LMFDB - Embedded newform 637.2.bb.a.423.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			423.1
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.a.509.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72056 - 1.72056i) q^{2} +(1.70689 - 0.985473i) q^{3} +3.92067i q^{4} +(-0.227080 - 0.0608458i) q^{5} +(-4.63238 - 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +O(q^{10})$	\(q+(-1.72056 - 1.72056i) q^{2} +(1.70689 - 0.985473i) q^{3} +3.92067i q^{4} +(-0.227080 - 0.0608458i) q^{5} +(-4.63238 - 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +(0.286016 + 0.495394i) q^{10} +(2.76307 + 0.740362i) q^{11} +(3.86372 + 6.69215i) q^{12} +(2.03197 - 2.97844i) q^{13} +(-0.447562 + 0.119924i) q^{15} -3.53033 q^{16} +4.03177 q^{17} +(-2.07916 + 0.557110i) q^{18} +(-1.42261 - 5.30924i) q^{19} +(0.238557 - 0.890305i) q^{20} +(-3.48019 - 6.02787i) q^{22} +6.05019i q^{23} +(2.38402 - 8.89728i) q^{24} +(-4.28226 - 2.47237i) q^{25} +(-8.62072 + 1.62847i) q^{26} +4.16929i q^{27} +(3.54072 - 6.13271i) q^{29} +(0.976395 + 0.563722i) q^{30} +(-0.595317 - 2.22176i) q^{31} +(-0.535124 - 0.535124i) q^{32} +(5.44585 - 1.45921i) q^{33} +(-6.93691 - 6.93691i) q^{34} +(3.00366 + 1.73416i) q^{36} +(7.34878 - 7.34878i) q^{37} +(-6.68720 + 11.5826i) q^{38} +(0.533171 - 7.08632i) q^{39} +(-0.951490 + 0.549343i) q^{40} +(0.0713473 + 0.266272i) q^{41} +(3.91398 - 2.25974i) q^{43} +(-2.90272 + 10.8331i) q^{44} +(-0.147055 + 0.147055i) q^{45} +(10.4097 - 10.4097i) q^{46} +(0.842735 - 3.14513i) q^{47} +(-6.02588 + 3.47904i) q^{48} +(3.11404 + 11.6218i) q^{50} +(6.88178 - 3.97320i) q^{51} +(11.6775 + 7.96668i) q^{52} +(-3.96785 + 6.87251i) q^{53} +(7.17352 - 7.17352i) q^{54} +(-0.582389 - 0.336242i) q^{55} +(-7.66035 - 7.66035i) q^{57} +(-16.6437 + 4.45968i) q^{58} +(0.514009 + 0.514009i) q^{59} +(-0.470182 - 1.75474i) q^{60} +(-1.97520 - 1.14038i) q^{61} +(-2.79839 + 4.84695i) q^{62} +8.90209i q^{64} +(-0.642644 + 0.552707i) q^{65} +(-11.8806 - 6.85927i) q^{66} +(0.688941 - 2.57116i) q^{67} +15.8072i q^{68} +(5.96230 + 10.3270i) q^{69} +(-0.362587 + 1.35319i) q^{71} +(-1.07003 - 3.99339i) q^{72} +(-13.0894 + 3.50729i) q^{73} -25.2881 q^{74} -9.74580 q^{75} +(20.8158 - 5.57758i) q^{76} +(-13.1098 + 11.2751i) q^{78} +(-1.91392 - 3.31501i) q^{79} +(0.801666 + 0.214806i) q^{80} +(5.43566 + 9.41483i) q^{81} +(0.335380 - 0.580895i) q^{82} +(-4.19588 + 4.19588i) q^{83} +(-0.915533 - 0.245316i) q^{85} +(-10.6223 - 2.84623i) q^{86} -13.9571i q^{87} +(11.5776 - 6.68431i) q^{88} +(-2.44076 - 2.44076i) q^{89} +0.506034 q^{90} -23.7208 q^{92} +(-3.20562 - 3.20562i) q^{93} +(-6.86137 + 3.96141i) q^{94} +1.29218i q^{95} +(-1.44075 - 0.386047i) q^{96} +(-2.61723 - 0.701285i) q^{97} +(1.78934 - 1.78934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.72056	−	1.72056i	−1.21662	−	1.21662i	−0.968808	−	0.247814i	$-0.920288\pi$
$2$	−1.72056	−	1.72056i	−1.21662	−	1.21662i	−0.247814	−	0.968808i	$-0.579712\pi$
$3$	1.70689	−	0.985473i	0.985473	−	0.568963i	0.0815547	−	0.996669i	$-0.474011\pi$
$3$	1.70689	−	0.985473i	0.985473	−	0.568963i	0.903918	+	0.427706i	$0.140678\pi$
$4$			3.92067i			1.96034i
$5$	−0.227080	−	0.0608458i	−0.101553	−	0.0272111i	0.207685	−	0.978196i	$-0.433407\pi$
$5$	−0.227080	−	0.0608458i	−0.101553	−	0.0272111i	−0.309238	+	0.950985i	$0.600074\pi$
$6$	−4.63238	−	1.24124i	−1.89116	−	0.506735i
$7$		0			0
$7$		0			0
$8$	3.30464	−	3.30464i	1.16837	−	1.16837i
$9$	0.442313	−	0.766108i	0.147438	−	0.255369i
$10$	0.286016	+	0.495394i	0.0904462	+	0.156657i
$11$	2.76307	+	0.740362i	0.833096	+	0.223227i	0.650064	−	0.759880i	$-0.274742\pi$
$11$	2.76307	+	0.740362i	0.833096	+	0.223227i	0.183032	+	0.983107i	$0.441409\pi$
$12$	3.86372	+	6.69215i	1.11536	+	1.93186i
$13$	2.03197	−	2.97844i	0.563566	−	0.826071i
$13$	2.03197	−	2.97844i	0.563566	−	0.826071i
$14$		0			0
$15$	−0.447562	+	0.119924i	−0.115560	+	0.0309642i
$16$	−3.53033			−0.882582
$17$	4.03177			0.977847			0.488924	−	0.872327i	$-0.337390\pi$
$17$	4.03177			0.977847			0.488924	+	0.872327i	$0.337390\pi$
$18$	−2.07916	+	0.557110i	−0.490064	+	0.131312i
$19$	−1.42261	−	5.30924i	−0.326368	−	1.21802i	−0.912929	−	0.408118i	$-0.866185\pi$
$19$	−1.42261	−	5.30924i	−0.326368	−	1.21802i	0.586561	−	0.809905i	$-0.300482\pi$
$20$	0.238557	−	0.890305i	0.0533429	−	0.199078i
$21$		0			0
$22$	−3.48019	−	6.02787i	−0.741979	−	1.28515i
$23$			6.05019i			1.26155i	0.775965	+	0.630776i	$0.217263\pi$
$23$			6.05019i			1.26155i	−0.775965	+	0.630776i	$0.782737\pi$
$24$	2.38402	−	8.89728i	0.486636	−	1.81615i
$25$	−4.28226	−	2.47237i	−0.856453	−	0.494473i
$26$	−8.62072	+	1.62847i	−1.69066	+	0.319368i
$27$			4.16929i			0.802380i
$28$		0			0
$29$	3.54072	−	6.13271i	0.657495	−	1.13882i	−0.323766	−	0.946137i	$-0.604949\pi$
$29$	3.54072	−	6.13271i	0.657495	−	1.13882i	0.981262	−	0.192679i	$-0.0617175\pi$
$30$	0.976395	+	0.563722i	0.178264	+	0.102921i
$31$	−0.595317	−	2.22176i	−0.106922	−	0.399039i	0.891634	−	0.452757i	$-0.149559\pi$
$31$	−0.595317	−	2.22176i	−0.106922	−	0.399039i	−0.998556	+	0.0537180i	$0.982893\pi$
$32$	−0.535124	−	0.535124i	−0.0945975	−	0.0945975i
$33$	5.44585	−	1.45921i	0.948002	−	0.254016i
$34$	−6.93691	−	6.93691i	−1.18967	−	1.18967i
$35$		0			0
$36$	3.00366	+	1.73416i	0.500610	+	0.289027i
$37$	7.34878	−	7.34878i	1.20813	−	1.20813i	0.236500	−	0.971632i	$-0.424000\pi$
$37$	7.34878	−	7.34878i	1.20813	−	1.20813i	0.971632	−	0.236500i	$-0.0760002\pi$
$38$	−6.68720	+	11.5826i	−1.08481	+	1.87894i
$39$	0.533171	−	7.08632i	0.0853757	−	1.13472i
$40$	−0.951490	+	0.549343i	−0.150444	+	0.0868587i
$41$	0.0713473	+	0.266272i	0.0111426	+	0.0415847i	0.971273	−	0.237967i	$-0.0764809\pi$
$41$	0.0713473	+	0.266272i	0.0111426	+	0.0415847i	−0.960131	+	0.279551i	$0.909814\pi$
$42$		0			0
$43$	3.91398	−	2.25974i	0.596877	−	0.344607i	−0.170935	−	0.985282i	$-0.554679\pi$
$43$	3.91398	−	2.25974i	0.596877	−	0.344607i	0.767812	+	0.640675i	$0.221345\pi$
$44$	−2.90272	+	10.8331i	−0.437601	+	1.63315i
$45$	−0.147055	+	0.147055i	−0.0219216	+	0.0219216i
$46$	10.4097	−	10.4097i	1.53483	−	1.53483i
$47$	0.842735	−	3.14513i	0.122926	−	0.458764i	−0.876832	−	0.480797i	$-0.840347\pi$
$47$	0.842735	−	3.14513i	0.122926	−	0.458764i	0.999757	+	0.0220331i	$0.00701391\pi$
$48$	−6.02588	+	3.47904i	−0.869760	+	0.502156i
$49$		0			0
$50$	3.11404	+	11.6218i	0.440392	+	1.64357i
$51$	6.88178	−	3.97320i	0.963642	−	0.556359i
$52$	11.6775	+	7.96668i	1.61938	+	1.10478i
$53$	−3.96785	+	6.87251i	−0.545026	+	0.944012i	0.453580	+	0.891216i	$0.350147\pi$
$53$	−3.96785	+	6.87251i	−0.545026	+	0.944012i	−0.998605	+	0.0527963i	$0.983187\pi$
$54$	7.17352	−	7.17352i	0.976193	−	0.976193i
$55$	−0.582389	−	0.336242i	−0.0785293	−	0.0453389i
$56$		0			0
$57$	−7.66035	−	7.66035i	−1.01464	−	1.01464i
$58$	−16.6437	+	4.45968i	−2.18543	+	0.585584i
$59$	0.514009	+	0.514009i	0.0669183	+	0.0669183i	0.739774	−	0.672856i	$-0.234932\pi$
$59$	0.514009	+	0.514009i	0.0669183	+	0.0669183i	−0.672856	+	0.739774i	$0.734932\pi$
$60$	−0.470182	−	1.75474i	−0.0607002	−	0.226536i
$61$	−1.97520	−	1.14038i	−0.252899	−	0.146011i	0.368192	−	0.929750i	$-0.379977\pi$
$61$	−1.97520	−	1.14038i	−0.252899	−	0.146011i	−0.621091	+	0.783739i	$0.713310\pi$
$62$	−2.79839	+	4.84695i	−0.355396	+	0.615563i
$63$		0			0
$64$			8.90209i			1.11276i
$65$	−0.642644	+	0.552707i	−0.0797102	+	0.0685548i
$66$	−11.8806	−	6.85927i	−1.46240	−	0.844318i
$67$	0.688941	−	2.57116i	0.0841676	−	0.314118i	−0.910988	−	0.412434i	$-0.864679\pi$
$67$	0.688941	−	2.57116i	0.0841676	−	0.314118i	0.995155	+	0.0983159i	$0.0313456\pi$
$68$			15.8072i			1.91691i
$69$	5.96230	+	10.3270i	0.717776	+	1.24323i
$70$		0			0
$71$	−0.362587	+	1.35319i	−0.0430312	+	0.160595i	−0.984098	−	0.177626i	$-0.943158\pi$
$71$	−0.362587	+	1.35319i	−0.0430312	+	0.160595i	0.941067	+	0.338220i	$0.109825\pi$
$72$	−1.07003	−	3.99339i	−0.126104	−	0.470626i
$73$	−13.0894	+	3.50729i	−1.53200	+	0.410497i	−0.923670	−	0.383190i	$-0.874826\pi$
$73$	−13.0894	+	3.50729i	−1.53200	+	0.410497i	−0.608326	+	0.793687i	$0.708159\pi$
$74$	−25.2881			−2.93968
$75$	−9.74580			−1.12535
$76$	20.8158	−	5.57758i	2.38774	−	0.639792i
$77$		0			0
$78$	−13.1098	+	11.2751i	−1.48439	+	1.27665i
$79$	−1.91392	−	3.31501i	−0.215333	−	0.372967i	0.738043	−	0.674754i	$-0.235750\pi$
$79$	−1.91392	−	3.31501i	−0.215333	−	0.372967i	−0.953375	+	0.301787i	$0.902417\pi$
$80$	0.801666	+	0.214806i	0.0896290	+	0.0240160i
$81$	5.43566	+	9.41483i	0.603962	+	1.04609i
$82$	0.335380	−	0.580895i	0.0370365	−	0.0641491i
$83$	−4.19588	+	4.19588i	−0.460558	+	0.460558i	−0.898838	−	0.438280i	$-0.855588\pi$
$83$	−4.19588	+	4.19588i	−0.460558	+	0.460558i	0.438280	+	0.898838i	$0.355588\pi$
$84$		0			0
$85$	−0.915533	−	0.245316i	−0.0993035	−	0.0266083i
$86$	−10.6223	−	2.84623i	−1.14543	−	0.306917i
$87$		−	13.9571i		−	1.49636i
$88$	11.5776	−	6.68431i	1.23417	−	0.712550i
$89$	−2.44076	−	2.44076i	−0.258720	−	0.258720i	0.565813	−	0.824533i	$-0.308562\pi$
$89$	−2.44076	−	2.44076i	−0.258720	−	0.258720i	−0.824533	+	0.565813i	$0.808562\pi$
$90$	0.506034			0.0533407
$91$		0			0
$92$	−23.7208			−2.47307
$93$	−3.20562	−	3.20562i	−0.332407	−	0.332407i
$94$	−6.86137	+	3.96141i	−0.707696	+	0.408589i
$95$			1.29218i			0.132575i
$96$	−1.44075	−	0.386047i	−0.147046	−	0.0394008i
$97$	−2.61723	−	0.701285i	−0.265739	−	0.0712047i	0.123489	−	0.992346i	$-0.460592\pi$
$97$	−2.61723	−	0.701285i	−0.265739	−	0.0712047i	−0.389228	+	0.921141i	$0.627258\pi$
$98$		0			0
$99$	1.78934	−	1.78934i	0.179835	−	0.179835i
$100$	9.69334	−	16.7894i	0.969334	−	1.67894i
$101$	6.89116	+	11.9358i	0.685697	+	1.18766i	0.973217	+	0.229887i	$0.0738356\pi$
$101$	6.89116	+	11.9358i	0.685697	+	1.18766i	−0.287521	+	0.957774i	$0.592831\pi$
$102$	−18.6767	−	5.00440i	−1.84927	−	0.495509i
$103$	4.01282	+	6.95040i	0.395395	+	0.684843i	0.993151	−	0.116834i	$-0.0372745\pi$
$103$	4.01282	+	6.95040i	0.395395	+	0.684843i	−0.597757	+	0.801677i	$0.703941\pi$
$104$	−3.12775	−	16.5576i	−0.306701	−	1.62360i
$105$		0			0
$106$	18.6515	−	4.99766i	1.81160	−	0.485415i
$107$	4.17877			0.403977			0.201988	−	0.979388i	$-0.435260\pi$
$107$	4.17877			0.403977			0.201988	+	0.979388i	$0.435260\pi$
$108$	−16.3464			−1.57293
$109$	13.6069	−	3.64596i	1.30331	−	0.349220i	0.460607	−	0.887604i	$-0.347632\pi$
$109$	13.6069	−	3.64596i	1.30331	−	0.349220i	0.842699	+	0.538385i	$0.180965\pi$
$110$	0.423510	+	1.58056i	0.0403801	+	0.150701i
$111$	5.30152	−	19.7856i	0.503198	−	1.87796i
$112$		0			0
$113$	2.30697	+	3.99579i	0.217022	+	0.375892i	0.953896	−	0.300137i	$-0.0970325\pi$
$113$	2.30697	+	3.99579i	0.217022	+	0.375892i	−0.736874	+	0.676030i	$0.763699\pi$
$114$			26.3602i			2.46886i
$115$	0.368129	−	1.37388i	0.0343282	−	0.128115i
$116$	24.0443	+	13.8820i	2.23246	+	1.28891i
$117$	−1.38304	−	2.87411i	−0.127862	−	0.265712i
$118$		−	1.76877i		−	0.162828i
$119$		0			0
$120$	−1.08272	+	1.87533i	−0.0988388	+	0.171194i
$121$	−2.43987	−	1.40866i	−0.221807	−	0.128060i
$122$	1.43636	+	5.36056i	0.130042	+	0.485322i
$123$	0.384185	+	0.384185i	0.0346408	+	0.0346408i
$124$	8.71077	−	2.33404i	0.782251	−	0.209603i
$125$	1.65315	+	1.65315i	0.147862	+	0.147862i
$126$		0			0
$127$	3.63943	+	2.10123i	0.322947	+	0.186454i	0.652705	−	0.757612i	$-0.273634\pi$
$127$	3.63943	+	2.10123i	0.322947	+	0.186454i	−0.329758	+	0.944065i	$0.606967\pi$
$128$	14.2463	−	14.2463i	1.25921	−	1.25921i
$129$	4.45382	−	7.71425i	0.392137	−	0.679202i
$130$	2.05668	+	0.154743i	0.180382	+	0.0135719i
$131$	11.9149	−	6.87908i	1.04101	−	0.601028i	0.120891	−	0.992666i	$-0.461425\pi$
$131$	11.9149	−	6.87908i	1.04101	−	0.601028i	0.920119	+	0.391638i	$0.128092\pi$
$132$	5.72109	+	21.3514i	0.497957	+	1.85840i
$133$		0			0
$134$	−5.60922	+	3.23848i	−0.484562	+	0.279762i
$135$	0.253684	−	0.946761i	0.0218336	−	0.0814842i
$136$	13.3235	−	13.3235i	1.14248	−	1.14248i
$137$	−9.75631	+	9.75631i	−0.833538	+	0.833538i	−0.987999	−	0.154461i	$-0.950636\pi$
$137$	−9.75631	+	9.75631i	−0.833538	+	0.833538i	0.154461	+	0.987999i	$0.450636\pi$
$138$	7.50975	−	28.0268i	0.639272	−	2.38580i
$139$	−12.9252	+	7.46236i	−1.09630	+	0.632949i	−0.935247	−	0.353997i	$-0.884822\pi$
$139$	−12.9252	+	7.46236i	−1.09630	+	0.632949i	−0.161053	+	0.986946i	$0.551489\pi$
$140$		0			0
$141$	−1.66098	−	6.19888i	−0.139880	−	0.522040i
$142$	2.95211	−	1.70440i	0.247735	−	0.143030i
$143$	7.81959	−	6.72524i	0.653907	−	0.562393i
$144$	−1.56151	+	2.70461i	−0.130126	+	0.225384i
$145$	−1.17718	+	1.17718i	−0.0977592	+	0.0977592i
$146$	28.5556	+	16.4866i	2.36328	+	1.36444i
$147$		0			0
$148$	28.8121	+	28.8121i	2.36834	+	2.36834i
$149$	10.2136	−	2.73674i	0.836735	−	0.224202i	0.185085	−	0.982723i	$-0.440744\pi$
$149$	10.2136	−	2.73674i	0.836735	−	0.224202i	0.651650	+	0.758520i	$0.274077\pi$
$150$	16.7683	+	16.7683i	1.36912	+	1.36912i
$151$	−1.16428	−	4.34514i	−0.0947476	−	0.353603i	0.902233	−	0.431248i	$-0.141927\pi$
$151$	−1.16428	−	4.34514i	−0.0947476	−	0.353603i	−0.996981	+	0.0776451i	$0.975260\pi$
$152$	−22.2463	−	12.8439i	−1.80442	−	1.04178i
$153$	1.78330	−	3.08877i	0.144171	−	0.249712i
$154$		0			0
$155$			0.540738i			0.0434331i
$156$	27.7831	+	2.09039i	2.22443	+	0.167365i
$157$	−11.2646	−	6.50360i	−0.899010	−	0.519044i	−0.0221312	−	0.999755i	$-0.507045\pi$
$157$	−11.2646	−	6.50360i	−0.899010	−	0.519044i	−0.876879	+	0.480711i	$0.840378\pi$
$158$	−2.41066	+	8.99670i	−0.191782	+	0.715739i
$159$			15.6408i			1.24040i
$160$	0.0889558	+	0.154076i	0.00703257	+	0.0121808i
$161$		0			0
$162$	6.84642	−	25.5512i	0.537906	−	2.00749i
$163$	4.24621	+	15.8471i	0.332589	+	1.24124i	0.906459	+	0.422293i	$0.138775\pi$
$163$	4.24621	+	15.8471i	0.332589	+	1.24124i	−0.573870	+	0.818946i	$0.694559\pi$
$164$	−1.04396	+	0.279729i	−0.0815199	+	0.0218432i
$165$	−1.32543			−0.103185
$166$	14.4386			1.12065
$167$	−9.84852	+	2.63890i	−0.762101	+	0.204204i	−0.618879	−	0.785486i	$-0.712413\pi$
$167$	−9.84852	+	2.63890i	−0.762101	+	0.204204i	−0.143222	+	0.989691i	$0.545746\pi$
$168$		0			0
$169$	−4.74221	−	12.1042i	−0.364786	−	0.931091i
$170$	1.15315	+	1.99731i	0.0884426	+	0.153187i
$171$	−4.69669	−	1.25847i	−0.359165	−	0.0962380i
$172$	8.85970	+	15.3455i	0.675546	+	1.17008i
$173$	−7.48809	+	12.9698i	−0.569309	+	0.986072i	0.427325	+	0.904098i	$0.359456\pi$
$173$	−7.48809	+	12.9698i	−0.569309	+	0.986072i	−0.996634	+	0.0819744i	$0.973877\pi$
$174$	−24.0141	+	24.0141i	−1.82051	+	1.82051i
$175$		0			0
$176$	−9.75453	−	2.61372i	−0.735276	−	0.197017i
$177$	1.38390	+	0.370814i	0.104020	+	0.0278721i
$178$			8.39897i			0.629529i
$179$	7.95325	−	4.59181i	0.594454	−	0.343208i	−0.172403	−	0.985027i	$-0.555153\pi$
$179$	7.95325	−	4.59181i	0.594454	−	0.343208i	0.766857	+	0.641819i	$0.221820\pi$
$180$	−0.576554	−	0.576554i	−0.0429738	−	0.0429738i
$181$	12.8202			0.952919			0.476459	−	0.879197i	$-0.341920\pi$
$181$	12.8202			0.952919			0.476459	+	0.879197i	$0.341920\pi$
$182$		0			0
$183$	−4.49527			−0.332300
$184$	19.9937	+	19.9937i	1.47395	+	1.47395i
$185$	−2.11590	+	1.22162i	−0.155564	+	0.0898150i
$186$			11.0309i			0.808828i
$187$	11.1400	+	2.98497i	0.814641	+	0.218282i
$188$	12.3310	+	3.30409i	0.899332	+	0.240975i
$189$		0			0
$190$	2.22328	−	2.22328i	0.161294	−	0.161294i
$191$	2.69581	−	4.66928i	0.195062	−	0.337857i	−0.751859	−	0.659324i	$-0.770843\pi$
$191$	2.69581	−	4.66928i	0.195062	−	0.337857i	0.946921	+	0.321467i	$0.104176\pi$
$192$	8.77276	+	15.1949i	0.633120	+	1.09660i
$193$	3.22754	+	0.864817i	0.232323	+	0.0622509i	0.373102	−	0.927790i	$-0.378294\pi$
$193$	3.22754	+	0.864817i	0.232323	+	0.0622509i	−0.140779	+	0.990041i	$0.544961\pi$
$194$	3.29650	+	5.70971i	0.236675	+	0.409933i
$195$	−0.552245	+	1.57672i	−0.0395471	+	0.112911i
$196$		0			0
$197$	3.67856	−	0.985668i	0.262087	−	0.0702259i	−0.125383	−	0.992108i	$-0.540016\pi$
$197$	3.67856	−	0.985668i	0.262087	−	0.0702259i	0.387470	+	0.921882i	$0.373349\pi$
$198$	−6.15733			−0.437583
$199$	22.2669			1.57846			0.789229	−	0.614099i	$-0.210480\pi$
$199$	22.2669			1.57846			0.789229	+	0.614099i	$0.210480\pi$
$200$	−22.3216	+	5.98106i	−1.57838	+	0.422925i
$201$	−1.35787	−	5.06762i	−0.0957765	−	0.357443i
$202$	8.67969	−	32.3931i	0.610701	−	2.27917i
$203$		0			0
$204$	15.5776	+	26.9812i	1.09065	+	1.88906i
$205$		−	0.0648061i		−	0.00452626i
$206$	5.05430	−	18.8629i	0.352150	−	1.31424i
$207$	4.63510	+	2.67608i	0.322162	+	0.186000i
$208$	−7.17351	+	10.5149i	−0.497394	+	0.729075i
$209$		−	15.7230i		−	1.08759i
$210$		0			0
$211$	−7.76031	+	13.4412i	−0.534242	+	0.925334i	0.464958	+	0.885333i	$0.346069\pi$
$211$	−7.76031	+	13.4412i	−0.534242	+	0.925334i	−0.999200	+	0.0400009i	$0.987264\pi$
$212$	−26.9449	−	15.5566i	−1.85058	−	1.06843i
$213$	0.714640	+	2.66707i	0.0489663	+	0.182745i
$214$	−7.18983	−	7.18983i	−0.491487	−	0.491487i
$215$	−1.02628	+	0.274992i	−0.0699919	+	0.0187543i
$216$	13.7780	+	13.7780i	0.937473	+	0.937473i
$217$		0			0
$218$	−29.6846	−	17.1384i	−2.01050	−	1.16076i
$219$	−18.8858	+	18.8858i	−1.27618	+	1.27618i
$220$	1.31830	−	2.28336i	0.0888795	−	0.153944i
$221$	8.19242	−	12.0084i	0.551082	−	0.807771i
$222$	−43.1639	+	24.9207i	−2.89697	+	1.67257i
$223$	−1.32002	−	4.92639i	−0.0883952	−	0.329895i	0.907540	−	0.419965i	$-0.137958\pi$
$223$	−1.32002	−	4.92639i	−0.0883952	−	0.329895i	−0.995935	+	0.0900697i	$0.971291\pi$
$224$		0			0
$225$	−3.78820	+	2.18712i	−0.252547	+	0.145808i
$226$	2.90572	−	10.8443i	0.193286	−	0.721352i
$227$	7.63959	−	7.63959i	0.507057	−	0.507057i	−0.406565	−	0.913622i	$-0.633273\pi$
$227$	7.63959	−	7.63959i	0.507057	−	0.507057i	0.913622	+	0.406565i	$0.133273\pi$
$228$	30.0337	−	30.0337i	1.98903	−	1.98903i
$229$	−3.42227	+	12.7721i	−0.226150	+	0.844002i	0.755791	+	0.654813i	$0.227253\pi$
$229$	−3.42227	+	12.7721i	−0.226150	+	0.844002i	−0.981941	+	0.189189i	$0.939414\pi$
$230$	−2.99723	+	1.73045i	−0.197631	+	0.114103i
$231$		0			0
$232$	−8.56558	−	31.9672i	−0.562358	−	2.09875i
$233$	−10.5909	+	6.11465i	−0.693832	+	0.400584i	−0.805046	−	0.593212i	$-0.797859\pi$
$233$	−10.5909	+	6.11465i	−0.693832	+	0.400584i	0.111214	+	0.993796i	$0.464526\pi$
$234$	−2.56547	+	7.32470i	−0.167710	+	0.478830i
$235$	−0.382736	+	0.662918i	−0.0249670	+	0.0432440i
$236$	−2.01526	+	2.01526i	−0.131182	+	0.131182i
$237$	−6.53370	−	3.77223i	−0.424409	−	0.245033i
$238$		0			0
$239$	4.36940	+	4.36940i	0.282633	+	0.282633i	0.834158	−	0.551525i	$-0.185954\pi$
$239$	4.36940	+	4.36940i	0.282633	+	0.282633i	−0.551525	+	0.834158i	$0.685954\pi$
$240$	1.58004	−	0.423370i	0.101991	−	0.0273284i
$241$	8.64343	+	8.64343i	0.556772	+	0.556772i	0.928387	−	0.371615i	$-0.121196\pi$
$241$	8.64343	+	8.64343i	0.556772	+	0.556772i	−0.371615	+	0.928387i	$0.621196\pi$
$242$	1.77427	+	6.62165i	0.114054	+	0.425656i
$243$	7.72400	+	4.45945i	0.495495	+	0.286074i
$244$	4.47107	−	7.74412i	0.286231	−	0.495767i
$245$		0			0
$246$		−	1.32203i		−	0.0842896i
$247$	−18.7040	−	6.55106i	−1.19010	−	0.416834i
$248$	−9.30940	−	5.37479i	−0.591148	−	0.341299i
$249$	−3.02698	+	11.2968i	−0.191827	+	0.715908i
$250$		−	5.68870i		−	0.359785i
$251$	−13.4971	−	23.3777i	−0.851929	−	1.47558i	−0.879465	−	0.475964i	$-0.842099\pi$
$251$	−13.4971	−	23.3777i	−0.851929	−	1.47558i	0.0275356	−	0.999621i	$-0.491234\pi$
$252$		0			0
$253$	−4.47933	+	16.7171i	−0.281613	+	1.05099i
$254$	−2.64658	−	9.87716i	−0.166061	−	0.619748i
$255$	−1.80447	+	0.483505i	−0.113000	+	0.0302783i
$256$	−31.2193			−1.95121
$257$	−19.2922			−1.20341			−0.601707	−	0.798717i	$-0.705513\pi$
$257$	−19.2922			−1.20341			−0.601707	+	0.798717i	$0.705513\pi$
$258$	−20.9359	+	5.60977i	−1.30341	+	0.349249i
$259$		0			0
$260$	−2.16698	−	2.51960i	−0.134391	−	0.156259i
$261$	−3.13221	−	5.42515i	−0.193879	−	0.335808i
$262$	−32.3362	−	8.66447i	−1.99774	−	0.535293i
$263$	9.95932	+	17.2501i	0.614118	+	1.06368i	0.990539	+	0.137235i	$0.0438215\pi$
$263$	9.95932	+	17.2501i	0.614118	+	1.06368i	−0.376420	+	0.926449i	$0.622845\pi$
$264$	13.1744	−	22.8187i	0.810829	−	1.40440i
$265$	1.31918	−	1.31918i	0.0810367	−	0.0810367i
$266$		0			0
$267$	−6.57142	−	1.76081i	−0.402164	−	0.107760i
$268$	10.0807	+	2.70111i	0.615776	+	0.164997i
$269$		−	26.2749i		−	1.60201i	−0.598657	−	0.801006i	$-0.704299\pi$
$269$		−	26.2749i		−	1.60201i	0.598657	−	0.801006i	$-0.295701\pi$
$270$	−2.06544	+	1.19248i	−0.125699	+	0.0725722i
$271$	−3.79858	−	3.79858i	−0.230747	−	0.230747i	0.582257	−	0.813005i	$-0.302170\pi$
$271$	−3.79858	−	3.79858i	−0.230747	−	0.230747i	−0.813005	+	0.582257i	$0.802170\pi$
$272$	−14.2335			−0.863031
$273$		0			0
$274$	33.5727			2.02820
$275$	−10.0017	−	10.0017i	−0.603127	−	0.603127i
$276$	−40.4888	+	23.3762i	−2.43714	+	1.40708i
$277$		−	6.51116i		−	0.391218i	−0.980682	−	0.195609i	$-0.937332\pi$
$277$		−	6.51116i		−	0.391218i	0.980682	−	0.195609i	$-0.0626683\pi$
$278$	35.0780	+	9.39913i	2.10384	+	0.563722i
$279$	−1.96542	−	0.526633i	−0.117667	−	0.0315287i
$280$		0			0
$281$	−11.1540	+	11.1540i	−0.665390	+	0.665390i	−0.956645	−	0.291255i	$-0.905927\pi$
$281$	−11.1540	+	11.1540i	−0.665390	+	0.665390i	0.291255	+	0.956645i	$0.405927\pi$
$282$	−7.80773	+	13.5234i	−0.464944	+	0.805306i
$283$	−1.18900	−	2.05940i	−0.0706784	−	0.122419i	0.828520	−	0.559959i	$-0.189183\pi$
$283$	−1.18900	−	2.05940i	−0.0706784	−	0.122419i	−0.899199	+	0.437540i	$0.855850\pi$
$284$	−5.30543	−	1.42159i	−0.314819	−	0.0843556i
$285$	1.27341	+	2.20561i	0.0754303	+	0.130649i
$286$	−25.0253	−	1.88289i	−1.47978	−	0.111338i
$287$		0			0
$288$	−0.646655	+	0.173271i	−0.0381045	+	0.0102101i
$289$	−0.744846			−0.0438145
$290$	4.05081			0.237872
$291$	−5.15842	+	1.38219i	−0.302392	+	0.0810256i
$292$	−13.7509	−	51.3192i	−0.804712	−	3.00323i
$293$	−8.69014	+	32.4321i	−0.507684	+	1.89470i	−0.0653221	+	0.997864i	$0.520807\pi$
$293$	−8.69014	+	32.4321i	−0.507684	+	1.89470i	−0.442361	+	0.896837i	$0.645859\pi$
$294$		0			0
$295$	−0.0854457	−	0.147996i	−0.00497484	−	0.00861668i
$296$		−	48.5701i		−	2.82308i
$297$	−3.08678	+	11.5200i	−0.179113	+	0.668459i
$298$	−22.2820	−	12.8645i	−1.29076	−	0.745220i
$299$	18.0201	+	12.2938i	1.04213	+	0.710968i
$300$		−	38.2101i		−	2.20606i
$301$		0			0
$302$	−5.47288	+	9.47931i	−0.314929	+	0.545473i
$303$	23.5249	+	13.5821i	1.35147	+	0.780272i
$304$	5.02227	+	18.7434i	0.288047	+	1.07501i
$305$	0.379141	+	0.379141i	0.0217095	+	0.0217095i
$306$	−8.38271	+	2.24614i	−0.479208	+	0.128403i
$307$	19.1548	+	19.1548i	1.09322	+	1.09322i	0.995183	+	0.0980380i	$0.0312567\pi$
$307$	19.1548	+	19.1548i	1.09322	+	1.09322i	0.0980380	+	0.995183i	$0.468743\pi$
$308$		0			0
$309$	13.6989	+	7.90904i	0.779301	+	0.449930i
$310$	0.930374	−	0.930374i	0.0528417	−	0.0528417i
$311$	−16.5705	+	28.7009i	−0.939627	+	1.62748i	−0.173458	+	0.984841i	$0.555494\pi$
$311$	−16.5705	+	28.7009i	−0.939627	+	1.62748i	−0.766168	+	0.642640i	$0.777839\pi$
$312$	−21.6558	−	25.1796i	−1.22602	−	1.42552i
$313$	1.14049	−	0.658460i	0.0644641	−	0.0372183i	−0.467422	−	0.884035i	$-0.654817\pi$
$313$	1.14049	−	0.658460i	0.0644641	−	0.0372183i	0.531886	+	0.846816i	$0.321484\pi$
$314$	8.19154	+	30.5712i	0.462275	+	1.72523i
$315$		0			0
$316$	12.9971	−	7.50385i	0.731142	−	0.422125i
$317$	2.24279	−	8.37022i	0.125968	−	0.470118i	−0.873904	−	0.486098i	$-0.838420\pi$
$317$	2.24279	−	8.37022i	0.125968	−	0.470118i	0.999872	+	0.0159793i	$0.00508657\pi$
$318$	26.9110	−	26.9110i	1.50909	−	1.50909i
$319$	14.3237	−	14.3237i	0.801972	−	0.801972i
$320$	0.541655	−	2.02148i	0.0302794	−	0.113004i
$321$	7.13269	−	4.11806i	0.398108	−	0.229848i
$322$		0			0
$323$	−5.73562	−	21.4056i	−0.319139	−	1.19104i
$324$	−36.9125	+	21.3114i	−2.05069	+	1.18397i
$325$	−16.0652	+	7.73070i	−0.891138	+	0.428822i
$326$	19.9600	−	34.5718i	1.10548	−	1.91475i
$327$	19.6325	−	19.6325i	1.08568	−	1.08568i
$328$	1.11571	+	0.644155i	0.0616047	+	0.0355675i
$329$		0			0
$330$	2.28049	+	2.28049i	0.125537	+	0.125537i
$331$	−22.5870	+	6.05217i	−1.24149	+	0.332657i	−0.819045	−	0.573729i	$-0.805496\pi$
$331$	−22.5870	+	6.05217i	−1.24149	+	0.332657i	−0.422449	+	0.906387i	$0.638829\pi$
$332$	−16.4507	−	16.4507i	−0.902848	−	0.902848i
$333$	−2.37950	−	8.88041i	−0.130396	−	0.486644i
$334$	21.4854	+	12.4046i	1.17563	+	0.678749i
$335$	−0.312889	+	0.541940i	−0.0170950	+	0.0296094i
$336$		0			0
$337$			5.08165i			0.276815i	0.990375	+	0.138407i	$0.0441984\pi$
$337$			5.08165i			0.276815i	−0.990375	+	0.138407i	$0.955802\pi$
$338$	−12.6667	+	28.9853i	−0.688980	+	1.57659i
$339$	7.87549	+	4.54691i	0.427738	+	0.246955i
$340$	0.961805	−	3.58951i	0.0521612	−	0.194668i
$341$		−	6.57961i		−	0.356306i
$342$	5.91567	+	10.2462i	0.319883	+	0.554053i
$343$		0			0
$344$	5.46668	−	20.4019i	0.294744	−	1.10000i
$345$	−0.725562	−	2.70783i	−0.0390630	−	0.145785i
$346$	35.1990	−	9.43155i	1.89231	−	0.507043i
$347$	0.683981			0.0367180			0.0183590	−	0.999831i	$-0.494156\pi$
$347$	0.683981			0.0367180			0.0183590	+	0.999831i	$0.494156\pi$
$348$	54.7214			2.93337
$349$	−5.07510	+	1.35987i	−0.271664	+	0.0727921i	−0.392079	−	0.919932i	$-0.628244\pi$
$349$	−5.07510	+	1.35987i	−0.271664	+	0.0727921i	0.120415	+	0.992724i	$0.461577\pi$
$350$		0			0
$351$	12.4180	+	8.47186i	0.662822	+	0.452194i
$352$	−1.08240	−	1.87477i	−0.0576920	−	0.0999256i
$353$	−20.9733	−	5.61978i	−1.11630	−	0.299111i	−0.346913	−	0.937897i	$-0.612770\pi$
$353$	−20.9733	−	5.61978i	−1.11630	−	0.299111i	−0.769384	+	0.638787i	$0.779437\pi$
$354$	−1.74307	−	3.01909i	−0.0926434	−	0.160463i
$355$	0.164672	−	0.285221i	0.00873991	−	0.0151380i
$356$	9.56943	−	9.56943i	0.507179	−	0.507179i
$357$		0			0
$358$	−21.5846	−	5.78356i	−1.14078	−	0.305671i
$359$	13.7143	+	3.67473i	0.723812	+	0.193945i	0.601872	−	0.798593i	$-0.294422\pi$
$359$	13.7143	+	3.67473i	0.723812	+	0.193945i	0.121940	+	0.992537i	$0.461088\pi$
$360$			0.971926i			0.0512250i
$361$	−9.70976	+	5.60593i	−0.511040	+	0.295049i
$362$	−22.0580	−	22.0580i	−1.15934	−	1.15934i
$363$	−5.55279			−0.291446
$364$		0			0
$365$	3.18574			0.166749
$366$	7.73439	+	7.73439i	0.404283	+	0.404283i
$367$	−2.60256	+	1.50259i	−0.135853	+	0.0784346i	−0.566386	−	0.824140i	$-0.691659\pi$
$367$	−2.60256	+	1.50259i	−0.135853	+	0.0784346i	0.430533	+	0.902575i	$0.358326\pi$
$368$		−	21.3592i		−	1.11342i
$369$	0.235551	+	0.0631157i	0.0122623	+	0.00328567i
$370$	5.74241	+	1.53867i	0.298534	+	0.0799918i
$371$		0			0
$372$	12.5682	−	12.5682i	0.651630	−	0.651630i
$373$	13.0925	−	22.6769i	0.677906	−	1.17417i	−0.297705	−	0.954658i	$-0.596221\pi$
$373$	13.0925	−	22.6769i	0.677906	−	1.17417i	0.975610	−	0.219509i	$-0.0704456\pi$
$374$	−14.0313	−	24.3030i	−0.725543	−	1.25668i
$375$	4.45088	+	1.19261i	0.229843	+	0.0615861i
$376$	−7.60858	−	13.1784i	−0.392383	−	0.679627i
$377$	−11.0713	−	23.0073i	−0.570200	−	1.18494i
$378$		0			0
$379$	−5.54850	+	1.48672i	−0.285007	+	0.0763675i	−0.398491	−	0.917172i	$-0.630466\pi$
$379$	−5.54850	+	1.48672i	−0.285007	+	0.0763675i	0.113483	+	0.993540i	$0.463799\pi$
$380$	−5.06622			−0.259892
$381$	8.28280			0.424341
$382$	−12.6721	+	3.39548i	−0.648361	+	0.173728i
$383$	4.20381	+	15.6888i	0.214804	+	0.801661i	0.986235	+	0.165348i	$0.0528747\pi$
$383$	4.20381	+	15.6888i	0.214804	+	0.801661i	−0.771431	+	0.636313i	$0.780459\pi$
$384$	10.2775	−	38.3563i	0.524474	−	1.95736i
$385$		0			0
$386$	−4.06521	−	7.04116i	−0.206914	−	0.358385i
$387$		−	3.99805i		−	0.203232i
$388$	2.74951	−	10.2613i	0.139585	−	0.520939i
$389$	−8.04726	−	4.64609i	−0.408012	−	0.235566i	0.281923	−	0.959437i	$-0.409028\pi$
$389$	−8.04726	−	4.64609i	−0.408012	−	0.235566i	−0.689935	+	0.723871i	$0.742361\pi$
$390$	3.66301	−	1.76267i	0.185484	−	0.0892562i
$391$			24.3930i			1.23361i
$392$		0			0
$393$	13.5583	−	23.4836i	0.683925	−	1.18459i
$394$	−8.02510	−	4.63330i	−0.404299	−	0.233422i
$395$	0.232908	+	0.869225i	0.0117189	+	0.0437355i
$396$	7.01540	+	7.01540i	0.352537	+	0.352537i
$397$	−18.2054	+	4.87812i	−0.913703	+	0.244826i	−0.684892	−	0.728645i	$-0.740151\pi$
$397$	−18.2054	+	4.87812i	−0.913703	+	0.244826i	−0.228811	+	0.973471i	$0.573484\pi$
$398$	−38.3116	−	38.3116i	−1.92039	−	1.92039i
$399$		0			0
$400$	15.1178	+	8.72826i	0.755890	+	0.436413i
$401$	−26.4901	+	26.4901i	−1.32285	+	1.32285i	−0.411393	+	0.911458i	$0.634958\pi$
$401$	−26.4901	+	26.4901i	−1.32285	+	1.32285i	−0.911458	+	0.411393i	$0.865042\pi$
$402$	−6.38287	+	11.0555i	−0.318349	+	0.551396i
$403$	−7.82703	−	2.74142i	−0.389892	−	0.136560i
$404$	−46.7965	+	27.0180i	−2.32822	+	1.34420i
$405$	−0.661474	−	2.46866i	−0.0328689	−	0.122668i
$406$		0			0
$407$	25.7459	−	14.8644i	1.27618	−	0.736801i
$408$	9.61181	−	35.8718i	0.475856	−	1.77592i
$409$	−14.4159	+	14.4159i	−0.712820	+	0.712820i	−0.967124	−	0.254304i	$-0.918154\pi$
$409$	−14.4159	+	14.4159i	−0.712820	+	0.712820i	0.254304	+	0.967124i	$0.418154\pi$
$410$	−0.111503	+	0.111503i	−0.00550674	+	0.00550674i
$411$	−7.03836	+	26.2675i	−0.347177	+	1.29568i
$412$	−27.2502	+	15.7329i	−1.34252	+	0.775106i
$413$		0			0
$414$	−3.37062	−	12.5793i	−0.165657	−	0.618241i
$415$	1.20810	−	0.697498i	0.0593034	−	0.0342388i
$416$	−2.68119	+	0.506481i	−0.131456	+	0.0248323i
$417$	−14.7079	+	25.4748i	−0.720249	+	1.24751i
$418$	−27.0525	+	27.0525i	−1.32318	+	1.32318i
$419$	9.48347	+	5.47529i	0.463298	+	0.267485i	0.713430	−	0.700727i	$-0.247141\pi$
$419$	9.48347	+	5.47529i	0.463298	+	0.267485i	−0.250132	+	0.968212i	$0.580474\pi$
$420$		0			0
$421$	−7.99908	−	7.99908i	−0.389852	−	0.389852i	0.484783	−	0.874634i	$-0.338899\pi$
$421$	−7.99908	−	7.99908i	−0.389852	−	0.389852i	−0.874634	+	0.484783i	$0.838899\pi$
$422$	36.4786	−	9.77441i	1.77575	−	0.475811i
$423$	−2.03676	−	2.03676i	−0.0990305	−	0.0990305i
$424$	9.59886	+	35.8235i	0.466162	+	1.73974i
$425$	−17.2651	−	9.96801i	−0.837480	−	0.483519i
$426$	3.35928	−	5.81845i	0.162758	−	0.281905i
$427$		0			0
$428$			16.3836i			0.791930i
$429$	6.71962	−	19.1852i	0.324426	−	0.926271i
$430$	2.23892	+	1.29264i	0.107970	+	0.0623368i
$431$	−4.52862	+	16.9010i	−0.218136	+	0.814095i	0.766903	+	0.641763i	$0.221797\pi$
$431$	−4.52862	+	16.9010i	−0.218136	+	0.814095i	−0.985039	+	0.172332i	$0.944870\pi$
$432$		−	14.7190i		−	0.708166i
$433$	3.05668	+	5.29433i	0.146895	+	0.254429i	0.930078	−	0.367361i	$-0.119739\pi$
$433$	3.05668	+	5.29433i	0.146895	+	0.254429i	−0.783183	+	0.621791i	$0.786405\pi$
$434$		0			0
$435$	−0.849234	+	3.16938i	−0.0407176	+	0.151960i
$436$	14.2946	+	53.3482i	0.684588	+	2.55492i
$437$	32.1219	−	8.60704i	1.53660	−	0.411731i
$438$	64.9883			3.10526
$439$	15.7233			0.750434			0.375217	−	0.926937i	$-0.377568\pi$
$439$	15.7233			0.750434			0.375217	+	0.926937i	$0.377568\pi$
$440$	−3.03574	+	0.813425i	−0.144723	+	0.0387785i
$441$		0			0
$442$	−34.7568	+	6.56560i	−1.65321	+	0.312294i
$443$	5.63934	+	9.76763i	0.267933	+	0.464074i	0.968328	−	0.249682i	$-0.0803260\pi$
$443$	5.63934	+	9.76763i	0.267933	+	0.464074i	−0.700395	+	0.713756i	$0.746993\pi$
$444$	77.5727	+	20.7855i	3.68144	+	0.986438i
$445$	0.405738	+	0.702758i	0.0192338	+	0.0333139i
$446$	−6.20498	+	10.7473i	−0.293814	+	0.508901i
$447$	14.7366	−	14.7366i	0.697016	−	0.697016i
$448$		0			0
$449$	4.69271	+	1.25741i	0.221463	+	0.0593407i	0.367844	−	0.929888i	$-0.380096\pi$
$449$	4.69271	+	1.25741i	0.221463	+	0.0593407i	−0.146381	+	0.989228i	$0.546763\pi$
$450$	10.2809	+	2.75476i	0.484647	+	0.129861i
$451$			0.788550i			0.0371313i
$452$	−15.6662	+	9.04488i	−0.736876	+	0.425435i
$453$	−6.26931	−	6.26931i	−0.294558	−	0.294558i
$454$	−26.2888			−1.23379
$455$		0			0
$456$	−50.6293			−2.37094
$457$	−6.30355	−	6.30355i	−0.294868	−	0.294868i	0.544132	−	0.839000i	$-0.316859\pi$
$457$	−6.30355	−	6.30355i	−0.294868	−	0.294868i	−0.839000	+	0.544132i	$0.816859\pi$
$458$	27.8634	−	16.0869i	1.30197	−	0.751693i
$459$			16.8096i			0.784605i
$460$	5.38652	+	1.44331i	0.251148	+	0.0672948i
$461$	11.4373	+	3.06461i	0.532688	+	0.142733i	0.515129	−	0.857113i	$-0.327744\pi$
$461$	11.4373	+	3.06461i	0.532688	+	0.142733i	0.0175587	+	0.999846i	$0.494411\pi$
$462$		0			0
$463$	−19.6291	+	19.6291i	−0.912240	+	0.912240i	−0.996448	−	0.0842083i	$-0.973164\pi$
$463$	−19.6291	+	19.6291i	−0.912240	+	0.912240i	0.0842083	+	0.996448i	$0.473164\pi$
$464$	−12.4999	+	21.6505i	−0.580294	+	1.00510i
$465$	0.532883	+	0.922980i	0.0247118	+	0.0428022i
$466$	28.7429	+	7.70164i	1.33149	+	0.356772i
$467$	12.2870	+	21.2818i	0.568576	+	0.984803i	0.996707	+	0.0810863i	$0.0258389\pi$
$467$	12.2870	+	21.2818i	0.568576	+	0.984803i	−0.428131	+	0.903717i	$0.640828\pi$
$468$	11.2684	−	5.42246i	0.520884	−	0.250653i
$469$		0			0
$470$	1.79911	−	0.482071i	0.0829870	−	0.0222363i
$471$	−25.6365			−1.18127
$472$	3.39723			0.156370
$473$	12.4876	−	3.34605i	0.574182	−	0.153852i
$474$	4.75127	+	17.7320i	0.218233	+	0.814458i
$475$	−7.03441	+	26.2528i	−0.322761	+	1.20456i
$476$		0			0
$477$	3.51006	+	6.07960i	0.160715	+	0.278366i
$478$		−	15.0357i		−	0.687715i
$479$	−5.47147	+	20.4198i	−0.249998	+	0.933004i	0.720808	+	0.693135i	$0.243771\pi$
$479$	−5.47147	+	20.4198i	−0.249998	+	0.933004i	−0.970805	+	0.239869i	$0.922896\pi$
$480$	0.303675	+	0.175327i	0.0138608	+	0.00800255i
$481$	−6.95542	−	36.8204i	−0.317140	−	1.67886i
$482$		−	29.7431i		−	1.35476i
$483$		0			0
$484$	5.52290	−	9.56595i	0.251041	−	0.434816i
$485$	0.551650	+	0.318495i	0.0250491	+	0.0144621i
$486$	−5.61686	−	20.9624i	−0.254786	−	0.950873i
$487$	−10.9256	−	10.9256i	−0.495085	−	0.495085i	0.414819	−	0.909904i	$-0.363845\pi$
$487$	−10.9256	−	10.9256i	−0.495085	−	0.495085i	−0.909904	+	0.414819i	$0.863845\pi$
$488$	−10.2959	+	2.75877i	−0.466073	+	0.124884i
$489$	22.8647	+	22.8647i	1.03398	+	1.03398i
$490$		0			0
$491$	19.0691	+	11.0096i	0.860578	+	0.496855i	0.864206	−	0.503139i	$-0.167822\pi$
$491$	19.0691	+	11.0096i	0.860578	+	0.496855i	−0.00362809	+	0.999993i	$0.501155\pi$
$492$	−1.50627	+	1.50627i	−0.0679077	+	0.0679077i
$493$	14.2754	−	24.7257i	0.642930	−	1.11359i
$494$	20.9098	+	43.4528i	0.940777	+	1.95504i
$495$	−0.515196	+	0.297449i	−0.0231563	+	0.0133693i
$496$	2.10167	+	7.84352i	0.0943676	+	0.352185i
$497$		0			0
$498$	24.6450	−	14.2288i	1.10437	−	0.637608i
$499$	−7.46375	+	27.8551i	−0.334123	+	1.24697i	0.570693	+	0.821164i	$0.306675\pi$
$499$	−7.46375	+	27.8551i	−0.334123	+	1.24697i	−0.904816	+	0.425802i	$0.859992\pi$
$500$	−6.48147	+	6.48147i	−0.289860	+	0.289860i
$501$	−14.2098	+	14.2098i	−0.634845	+	0.634845i
$502$	−17.0001	+	63.4453i	−0.758753	+	2.83170i
$503$	−7.32350	+	4.22823i	−0.326539	+	0.188527i	−0.654303	−	0.756232i	$-0.727038\pi$
$503$	−7.32350	+	4.22823i	−0.326539	+	0.188527i	0.327764	+	0.944759i	$0.393705\pi$
$504$		0			0
$505$	−0.838597	−	3.12969i	−0.0373171	−	0.139269i
$506$	36.4698	−	21.0558i	1.62128	−	0.936046i
$507$	−20.0228	−	15.9872i	−0.889243	−	0.710016i
$508$	−8.23822	+	14.2690i	−0.365512	+	0.633085i
$509$	14.3892	−	14.3892i	0.637789	−	0.637789i	−0.312221	−	0.950010i	$-0.601073\pi$
$509$	14.3892	−	14.3892i	0.637789	−	0.637789i	0.950010	+	0.312221i	$0.101073\pi$
$510$	3.93660	+	2.27280i	0.174315	+	0.100641i
$511$		0			0
$512$	25.2221	+	25.2221i	1.11467	+	1.11467i
$513$	22.1358	−	5.93126i	0.977317	−	0.261871i
$514$	33.1934	+	33.1934i	1.46410	+	1.46410i
$515$	−0.488326	−	1.82246i	−0.0215182	−	0.0803071i
$516$	30.2450	+	17.4620i	1.33146	+	0.768721i
$517$	4.65707	−	8.06628i	0.204818	−	0.354754i
$518$		0			0
$519$			29.5172i			1.29566i
$520$	−0.297211	+	3.95020i	−0.0130336	+	0.173228i
$521$	15.2229	+	8.78895i	0.666928	+	0.385051i	0.794911	−	0.606725i	$-0.207517\pi$
$521$	15.2229	+	8.78895i	0.666928	+	0.385051i	−0.127984	+	0.991776i	$0.540851\pi$
$522$	−3.94515	+	14.7235i	−0.172674	+	0.644429i
$523$		−	28.3430i		−	1.23935i	−0.784857	−	0.619677i	$-0.787264\pi$
$523$		−	28.3430i		−	1.23935i	0.784857	−	0.619677i	$-0.212736\pi$
$524$	26.9706	+	46.7145i	1.17822	+	2.04073i
$525$		0			0
$526$	12.5442	−	46.8154i	0.546951	−	2.04125i
$527$	−2.40018	−	8.95760i	−0.104554	−	0.390199i
$528$	−19.2257	+	5.15150i	−0.836689	+	0.224190i
$529$	−13.6048			−0.591514
$530$	−4.53947			−0.197182
$531$	0.621139	−	0.166434i	0.0269552	−	0.00722261i
$532$		0			0
$533$	0.938050	+	0.328552i	0.0406315	+	0.0142312i
$534$	8.27696	+	14.3361i	0.358179	+	0.620384i
$535$	−0.948914	−	0.254261i	−0.0410251	−	0.0109926i
$536$	−6.22006	−	10.7735i	−0.268666	−	0.465343i
$537$	9.05021	−	15.6754i	0.390545	−	0.676444i
$538$	−45.2077	+	45.2077i	−1.94904	+	1.94904i
$539$		0			0
$540$	3.71194	+	0.994611i	0.159736	+	0.0428012i
$541$	12.8053	+	3.43118i	0.550545	+	0.147518i	0.523359	−	0.852112i	$-0.324679\pi$
$541$	12.8053	+	3.43118i	0.550545	+	0.147518i	0.0271858	+	0.999630i	$0.491345\pi$
$542$			13.0714i			0.561464i
$543$	21.8827	−	12.6340i	0.939075	−	0.542175i
$544$	−2.15750	−	2.15750i	−0.0925019	−	0.0925019i
$545$	−3.31170			−0.141857
$546$		0			0
$547$	−28.5769			−1.22186			−0.610930	−	0.791685i	$-0.709204\pi$
$547$	−28.5769			−1.22186			−0.610930	+	0.791685i	$0.709204\pi$
$548$	−38.2513	−	38.2513i	−1.63401	−	1.63401i
$549$	−1.74731	+	1.00881i	−0.0745736	+	0.0430551i
$550$			34.4172i			1.46756i
$551$	−37.5971	−	10.0741i	−1.60169	−	0.429172i
$552$	53.8302	+	14.4238i	2.29117	+	0.613916i
$553$		0			0
$554$	−11.2029	+	11.2029i	−0.475964	+	0.475964i
$555$	−2.40774	+	4.17032i	−0.102203	+	0.177020i
$556$	−29.2575	−	50.6754i	−1.24079	−	2.14912i
$557$	−42.3739	−	11.3540i	−1.79544	−	0.481086i	−0.802187	−	0.597073i	$-0.796330\pi$
$557$	−42.3739	−	11.3540i	−1.79544	−	0.481086i	−0.993251	+	0.115987i	$0.962997\pi$
$558$	2.47553	+	4.28774i	0.104797	+	0.181514i
$559$	1.22259	−	16.2493i	0.0517100	−	0.687272i
$560$		0			0
$561$	21.9564	−	5.88321i	0.927001	−	0.248389i
$562$	38.3822			1.61906
$563$	6.62349			0.279147			0.139573	−	0.990212i	$-0.455427\pi$
$563$	6.62349			0.279147			0.139573	+	0.990212i	$0.455427\pi$
$564$	24.3038	−	6.51218i	1.02337	−	0.274212i
$565$	−0.280739	−	1.04773i	−0.0118108	−	0.0440785i
$566$	−1.49759	+	5.58907i	−0.0629482	+	0.234926i
$567$		0			0
$568$	3.27360	+	5.67003i	0.137357	+	0.237909i
$569$		−	0.438350i		−	0.0183766i	−0.999958	−	0.00918829i	$-0.997075\pi$
$569$		−	0.438350i		−	0.0183766i	0.999958	−	0.00918829i	$-0.00292477\pi$
$570$	1.60391	−	5.98587i	0.0671804	−	0.250721i
$571$	−1.04982	−	0.606116i	−0.0439338	−	0.0253652i	0.477872	−	0.878429i	$-0.341408\pi$
$571$	−1.04982	−	0.606116i	−0.0439338	−	0.0253652i	−0.521806	+	0.853064i	$0.674742\pi$
$572$	26.3675	+	30.6580i	1.10248	+	1.28188i
$573$		−	10.6266i		−	0.443932i
$574$		0			0
$575$	14.9583	−	25.9085i	0.623804	−	1.08046i
$576$	6.81996	+	3.93751i	0.284165	+	0.164063i
$577$	0.402507	+	1.50218i	0.0167566	+	0.0625365i	0.973798	−	0.227415i	$-0.0730274\pi$
$577$	0.402507	+	1.50218i	0.0167566	+	0.0625365i	−0.957041	+	0.289952i	$0.906361\pi$
$578$	1.28155	+	1.28155i	0.0533057	+	0.0533057i
$579$	6.36131	−	1.70451i	0.264367	−	0.0708369i
$580$	−4.61532	−	4.61532i	−0.191641	−	0.191641i
$581$		0			0
$582$	11.2535	+	6.49723i	0.466474	+	0.269319i
$583$	−16.0516	+	16.0516i	−0.664788	+	0.664788i
$584$	−31.6653	+	54.8460i	−1.31032	+	2.26954i
$585$	0.139183	+	0.736805i	0.00575452	+	0.0304631i
$586$	70.7533	−	40.8495i	2.92279	−	1.68748i
$587$	−4.96434	−	18.5272i	−0.204900	−	0.764698i	−0.989480	−	0.144670i	$-0.953788\pi$
$587$	−4.96434	−	18.5272i	−0.204900	−	0.764698i	0.784580	−	0.620028i	$-0.212879\pi$
$588$		0			0
$589$	−10.9489	+	6.32137i	−0.451143	+	0.260467i
$590$	−0.107622	+	0.401652i	−0.00443074	+	0.0165357i
$591$	5.30755	−	5.30755i	0.218323	−	0.218323i
$592$	−25.9436	+	25.9436i	−1.06627	+	1.06627i
$593$	1.95948	−	7.31288i	0.0804662	−	0.300304i	−0.913951	−	0.405825i	$-0.866984\pi$
$593$	1.95948	−	7.31288i	0.0804662	−	0.300304i	0.994417	+	0.105521i	$0.0336510\pi$
$594$	25.1319	−	14.5099i	1.03118	−	0.595349i
$595$		0			0
$596$	10.7299	+	40.0444i	0.439512	+	1.64028i
$597$	38.0071	−	21.9434i	1.55553	−	0.898084i
$598$	−9.85253	−	52.1570i	−0.402900	−	2.13286i
$599$	18.9239	−	32.7771i	0.773208	−	1.33924i	−0.162588	−	0.986694i	$-0.551984\pi$
$599$	18.9239	−	32.7771i	0.773208	−	1.33924i	0.935796	−	0.352542i	$-0.114683\pi$
$600$	−32.2063	+	32.2063i	−1.31482	+	1.31482i
$601$	−20.0340	−	11.5666i	−0.817205	−	0.471813i	0.0322469	−	0.999480i	$-0.489734\pi$
$601$	−20.0340	−	11.5666i	−0.817205	−	0.471813i	−0.849452	+	0.527667i	$0.823067\pi$
$602$		0			0
$603$	−1.66506	−	1.66506i	−0.0678066	−	0.0678066i
$604$	17.0359	−	4.56475i	0.693181	−	0.185737i
$605$	0.468335	+	0.468335i	0.0190405	+	0.0190405i
$606$	−17.1072	−	63.8449i	−0.694933	−	2.59352i
$607$	8.49783	+	4.90622i	0.344916	+	0.199137i	0.662444	−	0.749112i	$-0.269519\pi$
$607$	8.49783	+	4.90622i	0.344916	+	0.199137i	−0.317528	+	0.948249i	$0.602853\pi$
$608$	−2.07983	+	3.60238i	−0.0843483	+	0.146096i
$609$		0			0
$610$		−	1.30467i		−	0.0528246i
$611$	−7.65517	−	8.90084i	−0.309695	−	0.360089i
$612$	12.1101	+	6.99175i	0.489520	+	0.282625i
$613$	9.62949	−	35.9377i	0.388931	−	1.45151i	−0.442944	−	0.896549i	$-0.646066\pi$
$613$	9.62949	−	35.9377i	0.388931	−	1.45151i	0.831875	−	0.554962i	$-0.187267\pi$
$614$		−	65.9140i		−	2.66007i
$615$	−0.0638647	−	0.110617i	−0.00257527	−	0.00446050i
$616$		0			0
$617$	−2.10572	+	7.85866i	−0.0847732	+	0.316378i	−0.995271	−	0.0971357i	$-0.969032\pi$
$617$	−2.10572	+	7.85866i	−0.0847732	+	0.316378i	0.910498	+	0.413514i	$0.135699\pi$
$618$	−9.96175	−	37.1778i	−0.400720	−	1.49551i
$619$	−44.4523	+	11.9110i	−1.78669	+	0.478742i	−0.991776	−	0.127984i	$-0.959149\pi$
$619$	−44.4523	+	11.9110i	−1.78669	+	0.478742i	−0.794912	+	0.606725i	$0.792483\pi$
$620$	−2.12006			−0.0851436
$621$	−25.2250			−1.01224
$622$	77.8924	−	20.8712i	3.12320	−	0.836859i
$623$		0			0
$624$	−1.88227	+	25.0170i	−0.0753511	+	1.00148i
$625$	12.0870	+	20.9353i	0.483481	+	0.837413i
$626$	−3.09520	−	0.829356i	−0.123709	−	0.0331477i
$627$	−15.4946	−	26.8375i	−0.618796	−	1.07179i
$628$	25.4985	−	44.1647i	1.01750	−	1.76236i
$629$	29.6286	−	29.6286i	1.18137	−	1.18137i
$630$		0			0
$631$	5.64724	+	1.51317i	0.224813	+	0.0602384i	0.369467	−	0.929244i	$-0.379540\pi$
$631$	5.64724	+	1.51317i	0.224813	+	0.0602384i	−0.144654	+	0.989482i	$0.546207\pi$
$632$	−17.2797	−	4.63008i	−0.687350	−	0.184175i
$633$			30.5903i			1.21585i
$634$	−18.2604	+	10.5426i	−0.725211	+	0.418701i
$635$	−0.698590	−	0.698590i	−0.0277227	−	0.0277227i
$636$	−61.3225			−2.43160
$637$		0			0
$638$	−49.2896			−1.95139
$639$	0.876316	+	0.876316i	0.0346665	+	0.0346665i
$640$	−4.10189	+	2.36823i	−0.162141	+	0.0936124i
$641$		−	44.4981i		−	1.75757i	−0.477219	−	0.878785i	$-0.658355\pi$
$641$		−	44.4981i		−	1.75757i	0.477219	−	0.878785i	$-0.341645\pi$
$642$	−19.3576	−	5.18686i	−0.763985	−	0.204709i
$643$	27.5723	+	7.38796i	1.08734	+	0.291353i	0.757601	−	0.652718i	$-0.226371\pi$
$643$	27.5723	+	7.38796i	1.08734	+	0.291353i	0.329743	+	0.944071i	$0.393038\pi$
$644$		0			0
$645$	−1.48075	+	1.48075i	−0.0583046	+	0.0583046i
$646$	−26.9612	+	46.6982i	−1.06078	+	1.83732i
$647$	17.6121	+	30.5051i	0.692404	+	1.19928i	0.971048	+	0.238885i	$0.0767818\pi$
$647$	17.6121	+	30.5051i	0.692404	+	1.19928i	−0.278644	+	0.960395i	$0.589885\pi$
$648$	49.0755	+	13.1497i	1.92787	+	0.516571i
$649$	1.03969	+	1.80079i	0.0408114	+	0.0706874i
$650$	40.9424	+	14.3401i	1.60589	+	0.562463i
$651$		0			0
$652$	−62.1312	+	16.6480i	−2.43325	+	0.651987i
$653$	−15.3961			−0.602498			−0.301249	−	0.953546i	$-0.597403\pi$
$653$	−15.3961			−0.602498			−0.301249	+	0.953546i	$0.597403\pi$
$654$	−67.5579			−2.64172
$655$	−3.12420	+	0.837126i	−0.122073	+	0.0327092i
$656$	−0.251879	−	0.940027i	−0.00983424	−	0.0367019i
$657$	−3.10264	+	11.5792i	−0.121045	+	0.451748i
$658$		0			0
$659$	5.17792	+	8.96841i	0.201703	+	0.349360i	0.949077	−	0.315043i	$-0.102019\pi$
$659$	5.17792	+	8.96841i	0.201703	+	0.349360i	−0.747374	+	0.664403i	$0.768686\pi$
$660$		−	5.19658i		−	0.202277i
$661$	−5.27256	+	19.6775i	−0.205079	+	0.765365i	0.784347	+	0.620323i	$0.212998\pi$
$661$	−5.27256	+	19.6775i	−0.205079	+	0.765365i	−0.989425	+	0.145042i	$0.953668\pi$
$662$	49.2755	+	28.4492i	1.91515	+	1.10571i
$663$	2.14962	−	28.5704i	0.0834844	−	1.10958i
$664$			27.7317i			1.07620i
$665$		0			0
$666$	−11.1852	+	19.3734i	−0.433419	+	0.750704i
$667$	37.1041	+	21.4220i	1.43668	+	0.829465i
$668$	−10.3463	−	38.6128i	−0.400309	−	1.49397i
$669$	−7.10795	−	7.10795i	−0.274809	−	0.274809i
$670$	1.47079	−	0.394096i	0.0568215	−	0.0152253i
$671$	−4.61332	−	4.61332i	−0.178095	−	0.178095i
$672$		0			0
$673$	−28.0255	−	16.1805i	−1.08030	−	0.623714i	−0.149326	−	0.988788i	$-0.547710\pi$
$673$	−28.0255	−	16.1805i	−1.08030	−	0.623714i	−0.930979	+	0.365074i	$0.881044\pi$
$674$	8.74329	−	8.74329i	0.336779	−	0.336779i
$675$	10.3080	−	17.8540i	0.396755	−	0.687200i
$676$	47.4566	−	18.5927i	1.82525	−	0.715103i
$677$	−11.3616	+	6.55960i	−0.436660	+	0.252106i	−0.702180	−	0.712000i	$-0.747790\pi$
$677$	−11.3616	+	6.55960i	−0.436660	+	0.252106i	0.265520	+	0.964105i	$0.414456\pi$
$678$	−5.72702	−	21.3735i	−0.219945	−	0.820845i
$679$		0			0
$680$	−3.83619	+	2.21482i	−0.147111	+	0.0849346i
$681$	5.51132	−	20.5685i	0.211194	−	0.788188i
$682$	−11.3206	+	11.3206i	−0.433489	+	0.433489i
$683$	−27.1767	+	27.1767i	−1.03989	+	1.03989i	−0.0407173	+	0.999171i	$0.512964\pi$
$683$	−27.1767	+	27.1767i	−1.03989	+	1.03989i	−0.999171	+	0.0407173i	$0.987036\pi$
$684$	4.93407	−	18.4142i	0.188659	−	0.704084i
$685$	2.80909	−	1.62183i	0.107330	−	0.0619669i
$686$		0			0
$687$	6.74510	+	25.1731i	0.257342	+	0.960412i
$688$	−13.8177	+	7.97762i	−0.526793	+	0.304144i
$689$	12.4068	+	25.7827i	0.472663	+	0.982243i
$690$	−3.41062	+	5.90737i	−0.129840	+	0.224890i
$691$	11.8354	−	11.8354i	0.450240	−	0.450240i	−0.445194	−	0.895434i	$-0.646865\pi$
$691$	11.8354	−	11.8354i	0.450240	−	0.450240i	0.895434	+	0.445194i	$0.146865\pi$
$692$	−50.8502	−	29.3584i	−1.93303	−	1.11604i
$693$		0			0
$694$	−1.17683	−	1.17683i	−0.0446720	−	0.0446720i
$695$	3.38910	−	0.908107i	0.128556	−	0.0344464i
$696$	−46.1233	−	46.1233i	−1.74830	−	1.74830i
$697$	0.287656	+	1.07355i	0.0108957	+	0.0406635i
$698$	11.0718	+	6.39229i	0.419072	+	0.241952i
$699$	−12.0516	+	20.8741i	−0.455835	+	0.789529i
$700$		0			0
$701$		−	22.9034i		−	0.865051i	−0.901622	−	0.432525i	$-0.857623\pi$
$701$		−	22.9034i		−	0.865051i	0.901622	−	0.432525i	$-0.142377\pi$
$702$	−6.78954	−	35.9423i	−0.256255	−	1.35655i
$703$	−49.4708	−	28.5620i	−1.86583	−	1.07724i
$704$	−6.59076	+	24.5971i	−0.248399	+	0.927037i
$705$			1.50870i			0.0568211i
$706$	26.4167	+	45.7551i	0.994206	+	1.72201i
$707$		0			0
$708$	−1.45384	+	5.42581i	−0.0546387	+	0.203914i
$709$	−1.72913	−	6.45322i	−0.0649390	−	0.242356i	0.925825	−	0.377952i	$-0.123372\pi$
$709$	−1.72913	−	6.45322i	−0.0649390	−	0.242356i	−0.990764	+	0.135596i	$0.956705\pi$
$710$	−0.774070	+	0.207411i	−0.0290503	+	0.00778401i
$711$	−3.38621			−0.126993
$712$	−16.1317			−0.604560
$713$	13.4420	−	3.60178i	0.503408	−	0.134888i
$714$		0			0
$715$	−2.18487	+	1.05138i	−0.0817096	+	0.0393193i
$716$	18.0030	+	31.1821i	0.672803	+	1.16533i
$717$	11.7640	+	3.15216i	0.439335	+	0.117719i
$718$	−17.2737	−	29.9189i	−0.644648	−	1.11656i
$719$	5.57246	−	9.65178i	0.207818	−	0.359951i	−0.743209	−	0.669059i	$-0.766697\pi$
$719$	5.57246	−	9.65178i	0.207818	−	0.359951i	0.951027	+	0.309108i	$0.100031\pi$
$720$	0.519152	−	0.519152i	0.0193476	−	0.0193476i
$721$		0			0
$722$	26.3516	+	7.06089i	0.980705	+	0.262779i
$723$	23.2712	+	6.23551i	0.865466	+	0.231901i
$724$			50.2638i			1.86804i
$725$	−30.3246	+	17.5079i	−1.12623	+	0.650228i
$726$	9.55393	+	9.55393i	0.354580	+	0.354580i
$727$	2.66009			0.0986574			0.0493287	−	0.998783i	$-0.484292\pi$
$727$	2.66009			0.0986574			0.0493287	+	0.998783i	$0.484292\pi$
$728$		0			0
$729$	−15.0353			−0.556862
$730$	−5.48126	−	5.48126i	−0.202871	−	0.202871i
$731$	15.7803	−	9.11075i	0.583655	−	0.336973i
$732$		−	17.6245i		−	0.651419i
$733$	18.2289	+	4.88442i	0.673299	+	0.180410i	0.579241	−	0.815157i	$-0.303349\pi$
$733$	18.2289	+	4.88442i	0.673299	+	0.180410i	0.0940588	+	0.995567i	$0.470016\pi$
$734$	7.06318	+	1.89257i	0.260707	+	0.0698561i
$735$		0			0
$736$	3.23760	−	3.23760i	0.119340	−	0.119340i
$737$	3.80718	−	6.59423i	0.140239	−	0.242902i
$738$	−0.296686	−	0.513874i	−0.0109211	−	0.0189160i
$739$	40.8109	+	10.9352i	1.50125	+	0.402259i	0.913519	−	0.406795i	$-0.133354\pi$
$739$	40.8109	+	10.9352i	1.50125	+	0.402259i	0.587733	+	0.809055i	$0.300020\pi$
$740$	−4.78956	−	8.29575i	−0.176068	−	0.304958i
$741$	−38.3815	+	7.25031i	−1.40998	+	0.266347i
$742$		0			0
$743$	23.2394	−	6.22698i	0.852571	−	0.228446i	0.194035	−	0.980995i	$-0.437842\pi$
$743$	23.2394	−	6.22698i	0.852571	−	0.228446i	0.658536	+	0.752549i	$0.271176\pi$
$744$	−21.1868			−0.776747
$745$	−2.48583			−0.0910738
$746$	−61.5436	+	16.4906i	−2.25327	+	0.603762i
$747$	1.35861	+	5.07039i	0.0497088	+	0.185516i
$748$	−11.7031	+	43.6765i	−0.427907	+	1.59697i
$749$		0			0
$750$	−5.60606	−	9.70998i	−0.204704	−	0.354558i
$751$		−	16.7433i		−	0.610973i	−0.952196	−	0.305486i	$-0.901181\pi$
$751$		−	16.7433i		−	0.610973i	0.952196	−	0.305486i	$-0.0988191\pi$
$752$	−2.97513	+	11.1033i	−0.108492	+	0.404897i
$753$	−46.0761	−	26.6020i	−1.67911	−	0.969432i
$754$	−20.5367	+	58.6343i	−0.747901	+	2.13534i
$755$			1.05754i			0.0384877i
$756$		0			0
$757$	−13.8538	+	23.9955i	−0.503524	+	0.872130i	0.496467	+	0.868055i	$0.334630\pi$
$757$	−13.8538	+	23.9955i	−0.503524	+	0.872130i	−0.999992	+	0.00407434i	$0.998703\pi$
$758$	12.1045	+	6.98855i	0.439656	+	0.253836i
$759$	8.82851	+	32.9485i	0.320455	+	1.19595i
$760$	4.27019	+	4.27019i	0.154896	+	0.154896i
$761$	−21.8743	+	5.86120i	−0.792943	+	0.212468i	−0.632483	−	0.774574i	$-0.717964\pi$
$761$	−21.8743	+	5.86120i	−0.792943	+	0.212468i	−0.160459	+	0.987042i	$0.551298\pi$
$762$	−14.2511	−	14.2511i	−0.516262	−	0.516262i
$763$		0			0
$764$	18.3067	+	10.5694i	0.662314	+	0.382387i
$765$	−0.592891	+	0.592891i	−0.0214360	+	0.0214360i
$766$	19.7607	−	34.2265i	0.713983	−	1.23665i
$767$	2.57540	−	0.486496i	0.0929921	−	0.0175663i
$768$	−53.2879	+	30.7658i	−1.92286	+	1.11016i
$769$	−5.25290	−	19.6041i	−0.189424	−	0.706941i	−0.993640	−	0.112604i	$-0.964081\pi$
$769$	−5.25290	−	19.6041i	−0.189424	−	0.706941i	0.804216	−	0.594338i	$-0.202586\pi$
$770$		0			0
$771$	−32.9296	+	19.0119i	−1.18593	+	0.684698i
$772$	−3.39066	+	12.6541i	−0.122033	+	0.455432i
$773$	−14.4404	+	14.4404i	−0.519384	+	0.519384i	−0.917385	−	0.398001i	$-0.869704\pi$
$773$	−14.4404	+	14.4404i	−0.519384	+	0.519384i	0.398001	+	0.917385i	$0.369704\pi$
$774$	−6.87889	+	6.87889i	−0.247257	+	0.247257i
$775$	−2.94369	+	10.9860i	−0.105740	+	0.394628i
$776$	−10.9665	+	6.33150i	−0.393674	+	0.227288i
$777$		0			0
$778$	5.85193	+	21.8397i	0.209802	+	0.782991i
$779$	1.31220	−	0.757600i	0.0470145	−	0.0271438i
$780$	−6.18179	−	2.16517i	−0.221344	−	0.0775256i
$781$	−2.00371	+	3.47052i	−0.0716982	+	0.124185i
$782$	41.9696	−	41.9696i	1.50083	−	1.50083i
$783$	25.5690	+	14.7623i	0.913763	+	0.527561i
$784$		0			0
$785$	2.16224	+	2.16224i	0.0771736	+	0.0771736i
$786$	−63.7329	+	17.0772i	−2.27328	+	0.609123i
$787$	−24.9260	−	24.9260i	−0.888517	−	0.888517i	0.105864	−	0.994381i	$-0.466239\pi$
$787$	−24.9260	−	24.9260i	−0.888517	−	0.888517i	−0.994381	+	0.105864i	$0.966239\pi$
$788$	3.86448	+	14.4224i	0.137666	+	0.513778i
$789$	33.9989	+	19.6293i	1.21039	+	0.698821i
$790$	1.09482	−	1.89629i	0.0389521	−	0.0674670i
$791$		0			0
$792$		−	11.8262i		−	0.420226i
$793$	−7.41011	+	3.56580i	−0.263141	+	0.126625i
$794$	39.7167	+	22.9304i	1.40949	+	0.813770i
$795$	0.951679	−	3.55171i	0.0337526	−	0.125966i
$796$			87.3012i			3.09431i
$797$	−10.0235	−	17.3612i	−0.355050	−	0.614964i	0.632077	−	0.774906i	$-0.282203\pi$
$797$	−10.0235	−	17.3612i	−0.355050	−	0.614964i	−0.987126	+	0.159942i	$0.948869\pi$
$798$		0			0
$799$	3.39771	−	12.6804i	0.120202	−	0.448602i
$800$	0.968520	+	3.61457i	0.0342424	+	0.127794i
$801$	−2.94947	+	0.790308i	−0.104214	+	0.0279242i
$802$	91.1557			3.21882
$803$	−38.7635			−1.36793
$804$	19.8685	−	5.32375i	0.700708	−	0.187754i
$805$		0			0
$806$	8.75012	+	18.1837i	0.308210	+	0.640493i
$807$	−25.8932	−	44.8484i	−0.911485	−	1.57874i
$808$	62.2165	+	16.6708i	2.18877	+	0.586478i
$809$	−17.2473	−	29.8731i	−0.606381	−	1.05028i	−0.991832	−	0.127555i	$-0.959287\pi$
$809$	−17.2473	−	29.8731i	−0.606381	−	1.05028i	0.385450	−	0.922729i	$-0.374046\pi$
$810$	−3.10937	+	5.38559i	−0.109252	+	0.189230i
$811$	−15.8161	+	15.8161i	−0.555379	+	0.555379i	−0.927988	−	0.372609i	$-0.878463\pi$
$811$	−15.8161	+	15.8161i	−0.555379	+	0.555379i	0.372609	+	0.927988i	$0.378463\pi$
$812$		0			0
$813$	−10.2272	−	2.74036i	−0.358682	−	0.0961085i
$814$	−69.8726	−	18.7223i	−2.44903	−	0.656217i
$815$		−	3.85692i		−	0.135102i
$816$	−24.2949	+	14.0267i	−0.850493	+	0.491032i
$817$	−17.5656	−	17.5656i	−0.614541	−	0.614541i
$818$	49.6069			1.73447
$819$		0			0
$820$	0.254084			0.00887298
$821$	−27.2867	−	27.2867i	−0.952313	−	0.952313i	0.0466003	−	0.998914i	$-0.485161\pi$
$821$	−27.2867	−	27.2867i	−0.952313	−	0.952313i	−0.998914	+	0.0466003i	$0.985161\pi$
$822$	57.3049	−	33.0850i	1.99874	−	1.15397i
$823$		−	9.45706i		−	0.329653i	−0.986323	−	0.164826i	$-0.947294\pi$
$823$		−	9.45706i		−	0.329653i	0.986323	−	0.164826i	$-0.0527063\pi$
$824$	36.2295	+	9.70766i	1.26211	+	0.338182i
$825$	−26.9283	−	7.21541i	−0.937523	−	0.251208i
$826$		0			0
$827$	12.1614	−	12.1614i	0.422895	−	0.422895i	−0.463304	−	0.886199i	$-0.653336\pi$
$827$	12.1614	−	12.1614i	0.422895	−	0.422895i	0.886199	+	0.463304i	$0.153336\pi$
$828$	−10.4920	+	18.1727i	−0.364623	+	0.631545i
$829$	−2.94122	−	5.09434i	−0.102153	−	0.176934i	0.810419	−	0.585851i	$-0.199240\pi$
$829$	−2.94122	−	5.09434i	−0.102153	−	0.176934i	−0.912571	+	0.408918i	$0.865906\pi$
$830$	−3.27870	−	0.878526i	−0.113805	−	0.0304941i
$831$	−6.41657	−	11.1138i	−0.222588	−	0.385534i
$832$	26.5143	+	18.0888i	0.919219	+	0.627115i
$833$		0			0
$834$	69.1369	−	18.5252i	2.39401	−	0.641474i
$835$	2.39697			0.0829504
$836$	61.6449			2.13203
$837$	9.26314	−	2.48205i	0.320181	−	0.0857922i
$838$	−6.89634	−	25.7375i	−0.238230	−	0.889087i
$839$	3.66834	−	13.6904i	0.126645	−	0.472646i	−0.873248	−	0.487276i	$-0.837991\pi$
$839$	3.66834	−	13.6904i	0.126645	−	0.472646i	0.999893	+	0.0146305i	$0.00465719\pi$
$840$		0			0
$841$	−10.5734	−	18.3137i	−0.364601	−	0.631507i
$842$			27.5259i			0.948604i
$843$	−8.04666	+	30.0305i	−0.277142	+	1.03431i
$844$	−52.6987	−	30.4256i	−1.81397	−	1.04729i
$845$	0.340371	+	3.03716i	0.0117091	+	0.104482i
$846$			7.00874i			0.240965i
$847$		0			0
$848$	14.0078	−	24.2622i	0.481030	−	0.833168i
$849$	−4.05896	−	2.34344i	−0.139303	−	0.0804268i
$850$	12.5551	+	46.8563i	0.430636	+	1.60716i
$851$	44.4615	+	44.4615i	1.52412	+	1.52412i
$852$	−10.4567	+	2.80187i	−0.358241	+	0.0959904i
$853$	0.313002	+	0.313002i	0.0107170	+	0.0107170i	0.712445	−	0.701728i	$-0.247588\pi$
$853$	0.313002	+	0.313002i	0.0107170	+	0.0107170i	−0.701728	+	0.712445i	$0.747588\pi$
$854$		0			0
$855$	0.989951	+	0.571548i	0.0338556	+	0.0195465i
$856$	13.8093	−	13.8093i	0.471993	−	0.471993i
$857$	17.0917	−	29.6037i	0.583842	−	1.01124i	−0.411176	−	0.911556i	$-0.634882\pi$
$857$	17.0917	−	29.6037i	0.583842	−	1.01124i	0.995019	−	0.0996889i	$-0.0317848\pi$
$858$	−44.5709	+	21.4479i	−1.52163	+	0.732218i
$859$	3.41700	−	1.97280i	0.116586	−	0.0673112i	−0.440573	−	0.897717i	$-0.645225\pi$
$859$	3.41700	−	1.97280i	0.116586	−	0.0673112i	0.557159	+	0.830406i	$0.311891\pi$
$860$	−1.07815	−	4.02372i	−0.0367647	−	0.137208i
$861$		0			0
$862$	36.8711	−	21.2875i	1.25583	−	0.725056i
$863$	−9.37524	+	34.9889i	−0.319137	+	1.19104i	0.600939	+	0.799295i	$0.294794\pi$
$863$	−9.37524	+	34.9889i	−0.319137	+	1.19104i	−0.920076	+	0.391740i	$0.871873\pi$
$864$	2.23109	−	2.23109i	0.0759031	−	0.0759031i
$865$	2.48955	−	2.48955i	0.0846472	−	0.0846472i
$866$	3.85001	−	14.3684i	0.130829	−	0.488260i
$867$	−1.27137	+	0.734026i	−0.0431780	+	0.0249288i
$868$		0			0
$869$	−2.83399	−	10.5766i	−0.0961364	−	0.358786i
$870$	6.91428	−	3.99196i	0.234416	−	0.135340i
$871$	−6.25815	−	7.27649i	−0.212049	−	0.246555i
$872$	32.9173	−	57.0145i	1.11472	−	1.93075i
$873$	−1.69489	+	1.69489i	−0.0573635	+	0.0573635i
$874$	−70.0768	−	40.4588i	−2.37038	−	1.36854i
$875$		0			0
$876$	−74.0450	−	74.0450i	−2.50175	−	2.50175i
$877$	38.1725	−	10.2283i	1.28899	−	0.345385i	0.451716	−	0.892162i	$-0.350812\pi$
$877$	38.1725	−	10.2283i	1.28899	−	0.345385i	0.837278	+	0.546777i	$0.184146\pi$
$878$	−27.0530	−	27.0530i	−0.912994	−	0.912994i
$879$	17.1278	+	63.9218i	0.577706	+	2.15603i
$880$	2.05602	+	1.18705i	0.0693085	+	0.0400153i
$881$	−3.07636	+	5.32841i	−0.103645	+	0.179519i	−0.913184	−	0.407548i	$-0.866384\pi$
$881$	−3.07636	+	5.32841i	−0.103645	+	0.179519i	0.809539	+	0.587067i	$0.199717\pi$
$882$		0			0
$883$		−	2.86401i		−	0.0963817i	−0.998838	−	0.0481909i	$-0.984654\pi$
$883$		−	2.86401i		−	0.0963817i	0.998838	−	0.0481909i	$-0.0153456\pi$
$884$	47.0809	+	32.1198i	1.58350	+	1.08031i
$885$	−0.291693	−	0.168409i	−0.00980515	−	0.00566100i
$886$	7.10297	−	26.5087i	0.238629	−	0.890576i
$887$			54.0214i			1.81386i	0.421281	+	0.906930i	$0.361581\pi$
$887$			54.0214i			1.81386i	−0.421281	+	0.906930i	$0.638419\pi$
$888$	−47.8645	−	82.9037i	−1.60623	−	2.78207i
$889$		0			0
$890$	0.511042	−	1.90724i	0.0171302	−	0.0639307i
$891$	8.04870	+	30.0382i	0.269642	+	1.00632i
$892$	19.3148	−	5.17537i	0.646706	−	0.173284i
$893$	−17.8971			−0.598905
$894$	−50.7104			−1.69601
$895$	−2.08541	+	0.558785i	−0.0697077	+	0.0186781i
$896$		0			0
$897$	42.8736	+	3.22579i	1.43151	+	0.107706i
$898$	−5.91065	−	10.2375i	−0.197241	−	0.341631i
$899$	−15.7332	−	4.21571i	−0.524733	−	0.140602i
$900$	−8.57498	−	14.8523i	−0.285833	−	0.495076i
$901$	−15.9974	+	27.7084i	−0.532952	+	0.923100i
$902$	1.35675	−	1.35675i	0.0451748	−	0.0451748i
$903$		0			0
$904$	20.8283	+	5.58094i	0.692741	+	0.185619i
$905$	−2.91121	−	0.780056i	−0.0967719	−	0.0259299i
$906$			21.5735i			0.716731i
$907$	−2.95673	+	1.70707i	−0.0981766	+	0.0566823i	−0.548284	−	0.836292i	$-0.684719\pi$
$907$	−2.95673	+	1.70707i	−0.0981766	+	0.0566823i	0.450108	+	0.892974i	$0.351386\pi$
$908$	29.9523	+	29.9523i	0.994003	+	0.994003i
$909$	12.1922			0.404390
$910$		0			0
$911$	40.6913			1.34816			0.674082	−	0.738656i	$-0.264539\pi$
$911$	40.6913			1.34816			0.674082	+	0.738656i	$0.264539\pi$
$912$	27.0435	+	27.0435i	0.895501	+	0.895501i
$913$	−14.7000	+	8.48703i	−0.486498	+	0.280880i
$914$			21.6913i			0.717484i
$915$	1.02078	+	0.273518i	0.0337461	+	0.00904224i
$916$	−50.0751	−	13.4176i	−1.65453	−	0.443330i
$917$		0			0
$918$	28.9220	−	28.9220i	0.954567	−	0.954567i
$919$	11.1365	−	19.2890i	0.367359	−	0.636285i	−0.621793	−	0.783182i	$-0.713595\pi$
$919$	11.1365	−	19.2890i	0.367359	−	0.636285i	0.989152	+	0.146897i	$0.0469287\pi$
$920$	−3.32363	−	5.75670i	−0.109577	−	0.189793i
$921$	51.5716	+	13.8186i	1.69934	+	0.455337i
$922$	−14.4057	−	24.9514i	−0.474427	−	0.821732i
$923$	3.29364	+	3.82959i	0.108412	+	0.126053i
$924$		0			0
$925$	−49.6383	+	13.3005i	−1.63210	+	0.437319i
$926$	67.5461			2.21970
$927$	7.09968			0.233184
$928$	−5.17649	+	1.38704i	−0.169927	+	0.0455317i
$929$	−13.8098	−	51.5390i	−0.453086	−	1.69094i	−0.693654	−	0.720308i	$-0.744000\pi$
$929$	−13.8098	−	51.5390i	−0.453086	−	1.69094i	0.240568	−	0.970632i	$-0.422666\pi$
$930$	0.671187	−	2.50490i	0.0220091	−	0.0821390i
$931$		0			0
$932$	−23.9735	−	41.5234i	−0.785280	−	1.36014i
$933$			65.3191i			2.13845i
$934$	15.4760	−	57.7572i	0.506390	−	1.88987i
$935$	−2.34806	−	1.35565i	−0.0767897	−	0.0443345i
$936$	−14.0683	−	4.92744i	−0.459838	−	0.161058i
$937$			41.0483i			1.34099i	0.741914	+	0.670495i	$0.233918\pi$
$937$			41.0483i			1.34099i	−0.741914	+	0.670495i	$0.766082\pi$
$938$		0			0
$939$	1.29779	−	2.24784i	0.0423517	−	0.0733553i
$940$	−2.59909	−	1.50058i	−0.0847728	−	0.0489436i
$941$	0.900623	+	3.36117i	0.0293595	+	0.109571i	0.979051	−	0.203617i	$-0.0652697\pi$
$941$	0.900623	+	3.36117i	0.0293595	+	0.109571i	−0.949691	+	0.313188i	$0.898603\pi$
$942$	44.1092	+	44.1092i	1.43715	+	1.43715i
$943$	−1.61100	+	0.431665i	−0.0524612	+	0.0140569i
$944$	−1.81462	−	1.81462i	−0.0590609	−	0.0590609i
$945$		0			0
$946$	−27.2428	−	15.7287i	−0.885741	−	0.511383i
$947$	9.62580	−	9.62580i	0.312796	−	0.312796i	−0.533196	−	0.845992i	$-0.679009\pi$
$947$	9.62580	−	9.62580i	0.312796	−	0.312796i	0.845992	+	0.533196i	$0.179009\pi$
$948$	14.7897	−	25.6165i	0.480347	−	0.831985i
$949$	−16.1509	+	46.1126i	−0.524282	+	1.49688i
$950$	57.2727	−	33.0664i	1.85817	−	1.07282i
$951$	−4.42042	−	16.4972i	−0.143342	−	0.534960i
$952$		0			0
$953$	−50.4563	+	29.1309i	−1.63444	+	0.943643i	−0.651737	+	0.758445i	$0.725960\pi$
$953$	−50.4563	+	29.1309i	−1.63444	+	0.943643i	−0.982701	+	0.185199i	$0.940707\pi$
$954$	4.42106	−	16.4996i	0.143137	−	0.534195i
$955$	−0.896270	+	0.896270i	−0.0290026	+	0.0290026i
$956$	−17.1310	+	17.1310i	−0.554056	+	0.554056i
$957$	10.3333	−	38.5645i	0.334029	−	1.24661i
$958$	44.5475	−	25.7195i	1.43927	−	0.830960i
$959$		0			0
$960$	−1.06757	−	3.98423i	−0.0344557	−	0.128591i
$961$	22.2650	−	12.8547i	0.718226	−	0.414668i
$962$	−51.3845	+	75.3190i	−1.65670	+	2.42838i
$963$	1.84832	−	3.20139i	0.0595614	−	0.103163i
$964$	−33.8880	+	33.8880i	−1.09146	+	1.09146i
$965$	−0.680289	−	0.392765i	−0.0218993	−	0.0126435i
$966$		0			0
$967$	29.7856	+	29.7856i	0.957840	+	0.957840i	0.999147	−	0.0413063i	$-0.0131520\pi$
$967$	29.7856	+	29.7856i	0.957840	+	0.957840i	−0.0413063	+	0.999147i	$0.513152\pi$
$968$	−12.7180	+	3.40778i	−0.408773	+	0.109530i
$969$	−30.8847	−	30.8847i	−0.992161	−	0.992161i
$970$	−0.401157	−	1.49714i	−0.0128804	−	0.0480702i
$971$	14.2112	+	8.20486i	0.456060	+	0.263306i	0.710386	−	0.703812i	$-0.248520\pi$
$971$	14.2112	+	8.20486i	0.456060	+	0.263306i	−0.254326	+	0.967119i	$0.581854\pi$
$972$	−17.4841	+	30.2833i	−0.560801	+	0.971336i
$973$		0			0
$974$			37.5963i			1.20466i
$975$	−19.8031	+	29.0273i	−0.634208	+	0.929617i
$976$	6.97311	+	4.02593i	0.223204	+	0.128867i
$977$	5.82122	−	21.7251i	0.186237	−	0.695047i	−0.808125	−	0.589011i	$-0.799517\pi$
$977$	5.82122	−	21.7251i	0.186237	−	0.695047i	0.994362	−	0.106036i	$-0.0338159\pi$
$978$		−	78.6802i		−	2.51592i
$979$	−4.93694	−	8.55104i	−0.157785	−	0.273292i
$980$		0			0
$981$	3.22531	−	12.0370i	0.102976	−	0.384313i
$982$	−13.8670	−	51.7523i	−0.442513	−	1.65148i
$983$	55.3533	−	14.8319i	1.76550	−	0.473063i	0.777675	−	0.628666i	$-0.216399\pi$
$983$	55.3533	−	14.8319i	1.76550	−	0.473063i	0.987820	+	0.155603i	$0.0497320\pi$
$984$	2.53919			0.0809463
$985$	−0.895301			−0.0285267
$986$	−67.1037	+	17.9804i	−2.13702	+	0.572612i
$987$		0			0
$988$	25.6846	−	73.3321i	0.817134	−	2.33300i
$989$	13.6719	+	23.6804i	0.434740	+	0.752991i
$990$	1.39821	+	0.374648i	0.0444379	+	0.0119071i
$991$	−8.78106	−	15.2092i	−0.278940	−	0.483138i	0.692182	−	0.721723i	$-0.256650\pi$
$991$	−8.78106	−	15.2092i	−0.278940	−	0.483138i	−0.971122	+	0.238585i	$0.923316\pi$
$992$	−0.870346	+	1.50748i	−0.0276335	+	0.0478627i
$993$	−32.5893	+	32.5893i	−1.03419	+	1.03419i
$994$		0			0
$995$	−5.05636	−	1.35485i	−0.160297	−	0.0429516i
$996$	−44.2912	−	11.8678i	−1.40342	−	0.376045i
$997$		−	54.1792i		−	1.71587i	−0.513756	−	0.857936i	$-0.671746\pi$
$997$		−	54.1792i		−	1.71587i	0.513756	−	0.857936i	$-0.328254\pi$
$998$	60.7683	−	35.0846i	1.92359	−	1.11058i
$999$	30.6392	+	30.6392i	0.969380	+	0.969380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.423.1		28
7.2	even	3		91.2.w.a.33.1	✓	28
7.3	odd	6		637.2.bd.b.293.7		28
7.4	even	3		637.2.bd.a.293.7		28
7.5	odd	6		637.2.x.a.215.1		28
7.6	odd	2		91.2.ba.a.59.1	yes	28
13.2	odd	12		637.2.x.a.80.1		28
21.2	odd	6		819.2.gh.b.397.7		28
21.20	even	2		819.2.et.b.514.7		28
91.2	odd	12		91.2.ba.a.54.1	yes	28
91.41	even	12		91.2.w.a.80.1	yes	28
91.54	even	12	inner	637.2.bb.a.509.1		28
91.67	odd	12		637.2.bd.b.587.7		28
91.80	even	12		637.2.bd.a.587.7		28
273.2	even	12		819.2.et.b.145.7		28
273.41	odd	12		819.2.gh.b.262.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.1	✓	28	7.2	even	3
91.2.w.a.80.1	yes	28	91.41	even	12
91.2.ba.a.54.1	yes	28	91.2	odd	12
91.2.ba.a.59.1	yes	28	7.6	odd	2
637.2.x.a.80.1		28	13.2	odd	12
637.2.x.a.215.1		28	7.5	odd	6
637.2.bb.a.423.1		28	1.1	even	1	trivial
637.2.bb.a.509.1		28	91.54	even	12	inner
637.2.bd.a.293.7		28	7.4	even	3
637.2.bd.a.587.7		28	91.80	even	12
637.2.bd.b.293.7		28	7.3	odd	6
637.2.bd.b.587.7		28	91.67	odd	12
819.2.et.b.145.7		28	273.2	even	12
819.2.et.b.514.7		28	21.20	even	2
819.2.gh.b.262.7		28	273.41	odd	12
819.2.gh.b.397.7		28	21.2	odd	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72056 - 1.72056i) q^{2} +(1.70689 - 0.985473i) q^{3} +3.92067i q^{4} +(-0.227080 - 0.0608458i) q^{5} +(-4.63238 - 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +O(q^{10})\)	\(q+(-1.72056 - 1.72056i) q^{2} +(1.70689 - 0.985473i) q^{3} +3.92067i q^{4} +(-0.227080 - 0.0608458i) q^{5} +(-4.63238 - 1.24124i) q^{6} +(3.30464 - 3.30464i) q^{8} +(0.442313 - 0.766108i) q^{9} +(0.286016 + 0.495394i) q^{10} +(2.76307 + 0.740362i) q^{11} +(3.86372 + 6.69215i) q^{12} +(2.03197 - 2.97844i) q^{13} +(-0.447562 + 0.119924i) q^{15} -3.53033 q^{16} +4.03177 q^{17} +(-2.07916 + 0.557110i) q^{18} +(-1.42261 - 5.30924i) q^{19} +(0.238557 - 0.890305i) q^{20} +(-3.48019 - 6.02787i) q^{22} +6.05019i q^{23} +(2.38402 - 8.89728i) q^{24} +(-4.28226 - 2.47237i) q^{25} +(-8.62072 + 1.62847i) q^{26} +4.16929i q^{27} +(3.54072 - 6.13271i) q^{29} +(0.976395 + 0.563722i) q^{30} +(-0.595317 - 2.22176i) q^{31} +(-0.535124 - 0.535124i) q^{32} +(5.44585 - 1.45921i) q^{33} +(-6.93691 - 6.93691i) q^{34} +(3.00366 + 1.73416i) q^{36} +(7.34878 - 7.34878i) q^{37} +(-6.68720 + 11.5826i) q^{38} +(0.533171 - 7.08632i) q^{39} +(-0.951490 + 0.549343i) q^{40} +(0.0713473 + 0.266272i) q^{41} +(3.91398 - 2.25974i) q^{43} +(-2.90272 + 10.8331i) q^{44} +(-0.147055 + 0.147055i) q^{45} +(10.4097 - 10.4097i) q^{46} +(0.842735 - 3.14513i) q^{47} +(-6.02588 + 3.47904i) q^{48} +(3.11404 + 11.6218i) q^{50} +(6.88178 - 3.97320i) q^{51} +(11.6775 + 7.96668i) q^{52} +(-3.96785 + 6.87251i) q^{53} +(7.17352 - 7.17352i) q^{54} +(-0.582389 - 0.336242i) q^{55} +(-7.66035 - 7.66035i) q^{57} +(-16.6437 + 4.45968i) q^{58} +(0.514009 + 0.514009i) q^{59} +(-0.470182 - 1.75474i) q^{60} +(-1.97520 - 1.14038i) q^{61} +(-2.79839 + 4.84695i) q^{62} +8.90209i q^{64} +(-0.642644 + 0.552707i) q^{65} +(-11.8806 - 6.85927i) q^{66} +(0.688941 - 2.57116i) q^{67} +15.8072i q^{68} +(5.96230 + 10.3270i) q^{69} +(-0.362587 + 1.35319i) q^{71} +(-1.07003 - 3.99339i) q^{72} +(-13.0894 + 3.50729i) q^{73} -25.2881 q^{74} -9.74580 q^{75} +(20.8158 - 5.57758i) q^{76} +(-13.1098 + 11.2751i) q^{78} +(-1.91392 - 3.31501i) q^{79} +(0.801666 + 0.214806i) q^{80} +(5.43566 + 9.41483i) q^{81} +(0.335380 - 0.580895i) q^{82} +(-4.19588 + 4.19588i) q^{83} +(-0.915533 - 0.245316i) q^{85} +(-10.6223 - 2.84623i) q^{86} -13.9571i q^{87} +(11.5776 - 6.68431i) q^{88} +(-2.44076 - 2.44076i) q^{89} +0.506034 q^{90} -23.7208 q^{92} +(-3.20562 - 3.20562i) q^{93} +(-6.86137 + 3.96141i) q^{94} +1.29218i q^{95} +(-1.44075 - 0.386047i) q^{96} +(-2.61723 - 0.701285i) q^{97} +(1.78934 - 1.78934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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