LMFDB - Embedded newform 91.10.h.a.16.18

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			16.18
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.4349 q^{2} +(122.315 - 211.855i) q^{3} +354.414 q^{4} +(-310.503 + 537.807i) q^{5} +(-3600.32 + 6235.94i) q^{6} +(-5780.64 + 2633.98i) q^{7} +4638.52 q^{8} +(-20080.3 - 34780.0i) q^{9} +O(q^{10})$	\(q-29.4349 q^{2} +(122.315 - 211.855i) q^{3} +354.414 q^{4} +(-310.503 + 537.807i) q^{5} +(-3600.32 + 6235.94i) q^{6} +(-5780.64 + 2633.98i) q^{7} +4638.52 q^{8} +(-20080.3 - 34780.0i) q^{9} +(9139.63 - 15830.3i) q^{10} +(12141.0 - 21028.8i) q^{11} +(43350.1 - 75084.5i) q^{12} +(2686.70 - 102943. i) q^{13} +(170153. - 77530.9i) q^{14} +(75958.1 + 131563. i) q^{15} -317995. q^{16} -190069. q^{17} +(591061. + 1.02375e6i) q^{18} +(16631.6 + 28806.8i) q^{19} +(-110047. + 190606. i) q^{20} +(-149035. + 1.54683e6i) q^{21} +(-357369. + 618981. i) q^{22} -2.09430e6 q^{23} +(567359. - 982695. i) q^{24} +(783738. + 1.35747e6i) q^{25} +(-79082.7 + 3.03012e6i) q^{26} -5.00940e6 q^{27} +(-2.04874e6 + 933520. i) q^{28} +(3.12331e6 + 5.40973e6i) q^{29} +(-2.23582e6 - 3.87256e6i) q^{30} +(-4.31144e6 - 7.46764e6i) q^{31} +6.98522e6 q^{32} +(-2.97004e6 - 5.14426e6i) q^{33} +5.59467e6 q^{34} +(378333. - 3.92672e6i) q^{35} +(-7.11673e6 - 1.23265e7i) q^{36} +4.76995e6 q^{37} +(-489550. - 847926. i) q^{38} +(-2.14804e7 - 1.31606e7i) q^{39} +(-1.44027e6 + 2.49463e6i) q^{40} +(-7.91967e6 - 1.37173e7i) q^{41} +(4.38682e6 - 4.55309e7i) q^{42} +(-1.58038e7 + 2.73729e7i) q^{43} +(4.30294e6 - 7.45291e6i) q^{44} +2.49399e7 q^{45} +6.16456e7 q^{46} +(-2.45985e7 + 4.26059e7i) q^{47} +(-3.88954e7 + 6.73688e7i) q^{48} +(2.64779e7 - 3.04521e7i) q^{49} +(-2.30693e7 - 3.99572e7i) q^{50} +(-2.32483e7 + 4.02672e7i) q^{51} +(952203. - 3.64845e7i) q^{52} +(3.04955e7 + 5.28198e7i) q^{53} +1.47451e8 q^{54} +(7.53962e6 + 1.30590e7i) q^{55} +(-2.68136e7 + 1.22178e7i) q^{56} +8.13717e6 q^{57} +(-9.19344e7 - 1.59235e8i) q^{58} +1.01130e8 q^{59} +(2.69206e7 + 4.66279e7i) q^{60} +(-1.91445e7 - 3.31593e7i) q^{61} +(1.26907e8 + 2.19809e8i) q^{62} +(2.07687e8 + 1.48160e8i) q^{63} -4.27962e7 q^{64} +(5.45293e7 + 3.34091e7i) q^{65} +(8.74229e7 + 1.51421e8i) q^{66} +(7.75715e7 - 1.34358e8i) q^{67} -6.73633e7 q^{68} +(-2.56164e8 + 4.43689e8i) q^{69} +(-1.11362e7 + 1.15583e8i) q^{70} +(6.20910e7 - 1.07545e8i) q^{71} +(-9.31427e7 - 1.61328e8i) q^{72} +(9.67838e7 + 1.67634e8i) q^{73} -1.40403e8 q^{74} +3.83451e8 q^{75} +(5.89448e6 + 1.02095e7i) q^{76} +(-1.47932e7 + 1.53539e8i) q^{77} +(6.32274e8 + 3.87382e8i) q^{78} +(-2.18465e8 + 3.78392e8i) q^{79} +(9.87383e7 - 1.71020e8i) q^{80} +(-2.17484e8 + 3.76693e8i) q^{81} +(2.33115e8 + 4.03767e8i) q^{82} -1.48326e8 q^{83} +(-5.28200e7 + 5.48219e8i) q^{84} +(5.90171e7 - 1.02221e8i) q^{85} +(4.65182e8 - 8.05719e8i) q^{86} +1.52811e9 q^{87} +(5.63162e7 - 9.75426e7i) q^{88} +2.50507e8 q^{89} -7.34104e8 q^{90} +(2.55619e8 + 6.02153e8i) q^{91} -7.42251e8 q^{92} -2.10941e9 q^{93} +(7.24055e8 - 1.25410e9i) q^{94} -2.06567e7 q^{95} +(8.54395e8 - 1.47986e9i) q^{96} +(-3.02604e7 + 5.24125e7i) q^{97} +(-7.79375e8 + 8.96356e8i) q^{98} -9.75177e8 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 $

$2$	−29.4349			−1.30085			−0.650426	−	0.759570i	$-0.725410\pi$
$2$	−29.4349			−1.30085			−0.650426	+	0.759570i	$0.725410\pi$
$3$	122.315	−	211.855i	0.871832	−	1.51006i	0.0117328	−	0.999931i	$-0.496265\pi$
$3$	122.315	−	211.855i	0.871832	−	1.51006i	0.860099	−	0.510127i	$-0.170401\pi$
$4$	354.414			0.692215
$5$	−310.503	+	537.807i	−0.222178	+	0.384823i	−0.955469	−	0.295091i	$-0.904650\pi$
$5$	−310.503	+	537.807i	−0.222178	+	0.384823i	0.733291	+	0.679915i	$0.237983\pi$
$6$	−3600.32	+	6235.94i	−1.13412	+	1.96436i
$7$	−5780.64	+	2633.98i	−0.909986	+	0.414640i
$7$	−5780.64	+	2633.98i	−0.909986	+	0.414640i
$8$	4638.52			0.400382
$9$	−20080.3	−	34780.0i	−1.02018	−	1.76701i
$10$	9139.63	−	15830.3i	0.289020	−	0.500598i
$11$	12141.0	−	21028.8i	0.250027	−	0.433060i	−0.713506	−	0.700649i	$-0.752894\pi$
$11$	12141.0	−	21028.8i	0.250027	−	0.433060i	0.963533	+	0.267590i	$0.0862272\pi$
$12$	43350.1	−	75084.5i	0.603496	−	1.04529i
$13$	2686.70	−	102943.i	0.0260900	−	0.999660i
$13$	2686.70	−	102943.i	0.0260900	−	0.999660i
$14$	170153.	−	77530.9i	1.18376	−	0.539385i
$15$	75958.1	+	131563.i	0.387404	+	0.671003i
$16$	−317995.			−1.21305
$17$	−190069.			−0.551940			−0.275970	−	0.961166i	$-0.588999\pi$
$17$	−190069.			−0.551940			−0.275970	+	0.961166i	$0.588999\pi$
$18$	591061.	+	1.02375e6i	1.32711	+	2.29862i
$19$	16631.6	+	28806.8i	0.0292781	+	0.0507112i	0.880293	−	0.474430i	$-0.157346\pi$
$19$	16631.6	+	28806.8i	0.0292781	+	0.0507112i	−0.851015	+	0.525141i	$0.824012\pi$
$20$	−110047.	+	190606.i	−0.153795	+	0.266381i
$21$	−149035.	+	1.54683e6i	−0.167225	+	1.73563i
$22$	−357369.	+	618981.i	−0.325248	+	0.563346i
$23$	−2.09430e6			−1.56050			−0.780251	−	0.625467i	$-0.784909\pi$
$23$	−2.09430e6			−1.56050			−0.780251	+	0.625467i	$0.784909\pi$
$24$	567359.	−	982695.i	0.349066	−	0.604600i
$25$	783738.	+	1.35747e6i	0.401274	+	0.695027i
$26$	−79082.7	+	3.03012e6i	−0.0339392	+	1.30041i
$27$	−5.00940e6			−1.81405
$28$	−2.04874e6	+	933520.i	−0.629906	+	0.287020i
$29$	3.12331e6	+	5.40973e6i	0.820019	+	1.42032i	0.905667	+	0.423990i	$0.139371\pi$
$29$	3.12331e6	+	5.40973e6i	0.820019	+	1.42032i	−0.0856477	+	0.996325i	$0.527296\pi$
$30$	−2.23582e6	−	3.87256e6i	−0.503955	−	0.872875i
$31$	−4.31144e6	−	7.46764e6i	−0.838485	−	1.45230i	−0.891161	−	0.453686i	$-0.850109\pi$
$31$	−4.31144e6	−	7.46764e6i	−0.838485	−	1.45230i	0.0526767	−	0.998612i	$-0.483225\pi$
$32$	6.98522e6			1.17762
$33$	−2.97004e6	−	5.14426e6i	−0.435963	−	0.755111i
$34$	5.59467e6			0.717992
$35$	378333.	−	3.92672e6i	0.0426156	−	0.442307i
$36$	−7.11673e6	−	1.23265e7i	−0.706186	−	1.22315i
$37$	4.76995e6			0.418414			0.209207	−	0.977871i	$-0.432912\pi$
$37$	4.76995e6			0.418414			0.209207	+	0.977871i	$0.432912\pi$
$38$	−489550.	−	847926.i	−0.0380865	−	0.0659678i
$39$	−2.14804e7	−	1.31606e7i	−1.48680	−	0.910933i
$40$	−1.44027e6	+	2.49463e6i	−0.0889560	+	0.154076i
$41$	−7.91967e6	−	1.37173e7i	−0.437703	−	0.758124i	0.559809	−	0.828622i	$-0.310875\pi$
$41$	−7.91967e6	−	1.37173e7i	−0.437703	−	0.758124i	−0.997512	+	0.0704975i	$0.977541\pi$
$42$	4.38682e6	−	4.55309e7i	0.217535	−	2.25779i
$43$	−1.58038e7	+	2.73729e7i	−0.704940	+	1.22099i	0.261773	+	0.965129i	$0.415693\pi$
$43$	−1.58038e7	+	2.73729e7i	−0.704940	+	1.22099i	−0.966713	+	0.255862i	$0.917641\pi$
$44$	4.30294e6	−	7.45291e6i	0.173073	−	0.299770i
$45$	2.49399e7			0.906648
$46$	6.16456e7			2.02998
$47$	−2.45985e7	+	4.26059e7i	−0.735306	+	1.27359i	0.219282	+	0.975661i	$0.429628\pi$
$47$	−2.45985e7	+	4.26059e7i	−0.735306	+	1.27359i	−0.954589	+	0.297927i	$0.903705\pi$
$48$	−3.88954e7	+	6.73688e7i	−1.05758	+	1.83178i
$49$	2.64779e7	−	3.04521e7i	0.656148	−	0.754633i
$50$	−2.30693e7	−	3.99572e7i	−0.521998	−	0.904127i
$51$	−2.32483e7	+	4.02672e7i	−0.481199	+	0.833461i
$52$	952203.	−	3.64845e7i	0.0180599	−	0.691980i
$53$	3.04955e7	+	5.28198e7i	0.530878	+	0.919508i	0.999351	+	0.0360301i	$0.0114712\pi$
$53$	3.04955e7	+	5.28198e7i	0.530878	+	0.919508i	−0.468472	+	0.883478i	$0.655195\pi$
$54$	1.47451e8			2.35981
$55$	7.53962e6	+	1.30590e7i	0.111101	+	0.192432i
$56$	−2.68136e7	+	1.22178e7i	−0.364342	+	0.166014i
$57$	8.13717e6			0.102102
$58$	−9.19344e7	−	1.59235e8i	−1.06672	−	1.84762i
$59$	1.01130e8			1.08654			0.543270	−	0.839558i	$-0.317186\pi$
$59$	1.01130e8			1.08654			0.543270	+	0.839558i	$0.317186\pi$
$60$	2.69206e7	+	4.66279e7i	0.268167	+	0.464478i
$61$	−1.91445e7	−	3.31593e7i	−0.177035	−	0.306634i	0.763828	−	0.645419i	$-0.223317\pi$
$61$	−1.91445e7	−	3.31593e7i	−0.177035	−	0.306634i	−0.940864	+	0.338785i	$0.889984\pi$
$62$	1.26907e8	+	2.19809e8i	1.09074	+	1.88922i
$63$	2.07687e8	+	1.48160e8i	1.66102	+	1.18494i
$64$	−4.27962e7			−0.318856
$65$	5.45293e7	+	3.34091e7i	0.378896	+	0.232142i
$66$	8.74229e7	+	1.51421e8i	0.567124	+	0.982287i
$67$	7.75715e7	−	1.34358e8i	0.470290	−	0.814566i	−0.529133	−	0.848539i	$-0.677483\pi$
$67$	7.75715e7	−	1.34358e8i	0.470290	−	0.814566i	0.999423	+	0.0339731i	$0.0108160\pi$
$68$	−6.73633e7			−0.382061
$69$	−2.56164e8	+	4.43689e8i	−1.36050	+	2.35645i
$70$	−1.11362e7	+	1.15583e8i	−0.0554365	+	0.575376i
$71$	6.20910e7	−	1.07545e8i	0.289979	−	0.502258i	−0.683826	−	0.729645i	$-0.739685\pi$
$71$	6.20910e7	−	1.07545e8i	0.289979	−	0.502258i	0.973804	+	0.227388i	$0.0730184\pi$
$72$	−9.31427e7	−	1.61328e8i	−0.408463	−	0.707479i
$73$	9.67838e7	+	1.67634e8i	0.398887	+	0.690892i	0.993589	−	0.113054i	$-0.0360632\pi$
$73$	9.67838e7	+	1.67634e8i	0.398887	+	0.690892i	−0.594702	+	0.803946i	$0.702730\pi$
$74$	−1.40403e8			−0.544294
$75$	3.83451e8			1.39937
$76$	5.89448e6	+	1.02095e7i	0.0202668	+	0.0351031i
$77$	−1.47932e7	+	1.53539e8i	−0.0479573	+	0.497749i
$78$	6.32274e8	+	3.87382e8i	1.93410	+	1.18499i
$79$	−2.18465e8	+	3.78392e8i	−0.631044	+	1.09300i	0.356294	+	0.934374i	$0.384040\pi$
$79$	−2.18465e8	+	3.78392e8i	−0.631044	+	1.09300i	−0.987339	+	0.158627i	$0.949293\pi$
$80$	9.87383e7	−	1.71020e8i	0.269513	−	0.466811i
$81$	−2.17484e8	+	3.76693e8i	−0.561363	+	0.972309i
$82$	2.33115e8	+	4.03767e8i	0.569387	+	0.986207i
$83$	−1.48326e8			−0.343056			−0.171528	−	0.985179i	$-0.554870\pi$
$83$	−1.48326e8			−0.343056			−0.171528	+	0.985179i	$0.554870\pi$
$84$	−5.28200e7	+	5.48219e8i	−0.115756	+	1.20143i
$85$	5.90171e7	−	1.02221e8i	0.122629	−	0.212399i
$86$	4.65182e8	−	8.05719e8i	0.917022	−	1.58833i
$87$	1.52811e9			2.85968
$88$	5.63162e7	−	9.75426e7i	0.100106	−	0.173389i
$89$	2.50507e8			0.423219			0.211609	−	0.977354i	$-0.432130\pi$
$89$	2.50507e8			0.423219			0.211609	+	0.977354i	$0.432130\pi$
$90$	−7.34104e8			−1.17941
$91$	2.55619e8	+	6.02153e8i	0.390757	+	0.920494i
$92$	−7.42251e8			−1.08020
$93$	−2.10941e9			−2.92407
$94$	7.24055e8	−	1.25410e9i	0.956525	−	1.65675i
$95$	−2.06567e7			−0.0260198
$96$	8.54395e8	−	1.47986e9i	1.02669	−	1.77827i
$97$	−3.02604e7	+	5.24125e7i	−0.0347057	+	0.0601121i	−0.882857	−	0.469643i	$-0.844383\pi$
$97$	−3.02604e7	+	5.24125e7i	−0.0347057	+	0.0601121i	0.848151	+	0.529755i	$0.177716\pi$
$98$	−7.79375e8	+	8.96356e8i	−0.853551	+	0.981665i
$99$	−9.75177e8			−1.02029
$100$	2.77768e8	+	4.81108e8i	0.277768	+	0.481108i
$101$	2.58760e8	−	4.48185e8i	0.247429	−	0.428560i	−0.715383	−	0.698733i	$-0.753748\pi$
$101$	2.58760e8	−	4.48185e8i	0.247429	−	0.428560i	0.962812	+	0.270173i	$0.0870809\pi$
$102$	6.84311e8	−	1.18526e9i	0.625968	−	1.08421i
$103$	1.01806e7	−	1.76332e7i	0.00891259	−	0.0154371i	−0.861535	−	0.507699i	$-0.830496\pi$
$103$	1.01806e7	−	1.76332e7i	0.00891259	−	0.0154371i	0.870447	+	0.492262i	$0.163830\pi$
$104$	1.24623e7	−	4.77504e8i	0.0104460	−	0.400246i
$105$	−7.85621e8	−	5.60448e8i	−0.630756	−	0.449970i
$106$	−8.97634e8	−	1.55475e9i	−0.690594	−	1.19614i
$107$	2.03300e9			1.49938			0.749688	−	0.661792i	$-0.230204\pi$
$107$	2.03300e9			1.49938			0.749688	+	0.661792i	$0.230204\pi$
$108$	−1.77540e9			−1.25571
$109$	7.55368e8	+	1.30834e9i	0.512553	+	0.887769i	0.999894	+	0.0145567i	$0.00463369\pi$
$109$	7.55368e8	+	1.30834e9i	0.512553	+	0.887769i	−0.487341	+	0.873212i	$0.662033\pi$
$110$	−2.21928e8	−	3.84391e8i	−0.144526	−	0.250326i
$111$	5.83435e8	−	1.01054e9i	0.364787	−	0.631829i
$112$	1.83821e9	−	8.37591e8i	1.10386	−	0.502980i
$113$	1.38128e9	−	2.39245e9i	0.796947	−	1.38035i	−0.124648	−	0.992201i	$-0.539780\pi$
$113$	1.38128e9	−	2.39245e9i	0.796947	−	1.38035i	0.921595	−	0.388152i	$-0.126886\pi$
$114$	−2.39517e8			−0.132820
$115$	6.50287e8	−	1.12633e9i	0.346709	−	0.600517i
$116$	1.10695e9	+	1.91729e9i	0.567630	+	0.983164i
$117$	−3.63431e9	+	1.97368e9i	−1.79302	+	0.973734i
$118$	−2.97675e9			−1.41343
$119$	1.09872e9	−	5.00638e8i	0.502257	−	0.228856i
$120$	3.52333e8	+	6.10259e8i	0.155109	+	0.268657i
$121$	8.84167e8	+	1.53142e9i	0.374973	+	0.649472i
$122$	5.63517e8	+	9.76040e8i	0.230297	+	0.398886i
$123$	−3.87477e9			−1.52642
$124$	−1.52804e9	−	2.64664e9i	−0.580412	−	1.00530i
$125$	−2.18631e9			−0.800972
$126$	−6.11324e9	−	4.36107e9i	−2.16075	−	1.54144i
$127$	3.39973e8	+	5.88851e8i	0.115965	+	0.200858i	0.918165	−	0.396198i	$-0.129671\pi$
$127$	3.39973e8	+	5.88851e8i	0.115965	+	0.200858i	−0.802200	+	0.597055i	$0.796337\pi$
$128$	−2.31673e9			−0.762836
$129$	3.86606e9	+	6.69622e9i	1.22918	+	2.12900i
$130$	−1.60506e9	−	9.83393e8i	−0.492887	−	0.301983i
$131$	−2.94798e9	+	5.10606e9i	−0.874590	+	1.51483i	−0.0173908	+	0.999849i	$0.505536\pi$
$131$	−2.94798e9	+	5.10606e9i	−0.874590	+	1.51483i	−0.857199	+	0.514985i	$0.827797\pi$
$132$	−1.05263e9	−	1.82320e9i	−0.301780	−	0.522699i
$133$	−1.72018e8	−	1.22714e8i	−0.0476696	−	0.0340066i
$134$	−2.28331e9	+	3.95481e9i	−0.611777	+	1.05963i
$135$	1.55543e9	−	2.69409e9i	0.403041	−	0.698088i
$136$	−8.81640e8			−0.220987
$137$	4.40650e9			1.06869			0.534344	−	0.845267i	$-0.320559\pi$
$137$	4.40650e9			1.06869			0.534344	+	0.845267i	$0.320559\pi$
$138$	7.54017e9	−	1.30600e10i	1.76980	−	3.06539i
$139$	−1.65912e9	+	2.87368e9i	−0.376974	+	0.652938i	−0.990620	−	0.136643i	$-0.956369\pi$
$139$	−1.65912e9	+	2.87368e9i	−0.376974	+	0.652938i	0.613647	+	0.789581i	$0.289702\pi$
$140$	1.34087e8	−	1.39169e9i	0.0294991	−	0.306172i
$141$	6.01752e9	+	1.04226e10i	1.28213	+	2.22071i
$142$	−1.82764e9	+	3.16557e9i	−0.377219	+	0.653363i
$143$	−2.13215e9	−	1.30633e9i	−0.426389	−	0.261240i
$144$	6.38541e9	+	1.10599e10i	1.23754	+	2.14348i
$145$	−3.87919e9			−0.728760
$146$	−2.84882e9	−	4.93431e9i	−0.518893	−	0.898749i
$147$	−3.21281e9	−	9.33423e9i	−0.567488	−	1.64873i
$148$	1.69054e9			0.289632
$149$	−4.32746e9	−	7.49539e9i	−0.719275	−	1.24582i	−0.961287	−	0.275548i	$-0.911141\pi$
$149$	−4.32746e9	−	7.49539e9i	−0.719275	−	1.24582i	0.242012	−	0.970273i	$-0.422193\pi$
$150$	−1.12868e10			−1.82038
$151$	5.00908e9	+	8.67598e9i	0.784082	+	1.35807i	0.929546	+	0.368707i	$0.120199\pi$
$151$	5.00908e9	+	8.67598e9i	0.784082	+	1.35807i	−0.145464	+	0.989364i	$0.546467\pi$
$152$	7.71461e7	+	1.33621e8i	0.0117224	+	0.0203039i
$153$	3.81664e9	+	6.61061e9i	0.563080	+	0.975282i
$154$	4.35437e8	−	4.51941e9i	0.0623853	−	0.647498i
$155$	5.35486e9			0.745171
$156$	−7.61296e9	−	4.66432e9i	−1.02918	−	0.630562i
$157$	−2.41862e8	−	4.18916e8i	−0.0317701	−	0.0550274i	0.849703	−	0.527261i	$-0.176781\pi$
$157$	−2.41862e8	−	4.18916e8i	−0.0317701	−	0.0550274i	−0.881473	+	0.472234i	$0.843448\pi$
$158$	6.43050e9	−	1.11379e10i	0.820895	−	1.42183i
$159$	1.49202e10			1.85135
$160$	−2.16893e9	+	3.75670e9i	−0.261641	+	0.453176i
$161$	1.21064e10	−	5.51635e9i	1.42003	−	0.647046i
$162$	6.40161e9	−	1.10879e10i	0.730250	−	1.26483i
$163$	8.26462e9	+	1.43147e10i	0.917020	+	1.58832i	0.803917	+	0.594742i	$0.202746\pi$
$163$	8.26462e9	+	1.43147e10i	0.917020	+	1.58832i	0.113103	+	0.993583i	$0.463921\pi$
$164$	−2.80684e9	−	4.86160e9i	−0.302985	−	0.524785i
$165$	3.68883e9			0.387445
$166$	4.36595e9			0.446265
$167$	−1.65861e9	−	2.87279e9i	−0.165013	−	0.285812i	0.771647	−	0.636051i	$-0.219433\pi$
$167$	−1.65861e9	−	2.87279e9i	−0.165013	−	0.285812i	−0.936660	+	0.350240i	$0.886100\pi$
$168$	−6.91301e8	+	7.17502e9i	−0.0669538	+	0.694914i
$169$	−1.05901e10	−	5.53154e8i	−0.998639	−	0.0521622i
$170$	−1.73716e9	+	3.00885e9i	−0.159522	+	0.276300i
$171$	6.67934e8	−	1.15690e9i	0.0597381	−	0.103469i
$172$	−5.60108e9	+	9.70135e9i	−0.487970	+	0.845189i
$173$	−4.79214e8	−	8.30023e8i	−0.0406745	−	0.0704503i	0.844971	−	0.534811i	$-0.179617\pi$
$173$	−4.79214e8	−	8.30023e8i	−0.0406745	−	0.0704503i	−0.885646	+	0.464361i	$0.846284\pi$
$174$	−4.49797e10			−3.72002
$175$	−8.10607e9	−	5.78272e9i	−0.653340	−	0.466080i
$176$	−3.86077e9	+	6.68705e9i	−0.303296	+	0.525324i
$177$	1.23697e10	−	2.14249e10i	0.947281	−	1.64074i
$178$	−7.37365e9			−0.550545
$179$	7.64692e8	−	1.32448e9i	0.0556734	−	0.0964291i	−0.836846	−	0.547439i	$-0.815603\pi$
$179$	7.64692e8	−	1.32448e9i	0.0556734	−	0.0964291i	0.892519	+	0.451010i	$0.148936\pi$
$180$	8.83906e9			0.627596
$181$	−2.09108e10			−1.44816			−0.724082	−	0.689714i	$-0.757736\pi$
$181$	−2.09108e10			−1.44816			−0.724082	+	0.689714i	$0.757736\pi$
$182$	−7.52413e9	−	1.77243e10i	−0.508317	−	1.19743i
$183$	−9.36662e9			−0.617381
$184$	−9.71447e9			−0.624797
$185$	−1.48108e9	+	2.56531e9i	−0.0929622	+	0.161015i
$186$	6.20904e10			3.80378
$187$	−2.30763e9	+	3.99693e9i	−0.138000	+	0.239023i
$188$	−8.71806e9	+	1.51001e10i	−0.508990	+	0.881597i
$189$	2.89575e10	−	1.31947e10i	1.65076	−	0.752177i
$190$	6.08027e8			0.0338479
$191$	−4.34982e9	−	7.53411e9i	−0.236495	−	0.409621i	0.723211	−	0.690627i	$-0.242665\pi$
$191$	−4.34982e9	−	7.53411e9i	−0.236495	−	0.409621i	−0.959706	+	0.281006i	$0.909332\pi$
$192$	−5.23460e9	+	9.06659e9i	−0.277989	+	0.481491i
$193$	−6.28729e9	+	1.08899e10i	−0.326179	+	0.564958i	−0.981750	−	0.190175i	$-0.939094\pi$
$193$	−6.28729e9	+	1.08899e10i	−0.326179	+	0.564958i	0.655572	+	0.755133i	$0.272428\pi$
$194$	8.90711e8	−	1.54276e9i	0.0451470	−	0.0781969i
$195$	1.37476e10	−	7.46589e9i	0.680882	−	0.369765i
$196$	9.38415e9	−	1.07927e10i	0.454195	−	0.522368i
$197$	2.37122e9	+	4.10707e9i	0.112169	+	0.194283i	0.916645	−	0.399703i	$-0.130887\pi$
$197$	2.37122e9	+	4.10707e9i	0.112169	+	0.194283i	−0.804475	+	0.593986i	$0.797553\pi$
$198$	2.87042e10			1.32725
$199$	−2.18593e10			−0.988091			−0.494046	−	0.869436i	$-0.664482\pi$
$199$	−2.18593e10			−0.988091			−0.494046	+	0.869436i	$0.664482\pi$
$200$	3.63539e9	+	6.29668e9i	0.160663	+	0.278276i
$201$	−1.89763e10	−	3.28679e10i	−0.820028	−	1.42033i
$202$	−7.61658e9	+	1.31923e10i	−0.321869	+	0.557493i
$203$	−3.23038e10	−	2.30450e10i	−1.33513	−	0.952454i
$204$	−8.23951e9	+	1.42713e10i	−0.333093	+	0.576935i
$205$	9.83632e9			0.388992
$206$	−2.99664e8	+	5.19033e8i	−0.0115940	+	0.0200813i
$207$	4.20542e10	+	7.28399e10i	1.59200	+	2.75742i
$208$	−8.54355e8	+	3.27354e10i	−0.0316485	+	1.21264i
$209$	8.07697e8			0.0292813
$210$	2.31247e10	+	1.64967e10i	0.820520	+	0.585344i
$211$	1.91693e9	+	3.32023e9i	0.0665788	+	0.115318i	0.897393	−	0.441232i	$-0.145458\pi$
$211$	1.91693e9	+	3.32023e9i	0.0665788	+	0.115318i	−0.830814	+	0.556550i	$0.812125\pi$
$212$	1.08081e10	+	1.87201e10i	0.367482	+	0.636498i
$213$	−1.51893e10	−	2.63086e10i	−0.505626	−	0.875769i
$214$	−5.98412e10			−1.95047
$215$	−9.81422e9	−	1.69987e10i	−0.313244	−	0.542555i
$216$	−2.32362e10			−0.726313
$217$	4.45925e10	+	3.18115e10i	1.36519	+	0.973901i
$218$	−2.22342e10	−	3.85107e10i	−0.666756	−	1.15486i
$219$	4.73523e10			1.39105
$220$	2.67215e9	+	4.62830e9i	0.0769058	+	0.133205i
$221$	−5.10658e8	+	1.95663e10i	−0.0144001	+	0.551752i
$222$	−1.71733e10	+	2.97451e10i	−0.474533	+	0.821916i
$223$	−8.25181e9	−	1.42926e10i	−0.223449	−	0.387024i	0.732404	−	0.680870i	$-0.238398\pi$
$223$	−8.25181e9	−	1.42926e10i	−0.223449	−	0.387024i	−0.955853	+	0.293846i	$0.905065\pi$
$224$	−4.03790e10	+	1.83989e10i	−1.07162	+	0.488288i
$225$	3.14753e10	−	5.45169e10i	0.818746	−	1.41811i
$226$	−4.06579e10	+	7.04216e10i	−1.03671	+	1.79563i
$227$	3.33355e10			0.833279			0.416639	−	0.909072i	$-0.363208\pi$
$227$	3.33355e10			0.833279			0.416639	+	0.909072i	$0.363208\pi$
$228$	2.88393e9			0.0706769
$229$	−1.09058e10	+	1.88894e10i	−0.262058	+	0.453898i	−0.966789	−	0.255577i	$-0.917735\pi$
$229$	−1.09058e10	+	1.88894e10i	−0.262058	+	0.453898i	0.704730	+	0.709475i	$0.251068\pi$
$230$	−1.91412e10	+	3.31534e10i	−0.451017	+	0.781184i
$231$	3.07186e10	+	2.19141e10i	0.709819	+	0.506372i
$232$	1.44875e10	+	2.50932e10i	0.328321	+	0.568669i
$233$	1.34332e10	−	2.32670e10i	0.298591	−	0.517176i	−0.677222	−	0.735778i	$-0.736817\pi$
$233$	1.34332e10	−	2.32670e10i	0.298591	−	0.517176i	0.975814	+	0.218603i	$0.0701499\pi$
$234$	1.06976e11	−	5.80951e10i	2.33246	−	1.26668i
$235$	−1.52758e10	−	2.64585e10i	−0.326738	−	0.565926i
$236$	3.58419e10			0.752120
$237$	5.34429e10	+	9.25659e10i	1.10033	+	1.90583i
$238$	−3.23408e10	+	1.47362e10i	−0.653362	+	0.297708i
$239$	−2.05741e10			−0.407877			−0.203939	−	0.978984i	$-0.565374\pi$
$239$	−2.05741e10			−0.407877			−0.203939	+	0.978984i	$0.565374\pi$
$240$	−2.41543e10	−	4.18364e10i	−0.469941	−	0.813962i
$241$	4.11149e10			0.785095			0.392548	−	0.919732i	$-0.371594\pi$
$241$	4.11149e10			0.785095			0.392548	+	0.919732i	$0.371594\pi$
$242$	−2.60254e10	−	4.50773e10i	−0.487784	−	0.844867i
$243$	3.90284e9	+	6.75992e9i	0.0718047	+	0.124369i
$244$	−6.78509e9	−	1.17521e10i	−0.122547	−	0.212257i
$245$	8.15590e9	+	2.36955e10i	0.144619	+	0.420163i
$246$	1.14053e11			1.98564
$247$	3.01015e9	−	1.63472e9i	0.0514578	−	0.0279451i
$248$	−1.99987e10	−	3.46388e10i	−0.335714	−	0.581474i
$249$	−1.81424e10	+	3.14236e10i	−0.299087	+	0.518034i
$250$	6.43540e10			1.04195
$251$	−4.26014e10	+	7.37878e10i	−0.677473	+	1.17342i	0.298266	+	0.954483i	$0.403592\pi$
$251$	−4.26014e10	+	7.37878e10i	−0.677473	+	1.17342i	−0.975739	+	0.218935i	$0.929742\pi$
$252$	7.36071e10	+	5.25099e10i	1.14979	+	0.820236i
$253$	−2.54269e10	+	4.40407e10i	−0.390168	+	0.675790i
$254$	−1.00071e10	−	1.73328e10i	−0.150854	−	0.261286i
$255$	−1.44373e10	−	2.50061e10i	−0.213823	−	0.370353i
$256$	9.01044e10			1.31119
$257$	−1.10905e10			−0.158581			−0.0792904	−	0.996852i	$-0.525265\pi$
$257$	−1.10905e10			−0.158581			−0.0792904	+	0.996852i	$0.525265\pi$
$258$	−1.13797e11	−	1.97103e11i	−1.59898	−	2.76951i
$259$	−2.75733e10	+	1.25639e10i	−0.380750	+	0.173491i
$260$	1.93260e10	+	1.18406e10i	0.262277	+	0.160692i
$261$	1.25434e11	−	2.17258e11i	1.67314	−	2.89796i
$262$	8.67737e10	−	1.50296e11i	1.13771	−	1.97057i
$263$	−5.25506e10	+	9.10203e10i	−0.677293	+	1.17311i	0.298499	+	0.954410i	$0.403514\pi$
$263$	−5.25506e10	+	9.10203e10i	−0.677293	+	1.17311i	−0.975793	+	0.218697i	$0.929819\pi$
$264$	−1.37766e10	−	2.38618e10i	−0.174552	−	0.302333i
$265$	−3.78758e10			−0.471798
$266$	5.06333e9	+	3.61209e9i	0.0620110	+	0.0442375i
$267$	3.06407e10	−	5.30712e10i	0.368976	−	0.639084i
$268$	2.74924e10	−	4.76183e10i	0.325542	−	0.563855i
$269$	−1.28681e11			−1.49840			−0.749200	−	0.662344i	$-0.769562\pi$
$269$	−1.28681e11			−1.49840			−0.749200	+	0.662344i	$0.769562\pi$
$270$	−4.57841e10	+	7.93003e10i	−0.524297	+	0.908109i
$271$	−9.52838e10			−1.07314			−0.536571	−	0.843855i	$-0.680281\pi$
$271$	−9.52838e10			−1.07314			−0.536571	+	0.843855i	$0.680281\pi$
$272$	6.04410e10			0.669532
$273$	1.58835e11	+	1.94980e10i	1.73067	+	0.212450i
$274$	−1.29705e11			−1.39020
$275$	3.80614e10			0.401317
$276$	−9.07882e10	+	1.57250e11i	−0.941756	+	1.63117i
$277$	−4.40555e9			−0.0449616			−0.0224808	−	0.999747i	$-0.507156\pi$
$277$	−4.40555e9			−0.0449616			−0.0224808	+	0.999747i	$0.507156\pi$
$278$	4.88360e10	−	8.45865e10i	0.490387	−	0.849375i
$279$	−1.73150e11	+	2.99904e11i	−1.71082	+	2.96322i
$280$	1.75491e9	−	1.82142e10i	0.0170625	−	0.177092i
$281$	−6.52112e10			−0.623941			−0.311971	−	0.950092i	$-0.600989\pi$
$281$	−6.52112e10			−0.623941			−0.311971	+	0.950092i	$0.600989\pi$
$282$	−1.77125e11	−	3.06790e11i	−1.66786	−	2.88881i
$283$	−6.99602e10	+	1.21175e11i	−0.648354	+	1.12298i	0.335162	+	0.942160i	$0.391209\pi$
$283$	−6.99602e10	+	1.21175e11i	−0.648354	+	1.12298i	−0.983516	+	0.180821i	$0.942125\pi$
$284$	2.20059e10	−	3.81154e10i	0.200728	−	0.347671i
$285$	−2.52661e9	+	4.37622e9i	−0.0226849	+	0.0392914i
$286$	6.27597e10	+	3.84517e10i	0.554669	+	0.339835i
$287$	8.19118e10	+	5.84343e10i	0.712652	+	0.508393i
$288$	−1.40265e11	−	2.42946e11i	−1.20139	−	2.08087i
$289$	−8.24616e10			−0.695362
$290$	1.14184e11			0.948009
$291$	7.40257e9	+	1.28216e10i	0.0605152	+	0.104815i
$292$	3.43016e10	+	5.94121e10i	0.276116	+	0.478246i
$293$	−1.08867e10	+	1.88563e10i	−0.0862963	+	0.149470i	−0.905943	−	0.423400i	$-0.860837\pi$
$293$	−1.08867e10	+	1.88563e10i	−0.0862963	+	0.149470i	0.819647	+	0.572870i	$0.194170\pi$
$294$	9.45687e10	+	2.74752e11i	0.738218	+	2.14476i
$295$	−3.14011e10	+	5.43884e10i	−0.241405	+	0.418126i
$296$	2.21255e10			0.167525
$297$	−6.08191e10	+	1.05342e11i	−0.453561	+	0.785591i
$298$	1.27379e11	+	2.20626e11i	0.935671	+	1.62063i
$299$	−5.62676e9	+	2.15594e11i	−0.0407134	+	1.55997i
$300$	1.35900e11			0.968669
$301$	1.92561e10	−	1.99860e11i	0.135213	−	1.40338i
$302$	−1.47442e11	−	2.55377e11i	−1.01997	−	1.76665i
$303$	−6.33003e10	−	1.09639e11i	−0.431433	−	0.747264i
$304$	−5.28877e9	−	9.16041e9i	−0.0355159	−	0.0615154i
$305$	2.37777e10			0.157333
$306$	−1.12342e11	−	1.94583e11i	−0.732483	−	1.26870i
$307$	1.77058e11			1.13761			0.568805	−	0.822473i	$-0.307406\pi$
$307$	1.77058e11			1.13761			0.568805	+	0.822473i	$0.307406\pi$
$308$	−5.24293e9	+	5.44164e10i	−0.0331968	+	0.344550i
$309$	−2.49046e9	−	4.31361e9i	−0.0155406	−	0.0269171i
$310$	−1.57620e11			−0.969357
$311$	−5.64797e10	−	9.78258e10i	−0.342350	−	0.592968i	0.642518	−	0.766270i	$-0.277890\pi$
$311$	−5.64797e10	−	9.78258e10i	−0.342350	−	0.592968i	−0.984869	+	0.173302i	$0.944556\pi$
$312$	−9.96374e10	−	6.10459e10i	−0.595287	−	0.364721i
$313$	−1.25791e11	+	2.17877e11i	−0.740800	+	1.28310i	0.211332	+	0.977414i	$0.432220\pi$
$313$	−1.25791e11	+	2.17877e11i	−0.740800	+	1.28310i	−0.952132	+	0.305688i	$0.901114\pi$
$314$	7.11917e9	+	1.23308e10i	0.0413282	+	0.0715825i
$315$	−1.44169e11	+	6.56912e10i	−0.825037	+	0.375932i
$316$	−7.74271e10	+	1.34108e11i	−0.436819	+	0.756592i
$317$	5.53012e10	−	9.57844e10i	0.307587	−	0.532756i	−0.670247	−	0.742138i	$-0.733812\pi$
$317$	5.53012e10	−	9.57844e10i	0.307587	−	0.532756i	0.977834	+	0.209382i	$0.0671452\pi$
$318$	−4.39175e11			−2.40833
$319$	1.51680e11			0.820108
$320$	1.32883e10	−	2.30161e10i	0.0708428	−	0.122703i
$321$	2.48666e11	−	4.30702e11i	1.30720	−	2.26414i
$322$	−3.56351e11	+	1.62373e11i	−1.84725	+	0.841711i
$323$	−3.16116e9	−	5.47529e9i	−0.0161598	−	0.0279895i
$324$	−7.70793e10	+	1.33505e11i	−0.388584	+	0.673048i
$325$	1.41848e11	−	7.70333e10i	0.705260	−	0.383004i
$326$	−2.43268e11	−	4.21353e11i	−1.19291	−	2.06618i
$327$	3.69570e11			1.78744
$328$	−3.67356e10	−	6.36279e10i	−0.175249	−	0.303539i
$329$	2.99721e10	−	3.11081e11i	0.141038	−	1.46383i
$330$	−1.08580e11			−0.504009
$331$	9.50023e10	+	1.64549e11i	0.435019	+	0.753475i	0.997297	−	0.0734730i	$-0.0234083\pi$
$331$	9.50023e10	+	1.64549e11i	0.435019	+	0.753475i	−0.562278	+	0.826948i	$0.690075\pi$
$332$	−5.25687e10			−0.237469
$333$	−9.57818e10	−	1.65899e11i	−0.426858	−	0.739341i
$334$	4.88209e10	+	8.45603e10i	0.214658	+	0.371798i
$335$	4.81724e10	+	8.34370e10i	0.208976	+	0.361957i
$336$	4.73922e10	−	4.91884e11i	0.202852	−	2.10541i
$337$	2.35998e11			0.996723			0.498362	−	0.866969i	$-0.333935\pi$
$337$	2.35998e11			0.996723			0.498362	+	0.866969i	$0.333935\pi$
$338$	3.11718e11	+	1.62820e10i	1.29908	+	0.0678552i
$339$	−3.37902e11	−	5.85264e11i	−1.38961	−	2.40687i
$340$	2.09165e10	−	3.62284e10i	0.0848855	−	0.147026i
$341$	−2.09381e11			−0.838575
$342$	−1.96606e10	+	3.40532e10i	−0.0777104	+	0.134598i
$343$	−7.28490e10	+	2.45775e11i	−0.284184	+	0.958770i
$344$	−7.33061e10	+	1.26970e11i	−0.282245	+	0.488863i
$345$	−1.59079e11	−	2.75534e11i	−0.604544	−	1.04710i
$346$	1.41056e10	+	2.44317e10i	0.0529115	+	0.0916453i
$347$	−1.99799e11			−0.739793			−0.369896	−	0.929073i	$-0.620607\pi$
$347$	−1.99799e11			−0.739793			−0.369896	+	0.929073i	$0.620607\pi$
$348$	5.41583e11			1.97951
$349$	−1.92466e11	−	3.33361e11i	−0.694449	−	1.20282i	−0.970366	−	0.241639i	$-0.922315\pi$
$349$	−1.92466e11	−	3.33361e11i	−0.694449	−	1.20282i	0.275917	−	0.961181i	$-0.411018\pi$
$350$	2.38601e11	+	1.70214e11i	0.849898	+	0.606302i
$351$	−1.34587e10	+	5.15683e11i	−0.0473285	+	1.81343i
$352$	8.48075e10	−	1.46891e11i	0.294437	−	0.509980i
$353$	6.64362e10	−	1.15071e11i	0.227729	−	0.394438i	−0.729406	−	0.684081i	$-0.760203\pi$
$353$	6.64362e10	−	1.15071e11i	0.227729	−	0.394438i	0.957135	+	0.289643i	$0.0935366\pi$
$354$	−3.64100e11	+	6.30640e11i	−1.23227	+	2.13436i
$355$	3.85589e10	+	6.67859e10i	0.128854	+	0.223181i
$356$	8.87832e10			0.292958
$357$	2.83269e10	−	2.94005e11i	0.0922980	−	0.957962i
$358$	−2.25086e10	+	3.89861e10i	−0.0724228	+	0.125440i
$359$	4.37150e10	−	7.57167e10i	0.138901	−	0.240584i	−0.788180	−	0.615445i	$-0.788976\pi$
$359$	4.37150e10	−	7.57167e10i	0.138901	−	0.240584i	0.927081	+	0.374861i	$0.122310\pi$
$360$	1.15684e11			0.363006
$361$	1.60791e11	−	2.78498e11i	0.498286	−	0.863056i
$362$	6.15509e11			1.88385
$363$	4.32586e11			1.30765
$364$	9.05950e10	+	2.13412e11i	0.270488	+	0.637180i
$365$	−1.20207e11			−0.354495
$366$	2.75706e11			0.803121
$367$	−1.22666e11	+	2.12464e11i	−0.352961	+	0.611347i	−0.986767	−	0.162145i	$-0.948159\pi$
$367$	−1.22666e11	+	2.12464e11i	−0.352961	+	0.611347i	0.633805	+	0.773493i	$0.281492\pi$
$368$	6.65977e11			1.89297
$369$	−3.18058e11	+	5.50893e11i	−0.893075	+	1.54685i
$370$	4.35955e10	−	7.55097e10i	0.120930	−	0.209457i
$371$	−3.15410e11	−	2.25008e11i	−0.864356	−	0.616616i
$372$	−7.47606e11			−2.02409
$373$	3.37581e11	+	5.84707e11i	0.903001	+	1.56404i	0.823579	+	0.567202i	$0.191974\pi$
$373$	3.37581e11	+	5.84707e11i	0.903001	+	1.56404i	0.0794218	+	0.996841i	$0.474693\pi$
$374$	6.79249e10	−	1.17649e11i	0.179517	−	0.310933i
$375$	−2.67418e11	+	4.63182e11i	−0.698313	+	1.20951i
$376$	−1.14101e11	+	1.97628e11i	−0.294404	+	0.509922i
$377$	5.65286e11	−	3.06989e11i	1.44123	−	0.782684i
$378$	−8.52363e11	+	3.88384e11i	−2.14739	+	0.978471i
$379$	2.48396e11	+	4.30234e11i	0.618397	+	1.07110i	0.989778	+	0.142615i	$0.0455510\pi$
$379$	2.48396e11	+	4.30234e11i	0.618397	+	1.07110i	−0.371381	+	0.928480i	$0.621116\pi$
$380$	−7.32102e9			−0.0180113
$381$	1.66335e11			0.404409
$382$	1.28037e11	+	2.21766e11i	0.307644	+	0.532856i
$383$	1.52235e11	+	2.63678e11i	0.361509	+	0.626152i	0.988209	−	0.153108i	$-0.0489283\pi$
$383$	1.52235e11	+	2.63678e11i	0.361509	+	0.626152i	−0.626700	+	0.779260i	$0.715595\pi$
$384$	−2.83370e11	+	4.90812e11i	−0.665065	+	1.15193i
$385$	−7.79810e10	−	5.56302e10i	−0.180890	−	0.129044i
$386$	1.85066e11	−	3.20543e11i	0.424310	−	0.734927i
$387$	1.26937e12			2.87667
$388$	−1.07247e10	+	1.85757e10i	−0.0240238	+	0.0416105i
$389$	9.49965e10	+	1.64539e11i	0.210346	+	0.364330i	0.951823	−	0.306648i	$-0.0992076\pi$
$389$	9.49965e10	+	1.64539e11i	0.210346	+	0.364330i	−0.741477	+	0.670979i	$0.765874\pi$
$390$	−4.04660e11	+	2.19758e11i	−0.885726	+	0.481010i
$391$	3.98063e11			0.861303
$392$	1.22818e11	−	1.41253e11i	0.262710	−	0.302141i
$393$	7.21164e11	+	1.24909e12i	1.52499	+	2.64136i
$394$	−6.97967e10	−	1.20891e11i	−0.145916	−	0.252733i
$395$	−1.35668e11	−	2.34984e11i	−0.280408	−	0.485681i
$396$	−3.45617e11			−0.706263
$397$	−2.19810e11	−	3.80723e11i	−0.444110	−	0.769222i	0.553879	−	0.832597i	$-0.313147\pi$
$397$	−2.19810e11	−	3.80723e11i	−0.444110	−	0.769222i	−0.997990	+	0.0633752i	$0.979814\pi$
$398$	6.43426e11			1.28536
$399$	−4.70380e10	+	2.14331e10i	−0.0929118	+	0.0423358i
$400$	−2.49225e11	−	4.31670e11i	−0.486767	−	0.843105i
$401$	−1.84685e11			−0.356682			−0.178341	−	0.983969i	$-0.557073\pi$
$401$	−1.84685e11			−0.356682			−0.178341	+	0.983969i	$0.557073\pi$
$402$	5.58565e11	+	9.67463e11i	1.06673	+	1.84764i
$403$	−7.80326e11	+	4.23770e11i	−1.47368	+	0.800309i
$404$	9.17082e10	−	1.58843e11i	0.171274	−	0.296656i
$405$	−1.35059e11	−	2.33928e11i	−0.249445	−	0.432051i
$406$	9.50861e11	+	6.78327e11i	1.73680	+	1.23900i
$407$	5.79119e10	−	1.00306e11i	0.104615	−	0.181198i
$408$	−1.07838e11	+	1.86780e11i	−0.192663	+	0.333703i
$409$	−1.54191e11			−0.272460			−0.136230	−	0.990677i	$-0.543499\pi$
$409$	−1.54191e11			−0.272460			−0.136230	+	0.990677i	$0.543499\pi$
$410$	−2.89531e11			−0.506021
$411$	5.38979e11	−	9.33539e11i	0.931716	−	1.61378i
$412$	3.60814e9	−	6.24947e9i	0.00616943	−	0.0106858i
$413$	−5.84596e11	+	2.66374e11i	−0.988736	+	0.450523i
$414$	−1.23786e12	−	2.14404e12i	−2.07095	−	3.58700i
$415$	4.60556e10	−	7.97706e10i	0.0762194	−	0.132016i
$416$	1.87672e10	−	7.19080e11i	0.0307241	−	1.17722i
$417$	4.05869e11	+	7.02986e11i	0.657316	+	1.13850i
$418$	−2.37745e10			−0.0380906
$419$	3.51410e11	+	6.08660e11i	0.556995	+	0.964744i	0.997745	+	0.0671138i	$0.0213791\pi$
$419$	3.51410e11	+	6.08660e11i	0.556995	+	0.964744i	−0.440750	+	0.897630i	$0.645288\pi$
$420$	−2.78435e11	−	1.98631e11i	−0.436619	−	0.311476i
$421$	−7.66453e11			−1.18909			−0.594547	−	0.804061i	$-0.702669\pi$
$421$	−7.66453e11			−1.18909			−0.594547	+	0.804061i	$0.702669\pi$
$422$	−5.64248e10	−	9.77306e10i	−0.0866092	−	0.150012i
$423$	1.97578e12			3.00059
$424$	1.41454e11	+	2.45006e11i	0.212554	+	0.368155i
$425$	−1.48965e11	−	2.58014e11i	−0.221479	−	0.383613i
$426$	4.47095e11	+	7.74392e11i	0.657744	+	1.13925i
$427$	1.98008e11	+	1.41255e11i	0.288242	+	0.205627i
$428$	7.20524e11			1.03789
$429$	−5.37546e11	+	2.91924e11i	−0.766228	+	0.416114i
$430$	2.88881e11	+	5.00356e11i	0.407484	+	0.705783i
$431$	3.19439e11	−	5.53285e11i	0.445903	−	0.772327i	−0.552211	−	0.833704i	$-0.686216\pi$
$431$	3.19439e11	−	5.53285e11i	0.445903	−	0.772327i	0.998115	+	0.0613768i	$0.0195491\pi$
$432$	1.59296e12			2.20054
$433$	1.44112e11	−	2.49610e11i	0.197018	−	0.341245i	−0.750542	−	0.660822i	$-0.770208\pi$
$433$	1.44112e11	−	2.49610e11i	0.197018	−	0.341245i	0.947560	+	0.319578i	$0.103541\pi$
$434$	−1.31258e12	−	9.36368e11i	−1.77591	−	1.26690i
$435$	−4.74482e11	+	8.21826e11i	−0.635357	+	1.10047i
$436$	2.67713e11	+	4.63693e11i	0.354797	+	0.614527i
$437$	−3.48317e10	−	6.03302e10i	−0.0456886	−	0.0791349i
$438$	−1.39381e12			−1.80955
$439$	−1.12554e12			−1.44634			−0.723168	−	0.690672i	$-0.757315\pi$
$439$	−1.12554e12			−1.44634			−0.723168	+	0.690672i	$0.757315\pi$
$440$	3.49727e10	+	6.05745e10i	0.0444828	+	0.0770465i
$441$	−1.59081e12	−	3.09416e11i	−2.00283	−	0.389555i
$442$	1.50312e10	−	5.75933e11i	0.0187324	−	0.717747i
$443$	−4.98130e11	+	8.62787e11i	−0.614506	+	1.06436i	0.375965	+	0.926634i	$0.377311\pi$
$443$	−4.98130e11	+	8.62787e11i	−0.614506	+	1.06436i	−0.990471	+	0.137722i	$0.956022\pi$
$444$	2.06778e11	−	3.58149e11i	0.252511	−	0.437362i
$445$	−7.77831e10	+	1.34724e11i	−0.0940298	+	0.162864i
$446$	2.42891e11	+	4.20700e11i	0.290673	+	0.503461i
$447$	−2.11725e12			−2.50835
$448$	2.47389e11	−	1.12724e11i	0.290155	−	0.132211i
$449$	5.26188e11	−	9.11384e11i	0.610988	−	1.05826i	−0.380087	−	0.924951i	$-0.624106\pi$
$449$	5.26188e11	−	9.11384e11i	0.610988	−	1.05826i	0.991074	−	0.133311i	$-0.0425609\pi$
$450$	−9.26474e11	+	1.60470e12i	−1.06507	+	1.84475i
$451$	−3.84611e11			−0.437751
$452$	4.89546e11	−	8.47919e11i	0.551659	−	0.955502i
$453$	2.45074e12			2.73435
$454$	−9.81227e11			−1.08397
$455$	−4.03213e11	−	4.94967e10i	−0.441045	−	0.0541408i
$456$	3.77444e10			0.0408800
$457$	−9.51794e11			−1.02075			−0.510376	−	0.859952i	$-0.670494\pi$
$457$	−9.51794e11			−1.02075			−0.510376	+	0.859952i	$0.670494\pi$
$458$	3.21011e11	−	5.56008e11i	0.340899	−	0.590454i
$459$	9.52133e11			1.00125
$460$	2.30471e11	−	3.99188e11i	0.239997	−	0.415687i
$461$	1.79027e11	−	3.10084e11i	0.184614	−	0.319761i	−0.758832	−	0.651286i	$-0.774230\pi$
$461$	1.79027e11	−	3.10084e11i	0.184614	−	0.319761i	0.943446	+	0.331525i	$0.107563\pi$
$462$	−9.04200e11	−	6.45040e11i	−0.923370	−	0.658715i
$463$	2.08403e11			0.210761			0.105380	−	0.994432i	$-0.466394\pi$
$463$	2.08403e11			0.210761			0.105380	+	0.994432i	$0.466394\pi$
$464$	−9.93196e11	−	1.72027e12i	−0.994727	−	1.72292i
$465$	6.54978e11	−	1.13446e12i	0.649664	−	1.12525i
$466$	−3.95405e11	+	6.84861e11i	−0.388423	+	0.672769i
$467$	3.25952e11	−	5.64565e11i	0.317123	−	0.549273i	−0.662764	−	0.748829i	$-0.730617\pi$
$467$	3.25952e11	−	5.64565e11i	0.317123	−	0.549273i	0.979886	+	0.199556i	$0.0639500\pi$
$468$	−1.28805e12	+	6.99501e11i	−1.24116	+	0.674034i
$469$	−9.45172e10	+	9.80995e11i	−0.0902055	+	0.936244i
$470$	4.49642e11	+	7.78803e11i	0.425037	+	0.736186i
$471$	−1.18333e11			−0.110793
$472$	4.69094e11			0.435031
$473$	3.83746e11	+	6.64668e11i	0.352508	+	0.610562i
$474$	−1.57309e12	−	2.72467e12i	−1.43137	−	2.47920i
$475$	−2.60697e10	+	4.51540e10i	−0.0234971	+	0.0406982i
$476$	3.89403e11	−	1.77433e11i	0.347670	−	0.158418i
$477$	1.22472e12	−	2.12127e12i	1.08319	−	1.87613i
$478$	6.05596e11			0.530588
$479$	2.72171e10	−	4.71413e10i	0.0236228	−	0.0409159i	−0.853972	−	0.520318i	$-0.825813\pi$
$479$	2.72171e10	−	4.71413e10i	0.0236228	−	0.0409159i	0.877595	+	0.479403i	$0.159147\pi$
$480$	5.30584e11	+	9.18999e11i	0.456214	+	0.790186i
$481$	1.28154e10	−	4.91033e11i	0.0109164	−	0.418271i
$482$	−1.21021e12			−1.02129
$483$	3.12124e11	−	3.23954e12i	0.260955	−	2.70845i
$484$	3.13361e11	+	5.42758e11i	0.259562	+	0.449575i
$485$	−1.87919e10	−	3.25485e10i	−0.0154217	−	0.0267112i
$486$	−1.14880e11	−	1.98978e11i	−0.0934072	−	0.161786i
$487$	−7.24842e11			−0.583933			−0.291966	−	0.956429i	$-0.594310\pi$
$487$	−7.24842e11			−0.583933			−0.291966	+	0.956429i	$0.594310\pi$
$488$	−8.88023e10	−	1.53810e11i	−0.0708818	−	0.122771i
$489$	4.04354e12			3.19795
$490$	−2.40068e11	−	6.97475e11i	−0.188127	−	0.546570i
$491$	−3.38528e11	−	5.86347e11i	−0.262862	−	0.455290i	0.704139	−	0.710062i	$-0.251333\pi$
$491$	−3.38528e11	−	5.86347e11i	−0.262862	−	0.455290i	−0.967001	+	0.254772i	$0.918000\pi$
$492$	−1.37327e12			−1.05661
$493$	−5.93645e11	−	1.02822e12i	−0.452601	−	0.783928i
$494$	−8.86034e10	+	4.81177e10i	−0.0669390	+	0.0363524i
$495$	3.02795e11	−	5.24457e11i	0.226686	−	0.392633i
$496$	1.37102e12	+	2.37467e12i	1.01713	+	1.76171i
$497$	−7.56550e10	+	7.85224e11i	−0.0556203	+	0.577284i
$498$	5.34020e11	−	9.24950e11i	0.389068	−	0.673886i
$499$	−7.13817e11	+	1.23637e12i	−0.515388	+	0.892679i	0.484452	+	0.874818i	$0.339019\pi$
$499$	−7.13817e11	+	1.23637e12i	−0.515388	+	0.892679i	−0.999840	+	0.0178609i	$0.994314\pi$
$500$	−7.74861e11			−0.554445
$501$	−8.11487e11			−0.575456
$502$	1.25397e12	−	2.17194e12i	0.881292	−	1.52644i
$503$	−2.11807e11	+	3.66860e11i	−0.147531	+	0.255531i	−0.930314	−	0.366763i	$-0.880466\pi$
$503$	−2.11807e11	+	3.66860e11i	−0.147531	+	0.255531i	0.782783	+	0.622294i	$0.213799\pi$
$504$	9.63359e11	+	6.87242e11i	0.665044	+	0.474430i
$505$	1.60691e11	+	2.78326e11i	0.109947	+	0.190433i
$506$	7.48439e11	−	1.29633e12i	0.507550	−	0.879103i
$507$	−1.41251e12	+	2.17590e12i	−0.949413	+	1.46253i
$508$	1.20491e11	+	2.08697e11i	0.0802729	+	0.139037i
$509$	−1.98171e12			−1.30861			−0.654305	−	0.756231i	$-0.727039\pi$
$509$	−1.98171e12			−1.30861			−0.654305	+	0.756231i	$0.727039\pi$
$510$	4.24961e11	+	7.36054e11i	0.278153	+	0.481774i
$511$	−1.00102e12	−	7.14108e11i	−0.649453	−	0.463308i
$512$	−1.46605e12			−0.942831
$513$	−8.33145e10	−	1.44305e11i	−0.0531120	−	0.0919926i
$514$	3.26447e11			0.206290
$515$	6.32219e9	+	1.09503e10i	0.00396036	+	0.00685955i
$516$	1.37019e12	+	2.37323e12i	0.850857	+	1.47373i
$517$	5.97300e11	+	1.03455e12i	0.367693	+	0.636863i
$518$	8.11619e11	−	3.69818e11i	0.495300	−	0.225686i
$519$	−2.34460e11			−0.141845
$520$	2.52935e11	+	1.54969e11i	0.151703	+	0.0929456i
$521$	2.33860e11	+	4.05057e11i	0.139055	+	0.240850i	0.927139	−	0.374718i	$-0.122260\pi$
$521$	2.33860e11	+	4.05057e11i	0.139055	+	0.240850i	−0.788084	+	0.615567i	$0.788927\pi$
$522$	−3.69213e12	+	6.39496e12i	−2.17651	+	3.76982i
$523$	2.16140e11			0.126322			0.0631608	−	0.998003i	$-0.479882\pi$
$523$	2.16140e11			0.126322			0.0631608	+	0.998003i	$0.479882\pi$
$524$	−1.04481e12	+	1.80966e12i	−0.605405	+	1.04859i
$525$	−2.21659e12	+	1.01000e12i	−1.27341	+	0.580236i
$526$	1.54682e12	−	2.67918e12i	0.881058	−	1.52604i
$527$	8.19473e11	+	1.41937e12i	0.462793	+	0.801581i
$528$	9.44457e11	+	1.63585e12i	0.528847	+	0.915989i
$529$	2.58495e12			1.43517
$530$	1.11487e12			0.613739
$531$	−2.03072e12	−	3.51730e12i	−1.10847	−	1.91993i
$532$	−6.09656e10	−	4.34917e10i	−0.0329976	−	0.0235399i
$533$	−1.43338e12	+	7.78421e11i	−0.769286	+	0.417775i
$534$	−9.01906e11	+	1.56215e12i	−0.479983	+	0.831354i
$535$	−6.31253e11	+	1.09336e12i	−0.333128	+	0.576995i
$536$	3.59817e11	−	6.23222e11i	0.188296	−	0.326138i
$537$	−1.87066e11	−	3.24008e11i	−0.0970757	−	0.168140i
$538$	3.78770e12			1.94920
$539$	−3.18904e11	−	9.26518e11i	−0.162746	−	0.472830i
$540$	5.51268e11	−	9.54824e11i	0.278991	−	0.483227i
$541$	−1.20272e12	+	2.08317e12i	−0.603638	+	1.04553i	0.388627	+	0.921395i	$0.372949\pi$
$541$	−1.20272e12	+	2.08317e12i	−0.603638	+	1.04553i	−0.992265	+	0.124137i	$0.960384\pi$
$542$	2.80467e12			1.39600
$543$	−2.55770e12	+	4.43007e12i	−1.26256	+	2.18681i
$544$	−1.32768e12			−0.649976
$545$	−9.38175e11			−0.455512
$546$	−4.67530e12	−	5.73921e11i	−2.25135	−	0.276366i
$547$	−9.28183e11			−0.443293			−0.221646	−	0.975127i	$-0.571143\pi$
$547$	−9.28183e11			−0.443293			−0.221646	+	0.975127i	$0.571143\pi$
$548$	1.56173e12			0.739762
$549$	−7.68854e11	+	1.33169e12i	−0.361217	+	0.625646i
$550$	−1.12034e12			−0.522055
$551$	−1.03891e11	+	1.79945e11i	−0.0480173	+	0.0831683i
$552$	−1.18822e12	+	2.05806e12i	−0.544718	+	0.943480i
$553$	2.66189e11	−	2.76278e12i	0.121040	−	1.25627i
$554$	1.29677e11			0.0584883
$555$	3.62316e11	+	6.27550e11i	0.162095	+	0.280757i
$556$	−5.88016e11	+	1.01847e12i	−0.260947	+	0.451973i
$557$	1.51744e12	−	2.62828e12i	0.667978	−	1.15697i	−0.310490	−	0.950577i	$-0.600493\pi$
$557$	1.51744e12	−	2.62828e12i	0.667978	−	1.15697i	0.978469	−	0.206396i	$-0.0661734\pi$
$558$	5.09665e12	−	8.82766e12i	2.22552	−	3.85471i
$559$	2.77539e12	+	1.70043e12i	1.20218	+	0.736556i
$560$	−1.20308e11	+	1.24868e12i	−0.0516949	+	0.536542i
$561$	5.64514e11	+	9.77766e11i	0.240625	+	0.416776i
$562$	1.91949e12			0.811655
$563$	−2.56963e12			−1.07791			−0.538955	−	0.842335i	$-0.681181\pi$
$563$	−2.56963e12			−1.07791			−0.538955	+	0.842335i	$0.681181\pi$
$564$	2.13269e12	+	3.69393e12i	0.887509	+	1.53721i
$565$	8.57785e11	+	1.48573e12i	0.354128	+	0.613368i
$566$	2.05927e12	−	3.56676e12i	0.843412	−	1.46083i
$567$	2.64994e11	−	2.75037e12i	0.107674	−	1.11755i
$568$	2.88011e11	−	4.98849e11i	0.116102	−	0.201095i
$569$	3.86108e12			1.54420			0.772100	−	0.635501i	$-0.219206\pi$
$569$	3.86108e12			1.54420			0.772100	+	0.635501i	$0.219206\pi$
$570$	7.43707e10	−	1.28814e11i	0.0295097	−	0.0511123i
$571$	−2.29431e12	−	3.97386e12i	−0.903213	−	1.56441i	−0.823299	−	0.567608i	$-0.807869\pi$
$571$	−2.29431e12	−	3.97386e12i	−0.903213	−	1.56441i	−0.0799138	−	0.996802i	$-0.525465\pi$
$572$	−7.55665e11	−	4.62982e11i	−0.295153	−	0.180835i
$573$	−2.12819e12			−0.824734
$574$	−2.41107e12	−	1.72001e12i	−0.927055	−	0.661344i
$575$	−1.64139e12	−	2.84296e12i	−0.626189	−	1.08459i
$576$	8.59358e11	+	1.48845e12i	0.325292	+	0.563422i
$577$	−2.14422e12	−	3.71390e12i	−0.805338	−	1.39489i	−0.916063	−	0.401035i	$-0.868651\pi$
$577$	−2.14422e12	−	3.71390e12i	−0.805338	−	1.39489i	0.110725	−	0.993851i	$-0.464683\pi$
$578$	2.42725e12			0.904563
$579$	1.53806e12	+	2.66399e12i	0.568746	+	0.985097i
$580$	−1.37484e12			−0.504459
$581$	8.57417e11	−	3.90687e11i	0.312176	−	0.142245i
$582$	−2.17894e11	−	3.77404e11i	−0.0787213	−	0.136349i
$583$	1.48098e12			0.530936
$584$	4.48934e11	+	7.77576e11i	0.159707	+	0.276621i
$585$	6.70060e10	−	2.56739e12i	0.0236544	−	0.906339i
$586$	3.20449e11	−	5.55034e11i	0.112259	−	0.194438i
$587$	−2.16685e12	−	3.75309e12i	−0.753281	−	1.30472i	−0.946225	−	0.323510i	$-0.895137\pi$
$587$	−2.16685e12	−	3.75309e12i	−0.753281	−	1.30472i	0.192944	−	0.981210i	$-0.438196\pi$
$588$	−1.13866e12	−	3.30818e12i	−0.392824	−	1.14128i
$589$	1.43413e11	−	2.48398e11i	0.0490985	−	0.0850412i
$590$	9.24290e11	−	1.60092e12i	0.314032	−	0.543920i
$591$	1.16014e12			0.391171
$592$	−1.51682e12			−0.507558
$593$	1.44511e12	−	2.50301e12i	0.479905	−	0.831219i	−0.519830	−	0.854270i	$-0.674005\pi$
$593$	1.44511e12	−	2.50301e12i	0.479905	−	0.831219i	0.999734	+	0.0230507i	$0.00733791\pi$
$594$	1.79020e12	−	3.10073e12i	0.590016	−	1.02194i
$595$	−7.19095e10	+	7.46349e11i	−0.0235212	+	0.244127i
$596$	−1.53372e12	−	2.65647e12i	−0.497894	−	0.862377i
$597$	−2.67371e12	+	4.63100e12i	−0.861450	+	1.49207i
$598$	1.65623e11	−	6.34599e12i	0.0529621	−	2.02929i
$599$	−6.00618e11	−	1.04030e12i	−0.190624	−	0.330170i	0.754833	−	0.655917i	$-0.227718\pi$
$599$	−6.00618e11	−	1.04030e12i	−0.190624	−	0.330170i	−0.945457	+	0.325746i	$0.894384\pi$
$600$	1.77865e12			0.560285
$601$	−9.49956e11	−	1.64537e12i	−0.297008	−	0.514433i	0.678442	−	0.734654i	$-0.262655\pi$
$601$	−9.49956e11	−	1.64537e12i	−0.297008	−	0.514433i	−0.975450	+	0.220221i	$0.929322\pi$
$602$	−5.66802e11	+	5.88285e12i	−0.175893	+	1.82559i
$603$	−6.23062e12			−1.91913
$604$	1.77529e12	+	3.07489e12i	0.542754	+	0.940077i
$605$	−1.09815e12			−0.333243
$606$	1.86324e12	+	3.22722e12i	0.561231	+	0.972080i
$607$	1.45349e12	+	2.51751e12i	0.434572	+	0.752701i	0.997261	−	0.0739682i	$-0.0235663\pi$
$607$	1.45349e12	+	2.51751e12i	0.434572	+	0.752701i	−0.562689	+	0.826669i	$0.690233\pi$
$608$	1.16176e11	+	2.01222e11i	0.0344785	+	0.0597186i
$609$	−8.83343e12	+	4.02500e12i	−2.60226	+	1.18574i
$610$	−6.99895e11			−0.204667
$611$	4.31989e12	+	2.64672e12i	1.25397	+	0.768284i
$612$	1.35267e12	+	2.34290e12i	0.389772	+	0.675105i
$613$	−3.05824e11	+	5.29703e11i	−0.0874782	+	0.151517i	−0.906445	−	0.422325i	$-0.861214\pi$
$613$	−3.05824e11	+	5.29703e11i	−0.0874782	+	0.151517i	0.818966	+	0.573842i	$0.194547\pi$
$614$	−5.21169e12			−1.47986
$615$	1.20313e12	−	2.08388e12i	0.339136	−	0.587400i
$616$	−6.86187e10	+	7.12194e11i	−0.0192012	+	0.199290i
$617$	−1.87737e12	+	3.25169e12i	−0.521514	+	0.903288i	0.478173	+	0.878266i	$0.341299\pi$
$617$	−1.87737e12	+	3.25169e12i	−0.521514	+	0.903288i	−0.999687	+	0.0250227i	$0.992034\pi$
$618$	7.33066e10	+	1.26971e11i	0.0202160	+	0.0350151i
$619$	2.09640e12	+	3.63107e12i	0.573939	+	0.994092i	0.996156	+	0.0875973i	$0.0279189\pi$
$619$	2.09640e12	+	3.63107e12i	0.573939	+	0.994092i	−0.422217	+	0.906495i	$0.638748\pi$
$620$	1.89784e12			0.515819
$621$	1.04912e13			2.83083
$622$	1.66248e12	+	2.87949e12i	0.445347	+	0.771364i
$623$	−1.44809e12	+	6.59830e11i	−0.385123	+	0.175483i
$624$	6.83066e12	+	4.18501e12i	1.80356	+	1.10501i
$625$	−8.51882e11	+	1.47550e12i	−0.223316	+	0.386794i
$626$	3.70265e12	−	6.41318e12i	0.963670	−	1.66913i
$627$	9.87932e10	−	1.71115e11i	0.0255284	−	0.0442165i
$628$	−8.57192e10	−	1.48470e11i	−0.0219917	−	0.0380908i
$629$	−9.06620e11			−0.230939
$630$	4.24359e12	−	1.93361e12i	1.07325	−	0.489032i
$631$	4.53237e11	−	7.85029e11i	0.113813	−	0.197130i	−0.803491	−	0.595316i	$-0.797027\pi$
$631$	4.53237e11	−	7.85029e11i	0.113813	−	0.197130i	0.917305	+	0.398186i	$0.130360\pi$
$632$	−1.01335e12	+	1.75518e12i	−0.252659	+	0.437618i
$633$	9.37877e11			0.232182
$634$	−1.62779e12	+	2.81941e12i	−0.400125	+	0.693036i
$635$	−4.22251e11			−0.103060
$636$	5.28794e12			1.28153
$637$	−3.06370e12	−	2.80754e12i	−0.737257	−	0.675613i
$638$	−4.46470e12			−1.06684
$639$	−4.98721e12			−1.18333
$640$	7.19352e11	−	1.24595e12i	0.169485	−	0.293557i
$641$	5.56702e12			1.30245			0.651226	−	0.758884i	$-0.274255\pi$
$641$	5.56702e12			1.30245			0.651226	+	0.758884i	$0.274255\pi$
$642$	−7.31946e12	+	1.26777e13i	−1.70048	+	2.94532i
$643$	−3.42162e11	+	5.92642e11i	−0.0789373	+	0.136723i	−0.902792	−	0.430078i	$-0.858486\pi$
$643$	−3.42162e11	+	5.92642e11i	−0.0789373	+	0.136723i	0.823854	+	0.566802i	$0.191819\pi$
$644$	4.29068e12	−	1.95507e12i	0.982970	−	0.447895i
$645$	−4.80169e12			−1.09238
$646$	9.30485e10	+	1.61165e11i	0.0210215	+	0.0364102i
$647$	−1.96724e12	+	3.40737e12i	−0.441356	+	0.764451i	−0.997790	−	0.0664405i	$-0.978836\pi$
$647$	−1.96724e12	+	3.40737e12i	−0.441356	+	0.764451i	0.556434	+	0.830892i	$0.312169\pi$
$648$	−1.00880e12	+	1.74730e12i	−0.224760	+	0.389295i
$649$	1.22782e12	−	2.12664e12i	0.271664	−	0.470537i
$650$	−4.17529e12	+	2.26747e12i	−0.917438	+	0.498232i
$651$	1.21937e13	−	5.55614e12i	2.66086	−	1.21244i
$652$	2.92910e12	+	5.07335e12i	0.634775	+	1.09946i
$653$	6.02265e12			1.29622			0.648109	−	0.761547i	$-0.275560\pi$
$653$	6.02265e12			1.29622			0.648109	+	0.761547i	$0.275560\pi$
$654$	−1.08783e13			−2.32520
$655$	−1.83072e12	−	3.17089e12i	−0.388629	−	0.673125i
$656$	2.51841e12	+	4.36202e12i	0.530957	+	0.919645i
$657$	3.88689e12	−	6.73229e12i	0.813875	−	1.40967i
$658$	−8.82227e11	+	9.15664e12i	−0.183469	+	1.90423i
$659$	1.38949e12	−	2.40667e12i	0.286993	−	0.497087i	−0.686097	−	0.727510i	$-0.740678\pi$
$659$	1.38949e12	−	2.40667e12i	0.286993	−	0.497087i	0.973091	+	0.230423i	$0.0740109\pi$
$660$	1.30737e12			0.268196
$661$	−4.06038e12	+	7.03278e12i	−0.827294	+	1.43292i	0.0728595	+	0.997342i	$0.476788\pi$
$661$	−4.06038e12	+	7.03278e12i	−0.827294	+	1.43292i	−0.900153	+	0.435573i	$0.856546\pi$
$662$	−2.79639e12	−	4.84348e12i	−0.565895	−	0.980160i
$663$	4.08277e12	+	2.50143e12i	0.820623	+	0.502780i
$664$	−6.88012e11			−0.137353
$665$	1.19409e11	−	5.44092e10i	0.0236776	−	0.0107888i
$666$	2.81933e12	+	4.88322e12i	0.555280	+	0.961772i
$667$	−6.54116e12	−	1.13296e13i	−1.27964	−	2.21640i
$668$	−5.87834e11	−	1.01816e12i	−0.114225	−	0.197843i
$669$	−4.03727e12			−0.779239
$670$	−1.41795e12	−	2.45596e12i	−0.271847	−	0.470852i
$671$	−9.29733e11			−0.177055
$672$	−1.04104e12	+	1.08050e13i	−0.196927	+	2.04391i
$673$	−2.10965e12	−	3.65403e12i	−0.396409	−	0.686601i	0.596871	−	0.802337i	$-0.296410\pi$
$673$	−2.10965e12	−	3.65403e12i	−0.396409	−	0.686601i	−0.993280	+	0.115737i	$0.963077\pi$
$674$	−6.94659e12			−1.29659
$675$	−3.92606e12	−	6.80014e12i	−0.727931	−	1.26081i
$676$	−3.75327e12	−	1.96046e11i	−0.691273	−	0.0361075i
$677$	1.09652e12	−	1.89922e12i	0.200616	−	0.347478i	−0.748111	−	0.663574i	$-0.769039\pi$
$677$	1.09652e12	−	1.89922e12i	0.200616	−	0.347478i	0.948727	+	0.316096i	$0.102372\pi$
$678$	9.94612e12	+	1.72272e13i	1.80767	+	3.13098i
$679$	3.68708e10	−	3.82683e11i	0.00665685	−	0.0690915i
$680$	2.73752e11	−	4.74152e11i	0.0490984	−	0.0850409i
$681$	4.07742e12	−	7.06229e12i	0.726479	−	1.25830i
$682$	6.16311e12			1.09086
$683$	−7.94846e12			−1.39762			−0.698811	−	0.715306i	$-0.746287\pi$
$683$	−7.94846e12			−1.39762			−0.698811	+	0.715306i	$0.746287\pi$
$684$	2.36726e11	−	4.10021e11i	0.0413516	−	0.0716231i
$685$	−1.36823e12	+	2.36984e12i	−0.237439	+	0.411256i
$686$	2.14430e12	−	7.23437e12i	0.369682	−	1.24722i
$687$	2.66788e12	+	4.62090e12i	0.456942	+	0.791446i
$688$	5.02551e12	−	8.70444e12i	0.855130	−	1.48113i
$689$	5.51937e12	−	2.99740e12i	0.933046	−	0.506708i
$690$	4.68249e12	+	8.11031e12i	0.786422	+	1.36212i
$691$	−4.35415e12			−0.726527			−0.363264	−	0.931686i	$-0.618338\pi$
$691$	−4.35415e12			−0.726527			−0.363264	+	0.931686i	$0.618338\pi$
$692$	−1.69840e11	−	2.94172e11i	−0.0281555	−	0.0487668i
$693$	5.63714e12	−	2.56859e12i	0.928452	−	0.423054i
$694$	5.88106e12			0.962361
$695$	−1.03032e12	−	1.78457e12i	−0.167510	−	0.290136i
$696$	7.08816e12			1.14496
$697$	1.50529e12	+	2.60723e12i	0.241586	+	0.418439i
$698$	5.66523e12	+	9.81246e12i	0.903375	+	1.56469i
$699$	−3.28615e12	−	5.69178e12i	−0.520643	−	0.901781i
$700$	−2.87291e12	−	2.04948e12i	−0.452252	−	0.322628i
$701$	−9.92904e12			−1.55302			−0.776508	−	0.630107i	$-0.783011\pi$
$701$	−9.92904e12			−1.55302			−0.776508	+	0.630107i	$0.783011\pi$
$702$	3.96157e11	−	1.51791e13i	0.0615673	−	2.35901i
$703$	7.93320e10	+	1.37407e11i	0.0122504	+	0.0212183i
$704$	−5.19588e11	+	8.99952e11i	−0.0797227	+	0.138084i
$705$	−7.47383e12			−1.13944
$706$	−1.95554e12	+	3.38710e12i	−0.296242	+	0.513106i
$707$	−3.15287e11	+	3.27236e12i	−0.0474590	+	0.492577i
$708$	4.38399e12	−	7.59329e12i	0.655722	−	1.13574i
$709$	−4.64385e12	−	8.04339e12i	−0.690193	−	1.19545i	−0.971774	−	0.235912i	$-0.924192\pi$
$709$	−4.64385e12	−	8.04339e12i	−0.690193	−	1.19545i	0.281581	−	0.959537i	$-0.409141\pi$
$710$	−1.13498e12	−	1.96584e12i	−0.167620	−	0.290326i
$711$	1.75473e13			2.57512
$712$	1.16198e12			0.169449
$713$	9.02947e12	+	1.56395e13i	1.30846	+	2.26631i
$714$	−8.33800e11	+	8.65402e12i	−0.120066	+	1.24617i
$715$	1.36459e12	−	7.41067e11i	0.195266	−	0.106043i
$716$	2.71018e11	−	4.69416e11i	0.0385380	−	0.0667497i
$717$	−2.51651e12	+	4.35872e12i	−0.355601	+	0.615918i
$718$	−1.28675e12	+	2.22871e12i	−0.180690	+	0.312964i
$719$	−7.13828e11	−	1.23639e12i	−0.0996125	−	0.172534i	0.811912	−	0.583780i	$-0.198427\pi$
$719$	−7.13828e11	−	1.23639e12i	−0.0996125	−	0.172534i	−0.911524	+	0.411246i	$0.865094\pi$
$720$	−7.93076e12			−1.09981
$721$	−1.24045e10	+	1.28747e11i	−0.00170951	+	0.0177430i
$722$	−4.73286e12	+	8.19755e12i	−0.648196	+	1.12271i
$723$	5.02895e12	−	8.71040e12i	0.684471	−	1.18554i
$724$	−7.41110e12			−1.00244
$725$	−4.89572e12	+	8.47963e12i	−0.658105	+	1.13987i
$726$	−1.27331e13			−1.70106
$727$	5.31663e12			0.705882			0.352941	−	0.935646i	$-0.385182\pi$
$727$	5.31663e12			0.705882			0.352941	+	0.935646i	$0.385182\pi$
$728$	1.18569e12	+	2.79310e12i	0.156452	+	0.368549i
$729$	−6.65196e12			−0.872320
$730$	3.53827e12			0.461146
$731$	3.00381e12	−	5.20275e12i	0.389084	−	0.673914i
$732$	−3.31966e12			−0.427360
$733$	−1.94038e12	+	3.36083e12i	−0.248266	+	0.430010i	−0.963045	−	0.269341i	$-0.913194\pi$
$733$	−1.94038e12	+	3.36083e12i	−0.248266	+	0.430010i	0.714778	+	0.699351i	$0.246528\pi$
$734$	3.61067e12	−	6.25386e12i	0.459151	−	0.795272i
$735$	6.01760e12	+	1.17044e12i	0.760554	+	0.147929i
$736$	−1.46292e13			−1.83768
$737$	−1.88359e12	−	3.26247e12i	−0.235170	−	0.407327i
$738$	9.36201e12	−	1.62155e13i	1.16176	−	2.01222i
$739$	6.38444e12	−	1.10582e13i	0.787450	−	1.36390i	−0.140075	−	0.990141i	$-0.544734\pi$
$739$	6.38444e12	−	1.10582e13i	0.787450	−	1.36390i	0.927525	−	0.373762i	$-0.121932\pi$
$740$	−5.24917e11	+	9.09183e11i	−0.0643499	+	0.111457i
$741$	2.18621e10	−	8.37665e11i	0.00266385	−	0.102068i
$742$	9.28407e12	+	6.62308e12i	1.12440	+	0.802126i
$743$	1.77075e12	+	3.06703e12i	0.213161	+	0.369206i	0.952702	−	0.303906i	$-0.0982907\pi$
$743$	1.77075e12	+	3.06703e12i	0.213161	+	0.369206i	−0.739541	+	0.673112i	$0.764957\pi$
$744$	−9.78455e12			−1.17075
$745$	5.37476e12			0.639228
$746$	−9.93666e12	−	1.72108e13i	−1.17467	−	2.03459i
$747$	2.97842e12	+	5.15877e12i	0.349980	+	0.606183i
$748$	−8.17857e11	+	1.41657e12i	−0.0955256	+	0.165455i
$749$	−1.17520e13	+	5.35488e12i	−1.36441	+	0.621701i
$750$	7.87144e12	−	1.36337e13i	0.908402	−	1.57340i
$751$	7.38930e12			0.847663			0.423832	−	0.905741i	$-0.360685\pi$
$751$	7.38930e12			0.847663			0.423832	+	0.905741i	$0.360685\pi$
$752$	7.82219e12	−	1.35484e13i	0.891966	−	1.54493i
$753$	1.04216e13	+	1.80507e13i	1.18129	+	2.04605i
$754$	−1.66391e13	+	9.03619e12i	−1.87482	+	1.01816i
$755$	−6.22133e12			−0.696823
$756$	1.02630e13	−	4.67637e12i	1.14268	−	0.520668i
$757$	4.54324e12	+	7.86912e12i	0.502845	+	0.870953i	0.999995	+	0.00328816i	$0.00104666\pi$
$757$	4.54324e12	+	7.86912e12i	0.502845	+	0.870953i	−0.497150	+	0.867665i	$0.665620\pi$
$758$	−7.31150e12	−	1.26639e13i	−0.804443	−	1.39334i
$759$	6.22017e12	+	1.07736e13i	0.680322	+	1.17835i
$760$	−9.58164e10			−0.0104179
$761$	−2.00210e12	−	3.46775e12i	−0.216399	−	0.374814i	0.737305	−	0.675560i	$-0.236098\pi$
$761$	−2.00210e12	−	3.46775e12i	−0.216399	−	0.374814i	−0.953705	+	0.300745i	$0.902765\pi$
$762$	−4.89605e12			−0.526076
$763$	−7.81263e12	−	5.57339e12i	−0.834521	−	0.595332i
$764$	−1.54164e12	−	2.67020e12i	−0.163705	−	0.283546i
$765$	−4.74031e12			−0.500415
$766$	−4.48102e12	−	7.76135e12i	−0.470270	−	0.814531i
$767$	2.71705e11	−	1.04106e13i	0.0283478	−	1.08617i
$768$	1.10211e13	−	1.90891e13i	1.14314	−	1.97998i
$769$	2.39095e12	+	4.14124e12i	0.246548	+	0.427034i	0.962566	−	0.271048i	$-0.0873703\pi$
$769$	2.39095e12	+	4.14124e12i	0.246548	+	0.427034i	−0.716018	+	0.698082i	$0.754037\pi$
$770$	2.29536e12	+	1.63747e12i	0.235312	+	0.167867i
$771$	−1.35653e12	+	2.34957e12i	−0.138256	+	0.239466i
$772$	−2.22831e12	+	3.85954e12i	−0.225786	+	0.391073i
$773$	−1.14702e13			−1.15548			−0.577741	−	0.816220i	$-0.696066\pi$
$773$	−1.14702e13			−1.15548			−0.577741	+	0.816220i	$0.696066\pi$
$774$	−3.73639e13			−3.74212
$775$	6.75809e12	−	1.17054e13i	0.672924	−	1.16554i
$776$	−1.40363e11	+	2.43116e11i	−0.0138956	+	0.0240678i
$777$	−7.10888e11	+	7.37831e12i	−0.0699691	+	0.726210i
$778$	−2.79621e12	−	4.84319e12i	−0.273629	−	0.473939i
$779$	2.63434e11	−	4.56281e11i	0.0256303	−	0.0443929i
$780$	4.87235e12	−	2.64602e12i	0.471317	−	0.255957i
$781$	−1.50769e12	−	2.61140e12i	−0.145005	−	0.251156i
$782$	−1.17169e13			−1.12043
$783$	−1.56459e13	−	2.70995e13i	−1.48755	−	2.57652i
$784$	−8.41984e12	+	9.68362e12i	−0.795942	+	0.915409i
$785$	3.00395e11			0.0282344
$786$	−2.12274e13	−	3.67669e13i	−1.98379	−	3.43602i
$787$	−2.19788e11			−0.0204229			−0.0102115	−	0.999948i	$-0.503250\pi$
$787$	−2.19788e11			−0.0204229			−0.0102115	+	0.999948i	$0.503250\pi$
$788$	8.40394e11	+	1.45561e12i	0.0776453	+	0.134486i
$789$	1.28554e13	+	2.22662e13i	1.18097	+	2.04550i
$790$	3.99338e12	+	6.91673e12i	0.364769	+	0.631799i
$791$	−1.68303e12	+	1.74682e13i	−0.152861	+	1.58655i
$792$	−4.52338e12			−0.408507
$793$	−3.46495e12	+	1.88171e12i	−0.311149	+	0.168975i
$794$	6.47010e12	+	1.12065e13i	0.577722	+	1.00064i
$795$	−4.63277e12	+	8.02419e12i	−0.411328	+	0.712441i
$796$	−7.74724e12			−0.683972
$797$	8.99708e12	−	1.55834e13i	0.789840	−	1.36804i	−0.136224	−	0.990678i	$-0.543497\pi$
$797$	8.99708e12	−	1.55834e13i	0.789840	−	1.36804i	0.926064	−	0.377365i	$-0.123170\pi$
$798$	1.38456e12	−	6.30882e11i	0.120864	−	0.0550725i
$799$	4.67542e12	−	8.09806e12i	0.405845	−	0.702944i
$800$	5.47459e12	+	9.48226e12i	0.472548	+	0.818478i
$801$	−5.03024e12	−	8.71264e12i	−0.431760	−	0.747831i
$802$	5.43617e12			0.463990
$803$	4.70020e12			0.398930
$804$	−6.72546e12	−	1.16488e13i	−0.567636	−	0.983174i
$805$	−7.92344e11	+	8.22375e12i	−0.0665017	+	0.690222i
$806$	2.29688e13	−	1.24736e13i	1.91704	−	1.04108i
$807$	−1.57395e13	+	2.72617e13i	−1.30635	+	2.26267i
$808$	1.20026e12	−	2.07892e12i	0.0990662	−	0.171588i
$809$	6.98141e12	−	1.20922e13i	0.573027	−	0.992511i	−0.423226	−	0.906024i	$-0.639102\pi$
$809$	6.98141e12	−	1.20922e13i	0.573027	−	0.992511i	0.996253	−	0.0864872i	$-0.0275642\pi$
$810$	3.97544e12	+	6.88566e12i	0.324491	+	0.562035i
$811$	2.76656e12			0.224567			0.112284	−	0.993676i	$-0.464184\pi$
$811$	2.76656e12			0.224567			0.112284	+	0.993676i	$0.464184\pi$
$812$	−1.14489e13	−	8.16746e12i	−0.924194	−	0.659303i
$813$	−1.16546e13	+	2.01864e13i	−0.935600	+	1.62051i
$814$	−1.70463e12	+	2.95251e12i	−0.136088	+	0.235712i
$815$	−1.02648e13			−0.814966
$816$	7.39282e12	−	1.28047e13i	0.583720	−	1.01103i
$817$	−1.05137e12			−0.0825573
$818$	4.53859e12			0.354431
$819$	1.58100e13	−	2.09818e13i	1.22788	−	1.62954i
$820$	3.48613e12			0.269266
$821$	2.53938e13			1.95067			0.975333	−	0.220739i	$-0.0708469\pi$
$821$	2.53938e13			1.95067			0.975333	+	0.220739i	$0.0708469\pi$
$822$	−1.58648e13	+	2.74786e13i	−1.21202	+	2.09929i
$823$	7.67654e12			0.583266			0.291633	−	0.956530i	$-0.405801\pi$
$823$	7.67654e12			0.583266			0.291633	+	0.956530i	$0.405801\pi$
$824$	4.72228e10	−	8.17922e10i	0.00356844	−	0.00618073i
$825$	4.65547e12	−	8.06351e12i	0.349881	−	0.606013i
$826$	1.72075e13	−	7.84070e12i	1.28620	−	0.586063i
$827$	5.29541e12			0.393663			0.196831	−	0.980437i	$-0.436935\pi$
$827$	5.29541e12			0.393663			0.196831	+	0.980437i	$0.436935\pi$
$828$	1.49046e13	+	2.58155e13i	1.10201	+	1.90873i
$829$	−7.45357e12	+	1.29100e13i	−0.548111	+	0.949357i	0.450293	+	0.892881i	$0.351320\pi$
$829$	−7.45357e12	+	1.29100e13i	−0.548111	+	0.949357i	−0.998404	+	0.0564756i	$0.982014\pi$
$830$	−1.35564e12	+	2.34804e12i	−0.0991502	+	0.171733i
$831$	−5.38864e11	+	9.33339e11i	−0.0391989	+	0.0678946i
$832$	−1.14980e11	+	4.40557e12i	−0.00831895	+	0.318748i
$833$	−5.03264e12	+	5.78802e12i	−0.362154	+	0.416512i
$834$	−1.19467e13	−	2.06923e13i	−0.855070	−	1.48102i
$835$	2.06001e12			0.146649
$836$	2.86259e11			0.0202690
$837$	2.15978e13	+	3.74084e13i	1.52105	+	2.63454i
$838$	−1.03437e13	−	1.79159e13i	−0.724568	−	1.25499i
$839$	−1.15305e13	+	1.99715e13i	−0.803379	+	1.39149i	0.114002	+	0.993481i	$0.463633\pi$
$839$	−1.15305e13	+	1.99715e13i	−0.803379	+	1.39149i	−0.917380	+	0.398012i	$0.869700\pi$
$840$	−3.64412e12	−	2.59965e12i	−0.252543	−	0.180160i
$841$	−1.22566e13	+	2.12290e13i	−0.844863	+	1.46335i
$842$	2.25605e13			1.54684
$843$	−7.97628e12	+	1.38153e13i	−0.543972	+	0.942187i
$844$	6.79389e11	+	1.17674e12i	0.0460869	+	0.0798248i
$845$	3.58574e12	−	5.52365e12i	0.241949	−	0.372710i
$846$	−5.81568e13			−3.90332
$847$	−9.14478e12	−	6.52372e12i	−0.610517	−	0.435532i
$848$	−9.69742e12	−	1.67964e13i	−0.643984	−	1.11541i
$849$	1.71143e13	+	2.96429e13i	1.13051	+	1.95810i
$850$	4.38476e12	+	7.59463e12i	0.288112	+	0.499024i
$851$	−9.98972e12			−0.652935
$852$	−5.38330e12	−	9.32415e12i	−0.350002	−	0.606221i
$853$	2.62726e13			1.69915			0.849577	−	0.527464i	$-0.176857\pi$
$853$	2.62726e13			1.69915			0.849577	+	0.527464i	$0.176857\pi$
$854$	−5.82836e12	−	4.15784e12i	−0.374961	−	0.267490i
$855$	4.14791e11	+	7.18439e11i	0.0265450	+	0.0459772i
$856$	9.43012e12			0.600323
$857$	2.52192e12	+	4.36809e12i	0.159705	+	0.276616i	0.934762	−	0.355274i	$-0.115613\pi$
$857$	2.52192e12	+	4.36809e12i	0.159705	+	0.276616i	−0.775058	+	0.631891i	$0.782279\pi$
$858$	1.58226e13	−	8.59277e12i	0.996749	−	0.541303i
$859$	−1.16418e13	+	2.01641e13i	−0.729541	+	1.26360i	0.227536	+	0.973770i	$0.426933\pi$
$859$	−1.16418e13	+	2.01641e13i	−0.729541	+	1.26360i	−0.957077	+	0.289832i	$0.906400\pi$
$860$	−3.47830e12	−	6.02459e12i	−0.216832	−	0.375565i
$861$	2.23986e13	−	1.02061e13i	1.38902	−	0.632913i
$862$	−9.40267e12	+	1.62859e13i	−0.580054	+	1.00468i
$863$	5.14337e12	−	8.90859e12i	0.315645	−	0.546714i	−0.663929	−	0.747796i	$-0.731112\pi$
$863$	5.14337e12	−	8.90859e12i	0.315645	−	0.546714i	0.979574	+	0.201082i	$0.0644456\pi$
$864$	−3.49918e13			−2.13626
$865$	5.95189e11			0.0361479
$866$	−4.24193e12	+	7.34724e12i	−0.256291	+	0.443909i
$867$	−1.00863e13	+	1.74699e13i	−0.606239	+	1.05004i
$868$	1.58042e13	+	1.12744e13i	0.945005	+	0.674149i
$869$	5.30476e12	+	9.18811e12i	0.315556	+	0.546559i
$870$	1.39663e13	−	2.41904e13i	0.826505	−	1.43155i
$871$	−1.36228e13	−	8.34643e12i	−0.802019	−	0.491382i
$872$	3.50379e12	+	6.06874e12i	0.205217	+	0.355447i
$873$	2.43054e12			0.141625
$874$	1.02527e12	+	1.77581e12i	0.0594341	+	0.102943i
$875$	1.26383e13	−	5.75870e12i	0.728873	−	0.332115i
$876$	1.67823e13			0.962906
$877$	3.16178e12	+	5.47636e12i	0.180482	+	0.312604i	0.942045	−	0.335487i	$-0.108901\pi$
$877$	3.16178e12	+	5.47636e12i	0.180482	+	0.312604i	−0.761563	+	0.648091i	$0.775568\pi$
$878$	3.31301e13			1.88147
$879$	2.66321e12	+	4.61281e12i	0.150472	+	0.260625i
$880$	−2.39756e12	−	4.15270e12i	−0.134771	−	0.233431i
$881$	−4.31112e12	−	7.46708e12i	−0.241101	−	0.417599i	0.719927	−	0.694049i	$-0.244175\pi$
$881$	−4.31112e12	−	7.46708e12i	−0.241101	−	0.417599i	−0.961028	+	0.276451i	$0.910842\pi$
$882$	4.68254e13	+	9.10763e12i	2.60539	+	0.506754i
$883$	1.49492e13			0.827554			0.413777	−	0.910378i	$-0.364209\pi$
$883$	1.49492e13			0.827554			0.413777	+	0.910378i	$0.364209\pi$
$884$	−1.80985e11	+	6.93458e12i	−0.00996796	+	0.381931i
$885$	7.68164e12	+	1.33050e13i	0.420929	+	0.729071i
$886$	1.46624e13	−	2.53961e13i	0.799381	−	1.38457i
$887$	−2.95807e13			−1.60455			−0.802274	−	0.596956i	$-0.796377\pi$
$887$	−2.95807e13			−1.60455			−0.802274	+	0.596956i	$0.796377\pi$
$888$	2.70627e12	−	4.68740e12i	0.146054	−	0.252973i
$889$	−3.51628e12	−	2.50845e12i	−0.188810	−	0.134694i
$890$	2.28954e12	−	3.96560e12i	0.122319	−	0.211862i
$891$	5.28093e12	+	9.14684e12i	0.280712	+	0.486207i
$892$	−2.92456e12	−	5.06549e12i	−0.154675	−	0.267904i
$893$	−1.63645e12			−0.0861136
$894$	6.23211e13			3.26299
$895$	4.74878e11	+	8.22513e11i	0.0247388	+	0.0428488i
$896$	1.33922e13	−	6.10222e12i	0.694169	−	0.316302i
$897$	4.49865e13	+	2.75624e13i	2.32015	+	1.42151i
$898$	−1.54883e13	+	2.68265e13i	−0.794804	+	1.37664i
$899$	2.69320e13	−	4.66475e13i	1.37515	−	2.38182i
$900$	1.11553e13	−	1.93216e13i	0.566748	−	0.981637i
$901$	−5.79627e12	−	1.00394e13i	−0.293013	−	0.507513i
$902$	1.13210e13			0.569449
$903$	−3.99860e13	−	2.85253e13i	−2.00130	−	1.42769i
$904$	6.40711e12	−	1.10974e13i	0.319083	−	0.552669i
$905$	6.49288e12	−	1.12460e13i	0.321750	−	0.557287i
$906$	−7.21372e13			−3.55699
$907$	5.93945e11	−	1.02874e12i	0.0291416	−	0.0504747i	−0.851087	−	0.525025i	$-0.824056\pi$
$907$	5.93945e11	−	1.02874e12i	0.0291416	−	0.0504747i	0.880228	+	0.474550i	$0.157389\pi$
$908$	1.18146e13			0.576808
$909$	−2.07839e13			−1.00969
$910$	1.18685e13	+	1.45693e12i	0.573734	+	0.0704292i
$911$	6.60849e12			0.317884			0.158942	−	0.987288i	$-0.449192\pi$
$911$	6.60849e12			0.317884			0.158942	+	0.987288i	$0.449192\pi$
$912$	−2.58757e12			−0.123856
$913$	−1.80082e12	+	3.11911e12i	−0.0857733	+	0.148564i
$914$	2.80160e13			1.32785
$915$	2.90836e12	−	5.03743e12i	0.137168	−	0.237582i
$916$	−3.86517e12	+	6.69467e12i	−0.181401	+	0.314195i
$917$	3.59198e12	−	3.72812e13i	0.167754	−	1.74112i
$918$	−2.80260e13			−1.30247
$919$	2.54788e12	+	4.41305e12i	0.117831	+	0.204089i	0.918908	−	0.394472i	$-0.129073\pi$
$919$	2.54788e12	+	4.41305e12i	0.117831	+	0.204089i	−0.801077	+	0.598561i	$0.795739\pi$
$920$	3.01637e12	−	5.22451e12i	0.138816	−	0.240436i
$921$	2.16568e13	−	3.75107e13i	0.991805	−	1.71786i
$922$	−5.26966e12	+	9.12731e12i	−0.240156	+	0.415962i
$923$	−1.09042e13	−	6.68078e12i	−0.494521	−	0.302984i
$924$	1.08871e13	+	7.76667e12i	0.491348	+	0.350518i
$925$	3.73839e12	+	6.47508e12i	0.167899	+	0.290809i
$926$	−6.13433e12			−0.274169
$927$	−8.17713e11			−0.0363699
$928$	2.18170e13	+	3.77882e13i	0.965671	+	1.67259i
$929$	−8.39681e12	−	1.45437e13i	−0.369865	−	0.640626i	0.619679	−	0.784856i	$-0.287263\pi$
$929$	−8.39681e12	−	1.45437e13i	−0.369865	−	0.640626i	−0.989544	+	0.144230i	$0.953930\pi$
$930$	−1.92792e13	+	3.33926e13i	−0.845116	+	1.46378i
$931$	1.31760e12	+	2.56276e11i	0.0574791	+	0.0111798i
$932$	4.76091e12	−	8.24614e12i	0.206690	−	0.357997i
$933$	−2.76332e13			−1.19389
$934$	−9.59436e12	+	1.66179e13i	−0.412530	+	0.714522i
$935$	−1.43305e12	−	2.48212e12i	−0.0613210	−	0.106211i
$936$	−1.68578e13	+	9.15496e12i	−0.717895	+	0.389866i
$937$	7.87570e12			0.333781			0.166890	−	0.985975i	$-0.446627\pi$
$937$	7.87570e12			0.333781			0.166890	+	0.985975i	$0.446627\pi$
$938$	2.78211e12	−	2.88755e13i	0.117344	−	1.21791i
$939$	3.07722e13	+	5.32990e13i	1.29171	+	2.23730i
$940$	−5.41397e12	−	9.37727e12i	−0.226173	−	0.391743i
$941$	1.07860e13	+	1.86820e13i	0.448444	+	0.776728i	0.998285	−	0.0585412i	$-0.0186449\pi$
$941$	1.07860e13	+	1.86820e13i	0.448444	+	0.776728i	−0.549841	+	0.835270i	$0.685312\pi$
$942$	3.48312e12			0.144125
$943$	1.65862e13	+	2.87281e13i	0.683037	+	1.18305i
$944$	−3.21588e13			−1.31803
$945$	−1.89522e12	+	1.96705e13i	−0.0773067	+	0.802367i
$946$	−1.12955e13	−	1.95645e13i	−0.458561	−	0.794251i
$947$	−1.30837e13			−0.528635			−0.264317	−	0.964436i	$-0.585147\pi$
$947$	−1.30837e13			−0.528635			−0.264317	+	0.964436i	$0.585147\pi$
$948$	1.89409e13	+	3.28067e13i	0.761665	+	1.31924i
$949$	1.75168e13	−	9.51284e12i	0.701064	−	0.380726i
$950$	7.67359e11	−	1.32910e12i	0.0305663	−	0.0529423i
$951$	−1.35283e13	−	2.34317e13i	−0.536328	−	0.928947i
$952$	5.09644e12	−	2.32222e12i	0.201095	−	0.0916299i
$953$	−2.28721e13	+	3.96157e13i	−0.898233	+	1.55578i	−0.0684803	+	0.997652i	$0.521815\pi$
$953$	−2.28721e13	+	3.96157e13i	−0.898233	+	1.55578i	−0.829752	+	0.558132i	$0.811518\pi$
$954$	−3.60494e13	+	6.24395e13i	−1.40906	+	2.44057i
$955$	5.40253e12			0.210175
$956$	−7.29174e12			−0.282339
$957$	1.85527e13	−	3.21343e13i	0.714997	−	1.23841i
$958$	−8.01132e11	+	1.38760e12i	−0.0307298	+	0.0532255i
$959$	−2.54724e13	+	1.16066e13i	−0.972490	+	0.443120i
$960$	−3.25072e12	−	5.63041e12i	−0.123526	−	0.213953i
$961$	−2.39573e13	+	4.14952e13i	−0.906113	+	1.56943i
$962$	−3.77220e11	+	1.44535e13i	−0.0142006	+	0.544109i
$963$	−4.08232e13	−	7.07078e13i	−1.52964	−	2.64941i
$964$	1.45717e13			0.543455
$965$	−3.90444e12	−	6.76269e12i	−0.144939	−	0.251042i
$966$	−9.18734e12	+	9.53555e13i	−0.339463	+	3.52329i
$967$	2.94633e13			1.08358			0.541792	−	0.840512i	$-0.317746\pi$
$967$	2.94633e13			1.08358			0.541792	+	0.840512i	$0.317746\pi$
$968$	4.10123e12	+	7.10353e12i	0.150132	+	0.260037i
$969$	−1.54662e12			−0.0563544
$970$	5.53137e11	+	9.58061e11i	0.0200613	+	0.0347472i
$971$	5.78721e12	+	1.00237e13i	0.208921	+	0.361862i	0.951375	−	0.308035i	$-0.0996714\pi$
$971$	5.78721e12	+	1.00237e13i	0.208921	+	0.361862i	−0.742454	+	0.669897i	$0.766338\pi$
$972$	1.38322e12	+	2.39581e12i	0.0497043	+	0.0860904i
$973$	2.02156e12	−	2.09818e13i	0.0723067	−	0.750472i
$974$	2.13357e13			0.759610
$975$	1.03022e12	−	3.94736e13i	0.0365096	−	1.39890i
$976$	6.08785e12	+	1.05445e13i	0.214753	+	0.371964i
$977$	−2.32524e13	+	4.02743e13i	−0.816472	+	1.41417i	0.0917940	+	0.995778i	$0.470740\pi$
$977$	−2.32524e13	+	4.02743e13i	−0.816472	+	1.41417i	−0.908266	+	0.418393i	$0.862593\pi$
$978$	−1.19021e14			−4.16006
$979$	3.04140e12	−	5.26786e12i	0.105816	−	0.183279i
$980$	2.89057e12	+	8.39802e12i	0.100107	+	0.290844i
$981$	3.03360e13	−	5.25434e13i	1.04580	−	1.81137i
$982$	9.96454e12	+	1.72591e13i	0.341944	+	0.592265i
$983$	2.00779e12	+	3.47760e12i	0.0685849	+	0.118792i	0.898279	−	0.439426i	$-0.144818\pi$
$983$	2.00779e12	+	3.47760e12i	0.0685849	+	0.118792i	−0.829694	+	0.558219i	$0.811485\pi$
$984$	−1.79732e13			−0.611149
$985$	−2.94508e12			−0.0996861
$986$	1.74739e13	+	3.02657e13i	0.588767	+	1.01977i
$987$	−6.22381e13	−	4.43995e13i	−2.08751	−	1.48919i
$988$	1.06684e12	−	5.79366e11i	0.0356199	−	0.0193440i
$989$	3.30979e13	−	5.73272e13i	1.10006	−	1.90536i
$990$	−8.91275e12	+	1.54373e13i	−0.294886	+	0.510757i
$991$	1.24002e13	−	2.14777e13i	0.408410	−	0.707386i	−0.586302	−	0.810092i	$-0.699417\pi$
$991$	1.24002e13	−	2.14777e13i	0.408410	−	0.707386i	0.994712	+	0.102706i	$0.0327502\pi$
$992$	−3.01164e13	−	5.21631e13i	−0.987417	−	1.71026i
$993$	4.64807e13			1.51705
$994$	2.22690e12	−	2.31130e13i	0.0723538	−	0.750961i
$995$	6.78737e12	−	1.17561e13i	0.219532	−	0.380240i
$996$	−6.42993e12	+	1.11370e13i	−0.207033	+	0.358591i
$997$	3.16424e13			1.01424			0.507120	−	0.861875i	$-0.330710\pi$
$997$	3.16424e13			1.01424			0.507120	+	0.861875i	$0.330710\pi$
$998$	2.10111e13	−	3.63924e13i	0.670444	−	1.16124i
$999$	−2.38946e13			−0.759023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.18	yes	164
7.4	even	3		91.10.g.a.81.65	yes	164
13.9	even	3		91.10.g.a.9.65	✓	164
91.74	even	3	inner	91.10.h.a.74.18	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.65	✓	164	13.9	even	3
91.10.g.a.81.65	yes	164	7.4	even	3
91.10.h.a.16.18	yes	164	1.1	even	1	trivial
91.10.h.a.74.18	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)

\(f(q)\)	\(=\)	\(q-29.4349 q^{2} +(122.315 - 211.855i) q^{3} +354.414 q^{4} +(-310.503 + 537.807i) q^{5} +(-3600.32 + 6235.94i) q^{6} +(-5780.64 + 2633.98i) q^{7} +4638.52 q^{8} +(-20080.3 - 34780.0i) q^{9} +O(q^{10})\)	\(q-29.4349 q^{2} +(122.315 - 211.855i) q^{3} +354.414 q^{4} +(-310.503 + 537.807i) q^{5} +(-3600.32 + 6235.94i) q^{6} +(-5780.64 + 2633.98i) q^{7} +4638.52 q^{8} +(-20080.3 - 34780.0i) q^{9} +(9139.63 - 15830.3i) q^{10} +(12141.0 - 21028.8i) q^{11} +(43350.1 - 75084.5i) q^{12} +(2686.70 - 102943. i) q^{13} +(170153. - 77530.9i) q^{14} +(75958.1 + 131563. i) q^{15} -317995. q^{16} -190069. q^{17} +(591061. + 1.02375e6i) q^{18} +(16631.6 + 28806.8i) q^{19} +(-110047. + 190606. i) q^{20} +(-149035. + 1.54683e6i) q^{21} +(-357369. + 618981. i) q^{22} -2.09430e6 q^{23} +(567359. - 982695. i) q^{24} +(783738. + 1.35747e6i) q^{25} +(-79082.7 + 3.03012e6i) q^{26} -5.00940e6 q^{27} +(-2.04874e6 + 933520. i) q^{28} +(3.12331e6 + 5.40973e6i) q^{29} +(-2.23582e6 - 3.87256e6i) q^{30} +(-4.31144e6 - 7.46764e6i) q^{31} +6.98522e6 q^{32} +(-2.97004e6 - 5.14426e6i) q^{33} +5.59467e6 q^{34} +(378333. - 3.92672e6i) q^{35} +(-7.11673e6 - 1.23265e7i) q^{36} +4.76995e6 q^{37} +(-489550. - 847926. i) q^{38} +(-2.14804e7 - 1.31606e7i) q^{39} +(-1.44027e6 + 2.49463e6i) q^{40} +(-7.91967e6 - 1.37173e7i) q^{41} +(4.38682e6 - 4.55309e7i) q^{42} +(-1.58038e7 + 2.73729e7i) q^{43} +(4.30294e6 - 7.45291e6i) q^{44} +2.49399e7 q^{45} +6.16456e7 q^{46} +(-2.45985e7 + 4.26059e7i) q^{47} +(-3.88954e7 + 6.73688e7i) q^{48} +(2.64779e7 - 3.04521e7i) q^{49} +(-2.30693e7 - 3.99572e7i) q^{50} +(-2.32483e7 + 4.02672e7i) q^{51} +(952203. - 3.64845e7i) q^{52} +(3.04955e7 + 5.28198e7i) q^{53} +1.47451e8 q^{54} +(7.53962e6 + 1.30590e7i) q^{55} +(-2.68136e7 + 1.22178e7i) q^{56} +8.13717e6 q^{57} +(-9.19344e7 - 1.59235e8i) q^{58} +1.01130e8 q^{59} +(2.69206e7 + 4.66279e7i) q^{60} +(-1.91445e7 - 3.31593e7i) q^{61} +(1.26907e8 + 2.19809e8i) q^{62} +(2.07687e8 + 1.48160e8i) q^{63} -4.27962e7 q^{64} +(5.45293e7 + 3.34091e7i) q^{65} +(8.74229e7 + 1.51421e8i) q^{66} +(7.75715e7 - 1.34358e8i) q^{67} -6.73633e7 q^{68} +(-2.56164e8 + 4.43689e8i) q^{69} +(-1.11362e7 + 1.15583e8i) q^{70} +(6.20910e7 - 1.07545e8i) q^{71} +(-9.31427e7 - 1.61328e8i) q^{72} +(9.67838e7 + 1.67634e8i) q^{73} -1.40403e8 q^{74} +3.83451e8 q^{75} +(5.89448e6 + 1.02095e7i) q^{76} +(-1.47932e7 + 1.53539e8i) q^{77} +(6.32274e8 + 3.87382e8i) q^{78} +(-2.18465e8 + 3.78392e8i) q^{79} +(9.87383e7 - 1.71020e8i) q^{80} +(-2.17484e8 + 3.76693e8i) q^{81} +(2.33115e8 + 4.03767e8i) q^{82} -1.48326e8 q^{83} +(-5.28200e7 + 5.48219e8i) q^{84} +(5.90171e7 - 1.02221e8i) q^{85} +(4.65182e8 - 8.05719e8i) q^{86} +1.52811e9 q^{87} +(5.63162e7 - 9.75426e7i) q^{88} +2.50507e8 q^{89} -7.34104e8 q^{90} +(2.55619e8 + 6.02153e8i) q^{91} -7.42251e8 q^{92} -2.10941e9 q^{93} +(7.24055e8 - 1.25410e9i) q^{94} -2.06567e7 q^{95} +(8.54395e8 - 1.47986e9i) q^{96} +(-3.02604e7 + 5.24125e7i) q^{97} +(-7.79375e8 + 8.96356e8i) q^{98} -9.75177e8 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

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