LMFDB - Embedded newform 637.2.cc.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(5,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([58, 63]))

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

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

chi := DirichletCharacter("637.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.cc (of order $84$, degree $24$, 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:	$1536$
Relative dimension:	$64$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	637.5
Dual form			637.2.cc.a.255.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.49274 + 2.02259i) q^{2} +(0.837048 - 1.22772i) q^{3} +(-1.27309 - 4.12726i) q^{4} +(2.40257 - 2.06758i) q^{5} +(1.23369 + 3.52568i) q^{6} +(0.937355 + 2.47414i) q^{7} +(5.50271 + 1.92548i) q^{8} +(0.289366 + 0.737293i) q^{9} +(0.595454 + 7.94578i) q^{10} +(-0.241828 + 0.105509i) q^{11} +(-6.13278 - 1.89171i) q^{12} +(-1.50365 + 3.27705i) q^{13} +(-6.40340 - 1.79736i) q^{14} +(-0.527350 - 4.68036i) q^{15} +(-4.97128 + 3.38936i) q^{16} +(3.67913 - 3.41373i) q^{17} +(-1.92319 - 0.515317i) q^{18} +(2.67157 - 0.715845i) q^{19} +(-11.5921 - 7.28382i) q^{20} +(3.82217 + 0.920161i) q^{21} +(0.147586 - 0.646617i) q^{22} +(-4.09036 + 4.40836i) q^{23} +(6.96999 - 5.14409i) q^{24} +(0.752252 - 4.99086i) q^{25} +(-4.38358 - 7.93304i) q^{26} +(5.49340 + 1.25383i) q^{27} +(9.01808 - 7.01851i) q^{28} +(1.11838 + 4.89994i) q^{29} +(10.2537 + 5.91995i) q^{30} +(2.51710 - 9.39396i) q^{31} +(0.129566 - 3.46273i) q^{32} +(-0.0728864 + 0.385214i) q^{33} +(1.41260 + 12.5372i) q^{34} +(7.36754 + 4.00624i) q^{35} +(2.67461 - 2.13293i) q^{36} +(-1.87685 - 3.55117i) q^{37} +(-2.54010 + 6.47207i) q^{38} +(2.76469 + 4.58911i) q^{39} +(17.2017 - 6.75118i) q^{40} +(9.30665 + 3.25654i) q^{41} +(-7.56662 + 6.35713i) q^{42} +(-3.13028 + 6.50009i) q^{43} +(0.743331 + 0.863766i) q^{44} +(2.21963 + 1.17311i) q^{45} +(-2.81046 - 14.8537i) q^{46} +(6.53832 - 8.85910i) q^{47} +8.94041i q^{48} +(-5.24273 + 4.63829i) q^{49} +(8.97156 + 8.97156i) q^{50} +(-1.11151 - 7.37441i) q^{51} +(15.4395 + 2.03396i) q^{52} +(4.36450 - 1.34627i) q^{53} +(-10.7362 + 9.23925i) q^{54} +(-0.362862 + 0.753491i) q^{55} +(0.394081 + 15.4193i) q^{56} +(1.35737 - 3.87915i) q^{57} +(-11.5800 - 5.05231i) q^{58} +(-9.07278 - 7.80775i) q^{59} +(-18.6457 + 8.13504i) q^{60} +(2.88378 - 9.34899i) q^{61} +(15.2428 + 19.1138i) q^{62} +(-1.55293 + 1.40704i) q^{63} +(-2.59790 - 2.07176i) q^{64} +(3.16294 + 10.9823i) q^{65} +(-0.670330 - 0.722444i) q^{66} +(-4.56051 - 1.22198i) q^{67} +(-18.7732 - 10.8387i) q^{68} +(1.98842 + 8.71184i) q^{69} +(-19.1008 + 8.92125i) q^{70} +(1.32419 + 2.10744i) q^{71} +(0.172654 + 4.61427i) q^{72} +(-6.83624 + 5.04538i) q^{73} +(9.98421 + 1.50488i) q^{74} +(-5.49773 - 5.10115i) q^{75} +(-6.35564 - 10.1149i) q^{76} +(-0.487722 - 0.499418i) q^{77} +(-13.4089 - 1.25852i) q^{78} +(1.18799 - 2.05765i) q^{79} +(-4.93608 + 18.4217i) q^{80} +(4.39577 - 4.07868i) q^{81} +(-20.4791 + 13.9624i) q^{82} +(-3.54779 + 0.399740i) q^{83} +(-1.06823 - 16.9466i) q^{84} +(1.78120 - 15.8086i) q^{85} +(-8.47433 - 16.0342i) q^{86} +(6.95191 + 2.72842i) q^{87} +(-1.53386 + 0.114947i) q^{88} +(8.56180 + 3.73548i) q^{89} +(-5.68606 + 2.73826i) q^{90} +(-9.51733 - 0.648474i) q^{91} +(23.4019 + 11.2697i) q^{92} +(-9.42625 - 10.9535i) q^{93} +(8.15834 + 26.4487i) q^{94} +(4.93857 - 7.24356i) q^{95} +(-4.14282 - 3.05754i) q^{96} +(-0.440623 - 0.440623i) q^{97} +(-1.55533 - 17.5277i) q^{98} +(-0.147768 - 0.147768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1536 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 28 q^{6} - 22 q^{7} - 12 q^{8} - 176 q^{9} - 22 q^{11} - 28 q^{13} - 84 q^{14} - 8 q^{15} - 180 q^{16} - 18 q^{18} - 54 q^{19} - 28 q^{20} - 2 q^{21} - 48 q^{22}+ \cdots - 32 q^{99}+O(q^{100}) $ 1536 * q - 26 * q^2 - 44 * q^3 - 22 * q^5 - 28 * q^6 - 22 * q^7 - 12 * q^8 - 176 * q^9 - 22 * q^11 - 28 * q^13 - 84 * q^14 - 8 * q^15 - 180 * q^16 - 18 * q^18 - 54 * q^19 - 28 * q^20 - 2 * q^21 - 48 * q^22 + 68 * q^24 - 52 * q^26 - 56 * q^27 + 62 * q^28 - 48 * q^29 - 66 * q^31 - 32 * q^32 - 76 * q^33 + 28 * q^34 - 140 * q^35 - 62 * q^37 - 16 * q^39 + 76 * q^40 - 28 * q^41 + 128 * q^42 - 226 * q^44 + 66 * q^45 - 32 * q^46 + 68 * q^47 + 156 * q^50 + 48 * q^52 - 48 * q^53 - 64 * q^54 + 28 * q^55 - 62 * q^57 - 22 * q^58 + 54 * q^59 - 88 * q^60 - 8 * q^61 - 150 * q^63 - 12 * q^65 + 72 * q^66 - 30 * q^67 - 36 * q^68 + 62 * q^70 + 104 * q^71 - 54 * q^72 - 136 * q^73 + 12 * q^74 + 28 * q^76 + 68 * q^78 - 16 * q^79 - 180 * q^80 + 64 * q^81 + 70 * q^83 + 30 * q^84 - 96 * q^85 + 30 * q^86 + 416 * q^87 - 38 * q^89 - 196 * q^91 - 180 * q^92 + 38 * q^93 - 264 * q^94 - 350 * q^96 - 390 * q^98 - 32 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−1.49274	+	2.02259i	−1.05553	+	1.43019i	−0.158957	+	0.987285i	$0.550813\pi$
$2$	−1.49274	+	2.02259i	−1.05553	+	1.43019i	−0.896570	+	0.442903i	$0.853949\pi$
$3$	0.837048	−	1.22772i	0.483270	−	0.708827i	−0.504731	−	0.863277i	$-0.668408\pi$
$3$	0.837048	−	1.22772i	0.483270	−	0.708827i	0.988001	+	0.154450i	$0.0493606\pi$
$4$	−1.27309	−	4.12726i	−0.636546	−	2.06363i
$5$	2.40257	−	2.06758i	1.07446	−	0.924650i	0.0770852	−	0.997025i	$-0.475439\pi$
$5$	2.40257	−	2.06758i	1.07446	−	0.924650i	0.997378	+	0.0723746i	$0.0230577\pi$
$6$	1.23369	+	3.52568i	0.503651	+	1.43935i
$7$	0.937355	+	2.47414i	0.354287	+	0.935137i
$7$	0.937355	+	2.47414i	0.354287	+	0.935137i
$8$	5.50271	+	1.92548i	1.94550	+	0.680760i
$9$	0.289366	+	0.737293i	0.0964554	+	0.245764i
$10$	0.595454	+	7.94578i	0.188299	+	2.51268i
$11$	−0.241828	+	0.105509i	−0.0729140	+	0.0318120i	−0.436033	−	0.899931i	$-0.643617\pi$
$11$	−0.241828	+	0.105509i	−0.0729140	+	0.0318120i	0.363119	+	0.931743i	$0.381712\pi$
$12$	−6.13278	−	1.89171i	−1.77038	−	0.546090i
$13$	−1.50365	+	3.27705i	−0.417036	+	0.908890i
$13$	−1.50365	+	3.27705i	−0.417036	+	0.908890i
$14$	−6.40340	−	1.79736i	−1.71138	−	0.480365i
$15$	−0.527350	−	4.68036i	−0.136161	−	1.20846i
$16$	−4.97128	+	3.38936i	−1.24282	+	0.847340i
$17$	3.67913	−	3.41373i	0.892320	−	0.827952i	−0.0935242	−	0.995617i	$-0.529813\pi$
$17$	3.67913	−	3.41373i	0.892320	−	0.827952i	0.985844	+	0.167665i	$0.0536228\pi$
$18$	−1.92319	−	0.515317i	−0.453300	−	0.121461i
$19$	2.67157	−	0.715845i	0.612900	−	0.164226i	0.0610022	−	0.998138i	$-0.480570\pi$
$19$	2.67157	−	0.715845i	0.612900	−	0.164226i	0.551898	+	0.833911i	$0.313904\pi$
$20$	−11.5921	−	7.28382i	−2.59208	−	1.62871i
$21$	3.82217	+	0.920161i	0.834066	+	0.200796i
$22$	0.147586	−	0.646617i	0.0314654	−	0.137859i
$23$	−4.09036	+	4.40836i	−0.852899	+	0.919206i	−0.997527	−	0.0702798i	$-0.977611\pi$
$23$	−4.09036	+	4.40836i	−0.852899	+	0.919206i	0.144629	+	0.989486i	$0.453801\pi$
$24$	6.96999	−	5.14409i	1.42274	−	1.05003i
$25$	0.752252	−	4.99086i	0.150450	−	0.998173i
$26$	−4.38358	−	7.93304i	−0.859690	−	1.55580i
$27$	5.49340	+	1.25383i	1.05720	+	0.241300i
$28$	9.01808	−	7.01851i	1.70426	−	1.32637i
$29$	1.11838	+	4.89994i	0.207678	+	0.909896i	0.966107	+	0.258141i	$0.0831098\pi$
$29$	1.11838	+	4.89994i	0.207678	+	0.909896i	−0.758430	+	0.651755i	$0.774033\pi$
$30$	10.2537	+	5.91995i	1.87205	+	1.08083i
$31$	2.51710	−	9.39396i	0.452085	−	1.68720i	−0.244434	−	0.969666i	$-0.578602\pi$
$31$	2.51710	−	9.39396i	0.452085	−	1.68720i	0.696519	−	0.717538i	$-0.254731\pi$
$32$	0.129566	−	3.46273i	0.0229043	−	0.612129i
$33$	−0.0728864	+	0.385214i	−0.0126879	+	0.0670572i
$34$	1.41260	+	12.5372i	0.242259	+	2.15011i
$35$	7.36754	+	4.00624i	1.24534	+	0.677178i
$36$	2.67461	−	2.13293i	0.445768	−	0.355488i
$37$	−1.87685	−	3.55117i	−0.308552	−	0.583809i	0.680261	−	0.732970i	$-0.261866\pi$
$37$	−1.87685	−	3.55117i	−0.308552	−	0.583809i	−0.988813	+	0.149161i	$0.952343\pi$
$38$	−2.54010	+	6.47207i	−0.412059	+	1.04991i
$39$	2.76469	+	4.58911i	0.442704	+	0.734846i
$40$	17.2017	−	6.75118i	2.71983	−	1.06746i
$41$	9.30665	+	3.25654i	1.45345	+	0.508586i	0.937486	−	0.348022i	$-0.113146\pi$
$41$	9.30665	+	3.25654i	1.45345	+	0.508586i	0.515968	+	0.856608i	$0.327432\pi$
$42$	−7.56662	+	6.35713i	−1.16755	+	0.980927i
$43$	−3.13028	+	6.50009i	−0.477363	+	0.991254i	0.513714	+	0.857961i	$0.328269\pi$
$43$	−3.13028	+	6.50009i	−0.477363	+	0.991254i	−0.991077	+	0.133292i	$0.957445\pi$
$44$	0.743331	+	0.863766i	0.112061	+	0.130218i
$45$	2.21963	+	1.17311i	0.330884	+	0.174877i
$46$	−2.81046	−	14.8537i	−0.414380	−	2.19005i
$47$	6.53832	−	8.85910i	0.953711	−	1.29223i	−0.00263467	−	0.999997i	$-0.500839\pi$
$47$	6.53832	−	8.85910i	0.953711	−	1.29223i	0.956346	−	0.292237i	$-0.0943995\pi$
$48$			8.94041i			1.29044i
$49$	−5.24273	+	4.63829i	−0.748962	+	0.662613i
$50$	8.97156	+	8.97156i	1.26877	+	1.26877i
$51$	−1.11151	−	7.37441i	−0.155643	−	1.03262i
$52$	15.4395	+	2.03396i	2.14108	+	0.282059i
$53$	4.36450	−	1.34627i	0.599511	−	0.184925i	0.0198779	−	0.999802i	$-0.493672\pi$
$53$	4.36450	−	1.34627i	0.599511	−	0.184925i	0.579633	+	0.814878i	$0.303196\pi$
$54$	−10.7362	+	9.23925i	−1.46101	+	1.25730i
$55$	−0.362862	+	0.753491i	−0.0489283	+	0.101601i
$56$	0.394081	+	15.4193i	0.0526612	+	2.06049i
$57$	1.35737	−	3.87915i	0.179788	−	0.513806i
$58$	−11.5800	−	5.05231i	−1.52053	−	0.663401i
$59$	−9.07278	−	7.80775i	−1.18117	−	1.01648i	−0.999451	−	0.0331335i	$-0.989451\pi$
$59$	−9.07278	−	7.80775i	−1.18117	−	1.01648i	−0.181724	−	0.983350i	$-0.558168\pi$
$60$	−18.6457	+	8.13504i	−2.40715	+	1.05023i
$61$	2.88378	−	9.34899i	0.369231	−	1.19702i	−0.560306	−	0.828286i	$-0.689316\pi$
$61$	2.88378	−	9.34899i	0.369231	−	1.19702i	0.929536	−	0.368730i	$-0.120207\pi$
$62$	15.2428	+	19.1138i	1.93583	+	2.42746i
$63$	−1.55293	+	1.40704i	−0.195650	+	0.177270i
$64$	−2.59790	−	2.07176i	−0.324738	−	0.258970i
$65$	3.16294	+	10.9823i	0.392315	+	1.36218i
$66$	−0.670330	−	0.722444i	−0.0825120	−	0.0889267i
$67$	−4.56051	−	1.22198i	−0.557154	−	0.149289i	−0.0307557	−	0.999527i	$-0.509791\pi$
$67$	−4.56051	−	1.22198i	−0.557154	−	0.149289i	−0.526399	+	0.850238i	$0.676458\pi$
$68$	−18.7732	−	10.8387i	−2.27659	−	1.31439i
$69$	1.98842	+	8.71184i	0.239378	+	1.04878i
$70$	−19.1008	+	8.92125i	−2.28298	+	1.06629i
$71$	1.32419	+	2.10744i	0.157153	+	0.250108i	0.916015	−	0.401144i	$-0.131387\pi$
$71$	1.32419	+	2.10744i	0.157153	+	0.250108i	−0.758862	+	0.651251i	$0.774244\pi$
$72$	0.172654	+	4.61427i	0.0203475	+	0.543797i
$73$	−6.83624	+	5.04538i	−0.800121	+	0.590516i	−0.915274	−	0.402831i	$-0.868026\pi$
$73$	−6.83624	+	5.04538i	−0.800121	+	0.590516i	0.115153	+	0.993348i	$0.463264\pi$
$74$	9.98421	+	1.50488i	1.16064	+	0.174939i
$75$	−5.49773	−	5.10115i	−0.634824	−	0.589030i
$76$	−6.35564	−	10.1149i	−0.729042	−	1.16026i
$77$	−0.487722	−	0.499418i	−0.0555811	−	0.0569139i
$78$	−13.4089	−	1.25852i	−1.51825	−	0.142499i
$79$	1.18799	−	2.05765i	0.133659	−	0.231504i	−0.791425	−	0.611266i	$-0.790661\pi$
$79$	1.18799	−	2.05765i	0.133659	−	0.231504i	0.925084	+	0.379762i	$0.123994\pi$
$80$	−4.93608	+	18.4217i	−0.551870	+	2.05961i
$81$	4.39577	−	4.07868i	0.488419	−	0.453187i
$82$	−20.4791	+	13.9624i	−2.26153	+	1.54189i
$83$	−3.54779	+	0.399740i	−0.389421	+	0.0438772i	−0.304505	−	0.952511i	$-0.598491\pi$
$83$	−3.54779	+	0.399740i	−0.389421	+	0.0438772i	−0.0849164	+	0.996388i	$0.527062\pi$
$84$	−1.06823	−	16.9466i	−0.116553	−	1.84902i
$85$	1.78120	−	15.8086i	0.193199	−	1.71469i
$86$	−8.47433	−	16.0342i	−0.913810	−	1.72901i
$87$	6.95191	+	2.72842i	0.745323	+	0.292518i
$88$	−1.53386	+	0.114947i	−0.163511	+	0.0122534i
$89$	8.56180	+	3.73548i	0.907549	+	0.395960i	0.801219	−	0.598371i	$-0.204185\pi$
$89$	8.56180	+	3.73548i	0.907549	+	0.395960i	0.106330	+	0.994331i	$0.466090\pi$
$90$	−5.68606	+	2.73826i	−0.599364	+	0.288638i
$91$	−9.51733	−	0.648474i	−0.997687	−	0.0679786i
$92$	23.4019	+	11.2697i	2.43981	+	1.17495i
$93$	−9.42625	−	10.9535i	−0.977457	−	1.13583i
$94$	8.15834	+	26.4487i	0.841468	+	2.72797i
$95$	4.93857	−	7.24356i	0.506687	−	0.743173i
$96$	−4.14282	−	3.05754i	−0.422825	−	0.312059i
$97$	−0.440623	−	0.440623i	−0.0447385	−	0.0447385i	0.684384	−	0.729122i	$-0.260071\pi$
$97$	−0.440623	−	0.440623i	−0.0447385	−	0.0447385i	−0.729122	+	0.684384i	$0.760071\pi$
$98$	−1.55533	−	17.5277i	−0.157112	−	1.77056i
$99$	−0.147768	−	0.147768i	−0.0148512	−	0.0148512i
$100$	−21.5563	+	3.24909i	−2.15563	+	0.324909i
$101$	7.21765	+	4.92091i	0.718183	+	0.489649i	0.866428	−	0.499302i	$-0.166410\pi$
$101$	7.21765	+	4.92091i	0.718183	+	0.489649i	−0.148245	+	0.988951i	$0.547362\pi$
$102$	16.5746	+	8.75995i	1.64113	+	0.867364i
$103$	−1.01274	+	13.5140i	−0.0997879	+	1.33158i	0.692495	+	0.721423i	$0.256512\pi$
$103$	−1.01274	+	13.5140i	−0.0997879	+	1.33158i	−0.792282	+	0.610154i	$0.791107\pi$
$104$	−14.5840	+	15.1374i	−1.43008	+	1.48434i
$105$	11.0855	−	5.69189i	1.08184	−	0.555472i
$106$	−3.79211	+	10.8372i	−0.368323	+	1.05261i
$107$	0.461458	+	1.17578i	0.0446108	+	0.113667i	0.951443	−	0.307826i	$-0.0996015\pi$
$107$	0.461458	+	1.17578i	0.0446108	+	0.113667i	−0.906832	+	0.421493i	$0.861506\pi$
$108$	−1.81871	−	24.2689i	−0.175005	−	2.33528i
$109$	−2.88988	−	6.62368i	−0.276801	−	0.634434i	0.721518	−	0.692395i	$-0.243445\pi$
$109$	−2.88988	−	6.62368i	−0.276801	−	0.634434i	−0.998319	+	0.0579617i	$0.981540\pi$
$110$	−0.982346	−	1.85869i	−0.0936630	−	0.177219i
$111$	−5.93087	−	0.668249i	−0.562933	−	0.0634274i
$112$	−13.0456	−	9.12260i	−1.23269	−	0.862005i
$113$	−2.58421	+	3.24050i	−0.243102	+	0.304841i	−0.888381	−	0.459106i	$-0.848170\pi$
$113$	−2.58421	+	3.24050i	−0.243102	+	0.304841i	0.645279	+	0.763947i	$0.276741\pi$
$114$	5.81973	+	8.53597i	0.545068	+	0.799467i
$115$	−0.712746	+	19.0485i	−0.0664639	+	1.77629i
$116$	18.7995	−	10.8539i	1.74549	−	1.00776i
$117$	−2.85125	−	0.160361i	−0.263598	−	0.0148254i
$118$	29.3352	−	6.69557i	2.70052	−	0.616377i
$119$	11.8947	+	5.90280i	1.09039	+	0.541109i
$120$	6.11009	−	26.7701i	0.557772	−	2.44376i
$121$	−7.43455	+	8.01254i	−0.675868	+	0.728413i
$122$	14.6045	+	19.7883i	1.32223	+	1.79155i
$123$	11.7882	−	8.70012i	1.06291	−	0.784464i
$124$	−41.9758	+	1.57062i	−3.76954	+	0.141046i
$125$	−0.0796614	−	0.126780i	−0.00712513	−	0.0113396i
$126$	−0.527744	−	5.24128i	−0.0470152	−	0.466930i
$127$	−4.56694	+	1.04237i	−0.405251	+	0.0924958i	−0.420287	−	0.907391i	$-0.638071\pi$
$127$	−4.56694	+	1.04237i	−0.405251	+	0.0924958i	0.0150366	+	0.999887i	$0.495214\pi$
$128$	14.7625	−	3.95559i	1.30483	−	0.349628i
$129$	5.36012	+	9.28400i	0.471932	+	0.817411i
$130$	−26.9341	−	9.99631i	−2.36227	−	0.876735i
$131$	−0.318478	−	0.467122i	−0.0278256	−	0.0408126i	0.812074	−	0.583555i	$-0.198339\pi$
$131$	−0.318478	−	0.467122i	−0.0278256	−	0.0408126i	−0.839900	+	0.542742i	$0.817386\pi$
$132$	1.68267	−	0.189591i	0.146458	−	0.0165018i
$133$	4.27531	+	5.93884i	0.370716	+	0.514963i
$134$	9.27923	−	7.39994i	0.801603	−	0.639257i
$135$	15.7907	−	8.34562i	1.35905	−	0.718276i
$136$	26.8182	−	11.7007i	2.29965	−	1.00333i
$137$	−6.11078	+	7.10086i	−0.522079	+	0.606667i	−0.955669	−	0.294443i	$-0.904866\pi$
$137$	−6.11078	+	7.10086i	−0.522079	+	0.606667i	0.433590	+	0.901110i	$0.357247\pi$
$138$	−20.5887	−	8.98275i	−1.75263	−	0.764663i
$139$	−9.08056	−	18.8560i	−0.770203	−	1.59934i	−0.800156	−	0.599793i	$-0.795250\pi$
$139$	−9.08056	−	18.8560i	−0.770203	−	1.59934i	0.0299521	−	0.999551i	$-0.490465\pi$
$140$	7.15525	−	35.5081i	0.604729	−	3.00098i
$141$	−5.40365	−	15.4427i	−0.455069	−	1.30051i
$142$	−6.23918	−	0.467562i	−0.523580	−	0.0392369i
$143$	0.0178674	−	0.951130i	0.00149415	−	0.0795375i
$144$	−3.93747	−	2.68452i	−0.328122	−	0.223710i
$145$	12.8180	+	9.46011i	1.06448	+	0.785620i
$146$		−	21.3584i		−	1.76763i
$147$	1.30612	+	10.3191i	0.107727	+	0.851105i
$148$	−12.2672	+	12.2672i	−1.00836	+	1.00836i
$149$	−7.06844	+	9.57740i	−0.579069	+	0.784611i	−0.992012	−	0.126146i	$-0.959739\pi$
$149$	−7.06844	+	9.57740i	−0.579069	+	0.784611i	0.412942	+	0.910757i	$0.364501\pi$
$150$	18.5242	−	3.50497i	1.51250	−	0.286180i
$151$	−10.8644	−	5.74201i	−0.884133	−	0.467278i	−0.0374026	−	0.999300i	$-0.511908\pi$
$151$	−10.8644	−	5.74201i	−0.884133	−	0.467278i	−0.846730	+	0.532022i	$0.821432\pi$
$152$	16.0792	+	1.20497i	1.30420	+	0.0977361i
$153$	3.58154	+	1.72478i	0.289550	+	0.139440i
$154$	1.73816	−	0.240961i	0.140065	−	0.0194172i
$155$	−13.3752	−	27.7740i	−1.07432	−	2.23086i
$156$	15.4208	−	17.2529i	1.23465	−	1.38134i
$157$	−3.16391	+	0.237103i	−0.252508	+	0.0189228i	−0.200383	−	0.979718i	$-0.564219\pi$
$157$	−3.16391	+	0.237103i	−0.252508	+	0.0189228i	−0.0521252	+	0.998641i	$0.516599\pi$
$158$	2.38844	+	5.47435i	0.190014	+	0.435516i
$159$	2.00045	−	6.48530i	0.158646	−	0.514318i
$160$	−6.84817	−	8.58734i	−0.541396	−	0.678889i
$161$	−14.7410	−	5.98792i	−1.16175	−	0.471914i
$162$	1.68776	+	14.9793i	0.132603	+	1.17688i
$163$	6.21163	+	1.17530i	0.486533	+	0.0920570i	0.423390	−	0.905948i	$-0.360840\pi$
$163$	6.21163	+	1.17530i	0.486533	+	0.0920570i	0.0631428	+	0.998005i	$0.479888\pi$
$164$	1.59237	−	42.5569i	0.124343	−	3.32313i
$165$	0.621346	+	1.07620i	0.0483717	+	0.0837823i
$166$	4.48742	−	7.77245i	0.348292	−	0.603259i
$167$	−9.21927	−	5.79285i	−0.713408	−	0.448264i	0.125813	−	0.992054i	$-0.459846\pi$
$167$	−9.21927	−	5.79285i	−0.713408	−	0.448264i	−0.839221	+	0.543790i	$0.816989\pi$
$168$	19.2605	+	12.4229i	1.48598	+	0.958447i
$169$	−8.47810	−	9.85504i	−0.652161	−	0.758080i
$170$	29.3155	+	27.2008i	2.24840	+	2.08621i
$171$	1.30085	+	1.76259i	0.0994785	+	0.134789i
$172$	30.8127	+	4.64427i	2.34945	+	0.354122i
$173$	2.85592	+	2.64991i	0.217132	+	0.201469i	0.781238	−	0.624234i	$-0.214589\pi$
$173$	2.85592	+	2.64991i	0.217132	+	0.201469i	−0.564106	+	0.825702i	$0.690779\pi$
$174$	−15.8959	+	9.98804i	−1.20506	+	0.757192i
$175$	13.0532	−	2.81703i	0.986731	−	0.212948i
$176$	0.844589	−	1.34415i	0.0636633	−	0.101319i
$177$	−17.1801	+	4.60340i	−1.29134	+	0.346013i
$178$	−20.3359	+	11.7409i	−1.52424	+	0.880020i
$179$	10.1225	+	10.9094i	0.756588	+	0.815408i	0.987509	−	0.157564i	$-0.0503642\pi$
$179$	10.1225	+	10.9094i	0.756588	+	0.815408i	−0.230921	+	0.972973i	$0.574174\pi$
$180$	2.01594	−	10.6545i	0.150259	−	0.794139i
$181$	7.79854	−	9.77906i	0.579661	−	0.726872i	−0.402394	−	0.915467i	$-0.631822\pi$
$181$	7.79854	−	9.77906i	0.579661	−	0.726872i	0.982055	+	0.188595i	$0.0603932\pi$
$182$	15.5185	−	18.2817i	1.15031	−	1.35513i
$183$	−9.06412	−	11.3660i	−0.670039	−	0.840202i
$184$	−30.9963	+	16.3820i	−2.28507	+	1.20770i
$185$	−11.8516	−	4.65141i	−0.871346	−	0.341978i
$186$	36.2254	−	2.71472i	2.65618	−	0.199053i
$187$	−0.529539	+	1.21372i	−0.0387237	+	0.0887558i
$188$	−44.8877	−	15.7069i	−3.27377	−	1.14554i
$189$	2.04711	+	14.7667i	0.148905	+	1.07412i
$190$	7.27875	+	20.8015i	0.528056	+	1.50910i
$191$	0.790797	−	10.5524i	0.0572200	−	0.763548i	−0.892620	−	0.450811i	$-0.851135\pi$
$191$	0.790797	−	10.5524i	0.0572200	−	0.763548i	0.949840	−	0.312738i	$-0.101246\pi$
$192$	−4.71812	+	1.45535i	−0.340501	+	0.105031i
$193$	−3.79820	−	20.0739i	−0.273400	−	1.44495i	−0.802631	−	0.596476i	$-0.796567\pi$
$193$	−3.79820	−	20.0739i	−0.273400	−	1.44495i	0.529231	−	0.848478i	$-0.322481\pi$
$194$	1.54893	−	0.233464i	0.111207	−	0.0167618i
$195$	16.1307	+	5.30945i	1.15514	+	0.380218i
$196$	25.8179	+	15.7332i	1.84414	+	1.12380i
$197$	11.3449	−	11.3449i	0.808288	−	0.808288i	−0.176087	−	0.984375i	$-0.556344\pi$
$197$	11.3449	−	11.3449i	0.808288	−	0.808288i	0.984375	+	0.176087i	$0.0563439\pi$
$198$	0.519452	−	0.0782948i	0.0369159	−	0.00556417i
$199$	−15.1024	−	10.2967i	−1.07058	−	0.729911i	−0.106179	−	0.994347i	$-0.533862\pi$
$199$	−15.1024	−	10.2967i	−1.07058	−	0.729911i	−0.964403	+	0.264436i	$0.914814\pi$
$200$	13.7492	−	26.0148i	0.972218	−	1.83953i
$201$	−5.31762	+	4.57618i	−0.375076	+	0.322779i
$202$	−20.7271	+	7.25272i	−1.45835	+	0.510299i
$203$	−11.0748	+	7.36001i	−0.777300	+	0.516571i
$204$	−29.0211	+	13.9758i	−2.03188	+	0.978503i
$205$	29.0931	−	11.4182i	2.03195	−	0.797480i
$206$	−25.8216	−	22.2213i	−1.79908	−	1.54823i
$207$	−4.43386	−	1.74016i	−0.308175	−	0.120950i
$208$	−3.63205	−	21.3875i	−0.251837	−	1.48296i
$209$	−0.570534	+	0.454985i	−0.0394646	+	0.0314720i
$210$	−5.03547	+	30.9181i	−0.347480	+	2.13355i
$211$	−13.3132	+	16.6942i	−0.916517	+	1.14928i	0.0718840	+	0.997413i	$0.477099\pi$
$211$	−13.3132	+	16.6942i	−0.916517	+	1.14928i	−0.988401	+	0.151864i	$0.951473\pi$
$212$	−11.1128	−	16.2995i	−0.763232	−	1.11946i
$213$	3.69578	+	0.138286i	0.253230	+	0.00947521i
$214$	−3.06695	−	0.821787i	−0.209653	−	0.0561762i
$215$	5.91873	+	22.0890i	0.403654	+	1.50646i
$216$	27.8143	+	17.4769i	1.89253	+	1.18915i
$217$	25.6014	−	2.57780i	1.73793	−	0.174993i
$218$	17.7108	+	4.04239i	1.19953	+	0.273785i
$219$	0.472066	+	12.6162i	0.0318993	+	0.852526i
$220$	3.57181	+	0.538364i	0.240812	+	0.0362965i
$221$	5.65486	+	17.1897i	0.380387	+	1.15631i
$222$	10.2048	−	10.9982i	0.684904	−	0.738151i
$223$	−2.51144	+	1.57804i	−0.168179	+	0.105674i	−0.613491	−	0.789702i	$-0.710235\pi$
$223$	−2.51144	+	1.57804i	−0.168179	+	0.105674i	0.445313	+	0.895375i	$0.353093\pi$
$224$	8.68872	−	2.92524i	0.580539	−	0.195451i
$225$	3.89740	−	0.889557i	0.259827	−	0.0593038i
$226$	−2.69665	−	10.0640i	−0.179379	−	0.669450i
$227$	−3.71069	+	13.8485i	−0.246287	+	0.919157i	0.726445	+	0.687225i	$0.241171\pi$
$227$	−3.71069	+	13.8485i	−0.246287	+	0.919157i	−0.972732	+	0.231932i	$0.925495\pi$
$228$	−17.7383	−	0.663721i	−1.17475	−	0.0439560i
$229$	−0.301368	+	1.59277i	−0.0199150	+	0.105253i	−0.991114	−	0.133018i	$-0.957533\pi$
$229$	−0.301368	+	1.59277i	−0.0199150	+	0.105253i	0.971199	+	0.238271i	$0.0765807\pi$
$230$	−37.4635	−	29.8761i	−2.47027	−	1.96997i
$231$	−1.02139	+	0.180751i	−0.0672028	+	0.0118925i
$232$	−3.28062	+	29.1163i	−0.215384	+	1.91158i
$233$	−4.99665	+	16.1988i	−0.327342	+	1.06122i	0.631046	+	0.775745i	$0.282626\pi$
$233$	−4.99665	+	16.1988i	−0.327342	+	1.06122i	−0.958388	+	0.285470i	$0.907850\pi$
$234$	4.58052	−	5.52753i	0.299438	−	0.361346i
$235$	−2.60813	−	34.8031i	−0.170136	−	2.27031i
$236$	−20.6742	+	47.3857i	−1.34577	+	3.08455i
$237$	−1.53183	−	3.18087i	−0.0995029	−	0.206620i
$238$	−29.6947	+	15.2468i	−1.92482	+	0.988301i
$239$	−19.2123	+	6.72268i	−1.24274	+	0.434854i	−0.869987	−	0.493075i	$-0.835873\pi$
$239$	−19.2123	+	6.72268i	−1.24274	+	0.434854i	−0.372755	+	0.927930i	$0.621587\pi$
$240$	18.4850	+	21.4800i	1.19320	+	1.38653i
$241$	5.17553	−	9.79258i	0.333385	−	0.630796i	−0.659252	−	0.751922i	$-0.729127\pi$
$241$	5.17553	−	9.79258i	0.333385	−	0.630796i	0.992637	+	0.121127i	$0.0386507\pi$
$242$	−5.10824	−	26.9977i	−0.328370	−	1.73548i
$243$	1.19139	+	7.90436i	0.0764278	+	0.507065i
$244$	−42.2571			−2.70523
$245$	−3.00600	+	21.9836i	−0.192046	+	1.40448i
$246$			36.8298i			2.34818i
$247$	−1.67124	+	9.83125i	−0.106338	+	0.625547i
$248$	31.9388	−	46.8456i	2.02811	−	2.97470i
$249$	−2.47890	+	4.69031i	−0.157094	+	0.297237i
$250$	0.375339	+	0.0281278i	0.0237385	+	0.00177896i
$251$	−14.3253	−	6.89868i	−0.904202	−	0.435441i	−0.0767971	−	0.997047i	$-0.524469\pi$
$251$	−14.3253	−	6.89868i	−0.904202	−	0.435441i	−0.827405	+	0.561606i	$0.810184\pi$
$252$	7.78423	+	4.61805i	0.490360	+	0.290910i
$253$	0.524045	−	1.49763i	0.0329464	−	0.0941554i
$254$	4.70896	−	10.7931i	0.295467	−	0.677216i
$255$	−17.9177	−	15.4194i	−1.12205	−	0.965601i
$256$	−11.6081	+	29.5768i	−0.725503	+	1.84855i
$257$	−30.1491	−	9.29976i	−1.88065	−	0.580103i	−0.992771	−	0.120024i	$-0.961703\pi$
$257$	−30.1491	−	9.29976i	−1.88065	−	0.580103i	−0.887878	−	0.460079i	$-0.847821\pi$
$258$	−26.7790	−	3.01727i	−1.66719	−	0.187847i
$259$	7.02682	−	7.97229i	0.436625	−	0.495374i
$260$	41.2999	−	27.0357i	2.56131	−	1.67668i
$261$	−3.28907	+	2.24245i	−0.203588	+	0.138804i
$262$	1.42020	+	0.0531402i	0.0877403	+	0.00328301i
$263$	3.02752	+	5.24381i	0.186685	+	0.323347i	0.944143	−	0.329536i	$-0.106892\pi$
$263$	3.02752	+	5.24381i	0.186685	+	0.323347i	−0.757458	+	0.652884i	$0.773559\pi$
$264$	−1.14280	+	1.97938i	−0.0703342	+	0.121822i
$265$	7.70251	−	12.2585i	0.473161	−	0.753032i
$266$	−18.3938	−	0.217938i	−1.12779	−	0.0133626i
$267$	11.7528	−	7.38476i	0.719258	−	0.451940i
$268$	0.762495	+	20.3781i	0.0465768	+	1.24479i
$269$	0.519087	−	3.44391i	0.0316493	−	0.209979i	−0.967417	−	0.253189i	$-0.918520\pi$
$269$	0.519087	−	3.44391i	0.0316493	−	0.209979i	0.999066	+	0.0432102i	$0.0137585\pi$
$270$	−6.69161	+	44.3959i	−0.407238	+	2.70185i
$271$	−20.2268	+	0.756835i	−1.22869	+	0.0459744i	−0.643837	−	0.765163i	$-0.722658\pi$
$271$	−20.2268	+	0.756835i	−1.22869	+	0.0459744i	−0.584856	+	0.811137i	$0.698849\pi$
$272$	−6.71960	+	29.4405i	−0.407436	+	1.78509i
$273$	−8.76261	+	11.1418i	−0.530337	+	0.674335i
$274$	−5.24032	−	22.9594i	−0.316580	−	1.38703i
$275$	0.344663	+	1.28630i	0.0207840	+	0.0775669i
$276$	33.4246	−	19.2977i	2.01192	−	1.16159i
$277$	20.0925	+	21.6546i	1.20724	+	1.30110i	0.941484	+	0.337058i	$0.109432\pi$
$277$	20.0925	+	21.6546i	1.20724	+	1.30110i	0.265758	+	0.964040i	$0.414378\pi$
$278$	51.6929	+	9.78082i	3.10033	+	0.586615i
$279$	7.65446	−	0.862450i	0.458261	−	0.0516336i
$280$	32.8275	+	36.2312i	1.96182	+	2.16523i
$281$	−0.891263	+	7.91017i	−0.0531683	+	0.471881i	0.938712	+	0.344703i	$0.112021\pi$
$281$	−0.891263	+	7.91017i	−0.0531683	+	0.471881i	−0.991880	+	0.127178i	$0.959408\pi$
$282$	39.3006	+	12.1226i	2.34032	+	0.721892i
$283$	−2.82277	+	7.19231i	−0.167796	+	0.427538i	−0.989894	−	0.141808i	$-0.954708\pi$
$283$	−2.82277	+	7.19231i	−0.167796	+	0.427538i	0.822098	+	0.569346i	$0.192804\pi$
$284$	7.01215	−	8.14827i	0.416095	−	0.483511i
$285$	−4.75927	−	12.1264i	−0.281915	−	0.718307i
$286$	1.89708	+	1.45593i	0.112177	+	0.0860909i
$287$	0.666503	+	26.0785i	0.0393424	+	1.53936i
$288$	2.59054	−	0.906468i	0.152649	−	0.0534141i
$289$	0.612007	−	8.16666i	0.0360004	−	0.480392i
$290$	−38.2679	+	11.8041i	−2.24717	+	0.693160i
$291$	−0.909785	+	0.172141i	−0.0533326	+	0.0100911i
$292$	29.5267	+	21.7917i	1.72792	+	1.27526i
$293$	14.9890	−	14.9890i	0.875668	−	0.875668i	−0.117415	−	0.993083i	$-0.537461\pi$
$293$	14.9890	−	14.9890i	0.875668	−	0.875668i	0.993083	+	0.117415i	$0.0374607\pi$
$294$	−22.8210	−	12.7620i	−1.33095	−	0.744294i
$295$	−37.9412			−2.20902
$296$	−3.49004	−	23.1549i	−0.202854	−	1.34585i
$297$	−1.46075	+	0.276389i	−0.0847612	+	0.0160377i
$298$	−8.81981	−	28.5931i	−0.510918	−	1.65636i
$299$	−8.29595	−	20.0329i	−0.479767	−	1.15853i
$300$	−14.0547	+	29.1848i	−0.811447	+	1.68499i
$301$	−19.0163	−	1.65185i	−1.09608	−	0.0952113i
$302$	27.8315	−	13.4029i	1.60152	−	0.771252i
$303$	12.0830	−	4.74224i	0.694153	−	0.272435i
$304$	−10.8549	+	12.6136i	−0.622569	+	0.723438i
$305$	−12.4013	−	28.4241i	−0.710096	−	1.62756i
$306$	−8.83482	+	4.66934i	−0.505053	+	0.266928i
$307$	5.24107	+	0.590527i	0.299124	+	0.0337031i	0.260251	−	0.965541i	$-0.416195\pi$
$307$	5.24107	+	0.590527i	0.299124	+	0.0337031i	0.0388728	+	0.999244i	$0.487623\pi$
$308$	−1.44031	+	2.64876i	−0.0820695	+	0.150927i
$309$	15.7438	+	12.5553i	0.895634	+	0.714244i
$310$	76.1411	+	14.4067i	4.32453	+	0.818245i
$311$	4.63208	−	4.29795i	0.262661	−	0.243714i	−0.537837	−	0.843049i	$-0.680759\pi$
$311$	4.63208	−	4.29795i	0.262661	−	0.243714i	0.800499	+	0.599335i	$0.204568\pi$
$312$	6.37702	+	30.5759i	0.361028	+	1.73102i
$313$	−21.1882	−	12.2330i	−1.19763	−	0.691450i	−0.237601	−	0.971363i	$-0.576361\pi$
$313$	−21.1882	−	12.2330i	−1.19763	−	0.691450i	−0.960025	+	0.279913i	$0.909695\pi$
$314$	4.24334	−	6.75324i	0.239466	−	0.381107i
$315$	−0.821856	+	6.59131i	−0.0463063	+	0.371378i
$316$	−10.0049	−	2.28355i	−0.562819	−	0.128460i
$317$	8.50488	−	0.318230i	0.477681	−	0.0178736i	0.202533	−	0.979275i	$-0.435083\pi$
$317$	8.50488	−	0.318230i	0.477681	−	0.0178736i	0.275148	+	0.961402i	$0.411273\pi$
$318$	10.1310	+	13.7270i	0.568116	+	0.769770i
$319$	−0.787441	−	1.06694i	−0.0440882	−	0.0597374i
$320$	−10.5252	+	0.393824i	−0.588375	+	0.0220154i
$321$	1.82979	+	0.417638i	0.102129	+	0.0233103i
$322$	34.1156	−	20.8766i	1.90119	−	1.16341i
$323$	7.38535	−	11.7537i	0.410932	−	0.653994i
$324$	−22.4300	−	12.9500i	−1.24611	−	0.719443i
$325$	15.2242	+	9.96966i	0.844486	+	0.553017i
$326$	−11.6495	+	10.8092i	−0.645207	+	0.598665i
$327$	−10.5510	−	1.99636i	−0.583473	−	0.110399i
$328$	44.9414	+	35.8396i	2.48147	+	1.97891i
$329$	28.0474	+	7.87258i	1.54630	+	0.434030i
$330$	−3.10423	−	0.349762i	−0.170882	−	0.0192538i
$331$	−10.1202	+	5.34868i	−0.556257	+	0.293990i	−0.721674	−	0.692234i	$-0.756627\pi$
$331$	−10.1202	+	5.34868i	−0.556257	+	0.293990i	0.165417	+	0.986224i	$0.447103\pi$
$332$	6.16650	+	14.1338i	0.338431	+	0.775691i
$333$	2.07516	−	2.41137i	0.113718	−	0.132143i
$334$	25.4785	−	9.99959i	1.39412	−	0.547153i
$335$	−13.4835	+	6.49331i	−0.736682	+	0.354767i
$336$	−22.1198	+	8.38034i	−1.20674	+	0.457185i
$337$	14.7986	−	30.7297i	0.806132	−	1.67395i	0.0695746	−	0.997577i	$-0.477836\pi$
$337$	14.7986	−	30.7297i	0.806132	−	1.67395i	0.736558	−	0.676375i	$-0.236450\pi$
$338$	32.5883	−	2.43670i	1.77257	−	0.132539i
$339$	1.81533	+	5.88516i	0.0985953	+	0.319638i
$340$	−67.5140	+	12.7743i	−3.66146	+	0.692786i
$341$	0.382436	+	2.53730i	0.0207101	+	0.137403i
$342$	−5.50683			−0.297775
$343$	−16.3901	−	8.62353i	−0.884981	−	0.465627i
$344$	−29.7408	+	29.7408i	−1.60352	+	1.60352i
$345$	22.7897	+	16.8196i	1.22696	+	0.905537i
$346$	−9.62283	+	1.82074i	−0.517327	+	0.0978835i
$347$	11.3370	−	3.49700i	0.608602	−	0.187729i	0.0248909	−	0.999690i	$-0.492076\pi$
$347$	11.3370	−	3.49700i	0.608602	−	0.187729i	0.583711	+	0.811961i	$0.301600\pi$
$348$	2.41050	−	32.1659i	0.129216	−	1.72427i
$349$	−13.7559	+	4.81341i	−0.736339	+	0.257656i	−0.672287	−	0.740291i	$-0.734688\pi$
$349$	−13.7559	+	4.81341i	−0.736339	+	0.257656i	−0.0640515	+	0.997947i	$0.520402\pi$
$350$	−13.7874	+	30.6064i	−0.736965	+	1.63598i
$351$	−12.3690	+	16.1168i	−0.660208	+	0.860252i
$352$	0.334015	+	0.851056i	0.0178030	+	0.0453614i
$353$	0.232877	−	0.270608i	0.0123948	−	0.0144030i	−0.751740	−	0.659459i	$-0.770785\pi$
$353$	0.232877	−	0.270608i	0.0123948	−	0.0144030i	0.764135	+	0.645056i	$0.223166\pi$
$354$	16.3347	−	41.6200i	0.868178	−	2.21208i
$355$	7.53878	+	2.32541i	0.400117	+	0.123420i
$356$	4.51733	−	40.0924i	0.239418	−	2.12489i
$357$	17.2034	−	9.66248i	0.910503	−	0.511393i
$358$	−37.1755	+	4.18867i	−1.96479	+	0.221378i
$359$	15.6575	+	2.96255i	0.826370	+	0.156358i	0.581860	−	0.813289i	$-0.302325\pi$
$359$	15.6575	+	2.96255i	0.826370	+	0.156358i	0.244510	+	0.969647i	$0.421373\pi$
$360$	9.95520	+	10.7291i	0.524685	+	0.565476i
$361$	−9.82962	+	5.67514i	−0.517349	+	0.298691i
$362$	8.13785	+	30.3709i	0.427716	+	1.59626i
$363$	3.61411	+	15.8345i	0.189692	+	0.831094i
$364$	9.44001	+	40.1061i	0.494791	+	2.10213i
$365$	−5.99284	+	26.2563i	−0.313680	+	1.37432i
$366$	36.5192	−	1.36645i	1.90889	−	0.0714257i
$367$	−3.19577	+	21.2026i	−0.166818	+	1.10676i	0.736075	+	0.676899i	$0.236677\pi$
$367$	−3.19577	+	21.2026i	−0.166818	+	1.10676i	−0.902893	+	0.429865i	$0.858561\pi$
$368$	5.39280	−	35.7789i	0.281119	−	1.86510i
$369$	0.292007	+	7.80406i	0.0152013	+	0.406263i
$370$	27.0992	−	17.0276i	1.40882	−	0.885222i
$371$	7.42195	+	9.53646i	0.385328	+	0.495108i
$372$	−33.2075	+	52.8494i	−1.72173	+	2.74011i
$373$	−0.311855	+	0.540149i	−0.0161472	+	0.0279679i	−0.873986	−	0.485951i	$-0.838473\pi$
$373$	−0.311855	+	0.540149i	−0.0161472	+	0.0279679i	0.857839	+	0.513919i	$0.171807\pi$
$374$	−1.66439	−	2.88281i	−0.0860635	−	0.149066i
$375$	−0.222332	−	0.00831907i	−0.0114812	−	0.000429595i
$376$	53.0365	−	36.1597i	2.73515	−	1.86479i
$377$	−17.7390	−	3.70279i	−0.913604	−	0.190704i
$378$	−32.9228	−	17.9024i	−1.69337	−	0.920801i
$379$	−17.8630	−	2.01268i	−0.917561	−	0.103384i	−0.359463	−	0.933159i	$-0.617040\pi$
$379$	−17.8630	−	2.01268i	−0.917561	−	0.103384i	−0.558098	+	0.829775i	$0.688469\pi$
$380$	−36.1833	−	11.1611i	−1.85616	−	0.572551i
$381$	−2.54300	+	6.47946i	−0.130282	+	0.331953i
$382$	20.1628	+	17.3515i	1.03162	+	0.887781i
$383$	1.27809	−	2.92942i	0.0653074	−	0.149686i	−0.880848	−	0.473400i	$-0.843027\pi$
$383$	1.27809	−	2.92942i	0.0653074	−	0.149686i	0.946155	+	0.323713i	$0.104931\pi$
$384$	7.50052	−	21.4353i	0.382760	−	1.09386i
$385$	−2.20437	−	0.191483i	−0.112345	−	0.00975889i
$386$	46.2711	+	22.2830i	2.35514	+	1.13417i
$387$	−5.69826	−	0.427026i	−0.289659	−	0.0217069i
$388$	−1.25761	+	2.37952i	−0.0638456	+	0.120802i
$389$	−5.28088	+	7.74563i	−0.267751	+	0.392719i	−0.936442	−	0.350821i	$-0.885902\pi$
$389$	−5.28088	+	7.74563i	−0.267751	+	0.392719i	0.668691	+	0.743540i	$0.266855\pi$
$390$	−34.8178	+	24.7002i	−1.76307	+	1.25074i
$391$			30.1823i			1.52638i
$392$	−37.7802	+	15.4284i	−1.90819	+	0.779251i
$393$	−0.840078			−0.0423763
$394$	6.01109	+	39.8810i	0.302834	+	2.00917i
$395$	−1.40014	−	7.39991i	−0.0704487	−	0.372330i
$396$	−0.421754	+	0.797997i	−0.0211939	+	0.0401009i
$397$	2.18999	+	2.54481i	0.109912	+	0.127721i	0.810233	−	0.586108i	$-0.199341\pi$
$397$	2.18999	+	2.54481i	0.109912	+	0.127721i	−0.700321	+	0.713828i	$0.746960\pi$
$398$	43.3699	−	15.1758i	2.17394	−	0.760694i
$399$	10.8699	−	0.277808i	0.544176	−	0.0139078i
$400$	13.1762	+	27.3606i	0.658809	+	1.36803i
$401$	8.34910	−	19.1363i	0.416934	−	0.955623i	−0.573698	−	0.819067i	$-0.694492\pi$
$401$	8.34910	−	19.1363i	0.416934	−	0.955623i	0.990632	−	0.136557i	$-0.0436035\pi$
$402$	−1.31792	−	17.5864i	−0.0657319	−	0.877131i
$403$	26.9996	+	22.3739i	1.34495	+	1.11452i
$404$	11.1212	−	36.0539i	0.553298	−	1.79375i
$405$	2.12816	−	18.8879i	0.105749	−	0.938549i
$406$	1.64554	−	33.3864i	0.0816666	−	1.65694i
$407$	0.828554	+	0.660750i	0.0410699	+	0.0327521i
$408$	8.08295	−	42.7194i	0.400166	−	2.11493i
$409$	2.89209	+	0.108215i	0.143005	+	0.00535086i	0.108798	−	0.994064i	$-0.465300\pi$
$409$	2.89209	+	0.108215i	0.143005	+	0.00535086i	0.0342071	+	0.999415i	$0.489109\pi$
$410$	−20.3341	+	75.8877i	−1.00423	+	3.74783i
$411$	3.60288	+	13.4461i	0.177717	+	0.663248i
$412$	57.0653	−	13.0248i	2.81140	−	0.641685i
$413$	10.8131	−	29.7659i	0.532076	−	1.46469i
$414$	10.1382	−	6.37028i	0.498267	−	0.313082i
$415$	−7.69733	+	8.29575i	−0.377847	+	0.407222i
$416$	11.1527	+	5.63131i	0.546806	+	0.276098i
$417$	−30.7508	−	4.63494i	−1.50587	−	0.226974i
$418$	−0.0685909	−	1.83313i	−0.00335489	−	0.0896614i
$419$	−8.45526	−	1.92986i	−0.413066	−	0.0942797i	0.0109372	−	0.999940i	$-0.496519\pi$
$419$	−8.45526	−	1.92986i	−0.413066	−	0.0942797i	−0.424004	+	0.905660i	$0.639376\pi$
$420$	−37.6049	−	38.5067i	−1.83493	−	1.87893i
$421$	7.81095	+	4.90794i	0.380682	+	0.239199i	0.708756	−	0.705454i	$-0.249257\pi$
$421$	7.81095	+	4.90794i	0.380682	+	0.239199i	−0.328074	+	0.944652i	$0.606399\pi$
$422$	−13.8924	−	51.8472i	−0.676273	−	2.52388i
$423$	8.42372	+	2.25713i	0.409575	+	0.109745i
$424$	26.6088	+	0.995631i	1.29224	+	0.0483521i
$425$	−14.2698	−	20.9300i	−0.692189	−	1.01526i
$426$	−5.79653	+	7.26862i	−0.280843	+	0.352166i
$427$	25.8338	−	1.62844i	1.25019	−	0.0788058i
$428$	4.26526	−	3.40143i	0.206169	−	0.164414i
$429$	−1.15277	−	0.818078i	−0.0556563	−	0.0394972i
$430$	−53.5122	−	21.0020i	−2.58059	−	1.01281i
$431$	−27.3059	−	23.4986i	−1.31528	−	1.13189i	−0.981963	−	0.189071i	$-0.939452\pi$
$431$	−27.3059	−	23.4986i	−1.31528	−	1.13189i	−0.333314	−	0.942816i	$-0.608167\pi$
$432$	−31.5589	+	12.3860i	−1.51838	+	0.595919i
$433$	5.68526	−	2.73787i	0.273216	−	0.131574i	−0.292259	−	0.956339i	$-0.594407\pi$
$433$	5.68526	−	2.73787i	0.273216	−	0.131574i	0.565475	+	0.824765i	$0.308693\pi$
$434$	−33.0024	+	55.6291i	−1.58416	+	2.67028i
$435$	22.3437	−	7.81840i	1.07130	−	0.374863i
$436$	−23.6586	+	20.3599i	−1.13304	+	0.975061i
$437$	−7.77198	+	14.7053i	−0.371784	+	0.703450i
$438$	−26.2222	−	17.8780i	−1.25294	−	0.854243i
$439$	−24.0240	+	3.62103i	−1.14660	+	0.172822i	−0.694737	−	0.719264i	$-0.744479\pi$
$439$	−24.0240	+	3.62103i	−1.14660	+	0.172822i	−0.451865	+	0.892086i	$0.649241\pi$
$440$	−3.44756	+	3.44756i	−0.164356	+	0.164356i
$441$	−4.93685	−	2.52326i	−0.235088	−	0.120155i
$442$	−43.2090	−	14.2223i	−2.05524	−	0.676488i
$443$	−16.6821	+	2.51443i	−0.792592	+	0.119464i	−0.532845	−	0.846213i	$-0.678877\pi$
$443$	−16.6821	+	2.51443i	−0.792592	+	0.119464i	−0.259747	+	0.965677i	$0.583639\pi$
$444$	4.79251	+	25.3290i	0.227442	+	1.20206i
$445$	28.2937	−	8.72747i	1.34125	−	0.413722i
$446$	0.557193	−	7.43523i	0.0263839	−	0.352068i
$447$	5.84178	+	16.6948i	0.276307	+	0.789639i
$448$	2.69066	−	8.36955i	0.127122	−	0.395424i
$449$	−4.19612	−	1.46829i	−0.198027	−	0.0692927i	0.229443	−	0.973322i	$-0.426309\pi$
$449$	−4.19612	−	1.46829i	−0.198027	−	0.0692927i	−0.427470	+	0.904029i	$0.640595\pi$
$450$	−4.01860	+	9.21073i	−0.189439	+	0.434198i
$451$	−2.59420	+	0.194409i	−0.122156	+	0.00915435i
$452$	16.6643	+	6.54027i	0.783825	+	0.307629i
$453$	−16.1436	+	8.53216i	−0.758494	+	0.400876i
$454$	−22.4707	−	28.1774i	−1.05460	−	1.32243i
$455$	−24.2068	+	18.1198i	−1.13483	+	0.849471i
$456$	14.9385	−	18.7322i	0.699557	−	0.877217i
$457$	−4.98148	+	26.3278i	−0.233024	+	1.23156i	0.649159	+	0.760653i	$0.275121\pi$
$457$	−4.98148	+	26.3278i	−0.233024	+	1.23156i	−0.882182	+	0.470908i	$0.843926\pi$
$458$	−2.77166	−	2.98713i	−0.129511	−	0.139580i
$459$	24.4912	−	14.1400i	1.14315	−	0.659998i
$460$	79.5257	−	21.3088i	3.70791	−	0.993530i
$461$	13.8060	−	21.9722i	0.643011	−	1.02335i	−0.353130	−	0.935574i	$-0.614883\pi$
$461$	13.8060	−	21.9722i	0.643011	−	1.02335i	0.996141	−	0.0877713i	$-0.0279745\pi$
$462$	1.15909	−	2.33568i	0.0539258	−	0.108666i
$463$	12.2680	−	7.70851i	0.570144	−	0.358245i	−0.215901	−	0.976415i	$-0.569269\pi$
$463$	12.2680	−	7.70851i	0.570144	−	0.358245i	0.786044	+	0.618170i	$0.212126\pi$
$464$	−22.1674	−	20.5684i	−1.02910	−	0.954862i
$465$	−45.2945	−	6.82705i	−2.10048	−	0.316597i
$466$	−25.3048	−	34.2867i	−1.17222	−	1.58830i
$467$	12.1154	+	11.2415i	0.560635	+	0.520193i	0.908796	−	0.417242i	$-0.137003\pi$
$467$	12.1154	+	11.2415i	0.560635	+	0.520193i	−0.348160	+	0.937435i	$0.613194\pi$
$468$	2.96805	+	11.9720i	0.137198	+	0.553406i
$469$	−1.25145	−	12.4288i	−0.0577867	−	0.573907i
$470$	74.2858	+	46.6768i	3.42655	+	2.15304i
$471$	−2.35725	+	4.08288i	−0.108616	+	0.188129i
$472$	−34.8912	−	60.4332i	−1.60600	−	2.78167i
$473$	0.0711744	−	1.90218i	0.00327260	−	0.0874621i
$474$	8.72023	+	1.64996i	0.400533	+	0.0757850i
$475$	−1.56299	−	13.8719i	−0.0717150	−	0.636488i
$476$	9.21936	−	56.6073i	0.422569	−	2.59459i
$477$	2.25553	+	2.82835i	0.103274	+	0.129501i
$478$	15.0818	−	48.8939i	0.689824	−	2.23636i
$479$	−13.2258	−	30.3139i	−0.604302	−	1.38508i	−0.902549	−	0.430587i	$-0.858307\pi$
$479$	−13.2258	−	30.3139i	−0.604302	−	1.38508i	0.298247	−	0.954489i	$-0.403598\pi$
$480$	−16.2751	+	1.21965i	−0.742855	+	0.0556693i
$481$	14.4595	−	0.810819i	0.659295	−	0.0369702i
$482$	12.0807	+	25.0858i	0.550259	+	1.14263i
$483$	−19.6905	+	13.0857i	−0.895947	+	0.595421i
$484$	42.5347	+	20.4836i	1.93340	+	0.931075i
$485$	−1.96965	−	0.147605i	−0.0894372	−	0.00670239i
$486$	−17.7657	−	9.38946i	−0.805870	−	0.425915i
$487$	10.7067	−	2.02582i	0.485167	−	0.0917986i	0.0624270	−	0.998050i	$-0.480116\pi$
$487$	10.7067	−	2.02582i	0.485167	−	0.0917986i	0.422740	+	0.906251i	$0.361068\pi$
$488$	33.8699	−	45.8921i	1.53322	−	2.07744i
$489$	6.64239	−	6.64239i	0.300379	−	0.300379i
$490$	−39.9767	−	38.8957i	−1.80596	−	1.75713i
$491$		−	8.43690i		−	0.380752i	−0.981711	−	0.190376i	$-0.939029\pi$
$491$		−	8.43690i		−	0.380752i	0.981711	−	0.190376i	$-0.0609707\pi$
$492$	−50.9152	−	37.5771i	−2.29543	−	1.69411i
$493$	20.8417	+	14.2097i	0.938665	+	0.639971i
$494$	−17.3899	−	18.0557i	−0.782407	−	0.812366i
$495$	−0.660544	−	0.0495009i	−0.0296892	−	0.00222490i
$496$	19.3263	+	55.2313i	0.867775	+	2.47996i
$497$	−3.97287	+	5.25167i	−0.178208	+	0.235569i
$498$	−5.78623	−	12.0152i	−0.259287	−	0.538415i
$499$	−8.72548	−	3.80689i	−0.390606	−	0.170420i	0.195405	−	0.980723i	$-0.437398\pi$
$499$	−8.72548	−	3.80689i	−0.390606	−	0.170420i	−0.586011	+	0.810303i	$0.699303\pi$
$500$	−0.421840	+	0.490187i	−0.0188652	+	0.0219218i
$501$	−14.8290	+	6.46982i	−0.662511	+	0.289050i
$502$	35.3371	−	18.6762i	1.57717	−	0.833559i
$503$	−18.1650	+	14.4861i	−0.809936	+	0.645903i	−0.938299	−	0.345825i	$-0.887599\pi$
$503$	−18.1650	+	14.4861i	−0.809936	+	0.645903i	0.128363	+	0.991727i	$0.459028\pi$
$504$	−11.2545	+	4.75238i	−0.501316	+	0.211688i
$505$	27.5153	−	3.10023i	1.22441	−	0.137958i
$506$	2.24684	+	3.29551i	0.0998841	+	0.146503i
$507$	−19.1959	+	2.15962i	−0.852518	+	0.0959119i
$508$	10.1163	+	17.5219i	0.448838	+	0.777410i
$509$	29.4031	−	7.87855i	1.30327	−	0.349210i	0.460585	−	0.887616i	$-0.347640\pi$
$509$	29.4031	−	7.87855i	1.30327	−	0.349210i	0.842686	+	0.538405i	$0.180973\pi$
$510$	57.9336	−	13.2230i	2.56534	−	0.585523i
$511$	−18.8909	−	12.1845i	−0.835686	−	0.539011i
$512$	−26.2317	−	41.7475i	−1.15929	−	1.84500i
$513$	15.5736	−	0.582721i	0.687589	−	0.0257278i
$514$	63.8144	−	47.0972i	2.81473	−	2.07737i
$515$	25.5082	+	34.5624i	1.12402	+	1.52300i
$516$	31.4936	−	33.9420i	1.38643	−	1.49421i
$517$	−0.646438	+	2.83223i	−0.0284303	+	0.124561i
$518$	5.63547	+	26.1129i	0.247608	+	1.14734i
$519$	5.64390	−	1.28818i	0.247740	−	0.0565450i
$520$	−3.74137	+	66.5223i	−0.164070	+	2.91720i
$521$	−16.1811	+	9.34215i	−0.708906	+	0.409287i	−0.810656	−	0.585523i	$-0.800889\pi$
$521$	−16.1811	+	9.34215i	−0.708906	+	0.409287i	0.101750	+	0.994810i	$0.467556\pi$
$522$	0.374167	−	9.99983i	0.0163769	−	0.437681i
$523$	4.95457	+	7.26702i	0.216648	+	0.317765i	0.919143	−	0.393925i	$-0.128883\pi$
$523$	4.95457	+	7.26702i	0.216648	+	0.317765i	−0.702495	+	0.711689i	$0.747930\pi$
$524$	−1.52248	+	1.90913i	−0.0665099	+	0.0834008i
$525$	7.46763	−	18.3837i	0.325914	−	0.802333i
$526$	−15.1254	−	1.70422i	−0.659498	−	0.0743076i
$527$	−22.8077	−	43.1543i	−0.993520	−	1.87983i
$528$	−0.943290	−	2.16204i	−0.0410514	−	0.0940909i
$529$	−0.983796	−	13.1278i	−0.0427737	−	0.570776i
$530$	13.2960	+	33.8777i	0.577543	+	1.47156i
$531$	3.13125	−	8.94859i	0.135885	−	0.388336i
$532$	19.0683	−	25.2060i	0.826715	−	1.09282i
$533$	−24.6657	+	25.6017i	−1.06839	+	1.10893i
$534$	−2.60749	+	34.7946i	−0.112837	+	1.50571i
$535$	3.53970	+	1.87078i	0.153034	+	0.0808811i
$536$	−22.7422	−	15.5054i	−0.982314	−	0.669731i
$537$	21.8667	−	3.29588i	0.943620	−	0.142228i
$538$	6.19077	+	6.19077i	0.266903	+	0.266903i
$539$	0.778461	−	1.67482i	0.0335307	−	0.0721397i
$540$	−54.5475	−	54.5475i	−2.34735	−	2.34735i
$541$	−26.6436	−	19.6639i	−1.14550	−	0.845416i	−0.155687	−	0.987806i	$-0.549759\pi$
$541$	−26.6436	−	19.6639i	−1.14550	−	0.845416i	−0.989811	+	0.142390i	$0.954521\pi$
$542$	28.6626	−	42.0404i	1.23117	−	1.80579i
$543$	−5.47824	−	17.7600i	−0.235094	−	0.762155i
$544$	−11.3441	−	13.1821i	−0.486376	−	0.565179i
$545$	−20.6381	−	9.93881i	−0.884041	−	0.425732i
$546$	−9.45510	−	34.3551i	−0.404641	−	1.47026i
$547$	4.15983	−	2.00327i	0.177861	−	0.0856536i	−0.342834	−	0.939396i	$-0.611387\pi$
$547$	4.15983	−	2.00327i	0.177861	−	0.0856536i	0.520696	+	0.853742i	$0.325673\pi$
$548$	37.0867	+	16.1808i	1.58427	+	0.691208i
$549$	7.72741	−	0.579090i	0.329798	−	0.0247149i
$550$	−3.11615	−	1.22300i	−0.132873	−	0.0521489i
$551$	6.49543	+	12.2899i	0.276714	+	0.523569i
$552$	−5.83278	+	51.7674i	−0.248260	+	2.20337i
$553$	6.20448	+	1.01049i	0.263841	+	0.0429706i
$554$	−73.7913	+	8.31428i	−3.13509	+	0.353240i
$555$	−15.6310	+	10.6570i	−0.663499	+	0.452366i
$556$	−66.2632	+	61.4833i	−2.81019	+	2.60747i
$557$	−4.95580	+	18.4953i	−0.209984	+	0.783672i	0.777888	+	0.628403i	$0.216291\pi$
$557$	−4.95580	+	18.4953i	−0.209984	+	0.783672i	−0.987872	+	0.155269i	$0.950376\pi$
$558$	−9.68174	+	16.7693i	−0.409861	+	0.709899i
$559$	−16.5943	−	20.0319i	−0.701863	−	0.847259i
$560$	−50.2047	+	5.05511i	−2.12154	+	0.213618i
$561$	1.04686	+	1.66607i	0.0441984	+	0.0703414i
$562$	−14.6686	−	13.6105i	−0.618759	−	0.574124i
$563$	−35.5717	−	5.36157i	−1.49917	−	0.225963i	−0.652379	−	0.757893i	$-0.726229\pi$
$563$	−35.5717	−	5.36157i	−1.49917	−	0.225963i	−0.846789	+	0.531930i	$0.821467\pi$
$564$	−56.8569	+	41.9623i	−2.39411	+	1.76693i
$565$	0.491238	+	13.1286i	0.0206665	+	0.552325i
$566$	−10.3334	−	16.4456i	−0.434347	−	0.691259i
$567$	14.2116	+	7.05258i	0.596832	+	0.296181i
$568$	3.22881	+	14.1464i	0.135478	+	0.593568i
$569$	20.4915	+	11.8308i	0.859048	+	0.495972i	0.863693	−	0.504017i	$-0.168145\pi$
$569$	20.4915	+	11.8308i	0.859048	+	0.495972i	−0.00464516	+	0.999989i	$0.501479\pi$
$570$	31.6311	+	8.47553i	1.32488	+	0.355001i
$571$	25.7982	+	27.8039i	1.07962	+	1.16356i	0.985792	+	0.167968i	$0.0537205\pi$
$571$	25.7982	+	27.8039i	1.07962	+	1.16356i	0.0938298	+	0.995588i	$0.470089\pi$
$572$	−3.94831	+	1.13713i	−0.165087	+	0.0475459i
$573$	−12.2936	−	9.80379i	−0.513571	−	0.409559i
$574$	−53.7410	−	37.5803i	−2.24311	−	1.56857i
$575$	18.9245	+	23.7306i	0.789208	+	0.989635i
$576$	0.775748	−	2.51491i	0.0323228	−	0.104788i
$577$	4.72710	−	2.06241i	0.196792	−	0.0858594i	−0.299185	−	0.954195i	$-0.596715\pi$
$577$	4.72710	−	2.06241i	0.196792	−	0.0858594i	0.495977	+	0.868336i	$0.334810\pi$
$578$	15.6043	+	13.4285i	0.649051	+	0.558554i
$579$	−27.8245	−	12.1397i	−1.15635	−	0.504510i
$580$	22.7259	−	64.9468i	0.943641	−	2.69677i
$581$	−4.31455	−	8.40304i	−0.178998	−	0.348617i
$582$	1.00990	−	2.09709i	0.0418618	−	0.0869270i
$583$	−0.913417	+	0.786059i	−0.0378299	+	0.0325552i
$584$	−47.3326	+	14.6002i	−1.95864	+	0.604160i
$585$	−7.18189	+	5.50991i	−0.296934	+	0.227807i
$586$	7.94195	+	52.6914i	0.328079	+	2.17666i
$587$	30.5562	+	30.5562i	1.26119	+	1.26119i	0.950518	+	0.310671i	$0.100554\pi$
$587$	30.5562	+	30.5562i	1.26119	+	1.26119i	0.310671	+	0.950518i	$0.399446\pi$
$588$	40.9268	−	18.5279i	1.68779	−	0.764077i
$589$		−	26.8985i		−	1.10833i
$590$	56.6363	−	76.7394i	2.33168	−	3.15931i
$591$	−4.43217	−	23.4246i	−0.182315	−	0.963558i
$592$	21.3665	+	11.2925i	0.878159	+	0.464120i
$593$	14.7867	+	17.1824i	0.607216	+	0.705597i	0.974469	−	0.224524i	$-0.0720826\pi$
$593$	14.7867	+	17.1824i	0.607216	+	0.705597i	−0.367253	+	0.930121i	$0.619702\pi$
$594$	1.62150	−	3.36707i	0.0665309	−	0.138153i
$595$	40.7824	−	10.4113i	1.67191	−	0.426823i
$596$	48.5272	+	16.9804i	1.98775	+	0.695544i
$597$	−25.2829	+	9.92281i	−1.03476	+	0.406114i
$598$	52.9021	+	13.1246i	2.16333	+	0.536706i
$599$	−8.38057	+	21.3533i	−0.342421	+	0.872474i	0.651117	+	0.758977i	$0.274301\pi$
$599$	−8.38057	+	21.3533i	−0.342421	+	0.872474i	−0.993538	+	0.113497i	$0.963795\pi$
$600$	−20.4303	−	38.6559i	−0.834062	−	1.57812i
$601$	−2.66884	+	2.12833i	−0.108864	+	0.0868164i	−0.676409	−	0.736526i	$-0.736465\pi$
$601$	−2.66884	+	2.12833i	−0.108864	+	0.0868164i	0.567545	+	0.823343i	$0.307893\pi$
$602$	31.7274	−	35.9964i	1.29311	−	1.46710i
$603$	−0.418696	−	3.71603i	−0.0170506	−	0.151328i
$604$	−9.86738	+	52.1504i	−0.401498	+	2.12197i
$605$	−1.29547	+	34.6222i	−0.0526684	+	1.40759i
$606$	−8.44522	+	31.5180i	−0.343064	+	1.28033i
$607$	35.8452	+	20.6952i	1.45491	+	0.839994i	0.998754	−	0.0499044i	$-0.0158917\pi$
$607$	35.8452	+	20.6952i	1.45491	+	0.839994i	0.456158	+	0.889899i	$0.349225\pi$
$608$	−2.13263	−	9.34367i	−0.0864896	−	0.378936i
$609$	−0.234096	+	19.7575i	−0.00948603	+	0.800614i
$610$	76.0022	+	17.3470i	3.07724	+	0.702360i
$611$	19.2004	+	34.7473i	0.776765	+	1.40573i
$612$	2.55898	−	16.9777i	0.103441	−	0.686284i
$613$	16.4974	−	12.1756i	0.666323	−	0.491769i	−0.207360	−	0.978265i	$-0.566487\pi$
$613$	16.4974	−	12.1756i	0.666323	−	0.491769i	0.873683	+	0.486496i	$0.161725\pi$
$614$	−9.01795	+	9.71904i	−0.363935	+	0.392229i
$615$	10.3339	−	45.2758i	0.416703	−	1.82570i
$616$	−1.72217	−	3.68725i	−0.0693882	−	0.148564i
$617$	−1.99272	−	1.25211i	−0.0802237	−	0.0504079i	0.491323	−	0.870978i	$-0.336514\pi$
$617$	−1.99272	−	1.25211i	−0.0802237	−	0.0504079i	−0.571547	+	0.820570i	$0.693656\pi$
$618$	−48.8956	+	13.1015i	−1.96687	+	0.527021i
$619$	−23.5016	−	6.29724i	−0.944611	−	0.253108i	−0.246537	−	0.969133i	$-0.579293\pi$
$619$	−23.5016	−	6.29724i	−0.944611	−	0.253108i	−0.698074	+	0.716026i	$0.745959\pi$
$620$	−97.6025	+	90.5619i	−3.91981	+	3.63705i
$621$	−27.9973	+	19.0882i	−1.12349	+	0.765985i
$622$	1.77849	+	15.7845i	0.0713109	+	0.632902i
$623$	−1.21664	+	24.6846i	−0.0487438	+	0.988966i
$624$	−29.2982	−	13.4432i	−1.17287	−	0.538159i
$625$	23.6615	+	7.29860i	0.946460	+	0.291944i
$626$	56.3708	−	24.5943i	2.25303	−	0.982987i
$627$	0.0810324	+	1.08130i	0.00323612	+	0.0431831i
$628$	5.00654	+	12.7565i	0.199783	+	0.509038i
$629$	−19.0279	−	6.65816i	−0.758693	−	0.265478i
$630$	−12.1047	−	11.5014i	−0.482263	−	0.458226i
$631$	4.31139	+	12.3212i	0.171634	+	0.490501i	0.997282	−	0.0736848i	$-0.0234759\pi$
$631$	4.31139	+	12.3212i	0.171634	+	0.490501i	−0.825648	+	0.564186i	$0.809190\pi$
$632$	10.4991	−	9.03522i	0.417632	−	0.359402i
$633$	9.35210	+	30.3188i	0.371713	+	1.20506i
$634$	−12.0519	+	17.6769i	−0.478643	+	0.702040i
$635$	−8.81721	+	11.9469i	−0.349900	+	0.474098i
$636$	−29.3133			−1.16235
$637$	−7.31669	−	24.1550i	−0.289898	−	0.957058i
$638$	3.33344			0.131972
$639$	−1.17063	+	1.58614i	−0.0463093	+	0.0627468i
$640$	27.2894	−	40.0262i	1.07871	−	1.58217i
$641$	8.66385	+	28.0875i	0.342202	+	1.10939i	0.949196	+	0.314684i	$0.101899\pi$
$641$	8.66385	+	28.0875i	0.342202	+	1.10939i	−0.606995	+	0.794706i	$0.707625\pi$
$642$	−3.57611	+	3.07750i	−0.141138	+	0.121459i
$643$	−12.1485	−	34.7183i	−0.479089	−	1.36916i	−0.889366	−	0.457196i	$-0.848854\pi$
$643$	−12.1485	−	34.7183i	−0.479089	−	1.36916i	0.410278	−	0.911961i	$-0.365432\pi$
$644$	−5.94707	+	68.4632i	−0.234347	+	2.69783i
$645$	32.0735	+	11.2230i	1.26289	+	0.441905i
$646$	12.7486	+	32.4828i	0.501585	+	1.27802i
$647$	−2.18714	−	29.1854i	−0.0859855	−	1.14740i	−0.858643	−	0.512574i	$-0.828692\pi$
$647$	−2.18714	−	29.1854i	−0.0859855	−	1.14740i	0.772658	−	0.634823i	$-0.218927\pi$
$648$	32.0421	−	13.9798i	1.25873	−	0.549179i
$649$	3.01784	+	0.930880i	0.118461	+	0.0365402i
$650$	−42.8903	+	15.9102i	−1.68230	+	0.624049i
$651$	18.2648	−	33.5892i	0.715852	−	1.31646i
$652$	−3.05719	−	27.1333i	−0.119729	−	1.06262i
$653$	8.45511	−	5.76460i	0.330874	−	0.225586i	−0.386475	−	0.922300i	$-0.626308\pi$
$653$	8.45511	−	5.76460i	0.330874	−	0.225586i	0.717349	+	0.696714i	$0.245355\pi$
$654$	19.7878	−	18.3604i	0.773763	−	0.717947i
$655$	−1.73098	−	0.463814i	−0.0676349	−	0.0181227i
$656$	−57.3035	+	15.3544i	−2.23733	+	0.599490i
$657$	−5.69809	−	3.58035i	−0.222304	−	0.139683i
$658$	−57.7905	+	44.9767i	−2.25291	+	1.75337i
$659$	10.8841	−	47.6865i	0.423986	−	1.85760i	−0.0843402	−	0.996437i	$-0.526878\pi$
$659$	10.8841	−	47.6865i	0.423986	−	1.85760i	0.508326	−	0.861165i	$-0.330265\pi$
$660$	3.65074	−	3.93456i	0.142105	−	0.153153i
$661$	27.3703	−	20.2002i	1.06458	−	0.785697i	0.0869902	−	0.996209i	$-0.472275\pi$
$661$	27.3703	−	20.2002i	1.06458	−	0.785697i	0.977591	+	0.210512i	$0.0675132\pi$
$662$	4.28863	−	28.4532i	0.166683	−	1.10587i
$663$	25.8376	+	7.44603i	1.00345	+	0.289180i
$664$	−20.2922	−	4.63155i	−0.787489	−	0.179739i
$665$	22.5508	+	5.42894i	0.874481	+	0.210525i
$666$	1.77956	+	7.79675i	0.0689564	+	0.302118i
$667$	−26.1753	−	15.1123i	−1.01351	−	0.585150i
$668$	−12.1716	+	45.4252i	−0.470935	+	1.75755i
$669$	−0.164796	+	4.40425i	−0.00637137	+	0.170278i
$670$	6.99404	−	36.9644i	0.270204	−	1.42806i
$671$	0.289019	+	2.56511i	0.0111575	+	0.0990251i
$672$	3.68149	−	13.1159i	0.142017	−	0.505957i
$673$	−29.9649	+	23.8962i	−1.15506	+	0.921133i	−0.997792	−	0.0664226i	$-0.978841\pi$
$673$	−29.9649	+	23.8962i	−1.15506	+	0.921133i	−0.157272	+	0.987555i	$0.550270\pi$
$674$	40.0630	+	75.8030i	1.54317	+	2.91982i
$675$	10.3901	−	26.4736i	0.399916	−	1.01897i
$676$	−29.8810	+	47.5377i	−1.14927	+	1.82837i
$677$	18.5508	−	7.28065i	0.712965	−	0.279818i	0.0189926	−	0.999820i	$-0.493954\pi$
$677$	18.5508	−	7.28065i	0.712965	−	0.279818i	0.693973	+	0.720001i	$0.255859\pi$
$678$	−14.6131	−	5.11334i	−0.561212	−	0.196377i
$679$	0.677142	−	1.50318i	0.0259863	−	0.0576868i
$680$	40.2407	−	83.5606i	1.54316	−	3.20440i
$681$	13.8961	+	16.1476i	0.532500	+	0.618776i
$682$	−5.70280	−	3.01402i	−0.218371	−	0.115413i
$683$	−3.26200	−	17.2401i	−0.124817	−	0.659673i	−0.987959	−	0.154713i	$-0.950555\pi$
$683$	−3.26200	−	17.2401i	−0.124817	−	0.659673i	0.863143	−	0.504960i	$-0.168493\pi$
$684$	5.61856	−	7.61288i	0.214831	−	0.291086i
$685$			29.6949i			1.13458i
$686$	41.9080	−	20.2778i	1.60006	−	0.774208i
$687$	1.70322	+	1.70322i	0.0649819	+	0.0649819i
$688$	−6.46965	−	42.9234i	−0.246653	−	1.63644i
$689$	−2.15087	+	16.3270i	−0.0819418	+	0.622009i
$690$	−68.0384	+	20.9871i	−2.59018	+	0.798964i
$691$	−10.4286	+	8.97455i	−0.396723	+	0.341408i	−0.827916	−	0.560852i	$-0.810474\pi$
$691$	−10.4286	+	8.97455i	−0.396723	+	0.341408i	0.431193	+	0.902260i	$0.358093\pi$
$692$	7.30102	−	15.1607i	0.277543	−	0.576324i
$693$	0.227087	−	0.504108i	0.00862632	−	0.0191495i
$694$	−9.85020	+	28.1502i	−0.373908	+	1.06857i
$695$	−60.8030	−	26.5281i	−2.30639	−	1.00627i
$696$	33.0008	+	28.3995i	1.25089	+	1.07648i
$697$	45.3573	−	19.7892i	1.71803	−	0.749569i
$698$	10.7985	−	35.0078i	0.408729	−	1.32507i
$699$	15.7052	+	19.6936i	0.594024	+	0.744882i
$700$	−28.2446	−	50.2877i	−1.06754	−	1.90070i
$701$	20.0929	+	16.0235i	0.758898	+	0.605201i	0.924584	−	0.380978i	$-0.124412\pi$
$701$	20.0929	+	16.0235i	0.758898	+	0.605201i	−0.165686	+	0.986179i	$0.552984\pi$
$702$	−14.1340	−	49.0756i	−0.533454	−	1.85224i
$703$	−7.55622	−	8.14367i	−0.284988	−	0.307144i
$704$	0.846835	+	0.226909i	0.0319163	+	0.00855194i
$705$	−44.9118	−	25.9298i	−1.69148	−	0.976574i
$706$	0.199705	+	0.874963i	0.00751598	+	0.0329297i
$707$	−5.40952	+	22.4701i	−0.203446	+	0.845076i
$708$	40.8713	+	65.0463i	1.53604	+	2.44459i
$709$	0.532094	+	14.2205i	0.0199832	+	0.534062i	0.972954	+	0.231000i	$0.0741996\pi$
$709$	0.532094	+	14.2205i	0.0199832	+	0.534062i	−0.952971	+	0.303063i	$0.901991\pi$
$710$	−15.9568	+	11.7766i	−0.598848	+	0.441970i
$711$	1.86086	+	0.280479i	0.0697875	+	0.0105188i
$712$	39.9205	+	37.0408i	1.49608	+	1.38816i
$713$	31.1161	+	49.5209i	1.16531	+	1.85457i
$714$	−6.13703	+	49.2191i	−0.229672	+	1.84198i
$715$	−1.92361	−	2.32210i	−0.0719390	−	0.0868417i
$716$	32.1392	−	55.6667i	1.20110	−	2.08036i
$717$	−7.82804	+	29.2146i	−0.292344	+	1.09104i
$718$	−29.3646	+	27.2464i	−1.09588	+	1.01682i
$719$	−17.5473	+	11.9635i	−0.654403	+	0.446164i	−0.844467	−	0.535607i	$-0.820083\pi$
$719$	−17.5473	+	11.9635i	−0.654403	+	0.446164i	0.190064	+	0.981772i	$0.439130\pi$
$720$	−15.0105	+	1.69128i	−0.559409	+	0.0630302i
$721$	−34.3849	+	10.1618i	−1.28056	+	0.378445i
$722$	3.19460	−	28.3528i	0.118891	−	1.05518i
$723$	−7.69042	−	14.5510i	−0.286010	−	0.541157i
$724$	−50.2890	−	19.7370i	−1.86898	−	0.733519i
$725$	25.2962	−	1.89569i	0.939478	−	0.0704042i
$726$	−37.4216	−	16.3269i	−1.38884	−	0.605947i
$727$	19.6648	−	9.47006i	0.729326	−	0.351225i	−0.0320928	−	0.999485i	$-0.510217\pi$
$727$	19.6648	−	9.47006i	0.729326	−	0.351225i	0.761419	+	0.648260i	$0.224503\pi$
$728$	−51.1224	−	21.8938i	−1.89472	−	0.811438i
$729$	26.9097	+	12.9590i	0.996656	+	0.479964i
$730$	−44.1601	−	51.3150i	−1.63444	−	1.89925i
$731$	10.6729	+	34.6006i	0.394750	+	1.27975i
$732$	−35.3712	+	51.8800i	−1.30736	+	1.91754i
$733$	−27.5997	−	20.3695i	−1.01942	−	0.752365i	−0.0502434	−	0.998737i	$-0.516000\pi$
$733$	−27.5997	−	20.3695i	−1.01942	−	0.752365i	−0.969175	+	0.246372i	$0.920762\pi$
$734$	−38.1136	−	38.1136i	−1.40680	−	1.40680i
$735$	24.4736	+	22.0919i	0.902723	+	0.814871i
$736$	14.7350	+	14.7350i	0.543138	+	0.543138i
$737$	1.23179	−	0.185662i	0.0453735	−	0.00683896i
$738$	−16.2203	−	11.0588i	−0.597078	−	0.407081i
$739$	−0.161314	−	0.0852568i	−0.00593402	−	0.00313622i	0.464299	−	0.885679i	$-0.346306\pi$
$739$	−0.161314	−	0.0852568i	−0.00593402	−	0.00313622i	−0.470233	+	0.882542i	$0.655830\pi$
$740$	−4.10941	+	54.8363i	−0.151065	+	2.01582i
$741$	10.6712	+	10.2810i	0.392015	+	0.377684i
$742$	−30.3674	+	0.776117i	−1.11482	+	0.0284922i
$743$	11.0282	−	31.5169i	0.404587	−	1.15624i	−0.543825	−	0.839199i	$-0.683024\pi$
$743$	11.0282	−	31.5169i	0.404587	−	1.15624i	0.948411	−	0.317043i	$-0.102690\pi$
$744$	−30.7791	−	78.4240i	−1.12842	−	2.87516i
$745$	2.81960	+	37.6250i	0.103302	+	1.37847i
$746$	−0.626982	−	1.43706i	−0.0229554	−	0.0526144i
$747$	−1.32134	−	2.50009i	−0.0483452	−	0.0914736i
$748$	5.68348	+	0.640374i	0.207809	+	0.0234144i
$749$	−2.47648	+	2.24383i	−0.0904888	+	0.0819878i
$750$	0.348710	−	0.437268i	0.0127331	−	0.0159668i
$751$	11.2949	+	16.5666i	0.412158	+	0.604525i	0.975045	−	0.222009i	$-0.0712615\pi$
$751$	11.2949	+	16.5666i	0.412158	+	0.604525i	−0.562886	+	0.826534i	$0.690309\pi$
$752$	−2.47709	+	66.2017i	−0.0903303	+	2.41413i
$753$	−20.4606	+	11.8129i	−0.745626	+	0.430487i
$754$	33.9689	−	30.3514i	1.23708	−	1.10533i
$755$	−37.9746	+	8.66745i	−1.38204	+	0.315441i
$756$	58.3400	−	27.2483i	2.12180	−	0.991012i
$757$	−2.74169	+	12.0121i	−0.0996485	+	0.436588i	0.900351	+	0.435165i	$0.143310\pi$
$757$	−2.74169	+	12.0121i	−0.0996485	+	0.436588i	−0.999999	+	0.00142302i	$0.999547\pi$
$758$	30.7357	−	33.1252i	1.11637	−	1.20316i
$759$	−1.40003	−	1.89697i	−0.0508179	−	0.0688558i
$760$	41.1229	−	30.3500i	1.49168	−	1.10091i
$761$	44.6322	−	1.67002i	1.61792	−	0.0605381i	0.787006	−	0.616946i	$-0.211630\pi$
$761$	44.6322	−	1.67002i	1.61792	−	0.0605381i	0.830910	+	0.556407i	$0.187821\pi$
$762$	−9.30927	−	14.8156i	−0.337239	−	0.536713i
$763$	13.6791	−	13.3587i	0.495216	−	0.483618i
$764$	−44.5595	+	10.1704i	−1.61211	+	0.367953i
$765$	12.1710	−	3.26121i	0.440044	−	0.117909i
$766$	4.01716	+	6.95792i	0.145146	+	0.251400i
$767$	39.2286	−	17.9918i	1.41646	−	0.649647i
$768$	26.5957	+	39.0087i	0.959689	+	1.40761i
$769$	−25.6251	+	2.88726i	−0.924065	+	0.104117i	−0.561159	−	0.827708i	$-0.689644\pi$
$769$	−25.6251	+	2.88726i	−0.924065	+	0.104117i	−0.362907	+	0.931825i	$0.618216\pi$
$770$	3.67785	−	4.17271i	0.132540	−	0.150374i
$771$	−36.6538	+	29.2304i	−1.32005	+	1.05271i
$772$	−78.0150	+	41.2321i	−2.80782	+	1.48398i
$773$	18.6128	−	8.12069i	0.669456	−	0.292081i	−0.0375430	−	0.999295i	$-0.511953\pi$
$773$	18.6128	−	8.12069i	0.669456	−	0.292081i	0.706999	+	0.707214i	$0.250048\pi$
$774$	9.36972	−	10.8878i	0.336788	−	0.391354i
$775$	−44.9905	−	19.6291i	−1.61611	−	0.705100i
$776$	−1.57621	−	3.27303i	−0.0565825	−	0.117495i
$777$	−3.90599	−	15.3002i	−0.140127	−	0.548891i
$778$	−7.78326	−	22.2433i	−0.279043	−	0.797460i
$779$	27.1946	+	2.03795i	0.974346	+	0.0730172i
$780$	1.37763	−	73.3351i	0.0493271	−	2.62582i
$781$	−0.542581	−	0.369926i	−0.0194151	−	0.0132370i
$782$	−61.0465	−	45.0544i	−2.18302	−	1.61114i
$783$			28.3196i			1.01206i
$784$	10.3422	−	40.8277i	0.369366	−	1.45813i
$785$	−7.11130	+	7.11130i	−0.253813	+	0.253813i
$786$	1.25402	−	1.69913i	0.0447293	−	0.0606061i
$787$	2.99313	−	0.566332i	0.106694	−	0.0201875i	−0.132291	−	0.991211i	$-0.542233\pi$
$787$	2.99313	−	0.566332i	0.106694	−	0.0201875i	0.238984	+	0.971023i	$0.423186\pi$
$788$	−61.2663	−	32.3802i	−2.18252	−	1.15350i
$789$	8.97213	+	0.672368i	0.319416	+	0.0239369i
$790$	17.0570	+	8.21424i	0.606863	+	0.292250i
$791$	−10.4398	−	3.35621i	−0.371196	−	0.119333i
$792$	−0.528598	−	1.09765i	−0.0187829	−	0.0390031i
$793$	26.3009	+	23.5079i	0.933973	+	0.834789i
$794$	−8.41620	+	0.630707i	−0.298680	+	0.0223830i
$795$	−8.60265	−	19.7175i	−0.305105	−	0.699307i
$796$	−23.2702	+	75.4402i	−0.824792	+	2.67391i
$797$	34.7655	+	43.5945i	1.23146	+	1.54420i	0.738706	+	0.674028i	$0.235437\pi$
$797$	34.7655	+	43.5945i	1.23146	+	1.54420i	0.492751	+	0.870171i	$0.335991\pi$
$798$	−15.6640	+	22.4001i	−0.554501	+	0.792953i
$799$	−6.18730	−	54.9138i	−0.218891	−	1.94271i
$800$	−17.1845	−	3.25149i	−0.607565	−	0.114958i
$801$	−0.276644	+	7.39348i	−0.00977475	+	0.261236i
$802$	26.2420	+	45.4524i	0.926636	+	1.60498i
$803$	1.12087	−	1.94140i	0.0395545	−	0.0685104i
$804$	25.6569	+	16.1213i	0.904850	+	0.568555i
$805$	−47.7968	+	16.0918i	−1.68462	+	0.567162i
$806$	−85.5566	+	21.2108i	−3.01360	+	0.747120i
$807$	−3.79368	−	3.52002i	−0.133544	−	0.123910i
$808$	30.2415	+	40.9758i	1.06389	+	1.44152i
$809$	−24.4747	−	3.68897i	−0.860486	−	0.129697i	−0.296048	−	0.955173i	$-0.595669\pi$
$809$	−24.4747	−	3.68897i	−0.860486	−	0.129697i	−0.564438	+	0.825476i	$0.690907\pi$
$810$	35.0258	+	32.4992i	1.23068	+	1.14190i
$811$	16.7010	−	10.4939i	0.586452	−	0.368492i	−0.205885	−	0.978576i	$-0.566007\pi$
$811$	16.7010	−	10.4939i	0.586452	−	0.368492i	0.792337	+	0.610084i	$0.208864\pi$
$812$	44.4759	+	36.3387i	1.56080	+	1.27524i
$813$	−16.0016	+	25.4665i	−0.561202	+	0.893148i
$814$	−2.57324	+	0.689498i	−0.0901921	+	0.0241669i
$815$	17.3539	−	10.0193i	0.607882	−	0.350961i
$816$	30.5202	+	32.8929i	1.06842	+	1.15148i
$817$	−3.70970	+	19.6062i	−0.129786	+	0.685935i
$818$	−4.53602	+	5.68799i	−0.158598	+	0.198876i
$819$	−2.27588	−	7.20470i	−0.0795255	−	0.251753i
$820$	−84.1639	−	105.538i	−2.93913	−	3.68556i
$821$	40.6527	−	21.4856i	1.41879	−	0.749852i	0.430521	−	0.902581i	$-0.358330\pi$
$821$	40.6527	−	21.4856i	1.41879	−	0.749852i	0.988268	+	0.152729i	$0.0488060\pi$
$822$	−32.5742	−	12.7844i	−1.13615	−	0.445908i
$823$	44.5573	−	3.33911i	1.55317	−	0.116394i	0.729705	−	0.683762i	$-0.239657\pi$
$823$	44.5573	−	3.33911i	1.55317	−	0.116394i	0.823465	+	0.567368i	$0.192038\pi$
$824$	−31.5938	+	72.4138i	−1.10062	+	2.52265i
$825$	1.86772	+	0.653544i	0.0650257	+	0.0227535i
$826$	44.0632	+	66.3032i	1.53316	+	2.30699i
$827$	−6.07103	−	17.3500i	−0.211111	−	0.603319i	0.788826	−	0.614617i	$-0.210689\pi$
$827$	−6.07103	−	17.3500i	−0.211111	−	0.603319i	−0.999936	+	0.0112978i	$0.996404\pi$
$828$	−1.53739	+	20.5151i	−0.0534281	+	0.712949i
$829$	42.8943	−	13.2311i	1.48978	−	0.459536i	0.560263	−	0.828315i	$-0.310700\pi$
$829$	42.8943	−	13.2311i	1.48978	−	0.459536i	0.929517	+	0.368779i	$0.120224\pi$
$830$	−5.28880	−	27.9520i	−0.183577	−	0.970227i
$831$	43.4042	−	6.54214i	1.50568	−	0.226944i
$832$	10.6956	−	5.39826i	0.370803	−	0.187151i
$833$	−3.45480	+	34.9622i	−0.119702	+	1.21137i
$834$	55.2776	−	55.2776i	1.91411	−	1.91411i
$835$	−34.1271	+	5.14384i	−1.18102	+	0.178010i
$836$	2.60419	+	1.77550i	0.0900676	+	0.0614071i
$837$	25.6059	−	48.4487i	0.885069	−	1.67463i
$838$	16.5248	−	14.2208i	0.570841	−	0.491248i
$839$	−21.6179	+	7.56441i	−0.746331	+	0.261153i	−0.676537	−	0.736409i	$-0.736520\pi$
$839$	−21.6179	+	7.56441i	−0.746331	+	0.261153i	−0.0697943	+	0.997561i	$0.522234\pi$
$840$	71.9602	−	9.97582i	2.48286	−	0.344198i
$841$	3.36947	−	1.62265i	0.116189	−	0.0559535i
$842$	−21.5865	+	8.47207i	−0.743919	+	0.291967i
$843$	8.96548	+	7.71542i	0.308788	+	0.265733i
$844$	85.8503	+	33.6937i	2.95509	+	1.15979i
$845$	−40.7453	−	6.14831i	−1.40168	−	0.211508i
$846$	−17.1397	+	13.6684i	−0.589274	+	0.469930i
$847$	−26.7930	−	10.8835i	−0.920617	−	0.373962i
$848$	−17.1342	+	21.4856i	−0.588389	+	0.737817i
$849$	6.46738	+	9.48590i	0.221960	+	0.325555i
$850$	63.6340	+	2.38102i	2.18263	+	0.0816682i
$851$	23.3318	+	6.25174i	0.799804	+	0.214307i
$852$	−4.13432	−	15.4295i	−0.141639	−	0.528605i
$853$	22.9936	+	14.4478i	0.787286	+	0.494685i	0.864684	−	0.502316i	$-0.167518\pi$
$853$	22.9936	+	14.4478i	0.787286	+	0.494685i	−0.0773982	+	0.997000i	$0.524661\pi$
$854$	−35.2695	+	54.6821i	−1.20690	+	1.87118i
$855$	6.76968	+	1.54513i	0.231518	+	0.0528425i
$856$	0.275335	+	7.35848i	0.00941076	+	0.251508i
$857$	−51.8591	−	7.81650i	−1.77147	−	0.267006i	−0.819475	−	0.573115i	$-0.805735\pi$
$857$	−51.8591	−	7.81650i	−1.77147	−	0.267006i	−0.951997	+	0.306108i	$0.900973\pi$
$858$	3.37542	−	1.11040i	0.115235	−	0.0379086i
$859$	−0.308113	+	0.332067i	−0.0105127	+	0.0113300i	−0.738286	−	0.674487i	$-0.764365\pi$
$859$	−0.308113	+	0.332067i	−0.0105127	+	0.0113300i	0.727774	+	0.685817i	$0.240555\pi$
$860$	83.6321	−	52.5495i	2.85183	−	1.79192i
$861$	32.5751	+	21.0107i	1.11016	+	0.716042i
$862$	88.2886	−	20.1513i	3.00712	−	0.686356i
$863$	−6.59373	−	24.6081i	−0.224453	−	0.837671i	−0.982623	−	0.185613i	$-0.940573\pi$
$863$	−6.59373	−	24.6081i	−0.224453	−	0.837671i	0.758170	−	0.652057i	$-0.226094\pi$
$864$	5.05344	−	18.8597i	0.171921	−	0.641620i
$865$	12.3405	+	0.461747i	0.419588	+	0.0156999i
$866$	−2.94901	+	15.5859i	−0.100211	+	0.529630i
$867$	−9.51413	−	7.58726i	−0.323117	−	0.257677i
$868$	−43.2322	−	102.382i	−1.46740	−	3.47507i
$869$	−0.0701886	+	0.622941i	−0.00238099	+	0.0211318i
$870$	−17.5399	+	56.8630i	−0.594659	+	1.92784i
$871$	10.8619	−	13.1076i	0.368041	−	0.444133i
$872$	−3.14841	−	42.0126i	−0.106619	−	1.42273i
$873$	0.197367	−	0.452369i	0.00667985	−	0.0153104i
$874$	−18.1413	−	37.6707i	−0.613638	−	1.27423i
$875$	0.239001	−	0.315932i	0.00807972	−	0.0106804i
$876$	51.4695	−	18.0100i	1.73899	−	0.608501i
$877$	5.77565	+	6.71143i	0.195030	+	0.226629i	0.846969	−	0.531643i	$-0.178425\pi$
$877$	5.77565	+	6.71143i	0.195030	+	0.226629i	−0.651939	+	0.758272i	$0.726044\pi$
$878$	28.5377	−	53.9959i	0.963100	−	1.82227i
$879$	−5.85585	−	30.9489i	−0.197513	−	1.04388i
$880$	−0.749964	−	4.97568i	−0.0252813	−	0.167730i
$881$	−38.5788			−1.29975			−0.649876	−	0.760040i	$-0.725179\pi$
$881$	−38.5788			−1.29975			−0.649876	+	0.760040i	$0.725179\pi$
$882$	12.4730	−	6.21865i	0.419987	−	0.209393i
$883$			47.6393i			1.60319i	0.597867	+	0.801595i	$0.296015\pi$
$883$			47.6393i			1.60319i	−0.597867	+	0.801595i	$0.703985\pi$
$884$	63.7474	−	45.2232i	2.14406	−	1.52102i
$885$	−31.7586	+	46.5813i	−1.06755	+	1.56581i
$886$	19.8164	−	37.4945i	0.665746	−	1.25965i
$887$	−51.1961	−	3.83662i	−1.71900	−	0.128821i	−0.821605	−	0.570057i	$-0.806921\pi$
$887$	−51.1961	−	3.83662i	−1.71900	−	0.128821i	−0.897391	+	0.441236i	$0.854540\pi$
$888$	−31.3491	−	15.0970i	−1.05201	−	0.506621i
$889$	−6.85983	−	10.3222i	−0.230071	−	0.346195i
$890$	−24.5831	+	70.2545i	−0.824028	+	2.35494i
$891$	−0.632686	+	1.45013i	−0.0211958	+	0.0485812i
$892$	9.71029	+	8.35638i	0.325125	+	0.279792i
$893$	11.1258	−	28.3481i	0.372312	−	0.948635i
$894$	−42.4871	−	13.1055i	−1.42098	−	0.438315i
$895$	46.8760	+	5.28166i	1.56689	+	0.176546i
$896$	23.6244	+	32.8166i	0.789235	+	1.09633i
$897$	−31.5390	−	6.58338i	−1.05306	−	0.219813i
$898$	9.23346	−	6.29527i	0.308124	−	0.210076i
$899$	48.8449	+	1.82765i	1.62907	+	0.0609554i
$900$	−8.63319	−	14.9531i	−0.287773	−	0.498437i
$901$	11.4618	−	19.8524i	0.381847	−	0.661378i
$902$	3.47926	−	5.53722i	0.115847	−	0.184369i
$903$	−17.9456	+	21.9641i	−0.597191	+	0.730919i
$904$	−20.4597	+	12.8557i	−0.680480	+	0.427574i
$905$	−1.48244	−	39.6190i	−0.0492779	−	1.31698i
$906$	6.84118	−	45.3883i	0.227283	−	1.50792i
$907$	8.76742	−	58.1680i	0.291117	−	1.93144i	−0.0669840	−	0.997754i	$-0.521338\pi$
$907$	8.76742	−	58.1680i	0.291117	−	1.93144i	0.358101	−	0.933683i	$-0.383424\pi$
$908$	61.8804	−	2.31540i	2.05357	−	0.0768393i
$909$	−1.53961	+	6.74547i	−0.0510656	+	0.223733i
$910$	−0.514495	−	76.0087i	−0.0170554	−	2.51966i
$911$	−10.4862	−	45.9430i	−0.347423	−	1.52216i	−0.783007	−	0.622013i	$-0.786315\pi$
$911$	−10.4862	−	45.9430i	−0.347423	−	1.52216i	0.435584	−	0.900148i	$-0.356542\pi$
$912$	6.39995	+	23.8849i	0.211924	+	0.790910i
$913$	0.815781	−	0.470991i	0.0269984	−	0.0155875i
$914$	−45.8143	−	49.3760i	−1.51540	−	1.63321i
$915$	−45.2774	−	8.56695i	−1.49683	−	0.283215i
$916$	6.95744	−	0.783916i	0.229880	−	0.0259013i
$917$	0.857197	−	1.22582i	0.0283071	−	0.0404801i
$918$	−7.95955	+	70.6429i	−0.262704	+	2.33156i
$919$	19.8067	+	6.10955i	0.653362	+	0.201535i	0.603676	−	0.797230i	$-0.293702\pi$
$919$	19.8067	+	6.10955i	0.653362	+	0.201535i	0.0496853	+	0.998765i	$0.484178\pi$
$920$	−40.5996	+	103.446i	−1.33853	+	3.41052i
$921$	5.11203	−	5.94029i	0.168447	−	0.195739i
$922$	23.8319	+	60.7227i	0.784862	+	1.99979i
$923$	−8.89732	+	1.17060i	−0.292859	+	0.0385308i
$924$	2.04634	+	3.98545i	0.0673195	+	0.131112i
$925$	−19.1353	+	6.69572i	−0.629164	+	0.220154i
$926$	−2.72181	+	36.3200i	−0.0894442	+	1.19355i
$927$	−10.2569	+	3.16382i	−0.336879	+	0.103913i
$928$	17.1121	−	3.23778i	0.561731	−	0.106285i
$929$	15.6005	+	11.5137i	0.511837	+	0.377753i	0.818900	−	0.573936i	$-0.194584\pi$
$929$	15.6005	+	11.5137i	0.511837	+	0.377753i	−0.307063	+	0.951689i	$0.599346\pi$
$930$	81.4212	−	81.4212i	2.66991	−	2.66991i
$931$	−10.6860	+	16.1445i	−0.350221	+	0.529115i
$932$	73.2177			2.39833
$933$	−1.39941	−	9.28451i	−0.0458148	−	0.303961i
$934$	−40.8221	+	7.72396i	−1.33574	+	0.252736i
$935$	1.23720	+	4.01091i	0.0404608	+	0.131171i
$936$	−15.3808	−	6.37244i	−0.502738	−	0.208290i
$937$	−12.7294	+	26.4329i	−0.415852	+	0.863525i	0.582849	+	0.812580i	$0.301938\pi$
$937$	−12.7294	+	26.4329i	−0.415852	+	0.863525i	−0.998701	+	0.0509453i	$0.983777\pi$
$938$	27.0064	+	16.0217i	0.881790	+	0.523128i
$939$	−32.7543	+	15.7736i	−1.06890	+	0.514753i
$940$	−140.321	+	55.0720i	−4.57677	+	1.79625i
$941$	4.45558	−	5.17748i	0.145248	−	0.168781i	−0.680635	−	0.732622i	$-0.738296\pi$
$941$	4.45558	−	5.17748i	0.145248	−	0.168781i	0.825883	+	0.563841i	$0.190677\pi$
$942$	−4.73923	−	10.8624i	−0.154413	−	0.353917i
$943$	−52.4235	+	27.7066i	−1.70714	+	0.902252i
$944$	71.5666	+	8.06361i	2.32929	+	0.262448i
$945$	35.4497	+	31.2455i	1.15318	+	1.01642i
$946$	3.74108	+	2.98341i	0.121633	+	0.0969990i
$947$	3.04125	+	0.575436i	0.0988275	+	0.0186992i	0.235090	−	0.971974i	$-0.424461\pi$
$947$	3.04125	+	0.575436i	0.0988275	+	0.0186992i	−0.136263	+	0.990673i	$0.543509\pi$
$948$	−11.1781	+	10.3718i	−0.363049	+	0.336860i
$949$	−6.25465	−	29.9892i	−0.203035	−	0.973489i
$950$	30.3904	+	17.5459i	0.985995	+	0.569265i
$951$	6.72829	−	10.7080i	0.218180	−	0.347231i
$952$	54.0873	+	55.3844i	1.75298	+	1.79502i
$953$	18.4163	+	4.20339i	0.596561	+	0.136161i	0.510131	−	0.860097i	$-0.329597\pi$
$953$	18.4163	+	4.20339i	0.596561	+	0.136161i	0.0864302	+	0.996258i	$0.472454\pi$
$954$	−9.08753	+	0.340031i	−0.294220	+	0.0110089i
$955$	−19.9181	−	26.9880i	−0.644534	−	0.873313i
$956$	52.2053	+	70.7357i	1.68844	+	2.28776i
$957$	−1.96904	+	0.0736763i	−0.0636500	+	0.00238162i
$958$	81.0552	+	18.5003i	2.61878	+	0.597718i
$959$	−23.2965	−	8.46291i	−0.752283	−	0.273282i
$960$	−8.32657	+	13.2517i	−0.268739	+	0.427696i
$961$	−55.0638	−	31.7911i	−1.77625	−	1.02552i
$962$	−19.9443	+	30.4560i	−0.643030	+	0.981939i
$963$	−0.733361	+	0.680459i	−0.0236322	+	0.0219275i
$964$	−47.0055	−	8.89392i	−1.51394	−	0.286454i
$965$	−50.6299	−	40.3760i	−1.62984	−	1.29975i
$966$	2.92568	−	59.3593i	0.0941323	−	1.90985i
$967$	14.4570	+	1.62891i	0.464906	+	0.0523823i	0.341311	−	0.939950i	$-0.389129\pi$
$967$	14.4570	+	1.62891i	0.464906	+	0.0523823i	0.123595	+	0.992333i	$0.460558\pi$
$968$	−56.3382	+	29.7756i	−1.81078	+	0.957023i
$969$	−8.24843	−	18.9056i	−0.264978	−	0.607335i
$970$	3.23872	−	3.76346i	0.103989	−	0.120837i
$971$	36.4115	−	14.2904i	1.16850	−	0.458602i	0.299829	−	0.953993i	$-0.403070\pi$
$971$	36.4115	−	14.2904i	1.16850	−	0.458602i	0.868670	+	0.495391i	$0.164975\pi$
$972$	31.1066	−	14.9802i	0.997745	−	0.480489i
$973$	38.1406	−	40.1413i	1.22273	−	1.28687i
$974$	−11.8849	+	24.6793i	−0.380818	+	0.790776i
$975$	24.9834	−	10.3460i	0.800108	−	0.331338i
$976$	17.3510	+	56.2506i	0.555392	+	1.80054i
$977$	−22.4661	+	4.25082i	−0.718755	+	0.135996i	−0.532408	−	0.846488i	$-0.678713\pi$
$977$	−22.4661	+	4.25082i	−0.718755	+	0.135996i	−0.186348	+	0.982484i	$0.559665\pi$
$978$	3.51948	+	23.3502i	0.112540	+	0.746657i
$979$	−2.46461			−0.0787693
$980$	94.5590	−	15.5806i	3.02058	−	0.497704i
$981$	4.04736	−	4.04736i	0.129222	−	0.129222i
$982$	17.0644	+	12.5941i	0.544547	+	0.401894i
$983$	−1.53075	+	0.289634i	−0.0488234	+	0.00923789i	−0.210266	−	0.977644i	$-0.567433\pi$
$983$	−1.53075	+	0.289634i	−0.0488234	+	0.00923789i	0.161443	+	0.986882i	$0.448385\pi$
$984$	81.6192	−	25.1762i	2.60192	−	0.802587i
$985$	3.80043	−	50.7133i	0.121092	−	1.61586i
$986$	−59.8516	+	20.9430i	−1.90606	+	0.666961i
$987$	33.1424	−	27.8447i	1.05493	−	0.886307i
$988$	42.7038	−	5.61844i	1.35859	−	0.178746i
$989$	−15.8508	−	40.3871i	−0.504025	−	1.28423i
$990$	1.08614	−	1.26212i	0.0345198	−	0.0401127i
$991$	14.2701	−	36.3597i	0.453306	−	1.15500i	−0.503428	−	0.864037i	$-0.667928\pi$
$991$	14.2701	−	36.3597i	0.453306	−	1.15500i	0.956733	−	0.290966i	$-0.0939768\pi$
$992$	−32.2026	−	9.93318i	−1.02243	−	0.315379i
$993$	−1.90439	+	16.9019i	−0.0604340	+	0.536366i
$994$	−4.69151	−	15.8749i	−0.148806	−	0.503520i
$995$	−57.5738	+	6.48701i	−1.82521	+	0.205652i
$996$	22.5140	+	4.25988i	0.713384	+	0.134980i
$997$	−28.8974	−	31.1440i	−0.915190	−	0.986340i	0.0847598	−	0.996401i	$-0.472988\pi$
$997$	−28.8974	−	31.1440i	−0.915190	−	0.986340i	−0.999949	+	0.0100616i	$0.996797\pi$
$998$	20.7247	−	11.9654i	0.656028	−	0.378758i
$999$	−5.85770	−	21.8612i	−0.185330	−	0.691659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.cc.a.5.6	✓	1536
13.8	odd	4	inner	637.2.cc.a.593.6	yes	1536
49.10	odd	42	inner	637.2.cc.a.304.6	yes	1536
637.255	even	84	inner	637.2.cc.a.255.6	yes	1536

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.cc.a.5.6	✓	1536	1.1	even	1	trivial
637.2.cc.a.255.6	yes	1536	637.255	even	84	inner
637.2.cc.a.304.6	yes	1536	49.10	odd	42	inner
637.2.cc.a.593.6	yes	1536	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.cc (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49274 + 2.02259i) q^{2} +(0.837048 - 1.22772i) q^{3} +(-1.27309 - 4.12726i) q^{4} +(2.40257 - 2.06758i) q^{5} +(1.23369 + 3.52568i) q^{6} +(0.937355 + 2.47414i) q^{7} +(5.50271 + 1.92548i) q^{8} +(0.289366 + 0.737293i) q^{9} +(0.595454 + 7.94578i) q^{10} +(-0.241828 + 0.105509i) q^{11} +(-6.13278 - 1.89171i) q^{12} +(-1.50365 + 3.27705i) q^{13} +(-6.40340 - 1.79736i) q^{14} +(-0.527350 - 4.68036i) q^{15} +(-4.97128 + 3.38936i) q^{16} +(3.67913 - 3.41373i) q^{17} +(-1.92319 - 0.515317i) q^{18} +(2.67157 - 0.715845i) q^{19} +(-11.5921 - 7.28382i) q^{20} +(3.82217 + 0.920161i) q^{21} +(0.147586 - 0.646617i) q^{22} +(-4.09036 + 4.40836i) q^{23} +(6.96999 - 5.14409i) q^{24} +(0.752252 - 4.99086i) q^{25} +(-4.38358 - 7.93304i) q^{26} +(5.49340 + 1.25383i) q^{27} +(9.01808 - 7.01851i) q^{28} +(1.11838 + 4.89994i) q^{29} +(10.2537 + 5.91995i) q^{30} +(2.51710 - 9.39396i) q^{31} +(0.129566 - 3.46273i) q^{32} +(-0.0728864 + 0.385214i) q^{33} +(1.41260 + 12.5372i) q^{34} +(7.36754 + 4.00624i) q^{35} +(2.67461 - 2.13293i) q^{36} +(-1.87685 - 3.55117i) q^{37} +(-2.54010 + 6.47207i) q^{38} +(2.76469 + 4.58911i) q^{39} +(17.2017 - 6.75118i) q^{40} +(9.30665 + 3.25654i) q^{41} +(-7.56662 + 6.35713i) q^{42} +(-3.13028 + 6.50009i) q^{43} +(0.743331 + 0.863766i) q^{44} +(2.21963 + 1.17311i) q^{45} +(-2.81046 - 14.8537i) q^{46} +(6.53832 - 8.85910i) q^{47} +8.94041i q^{48} +(-5.24273 + 4.63829i) q^{49} +(8.97156 + 8.97156i) q^{50} +(-1.11151 - 7.37441i) q^{51} +(15.4395 + 2.03396i) q^{52} +(4.36450 - 1.34627i) q^{53} +(-10.7362 + 9.23925i) q^{54} +(-0.362862 + 0.753491i) q^{55} +(0.394081 + 15.4193i) q^{56} +(1.35737 - 3.87915i) q^{57} +(-11.5800 - 5.05231i) q^{58} +(-9.07278 - 7.80775i) q^{59} +(-18.6457 + 8.13504i) q^{60} +(2.88378 - 9.34899i) q^{61} +(15.2428 + 19.1138i) q^{62} +(-1.55293 + 1.40704i) q^{63} +(-2.59790 - 2.07176i) q^{64} +(3.16294 + 10.9823i) q^{65} +(-0.670330 - 0.722444i) q^{66} +(-4.56051 - 1.22198i) q^{67} +(-18.7732 - 10.8387i) q^{68} +(1.98842 + 8.71184i) q^{69} +(-19.1008 + 8.92125i) q^{70} +(1.32419 + 2.10744i) q^{71} +(0.172654 + 4.61427i) q^{72} +(-6.83624 + 5.04538i) q^{73} +(9.98421 + 1.50488i) q^{74} +(-5.49773 - 5.10115i) q^{75} +(-6.35564 - 10.1149i) q^{76} +(-0.487722 - 0.499418i) q^{77} +(-13.4089 - 1.25852i) q^{78} +(1.18799 - 2.05765i) q^{79} +(-4.93608 + 18.4217i) q^{80} +(4.39577 - 4.07868i) q^{81} +(-20.4791 + 13.9624i) q^{82} +(-3.54779 + 0.399740i) q^{83} +(-1.06823 - 16.9466i) q^{84} +(1.78120 - 15.8086i) q^{85} +(-8.47433 - 16.0342i) q^{86} +(6.95191 + 2.72842i) q^{87} +(-1.53386 + 0.114947i) q^{88} +(8.56180 + 3.73548i) q^{89} +(-5.68606 + 2.73826i) q^{90} +(-9.51733 - 0.648474i) q^{91} +(23.4019 + 11.2697i) q^{92} +(-9.42625 - 10.9535i) q^{93} +(8.15834 + 26.4487i) q^{94} +(4.93857 - 7.24356i) q^{95} +(-4.14282 - 3.05754i) q^{96} +(-0.440623 - 0.440623i) q^{97} +(-1.55533 - 17.5277i) q^{98} +(-0.147768 - 0.147768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1536 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 28 q^{6} - 22 q^{7} - 12 q^{8} - 176 q^{9} - 22 q^{11} - 28 q^{13} - 84 q^{14} - 8 q^{15} - 180 q^{16} - 18 q^{18} - 54 q^{19} - 28 q^{20} - 2 q^{21} - 48 q^{22}+ \cdots - 32 q^{99}+O(q^{100}) \) 1536 * q - 26 * q^2 - 44 * q^3 - 22 * q^5 - 28 * q^6 - 22 * q^7 - 12 * q^8 - 176 * q^9 - 22 * q^11 - 28 * q^13 - 84 * q^14 - 8 * q^15 - 180 * q^16 - 18 * q^18 - 54 * q^19 - 28 * q^20 - 2 * q^21 - 48 * q^22 + 68 * q^24 - 52 * q^26 - 56 * q^27 + 62 * q^28 - 48 * q^29 - 66 * q^31 - 32 * q^32 - 76 * q^33 + 28 * q^34 - 140 * q^35 - 62 * q^37 - 16 * q^39 + 76 * q^40 - 28 * q^41 + 128 * q^42 - 226 * q^44 + 66 * q^45 - 32 * q^46 + 68 * q^47 + 156 * q^50 + 48 * q^52 - 48 * q^53 - 64 * q^54 + 28 * q^55 - 62 * q^57 - 22 * q^58 + 54 * q^59 - 88 * q^60 - 8 * q^61 - 150 * q^63 - 12 * q^65 + 72 * q^66 - 30 * q^67 - 36 * q^68 + 62 * q^70 + 104 * q^71 - 54 * q^72 - 136 * q^73 + 12 * q^74 + 28 * q^76 + 68 * q^78 - 16 * q^79 - 180 * q^80 + 64 * q^81 + 70 * q^83 + 30 * q^84 - 96 * q^85 + 30 * q^86 + 416 * q^87 - 38 * q^89 - 196 * q^91 - 180 * q^92 + 38 * q^93 - 264 * q^94 - 350 * q^96 - 390 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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