LMFDB - Embedded newform 91.10.h.a.16.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(16,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$82$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.17
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.17

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.7072 q^{2} +(-48.0812 + 83.2791i) q^{3} +370.519 q^{4} +(-95.8890 + 166.085i) q^{5} +(1428.36 - 2473.99i) q^{6} +(-1720.94 - 6114.90i) q^{7} +4203.00 q^{8} +(5217.89 + 9037.66i) q^{9} +O(q^{10})$	\(q-29.7072 q^{2} +(-48.0812 + 83.2791i) q^{3} +370.519 q^{4} +(-95.8890 + 166.085i) q^{5} +(1428.36 - 2473.99i) q^{6} +(-1720.94 - 6114.90i) q^{7} +4203.00 q^{8} +(5217.89 + 9037.66i) q^{9} +(2848.60 - 4933.91i) q^{10} +(24030.1 - 41621.4i) q^{11} +(-17815.0 + 30856.5i) q^{12} +(71178.6 - 74418.5i) q^{13} +(51124.5 + 181657. i) q^{14} +(-9220.91 - 15971.1i) q^{15} -314565. q^{16} -11945.7 q^{17} +(-155009. - 268484. i) q^{18} +(-156052. - 270291. i) q^{19} +(-35528.7 + 61537.6i) q^{20} +(591988. + 150693. i) q^{21} +(-713869. + 1.23646e6i) q^{22} -218795. q^{23} +(-202085. + 350022. i) q^{24} +(958173. + 1.65960e6i) q^{25} +(-2.11452e6 + 2.21077e6i) q^{26} -2.89630e6 q^{27} +(-637643. - 2.26569e6i) q^{28} +(-753351. - 1.30484e6i) q^{29} +(273928. + 474457. i) q^{30} +(4.55566e6 + 7.89063e6i) q^{31} +7.19293e6 q^{32} +(2.31080e6 + 4.00242e6i) q^{33} +354873. q^{34} +(1.18061e6 + 300529. i) q^{35} +(1.93333e6 + 3.34863e6i) q^{36} +1.07060e6 q^{37} +(4.63588e6 + 8.02959e6i) q^{38} +(2.77515e6 + 9.50582e6i) q^{39} +(-403021. + 698053. i) q^{40} +(-5.86238e6 - 1.01539e7i) q^{41} +(-1.75863e7 - 4.47667e6i) q^{42} +(-1.01114e7 + 1.75135e7i) q^{43} +(8.90364e6 - 1.54215e7i) q^{44} -2.00135e6 q^{45} +6.49979e6 q^{46} +(-603514. + 1.04532e6i) q^{47} +(1.51247e7 - 2.61967e7i) q^{48} +(-3.44303e7 + 2.10468e7i) q^{49} +(-2.84647e7 - 4.93023e7i) q^{50} +(574363. - 994825. i) q^{51} +(2.63730e7 - 2.75735e7i) q^{52} +(-1.98127e7 - 3.43165e7i) q^{53} +8.60409e7 q^{54} +(4.60845e6 + 7.98207e6i) q^{55} +(-7.23312e6 - 2.57009e7i) q^{56} +3.00128e7 q^{57} +(2.23800e7 + 3.87633e7i) q^{58} +5.36794e7 q^{59} +(-3.41653e6 - 5.91760e6i) q^{60} +(-8.40269e7 - 1.45539e8i) q^{61} +(-1.35336e8 - 2.34409e8i) q^{62} +(4.62846e7 - 4.74602e7i) q^{63} -5.26246e7 q^{64} +(5.53453e6 + 1.89576e7i) q^{65} +(-6.86474e7 - 1.18901e8i) q^{66} +(1.05619e8 - 1.82938e8i) q^{67} -4.42611e6 q^{68} +(1.05199e7 - 1.82210e7i) q^{69} +(-3.50726e7 - 8.92788e6i) q^{70} +(-5.28700e7 + 9.15736e7i) q^{71} +(2.19308e7 + 3.79852e7i) q^{72} +(-1.17526e8 - 2.03561e8i) q^{73} -3.18045e7 q^{74} -1.84280e8 q^{75} +(-5.78204e7 - 1.00148e8i) q^{76} +(-2.95865e8 - 7.53137e7i) q^{77} +(-8.24421e7 - 2.82391e8i) q^{78} +(7.94558e7 - 1.37621e8i) q^{79} +(3.01633e7 - 5.22444e7i) q^{80} +(3.65536e7 - 6.33127e7i) q^{81} +(1.74155e8 + 3.01646e8i) q^{82} -2.33775e8 q^{83} +(2.19343e8 + 5.58346e7i) q^{84} +(1.14546e6 - 1.98399e6i) q^{85} +(3.00383e8 - 5.20278e8i) q^{86} +1.44888e8 q^{87} +(1.00999e8 - 1.74935e8i) q^{88} +4.67294e8 q^{89} +5.94547e7 q^{90} +(-5.77556e8 - 3.07179e8i) q^{91} -8.10677e7 q^{92} -8.76166e8 q^{93} +(1.79287e7 - 3.10535e7i) q^{94} +5.98548e7 q^{95} +(-3.45845e8 + 5.99021e8i) q^{96} +(2.67275e8 - 4.62933e8i) q^{97} +(1.02283e9 - 6.25242e8i) q^{98} +5.01547e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) $ 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−29.7072			−1.31289			−0.656443	−	0.754375i	$-0.727940\pi$
$2$	−29.7072			−1.31289			−0.656443	+	0.754375i	$0.727940\pi$
$3$	−48.0812	+	83.2791i	−0.342712	+	0.593595i	−0.984935	−	0.172923i	$-0.944679\pi$
$3$	−48.0812	+	83.2791i	−0.342712	+	0.593595i	0.642223	+	0.766518i	$0.278012\pi$
$4$	370.519			0.723671
$5$	−95.8890	+	166.085i	−0.0686126	+	0.118840i	−0.898291	−	0.439401i	$-0.855191\pi$
$5$	−95.8890	+	166.085i	−0.0686126	+	0.118840i	0.829678	+	0.558242i	$0.188524\pi$
$6$	1428.36	−	2473.99i	0.449942	−	0.779323i
$7$	−1720.94	−	6114.90i	−0.270910	−	0.962605i
$7$	−1720.94	−	6114.90i	−0.270910	−	0.962605i
$8$	4203.00			0.362789
$9$	5217.89	+	9037.66i	0.265096	+	0.459161i
$10$	2848.60	−	4933.91i	0.0900805	−	0.156024i
$11$	24030.1	−	41621.4i	0.494868	−	0.857136i	−0.505115	−	0.863052i	$-0.668550\pi$
$11$	24030.1	−	41621.4i	0.494868	−	0.857136i	0.999983	+	0.00591589i	$0.00188310\pi$
$12$	−17815.0	+	30856.5i	−0.248011	+	0.429567i
$13$	71178.6	−	74418.5i	0.691201	−	0.722663i
$13$	71178.6	−	74418.5i	0.691201	−	0.722663i
$14$	51124.5	+	181657.i	0.355675	+	1.26379i
$15$	−9220.91	−	15971.1i	−0.0470287	−	0.0814562i
$16$	−314565.			−1.19997
$17$	−11945.7			−0.0346889			−0.0173445	−	0.999850i	$-0.505521\pi$
$17$	−11945.7			−0.0346889			−0.0173445	+	0.999850i	$0.505521\pi$
$18$	−155009.	−	268484.i	−0.348042	−	0.602826i
$19$	−156052.	−	270291.i	−0.274713	−	0.475817i	0.695350	−	0.718672i	$-0.255250\pi$
$19$	−156052.	−	270291.i	−0.274713	−	0.475817i	−0.970063	+	0.242855i	$0.921916\pi$
$20$	−35528.7	+	61537.6i	−0.0496529	+	0.0860013i
$21$	591988.	+	150693.i	0.664242	+	0.169085i
$22$	−713869.	+	1.23646e6i	−0.649705	+	1.12532i
$23$	−218795.			−0.163028			−0.0815139	−	0.996672i	$-0.525976\pi$
$23$	−218795.			−0.163028			−0.0815139	+	0.996672i	$0.525976\pi$
$24$	−202085.	+	350022.i	−0.124332	+	0.215350i
$25$	958173.	+	1.65960e6i	0.490585	+	0.849718i
$26$	−2.11452e6	+	2.21077e6i	−0.907468	+	0.948774i
$27$	−2.89630e6			−1.04883
$28$	−637643.	−	2.26569e6i	−0.196050	−	0.696609i
$29$	−753351.	−	1.30484e6i	−0.197791	−	0.342584i	0.750021	−	0.661414i	$-0.230043\pi$
$29$	−753351.	−	1.30484e6i	−0.197791	−	0.342584i	−0.947812	+	0.318830i	$0.896710\pi$
$30$	273928.	+	474457.i	0.0617434	+	0.106943i
$31$	4.55566e6	+	7.89063e6i	0.885979	+	1.53456i	0.844587	+	0.535418i	$0.179846\pi$
$31$	4.55566e6	+	7.89063e6i	0.885979	+	1.53456i	0.0413917	+	0.999143i	$0.486821\pi$
$32$	7.19293e6			1.21264
$33$	2.31080e6	+	4.00242e6i	0.339195	+	0.587502i
$34$	354873.			0.0455426
$35$	1.18061e6	+	300529.i	0.132984	+	0.0338516i
$36$	1.93333e6	+	3.34863e6i	0.191843	+	0.332281i
$37$	1.07060e6			0.0939115			0.0469557	−	0.998897i	$-0.485048\pi$
$37$	1.07060e6			0.0939115			0.0469557	+	0.998897i	$0.485048\pi$
$38$	4.63588e6	+	8.02959e6i	0.360667	+	0.624694i
$39$	2.77515e6	+	9.50582e6i	0.192086	+	0.657959i
$40$	−403021.	+	698053.i	−0.0248919	+	0.0431140i
$41$	−5.86238e6	−	1.01539e7i	−0.324001	−	0.561187i	0.657308	−	0.753622i	$-0.271695\pi$
$41$	−5.86238e6	−	1.01539e7i	−0.324001	−	0.561187i	−0.981310	+	0.192435i	$0.938362\pi$
$42$	−1.75863e7	−	4.47667e6i	−0.872074	−	0.221990i
$43$	−1.01114e7	+	1.75135e7i	−0.451029	+	0.781205i	−0.998450	−	0.0556520i	$-0.982276\pi$
$43$	−1.01114e7	+	1.75135e7i	−0.451029	+	0.781205i	0.547421	+	0.836857i	$0.315610\pi$
$44$	8.90364e6	−	1.54215e7i	0.358121	−	0.620285i
$45$	−2.00135e6			−0.0727558
$46$	6.49979e6			0.214037
$47$	−603514.	+	1.04532e6i	−0.0180404	+	0.0312469i	−0.874905	−	0.484295i	$-0.839076\pi$
$47$	−603514.	+	1.04532e6i	−0.0180404	+	0.0312469i	0.856864	+	0.515542i	$0.172409\pi$
$48$	1.51247e7	−	2.61967e7i	0.411245	−	0.712297i
$49$	−3.44303e7	+	2.10468e7i	−0.853215	+	0.521559i
$50$	−2.84647e7	−	4.93023e7i	−0.644082	−	1.11558i
$51$	574363.	−	994825.i	0.0118883	−	0.0205912i
$52$	2.63730e7	−	2.75735e7i	0.500202	−	0.522970i
$53$	−1.98127e7	−	3.43165e7i	−0.344907	−	0.597396i	0.640430	−	0.768016i	$-0.278756\pi$
$53$	−1.98127e7	−	3.43165e7i	−0.344907	−	0.597396i	−0.985337	+	0.170621i	$0.945423\pi$
$54$	8.60409e7			1.37700
$55$	4.60845e6	+	7.98207e6i	0.0679083	+	0.117621i
$56$	−7.23312e6	−	2.57009e7i	−0.0982833	−	0.349222i
$57$	3.00128e7			0.376590
$58$	2.23800e7	+	3.87633e7i	0.259677	+	0.449774i
$59$	5.36794e7			0.576731			0.288366	−	0.957520i	$-0.406888\pi$
$59$	5.36794e7			0.576731			0.288366	+	0.957520i	$0.406888\pi$
$60$	−3.41653e6	−	5.91760e6i	−0.0340333	−	0.0589474i
$61$	−8.40269e7	−	1.45539e8i	−0.777023	−	1.34584i	−0.933650	−	0.358186i	$-0.883395\pi$
$61$	−8.40269e7	−	1.45539e8i	−0.777023	−	1.34584i	0.156627	−	0.987658i	$-0.449938\pi$
$62$	−1.35336e8	−	2.34409e8i	−1.16319	−	2.01470i
$63$	4.62846e7	−	4.74602e7i	0.370173	−	0.379574i
$64$	−5.26246e7			−0.392083
$65$	5.53453e6	+	1.89576e7i	0.0384565	+	0.131726i
$66$	−6.86474e7	−	1.18901e8i	−0.445324	−	0.771324i
$67$	1.05619e8	−	1.82938e8i	0.640333	−	1.10909i	−0.345025	−	0.938594i	$-0.612130\pi$
$67$	1.05619e8	−	1.82938e8i	0.640333	−	1.10909i	0.985358	−	0.170496i	$-0.0545371\pi$
$68$	−4.42611e6			−0.0251034
$69$	1.05199e7	−	1.82210e7i	0.0558717	−	0.0967726i
$70$	−3.50726e7	−	8.92788e6i	−0.174593	−	0.0444434i
$71$	−5.28700e7	+	9.15736e7i	−0.246915	+	0.427669i	−0.962668	−	0.270684i	$-0.912750\pi$
$71$	−5.28700e7	+	9.15736e7i	−0.246915	+	0.427669i	0.715753	+	0.698353i	$0.246083\pi$
$72$	2.19308e7	+	3.79852e7i	0.0961741	+	0.166578i
$73$	−1.17526e8	−	2.03561e8i	−0.484373	−	0.838959i	0.515466	−	0.856910i	$-0.327619\pi$
$73$	−1.17526e8	−	2.03561e8i	−0.484373	−	0.838959i	−0.999839	+	0.0179511i	$0.994286\pi$
$74$	−3.18045e7			−0.123295
$75$	−1.84280e8			−0.672518
$76$	−5.78204e7	−	1.00148e8i	−0.198802	−	0.344335i
$77$	−2.95865e8	−	7.53137e7i	−0.959148	−	0.244155i
$78$	−8.24421e7	−	2.82391e8i	−0.252188	−	0.863825i
$79$	7.94558e7	−	1.37621e8i	0.229511	−	0.397525i	−0.728152	−	0.685415i	$-0.759621\pi$
$79$	7.94558e7	−	1.37621e8i	0.229511	−	0.397525i	0.957663	+	0.287891i	$0.0929540\pi$
$80$	3.01633e7	−	5.22444e7i	0.0823331	−	0.142605i
$81$	3.65536e7	−	6.33127e7i	0.0943512	−	0.163421i
$82$	1.74155e8	+	3.01646e8i	0.425377	+	0.736775i
$83$	−2.33775e8			−0.540687			−0.270343	−	0.962764i	$-0.587137\pi$
$83$	−2.33775e8			−0.540687			−0.270343	+	0.962764i	$0.587137\pi$
$84$	2.19343e8	+	5.58346e7i	0.480692	+	0.122362i
$85$	1.14546e6	−	1.98399e6i	0.00238010	−	0.00412245i
$86$	3.00383e8	−	5.20278e8i	0.592150	−	1.02563i
$87$	1.44888e8			0.271142
$88$	1.00999e8	−	1.74935e8i	0.179533	−	0.310960i
$89$	4.67294e8			0.789470			0.394735	−	0.918795i	$-0.370836\pi$
$89$	4.67294e8			0.789470			0.394735	+	0.918795i	$0.370836\pi$
$90$	5.94547e7			0.0955201
$91$	−5.77556e8	−	3.07179e8i	−0.882892	−	0.469576i
$92$	−8.10677e7			−0.117978
$93$	−8.76166e8			−1.21454
$94$	1.79287e7	−	3.10535e7i	0.0236850	−	0.0410237i
$95$	5.98548e7			0.0753951
$96$	−3.45845e8	+	5.99021e8i	−0.415586	+	0.719816i
$97$	2.67275e8	−	4.62933e8i	0.306538	−	0.530940i	−0.671064	−	0.741399i	$-0.734163\pi$
$97$	2.67275e8	−	4.62933e8i	0.306538	−	0.530940i	0.977603	+	0.210459i	$0.0674959\pi$
$98$	1.02283e9	−	6.25242e8i	1.12017	−	0.684748i
$99$	5.01547e8			0.524751
$100$	3.55022e8	+	6.14916e8i	0.355022	+	0.614916i
$101$	−3.88283e8	+	6.72526e8i	−0.371281	+	0.643077i	−0.989763	−	0.142722i	$-0.954415\pi$
$101$	−3.88283e8	+	6.72526e8i	−0.371281	+	0.643077i	0.618482	+	0.785799i	$0.287748\pi$
$102$	−1.70627e7	+	2.95535e7i	−0.0156080	+	0.0270339i
$103$	5.87289e8	−	1.01721e9i	0.514144	−	0.890523i	−0.485722	−	0.874113i	$-0.661443\pi$
$103$	5.87289e8	−	1.01721e9i	0.514144	−	0.890523i	0.999865	−	0.0164094i	$-0.00522351\pi$
$104$	2.99163e8	−	3.12781e8i	0.250760	−	0.262174i
$105$	−8.17929e7	+	8.38703e7i	−0.0656695	+	0.0673374i
$106$	5.88579e8	+	1.01945e9i	0.452823	+	0.784313i
$107$	−4.74131e8			−0.349680			−0.174840	−	0.984597i	$-0.555941\pi$
$107$	−4.74131e8			−0.349680			−0.174840	+	0.984597i	$0.555941\pi$
$108$	−1.07313e9			−0.759009
$109$	2.05509e8	+	3.55952e8i	0.139448	+	0.241531i	0.927288	−	0.374349i	$-0.122134\pi$
$109$	2.05509e8	+	3.55952e8i	0.139448	+	0.241531i	−0.787840	+	0.615880i	$0.788801\pi$
$110$	−1.36904e8	−	2.37125e8i	−0.0891559	−	0.154423i
$111$	−5.14757e7	+	8.91585e7i	−0.0321846	+	0.0557454i
$112$	5.41350e8	+	1.92353e9i	0.325085	+	1.15510i
$113$	5.71466e7	−	9.89808e7i	0.0329714	−	0.0571081i	−0.849069	−	0.528282i	$-0.822836\pi$
$113$	5.71466e7	−	9.89808e7i	0.0329714	−	0.0571081i	0.882040	+	0.471174i	$0.156170\pi$
$114$	−8.91596e8			−0.494420
$115$	2.09800e7	−	3.63384e7i	0.0111858	−	0.0193743i
$116$	−2.79131e8	−	4.83470e8i	−0.143136	−	0.247918i
$117$	1.04397e9	+	2.54980e8i	0.515053	+	0.125797i
$118$	−1.59467e9			−0.757183
$119$	2.05579e7	+	7.30466e7i	0.00939759	+	0.0333917i
$120$	−3.87555e7	−	6.71264e7i	−0.0170615	−	0.0295514i
$121$	2.40780e7	+	4.17044e7i	0.0102114	+	0.0176867i
$122$	2.49621e9	+	4.32355e9i	1.02014	+	1.76694i
$123$	1.12748e9			0.444157
$124$	1.68796e9	+	2.92363e9i	0.641157	+	1.11052i
$125$	−7.42079e8			−0.271866
$126$	−1.37499e9	+	1.40991e9i	−0.485995	+	0.498338i
$127$	2.80341e9	+	4.85565e9i	0.956246	+	1.65627i	0.731490	+	0.681852i	$0.238825\pi$
$127$	2.80341e9	+	4.85565e9i	0.956246	+	1.65627i	0.224757	+	0.974415i	$0.427841\pi$
$128$	−2.11945e9			−0.697876
$129$	−9.72340e8	−	1.68414e9i	−0.309146	−	0.535457i
$130$	−1.64415e8	−	5.63177e8i	−0.0504891	−	0.172942i
$131$	−3.61410e8	+	6.25981e8i	−0.107221	+	0.185712i	−0.914643	−	0.404262i	$-0.867529\pi$
$131$	−3.61410e8	+	6.25981e8i	−0.107221	+	0.185712i	0.807423	+	0.589974i	$0.200862\pi$
$132$	8.56195e8	+	1.48297e9i	0.245465	+	0.425158i
$133$	−1.38424e9	+	1.41940e9i	−0.383601	+	0.393344i
$134$	−3.13765e9	+	5.43457e9i	−0.840685	+	1.45611i
$135$	2.77723e8	−	4.81030e8i	0.0719630	−	0.124644i
$136$	−5.02076e7			−0.0125848
$137$	−4.75920e9			−1.15423			−0.577113	−	0.816664i	$-0.695821\pi$
$137$	−4.75920e9			−1.15423			−0.577113	+	0.816664i	$0.695821\pi$
$138$	−3.12518e8	+	5.41297e8i	−0.0733531	+	0.127051i
$139$	2.82910e9	−	4.90014e9i	0.642808	−	1.11338i	−0.341996	−	0.939702i	$-0.611103\pi$
$139$	2.82910e9	−	4.90014e9i	0.642808	−	1.11338i	0.984803	−	0.173674i	$-0.0555639\pi$
$140$	4.37439e8	+	1.11352e8i	0.0962368	+	0.0244974i
$141$	−5.80354e7	−	1.00520e8i	−0.0123654	−	0.0214174i
$142$	1.57062e9	−	2.72040e9i	0.324171	−	0.561481i
$143$	−1.38697e9	−	4.75084e9i	−0.277368	−	0.950076i
$144$	−1.64137e9	−	2.84293e9i	−0.318108	−	0.550980i
$145$	2.88952e8			0.0542838
$146$	3.49136e9	+	6.04722e9i	0.635927	+	1.10146i
$147$	−9.73076e7	−	3.87928e9i	−0.0171877	−	0.685209i
$148$	3.96677e8			0.0679610
$149$	−5.07173e9	−	8.78449e9i	−0.842981	−	1.46009i	−0.887363	−	0.461071i	$-0.847465\pi$
$149$	−5.07173e9	−	8.78449e9i	−0.842981	−	1.46009i	0.0443822	−	0.999015i	$-0.485868\pi$
$150$	5.47446e9			0.882939
$151$	2.71419e9	+	4.70112e9i	0.424859	+	0.735877i	0.996407	−	0.0846915i	$-0.0269905\pi$
$151$	2.71419e9	+	4.70112e9i	0.424859	+	0.735877i	−0.571549	+	0.820568i	$0.693657\pi$
$152$	−6.55888e8	−	1.13603e9i	−0.0996629	−	0.172621i
$153$	−6.23313e7	−	1.07961e8i	−0.00919591	−	0.0159278i
$154$	8.78934e9	+	2.23736e9i	1.25925	+	0.320548i
$155$	−1.74735e9			−0.243157
$156$	1.02825e9	+	3.52209e9i	0.139007	+	0.476146i
$157$	−4.95637e9	−	8.58469e9i	−0.651052	−	1.12765i	−0.982868	−	0.184311i	$-0.940995\pi$
$157$	−4.95637e9	−	8.58469e9i	−0.651052	−	1.12765i	0.331816	−	0.943344i	$-0.392339\pi$
$158$	−2.36041e9	+	4.08835e9i	−0.301322	+	0.521905i
$159$	3.81047e9			0.472815
$160$	−6.89723e8	+	1.19463e9i	−0.0832021	+	0.144110i
$161$	3.76534e8	+	1.33791e9i	0.0441659	+	0.156931i
$162$	−1.08591e9	+	1.88084e9i	−0.123872	+	0.214553i
$163$	−7.83212e9	−	1.35656e10i	−0.869030	−	1.50520i	−0.862989	−	0.505223i	$-0.831410\pi$
$163$	−7.83212e9	−	1.35656e10i	−0.869030	−	1.50520i	−0.00604162	−	0.999982i	$-0.501923\pi$
$164$	−2.17213e9	−	3.76224e9i	−0.234470	−	0.406115i
$165$	−8.86320e8			−0.0930921
$166$	6.94480e9			0.709861
$167$	6.37837e9	+	1.10477e10i	0.634578	+	1.09912i	0.986604	+	0.163132i	$0.0521596\pi$
$167$	6.37837e9	+	1.10477e10i	0.634578	+	1.09912i	−0.352026	+	0.935990i	$0.614507\pi$
$168$	2.48812e9	+	6.33362e8i	0.240980	+	0.0613423i
$169$	−4.71726e8	−	1.05940e10i	−0.0444836	−	0.999010i
$170$	−3.40284e7	+	5.89389e7i	−0.00312479	+	0.00541230i
$171$	1.62853e9	−	2.82070e9i	0.145651	−	0.252275i
$172$	−3.74648e9	+	6.48910e9i	−0.326397	+	0.565335i
$173$	1.58841e9	+	2.75121e9i	0.134821	+	0.233516i	0.925529	−	0.378677i	$-0.123621\pi$
$173$	1.58841e9	+	2.75121e9i	0.134821	+	0.233516i	−0.790708	+	0.612193i	$0.790288\pi$
$174$	−4.30423e9			−0.355978
$175$	8.49935e9	−	8.71522e9i	0.685037	−	0.702436i
$176$	−7.55905e9	+	1.30927e10i	−0.593827	+	1.02854i
$177$	−2.58097e9	+	4.47037e9i	−0.197653	+	0.342345i
$178$	−1.38820e10			−1.03648
$179$	−5.13677e9	+	8.89714e9i	−0.373983	+	0.647757i	−0.990174	−	0.139839i	$-0.955341\pi$
$179$	−5.13677e9	+	8.89714e9i	−0.373983	+	0.647757i	0.616192	+	0.787596i	$0.288675\pi$
$180$	−7.41540e8			−0.0526512
$181$	−9.99607e9			−0.692270			−0.346135	−	0.938185i	$-0.612506\pi$
$181$	−9.99607e9			−0.692270			−0.346135	+	0.938185i	$0.612506\pi$
$182$	1.71576e10	+	9.12545e9i	1.15914	+	0.616500i
$183$	1.61605e10			1.06518
$184$	−9.19594e8			−0.0591447
$185$	−1.02659e8	+	1.77810e8i	−0.00644351	+	0.0111605i
$186$	2.60285e10			1.59456
$187$	−2.87056e8	+	4.97196e8i	−0.0171664	+	0.0297331i
$188$	−2.23614e8	+	3.87310e8i	−0.0130553	+	0.0226125i
$189$	4.98436e9	+	1.77105e10i	0.284140	+	1.00961i
$190$	−1.77812e9			−0.0989851
$191$	−1.23446e10	−	2.13815e10i	−0.671161	−	1.16248i	−0.977575	−	0.210586i	$-0.932463\pi$
$191$	−1.23446e10	−	2.13815e10i	−0.671161	−	1.16248i	0.306415	−	0.951898i	$-0.400871\pi$
$192$	2.53025e9	−	4.38253e9i	0.134372	−	0.232739i
$193$	1.03850e10	−	1.79873e10i	0.538763	−	0.933165i	−0.460208	−	0.887811i	$-0.652225\pi$
$193$	1.03850e10	−	1.79873e10i	0.538763	−	0.933165i	0.998971	−	0.0453540i	$-0.0144416\pi$
$194$	−7.93999e9	+	1.37525e10i	−0.402450	+	0.697064i
$195$	−1.84488e9	−	4.50593e8i	−0.0913716	−	0.0223166i
$196$	−1.27571e10	+	7.79825e9i	−0.617447	+	0.377437i
$197$	−6.35754e9	−	1.10116e10i	−0.300740	−	0.520897i	0.675564	−	0.737301i	$-0.263900\pi$
$197$	−6.35754e9	−	1.10116e10i	−0.300740	−	0.520897i	−0.976304	+	0.216405i	$0.930567\pi$
$198$	−1.48996e10			−0.688938
$199$	2.56596e9			0.115987			0.0579936	−	0.998317i	$-0.481530\pi$
$199$	2.56596e9			0.115987			0.0579936	+	0.998317i	$0.481530\pi$
$200$	4.02720e9	+	6.97531e9i	0.177979	+	0.308268i
$201$	1.01566e10	+	1.75917e10i	0.438900	+	0.760198i
$202$	1.15348e10	−	1.99789e10i	0.487449	−	0.844287i
$203$	−6.68250e9	+	6.85223e9i	−0.276189	+	0.283204i
$204$	2.12813e8	−	3.68602e8i	0.00860323	−	0.0149012i
$205$	2.24855e9			0.0889223
$206$	−1.74467e10	+	3.02186e10i	−0.675012	+	1.16916i
$207$	−1.14165e9	−	1.97739e9i	−0.0432181	−	0.0748560i
$208$	−2.23903e10	+	2.34095e10i	−0.829421	+	0.867175i
$209$	−1.49998e10			−0.543787
$210$	2.42984e9	−	2.49155e9i	0.0862166	−	0.0884064i
$211$	−1.30867e10	−	2.26668e10i	−0.454526	−	0.787262i	0.544135	−	0.838998i	$-0.316858\pi$
$211$	−1.30867e10	−	2.26668e10i	−0.454526	−	0.787262i	−0.998661	+	0.0517357i	$0.983525\pi$
$212$	−7.34098e9	−	1.27149e10i	−0.249599	−	0.432318i
$213$	−5.08411e9	−	8.80594e9i	−0.169241	−	0.293135i
$214$	1.40851e10			0.459091
$215$	−1.93915e9	−	3.35870e9i	−0.0618925	−	0.107201i
$216$	−1.21731e10			−0.380505
$217$	4.04104e10	−	4.14367e10i	1.23715	−	1.26858i
$218$	−6.10511e9	−	1.05744e10i	−0.183079	−	0.317103i
$219$	2.26031e10			0.664003
$220$	1.70752e9	+	2.95751e9i	0.0491433	+	0.0851186i
$221$	−8.50276e8	+	8.88980e8i	−0.0239770	+	0.0250684i
$222$	1.52920e9	−	2.64865e9i	0.0422548	−	0.0731874i
$223$	6.53809e9	+	1.13243e10i	0.177043	+	0.306648i	0.940866	−	0.338778i	$-0.110013\pi$
$223$	6.53809e9	+	1.13243e10i	0.177043	+	0.306648i	−0.763823	+	0.645425i	$0.776680\pi$
$224$	−1.23786e10	−	4.39840e10i	−0.328516	−	1.16729i
$225$	−9.99929e9	+	1.73193e10i	−0.260105	+	0.450514i
$226$	−1.69767e9	+	2.94044e9i	−0.0432877	+	0.0749765i
$227$	5.96245e9			0.149042			0.0745209	−	0.997219i	$-0.476257\pi$
$227$	5.96245e9			0.149042			0.0745209	+	0.997219i	$0.476257\pi$
$228$	1.11203e10			0.272527
$229$	1.68722e10	−	2.92235e10i	0.405426	−	0.702219i	−0.588945	−	0.808173i	$-0.700456\pi$
$229$	1.68722e10	−	2.92235e10i	0.405426	−	0.702219i	0.994371	+	0.105954i	$0.0337897\pi$
$230$	−6.23258e8	+	1.07951e9i	−0.0146856	+	0.0254363i
$231$	2.04976e10	−	2.10182e10i	0.473641	−	0.485671i
$232$	−3.16633e9	−	5.48425e9i	−0.0717564	−	0.124286i
$233$	2.79027e10	−	4.83289e10i	0.620219	−	1.07425i	−0.369226	−	0.929340i	$-0.620377\pi$
$233$	2.79027e10	−	4.83289e10i	0.620219	−	1.07425i	0.989445	−	0.144911i	$-0.0462896\pi$
$234$	−3.10135e10	−	7.57474e9i	−0.676206	−	0.165157i
$235$	−1.15741e8	−	2.00469e8i	−0.00247560	−	0.00428787i
$236$	1.98893e10			0.417364
$237$	7.64066e9	+	1.32340e10i	0.157313	+	0.272473i
$238$	−6.10717e8	−	2.17001e9i	−0.0123380	−	0.0438395i
$239$	−5.13898e10			−1.01879			−0.509397	−	0.860532i	$-0.670132\pi$
$239$	−5.13898e10			−1.01879			−0.509397	+	0.860532i	$0.670132\pi$
$240$	2.90058e9	+	5.02395e9i	0.0564331	+	0.0977451i
$241$	−3.48578e10			−0.665615			−0.332807	−	0.942995i	$-0.607996\pi$
$241$	−3.48578e10			−0.665615			−0.332807	+	0.942995i	$0.607996\pi$
$242$	−7.15292e8	−	1.23892e9i	−0.0134065	−	0.0232207i
$243$	−2.49888e10	−	4.32819e10i	−0.459745	−	0.796302i
$244$	−3.11336e10	−	5.39250e10i	−0.562309	−	0.973948i
$245$	−1.94062e8	−	7.73650e9i	−0.00344106	−	0.137182i
$246$	−3.34944e10			−0.583128
$247$	−3.12222e10	−	7.62572e9i	−0.533737	−	0.130360i
$248$	1.91474e10	+	3.31643e10i	0.321423	+	0.556722i
$249$	1.12402e10	−	1.94685e10i	0.185300	−	0.320949i
$250$	2.20451e10			0.356929
$251$	−5.49763e10	+	9.52217e10i	−0.874266	+	1.51427i	−0.0167226	+	0.999860i	$0.505323\pi$
$251$	−5.49763e10	+	9.52217e10i	−0.874266	+	1.51427i	−0.857543	+	0.514412i	$0.828010\pi$
$252$	1.71494e10	−	1.75849e10i	0.267883	−	0.274687i
$253$	−5.25767e9	+	9.10655e9i	−0.0806773	+	0.139737i
$254$	−8.32815e10	−	1.44248e11i	−1.25544	−	2.17449i
$255$	1.10150e8	+	1.90786e8i	0.00163138	+	0.00282563i
$256$	8.99068e10			1.30832
$257$	1.28826e11			1.84207			0.921033	−	0.389484i	$-0.127347\pi$
$257$	1.28826e11			1.84207			0.921033	+	0.389484i	$0.127347\pi$
$258$	2.88855e10	+	5.00312e10i	0.405874	+	0.702995i
$259$	−1.84244e9	−	6.54660e9i	−0.0254416	−	0.0903996i
$260$	2.05065e9	+	7.02415e9i	0.0278299	+	0.0953265i
$261$	7.86182e9	−	1.36171e10i	0.104867	−	0.181636i
$262$	1.07365e10	−	1.85961e10i	0.140769	−	0.243819i
$263$	3.00748e10	−	5.20910e10i	0.387616	−	0.671370i	−0.604513	−	0.796596i	$-0.706632\pi$
$263$	3.00748e10	−	5.20910e10i	0.387616	−	0.671370i	0.992128	+	0.125226i	$0.0399654\pi$
$264$	9.71227e9	+	1.68221e10i	0.123056	+	0.213139i
$265$	7.59926e9			0.0946597
$266$	4.11220e10	−	4.21664e10i	0.503624	−	0.516416i
$267$	−2.24681e10	+	3.89159e10i	−0.270561	+	0.468626i
$268$	3.91340e10	−	6.77820e10i	0.463391	−	0.802616i
$269$	−1.64407e11			−1.91440			−0.957202	−	0.289420i	$-0.906538\pi$
$269$	−1.64407e11			−1.91440			−0.957202	+	0.289420i	$0.906538\pi$
$270$	−8.25037e9	+	1.42901e10i	−0.0944793	+	0.163643i
$271$	−2.99782e10			−0.337632			−0.168816	−	0.985648i	$-0.553994\pi$
$271$	−2.99782e10			−0.337632			−0.168816	+	0.985648i	$0.553994\pi$
$272$	3.75770e9			0.0416257
$273$	5.33512e10	−	3.33288e10i	0.581316	−	0.363151i
$274$	1.41383e11			1.51537
$275$	9.21002e10			0.971098
$276$	3.89783e9	−	6.75125e9i	0.0404327	−	0.0700315i
$277$	5.88081e10			0.600175			0.300088	−	0.953912i	$-0.402984\pi$
$277$	5.88081e10			0.600175			0.300088	+	0.953912i	$0.402984\pi$
$278$	−8.40446e10	+	1.45570e11i	−0.843933	+	1.46174i
$279$	−4.75419e10	+	8.23450e10i	−0.469740	+	0.813613i
$280$	4.96210e9	+	1.26312e9i	0.0482452	+	0.0122810i
$281$	−1.08850e11			−1.04148			−0.520739	−	0.853716i	$-0.674343\pi$
$281$	−1.08850e11			−1.04148			−0.520739	+	0.853716i	$0.674343\pi$
$282$	1.72407e9	+	2.98618e9i	0.0162343	+	0.0281186i
$283$	1.45586e9	−	2.52162e9i	0.0134921	−	0.0233690i	−0.859201	−	0.511639i	$-0.829039\pi$
$283$	1.45586e9	−	2.52162e9i	0.0134921	−	0.0233690i	0.872693	+	0.488270i	$0.162372\pi$
$284$	−1.95894e10	+	3.39298e10i	−0.178685	+	0.309491i
$285$	−2.87789e9	+	4.98466e9i	−0.0258388	+	0.0447541i
$286$	4.12031e10	+	1.41134e11i	0.364152	+	1.24734i
$287$	−5.20015e10	+	5.33223e10i	−0.452426	+	0.463917i
$288$	3.75319e10	+	6.50072e10i	0.321466	+	0.556795i
$289$	−1.18445e11			−0.998797
$290$	−8.58397e9			−0.0712685
$291$	2.57018e10	+	4.45168e10i	0.210109	+	0.363920i
$292$	−4.35456e10	−	7.54231e10i	−0.350527	−	0.607130i
$293$	−2.62703e10	+	4.55015e10i	−0.208239	+	0.360680i	−0.951160	−	0.308699i	$-0.900106\pi$
$293$	−2.62703e10	+	4.55015e10i	−0.208239	+	0.360680i	0.742921	+	0.669379i	$0.233440\pi$
$294$	2.89074e9	+	1.15243e11i	0.0225655	+	0.899602i
$295$	−5.14726e9	+	8.91532e9i	−0.0395710	+	0.0685390i
$296$	4.49972e9			0.0340701
$297$	−6.95984e10	+	1.20548e11i	−0.519033	+	0.898992i
$298$	1.50667e11	+	2.60963e11i	1.10674	+	1.91693i
$299$	−1.55735e10	+	1.62824e10i	−0.112685	+	0.117814i
$300$	−6.82795e10			−0.486681
$301$	1.24495e11	+	3.16906e10i	0.874180	+	0.222526i
$302$	−8.06312e10	−	1.39657e11i	−0.557791	−	0.966123i
$303$	−3.73382e10	−	6.46717e10i	−0.254485	−	0.440781i
$304$	4.90887e10	+	8.50241e10i	0.329648	+	0.570967i
$305$	3.22290e10			0.213254
$306$	1.85169e9	+	3.20722e9i	0.0120732	+	0.0209114i
$307$	−8.18293e10			−0.525758			−0.262879	−	0.964829i	$-0.584672\pi$
$307$	−8.18293e10			−0.525758			−0.262879	+	0.964829i	$0.584672\pi$
$308$	−1.09624e11	−	2.79052e10i	−0.694108	−	0.176688i
$309$	5.64751e10	+	9.78178e10i	0.352407	+	0.610386i
$310$	5.19089e10			0.319238
$311$	−5.21107e10	−	9.02583e10i	−0.315867	−	0.547099i	0.663754	−	0.747951i	$-0.268962\pi$
$311$	−5.21107e10	−	9.02583e10i	−0.315867	−	0.547099i	−0.979622	+	0.200852i	$0.935629\pi$
$312$	1.16640e10	+	3.99529e10i	0.0696868	+	0.238700i
$313$	8.44849e10	−	1.46332e11i	0.497542	−	0.861768i	−0.502454	−	0.864604i	$-0.667569\pi$
$313$	8.44849e10	−	1.46332e11i	0.497542	−	0.861768i	0.999996	+	0.00283603i	$0.000902737\pi$
$314$	1.47240e11	+	2.55027e11i	0.854757	+	1.48048i
$315$	3.44422e9	+	1.22381e10i	0.0197103	+	0.0700351i
$316$	2.94399e10	−	5.09914e10i	0.166090	−	0.287677i
$317$	−8.44496e10	+	1.46271e11i	−0.469711	+	0.813564i	−0.999400	−	0.0346282i	$-0.988975\pi$
$317$	−8.44496e10	+	1.46271e11i	−0.469711	+	0.813564i	0.529689	+	0.848192i	$0.322309\pi$
$318$	−1.13198e11			−0.620752
$319$	−7.24126e10			−0.391522
$320$	5.04611e9	−	8.74013e9i	0.0269018	−	0.0465954i
$321$	2.27968e10	−	3.94852e10i	0.119840	−	0.207569i
$322$	−1.11858e10	−	3.97455e10i	−0.0579849	−	0.206033i
$323$	1.86415e9	+	3.22881e9i	0.00952950	+	0.0165056i
$324$	1.35438e10	−	2.34586e10i	0.0682792	−	0.118263i
$325$	1.91707e11	+	4.68224e10i	0.953152	+	0.232798i
$326$	2.32671e11	+	4.02997e11i	1.14094	+	1.97616i
$327$	−3.95245e10			−0.191162
$328$	−2.46396e10	−	4.26770e10i	−0.117544	−	0.203592i
$329$	7.43062e9	+	1.89149e9i	0.0349658	+	0.00890068i
$330$	2.63301e10			0.122219
$331$	1.53568e10	+	2.65988e10i	0.0703194	+	0.121797i	0.899041	−	0.437864i	$-0.144265\pi$
$331$	1.53568e10	+	2.65988e10i	0.0703194	+	0.121797i	−0.828722	+	0.559661i	$0.810931\pi$
$332$	−8.66180e10			−0.391279
$333$	5.58627e9	+	9.67570e9i	0.0248956	+	0.0431205i
$334$	−1.89484e11	−	3.28195e11i	−0.833129	−	1.44302i
$335$	2.02554e10	+	3.50834e10i	0.0878698	+	0.152195i
$336$	−1.86219e11	−	4.74028e10i	−0.797071	−	0.202898i
$337$	−6.42268e10			−0.271258			−0.135629	−	0.990760i	$-0.543305\pi$
$337$	−6.42268e10			−0.271258			−0.135629	+	0.990760i	$0.543305\pi$
$338$	1.40137e10	+	3.14718e11i	0.0584019	+	1.31159i
$339$	5.49535e9	+	9.51823e9i	0.0225994	+	0.0391433i
$340$	4.24415e8	−	7.35108e8i	0.00172241	−	0.00298329i
$341$	4.37892e11			1.75377
$342$	−4.83791e10	+	8.37951e10i	−0.191223	+	0.331208i
$343$	1.87952e11	+	1.74317e11i	0.733200	+	0.680013i
$344$	−4.24983e10	+	7.36092e10i	−0.163628	+	0.283413i
$345$	2.01749e9	+	3.49439e9i	0.00766699	+	0.0132796i
$346$	−4.71874e10	−	8.17309e10i	−0.177004	−	0.306580i
$347$	−9.44919e10			−0.349874			−0.174937	−	0.984580i	$-0.555972\pi$
$347$	−9.44919e10			−0.349874			−0.174937	+	0.984580i	$0.555972\pi$
$348$	5.36839e10			0.196217
$349$	3.09274e10	+	5.35677e10i	0.111591	+	0.193281i	0.916412	−	0.400237i	$-0.131072\pi$
$349$	3.09274e10	+	5.35677e10i	0.111591	+	0.193281i	−0.804821	+	0.593518i	$0.797739\pi$
$350$	−2.52492e11	+	2.58905e11i	−0.899376	+	0.922219i
$351$	−2.06154e11	+	2.15538e11i	−0.724953	+	0.757952i
$352$	1.72847e11	−	2.99380e11i	0.600095	−	1.03940i
$353$	2.24240e11	−	3.88395e11i	0.768647	−	1.33134i	−0.169650	−	0.985504i	$-0.554264\pi$
$353$	2.24240e11	−	3.88395e11i	0.768647	−	1.33134i	0.938297	−	0.345831i	$-0.112403\pi$
$354$	7.66735e10	−	1.32802e11i	0.259496	−	0.449460i
$355$	−1.01393e10	−	1.75618e10i	−0.0338829	−	0.0586869i
$356$	1.73142e11			0.571316
$357$	−7.07170e9	−	1.80013e9i	−0.0230418	−	0.00586539i
$358$	1.52599e11	−	2.64309e11i	0.490997	−	0.850431i
$359$	2.60524e11	−	4.51241e11i	0.827795	−	1.43378i	−0.0719699	−	0.997407i	$-0.522929\pi$
$359$	2.60524e11	−	4.51241e11i	0.827795	−	1.43378i	0.899765	−	0.436376i	$-0.143738\pi$
$360$	−8.41168e9			−0.0263950
$361$	1.12639e11	−	1.95097e11i	0.349065	−	0.604599i
$362$	2.96956e11			0.908872
$363$	−4.63080e9			−0.0139983
$364$	−2.13996e11	−	1.13816e11i	−0.638923	−	0.339818i
$365$	4.50777e10			0.132936
$366$	−4.80082e11			−1.39846
$367$	2.27981e11	−	3.94875e11i	0.655997	−	1.13622i	−0.325646	−	0.945492i	$-0.605582\pi$
$367$	2.27981e11	−	3.94875e11i	0.655997	−	1.13622i	0.981643	−	0.190728i	$-0.0610849\pi$
$368$	6.88253e10			0.195629
$369$	6.11786e10	−	1.05964e11i	0.171783	−	0.297537i
$370$	3.04970e9	−	5.28224e9i	0.00845959	−	0.0146524i
$371$	−1.75746e11	+	1.80209e11i	−0.481617	+	0.493849i
$372$	−3.24637e11			−0.878930
$373$	−1.96343e11	−	3.40076e11i	−0.525201	−	0.909675i	−0.999569	−	0.0293482i	$-0.990657\pi$
$373$	−1.96343e11	−	3.40076e11i	−0.525201	−	0.909675i	0.474368	−	0.880326i	$-0.342677\pi$
$374$	8.52765e9	−	1.47703e10i	0.0225376	−	0.0390362i
$375$	3.56801e10	−	6.17997e10i	0.0931719	−	0.161378i
$376$	−2.53657e9	+	4.39346e9i	−0.00654487	+	0.0113360i
$377$	−1.50727e11	−	3.68136e10i	−0.384286	−	0.0938581i
$378$	−1.48072e11	−	5.26131e11i	−0.373043	−	1.32550i
$379$	−1.29156e11	−	2.23704e11i	−0.321541	−	0.556926i	0.659265	−	0.751911i	$-0.270868\pi$
$379$	−1.29156e11	−	2.23704e11i	−0.321541	−	0.556926i	−0.980806	+	0.194985i	$0.937534\pi$
$380$	2.21774e10			0.0545612
$381$	−5.39165e11			−1.31087
$382$	3.66724e11	+	6.35184e11i	0.881158	+	1.52621i
$383$	−3.07640e11	−	5.32849e11i	−0.730548	−	1.26535i	−0.956649	−	0.291243i	$-0.905931\pi$
$383$	−3.07640e11	−	5.32849e11i	−0.730548	−	1.26535i	0.226101	−	0.974104i	$-0.427402\pi$
$384$	1.01906e11	−	1.76506e11i	0.239171	−	0.414256i
$385$	4.08787e10	−	4.19169e10i	0.0948251	−	0.0972335i
$386$	−3.08509e11	+	5.34353e11i	−0.707335	+	1.22514i
$387$	−2.11041e11			−0.478265
$388$	9.90304e10	−	1.71526e11i	0.221833	−	0.384226i
$389$	−3.77737e11	−	6.54260e11i	−0.836405	−	1.44870i	−0.892881	−	0.450293i	$-0.851320\pi$
$389$	−3.77737e11	−	6.54260e11i	−0.836405	−	1.44870i	0.0564757	−	0.998404i	$-0.482014\pi$
$390$	5.48062e10	+	1.33859e10i	0.119961	+	0.0292992i
$391$	2.61365e9			0.00565526
$392$	−1.44710e11	+	8.84596e10i	−0.309537	+	0.189216i
$393$	−3.47541e10	−	6.01958e10i	−0.0734919	−	0.127292i
$394$	1.88865e11	+	3.27124e11i	0.394837	+	0.683878i
$395$	1.52379e10	+	2.63928e10i	0.0314947	+	0.0545504i
$396$	1.85833e11			0.379747
$397$	−8.42912e10	−	1.45997e11i	−0.170304	−	0.294975i	0.768222	−	0.640183i	$-0.221142\pi$
$397$	−8.42912e10	−	1.45997e11i	−0.170304	−	0.294975i	−0.938526	+	0.345208i	$0.887808\pi$
$398$	−7.62274e10			−0.152278
$399$	−5.16503e10	−	1.83525e11i	−0.102022	−	0.362507i
$400$	−3.01408e11	−	5.22054e11i	−0.588688	−	1.01964i
$401$	−9.01757e11			−1.74157			−0.870783	−	0.491668i	$-0.836387\pi$
$401$	−9.01757e11			−1.74157			−0.870783	+	0.491668i	$0.836387\pi$
$402$	−3.01724e11	−	5.22602e11i	−0.576226	−	0.998053i
$403$	9.11474e11	+	2.22618e11i	1.72136	+	0.420425i
$404$	−1.43866e11	+	2.49184e11i	−0.268685	+	0.465376i
$405$	7.01017e9	+	1.21420e10i	0.0129474	+	0.0224255i
$406$	1.98519e11	−	2.03561e11i	0.362605	−	0.371815i
$407$	2.57266e10	−	4.45598e10i	0.0464738	−	0.0804950i
$408$	2.41404e9	−	4.18125e9i	0.00431295	−	0.00747025i
$409$	9.56217e11			1.68967			0.844835	−	0.535027i	$-0.179699\pi$
$409$	9.56217e11			1.68967			0.844835	+	0.535027i	$0.179699\pi$
$410$	−6.67982e10			−0.116745
$411$	2.28828e11	−	3.96342e11i	0.395568	−	0.685143i
$412$	2.17602e11	−	3.76898e11i	0.372071	−	0.644445i
$413$	−9.23793e10	−	3.28244e11i	−0.156243	−	0.555164i
$414$	3.39152e10	+	5.87429e10i	0.0567405	+	0.0982774i
$415$	2.24164e10	−	3.88263e10i	0.0370979	−	0.0642555i
$416$	5.11982e11	−	5.35287e11i	0.838175	−	0.876328i
$417$	2.72053e11	+	4.71209e11i	0.440596	+	0.763135i
$418$	4.45604e11			0.713930
$419$	−2.24059e11	−	3.88081e11i	−0.355139	−	0.615119i	0.632002	−	0.774966i	$-0.282233\pi$
$419$	−2.24059e11	−	3.88081e11i	−0.355139	−	0.615119i	−0.987142	+	0.159847i	$0.948900\pi$
$420$	−3.03059e10	+	3.10756e10i	−0.0475231	+	0.0487301i
$421$	8.91371e9			0.0138289			0.00691447	−	0.999976i	$-0.497799\pi$
$421$	8.91371e9			0.0138289			0.00691447	+	0.999976i	$0.497799\pi$
$422$	3.88769e11	+	6.73368e11i	0.596741	+	1.03359i
$423$	−1.25963e10			−0.0191298
$424$	−8.32726e10	−	1.44232e11i	−0.125128	−	0.216729i
$425$	−1.14460e10	−	1.98251e10i	−0.0170178	−	0.0294758i
$426$	1.51035e11	+	2.61600e11i	0.222195	+	0.384853i
$427$	−7.45349e11	+	7.64280e11i	−1.08501	+	1.11257i
$428$	−1.75675e11			−0.253053
$429$	4.62333e11	+	1.12920e11i	0.659018	+	0.160959i
$430$	5.76067e10	+	9.97778e10i	0.0812578	+	0.140743i
$431$	−5.31916e11	+	9.21306e11i	−0.742498	+	1.28605i	0.208856	+	0.977946i	$0.433026\pi$
$431$	−5.31916e11	+	9.21306e11i	−0.742498	+	1.28605i	−0.951354	+	0.308099i	$0.900307\pi$
$432$	9.11074e11			1.25857
$433$	4.85539e11	−	8.40979e11i	0.663787	−	1.14971i	−0.315826	−	0.948817i	$-0.602281\pi$
$433$	4.85539e11	−	8.40979e11i	0.663787	−	1.14971i	0.979613	−	0.200896i	$-0.0643852\pi$
$434$	−1.20048e12	+	1.23097e12i	−1.62424	+	1.66550i
$435$	−1.38932e10	+	2.40637e10i	−0.0186037	+	0.0322226i
$436$	7.61451e10	+	1.31887e11i	0.100914	+	0.174789i
$437$	3.41435e10	+	5.91382e10i	0.0447859	+	0.0775714i
$438$	−6.71476e11			−0.871760
$439$	−3.20507e11			−0.411858			−0.205929	−	0.978567i	$-0.566022\pi$
$439$	−3.20507e11			−0.411858			−0.205929	+	0.978567i	$0.566022\pi$
$440$	1.93693e10	+	3.35486e10i	0.0246364	+	0.0426715i
$441$	−3.69867e11	−	2.01349e11i	−0.465664	−	0.253499i
$442$	2.52593e10	−	2.64091e10i	0.0314791	−	0.0329120i
$443$	−6.64063e11	+	1.15019e12i	−0.819204	+	1.41890i	0.0870646	+	0.996203i	$0.472251\pi$
$443$	−6.64063e11	+	1.15019e12i	−0.819204	+	1.41890i	−0.906269	+	0.422701i	$0.861082\pi$
$444$	−1.90727e10	+	3.30349e10i	−0.0232911	+	0.0403413i
$445$	−4.48084e10	+	7.76104e10i	−0.0541676	+	0.0938210i
$446$	−1.94229e11	−	3.36414e11i	−0.232437	−	0.402594i
$447$	9.75419e11			1.15560
$448$	9.05640e10	+	3.21794e11i	0.106220	+	0.377421i
$449$	−2.84640e11	+	4.93010e11i	−0.330512	+	0.572463i	−0.982612	−	0.185670i	$-0.940555\pi$
$449$	−2.84640e11	+	4.93010e11i	−0.330512	+	0.572463i	0.652101	+	0.758132i	$0.273888\pi$
$450$	2.97051e11	−	5.14508e11i	0.341488	−	0.591474i
$451$	−5.63496e11			−0.641352
$452$	2.11739e10	−	3.66743e10i	0.0238604	−	0.0413275i
$453$	−5.22007e11			−0.582417
$454$	−1.77128e11			−0.195675
$455$	1.06399e11	−	6.64680e10i	0.116382	−	0.0727045i
$456$	1.26143e11			0.136623
$457$	1.68242e12			1.80431			0.902153	−	0.431416i	$-0.141986\pi$
$457$	1.68242e12			1.80431			0.902153	+	0.431416i	$0.141986\pi$
$458$	−5.01226e11	+	8.68150e11i	−0.532279	+	0.921934i
$459$	3.45982e10			0.0363828
$460$	7.77350e9	−	1.34641e10i	0.00809481	−	0.0140206i
$461$	5.46456e11	−	9.46490e11i	0.563510	−	0.976027i	−0.433677	−	0.901068i	$-0.642784\pi$
$461$	5.46456e11	−	9.46490e11i	0.563510	−	0.976027i	0.997187	−	0.0749590i	$-0.0238826\pi$
$462$	−6.08927e11	+	6.24393e11i	−0.621837	+	0.637631i
$463$	5.66744e11			0.573156			0.286578	−	0.958057i	$-0.407482\pi$
$463$	5.66744e11			0.573156			0.286578	+	0.958057i	$0.407482\pi$
$464$	2.36978e11	+	4.10458e11i	0.237344	+	0.411091i
$465$	8.40147e10	−	1.45518e11i	0.0833330	−	0.144337i
$466$	−8.28913e11	+	1.43572e12i	−0.814277	+	1.41037i
$467$	−5.48785e10	+	9.50524e10i	−0.0533920	+	0.0924777i	−0.891486	−	0.453048i	$-0.850337\pi$
$467$	−5.48785e10	+	9.50524e10i	−0.0533920	+	0.0924777i	0.838094	+	0.545526i	$0.183670\pi$
$468$	3.86812e11	+	9.44749e10i	0.372729	+	0.0910353i
$469$	−1.30041e12	−	3.31024e11i	−1.24109	−	0.315924i
$470$	3.43833e9	+	5.95537e9i	0.00325018	+	0.00562948i
$471$	9.53233e11			0.892494
$472$	2.25614e11			0.209232
$473$	4.85958e11	+	8.41704e11i	0.446400	+	0.773187i
$474$	−2.26983e11	−	3.93146e11i	−0.206534	−	0.357727i
$475$	2.99050e11	−	5.17971e11i	0.269540	−	0.466857i
$476$	7.61708e9	+	2.70652e10i	0.00680076	+	0.0241646i
$477$	2.06761e11	−	3.58120e11i	0.182867	−	0.316735i
$478$	1.52665e12			1.33756
$479$	−5.89918e11	+	1.02177e12i	−0.512014	+	0.886834i	0.487889	+	0.872906i	$0.337767\pi$
$479$	−5.89918e11	+	1.02177e12i	−0.512014	+	0.886834i	−0.999903	+	0.0139285i	$0.995566\pi$
$480$	−6.63254e10	−	1.14879e11i	−0.0570288	−	0.0987768i
$481$	7.62036e10	−	7.96723e10i	0.0649117	−	0.0678664i
$482$	1.03553e12			0.873876
$483$	−1.29524e11	−	3.29708e10i	−0.108290	−	0.0275656i
$484$	8.92138e9	+	1.54523e10i	0.00738972	+	0.0127994i
$485$	5.12574e10	+	8.87804e10i	0.0420648	+	0.0728583i
$486$	7.42348e11	+	1.28579e12i	0.603593	+	1.04545i
$487$	−1.30273e12			−1.04948			−0.524742	−	0.851261i	$-0.675838\pi$
$487$	−1.30273e12			−1.04948			−0.524742	+	0.851261i	$0.675838\pi$
$488$	−3.53165e11	−	6.11699e11i	−0.281895	−	0.488257i
$489$	1.50631e12			1.19131
$490$	5.76504e9	+	2.29830e11i	0.00451772	+	0.180104i
$491$	−5.71529e11	−	9.89917e11i	−0.443784	−	0.768656i	0.554183	−	0.832395i	$-0.313031\pi$
$491$	−5.71529e11	−	9.89917e11i	−0.443784	−	0.768656i	−0.997967	+	0.0637389i	$0.979698\pi$
$492$	4.17754e11			0.321424
$493$	8.99930e9	+	1.55872e10i	0.00686116	+	0.0118839i
$494$	9.27525e11	+	2.26539e11i	0.700736	+	0.171148i
$495$	−4.80928e10	+	8.32992e10i	−0.0360045	+	0.0623616i
$496$	−1.43305e12	−	2.48212e12i	−1.06315	−	1.84143i
$497$	6.50949e11	+	1.65702e11i	0.478568	+	0.121821i
$498$	−3.33914e11	+	5.78356e11i	−0.243278	+	0.421370i
$499$	−2.53703e11	+	4.39427e11i	−0.183178	+	0.317274i	−0.942961	−	0.332903i	$-0.891972\pi$
$499$	−2.53703e11	+	4.39427e11i	−0.183178	+	0.317274i	0.759783	+	0.650177i	$0.225305\pi$
$500$	−2.74955e11			−0.196742
$501$	−1.22672e12			−0.869912
$502$	1.63319e12	−	2.82877e12i	1.14781	−	1.98807i
$503$	−2.74308e11	+	4.75115e11i	−0.191065	+	0.330935i	−0.945604	−	0.325321i	$-0.894528\pi$
$503$	−2.74308e11	+	4.75115e11i	−0.191065	+	0.330935i	0.754538	+	0.656256i	$0.227861\pi$
$504$	1.94534e11	−	1.99475e11i	0.134295	−	0.137705i
$505$	−7.44641e10	−	1.28976e11i	−0.0509490	−	0.0882463i
$506$	1.56191e11	−	2.70531e11i	0.105920	−	0.183459i
$507$	9.04940e11	+	4.70088e11i	0.608253	+	0.315968i
$508$	1.03872e12	+	1.79911e12i	0.692008	+	1.19859i
$509$	4.83245e11			0.319108			0.159554	−	0.987189i	$-0.448994\pi$
$509$	4.83245e11			0.319108			0.159554	+	0.987189i	$0.448994\pi$
$510$	−3.27225e9	−	5.66771e9i	−0.00214181	−	0.00370973i
$511$	−1.04250e12	+	1.06897e12i	−0.676364	+	0.693543i
$512$	−1.58572e12			−1.01979
$513$	4.51974e11	+	7.82842e11i	0.288128	+	0.499052i
$514$	−3.82707e12			−2.41842
$515$	1.12629e11	+	1.95079e11i	0.0705534	+	0.122202i
$516$	−3.60271e11	−	6.24007e11i	−0.223720	−	0.387495i
$517$	2.90051e10	+	5.02382e10i	0.0178553	+	0.0309262i
$518$	5.47338e10	+	1.94481e11i	0.0334019	+	0.118684i
$519$	−3.05492e11			−0.184819
$520$	2.32616e10	+	7.96786e10i	0.0139516	+	0.0477889i
$521$	−6.14800e11	−	1.06486e12i	−0.365564	−	0.633176i	0.623302	−	0.781981i	$-0.285791\pi$
$521$	−6.14800e11	−	1.06486e12i	−0.365564	−	0.633176i	−0.988867	+	0.148805i	$0.952457\pi$
$522$	−2.33553e11	+	4.04525e11i	−0.137679	+	0.238467i
$523$	2.59064e12			1.51408			0.757042	−	0.653366i	$-0.226644\pi$
$523$	2.59064e12			1.51408			0.757042	+	0.653366i	$0.226644\pi$
$524$	−1.33909e11	+	2.31938e11i	−0.0775926	+	0.134394i
$525$	3.17137e11	+	1.12686e12i	0.182192	+	0.647369i
$526$	−8.93438e11	+	1.54748e12i	−0.508895	+	0.881433i
$527$	−5.44204e10	−	9.42589e10i	−0.0307337	−	0.0532322i
$528$	−7.26897e11	−	1.25902e12i	−0.407024	−	0.704986i
$529$	−1.75328e12			−0.973422
$530$	−2.25753e11			−0.124277
$531$	2.80093e11	+	4.85136e11i	0.152889	+	0.264812i
$532$	−5.12889e11	+	5.25915e11i	−0.277601	+	0.284651i
$533$	−1.17292e12	−	2.86473e11i	−0.629499	−	0.153749i
$534$	6.67465e11	−	1.15608e12i	0.355216	−	0.615252i
$535$	4.54639e10	−	7.87458e10i	0.0239925	−	0.0415562i
$536$	4.43917e11	−	7.68887e11i	0.232306	−	0.402366i
$537$	−4.93964e11	−	8.55571e11i	−0.256337	−	0.443989i
$538$	4.88406e12			2.51340
$539$	4.86326e10	+	1.93880e12i	0.0248187	+	0.989425i
$540$	1.02902e11	−	1.78231e11i	0.0520776	−	0.0902010i
$541$	−7.42126e11	+	1.28540e12i	−0.372469	+	0.645135i	−0.989945	−	0.141455i	$-0.954822\pi$
$541$	−7.42126e11	+	1.28540e12i	−0.372469	+	0.645135i	0.617476	+	0.786590i	$0.288155\pi$
$542$	8.90568e11			0.443272
$543$	4.80623e11	−	8.32464e11i	0.237250	−	0.410928i
$544$	−8.59244e10			−0.0420651
$545$	−7.88242e10			−0.0382715
$546$	−1.58492e12	+	9.90105e11i	−0.763202	+	0.476776i
$547$	−8.57635e11			−0.409599			−0.204800	−	0.978804i	$-0.565654\pi$
$547$	−8.57635e11			−0.409599			−0.204800	+	0.978804i	$0.565654\pi$
$548$	−1.76337e12			−0.835280
$549$	8.76887e11	−	1.51881e12i	0.411972	−	0.713557i
$550$	−2.73604e12			−1.27494
$551$	−2.35125e11	+	4.07248e11i	−0.108672	+	0.188225i
$552$	4.42152e10	−	7.65830e10i	0.0202696	−	0.0351080i
$553$	−9.78280e11	−	2.49025e11i	−0.444836	−	0.113235i
$554$	−1.74703e12			−0.787962
$555$	−9.87190e9	−	1.70986e10i	−0.00441654	−	0.00764967i
$556$	1.04823e12	−	1.81560e12i	0.465181	−	0.805717i
$557$	−1.87982e12	+	3.25594e12i	−0.827498	+	1.43327i	0.0724979	+	0.997369i	$0.476903\pi$
$557$	−1.87982e12	+	3.25594e12i	−0.827498	+	1.43327i	−0.899995	+	0.435899i	$0.856430\pi$
$558$	1.41234e12	−	2.44624e12i	0.616715	−	1.06818i
$559$	5.83612e11	+	1.99906e12i	0.252797	+	0.865911i
$560$	−3.71379e11	−	9.45359e10i	−0.159577	−	0.0406210i
$561$	−2.76040e10	−	4.78116e10i	−0.0117663	−	0.0203798i
$562$	3.23363e12			1.36734
$563$	2.94126e12			1.23380			0.616900	−	0.787041i	$-0.288388\pi$
$563$	2.94126e12			1.23380			0.616900	+	0.787041i	$0.288388\pi$
$564$	−2.15032e10	−	3.72447e10i	−0.00894845	−	0.0154992i
$565$	1.09595e10	+	1.89823e10i	0.00452450	+	0.00783667i
$566$	−4.32495e10	+	7.49104e10i	−0.0177136	+	0.0306809i
$567$	−4.50057e11	−	1.14564e11i	−0.182871	−	0.0465504i
$568$	−2.22213e11	+	3.84883e11i	−0.0895780	+	0.155154i
$569$	−1.34996e12			−0.539903			−0.269952	−	0.962874i	$-0.587008\pi$
$569$	−1.34996e12			−0.539903			−0.269952	+	0.962874i	$0.587008\pi$
$570$	8.54942e10	−	1.48080e11i	0.0339234	−	0.0587571i
$571$	1.76993e12	+	3.06561e12i	0.696776	+	1.20685i	0.969578	+	0.244782i	$0.0787164\pi$
$571$	1.76993e12	+	3.06561e12i	0.696776	+	1.20685i	−0.272802	+	0.962070i	$0.587950\pi$
$572$	−5.13901e11	−	1.76028e12i	−0.200723	−	0.687542i
$573$	2.37417e12			0.920060
$574$	1.54482e12	−	1.58406e12i	0.593984	−	0.609070i
$575$	−2.09643e11	−	3.63113e11i	−0.0799790	−	0.138528i
$576$	−2.74589e11	−	4.75603e11i	−0.103940	−	0.180029i
$577$	8.15670e11	+	1.41278e12i	0.306354	+	0.530621i	0.977562	−	0.210649i	$-0.0675576\pi$
$577$	8.15670e11	+	1.41278e12i	0.306354	+	0.530621i	−0.671208	+	0.741269i	$0.734224\pi$
$578$	3.51868e12			1.31131
$579$	9.98645e11	+	1.72970e12i	0.369282	+	0.639615i
$580$	1.07062e11			0.0392836
$581$	4.02313e11	+	1.42951e12i	0.146478	+	0.520468i
$582$	−7.63529e11	−	1.32247e12i	−0.275849	−	0.477785i
$583$	−1.90441e12			−0.682733
$584$	−4.93960e11	−	8.55564e11i	−0.175725	−	0.304365i
$585$	−1.42453e11	+	1.48938e11i	−0.0502888	+	0.0525779i
$586$	7.80419e11	−	1.35172e12i	0.273394	−	0.473532i
$587$	−1.24372e12	−	2.15418e12i	−0.432364	−	0.748877i	0.564712	−	0.825288i	$-0.308987\pi$
$587$	−1.24372e12	−	2.15418e12i	−0.432364	−	0.748877i	−0.997076	+	0.0764109i	$0.975654\pi$
$588$	−3.60543e10	−	1.43735e12i	−0.0124383	−	0.495866i
$589$	1.42184e12	−	2.46270e12i	0.486780	−	0.843128i
$590$	1.52911e11	−	2.64849e11i	0.0519522	−	0.0899839i
$591$	1.22271e12			0.412269
$592$	−3.36773e11			−0.112691
$593$	−2.46531e12	+	4.27005e12i	−0.818702	+	1.41803i	0.0879370	+	0.996126i	$0.471973\pi$
$593$	−2.46531e12	+	4.27005e12i	−0.818702	+	1.41803i	−0.906639	+	0.421907i	$0.861361\pi$
$594$	2.06758e12	−	3.58115e12i	0.681432	−	1.18027i
$595$	−1.41032e10	−	3.59002e9i	−0.00461308	−	0.00117428i
$596$	−1.87917e12	−	3.25482e12i	−0.610041	−	1.05662i
$597$	−1.23374e11	+	2.13691e11i	−0.0397503	+	0.0688495i
$598$	4.62646e11	−	4.83704e11i	0.147943	−	0.154677i
$599$	2.22176e12	+	3.84821e12i	0.705143	+	1.22134i	0.966640	+	0.256139i	$0.0824506\pi$
$599$	2.22176e12	+	3.84821e12i	0.705143	+	1.22134i	−0.261497	+	0.965204i	$0.584216\pi$
$600$	−7.74530e11			−0.243982
$601$	5.53017e11	+	9.57853e11i	0.172903	+	0.299477i	0.939434	−	0.342731i	$-0.111352\pi$
$601$	5.53017e11	+	9.57853e11i	0.172903	+	0.299477i	−0.766530	+	0.642208i	$0.778019\pi$
$602$	−3.69839e12	−	9.41439e11i	−1.14770	−	0.292151i
$603$	2.20444e12			0.679001
$604$	1.00566e12	+	1.74186e12i	0.307458	+	0.532532i
$605$	−9.23527e9			−0.00280253
$606$	1.10922e12	+	1.92122e12i	0.334110	+	0.578695i
$607$	−1.71819e12	−	2.97599e12i	−0.513715	−	0.889781i	−0.999873	−	0.0159099i	$-0.994936\pi$
$607$	−1.71819e12	−	2.97599e12i	−0.513715	−	0.889781i	0.486158	−	0.873871i	$-0.338398\pi$
$608$	−1.12247e12	−	1.94418e12i	−0.333127	−	0.576993i
$609$	−2.49345e11	−	8.85976e11i	−0.0734551	−	0.261002i
$610$	−9.57434e11			−0.279978
$611$	3.48337e10	+	1.19317e11i	0.0101115	+	0.0346351i
$612$	−2.30950e10	−	4.00016e10i	−0.00665481	−	0.0115265i
$613$	−1.38273e11	+	2.39495e11i	−0.0395516	+	0.0685054i	−0.885124	−	0.465356i	$-0.845926\pi$
$613$	−1.38273e11	+	2.39495e11i	−0.0395516	+	0.0685054i	0.845572	+	0.533861i	$0.179260\pi$
$614$	2.43092e12			0.690261
$615$	−1.08113e11	+	1.87257e11i	−0.0304748	+	0.0527838i
$616$	−1.24352e12	−	3.16543e11i	−0.347968	−	0.0885767i
$617$	−1.79778e12	+	3.11384e12i	−0.499404	+	0.864994i	−1.00000		0.000687532i	$-0.999781\pi$
$617$	−1.79778e12	+	3.11384e12i	−0.499404	+	0.864994i	0.500595	+	0.865681i	$0.333114\pi$
$618$	−1.67772e12	−	2.90590e12i	−0.462670	−	0.801368i
$619$	−2.08254e12	−	3.60706e12i	−0.570145	−	0.987520i	−0.996551	−	0.0829882i	$-0.973554\pi$
$619$	−2.08254e12	−	3.60706e12i	−0.570145	−	0.987520i	0.426405	−	0.904532i	$-0.359780\pi$
$620$	−6.47427e11			−0.175966
$621$	6.33695e11			0.170989
$622$	1.54806e12	+	2.68132e12i	0.414698	+	0.718278i
$623$	−8.04188e11	−	2.85746e12i	−0.213876	−	0.759947i
$624$	−8.72967e11	−	2.99020e12i	−0.230498	−	0.789532i
$625$	−1.80027e12	+	3.11817e12i	−0.471931	+	0.817409i
$626$	−2.50981e12	+	4.34712e12i	−0.653216	+	1.13140i
$627$	7.21211e11	−	1.24917e12i	0.186362	−	0.322789i
$628$	−1.83643e12	−	3.18079e12i	−0.471147	−	0.816051i
$629$	−1.27890e10			−0.00325769
$630$	−1.02318e11	−	3.63559e11i	−0.0258774	−	0.0919481i
$631$	−2.71466e12	+	4.70194e12i	−0.681685	+	1.18071i	0.292781	+	0.956180i	$0.405419\pi$
$631$	−2.71466e12	+	4.70194e12i	−0.681685	+	1.18071i	−0.974466	+	0.224534i	$0.927914\pi$
$632$	3.33952e11	−	5.78423e11i	0.0832641	−	0.144218i
$633$	2.51690e12			0.623087
$634$	2.50876e12	−	4.34531e12i	0.616678	−	1.06812i
$635$	−1.07526e12			−0.262442
$636$	1.41185e12			0.342162
$637$	−8.84428e11	+	4.06033e12i	−0.212831	+	0.977089i
$638$	2.15118e12			0.514024
$639$	−1.10348e12			−0.261825
$640$	2.03232e11	−	3.52008e11i	0.0478831	−	0.0829359i
$641$	4.52327e12			1.05826			0.529129	−	0.848542i	$-0.322519\pi$
$641$	4.52327e12			1.05826			0.529129	+	0.848542i	$0.322519\pi$
$642$	−6.77229e11	+	1.17300e12i	−0.157336	+	0.272514i
$643$	−2.28177e12	+	3.95214e12i	−0.526407	+	0.911764i	0.473119	+	0.880998i	$0.343128\pi$
$643$	−2.28177e12	+	3.95214e12i	−0.526407	+	0.911764i	−0.999527	+	0.0307658i	$0.990205\pi$
$644$	1.39513e11	+	4.95721e11i	0.0319616	+	0.113567i
$645$	3.72947e11			0.0848453
$646$	−5.53788e10	−	9.59189e10i	−0.0125111	−	0.0216699i
$647$	3.08662e12	−	5.34618e12i	0.692490	−	1.19943i	−0.278529	−	0.960428i	$-0.589847\pi$
$647$	3.08662e12	−	5.34618e12i	0.692490	−	1.19943i	0.971019	−	0.239001i	$-0.0768198\pi$
$648$	1.53635e11	−	2.66103e11i	0.0342296	−	0.0592874i
$649$	1.28992e12	−	2.23421e12i	0.285406	−	0.494337i
$650$	−5.69507e12	−	1.39097e12i	−1.25138	−	0.305637i
$651$	1.50783e12	+	5.35767e12i	0.329033	+	1.16913i
$652$	−2.90195e12	−	5.02633e12i	−0.628892	−	1.08927i
$653$	−3.85243e11			−0.0829136			−0.0414568	−	0.999140i	$-0.513200\pi$
$653$	−3.85243e11			−0.0829136			−0.0414568	+	0.999140i	$0.513200\pi$
$654$	1.17416e12			0.250974
$655$	−6.93105e10	−	1.20049e11i	−0.0147134	−	0.0254844i
$656$	1.84410e12	+	3.19408e12i	0.388792	+	0.673408i
$657$	1.22647e12	−	2.12432e12i	0.256811	−	0.444810i
$658$	−2.20743e11	−	5.61910e10i	−0.0459061	−	0.0116856i
$659$	2.79656e11	−	4.84378e11i	0.0577617	−	0.100046i	−0.835699	−	0.549188i	$-0.814937\pi$
$659$	2.79656e11	−	4.84378e11i	0.0577617	−	0.100046i	0.893460	+	0.449142i	$0.148270\pi$
$660$	−3.28399e11			−0.0673680
$661$	2.16316e11	−	3.74670e11i	0.0440739	−	0.0763382i	−0.843147	−	0.537683i	$-0.819300\pi$
$661$	2.16316e11	−	3.74670e11i	0.0440739	−	0.0763382i	0.887221	+	0.461345i	$0.152633\pi$
$662$	−4.56209e11	−	7.90176e11i	−0.0923214	−	0.159905i
$663$	−3.31511e10	−	1.13553e11i	−0.00666327	−	0.0228239i
$664$	−9.82554e11			−0.196155
$665$	−1.03007e11	−	3.66006e11i	−0.0204253	−	0.0725756i
$666$	−1.65953e11	−	2.87438e11i	−0.0326851	−	0.0566123i
$667$	1.64829e11	+	2.85493e11i	0.0322455	+	0.0558508i
$668$	2.36331e12	+	4.09337e12i	0.459226	+	0.795403i
$669$	−1.25744e12			−0.242699
$670$	−6.01733e11	−	1.04223e12i	−0.115363	−	0.199815i
$671$	−8.07671e12			−1.53810
$672$	4.25813e12	+	1.08392e12i	0.805484	+	0.205039i
$673$	1.09884e12	+	1.90324e12i	0.206474	+	0.357623i	0.950601	−	0.310414i	$-0.100468\pi$
$673$	1.09884e12	+	1.90324e12i	0.206474	+	0.357623i	−0.744127	+	0.668038i	$0.767135\pi$
$674$	1.90800e12			0.356130
$675$	−2.77515e12	−	4.80671e12i	−0.514541	−	0.891211i
$676$	−1.74784e11	−	3.92528e12i	−0.0321915	−	0.722954i
$677$	1.96758e12	−	3.40794e12i	0.359983	−	0.623509i	−0.627974	−	0.778234i	$-0.716116\pi$
$677$	1.96758e12	−	3.40794e12i	0.359983	−	0.623509i	0.987958	+	0.154725i	$0.0494490\pi$
$678$	−1.63252e11	−	2.82760e11i	−0.0296705	−	0.0513907i
$679$	−3.29075e12	−	8.37674e11i	−0.594130	−	0.151238i
$680$	4.81436e9	−	8.33871e9i	0.000863472	−	0.00149558i
$681$	−2.86682e11	+	4.96547e11i	−0.0510785	+	0.0884705i
$682$	−1.30086e13			−2.30250
$683$	1.01510e13			1.78492			0.892458	−	0.451130i	$-0.148979\pi$
$683$	1.01510e13			1.78492			0.892458	+	0.451130i	$0.148979\pi$
$684$	6.03402e11	−	1.04512e12i	0.105403	−	0.182564i
$685$	4.56354e11	−	7.90429e11i	0.0791944	−	0.137169i
$686$	−5.58352e12	−	5.17849e12i	−0.962609	−	0.892780i
$687$	1.62247e12	+	2.81020e12i	0.277889	+	0.481318i
$688$	3.18070e12	−	5.50914e12i	0.541222	−	0.937424i
$689$	−3.96402e12	−	9.68173e11i	−0.670115	−	0.163669i
$690$	−5.99340e10	−	1.03809e11i	−0.0100659	−	0.0174346i
$691$	6.20535e12			1.03542			0.517708	−	0.855557i	$-0.326785\pi$
$691$	6.20535e12			1.03542			0.517708	+	0.855557i	$0.326785\pi$
$692$	5.88538e11	+	1.01938e12i	0.0975657	+	0.168989i
$693$	−8.63135e11	−	3.06691e12i	−0.142161	−	0.505128i
$694$	2.80709e12			0.459345
$695$	5.42558e11	+	9.39738e11i	0.0882094	+	0.152783i
$696$	6.08965e11			0.0983672
$697$	7.00302e10	+	1.21296e11i	0.0112393	+	0.0194670i
$698$	−9.18766e11	−	1.59135e12i	−0.146506	−	0.253756i
$699$	2.68319e12	+	4.64743e12i	0.425113	+	0.736318i
$700$	3.14917e12	−	3.22916e12i	0.495742	−	0.508333i
$701$	3.23633e12			0.506199			0.253100	−	0.967440i	$-0.418550\pi$
$701$	3.23633e12			0.506199			0.253100	+	0.967440i	$0.418550\pi$
$702$	6.12427e12	−	6.40304e12i	0.951781	−	0.995105i
$703$	−1.67069e11	−	2.89373e11i	−0.0257987	−	0.0446847i
$704$	−1.26458e12	+	2.19031e12i	−0.194030	+	0.336069i
$705$	2.22598e10			0.00339368
$706$	−6.66155e12	+	1.15381e13i	−1.00915	+	1.74789i
$707$	4.78064e12	+	1.21693e12i	0.719612	+	0.183180i
$708$	−9.56300e11	+	1.65636e12i	−0.143036	+	0.247745i
$709$	−4.37436e12	−	7.57661e12i	−0.650139	−	1.12607i	−0.983089	−	0.183129i	$-0.941377\pi$
$709$	−4.37436e12	−	7.57661e12i	−0.650139	−	1.12607i	0.332950	−	0.942944i	$-0.391956\pi$
$710$	3.01211e11	+	5.21712e11i	0.0444844	+	0.0770493i
$711$	1.65837e12			0.243370
$712$	1.96404e12			0.286411
$713$	−9.96754e11	−	1.72643e12i	−0.144439	−	0.250176i
$714$	2.10081e11	+	5.34768e10i	0.0302513	+	0.00770059i
$715$	9.22037e11	+	2.25198e11i	0.131938	+	0.0322246i
$716$	−1.90327e12	+	3.29656e12i	−0.270640	+	0.468763i
$717$	2.47088e12	−	4.27970e12i	0.349153	−	0.604751i
$718$	−7.73944e12	+	1.34051e13i	−1.08680	+	1.88239i
$719$	8.68756e11	+	1.50473e12i	0.121232	+	0.209980i	0.920254	−	0.391322i	$-0.127982\pi$
$719$	8.68756e11	+	1.50473e12i	0.121232	+	0.209980i	−0.799022	+	0.601302i	$0.794649\pi$
$720$	6.29556e11			0.0873049
$721$	−7.23085e12	−	1.84064e12i	−0.996508	−	0.253665i
$722$	−3.34620e12	+	5.79578e12i	−0.458283	+	0.793770i
$723$	1.67600e12	−	2.90292e12i	0.228114	−	0.395106i
$724$	−3.70374e12			−0.500976
$725$	1.44368e12	−	2.50053e12i	0.194067	−	0.336133i
$726$	1.37568e11			0.0183782
$727$	−9.06597e11			−0.120367			−0.0601837	−	0.998187i	$-0.519169\pi$
$727$	−9.06597e11			−0.120367			−0.0601837	+	0.998187i	$0.519169\pi$
$728$	−2.42746e12	−	1.29107e12i	−0.320304	−	0.170357i
$729$	6.24494e12			0.818944
$730$	−1.33913e12			−0.174530
$731$	1.20788e11	−	2.09211e11i	0.0156457	−	0.0270992i
$732$	5.98776e12			0.770841
$733$	1.62882e12	−	2.82120e12i	0.208404	−	0.360966i	−0.742808	−	0.669504i	$-0.766507\pi$
$733$	1.62882e12	−	2.82120e12i	0.208404	−	0.360966i	0.951212	+	0.308539i	$0.0998399\pi$
$734$	−6.77269e12	+	1.17306e13i	−0.861249	+	1.49173i
$735$	6.53619e11	+	3.55819e11i	0.0826098	+	0.0449714i
$736$	−1.57378e12			−0.197694
$737$	−5.07609e12	−	8.79204e12i	−0.633761	−	1.09771i
$738$	−1.81745e12	+	3.14791e12i	−0.225532	+	0.390633i
$739$	1.66466e12	−	2.88328e12i	0.205318	−	0.355621i	−0.744916	−	0.667158i	$-0.767511\pi$
$739$	1.66466e12	−	2.88328e12i	0.205318	−	0.355621i	0.950234	+	0.311537i	$0.100844\pi$
$740$	−3.80370e10	+	6.58820e10i	−0.00466298	+	0.00807652i
$741$	2.13626e12	−	2.23350e12i	0.260299	−	0.272148i
$742$	5.22092e12	−	5.35352e12i	0.632309	−	0.648368i
$743$	1.31415e12	+	2.27617e12i	0.158196	+	0.274003i	0.934218	−	0.356702i	$-0.116099\pi$
$743$	1.31415e12	+	2.27617e12i	0.158196	+	0.274003i	−0.776022	+	0.630705i	$0.782766\pi$
$744$	−3.68252e12			−0.440623
$745$	1.94529e12			0.231356
$746$	5.83280e12	+	1.01027e13i	0.689529	+	1.19430i
$747$	−1.21981e12	−	2.11277e12i	−0.143334	−	0.248262i
$748$	−1.06360e11	+	1.84221e11i	−0.0124228	+	0.0215170i
$749$	8.15953e11	+	2.89926e12i	0.0947321	+	0.336604i
$750$	−1.05996e12	+	1.83590e12i	−0.122324	+	0.211872i
$751$	−6.25905e12			−0.718007			−0.359004	−	0.933336i	$-0.616883\pi$
$751$	−6.25905e12			−0.718007			−0.359004	+	0.933336i	$0.616883\pi$
$752$	1.89845e11	−	3.28820e11i	0.0216480	−	0.0374954i
$753$	−5.28665e12	−	9.15675e12i	−0.599243	−	1.03792i
$754$	4.47768e12	+	1.09363e12i	0.504524	+	0.123225i
$755$	−1.04104e12			−0.116603
$756$	1.84680e12	+	6.56210e12i	0.205623	+	0.730626i
$757$	2.01450e12	+	3.48921e12i	0.222964	+	0.386186i	0.955707	−	0.294320i	$-0.0950933\pi$
$757$	2.01450e12	+	3.48921e12i	0.222964	+	0.386186i	−0.732742	+	0.680506i	$0.761760\pi$
$758$	3.83686e12	+	6.64563e12i	0.422147	+	0.731181i
$759$	−5.05590e11	−	8.75708e11i	−0.0552982	−	0.0957793i
$760$	2.51570e11			0.0273525
$761$	−1.96232e11	−	3.39883e11i	−0.0212099	−	0.0367366i	0.855226	−	0.518256i	$-0.173418\pi$
$761$	−1.96232e11	−	3.39883e11i	−0.0212099	−	0.0367366i	−0.876436	+	0.481519i	$0.840085\pi$
$762$	1.60171e13			1.72102
$763$	1.82294e12	−	1.86924e12i	0.194721	−	0.199666i
$764$	−4.57391e12	−	7.92224e12i	−0.485699	−	0.841256i
$765$	2.39075e10			0.00252382
$766$	9.13914e12	+	1.58295e13i	0.959127	+	1.66126i
$767$	3.82082e12	−	3.99474e12i	0.398637	−	0.416782i
$768$	−4.32283e12	+	7.48735e12i	−0.448376	+	0.776610i
$769$	1.45961e12	+	2.52812e12i	0.150511	+	0.260693i	0.931415	−	0.363958i	$-0.118575\pi$
$769$	1.45961e12	+	2.52812e12i	0.150511	+	0.260693i	−0.780904	+	0.624651i	$0.785241\pi$
$770$	−1.21439e12	+	1.24524e12i	−0.124495	+	0.127657i
$771$	−6.19412e12	+	1.07285e13i	−0.631299	+	1.09344i
$772$	3.84784e12	−	6.66465e12i	0.389887	−	0.675304i
$773$	−3.85730e12			−0.388575			−0.194288	−	0.980945i	$-0.562240\pi$
$773$	−3.85730e12			−0.388575			−0.194288	+	0.980945i	$0.562240\pi$
$774$	6.26946e12			0.627907
$775$	−8.73022e12	+	1.51212e13i	−0.869295	+	1.50566i
$776$	1.12335e12	−	1.94571e12i	0.111209	−	0.192619i
$777$	6.33782e11	+	1.61332e11i	0.0623799	+	0.0158791i
$778$	1.12215e13	+	1.94363e13i	1.09811	+	1.90197i
$779$	−1.82968e12	+	3.16910e12i	−0.178015	+	0.308331i
$780$	−6.83562e11	−	1.66953e11i	−0.0661230	−	0.0161499i
$781$	2.54095e12	+	4.40105e12i	0.244380	+	0.423279i
$782$	−7.76444e10			−0.00742471
$783$	2.18193e12	+	3.77921e12i	0.207450	+	0.359313i
$784$	1.08306e13	−	6.62059e12i	1.02383	−	0.625856i
$785$	1.90105e12			0.178681
$786$	1.03245e12	+	1.78825e12i	0.0964865	+	0.167119i
$787$	−5.35213e12			−0.497325			−0.248662	−	0.968590i	$-0.579991\pi$
$787$	−5.35213e12			−0.497325			−0.248662	+	0.968590i	$0.579991\pi$
$788$	−2.35559e12	−	4.08000e12i	−0.217637	−	0.376958i
$789$	2.89206e12	+	5.00920e12i	0.265681	+	0.460174i
$790$	−4.52675e11	−	7.84056e11i	−0.0413489	−	0.0716185i
$791$	−7.03603e11	−	1.79105e11i	−0.0639048	−	0.0162672i
$792$	2.10800e12			0.190374
$793$	−1.68117e13	−	4.10609e12i	−1.50967	−	0.368722i
$794$	2.50406e12	+	4.33715e12i	0.223590	+	0.387269i
$795$	−3.65382e11	+	6.32860e11i	−0.0324410	+	0.0561895i
$796$	9.50736e11			0.0839366
$797$	8.86851e11	−	1.53607e12i	0.0778553	−	0.134849i	−0.824469	−	0.565907i	$-0.808526\pi$
$797$	8.86851e11	−	1.53607e12i	0.0778553	−	0.134849i	0.902324	+	0.431058i	$0.141859\pi$
$798$	1.53439e12	+	5.45202e12i	0.133944	+	0.475931i
$799$	7.20938e9	−	1.24870e10i	0.000625803	−	0.00108392i
$800$	6.89207e12	+	1.19374e13i	0.594901	+	1.03040i
$801$	2.43829e12	+	4.22325e12i	0.209286	+	0.362493i
$802$	2.67887e13			2.28648
$803$	−1.12966e13			−0.958803
$804$	3.76322e12	+	6.51808e12i	0.317619	+	0.550133i
$805$	−2.58311e11	−	6.57541e10i	−0.0216801	−	0.00551876i
$806$	−2.70774e13	−	6.61338e12i	−2.25995	−	0.551970i
$807$	7.90486e12	−	1.36916e13i	0.656090	−	1.13638i
$808$	−1.63195e12	+	2.82662e12i	−0.134696	+	0.233301i
$809$	−9.46870e12	+	1.64003e13i	−0.777181	+	1.34612i	0.156379	+	0.987697i	$0.450018\pi$
$809$	−9.46870e12	+	1.64003e13i	−0.777181	+	1.34612i	−0.933560	+	0.358420i	$0.883316\pi$
$810$	−2.08253e11	−	3.60704e11i	−0.0169984	−	0.0294421i
$811$	−4.55539e12			−0.369770			−0.184885	−	0.982760i	$-0.559191\pi$
$811$	−4.55539e12			−0.369770			−0.184885	+	0.982760i	$0.559191\pi$
$812$	−2.47600e12	+	2.53888e12i	−0.199870	+	0.204947i
$813$	1.44139e12	−	2.49655e12i	0.115711	−	0.200416i
$814$	−7.64267e11	+	1.32375e12i	−0.0610148	+	0.105681i
$815$	3.00405e12			0.238506
$816$	−1.80675e11	+	3.12938e11i	−0.0142656	+	0.0247088i
$817$	6.31165e12			0.495614
$818$	−2.84066e13			−2.21834
$819$	−2.37443e11	−	6.82258e12i	−0.0184409	−	0.529872i
$820$	8.33132e11			0.0643504
$821$	−1.37759e13			−1.05822			−0.529110	−	0.848553i	$-0.677474\pi$
$821$	−1.37759e13			−1.05822			−0.529110	+	0.848553i	$0.677474\pi$
$822$	−6.79784e12	+	1.17742e13i	−0.519335	+	0.899515i
$823$	−4.31215e12			−0.327639			−0.163819	−	0.986490i	$-0.552381\pi$
$823$	−4.31215e12			−0.327639			−0.163819	+	0.986490i	$0.552381\pi$
$824$	2.46837e12	−	4.27535e12i	0.186526	−	0.323072i
$825$	−4.42829e12	+	7.67002e12i	−0.332807	+	0.576439i
$826$	2.74433e12	+	9.75122e12i	0.205129	+	0.728868i
$827$	2.38754e13			1.77491			0.887455	−	0.460894i	$-0.152471\pi$
$827$	2.38754e13			1.77491			0.887455	+	0.460894i	$0.152471\pi$
$828$	−4.23003e11	−	7.32662e11i	−0.0312757	−	0.0541711i
$829$	2.33566e11	−	4.04549e11i	0.0171757	−	0.0297492i	−0.857310	−	0.514801i	$-0.827866\pi$
$829$	2.33566e11	−	4.04549e11i	0.0171757	−	0.0297492i	0.874486	+	0.485052i	$0.161199\pi$
$830$	−6.65929e11	+	1.15342e12i	−0.0487053	+	0.0843601i
$831$	−2.82757e12	+	4.89749e12i	−0.205688	+	0.356261i
$832$	−3.74574e12	+	3.91624e12i	−0.271008	+	0.283344i
$833$	4.11293e11	−	2.51418e11i	0.0295971	−	0.0180923i
$834$	−8.08193e12	−	1.39983e13i	−0.578453	−	1.00191i
$835$	−2.44646e12			−0.174160
$836$	−5.55773e12			−0.393523
$837$	−1.31945e13	−	2.28536e13i	−0.929243	−	1.60950i
$838$	6.65616e12	+	1.15288e13i	0.466258	+	0.807582i
$839$	−9.67397e12	+	1.67558e13i	−0.674025	+	1.16745i	0.302728	+	0.953077i	$0.402103\pi$
$839$	−9.67397e12	+	1.67558e13i	−0.674025	+	1.16745i	−0.976753	+	0.214369i	$0.931231\pi$
$840$	−3.43775e11	+	3.52507e11i	−0.0238242	+	0.0244293i
$841$	6.11850e12	−	1.05975e13i	0.421757	−	0.730505i
$842$	−2.64802e11			−0.0181558
$843$	5.23364e12	−	9.06493e12i	0.356927	−	0.618216i
$844$	−4.84887e12	−	8.39849e12i	−0.328927	−	0.569719i
$845$	1.80473e12	+	9.37501e11i	0.121775	+	0.0632582i
$846$	3.74201e11			0.0251153
$847$	2.13581e11	−	2.19006e11i	0.0142589	−	0.0146211i
$848$	6.23238e12	+	1.07948e13i	0.413878	+	0.716858i
$849$	1.39999e11	+	2.42485e11i	0.00924783	+	0.0160177i
$850$	3.40030e11	+	5.88949e11i	0.0223425	+	0.0386984i
$851$	−2.34241e11			−0.0153102
$852$	−1.88376e12	−	3.26277e12i	−0.122475	−	0.212133i
$853$	1.33655e13			0.864398			0.432199	−	0.901778i	$-0.357738\pi$
$853$	1.33655e13			0.864398			0.432199	+	0.901778i	$0.357738\pi$
$854$	2.21423e13	−	2.27046e13i	1.42450	−	1.46068i
$855$	3.12316e11	+	5.40947e11i	0.0199870	+	0.0346184i
$856$	−1.99277e12			−0.126860
$857$	−4.26994e12	−	7.39575e12i	−0.270401	−	0.468348i	0.698564	−	0.715548i	$-0.253823\pi$
$857$	−4.26994e12	−	7.39575e12i	−0.270401	−	0.468348i	−0.968964	+	0.247200i	$0.920489\pi$
$858$	−1.37346e13	−	3.35455e12i	−0.865216	−	0.211320i
$859$	1.06101e13	−	1.83773e13i	0.664892	−	1.15163i	−0.314423	−	0.949283i	$-0.601811\pi$
$859$	1.06101e13	−	1.83773e13i	0.664892	−	1.15163i	0.979315	−	0.202344i	$-0.0648558\pi$
$860$	−7.18492e11	−	1.24447e12i	−0.0447898	−	0.0775782i
$861$	−1.94033e12	−	6.89444e12i	−0.120327	−	0.427548i
$862$	1.58018e13	−	2.73694e13i	0.974816	−	1.68843i
$863$	6.07349e12	−	1.05196e13i	0.372726	−	0.645581i	−0.617258	−	0.786761i	$-0.711756\pi$
$863$	6.07349e12	−	1.05196e13i	0.372726	−	0.645581i	0.989984	+	0.141180i	$0.0450897\pi$
$864$	−2.08328e13			−1.27185
$865$	−6.09246e11			−0.0370015
$866$	−1.44240e13	+	2.49831e13i	−0.871477	+	1.50944i
$867$	5.69499e12	−	9.86401e12i	0.342300	−	0.592881i
$868$	1.49728e13	−	1.53531e13i	0.895292	−	0.918031i
$869$	−3.81867e12	−	6.61413e12i	−0.227155	−	0.393445i
$870$	4.12728e11	−	7.14866e11i	0.0244246	−	0.0423046i
$871$	−6.09613e12	−	2.08813e13i	−0.358899	−	1.22935i
$872$	8.63754e11	+	1.49607e12i	0.0505902	+	0.0876247i
$873$	5.57844e12			0.325049
$874$	−1.01431e12	−	1.75683e12i	−0.0587988	−	0.101842i
$875$	1.27708e12	+	4.53774e12i	0.0736514	+	0.261700i
$876$	8.37490e12			0.480519
$877$	−7.69758e12	−	1.33326e13i	−0.439396	−	0.761056i	0.558247	−	0.829675i	$-0.311474\pi$
$877$	−7.69758e12	−	1.33326e13i	−0.439396	−	0.761056i	−0.997643	+	0.0686187i	$0.978141\pi$
$878$	9.52139e12			0.540723
$879$	−2.52622e12	−	4.37554e12i	−0.142732	−	0.247219i
$880$	−1.44966e12	−	2.51088e12i	−0.0814880	−	0.141141i
$881$	−1.62701e13	−	2.81807e13i	−0.909911	−	1.57601i	−0.814186	−	0.580604i	$-0.802817\pi$
$881$	−1.62701e13	−	2.81807e13i	−0.909911	−	1.57601i	−0.0957246	−	0.995408i	$-0.530517\pi$
$882$	1.09877e13	+	5.98153e12i	0.611364	+	0.332816i
$883$	−1.81780e13			−1.00629			−0.503145	−	0.864202i	$-0.667824\pi$
$883$	−1.81780e13			−1.00629			−0.503145	+	0.864202i	$0.667824\pi$
$884$	−3.15044e11	+	3.29384e11i	−0.0173515	+	0.0181413i
$885$	−4.94973e11	−	8.57319e11i	−0.0271230	−	0.0469783i
$886$	1.97275e13	−	3.41690e13i	1.07552	−	1.86286i
$887$	6.84719e12			0.371412			0.185706	−	0.982605i	$-0.440543\pi$
$887$	6.84719e12			0.371412			0.185706	+	0.982605i	$0.440543\pi$
$888$	−2.16352e11	+	3.74733e11i	−0.0116762	+	0.0202238i
$889$	2.48673e13	−	2.54989e13i	1.33527	−	1.36919i
$890$	1.33113e12	−	2.30559e12i	0.0711158	−	0.123176i
$891$	−1.75678e12	−	3.04283e12i	−0.0933828	−	0.161744i
$892$	2.42249e12	+	4.19587e12i	0.128121	+	0.221912i
$893$	3.76719e11			0.0198238
$894$	−2.89770e13			−1.51717
$895$	−9.85119e11	−	1.70628e12i	−0.0513198	−	0.0888885i
$896$	3.64746e12	+	1.29602e13i	0.189062	+	0.671779i
$897$	−6.07189e11	−	2.07982e12i	−0.0313154	−	0.107266i
$898$	8.45585e12	−	1.46460e13i	0.433924	−	0.751579i
$899$	6.86402e12	−	1.18888e13i	0.350477	−	0.607045i
$900$	−3.70493e12	+	6.41713e12i	−0.188230	+	0.326024i
$901$	2.36676e11	+	4.09934e11i	0.0119644	+	0.0207230i
$902$	1.67399e13			0.842022
$903$	−8.62501e12	+	8.84407e12i	−0.431683	+	0.442647i
$904$	2.40187e11	−	4.16016e11i	0.0119617	−	0.0207182i
$905$	9.58513e11	−	1.66019e12i	0.0474984	−	0.0822697i
$906$	1.55074e13			0.764648
$907$	1.56113e13	−	2.70395e13i	0.765958	−	1.32668i	−0.173780	−	0.984784i	$-0.555598\pi$
$907$	1.56113e13	−	2.70395e13i	0.765958	−	1.32668i	0.939739	−	0.341894i	$-0.111068\pi$
$908$	2.20920e12			0.107857
$909$	−8.10408e12			−0.393701
$910$	−3.16082e12	+	1.97458e12i	−0.152796	+	0.0954527i
$911$	−2.27070e13			−1.09226			−0.546132	−	0.837699i	$-0.683900\pi$
$911$	−2.27070e13			−1.09226			−0.546132	+	0.837699i	$0.683900\pi$
$912$	−9.44097e12			−0.451897
$913$	−5.61764e12	+	9.73003e12i	−0.267569	+	0.463442i
$914$	−4.99799e13			−2.36885
$915$	−1.54961e12	+	2.68400e12i	−0.0730848	+	0.126587i
$916$	6.25148e12	−	1.08279e13i	0.293395	−	0.508176i
$917$	4.44977e12	+	1.13271e12i	0.207815	+	0.0529000i
$918$	−1.02782e12			−0.0477665
$919$	1.98062e13	+	3.43053e13i	0.915968	+	1.58650i	0.805477	+	0.592627i	$0.201909\pi$
$919$	1.98062e13	+	3.43053e13i	0.915968	+	1.58650i	0.110491	+	0.993877i	$0.464758\pi$
$920$	8.81789e10	−	1.52730e11i	0.00405807	−	0.00702878i
$921$	3.93445e12	−	6.81467e12i	0.180184	−	0.312088i
$922$	−1.62337e13	+	2.81176e13i	−0.739824	+	1.28141i
$923$	3.05156e12	+	1.04526e13i	0.138393	+	0.474041i
$924$	7.59476e12	−	7.78766e12i	0.342760	−	0.351466i
$925$	1.02582e12	+	1.77677e12i	0.0460715	+	0.0797982i
$926$	−1.68364e13			−0.752489
$927$	1.22577e13			0.545191
$928$	−5.41880e12	−	9.38564e12i	−0.239849	−	0.415430i
$929$	−1.77533e13	−	3.07497e13i	−0.782004	−	1.35447i	−0.930773	−	0.365598i	$-0.880864\pi$
$929$	−1.77533e13	−	3.07497e13i	−0.782004	−	1.35447i	0.148769	−	0.988872i	$-0.452469\pi$
$930$	−2.49584e12	+	4.32293e12i	−0.109407	+	0.189498i
$931$	1.10617e13	+	6.02179e12i	0.482556	+	0.262695i
$932$	1.03385e13	−	1.79068e13i	0.448834	−	0.777404i
$933$	1.00222e13			0.433007
$934$	1.63029e12	−	2.82374e12i	0.0700976	−	0.121413i
$935$	−5.50511e10	−	9.53513e10i	−0.00235567	−	0.00408013i
$936$	4.38781e12	+	1.07168e12i	0.186856	+	0.0456376i
$937$	1.74534e12			0.0739695			0.0369848	−	0.999316i	$-0.488225\pi$
$937$	1.74534e12			0.0739695			0.0369848	+	0.999316i	$0.488225\pi$
$938$	3.86316e13	+	9.83382e12i	1.62941	+	0.414772i
$939$	8.12427e12	+	1.40717e13i	0.341028	+	0.590677i
$940$	−4.28842e10	−	7.42775e10i	−0.00179152	−	0.00310300i
$941$	−1.55403e11	−	2.69167e11i	−0.00646111	−	0.0111910i	0.862777	−	0.505585i	$-0.168723\pi$
$941$	−1.55403e11	−	2.69167e11i	−0.00646111	−	0.0111910i	−0.869238	+	0.494394i	$0.835390\pi$
$942$	−2.83179e13			−1.17174
$943$	1.28266e12	+	2.22163e12i	0.0528213	+	0.0914891i
$944$	−1.68857e13			−0.692061
$945$	−3.41939e12	−	8.70420e11i	−0.139478	−	0.0355047i
$946$	−1.44365e13	−	2.50047e13i	−0.586072	−	1.01511i
$947$	3.10822e13			1.25585			0.627924	−	0.778275i	$-0.283905\pi$
$947$	3.10822e13			1.25585			0.627924	+	0.778275i	$0.283905\pi$
$948$	2.83101e12	+	4.90346e12i	0.113842	+	0.197181i
$949$	−2.35140e13	−	5.74306e12i	−0.941084	−	0.229850i
$950$	−8.88396e12	+	1.53875e13i	−0.353875	+	0.612930i
$951$	−8.12088e12	−	1.40658e13i	−0.321952	−	0.557637i
$952$	8.64046e10	+	3.07015e11i	0.00340934	+	0.0121141i
$953$	−1.08350e13	+	1.87668e13i	−0.425511	+	0.737007i	−0.996468	−	0.0839732i	$-0.973239\pi$
$953$	−1.08350e13	+	1.87668e13i	−0.425511	+	0.737007i	0.570957	+	0.820980i	$0.306572\pi$
$954$	−6.14229e12	+	1.06388e13i	−0.240084	+	0.415837i
$955$	4.73484e12			0.184200
$956$	−1.90409e13			−0.737272
$957$	3.48168e12	−	6.03045e12i	0.134179	−	0.232405i
$958$	1.75248e13	−	3.03539e13i	0.672216	−	1.16431i
$959$	8.19031e12	+	2.91020e13i	0.312692	+	1.11106i
$960$	4.85247e11	+	8.40472e11i	0.0184392	+	0.0319376i
$961$	−2.82882e13	+	4.89966e13i	−1.06992	+	1.85315i
$962$	−2.26380e12	+	2.36684e12i	−0.0852217	+	0.0891008i
$963$	−2.47397e12	−	4.28503e12i	−0.0926990	−	0.160559i
$964$	−1.29155e13			−0.481686
$965$	1.99161e12	+	3.44957e12i	0.0739318	+	0.128054i
$966$	3.84780e12	+	9.79472e11i	0.142172	+	0.0361905i
$967$	5.88349e12			0.216379			0.108190	−	0.994130i	$-0.465495\pi$
$967$	5.88349e12			0.216379			0.108190	+	0.994130i	$0.465495\pi$
$968$	1.01200e11	+	1.75283e11i	0.00370460	+	0.00641655i
$969$	−3.58523e11			−0.0130635
$970$	−1.52271e12	−	2.63742e12i	−0.0552263	−	0.0956547i
$971$	2.41961e13	+	4.19089e13i	0.873491	+	1.51293i	0.858361	+	0.513046i	$0.171483\pi$
$971$	2.41961e13	+	4.19089e13i	0.873491	+	1.51293i	0.0151302	+	0.999886i	$0.495184\pi$
$972$	−9.25884e12	−	1.60368e13i	−0.332704	−	0.576261i
$973$	−3.48326e13	−	8.86676e12i	−1.24588	−	0.317145i
$974$	3.87006e13			1.37785
$975$	−1.31168e13	+	1.37139e13i	−0.464845	+	0.486004i
$976$	2.64319e13	+	4.57815e13i	0.932406	+	1.61497i
$977$	4.36069e12	−	7.55294e12i	0.153119	−	0.265211i	−0.779253	−	0.626709i	$-0.784401\pi$
$977$	4.36069e12	−	7.55294e12i	0.153119	−	0.265211i	0.932373	+	0.361499i	$0.117735\pi$
$978$	−4.47483e13			−1.56405
$979$	1.12292e13	−	1.94495e13i	0.390683	−	0.676683i
$980$	−7.19036e10	−	2.86652e12i	−0.00249020	−	0.0992746i
$981$	−2.14465e12	+	3.71464e12i	−0.0739343	+	0.128058i
$982$	1.69785e13	+	2.94077e13i	0.582638	+	1.00916i
$983$	7.02367e12	+	1.21653e13i	0.239924	+	0.415560i	0.960692	−	0.277616i	$-0.0895442\pi$
$983$	7.02367e12	+	1.21653e13i	0.239924	+	0.415560i	−0.720768	+	0.693176i	$0.756211\pi$
$984$	4.73880e12			0.161135
$985$	2.43847e12			0.0825381
$986$	−2.67344e11	−	4.63054e11i	−0.00900792	−	0.0156022i
$987$	−5.14795e11	+	5.27870e11i	−0.0172666	+	0.0177052i
$988$	−1.15684e13	−	2.82548e12i	−0.386250	−	0.0943377i
$989$	2.21233e12	−	3.83187e12i	0.0735303	−	0.127358i
$990$	1.42870e12	−	2.47459e12i	0.0472698	−	0.0818737i
$991$	−2.19398e13	+	3.80009e13i	−0.722606	+	1.25159i	0.237346	+	0.971425i	$0.423723\pi$
$991$	−2.19398e13	+	3.80009e13i	−0.722606	+	1.25159i	−0.959952	+	0.280165i	$0.909611\pi$
$992$	3.27685e13	+	5.67567e13i	1.07437	+	1.86087i
$993$	−2.95350e12			−0.0963973
$994$	−1.93379e13	−	4.92254e12i	−0.628305	−	0.159938i
$995$	−2.46047e11	+	4.26166e11i	−0.00795818	+	0.0137840i
$996$	4.16470e12	−	7.21347e12i	0.134096	−	0.232262i
$997$	5.47031e13			1.75341			0.876706	−	0.481027i	$-0.159736\pi$
$997$	5.47031e13			1.75341			0.876706	+	0.481027i	$0.159736\pi$
$998$	7.53681e12	−	1.30541e13i	0.240492	−	0.416544i
$999$	−3.10077e12			−0.0984974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.17	yes	164
7.4	even	3		91.10.g.a.81.66	yes	164
13.9	even	3		91.10.g.a.9.66	✓	164
91.74	even	3	inner	91.10.h.a.74.17	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.66	✓	164	13.9	even	3
91.10.g.a.81.66	yes	164	7.4	even	3
91.10.h.a.16.17	yes	164	1.1	even	1	trivial
91.10.h.a.74.17	yes	164	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-29.7072 q^{2} +(-48.0812 + 83.2791i) q^{3} +370.519 q^{4} +(-95.8890 + 166.085i) q^{5} +(1428.36 - 2473.99i) q^{6} +(-1720.94 - 6114.90i) q^{7} +4203.00 q^{8} +(5217.89 + 9037.66i) q^{9} +O(q^{10})\)	\(q-29.7072 q^{2} +(-48.0812 + 83.2791i) q^{3} +370.519 q^{4} +(-95.8890 + 166.085i) q^{5} +(1428.36 - 2473.99i) q^{6} +(-1720.94 - 6114.90i) q^{7} +4203.00 q^{8} +(5217.89 + 9037.66i) q^{9} +(2848.60 - 4933.91i) q^{10} +(24030.1 - 41621.4i) q^{11} +(-17815.0 + 30856.5i) q^{12} +(71178.6 - 74418.5i) q^{13} +(51124.5 + 181657. i) q^{14} +(-9220.91 - 15971.1i) q^{15} -314565. q^{16} -11945.7 q^{17} +(-155009. - 268484. i) q^{18} +(-156052. - 270291. i) q^{19} +(-35528.7 + 61537.6i) q^{20} +(591988. + 150693. i) q^{21} +(-713869. + 1.23646e6i) q^{22} -218795. q^{23} +(-202085. + 350022. i) q^{24} +(958173. + 1.65960e6i) q^{25} +(-2.11452e6 + 2.21077e6i) q^{26} -2.89630e6 q^{27} +(-637643. - 2.26569e6i) q^{28} +(-753351. - 1.30484e6i) q^{29} +(273928. + 474457. i) q^{30} +(4.55566e6 + 7.89063e6i) q^{31} +7.19293e6 q^{32} +(2.31080e6 + 4.00242e6i) q^{33} +354873. q^{34} +(1.18061e6 + 300529. i) q^{35} +(1.93333e6 + 3.34863e6i) q^{36} +1.07060e6 q^{37} +(4.63588e6 + 8.02959e6i) q^{38} +(2.77515e6 + 9.50582e6i) q^{39} +(-403021. + 698053. i) q^{40} +(-5.86238e6 - 1.01539e7i) q^{41} +(-1.75863e7 - 4.47667e6i) q^{42} +(-1.01114e7 + 1.75135e7i) q^{43} +(8.90364e6 - 1.54215e7i) q^{44} -2.00135e6 q^{45} +6.49979e6 q^{46} +(-603514. + 1.04532e6i) q^{47} +(1.51247e7 - 2.61967e7i) q^{48} +(-3.44303e7 + 2.10468e7i) q^{49} +(-2.84647e7 - 4.93023e7i) q^{50} +(574363. - 994825. i) q^{51} +(2.63730e7 - 2.75735e7i) q^{52} +(-1.98127e7 - 3.43165e7i) q^{53} +8.60409e7 q^{54} +(4.60845e6 + 7.98207e6i) q^{55} +(-7.23312e6 - 2.57009e7i) q^{56} +3.00128e7 q^{57} +(2.23800e7 + 3.87633e7i) q^{58} +5.36794e7 q^{59} +(-3.41653e6 - 5.91760e6i) q^{60} +(-8.40269e7 - 1.45539e8i) q^{61} +(-1.35336e8 - 2.34409e8i) q^{62} +(4.62846e7 - 4.74602e7i) q^{63} -5.26246e7 q^{64} +(5.53453e6 + 1.89576e7i) q^{65} +(-6.86474e7 - 1.18901e8i) q^{66} +(1.05619e8 - 1.82938e8i) q^{67} -4.42611e6 q^{68} +(1.05199e7 - 1.82210e7i) q^{69} +(-3.50726e7 - 8.92788e6i) q^{70} +(-5.28700e7 + 9.15736e7i) q^{71} +(2.19308e7 + 3.79852e7i) q^{72} +(-1.17526e8 - 2.03561e8i) q^{73} -3.18045e7 q^{74} -1.84280e8 q^{75} +(-5.78204e7 - 1.00148e8i) q^{76} +(-2.95865e8 - 7.53137e7i) q^{77} +(-8.24421e7 - 2.82391e8i) q^{78} +(7.94558e7 - 1.37621e8i) q^{79} +(3.01633e7 - 5.22444e7i) q^{80} +(3.65536e7 - 6.33127e7i) q^{81} +(1.74155e8 + 3.01646e8i) q^{82} -2.33775e8 q^{83} +(2.19343e8 + 5.58346e7i) q^{84} +(1.14546e6 - 1.98399e6i) q^{85} +(3.00383e8 - 5.20278e8i) q^{86} +1.44888e8 q^{87} +(1.00999e8 - 1.74935e8i) q^{88} +4.67294e8 q^{89} +5.94547e7 q^{90} +(-5.77556e8 - 3.07179e8i) q^{91} -8.10677e7 q^{92} -8.76166e8 q^{93} +(1.79287e7 - 3.10535e7i) q^{94} +5.98548e7 q^{95} +(-3.45845e8 + 5.99021e8i) q^{96} +(2.67275e8 - 4.62933e8i) q^{97} +(1.02283e9 - 6.25242e8i) q^{98} +5.01547e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Introduction

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