LMFDB - Embedded newform 637.2.e.o.508.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.2
Root			$-0.0731214 - 0.126650i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.o.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.916185 - 1.58688i) q^{2} +(0.426879 - 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(1.31278 + 2.27379i) q^{5} -1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +O(q^{10})$	\(q+(-0.916185 - 1.58688i) q^{2} +(0.426879 - 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(1.31278 + 2.27379i) q^{5} -1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +(2.40549 - 4.16643i) q^{10} +(-1.63234 + 2.82730i) q^{11} +(0.579522 + 1.00376i) q^{12} -1.00000 q^{13} +2.24158 q^{15} +(2.43607 + 4.21939i) q^{16} +(2.26511 - 3.92328i) q^{17} +(2.08075 - 3.60396i) q^{18} +(2.03308 + 3.52139i) q^{19} -3.56440 q^{20} +5.98212 q^{22} +(2.26633 + 3.92540i) q^{23} +(-0.502500 + 0.870355i) q^{24} +(-0.946761 + 1.63984i) q^{25} +(0.916185 + 1.58688i) q^{26} +4.50024 q^{27} -1.42268 q^{29} +(-2.05371 - 3.55712i) q^{30} +(-1.40164 + 2.42771i) q^{31} +(3.28663 - 5.69261i) q^{32} +(1.39363 + 2.41383i) q^{33} -8.30102 q^{34} -3.08320 q^{36} +(5.02517 + 8.70385i) q^{37} +(3.72535 - 6.45249i) q^{38} +(-0.426879 + 0.739375i) q^{39} +(-1.54533 - 2.67660i) q^{40} +2.84271 q^{41} +9.72632 q^{43} +(-2.21604 - 3.83829i) q^{44} +(-2.98144 + 5.16401i) q^{45} +(4.15276 - 7.19278i) q^{46} +(-4.72478 - 8.18356i) q^{47} +4.15962 q^{48} +3.46963 q^{50} +(-1.93385 - 3.34953i) q^{51} +(0.678791 - 1.17570i) q^{52} +(-2.63219 + 4.55909i) q^{53} +(-4.12305 - 7.14134i) q^{54} -8.57161 q^{55} +3.47151 q^{57} +(1.30344 + 2.25762i) q^{58} +(-1.28395 + 2.22387i) q^{59} +(-1.52157 + 2.63543i) q^{60} +(-5.59149 - 9.68475i) q^{61} +5.13664 q^{62} -2.30037 q^{64} +(-1.31278 - 2.27379i) q^{65} +(2.55364 - 4.42303i) q^{66} +(0.990861 - 1.71622i) q^{67} +(3.07506 + 5.32617i) q^{68} +3.86979 q^{69} -11.7544 q^{71} +(-1.33671 - 2.31525i) q^{72} +(6.06956 - 10.5128i) q^{73} +(9.20797 - 15.9487i) q^{74} +(0.808304 + 1.40002i) q^{75} -5.52013 q^{76} +1.56440 q^{78} +(-5.95445 - 10.3134i) q^{79} +(-6.39602 + 11.0782i) q^{80} +(-1.48559 + 2.57312i) q^{81} +(-2.60444 - 4.51103i) q^{82} -13.2233 q^{83} +11.8943 q^{85} +(-8.91111 - 15.4345i) q^{86} +(-0.607310 + 1.05189i) q^{87} +(1.92151 - 3.32816i) q^{88} +(5.33328 + 9.23751i) q^{89} +10.9262 q^{90} -6.15345 q^{92} +(1.19666 + 2.07268i) q^{93} +(-8.65755 + 14.9953i) q^{94} +(-5.33795 + 9.24560i) q^{95} +(-2.80598 - 4.86011i) q^{96} +13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.916185	−	1.58688i	−0.647841	−	1.12209i	−0.983638	−	0.180159i	$-0.942339\pi$
$2$	−0.916185	−	1.58688i	−0.647841	−	1.12209i	0.335797	−	0.941934i	$-0.390994\pi$
$3$	0.426879	−	0.739375i	0.246458	−	0.426879i	−0.716082	−	0.698016i	$-0.754066\pi$
$3$	0.426879	−	0.739375i	0.246458	−	0.426879i	0.962541	+	0.271137i	$0.0873998\pi$
$4$	−0.678791	+	1.17570i	−0.339395	+	0.587850i
$5$	1.31278	+	2.27379i	0.587091	+	1.01687i	0.994611	+	0.103676i	$0.0330604\pi$
$5$	1.31278	+	2.27379i	0.587091	+	1.01687i	−0.407520	+	0.913196i	$0.633606\pi$
$6$	−1.56440			−0.638663
$7$		0			0
$7$		0			0
$8$	−1.17715			−0.416185
$9$	1.13555	+	1.96683i	0.378516	+	0.655610i
$10$	2.40549	−	4.16643i	0.760683	−	1.31754i
$11$	−1.63234	+	2.82730i	−0.492170	+	0.852464i	−0.999959	−	0.00901745i	$-0.997130\pi$
$11$	−1.63234	+	2.82730i	−0.492170	+	0.852464i	0.507789	+	0.861481i	$0.330463\pi$
$12$	0.579522	+	1.00376i	0.167294	+	0.289761i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	2.24158			0.578775
$16$	2.43607	+	4.21939i	0.609017	+	1.05485i
$17$	2.26511	−	3.92328i	0.549369	−	0.951535i	−0.448949	−	0.893557i	$-0.648202\pi$
$17$	2.26511	−	3.92328i	0.549369	−	0.951535i	0.998318	−	0.0579773i	$-0.0184651\pi$
$18$	2.08075	−	3.60396i	0.490437	−	0.849461i
$19$	2.03308	+	3.52139i	0.466420	+	0.807863i	0.999264	−	0.0383505i	$-0.0122103\pi$
$19$	2.03308	+	3.52139i	0.466420	+	0.807863i	−0.532845	+	0.846213i	$0.678877\pi$
$20$	−3.56440			−0.797024
$21$		0			0
$22$	5.98212			1.27539
$23$	2.26633	+	3.92540i	0.472562	+	0.818502i	0.999507	−	0.0313975i	$-0.00999579\pi$
$23$	2.26633	+	3.92540i	0.472562	+	0.818502i	−0.526945	+	0.849900i	$0.676662\pi$
$24$	−0.502500	+	0.870355i	−0.102572	+	0.177661i
$25$	−0.946761	+	1.63984i	−0.189352	+	0.327968i
$26$	0.916185	+	1.58688i	0.179679	+	0.311213i
$27$	4.50024			0.866071
$28$		0			0
$29$	−1.42268			−0.264184			−0.132092	−	0.991237i	$-0.542169\pi$
$29$	−1.42268			−0.264184			−0.132092	+	0.991237i	$0.542169\pi$
$30$	−2.05371	−	3.55712i	−0.374954	−	0.649439i
$31$	−1.40164	+	2.42771i	−0.251742	+	0.436030i	−0.964005	−	0.265882i	$-0.914337\pi$
$31$	−1.40164	+	2.42771i	−0.251742	+	0.436030i	0.712264	+	0.701912i	$0.247670\pi$
$32$	3.28663	−	5.69261i	0.580999	−	1.00632i
$33$	1.39363	+	2.41383i	0.242599	+	0.420194i
$34$	−8.30102			−1.42361
$35$		0			0
$36$	−3.08320			−0.513867
$37$	5.02517	+	8.70385i	0.826133	+	1.43090i	0.901050	+	0.433715i	$0.142797\pi$
$37$	5.02517	+	8.70385i	0.826133	+	1.43090i	−0.0749173	+	0.997190i	$0.523869\pi$
$38$	3.72535	−	6.45249i	0.604331	−	1.04673i
$39$	−0.426879	+	0.739375i	−0.0683553	+	0.118395i
$40$	−1.54533	−	2.67660i	−0.244339	−	0.423207i
$41$	2.84271			0.443956			0.221978	−	0.975052i	$-0.428749\pi$
$41$	2.84271			0.443956			0.221978	+	0.975052i	$0.428749\pi$
$42$		0			0
$43$	9.72632			1.48325			0.741625	−	0.670815i	$-0.234056\pi$
$43$	9.72632			1.48325			0.741625	+	0.670815i	$0.234056\pi$
$44$	−2.21604	−	3.83829i	−0.334081	−	0.578644i
$45$	−2.98144	+	5.16401i	−0.444447	+	0.769805i
$46$	4.15276	−	7.19278i	0.612290	−	1.06052i
$47$	−4.72478	−	8.18356i	−0.689180	−	1.19369i	−0.972103	−	0.234552i	$-0.924638\pi$
$47$	−4.72478	−	8.18356i	−0.689180	−	1.19369i	0.282923	−	0.959142i	$-0.408696\pi$
$48$	4.15962			0.600390
$49$		0			0
$50$	3.46963			0.490680
$51$	−1.93385	−	3.34953i	−0.270793	−	0.469028i
$52$	0.678791	−	1.17570i	0.0941313	−	0.163040i
$53$	−2.63219	+	4.55909i	−0.361559	+	0.626239i	−0.988218	−	0.153055i	$-0.951089\pi$
$53$	−2.63219	+	4.55909i	−0.361559	+	0.626239i	0.626658	+	0.779294i	$0.284422\pi$
$54$	−4.12305	−	7.14134i	−0.561076	−	0.971813i
$55$	−8.57161			−1.15580
$56$		0			0
$57$	3.47151			0.459812
$58$	1.30344	+	2.25762i	0.171149	+	0.296440i
$59$	−1.28395	+	2.22387i	−0.167156	+	0.289523i	−0.937419	−	0.348204i	$-0.886792\pi$
$59$	−1.28395	+	2.22387i	−0.167156	+	0.289523i	0.770263	+	0.637727i	$0.220125\pi$
$60$	−1.52157	+	2.63543i	−0.196433	+	0.340233i
$61$	−5.59149	−	9.68475i	−0.715917	−	1.24000i	−0.962605	−	0.270910i	$-0.912676\pi$
$61$	−5.59149	−	9.68475i	−0.715917	−	1.24000i	0.246688	−	0.969095i	$-0.420658\pi$
$62$	5.13664			0.652354
$63$		0			0
$64$	−2.30037			−0.287546
$65$	−1.31278	−	2.27379i	−0.162830	−	0.282030i
$66$	2.55364	−	4.42303i	0.314331	−	0.544438i
$67$	0.990861	−	1.71622i	0.121053	−	0.209670i	−0.799130	−	0.601158i	$-0.794706\pi$
$67$	0.990861	−	1.71622i	0.121053	−	0.209670i	0.920183	+	0.391488i	$0.128040\pi$
$68$	3.07506	+	5.32617i	0.372906	+	0.645893i
$69$	3.86979			0.465868
$70$		0			0
$71$	−11.7544			−1.39499			−0.697495	−	0.716590i	$-0.745702\pi$
$71$	−11.7544			−1.39499			−0.697495	+	0.716590i	$0.745702\pi$
$72$	−1.33671	−	2.31525i	−0.157533	−	0.272855i
$73$	6.06956	−	10.5128i	0.710388	−	1.23043i	−0.254323	−	0.967119i	$-0.581853\pi$
$73$	6.06956	−	10.5128i	0.710388	−	1.23043i	0.964711	−	0.263309i	$-0.0848139\pi$
$74$	9.20797	−	15.9487i	1.07041	−	1.85400i
$75$	0.808304	+	1.40002i	0.0933350	+	0.161661i
$76$	−5.52013			−0.633202
$77$		0			0
$78$	1.56440			0.177133
$79$	−5.95445	−	10.3134i	−0.669928	−	1.16035i	−0.977924	−	0.208961i	$-0.932992\pi$
$79$	−5.95445	−	10.3134i	−0.669928	−	1.16035i	0.307996	−	0.951388i	$-0.400342\pi$
$80$	−6.39602	+	11.0782i	−0.715097	+	1.23858i
$81$	−1.48559	+	2.57312i	−0.165066	+	0.285902i
$82$	−2.60444	−	4.51103i	−0.287613	−	0.498160i
$83$	−13.2233			−1.45145			−0.725723	−	0.687987i	$-0.758495\pi$
$83$	−13.2233			−1.45145			−0.725723	+	0.687987i	$0.758495\pi$
$84$		0			0
$85$	11.8943			1.29012
$86$	−8.91111	−	15.4345i	−0.960909	−	1.66434i
$87$	−0.607310	+	1.05189i	−0.0651105	+	0.112775i
$88$	1.92151	−	3.32816i	0.204834	−	0.354783i
$89$	5.33328	+	9.23751i	0.565326	+	0.979174i	0.997019	+	0.0771532i	$0.0245831\pi$
$89$	5.33328	+	9.23751i	0.565326	+	0.979174i	−0.431693	+	0.902021i	$0.642084\pi$
$90$	10.9262			1.15172
$91$		0			0
$92$	−6.15345			−0.641542
$93$	1.19666	+	2.07268i	0.124088	+	0.214926i
$94$	−8.65755	+	14.9953i	−0.892958	+	1.54665i
$95$	−5.33795	+	9.24560i	−0.547662	+	0.948578i
$96$	−2.80598	−	4.86011i	−0.286384	−	0.496032i
$97$	13.7422			1.39531			0.697655	−	0.716433i	$-0.254227\pi$
$97$	13.7422			1.39531			0.697655	+	0.716433i	$0.254227\pi$
$98$		0			0
$99$	−7.41443			−0.745178
$100$	−1.28531	−	2.22621i	−0.128531	−	0.222621i
$101$	2.94729	−	5.10486i	0.293266	−	0.507952i	−0.681314	−	0.731991i	$-0.738591\pi$
$101$	2.94729	−	5.10486i	0.293266	−	0.507952i	0.974580	+	0.224039i	$0.0719244\pi$
$102$	−3.54353	+	6.13757i	−0.350862	+	0.607710i
$103$	1.39368	+	2.41393i	0.137324	+	0.237852i	0.926483	−	0.376337i	$-0.122817\pi$
$103$	1.39368	+	2.41393i	0.137324	+	0.237852i	−0.789159	+	0.614189i	$0.789483\pi$
$104$	1.17715			0.115429
$105$		0			0
$106$	9.64630			0.936932
$107$	8.83236	+	15.2981i	0.853856	+	1.47892i	0.877702	+	0.479207i	$0.159076\pi$
$107$	8.83236	+	15.2981i	0.853856	+	1.47892i	−0.0238454	+	0.999716i	$0.507591\pi$
$108$	−3.05472	+	5.29093i	−0.293941	+	0.509120i
$109$	4.78225	−	8.28310i	0.458057	−	0.793377i	−0.540802	−	0.841150i	$-0.681879\pi$
$109$	4.78225	−	8.28310i	0.458057	−	0.793377i	0.998858	+	0.0477730i	$0.0152124\pi$
$110$	7.85318	+	13.6021i	0.748771	+	1.29691i
$111$	8.58055			0.814430
$112$		0			0
$113$	−17.6017			−1.65583			−0.827916	−	0.560852i	$-0.810474\pi$
$113$	−17.6017			−1.65583			−0.827916	+	0.560852i	$0.810474\pi$
$114$	−3.18054	−	5.50886i	−0.297885	−	0.515952i
$115$	−5.95037	+	10.3063i	−0.554875	+	0.961071i
$116$	0.965699	−	1.67264i	0.0896629	−	0.155301i
$117$	−1.13555	−	1.96683i	−0.104982	−	0.181833i
$118$	4.70535			0.433163
$119$		0			0
$120$	−2.63868			−0.240877
$121$	0.170904	+	0.296015i	0.0155367	+	0.0269104i
$122$	−10.2457	+	17.7460i	−0.927600	+	1.60665i
$123$	1.21349	−	2.10183i	0.109417	−	0.189515i
$124$	−1.90284	−	3.29581i	−0.170880	−	0.295973i
$125$	8.15622			0.729514
$126$		0			0
$127$	−1.59482			−0.141517			−0.0707586	−	0.997493i	$-0.522542\pi$
$127$	−1.59482			−0.141517			−0.0707586	+	0.997493i	$0.522542\pi$
$128$	−4.46569	−	7.73480i	−0.394715	−	0.683667i
$129$	4.15196	−	7.19140i	0.365559	−	0.633167i
$130$	−2.40549	+	4.16643i	−0.210976	+	0.365420i
$131$	2.15140	+	3.72633i	0.187968	+	0.325571i	0.944573	−	0.328302i	$-0.106476\pi$
$131$	2.15140	+	3.72633i	0.187968	+	0.325571i	−0.756604	+	0.653873i	$0.773143\pi$
$132$	−3.78392			−0.329348
$133$		0			0
$134$	−3.63125			−0.313692
$135$	5.90781	+	10.2326i	0.508463	+	0.880684i
$136$	−2.66637	+	4.61828i	−0.228639	+	0.396015i
$137$	−4.91117	+	8.50640i	−0.419590	+	0.726751i	−0.995898	−	0.0904816i	$-0.971159\pi$
$137$	−4.91117	+	8.50640i	−0.419590	+	0.726751i	0.576308	+	0.817232i	$0.304493\pi$
$138$	−3.54545	−	6.14089i	−0.301808	−	0.522747i
$139$	−10.0811			−0.855070			−0.427535	−	0.903999i	$-0.640618\pi$
$139$	−10.0811			−0.855070			−0.427535	+	0.903999i	$0.640618\pi$
$140$		0			0
$141$	−8.06763			−0.679417
$142$	10.7692	+	18.6528i	0.903731	+	1.56531i
$143$	1.63234	−	2.82730i	0.136503	−	0.236431i
$144$	−5.53255	+	9.58266i	−0.461046	+	0.798555i
$145$	−1.86766	−	3.23487i	−0.155100	−	0.268642i
$146$	−22.2434			−1.84087
$147$		0			0
$148$	−13.6442			−1.12154
$149$	6.90619	+	11.9619i	0.565777	+	0.979955i	0.996977	+	0.0776983i	$0.0247571\pi$
$149$	6.90619	+	11.9619i	0.565777	+	0.979955i	−0.431200	+	0.902256i	$0.641910\pi$
$150$	1.48111	−	2.56536i	0.120932	−	0.209461i
$151$	−10.6062	+	18.3704i	−0.863117	+	1.49496i	0.00578805	+	0.999983i	$0.498158\pi$
$151$	−10.6062	+	18.3704i	−0.863117	+	1.49496i	−0.868905	+	0.494979i	$0.835176\pi$
$152$	−2.39323	−	4.14520i	−0.194117	−	0.336220i
$153$	10.2886			0.831780
$154$		0			0
$155$	−7.36015			−0.591182
$156$	−0.579522	−	1.00376i	−0.0463989	−	0.0803653i
$157$	11.7578	−	20.3650i	0.938372	−	1.62531i	0.169864	−	0.985468i	$-0.445667\pi$
$157$	11.7578	−	20.3650i	0.938372	−	1.62531i	0.768508	−	0.639840i	$-0.221000\pi$
$158$	−10.9108	+	18.8980i	−0.868013	+	1.50344i
$159$	2.24725	+	3.89236i	0.178219	+	0.308684i
$160$	17.2584			1.36440
$161$		0			0
$162$	5.44431			0.427745
$163$	−3.91531	−	6.78151i	−0.306671	−	0.531169i	0.670961	−	0.741492i	$-0.265882\pi$
$163$	−3.91531	−	6.78151i	−0.306671	−	0.531169i	−0.977632	+	0.210323i	$0.932548\pi$
$164$	−1.92960	+	3.34217i	−0.150677	+	0.260979i
$165$	−3.65904	+	6.33764i	−0.284856	+	0.493384i
$166$	12.1150	+	20.9838i	0.940306	+	1.62866i
$167$	−12.7116			−0.983654			−0.491827	−	0.870693i	$-0.663671\pi$
$167$	−12.7116			−0.983654			−0.491827	+	0.870693i	$0.663671\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−10.8974	−	18.8748i	−0.835791	−	1.44763i
$171$	−4.61732	+	7.99743i	−0.353095	+	0.611578i
$172$	−6.60213	+	11.4352i	−0.503408	+	0.871928i
$173$	2.62454	+	4.54583i	0.199540	+	0.345613i	0.948379	−	0.317138i	$-0.102722\pi$
$173$	2.62454	+	4.54583i	0.199540	+	0.345613i	−0.748840	+	0.662751i	$0.769389\pi$
$174$	2.22563			0.168725
$175$		0			0
$176$	−15.9060			−1.19896
$177$	1.09618	+	1.89865i	0.0823942	+	0.142711i
$178$	9.77254	−	16.9265i	0.732483	−	1.26870i
$179$	5.26275	−	9.11536i	0.393357	−	0.681314i	−0.599533	−	0.800350i	$-0.704647\pi$
$179$	5.26275	−	9.11536i	0.393357	−	0.681314i	0.992890	+	0.119036i	$0.0379804\pi$
$180$	−4.04755	−	7.01056i	−0.301687	−	0.522537i
$181$	18.8177			1.39871			0.699356	−	0.714774i	$-0.253470\pi$
$181$	18.8177			1.39871			0.699356	+	0.714774i	$0.253470\pi$
$182$		0			0
$183$	−9.54755			−0.705775
$184$	−2.66781	−	4.62078i	−0.196673	−	0.340648i
$185$	−13.1938	+	22.8524i	−0.970031	+	1.68014i
$186$	2.19272	−	3.79791i	0.160778	−	0.278476i
$187$	7.39486	+	12.8083i	0.540766	+	0.936634i
$188$	12.8285			0.935618
$189$		0			0
$190$	19.5622			1.41919
$191$	−7.45722	−	12.9163i	−0.539585	−	0.934589i	−0.998926	−	0.0463292i	$-0.985248\pi$
$191$	−7.45722	−	12.9163i	−0.539585	−	0.934589i	0.459341	−	0.888260i	$-0.348086\pi$
$192$	−0.981980	+	1.70084i	−0.0708683	+	0.122747i
$193$	0.0265678	−	0.0460168i	0.00191239	−	0.00331236i	−0.865068	−	0.501655i	$-0.832725\pi$
$193$	0.0265678	−	0.0460168i	0.00191239	−	0.00331236i	0.866980	+	0.498343i	$0.166058\pi$
$194$	−12.5904	−	21.8072i	−0.903939	−	1.56567i
$195$	−2.24158			−0.160523
$196$		0			0
$197$	10.0478			0.715875			0.357938	−	0.933745i	$-0.383480\pi$
$197$	10.0478			0.715875			0.357938	+	0.933745i	$0.383480\pi$
$198$	6.79299	+	11.7658i	0.482757	+	0.836159i
$199$	11.6457	−	20.1710i	0.825543	−	1.42988i	−0.0759612	−	0.997111i	$-0.524202\pi$
$199$	11.6457	−	20.1710i	0.825543	−	1.42988i	0.901504	−	0.432771i	$-0.142464\pi$
$200$	1.11448	−	1.93034i	0.0788056	−	0.136495i
$201$	−0.845955	−	1.46524i	−0.0596691	−	0.103350i
$202$	−10.8011			−0.759959
$203$		0			0
$204$	5.25072			0.367624
$205$	3.73184	+	6.46373i	0.260643	+	0.451446i
$206$	2.55374	−	4.42321i	0.177928	−	0.308180i
$207$	−5.14706	+	8.91497i	−0.357745	+	0.619633i
$208$	−2.43607	−	4.21939i	−0.168911	−	0.292562i
$209$	−13.2747			−0.918232
$210$		0			0
$211$	−2.47457			−0.170356			−0.0851780	−	0.996366i	$-0.527146\pi$
$211$	−2.47457			−0.170356			−0.0851780	+	0.996366i	$0.527146\pi$
$212$	−3.57342	−	6.18934i	−0.245423	−	0.425085i
$213$	−5.01770	+	8.69091i	−0.343807	+	0.595491i
$214$	16.1842	−	28.0318i	1.10633	−	1.91621i
$215$	12.7685	+	22.1156i	0.870803	+	1.50827i
$216$	−5.29745			−0.360446
$217$		0			0
$218$	−17.5257			−1.18699
$219$	−5.18193	−	8.97537i	−0.350162	−	0.606499i
$220$	5.81833	−	10.0776i	0.392272	−	0.679434i
$221$	−2.26511	+	3.92328i	−0.152367	+	0.263908i
$222$	−7.86137	−	13.6163i	−0.527621	−	0.913866i
$223$	−6.17027			−0.413192			−0.206596	−	0.978426i	$-0.566239\pi$
$223$	−6.17027			−0.413192			−0.206596	+	0.978426i	$0.566239\pi$
$224$		0			0
$225$	−4.30038			−0.286692
$226$	16.1264	+	27.9318i	1.07272	+	1.85800i
$227$	5.79694	−	10.0406i	0.384757	−	0.666418i	−0.606979	−	0.794718i	$-0.707619\pi$
$227$	5.79694	−	10.0406i	0.384757	−	0.666418i	0.991735	+	0.128300i	$0.0409520\pi$
$228$	−2.35643	+	4.08145i	−0.156058	+	0.270301i
$229$	−5.11909	−	8.86653i	−0.338279	−	0.585917i	0.645830	−	0.763481i	$-0.276511\pi$
$229$	−5.11909	−	8.86653i	−0.338279	−	0.585917i	−0.984109	+	0.177565i	$0.943178\pi$
$230$	21.8065			1.43788
$231$		0			0
$232$	1.67470			0.109950
$233$	−10.7411	−	18.6041i	−0.703673	−	1.21880i	−0.967168	−	0.254137i	$-0.918208\pi$
$233$	−10.7411	−	18.6041i	−0.703673	−	1.21880i	0.263495	−	0.964661i	$-0.415125\pi$
$234$	−2.08075	+	3.60396i	−0.136023	+	0.235598i
$235$	12.4052	−	21.4864i	0.809223	−	1.40162i
$236$	−1.74307	−	3.01909i	−0.113464	−	0.196526i
$237$	−10.1673			−0.660437
$238$		0			0
$239$	1.08591			0.0702414			0.0351207	−	0.999383i	$-0.488818\pi$
$239$	1.08591			0.0702414			0.0351207	+	0.999383i	$0.488818\pi$
$240$	5.46065	+	9.45812i	0.352483	+	0.610519i
$241$	−9.99149	+	17.3058i	−0.643608	+	1.11476i	0.341013	+	0.940059i	$0.389230\pi$
$241$	−9.99149	+	17.3058i	−0.643608	+	1.11476i	−0.984621	+	0.174704i	$0.944103\pi$
$242$	0.313160	−	0.542408i	0.0201307	−	0.0348673i
$243$	8.01869	+	13.8888i	0.514399	+	0.890966i
$244$	15.1818			0.971915
$245$		0			0
$246$	−4.44713			−0.283538
$247$	−2.03308	−	3.52139i	−0.129362	−	0.224061i
$248$	1.64994	−	2.85778i	0.104771	−	0.181469i
$249$	−5.64475	+	9.77699i	−0.357721	+	0.619592i
$250$	−7.47261	−	12.9429i	−0.472609	−	0.818583i
$251$	−20.1497			−1.27184			−0.635920	−	0.771755i	$-0.719379\pi$
$251$	−20.1497			−1.27184			−0.635920	+	0.771755i	$0.719379\pi$
$252$		0			0
$253$	−14.7977			−0.930325
$254$	1.46115	+	2.53078i	0.0916806	+	0.158795i
$255$	5.07742	−	8.79436i	0.317961	−	0.550724i
$256$	−10.4832	+	18.1574i	−0.655198	+	1.13484i
$257$	−7.50869	−	13.0054i	−0.468379	−	0.811257i	0.530968	−	0.847392i	$-0.321829\pi$
$257$	−7.50869	−	13.0054i	−0.468379	−	0.811257i	−0.999347	+	0.0361353i	$0.988495\pi$
$258$	−15.2158			−0.947297
$259$		0			0
$260$	3.56440			0.221055
$261$	−1.61552	−	2.79816i	−0.0999981	−	0.173202i
$262$	3.94216	−	6.82801i	0.243547	−	0.421836i
$263$	10.5831	−	18.3305i	0.652582	−	1.13031i	−0.329912	−	0.944012i	$-0.607019\pi$
$263$	10.5831	−	18.3305i	0.652582	−	1.13031i	0.982494	−	0.186294i	$-0.0596477\pi$
$264$	−1.64051	−	2.84144i	−0.100966	−	0.174879i
$265$	−13.8219			−0.849074
$266$		0			0
$267$	9.10665			0.557318
$268$	1.34517	+	2.32991i	0.0821696	+	0.142322i
$269$	−2.05240	+	3.55486i	−0.125137	+	0.216744i	−0.921786	−	0.387698i	$-0.873270\pi$
$269$	−2.05240	+	3.55486i	−0.125137	+	0.216744i	0.796650	+	0.604442i	$0.206604\pi$
$270$	10.8253	−	18.7499i	0.658806	−	1.14109i
$271$	1.71622	+	2.97258i	0.104253	+	0.180571i	0.913433	−	0.406990i	$-0.133422\pi$
$271$	1.71622	+	2.97258i	0.104253	+	0.180571i	−0.809180	+	0.587561i	$0.800088\pi$
$272$	22.0718			1.33830
$273$		0			0
$274$	17.9982			1.08731
$275$	−3.09088	−	5.35356i	−0.186387	−	0.322832i
$276$	−2.62678	+	4.54971i	−0.158113	+	0.273860i
$277$	0.180506	−	0.312645i	0.0108455	−	0.0187850i	−0.860552	−	0.509363i	$-0.829881\pi$
$277$	0.180506	−	0.312645i	0.0108455	−	0.0187850i	0.871397	+	0.490578i	$0.163214\pi$
$278$	9.23618	+	15.9975i	0.553949	+	0.959468i
$279$	−6.36652			−0.381154
$280$		0			0
$281$	18.5213			1.10489			0.552445	−	0.833550i	$-0.313695\pi$
$281$	18.5213			1.10489			0.552445	+	0.833550i	$0.313695\pi$
$282$	7.39144	+	12.8024i	0.440154	+	0.762369i
$283$	−0.805788	+	1.39567i	−0.0478991	+	0.0829637i	−0.888981	−	0.457944i	$-0.848586\pi$
$283$	−0.805788	+	1.39567i	−0.0478991	+	0.0829637i	0.841082	+	0.540908i	$0.181919\pi$
$284$	7.97877	−	13.8196i	0.473453	−	0.820045i
$285$	4.55731	+	7.89349i	0.269952	+	0.467570i
$286$	−5.98212			−0.353730
$287$		0			0
$288$	14.9285			0.879671
$289$	−1.76140	−	3.05084i	−0.103612	−	0.179461i
$290$	−3.42224	+	5.92749i	−0.200961	+	0.348074i
$291$	5.86626	−	10.1607i	0.343886	−	0.595628i
$292$	8.23992	+	14.2720i	0.482205	+	0.835203i
$293$	4.41671			0.258027			0.129013	−	0.991643i	$-0.458819\pi$
$293$	4.41671			0.258027			0.129013	+	0.991643i	$0.458819\pi$
$294$		0			0
$295$	−6.74217			−0.392544
$296$	−5.91538	−	10.2457i	−0.343824	−	0.595521i
$297$	−7.34594	+	12.7235i	−0.426255	+	0.738295i
$298$	12.6547	−	21.9186i	0.733067	−	1.26971i
$299$	−2.26633	−	3.92540i	−0.131065	−	0.227012i
$300$	−2.19468			−0.126710
$301$		0			0
$302$	38.8688			2.23665
$303$	−2.51627	−	4.35831i	−0.144556	−	0.250378i
$304$	−9.90542	+	17.1567i	−0.568115	+	0.984004i
$305$	14.6807	−	25.4278i	0.840617	−	1.45599i
$306$	−9.42622	−	16.3267i	−0.538861	−	0.933335i
$307$	5.78353			0.330083			0.165042	−	0.986287i	$-0.447224\pi$
$307$	5.78353			0.330083			0.165042	+	0.986287i	$0.447224\pi$
$308$		0			0
$309$	2.37973			0.135378
$310$	6.74326	+	11.6797i	0.382992	+	0.663361i
$311$	7.14476	−	12.3751i	0.405142	−	0.701727i	−0.589196	−	0.807990i	$-0.700555\pi$
$311$	7.14476	−	12.3751i	0.405142	−	0.701727i	0.994338	+	0.106264i	$0.0338887\pi$
$312$	0.502500	−	0.870355i	0.0284485	−	0.0492742i
$313$	1.36862	+	2.37053i	0.0773592	+	0.133990i	0.902110	−	0.431507i	$-0.142018\pi$
$313$	1.36862	+	2.37053i	0.0773592	+	0.133990i	−0.824751	+	0.565497i	$0.808685\pi$
$314$	−43.0892			−2.43166
$315$		0			0
$316$	16.1673			0.909481
$317$	−5.32560	−	9.22422i	−0.299116	−	0.518084i	0.676818	−	0.736150i	$-0.263358\pi$
$317$	−5.32560	−	9.22422i	−0.299116	−	0.518084i	−0.975934	+	0.218067i	$0.930025\pi$
$318$	4.11780	−	7.13224i	0.230915	−	0.399956i
$319$	2.32230	−	4.02234i	0.130024	−	0.225208i
$320$	−3.01987	−	5.23057i	−0.168816	−	0.292398i
$321$	15.0814			0.841761
$322$		0			0
$323$	18.4205			1.02495
$324$	−2.01681	−	3.49322i	−0.112045	−	0.194068i
$325$	0.946761	−	1.63984i	0.0525169	−	0.0909619i
$326$	−7.17430	+	12.4262i	−0.397347	+	0.688226i
$327$	−4.08288	−	7.07176i	−0.225784	−	0.391069i
$328$	−3.34629			−0.184768
$329$		0			0
$330$	13.4094			0.738164
$331$	1.70813	+	2.95856i	0.0938872	+	0.162617i	0.909144	−	0.416483i	$-0.136737\pi$
$331$	1.70813	+	2.95856i	0.0938872	+	0.162617i	−0.815256	+	0.579100i	$0.803404\pi$
$332$	8.97586	−	15.5466i	0.492614	−	0.853233i
$333$	−11.4127	+	19.7673i	−0.625410	+	1.08324i
$334$	11.6462	+	20.1718i	0.637251	+	1.10375i
$335$	5.20312			0.284277
$336$		0			0
$337$	24.9606			1.35969			0.679844	−	0.733357i	$-0.262047\pi$
$337$	24.9606			1.35969			0.679844	+	0.733357i	$0.262047\pi$
$338$	−0.916185	−	1.58688i	−0.0498339	−	0.0863149i
$339$	−7.51380	+	13.0143i	−0.408094	+	0.706839i
$340$	−8.07374	+	13.9841i	−0.437860	+	0.758396i
$341$	−4.57591	−	7.92572i	−0.247800	−	0.429202i
$342$	16.9213			0.914997
$343$		0			0
$344$	−11.4493			−0.617306
$345$	5.08017	+	8.79911i	0.273507	+	0.473728i
$346$	4.80912	−	8.32964i	0.258540	−	0.447804i
$347$	9.59165	−	16.6132i	0.514907	−	0.891845i	−0.484944	−	0.874545i	$-0.661160\pi$
$347$	9.59165	−	16.6132i	0.514907	−	0.891845i	0.999850	−	0.0172992i	$-0.00550678\pi$
$348$	−0.824473	−	1.42803i	−0.0441964	−	0.0765504i
$349$	3.94421			0.211129			0.105564	−	0.994412i	$-0.466335\pi$
$349$	3.94421			0.211129			0.105564	+	0.994412i	$0.466335\pi$
$350$		0			0
$351$	−4.50024			−0.240205
$352$	10.7298	+	18.5846i	0.571901	+	0.990562i
$353$	14.0116	−	24.2688i	0.745762	−	1.29170i	−0.204076	−	0.978955i	$-0.565419\pi$
$353$	14.0116	−	24.2688i	0.745762	−	1.29170i	0.949838	−	0.312743i	$-0.101248\pi$
$354$	2.00861	−	3.47902i	0.106757	−	0.184908i
$355$	−15.4309	−	26.7271i	−0.818986	−	1.41853i
$356$	−14.4807			−0.767476
$357$		0			0
$358$	−19.2866			−1.01933
$359$	−16.6116	−	28.7721i	−0.876726	−	1.51853i	−0.854912	−	0.518773i	$-0.826389\pi$
$359$	−16.6116	−	28.7721i	−0.876726	−	1.51853i	−0.0218141	−	0.999762i	$-0.506944\pi$
$360$	3.50960	−	6.07881i	0.184972	−	0.320382i
$361$	1.23320	−	2.13597i	0.0649054	−	0.112419i
$362$	−17.2405	−	29.8615i	−0.906142	−	1.56948i
$363$	0.291821			0.0153166
$364$		0			0
$365$	31.8719			1.66825
$366$	8.74733	+	15.1508i	0.457230	+	0.791946i
$367$	−14.1546	+	24.5164i	−0.738862	+	1.27975i	0.214146	+	0.976802i	$0.431303\pi$
$367$	−14.1546	+	24.5164i	−0.738862	+	1.27975i	−0.953008	+	0.302945i	$0.902030\pi$
$368$	−11.0419	+	19.1251i	−0.575597	+	0.996963i
$369$	3.22803	+	5.59112i	0.168045	+	0.291062i
$370$	48.3520			2.51370
$371$		0			0
$372$	−3.24912			−0.168459
$373$	6.47573	+	11.2163i	0.335301	+	0.580758i	0.983543	−	0.180677i	$-0.0578287\pi$
$373$	6.47573	+	11.2163i	0.335301	+	0.580758i	−0.648242	+	0.761435i	$0.724495\pi$
$374$	13.5501	−	23.4695i	0.700660	−	1.21358i
$375$	3.48171	−	6.03051i	0.179795	−	0.311414i
$376$	5.56177	+	9.63327i	0.286827	+	0.496798i
$377$	1.42268			0.0732716
$378$		0			0
$379$	0.168981			0.00867995			0.00433997	−	0.999991i	$-0.498619\pi$
$379$	0.168981			0.00867995			0.00433997	+	0.999991i	$0.498619\pi$
$380$	−7.24670	−	12.5516i	−0.371748	−	0.643886i
$381$	−0.680794	+	1.17917i	−0.0348781	+	0.0604107i
$382$	−13.6644	+	23.6674i	−0.699131	+	1.21093i
$383$	5.09665	+	8.82766i	0.260427	+	0.451073i	0.966355	−	0.257210i	$-0.0828034\pi$
$383$	5.09665	+	8.82766i	0.260427	+	0.451073i	−0.705929	+	0.708283i	$0.749470\pi$
$384$	−7.62523			−0.389124
$385$		0			0
$386$	−0.0973641			−0.00495570
$387$	11.0447	+	19.1300i	0.561434	+	0.972432i
$388$	−9.32809	+	16.1567i	−0.473562	+	0.820233i
$389$	14.3332	−	24.8259i	0.726723	−	1.25872i	−0.231537	−	0.972826i	$-0.574376\pi$
$389$	14.3332	−	24.8259i	0.726723	−	1.25872i	0.958261	−	0.285896i	$-0.0922911\pi$
$390$	2.05371	+	3.55712i	0.103993	+	0.180122i
$391$	20.5339			1.03844
$392$		0			0
$393$	3.67354			0.185306
$394$	−9.20564	−	15.9446i	−0.463773	−	0.803279i
$395$	15.6337	−	27.0784i	0.786617	−	1.36246i
$396$	5.03284	−	8.71714i	0.252910	−	0.438053i
$397$	−14.3206	−	24.8039i	−0.718728	−	1.24487i	−0.961504	−	0.274791i	$-0.911391\pi$
$397$	−14.3206	−	24.8039i	−0.718728	−	1.24487i	0.242776	−	0.970082i	$-0.421942\pi$
$398$	−42.6785			−2.13928
$399$		0			0
$400$	−9.22550			−0.461275
$401$	7.14814	+	12.3809i	0.356961	+	0.618275i	0.987452	−	0.157922i	$-0.0504795\pi$
$401$	7.14814	+	12.3809i	0.356961	+	0.618275i	−0.630490	+	0.776197i	$0.717146\pi$
$402$	−1.55010	+	2.68486i	−0.0773121	+	0.133909i
$403$	1.40164	−	2.42771i	0.0698206	−	0.120933i
$404$	4.00118	+	6.93026i	0.199066	+	0.344793i
$405$	−7.80100			−0.387635
$406$		0			0
$407$	−32.8112			−1.62639
$408$	2.27643	+	3.94289i	0.112700	+	0.195202i
$409$	12.8494	−	22.2558i	0.635362	−	1.10048i	−0.351077	−	0.936347i	$-0.614184\pi$
$409$	12.8494	−	22.2558i	0.635362	−	1.10048i	0.986438	−	0.164132i	$-0.0524824\pi$
$410$	6.83810	−	11.8439i	0.337710	−	0.584931i
$411$	4.19295	+	7.26240i	0.206823	+	0.358228i
$412$	−3.78408			−0.186428
$413$		0			0
$414$	18.8626			0.927048
$415$	−17.3592	−	30.0671i	−0.852132	−	1.47594i
$416$	−3.28663	+	5.69261i	−0.161140	+	0.279103i
$417$	−4.30342	+	7.45374i	−0.210739	+	0.365011i
$418$	12.1621	+	21.0654i	0.594868	+	1.03034i
$419$	−18.7999			−0.918433			−0.459216	−	0.888324i	$-0.651870\pi$
$419$	−18.7999			−0.918433			−0.459216	+	0.888324i	$0.651870\pi$
$420$		0			0
$421$	−18.0283			−0.878645			−0.439322	−	0.898329i	$-0.644781\pi$
$421$	−18.0283			−0.878645			−0.439322	+	0.898329i	$0.644781\pi$
$422$	2.26716	+	3.92684i	0.110364	+	0.191155i
$423$	10.7304	−	18.5857i	0.521732	−	0.903666i
$424$	3.09848	−	5.36673i	0.150476	−	0.260632i
$425$	4.28903	+	7.42882i	0.208048	+	0.360350i
$426$	18.3886			0.890929
$427$		0			0
$428$	−23.9813			−1.15918
$429$	−1.39363	−	2.41383i	−0.0672849	−	0.116541i
$430$	23.3966	−	40.5240i	1.12828	−	1.95424i
$431$	−10.2791	+	17.8040i	−0.495128	+	0.857587i	−0.999984	−	0.00561653i	$-0.998212\pi$
$431$	−10.2791	+	17.8040i	−0.495128	+	0.857587i	0.504856	+	0.863203i	$0.331546\pi$
$432$	10.9629	+	18.9883i	0.527452	+	0.913574i
$433$	−18.9235			−0.909404			−0.454702	−	0.890644i	$-0.650254\pi$
$433$	−18.9235			−0.909404			−0.454702	+	0.890644i	$0.650254\pi$
$434$		0			0
$435$	−3.18905			−0.152903
$436$	6.49229	+	11.2450i	0.310924	+	0.538537i
$437$	−9.21524	+	15.9613i	−0.440825	+	0.763531i
$438$	−9.49522	+	16.4462i	−0.453699	+	0.785830i
$439$	−7.32750	−	12.6916i	−0.349723	−	0.605737i	0.636477	−	0.771295i	$-0.280391\pi$
$439$	−7.32750	−	12.6916i	−0.349723	−	0.605737i	−0.986200	+	0.165558i	$0.947058\pi$
$440$	10.0901			0.481025
$441$		0			0
$442$	8.30102			0.394839
$443$	5.97962	+	10.3570i	0.284100	+	0.492076i	0.972391	−	0.233359i	$-0.0749718\pi$
$443$	5.97962	+	10.3570i	0.284100	+	0.492076i	−0.688290	+	0.725435i	$0.741638\pi$
$444$	−5.82440	+	10.0882i	−0.276414	+	0.478763i
$445$	−14.0028	+	24.2536i	−0.663796	+	1.14973i
$446$	5.65311	+	9.79148i	0.267683	+	0.463640i
$447$	11.7924			0.557762
$448$		0			0
$449$	−2.32245			−0.109603			−0.0548015	−	0.998497i	$-0.517453\pi$
$449$	−2.32245			−0.109603			−0.0548015	+	0.998497i	$0.517453\pi$
$450$	3.93994	+	6.82418i	0.185731	+	0.321695i
$451$	−4.64027	+	8.03719i	−0.218502	+	0.378457i
$452$	11.9479	−	20.6944i	0.561981	−	0.973380i
$453$	9.05508	+	15.6839i	0.425445	+	0.736892i
$454$	−21.2443			−0.997044
$455$		0			0
$456$	−4.08648			−0.191367
$457$	9.29023	+	16.0912i	0.434579	+	0.752712i	0.997261	−	0.0739607i	$-0.0235639\pi$
$457$	9.29023	+	16.0912i	0.434579	+	0.752712i	−0.562682	+	0.826673i	$0.690231\pi$
$458$	−9.38007	+	16.2468i	−0.438302	+	0.759161i
$459$	10.1935	−	17.6557i	0.475793	−	0.824097i
$460$	−8.07810	−	13.9917i	−0.376644	−	0.652366i
$461$	−27.8926			−1.29909			−0.649543	−	0.760325i	$-0.725040\pi$
$461$	−27.8926			−1.29909			−0.649543	+	0.760325i	$0.725040\pi$
$462$		0			0
$463$	−3.66462			−0.170309			−0.0851547	−	0.996368i	$-0.527138\pi$
$463$	−3.66462			−0.170309			−0.0851547	+	0.996368i	$0.527138\pi$
$464$	−3.46574	−	6.00283i	−0.160893	−	0.278674i
$465$	−3.14189	+	5.44192i	−0.145702	+	0.252363i
$466$	−19.6817	+	34.0897i	−0.911737	+	1.57917i
$467$	19.3766	+	33.5612i	0.896641	+	1.55303i	0.831760	+	0.555136i	$0.187334\pi$
$467$	19.3766	+	33.5612i	0.896641	+	1.55303i	0.0648815	+	0.997893i	$0.479333\pi$
$468$	3.08320			0.142521
$469$		0			0
$470$	−45.4617			−2.09699
$471$	−10.0383	−	17.3868i	−0.462539	−	0.801142i
$472$	1.51140	−	2.61783i	0.0695680	−	0.120495i
$473$	−15.8767	+	27.4992i	−0.730011	+	1.26442i
$474$	9.31513	+	16.1343i	0.427858	+	0.741072i
$475$	−7.69935			−0.353270
$476$		0			0
$477$	−11.9559			−0.547425
$478$	−0.994891	−	1.72320i	−0.0455052	−	0.0788174i
$479$	−3.01715	+	5.22585i	−0.137857	+	0.238775i	−0.926685	−	0.375838i	$-0.877355\pi$
$479$	−3.01715	+	5.22585i	−0.137857	+	0.238775i	0.788828	+	0.614614i	$0.210688\pi$
$480$	7.36726	−	12.7605i	0.336268	−	0.582433i
$481$	−5.02517	−	8.70385i	−0.229128	−	0.396861i
$482$	36.6162			1.66782
$483$		0			0
$484$	−0.464032			−0.0210924
$485$	18.0405	+	31.2470i	0.819175	+	1.41885i
$486$	14.6932	−	25.4494i	0.666498	−	1.15441i
$487$	1.90125	−	3.29305i	0.0861537	−	0.149223i	−0.819729	−	0.572752i	$-0.805876\pi$
$487$	1.90125	−	3.29305i	0.0861537	−	0.149223i	0.905882	+	0.423530i	$0.139209\pi$
$488$	6.58202	+	11.4004i	0.297954	+	0.516072i
$489$	−6.68545			−0.302326
$490$		0			0
$491$	−0.381464			−0.0172152			−0.00860761	−	0.999963i	$-0.502740\pi$
$491$	−0.381464			−0.0172152			−0.00860761	+	0.999963i	$0.502740\pi$
$492$	1.64741	+	2.85340i	0.0742710	+	0.128641i
$493$	−3.22251	+	5.58156i	−0.145135	+	0.251381i
$494$	−3.72535	+	6.45249i	−0.167611	+	0.290311i
$495$	−9.73348	−	16.8589i	−0.437488	−	0.757751i
$496$	−13.6580			−0.613260
$497$		0			0
$498$	20.6865			0.926986
$499$	−17.2870	−	29.9419i	−0.773871	−	1.34038i	−0.935427	−	0.353520i	$-0.884985\pi$
$499$	−17.2870	−	29.9419i	−0.773871	−	1.34038i	0.161556	−	0.986864i	$-0.448349\pi$
$500$	−5.53636	+	9.58926i	−0.247594	+	0.428845i
$501$	−5.42632	+	9.39866i	−0.242430	+	0.419901i
$502$	18.4609	+	31.9752i	0.823950	+	1.42712i
$503$	2.41090			0.107497			0.0537485	−	0.998555i	$-0.482883\pi$
$503$	2.41090			0.107497			0.0537485	+	0.998555i	$0.482883\pi$
$504$		0			0
$505$	15.4765			0.688696
$506$	13.5575	+	23.4822i	0.602702	+	1.04391i
$507$	0.426879	−	0.739375i	0.0189583	−	0.0328368i
$508$	1.08255	−	1.87503i	0.0480303	−	0.0831908i
$509$	−10.9577	−	18.9792i	−0.485690	−	0.841239i	0.514175	−	0.857685i	$-0.328098\pi$
$509$	−10.9577	−	18.9792i	−0.485690	−	0.841239i	−0.999865	+	0.0164459i	$0.994765\pi$
$510$	−18.6074			−0.823951
$511$		0			0
$512$	20.5553			0.908426
$513$	9.14933	+	15.8471i	0.403953	+	0.699667i
$514$	−13.7587	+	23.8308i	−0.606871	+	1.05113i
$515$	−3.65919	+	6.33790i	−0.161243	+	0.279281i
$516$	5.63662	+	9.76291i	0.248138	+	0.429788i
$517$	30.8499			1.35678
$518$		0			0
$519$	4.48143			0.196713
$520$	1.54533	+	2.67660i	0.0677674	+	0.117377i
$521$	−15.0725	+	26.1063i	−0.660338	+	1.14374i	0.320188	+	0.947354i	$0.396254\pi$
$521$	−15.0725	+	26.1063i	−0.660338	+	1.14374i	−0.980527	+	0.196386i	$0.937079\pi$
$522$	−2.96023	+	5.12727i	−0.129566	+	0.224414i
$523$	−9.04966	−	15.6745i	−0.395714	−	0.685397i	0.597478	−	0.801885i	$-0.296170\pi$
$523$	−9.04966	−	15.6745i	−0.395714	−	0.685397i	−0.993192	+	0.116489i	$0.962836\pi$
$524$	−5.84139			−0.255182
$525$		0			0
$526$	−38.7843			−1.69108
$527$	6.34972	+	10.9980i	0.276598	+	0.479082i
$528$	−6.78993	+	11.7605i	−0.295494	+	0.511811i
$529$	1.22750	−	2.12609i	0.0533695	−	0.0924387i
$530$	12.6634	+	21.9337i	0.550065	+	0.952740i
$531$	−5.83197			−0.253086
$532$		0			0
$533$	−2.84271			−0.123131
$534$	−8.34338	−	14.4512i	−0.361053	−	0.625363i
$535$	−23.1898	+	40.1659i	−1.00258	+	1.73653i
$536$	−1.16639	+	2.02025i	−0.0503805	+	0.0872615i
$537$	−4.49312	−	7.78230i	−0.193892	−	0.335831i
$538$	7.52151			0.324275
$539$		0			0
$540$	−16.0406			−0.690280
$541$	−2.04445	−	3.54109i	−0.0878977	−	0.152243i	0.818725	−	0.574186i	$-0.194682\pi$
$541$	−2.04445	−	3.54109i	−0.0878977	−	0.152243i	−0.906622	+	0.421943i	$0.861348\pi$
$542$	3.14475	−	5.44686i	0.135079	−	0.233963i
$543$	8.03289	−	13.9134i	0.344724	−	0.597080i
$544$	−14.8891	−	25.7887i	−0.638366	−	1.10568i
$545$	25.1121			1.07568
$546$		0			0
$547$	−40.4264			−1.72851			−0.864255	−	0.503055i	$-0.832209\pi$
$547$	−40.4264			−1.72851			−0.864255	+	0.503055i	$0.832209\pi$
$548$	−6.66731	−	11.5481i	−0.284814	−	0.493311i
$549$	12.6988	−	21.9950i	0.541973	−	0.938724i
$550$	−5.66364	+	9.80971i	−0.241498	+	0.418287i
$551$	−2.89241	−	5.00980i	−0.123221	−	0.213425i
$552$	−4.55532			−0.193887
$553$		0			0
$554$	−0.661507			−0.0281047
$555$	11.2643	+	19.5104i	0.478145	+	0.828171i
$556$	6.84297	−	11.8524i	0.290207	−	0.502653i
$557$	−9.88450	+	17.1205i	−0.418820	+	0.725417i	−0.995821	−	0.0913260i	$-0.970889\pi$
$557$	−9.88450	+	17.1205i	−0.418820	+	0.725417i	0.577001	+	0.816743i	$0.304223\pi$
$558$	5.83291	+	10.1029i	0.246927	+	0.427690i
$559$	−9.72632			−0.411379
$560$		0			0
$561$	12.6268			0.533105
$562$	−16.9690	−	29.3911i	−0.715792	−	1.23979i
$563$	4.11196	−	7.12212i	0.173298	−	0.300162i	−0.766273	−	0.642515i	$-0.777891\pi$
$563$	4.11196	−	7.12212i	0.173298	−	0.300162i	0.939571	+	0.342354i	$0.111224\pi$
$564$	5.47623	−	9.48511i	0.230591	−	0.399395i
$565$	−23.1071	−	40.0227i	−0.972124	−	1.68377i
$566$	2.95300			0.124124
$567$		0			0
$568$	13.8367			0.580574
$569$	−7.28849	−	12.6240i	−0.305550	−	0.529227i	0.671834	−	0.740702i	$-0.265507\pi$
$569$	−7.28849	−	12.6240i	−0.305550	−	0.529227i	−0.977384	+	0.211474i	$0.932174\pi$
$570$	8.35068	−	14.4638i	0.349772	−	0.605822i
$571$	1.29411	−	2.24146i	0.0541568	−	0.0938023i	−0.837676	−	0.546167i	$-0.816086\pi$
$571$	1.29411	−	2.24146i	0.0541568	−	0.0938023i	0.891833	+	0.452365i	$0.149420\pi$
$572$	2.21604	+	3.83829i	0.0926573	+	0.160487i
$573$	−12.7333			−0.531942
$574$		0			0
$575$	−8.58269			−0.357923
$576$	−2.61219	−	4.52444i	−0.108841	−	0.188518i
$577$	−11.9468	+	20.6925i	−0.497353	+	0.861441i	−0.999995	−	0.00305340i	$-0.999028\pi$
$577$	−11.9468	+	20.6925i	−0.497353	+	0.861441i	0.502642	+	0.864495i	$0.332361\pi$
$578$	−3.22754	+	5.59027i	−0.134248	+	0.232525i
$579$	−0.0226825	−	0.0392872i	−0.000942651	−	0.00163272i
$580$	5.07099			0.210561
$581$		0			0
$582$	−21.4983			−0.891134
$583$	−8.59329	−	14.8840i	−0.355898	−	0.616433i
$584$	−7.14478	+	12.3751i	−0.295653	+	0.512086i
$585$	2.98144	−	5.16401i	0.123268	−	0.213506i
$586$	−4.04652	−	7.00878i	−0.167160	−	0.289530i
$587$	−28.5759			−1.17945			−0.589726	−	0.807604i	$-0.700764\pi$
$587$	−28.5759			−1.17945			−0.589726	+	0.807604i	$0.700764\pi$
$588$		0			0
$589$	−11.3986			−0.469669
$590$	6.17707	+	10.6990i	0.254306	+	0.440471i
$591$	4.28919	−	7.42909i	0.176434	−	0.305592i
$592$	−24.4833	+	42.4063i	−1.00626	+	1.74289i
$593$	−9.97874	−	17.2837i	−0.409778	−	0.709756i	0.585087	−	0.810971i	$-0.301060\pi$
$593$	−9.97874	−	17.2837i	−0.409778	−	0.709756i	−0.994865	+	0.101215i	$0.967727\pi$
$594$	26.9210			1.10458
$595$		0			0
$596$	−18.7514			−0.768088
$597$	−9.94261	−	17.2211i	−0.406924	−	0.704813i
$598$	−4.15276	+	7.19278i	−0.169819	+	0.294135i
$599$	−0.588578	+	1.01945i	−0.0240486	+	0.0416535i	−0.877799	−	0.479029i	$-0.840989\pi$
$599$	−0.588578	+	1.01945i	−0.0240486	+	0.0416535i	0.853751	+	0.520682i	$0.174322\pi$
$600$	−0.951495	−	1.64804i	−0.0388446	−	0.0672809i
$601$	30.9250			1.26146			0.630729	−	0.776003i	$-0.282756\pi$
$601$	30.9250			1.26146			0.630729	+	0.776003i	$0.282756\pi$
$602$		0			0
$603$	4.50069			0.183282
$604$	−14.3987	−	24.9393i	−0.585876	−	1.01477i
$605$	−0.448718	+	0.777202i	−0.0182430	+	0.0315977i
$606$	−4.61074	+	7.98603i	−0.187298	+	0.324410i
$607$	1.20354	+	2.08460i	0.0488503	+	0.0846111i	0.889417	−	0.457097i	$-0.151111\pi$
$607$	1.20354	+	2.08460i	0.0488503	+	0.0846111i	−0.840566	+	0.541709i	$0.817778\pi$
$608$	26.7279			1.08396
$609$		0			0
$610$	−53.8011			−2.17834
$611$	4.72478	+	8.18356i	0.191144	+	0.331071i
$612$	−6.98377	+	12.0963i	−0.282302	+	0.488962i
$613$	13.8871	−	24.0532i	0.560895	−	0.971499i	−0.436524	−	0.899693i	$-0.643790\pi$
$613$	13.8871	−	24.0532i	0.560895	−	0.971499i	0.997419	−	0.0718060i	$-0.0228762\pi$
$614$	−5.29878	−	9.17776i	−0.213841	−	0.370384i
$615$	6.37216			0.256950
$616$		0			0
$617$	26.2125			1.05527			0.527637	−	0.849470i	$-0.323078\pi$
$617$	26.2125			1.05527			0.527637	+	0.849470i	$0.323078\pi$
$618$	−2.18028	−	3.77635i	−0.0877036	−	0.151907i
$619$	−8.61787	+	14.9266i	−0.346381	+	0.599950i	−0.985604	−	0.169072i	$-0.945923\pi$
$619$	−8.61787	+	14.9266i	−0.346381	+	0.599950i	0.639222	+	0.769022i	$0.279256\pi$
$620$	4.99600	−	8.65333i	0.200644	−	0.347526i
$621$	10.1990	+	17.6652i	0.409273	+	0.708881i
$622$	−26.1837			−1.04987
$623$		0			0
$624$	−4.15962			−0.166518
$625$	15.4411	+	26.7448i	0.617644	+	1.06979i
$626$	2.50783	−	4.34368i	0.100233	−	0.173608i
$627$	−5.66669	+	9.81500i	−0.226306	+	0.391973i
$628$	15.9621	+	27.6472i	0.636958	+	1.10324i
$629$	45.5302			1.81541
$630$		0			0
$631$	39.2125			1.56103			0.780513	−	0.625140i	$-0.214958\pi$
$631$	39.2125			1.56103			0.780513	+	0.625140i	$0.214958\pi$
$632$	7.00927	+	12.1404i	0.278814	+	0.482920i
$633$	−1.05634	+	1.82963i	−0.0419857	+	0.0727214i
$634$	−9.75848	+	16.9022i	−0.387559	+	0.671271i
$635$	−2.09364	−	3.62629i	−0.0830835	−	0.143905i
$636$	−6.10166			−0.241946
$637$		0			0
$638$	−8.51062			−0.336939
$639$	−13.3477	−	23.1189i	−0.528027	−	0.914569i
$640$	11.7249	−	20.3081i	0.463468	−	0.802749i
$641$	11.4368	−	19.8091i	0.451725	−	0.782411i	−0.546768	−	0.837284i	$-0.684142\pi$
$641$	11.4368	−	19.8091i	0.451725	−	0.782411i	0.998493	+	0.0548728i	$0.0174753\pi$
$642$	−13.8173	−	23.9323i	−0.545327	−	0.944534i
$643$	46.7072			1.84195			0.920976	−	0.389620i	$-0.127394\pi$
$643$	46.7072			1.84195			0.920976	+	0.389620i	$0.127394\pi$
$644$		0			0
$645$	21.8024			0.858467
$646$	−16.8766	−	29.2312i	−0.664001	−	1.15008i
$647$	2.96538	−	5.13618i	0.116581	−	0.201924i	−0.801830	−	0.597553i	$-0.796140\pi$
$647$	2.96538	−	5.13618i	0.116581	−	0.201924i	0.918411	+	0.395629i	$0.129473\pi$
$648$	1.74876	−	3.02895i	0.0686979	−	0.118988i
$649$	−4.19171	−	7.26025i	−0.164539	−	0.284990i
$650$	−3.46963			−0.136090
$651$		0			0
$652$	10.6307			0.416330
$653$	9.40230	+	16.2853i	0.367940	+	0.637292i	0.989243	−	0.146279i	$-0.0467297\pi$
$653$	9.40230	+	16.2853i	0.367940	+	0.637292i	−0.621303	+	0.783570i	$0.713396\pi$
$654$	−7.48135	+	12.9581i	−0.292544	+	0.506701i
$655$	−5.64860	+	9.78367i	−0.220709	+	0.382280i
$656$	6.92502	+	11.9945i	0.270377	+	0.468306i
$657$	27.5691			1.07557
$658$		0			0
$659$	23.1086			0.900184			0.450092	−	0.892982i	$-0.351391\pi$
$659$	23.1086			0.900184			0.450092	+	0.892982i	$0.351391\pi$
$660$	−4.96744	−	8.60386i	−0.193357	−	0.334905i
$661$	−16.9543	+	29.3658i	−0.659447	+	1.14220i	0.321312	+	0.946973i	$0.395876\pi$
$661$	−16.9543	+	29.3658i	−0.659447	+	1.14220i	−0.980759	+	0.195222i	$0.937457\pi$
$662$	3.12992	−	5.42119i	0.121648	−	0.210700i
$663$	1.93385	+	3.34953i	0.0751045	+	0.130085i
$664$	15.5658			0.604071
$665$		0			0
$666$	41.8244			1.62066
$667$	−3.22425	−	5.58457i	−0.124844	−	0.216236i
$668$	8.62852	−	14.9450i	0.333848	−	0.578241i
$669$	−2.63396	+	4.56215i	−0.101835	+	0.176383i
$670$	−4.76702	−	8.25672i	−0.184166	−	0.318985i
$671$	36.5090			1.40941
$672$		0			0
$673$	6.00430			0.231449			0.115724	−	0.993281i	$-0.463081\pi$
$673$	6.00430			0.231449			0.115724	+	0.993281i	$0.463081\pi$
$674$	−22.8685	−	39.6094i	−0.880862	−	1.52570i
$675$	−4.26065	+	7.37967i	−0.163993	+	0.284043i
$676$	−0.678791	+	1.17570i	−0.0261073	+	0.0452192i
$677$	10.1037	+	17.5002i	0.388318	+	0.672587i	0.992224	−	0.124469i	$-0.0397227\pi$
$677$	10.1037	+	17.5002i	0.388318	+	0.672587i	−0.603905	+	0.797056i	$0.706389\pi$
$678$	27.5361			1.05752
$679$		0			0
$680$	−14.0014			−0.536928
$681$	−4.94918	−	8.57224i	−0.189653	−	0.328489i
$682$	−8.38477	+	14.5228i	−0.321069	+	0.556109i
$683$	15.8254	−	27.4104i	0.605541	−	1.04883i	−0.386424	−	0.922321i	$-0.626290\pi$
$683$	15.8254	−	27.4104i	0.605541	−	1.04883i	0.991966	−	0.126507i	$-0.0403767\pi$
$684$	−6.26838	−	10.8572i	−0.239678	−	0.415134i
$685$	−25.7891			−0.985350
$686$		0			0
$687$	−8.74092			−0.333487
$688$	23.6940	+	41.0391i	0.903324	+	1.56460i
$689$	2.63219	−	4.55909i	0.100279	−	0.173688i
$690$	9.30875	−	16.1232i	0.354378	−	0.613801i
$691$	4.84600	+	8.39351i	0.184350	+	0.319304i	0.943357	−	0.331778i	$-0.107649\pi$
$691$	4.84600	+	8.39351i	0.184350	+	0.319304i	−0.759007	+	0.651082i	$0.774315\pi$
$692$	−7.12604			−0.270891
$693$		0			0
$694$	−35.1509			−1.33431
$695$	−13.2343	−	22.9224i	−0.502004	−	0.869497i
$696$	0.714895	−	1.23823i	0.0270980	−	0.0469352i
$697$	6.43903	−	11.1527i	0.243896	−	0.422440i
$698$	−3.61363	−	6.25898i	−0.136778	−	0.236906i
$699$	−18.3406			−0.693705
$700$		0			0
$701$	−5.10365			−0.192762			−0.0963811	−	0.995345i	$-0.530727\pi$
$701$	−5.10365			−0.192762			−0.0963811	+	0.995345i	$0.530727\pi$
$702$	4.12305	+	7.14134i	0.155615	+	0.269532i
$703$	−20.4331	+	35.3912i	−0.770649	+	1.33480i
$704$	3.75500	−	6.50385i	0.141522	−	0.245123i
$705$	−10.5910	−	18.3441i	−0.398880	−	0.690880i
$706$	−51.3489			−1.93254
$707$		0			0
$708$	−2.97632			−0.111857
$709$	−13.0723	−	22.6418i	−0.490939	−	0.850332i	0.509006	−	0.860763i	$-0.330013\pi$
$709$	−13.0723	−	22.6418i	−0.490939	−	0.850332i	−0.999946	+	0.0104312i	$0.996680\pi$
$710$	−28.2751	+	48.9739i	−1.06115	+	1.83796i
$711$	13.5231	−	23.4228i	0.507157	−	0.878422i
$712$	−6.27806	−	10.8739i	−0.235280	−	0.407518i
$713$	−12.7063			−0.475855
$714$		0			0
$715$	8.57161			0.320560
$716$	7.14462	+	12.3748i	0.267007	+	0.462469i
$717$	0.463550	−	0.802892i	0.0173116	−	0.0299846i
$718$	−30.4386	+	52.7212i	−1.13596	+	1.96754i
$719$	−4.36442	−	7.55939i	−0.162765	−	0.281918i	0.773094	−	0.634291i	$-0.218708\pi$
$719$	−4.36442	−	7.55939i	−0.162765	−	0.281918i	−0.935859	+	0.352373i	$0.885375\pi$
$720$	−29.0520			−1.08270
$721$		0			0
$722$	−4.51937			−0.168193
$723$	8.53031	+	14.7749i	0.317245	+	0.549485i
$724$	−12.7733	+	22.1240i	−0.474716	+	0.822232i
$725$	1.34694	−	2.33296i	0.0500239	−	0.0866440i
$726$	−0.267362	−	0.463085i	−0.00992275	−	0.0171867i
$727$	21.8712			0.811158			0.405579	−	0.914060i	$-0.367070\pi$
$727$	21.8712			0.811158			0.405579	+	0.914060i	$0.367070\pi$
$728$		0			0
$729$	4.77848			0.176981
$730$	−29.2005	−	50.5768i	−1.08076	−	1.87193i
$731$	22.0311	−	38.1590i	0.814851	−	1.41136i
$732$	6.48079	−	11.2251i	0.239537	−	0.414890i
$733$	−17.7820	−	30.7993i	−0.656793	−	1.13760i	−0.981441	−	0.191764i	$-0.938579\pi$
$733$	−17.7820	−	30.7993i	−0.656793	−	1.13760i	0.324648	−	0.945835i	$-0.394754\pi$
$734$	51.8728			1.91466
$735$		0			0
$736$	29.7943			1.09823
$737$	3.23485	+	5.60293i	0.119157	+	0.206387i
$738$	5.91495	−	10.2450i	0.217732	−	0.377123i
$739$	18.2447	−	31.6007i	0.671142	−	1.16245i	−0.306439	−	0.951890i	$-0.599137\pi$
$739$	18.2447	−	31.6007i	0.671142	−	1.16245i	0.977581	−	0.210561i	$-0.0675292\pi$
$740$	−17.9117	−	31.0240i	−0.658448	−	1.14047i
$741$	−3.47151			−0.127529
$742$		0			0
$743$	12.4588			0.457071			0.228535	−	0.973536i	$-0.426606\pi$
$743$	12.4588			0.457071			0.228535	+	0.973536i	$0.426606\pi$
$744$	−1.40865	−	2.43985i	−0.0516435	−	0.0894492i
$745$	−18.1326	+	31.4065i	−0.664326	+	1.15065i
$746$	11.8659	−	20.5524i	0.434443	−	0.752477i
$747$	−15.0157	−	26.0080i	−0.549396	−	0.951582i
$748$	−20.0783			−0.734134
$749$		0			0
$750$	−12.7596			−0.465914
$751$	9.47118	+	16.4046i	0.345608	+	0.598611i	0.985464	−	0.169884i	$-0.0543393\pi$
$751$	9.47118	+	16.4046i	0.345608	+	0.598611i	−0.639856	+	0.768495i	$0.721006\pi$
$752$	23.0198	−	39.8714i	0.839445	−	1.45396i
$753$	−8.60150	+	14.8982i	−0.313456	+	0.542922i
$754$	−1.30344	−	2.25762i	−0.0474683	−	0.0822175i
$755$	−55.6940			−2.02691
$756$		0			0
$757$	−25.0956			−0.912114			−0.456057	−	0.889951i	$-0.650739\pi$
$757$	−25.0956			−0.912114			−0.456057	+	0.889951i	$0.650739\pi$
$758$	−0.154817	−	0.268152i	−0.00562322	−	0.00973971i
$759$	−6.31683	+	10.9411i	−0.229286	+	0.397136i
$760$	6.28356	−	10.8834i	0.227929	−	0.394784i
$761$	14.0308	+	24.3021i	0.508617	+	0.880951i	0.999950	+	0.00997886i	$0.00317642\pi$
$761$	14.0308	+	24.3021i	0.508617	+	0.880951i	−0.491333	+	0.870972i	$0.663490\pi$
$762$	2.49493			0.0903818
$763$		0			0
$764$	20.2476			0.732531
$765$	13.5066	+	23.3941i	0.488331	+	0.845814i
$766$	9.33896	−	16.1756i	0.337430	−	0.584446i
$767$	1.28395	−	2.22387i	0.0463608	−	0.0802993i
$768$	8.95009	+	15.5020i	0.322958	+	0.559380i
$769$	23.2636			0.838907			0.419454	−	0.907777i	$-0.362222\pi$
$769$	23.2636			0.838907			0.419454	+	0.907777i	$0.362222\pi$
$770$		0			0
$771$	−12.8212			−0.461744
$772$	0.0360680	+	0.0624715i	0.00129811	+	0.00224840i
$773$	22.9059	−	39.6742i	0.823869	−	1.42698i	−0.0789122	−	0.996882i	$-0.525145\pi$
$773$	22.9059	−	39.6742i	0.823869	−	1.42698i	0.902781	−	0.430101i	$-0.141522\pi$
$774$	20.2380	−	35.0532i	0.727440	−	1.25996i
$775$	−2.65404	−	4.59692i	−0.0953358	−	0.165126i
$776$	−16.1766			−0.580708
$777$		0			0
$778$	−52.5276			−1.88320
$779$	5.77944	+	10.0103i	0.207070	+	0.358655i
$780$	1.52157	−	2.63543i	0.0544808	−	0.0943635i
$781$	19.1872	−	33.2332i	0.686573	−	1.18918i
$782$	−18.8129	−	32.5848i	−0.672746	−	1.16523i
$783$	−6.40238			−0.228803
$784$		0			0
$785$	61.7413			2.20364
$786$	−3.36564	−	5.82947i	−0.120049	−	0.207930i
$787$	15.6358	−	27.0819i	0.557355	−	0.965367i	−0.440361	−	0.897821i	$-0.645150\pi$
$787$	15.6358	−	27.0819i	0.557355	−	0.965367i	0.997716	−	0.0675464i	$-0.0215171\pi$
$788$	−6.82035	+	11.8132i	−0.242965	+	0.420827i
$789$	−9.03541	−	15.6498i	−0.321669	−	0.557147i
$790$	−57.2935			−2.03841
$791$		0			0
$792$	8.72789			0.310132
$793$	5.59149	+	9.68475i	0.198560	+	0.343915i
$794$	−26.2406	+	45.4500i	−0.931242	+	1.61296i
$795$	−5.90028	+	10.2196i	−0.209261	+	0.362451i
$796$	15.8100	+	27.3837i	0.560371	+	0.970590i
$797$	11.6121			0.411323			0.205661	−	0.978623i	$-0.434065\pi$
$797$	11.6121			0.411323			0.205661	+	0.978623i	$0.434065\pi$
$798$		0			0
$799$	−42.8085			−1.51446
$800$	6.22331	+	10.7791i	0.220027	+	0.381098i
$801$	−12.1124	+	20.9793i	−0.427971	+	0.741267i
$802$	13.0980	−	22.6865i	0.462508	−	0.801087i
$803$	19.8152	+	34.3210i	0.699264	+	1.21116i
$804$	2.29691			0.0810056
$805$		0			0
$806$	−5.13664			−0.180931
$807$	1.75225	+	3.03499i	0.0616821	+	0.106837i
$808$	−3.46940	+	6.00918i	−0.122053	+	0.211402i
$809$	−3.65333	+	6.32775i	−0.128444	+	0.222472i	−0.923074	−	0.384623i	$-0.874332\pi$
$809$	−3.65333	+	6.32775i	−0.128444	+	0.222472i	0.794630	+	0.607094i	$0.207665\pi$
$810$	7.14716	+	12.3792i	0.251126	+	0.434962i
$811$	15.9662			0.560651			0.280325	−	0.959905i	$-0.409558\pi$
$811$	15.9662			0.560651			0.280325	+	0.959905i	$0.409558\pi$
$812$		0			0
$813$	2.93047			0.102776
$814$	30.0612	+	52.0675i	1.05364	+	1.82496i
$815$	10.2798	−	17.8052i	0.360087	−	0.623690i
$816$	9.42198	−	16.3193i	0.329835	−	0.571291i
$817$	19.7743	+	34.2502i	0.691817	+	1.19826i
$818$	−47.0897			−1.64645
$819$		0			0
$820$	−10.1325			−0.353844
$821$	−0.563942	−	0.976775i	−0.0196817	−	0.0340897i	0.856017	−	0.516948i	$-0.172932\pi$
$821$	−0.563942	−	0.976775i	−0.0196817	−	0.0340897i	−0.875699	+	0.482858i	$0.839599\pi$
$822$	7.68303	−	13.3074i	0.267977	−	0.464149i
$823$	−11.2022	+	19.4028i	−0.390484	+	0.676338i	−0.992513	−	0.122136i	$-0.961026\pi$
$823$	−11.2022	+	19.4028i	−0.390484	+	0.676338i	0.602030	+	0.798474i	$0.294359\pi$
$824$	−1.64057	−	2.84156i	−0.0571521	−	0.0989903i
$825$	−5.27772			−0.183747
$826$		0			0
$827$	−6.32296			−0.219871			−0.109935	−	0.993939i	$-0.535064\pi$
$827$	−6.32296			−0.219871			−0.109935	+	0.993939i	$0.535064\pi$
$828$	−6.98755	−	12.1028i	−0.242834	−	0.420601i
$829$	−22.1852	+	38.4259i	−0.770523	+	1.33459i	0.166753	+	0.985999i	$0.446672\pi$
$829$	−22.1852	+	38.4259i	−0.770523	+	1.33459i	−0.937276	+	0.348587i	$0.886662\pi$
$830$	−31.8086	+	55.0940i	−1.10409	+	1.91234i
$831$	−0.154108	−	0.266923i	−0.00534595	−	0.00925946i
$832$	2.30037			0.0797510
$833$		0			0
$834$	15.7709			0.546102
$835$	−16.6875	−	28.9036i	−0.577495	−	1.00025i
$836$	9.01075	−	15.6071i	0.311643	−	0.539782i
$837$	−6.30771	+	10.9253i	−0.218026	+	0.377633i
$838$	17.2241	+	29.8331i	0.594998	+	1.03057i
$839$	9.89476			0.341605			0.170803	−	0.985305i	$-0.445364\pi$
$839$	9.89476			0.341605			0.170803	+	0.985305i	$0.445364\pi$
$840$		0			0
$841$	−26.9760			−0.930207
$842$	16.5172	+	28.6087i	0.569222	+	0.985921i
$843$	7.90636	−	13.6942i	0.272309	−	0.471654i
$844$	1.67971	−	2.90935i	0.0578181	−	0.100144i
$845$	1.31278	+	2.27379i	0.0451609	+	0.0782209i
$846$	−39.3243			−1.35200
$847$		0			0
$848$	−25.6488			−0.880783
$849$	0.687947	+	1.19156i	0.0236103	+	0.0408942i
$850$	7.85909	−	13.6123i	0.269565	−	0.466899i
$851$	−22.7774	+	39.4516i	−0.780799	+	1.35238i
$852$	−6.81193	−	11.7986i	−0.233373	−	0.404214i
$853$	−25.9407			−0.888193			−0.444097	−	0.895979i	$-0.646475\pi$
$853$	−25.9407			−0.888193			−0.444097	+	0.895979i	$0.646475\pi$
$854$		0			0
$855$	−24.2460			−0.829196
$856$	−10.3970	−	18.0081i	−0.355362	−	0.615506i
$857$	5.01219	−	8.68137i	0.171213	−	0.296550i	−0.767631	−	0.640892i	$-0.778565\pi$
$857$	5.01219	−	8.68137i	0.171213	−	0.296550i	0.938844	+	0.344342i	$0.111898\pi$
$858$	−2.55364	+	4.42303i	−0.0871798	+	0.151000i
$859$	18.7189	+	32.4221i	0.638680	+	1.10623i	0.985723	+	0.168377i	$0.0538527\pi$
$859$	18.7189	+	32.4221i	0.638680	+	1.10623i	−0.347042	+	0.937850i	$0.612814\pi$
$860$	−34.6685			−1.18219
$861$		0			0
$862$	37.6703			1.28306
$863$	−10.5013	−	18.1888i	−0.357469	−	0.619155i	0.630068	−	0.776540i	$-0.283027\pi$
$863$	−10.5013	−	18.1888i	−0.357469	−	0.619155i	−0.987537	+	0.157385i	$0.949694\pi$
$864$	14.7906	−	25.6181i	0.503187	−	0.871545i
$865$	−6.89085	+	11.9353i	−0.234296	+	0.405813i
$866$	17.3374	+	30.0293i	0.589149	+	1.02044i
$867$	−3.00762			−0.102144
$868$		0			0
$869$	38.8788			1.31887
$870$	2.92176	+	5.06064i	0.0990569	+	0.171572i
$871$	−0.990861	+	1.71622i	−0.0335741	+	0.0581520i
$872$	−5.62942	+	9.75045i	−0.190636	+	0.330192i
$873$	15.6050	+	27.0286i	0.528148	+	0.914779i
$874$	33.7715			1.14234
$875$		0			0
$876$	14.0698			0.475374
$877$	−3.78151	−	6.54976i	−0.127692	−	0.221170i	0.795090	−	0.606492i	$-0.207424\pi$
$877$	−3.78151	−	6.54976i	−0.127692	−	0.221170i	−0.922782	+	0.385322i	$0.874090\pi$
$878$	−13.4267	+	23.2557i	−0.453129	+	0.784843i
$879$	1.88540	−	3.26560i	0.0635929	−	0.110146i
$880$	−20.8810	−	36.1670i	−0.703899	−	1.21919i
$881$	34.3550			1.15745			0.578725	−	0.815522i	$-0.303550\pi$
$881$	34.3550			1.15745			0.578725	+	0.815522i	$0.303550\pi$
$882$		0			0
$883$	49.6697			1.67152			0.835759	−	0.549096i	$-0.185028\pi$
$883$	49.6697			1.67152			0.835759	+	0.549096i	$0.185028\pi$
$884$	−3.07506	−	5.32617i	−0.103426	−	0.179138i
$885$	−2.87809	+	4.98499i	−0.0967459	+	0.167569i
$886$	10.9569	−	18.9779i	0.368104	−	0.637574i
$887$	−24.0162	−	41.5973i	−0.806386	−	1.39670i	−0.915351	−	0.402656i	$-0.868087\pi$
$887$	−24.0162	−	41.5973i	−0.806386	−	1.39670i	0.108965	−	0.994046i	$-0.465246\pi$
$888$	−10.1006			−0.338954
$889$		0			0
$890$	51.3166			1.72014
$891$	−4.85000	−	8.40044i	−0.162481	−	0.281425i
$892$	4.18832	−	7.25439i	0.140235	−	0.242895i
$893$	19.2117	−	33.2756i	0.642894	−	1.11353i
$894$	−10.8040	−	18.7131i	−0.361341	−	0.625861i
$895$	27.6353			0.923745
$896$		0			0
$897$	−3.86979			−0.129209
$898$	2.12779	+	3.68544i	0.0710053	+	0.122985i
$899$	1.99408	−	3.45385i	0.0665063	−	0.115192i
$900$	2.91905	−	5.05595i	0.0973018	−	0.168532i
$901$	11.9244	+	20.6536i	0.397259	+	0.688073i
$902$	17.0054			0.566218
$903$		0			0
$904$	20.7199			0.689133
$905$	24.7035	+	42.7877i	0.821171	+	1.42231i
$906$	16.5923	−	28.7387i	0.551241	−	0.954778i
$907$	−1.20098	+	2.08015i	−0.0398778	+	0.0690704i	−0.885275	−	0.465067i	$-0.846030\pi$
$907$	−1.20098	+	2.08015i	−0.0398778	+	0.0690704i	0.845398	+	0.534137i	$0.179364\pi$
$908$	7.86982	+	13.6309i	0.261169	+	0.452358i
$909$	13.3872			0.444024
$910$		0			0
$911$	−33.9555			−1.12500			−0.562499	−	0.826798i	$-0.690160\pi$
$911$	−33.9555			−1.12500			−0.562499	+	0.826798i	$0.690160\pi$
$912$	8.45683	+	14.6477i	0.280034	+	0.485032i
$913$	21.5850	−	37.3863i	0.714359	−	1.23731i
$914$	17.0231	−	29.4850i	0.563076	−	0.975276i
$915$	−12.5338	−	21.7092i	−0.414355	−	0.717683i
$916$	13.8992			0.459241
$917$		0			0
$918$	−37.3566			−1.23295
$919$	4.68567	+	8.11582i	0.154566	+	0.267716i	0.932901	−	0.360133i	$-0.117269\pi$
$919$	4.68567	+	8.11582i	0.154566	+	0.267716i	−0.778335	+	0.627849i	$0.783935\pi$
$920$	7.00447	−	12.1321i	0.230931	−	0.399983i
$921$	2.46886	−	4.27620i	0.0813518	−	0.140906i
$922$	25.5547	+	44.2621i	0.841601	+	1.45770i
$923$	11.7544			0.386901
$924$		0			0
$925$	−19.0306			−0.625721
$926$	3.35747	+	5.81531i	0.110333	+	0.191103i
$927$	−3.16519	+	5.48227i	−0.103959	+	0.180061i
$928$	−4.67581	+	8.09874i	−0.153491	+	0.265854i
$929$	−21.7137	−	37.6092i	−0.712402	−	1.23392i	−0.963953	−	0.266073i	$-0.914274\pi$
$929$	−21.7137	−	37.6092i	−0.712402	−	1.23392i	0.251551	−	0.967844i	$-0.419059\pi$
$930$	11.5142			0.377566
$931$		0			0
$932$	29.1639			0.955294
$933$	−6.09989	−	10.5653i	−0.199701	−	0.345893i
$934$	35.5051	−	61.4966i	1.16176	−	2.01223i
$935$	−19.4156	+	33.6288i	−0.634958	+	1.09978i
$936$	1.33671	+	2.31525i	0.0436918	+	0.0756764i
$937$	−2.59416			−0.0847476			−0.0423738	−	0.999102i	$-0.513492\pi$
$937$	−2.59416			−0.0847476			−0.0423738	+	0.999102i	$0.513492\pi$
$938$		0			0
$939$	2.33695			0.0762633
$940$	16.8410	+	29.1695i	0.549293	+	0.951403i
$941$	21.7030	−	37.5907i	0.707497	−	1.22542i	−0.258286	−	0.966069i	$-0.583158\pi$
$941$	21.7030	−	37.5907i	0.707497	−	1.22542i	0.965783	−	0.259352i	$-0.0835090\pi$
$942$	−18.3938	+	31.8591i	−0.599304	+	1.03802i
$943$	6.44251	+	11.1588i	0.209797	+	0.363379i
$944$	−12.5112			−0.407204
$945$		0			0
$946$	58.1840			1.89172
$947$	3.75029	+	6.49569i	0.121868	+	0.211082i	0.920504	−	0.390732i	$-0.127778\pi$
$947$	3.75029	+	6.49569i	0.121868	+	0.211082i	−0.798636	+	0.601814i	$0.794445\pi$
$948$	6.90147	−	11.9537i	0.224149	−	0.388238i
$949$	−6.06956	+	10.5128i	−0.197026	+	0.341259i
$950$	7.05403	+	12.2179i	0.228863	+	0.396402i
$951$	−9.09355			−0.294878
$952$		0			0
$953$	−0.708439			−0.0229486			−0.0114743	−	0.999934i	$-0.503652\pi$
$953$	−0.708439			−0.0229486			−0.0114743	+	0.999934i	$0.503652\pi$
$954$	10.9539	+	18.9726i	0.354644	+	0.614262i
$955$	19.5793	−	33.9124i	0.633572	−	1.09738i
$956$	−0.737103	+	1.27670i	−0.0238396	+	0.0412914i
$957$	−1.98268	−	3.43410i	−0.0640909	−	0.111009i
$958$	11.0571			0.357238
$959$		0			0
$960$	−5.15648			−0.166425
$961$	11.5708	+	20.0412i	0.373252	+	0.646492i
$962$	−9.20797	+	15.9487i	−0.296877	+	0.514206i
$963$	−20.0592	+	34.7435i	−0.646397	+	1.11959i
$964$	−13.5643	−	23.4940i	−0.436875	−	0.756690i
$965$	0.139510			0.00449100
$966$		0			0
$967$	−16.9761			−0.545915			−0.272957	−	0.962026i	$-0.588002\pi$
$967$	−16.9761			−0.545915			−0.272957	+	0.962026i	$0.588002\pi$
$968$	−0.201180	−	0.348453i	−0.00646616	−	0.0111997i
$969$	7.86333	−	13.6197i	0.252607	−	0.437527i
$970$	33.0568	−	57.2560i	1.06139	−	1.83838i
$971$	−3.43179	−	5.94404i	−0.110132	−	0.190753i	0.805692	−	0.592335i	$-0.201794\pi$
$971$	−3.43179	−	5.94404i	−0.110132	−	0.190753i	−0.915823	+	0.401582i	$0.868461\pi$
$972$	−21.7721			−0.698339
$973$		0			0
$974$	−6.96757			−0.223255
$975$	−0.808304	−	1.40002i	−0.0258865	−	0.0448367i
$976$	27.2425	−	47.1854i	0.872011	−	1.51037i
$977$	−0.290957	+	0.503952i	−0.00930853	+	0.0161228i	−0.870642	−	0.491917i	$-0.836296\pi$
$977$	−0.290957	+	0.503952i	−0.00930853	+	0.0161228i	0.861334	+	0.508040i	$0.169630\pi$
$978$	6.12511	+	10.6090i	0.195859	+	0.339238i
$979$	−34.8230			−1.11295
$980$		0			0
$981$	21.7219			0.693528
$982$	0.349491	+	0.605337i	0.0111527	+	0.0193171i
$983$	17.3597	−	30.0679i	0.553689	−	0.959018i	−0.444315	−	0.895871i	$-0.646553\pi$
$983$	17.3597	−	30.0679i	0.553689	−	0.959018i	0.998004	−	0.0631474i	$-0.0201138\pi$
$984$	−1.42846	+	2.47416i	−0.0455376	+	0.0788735i
$985$	13.1905	+	22.8466i	0.420284	+	0.727954i
$986$	11.8097			0.376097
$987$		0			0
$988$	5.52013			0.175619
$989$	22.0430	+	38.1797i	0.700928	+	1.21404i
$990$	−17.8353	+	30.8917i	−0.566845	+	0.981804i
$991$	−12.0844	+	20.9308i	−0.383874	+	0.664889i	−0.991612	−	0.129248i	$-0.958744\pi$
$991$	−12.0844	+	20.9308i	−0.383874	+	0.664889i	0.607738	+	0.794137i	$0.292077\pi$
$992$	9.21334	+	15.9580i	0.292524	+	0.506666i
$993$	2.91665			0.0925572
$994$		0			0
$995$	61.1528			1.93868
$996$	−7.66320	−	13.2731i	−0.242818	−	0.420573i
$997$	−17.5926	+	30.4713i	−0.557163	+	0.965035i	0.440569	+	0.897719i	$0.354777\pi$
$997$	−17.5926	+	30.4713i	−0.557163	+	0.965035i	−0.997732	+	0.0673158i	$0.978556\pi$
$998$	−31.6761	+	54.8647i	−1.00269	+	1.73671i
$999$	22.6145	+	39.1694i	0.715490	+	1.23927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.o.508.2		12
7.2	even	3	inner	637.2.e.o.79.2		12
7.3	odd	6		637.2.a.n.1.5	yes	6
7.4	even	3		637.2.a.m.1.5	✓	6
7.5	odd	6		637.2.e.n.79.2		12
7.6	odd	2		637.2.e.n.508.2		12
21.11	odd	6		5733.2.a.bu.1.2		6
21.17	even	6		5733.2.a.br.1.2		6
91.25	even	6		8281.2.a.cc.1.2		6
91.38	odd	6		8281.2.a.cd.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.5	✓	6	7.4	even	3
637.2.a.n.1.5	yes	6	7.3	odd	6
637.2.e.n.79.2		12	7.5	odd	6
637.2.e.n.508.2		12	7.6	odd	2
637.2.e.o.79.2		12	7.2	even	3	inner
637.2.e.o.508.2		12	1.1	even	1	trivial
5733.2.a.br.1.2		6	21.17	even	6
5733.2.a.bu.1.2		6	21.11	odd	6
8281.2.a.cc.1.2		6	91.25	even	6
8281.2.a.cd.1.2		6	91.38	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.916185 - 1.58688i) q^{2} +(0.426879 - 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(1.31278 + 2.27379i) q^{5} -1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +O(q^{10})\)	\(q+(-0.916185 - 1.58688i) q^{2} +(0.426879 - 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(1.31278 + 2.27379i) q^{5} -1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +(2.40549 - 4.16643i) q^{10} +(-1.63234 + 2.82730i) q^{11} +(0.579522 + 1.00376i) q^{12} -1.00000 q^{13} +2.24158 q^{15} +(2.43607 + 4.21939i) q^{16} +(2.26511 - 3.92328i) q^{17} +(2.08075 - 3.60396i) q^{18} +(2.03308 + 3.52139i) q^{19} -3.56440 q^{20} +5.98212 q^{22} +(2.26633 + 3.92540i) q^{23} +(-0.502500 + 0.870355i) q^{24} +(-0.946761 + 1.63984i) q^{25} +(0.916185 + 1.58688i) q^{26} +4.50024 q^{27} -1.42268 q^{29} +(-2.05371 - 3.55712i) q^{30} +(-1.40164 + 2.42771i) q^{31} +(3.28663 - 5.69261i) q^{32} +(1.39363 + 2.41383i) q^{33} -8.30102 q^{34} -3.08320 q^{36} +(5.02517 + 8.70385i) q^{37} +(3.72535 - 6.45249i) q^{38} +(-0.426879 + 0.739375i) q^{39} +(-1.54533 - 2.67660i) q^{40} +2.84271 q^{41} +9.72632 q^{43} +(-2.21604 - 3.83829i) q^{44} +(-2.98144 + 5.16401i) q^{45} +(4.15276 - 7.19278i) q^{46} +(-4.72478 - 8.18356i) q^{47} +4.15962 q^{48} +3.46963 q^{50} +(-1.93385 - 3.34953i) q^{51} +(0.678791 - 1.17570i) q^{52} +(-2.63219 + 4.55909i) q^{53} +(-4.12305 - 7.14134i) q^{54} -8.57161 q^{55} +3.47151 q^{57} +(1.30344 + 2.25762i) q^{58} +(-1.28395 + 2.22387i) q^{59} +(-1.52157 + 2.63543i) q^{60} +(-5.59149 - 9.68475i) q^{61} +5.13664 q^{62} -2.30037 q^{64} +(-1.31278 - 2.27379i) q^{65} +(2.55364 - 4.42303i) q^{66} +(0.990861 - 1.71622i) q^{67} +(3.07506 + 5.32617i) q^{68} +3.86979 q^{69} -11.7544 q^{71} +(-1.33671 - 2.31525i) q^{72} +(6.06956 - 10.5128i) q^{73} +(9.20797 - 15.9487i) q^{74} +(0.808304 + 1.40002i) q^{75} -5.52013 q^{76} +1.56440 q^{78} +(-5.95445 - 10.3134i) q^{79} +(-6.39602 + 11.0782i) q^{80} +(-1.48559 + 2.57312i) q^{81} +(-2.60444 - 4.51103i) q^{82} -13.2233 q^{83} +11.8943 q^{85} +(-8.91111 - 15.4345i) q^{86} +(-0.607310 + 1.05189i) q^{87} +(1.92151 - 3.32816i) q^{88} +(5.33328 + 9.23751i) q^{89} +10.9262 q^{90} -6.15345 q^{92} +(1.19666 + 2.07268i) q^{93} +(-8.65755 + 14.9953i) q^{94} +(-5.33795 + 9.24560i) q^{95} +(-2.80598 - 4.86011i) q^{96} +13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Introduction

L-functions

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