LMFDB - Embedded newform 552.2.q.c.265.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.2
Character	$\chi$	$=$	552.265
Dual form			552.2.q.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{3} +(-0.991724 + 0.291196i) q^{5} +(-2.31042 - 2.66637i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{3} +(-0.991724 + 0.291196i) q^{5} +(-2.31042 - 2.66637i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-1.40006 - 0.899767i) q^{11} +(-3.21506 + 3.71038i) q^{13} +(0.147095 + 1.02307i) q^{15} +(0.654168 + 1.43243i) q^{17} +(-3.15045 + 6.89851i) q^{19} +(-2.96803 + 1.90744i) q^{21} +(1.47281 - 4.56408i) q^{23} +(-3.30755 + 2.12563i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-3.54108 - 7.75389i) q^{29} +(-0.990247 - 6.88732i) q^{31} +(-1.08986 + 1.25776i) q^{33} +(3.06773 + 1.97151i) q^{35} +(8.02252 + 2.35562i) q^{37} +(3.21506 + 3.71038i) q^{39} +(-11.4839 + 3.37199i) q^{41} +(0.212305 - 1.47661i) q^{43} +1.03359 q^{45} -3.84862 q^{47} +(-0.775266 + 5.39209i) q^{49} +(1.51095 - 0.443654i) q^{51} +(-4.28703 - 4.94749i) q^{53} +(1.65049 + 0.484626i) q^{55} +(6.37994 + 4.10014i) q^{57} +(8.34611 - 9.63192i) q^{59} +(0.641196 + 4.45962i) q^{61} +(1.46563 + 3.20928i) q^{63} +(2.10800 - 4.61589i) q^{65} +(-3.57483 + 2.29741i) q^{67} +(-4.30802 - 2.10735i) q^{69} +(-2.75118 + 1.76808i) q^{71} +(-4.00312 + 8.76562i) q^{73} +(1.63328 + 3.57639i) q^{75} +(0.835628 + 5.81192i) q^{77} +(11.3200 - 13.0639i) q^{79} +(0.841254 + 0.540641i) q^{81} +(2.51280 + 0.737824i) q^{83} +(-1.06587 - 1.23008i) q^{85} +(-8.17891 + 2.40155i) q^{87} +(2.21930 - 15.4355i) q^{89} +17.3214 q^{91} -6.95815 q^{93} +(1.11555 - 7.75882i) q^{95} +(-4.37419 + 1.28438i) q^{97} +(1.08986 + 1.25776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$		0			0
$5$	−0.991724	+	0.291196i	−0.443512	+	0.130227i	−0.495861	−	0.868402i	$-0.665147\pi$
$5$	−0.991724	+	0.291196i	−0.443512	+	0.130227i	0.0523487	+	0.998629i	$0.483329\pi$
$6$		0			0
$7$	−2.31042	−	2.66637i	−0.873256	−	1.00779i	−0.999875	−	0.0158399i	$-0.994958\pi$
$7$	−2.31042	−	2.66637i	−0.873256	−	1.00779i	0.126618	−	0.991952i	$-0.459588\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	−1.40006	−	0.899767i	−0.422135	−	0.271290i	0.312280	−	0.949990i	$-0.398907\pi$
$11$	−1.40006	−	0.899767i	−0.422135	−	0.271290i	−0.734415	+	0.678700i	$0.762544\pi$
$12$		0			0
$13$	−3.21506	+	3.71038i	−0.891698	+	1.02907i	0.107693	+	0.994184i	$0.465654\pi$
$13$	−3.21506	+	3.71038i	−0.891698	+	1.02907i	−0.999391	+	0.0348900i	$0.988892\pi$
$14$		0			0
$15$	0.147095	+	1.02307i	0.0379799	+	0.264156i
$16$		0			0
$17$	0.654168	+	1.43243i	0.158659	+	0.347415i	0.972222	−	0.234063i	$-0.0752021\pi$
$17$	0.654168	+	1.43243i	0.158659	+	0.347415i	−0.813562	+	0.581478i	$0.802475\pi$
$18$		0			0
$19$	−3.15045	+	6.89851i	−0.722762	+	1.58263i	0.0872314	+	0.996188i	$0.472198\pi$
$19$	−3.15045	+	6.89851i	−0.722762	+	1.58263i	−0.809993	+	0.586439i	$0.800529\pi$
$20$		0			0
$21$	−2.96803	+	1.90744i	−0.647678	+	0.416237i
$22$		0			0
$23$	1.47281	−	4.56408i	0.307101	−	0.951677i
$23$	1.47281	−	4.56408i	0.307101	−	0.951677i
$24$		0			0
$25$	−3.30755	+	2.12563i	−0.661509	+	0.425126i
$26$		0			0
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$		0			0
$29$	−3.54108	−	7.75389i	−0.657562	−	1.43986i	−0.884776	−	0.466016i	$-0.845689\pi$
$29$	−3.54108	−	7.75389i	−0.657562	−	1.43986i	0.227214	−	0.973845i	$-0.427038\pi$
$30$		0			0
$31$	−0.990247	−	6.88732i	−0.177854	−	1.23700i	−0.861717	−	0.507389i	$-0.830611\pi$
$31$	−0.990247	−	6.88732i	−0.177854	−	1.23700i	0.683863	−	0.729610i	$-0.260298\pi$
$32$		0			0
$33$	−1.08986	+	1.25776i	−0.189720	+	0.218948i
$34$		0			0
$35$	3.06773	+	1.97151i	0.518542	+	0.333246i
$36$		0			0
$37$	8.02252	+	2.35562i	1.31889	+	0.387262i	0.864094	−	0.503331i	$-0.167892\pi$
$37$	8.02252	+	2.35562i	1.31889	+	0.387262i	0.454801	+	0.890593i	$0.349711\pi$
$38$		0			0
$39$	3.21506	+	3.71038i	0.514822	+	0.594136i
$40$		0			0
$41$	−11.4839	+	3.37199i	−1.79349	+	0.526617i	−0.996955	−	0.0779742i	$-0.975155\pi$
$41$	−11.4839	+	3.37199i	−1.79349	+	0.526617i	−0.796536	+	0.604591i	$0.793337\pi$
$42$		0			0
$43$	0.212305	−	1.47661i	0.0323761	−	0.225181i	−0.967209	−	0.253982i	$-0.918260\pi$
$43$	0.212305	−	1.47661i	0.0323761	−	0.225181i	0.999585	+	0.0288006i	$0.00916879\pi$
$44$		0			0
$45$	1.03359			0.154079
$46$		0			0
$47$	−3.84862			−0.561379			−0.280689	−	0.959799i	$-0.590563\pi$
$47$	−3.84862			−0.561379			−0.280689	+	0.959799i	$0.590563\pi$
$48$		0			0
$49$	−0.775266	+	5.39209i	−0.110752	+	0.770299i
$50$		0			0
$51$	1.51095	−	0.443654i	0.211575	−	0.0621240i
$52$		0			0
$53$	−4.28703	−	4.94749i	−0.588868	−	0.679590i	0.380619	−	0.924732i	$-0.375711\pi$
$53$	−4.28703	−	4.94749i	−0.588868	−	0.679590i	−0.969487	+	0.245142i	$0.921165\pi$
$54$		0			0
$55$	1.65049	+	0.484626i	0.222551	+	0.0653470i
$56$		0			0
$57$	6.37994	+	4.10014i	0.845044	+	0.543077i
$58$		0			0
$59$	8.34611	−	9.63192i	1.08657	−	1.25397i	0.121328	−	0.992612i	$-0.461285\pi$
$59$	8.34611	−	9.63192i	1.08657	−	1.25397i	0.965242	−	0.261357i	$-0.0841699\pi$
$60$		0			0
$61$	0.641196	+	4.45962i	0.0820967	+	0.570995i	0.988802	+	0.149231i	$0.0476799\pi$
$61$	0.641196	+	4.45962i	0.0820967	+	0.570995i	−0.906706	+	0.421764i	$0.861411\pi$
$62$		0			0
$63$	1.46563	+	3.20928i	0.184652	+	0.404331i
$64$		0			0
$65$	2.10800	−	4.61589i	0.261466	−	0.572530i
$66$		0			0
$67$	−3.57483	+	2.29741i	−0.436735	+	0.280673i	−0.740477	−	0.672082i	$-0.765400\pi$
$67$	−3.57483	+	2.29741i	−0.436735	+	0.280673i	0.303742	+	0.952754i	$0.401764\pi$
$68$		0			0
$69$	−4.30802	−	2.10735i	−0.518625	−	0.253695i
$70$		0			0
$71$	−2.75118	+	1.76808i	−0.326505	+	0.209832i	−0.693616	−	0.720345i	$-0.743983\pi$
$71$	−2.75118	+	1.76808i	−0.326505	+	0.209832i	0.367111	+	0.930177i	$0.380347\pi$
$72$		0			0
$73$	−4.00312	+	8.76562i	−0.468530	+	1.02594i	0.516929	+	0.856028i	$0.327075\pi$
$73$	−4.00312	+	8.76562i	−0.468530	+	1.02594i	−0.985460	+	0.169910i	$0.945652\pi$
$74$		0			0
$75$	1.63328	+	3.57639i	0.188595	+	0.412966i
$76$		0			0
$77$	0.835628	+	5.81192i	0.0952286	+	0.662330i
$78$		0			0
$79$	11.3200	−	13.0639i	1.27360	−	1.46981i	0.460522	−	0.887648i	$-0.347662\pi$
$79$	11.3200	−	13.0639i	1.27360	−	1.46981i	0.813074	−	0.582160i	$-0.197792\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	2.51280	+	0.737824i	0.275815	+	0.0809867i	0.416715	−	0.909037i	$-0.363181\pi$
$83$	2.51280	+	0.737824i	0.275815	+	0.0809867i	−0.140900	+	0.990024i	$0.544999\pi$
$84$		0			0
$85$	−1.06587	−	1.23008i	−0.115610	−	0.133421i
$86$		0			0
$87$	−8.17891	+	2.40155i	−0.876872	+	0.257473i
$88$		0			0
$89$	2.21930	−	15.4355i	0.235245	−	1.63616i	−0.439593	−	0.898197i	$-0.644877\pi$
$89$	2.21930	−	15.4355i	0.235245	−	1.63616i	0.674837	−	0.737966i	$-0.264214\pi$
$90$		0			0
$91$	17.3214			1.81577
$92$		0			0
$93$	−6.95815			−0.721526
$94$		0			0
$95$	1.11555	−	7.75882i	0.114453	−	0.796038i
$96$		0			0
$97$	−4.37419	+	1.28438i	−0.444131	+	0.130409i	−0.496149	−	0.868237i	$-0.665253\pi$
$97$	−4.37419	+	1.28438i	−0.444131	+	0.130409i	0.0520176	+	0.998646i	$0.483435\pi$
$98$		0			0
$99$	1.08986	+	1.25776i	0.109535	+	0.126410i
$100$		0			0
$101$	6.97416	+	2.04780i	0.693955	+	0.203764i	0.609643	−	0.792676i	$-0.291313\pi$
$101$	6.97416	+	2.04780i	0.693955	+	0.203764i	0.0843118	+	0.996439i	$0.473131\pi$
$102$		0			0
$103$	−8.23195	−	5.29035i	−0.811118	−	0.521274i	0.0681086	−	0.997678i	$-0.478304\pi$
$103$	−8.23195	−	5.29035i	−0.811118	−	0.521274i	−0.879226	+	0.476404i	$0.841940\pi$
$104$		0			0
$105$	2.38803	−	2.75593i	0.233048	−	0.268951i
$106$		0			0
$107$	0.502603	+	3.49568i	0.0485884	+	0.337940i	0.999587	+	0.0287440i	$0.00915077\pi$
$107$	0.502603	+	3.49568i	0.0485884	+	0.337940i	−0.950998	+	0.309196i	$0.899940\pi$
$108$		0			0
$109$	1.64155	+	3.59449i	0.157232	+	0.344289i	0.971810	−	0.235764i	$-0.0757591\pi$
$109$	1.64155	+	3.59449i	0.157232	+	0.344289i	−0.814579	+	0.580053i	$0.803032\pi$
$110$		0			0
$111$	3.47337	−	7.60562i	0.329678	−	0.721894i
$112$		0			0
$113$	2.94359	−	1.89173i	0.276910	−	0.177959i	−0.394814	−	0.918761i	$-0.629191\pi$
$113$	2.94359	−	1.89173i	0.276910	−	0.177959i	0.671723	+	0.740802i	$0.265554\pi$
$114$		0			0
$115$	−0.131574	+	4.95518i	−0.0122693	+	0.462073i
$116$		0			0
$117$	4.13016	−	2.65430i	0.381834	−	0.245390i
$118$		0			0
$119$	2.30798	−	5.05376i	0.211572	−	0.463278i
$120$		0			0
$121$	−3.41897	−	7.48649i	−0.310815	−	0.680590i
$122$		0			0
$123$	1.70333	+	11.8469i	0.153584	+	1.06820i
$124$		0			0
$125$	6.04549	−	6.97687i	0.540725	−	0.624030i
$126$		0			0
$127$	−3.36108	−	2.16004i	−0.298248	−	0.191672i	0.382955	−	0.923767i	$-0.374906\pi$
$127$	−3.36108	−	2.16004i	−0.298248	−	0.191672i	−0.681203	+	0.732095i	$0.738543\pi$
$128$		0			0
$129$	−1.43137	−	0.420287i	−0.126025	−	0.0370042i
$130$		0			0
$131$	0.454408	+	0.524415i	0.0397018	+	0.0458184i	0.775253	−	0.631651i	$-0.217622\pi$
$131$	0.454408	+	0.524415i	0.0397018	+	0.0458184i	−0.735551	+	0.677469i	$0.763077\pi$
$132$		0			0
$133$	25.6728	−	7.53822i	2.22611	−	0.653646i
$134$		0			0
$135$	0.147095	−	1.02307i	0.0126600	−	0.0880519i
$136$		0			0
$137$	14.2298			1.21573			0.607866	−	0.794039i	$-0.292026\pi$
$137$	14.2298			1.21573			0.607866	+	0.794039i	$0.292026\pi$
$138$		0			0
$139$	−7.78985			−0.660726			−0.330363	−	0.943854i	$-0.607171\pi$
$139$	−7.78985			−0.660726			−0.330363	+	0.943854i	$0.607171\pi$
$140$		0			0
$141$	−0.547716	+	3.80945i	−0.0461260	+	0.320813i
$142$		0			0
$143$	7.83977	−	2.30196i	0.655594	−	0.192500i
$144$		0			0
$145$	5.76968	+	6.65857i	0.479146	+	0.552964i
$146$		0			0
$147$	5.22687	+	1.53475i	0.431105	+	0.126584i
$148$		0			0
$149$	4.50459	+	2.89492i	0.369030	+	0.237161i	0.711991	−	0.702188i	$-0.247794\pi$
$149$	4.50459	+	2.89492i	0.369030	+	0.237161i	−0.342961	+	0.939350i	$0.611430\pi$
$150$		0			0
$151$	−3.20465	+	3.69836i	−0.260791	+	0.300968i	−0.871011	−	0.491263i	$-0.836535\pi$
$151$	−3.20465	+	3.69836i	−0.260791	+	0.300968i	0.610221	+	0.792232i	$0.291081\pi$
$152$		0			0
$153$	−0.224108	−	1.55871i	−0.0181181	−	0.126014i
$154$		0			0
$155$	2.98762	+	6.54196i	0.239971	+	0.525463i
$156$		0			0
$157$	−2.67476	+	5.85691i	−0.213469	+	0.467432i	−0.985829	−	0.167753i	$-0.946349\pi$
$157$	−2.67476	+	5.85691i	−0.213469	+	0.467432i	0.772360	+	0.635185i	$0.219076\pi$
$158$		0			0
$159$	−5.50724	+	3.53929i	−0.436753	+	0.280684i
$160$		0			0
$161$	−15.5723	+	6.61790i	−1.22727	+	0.521563i
$162$		0			0
$163$	−18.1699	+	11.6771i	−1.42318	+	0.914620i	−0.423214	+	0.906030i	$0.639098\pi$
$163$	−18.1699	+	11.6771i	−1.42318	+	0.914620i	−0.999963	+	0.00859017i	$0.997266\pi$
$164$		0			0
$165$	0.714582	−	1.56472i	0.0556301	−	0.121813i
$166$		0			0
$167$	3.34792	+	7.33093i	0.259070	+	0.567284i	0.993814	−	0.111061i	$-0.0354248\pi$
$167$	3.34792	+	7.33093i	0.259070	+	0.567284i	−0.734743	+	0.678345i	$0.762697\pi$
$168$		0			0
$169$	−1.58020	−	10.9905i	−0.121554	−	0.845425i
$170$		0			0
$171$	4.96637	−	5.73149i	0.379787	−	0.438298i
$172$		0			0
$173$	0.518340	+	0.333117i	0.0394086	+	0.0253264i	0.560197	−	0.828360i	$-0.310725\pi$
$173$	0.518340	+	0.333117i	0.0394086	+	0.0253264i	−0.520788	+	0.853686i	$0.674362\pi$
$174$		0			0
$175$	13.3095	+	3.90803i	1.00611	+	0.295419i
$176$		0			0
$177$	−8.34611	−	9.63192i	−0.627332	−	0.723979i
$178$		0			0
$179$	8.08268	−	2.37329i	0.604128	−	0.177388i	0.0346566	−	0.999399i	$-0.488966\pi$
$179$	8.08268	−	2.37329i	0.604128	−	0.177388i	0.569471	+	0.822011i	$0.307148\pi$
$180$		0			0
$181$	−0.239592	+	1.66640i	−0.0178087	+	0.123862i	−0.996786	−	0.0801048i	$-0.974475\pi$
$181$	−0.239592	+	1.66640i	−0.0178087	+	0.123862i	0.978978	+	0.203967i	$0.0653836\pi$
$182$		0			0
$183$	4.50548			0.333054
$184$		0			0
$185$	−8.64207			−0.635378
$186$		0			0
$187$	0.372974	−	2.59409i	0.0272746	−	0.189699i
$188$		0			0
$189$	3.38519	−	0.993983i	0.246237	−	0.0723016i
$190$		0			0
$191$	−13.8067	−	15.9338i	−0.999018	−	1.15293i	−0.988228	−	0.152987i	$-0.951111\pi$
$191$	−13.8067	−	15.9338i	−0.999018	−	1.15293i	−0.0107901	−	0.999942i	$-0.503435\pi$
$192$		0			0
$193$	15.3375	+	4.50348i	1.10401	+	0.324168i	0.782446	−	0.622719i	$-0.213972\pi$
$193$	15.3375	+	4.50348i	1.10401	+	0.324168i	0.321568	+	0.946886i	$0.395790\pi$
$194$		0			0
$195$	−4.26890	−	2.74346i	−0.305702	−	0.196463i
$196$		0			0
$197$	−2.75588	+	3.18045i	−0.196348	+	0.226598i	−0.845383	−	0.534161i	$-0.820628\pi$
$197$	−2.75588	+	3.18045i	−0.196348	+	0.226598i	0.649035	+	0.760759i	$0.275173\pi$
$198$		0			0
$199$	1.81524	+	12.6253i	0.128679	+	0.894983i	0.947231	+	0.320551i	$0.103868\pi$
$199$	1.81524	+	12.6253i	0.128679	+	0.894983i	−0.818552	+	0.574432i	$0.805223\pi$
$200$		0			0
$201$	1.76527	+	3.86540i	0.124513	+	0.272644i
$202$		0			0
$203$	−12.4933	+	27.3565i	−0.876859	+	1.92005i
$204$		0			0
$205$	10.4070	−	6.68817i	0.726856	−	0.467122i
$206$		0			0
$207$	−2.69900	+	3.96427i	−0.187593	+	0.275536i
$208$		0			0
$209$	10.6179	−	6.82369i	0.734454	−	0.472005i
$210$		0			0
$211$	−0.857778	+	1.87827i	−0.0590519	+	0.129306i	−0.936857	−	0.349712i	$-0.886280\pi$
$211$	−0.857778	+	1.87827i	−0.0590519	+	0.129306i	0.877806	+	0.479017i	$0.159007\pi$
$212$		0			0
$213$	1.35855	+	2.97480i	0.0930861	+	0.203830i
$214$		0			0
$215$	0.219436	+	1.52621i	0.0149654	+	0.104087i
$216$		0			0
$217$	−16.0762	+	18.5530i	−1.09133	+	1.25946i
$218$		0			0
$219$	8.10669	+	5.20986i	0.547800	+	0.352049i
$220$		0			0
$221$	−7.41805	−	2.17814i	−0.498992	−	0.146517i
$222$		0			0
$223$	−18.1999	−	21.0038i	−1.21876	−	1.40652i	−0.886115	−	0.463466i	$-0.846606\pi$
$223$	−18.1999	−	21.0038i	−1.21876	−	1.40652i	−0.332641	−	0.943054i	$-0.607940\pi$
$224$		0			0
$225$	3.77243	−	1.10768i	0.251495	−	0.0738456i
$226$		0			0
$227$	0.488478	−	3.39744i	0.0324214	−	0.225496i	−0.967168	−	0.254136i	$-0.918209\pi$
$227$	0.488478	−	3.39744i	0.0324214	−	0.225496i	0.999590	+	0.0286406i	$0.00911784\pi$
$228$		0			0
$229$	14.0758			0.930152			0.465076	−	0.885271i	$-0.346027\pi$
$229$	14.0758			0.930152			0.465076	+	0.885271i	$0.346027\pi$
$230$		0			0
$231$	5.87168			0.386329
$232$		0			0
$233$	−0.0416499	+	0.289682i	−0.00272858	+	0.0189777i	−0.991140	−	0.132819i	$-0.957597\pi$
$233$	−0.0416499	+	0.289682i	−0.00272858	+	0.0189777i	0.988412	+	0.151797i	$0.0485060\pi$
$234$		0			0
$235$	3.81677	−	1.12070i	0.248978	−	0.0731067i
$236$		0			0
$237$	−11.3200	−	13.0639i	−0.735311	−	0.848594i
$238$		0			0
$239$	−23.6927	−	6.95680i	−1.53255	−	0.449998i	−0.596722	−	0.802448i	$-0.703531\pi$
$239$	−23.6927	−	6.95680i	−1.53255	−	0.449998i	−0.935831	+	0.352449i	$0.885349\pi$
$240$		0			0
$241$	11.2092	+	7.20374i	0.722050	+	0.464033i	0.849349	−	0.527831i	$-0.176995\pi$
$241$	11.2092	+	7.20374i	0.722050	+	0.464033i	−0.127299	+	0.991864i	$0.540631\pi$
$242$		0			0
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$		0			0
$245$	−0.801308	−	5.57322i	−0.0511937	−	0.356060i
$246$		0			0
$247$	−15.4672	−	33.8685i	−0.984156	−	2.15500i
$248$		0			0
$249$	1.08792	−	2.38222i	0.0689443	−	0.150967i
$250$		0			0
$251$	−17.3312	+	11.1381i	−1.09394	+	0.703030i	−0.957735	−	0.287651i	$-0.907126\pi$
$251$	−17.3312	+	11.1381i	−1.09394	+	0.703030i	−0.136201	+	0.990681i	$0.543489\pi$
$252$		0			0
$253$	−6.16863	+	5.06482i	−0.387819	+	0.318423i
$254$		0			0
$255$	−1.36925	+	0.879964i	−0.0857458	+	0.0551055i
$256$		0			0
$257$	5.86862	−	12.8505i	0.366074	−	0.801591i	−0.633537	−	0.773712i	$-0.718398\pi$
$257$	5.86862	−	12.8505i	0.366074	−	0.801591i	0.999611	−	0.0278786i	$-0.00887518\pi$
$258$		0			0
$259$	−12.2544	−	26.8335i	−0.761453	−	1.66735i
$260$		0			0
$261$	1.21312	+	8.43744i	0.0750903	+	0.522264i
$262$		0			0
$263$	−12.3024	+	14.1978i	−0.758601	+	0.875473i	−0.995372	−	0.0960929i	$-0.969365\pi$
$263$	−12.3024	+	14.1978i	−0.758601	+	0.875473i	0.236771	+	0.971565i	$0.423911\pi$
$264$		0			0
$265$	5.69224	+	3.65818i	0.349671	+	0.224720i
$266$		0			0
$267$	−14.9626	−	4.39341i	−0.915695	−	0.268872i
$268$		0			0
$269$	−13.2378	−	15.2772i	−0.807124	−	0.931470i	0.191626	−	0.981468i	$-0.438624\pi$
$269$	−13.2378	−	15.2772i	−0.807124	−	0.931470i	−0.998749	+	0.0499978i	$0.984079\pi$
$270$		0			0
$271$	−20.3159	+	5.96528i	−1.23410	+	0.362365i	−0.832796	−	0.553579i	$-0.813262\pi$
$271$	−20.3159	+	5.96528i	−1.23410	+	0.362365i	−0.401305	+	0.915944i	$0.631443\pi$
$272$		0			0
$273$	2.46509	−	17.1451i	0.149194	−	1.03767i
$274$		0			0
$275$	6.54335			0.394579
$276$		0			0
$277$	−29.4561			−1.76984			−0.884922	−	0.465740i	$-0.845788\pi$
$277$	−29.4561			−1.76984			−0.884922	+	0.465740i	$0.845788\pi$
$278$		0			0
$279$	−0.990247	+	6.88732i	−0.0592846	+	0.412333i
$280$		0			0
$281$	−12.5173	+	3.67541i	−0.746719	+	0.219256i	−0.632888	−	0.774244i	$-0.718131\pi$
$281$	−12.5173	+	3.67541i	−0.746719	+	0.219256i	−0.113831	+	0.993500i	$0.536312\pi$
$282$		0			0
$283$	15.4824	+	17.8676i	0.920333	+	1.06212i	0.997877	+	0.0651315i	$0.0207467\pi$
$283$	15.4824	+	17.8676i	0.920333	+	1.06212i	−0.0775441	+	0.996989i	$0.524708\pi$
$284$		0			0
$285$	−7.52108	−	2.20839i	−0.445511	−	0.130814i
$286$		0			0
$287$	35.5237	+	22.8297i	2.09690	+	1.34759i
$288$		0			0
$289$	9.50872	−	10.9736i	0.559336	−	0.645508i
$290$		0			0
$291$	0.648792	+	4.51245i	0.0380329	+	0.264524i
$292$		0			0
$293$	11.2008	+	24.5262i	0.654355	+	1.43284i	0.887690	+	0.460441i	$0.152309\pi$
$293$	11.2008	+	24.5262i	0.654355	+	1.43284i	−0.233335	+	0.972396i	$0.574964\pi$
$294$		0			0
$295$	−5.47225	+	11.9826i	−0.318607	+	0.697652i
$296$		0			0
$297$	1.40006	−	0.899767i	0.0812400	−	0.0522097i
$298$		0			0
$299$	12.1993	+	20.1385i	0.705504	+	1.16464i
$300$		0			0
$301$	−4.42770	+	2.84551i	−0.255208	+	0.164012i
$302$		0			0
$303$	3.01948	−	6.61175i	0.173465	−	0.379835i
$304$		0			0
$305$	−1.93451	−	4.23599i	−0.110770	−	0.242552i
$306$		0			0
$307$	−0.294429	−	2.04780i	−0.0168040	−	0.116874i	0.979693	−	0.200504i	$-0.0642578\pi$
$307$	−0.294429	−	2.04780i	−0.0168040	−	0.116874i	−0.996497	+	0.0836296i	$0.973349\pi$
$308$		0			0
$309$	−6.40803	+	7.39526i	−0.364540	+	0.420702i
$310$		0			0
$311$	−3.49958	−	2.24904i	−0.198443	−	0.127531i	0.437646	−	0.899147i	$-0.355812\pi$
$311$	−3.49958	−	2.24904i	−0.198443	−	0.127531i	−0.636089	+	0.771616i	$0.719449\pi$
$312$		0			0
$313$	0.116259	+	0.0341368i	0.00657135	+	0.00192952i	0.285017	−	0.958523i	$-0.408001\pi$
$313$	0.116259	+	0.0341368i	0.00657135	+	0.00192952i	−0.278445	+	0.960452i	$0.589819\pi$
$314$		0			0
$315$	−2.38803	−	2.75593i	−0.134550	−	0.155279i
$316$		0			0
$317$	−22.4651	+	6.59633i	−1.26176	+	0.370487i	−0.843150	−	0.537678i	$-0.819302\pi$
$317$	−22.4651	+	6.59633i	−1.26176	+	0.370487i	−0.418613	+	0.908165i	$0.637484\pi$
$318$		0			0
$319$	−2.01895	+	14.0421i	−0.113039	+	0.786206i
$320$		0			0
$321$	3.53162			0.197116
$322$		0			0
$323$	−11.9426			−0.664501
$324$		0			0
$325$	2.74707	−	19.1063i	0.152380	−	1.05983i
$326$		0			0
$327$	3.79152	−	1.11329i	0.209671	−	0.0615651i
$328$		0			0
$329$	8.89192	+	10.2618i	0.490227	+	0.565753i
$330$		0			0
$331$	−19.8004	−	5.81391i	−1.08833	−	0.319562i	−0.312122	−	0.950042i	$-0.601040\pi$
$331$	−19.8004	−	5.81391i	−1.08833	−	0.319562i	−0.776205	+	0.630481i	$0.782858\pi$
$332$		0			0
$333$	−7.03390	−	4.52041i	−0.385455	−	0.247717i
$334$		0			0
$335$	2.87625	−	3.31937i	0.157146	−	0.181357i
$336$		0			0
$337$	−1.79716	−	12.4995i	−0.0978975	−	0.680892i	−0.978380	−	0.206814i	$-0.933690\pi$
$337$	−1.79716	−	12.4995i	−0.0978975	−	0.680892i	0.880483	−	0.474078i	$-0.157219\pi$
$338$		0			0
$339$	−1.45356	−	3.18285i	−0.0789464	−	0.172869i
$340$		0			0
$341$	−4.81057	+	10.5337i	−0.260507	+	0.570431i
$342$		0			0
$343$	−4.60776	+	2.96122i	−0.248795	+	0.159891i
$344$		0			0
$345$	4.88602	+	0.835431i	0.263055	+	0.0449781i
$346$		0			0
$347$	0.120158	−	0.0772208i	0.00645041	−	0.00414543i	−0.537412	−	0.843320i	$-0.680598\pi$
$347$	0.120158	−	0.0772208i	0.00645041	−	0.00414543i	0.543862	+	0.839175i	$0.316961\pi$
$348$		0			0
$349$	9.93357	−	21.7515i	0.531732	−	1.16433i	−0.433072	−	0.901359i	$-0.642570\pi$
$349$	9.93357	−	21.7515i	0.531732	−	1.16433i	0.964804	−	0.262971i	$-0.0847024\pi$
$350$		0			0
$351$	−2.03949	−	4.46587i	−0.108860	−	0.238371i
$352$		0			0
$353$	3.66415	+	25.4847i	0.195023	+	1.35641i	0.818470	+	0.574549i	$0.194823\pi$
$353$	3.66415	+	25.4847i	0.195023	+	1.35641i	−0.623447	+	0.781866i	$0.714268\pi$
$354$		0			0
$355$	2.21356	−	2.55458i	0.117483	−	0.135583i
$356$		0			0
$357$	−4.67386	−	3.00371i	−0.247367	−	0.158973i
$358$		0			0
$359$	9.04144	+	2.65481i	0.477189	+	0.140115i	0.511478	−	0.859297i	$-0.329098\pi$
$359$	9.04144	+	2.65481i	0.477189	+	0.140115i	−0.0342885	+	0.999412i	$0.510917\pi$
$360$		0			0
$361$	−25.2218	−	29.1075i	−1.32746	−	1.53198i
$362$		0			0
$363$	−7.89686	+	2.31873i	−0.414478	+	0.121702i
$364$		0			0
$365$	1.41748	−	9.85877i	0.0741941	−	0.516031i
$366$		0			0
$367$	−1.61632			−0.0843711			−0.0421856	−	0.999110i	$-0.513432\pi$
$367$	−1.61632			−0.0843711			−0.0421856	+	0.999110i	$0.513432\pi$
$368$		0			0
$369$	11.9688			0.623069
$370$		0			0
$371$	−3.28699	+	22.8615i	−0.170652	+	1.18691i
$372$		0			0
$373$	15.5498	−	4.56583i	0.805137	−	0.236410i	0.146833	−	0.989161i	$-0.453092\pi$
$373$	15.5498	−	4.56583i	0.805137	−	0.236410i	0.658304	+	0.752752i	$0.271274\pi$
$374$		0			0
$375$	−6.04549	−	6.97687i	−0.312188	−	0.360284i
$376$		0			0
$377$	40.1547	+	11.7905i	2.06807	+	0.607240i
$378$		0			0
$379$	9.68657	+	6.22518i	0.497566	+	0.319766i	0.765242	−	0.643743i	$-0.222619\pi$
$379$	9.68657	+	6.22518i	0.497566	+	0.319766i	−0.267676	+	0.963509i	$0.586256\pi$
$380$		0			0
$381$	−2.61638	+	3.01946i	−0.134041	+	0.154692i
$382$		0			0
$383$	2.18330	+	15.1852i	0.111562	+	0.775928i	0.966402	+	0.257037i	$0.0827461\pi$
$383$	2.18330	+	15.1852i	0.111562	+	0.775928i	−0.854840	+	0.518892i	$0.826345\pi$
$384$		0			0
$385$	−2.52112	−	5.52049i	−0.128488	−	0.281350i
$386$		0			0
$387$	−0.619714	+	1.35698i	−0.0315018	+	0.0689794i
$388$		0			0
$389$	−8.31216	+	5.34190i	−0.421443	+	0.270845i	−0.734127	−	0.679012i	$-0.762408\pi$
$389$	−8.31216	+	5.34190i	−0.421443	+	0.270845i	0.312684	+	0.949857i	$0.398772\pi$
$390$		0			0
$391$	7.50119	−	0.875987i	0.379351	−	0.0443005i
$392$		0			0
$393$	0.583746	−	0.375151i	0.0294461	−	0.0189239i
$394$		0			0
$395$	−7.42211	+	16.2522i	−0.373447	+	0.817735i
$396$		0			0
$397$	−0.831601	−	1.82095i	−0.0417368	−	0.0913909i	0.887615	−	0.460586i	$-0.152361\pi$
$397$	−0.831601	−	1.82095i	−0.0417368	−	0.0913909i	−0.929352	+	0.369195i	$0.879633\pi$
$398$		0			0
$399$	−3.80787	−	26.4843i	−0.190632	−	1.32587i
$400$		0			0
$401$	15.9698	−	18.4302i	0.797496	−	0.920360i	−0.200745	−	0.979644i	$-0.564336\pi$
$401$	15.9698	−	18.4302i	0.797496	−	0.920360i	0.998241	+	0.0592840i	$0.0188817\pi$
$402$		0			0
$403$	28.7383	+	18.4690i	1.43156	+	0.920005i
$404$		0			0
$405$	−0.991724	−	0.291196i	−0.0492791	−	0.0144697i
$406$		0			0
$407$	−9.11253	−	10.5164i	−0.451691	−	0.521280i
$408$		0			0
$409$	−6.67698	+	1.96054i	−0.330155	+	0.0969424i	−0.442609	−	0.896715i	$-0.645947\pi$
$409$	−6.67698	+	1.96054i	−0.330155	+	0.0969424i	0.112454	+	0.993657i	$0.464129\pi$
$410$		0			0
$411$	2.02511	−	14.0849i	0.0998913	−	0.694759i
$412$		0			0
$413$	−44.9652			−2.21259
$414$		0			0
$415$	−2.70685			−0.132874
$416$		0			0
$417$	−1.10861	+	7.71056i	−0.0542889	+	0.377588i
$418$		0			0
$419$	23.9361	−	7.02827i	1.16935	−	0.343353i	0.361293	−	0.932452i	$-0.382335\pi$
$419$	23.9361	−	7.02827i	1.16935	−	0.343353i	0.808061	+	0.589099i	$0.200517\pi$
$420$		0			0
$421$	−1.50692	−	1.73908i	−0.0734427	−	0.0847574i	0.717839	−	0.696209i	$-0.245131\pi$
$421$	−1.50692	−	1.73908i	−0.0734427	−	0.0847574i	−0.791282	+	0.611452i	$0.790586\pi$
$422$		0			0
$423$	3.69272	+	1.08428i	0.179546	+	0.0527196i
$424$		0			0
$425$	−5.20851	−	3.34731i	−0.252650	−	0.162368i
$426$		0			0
$427$	10.4095	−	12.0132i	0.503753	−	0.581362i
$428$		0			0
$429$	−1.16282	−	8.08757i	−0.0561414	−	0.390472i
$430$		0			0
$431$	−8.69041	−	19.0293i	−0.418602	−	0.916611i	−0.995041	−	0.0994703i	$-0.968285\pi$
$431$	−8.69041	−	19.0293i	−0.418602	−	0.916611i	0.576438	−	0.817141i	$-0.304442\pi$
$432$		0			0
$433$	−15.6536	+	34.2766i	−0.752263	+	1.64723i	0.00999130	+	0.999950i	$0.496820\pi$
$433$	−15.6536	+	34.2766i	−0.752263	+	1.64723i	−0.762255	+	0.647277i	$0.775908\pi$
$434$		0			0
$435$	7.41190	−	4.76334i	0.355373	−	0.228385i
$436$		0			0
$437$	26.8454	+	24.5391i	1.28419	+	1.17386i
$438$		0			0
$439$	17.0867	−	10.9809i	0.815502	−	0.524091i	−0.0651387	−	0.997876i	$-0.520749\pi$
$439$	17.0867	−	10.9809i	0.815502	−	0.524091i	0.880641	+	0.473785i	$0.157113\pi$
$440$		0			0
$441$	2.26299	−	4.95526i	0.107761	−	0.235965i
$442$		0			0
$443$	9.72531	+	21.2955i	0.462063	+	1.01178i	0.987012	+	0.160644i	$0.0513571\pi$
$443$	9.72531	+	21.2955i	0.462063	+	1.01178i	−0.524949	+	0.851134i	$0.675916\pi$
$444$		0			0
$445$	2.29384	+	15.9540i	0.108739	+	0.756294i
$446$		0			0
$447$	3.50653	−	4.04675i	0.165853	−	0.191405i
$448$		0			0
$449$	8.41666	+	5.40906i	0.397207	+	0.255269i	0.723962	−	0.689840i	$-0.242319\pi$
$449$	8.41666	+	5.40906i	0.397207	+	0.255269i	−0.326756	+	0.945109i	$0.605955\pi$
$450$		0			0
$451$	19.1123	+	5.61187i	0.899962	+	0.264253i
$452$		0			0
$453$	3.20465	+	3.69836i	0.150568	+	0.173764i
$454$		0			0
$455$	−17.1780	+	5.04392i	−0.805318	+	0.236463i
$456$		0			0
$457$	0.484884	−	3.37244i	0.0226819	−	0.157756i	−0.975333	−	0.220740i	$-0.929153\pi$
$457$	0.484884	−	3.37244i	0.0226819	−	0.157756i	0.998015	+	0.0629841i	$0.0200618\pi$
$458$		0			0
$459$	−1.57473			−0.0735023
$460$		0			0
$461$	−1.96052			−0.0913104			−0.0456552	−	0.998957i	$-0.514538\pi$
$461$	−1.96052			−0.0913104			−0.0456552	+	0.998957i	$0.514538\pi$
$462$		0			0
$463$	−1.53400	+	10.6692i	−0.0712912	+	0.495841i	0.922625	+	0.385699i	$0.126040\pi$
$463$	−1.53400	+	10.6692i	−0.0712912	+	0.495841i	−0.993916	+	0.110142i	$0.964869\pi$
$464$		0			0
$465$	6.90056	−	2.02619i	0.320006	−	0.0939622i
$466$		0			0
$467$	−15.2326	−	17.5794i	−0.704881	−	0.813476i	0.284523	−	0.958669i	$-0.408165\pi$
$467$	−15.2326	−	17.5794i	−0.704881	−	0.813476i	−0.989403	+	0.145194i	$0.953619\pi$
$468$		0			0
$469$	14.3851	+	4.22384i	0.664242	+	0.195039i
$470$		0			0
$471$	5.41664	+	3.48106i	0.249586	+	0.160399i
$472$		0			0
$473$	−1.62585	+	1.87633i	−0.0747564	+	0.0862735i
$474$		0			0
$475$	−4.24345	−	29.5138i	−0.194703	−	1.35419i
$476$		0			0
$477$	2.71950	+	5.95488i	0.124517	+	0.272655i
$478$		0			0
$479$	3.63899	−	7.96828i	0.166270	−	0.364080i	−0.808096	−	0.589051i	$-0.799502\pi$
$479$	3.63899	−	7.96828i	0.166270	−	0.364080i	0.974365	+	0.224971i	$0.0722288\pi$
$480$		0			0
$481$	−34.5332	+	22.1931i	−1.57458	+	1.01192i
$482$		0			0
$483$	4.33437	+	16.3556i	0.197221	+	0.744207i
$484$		0			0
$485$	3.96398	−	2.54749i	0.179995	−	0.115676i
$486$		0			0
$487$	1.60050	−	3.50461i	0.0725256	−	0.158809i	−0.869897	−	0.493234i	$-0.835815\pi$
$487$	1.60050	−	3.50461i	0.0725256	−	0.158809i	0.942422	+	0.334425i	$0.108542\pi$
$488$		0			0
$489$	8.97239	+	19.6468i	0.405745	+	0.888458i
$490$		0			0
$491$	−4.55862	−	31.7059i	−0.205728	−	1.43087i	−0.786897	−	0.617084i	$-0.788314\pi$
$491$	−4.55862	−	31.7059i	−0.205728	−	1.43087i	0.581170	−	0.813782i	$-0.302595\pi$
$492$		0			0
$493$	8.79043	−	10.1447i	0.395901	−	0.456894i
$494$		0			0
$495$	−1.44709	−	0.929991i	−0.0650420	−	0.0418000i
$496$		0			0
$497$	11.0707	+	3.25066i	0.496590	+	0.145812i
$498$		0			0
$499$	9.33598	+	10.7743i	0.417936	+	0.482324i	0.925207	−	0.379463i	$-0.123891\pi$
$499$	9.33598	+	10.7743i	0.417936	+	0.482324i	−0.507271	+	0.861787i	$0.669346\pi$
$500$		0			0
$501$	7.73277	−	2.27055i	0.345475	−	0.101441i
$502$		0			0
$503$	5.40622	−	37.6011i	0.241051	−	1.67655i	−0.405822	−	0.913952i	$-0.633015\pi$
$503$	5.40622	−	37.6011i	0.241051	−	1.67655i	0.646873	−	0.762598i	$-0.276076\pi$
$504$		0			0
$505$	−7.51276			−0.334313
$506$		0			0
$507$	−11.1035			−0.493126
$508$		0			0
$509$	−6.16393	+	42.8711i	−0.273211	+	1.90023i	0.140938	+	0.990018i	$0.454988\pi$
$509$	−6.16393	+	42.8711i	−0.273211	+	1.90023i	−0.414150	+	0.910209i	$0.635921\pi$
$510$		0			0
$511$	32.6212	−	9.57846i	1.44308	−	0.423726i
$512$		0			0
$513$	−4.96637	−	5.73149i	−0.219270	−	0.253052i
$514$		0			0
$515$	9.70435	+	2.84945i	0.427625	+	0.125562i
$516$		0			0
$517$	5.38831	+	3.46286i	0.236978	+	0.152296i
$518$		0			0
$519$	0.403494	−	0.465656i	0.0177114	−	0.0204400i
$520$		0			0
$521$	4.79984	+	33.3836i	0.210285	+	1.46256i	0.772206	+	0.635373i	$0.219153\pi$
$521$	4.79984	+	33.3836i	0.210285	+	1.46256i	−0.561921	+	0.827191i	$0.689937\pi$
$522$		0			0
$523$	−9.66803	−	21.1700i	−0.422753	−	0.925700i	−0.994448	−	0.105234i	$-0.966441\pi$
$523$	−9.66803	−	21.1700i	−0.422753	−	0.925700i	0.571694	−	0.820467i	$-0.306286\pi$
$524$		0			0
$525$	5.76240	−	12.6179i	0.251492	−	0.550690i
$526$		0			0
$527$	9.21781	−	5.92393i	0.401534	−	0.258050i
$528$		0			0
$529$	−18.6617	−	13.4440i	−0.811377	−	0.584523i
$530$		0			0
$531$	−10.7217	+	6.89039i	−0.465280	+	0.299017i
$532$		0			0
$533$	24.4102	−	53.4510i	1.05732	−	2.31522i
$534$		0			0
$535$	−1.51637	−	3.32039i	−0.0655584	−	0.143553i
$536$		0			0
$537$	−1.19885	−	8.33816i	−0.0517340	−	0.359818i
$538$		0			0
$539$	5.93704	−	6.85171i	0.255727	−	0.295124i
$540$		0			0
$541$	30.5905	+	19.6593i	1.31519	+	0.845221i	0.994778	−	0.102058i	$-0.0325426\pi$
$541$	30.5905	+	19.6593i	1.31519	+	0.845221i	0.320411	+	0.947279i	$0.396179\pi$
$542$		0			0
$543$	1.61534	+	0.474307i	0.0693209	+	0.0203544i
$544$		0			0
$545$	−2.67466	−	3.08673i	−0.114570	−	0.132221i
$546$		0			0
$547$	33.4258	−	9.81469i	1.42918	−	0.419646i	0.526582	−	0.850125i	$-0.323473\pi$
$547$	33.4258	−	9.81469i	1.42918	−	0.419646i	0.902601	+	0.430479i	$0.141655\pi$
$548$		0			0
$549$	0.641196	−	4.45962i	0.0273656	−	0.190332i
$550$		0			0
$551$	64.6463			2.75402
$552$		0			0
$553$	−60.9871			−2.59344
$554$		0			0
$555$	−1.22990	+	8.55411i	−0.0522062	+	0.363102i
$556$		0			0
$557$	−9.69664	+	2.84719i	−0.410860	+	0.120639i	−0.480629	−	0.876924i	$-0.659592\pi$
$557$	−9.69664	+	2.84719i	−0.410860	+	0.120639i	0.0697697	+	0.997563i	$0.477774\pi$
$558$		0			0
$559$	4.79621	+	5.53513i	0.202858	+	0.234111i
$560$		0			0
$561$	−2.51461	−	0.738355i	−0.106167	−	0.0311734i
$562$		0			0
$563$	−23.1636	−	14.8863i	−0.976229	−	0.627384i	−0.0477851	−	0.998858i	$-0.515216\pi$
$563$	−23.1636	−	14.8863i	−0.976229	−	0.627384i	−0.928443	+	0.371474i	$0.878853\pi$
$564$		0			0
$565$	−2.36836	+	2.73324i	−0.0996377	+	0.114988i
$566$		0			0
$567$	−0.502102	−	3.49220i	−0.0210863	−	0.146658i
$568$		0			0
$569$	−17.8207	−	39.0219i	−0.747083	−	1.63588i	−0.771539	−	0.636182i	$-0.780513\pi$
$569$	−17.8207	−	39.0219i	−0.747083	−	1.63588i	0.0244566	−	0.999701i	$-0.492214\pi$
$570$		0			0
$571$	−11.9388	+	26.1423i	−0.499622	+	1.09402i	0.476970	+	0.878920i	$0.341735\pi$
$571$	−11.9388	+	26.1423i	−0.499622	+	1.09402i	−0.976592	+	0.215100i	$0.930992\pi$
$572$		0			0
$573$	−17.7365	+	11.3986i	−0.740953	+	0.476182i
$574$		0			0
$575$	4.83018	+	18.2266i	0.201432	+	0.760100i
$576$		0			0
$577$	23.6912	−	15.2254i	0.986277	−	0.633842i	0.0551276	−	0.998479i	$-0.482443\pi$
$577$	23.6912	−	15.2254i	0.986277	−	0.633842i	0.931150	+	0.364637i	$0.118807\pi$
$578$		0			0
$579$	6.64039	−	14.5404i	0.275965	−	0.604279i
$580$		0			0
$581$	−3.83831	−	8.40472i	−0.159240	−	0.348687i
$582$		0			0
$583$	1.55052	+	10.7841i	0.0642161	+	0.446633i
$584$		0			0
$585$	−3.32306	+	3.83502i	−0.137392	+	0.158558i
$586$		0			0
$587$	−12.7852	−	8.21653i	−0.527700	−	0.339132i	0.249511	−	0.968372i	$-0.419730\pi$
$587$	−12.7852	−	8.21653i	−0.527700	−	0.339132i	−0.777211	+	0.629240i	$0.783366\pi$
$588$		0			0
$589$	50.6320	+	14.8669i	2.08626	+	0.612580i
$590$		0			0
$591$	2.75588	+	3.18045i	0.113362	+	0.130826i
$592$		0			0
$593$	26.0136	−	7.63827i	1.06825	−	0.313666i	0.300081	−	0.953914i	$-0.402986\pi$
$593$	26.0136	−	7.63827i	1.06825	−	0.313666i	0.768169	+	0.640248i	$0.221168\pi$
$594$		0			0
$595$	−0.817237	+	5.68401i	−0.0335035	+	0.233022i
$596$		0			0
$597$	12.7551			0.522032
$598$		0			0
$599$	−9.79350			−0.400152			−0.200076	−	0.979780i	$-0.564119\pi$
$599$	−9.79350			−0.400152			−0.200076	+	0.979780i	$0.564119\pi$
$600$		0			0
$601$	4.84570	−	33.7026i	0.197660	−	1.37476i	−0.613390	−	0.789780i	$-0.710195\pi$
$601$	4.84570	−	33.7026i	0.197660	−	1.37476i	0.811050	−	0.584977i	$-0.198896\pi$
$602$		0			0
$603$	4.07728	−	1.19720i	0.166040	−	0.0487537i
$604$		0			0
$605$	5.57071	+	6.42894i	0.226481	+	0.261374i
$606$		0			0
$607$	23.7870	+	6.98449i	0.965483	+	0.283492i	0.726219	−	0.687463i	$-0.241276\pi$
$607$	23.7870	+	6.98449i	0.965483	+	0.283492i	0.239264	+	0.970955i	$0.423094\pi$
$608$		0			0
$609$	25.3001	+	16.2594i	1.02521	+	0.658864i
$610$		0			0
$611$	12.3735	−	14.2798i	0.500580	−	0.577700i
$612$		0			0
$613$	−1.24139	−	8.63407i	−0.0501393	−	0.348727i	−0.999412	−	0.0342740i	$-0.989088\pi$
$613$	−1.24139	−	8.63407i	−0.0501393	−	0.348727i	0.949273	−	0.314453i	$-0.101821\pi$
$614$		0			0
$615$	−5.13902	−	11.2529i	−0.207225	−	0.453760i
$616$		0			0
$617$	−2.13710	+	4.67959i	−0.0860363	+	0.188393i	−0.947760	−	0.318985i	$-0.896658\pi$
$617$	−2.13710	+	4.67959i	−0.0860363	+	0.188393i	0.861723	+	0.507378i	$0.169385\pi$
$618$		0			0
$619$	20.9862	−	13.4870i	0.843506	−	0.542088i	−0.0460371	−	0.998940i	$-0.514659\pi$
$619$	20.9862	−	13.4870i	0.843506	−	0.542088i	0.889543	+	0.456851i	$0.151023\pi$
$620$		0			0
$621$	3.53981	+	3.23570i	0.142048	+	0.129844i
$622$		0			0
$623$	−46.2843	+	29.7451i	−1.85434	+	1.19171i
$624$		0			0
$625$	4.20260	−	9.20240i	0.168104	−	0.368096i
$626$		0			0
$627$	−5.24316	−	11.4809i	−0.209392	−	0.458504i
$628$		0			0
$629$	1.87381	+	13.0327i	0.0747139	+	0.519646i
$630$		0			0
$631$	5.23956	−	6.04678i	0.208584	−	0.240719i	−0.641812	−	0.766862i	$-0.721817\pi$
$631$	5.23956	−	6.04678i	0.208584	−	0.240719i	0.850396	+	0.526143i	$0.176363\pi$
$632$		0			0
$633$	1.73708	+	1.11635i	0.0690427	+	0.0443710i
$634$		0			0
$635$	3.96226	+	1.16342i	0.157237	+	0.0461691i
$636$		0			0
$637$	−17.5142	−	20.2124i	−0.693937	−	0.800846i
$638$		0			0
$639$	3.13787	−	0.921360i	0.124132	−	0.0364485i
$640$		0			0
$641$	−4.71571	+	32.7985i	−0.186259	+	1.29546i	0.655329	+	0.755344i	$0.272530\pi$
$641$	−4.71571	+	32.7985i	−0.186259	+	1.29546i	−0.841588	+	0.540119i	$0.818379\pi$
$642$		0			0
$643$	−28.7881			−1.13529			−0.567646	−	0.823273i	$-0.692146\pi$
$643$	−28.7881			−1.13529			−0.567646	+	0.823273i	$0.692146\pi$
$644$		0			0
$645$	1.54191			0.0607125
$646$		0			0
$647$	0.277401	−	1.92936i	0.0109057	−	0.0758511i	−0.983642	−	0.180136i	$-0.942346\pi$
$647$	0.277401	−	1.92936i	0.0109057	−	0.0758511i	0.994547	+	0.104285i	$0.0332553\pi$
$648$		0			0
$649$	−20.3516	+	5.97576i	−0.798869	+	0.234569i
$650$		0			0
$651$	16.0762	+	18.5530i	0.630077	+	0.727148i
$652$		0			0
$653$	−36.4320	−	10.6974i	−1.42569	−	0.418622i	−0.524268	−	0.851553i	$-0.675661\pi$
$653$	−36.4320	−	10.6974i	−1.42569	−	0.418622i	−0.901427	+	0.432932i	$0.857479\pi$
$654$		0			0
$655$	−0.603355	−	0.387753i	−0.0235750	−	0.0151508i
$656$		0			0
$657$	6.31053	−	7.28274i	0.246197	−	0.284127i
$658$		0			0
$659$	−3.24554	−	22.5733i	−0.126428	−	0.879329i	−0.950030	−	0.312160i	$-0.898948\pi$
$659$	−3.24554	−	22.5733i	−0.126428	−	0.879329i	0.823601	−	0.567169i	$-0.191962\pi$
$660$		0			0
$661$	6.76138	+	14.8054i	0.262987	+	0.575862i	0.994353	−	0.106124i	$-0.0338439\pi$
$661$	6.76138	+	14.8054i	0.262987	+	0.575862i	−0.731366	+	0.681986i	$0.761117\pi$
$662$		0			0
$663$	−3.21166	+	7.03256i	−0.124731	+	0.273122i
$664$		0			0
$665$	−23.2652	+	14.9517i	−0.902187	+	0.579800i
$666$		0			0
$667$	−40.6047	+	4.74181i	−1.57222	+	0.183604i
$668$		0			0
$669$	−23.3801	+	15.0255i	−0.903928	+	0.580919i
$670$		0			0
$671$	3.11490	−	6.82068i	0.120249	−	0.263309i
$672$		0			0
$673$	−1.24413	−	2.72427i	−0.0479578	−	0.105013i	0.884136	−	0.467229i	$-0.154748\pi$
$673$	−1.24413	−	2.72427i	−0.0479578	−	0.105013i	−0.932094	+	0.362216i	$0.882020\pi$
$674$		0			0
$675$	−0.559538	−	3.89167i	−0.0215366	−	0.149790i
$676$		0			0
$677$	−10.5688	+	12.1971i	−0.406193	+	0.468771i	−0.921581	−	0.388185i	$-0.873102\pi$
$677$	−10.5688	+	12.1971i	−0.406193	+	0.468771i	0.515389	+	0.856957i	$0.327648\pi$
$678$		0			0
$679$	13.5308	+	8.69573i	0.519265	+	0.333712i
$680$		0			0
$681$	−3.29334	−	0.967012i	−0.126201	−	0.0370560i
$682$		0			0
$683$	28.3323	+	32.6972i	1.08411	+	1.25113i	0.966115	+	0.258111i	$0.0830999\pi$
$683$	28.3323	+	32.6972i	1.08411	+	1.25113i	0.117991	+	0.993015i	$0.462355\pi$
$684$		0			0
$685$	−14.1120	+	4.14366i	−0.539192	+	0.158321i
$686$		0			0
$687$	2.00319	−	13.9325i	0.0764264	−	0.531558i
$688$		0			0
$689$	32.1401			1.22444
$690$		0			0
$691$	−4.97874			−0.189400			−0.0947001	−	0.995506i	$-0.530189\pi$
$691$	−4.97874			−0.189400			−0.0947001	+	0.995506i	$0.530189\pi$
$692$		0			0
$693$	0.835628	−	5.81192i	0.0317429	−	0.220777i
$694$		0			0
$695$	7.72538	−	2.26838i	0.293040	−	0.0860444i
$696$		0			0
$697$	−12.3426	−	14.2441i	−0.467508	−	0.539533i
$698$		0			0
$699$	0.280806	+	0.0824520i	0.0106210	+	0.00311862i
$700$		0			0
$701$	25.1883	+	16.1875i	0.951349	+	0.611395i	0.921591	−	0.388162i	$-0.126890\pi$
$701$	25.1883	+	16.1875i	0.951349	+	0.611395i	0.0297579	+	0.999557i	$0.490526\pi$
$702$		0			0
$703$	−41.5248	+	47.9222i	−1.56614	+	1.80742i
$704$		0			0
$705$	−0.566114	−	3.93741i	−0.0213211	−	0.148291i
$706$		0			0
$707$	−10.6531	−	23.3269i	−0.400649	−	0.877300i
$708$		0			0
$709$	16.3975	−	35.9054i	0.615820	−	1.34846i	−0.302701	−	0.953085i	$-0.597889\pi$
$709$	16.3975	−	35.9054i	0.615820	−	1.34846i	0.918521	−	0.395372i	$-0.129384\pi$
$710$		0			0
$711$	−14.5420	+	9.34556i	−0.545366	+	0.350486i
$712$		0			0
$713$	−32.8927	−	5.62413i	−1.23184	−	0.210625i
$714$		0			0
$715$	−7.10456	+	4.56582i	−0.265696	+	0.170752i
$716$		0			0
$717$	−10.2578	+	22.4615i	−0.383085	+	0.838840i
$718$		0			0
$719$	−13.9523	−	30.5512i	−0.520331	−	1.13937i	−0.969314	−	0.245826i	$-0.920941\pi$
$719$	−13.9523	−	30.5512i	−0.520331	−	1.13937i	0.448982	−	0.893541i	$-0.351787\pi$
$720$		0			0
$721$	4.91324	+	34.1723i	0.182978	+	1.27264i
$722$		0			0
$723$	8.72565	−	10.0699i	0.324511	−	0.374505i
$724$		0			0
$725$	28.1942	+	18.1193i	1.04711	+	0.672935i
$726$		0			0
$727$	15.2866	+	4.48856i	0.566950	+	0.166471i	0.552631	−	0.833426i	$-0.313624\pi$
$727$	15.2866	+	4.48856i	0.566950	+	0.166471i	0.0143186	+	0.999897i	$0.495442\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	2.25402	−	0.661841i	0.0833681	−	0.0244791i
$732$		0			0
$733$	1.90011	−	13.2156i	0.0701822	−	0.488128i	−0.924169	−	0.381985i	$-0.875241\pi$
$733$	1.90011	−	13.2156i	0.0701822	−	0.488128i	0.994351	−	0.106143i	$-0.0338502\pi$
$734$		0			0
$735$	−5.63053			−0.207685
$736$		0			0
$737$	7.07213			0.260505
$738$		0			0
$739$	−0.777628	+	5.40852i	−0.0286055	+	0.198956i	−0.999113	−	0.0421164i	$-0.986590\pi$
$739$	−0.777628	+	5.40852i	−0.0286055	+	0.198956i	0.970507	+	0.241072i	$0.0774991\pi$
$740$		0			0
$741$	−35.7250	+	10.4898i	−1.31239	+	0.385352i
$742$		0			0
$743$	−1.58557	−	1.82985i	−0.0581690	−	0.0671307i	0.725919	−	0.687780i	$-0.241415\pi$
$743$	−1.58557	−	1.82985i	−0.0581690	−	0.0671307i	−0.784088	+	0.620649i	$0.786869\pi$
$744$		0			0
$745$	−5.31030	−	1.55924i	−0.194554	−	0.0571263i
$746$		0			0
$747$	−2.20314	−	1.41587i	−0.0806088	−	0.0518041i
$748$		0			0
$749$	8.15953	−	9.41660i	0.298143	−	0.344075i
$750$		0			0
$751$	4.30969	+	29.9746i	0.157263	+	1.09379i	0.903649	+	0.428274i	$0.140878\pi$
$751$	4.30969	+	29.9746i	0.157263	+	1.09379i	−0.746386	+	0.665513i	$0.768213\pi$
$752$		0			0
$753$	8.55823	+	18.7399i	0.311879	+	0.682920i
$754$		0			0
$755$	2.10118	−	4.60093i	0.0764696	−	0.167445i
$756$		0			0
$757$	−33.8652	+	21.7639i	−1.23085	+	0.791021i	−0.984024	−	0.178038i	$-0.943025\pi$
$757$	−33.8652	+	21.7639i	−1.23085	+	0.791021i	−0.246829	+	0.969059i	$0.579389\pi$
$758$		0			0
$759$	4.13538	+	6.82664i	0.150105	+	0.247791i
$760$		0			0
$761$	−15.5192	+	9.97356i	−0.562569	+	0.361541i	−0.790808	−	0.612064i	$-0.790340\pi$
$761$	−15.5192	+	9.97356i	−0.562569	+	0.361541i	0.228239	+	0.973605i	$0.426703\pi$
$762$		0			0
$763$	5.79155	−	12.6817i	0.209668	−	0.459110i
$764$		0			0
$765$	0.676143	+	1.48055i	0.0244460	+	0.0535293i
$766$		0			0
$767$	8.90483	+	61.9344i	0.321535	+	2.23632i
$768$		0			0
$769$	−12.7216	+	14.6815i	−0.458752	+	0.529428i	−0.937249	−	0.348662i	$-0.886636\pi$
$769$	−12.7216	+	14.6815i	−0.458752	+	0.529428i	0.478497	+	0.878089i	$0.341182\pi$
$770$		0			0
$771$	−11.8845	−	7.63770i	−0.428009	−	0.275065i
$772$		0			0
$773$	−18.5056	−	5.43374i	−0.665601	−	0.195438i	−0.0685578	−	0.997647i	$-0.521840\pi$
$773$	−18.5056	−	5.43374i	−0.665601	−	0.195438i	−0.597043	+	0.802209i	$0.703658\pi$
$774$		0			0
$775$	17.9152	+	20.6752i	0.643533	+	0.742677i
$776$		0			0
$777$	−28.3043	+	8.31090i	−1.01541	+	0.298152i
$778$		0			0
$779$	12.9178	−	89.8455i	0.462829	−	3.21905i
$780$		0			0
$781$	5.44269			0.194755
$782$		0			0
$783$	8.52420			0.304630
$784$		0			0
$785$	0.947113	−	6.58732i	0.0338039	−	0.235111i
$786$		0			0
$787$	13.6794	−	4.01663i	0.487617	−	0.143177i	−0.0286767	−	0.999589i	$-0.509129\pi$
$787$	13.6794	−	4.01663i	0.487617	−	0.143177i	0.516294	+	0.856411i	$0.327311\pi$
$788$		0			0
$789$	12.3024	+	14.1978i	0.437979	+	0.505454i
$790$		0			0
$791$	−11.8450	−	3.47800i	−0.421158	−	0.123663i
$792$		0			0
$793$	−18.6084	−	11.9589i	−0.660802	−	0.424672i
$794$		0			0
$795$	4.43103	−	5.11368i	0.157153	−	0.181364i
$796$		0			0
$797$	−4.07734	−	28.3585i	−0.144427	−	1.00451i	−0.925142	−	0.379622i	$-0.876054\pi$
$797$	−4.07734	−	28.3585i	−0.144427	−	1.00451i	0.780715	−	0.624888i	$-0.214855\pi$
$798$		0			0
$799$	−2.51764	−	5.51287i	−0.0890679	−	0.195031i
$800$		0			0
$801$	−6.47809	+	14.1850i	−0.228892	+	0.501204i
$802$		0			0
$803$	13.4916	−	8.67055i	0.476110	−	0.305977i
$804$		0			0
$805$	13.5163	−	11.0977i	0.476388	−	0.391143i
$806$		0			0
$807$	−17.0057	+	10.9289i	−0.598628	+	0.384715i
$808$		0			0
$809$	12.9460	−	28.3477i	0.455155	−	0.996652i	−0.533410	−	0.845857i	$-0.679090\pi$
$809$	12.9460	−	28.3477i	0.455155	−	0.996652i	0.988565	−	0.150794i	$-0.0481832\pi$
$810$		0			0
$811$	5.94761	+	13.0234i	0.208849	+	0.457315i	0.984848	−	0.173419i	$-0.0554813\pi$
$811$	5.94761	+	13.0234i	0.208849	+	0.457315i	−0.775999	+	0.630734i	$0.782754\pi$
$812$		0			0
$813$	3.01331	+	20.9580i	0.105681	+	0.735031i
$814$		0			0
$815$	14.6192	−	16.8715i	0.512088	−	0.590981i
$816$		0			0
$817$	9.51757	+	6.11657i	0.332977	+	0.213992i
$818$		0			0
$819$	−16.6197	−	4.87999i	−0.580740	−	0.170521i
$820$		0			0
$821$	−26.9758	−	31.1317i	−0.941462	−	1.08650i	−0.996120	−	0.0879999i	$-0.971952\pi$
$821$	−26.9758	−	31.1317i	−0.941462	−	1.08650i	0.0546586	−	0.998505i	$-0.482593\pi$
$822$		0			0
$823$	−8.69069	+	2.55182i	−0.302939	+	0.0889508i	−0.429669	−	0.902986i	$-0.641370\pi$
$823$	−8.69069	+	2.55182i	−0.302939	+	0.0889508i	0.126731	+	0.991937i	$0.459552\pi$
$824$		0			0
$825$	0.931216	−	6.47675i	0.0324208	−	0.225491i
$826$		0			0
$827$	−20.4672			−0.711716			−0.355858	−	0.934540i	$-0.615811\pi$
$827$	−20.4672			−0.711716			−0.355858	+	0.934540i	$0.615811\pi$
$828$		0			0
$829$	−22.4690			−0.780380			−0.390190	−	0.920734i	$-0.627591\pi$
$829$	−22.4690			−0.780380			−0.390190	+	0.920734i	$0.627591\pi$
$830$		0			0
$831$	−4.19204	+	29.1562i	−0.145420	+	1.01142i
$832$		0			0
$833$	−8.23094	+	2.41682i	−0.285185	+	0.0837379i
$834$		0			0
$835$	−5.45496	−	6.29536i	−0.188777	−	0.217860i
$836$		0			0
$837$	6.67629	+	1.96034i	0.230766	+	0.0677591i
$838$		0			0
$839$	4.78410	+	3.07455i	0.165165	+	0.106145i	0.620612	−	0.784118i	$-0.286884\pi$
$839$	4.78410	+	3.07455i	0.165165	+	0.106145i	−0.455447	+	0.890263i	$0.650520\pi$
$840$		0			0
$841$	−28.5926	+	32.9976i	−0.985951	+	1.13785i
$842$		0			0
$843$	1.85660	+	12.9129i	0.0639448	+	0.444746i
$844$		0			0
$845$	4.76752	+	10.4394i	0.164008	+	0.359127i
$846$		0			0
$847$	−12.0625	+	26.4131i	−0.414472	+	0.907566i
$848$		0			0
$849$	19.8891	−	12.7820i	0.682593	−	0.438676i
$850$		0			0
$851$	22.5669	−	33.1461i	0.773583	−	1.13623i
$852$		0			0
$853$	28.8072	−	18.5133i	0.986341	−	0.633883i	0.0551744	−	0.998477i	$-0.482429\pi$
$853$	28.8072	−	18.5133i	0.986341	−	0.633883i	0.931167	+	0.364594i	$0.118792\pi$
$854$		0			0
$855$	−3.25627	+	7.13024i	−0.111362	+	0.243849i
$856$		0			0
$857$	−5.41151	−	11.8496i	−0.184854	−	0.404773i	0.794405	−	0.607389i	$-0.207783\pi$
$857$	−5.41151	−	11.8496i	−0.184854	−	0.404773i	−0.979258	+	0.202616i	$0.935056\pi$
$858$		0			0
$859$	−1.92425	−	13.3834i	−0.0656544	−	0.456637i	−0.995956	−	0.0898413i	$-0.971364\pi$
$859$	−1.92425	−	13.3834i	−0.0656544	−	0.456637i	0.930302	−	0.366795i	$-0.119545\pi$
$860$		0			0
$861$	27.6529	−	31.9131i	0.942407	−	1.08760i
$862$		0			0
$863$	−20.4871	−	13.1663i	−0.697389	−	0.448185i	0.143317	−	0.989677i	$-0.454223\pi$
$863$	−20.4871	−	13.1663i	−0.697389	−	0.448185i	−0.840706	+	0.541492i	$0.817860\pi$
$864$		0			0
$865$	−0.611052	−	0.179421i	−0.0207764	−	0.00610050i
$866$		0			0
$867$	−9.50872	−	10.9736i	−0.322933	−	0.372684i
$868$		0			0
$869$	−27.6032	+	8.10503i	−0.936374	+	0.274944i
$870$		0			0
$871$	2.96906	−	20.6503i	0.100603	−	0.699709i
$872$		0			0
$873$	4.55885			0.154294
$874$		0			0
$875$	−32.5705			−1.10108
$876$		0			0
$877$	4.90519	−	34.1164i	0.165637	−	1.15203i	−0.722138	−	0.691749i	$-0.756840\pi$
$877$	4.90519	−	34.1164i	0.165637	−	1.15203i	0.887774	−	0.460279i	$-0.152251\pi$
$878$		0			0
$879$	25.8706	−	7.59630i	0.872594	−	0.256217i
$880$		0			0
$881$	−17.4065	−	20.0882i	−0.586440	−	0.676788i	0.382536	−	0.923940i	$-0.375051\pi$
$881$	−17.4065	−	20.0882i	−0.586440	−	0.676788i	−0.968977	+	0.247152i	$0.920505\pi$
$882$		0			0
$883$	−6.68068	−	1.96163i	−0.224823	−	0.0660140i	0.167381	−	0.985892i	$-0.446469\pi$
$883$	−6.68068	−	1.96163i	−0.224823	−	0.0660140i	−0.392204	+	0.919878i	$0.628287\pi$
$884$		0			0
$885$	11.0818	+	7.12185i	0.372511	+	0.239398i
$886$		0			0
$887$	−37.0884	+	42.8023i	−1.24531	+	1.43716i	−0.388562	+	0.921423i	$0.627028\pi$
$887$	−37.0884	+	42.8023i	−1.24531	+	1.43716i	−0.856746	+	0.515739i	$0.827517\pi$
$888$		0			0
$889$	2.00606	+	13.9525i	0.0672811	+	0.467950i
$890$		0			0
$891$	−0.691358	−	1.51386i	−0.0231614	−	0.0507163i
$892$		0			0
$893$	12.1249	−	26.5497i	0.405743	−	0.888453i
$894$		0			0
$895$	−7.32469	+	4.70729i	−0.244837	+	0.157347i
$896$		0			0
$897$	21.6696	−	9.20913i	0.723528	−	0.307484i
$898$		0			0
$899$	−49.8970	+	32.0668i	−1.66416	+	1.06949i
$900$		0			0
$901$	4.28249	−	9.37735i	0.142671	−	0.312405i
$902$		0			0
$903$	2.18642	+	4.78759i	0.0727594	+	0.159321i
$904$		0			0
$905$	−0.247640	−	1.72238i	−0.00823184	−	0.0572537i
$906$		0			0
$907$	−15.3091	+	17.6676i	−0.508329	+	0.586643i	−0.950670	−	0.310204i	$-0.899603\pi$
$907$	−15.3091	+	17.6676i	−0.508329	+	0.586643i	0.442341	+	0.896847i	$0.354148\pi$
$908$		0			0
$909$	−6.11473	−	3.92970i	−0.202813	−	0.130340i
$910$		0			0
$911$	−1.29472	−	0.380163i	−0.0428959	−	0.0125954i	0.260214	−	0.965551i	$-0.416207\pi$
$911$	−1.29472	−	0.380163i	−0.0428959	−	0.0125954i	−0.303110	+	0.952956i	$0.598025\pi$
$912$		0			0
$913$	−2.85421	−	3.29393i	−0.0944605	−	0.109013i
$914$		0			0
$915$	−4.46819	+	1.31198i	−0.147714	+	0.0433727i
$916$		0			0
$917$	0.348409	−	2.42324i	0.0115055	−	0.0800223i
$918$		0			0
$919$	23.3419			0.769978			0.384989	−	0.922921i	$-0.374205\pi$
$919$	23.3419			0.769978			0.384989	+	0.922921i	$0.374205\pi$
$920$		0			0
$921$	−2.06886			−0.0681711
$922$		0			0
$923$	2.28498	−	15.8924i	0.0752112	−	0.523105i
$924$		0			0
$925$	−31.5421	+	9.26158i	−1.03710	+	0.304519i
$926$		0			0
$927$	6.40803	+	7.39526i	0.210467	+	0.242892i
$928$		0			0
$929$	26.7292	+	7.84840i	0.876956	+	0.257497i	0.689071	−	0.724694i	$-0.258019\pi$
$929$	26.7292	+	7.84840i	0.876956	+	0.257497i	0.187885	+	0.982191i	$0.439837\pi$
$930$		0			0
$931$	−34.7550	−	22.3357i	−1.13905	−	0.732022i
$932$		0			0
$933$	−2.72419	+	3.14388i	−0.0891860	+	0.102926i
$934$		0			0
$935$	0.385503	+	2.68123i	0.0126073	+	0.0876856i
$936$		0			0
$937$	21.7029	+	47.5228i	0.709004	+	1.55250i	0.828701	+	0.559692i	$0.189080\pi$
$937$	21.7029	+	47.5228i	0.709004	+	1.55250i	−0.119697	+	0.992810i	$0.538192\pi$
$938$		0			0
$939$	0.0503347	−	0.110218i	0.00164261	−	0.00359681i
$940$		0			0
$941$	−11.5432	+	7.41835i	−0.376297	+	0.241831i	−0.715094	−	0.699028i	$-0.753616\pi$
$941$	−11.5432	+	7.41835i	−0.376297	+	0.241831i	0.338797	+	0.940859i	$0.389980\pi$
$942$		0			0
$943$	−1.52360	+	57.3800i	−0.0496151	+	1.86855i
$944$		0			0
$945$	−3.06773	+	1.97151i	−0.0997934	+	0.0641333i
$946$		0			0
$947$	−12.5118	+	27.3969i	−0.406577	+	0.890280i	0.589984	+	0.807415i	$0.299134\pi$
$947$	−12.5118	+	27.3969i	−0.406577	+	0.890280i	−0.996561	+	0.0828647i	$0.973593\pi$
$948$		0			0
$949$	−19.6535	−	43.0351i	−0.637979	−	1.39698i
$950$		0			0
$951$	3.33208	+	23.1751i	0.108050	+	0.751506i
$952$		0			0
$953$	27.7665	−	32.0443i	0.899446	−	1.03802i	−0.0996293	−	0.995025i	$-0.531766\pi$
$953$	27.7665	−	32.0443i	0.899446	−	1.03802i	0.999075	−	0.0429916i	$-0.0136889\pi$
$954$		0			0
$955$	18.3323	+	11.7815i	0.593219	+	0.381239i
$956$		0			0
$957$	13.6118	+	3.99680i	0.440008	+	0.129198i
$958$		0			0
$959$	−32.8768	−	37.9418i	−1.06165	−	1.22520i
$960$		0			0
$961$	−16.7103	+	4.90660i	−0.539043	+	0.158277i
$962$		0			0
$963$	0.502603	−	3.49568i	0.0161961	−	0.112647i
$964$		0			0
$965$	−16.5219			−0.531859
$966$		0			0
$967$	29.9683			0.963715			0.481858	−	0.876250i	$-0.339962\pi$
$967$	29.9683			0.963715			0.481858	+	0.876250i	$0.339962\pi$
$968$		0			0
$969$	−1.69960	+	11.8210i	−0.0545991	+	0.379745i
$970$		0			0
$971$	−52.4916	+	15.4129i	−1.68454	+	0.494625i	−0.977212	−	0.212264i	$-0.931916\pi$
$971$	−52.4916	+	15.4129i	−1.68454	+	0.494625i	−0.707325	+	0.706889i	$0.750098\pi$
$972$		0			0
$973$	17.9978	+	20.7706i	0.576983	+	0.665874i
$974$		0			0
$975$	−18.5209	−	5.43822i	−0.593143	−	0.174162i
$976$		0			0
$977$	25.9733	+	16.6920i	0.830959	+	0.534025i	0.885582	−	0.464482i	$-0.153760\pi$
$977$	25.9733	+	16.6920i	0.830959	+	0.534025i	−0.0546236	+	0.998507i	$0.517396\pi$
$978$		0			0
$979$	−16.9955	+	19.6139i	−0.543180	+	0.626863i
$980$		0			0
$981$	−0.562369	−	3.91136i	−0.0179551	−	0.124880i
$982$		0			0
$983$	4.35540	+	9.53701i	0.138916	+	0.304183i	0.966285	−	0.257476i	$-0.0828907\pi$
$983$	4.35540	+	9.53701i	0.138916	+	0.304183i	−0.827369	+	0.561659i	$0.810163\pi$
$984$		0			0
$985$	1.80693	−	3.95663i	0.0575737	−	0.126069i
$986$		0			0
$987$	11.4228	−	7.34100i	0.363593	−	0.233667i
$988$		0			0
$989$	−6.42669	−	3.14374i	−0.204357	−	0.0999651i
$990$		0			0
$991$	25.6356	−	16.4750i	0.814340	−	0.523345i	−0.0659260	−	0.997825i	$-0.521000\pi$
$991$	25.6356	−	16.4750i	0.814340	−	0.523345i	0.880266	+	0.474480i	$0.157364\pi$
$992$		0			0
$993$	−8.57262	+	18.7714i	−0.272044	+	0.595693i
$994$		0			0
$995$	−5.47666	−	11.9922i	−0.173622	−	0.380178i
$996$		0			0
$997$	1.42385	+	9.90308i	0.0450937	+	0.313634i	0.999867	+	0.0162993i	$0.00518847\pi$
$997$	1.42385	+	9.90308i	0.0450937	+	0.313634i	−0.954773	+	0.297334i	$0.903902\pi$
$998$		0			0
$999$	−5.47543	+	6.31898i	−0.173235	+	0.199924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.265.2	yes	30
23.2	even	11	inner	552.2.q.c.25.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.25.2	✓	30	23.2	even	11	inner
552.2.q.c.265.2	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{3} +(-0.991724 + 0.291196i) q^{5} +(-2.31042 - 2.66637i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{3} +(-0.991724 + 0.291196i) q^{5} +(-2.31042 - 2.66637i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-1.40006 - 0.899767i) q^{11} +(-3.21506 + 3.71038i) q^{13} +(0.147095 + 1.02307i) q^{15} +(0.654168 + 1.43243i) q^{17} +(-3.15045 + 6.89851i) q^{19} +(-2.96803 + 1.90744i) q^{21} +(1.47281 - 4.56408i) q^{23} +(-3.30755 + 2.12563i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-3.54108 - 7.75389i) q^{29} +(-0.990247 - 6.88732i) q^{31} +(-1.08986 + 1.25776i) q^{33} +(3.06773 + 1.97151i) q^{35} +(8.02252 + 2.35562i) q^{37} +(3.21506 + 3.71038i) q^{39} +(-11.4839 + 3.37199i) q^{41} +(0.212305 - 1.47661i) q^{43} +1.03359 q^{45} -3.84862 q^{47} +(-0.775266 + 5.39209i) q^{49} +(1.51095 - 0.443654i) q^{51} +(-4.28703 - 4.94749i) q^{53} +(1.65049 + 0.484626i) q^{55} +(6.37994 + 4.10014i) q^{57} +(8.34611 - 9.63192i) q^{59} +(0.641196 + 4.45962i) q^{61} +(1.46563 + 3.20928i) q^{63} +(2.10800 - 4.61589i) q^{65} +(-3.57483 + 2.29741i) q^{67} +(-4.30802 - 2.10735i) q^{69} +(-2.75118 + 1.76808i) q^{71} +(-4.00312 + 8.76562i) q^{73} +(1.63328 + 3.57639i) q^{75} +(0.835628 + 5.81192i) q^{77} +(11.3200 - 13.0639i) q^{79} +(0.841254 + 0.540641i) q^{81} +(2.51280 + 0.737824i) q^{83} +(-1.06587 - 1.23008i) q^{85} +(-8.17891 + 2.40155i) q^{87} +(2.21930 - 15.4355i) q^{89} +17.3214 q^{91} -6.95815 q^{93} +(1.11555 - 7.75882i) q^{95} +(-4.37419 + 1.28438i) q^{97} +(1.08986 + 1.25776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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