LMFDB - Embedded newform 91.10.h.a.16.13

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			16.13
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-33.6954 q^{2} +(-7.73692 + 13.4007i) q^{3} +623.381 q^{4} +(-406.981 + 704.911i) q^{5} +(260.699 - 451.543i) q^{6} +(-6248.30 + 1145.56i) q^{7} -3753.02 q^{8} +(9721.78 + 16838.6i) q^{9} +O(q^{10})$	\(q-33.6954 q^{2} +(-7.73692 + 13.4007i) q^{3} +623.381 q^{4} +(-406.981 + 704.911i) q^{5} +(260.699 - 451.543i) q^{6} +(-6248.30 + 1145.56i) q^{7} -3753.02 q^{8} +(9721.78 + 16838.6i) q^{9} +(13713.4 - 23752.3i) q^{10} +(-3518.45 + 6094.13i) q^{11} +(-4823.05 + 8353.76i) q^{12} +(-13976.7 + 102025. i) q^{13} +(210539. - 38600.2i) q^{14} +(-6297.56 - 10907.7i) q^{15} -192711. q^{16} -545570. q^{17} +(-327579. - 567384. i) q^{18} +(216125. + 374340. i) q^{19} +(-253704. + 439428. i) q^{20} +(32991.2 - 92595.0i) q^{21} +(118555. - 205344. i) q^{22} +1.70291e6 q^{23} +(29036.8 - 50293.2i) q^{24} +(645296. + 1.11768e6i) q^{25} +(470950. - 3.43778e6i) q^{26} -605438. q^{27} +(-3.89507e6 + 714122. i) q^{28} +(3.37952e6 + 5.85351e6i) q^{29} +(212199. + 367539. i) q^{30} +(1.82227e6 + 3.15627e6i) q^{31} +8.41504e6 q^{32} +(-54443.9 - 94299.5i) q^{33} +1.83832e7 q^{34} +(1.73542e6 - 4.87072e6i) q^{35} +(6.06037e6 + 1.04969e7i) q^{36} +1.36624e6 q^{37} +(-7.28243e6 - 1.26135e7i) q^{38} +(-1.25908e6 - 976659. i) q^{39} +(1.52741e6 - 2.64555e6i) q^{40} +(1.13725e7 + 1.96978e7i) q^{41} +(-1.11165e6 + 3.12003e6i) q^{42} +(4.93957e6 - 8.55559e6i) q^{43} +(-2.19333e6 + 3.79896e6i) q^{44} -1.58263e7 q^{45} -5.73803e7 q^{46} +(-9.19899e6 + 1.59331e7i) q^{47} +(1.49099e6 - 2.58247e6i) q^{48} +(3.77290e7 - 1.43156e7i) q^{49} +(-2.17435e7 - 3.76609e7i) q^{50} +(4.22103e6 - 7.31104e6i) q^{51} +(-8.71279e6 + 6.36006e7i) q^{52} +(1.05627e7 + 1.82952e7i) q^{53} +2.04005e7 q^{54} +(-2.86388e6 - 4.96039e6i) q^{55} +(2.34500e7 - 4.29932e6i) q^{56} -6.68858e6 q^{57} +(-1.13874e8 - 1.97236e8i) q^{58} -1.26573e8 q^{59} +(-3.92577e6 - 6.79964e6i) q^{60} +(2.00885e7 + 3.47943e7i) q^{61} +(-6.14022e7 - 1.06352e8i) q^{62} +(-8.00343e7 - 9.40759e7i) q^{63} -1.84880e8 q^{64} +(-6.62305e7 - 5.13746e7i) q^{65} +(1.83451e6 + 3.17746e6i) q^{66} +(-2.00792e7 + 3.47782e7i) q^{67} -3.40098e8 q^{68} +(-1.31753e7 + 2.28203e7i) q^{69} +(-5.84757e7 + 1.64121e8i) q^{70} +(9.83948e7 - 1.70425e8i) q^{71} +(-3.64860e7 - 6.31957e7i) q^{72} +(-4.10213e7 - 7.10509e7i) q^{73} -4.60360e7 q^{74} -1.99704e7 q^{75} +(1.34728e8 + 2.33356e8i) q^{76} +(1.50031e7 - 4.21086e7i) q^{77} +(4.24251e7 + 3.29089e7i) q^{78} +(-1.48253e8 + 2.56782e8i) q^{79} +(7.84298e7 - 1.35844e8i) q^{80} +(-1.86670e8 + 3.23321e8i) q^{81} +(-3.83203e8 - 6.63726e8i) q^{82} -5.21475e8 q^{83} +(2.05661e7 - 5.77219e7i) q^{84} +(2.22036e8 - 3.84578e8i) q^{85} +(-1.66441e8 + 2.88284e8i) q^{86} -1.04588e8 q^{87} +(1.32048e7 - 2.28714e7i) q^{88} -4.49175e8 q^{89} +5.33274e8 q^{90} +(-2.95459e7 - 6.53496e8i) q^{91} +1.06156e9 q^{92} -5.63951e7 q^{93} +(3.09964e8 - 5.36873e8i) q^{94} -3.51836e8 q^{95} +(-6.51064e7 + 1.12768e8i) q^{96} +(-3.91079e8 + 6.77369e8i) q^{97} +(-1.27129e9 + 4.82372e8i) q^{98} -1.36822e8 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 $

$2$	−33.6954			−1.48914			−0.744570	−	0.667544i	$-0.767346\pi$
$2$	−33.6954			−1.48914			−0.744570	+	0.667544i	$0.767346\pi$
$3$	−7.73692	+	13.4007i	−0.0551471	+	0.0955175i	−0.892281	−	0.451480i	$-0.850896\pi$
$3$	−7.73692	+	13.4007i	−0.0551471	+	0.0955175i	0.837134	+	0.546998i	$0.184229\pi$
$4$	623.381			1.21754
$5$	−406.981	+	704.911i	−0.291212	+	0.504394i	−0.974097	−	0.226133i	$-0.927392\pi$
$5$	−406.981	+	704.911i	−0.291212	+	0.504394i	0.682885	+	0.730526i	$0.260725\pi$
$6$	260.699	−	451.543i	0.0821217	−	0.142239i
$7$	−6248.30	+	1145.56i	−0.983605	+	0.180334i
$7$	−6248.30	+	1145.56i	−0.983605	+	0.180334i
$8$	−3753.02			−0.323948
$9$	9721.78	+	16838.6i	0.493918	+	0.855490i
$10$	13713.4	−	23752.3i	0.433655	−	0.751113i
$11$	−3518.45	+	6094.13i	−0.0724576	+	0.125500i	−0.899978	−	0.435936i	$-0.856418\pi$
$11$	−3518.45	+	6094.13i	−0.0724576	+	0.125500i	0.827520	+	0.561436i	$0.189751\pi$
$12$	−4823.05	+	8353.76i	−0.0671438	+	0.116296i
$13$	−13976.7	+	102025.i	−0.135725	+	0.990747i
$13$	−13976.7	+	102025.i	−0.135725	+	0.990747i
$14$	210539.	−	38600.2i	1.46473	−	0.268543i
$15$	−6297.56	−	10907.7i	−0.0321189	−	0.0556317i
$16$	−192711.			−0.735136
$17$	−545570.			−1.58427			−0.792137	−	0.610344i	$-0.791031\pi$
$17$	−545570.			−1.58427			−0.792137	+	0.610344i	$0.791031\pi$
$18$	−327579.	−	567384.i	−0.735513	−	1.27395i
$19$	216125.	+	374340.i	0.380465	+	0.658985i	0.991129	−	0.132905i	$-0.0424307\pi$
$19$	216125.	+	374340.i	0.380465	+	0.658985i	−0.610664	+	0.791890i	$0.709097\pi$
$20$	−253704.	+	439428.i	−0.354562	+	0.614120i
$21$	32991.2	−	92595.0i	0.0370179	−	0.103896i
$22$	118555.	−	205344.i	0.107900	−	0.186887i
$23$	1.70291e6			1.26887			0.634434	−	0.772977i	$-0.281233\pi$
$23$	1.70291e6			1.26887			0.634434	+	0.772977i	$0.281233\pi$
$24$	29036.8	−	50293.2i	0.0178648	−	0.0309427i
$25$	645296.	+	1.11768e6i	0.330391	+	0.572255i
$26$	470950.	−	3.43778e6i	0.202113	−	1.47536i
$27$	−605438.			−0.219247
$28$	−3.89507e6	+	714122.i	−1.19758	+	0.219564i
$29$	3.37952e6	+	5.85351e6i	0.887288	+	1.53683i	0.843068	+	0.537806i	$0.180747\pi$
$29$	3.37952e6	+	5.85351e6i	0.887288	+	1.53683i	0.0442196	+	0.999022i	$0.485920\pi$
$30$	212199.	+	367539.i	0.0478296	+	0.0828434i
$31$	1.82227e6	+	3.15627e6i	0.354393	+	0.613827i	0.987014	−	0.160635i	$-0.0513540\pi$
$31$	1.82227e6	+	3.15627e6i	0.354393	+	0.613827i	−0.632621	+	0.774462i	$0.718021\pi$
$32$	8.41504e6			1.41867
$33$	−54443.9	−	94299.5i	−0.00799164	−	0.0138419i
$34$	1.83832e7			2.35921
$35$	1.73542e6	−	4.87072e6i	0.195478	−	0.548640i
$36$	6.06037e6	+	1.04969e7i	0.601365	+	1.04159i
$37$	1.36624e6			0.119845			0.0599224	−	0.998203i	$-0.480915\pi$
$37$	1.36624e6			0.119845			0.0599224	+	0.998203i	$0.480915\pi$
$38$	−7.28243e6	−	1.26135e7i	−0.566566	−	0.981321i
$39$	−1.25908e6	−	976659.i	−0.0871488	−	0.0676008i
$40$	1.52741e6	−	2.64555e6i	0.0943376	−	0.163398i
$41$	1.13725e7	+	1.96978e7i	0.628536	+	1.08866i	0.987846	+	0.155438i	$0.0496790\pi$
$41$	1.13725e7	+	1.96978e7i	0.628536	+	1.08866i	−0.359309	+	0.933219i	$0.616988\pi$
$42$	−1.11165e6	+	3.12003e6i	−0.0551248	+	0.154716i
$43$	4.93957e6	−	8.55559e6i	0.220334	−	0.381630i	−0.734575	−	0.678527i	$-0.762619\pi$
$43$	4.93957e6	−	8.55559e6i	0.220334	−	0.381630i	0.954909	+	0.296897i	$0.0959520\pi$
$44$	−2.19333e6	+	3.79896e6i	−0.0882200	+	0.152802i
$45$	−1.58263e7			−0.575338
$46$	−5.73803e7			−1.88952
$47$	−9.19899e6	+	1.59331e7i	−0.274979	+	0.476278i	−0.970130	−	0.242586i	$-0.922004\pi$
$47$	−9.19899e6	+	1.59331e7i	−0.274979	+	0.476278i	0.695151	+	0.718864i	$0.255338\pi$
$48$	1.49099e6	−	2.58247e6i	0.0405406	−	0.0702183i
$49$	3.77290e7	−	1.43156e7i	0.934959	−	0.354755i
$50$	−2.17435e7	−	3.76609e7i	−0.491999	−	0.852168i
$51$	4.22103e6	−	7.31104e6i	0.0873680	−	0.151326i
$52$	−8.71279e6	+	6.36006e7i	−0.165250	+	1.20627i
$53$	1.05627e7	+	1.82952e7i	0.183880	+	0.318489i	0.943198	−	0.332230i	$-0.107801\pi$
$53$	1.05627e7	+	1.82952e7i	0.183880	+	0.318489i	−0.759319	+	0.650719i	$0.774468\pi$
$54$	2.04005e7			0.326489
$55$	−2.86388e6	−	4.96039e6i	−0.0422010	−	0.0730943i
$56$	2.34500e7	−	4.29932e6i	0.318637	−	0.0584189i
$57$	−6.68858e6			−0.0839261
$58$	−1.13874e8	−	1.97236e8i	−1.32130	−	2.28855i
$59$	−1.26573e8			−1.35990			−0.679948	−	0.733260i	$-0.737998\pi$
$59$	−1.26573e8			−1.35990			−0.679948	+	0.733260i	$0.737998\pi$
$60$	−3.92577e6	−	6.79964e6i	−0.0391061	−	0.0677338i
$61$	2.00885e7	+	3.47943e7i	0.185765	+	0.321754i	0.943834	−	0.330420i	$-0.107190\pi$
$61$	2.00885e7	+	3.47943e7i	0.185765	+	0.321754i	−0.758069	+	0.652174i	$0.773857\pi$
$62$	−6.14022e7	−	1.06352e8i	−0.527742	−	0.914075i
$63$	−8.00343e7	−	9.40759e7i	−0.640094	−	0.752395i
$64$	−1.84880e8			−1.37746
$65$	−6.62305e7	−	5.13746e7i	−0.460202	−	0.356976i
$66$	1.83451e6	+	3.17746e6i	0.0119007	+	0.0206126i
$67$	−2.00792e7	+	3.47782e7i	−0.121734	+	0.210849i	−0.920451	−	0.390857i	$-0.872179\pi$
$67$	−2.00792e7	+	3.47782e7i	−0.121734	+	0.210849i	0.798718	+	0.601706i	$0.205512\pi$
$68$	−3.40098e8			−1.92892
$69$	−1.31753e7	+	2.28203e7i	−0.0699744	+	0.121199i
$70$	−5.84757e7	+	1.64121e8i	−0.291094	+	0.817002i
$71$	9.83948e7	−	1.70425e8i	0.459525	−	0.795921i	−0.539410	−	0.842043i	$-0.681353\pi$
$71$	9.83948e7	−	1.70425e8i	0.459525	−	0.795921i	0.998936	+	0.0461217i	$0.0146862\pi$
$72$	−3.64860e7	−	6.31957e7i	−0.160004	−	0.277135i
$73$	−4.10213e7	−	7.10509e7i	−0.169066	−	0.292831i	0.769026	−	0.639218i	$-0.220742\pi$
$73$	−4.10213e7	−	7.10509e7i	−0.169066	−	0.292831i	−0.938092	+	0.346387i	$0.887408\pi$
$74$	−4.60360e7			−0.178466
$75$	−1.99704e7			−0.0728805
$76$	1.34728e8	+	2.33356e8i	0.463231	+	0.802340i
$77$	1.50031e7	−	4.21086e7i	0.0486377	−	0.136509i
$78$	4.24251e7	+	3.29089e7i	0.129777	+	0.100667i
$79$	−1.48253e8	+	2.56782e8i	−0.428235	+	0.741724i	−0.996716	−	0.0809715i	$-0.974198\pi$
$79$	−1.48253e8	+	2.56782e8i	−0.428235	+	0.741724i	0.568482	+	0.822696i	$0.307531\pi$
$80$	7.84298e7	−	1.35844e8i	0.214080	−	0.370798i
$81$	−1.86670e8	+	3.23321e8i	−0.481827	+	0.834548i
$82$	−3.83203e8	−	6.63726e8i	−0.935979	−	1.62116i
$83$	−5.21475e8			−1.20610			−0.603048	−	0.797705i	$-0.706047\pi$
$83$	−5.21475e8			−1.20610			−0.603048	+	0.797705i	$0.706047\pi$
$84$	2.05661e7	−	5.77219e7i	0.0450708	−	0.126498i
$85$	2.22036e8	−	3.84578e8i	0.461359	−	0.799097i
$86$	−1.66441e8	+	2.88284e8i	−0.328108	+	0.568300i
$87$	−1.04588e8			−0.195725
$88$	1.32048e7	−	2.28714e7i	0.0234725	−	0.0406556i
$89$	−4.49175e8			−0.758859			−0.379429	−	0.925221i	$-0.623880\pi$
$89$	−4.49175e8			−0.758859			−0.379429	+	0.925221i	$0.623880\pi$
$90$	5.33274e8			0.856760
$91$	−2.95459e7	−	6.53496e8i	−0.0451659	−	0.998980i
$92$	1.06156e9			1.54490
$93$	−5.63951e7			−0.0781750
$94$	3.09964e8	−	5.36873e8i	0.409483	−	0.709245i
$95$	−3.51836e8			−0.443183
$96$	−6.51064e7	+	1.12768e8i	−0.0782354	+	0.135508i
$97$	−3.91079e8	+	6.77369e8i	−0.448530	+	0.776877i	−0.998291	−	0.0584452i	$-0.981386\pi$
$97$	−3.91079e8	+	6.77369e8i	−0.448530	+	0.776877i	0.549760	+	0.835322i	$0.314719\pi$
$98$	−1.27129e9	+	4.82372e8i	−1.39229	+	0.528280i
$99$	−1.36822e8			−0.143152
$100$	4.02265e8	+	6.96743e8i	0.402265	+	0.696743i
$101$	−7.99225e8	+	1.38430e9i	−0.764228	+	1.32368i	0.176426	+	0.984314i	$0.443546\pi$
$101$	−7.99225e8	+	1.38430e9i	−0.764228	+	1.32368i	−0.940654	+	0.339367i	$0.889787\pi$
$102$	−1.42229e8	+	2.46348e8i	−0.130103	+	0.225346i
$103$	8.17560e8	−	1.41606e9i	0.715735	−	1.23969i	−0.246941	−	0.969031i	$-0.579425\pi$
$103$	8.17560e8	−	1.41606e9i	0.715735	−	1.23969i	0.962676	−	0.270658i	$-0.0872413\pi$
$104$	5.24547e7	−	3.82903e8i	0.0439678	−	0.320951i
$105$	5.18445e7	+	6.09403e7i	0.0416247	+	0.0489275i
$106$	−3.55915e8	−	6.16463e8i	−0.273823	−	0.474275i
$107$	2.64188e9			1.94844			0.974220	−	0.225602i	$-0.0724348\pi$
$107$	2.64188e9			1.94844			0.974220	+	0.225602i	$0.0724348\pi$
$108$	−3.77418e8			−0.266942
$109$	−1.37654e9	−	2.38424e9i	−0.934051	−	1.61782i	−0.776318	−	0.630341i	$-0.782915\pi$
$109$	−1.37654e9	−	2.38424e9i	−0.934051	−	1.61782i	−0.157733	−	0.987482i	$-0.550418\pi$
$110$	9.64996e7	+	1.67142e8i	0.0628432	+	0.108848i
$111$	−1.05705e7	+	1.83086e7i	−0.00660909	+	0.0114473i
$112$	1.20412e9	−	2.20763e8i	0.723083	−	0.132570i
$113$	6.86460e8	−	1.18898e9i	0.396061	−	0.685998i	−0.597175	−	0.802111i	$-0.703710\pi$
$113$	6.86460e8	−	1.18898e9i	0.396061	−	0.685998i	0.993236	+	0.116113i	$0.0370434\pi$
$114$	2.25374e8			0.124978
$115$	−6.93052e8	+	1.20040e9i	−0.369510	+	0.640009i
$116$	2.10673e9	+	3.64896e9i	1.08031	+	1.87115i
$117$	−1.85384e9	+	7.56519e8i	−0.914611	+	0.373236i
$118$	4.26492e9			2.02508
$119$	3.40889e9	−	6.24985e8i	1.55830	−	0.285698i
$120$	2.36348e7	+	4.09368e7i	0.0104049	+	0.0180218i
$121$	1.15421e9	+	1.99916e9i	0.489500	+	0.847839i
$122$	−6.76891e8	−	1.17241e9i	−0.276630	−	0.479137i
$123$	−3.51954e8			−0.138648
$124$	1.13597e9	+	1.96756e9i	0.431488	+	0.747360i
$125$	−2.64026e9			−0.967279
$126$	2.69679e9	+	3.16993e9i	0.953190	+	1.12042i
$127$	4.12229e8	+	7.14002e8i	0.140612	+	0.243547i	0.927727	−	0.373259i	$-0.121760\pi$
$127$	4.12229e8	+	7.14002e8i	0.140612	+	0.243547i	−0.787115	+	0.616806i	$0.788426\pi$
$128$	1.92110e9			0.632566
$129$	7.64342e7	+	1.32388e8i	0.0243015	+	0.0420915i
$130$	2.23167e9	+	1.73109e9i	0.685305	+	0.531587i
$131$	−3.32448e8	+	5.75817e8i	−0.0986286	+	0.170830i	−0.911117	−	0.412147i	$-0.864779\pi$
$131$	−3.32448e8	+	5.75817e8i	−0.0986286	+	0.170830i	0.812489	+	0.582977i	$0.198112\pi$
$132$	−3.39393e7	−	5.87845e7i	−0.00973015	−	0.0168531i
$133$	−1.77925e9	−	2.09141e9i	−0.493065	−	0.579570i
$134$	6.76578e8	−	1.17187e9i	0.181278	−	0.313984i
$135$	2.46402e8	−	4.26780e8i	0.0638472	−	0.110587i
$136$	2.04753e9			0.513223
$137$	−2.13379e9			−0.517499			−0.258749	−	0.965944i	$-0.583310\pi$
$137$	−2.13379e9			−0.517499			−0.258749	+	0.965944i	$0.583310\pi$
$138$	4.43947e8	−	7.68938e8i	0.104202	−	0.180483i
$139$	6.62798e8	−	1.14800e9i	0.150596	−	0.260841i	−0.780850	−	0.624718i	$-0.785214\pi$
$139$	6.62798e8	−	1.14800e9i	0.150596	−	0.260841i	0.931447	+	0.363877i	$0.118547\pi$
$140$	1.08183e9	−	3.03631e9i	0.238003	−	0.667991i
$141$	−1.42344e8	−	2.46547e8i	−0.0303286	−	0.0525307i
$142$	−3.31545e9	+	5.74253e9i	−0.684298	+	1.18524i
$143$	−5.72579e8	−	4.44146e8i	−0.114505	−	0.0888206i
$144$	−1.87350e9	−	3.24499e9i	−0.363096	−	0.628901i
$145$	−5.50161e9			−1.03355
$146$	1.38223e9	+	2.39409e9i	0.251763	+	0.436067i
$147$	−1.00066e8	+	6.16355e8i	−0.0176749	+	0.108869i
$148$	8.51688e8			0.145916
$149$	5.73737e9	+	9.93742e9i	0.953618	+	1.65172i	0.737498	+	0.675349i	$0.236007\pi$
$149$	5.73737e9	+	9.93742e9i	0.953618	+	1.65172i	0.216120	+	0.976367i	$0.430660\pi$
$150$	6.72911e8			0.108529
$151$	−5.03129e9	−	8.71446e9i	−0.787560	−	1.36409i	−0.927458	−	0.373927i	$-0.878011\pi$
$151$	−5.03129e9	−	8.71446e9i	−0.787560	−	1.36409i	0.139898	−	0.990166i	$-0.455322\pi$
$152$	−8.11123e8	−	1.40491e9i	−0.123251	−	0.213477i
$153$	−5.30391e9	−	9.18664e9i	−0.782501	−	1.35533i
$154$	−5.05536e8	+	1.41886e9i	−0.0724284	+	0.203281i
$155$	−2.96652e9			−0.412814
$156$	−7.84884e8	−	6.08830e8i	−0.106107	−	0.0823068i
$157$	−4.40879e9	−	7.63624e9i	−0.579123	−	1.00307i	−0.995580	−	0.0939147i	$-0.970062\pi$
$157$	−4.40879e9	−	7.63624e9i	−0.579123	−	1.00307i	0.416458	−	0.909155i	$-0.363271\pi$
$158$	4.99545e9	−	8.65237e9i	0.637702	−	1.10453i
$159$	−3.26891e8			−0.0405617
$160$	−3.42476e9	+	5.93186e9i	−0.413133	+	0.715568i
$161$	−1.06403e10	+	1.95079e9i	−1.24807	+	0.228820i
$162$	6.28991e9	−	1.08944e10i	0.717508	−	1.24276i
$163$	−4.02040e9	−	6.96353e9i	−0.446092	−	0.772654i	0.552035	−	0.833821i	$-0.313851\pi$
$163$	−4.02040e9	−	6.96353e9i	−0.446092	−	0.772654i	−0.998128	+	0.0611664i	$0.980518\pi$
$164$	7.08943e9	+	1.22792e10i	0.765268	+	1.32548i
$165$	8.86304e7			0.00930904
$166$	1.75713e10			1.79605
$167$	6.16373e9	+	1.06759e10i	0.613224	+	1.06214i	0.990693	+	0.136113i	$0.0434611\pi$
$167$	6.16373e9	+	1.06759e10i	0.613224	+	1.06214i	−0.377469	+	0.926022i	$0.623206\pi$
$168$	−1.23817e8	+	3.47511e8i	−0.0119919	+	0.0336571i
$169$	−1.02138e10	−	2.85195e9i	−0.963158	−	0.268937i
$170$	−7.48161e9	+	1.29585e10i	−0.687029	+	1.18997i
$171$	−4.20225e9	+	7.27851e9i	−0.375837	+	0.650968i
$172$	3.07924e9	−	5.33339e9i	0.268266	−	0.464650i
$173$	−1.65394e9	−	2.86471e9i	−0.140382	−	0.243149i	0.787258	−	0.616623i	$-0.211500\pi$
$173$	−1.65394e9	−	2.86471e9i	−0.140382	−	0.243149i	−0.927641	+	0.373474i	$0.878166\pi$
$174$	3.52415e9			0.291463
$175$	−5.31238e9	−	6.24441e9i	−0.428172	−	0.503292i
$176$	6.78045e8	−	1.17441e9i	0.0532661	−	0.0922597i
$177$	9.79282e8	−	1.69617e9i	0.0749943	−	0.129894i
$178$	1.51351e10			1.13005
$179$	−7.37448e9	+	1.27730e10i	−0.536899	+	0.929937i	0.462170	+	0.886792i	$0.347071\pi$
$179$	−7.37448e9	+	1.27730e10i	−0.536899	+	0.929937i	−0.999069	+	0.0431452i	$0.986262\pi$
$180$	−9.86582e9			−0.700498
$181$	2.33214e10			1.61510			0.807552	−	0.589796i	$-0.200792\pi$
$181$	2.33214e10			1.61510			0.807552	+	0.589796i	$0.200792\pi$
$182$	9.95560e8	+	2.20198e10i	0.0672584	+	1.48762i
$183$	−6.21693e8			−0.0409776
$184$	−6.39106e9			−0.411048
$185$	−5.56033e8	+	9.63078e8i	−0.0349002	+	0.0604490i
$186$	1.90026e9			0.116414
$187$	1.91956e9	−	3.32477e9i	0.114793	−	0.198827i
$188$	−5.73447e9	+	9.93240e9i	−0.334798	+	0.579888i
$189$	3.78296e9	−	6.93567e8i	0.215652	−	0.0395376i
$190$	1.18552e10			0.659963
$191$	8.25840e9	+	1.43040e10i	0.448999	+	0.777690i	0.998321	−	0.0579213i	$-0.0184472\pi$
$191$	8.25840e9	+	1.43040e10i	0.448999	+	0.777690i	−0.549322	+	0.835611i	$0.685114\pi$
$192$	1.43040e9	−	2.47753e9i	0.0759630	−	0.131572i
$193$	1.04442e9	−	1.80899e9i	0.0541835	−	0.0938486i	−0.837661	−	0.546190i	$-0.816078\pi$
$193$	1.04442e9	−	1.80899e9i	0.0541835	−	0.0938486i	0.891845	+	0.452341i	$0.149411\pi$
$194$	1.31776e10	−	2.28242e10i	0.667925	−	1.15688i
$195$	1.20088e9	−	4.90057e8i	0.0594762	−	0.0242712i
$196$	2.35195e10	−	8.92410e9i	1.13835	−	0.431929i
$197$	6.14350e9	+	1.06409e10i	0.290615	+	0.503360i	0.973955	−	0.226740i	$-0.0728068\pi$
$197$	6.14350e9	+	1.06409e10i	0.290615	+	0.503360i	−0.683340	+	0.730100i	$0.739473\pi$
$198$	4.61028e9			0.213174
$199$	−1.29625e10			−0.585937			−0.292968	−	0.956122i	$-0.594643\pi$
$199$	−1.29625e10			−0.585937			−0.292968	+	0.956122i	$0.594643\pi$
$200$	−2.42181e9	−	4.19469e9i	−0.107030	−	0.185381i
$201$	−3.10703e8	−	5.38153e8i	−0.0134265	−	0.0232554i
$202$	2.69302e10	−	4.66445e10i	1.13804	−	1.97115i
$203$	−2.78219e10	−	3.27030e10i	−1.14988	−	1.35162i
$204$	2.63131e9	−	4.55756e9i	0.106374	−	0.184245i
$205$	−1.85136e10			−0.732149
$206$	−2.75480e10	+	4.77146e10i	−1.06583	+	1.84607i
$207$	1.65553e10	+	2.86747e10i	0.626717	+	1.08550i
$208$	2.69346e9	−	1.96614e10i	0.0997760	−	0.728333i
$209$	−3.04170e9			−0.110270
$210$	−1.74692e9	−	2.05341e9i	−0.0619850	−	0.0728599i
$211$	−1.77651e10	−	3.07701e10i	−0.617017	−	1.06870i	−0.990027	−	0.140877i	$-0.955008\pi$
$211$	−1.77651e10	−	3.07701e10i	−0.617017	−	1.06870i	0.373010	−	0.927827i	$-0.378326\pi$
$212$	6.58459e9	+	1.14048e10i	0.223881	+	0.387773i
$213$	1.52254e9	+	2.63712e9i	0.0506829	+	0.0877854i
$214$	−8.90194e10			−2.90150
$215$	4.02062e9	+	6.96392e9i	0.128328	+	0.222270i
$216$	2.27222e9			0.0710246
$217$	−1.50018e10	−	1.76338e10i	−0.459277	−	0.539855i
$218$	4.63832e10	+	8.03380e10i	1.39093	+	2.40917i
$219$	1.26951e9			0.0372940
$220$	−1.78529e9	−	3.09221e9i	−0.0513814	−	0.0889952i
$221$	7.62525e9	−	5.56619e10i	0.215025	−	1.56961i
$222$	3.56177e8	−	6.16916e8i	0.00984186	−	0.0170466i
$223$	−1.23776e10	−	2.14386e10i	−0.335170	−	0.580531i	0.648348	−	0.761344i	$-0.275460\pi$
$223$	−1.23776e10	−	2.14386e10i	−0.335170	−	0.580531i	−0.983517	+	0.180813i	$0.942127\pi$
$224$	−5.25797e10	+	9.63995e9i	−1.39541	+	0.255834i
$225$	−1.25468e10	+	2.17318e10i	−0.326372	+	0.565293i
$226$	−2.31306e10	+	4.00633e10i	−0.589791	+	1.02155i
$227$	3.86319e10			0.965673			0.482836	−	0.875711i	$-0.339607\pi$
$227$	3.86319e10			0.965673			0.482836	+	0.875711i	$0.339607\pi$
$228$	−4.16953e9			−0.102183
$229$	1.13599e10	−	1.96759e10i	0.272969	−	0.472797i	−0.696651	−	0.717410i	$-0.745328\pi$
$229$	1.13599e10	−	1.96759e10i	0.272969	−	0.472797i	0.969621	+	0.244613i	$0.0786609\pi$
$230$	2.33527e10	−	4.04480e10i	0.550252	−	0.953064i
$231$	4.48208e8	+	5.26843e8i	0.0103568	+	0.0121738i
$232$	−1.26834e10	−	2.19683e10i	−0.287436	−	0.497853i
$233$	−2.68012e10	+	4.64210e10i	−0.595733	+	1.03184i	0.397709	+	0.917511i	$0.369805\pi$
$233$	−2.68012e10	+	4.64210e10i	−0.595733	+	1.03184i	−0.993443	+	0.114329i	$0.963528\pi$
$234$	6.24660e10	−	2.54912e10i	1.36198	−	0.555801i
$235$	−7.48763e9	−	1.29690e10i	−0.160154	−	0.277396i
$236$	−7.89029e10			−1.65573
$237$	−2.29404e9	−	3.97340e9i	−0.0472318	−	0.0818079i
$238$	−1.14864e11	+	2.10591e10i	−2.32053	+	0.425445i
$239$	1.90048e9			0.0376767			0.0188383	−	0.999823i	$-0.494003\pi$
$239$	1.90048e9			0.0376767			0.0188383	+	0.999823i	$0.494003\pi$
$240$	1.21361e9	+	2.10204e9i	0.0236118	+	0.0408968i
$241$	3.12382e10			0.596499			0.298250	−	0.954488i	$-0.403597\pi$
$241$	3.12382e10			0.596499			0.298250	+	0.954488i	$0.403597\pi$
$242$	−3.88917e10	−	6.73625e10i	−0.728934	−	1.26255i
$243$	−8.84691e9	−	1.53233e10i	−0.162766	−	0.281919i
$244$	1.25228e10	+	2.16901e10i	0.226176	+	0.391749i
$245$	−5.26371e9	+	3.24218e10i	−0.0933349	+	0.574896i
$246$	1.18592e10			0.206466
$247$	−4.12129e10	+	1.68182e10i	−0.704525	+	0.287504i
$248$	−6.83902e9	−	1.18455e10i	−0.114805	−	0.198848i
$249$	4.03461e9	−	6.98814e9i	0.0665126	−	0.115203i
$250$	8.89647e10			1.44041
$251$	4.65240e10	−	8.05819e10i	0.739853	−	1.28146i	−0.212709	−	0.977116i	$-0.568228\pi$
$251$	4.65240e10	−	8.05819e10i	0.739853	−	1.28146i	0.952561	−	0.304347i	$-0.0984382\pi$
$252$	−4.98919e10	−	5.86451e10i	−0.779340	−	0.916071i
$253$	−5.99160e9	+	1.03778e10i	−0.0919391	+	0.159243i
$254$	−1.38902e10	−	2.40586e10i	−0.209391	−	0.362676i
$255$	3.43576e9	+	5.95090e9i	0.0508852	+	0.0881357i
$256$	2.99261e10			0.435482
$257$	−9.43225e10			−1.34870			−0.674352	−	0.738410i	$-0.735577\pi$
$257$	−9.43225e10			−1.34870			−0.674352	+	0.738410i	$0.735577\pi$
$258$	−2.57548e9	−	4.46086e9i	−0.0361884	−	0.0626802i
$259$	−8.53668e9	+	1.56511e9i	−0.117880	+	0.0216121i
$260$	−4.12868e10	−	3.20260e10i	−0.560314	−	0.434632i
$261$	−6.57100e10	+	1.13813e11i	−0.876494	+	1.51813i
$262$	1.12020e10	−	1.94024e10i	0.146872	−	0.254389i
$263$	6.57728e9	−	1.13922e10i	0.0847707	−	0.146827i	−0.820523	−	0.571614i	$-0.806318\pi$
$263$	6.57728e9	−	1.13922e10i	0.0847707	−	0.146827i	0.905293	+	0.424787i	$0.139651\pi$
$264$	2.04329e8	+	3.53908e8i	0.00258888	+	0.00448407i
$265$	−1.71953e10			−0.214192
$266$	5.99525e10	+	7.04708e10i	0.734243	+	0.863061i
$267$	3.47523e9	−	6.01928e9i	0.0418488	−	0.0724843i
$268$	−1.25170e10	+	2.16801e10i	−0.148216	+	0.256717i
$269$	1.52441e11			1.77507			0.887536	−	0.460737i	$-0.152415\pi$
$269$	1.52441e11			1.77507			0.887536	+	0.460737i	$0.152415\pi$
$270$	−8.30261e9	+	1.43805e10i	−0.0950774	+	0.164679i
$271$	−1.61943e10			−0.182390			−0.0911948	−	0.995833i	$-0.529069\pi$
$271$	−1.61943e10			−0.182390			−0.0911948	+	0.995833i	$0.529069\pi$
$272$	1.05138e11			1.16466
$273$	8.98592e9	+	4.66011e9i	0.0979108	+	0.0507767i
$274$	7.18990e10			0.770629
$275$	−9.08175e9			−0.0957574
$276$	−8.21322e9	+	1.42257e10i	−0.0851966	+	0.147565i
$277$	−3.06593e10			−0.312899			−0.156449	−	0.987686i	$-0.550005\pi$
$277$	−3.06593e10			−0.312899			−0.156449	+	0.987686i	$0.550005\pi$
$278$	−2.23333e10	+	3.86823e10i	−0.224259	+	0.388429i
$279$	−3.54315e10	+	6.13691e10i	−0.350082	+	0.606360i
$280$	−6.51306e9	+	1.82799e10i	−0.0633248	+	0.177731i
$281$	−3.97350e10			−0.380185			−0.190092	−	0.981766i	$-0.560879\pi$
$281$	−3.97350e10			−0.380185			−0.190092	+	0.981766i	$0.560879\pi$
$282$	4.79633e9	+	8.30749e9i	0.0451635	+	0.0782256i
$283$	−6.46486e10	+	1.11975e11i	−0.599129	+	1.03772i	0.393821	+	0.919187i	$0.371153\pi$
$283$	−6.46486e10	+	1.11975e11i	−0.599129	+	1.03772i	−0.992950	+	0.118535i	$0.962180\pi$
$284$	6.13374e10	−	1.06240e11i	0.559491	−	0.969066i
$285$	2.72212e9	−	4.71486e9i	0.0244403	−	0.0423318i
$286$	1.92933e10	+	1.49657e10i	0.170513	+	0.132266i
$287$	−9.36242e10	−	1.10050e11i	−0.814554	−	0.957462i
$288$	8.18091e10	+	1.41698e11i	0.700706	+	1.21366i
$289$	1.79058e11			1.50992
$290$	1.85379e11			1.53911
$291$	−6.05149e9	−	1.04815e10i	−0.0494703	−	0.0856850i
$292$	−2.55719e10	−	4.42918e10i	−0.205845	−	0.356534i
$293$	1.14928e11	−	1.99061e11i	0.911007	−	1.57791i	0.0983619	−	0.995151i	$-0.468640\pi$
$293$	1.14928e11	−	1.99061e11i	0.911007	−	1.57791i	0.812645	−	0.582759i	$-0.198027\pi$
$294$	3.37176e9	−	2.07683e10i	0.0263205	−	0.162121i
$295$	5.15126e10	−	8.92225e10i	0.396018	−	0.685923i
$296$	−5.12753e9			−0.0388235
$297$	2.13020e9	−	3.68962e9i	0.0158861	−	0.0275155i
$298$	−1.93323e11	−	3.34845e11i	−1.42007	−	2.45964i
$299$	−2.38010e10	+	1.73740e11i	−0.172217	+	1.25713i
$300$	−1.24492e10			−0.0887349
$301$	−2.10630e10	+	5.91165e10i	−0.147901	+	0.415107i
$302$	1.69532e11	+	2.93637e11i	1.17279	+	2.03133i
$303$	−1.23671e10	−	2.14204e10i	−0.0842898	−	0.145994i
$304$	−4.16498e10	−	7.21396e10i	−0.279693	−	0.484443i
$305$	−3.27026e10			−0.216388
$306$	1.78717e11	+	3.09548e11i	1.16525	+	2.01828i
$307$	8.96679e10			0.576122			0.288061	−	0.957612i	$-0.406989\pi$
$307$	8.96679e10			0.576122			0.288061	+	0.957612i	$0.406989\pi$
$308$	9.35265e9	−	2.62497e10i	0.0592184	−	0.166206i
$309$	1.26508e10	+	2.19118e10i	0.0789413	+	0.136730i
$310$	9.99581e10			0.614738
$311$	4.67321e10	+	8.09424e10i	0.283265	+	0.490630i	0.972187	−	0.234206i	$-0.0752489\pi$
$311$	4.67321e10	+	8.09424e10i	0.283265	+	0.490630i	−0.688922	+	0.724836i	$0.741916\pi$
$312$	4.72534e9	+	3.66542e9i	0.0282317	+	0.0218992i
$313$	7.76264e10	−	1.34453e11i	0.457151	−	0.791809i	−0.541658	−	0.840599i	$-0.682203\pi$
$313$	7.76264e10	−	1.34453e11i	0.457151	−	0.791809i	0.998809	+	0.0487900i	$0.0155365\pi$
$314$	1.48556e11	+	2.57306e11i	0.862395	+	1.49371i
$315$	9.88876e10	−	1.81300e10i	0.565906	−	0.103753i
$316$	−9.24182e10	+	1.60073e11i	−0.521393	+	0.903080i
$317$	−1.25038e11	+	2.16573e11i	−0.695468	+	1.20459i	0.274555	+	0.961571i	$0.411469\pi$
$317$	−1.25038e11	+	2.16573e11i	−0.695468	+	1.20459i	−0.970023	+	0.243014i	$0.921864\pi$
$318$	1.10147e10			0.0604021
$319$	−4.75627e10			−0.257163
$320$	7.52426e10	−	1.30324e11i	0.401133	−	0.694783i
$321$	−2.04400e10	+	3.54032e10i	−0.107451	+	0.186110i
$322$	3.58529e11	−	6.57327e10i	1.85855	−	0.340746i
$323$	−1.17911e11	−	2.04229e11i	−0.602760	−	1.04401i
$324$	−1.16366e11	+	2.01552e11i	−0.586644	+	1.01610i
$325$	−1.23051e11	+	5.02149e10i	−0.611802	+	0.249665i
$326$	1.35469e11	+	2.34639e11i	0.664294	+	1.15059i
$327$	4.26008e10			0.206041
$328$	−4.26814e10	−	7.39263e10i	−0.203613	−	0.352669i
$329$	3.92257e10	−	1.10093e11i	0.184582	−	0.518058i
$330$	−2.98644e9			−0.0138625
$331$	3.56007e9	+	6.16622e9i	0.0163017	+	0.0282353i	0.874061	−	0.485816i	$-0.161477\pi$
$331$	3.56007e9	+	6.16622e9i	0.0163017	+	0.0282353i	−0.857759	+	0.514051i	$0.828144\pi$
$332$	−3.25077e11			−1.46847
$333$	1.32823e10	+	2.30056e10i	0.0591935	+	0.102526i
$334$	−2.07689e11	−	3.59728e11i	−0.913177	−	1.58167i
$335$	−1.63437e10	−	2.83082e10i	−0.0709005	−	0.122803i
$336$	−6.35779e9	+	1.78441e10i	−0.0272132	+	0.0763780i
$337$	3.20655e11			1.35426			0.677131	−	0.735862i	$-0.263223\pi$
$337$	3.20655e11			1.35426			0.677131	+	0.735862i	$0.263223\pi$
$338$	3.44158e11	+	9.60975e10i	1.43428	+	0.400486i
$339$	1.06222e10	+	1.83982e10i	0.0436832	+	0.0756616i
$340$	1.38413e11	−	2.39739e11i	0.561723	−	0.972933i
$341$	−2.56463e10			−0.102714
$342$	1.41596e11	−	2.45252e11i	0.559674	−	0.969383i
$343$	−2.19343e11	+	1.32669e11i	−0.855657	+	0.517544i
$344$	−1.85383e10	+	3.21093e10i	−0.0713768	+	0.123628i
$345$	−1.07242e10	−	1.85748e10i	−0.0407547	−	0.0705893i
$346$	5.57302e10	+	9.65275e10i	0.209049	+	0.362083i
$347$	2.78860e11			1.03253			0.516267	−	0.856428i	$-0.327321\pi$
$347$	2.78860e11			1.03253			0.516267	+	0.856428i	$0.327321\pi$
$348$	−6.51984e10			−0.238304
$349$	−7.71244e8	−	1.33583e9i	−0.00278277	−	0.00481990i	0.864631	−	0.502408i	$-0.167552\pi$
$349$	−7.71244e8	−	1.33583e9i	−0.00278277	−	0.00481990i	−0.867413	+	0.497588i	$0.834219\pi$
$350$	1.79003e11	+	2.10408e11i	0.637608	+	0.749473i
$351$	8.46201e9	−	6.17700e10i	0.0297572	−	0.217218i
$352$	−2.96078e10	+	5.12823e10i	−0.102793	+	0.178043i
$353$	3.95528e10	−	6.85075e10i	0.135579	−	0.234829i	−0.790240	−	0.612798i	$-0.790044\pi$
$353$	3.95528e10	−	6.85075e10i	0.135579	−	0.234829i	0.925818	+	0.377969i	$0.123377\pi$
$354$	−3.29973e10	+	5.71530e10i	−0.111677	+	0.193430i
$355$	8.00896e10	+	1.38719e11i	0.267638	+	0.463563i
$356$	−2.80007e11			−0.923941
$357$	−1.79990e10	+	5.05170e10i	−0.0586465	+	0.164600i
$358$	2.48486e11	−	4.30391e11i	0.799519	−	1.38481i
$359$	−8.52930e10	+	1.47732e11i	−0.271012	+	0.469406i	−0.969121	−	0.246585i	$-0.920692\pi$
$359$	−8.52930e10	+	1.47732e11i	−0.271012	+	0.469406i	0.698109	+	0.715991i	$0.254025\pi$
$360$	5.93965e10			0.186380
$361$	6.79235e10	−	1.17647e11i	0.210493	−	0.364584i
$362$	−7.85823e11			−2.40512
$363$	−3.57203e10			−0.107978
$364$	−1.84183e10	−	4.07377e11i	−0.0549913	−	1.21630i
$365$	6.67795e10			0.196936
$366$	2.09482e10			0.0610213
$367$	7.22045e9	−	1.25062e10i	0.0207762	−	0.0359855i	−0.855450	−	0.517885i	$-0.826720\pi$
$367$	7.22045e9	−	1.25062e10i	0.0207762	−	0.0359855i	0.876227	+	0.481899i	$0.160053\pi$
$368$	−3.28170e11			−0.932791
$369$	−2.21123e11	+	3.82996e11i	−0.620890	+	1.07541i
$370$	1.87358e10	−	3.24513e10i	0.0519713	−	0.0900170i
$371$	−8.69573e10	−	1.02213e11i	−0.238300	−	0.280108i
$372$	−3.51556e10			−0.0951812
$373$	−6.28356e10	−	1.08834e11i	−0.168080	−	0.291123i	0.769665	−	0.638448i	$-0.220423\pi$
$373$	−6.28356e10	−	1.08834e11i	−0.168080	−	0.291123i	−0.937745	+	0.347325i	$0.887090\pi$
$374$	−6.46803e10	+	1.12030e11i	−0.170942	+	0.296081i
$375$	2.04275e10	−	3.53814e10i	0.0533426	−	0.0923921i
$376$	3.45240e10	−	5.97973e10i	0.0890791	−	0.154290i
$377$	−6.44440e11	+	2.62984e11i	−1.64303	+	0.670492i
$378$	−1.27468e11	+	2.33700e10i	−0.321136	+	0.0588771i
$379$	−6.15106e10	−	1.06540e11i	−0.153135	−	0.265237i	0.779244	−	0.626721i	$-0.215604\pi$
$379$	−6.15106e10	−	1.06540e11i	−0.153135	−	0.265237i	−0.932378	+	0.361484i	$0.882270\pi$
$380$	−2.19328e11			−0.539594
$381$	−1.27575e10			−0.0310173
$382$	−2.78270e11	−	4.81978e11i	−0.668623	−	1.15809i
$383$	−2.57690e11	−	4.46332e11i	−0.611932	−	1.05990i	−0.990914	−	0.134494i	$-0.957059\pi$
$383$	−2.57690e11	−	4.46332e11i	−0.611932	−	1.05990i	0.378982	−	0.925404i	$-0.376274\pi$
$384$	−1.48634e10	+	2.57442e10i	−0.0348842	+	0.0604212i
$385$	2.35768e10	+	2.77132e10i	0.0546905	+	0.0642856i
$386$	−3.51921e10	+	6.09546e10i	−0.0806868	+	0.139754i
$387$	1.92086e11			0.435307
$388$	−2.43791e11	+	4.22259e11i	−0.546104	+	0.945879i
$389$	−3.02092e11	−	5.23239e11i	−0.668907	−	1.15858i	−0.978210	−	0.207618i	$-0.933429\pi$
$389$	−3.02092e11	−	5.23239e11i	−0.668907	−	1.15858i	0.309303	−	0.950964i	$-0.399904\pi$
$390$	−4.04641e10	+	1.65127e10i	−0.0885684	+	0.0361432i
$391$	−9.29057e11			−2.01023
$392$	−1.41598e11	+	5.37269e10i	−0.302879	+	0.114922i
$393$	−5.14424e9	−	8.91009e9i	−0.0108781	−	0.0188415i
$394$	−2.07008e11	−	3.58548e11i	−0.432767	−	0.749574i
$395$	−1.20672e11	−	2.09011e11i	−0.249414	−	0.431998i
$396$	−8.52923e10			−0.174294
$397$	−2.64059e11	−	4.57364e11i	−0.533512	−	0.924070i	−0.999234	−	0.0391390i	$-0.987538\pi$
$397$	−2.64059e11	−	4.57364e11i	−0.533512	−	0.924070i	0.465722	−	0.884931i	$-0.345795\pi$
$398$	4.36777e11			0.872542
$399$	4.17923e10	−	7.66219e9i	0.0825502	−	0.0151347i
$400$	−1.24356e11	−	2.15391e11i	−0.242882	−	0.420685i
$401$	−4.19372e11			−0.809934			−0.404967	−	0.914331i	$-0.632717\pi$
$401$	−4.19372e11			−0.809934			−0.404967	+	0.914331i	$0.632717\pi$
$402$	1.04693e10	+	1.81333e10i	0.0199939	+	0.0346305i
$403$	−3.47488e11	+	1.41804e11i	−0.656247	+	0.267803i
$404$	−4.98221e11	+	8.62945e11i	−0.930478	+	1.61164i
$405$	−1.51942e11	−	2.63171e11i	−0.280627	−	0.486061i
$406$	9.37469e11	+	1.10194e12i	1.71234	+	2.01276i
$407$	−4.80704e9	+	8.32604e9i	−0.00868366	+	0.0150405i
$408$	−1.58416e10	+	2.74385e10i	−0.0283027	+	0.0490218i
$409$	−5.43396e11			−0.960200			−0.480100	−	0.877214i	$-0.659400\pi$
$409$	−5.43396e11			−0.960200			−0.480100	+	0.877214i	$0.659400\pi$
$410$	6.23824e11			1.09027
$411$	1.65090e10	−	2.85944e10i	0.0285385	−	0.0494302i
$412$	5.09651e11	−	8.82741e11i	0.871436	−	1.50937i
$413$	7.90864e11	−	1.44997e11i	1.33760	−	0.245236i
$414$	−5.57839e11	−	9.66205e11i	−0.933269	−	1.61647i
$415$	2.12230e11	−	3.67593e11i	0.351229	−	0.608347i
$416$	−1.17614e11	+	8.58546e11i	−0.192548	+	1.40554i
$417$	1.02560e10	+	1.77640e10i	0.0166099	+	0.0287692i
$418$	1.02491e11			0.164208
$419$	4.15298e11	+	7.19317e11i	0.658259	+	1.14014i	0.981066	+	0.193673i	$0.0620400\pi$
$419$	4.15298e11	+	7.19317e11i	0.658259	+	1.14014i	−0.322807	+	0.946465i	$0.604627\pi$
$420$	3.23188e10	+	3.79890e10i	0.0506797	+	0.0595712i
$421$	−4.58624e11			−0.711520			−0.355760	−	0.934577i	$-0.615778\pi$
$421$	−4.58624e11			−0.711520			−0.355760	+	0.934577i	$0.615778\pi$
$422$	5.98603e11	+	1.03681e12i	0.918825	+	1.59145i
$423$	−3.57722e11			−0.543268
$424$	−3.96421e10	−	6.86621e10i	−0.0595676	−	0.103174i
$425$	−3.52054e11	−	6.09775e11i	−0.523430	−	0.906608i
$426$	−5.13028e10	−	8.88590e10i	−0.0754740	−	0.130725i
$427$	−1.65378e11	−	1.94393e11i	−0.240743	−	0.282979i
$428$	1.64690e12			2.37230
$429$	1.03819e10	−	4.23665e9i	0.0147985	−	0.00603900i
$430$	−1.35477e11	−	2.34652e11i	−0.191098	−	0.330991i
$431$	−2.13253e11	+	3.69365e11i	−0.297679	+	0.515595i	−0.975604	−	0.219536i	$-0.929546\pi$
$431$	−2.13253e11	+	3.69365e11i	−0.297679	+	0.515595i	0.677926	+	0.735130i	$0.262879\pi$
$432$	1.16675e11			0.161176
$433$	4.13478e11	−	7.16164e11i	0.565271	−	0.979078i	−0.431754	−	0.901992i	$-0.642105\pi$
$433$	4.13478e11	−	7.16164e11i	0.565271	−	0.979078i	0.997024	−	0.0770861i	$-0.0245616\pi$
$434$	5.05492e11	+	5.94178e11i	0.683929	+	0.803920i
$435$	4.25655e10	−	7.37256e10i	0.0569975	−	0.0987226i
$436$	−8.58110e11	−	1.48629e12i	−1.13724	−	1.96977i
$437$	3.68042e11	+	6.37468e11i	0.482760	+	0.836165i
$438$	−4.27768e10			−0.0555360
$439$	2.24803e11			0.288876			0.144438	−	0.989514i	$-0.453863\pi$
$439$	2.24803e11			0.288876			0.144438	+	0.989514i	$0.453863\pi$
$440$	1.07482e10	+	1.86164e10i	0.0136709	+	0.0236788i
$441$	6.07849e11	+	4.96130e11i	0.765282	+	0.624629i
$442$	−2.56936e11	+	1.87555e12i	−0.320202	+	2.33738i
$443$	3.16772e11	−	5.48666e11i	0.390778	−	0.676848i	−0.601774	−	0.798666i	$-0.705539\pi$
$443$	3.16772e11	−	5.48666e11i	0.390778	−	0.676848i	0.992552	+	0.121818i	$0.0388725\pi$
$444$	−6.58944e9	+	1.14132e10i	−0.00804683	+	0.0139375i
$445$	1.82806e11	−	3.16629e11i	0.220989	−	0.382763i
$446$	4.17069e11	+	7.22384e11i	0.499115	+	0.864493i
$447$	−1.77558e11			−0.210357
$448$	1.15519e12	−	2.11792e11i	1.35488	−	0.248403i
$449$	−3.22968e11	+	5.59396e11i	−0.375017	+	0.649548i	−0.990330	−	0.138735i	$-0.955696\pi$
$449$	−3.22968e11	+	5.59396e11i	−0.375017	+	0.649548i	0.615313	+	0.788283i	$0.289030\pi$
$450$	4.22771e11	−	7.32261e11i	0.486014	−	0.841801i
$451$	−1.60055e11			−0.182169
$452$	4.27926e11	−	7.41190e11i	0.482221	−	0.835231i
$453$	1.55707e11			0.173726
$454$	−1.30172e12			−1.43802
$455$	4.72681e11	+	2.45133e11i	0.517032	+	0.268133i
$456$	2.51024e10			0.0271877
$457$	4.15604e11			0.445714			0.222857	−	0.974851i	$-0.428462\pi$
$457$	4.15604e11			0.445714			0.222857	+	0.974851i	$0.428462\pi$
$458$	−3.82776e11	+	6.62987e11i	−0.406490	+	0.704061i
$459$	3.30309e11			0.347346
$460$	−4.32035e11	+	7.48307e11i	−0.449893	+	0.779237i
$461$	−6.08880e11	+	1.05461e12i	−0.627882	+	1.08752i	0.360094	+	0.932916i	$0.382745\pi$
$461$	−6.08880e11	+	1.05461e12i	−0.627882	+	1.08752i	−0.987976	+	0.154607i	$0.950589\pi$
$462$	−1.51025e10	−	1.77522e10i	−0.0154227	−	0.0181286i
$463$	1.54999e12			1.56753			0.783763	−	0.621060i	$-0.213298\pi$
$463$	1.54999e12			1.56753			0.783763	+	0.621060i	$0.213298\pi$
$464$	−6.51273e11	−	1.12804e12i	−0.652277	−	1.12978i
$465$	2.29517e10	−	3.97535e10i	0.0227655	−	0.0394310i
$466$	9.03076e11	−	1.56417e12i	0.887131	−	1.53656i
$467$	−6.11480e11	+	1.05911e12i	−0.594917	+	1.03043i	0.398642	+	0.917107i	$0.369482\pi$
$467$	−6.11480e11	+	1.05911e12i	−0.594917	+	1.03043i	−0.993559	+	0.113320i	$0.963852\pi$
$468$	−1.15565e12	+	4.71600e11i	−1.11358	+	0.454430i
$469$	8.56204e10	−	2.40307e11i	0.0817146	−	0.229345i
$470$	2.52299e11	+	4.36994e11i	0.238492	+	0.413081i
$471$	1.36442e11			0.127748
$472$	4.75030e11			0.440536
$473$	3.47592e10	+	6.02048e10i	0.0319297	+	0.0553039i
$474$	7.72988e10	+	1.33885e11i	0.0703348	+	0.121823i
$475$	−2.78930e11	+	4.83120e11i	−0.251405	+	0.435446i
$476$	2.12503e12	−	3.89603e11i	1.89729	−	0.347849i
$477$	−2.05377e11	+	3.55723e11i	−0.181643	+	0.314615i
$478$	−6.40374e10			−0.0561058
$479$	9.67182e11	−	1.67521e12i	0.839457	−	1.45398i	−0.0508927	−	0.998704i	$-0.516207\pi$
$479$	9.67182e11	−	1.67521e12i	0.839457	−	1.45398i	0.890349	−	0.455278i	$-0.150460\pi$
$480$	−5.29942e10	−	9.17886e10i	−0.0455662	−	0.0789229i
$481$	−1.90955e10	+	1.39391e11i	−0.0162659	+	0.118736i
$482$	−1.05259e12			−0.888272
$483$	5.61811e10	−	1.57681e11i	0.0469708	−	0.131831i
$484$	7.19515e11	+	1.24624e12i	0.595986	+	1.03228i
$485$	−3.18323e11	−	5.51352e11i	−0.261235	−	0.452472i
$486$	2.98100e11	+	5.16325e11i	0.242381	+	0.419817i
$487$	1.38687e12			1.11726			0.558631	−	0.829416i	$-0.311327\pi$
$487$	1.38687e12			1.11726			0.558631	+	0.829416i	$0.311327\pi$
$488$	−7.53926e10	−	1.30584e11i	−0.0601782	−	0.104232i
$489$	1.24422e11			0.0984027
$490$	1.77363e11	−	1.09247e12i	0.138989	−	0.856102i
$491$	7.66925e11	+	1.32835e12i	0.595506	+	1.03145i	0.993475	+	0.114048i	$0.0363817\pi$
$491$	7.66925e11	+	1.32835e12i	0.595506	+	1.03145i	−0.397969	+	0.917399i	$0.630285\pi$
$492$	−2.19401e11			−0.168809
$493$	−1.84377e12	−	3.19350e12i	−1.40571	−	2.43476i
$494$	1.38868e12	−	5.66697e11i	1.04914	−	0.428134i
$495$	5.56840e10	−	9.64476e10i	0.0416876	−	0.0722051i
$496$	−3.51173e11	−	6.08249e11i	−0.260527	−	0.451246i
$497$	−4.19568e11	+	1.17758e12i	−0.308460	+	0.865741i
$498$	−1.35948e11	+	2.35468e11i	−0.0990467	+	0.171554i
$499$	−6.42629e11	+	1.11307e12i	−0.463989	+	0.803652i	−0.999155	−	0.0410943i	$-0.986916\pi$
$499$	−6.42629e11	+	1.11307e12i	−0.463989	+	0.803652i	0.535166	+	0.844747i	$0.320249\pi$
$500$	−1.64589e12			−1.17770
$501$	−1.90753e11			−0.135270
$502$	−1.56765e12	+	2.71524e12i	−1.10174	+	1.90828i
$503$	−8.24264e11	+	1.42767e12i	−0.574130	+	0.994422i	0.422006	+	0.906593i	$0.361326\pi$
$503$	−8.24264e11	+	1.42767e12i	−0.574130	+	0.994422i	−0.996136	+	0.0878291i	$0.972007\pi$
$504$	3.00370e11	+	3.53069e11i	0.207357	+	0.243737i
$505$	−6.50538e11	−	1.12677e12i	−0.445104	−	0.770943i
$506$	2.01889e11	−	3.49683e11i	0.136910	−	0.237136i
$507$	1.17242e11	−	1.14807e11i	0.0788036	−	0.0771673i
$508$	2.56976e11	+	4.45095e11i	0.171201	+	0.296528i
$509$	−2.52832e11			−0.166956			−0.0834781	−	0.996510i	$-0.526603\pi$
$509$	−2.52832e11			−0.166956			−0.0834781	+	0.996510i	$0.526603\pi$
$510$	−1.15769e11	−	2.00518e11i	−0.0757752	−	0.131247i
$511$	3.37707e11	+	3.96955e11i	0.219102	+	0.257542i
$512$	−1.99198e12			−1.28106
$513$	−1.30851e11	−	2.26640e11i	−0.0834156	−	0.144480i
$514$	3.17824e12			2.00841
$515$	6.65462e11	+	1.15261e12i	0.416861	+	0.722024i
$516$	4.76476e10	+	8.25280e10i	0.0295881	+	0.0512481i
$517$	−6.47323e10	−	1.12120e11i	−0.0398487	−	0.0690199i
$518$	2.87647e11	−	5.27372e10i	0.175540	−	0.0321835i
$519$	5.11856e10			0.0309667
$520$	2.48564e11	+	1.92810e11i	0.149082	+	0.115642i
$521$	8.50471e11	+	1.47306e12i	0.505696	+	0.875891i	0.999978	+	0.00658973i	$0.00209759\pi$
$521$	8.50471e11	+	1.47306e12i	0.505696	+	0.875891i	−0.494282	+	0.869301i	$0.664569\pi$
$522$	2.21413e12	−	3.83498e12i	1.30522	−	2.26071i
$523$	1.65256e12			0.965830			0.482915	−	0.875667i	$-0.339578\pi$
$523$	1.65256e12			0.965830			0.482915	+	0.875667i	$0.339578\pi$
$524$	−2.07242e11	+	3.58953e11i	−0.120084	+	0.207992i
$525$	1.24781e11	−	2.28774e10i	0.0716856	−	0.0131428i
$526$	−2.21624e11	+	3.83865e11i	−0.126236	+	0.218646i
$527$	−9.94177e11	−	1.72196e12i	−0.561456	−	0.972470i
$528$	1.04920e10	+	1.81726e10i	0.00587494	+	0.0101757i
$529$	1.09875e12			0.610028
$530$	5.79402e11			0.318962
$531$	−1.23051e12	−	2.13131e12i	−0.671677	−	1.16338i
$532$	−1.10915e12	−	1.30374e12i	−0.600326	−	0.705650i
$533$	−2.16863e12	+	8.84977e11i	−1.16389	+	0.474963i
$534$	−1.17099e11	+	2.02822e11i	−0.0623188	+	0.107939i
$535$	−1.07520e12	+	1.86229e12i	−0.567408	+	0.982780i
$536$	7.53577e10	−	1.30523e11i	0.0394354	−	0.0683041i
$537$	−1.14112e11	−	1.97647e11i	−0.0592168	−	0.102567i
$538$	−5.13656e12			−2.64333
$539$	−4.55060e10	+	2.80294e11i	−0.0232230	+	0.143042i
$540$	1.53602e11	−	2.66047e11i	0.0777365	−	0.134644i
$541$	5.16932e11	−	8.95353e11i	0.259445	−	0.449372i	−0.706648	−	0.707565i	$-0.749794\pi$
$541$	5.16932e11	−	8.95353e11i	0.259445	−	0.449372i	0.966093	+	0.258193i	$0.0831269\pi$
$542$	5.45673e11			0.271604
$543$	−1.80436e11	+	3.12524e11i	−0.0890682	+	0.154271i
$544$	−4.59099e12			−2.24756
$545$	2.24091e12			1.08803
$546$	−3.02784e11	−	1.57024e11i	−0.145803	−	0.0756136i
$547$	3.98443e12			1.90293			0.951467	−	0.307751i	$-0.0995765\pi$
$547$	3.98443e12			1.90293			0.951467	+	0.307751i	$0.0995765\pi$
$548$	−1.33016e12			−0.630076
$549$	−3.90592e11	+	6.76526e11i	−0.183505	+	0.317840i
$550$	3.06013e11			0.142596
$551$	−1.46080e12	+	2.53018e12i	−0.675164	+	1.16942i
$552$	4.94471e10	−	8.56449e10i	0.0226681	−	0.0392623i
$553$	6.32171e11	−	1.77428e12i	0.287456	−	0.806790i
$554$	1.03308e12			0.465950
$555$	−8.60397e9	−	1.49025e10i	−0.00384929	−	0.00666716i
$556$	4.13176e11	−	7.15641e11i	0.183357	−	0.317584i
$557$	−1.17922e11	+	2.04247e11i	−0.0519096	+	0.0899100i	−0.890813	−	0.454371i	$-0.849864\pi$
$557$	−1.17922e11	+	2.04247e11i	−0.0519096	+	0.0899100i	0.838903	+	0.544281i	$0.183197\pi$
$558$	1.19388e12	−	2.06786e12i	0.521322	−	0.902956i
$559$	8.03848e11	+	6.23540e11i	0.348193	+	0.270092i
$560$	−3.34435e11	+	9.38644e11i	−0.143703	+	0.403325i
$561$	2.97029e10	+	5.14470e10i	0.0126609	+	0.0219294i
$562$	1.33889e12			0.566149
$563$	1.40379e12			0.588862			0.294431	−	0.955673i	$-0.404870\pi$
$563$	1.40379e12			0.588862			0.294431	+	0.955673i	$0.404870\pi$
$564$	−8.87343e10	−	1.53692e11i	−0.0369263	−	0.0639582i
$565$	5.58752e11	+	9.67788e11i	0.230675	+	0.399542i
$566$	2.17836e12	−	3.77303e12i	0.892188	−	1.54531i
$567$	7.95983e11	−	2.23405e12i	0.323430	−	0.907756i
$568$	−3.69278e11	+	6.39607e11i	−0.148863	+	0.257837i
$569$	4.75781e12			1.90284			0.951418	−	0.307901i	$-0.0996266\pi$
$569$	4.75781e12			1.90284			0.951418	+	0.307901i	$0.0996266\pi$
$570$	−9.17231e10	+	1.58869e11i	−0.0363950	+	0.0630380i
$571$	1.36078e12	+	2.35694e12i	0.535704	+	0.927866i	0.999129	+	0.0417303i	$0.0132870\pi$
$571$	1.36078e12	+	2.35694e12i	0.535704	+	0.927866i	−0.463425	+	0.886136i	$0.653380\pi$
$572$	−3.56934e11	−	2.76872e11i	−0.139414	−	0.108143i
$573$	−2.55578e11			−0.0990440
$574$	3.15471e12	+	3.70818e12i	1.21298	+	1.42580i
$575$	1.09888e12	+	1.90332e12i	0.419223	+	0.726116i
$576$	−1.79736e12	−	3.11312e12i	−0.680353	−	1.17841i
$577$	1.08989e12	+	1.88775e12i	0.409347	+	0.709010i	0.994817	−	0.101684i	$-0.0324232\pi$
$577$	1.08989e12	+	1.88775e12i	0.409347	+	0.709010i	−0.585470	+	0.810694i	$0.699090\pi$
$578$	−6.03345e12			−2.24849
$579$	1.61612e10	+	2.79920e10i	0.00597612	+	0.0103509i
$580$	−3.42960e12			−1.25840
$581$	3.25833e12	−	5.97382e11i	1.18632	−	0.217500i
$582$	2.03908e11	+	3.53178e11i	0.0736682	+	0.127597i
$583$	−1.48657e11			−0.0532939
$584$	1.53954e11	+	2.66656e11i	0.0547687	+	0.0948621i
$585$	2.21199e11	−	1.61468e12i	0.0780876	−	0.570015i
$586$	−3.87255e12	+	6.70745e12i	−1.35662	+	2.34973i
$587$	−1.35856e12	−	2.35309e12i	−0.472287	−	0.818026i	0.527210	−	0.849735i	$-0.323238\pi$
$587$	−1.35856e12	−	2.35309e12i	−0.472287	−	0.818026i	−0.999497	+	0.0317094i	$0.989905\pi$
$588$	−6.23791e10	+	3.84224e11i	−0.0215199	+	0.132552i
$589$	−7.87679e11	+	1.36430e12i	−0.269668	+	0.467080i
$590$	−1.73574e12	+	3.00639e12i	−0.589726	+	1.02144i
$591$	−1.90127e11			−0.0641063
$592$	−2.63290e11			−0.0881022
$593$	2.06639e12	−	3.57909e12i	0.686224	−	1.18858i	−0.286826	−	0.957983i	$-0.592600\pi$
$593$	2.06639e12	−	3.57909e12i	0.686224	−	1.18858i	0.973050	−	0.230592i	$-0.0740664\pi$
$594$	−7.17780e10	+	1.24323e11i	−0.0236566	+	0.0409744i
$595$	−9.46792e11	+	2.65732e12i	−0.309691	+	0.869195i
$596$	3.57657e12	+	6.19479e12i	1.16107	+	2.01103i
$597$	1.00290e11	−	1.73707e11i	0.0323127	−	0.0559672i
$598$	8.01985e11	−	5.85424e12i	0.256455	−	1.87204i
$599$	−1.90490e12	−	3.29939e12i	−0.604578	−	1.04716i	−0.992118	−	0.125307i	$-0.960008\pi$
$599$	−1.90490e12	−	3.29939e12i	−0.604578	−	1.04716i	0.387540	−	0.921853i	$-0.373325\pi$
$600$	7.49493e10			0.0236095
$601$	2.24502e12	+	3.88849e12i	0.701917	+	1.21576i	0.967793	+	0.251748i	$0.0810054\pi$
$601$	2.24502e12	+	3.88849e12i	0.701917	+	1.21576i	−0.265876	+	0.964007i	$0.585661\pi$
$602$	7.09726e11	−	1.99196e12i	0.220245	−	0.618152i
$603$	−7.80823e11			−0.240505
$604$	−3.13641e12	−	5.43242e12i	−0.958886	−	1.66084i
$605$	−1.87897e12			−0.570192
$606$	4.16714e11	+	7.21769e11i	0.125519	+	0.217406i
$607$	−3.26857e9	−	5.66134e9i	−0.000977258	−	0.00169266i	0.865536	−	0.500846i	$-0.166978\pi$
$607$	−3.26857e9	−	5.66134e9i	−0.000977258	−	0.00169266i	−0.866514	+	0.499153i	$0.833644\pi$
$608$	1.81870e12	+	3.15009e12i	0.539754	+	0.934881i
$609$	6.53500e11	−	1.19813e11i	0.192516	−	0.0352959i
$610$	1.10193e12			0.322232
$611$	−1.49701e12	−	1.16122e12i	−0.434549	−	0.337077i
$612$	−3.30635e12	−	5.72677e12i	−0.952726	−	1.65017i
$613$	−5.71710e11	+	9.90231e11i	−0.163532	+	0.283246i	−0.936133	−	0.351646i	$-0.885622\pi$
$613$	−5.71710e11	+	9.90231e11i	−0.163532	+	0.283246i	0.772601	+	0.634892i	$0.218955\pi$
$614$	−3.02140e12			−0.857926
$615$	1.43238e11	−	2.48096e11i	0.0403758	−	0.0699330i
$616$	−5.63070e10	+	1.58034e11i	−0.0157561	+	0.0442220i
$617$	4.76024e11	−	8.24498e11i	0.132235	−	0.229037i	−0.792303	−	0.610128i	$-0.791118\pi$
$617$	4.76024e11	−	8.24498e11i	0.132235	−	0.229037i	0.924538	+	0.381091i	$0.124451\pi$
$618$	−4.26273e11	−	7.38327e11i	−0.117555	−	0.203611i
$619$	3.98351e11	+	6.89964e11i	0.109058	+	0.188894i	0.915389	−	0.402571i	$-0.131883\pi$
$619$	3.98351e11	+	6.89964e11i	0.109058	+	0.188894i	−0.806331	+	0.591465i	$0.798550\pi$
$620$	−1.84927e12			−0.502618
$621$	−1.03101e12			−0.278195
$622$	−1.57466e12	−	2.72739e12i	−0.421822	−	0.730618i
$623$	2.80658e12	−	5.14559e11i	0.746417	−	0.136848i
$624$	2.42639e11	+	1.88213e11i	0.0640662	+	0.0496958i
$625$	−1.85808e11	+	3.21828e11i	−0.0487084	+	0.0843653i
$626$	−2.61565e12	+	4.53044e12i	−0.680762	+	1.17912i
$627$	2.35334e10	−	4.07610e10i	0.00608108	−	0.0105327i
$628$	−2.74835e12	−	4.76028e12i	−0.705105	−	1.22128i
$629$	−7.45379e11			−0.189867
$630$	−3.33206e12	+	6.10899e11i	−0.842714	+	0.154503i
$631$	1.13289e12	−	1.96222e12i	0.284481	−	0.492736i	−0.688002	−	0.725709i	$-0.741512\pi$
$631$	1.13289e12	−	1.96222e12i	0.284481	−	0.492736i	0.972483	+	0.232973i	$0.0748453\pi$
$632$	5.56397e11	−	9.63708e11i	0.138726	−	0.240280i
$633$	5.49789e11			0.136107
$634$	4.21322e12	−	7.29751e12i	1.03565	−	1.79380i
$635$	−6.71077e11			−0.163791
$636$	−2.03778e11			−0.0493855
$637$	9.33232e11	+	4.04939e12i	0.224575	+	0.974457i
$638$	1.60264e12			0.382952
$639$	3.82629e12			0.907871
$640$	−7.81853e11	+	1.35421e12i	−0.184211	+	0.319062i
$641$	9.55097e11			0.223453			0.111727	−	0.993739i	$-0.464362\pi$
$641$	9.55097e11			0.223453			0.111727	+	0.993739i	$0.464362\pi$
$642$	6.88736e11	−	1.19293e12i	0.160009	−	0.277144i
$643$	6.80755e11	−	1.17910e12i	0.157051	−	0.272021i	−0.776753	−	0.629806i	$-0.783135\pi$
$643$	6.80755e11	−	1.17910e12i	0.157051	−	0.272021i	0.933804	+	0.357785i	$0.116468\pi$
$644$	−6.63296e12	+	1.21609e12i	−1.51957	+	0.278598i
$645$	−1.24429e11			−0.0283076
$646$	3.97308e12	+	6.88157e12i	0.897595	+	1.55468i
$647$	−3.88045e12	+	6.72114e12i	−0.870589	+	1.50791i	−0.00920125	+	0.999958i	$0.502929\pi$
$647$	−3.88045e12	+	6.72114e12i	−0.870589	+	1.50791i	−0.861388	+	0.507947i	$0.830404\pi$
$648$	7.00575e11	−	1.21343e12i	0.156087	−	0.270351i
$649$	4.45339e11	−	7.71350e11i	0.0985348	−	0.170667i
$650$	4.14626e12	−	1.69201e12i	0.911059	−	0.371786i
$651$	3.52374e11	−	6.46041e10i	0.0768934	−	0.0140976i
$652$	−2.50624e12	−	4.34093e12i	−0.543135	−	0.940738i
$653$	−3.92762e12			−0.845318			−0.422659	−	0.906289i	$-0.638903\pi$
$653$	−3.92762e12			−0.845318			−0.422659	+	0.906289i	$0.638903\pi$
$654$	−1.43545e12			−0.306823
$655$	−2.70600e11	−	4.68693e11i	−0.0574436	−	0.0994952i
$656$	−2.19162e12	−	3.79600e12i	−0.462059	−	0.800310i
$657$	7.97600e11	−	1.38148e12i	0.167009	−	0.289269i
$658$	−1.32173e12	+	3.70963e12i	−0.274868	+	0.771461i
$659$	4.20591e12	−	7.28484e12i	0.868711	−	1.50465i	0.00539642	−	0.999985i	$-0.498282\pi$
$659$	4.20591e12	−	7.28484e12i	0.868711	−	1.50465i	0.863315	−	0.504666i	$-0.168384\pi$
$660$	5.52505e10			0.0113341
$661$	−3.31234e12	+	5.73714e12i	−0.674883	+	1.16893i	0.301620	+	0.953428i	$0.402473\pi$
$661$	−3.31234e12	+	5.73714e12i	−0.674883	+	1.16893i	−0.976503	+	0.215503i	$0.930861\pi$
$662$	−1.19958e11	−	2.07773e11i	−0.0242755	−	0.0420464i
$663$	6.86914e11	+	5.32835e11i	0.138068	+	0.107098i
$664$	1.95710e12			0.390713
$665$	2.19838e12	−	4.03050e11i	0.435918	−	0.0799211i
$666$	−4.47552e11	−	7.75183e11i	−0.0881474	−	0.152676i
$667$	5.75503e12	+	9.96800e12i	1.12585	+	1.95003i
$668$	3.84235e12	+	6.65514e12i	0.746625	+	1.29319i
$669$	3.83058e11			0.0739345
$670$	5.50708e11	+	9.53855e11i	0.105581	+	0.182871i
$671$	−2.82721e11			−0.0538403
$672$	2.77622e11	−	7.79190e11i	0.0525161	−	0.147395i
$673$	−2.79642e12	−	4.84355e12i	−0.525455	−	0.910114i	−0.999560	−	0.0296462i	$-0.990562\pi$
$673$	−2.79642e12	−	4.84355e12i	−0.525455	−	0.910114i	0.474106	−	0.880468i	$-0.342771\pi$
$674$	−1.08046e13			−2.01669
$675$	−3.90687e11	−	6.76689e11i	−0.0724372	−	0.125465i
$676$	−6.36709e12	−	1.77785e12i	−1.17268	−	0.327442i
$677$	−1.30960e12	+	2.26830e12i	−0.239602	+	0.415003i	−0.960600	−	0.277934i	$-0.910350\pi$
$677$	−1.30960e12	+	2.26830e12i	−0.239602	+	0.415003i	0.720998	+	0.692937i	$0.243684\pi$
$678$	−3.57919e11	−	6.19933e11i	−0.0650505	−	0.112671i
$679$	1.66761e12	−	4.68041e12i	0.301079	−	0.845026i
$680$	−8.33307e11	+	1.44333e12i	−0.149457	+	0.258866i
$681$	−2.98892e11	+	5.17696e11i	−0.0532540	+	0.0922387i
$682$	8.64161e11			0.152956
$683$	4.68061e12			0.823017			0.411509	−	0.911406i	$-0.365002\pi$
$683$	4.68061e12			0.823017			0.411509	+	0.911406i	$0.365002\pi$
$684$	−2.61960e12	+	4.53728e12i	−0.457596	+	0.792580i
$685$	8.68412e11	−	1.50413e12i	0.150702	−	0.261023i
$686$	7.39084e12	−	4.47035e12i	1.27419	−	0.770696i
$687$	1.75781e11	+	3.04461e11i	0.0301069	+	0.0521467i
$688$	−9.51912e11	+	1.64876e12i	−0.161975	+	0.280550i
$689$	−2.01420e12	+	8.21958e11i	−0.340499	+	0.138951i
$690$	3.61356e11	+	6.25886e11i	0.0606895	+	0.105117i
$691$	−1.22796e12			−0.204896			−0.102448	−	0.994738i	$-0.532667\pi$
$691$	−1.22796e12			−0.204896			−0.102448	+	0.994738i	$0.532667\pi$
$692$	−1.03103e12	−	1.78580e12i	−0.170921	−	0.296044i
$693$	8.54907e11	−	1.56738e11i	0.140805	−	0.0258152i
$694$	−9.39631e12			−1.53759
$695$	5.39492e11	+	9.34428e11i	0.0877109	+	0.151920i
$696$	3.92522e11			0.0634049
$697$	−6.20452e12	−	1.07465e13i	−0.995773	−	1.72473i
$698$	2.59874e10	+	4.50115e10i	0.00414394	+	0.00717751i
$699$	−4.14717e11	−	7.18311e11i	−0.0657059	−	0.113806i
$700$	−3.31164e12	−	3.89264e12i	−0.521316	−	0.612778i
$701$	7.49845e12			1.17284			0.586422	−	0.810005i	$-0.300536\pi$
$701$	7.49845e12			1.17284			0.586422	+	0.810005i	$0.300536\pi$
$702$	−2.85131e11	+	2.08136e12i	−0.0443126	+	0.323468i
$703$	2.95279e11	+	5.11438e11i	0.0455967	+	0.0789759i
$704$	6.50490e11	−	1.12668e12i	0.0998076	−	0.172872i
$705$	2.31725e11			0.0353282
$706$	−1.33275e12	+	2.30839e12i	−0.201896	+	0.349694i
$707$	3.40800e12	−	9.56507e12i	0.512994	−	1.43980i
$708$	6.10466e11	−	1.05736e12i	0.0913086	−	0.158151i
$709$	2.03640e12	+	3.52714e12i	0.302660	+	0.524222i	0.976737	−	0.214439i	$-0.0687922\pi$
$709$	2.03640e12	+	3.52714e12i	0.302660	+	0.524222i	−0.674078	+	0.738660i	$0.735459\pi$
$710$	−2.69865e12	−	4.67420e12i	−0.398551	−	0.690311i
$711$	−5.76514e12			−0.846051
$712$	1.68576e12			0.245831
$713$	3.10317e12	+	5.37484e12i	0.449679	+	0.778866i
$714$	6.06484e11	−	1.70219e12i	0.0873328	−	0.245113i
$715$	5.46112e11	−	2.22858e11i	0.0781456	−	0.0318898i
$716$	−4.59711e12	+	7.96243e12i	−0.653697	+	1.13224i
$717$	−1.47038e10	+	2.54678e10i	−0.00207776	+	0.00359878i
$718$	2.87398e12	−	4.97789e12i	0.403575	−	0.699012i
$719$	−1.24217e12	−	2.15150e12i	−0.173341	−	0.300235i	0.766245	−	0.642549i	$-0.222123\pi$
$719$	−1.24217e12	−	2.15150e12i	−0.173341	−	0.300235i	−0.939586	+	0.342313i	$0.888790\pi$
$720$	3.04991e12			0.422952
$721$	−3.48618e12	+	9.78451e12i	−0.480442	+	1.34844i
$722$	−2.28871e12	+	3.96416e12i	−0.313454	+	0.542918i
$723$	−2.41688e11	+	4.18616e11i	−0.0328952	+	0.0569761i
$724$	1.45381e13			1.96645
$725$	−4.36159e12	+	7.55449e12i	−0.586305	+	1.01551i
$726$	1.20361e12			0.160794
$727$	−7.42136e12			−0.985322			−0.492661	−	0.870221i	$-0.663976\pi$
$727$	−7.42136e12			−0.985322			−0.492661	+	0.870221i	$0.663976\pi$
$728$	1.10886e11	+	2.45258e12i	0.0146314	+	0.323618i
$729$	−7.07464e12			−0.927749
$730$	−2.25016e12			−0.293266
$731$	−2.69488e12	+	4.66767e12i	−0.349069	+	0.604606i
$732$	−3.87551e11			−0.0498918
$733$	−1.05719e12	+	1.83111e12i	−0.135265	+	0.234287i	−0.925699	−	0.378261i	$-0.876522\pi$
$733$	−1.05719e12	+	1.83111e12i	−0.135265	+	0.234287i	0.790433	+	0.612548i	$0.209855\pi$
$734$	−2.43296e11	+	4.21401e11i	−0.0309388	+	0.0535875i
$735$	−3.93751e11	−	3.21382e11i	−0.0497655	−	0.0406190i
$736$	1.43301e13			1.80010
$737$	−1.41295e11	−	2.44731e11i	−0.0176410	−	0.0305552i
$738$	7.45082e12	−	1.29052e13i	0.924593	−	1.60144i
$739$	−8.07415e11	+	1.39848e12i	−0.0995857	+	0.172487i	−0.911513	−	0.411271i	$-0.865085\pi$
$739$	−8.07415e11	+	1.39848e12i	−0.0995857	+	0.172487i	0.811928	+	0.583758i	$0.198418\pi$
$740$	−3.46621e11	+	6.00364e11i	−0.0424924	+	0.0735990i
$741$	9.34841e10	−	6.82404e11i	0.0113908	−	0.0831495i
$742$	2.93006e12	+	3.44412e12i	0.354862	+	0.417120i
$743$	−4.43914e12	−	7.68881e12i	−0.534379	−	0.925571i	−0.999193	−	0.0401628i	$-0.987212\pi$
$743$	−4.43914e12	−	7.68881e12i	−0.534379	−	0.925571i	0.464815	−	0.885408i	$-0.346121\pi$
$744$	2.11652e11			0.0253247
$745$	−9.34000e12			−1.11082
$746$	2.11727e12	+	3.66722e12i	0.250295	+	0.433523i
$747$	−5.06966e12	−	8.78091e12i	−0.595712	−	1.03180i
$748$	1.19662e12	−	2.07260e12i	0.139765	−	0.242079i
$749$	−1.65073e13	+	3.02645e12i	−1.91650	+	0.351370i
$750$	−6.88312e11	+	1.19219e12i	−0.0794346	+	0.137585i
$751$	1.02677e13			1.17786			0.588931	−	0.808183i	$-0.299549\pi$
$751$	1.02677e13			1.17786			0.588931	+	0.808183i	$0.299549\pi$
$752$	1.77275e12	−	3.07049e12i	0.202147	−	0.350129i
$753$	7.19905e11	+	1.24691e12i	0.0816014	+	0.141338i
$754$	2.17147e13	−	8.86136e12i	2.44671	−	0.998457i
$755$	8.19056e12			0.917387
$756$	2.35822e12	−	4.32357e11i	0.262565	−	0.0481387i
$757$	−8.16242e12	−	1.41377e13i	−0.903415	−	1.56476i	−0.823031	−	0.567997i	$-0.807719\pi$
$757$	−8.16242e12	−	1.41377e13i	−0.903415	−	1.56476i	−0.0803840	−	0.996764i	$-0.525615\pi$
$758$	2.07263e12	+	3.58989e12i	0.228039	+	0.394975i
$759$	−9.27130e10	−	1.60584e11i	−0.0101403	−	0.0175636i
$760$	1.32045e12			0.143569
$761$	−3.85732e12	−	6.68107e12i	−0.416922	−	0.722130i	0.578706	−	0.815536i	$-0.303558\pi$
$761$	−3.85732e12	−	6.68107e12i	−0.416922	−	0.722130i	−0.995628	+	0.0934062i	$0.970224\pi$
$762$	4.29870e11			0.0461892
$763$	1.13324e13	+	1.33205e13i	1.21049	+	1.42286i
$764$	5.14813e12	+	8.91682e12i	0.546675	+	0.946869i
$765$	8.63436e12			0.911493
$766$	8.68298e12	+	1.50394e13i	0.911253	+	1.57834i
$767$	1.76906e12	−	1.29136e13i	0.184571	−	1.34731i
$768$	−2.31536e11	+	4.01032e11i	−0.0240155	+	0.0415961i
$769$	4.12629e12	+	7.14694e12i	0.425492	+	0.736973i	0.996466	−	0.0839947i	$-0.0267679\pi$
$769$	4.12629e12	+	7.14694e12i	0.425492	+	0.736973i	−0.570975	+	0.820968i	$0.693435\pi$
$770$	−7.94431e11	−	9.33809e11i	−0.0814419	−	0.0957304i
$771$	7.29766e11	−	1.26399e12i	0.0743770	−	0.128825i
$772$	6.51071e11	−	1.12769e12i	0.0659706	−	0.114264i
$773$	2.54053e12			0.255927			0.127963	−	0.991779i	$-0.459156\pi$
$773$	2.54053e12			0.255927			0.127963	+	0.991779i	$0.459156\pi$
$774$	−6.47241e12			−0.648234
$775$	−2.35181e12	+	4.07345e12i	−0.234177	+	0.405607i
$776$	1.46773e12	−	2.54218e12i	0.145301	−	0.251668i
$777$	4.50739e10	−	1.26507e11i	0.00443640	−	0.0124514i
$778$	1.01791e13	+	1.76307e13i	0.996097	+	1.72529i
$779$	−4.91579e12	+	8.51440e12i	−0.478272	+	0.828391i
$780$	7.48604e11	−	3.05492e11i	0.0724147	−	0.0295511i
$781$	6.92393e11	+	1.19926e12i	0.0665922	+	0.115341i
$782$	3.13049e13			2.99352
$783$	−2.04609e12	−	3.54394e12i	−0.194535	−	0.336944i
$784$	−7.27080e12	+	2.75879e12i	−0.687322	+	0.260793i
$785$	7.17716e12			0.674589
$786$	1.73337e11	+	3.00229e11i	0.0161991	+	0.0280577i
$787$	−2.11205e12			−0.196254			−0.0981268	−	0.995174i	$-0.531285\pi$
$787$	−2.11205e12			−0.196254			−0.0981268	+	0.995174i	$0.531285\pi$
$788$	3.82974e12	+	6.63331e12i	0.353836	+	0.612861i
$789$	1.01776e11	+	1.76281e11i	0.00934971	+	0.0161942i
$790$	4.06611e12	+	7.04270e12i	0.371413	+	0.643306i
$791$	−2.92716e12	+	8.21552e12i	−0.265859	+	0.746175i
$792$	5.13496e11			0.0463740
$793$	−3.83067e12	+	1.56323e12i	−0.343990	+	0.140376i
$794$	8.89759e12	+	1.54111e13i	0.794475	+	1.37607i
$795$	1.33039e11	−	2.30429e11i	0.0118121	−	0.0204591i
$796$	−8.08058e12			−0.713401
$797$	2.72832e12	−	4.72559e12i	0.239515	−	0.414852i	−0.721060	−	0.692872i	$-0.756345\pi$
$797$	2.72832e12	−	4.72559e12i	0.239515	−	0.414852i	0.960575	+	0.278020i	$0.0896783\pi$
$798$	−1.40821e12	+	2.58181e11i	−0.122929	+	0.0225377i
$799$	5.01869e12	−	8.69263e12i	0.435642	−	0.754555i
$800$	5.43019e12	+	9.40536e12i	0.468716	+	0.811840i
$801$	−4.36678e12	−	7.56349e12i	−0.374814	−	0.649196i
$802$	1.41309e13			1.20611
$803$	5.77325e11			0.0490005
$804$	−1.93686e11	−	3.35474e11i	−0.0163473	−	0.0283144i
$805$	2.95526e12	−	8.29441e12i	0.248036	−	0.696152i
$806$	1.17088e13	−	4.77813e12i	0.977245	−	0.398796i
$807$	−1.17942e12	+	2.04282e12i	−0.0978901	+	0.169551i
$808$	2.99951e12	−	5.19530e12i	0.247570	−	0.428804i
$809$	−5.01896e12	+	8.69309e12i	−0.411951	+	0.713519i	−0.995103	−	0.0988434i	$-0.968486\pi$
$809$	−5.01896e12	+	8.69309e12i	−0.411951	+	0.713519i	0.583152	+	0.812363i	$0.301819\pi$
$810$	5.11974e12	+	8.86766e12i	0.417894	+	0.723813i
$811$	1.57634e13			1.27955			0.639775	−	0.768562i	$-0.279028\pi$
$811$	1.57634e13			1.27955			0.639775	+	0.768562i	$0.279028\pi$
$812$	−1.73436e13	−	2.03864e13i	−1.40003	−	1.64566i
$813$	1.25294e11	−	2.17015e11i	0.0100583	−	0.0174214i
$814$	1.61975e11	−	2.80549e11i	0.0129312	−	0.0223975i
$815$	6.54490e12			0.519629
$816$	−8.13440e11	+	1.40892e12i	−0.0642273	+	0.111245i
$817$	4.27027e12			0.335317
$818$	1.83100e13			1.42987
$819$	1.07167e13	−	6.85065e12i	0.832309	−	0.532053i
$820$	−1.15410e13			−0.891421
$821$	3.46057e12			0.265830			0.132915	−	0.991127i	$-0.457566\pi$
$821$	3.46057e12			0.265830			0.132915	+	0.991127i	$0.457566\pi$
$822$	−5.56276e11	+	9.63499e11i	−0.0424979	+	0.0736085i
$823$	−1.97140e13			−1.49788			−0.748939	−	0.662639i	$-0.769436\pi$
$823$	−1.97140e13			−1.49788			−0.748939	+	0.662639i	$0.769436\pi$
$824$	−3.06832e12	+	5.31448e12i	−0.231861	+	0.401595i
$825$	7.02648e10	−	1.21702e11i	0.00528074	−	0.00914651i
$826$	−2.66485e13	+	4.88573e12i	−1.99188	+	0.365190i
$827$	−1.76140e13			−1.30944			−0.654718	−	0.755873i	$-0.727213\pi$
$827$	−1.76140e13			−1.30944			−0.654718	+	0.755873i	$0.727213\pi$
$828$	1.03203e13	+	1.78752e13i	0.763053	+	1.32165i
$829$	9.87033e12	−	1.70959e13i	0.725832	−	1.25718i	−0.232798	−	0.972525i	$-0.574788\pi$
$829$	9.87033e12	−	1.70959e13i	0.725832	−	1.25718i	0.958630	−	0.284653i	$-0.0918785\pi$
$830$	−7.15118e12	+	1.23862e13i	−0.523030	+	0.905914i
$831$	2.37209e11	−	4.10858e11i	0.0172554	−	0.0298873i
$832$	2.58401e12	−	1.88624e13i	0.186956	−	1.36472i
$833$	−2.05838e13	+	7.81019e12i	−1.48123	+	0.562029i
$834$	−3.45581e11	−	5.98564e11i	−0.0247345	−	0.0428414i
$835$	−1.00341e13			−0.714312
$836$	−1.89614e12			−0.134258
$837$	−1.10327e12	−	1.91092e12i	−0.0776995	−	0.134580i
$838$	−1.39936e13	−	2.42377e13i	−0.980240	−	1.69783i
$839$	−5.07750e12	+	8.79449e12i	−0.353770	+	0.612748i	−0.986907	−	0.161292i	$-0.948434\pi$
$839$	−5.07750e12	+	8.79449e12i	−0.353770	+	0.612748i	0.633137	+	0.774040i	$0.281767\pi$
$840$	−1.94573e11	−	2.28710e11i	−0.0134842	−	0.0158500i
$841$	−1.55888e13	+	2.70006e13i	−1.07456	+	1.86119i
$842$	1.54535e13			1.05955
$843$	3.07427e11	−	5.32478e11i	0.0209661	−	0.0363143i
$844$	−1.10744e13	−	1.91815e13i	−0.751243	−	1.30119i
$845$	6.16719e12	−	6.03914e12i	0.416133	−	0.407493i
$846$	1.20536e13			0.809003
$847$	−9.50205e12	−	1.11691e13i	−0.634369	−	0.745665i
$848$	−2.03555e12	−	3.52568e12i	−0.135177	−	0.234133i
$849$	−1.00036e12	−	1.73268e12i	−0.0660804	−	0.114455i
$850$	1.18626e13	+	2.05466e13i	0.779461	+	1.35007i
$851$	2.32658e12			0.152067
$852$	9.49125e11	+	1.64393e12i	0.0617085	+	0.106882i
$853$	7.07455e12			0.457539			0.228770	−	0.973481i	$-0.426530\pi$
$853$	7.07455e12			0.457539			0.228770	+	0.973481i	$0.426530\pi$
$854$	5.57249e12	+	6.55015e12i	0.358500	+	0.421396i
$855$	−3.42047e12	−	5.92442e12i	−0.218896	−	0.379139i
$856$	−9.91505e12			−0.631194
$857$	−1.53404e13	−	2.65704e13i	−0.971457	−	1.68261i	−0.691163	−	0.722699i	$-0.742901\pi$
$857$	−1.53404e13	−	2.65704e13i	−0.971457	−	1.68261i	−0.280295	−	0.959914i	$-0.590432\pi$
$858$	−3.49822e11	+	1.42756e11i	−0.0220371	+	0.00899293i
$859$	−8.62870e11	+	1.49454e12i	−0.0540725	+	0.0936563i	−0.891795	−	0.452440i	$-0.850554\pi$
$859$	−8.62870e11	+	1.49454e12i	−0.0540725	+	0.0936563i	0.837722	+	0.546097i	$0.183887\pi$
$860$	2.50638e12	+	4.34118e12i	0.156244	+	0.270623i
$861$	2.19911e12	−	4.03185e11i	0.136375	−	0.0250029i
$862$	7.18565e12	−	1.24459e13i	0.443285	−	0.767793i
$863$	−9.51239e12	+	1.64759e13i	−0.583769	+	1.01112i	0.411259	+	0.911519i	$0.365089\pi$
$863$	−9.51239e12	+	1.64759e13i	−0.583769	+	1.01112i	−0.995028	+	0.0995989i	$0.968244\pi$
$864$	−5.09478e12			−0.311038
$865$	2.69249e12			0.163524
$866$	−1.39323e13	+	2.41314e13i	−0.841768	+	1.45798i
$867$	−1.38536e12	+	2.39952e12i	−0.0832678	+	0.144224i
$868$	−9.35184e12	−	1.09926e13i	−0.559189	−	0.657295i
$869$	−1.04324e12	−	1.80695e12i	−0.0620577	−	0.107487i
$870$	−1.43426e12	+	2.48421e12i	−0.0848773	+	0.147012i
$871$	−3.26762e12	−	2.53467e12i	−0.192375	−	0.149225i
$872$	5.16619e12	+	8.94811e12i	0.302584	+	0.524091i
$873$	−1.52079e13			−0.886148
$874$	−1.24013e13	−	2.14797e13i	−0.718898	−	1.24517i
$875$	1.64971e13	−	3.02459e12i	0.951421	−	0.174433i
$876$	7.91390e11			0.0454069
$877$	−1.44326e13	−	2.49979e13i	−0.823845	−	1.42694i	−0.902799	−	0.430063i	$-0.858491\pi$
$877$	−1.44326e13	−	2.49979e13i	−0.823845	−	1.42694i	0.0789544	−	0.996878i	$-0.474842\pi$
$878$	−7.57483e12			−0.430177
$879$	1.77838e12	+	3.08024e12i	0.100479	+	0.174034i
$880$	5.51902e11	+	9.55923e11i	0.0310235	+	0.0537342i
$881$	−3.80119e12	−	6.58385e12i	−0.212583	−	0.368204i	0.739939	−	0.672673i	$-0.234854\pi$
$881$	−3.80119e12	−	6.58385e12i	−0.212583	−	0.368204i	−0.952522	+	0.304470i	$0.901521\pi$
$882$	−2.04817e13	−	1.67173e13i	−1.13961	−	0.930160i
$883$	−1.40735e13			−0.779072			−0.389536	−	0.921011i	$-0.627365\pi$
$883$	−1.40735e13			−0.779072			−0.389536	+	0.921011i	$0.627365\pi$
$884$	4.75343e12	−	3.46986e13i	0.261802	−	1.91107i
$885$	7.97098e11	+	1.38061e12i	0.0436784	+	0.0756533i
$886$	−1.06738e13	+	1.84875e13i	−0.581924	+	1.00792i
$887$	−1.70083e13			−0.922582			−0.461291	−	0.887249i	$-0.652614\pi$
$887$	−1.70083e13			−0.922582			−0.461291	+	0.887249i	$0.652614\pi$
$888$	3.96712e10	−	6.87126e10i	0.00214100	−	0.00370833i
$889$	−3.39367e12	−	3.98907e12i	−0.182226	−	0.214197i
$890$	−6.15971e12	+	1.06689e13i	−0.329083	+	0.569989i
$891$	−1.31357e12	−	2.27518e12i	−0.0698240	−	0.120939i
$892$	−7.71596e12	−	1.33644e13i	−0.408083	−	0.706820i
$893$	−7.95254e12			−0.418480
$894$	5.98290e12			0.313251
$895$	−6.00254e12	−	1.03967e13i	−0.312703	−	0.541617i
$896$	−1.20036e13	+	2.20075e12i	−0.622196	+	0.114073i
$897$	−2.14410e12	−	1.66316e12i	−0.110580	−	0.0857766i
$898$	1.08825e13	−	1.88491e13i	0.558452	−	0.967268i
$899$	−1.23168e13	+	2.13334e13i	−0.628898	+	1.08928i
$900$	−7.82146e12	+	1.35472e13i	−0.397371	+	0.688268i
$901$	−5.76270e12	−	9.98128e12i	−0.291316	−	0.504574i
$902$	5.39311e12			0.271275
$903$	−6.29242e11	−	7.39639e11i	−0.0314937	−	0.0370190i
$904$	−2.57630e12	+	4.46228e12i	−0.128303	+	0.222228i
$905$	−9.49135e12	+	1.64395e13i	−0.470337	+	0.814648i
$906$	−5.24661e12			−0.258703
$907$	6.66586e12	−	1.15456e13i	0.327057	−	0.566479i	−0.654870	−	0.755742i	$-0.727276\pi$
$907$	6.66586e12	−	1.15456e13i	0.327057	−	0.566479i	0.981926	+	0.189263i	$0.0606098\pi$
$908$	2.40824e13			1.17575
$909$	−3.10795e13			−1.50986
$910$	−1.59272e13	−	8.25986e12i	−0.769933	−	0.399288i
$911$	2.37830e13			1.14402			0.572011	−	0.820246i	$-0.306163\pi$
$911$	2.37830e13			1.14402			0.572011	+	0.820246i	$0.306163\pi$
$912$	1.28897e12			0.0616971
$913$	1.83478e12	−	3.17793e12i	0.0873907	−	0.151365i
$914$	−1.40039e13			−0.663731
$915$	2.53017e11	−	4.38238e11i	0.0119331	−	0.0206688i
$916$	7.08153e12	−	1.22656e13i	0.332351	−	0.575649i
$917$	1.41760e12	−	3.97872e12i	0.0662052	−	0.185815i
$918$	−1.11299e13			−0.517248
$919$	−4.61086e12	−	7.98625e12i	−0.213237	−	0.369337i	0.739489	−	0.673169i	$-0.235067\pi$
$919$	−4.61086e12	−	7.98625e12i	−0.213237	−	0.369337i	−0.952726	+	0.303832i	$0.901734\pi$
$920$	2.60104e12	−	4.50513e12i	0.119702	−	0.207330i
$921$	−6.93753e11	+	1.20162e12i	−0.0317714	+	0.0550297i
$922$	2.05165e13	−	3.55356e13i	0.935004	−	1.61948i
$923$	1.60124e13	+	1.24207e13i	0.726187	+	0.563299i
$924$	2.79404e11	+	3.28424e11i	0.0126098	+	0.0148221i
$925$	8.81629e11	+	1.52703e12i	0.0395957	+	0.0685818i
$926$	−5.22276e13			−2.33427
$927$	3.17925e13			1.41406
$928$	2.84388e13	+	4.92575e13i	1.25877	+	2.18025i
$929$	2.37899e12	+	4.12054e12i	0.104791	+	0.181503i	0.913653	−	0.406496i	$-0.133249\pi$
$929$	2.37899e12	+	4.12054e12i	0.104791	+	0.181503i	−0.808862	+	0.587999i	$0.799916\pi$
$930$	−7.73368e11	+	1.33951e12i	−0.0339010	+	0.0587183i
$931$	1.35131e13	+	1.10295e13i	0.589497	+	0.481152i
$932$	−1.67073e13	+	2.89379e13i	−0.725330	+	1.25631i
$933$	−1.44625e12			−0.0624850
$934$	2.06041e13	−	3.56873e13i	0.885915	−	1.53445i
$935$	1.56245e12	+	2.70624e12i	0.0668579	+	0.115801i
$936$	6.95751e12	−	2.83923e12i	0.296287	−	0.120909i
$937$	−3.64273e13			−1.54383			−0.771913	−	0.635728i	$-0.780700\pi$
$937$	−3.64273e13			−1.54383			−0.771913	+	0.635728i	$0.780700\pi$
$938$	−2.88502e12	+	8.09724e12i	−0.121685	+	0.341527i
$939$	1.20118e12	+	2.08050e12i	0.0504211	+	0.0873319i
$940$	−4.66764e12	−	8.08459e12i	−0.194994	−	0.337740i
$941$	−7.26921e11	−	1.25906e12i	−0.0302228	−	0.0523473i	0.850518	−	0.525945i	$-0.176288\pi$
$941$	−7.26921e11	−	1.25906e12i	−0.0302228	−	0.0523473i	−0.880741	+	0.473598i	$0.842955\pi$
$942$	−4.59746e12			−0.190234
$943$	1.93664e13	+	3.35436e13i	0.797530	+	1.38136i
$944$	2.43920e13			0.999708
$945$	−1.05069e12	+	2.94892e12i	−0.0428579	+	0.120287i
$946$	−1.17123e12	−	2.02862e12i	−0.0475479	−	0.0823553i
$947$	3.42949e12			0.138565			0.0692827	−	0.997597i	$-0.477929\pi$
$947$	3.42949e12			0.138565			0.0692827	+	0.997597i	$0.477929\pi$
$948$	−1.43006e12	−	2.47694e12i	−0.0575066	−	0.0996044i
$949$	7.82233e12	−	3.19215e12i	0.313068	−	0.127757i
$950$	9.39865e12	−	1.62789e13i	0.374377	−	0.648440i
$951$	−1.93482e12	−	3.35121e12i	−0.0767060	−	0.132859i
$952$	−1.27936e13	+	2.34558e12i	−0.504809	+	0.0925516i
$953$	7.88384e12	−	1.36552e13i	0.309613	−	0.536266i	−0.668664	−	0.743564i	$-0.733134\pi$
$953$	7.88384e12	−	1.36552e13i	0.309613	−	0.536266i	0.978278	+	0.207298i	$0.0664671\pi$
$954$	6.92025e12	−	1.19862e13i	0.270492	−	0.468506i
$955$	−1.34440e13			−0.523016
$956$	1.18472e12			0.0458729
$957$	3.67989e11	−	6.37375e11i	0.0141818	−	0.0245636i
$958$	−3.25896e13	+	5.64468e13i	−1.25007	+	2.16518i
$959$	1.33326e13	−	2.44439e12i	0.509015	−	0.0933227i
$960$	1.16429e12	+	2.01661e12i	0.0442426	+	0.0766305i
$961$	6.57846e12	−	1.13942e13i	0.248811	−	0.430953i
$962$	6.43430e11	−	4.69684e12i	0.0242222	−	0.176814i
$963$	2.56838e13	+	4.44857e13i	0.962368	+	1.66687i
$964$	1.94733e13			0.726262
$965$	8.50117e11	+	1.47245e12i	0.0315577	+	0.0546596i
$966$	−1.89305e12	+	5.31313e12i	−0.0699462	+	0.196315i
$967$	3.78907e13			1.39352			0.696760	−	0.717304i	$-0.254624\pi$
$967$	3.78907e13			1.39352			0.696760	+	0.717304i	$0.254624\pi$
$968$	−4.33179e12	−	7.50288e12i	−0.158573	−	0.274656i
$969$	3.64909e12			0.132962
$970$	1.07260e13	+	1.85780e13i	0.389015	+	0.673794i
$971$	6.92033e12	+	1.19864e13i	0.249827	+	0.432714i	0.963478	−	0.267788i	$-0.0862928\pi$
$971$	6.92033e12	+	1.19864e13i	0.249827	+	0.432714i	−0.713650	+	0.700502i	$0.752959\pi$
$972$	−5.51500e12	−	9.55225e12i	−0.198174	−	0.343248i
$973$	−2.82626e12	+	7.93233e12i	−0.101089	+	0.283722i
$974$	−4.67311e13			−1.66376
$975$	2.79120e11	−	2.03749e12i	0.00989167	−	0.0722061i
$976$	−3.87129e12	−	6.70526e12i	−0.136562	−	0.236533i
$977$	2.02280e13	−	3.50359e13i	0.710275	−	1.23023i	−0.254478	−	0.967078i	$-0.581904\pi$
$977$	2.02280e13	−	3.50359e13i	0.710275	−	1.23023i	0.964754	−	0.263155i	$-0.0847629\pi$
$978$	−4.19245e12			−0.146535
$979$	1.58040e12	−	2.73733e12i	0.0549850	−	0.0952369i
$980$	−3.28129e12	+	2.02111e13i	−0.113639	+	0.699960i
$981$	2.67649e13	−	4.63582e13i	0.922688	−	1.59814i
$982$	−2.58418e13	−	4.47594e13i	−0.886792	−	1.53597i
$983$	1.91190e13	+	3.31151e13i	0.653093	+	1.13119i	0.982368	+	0.186956i	$0.0598622\pi$
$983$	1.91190e13	+	3.31151e13i	0.653093	+	1.13119i	−0.329275	+	0.944234i	$0.606804\pi$
$984$	1.32089e12			0.0449147
$985$	−1.00012e13			−0.338522
$986$	6.21265e13	+	1.07606e14i	2.09330	+	3.62569i
$987$	1.17184e12	+	1.37743e12i	0.0393044	+	0.0462002i
$988$	−2.56913e13	+	1.04842e13i	−0.857788	+	0.350048i
$989$	8.41165e12	−	1.45694e13i	0.279575	−	0.484238i
$990$	−1.87630e12	+	3.24984e12i	−0.0620788	+	0.107524i
$991$	−2.64750e13	+	4.58561e13i	−0.871978	+	1.51031i	−0.0120297	+	0.999928i	$0.503829\pi$
$991$	−2.64750e13	+	4.58561e13i	−0.871978	+	1.51031i	−0.859948	+	0.510382i	$0.829504\pi$
$992$	1.53345e13	+	2.65601e13i	0.502767	+	0.870818i
$993$	−1.10176e11			−0.00359596
$994$	1.41375e13	−	3.96791e13i	0.459340	−	1.28921i
$995$	5.27550e12	−	9.13743e12i	0.170632	−	0.295543i
$996$	2.51510e12	−	4.35627e12i	0.0809818	−	0.140265i
$997$	−4.66250e13			−1.49448			−0.747241	−	0.664553i	$-0.768622\pi$
$997$	−4.66250e13			−1.49448			−0.747241	+	0.664553i	$0.768622\pi$
$998$	2.16536e13	−	3.75052e13i	0.690945	−	1.19675i
$999$	−8.27174e11			−0.0262756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.13	yes	164
7.4	even	3		91.10.g.a.81.70	yes	164
13.9	even	3		91.10.g.a.9.70	✓	164
91.74	even	3	inner	91.10.h.a.74.13	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.70	✓	164	13.9	even	3
91.10.g.a.81.70	yes	164	7.4	even	3
91.10.h.a.16.13	yes	164	1.1	even	1	trivial
91.10.h.a.74.13	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)

\(f(q)\)	\(=\)	\(q-33.6954 q^{2} +(-7.73692 + 13.4007i) q^{3} +623.381 q^{4} +(-406.981 + 704.911i) q^{5} +(260.699 - 451.543i) q^{6} +(-6248.30 + 1145.56i) q^{7} -3753.02 q^{8} +(9721.78 + 16838.6i) q^{9} +O(q^{10})\)	\(q-33.6954 q^{2} +(-7.73692 + 13.4007i) q^{3} +623.381 q^{4} +(-406.981 + 704.911i) q^{5} +(260.699 - 451.543i) q^{6} +(-6248.30 + 1145.56i) q^{7} -3753.02 q^{8} +(9721.78 + 16838.6i) q^{9} +(13713.4 - 23752.3i) q^{10} +(-3518.45 + 6094.13i) q^{11} +(-4823.05 + 8353.76i) q^{12} +(-13976.7 + 102025. i) q^{13} +(210539. - 38600.2i) q^{14} +(-6297.56 - 10907.7i) q^{15} -192711. q^{16} -545570. q^{17} +(-327579. - 567384. i) q^{18} +(216125. + 374340. i) q^{19} +(-253704. + 439428. i) q^{20} +(32991.2 - 92595.0i) q^{21} +(118555. - 205344. i) q^{22} +1.70291e6 q^{23} +(29036.8 - 50293.2i) q^{24} +(645296. + 1.11768e6i) q^{25} +(470950. - 3.43778e6i) q^{26} -605438. q^{27} +(-3.89507e6 + 714122. i) q^{28} +(3.37952e6 + 5.85351e6i) q^{29} +(212199. + 367539. i) q^{30} +(1.82227e6 + 3.15627e6i) q^{31} +8.41504e6 q^{32} +(-54443.9 - 94299.5i) q^{33} +1.83832e7 q^{34} +(1.73542e6 - 4.87072e6i) q^{35} +(6.06037e6 + 1.04969e7i) q^{36} +1.36624e6 q^{37} +(-7.28243e6 - 1.26135e7i) q^{38} +(-1.25908e6 - 976659. i) q^{39} +(1.52741e6 - 2.64555e6i) q^{40} +(1.13725e7 + 1.96978e7i) q^{41} +(-1.11165e6 + 3.12003e6i) q^{42} +(4.93957e6 - 8.55559e6i) q^{43} +(-2.19333e6 + 3.79896e6i) q^{44} -1.58263e7 q^{45} -5.73803e7 q^{46} +(-9.19899e6 + 1.59331e7i) q^{47} +(1.49099e6 - 2.58247e6i) q^{48} +(3.77290e7 - 1.43156e7i) q^{49} +(-2.17435e7 - 3.76609e7i) q^{50} +(4.22103e6 - 7.31104e6i) q^{51} +(-8.71279e6 + 6.36006e7i) q^{52} +(1.05627e7 + 1.82952e7i) q^{53} +2.04005e7 q^{54} +(-2.86388e6 - 4.96039e6i) q^{55} +(2.34500e7 - 4.29932e6i) q^{56} -6.68858e6 q^{57} +(-1.13874e8 - 1.97236e8i) q^{58} -1.26573e8 q^{59} +(-3.92577e6 - 6.79964e6i) q^{60} +(2.00885e7 + 3.47943e7i) q^{61} +(-6.14022e7 - 1.06352e8i) q^{62} +(-8.00343e7 - 9.40759e7i) q^{63} -1.84880e8 q^{64} +(-6.62305e7 - 5.13746e7i) q^{65} +(1.83451e6 + 3.17746e6i) q^{66} +(-2.00792e7 + 3.47782e7i) q^{67} -3.40098e8 q^{68} +(-1.31753e7 + 2.28203e7i) q^{69} +(-5.84757e7 + 1.64121e8i) q^{70} +(9.83948e7 - 1.70425e8i) q^{71} +(-3.64860e7 - 6.31957e7i) q^{72} +(-4.10213e7 - 7.10509e7i) q^{73} -4.60360e7 q^{74} -1.99704e7 q^{75} +(1.34728e8 + 2.33356e8i) q^{76} +(1.50031e7 - 4.21086e7i) q^{77} +(4.24251e7 + 3.29089e7i) q^{78} +(-1.48253e8 + 2.56782e8i) q^{79} +(7.84298e7 - 1.35844e8i) q^{80} +(-1.86670e8 + 3.23321e8i) q^{81} +(-3.83203e8 - 6.63726e8i) q^{82} -5.21475e8 q^{83} +(2.05661e7 - 5.77219e7i) q^{84} +(2.22036e8 - 3.84578e8i) q^{85} +(-1.66441e8 + 2.88284e8i) q^{86} -1.04588e8 q^{87} +(1.32048e7 - 2.28714e7i) q^{88} -4.49175e8 q^{89} +5.33274e8 q^{90} +(-2.95459e7 - 6.53496e8i) q^{91} +1.06156e9 q^{92} -5.63951e7 q^{93} +(3.09964e8 - 5.36873e8i) q^{94} -3.51836e8 q^{95} +(-6.51064e7 + 1.12768e8i) q^{96} +(-3.91079e8 + 6.77369e8i) q^{97} +(-1.27129e9 + 4.82372e8i) q^{98} -1.36822e8 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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