LMFDB - Embedded newform 425.2.r.a.69.5

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			69.5
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.20587 + 0.716731i) q^{2} +(-0.551084 - 0.758502i) q^{3} +(2.73413 - 1.98646i) q^{4} +(1.11977 - 1.93549i) q^{5} +(1.75926 + 1.27818i) q^{6} -3.09233i q^{7} +(-1.88077 + 2.58866i) q^{8} +(0.655419 - 2.01717i) q^{9} +(-1.08286 + 5.07201i) q^{10} +(-0.898962 - 2.76672i) q^{11} +(-3.01347 - 0.979135i) q^{12} +(-1.22874 - 0.399243i) q^{13} +(2.21637 + 6.82128i) q^{14} +(-2.08516 + 0.217264i) q^{15} +(0.204676 - 0.629927i) q^{16} +(-0.587785 + 0.809017i) q^{17} +4.91938i q^{18} +(5.74997 + 4.17760i) q^{19} +(-0.783159 - 7.51625i) q^{20} +(-2.34554 + 1.70413i) q^{21} +(3.96599 + 5.45871i) q^{22} +(-6.15964 + 2.00139i) q^{23} +2.99996 q^{24} +(-2.49221 - 4.33461i) q^{25} +2.99660 q^{26} +(-4.56624 + 1.48366i) q^{27} +(-6.14279 - 8.45483i) q^{28} +(-2.44827 + 1.77877i) q^{29} +(4.44387 - 1.97375i) q^{30} +(2.83413 + 2.05911i) q^{31} -4.86328i q^{32} +(-1.60316 + 2.20656i) q^{33} +(0.716731 - 2.20587i) q^{34} +(-5.98516 - 3.46271i) q^{35} +(-2.21503 - 6.81718i) q^{36} +(3.80367 + 1.23589i) q^{37} +(-15.6779 - 5.09406i) q^{38} +(0.374314 + 1.15202i) q^{39} +(2.90427 + 6.53891i) q^{40} +(2.15690 - 6.63826i) q^{41} +(3.95255 - 5.44022i) q^{42} -0.886046i q^{43} +(-7.95386 - 5.77881i) q^{44} +(-3.17029 - 3.52733i) q^{45} +(12.1529 - 8.82961i) q^{46} +(-4.18135 - 5.75513i) q^{47} +(-0.590594 + 0.191896i) q^{48} -2.56251 q^{49} +(8.60425 + 7.77536i) q^{50} +0.937560 q^{51} +(-4.15262 + 1.34927i) q^{52} +(4.82566 + 6.64195i) q^{53} +(9.00914 - 6.54553i) q^{54} +(-6.36158 - 1.35817i) q^{55} +(8.00498 + 5.81596i) q^{56} -6.66357i q^{57} +(4.12566 - 5.67848i) q^{58} +(-2.24858 + 6.92043i) q^{59} +(-5.26950 + 4.73611i) q^{60} +(-4.75137 - 14.6232i) q^{61} +(-7.72754 - 2.51083i) q^{62} +(-6.23777 - 2.02677i) q^{63} +(3.89501 + 11.9876i) q^{64} +(-2.14865 + 1.93115i) q^{65} +(1.95485 - 6.01642i) q^{66} +(3.34391 - 4.60249i) q^{67} +3.37957i q^{68} +(4.91253 + 3.56917i) q^{69} +(15.6843 + 3.34855i) q^{70} +(-7.89854 + 5.73863i) q^{71} +(3.98908 + 5.49049i) q^{72} +(11.7044 - 3.80298i) q^{73} -9.27620 q^{74} +(-1.91440 + 4.27908i) q^{75} +24.0198 q^{76} +(-8.55561 + 2.77989i) q^{77} +(-1.65138 - 2.27293i) q^{78} +(-8.09824 + 5.88371i) q^{79} +(-0.990024 - 1.10152i) q^{80} +(-1.50599 - 1.09417i) q^{81} +16.1891i q^{82} +(-1.97631 + 2.72016i) q^{83} +(-3.02781 + 9.31864i) q^{84} +(0.907654 + 2.04357i) q^{85} +(0.635057 + 1.95450i) q^{86} +(2.69840 + 0.876763i) q^{87} +(8.85283 + 2.87646i) q^{88} +(-0.570905 - 1.75707i) q^{89} +(9.52140 + 5.50860i) q^{90} +(-1.23459 + 3.79968i) q^{91} +(-12.8656 + 17.7079i) q^{92} -3.28443i q^{93} +(13.3484 + 9.69818i) q^{94} +(14.5244 - 6.45102i) q^{95} +(-3.68880 + 2.68007i) q^{96} +(4.32185 + 5.94852i) q^{97} +(5.65256 - 1.83663i) q^{98} -6.17015 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 $

$2$	−2.20587	+	0.716731i	−1.55979	+	0.506805i	−0.956751	−	0.290909i	$-0.906042\pi$
$2$	−2.20587	+	0.716731i	−1.55979	+	0.506805i	−0.603035	+	0.797714i	$0.706042\pi$
$3$	−0.551084	−	0.758502i	−0.318168	−	0.437921i	0.619738	−	0.784808i	$-0.287239\pi$
$3$	−0.551084	−	0.758502i	−0.318168	−	0.437921i	−0.937907	+	0.346887i	$0.887239\pi$
$4$	2.73413	−	1.98646i	1.36706	−	0.993230i
$5$	1.11977	−	1.93549i	0.500778	−	0.865576i
$5$	1.11977	−	1.93549i	0.500778	−	0.865576i
$6$	1.75926	+	1.27818i	0.718215	+	0.521814i
$7$		−	3.09233i		−	1.16879i	−0.811469	−	0.584396i	$-0.801332\pi$
$7$		−	3.09233i		−	1.16879i	0.811469	−	0.584396i	$-0.198668\pi$
$8$	−1.88077	+	2.58866i	−0.664952	+	0.915228i
$9$	0.655419	−	2.01717i	0.218473	−	0.672391i
$10$	−1.08286	+	5.07201i	−0.342429	+	1.60391i
$11$	−0.898962	−	2.76672i	−0.271047	−	0.834197i	−0.990238	−	0.139385i	$-0.955487\pi$
$11$	−0.898962	−	2.76672i	−0.271047	−	0.834197i	0.719191	−	0.694812i	$-0.244513\pi$
$12$	−3.01347	−	0.979135i	−0.869913	−	0.282652i
$13$	−1.22874	−	0.399243i	−0.340792	−	0.110730i	0.133621	−	0.991033i	$-0.457340\pi$
$13$	−1.22874	−	0.399243i	−0.340792	−	0.110730i	−0.474413	+	0.880302i	$0.657340\pi$
$14$	2.21637	+	6.82128i	0.592349	+	1.82306i
$15$	−2.08516	+	0.217264i	−0.538386	+	0.0560973i
$16$	0.204676	−	0.629927i	0.0511689	−	0.157482i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			4.91938i			1.15951i
$19$	5.74997	+	4.17760i	1.31913	+	0.958407i	0.999943	+	0.0107164i	$0.00341119\pi$
$19$	5.74997	+	4.17760i	1.31913	+	0.958407i	0.319191	+	0.947690i	$0.396589\pi$
$20$	−0.783159	−	7.51625i	−0.175120	−	1.68069i
$21$	−2.34554	+	1.70413i	−0.511838	+	0.371872i
$22$	3.96599	+	5.45871i	0.845551	+	1.16380i
$23$	−6.15964	+	2.00139i	−1.28437	+	0.417318i	−0.870119	−	0.492842i	$-0.835958\pi$
$23$	−6.15964	+	2.00139i	−1.28437	+	0.417318i	−0.414255	+	0.910161i	$0.635958\pi$
$24$	2.99996			0.612365
$25$	−2.49221	−	4.33461i	−0.498442	−	0.866923i
$26$	2.99660			0.587682
$27$	−4.56624	+	1.48366i	−0.878773	+	0.285531i
$28$	−6.14279	−	8.45483i	−1.16088	−	1.59781i
$29$	−2.44827	+	1.77877i	−0.454632	+	0.330309i	−0.791422	−	0.611271i	$-0.790659\pi$
$29$	−2.44827	+	1.77877i	−0.454632	+	0.330309i	0.336790	+	0.941580i	$0.390659\pi$
$30$	4.44387	−	1.97375i	0.811336	−	0.360357i
$31$	2.83413	+	2.05911i	0.509024	+	0.369828i	0.812453	−	0.583026i	$-0.198132\pi$
$31$	2.83413	+	2.05911i	0.509024	+	0.369828i	−0.303429	+	0.952854i	$0.598132\pi$
$32$		−	4.86328i		−	0.859714i
$33$	−1.60316	+	2.20656i	−0.279074	+	0.384113i
$34$	0.716731	−	2.20587i	0.122918	−	0.378304i
$35$	−5.98516	−	3.46271i	−1.01168	−	0.585305i
$36$	−2.21503	−	6.81718i	−0.369172	−	1.13620i
$37$	3.80367	+	1.23589i	0.625320	+	0.203179i	0.604501	−	0.796605i	$-0.293373\pi$
$37$	3.80367	+	1.23589i	0.625320	+	0.203179i	0.0208189	+	0.999783i	$0.493373\pi$
$38$	−15.6779	−	5.09406i	−2.54329	−	0.826366i
$39$	0.374314	+	1.15202i	0.0599382	+	0.184471i
$40$	2.90427	+	6.53891i	0.459206	+	1.03389i
$41$	2.15690	−	6.63826i	0.336851	−	1.03672i	−0.628952	−	0.777444i	$-0.716516\pi$
$41$	2.15690	−	6.63826i	0.336851	−	1.03672i	0.965803	−	0.259277i	$-0.0834843\pi$
$42$	3.95255	−	5.44022i	0.609892	−	0.839444i
$43$		−	0.886046i		−	0.135121i	−0.997715	−	0.0675604i	$-0.978478\pi$
$43$		−	0.886046i		−	0.135121i	0.997715	−	0.0675604i	$-0.0215215\pi$
$44$	−7.95386	−	5.77881i	−1.19909	−	0.871189i
$45$	−3.17029	−	3.52733i	−0.472599	−	0.525824i
$46$	12.1529	−	8.82961i	1.79185	−	1.30185i
$47$	−4.18135	−	5.75513i	−0.609912	−	0.839472i	0.386658	−	0.922223i	$-0.373629\pi$
$47$	−4.18135	−	5.75513i	−0.609912	−	0.839472i	−0.996570	+	0.0827508i	$0.973629\pi$
$48$	−0.590594	+	0.191896i	−0.0852449	+	0.0276977i
$49$	−2.56251			−0.366073
$50$	8.60425	+	7.77536i	1.21682	+	1.09960i
$51$	0.937560			0.131285
$52$	−4.15262	+	1.34927i	−0.575865	+	0.187110i
$53$	4.82566	+	6.64195i	0.662856	+	0.912342i	0.999572	−	0.0292638i	$-0.00931627\pi$
$53$	4.82566	+	6.64195i	0.662856	+	0.912342i	−0.336716	+	0.941606i	$0.609316\pi$
$54$	9.00914	−	6.54553i	1.22599	−	0.890733i
$55$	−6.36158	−	1.35817i	−0.857796	−	0.183136i
$56$	8.00498	+	5.81596i	1.06971	+	0.777190i
$57$		−	6.66357i		−	0.882611i
$58$	4.12566	−	5.67848i	0.541725	−	0.745621i
$59$	−2.24858	+	6.92043i	−0.292741	+	0.900963i	0.691231	+	0.722634i	$0.257069\pi$
$59$	−2.24858	+	6.92043i	−0.292741	+	0.900963i	−0.983971	+	0.178328i	$0.942931\pi$
$60$	−5.26950	+	4.73611i	−0.680290	+	0.611430i
$61$	−4.75137	−	14.6232i	−0.608350	−	1.87231i	−0.471873	−	0.881667i	$-0.656422\pi$
$61$	−4.75137	−	14.6232i	−0.608350	−	1.87231i	−0.136478	−	0.990643i	$-0.543578\pi$
$62$	−7.72754	−	2.51083i	−0.981399	−	0.318876i
$63$	−6.23777	−	2.02677i	−0.785885	−	0.255349i
$64$	3.89501	+	11.9876i	0.486876	+	1.49845i
$65$	−2.14865	+	1.93115i	−0.266507	+	0.239530i
$66$	1.95485	−	6.01642i	0.240626	−	0.740570i
$67$	3.34391	−	4.60249i	0.408523	−	0.562284i	−0.554334	−	0.832294i	$-0.687027\pi$
$67$	3.34391	−	4.60249i	0.408523	−	0.562284i	0.962857	+	0.270010i	$0.0870271\pi$
$68$			3.37957i			0.409833i
$69$	4.91253	+	3.56917i	0.591400	+	0.429677i
$70$	15.6843	+	3.34855i	1.87464	+	0.400228i
$71$	−7.89854	+	5.73863i	−0.937384	+	0.681050i	−0.947790	−	0.318896i	$-0.896688\pi$
$71$	−7.89854	+	5.73863i	−0.937384	+	0.681050i	0.0104053	+	0.999946i	$0.496688\pi$
$72$	3.98908	+	5.49049i	0.470117	+	0.647061i
$73$	11.7044	−	3.80298i	1.36989	−	0.445106i	0.470560	−	0.882368i	$-0.344052\pi$
$73$	11.7044	−	3.80298i	1.36989	−	0.445106i	0.899334	+	0.437262i	$0.144052\pi$
$74$	−9.27620			−1.07834
$75$	−1.91440	+	4.27908i	−0.221055	+	0.494106i
$76$	24.0198			2.75526
$77$	−8.55561	+	2.77989i	−0.975003	+	0.316798i
$78$	−1.65138	−	2.27293i	−0.186982	−	0.257358i
$79$	−8.09824	+	5.88371i	−0.911123	+	0.661970i	−0.941299	−	0.337575i	$-0.890393\pi$
$79$	−8.09824	+	5.88371i	−0.911123	+	0.661970i	0.0301757	+	0.999545i	$0.490393\pi$
$80$	−0.990024	−	1.10152i	−0.110688	−	0.123154i
$81$	−1.50599	−	1.09417i	−0.167332	−	0.121574i
$82$			16.1891i			1.78778i
$83$	−1.97631	+	2.72016i	−0.216928	+	0.298576i	−0.903588	−	0.428403i	$-0.859076\pi$
$83$	−1.97631	+	2.72016i	−0.216928	+	0.298576i	0.686659	+	0.726979i	$0.259076\pi$
$84$	−3.02781	+	9.31864i	−0.330361	+	1.01675i
$85$	0.907654	+	2.04357i	0.0984489	+	0.221656i
$86$	0.635057	+	1.95450i	0.0684799	+	0.210759i
$87$	2.69840	+	0.876763i	0.289299	+	0.0939989i
$88$	8.85283	+	2.87646i	0.943715	+	0.306632i
$89$	−0.570905	−	1.75707i	−0.0605158	−	0.186249i	0.916228	−	0.400656i	$-0.131218\pi$
$89$	−0.570905	−	1.75707i	−0.0605158	−	0.186249i	−0.976744	+	0.214408i	$0.931218\pi$
$90$	9.52140	+	5.50860i	1.00364	+	0.580657i
$91$	−1.23459	+	3.79968i	−0.129420	+	0.398315i
$92$	−12.8656	+	17.7079i	−1.34133	+	1.84618i
$93$		−	3.28443i		−	0.340580i
$94$	13.3484	+	9.69818i	1.37678	+	1.00029i
$95$	14.5244	−	6.45102i	1.49017	−	0.661861i
$96$	−3.68880	+	2.68007i	−0.376487	+	0.273534i
$97$	4.32185	+	5.94852i	0.438818	+	0.603981i	0.969949	−	0.243309i	$-0.0782329\pi$
$97$	4.32185	+	5.94852i	0.438818	+	0.603981i	−0.531131	+	0.847290i	$0.678233\pi$
$98$	5.65256	−	1.83663i	0.570995	−	0.185528i
$99$	−6.17015			−0.620124
$100$	−15.4246	−	6.90071i	−1.54246	−	0.690071i
$101$	13.3500			1.32837			0.664187	−	0.747566i	$-0.268778\pi$
$101$	13.3500			1.32837			0.664187	+	0.747566i	$0.268778\pi$
$102$	−2.06814	+	0.671978i	−0.204776	+	0.0665357i
$103$	9.14382	+	12.5854i	0.900968	+	1.24008i	0.970158	+	0.242472i	$0.0779583\pi$
$103$	9.14382	+	12.5854i	0.900968	+	1.24008i	−0.0691908	+	0.997603i	$0.522042\pi$
$104$	3.34449	−	2.42991i	0.327954	−	0.238272i
$105$	0.671852	+	6.44800i	0.0655661	+	0.629260i
$106$	−15.4053	−	11.1926i	−1.49629	−	1.08712i
$107$		−	12.7386i		−	1.23148i	−0.787948	−	0.615742i	$-0.788857\pi$
$107$		−	12.7386i		−	1.23148i	0.787948	−	0.615742i	$-0.211143\pi$
$108$	−9.53745	+	13.1272i	−0.917741	+	1.26316i
$109$	−0.339816	+	1.04585i	−0.0325485	+	0.100174i	−0.966011	−	0.258501i	$-0.916771\pi$
$109$	−0.339816	+	1.04585i	−0.0325485	+	0.100174i	0.933462	+	0.358675i	$0.116771\pi$
$110$	15.0063	−	1.56358i	1.43079	−	0.149082i
$111$	−1.15872	−	3.56617i	−0.109981	−	0.338486i
$112$	−1.94794	−	0.632925i	−0.184063	−	0.0598058i
$113$	−1.71491	−	0.557209i	−0.161325	−	0.0524178i	0.227241	−	0.973839i	$-0.427030\pi$
$113$	−1.71491	−	0.557209i	−0.161325	−	0.0524178i	−0.388566	+	0.921421i	$0.627030\pi$
$114$	4.77599	+	14.6990i	0.447312	+	1.37668i
$115$	−3.02375	+	14.1630i	−0.281966	+	1.32071i
$116$	−3.16042	+	9.72676i	−0.293437	+	0.903107i
$117$	−1.61069	+	2.21692i	−0.148908	+	0.204954i
$118$		−	16.8772i		−	1.55367i
$119$	2.50175	+	1.81763i	0.229335	+	0.166622i
$120$	3.35928	−	5.80638i	0.306659	−	0.530048i
$121$	2.05258	−	1.49129i	0.186598	−	0.135571i
$122$	20.9618	+	28.8515i	1.89779	+	2.61209i
$123$	−6.22376	+	2.02222i	−0.561178	+	0.182338i
$124$	11.8392			1.06319
$125$	−11.1803	−	0.0301521i	−0.999996	−	0.00269688i
$126$	15.2124			1.35522
$127$	−2.66963	+	0.867416i	−0.236892	+	0.0769707i	−0.425057	−	0.905167i	$-0.639746\pi$
$127$	−2.66963	+	0.867416i	−0.236892	+	0.0769707i	0.188165	+	0.982137i	$0.439746\pi$
$128$	−11.4667	−	15.7825i	−1.01352	−	1.39499i
$129$	−0.672068	+	0.488286i	−0.0591723	+	0.0429912i
$130$	3.35552	−	5.79988i	0.294298	−	0.508683i
$131$	−14.9083	−	10.8315i	−1.30255	−	0.946357i	−0.302571	−	0.953127i	$-0.597845\pi$
$131$	−14.9083	−	10.8315i	−1.30255	−	0.946357i	−0.999977	+	0.00677031i	$0.997845\pi$
$132$			9.21763i			0.802291i
$133$	12.9185	−	17.7808i	1.12018	−	1.54179i
$134$	−4.07748	+	12.5492i	−0.352240	+	1.08408i
$135$	−2.24155	+	10.4993i	−0.192922	+	0.903632i
$136$	−0.988779	−	3.04315i	−0.0847871	−	0.260948i
$137$	−3.26232	−	1.05999i	−0.278719	−	0.0905612i	0.166322	−	0.986071i	$-0.446811\pi$
$137$	−3.26232	−	1.05999i	−0.278719	−	0.0905612i	−0.445041	+	0.895510i	$0.646811\pi$
$138$	−13.3945	−	4.35215i	−1.14022	−	0.370480i
$139$	−3.66824	−	11.2897i	−0.311136	−	0.957578i	−0.977316	−	0.211787i	$-0.932072\pi$
$139$	−3.66824	−	11.2897i	−0.311136	−	0.957578i	0.666180	−	0.745791i	$-0.267928\pi$
$140$	−23.2427	+	2.42179i	−1.96437	+	0.204678i
$141$	−2.06100	+	6.34312i	−0.173568	+	0.534187i
$142$	13.3101	−	18.3198i	1.11696	−	1.53736i
$143$			3.75849i			0.314301i
$144$	−1.13652	−	0.825733i	−0.0947103	−	0.0688110i
$145$	0.701277	+	6.73040i	0.0582379	+	0.558930i
$146$	−23.0926	+	16.7778i	−1.91116	+	1.38854i
$147$	1.41216	+	1.94367i	0.116473	+	0.160311i
$148$	12.8548	−	4.17677i	1.05666	−	0.343328i
$149$	11.4245			0.935927			0.467964	−	0.883748i	$-0.344988\pi$
$149$	11.4245			0.935927			0.467964	+	0.883748i	$0.344988\pi$
$150$	1.15596	−	10.8112i	0.0943837	−	0.882731i
$151$	−15.0297			−1.22310			−0.611550	−	0.791206i	$-0.709454\pi$
$151$	−15.0297			−1.22310			−0.611550	+	0.791206i	$0.709454\pi$
$152$	−21.6287	+	7.02760i	−1.75432	+	0.570014i
$153$	1.24668	+	1.71591i	0.100788	+	0.138723i
$154$	16.8801	−	12.2641i	1.36024	−	0.988273i
$155$	7.15896	−	3.17967i	0.575022	−	0.255397i
$156$	3.31187	+	2.40621i	0.265162	+	0.192651i
$157$			10.1941i			0.813580i	0.913522	+	0.406790i	$0.133352\pi$
$157$			10.1941i			0.813580i	−0.913522	+	0.406790i	$0.866648\pi$
$158$	13.6466	−	18.7830i	1.08567	−	1.49429i
$159$	2.37859	−	7.32055i	0.188634	−	0.580557i
$160$	−9.41280	−	5.44577i	−0.744148	−	0.430526i
$161$	6.18896	+	19.0476i	0.487758	+	1.50116i
$162$	4.10625	+	1.33420i	0.322617	+	0.104825i
$163$	4.23068	+	1.37463i	0.331372	+	0.107669i	0.469978	−	0.882678i	$-0.344262\pi$
$163$	4.23068	+	1.37463i	0.331372	+	0.107669i	−0.138605	+	0.990348i	$0.544262\pi$
$164$	−7.28939	−	22.4344i	−0.569206	−	1.75184i
$165$	2.47559	+	5.57374i	0.192724	+	0.433915i
$166$	2.40986	−	7.41680i	0.187042	−	0.575655i
$167$	6.21030	−	8.54775i	0.480568	−	0.661445i	−0.498046	−	0.867150i	$-0.665949\pi$
$167$	6.21030	−	8.54775i	0.480568	−	0.661445i	0.978614	+	0.205706i	$0.0659490\pi$
$168$		−	9.27688i		−	0.715726i
$169$	−9.16680	−	6.66007i	−0.705139	−	0.512313i
$170$	−3.46685	−	3.85730i	−0.265896	−	0.295841i
$171$	12.1956	−	8.86061i	0.932619	−	0.677588i
$172$	−1.76010	−	2.42256i	−0.134206	−	0.184719i
$173$	21.0904	−	6.85270i	1.60348	−	0.521001i	0.635512	−	0.772091i	$-0.280789\pi$
$173$	21.0904	−	6.85270i	1.60348	−	0.521001i	0.967964	+	0.251090i	$0.0807889\pi$
$174$	−6.58072			−0.498883
$175$	−13.4041	+	7.70674i	−1.01325	+	0.582575i
$176$	−1.92683			−0.145240
$177$	6.48831	−	2.10818i	0.487691	−	0.158461i
$178$	2.51869	+	3.46667i	0.188784	+	0.259838i
$179$	8.90244	−	6.46800i	0.665400	−	0.483441i	−0.203082	−	0.979162i	$-0.565096\pi$
$179$	8.90244	−	6.46800i	0.665400	−	0.483441i	0.868482	+	0.495720i	$0.165096\pi$
$180$	−15.6749	−	3.34653i	−1.16834	−	0.249436i
$181$	−13.7584	−	9.99608i	−1.02266	−	0.743003i	−0.0558303	−	0.998440i	$-0.517781\pi$
$181$	−13.7584	−	9.99608i	−1.02266	−	0.743003i	−0.966826	+	0.255437i	$0.917781\pi$
$182$		−	9.26648i		−	0.686877i
$183$	−8.47333	+	11.6625i	−0.626366	+	0.862119i
$184$	6.40395	−	19.7093i	0.472106	−	1.45299i
$185$	6.65130	−	5.97804i	0.489013	−	0.439514i
$186$	2.35405	+	7.24503i	0.172608	+	0.531232i
$187$	2.76672	+	0.898962i	0.202323	+	0.0657386i
$188$	−22.8647	−	7.42919i	−1.66758	−	0.541829i
$189$	4.58797	+	14.1203i	0.333726	+	1.02710i
$190$	−27.4152	+	24.6402i	−1.98891	+	1.78759i
$191$	4.80000	−	14.7729i	0.347316	−	1.06893i	−0.613017	−	0.790070i	$-0.710044\pi$
$191$	4.80000	−	14.7729i	0.347316	−	1.06893i	0.960332	−	0.278858i	$-0.0899558\pi$
$192$	6.94615	−	9.56055i	0.501295	−	0.689973i
$193$		−	2.76730i		−	0.199195i	−0.995028	−	0.0995974i	$-0.968245\pi$
$193$		−	2.76730i		−	0.199195i	0.995028	−	0.0995974i	$-0.0317555\pi$
$194$	−13.7969	−	10.0241i	−0.990562	−	0.719686i
$195$	2.64887	+	0.565523i	0.189689	+	0.0404980i
$196$	−7.00623	+	5.09032i	−0.500445	+	0.363595i
$197$	2.25971	+	3.11023i	0.160998	+	0.221594i	0.881893	−	0.471450i	$-0.156269\pi$
$197$	2.25971	+	3.11023i	0.160998	+	0.221594i	−0.720895	+	0.693044i	$0.756269\pi$
$198$	13.6106	−	4.42234i	0.967260	−	0.314282i
$199$	21.5698			1.52904			0.764520	−	0.644600i	$-0.222976\pi$
$199$	21.5698			1.52904			0.764520	+	0.644600i	$0.222976\pi$
$200$	15.9081	+	1.70093i	1.12487	+	0.120274i
$201$	−5.33377			−0.376215
$202$	−29.4484	+	9.56835i	−2.07198	+	0.673227i
$203$	5.50054	+	7.57085i	0.386062	+	0.531369i
$204$	2.56341	−	1.86243i	0.179474	−	0.130396i
$205$	−10.4330	−	11.6080i	−0.728673	−	0.810738i
$206$	−29.1904	−	21.2081i	−2.03379	−	1.47764i
$207$			13.7368i			0.954775i
$208$	−0.502988	+	0.692303i	−0.0348759	+	0.0480026i
$209$	6.38924	−	19.6641i	0.441953	−	1.36019i
$210$	−6.10350	−	13.7419i	−0.421182	−	0.948282i
$211$	−1.85214	−	5.70030i	−0.127507	−	0.392425i	0.866843	−	0.498581i	$-0.166146\pi$
$211$	−1.85214	−	5.70030i	−0.127507	−	0.392425i	−0.994349	+	0.106157i	$0.966146\pi$
$212$	26.3880	+	8.57397i	1.81233	+	0.588862i
$213$	8.70552	+	2.82859i	0.596492	+	0.193812i
$214$	9.13012	+	28.0996i	0.624122	+	1.92085i
$215$	−1.71493	−	0.992172i	−0.116957	−	0.0676656i
$216$	4.74735	−	14.6108i	0.323016	−	0.994142i
$217$	6.36746	−	8.76405i	0.432251	−	0.594943i
$218$		−	2.55056i		−	0.172746i
$219$	−9.33466	−	6.78203i	−0.630778	−	0.458287i
$220$	−20.0913	+	8.92361i	−1.35456	+	0.601629i
$221$	1.04523	−	0.759405i	0.0703099	−	0.0510831i
$222$	5.11197	+	7.03602i	0.343093	+	0.472227i
$223$	3.00547	−	0.976536i	0.201261	−	0.0653937i	−0.206652	−	0.978415i	$-0.566257\pi$
$223$	3.00547	−	0.976536i	0.201261	−	0.0653937i	0.407913	+	0.913021i	$0.366257\pi$
$224$	−15.0389			−1.00483
$225$	−10.3771	+	2.18623i	−0.691808	+	0.145749i
$226$	4.18224			0.278199
$227$	−17.5337	+	5.69703i	−1.16375	+	0.378125i	−0.826307	−	0.563220i	$-0.809562\pi$
$227$	−17.5337	+	5.69703i	−1.16375	+	0.378125i	−0.337444	+	0.941346i	$0.609562\pi$
$228$	−13.2369	−	18.2191i	−0.876636	−	1.20659i
$229$	−14.5435	+	10.5664i	−0.961058	+	0.698250i	−0.953396	−	0.301721i	$-0.902439\pi$
$229$	−14.5435	+	10.5664i	−0.961058	+	0.698250i	−0.00766206	+	0.999971i	$0.502439\pi$
$230$	−3.48106	−	33.4090i	−0.229534	−	2.20292i
$231$	6.82341	+	4.95750i	0.448947	+	0.326179i
$232$		−	9.68317i		−	0.635731i
$233$	−10.0185	+	13.7893i	−0.656334	+	0.903367i	−0.999353	−	0.0359617i	$-0.988551\pi$
$233$	−10.0185	+	13.7893i	−0.656334	+	0.903367i	0.343019	+	0.939329i	$0.388551\pi$
$234$	1.96403	−	6.04466i	0.128393	−	0.395152i
$235$	−15.8211	+	1.64849i	−1.03206	+	0.107536i
$236$	7.59924	+	23.3880i	0.494668	+	1.52243i
$237$	8.92561	+	2.90011i	0.579781	+	0.188382i
$238$	−6.82128	−	2.21637i	−0.442158	−	0.143666i
$239$	3.22055	+	9.91184i	0.208320	+	0.641144i	0.999561	+	0.0296385i	$0.00943560\pi$
$239$	3.22055	+	9.91184i	0.208320	+	0.641144i	−0.791241	+	0.611505i	$0.790564\pi$
$240$	−0.289921	+	1.35797i	−0.0187143	+	0.0876563i
$241$	3.72252	−	11.4567i	0.239788	−	0.737993i	−0.756662	−	0.653807i	$-0.773171\pi$
$241$	3.72252	−	11.4567i	0.239788	−	0.737993i	0.996450	−	0.0841862i	$-0.0268291\pi$
$242$	−3.45887	+	4.76073i	−0.222345	+	0.306031i
$243$			16.1490i			1.03596i
$244$	−42.0393	−	30.5433i	−2.69129	−	1.95534i
$245$	−2.86943	+	4.95970i	−0.183321	+	0.316864i
$246$	12.2794	−	8.92152i	0.782907	−	0.568816i
$247$	−5.39736	−	7.42883i	−0.343426	−	0.472685i
$248$	−10.6607	+	3.46386i	−0.676953	+	0.219955i
$249$	3.15236			0.199773
$250$	24.6839	−	7.94675i	1.56115	−	0.502597i
$251$	10.4622			0.660368			0.330184	−	0.943917i	$-0.392889\pi$
$251$	10.4622			0.660368			0.330184	+	0.943917i	$0.392889\pi$
$252$	−21.0810	+	6.84962i	−1.32798	+	0.431485i
$253$	11.0746	+	15.2428i	0.696252	+	0.958309i
$254$	5.26716	−	3.82681i	0.330491	−	0.240116i
$255$	1.04986	−	1.81463i	0.0657445	−	0.113637i
$256$	16.2112	+	11.7781i	1.01320	+	0.736134i
$257$		−	15.0456i		−	0.938520i	−0.883060	−	0.469260i	$-0.844521\pi$
$257$		−	15.0456i		−	0.938520i	0.883060	−	0.469260i	$-0.155479\pi$
$258$	1.13252	−	1.55879i	0.0705079	−	0.0970458i
$259$	3.82177	−	11.7622i	0.237473	−	0.730868i
$260$	−2.03851	+	9.54822i	−0.126423	+	0.592156i
$261$	1.98345	+	6.10442i	0.122772	+	0.377854i
$262$	40.6492	+	13.2077i	2.51131	+	0.815976i
$263$	19.8092	+	6.43639i	1.22149	+	0.396885i	0.847623	−	0.530600i	$-0.178033\pi$
$263$	19.8092	+	6.43639i	1.22149	+	0.396885i	0.373862	+	0.927484i	$0.378033\pi$
$264$	−2.69685	−	8.30006i	−0.165980	−	0.510833i
$265$	18.2591	−	1.90251i	1.12165	−	0.116870i
$266$	−15.7525	+	48.4813i	−0.965849	+	2.97258i
$267$	−1.01812	+	1.40132i	−0.0623080	+	0.0857596i
$268$		−	19.2263i		−	1.17444i
$269$	−3.95141	−	2.87087i	−0.240922	−	0.175040i	0.460772	−	0.887518i	$-0.347573\pi$
$269$	−3.95141	−	2.87087i	−0.240922	−	0.175040i	−0.701694	+	0.712479i	$0.747573\pi$
$270$	−2.58056	−	24.7666i	−0.157048	−	1.50725i
$271$	−19.9988	+	14.5300i	−1.21484	+	0.882635i	−0.995661	−	0.0930494i	$-0.970339\pi$
$271$	−19.9988	+	14.5300i	−1.21484	+	0.882635i	−0.219181	+	0.975684i	$0.570339\pi$
$272$	0.389316	+	0.535848i	0.0236058	+	0.0324905i
$273$	3.56243	−	1.15750i	0.215608	−	0.0700553i
$274$	7.95598			0.480639
$275$	−9.75226	+	10.7919i	−0.588084	+	0.650776i
$276$	20.5215			1.23525
$277$	5.03669	−	1.63652i	0.302625	−	0.0983289i	−0.153768	−	0.988107i	$-0.549141\pi$
$277$	5.03669	−	1.63652i	0.302625	−	0.0983289i	0.456394	+	0.889778i	$0.349141\pi$
$278$	16.1833	+	22.2744i	0.970611	+	1.33593i
$279$	6.01113	−	4.36734i	0.359877	−	0.261466i
$280$	20.2205	−	8.98097i	1.20841	−	0.536715i
$281$	25.2840	+	18.3699i	1.50832	+	1.09586i	0.966918	+	0.255088i	$0.0821045\pi$
$281$	25.2840	+	18.3699i	1.50832	+	1.09586i	0.541397	+	0.840767i	$0.317895\pi$
$282$		−	15.4693i		−	0.921183i
$283$	2.31625	−	3.18805i	0.137687	−	0.189510i	−0.734605	−	0.678495i	$-0.762633\pi$
$283$	2.31625	−	3.18805i	0.137687	−	0.189510i	0.872292	+	0.488985i	$0.162633\pi$
$284$	−10.1961	+	31.3803i	−0.605025	+	1.86208i
$285$	−12.8972	−	7.46169i	−0.763967	−	0.441993i
$286$	−2.69383	−	8.29075i	−0.159289	−	0.490242i
$287$	−20.5277	−	6.66985i	−1.21171	−	0.393709i
$288$	−9.81007	−	3.18749i	−0.578064	−	0.187824i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−6.37081	−	14.3438i	−0.374107	−	0.842295i
$291$	2.13026	−	6.55627i	0.124878	−	0.384335i
$292$	24.4468	−	33.6481i	1.43064	−	1.96911i
$293$		−	20.4107i		−	1.19241i	−0.802834	−	0.596203i	$-0.796675\pi$
$293$		−	20.4107i		−	1.19241i	0.802834	−	0.596203i	$-0.203325\pi$
$294$	−4.50812	−	3.27534i	−0.262919	−	0.191022i
$295$	10.8765	+	12.1014i	0.633253	+	0.704572i
$296$	−10.3531	+	7.52198i	−0.601763	+	0.437206i
$297$	8.20975	+	11.2997i	0.476378	+	0.655678i
$298$	−25.2009	+	8.18826i	−1.45985	+	0.474333i
$299$	8.36766			0.483914
$300$	3.26602	+	15.5024i	0.188564	+	0.895033i
$301$	−2.73995			−0.157928
$302$	33.1536	−	10.7723i	1.90777	−	0.619873i
$303$	−7.35697	−	10.1260i	−0.422647	−	0.581723i
$304$	3.80846	−	2.76701i	0.218430	−	0.158699i
$305$	−33.6235	−	7.17849i	−1.92527	−	0.411039i
$306$	−3.97986	−	2.89154i	−0.227514	−	0.165298i
$307$		−	2.89935i		−	0.165475i	−0.996571	−	0.0827374i	$-0.973634\pi$
$307$		−	2.89935i		−	0.165475i	0.996571	−	0.0827374i	$-0.0263663\pi$
$308$	−17.8700	+	24.5960i	−1.01824	+	1.40148i
$309$	4.50703	−	13.8712i	0.256396	−	0.789106i
$310$	−13.5128	+	12.1450i	−0.767474	+	0.689789i
$311$	10.7024	+	32.9387i	0.606879	+	1.86778i	0.483320	+	0.875444i	$0.339431\pi$
$311$	10.7024	+	32.9387i	0.606879	+	1.86778i	0.123559	+	0.992337i	$0.460569\pi$
$312$	−3.68619	−	1.19771i	−0.208689	−	0.0678072i
$313$	10.7999	+	3.50909i	0.610444	+	0.198345i	0.597893	−	0.801576i	$-0.296005\pi$
$313$	10.7999	+	3.50909i	0.610444	+	0.198345i	0.0125513	+	0.999921i	$0.496005\pi$
$314$	−7.30644	−	22.4869i	−0.412326	−	1.26901i
$315$	−10.9077	+	9.80358i	−0.614578	+	0.552369i
$316$	−10.4539	+	32.1737i	−0.588075	+	1.80991i
$317$	17.6501	−	24.2933i	0.991328	−	1.36445i	0.0608307	−	0.998148i	$-0.480625\pi$
$317$	17.6501	−	24.2933i	0.991328	−	1.36445i	0.930498	−	0.366298i	$-0.119375\pi$
$318$			17.8530i			1.00115i
$319$	7.12225	+	5.17462i	0.398770	+	0.289723i
$320$	27.5634	+	5.88468i	1.54084	+	0.328964i
$321$	−9.66222	+	7.02001i	−0.539293	+	0.391819i
$322$	−27.3041	−	37.5808i	−1.52160	−	2.09430i
$323$	−6.75950	+	2.19629i	−0.376108	+	0.122205i
$324$	−6.29110			−0.349505
$325$	1.33172	+	6.32113i	0.0738707	+	0.350633i
$326$	−10.3176			−0.571437
$327$	0.980544	−	0.318598i	0.0542242	−	0.0176185i
$328$	13.1275	+	18.0685i	0.724847	+	0.997666i
$329$	−17.7968	+	12.9301i	−0.981168	+	0.712860i
$330$	−9.45570	−	10.5206i	−0.520519	−	0.579141i
$331$	−13.2306	−	9.61260i	−0.727220	−	0.528357i	0.161463	−	0.986879i	$-0.448379\pi$
$331$	−13.2306	−	9.61260i	−0.727220	−	0.528357i	−0.888683	+	0.458522i	$0.848379\pi$
$332$			11.3631i			0.623633i
$333$	4.98600	−	6.86264i	0.273231	−	0.376070i
$334$	−7.57269	+	23.3063i	−0.414359	+	1.27527i
$335$	−5.16364	−	11.6258i	−0.282120	−	0.635187i
$336$	0.593405	+	1.82631i	0.0323729	+	0.0996335i
$337$	−13.1360	−	4.26815i	−0.715564	−	0.232501i	−0.0714653	−	0.997443i	$-0.522768\pi$
$337$	−13.1360	−	4.26815i	−0.715564	−	0.232501i	−0.644099	+	0.764942i	$0.722768\pi$
$338$	24.9943	+	8.12113i	1.35951	+	0.441731i
$339$	0.522416	+	1.60783i	0.0283738	+	0.0873255i
$340$	6.54111	+	3.78435i	0.354741	+	0.205235i
$341$	3.14922	−	9.69230i	0.170540	−	0.524867i
$342$	−20.5512	+	28.2863i	−1.11128	+	1.52955i
$343$		−	13.7222i		−	0.740929i
$344$	2.29367	+	1.66645i	0.123666	+	0.0898489i
$345$	12.4090	−	5.51148i	0.668078	−	0.296728i
$346$	−41.6112	+	30.2323i	−2.23703	+	1.62530i
$347$	6.21923	+	8.56003i	0.333866	+	0.459527i	0.942637	−	0.333819i	$-0.108337\pi$
$347$	6.21923	+	8.56003i	0.333866	+	0.459527i	−0.608772	+	0.793346i	$0.708337\pi$
$348$	9.11942	−	2.96308i	0.488852	−	0.158838i
$349$	34.7761			1.86152			0.930762	−	0.365626i	$-0.119145\pi$
$349$	34.7761			1.86152			0.930762	+	0.365626i	$0.119145\pi$
$350$	24.0440	−	26.6072i	1.28520	−	1.42221i
$351$	6.20308			0.331096
$352$	−13.4553	+	4.37190i	−0.717171	+	0.233023i
$353$	4.89840	+	6.74207i	0.260715	+	0.358844i	0.919228	−	0.393726i	$-0.128814\pi$
$353$	4.89840	+	6.74207i	0.260715	+	0.358844i	−0.658512	+	0.752570i	$0.728814\pi$
$354$	−12.8014	+	9.30075i	−0.680386	+	0.494329i
$355$	2.26245	+	21.7135i	0.120078	+	1.15243i
$356$	−5.05127	−	3.66996i	−0.267717	−	0.194508i
$357$		−	2.89924i		−	0.153444i
$358$	−15.0018	+	20.6482i	−0.792871	+	1.09129i
$359$	−0.663713	+	2.04270i	−0.0350294	+	0.107809i	−0.967042	−	0.254616i	$-0.918051\pi$
$359$	−0.663713	+	2.04270i	−0.0350294	+	0.107809i	0.932013	+	0.362425i	$0.118051\pi$
$360$	15.0936	−	1.57269i	0.795505	−	0.0828879i
$361$	9.73851	+	29.9721i	0.512553	+	1.57748i
$362$	37.5138	+	12.1890i	1.97168	+	0.640638i
$363$	−2.26229	−	0.735061i	−0.118739	−	0.0385807i
$364$	4.17239	+	12.8413i	0.218692	+	0.673066i
$365$	5.74564	−	26.9121i	0.300741	−	1.40865i
$366$	10.3322	−	31.7991i	0.540071	−	1.66217i
$367$	−1.47342	+	2.02799i	−0.0769119	+	0.105860i	−0.845740	−	0.533596i	$-0.820840\pi$
$367$	−1.47342	+	2.02799i	−0.0769119	+	0.105860i	0.768828	+	0.639456i	$0.220840\pi$
$368$			4.28976i			0.223619i
$369$	−11.9768	−	8.70168i	−0.623489	−	0.452992i
$370$	−10.3873	+	17.9540i	−0.540008	+	0.933382i
$371$	20.5391	−	14.9225i	1.06634	−	0.774740i
$372$	−6.52439	−	8.98006i	−0.338274	−	0.465594i
$373$	21.6175	−	7.02394i	1.11931	−	0.363686i	0.309805	−	0.950800i	$-0.399736\pi$
$373$	21.6175	−	7.02394i	1.11931	−	0.363686i	0.809504	+	0.587114i	$0.199736\pi$
$374$	−6.74734			−0.348897
$375$	6.13841	+	8.49689i	0.316986	+	0.438778i
$376$	22.7622			1.17387
$377$	3.71845	−	1.20820i	0.191510	−	0.0622254i
$378$	−20.2409	−	27.8593i	−1.04108	−	1.43293i
$379$	19.3685	−	14.0720i	0.994893	−	0.722832i	0.0339056	−	0.999425i	$-0.489205\pi$
$379$	19.3685	−	14.0720i	0.994893	−	0.722832i	0.960987	+	0.276593i	$0.0892055\pi$
$380$	26.8967	−	46.4900i	1.37977	−	2.38488i
$381$	2.12913	+	1.54690i	0.109079	+	0.0792502i
$382$			36.0274i			1.84332i
$383$	3.02071	−	4.15766i	0.154351	−	0.212446i	−0.724838	−	0.688920i	$-0.758085\pi$
$383$	3.02071	−	4.15766i	0.154351	−	0.212446i	0.879189	+	0.476474i	$0.158085\pi$
$384$	−5.65197	+	17.3950i	−0.288426	+	0.887683i
$385$	−4.19992	+	19.6721i	−0.214048	+	1.00258i
$386$	1.98341	+	6.10431i	0.100953	+	0.310701i
$387$	−1.78731	−	0.580732i	−0.0908540	−	0.0295203i
$388$	23.6330	+	7.67883i	1.19978	+	0.389833i
$389$	5.36432	+	16.5097i	0.271982	+	0.837073i	0.990002	+	0.141051i	$0.0450483\pi$
$389$	5.36432	+	16.5097i	0.271982	+	0.837073i	−0.718021	+	0.696022i	$0.754952\pi$
$390$	−6.24839	+	0.651053i	−0.316399	+	0.0329674i
$391$	2.00139	−	6.15964i	0.101215	−	0.311506i
$392$	4.81949	−	6.63346i	0.243421	−	0.335040i
$393$			17.2771i			0.871514i
$394$	−7.21382	−	5.24115i	−0.363427	−	0.264045i
$395$	2.31965	+	22.2625i	0.116714	+	1.12015i
$396$	−16.8700	+	12.2568i	−0.847749	+	0.615925i
$397$	−17.7889	−	24.4844i	−0.892801	−	1.22884i	−0.972708	−	0.232033i	$-0.925462\pi$
$397$	−17.7889	−	24.4844i	−0.892801	−	1.22884i	0.0799068	−	0.996802i	$-0.474538\pi$
$398$	−47.5801	+	15.4597i	−2.38498	+	0.774925i
$399$	−20.6060			−1.03159
$400$	−3.24058	+	0.682720i	−0.162029	+	0.0341360i
$401$	3.54423			0.176990			0.0884952	−	0.996077i	$-0.471794\pi$
$401$	3.54423			0.176990			0.0884952	+	0.996077i	$0.471794\pi$
$402$	11.7656	−	3.82288i	0.586815	−	0.190668i
$403$	−2.66033	−	3.66163i	−0.132520	−	0.182399i
$404$	36.5006	−	26.5192i	1.81597	−	1.31938i
$405$	−3.80412	+	1.68961i	−0.189028	+	0.0839572i
$406$	−17.5597	−	12.7579i	−0.871475	−	0.633164i
$407$		−	11.6347i		−	0.576711i
$408$	−1.76333	+	2.42702i	−0.0872980	+	0.120155i
$409$	−3.51772	+	10.8264i	−0.173940	+	0.535333i	−0.999583	−	0.0288598i	$-0.990812\pi$
$409$	−3.51772	+	10.8264i	−0.173940	+	0.535333i	0.825643	+	0.564192i	$0.190812\pi$
$410$	31.3337	+	18.1281i	1.54746	+	0.895282i
$411$	0.993806	+	3.05862i	0.0490208	+	0.150871i
$412$	50.0008	+	16.2462i	2.46336	+	0.800394i
$413$	21.4002	+	6.95336i	1.05304	+	0.342153i
$414$	−9.84560	−	30.3016i	−0.483885	−	1.48924i
$415$	3.05181	+	6.87109i	0.149807	+	0.337288i
$416$	−1.94163	+	5.97572i	−0.0951962	+	0.292984i
$417$	−6.54173	+	9.00392i	−0.320350	+	0.440924i
$418$			47.9557i			2.34559i
$419$	−6.82392	−	4.95787i	−0.333370	−	0.242208i	0.408489	−	0.912763i	$-0.366056\pi$
$419$	−6.82392	−	4.95787i	−0.333370	−	0.242208i	−0.741859	+	0.670556i	$0.766056\pi$
$420$	14.6456	+	16.2951i	0.714633	+	0.795117i
$421$	2.92711	−	2.12667i	0.142659	−	0.103648i	−0.514167	−	0.857690i	$-0.671899\pi$
$421$	2.92711	−	2.12667i	0.142659	−	0.103648i	0.656826	+	0.754043i	$0.271899\pi$
$422$	8.17116	+	11.2466i	0.397766	+	0.547478i
$423$	−14.3496	+	4.66248i	−0.697703	+	0.226698i
$424$	−26.2697			−1.27577
$425$	4.97166	+	0.531582i	0.241161	+	0.0257855i
$426$	−21.2306			−1.02862
$427$	−45.2198	+	14.6928i	−2.18834	+	0.711035i
$428$	−25.3046	−	34.8289i	−1.22315	−	1.68352i
$429$	2.85082	−	2.07125i	0.137639	−	0.100001i
$430$	4.49403	+	0.959460i	0.216722	+	0.0462692i
$431$	18.7020	+	13.5878i	0.900841	+	0.654499i	0.938682	−	0.344784i	$-0.112048\pi$
$431$	18.7020	+	13.5878i	0.900841	+	0.654499i	−0.0378407	+	0.999284i	$0.512048\pi$
$432$			3.18006i			0.153001i
$433$	−3.44617	+	4.74324i	−0.165612	+	0.227946i	−0.883755	−	0.467950i	$-0.844993\pi$
$433$	−3.44617	+	4.74324i	−0.165612	+	0.227946i	0.718142	+	0.695896i	$0.244993\pi$
$434$	−7.76432	+	23.8961i	−0.372699	+	1.14705i
$435$	4.71856	−	4.24094i	0.226238	−	0.203337i
$436$	1.14843	+	3.53451i	0.0549999	+	0.169272i
$437$	−43.7788	−	14.2246i	−2.09422	−	0.680454i
$438$	25.4520	+	8.26984i	1.21614	+	0.395148i
$439$	−0.963716	−	2.96601i	−0.0459957	−	0.141560i	0.925421	−	0.378940i	$-0.123711\pi$
$439$	−0.963716	−	2.96601i	−0.0459957	−	0.141560i	−0.971417	+	0.237380i	$0.923711\pi$
$440$	15.4805	−	13.9135i	0.738005	−	0.663302i
$441$	−1.67952	+	5.16903i	−0.0799771	+	0.246144i
$442$	−1.76136	+	2.42430i	−0.0837792	+	0.115312i
$443$			1.77386i			0.0842786i	0.999112	+	0.0421393i	$0.0134173\pi$
$443$			1.77386i			0.0842786i	−0.999112	+	0.0421393i	$0.986583\pi$
$444$	−10.2521	−	7.44861i	−0.486545	−	0.353496i
$445$	−4.04006	−	0.862538i	−0.191517	−	0.0408882i
$446$	−5.92976	+	4.30822i	−0.280782	+	0.204000i
$447$	−6.29583	−	8.66547i	−0.297783	−	0.409862i
$448$	37.0697	−	12.0447i	1.75138	−	0.569057i
$449$	8.33800			0.393494			0.196747	−	0.980454i	$-0.436962\pi$
$449$	8.33800			0.393494			0.196747	+	0.980454i	$0.436962\pi$
$450$	21.3236	−	12.2601i	1.00521	−	0.577948i
$451$	−20.3052			−0.956133
$452$	−5.79566	+	1.88312i	−0.272605	+	0.0885747i
$453$	8.28263	+	11.4001i	0.389152	+	0.535621i
$454$	34.5938	−	25.1338i	1.62357	−	1.17959i
$455$	5.97177	+	6.64432i	0.279961	+	0.311491i
$456$	17.2497	+	12.5326i	0.807791	+	0.586894i
$457$		−	28.4956i		−	1.33297i	−0.745519	−	0.666484i	$-0.767798\pi$
$457$		−	28.4956i		−	1.33297i	0.745519	−	0.666484i	$-0.232202\pi$
$458$	24.5077	−	33.7319i	1.14517	−	1.57619i
$459$	1.48366	−	4.56624i	0.0692513	−	0.213134i
$460$	19.8669	+	44.7300i	0.926300	+	2.08555i
$461$	−10.4863	−	32.2737i	−0.488398	−	1.50313i	−0.826999	−	0.562204i	$-0.809954\pi$
$461$	−10.4863	−	32.2737i	−0.488398	−	1.50313i	0.338601	−	0.940930i	$-0.390046\pi$
$462$	−18.6047	−	6.04505i	−0.865571	−	0.281241i
$463$	−28.0728	−	9.12140i	−1.30465	−	0.423907i	−0.427455	−	0.904037i	$-0.640590\pi$
$463$	−28.0728	−	9.12140i	−1.30465	−	0.423907i	−0.877198	+	0.480129i	$0.840590\pi$
$464$	0.619394	+	1.90630i	0.0287546	+	0.0884977i
$465$	−6.35697	−	3.67782i	−0.294798	−	0.170555i
$466$	12.2163	−	37.5980i	0.565910	−	1.74169i
$467$	11.0908	−	15.2652i	0.513221	−	0.706388i	−0.471237	−	0.882006i	$-0.656192\pi$
$467$	11.0908	−	15.2652i	0.513221	−	0.706388i	0.984458	+	0.175618i	$0.0561924\pi$
$468$			9.26090i			0.428085i
$469$	−14.2324	−	10.3405i	−0.657192	−	0.477478i
$470$	33.7179	−	14.9759i	1.55529	−	0.690785i
$471$	7.73226	−	5.61782i	0.356284	−	0.258855i
$472$	−13.6855	−	18.8365i	−0.629928	−	0.867022i
$473$	−2.45144	+	0.796522i	−0.112717	+	0.0366241i
$474$	−21.7673			−0.999807
$475$	3.77814	−	35.3354i	0.173353	−	1.62130i
$476$	10.4507			0.479009
$477$	16.5608	−	5.38093i	0.758267	−	0.246376i
$478$	−14.2082	−	19.5560i	−0.649870	−	0.894469i
$479$	−22.7060	+	16.4968i	−1.03746	+	0.753760i	−0.969788	−	0.243947i	$-0.921558\pi$
$479$	−22.7060	+	16.4968i	−1.03746	+	0.753760i	−0.0676734	+	0.997708i	$0.521558\pi$
$480$	1.05662	+	10.1407i	0.0482277	+	0.462858i
$481$	−4.18032	−	3.03718i	−0.190606	−	0.138483i
$482$			27.9401i			1.27264i
$483$	11.0370	−	15.1912i	0.502203	−	0.691223i
$484$	2.64963	−	8.15473i	0.120438	−	0.370670i
$485$	16.3528	−	1.70388i	0.742541	−	0.0773694i
$486$	−11.5745	−	35.6225i	−0.525028	−	1.61587i
$487$	30.6682	+	9.96471i	1.38971	+	0.451544i	0.905849	−	0.423600i	$-0.139234\pi$
$487$	30.6682	+	9.96471i	1.38971	+	0.451544i	0.483861	+	0.875145i	$0.339234\pi$
$488$	46.7907	+	15.2032i	2.11812	+	0.688217i
$489$	−1.28880	−	3.96651i	−0.0582815	−	0.179372i
$490$	2.77483	−	12.9971i	0.125354	−	0.587148i
$491$	12.1038	−	37.2518i	0.546238	−	1.68115i	−0.171790	−	0.985134i	$-0.554955\pi$
$491$	12.1038	−	37.2518i	0.546238	−	1.68115i	0.718028	−	0.696014i	$-0.245045\pi$
$492$	−12.9995	+	17.8923i	−0.586063	+	0.806646i
$493$		−	3.02622i		−	0.136294i
$494$	17.2304	+	12.5186i	0.775231	+	0.563238i
$495$	−6.90918	+	11.9422i	−0.310544	+	0.536764i
$496$	1.87717	−	1.36384i	0.0842873	−	0.0612383i
$497$	17.7457	+	24.4249i	0.796005	+	1.09561i
$498$	−6.95369	+	2.25939i	−0.311603	+	0.101246i
$499$	−14.5610			−0.651840			−0.325920	−	0.945397i	$-0.605674\pi$
$499$	−14.5610			−0.651840			−0.325920	+	0.945397i	$0.605674\pi$
$500$	−30.6283	+	22.1268i	−1.36974	+	0.989540i
$501$	−9.90588			−0.442562
$502$	−23.0783	+	7.49858i	−1.03003	+	0.334678i
$503$	3.86371	+	5.31794i	0.172274	+	0.237115i	0.886420	−	0.462882i	$-0.153185\pi$
$503$	3.86371	+	5.31794i	0.172274	+	0.237115i	−0.714146	+	0.699997i	$0.753185\pi$
$504$	16.9784	−	12.3355i	0.756279	−	0.549469i
$505$	14.9490	−	25.8387i	0.665221	−	1.14981i
$506$	−35.3541	−	25.6862i	−1.57168	−	1.14189i
$507$			10.6233i			0.471797i
$508$	−5.57603	+	7.67474i	−0.247396	+	0.340512i
$509$	−5.92352	+	18.2307i	−0.262556	+	0.808063i	0.729691	+	0.683777i	$0.239664\pi$
$509$	−5.92352	+	18.2307i	−0.262556	+	0.808063i	−0.992246	+	0.124286i	$0.960336\pi$
$510$	−1.01524	+	4.75531i	−0.0449556	+	0.210569i
$511$	−11.7601	−	36.1938i	−0.520235	−	1.60112i
$512$	−7.09473	−	2.30522i	−0.313546	−	0.101877i
$513$	−32.4539	−	10.5449i	−1.43287	−	0.465569i
$514$	10.7837	+	33.1887i	0.475647	+	1.46389i
$515$	34.5979	−	3.60494i	1.52456	−	0.158853i
$516$	−0.867559	+	2.67007i	−0.0381921	+	0.117543i
$517$	−12.1640	+	16.7423i	−0.534971	+	0.736324i
$518$			28.6851i			1.26035i
$519$	−16.8204	−	12.2207i	−0.738333	−	0.536430i
$520$	−0.957990	−	9.19416i	−0.0420106	−	0.403191i
$521$	21.6272	−	15.7131i	0.947505	−	0.688403i	−0.00271037	−	0.999996i	$-0.500863\pi$
$521$	21.6272	−	15.7131i	0.947505	−	0.688403i	0.950215	+	0.311594i	$0.100863\pi$
$522$	−8.75045	−	12.0440i	−0.382997	−	0.527150i
$523$	−29.1186	+	9.46120i	−1.27327	+	0.413710i	−0.866204	−	0.499690i	$-0.833447\pi$
$523$	−29.1186	+	9.46120i	−1.27327	+	0.413710i	−0.407063	+	0.913400i	$0.633447\pi$
$524$	−62.2778			−2.72062
$525$	13.2323	+	5.91995i	0.577507	+	0.258368i
$526$	−48.3096			−2.10640
$527$	−3.33171	+	1.08254i	−0.145132	+	0.0471562i
$528$	1.06184	+	1.46150i	0.0462108	+	0.0636037i
$529$	15.3282	−	11.1366i	0.666445	−	0.484200i
$530$	−38.9135	+	17.2835i	−1.69030	+	0.750748i
$531$	12.4859	+	9.07156i	0.541843	+	0.393672i
$532$		−	74.2771i		−	3.22032i
$533$	−5.30056	+	7.29559i	−0.229593	+	0.316007i
$534$	1.24147	−	3.82086i	0.0537237	−	0.165345i
$535$	−24.6553	−	14.2643i	−1.06594	−	0.616700i
$536$	5.62516	+	17.3125i	0.242970	+	0.747784i
$537$	−9.81198	−	3.18811i	−0.423418	−	0.137577i
$538$	10.7739	+	3.50066i	0.464497	+	0.150924i
$539$	2.30360	+	7.08975i	0.0992230	+	0.305377i
$540$	14.7277	+	33.1591i	0.633778	+	1.42694i
$541$	3.27942	−	10.0930i	0.140993	−	0.433933i	−0.855481	−	0.517835i	$-0.826738\pi$
$541$	3.27942	−	10.0930i	0.140993	−	0.433933i	0.996474	+	0.0839020i	$0.0267383\pi$
$542$	33.7007	−	46.3851i	1.44757	−	1.99241i
$543$			15.9445i			0.684243i
$544$	3.93447	+	2.85856i	0.168689	+	0.122560i
$545$	1.64370	+	1.82882i	0.0704086	+	0.0783382i
$546$	−7.02864	+	5.10661i	−0.300798	+	0.218543i
$547$	4.98593	+	6.86254i	0.213183	+	0.293421i	0.902195	−	0.431329i	$-0.141955\pi$
$547$	4.98593	+	6.86254i	0.213183	+	0.293421i	−0.689012	+	0.724750i	$0.741955\pi$
$548$	−11.0252	+	3.58232i	−0.470975	+	0.153029i
$549$	−32.6117			−1.39183
$550$	13.7773	−	30.7953i	0.587468	−	1.31312i
$551$	−21.5084			−0.916290
$552$	−18.4787	+	6.00409i	−0.786505	+	0.255551i
$553$	18.1944	+	25.0424i	0.773704	+	1.06491i
$554$	−9.93734	+	7.21990i	−0.422197	+	0.306744i
$555$	−8.19977	−	1.75062i	−0.348061	−	0.0743097i
$556$	−32.4559	−	23.5806i	−1.37644	−	1.00004i
$557$			32.6854i			1.38493i	0.721453	+	0.692463i	$0.243475\pi$
$557$			32.6854i			1.38493i	−0.721453	+	0.692463i	$0.756525\pi$
$558$	−10.1296	+	13.9421i	−0.428819	+	0.590218i
$559$	−0.353748	+	1.08872i	−0.0149619	+	0.0460481i
$560$	−3.40627	+	3.06148i	−0.143941	+	0.129371i
$561$	−0.842830	−	2.59397i	−0.0355843	−	0.109517i
$562$	−68.9394	−	22.3998i	−2.90803	−	0.944877i
$563$	−21.4928	−	6.98342i	−0.905812	−	0.294316i	−0.181178	−	0.983450i	$-0.557991\pi$
$563$	−21.4928	−	6.98342i	−0.905812	−	0.294316i	−0.724634	+	0.689134i	$0.757991\pi$
$564$	6.96531	+	21.4370i	0.293292	+	0.902661i
$565$	−2.99878	+	2.69524i	−0.126160	+	0.113390i
$566$	−2.82438	+	8.69255i	−0.118718	+	0.365375i
$567$	−3.38353	+	4.65703i	−0.142095	+	0.195577i
$568$		−	31.2396i		−	1.31079i
$569$	−21.9380	−	15.9389i	−0.919688	−	0.668192i	0.0237587	−	0.999718i	$-0.492437\pi$
$569$	−21.9380	−	15.9389i	−0.919688	−	0.668192i	−0.943446	+	0.331526i	$0.892437\pi$
$570$	33.7977	+	7.21568i	1.41563	+	0.302232i
$571$	24.2729	−	17.6353i	1.01579	−	0.738015i	0.0503744	−	0.998730i	$-0.483959\pi$
$571$	24.2729	−	17.6353i	1.01579	−	0.738015i	0.965416	+	0.260716i	$0.0839585\pi$
$572$	7.46610	+	10.2762i	0.312173	+	0.429670i
$573$	−13.8505	+	4.50028i	−0.578611	+	0.188002i
$574$	50.0619			2.08954
$575$	24.0264	+	21.7118i	1.00197	+	0.905444i
$576$	26.7340			1.11392
$577$	27.4271	−	8.91160i	1.14180	−	0.370995i	0.323754	−	0.946141i	$-0.395055\pi$
$577$	27.4271	−	8.91160i	1.14180	−	0.370995i	0.818050	+	0.575147i	$0.195055\pi$
$578$	1.36330	+	1.87643i	0.0567059	+	0.0780490i
$579$	−2.09900	+	1.52502i	−0.0872316	+	0.0633775i
$580$	15.2871	+	17.0087i	0.634761	+	0.706249i
$581$	8.41163	+	6.11141i	0.348973	+	0.253544i
$582$			15.9891i			0.662769i
$583$	14.0383	−	19.3221i	0.581409	−	0.800240i
$584$	−12.1686	+	37.4512i	−0.503541	+	1.54974i
$585$	2.48721	+	5.59991i	0.102833	+	0.231528i
$586$	14.6290	+	45.0234i	0.604318	+	1.85990i
$587$	12.8878	+	4.18751i	0.531938	+	0.172837i	0.562656	−	0.826691i	$-0.309780\pi$
$587$	12.8878	+	4.18751i	0.531938	+	0.172837i	−0.0307185	+	0.999528i	$0.509780\pi$
$588$	7.72204	+	2.50904i	0.318452	+	0.103471i
$589$	7.69399	+	23.6797i	0.317025	+	0.975704i
$590$	−32.6656	−	18.8986i	−1.34482	−	0.778045i
$591$	1.11382	−	3.42799i	0.0458165	−	0.141009i
$592$	1.55704	−	2.14308i	0.0639938	−	0.0880800i
$593$			22.5206i			0.924810i	0.886669	+	0.462405i	$0.153013\pi$
$593$			22.5206i			0.924810i	−0.886669	+	0.462405i	$0.846987\pi$
$594$	−26.2085	−	19.0416i	−1.07535	−	0.781286i
$595$	6.31938	−	2.80677i	0.259069	−	0.115066i
$596$	31.2359	−	22.6942i	1.27947	−	0.929591i
$597$	−11.8867	−	16.3607i	−0.486492	−	0.669599i
$598$	−18.4580	+	5.99736i	−0.754803	+	0.245250i
$599$	24.1879			0.988291			0.494145	−	0.869379i	$-0.335481\pi$
$599$	24.1879			0.988291			0.494145	+	0.869379i	$0.335481\pi$
$600$	−7.47654	−	13.0037i	−0.305228	−	0.530873i
$601$	−3.59512			−0.146648			−0.0733241	−	0.997308i	$-0.523361\pi$
$601$	−3.59512			−0.146648			−0.0733241	+	0.997308i	$0.523361\pi$
$602$	6.04397	−	1.96381i	0.246334	−	0.0800387i
$603$	−7.09236	−	9.76180i	−0.288823	−	0.397531i
$604$	−41.0931	+	29.8559i	−1.67206	+	1.21482i
$605$	−0.587937	−	5.64264i	−0.0239031	−	0.229406i
$606$	23.4861	+	17.0637i	0.954059	+	0.693164i
$607$		−	2.47793i		−	0.100576i	−0.998735	−	0.0502880i	$-0.983986\pi$
$607$		−	2.47793i		−	0.100576i	0.998735	−	0.0502880i	$-0.0160139\pi$
$608$	20.3168	−	27.9637i	0.823956	−	1.13408i
$609$	2.71124	−	8.34434i	0.109865	−	0.338130i
$610$	79.3141	−	8.26416i	3.21133	−	0.334606i
$611$	2.84011	+	8.74096i	0.114899	+	0.353621i
$612$	6.81718	+	2.21503i	0.275568	+	0.0895375i
$613$	−36.5904	−	11.8889i	−1.47787	−	0.480189i	−0.544395	−	0.838829i	$-0.683241\pi$
$613$	−36.5904	−	11.8889i	−1.47787	−	0.480189i	−0.933476	+	0.358639i	$0.883241\pi$
$614$	2.07806	+	6.39560i	0.0838635	+	0.258105i
$615$	−3.05523	+	14.3104i	−0.123199	+	0.577052i
$616$	8.89496	−	27.3759i	0.358388	−	1.10301i
$617$	−14.6329	+	20.1405i	−0.589098	+	0.810824i	−0.994656	−	0.103245i	$-0.967077\pi$
$617$	−14.6329	+	20.1405i	−0.589098	+	0.810824i	0.405558	+	0.914069i	$0.367077\pi$
$618$			33.8284i			1.36078i
$619$	−1.49530	−	1.08640i	−0.0601013	−	0.0436661i	0.557329	−	0.830292i	$-0.311826\pi$
$619$	−1.49530	−	1.08640i	−0.0601013	−	0.0436661i	−0.617430	+	0.786626i	$0.711826\pi$
$620$	13.2572	−	22.9146i	0.532424	−	0.920273i
$621$	25.1570	−	18.2776i	1.00952	−	0.733456i
$622$	−47.2163	−	64.9877i	−1.89320	−	2.60577i
$623$	−5.43343	+	1.76543i	−0.217686	+	0.0707304i
$624$	0.802302			0.0321178
$625$	−12.5778	+	21.6055i	−0.503111	+	0.864222i
$626$	−26.3382			−1.05269
$627$	−18.4362	+	5.99029i	−0.736272	+	0.239229i
$628$	20.2502	+	27.8720i	0.808072	+	1.11222i
$629$	−3.23560	+	2.35080i	−0.129012	+	0.0937324i
$630$	17.0344	−	29.4433i	0.678667	−	1.17305i
$631$	−9.59683	−	6.97250i	−0.382044	−	0.277571i	0.380144	−	0.924927i	$-0.375875\pi$
$631$	−9.59683	−	6.97250i	−0.382044	−	0.277571i	−0.762187	+	0.647356i	$0.775875\pi$
$632$		−	32.0295i		−	1.27406i
$633$	−3.30300	+	4.54619i	−0.131283	+	0.180695i
$634$	−21.5221	+	66.2382i	−0.854751	+	2.63065i
$635$	−1.31051	+	6.13835i	−0.0520062	+	0.243593i
$636$	−8.03860	−	24.7403i	−0.318751	−	0.981016i
$637$	3.14867	+	1.02306i	0.124755	+	0.0405353i
$638$	−19.4196	−	6.30980i	−0.768828	−	0.249808i
$639$	6.39895	+	19.6939i	0.253138	+	0.779080i
$640$	−43.3869	+	4.52071i	−1.71502	+	0.178697i
$641$	−9.74174	+	29.9820i	−0.384776	+	1.18422i	0.551867	+	0.833932i	$0.313915\pi$
$641$	−9.74174	+	29.9820i	−0.384776	+	1.18422i	−0.936643	+	0.350286i	$0.886085\pi$
$642$	16.2821	−	22.4105i	0.642605	−	0.884470i
$643$			10.9134i			0.430382i	0.976572	+	0.215191i	$0.0690374\pi$
$643$			10.9134i			0.430382i	−0.976572	+	0.215191i	$0.930963\pi$
$644$	54.7588	+	39.7846i	2.15780	+	1.56773i
$645$	0.192506	+	1.84755i	0.00757991	+	0.0727471i
$646$	13.3364	−	9.68948i	0.524714	−	0.381227i
$647$	26.2994	+	36.1980i	1.03394	+	1.42309i	0.901951	+	0.431838i	$0.142135\pi$
$647$	26.2994	+	36.1980i	1.03394	+	1.42309i	0.131984	+	0.991252i	$0.457865\pi$
$648$	5.66485	−	1.84062i	0.222536	−	0.0723064i
$649$	21.1683			0.830927
$650$	−7.46816	−	12.9891i	−0.292925	−	0.509475i
$651$	−10.1566			−0.398067
$652$	14.2979	−	4.64566i	0.559948	−	0.181938i
$653$	−3.07809	−	4.23663i	−0.120455	−	0.165792i	0.744531	−	0.667588i	$-0.232673\pi$
$653$	−3.07809	−	4.23663i	−0.120455	−	0.165792i	−0.864986	+	0.501795i	$0.832673\pi$
$654$	−1.93460	+	1.40557i	−0.0756490	+	0.0549622i
$655$	−37.6583	+	16.7260i	−1.47143	+	0.653539i
$656$	−3.74015	−	2.71738i	−0.146028	−	0.106096i
$657$		−	26.1023i		−	1.01835i
$658$	29.9900	−	41.2777i	1.16913	−	1.60917i
$659$	−1.57636	+	4.85153i	−0.0614062	+	0.188989i	−0.977054	−	0.212993i	$-0.931679\pi$
$659$	−1.57636	+	4.85153i	−0.0614062	+	0.188989i	0.915647	+	0.401982i	$0.131679\pi$
$660$	17.8406	+	10.3217i	0.694444	+	0.401770i
$661$	12.3847	+	38.1163i	0.481711	+	1.48255i	0.836689	+	0.547679i	$0.184488\pi$
$661$	12.3847	+	38.1163i	0.481711	+	1.48255i	−0.354978	+	0.934875i	$0.615512\pi$
$662$	36.0747	+	11.7214i	1.40208	+	0.455564i
$663$	−1.15202	−	0.374314i	−0.0447408	−	0.0145372i
$664$	−3.32457	−	10.2320i	−0.129018	−	0.397078i
$665$	−19.9487	−	44.9141i	−0.773577	−	1.74169i
$666$	−6.07980	+	18.7117i	−0.235588	+	0.725064i
$667$	11.5204	−	15.8565i	0.446073	−	0.613966i
$668$		−	35.7072i		−	1.38155i
$669$	−2.39697	−	1.74150i	−0.0926722	−	0.0673303i
$670$	19.7229	+	21.9441i	0.761962	+	0.847776i
$671$	−36.1870	+	26.2914i	−1.39698	+	1.01497i
$672$	8.28767	+	11.4070i	0.319704	+	0.440035i
$673$	36.5445	−	11.8740i	1.40869	−	0.457710i	0.496698	−	0.867923i	$-0.334546\pi$
$673$	36.5445	−	11.8740i	1.40869	−	0.457710i	0.911990	+	0.410213i	$0.134546\pi$
$674$	32.0355			1.23396
$675$	17.8111	+	16.0953i	0.685550	+	0.619508i
$676$	−38.2932			−1.47281
$677$	26.7045	−	8.67682i	1.02634	−	0.333477i	0.252996	−	0.967467i	$-0.418584\pi$
$677$	26.7045	−	8.67682i	1.02634	−	0.333477i	0.773341	+	0.633990i	$0.218584\pi$
$678$	−2.30477	−	3.17224i	−0.0885140	−	0.121829i
$679$	18.3948	−	13.3646i	0.705927	−	0.512886i
$680$	−6.99718	−	1.49387i	−0.268330	−	0.0572874i
$681$	13.9837	+	10.1598i	0.535858	+	0.389323i
$682$			23.6371i			0.905111i
$683$	11.6927	−	16.0936i	0.447409	−	0.615805i	−0.524430	−	0.851454i	$-0.675721\pi$
$683$	11.6927	−	16.0936i	0.447409	−	0.615805i	0.971838	+	0.235649i	$0.0757214\pi$
$684$	15.7430	−	48.4521i	0.601950	−	1.85261i
$685$	−5.70466	+	5.12722i	−0.217964	+	0.195901i
$686$	9.83511	+	30.2694i	0.375506	+	1.15569i
$687$	16.0293	+	5.20824i	0.611557	+	0.198707i
$688$	−0.558144	−	0.181352i	−0.0212790	−	0.00691398i
$689$	−3.27775	−	10.0879i	−0.124872	−	0.384317i
$690$	−23.4224	+	21.0515i	−0.891676	+	0.801418i
$691$	0.0387259	−	0.119186i	0.00147320	−	0.00453405i	−0.950317	−	0.311283i	$-0.899241\pi$
$691$	0.0387259	−	0.119186i	0.00147320	−	0.00453405i	0.951790	+	0.306749i	$0.0992412\pi$
$692$	44.0513	−	60.6315i	1.67458	−	2.30486i
$693$			19.0801i			0.724795i
$694$	−19.8541	−	14.4248i	−0.753650	−	0.547558i
$695$	−25.9586	−	5.54207i	−0.984666	−	0.210223i
$696$	−7.34470	+	5.33624i	−0.278400	+	0.202270i
$697$	4.10267	+	5.64684i	0.155400	+	0.213889i
$698$	−76.7117	+	24.9251i	−2.90358	+	0.943430i
$699$	15.9802			0.604428
$700$	−21.3393	+	47.6979i	−0.806549	+	1.80281i
$701$	−5.54505			−0.209434			−0.104717	−	0.994502i	$-0.533394\pi$
$701$	−5.54505			−0.209434			−0.104717	+	0.994502i	$0.533394\pi$
$702$	−13.6832	+	4.44594i	−0.516439	+	0.167801i
$703$	16.7080	+	22.9965i	0.630152	+	0.867330i
$704$	29.6649	−	21.5528i	1.11804	−	0.812302i
$705$	9.96916	+	11.0919i	0.375460	+	0.417745i
$706$	−15.6375	−	11.3613i	−0.588524	−	0.427588i
$707$		−	41.2826i		−	1.55259i
$708$	13.5521	−	18.6528i	0.509318	−	0.701016i
$709$	−13.0974	+	40.3097i	−0.491884	+	1.51386i	0.329873	+	0.944025i	$0.392994\pi$
$709$	−13.0974	+	40.3097i	−0.491884	+	1.51386i	−0.821757	+	0.569838i	$0.807006\pi$
$710$	−20.5534	−	46.2756i	−0.771355	−	1.73669i
$711$	6.56073	+	20.1919i	0.246047	+	0.757254i
$712$	5.62218	+	1.82676i	0.210700	+	0.0684606i
$713$	−21.5783	−	7.01121i	−0.808113	−	0.262572i
$714$	2.07798	+	6.39536i	0.0777664	+	0.239340i
$715$	7.27451	+	4.20867i	0.272051	+	0.157395i
$716$	11.4920	−	35.3687i	0.429476	−	1.32179i
$717$	5.74335	−	7.90505i	0.214489	−	0.295219i
$718$		−	4.98163i		−	0.185913i
$719$	−19.6464	−	14.2739i	−0.732686	−	0.532327i	0.157726	−	0.987483i	$-0.449584\pi$
$719$	−19.6464	−	14.2739i	−0.732686	−	0.532327i	−0.890412	+	0.455156i	$0.849584\pi$
$720$	−2.87084	+	1.27509i	−0.106990	+	0.0475198i
$721$	38.9182	−	28.2757i	1.44939	−	1.05304i
$722$	−42.9638	−	59.1346i	−1.59895	−	2.20076i
$723$	−10.7414	+	3.49008i	−0.399476	+	0.129798i
$724$	−57.4741			−2.13601
$725$	13.8119	+	6.17922i	0.512960	+	0.229491i
$726$	5.51715			0.204761
$727$	−41.7020	+	13.5498i	−1.54664	+	0.502534i	−0.953199	−	0.302343i	$-0.902231\pi$
$727$	−41.7020	+	13.5498i	−1.54664	+	0.502534i	−0.593441	+	0.804877i	$0.702231\pi$
$728$	−7.51409	−	10.3423i	−0.278491	−	0.383310i
$729$	7.73103	−	5.61692i	0.286335	−	0.208034i
$730$	6.61462	+	63.4828i	0.244818	+	2.34960i
$731$	0.716826	+	0.520805i	0.0265128	+	0.0192627i
$732$			48.7188i			1.80070i
$733$	−29.7169	+	40.9017i	−1.09762	+	1.51074i	−0.259112	+	0.965847i	$0.583430\pi$
$733$	−29.7169	+	40.9017i	−1.09762	+	1.51074i	−0.838506	+	0.544893i	$0.816570\pi$
$734$	1.79665	−	5.52952i	0.0663156	−	0.204098i
$735$	5.34324	−	0.556741i	0.197088	−	0.0205357i
$736$	9.73331	+	29.9560i	0.358774	+	1.10419i
$737$	−15.7399	−	5.11419i	−0.579785	−	0.188384i
$738$	32.6561	+	10.6106i	1.20209	+	0.390582i
$739$	−7.72721	−	23.7819i	−0.284250	−	0.874832i	−0.986622	−	0.163022i	$-0.947876\pi$
$739$	−7.72721	−	23.7819i	−0.284250	−	0.874832i	0.702372	−	0.711810i	$-0.252124\pi$
$740$	6.31036	−	29.5572i	0.231974	−	1.08655i
$741$	−2.66038	+	8.18782i	−0.0977316	+	0.300787i
$742$	−34.6112	+	47.6382i	−1.27062	+	1.74885i
$743$		−	6.26573i		−	0.229867i	−0.993373	−	0.114934i	$-0.963334\pi$
$743$		−	6.26573i		−	0.229867i	0.993373	−	0.114934i	$-0.0366655\pi$
$744$	8.50227	+	6.17726i	0.311708	+	0.226469i
$745$	12.7928	−	22.1119i	0.468692	−	0.810116i
$746$	−42.6510	+	30.9878i	−1.56157	+	1.13454i
$747$	4.19172	+	5.76941i	0.153367	+	0.211092i
$748$	9.35032	−	3.03810i	0.341882	−	0.111084i
$749$	−39.3918			−1.43935
$750$	−19.6305	−	14.3435i	−0.716805	−	0.523749i
$751$	13.9499			0.509041			0.254520	−	0.967067i	$-0.418082\pi$
$751$	13.9499			0.509041			0.254520	+	0.967067i	$0.418082\pi$
$752$	−4.48113	+	1.45601i	−0.163410	+	0.0530952i
$753$	−5.76555	−	7.93560i	−0.210108	−	0.289189i
$754$	−7.33647	+	5.33026i	−0.267179	+	0.194117i
$755$	−16.8299	+	29.0898i	−0.612502	+	1.05869i
$756$	40.5935	+	29.4929i	1.47637	+	1.07265i
$757$		−	5.22773i		−	0.190005i	−0.995477	−	0.0950026i	$-0.969714\pi$
$757$		−	5.22773i		−	0.190005i	0.995477	−	0.0950026i	$-0.0302859\pi$
$758$	−32.6385	+	44.9231i	−1.18548	+	1.63168i
$759$	5.45870	−	16.8002i	0.198138	−	0.609807i
$760$	−10.6175	+	49.7314i	−0.385136	+	1.80395i
$761$	−1.78088	−	5.48099i	−0.0645569	−	0.198686i	0.913575	−	0.406669i	$-0.133310\pi$
$761$	−1.78088	−	5.48099i	−0.0645569	−	0.198686i	−0.978132	+	0.207984i	$0.933310\pi$
$762$	−5.80529	−	1.88625i	−0.210304	−	0.0683318i
$763$	3.23411	+	1.05082i	0.117082	+	0.0380424i
$764$	−16.2219	−	49.9259i	−0.586888	−	1.80626i
$765$	4.71712	−	0.491503i	0.170548	−	0.0177703i
$766$	−3.68338	+	11.3363i	−0.133086	+	0.409597i
$767$	5.52586	−	7.60570i	0.199527	−	0.274626i
$768$		−	18.7870i		−	0.677917i
$769$	−10.7170	−	7.78638i	−0.386466	−	0.280784i	0.377540	−	0.925993i	$-0.376770\pi$
$769$	−10.7170	−	7.78638i	−0.386466	−	0.280784i	−0.764006	+	0.645209i	$0.776770\pi$
$770$	−4.83512	−	46.4044i	−0.174246	−	1.67230i
$771$	−11.4121	+	8.29139i	−0.410998	+	0.298607i
$772$

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+(-2.20587 + 0.716731i) q^{2} +(-0.551084 - 0.758502i) q^{3} +(2.73413 - 1.98646i) q^{4} +(1.11977 - 1.93549i) q^{5} +(1.75926 + 1.27818i) q^{6} -3.09233i q^{7} +(-1.88077 + 2.58866i) q^{8} +(0.655419 - 2.01717i) q^{9} +(-1.08286 + 5.07201i) q^{10} +(-0.898962 - 2.76672i) q^{11} +(-3.01347 - 0.979135i) q^{12} +(-1.22874 - 0.399243i) q^{13} +(2.21637 + 6.82128i) q^{14} +(-2.08516 + 0.217264i) q^{15} +(0.204676 - 0.629927i) q^{16} +(-0.587785 + 0.809017i) q^{17} +4.91938i q^{18} +(5.74997 + 4.17760i) q^{19} +(-0.783159 - 7.51625i) q^{20} +(-2.34554 + 1.70413i) q^{21} +(3.96599 + 5.45871i) q^{22} +(-6.15964 + 2.00139i) q^{23} +2.99996 q^{24} +(-2.49221 - 4.33461i) q^{25} +2.99660 q^{26} +(-4.56624 + 1.48366i) q^{27} +(-6.14279 - 8.45483i) q^{28} +(-2.44827 + 1.77877i) q^{29} +(4.44387 - 1.97375i) q^{30} +(2.83413 + 2.05911i) q^{31} -4.86328i q^{32} +(-1.60316 + 2.20656i) q^{33} +(0.716731 - 2.20587i) q^{34} +(-5.98516 - 3.46271i) q^{35} +(-2.21503 - 6.81718i) q^{36} +(3.80367 + 1.23589i) q^{37} +(-15.6779 - 5.09406i) q^{38} +(0.374314 + 1.15202i) q^{39} +(2.90427 + 6.53891i) q^{40} +(2.15690 - 6.63826i) q^{41} +(3.95255 - 5.44022i) q^{42} -0.886046i q^{43} +(-7.95386 - 5.77881i) q^{44} +(-3.17029 - 3.52733i) q^{45} +(12.1529 - 8.82961i) q^{46} +(-4.18135 - 5.75513i) q^{47} +(-0.590594 + 0.191896i) q^{48} -2.56251 q^{49} +(8.60425 + 7.77536i) q^{50} +0.937560 q^{51} +(-4.15262 + 1.34927i) q^{52} +(4.82566 + 6.64195i) q^{53} +(9.00914 - 6.54553i) q^{54} +(-6.36158 - 1.35817i) q^{55} +(8.00498 + 5.81596i) q^{56} -6.66357i q^{57} +(4.12566 - 5.67848i) q^{58} +(-2.24858 + 6.92043i) q^{59} +(-5.26950 + 4.73611i) q^{60} +(-4.75137 - 14.6232i) q^{61} +(-7.72754 - 2.51083i) q^{62} +(-6.23777 - 2.02677i) q^{63} +(3.89501 + 11.9876i) q^{64} +(-2.14865 + 1.93115i) q^{65} +(1.95485 - 6.01642i) q^{66} +(3.34391 - 4.60249i) q^{67} +3.37957i q^{68} +(4.91253 + 3.56917i) q^{69} +(15.6843 + 3.34855i) q^{70} +(-7.89854 + 5.73863i) q^{71} +(3.98908 + 5.49049i) q^{72} +(11.7044 - 3.80298i) q^{73} -9.27620 q^{74} +(-1.91440 + 4.27908i) q^{75} +24.0198 q^{76} +(-8.55561 + 2.77989i) q^{77} +(-1.65138 - 2.27293i) q^{78} +(-8.09824 + 5.88371i) q^{79} +(-0.990024 - 1.10152i) q^{80} +(-1.50599 - 1.09417i) q^{81} +16.1891i q^{82} +(-1.97631 + 2.72016i) q^{83} +(-3.02781 + 9.31864i) q^{84} +(0.907654 + 2.04357i) q^{85} +(0.635057 + 1.95450i) q^{86} +(2.69840 + 0.876763i) q^{87} +(8.85283 + 2.87646i) q^{88} +(-0.570905 - 1.75707i) q^{89} +(9.52140 + 5.50860i) q^{90} +(-1.23459 + 3.79968i) q^{91} +(-12.8656 + 17.7079i) q^{92} -3.28443i q^{93} +(13.3484 + 9.69818i) q^{94} +(14.5244 - 6.45102i) q^{95} +(-3.68880 + 2.68007i) q^{96} +(4.32185 + 5.94852i) q^{97} +(5.65256 - 1.83663i) q^{98} -6.17015 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more