LMFDB - Embedded newform 637.2.bl.a.235.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.27
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.a.534.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.72488 + 0.410710i) q^{2} +(0.680220 - 0.463766i) q^{3} +(5.34515 + 1.64876i) q^{4} +(0.189463 + 2.52821i) q^{5} +(2.04399 - 0.984335i) q^{6} +(-1.91733 - 1.82314i) q^{7} +(8.92220 + 4.29671i) q^{8} +(-0.848403 + 2.16170i) q^{9} +O(q^{10})$	\(q+(2.72488 + 0.410710i) q^{2} +(0.680220 - 0.463766i) q^{3} +(5.34515 + 1.64876i) q^{4} +(0.189463 + 2.52821i) q^{5} +(2.04399 - 0.984335i) q^{6} +(-1.91733 - 1.82314i) q^{7} +(8.92220 + 4.29671i) q^{8} +(-0.848403 + 2.16170i) q^{9} +(-0.522097 + 6.96690i) q^{10} +(-2.37076 - 6.04061i) q^{11} +(4.40052 - 1.35738i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-4.47571 - 5.75531i) q^{14} +(1.30138 + 1.63188i) q^{15} +(13.3038 + 9.07041i) q^{16} +(-3.06627 - 2.84508i) q^{17} +(-3.19963 + 5.54191i) q^{18} +(-0.335953 - 0.581888i) q^{19} +(-3.15571 + 13.8261i) q^{20} +(-2.14972 - 0.350945i) q^{21} +(-3.97911 - 17.4336i) q^{22} +(0.258963 - 0.240283i) q^{23} +(8.06173 - 1.21511i) q^{24} +(-1.41182 + 0.212797i) q^{25} +(-2.02004 + 1.87432i) q^{26} +(0.975007 + 4.27178i) q^{27} +(-7.24249 - 12.9062i) q^{28} +(1.18836 - 5.20655i) q^{29} +(2.87587 + 4.98115i) q^{30} +(-3.77071 + 6.53106i) q^{31} +(18.0074 + 16.7084i) q^{32} +(-4.41407 - 3.00946i) q^{33} +(-7.18671 - 9.01185i) q^{34} +(4.24603 - 5.19284i) q^{35} +(-8.09895 + 10.1558i) q^{36} +(2.53064 - 0.780600i) q^{37} +(-0.676446 - 1.72356i) q^{38} +(-0.0615233 + 0.820971i) q^{39} +(-9.17256 + 23.3713i) q^{40} +(-7.57825 - 3.64949i) q^{41} +(-5.71359 - 1.83919i) q^{42} +(5.72717 - 2.75806i) q^{43} +(-2.71257 - 36.1968i) q^{44} +(-5.62597 - 1.73538i) q^{45} +(0.804330 - 0.548383i) q^{46} +(9.21729 + 1.38928i) q^{47} +13.2561 q^{48} +(0.352309 + 6.99113i) q^{49} -3.93443 q^{50} +(-3.40519 - 0.513250i) q^{51} +(-4.62170 + 3.15102i) q^{52} +(-0.141235 - 0.0435651i) q^{53} +(0.902314 + 12.0405i) q^{54} +(14.8228 - 7.13827i) q^{55} +(-9.27330 - 24.5046i) q^{56} +(-0.498382 - 0.240008i) q^{57} +(5.37653 - 13.6992i) q^{58} +(0.485859 - 6.48333i) q^{59} +(4.26548 + 10.8683i) q^{60} +(0.758961 - 0.234108i) q^{61} +(-12.9571 + 16.2477i) q^{62} +(5.56774 - 2.59792i) q^{63} +(22.1272 + 27.7467i) q^{64} +(-2.09477 - 1.42819i) q^{65} +(-10.7918 - 10.0133i) q^{66} +(-4.66527 + 8.08048i) q^{67} +(-11.6988 - 20.2629i) q^{68} +(0.0647170 - 0.283543i) q^{69} +(13.7027 - 12.4060i) q^{70} +(2.58433 + 11.3227i) q^{71} +(-16.8578 + 15.6417i) q^{72} +(-12.3313 + 1.85865i) q^{73} +(7.21631 - 1.08768i) q^{74} +(-0.861657 + 0.799501i) q^{75} +(-0.836327 - 3.66419i) q^{76} +(-6.46735 + 15.9041i) q^{77} +(-0.504824 + 2.21178i) q^{78} +(-2.18860 - 3.79077i) q^{79} +(-20.4113 + 35.3535i) q^{80} +(-2.46260 - 2.28496i) q^{81} +(-19.1509 - 13.0569i) q^{82} +(8.55442 + 10.7269i) q^{83} +(-10.9119 - 5.42022i) q^{84} +(6.61203 - 8.29122i) q^{85} +(16.7386 - 5.16318i) q^{86} +(-1.60628 - 4.09272i) q^{87} +(4.80228 - 64.0820i) q^{88} +(-0.924152 + 2.35470i) q^{89} +(-14.6174 - 7.03935i) q^{90} +(2.62083 - 0.362319i) q^{91} +(1.78036 - 0.857378i) q^{92} +(0.463973 + 6.19129i) q^{93} +(24.5454 + 7.57126i) q^{94} +(1.40749 - 0.959609i) q^{95} +(19.9978 + 3.01418i) q^{96} -5.30298 q^{97} +(-1.91132 + 19.1947i) q^{98} +15.0693 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	2.72488	+	0.410710i	1.92678	+	0.290416i	0.996981	−	0.0776474i	$-0.0247409\pi$
$2$	2.72488	+	0.410710i	1.92678	+	0.290416i	0.929801	+	0.368063i	$0.119979\pi$
$3$	0.680220	−	0.463766i	0.392725	−	0.267756i	−0.350818	−	0.936444i	$-0.614096\pi$
$3$	0.680220	−	0.463766i	0.392725	−	0.267756i	0.743543	+	0.668688i	$0.233144\pi$
$4$	5.34515	+	1.64876i	2.67257	+	0.824380i
$5$	0.189463	+	2.52821i	0.0847306	+	1.13065i	0.863841	+	0.503765i	$0.168052\pi$
$5$	0.189463	+	2.52821i	0.0847306	+	1.13065i	−0.779110	+	0.626887i	$0.784329\pi$
$6$	2.04399	−	0.984335i	0.834456	−	0.401853i
$7$	−1.91733	−	1.82314i	−0.724683	−	0.689083i
$7$	−1.91733	−	1.82314i	−0.724683	−	0.689083i
$8$	8.92220	+	4.29671i	3.15447	+	1.51911i
$9$	−0.848403	+	2.16170i	−0.282801	+	0.720565i
$10$	−0.522097	+	6.96690i	−0.165101	+	2.20313i
$11$	−2.37076	−	6.04061i	−0.714812	−	1.82131i	−0.550362	−	0.834926i	$-0.685510\pi$
$11$	−2.37076	−	6.04061i	−0.714812	−	1.82131i	−0.164451	−	0.986385i	$-0.552585\pi$
$12$	4.40052	−	1.35738i	1.27032	−	0.391842i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$13$	−0.623490	+	0.781831i	−0.172925	+	0.216841i
$14$	−4.47571	−	5.75531i	−1.19618	−	1.53817i
$15$	1.30138	+	1.63188i	0.336014	+	0.421348i
$16$	13.3038	+	9.07041i	3.32596	+	2.26760i
$17$	−3.06627	−	2.84508i	−0.743679	−	0.690033i	0.214333	−	0.976761i	$-0.431242\pi$
$17$	−3.06627	−	2.84508i	−0.743679	−	0.690033i	−0.958012	+	0.286727i	$0.907433\pi$
$18$	−3.19963	+	5.54191i	−0.754159	+	1.30624i
$19$	−0.335953	−	0.581888i	−0.0770730	−	0.133494i	0.824913	−	0.565260i	$-0.191224\pi$
$19$	−0.335953	−	0.581888i	−0.0770730	−	0.133494i	−0.901986	+	0.431766i	$0.857891\pi$
$20$	−3.15571	+	13.8261i	−0.705638	+	3.09160i
$21$	−2.14972	−	0.350945i	−0.469107	−	0.0765824i
$22$	−3.97911	−	17.4336i	−0.848350	−	3.71686i
$23$	0.258963	−	0.240283i	0.0539976	−	0.0501024i	−0.652712	−	0.757606i	$-0.726369\pi$
$23$	0.258963	−	0.240283i	0.0539976	−	0.0501024i	0.706710	+	0.707503i	$0.250179\pi$
$24$	8.06173	−	1.21511i	1.64559	−	0.248033i
$25$	−1.41182	+	0.212797i	−0.282363	+	0.0425594i
$26$	−2.02004	+	1.87432i	−0.396163	+	0.367585i
$27$	0.975007	+	4.27178i	0.187640	+	0.822105i
$28$	−7.24249	−	12.9062i	−1.36870	−	2.43904i
$29$	1.18836	−	5.20655i	0.220673	−	0.966832i	−0.736300	−	0.676655i	$-0.763429\pi$
$29$	1.18836	−	5.20655i	0.220673	−	0.966832i	0.956973	−	0.290177i	$-0.0937142\pi$
$30$	2.87587	+	4.98115i	0.525060	+	0.909430i
$31$	−3.77071	+	6.53106i	−0.677240	+	1.17301i	0.298569	+	0.954388i	$0.403491\pi$
$31$	−3.77071	+	6.53106i	−0.677240	+	1.17301i	−0.975809	+	0.218626i	$0.929843\pi$
$32$	18.0074	+	16.7084i	3.18329	+	2.95366i
$33$	−4.41407	−	3.00946i	−0.768391	−	0.523880i
$34$	−7.18671	−	9.01185i	−1.23251	−	1.54552i
$35$	4.24603	−	5.19284i	0.717710	−	0.877750i
$36$	−8.09895	+	10.1558i	−1.34983	+	1.69263i
$37$	2.53064	−	0.780600i	0.416035	−	0.128330i	−0.0796687	−	0.996821i	$-0.525386\pi$
$37$	2.53064	−	0.780600i	0.416035	−	0.128330i	0.495704	+	0.868491i	$0.334910\pi$
$38$	−0.676446	−	1.72356i	−0.109734	−	0.279598i
$39$	−0.0615233	+	0.820971i	−0.00985161	+	0.131461i
$40$	−9.17256	+	23.3713i	−1.45031	+	3.69533i
$41$	−7.57825	−	3.64949i	−1.18352	−	0.569955i	−0.264587	−	0.964362i	$-0.585236\pi$
$41$	−7.57825	−	3.64949i	−1.18352	−	0.569955i	−0.918936	+	0.394407i	$0.870950\pi$
$42$	−5.71359	−	1.83919i	−0.881626	−	0.283794i
$43$	5.72717	−	2.75806i	0.873385	−	0.420600i	0.0571810	−	0.998364i	$-0.481789\pi$
$43$	5.72717	−	2.75806i	0.873385	−	0.420600i	0.816204	+	0.577764i	$0.196074\pi$
$44$	−2.71257	−	36.1968i	−0.408936	−	5.45687i
$45$	−5.62597	−	1.73538i	−0.838670	−	0.258695i
$46$	0.804330	−	0.548383i	0.118592	−	0.0808547i
$47$	9.21729	+	1.38928i	1.34448	+	0.202648i	0.781543	−	0.623852i	$-0.214433\pi$
$47$	9.21729	+	1.38928i	1.34448	+	0.202648i	0.562937	+	0.826500i	$0.309671\pi$
$48$	13.2561			1.91335
$49$	0.352309	+	6.99113i	0.0503299	+	0.998733i
$50$	−3.93443			−0.556412
$51$	−3.40519	−	0.513250i	−0.476822	−	0.0718693i
$52$	−4.62170	+	3.15102i	−0.640914	+	0.436968i
$53$	−0.141235	−	0.0435651i	−0.0194001	−	0.00598413i	0.285040	−	0.958516i	$-0.407993\pi$
$53$	−0.141235	−	0.0435651i	−0.0194001	−	0.00598413i	−0.304440	+	0.952532i	$0.598469\pi$
$54$	0.902314	+	12.0405i	0.122789	+	1.63851i
$55$	14.8228	−	7.13827i	1.99870	−	0.962524i
$56$	−9.27330	−	24.5046i	−1.23920	−	3.27457i
$57$	−0.498382	−	0.240008i	−0.0660124	−	0.0317899i
$58$	5.37653	−	13.6992i	0.705972	−	1.79879i
$59$	0.485859	−	6.48333i	0.0632534	−	0.844058i	−0.871870	−	0.489737i	$-0.837093\pi$
$59$	0.485859	−	6.48333i	0.0632534	−	0.844058i	0.935124	−	0.354321i	$-0.115288\pi$
$60$	4.26548	+	10.8683i	0.550671	+	1.40309i
$61$	0.758961	−	0.234108i	0.0971750	−	0.0299745i	−0.245786	−	0.969324i	$-0.579046\pi$
$61$	0.758961	−	0.234108i	0.0971750	−	0.0299745i	0.342961	+	0.939349i	$0.388570\pi$
$62$	−12.9571	+	16.2477i	−1.64555	+	2.06346i
$63$	5.56774	−	2.59792i	0.701470	−	0.327308i
$64$	22.1272	+	27.7467i	2.76591	+	3.46834i
$65$	−2.09477	−	1.42819i	−0.259824	−	0.177145i
$66$	−10.7918	−	10.0133i	−1.32838	−	1.23256i
$67$	−4.66527	+	8.08048i	−0.569953	+	0.987188i	0.426617	+	0.904432i	$0.359705\pi$
$67$	−4.66527	+	8.08048i	−0.569953	+	0.987188i	−0.996570	+	0.0827553i	$0.973628\pi$
$68$	−11.6988	−	20.2629i	−1.41869	−	2.45724i
$69$	0.0647170	−	0.283543i	0.00779101	−	0.0341346i
$70$	13.7027	−	12.4060i	1.63778	−	1.48280i
$71$	2.58433	+	11.3227i	0.306704	+	1.34376i	0.859796	+	0.510638i	$0.170591\pi$
$71$	2.58433	+	11.3227i	0.306704	+	1.34376i	−0.553092	+	0.833120i	$0.686552\pi$
$72$	−16.8578	+	15.6417i	−1.98671	+	1.84340i
$73$	−12.3313	+	1.85865i	−1.44327	+	0.217538i	−0.823532	−	0.567270i	$-0.807999\pi$
$73$	−12.3313	+	1.85865i	−1.44327	+	0.217538i	−0.619739	+	0.784808i	$0.712761\pi$
$74$	7.21631	−	1.08768i	0.838878	−	0.126441i
$75$	−0.861657	+	0.799501i	−0.0994956	+	0.0923184i
$76$	−0.836327	−	3.66419i	−0.0959332	−	0.420311i
$77$	−6.46735	+	15.9041i	−0.737023	+	1.81244i
$78$	−0.504824	+	2.21178i	−0.0571601	+	0.250435i
$79$	−2.18860	−	3.79077i	−0.246237	−	0.426495i	0.716242	−	0.697852i	$-0.245861\pi$
$79$	−2.18860	−	3.79077i	−0.246237	−	0.426495i	−0.962479	+	0.271357i	$0.912528\pi$
$80$	−20.4113	+	35.3535i	−2.28206	+	3.95264i
$81$	−2.46260	−	2.28496i	−0.273622	−	0.253884i
$82$	−19.1509	−	13.0569i	−2.11487	−	1.44189i
$83$	8.55442	+	10.7269i	0.938970	+	1.17743i	0.983950	+	0.178443i	$0.0571060\pi$
$83$	8.55442	+	10.7269i	0.938970	+	1.17743i	−0.0449806	+	0.998988i	$0.514323\pi$
$84$	−10.9119	−	5.42022i	−1.19059	−	0.591394i
$85$	6.61203	−	8.29122i	0.717175	−	0.899309i
$86$	16.7386	−	5.16318i	1.80497	−	0.556760i
$87$	−1.60628	−	4.09272i	−0.172211	−	0.438786i
$88$	4.80228	−	64.0820i	0.511925	−	6.83116i
$89$	−0.924152	+	2.35470i	−0.0979599	+	0.249598i	−0.971450	−	0.237244i	$-0.923756\pi$
$89$	−0.924152	+	2.35470i	−0.0979599	+	0.249598i	0.873490	+	0.486842i	$0.161851\pi$
$90$	−14.6174	−	7.03935i	−1.54080	−	0.742012i
$91$	2.62083	−	0.362319i	0.274737	−	0.0379813i
$92$	1.78036	−	0.857378i	0.185616	−	0.0893879i
$93$	0.463973	+	6.19129i	0.0481118	+	0.642007i
$94$	24.5454	+	7.57126i	2.53167	+	0.780916i
$95$	1.40749	−	0.959609i	0.144405	−	0.0984538i
$96$	19.9978	+	3.01418i	2.04102	+	0.307634i
$97$	−5.30298			−0.538436			−0.269218	−	0.963079i	$-0.586765\pi$
$97$	−5.30298			−0.538436			−0.269218	+	0.963079i	$0.586765\pi$
$98$	−1.91132	+	19.1947i	−0.193073	+	1.93896i
$99$	15.0693			1.51452
$100$	−7.89721	−	1.19031i	−0.789721	−	0.119031i
$101$	−2.27857	+	1.55351i	−0.226727	+	0.154580i	−0.671356	−	0.741135i	$-0.734288\pi$
$101$	−2.27857	+	1.55351i	−0.226727	+	0.154580i	0.444629	+	0.895715i	$0.353335\pi$
$102$	−9.06794	−	2.79709i	−0.897860	−	0.276953i
$103$	−0.293260	−	3.91329i	−0.0288958	−	0.385588i	−0.992837	−	0.119474i	$-0.961879\pi$
$103$	−0.293260	−	3.91329i	−0.0288958	−	0.385588i	0.963942	−	0.266114i	$-0.0857398\pi$
$104$	−8.92220	+	4.29671i	−0.874894	+	0.421327i
$105$	0.479970	−	5.50144i	0.0468403	−	0.536885i
$106$	−0.366955	−	0.176716i	−0.0356418	−	0.0171642i
$107$	1.58968	−	4.05043i	0.153680	−	0.391570i	−0.833212	−	0.552954i	$-0.813501\pi$
$107$	1.58968	−	4.05043i	0.153680	−	0.391570i	0.986892	+	0.161384i	$0.0515958\pi$
$108$	−1.83159	+	24.4409i	−0.176245	+	2.35182i
$109$	−2.68673	−	6.84569i	−0.257342	−	0.655698i	0.742558	−	0.669781i	$-0.233612\pi$
$109$	−2.68673	−	6.84569i	−0.257342	−	0.655698i	−0.999901	+	0.0140834i	$0.995517\pi$
$110$	43.3221	−	13.3631i	4.13060	−	1.27412i
$111$	1.35938	−	1.70461i	0.129027	−	0.161794i
$112$	−8.97122	−	41.6458i	−0.847701	−	3.93515i
$113$	0.521760	+	0.654267i	0.0490831	+	0.0615482i	0.805767	−	0.592232i	$-0.201753\pi$
$113$	0.521760	+	0.654267i	0.0490831	+	0.0615482i	−0.756684	+	0.653781i	$0.773182\pi$
$114$	−1.25946	−	0.858685i	−0.117959	−	0.0804232i
$115$	0.656550	+	0.609190i	0.0612236	+	0.0568072i
$116$	14.9363	−	25.8705i	1.38680	−	2.40201i
$117$	−1.16111	−	2.01110i	−0.107345	−	0.185927i
$118$	3.98667	−	17.4668i	0.367003	−	1.60795i
$119$	0.692062	+	11.0452i	0.0634412	+	1.01251i
$120$	4.59946	+	20.1516i	0.419871	+	1.83958i
$121$	−22.8048	+	21.1598i	−2.07317	+	1.92362i
$122$	2.16423	−	0.326205i	0.195940	−	0.0295332i
$123$	−6.84739	+	1.03208i	−0.617408	+	0.0930593i
$124$	−30.9232	+	28.6925i	−2.77698	+	2.57666i
$125$	2.01531	+	8.82964i	0.180255	+	0.789747i
$126$	16.2384	−	4.79231i	1.44663	−	0.426933i
$127$	−1.09765	+	4.80914i	−0.0974010	+	0.426742i	−0.999993	−	0.00375539i	$-0.998805\pi$
$127$	−1.09765	+	4.80914i	−0.0974010	+	0.426742i	0.902592	+	0.430497i	$0.141662\pi$
$128$	24.3333	+	42.1465i	2.15078	+	3.72526i
$129$	2.61664	−	4.53215i	0.230382	−	0.399034i
$130$	−5.12142	−	4.75198i	−0.449178	−	0.416776i
$131$	7.88438	+	5.37548i	0.688862	+	0.469658i	0.856471	−	0.516196i	$-0.172652\pi$
$131$	7.88438	+	5.37548i	0.688862	+	0.469658i	−0.167609	+	0.985854i	$0.553605\pi$
$132$	−18.6320	−	23.3638i	−1.62171	−	2.03355i
$133$	−0.416731	+	1.72816i	−0.0361352	+	0.149851i
$134$	−16.0310	+	20.1023i	−1.38487	+	1.73657i
$135$	−10.6153	+	3.27437i	−0.913616	+	0.281813i
$136$	−15.1334	−	38.5592i	−1.29768	−	3.30643i
$137$	−0.467638	+	6.24019i	−0.0399530	+	0.533136i	0.940938	+	0.338578i	$0.109946\pi$
$137$	−0.467638	+	6.24019i	−0.0399530	+	0.533136i	−0.980891	+	0.194557i	$0.937673\pi$
$138$	0.292800	−	0.746042i	0.0249248	−	0.0635073i
$139$	−1.26209	−	0.607789i	−0.107049	−	0.0515520i	0.379593	−	0.925154i	$-0.376064\pi$
$139$	−1.26209	−	0.607789i	−0.107049	−	0.0515520i	−0.486642	+	0.873602i	$0.661778\pi$
$140$	31.2574	−	20.7558i	2.64173	−	1.75419i
$141$	6.91409	−	3.32965i	0.582271	−	0.280407i
$142$	2.39166	+	31.9144i	0.200703	+	2.67820i
$143$	6.20088	+	1.91272i	0.518544	+	0.159950i
$144$	−30.8945	+	21.0635i	−2.57454	+	1.75529i
$145$	13.3884	+	2.01798i	1.11185	+	0.167584i
$146$	−34.3647			−2.84404
$147$	3.48190	+	4.59212i	0.287182	+	0.378751i
$148$	14.8137			1.21768
$149$	−4.39572	−	0.662548i	−0.360111	−	0.0542780i	−0.0335051	−	0.999439i	$-0.510667\pi$
$149$	−4.39572	−	0.662548i	−0.360111	−	0.0542780i	−0.326606	+	0.945161i	$0.605905\pi$
$150$	−2.67628	+	1.82465i	−0.218517	+	0.148982i
$151$	−7.51666	−	2.31858i	−0.611697	−	0.188684i	−0.0265991	−	0.999646i	$-0.508468\pi$
$151$	−7.51666	−	2.31858i	−0.611697	−	0.188684i	−0.585098	+	0.810963i	$0.698944\pi$
$152$	−0.497241	−	6.63522i	−0.0403316	−	0.538187i
$153$	8.75163	−	4.21456i	0.707527	−	0.340727i
$154$	−24.1547	+	40.6805i	−1.94644	+	3.27813i
$155$	−17.2263	−	8.29577i	−1.38365	−	0.666332i
$156$	−1.68243	+	4.28677i	−0.134703	+	0.343217i
$157$	0.525607	−	7.01374i	0.0419480	−	0.559758i	−0.936148	−	0.351605i	$-0.885636\pi$
$157$	0.525607	−	7.01374i	0.0419480	−	0.559758i	0.978096	−	0.208152i	$-0.0667450\pi$
$158$	−4.40678	−	11.2283i	−0.350584	−	0.893275i
$159$	−0.116275	+	0.0358660i	−0.00922118	+	0.00284436i
$160$	−38.8308	+	48.6922i	−3.06984	+	3.84946i
$161$	−0.934587	−	0.0114253i	−0.0736558	−	0.000900439i
$162$	−5.77183	−	7.23765i	−0.453478	−	0.568643i
$163$	−16.1903	−	11.0383i	−1.26812	−	0.864589i	−0.272880	−	0.962048i	$-0.587976\pi$
$163$	−16.1903	−	11.0383i	−1.26812	−	0.864589i	−0.995240	+	0.0974591i	$0.968928\pi$
$164$	−34.4897	−	32.0018i	−2.69319	−	2.49892i
$165$	6.77226	−	11.7299i	0.527220	−	0.913171i
$166$	18.9041	+	32.7429i	1.46725	+	2.54134i
$167$	0.787289	−	3.44934i	0.0609223	−	0.266918i	−0.935289	−	0.353885i	$-0.884860\pi$
$167$	0.787289	−	3.44934i	0.0609223	−	0.266918i	0.996211	+	0.0869672i	$0.0277175\pi$
$168$	−17.6723	−	12.3679i	−1.36345	−	0.954205i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	21.4223	−	19.8770i	1.64301	−	1.52449i
$171$	1.54289	−	0.232553i	0.117988	−	0.0177838i
$172$	35.1599	−	5.29951i	2.68092	−	0.404084i
$173$	8.84278	−	8.20490i	0.672304	−	0.623807i	−0.268291	−	0.963338i	$-0.586459\pi$
$173$	8.84278	−	8.20490i	0.672304	−	0.623807i	0.940595	+	0.339531i	$0.110268\pi$
$174$	−2.69599	−	11.8119i	−0.204382	−	0.895458i
$175$	3.09487	+	2.16594i	0.233951	+	0.163729i
$176$	23.2505	−	101.867i	1.75257	−	7.67852i
$177$	−2.67626	−	4.63542i	−0.201160	−	0.348419i
$178$	−3.48530	+	6.03672i	−0.261234	+	0.452471i
$179$	13.9409	+	12.9352i	1.04199	+	0.966826i	0.999479	−	0.0322704i	$-0.0102738\pi$
$179$	13.9409	+	12.9352i	1.04199	+	0.966826i	0.0425110	+	0.999096i	$0.486464\pi$
$180$	−27.2104	−	18.5517i	−2.02814	−	1.38277i
$181$	−2.21799	−	2.78127i	−0.164862	−	0.206730i	0.692538	−	0.721382i	$-0.256493\pi$
$181$	−2.21799	−	2.78127i	−0.164862	−	0.206730i	−0.857399	+	0.514652i	$0.827921\pi$
$182$	7.29024	+	0.0891229i	0.540389	+	0.00660623i
$183$	0.407689	−	0.511226i	0.0301372	−	0.0377909i
$184$	3.34295	−	1.03116i	0.246445	−	0.0760183i
$185$	2.45299	+	6.25012i	0.180347	+	0.459518i
$186$	−1.27855	+	17.0611i	−0.0937479	+	1.25098i
$187$	−9.91662	+	25.2671i	−0.725175	+	1.84772i
$188$	46.9772	+	22.6230i	3.42616	+	1.64995i
$189$	5.91866	−	9.96800i	0.430519	−	0.725065i
$190$	4.22936	−	2.03675i	0.306830	−	0.147761i
$191$	1.06906	+	14.2656i	0.0773543	+	1.03222i	0.891933	+	0.452168i	$0.149349\pi$
$191$	1.06906	+	14.2656i	0.0773543	+	1.03222i	−0.814579	+	0.580053i	$0.803032\pi$
$192$	27.9194	+	8.61199i	2.01491	+	0.621517i
$193$	−1.26417	+	0.861900i	−0.0909973	+	0.0620409i	−0.607964	−	0.793965i	$-0.708013\pi$
$193$	−1.26417	+	0.861900i	−0.0909973	+	0.0620409i	0.516967	+	0.856006i	$0.327061\pi$
$194$	−14.4500	−	2.17799i	−1.03745	−	0.156370i
$195$	−2.08725			−0.149471
$196$	−9.64355	+	37.9495i	−0.688825	+	2.71068i
$197$	8.81475			0.628025			0.314012	−	0.949419i	$-0.398327\pi$
$197$	8.81475			0.628025			0.314012	+	0.949419i	$0.398327\pi$
$198$	41.0621	+	6.18911i	2.91816	+	0.439841i
$199$	12.0120	−	8.18967i	0.851511	−	0.580550i	−0.0570176	−	0.998373i	$-0.518159\pi$
$199$	12.0120	−	8.18967i	0.851511	−	0.580550i	0.908528	+	0.417823i	$0.137207\pi$
$200$	−13.5108	−	4.16754i	−0.955360	−	0.294689i
$201$	0.574045	+	7.66010i	0.0404900	+	0.540302i
$202$	−6.84688	+	3.29729i	−0.481745	+	0.231996i
$203$	−11.7708	+	7.81613i	−0.826146	+	0.548585i
$204$	−17.3550	−	8.35773i	−1.21509	−	0.585158i
$205$	7.79089	−	19.8509i	0.544140	−	1.38645i
$206$	0.808126	−	10.7837i	0.0563048	−	0.751335i
$207$	0.299713	+	0.763656i	0.0208315	+	0.0530778i
$208$	−15.3863	+	4.74606i	−1.06685	+	0.329080i
$209$	−2.71849	+	3.40888i	−0.188042	+	0.235797i
$210$	3.56736	−	14.7936i	0.246171	−	1.02086i
$211$	4.37227	+	5.48265i	0.300999	+	0.377441i	0.909212	−	0.416333i	$-0.136685\pi$
$211$	4.37227	+	5.48265i	0.300999	+	0.377441i	−0.608213	+	0.793774i	$0.708113\pi$
$212$	−0.683092	−	0.465724i	−0.0469149	−	0.0319860i
$213$	7.00901	+	6.50341i	0.480249	+	0.445606i
$214$	5.99523	−	10.3840i	0.409825	−	0.709839i
$215$	8.05805	+	13.9570i	0.549555	+	0.951857i
$216$	−9.65539	+	42.3030i	−0.656966	+	2.87836i
$217$	19.1368	−	5.64766i	1.29909	−	0.383388i
$218$	−4.50944	−	19.7572i	−0.305418	−	1.33812i
$219$	−7.52602	+	6.98313i	−0.508562	+	0.471876i
$220$	90.9992	−	13.7159i	6.13517	−	0.924727i
$221$	4.13616	−	0.623426i	0.278228	−	0.0419362i
$222$	4.40425	−	4.08654i	0.295594	−	0.274271i
$223$	−5.44009	−	23.8346i	−0.364295	−	1.59608i	−0.742161	−	0.670222i	$-0.766199\pi$
$223$	−5.44009	−	23.8346i	−0.364295	−	1.59608i	0.377865	−	0.925861i	$-0.376658\pi$
$224$	−4.06430	−	64.8656i	−0.271558	−	4.33402i
$225$	0.737786	−	3.23245i	0.0491857	−	0.215497i
$226$	1.15302	+	1.99709i	0.0766978	+	0.132845i
$227$	7.84413	−	13.5864i	0.520633	−	0.901763i	−0.479079	−	0.877772i	$-0.659029\pi$
$227$	7.84413	−	13.5864i	0.520633	−	0.901763i	0.999712	−	0.0239914i	$-0.00763744\pi$
$228$	−2.26821	−	2.10459i	−0.150216	−	0.139380i
$229$	1.57541	+	1.07410i	0.104106	+	0.0709783i	0.614254	−	0.789108i	$-0.289457\pi$
$229$	1.57541	+	1.07410i	0.104106	+	0.0709783i	−0.510148	+	0.860087i	$0.670409\pi$
$230$	1.53882	+	1.92962i	0.101467	+	0.127235i
$231$	2.97655	+	13.8176i	0.195843	+	0.909132i
$232$	32.9738	−	41.3479i	2.16484	−	2.71462i
$233$	1.94304	−	0.599349i	0.127293	−	0.0392647i	−0.230454	−	0.973083i	$-0.574021\pi$
$233$	1.94304	−	0.599349i	0.127293	−	0.0392647i	0.357747	+	0.933819i	$0.383545\pi$
$234$	−2.33791	−	5.95689i	−0.152834	−	0.389414i
$235$	−1.76606	+	23.5665i	−0.115205	+	1.53731i
$236$	13.2864	−	33.8533i	0.864874	−	2.20366i
$237$	−3.24677	−	1.56356i	−0.210900	−	0.101564i
$238$	−2.65058	+	30.3811i	−0.171812	+	1.96931i
$239$	3.60058	−	1.73395i	0.232902	−	0.112160i	−0.313793	−	0.949491i	$-0.601600\pi$
$239$	3.60058	−	1.73395i	0.232902	−	0.112160i	0.546695	+	0.837332i	$0.315886\pi$
$240$	2.51154	+	33.5142i	0.162120	+	2.16333i
$241$	−1.47181	−	0.453993i	−0.0948076	−	0.0292443i	0.246988	−	0.969018i	$-0.420559\pi$
$241$	−1.47181	−	0.453993i	−0.0948076	−	0.0292443i	−0.341796	+	0.939774i	$0.611035\pi$
$242$	−70.8310	+	48.2918i	−4.55319	+	3.10431i
$243$	−15.7329	−	2.37135i	−1.00927	−	0.152122i
$244$	4.44275			0.284418
$245$	−17.6083	+	2.21528i	−1.12495	+	0.141529i
$246$	−19.0822			−1.21664
$247$	0.664402	+	0.100143i	0.0422749	+	0.00637192i
$248$	−61.7051	+	42.0698i	−3.91828	+	2.67144i
$249$	10.7937	+	3.32940i	0.684021	+	0.210992i
$250$	1.86505	+	24.8874i	0.117956	+	1.57402i
$251$	9.39504	−	4.52441i	0.593010	−	0.285578i	−0.113210	−	0.993571i	$-0.536113\pi$
$251$	9.39504	−	4.52441i	0.593010	−	0.285578i	0.706220	+	0.707993i	$0.250399\pi$
$252$	34.0438	−	4.70642i	2.14456	−	0.296476i
$253$	−2.06539	−	0.994641i	−0.129850	−	0.0625326i
$254$	−4.96613	+	12.6535i	−0.311603	+	0.793951i
$255$	0.652446	−	8.70629i	0.0408578	−	0.545209i
$256$	23.0639	+	58.7659i	1.44149	+	3.67287i
$257$	23.7910	−	7.33855i	1.48404	−	0.457766i	0.556297	−	0.830984i	$-0.312222\pi$
$257$	23.7910	−	7.33855i	1.48404	−	0.457766i	0.927744	+	0.373218i	$0.121746\pi$
$258$	8.99143	−	11.2749i	0.559782	−	0.701945i
$259$	−6.27523	−	3.11705i	−0.389924	−	0.193684i
$260$	−8.84209	−	11.0876i	−0.548363	−	0.687626i
$261$	10.2468	+	6.98613i	0.634259	+	0.432431i
$262$	19.2762	+	17.8857i	1.19089	+	1.10498i
$263$	4.82454	−	8.35635i	0.297494	−	0.515275i	−0.678068	−	0.734999i	$-0.737182\pi$
$263$	4.82454	−	8.35635i	0.297494	−	0.515275i	0.975562	+	0.219724i	$0.0705158\pi$
$264$	−26.4525	−	45.8170i	−1.62804	−	2.81984i
$265$	0.0833831	−	0.365325i	0.00512218	−	0.0224418i
$266$	−1.84532	+	4.53788i	−0.113144	+	0.278235i
$267$	0.463404	+	2.03030i	0.0283598	+	0.124253i
$268$	−38.2593	+	35.4995i	−2.33706	+	2.16847i
$269$	15.9601	−	2.40560i	0.973106	−	0.146672i	0.356802	−	0.934180i	$-0.383867\pi$
$269$	15.9601	−	2.40560i	0.973106	−	0.146672i	0.616305	+	0.787508i	$0.288629\pi$
$270$	−30.2701	+	4.56249i	−1.84218	+	0.277664i
$271$	11.4995	−	10.6700i	0.698545	−	0.648155i	−0.248731	−	0.968572i	$-0.580014\pi$
$271$	11.4995	−	10.6700i	0.698545	−	0.648155i	0.947276	+	0.320417i	$0.103823\pi$
$272$	−14.9871	−	65.6628i	−0.908727	−	3.98139i
$273$	1.61471	−	1.46191i	0.0977265	−	0.0884786i
$274$	−3.83717	+	16.8117i	−0.231812	+	1.01563i
$275$	4.63250	+	8.02373i	0.279350	+	0.483849i
$276$	0.813417	−	1.40888i	0.0489619	−	0.0848046i
$277$	19.5810	+	18.1685i	1.17651	+	1.09164i	0.994105	+	0.108417i	$0.0345783\pi$
$277$	19.5810	+	18.1685i	1.17651	+	1.09164i	0.182404	+	0.983224i	$0.441612\pi$
$278$	−3.18941	−	2.17450i	−0.191288	−	0.130418i
$279$	−10.9191	−	13.6921i	−0.653709	−	0.819725i
$280$	60.1960	−	28.0876i	3.59740	−	1.67856i
$281$	7.30407	−	9.15901i	0.435724	−	0.546381i	−0.514686	−	0.857378i	$-0.672092\pi$
$281$	7.30407	−	9.15901i	0.435724	−	0.546381i	0.950411	+	0.310998i	$0.100663\pi$
$282$	20.2076	−	6.23321i	1.20334	−	0.371183i
$283$	−8.87513	−	22.6135i	−0.527572	−	1.34423i	−0.907825	−	0.419349i	$-0.862258\pi$
$283$	−8.87513	−	22.6135i	−0.527572	−	1.34423i	0.380253	−	0.924882i	$-0.375837\pi$
$284$	−4.85478	+	64.7825i	−0.288078	+	3.84413i
$285$	0.512367	−	1.30549i	0.0303500	−	0.0773306i
$286$	16.1111	+	7.75870i	0.952669	+	0.458781i
$287$	7.87646	+	20.8135i	0.464933	+	1.22858i
$288$	−51.3961	+	24.7510i	−3.02854	+	1.45847i
$289$	0.0371024	+	0.495097i	0.00218249	+	0.0291233i
$290$	35.6531	+	10.9975i	2.09362	+	0.645796i
$291$	−3.60719	+	2.45934i	−0.211457	+	0.144169i
$292$	−68.9771	−	10.3966i	−4.03658	−	0.608416i
$293$	−29.8667			−1.74483			−0.872414	−	0.488767i	$-0.837447\pi$
$293$	−29.8667			−1.74483			−0.872414	+	0.488767i	$0.837447\pi$
$294$	7.60173	+	13.9430i	0.443342	+	0.813173i
$295$	16.4833			0.959695
$296$	25.9329	+	3.90876i	1.50732	+	0.227192i
$297$	23.4927	−	16.0170i	1.36318	−	0.929402i
$298$	−11.7057	−	3.61073i	−0.678093	−	0.209164i
$299$	0.0263997	+	0.352279i	0.00152673	+	0.0203728i
$300$	−5.92387	+	2.85279i	−0.342015	+	0.164706i
$301$	−16.0092	−	5.15333i	−0.922755	−	0.297033i
$302$	−19.5297	−	9.40503i	−1.12381	−	0.541198i
$303$	−0.829469	+	2.11345i	−0.0476517	+	0.121415i
$304$	0.808493	−	10.7886i	0.0463702	−	0.618768i
$305$	0.735672	+	1.87446i	0.0421244	+	0.107331i
$306$	25.5781	−	7.88980i	1.46220	−	0.451030i
$307$	12.0380	−	15.0951i	0.687043	−	0.861525i	−0.308939	−	0.951082i	$-0.599974\pi$
$307$	12.0380	−	15.0951i	0.687043	−	0.861525i	0.995982	+	0.0895573i	$0.0285452\pi$
$308$	−60.7909	+	74.3465i	−3.46388	+	4.23629i
$309$	−2.01433	−	2.52589i	−0.114591	−	0.143693i
$310$	−43.5326	−	29.6800i	−2.47248	−	1.68571i
$311$	18.8930	+	17.5301i	1.07132	+	0.994042i	0.999994	−	0.00341105i	$-0.00108577\pi$
$311$	18.8930	+	17.5301i	1.07132	+	0.994042i	0.0713281	+	0.997453i	$0.477276\pi$
$312$	−4.07639	+	7.06052i	−0.230780	+	0.399723i
$313$	9.41898	+	16.3141i	0.532392	+	0.922130i	0.999285	+	0.0378161i	$0.0120401\pi$
$313$	9.41898	+	16.3141i	0.532392	+	0.922130i	−0.466893	+	0.884314i	$0.654627\pi$
$314$	4.31283	−	18.8957i	0.243387	−	1.06635i
$315$	7.62299	+	13.5842i	0.429507	+	0.765385i
$316$	−5.44834	−	23.8707i	−0.306493	−	1.34283i
$317$	−22.2688	+	20.6625i	−1.25074	+	1.16052i	−0.270500	+	0.962720i	$0.587189\pi$
$317$	−22.2688	+	20.6625i	−1.25074	+	1.16052i	−0.980242	+	0.197800i	$0.936620\pi$
$318$	−0.331565	+	0.0499754i	−0.0185932	+	0.00280248i
$319$	−34.2681	+	5.16508i	−1.91864	+	0.289189i
$320$	−65.9573	+	61.1994i	−3.68712	+	3.42115i
$321$	−0.797123	−	3.49242i	−0.0444910	−	0.194928i
$322$	−2.54195	−	0.414977i	−0.141657	−	0.0231257i
$323$	−0.625396	+	2.74004i	−0.0347980	+	0.152460i
$324$	−9.39560	−	16.2737i	−0.521978	−	0.904092i
$325$	0.713881	−	1.23648i	0.0395990	−	0.0685875i
$326$	−39.5830	−	36.7276i	−2.19230	−	2.03416i
$327$	−5.00237	−	3.41056i	−0.276632	−	0.188604i
$328$	−51.9339	−	65.1230i	−2.86757	−	3.59582i
$329$	−15.1397	−	19.4681i	−0.834680	−	1.07331i
$330$	23.2712	−	29.1811i	1.28104	−	1.60637i
$331$	20.5242	−	6.33086i	1.12811	−	0.347976i	0.326129	−	0.945325i	$-0.394256\pi$
$331$	20.5242	−	6.33086i	1.12811	−	0.347976i	0.801981	+	0.597350i	$0.203780\pi$
$332$	28.0386	+	71.4411i	1.53882	+	3.92084i
$333$	−0.459586	+	6.13275i	−0.0251851	+	0.336072i
$334$	3.56195	−	9.07569i	0.194901	−	0.496600i
$335$	−21.3131	−	10.2638i	−1.16446	−	0.560773i
$336$	−25.4163	−	24.1677i	−1.38657	−	1.31846i
$337$	−32.2864	+	15.5483i	−1.75875	+	0.846969i	−0.784952	+	0.619557i	$0.787312\pi$
$337$	−32.2864	+	15.5483i	−1.75875	+	0.846969i	−0.973799	+	0.227412i	$0.926973\pi$
$338$	−0.205931	−	2.74795i	−0.0112012	−	0.149469i
$339$	0.658339	+	0.203071i	0.0357561	+	0.0110293i
$340$	49.0125	−	33.4162i	2.65808	−	1.81225i
$341$	48.3911	+	7.29378i	2.62052	+	0.394980i
$342$	4.29970			0.232501
$343$	12.0703	−	14.0466i	0.651736	−	0.758446i
$344$	62.9495			3.39401
$345$	0.729120	+	0.109897i	0.0392545	+	0.00591667i
$346$	27.4654	−	18.7256i	1.47655	−	1.00669i
$347$	−17.7091	−	5.46252i	−0.950672	−	0.293244i	−0.219636	−	0.975582i	$-0.570487\pi$
$347$	−17.7091	−	5.46252i	−0.950672	−	0.293244i	−0.731036	+	0.682338i	$0.760963\pi$
$348$	−1.83786	−	24.5246i	−0.0985198	−	1.31466i
$349$	−29.2706	+	14.0960i	−1.56682	+	0.754539i	−0.997704	−	0.0677206i	$-0.978427\pi$
$349$	−29.2706	+	14.0960i	−1.56682	+	0.754539i	−0.569112	+	0.822260i	$0.692713\pi$
$350$	7.54359	+	7.17302i	0.403222	+	0.383414i
$351$	−3.94772	−	1.90112i	−0.210714	−	0.101474i
$352$	58.2378	−	148.387i	3.10408	−	7.90908i
$353$	−0.211197	+	2.81823i	−0.0112409	+	0.149999i	0.988759	+	0.149518i	$0.0477723\pi$
$353$	−0.211197	+	2.81823i	−0.0112409	+	0.149999i	−1.00000		0.000481300i	$0.999847\pi$
$354$	−5.38868	−	13.7301i	−0.286405	−	0.729748i
$355$	−28.1366	+	8.67899i	−1.49334	+	0.460633i
$356$	−8.82206	+	11.0625i	−0.467568	+	0.586312i
$357$	5.59315	+	7.19221i	0.296021	+	0.380652i
$358$	32.6746	+	40.9727i	1.72691	+	2.16547i
$359$	7.38391	+	5.03427i	0.389708	+	0.265698i	0.742285	−	0.670084i	$-0.233742\pi$
$359$	7.38391	+	5.03427i	0.389708	+	0.265698i	−0.352577	+	0.935783i	$0.614694\pi$
$360$	−42.7396	−	39.6566i	−2.25257	−	2.09008i
$361$	9.27427	−	16.0635i	0.488120	−	0.845448i
$362$	−4.90146	−	8.48958i	−0.257615	−	0.446203i
$363$	−5.69911	+	24.9694i	−0.299126	+	1.31056i
$364$	14.6061	+	2.38446i	0.765566	+	0.124980i
$365$	−7.03538	−	30.8240i	−0.368249	−	1.61340i
$366$	1.32087	−	1.22559i	0.0690429	−	0.0640625i
$367$	−1.21941	+	0.183797i	−0.0636529	+	0.00959412i	−0.180791	−	0.983521i	$-0.557866\pi$
$367$	−1.21941	+	0.183797i	−0.0636529	+	0.00959412i	0.117139	+	0.993116i	$0.462628\pi$
$368$	5.62467	−	0.847782i	0.293206	−	0.0441937i
$369$	14.3185	−	13.2856i	0.745391	−	0.691622i
$370$	4.11712	+	18.0383i	0.214039	+	0.937766i
$371$	0.191368	+	0.341019i	0.00993533	+	0.0177048i
$372$	−7.72794	+	33.8583i	−0.400675	+	1.75547i
$373$	7.70510	+	13.3456i	0.398955	+	0.691011i	0.993597	−	0.112980i	$-0.0360396\pi$
$373$	7.70510	+	13.3456i	0.398955	+	0.691011i	−0.594642	+	0.803991i	$0.702706\pi$
$374$	−37.3991	+	64.7771i	−1.93386	+	3.34954i
$375$	5.46574	+	5.07146i	0.282250	+	0.261889i
$376$	76.2692	+	51.9994i	3.93328	+	2.68167i
$377$	3.32972	+	4.17533i	0.171489	+	0.215040i
$378$	20.2216	−	24.7308i	1.04009	−	1.27201i
$379$	−5.25933	+	6.59499i	−0.270154	+	0.338762i	−0.898340	−	0.439301i	$-0.855226\pi$
$379$	−5.25933	+	6.59499i	−0.270154	+	0.338762i	0.628186	+	0.778063i	$0.283798\pi$
$380$	9.10539	−	2.80864i	0.467097	−	0.144080i
$381$	1.48367	+	3.78033i	0.0760106	+	0.193672i
$382$	−2.94596	+	39.3111i	−0.150728	+	2.01133i
$383$	2.24213	−	5.71284i	0.114567	−	0.291913i	−0.862076	−	0.506779i	$-0.830836\pi$
$383$	2.24213	−	5.71284i	0.114567	−	0.291913i	0.976644	+	0.214866i	$0.0689314\pi$
$384$	36.0981	+	17.3839i	1.84212	+	0.887120i
$385$	−41.4342	−	13.3376i	−2.11168	−	0.679747i
$386$	−3.79872	+	1.82936i	−0.193350	+	0.0931122i
$387$	1.10314	+	14.7203i	0.0560756	+	0.748277i
$388$	−28.3452	−	8.74334i	−1.43901	−	0.443876i
$389$	8.51432	−	5.80496i	0.431693	−	0.294323i	−0.327912	−	0.944708i	$-0.606345\pi$
$389$	8.51432	−	5.80496i	0.431693	−	0.294323i	0.759605	+	0.650385i	$0.225392\pi$
$390$	−5.68750	−	0.857252i	−0.287998	−	0.0434087i
$391$	−1.47767			−0.0747292
$392$	−26.8955	+	63.8900i	−1.35843	+	3.22693i
$393$	7.85608			0.396287
$394$	24.0191	+	3.62030i	1.21007	+	0.182388i
$395$	9.16923	−	6.25147i	0.461354	−	0.314546i
$396$	80.5477	+	24.8457i	4.04767	+	1.24854i
$397$	0.539043	+	7.19303i	0.0270538	+	0.361008i	0.994258	+	0.107008i	$0.0341271\pi$
$397$	0.539043	+	7.19303i	0.0270538	+	0.361008i	−0.967204	+	0.253999i	$0.918254\pi$
$398$	36.0950	−	17.3824i	1.80928	−	0.871302i
$399$	0.517994	+	1.36880i	0.0259322	+	0.0685256i
$400$	−20.7127	−	9.97472i	−1.03564	−	0.498736i
$401$	−7.72038	+	19.6712i	−0.385537	+	0.982333i	0.597979	+	0.801512i	$0.295971\pi$
$401$	−7.72038	+	19.6712i	−0.385537	+	0.982333i	−0.983516	+	0.180821i	$0.942124\pi$
$402$	−1.58187	+	21.1086i	−0.0788966	+	1.05280i
$403$	−2.75519	−	7.02011i	−0.137246	−	0.349697i
$404$	−14.7407	+	4.54690i	−0.733376	+	0.226217i
$405$	5.31029	−	6.65889i	0.263870	−	0.330883i
$406$	−35.2841	+	16.4636i	−1.75112	+	0.817077i
$407$	−10.7149	−	13.4360i	−0.531116	−	0.665998i
$408$	−28.1765	−	19.2104i	−1.39494	−	0.951057i
$409$	−6.21590	−	5.76751i	−0.307356	−	0.285185i	0.511380	−	0.859355i	$-0.329135\pi$
$409$	−6.21590	−	5.76751i	−0.307356	−	0.285185i	−0.818736	+	0.574170i	$0.805325\pi$
$410$	29.3822	−	50.8915i	1.45108	−	2.51335i
$411$	2.57589	+	4.46158i	0.127060	+	0.220074i
$412$	4.88455	−	21.4006i	0.240645	−	1.05433i
$413$	−12.7516	+	11.5449i	−0.627464	+	0.568087i
$414$	0.503041	+	2.20397i	0.0247231	+	0.108319i
$415$	−25.4992	+	23.6598i	−1.25170	+	1.16141i
$416$	−24.2906	+	3.66122i	−1.19095	+	0.179506i
$417$	−1.14037	+	0.171883i	−0.0558441	+	0.00841714i
$418$	−8.80763	+	8.17229i	−0.430795	+	0.399720i
$419$	7.08967	+	31.0619i	0.346353	+	1.51747i	0.785389	+	0.619002i	$0.212463\pi$
$419$	7.08967	+	31.0619i	0.346353	+	1.51747i	−0.439037	+	0.898469i	$0.644680\pi$
$420$	11.6361	−	28.6146i	0.567782	−	1.39625i
$421$	2.07327	−	9.08361i	0.101045	−	0.442708i	−0.898944	−	0.438063i	$-0.855665\pi$
$421$	2.07327	−	9.08361i	0.101045	−	0.442708i	0.999989	−	0.00464438i	$-0.00147836\pi$
$422$	9.66213	+	16.7353i	0.470345	+	0.814661i
$423$	−10.8232	+	18.7463i	−0.526241	+	0.911476i
$424$	−1.07294	−	0.995540i	−0.0521064	−	0.0483477i
$425$	4.93443	+	3.36424i	0.239355	+	0.163189i
$426$	16.4277	+	20.5997i	0.795924	+	0.998058i
$427$	−1.88199	−	0.934830i	−0.0910759	−	0.0452396i
$428$	15.1752	−	19.0292i	0.733523	−	0.919809i
$429$	5.10502	−	1.57469i	0.246473	−	0.0760268i
$430$	16.2250	+	41.3406i	0.782438	+	1.99362i
$431$	2.16456	−	28.8841i	0.104263	−	1.39130i	−0.662353	−	0.749192i	$-0.730442\pi$
$431$	2.16456	−	28.8841i	0.104263	−	1.39130i	0.766616	−	0.642106i	$-0.221939\pi$
$432$	−25.7755	+	65.6749i	−1.24012	+	3.15978i
$433$	11.3668	+	5.47396i	0.546253	+	0.263062i	0.686593	−	0.727042i	$-0.259105\pi$
$433$	11.3668	+	5.47396i	0.546253	+	0.263062i	−0.140340	+	0.990103i	$0.544820\pi$
$434$	54.4649	−	7.52956i	2.61440	−	0.361430i
$435$	10.0430	−	4.83643i	0.481523	−	0.231889i
$436$	−3.07410	−	41.0210i	−0.147223	−	1.96455i
$437$	−0.226817	−	0.0699639i	−0.0108501	−	0.00334683i
$438$	−23.3756	+	15.9372i	−1.11693	+	0.761508i
$439$	19.8591	+	2.99328i	0.947823	+	0.142861i	0.604722	−	0.796437i	$-0.293284\pi$
$439$	19.8591	+	2.99328i	0.947823	+	0.142861i	0.343102	+	0.939298i	$0.388522\pi$
$440$	162.923			7.76704
$441$	−15.4116	−	5.16971i	−0.733885	−	0.246177i
$442$	11.5266			0.548264
$443$	−35.1936	−	5.30459i	−1.67210	−	0.252029i	−0.756463	−	0.654036i	$-0.773074\pi$
$443$	−35.1936	−	5.30459i	−1.67210	−	0.252029i	−0.915636	+	0.402007i	$0.868313\pi$
$444$	10.0766	−	6.87009i	0.478213	−	0.326040i
$445$	−6.12828	−	1.89032i	−0.290508	−	0.0896099i
$446$	−5.03450	−	67.1807i	−0.238390	−	3.18110i
$447$	−3.29732	+	1.58791i	−0.155958	+	0.0751054i
$448$	8.16091	−	93.5407i	0.385567	−	4.41938i
$449$	0.857959	+	0.413171i	0.0404896	+	0.0194988i	0.454019	−	0.890992i	$-0.349990\pi$
$449$	0.857959	+	0.413171i	0.0404896	+	0.0194988i	−0.413529	+	0.910491i	$0.635704\pi$
$450$	3.33798	−	8.50503i	0.157354	−	0.400931i
$451$	−4.07891	+	54.4293i	−0.192068	+	2.56298i
$452$	1.71016	+	4.35741i	0.0804390	+	0.204955i
$453$	−6.18826	+	1.90883i	−0.290750	+	0.0896845i
$454$	26.9544	−	33.7998i	1.26503	−	1.58630i
$455$	1.41257	+	6.55736i	0.0662223	+	0.307414i
$456$	−3.41542	−	4.28281i	−0.159942	−	0.200561i
$457$	13.8223	+	9.42392i	0.646582	+	0.440832i	0.841698	−	0.539948i	$-0.181556\pi$
$457$	13.8223	+	9.42392i	0.646582	+	0.440832i	−0.195116	+	0.980780i	$0.562508\pi$
$458$	3.85167	+	3.57382i	0.179977	+	0.166994i
$459$	9.16394	−	15.8724i	0.427736	−	0.740861i
$460$	2.50495	+	4.33870i	0.116794	+	0.202293i
$461$	2.05007	−	8.98192i	0.0954811	−	0.418330i	−0.904486	−	0.426504i	$-0.859745\pi$
$461$	2.05007	−	8.98192i	0.0954811	−	0.418330i	0.999967	+	0.00817444i	$0.00260203\pi$
$462$	2.43573	+	38.8738i	0.113320	+	1.80857i
$463$	−5.41009	−	23.7031i	−0.251428	−	1.10158i	−0.930149	−	0.367182i	$-0.880323\pi$
$463$	−5.41009	−	23.7031i	−0.251428	−	1.10158i	0.678721	−	0.734396i	$-0.262535\pi$
$464$	63.0353	−	58.4882i	2.92634	−	2.71525i
$465$	−15.5650	+	2.34605i	−0.721810	+	0.108795i
$466$	5.54072	−	0.835128i	0.256669	−	0.0386866i
$467$	−11.2313	+	10.4211i	−0.519722	+	0.482231i	−0.895863	−	0.444331i	$-0.853441\pi$
$467$	−11.2313	+	10.4211i	−0.519722	+	0.482231i	0.376141	+	0.926563i	$0.377251\pi$
$468$	−2.89048	−	12.6640i	−0.133613	−	0.585395i
$469$	23.6767	−	6.98750i	1.09329	−	0.322653i
$470$	−14.4913	+	63.4906i	−0.668434	+	2.92860i
$471$	−2.89521	−	5.01465i	−0.133404	−	0.231063i
$472$	32.1919	−	55.7580i	1.48175	−	2.56647i
$473$	−30.2381	−	28.0569i	−1.39035	−	1.29006i
$474$	−8.20488	−	5.59399i	−0.376863	−	0.256941i
$475$	0.598128	+	0.750029i	0.0274440	+	0.0344137i
$476$	−14.5117	+	60.1793i	−0.665143	+	2.75831i
$477$	0.213998	−	0.268345i	0.00979831	−	0.0122867i
$478$	10.5233	−	3.24600i	0.481324	−	0.148469i
$479$	−9.13767	−	23.2824i	−0.417511	−	1.06380i	−0.972698	−	0.232074i	$-0.925449\pi$
$479$	−9.13767	−	23.2824i	−0.417511	−	1.06380i	0.555187	−	0.831725i	$-0.312647\pi$
$480$	−3.83165	+	51.1298i	−0.174890	+	2.33375i
$481$	−0.967533	+	2.46523i	−0.0441157	+	0.112405i
$482$	−3.82405	−	1.84156i	−0.174181	−	0.0838810i
$483$	−0.641024	+	0.425658i	−0.0291676	+	0.0193681i
$484$	−156.783	+	75.5026i	−7.12649	+	3.43194i
$485$	−1.00472	−	13.4071i	−0.0456220	−	0.608784i
$486$	−41.8963	−	12.9233i	−1.90046	−	0.586213i
$487$	8.51120	−	5.80284i	0.385679	−	0.262952i	−0.354923	−	0.934896i	$-0.615493\pi$
$487$	8.51120	−	5.80284i	0.385679	−	0.262952i	0.740602	+	0.671944i	$0.234540\pi$
$488$	7.77750	+	1.17227i	0.352071	+	0.0530661i
$489$	−16.1321			−0.729521
$490$	−48.8904	−	1.19554i	−2.20864	−	0.0540092i
$491$	17.6737			0.797603			0.398802	−	0.917037i	$-0.369426\pi$
$491$	17.6737			0.797603			0.398802	+	0.917037i	$0.369426\pi$
$492$	−38.3019	−	5.77309i	−1.72678	−	0.260271i
$493$	−18.4569	+	12.5837i	−0.831257	+	0.566741i
$494$	1.76929	+	0.545753i	0.0796040	+	0.0245546i
$495$	2.85508	+	38.0985i	0.128326	+	1.71240i
$496$	−109.404	+	52.6864i	−4.91240	+	2.36569i
$497$	15.6879	−	26.4210i	0.703698	−	1.18514i
$498$	28.0440	+	13.5053i	1.25668	+	0.605187i
$499$	−4.99574	+	12.7289i	−0.223640	+	0.569825i	−0.998020	−	0.0628954i	$-0.979967\pi$
$499$	−4.99574	+	12.7289i	−0.223640	+	0.569825i	0.774380	+	0.632721i	$0.218062\pi$
$500$	−3.78584	+	50.5185i	−0.169308	+	2.25925i
$501$	−1.06416	−	2.71143i	−0.0475430	−	0.121138i
$502$	27.4586	−	8.46985i	1.22554	−	0.378028i
$503$	−14.4005	+	18.0577i	−0.642087	+	0.805151i	−0.991262	−	0.131906i	$-0.957890\pi$
$503$	−14.4005	+	18.0577i	−0.642087	+	0.805151i	0.349176	+	0.937057i	$0.386462\pi$
$504$	60.8391	+	0.743755i	2.70999	+	0.0331295i
$505$	−4.35930	−	5.46639i	−0.193986	−	0.243251i
$506$	−5.21944	−	3.55856i	−0.232033	−	0.158197i
$507$	−0.603502	−	0.559968i	−0.0268025	−	0.0248690i
$508$	−13.7962	+	23.8958i	−0.612109	+	1.06020i
$509$	−20.4830	−	35.4776i	−0.907893	−	1.57252i	−0.816986	−	0.576658i	$-0.804357\pi$
$509$	−20.4830	−	35.4776i	−0.907893	−	1.57252i	−0.0909075	−	0.995859i	$-0.528977\pi$
$510$	5.35360	−	23.4556i	0.237061	−	1.03863i
$511$	27.0318	+	18.9181i	1.19581	+	0.836887i
$512$	17.0520	+	74.7098i	0.753600	+	3.30174i
$513$	2.15815	−	2.00247i	0.0952844	−	0.0884110i
$514$	67.8416	−	10.2255i	2.99236	−	0.451026i
$515$	9.83807	−	1.48285i	0.433517	−	0.0653422i
$516$	21.4588	−	19.9108i	0.944669	−	0.876525i
$517$	−13.4599	−	58.9717i	−0.591966	−	2.59357i
$518$	−15.8190	−	11.0709i	−0.695049	−	0.486427i
$519$	2.20988	−	9.68213i	0.0970031	−	0.424998i
$520$	−12.5534	−	21.7432i	−0.550504	−	0.953501i
$521$	3.15057	−	5.45695i	0.138029	−	0.239073i	−0.788721	−	0.614751i	$-0.789257\pi$
$521$	3.15057	−	5.45695i	0.138029	−	0.239073i	0.926750	+	0.375677i	$0.122590\pi$
$522$	25.0520	+	23.2448i	1.09649	+	1.01740i
$523$	−12.5529	−	8.55843i	−0.548901	−	0.374234i	0.256885	−	0.966442i	$-0.417304\pi$
$523$	−12.5529	−	8.55843i	−0.548901	−	0.374234i	−0.805785	+	0.592208i	$0.798256\pi$
$524$	33.2803	+	41.7322i	1.45386	+	1.82308i
$525$	3.10968	+	0.0380158i	0.135718	+	0.00165914i
$526$	16.5783	−	20.7886i	0.722850	−	0.906425i
$527$	30.1434	−	9.29801i	1.31307	−	0.405028i
$528$	−31.4271	−	80.0748i	−1.36769	−	3.48481i
$529$	−1.70947	+	22.8112i	−0.0743246	+	0.991793i
$530$	0.377252	−	0.961222i	0.0163868	−	0.0417528i
$531$	13.6028	+	6.55076i	0.590311	+	0.284279i
$532$	−5.07682	+	8.55020i	−0.220108	+	0.370698i
$533$	7.57825	−	3.64949i	0.328250	−	0.158077i
$534$	0.428854	+	5.72266i	0.0185583	+	0.247644i
$535$	10.5415	+	3.25163i	0.455750	+	0.140580i
$536$	−76.3439	+	52.0504i	−3.29755	+	2.24823i
$537$	15.4818	+	2.33351i	0.668089	+	0.100698i
$538$	44.4775			1.91756
$539$	41.3954	−	18.7025i	1.78303	−	0.805573i
$540$	−62.1388			−2.67403
$541$	−2.23946	−	0.337544i	−0.0962819	−	0.0145122i	0.100725	−	0.994914i	$-0.467884\pi$
$541$	−2.23946	−	0.337544i	−0.0962819	−	0.0145122i	−0.197006	+	0.980402i	$0.563122\pi$
$542$	35.7170	−	24.3515i	1.53418	−	1.04598i
$543$	−2.79858	−	0.863248i	−0.120099	−	0.0370455i
$544$	−7.67870	−	102.465i	−0.329221	−	4.39315i
$545$	16.7983	−	8.08965i	0.719561	−	0.346522i
$546$	5.00030	−	3.32035i	0.213993	−	0.142098i
$547$	17.3551	+	8.35779i	0.742052	+	0.357353i	0.766411	−	0.642350i	$-0.222040\pi$
$547$	17.3551	+	8.35779i	0.742052	+	0.357353i	−0.0243598	+	0.999703i	$0.507755\pi$
$548$	−12.7882	+	32.5837i	−0.546284	+	1.39191i
$549$	−0.137834	+	1.83926i	−0.00588259	+	0.0784977i
$550$	9.32760	+	23.7663i	0.397730	+	1.01340i
$551$	−3.42887	+	1.05767i	−0.146075	+	0.0450581i
$552$	1.79572	−	2.25176i	0.0764310	−	0.0958414i
$553$	−2.71484	+	11.2583i	−0.115447	+	0.478752i
$554$	45.8939	+	57.5492i	1.94985	+	2.44503i
$555$	4.56717	+	3.11384i	0.193865	+	0.132175i
$556$	−5.74394	−	5.32960i	−0.243597	−	0.226025i
$557$	6.52994	−	11.3102i	0.276682	−	0.479228i	−0.693876	−	0.720095i	$-0.744098\pi$
$557$	6.52994	−	11.3102i	0.276682	−	0.479228i	0.970558	+	0.240867i	$0.0774317\pi$
$558$	−24.1297	−	41.7939i	−1.02149	−	1.76928i
$559$	−1.41449	+	6.19730i	−0.0598267	+	0.262118i
$560$	103.590	−	30.5715i	4.37746	−	1.29188i
$561$	4.97256	+	21.7862i	0.209942	+	0.919814i
$562$	23.6644	−	21.9574i	0.998223	−	0.926216i
$563$	36.8269	−	5.55076i	1.55207	−	0.233937i	0.683666	−	0.729795i	$-0.260385\pi$
$563$	36.8269	−	5.55076i	1.55207	−	0.233937i	0.868403	+	0.495858i	$0.165146\pi$
$564$	42.4466	−	6.39780i	1.78732	−	0.269396i
$565$	−1.55527	+	1.44308i	−0.0654308	+	0.0607109i
$566$	−14.8961	−	65.2641i	−0.626130	−	2.74325i
$567$	0.555813	+	8.87068i	0.0233419	+	0.372534i
$568$	−25.5924	+	112.128i	−1.07383	+	4.70477i
$569$	−2.96020	−	5.12722i	−0.124098	−	0.214944i	0.797282	−	0.603607i	$-0.206270\pi$
$569$	−2.96020	−	5.12722i	−0.124098	−	0.214944i	−0.921380	+	0.388663i	$0.872937\pi$
$570$	1.93232	−	3.34687i	0.0809359	−	0.140185i
$571$	−24.2584	−	22.5086i	−1.01518	−	0.941954i	−0.0168623	−	0.999858i	$-0.505368\pi$
$571$	−24.2584	−	22.5086i	−1.01518	−	0.941954i	−0.998322	+	0.0579043i	$0.981558\pi$
$572$	29.9910	+	20.4475i	1.25399	+	0.854954i
$573$	7.34309	+	9.20794i	0.306762	+	0.384667i
$574$	12.9141	+	59.9492i	0.539025	+	2.50223i
$575$	−0.314477	+	0.394341i	−0.0131146	+	0.0164452i
$576$	−78.7527	+	24.2920i	−3.28136	+	1.01217i
$577$	−2.19757	−	5.59933i	−0.0914862	−	0.233103i	0.877805	−	0.479018i	$-0.159007\pi$
$577$	−2.19757	−	5.59933i	−0.0914862	−	0.233103i	−0.969292	+	0.245915i	$0.920912\pi$
$578$	−0.102241	+	1.36432i	−0.00425268	+	0.0567481i
$579$	−0.460197	+	1.17256i	−0.0191251	+	0.0487300i
$580$	68.2360	+	32.8607i	2.83334	+	1.36447i
$581$	3.15502	−	36.1629i	0.130892	−	1.50029i
$582$	−10.8392	+	5.21991i	−0.449301	+	0.216372i
$583$	0.0716742	+	0.956426i	0.00296844	+	0.0396111i
$584$	−118.008	−	36.4008i	−4.88322	−	1.50628i
$585$	4.86451	−	3.31657i	0.201123	−	0.137123i
$586$	−81.3831	−	12.2665i	−3.36190	−	0.506725i
$587$	−2.70414			−0.111612			−0.0558059	−	0.998442i	$-0.517773\pi$
$587$	−2.70414			−0.111612			−0.0558059	+	0.998442i	$0.517773\pi$
$588$	11.0400	+	30.2864i	0.455280	+	1.24899i
$589$	5.06713			0.208788
$590$	44.9150	+	6.76985i	1.84912	+	0.278710i
$591$	5.99597	−	4.08798i	0.246641	−	0.168157i
$592$	40.7477	+	12.5690i	1.67472	+	0.516582i
$593$	−1.37114	−	18.2966i	−0.0563059	−	0.751350i	−0.951887	−	0.306451i	$-0.900859\pi$
$593$	−1.37114	−	18.2966i	−0.0563059	−	0.751350i	0.895581	−	0.444899i	$-0.146760\pi$
$594$	70.5931	−	33.9958i	2.89647	−	1.39487i
$595$	−27.7935	+	3.84234i	−1.13942	+	0.157521i
$596$	−22.4034	−	10.7889i	−0.917678	−	0.441931i
$597$	4.37274	−	11.1416i	0.178964	−	0.455994i
$598$	−0.0727485	+	0.970762i	−0.00297491	+	0.0396974i
$599$	−15.3835	−	39.1964i	−0.628551	−	1.60152i	−0.788941	−	0.614469i	$-0.789370\pi$
$599$	−15.3835	−	39.1964i	−0.628551	−	1.60152i	0.160389	−	0.987054i	$-0.448725\pi$
$600$	−11.1231	+	3.43102i	−0.454099	+	0.140071i
$601$	−10.9447	+	13.7242i	−0.446443	+	0.559821i	−0.953228	−	0.302251i	$-0.902262\pi$
$601$	−10.9447	+	13.7242i	−0.446443	+	0.559821i	0.506786	+	0.862072i	$0.330833\pi$
$602$	−41.5067	−	20.6173i	−1.69168	−	0.840300i
$603$	−13.5095	−	16.9404i	−0.550150	−	0.689866i
$604$	−36.3549	−	24.7863i	−1.47926	−	1.00854i
$605$	−57.8172	−	53.6465i	−2.35060	−	2.18104i
$606$	−3.12822	+	5.41823i	−0.127075	+	0.220101i
$607$	−2.35803	−	4.08423i	−0.0957095	−	0.165774i	0.814195	−	0.580591i	$-0.197179\pi$
$607$	−2.35803	−	4.08423i	−0.0957095	−	0.165774i	−0.909904	+	0.414818i	$0.863845\pi$
$608$	3.67279	−	16.0916i	0.148951	−	0.652599i
$609$	−4.38185	+	10.7756i	−0.177562	+	0.436648i
$610$	1.23476	+	5.40983i	0.0499939	+	0.219038i
$611$	−6.83307	+	6.34016i	−0.276436	+	0.256496i
$612$	53.7275	−	8.09812i	2.17181	−	0.327347i
$613$	−7.85740	+	1.18431i	−0.317357	+	0.0478339i	−0.305789	−	0.952099i	$-0.598920\pi$
$613$	−7.85740	+	1.18431i	−0.317357	+	0.0478339i	−0.0115679	+	0.999933i	$0.503682\pi$
$614$	39.0017	−	36.1883i	1.57398	−	1.46044i
$615$	−3.90664	−	17.1161i	−0.157531	−	0.690188i
$616$	−126.038	+	114.111i	−5.07822	+	4.59767i
$617$	−1.28951	+	5.64969i	−0.0519135	+	0.227448i	−0.994229	−	0.107278i	$-0.965787\pi$
$617$	−1.28951	+	5.64969i	−0.0519135	+	0.227448i	0.942316	+	0.334726i	$0.108644\pi$
$618$	−4.45141	−	7.71006i	−0.179062	−	0.310144i
$619$	7.39318	−	12.8054i	0.297157	−	0.514691i	−0.678327	−	0.734760i	$-0.737295\pi$
$619$	7.39318	−	12.8054i	0.297157	−	0.514691i	0.975484	+	0.220069i	$0.0706282\pi$
$620$	−78.3996	−	72.7442i	−3.14860	−	2.92148i
$621$	1.27893	+	0.871958i	0.0513216	+	0.0349905i
$622$	44.2813	+	55.5270i	1.77552	+	2.22643i
$623$	6.06485	−	2.82988i	0.242983	−	0.113377i
$624$	−8.26504	+	10.3640i	−0.330866	+	0.414893i
$625$	−28.7630	+	8.87222i	−1.15052	+	0.354889i
$626$	18.9652	+	48.3226i	0.758002	+	1.93136i
$627$	−0.268249	+	3.57954i	−0.0107128	+	0.142953i
$628$	14.3734	−	36.6229i	0.573562	−	1.46141i
$629$	−9.98051	−	4.80636i	−0.397949	−	0.191642i
$630$	15.1926	+	40.1463i	0.605286	+	1.59947i
$631$	6.62749	−	3.19163i	0.263836	−	0.127057i	−0.297290	−	0.954787i	$-0.596083\pi$
$631$	6.62749	−	3.19163i	0.263836	−	0.127057i	0.561126	+	0.827731i	$0.310368\pi$
$632$	−3.23933	−	43.2258i	−0.128854	−	1.71943i
$633$	5.51677	+	1.70170i	0.219272	+	0.0676364i
$634$	−69.1662	+	47.1567i	−2.74694	+	1.87283i
$635$	−12.3665	−	1.86395i	−0.490749	−	0.0739685i
$636$	−0.680640			−0.0269891
$637$	−5.68555	−	4.08345i	−0.225270	−	0.161792i
$638$	−95.4977			−3.78079
$639$	−26.6688	−	4.01967i	−1.05500	−	0.159016i
$640$	−101.945	+	69.5050i	−4.02973	+	2.74743i
$641$	8.32061	+	2.56657i	0.328644	+	0.101373i	0.454687	−	0.890651i	$-0.349751\pi$
$641$	8.32061	+	2.56657i	0.328644	+	0.101373i	−0.126042	+	0.992025i	$0.540227\pi$
$642$	−0.737692	−	9.84382i	−0.0291144	−	0.388505i
$643$	−16.6158	+	8.00174i	−0.655263	+	0.315558i	−0.731811	−	0.681508i	$-0.761324\pi$
$643$	−16.6158	+	8.00174i	−0.655263	+	0.315558i	0.0765478	+	0.997066i	$0.475610\pi$
$644$	−4.97667	−	1.60198i	−0.196108	−	0.0631268i
$645$	11.9540	+	5.75675i	0.470689	+	0.226672i
$646$	−2.82949	+	7.20943i	−0.111325	+	0.283651i
$647$	−0.861864	+	11.5008i	−0.0338834	+	0.452142i	0.954298	+	0.298855i	$0.0966048\pi$
$647$	−0.861864	+	11.5008i	−0.0338834	+	0.452142i	−0.988182	+	0.153287i	$0.951014\pi$
$648$	−12.1540	−	30.9679i	−0.477454	−	1.21653i
$649$	−40.3151	+	12.4356i	−1.58251	+	0.488139i
$650$	2.45307	−	3.07606i	0.0962175	−	0.120653i
$651$	10.3980	−	12.7166i	0.407530	−	0.498404i
$652$	−68.3398	−	85.6954i	−2.67639	−	3.35609i
$653$	−36.7456	−	25.0528i	−1.43797	−	0.980390i	−0.996542	−	0.0830924i	$-0.973520\pi$
$653$	−36.7456	−	25.0528i	−1.43797	−	0.980390i	−0.441426	−	0.897298i	$-0.645527\pi$
$654$	−12.2301	−	11.3479i	−0.478235	−	0.443737i
$655$	−12.0966	+	20.9519i	−0.472652	+	0.818657i
$656$	−67.7174	−	117.290i	−2.64392	−	4.57941i
$657$	6.44409	−	28.2334i	0.251408	−	1.10149i
$658$	−33.2582	−	59.2664i	−1.29654	−	2.31044i
$659$	5.60280	+	24.5475i	0.218254	+	0.956233i	0.958767	+	0.284192i	$0.0917252\pi$
$659$	5.60280	+	24.5475i	0.218254	+	0.956233i	−0.740514	+	0.672041i	$0.765418\pi$
$660$	55.5385	−	51.5322i	2.16183	−	2.00589i
$661$	3.21869	−	0.485140i	0.125193	−	0.0188697i	−0.0861470	−	0.996282i	$-0.527455\pi$
$661$	3.21869	−	0.485140i	0.125193	−	0.0188697i	0.211340	+	0.977413i	$0.432217\pi$
$662$	58.5260	−	8.82138i	2.27468	−	0.342853i
$663$	2.52438	−	2.34228i	0.0980386	−	0.0909666i
$664$	30.2339	+	132.463i	1.17330	+	5.14058i
$665$	−4.44812	−	0.726162i	−0.172491	−	0.0281594i
$666$	−3.77109	+	16.5222i	−0.146127	+	0.640224i
$667$	−0.943303	−	1.63385i	−0.0365248	−	0.0632628i
$668$	9.89531	−	17.1392i	0.382861	−	0.663134i
$669$	−14.7541	−	13.6898i	−0.570428	−	0.529280i
$670$	−53.8601	−	36.7212i	−2.08080	−	1.41866i
$671$	−3.21347	−	4.02957i	−0.124055	−	0.155560i
$672$	−32.8471	−	42.2380i	−1.26711	−	1.62937i
$673$	−22.0825	+	27.6905i	−0.851216	+	1.06739i	0.145732	+	0.989324i	$0.453446\pi$
$673$	−22.0825	+	27.6905i	−0.851216	+	1.06739i	−0.996948	+	0.0780670i	$0.975125\pi$
$674$	−94.3623	+	29.1069i	−3.63470	+	1.12116i
$675$	−2.28555	−	5.82349i	−0.0879709	−	0.224146i
$676$	0.418015	−	5.57802i	0.0160775	−	0.214539i
$677$	2.84565	−	7.25059i	0.109367	−	0.278663i	−0.865704	−	0.500557i	$-0.833129\pi$
$677$	2.84565	−	7.25059i	0.109367	−	0.278663i	0.975071	+	0.221894i	$0.0712239\pi$
$678$	1.71049	+	0.823729i	0.0656910	+	0.0316351i
$679$	10.1676	+	9.66808i	0.390195	+	0.371027i
$680$	94.6188	−	45.5660i	3.62846	−	1.74738i
$681$	−0.965193	−	12.8796i	−0.0369863	−	0.493548i
$682$	128.864	+	39.7494i	4.93447	+	1.52208i
$683$	−22.6400	+	15.4357i	−0.866294	+	0.590629i	−0.912854	−	0.408286i	$-0.866126\pi$
$683$	−22.6400	+	15.4357i	−0.866294	+	0.590629i	0.0465601	+	0.998915i	$0.485174\pi$
$684$	8.63039	+	1.30082i	0.329991	+	0.0497382i
$685$	−15.8651			−0.606176
$686$	38.6593	−	33.3179i	1.47602	−	1.27208i
$687$	1.56976			0.0598899
$688$	101.210	+	15.2550i	3.85860	+	0.581590i
$689$	0.122119	−	0.0832593i	0.00465236	−	0.00317193i
$690$	1.94163	+	0.598913i	0.0739166	+	0.0228002i
$691$	−0.774971	−	10.3413i	−0.0294813	−	0.393400i	−0.992352	−	0.123438i	$-0.960608\pi$
$691$	−0.774971	−	10.3413i	−0.0294813	−	0.393400i	0.962871	−	0.269962i	$-0.0870111\pi$
$692$	60.7939	−	29.2768i	2.31104	−	1.11294i
$693$	−28.8928	−	27.4735i	−1.09755	−	1.04363i
$694$	−46.0116	−	22.1580i	−1.74658	−	0.841106i
$695$	1.29750	−	3.30598i	0.0492170	−	0.125403i
$696$	3.25371	−	43.4178i	0.123332	−	1.64575i
$697$	12.8538	+	32.7510i	0.486874	+	1.24053i
$698$	−85.5481	+	26.3881i	−3.23804	+	0.998804i
$699$	1.04374	−	1.30881i	0.0394778	−	0.0495036i
$700$	12.9715	+	16.6800i	0.490275	+	0.630443i
$701$	2.97189	+	3.72663i	0.112247	+	0.140753i	0.834781	−	0.550582i	$-0.185594\pi$
$701$	2.97189	+	3.72663i	0.112247	+	0.140753i	−0.722534	+	0.691335i	$0.757023\pi$
$702$	−9.97626	−	6.80170i	−0.376530	−	0.256714i
$703$	−1.30440	−	1.21031i	−0.0491964	−	0.0456476i
$704$	115.148	−	199.443i	4.33982	−	7.51679i
$705$	9.72803	+	16.8494i	0.366379	+	0.634587i
$706$	−1.73296	+	7.59261i	−0.0652210	+	0.285752i
$707$	7.20104	+	1.17558i	0.270823	+	0.0442123i
$708$	−6.66231	−	29.1895i	−0.250385	−	1.09701i
$709$	−14.2651	+	13.2360i	−0.535735	+	0.497090i	−0.901003	−	0.433813i	$-0.857168\pi$
$709$	−14.2651	+	13.2360i	−0.535735	+	0.497090i	0.365268	+	0.930903i	$0.380977\pi$
$710$	−80.2334	+	12.0932i	−3.01111	+	0.453851i
$711$	10.0513	−	1.51499i	0.376954	−	0.0568166i
$712$	−18.3629	+	17.0383i	−0.688179	+	0.638537i
$713$	0.592826	+	2.59734i	0.0222015	+	0.0972712i
$714$	12.2867	+	21.8951i	0.459820	+	0.819403i
$715$	−3.66092	+	16.0396i	−0.136911	+	0.599845i
$716$	53.1889	+	92.1259i	1.98776	+	3.44291i
$717$	1.64504	−	2.84929i	0.0614351	−	0.106409i
$718$	18.0527	+	16.7504i	0.673719	+	0.625120i
$719$	25.9770	+	17.7108i	0.968778	+	0.660501i	0.940748	−	0.339106i	$-0.110124\pi$
$719$	25.9770	+	17.7108i	0.968778	+	0.660501i	0.0280294	+	0.999607i	$0.491077\pi$
$720$	−59.1064	−	74.1171i	−2.20277	−	2.76218i
$721$	−6.57220	+	8.03772i	−0.244762	+	0.299340i
$722$	31.8687	−	39.9621i	1.18603	−	1.48724i
$723$	−1.21170	+	0.373760i	−0.0450637	+	0.0139003i
$724$	−7.26984	−	18.5232i	−0.270181	−	0.688411i
$725$	−0.569809	+	7.60357i	−0.0211622	+	0.282389i
$726$	−25.7846	+	65.6981i	−0.956956	+	2.43828i
$727$	−32.2954	−	15.5527i	−1.19777	−	0.576816i	−0.274731	−	0.961521i	$-0.588589\pi$
$727$	−32.2954	−	15.5527i	−1.19777	−	0.576816i	−0.923040	+	0.384705i	$0.874303\pi$
$728$	24.9403	+	8.02823i	0.924349	+	0.297546i
$729$	−2.72151	+	1.31061i	−0.100797	+	0.0485411i
$730$	−6.51085	−	86.8813i	−0.240978	−	3.21562i
$731$	−25.4079	−	7.83731i	−0.939746	−	0.289873i
$732$	3.02205	−	2.06040i	0.111698	−	0.0761544i
$733$	−32.8487	−	4.95115i	−1.21329	−	0.182875i	−0.488949	−	0.872312i	$-0.662620\pi$
$733$	−32.8487	−	4.95115i	−1.21329	−	0.182875i	−0.724345	+	0.689437i	$0.757858\pi$
$734$	−3.39824			−0.125431
$735$	−10.9502	+	9.67302i	−0.403903	+	0.356795i
$736$	8.67800			0.319875
$737$	59.8713	+	9.02414i	2.20539	+	0.332408i
$738$	44.4727	−	30.3210i	1.63706	−	1.11613i
$739$	8.79171	+	2.71188i	0.323408	+	0.0997583i	0.452208	−	0.891912i	$-0.350636\pi$
$739$	8.79171	+	2.71188i	0.323408	+	0.0997583i	−0.128800	+	0.991671i	$0.541113\pi$
$740$	2.80665	+	37.4522i	0.103175	+	1.37677i
$741$	0.498382	−	0.240008i	0.0183085	−	0.00881693i
$742$	0.381395	+	1.00783i	0.0140015	+	0.0369988i
$743$	−8.87458	−	4.27377i	−0.325577	−	0.156789i	0.263954	−	0.964535i	$-0.414973\pi$
$743$	−8.87458	−	4.27377i	−0.325577	−	0.156789i	−0.589531	+	0.807746i	$0.700687\pi$
$744$	−22.4625	+	57.2335i	−0.823515	+	2.09828i
$745$	0.842235	−	11.2388i	0.0308571	−	0.411759i
$746$	15.5143	+	39.5298i	0.568019	+	1.44729i
$747$	−30.4459	+	9.39131i	−1.11396	+	0.343610i
$748$	−94.6652	+	118.706i	−3.46130	+	4.34034i
$749$	−10.4324	+	4.86781i	−0.381193	+	0.177866i
$750$	12.8106	+	16.0640i	0.467776	+	0.586573i
$751$	−24.1445	−	16.4614i	−0.881045	−	0.600686i	0.0360522	−	0.999350i	$-0.488522\pi$
$751$	−24.1445	−	16.4614i	−0.881045	−	0.600686i	−0.917097	+	0.398664i	$0.869474\pi$
$752$	110.024	+	102.087i	4.01216	+	3.72274i
$753$	4.29243	−	7.43470i	0.156425	−	0.270936i
$754$	7.35823	+	12.7448i	0.267971	+	0.464139i
$755$	4.43774	−	19.4430i	0.161506	−	0.707604i
$756$	48.0709	−	43.5220i	1.74832	−	1.58288i
$757$	−6.49507	−	28.4568i	−0.236067	−	1.03428i	−0.944503	−	0.328503i	$-0.893456\pi$
$757$	−6.49507	−	28.4568i	−0.236067	−	1.03428i	0.708436	−	0.705775i	$-0.249401\pi$
$758$	−17.0397	+	15.8105i	−0.618909	+	0.574264i
$759$	−1.86620	+	0.281285i	−0.0677389	+	0.0102100i
$760$	16.6810	−	2.51426i	0.605085	−	0.0912019i
$761$	−15.4210	+	14.3086i	−0.559010	+	0.518686i	−0.908295	−	0.418331i	$-0.862615\pi$
$761$	−15.4210	+	14.3086i	−0.559010	+	0.518686i	0.349284	+	0.937017i	$0.386425\pi$
$762$	2.49020	+	10.9103i	0.0902106	+	0.395238i
$763$	−7.32930	+	18.0237i	−0.265339	+	0.652503i
$764$	−17.8062	+	78.0143i	−0.644207	+	2.82246i
$765$	12.3134	+	21.3275i	0.445193	+	0.771097i
$766$	8.45585	−	14.6460i	0.305522	−	0.529180i
$767$	4.76595	+	4.42215i	0.172088	+	0.159675i
$768$	42.9422	+	29.2775i	1.54954	+	1.05646i
$769$	−15.6371	−	19.6083i	−0.563889	−	0.707095i	0.415382	−	0.909647i	$-0.363648\pi$
$769$	−15.6371	−	19.6083i	−0.563889	−	0.707095i	−0.979271	+	0.202552i	$0.935076\pi$
$770$	−107.425	−	53.3608i	−3.87135	−	1.92299i
$771$	12.7797	−	16.0253i	0.460251	−	0.577136i
$772$	−8.17826	+	2.52266i	−0.294342	+	0.0907925i
$773$	12.2973	+	31.3330i	0.442303	+	1.12697i	0.962104	+	0.272682i	$0.0879108\pi$
$773$	12.2973	+	31.3330i	0.442303	+	1.12697i	−0.519801	+	0.854287i	$0.673994\pi$
$774$	−3.03987	+	40.5642i	−0.109266	+	1.45805i
$775$	3.93376	−	10.0231i	0.141305	−	0.360039i
$776$	−47.3143	−	22.7853i	−1.69848	−	0.817946i
$777$	−5.71412	+	0.789955i	−0.204993	+	0.0283395i
$778$	25.5847	−	12.3209i	0.917254	−	0.441726i
$779$	0.422341	+	5.63575i	0.0151319	+	0.201922i
$780$	−11.1566	−	3.44137i	−0.399472	−	0.123221i
$781$	62.2692	−	42.4544i	2.22817	−	1.51914i
$782$	−4.02649	−	0.606895i	−0.143987	−	0.0217025i
$783$	23.3999			0.836245
$784$	−58.7253	+	96.2045i	−2.09733	+	3.43587i
$785$	17.8318			0.636445
$786$	21.4069	+	3.22657i	0.763558	+	0.115088i
$787$	−41.4578	+	28.2655i	−1.47781	+	1.00756i	−0.486840	+	0.873491i	$0.661851\pi$
$787$	−41.4578	+	28.2655i	−1.47781	+	1.00756i	−0.990973	+	0.134064i	$0.957197\pi$
$788$	47.1161	+	14.5334i	1.67844	+	0.517731i
$789$	−0.593643	−	7.92162i	−0.0211343	−	0.282017i
$790$	27.5526	−	13.2686i	0.980277	−	0.472077i
$791$	0.192434	−	2.20569i	0.00684217	−	0.0784253i
$792$	134.451	+	64.7484i	4.77752	+	2.30073i
$793$	−0.290171	+	0.739344i	−0.0103043	+	0.0262549i
$794$	−1.48542	+	19.8215i	−0.0527155	+	0.703440i
$795$	−0.112707	−	0.287172i	−0.00399729	−	0.0101849i
$796$	77.7089	−	23.9700i	2.75432	−	0.849595i
$797$	3.68988	−	4.62697i	0.130702	−	0.163896i	−0.712174	−	0.702003i	$-0.752289\pi$
$797$	3.68988	−	4.62697i	0.130702	−	0.163896i	0.842876	+	0.538108i	$0.180861\pi$
$798$	0.849295	+	3.94255i	0.0300647	+	0.139565i
$799$	−24.3101	−	30.4838i	−0.860028	−	1.07844i
$800$	−28.9786	−	19.7573i	−1.02455	−	0.698526i
$801$	−4.30609	−	3.99547i	−0.152148	−	0.141173i
$802$	−29.1163	+	50.4309i	−1.02813	+	1.78078i
$803$	40.4620	+	70.0822i	1.42787	+	2.47315i
$804$	−9.56131	+	41.8908i	−0.337201	+	1.47738i
$805$	−0.148185	−	2.36500i	−0.00522282	−	0.0833553i
$806$	−4.62434	−	20.2606i	−0.162885	−	0.713648i
$807$	9.74076	−	9.03811i	0.342891	−	0.318156i
$808$	−27.0049	+	4.07033i	−0.950028	+	0.143194i
$809$	1.09754	−	0.165427i	0.0385873	−	0.00581610i	−0.129720	−	0.991551i	$-0.541408\pi$
$809$	1.09754	−	0.165427i	0.0385873	−	0.00581610i	0.168308	+	0.985735i	$0.446170\pi$
$810$	17.2048	−	15.9637i	0.604514	−	0.560907i
$811$	−7.16599	−	31.3963i	−0.251632	−	1.10247i	−0.929945	−	0.367699i	$-0.880146\pi$
$811$	−7.16599	−	31.3963i	−0.251632	−	1.10247i	0.678313	−	0.734773i	$-0.262711\pi$
$812$	−75.8034	+	22.3712i	−2.66018	+	0.785075i
$813$	2.87382	−	12.5910i	0.100789	−	0.441586i
$814$	−23.6784	−	41.0122i	−0.829928	−	1.43748i
$815$	24.8398	−	43.0238i	0.870101	−	1.50706i
$816$	−40.6467	−	37.7146i	−1.42292	−	1.32028i
$817$	−3.52894	−	2.40599i	−0.123462	−	0.0841751i
$818$	−14.5688	−	18.2687i	−0.509387	−	0.638751i
$819$	−1.44029	+	5.97282i	−0.0503279	+	0.208707i
$820$	74.3728	−	93.2605i	2.59721	−	3.25680i
$821$	25.2335	−	7.78349i	0.880654	−	0.271646i	0.178730	−	0.983898i	$-0.442801\pi$
$821$	25.2335	−	7.78349i	0.880654	−	0.271646i	0.701923	+	0.712252i	$0.252325\pi$
$822$	5.18659	+	13.2152i	0.180903	+	0.460934i
$823$	−0.229821	+	3.06675i	−0.00801107	+	0.106900i	−0.999776	−	0.0211725i	$-0.993260\pi$
$823$	−0.229821	+	3.06675i	−0.00801107	+	0.106900i	0.991765	+	0.128073i	$0.0408791\pi$
$824$	14.1977	−	36.1752i	0.494601	−	1.26022i
$825$	6.87226	+	3.30950i	0.239261	+	0.115222i
$826$	−39.4882	+	26.2213i	−1.37397	+	0.912355i
$827$	26.3185	−	12.6743i	0.915183	−	0.440729i	0.0838341	−	0.996480i	$-0.473283\pi$
$827$	26.3185	−	12.6743i	0.915183	−	0.440729i	0.831349	+	0.555751i	$0.187569\pi$
$828$	0.342924	+	4.57601i	0.0119174	+	0.159027i
$829$	−27.3355	−	8.43187i	−0.949400	−	0.292851i	−0.218887	−	0.975750i	$-0.570243\pi$
$829$	−27.3355	−	8.43187i	−0.949400	−	0.292851i	−0.730513	+	0.682899i	$0.760719\pi$
$830$	−79.1995	+	53.9973i	−2.74905	+	1.87427i
$831$	21.7454	+	3.27758i	0.754338	+	0.113698i
$832$	−35.4893			−1.23037
$833$	18.8101	−	22.4390i	0.651730	−	0.777466i
$834$	−3.17796			−0.110044
$835$	8.86983	+	1.33691i	0.306953	+	0.0462657i
$836$	−20.1512	+	13.7388i	−0.696943	+	0.475168i
$837$	−31.5758	−	9.73983i	−1.09142	−	0.336658i
$838$	6.56109	+	87.5517i	0.226649	+	3.02442i
$839$	23.0822	−	11.1158i	0.796887	−	0.383761i	0.00929451	−	0.999957i	$-0.497041\pi$
$839$	23.0822	−	11.1158i	0.796887	−	0.383761i	0.787593	+	0.616196i	$0.211327\pi$
$840$	27.9205	−	47.0227i	0.963347	−	1.62244i
$841$	0.432113	+	0.208095i	0.0149005	+	0.00717568i
$842$	9.38015	−	23.9002i	0.323261	−	0.823656i
$843$	0.720734	−	9.61753i	0.0248234	−	0.331245i
$844$	14.3308	+	36.5144i	0.493288	+	1.25688i
$845$	2.42267	−	0.747294i	0.0833423	−	0.0257077i
$846$	−37.1912	+	46.6362i	−1.27866	+	1.60339i
$847$	82.3018	+	1.00614i	2.82792	+	0.0345712i
$848$	−1.48381	−	1.86064i	−0.0509542	−	0.0638946i
$849$	−16.5244	−	11.2661i	−0.567116	−	0.386653i
$850$	12.0640	+	11.1938i	0.413792	+	0.383943i
$851$	0.467779	−	0.810217i	0.0160353	−	0.0277739i
$852$	26.7416	+	46.3178i	0.916153	+	1.58682i
$853$	−0.00132122	+	0.00578862i	−4.52376e−5	+	0.000198199i	−0.974951	−	0.222422i	$-0.928604\pi$
$853$	−0.00132122	+	0.00578862i	−4.52376e−5	+	0.000198199i	0.974905	+	0.222620i	$0.0714609\pi$
$854$	−4.74426	−	3.32025i	−0.162345	−	0.113617i
$855$	0.880265	+	3.85669i	0.0301044	+	0.131896i
$856$	31.5869	−	29.3084i	1.07962	−	1.00174i
$857$	6.30374	−	0.950136i	0.215332	−	0.0324560i	−0.0404904	−	0.999180i	$-0.512892\pi$
$857$	6.30374	−	0.950136i	0.215332	−	0.0324560i	0.255822	+	0.966724i	$0.417654\pi$
$858$	14.5573	−	2.19416i	0.496979	−	0.0749075i
$859$	6.53794	−	6.06632i	0.223072	−	0.206980i	−0.560718	−	0.828007i	$-0.689475\pi$
$859$	6.53794	−	6.06632i	0.223072	−	0.206980i	0.783789	+	0.621027i	$0.213284\pi$
$860$	20.0598	+	87.8878i	0.684034	+	2.99695i
$861$	15.0103	+	10.5049i	0.511550	+	0.358007i
$862$	17.7612	−	77.8167i	0.604947	−	2.65045i
$863$	14.7469	+	25.5424i	0.501991	+	0.869474i	0.999997	+	0.00230048i	$0.000732265\pi$
$863$	14.7469	+	25.5424i	0.501991	+	0.869474i	−0.498006	+	0.867173i	$0.665934\pi$
$864$	−53.8175	+	93.2146i	−1.83091	+	3.17123i
$865$	22.4191	+	20.8019i	0.762274	+	0.707287i
$866$	28.7250	+	19.5843i	0.976114	+	0.665503i
$867$	0.254847	+	0.319568i	0.00865505	+	0.0108531i
$868$	111.600	+	1.36431i	3.78796	+	0.0463077i
$869$	−17.7099	+	22.2075i	−0.600768	+	0.753339i
$870$	29.3522	−	9.05396i	0.995133	−	0.306958i
$871$	−3.40883	−	8.68555i	−0.115504	−	0.294299i
$872$	5.44232	−	72.6227i	0.184300	−	2.45932i
$873$	4.49906	−	11.4634i	0.152270	−	0.387978i
$874$	−0.589315	−	0.283799i	−0.0199339	−	0.00959965i
$875$	12.2337	−	20.6035i	0.413573	−	0.696526i
$876$	−51.7412	+	24.9173i	−1.74817	+	0.841876i
$877$	1.49793	+	19.9885i	0.0505816	+	0.674965i	0.963652	+	0.267162i	$0.0860859\pi$
$877$	1.49793	+	19.9885i	0.0505816	+	0.674965i	−0.913070	+	0.407803i	$0.866295\pi$
$878$	52.8843	+	16.3127i	1.78476	+	0.550525i
$879$	−20.3159	+	13.8511i	−0.685238	+	0.467187i
$880$	261.947	+	39.4821i	8.83023	+	1.33094i
$881$	15.1843			0.511571			0.255786	−	0.966734i	$-0.417666\pi$
$881$	15.1843			0.511571			0.255786	+	0.966734i	$0.417666\pi$
$882$	−39.8715	−	20.4165i	−1.34254	−	0.687460i
$883$	−37.6084			−1.26562			−0.632812	−	0.774305i	$-0.718099\pi$
$883$	−37.6084			−1.26562			−0.632812	+	0.774305i	$0.718099\pi$
$884$	23.1363	+	3.48723i	0.778157	+	0.117288i
$885$	11.2123	−	7.64440i	0.376896	−	0.256964i
$886$	−93.7198	−	28.9087i	−3.14858	−	0.971208i
$887$	0.720269	+	9.61132i	0.0241843	+	0.322716i	0.996155	+	0.0876130i	$0.0279239\pi$
$887$	0.720269	+	9.61132i	0.0241843	+	0.322716i	−0.971970	+	0.235104i	$0.924457\pi$
$888$	19.4529	−	9.36800i	0.652795	−	0.314370i
$889$	10.8723	−	7.21952i	0.364645	−	0.242135i
$890$	−15.9225	−	7.66785i	−0.533722	−	0.257027i
$891$	−7.96429	+	20.2927i	−0.266814	+	0.679830i
$892$	10.2194	−	136.369i	0.342172	−	4.56597i
$893$	−2.28817	−	5.83017i	−0.0765708	−	0.195099i
$894$	−9.63698	+	2.97262i	−0.322309	+	0.0994191i
$895$	−30.0618	+	37.6963i	−1.00485	+	1.26005i
$896$	30.1841	−	125.172i	1.00838	−	4.18170i
$897$	0.181333	+	0.227384i	0.00605453	+	0.00759214i
$898$	2.16814	+	1.47821i	0.0723518	+	0.0493286i
$899$	29.5234	+	27.3937i	0.984659	+	0.913630i
$900$	9.27311	−	16.0615i	0.309104	−	0.535383i
$901$	0.309117	+	0.535406i	0.0102982	+	0.0178370i
$902$	−33.4692	+	146.638i	−1.11440	+	4.88251i
$903$	−13.2797	+	3.91913i	−0.441922	+	0.130420i
$904$	1.84406	+	8.07935i	0.0613325	+	0.268715i
$905$	6.61142	−	6.13450i	0.219771	−	0.203918i
$906$	−17.6463	+	2.65974i	−0.586258	+	0.0883641i
$907$	39.2677	−	5.91865i	1.30386	−	0.196525i	0.539868	−	0.841750i	$-0.318474\pi$
$907$	39.2677	−	5.91865i	1.30386	−	0.196525i	0.763993	+	0.645224i	$0.223236\pi$
$908$	64.3288	−	59.6884i	2.13483	−	1.98083i
$909$	−1.42506	−	6.24358i	−0.0472662	−	0.207087i
$910$	1.15591	+	18.4482i	0.0383181	+	0.611551i
$911$	11.3763	−	49.8427i	0.376912	−	1.65136i	−0.329941	−	0.944001i	$-0.607029\pi$
$911$	11.3763	−	49.8427i	0.376912	−	1.65136i	0.706854	−	0.707360i	$-0.250114\pi$
$912$	−4.45343	−	7.71357i	−0.147468	−	0.255422i
$913$	44.5165	−	77.1049i	1.47328	−	2.55180i
$914$	33.7938	+	31.3560i	1.11780	+	1.03717i
$915$	1.36973	+	0.933866i	0.0452819	+	0.0308727i
$916$	6.64988	+	8.33868i	0.219718	+	0.275518i
$917$	−5.31670	−	24.6809i	−0.175573	−	0.815036i
$918$	31.4896	−	39.4867i	1.03931	−	1.30326i
$919$	16.4100	−	5.06183i	0.541317	−	0.166974i	−0.0120258	−	0.999928i	$-0.503828\pi$
$919$	16.4100	−	5.06183i	0.541317	−	0.166974i	0.553343	+	0.832953i	$0.313352\pi$
$920$	3.24036	+	8.25631i	0.106832	+	0.272203i
$921$	1.18785	−	15.8508i	0.0391411	−	0.522302i
$922$	9.27515	−	23.6327i	0.305461	−	0.778301i
$923$	−10.4638	−	5.03908i	−0.344419	−	0.165863i
$924$	−6.87180	+	78.7648i	−0.226065	+	2.59117i
$925$	−3.40669	+	1.64058i	−0.112011	+	0.0539418i
$926$	−5.00673	−	66.8102i	−0.164531	−	2.19552i
$927$	8.70814	+	2.68611i	0.286013	+	0.0882233i
$928$	108.393	−	73.9009i	3.55816	−	2.42591i
$929$	15.3667	+	2.31616i	0.504166	+	0.0759908i	0.396201	−	0.918164i	$-0.370328\pi$
$929$	15.3667	+	2.31616i	0.504166	+	0.0759908i	0.107965	+	0.994155i	$0.465567\pi$
$930$	−43.3763			−1.42237
$931$	3.94970	−	2.55370i	0.129446	−	0.0836941i
$932$	11.3740			0.372569
$933$	20.9813	+	3.16242i	0.686896	+	0.103533i
$934$	−34.8840	+	23.7835i	−1.14144	+	0.778219i
$935$	−65.7596	−	20.2841i	−2.15057	−	0.663362i
$936$	−1.71855	−	22.9324i	−0.0561725	−	0.749569i
$937$	−30.5994	+	14.7359i	−0.999639	+	0.481401i	−0.860816	−	0.508916i	$-0.830046\pi$
$937$	−30.5994	+	14.7359i	−0.999639	+	0.481401i	−0.138823	+	0.990317i	$0.544332\pi$
$938$	67.3861	−	9.31586i	2.20023	−	0.304174i
$939$	13.9729	+	6.72901i	0.455989	+	0.219593i
$940$	−48.2954	+	123.055i	−1.57522	+	4.01360i
$941$	−3.80001	+	50.7076i	−0.123877	+	1.65302i	0.496000	+	0.868322i	$0.334801\pi$
$941$	−3.80001	+	50.7076i	−0.123877	+	1.65302i	−0.619877	+	0.784699i	$0.712818\pi$
$942$	−5.82953	−	14.8534i	−0.189936	−	0.483950i
$943$	−2.83940	+	0.875838i	−0.0924635	+	0.0285212i
$944$	65.2703	−	81.8463i	2.12437	−	2.66387i
$945$	26.3226	+	13.0751i	0.856274	+	0.425332i
$946$	−70.8720	−	88.8707i	−2.30425	−	2.88944i
$947$	−12.1596	−	8.29030i	−0.395135	−	0.269399i	0.349411	−	0.936970i	$-0.386382\pi$
$947$	−12.1596	−	8.29030i	−0.395135	−	0.269399i	−0.744546	+	0.667571i	$0.767334\pi$
$948$	−14.7765	−	13.7106i	−0.479919	−	0.445299i
$949$	6.23530	−	10.7998i	0.202406	−	0.350578i
$950$	1.32178	+	2.28940i	0.0428843	+	0.0742778i
$951$	−5.56516	+	24.3826i	−0.180463	+	0.790659i
$952$	−41.2833	+	101.521i	−1.33800	+	3.29032i
$953$	−2.50833	−	10.9897i	−0.0812529	−	0.355992i	0.917915	−	0.396777i	$-0.129871\pi$
$953$	−2.50833	−	10.9897i	−0.0812529	−	0.355992i	−0.999168	+	0.0407847i	$0.987014\pi$
$954$	0.693332	−	0.643318i	0.0224475	−	0.0208282i
$955$	−35.8639	+	5.40561i	−1.16053	+	0.174922i
$956$	22.1045	−	3.33171i	0.714909	−	0.107755i
$957$	−20.9144	+	19.4058i	−0.676068	+	0.627299i
$958$	−15.3367	−	67.1947i	−0.495508	−	2.17096i
$959$	12.2734	−	11.1119i	0.396328	−	0.358823i
$960$	−16.4832	+	72.2178i	−0.531994	+	2.33082i
$961$	−12.9365	−	22.4067i	−0.417307	−	0.722798i
$962$	−3.64891	+	6.32009i	−0.117646	+	0.203768i
$963$	7.40711	+	6.87279i	0.238691	+	0.221473i
$964$	−7.11852	−	4.85332i	−0.229272	−	0.156315i
$965$	−2.41858	−	3.03281i	−0.0778569	−	0.0976295i
$966$	−1.92154	+	0.896593i	−0.0618244	+	0.0288474i
$967$	−12.4785	+	15.6476i	−0.401283	+	0.503193i	−0.940884	−	0.338728i	$-0.890003\pi$
$967$	−12.4785	+	15.6476i	−0.401283	+	0.503193i	0.539602	+	0.841921i	$0.318575\pi$
$968$	−294.387	+	90.8063i	−9.46195	+	2.91863i
$969$	0.845331	+	2.15387i	0.0271559	+	0.0691922i
$970$	2.76867	−	36.9453i	0.0888966	−	1.18624i
$971$	−12.9225	+	32.9261i	−0.414704	+	1.05665i	0.559068	+	0.829122i	$0.311159\pi$
$971$	−12.9225	+	32.9261i	−0.414704	+	1.05665i	−0.973772	+	0.227527i	$0.926936\pi$
$972$	−80.1849	−	38.6150i	−2.57193	−	1.23858i
$973$	1.31175	+	3.46629i	0.0420528	+	0.111124i
$974$	25.5753	−	12.3164i	0.819485	−	0.394643i
$975$	−0.0878406	−	1.17215i	−0.00281315	−	0.0375389i
$976$	12.2206	+	3.76954i	0.391170	+	0.120660i
$977$	−45.4500	+	30.9873i	−1.45407	+	0.991371i	−0.459408	+	0.888226i	$0.651938\pi$
$977$	−45.4500	+	30.9873i	−1.45407	+	0.991371i	−0.994666	+	0.103145i	$0.967109\pi$
$978$	−43.9582	−	6.62563i	−1.40563	−	0.211864i
$979$	16.4148			0.524618
$980$	−97.7715	−	17.1909i	−3.12320	−	0.549143i
$981$	17.0777			0.545250
$982$	48.1587	+	7.25876i	1.53681	+	0.231636i
$983$	25.9821	−	17.7143i	0.828700	−	0.564998i	−0.0730139	−	0.997331i	$-0.523262\pi$
$983$	25.9821	−	17.7143i	0.828700	−	0.564998i	0.901714	+	0.432333i	$0.142309\pi$
$984$	−65.5283	−	20.2128i	−2.08897	−	0.644361i
$985$	1.67007	+	22.2856i	0.0532129	+	0.710077i
$986$	−55.4611	+	26.7087i	−1.76624	+	0.850577i
$987$	−19.3270	−	6.22133i	−0.615186	−	0.198027i
$988$	3.38622	+	1.63072i	0.107730	+	0.0518800i
$989$	0.820412	−	2.09038i	0.0260876	−	0.0664701i
$990$	−7.86764	+	104.986i	−0.250050	+	3.33669i
$991$	6.39207	+	16.2867i	0.203051	+	0.517365i	0.995734	−	0.0922684i	$-0.0294118\pi$
$991$	6.39207	+	16.2867i	0.203051	+	0.517365i	−0.792683	+	0.609634i	$0.791317\pi$
$992$	−177.025	+	54.6049i	−5.62054	+	1.73371i
$993$	11.0249	−	13.8248i	0.349865	−	0.438716i
$994$	53.5990	−	65.5509i	1.70006	−	2.07915i
$995$	22.9811	+	28.8174i	0.728549	+	0.913572i
$996$	52.2043	+	35.5923i	1.65416	+	1.12779i
$997$	−4.01623	−	3.72651i	−0.127195	−	0.118020i	0.614011	−	0.789298i	$-0.289555\pi$
$997$	−4.01623	−	3.72651i	−0.127195	−	0.118020i	−0.741206	+	0.671278i	$0.765746\pi$
$998$	−18.8407	+	32.6330i	−0.596391	+	1.03298i
$999$	5.80195	+	10.0493i	0.183566	+	0.317945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.235.27	✓	324
49.44	even	21	inner	637.2.bl.a.534.27	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.235.27	✓	324	1.1	even	1	trivial
637.2.bl.a.534.27	yes	324	49.44	even	21	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.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.72488 + 0.410710i) q^{2} +(0.680220 - 0.463766i) q^{3} +(5.34515 + 1.64876i) q^{4} +(0.189463 + 2.52821i) q^{5} +(2.04399 - 0.984335i) q^{6} +(-1.91733 - 1.82314i) q^{7} +(8.92220 + 4.29671i) q^{8} +(-0.848403 + 2.16170i) q^{9} +O(q^{10})\)	\(q+(2.72488 + 0.410710i) q^{2} +(0.680220 - 0.463766i) q^{3} +(5.34515 + 1.64876i) q^{4} +(0.189463 + 2.52821i) q^{5} +(2.04399 - 0.984335i) q^{6} +(-1.91733 - 1.82314i) q^{7} +(8.92220 + 4.29671i) q^{8} +(-0.848403 + 2.16170i) q^{9} +(-0.522097 + 6.96690i) q^{10} +(-2.37076 - 6.04061i) q^{11} +(4.40052 - 1.35738i) q^{12} +(-0.623490 + 0.781831i) q^{13} +(-4.47571 - 5.75531i) q^{14} +(1.30138 + 1.63188i) q^{15} +(13.3038 + 9.07041i) q^{16} +(-3.06627 - 2.84508i) q^{17} +(-3.19963 + 5.54191i) q^{18} +(-0.335953 - 0.581888i) q^{19} +(-3.15571 + 13.8261i) q^{20} +(-2.14972 - 0.350945i) q^{21} +(-3.97911 - 17.4336i) q^{22} +(0.258963 - 0.240283i) q^{23} +(8.06173 - 1.21511i) q^{24} +(-1.41182 + 0.212797i) q^{25} +(-2.02004 + 1.87432i) q^{26} +(0.975007 + 4.27178i) q^{27} +(-7.24249 - 12.9062i) q^{28} +(1.18836 - 5.20655i) q^{29} +(2.87587 + 4.98115i) q^{30} +(-3.77071 + 6.53106i) q^{31} +(18.0074 + 16.7084i) q^{32} +(-4.41407 - 3.00946i) q^{33} +(-7.18671 - 9.01185i) q^{34} +(4.24603 - 5.19284i) q^{35} +(-8.09895 + 10.1558i) q^{36} +(2.53064 - 0.780600i) q^{37} +(-0.676446 - 1.72356i) q^{38} +(-0.0615233 + 0.820971i) q^{39} +(-9.17256 + 23.3713i) q^{40} +(-7.57825 - 3.64949i) q^{41} +(-5.71359 - 1.83919i) q^{42} +(5.72717 - 2.75806i) q^{43} +(-2.71257 - 36.1968i) q^{44} +(-5.62597 - 1.73538i) q^{45} +(0.804330 - 0.548383i) q^{46} +(9.21729 + 1.38928i) q^{47} +13.2561 q^{48} +(0.352309 + 6.99113i) q^{49} -3.93443 q^{50} +(-3.40519 - 0.513250i) q^{51} +(-4.62170 + 3.15102i) q^{52} +(-0.141235 - 0.0435651i) q^{53} +(0.902314 + 12.0405i) q^{54} +(14.8228 - 7.13827i) q^{55} +(-9.27330 - 24.5046i) q^{56} +(-0.498382 - 0.240008i) q^{57} +(5.37653 - 13.6992i) q^{58} +(0.485859 - 6.48333i) q^{59} +(4.26548 + 10.8683i) q^{60} +(0.758961 - 0.234108i) q^{61} +(-12.9571 + 16.2477i) q^{62} +(5.56774 - 2.59792i) q^{63} +(22.1272 + 27.7467i) q^{64} +(-2.09477 - 1.42819i) q^{65} +(-10.7918 - 10.0133i) q^{66} +(-4.66527 + 8.08048i) q^{67} +(-11.6988 - 20.2629i) q^{68} +(0.0647170 - 0.283543i) q^{69} +(13.7027 - 12.4060i) q^{70} +(2.58433 + 11.3227i) q^{71} +(-16.8578 + 15.6417i) q^{72} +(-12.3313 + 1.85865i) q^{73} +(7.21631 - 1.08768i) q^{74} +(-0.861657 + 0.799501i) q^{75} +(-0.836327 - 3.66419i) q^{76} +(-6.46735 + 15.9041i) q^{77} +(-0.504824 + 2.21178i) q^{78} +(-2.18860 - 3.79077i) q^{79} +(-20.4113 + 35.3535i) q^{80} +(-2.46260 - 2.28496i) q^{81} +(-19.1509 - 13.0569i) q^{82} +(8.55442 + 10.7269i) q^{83} +(-10.9119 - 5.42022i) q^{84} +(6.61203 - 8.29122i) q^{85} +(16.7386 - 5.16318i) q^{86} +(-1.60628 - 4.09272i) q^{87} +(4.80228 - 64.0820i) q^{88} +(-0.924152 + 2.35470i) q^{89} +(-14.6174 - 7.03935i) q^{90} +(2.62083 - 0.362319i) q^{91} +(1.78036 - 0.857378i) q^{92} +(0.463973 + 6.19129i) q^{93} +(24.5454 + 7.57126i) q^{94} +(1.40749 - 0.959609i) q^{95} +(19.9978 + 3.01418i) q^{96} -5.30298 q^{97} +(-1.91132 + 19.1947i) q^{98} +15.0693 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

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Database

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