LMFDB - Embedded newform 425.2.r.a.69.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.16
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.628349 + 0.204163i) q^{2} +(0.482449 + 0.664034i) q^{3} +(-1.26489 + 0.918999i) q^{4} +(2.18757 - 0.463165i) q^{5} +(-0.438718 - 0.318747i) q^{6} -4.33633i q^{7} +(1.38385 - 1.90471i) q^{8} +(0.718867 - 2.21244i) q^{9} +(-1.28000 + 0.737651i) q^{10} +(0.471027 + 1.44967i) q^{11} +(-1.22049 - 0.396562i) q^{12} +(-6.34940 - 2.06304i) q^{13} +(0.885318 + 2.72473i) q^{14} +(1.36295 + 1.22917i) q^{15} +(0.485622 - 1.49459i) q^{16} +(0.587785 - 0.809017i) q^{17} +1.53695i q^{18} +(-3.52786 - 2.56314i) q^{19} +(-2.34140 + 2.59623i) q^{20} +(2.87947 - 2.09206i) q^{21} +(-0.591939 - 0.814734i) q^{22} +(5.09722 - 1.65619i) q^{23} +1.93243 q^{24} +(4.57096 - 2.02641i) q^{25} +4.41084 q^{26} +(4.15781 - 1.35095i) q^{27} +(3.98508 + 5.48499i) q^{28} +(-0.798778 + 0.580346i) q^{29} +(-1.10736 - 0.494084i) q^{30} +(5.66269 + 4.11419i) q^{31} +5.74697i q^{32} +(-0.735385 + 1.01217i) q^{33} +(-0.204163 + 0.628349i) q^{34} +(-2.00843 - 9.48604i) q^{35} +(1.12394 + 3.45915i) q^{36} +(1.72441 + 0.560296i) q^{37} +(2.74003 + 0.890289i) q^{38} +(-1.69333 - 5.21153i) q^{39} +(2.14508 - 4.80764i) q^{40} +(-1.09444 + 3.36833i) q^{41} +(-1.38219 + 1.90242i) q^{42} +0.221105i q^{43} +(-1.92805 - 1.40081i) q^{44} +(0.547848 - 5.17284i) q^{45} +(-2.86470 + 2.08133i) q^{46} +(-5.50531 - 7.57741i) q^{47} +(1.22675 - 0.398594i) q^{48} -11.8037 q^{49} +(-2.45844 + 2.20652i) q^{50} +0.820791 q^{51} +(9.92725 - 3.22556i) q^{52} +(7.56730 + 10.4155i) q^{53} +(-2.33674 + 1.69774i) q^{54} +(1.70184 + 2.95310i) q^{55} +(-8.25944 - 6.00083i) q^{56} -3.57920i q^{57} +(0.383426 - 0.527741i) q^{58} +(1.66288 - 5.11782i) q^{59} +(-2.85359 - 0.302220i) q^{60} +(2.40931 + 7.41510i) q^{61} +(-4.39811 - 1.42903i) q^{62} +(-9.59388 - 3.11724i) q^{63} +(-0.202075 - 0.621922i) q^{64} +(-14.8453 - 1.57224i) q^{65} +(0.255431 - 0.786135i) q^{66} +(-4.91621 + 6.76658i) q^{67} +1.56349i q^{68} +(3.55891 + 2.58570i) q^{69} +(3.19870 + 5.55050i) q^{70} +(-9.83939 + 7.14874i) q^{71} +(-3.21926 - 4.43093i) q^{72} +(13.1344 - 4.26763i) q^{73} -1.19793 q^{74} +(3.55086 + 2.05763i) q^{75} +6.81789 q^{76} +(6.28625 - 2.04253i) q^{77} +(2.12800 + 2.92895i) q^{78} +(-4.36847 + 3.17388i) q^{79} +(0.370092 - 3.49445i) q^{80} +(-2.74304 - 1.99294i) q^{81} -2.33993i q^{82} +(10.0350 - 13.8120i) q^{83} +(-1.71962 + 5.29246i) q^{84} +(0.911115 - 2.04203i) q^{85} +(-0.0451415 - 0.138931i) q^{86} +(-0.770740 - 0.250429i) q^{87} +(3.41303 + 1.10896i) q^{88} +(1.41713 + 4.36148i) q^{89} +(0.711863 + 3.36220i) q^{90} +(-8.94604 + 27.5331i) q^{91} +(-4.92540 + 6.77924i) q^{92} +5.74511i q^{93} +(5.00629 + 3.63728i) q^{94} +(-8.90461 - 3.97308i) q^{95} +(-3.81618 + 2.77262i) q^{96} +(2.68545 + 3.69620i) q^{97} +(7.41687 - 2.40989i) q^{98} +3.54592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−0.628349	+	0.204163i	−0.444310	+	0.144365i	−0.522623	−	0.852564i	$-0.675047\pi$
$2$	−0.628349	+	0.204163i	−0.444310	+	0.144365i	0.0783133	+	0.996929i	$0.475047\pi$
$3$	0.482449	+	0.664034i	0.278542	+	0.383380i	0.925250	−	0.379357i	$-0.123855\pi$
$3$	0.482449	+	0.664034i	0.278542	+	0.383380i	−0.646708	+	0.762737i	$0.723855\pi$
$4$	−1.26489	+	0.918999i	−0.632447	+	0.459500i
$5$	2.18757	−	0.463165i	0.978313	−	0.207134i
$5$	2.18757	−	0.463165i	0.978313	−	0.207134i
$6$	−0.438718	−	0.318747i	−0.179106	−	0.130128i
$7$		−	4.33633i		−	1.63898i	−0.573095	−	0.819489i	$-0.694257\pi$
$7$		−	4.33633i		−	1.63898i	0.573095	−	0.819489i	$-0.305743\pi$
$8$	1.38385	−	1.90471i	0.489265	−	0.673416i
$9$	0.718867	−	2.21244i	0.239622	−	0.737481i
$10$	−1.28000	+	0.737651i	−0.404771	+	0.233266i
$11$	0.471027	+	1.44967i	0.142020	+	0.437092i	0.996616	−	0.0822014i	$-0.0261951\pi$
$11$	0.471027	+	1.44967i	0.142020	+	0.437092i	−0.854596	+	0.519294i	$0.826195\pi$
$12$	−1.22049	−	0.396562i	−0.352326	−	0.114478i
$13$	−6.34940	−	2.06304i	−1.76101	−	0.572185i	−0.763702	−	0.645569i	$-0.776620\pi$
$13$	−6.34940	−	2.06304i	−1.76101	−	0.572185i	−0.997304	+	0.0733836i	$0.976620\pi$
$14$	0.885318	+	2.72473i	0.236611	+	0.728214i
$15$	1.36295	+	1.22917i	0.351912	+	0.317370i
$16$	0.485622	−	1.49459i	0.121405	−	0.373648i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$			1.53695i			0.362263i
$19$	−3.52786	−	2.56314i	−0.809347	−	0.588025i	0.104295	−	0.994546i	$-0.466742\pi$
$19$	−3.52786	−	2.56314i	−0.809347	−	0.588025i	−0.913641	+	0.406522i	$0.866742\pi$
$20$	−2.34140	+	2.59623i	−0.523553	+	0.580535i
$21$	2.87947	−	2.09206i	0.628352	−	0.456524i
$22$	−0.591939	−	0.814734i	−0.126202	−	0.173702i
$23$	5.09722	−	1.65619i	1.06284	−	0.345339i	0.275147	−	0.961402i	$-0.411274\pi$
$23$	5.09722	−	1.65619i	1.06284	−	0.345339i	0.787696	+	0.616064i	$0.211274\pi$
$24$	1.93243			0.394455
$25$	4.57096	−	2.02641i	0.914191	−	0.405283i
$26$	4.41084			0.865036
$27$	4.15781	−	1.35095i	0.800171	−	0.259991i
$28$	3.98508	+	5.48499i	0.753110	+	1.03657i
$29$	−0.798778	+	0.580346i	−0.148329	+	0.107768i	−0.659475	−	0.751727i	$-0.729221\pi$
$29$	−0.798778	+	0.580346i	−0.148329	+	0.107768i	0.511145	+	0.859494i	$0.329221\pi$
$30$	−1.10736	−	0.494084i	−0.202175	−	0.0902070i
$31$	5.66269	+	4.11419i	1.01705	+	0.738930i	0.965676	−	0.259750i	$-0.0836400\pi$
$31$	5.66269	+	4.11419i	1.01705	+	0.738930i	0.0513738	+	0.998679i	$0.483640\pi$
$32$			5.74697i			1.01593i
$33$	−0.735385	+	1.01217i	−0.128014	+	0.176196i
$34$	−0.204163	+	0.628349i	−0.0350137	+	0.107761i
$35$	−2.00843	−	9.48604i	−0.339487	−	1.60343i
$36$	1.12394	+	3.45915i	0.187324	+	0.576524i
$37$	1.72441	+	0.560296i	0.283492	+	0.0921121i	0.447312	−	0.894378i	$-0.352382\pi$
$37$	1.72441	+	0.560296i	0.283492	+	0.0921121i	−0.163820	+	0.986490i	$0.552382\pi$
$38$	2.74003	+	0.890289i	0.444491	+	0.144424i
$39$	−1.69333	−	5.21153i	−0.271150	−	0.834513i
$40$	2.14508	−	4.80764i	0.339168	−	0.760155i
$41$	−1.09444	+	3.36833i	−0.170922	+	0.526044i	−0.999424	−	0.0339422i	$-0.989194\pi$
$41$	−1.09444	+	3.36833i	−0.170922	+	0.526044i	0.828502	+	0.559987i	$0.189194\pi$
$42$	−1.38219	+	1.90242i	−0.213277	+	0.293550i
$43$			0.221105i			0.0337182i	0.999858	+	0.0168591i	$0.00536668\pi$
$43$			0.221105i			0.0337182i	−0.999858	+	0.0168591i	$0.994633\pi$
$44$	−1.92805	−	1.40081i	−0.290664	−	0.211180i
$45$	0.547848	−	5.17284i	0.0816684	−	0.771121i
$46$	−2.86470	+	2.08133i	−0.422377	+	0.306875i
$47$	−5.50531	−	7.57741i	−0.803032	−	1.10528i	−0.992361	−	0.123366i	$-0.960631\pi$
$47$	−5.50531	−	7.57741i	−0.803032	−	1.10528i	0.189329	−	0.981914i	$-0.439369\pi$
$48$	1.22675	−	0.398594i	0.177066	−	0.0575321i
$49$	−11.8037			−1.68625
$50$	−2.45844	+	2.20652i	−0.347676	+	0.312048i
$51$	0.820791			0.114934
$52$	9.92725	−	3.22556i	1.37666	−	0.447304i
$53$	7.56730	+	10.4155i	1.03945	+	1.43068i	0.897611	+	0.440788i	$0.145301\pi$
$53$	7.56730	+	10.4155i	1.03945	+	1.43068i	0.141837	+	0.989890i	$0.454699\pi$
$54$	−2.33674	+	1.69774i	−0.317990	+	0.231034i
$55$	1.70184	+	2.95310i	0.229476	+	0.398196i
$56$	−8.25944	−	6.00083i	−1.10371	−	0.801895i
$57$		−	3.57920i		−	0.474077i
$58$	0.383426	−	0.527741i	0.0503464	−	0.0692958i
$59$	1.66288	−	5.11782i	0.216489	−	0.666284i	−0.782556	−	0.622580i	$-0.786084\pi$
$59$	1.66288	−	5.11782i	0.216489	−	0.666284i	0.999045	−	0.0437033i	$-0.0139156\pi$
$60$	−2.85359	−	0.302220i	−0.368397	−	0.0390164i
$61$	2.40931	+	7.41510i	0.308481	+	0.949407i	0.978355	+	0.206932i	$0.0663480\pi$
$61$	2.40931	+	7.41510i	0.308481	+	0.949407i	−0.669874	+	0.742475i	$0.733652\pi$
$62$	−4.39811	−	1.42903i	−0.558561	−	0.181487i
$63$	−9.59388	−	3.11724i	−1.20872	−	0.392736i
$64$	−0.202075	−	0.621922i	−0.0252594	−	0.0777403i
$65$	−14.8453	−	1.57224i	−1.84133	−	0.195013i
$66$	0.255431	−	0.786135i	0.0314413	−	0.0967665i
$67$	−4.91621	+	6.76658i	−0.600610	+	0.826669i	−0.995764	−	0.0919460i	$-0.970691\pi$
$67$	−4.91621	+	6.76658i	−0.600610	+	0.826669i	0.395154	+	0.918615i	$0.370691\pi$
$68$			1.56349i			0.189602i
$69$	3.55891	+	2.58570i	0.428443	+	0.311282i
$70$	3.19870	+	5.55050i	0.382317	+	0.663411i
$71$	−9.83939	+	7.14874i	−1.16772	+	0.848399i	−0.990734	−	0.135815i	$-0.956635\pi$
$71$	−9.83939	+	7.14874i	−1.16772	+	0.848399i	−0.176986	+	0.984213i	$0.556635\pi$
$72$	−3.21926	−	4.43093i	−0.379393	−	0.522190i
$73$	13.1344	−	4.26763i	1.53727	−	0.499488i	0.586645	−	0.809844i	$-0.300448\pi$
$73$	13.1344	−	4.26763i	1.53727	−	0.499488i	0.950620	+	0.310356i	$0.100448\pi$
$74$	−1.19793			−0.139256
$75$	3.55086	+	2.05763i	0.410018	+	0.237595i
$76$	6.81789			0.782066
$77$	6.28625	−	2.04253i	0.716385	−	0.232768i
$78$	2.12800	+	2.92895i	0.240949	+	0.331638i
$79$	−4.36847	+	3.17388i	−0.491491	+	0.357089i	−0.805757	−	0.592246i	$-0.798241\pi$
$79$	−4.36847	+	3.17388i	−0.491491	+	0.357089i	0.314267	+	0.949335i	$0.398241\pi$
$80$	0.370092	−	3.49445i	0.0413776	−	0.390691i
$81$	−2.74304	−	1.99294i	−0.304782	−	0.221437i
$82$		−	2.33993i		−	0.258402i
$83$	10.0350	−	13.8120i	1.10149	−	1.51606i	0.268084	−	0.963396i	$-0.413610\pi$
$83$	10.0350	−	13.8120i	1.10149	−	1.51606i	0.833401	−	0.552669i	$-0.186390\pi$
$84$	−1.71962	+	5.29246i	−0.187626	+	0.577455i
$85$	0.911115	−	2.04203i	0.0988243	−	0.221489i
$86$	−0.0451415	−	0.138931i	−0.00486773	−	0.0149813i
$87$	−0.770740	−	0.250429i	−0.0826320	−	0.0268488i
$88$	3.41303	+	1.10896i	0.363831	+	0.118216i
$89$	1.41713	+	4.36148i	0.150216	+	0.462316i	0.997645	−	0.0685923i	$-0.0218508\pi$
$89$	1.41713	+	4.36148i	0.150216	+	0.462316i	−0.847429	+	0.530909i	$0.821851\pi$
$90$	0.711863	+	3.36220i	0.0750369	+	0.354407i
$91$	−8.94604	+	27.5331i	−0.937799	+	2.88625i
$92$	−4.92540	+	6.77924i	−0.513509	+	0.706784i
$93$			5.74511i			0.595740i
$94$	5.00629	+	3.63728i	0.516359	+	0.375157i
$95$	−8.90461	−	3.97308i	−0.913594	−	0.407629i
$96$	−3.81618	+	2.77262i	−0.389488	+	0.282979i
$97$	2.68545	+	3.69620i	0.272666	+	0.375292i	0.923287	−	0.384110i	$-0.125492\pi$
$97$	2.68545	+	3.69620i	0.272666	+	0.375292i	−0.650622	+	0.759402i	$0.725492\pi$
$98$	7.41687	−	2.40989i	0.749217	−	0.243435i
$99$	3.54592			0.356379
$100$	−3.91950	+	6.76390i	−0.391950	+	0.676390i
$101$	−5.49909			−0.547180			−0.273590	−	0.961846i	$-0.588211\pi$
$101$	−5.49909			−0.547180			−0.273590	+	0.961846i	$0.588211\pi$
$102$	−0.515744	+	0.167575i	−0.0510662	+	0.0165924i
$103$	−10.9162	−	15.0248i	−1.07560	−	1.48044i	−0.864273	−	0.503022i	$-0.832221\pi$
$103$	−10.9162	−	15.0248i	−1.07560	−	1.48044i	−0.211327	−	0.977415i	$-0.567779\pi$
$104$	−12.7161	+	9.23880i	−1.24692	+	0.905939i
$105$	5.33009	−	5.91020i	0.520163	−	0.576776i
$106$	−6.88136	−	4.99960i	−0.668377	−	0.485604i
$107$		−	6.89809i		−	0.666864i	−0.942774	−	0.333432i	$-0.891793\pi$
$107$		−	6.89809i		−	0.666864i	0.942774	−	0.333432i	$-0.108207\pi$
$108$	−4.01766	+	5.52984i	−0.386600	+	0.532109i
$109$	−3.02006	+	9.29480i	−0.289270	+	0.890280i	0.695817	+	0.718219i	$0.255043\pi$
$109$	−3.02006	+	9.29480i	−0.289270	+	0.890280i	−0.985086	+	0.172061i	$0.944957\pi$
$110$	−1.67227	−	1.50812i	−0.159444	−	0.143794i
$111$	0.459886	+	1.41538i	0.0436504	+	0.134342i
$112$	−6.48103	−	2.10582i	−0.612400	−	0.198981i
$113$	8.69640	+	2.82563i	0.818089	+	0.265813i	0.688020	−	0.725692i	$-0.258480\pi$
$113$	8.69640	+	2.82563i	0.818089	+	0.265813i	0.130069	+	0.991505i	$0.458480\pi$
$114$	0.730741	+	2.24899i	0.0684402	+	0.210637i
$115$	10.3835	−	5.98388i	0.968262	−	0.558000i
$116$	0.477032	−	1.46815i	0.0442913	−	0.136315i
$117$	−9.12874	+	12.5646i	−0.843952	+	1.16160i
$118$			3.55528i			0.327290i
$119$	−3.50816	−	2.54883i	−0.321593	−	0.233651i
$120$	4.22733	−	0.895033i	0.385901	−	0.0817050i
$121$	7.01951	−	5.09997i	0.638137	−	0.463634i
$122$	−3.02778	−	4.16738i	−0.274122	−	0.377297i
$123$	−2.76469	+	0.898304i	−0.249284	+	0.0809973i
$124$	−10.9436			−0.982768
$125$	9.06074	−	6.55003i	0.810417	−	0.585853i
$126$	6.66474			0.593742
$127$	−0.544100	+	0.176789i	−0.0482811	+	0.0156875i	−0.333058	−	0.942906i	$-0.608080\pi$
$127$	−0.544100	+	0.176789i	−0.0482811	+	0.0156875i	0.284777	+	0.958594i	$0.408080\pi$
$128$	−6.50202	−	8.94926i	−0.574703	−	0.791011i
$129$	−0.146821	+	0.106672i	−0.0129269	+	0.00939194i
$130$	9.64903	−	2.04294i	0.846276	−	0.179178i
$131$	8.80643	+	6.39825i	0.769422	+	0.559018i	0.901786	−	0.432184i	$-0.142257\pi$
$131$	8.80643	+	6.39825i	0.769422	+	0.559018i	−0.132364	+	0.991201i	$0.542257\pi$
$132$		−	1.95611i		−	0.170257i
$133$	−11.1146	+	15.2980i	−0.963759	+	1.32650i
$134$	1.70761	−	5.25548i	0.147515	−	0.454004i
$135$	8.46980	−	4.88106i	0.728965	−	0.420095i
$136$	−0.727534	−	2.23912i	−0.0623855	−	0.192003i
$137$	−1.67535	−	0.544353i	−0.143134	−	0.0465072i	0.236574	−	0.971614i	$-0.423976\pi$
$137$	−1.67535	−	0.544353i	−0.143134	−	0.0465072i	−0.379708	+	0.925106i	$0.623976\pi$
$138$	−2.76414	−	0.898125i	−0.235300	−	0.0764534i
$139$	−3.49967	−	10.7709i	−0.296839	−	0.913575i	−0.982598	−	0.185747i	$-0.940530\pi$
$139$	−3.49967	−	10.7709i	−0.296839	−	0.913575i	0.685759	−	0.727829i	$-0.259470\pi$
$140$	11.2581	+	10.1531i	0.951484	+	0.858092i
$141$	2.37563	−	7.31143i	0.200064	−	0.615734i
$142$	4.72307	−	6.50074i	0.396351	−	0.545530i
$143$		−	10.1763i		−	0.850984i
$144$	−2.95760	−	2.14882i	−0.246467	−	0.179069i
$145$	−1.47859	+	1.63952i	−0.122790	+	0.136154i
$146$	−7.38170	+	5.36312i	−0.610914	+	0.443855i
$147$	−5.69470	−	7.83809i	−0.469691	−	0.646474i
$148$	−2.69611	+	0.876020i	−0.221619	+	0.0720084i
$149$	−8.06190			−0.660456			−0.330228	−	0.943901i	$-0.607126\pi$
$149$	−8.06190			−0.660456			−0.330228	+	0.943901i	$0.607126\pi$
$150$	−2.65127	−	0.567956i	−0.216476	−	0.0463734i
$151$	6.90619			0.562018			0.281009	−	0.959705i	$-0.409331\pi$
$151$	6.90619			0.562018			0.281009	+	0.959705i	$0.409331\pi$
$152$	−9.76407	+	3.17254i	−0.791971	+	0.257327i
$153$	−1.36737	−	1.88202i	−0.110545	−	0.152152i
$154$	−3.53295	+	2.56684i	−0.284693	+	0.206842i
$155$	14.2931	+	6.37733i	1.14805	+	0.512239i
$156$	6.93127	+	5.03586i	0.554946	+	0.403192i
$157$			20.4112i			1.62899i	0.580167	+	0.814497i	$0.302987\pi$
$157$			20.4112i			1.62899i	−0.580167	+	0.814497i	$0.697013\pi$
$158$	2.09693	−	2.88618i	0.166823	−	0.229612i
$159$	−3.26541	+	10.0499i	−0.258964	+	0.797008i
$160$	2.66179	+	12.5719i	0.210433	+	0.993897i
$161$	−7.18177	−	22.1032i	−0.566002	−	1.74198i
$162$	2.13047	+	0.692232i	0.167386	+	0.0543869i
$163$	6.55802	+	2.13083i	0.513663	+	0.166899i	0.554368	−	0.832272i	$-0.312960\pi$
$163$	6.55802	+	2.13083i	0.513663	+	0.166899i	−0.0407042	+	0.999171i	$0.512960\pi$
$164$	−1.71115	−	5.26636i	−0.133618	−	0.411234i
$165$	−1.13991	+	2.55480i	−0.0887416	+	0.198891i
$166$	−3.48559	+	10.7275i	−0.270534	+	0.832618i
$167$	−1.43941	+	1.98117i	−0.111385	+	0.153308i	−0.861070	−	0.508487i	$-0.830205\pi$
$167$	−1.43941	+	1.98117i	−0.111385	+	0.153308i	0.749685	+	0.661795i	$0.230205\pi$
$168$		−	8.37965i		−	0.646504i
$169$	25.5415	+	18.5570i	1.96473	+	1.42746i
$170$	−0.155593	+	1.46912i	−0.0119334	+	0.112676i
$171$	−8.20687	+	5.96264i	−0.627595	+	0.455974i
$172$	−0.203195	−	0.279675i	−0.0154935	−	0.0213250i
$173$	0.00838935	−	0.00272587i	0.000637831	−	0.000207244i	−0.308698	−	0.951160i	$-0.599893\pi$
$173$	0.00838935	−	0.00272587i	0.000637831	−	0.000207244i	0.309336	+	0.950953i	$0.399893\pi$
$174$	0.535422			0.0405902
$175$	−8.78719	−	19.8212i	−0.664249	−	1.49834i
$176$	2.39541			0.180561
$177$	4.20066	−	1.36488i	0.315741	−	0.102591i
$178$	−1.78091	−	2.45121i	−0.133485	−	0.183726i
$179$	−9.78547	+	7.10956i	−0.731400	+	0.531393i	−0.890006	−	0.455949i	$-0.849300\pi$
$179$	−9.78547	+	7.10956i	−0.731400	+	0.531393i	0.158606	+	0.987342i	$0.449300\pi$
$180$	4.06086	+	7.04656i	0.302679	+	0.525220i
$181$	1.90208	+	1.38194i	0.141381	+	0.102719i	0.656227	−	0.754563i	$-0.272151\pi$
$181$	1.90208	+	1.38194i	0.141381	+	0.102719i	−0.514847	+	0.857282i	$0.672151\pi$
$182$		−	19.1268i		−	1.41777i
$183$	−3.76151	+	5.17728i	−0.278059	+	0.382715i
$184$	3.89924	−	12.0006i	0.287456	−	0.884698i
$185$	4.03179	+	0.427001i	0.296423	+	0.0313938i
$186$	−1.17294	−	3.60993i	−0.0860040	−	0.264693i
$187$	1.44967	+	0.471027i	0.106010	+	0.0344449i
$188$	13.9273	+	4.52525i	1.01575	+	0.330037i
$189$	−5.85818	−	18.0296i	−0.426120	−	1.31146i
$190$	6.40636	+	0.678488i	0.464766	+	0.0492227i
$191$	2.08491	−	6.41668i	0.150858	−	0.464295i	−0.846859	−	0.531817i	$-0.821509\pi$
$191$	2.08491	−	6.41668i	0.150858	−	0.464295i	0.997718	+	0.0675224i	$0.0215094\pi$
$192$	0.315487	−	0.434230i	0.0227683	−	0.0313379i
$193$			26.0320i			1.87382i	0.349565	+	0.936912i	$0.386329\pi$
$193$			26.0320i			1.87382i	−0.349565	+	0.936912i	$0.613671\pi$
$194$	−2.44202	−	1.77423i	−0.175327	−	0.127383i
$195$	−6.11808	−	10.6163i	−0.438125	−	0.760250i
$196$	14.9305	−	10.8476i	1.06646	−	0.774831i
$197$	−3.99857	−	5.50356i	−0.284886	−	0.392112i	0.642459	−	0.766320i	$-0.277914\pi$
$197$	−3.99857	−	5.50356i	−0.284886	−	0.392112i	−0.927345	+	0.374208i	$0.877914\pi$
$198$	−2.22808	+	0.723946i	−0.158343	+	0.0514486i
$199$	23.9541			1.69806			0.849029	−	0.528346i	$-0.177188\pi$
$199$	23.9541			1.69806			0.849029	+	0.528346i	$0.177188\pi$
$200$	2.46580	−	11.5106i	0.174358	−	0.813922i
$201$	−6.86506			−0.484224
$202$	3.45535	−	1.12271i	0.243117	−	0.0789936i
$203$	2.51657	+	3.46377i	0.176629	+	0.243109i
$204$	−1.03821	+	0.754307i	−0.0726895	+	0.0528120i
$205$	−0.834069	+	7.87537i	−0.0582539	+	0.550040i
$206$	9.92667	+	7.21215i	0.691624	+	0.502494i
$207$		−	12.4679i		−	0.866578i
$208$	−6.16681	+	8.48789i	−0.427591	+	0.588529i
$209$	2.05399	−	6.32155i	0.142078	−	0.437270i
$210$	−2.14251	+	4.80187i	−0.147847	+	0.331361i
$211$	−5.50737	−	16.9500i	−0.379143	−	1.16688i	−0.940641	−	0.339404i	$-0.889774\pi$
$211$	−5.50737	−	16.9500i	−0.379143	−	1.16688i	0.561497	−	0.827479i	$-0.310226\pi$
$212$	−19.1437	−	6.22015i	−1.31479	−	0.427202i
$213$	−9.49401	−	3.08479i	−0.650519	−	0.211366i
$214$	1.40834	+	4.33441i	0.0962718	+	0.296294i
$215$	0.102408	+	0.483684i	0.00698417	+	0.0329870i
$216$	3.18062	−	9.78894i	0.216414	−	0.666053i
$217$	17.8405	−	24.5553i	1.21109	−	1.66692i
$218$		−	6.45696i		−	0.437321i
$219$	9.17053	+	6.66278i	0.619687	+	0.450229i
$220$	−4.86655	−	2.17137i	−0.328102	−	0.146393i
$221$	−5.40112	+	3.92414i	−0.363319	+	0.263966i
$222$	−0.577938	−	0.795463i	−0.0387887	−	0.0533880i
$223$	5.83604	−	1.89625i	0.390810	−	0.126982i	−0.107019	−	0.994257i	$-0.534131\pi$
$223$	5.83604	−	1.89625i	0.390810	−	0.126982i	0.497829	+	0.867275i	$0.334131\pi$
$224$	24.9207			1.66509
$225$	−1.19742	−	11.5697i	−0.0798279	−	0.771314i
$226$	−6.04127			−0.401859
$227$	7.29029	−	2.36876i	0.483873	−	0.157220i	−0.0569143	−	0.998379i	$-0.518126\pi$
$227$	7.29029	−	2.36876i	0.483873	−	0.157220i	0.540788	+	0.841159i	$0.318126\pi$
$228$	3.28929	+	4.52731i	0.217838	+	0.299829i
$229$	−4.15973	+	3.02222i	−0.274883	+	0.199714i	−0.716682	−	0.697400i	$-0.754340\pi$
$229$	−4.15973	+	3.02222i	−0.274883	+	0.199714i	0.441800	+	0.897114i	$0.354340\pi$
$230$	−5.30275	+	5.87988i	−0.349653	+	0.387708i
$231$	4.38910	+	3.18887i	0.288782	+	0.209812i
$232$			2.32455i			0.152614i
$233$	9.42748	−	12.9758i	0.617615	−	0.850074i	−0.379562	−	0.925166i	$-0.623925\pi$
$233$	9.42748	−	12.9758i	0.617615	−	0.850074i	0.997177	+	0.0750924i	$0.0239252\pi$
$234$	3.17080	−	9.75873i	0.207282	−	0.637948i
$235$	−15.5529	−	14.0263i	−1.01456	−	0.914974i
$236$	2.59991	+	8.00169i	0.169239	+	0.520865i
$237$	−4.21512	−	1.36958i	−0.273802	−	0.0889636i
$238$	2.72473	+	0.885318i	0.176618	+	0.0573866i
$239$	4.46483	+	13.7413i	0.288806	+	0.888852i	0.985232	+	0.171224i	$0.0547722\pi$
$239$	4.46483	+	13.7413i	0.288806	+	0.888852i	−0.696427	+	0.717628i	$0.745228\pi$
$240$	2.49898	−	1.44014i	0.161309	−	0.0929606i
$241$	−3.28979	+	10.1249i	−0.211914	+	0.652204i	0.787444	+	0.616386i	$0.211404\pi$
$241$	−3.28979	+	10.1249i	−0.211914	+	0.652204i	−0.999358	+	0.0358185i	$0.988596\pi$
$242$	−3.36948	+	4.63769i	−0.216598	+	0.298122i
$243$		−	15.8983i		−	1.01988i
$244$	−9.86200	−	7.16516i	−0.631350	−	0.458703i
$245$	−25.8216	+	5.46708i	−1.64968	+	0.349279i
$246$	1.55379	−	1.12890i	0.0990662	−	0.0719758i
$247$	17.1119	+	23.5525i	1.08880	+	1.49861i
$248$	15.6727	−	5.09235i	0.995215	−	0.323365i
$249$	14.0130			0.888039
$250$	−4.35603	+	5.96558i	−0.275500	+	0.377296i
$251$	−6.33159			−0.399647			−0.199823	−	0.979832i	$-0.564037\pi$
$251$	−6.33159			−0.399647			−0.199823	+	0.979832i	$0.564037\pi$
$252$	15.0000	−	4.87379i	0.944910	−	0.307020i
$253$	4.80185	+	6.60918i	0.301890	+	0.415516i
$254$	0.305791	−	0.222170i	0.0191870	−	0.0139402i
$255$	1.79554	−	0.380162i	0.112441	−	0.0238066i
$256$	6.97072	+	5.06453i	0.435670	+	0.316533i
$257$		−	22.3079i		−	1.39153i	−0.718269	−	0.695765i	$-0.755065\pi$
$257$		−	22.3079i		−	1.39153i	0.718269	−	0.695765i	$-0.244935\pi$
$258$	0.0704766	−	0.0970027i	0.00438768	−	0.00603913i
$259$	2.42963	−	7.47762i	0.150970	−	0.464637i
$260$	20.2226	−	11.6541i	1.25415	−	0.722756i
$261$	0.709769	+	2.18444i	0.0439336	+	0.135214i
$262$	−6.83980	−	2.22239i	−0.422564	−	0.137299i
$263$	0.897902	+	0.291746i	0.0553670	+	0.0179898i	0.336570	−	0.941659i	$-0.390733\pi$
$263$	0.897902	+	0.291746i	0.0553670	+	0.0179898i	−0.281203	+	0.959648i	$0.590733\pi$
$264$	0.910226	+	2.80139i	0.0560205	+	0.172413i
$265$	21.3781	+	19.2797i	1.31325	+	1.18435i
$266$	3.86058	−	11.8817i	0.236708	−	0.728511i
$267$	−2.21248	+	3.04522i	−0.135402	+	0.186364i
$268$		−	13.0770i		−	0.798804i
$269$	10.5115	+	7.63708i	0.640900	+	0.465641i	0.860159	−	0.510026i	$-0.170364\pi$
$269$	10.5115	+	7.63708i	0.640900	+	0.465641i	−0.219259	+	0.975667i	$0.570364\pi$
$270$	−4.32546	+	4.79623i	−0.263239	+	0.291890i
$271$	3.82638	−	2.78003i	0.232436	−	0.168875i	−0.465471	−	0.885063i	$-0.654115\pi$
$271$	3.82638	−	2.78003i	0.232436	−	0.168875i	0.697907	+	0.716189i	$0.254115\pi$
$272$	−0.923708	−	1.27137i	−0.0560080	−	0.0770884i
$273$	−22.5989	+	7.34283i	−1.36775	+	0.444408i
$274$	1.16384			0.0703101
$275$	5.09068	+	5.67189i	0.306979	+	0.342028i
$276$	−6.87790			−0.414001
$277$	−6.11474	+	1.98680i	−0.367399	+	0.119375i	−0.486897	−	0.873459i	$-0.661871\pi$
$277$	−6.11474	+	1.98680i	−0.367399	+	0.119375i	0.119498	+	0.992834i	$0.461871\pi$
$278$	4.39804	+	6.05338i	0.263777	+	0.363057i
$279$	13.1731	−	9.57084i	0.788655	−	0.572991i
$280$	−20.8475	−	9.30179i	−1.24588	−	0.555888i
$281$	−15.8111	−	11.4874i	−0.943209	−	0.685282i	0.00598176	−	0.999982i	$-0.498096\pi$
$281$	−15.8111	−	11.4874i	−0.943209	−	0.685282i	−0.949191	+	0.314700i	$0.898096\pi$
$282$			5.07915i			0.302459i
$283$	−2.84632	+	3.91762i	−0.169196	+	0.232879i	−0.885192	−	0.465226i	$-0.845973\pi$
$283$	−2.84632	+	3.91762i	−0.169196	+	0.232879i	0.715996	+	0.698105i	$0.245973\pi$
$284$	5.87610	−	18.0848i	0.348682	−	1.07313i
$285$	−1.65776	−	7.82977i	−0.0981973	−	0.463796i
$286$	2.07762	+	6.39426i	0.122852	+	0.378101i
$287$	14.6062	+	4.74583i	0.862175	+	0.280138i
$288$	12.7148	+	4.13130i	0.749230	+	0.243439i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	0.594343	−	1.33206i	0.0349010	−	0.0782214i
$291$	−1.15881	+	3.56645i	−0.0679307	+	0.209069i
$292$	−12.6917	+	17.4686i	−0.742724	+	1.02227i
$293$			19.7008i			1.15093i	0.817826	+	0.575465i	$0.195179\pi$
$293$			19.7008i			1.15093i	−0.817826	+	0.575465i	$0.804821\pi$
$294$	5.17851	+	3.76241i	0.302017	+	0.219428i
$295$	1.26728	−	11.9658i	0.0737839	−	0.696676i
$296$	3.45353	−	2.50914i	0.200733	−	0.145841i
$297$	3.91688	+	5.39113i	0.227281	+	0.312825i
$298$	5.06569	−	1.64594i	0.293447	−	0.0953468i
$299$	−35.7810			−2.06927
$300$	−6.38242	+	0.660555i	−0.368489	+	0.0381372i
$301$	0.958785			0.0552634
$302$	−4.33950	+	1.40999i	−0.249710	+	0.0811357i
$303$	−2.65303	−	3.65158i	−0.152413	−	0.209778i
$304$	−5.54405	+	4.02799i	−0.317973	+	0.231021i
$305$	8.70496	+	15.1052i	0.498445	+	0.864920i
$306$	1.24342	+	0.903399i	0.0710817	+	0.0516439i
$307$			18.0701i			1.03131i	0.856796	+	0.515656i	$0.172452\pi$
$307$			18.0701i			1.03131i	−0.856796	+	0.515656i	$0.827548\pi$
$308$	−6.07436	+	8.36064i	−0.346119	+	0.476392i
$309$	4.71049	−	14.4974i	0.267970	−	0.824728i
$310$	−10.2831	−	1.08907i	−0.584039	−	0.0618548i
$311$	−1.25019	−	3.84769i	−0.0708918	−	0.218182i	0.909333	−	0.416069i	$-0.136592\pi$
$311$	−1.25019	−	3.84769i	−0.0708918	−	0.218182i	−0.980225	+	0.197886i	$0.936592\pi$
$312$	−12.2698	−	3.98669i	−0.694638	−	0.225702i
$313$	−2.31881	−	0.753428i	−0.131067	−	0.0425863i	0.242749	−	0.970089i	$-0.421951\pi$
$313$	−2.31881	−	0.753428i	−0.131067	−	0.0425863i	−0.373816	+	0.927503i	$0.621951\pi$
$314$	−4.16722	−	12.8254i	−0.235170	−	0.723779i
$315$	−22.4311	−	2.37565i	−1.26385	−	0.133853i
$316$	2.60886	−	8.02923i	0.146760	−	0.451680i
$317$	−4.26769	+	5.87397i	−0.239697	+	0.329915i	−0.911870	−	0.410480i	$-0.865361\pi$
$317$	−4.26769	+	5.87397i	−0.239697	+	0.329915i	0.672172	+	0.740395i	$0.265361\pi$
$318$		−	6.98151i		−	0.391504i
$319$	−1.21756	−	0.884607i	−0.0681701	−	0.0495285i
$320$	−0.730106	−	1.26691i	−0.0408142	−	0.0708223i
$321$	4.58057	−	3.32798i	0.255662	−	0.185750i
$322$	9.02531	+	12.4223i	0.502961	+	0.692267i
$323$	−4.14725	+	1.34752i	−0.230759	+	0.0749782i
$324$	5.30116			0.294509
$325$	−33.2034	+	3.43642i	−1.84179	+	0.190618i
$326$	−4.55576			−0.252320
$327$	−7.62909	+	2.47884i	−0.421890	+	0.137080i
$328$	4.90115	+	6.74585i	0.270620	+	0.372477i
$329$	−32.8581	+	23.8728i	−1.81153	+	1.31615i
$330$	0.194664	−	1.83803i	0.0107159	−	0.101180i
$331$	23.7297	+	17.2406i	1.30430	+	0.947631i	0.999988	−	0.00494014i	$-0.00157250\pi$
$331$	23.7297	+	17.2406i	1.30430	+	0.947631i	0.304315	+	0.952571i	$0.401573\pi$
$332$			26.6929i			1.46496i
$333$	2.47925	−	3.41239i	0.135862	−	0.186998i
$334$	0.499967	−	1.53874i	0.0273570	−	0.0841962i
$335$	−7.62052	+	17.0794i	−0.416354	+	0.933147i
$336$	−1.72844	−	5.31958i	−0.0942939	−	0.290207i
$337$	−9.05066	−	2.94074i	−0.493021	−	0.160192i	0.0519457	−	0.998650i	$-0.483458\pi$
$337$	−9.05066	−	2.94074i	−0.493021	−	0.160192i	−0.544967	+	0.838458i	$0.683458\pi$
$338$	−19.8376	−	6.44563i	−1.07902	−	0.350596i
$339$	2.31925	+	7.13793i	0.125965	+	0.387679i
$340$	0.724156	+	3.42026i	0.0392728	+	0.185490i
$341$	−3.29694	+	10.1469i	−0.178539	+	0.549488i
$342$	3.93943	−	5.42216i	0.213020	−	0.293197i
$343$			20.8306i			1.12475i
$344$	0.421141	+	0.305977i	0.0227064	+	0.0164972i
$345$	8.98299	+	4.00805i	0.483628	+	0.215786i
$346$	−0.00471492	+	0.00342559i	−0.000253476	+	0.000184161i
$347$	13.5384	+	18.6341i	0.726782	+	1.00033i	0.999271	+	0.0381705i	$0.0121530\pi$
$347$	13.5384	+	18.6341i	0.726782	+	1.00033i	−0.272490	+	0.962159i	$0.587847\pi$
$348$	1.20505	−	0.391544i	0.0645973	−	0.0209889i
$349$	7.78577			0.416763			0.208381	−	0.978048i	$-0.433180\pi$
$349$	7.78577			0.416763			0.208381	+	0.978048i	$0.433180\pi$
$350$	9.56818	+	10.6606i	0.511441	+	0.569833i
$351$	−29.1867			−1.55787
$352$	−8.33122	+	2.70698i	−0.444055	+	0.144282i
$353$	−2.38387	−	3.28111i	−0.126881	−	0.174636i	0.740851	−	0.671670i	$-0.234423\pi$
$353$	−2.38387	−	3.28111i	−0.126881	−	0.174636i	−0.867731	+	0.497034i	$0.834423\pi$
$354$	−2.36083	+	1.71524i	−0.125476	+	0.0911640i
$355$	−18.2133	+	20.1956i	−0.966664	+	1.07187i
$356$	−5.80072	−	4.21447i	−0.307438	−	0.223366i
$357$		−	3.55922i		−	0.188374i
$358$	4.69718	−	6.46512i	0.248254	−	0.341692i
$359$	−4.69086	+	14.4370i	−0.247574	+	0.761955i	0.747628	+	0.664117i	$0.231192\pi$
$359$	−4.69086	+	14.4370i	−0.247574	+	0.761955i	−0.995202	+	0.0978373i	$0.968808\pi$
$360$	−9.09461	−	8.20193i	−0.479328	−	0.432280i
$361$	0.00478427	+	0.0147245i	0.000251804	+	0.000774972i
$362$	−1.47731	−	0.480008i	−0.0776458	−	0.0252287i
$363$	6.77311	+	2.20072i	0.355496	+	0.115508i
$364$	−13.9871	−	43.0478i	−0.733122	−	2.25632i
$365$	26.7559	−	15.4191i	1.40047	−	0.807075i
$366$	1.30653	−	4.02110i	0.0682936	−	0.210186i
$367$	4.14167	−	5.70053i	0.216194	−	0.297565i	−0.687122	−	0.726542i	$-0.741126\pi$
$367$	4.14167	−	5.70053i	0.216194	−	0.297565i	0.903315	+	0.428977i	$0.141126\pi$
$368$		−	8.42253i		−	0.439055i
$369$	6.66548	+	4.84276i	0.346991	+	0.252104i
$370$	−2.62055	+	0.554837i	−0.136236	+	0.0288446i
$371$	45.1650	−	32.8143i	2.34485	−	1.70363i
$372$	−5.27975	−	7.26695i	−0.273742	−	0.376774i
$373$	−25.1600	+	8.17499i	−1.30274	+	0.423285i	−0.876533	−	0.481342i	$-0.840149\pi$
$373$	−25.1600	+	8.17499i	−1.30274	+	0.423285i	−0.426204	+	0.904627i	$0.640149\pi$
$374$	−1.00707			−0.0520742
$375$	8.72079	+	2.85658i	0.450340	+	0.147513i
$376$	−22.0513			−1.13721
$377$	6.26904	−	2.03693i	0.322872	−	0.104907i
$378$	7.36197	+	10.1329i	0.378659	+	0.521179i
$379$	−1.07072	+	0.777920i	−0.0549989	+	0.0399591i	−0.614945	−	0.788570i	$-0.710822\pi$
$379$	−1.07072	+	0.777920i	−0.0549989	+	0.0399591i	0.559946	+	0.828529i	$0.310822\pi$
$380$	14.9146	−	3.15781i	0.765105	−	0.161992i
$381$	−0.379894	−	0.276009i	−0.0194626	−	0.0141404i
$382$			4.45758i			0.228069i
$383$	−7.80056	+	10.7366i	−0.398590	+	0.548612i	−0.960389	−	0.278661i	$-0.910109\pi$
$383$	−7.80056	+	10.7366i	−0.398590	+	0.548612i	0.561799	+	0.827274i	$0.310109\pi$
$384$	2.80572	−	8.63513i	0.143179	−	0.440659i
$385$	12.8056	−	7.37975i	0.652634	−	0.376107i
$386$	−5.31477	−	16.3572i	−0.270515	−	0.832559i
$387$	0.489183	+	0.158945i	0.0248666	+	0.00807964i
$388$	−6.79361	−	2.20738i	−0.344893	−	0.112063i
$389$	4.92150	+	15.1468i	0.249530	+	0.767975i	0.994858	+	0.101277i	$0.0322928\pi$
$389$	4.92150	+	15.1468i	0.249530	+	0.767975i	−0.745328	+	0.666698i	$0.767707\pi$
$390$	6.01175	+	5.42167i	0.304417	+	0.274537i
$391$	1.65619	−	5.09722i	0.0837569	−	0.257777i
$392$	−16.3346	+	22.4827i	−0.825023	+	1.13555i
$393$			8.93460i			0.450691i
$394$	3.63612	+	2.64180i	0.183185	+	0.133092i
$395$	−8.08631	+	8.96641i	−0.406867	+	0.451149i
$396$	−4.48522	+	3.25870i	−0.225391	+	0.163756i
$397$	16.0616	+	22.1069i	0.806108	+	1.10951i	0.991912	+	0.126925i	$0.0405108\pi$
$397$	16.0616	+	22.1069i	0.806108	+	1.10951i	−0.185805	+	0.982587i	$0.559489\pi$
$398$	−15.0515	+	4.89053i	−0.754464	+	0.245140i
$399$	−15.5206			−0.777002
$400$	−0.808902	−	7.81578i	−0.0404451	−	0.390789i
$401$	10.0879			0.503765			0.251882	−	0.967758i	$-0.418950\pi$
$401$	10.0879			0.503765			0.251882	+	0.967758i	$0.418950\pi$
$402$	4.31365	−	1.40159i	0.215145	−	0.0699050i
$403$	−27.4669	−	37.8050i	−1.36823	−	1.88320i
$404$	6.95576	−	5.05366i	0.346062	−	0.251429i
$405$	−6.92366	−	3.08921i	−0.344039	−	0.153504i
$406$	−2.28846	−	1.66266i	−0.113574	−	0.0825166i
$407$			2.76375i			0.136994i
$408$	1.13585	−	1.56337i	0.0562331	−	0.0773983i
$409$	−0.245210	+	0.754680i	−0.0121249	+	0.0373165i	−0.956936	−	0.290299i	$-0.906245\pi$
$409$	−0.245210	+	0.754680i	−0.0121249	+	0.0373165i	0.944811	+	0.327616i	$0.106245\pi$
$410$	−1.08377	−	5.11877i	−0.0535237	−	0.252798i
$411$	−0.446800	−	1.37511i	−0.0220390	−	0.0678291i
$412$	27.6156	+	8.97284i	1.36052	+	0.442060i
$413$	−22.1926	−	7.21080i	−1.09202	−	0.354820i
$414$	2.54548	+	7.83419i	0.125104	+	0.385029i
$415$	15.5551	−	34.8626i	0.763569	−	1.71134i
$416$	11.8562	−	36.4898i	0.581300	−	1.78906i
$417$	5.46382	−	7.52031i	0.267565	−	0.368271i
$418$			4.39149i			0.214795i
$419$	−4.26011	−	3.09515i	−0.208120	−	0.151208i	0.478843	−	0.877901i	$-0.341056\pi$
$419$	−4.26011	−	3.09515i	−0.208120	−	0.151208i	−0.686963	+	0.726693i	$0.741056\pi$
$420$	−1.31052	+	12.3741i	−0.0639471	+	0.603795i
$421$	0.217609	−	0.158102i	0.0106056	−	0.00770544i	−0.582470	−	0.812852i	$-0.697914\pi$
$421$	0.217609	−	0.158102i	0.0106056	−	0.00770544i	0.593075	+	0.805147i	$0.297914\pi$
$422$	6.92111	+	9.52609i	0.336914	+	0.463723i
$423$	−20.7222	+	6.73305i	−1.00755	+	0.327372i
$424$	30.3105			1.47201
$425$	1.04734	−	4.88908i	0.0508034	−	0.237155i
$426$	6.59535			0.319546
$427$	32.1543	−	10.4476i	1.55606	−	0.505593i
$428$	6.33934	+	8.72535i	0.306424	+	0.421756i
$429$	6.75740	−	4.90954i	0.326250	−	0.237035i
$430$	−0.163098	−	0.283014i	−0.00786530	−	0.0136482i
$431$	7.21468	+	5.24178i	0.347519	+	0.252487i	0.747828	−	0.663893i	$-0.231097\pi$
$431$	7.21468	+	5.24178i	0.347519	+	0.252487i	−0.400308	+	0.916380i	$0.631097\pi$
$432$		−	6.87028i		−	0.330546i
$433$	−1.20339	+	1.65632i	−0.0578310	+	0.0795976i	−0.836953	−	0.547275i	$-0.815665\pi$
$433$	−1.20339	+	1.65632i	−0.0578310	+	0.0795976i	0.779122	+	0.626872i	$0.215665\pi$
$434$	−6.19676	+	19.0717i	−0.297454	+	0.915469i
$435$	−1.80204	−	0.190851i	−0.0864012	−	0.00915063i
$436$	−4.72185	−	14.5324i	−0.226136	−	0.695974i
$437$	−22.2273	−	7.22209i	−1.06328	−	0.345479i
$438$	−7.12259	−	2.31427i	−0.340330	−	0.110580i
$439$	−3.52005	−	10.8336i	−0.168003	−	0.517059i	0.831242	−	0.555910i	$-0.187630\pi$
$439$	−3.52005	−	10.8336i	−0.168003	−	0.517059i	−0.999245	+	0.0388510i	$0.987630\pi$
$440$	7.97989	+	0.845139i	0.380426	+	0.0402904i
$441$	−8.48532	+	26.1151i	−0.404063	+	1.24358i
$442$	2.59262	−	3.56844i	0.123319	−	0.169733i
$443$		−	10.0503i		−	0.477506i	−0.971080	−	0.238753i	$-0.923261\pi$
$443$		−	10.0503i		−	0.477506i	0.971080	−	0.238753i	$-0.0767387\pi$
$444$	−1.88244	−	1.36768i	−0.0893368	−	0.0649070i
$445$	5.12016	+	8.88470i	0.242719	+	0.421175i
$446$	−3.27993	+	2.38301i	−0.155309	+	0.112839i
$447$	−3.88945	−	5.35337i	−0.183965	−	0.253206i
$448$	−2.69686	+	0.876263i	−0.127415	+	0.0413995i
$449$	28.2771			1.33448			0.667241	−	0.744842i	$-0.267475\pi$
$449$	28.2771			1.33448			0.667241	+	0.744842i	$0.267475\pi$
$450$	3.11450	+	7.02535i	0.146819	+	0.331178i
$451$	−5.39848			−0.254204
$452$	−13.5968	+	4.41786i	−0.639539	+	0.207799i
$453$	3.33188	+	4.58595i	0.156546	+	0.215467i
$454$	−4.09723	+	2.97681i	−0.192293	+	0.139709i
$455$	−6.81777	+	64.3741i	−0.319622	+	3.01790i
$456$	−6.81734	−	4.95309i	−0.319251	−	0.231950i
$457$		−	25.0501i		−	1.17179i	−0.810386	−	0.585897i	$-0.800742\pi$
$457$		−	25.0501i		−	1.17179i	0.810386	−	0.585897i	$-0.199258\pi$
$458$	1.99674	−	2.74827i	0.0933014	−	0.128418i
$459$	1.35095	−	4.15781i	0.0630572	−	0.194070i
$460$	−7.63478	+	17.1114i	−0.355974	+	0.797821i
$461$	13.0070	+	40.0316i	0.605799	+	1.86446i	0.491205	+	0.871044i	$0.336556\pi$
$461$	13.0070	+	40.0316i	0.605799	+	1.86446i	0.114593	+	0.993413i	$0.463444\pi$
$462$	−3.40894	−	1.10763i	−0.158598	−	0.0515317i
$463$	−17.5172	−	5.69169i	−0.814095	−	0.264515i	−0.127764	−	0.991805i	$-0.540780\pi$
$463$	−17.5172	−	5.69169i	−0.814095	−	0.264515i	−0.686331	+	0.727289i	$0.740780\pi$
$464$	0.479476	+	1.47568i	0.0222591	+	0.0685065i
$465$	2.66093	+	12.5678i	0.123398	+	0.582820i
$466$	−3.27457	+	10.0781i	−0.151691	+	0.466858i
$467$	−0.614318	+	0.845537i	−0.0284273	+	0.0391268i	−0.822994	−	0.568050i	$-0.807698\pi$
$467$	−0.614318	+	0.845537i	−0.0284273	+	0.0391268i	0.794567	+	0.607177i	$0.207698\pi$
$468$		−	24.2822i		−	1.12245i
$469$	29.3421	+	21.3183i	1.35489	+	0.984387i
$470$	12.6363	+	5.63808i	0.582868	+	0.260065i
$471$	−13.5538	+	9.84739i	−0.624524	+	0.453744i
$472$	−7.44678	−	10.2496i	−0.342766	−	0.471777i
$473$	−0.320530	+	0.104146i	−0.0147380	+	0.00478866i
$474$	2.92819			0.134496
$475$	−21.3197	−	4.56710i	−0.978214	−	0.209553i
$476$	6.77983			0.310753
$477$	28.4836	−	9.25487i	1.30417	−	0.423752i
$478$	−5.61094	−	7.72279i	−0.256638	−	0.353232i
$479$	−1.70346	+	1.23764i	−0.0778331	+	0.0565491i	−0.626021	−	0.779806i	$-0.715318\pi$
$479$	−1.70346	+	1.23764i	−0.0778331	+	0.0565491i	0.548188	+	0.836355i	$0.315318\pi$
$480$	−7.06400	+	7.83283i	−0.322426	+	0.357518i
$481$	−9.79307	−	7.11508i	−0.446526	−	0.324420i
$482$		−	7.03365i		−	0.320374i
$483$	11.2124	−	15.4326i	0.510184	−	0.702208i
$484$	−4.19206	+	12.9018i	−0.190548	+	0.586447i
$485$	7.58656	+	6.84190i	0.344488	+	0.310675i
$486$	3.24585	+	9.98969i	0.147235	+	0.453141i
$487$	−25.9859	−	8.44333i	−1.17753	−	0.382604i	−0.346084	−	0.938204i	$-0.612489\pi$
$487$	−25.9859	−	8.44333i	−1.17753	−	0.382604i	−0.831450	+	0.555600i	$0.812489\pi$
$488$	17.4577	+	5.67236i	0.790275	+	0.256776i
$489$	1.74897	+	5.38276i	0.0790910	+	0.243417i
$490$	15.1088	−	8.70704i	0.682545	−	0.393344i
$491$	−4.91501	+	15.1269i	−0.221812	+	0.682666i	0.776788	+	0.629762i	$0.216848\pi$
$491$	−4.91501	+	15.1269i	−0.221812	+	0.682666i	−0.998600	+	0.0529036i	$0.983152\pi$
$492$	2.67150	−	3.67701i	0.120441	−	0.165772i
$493$			0.987344i			0.0444678i
$494$	−15.5608	−	11.3056i	−0.700114	−	0.508663i
$495$	7.75697	−	1.64235i	0.348650	−	0.0738180i
$496$	8.89895	−	6.46547i	0.399575	−	0.290308i
$497$	30.9993	+	42.6668i	1.39051	+	1.91387i
$498$	−8.80507	+	2.86094i	−0.394565	+	0.128202i
$499$	5.43557			0.243330			0.121665	−	0.992571i	$-0.461177\pi$
$499$	5.43557			0.243330			0.121665	+	0.992571i	$0.461177\pi$
$500$	−5.44140	+	16.6119i	−0.243347	+	0.742907i
$501$	−2.01001			−0.0898004
$502$	3.97845	−	1.29268i	0.177567	−	0.0576950i
$503$	−21.8353	−	30.0537i	−0.973586	−	1.34003i	−0.940214	−	0.340583i	$-0.889375\pi$
$503$	−21.8353	−	30.0537i	−0.973586	−	1.34003i	−0.0333717	−	0.999443i	$-0.510625\pi$
$504$	−19.2140	+	13.9598i	−0.855857	+	0.621817i
$505$	−12.0297	+	2.54698i	−0.535313	+	0.113339i
$506$	−4.36659	−	3.17251i	−0.194119	−	0.141035i
$507$			25.9132i			1.15085i
$508$	0.525760	−	0.723647i	0.0233268	−	0.0321066i
$509$	6.17623	−	19.0085i	0.273757	−	0.842536i	−0.715789	−	0.698316i	$-0.753933\pi$
$509$	6.17623	−	19.0085i	0.273757	−	0.842536i	0.989546	−	0.144220i	$-0.0460672\pi$
$510$	−1.05061	+	0.605457i	−0.0465219	+	0.0268101i
$511$	−18.5058	−	56.9551i	−0.818650	−	2.51954i
$512$	15.6269	+	5.07750i	0.690620	+	0.224396i
$513$	−18.1309	−	5.89107i	−0.800497	−	0.260097i
$514$	4.55446	+	14.0172i	0.200888	+	0.618271i
$515$	−30.8389	−	27.8119i	−1.35892	−	1.22554i
$516$	0.0876820	−	0.269857i	0.00385998	−	0.0118798i
$517$	8.39161	−	11.5501i	0.369063	−	0.507971i
$518$			5.19460i			0.228238i
$519$	0.00585750	+	0.00425573i	0.000257116	+	0.000186806i
$520$	−23.5384	+	26.1002i	−1.03223	+	1.14457i
$521$	4.73573	−	3.44071i	0.207476	−	0.150740i	−0.479195	−	0.877708i	$-0.659071\pi$
$521$	4.73573	−	3.44071i	0.207476	−	0.150740i	0.686671	+	0.726968i	$0.259071\pi$
$522$	−0.891966	−	1.22769i	−0.0390403	−	0.0537343i
$523$	21.5373	−	6.99790i	0.941761	−	0.305997i	0.202398	−	0.979303i	$-0.435127\pi$
$523$	21.5373	−	6.99790i	0.941761	−	0.305997i	0.739363	+	0.673307i	$0.235127\pi$
$524$	−17.0192			−0.743487
$525$	8.92256	−	15.3977i	0.389412	−	0.672011i
$526$	−0.623759			−0.0271972
$527$	6.65690	−	2.16296i	0.289979	−	0.0942199i
$528$	1.15566	+	1.59063i	0.0502937	+	0.0692233i
$529$	4.63127	−	3.36482i	0.201360	−	0.146296i
$530$	−17.3691	−	7.74980i	−0.754467	−	0.336630i
$531$	−10.1275	−	7.35806i	−0.439496	−	0.319313i
$532$		−	29.5646i		−	1.28179i
$533$	13.8980	−	19.1290i	0.601990	−	0.828568i
$534$	0.768489	−	2.36517i	0.0332558	−	0.102351i
$535$	−3.19495	−	15.0901i	−0.138130	−	0.652401i
$536$	6.08506	+	18.7279i	0.262834	+	0.808921i
$537$	−9.44198	−	3.06788i	−0.407451	−	0.132389i
$538$	−8.16412	−	2.65268i	−0.351980	−	0.114365i
$539$	−5.55988	−	17.1115i	−0.239481	−	0.737046i
$540$	−6.22771	+	13.9578i	−0.267998	+	0.600647i
$541$	11.1562	−	34.3352i	0.479642	−	1.47619i	−0.359952	−	0.932971i	$-0.617207\pi$
$541$	11.1562	−	34.3352i	0.479642	−	1.47619i	0.839594	−	0.543214i	$-0.182793\pi$
$542$	−1.83672	+	2.52803i	−0.0788940	+	0.108588i
$543$			1.92976i			0.0828141i
$544$	4.64940	+	3.37798i	0.199341	+	0.144830i
$545$	−2.30159	+	21.7318i	−0.0985892	+	0.930890i
$546$	12.7009	−	9.22772i	0.543547	−	0.394910i
$547$	−13.3156	−	18.3274i	−0.569335	−	0.783623i	0.423141	−	0.906064i	$-0.360928\pi$
$547$	−13.3156	−	18.3274i	−0.569335	−	0.783623i	−0.992476	+	0.122441i	$0.960928\pi$
$548$	2.61939	−	0.851092i	0.111895	−	0.0363569i
$549$	18.1375			0.774089
$550$	−4.35671	−	2.52460i	−0.185771	−	0.107649i
$551$	4.30549			0.183420
$552$	9.85001	−	3.20046i	0.419244	−	0.136221i
$553$	13.7630	+	18.9431i	0.585261	+	0.805543i
$554$	3.43656	−	2.49681i	0.146006	−	0.106079i
$555$	1.66159	+	2.88325i	0.0705306	+	0.122387i
$556$	14.3252	+	10.4078i	0.607522	+	0.441391i
$557$			40.3585i			1.71004i	0.518591	+	0.855022i	$0.326457\pi$
$557$			40.3585i			1.71004i	−0.518591	+	0.855022i	$0.673543\pi$
$558$	−6.32332	+	8.70330i	−0.267687	+	0.368440i
$559$	0.456150	−	1.40388i	0.0192931	−	0.0593780i
$560$	−15.1531	−	1.60484i	−0.640334	−	0.0678169i
$561$	0.386615	+	1.18988i	0.0163229	+	0.0502367i
$562$	12.2802	+	3.99007i	0.518008	+	0.168311i
$563$	−15.9363	−	5.17803i	−0.671636	−	0.218228i	−0.0467063	−	0.998909i	$-0.514872\pi$
$563$	−15.9363	−	5.17803i	−0.671636	−	0.218228i	−0.624930	+	0.780681i	$0.714872\pi$
$564$	3.71428	+	11.4314i	0.156399	+	0.481348i
$565$	20.3328	+	2.15341i	0.855405	+	0.0905948i
$566$	0.988649	−	3.04275i	0.0415560	−	0.127896i
$567$	−8.64202	+	11.8947i	−0.362931	+	0.499531i
$568$			28.6340i			1.20145i
$569$	7.24970	+	5.26721i	0.303923	+	0.220813i	0.729285	−	0.684210i	$-0.239853\pi$
$569$	7.24970	+	5.26721i	0.303923	+	0.220813i	−0.425361	+	0.905024i	$0.639853\pi$
$570$	2.64020	+	4.58138i	0.110586	+	0.191893i
$571$	−19.0433	+	13.8358i	−0.796937	+	0.579009i	−0.910014	−	0.414577i	$-0.863929\pi$
$571$	−19.0433	+	13.8358i	−0.796937	+	0.579009i	0.113077	+	0.993586i	$0.463929\pi$
$572$	9.35200	+	12.8719i	0.391027	+	0.538202i
$573$	5.26675	−	1.71127i	0.220022	−	0.0714894i
$574$	−10.1467			−0.423515
$575$	19.9430	−	17.8994i	0.831682	−	0.746458i
$576$	−1.52123			−0.0633847
$577$	−5.21609	+	1.69481i	−0.217149	+	0.0705559i	−0.415571	−	0.909561i	$-0.636418\pi$
$577$	−5.21609	+	1.69481i	−0.217149	+	0.0705559i	0.198422	+	0.980117i	$0.436418\pi$
$578$	0.388341	+	0.534506i	0.0161529	+	0.0222325i
$579$	−17.2861	+	12.5591i	−0.718387	+	0.521939i
$580$	0.363546	−	3.43264i	0.0150954	−	0.142533i
$581$	−59.8934	−	43.5151i	−2.48480	−	1.80531i
$582$		−	2.47757i		−	0.102698i
$583$	−11.5346	+	15.8761i	−0.477716	+	0.657520i
$584$	10.0475	−	30.9230i	0.415768	−	1.27960i
$585$	−14.1503	+	31.7142i	−0.585043	+	1.31122i
$586$	−4.02217	−	12.3790i	−0.166154	−	0.511370i
$587$	−8.54386	−	2.77607i	−0.352643	−	0.114581i	0.127338	−	0.991859i	$-0.459357\pi$
$587$	−8.54386	−	2.77607i	−0.352643	−	0.114581i	−0.479981	+	0.877279i	$0.659357\pi$
$588$	14.4064	+	4.68092i	0.594109	+	0.193038i
$589$	−9.43195	−	29.0286i	−0.388637	−	1.19610i
$590$	1.64668	+	7.77743i	0.0677927	+	0.320192i
$591$	1.72544	−	5.31037i	0.0709753	−	0.218439i
$592$	1.67483	−	2.30520i	0.0688349	−	0.0947431i
$593$		−	13.5739i		−	0.557415i	−0.960376	−	0.278707i	$-0.910094\pi$
$593$		−	13.5739i		−	0.557415i	0.960376	−	0.278707i	$-0.0899059\pi$
$594$	−3.56184	−	2.58783i	−0.146144	−	0.106180i
$595$	−8.85489	−	3.95090i	−0.363015	−	0.161971i
$596$	10.1974	−	7.40887i	0.417703	−	0.303479i
$597$	11.5566	+	15.9063i	0.472981	+	0.651002i
$598$	22.4830	−	7.30516i	0.919398	−	0.298730i
$599$	−11.8784			−0.485340			−0.242670	−	0.970109i	$-0.578023\pi$
$599$	−11.8784			−0.485340			−0.242670	+	0.970109i	$0.578023\pi$
$600$	8.83305	−	3.91590i	0.360608	−	0.159866i
$601$	29.3035			1.19531			0.597656	−	0.801752i	$-0.296099\pi$
$601$	29.3035			1.19531			0.597656	+	0.801752i	$0.296099\pi$
$602$	−0.602452	+	0.195748i	−0.0245541	+	0.00797811i
$603$	11.4366	+	15.7411i	0.465733	+	0.641027i
$604$	−8.73560	+	6.34678i	−0.355446	+	0.258247i
$605$	12.9936	−	14.4077i	0.528263	−	0.585758i
$606$	2.41255	+	1.75282i	0.0980030	+	0.0712034i
$607$		−	24.7537i		−	1.00472i	−0.864658	−	0.502361i	$-0.832465\pi$
$607$		−	24.7537i		−	1.00472i	0.864658	−	0.502361i	$-0.167535\pi$
$608$	14.7303	−	20.2745i	0.597392	−	0.822240i
$609$	−1.08594	+	3.34218i	−0.0440045	+	0.135432i
$610$	−8.55368	−	7.71409i	−0.346328	−	0.312335i
$611$	19.3229	+	59.4697i	0.781720	+	2.40589i
$612$	3.45915	+	1.12394i	0.139828	+	0.0454328i
$613$	16.9613	+	5.51105i	0.685059	+	0.222589i	0.630809	−	0.775938i	$-0.282723\pi$
$613$	16.9613	+	5.51105i	0.685059	+	0.222589i	0.0542503	+	0.998527i	$0.482723\pi$
$614$	−3.68924	−	11.3543i	−0.148886	−	0.458222i
$615$	−5.63191	+	3.24561i	−0.227101	+	0.130876i
$616$	4.80882	−	14.8000i	0.193753	−	0.596310i
$617$	−14.1250	+	19.4414i	−0.568651	+	0.782681i	−0.992394	−	0.123102i	$-0.960716\pi$
$617$	−14.1250	+	19.4414i	−0.568651	+	0.782681i	0.423743	+	0.905782i	$0.360716\pi$
$618$			10.0711i			0.405121i
$619$	31.4664	+	22.8617i	1.26474	+	0.918888i	0.998980	−	0.0451509i	$-0.0143769\pi$
$619$	31.4664	+	22.8617i	1.26474	+	0.918888i	0.265761	+	0.964039i	$0.414377\pi$
$620$	−23.9400	+	5.06871i	−0.961454	+	0.203564i
$621$	18.9558	−	13.7722i	0.760671	−	0.552660i
$622$	1.57111	+	2.16245i	0.0629958	+	0.0867063i
$623$	18.9128	−	6.14515i	0.757726	−	0.246200i
$624$	−8.61142			−0.344733
$625$	16.7873	−	18.5253i	0.671492	−	0.741012i
$626$	1.61085			0.0643824
$627$	5.18867	−	1.68590i	0.207215	−	0.0673284i
$628$	−18.7579	−	25.8181i	−0.748522	−	1.03025i
$629$	1.46687	−	1.06575i	0.0584881	−	0.0424941i
$630$	14.5796	−	3.08687i	0.580865	−	0.122984i
$631$	−3.36474	−	2.44463i	−0.133948	−	0.0973190i	0.518794	−	0.854900i	$-0.326381\pi$
$631$	−3.36474	−	2.44463i	−0.133948	−	0.0973190i	−0.652742	+	0.757581i	$0.726381\pi$
$632$			12.7128i			0.505689i
$633$	8.59832	−	11.8346i	0.341753	−	0.470382i
$634$	1.48235	−	4.56221i	0.0588717	−	0.181188i
$635$	−1.10838	+	0.638747i	−0.0439846	+	0.0253479i
$636$	−5.10545	−	15.7129i	−0.202444	−	0.623059i
$637$	74.9466	+	24.3516i	2.96949	+	0.964847i
$638$	0.945656	+	0.307262i	0.0374389	+	0.0121646i
$639$	8.74297	+	26.9081i	0.345866	+	1.06447i
$640$	−18.3686	−	16.5657i	−0.726084	−	0.654815i
$641$	−4.75485	+	14.6339i	−0.187805	+	0.578005i	−0.999985	−	0.00540175i	$-0.998281\pi$
$641$	−4.75485	+	14.6339i	−0.187805	+	0.578005i	0.812180	+	0.583407i	$0.198281\pi$
$642$	−2.19875	+	3.02631i	−0.0867776	+	0.119439i
$643$			2.00001i			0.0788725i	0.999222	+	0.0394363i	$0.0125562\pi$
$643$			2.00001i			0.0788725i	−0.999222	+	0.0394363i	$0.987444\pi$
$644$	29.3970	+	21.3582i	1.15840	+	0.841630i
$645$	−0.271776	+	0.301355i	−0.0107012	+	0.0118659i
$646$	2.33081	−	1.69343i	0.0917043	−	0.0666271i
$647$	0.518924	+	0.714238i	0.0204010	+	0.0280796i	0.819096	−	0.573657i	$-0.194476\pi$
$647$	0.518924	+	0.714238i	0.0204010	+	0.0280796i	−0.798695	+	0.601737i	$0.794476\pi$
$648$	−7.59192	+	2.46677i	−0.298239	+	0.0969037i
$649$	8.20242			0.321973
$650$	20.1617	−	8.93818i	0.790808	−	0.350584i
$651$	24.9127			0.976405
$652$	−10.2534	+	3.33154i	−0.401555	+	0.130473i
$653$	−21.4194	−	29.4813i	−0.838206	−	1.15369i	−0.986340	−	0.164725i	$-0.947326\pi$
$653$	−21.4194	−	29.4813i	−0.838206	−	1.15369i	0.148133	−	0.988967i	$-0.452674\pi$
$654$	4.28764	−	3.11516i	0.167660	−	0.121812i
$655$	22.2282	+	9.91781i	0.868526	+	0.387521i
$656$	4.50279	+	3.27147i	0.175804	+	0.127729i
$657$		−	32.1270i		−	1.25339i
$658$	15.7724	−	21.7089i	0.614874	−	0.846301i
$659$	13.6562	−	42.0295i	0.531970	−	1.63724i	−0.218135	−	0.975919i	$-0.569997\pi$
$659$	13.6562	−	42.0295i	0.531970	−	1.63724i	0.750106	−	0.661318i	$-0.230003\pi$
$660$	−0.905999	−	4.27913i	−0.0352660	−	0.166565i
$661$	7.32242	+	22.5361i	0.284809	+	0.876552i	0.986456	+	0.164027i	$0.0524485\pi$
$661$	7.32242	+	22.5361i	0.284809	+	0.876552i	−0.701647	+	0.712525i	$0.747551\pi$
$662$	−18.4304	−	5.98841i	−0.716320	−	0.232746i
$663$	−5.21153	−	1.69333i	−0.202399	−	0.0657634i
$664$	−12.4209	−	38.2275i	−0.482023	−	1.48352i
$665$	−17.2286	+	38.6133i	−0.668095	+	1.49736i
$666$	−0.861149	+	2.65034i	−0.0333688	+	0.102699i
$667$	−3.11038	+	4.28108i	−0.120435	+	0.165764i
$668$		−	3.82879i		−	0.148140i
$669$	4.07477	+	2.96049i	0.157540	+	0.114459i
$670$	1.30137	−	12.2877i	0.0502762	−	0.474714i
$671$	−9.61461	+	6.98543i	−0.371168	+	0.269669i
$672$	12.0230	+	16.5482i	0.463797	+	0.638362i
$673$	−12.0785	+	3.92454i	−0.465592	+	0.151280i	−0.532413	−	0.846485i	$-0.678715\pi$
$673$	−12.0785	+	3.92454i	−0.465592	+	0.151280i	0.0668204	+	0.997765i	$0.478715\pi$
$674$	6.28737			0.242180
$675$	16.2676	−	14.6006i	0.626140	−	0.561977i
$676$	−49.3611			−1.89850
$677$	14.4488	−	4.69471i	0.555314	−	0.180432i	−0.0178978	−	0.999840i	$-0.505697\pi$
$677$	14.4488	−	4.69471i	0.555314	−	0.180432i	0.573211	+	0.819407i	$0.305697\pi$
$678$	−2.91460	−	4.01161i	−0.111935	−	0.154065i
$679$	16.0279	−	11.6450i	0.615095	−	0.446893i
$680$	−2.62861	−	4.56127i	−0.100803	−	0.174917i
$681$	5.09013	+	3.69820i	0.195054	+	0.141715i
$682$		−	7.04893i		−	0.269918i
$683$	−3.29300	+	4.53243i	−0.126003	+	0.173428i	−0.867358	−	0.497685i	$-0.834184\pi$
$683$	−3.29300	+	4.53243i	−0.126003	+	0.173428i	0.741355	+	0.671113i	$0.234184\pi$
$684$	4.90116	−	15.0842i	0.187400	−	0.576759i
$685$	−3.91707	−	0.414851i	−0.149663	−	0.0158506i
$686$	−4.25284	−	13.0889i	−0.162374	−	0.499736i
$687$	−4.01372	−	1.30414i	−0.153133	−	0.0497559i
$688$	0.330462	+	0.107374i	0.0125987	+	0.00409358i
$689$	−26.5602	−	81.7437i	−1.01186	−	3.11419i
$690$	−6.46275	−	0.684460i	−0.246033	−	0.0260570i
$691$	−1.56047	+	4.80264i	−0.0593632	+	0.182701i	−0.976341	−	0.216238i	$-0.930621\pi$
$691$	−1.56047	+	4.80264i	−0.0593632	+	0.182701i	0.916978	+	0.398939i	$0.130621\pi$
$692$	−0.00810657	+	0.0111577i	−0.000308166	+	0.000424154i
$693$		−	15.3763i		−	0.584097i
$694$	−12.3113	−	8.94465i	−0.467329	−	0.339534i
$695$	−12.6445	−	21.9412i	−0.479633	−	0.832277i
$696$	−1.54358	+	1.12148i	−0.0585094	+	0.0425095i
$697$	2.08174	+	2.86527i	0.0788516	+	0.108530i
$698$	−4.89218	+	1.58957i	−0.185172	+	0.0601660i
$699$	13.1647			0.497933
$700$	29.3305	+	16.9963i	1.10859	+	0.642398i
$701$	−11.0138			−0.415986			−0.207993	−	0.978130i	$-0.566693\pi$
$701$	−11.0138			−0.415986			−0.207993	+	0.978130i	$0.566693\pi$
$702$	18.3394	−	5.95884i	0.692177	−	0.224902i
$703$	−4.64737	−	6.39656i	−0.175279	−	0.241251i
$704$	0.806400	−	0.585884i	0.0303924	−	0.0220813i
$705$	1.81046	−	17.0946i	0.0681860	−	0.643820i
$706$	2.16778	+	1.57499i	0.0815856	+	0.0592754i
$707$			23.8458i			0.896815i
$708$	−4.05907	+	5.58683i	−0.152549	+	0.209966i
$709$	−9.97009	+	30.6848i	−0.374435	+	1.15239i	0.569425	+	0.822044i	$0.307166\pi$
$709$	−9.97009	+	30.6848i	−0.374435	+	1.15239i	−0.943859	+	0.330348i	$0.892834\pi$
$710$	7.32114	−	16.4084i	0.274757	−	0.615797i
$711$	3.88168	+	11.9466i	0.145574	+	0.448032i
$712$	10.2685	+	3.33642i	0.384827	+	0.125038i
$713$	35.6778	+	11.5924i	1.33615	+	0.434140i
$714$	0.726661	+	2.23643i	0.0271946	+	0.0836964i
$715$	−4.71330	−	22.2614i	−0.176267	−	0.832528i
$716$	5.84390	−	17.9857i	0.218397	−	0.672156i
$717$	−6.97065	+	9.59428i	−0.260324	+	0.358305i
$718$		−	10.0292i		−	0.374285i
$719$	10.1001	+	7.33813i	0.376669	+	0.273666i	0.759971	−	0.649957i	$-0.225213\pi$
$719$	10.1001	+	7.33813i	0.376669	+	0.273666i	−0.383302	+	0.923623i	$0.625213\pi$
$720$	−7.46523	−	3.33085i	−0.278213	−	0.124134i
$721$	−65.1525	+	47.3360i	−2.42640	+	1.76289i
$722$	−0.00601239	−	0.00827534i	−0.000223758	−	0.000307976i
$723$	−8.31046	+	2.70023i	−0.309069	+	0.100423i
$724$	−3.67594			−0.136615
$725$	−2.47516	+	4.27139i	−0.0919251	+	0.158636i
$726$	−4.70518			−0.174626
$727$	−4.68090	+	1.52092i	−0.173605	+	0.0564077i	−0.394530	−	0.918883i	$-0.629092\pi$
$727$	−4.68090	+	1.52092i	−0.173605	+	0.0564077i	0.220925	+	0.975291i	$0.429092\pi$
$728$	40.0625	+	55.1413i	1.48481	+	2.04367i
$729$	2.32790	−	1.69132i	0.0862184	−	0.0626413i
$730$	−13.6640	+	15.1512i	−0.505728	+	0.560770i
$731$	0.178878	+	0.129962i	0.00661604	+	0.00480683i
$732$		−	10.0055i		−	0.369815i
$733$	−12.2853	+	16.9092i	−0.453767	+	0.624556i	−0.973202	−	0.229954i	$-0.926143\pi$
$733$	−12.2853	+	16.9092i	−0.453767	+	0.624556i	0.519435	+	0.854510i	$0.326143\pi$
$734$	−1.43858	+	4.42750i	−0.0530990	+	0.163422i
$735$	−16.0879	−	14.5088i	−0.593411	−	0.535165i
$736$	9.51805	+	29.2935i	0.350840	+	1.07977i
$737$	−12.1250	−	3.93964i	−0.446629	−	0.145119i
$738$	−5.17696	−	1.68210i	−0.190567	−	0.0619189i
$739$	4.44023	+	13.6656i	0.163336	+	0.502698i	0.998910	−	0.0466811i	$-0.0148645\pi$
$739$	4.44023	+	13.6656i	0.163336	+	0.502698i	−0.835574	+	0.549379i	$0.814864\pi$
$740$	−5.49220	+	3.16510i	−0.201897	+	0.116351i
$741$	−7.38405	+	22.7258i	−0.271260	+	0.834852i
$742$	−21.6799	+	29.8398i	−0.795895	+	1.09546i
$743$		−	31.3724i		−	1.15094i	−0.817823	−	0.575470i	$-0.804819\pi$
$743$		−	31.3724i		−	1.15094i	0.817823	−	0.575470i	$-0.195181\pi$
$744$	10.9428	+	7.95038i	0.401181	+	0.291475i
$745$	−17.6360	+	3.73398i	−0.646133	+	0.136803i
$746$	14.1402	−	10.2735i	0.517711	−	0.376139i
$747$	−23.3445	−	32.1309i	−0.854129	−	1.17561i
$748$	−2.26655	+	0.736448i	−0.0828734	+	0.0269272i
$749$	−29.9124			−1.09297
$750$	−6.06291	−	0.0144688i	−0.221386	−	0.000528326i
$751$	14.1191			0.515213			0.257606	−	0.966250i	$-0.417066\pi$
$751$	14.1191			0.515213			0.257606	+	0.966250i	$0.417066\pi$
$752$	−13.9986	+	4.54843i	−0.510477	+	0.165864i
$753$	−3.05467	−	4.20439i	−0.111318	−	0.153217i
$754$	−3.52328	+	2.55981i	−0.128310	+	0.0932229i
$755$	15.1078	−	3.19870i	0.549829	−	0.116413i
$756$	23.9792	+	17.4219i	0.872115	+	0.633629i
$757$		−	50.4329i		−	1.83301i	−0.400018	−	0.916507i	$-0.630996\pi$
$757$		−	50.4329i		−	1.83301i	0.400018	−	0.916507i	$-0.369004\pi$
$758$	0.513960	−	0.707406i	0.0186679	−	0.0256941i
$759$	−2.07207	+	6.37719i	−0.0752115	+	0.231477i
$760$	−19.8902	+	11.4625i	−0.721494	+	0.415790i
$761$	−9.07982	−	27.9448i	−0.329143	−	1.01300i	−0.969535	−	0.244951i	$-0.921228\pi$
$761$	−9.07982	−	27.9448i	−0.329143	−	1.01300i	0.640392	−	0.768048i	$-0.278772\pi$
$762$	0.295057	+	0.0958699i	0.0106888	+	0.00347300i
$763$	40.3053	+	13.0960i	1.45915	+	0.474106i
$764$	3.25974	+	10.0324i	0.117933	+	0.362961i
$765$	−3.86290	−	3.48374i	−0.139663	−	0.125955i
$766$	2.70947	−	8.33889i	0.0978971	−	0.301296i
$767$	−21.1166	+	29.0645i	−0.762476	+	1.04946i
$768$			7.07218i			0.255195i
$769$	−5.22161	−	3.79373i	−0.188296	−	0.136805i	0.489643	−	0.871923i	$-0.337127\pi$
$769$	−5.22161	−	3.79373i	−0.188296	−	0.136805i	−0.677940	+	0.735118i	$0.737127\pi$
$770$	−6.53972	+	7.25149i	−0.235675	+	0.261326i
$771$	14.8132	−	10.7624i	0.533485	−

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.628349 + 0.204163i) q^{2} +(0.482449 + 0.664034i) q^{3} +(-1.26489 + 0.918999i) q^{4} +(2.18757 - 0.463165i) q^{5} +(-0.438718 - 0.318747i) q^{6} -4.33633i q^{7} +(1.38385 - 1.90471i) q^{8} +(0.718867 - 2.21244i) q^{9} +(-1.28000 + 0.737651i) q^{10} +(0.471027 + 1.44967i) q^{11} +(-1.22049 - 0.396562i) q^{12} +(-6.34940 - 2.06304i) q^{13} +(0.885318 + 2.72473i) q^{14} +(1.36295 + 1.22917i) q^{15} +(0.485622 - 1.49459i) q^{16} +(0.587785 - 0.809017i) q^{17} +1.53695i q^{18} +(-3.52786 - 2.56314i) q^{19} +(-2.34140 + 2.59623i) q^{20} +(2.87947 - 2.09206i) q^{21} +(-0.591939 - 0.814734i) q^{22} +(5.09722 - 1.65619i) q^{23} +1.93243 q^{24} +(4.57096 - 2.02641i) q^{25} +4.41084 q^{26} +(4.15781 - 1.35095i) q^{27} +(3.98508 + 5.48499i) q^{28} +(-0.798778 + 0.580346i) q^{29} +(-1.10736 - 0.494084i) q^{30} +(5.66269 + 4.11419i) q^{31} +5.74697i q^{32} +(-0.735385 + 1.01217i) q^{33} +(-0.204163 + 0.628349i) q^{34} +(-2.00843 - 9.48604i) q^{35} +(1.12394 + 3.45915i) q^{36} +(1.72441 + 0.560296i) q^{37} +(2.74003 + 0.890289i) q^{38} +(-1.69333 - 5.21153i) q^{39} +(2.14508 - 4.80764i) q^{40} +(-1.09444 + 3.36833i) q^{41} +(-1.38219 + 1.90242i) q^{42} +0.221105i q^{43} +(-1.92805 - 1.40081i) q^{44} +(0.547848 - 5.17284i) q^{45} +(-2.86470 + 2.08133i) q^{46} +(-5.50531 - 7.57741i) q^{47} +(1.22675 - 0.398594i) q^{48} -11.8037 q^{49} +(-2.45844 + 2.20652i) q^{50} +0.820791 q^{51} +(9.92725 - 3.22556i) q^{52} +(7.56730 + 10.4155i) q^{53} +(-2.33674 + 1.69774i) q^{54} +(1.70184 + 2.95310i) q^{55} +(-8.25944 - 6.00083i) q^{56} -3.57920i q^{57} +(0.383426 - 0.527741i) q^{58} +(1.66288 - 5.11782i) q^{59} +(-2.85359 - 0.302220i) q^{60} +(2.40931 + 7.41510i) q^{61} +(-4.39811 - 1.42903i) q^{62} +(-9.59388 - 3.11724i) q^{63} +(-0.202075 - 0.621922i) q^{64} +(-14.8453 - 1.57224i) q^{65} +(0.255431 - 0.786135i) q^{66} +(-4.91621 + 6.76658i) q^{67} +1.56349i q^{68} +(3.55891 + 2.58570i) q^{69} +(3.19870 + 5.55050i) q^{70} +(-9.83939 + 7.14874i) q^{71} +(-3.21926 - 4.43093i) q^{72} +(13.1344 - 4.26763i) q^{73} -1.19793 q^{74} +(3.55086 + 2.05763i) q^{75} +6.81789 q^{76} +(6.28625 - 2.04253i) q^{77} +(2.12800 + 2.92895i) q^{78} +(-4.36847 + 3.17388i) q^{79} +(0.370092 - 3.49445i) q^{80} +(-2.74304 - 1.99294i) q^{81} -2.33993i q^{82} +(10.0350 - 13.8120i) q^{83} +(-1.71962 + 5.29246i) q^{84} +(0.911115 - 2.04203i) q^{85} +(-0.0451415 - 0.138931i) q^{86} +(-0.770740 - 0.250429i) q^{87} +(3.41303 + 1.10896i) q^{88} +(1.41713 + 4.36148i) q^{89} +(0.711863 + 3.36220i) q^{90} +(-8.94604 + 27.5331i) q^{91} +(-4.92540 + 6.77924i) q^{92} +5.74511i q^{93} +(5.00629 + 3.63728i) q^{94} +(-8.90461 - 3.97308i) q^{95} +(-3.81618 + 2.77262i) q^{96} +(2.68545 + 3.69620i) q^{97} +(7.41687 - 2.40989i) q^{98} +3.54592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

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