LMFDB - Embedded newform 552.2.q.b.49.2

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			49.2
Character	$\chi$	$=$	552.49
Dual form			552.2.q.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(1.31805 - 1.52111i) q^{5} +(4.20804 - 2.70434i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(1.31805 - 1.52111i) q^{5} +(4.20804 - 2.70434i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.430370 + 2.99329i) q^{11} +(-3.78416 - 2.43193i) q^{13} +(-0.836116 - 1.83084i) q^{15} +(7.13503 + 2.09503i) q^{17} +(-6.04192 + 1.77407i) q^{19} +(-0.711873 - 4.95119i) q^{21} +(-4.79209 - 0.189368i) q^{23} +(0.135049 + 0.939285i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(4.74955 + 1.39459i) q^{29} +(-2.69124 - 5.89300i) q^{31} +(2.54401 + 1.63493i) q^{33} +(1.43280 - 9.96537i) q^{35} +(1.67856 + 1.93716i) q^{37} +(-3.78416 + 2.43193i) q^{39} +(1.95121 - 2.25182i) q^{41} +(-1.27884 + 2.80026i) q^{43} -2.01272 q^{45} +6.39159 q^{47} +(7.48621 - 16.3925i) q^{49} +(4.86971 - 5.61994i) q^{51} +(-0.0481637 + 0.0309530i) q^{53} +(3.98588 + 4.59996i) q^{55} +(-0.896155 + 6.23290i) q^{57} +(-5.43920 - 3.49556i) q^{59} +(2.41163 + 5.28073i) q^{61} +(-4.79948 - 1.40926i) q^{63} +(-8.68697 + 2.55072i) q^{65} +(0.928880 + 6.46050i) q^{67} +(-2.16296 + 4.28037i) q^{69} +(0.915896 + 6.37019i) q^{71} +(-10.8149 + 3.17554i) q^{73} +(0.910505 + 0.267348i) q^{75} +(6.28386 + 13.7597i) q^{77} +(-12.0856 - 7.76693i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(9.00270 + 10.3897i) q^{83} +(12.5911 - 8.09183i) q^{85} +(3.24160 - 3.74100i) q^{87} +(-1.12991 + 2.47416i) q^{89} -22.5007 q^{91} -6.47844 q^{93} +(-5.26501 + 11.5288i) q^{95} +(11.8213 - 13.6426i) q^{97} +(2.54401 - 1.63493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$	$1$	$1$

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
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	1.31805	−	1.52111i	0.589452	−	0.680263i	−0.380158	−	0.924922i	$-0.624130\pi$
$5$	1.31805	−	1.52111i	0.589452	−	0.680263i	0.969609	+	0.244658i	$0.0786758\pi$
$6$		0			0
$7$	4.20804	−	2.70434i	1.59049	−	1.02214i	0.618899	−	0.785470i	$-0.287579\pi$
$7$	4.20804	−	2.70434i	1.59049	−	1.02214i	0.971589	−	0.236675i	$-0.0760575\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	−0.430370	+	2.99329i	−0.129761	+	0.902510i	0.816093	+	0.577920i	$0.196135\pi$
$11$	−0.430370	+	2.99329i	−0.129761	+	0.902510i	−0.945855	+	0.324590i	$0.894774\pi$
$12$		0			0
$13$	−3.78416	−	2.43193i	−1.04954	−	0.674496i	−0.102209	−	0.994763i	$-0.532591\pi$
$13$	−3.78416	−	2.43193i	−1.04954	−	0.674496i	−0.947327	+	0.320267i	$0.896228\pi$
$14$		0			0
$15$	−0.836116	−	1.83084i	−0.215884	−	0.472720i
$16$		0			0
$17$	7.13503	+	2.09503i	1.73050	+	0.508120i	0.987014	−	0.160633i	$-0.0513534\pi$
$17$	7.13503	+	2.09503i	1.73050	+	0.508120i	0.743485	+	0.668753i	$0.233172\pi$
$18$		0			0
$19$	−6.04192	+	1.77407i	−1.38611	+	0.406999i	−0.887892	−	0.460052i	$-0.847831\pi$
$19$	−6.04192	+	1.77407i	−1.38611	+	0.406999i	−0.498219	+	0.867051i	$0.666013\pi$
$20$		0			0
$21$	−0.711873	−	4.95119i	−0.155344	−	1.08044i
$22$		0			0
$23$	−4.79209	−	0.189368i	−0.999220	−	0.0394859i
$23$	−4.79209	−	0.189368i	−0.999220	−	0.0394859i
$24$		0			0
$25$	0.135049	+	0.939285i	0.0270098	+	0.187857i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	4.74955	+	1.39459i	0.881968	+	0.258969i	0.691198	−	0.722665i	$-0.257083\pi$
$29$	4.74955	+	1.39459i	0.881968	+	0.258969i	0.190770	+	0.981635i	$0.438901\pi$
$30$		0			0
$31$	−2.69124	−	5.89300i	−0.483361	−	1.05841i	−0.981526	−	0.191331i	$-0.938720\pi$
$31$	−2.69124	−	5.89300i	−0.483361	−	1.05841i	0.498164	−	0.867083i	$-0.334008\pi$
$32$		0			0
$33$	2.54401	+	1.63493i	0.442855	+	0.284606i
$34$		0			0
$35$	1.43280	−	9.96537i	0.242188	−	1.68446i
$36$		0			0
$37$	1.67856	+	1.93716i	0.275953	+	0.318467i	0.876761	−	0.480927i	$-0.159700\pi$
$37$	1.67856	+	1.93716i	0.275953	+	0.318467i	−0.600808	+	0.799394i	$0.705154\pi$
$38$		0			0
$39$	−3.78416	+	2.43193i	−0.605950	+	0.389421i
$40$		0			0
$41$	1.95121	−	2.25182i	0.304728	−	0.351675i	−0.582645	−	0.812727i	$-0.697982\pi$
$41$	1.95121	−	2.25182i	0.304728	−	0.351675i	0.887373	+	0.461051i	$0.152528\pi$
$42$		0			0
$43$	−1.27884	+	2.80026i	−0.195021	+	0.427035i	−0.981728	−	0.190291i	$-0.939057\pi$
$43$	−1.27884	+	2.80026i	−0.195021	+	0.427035i	0.786707	+	0.617326i	$0.211784\pi$
$44$		0			0
$45$	−2.01272			−0.300039
$46$		0			0
$47$	6.39159			0.932309			0.466155	−	0.884703i	$-0.345639\pi$
$47$	6.39159			0.932309			0.466155	+	0.884703i	$0.345639\pi$
$48$		0			0
$49$	7.48621	−	16.3925i	1.06946	−	2.34179i
$50$		0			0
$51$	4.86971	−	5.61994i	0.681896	−	0.786949i
$52$		0			0
$53$	−0.0481637	+	0.0309530i	−0.00661580	+	0.00425172i	−0.543945	−	0.839121i	$-0.683070\pi$
$53$	−0.0481637	+	0.0309530i	−0.00661580	+	0.00425172i	0.537329	+	0.843373i	$0.319433\pi$
$54$		0			0
$55$	3.98588	+	4.59996i	0.537456	+	0.620258i
$56$		0			0
$57$	−0.896155	+	6.23290i	−0.118699	+	0.825567i
$58$		0			0
$59$	−5.43920	−	3.49556i	−0.708123	−	0.455083i	0.136364	−	0.990659i	$-0.456458\pi$
$59$	−5.43920	−	3.49556i	−0.708123	−	0.455083i	−0.844487	+	0.535576i	$0.820095\pi$
$60$		0			0
$61$	2.41163	+	5.28073i	0.308778	+	0.676129i	0.998867	−	0.0475958i	$-0.0151559\pi$
$61$	2.41163	+	5.28073i	0.308778	+	0.676129i	−0.690089	+	0.723724i	$0.742429\pi$
$62$		0			0
$63$	−4.79948	−	1.40926i	−0.604678	−	0.177549i
$64$		0			0
$65$	−8.68697	+	2.55072i	−1.07749	+	0.316378i
$66$		0			0
$67$	0.928880	+	6.46050i	0.113481	+	0.789276i	0.964489	+	0.264123i	$0.0850826\pi$
$67$	0.928880	+	6.46050i	0.113481	+	0.789276i	−0.851008	+	0.525152i	$0.824008\pi$
$68$		0			0
$69$	−2.16296	+	4.28037i	−0.260390	+	0.515296i
$70$		0			0
$71$	0.915896	+	6.37019i	0.108697	+	0.756003i	0.969150	+	0.246473i	$0.0792716\pi$
$71$	0.915896	+	6.37019i	0.108697	+	0.756003i	−0.860453	+	0.509530i	$0.829819\pi$
$72$		0			0
$73$	−10.8149	+	3.17554i	−1.26579	+	0.371669i	−0.844646	−	0.535325i	$-0.820189\pi$
$73$	−10.8149	+	3.17554i	−1.26579	+	0.371669i	−0.421143	+	0.906994i	$0.638371\pi$
$74$		0			0
$75$	0.910505	+	0.267348i	0.105136	+	0.0308707i
$76$		0			0
$77$	6.28386	+	13.7597i	0.716112	+	1.56807i
$78$		0			0
$79$	−12.0856	−	7.76693i	−1.35973	−	0.873848i	−0.361450	−	0.932392i	$-0.617718\pi$
$79$	−12.0856	−	7.76693i	−1.35973	−	0.873848i	−0.998285	+	0.0585433i	$0.981354\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	9.00270	+	10.3897i	0.988175	+	1.14041i	0.990092	+	0.140417i	$0.0448443\pi$
$83$	9.00270	+	10.3897i	0.988175	+	1.14041i	−0.00191727	+	0.999998i	$0.500610\pi$
$84$		0			0
$85$	12.5911	−	8.09183i	1.36570	−	0.877683i
$86$		0			0
$87$	3.24160	−	3.74100i	0.347536	−	0.401078i
$88$		0			0
$89$	−1.12991	+	2.47416i	−0.119770	+	0.262260i	−0.960016	−	0.279946i	$-0.909684\pi$
$89$	−1.12991	+	2.47416i	−0.119770	+	0.262260i	0.840246	+	0.542206i	$0.182411\pi$
$90$		0			0
$91$	−22.5007			−2.35871
$92$		0			0
$93$	−6.47844			−0.671783
$94$		0			0
$95$	−5.26501	+	11.5288i	−0.540179	+	1.18283i
$96$		0			0
$97$	11.8213	−	13.6426i	1.20028	−	1.38519i	0.297700	−	0.954660i	$-0.403781\pi$
$97$	11.8213	−	13.6426i	1.20028	−	1.38519i	0.902575	−	0.430532i	$-0.141674\pi$
$98$		0			0
$99$	2.54401	−	1.63493i	0.255682	−	0.164317i
$100$		0			0
$101$	−0.148904	−	0.171845i	−0.0148165	−	0.0170992i	0.748293	−	0.663368i	$-0.230874\pi$
$101$	−0.148904	−	0.171845i	−0.0148165	−	0.0170992i	−0.763109	+	0.646269i	$0.776328\pi$
$102$		0			0
$103$	0.143758	−	0.999862i	0.0141649	−	0.0985193i	−0.981512	−	0.191398i	$-0.938698\pi$
$103$	0.143758	−	0.999862i	0.0141649	−	0.0985193i	0.995677	+	0.0928788i	$0.0296069\pi$
$104$		0			0
$105$	−8.46961	−	5.44309i	−0.826550	−	0.531191i
$106$		0			0
$107$	1.57568	+	3.45027i	0.152327	+	0.333550i	0.970376	−	0.241598i	$-0.0776716\pi$
$107$	1.57568	+	3.45027i	0.152327	+	0.333550i	−0.818049	+	0.575148i	$0.804944\pi$
$108$		0			0
$109$	6.22477	+	1.82776i	0.596225	+	0.175067i	0.565902	−	0.824473i	$-0.308528\pi$
$109$	6.22477	+	1.82776i	0.596225	+	0.175067i	0.0303230	+	0.999540i	$0.490346\pi$
$110$		0			0
$111$	2.45940	−	0.722145i	0.233436	−	0.0685430i
$112$		0			0
$113$	2.52203	+	17.5411i	0.237253	+	1.65013i	0.665448	+	0.746445i	$0.268241\pi$
$113$	2.52203	+	17.5411i	0.237253	+	1.65013i	−0.428195	+	0.903687i	$0.640850\pi$
$114$		0			0
$115$	−6.60428	+	7.03972i	−0.615853	+	0.656458i
$116$		0			0
$117$	0.640166	+	4.45245i	0.0591834	+	0.411629i
$118$		0			0
$119$	35.6902	−	10.4796i	3.27171	−	0.960661i
$120$		0			0
$121$	1.77987	+	0.522617i	0.161806	+	0.0475107i
$122$		0			0
$123$	−1.23776	−	2.71033i	−0.111605	−	0.244382i
$124$		0			0
$125$	10.0728	+	6.47341i	0.900940	+	0.578999i
$126$		0			0
$127$	−0.550711	+	3.83028i	−0.0488677	+	0.339882i	0.950690	+	0.310143i	$0.100377\pi$
$127$	−0.550711	+	3.83028i	−0.0488677	+	0.339882i	−0.999558	+	0.0297396i	$0.990532\pi$
$128$		0			0
$129$	2.01596	+	2.32654i	0.177495	+	0.204840i
$130$		0			0
$131$	−14.2689	+	9.17008i	−1.24668	+	0.801193i	−0.986404	−	0.164340i	$-0.947450\pi$
$131$	−14.2689	+	9.17008i	−1.24668	+	0.801193i	−0.260278	+	0.965534i	$0.583814\pi$
$132$		0			0
$133$	−20.6269	+	23.8047i	−1.78858	+	2.06413i
$134$		0			0
$135$	−0.836116	+	1.83084i	−0.0719614	+	0.157573i
$136$		0			0
$137$	−16.0596			−1.37206			−0.686032	−	0.727571i	$-0.740649\pi$
$137$	−16.0596			−1.37206			−0.686032	+	0.727571i	$0.740649\pi$
$138$		0			0
$139$	−11.2165			−0.951369			−0.475684	−	0.879616i	$-0.657800\pi$
$139$	−11.2165			−0.951369			−0.475684	+	0.879616i	$0.657800\pi$
$140$		0			0
$141$	2.65516	−	5.81399i	0.223605	−	0.489627i
$142$		0			0
$143$	8.90806	−	10.2804i	0.744929	−	0.859694i
$144$		0			0
$145$	8.38149	−	5.38646i	0.696045	−	0.447321i
$146$		0			0
$147$	−11.8013	−	13.6194i	−0.973352	−	1.12331i
$148$		0			0
$149$	0.239378	−	1.66491i	0.0196106	−	0.136395i	−0.977664	−	0.210174i	$-0.932597\pi$
$149$	0.239378	−	1.66491i	0.0196106	−	0.136395i	0.997275	+	0.0737792i	$0.0235060\pi$
$150$		0			0
$151$	20.5413	+	13.2011i	1.67163	+	1.07429i	0.897201	+	0.441622i	$0.145597\pi$
$151$	20.5413	+	13.2011i	1.67163	+	1.07429i	0.774424	+	0.632667i	$0.218040\pi$
$152$		0			0
$153$	−3.08913	−	6.76425i	−0.249741	−	0.546857i
$154$		0			0
$155$	−12.5111	−	3.67360i	−1.00492	−	0.295071i
$156$		0			0
$157$	−5.93902	+	1.74385i	−0.473986	+	0.139175i	−0.509996	−	0.860177i	$-0.670353\pi$
$157$	−5.93902	+	1.74385i	−0.473986	+	0.139175i	0.0360105	+	0.999351i	$0.488535\pi$
$158$		0			0
$159$	0.00814786	+	0.0566696i	0.000646167	+	0.00449419i
$160$		0			0
$161$	−20.6774	+	12.1626i	−1.62961	+	0.958546i
$162$		0			0
$163$	−1.43102	−	9.95299i	−0.112086	−	0.779578i	−0.965884	−	0.258974i	$-0.916616\pi$
$163$	−1.43102	−	9.95299i	−0.112086	−	0.779578i	0.853798	−	0.520604i	$-0.174293\pi$
$164$		0			0
$165$	5.84006	−	1.71480i	0.454648	−	0.133497i
$166$		0			0
$167$	−9.13788	−	2.68312i	−0.707110	−	0.207626i	−0.0916467	−	0.995792i	$-0.529213\pi$
$167$	−9.13788	−	2.68312i	−0.707110	−	0.207626i	−0.615464	+	0.788165i	$0.711031\pi$
$168$		0			0
$169$	3.00517	+	6.58041i	0.231167	+	0.506186i
$170$		0			0
$171$	5.29737	+	3.40441i	0.405100	+	0.260342i
$172$		0			0
$173$	1.28737	−	8.95387i	0.0978771	−	0.680750i	−0.880519	−	0.474011i	$-0.842806\pi$
$173$	1.28737	−	8.95387i	0.0978771	−	0.680750i	0.978396	−	0.206739i	$-0.0662852\pi$
$174$		0			0
$175$	3.10844	+	3.58733i	0.234976	+	0.271176i
$176$		0			0
$177$	−5.43920	+	3.49556i	−0.408835	+	0.262742i
$178$		0			0
$179$	−2.78964	+	3.21941i	−0.208507	+	0.240630i	−0.850365	−	0.526194i	$-0.823619\pi$
$179$	−2.78964	+	3.21941i	−0.208507	+	0.240630i	0.641857	+	0.766824i	$0.278164\pi$
$180$		0			0
$181$	6.09167	−	13.3389i	0.452790	−	0.991472i	−0.536282	−	0.844039i	$-0.680172\pi$
$181$	6.09167	−	13.3389i	0.452790	−	0.991472i	0.989072	−	0.147433i	$-0.0471012\pi$
$182$		0			0
$183$	5.80535			0.429144
$184$		0			0
$185$	5.15907			0.379303
$186$		0			0
$187$	−9.34174	+	20.4556i	−0.683136	+	1.49586i
$188$		0			0
$189$	−3.27568	+	3.78034i	−0.238271	+	0.274979i
$190$		0			0
$191$	−3.91979	+	2.51909i	−0.283626	+	0.182275i	−0.674717	−	0.738077i	$-0.735734\pi$
$191$	−3.91979	+	2.51909i	−0.283626	+	0.182275i	0.391091	+	0.920352i	$0.372098\pi$
$192$		0			0
$193$	−1.24319	−	1.43472i	−0.0894866	−	0.103273i	0.709240	−	0.704967i	$-0.249038\pi$
$193$	−1.24319	−	1.43472i	−0.0894866	−	0.103273i	−0.798727	+	0.601694i	$0.794493\pi$
$194$		0			0
$195$	−1.28848	+	8.96156i	−0.0922698	+	0.641750i
$196$		0			0
$197$	7.17874	+	4.61349i	0.511464	+	0.328698i	0.770787	−	0.637093i	$-0.219863\pi$
$197$	7.17874	+	4.61349i	0.511464	+	0.328698i	−0.259323	+	0.965791i	$0.583500\pi$
$198$		0			0
$199$	8.09447	+	17.7244i	0.573801	+	1.25645i	0.944749	+	0.327796i	$0.106306\pi$
$199$	8.09447	+	17.7244i	0.573801	+	1.25645i	−0.370947	+	0.928654i	$0.620967\pi$
$200$		0			0
$201$	6.26255	+	1.83885i	0.441726	+	0.129702i
$202$		0			0
$203$	23.7577	−	6.97589i	1.66746	−	0.489612i
$204$		0			0
$205$	−0.853474	−	5.93604i	−0.0596092	−	0.414591i
$206$		0			0
$207$	2.99504	+	3.74563i	0.208170	+	0.260339i
$208$		0			0
$209$	−2.71003	−	18.8487i	−0.187457	−	1.30379i
$210$		0			0
$211$	0.447028	−	0.131259i	0.0307747	−	0.00903627i	−0.266309	−	0.963888i	$-0.585804\pi$
$211$	0.447028	−	0.131259i	0.0307747	−	0.00903627i	0.297084	+	0.954851i	$0.403986\pi$
$212$		0			0
$213$	6.17501	+	1.81315i	0.423105	+	0.124235i
$214$		0			0
$215$	2.57394	+	5.63615i	0.175541	+	0.384382i
$216$		0			0
$217$	−27.2615	−	17.5199i	−1.85063	−	1.18933i
$218$		0			0
$219$	−1.60410	+	11.1568i	−0.108395	+	0.753903i
$220$		0			0
$221$	−21.9051	−	25.2798i	−1.47350	−	1.70051i
$222$		0			0
$223$	5.60029	−	3.59909i	0.375023	−	0.241013i	−0.339528	−	0.940596i	$-0.610267\pi$
$223$	5.60029	−	3.59909i	0.375023	−	0.241013i	0.714551	+	0.699583i	$0.246631\pi$
$224$		0			0
$225$	0.621426	−	0.717164i	0.0414284	−	0.0478109i
$226$		0			0
$227$	5.61884	−	12.3035i	0.372935	−	0.816614i	−0.626377	−	0.779521i	$-0.715463\pi$
$227$	5.61884	−	12.3035i	0.372935	−	0.816614i	0.999312	−	0.0370936i	$-0.0118100\pi$
$228$		0			0
$229$	−6.50334			−0.429753			−0.214876	−	0.976641i	$-0.568935\pi$
$229$	−6.50334			−0.429753			−0.214876	+	0.976641i	$0.568935\pi$
$230$		0			0
$231$	15.1267			0.995264
$232$		0			0
$233$	−2.37648	+	5.20376i	−0.155688	+	0.340910i	−0.971363	−	0.237601i	$-0.923639\pi$
$233$	−2.37648	+	5.20376i	−0.155688	+	0.340910i	0.815674	+	0.578511i	$0.196366\pi$
$234$		0			0
$235$	8.42446	−	9.72234i	0.549551	−	0.634216i
$236$		0			0
$237$	−12.0856	+	7.76693i	−0.785043	+	0.504517i
$238$		0			0
$239$	3.43863	+	3.96839i	0.222427	+	0.256694i	0.855985	−	0.517001i	$-0.172952\pi$
$239$	3.43863	+	3.96839i	0.222427	+	0.256694i	−0.633558	+	0.773695i	$0.718406\pi$
$240$		0			0
$241$	1.56802	−	10.9058i	0.101005	−	0.702506i	−0.874899	−	0.484306i	$-0.839072\pi$
$241$	1.56802	−	10.9058i	0.101005	−	0.702506i	0.975904	−	0.218200i	$-0.0700186\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	−15.0677	−	32.9936i	−0.962638	−	2.10788i
$246$		0			0
$247$	27.1780	+	7.98018i	1.72929	+	0.507767i
$248$		0			0
$249$	13.1906	−	3.87312i	0.835923	−	0.245449i
$250$		0			0
$251$	−2.98817	−	20.7832i	−0.188612	−	1.31182i	−0.835607	−	0.549328i	$-0.814884\pi$
$251$	−2.98817	−	20.7832i	−0.188612	−	1.31182i	0.646995	−	0.762494i	$-0.276025\pi$
$252$		0			0
$253$	2.62920	−	14.2626i	0.165297	−	0.896683i
$254$		0			0
$255$	−2.13004	−	14.8148i	−0.133388	−	0.927737i
$256$		0			0
$257$	4.27564	−	1.25544i	0.266707	−	0.0783122i	−0.145645	−	0.989337i	$-0.546526\pi$
$257$	4.27564	−	1.25544i	0.266707	−	0.0783122i	0.412352	+	0.911025i	$0.364707\pi$
$258$		0			0
$259$	12.3022	+	3.61225i	0.764420	+	0.224454i
$260$		0			0
$261$	−2.05633	−	4.50273i	−0.127284	−	0.278712i
$262$		0			0
$263$	−6.13742	−	3.94428i	−0.378450	−	0.243215i	0.337562	−	0.941303i	$-0.390398\pi$
$263$	−6.13742	−	3.94428i	−0.378450	−	0.243215i	−0.716011	+	0.698089i	$0.754034\pi$
$264$		0			0
$265$	−0.0163994	+	0.114060i	−0.00100741	+	0.00700667i
$266$		0			0
$267$	1.78119	+	2.05561i	0.109007	+	0.125801i
$268$		0			0
$269$	2.20083	−	1.41439i	0.134187	−	0.0862367i	−0.471825	−	0.881692i	$-0.656405\pi$
$269$	2.20083	−	1.41439i	0.134187	−	0.0862367i	0.606012	+	0.795455i	$0.292768\pi$
$270$		0			0
$271$	4.21019	−	4.85882i	0.255751	−	0.295152i	−0.613325	−	0.789830i	$-0.710169\pi$
$271$	4.21019	−	4.85882i	0.255751	−	0.295152i	0.869076	+	0.494678i	$0.164714\pi$
$272$		0			0
$273$	−9.34711	+	20.4673i	−0.565713	+	1.23874i
$274$		0			0
$275$	−2.86967			−0.173048
$276$		0			0
$277$	−8.48518			−0.509825			−0.254913	−	0.966964i	$-0.582047\pi$
$277$	−8.48518			−0.509825			−0.254913	+	0.966964i	$0.582047\pi$
$278$		0			0
$279$	−2.69124	+	5.89300i	−0.161120	+	0.352805i
$280$		0			0
$281$	−9.61727	+	11.0989i	−0.573718	+	0.662106i	−0.966242	−	0.257636i	$-0.917057\pi$
$281$	−9.61727	+	11.0989i	−0.573718	+	0.662106i	0.392524	+	0.919742i	$0.371602\pi$
$282$		0			0
$283$	17.8680	−	11.4831i	1.06214	−	0.682598i	0.111778	−	0.993733i	$-0.464345\pi$
$283$	17.8680	−	11.4831i	1.06214	−	0.682598i	0.950366	+	0.311135i	$0.100709\pi$
$284$		0			0
$285$	8.29977	+	9.57845i	0.491636	+	0.567378i
$286$		0			0
$287$	2.12109	−	14.7525i	0.125204	−	0.870812i
$288$		0			0
$289$	32.2182	+	20.7054i	1.89519	+	1.21796i
$290$		0			0
$291$	−7.49894	−	16.4204i	−0.439596	−	0.962580i
$292$		0			0
$293$	−4.71547	−	1.38459i	−0.275481	−	0.0808884i	0.141074	−	0.989999i	$-0.454944\pi$
$293$	−4.71547	−	1.38459i	−0.275481	−	0.0808884i	−0.416555	+	0.909111i	$0.636763\pi$
$294$		0			0
$295$	−12.4863	+	3.66631i	−0.726980	+	0.213461i
$296$		0			0
$297$	−0.430370	−	2.99329i	−0.0249726	−	0.173688i
$298$		0			0
$299$	17.6735	+	12.3706i	1.02209	+	0.715412i
$300$		0			0
$301$	2.19147	+	15.2420i	0.126314	+	0.878534i
$302$		0			0
$303$	−0.218172	+	0.0640612i	−0.0125337	+	0.00368022i
$304$		0			0
$305$	11.2113	+	3.29192i	0.641955	+	0.188495i
$306$		0			0
$307$	−6.05457	−	13.2577i	−0.345553	−	0.756655i	−1.00000		0.000546917i	$-0.999826\pi$
$307$	−6.05457	−	13.2577i	−0.345553	−	0.756655i	0.654447	−	0.756108i	$-0.272901\pi$
$308$		0			0
$309$	−0.849787	−	0.546125i	−0.0483427	−	0.0310680i
$310$		0			0
$311$	0.444076	−	3.08862i	0.0251812	−	0.175139i	−0.973350	−	0.229326i	$-0.926348\pi$
$311$	0.444076	−	3.08862i	0.0251812	−	0.175139i	0.998531	+	0.0541871i	$0.0172567\pi$
$312$		0			0
$313$	7.56117	+	8.72606i	0.427383	+	0.493226i	0.928072	−	0.372401i	$-0.121465\pi$
$313$	7.56117	+	8.72606i	0.427383	+	0.493226i	−0.500689	+	0.865627i	$0.666920\pi$
$314$		0			0
$315$	−8.46961	+	5.44309i	−0.477209	+	0.306683i
$316$		0			0
$317$	−5.71437	+	6.59473i	−0.320951	+	0.370397i	−0.893182	−	0.449695i	$-0.851533\pi$
$317$	−5.71437	+	6.59473i	−0.320951	+	0.370397i	0.572231	+	0.820092i	$0.306078\pi$
$318$		0			0
$319$	−6.21848	+	13.6166i	−0.348168	+	0.762381i
$320$		0			0
$321$	3.79304			0.211707
$322$		0			0
$323$	−46.8260			−2.60547
$324$		0			0
$325$	1.77323	−	3.88283i	0.0983611	−	0.215381i
$326$		0			0
$327$	4.24845	−	4.90297i	0.234940	−	0.271135i
$328$		0			0
$329$	26.8960	−	17.2850i	1.48283	−	0.952955i
$330$		0			0
$331$	−9.67587	−	11.1666i	−0.531834	−	0.613769i	0.424720	−	0.905325i	$-0.360373\pi$
$331$	−9.67587	−	11.1666i	−0.531834	−	0.613769i	−0.956554	+	0.291556i	$0.905827\pi$
$332$		0			0
$333$	0.364786	−	2.53714i	0.0199901	−	0.139034i
$334$		0			0
$335$	11.0515	+	7.10235i	0.603807	+	0.388043i
$336$		0			0
$337$	−10.9242	−	23.9206i	−0.595077	−	1.30304i	−0.932325	−	0.361620i	$-0.882224\pi$
$337$	−10.9242	−	23.9206i	−0.595077	−	1.30304i	0.337249	−	0.941416i	$-0.390504\pi$
$338$		0			0
$339$	17.0037	+	4.99273i	0.923512	+	0.271168i
$340$		0			0
$341$	18.7977	−	5.51949i	1.01795	−	0.298897i
$342$		0			0
$343$	−7.84558	−	54.5672i	−0.423622	−	2.94635i
$344$		0			0
$345$	3.66004	+	8.93188i	0.197050	+	0.480876i
$346$		0			0
$347$	0.0565300	+	0.393175i	0.00303469	+	0.0211067i	0.991283	−	0.131753i	$-0.0420607\pi$
$347$	0.0565300	+	0.393175i	0.00303469	+	0.0211067i	−0.988248	+	0.152860i	$0.951152\pi$
$348$		0			0
$349$	−22.4624	+	6.59556i	−1.20239	+	0.353052i	−0.820765	−	0.571266i	$-0.806452\pi$
$349$	−22.4624	+	6.59556i	−1.20239	+	0.353052i	−0.381621	+	0.924319i	$0.624634\pi$
$350$		0			0
$351$	4.31603	+	1.26730i	0.230373	+	0.0676435i
$352$		0			0
$353$	10.3078	+	22.5709i	0.548627	+	1.20133i	0.957420	+	0.288699i	$0.0932228\pi$
$353$	10.3078	+	22.5709i	0.548627	+	1.20133i	−0.408792	+	0.912627i	$0.634050\pi$
$354$		0			0
$355$	10.8970	+	7.00308i	0.578353	+	0.371685i
$356$		0			0
$357$	5.29367	−	36.8183i	0.280171	−	1.94863i
$358$		0			0
$359$	−1.63444	−	1.88624i	−0.0862624	−	0.0995521i	0.710977	−	0.703215i	$-0.248253\pi$
$359$	−1.63444	−	1.88624i	−0.0862624	−	0.0995521i	−0.797240	+	0.603663i	$0.793707\pi$
$360$		0			0
$361$	17.3736	−	11.1654i	0.914402	−	0.587651i
$362$		0			0
$363$	1.21477	−	1.40192i	0.0637591	−	0.0735819i
$364$		0			0
$365$	−9.42426	+	20.6363i	−0.493288	+	1.08015i
$366$		0			0
$367$	10.4296			0.544418			0.272209	−	0.962238i	$-0.412246\pi$
$367$	10.4296			0.544418			0.272209	+	0.962238i	$0.412246\pi$
$368$		0			0
$369$	−2.97959			−0.155111
$370$		0			0
$371$	−0.118967	+	0.260502i	−0.00617648	+	0.0135246i
$372$		0			0
$373$	−9.87125	+	11.3920i	−0.511114	+	0.589857i	−0.951383	−	0.308009i	$-0.900337\pi$
$373$	−9.87125	+	11.3920i	−0.511114	+	0.589857i	0.440270	+	0.897866i	$0.354883\pi$
$374$		0			0
$375$	10.0728	−	6.47341i	0.520158	−	0.334285i
$376$		0			0
$377$	−14.5815	−	16.8279i	−0.750985	−	0.866682i
$378$		0			0
$379$	1.72935	−	12.0279i	0.0888310	−	0.617833i	−0.895966	−	0.444123i	$-0.853515\pi$
$379$	1.72935	−	12.0279i	0.0888310	−	0.617833i	0.984797	−	0.173710i	$-0.0555756\pi$
$380$		0			0
$381$	3.25537	+	2.09210i	0.166778	+	0.107182i
$382$		0			0
$383$	−13.8735	−	30.3787i	−0.708902	−	1.55228i	−0.828832	−	0.559497i	$-0.810994\pi$
$383$	−13.8735	−	30.3787i	−0.708902	−	1.55228i	0.119930	−	0.992782i	$-0.461733\pi$
$384$		0			0
$385$	29.2126	+	8.57759i	1.48881	+	0.437155i
$386$		0			0
$387$	2.95375	−	0.867300i	0.150148	−	0.0440873i
$388$		0			0
$389$	1.47211	+	10.2388i	0.0746391	+	0.519127i	0.992502	+	0.122229i	$0.0390042\pi$
$389$	1.47211	+	10.2388i	0.0746391	+	0.519127i	−0.917863	+	0.396898i	$0.870087\pi$
$390$		0			0
$391$	−33.7950	−	11.3907i	−1.70909	−	0.576054i
$392$		0			0
$393$	2.41387	+	16.7889i	0.121764	+	0.846886i
$394$		0			0
$395$	−27.7438	+	8.14633i	−1.39594	+	0.409886i
$396$		0			0
$397$	−7.34966	−	2.15806i	−0.368869	−	0.108310i	0.0920442	−	0.995755i	$-0.470660\pi$
$397$	−7.34966	−	2.15806i	−0.368869	−	0.108310i	−0.460913	+	0.887445i	$0.652478\pi$
$398$		0			0
$399$	13.0848	+	28.6518i	0.655060	+	1.43438i
$400$		0			0
$401$	−18.7384	−	12.0424i	−0.935751	−	0.601371i	−0.0185639	−	0.999828i	$-0.505909\pi$
$401$	−18.7384	−	12.0424i	−0.935751	−	0.601371i	−0.917187	+	0.398457i	$0.869546\pi$
$402$		0			0
$403$	−4.14728	+	28.8450i	−0.206591	+	1.43687i
$404$		0			0
$405$	1.31805	+	1.52111i	0.0654946	+	0.0755848i
$406$		0			0
$407$	−6.52088	+	4.19071i	−0.323228	+	0.207726i
$408$		0			0
$409$	−8.33240	+	9.61611i	−0.412011	+	0.475486i	−0.923387	−	0.383871i	$-0.874591\pi$
$409$	−8.33240	+	9.61611i	−0.412011	+	0.475486i	0.511376	+	0.859357i	$0.329136\pi$
$410$		0			0
$411$	−6.67140	+	14.6083i	−0.329076	+	0.720576i
$412$		0			0
$413$	−32.3415			−1.59142
$414$		0			0
$415$	27.6699			1.35826
$416$		0			0
$417$	−4.65949	+	10.2029i	−0.228176	+	0.499636i
$418$		0			0
$419$	16.7731	−	19.3572i	0.819420	−	0.945661i	−0.179857	−	0.983693i	$-0.557563\pi$
$419$	16.7731	−	19.3572i	0.819420	−	0.945661i	0.999277	+	0.0380321i	$0.0121089\pi$
$420$		0			0
$421$	−4.77985	+	3.07182i	−0.232956	+	0.149712i	−0.651911	−	0.758295i	$-0.726033\pi$
$421$	−4.77985	+	3.07182i	−0.232956	+	0.149712i	0.418956	+	0.908007i	$0.362396\pi$
$422$		0			0
$423$	−4.18560	−	4.83044i	−0.203511	−	0.234864i
$424$		0			0
$425$	−1.00426	+	6.98476i	−0.0487136	+	0.338811i
$426$		0			0
$427$	24.4291	+	15.6997i	1.18221	+	0.759759i
$428$		0			0
$429$	−5.65088	−	12.3737i	−0.272827	−	0.597408i
$430$		0			0
$431$	17.1472	+	5.03487i	0.825951	+	0.242521i	0.667277	−	0.744810i	$-0.267460\pi$
$431$	17.1472	+	5.03487i	0.825951	+	0.242521i	0.158674	+	0.987331i	$0.449278\pi$
$432$		0			0
$433$	−6.92156	+	2.03235i	−0.332629	+	0.0976686i	−0.443782	−	0.896135i	$-0.646364\pi$
$433$	−6.92156	+	2.03235i	−0.332629	+	0.0976686i	0.111154	+	0.993803i	$0.464545\pi$
$434$		0			0
$435$	−1.41790	−	9.86169i	−0.0679829	−	0.472832i
$436$		0			0
$437$	29.2894	−	7.35735i	1.40110	−	0.351950i
$438$		0			0
$439$	1.52494	+	10.6062i	0.0727813	+	0.506205i	0.993305	+	0.115519i	$0.0368531\pi$
$439$	1.52494	+	10.6062i	0.0727813	+	0.506205i	−0.920524	+	0.390686i	$0.872238\pi$
$440$		0			0
$441$	−17.2911	+	5.07711i	−0.823384	+	0.241767i
$442$		0			0
$443$	−20.8316	−	6.11670i	−0.989738	−	0.290613i	−0.253499	−	0.967336i	$-0.581582\pi$
$443$	−20.8316	−	6.11670i	−0.989738	−	0.290613i	−0.736238	+	0.676722i	$0.763400\pi$
$444$		0			0
$445$	2.27420	+	4.97980i	0.107807	+	0.236065i
$446$		0			0
$447$	−1.41502	−	0.909375i	−0.0669280	−	0.0430120i
$448$		0			0
$449$	2.11391	−	14.7026i	0.0997617	−	0.693858i	−0.877150	−	0.480216i	$-0.840558\pi$
$449$	2.11391	−	14.7026i	0.0997617	−	0.693858i	0.976912	−	0.213642i	$-0.0685326\pi$
$450$		0			0
$451$	5.90060	+	6.80966i	0.277849	+	0.320654i
$452$		0			0
$453$	20.5413	−	13.2011i	0.965113	−	0.620241i
$454$		0			0
$455$	−29.6571	+	34.2261i	−1.39034	+	1.60454i
$456$		0			0
$457$	−0.687808	+	1.50609i	−0.0321743	+	0.0704519i	−0.925037	−	0.379877i	$-0.875966\pi$
$457$	−0.687808	+	1.50609i	−0.0321743	+	0.0704519i	0.892863	+	0.450329i	$0.148693\pi$
$458$		0			0
$459$	−7.43625			−0.347094
$460$		0			0
$461$	−27.5437			−1.28284			−0.641420	−	0.767190i	$-0.721654\pi$
$461$	−27.5437			−1.28284			−0.641420	+	0.767190i	$0.721654\pi$
$462$		0			0
$463$	−13.4032	+	29.3488i	−0.622898	+	1.36396i	0.290495	+	0.956877i	$0.406180\pi$
$463$	−13.4032	+	29.3488i	−0.622898	+	1.36396i	−0.913393	+	0.407080i	$0.866547\pi$
$464$		0			0
$465$	−8.53893	+	9.85445i	−0.395984	+	0.456989i
$466$		0			0
$467$	−19.9372	+	12.8129i	−0.922585	+	0.592909i	−0.913407	−	0.407049i	$-0.866558\pi$
$467$	−19.9372	+	12.8129i	−0.922585	+	0.592909i	−0.00917844	+	0.999958i	$0.502922\pi$
$468$		0			0
$469$	21.3802	+	24.6740i	0.987244	+	1.13934i
$470$		0			0
$471$	−0.880894	+	6.12675i	−0.0405894	+	0.282306i
$472$		0			0
$473$	−7.83161	−	5.03307i	−0.360098	−	0.231421i
$474$		0			0
$475$	−2.48231	−	5.43550i	−0.113896	−	0.249398i
$476$		0			0
$477$	0.0549332	+	0.0161299i	0.00251522	+	0.000738535i
$478$		0			0
$479$	31.0270	−	9.11036i	1.41766	−	0.416263i	0.518950	−	0.854805i	$-0.326323\pi$
$479$	31.0270	−	9.11036i	1.41766	−	0.416263i	0.898711	+	0.438542i	$0.144505\pi$
$480$		0			0
$481$	−1.64089	−	11.4127i	−0.0748183	−	0.520373i
$482$		0			0
$483$	2.47377	+	23.8614i	0.112560	+	1.08573i
$484$		0			0
$485$	−5.17073	−	35.9632i	−0.234791	−	1.63301i
$486$		0			0
$487$	−25.1282	+	7.37830i	−1.13867	+	0.334343i	−0.796108	−	0.605154i	$-0.793111\pi$
$487$	−25.1282	+	7.37830i	−1.13867	+	0.334343i	−0.342558	+	0.939497i	$0.611293\pi$
$488$		0			0
$489$	−9.64802	−	2.83292i	−0.436299	−	0.128109i
$490$		0			0
$491$	1.89331	+	4.14578i	0.0854440	+	0.187096i	0.947531	−	0.319664i	$-0.103570\pi$
$491$	1.89331	+	4.14578i	0.0854440	+	0.187096i	−0.862087	+	0.506761i	$0.830843\pi$
$492$		0			0
$493$	30.9664	+	19.9009i	1.39466	+	0.896292i
$494$		0			0
$495$	0.866215	−	6.02466i	0.0389335	−	0.270788i
$496$		0			0
$497$	21.0813	+	24.3291i	0.945626	+	1.09131i
$498$		0			0
$499$	−25.9099	+	16.6513i	−1.15989	+	0.745415i	−0.971584	−	0.236696i	$-0.923936\pi$
$499$	−25.9099	+	16.6513i	−1.15989	+	0.745415i	−0.188305	+	0.982111i	$0.560299\pi$
$500$		0			0
$501$	−6.23667	+	7.19750i	−0.278634	+	0.321560i
$502$		0			0
$503$	6.22158	−	13.6234i	0.277406	−	0.607435i	−0.718727	−	0.695293i	$-0.755275\pi$
$503$	6.22158	−	13.6234i	0.277406	−	0.607435i	0.996133	+	0.0878574i	$0.0280020\pi$
$504$		0			0
$505$	−0.457659			−0.0203656
$506$		0			0
$507$	7.23415			0.321280
$508$		0			0
$509$	−6.72982	+	14.7363i	−0.298294	+	0.653173i	−0.998130	−	0.0611308i	$-0.980529\pi$
$509$	−6.72982	+	14.7363i	−0.298294	+	0.653173i	0.699836	+	0.714304i	$0.253257\pi$
$510$		0			0
$511$	−36.9218	+	42.6100i	−1.63332	+	1.88496i
$512$		0			0
$513$	5.29737	−	3.40441i	0.233884	−	0.150308i
$514$		0			0
$515$	−1.33142	−	1.53654i	−0.0586695	−	0.0677082i
$516$		0			0
$517$	−2.75075	+	19.1319i	−0.120978	+	0.841418i
$518$		0			0
$519$	−7.60994	−	4.89061i	−0.334039	−	0.214674i
$520$		0			0
$521$	2.38152	+	5.21480i	0.104336	+	0.228464i	0.954599	−	0.297894i	$-0.0962842\pi$
$521$	2.38152	+	5.21480i	0.104336	+	0.228464i	−0.850263	+	0.526359i	$0.823557\pi$
$522$		0			0
$523$	−1.40391	−	0.412224i	−0.0613885	−	0.0180253i	0.250894	−	0.968015i	$-0.419275\pi$
$523$	−1.40391	−	0.412224i	−0.0613885	−	0.0180253i	−0.312283	+	0.949989i	$0.601094\pi$
$524$		0			0
$525$	4.55444	−	1.33730i	0.198772	−	0.0583647i
$526$		0			0
$527$	−6.85606	−	47.6850i	−0.298655	−	2.07719i
$528$		0			0
$529$	22.9283	+	1.81494i	0.996882	+	0.0789103i
$530$		0			0
$531$	0.920149	+	6.39977i	0.0399310	+	0.277727i
$532$		0			0
$533$	−12.8600	+	3.77603i	−0.557027	+	0.163558i
$534$		0			0
$535$	7.32509	+	2.15084i	0.316691	+	0.0929889i
$536$		0			0
$537$	1.76962	+	3.87494i	0.0763649	+	0.167216i
$538$		0			0
$539$	45.8457	+	29.4632i	1.97471	+	1.26907i
$540$		0			0
$541$	5.89126	−	40.9746i	0.253285	−	1.76163i	−0.324918	−	0.945742i	$-0.605337\pi$
$541$	5.89126	−	40.9746i	0.253285	−	1.76163i	0.578203	−	0.815893i	$-0.303754\pi$
$542$		0			0
$543$	−9.60292	−	11.0824i	−0.412101	−	0.475589i
$544$		0			0
$545$	10.9848	−	7.05950i	0.470537	−	0.302396i
$546$		0			0
$547$	−5.07226	+	5.85370i	−0.216874	+	0.250286i	−0.853753	−	0.520677i	$-0.825679\pi$
$547$	−5.07226	+	5.85370i	−0.216874	+	0.250286i	0.636879	+	0.770963i	$0.280225\pi$
$548$		0			0
$549$	2.41163	−	5.28073i	0.102926	−	0.225376i
$550$		0			0
$551$	−31.1705			−1.32791
$552$		0			0
$553$	−71.8610			−3.05584
$554$		0			0
$555$	2.14316	−	4.69286i	0.0909719	−	0.199201i
$556$		0			0
$557$	18.8007	−	21.6972i	0.796613	−	0.919341i	−0.201577	−	0.979473i	$-0.564607\pi$
$557$	18.8007	−	21.6972i	0.796613	−	0.919341i	0.998190	+	0.0601319i	$0.0191521\pi$
$558$		0			0
$559$	11.6494	−	7.48658i	0.492715	−	0.316649i
$560$		0			0
$561$	14.7263	+	16.9951i	0.621746	+	0.717533i
$562$		0			0
$563$	−4.47051	+	31.0931i	−0.188409	+	1.31042i	0.647717	+	0.761881i	$0.275724\pi$
$563$	−4.47051	+	31.0931i	−0.188409	+	1.31042i	−0.836127	+	0.548536i	$0.815185\pi$
$564$		0			0
$565$	30.0063	+	19.2839i	1.26237	+	0.811278i
$566$		0			0
$567$	2.07795	+	4.55007i	0.0872656	+	0.191085i
$568$		0			0
$569$	−19.8788	−	5.83694i	−0.833363	−	0.244697i	−0.162902	−	0.986642i	$-0.552085\pi$
$569$	−19.8788	−	5.83694i	−0.833363	−	0.244697i	−0.670461	+	0.741945i	$0.733904\pi$
$570$		0			0
$571$	40.9638	−	12.0281i	1.71428	−	0.503359i	0.730529	−	0.682881i	$-0.239273\pi$
$571$	40.9638	−	12.0281i	1.71428	−	0.503359i	0.983754	+	0.179522i	$0.0574552\pi$
$572$		0			0
$573$	0.663110	+	4.61203i	0.0277018	+	0.192670i
$574$		0			0
$575$	−0.469296	−	4.52671i	−0.0195710	−	0.188777i
$576$		0			0
$577$	−5.30107	−	36.8698i	−0.220686	−	1.53491i	−0.735452	−	0.677577i	$-0.763030\pi$
$577$	−5.30107	−	36.8698i	−0.220686	−	1.53491i	0.514766	−	0.857331i	$-0.327879\pi$
$578$		0			0
$579$	−1.82150	+	0.534841i	−0.0756990	+	0.0222272i
$580$		0			0
$581$	65.9809	+	19.3738i	2.73735	+	0.803759i
$582$		0			0
$583$	−0.0719229	−	0.157489i	−0.00297874	−	0.00652253i
$584$		0			0
$585$	7.61647	+	4.89481i	0.314902	+	0.202375i
$586$		0			0
$587$	−0.832963	+	5.79339i	−0.0343801	+	0.239119i	−0.999764	−	0.0217135i	$-0.993088\pi$
$587$	−0.832963	+	5.79339i	−0.0343801	+	0.239119i	0.965384	+	0.260832i	$0.0839969\pi$
$588$		0			0
$589$	26.7148	+	30.8306i	1.10077	+	1.27035i
$590$		0			0
$591$	7.17874	−	4.61349i	0.295294	−	0.189774i
$592$		0			0
$593$	11.5391	−	13.3169i	0.473856	−	0.546859i	−0.467624	−	0.883927i	$-0.654890\pi$
$593$	11.5391	−	13.3169i	0.473856	−	0.546859i	0.941480	+	0.337068i	$0.109435\pi$
$594$		0			0
$595$	31.1009	−	68.1015i	1.27501	−	2.79189i
$596$		0			0
$597$	19.4853			0.797478
$598$		0			0
$599$	−1.21320			−0.0495700			−0.0247850	−	0.999693i	$-0.507890\pi$
$599$	−1.21320			−0.0495700			−0.0247850	+	0.999693i	$0.507890\pi$
$600$		0			0
$601$	−10.4184	+	22.8131i	−0.424976	+	0.930567i	0.569140	+	0.822241i	$0.307276\pi$
$601$	−10.4184	+	22.8131i	−0.424976	+	0.930567i	−0.994115	+	0.108326i	$0.965451\pi$
$602$		0			0
$603$	4.27423	−	4.93273i	0.174060	−	0.200876i
$604$		0			0
$605$	3.14093	−	2.01855i	0.127697	−	0.0820657i
$606$		0			0
$607$	−7.30562	−	8.43113i	−0.296526	−	0.342209i	0.587863	−	0.808961i	$-0.299970\pi$
$607$	−7.30562	−	8.43113i	−0.296526	−	0.342209i	−0.884388	+	0.466752i	$0.845424\pi$
$608$		0			0
$609$	3.52381	−	24.5087i	0.142792	−	0.993141i
$610$		0			0
$611$	−24.1868	−	15.5439i	−0.978493	−	0.628839i
$612$		0			0
$613$	16.7511	+	36.6798i	0.676570	+	1.48148i	0.866237	+	0.499633i	$0.166532\pi$
$613$	16.7511	+	36.6798i	0.676570	+	1.48148i	−0.189667	+	0.981848i	$0.560741\pi$
$614$		0			0
$615$	−5.75416	−	1.68957i	−0.232030	−	0.0681302i
$616$		0			0
$617$	−17.4701	+	5.12968i	−0.703319	+	0.206513i	−0.613788	−	0.789471i	$-0.710355\pi$
$617$	−17.4701	+	5.12968i	−0.703319	+	0.206513i	−0.0895309	+	0.995984i	$0.528537\pi$
$618$		0			0
$619$	1.05208	+	7.31738i	0.0422867	+	0.294111i	0.999980	+	0.00631979i	$0.00201166\pi$
$619$	1.05208	+	7.31738i	0.0422867	+	0.294111i	−0.957693	+	0.287791i	$0.907079\pi$
$620$		0			0
$621$	4.65133	−	1.16839i	0.186651	−	0.0468859i
$622$		0			0
$623$	1.93626	+	13.4670i	0.0775748	+	0.539545i
$624$		0			0
$625$	18.5708	−	5.45287i	0.742831	−	0.218115i
$626$		0			0
$627$	−18.2712	−	5.36490i	−0.729680	−	0.214253i
$628$		0			0
$629$	7.91815	+	17.3383i	0.315717	+	0.691325i
$630$		0			0
$631$	−16.8961	−	10.8584i	−0.672622	−	0.432268i	0.159248	−	0.987239i	$-0.449093\pi$
$631$	−16.8961	−	10.8584i	−0.672622	−	0.432268i	−0.831870	+	0.554971i	$0.812729\pi$
$632$		0			0
$633$	0.0663046	−	0.461158i	0.00263537	−	0.0183294i
$634$		0			0
$635$	5.10043	+	5.88621i	0.202404	+	0.233587i
$636$		0			0
$637$	−68.1945	+	43.8259i	−2.70196	+	1.73645i
$638$		0			0
$639$	4.21449	−	4.86378i	0.166723	−	0.192408i
$640$		0			0
$641$	9.73401	−	21.3145i	0.384470	−	0.841873i	−0.614141	−	0.789196i	$-0.710497\pi$
$641$	9.73401	−	21.3145i	0.384470	−	0.841873i	0.998612	−	0.0526766i	$-0.0167753\pi$
$642$		0			0
$643$	−35.1576			−1.38648			−0.693240	−	0.720707i	$-0.743817\pi$
$643$	−35.1576			−1.38648			−0.693240	+	0.720707i	$0.743817\pi$
$644$		0			0
$645$	6.19607			0.243970
$646$		0			0
$647$	−17.3223	+	37.9305i	−0.681009	+	1.49120i	0.180561	+	0.983564i	$0.442209\pi$
$647$	−17.3223	+	37.9305i	−0.681009	+	1.49120i	−0.861570	+	0.507639i	$0.830519\pi$
$648$		0			0
$649$	12.8041	−	14.7767i	0.502604	−	0.580036i
$650$		0			0
$651$	−27.2615	+	17.5199i	−1.06846	+	0.686660i
$652$		0			0
$653$	−0.663117	−	0.765278i	−0.0259498	−	0.0299476i	0.742626	−	0.669706i	$-0.233580\pi$
$653$	−0.663117	−	0.765278i	−0.0259498	−	0.0299476i	−0.768576	+	0.639758i	$0.779034\pi$
$654$		0			0
$655$	−4.85846	+	33.7913i	−0.189836	+	1.32034i
$656$		0			0
$657$	9.48217	+	6.09382i	0.369935	+	0.237743i
$658$		0			0
$659$	−1.13211	−	2.47898i	−0.0441009	−	0.0965675i	0.886299	−	0.463113i	$-0.153268\pi$
$659$	−1.13211	−	2.47898i	−0.0441009	−	0.0965675i	−0.930400	+	0.366546i	$0.880540\pi$
$660$		0			0
$661$	−2.74545	−	0.806138i	−0.106786	−	0.0313551i	0.227903	−	0.973684i	$-0.426813\pi$
$661$	−2.74545	−	0.806138i	−0.106786	−	0.0313551i	−0.334689	+	0.942329i	$0.608631\pi$
$662$		0			0
$663$	−32.0951	+	9.42396i	−1.24647	+	0.365996i
$664$		0			0
$665$	9.02236	+	62.7519i	0.349872	+	2.43341i
$666$		0			0
$667$	−22.4962	−	7.58243i	−0.871055	−	0.293593i
$668$		0			0
$669$	−0.947401	−	6.58932i	−0.0366287	−	0.254758i
$670$		0			0
$671$	−16.8446	+	4.94603i	−0.650280	+	0.190940i
$672$		0			0
$673$	−13.4868	−	3.96008i	−0.519878	−	0.152650i	0.0112579	−	0.999937i	$-0.496416\pi$
$673$	−13.4868	−	3.96008i	−0.519878	−	0.152650i	−0.531136	+	0.847287i	$0.678235\pi$
$674$		0			0
$675$	−0.394206	−	0.863190i	−0.0151730	−	0.0332242i
$676$		0			0
$677$	−31.7494	−	20.4041i	−1.22023	−	0.784192i	−0.237886	−	0.971293i	$-0.576455\pi$
$677$	−31.7494	−	20.4041i	−1.22023	−	0.784192i	−0.982341	+	0.187101i	$0.940091\pi$
$678$		0			0
$679$	12.8505	−	89.3773i	0.493158	−	3.42999i
$680$		0			0
$681$	−8.85754	−	10.2221i	−0.339422	−	0.391713i
$682$		0			0
$683$	10.9190	−	7.01720i	0.417803	−	0.268506i	−0.314805	−	0.949156i	$-0.601939\pi$
$683$	10.9190	−	7.01720i	0.417803	−	0.268506i	0.732608	+	0.680650i	$0.238303\pi$
$684$		0			0
$685$	−21.1674	+	24.4285i	−0.808765	+	0.933365i
$686$		0			0
$687$	−2.70159	+	5.91565i	−0.103072	+	0.225696i
$688$		0			0
$689$	0.257535			0.00981129
$690$		0			0
$691$	26.4441			1.00598			0.502990	−	0.864292i	$-0.332233\pi$
$691$	26.4441			1.00598			0.502990	+	0.864292i	$0.332233\pi$
$692$		0			0
$693$	6.28386	−	13.7597i	0.238704	−	0.522689i
$694$		0			0
$695$	−14.7839	+	17.0615i	−0.560786	+	0.647181i
$696$		0			0
$697$	18.6396	−	11.9789i	0.706025	−	0.453735i
$698$		0			0
$699$	3.74628	+	4.32344i	0.141697	+	0.163528i
$700$		0			0
$701$	3.39522	−	23.6143i	0.128236	−	0.891900i	−0.819554	−	0.573003i	$-0.805778\pi$
$701$	3.39522	−	23.6143i	0.128236	−	0.891900i	0.947789	−	0.318897i	$-0.103312\pi$
$702$		0			0
$703$	−13.5784	−	8.72629i	−0.512118	−	0.329118i
$704$		0			0
$705$	−5.34411	−	11.7020i	−0.201271	−	0.440721i
$706$		0			0
$707$	−1.09132	−	0.320441i	−0.0410434	−	0.0120514i
$708$		0			0
$709$	−22.6780	+	6.65887i	−0.851691	+	0.250079i	−0.678310	−	0.734776i	$-0.737287\pi$
$709$	−22.6780	+	6.65887i	−0.851691	+	0.250079i	−0.173381	+	0.984855i	$0.555469\pi$
$710$		0			0
$711$	2.04452	+	14.2199i	0.0766754	+	0.533289i
$712$		0			0
$713$	11.7807	+	28.7494i	0.441192	+	1.07667i
$714$		0			0
$715$	−3.89644	−	27.1004i	−0.145719	−	1.01350i
$716$		0			0
$717$	5.03824	−	1.47936i	0.188156	−	0.0552477i
$718$		0			0
$719$	15.8085	+	4.64181i	0.589559	+	0.173110i	0.562887	−	0.826534i	$-0.309691\pi$
$719$	15.8085	+	4.64181i	0.589559	+	0.173110i	0.0266724	+	0.999644i	$0.491509\pi$
$720$		0			0
$721$	−2.09903	−	4.59623i	−0.0781718	−	0.171172i
$722$		0			0
$723$	−9.26890	−	5.95676i	−0.344714	−	0.221534i
$724$		0			0
$725$	−0.668499	+	4.64951i	−0.0248274	+	0.172679i
$726$		0			0
$727$	4.61182	+	5.32233i	0.171043	+	0.197394i	0.834799	−	0.550555i	$-0.185584\pi$
$727$	4.61182	+	5.32233i	0.171043	+	0.197394i	−0.663756	+	0.747949i	$0.731039\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	−14.9912	+	17.3007i	−0.554468	+	0.639890i
$732$		0			0
$733$	17.0349	−	37.3012i	0.629197	−	1.37775i	−0.279440	−	0.960163i	$-0.590149\pi$
$733$	17.0349	−	37.3012i	0.629197	−	1.37775i	0.908637	−	0.417586i	$-0.137124\pi$
$734$		0			0
$735$	−36.2714			−1.33789
$736$		0			0
$737$	−19.7379			−0.727055
$738$		0			0
$739$	12.4321	−	27.2226i	0.457323	−	1.00140i	−0.530766	−	0.847518i	$-0.678096\pi$
$739$	12.4321	−	27.2226i	0.457323	−	1.00140i	0.988090	−	0.153880i	$-0.0491769\pi$
$740$		0			0
$741$	18.5492	−	21.4069i	0.681421	−	0.786401i
$742$		0			0
$743$	2.12810	−	1.36765i	0.0780724	−	0.0501741i	−0.501022	−	0.865434i	$-0.667043\pi$
$743$	2.12810	−	1.36765i	0.0780724	−	0.0501741i	0.579095	+	0.815260i	$0.303406\pi$
$744$		0			0
$745$	−2.21701	−	2.55856i	−0.0812249	−	0.0937386i
$746$		0			0
$747$	1.95647	−	13.6076i	0.0715837	−	0.497875i
$748$		0			0
$749$	15.9612	+	10.2577i	0.583211	+	0.374807i
$750$		0			0
$751$	−16.9524	−	37.1206i	−0.618603	−	1.35455i	−0.916531	−	0.399963i	$-0.869023\pi$
$751$	−16.9524	−	37.1206i	−0.618603	−	1.35455i	0.297928	−	0.954588i	$-0.403704\pi$
$752$		0			0
$753$	−20.1464	−	5.91551i	−0.734174	−	0.215573i
$754$		0			0
$755$	47.1549	−	13.8459i	1.71614	−	0.503905i
$756$		0			0
$757$	−4.67714	−	32.5302i	−0.169994	−	1.18233i	−0.878892	−	0.477021i	$-0.841717\pi$
$757$	−4.67714	−	32.5302i	−0.169994	−	1.18233i	0.708898	−	0.705311i	$-0.249192\pi$
$758$		0			0
$759$	−11.8815	−	8.31651i	−0.431272	−	0.301870i
$760$		0			0
$761$	7.14381	+	49.6863i	0.258963	+	1.80113i	0.540251	+	0.841504i	$0.318329\pi$
$761$	7.14381	+	49.6863i	0.258963	+	1.80113i	−0.281289	+	0.959623i	$0.590762\pi$
$762$		0			0
$763$	31.1369	−	9.14263i	1.12723	−	0.330985i
$764$		0			0
$765$	−14.3608	−	4.21672i	−0.519217	−	0.152456i
$766$		0			0
$767$	12.0818	+	26.4555i	0.436249	+	0.955253i
$768$		0			0
$769$	−20.2578	−	13.0189i	−0.730515	−	0.469473i	0.121765	−	0.992559i	$-0.461144\pi$
$769$	−20.2578	−	13.0189i	−0.730515	−	0.469473i	−0.852280	+	0.523086i	$0.824781\pi$
$770$		0			0
$771$	0.634175	−	4.41079i	0.0228393	−	0.158851i
$772$		0			0
$773$	−10.0732	−	11.6251i	−0.362308	−	0.418126i	0.545103	−	0.838369i	$-0.316490\pi$
$773$	−10.0732	−	11.6251i	−0.362308	−	0.418126i	−0.907412	+	0.420243i	$0.861945\pi$
$774$		0			0
$775$	5.17175	−	3.32368i	0.185775	−	0.119390i
$776$		0			0
$777$	8.39632	−	9.68987i	0.301216	−	0.347622i
$778$		0			0
$779$	−7.79419	+	17.0669i	−0.279256	+	0.611485i
$780$		0			0
$781$	−19.4620			−0.696405
$782$		0			0
$783$	−4.95006			−0.176901
$784$		0			0
$785$	−5.17535	+	11.3324i	−0.184716	+	0.404472i
$786$		0			0
$787$	17.1317	−	19.7711i	0.610681	−	0.704763i	−0.363229	−	0.931700i	$-0.618326\pi$
$787$	17.1317	−	19.7711i	0.610681	−	0.704763i	0.973910	+	0.226937i	$0.0728711\pi$
$788$		0			0
$789$	−6.13742	+	3.94428i	−0.218498	+	0.140420i
$790$		0			0
$791$	58.0500	+	66.9933i	2.06402	+	2.38201i
$792$		0			0
$793$	3.71639	−	25.8481i	0.131973	−	0.917891i
$794$		0			0
$795$	0.0969403	+	0.0622998i	0.00343812	+	0.00220954i
$796$		0			0
$797$	7.01639	+	15.3638i	0.248533	+	0.544212i	0.992246	−	0.124287i	$-0.0396643\pi$
$797$	7.01639	+	15.3638i	0.248533	+	0.544212i	−0.743713	+	0.668499i	$0.766937\pi$
$798$		0			0
$799$	45.6042	+	13.3906i	1.61336	+	0.473725i
$800$		0			0
$801$	2.60978	−	0.766300i	0.0922120	−	0.0270759i
$802$		0			0
$803$	−4.85090	−	33.7388i	−0.171185	−	1.19062i
$804$		0			0
$805$	−8.75325	+	47.4837i	−0.308512	+	1.67358i
$806$		0			0
$807$	−0.372314	−	2.58950i	−0.0131061	−	0.0911548i
$808$		0			0
$809$	39.7755	−	11.6791i	1.39843	−	0.410616i	0.506286	−	0.862366i	$-0.331018\pi$
$809$	39.7755	−	11.6791i	1.39843	−	0.410616i	0.892145	+	0.451749i	$0.149200\pi$
$810$		0			0
$811$	40.0589	+	11.7624i	1.40666	+	0.413032i	0.894965	−	0.446136i	$-0.147200\pi$
$811$	40.0589	+	11.7624i	1.40666	+	0.413032i	0.511693	+	0.859168i	$0.329018\pi$
$812$		0			0
$813$	−2.67076	−	5.84815i	−0.0936677	−	0.205104i
$814$		0			0
$815$	−17.0258	−	10.9418i	−0.596388	−	0.383275i
$816$		0			0
$817$	2.75877	−	19.1877i	0.0965172	−	0.671292i
$818$		0			0
$819$	14.7348	+	17.0049i	0.514875	+	0.594198i
$820$		0			0
$821$	42.6886	−	27.4343i	1.48984	−	0.957463i	0.493706	−	0.869629i	$-0.335642\pi$
$821$	42.6886	−	27.4343i	1.48984	−	0.957463i	0.996135	−	0.0878335i	$-0.0279943\pi$
$822$		0			0
$823$	−10.8933	+	12.5716i	−0.379718	+	0.438217i	−0.913149	−	0.407626i	$-0.866357\pi$
$823$	−10.8933	+	12.5716i	−0.379718	+	0.438217i	0.533431	+	0.845843i	$0.320902\pi$
$824$		0			0
$825$	−1.19210	+	2.61034i	−0.0415037	+	0.0908805i
$826$		0			0
$827$	−0.983710			−0.0342069			−0.0171035	−	0.999854i	$-0.505444\pi$
$827$	−0.983710			−0.0342069			−0.0171035	+	0.999854i	$0.505444\pi$
$828$		0			0
$829$	−22.7205			−0.789115			−0.394557	−	0.918871i	$-0.629102\pi$
$829$	−22.7205			−0.789115			−0.394557	+	0.918871i	$0.629102\pi$
$830$		0			0
$831$	−3.52487	+	7.71839i	−0.122276	+	0.267748i
$832$		0			0
$833$	87.7572	−	101.277i	3.04061	−	3.50905i
$834$		0			0
$835$	−16.1256	+	10.3633i	−0.558048	+	0.358636i
$836$		0			0
$837$	4.24248	+	4.89608i	0.146641	+	0.169233i
$838$		0			0
$839$	6.88818	−	47.9083i	0.237806	−	1.65398i	−0.425004	−	0.905191i	$-0.639727\pi$
$839$	6.88818	−	47.9083i	0.237806	−	1.65398i	0.662810	−	0.748787i	$-0.269364\pi$
$840$		0			0
$841$	−3.78306	−	2.43122i	−0.130450	−	0.0838353i
$842$		0			0
$843$	6.10078	+	13.3588i	0.210122	+	0.460103i
$844$		0			0
$845$	13.9705	+	4.10212i	0.480601	+	0.141117i
$846$		0			0
$847$	8.90310	−	2.61419i	0.305914	−	0.0898245i
$848$		0			0
$849$	−3.02273	−	21.0236i	−0.103740	−	0.721527i
$850$		0			0
$851$	−7.67697	−	9.60091i	−0.263163	−	0.329115i
$852$		0			0
$853$	−1.08277	−	7.53080i	−0.0370732	−	0.257850i	0.962853	−	0.270027i	$-0.0870327\pi$
$853$	−1.08277	−	7.53080i	−0.0370732	−	0.257850i	−0.999926	+	0.0121776i	$0.996124\pi$
$854$		0			0
$855$	12.1607	−	3.57071i	0.415888	−	0.122116i
$856$		0			0
$857$	−17.9079	−	5.25823i	−0.611721	−	0.179618i	−0.0388259	−	0.999246i	$-0.512362\pi$
$857$	−17.9079	−	5.25823i	−0.611721	−	0.179618i	−0.572896	+	0.819628i	$0.694180\pi$
$858$		0			0
$859$	−8.09886	−	17.7340i	−0.276329	−	0.605077i	0.719682	−	0.694304i	$-0.244288\pi$
$859$	−8.09886	−	17.7340i	−0.276329	−	0.605077i	−0.996011	+	0.0892268i	$0.971560\pi$
$860$		0			0
$861$	−12.5382	−	8.05781i	−0.427301	−	0.274610i
$862$		0			0
$863$	1.91221	−	13.2997i	0.0650923	−	0.452727i	−0.931044	−	0.364907i	$-0.881101\pi$
$863$	1.91221	−	13.2997i	0.0650923	−	0.452727i	0.996136	−	0.0878200i	$-0.0279900\pi$
$864$		0			0
$865$	−11.9230	−	13.7599i	−0.405396	−	0.467852i
$866$		0			0
$867$	32.2182	−	20.7054i	1.09419	−	0.703191i
$868$		0			0
$869$	28.4499	−	32.8330i	0.965098	−	1.11378i
$870$		0			0
$871$	12.1965	−	26.7065i	0.413261	−	0.904916i
$872$		0			0
$873$	−18.0517			−0.610957
$874$		0			0
$875$	59.8931			2.02476
$876$		0			0
$877$	12.0217	−	26.3238i	0.405944	−	0.888893i	−0.590689	−	0.806899i	$-0.701144\pi$
$877$	12.0217	−	26.3238i	0.405944	−	0.888893i	0.996633	−	0.0819935i	$-0.0261287\pi$
$878$		0			0
$879$	−3.21834	+	3.71416i	−0.108552	+	0.125276i
$880$		0			0
$881$	−45.2407	+	29.0744i	−1.52420	+	0.979542i	−0.533151	+	0.846020i	$0.678992\pi$
$881$	−45.2407	+	29.0744i	−1.52420	+	0.979542i	−0.991046	+	0.133522i	$0.957371\pi$
$882$		0			0
$883$	−20.1952	−	23.3065i	−0.679623	−	0.784326i	0.306227	−	0.951959i	$-0.400933\pi$
$883$	−20.1952	−	23.3065i	−0.679623	−	0.784326i	−0.985850	+	0.167632i	$0.946388\pi$
$884$		0			0
$885$	−1.85200	+	12.8810i	−0.0622545	+	0.432989i
$886$		0			0
$887$	−8.62325	−	5.54183i	−0.289540	−	0.186076i	0.387805	−	0.921741i	$-0.373233\pi$
$887$	−8.62325	−	5.54183i	−0.289540	−	0.186076i	−0.677345	+	0.735665i	$0.736870\pi$
$888$		0			0
$889$	8.04097	+	17.6073i	0.269686	+	0.590529i
$890$		0			0
$891$	−2.90157	−	0.851978i	−0.0972063	−	0.0285424i
$892$		0			0
$893$	−38.6175	+	11.3391i	−1.29228	+	0.379449i
$894$		0			0
$895$	1.22021	+	8.48672i	0.0407870	+	0.283680i
$896$		0			0
$897$	18.5946	−	10.9374i	0.620854	−	0.365190i
$898$		0			0
$899$	−4.56385	−	31.7422i	−0.152213	−	1.05866i
$900$		0			0
$901$	−0.408497	+	0.119946i	−0.0136090	+	0.00399597i
$902$		0			0
$903$	14.7750	+	4.33832i	0.491680	+	0.144370i
$904$		0			0
$905$	−12.2608	−	26.8475i	−0.407564	−	0.892441i
$906$		0			0
$907$	−4.36116	−	2.80275i	−0.144810	−	0.0930637i	0.466230	−	0.884664i	$-0.345612\pi$
$907$	−4.36116	−	2.80275i	−0.144810	−	0.0930637i	−0.611040	+	0.791600i	$0.709248\pi$
$908$		0			0
$909$	−0.0323600	+	0.225069i	−0.00107331	+	0.00746506i
$910$		0			0
$911$	−19.0442	−	21.9782i	−0.630964	−	0.728171i	0.346786	−	0.937944i	$-0.387273\pi$
$911$	−19.0442	−	21.9782i	−0.630964	−	0.728171i	−0.977750	+	0.209773i	$0.932728\pi$
$912$		0			0
$913$	−34.9738	+	22.4763i	−1.15746	+	0.743856i
$914$		0			0
$915$	7.65176	−	8.83061i	0.252960	−	0.291931i
$916$		0			0
$917$	−35.2451	+	77.1761i	−1.16390	+	2.54858i
$918$		0			0
$919$	−15.7778			−0.520463			−0.260231	−	0.965546i	$-0.583799\pi$
$919$	−15.7778			−0.520463			−0.260231	+	0.965546i	$0.583799\pi$
$920$		0			0
$921$	−14.5747			−0.480254
$922$		0			0
$923$	12.0260	−	26.3332i	0.395840	−	0.866769i
$924$		0			0
$925$	−1.59286	+	1.83826i	−0.0523728	+	0.0604415i
$926$		0			0
$927$	−0.849787	+	0.546125i	−0.0279107	+	0.0179371i
$928$		0			0
$929$	17.4268	+	20.1116i	0.571756	+	0.659841i	0.965812	−	0.259245i	$-0.0834737\pi$
$929$	17.4268	+	20.1116i	0.571756	+	0.659841i	−0.394056	+	0.919087i	$0.628928\pi$
$930$		0			0
$931$	−16.1496	+	112.323i	−0.529283	+	3.68125i
$932$		0			0
$933$	−2.62503	−	1.68700i	−0.0859396	−	0.0552300i
$934$		0			0
$935$	18.8023	+	41.1714i	0.614902	+	1.34645i
$936$		0			0
$937$	21.7415	+	6.38387i	0.710263	+	0.208552i	0.616856	−	0.787076i	$-0.288406\pi$
$937$	21.7415	+	6.38387i	0.710263	+	0.208552i	0.0934069	+	0.995628i	$0.470224\pi$
$938$		0			0
$939$	11.0785	−	3.25295i	0.361534	−	0.106156i
$940$		0			0
$941$	−8.00943	−	55.7068i	−0.261100	−	1.81599i	−0.524620	−	0.851336i	$-0.675793\pi$
$941$	−8.00943	−	55.7068i	−0.261100	−	1.81599i	0.263520	−	0.964654i	$-0.415116\pi$
$942$		0			0
$943$	−9.77682	+	10.4214i	−0.318377	+	0.339369i
$944$		0			0
$945$	1.43280	+	9.96537i	0.0466091	+	0.324174i
$946$		0			0
$947$	7.24610	−	2.12765i	0.235467	−	0.0691392i	−0.161870	−	0.986812i	$-0.551753\pi$
$947$	7.24610	−	2.12765i	0.235467	−	0.0691392i	0.397337	+	0.917673i	$0.369934\pi$
$948$		0			0
$949$	48.6480	+	14.2843i	1.57918	+	0.463690i
$950$		0			0
$951$	3.62494	+	7.93752i	0.117547	+	0.257392i
$952$		0			0
$953$	−45.4436	−	29.2048i	−1.47206	−	0.946036i	−0.997844	−	0.0656284i	$-0.979095\pi$
$953$	−45.4436	−	29.2048i	−1.47206	−	0.946036i	−0.474217	−	0.880408i	$-0.657269\pi$
$954$		0			0
$955$	−1.33466	+	9.28275i	−0.0431885	+	0.300383i
$956$		0			0
$957$	9.80281	+	11.3131i	0.316880	+	0.365699i
$958$		0			0
$959$	−67.5794	+	43.4306i	−2.18225	+	1.40245i
$960$		0			0
$961$	−7.18395	+	8.29072i	−0.231740	+	0.267443i
$962$		0			0
$963$	1.57568	−	3.45027i	0.0507757	−	0.111183i
$964$		0			0
$965$	−3.82096			−0.123001
$966$		0			0
$967$	36.5036			1.17388			0.586938	−	0.809632i	$-0.300333\pi$
$967$	36.5036			1.17388			0.586938	+	0.809632i	$0.300333\pi$
$968$		0			0
$969$	−19.4522	+	42.5944i	−0.624895	+	1.36833i
$970$		0			0
$971$	−16.1895	+	18.6836i	−0.519544	+	0.599586i	−0.953517	−	0.301340i	$-0.902566\pi$
$971$	−16.1895	+	18.6836i	−0.519544	+	0.599586i	0.433972	+	0.900926i	$0.357112\pi$
$972$		0			0
$973$	−47.1993	+	30.3332i	−1.51314	+	0.972437i
$974$		0			0
$975$	−2.79532	−	3.22597i	−0.0895220	−	0.103314i
$976$		0			0
$977$	−8.45499	+	58.8057i	−0.270499	+	1.88136i	0.172752	+	0.984965i	$0.444734\pi$
$977$	−8.45499	+	58.8057i	−0.270499	+	1.88136i	−0.443251	+	0.896397i	$0.646175\pi$
$978$		0			0
$979$	−6.91959	−	4.44695i	−0.221151	−	0.142125i
$980$		0			0
$981$	−2.69503	−	5.90129i	−0.0860457	−	0.188414i
$982$		0			0
$983$	−16.0446	−	4.71113i	−0.511744	−	0.150262i	0.0156581	−	0.999877i	$-0.495016\pi$
$983$	−16.0446	−	4.71113i	−0.511744	−	0.150262i	−0.527402	+	0.849616i	$0.676834\pi$
$984$		0			0
$985$	16.4796	−	4.83885i	0.525084	−	0.154179i
$986$		0			0
$987$	−4.55000	−	31.6460i	−0.144828	−	1.00730i
$988$		0			0
$989$	6.65857	−	13.1769i	0.211730	−	0.419002i
$990$		0			0
$991$	−0.152124	−	1.05804i	−0.00483237	−	0.0336099i	0.987263	−	0.159099i	$-0.0508590\pi$
$991$	−0.152124	−	1.05804i	−0.00483237	−	0.0336099i	−0.992095	+	0.125489i	$0.959950\pi$
$992$		0			0
$993$	−14.1770	+	4.16273i	−0.449892	+	0.132100i
$994$		0			0
$995$	37.6298	+	11.0491i	1.19294	+	0.350280i
$996$		0			0
$997$	4.72144	+	10.3385i	0.149530	+	0.327424i	0.969543	−	0.244920i	$-0.0787616\pi$
$997$	4.72144	+	10.3385i	0.149530	+	0.327424i	−0.820014	+	0.572344i	$0.806034\pi$
$998$		0			0
$999$	−2.15633	−	1.38579i	−0.0682231	−	0.0438444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.49.2	✓	30
23.8	even	11	inner	552.2.q.b.169.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.49.2	✓	30	1.1	even	1	trivial
552.2.q.b.169.2	yes	30	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(1.31805 - 1.52111i) q^{5} +(4.20804 - 2.70434i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(1.31805 - 1.52111i) q^{5} +(4.20804 - 2.70434i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-0.430370 + 2.99329i) q^{11} +(-3.78416 - 2.43193i) q^{13} +(-0.836116 - 1.83084i) q^{15} +(7.13503 + 2.09503i) q^{17} +(-6.04192 + 1.77407i) q^{19} +(-0.711873 - 4.95119i) q^{21} +(-4.79209 - 0.189368i) q^{23} +(0.135049 + 0.939285i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(4.74955 + 1.39459i) q^{29} +(-2.69124 - 5.89300i) q^{31} +(2.54401 + 1.63493i) q^{33} +(1.43280 - 9.96537i) q^{35} +(1.67856 + 1.93716i) q^{37} +(-3.78416 + 2.43193i) q^{39} +(1.95121 - 2.25182i) q^{41} +(-1.27884 + 2.80026i) q^{43} -2.01272 q^{45} +6.39159 q^{47} +(7.48621 - 16.3925i) q^{49} +(4.86971 - 5.61994i) q^{51} +(-0.0481637 + 0.0309530i) q^{53} +(3.98588 + 4.59996i) q^{55} +(-0.896155 + 6.23290i) q^{57} +(-5.43920 - 3.49556i) q^{59} +(2.41163 + 5.28073i) q^{61} +(-4.79948 - 1.40926i) q^{63} +(-8.68697 + 2.55072i) q^{65} +(0.928880 + 6.46050i) q^{67} +(-2.16296 + 4.28037i) q^{69} +(0.915896 + 6.37019i) q^{71} +(-10.8149 + 3.17554i) q^{73} +(0.910505 + 0.267348i) q^{75} +(6.28386 + 13.7597i) q^{77} +(-12.0856 - 7.76693i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(9.00270 + 10.3897i) q^{83} +(12.5911 - 8.09183i) q^{85} +(3.24160 - 3.74100i) q^{87} +(-1.12991 + 2.47416i) q^{89} -22.5007 q^{91} -6.47844 q^{93} +(-5.26501 + 11.5288i) q^{95} +(11.8213 - 13.6426i) q^{97} +(2.54401 - 1.63493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more