LMFDB - Embedded newform 552.2.q.b.169.2

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			169.2
Character	$\chi$	$=$	552.169
Dual form			552.2.q.b.49.2

$q$-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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

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	0.969609	−	0.244658i	$-0.0786758\pi$
$5$	1.31805	+	1.52111i	0.589452	+	0.680263i	−0.380158	+	0.924922i	$0.624130\pi$
$6$		0			0
$7$	4.20804	+	2.70434i	1.59049	+	1.02214i	0.971589	+	0.236675i	$0.0760575\pi$
$7$	4.20804	+	2.70434i	1.59049	+	1.02214i	0.618899	+	0.785470i	$0.287579\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.430370	−	2.99329i	−0.129761	−	0.902510i	−0.945855	−	0.324590i	$-0.894774\pi$
$11$	−0.430370	−	2.99329i	−0.129761	−	0.902510i	0.816093	−	0.577920i	$-0.196135\pi$
$12$		0			0
$13$	−3.78416	+	2.43193i	−1.04954	+	0.674496i	−0.947327	−	0.320267i	$-0.896228\pi$
$13$	−3.78416	+	2.43193i	−1.04954	+	0.674496i	−0.102209	+	0.994763i	$0.532591\pi$
$14$		0			0
$15$	−0.836116	+	1.83084i	−0.215884	+	0.472720i
$16$		0			0
$17$	7.13503	−	2.09503i	1.73050	−	0.508120i	0.743485	−	0.668753i	$-0.233172\pi$
$17$	7.13503	−	2.09503i	1.73050	−	0.508120i	0.987014	+	0.160633i	$0.0513534\pi$
$18$		0			0
$19$	−6.04192	−	1.77407i	−1.38611	−	0.406999i	−0.498219	−	0.867051i	$-0.666013\pi$
$19$	−6.04192	−	1.77407i	−1.38611	−	0.406999i	−0.887892	+	0.460052i	$0.847831\pi$
$20$		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	0.190770	−	0.981635i	$-0.438901\pi$
$29$	4.74955	−	1.39459i	0.881968	−	0.258969i	0.691198	+	0.722665i	$0.257083\pi$
$30$		0			0
$31$	−2.69124	+	5.89300i	−0.483361	+	1.05841i	0.498164	+	0.867083i	$0.334008\pi$
$31$	−2.69124	+	5.89300i	−0.483361	+	1.05841i	−0.981526	+	0.191331i	$0.938720\pi$
$32$		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	−0.600808	−	0.799394i	$-0.705154\pi$
$37$	1.67856	−	1.93716i	0.275953	−	0.318467i	0.876761	+	0.480927i	$0.159700\pi$
$38$		0			0
$39$	−3.78416	−	2.43193i	−0.605950	−	0.389421i
$40$		0			0
$41$	1.95121	+	2.25182i	0.304728	+	0.351675i	0.887373	−	0.461051i	$-0.152528\pi$
$41$	1.95121	+	2.25182i	0.304728	+	0.351675i	−0.582645	+	0.812727i	$0.697982\pi$
$42$		0			0
$43$	−1.27884	−	2.80026i	−0.195021	−	0.427035i	0.786707	−	0.617326i	$-0.211784\pi$
$43$	−1.27884	−	2.80026i	−0.195021	−	0.427035i	−0.981728	+	0.190291i	$0.939057\pi$
$44$		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	0.537329	−	0.843373i	$-0.319433\pi$
$53$	−0.0481637	−	0.0309530i	−0.00661580	−	0.00425172i	−0.543945	+	0.839121i	$0.683070\pi$
$54$		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	−0.844487	−	0.535576i	$-0.820095\pi$
$59$	−5.43920	+	3.49556i	−0.708123	+	0.455083i	0.136364	+	0.990659i	$0.456458\pi$
$60$		0			0
$61$	2.41163	−	5.28073i	0.308778	−	0.676129i	−0.690089	−	0.723724i	$-0.742429\pi$
$61$	2.41163	−	5.28073i	0.308778	−	0.676129i	0.998867	+	0.0475958i	$0.0151559\pi$
$62$		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	−0.851008	−	0.525152i	$-0.824008\pi$
$67$	0.928880	−	6.46050i	0.113481	−	0.789276i	0.964489	−	0.264123i	$-0.0850826\pi$
$68$		0			0
$69$	−2.16296	−	4.28037i	−0.260390	−	0.515296i
$70$		0			0
$71$	0.915896	−	6.37019i	0.108697	−	0.756003i	−0.860453	−	0.509530i	$-0.829819\pi$
$71$	0.915896	−	6.37019i	0.108697	−	0.756003i	0.969150	−	0.246473i	$-0.0792716\pi$
$72$		0			0
$73$	−10.8149	−	3.17554i	−1.26579	−	0.371669i	−0.421143	−	0.906994i	$-0.638371\pi$
$73$	−10.8149	−	3.17554i	−1.26579	−	0.371669i	−0.844646	+	0.535325i	$0.820189\pi$
$74$		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	−0.998285	−	0.0585433i	$-0.981354\pi$
$79$	−12.0856	+	7.76693i	−1.35973	+	0.873848i	−0.361450	+	0.932392i	$0.617718\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	9.00270	−	10.3897i	0.988175	−	1.14041i	−0.00191727	−	0.999998i	$-0.500610\pi$
$83$	9.00270	−	10.3897i	0.988175	−	1.14041i	0.990092	−	0.140417i	$-0.0448443\pi$
$84$		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	0.840246	−	0.542206i	$-0.182411\pi$
$89$	−1.12991	−	2.47416i	−0.119770	−	0.262260i	−0.960016	+	0.279946i	$0.909684\pi$
$90$		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	0.902575	+	0.430532i	$0.141674\pi$
$97$	11.8213	+	13.6426i	1.20028	+	1.38519i	0.297700	+	0.954660i	$0.403781\pi$
$98$		0			0
$99$	2.54401	+	1.63493i	0.255682	+	0.164317i
$100$		0			0
$101$	−0.148904	+	0.171845i	−0.0148165	+	0.0170992i	−0.763109	−	0.646269i	$-0.776328\pi$
$101$	−0.148904	+	0.171845i	−0.0148165	+	0.0170992i	0.748293	+	0.663368i	$0.230874\pi$
$102$		0			0
$103$	0.143758	+	0.999862i	0.0141649	+	0.0985193i	0.995677	−	0.0928788i	$-0.0296069\pi$
$103$	0.143758	+	0.999862i	0.0141649	+	0.0985193i	−0.981512	+	0.191398i	$0.938698\pi$
$104$		0			0
$105$	−8.46961	+	5.44309i	−0.826550	+	0.531191i
$106$		0			0
$107$	1.57568	−	3.45027i	0.152327	−	0.333550i	−0.818049	−	0.575148i	$-0.804944\pi$
$107$	1.57568	−	3.45027i	0.152327	−	0.333550i	0.970376	+	0.241598i	$0.0776716\pi$
$108$		0			0
$109$	6.22477	−	1.82776i	0.596225	−	0.175067i	0.0303230	−	0.999540i	$-0.490346\pi$
$109$	6.22477	−	1.82776i	0.596225	−	0.175067i	0.565902	+	0.824473i	$0.308528\pi$
$110$		0			0
$111$	2.45940	+	0.722145i	0.233436	+	0.0685430i
$112$		0			0
$113$	2.52203	−	17.5411i	0.237253	−	1.65013i	−0.428195	−	0.903687i	$-0.640850\pi$
$113$	2.52203	−	17.5411i	0.237253	−	1.65013i	0.665448	−	0.746445i	$-0.268241\pi$
$114$		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	−0.999558	−	0.0297396i	$-0.990532\pi$
$127$	−0.550711	−	3.83028i	−0.0488677	−	0.339882i	0.950690	−	0.310143i	$-0.100377\pi$
$128$		0			0
$129$	2.01596	−	2.32654i	0.177495	−	0.204840i
$130$		0			0
$131$	−14.2689	−	9.17008i	−1.24668	−	0.801193i	−0.260278	−	0.965534i	$-0.583814\pi$
$131$	−14.2689	−	9.17008i	−1.24668	−	0.801193i	−0.986404	+	0.164340i	$0.947450\pi$
$132$		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	0.997275	−	0.0737792i	$-0.0235060\pi$
$149$	0.239378	+	1.66491i	0.0196106	+	0.136395i	−0.977664	+	0.210174i	$0.932597\pi$
$150$		0			0
$151$	20.5413	−	13.2011i	1.67163	−	1.07429i	0.774424	−	0.632667i	$-0.218040\pi$
$151$	20.5413	−	13.2011i	1.67163	−	1.07429i	0.897201	−	0.441622i	$-0.145597\pi$
$152$		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	0.0360105	−	0.999351i	$-0.488535\pi$
$157$	−5.93902	−	1.74385i	−0.473986	−	0.139175i	−0.509996	+	0.860177i	$0.670353\pi$
$158$		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	0.853798	+	0.520604i	$0.174293\pi$
$163$	−1.43102	+	9.95299i	−0.112086	+	0.779578i	−0.965884	+	0.258974i	$0.916616\pi$
$164$		0			0
$165$	5.84006	+	1.71480i	0.454648	+	0.133497i
$166$		0			0
$167$	−9.13788	+	2.68312i	−0.707110	+	0.207626i	−0.615464	−	0.788165i	$-0.711031\pi$
$167$	−9.13788	+	2.68312i	−0.707110	+	0.207626i	−0.0916467	+	0.995792i	$0.529213\pi$
$168$		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	0.978396	+	0.206739i	$0.0662852\pi$
$173$	1.28737	+	8.95387i	0.0978771	+	0.680750i	−0.880519	+	0.474011i	$0.842806\pi$
$174$		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	0.641857	−	0.766824i	$-0.278164\pi$
$179$	−2.78964	−	3.21941i	−0.208507	−	0.240630i	−0.850365	+	0.526194i	$0.823619\pi$
$180$		0			0
$181$	6.09167	+	13.3389i	0.452790	+	0.991472i	0.989072	+	0.147433i	$0.0471012\pi$
$181$	6.09167	+	13.3389i	0.452790	+	0.991472i	−0.536282	+	0.844039i	$0.680172\pi$
$182$		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	0.391091	−	0.920352i	$-0.372098\pi$
$191$	−3.91979	−	2.51909i	−0.283626	−	0.182275i	−0.674717	+	0.738077i	$0.735734\pi$
$192$		0			0
$193$	−1.24319	+	1.43472i	−0.0894866	+	0.103273i	−0.798727	−	0.601694i	$-0.794493\pi$
$193$	−1.24319	+	1.43472i	−0.0894866	+	0.103273i	0.709240	+	0.704967i	$0.249038\pi$
$194$		0			0
$195$	−1.28848	−	8.96156i	−0.0922698	−	0.641750i
$196$		0			0
$197$	7.17874	−	4.61349i	0.511464	−	0.328698i	−0.259323	−	0.965791i	$-0.583500\pi$
$197$	7.17874	−	4.61349i	0.511464	−	0.328698i	0.770787	+	0.637093i	$0.219863\pi$
$198$		0			0
$199$	8.09447	−	17.7244i	0.573801	−	1.25645i	−0.370947	−	0.928654i	$-0.620967\pi$
$199$	8.09447	−	17.7244i	0.573801	−	1.25645i	0.944749	−	0.327796i	$-0.106306\pi$
$200$		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	0.297084	−	0.954851i	$-0.403986\pi$
$211$	0.447028	+	0.131259i	0.0307747	+	0.00903627i	−0.266309	+	0.963888i	$0.585804\pi$
$212$		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	0.714551	−	0.699583i	$-0.246631\pi$
$223$	5.60029	+	3.59909i	0.375023	+	0.241013i	−0.339528	+	0.940596i	$0.610267\pi$
$224$		0			0
$225$	0.621426	+	0.717164i	0.0414284	+	0.0478109i
$226$		0			0
$227$	5.61884	+	12.3035i	0.372935	+	0.816614i	0.999312	+	0.0370936i	$0.0118100\pi$
$227$	5.61884	+	12.3035i	0.372935	+	0.816614i	−0.626377	+	0.779521i	$0.715463\pi$
$228$		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	0.815674	−	0.578511i	$-0.196366\pi$
$233$	−2.37648	−	5.20376i	−0.155688	−	0.340910i	−0.971363	+	0.237601i	$0.923639\pi$
$234$		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	−0.633558	−	0.773695i	$-0.718406\pi$
$239$	3.43863	−	3.96839i	0.222427	−	0.256694i	0.855985	+	0.517001i	$0.172952\pi$
$240$		0			0
$241$	1.56802	+	10.9058i	0.101005	+	0.702506i	0.975904	+	0.218200i	$0.0700186\pi$
$241$	1.56802	+	10.9058i	0.101005	+	0.702506i	−0.874899	+	0.484306i	$0.839072\pi$
$242$		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	0.646995	+	0.762494i	$0.276025\pi$
$251$	−2.98817	+	20.7832i	−0.188612	+	1.31182i	−0.835607	+	0.549328i	$0.814884\pi$
$252$		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	0.412352	−	0.911025i	$-0.364707\pi$
$257$	4.27564	+	1.25544i	0.266707	+	0.0783122i	−0.145645	+	0.989337i	$0.546526\pi$
$258$		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	−0.716011	−	0.698089i	$-0.754034\pi$
$263$	−6.13742	+	3.94428i	−0.378450	+	0.243215i	0.337562	+	0.941303i	$0.390398\pi$
$264$		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	0.606012	−	0.795455i	$-0.292768\pi$
$269$	2.20083	+	1.41439i	0.134187	+	0.0862367i	−0.471825	+	0.881692i	$0.656405\pi$
$270$		0			0
$271$	4.21019	+	4.85882i	0.255751	+	0.295152i	0.869076	−	0.494678i	$-0.164714\pi$
$271$	4.21019	+	4.85882i	0.255751	+	0.295152i	−0.613325	+	0.789830i	$0.710169\pi$
$272$		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	0.392524	−	0.919742i	$-0.371602\pi$
$281$	−9.61727	−	11.0989i	−0.573718	−	0.662106i	−0.966242	+	0.257636i	$0.917057\pi$
$282$		0			0
$283$	17.8680	+	11.4831i	1.06214	+	0.682598i	0.950366	−	0.311135i	$-0.100709\pi$
$283$	17.8680	+	11.4831i	1.06214	+	0.682598i	0.111778	+	0.993733i	$0.464345\pi$
$284$		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	−0.416555	−	0.909111i	$-0.636763\pi$
$293$	−4.71547	+	1.38459i	−0.275481	+	0.0808884i	0.141074	+	0.989999i	$0.454944\pi$
$294$		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	0.654447	+	0.756108i	$0.272901\pi$
$307$	−6.05457	+	13.2577i	−0.345553	+	0.756655i	−1.00000		0.000546917i	$0.999826\pi$
$308$		0			0
$309$	−0.849787	+	0.546125i	−0.0483427	+	0.0310680i
$310$		0			0
$311$	0.444076	+	3.08862i	0.0251812	+	0.175139i	0.998531	−	0.0541871i	$-0.0172567\pi$
$311$	0.444076	+	3.08862i	0.0251812	+	0.175139i	−0.973350	+	0.229326i	$0.926348\pi$
$312$		0			0
$313$	7.56117	−	8.72606i	0.427383	−	0.493226i	−0.500689	−	0.865627i	$-0.666920\pi$
$313$	7.56117	−	8.72606i	0.427383	−	0.493226i	0.928072	+	0.372401i	$0.121465\pi$
$314$		0			0
$315$	−8.46961	−	5.44309i	−0.477209	−	0.306683i
$316$		0			0
$317$	−5.71437	−	6.59473i	−0.320951	−	0.370397i	0.572231	−	0.820092i	$-0.306078\pi$
$317$	−5.71437	−	6.59473i	−0.320951	−	0.370397i	−0.893182	+	0.449695i	$0.851533\pi$
$318$		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	−0.956554	−	0.291556i	$-0.905827\pi$
$331$	−9.67587	+	11.1666i	−0.531834	+	0.613769i	0.424720	+	0.905325i	$0.360373\pi$
$332$		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	0.337249	+	0.941416i	$0.390504\pi$
$337$	−10.9242	+	23.9206i	−0.595077	+	1.30304i	−0.932325	+	0.361620i	$0.882224\pi$
$338$		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	−0.988248	−	0.152860i	$-0.951152\pi$
$347$	0.0565300	−	0.393175i	0.00303469	−	0.0211067i	0.991283	+	0.131753i	$0.0420607\pi$
$348$		0			0
$349$	−22.4624	−	6.59556i	−1.20239	−	0.353052i	−0.381621	−	0.924319i	$-0.624634\pi$
$349$	−22.4624	−	6.59556i	−1.20239	−	0.353052i	−0.820765	+	0.571266i	$0.806452\pi$
$350$		0			0
$351$	4.31603	−	1.26730i	0.230373	−	0.0676435i
$352$		0			0
$353$	10.3078	−	22.5709i	0.548627	−	1.20133i	−0.408792	−	0.912627i	$-0.634050\pi$
$353$	10.3078	−	22.5709i	0.548627	−	1.20133i	0.957420	−	0.288699i	$-0.0932228\pi$
$354$		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	−0.797240	−	0.603663i	$-0.793707\pi$
$359$	−1.63444	+	1.88624i	−0.0862624	+	0.0995521i	0.710977	+	0.703215i	$0.248253\pi$
$360$		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	0.440270	−	0.897866i	$-0.354883\pi$
$373$	−9.87125	−	11.3920i	−0.511114	−	0.589857i	−0.951383	+	0.308009i	$0.900337\pi$
$374$		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	0.984797	+	0.173710i	$0.0555756\pi$
$379$	1.72935	+	12.0279i	0.0888310	+	0.617833i	−0.895966	+	0.444123i	$0.853515\pi$
$380$		0			0
$381$	3.25537	−	2.09210i	0.166778	−	0.107182i
$382$		0			0
$383$	−13.8735	+	30.3787i	−0.708902	+	1.55228i	0.119930	+	0.992782i	$0.461733\pi$
$383$	−13.8735	+	30.3787i	−0.708902	+	1.55228i	−0.828832	+	0.559497i	$0.810994\pi$
$384$		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	−0.917863	−	0.396898i	$-0.870087\pi$
$389$	1.47211	−	10.2388i	0.0746391	−	0.519127i	0.992502	−	0.122229i	$-0.0390042\pi$
$390$		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	−0.460913	−	0.887445i	$-0.652478\pi$
$397$	−7.34966	+	2.15806i	−0.368869	+	0.108310i	0.0920442	+	0.995755i	$0.470660\pi$
$398$		0			0
$399$	13.0848	−	28.6518i	0.655060	−	1.43438i
$400$		0			0
$401$	−18.7384	+	12.0424i	−0.935751	+	0.601371i	−0.917187	−	0.398457i	$-0.869546\pi$
$401$	−18.7384	+	12.0424i	−0.935751	+	0.601371i	−0.0185639	+	0.999828i	$0.505909\pi$
$402$		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	0.511376	−	0.859357i	$-0.329136\pi$
$409$	−8.33240	−	9.61611i	−0.412011	−	0.475486i	−0.923387	+	0.383871i	$0.874591\pi$
$410$		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	0.999277	−	0.0380321i	$-0.0121089\pi$
$419$	16.7731	+	19.3572i	0.819420	+	0.945661i	−0.179857	+	0.983693i	$0.557563\pi$
$420$		0			0
$421$	−4.77985	−	3.07182i	−0.232956	−	0.149712i	0.418956	−	0.908007i	$-0.362396\pi$
$421$	−4.77985	−	3.07182i	−0.232956	−	0.149712i	−0.651911	+	0.758295i	$0.726033\pi$
$422$		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	0.158674	−	0.987331i	$-0.449278\pi$
$431$	17.1472	−	5.03487i	0.825951	−	0.242521i	0.667277	+	0.744810i	$0.267460\pi$
$432$		0			0
$433$	−6.92156	−	2.03235i	−0.332629	−	0.0976686i	0.111154	−	0.993803i	$-0.464545\pi$
$433$	−6.92156	−	2.03235i	−0.332629	−	0.0976686i	−0.443782	+	0.896135i	$0.646364\pi$
$434$		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	−0.920524	−	0.390686i	$-0.872238\pi$
$439$	1.52494	−	10.6062i	0.0727813	−	0.506205i	0.993305	−	0.115519i	$-0.0368531\pi$
$440$		0			0
$441$	−17.2911	−	5.07711i	−0.823384	−	0.241767i
$442$		0			0
$443$	−20.8316	+	6.11670i	−0.989738	+	0.290613i	−0.736238	−	0.676722i	$-0.763400\pi$
$443$	−20.8316	+	6.11670i	−0.989738	+	0.290613i	−0.253499	+	0.967336i	$0.581582\pi$
$444$		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	0.976912	+	0.213642i	$0.0685326\pi$
$449$	2.11391	+	14.7026i	0.0997617	+	0.693858i	−0.877150	+	0.480216i	$0.840558\pi$
$450$		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	0.892863	−	0.450329i	$-0.148693\pi$
$457$	−0.687808	−	1.50609i	−0.0321743	−	0.0704519i	−0.925037	+	0.379877i	$0.875966\pi$
$458$		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	−0.913393	−	0.407080i	$-0.866547\pi$
$463$	−13.4032	−	29.3488i	−0.622898	−	1.36396i	0.290495	−	0.956877i	$-0.406180\pi$
$464$		0			0
$465$	−8.53893	−	9.85445i	−0.395984	−	0.456989i
$466$		0			0
$467$	−19.9372	−	12.8129i	−0.922585	−	0.592909i	−0.00917844	−	0.999958i	$-0.502922\pi$
$467$	−19.9372	−	12.8129i	−0.922585	−	0.592909i	−0.913407	+	0.407049i	$0.866558\pi$
$468$		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	0.898711	−	0.438542i	$-0.144505\pi$
$479$	31.0270	+	9.11036i	1.41766	+	0.416263i	0.518950	+	0.854805i	$0.326323\pi$
$480$		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	−0.342558	−	0.939497i	$-0.611293\pi$
$487$	−25.1282	−	7.37830i	−1.13867	−	0.334343i	−0.796108	+	0.605154i	$0.793111\pi$
$488$		0			0
$489$	−9.64802	+	2.83292i	−0.436299	+	0.128109i
$490$		0			0
$491$	1.89331	−	4.14578i	0.0854440	−	0.187096i	−0.862087	−	0.506761i	$-0.830843\pi$
$491$	1.89331	−	4.14578i	0.0854440	−	0.187096i	0.947531	+	0.319664i	$0.103570\pi$
$492$		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	−0.188305	−	0.982111i	$-0.560299\pi$
$499$	−25.9099	−	16.6513i	−1.15989	−	0.745415i	−0.971584	+	0.236696i	$0.923936\pi$
$500$		0			0
$501$	−6.23667	−	7.19750i	−0.278634	−	0.321560i
$502$		0			0
$503$	6.22158	+	13.6234i	0.277406	+	0.607435i	0.996133	−	0.0878574i	$-0.0280020\pi$
$503$	6.22158	+	13.6234i	0.277406	+	0.607435i	−0.718727	+	0.695293i	$0.755275\pi$
$504$		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	0.699836	−	0.714304i	$-0.253257\pi$
$509$	−6.72982	−	14.7363i	−0.298294	−	0.653173i	−0.998130	+	0.0611308i	$0.980529\pi$
$510$		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	−0.850263	−	0.526359i	$-0.823557\pi$
$521$	2.38152	−	5.21480i	0.104336	−	0.228464i	0.954599	+	0.297894i	$0.0962842\pi$
$522$		0			0
$523$	−1.40391	+	0.412224i	−0.0613885	+	0.0180253i	−0.312283	−	0.949989i	$-0.601094\pi$
$523$	−1.40391	+	0.412224i	−0.0613885	+	0.0180253i	0.250894	+	0.968015i	$0.419275\pi$
$524$		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	0.578203	+	0.815893i	$0.303754\pi$
$541$	5.89126	+	40.9746i	0.253285	+	1.76163i	−0.324918	+	0.945742i	$0.605337\pi$
$542$		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	0.636879	−	0.770963i	$-0.280225\pi$
$547$	−5.07226	−	5.85370i	−0.216874	−	0.250286i	−0.853753	+	0.520677i	$0.825679\pi$
$548$		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	0.998190	−	0.0601319i	$-0.0191521\pi$
$557$	18.8007	+	21.6972i	0.796613	+	0.919341i	−0.201577	+	0.979473i	$0.564607\pi$
$558$		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	−0.836127	−	0.548536i	$-0.815185\pi$
$563$	−4.47051	−	31.0931i	−0.188409	−	1.31042i	0.647717	−	0.761881i	$-0.275724\pi$
$564$		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	−0.670461	−	0.741945i	$-0.733904\pi$
$569$	−19.8788	+	5.83694i	−0.833363	+	0.244697i	−0.162902	+	0.986642i	$0.552085\pi$
$570$		0			0
$571$	40.9638	+	12.0281i	1.71428	+	0.503359i	0.983754	−	0.179522i	$-0.0574552\pi$
$571$	40.9638	+	12.0281i	1.71428	+	0.503359i	0.730529	+	0.682881i	$0.239273\pi$
$572$		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	0.514766	+	0.857331i	$0.327879\pi$
$577$	−5.30107	+	36.8698i	−0.220686	+	1.53491i	−0.735452	+	0.677577i	$0.763030\pi$
$578$		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	0.965384	−	0.260832i	$-0.0839969\pi$
$587$	−0.832963	−	5.79339i	−0.0343801	−	0.239119i	−0.999764	+	0.0217135i	$0.993088\pi$
$588$		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	0.941480	−	0.337068i	$-0.109435\pi$
$593$	11.5391	+	13.3169i	0.473856	+	0.546859i	−0.467624	+	0.883927i	$0.654890\pi$
$594$		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	−0.994115	−	0.108326i	$-0.965451\pi$
$601$	−10.4184	−	22.8131i	−0.424976	−	0.930567i	0.569140	−	0.822241i	$-0.307276\pi$
$602$		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	−0.884388	−	0.466752i	$-0.845424\pi$
$607$	−7.30562	+	8.43113i	−0.296526	+	0.342209i	0.587863	+	0.808961i	$0.299970\pi$
$608$		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	−0.189667	−	0.981848i	$-0.560741\pi$
$613$	16.7511	−	36.6798i	0.676570	−	1.48148i	0.866237	−	0.499633i	$-0.166532\pi$
$614$		0			0
$615$	−5.75416	+	1.68957i	−0.232030	+	0.0681302i
$616$		0			0
$617$	−17.4701	−	5.12968i	−0.703319	−	0.206513i	−0.0895309	−	0.995984i	$-0.528537\pi$
$617$	−17.4701	−	5.12968i	−0.703319	−	0.206513i	−0.613788	+	0.789471i	$0.710355\pi$
$618$		0			0
$619$	1.05208	−	7.31738i	0.0422867	−	0.294111i	−0.957693	−	0.287791i	$-0.907079\pi$
$619$	1.05208	−	7.31738i	0.0422867	−	0.294111i	0.999980	−	0.00631979i	$-0.00201166\pi$
$620$		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	−0.831870	−	0.554971i	$-0.812729\pi$
$631$	−16.8961	+	10.8584i	−0.672622	+	0.432268i	0.159248	+	0.987239i	$0.449093\pi$
$632$		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	0.998612	+	0.0526766i	$0.0167753\pi$
$641$	9.73401	+	21.3145i	0.384470	+	0.841873i	−0.614141	+	0.789196i	$0.710497\pi$
$642$		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	−0.861570	−	0.507639i	$-0.830519\pi$
$647$	−17.3223	−	37.9305i	−0.681009	−	1.49120i	0.180561	−	0.983564i	$-0.442209\pi$
$648$		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	−0.768576	−	0.639758i	$-0.779034\pi$
$653$	−0.663117	+	0.765278i	−0.0259498	+	0.0299476i	0.742626	+	0.669706i	$0.233580\pi$
$654$		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	−0.930400	−	0.366546i	$-0.880540\pi$
$659$	−1.13211	+	2.47898i	−0.0441009	+	0.0965675i	0.886299	+	0.463113i	$0.153268\pi$
$660$		0			0
$661$	−2.74545	+	0.806138i	−0.106786	+	0.0313551i	−0.334689	−	0.942329i	$-0.608631\pi$
$661$	−2.74545	+	0.806138i	−0.106786	+	0.0313551i	0.227903	+	0.973684i	$0.426813\pi$
$662$		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	−0.531136	−	0.847287i	$-0.678235\pi$
$673$	−13.4868	+	3.96008i	−0.519878	+	0.152650i	0.0112579	+	0.999937i	$0.496416\pi$
$674$		0			0
$675$	−0.394206	+	0.863190i	−0.0151730	+	0.0332242i
$676$		0			0
$677$	−31.7494	+	20.4041i	−1.22023	+	0.784192i	−0.982341	−	0.187101i	$-0.940091\pi$
$677$	−31.7494	+	20.4041i	−1.22023	+	0.784192i	−0.237886	+	0.971293i	$0.576455\pi$
$678$		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	0.732608	−	0.680650i	$-0.238303\pi$
$683$	10.9190	+	7.01720i	0.417803	+	0.268506i	−0.314805	+	0.949156i	$0.601939\pi$
$684$		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	0.947789	+	0.318897i	$0.103312\pi$
$701$	3.39522	+	23.6143i	0.128236	+	0.891900i	−0.819554	+	0.573003i	$0.805778\pi$
$702$		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	−0.173381	−	0.984855i	$-0.555469\pi$
$709$	−22.6780	−	6.65887i	−0.851691	−	0.250079i	−0.678310	+	0.734776i	$0.737287\pi$
$710$		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	0.0266724	−	0.999644i	$-0.491509\pi$
$719$	15.8085	−	4.64181i	0.589559	−	0.173110i	0.562887	+	0.826534i	$0.309691\pi$
$720$		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	−0.663756	−	0.747949i	$-0.731039\pi$
$727$	4.61182	−	5.32233i	0.171043	−	0.197394i	0.834799	+	0.550555i	$0.185584\pi$
$728$		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	0.908637	+	0.417586i	$0.137124\pi$
$733$	17.0349	+	37.3012i	0.629197	+	1.37775i	−0.279440	+	0.960163i	$0.590149\pi$
$734$		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	0.988090	+	0.153880i	$0.0491769\pi$
$739$	12.4321	+	27.2226i	0.457323	+	1.00140i	−0.530766	+	0.847518i	$0.678096\pi$
$740$		0			0
$741$	18.5492	+	21.4069i	0.681421	+	0.786401i
$742$		0			0
$743$	2.12810	+	1.36765i	0.0780724	+	0.0501741i	0.579095	−	0.815260i	$-0.303406\pi$
$743$	2.12810	+	1.36765i	0.0780724	+	0.0501741i	−0.501022	+	0.865434i	$0.667043\pi$
$744$		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	0.297928	+	0.954588i	$0.403704\pi$
$751$	−16.9524	+	37.1206i	−0.618603	+	1.35455i	−0.916531	+	0.399963i	$0.869023\pi$
$752$		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	0.708898	+	0.705311i	$0.249192\pi$
$757$	−4.67714	+	32.5302i	−0.169994	+	1.18233i	−0.878892	+	0.477021i	$0.841717\pi$
$758$		0			0
$759$	−11.8815	+	8.31651i	−0.431272	+	0.301870i
$760$		0			0
$761$	7.14381	−	49.6863i	0.258963	−	1.80113i	−0.281289	−	0.959623i	$-0.590762\pi$
$761$	7.14381	−	49.6863i	0.258963	−	1.80113i	0.540251	−	0.841504i	$-0.318329\pi$
$762$		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	−0.852280	−	0.523086i	$-0.824781\pi$
$769$	−20.2578	+	13.0189i	−0.730515	+	0.469473i	0.121765	+	0.992559i	$0.461144\pi$
$770$		0			0
$771$	0.634175	+	4.41079i	0.0228393	+	0.158851i
$772$		0			0
$773$	−10.0732	+	11.6251i	−0.362308	+	0.418126i	−0.907412	−	0.420243i	$-0.861945\pi$
$773$	−10.0732	+	11.6251i	−0.362308	+	0.418126i	0.545103	+	0.838369i	$0.316490\pi$
$774$		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	0.973910	−	0.226937i	$-0.0728711\pi$
$787$	17.1317	+	19.7711i	0.610681	+	0.704763i	−0.363229	+	0.931700i	$0.618326\pi$
$788$		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	−0.743713	−	0.668499i	$-0.766937\pi$
$797$	7.01639	−	15.3638i	0.248533	−	0.544212i	0.992246	+	0.124287i	$0.0396643\pi$
$798$		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	0.892145	−	0.451749i	$-0.149200\pi$
$809$	39.7755	+	11.6791i	1.39843	+	0.410616i	0.506286	+	0.862366i	$0.331018\pi$
$810$		0			0
$811$	40.0589	−	11.7624i	1.40666	−	0.413032i	0.511693	−	0.859168i	$-0.329018\pi$
$811$	40.0589	−	11.7624i	1.40666	−	0.413032i	0.894965	+	0.446136i	$0.147200\pi$
$812$		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	0.996135	+	0.0878335i	$0.0279943\pi$
$821$	42.6886	+	27.4343i	1.48984	+	0.957463i	0.493706	+	0.869629i	$0.335642\pi$
$822$		0			0
$823$	−10.8933	−	12.5716i	−0.379718	−	0.438217i	0.533431	−	0.845843i	$-0.320902\pi$
$823$	−10.8933	−	12.5716i	−0.379718	−	0.438217i	−0.913149	+	0.407626i	$0.866357\pi$
$824$		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	0.662810	+	0.748787i	$0.269364\pi$
$839$	6.88818	+	47.9083i	0.237806	+	1.65398i	−0.425004	+	0.905191i	$0.639727\pi$
$840$		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	−0.999926	−	0.0121776i	$-0.996124\pi$
$853$	−1.08277	+	7.53080i	−0.0370732	+	0.257850i	0.962853	+	0.270027i	$0.0870327\pi$
$854$		0			0
$855$	12.1607	+	3.57071i	0.415888	+	0.122116i
$856$		0			0
$857$	−17.9079	+	5.25823i	−0.611721	+	0.179618i	−0.572896	−	0.819628i	$-0.694180\pi$
$857$	−17.9079	+	5.25823i	−0.611721	+	0.179618i	−0.0388259	+	0.999246i	$0.512362\pi$
$858$		0			0
$859$	−8.09886	+	17.7340i	−0.276329	+	0.605077i	−0.996011	−	0.0892268i	$-0.971560\pi$
$859$	−8.09886	+	17.7340i	−0.276329	+	0.605077i	0.719682	+	0.694304i	$0.244288\pi$
$860$		0			0
$861$	−12.5382	+	8.05781i	−0.427301	+	0.274610i
$862$		0			0
$863$	1.91221	+	13.2997i	0.0650923	+	0.452727i	0.996136	+	0.0878200i	$0.0279900\pi$
$863$	1.91221	+	13.2997i	0.0650923	+	0.452727i	−0.931044	+	0.364907i	$0.881101\pi$
$864$		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	0.996633	+	0.0819935i	$0.0261287\pi$
$877$	12.0217	+	26.3238i	0.405944	+	0.888893i	−0.590689	+	0.806899i	$0.701144\pi$
$878$		0			0
$879$	−3.21834	−	3.71416i	−0.108552	−	0.125276i
$880$		0			0
$881$	−45.2407	−	29.0744i	−1.52420	−	0.979542i	−0.991046	−	0.133522i	$-0.957371\pi$
$881$	−45.2407	−	29.0744i	−1.52420	−	0.979542i	−0.533151	−	0.846020i	$-0.678992\pi$
$882$		0			0
$883$	−20.1952	+	23.3065i	−0.679623	+	0.784326i	−0.985850	−	0.167632i	$-0.946388\pi$
$883$	−20.1952	+	23.3065i	−0.679623	+	0.784326i	0.306227	+	0.951959i	$0.400933\pi$
$884$		0			0
$885$	−1.85200	−	12.8810i	−0.0622545	−	0.432989i
$886$		0			0
$887$	−8.62325	+	5.54183i	−0.289540	+	0.186076i	−0.677345	−	0.735665i	$-0.736870\pi$
$887$	−8.62325	+	5.54183i	−0.289540	+	0.186076i	0.387805	+	0.921741i	$0.373233\pi$
$888$		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	−0.611040	−	0.791600i	$-0.709248\pi$
$907$	−4.36116	+	2.80275i	−0.144810	+	0.0930637i	0.466230	+	0.884664i	$0.345612\pi$
$908$		0			0
$909$	−0.0323600	−	0.225069i	−0.00107331	−	0.00746506i
$910$		0			0
$911$	−19.0442	+	21.9782i	−0.630964	+	0.728171i	−0.977750	−	0.209773i	$-0.932728\pi$
$911$	−19.0442	+	21.9782i	−0.630964	+	0.728171i	0.346786	+	0.937944i	$0.387273\pi$
$912$		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	−0.394056	−	0.919087i	$-0.628928\pi$
$929$	17.4268	−	20.1116i	0.571756	−	0.659841i	0.965812	+	0.259245i	$0.0834737\pi$
$930$		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	0.0934069	−	0.995628i	$-0.470224\pi$
$937$	21.7415	−	6.38387i	0.710263	−	0.208552i	0.616856	+	0.787076i	$0.288406\pi$
$938$		0			0
$939$	11.0785	+	3.25295i	0.361534	+	0.106156i
$940$		0			0
$941$	−8.00943	+	55.7068i	−0.261100	+	1.81599i	0.263520	+	0.964654i	$0.415116\pi$
$941$	−8.00943	+	55.7068i	−0.261100	+	1.81599i	−0.524620	+	0.851336i	$0.675793\pi$
$942$		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	0.397337	−	0.917673i	$-0.369934\pi$
$947$	7.24610	+	2.12765i	0.235467	+	0.0691392i	−0.161870	+	0.986812i	$0.551753\pi$
$948$		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	−0.474217	+	0.880408i	$0.657269\pi$
$953$	−45.4436	+	29.2048i	−1.47206	+	0.946036i	−0.997844	+	0.0656284i	$0.979095\pi$
$954$		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	0.433972	−	0.900926i	$-0.357112\pi$
$971$	−16.1895	−	18.6836i	−0.519544	−	0.599586i	−0.953517	+	0.301340i	$0.902566\pi$
$972$		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	−0.443251	−	0.896397i	$-0.646175\pi$
$977$	−8.45499	−	58.8057i	−0.270499	−	1.88136i	0.172752	−	0.984965i	$-0.444734\pi$
$978$		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	−0.527402	−	0.849616i	$-0.676834\pi$
$983$	−16.0446	+	4.71113i	−0.511744	+	0.150262i	0.0156581	+	0.999877i	$0.495016\pi$
$984$		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	−0.992095	−	0.125489i	$-0.959950\pi$
$991$	−0.152124	+	1.05804i	−0.00483237	+	0.0336099i	0.987263	+	0.159099i	$0.0508590\pi$
$992$		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	−0.820014	−	0.572344i	$-0.806034\pi$
$997$	4.72144	−	10.3385i	0.149530	−	0.327424i	0.969543	+	0.244920i	$0.0787616\pi$
$998$		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.169.2	yes	30
23.3	even	11	inner	552.2.q.b.49.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.49.2	✓	30	23.3	even	11	inner
552.2.q.b.169.2	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)

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