LMFDB - Embedded newform 1205.2.b.c.724.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (of order $2$, degree $1$, 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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.11
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70963i q^{2} +1.38336i q^{3} -0.922819 q^{4} +(-1.53605 - 1.62498i) q^{5} +2.36503 q^{6} -5.05937i q^{7} -1.84158i q^{8} +1.08631 q^{9} +O(q^{10})$	\(q-1.70963i q^{2} +1.38336i q^{3} -0.922819 q^{4} +(-1.53605 - 1.62498i) q^{5} +2.36503 q^{6} -5.05937i q^{7} -1.84158i q^{8} +1.08631 q^{9} +(-2.77811 + 2.62606i) q^{10} -5.25074 q^{11} -1.27659i q^{12} -2.84467i q^{13} -8.64964 q^{14} +(2.24794 - 2.12490i) q^{15} -4.99404 q^{16} +6.16813i q^{17} -1.85719i q^{18} -1.47178 q^{19} +(1.41749 + 1.49956i) q^{20} +6.99894 q^{21} +8.97680i q^{22} +2.54443i q^{23} +2.54756 q^{24} +(-0.281131 + 4.99209i) q^{25} -4.86332 q^{26} +5.65285i q^{27} +4.66889i q^{28} +9.53193 q^{29} +(-3.63279 - 3.84313i) q^{30} -7.94968 q^{31} +4.85479i q^{32} -7.26367i q^{33} +10.5452 q^{34} +(-8.22139 + 7.77143i) q^{35} -1.00247 q^{36} -8.85694i q^{37} +2.51619i q^{38} +3.93520 q^{39} +(-2.99253 + 2.82874i) q^{40} +1.60908 q^{41} -11.9656i q^{42} +0.0179130i q^{43} +4.84548 q^{44} +(-1.66863 - 1.76524i) q^{45} +4.35003 q^{46} +5.95134i q^{47} -6.90856i q^{48} -18.5973 q^{49} +(8.53460 + 0.480629i) q^{50} -8.53275 q^{51} +2.62511i q^{52} -8.07317i q^{53} +9.66425 q^{54} +(8.06538 + 8.53236i) q^{55} -9.31723 q^{56} -2.03600i q^{57} -16.2960i q^{58} +3.28732 q^{59} +(-2.07444 + 1.96090i) q^{60} +7.19911 q^{61} +13.5910i q^{62} -5.49606i q^{63} -1.68822 q^{64} +(-4.62253 + 4.36954i) q^{65} -12.4182 q^{66} +2.92491i q^{67} -5.69207i q^{68} -3.51987 q^{69} +(13.2862 + 14.0555i) q^{70} -4.49618 q^{71} -2.00053i q^{72} +4.29619i q^{73} -15.1421 q^{74} +(-6.90586 - 0.388906i) q^{75} +1.35819 q^{76} +26.5655i q^{77} -6.72772i q^{78} -2.34077 q^{79} +(7.67107 + 8.11523i) q^{80} -4.56099 q^{81} -2.75093i q^{82} -9.27436i q^{83} -6.45875 q^{84} +(10.0231 - 9.47453i) q^{85} +0.0306245 q^{86} +13.1861i q^{87} +9.66964i q^{88} -13.8608 q^{89} +(-3.01790 + 2.85272i) q^{90} -14.3922 q^{91} -2.34805i q^{92} -10.9973i q^{93} +10.1746 q^{94} +(2.26072 + 2.39161i) q^{95} -6.71593 q^{96} -11.0653i q^{97} +31.7944i q^{98} -5.70395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.70963i		−	1.20889i	−0.796648	−	0.604444i	$-0.793395\pi$
$2$		−	1.70963i		−	1.20889i	0.796648	−	0.604444i	$-0.206605\pi$
$3$			1.38336i			0.798684i	0.916802	+	0.399342i	$0.130761\pi$
$3$			1.38336i			0.798684i	−0.916802	+	0.399342i	$0.869239\pi$
$4$	−0.922819			−0.461409
$5$	−1.53605	−	1.62498i	−0.686940	−	0.726714i
$5$	−1.53605	−	1.62498i	−0.686940	−	0.726714i
$6$	2.36503			0.965519
$7$		−	5.05937i		−	1.91226i	−0.292936	−	0.956132i	$-0.594632\pi$
$7$		−	5.05937i		−	1.91226i	0.292936	−	0.956132i	$-0.405368\pi$
$8$		−	1.84158i		−	0.651096i
$9$	1.08631			0.362104
$10$	−2.77811	+	2.62606i	−0.878515	+	0.830434i
$11$	−5.25074			−1.58316			−0.791579	−	0.611066i	$-0.790741\pi$
$11$	−5.25074			−1.58316			−0.791579	+	0.611066i	$0.790741\pi$
$12$		−	1.27659i		−	0.368520i
$13$		−	2.84467i		−	0.788969i	−0.918903	−	0.394485i	$-0.870923\pi$
$13$		−	2.84467i		−	0.788969i	0.918903	−	0.394485i	$-0.129077\pi$
$14$	−8.64964			−2.31171
$15$	2.24794	−	2.12490i	0.580415	−	0.548648i
$16$	−4.99404			−1.24851
$17$			6.16813i			1.49599i	0.663704	+	0.747996i	$0.268984\pi$
$17$			6.16813i			1.49599i	−0.663704	+	0.747996i	$0.731016\pi$
$18$		−	1.85719i		−	0.437743i
$19$	−1.47178			−0.337649			−0.168825	−	0.985646i	$-0.553997\pi$
$19$	−1.47178			−0.337649			−0.168825	+	0.985646i	$0.553997\pi$
$20$	1.41749	+	1.49956i	0.316961	+	0.335313i
$21$	6.99894			1.52729
$22$			8.97680i			1.91386i
$23$			2.54443i			0.530551i	0.964173	+	0.265275i	$0.0854629\pi$
$23$			2.54443i			0.530551i	−0.964173	+	0.265275i	$0.914537\pi$
$24$	2.54756			0.520019
$25$	−0.281131	+	4.99209i	−0.0562263	+	0.998418i
$26$	−4.86332			−0.953775
$27$			5.65285i			1.08789i
$28$			4.66889i			0.882336i
$29$	9.53193			1.77003			0.885017	−	0.465558i	$-0.154146\pi$
$29$	9.53193			1.77003			0.885017	+	0.465558i	$0.154146\pi$
$30$	−3.63279	−	3.84313i	−0.663254	−	0.701656i
$31$	−7.94968			−1.42780			−0.713902	−	0.700245i	$-0.753074\pi$
$31$	−7.94968			−1.42780			−0.713902	+	0.700245i	$0.753074\pi$
$32$			4.85479i			0.858214i
$33$		−	7.26367i		−	1.26444i
$34$	10.5452			1.80849
$35$	−8.22139	+	7.77143i	−1.38967	+	1.31361i
$36$	−1.00247			−0.167078
$37$		−	8.85694i		−	1.45607i	−0.685539	−	0.728036i	$-0.740433\pi$
$37$		−	8.85694i		−	1.45607i	0.685539	−	0.728036i	$-0.259567\pi$
$38$			2.51619i			0.408180i
$39$	3.93520			0.630137
$40$	−2.99253	+	2.82874i	−0.473160	+	0.447264i
$41$	1.60908			0.251297			0.125648	−	0.992075i	$-0.459899\pi$
$41$	1.60908			0.251297			0.125648	+	0.992075i	$0.459899\pi$
$42$		−	11.9656i		−	1.84633i
$43$			0.0179130i			0.00273171i	0.999999	+	0.00136585i	$0.000434765\pi$
$43$			0.0179130i			0.00273171i	−0.999999	+	0.00136585i	$0.999565\pi$
$44$	4.84548			0.730484
$45$	−1.66863	−	1.76524i	−0.248744	−	0.263146i
$46$	4.35003			0.641376
$47$			5.95134i			0.868092i	0.900891	+	0.434046i	$0.142915\pi$
$47$			5.95134i			0.868092i	−0.900891	+	0.434046i	$0.857085\pi$
$48$		−	6.90856i		−	0.997165i
$49$	−18.5973			−2.65675
$50$	8.53460	+	0.480629i	1.20698	+	0.0679713i
$51$	−8.53275			−1.19482
$52$			2.62511i			0.364038i
$53$		−	8.07317i		−	1.10894i	−0.832205	−	0.554468i	$-0.812922\pi$
$53$		−	8.07317i		−	1.10894i	0.832205	−	0.554468i	$-0.187078\pi$
$54$	9.66425			1.31514
$55$	8.06538	+	8.53236i	1.08754	+	1.15050i
$56$	−9.31723			−1.24507
$57$		−	2.03600i		−	0.269675i
$58$		−	16.2960i		−	2.13977i
$59$	3.28732			0.427973			0.213986	−	0.976837i	$-0.431355\pi$
$59$	3.28732			0.427973			0.213986	+	0.976837i	$0.431355\pi$
$60$	−2.07444	+	1.96090i	−0.267809	+	0.253151i
$61$	7.19911			0.921751			0.460876	−	0.887465i	$-0.347535\pi$
$61$	7.19911			0.921751			0.460876	+	0.887465i	$0.347535\pi$
$62$			13.5910i			1.72606i
$63$		−	5.49606i		−	0.692439i
$64$	−1.68822			−0.211027
$65$	−4.62253	+	4.36954i	−0.573355	+	0.541975i
$66$	−12.4182			−1.52857
$67$			2.92491i			0.357335i	0.983910	+	0.178667i	$0.0571786\pi$
$67$			2.92491i			0.357335i	−0.983910	+	0.178667i	$0.942821\pi$
$68$		−	5.69207i		−	0.690264i
$69$	−3.51987			−0.423742
$70$	13.2862	+	14.0555i	1.58801	+	1.67995i
$71$	−4.49618			−0.533599			−0.266799	−	0.963752i	$-0.585966\pi$
$71$	−4.49618			−0.533599			−0.266799	+	0.963752i	$0.585966\pi$
$72$		−	2.00053i		−	0.235765i
$73$			4.29619i			0.502831i	0.967879	+	0.251416i	$0.0808961\pi$
$73$			4.29619i			0.502831i	−0.967879	+	0.251416i	$0.919104\pi$
$74$	−15.1421			−1.76023
$75$	−6.90586	−	0.388906i	−0.797420	−	0.0449070i
$76$	1.35819			0.155795
$77$			26.5655i			3.02742i
$78$		−	6.72772i		−	0.761765i
$79$	−2.34077			−0.263357			−0.131679	−	0.991292i	$-0.542037\pi$
$79$	−2.34077			−0.263357			−0.131679	+	0.991292i	$0.542037\pi$
$80$	7.67107	+	8.11523i	0.857652	+	0.907310i
$81$	−4.56099			−0.506776
$82$		−	2.75093i		−	0.303790i
$83$		−	9.27436i		−	1.01799i	−0.860768	−	0.508997i	$-0.830016\pi$
$83$		−	9.27436i		−	1.01799i	0.860768	−	0.508997i	$-0.169984\pi$
$84$	−6.45875			−0.704708
$85$	10.0231	−	9.47453i	1.08716	−	1.02766i
$86$	0.0306245			0.00330232
$87$			13.1861i			1.41370i
$88$			9.66964i			1.03079i
$89$	−13.8608			−1.46924			−0.734619	−	0.678479i	$-0.762639\pi$
$89$	−13.8608			−1.46924			−0.734619	+	0.678479i	$0.762639\pi$
$90$	−3.01790	+	2.85272i	−0.318114	+	0.300704i
$91$	−14.3922			−1.50872
$92$		−	2.34805i		−	0.244801i
$93$		−	10.9973i		−	1.14036i
$94$	10.1746			1.04943
$95$	2.26072	+	2.39161i	0.231945	+	0.245374i
$96$	−6.71593			−0.685441
$97$		−	11.0653i		−	1.12351i	−0.827303	−	0.561756i	$-0.810126\pi$
$97$		−	11.0653i		−	1.12351i	0.827303	−	0.561756i	$-0.189874\pi$
$98$			31.7944i			3.21172i
$99$	−5.70395			−0.573269
$100$	0.259433	−	4.60679i	0.0259433	−	0.460679i
$101$	0.249085			0.0247849			0.0123924	−	0.999923i	$-0.496055\pi$
$101$	0.249085			0.0247849			0.0123924	+	0.999923i	$0.496055\pi$
$102$			14.5878i			1.44441i
$103$		−	13.4549i		−	1.32575i	−0.748730	−	0.662875i	$-0.769336\pi$
$103$		−	13.4549i		−	1.32575i	0.748730	−	0.662875i	$-0.230664\pi$
$104$	−5.23867			−0.513694
$105$	−10.7507	−	11.3732i	−1.04916	−	1.10991i
$106$	−13.8021			−1.34058
$107$			1.30787i			0.126437i	0.998000	+	0.0632185i	$0.0201365\pi$
$107$			1.30787i			0.126437i	−0.998000	+	0.0632185i	$0.979864\pi$
$108$		−	5.21655i		−	0.501963i
$109$	−19.2547			−1.84426			−0.922131	−	0.386878i	$-0.873554\pi$
$109$	−19.2547			−1.84426			−0.922131	+	0.386878i	$0.873554\pi$
$110$	14.5871	−	13.7888i	1.39083	−	1.31471i
$111$	12.2523			1.16294
$112$			25.2667i			2.38748i
$113$		−	17.0383i		−	1.60283i	−0.598108	−	0.801415i	$-0.704081\pi$
$113$		−	17.0383i		−	1.60283i	0.598108	−	0.801415i	$-0.295919\pi$
$114$	−3.48080			−0.326007
$115$	4.13466	−	3.90836i	0.385559	−	0.364457i
$116$	−8.79624			−0.816710
$117$		−	3.09020i		−	0.285689i
$118$		−	5.62009i		−	0.517371i
$119$	31.2069			2.86073
$120$	−3.91317	−	4.13975i	−0.357222	−	0.377905i
$121$	16.5703			1.50639
$122$		−	12.3078i		−	1.11429i
$123$			2.22594i			0.200707i
$124$	7.33611			0.658802
$125$	8.54389	−	7.21124i	0.764188	−	0.644993i
$126$	−9.39621			−0.837081
$127$		−	10.0749i		−	0.894007i	−0.894532	−	0.447004i	$-0.852491\pi$
$127$		−	10.0749i		−	0.894007i	0.894532	−	0.447004i	$-0.147509\pi$
$128$			12.5958i			1.11332i
$129$	−0.0247801			−0.00218177
$130$	7.47027	+	7.90280i	0.655186	+	0.693122i
$131$	5.37122			0.469285			0.234643	−	0.972082i	$-0.424608\pi$
$131$	5.37122			0.469285			0.234643	+	0.972082i	$0.424608\pi$
$132$			6.70305i			0.583426i
$133$			7.44628i			0.645675i
$134$	5.00050			0.431978
$135$	9.18577	−	8.68302i	0.790585	−	0.747316i
$136$	11.3591			0.974034
$137$		−	10.2584i		−	0.876436i	−0.898869	−	0.438218i	$-0.855610\pi$
$137$		−	10.2584i		−	0.876436i	0.898869	−	0.438218i	$-0.144390\pi$
$138$			6.01766i			0.512257i
$139$	−14.6133			−1.23949			−0.619743	−	0.784805i	$-0.712763\pi$
$139$	−14.6133			−1.23949			−0.619743	+	0.784805i	$0.712763\pi$
$140$	7.58685	−	7.17162i	0.641206	−	0.606112i
$141$	−8.23285			−0.693331
$142$			7.68679i			0.645061i
$143$			14.9366i			1.24906i
$144$	−5.42509			−0.452091
$145$	−14.6415	−	15.4892i	−1.21591	−	1.28631i
$146$	7.34488			0.607866
$147$		−	25.7267i		−	2.12191i
$148$			8.17335i			0.671845i
$149$	15.8135			1.29549			0.647747	−	0.761856i	$-0.275711\pi$
$149$	15.8135			1.29549			0.647747	+	0.761856i	$0.275711\pi$
$150$	−0.664884	+	11.8064i	−0.0542875	+	0.963991i
$151$	−15.2888			−1.24419			−0.622093	−	0.782944i	$-0.713717\pi$
$151$	−15.2888			−1.24419			−0.622093	+	0.782944i	$0.713717\pi$
$152$			2.71039i			0.219842i
$153$			6.70052i			0.541705i
$154$	45.4170			3.65981
$155$	12.2111	+	12.9181i	0.980817	+	1.03761i
$156$	−3.63148			−0.290751
$157$		−	0.857546i		−	0.0684396i	−0.999414	−	0.0342198i	$-0.989105\pi$
$157$		−	0.857546i		−	0.0684396i	0.999414	−	0.0342198i	$-0.0108946\pi$
$158$			4.00184i			0.318369i
$159$	11.1681			0.885689
$160$	7.88894	−	7.45717i	0.623676	−	0.589541i
$161$	12.8732			1.01455
$162$			7.79758i			0.612635i
$163$			9.36765i			0.733731i	0.930274	+	0.366866i	$0.119569\pi$
$163$			9.36765i			0.733731i	−0.930274	+	0.366866i	$0.880431\pi$
$164$	−1.48489			−0.115951
$165$	−11.8033	+	11.1573i	−0.918888	+	0.868597i
$166$	−15.8557			−1.23064
$167$		−	2.74053i		−	0.212069i	−0.994362	−	0.106034i	$-0.966185\pi$
$167$		−	2.74053i		−	0.212069i	0.994362	−	0.106034i	$-0.0338154\pi$
$168$		−	12.8891i		−	0.994415i
$169$	4.90786			0.377528
$170$	−16.1979	−	17.1357i	−1.24232	−	1.31425i
$171$	−1.59881			−0.122264
$172$		−	0.0165304i		−	0.00126043i
$173$			1.88911i			0.143627i	0.997418	+	0.0718134i	$0.0228786\pi$
$173$			1.88911i			0.143627i	−0.997418	+	0.0718134i	$0.977121\pi$
$174$	22.5433			1.70900
$175$	25.2569	+	1.42235i	1.90924	+	0.107519i
$176$	26.2224			1.97659
$177$			4.54755i			0.341815i
$178$			23.6967i			1.77614i
$179$	0.490228			0.0366413			0.0183207	−	0.999832i	$-0.494168\pi$
$179$	0.490228			0.0366413			0.0183207	+	0.999832i	$0.494168\pi$
$180$	1.53984	+	1.62900i	0.114773	+	0.121418i
$181$	0.282628			0.0210076			0.0105038	−	0.999945i	$-0.496656\pi$
$181$	0.282628			0.0210076			0.0105038	+	0.999945i	$0.496656\pi$
$182$			24.6053i			1.82387i
$183$			9.95896i			0.736188i
$184$	4.68577			0.345439
$185$	−14.3924	+	13.6047i	−1.05815	+	1.00023i
$186$	−18.8012			−1.37857
$187$		−	32.3873i		−	2.36839i
$188$		−	5.49201i		−	0.400546i
$189$	28.5999			2.08033
$190$	4.08876	−	3.86498i	0.296630	−	0.280395i
$191$	18.5700			1.34368			0.671840	−	0.740696i	$-0.265504\pi$
$191$	18.5700			1.34368			0.671840	+	0.740696i	$0.265504\pi$
$192$		−	2.33541i		−	0.168544i
$193$		−	25.6312i		−	1.84498i	−0.386026	−	0.922488i	$-0.626153\pi$
$193$		−	25.6312i		−	1.84498i	0.386026	−	0.922488i	$-0.373847\pi$
$194$	−18.9175			−1.35820
$195$	−6.04465	−	6.39463i	−0.432866	−	0.457929i
$196$	17.1619			1.22585
$197$			12.1900i			0.868499i	0.900793	+	0.434250i	$0.142986\pi$
$197$			12.1900i			0.868499i	−0.900793	+	0.434250i	$0.857014\pi$
$198$			9.75162i			0.693017i
$199$	−6.70955			−0.475628			−0.237814	−	0.971311i	$-0.576431\pi$
$199$	−6.70955			−0.475628			−0.237814	+	0.971311i	$0.576431\pi$
$200$	9.19332	+	0.517725i	0.650066	+	0.0366087i
$201$	−4.04621			−0.285398
$202$		−	0.425842i		−	0.0299621i
$203$		−	48.2256i		−	3.38477i
$204$	7.87418			0.551303
$205$	−2.47163	−	2.61473i	−0.172626	−	0.182621i
$206$	−23.0028			−1.60268
$207$			2.76405i			0.192115i
$208$			14.2064i			0.985036i
$209$	7.72794			0.534552
$210$	−19.4438	+	18.3796i	−1.34175	+	1.26832i
$211$	7.92574			0.545630			0.272815	−	0.962066i	$-0.412045\pi$
$211$	7.92574			0.545630			0.272815	+	0.962066i	$0.412045\pi$
$212$			7.45007i			0.511673i
$213$		−	6.21984i		−	0.426177i
$214$	2.23597			0.152848
$215$	0.0291083	−	0.0275152i	0.00198517	−	0.00187652i
$216$	10.4101			0.708321
$217$			40.2204i			2.73034i
$218$			32.9183i			2.22951i
$219$	−5.94318			−0.401603
$220$	−7.44288	−	7.87382i	−0.501799	−	0.530853i
$221$	17.5463			1.18029
$222$		−	20.9469i		−	1.40587i
$223$		−	18.7959i		−	1.25867i	−0.777134	−	0.629335i	$-0.783327\pi$
$223$		−	18.7959i		−	1.25867i	0.777134	−	0.629335i	$-0.216673\pi$
$224$	24.5622			1.64113
$225$	−0.305397	+	5.42297i	−0.0203598	+	0.361531i
$226$	−29.1292			−1.93764
$227$		−	1.76519i		−	0.117160i	−0.998283	−	0.0585799i	$-0.981343\pi$
$227$		−	1.76519i		−	0.117160i	0.998283	−	0.0585799i	$-0.0186572\pi$
$228$			1.87886i			0.124431i
$229$	21.1776			1.39945			0.699726	−	0.714411i	$-0.253305\pi$
$229$	21.1776			1.39945			0.699726	+	0.714411i	$0.253305\pi$
$230$	−6.68184	−	7.06871i	−0.440587	−	0.466097i
$231$	−36.7496			−2.41795
$232$		−	17.5538i		−	1.15246i
$233$		−	6.09009i		−	0.398975i	−0.979900	−	0.199488i	$-0.936072\pi$
$233$		−	6.09009i		−	0.398975i	0.979900	−	0.199488i	$-0.0639278\pi$
$234$	−5.28308			−0.345366
$235$	9.67082	−	9.14153i	0.630855	−	0.596327i
$236$	−3.03360			−0.197471
$237$		−	3.23813i		−	0.210339i
$238$		−	53.3521i		−	3.45830i
$239$	1.39490			0.0902286			0.0451143	−	0.998982i	$-0.485635\pi$
$239$	1.39490			0.0902286			0.0451143	+	0.998982i	$0.485635\pi$
$240$	−11.2263	+	10.6119i	−0.724654	+	0.684993i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	28.3290i		−	1.82106i
$243$			10.6490i			0.683137i
$244$	−6.64347			−0.425305
$245$	28.5663	+	30.2202i	1.82503	+	1.93070i
$246$	3.80553			0.242632
$247$			4.18672i			0.266395i
$248$			14.6399i			0.929637i
$249$	12.8298			0.813055
$250$	−12.3285	−	14.6068i	−0.779724	−	0.923818i
$251$	10.4868			0.661920			0.330960	−	0.943645i	$-0.392627\pi$
$251$	10.4868			0.661920			0.330960	+	0.943645i	$0.392627\pi$
$252$			5.07187i			0.319498i
$253$		−	13.3602i		−	0.839946i
$254$	−17.2244			−1.08075
$255$	13.1067	+	13.8656i	0.820773	+	0.868295i
$256$	18.1577			1.13485
$257$			14.8521i			0.926448i	0.886241	+	0.463224i	$0.153308\pi$
$257$			14.8521i			0.926448i	−0.886241	+	0.463224i	$0.846692\pi$
$258$			0.0423647i			0.00263751i
$259$	−44.8106			−2.78439
$260$	4.26576	−	4.03229i	0.264551	−	0.250072i
$261$	10.3547			0.640937
$262$		−	9.18277i		−	0.567313i
$263$			1.20965i			0.0745901i	0.999304	+	0.0372951i	$0.0118741\pi$
$263$			1.20965i			0.0745901i	−0.999304	+	0.0372951i	$0.988126\pi$
$264$	−13.3766			−0.823273
$265$	−13.1188	+	12.4008i	−0.805879	+	0.761772i
$266$	12.7304			0.780548
$267$		−	19.1744i		−	1.17346i
$268$		−	2.69916i		−	0.164878i
$269$	−15.6437			−0.953811			−0.476905	−	0.878955i	$-0.658242\pi$
$269$	−15.6437			−0.953811			−0.476905	+	0.878955i	$0.658242\pi$
$270$	−14.8447	−	15.7042i	−0.903421	−	0.955729i
$271$	−25.9732			−1.57776			−0.788880	−	0.614547i	$-0.789339\pi$
$271$	−25.9732			−1.57776			−0.788880	+	0.614547i	$0.789339\pi$
$272$		−	30.8039i		−	1.86776i
$273$		−	19.9097i		−	1.20499i
$274$	−17.5380			−1.05951
$275$	1.47615	−	26.2122i	0.0890151	−	1.58065i
$276$	3.24820			0.195519
$277$		−	11.7554i		−	0.706312i	−0.935564	−	0.353156i	$-0.885108\pi$
$277$		−	11.7554i		−	0.706312i	0.935564	−	0.353156i	$-0.114892\pi$
$278$			24.9833i			1.49840i
$279$	−8.63584			−0.517014
$280$	14.3117	+	15.1403i	0.855286	+	0.904807i
$281$	−6.68164			−0.398593			−0.199297	−	0.979939i	$-0.563866\pi$
$281$	−6.68164			−0.398593			−0.199297	+	0.979939i	$0.563866\pi$
$282$			14.0751i			0.838159i
$283$			7.36154i			0.437598i	0.975770	+	0.218799i	$0.0702140\pi$
$283$			7.36154i			0.437598i	−0.975770	+	0.218799i	$0.929786\pi$
$284$	4.14916			0.246207
$285$	−3.30847	+	3.12739i	−0.195977	+	0.185251i
$286$	25.5360			1.50998
$287$		−	8.14096i		−	0.480546i
$288$			5.27382i			0.310763i
$289$	−21.0458			−1.23799
$290$	−26.4807	+	25.0314i	−1.55500	+	1.46990i
$291$	15.3073			0.897331
$292$		−	3.96461i		−	0.232011i
$293$			12.0504i			0.703992i	0.936001	+	0.351996i	$0.114497\pi$
$293$			12.0504i			0.703992i	−0.936001	+	0.351996i	$0.885503\pi$
$294$	−43.9831			−2.56515
$295$	−5.04947	−	5.34184i	−0.293992	−	0.311014i
$296$	−16.3107			−0.948042
$297$		−	29.6816i		−	1.72230i
$298$		−	27.0352i		−	1.56611i
$299$	7.23807			0.418588
$300$	6.37286	+	0.358890i	0.367937	+	0.0207205i
$301$	0.0906285			0.00522374
$302$			26.1381i			1.50408i
$303$			0.344574i			0.0197953i
$304$	7.35013			0.421559
$305$	−11.0582	−	11.6984i	−0.633188	−	0.669850i
$306$	11.4554			0.654860
$307$			25.7906i			1.47195i	0.677010	+	0.735974i	$0.263275\pi$
$307$			25.7906i			1.47195i	−0.677010	+	0.735974i	$0.736725\pi$
$308$		−	24.5151i		−	1.39688i
$309$	18.6130			1.05886
$310$	22.0851	−	20.8763i	1.25435	−	1.18570i
$311$	−19.1825			−1.08774			−0.543869	−	0.839170i	$-0.683041\pi$
$311$	−19.1825			−1.08774			−0.543869	+	0.839170i	$0.683041\pi$
$312$		−	7.24698i		−	0.410279i
$313$			4.33448i			0.245000i	0.992469	+	0.122500i	$0.0390911\pi$
$313$			4.33448i			0.245000i	−0.992469	+	0.122500i	$0.960909\pi$
$314$	−1.46608			−0.0827358
$315$	−8.93100	+	8.44220i	−0.503205	+	0.475664i
$316$	2.16011			0.121516
$317$			7.30667i			0.410383i	0.978722	+	0.205192i	$0.0657818\pi$
$317$			7.30667i			0.410383i	−0.978722	+	0.205192i	$0.934218\pi$
$318$		−	19.0933i		−	1.07070i
$319$	−50.0497			−2.80225
$320$	2.59318	+	2.74332i	0.144963	+	0.153356i
$321$	−1.80926			−0.100983
$322$		−	22.0084i		−	1.22648i
$323$		−	9.07813i		−	0.505121i
$324$	4.20896			0.233831
$325$	14.2008	+	0.799726i	0.787721	+	0.0443608i
$326$	16.0152			0.886998
$327$		−	26.6361i		−	1.47298i
$328$		−	2.96325i		−	0.163618i
$329$	30.1101			1.66002
$330$	19.0748	+	20.1793i	1.05004	+	1.11083i
$331$	1.02032			0.0560821			0.0280411	−	0.999607i	$-0.491073\pi$
$331$	1.02032			0.0560821			0.0280411	+	0.999607i	$0.491073\pi$
$332$			8.55856i			0.469712i
$333$		−	9.62141i		−	0.527250i
$334$	−4.68529			−0.256367
$335$	4.75293	−	4.49280i	0.259680	−	0.245468i
$336$	−34.9530			−1.90684
$337$			18.9655i			1.03312i	0.856251	+	0.516559i	$0.172787\pi$
$337$			18.9655i			1.03312i	−0.856251	+	0.516559i	$0.827213\pi$
$338$		−	8.39060i		−	0.456389i
$339$	23.5702			1.28015
$340$	−9.24950	+	8.74327i	−0.501625	+	0.474170i
$341$	41.7417			2.26044
$342$			2.73337i			0.147804i
$343$			58.6750i			3.16815i
$344$	0.0329881			0.00177860
$345$	5.40668	+	5.71972i	0.291086	+	0.307939i
$346$	3.22968			0.173629
$347$		−	31.3900i		−	1.68510i	−0.538617	−	0.842550i	$-0.681053\pi$
$347$		−	31.3900i		−	1.68510i	0.538617	−	0.842550i	$-0.318947\pi$
$348$		−	12.1684i		−	0.652293i
$349$	12.0895			0.647139			0.323569	−	0.946204i	$-0.395117\pi$
$349$	12.0895			0.647139			0.323569	+	0.946204i	$0.395117\pi$
$350$	2.43168	−	43.1798i	0.129979	−	2.30806i
$351$	16.0805			0.858312
$352$		−	25.4913i		−	1.35869i
$353$			4.93700i			0.262770i	0.991331	+	0.131385i	$0.0419424\pi$
$353$			4.93700i			0.262770i	−0.991331	+	0.131385i	$0.958058\pi$
$354$	7.77461			0.413216
$355$	6.90634	+	7.30621i	0.366550	+	0.387774i
$356$	12.7910			0.677921
$357$			43.1704i			2.28482i
$358$		−	0.838106i		−	0.0442953i
$359$	−0.458022			−0.0241735			−0.0120867	−	0.999927i	$-0.503847\pi$
$359$	−0.458022			−0.0241735			−0.0120867	+	0.999927i	$0.503847\pi$
$360$	−3.25082	+	3.07290i	−0.171333	+	0.161956i
$361$	−16.8339			−0.885993
$362$		−	0.483189i		−	0.0253958i
$363$			22.9227i			1.20313i
$364$	13.2814			0.696136
$365$	6.98123	−	6.59914i	0.365414	−	0.345415i
$366$	17.0261			0.889968
$367$		−	16.2642i		−	0.848987i	−0.905431	−	0.424493i	$-0.860452\pi$
$367$		−	16.2642i		−	0.848987i	0.905431	−	0.424493i	$-0.139548\pi$
$368$		−	12.7070i		−	0.662398i
$369$	1.74797			0.0909957
$370$	23.2589	+	24.6056i	1.20917	+	1.27918i
$371$	−40.8452			−2.12058
$372$			10.1485i			0.526175i
$373$		−	19.6620i		−	1.01806i	−0.860749	−	0.509029i	$-0.830005\pi$
$373$		−	19.6620i		−	1.01806i	0.860749	−	0.509029i	$-0.169995\pi$
$374$	−55.3701			−2.86312
$375$	9.97575	+	11.8193i	0.515145	+	0.610345i
$376$	10.9598			0.565211
$377$		−	27.1152i		−	1.39650i
$378$		−	48.8950i		−	2.51489i
$379$	38.4555			1.97533			0.987664	−	0.156587i	$-0.0500493\pi$
$379$	38.4555			1.97533			0.987664	+	0.156587i	$0.0500493\pi$
$380$	−2.08623	−	2.20703i	−0.107022	−	0.113218i
$381$	13.9373			0.714029
$382$		−	31.7478i		−	1.62436i
$383$			25.5844i			1.30730i	0.756796	+	0.653652i	$0.226764\pi$
$383$			25.5844i			1.30730i	−0.756796	+	0.653652i	$0.773236\pi$
$384$	−17.4245			−0.889192
$385$	43.1684	−	40.8058i	2.20007	−	2.07965i
$386$	−43.8198			−2.23037
$387$			0.0194591i			0.000989162i
$388$			10.2113i			0.518399i
$389$	−1.54506			−0.0783376			−0.0391688	−	0.999233i	$-0.512471\pi$
$389$	−1.54506			−0.0783376			−0.0391688	+	0.999233i	$0.512471\pi$
$390$	−10.9324	+	10.3341i	−0.553585	+	0.523287i
$391$	−15.6944			−0.793699
$392$			34.2483i			1.72980i
$393$			7.43033i			0.374811i
$394$	20.8403			1.04992
$395$	3.59553	+	3.80371i	0.180911	+	0.191385i
$396$	5.26371			0.264511
$397$		−	15.9215i		−	0.799078i	−0.916716	−	0.399539i	$-0.869170\pi$
$397$		−	15.9215i		−	0.799078i	0.916716	−	0.399539i	$-0.130830\pi$
$398$			11.4708i			0.574980i
$399$	−10.3009			−0.515690
$400$	1.40398	−	24.9307i	0.0701991	−	1.24654i
$401$	−16.9817			−0.848024			−0.424012	−	0.905657i	$-0.639379\pi$
$401$	−16.9817			−0.848024			−0.424012	+	0.905657i	$0.639379\pi$
$402$			6.91750i			0.345014i
$403$			22.6142i			1.12649i
$404$	−0.229860			−0.0114360
$405$	7.00588	+	7.41152i	0.348125	+	0.368281i
$406$	−82.4477			−4.09181
$407$			46.5055i			2.30519i
$408$			15.7137i			0.777945i
$409$	26.2104			1.29602			0.648010	−	0.761631i	$-0.275601\pi$
$409$	26.2104			1.29602			0.648010	+	0.761631i	$0.275601\pi$
$410$	−4.47021	+	4.22556i	−0.220768	+	0.208685i
$411$	14.1911			0.699995
$412$			12.4164i			0.611714i
$413$		−	16.6318i		−	0.818397i
$414$	4.72549			0.232245
$415$	−15.0707	+	14.2458i	−0.739790	+	0.699301i
$416$	13.8103			0.677104
$417$		−	20.2155i		−	0.989957i
$418$		−	13.2119i		−	0.646214i
$419$	14.5100			0.708862			0.354431	−	0.935082i	$-0.384675\pi$
$419$	14.5100			0.708862			0.354431	+	0.935082i	$0.384675\pi$
$420$	9.92094	+	10.4954i	0.484092	+	0.512121i
$421$	14.9113			0.726732			0.363366	−	0.931646i	$-0.381627\pi$
$421$	14.9113			0.726732			0.363366	+	0.931646i	$0.381627\pi$
$422$		−	13.5500i		−	0.659606i
$423$			6.46502i			0.314340i
$424$	−14.8674			−0.722023
$425$	−30.7919	−	1.73406i	−1.49362	−	0.0841140i
$426$	−10.6336			−0.515200
$427$		−	36.4230i		−	1.76263i
$428$		−	1.20693i		−	0.0583392i
$429$	−20.6627			−0.997606
$430$	−0.0470406	−	0.0497643i	−0.00226850	−	0.00239985i
$431$	−27.0648			−1.30367			−0.651833	−	0.758363i	$-0.726000\pi$
$431$	−27.0648			−1.30367			−0.651833	+	0.758363i	$0.726000\pi$
$432$		−	28.2306i		−	1.35824i
$433$		−	32.9065i		−	1.58139i	−0.612212	−	0.790693i	$-0.709720\pi$
$433$		−	32.9065i		−	1.58139i	0.612212	−	0.790693i	$-0.290280\pi$
$434$	68.7618			3.30067
$435$	21.4272	−	20.2544i	1.02735	−	0.971126i
$436$	17.7686			0.850960
$437$		−	3.74484i		−	0.179140i
$438$			10.1606i			0.485493i
$439$	18.6369			0.889490			0.444745	−	0.895657i	$-0.353294\pi$
$439$	18.6369			0.889490			0.444745	+	0.895657i	$0.353294\pi$
$440$	15.7130	−	14.8530i	0.749088	−	0.708089i
$441$	−20.2025			−0.962022
$442$		−	29.9976i		−	1.42684i
$443$		−	0.950840i		−	0.0451758i	−0.999745	−	0.0225879i	$-0.992809\pi$
$443$		−	0.950840i		−	0.0451758i	0.999745	−	0.0225879i	$-0.00719056\pi$
$444$	−11.3067			−0.536592
$445$	21.2908	+	22.5235i	1.00928	+	1.06772i
$446$	−32.1340			−1.52159
$447$			21.8758i			1.03469i
$448$			8.54132i			0.403539i
$449$	−12.1598			−0.573858			−0.286929	−	0.957952i	$-0.592634\pi$
$449$	−12.1598			−0.573858			−0.286929	+	0.957952i	$0.592634\pi$
$450$	9.27125	+	0.522114i	0.437051	+	0.0246127i
$451$	−8.44889			−0.397843
$452$			15.7233i			0.739561i
$453$		−	21.1499i		−	0.993710i
$454$	−3.01781			−0.141633
$455$	22.1071	+	23.3871i	1.03640	+	1.09641i
$456$	−3.74945			−0.175584
$457$			34.9685i			1.63576i	0.575389	+	0.817880i	$0.304851\pi$
$457$			34.9685i			1.63576i	−0.575389	+	0.817880i	$0.695149\pi$
$458$		−	36.2057i		−	1.69178i
$459$	−34.8675			−1.62747
$460$	−3.81554	+	3.60671i	−0.177900	+	0.168164i
$461$	−10.2125			−0.475646			−0.237823	−	0.971309i	$-0.576434\pi$
$461$	−10.2125			−0.475646			−0.237823	+	0.971309i	$0.576434\pi$
$462$			62.8281i			2.92303i
$463$		−	17.4281i		−	0.809951i	−0.914328	−	0.404976i	$-0.867280\pi$
$463$		−	17.4281i		−	0.809951i	0.914328	−	0.404976i	$-0.132720\pi$
$464$	−47.6029			−2.20991
$465$	−17.8704	+	16.8923i	−0.828719	+	0.783362i
$466$	−10.4118			−0.482316
$467$			18.9150i			0.875281i	0.899150	+	0.437640i	$0.144186\pi$
$467$			18.9150i			0.875281i	−0.899150	+	0.437640i	$0.855814\pi$
$468$			2.85169i			0.131820i
$469$	14.7982			0.683318
$470$	−15.6286	−	16.5335i	−0.720893	−	0.762632i
$471$	1.18630			0.0546616
$472$		−	6.05385i		−	0.278651i
$473$		−	0.0940565i		−	0.00432472i
$474$	−5.53599			−0.254277
$475$	0.413763	−	7.34726i	0.0189848	−	0.337115i
$476$	−28.7983			−1.31997
$477$		−	8.76999i		−	0.401550i
$478$		−	2.38476i		−	0.109076i
$479$	19.0476			0.870306			0.435153	−	0.900357i	$-0.356694\pi$
$479$	19.0476			0.870306			0.435153	+	0.900357i	$0.356694\pi$
$480$	10.3160	+	10.9133i	0.470857	+	0.498120i
$481$	−25.1951			−1.14880
$482$		−	1.70963i		−	0.0778713i
$483$			17.8083i			0.810307i
$484$	−15.2914			−0.695063
$485$	−17.9809	+	16.9968i	−0.816472	+	0.771786i
$486$	18.2059			0.825835
$487$		−	22.4723i		−	1.01832i	−0.860673	−	0.509159i	$-0.829957\pi$
$487$		−	22.4723i		−	1.01832i	0.860673	−	0.509159i	$-0.170043\pi$
$488$		−	13.2577i		−	0.600148i
$489$	−12.9588			−0.586019
$490$	51.6653	−	48.8376i	2.33400	−	2.20626i
$491$	−7.02401			−0.316989			−0.158495	−	0.987360i	$-0.550664\pi$
$491$	−7.02401			−0.316989			−0.158495	+	0.987360i	$0.550664\pi$
$492$		−	2.05414i		−	0.0926079i
$493$			58.7942i			2.64796i
$494$	7.15773			0.322041
$495$	8.76152	+	9.26881i	0.393801	+	0.416602i
$496$	39.7010			1.78263
$497$			22.7479i			1.02038i
$498$		−	21.9341i		−	0.982892i
$499$	−21.8733			−0.979183			−0.489592	−	0.871952i	$-0.662854\pi$
$499$	−21.8733			−0.979183			−0.489592	+	0.871952i	$0.662854\pi$
$500$	−7.88446	+	6.65467i	−0.352604	+	0.297606i
$501$	3.79115			0.169376
$502$		−	17.9285i		−	0.800187i
$503$		−	30.0983i		−	1.34202i	−0.741449	−	0.671009i	$-0.765861\pi$
$503$		−	30.0983i		−	1.34202i	0.741449	−	0.671009i	$-0.234139\pi$
$504$	−10.1214			−0.450844
$505$	−0.382606	−	0.404759i	−0.0170257	−	0.0180115i
$506$	−22.8409			−1.01540
$507$			6.78934i			0.301525i
$508$			9.29735i			0.412503i
$509$	−7.77815			−0.344761			−0.172380	−	0.985030i	$-0.555146\pi$
$509$	−7.77815			−0.344761			−0.172380	+	0.985030i	$0.555146\pi$
$510$	23.7049	−	22.4075i	1.04967	−	0.992222i
$511$	21.7360			0.961546
$512$		−	5.85120i		−	0.258589i
$513$		−	8.31974i		−	0.367326i
$514$	25.3915			1.11997
$515$	−21.8640	+	20.6673i	−0.963441	+	0.910711i
$516$	0.0228676			0.00100669
$517$		−	31.2490i		−	1.37433i
$518$			76.6093i			3.36602i
$519$	−2.61333			−0.114712
$520$	8.04684	+	8.51275i	0.352877	+	0.373309i
$521$	−14.0318			−0.614746			−0.307373	−	0.951589i	$-0.599450\pi$
$521$	−14.0318			−0.614746			−0.307373	+	0.951589i	$0.599450\pi$
$522$		−	17.7026i		−	0.774821i
$523$			2.80012i			0.122440i	0.998124	+	0.0612202i	$0.0194992\pi$
$523$			2.80012i			0.122440i	−0.998124	+	0.0612202i	$0.980501\pi$
$524$	−4.95666			−0.216533
$525$	−1.96762	+	34.9393i	−0.0858741	+	1.52488i
$526$	2.06805			0.0901711
$527$		−	49.0347i		−	2.13598i
$528$			36.2751i			1.57867i
$529$	16.5259			0.718516
$530$	21.2006	+	22.4282i	0.920897	+	0.974217i
$531$	3.57106			0.154971
$532$		−	6.87157i		−	0.297920i
$533$		−	4.57731i		−	0.198265i
$534$	−32.7811			−1.41858
$535$	2.12527	−	2.00895i	0.0918835	−	0.0868546i
$536$	5.38645			0.232659
$537$			0.678162i			0.0292648i
$538$			26.7448i			1.15305i
$539$	97.6495			4.20606
$540$	−8.47680	+	8.01286i	−0.364783	+	0.344818i
$541$	31.2317			1.34276			0.671379	−	0.741114i	$-0.265702\pi$
$541$	31.2317			1.34276			0.671379	+	0.741114i	$0.265702\pi$
$542$			44.4045i			1.90734i
$543$			0.390977i			0.0167784i
$544$	−29.9450			−1.28388
$545$	29.5760	+	31.2885i	1.26690	+	1.34025i
$546$	−34.0381			−1.45669
$547$		−	42.9144i		−	1.83489i	−0.397865	−	0.917444i	$-0.630249\pi$
$547$		−	42.9144i		−	1.83489i	0.397865	−	0.917444i	$-0.369751\pi$
$548$			9.46666i			0.404396i
$549$	7.82048			0.333770
$550$	−44.8130	−	2.52366i	−1.91083	−	0.107609i
$551$	−14.0289			−0.597651
$552$			6.48211i			0.275897i
$553$			11.8428i			0.503609i
$554$	−20.0973			−0.853852
$555$	−18.8202	−	19.9098i	−0.798871	−	0.845126i
$556$	13.4854			0.571910
$557$		−	39.2314i		−	1.66229i	−0.556056	−	0.831145i	$-0.687686\pi$
$557$		−	39.2314i		−	1.66229i	0.556056	−	0.831145i	$-0.312314\pi$
$558$			14.7641i			0.625012i
$559$	0.0509565			0.00215523
$560$	41.0580	−	38.8108i	1.73502	−	1.64006i
$561$	44.8033			1.89160
$562$			11.4231i			0.481855i
$563$			9.68487i			0.408169i	0.978953	+	0.204084i	$0.0654217\pi$
$563$			9.68487i			0.408169i	−0.978953	+	0.204084i	$0.934578\pi$
$564$	7.59743			0.319909
$565$	−27.6870	+	26.1716i	−1.16480	+	1.10105i
$566$	12.5855			0.529007
$567$			23.0757i			0.969090i
$568$			8.28006i			0.347424i
$569$	12.8438			0.538441			0.269221	−	0.963079i	$-0.413234\pi$
$569$	12.8438			0.538441			0.269221	+	0.963079i	$0.413234\pi$
$570$	5.34667	+	5.65624i	0.223947	+	0.236914i
$571$	8.76755			0.366910			0.183455	−	0.983028i	$-0.441272\pi$
$571$	8.76755			0.366910			0.183455	+	0.983028i	$0.441272\pi$
$572$		−	13.7838i		−	0.576329i
$573$			25.6890i			1.07318i
$574$	−13.9180			−0.580926
$575$	−12.7020	−	0.715320i	−0.529712	−	0.0298309i
$576$	−1.83393			−0.0764138
$577$			42.9318i			1.78727i	0.448791	+	0.893637i	$0.351855\pi$
$577$			42.9318i			1.78727i	−0.448791	+	0.893637i	$0.648145\pi$
$578$			35.9805i			1.49659i
$579$	35.4572			1.47355
$580$	13.5114	+	14.2937i	0.561031	+	0.593515i
$581$	−46.9225			−1.94667
$582$		−	26.1698i		−	1.08477i
$583$			42.3901i			1.75562i
$584$	7.91177			0.327391
$585$	−5.02152	+	4.74669i	−0.207614	+	0.196251i
$586$	20.6017			0.851047
$587$			39.1573i			1.61619i	0.589049	+	0.808097i	$0.299503\pi$
$587$			39.1573i			1.61619i	−0.589049	+	0.808097i	$0.700497\pi$
$588$			23.7411i			0.979067i
$589$	11.7002			0.482097
$590$	−9.13254	+	8.63271i	−0.375981	+	0.355403i
$591$	−16.8631			−0.693656
$592$			44.2320i			1.81792i
$593$			21.3089i			0.875050i	0.899206	+	0.437525i	$0.144145\pi$
$593$			21.3089i			0.875050i	−0.899206	+	0.437525i	$0.855855\pi$
$594$	−50.7445			−2.08207
$595$	−47.9352	−	50.7106i	−1.96515	−	2.07893i
$596$	−14.5930			−0.597753
$597$		−	9.28173i		−	0.379876i
$598$		−	12.3744i		−	0.506026i
$599$	7.76975			0.317463			0.158732	−	0.987322i	$-0.449260\pi$
$599$	7.76975			0.317463			0.158732	+	0.987322i	$0.449260\pi$
$600$	−0.716200	+	12.7177i	−0.0292388	+	0.519197i
$601$	16.9993			0.693415			0.346707	−	0.937973i	$-0.387300\pi$
$601$	16.9993			0.693415			0.346707	+	0.937973i	$0.387300\pi$
$602$		−	0.154941i		−	0.00631492i
$603$			3.17737i			0.129392i
$604$	14.1088			0.574079
$605$	−25.4527	−	26.9264i	−1.03480	−	1.09472i
$606$	0.589093			0.0239303
$607$			20.7512i			0.842267i	0.906999	+	0.421133i	$0.138368\pi$
$607$			20.7512i			0.842267i	−0.906999	+	0.421133i	$0.861632\pi$
$608$		−	7.14518i		−	0.289775i
$609$	66.7134			2.70336
$610$	−19.9999	+	18.9053i	−0.809773	+	0.765453i
$611$	16.9296			0.684898
$612$		−	6.18337i		−	0.249948i
$613$		−	17.5567i		−	0.709108i	−0.935035	−	0.354554i	$-0.884633\pi$
$613$		−	17.5567i		−	0.709108i	0.935035	−	0.354554i	$-0.115367\pi$
$614$	44.0923			1.77942
$615$	3.61712	−	3.41915i	0.145856	−	0.137873i
$616$	48.9224			1.97114
$617$		−	6.03640i		−	0.243016i	−0.992590	−	0.121508i	$-0.961227\pi$
$617$		−	6.03640i		−	0.243016i	0.992590	−	0.121508i	$-0.0387731\pi$
$618$		−	31.8212i		−	1.28004i
$619$	21.4216			0.861008			0.430504	−	0.902589i	$-0.358336\pi$
$619$	21.4216			0.861008			0.430504	+	0.902589i	$0.358336\pi$
$620$	−11.2686	−	11.9211i	−0.452558	−	0.478761i
$621$	−14.3833			−0.577181
$622$			32.7948i			1.31495i
$623$			70.1268i			2.80957i
$624$	−19.6526			−0.786733
$625$	−24.8419	−	2.80687i	−0.993677	−	0.112275i
$626$	7.41034			0.296177
$627$			10.6905i			0.426938i
$628$			0.791359i			0.0315787i
$629$	54.6308			2.17827
$630$	14.4330	+	15.2687i	0.575025	+	0.608318i
$631$	17.0323			0.678044			0.339022	−	0.940778i	$-0.389904\pi$
$631$	17.0323			0.678044			0.339022	+	0.940778i	$0.389904\pi$
$632$			4.31071i			0.171471i
$633$			10.9642i			0.435786i
$634$	12.4917			0.496107
$635$	−16.3716	+	15.4756i	−0.649687	+	0.614129i
$636$	−10.3061			−0.408665
$637$			52.9031i			2.09610i
$638$			85.5662i			3.38760i
$639$	−4.88426			−0.193218
$640$	20.4679	−	19.3477i	0.809066	−	0.764785i
$641$	−5.88960			−0.232625			−0.116313	−	0.993213i	$-0.537107\pi$
$641$	−5.88960			−0.232625			−0.116313	+	0.993213i	$0.537107\pi$
$642$			3.09316i			0.122077i
$643$		−	27.5753i		−	1.08746i	−0.839259	−	0.543731i	$-0.817011\pi$
$643$		−	27.5753i		−	1.08746i	0.839259	−	0.543731i	$-0.182989\pi$
$644$	−11.8797			−0.468124
$645$	0.0380634	+	0.0402673i	0.00149874	+	0.00158552i
$646$	−15.5202			−0.610634
$647$		−	26.2229i		−	1.03093i	−0.856911	−	0.515465i	$-0.827619\pi$
$647$		−	26.2229i		−	1.03093i	0.856911	−	0.515465i	$-0.172381\pi$
$648$			8.39940i			0.329960i
$649$	−17.2609			−0.677549
$650$	1.36723	−	24.2781i	0.0536272	−	0.952266i
$651$	−55.6393			−2.18068
$652$		−	8.64464i		−	0.338550i
$653$		−	5.20569i		−	0.203714i	−0.994799	−	0.101857i	$-0.967522\pi$
$653$		−	5.20569i		−	0.203714i	0.994799	−	0.101857i	$-0.0324785\pi$
$654$	−45.5378			−1.78067
$655$	−8.25043	−	8.72813i	−0.322371	−	0.341036i
$656$	−8.03584			−0.313747
$657$			4.66701i			0.182077i
$658$		−	51.4769i		−	2.00678i
$659$	7.97812			0.310783			0.155392	−	0.987853i	$-0.450336\pi$
$659$	7.97812			0.310783			0.155392	+	0.987853i	$0.450336\pi$
$660$	10.8923	−	10.2962i	0.423984	−	0.400779i
$661$	17.0900			0.664724			0.332362	−	0.943152i	$-0.392154\pi$
$661$	17.0900			0.664724			0.332362	+	0.943152i	$0.392154\pi$
$662$		−	1.74437i		−	0.0677970i
$663$			24.2728i			0.942679i
$664$	−17.0795			−0.662811
$665$	12.1001	−	11.4378i	0.469221	−	0.443540i
$666$	−16.4490			−0.637386
$667$			24.2533i			0.939093i
$668$			2.52902i			0.0978506i
$669$	26.0016			1.00528
$670$	−7.68100	−	8.12573i	−0.296743	−	0.313924i
$671$	−37.8007			−1.45928
$672$			33.9784i			1.31074i
$673$		−	40.1751i		−	1.54864i	−0.632796	−	0.774319i	$-0.718093\pi$
$673$		−	40.1751i		−	1.54864i	0.632796	−	0.774319i	$-0.281907\pi$
$674$	32.4240			1.24892
$675$	−28.2195	−	1.58919i	−1.08617	−	0.0611680i
$676$	−4.52907			−0.174195
$677$		−	9.73259i		−	0.374054i	−0.982355	−	0.187027i	$-0.940115\pi$
$677$		−	9.73259i		−	0.374054i	0.982355	−	0.187027i	$-0.0598851\pi$
$678$		−	40.2961i		−	1.54756i
$679$	−55.9836			−2.14845
$680$	−17.4481	−	18.4583i	−0.669103	−	0.707844i
$681$	2.44190			0.0935736
$682$		−	71.3627i		−	2.73262i
$683$			9.78489i			0.374408i	0.982321	+	0.187204i	$0.0599426\pi$
$683$			9.78489i			0.374408i	−0.982321	+	0.187204i	$0.940057\pi$
$684$	1.47541			0.0564139
$685$	−16.6697	+	15.7574i	−0.636918	+	0.602059i
$686$	100.312			3.82994
$687$			29.2962i			1.11772i
$688$		−	0.0894582i		−	0.00341056i
$689$	−22.9655			−0.874916
$690$	9.77858	−	9.24339i	0.372264	−	0.351890i
$691$	3.54792			0.134969			0.0674846	−	0.997720i	$-0.478503\pi$
$691$	3.54792			0.134969			0.0674846	+	0.997720i	$0.478503\pi$
$692$		−	1.74331i		−	0.0662707i
$693$			28.8584i			1.09624i
$694$	−53.6651			−2.03710
$695$	22.4467	+	23.7464i	0.851452	+	0.900751i
$696$	24.2832			0.920452
$697$			9.92505i			0.375938i
$698$		−	20.6686i		−	0.782318i
$699$	8.42479			0.318655
$700$	−23.3075	−	1.31257i	−0.880941	−	0.0496105i
$701$	21.2003			0.800724			0.400362	−	0.916357i	$-0.368884\pi$
$701$	21.2003			0.800724			0.400362	+	0.916357i	$0.368884\pi$
$702$		−	27.4916i		−	1.03760i
$703$			13.0355i			0.491642i
$704$	8.86439			0.334089
$705$	12.6460	+	13.3782i	0.476277	+	0.503853i
$706$	8.44042			0.317659
$707$		−	1.26021i		−	0.0473952i
$708$		−	4.19656i		−	0.157717i
$709$	−35.8330			−1.34574			−0.672869	−	0.739762i	$-0.734938\pi$
$709$	−35.8330			−1.34574			−0.672869	+	0.739762i	$0.734938\pi$
$710$	12.4909	−	11.8073i	0.468775	−	0.443118i
$711$	−2.54281			−0.0953628
$712$			25.5257i			0.956615i
$713$		−	20.2274i		−	0.757523i
$714$	73.8052			2.76209
$715$	24.2717	−	22.9433i	0.907712	−	0.858032i
$716$	−0.452391			−0.0169067
$717$			1.92965i			0.0720641i
$718$			0.783046i			0.0292230i
$719$	17.4449			0.650586			0.325293	−	0.945613i	$-0.394537\pi$
$719$	17.4449			0.650586			0.325293	+	0.945613i	$0.394537\pi$
$720$	8.33319	+	8.81568i	0.310560	+	0.328541i
$721$	−68.0734			−2.53518
$722$			28.7796i			1.07107i
$723$			1.38336i			0.0514477i
$724$	−0.260815			−0.00969310
$725$	−2.67972	+	47.5842i	−0.0995225	+	1.76723i
$726$	39.1892			1.45445
$727$			2.83872i			0.105282i	0.998613	+	0.0526411i	$0.0167639\pi$
$727$			2.83872i			0.105282i	−0.998613	+	0.0526411i	$0.983236\pi$
$728$			26.5044i			0.982319i
$729$	−28.4144			−1.05239
$730$	−11.2821	−	11.9353i	−0.417568	−	0.441745i
$731$	−0.110490			−0.00408661
$732$		−	9.19032i		−	0.339684i
$733$		−	19.1179i		−	0.706135i	−0.935598	−	0.353067i	$-0.885139\pi$
$733$		−	19.1179i		−	0.706135i	0.935598	−	0.353067i	$-0.114861\pi$
$734$	−27.8058			−1.02633
$735$	−41.8055	+	39.5174i	−1.54202	+	1.45762i
$736$	−12.3527			−0.455326
$737$		−	15.3580i		−	0.565718i
$738$		−	2.98837i		−	0.110004i
$739$	10.7460			0.395299			0.197650	−	0.980273i	$-0.436669\pi$
$739$	10.7460			0.395299			0.197650	+	0.980273i	$0.436669\pi$
$740$	13.2815	−	12.5546i	0.488239	−	0.461518i
$741$	−5.79175			−0.212765
$742$			69.8300i			2.56354i
$743$		−	21.9385i		−	0.804846i	−0.915454	−	0.402423i	$-0.868168\pi$
$743$		−	21.9385i		−	0.804846i	0.915454	−	0.402423i	$-0.131832\pi$
$744$	−20.2523			−0.742486
$745$	−24.2903	−	25.6967i	−0.889927	−	0.941454i
$746$	−33.6146			−1.23072
$747$		−	10.0749i		−	0.368620i
$748$			29.8876i			1.09280i
$749$	6.61702			0.241781
$750$	20.2065	−	17.0548i	0.737838	−	0.622753i
$751$	−24.7399			−0.902773			−0.451386	−	0.892329i	$-0.649070\pi$
$751$	−24.7399			−0.902773			−0.451386	+	0.892329i	$0.649070\pi$
$752$		−	29.7212i		−	1.08382i
$753$			14.5070i			0.528665i
$754$	−46.3568			−1.68821
$755$	23.4843	+	24.8440i	0.854681	+	0.904167i
$756$	−26.3925			−0.959885
$757$		−	15.0100i		−	0.545546i	−0.962078	−	0.272773i	$-0.912059\pi$
$757$		−	15.0100i		−	0.545546i	0.962078	−	0.272773i	$-0.0879409\pi$
$758$		−	65.7446i		−	2.38795i
$759$	18.4819			0.670851
$760$	4.40434	−	4.16329i	0.159762	−	0.151018i
$761$	−26.0521			−0.944389			−0.472194	−	0.881495i	$-0.656538\pi$
$761$	−26.0521			−0.944389			−0.472194	+	0.881495i	$0.656538\pi$
$762$		−	23.8275i		−	0.863181i
$763$			97.4166i			3.52672i
$764$	−17.1368			−0.619987
$765$	10.8882	−	10.2923i	0.393665	−	0.372119i
$766$	43.7398			1.58038
$767$		−	9.35134i		−	0.337657i
$768$			25.1186i			0.906389i
$769$	24.4144			0.880407			0.440203	−	0.897898i	$-0.354906\pi$
$769$	24.4144			0.880407			0.440203	+	0.897898i	$0.354906\pi$
$770$	−69.7626	−	73.8018i	−2.51407	−	2.65963i
$771$	−20.5458			−0.739939
$772$			23.6530i			0.851289i
$773$			41.9248i			1.50793i	0.656914	+	0.753966i	$0.271862\pi$
$773$			41.9248i			1.50793i	−0.656914	+	0.753966i	$0.728138\pi$
$774$	0.0332678			0.00119579
$775$	2.23490	−	39.6855i	0.0802802	−	1.42555i
$776$	−20.3776			−0.731514
$777$		−	61.9892i		−	2.22385i
$778$			2.64147i			0.0947014i
$779$	−2.36822			−0.0848502
$780$	5.57811	+	5.90109i	0.199729	+	0.211293i
$781$	23.6083			0.844771
$782$			26.8315i			0.959494i
$783$			53.8825i			1.92560i
$784$	92.8756			3.31699
$785$	−1.39350	+	1.31723i	−0.0497360	+	0.0470139i
$786$	12.7031			0.453104
$787$		−	42.1295i		−	1.50176i	−0.660441	−	0.750878i	$-0.729631\pi$
$787$		−	42.1295i		−	1.50176i	0.660441	−	0.750878i	$-0.270369\pi$
$788$		−	11.2491i		−	0.400734i
$789$	−1.67338			−0.0595739
$790$	6.50292	−	6.14701i	0.231364	−	0.218701i
$791$	−86.2033			−3.06504
$792$			10.5043i			0.373253i
$793$		−	20.4791i		−	0.727233i
$794$	−27.2198			−0.965995
$795$	−17.1547	−	18.1480i	−0.608415	−	0.643642i
$796$	6.19170			0.219459
$797$		−	32.8495i		−	1.16359i	−0.813335	−	0.581795i	$-0.802351\pi$
$797$		−	32.8495i		−	1.16359i	0.813335	−	0.581795i	$-0.197649\pi$
$798$			17.6107i			0.623411i
$799$	−36.7086			−1.29866
$800$	−24.2355	−	1.36483i	−0.856856	−	0.0482542i
$801$	−15.0571			−0.532018
$802$			29.0323i			1.02517i
$803$		−	22.5582i		−	0.796062i
$804$	3.73392			0.131685
$805$	−19.7739	−	20.9188i	−0.696937	−	0.737290i
$806$	38.6618			1.36180
$807$		−	21.6408i		−	0.761793i
$808$		−	0.458709i		−	0.0161373i
$809$	−21.0371			−0.739625			−0.369812	−	0.929106i	$-0.620578\pi$
$809$	−21.0371			−0.739625			−0.369812	+	0.929106i	$0.620578\pi$
$810$	12.6709	−	11.9774i	0.445211	−	0.420844i
$811$	38.1121			1.33830			0.669149	−	0.743128i	$-0.266659\pi$
$811$	38.1121			1.33830			0.669149	+	0.743128i	$0.266659\pi$
$812$			44.5035i			1.56177i
$813$		−	35.9303i		−	1.26013i
$814$	79.5070			2.78672
$815$	15.2223	−	14.3891i	0.533213	−	0.504029i
$816$	42.6129			1.49175
$817$		−	0.0263640i		−	0.000922359i
$818$		−	44.8100i		−	1.56674i
$819$	−15.6345			−0.546313
$820$	2.28086	+	2.41292i	0.0796512	+	0.0842630i
$821$	−13.3082			−0.464459			−0.232230	−	0.972661i	$-0.574602\pi$
$821$	−13.3082			−0.464459			−0.232230	+	0.972661i	$0.574602\pi$
$822$		−	24.2614i		−	0.846215i
$823$			9.58043i			0.333953i	0.985961	+	0.166976i	$0.0534004\pi$
$823$			9.58043i			0.333953i	−0.985961	+	0.166976i	$0.946600\pi$
$824$	−24.7782			−0.863190
$825$	36.2609	+	2.04205i	1.26244	+	0.0710949i
$826$	−28.4341			−0.989350
$827$		−	5.10249i		−	0.177431i	−0.996057	−	0.0887154i	$-0.971724\pi$
$827$		−	5.10249i		−	0.177431i	0.996057	−	0.0887154i	$-0.0282762\pi$
$828$		−	2.55072i		−	0.0886435i
$829$	38.5370			1.33845			0.669223	−	0.743061i	$-0.266627\pi$
$829$	38.5370			1.33845			0.669223	+	0.743061i	$0.266627\pi$
$830$	24.3550	+	25.7652i	0.845376	+	0.894323i
$831$	16.2619			0.564120
$832$			4.80241i			0.166494i
$833$		−	114.710i		−	3.97448i
$834$	−34.5609			−1.19675
$835$	−4.45332	+	4.20958i	−0.154113	+	0.145679i
$836$	−7.13148			−0.246647
$837$		−	44.9383i		−	1.55330i
$838$		−	24.8067i		−	0.856934i
$839$	−9.97929			−0.344524			−0.172262	−	0.985051i	$-0.555107\pi$
$839$	−9.97929			−0.344524			−0.172262	+	0.985051i	$0.555107\pi$
$840$	−20.9445	+	19.7982i	−0.722655	+	0.683103i
$841$	61.8576			2.13302
$842$		−	25.4927i		−	0.878537i
$843$		−	9.24312i		−	0.318350i
$844$	−7.31402			−0.251759
$845$	−7.53870	−	7.97518i	−0.259339	−	0.274355i
$846$	11.0528			0.380002
$847$		−	83.8354i		−	2.88062i
$848$			40.3178i			1.38452i
$849$	−10.1837			−0.349503
$850$	−2.96458	+	52.6426i	−0.101684	+	1.80562i
$851$	22.5359			0.772520
$852$			5.73979i			0.196642i
$853$		−	0.528777i		−	0.0181050i	−0.999959	−	0.00905250i	$-0.997118\pi$
$853$		−	0.528777i		−	0.0181050i	0.999959	−	0.00905250i	$-0.00288154\pi$
$854$	−62.2697			−2.13082
$855$	2.45585	+	2.59804i	0.0839883	+	0.0888512i
$856$	2.40855			0.0823225
$857$		−	13.2208i		−	0.451615i	−0.974172	−	0.225808i	$-0.927498\pi$
$857$		−	13.2208i		−	0.451615i	0.974172	−	0.225808i	$-0.0725021\pi$
$858$			35.3255i			1.20599i
$859$	−15.8466			−0.540679			−0.270339	−	0.962765i	$-0.587136\pi$
$859$	−15.8466			−0.540679			−0.270339	+	0.962765i	$0.587136\pi$
$860$	−0.0268617	+	0.0253915i	−0.000915975	+	0.000865843i
$861$	11.2619			0.383804
$862$			46.2707i			1.57599i
$863$			42.9425i			1.46178i	0.682495	+	0.730890i	$0.260895\pi$
$863$			42.9425i			1.46178i	−0.682495	+	0.730890i	$0.739105\pi$
$864$	−27.4434			−0.933642
$865$	3.06978	−	2.90177i	0.104376	−	0.0986630i
$866$	−56.2578			−1.91172
$867$		−	29.1140i		−	0.988763i
$868$		−	37.1161i		−	1.25980i
$869$	12.2908			0.416937
$870$	−34.6275	−	36.6324i	−1.17398	−	1.24196i
$871$	8.32040			0.281926
$872$			35.4589i			1.20079i
$873$		−	12.0204i		−	0.406829i
$874$	−6.40228			−0.216560
$875$	−36.4844	−	43.2267i	−1.23340	−	1.46133i
$876$	5.48448			0.185303
$877$		−	13.9351i		−	0.470554i	−0.971928	−	0.235277i	$-0.924400\pi$
$877$		−	13.9351i		−	0.470554i	0.971928	−	0.235277i	$-0.0755997\pi$
$878$		−	31.8621i		−	1.07529i
$879$	−16.6701			−0.562267
$880$	−40.2788	−	42.6110i	−1.35780	−	1.43642i
$881$	38.0645			1.28243			0.641213	−	0.767363i	$-0.278431\pi$
$881$	38.0645			1.28243			0.641213	+	0.767363i	$0.278431\pi$
$882$			34.5386i			1.16298i
$883$		−	50.9419i		−	1.71433i	−0.515042	−	0.857165i	$-0.672224\pi$
$883$		−	50.9419i		−	1.71433i	0.515042	−	0.857165i	$-0.327776\pi$
$884$	−16.1920			−0.544597
$885$	7.38969	−	6.98524i	0.248402	−	0.234806i
$886$	−1.62558			−0.0546124
$887$		−	51.0399i		−	1.71375i	−0.515523	−	0.856875i	$-0.672403\pi$
$887$		−	51.0399i		−	1.71375i	0.515523	−	0.856875i	$-0.327597\pi$
$888$		−	22.5636i		−	0.757186i
$889$	−50.9729			−1.70958
$890$	38.5067	−	36.3992i	1.29075	−	1.22011i
$891$	23.9486			0.802307
$892$			17.3452i			0.580762i
$893$		−	8.75906i		−	0.293111i
$894$	37.3994			1.25082
$895$	−0.753012	−	0.796611i	−0.0251704	−	0.0266278i
$896$	63.7268			2.12896
$897$			10.0129i			0.334320i
$898$			20.7887i			0.693729i
$899$	−75.7758			−2.52726
$900$	0.281826	−	5.00442i	0.00939419	−	0.166814i
$901$	49.7964			1.65896
$902$			14.4444i			0.480947i
$903$			0.125372i			0.00417212i
$904$	−31.3774			−1.04360
$905$	−0.434130	−	0.459266i	−0.0144310	−	0.0152665i
$906$	−36.1585			−1.20128
$907$			20.9409i			0.695333i	0.937618	+	0.347666i	$0.113026\pi$
$907$			20.9409i			0.695333i	−0.937618	+	0.347666i	$0.886974\pi$
$908$			1.62895i			0.0540586i
$909$	0.270584			0.00897471
$910$	39.9832	−	37.7949i	1.32543	−	1.25289i
$911$	−28.0321			−0.928744			−0.464372	−	0.885640i	$-0.653720\pi$
$911$	−28.0321			−0.928744			−0.464372	+	0.885640i	$0.653720\pi$
$912$			10.1679i			0.336692i
$913$			48.6973i			1.61165i
$914$	59.7831			1.97745
$915$	16.1831	−	15.2974i	0.534998	−	0.505717i
$916$	−19.5430			−0.645720
$917$		−	27.1750i		−	0.897398i
$918$			59.6103i			1.96743i
$919$	21.5713			0.711572			0.355786	−	0.934567i	$-0.384213\pi$
$919$	21.5713			0.711572			0.355786	+	0.934567i	$0.384213\pi$
$920$	−7.19755	−	7.61429i	−0.237296	−	0.251036i
$921$	−35.6777			−1.17562
$922$			17.4596i			0.575002i
$923$			12.7901i			0.420993i
$924$	33.9133			1.11566
$925$	44.2147	+	2.48996i	1.45377	+	0.0818695i
$926$	−29.7955			−0.979140
$927$		−	14.6162i		−	0.480060i
$928$			46.2755i			1.51907i
$929$	−12.2984			−0.403499			−0.201749	−	0.979437i	$-0.564663\pi$
$929$	−12.2984			−0.403499			−0.201749	+	0.979437i	$0.564663\pi$
$930$	28.8795	+	30.5516i	0.946997	+	1.00183i
$931$	27.3711			0.897051
$932$			5.62005i			0.184091i
$933$		−	26.5363i		−	0.868758i
$934$	32.3375			1.05812
$935$	−52.6287	+	49.7483i	−1.72114	+	1.62694i
$936$	−5.69084			−0.186011
$937$			0.227516i			0.00743264i	0.999993	+	0.00371632i	$0.00118294\pi$
$937$			0.227516i			0.00743264i	−0.999993	+	0.00371632i	$0.998817\pi$
$938$		−	25.2994i		−	0.826055i
$939$	−5.99615			−0.195677
$940$	−8.92441	+	8.43597i	−0.291082	+	0.275151i
$941$	31.0857			1.01336			0.506682	−	0.862133i	$-0.330872\pi$
$941$	31.0857			1.01336			0.506682	+	0.862133i	$0.330872\pi$
$942$		−	2.02812i		−	0.0660797i
$943$			4.09421i			0.133326i
$944$	−16.4170			−0.534329
$945$	−43.9307	−	46.4743i	−1.42907	−	1.51181i
$946$	−0.160801			−0.00522810
$947$			28.5537i			0.927871i	0.885869	+	0.463935i	$0.153563\pi$
$947$			28.5537i			0.927871i	−0.885869	+	0.463935i	$0.846437\pi$
$948$			2.98821i			0.0970525i
$949$	12.2212			0.396718
$950$	−12.5611	−	0.707380i	−0.407534	−	0.0229505i
$951$	−10.1078			−0.327767
$952$		−	57.4699i		−	1.86261i
$953$			21.7444i			0.704372i	0.935930	+	0.352186i	$0.114561\pi$
$953$			21.7444i			0.704372i	−0.935930	+	0.352186i	$0.885439\pi$
$954$	−14.9934			−0.485429
$955$	−28.5244	−	30.1760i	−0.923028	−	0.976471i
$956$	−1.28724			−0.0416323
$957$		−	69.2368i		−	2.23811i
$958$		−	32.5642i		−	1.05210i
$959$	−51.9012			−1.67598
$960$	−3.79500	+	3.58730i	−0.122483	+	0.115780i
$961$	32.1974			1.03863
$962$			43.0741i			1.38877i
$963$			1.42076i			0.0457834i
$964$	−0.922819			−0.0297220
$965$	−41.6503	+	39.3707i	−1.34077	+	1.26739i
$966$	30.4456			0.979570
$967$			11.6791i			0.375576i	0.982210	+	0.187788i	$0.0601317\pi$
$967$			11.6791i			0.375576i	−0.982210	+	0.187788i	$0.939868\pi$
$968$		−	30.5155i		−	0.980805i
$969$	12.5583			0.403432
$970$	29.0582	+	30.7407i	0.933002	+	0.987023i
$971$	−8.70745			−0.279435			−0.139718	−	0.990191i	$-0.544619\pi$
$971$	−8.70745			−0.279435			−0.139718	+	0.990191i	$0.544619\pi$
$972$		−	9.82714i		−	0.315206i
$973$			73.9342i			2.37022i
$974$	−38.4192			−1.23103
$975$	−1.10631	+	19.6449i	−0.0354302	+	0.629140i
$976$	−35.9527			−1.15082
$977$		−	44.5056i		−	1.42386i	−0.702250	−	0.711930i	$-0.747821\pi$
$977$		−	44.5056i		−	1.42386i	0.702250	−	0.711930i	$-0.252179\pi$
$978$			22.1548i			0.708431i
$979$	72.7794			2.32604
$980$	−26.3615	−	27.8878i	−0.842086	−	0.890843i
$981$	−20.9166			−0.667815
$982$			12.0084i			0.383204i
$983$			43.9573i			1.40202i	0.713152	+	0.701010i	$0.247267\pi$
$983$			43.9573i			1.40202i	−0.713152	+	0.701010i	$0.752733\pi$
$984$	4.09925			0.130679
$985$	19.8085	−	18.7243i	0.631151	−	0.596607i
$986$	100.516			3.20108
$987$			41.6531i			1.32583i
$988$		−	3.86359i		−	0.122917i
$989$	−0.0455784			−0.00144931
$990$	15.8462	−	14.9789i	0.503625	−	0.476061i
$991$	19.5023			0.619510			0.309755	−	0.950816i	$-0.399753\pi$
$991$	19.5023			0.619510			0.309755	+	0.950816i	$0.399753\pi$
$992$		−	38.5940i		−	1.22536i
$993$			1.41148i			0.0447919i
$994$	38.8903			1.23353
$995$	10.3062	+	10.9029i	0.326728	+	0.345645i
$996$	−11.8396			−0.375151
$997$			53.0288i			1.67944i	0.543021	+	0.839719i	$0.317280\pi$
$997$			53.0288i			1.67944i	−0.543021	+	0.839719i	$0.682720\pi$
$998$			37.3951i			1.18372i
$999$	50.0669			1.58405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.11	✓	46
5.2	odd	4		6025.2.a.p.1.36		46
5.3	odd	4		6025.2.a.p.1.11		46
5.4	even	2	inner	1205.2.b.c.724.36	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.11	✓	46	1.1	even	1	trivial
1205.2.b.c.724.36	yes	46	5.4	even	2	inner
6025.2.a.p.1.11		46	5.3	odd	4
6025.2.a.p.1.36		46	5.2	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.70963i q^{2} +1.38336i q^{3} -0.922819 q^{4} +(-1.53605 - 1.62498i) q^{5} +2.36503 q^{6} -5.05937i q^{7} -1.84158i q^{8} +1.08631 q^{9} +O(q^{10})\)	\(q-1.70963i q^{2} +1.38336i q^{3} -0.922819 q^{4} +(-1.53605 - 1.62498i) q^{5} +2.36503 q^{6} -5.05937i q^{7} -1.84158i q^{8} +1.08631 q^{9} +(-2.77811 + 2.62606i) q^{10} -5.25074 q^{11} -1.27659i q^{12} -2.84467i q^{13} -8.64964 q^{14} +(2.24794 - 2.12490i) q^{15} -4.99404 q^{16} +6.16813i q^{17} -1.85719i q^{18} -1.47178 q^{19} +(1.41749 + 1.49956i) q^{20} +6.99894 q^{21} +8.97680i q^{22} +2.54443i q^{23} +2.54756 q^{24} +(-0.281131 + 4.99209i) q^{25} -4.86332 q^{26} +5.65285i q^{27} +4.66889i q^{28} +9.53193 q^{29} +(-3.63279 - 3.84313i) q^{30} -7.94968 q^{31} +4.85479i q^{32} -7.26367i q^{33} +10.5452 q^{34} +(-8.22139 + 7.77143i) q^{35} -1.00247 q^{36} -8.85694i q^{37} +2.51619i q^{38} +3.93520 q^{39} +(-2.99253 + 2.82874i) q^{40} +1.60908 q^{41} -11.9656i q^{42} +0.0179130i q^{43} +4.84548 q^{44} +(-1.66863 - 1.76524i) q^{45} +4.35003 q^{46} +5.95134i q^{47} -6.90856i q^{48} -18.5973 q^{49} +(8.53460 + 0.480629i) q^{50} -8.53275 q^{51} +2.62511i q^{52} -8.07317i q^{53} +9.66425 q^{54} +(8.06538 + 8.53236i) q^{55} -9.31723 q^{56} -2.03600i q^{57} -16.2960i q^{58} +3.28732 q^{59} +(-2.07444 + 1.96090i) q^{60} +7.19911 q^{61} +13.5910i q^{62} -5.49606i q^{63} -1.68822 q^{64} +(-4.62253 + 4.36954i) q^{65} -12.4182 q^{66} +2.92491i q^{67} -5.69207i q^{68} -3.51987 q^{69} +(13.2862 + 14.0555i) q^{70} -4.49618 q^{71} -2.00053i q^{72} +4.29619i q^{73} -15.1421 q^{74} +(-6.90586 - 0.388906i) q^{75} +1.35819 q^{76} +26.5655i q^{77} -6.72772i q^{78} -2.34077 q^{79} +(7.67107 + 8.11523i) q^{80} -4.56099 q^{81} -2.75093i q^{82} -9.27436i q^{83} -6.45875 q^{84} +(10.0231 - 9.47453i) q^{85} +0.0306245 q^{86} +13.1861i q^{87} +9.66964i q^{88} -13.8608 q^{89} +(-3.01790 + 2.85272i) q^{90} -14.3922 q^{91} -2.34805i q^{92} -10.9973i q^{93} +10.1746 q^{94} +(2.26072 + 2.39161i) q^{95} -6.71593 q^{96} -11.0653i q^{97} +31.7944i q^{98} -5.70395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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