LMFDB - Embedded newform 925.2.y.b.193.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.13
Character	$\chi$	$=$	925.193
Dual form			925.2.y.b.532.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.54509 - 0.892058i) q^{2} +(0.471934 + 1.76128i) q^{3} +(0.591534 - 1.02457i) q^{4} +(2.30034 + 2.30034i) q^{6} +(0.134169 + 0.500724i) q^{7} +1.45750i q^{8} +(-0.281310 + 0.162414i) q^{9} +5.59836i q^{11} +(2.08371 + 0.558329i) q^{12} +(-1.32347 - 0.764108i) q^{13} +(0.653977 + 0.653977i) q^{14} +(2.48324 + 4.30110i) q^{16} +(-3.63263 - 6.29189i) q^{17} +(-0.289766 + 0.501889i) q^{18} +(0.654716 + 2.44343i) q^{19} +(-0.818597 + 0.472617i) q^{21} +(4.99406 + 8.64996i) q^{22} +1.14851i q^{23} +(-2.56707 + 0.687844i) q^{24} -2.72651 q^{26} +(3.44922 + 3.44922i) q^{27} +(0.592390 + 0.158730i) q^{28} +(3.86835 + 3.86835i) q^{29} +(2.49059 - 2.49059i) q^{31} +(5.14920 + 2.97289i) q^{32} +(-9.86028 + 2.64205i) q^{33} +(-11.2255 - 6.48102i) q^{34} +0.384294i q^{36} +(1.49687 - 5.89571i) q^{37} +(3.19128 + 3.19128i) q^{38} +(0.721216 - 2.69162i) q^{39} +(-6.02783 - 3.48017i) q^{41} +(-0.843203 + 1.46047i) q^{42} +10.5642i q^{43} +(5.73589 + 3.31162i) q^{44} +(1.02454 + 1.77455i) q^{46} +(-1.35499 + 1.35499i) q^{47} +(-6.40352 + 6.40352i) q^{48} +(5.82945 - 3.36564i) q^{49} +(9.36743 - 9.36743i) q^{51} +(-1.56576 + 0.903991i) q^{52} +(2.14463 - 8.00388i) q^{53} +(8.40626 + 2.25245i) q^{54} +(-0.729806 + 0.195551i) q^{56} +(-3.99459 + 2.30628i) q^{57} +(9.42773 + 2.52615i) q^{58} +(3.01861 + 0.808835i) q^{59} +(-0.446001 - 1.66450i) q^{61} +(1.62643 - 6.06993i) q^{62} +(-0.119068 - 0.119068i) q^{63} +0.674985 q^{64} +(-12.8781 + 12.8781i) q^{66} +(4.42331 - 1.18522i) q^{67} -8.59528 q^{68} +(-2.02285 + 0.542020i) q^{69} +(2.78939 - 4.83137i) q^{71} +(-0.236719 - 0.410010i) q^{72} +(5.42800 - 5.42800i) q^{73} +(-2.94652 - 10.4447i) q^{74} +(2.89075 + 0.774573i) q^{76} +(-2.80323 + 0.751124i) q^{77} +(-1.28673 - 4.80215i) q^{78} +(-0.923868 - 3.44792i) q^{79} +(-4.93449 + 8.54678i) q^{81} -12.4181 q^{82} +(2.06428 - 7.70401i) q^{83} +1.11828i q^{84} +(9.42386 + 16.3226i) q^{86} +(-4.98764 + 8.63885i) q^{87} -8.15962 q^{88} +(-0.896627 + 3.34626i) q^{89} +(0.205039 - 0.765214i) q^{91} +(1.17672 + 0.679382i) q^{92} +(5.56202 + 3.21123i) q^{93} +(-0.884854 + 3.30232i) q^{94} +(-2.80601 + 10.4722i) q^{96} -13.3259 q^{97} +(6.00468 - 10.4004i) q^{98} +(-0.909254 - 1.57487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.54509	−	0.892058i	1.09254	−	0.630780i	0.158291	−	0.987393i	$-0.449402\pi$
$2$	1.54509	−	0.892058i	1.09254	−	0.630780i	0.934252	+	0.356613i	$0.116068\pi$
$3$	0.471934	+	1.76128i	0.272471	+	1.01688i	0.957517	+	0.288376i	$0.0931153\pi$
$3$	0.471934	+	1.76128i	0.272471	+	1.01688i	−0.685046	+	0.728500i	$0.740218\pi$
$4$	0.591534	−	1.02457i	0.295767	−	0.512283i
$5$		0			0
$5$		0			0
$6$	2.30034	+	2.30034i	0.939111	+	0.939111i
$7$	0.134169	+	0.500724i	0.0507110	+	0.189256i	0.986635	−	0.162946i	$-0.0520997\pi$
$7$	0.134169	+	0.500724i	0.0507110	+	0.189256i	−0.935924	+	0.352202i	$0.885433\pi$
$8$			1.45750i			0.515305i
$9$	−0.281310	+	0.162414i	−0.0937700	+	0.0541381i
$10$		0			0
$11$			5.59836i			1.68797i	0.536368	+	0.843984i	$0.319796\pi$
$11$			5.59836i			1.68797i	−0.536368	+	0.843984i	$0.680204\pi$
$12$	2.08371	+	0.558329i	0.601516	+	0.161176i
$13$	−1.32347	−	0.764108i	−0.367066	−	0.211925i	0.305110	−	0.952317i	$-0.401307\pi$
$13$	−1.32347	−	0.764108i	−0.367066	−	0.211925i	−0.672176	+	0.740392i	$0.734640\pi$
$14$	0.653977	+	0.653977i	0.174783	+	0.174783i
$15$		0			0
$16$	2.48324	+	4.30110i	0.620811	+	1.07528i
$17$	−3.63263	−	6.29189i	−0.881041	−	1.52601i	−0.850185	−	0.526484i	$-0.823510\pi$
$17$	−3.63263	−	6.29189i	−0.881041	−	1.52601i	−0.0308564	−	0.999524i	$-0.509823\pi$
$18$	−0.289766	+	0.501889i	−0.0682985	+	0.118296i
$19$	0.654716	+	2.44343i	0.150202	+	0.560562i	0.999469	+	0.0325976i	$0.0103780\pi$
$19$	0.654716	+	2.44343i	0.150202	+	0.560562i	−0.849266	+	0.527965i	$0.822955\pi$
$20$		0			0
$21$	−0.818597	+	0.472617i	−0.178632	+	0.103133i
$22$	4.99406	+	8.64996i	1.06474	+	1.84418i
$23$			1.14851i			0.239481i	0.992805	+	0.119740i	$0.0382062\pi$
$23$			1.14851i			0.239481i	−0.992805	+	0.119740i	$0.961794\pi$
$24$	−2.56707	+	0.687844i	−0.524001	+	0.140406i
$25$		0			0
$26$	−2.72651			−0.534713
$27$	3.44922	+	3.44922i	0.663803	+	0.663803i
$28$	0.592390	+	0.158730i	0.111951	+	0.0299972i
$29$	3.86835	+	3.86835i	0.718334	+	0.718334i	0.968264	−	0.249930i	$-0.0804075\pi$
$29$	3.86835	+	3.86835i	0.718334	+	0.718334i	−0.249930	+	0.968264i	$0.580408\pi$
$30$		0			0
$31$	2.49059	−	2.49059i	0.447323	−	0.447323i	−0.447141	−	0.894464i	$-0.647558\pi$
$31$	2.49059	−	2.49059i	0.447323	−	0.447323i	0.894464	+	0.447141i	$0.147558\pi$
$32$	5.14920	+	2.97289i	0.910258	+	0.525538i
$33$	−9.86028	+	2.64205i	−1.71645	+	0.459922i
$34$	−11.2255	−	6.48102i	−1.92515	−	1.11149i
$35$		0			0
$36$			0.384294i			0.0640490i
$37$	1.49687	−	5.89571i	0.246083	−	0.969249i
$37$	1.49687	−	5.89571i	0.246083	−	0.969249i
$38$	3.19128	+	3.19128i	0.517694	+	0.517694i
$39$	0.721216	−	2.69162i	0.115487	−	0.431003i
$40$		0			0
$41$	−6.02783	−	3.48017i	−0.941390	−	0.543512i	−0.0509939	−	0.998699i	$-0.516239\pi$
$41$	−6.02783	−	3.48017i	−0.941390	−	0.543512i	−0.890396	+	0.455187i	$0.849572\pi$
$42$	−0.843203	+	1.46047i	−0.130109	+	0.225356i
$43$			10.5642i			1.61102i	0.592580	+	0.805512i	$0.298109\pi$
$43$			10.5642i			1.61102i	−0.592580	+	0.805512i	$0.701891\pi$
$44$	5.73589	+	3.31162i	0.864718	+	0.499245i
$45$		0			0
$46$	1.02454	+	1.77455i	0.151060	+	0.261643i
$47$	−1.35499	+	1.35499i	−0.197646	+	0.197646i	−0.798990	−	0.601344i	$-0.794632\pi$
$47$	−1.35499	+	1.35499i	−0.197646	+	0.197646i	0.601344	+	0.798990i	$0.294632\pi$
$48$	−6.40352	+	6.40352i	−0.924269	+	0.924269i
$49$	5.82945	−	3.36564i	0.832779	−	0.480805i
$50$		0			0
$51$	9.36743	−	9.36743i	1.31170	−	1.31170i
$52$	−1.56576	+	0.903991i	−0.217132	+	0.125361i
$53$	2.14463	−	8.00388i	0.294588	−	1.09942i	−0.646956	−	0.762528i	$-0.723958\pi$
$53$	2.14463	−	8.00388i	0.294588	−	1.09942i	0.941544	−	0.336890i	$-0.109375\pi$
$54$	8.40626	+	2.25245i	1.14395	+	0.306520i
$55$		0			0
$56$	−0.729806	+	0.195551i	−0.0975245	+	0.0261316i
$57$	−3.99459	+	2.30628i	−0.529096	+	0.305474i
$58$	9.42773	+	2.52615i	1.23792	+	0.331700i
$59$	3.01861	+	0.808835i	0.392990	+	0.105301i	0.449902	−	0.893078i	$-0.351459\pi$
$59$	3.01861	+	0.808835i	0.392990	+	0.105301i	−0.0569123	+	0.998379i	$0.518126\pi$
$60$		0			0
$61$	−0.446001	−	1.66450i	−0.0571045	−	0.213117i	0.931478	−	0.363798i	$-0.118520\pi$
$61$	−0.446001	−	1.66450i	−0.0571045	−	0.213117i	−0.988582	+	0.150681i	$0.951853\pi$
$62$	1.62643	−	6.06993i	0.206557	−	0.770882i
$63$	−0.119068	−	0.119068i	−0.0150011	−	0.0150011i
$64$	0.674985			0.0843731
$65$		0			0
$66$	−12.8781	+	12.8781i	−1.58519	+	1.58519i
$67$	4.42331	−	1.18522i	0.540394	−	0.144798i	0.0217100	−	0.999764i	$-0.493089\pi$
$67$	4.42331	−	1.18522i	0.540394	−	0.144798i	0.518684	+	0.854966i	$0.326422\pi$
$68$	−8.59528			−1.04233
$69$	−2.02285	+	0.542020i	−0.243522	+	0.0652516i
$70$		0			0
$71$	2.78939	−	4.83137i	0.331040	−	0.573378i	−0.651676	−	0.758497i	$-0.725934\pi$
$71$	2.78939	−	4.83137i	0.331040	−	0.573378i	0.982716	+	0.185120i	$0.0592672\pi$
$72$	−0.236719	−	0.410010i	−0.0278976	−	0.0483201i
$73$	5.42800	−	5.42800i	0.635300	−	0.635300i	−0.314093	−	0.949392i	$-0.601700\pi$
$73$	5.42800	−	5.42800i	0.635300	−	0.635300i	0.949392	+	0.314093i	$0.101700\pi$
$74$	−2.94652	−	10.4447i	−0.342526	−	1.21417i
$75$		0			0
$76$	2.89075	+	0.774573i	0.331591	+	0.0888497i
$77$	−2.80323	+	0.751124i	−0.319458	+	0.0855985i
$78$	−1.28673	−	4.80215i	−0.145694	−	0.543737i
$79$	−0.923868	−	3.44792i	−0.103943	−	0.387922i	0.894280	−	0.447508i	$-0.147688\pi$
$79$	−0.923868	−	3.44792i	−0.103943	−	0.387922i	−0.998223	+	0.0595866i	$0.981022\pi$
$80$		0			0
$81$	−4.93449	+	8.54678i	−0.548276	+	0.949642i
$82$	−12.4181			−1.37134
$83$	2.06428	−	7.70401i	0.226584	−	0.845625i	−0.755179	−	0.655519i	$-0.772450\pi$
$83$	2.06428	−	7.70401i	0.226584	−	0.845625i	0.981764	−	0.190106i	$-0.0608832\pi$
$84$			1.11828i			0.122014i
$85$		0			0
$86$	9.42386	+	16.3226i	1.01620	+	1.76011i
$87$	−4.98764	+	8.63885i	−0.534731	+	0.926182i
$88$	−8.15962			−0.869818
$89$	−0.896627	+	3.34626i	−0.0950423	+	0.354703i	−0.997026	−	0.0770677i	$-0.975444\pi$
$89$	−0.896627	+	3.34626i	−0.0950423	+	0.354703i	0.901984	+	0.431770i	$0.142111\pi$
$90$		0			0
$91$	0.205039	−	0.765214i	0.0214939	−	0.0802162i
$92$	1.17672	+	0.679382i	0.122682	+	0.0708305i
$93$	5.56202	+	3.21123i	0.576754	+	0.332989i
$94$	−0.884854	+	3.30232i	−0.0912657	+	0.340608i
$95$		0			0
$96$	−2.80601	+	10.4722i	−0.286388	+	1.06881i
$97$	−13.3259			−1.35304			−0.676519	−	0.736425i	$-0.736513\pi$
$97$	−13.3259			−1.35304			−0.676519	+	0.736425i	$0.736513\pi$
$98$	6.00468	−	10.4004i	0.606565	−	1.05060i
$99$	−0.909254	−	1.57487i	−0.0913835	−	0.158281i
$100$		0			0
$101$		−	13.7961i		−	1.37276i	−0.727242	−	0.686381i	$-0.759198\pi$
$101$		−	13.7961i		−	1.37276i	0.727242	−	0.686381i	$-0.240802\pi$
$102$	6.11723	−	22.8298i	0.605696	−	2.26049i
$103$	1.57697			0.155384			0.0776920	−	0.996977i	$-0.475245\pi$
$103$	1.57697			0.155384			0.0776920	+	0.996977i	$0.475245\pi$
$104$	1.11369	−	1.92897i	0.109206	−	0.189151i
$105$		0			0
$106$	−3.82628	−	14.2799i	−0.371641	−	1.38698i
$107$	1.09735	+	4.09537i	0.106085	+	0.395915i	0.998466	−	0.0553681i	$-0.0176332\pi$
$107$	1.09735	+	4.09537i	0.106085	+	0.395915i	−0.892381	+	0.451283i	$0.850967\pi$
$108$	5.57429	−	1.49363i	0.536386	−	0.143724i
$109$	16.6734	+	4.46764i	1.59703	+	0.427922i	0.944143	−	0.329536i	$-0.106892\pi$
$109$	16.6734	+	4.46764i	1.59703	+	0.427922i	0.652883	+	0.757458i	$0.273559\pi$
$110$		0			0
$111$	11.0904	−	0.145983i	1.05266	−	0.0138561i
$112$	−1.82049	+	1.82049i	−0.172020	+	0.172020i
$113$	4.21859	+	7.30681i	0.396852	+	0.687367i	0.993336	−	0.115258i	$-0.0367695\pi$
$113$	4.21859	+	7.30681i	0.396852	+	0.687367i	−0.596484	+	0.802625i	$0.703436\pi$
$114$	−4.11466	+	7.12681i	−0.385374	+	0.667487i
$115$		0			0
$116$	6.25164	−	1.67512i	0.580450	−	0.155531i
$117$	0.496408			0.0458930
$118$	5.38555	−	1.44305i	0.495780	−	0.132844i
$119$	2.66312	−	2.66312i	0.244128	−	0.244128i
$120$		0			0
$121$	−20.3416			−1.84924
$122$	−2.17394	−	2.17394i	−0.196819	−	0.196819i
$123$	3.28482	−	12.2591i	0.296182	−	1.10537i
$124$	−1.07851	−	4.02504i	−0.0968527	−	0.361459i
$125$		0			0
$126$	−0.290186	−	0.0777550i	−0.0258518	−	0.00692696i
$127$	−16.4315	−	4.40281i	−1.45806	−	0.390686i	−0.559241	−	0.829005i	$-0.688907\pi$
$127$	−16.4315	−	4.40281i	−1.45806	−	0.390686i	−0.898819	+	0.438319i	$0.855574\pi$
$128$	−9.25548	+	5.34365i	−0.818077	+	0.472317i
$129$	−18.6065	+	4.98559i	−1.63821	+	0.438957i
$130$		0			0
$131$	−2.80001	−	0.750260i	−0.244638	−	0.0655505i	0.134417	−	0.990925i	$-0.457084\pi$
$131$	−2.80001	−	0.750260i	−0.244638	−	0.0655505i	−0.379054	+	0.925374i	$0.623751\pi$
$132$	−3.12573	+	11.6654i	−0.272060	+	1.01534i
$133$	−1.13564	+	0.655664i	−0.0984728	+	0.0568533i
$134$	5.77712	−	5.77712i	0.499068	−	0.499068i
$135$		0			0
$136$	9.17045	−	5.29456i	0.786359	−	0.454005i
$137$	14.2642	−	14.2642i	1.21868	−	1.21868i	0.250581	−	0.968096i	$-0.419378\pi$
$137$	14.2642	−	14.2642i	1.21868	−	1.21868i	0.968096	−	0.250581i	$-0.0806216\pi$
$138$	−2.64197	+	2.64197i	−0.224899	+	0.224899i
$139$	1.16560	+	2.01888i	0.0988651	+	0.171239i	0.911215	−	0.411931i	$-0.135145\pi$
$139$	1.16560	+	2.01888i	0.0988651	+	0.171239i	−0.812350	+	0.583170i	$0.801812\pi$
$140$		0			0
$141$	−3.02599	−	1.74706i	−0.254834	−	0.147129i
$142$		−	9.95319i		−	0.835253i
$143$	4.27775	−	7.40928i	0.357723	−	0.619595i
$144$	−1.39712	−	0.806629i	−0.116427	−	0.0672191i
$145$		0			0
$146$	3.54466	−	13.2288i	0.293358	−	1.09483i
$147$	8.67894	+	8.67894i	0.715827	+	0.715827i
$148$	−5.15510	−	5.02115i	−0.423747	−	0.412736i
$149$		−	11.6362i		−	0.953273i	−0.879101	−	0.476636i	$-0.841856\pi$
$149$		−	11.6362i		−	0.953273i	0.879101	−	0.476636i	$-0.158144\pi$
$150$		0			0
$151$	1.09708	+	0.633398i	0.0892790	+	0.0515452i	0.543975	−	0.839102i	$-0.316919\pi$
$151$	1.09708	+	0.633398i	0.0892790	+	0.0515452i	−0.454696	+	0.890647i	$0.650252\pi$
$152$	−3.56131	+	0.954250i	−0.288860	+	0.0773999i
$153$	2.04379	+	1.17998i	0.165230	+	0.0953958i
$154$	−3.66120	+	3.66120i	−0.295028	+	0.295028i
$155$		0			0
$156$	−2.33112	−	2.33112i	−0.186639	−	0.186639i
$157$	8.14942	+	2.18363i	0.650395	+	0.174273i	0.568907	−	0.822402i	$-0.307366\pi$
$157$	8.14942	+	2.18363i	0.650395	+	0.174273i	0.0814873	+	0.996674i	$0.474033\pi$
$158$	−4.50320	−	4.50320i	−0.358256	−	0.358256i
$159$	15.1092			1.19824
$160$		0			0
$161$	−0.575086	+	0.154094i	−0.0453232	+	0.0121443i
$162$			17.6074i			1.38337i
$163$	−10.4583	−	18.1144i	−0.819160	−	1.41883i	−0.906302	−	0.422631i	$-0.861107\pi$
$163$	−10.4583	−	18.1144i	−0.819160	−	1.41883i	0.0871421	−	0.996196i	$-0.472227\pi$
$164$	−7.13133	+	4.11728i	−0.556864	+	0.321505i
$165$		0			0
$166$	−3.68292	−	13.7448i	−0.285850	−	1.06681i
$167$	−8.29321	+	14.3643i	−0.641748	+	1.11154i	0.343294	+	0.939228i	$0.388457\pi$
$167$	−8.29321	+	14.3643i	−0.641748	+	1.11154i	−0.985042	+	0.172312i	$0.944876\pi$
$168$	−0.688840	−	1.19311i	−0.0531452	−	0.0920501i
$169$	−5.33228	−	9.23578i	−0.410175	−	0.710444i
$170$		0			0
$171$	−0.581027	−	0.581027i	−0.0444322	−	0.0444322i
$172$	10.8237	+	6.24907i	0.825300	+	0.476487i
$173$	−6.68355	−	1.79085i	−0.508141	−	0.136156i	−0.00436519	−	0.999990i	$-0.501389\pi$
$173$	−6.68355	−	1.79085i	−0.508141	−	0.136156i	−0.503776	+	0.863835i	$0.668056\pi$
$174$			17.7971i			1.34919i
$175$		0			0
$176$	−24.0791	+	13.9021i	−1.81503	+	1.04791i
$177$			5.69834i			0.428313i
$178$	1.59969	+	5.97011i	0.119902	+	0.447479i
$179$	−4.64628	−	4.64628i	−0.347279	−	0.347279i	0.511816	−	0.859095i	$-0.328973\pi$
$179$	−4.64628	−	4.64628i	−0.347279	−	0.347279i	−0.859095	+	0.511816i	$0.828973\pi$
$180$		0			0
$181$	7.11660	−	12.3263i	0.528973	−	0.916208i	−0.470456	−	0.882423i	$-0.655911\pi$
$181$	7.11660	−	12.3263i	0.528973	−	0.916208i	0.999429	−	0.0337848i	$-0.0107561\pi$
$182$	−0.365812	−	1.36523i	−0.0271158	−	0.101198i
$183$	2.72116	−	1.57106i	0.201154	−	0.116136i
$184$	−1.67396			−0.123406
$185$		0			0
$186$	11.4584			0.840172
$187$	35.2243	−	20.3367i	2.57585	−	1.48717i
$188$	0.586757	+	2.18981i	0.0427936	+	0.159708i
$189$	−1.26433	+	2.18989i	−0.0919666	+	0.159291i
$190$		0			0
$191$	−10.2203	−	10.2203i	−0.739518	−	0.739518i	0.232967	−	0.972485i	$-0.425157\pi$
$191$	−10.2203	−	10.2203i	−0.739518	−	0.739518i	−0.972485	+	0.232967i	$0.925157\pi$
$192$	0.318548	+	1.18884i	0.0229892	+	0.0857970i
$193$			11.2201i			0.807642i	0.914838	+	0.403821i	$0.132318\pi$
$193$			11.2201i			0.807642i	−0.914838	+	0.403821i	$0.867682\pi$
$194$	−20.5897	+	11.8875i	−1.47825	+	0.853470i
$195$		0			0
$196$		−	7.96355i		−	0.568825i
$197$	3.72926	+	0.999253i	0.265699	+	0.0711938i	0.389209	−	0.921149i	$-0.372748\pi$
$197$	3.72926	+	0.999253i	0.265699	+	0.0711938i	−0.123510	+	0.992343i	$0.539415\pi$
$198$	−2.80976	−	1.62221i	−0.199681	−	0.115286i
$199$	−3.32935	−	3.32935i	−0.236011	−	0.236011i	0.579185	−	0.815196i	$-0.303371\pi$
$199$	−3.32935	−	3.32935i	−0.236011	−	0.236011i	−0.815196	+	0.579185i	$0.803371\pi$
$200$		0			0
$201$	4.17502	+	7.23134i	0.294483	+	0.510060i
$202$	−12.3069	−	21.3162i	−0.865911	−	1.49980i
$203$	−1.41796	+	2.45599i	−0.0995215	+	0.172376i
$204$	−4.05640	−	15.1387i	−0.284005	−	1.05992i
$205$		0			0
$206$	2.43657	−	1.40675i	0.169764	−	0.0980131i
$207$	−0.186534	−	0.323087i	−0.0129650	−	0.0224561i
$208$		−	7.58986i		−	0.526262i
$209$	−13.6792	+	3.66534i	−0.946211	+	0.253537i
$210$		0			0
$211$	14.1666			0.975272			0.487636	−	0.873047i	$-0.337859\pi$
$211$	14.1666			0.975272			0.487636	+	0.873047i	$0.337859\pi$
$212$	−6.93189	−	6.93189i	−0.476084	−	0.476084i
$213$	9.82580	+	2.63281i	0.673253	+	0.180397i
$214$	5.34882	+	5.34882i	0.365637	+	0.365637i
$215$		0			0
$216$	−5.02725	+	5.02725i	−0.342061	+	0.342061i
$217$	1.58126	+	0.912939i	0.107343	+	0.0619743i
$218$	29.7473	−	7.97078i	2.01474	−	0.539849i
$219$	12.1219	+	6.99858i	0.819122	+	0.472920i
$220$		0			0
$221$			11.1029i			0.746860i
$222$	17.0055	−	10.1188i	1.14133	−	0.679133i
$223$	8.90135	+	8.90135i	0.596079	+	0.596079i	0.939267	−	0.343188i	$-0.111507\pi$
$223$	8.90135	+	8.90135i	0.596079	+	0.596079i	−0.343188	+	0.939267i	$0.611507\pi$
$224$	−0.797737	+	2.97719i	−0.0533010	+	0.198922i
$225$		0			0
$226$	13.0362	+	7.52645i	0.867155	+	0.500652i
$227$	−6.75561	+	11.7011i	−0.448386	+	0.776627i	−0.998281	−	0.0586067i	$-0.981334\pi$
$227$	−6.75561	+	11.7011i	−0.448386	+	0.776627i	0.549895	+	0.835233i	$0.314668\pi$
$228$			5.45696i			0.361396i
$229$	17.7518	+	10.2490i	1.17307	+	0.677273i	0.954402	−	0.298526i	$-0.0964948\pi$
$229$	17.7518	+	10.2490i	1.17307	+	0.677273i	0.218670	+	0.975799i	$0.429828\pi$
$230$		0			0
$231$	−2.64588	−	4.58280i	−0.174086	−	0.301526i
$232$	−5.63812	+	5.63812i	−0.370161	+	0.370161i
$233$	−2.52261	+	2.52261i	−0.165262	+	0.165262i	−0.784893	−	0.619631i	$-0.787282\pi$
$233$	−2.52261	+	2.52261i	−0.165262	+	0.165262i	0.619631	+	0.784893i	$0.287282\pi$
$234$	0.766995	−	0.442825i	0.0501400	−	0.0289484i
$235$		0			0
$236$	2.61432	−	2.61432i	0.170177	−	0.170177i
$237$	5.63675	−	3.25438i	0.366146	−	0.211395i
$238$	1.73910	−	6.49041i	0.112729	−	0.420711i
$239$	−19.2631	−	5.16154i	−1.24603	−	0.333872i	−0.425227	−	0.905087i	$-0.639806\pi$
$239$	−19.2631	−	5.16154i	−1.24603	−	0.333872i	−0.820801	+	0.571214i	$0.806473\pi$
$240$		0			0
$241$	24.3058	−	6.51271i	1.56567	−	0.419521i	0.631218	−	0.775605i	$-0.282555\pi$
$241$	24.3058	−	6.51271i	1.56567	−	0.419521i	0.934454	+	0.356085i	$0.115889\pi$
$242$	−31.4296	+	18.1459i	−2.02037	+	1.16646i
$243$	−3.24685	−	0.869990i	−0.208285	−	0.0558099i
$244$	−1.96921	−	0.527649i	−0.126066	−	0.0337792i
$245$		0			0
$246$	−5.86050	−	21.8717i	−0.373652	−	1.39449i
$247$	1.00055	−	3.73409i	0.0636633	−	0.237595i
$248$	3.63004	+	3.63004i	0.230508	+	0.230508i
$249$	14.5431			0.921633
$250$		0			0
$251$	−10.4158	+	10.4158i	−0.657439	+	0.657439i	−0.954773	−	0.297334i	$-0.903902\pi$
$251$	−10.4158	+	10.4158i	−0.657439	+	0.657439i	0.297334	+	0.954773i	$0.403902\pi$
$252$	−0.192425	+	0.0515602i	−0.0121217	+	0.00324799i
$253$	−6.42977			−0.404236
$254$	−29.3157	+	7.85512i	−1.83943	+	0.492874i
$255$		0			0
$256$	−10.2087	+	17.6820i	−0.638043	+	1.10512i
$257$	4.10172	+	7.10439i	0.255858	+	0.443160i	0.965128	−	0.261777i	$-0.0843086\pi$
$257$	4.10172	+	7.10439i	0.255858	+	0.443160i	−0.709270	+	0.704937i	$0.750975\pi$
$258$	−24.3013	+	24.3013i	−1.51293	+	1.51293i
$259$	3.15296	−	0.0415024i	0.195915	−	0.00257883i
$260$		0			0
$261$	−1.71648	−	0.459929i	−0.106247	−	0.0284689i
$262$	−4.99554	+	1.33855i	−0.308625	+	0.0826959i
$263$	7.65884	+	28.5832i	0.472264	+	1.76251i	0.631605	+	0.775290i	$0.282396\pi$
$263$	7.65884	+	28.5832i	0.472264	+	1.76251i	−0.159341	+	0.987224i	$0.550937\pi$
$264$	−3.85080	−	14.3714i	−0.237000	−	0.884497i
$265$		0			0
$266$	−1.16978	+	2.02612i	−0.0717238	+	0.124229i
$267$	−6.31685			−0.386585
$268$	1.40220	−	5.23308i	0.0856529	−	0.319661i
$269$		−	7.39825i		−	0.451079i	−0.974234	−	0.225540i	$-0.927586\pi$
$269$		−	7.39825i		−	0.451079i	0.974234	−	0.225540i	$-0.0724145\pi$
$270$		0			0
$271$	−8.75582	−	15.1655i	−0.531878	−	0.921240i	−0.999307	−	0.0372094i	$-0.988153\pi$
$271$	−8.75582	−	15.1655i	−0.531878	−	0.921240i	0.467429	−	0.884030i	$-0.345180\pi$
$272$	18.0414	−	31.2486i	1.09392	−	1.89472i
$273$	1.44452			0.0874264
$274$	9.31500	−	34.7641i	0.562740	−	2.10017i
$275$		0			0
$276$	−0.641247	+	2.39316i	−0.0385985	+	0.144052i
$277$	0.288374	+	0.166493i	0.0173267	+	0.0100036i	0.508638	−	0.860980i	$-0.330149\pi$
$277$	0.288374	+	0.166493i	0.0173267	+	0.0100036i	−0.491312	+	0.870984i	$0.663482\pi$
$278$	3.60192	+	2.07957i	0.216029	+	0.124724i
$279$	−0.296120	+	1.10513i	−0.0177282	+	0.0661627i
$280$		0			0
$281$	−8.01899	+	29.9273i	−0.478373	+	1.78531i	0.129836	+	0.991536i	$0.458555\pi$
$281$	−8.01899	+	29.9273i	−0.478373	+	1.78531i	−0.608209	+	0.793777i	$0.708112\pi$
$282$	−6.23390			−0.371224
$283$	−7.97950	+	13.8209i	−0.474332	+	0.821568i	−0.999568	−	0.0293891i	$-0.990644\pi$
$283$	−7.97950	+	13.8209i	−0.474332	+	0.821568i	0.525236	+	0.850957i	$0.323977\pi$
$284$	−3.30004	−	5.71583i	−0.195821	−	0.339172i
$285$		0			0
$286$		−	15.2640i		−	0.902579i
$287$	0.933859	−	3.48521i	0.0551240	−	0.205726i
$288$	−1.93136			−0.113806
$289$	−17.8919	+	30.9898i	−1.05247	+	1.82293i
$290$		0			0
$291$	−6.28893	−	23.4706i	−0.368664	−	1.37587i
$292$	−2.35050	−	8.77220i	−0.137553	−	0.513354i
$293$	−29.4468	+	7.89026i	−1.72030	+	0.460954i	−0.977913	−	0.209015i	$-0.932974\pi$
$293$	−29.4468	+	7.89026i	−1.72030	+	0.460954i	−0.742390	+	0.669968i	$0.766308\pi$
$294$	21.1519	+	5.66762i	1.23360	+	0.330543i
$295$		0			0
$296$	8.59301	+	2.18169i	0.499458	+	0.126808i
$297$	−19.3100	+	19.3100i	−1.12048	+	1.12048i
$298$	−10.3801	−	17.9789i	−0.601305	−	1.04149i
$299$	0.877585	−	1.52002i	0.0507521	−	0.0879052i
$300$		0			0
$301$	−5.28974	+	1.41738i	−0.304896	+	0.0816965i
$302$	2.26011			0.130055
$303$	24.2988	−	6.51084i	1.39593	−	0.374038i
$304$	−8.88364	+	8.88364i	−0.509512	+	0.509512i
$305$		0			0
$306$	4.21045			0.240695
$307$	−16.2385	−	16.2385i	−0.926780	−	0.926780i	0.0707164	−	0.997496i	$-0.477471\pi$
$307$	−16.2385	−	16.2385i	−0.926780	−	0.926780i	−0.997496	+	0.0707164i	$0.977471\pi$
$308$	−0.888630	+	3.31641i	−0.0506344	+	0.188970i
$309$	0.744227	+	2.77749i	0.0423376	+	0.158006i
$310$		0			0
$311$	19.8748	+	5.32544i	1.12700	+	0.301978i	0.773712	−	0.633537i	$-0.218398\pi$
$311$	19.8748	+	5.32544i	1.12700	+	0.301978i	0.353286	+	0.935515i	$0.385064\pi$
$312$	3.92304	+	1.05117i	0.222098	+	0.0595110i
$313$	1.96207	−	1.13280i	0.110903	−	0.0640299i	−0.443522	−	0.896263i	$-0.646271\pi$
$313$	1.96207	−	1.13280i	0.110903	−	0.0640299i	0.554426	+	0.832233i	$0.312938\pi$
$314$	14.5395	−	3.89585i	0.820512	−	0.219855i
$315$		0			0
$316$	−4.07912	−	1.09300i	−0.229469	−	0.0614859i
$317$	−0.786799	+	2.93637i	−0.0441910	+	0.164923i	−0.984495	−	0.175413i	$-0.943874\pi$
$317$	−0.786799	+	2.93637i	−0.0441910	+	0.164923i	0.940304	+	0.340336i	$0.110541\pi$
$318$	23.3451	−	13.4783i	1.30913	−	0.755825i
$319$	−21.6564	+	21.6564i	−1.21253	+	1.21253i
$320$		0			0
$321$	−6.69522	+	3.86549i	−0.373691	+	0.215751i
$322$	−0.751099	+	0.751099i	−0.0418571	+	0.0418571i
$323$	12.9955	−	12.9955i	0.723088	−	0.723088i
$324$	5.83783	+	10.1114i	0.324324	+	0.561745i
$325$		0			0
$326$	−32.3181	−	18.6589i	−1.78993	−	1.03342i
$327$			31.4750i			1.74057i
$328$	5.07236	−	8.78558i	0.280074	−	0.485103i
$329$	−0.860276	−	0.496681i	−0.0474285	−	0.0273829i
$330$		0			0
$331$	−8.80720	+	32.8689i	−0.484088	+	1.80664i	0.100047	+	0.994983i	$0.468101\pi$
$331$	−8.80720	+	32.8689i	−0.484088	+	1.80664i	−0.584135	+	0.811657i	$0.698566\pi$
$332$	−6.67217	−	6.67217i	−0.366183	−	0.366183i
$333$	0.536465	+	1.90163i	0.0293981	+	0.104209i
$334$			29.5921i			1.61921i
$335$		0			0
$336$	−4.06555	−	2.34725i	−0.221794	−	0.128053i
$337$	13.5915	−	3.64184i	0.740377	−	0.198383i	0.131131	−	0.991365i	$-0.458139\pi$
$337$	13.5915	−	3.64184i	0.740377	−	0.198383i	0.609246	+	0.792982i	$0.291472\pi$
$338$	−16.4777	−	9.51340i	−0.896268	−	0.517461i
$339$	−10.8784	+	10.8784i	−0.590836	+	0.590836i
$340$		0			0
$341$	13.9432	+	13.9432i	0.755067	+	0.755067i
$342$	−1.41605	−	0.379429i	−0.0765711	−	0.0205172i
$343$	5.03327	+	5.03327i	0.271771	+	0.271771i
$344$	−15.3973			−0.830168
$345$		0			0
$346$	−11.9242	+	3.19509i	−0.641050	+	0.171769i
$347$			1.28181i			0.0688112i	0.999408	+	0.0344056i	$0.0109538\pi$
$347$			1.28181i			0.0688112i	−0.999408	+	0.0344056i	$0.989046\pi$
$348$	5.90072	+	10.2203i	0.316312	+	0.547868i
$349$	12.5495	−	7.24548i	0.671761	−	0.387842i	−0.124982	−	0.992159i	$-0.539887\pi$
$349$	12.5495	−	7.24548i	0.671761	−	0.387842i	0.796744	+	0.604317i	$0.206554\pi$
$350$		0			0
$351$	−1.92938	−	7.20053i	−0.102983	−	0.384336i
$352$	−16.6433	+	28.8271i	−0.887091	+	1.53649i
$353$	−1.79288	−	3.10536i	−0.0954254	−	0.165282i	0.814361	−	0.580359i	$-0.197088\pi$
$353$	−1.79288	−	3.10536i	−0.0954254	−	0.165282i	−0.909786	+	0.415077i	$0.863754\pi$
$354$	5.08325	+	8.80444i	0.270171	+	0.467951i
$355$		0			0
$356$	2.89808	+	2.89808i	0.153598	+	0.153598i
$357$	5.94731	+	3.43368i	0.314765	+	0.181730i
$358$	−11.3237	−	3.03416i	−0.598474	−	0.160361i
$359$		−	8.45187i		−	0.446073i	−0.974810	−	0.223036i	$-0.928403\pi$
$359$		−	8.45187i		−	0.446073i	0.974810	−	0.223036i	$-0.0715969\pi$
$360$		0			0
$361$	10.9128	−	6.30049i	0.574356	−	0.331605i
$362$		−	25.3937i		−	1.33466i
$363$	−9.59990	−	35.8273i	−0.503864	−	1.88045i
$364$	−0.662726	−	0.662726i	−0.0347363	−	0.0347363i
$365$		0			0
$366$	2.80296	−	4.85487i	0.146513	−	0.253768i
$367$	0.171428	+	0.639778i	0.00894846	+	0.0333961i	0.970256	−	0.242082i	$-0.0778304\pi$
$367$	0.171428	+	0.639778i	0.00894846	+	0.0333961i	−0.961307	+	0.275478i	$0.911164\pi$
$368$	−4.93986	+	2.85203i	−0.257508	+	0.148672i
$369$	2.26092			0.117699
$370$		0			0
$371$	4.29548			0.223010
$372$	6.58024	−	3.79910i	0.341170	−	0.196974i
$373$	3.46797	+	12.9426i	0.179565	+	0.670144i	0.995729	+	0.0923244i	$0.0294297\pi$
$373$	3.46797	+	12.9426i	0.179565	+	0.670144i	−0.816164	+	0.577820i	$0.803904\pi$
$374$	36.2831	−	62.8442i	1.87615	−	3.24959i
$375$		0			0
$376$	−1.97491	−	1.97491i	−0.101848	−	0.101848i
$377$	−2.16382	−	8.07549i	−0.111442	−	0.415909i
$378$			4.51143i			0.232043i
$379$	−13.4140	+	7.74459i	−0.689032	+	0.397813i	−0.803249	−	0.595643i	$-0.796897\pi$
$379$	−13.4140	+	7.74459i	−0.689032	+	0.397813i	0.114217	+	0.993456i	$0.463564\pi$
$380$		0			0
$381$		−	31.0183i		−	1.58912i
$382$	−24.9085	−	6.67420i	−1.27443	−	0.341482i
$383$	−8.66601	−	5.00333i	−0.442813	−	0.255658i	0.261977	−	0.965074i	$-0.415625\pi$
$383$	−8.66601	−	5.00333i	−0.442813	−	0.255658i	−0.704790	+	0.709416i	$0.748959\pi$
$384$	−13.7796	−	13.7796i	−0.703190	−	0.703190i
$385$		0			0
$386$	10.0090	+	17.3361i	0.509444	+	0.882384i
$387$	−1.71578	−	2.97181i	−0.0872178	−	0.151066i
$388$	−7.88271	+	13.6533i	−0.400184	+	0.693139i
$389$	7.52118	+	28.0694i	0.381339	+	1.42318i	0.843858	+	0.536567i	$0.180279\pi$
$389$	7.52118	+	28.0694i	0.381339	+	1.42318i	−0.462519	+	0.886609i	$0.653054\pi$
$390$		0			0
$391$	7.22630	−	4.17211i	0.365450	−	0.210992i
$392$	4.90542	+	8.49644i	0.247761	+	0.429135i
$393$		−	5.28567i		−	0.266627i
$394$	6.65344	−	1.78278i	0.335195	−	0.0898153i
$395$		0			0
$396$	−2.15142			−0.108113
$397$	−4.87014	−	4.87014i	−0.244425	−	0.244425i	0.574253	−	0.818678i	$-0.305293\pi$
$397$	−4.87014	−	4.87014i	−0.244425	−	0.244425i	−0.818678	+	0.574253i	$0.805293\pi$
$398$	−8.11411	−	2.17417i	−0.406724	−	0.108981i
$399$	−1.69076	−	1.69076i	−0.0846437	−	0.0846437i
$400$		0			0
$401$	−12.2227	+	12.2227i	−0.610373	+	0.610373i	−0.943043	−	0.332670i	$-0.892050\pi$
$401$	−12.2227	+	12.2227i	−0.610373	+	0.610373i	0.332670	+	0.943043i	$0.392050\pi$
$402$	12.9016	+	7.44872i	0.643471	+	0.371508i
$403$	−5.19931	+	1.39315i	−0.258996	+	0.0693977i
$404$	−14.1350	−	8.16085i	−0.703243	−	0.406018i
$405$		0			0
$406$			5.05962i			0.251105i
$407$	33.0063	+	8.37999i	1.63606	+	0.415381i
$408$	13.6530	+	13.6530i	0.675926	+	0.675926i
$409$	5.14727	−	19.2099i	0.254516	−	0.949867i	−0.713843	−	0.700306i	$-0.753047\pi$
$409$	5.14727	−	19.2099i	0.254516	−	0.949867i	0.968359	−	0.249561i	$-0.0802863\pi$
$410$		0			0
$411$	31.8551	+	18.3916i	1.57130	+	0.907188i
$412$	0.932834	−	1.61572i	0.0459574	−	0.0796006i
$413$			1.62001i			0.0797156i
$414$	−0.576425	−	0.332799i	−0.0283297	−	0.0163562i
$415$		0			0
$416$	−4.54322	−	7.86908i	−0.222750	−	0.385814i
$417$	−3.00573	+	3.00573i	−0.147191	+	0.147191i
$418$	−17.8659	+	17.8659i	−0.873851	+	0.873851i
$419$	25.2333	−	14.5684i	1.23273	−	0.711715i	0.265129	−	0.964213i	$-0.414585\pi$
$419$	25.2333	−	14.5684i	1.23273	−	0.711715i	0.967597	+	0.252498i	$0.0812521\pi$
$420$		0			0
$421$	−10.7843	+	10.7843i	−0.525594	+	0.525594i	−0.919256	−	0.393661i	$-0.871208\pi$
$421$	−10.7843	+	10.7843i	−0.525594	+	0.525594i	0.393661	+	0.919256i	$0.371208\pi$
$422$	21.8887	−	12.6375i	1.06553	−	0.615182i
$423$	0.161103	−	0.601244i	0.00783309	−	0.0292335i
$424$	11.6657	+	3.12581i	0.566535	+	0.151803i
$425$		0			0
$426$	17.5304	−	4.69724i	0.849348	−	0.227582i
$427$	0.773614	−	0.446646i	0.0374378	−	0.0216147i
$428$	4.84510	+	1.29824i	0.234197	+	0.0627529i
$429$	15.0686	+	4.03763i	0.727520	+	0.194938i
$430$		0			0
$431$	2.59309	+	9.67755i	0.124905	+	0.466151i	0.999836	−	0.0180956i	$-0.00576032\pi$
$431$	2.59309	+	9.67755i	0.124905	+	0.466151i	−0.874931	+	0.484247i	$0.839094\pi$
$432$	−6.27020	+	23.4007i	−0.301675	+	1.12587i
$433$	−3.97942	−	3.97942i	−0.191239	−	0.191239i	0.604992	−	0.796231i	$-0.293176\pi$
$433$	−3.97942	−	3.97942i	−0.191239	−	0.191239i	−0.796231	+	0.604992i	$0.793176\pi$
$434$	3.25758			0.156369
$435$		0			0
$436$	14.4403	−	14.4403i	0.691565	−	0.691565i
$437$	−2.80631	+	0.751948i	−0.134244	+	0.0359705i
$438$	24.9725			1.19323
$439$	25.0684	−	6.71707i	1.19645	−	0.320588i	0.395018	−	0.918673i	$-0.370738\pi$
$439$	25.0684	−	6.71707i	1.19645	−	0.320588i	0.801433	+	0.598085i	$0.204072\pi$
$440$		0			0
$441$	−1.09326	+	1.89357i	−0.0520598	+	0.0901702i
$442$	9.90440	+	17.1549i	0.471104	+	0.815977i
$443$	13.4522	−	13.4522i	0.639135	−	0.639135i	−0.311207	−	0.950342i	$-0.600733\pi$
$443$	13.4522	−	13.4522i	0.639135	−	0.639135i	0.950342	+	0.311207i	$0.100733\pi$
$444$	6.41079	−	11.4492i	0.304242	−	0.543356i
$445$		0			0
$446$	21.6939	+	5.81287i	1.02724	+	0.275247i
$447$	20.4946	−	5.49150i	0.969360	−	0.259739i
$448$	0.0905618	+	0.337981i	0.00427864	+	0.0159681i
$449$	−7.64918	−	28.5471i	−0.360987	−	1.34722i	−0.872780	−	0.488114i	$-0.837685\pi$
$449$	−7.64918	−	28.5471i	−0.360987	−	1.34722i	0.511793	−	0.859109i	$-0.328982\pi$
$450$		0			0
$451$	19.4833	−	33.7460i	0.917430	−	1.58904i
$452$	9.98175			0.469502
$453$	−0.597844	+	2.23118i	−0.0280892	+	0.104830i
$454$			24.1056i			1.13133i
$455$		0			0
$456$	−3.36140	−	5.82212i	−0.157412	−	0.272646i
$457$	−0.940769	+	1.62946i	−0.0440073	+	0.0762229i	−0.887190	−	0.461404i	$-0.847346\pi$
$457$	−0.940769	+	1.62946i	−0.0440073	+	0.0762229i	0.843183	+	0.537627i	$0.180679\pi$
$458$	36.5708			1.70884
$459$	9.17240	−	34.2319i	0.428131	−	1.59781i
$460$		0			0
$461$	−3.29629	+	12.3019i	−0.153523	+	0.572957i	0.845704	+	0.533653i	$0.179181\pi$
$461$	−3.29629	+	12.3019i	−0.153523	+	0.572957i	−0.999227	+	0.0393048i	$0.987486\pi$
$462$	−8.17624	−	4.72055i	−0.380393	−	0.219620i
$463$	27.2476	+	15.7314i	1.26630	+	0.731100i	0.974286	−	0.225313i	$-0.0723405\pi$
$463$	27.2476	+	15.7314i	1.26630	+	0.731100i	0.292016	+	0.956413i	$0.405674\pi$
$464$	−7.03212	+	26.2442i	−0.326458	+	1.21836i
$465$		0			0
$466$	−1.64734	+	6.14797i	−0.0763117	+	0.284799i
$467$	0.00854231			0.000395291			0.000197645	−	1.00000i	$-0.499937\pi$
$467$	0.00854231			0.000395291			0.000197645		1.00000i	$0.499937\pi$
$468$	0.293642	−	0.508603i	0.0135736	−	0.0235102i
$469$	1.18694	+	2.05584i	0.0548078	+	0.0949298i
$470$		0			0
$471$			15.3839i			0.708855i
$472$	−1.17888	+	4.39963i	−0.0542623	+	0.202510i
$473$	−59.1421			−2.71936
$474$	5.80619	−	10.0566i	0.266687	−	0.461916i
$475$		0			0
$476$	−1.15322	−	4.30386i	−0.0528576	−	0.197267i
$477$	0.696639	+	2.59989i	0.0318969	+	0.119041i
$478$	−34.3676	+	9.20878i	−1.57194	+	0.421200i
$479$	29.4942	+	7.90296i	1.34763	+	0.361095i	0.859258	−	0.511543i	$-0.170926\pi$
$479$	29.4942	+	7.90296i	1.34763	+	0.361095i	0.488368	+	0.872638i	$0.337592\pi$
$480$		0			0
$481$	−6.48602	+	6.65905i	−0.295737	+	0.303626i
$482$	31.7449	−	31.7449i	1.44594	−	1.44594i
$483$	−0.542805	−	0.940166i	−0.0246985	−	0.0427790i
$484$	−12.0328	+	20.8413i	−0.546943	+	0.947334i
$485$		0			0
$486$	−5.79275	+	1.55216i	−0.262764	+	0.0704075i
$487$	8.10762			0.367391			0.183696	−	0.982983i	$-0.441194\pi$
$487$	8.10762			0.367391			0.183696	+	0.982983i	$0.441194\pi$
$488$	2.42601	−	0.650047i	0.109820	−	0.0294262i
$489$	26.9688	−	26.9688i	1.21957	−	1.21957i
$490$		0			0
$491$	−39.0457			−1.76211			−0.881055	−	0.473015i	$-0.843166\pi$
$491$	−39.0457			−1.76211			−0.881055	+	0.473015i	$0.843166\pi$
$492$	−10.6172	−	10.6172i	−0.478660	−	0.478660i
$493$	10.2870	−	38.3915i	0.463302	−	1.72907i
$494$	−1.78509	−	6.66205i	−0.0803151	−	0.299740i
$495$		0			0
$496$	16.8970	+	4.52754i	0.758698	+	0.203293i
$497$	2.79343	+	0.748497i	0.125302	+	0.0335747i
$498$	22.4704	−	12.9733i	1.00692	−	0.581347i
$499$	−20.2333	+	5.42151i	−0.905769	+	0.242700i	−0.681492	−	0.731825i	$-0.738669\pi$
$499$	−20.2333	+	5.42151i	−0.905769	+	0.242700i	−0.224277	+	0.974525i	$0.572002\pi$
$500$		0			0
$501$	−29.2133	−	7.82769i	−1.30516	−	0.349715i
$502$	−6.80184	+	25.3848i	−0.303581	+	1.13298i
$503$	−15.8054	+	9.12523i	−0.704726	+	0.406874i	−0.809105	−	0.587664i	$-0.800048\pi$
$503$	−15.8054	+	9.12523i	−0.704726	+	0.406874i	0.104379	+	0.994538i	$0.466715\pi$
$504$	0.173541	−	0.173541i	0.00773015	−	0.00773015i
$505$		0			0
$506$	−9.93457	+	5.73573i	−0.441645	+	0.254984i
$507$	13.7503	−	13.7503i	0.610673	−	0.610673i
$508$	−14.2308	+	14.2308i	−0.631388	+	0.631388i
$509$	−2.01917	−	3.49730i	−0.0894981	−	0.155015i	0.817801	−	0.575501i	$-0.195193\pi$
$509$	−2.01917	−	3.49730i	−0.0894981	−	0.155015i	−0.907299	+	0.420486i	$0.861860\pi$
$510$		0			0
$511$	3.44620	+	1.98966i	0.152451	+	0.0880176i
$512$			15.0523i			0.665224i
$513$	−6.16969	+	10.6862i	−0.272398	+	0.471808i
$514$	12.6750	+	7.31794i	0.559072	+	0.322781i
$515$		0			0
$516$	−5.89829	+	22.0127i	−0.259658	+	0.969057i
$517$	−7.58575	−	7.58575i	−0.333621	−	0.333621i
$518$	4.83458	−	2.87674i	0.212419	−	0.126397i
$519$		−	12.6168i		−	0.553814i
$520$		0			0
$521$	−24.7277	−	14.2766i	−1.08334	−	0.625468i	−0.151546	−	0.988450i	$-0.548425\pi$
$521$	−24.7277	−	14.2766i	−1.08334	−	0.625468i	−0.931796	+	0.362983i	$0.881758\pi$
$522$	−3.06240	+	0.820567i	−0.134038	+	0.0359152i
$523$	−11.7475	−	6.78240i	−0.513681	−	0.296574i	0.220665	−	0.975350i	$-0.429177\pi$
$523$	−11.7475	−	6.78240i	−0.513681	−	0.296574i	−0.734345	+	0.678776i	$0.762511\pi$
$524$	−2.42499	+	2.42499i	−0.105936	+	0.105936i
$525$		0			0
$526$	37.3314	+	37.3314i	1.62773	+	1.62773i
$527$	−24.7179	−	6.62314i	−1.07673	−	0.288508i
$528$	−35.8492	−	35.8492i	−1.56014	−	1.56014i
$529$	21.6809			0.942649
$530$		0			0
$531$	−0.980532	+	0.262733i	−0.0425515	+	0.0114016i
$532$			1.55139i			0.0672613i
$533$	5.31845	+	9.21183i	0.230368	+	0.399009i
$534$	−9.76009	+	5.63499i	−0.422360	+	0.243850i
$535$		0			0
$536$	1.72746	+	6.44699i	0.0746151	+	0.278467i
$537$	5.99066	−	10.3761i	0.258516	−	0.447763i
$538$	−6.59966	−	11.4310i	−0.284532	−	0.492823i
$539$	18.8420	+	32.6354i	0.811584	+	1.40571i
$540$		0			0
$541$	17.7354	+	17.7354i	0.762506	+	0.762506i	0.976775	−	0.214269i	$-0.0687368\pi$
$541$	17.7354	+	17.7354i	0.762506	+	0.762506i	−0.214269	+	0.976775i	$0.568737\pi$
$542$	−27.0570	−	15.6214i	−1.16220	−	0.670996i
$543$	25.0687	+	6.71713i	1.07580	+	0.288260i
$544$		−	43.1976i		−	1.85208i
$545$		0			0
$546$	2.23191	−	1.28860i	0.0955171	−	0.0551468i
$547$		−	5.95549i		−	0.254638i	−0.991862	−	0.127319i	$-0.959363\pi$
$547$		−	5.95549i		−	0.254638i	0.991862	−	0.127319i	$-0.0406372\pi$
$548$	−6.17688	−	23.0524i	−0.263863	−	0.984752i
$549$	0.395803	+	0.395803i	0.0168924	+	0.0168924i
$550$		0			0
$551$	−6.91938	+	11.9847i	−0.294776	+	0.510566i
$552$	−0.789996	−	2.94830i	−0.0336244	−	0.125488i
$553$	1.60250	−	0.925206i	0.0681454	−	0.0393437i
$554$	0.594084			0.0252402
$555$		0			0
$556$	2.75797			0.116964
$557$	−31.2534	+	18.0441i	−1.32425	+	0.764555i	−0.984403	−	0.175927i	$-0.943708\pi$
$557$	−31.2534	+	18.0441i	−1.32425	+	0.764555i	−0.339845	+	0.940482i	$0.610375\pi$
$558$	0.528312	+	1.97169i	0.0223652	+	0.0834682i
$559$	8.07218	−	13.9814i	0.341417	−	0.591351i
$560$		0			0
$561$	52.4422	+	52.4422i	2.21411	+	2.21411i
$562$	14.3068	+	53.3937i	0.603496	+	2.25228i
$563$		−	7.14047i		−	0.300935i	−0.988615	−	0.150467i	$-0.951922\pi$
$563$		−	7.14047i		−	0.300935i	0.988615	−	0.150467i	$-0.0480779\pi$
$564$	−3.57995	+	2.06689i	−0.150743	+	0.0870316i
$565$		0			0
$566$			28.4727i			1.19680i
$567$	−4.94163	−	1.32411i	−0.207529	−	0.0556072i
$568$	7.04173	+	4.06554i	0.295464	+	0.170586i
$569$	4.46279	+	4.46279i	0.187090	+	0.187090i	0.794437	−	0.607347i	$-0.207766\pi$
$569$	4.46279	+	4.46279i	0.187090	+	0.187090i	−0.607347	+	0.794437i	$0.707766\pi$
$570$		0			0
$571$	−13.7670	−	23.8452i	−0.576133	−	0.997891i	−0.995918	−	0.0902676i	$-0.971228\pi$
$571$	−13.7670	−	23.8452i	−0.576133	−	0.997891i	0.419785	−	0.907624i	$-0.362106\pi$
$572$	−5.06087	−	8.76568i	−0.211605	−	0.366511i
$573$	13.1776	−	22.8242i	0.550500	−	0.953495i
$574$	−1.66611	−	6.21802i	−0.0695422	−	0.259535i
$575$		0			0
$576$	−0.189880	+	0.109627i	−0.00791167	+	0.00456780i
$577$	9.79920	+	16.9727i	0.407946	+	0.706583i	0.994659	−	0.103212i	$-0.0329119\pi$
$577$	9.79920	+	16.9727i	0.407946	+	0.706583i	−0.586714	+	0.809795i	$0.699579\pi$
$578$			63.8426i			2.65550i
$579$	−19.7618	+	5.29515i	−0.821271	+	0.220059i
$580$		0			0
$581$	4.13454			0.171530
$582$	−30.6541	−	30.6541i	−1.27065	−	1.27065i
$583$	44.8086	+	12.0064i	1.85578	+	0.497256i
$584$	7.91133	+	7.91133i	0.327373	+	0.327373i
$585$		0			0
$586$	−38.4594	+	38.4594i	−1.58874	+	1.58874i
$587$	−4.50181	−	2.59912i	−0.185809	−	0.107277i	0.404210	−	0.914666i	$-0.367547\pi$
$587$	−4.50181	−	2.59912i	−0.185809	−	0.107277i	−0.590019	+	0.807389i	$0.700880\pi$
$588$	14.0260	−	3.75827i	0.578424	−	0.154988i
$589$	7.71622	+	4.45496i	0.317941	+	0.183563i
$590$		0			0
$591$			7.03986i			0.289581i
$592$	29.0751	−	8.20231i	1.19498	−	0.337113i
$593$	−31.9545	−	31.9545i	−1.31221	−	1.31221i	−0.919781	−	0.392432i	$-0.871634\pi$
$593$	−31.9545	−	31.9545i	−1.31221	−	1.31221i	−0.392432	−	0.919781i	$-0.628366\pi$
$594$	−12.6100	+	47.0613i	−0.517396	+	1.93095i
$595$		0			0
$596$	−11.9220	−	6.88319i	−0.488346	−	0.281947i
$597$	4.29268	−	7.43515i	0.175688	−	0.304300i
$598$		−	3.13143i		−	0.128054i
$599$	−24.4318	−	14.1057i	−0.998257	−	0.576344i	−0.0905247	−	0.995894i	$-0.528854\pi$
$599$	−24.4318	−	14.1057i	−0.998257	−	0.576344i	−0.907732	+	0.419550i	$0.862188\pi$
$600$		0			0
$601$	−16.5666	−	28.6942i	−0.675767	−	1.17046i	−0.976244	−	0.216674i	$-0.930479\pi$
$601$	−16.5666	−	28.6942i	−0.675767	−	1.17046i	0.300477	−	0.953789i	$-0.402854\pi$
$602$	−6.90874	+	6.90874i	−0.281579	+	0.281579i
$603$	−1.05182	+	1.05182i	−0.0428336	+	0.0428336i
$604$	1.29792	−	0.749353i	0.0528115	−	0.0304907i
$605$		0			0
$606$	31.7357	−	31.7357i	1.28918	−	1.28918i
$607$	39.6225	−	22.8760i	1.60823	−	0.928510i	0.618459	−	0.785817i	$-0.287757\pi$
$607$	39.6225	−	22.8760i	1.60823	−	0.928510i	0.989767	−	0.142693i	$-0.0455762\pi$
$608$	−3.89280	+	14.5281i	−0.157874	+	0.589193i
$609$	−4.99486	−	1.33837i	−0.202402	−	0.0542335i
$610$		0			0
$611$	2.82866	−	0.757937i	0.114435	−	0.0306629i
$612$	2.41794	−	1.39600i	0.0977394	−	0.0564298i
$613$	16.4808	+	4.41602i	0.665654	+	0.178362i	0.575796	−	0.817593i	$-0.304692\pi$
$613$	16.4808	+	4.41602i	0.665654	+	0.178362i	0.0898578	+	0.995955i	$0.471359\pi$
$614$	−39.5756	−	10.6043i	−1.59714	−	0.427953i
$615$		0			0
$616$	−1.09476	−	4.08572i	−0.0441093	−	0.164618i
$617$	1.82050	−	6.79418i	0.0732904	−	0.273524i	−0.919550	−	0.392973i	$-0.871446\pi$
$617$	1.82050	−	6.79418i	0.0732904	−	0.273524i	0.992840	+	0.119450i	$0.0381131\pi$
$618$	3.62758	+	3.62758i	0.145923	+	0.145923i
$619$	−33.5633			−1.34902			−0.674511	−	0.738265i	$-0.735645\pi$
$619$	−33.5633			−1.34902			−0.674511	+	0.738265i	$0.735645\pi$
$620$		0			0
$621$	−3.96147	+	3.96147i	−0.158968	+	0.158968i
$622$	35.4590	−	9.50120i	1.42178	−	0.380964i
$623$	−1.79585			−0.0719493
$624$	13.3679	−	3.58191i	0.535143	−	0.143391i
$625$		0			0
$626$	2.02105	−	3.50057i	0.0807776	−	0.139911i
$627$	−12.9114	−	22.3631i	−0.515630	−	0.893098i
$628$	7.05793	−	7.05793i	0.281642	−	0.281642i
$629$	−42.5327	+	11.9988i	−1.69589	+	0.478423i
$630$		0			0
$631$	14.5346	+	3.89453i	0.578613	+	0.155039i	0.536244	−	0.844063i	$-0.319843\pi$
$631$	14.5346	+	3.89453i	0.578613	+	0.155039i	0.0423693	+	0.999102i	$0.486509\pi$
$632$	5.02535	−	1.34654i	0.199898	−	0.0535625i
$633$	6.68571	+	24.9514i	0.265733	+	0.991730i
$634$	1.40374	+	5.23883i	0.0557496	+	0.208060i
$635$		0			0
$636$	8.93761	−	15.4804i	0.354399	−	0.613837i
$637$	−10.2868			−0.407579
$638$	−14.1423	+	52.7798i	−0.559899	+	2.08957i
$639$			1.81215i			0.0716875i
$640$		0			0
$641$	−6.51204	−	11.2792i	−0.257210	−	0.445501i	0.708283	−	0.705928i	$-0.249470\pi$
$641$	−6.51204	−	11.2792i	−0.257210	−	0.445501i	−0.965493	+	0.260427i	$0.916137\pi$
$642$	−6.89648	+	11.9450i	−0.272182	+	0.471433i
$643$	20.7795			0.819465			0.409732	−	0.912206i	$-0.365622\pi$
$643$	20.7795			0.819465			0.409732	+	0.912206i	$0.365622\pi$
$644$	−0.182304	+	0.680366i	−0.00718376	+	0.0268102i
$645$		0			0
$646$	8.48646	−	31.6719i	0.333895	−	1.24611i
$647$	−23.9186	−	13.8094i	−0.940336	−	0.542903i	−0.0502706	−	0.998736i	$-0.516008\pi$
$647$	−23.9186	−	13.8094i	−0.940336	−	0.542903i	−0.890066	+	0.455832i	$0.849342\pi$
$648$	−12.4569	−	7.19202i	−0.489355	−	0.282529i
$649$	−4.52815	+	16.8993i	−0.177745	+	0.663355i
$650$		0			0
$651$	−0.861693	+	3.21588i	−0.0337724	+	0.126040i
$652$	−24.7458			−0.969121
$653$	6.28388	−	10.8840i	0.245907	−	0.425924i	−0.716479	−	0.697609i	$-0.754247\pi$
$653$	6.28388	−	10.8840i	0.245907	−	0.425924i	0.962386	+	0.271685i	$0.0875808\pi$
$654$	28.0775	+	48.6317i	1.09792	+	1.90165i
$655$		0			0
$656$		−	34.5685i		−	1.34967i
$657$	−0.645366	+	2.40854i	−0.0251781	+	0.0939660i
$658$	−1.77227			−0.0690903
$659$	6.48868	−	11.2387i	0.252763	−	0.437799i	−0.711522	−	0.702663i	$-0.751994\pi$
$659$	6.48868	−	11.2387i	0.252763	−	0.437799i	0.964286	+	0.264865i	$0.0853273\pi$
$660$		0			0
$661$	−2.31806	−	8.65112i	−0.0901621	−	0.336490i	0.906079	−	0.423107i	$-0.139061\pi$
$661$	−2.31806	−	8.65112i	−0.0901621	−	0.336490i	−0.996242	+	0.0866179i	$0.972394\pi$
$662$	15.7131	+	58.6420i	0.610706	+	2.27918i
$663$	−19.5553	+	5.23982i	−0.759464	+	0.203498i
$664$	11.2286	+	3.00870i	0.435754	+	0.116760i
$665$		0			0
$666$	2.52525	+	2.45964i	0.0978516	+	0.0953090i
$667$	−4.44284	+	4.44284i	−0.172027	+	0.172027i
$668$	9.81143	+	16.9939i	0.379616	+	0.657513i
$669$	−11.4769	+	19.8786i	−0.443724	+	0.768552i
$670$		0			0
$671$	9.31845	−	2.49687i	0.359735	−	0.0963906i
$672$	−5.62015			−0.216802
$673$	−20.3974	+	5.46547i	−0.786262	+	0.210678i	−0.629544	−	0.776965i	$-0.716758\pi$
$673$	−20.3974	+	5.46547i	−0.786262	+	0.210678i	−0.156718	+	0.987643i	$0.550091\pi$
$674$	17.7514	−	17.7514i	0.683757	−	0.683757i
$675$		0			0
$676$	−12.6169			−0.485265
$677$	8.32530	+	8.32530i	0.319967	+	0.319967i	0.848754	−	0.528787i	$-0.177353\pi$
$677$	8.32530	+	8.32530i	0.319967	+	0.319967i	−0.528787	+	0.848754i	$0.677353\pi$
$678$	−7.10397	+	26.5124i	−0.272826	+	1.01820i
$679$	−1.78792	−	6.67259i	−0.0686139	−	0.256071i
$680$		0			0
$681$	−23.7970	−	6.37640i	−0.911905	−	0.244344i
$682$	33.9816	+	9.10535i	1.30122	+	0.348662i
$683$	−37.5275	+	21.6665i	−1.43595	+	0.829046i	−0.997565	−	0.0697413i	$-0.977783\pi$
$683$	−37.5275	+	21.6665i	−1.43595	+	0.829046i	−0.438385	+	0.898787i	$0.644449\pi$
$684$	−0.938998	+	0.251604i	−0.0359035	+	0.00962031i
$685$		0			0
$686$	12.2668	+	3.28689i	0.468350	+	0.125494i
$687$	−9.67370	+	36.1027i	−0.369075	+	1.37741i
$688$	−45.4377	+	26.2334i	−1.73229	+	1.00014i
$689$	−8.95420	+	8.95420i	−0.341128	+	0.341128i
$690$		0			0
$691$	−36.0683	+	20.8241i	−1.37210	+	0.792185i	−0.991193	−	0.132426i	$-0.957723\pi$
$691$	−36.0683	+	20.8241i	−1.37210	+	0.792185i	−0.380912	+	0.924611i	$0.624390\pi$
$692$	−5.78839	+	5.78839i	−0.220042	+	0.220042i
$693$	0.666584	−	0.666584i	0.0253214	−	0.0253214i
$694$	1.14345	+	1.98051i	0.0434047	+	0.0751792i
$695$		0			0
$696$	−12.5911	−	7.26950i	−0.477266	−	0.275550i
$697$			50.5687i			1.91542i
$698$	12.9268	−	22.3898i	0.489286	−	0.847467i
$699$	−5.63353	−	3.25252i	−0.213080	−	0.123022i
$700$		0			0
$701$	−1.36360	+	5.08902i	−0.0515024	+	0.192210i	−0.986884	−	0.161430i	$-0.948389\pi$
$701$	−1.36360	+	5.08902i	−0.0515024	+	0.192210i	0.935382	+	0.353640i	$0.115056\pi$
$702$	−9.40435	−	9.40435i	−0.354944	−	0.354944i
$703$	15.3858	−	0.202523i	0.580286	−	0.00763831i
$704$			3.77881i			0.142419i
$705$		0			0
$706$	−5.54032	−	3.19870i	−0.208513	−	0.120385i
$707$	6.90803	−	1.85100i	0.259803	−	0.0696141i
$708$	5.83833	+	3.37076i	0.219418	+	0.126681i
$709$	29.6747	−	29.6747i	1.11446	−	1.11446i	0.121918	−	0.992540i	$-0.461095\pi$
$709$	29.6747	−	29.6747i	1.11446	−	1.11446i	0.992540	−	0.121918i	$-0.0389046\pi$
$710$		0			0
$711$	0.819885	+	0.819885i	0.0307481	+	0.0307481i
$712$	−4.87718	−	1.30684i	−0.182780	−	0.0489757i
$713$	2.86046	+	2.86046i	0.107125	+	0.107125i
$714$	12.2522			0.458526
$715$		0			0
$716$	−7.50885	+	2.01199i	−0.280619	+	0.0751916i
$717$		−	36.3637i		−	1.35803i
$718$	−7.53956	−	13.0589i	−0.281374	−	0.487354i
$719$	−28.8381	+	16.6497i	−1.07548	+	0.620929i	−0.929674	−	0.368384i	$-0.879911\pi$
$719$	−28.8381	+	16.6497i	−1.07548	+	0.620929i	−0.145807	+	0.989313i	$0.546578\pi$
$720$		0			0
$721$	0.211580	+	0.789629i	0.00787967	+	0.0294073i
$722$	11.2408	−	19.4696i	0.418339	−	0.724585i
$723$	22.9414	+	39.7357i	0.853200	+	1.47779i
$724$	−8.41942	−	14.5829i	−0.312905	−	0.541968i
$725$		0			0
$726$	−46.7927	−	46.7927i	−1.73664	−	1.73664i
$727$	−39.0531	−	22.5473i	−1.44840	−	0.836233i	−0.450012	−	0.893023i	$-0.648580\pi$
$727$	−39.0531	−	22.5473i	−1.44840	−	0.836233i	−0.998386	+	0.0567895i	$0.981914\pi$
$728$	1.11530	+	0.298844i	0.0413358	+	0.0110759i
$729$			23.4777i			0.869546i
$730$		0			0
$731$	66.4687	−	38.3757i	2.45844	−	1.41938i
$732$		−	3.71735i		−	0.137397i
$733$	12.5896	+	46.9849i	0.465007	+	1.73543i	0.656867	+	0.754006i	$0.271881\pi$
$733$	12.5896	+	46.9849i	0.465007	+	1.73543i	−0.191861	+	0.981422i	$0.561452\pi$
$734$	0.835590	+	0.835590i	0.0308422	+	0.0308422i
$735$		0			0
$736$	−3.41439	+	5.91390i	−0.125856	+	0.217989i
$737$	6.63530	+	24.7633i	0.244415	+	0.912167i
$738$	3.49332	−	2.01687i	0.128591	−	0.0742420i
$739$	−44.4645			−1.63565			−0.817826	−	0.575466i	$-0.804821\pi$
$739$	−44.4645			−1.63565			−0.817826	+	0.575466i	$0.804821\pi$
$740$		0			0
$741$	7.04898			0.258951
$742$	6.63690	−	3.83182i	0.243648	−	0.140670i
$743$	−6.11311	−	22.8144i	−0.224268	−	0.836981i	−0.982696	−	0.185224i	$-0.940699\pi$
$743$	−6.11311	−	22.8144i	−0.224268	−	0.836981i	0.758428	−	0.651757i	$-0.225968\pi$
$744$	−4.68038	+	8.10665i	−0.171591	+	0.297204i
$745$		0			0
$746$	16.9039	+	16.9039i	0.618896	+	0.618896i
$747$	0.670538	+	2.50248i	0.0245337	+	0.0915611i
$748$		−	48.1195i		−	1.75942i
$749$	−1.90342	+	1.09894i	−0.0695495	+	0.0401544i
$750$		0			0
$751$			2.24894i			0.0820651i	0.999158	+	0.0410326i	$0.0130647\pi$
$751$			2.24894i			0.0820651i	−0.999158	+	0.0410326i	$0.986935\pi$
$752$	−9.19275	−	2.46319i	−0.335225	−	0.0898233i
$753$	−23.2607	−	13.4296i	−0.847667	−	0.489401i
$754$	−10.5471	−	10.5471i	−0.384103	−	0.384103i
$755$		0			0
$756$	1.49579	+	2.59078i	0.0544013	+	0.0942259i
$757$	12.0194	+	20.8182i	0.436851	+	0.756649i	0.997445	−	0.0714426i	$-0.0227603\pi$
$757$	12.0194	+	20.8182i	0.436851	+	0.756649i	−0.560593	+	0.828091i	$0.689427\pi$
$758$	−13.8172	+	23.9322i	−0.501865	+	0.869255i
$759$	−3.03442	−	11.3246i	−0.110143	−	0.411058i
$760$		0			0
$761$	1.34466	−	0.776338i	0.0487438	−	0.0281422i	−0.475430	−	0.879754i	$-0.657708\pi$
$761$	1.34466	−	0.776338i	0.0487438	−	0.0281422i	0.524174	+	0.851611i	$0.324374\pi$
$762$	−27.6701	−	47.9261i	−1.00238	−	1.73618i
$763$			8.94821i			0.323947i
$764$	−16.5171	+	4.42574i	−0.597567	+	0.160118i
$765$		0			0
$766$	−17.8530			−0.645056
$767$	−3.37702	−	3.37702i	−0.121937	−	0.121937i
$768$	−35.9607	−	9.63564i	−1.29762	−	0.347696i
$769$	−0.327336	−	0.327336i	−0.0118040	−	0.0118040i	0.701180	−	0.712984i	$-0.252657\pi$
$769$	−0.327336	−	0.327336i	−0.0118040	−	0.0118040i	−0.712984	+	0.701180i	$0.752657\pi$
$770$		0			0
$771$	−10.5771	+	10.5771i	−0.380924	+	0.380924i
$772$	11.4958	+	6.63708i	0.413741	+	0.238874i
$773$	8.07254	−	2.16303i	0.290349	−	0.0777988i	−0.110705	−	0.993853i	$-0.535311\pi$
$773$	8.07254	−	2.16303i	0.290349	−	0.0777988i	0.401054	+	0.916055i	$0.368644\pi$
$774$	−5.30205	−	3.06114i	−0.190578	−	0.110030i
$775$		0			0
$776$		−	19.4225i		−	0.697227i
$777$	1.56108	+	5.53365i	0.0560035	+	0.198519i
$778$	36.6604	+	36.6604i	1.31434	+	1.31434i
$779$	4.55705	−	17.0071i	0.163273	−	0.609344i
$780$		0			0
$781$	27.0477	+	15.6160i	0.967844	+	0.558785i
$782$	7.44352	−	12.8926i	0.266180	−	0.461037i
$783$			26.6856i			0.953665i
$784$	28.9519	+	16.7154i	1.03400	+	0.596978i
$785$		0			0
$786$	−4.71512	−	8.16683i	−0.168183	−	0.291301i
$787$	10.6002	−	10.6002i	0.377856	−	0.377856i	−0.492472	−	0.870328i	$-0.663907\pi$
$787$	10.6002	−	10.6002i	0.377856	−	0.377856i	0.870328	+	0.492472i	$0.163907\pi$
$788$	3.22979	−	3.22979i	0.115056	−	0.115056i
$789$	−46.7285	+	26.9787i	−1.66358	+	0.960468i
$790$		0			0
$791$	−3.09269	+	3.09269i	−0.109964	+	0.109964i
$792$	2.29538	−	1.32524i	0.0815628	−	0.0470903i
$793$	−0.681585	+	2.54371i	−0.0242038	+	0.0903298i
$794$	−11.8692	−	3.18035i	−0.421224	−	0.112867i
$795$		0			0
$796$	−5.38056	+	1.44172i	−0.190709	+	0.0511003i
$797$	−11.2338	+	6.48582i	−0.397921	+	0.229740i	−0.685586	−	0.727991i	$-0.740454\pi$
$797$	−11.2338	+	6.48582i	−0.397921	+	0.229740i	0.287666	+	0.957731i	$0.407121\pi$
$798$	−4.12062	−	1.10412i	−0.145868	−	0.0390853i
$799$	13.4477	+	3.60329i	0.475744	+	0.127475i
$800$		0			0
$801$	−0.291250	−	1.08696i	−0.0102908	−	0.0384059i
$802$	−7.98182	+	29.7885i	−0.281848	+	1.05187i
$803$	30.3879	+	30.3879i	1.07237	+	1.07237i
$804$	9.87866			0.348393
$805$		0			0
$806$	−6.79062	+	6.79062i	−0.239189	+	0.239189i
$807$	13.0304	−	3.49148i	0.458691	−	0.122906i
$808$	20.1078			0.707391
$809$	−33.4015	+	8.94991i	−1.17434	+	0.314662i	−0.792677	−	0.609641i	$-0.791313\pi$
$809$	−33.4015	+	8.94991i	−1.17434	+	0.314662i	−0.381658	+	0.924304i	$0.624647\pi$
$810$		0			0
$811$	−1.04400	+	1.80826i	−0.0366598	+	0.0634966i	−0.883773	−	0.467916i	$-0.845005\pi$
$811$	−1.04400	+	1.80826i	−0.0366598	+	0.0634966i	0.847113	+	0.531412i	$0.178338\pi$
$812$	1.67755	+	2.90560i	0.0588703	+	0.101966i
$813$	22.5786	−	22.5786i	0.791865	−	0.791865i
$814$	58.4731	−	16.4957i	2.04948	−	0.578173i
$815$		0			0
$816$	63.5519	+	17.0287i	2.22476	+	0.596123i
$817$	−25.8129	+	6.91654i	−0.903079	+	0.241979i
$818$	−9.18332	−	34.2726i	−0.321087	−	1.19831i
$819$	0.0666024	+	0.248564i	0.00232728	+	0.00868551i
$820$		0			0
$821$	4.52054	−	7.82980i	0.157768	−	0.273262i	−0.776296	−	0.630369i	$-0.782904\pi$
$821$	4.52054	−	7.82980i	0.157768	−	0.273262i	0.934063	+	0.357107i	$0.116237\pi$
$822$	65.6253			2.28895
$823$	14.4870	−	54.0662i	0.504985	−	1.88463i	0.0402289	−	0.999190i	$-0.487191\pi$
$823$	14.4870	−	54.0662i	0.504985	−	1.88463i	0.464756	−	0.885439i	$-0.346142\pi$
$824$			2.29844i			0.0800701i
$825$		0			0
$826$	1.44514	+	2.50306i	0.0502830	+	0.0870927i
$827$	17.2477	−	29.8739i	0.599761	−	1.03882i	−0.393095	−	0.919498i	$-0.628595\pi$
$827$	17.2477	−	29.8739i	0.599761	−	1.03882i	0.992856	−	0.119319i	$-0.0380712\pi$
$828$	−0.441366			−0.0153385
$829$	0.0403492	−	0.150585i	0.00140139	−	0.00523005i	−0.965222	−	0.261433i	$-0.915805\pi$
$829$	0.0403492	−	0.150585i	0.00140139	−	0.00523005i	0.966623	+	0.256203i	$0.0824716\pi$
$830$		0			0
$831$	−0.157147	+	0.586480i	−0.00545136	+	0.0203448i
$832$	−0.893325	−	0.515761i	−0.0309705	−	0.0178808i
$833$	−42.3525	−	24.4522i	−1.46743	−	0.847219i
$834$	−1.96284	+	7.32541i	−0.0679675	+	0.253658i
$835$		0			0
$836$	−4.33634	+	16.1834i	−0.149975	+	0.559716i
$837$	17.1812			0.593869
$838$	25.9918	−	45.0191i	0.897871	−	1.55516i
$839$	−20.0598	−	34.7446i	−0.692541	−	1.19952i	−0.971003	−	0.239069i	$-0.923158\pi$
$839$	−20.0598	−	34.7446i	−0.692541	−	1.19952i	0.278462	−	0.960447i	$-0.410175\pi$
$840$		0			0
$841$			0.928230i			0.0320079i
$842$	−7.04248	+	26.2829i	−0.242700	+	0.905769i
$843$	−56.4948			−1.94578
$844$	8.38005	−	14.5147i	0.288453	−	0.499615i
$845$		0			0
$846$	−0.287426	−	1.07269i	−0.00988191	−	0.0368798i
$847$	−2.72921	−	10.1855i	−0.0937767	−	0.349979i
$848$	39.7512	−	10.6513i	1.36506	−	0.365767i
$849$	−28.1083	−	7.53159i	−0.964674	−	0.258484i
$850$		0			0
$851$	6.77128	+	1.71917i	0.232116	+	0.0589322i
$852$	8.50978	−	8.50978i	0.291540	−	0.291540i
$853$	−3.24666	−	5.62338i	−0.111164	−	0.192541i	0.805076	−	0.593172i	$-0.202124\pi$
$853$	−3.24666	−	5.62338i	−0.111164	−	0.192541i	−0.916240	+	0.400631i	$0.868791\pi$
$854$	0.796869	−	1.38022i	0.0272683	−	0.0472301i
$855$		0			0
$856$	−5.96901	+	1.59939i	−0.204017	+	0.0546661i
$857$	25.9706			0.887137			0.443569	−	0.896240i	$-0.353712\pi$
$857$	25.9706			0.887137			0.443569	+	0.896240i	$0.353712\pi$
$858$	26.8842	−	7.20359i	0.917811	−	0.245927i
$859$	−17.4971	+	17.4971i	−0.596993	+	0.596993i	−0.939511	−	0.342518i	$-0.888720\pi$
$859$	−17.4971	+	17.4971i	−0.596993	+	0.596993i	0.342518	+	0.939511i	$0.388720\pi$
$860$		0			0
$861$	6.57915			0.224217
$862$	12.6395	+	12.6395i	0.430503	+	0.430503i
$863$	7.15937	−	26.7191i	0.243708	−	0.909530i	−0.730321	−	0.683104i	$-0.760629\pi$
$863$	7.15937	−	26.7191i	0.243708	−	0.909530i	0.974029	−	0.226425i	$-0.0727039\pi$
$864$	7.50657	+	28.0149i	0.255379	+	0.953086i
$865$		0			0
$866$	−9.69843	−	2.59869i	−0.329566	−	0.0883070i
$867$	−63.0254	−	16.8876i	−2.14046	−	0.573534i
$868$	1.87073	−	1.08007i	0.0634968	−	0.0366599i
$869$	19.3027	−	5.17214i	0.654799	−	0.175453i
$870$		0			0
$871$	−6.75977	−	1.81128i	−0.229046	−	0.0613727i
$872$	−6.51159	+	24.3016i	−0.220510	+	0.822955i
$873$	3.74870	−	2.16432i	0.126874	−	0.0732510i
$874$	−3.66521	+	3.66521i	−0.123978	+	0.123978i
$875$		0			0
$876$	14.3410	−	8.27979i	0.484538	−	0.279748i
$877$	−3.01345	+	3.01345i	−0.101757	+	0.101757i	−0.756152	−	0.654395i	$-0.772923\pi$
$877$	−3.01345	+	3.01345i	−0.101757	+	0.101757i	0.654395	+	0.756152i	$0.272923\pi$
$878$	32.7410	−	32.7410i	1.10495	−	1.10495i
$879$	−27.7939	−	48.1404i	−0.937465	−	1.62374i
$880$		0			0
$881$	25.4081	+	14.6694i	0.856021	+	0.494224i	0.862678	−	0.505754i	$-0.168786\pi$
$881$	25.4081	+	14.6694i	0.856021	+	0.494224i	−0.00665684	+	0.999978i	$0.502119\pi$
$882$			3.90099i			0.131353i
$883$	16.0263	−	27.7584i	0.539328	−	0.934144i	−0.459612	−	0.888120i	$-0.652011\pi$
$883$	16.0263	−	27.7584i	0.539328	−	0.934144i	0.998940	−	0.0460243i	$-0.0146552\pi$
$884$	11.3756	+	6.56772i	0.382604	+	0.220896i
$885$		0			0
$886$	8.78473	−	32.7851i	0.295129	−	1.10144i
$887$	−37.8878	−	37.8878i	−1.27215	−	1.27215i	−0.944959	−	0.327189i	$-0.893899\pi$
$887$	−37.8878	−	37.8878i	−1.27215	−	1.27215i	−0.327189	−	0.944959i	$-0.606101\pi$
$888$	0.212771	+	16.1643i	0.00714012	+	0.542439i
$889$		−	8.81837i		−	0.295759i
$890$		0			0
$891$	−47.8479	−	27.6250i	−1.60297	−	0.925473i
$892$	14.3855	−	3.85458i	0.481662	−	0.129061i
$893$	−4.19798	−	2.42370i	−0.140480	−	0.0811061i
$894$	26.7672	−	26.7672i	0.895229	−	0.895229i
$895$		0			0
$896$	−3.91749	−	3.91749i	−0.130874	−	0.130874i
$897$	3.09135	+	0.828324i	0.103217	+	0.0276569i
$898$	−37.2844	−	37.2844i	−1.24420	−	1.24420i
$899$	19.2689			0.642655
$900$		0			0
$901$	−58.1502	+	15.5813i	−1.93727	+	0.519089i
$902$		−	69.5207i		−	2.31479i
$903$	−4.99281	−	8.64781i	−0.166150	−	0.287781i
$904$	−10.6497	+	6.14860i	−0.354203	+	0.204499i
$905$		0			0
$906$	1.06662	+	3.98069i	0.0354362	+	0.132250i
$907$	15.3116	−	26.5205i	0.508414	−	0.880600i	−0.491538	−	0.870856i	$-0.663565\pi$
$907$	15.3116	−	26.5205i	0.508414	−	0.880600i	0.999953	−	0.00974360i	$-0.00310153\pi$
$908$	7.99234	+	13.8431i	0.265235	+	0.459401i
$909$	2.24068	+	3.88098i	0.0743188	+	0.128724i
$910$		0			0
$911$	−36.9318	−	36.9318i	−1.22361	−	1.22361i	−0.966341	−	0.257264i	$-0.917179\pi$
$911$	−36.9318	−	36.9318i	−1.22361	−	1.22361i	−0.257264	−	0.966341i	$-0.582821\pi$
$912$	−19.8391	−	11.4541i	−0.656937	−	0.379283i
$913$	43.1298	+	11.5566i	1.42739	+	0.382467i
$914$			3.35688i			0.111036i
$915$		0			0
$916$	21.0016	−	12.1253i	0.693911	−	0.400630i
$917$		−	1.50269i		−	0.0496233i
$918$	−16.3646	−	61.0736i	−0.540113	−	2.01573i
$919$	27.0236	+	27.0236i	0.891426	+	0.891426i	0.994657	−	0.103232i	$-0.0329183\pi$
$919$	27.0236	+	27.0236i	0.891426	+	0.891426i	−0.103232	+	0.994657i	$0.532918\pi$
$920$		0			0
$921$	20.9370	−	36.2640i	0.689899	−	1.19494i
$922$	5.88096	+	21.9480i	0.193679	+	0.722820i
$923$	−7.38337	+	4.26279i	−0.243027	+	0.140311i
$924$	−6.26051			−0.205956
$925$		0			0
$926$	56.1333			1.84465
$927$	−0.443619	+	0.256123i	−0.0145703	+	0.00841219i
$928$	8.41871	+	31.4191i	0.276358	+	1.03138i
$929$	12.6270	−	21.8706i	0.414279	−	0.717552i	−0.581073	−	0.813851i	$-0.697367\pi$
$929$	12.6270	−	21.8706i	0.414279	−	0.717552i	0.995352	+	0.0962988i	$0.0307004\pi$
$930$		0			0
$931$	12.0403	+	12.0403i	0.394607	+	0.394607i
$932$	1.09237	+	4.07679i	0.0357819	+	0.133540i
$933$			37.5184i			1.22830i
$934$	0.0131986	−	0.00762023i	0.000431872	−	0.000249342i
$935$		0			0
$936$			0.723516i			0.0236489i
$937$	8.40811	+	2.25295i	0.274681	+	0.0736006i	0.393530	−	0.919312i	$-0.371254\pi$
$937$	8.40811	+	2.25295i	0.274681	+	0.0736006i	−0.118849	+	0.992912i	$0.537920\pi$
$938$	3.66785	+	2.11764i	0.119760	+	0.0691433i
$939$	2.92116	+	2.92116i	0.0953283	+	0.0953283i
$940$		0			0
$941$	−19.3440	−	33.5049i	−0.630598	−	1.09223i	−0.987430	−	0.158059i	$-0.949476\pi$
$941$	−19.3440	−	33.5049i	−0.630598	−	1.09223i	0.356832	−	0.934169i	$-0.383857\pi$
$942$	13.7234	+	23.7696i	0.447131	+	0.774454i
$943$	3.99701	−	6.92303i	0.130161	−	0.225445i
$944$	4.01707	+	14.9919i	0.130744	+	0.487945i
$945$		0			0
$946$	−91.3798	+	52.7582i	−2.97101	+	1.71532i
$947$	−6.73712	−	11.6690i	−0.218927	−	0.379193i	0.735553	−	0.677467i	$-0.236922\pi$
$947$	−6.73712	−	11.6690i	−0.218927	−	0.379193i	−0.954480	+	0.298274i	$0.903589\pi$
$948$		−	7.70030i		−	0.250094i
$949$	−11.3314	+	3.03624i	−0.367833	+	0.0985605i
$950$		0			0
$951$	−5.54309			−0.179747
$952$	3.88150	+	3.88150i	0.125800	+	0.125800i
$953$	−23.8171	−	6.38179i	−0.771513	−	0.206726i	−0.148473	−	0.988916i	$-0.547436\pi$
$953$	−23.8171	−	6.38179i	−0.771513	−	0.206726i	−0.623040	+	0.782190i	$0.714103\pi$
$954$	3.39562	+	3.39562i	0.109937	+	0.109937i
$955$		0			0
$956$	−16.6831	+	16.6831i	−0.539571	+	0.539571i
$957$	−48.3634	−	27.9226i	−1.56337	−	0.902610i
$958$	52.6211	−	14.0998i	1.70011	−	0.455543i
$959$	9.05626	+	5.22864i	0.292442	+	0.168841i
$960$		0			0
$961$			18.5939i			0.599805i
$962$	−4.08122	+	16.0747i	−0.131584	+	0.518270i
$963$	−0.973843	−	0.973843i	−0.0313817	−	0.0313817i
$964$	7.70498	−	28.7554i	0.248161	−	0.926148i
$965$		0			0
$966$	−1.67736	−	0.968427i	−0.0539683	−	0.0311586i
$967$	2.76210	−	4.78411i	0.0888233	−	0.153846i	−0.818191	−	0.574947i	$-0.805023\pi$
$967$	2.76210	−	4.78411i	0.0888233	−	0.153846i	0.907014	+	0.421100i	$0.138356\pi$
$968$		−	29.6480i		−	0.952921i
$969$	29.0217	+	16.7557i	0.932311	+	0.538270i
$970$		0			0
$971$	8.56763	+	14.8396i	0.274948	+	0.476224i	0.970122	−	0.242617i	$-0.0780059\pi$
$971$	8.56763	+	14.8396i	0.274948	+	0.476224i	−0.695174	+	0.718842i	$0.744673\pi$
$972$	−2.81198	+	2.81198i	−0.0901944	+	0.0901944i
$973$	−0.854516	+	0.854516i	−0.0273945	+	0.0273945i
$974$	12.5270	−	7.23246i	0.401391	−	0.231743i
$975$		0			0
$976$	6.05164	−	6.05164i	0.193708	−	0.193708i
$977$	−22.5666	+	13.0289i	−0.721971	+	0.416830i	−0.815478	−	0.578789i	$-0.803526\pi$
$977$	−22.5666	+	13.0289i	−0.721971	+	0.416830i	0.0935067	+	0.995619i	$0.470192\pi$
$978$	17.6115	−	65.7270i	0.563154	−	2.10172i
$979$	−18.7336	−	5.01964i	−0.598727	−	0.160428i
$980$		0			0
$981$	−5.41601	+	1.45122i	−0.172920	+	0.0463338i
$982$	−60.3291	+	34.8310i	−1.92518	+	1.11150i
$983$	−16.0529	−	4.30135i	−0.512007	−	0.137192i	−0.00643984	−	0.999979i	$-0.502050\pi$
$983$	−16.0529	−	4.30135i	−0.512007	−	0.137192i	−0.505567	+	0.862788i	$0.668717\pi$
$984$	17.8677	+	4.78763i	0.569601	+	0.152624i
$985$		0			0
$986$	−18.3531	−	68.4948i	−0.584483	−	2.18132i
$987$	0.468800	−	1.74959i	0.0149221	−	0.0556900i
$988$	−3.23397	−	3.23397i	−0.102886	−	0.102886i
$989$	−12.1331			−0.385809
$990$		0			0
$991$	27.6853	−	27.6853i	0.879454	−	0.879454i	−0.114024	−	0.993478i	$-0.536374\pi$
$991$	27.6853	−	27.6853i	0.879454	−	0.879454i	0.993478	+	0.114024i	$0.0363742\pi$
$992$	20.2288	−	5.42028i	0.642264	−	0.172094i
$993$	−62.0478			−1.96903
$994$	4.98380	−	1.33541i	0.158077	−	0.0423565i
$995$		0			0
$996$	8.60274	−	14.9004i	0.272588	−	0.472137i
$997$	−6.37104	−	11.0350i	−0.201773	−	0.349481i	0.747327	−	0.664457i	$-0.231337\pi$
$997$	−6.37104	−	11.0350i	−0.201773	−	0.349481i	−0.949100	+	0.314976i	$0.898004\pi$
$998$	−26.4260	+	26.4260i	−0.836501	+	0.836501i
$999$	25.4986	−	15.1726i	0.806741	−	0.480040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.193.13		68
5.2	odd	4		925.2.t.b.82.13		68
5.3	odd	4		185.2.p.a.82.5	✓	68
5.4	even	2		185.2.u.a.8.5	yes	68
37.14	odd	12		925.2.t.b.643.13		68
185.14	odd	12		185.2.p.a.88.5	yes	68
185.88	even	12		185.2.u.a.162.5	yes	68
185.162	even	12	inner	925.2.y.b.532.13		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.82.5	✓	68	5.3	odd	4
185.2.p.a.88.5	yes	68	185.14	odd	12
185.2.u.a.8.5	yes	68	5.4	even	2
185.2.u.a.162.5	yes	68	185.88	even	12
925.2.t.b.82.13		68	5.2	odd	4
925.2.t.b.643.13		68	37.14	odd	12
925.2.y.b.193.13		68	1.1	even	1	trivial
925.2.y.b.532.13		68	185.162	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.54509 - 0.892058i) q^{2} +(0.471934 + 1.76128i) q^{3} +(0.591534 - 1.02457i) q^{4} +(2.30034 + 2.30034i) q^{6} +(0.134169 + 0.500724i) q^{7} +1.45750i q^{8} +(-0.281310 + 0.162414i) q^{9} +5.59836i q^{11} +(2.08371 + 0.558329i) q^{12} +(-1.32347 - 0.764108i) q^{13} +(0.653977 + 0.653977i) q^{14} +(2.48324 + 4.30110i) q^{16} +(-3.63263 - 6.29189i) q^{17} +(-0.289766 + 0.501889i) q^{18} +(0.654716 + 2.44343i) q^{19} +(-0.818597 + 0.472617i) q^{21} +(4.99406 + 8.64996i) q^{22} +1.14851i q^{23} +(-2.56707 + 0.687844i) q^{24} -2.72651 q^{26} +(3.44922 + 3.44922i) q^{27} +(0.592390 + 0.158730i) q^{28} +(3.86835 + 3.86835i) q^{29} +(2.49059 - 2.49059i) q^{31} +(5.14920 + 2.97289i) q^{32} +(-9.86028 + 2.64205i) q^{33} +(-11.2255 - 6.48102i) q^{34} +0.384294i q^{36} +(1.49687 - 5.89571i) q^{37} +(3.19128 + 3.19128i) q^{38} +(0.721216 - 2.69162i) q^{39} +(-6.02783 - 3.48017i) q^{41} +(-0.843203 + 1.46047i) q^{42} +10.5642i q^{43} +(5.73589 + 3.31162i) q^{44} +(1.02454 + 1.77455i) q^{46} +(-1.35499 + 1.35499i) q^{47} +(-6.40352 + 6.40352i) q^{48} +(5.82945 - 3.36564i) q^{49} +(9.36743 - 9.36743i) q^{51} +(-1.56576 + 0.903991i) q^{52} +(2.14463 - 8.00388i) q^{53} +(8.40626 + 2.25245i) q^{54} +(-0.729806 + 0.195551i) q^{56} +(-3.99459 + 2.30628i) q^{57} +(9.42773 + 2.52615i) q^{58} +(3.01861 + 0.808835i) q^{59} +(-0.446001 - 1.66450i) q^{61} +(1.62643 - 6.06993i) q^{62} +(-0.119068 - 0.119068i) q^{63} +0.674985 q^{64} +(-12.8781 + 12.8781i) q^{66} +(4.42331 - 1.18522i) q^{67} -8.59528 q^{68} +(-2.02285 + 0.542020i) q^{69} +(2.78939 - 4.83137i) q^{71} +(-0.236719 - 0.410010i) q^{72} +(5.42800 - 5.42800i) q^{73} +(-2.94652 - 10.4447i) q^{74} +(2.89075 + 0.774573i) q^{76} +(-2.80323 + 0.751124i) q^{77} +(-1.28673 - 4.80215i) q^{78} +(-0.923868 - 3.44792i) q^{79} +(-4.93449 + 8.54678i) q^{81} -12.4181 q^{82} +(2.06428 - 7.70401i) q^{83} +1.11828i q^{84} +(9.42386 + 16.3226i) q^{86} +(-4.98764 + 8.63885i) q^{87} -8.15962 q^{88} +(-0.896627 + 3.34626i) q^{89} +(0.205039 - 0.765214i) q^{91} +(1.17672 + 0.679382i) q^{92} +(5.56202 + 3.21123i) q^{93} +(-0.884854 + 3.30232i) q^{94} +(-2.80601 + 10.4722i) q^{96} -13.3259 q^{97} +(6.00468 - 10.4004i) q^{98} +(-0.909254 - 1.57487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Database

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