LMFDB - Embedded newform 690.2.m.h.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	690.121
Dual form			690.2.m.h.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.626720 - 4.35894i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.626720 - 4.35894i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-0.307739 - 0.673854i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.494288 + 3.43785i) q^{13} +(3.70468 + 2.38085i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.19187 + 5.99173i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.66688 - 1.92368i) q^{19} +(0.959493 + 0.281733i) q^{20} +(-1.82939 + 4.00580i) q^{21} +0.740799 q^{22} +(-3.39521 - 3.38712i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-3.33251 - 0.978513i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-3.70468 + 2.38085i) q^{28} +(-5.82184 + 6.71876i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(0.754354 - 0.221498i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.105427 + 0.733258i) q^{33} +(-3.29349 - 7.21174i) q^{34} +(1.82939 + 4.00580i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-8.83426 - 5.67743i) q^{37} +(2.44229 - 0.717120i) q^{38} +(0.494288 - 3.43785i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(9.19140 - 5.90695i) q^{41} +(-2.88385 - 3.32814i) q^{42} +(-0.408925 - 0.120071i) q^{43} +(-0.307739 + 0.673854i) q^{44} -1.00000 q^{45} +(4.49145 - 1.68133i) q^{46} -6.92253 q^{47} +(0.415415 - 0.909632i) q^{48} +(-11.8911 - 3.49154i) q^{49} +(0.654861 + 0.755750i) q^{50} +(6.66963 - 4.28631i) q^{51} +(2.27446 - 2.62487i) q^{52} +(0.588136 - 4.09058i) q^{53} +(0.959493 - 0.281733i) q^{54} +(0.623200 + 0.400506i) q^{55} +(-0.626720 - 4.35894i) q^{56} +(1.05739 + 2.31537i) q^{57} +(-3.69312 - 8.08681i) q^{58} +(1.23925 + 8.61915i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(-3.04556 + 0.894256i) q^{61} +(-0.111888 + 0.778198i) q^{62} +(2.88385 - 3.32814i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-2.27446 - 2.62487i) q^{65} +(-0.710791 - 0.208707i) q^{66} +(-5.32175 + 11.6530i) q^{67} +7.92820 q^{68} +(2.30342 + 4.20646i) q^{69} -4.40376 q^{70} +(-3.99369 + 8.74497i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-2.74556 - 3.16855i) q^{73} +(8.83426 - 5.67743i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(-0.362247 + 2.51948i) q^{76} +(-3.13015 + 0.919096i) q^{77} +(2.92184 + 1.87775i) q^{78} +(0.0190687 + 0.132626i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.55491 + 10.8146i) q^{82} +(-10.4200 - 6.69650i) q^{83} +(4.22538 - 1.24068i) q^{84} +(1.12830 - 7.84750i) q^{85} +(0.279094 - 0.322092i) q^{86} +(7.47891 - 4.80640i) q^{87} +(-0.485120 - 0.559858i) q^{88} +(-7.81366 - 2.29430i) q^{89} +(0.415415 - 0.909632i) q^{90} +15.2951 q^{91} +(-0.336424 + 4.78402i) q^{92} -0.786200 q^{93} +(2.87572 - 6.29696i) q^{94} +(2.44229 + 0.717120i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-8.12039 + 5.21866i) q^{97} +(8.11575 - 9.36608i) q^{98} +(0.105427 - 0.733258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	0.626720	−	4.35894i	0.236878	−	1.64752i	−0.430345	−	0.902665i	$-0.641608\pi$
$7$	0.626720	−	4.35894i	0.236878	−	1.64752i	0.667223	−	0.744858i	$-0.267483\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	−0.307739	−	0.673854i	−0.0927868	−	0.203175i	0.857548	−	0.514404i	$-0.171987\pi$
$11$	−0.307739	−	0.673854i	−0.0927868	−	0.203175i	−0.950335	+	0.311229i	$0.899259\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	0.494288	+	3.43785i	0.137091	+	0.953487i	0.935991	+	0.352024i	$0.114506\pi$
$13$	0.494288	+	3.43785i	0.137091	+	0.953487i	−0.798900	+	0.601463i	$0.794585\pi$
$14$	3.70468	+	2.38085i	0.990117	+	0.636310i
$15$	0.959493	−	0.281733i	0.247740	−	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−5.19187	+	5.99173i	−1.25921	+	1.45321i	−0.421752	+	0.906711i	$0.638585\pi$
$17$	−5.19187	+	5.99173i	−1.25921	+	1.45321i	−0.837461	+	0.546497i	$0.815961\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	−1.66688	−	1.92368i	−0.382408	−	0.441322i	0.531614	−	0.846987i	$-0.321586\pi$
$19$	−1.66688	−	1.92368i	−0.382408	−	0.441322i	−0.914022	+	0.405664i	$0.867040\pi$
$20$	0.959493	+	0.281733i	0.214549	+	0.0629973i
$21$	−1.82939	+	4.00580i	−0.399205	+	0.874137i
$22$	0.740799			0.157939
$23$	−3.39521	−	3.38712i	−0.707950	−	0.706263i
$23$	−3.39521	−	3.38712i	−0.707950	−	0.706263i
$24$	−1.00000			−0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−3.33251	−	0.978513i	−0.653559	−	0.191902i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−3.70468	+	2.38085i	−0.700118	+	0.449939i
$29$	−5.82184	+	6.71876i	−1.08109	+	1.24764i	−0.113925	+	0.993489i	$0.536342\pi$
$29$	−5.82184	+	6.71876i	−1.08109	+	1.24764i	−0.967164	+	0.254153i	$0.918203\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	0.754354	−	0.221498i	0.135486	−	0.0397823i	−0.213287	−	0.976990i	$-0.568417\pi$
$31$	0.754354	−	0.221498i	0.135486	−	0.0397823i	0.348772	+	0.937207i	$0.386599\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.105427	+	0.733258i	0.0183524	+	0.127644i
$34$	−3.29349	−	7.21174i	−0.564829	−	1.23680i
$35$	1.82939	+	4.00580i	0.309223	+	0.677104i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−8.83426	−	5.67743i	−1.45234	−	0.933364i	−0.999119	−	0.0419676i	$-0.986637\pi$
$37$	−8.83426	−	5.67743i	−1.45234	−	0.933364i	−0.453224	−	0.891397i	$-0.649726\pi$
$38$	2.44229	−	0.717120i	0.396191	−	0.116332i
$39$	0.494288	−	3.43785i	0.0791494	−	0.550496i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	9.19140	−	5.90695i	1.43546	−	0.922511i	0.435707	−	0.900089i	$-0.356499\pi$
$41$	9.19140	−	5.90695i	1.43546	−	0.922511i	0.999749	−	0.0224222i	$-0.00713782\pi$
$42$	−2.88385	−	3.32814i	−0.444988	−	0.513543i
$43$	−0.408925	−	0.120071i	−0.0623605	−	0.0183107i	0.250403	−	0.968142i	$-0.419437\pi$
$43$	−0.408925	−	0.120071i	−0.0623605	−	0.0183107i	−0.312764	+	0.949831i	$0.601255\pi$
$44$	−0.307739	+	0.673854i	−0.0463934	+	0.101587i
$45$	−1.00000			−0.149071
$46$	4.49145	−	1.68133i	0.662228	−	0.247899i
$47$	−6.92253			−1.00976			−0.504878	−	0.863191i	$-0.668462\pi$
$47$	−6.92253			−1.00976			−0.504878	+	0.863191i	$0.668462\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−11.8911	−	3.49154i	−1.69873	−	0.498791i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	6.66963	−	4.28631i	0.933934	−	0.600203i
$52$	2.27446	−	2.62487i	0.315411	−	0.364004i
$53$	0.588136	−	4.09058i	0.0807867	−	0.561884i	−0.908721	−	0.417404i	$-0.862940\pi$
$53$	0.588136	−	4.09058i	0.0807867	−	0.561884i	0.989508	−	0.144480i	$-0.0461509\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	0.623200	+	0.400506i	0.0840322	+	0.0540042i
$56$	−0.626720	−	4.35894i	−0.0837490	−	0.582487i
$57$	1.05739	+	2.31537i	0.140055	+	0.306678i
$58$	−3.69312	−	8.08681i	−0.484931	−	1.06185i
$59$	1.23925	+	8.61915i	0.161336	+	1.12212i	0.896119	+	0.443815i	$0.146375\pi$
$59$	1.23925	+	8.61915i	0.161336	+	1.12212i	−0.734783	+	0.678303i	$0.762716\pi$
$60$	−0.841254	−	0.540641i	−0.108605	−	0.0697964i
$61$	−3.04556	+	0.894256i	−0.389944	+	0.114498i	−0.470826	−	0.882226i	$-0.656044\pi$
$61$	−3.04556	+	0.894256i	−0.389944	+	0.114498i	0.0808829	+	0.996724i	$0.474226\pi$
$62$	−0.111888	+	0.778198i	−0.0142098	+	0.0988313i
$63$	2.88385	−	3.32814i	0.363331	−	0.419306i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−2.27446	−	2.62487i	−0.282112	−	0.325575i
$66$	−0.710791	−	0.208707i	−0.0874923	−	0.0256901i
$67$	−5.32175	+	11.6530i	−0.650156	+	1.42364i	0.241262	+	0.970460i	$0.422439\pi$
$67$	−5.32175	+	11.6530i	−0.650156	+	1.42364i	−0.891418	+	0.453183i	$0.850289\pi$
$68$	7.92820			0.961435
$69$	2.30342	+	4.20646i	0.277299	+	0.506398i
$70$	−4.40376			−0.526350
$71$	−3.99369	+	8.74497i	−0.473964	+	1.03784i	0.510115	+	0.860106i	$0.329603\pi$
$71$	−3.99369	+	8.74497i	−0.473964	+	1.03784i	−0.984079	+	0.177730i	$0.943124\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	−2.74556	−	3.16855i	−0.321344	−	0.370850i	0.571977	−	0.820269i	$-0.306176\pi$
$73$	−2.74556	−	3.16855i	−0.321344	−	0.370850i	−0.893321	+	0.449419i	$0.851631\pi$
$74$	8.83426	−	5.67743i	1.02696	−	0.659988i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	−0.362247	+	2.51948i	−0.0415526	+	0.289005i
$77$	−3.13015	+	0.919096i	−0.356714	+	0.104741i
$78$	2.92184	+	1.87775i	0.330833	+	0.212614i
$79$	0.0190687	+	0.132626i	0.00214539	+	0.0149215i	0.990866	−	0.134850i	$-0.0430553\pi$
$79$	0.0190687	+	0.132626i	0.00214539	+	0.0149215i	−0.988721	+	0.149772i	$0.952146\pi$
$80$	−0.415415	−	0.909632i	−0.0464448	−	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	1.55491	+	10.8146i	0.171711	+	1.19428i
$83$	−10.4200	−	6.69650i	−1.14374	−	0.735036i	−0.175356	−	0.984505i	$-0.556108\pi$
$83$	−10.4200	−	6.69650i	−1.14374	−	0.735036i	−0.968383	+	0.249469i	$0.919744\pi$
$84$	4.22538	−	1.24068i	0.461026	−	0.135370i
$85$	1.12830	−	7.84750i	0.122381	−	0.851181i
$86$	0.279094	−	0.322092i	0.0300955	−	0.0347321i
$87$	7.47891	−	4.80640i	0.801823	−	0.515301i
$88$	−0.485120	−	0.559858i	−0.0517140	−	0.0596811i
$89$	−7.81366	−	2.29430i	−0.828247	−	0.243195i	−0.159983	−	0.987120i	$-0.551144\pi$
$89$	−7.81366	−	2.29430i	−0.828247	−	0.243195i	−0.668264	+	0.743925i	$0.732962\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	15.2951			1.60337
$92$	−0.336424	+	4.78402i	−0.0350746	+	0.498768i
$93$	−0.786200			−0.0815252
$94$	2.87572	−	6.29696i	0.296608	−	0.649482i
$95$	2.44229	+	0.717120i	0.250573	+	0.0735750i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	−8.12039	+	5.21866i	−0.824501	+	0.529875i	−0.883526	−	0.468382i	$-0.844837\pi$
$97$	−8.12039	+	5.21866i	−0.824501	+	0.529875i	0.0590252	+	0.998256i	$0.481201\pi$
$98$	8.11575	−	9.36608i	0.819815	−	0.946117i
$99$	0.105427	−	0.733258i	0.0105958	−	0.0736953i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	14.8912	+	9.57001i	1.48173	+	0.952252i	0.996985	+	0.0775984i	$0.0247252\pi$
$101$	14.8912	+	9.57001i	1.48173	+	0.952252i	0.484748	+	0.874654i	$0.338911\pi$
$102$	1.12830	+	7.84750i	0.111718	+	0.777018i
$103$	−2.69428	−	5.89966i	−0.265476	−	0.581310i	0.729208	−	0.684292i	$-0.239889\pi$
$103$	−2.69428	−	5.89966i	−0.265476	−	0.581310i	−0.994683	+	0.102982i	$0.967162\pi$
$104$	1.44282	+	3.15933i	0.141480	+	0.309798i
$105$	−0.626720	−	4.35894i	−0.0611616	−	0.425389i
$106$	3.47660	+	2.23427i	0.337677	+	0.217012i
$107$	−0.836010	+	0.245475i	−0.0808201	+	0.0237309i	−0.321893	−	0.946776i	$-0.604319\pi$
$107$	−0.836010	+	0.245475i	−0.0808201	+	0.0237309i	0.241073	+	0.970507i	$0.422501\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−6.34803	+	7.32601i	−0.608031	+	0.701705i	−0.973388	−	0.229162i	$-0.926401\pi$
$109$	−6.34803	+	7.32601i	−0.608031	+	0.701705i	0.365357	+	0.930867i	$0.380947\pi$
$110$	−0.623200	+	0.400506i	−0.0594197	+	0.0381868i
$111$	6.87689	+	7.93635i	0.652726	+	0.753285i
$112$	4.22538	+	1.24068i	0.399261	+	0.117233i
$113$	3.24603	−	7.10781i	0.305361	−	0.668647i	−0.693286	−	0.720663i	$-0.743838\pi$
$113$	3.24603	−	7.10781i	0.305361	−	0.668647i	0.998646	+	0.0520163i	$0.0165648\pi$
$114$	−2.54539			−0.238398
$115$	4.68744	+	1.01384i	0.437106	+	0.0945407i
$116$	8.89020			0.825434
$117$	−1.44282	+	3.15933i	−0.133389	+	0.292080i
$118$	−8.35505	−	2.45326i	−0.769145	−	0.225841i
$119$	22.8637	+	26.3862i	2.09591	+	2.41881i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	6.84409	−	7.89850i	0.622190	−	0.718046i
$122$	0.451726	−	3.14182i	0.0408973	−	0.284447i
$123$	−10.4833	+	3.07816i	−0.945244	+	0.277549i
$124$	−0.661394	−	0.425052i	−0.0593949	−	0.0381708i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	1.82939	+	4.00580i	0.162975	+	0.356865i
$127$	−8.10170	−	17.7402i	−0.718909	−	1.57419i	−0.815426	−	0.578861i	$-0.803497\pi$
$127$	−8.10170	−	17.7402i	−0.718909	−	1.57419i	0.0965170	−	0.995331i	$-0.469230\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	0.358533	+	0.230415i	0.0315671	+	0.0202869i
$130$	3.33251	−	0.978513i	0.292280	−	0.0858213i
$131$	1.18469	−	8.23967i	0.103507	−	0.719904i	−0.870299	−	0.492523i	$-0.836075\pi$
$131$	1.18469	−	8.23967i	0.103507	−	0.719904i	0.973806	−	0.227381i	$-0.0730162\pi$
$132$	0.485120	−	0.559858i	0.0422243	−	0.0487294i
$133$	−9.42986	+	6.06020i	−0.817673	+	0.525486i
$134$	−8.38922	−	9.68168i	−0.724718	−	0.836369i
$135$	0.959493	+	0.281733i	0.0825800	+	0.0242477i
$136$	−3.29349	+	7.21174i	−0.282415	+	0.618402i
$137$	7.51893			0.642386			0.321193	−	0.947014i	$-0.395916\pi$
$137$	7.51893			0.642386			0.321193	+	0.947014i	$0.395916\pi$
$138$	−4.78320	+	0.347837i	−0.407173	+	0.0296099i
$139$	15.7837			1.33876			0.669379	−	0.742921i	$-0.266560\pi$
$139$	15.7837			1.33876			0.669379	+	0.742921i	$0.266560\pi$
$140$	1.82939	−	4.00580i	0.154611	−	0.338552i
$141$	6.64212	+	1.95030i	0.559368	+	0.164245i
$142$	−6.29566	−	7.26558i	−0.528320	−	0.609714i
$143$	2.16450	−	1.39104i	0.181004	−	0.116324i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	1.26521	−	8.79971i	0.105070	−	0.730776i
$146$	4.02276	−	1.18119i	0.332926	−	0.0977559i
$147$	10.4257	+	6.70022i	0.859900	+	0.552624i
$148$	1.49449	+	10.3944i	0.122846	+	0.854416i
$149$	−4.87508	−	10.6749i	−0.399382	−	0.874525i	−0.997333	−	0.0729916i	$-0.976745\pi$
$149$	−4.87508	−	10.6749i	−0.399382	−	0.874525i	0.597951	−	0.801533i	$-0.295982\pi$
$150$	−0.415415	−	0.909632i	−0.0339185	−	0.0742711i
$151$	0.546663	+	3.80213i	0.0444868	+	0.309413i	0.999900	+	0.0141405i	$0.00450122\pi$
$151$	0.546663	+	3.80213i	0.0444868	+	0.309413i	−0.955413	+	0.295272i	$0.904590\pi$
$152$	−2.14132	−	1.37614i	−0.173684	−	0.111620i
$153$	−7.60705	+	2.23363i	−0.614994	+	0.180578i
$154$	0.464274	−	3.22909i	0.0374122	−	0.260208i
$155$	−0.514852	+	0.594171i	−0.0413539	+	0.0477249i
$156$	−2.92184	+	1.87775i	−0.233935	+	0.150341i
$157$	4.80825	+	5.54902i	0.383740	+	0.442860i	0.914453	−	0.404692i	$-0.132621\pi$
$157$	4.80825	+	5.54902i	0.383740	+	0.442860i	−0.530713	+	0.847552i	$0.678076\pi$
$158$	−0.128562	−	0.0377492i	−0.0102278	−	0.00300316i
$159$	−1.71676	+	3.75918i	−0.136148	+	0.298123i
$160$	1.00000			0.0790569
$161$	−16.8921	+	12.6767i	−1.33128	+	0.999065i
$162$	−1.00000			−0.0785674
$163$	3.68234	−	8.06321i	0.288423	−	0.631559i	−0.708850	−	0.705360i	$-0.750785\pi$
$163$	3.68234	−	8.06321i	0.288423	−	0.631559i	0.997273	+	0.0738004i	$0.0235128\pi$
$164$	−10.4833	−	3.07816i	−0.818605	−	0.240364i
$165$	−0.485120	−	0.559858i	−0.0377665	−	0.0435849i
$166$	10.4200	−	6.69650i	0.808746	−	0.519749i
$167$	−2.50930	+	2.89589i	−0.194176	+	0.224091i	−0.844486	−	0.535578i	$-0.820094\pi$
$167$	−2.50930	+	2.89589i	−0.194176	+	0.224091i	0.650310	+	0.759669i	$0.274639\pi$
$168$	−0.626720	+	4.35894i	−0.0483525	+	0.336299i
$169$	0.898937	−	0.263952i	0.0691490	−	0.0203040i
$170$	6.66963	+	4.28631i	0.511537	+	0.328745i
$171$	−0.362247	−	2.51948i	−0.0277017	−	0.192670i
$172$	0.177045	+	0.387675i	0.0134996	+	0.0295599i
$173$	9.30504	+	20.3752i	0.707449	+	1.54910i	0.830699	+	0.556721i	$0.187941\pi$
$173$	9.30504	+	20.3752i	0.707449	+	1.54910i	−0.123251	+	0.992376i	$0.539332\pi$
$174$	1.26521	+	8.79971i	0.0959151	+	0.667104i
$175$	−3.70468	−	2.38085i	−0.280047	−	0.179976i
$176$	0.710791	−	0.208707i	0.0535779	−	0.0157319i
$177$	1.23925	−	8.61915i	0.0931474	−	0.647855i
$178$	5.33288	−	6.15447i	0.399716	−	0.461297i
$179$	−3.89278	+	2.50174i	−0.290960	+	0.186988i	−0.677975	−	0.735085i	$-0.737142\pi$
$179$	−3.89278	+	2.50174i	−0.290960	+	0.186988i	0.387016	+	0.922073i	$0.373506\pi$
$180$	0.654861	+	0.755750i	0.0488104	+	0.0563302i
$181$	−0.799531	−	0.234764i	−0.0594287	−	0.0174498i	0.251883	−	0.967758i	$-0.418950\pi$
$181$	−0.799531	−	0.234764i	−0.0594287	−	0.0174498i	−0.311312	+	0.950308i	$0.600768\pi$
$182$	−6.35383	+	13.9129i	−0.470977	+	1.03130i
$183$	3.17413			0.234639
$184$	−4.21194	−	2.29337i	−0.310508	−	0.169070i
$185$	10.5013			0.772071
$186$	0.326599	−	0.715153i	0.0239474	−	0.0524376i
$187$	5.63529	+	1.65467i	0.412094	+	0.121002i
$188$	4.53330	+	5.23170i	0.330625	+	0.381561i
$189$	−3.70468	+	2.38085i	−0.269476	+	0.173182i
$190$	−1.66688	+	1.92368i	−0.120928	+	0.139558i
$191$	−1.31972	+	9.17886i	−0.0954917	+	0.664159i	0.884708	+	0.466146i	$0.154358\pi$
$191$	−1.31972	+	9.17886i	−0.0954917	+	0.664159i	−0.980199	+	0.198013i	$0.936551\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	14.4615	+	9.29386i	1.04096	+	0.668987i	0.945225	−	0.326420i	$-0.105842\pi$
$193$	14.4615	+	9.29386i	1.04096	+	0.668987i	0.0957390	+	0.995406i	$0.469479\pi$
$194$	−1.37373	−	9.55448i	−0.0986278	−	0.685972i
$195$	1.44282	+	3.15933i	0.103322	+	0.226245i
$196$	5.14828	+	11.2732i	0.367734	+	0.805226i
$197$	−1.91317	−	13.3064i	−0.136308	−	0.948041i	−0.937091	−	0.349086i	$-0.886492\pi$
$197$	−1.91317	−	13.3064i	−0.136308	−	0.948041i	0.800783	−	0.598955i	$-0.204417\pi$
$198$	0.623200	+	0.400506i	0.0442889	+	0.0284627i
$199$	18.6640	−	5.48026i	1.32306	−	0.388485i	0.457463	−	0.889229i	$-0.348758\pi$
$199$	18.6640	−	5.48026i	1.32306	−	0.388485i	0.865596	+	0.500744i	$0.166940\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	8.38922	−	9.68168i	0.591730	−	0.682893i
$202$	−14.8912	+	9.57001i	−1.04774	+	0.673344i
$203$	25.6380	+	29.5878i	1.79943	+	2.07666i
$204$	−7.60705	−	2.23363i	−0.532600	−	0.156386i
$205$	−4.53876	+	9.93849i	−0.317000	+	0.694134i
$206$	6.48576			0.451884
$207$	−1.02502	−	4.68501i	−0.0712436	−	0.325631i
$208$	−3.47320			−0.240823
$209$	−0.783316	+	1.71522i	−0.0541831	+	0.118645i
$210$	4.22538	+	1.24068i	0.291579	+	0.0856152i
$211$	−4.72940	−	5.45802i	−0.325586	−	0.375746i	0.569233	−	0.822177i	$-0.307240\pi$
$211$	−4.72940	−	5.45802i	−0.325586	−	0.375746i	−0.894818	+	0.446431i	$0.852695\pi$
$212$	−3.47660	+	2.23427i	−0.238774	+	0.153451i
$213$	6.29566	−	7.26558i	0.431372	−	0.497829i
$214$	0.123999	−	0.862435i	0.00847643	−	0.0589548i
$215$	0.408925	−	0.120071i	0.0278885	−	0.00818879i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−0.492728	−	3.42700i	−0.0334485	−	0.232640i
$218$	−4.02691	−	8.81771i	−0.272737	−	0.597210i
$219$	1.74166	+	3.81371i	0.117691	+	0.257707i
$220$	−0.105427	−	0.733258i	−0.00710786	−	0.0494363i
$221$	−23.1649	−	14.8872i	−1.55824	−	1.00142i
$222$	−10.0759	+	2.95856i	−0.676252	+	0.198565i
$223$	−2.94680	+	20.4954i	−0.197332	+	1.37248i	0.614653	+	0.788798i	$0.289296\pi$
$223$	−2.94680	+	20.4954i	−0.197332	+	1.37248i	−0.811985	+	0.583678i	$0.801613\pi$
$224$	−2.88385	+	3.32814i	−0.192685	+	0.222371i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	5.11704	+	5.90538i	0.340381	+	0.392820i
$227$	9.39302	+	2.75804i	0.623436	+	0.183057i	0.578168	−	0.815917i	$-0.303768\pi$
$227$	9.39302	+	2.75804i	0.623436	+	0.183057i	0.0452680	+	0.998975i	$0.485586\pi$
$228$	1.05739	−	2.31537i	0.0700277	−	0.153339i
$229$	−20.7155			−1.36892			−0.684460	−	0.729051i	$-0.739962\pi$
$229$	−20.7155			−1.36892			−0.684460	+	0.729051i	$0.739962\pi$
$230$	−2.86945	+	3.84269i	−0.189206	+	0.253379i
$231$	3.26230			0.214644
$232$	−3.69312	+	8.08681i	−0.242465	+	0.530925i
$233$	−8.17503	−	2.40041i	−0.535564	−	0.157256i	0.00275613	−	0.999996i	$-0.499123\pi$
$233$	−8.17503	−	2.40041i	−0.535564	−	0.157256i	−0.538320	+	0.842740i	$0.680941\pi$
$234$	−2.27446	−	2.62487i	−0.148686	−	0.171593i
$235$	5.82361	−	3.74260i	0.379890	−	0.244141i
$236$	5.70238	−	6.58090i	0.371193	−	0.428380i
$237$	0.0190687	−	0.132626i	0.00123864	−	0.00861495i
$238$	−33.4996	+	9.83638i	−2.17146	+	0.637598i
$239$	−18.2636	−	11.7373i	−1.18137	−	0.759223i	−0.205736	−	0.978608i	$-0.565959\pi$
$239$	−18.2636	−	11.7373i	−1.18137	−	0.759223i	−0.975638	+	0.219385i	$0.929595\pi$
$240$	0.142315	+	0.989821i	0.00918638	+	0.0638927i
$241$	−3.93590	−	8.61842i	−0.253534	−	0.555161i	0.739478	−	0.673181i	$-0.235073\pi$
$241$	−3.93590	−	8.61842i	−0.253534	−	0.555161i	−0.993011	+	0.118020i	$0.962345\pi$
$242$	4.34159	+	9.50676i	0.279088	+	0.611118i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	2.67025	+	1.71606i	0.170945	+	0.109860i
$245$	11.8911	−	3.49154i	0.759694	−	0.223066i
$246$	1.55491	−	10.8146i	0.0991373	−	0.689515i
$247$	5.78940	−	6.68132i	0.368371	−	0.425122i
$248$	0.661394	−	0.425052i	0.0419986	−	0.0269908i
$249$	8.11125	+	9.36089i	0.514030	+	0.593222i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	4.57492	−	10.0177i	0.288766	−	0.632310i	−0.708539	−	0.705672i	$-0.750645\pi$
$251$	4.57492	−	10.0177i	0.288766	−	0.632310i	0.997305	+	0.0733614i	$0.0233727\pi$
$252$	−4.40376			−0.277411
$253$	−1.23759	+	3.33022i	−0.0778063	+	0.209369i
$254$	19.5027			1.22371
$255$	−3.29349	+	7.21174i	−0.206247	+	0.451617i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−8.42176	−	9.71923i	−0.525335	−	0.606269i	0.429624	−	0.903008i	$-0.358646\pi$
$257$	−8.42176	−	9.71923i	−0.525335	−	0.606269i	−0.954959	+	0.296739i	$0.904101\pi$
$258$	−0.358533	+	0.230415i	−0.0223213	+	0.0143450i
$259$	−30.2842	+	34.9498i	−1.88177	+	2.17167i
$260$	−0.494288	+	3.43785i	−0.0306544	+	0.213206i
$261$	−8.53008	+	2.50466i	−0.527999	+	0.155034i
$262$	7.00293	+	4.50051i	0.432643	+	0.278043i
$263$	−2.67313	−	18.5920i	−0.164832	−	1.14643i	−0.889367	−	0.457194i	$-0.848855\pi$
$263$	−2.67313	−	18.5920i	−0.164832	−	1.14643i	0.724535	−	0.689238i	$-0.242054\pi$
$264$	0.307739	+	0.673854i	0.0189400	+	0.0414729i
$265$	1.71676	+	3.75918i	0.105460	+	0.230925i
$266$	−1.59525	−	11.0952i	−0.0978110	−	0.680291i
$267$	6.85078	+	4.40273i	0.419261	+	0.269442i
$268$	12.2918	−	3.60919i	0.750839	−	0.220466i
$269$	2.63670	−	18.3387i	0.160763	−	1.11813i	−0.736438	−	0.676506i	$-0.763493\pi$
$269$	2.63670	−	18.3387i	0.160763	−	1.11813i	0.897200	−	0.441624i	$-0.145597\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	19.2305	−	12.3587i	1.16817	−	0.750736i	0.194994	−	0.980804i	$-0.437531\pi$
$271$	19.2305	−	12.3587i	1.16817	−	0.750736i	0.973175	+	0.230068i	$0.0738949\pi$
$272$	−5.19187	−	5.99173i	−0.314803	−	0.363302i
$273$	−14.6756	−	4.30914i	−0.888206	−	0.260801i
$274$	−3.12348	+	6.83946i	−0.188696	+	0.413187i
$275$	−0.740799			−0.0446718
$276$	1.67061	−	4.49545i	0.100559	−	0.270594i
$277$	21.4766			1.29040			0.645201	−	0.764013i	$-0.276774\pi$
$277$	21.4766			1.29040			0.645201	+	0.764013i	$0.276774\pi$
$278$	−6.55680	+	14.3574i	−0.393251	+	0.861099i
$279$	0.754354	+	0.221498i	0.0451620	+	0.0132608i
$280$	2.88385	+	3.32814i	0.172343	+	0.198894i
$281$	−1.87639	+	1.20588i	−0.111936	+	0.0719368i	−0.595411	−	0.803421i	$-0.703011\pi$
$281$	−1.87639	+	1.20588i	−0.111936	+	0.0719368i	0.483475	+	0.875358i	$0.339374\pi$
$282$	−4.53330	+	5.23170i	−0.269954	+	0.311543i
$283$	−0.672333	+	4.67618i	−0.0399661	+	0.277970i	−0.999998	−	0.00191988i	$-0.999389\pi$
$283$	−0.672333	+	4.67618i	−0.0399661	+	0.277970i	0.960032	+	0.279890i	$0.0902980\pi$
$284$	9.22432	−	2.70850i	0.547363	−	0.160720i
$285$	−2.14132	−	1.37614i	−0.126841	−	0.0815157i
$286$	0.366168	+	2.54675i	0.0216520	+	0.150593i
$287$	−19.9876	−	43.7667i	−1.17983	−	2.58347i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−6.52604	−	45.3896i	−0.383885	−	2.66998i
$290$	7.47891	+	4.80640i	0.439177	+	0.282242i
$291$	9.26173	−	2.71949i	0.542932	−	0.159419i
$292$	−0.596667	+	4.14991i	−0.0349173	+	0.242855i
$293$	2.33622	−	2.69614i	0.136483	−	0.157510i	−0.683393	−	0.730050i	$-0.739497\pi$
$293$	2.33622	−	2.69614i	0.136483	−	0.157510i	0.819877	+	0.572540i	$0.194042\pi$
$294$	−10.4257	+	6.70022i	−0.608041	+	0.390764i
$295$	−5.70238	−	6.58090i	−0.332006	−	0.383155i
$296$	−10.0759	−	2.95856i	−0.585651	−	0.171963i
$297$	−0.307739	+	0.673854i	−0.0178568	+	0.0391010i
$298$	11.7354			0.679816
$299$	9.96618	−	13.3464i	0.576359	−	0.771843i
$300$	1.00000			0.0577350
$301$	−0.779665	+	1.70723i	−0.0449391	+	0.0984030i
$302$	−3.68563	−	1.08220i	−0.212084	−	0.0622735i
$303$	−11.5918	−	13.3777i	−0.665934	−	0.768529i
$304$	2.14132	−	1.37614i	0.122813	−	0.0789272i
$305$	2.07861	−	2.39885i	0.119021	−	0.137358i
$306$	1.12830	−	7.84750i	0.0645006	−	0.448612i
$307$	16.5414	−	4.85700i	0.944069	−	0.277204i	0.226753	−	0.973952i	$-0.427189\pi$
$307$	16.5414	−	4.85700i	0.944069	−	0.277204i	0.717315	+	0.696749i	$0.245371\pi$
$308$	2.74442	+	1.76373i	0.156378	+	0.100498i
$309$	0.923020	+	6.41975i	0.0525088	+	0.365207i
$310$	−0.326599	−	0.715153i	−0.0185496	−	0.0406180i
$311$	−8.18969	−	17.9329i	−0.464395	−	1.01688i	−0.986464	−	0.163979i	$-0.947567\pi$
$311$	−8.18969	−	17.9329i	−0.464395	−	1.01688i	0.522069	−	0.852903i	$-0.325160\pi$
$312$	−0.494288	−	3.43785i	−0.0279835	−	0.194630i
$313$	8.17049	+	5.25085i	0.461823	+	0.296796i	0.750787	−	0.660544i	$-0.229674\pi$
$313$	8.17049	+	5.25085i	0.461823	+	0.296796i	−0.288964	+	0.957340i	$0.593311\pi$
$314$	−7.04498	+	2.06859i	−0.397571	+	0.116737i
$315$	−0.626720	+	4.35894i	−0.0353117	+	0.245598i
$316$	0.0877443	−	0.101262i	0.00493601	−	0.00569645i
$317$	−14.6500	+	9.41497i	−0.822825	+	0.528798i	−0.882991	−	0.469391i	$-0.844474\pi$
$317$	−14.6500	+	9.41497i	−0.822825	+	0.528798i	0.0601654	+	0.998188i	$0.480837\pi$
$318$	−2.70630	−	3.12324i	−0.151762	−	0.175143i
$319$	6.31907	+	1.85545i	0.353800	+	0.103885i
$320$	−0.415415	+	0.909632i	−0.0232224	+	0.0508500i
$321$	0.871304			0.0486314
$322$	−4.51393	−	20.6317i	−0.251551	−	1.14976i
$323$	20.1804			1.12287
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	3.33251	+	0.978513i	0.184854	+	0.0542782i
$326$	5.80485	+	6.69916i	0.321501	+	0.371032i
$327$	8.15486	−	5.24081i	0.450965	−	0.289818i
$328$	7.15490	−	8.25720i	0.395063	−	0.455927i
$329$	−4.33849	+	30.1749i	−0.239189	+	1.66359i
$330$	0.710791	−	0.208707i	0.0391278	−	0.0114889i
$331$	14.6192	+	9.39520i	0.803545	+	0.516407i	0.876771	−	0.480908i	$-0.159693\pi$
$331$	14.6192	+	9.39520i	0.803545	+	0.516407i	−0.0732260	+	0.997315i	$0.523329\pi$
$332$	1.76274	+	12.2602i	0.0967431	+	0.672863i
$333$	−4.36240	−	9.55232i	−0.239058	−	0.523464i
$334$	−1.59179	−	3.48554i	−0.0870990	−	0.190720i
$335$	−1.82315	−	12.6803i	−0.0996094	−	0.692799i
$336$	−3.70468	−	2.38085i	−0.202107	−	0.129886i
$337$	−19.5777	+	5.74854i	−1.06647	+	0.313143i	−0.767452	−	0.641106i	$-0.778476\pi$
$337$	−19.5777	+	5.74854i	−1.06647	+	0.313143i	−0.299014	+	0.954249i	$0.596658\pi$
$338$	−0.133333	+	0.927351i	−0.00725236	+	0.0504412i
$339$	−5.11704	+	5.90538i	−0.277920	+	0.320736i
$340$	−6.66963	+	4.28631i	−0.361711	+	0.232458i
$341$	−0.381402	−	0.440161i	−0.0206541	−	0.0238360i
$342$	2.44229	+	0.717120i	0.132064	+	0.0387774i
$343$	−9.86607	+	21.6037i	−0.532718	+	1.16649i
$344$	−0.426189			−0.0229786
$345$	−4.21194	−	2.29337i	−0.226763	−	0.123471i
$346$	−22.3994			−1.20420
$347$	−0.638796	+	1.39877i	−0.0342924	+	0.0750898i	−0.926003	−	0.377516i	$-0.876778\pi$
$347$	−0.638796	+	1.39877i	−0.0342924	+	0.0750898i	0.891711	+	0.452606i	$0.149506\pi$
$348$	−8.53008	−	2.50466i	−0.457260	−	0.134264i
$349$	−12.4612	−	14.3810i	−0.667034	−	0.769799i	0.316875	−	0.948467i	$-0.397366\pi$
$349$	−12.4612	−	14.3810i	−0.667034	−	0.769799i	−0.983909	+	0.178669i	$0.942821\pi$
$350$	3.70468	−	2.38085i	0.198023	−	0.127262i
$351$	2.27446	−	2.62487i	0.121402	−	0.140105i
$352$	−0.105427	+	0.733258i	−0.00561926	+	0.0390828i
$353$	2.63554	−	0.773865i	0.140276	−	0.0411887i	−0.210841	−	0.977520i	$-0.567620\pi$
$353$	2.63554	−	0.773865i	0.140276	−	0.0411887i	0.351117	+	0.936332i	$0.385802\pi$
$354$	7.32545	+	4.70778i	0.389343	+	0.250216i
$355$	−1.36818	−	9.51589i	−0.0726154	−	0.505051i
$356$	3.38295	+	7.40762i	0.179296	+	0.392603i
$357$	−14.5038	−	31.7588i	−0.767620	−	1.68085i
$358$	−0.658541	−	4.58025i	−0.0348050	−	0.242074i
$359$	−30.4854	−	19.5918i	−1.60896	−	1.03401i	−0.962581	−	0.270994i	$-0.912648\pi$
$359$	−30.4854	−	19.5918i	−1.60896	−	1.03401i	−0.646375	−	0.763020i	$-0.723716\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	1.78192	−	12.3935i	0.0937853	−	0.652291i
$362$	0.545686	−	0.629755i	0.0286806	−	0.0330992i
$363$	−8.79212	+	5.65035i	−0.461467	+	0.296567i
$364$	−10.0162	−	11.5593i	−0.524991	−	0.605871i
$365$	4.02276	+	1.18119i	0.210561	+	0.0618262i
$366$	−1.31858	+	2.88729i	−0.0689234	+	0.150921i
$367$	33.7513			1.76180			0.880901	−	0.473301i	$-0.156938\pi$
$367$	33.7513			1.76180			0.880901	+	0.473301i	$0.156938\pi$
$368$	3.83583	−	2.87861i	0.199956	−	0.150058i
$369$	10.9258			0.568776
$370$	−4.36240	+	9.55232i	−0.226790	+	0.496602i
$371$	−17.4620	−	5.12730i	−0.906580	−	0.266196i
$372$	0.514852	+	0.594171i	0.0266938	+	0.0308063i
$373$	−4.82913	+	3.10349i	−0.250043	+	0.160693i	−0.659659	−	0.751565i	$-0.729299\pi$
$373$	−4.82913	+	3.10349i	−0.250043	+	0.160693i	0.409616	+	0.912258i	$0.365663\pi$
$374$	−3.84613	+	4.43867i	−0.198879	+	0.229518i
$375$	0.142315	−	0.989821i	0.00734911	−	0.0511142i
$376$	−6.64212	+	1.95030i	−0.342541	+	0.100579i
$377$	−25.9757	−	16.6936i	−1.33782	−	0.859764i
$378$	−0.626720	−	4.35894i	−0.0322350	−	0.224199i
$379$	8.38458	+	18.3597i	0.430687	+	0.943073i	0.993215	+	0.116295i	$0.0371017\pi$
$379$	8.38458	+	18.3597i	0.430687	+	0.943073i	−0.562528	+	0.826778i	$0.690171\pi$
$380$	−1.05739	−	2.31537i	−0.0542432	−	0.118776i
$381$	2.77552	+	19.3042i	0.142194	+	0.988982i
$382$	−7.80116	−	5.01350i	−0.399142	−	0.256513i
$383$	−23.6434	+	6.94233i	−1.20812	+	0.354736i	−0.822953	−	0.568110i	$-0.807675\pi$
$383$	−23.6434	+	6.94233i	−1.20812	+	0.354736i	−0.385169	+	0.922846i	$0.625857\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	2.13635	−	2.46548i	0.108879	−	0.125653i
$386$	−14.4615	+	9.29386i	−0.736073	+	0.473045i
$387$	−0.279094	−	0.322092i	−0.0141872	−	0.0163729i
$388$	9.26173	+	2.71949i	0.470193	+	0.138061i
$389$	−7.96156	+	17.4334i	−0.403667	+	0.883907i	0.593218	+	0.805042i	$0.297857\pi$
$389$	−7.96156	+	17.4334i	−0.403667	+	0.883907i	−0.996885	+	0.0788657i	$0.974870\pi$
$390$	−3.47320			−0.175872
$391$	37.9222	−	2.75772i	1.91781	−	0.139464i
$392$	−12.3931			−0.625946
$393$	−3.45808	+	7.57214i	−0.174437	+	0.381964i
$394$	12.8987	+	3.78739i	0.649826	+	0.190806i
$395$	−0.0877443	−	0.101262i	−0.00441490	−	0.00509506i
$396$	−0.623200	+	0.400506i	−0.0313170	+	0.0201262i
$397$	−8.45851	+	9.76165i	−0.424521	+	0.489923i	−0.927209	−	0.374545i	$-0.877799\pi$
$397$	−8.45851	+	9.76165i	−0.424521	+	0.489923i	0.502688	+	0.864468i	$0.332344\pi$
$398$	−2.76831	+	19.2540i	−0.138763	+	0.965115i
$399$	10.7552	−	3.15802i	0.538436	−	0.158099i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	0.424702	+	2.95387i	0.0212086	+	0.147509i	0.997674	−	0.0681647i	$-0.0217143\pi$
$401$	0.424702	+	2.95387i	0.0212086	+	0.147509i	−0.976465	+	0.215674i	$0.930805\pi$
$402$	5.32175	+	11.6530i	0.265425	+	0.581200i
$403$	1.13435	+	2.48387i	0.0565058	+	0.123730i
$404$	−2.51915	−	17.5211i	−0.125332	−	0.871706i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	−37.5644	+	11.0299i	−1.86429	+	0.547405i
$407$	−1.10712	+	7.70017i	−0.0548778	+	0.381683i
$408$	5.19187	−	5.99173i	0.257036	−	0.296635i
$409$	−6.13241	+	3.94106i	−0.303228	+	0.194873i	−0.683402	−	0.730042i	$-0.739500\pi$
$409$	−6.13241	+	3.94106i	−0.303228	+	0.194873i	0.380174	+	0.924915i	$0.375864\pi$
$410$	−7.15490	−	8.25720i	−0.353355	−	0.407794i
$411$	−7.21436	−	2.11833i	−0.355858	−	0.104489i
$412$	−2.69428	+	5.89966i	−0.132738	+	0.290655i
$413$	38.3470			1.88693
$414$	4.68744	+	1.01384i	0.230375	+	0.0498273i
$415$	12.3862			0.608016
$416$	1.44282	−	3.15933i	0.0707400	−	0.154899i
$417$	−15.1444	−	4.44679i	−0.741624	−	0.217760i
$418$	−1.23482	−	1.42506i	−0.0603971	−	0.0697019i
$419$	11.7150	−	7.52879i	0.572317	−	0.367806i	−0.222243	−	0.974991i	$-0.571338\pi$
$419$	11.7150	−	7.52879i	0.572317	−	0.367806i	0.794560	+	0.607186i	$0.207702\pi$
$420$	−2.88385	+	3.32814i	−0.140717	+	0.162397i
$421$	−3.13747	+	21.8216i	−0.152911	+	1.06352i	0.758397	+	0.651793i	$0.225983\pi$
$421$	−3.13747	+	21.8216i	−0.152911	+	1.06352i	−0.911308	+	0.411726i	$0.864926\pi$
$422$	6.92946	−	2.03467i	0.337321	−	0.0990463i
$423$	−5.82361	−	3.74260i	−0.283153	−	0.181972i
$424$	−0.588136	−	4.09058i	−0.0285624	−	0.198656i
$425$	3.29349	+	7.21174i	0.159758	+	0.349821i
$426$	3.99369	+	8.74497i	0.193495	+	0.423695i
$427$	1.98929	+	13.8358i	0.0962686	+	0.669563i
$428$	0.732987	+	0.471062i	0.0354303	+	0.0227697i
$429$	−2.46872	+	0.724881i	−0.119191	+	0.0349976i
$430$	−0.0606530	+	0.421851i	−0.00292495	+	0.0203435i
$431$	−17.6950	+	20.4211i	−0.852339	+	0.983651i	−0.999985	−	0.00538892i	$-0.998285\pi$
$431$	−17.6950	+	20.4211i	−0.852339	+	0.983651i	0.147647	+	0.989040i	$0.452830\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	15.6526	+	18.0641i	0.752217	+	0.868105i	0.994781	−	0.102031i	$-0.0325340\pi$
$433$	15.6526	+	18.0641i	0.752217	+	0.868105i	−0.242564	+	0.970135i	$0.577989\pi$
$434$	3.32199	+	0.975425i	0.159461	+	0.0468219i
$435$	−3.69312	+	8.08681i	−0.177072	+	0.387733i
$436$	9.69371			0.464244
$437$	−0.856330	+	12.1772i	−0.0409638	+	0.582515i
$438$	−4.19259			−0.200330
$439$	4.16292	−	9.11553i	0.198685	−	0.435060i	−0.783896	−	0.620892i	$-0.786771\pi$
$439$	4.16292	−	9.11553i	0.198685	−	0.435060i	0.982582	+	0.185832i	$0.0594979\pi$
$440$	0.710791	+	0.208707i	0.0338856	+	0.00994972i
$441$	−8.11575	−	9.36608i	−0.386464	−	0.446004i
$442$	23.1649	−	14.8872i	1.10184	−	0.708112i
$443$	1.86149	−	2.14827i	0.0884419	−	0.102067i	−0.709804	−	0.704400i	$-0.751216\pi$
$443$	1.86149	−	2.14827i	0.0884419	−	0.102067i	0.798245	+	0.602332i	$0.205762\pi$
$444$	1.49449	−	10.3944i	0.0709254	−	0.493297i
$445$	7.81366	−	2.29430i	0.370403	−	0.108760i
$446$	−17.4192	−	11.1946i	−0.824821	−	0.530081i
$447$	1.67013	+	11.6160i	0.0789943	+	0.549418i
$448$	−1.82939	−	4.00580i	−0.0864305	−	0.189256i
$449$	9.93260	+	21.7494i	0.468748	+	1.02642i	0.985405	+	0.170223i	$0.0544489\pi$
$449$	9.93260	+	21.7494i	0.468748	+	1.02642i	−0.516657	+	0.856192i	$0.672824\pi$
$450$	0.142315	+	0.989821i	0.00670879	+	0.0466606i
$451$	−6.80898	−	4.37586i	−0.320622	−	0.206051i
$452$	−7.49742	+	2.20144i	−0.352649	+	0.103547i
$453$	0.546663	−	3.80213i	0.0256845	−	0.178639i
$454$	−6.41080	+	7.39846i	−0.300874	+	0.347227i
$455$	−12.8671	+	8.26917i	−0.603218	+	0.387665i
$456$	1.66688	+	1.92368i	0.0780587	+	0.0900845i
$457$	−2.85715	−	0.838935i	−0.133652	−	0.0392437i	0.214222	−	0.976785i	$-0.431278\pi$
$457$	−2.85715	−	0.838935i	−0.133652	−	0.0392437i	−0.347874	+	0.937541i	$0.613096\pi$
$458$	8.60553	−	18.8435i	0.402110	−	0.880498i
$459$	7.92820			0.370057
$460$	−2.30342	−	4.20646i	−0.107397	−	0.196127i
$461$	−15.7420			−0.733177			−0.366588	−	0.930383i	$-0.619474\pi$
$461$	−15.7420			−0.733177			−0.366588	+	0.930383i	$0.619474\pi$
$462$	−1.35521	+	2.96749i	−0.0630500	+	0.138060i
$463$	−34.2731	−	10.0635i	−1.59281	−	0.467690i	−0.639273	−	0.768980i	$-0.720765\pi$
$463$	−34.2731	−	10.0635i	−1.59281	−	0.467690i	−0.953533	+	0.301290i	$0.902583\pi$
$464$	−5.82184	−	6.71876i	−0.270272	−	0.311911i
$465$	0.661394	−	0.425052i	0.0306714	−	0.0197113i
$466$	5.57952	−	6.43910i	0.258466	−	0.298286i
$467$	2.54210	−	17.6807i	0.117634	−	0.818166i	−0.842514	−	0.538675i	$-0.818925\pi$
$467$	2.54210	−	17.6807i	0.117634	−	0.818166i	0.960148	−	0.279491i	$-0.0901657\pi$
$468$	3.33251	−	0.978513i	0.154045	−	0.0452318i
$469$	47.4595	+	30.5004i	2.19148	+	1.40838i
$470$	0.985179	+	6.85207i	0.0454429	+	0.316063i
$471$	−3.05014	−	6.67888i	−0.140543	−	0.307747i
$472$	3.61734	+	7.92087i	0.166502	+	0.364588i
$473$	0.0449317	+	0.312507i	0.00206596	+	0.0143691i
$474$	0.112719	+	0.0724401i	0.00517735	+	0.00332728i
$475$	−2.44229	+	0.717120i	−0.112060	+	0.0329037i
$476$	4.96876	−	34.5585i	0.227743	−	1.58399i
$477$	2.70630	−	3.12324i	0.123913	−	0.143003i
$478$	18.2636	−	11.7373i	0.835358	−	0.536852i
$479$	−22.5249	−	25.9951i	−1.02919	−	1.18775i	−0.982004	−	0.188859i	$-0.939521\pi$
$479$	−22.5249	−	25.9951i	−1.02919	−	1.18775i	−0.0471834	−	0.998886i	$-0.515025\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	15.1515	−	33.1771i	0.690848	−	1.51275i
$482$	9.47462			0.431557
$483$	19.7793	−	7.40418i	0.899988	−	0.336902i
$484$	−10.4512			−0.475055
$485$	4.00989	−	8.78043i	0.182080	−	0.398699i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−26.8034	−	30.9328i	−1.21458	−	1.40170i	−0.890074	−	0.455817i	$-0.849347\pi$
$487$	−26.8034	−	30.9328i	−1.21458	−	1.40170i	−0.324507	−	0.945883i	$-0.605198\pi$
$488$	−2.67025	+	1.71606i	−0.120876	+	0.0776826i
$489$	−5.80485	+	6.69916i	−0.262504	+	0.302946i
$490$	−1.76372	+	12.2670i	−0.0796768	+	0.554165i
$491$	−26.7675	+	7.85966i	−1.20800	+	0.354701i	−0.822907	−	0.568176i	$-0.807649\pi$
$491$	−26.7675	+	7.85966i	−1.20800	+	0.354701i	−0.385095	+	0.922877i	$0.625831\pi$
$492$	9.19140	+	5.90695i	0.414380	+	0.266306i
$493$	−10.0308	−	69.7658i	−0.451765	−	3.14210i
$494$	3.67254	+	8.04174i	0.165235	+	0.361815i
$495$	0.307739	+	0.673854i	0.0138318	+	0.0302875i
$496$	0.111888	+	0.778198i	0.00502392	+	0.0349421i
$497$	35.6158	+	22.8889i	1.59759	+	1.02671i
$498$	−11.8845	+	3.48960i	−0.532557	+	0.156373i
$499$	−3.17305	+	22.0691i	−0.142045	+	0.987947i	0.786728	+	0.617300i	$0.211773\pi$
$499$	−3.17305	+	22.0691i	−0.142045	+	0.987947i	−0.928774	+	0.370648i	$0.879136\pi$
$500$	0.654861	−	0.755750i	0.0292863	−	0.0337981i
$501$	3.22353	−	2.07164i	0.144017	−	0.0925538i
$502$	7.21191	+	8.32299i	0.321883	+	0.371473i
$503$	29.7910	+	8.74742i	1.32831	+	0.390028i	0.867486	−	0.497461i	$-0.165734\pi$
$503$	29.7910	+	8.74742i	1.32831	+	0.390028i	0.460828	+	0.887490i	$0.347553\pi$
$504$	1.82939	−	4.00580i	0.0814874	−	0.178433i
$505$	−17.7012			−0.787695
$506$	−2.51517	−	2.50917i	−0.111813	−	0.111546i
$507$	−0.936887			−0.0416086
$508$	−8.10170	+	17.7402i	−0.359455	+	0.787096i
$509$	−4.25140	−	1.24832i	−0.188440	−	0.0553310i	0.186151	−	0.982521i	$-0.440399\pi$
$509$	−4.25140	−	1.24832i	−0.188440	−	0.0553310i	−0.374591	+	0.927190i	$0.622217\pi$
$510$	−5.19187	−	5.99173i	−0.229900	−	0.265318i
$511$	−15.5322	+	9.98193i	−0.687104	+	0.441575i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	−0.362247	+	2.51948i	−0.0159936	+	0.111238i
$514$	12.3394	−	3.62319i	0.544270	−	0.159812i
$515$	5.45617	+	3.50647i	0.240428	+	0.154513i
$516$	−0.0606530	−	0.421851i	−0.00267010	−	0.0185710i
$517$	2.13033	+	4.66478i	0.0936919	+	0.205157i
$518$	−19.2110	−	42.0661i	−0.844081	−	1.84828i
$519$	−3.18776	−	22.1714i	−0.139927	−	0.973216i
$520$	−2.92184	−	1.87775i	−0.128131	−	0.0823449i
$521$	−2.48660	+	0.730131i	−0.108940	+	0.0319876i	−0.335748	−	0.941952i	$-0.608989\pi$
$521$	−2.48660	+	0.730131i	−0.108940	+	0.0319876i	0.226808	+	0.973939i	$0.427171\pi$
$522$	1.26521	−	8.79971i	0.0553766	−	0.385153i
$523$	0.123455	−	0.142475i	0.00539833	−	0.00623000i	−0.753044	−	0.657970i	$-0.771415\pi$
$523$	0.123455	−	0.142475i	0.00539833	−	0.00623000i	0.758442	+	0.651740i	$0.225961\pi$
$524$	−7.00293	+	4.50051i	−0.305925	+	0.196606i
$525$	2.88385	+	3.32814i	0.125862	+	0.145252i
$526$	18.0223	+	5.29183i	0.785811	+	0.230735i
$527$	−2.58935	+	5.66988i	−0.112794	+	0.246984i
$528$	−0.740799			−0.0322391
$529$	0.0548782	+	22.9999i	0.00238601	+	0.999997i
$530$	−4.13264			−0.179510
$531$	−3.61734	+	7.92087i	−0.156979	+	0.343737i
$532$	10.7552	+	3.15802i	0.466299	+	0.136918i
$533$	24.8504	+	28.6789i	1.07639	+	1.24222i
$534$	−6.85078	+	4.40273i	−0.296462	+	0.190525i
$535$	0.570583	−	0.658487i	0.0246684	−	0.0284689i
$536$	−1.82315	+	12.6803i	−0.0787482	+	0.547706i
$537$	4.43991	−	1.30368i	0.191596	−	0.0562578i
$538$	15.5861	+	10.0166i	0.671966	+	0.431846i
$539$	1.30656	+	9.08734i	0.0562777	+	0.391420i
$540$	−0.415415	−	0.909632i	−0.0178766	−	0.0391443i
$541$	13.6631	+	29.9181i	0.587424	+	1.28628i	0.936986	+	0.349366i	$0.113603\pi$
$541$	13.6631	+	29.9181i	0.587424	+	1.28628i	−0.349562	+	0.936913i	$0.613670\pi$
$542$	3.25322	+	22.6266i	0.139738	+	0.971898i
$543$	0.701004	+	0.450508i	0.0300830	+	0.0193331i
$544$	7.60705	−	2.23363i	0.326150	−	0.0957662i
$545$	1.37956	−	9.59504i	0.0590938	−	0.411006i
$546$	10.0162	−	11.5593i	0.428653	−	0.494692i
$547$	−14.8559	+	9.54733i	−0.635194	+	0.408215i	−0.818229	−	0.574892i	$-0.805044\pi$
$547$	−14.8559	+	9.54733i	−0.635194	+	0.408215i	0.183035	+	0.983106i	$0.441408\pi$
$548$	−4.92385	−	5.68243i	−0.210337	−	0.242741i
$549$	−3.04556	−	0.894256i	−0.129981	−	0.0381659i
$550$	0.307739	−	0.673854i	0.0131220	−	0.0287332i
$551$	22.6290			0.964030
$552$	3.39521	+	3.38712i	0.144510	+	0.144165i
$553$	0.590057			0.0250918
$554$	−8.92169	+	19.5358i	−0.379046	+	0.829996i
$555$	−10.0759	−	2.95856i	−0.427699	−	0.125584i
$556$	−10.3361	−	11.9285i	−0.438350	−	0.505883i
$557$	21.6681	−	13.9252i	0.918106	−	0.590031i	0.00599871	−	0.999982i	$-0.498091\pi$
$557$	21.6681	−	13.9252i	0.918106	−	0.590031i	0.912108	+	0.409951i	$0.134454\pi$
$558$	−0.514852	+	0.594171i	−0.0217954	+	0.0251533i
$559$	0.210660	−	1.46517i	0.00890997	−	0.0619702i
$560$	−4.22538	+	1.24068i	−0.178555	+	0.0524284i
$561$	−4.94085	−	3.17529i	−0.208603	−	0.134061i
$562$	−0.317428	−	2.20776i	−0.0133899	−	0.0931288i
$563$	−5.70255	−	12.4868i	−0.240334	−	0.526258i	0.750576	−	0.660784i	$-0.229776\pi$
$563$	−5.70255	−	12.4868i	−0.240334	−	0.526258i	−0.990910	+	0.134526i	$0.957049\pi$
$564$	−2.87572	−	6.29696i	−0.121090	−	0.265150i
$565$	1.11204	+	7.73441i	0.0467839	+	0.325389i
$566$	−3.97431	−	2.55413i	−0.167053	−	0.107358i
$567$	4.22538	−	1.24068i	0.177449	−	0.0521038i
$568$	−1.36818	+	9.51589i	−0.0574075	+	0.399278i
$569$	−21.0694	+	24.3154i	−0.883276	+	1.01935i	0.116382	+	0.993205i	$0.462870\pi$
$569$	−21.0694	+	24.3154i	−0.883276	+	1.01935i	−0.999658	+	0.0261503i	$0.991675\pi$
$570$	2.14132	−	1.37614i	0.0896901	−	0.0576403i
$571$	10.3422	+	11.9355i	0.432807	+	0.499486i	0.929696	−	0.368328i	$-0.120070\pi$
$571$	10.3422	+	11.9355i	0.432807	+	0.499486i	−0.496888	+	0.867814i	$0.665524\pi$
$572$	−2.46872	−	0.724881i	−0.103222	−	0.0303088i
$573$	3.85225	−	8.43525i	0.160930	−	0.352388i
$574$	48.1148			2.00827
$575$	−4.49145	+	1.68133i	−0.187306	+	0.0701163i
$576$	1.00000			0.0416667
$577$	−9.43442	+	20.6585i	−0.392760	+	0.860024i	0.605194	+	0.796078i	$0.293096\pi$
$577$	−9.43442	+	20.6585i	−0.392760	+	0.860024i	−0.997953	+	0.0639457i	$0.979632\pi$
$578$	43.9988	+	12.9192i	1.83011	+	0.537369i
$579$	−11.2574	−	12.9917i	−0.467840	−	0.539916i
$580$	−7.47891	+	4.80640i	−0.310545	+	0.199575i
$581$	−35.7200	+	41.2231i	−1.48192	+	1.71022i
$582$	−1.37373	+	9.55448i	−0.0569428	+	0.396046i
$583$	−2.93745	+	0.862512i	−0.121657	+	0.0357216i
$584$	−3.52703	−	2.26668i	−0.145950	−	0.0937961i
$585$	−0.494288	−	3.43785i	−0.0204363	−	0.142137i
$586$	1.48200	+	3.24512i	0.0612207	+	0.134055i
$587$	11.1288	+	24.3687i	0.459335	+	1.00580i	0.987639	+	0.156747i	$0.0501008\pi$
$587$	11.1288	+	24.3687i	0.459335	+	1.00580i	−0.528304	+	0.849055i	$0.677172\pi$
$588$	−1.76372	−	12.2670i	−0.0727347	−	0.505881i
$589$	−1.68351	−	1.08192i	−0.0693677	−	0.0445799i
$590$	8.35505	−	2.45326i	0.343972	−	0.100999i
$591$	−1.91317	+	13.3064i	−0.0786973	+	0.547351i
$592$	6.87689	−	7.93635i	0.282638	−	0.326182i
$593$	−6.15369	+	3.95473i	−0.252702	+	0.162401i	−0.660859	−	0.750510i	$-0.729808\pi$
$593$	−6.15369	+	3.95473i	−0.252702	+	0.162401i	0.408157	+	0.912912i	$0.366171\pi$
$594$	−0.485120	−	0.559858i	−0.0199047	−	0.0229713i
$595$	−33.4996	−	9.83638i	−1.37335	−	0.403252i
$596$	−4.87508	+	10.6749i	−0.199691	+	0.437262i
$597$	−19.4520			−0.796117
$598$	8.00023	+	14.6099i	0.327154	+	0.597442i
$599$	20.2365			0.826840			0.413420	−	0.910540i	$-0.364334\pi$
$599$	20.2365			0.826840			0.413420	+	0.910540i	$0.364334\pi$
$600$	−0.415415	+	0.909632i	−0.0169592	+	0.0371356i
$601$	2.26400	+	0.664770i	0.0923505	+	0.0271165i	0.327581	−	0.944823i	$-0.393766\pi$
$601$	2.26400	+	0.664770i	0.0923505	+	0.0271165i	−0.235231	+	0.971940i	$0.575585\pi$
$602$	−1.22906	−	1.41842i	−0.0500929	−	0.0578103i
$603$	−10.7770	+	6.92598i	−0.438875	+	0.282048i
$604$	2.51547	−	2.90300i	0.102353	−	0.118122i
$605$	−1.48736	+	10.3448i	−0.0604699	+	0.420578i
$606$	16.9842	−	4.98702i	0.689937	−	0.202584i
$607$	27.3932	+	17.6045i	1.11185	+	0.714546i	0.961697	−	0.274116i	$-0.0883853\pi$
$607$	27.3932	+	17.6045i	1.11185	+	0.714546i	0.150158	+	0.988662i	$0.452022\pi$
$608$	0.362247	+	2.51948i	0.0146911	+	0.102179i
$609$	−16.2636	−	35.6124i	−0.659035	−	1.44309i
$610$	1.31858	+	2.88729i	0.0533878	+	0.116903i
$611$	−3.42172	−	23.7986i	−0.138428	−	0.962789i
$612$	6.66963	+	4.28631i	0.269604	+	0.173264i
$613$	−22.3480	+	6.56196i	−0.902626	+	0.265035i	−0.699934	−	0.714208i	$-0.746787\pi$
$613$	−22.3480	+	6.56196i	−0.902626	+	0.265035i	−0.202692	+	0.979243i	$0.564969\pi$
$614$	−2.45347	+	17.0643i	−0.0990141	+	0.688658i
$615$	7.15490	−	8.25720i	0.288513	−	0.332962i
$616$	−2.74442	+	1.76373i	−0.110576	+	0.0710628i
$617$	1.80096	+	2.07842i	0.0725040	+	0.0836741i	0.790843	−	0.612020i	$-0.209643\pi$
$617$	1.80096	+	2.07842i	0.0725040	+	0.0836741i	−0.718339	+	0.695694i	$0.755097\pi$
$618$	−6.22304	−	1.82725i	−0.250327	−	0.0735028i
$619$	14.2515	−	31.2064i	0.572816	−	1.25429i	−0.372468	−	0.928045i	$-0.621488\pi$
$619$	14.2515	−	31.2064i	0.572816	−	1.25429i	0.945284	−	0.326247i	$-0.105784\pi$
$620$	0.786200			0.0315746
$621$	−0.336424	+	4.78402i	−0.0135002	+	0.191976i
$622$	19.7145			0.790478
$623$	−14.8977	+	32.6214i	−0.596863	+	1.30695i
$624$	3.33251	+	0.978513i	0.133407	+	0.0391719i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−8.17049	+	5.25085i	−0.326558	+	0.209866i
$627$	1.23482	−	1.42506i	0.0493140	−	0.0569114i
$628$	1.04493	−	7.26767i	0.0416973	−	0.290011i
$629$	79.8839	−	23.4560i	3.18518	−	0.935254i
$630$	−3.70468	−	2.38085i	−0.147598	−	0.0948554i
$631$	0.0135556	+	0.0942810i	0.000539638	+	0.00375327i	0.990089	−	0.140438i	$-0.0448511\pi$
$631$	0.0135556	+	0.0942810i	0.000539638	+	0.00375327i	−0.989550	+	0.144191i	$0.953942\pi$
$632$	0.0556612	+	0.121881i	0.00221408	+	0.00484816i
$633$	3.00013	+	6.56936i	0.119244	+	0.261109i
$634$	−2.47834	−	17.2372i	−0.0984274	−	0.684577i
$635$	16.4067	+	10.5439i	0.651079	+	0.418423i
$636$	3.96524	−	1.16430i	0.157232	−	0.0461675i
$637$	6.12576	−	42.6056i	0.242711	−	1.68809i
$638$	−4.31281	+	4.97725i	−0.170746	+	0.197051i
$639$	−8.08759	+	5.19758i	−0.319940	+	0.205613i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	−0.925618	−	0.271786i	−0.0365597	−	0.0107349i	0.263402	−	0.964686i	$-0.415156\pi$
$641$	−0.925618	−	0.271786i	−0.0365597	−	0.0107349i	−0.299961	+	0.953951i	$0.596974\pi$
$642$	−0.361953	+	0.792566i	−0.0142851	+	0.0312801i
$643$	−2.35413			−0.0928377			−0.0464189	−	0.998922i	$-0.514781\pi$
$643$	−2.35413			−0.0928377			−0.0464189	+	0.998922i	$0.514781\pi$
$644$	20.6424	+	4.46469i	0.813424	+	0.175933i
$645$	−0.426189			−0.0167812
$646$	−8.38323	+	18.3567i	−0.329834	+	0.722236i
$647$	−16.2686	−	4.77690i	−0.639586	−	0.187799i	−0.0541691	−	0.998532i	$-0.517251\pi$
$647$	−16.2686	−	4.77690i	−0.639586	−	0.187799i	−0.585417	+	0.810732i	$0.699069\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	5.42668	−	3.48752i	0.213016	−	0.136897i
$650$	−2.27446	+	2.62487i	−0.0892117	+	0.102956i
$651$	−0.492728	+	3.42700i	−0.0193115	+	0.134315i
$652$	−8.50519	+	2.49735i	−0.333089	+	0.0978037i
$653$	8.23974	+	5.29536i	0.322446	+	0.207223i	0.691842	−	0.722048i	$-0.256799\pi$
$653$	8.23974	+	5.29536i	0.322446	+	0.207223i	−0.369397	+	0.929272i	$0.620436\pi$
$654$	1.37956	+	9.59504i	0.0539450	+	0.375196i
$655$	3.45808	+	7.57214i	0.135118	+	0.295868i
$656$	4.53876	+	9.93849i	0.177209	+	0.388033i
$657$	−0.596667	−	4.14991i	−0.0232782	−	0.161904i
$658$	−25.6458	−	16.4815i	−0.999776	−	0.642517i
$659$	−11.9483	+	3.50834i	−0.465440	+	0.136665i	−0.506040	−	0.862510i	$-0.668891\pi$
$659$	−11.9483	+	3.50834i	−0.465440	+	0.136665i	0.0406003	+	0.999175i	$0.487073\pi$
$660$	−0.105427	+	0.733258i	−0.00410373	+	0.0285420i
$661$	18.3476	−	21.1742i	0.713638	−	0.823582i	−0.276889	−	0.960902i	$-0.589303\pi$
$661$	18.3476	−	21.1742i	0.713638	−	0.823582i	0.990527	+	0.137320i	$0.0438489\pi$
$662$	−14.6192	+	9.39520i	−0.568192	+	0.365155i
$663$	18.0324	+	20.8105i	0.700320	+	0.808212i
$664$	−11.8845	−	3.48960i	−0.461208	−	0.135423i
$665$	4.65651	−	10.1963i	0.180572	−	0.395397i
$666$	10.5013			0.406917
$667$	42.5236	−	3.09234i	1.64652	−	0.119736i
$668$	3.83181			0.148257
$669$	8.60167	−	18.8350i	0.332560	−	0.728204i
$670$	12.2918	+	3.60919i	0.474873	+	0.139435i
$671$	1.53983	+	1.77706i	0.0594447	+	0.0686028i
$672$	3.70468	−	2.38085i	0.142911	−	0.0918434i
$673$	1.98633	−	2.29235i	0.0765675	−	0.0883637i	−0.716173	−	0.697923i	$-0.754108\pi$
$673$	1.98633	−	2.29235i	0.0765675	−	0.0883637i	0.792741	+	0.609559i	$0.208653\pi$
$674$	2.90382	−	20.1965i	0.111851	−	0.777942i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−0.788160	−	0.506519i	−0.0303138	−	0.0194815i
$677$	−4.90925	−	34.1446i	−0.188678	−	1.31228i	−0.835436	−	0.549588i	$-0.814785\pi$
$677$	−4.90925	−	34.1446i	−0.188678	−	1.31228i	0.646758	−	0.762695i	$-0.276124\pi$
$678$	−3.24603	−	7.10781i	−0.124663	−	0.272974i
$679$	17.6586	+	38.6669i	0.677674	+	1.48390i
$680$	−1.12830	−	7.84750i	−0.0432683	−	0.300938i
$681$	−8.23550	−	5.29264i	−0.315585	−	0.202814i
$682$	0.558824	−	0.164086i	0.0213985	−	0.00628316i
$683$	−1.06719	+	7.42249i	−0.0408350	+	0.284014i	0.959164	+	0.282849i	$0.0912797\pi$
$683$	−1.06719	+	7.42249i	−0.0408350	+	0.284014i	−0.999999	+	0.00116417i	$0.999629\pi$
$684$	−1.66688	+	1.92368i	−0.0637347	+	0.0735537i
$685$	−6.32533	+	4.06504i	−0.241678	+	0.155317i
$686$	−15.5529	−	17.9490i	−0.593812	−	0.685295i
$687$	19.8764	+	5.83623i	0.758331	+	0.222666i
$688$	0.177045	−	0.387675i	0.00674979	−	0.0147800i
$689$	14.3535			0.546824
$690$	3.83583	−	2.87861i	0.146028	−	0.109587i
$691$	−28.4483			−1.08222			−0.541112	−	0.840950i	$-0.681997\pi$
$691$	−28.4483			−1.08222			−0.541112	+	0.840950i	$0.681997\pi$
$692$	9.30504	−	20.3752i	0.353724	−	0.774548i
$693$	−3.13015	−	0.919096i	−0.118905	−	0.0349136i
$694$	−1.00700	−	1.16214i	−0.0382251	−	0.0441142i
$695$	−13.2781	+	8.53333i	−0.503668	+	0.323688i
$696$	5.82184	−	6.71876i	0.220676	−	0.254674i
$697$	−12.3276	+	85.7405i	−0.466942	+	3.24765i
$698$	18.2580	−	5.36104i	0.691076	−	0.202918i
$699$	7.16761	+	4.60634i	0.271104	+	0.174228i
$700$	0.626720	+	4.35894i	0.0236878	+	0.164752i
$701$	−12.4807	−	27.3289i	−0.471389	−	1.03220i	−0.984742	−	0.174020i	$-0.944324\pi$
$701$	−12.4807	−	27.3289i	−0.471389	−	1.03220i	0.513354	−	0.858177i	$-0.328403\pi$
$702$	1.44282	+	3.15933i	0.0544557	+	0.119241i
$703$	3.80407	+	26.4579i	0.143473	+	0.997877i
$704$	−0.623200	−	0.400506i	−0.0234877	−	0.0150946i
$705$	−6.64212	+	1.95030i	−0.250157	+	0.0734527i
$706$	−0.390911	+	2.71885i	−0.0147121	+	0.102325i
$707$	51.0477	−	58.9122i	1.91985	−	2.21562i
$708$	−7.32545	+	4.70778i	−0.275307	+	0.176929i
$709$	−27.6853	−	31.9506i	−1.03974	−	1.19993i	−0.979437	−	0.201750i	$-0.935337\pi$
$709$	−27.6853	−	31.9506i	−1.03974	−	1.19993i	−0.0603077	−	0.998180i	$-0.519208\pi$
$710$	9.22432	+	2.70850i	0.346182	+	0.101648i
$711$	−0.0556612	+	0.121881i	−0.00208746	+	0.00457089i
$712$	−8.14353			−0.305192
$713$	−3.31143	−	1.80305i	−0.124014	−	0.0675248i
$714$	34.9139			1.30662
$715$	−1.06884	+	2.34043i	−0.0399723	+	0.0875271i
$716$	4.43991	+	1.30368i	0.165927	+	0.0487206i
$717$	14.2170	+	16.4073i	0.530944	+	0.612742i
$718$	30.4854	−	19.5918i	1.13770	−	0.731158i
$719$	−11.8271	+	13.6492i	−0.441078	+	0.509031i	−0.932142	−	0.362093i	$-0.882062\pi$
$719$	−11.8271	+	13.6492i	−0.441078	+	0.509031i	0.491065	+	0.871123i	$0.336608\pi$
$720$	0.142315	−	0.989821i	0.00530376	−	0.0368885i
$721$	−27.4048	+	8.04677i	−1.02061	+	0.299677i
$722$	10.5333	+	6.76935i	0.392009	+	0.251929i
$723$	1.34838	+	9.37819i	0.0501468	+	0.348778i
$724$	0.346159	+	0.757983i	0.0128649	+	0.0281702i
$725$	3.69312	+	8.08681i	0.137159	+	0.300336i
$726$	−1.48736	−	10.3448i	−0.0552012	−	0.383933i
$727$	−3.91626	−	2.51683i	−0.145246	−	0.0933440i	0.465999	−	0.884785i	$-0.345695\pi$
$727$	−3.91626	−	2.51683i	−0.145246	−	0.0933440i	−0.611246	+	0.791441i	$0.709331\pi$
$728$	14.6756	−	4.30914i	0.543913	−	0.159707i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−2.74556	+	3.16855i	−0.101618	+	0.117273i
$731$	2.84252	−	1.82678i	0.105134	−	0.0675658i
$732$	−2.07861	−	2.39885i	−0.0768278	−	0.0886640i
$733$	15.0542	+	4.42032i	0.556040	+	0.163268i	0.547666	−	0.836697i	$-0.315516\pi$
$733$	15.0542	+	4.42032i	0.556040	+	0.163268i	0.00837383	+	0.999965i	$0.497334\pi$
$734$	−14.0208	+	30.7012i	−0.517516	+	1.13320i
$735$	−12.3931			−0.457126
$736$	1.02502	+	4.68501i	0.0377826	+	0.172692i
$737$	9.49015			0.349574
$738$	−4.53876	+	9.93849i	−0.167074	+	0.365841i
$739$	26.3185	+	7.72780i	0.968140	+	0.284272i	0.727320	−	0.686298i	$-0.240765\pi$
$739$	26.3185	+	7.72780i	0.968140	+	0.284272i	0.240820	+	0.970570i	$0.422584\pi$
$740$	−6.87689	−	7.93635i	−0.252800	−	0.291746i
$741$	−7.43723	+	4.77962i	−0.273214	+	0.175584i
$742$	11.9179	−	13.7540i	0.437520	−	0.504926i
$743$	1.84294	−	12.8179i	0.0676109	−	0.470244i	−0.927685	−	0.373364i	$-0.878204\pi$
$743$	1.84294	−	12.8179i	0.0676109	−	0.470244i	0.995296	−	0.0968807i	$-0.0308865\pi$
$744$	−0.754354	+	0.221498i	−0.0276560	+	0.00812052i
$745$	9.87248	+	6.34466i	0.361700	+	0.232450i
$746$	−0.816944	−	5.68197i	−0.0299104	−	0.208032i
$747$	−5.14543	−	11.2669i	−0.188261	−	0.412235i
$748$	−2.43982	−	5.34245i	−0.0892085	−	0.195339i
$749$	0.546064	+	3.79796i	0.0199527	+	0.138774i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	12.4337	−	3.65088i	0.453714	−	0.133222i	−0.0468879	−	0.998900i	$-0.514930\pi$
$751$	12.4337	−	3.65088i	0.453714	−	0.133222i	0.500602	+	0.865678i	$0.333112\pi$
$752$	0.985179	−	6.85207i	0.0359258	−	0.249869i
$753$	−7.21191	+	8.32299i	−0.262817	+	0.303307i
$754$	25.9757	−	16.6936i	0.945981	−	0.607945i
$755$	−2.51547	−	2.90300i	−0.0915472	−	0.105651i
$756$	4.22538	+	1.24068i	0.153675	+	0.0451232i
$757$	−2.33919	+	5.12211i	−0.0850193	+	0.186166i	−0.947366	−	0.320151i	$-0.896266\pi$
$757$	−2.33919	+	5.12211i	−0.0850193	+	0.186166i	0.862347	+	0.506317i	$0.168994\pi$
$758$	−20.1836			−0.733102
$759$	2.12569	−	2.84666i	0.0771575	−	0.103327i
$760$	2.54539			0.0923311
$761$	−12.8187	+	28.0690i	−0.464678	+	1.01750i	0.521719	+	0.853118i	$0.325291\pi$
$761$	−12.8187	+	28.0690i	−0.464678	+	1.01750i	−0.986396	+	0.164385i	$0.947436\pi$
$762$	−18.7127	−	5.49453i	−0.677888	−	0.199046i
$763$	27.9552	+	32.2620i	1.01205	+	1.16796i
$764$	7.80116	−	5.01350i	0.282236	−	0.181382i
$765$	5.19187	−	5.99173i	0.187712	−	0.216632i
$766$	3.50686	−	24.3907i	0.126708	−	0.881273i
$767$	−29.0188	+	8.52068i	−1.04781	+	0.307664i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	−0.239280	−	1.66423i	−0.00862866	−	0.0600136i	0.985052	−	0.172256i	$-0.0551057\pi$
$769$	−0.239280	−	1.66423i	−0.00862866	−	0.0600136i	−0.993681	+	0.112243i	$0.964197\pi$
$770$	1.35521	+	2.96749i	0.0488383	+	0.106941i
$771$	5.34240	+	11.6982i	0.192402	+	0.421301i
$772$	−2.44646	−	17.0155i	−0.0880499	−	0.612401i
$773$	−19.9422	−	12.8161i	−0.717273	−	0.460963i	0.130414	−	0.991460i	$-0.458369\pi$
$773$	−19.9422	−	12.8161i	−0.717273	−	0.460963i	−0.847687	+	0.530496i	$0.822006\pi$
$774$	0.408925	−	0.120071i	0.0146985	−	0.00431587i
$775$	0.111888	−	0.778198i	0.00401914	−	0.0279537i
$776$	−6.32119	+	7.29505i	−0.226918	+	0.261877i
$777$	38.9039	−	25.0020i	1.39567	−	0.896944i
$778$	−12.5506	−	14.4842i	−0.449961	−	0.519283i
$779$	−26.6840	−	7.83514i	−0.956054	−	0.280723i
$780$	1.44282	−	3.15933i	0.0516612	−	0.113122i
$781$	7.12185			0.254840
$782$	−13.2449	+	35.6408i	−0.473638	+	1.27451i
$783$	8.89020			0.317710
$784$	5.14828	−	11.2732i	0.183867	−	0.402613i
$785$	−7.04498	−	2.06859i	−0.251446	−	0.0738313i
$786$	−5.45133	−	6.29116i	−0.194442	−	0.224398i
$787$	−17.3987	+	11.1814i	−0.620195	+	0.398575i	−0.812668	−	0.582727i	$-0.801986\pi$
$787$	−17.3987	+	11.1814i	−0.620195	+	0.398575i	0.192473	+	0.981302i	$0.438349\pi$
$788$	−8.80343	+	10.1597i	−0.313609	+	0.361924i
$789$	−2.67313	+	18.5920i	−0.0951658	+	0.661893i
$790$	0.128562	−	0.0377492i	0.00457402	−	0.00134305i
$791$	−28.9481	−	18.6038i	−1.02928	−	0.661476i
$792$	−0.105427	−	0.733258i	−0.00374617	−	0.0260552i
$793$	−4.57970	−	10.0281i	−0.162630	−	0.356110i
$794$	−5.36571	−	11.7493i	−0.190422	−	0.416966i
$795$	−0.588136	−	4.09058i	−0.0208590	−	0.145078i
$796$	−16.3640	−	10.5165i	−0.580008	−	0.372749i
$797$	37.6573	−	11.0572i	1.33389	−	0.391666i	0.464404	−	0.885623i	$-0.346268\pi$
$797$	37.6573	−	11.0572i	1.33389	−	0.391666i	0.869486	+	0.493958i	$0.164450\pi$
$798$	−1.59525	+	11.0952i	−0.0564712	+	0.392766i
$799$	35.9409	−	41.4780i	1.27150	−	1.46739i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	−5.33288	−	6.15447i	−0.188428	−	0.217458i
$802$	−2.86336	−	0.840758i	−0.101109	−	0.0296882i
$803$	−1.29022	+	2.82519i	−0.0455310	+	0.0996989i
$804$	−12.8107			−0.451798
$805$	7.35696	−	19.7969i	0.259299	−	0.697748i
$806$	−2.73063			−0.0961824
$807$	−7.69650	+	16.8530i	−0.270930	+	0.593253i
$808$	16.9842	+	4.98702i	0.597503	+	0.175443i
$809$	−1.55941	−	1.79965i	−0.0548259	−	0.0632725i	0.727674	−	0.685923i	$-0.240601\pi$
$809$	−1.55941	−	1.79965i	−0.0548259	−	0.0632725i	−0.782500	+	0.622650i	$0.786056\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	−0.0862680	+	0.0995585i	−0.00302928	+	0.00349597i	−0.757262	−	0.653111i	$-0.773463\pi$
$811$	−0.0862680	+	0.0995585i	−0.00302928	+	0.00349597i	0.754233	+	0.656607i	$0.228009\pi$
$812$	5.57167	−	38.7518i	0.195527	−	1.35992i
$813$	−21.9334	+	6.44021i	−0.769236	+	0.225868i
$814$	−6.54441	−	4.20584i	−0.229381	−	0.147414i
$815$	1.26151	+	8.77403i	0.0441889	+	0.307341i
$816$	3.29349	+	7.21174i	0.115295	+	0.252462i
$817$	0.450650	+	0.986785i	0.0157662	+	0.0345232i
$818$	−1.03742	−	7.21542i	−0.0362726	−	0.252281i
$819$	12.8671	+	8.26917i	0.449612	+	0.288948i
$820$	10.4833	−	3.07816i	0.366091	−	0.107494i
$821$	5.44612	−	37.8786i	0.190071	−	1.32197i	−0.641745	−	0.766918i	$-0.721789\pi$
$821$	5.44612	−	37.8786i	0.190071	−	1.32197i	0.831815	−	0.555053i	$-0.187302\pi$
$822$	4.92385	−	5.68243i	0.171739	−	0.198198i
$823$	−24.2543	+	15.5873i	−0.845453	+	0.543340i	−0.890153	−	0.455661i	$-0.849403\pi$
$823$	−24.2543	+	15.5873i	−0.845453	+	0.543340i	0.0447006	+	0.999000i	$0.485767\pi$
$824$	−4.24727	−	4.90161i	−0.147961	−	0.170756i
$825$	0.710791	+	0.208707i	0.0247466	+	0.00726625i
$826$	−15.9299	+	34.8816i	−0.554272	+	1.21369i
$827$	26.0146			0.904616			0.452308	−	0.891862i	$-0.350601\pi$
$827$	26.0146			0.904616			0.452308	+	0.891862i	$0.350601\pi$
$828$	−2.86945	+	3.84269i	−0.0997204	+	0.133543i
$829$	17.7466			0.616365			0.308183	−	0.951327i	$-0.400279\pi$
$829$	17.7466			0.616365			0.308183	+	0.951327i	$0.400279\pi$
$830$	−5.14543	+	11.2669i	−0.178600	+	0.391080i
$831$	−20.6066	−	6.05065i	−0.714836	−	0.209895i
$832$	2.27446	+	2.62487i	0.0788528	+	0.0910010i
$833$	82.6573	−	53.1206i	2.86391	−	1.84052i
$834$	10.3361	−	11.9285i	0.357912	−	0.413052i
$835$	0.545324	−	3.79281i	0.0188717	−	0.131256i
$836$	1.80924	−	0.531242i	0.0625740	−	0.0183734i
$837$	−0.661394	−	0.425052i	−0.0228611	−	0.0146919i
$838$	1.98183	+	13.7839i	0.0684612	+	0.476158i
$839$	−1.86301	−	4.07943i	−0.0643184	−	0.140838i	0.874743	−	0.484587i	$-0.161030\pi$
$839$	−1.86301	−	4.07943i	−0.0643184	−	0.140838i	−0.939061	+	0.343750i	$0.888303\pi$
$840$	−1.82939	−	4.00580i	−0.0631199	−	0.138213i
$841$	−7.12081	−	49.5263i	−0.245545	−	1.70780i
$842$	−18.5463	−	11.9190i	−0.639147	−	0.410755i
$843$	2.14012	−	0.628395i	0.0737095	−	0.0216431i
$844$	−1.02780	+	7.14849i	−0.0353783	+	0.246061i
$845$	−0.613531	+	0.708052i	−0.0211061	+	0.0243577i
$846$	5.82361	−	3.74260i	0.200220	−	0.128673i
$847$	−30.1397	−	34.7831i	−1.03561	−	1.19516i
$848$	3.96524	+	1.16430i	0.136167	+	0.0399822i
$849$	1.96253	−	4.29734i	0.0673539	−	0.147484i
$850$	−7.92820			−0.271935
$851$	10.7640	+	49.1987i	0.368986	+	1.68651i
$852$	−9.61374			−0.329361
$853$	0.863986	−	1.89187i	0.0295823	−	0.0647762i	−0.894264	−	0.447540i	$-0.852300\pi$
$853$	0.863986	−	1.89187i	0.0295823	−	0.0647762i	0.923846	+	0.382763i	$0.125028\pi$
$854$	−13.4119	−	3.93809i	−0.458946	−	0.134759i
$855$	1.66688	+	1.92368i	0.0570060	+	0.0657885i
$856$	−0.732987	+	0.471062i	−0.0250530	+	0.0161006i
$857$	−20.2359	+	23.3534i	−0.691244	+	0.797738i	−0.987542	−	0.157358i	$-0.949702\pi$
$857$	−20.2359	+	23.3534i	−0.691244	+	0.797738i	0.296298	+	0.955096i	$0.404248\pi$
$858$	0.366168	−	2.54675i	0.0125008	−	0.0869447i
$859$	−10.0685	+	2.95639i	−0.343534	+	0.100871i	−0.448948	−	0.893558i	$-0.648201\pi$
$859$	−10.0685	+	2.95639i	−0.343534	+	0.100871i	0.105414	+	0.994428i	$0.466383\pi$
$860$	−0.358533	−	0.230415i	−0.0122259	−	0.00785709i
$861$	6.84744	+	47.6250i	0.233360	+	1.62306i
$862$	−11.2249	−	24.5792i	−0.382323	−	0.837171i
$863$	−3.02978	−	6.63430i	−0.103135	−	0.225834i	0.851029	−	0.525119i	$-0.175979\pi$
$863$	−3.02978	−	6.63430i	−0.103135	−	0.225834i	−0.954164	+	0.299285i	$0.903252\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	−18.8436	−	12.1100i	−0.640700	−	0.411753i
$866$	−22.9340	+	6.73403i	−0.779329	+	0.228832i
$867$	−6.52604	+	45.3896i	−0.221636	+	1.54151i
$868$	−2.26728	+	2.61658i	−0.0769566	+	0.0888127i
$869$	0.0835021	−	0.0536635i	0.00283261	−	0.00182041i
$870$	−5.82184	−	6.71876i	−0.197379	−	0.227787i
$871$	−42.6918	−	12.5354i	−1.44656	−	0.424747i
$872$	−4.02691	+	8.81771i	−0.136368	+	0.298605i
$873$	−9.65273			−0.326695
$874$	−10.7210	−	5.83754i	−0.362645	−	0.197458i
$875$	4.40376			0.148874
$876$	1.74166	−	3.81371i	0.0588454	−	0.128853i
$877$	16.4150	+	4.81988i	0.554295	+	0.162756i	0.546871	−	0.837217i	$-0.315819\pi$
$877$	16.4150	+	4.81988i	0.554295	+	0.162756i	0.00742396	+	0.999972i	$0.497637\pi$
$878$	6.56243	+	7.57345i	0.221471	+	0.255592i
$879$	−3.00118	+	1.92874i	−0.101227	+	0.0650547i
$880$	−0.485120	+	0.559858i	−0.0163534	+	0.0188728i
$881$	−2.04478	+	14.2217i	−0.0688903	+	0.479142i	0.925947	+	0.377655i	$0.123269\pi$
$881$	−2.04478	+	14.2217i	−0.0688903	+	0.479142i	−0.994837	+	0.101488i	$0.967640\pi$
$882$	11.8911	−	3.49154i	0.400394	−	0.117566i
$883$	−16.0961	−	10.3443i	−0.541675	−	0.348114i	0.241018	−	0.970521i	$-0.422519\pi$
$883$	−16.0961	−	10.3443i	−0.541675	−	0.348114i	−0.782694	+	0.622407i	$0.786155\pi$
$884$	3.91881	+	27.2559i	0.131804	+	0.916716i
$885$	3.61734	+	7.92087i	0.121596	+	0.266257i
$886$	1.18085	+	2.58569i	0.0396713	+	0.0868680i
$887$	−3.65882	−	25.4476i	−0.122851	−	0.854448i	−0.954301	−	0.298848i	$-0.903398\pi$
$887$	−3.65882	−	25.4476i	−0.122851	−	0.854448i	0.831450	−	0.555600i	$-0.187511\pi$
$888$	8.83426	+	5.67743i	0.296458	+	0.190522i
$889$	−82.4061	+	24.1966i	−2.76381	+	0.811528i
$890$	−1.15895	+	8.06064i	−0.0388479	+	0.270193i
$891$	0.485120	−	0.559858i	0.0162521	−	0.0187560i
$892$	17.4192	−	11.1946i	0.583237	−	0.374824i
$893$	11.5390	+	13.3167i	0.386138	+	0.445628i
$894$	−11.2601	−	3.30626i	−0.376593	−	0.110578i
$895$	1.92227	−	4.20919i	0.0642544	−	0.140698i
$896$	4.40376			0.147119
$897$	−13.3226	+	9.99800i	−0.444829	+	0.333823i
$898$	−23.9101			−0.797889
$899$	−2.90353	+	6.35785i	−0.0968383	+	0.212046i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	21.4561	+	24.7617i	0.714807	+	0.824931i
$902$	6.80898	−	4.37586i	0.226714	−	0.145700i
$903$	1.22906	−	1.41842i	0.0409007	−	0.0472019i
$904$	1.11204	−	7.73441i	0.0369859	−	0.257243i
$905$	0.799531	−	0.234764i	0.0265773	−	0.00780381i
$906$	3.23144	+	2.07672i	0.107358	+	0.0689945i
$907$	−2.72927	−	18.9825i	−0.0906239	−	0.630303i	−0.983622	−	0.180243i	$-0.942312\pi$
$907$	−2.72927	−	18.9825i	−0.0906239	−	0.630303i	0.892998	−	0.450060i	$-0.148597\pi$
$908$	−4.06673	−	8.90490i	−0.134959	−	0.295519i
$909$	7.35336	+	16.1016i	0.243896	+	0.534057i
$910$	−2.17672	−	15.1395i	−0.0721577	−	0.501868i
$911$	4.65958	+	2.99453i	0.154379	+	0.0992132i	0.615550	−	0.788098i	$-0.288934\pi$
$911$	4.65958	+	2.99453i	0.154379	+	0.0992132i	−0.461171	+	0.887311i	$0.652570\pi$
$912$	−2.44229	+	0.717120i	−0.0808722	+	0.0237462i
$913$	−1.30584	+	9.08231i	−0.0432170	+	0.300580i
$914$	1.95003	−	2.25045i	0.0645011	−	0.0744383i
$915$	−2.67025	+	1.71606i	−0.0882757	+	0.0567314i
$916$	13.5658	+	15.6557i	0.448226	+	0.517280i
$917$	−35.1737	−	10.3279i	−1.16154	−	0.341059i
$918$	−3.29349	+	7.21174i	−0.108701	+	0.238023i
$919$	−25.8928			−0.854124			−0.427062	−	0.904222i	$-0.640451\pi$
$919$	−25.8928			−0.854124			−0.427062	+	0.904222i	$0.640451\pi$
$920$	4.78320	−	0.347837i	0.157697	−	0.0114679i
$921$	−17.2398			−0.568069
$922$	6.53945	−	14.3194i	0.215365	−	0.471584i
$923$	−32.0379	−	9.40717i	−1.05454	−	0.309641i
$924$	−2.13635	−	2.46548i	−0.0702808	−	0.0811084i
$925$	−8.83426	+	5.67743i	−0.290469	+	0.186673i
$926$	23.3916	−	26.9954i	0.768697	−	0.887123i
$927$	0.923020	−	6.41975i	0.0303160	−	0.210852i
$928$	8.53008	−	2.50466i	0.280014	−	0.0822194i
$929$	36.4517	+	23.4261i	1.19594	+	0.768584i	0.978249	−	0.207433i	$-0.0665110\pi$
$929$	36.4517	+	23.4261i	1.19594	+	0.768584i	0.217691	+	0.976018i	$0.430147\pi$
$930$	0.111888	+	0.778198i	0.00366895	+	0.0255181i
$931$	13.1044	+	28.6946i	0.429479	+	0.940428i
$932$	3.53940	+	7.75021i	0.115937	+	0.253866i
$933$	2.80566	+	19.5138i	0.0918532	+	0.638853i
$934$	15.0269	+	9.65721i	0.491696	+	0.315994i
$935$	−5.63529	+	1.65467i	−0.184294	+	0.0541136i
$936$	−0.494288	+	3.43785i	−0.0161563	+	0.112370i
$937$	−10.0265	+	11.5712i	−0.327552	+	0.378016i	−0.895509	−	0.445043i	$-0.853189\pi$
$937$	−10.0265	+	11.5712i	−0.327552	+	0.378016i	0.567957	+	0.823058i	$0.307734\pi$
$938$	−47.4595	+	30.5004i	−1.54961	+	0.995872i
$939$	−6.36019	−	7.34005i	−0.207557	−	0.239533i
$940$	−6.64212	−	1.95030i	−0.216642	−	0.0636119i
$941$	−23.6564	+	51.8004i	−0.771178	+	1.68864i	−0.0471348	+	0.998889i	$0.515009\pi$
$941$	−23.6564	+	51.8004i	−0.771178	+	1.68864i	−0.724043	+	0.689755i	$0.757718\pi$
$942$	7.34240			0.239228
$943$	−51.2142	−	11.0770i	−1.66777	−	0.360717i
$944$	−8.70778			−0.283414
$945$	1.82939	−	4.00580i	0.0595100	−	0.130309i
$946$	−0.302931	−	0.0889487i	−0.00984915	−	0.00289197i
$947$	22.3094	+	25.7464i	0.724958	+	0.836646i	0.991894	−	0.127068i	$-0.0405568\pi$
$947$	22.3094	+	25.7464i	0.724958	+	0.836646i	−0.266936	+	0.963714i	$0.586011\pi$
$948$	−0.112719	+	0.0724401i	−0.00366094	+	0.00235274i
$949$	9.53588	−	11.0050i	0.309548	−	0.357237i
$950$	0.362247	−	2.51948i	0.0117529	−	0.0817429i
$951$	16.7091	−	4.90622i	0.541828	−	0.159095i
$952$	29.3714	+	18.8759i	0.951933	+	0.611770i
$953$	−7.84153	−	54.5391i	−0.254012	−	1.76669i	−0.573599	−	0.819136i	$-0.694453\pi$
$953$	−7.84153	−	54.5391i	−0.254012	−	1.76669i	0.319587	−	0.947557i	$-0.396456\pi$
$954$	1.71676	+	3.75918i	0.0555822	+	0.121708i
$955$	−3.85225	−	8.43525i	−0.124656	−	0.272958i
$956$	3.08965	+	21.4890i	0.0999265	+	0.695004i
$957$	−5.54037	−	3.56058i	−0.179095	−	0.115097i
$958$	33.0031	−	9.69059i	1.06628	−	0.313089i
$959$	4.71227	−	32.7745i	0.152167	−	1.05835i
$960$	0.654861	−	0.755750i	0.0211355	−	0.0243917i
$961$	−25.5589	+	16.4257i	−0.824480	+	0.529861i
$962$	23.8848	+	27.5645i	0.770077	+	0.888716i
$963$	−0.836010	−	0.245475i	−0.0269400	−	0.00791031i
$964$	−3.93590	+	8.61842i	−0.126767	+	0.277581i
$965$	−17.1905			−0.553380
$966$	−1.48153	+	21.0677i	−0.0476674	+	0.677841i
$967$	25.3683			0.815788			0.407894	−	0.913029i	$-0.366263\pi$
$967$	25.3683			0.815788			0.407894	+	0.913029i	$0.366263\pi$
$968$	4.34159	−	9.50676i	0.139544	−	0.305559i
$969$	−19.3629	−	5.68547i	−0.622027	−	0.182644i
$970$	6.32119	+	7.29505i	0.202961	+	0.234230i
$971$	4.99745	−	3.21167i	0.160376	−	0.103067i	−0.457991	−	0.888957i	$-0.651431\pi$
$971$	4.99745	−	3.21167i	0.160376	−	0.103067i	0.618367	+	0.785889i	$0.287795\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	9.89199	−	68.8003i	0.317123	−	2.20564i
$974$	39.2720	−	11.5313i	1.25836	−	0.369487i
$975$	−2.92184	−	1.87775i	−0.0935738	−	0.0601362i
$976$	−0.451726	−	3.14182i	−0.0144594	−	0.100567i
$977$	9.98582	+	21.8659i	0.319475	+	0.699552i	0.999432	−	0.0336998i	$-0.0107290\pi$
$977$	9.98582	+	21.8659i	0.319475	+	0.699552i	−0.679957	+	0.733252i	$0.738002\pi$
$978$	−3.68234	−	8.06321i	−0.117748	−	0.257833i
$979$	0.858545	+	5.97131i	0.0274392	+	0.190844i
$980$	−10.4257	−	6.70022i	−0.333038	−	0.214031i
$981$	−9.30104	+	2.73103i	−0.296959	+	0.0871952i
$982$	3.97024	−	27.6136i	0.126695	−	0.881186i
$983$	33.9868	−	39.2228i	1.08401	−	1.25101i	0.117860	−	0.993030i	$-0.462397\pi$
$983$	33.9868	−	39.2228i	1.08401	−	1.25101i	0.966149	−	0.257983i	$-0.0830579\pi$
$984$	−9.19140	+	5.90695i	−0.293011	+	0.188307i
$985$	8.80343	+	10.1597i	0.280501	+	0.323715i
$986$	67.6282	+	19.8574i	2.15372	+	0.632389i
$987$	12.6640	−	27.7303i	0.403100	−	0.882665i
$988$	−8.84066			−0.281259
$989$	0.981691	+	1.79274i	0.0312160	+	0.0570060i
$990$	−0.740799			−0.0235441
$991$	17.3860	−	38.0701i	0.552286	−	1.20934i	−0.403420	−	0.915015i	$-0.632179\pi$
$991$	17.3860	−	38.0701i	0.552286	−	1.20934i	0.955706	−	0.294323i	$-0.0950940\pi$
$992$	−0.754354	−	0.221498i	−0.0239508	−	0.00703258i
$993$	−11.3801	−	13.1333i	−0.361137	−	0.416774i
$994$	−35.6158	+	22.8889i	−1.12967	+	0.725992i
$995$	−12.7383	+	14.7008i	−0.403832	+	0.466048i
$996$	1.76274	−	12.2602i	0.0558547	−	0.388478i
$997$	1.27409	−	0.374105i	0.0403507	−	0.0118480i	−0.261495	−	0.965205i	$-0.584215\pi$
$997$	1.27409	−	0.374105i	0.0403507	−	0.0118480i	0.301846	+	0.953357i	$0.402397\pi$
$998$	−18.7566	−	12.0541i	−0.593730	−	0.381567i
$999$	1.49449	+	10.3944i	0.0472836	+	0.328865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.121.3	✓	30
23.4	even	11	inner	690.2.m.h.211.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.121.3	✓	30	1.1	even	1	trivial
690.2.m.h.211.3	yes	30	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.626720 - 4.35894i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(0.626720 - 4.35894i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-0.307739 - 0.673854i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.494288 + 3.43785i) q^{13} +(3.70468 + 2.38085i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-5.19187 + 5.99173i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(-1.66688 - 1.92368i) q^{19} +(0.959493 + 0.281733i) q^{20} +(-1.82939 + 4.00580i) q^{21} +0.740799 q^{22} +(-3.39521 - 3.38712i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-3.33251 - 0.978513i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-3.70468 + 2.38085i) q^{28} +(-5.82184 + 6.71876i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(0.754354 - 0.221498i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.105427 + 0.733258i) q^{33} +(-3.29349 - 7.21174i) q^{34} +(1.82939 + 4.00580i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-8.83426 - 5.67743i) q^{37} +(2.44229 - 0.717120i) q^{38} +(0.494288 - 3.43785i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(9.19140 - 5.90695i) q^{41} +(-2.88385 - 3.32814i) q^{42} +(-0.408925 - 0.120071i) q^{43} +(-0.307739 + 0.673854i) q^{44} -1.00000 q^{45} +(4.49145 - 1.68133i) q^{46} -6.92253 q^{47} +(0.415415 - 0.909632i) q^{48} +(-11.8911 - 3.49154i) q^{49} +(0.654861 + 0.755750i) q^{50} +(6.66963 - 4.28631i) q^{51} +(2.27446 - 2.62487i) q^{52} +(0.588136 - 4.09058i) q^{53} +(0.959493 - 0.281733i) q^{54} +(0.623200 + 0.400506i) q^{55} +(-0.626720 - 4.35894i) q^{56} +(1.05739 + 2.31537i) q^{57} +(-3.69312 - 8.08681i) q^{58} +(1.23925 + 8.61915i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(-3.04556 + 0.894256i) q^{61} +(-0.111888 + 0.778198i) q^{62} +(2.88385 - 3.32814i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-2.27446 - 2.62487i) q^{65} +(-0.710791 - 0.208707i) q^{66} +(-5.32175 + 11.6530i) q^{67} +7.92820 q^{68} +(2.30342 + 4.20646i) q^{69} -4.40376 q^{70} +(-3.99369 + 8.74497i) q^{71} +(0.959493 + 0.281733i) q^{72} +(-2.74556 - 3.16855i) q^{73} +(8.83426 - 5.67743i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(-0.362247 + 2.51948i) q^{76} +(-3.13015 + 0.919096i) q^{77} +(2.92184 + 1.87775i) q^{78} +(0.0190687 + 0.132626i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.55491 + 10.8146i) q^{82} +(-10.4200 - 6.69650i) q^{83} +(4.22538 - 1.24068i) q^{84} +(1.12830 - 7.84750i) q^{85} +(0.279094 - 0.322092i) q^{86} +(7.47891 - 4.80640i) q^{87} +(-0.485120 - 0.559858i) q^{88} +(-7.81366 - 2.29430i) q^{89} +(0.415415 - 0.909632i) q^{90} +15.2951 q^{91} +(-0.336424 + 4.78402i) q^{92} -0.786200 q^{93} +(2.87572 - 6.29696i) q^{94} +(2.44229 + 0.717120i) q^{95} +(0.654861 + 0.755750i) q^{96} +(-8.12039 + 5.21866i) q^{97} +(8.11575 - 9.36608i) q^{98} +(0.105427 - 0.733258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

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