LMFDB - Embedded newform 504.2.bs.a.257.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.18
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.957290 - 1.44347i) q^{3} +(-1.80389 - 3.12442i) q^{5} +(2.05506 + 1.66636i) q^{7} +(-1.16719 - 2.76363i) q^{9} +O(q^{10})$	\(q+(0.957290 - 1.44347i) q^{3} +(-1.80389 - 3.12442i) q^{5} +(2.05506 + 1.66636i) q^{7} +(-1.16719 - 2.76363i) q^{9} +(-4.30356 - 2.48466i) q^{11} +(-0.167352 - 0.0966208i) q^{13} +(-6.23684 - 0.387129i) q^{15} +(0.257836 + 0.446584i) q^{17} +(1.69676 + 0.979624i) q^{19} +(4.37261 - 1.37122i) q^{21} +(4.75967 - 2.74800i) q^{23} +(-4.00801 + 6.94208i) q^{25} +(-5.10655 - 0.960796i) q^{27} +(-6.81428 + 3.93423i) q^{29} -3.21900i q^{31} +(-7.70629 + 3.83351i) q^{33} +(1.49931 - 9.42678i) q^{35} +(4.09961 - 7.10074i) q^{37} +(-0.299673 + 0.149073i) q^{39} +(-3.39731 + 5.88431i) q^{41} +(-5.07054 - 8.78243i) q^{43} +(-6.52928 + 8.63208i) q^{45} +11.5606 q^{47} +(1.44651 + 6.84891i) q^{49} +(0.891453 + 0.0553337i) q^{51} +(6.88707 - 3.97625i) q^{53} +17.9282i q^{55} +(3.03834 - 1.51143i) q^{57} +9.61678 q^{59} +0.692340i q^{61} +(2.20655 - 7.62438i) q^{63} +0.697172i q^{65} -2.52467 q^{67} +(0.589743 - 9.50105i) q^{69} -13.8891i q^{71} +(5.49489 - 3.17248i) q^{73} +(6.18383 + 12.4310i) q^{75} +(-4.70373 - 12.2774i) q^{77} +7.98485 q^{79} +(-6.27533 + 6.45138i) q^{81} +(4.86357 + 8.42395i) q^{83} +(0.930212 - 1.61117i) q^{85} +(-0.844318 + 13.6024i) q^{87} +(-4.42128 + 7.65787i) q^{89} +(-0.182913 - 0.477429i) q^{91} +(-4.64651 - 3.08151i) q^{93} -7.06852i q^{95} +(2.49132 - 1.43837i) q^{97} +(-1.84361 + 14.7935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.957290	−	1.44347i	0.552692	−	0.833386i
$3$	0.957290	−	1.44347i	0.552692	−	0.833386i
$4$		0			0
$5$	−1.80389	−	3.12442i	−0.806723	−	1.39728i	−0.915122	−	0.403177i	$-0.867906\pi$
$5$	−1.80389	−	3.12442i	−0.806723	−	1.39728i	0.108400	−	0.994107i	$-0.465427\pi$
$6$		0			0
$7$	2.05506	+	1.66636i	0.776738	+	0.629824i
$7$	2.05506	+	1.66636i	0.776738	+	0.629824i
$8$		0			0
$9$	−1.16719	−	2.76363i	−0.389064	−	0.921211i
$10$		0			0
$11$	−4.30356	−	2.48466i	−1.29757	−	0.749154i	−0.317589	−	0.948229i	$-0.602873\pi$
$11$	−4.30356	−	2.48466i	−1.29757	−	0.749154i	−0.979984	+	0.199074i	$0.936206\pi$
$12$		0			0
$13$	−0.167352	−	0.0966208i	−0.0464151	−	0.0267978i	0.476613	−	0.879113i	$-0.341864\pi$
$13$	−0.167352	−	0.0966208i	−0.0464151	−	0.0267978i	−0.523028	+	0.852315i	$0.675198\pi$
$14$		0			0
$15$	−6.23684	−	0.387129i	−1.61035	−	0.0999563i
$16$		0			0
$17$	0.257836	+	0.446584i	0.0625343	+	0.108313i	0.895598	−	0.444865i	$-0.146748\pi$
$17$	0.257836	+	0.446584i	0.0625343	+	0.108313i	−0.833063	+	0.553178i	$0.813415\pi$
$18$		0			0
$19$	1.69676	+	0.979624i	0.389263	+	0.224741i	0.681841	−	0.731501i	$-0.261180\pi$
$19$	1.69676	+	0.979624i	0.389263	+	0.224741i	−0.292578	+	0.956242i	$0.594513\pi$
$20$		0			0
$21$	4.37261	−	1.37122i	0.954183	−	0.299224i
$22$		0			0
$23$	4.75967	−	2.74800i	0.992460	−	0.572997i	0.0864511	−	0.996256i	$-0.472447\pi$
$23$	4.75967	−	2.74800i	0.992460	−	0.572997i	0.906009	+	0.423259i	$0.139114\pi$
$24$		0			0
$25$	−4.00801	+	6.94208i	−0.801602	+	1.38842i
$26$		0			0
$27$	−5.10655	−	0.960796i	−0.982756	−	0.184905i
$28$		0			0
$29$	−6.81428	+	3.93423i	−1.26538	+	0.730568i	−0.974110	−	0.226073i	$-0.927411\pi$
$29$	−6.81428	+	3.93423i	−1.26538	+	0.730568i	−0.291270	+	0.956641i	$0.594078\pi$
$30$		0			0
$31$		−	3.21900i		−	0.578149i	−0.957307	−	0.289074i	$-0.906652\pi$
$31$		−	3.21900i		−	0.578149i	0.957307	−	0.289074i	$-0.0933475\pi$
$32$		0			0
$33$	−7.70629	+	3.83351i	−1.34149	+	0.667328i
$34$		0			0
$35$	1.49931	−	9.42678i	0.253430	−	1.59342i
$36$		0			0
$37$	4.09961	−	7.10074i	0.673972	−	1.16735i	−0.302796	−	0.953055i	$-0.597920\pi$
$37$	4.09961	−	7.10074i	0.673972	−	1.16735i	0.976768	−	0.214299i	$-0.0687466\pi$
$38$		0			0
$39$	−0.299673	+	0.149073i	−0.0479861	+	0.0238708i
$40$		0			0
$41$	−3.39731	+	5.88431i	−0.530571	+	0.918976i	0.468793	+	0.883308i	$0.344689\pi$
$41$	−3.39731	+	5.88431i	−0.530571	+	0.918976i	−0.999364	+	0.0356675i	$0.988644\pi$
$42$		0			0
$43$	−5.07054	−	8.78243i	−0.773250	−	1.33931i	−0.935773	−	0.352603i	$-0.885297\pi$
$43$	−5.07054	−	8.78243i	−0.773250	−	1.33931i	0.162523	−	0.986705i	$-0.448037\pi$
$44$		0			0
$45$	−6.52928	+	8.63208i	−0.973327	+	1.28679i
$46$		0			0
$47$	11.5606			1.68629			0.843145	−	0.537687i	$-0.180702\pi$
$47$	11.5606			1.68629			0.843145	+	0.537687i	$0.180702\pi$
$48$		0			0
$49$	1.44651	+	6.84891i	0.206644	+	0.978416i
$50$		0			0
$51$	0.891453	+	0.0553337i	0.124828	+	0.00774826i
$52$		0			0
$53$	6.88707	−	3.97625i	0.946012	−	0.546180i	0.0541721	−	0.998532i	$-0.482748\pi$
$53$	6.88707	−	3.97625i	0.946012	−	0.546180i	0.891840	+	0.452351i	$0.149415\pi$
$54$		0			0
$55$			17.9282i			2.41744i
$56$		0			0
$57$	3.03834	−	1.51143i	0.402439	−	0.200194i
$58$		0			0
$59$	9.61678			1.25200			0.625999	−	0.779824i	$-0.284691\pi$
$59$	9.61678			1.25200			0.625999	+	0.779824i	$0.284691\pi$
$60$		0			0
$61$			0.692340i			0.0886450i	0.999017	+	0.0443225i	$0.0141129\pi$
$61$			0.692340i			0.0886450i	−0.999017	+	0.0443225i	$0.985887\pi$
$62$		0			0
$63$	2.20655	−	7.62438i	0.278000	−	0.960581i
$64$		0			0
$65$			0.697172i			0.0864735i
$66$		0			0
$67$	−2.52467			−0.308438			−0.154219	−	0.988037i	$-0.549286\pi$
$67$	−2.52467			−0.308438			−0.154219	+	0.988037i	$0.549286\pi$
$68$		0			0
$69$	0.589743	−	9.50105i	0.0709967	−	1.14379i
$70$		0			0
$71$		−	13.8891i		−	1.64833i	−0.566348	−	0.824166i	$-0.691644\pi$
$71$		−	13.8891i		−	1.64833i	0.566348	−	0.824166i	$-0.308356\pi$
$72$		0			0
$73$	5.49489	−	3.17248i	0.643128	−	0.371310i	−0.142690	−	0.989767i	$-0.545575\pi$
$73$	5.49489	−	3.17248i	0.643128	−	0.371310i	0.785819	+	0.618457i	$0.212242\pi$
$74$		0			0
$75$	6.18383	+	12.4310i	0.714047	+	1.43541i
$76$		0			0
$77$	−4.70373	−	12.2774i	−0.536040	−	1.39914i
$78$		0			0
$79$	7.98485			0.898366			0.449183	−	0.893440i	$-0.351715\pi$
$79$	7.98485			0.898366			0.449183	+	0.893440i	$0.351715\pi$
$80$		0			0
$81$	−6.27533	+	6.45138i	−0.697259	+	0.716820i
$82$		0			0
$83$	4.86357	+	8.42395i	0.533846	+	0.924649i	0.999218	+	0.0395336i	$0.0125872\pi$
$83$	4.86357	+	8.42395i	0.533846	+	0.924649i	−0.465372	+	0.885115i	$0.654079\pi$
$84$		0			0
$85$	0.930212	−	1.61117i	0.100896	−	0.174756i
$86$		0			0
$87$	−0.844318	+	13.6024i	−0.0905204	+	1.45833i
$88$		0			0
$89$	−4.42128	+	7.65787i	−0.468654	+	0.811733i	−0.999358	−	0.0358243i	$-0.988594\pi$
$89$	−4.42128	+	7.65787i	−0.468654	+	0.811733i	0.530704	+	0.847557i	$0.321928\pi$
$90$		0			0
$91$	−0.182913	−	0.477429i	−0.0191745	−	0.0500482i
$92$		0			0
$93$	−4.64651	−	3.08151i	−0.481821	−	0.319538i
$94$		0			0
$95$		−	7.06852i		−	0.725215i
$96$		0			0
$97$	2.49132	−	1.43837i	0.252956	−	0.146044i	−0.368161	−	0.929762i	$-0.620013\pi$
$97$	2.49132	−	1.43837i	0.252956	−	0.146044i	0.621117	+	0.783718i	$0.286679\pi$
$98$		0			0
$99$	−1.84361	+	14.7935i	−0.185290	+	1.48681i
$100$		0			0
$101$	0.611850	−	1.05975i	0.0608813	−	0.105450i	−0.833978	−	0.551797i	$-0.813942\pi$
$101$	0.611850	−	1.05975i	0.0608813	−	0.105450i	0.894860	+	0.446348i	$0.147276\pi$
$102$		0			0
$103$	1.22436	−	0.706887i	0.120640	−	0.0696516i	−0.438466	−	0.898748i	$-0.644478\pi$
$103$	1.22436	−	0.706887i	0.120640	−	0.0696516i	0.559106	+	0.829096i	$0.311145\pi$
$104$		0			0
$105$	−12.1720	−	11.1884i	−1.18786	−	1.09187i
$106$		0			0
$107$	−2.74499	−	1.58482i	−0.265368	−	0.153210i	0.361413	−	0.932406i	$-0.382295\pi$
$107$	−2.74499	−	1.58482i	−0.265368	−	0.153210i	−0.626781	+	0.779196i	$0.715628\pi$
$108$		0			0
$109$	9.94920	+	17.2325i	0.952961	+	1.65058i	0.738967	+	0.673741i	$0.235314\pi$
$109$	9.94920	+	17.2325i	0.952961	+	1.65058i	0.213993	+	0.976835i	$0.431353\pi$
$110$		0			0
$111$	−6.32516	−	12.7151i	−0.600357	−	1.20687i
$112$		0			0
$113$	3.08850	+	1.78315i	0.290542	+	0.167744i	0.638186	−	0.769882i	$-0.279685\pi$
$113$	3.08850	+	1.78315i	0.290542	+	0.167744i	−0.347644	+	0.937626i	$0.613018\pi$
$114$		0			0
$115$	−17.1718	−	9.91415i	−1.60128	−	0.924499i
$116$		0			0
$117$	−0.0716924	+	0.575275i	−0.00662796	+	0.0531842i
$118$		0			0
$119$	−0.214302	+	1.34740i	−0.0196450	+	0.123516i
$120$		0			0
$121$	6.84710	+	11.8595i	0.622464	+	1.07814i
$122$		0			0
$123$	5.24160	+	10.5369i	0.472619	+	0.950080i
$124$		0			0
$125$	10.8811			0.973238
$126$		0			0
$127$	15.1490			1.34425			0.672126	−	0.740436i	$-0.265381\pi$
$127$	15.1490			1.34425			0.672126	+	0.740436i	$0.265381\pi$
$128$		0			0
$129$	−17.5311	−	1.08818i	−1.54353	−	0.0958089i
$130$		0			0
$131$	0.331039	+	0.573376i	0.0289230	+	0.0500961i	0.880125	−	0.474743i	$-0.157459\pi$
$131$	0.331039	+	0.573376i	0.0289230	+	0.0500961i	−0.851202	+	0.524839i	$0.824126\pi$
$132$		0			0
$133$	1.85453	+	4.84059i	0.160808	+	0.419732i
$134$		0			0
$135$	6.20971	+	17.6882i	0.534447	+	1.52236i
$136$		0			0
$137$	−2.64994	−	1.52994i	−0.226399	−	0.130712i	0.382511	−	0.923951i	$-0.375060\pi$
$137$	−2.64994	−	1.52994i	−0.226399	−	0.130712i	−0.608910	+	0.793239i	$0.708393\pi$
$138$		0			0
$139$	−0.924289	−	0.533639i	−0.0783972	−	0.0452626i	0.460289	−	0.887769i	$-0.347746\pi$
$139$	−0.924289	−	0.533639i	−0.0783972	−	0.0452626i	−0.538686	+	0.842507i	$0.681079\pi$
$140$		0			0
$141$	11.0669	−	16.6874i	0.931998	−	1.40533i
$142$		0			0
$143$	0.480140	+	0.831627i	0.0401513	+	0.0695442i
$144$		0			0
$145$	24.5844	+	14.1938i	2.04162	+	1.17873i
$146$		0			0
$147$	11.2709	+	4.46840i	0.929609	+	0.368548i
$148$		0			0
$149$	−0.726445	+	0.419413i	−0.0595127	+	0.0343597i	−0.529461	−	0.848334i	$-0.677606\pi$
$149$	−0.726445	+	0.419413i	−0.0595127	+	0.0343597i	0.469948	+	0.882694i	$0.344273\pi$
$150$		0			0
$151$	3.26270	−	5.65117i	0.265515	−	0.459885i	−0.702183	−	0.711996i	$-0.747791\pi$
$151$	3.26270	−	5.65117i	0.265515	−	0.459885i	0.967698	+	0.252111i	$0.0811247\pi$
$152$		0			0
$153$	0.933251	−	1.23381i	0.0754489	−	0.0997478i
$154$		0			0
$155$	−10.0575	+	5.80670i	−0.807838	+	0.466406i
$156$		0			0
$157$			9.67730i			0.772332i	0.922429	+	0.386166i	$0.126201\pi$
$157$			9.67730i			0.772332i	−0.922429	+	0.386166i	$0.873799\pi$
$158$		0			0
$159$	0.853337	−	13.7477i	0.0676740	−	1.09026i
$160$		0			0
$161$	14.3605	+	2.28402i	1.13177	+	0.180006i
$162$		0			0
$163$	−2.98011	+	5.16171i	−0.233421	+	0.404296i	−0.958812	−	0.284040i	$-0.908325\pi$
$163$	−2.98011	+	5.16171i	−0.233421	+	0.404296i	0.725392	+	0.688336i	$0.241659\pi$
$164$		0			0
$165$	25.8788	+	17.1625i	2.01466	+	1.33610i
$166$		0			0
$167$	−6.25237	+	10.8294i	−0.483823	+	0.838005i	−0.999827	−	0.0185803i	$-0.994085\pi$
$167$	−6.25237	+	10.8294i	−0.483823	+	0.838005i	0.516005	+	0.856586i	$0.327419\pi$
$168$		0			0
$169$	−6.48133	−	11.2260i	−0.498564	−	0.863538i
$170$		0			0
$171$	0.726878	−	5.83262i	0.0555858	−	0.446032i
$172$		0			0
$173$	9.93547			0.755380			0.377690	−	0.925932i	$-0.376719\pi$
$173$	9.93547			0.755380			0.377690	+	0.925932i	$0.376719\pi$
$174$		0			0
$175$	−19.8047	+	7.58759i	−1.49709	+	0.573568i
$176$		0			0
$177$	9.20604	−	13.8815i	0.691969	−	1.04340i
$178$		0			0
$179$	−2.61642	+	1.51059i	−0.195560	+	0.112907i	−0.594583	−	0.804034i	$-0.702683\pi$
$179$	−2.61642	+	1.51059i	−0.195560	+	0.112907i	0.399023	+	0.916941i	$0.369349\pi$
$180$		0			0
$181$		−	13.6853i		−	1.01722i	−0.860997	−	0.508611i	$-0.830159\pi$
$181$		−	13.6853i		−	1.01722i	0.860997	−	0.508611i	$-0.169841\pi$
$182$		0			0
$183$	0.999369	+	0.662770i	0.0738755	+	0.0489934i
$184$		0			0
$185$	−29.5809			−2.17483
$186$		0			0
$187$		−	2.56254i		−	0.187391i
$188$		0			0
$189$	−8.89322	−	10.4838i	−0.646887	−	0.762586i
$190$		0			0
$191$		−	13.8893i		−	1.00499i	−0.864579	−	0.502497i	$-0.832415\pi$
$191$		−	13.8893i		−	1.00499i	0.864579	−	0.502497i	$-0.167585\pi$
$192$		0			0
$193$	−19.4756			−1.40189			−0.700944	−	0.713216i	$-0.747238\pi$
$193$	−19.4756			−1.40189			−0.700944	+	0.713216i	$0.747238\pi$
$194$		0			0
$195$	1.00634	+	0.667396i	0.0720658	+	0.0477932i
$196$		0			0
$197$			26.1835i			1.86549i	0.360531	+	0.932747i	$0.382596\pi$
$197$			26.1835i			1.86549i	−0.360531	+	0.932747i	$0.617404\pi$
$198$		0			0
$199$	−0.580026	+	0.334878i	−0.0411170	+	0.0237389i	−0.520418	−	0.853912i	$-0.674224\pi$
$199$	−0.580026	+	0.334878i	−0.0411170	+	0.0237389i	0.479301	+	0.877651i	$0.340890\pi$
$200$		0			0
$201$	−2.41685	+	3.64428i	−0.170471	+	0.257048i
$202$		0			0
$203$	−20.5596	−	3.26997i	−1.44300	−	0.229507i
$204$		0			0
$205$	24.5134			1.71209
$206$		0			0
$207$	−13.1499	−	9.94654i	−0.913981	−	0.691332i
$208$		0			0
$209$	−4.86807	−	8.43175i	−0.336732	−	0.583236i
$210$		0			0
$211$	−3.25422	+	5.63648i	−0.224030	+	0.388031i	−0.956028	−	0.293275i	$-0.905255\pi$
$211$	−3.25422	+	5.63648i	−0.224030	+	0.388031i	0.731998	+	0.681307i	$0.238588\pi$
$212$		0			0
$213$	−20.0484	−	13.2959i	−1.37370	−	0.911020i
$214$		0			0
$215$	−18.2934	+	31.6850i	−1.24760	+	2.16090i
$216$		0			0
$217$	5.36400	−	6.61522i	0.364132	−	0.449070i
$218$		0			0
$219$	0.680840	−	10.9687i	0.0460069	−	0.741194i
$220$		0			0
$221$		−	0.0996491i		−	0.00670312i
$222$		0			0
$223$	−21.4478	+	12.3829i	−1.43625	+	0.829221i	−0.997587	−	0.0694286i	$-0.977882\pi$
$223$	−21.4478	+	12.3829i	−1.43625	+	0.829221i	−0.438667	+	0.898650i	$0.644549\pi$
$224$		0			0
$225$	23.8635	+	2.97393i	1.59090	+	0.198262i
$226$		0			0
$227$	8.43231	−	14.6052i	0.559672	−	0.969381i	−0.437851	−	0.899047i	$-0.644260\pi$
$227$	8.43231	−	14.6052i	0.559672	−	0.969381i	0.997524	−	0.0703335i	$-0.0224063\pi$
$228$		0			0
$229$	−0.769864	+	0.444481i	−0.0508740	+	0.0293721i	−0.525221	−	0.850966i	$-0.676017\pi$
$229$	−0.769864	+	0.444481i	−0.0508740	+	0.0293721i	0.474347	+	0.880338i	$0.342684\pi$
$230$		0			0
$231$	−22.2248	−	4.96335i	−1.46229	−	0.326565i
$232$		0			0
$233$	−17.9798	−	10.3806i	−1.17789	−	0.680057i	−0.222367	−	0.974963i	$-0.571378\pi$
$233$	−17.9798	−	10.3806i	−1.17789	−	0.680057i	−0.955526	+	0.294906i	$0.904712\pi$
$234$		0			0
$235$	−20.8540	−	36.1203i	−1.36037	−	2.35623i
$236$		0			0
$237$	7.64382	−	11.5259i	0.496519	−	0.748686i
$238$		0			0
$239$	14.5617	+	8.40721i	0.941919	+	0.543817i	0.890561	−	0.454863i	$-0.150312\pi$
$239$	14.5617	+	8.40721i	0.941919	+	0.543817i	0.0513574	+	0.998680i	$0.483645\pi$
$240$		0			0
$241$	−14.2705	−	8.23906i	−0.919242	−	0.530725i	−0.0358487	−	0.999357i	$-0.511413\pi$
$241$	−14.2705	−	8.23906i	−0.919242	−	0.530725i	−0.883393	+	0.468633i	$0.844747\pi$
$242$		0			0
$243$	3.30504	+	15.2341i	0.212018	+	0.977266i
$244$		0			0
$245$	18.7896	−	16.8742i	1.20042	−	1.07805i
$246$		0			0
$247$	−0.189304	−	0.327884i	−0.0120451	−	0.0208628i
$248$		0			0
$249$	16.8155	+	1.04376i	1.06564	+	0.0661458i
$250$		0			0
$251$	23.9826			1.51377			0.756885	−	0.653548i	$-0.226720\pi$
$251$	23.9826			1.51377			0.756885	+	0.653548i	$0.226720\pi$
$252$		0			0
$253$	−27.3114			−1.71705
$254$		0			0
$255$	−1.43519	−	2.88509i	−0.0898753	−	0.180671i
$256$		0			0
$257$	1.65100	+	2.85962i	0.102987	+	0.178378i	0.912914	−	0.408152i	$-0.133827\pi$
$257$	1.65100	+	2.85962i	0.102987	+	0.178378i	−0.809927	+	0.586530i	$0.800493\pi$
$258$		0			0
$259$	20.2573	−	7.76100i	1.25873	−	0.482245i
$260$		0			0
$261$	18.8263	+	14.2402i	1.16532	+	0.881445i
$262$		0			0
$263$	−4.01855	−	2.32011i	−0.247794	−	0.143064i	0.370960	−	0.928649i	$-0.379029\pi$
$263$	−4.01855	−	2.32011i	−0.247794	−	0.143064i	−0.618754	+	0.785585i	$0.712362\pi$
$264$		0			0
$265$	−24.8470	−	14.3454i	−1.52634	−	0.881232i
$266$		0			0
$267$	6.82144	+	13.7128i	0.417466	+	0.839208i
$268$		0			0
$269$	−5.43824	−	9.41931i	−0.331575	−	0.574306i	0.651245	−	0.758867i	$-0.274247\pi$
$269$	−5.43824	−	9.41931i	−0.331575	−	0.574306i	−0.982821	+	0.184562i	$0.940913\pi$
$270$		0			0
$271$	−3.69645	−	2.13414i	−0.224543	−	0.129640i	0.383509	−	0.923537i	$-0.374716\pi$
$271$	−3.69645	−	2.13414i	−0.224543	−	0.129640i	−0.608052	+	0.793897i	$0.708049\pi$
$272$		0			0
$273$	−0.864255	−	0.193009i	−0.0523071	−	0.0116814i
$274$		0			0
$275$	34.4975	−	19.9171i	2.08028	−	1.20105i
$276$		0			0
$277$	10.7131	−	18.5556i	0.643686	−	1.11490i	−0.340917	−	0.940093i	$-0.610737\pi$
$277$	10.7131	−	18.5556i	0.643686	−	1.11490i	0.984603	−	0.174804i	$-0.0559292\pi$
$278$		0			0
$279$	−8.89612	+	3.75719i	−0.532597	+	0.224937i
$280$		0			0
$281$	−10.0127	+	5.78086i	−0.597310	+	0.344857i	−0.767983	−	0.640471i	$-0.778739\pi$
$281$	−10.0127	+	5.78086i	−0.597310	+	0.344857i	0.170672	+	0.985328i	$0.445406\pi$
$282$		0			0
$283$			15.1892i			0.902902i	0.892296	+	0.451451i	$0.149093\pi$
$283$			15.1892i			0.902902i	−0.892296	+	0.451451i	$0.850907\pi$
$284$		0			0
$285$	−10.2032	−	6.76662i	−0.604384	−	0.400820i
$286$		0			0
$287$	−16.7870	+	6.43147i	−0.990907	+	0.379637i
$288$		0			0
$289$	8.36704	−	14.4921i	0.492179	−	0.852479i
$290$		0			0
$291$	0.308686	−	4.97308i	0.0180955	−	0.291527i
$292$		0			0
$293$	−9.41545	+	16.3080i	−0.550057	+	0.952726i	0.448213	+	0.893927i	$0.352061\pi$
$293$	−9.41545	+	16.3080i	−0.550057	+	0.952726i	−0.998270	+	0.0587995i	$0.981273\pi$
$294$		0			0
$295$	−17.3476	−	30.0469i	−1.01001	−	1.74940i
$296$		0			0
$297$	19.5891	+	16.8229i	1.13668	+	0.976164i
$298$		0			0
$299$	−1.06205			−0.0614202
$300$		0			0
$301$	4.21442	−	26.4977i	0.242915	−	1.52730i
$302$		0			0
$303$	−0.944003	−	1.89768i	−0.0542316	−	0.109019i
$304$		0			0
$305$	2.16316	−	1.24890i	0.123862	−	0.0715119i
$306$		0			0
$307$			6.63205i			0.378511i	0.981928	+	0.189255i	$0.0606074\pi$
$307$			6.63205i			0.378511i	−0.981928	+	0.189255i	$0.939393\pi$
$308$		0			0
$309$	0.151704	−	2.44402i	0.00863013	−	0.139036i
$310$		0			0
$311$	11.7834			0.668174			0.334087	−	0.942542i	$-0.391572\pi$
$311$	11.7834			0.668174			0.334087	+	0.942542i	$0.391572\pi$
$312$		0			0
$313$		−	28.2405i		−	1.59625i	−0.602494	−	0.798124i	$-0.705826\pi$
$313$		−	28.2405i		−	1.59625i	0.602494	−	0.798124i	$-0.294174\pi$
$314$		0			0
$315$	−27.8021	+	6.85931i	−1.56647	+	0.386478i
$316$		0			0
$317$		−	3.09129i		−	0.173624i	−0.996225	−	0.0868121i	$-0.972332\pi$
$317$		−	3.09129i		−	0.173624i	0.996225	−	0.0868121i	$-0.0276680\pi$
$318$		0			0
$319$	39.1009			2.18923
$320$		0			0
$321$	−4.91538	+	2.44517i	−0.274350	+	0.136476i
$322$		0			0
$323$			1.01033i			0.0562161i
$324$		0			0
$325$	1.34150	−	0.774515i	0.0744130	−	0.0429623i
$326$		0			0
$327$	34.3988	+	2.13518i	1.90226	+	0.118076i
$328$		0			0
$329$	23.7577	+	19.2641i	1.30981	+	1.06206i
$330$		0			0
$331$	−0.0688739			−0.00378565			−0.00189283	−	0.999998i	$-0.500603\pi$
$331$	−0.0688739			−0.00378565			−0.00189283	+	0.999998i	$0.500603\pi$
$332$		0			0
$333$	−24.4089	−	3.04190i	−1.33760	−	0.166695i
$334$		0			0
$335$	4.55423	+	7.88815i	0.248824	+	0.430976i
$336$		0			0
$337$	−2.02979	+	3.51570i	−0.110570	+	0.191512i	−0.916000	−	0.401178i	$-0.868601\pi$
$337$	−2.02979	+	3.51570i	−0.110570	+	0.191512i	0.805430	+	0.592690i	$0.201934\pi$
$338$		0			0
$339$	5.53051	−	2.75116i	0.300376	−	0.149423i
$340$		0			0
$341$	−7.99812	+	13.8532i	−0.433123	+	0.750190i
$342$		0			0
$343$	−8.44007	+	16.4853i	−0.455721	+	0.890123i
$344$		0			0
$345$	−30.7491	+	15.2962i	−1.65548	+	0.823521i
$346$		0			0
$347$			28.2050i			1.51413i	0.653342	+	0.757063i	$0.273366\pi$
$347$			28.2050i			1.51413i	−0.653342	+	0.757063i	$0.726634\pi$
$348$		0			0
$349$	−2.52612	+	1.45846i	−0.135220	+	0.0780695i	−0.566084	−	0.824348i	$-0.691542\pi$
$349$	−2.52612	+	1.45846i	−0.135220	+	0.0780695i	0.430864	+	0.902417i	$0.358209\pi$
$350$		0			0
$351$	0.761759	+	0.654190i	0.0406597	+	0.0349181i
$352$		0			0
$353$	−12.3283	+	21.3533i	−0.656172	+	1.13652i	0.325427	+	0.945567i	$0.394492\pi$
$353$	−12.3283	+	21.3533i	−0.656172	+	1.13652i	−0.981599	+	0.190956i	$0.938841\pi$
$354$		0			0
$355$	−43.3954	+	25.0544i	−2.30319	+	1.32975i
$356$		0			0
$357$	1.73978	+	1.59919i	0.0920789	+	0.0846382i
$358$		0			0
$359$	−22.1427	−	12.7841i	−1.16865	−	0.674718i	−0.215285	−	0.976551i	$-0.569068\pi$
$359$	−22.1427	−	12.7841i	−1.16865	−	0.674718i	−0.953361	+	0.301834i	$0.902401\pi$
$360$		0			0
$361$	−7.58067	−	13.1301i	−0.398983	−	0.691059i
$362$		0			0
$363$	23.6735	+	1.46945i	1.24254	+	0.0771259i
$364$		0			0
$365$	−19.8243	−	11.4456i	−1.03765	−	0.599089i
$366$		0			0
$367$	18.3774	+	10.6102i	0.959291	+	0.553847i	0.895955	−	0.444146i	$-0.146493\pi$
$367$	18.3774	+	10.6102i	0.959291	+	0.553847i	0.0633360	+	0.997992i	$0.479826\pi$
$368$		0			0
$369$	20.2274	+	2.52080i	1.05300	+	0.131227i
$370$		0			0
$371$	20.7792	+	3.30489i	1.07880	+	0.171582i
$372$		0			0
$373$	2.46028	+	4.26133i	0.127388	+	0.220643i	0.922664	−	0.385605i	$-0.126007\pi$
$373$	2.46028	+	4.26133i	0.127388	+	0.220643i	−0.795276	+	0.606248i	$0.792674\pi$
$374$		0			0
$375$	10.4164	−	15.7065i	0.537900	−	0.811083i
$376$		0			0
$377$	1.52051			0.0783104
$378$		0			0
$379$	−6.48201			−0.332959			−0.166479	−	0.986045i	$-0.553240\pi$
$379$	−6.48201			−0.332959			−0.166479	+	0.986045i	$0.553240\pi$
$380$		0			0
$381$	14.5020	−	21.8670i	0.742957	−	1.12028i
$382$		0			0
$383$	−5.34846	−	9.26380i	−0.273293	−	0.473358i	0.696410	−	0.717644i	$-0.254780\pi$
$383$	−5.34846	−	9.26380i	−0.273293	−	0.473358i	−0.969703	+	0.244286i	$0.921446\pi$
$384$		0			0
$385$	−29.8748	+	36.8435i	−1.52256	+	1.87772i
$386$		0			0
$387$	−18.3531	+	24.2639i	−0.932941	+	1.23340i
$388$		0			0
$389$	−24.9170	−	14.3859i	−1.26334	−	0.729392i	−0.289624	−	0.957140i	$-0.593530\pi$
$389$	−24.9170	−	14.3859i	−1.26334	−	0.729392i	−0.973720	+	0.227748i	$0.926864\pi$
$390$		0			0
$391$	2.45442	+	1.41706i	0.124126	+	0.0716639i
$392$		0			0
$393$	1.14455	+	0.0710438i	0.0577349	+	0.00358368i
$394$		0			0
$395$	−14.4038	−	24.9481i	−0.724732	−	1.25527i
$396$		0			0
$397$	−9.94085	−	5.73935i	−0.498917	−	0.288050i	0.229349	−	0.973344i	$-0.426340\pi$
$397$	−9.94085	−	5.73935i	−0.498917	−	0.288050i	−0.728266	+	0.685294i	$0.759674\pi$
$398$		0			0
$399$	8.76255	+	1.95689i	0.438676	+	0.0979671i
$400$		0			0
$401$	5.74507	−	3.31692i	0.286895	−	0.165639i	−0.349646	−	0.936882i	$-0.613698\pi$
$401$	5.74507	−	3.31692i	0.286895	−	0.165639i	0.636541	+	0.771243i	$0.280365\pi$
$402$		0			0
$403$	−0.311022	+	0.538706i	−0.0154931	+	0.0268349i
$404$		0			0
$405$	31.4768	+	7.96923i	1.56410	+	0.395994i
$406$		0			0
$407$	−35.2859	+	20.3723i	−1.74906	+	1.00982i
$408$		0			0
$409$			27.9184i			1.38048i	0.723582	+	0.690239i	$0.242495\pi$
$409$			27.9184i			1.38048i	−0.723582	+	0.690239i	$0.757505\pi$
$410$		0			0
$411$	−4.74518	+	2.36050i	−0.234062	+	0.116435i
$412$		0			0
$413$	19.7630	+	16.0250i	0.972474	+	0.788538i
$414$		0			0
$415$	17.5467	−	30.3917i	0.861332	−	1.49187i
$416$		0			0
$417$	−1.65510	+	0.823334i	−0.0810507	+	0.0403188i
$418$		0			0
$419$	1.05772	−	1.83203i	0.0516732	−	0.0895006i	−0.839032	−	0.544082i	$-0.816878\pi$
$419$	1.05772	−	1.83203i	0.0516732	−	0.0895006i	0.890705	+	0.454582i	$0.150211\pi$
$420$		0			0
$421$	2.78690	+	4.82705i	0.135825	+	0.235256i	0.925912	−	0.377739i	$-0.123298\pi$
$421$	2.78690	+	4.82705i	0.135825	+	0.235256i	−0.790087	+	0.612994i	$0.789965\pi$
$422$		0			0
$423$	−13.4935	−	31.9493i	−0.656074	−	1.55343i
$424$		0			0
$425$	−4.13363			−0.200511
$426$		0			0
$427$	−1.15368	+	1.42280i	−0.0558307	+	0.0688540i
$428$		0			0
$429$	1.66006	+	0.103042i	0.0801484	+	0.00497492i
$430$		0			0
$431$	−23.5955	+	13.6228i	−1.13655	+	0.656189i	−0.945575	−	0.325405i	$-0.894499\pi$
$431$	−23.5955	+	13.6228i	−1.13655	+	0.656189i	−0.190978	+	0.981594i	$0.561166\pi$
$432$		0			0
$433$			39.5990i			1.90301i	0.307638	+	0.951503i	$0.400461\pi$
$433$			39.5990i			1.90301i	−0.307638	+	0.951503i	$0.599539\pi$
$434$		0			0
$435$	44.0227	−	21.8991i	2.11072	−	1.04998i
$436$		0			0
$437$	10.7680			0.515104
$438$		0			0
$439$		−	1.65855i		−	0.0791581i	−0.999216	−	0.0395791i	$-0.987398\pi$
$439$		−	1.65855i		−	0.0791581i	0.999216	−	0.0395791i	$-0.0126017\pi$
$440$		0			0
$441$	17.2395	−	11.9916i	0.820930	−	0.571029i
$442$		0			0
$443$			30.9025i			1.46822i	0.679029	+	0.734111i	$0.262401\pi$
$443$			30.9025i			1.46822i	−0.679029	+	0.734111i	$0.737599\pi$
$444$		0			0
$445$	31.9019			1.51230
$446$		0			0
$447$	−0.0900096	+	1.45010i	−0.00425731	+	0.0685873i
$448$		0			0
$449$			4.87116i			0.229884i	0.993372	+	0.114942i	$0.0366682\pi$
$449$			4.87116i			0.229884i	−0.993372	+	0.114942i	$0.963332\pi$
$450$		0			0
$451$	29.2411	−	16.8823i	1.37691	−	0.794959i
$452$		0			0
$453$	−5.03392	−	10.1194i	−0.236514	−	0.475451i
$454$		0			0
$455$	−1.16174	+	1.43273i	−0.0544631	+	0.0671673i
$456$		0			0
$457$	34.1700			1.59840			0.799202	−	0.601062i	$-0.205256\pi$
$457$	34.1700			1.59840			0.799202	+	0.601062i	$0.205256\pi$
$458$		0			0
$459$	−0.887574	−	2.52823i	−0.0414284	−	0.118008i
$460$		0			0
$461$	16.4992	+	28.5775i	0.768446	+	1.33099i	0.938405	+	0.345537i	$0.112303\pi$
$461$	16.4992	+	28.5775i	0.768446	+	1.33099i	−0.169959	+	0.985451i	$0.554363\pi$
$462$		0			0
$463$	12.5161	−	21.6785i	0.581673	−	1.00749i	−0.413609	−	0.910455i	$-0.635732\pi$
$463$	12.5161	−	21.6785i	0.581673	−	1.00749i	0.995281	−	0.0970318i	$-0.0309348\pi$
$464$		0			0
$465$	−1.24617	+	20.0764i	−0.0577896	+	0.931020i
$466$		0			0
$467$	18.6065	−	32.2274i	0.861005	−	1.49130i	−0.00995493	−	0.999950i	$-0.503169\pi$
$467$	18.6065	−	32.2274i	0.861005	−	1.49130i	0.870960	−	0.491354i	$-0.163498\pi$
$468$		0			0
$469$	−5.18835	−	4.20701i	−0.239576	−	0.194262i
$470$		0			0
$471$	13.9689	+	9.26398i	0.643651	+	0.426862i
$472$		0			0
$473$			50.3943i			2.31713i
$474$		0			0
$475$	−13.6013	+	7.85269i	−0.624068	+	0.360306i
$476$		0			0
$477$	−19.0274	−	14.3923i	−0.871206	−	0.658977i
$478$		0			0
$479$	−11.3068	+	19.5839i	−0.516620	+	0.894812i	0.483194	+	0.875513i	$0.339477\pi$
$479$	−11.3068	+	19.5839i	−0.516620	+	0.894812i	−0.999814	+	0.0192983i	$0.993857\pi$
$480$		0			0
$481$	−1.37216	+	0.792216i	−0.0625650	+	0.0361219i
$482$		0			0
$483$	17.0441	−	18.5425i	0.775533	−	0.843712i
$484$		0			0
$485$	−8.98813	−	5.18930i	−0.408130	−	0.235634i
$486$		0			0
$487$	8.84500	+	15.3200i	0.400805	+	0.694215i	0.993823	−	0.110974i	$-0.0353971\pi$
$487$	8.84500	+	15.3200i	0.400805	+	0.694215i	−0.593018	+	0.805189i	$0.702064\pi$
$488$		0			0
$489$	4.59792	+	9.24295i	0.207925	+	0.417981i
$490$		0			0
$491$	13.2084	+	7.62587i	0.596086	+	0.344151i	0.767500	−	0.641048i	$-0.221500\pi$
$491$	13.2084	+	7.62587i	0.596086	+	0.344151i	−0.171414	+	0.985199i	$0.554834\pi$
$492$		0			0
$493$	−3.51393	−	2.02877i	−0.158259	−	0.0913711i
$494$		0			0
$495$	49.5470	−	20.9256i	2.22697	−	0.940538i
$496$		0			0
$497$	23.1442	−	28.5429i	1.03816	−	1.28032i
$498$		0			0
$499$	−7.99221	−	13.8429i	−0.357780	−	0.619694i	0.629809	−	0.776750i	$-0.283133\pi$
$499$	−7.99221	−	13.8429i	−0.357780	−	0.619694i	−0.987590	+	0.157056i	$0.949800\pi$
$500$		0			0
$501$	9.64657	+	19.3920i	0.430977	+	0.866370i
$502$		0			0
$503$	12.2911			0.548034			0.274017	−	0.961725i	$-0.411648\pi$
$503$	12.2911			0.548034			0.274017	+	0.961725i	$0.411648\pi$
$504$		0			0
$505$	−4.41483			−0.196457
$506$		0			0
$507$	−22.4089	−	1.39095i	−0.995212	−	0.0617741i
$508$		0			0
$509$	0.401274	+	0.695027i	0.0177861	+	0.0308065i	0.874781	−	0.484518i	$-0.161005\pi$
$509$	0.401274	+	0.695027i	0.0177861	+	0.0308065i	−0.856995	+	0.515324i	$0.827672\pi$
$510$		0			0
$511$	16.5788	+	2.63683i	0.733402	+	0.116646i
$512$		0			0
$513$	−7.72337	−	6.63274i	−0.340995	−	0.292843i
$514$		0			0
$515$	−4.41722	−	2.55029i	−0.194646	−	0.112379i
$516$		0			0
$517$	−49.7518	−	28.7242i	−2.18808	−	1.26329i
$518$		0			0
$519$	9.51113	−	14.3415i	0.417492	−	0.629523i
$520$		0			0
$521$	2.76975	+	4.79734i	0.121345	+	0.210175i	0.920298	−	0.391217i	$-0.127946\pi$
$521$	2.76975	+	4.79734i	0.121345	+	0.210175i	−0.798953	+	0.601393i	$0.794613\pi$
$522$		0			0
$523$	5.68350	+	3.28137i	0.248522	+	0.143484i	0.619087	−	0.785322i	$-0.287503\pi$
$523$	5.68350	+	3.28137i	0.248522	+	0.143484i	−0.370565	+	0.928806i	$0.620836\pi$
$524$		0			0
$525$	−8.00639	+	35.8509i	−0.349427	+	1.56466i
$526$		0			0
$527$	1.43755	−	0.829972i	0.0626208	−	0.0361541i
$528$		0			0
$529$	3.60297	−	6.24053i	0.156651	−	0.271327i
$530$		0			0
$531$	−11.2246	−	26.5772i	−0.487107	−	1.15335i
$532$		0			0
$533$	1.13709	−	0.656502i	0.0492530	−	0.0284362i
$534$		0			0
$535$			11.4353i			0.494393i
$536$		0			0
$537$	−0.324185	+	5.22279i	−0.0139896	+	0.225380i
$538$		0			0
$539$	10.7921	−	33.0688i	0.464848	−	1.42437i
$540$		0			0
$541$	−19.8075	+	34.3075i	−0.851589	+	1.47500i	0.0281847	+	0.999603i	$0.491027\pi$
$541$	−19.8075	+	34.3075i	−0.851589	+	1.47500i	−0.879774	+	0.475393i	$0.842306\pi$
$542$		0			0
$543$	−19.7543	−	13.1008i	−0.847738	−	0.562210i
$544$		0			0
$545$	35.8945	−	62.1710i	1.53755	−	2.66311i
$546$		0			0
$547$	−1.47392	−	2.55291i	−0.0630203	−	0.109154i	0.832794	−	0.553583i	$-0.186740\pi$
$547$	−1.47392	−	2.55291i	−0.0630203	−	0.109154i	−0.895814	+	0.444429i	$0.853407\pi$
$548$		0			0
$549$	1.91337	−	0.808093i	0.0816607	−	0.0344886i
$550$		0			0
$551$	−15.4163			−0.656754
$552$		0			0
$553$	16.4093	+	13.3056i	0.697795	+	0.565812i
$554$		0			0
$555$	−28.3175	+	42.6991i	−1.20201	+	1.81248i
$556$		0			0
$557$	−8.23888	+	4.75672i	−0.349093	+	0.201549i	−0.664286	−	0.747479i	$-0.731264\pi$
$557$	−8.23888	+	4.75672i	−0.349093	+	0.201549i	0.315193	+	0.949028i	$0.397931\pi$
$558$		0			0
$559$			1.95968i			0.0828855i
$560$		0			0
$561$	−3.69894	−	2.45309i	−0.156169	−	0.103570i
$562$		0			0
$563$	−6.58667			−0.277595			−0.138798	−	0.990321i	$-0.544324\pi$
$563$	−6.58667			−0.277595			−0.138798	+	0.990321i	$0.544324\pi$
$564$		0			0
$565$		−	12.8664i		−	0.541293i
$566$		0			0
$567$	−23.6464	+	2.80101i	−0.993057	+	0.117631i
$568$		0			0
$569$		−	24.4094i		−	1.02330i	−0.859195	−	0.511648i	$-0.829035\pi$
$569$		−	24.4094i		−	1.02330i	0.859195	−	0.511648i	$-0.170965\pi$
$570$		0			0
$571$	23.3403			0.976762			0.488381	−	0.872630i	$-0.337588\pi$
$571$	23.3403			0.976762			0.488381	+	0.872630i	$0.337588\pi$
$572$		0			0
$573$	−20.0487	−	13.2961i	−0.837548	−	0.555452i
$574$		0			0
$575$			44.0560i			1.83726i
$576$		0			0
$577$	2.99702	−	1.73033i	0.124768	−	0.0720346i	−0.436317	−	0.899793i	$-0.643717\pi$
$577$	2.99702	−	1.73033i	0.124768	−	0.0720346i	0.561085	+	0.827758i	$0.310384\pi$
$578$		0			0
$579$	−18.6438	+	28.1124i	−0.774812	+	1.16831i
$580$		0			0
$581$	−4.04240	+	25.4161i	−0.167707	+	1.05444i
$582$		0			0
$583$	−39.5186			−1.63669
$584$		0			0
$585$	1.92673	−	0.813733i	0.0796603	−	0.0336437i
$586$		0			0
$587$	15.5563	+	26.9442i	0.642076	+	1.11211i	0.984969	+	0.172733i	$0.0552598\pi$
$587$	15.5563	+	26.9442i	0.642076	+	1.11211i	−0.342893	+	0.939374i	$0.611407\pi$
$588$		0			0
$589$	3.15341	−	5.46186i	0.129934	−	0.225052i
$590$		0			0
$591$	37.7950	+	25.0652i	1.55468	+	1.03104i
$592$		0			0
$593$	12.4614	−	21.5839i	0.511730	−	0.886343i	−0.488177	−	0.872745i	$-0.662338\pi$
$593$	12.4614	−	21.5839i	0.511730	−	0.886343i	0.999908	−	0.0135985i	$-0.00432865\pi$
$594$		0			0
$595$	4.59643	−	1.76099i	0.188435	−	0.0721935i
$596$		0			0
$597$	−0.0718677	+	1.15782i	−0.00294135	+	0.0473866i
$598$		0			0
$599$			16.7643i			0.684972i	0.939523	+	0.342486i	$0.111269\pi$
$599$			16.7643i			0.684972i	−0.939523	+	0.342486i	$0.888731\pi$
$600$		0			0
$601$	−4.25731	+	2.45796i	−0.173659	+	0.100262i	−0.584310	−	0.811530i	$-0.698635\pi$
$601$	−4.25731	+	2.45796i	−0.173659	+	0.100262i	0.410651	+	0.911793i	$0.365302\pi$
$602$		0			0
$603$	2.94678	+	6.97727i	0.120002	+	0.284136i
$604$		0			0
$605$	24.7028	−	42.7865i	1.00431	−	1.73952i
$606$		0			0
$607$	34.5704	−	19.9593i	1.40317	−	0.810121i	0.408454	−	0.912779i	$-0.366068\pi$
$607$	34.5704	−	19.9593i	1.40317	−	0.810121i	0.994717	+	0.102658i	$0.0327347\pi$
$608$		0			0
$609$	−24.4015	+	26.5467i	−0.988800	+	1.07573i
$610$		0			0
$611$	−1.93469	−	1.11700i	−0.0782693	−	0.0451888i
$612$		0			0
$613$	4.71228	+	8.16190i	0.190327	+	0.329656i	0.945359	−	0.326032i	$-0.105712\pi$
$613$	4.71228	+	8.16190i	0.190327	+	0.329656i	−0.755032	+	0.655688i	$0.772379\pi$
$614$		0			0
$615$	23.4665	−	35.3843i	0.946260	−	1.42683i
$616$		0			0
$617$	−16.7764	−	9.68589i	−0.675394	−	0.389939i	0.122723	−	0.992441i	$-0.460837\pi$
$617$	−16.7764	−	9.68589i	−0.675394	−	0.389939i	−0.798117	+	0.602502i	$0.794171\pi$
$618$		0			0
$619$	39.0961	+	22.5721i	1.57140	+	0.907250i	0.995997	+	0.0893829i	$0.0284895\pi$
$619$	39.0961	+	22.5721i	1.57140	+	0.907250i	0.575406	+	0.817868i	$0.304844\pi$
$620$		0			0
$621$	−26.9458	+	9.45972i	−1.08130	+	0.379605i
$622$		0			0
$623$	−21.8467	+	8.36994i	−0.875270	+	0.335335i
$624$		0			0
$625$	0.411737	+	0.713150i	0.0164695	+	0.0285260i
$626$		0			0
$627$	−16.8311	−	1.04473i	−0.672169	−	0.0417225i
$628$		0			0
$629$	4.22810			0.168586
$630$		0			0
$631$	29.0799			1.15765			0.578826	−	0.815451i	$-0.303511\pi$
$631$	29.0799			1.15765			0.578826	+	0.815451i	$0.303511\pi$
$632$		0			0
$633$	5.02084	+	10.0931i	0.199560	+	0.401165i
$634$		0			0
$635$	−27.3270	−	47.3318i	−1.08444	−	1.87830i
$636$		0			0
$637$	0.419671	−	1.28594i	0.0166280	−	0.0509509i
$638$		0			0
$639$	−38.3844	+	16.2112i	−1.51846	+	0.641307i
$640$		0			0
$641$	−0.283082	−	0.163438i	−0.0111811	−	0.00645540i	0.494399	−	0.869235i	$-0.335388\pi$
$641$	−0.283082	−	0.163438i	−0.0111811	−	0.00645540i	−0.505580	+	0.862780i	$0.668721\pi$
$642$		0			0
$643$	−28.5658	−	16.4925i	−1.12653	−	0.650401i	−0.183468	−	0.983026i	$-0.558732\pi$
$643$	−28.5658	−	16.4925i	−1.12653	−	0.650401i	−0.943059	+	0.332625i	$0.892066\pi$
$644$		0			0
$645$	28.2242	+	56.7376i	1.11133	+	2.23404i
$646$		0			0
$647$	2.78325	+	4.82074i	0.109421	+	0.189523i	0.915536	−	0.402236i	$-0.131767\pi$
$647$	2.78325	+	4.82074i	0.109421	+	0.189523i	−0.806115	+	0.591759i	$0.798434\pi$
$648$		0			0
$649$	−41.3864	−	23.8945i	−1.62456	−	0.937939i
$650$		0			0
$651$	−4.41395	−	14.0754i	−0.172996	−	0.551660i
$652$		0			0
$653$	−29.7096	+	17.1528i	−1.16262	+	0.671242i	−0.951932	−	0.306311i	$-0.900905\pi$
$653$	−29.7096	+	17.1528i	−1.16262	+	0.671242i	−0.210693	+	0.977552i	$0.567572\pi$
$654$		0			0
$655$	1.19431	−	2.06861i	0.0466657	−	0.0808274i
$656$		0			0
$657$	−15.1811	−	11.4830i	−0.592273	−	0.447993i
$658$		0			0
$659$	19.9447	−	11.5151i	0.776935	−	0.448564i	−0.0584078	−	0.998293i	$-0.518602\pi$
$659$	19.9447	−	11.5151i	0.776935	−	0.448564i	0.835343	+	0.549729i	$0.185269\pi$
$660$		0			0
$661$			49.6084i			1.92954i	0.263088	+	0.964772i	$0.415259\pi$
$661$			49.6084i			1.92954i	−0.263088	+	0.964772i	$0.584741\pi$
$662$		0			0
$663$	−0.143840	−	0.0953931i	−0.00558629	−	0.00370476i
$664$		0			0
$665$	11.7787	−	14.5262i	0.456757	−	0.563302i
$666$		0			0
$667$	−21.6225	+	37.4512i	−0.837226	+	1.45012i
$668$		0			0
$669$	−2.65748	+	42.8133i	−0.102744	+	1.65526i
$670$		0			0
$671$	1.72023	−	2.97953i	0.0664088	−	0.115023i
$672$		0			0
$673$	−19.7394	−	34.1896i	−0.760898	−	1.31791i	−0.942388	−	0.334521i	$-0.891426\pi$
$673$	−19.7394	−	34.1896i	−0.760898	−	1.31791i	0.181491	−	0.983393i	$-0.441908\pi$
$674$		0			0
$675$	27.1370	−	31.5992i	1.04451	−	1.21625i
$676$		0			0
$677$	13.2257			0.508304			0.254152	−	0.967164i	$-0.418204\pi$
$677$	13.2257			0.508304			0.254152	+	0.967164i	$0.418204\pi$
$678$		0			0
$679$	7.51664	+	1.19551i	0.288462	+	0.0458795i
$680$		0			0
$681$	−13.0099	−	26.1532i	−0.498542	−	1.00219i
$682$		0			0
$683$	13.6082	−	7.85669i	0.520703	−	0.300628i	−0.216519	−	0.976278i	$-0.569470\pi$
$683$	13.6082	−	7.85669i	0.520703	−	0.300628i	0.737222	+	0.675650i	$0.236137\pi$
$684$		0			0
$685$			11.0394i			0.421792i
$686$		0			0
$687$	−0.0953894	+	1.53677i	−0.00363933	+	0.0586314i
$688$		0			0
$689$	−1.53675			−0.0585457
$690$		0			0
$691$			25.2783i			0.961631i	0.876822	+	0.480815i	$0.159659\pi$
$691$			25.2783i			0.961631i	−0.876822	+	0.480815i	$0.840341\pi$
$692$		0			0
$693$	−28.4400	+	27.3294i	−1.08035	+	1.03816i
$694$		0			0
$695$			3.85049i			0.146058i
$696$		0			0
$697$	−3.50379			−0.132716
$698$		0			0
$699$	−32.1959	+	16.0159i	−1.21776	+	0.605777i
$700$		0			0
$701$		−	10.4870i		−	0.396089i	−0.980193	−	0.198044i	$-0.936541\pi$
$701$		−	10.4870i		−	0.396089i	0.980193	−	0.198044i	$-0.0634590\pi$
$702$		0			0
$703$	13.9121	−	8.03216i	0.524705	−	0.302939i
$704$		0			0
$705$	−72.1017	−	4.47545i	−2.71551	−	0.168555i
$706$		0			0
$707$	3.02331	−	1.15830i	0.113703	−	0.0435622i
$708$		0			0
$709$	−13.6978			−0.514432			−0.257216	−	0.966354i	$-0.582805\pi$
$709$	−13.6978			−0.514432			−0.257216	+	0.966354i	$0.582805\pi$
$710$		0			0
$711$	−9.31985	−	22.0672i	−0.349522	−	0.827585i
$712$		0			0
$713$	−8.84579	−	15.3214i	−0.331278	−	0.573790i
$714$		0			0
$715$	1.73224	−	3.00032i	0.0647820	−	0.112206i
$716$		0			0
$717$	26.0753	−	12.9712i	0.973800	−	0.484418i
$718$		0			0
$719$	16.8349	−	29.1589i	0.627836	−	1.08744i	−0.360149	−	0.932895i	$-0.617274\pi$
$719$	16.8349	−	29.1589i	0.627836	−	1.08744i	0.987985	−	0.154550i	$-0.0493927\pi$
$720$		0			0
$721$	3.69406	+	0.587534i	0.137574	+	0.0218809i
$722$		0			0
$723$	−25.5538	+	12.7118i	−0.950356	+	0.472756i
$724$		0			0
$725$		−	63.0737i		−	2.34250i
$726$		0			0
$727$	26.1600	−	15.1035i	0.970219	−	0.560156i	0.0709160	−	0.997482i	$-0.477408\pi$
$727$	26.1600	−	15.1035i	0.970219	−	0.560156i	0.899303	+	0.437326i	$0.144074\pi$
$728$		0			0
$729$	25.1537	+	9.81271i	0.931620	+	0.363434i
$730$		0			0
$731$	2.61473	−	4.52885i	0.0967093	−	0.167505i
$732$		0			0
$733$	15.6089	−	9.01178i	0.576526	−	0.332858i	−0.183225	−	0.983071i	$-0.558654\pi$
$733$	15.6089	−	9.01178i	0.576526	−	0.332858i	0.759752	+	0.650213i	$0.225320\pi$
$734$		0			0
$735$	−6.37025	−	43.2756i	−0.234970	−	1.59624i
$736$		0			0
$737$	10.8651	+	6.27297i	0.400221	+	0.231068i
$738$		0			0
$739$	−18.2362	−	31.5859i	−0.670828	−	1.16191i	−0.977670	−	0.210147i	$-0.932606\pi$
$739$	−18.2362	−	31.5859i	−0.670828	−	1.16191i	0.306842	−	0.951760i	$-0.400728\pi$
$740$		0			0
$741$	−0.654509	−	0.0406262i	−0.0240440	−	0.00149244i
$742$		0			0
$743$	−3.55209	−	2.05080i	−0.130314	−	0.0752366i	0.433426	−	0.901189i	$-0.357305\pi$
$743$	−3.55209	−	2.05080i	−0.130314	−	0.0752366i	−0.563740	+	0.825953i	$0.690638\pi$
$744$		0			0
$745$	2.62085	+	1.51315i	0.0960204	+	0.0554374i
$746$		0			0
$747$	17.6040	−	23.2735i	0.644096	−	0.851532i
$748$		0			0
$749$	−3.00023	−	7.83102i	−0.109626	−	0.286139i
$750$		0			0
$751$	3.57947	+	6.19982i	0.130617	+	0.226235i	0.923914	−	0.382599i	$-0.124971\pi$
$751$	3.57947	+	6.19982i	0.130617	+	0.226235i	−0.793298	+	0.608834i	$0.791638\pi$
$752$		0			0
$753$	22.9583	−	34.6181i	0.836648	−	1.26155i
$754$		0			0
$755$	−23.5422			−0.856787
$756$		0			0
$757$	5.91414			0.214953			0.107477	−	0.994208i	$-0.465723\pi$
$757$	5.91414			0.214953			0.107477	+	0.994208i	$0.465723\pi$
$758$		0			0
$759$	−26.1449	+	39.4231i	−0.949000	+	1.43097i
$760$		0			0
$761$	8.49258	+	14.7096i	0.307856	+	0.533222i	0.977893	−	0.209106i	$-0.0670552\pi$
$761$	8.49258	+	14.7096i	0.307856	+	0.533222i	−0.670037	+	0.742327i	$0.733722\pi$
$762$		0			0
$763$	−8.26936	+	51.9927i	−0.299371	+	1.88226i
$764$		0			0
$765$	−5.53843	−	0.690215i	−0.200242	−	0.0249548i
$766$		0			0
$767$	−1.60939	−	0.929181i	−0.0581116	−	0.0335508i
$768$		0			0
$769$	18.8525	+	10.8845i	0.679838	+	0.392505i	0.799794	−	0.600274i	$-0.204942\pi$
$769$	18.8525	+	10.8845i	0.679838	+	0.392505i	−0.119956	+	0.992779i	$0.538275\pi$
$770$		0			0
$771$	5.70825	+	0.354319i	0.205578	+	0.0127605i
$772$		0			0
$773$	5.78476	+	10.0195i	0.208063	+	0.360376i	0.951104	−	0.308870i	$-0.0999507\pi$
$773$	5.78476	+	10.0195i	0.208063	+	0.360376i	−0.743041	+	0.669246i	$0.766617\pi$
$774$		0			0
$775$	22.3465	+	12.9018i	0.802711	+	0.463446i
$776$		0			0
$777$	8.18937	−	36.6703i	0.293792	−	1.31554i
$778$		0			0
$779$	−11.5288	+	6.65617i	−0.413063	+	0.238482i
$780$		0			0
$781$	−34.5097	+	59.7726i	−1.23486	+	2.13883i
$782$		0			0
$783$	38.5775	−	13.5432i	1.37865	−	0.483995i
$784$		0			0
$785$	30.2360	−	17.4567i	1.07917	−	0.623058i
$786$		0			0
$787$		−	41.3722i		−	1.47476i	−0.675478	−	0.737380i	$-0.736063\pi$
$787$		−	41.3722i		−	1.47476i	0.675478	−	0.737380i	$-0.263937\pi$
$788$		0			0
$789$	−7.19592	+	3.57962i	−0.256181	+	0.127438i
$790$		0			0
$791$	3.37569	+	8.81101i	0.120026	+	0.313284i
$792$		0			0
$793$	0.0668944	−	0.115865i	0.00237549	−	0.00411447i
$794$		0			0
$795$	−44.4929	+	22.1331i	−1.57800	+	0.784979i
$796$		0			0
$797$	2.87203	−	4.97451i	0.101733	−	0.176206i	−0.810666	−	0.585509i	$-0.800895\pi$
$797$	2.87203	−	4.97451i	0.101733	−	0.176206i	0.912399	+	0.409303i	$0.134228\pi$
$798$		0			0
$799$	2.98074	+	5.16279i	0.105451	+	0.182646i
$800$		0			0
$801$	26.3240	+	3.28057i	0.930114	+	0.115913i
$802$		0			0
$803$	−31.5301			−1.11267
$804$		0			0
$805$	−18.7685	−	48.9885i	−0.661504	−	1.72662i
$806$		0			0
$807$	−18.8024	−	1.16709i	−0.661877	−	0.0410836i
$808$		0			0
$809$	20.0144	−	11.5553i	0.703667	−	0.406263i	−0.105045	−	0.994468i	$-0.533499\pi$
$809$	20.0144	−	11.5553i	0.703667	−	0.406263i	0.808712	+	0.588205i	$0.200165\pi$
$810$		0			0
$811$		−	26.7952i		−	0.940906i	−0.882425	−	0.470453i	$-0.844091\pi$
$811$		−	26.7952i		−	0.940906i	0.882425	−	0.470453i	$-0.155909\pi$
$812$		0			0
$813$	−6.61914	+	3.29270i	−0.232143	+	0.115480i
$814$		0			0
$815$	21.5031			0.753222
$816$		0			0
$817$		−	19.8689i		−	0.695124i
$818$		0			0
$819$	−1.10594	+	1.06276i	−0.0386448	+	0.0371357i
$820$		0			0
$821$		−	37.9622i		−	1.32489i	−0.749111	−	0.662444i	$-0.769519\pi$
$821$		−	37.9622i		−	1.32489i	0.749111	−	0.662444i	$-0.230481\pi$
$822$		0			0
$823$	12.3810			0.431576			0.215788	−	0.976440i	$-0.430768\pi$
$823$	12.3810			0.431576			0.215788	+	0.976440i	$0.430768\pi$
$824$		0			0
$825$	4.27438	−	68.8624i	0.148815	−	2.39748i
$826$		0			0
$827$			3.64308i			0.126682i	0.997992	+	0.0633412i	$0.0201756\pi$
$827$			3.64308i			0.126682i	−0.997992	+	0.0633412i	$0.979824\pi$
$828$		0			0
$829$	30.6504	−	17.6960i	1.06453	−	0.614607i	0.137849	−	0.990453i	$-0.455981\pi$
$829$	30.6504	−	17.6960i	1.06453	−	0.614607i	0.926682	+	0.375846i	$0.122648\pi$
$830$		0			0
$831$	−16.5289	−	33.2271i	−0.573380	−	1.15263i
$832$		0			0
$833$	−2.68565	+	2.41188i	−0.0930524	+	0.0835668i
$834$		0			0
$835$	45.1142			1.56124
$836$		0			0
$837$	−3.09280	+	16.4380i	−0.106903	+	0.568180i
$838$		0			0
$839$	−9.18501	−	15.9089i	−0.317102	−	0.549236i	0.662780	−	0.748814i	$-0.269376\pi$
$839$	−9.18501	−	15.9089i	−0.317102	−	0.549236i	−0.979882	+	0.199578i	$0.936043\pi$
$840$		0			0
$841$	16.4563	−	28.5031i	0.567458	−	0.982867i
$842$		0			0
$843$	−1.24062	+	19.9870i	−0.0427293	+	0.688390i
$844$		0			0
$845$	−23.3832	+	40.5008i	−0.804405	+	1.39327i
$846$		0			0
$847$	−5.69103	+	35.7817i	−0.195546	+	1.22947i
$848$		0			0
$849$	21.9250	+	14.5404i	0.752466	+	0.499026i
$850$		0			0
$851$		−	45.0629i		−	1.54474i
$852$		0			0
$853$	−30.7835	+	17.7728i	−1.05401	+	0.608531i	−0.923768	−	0.382952i	$-0.874907\pi$
$853$	−30.7835	+	17.7728i	−1.05401	+	0.608531i	−0.130238	+	0.991483i	$0.541574\pi$
$854$		0			0
$855$	−19.5348	+	8.25032i	−0.668076	+	0.282155i
$856$		0			0
$857$	−13.7151	+	23.7553i	−0.468500	+	0.811466i	−0.999352	−	0.0359989i	$-0.988539\pi$
$857$	−13.7151	+	23.7553i	−0.468500	+	0.811466i	0.530852	+	0.847465i	$0.321872\pi$
$858$		0			0
$859$	−22.8158	+	13.1727i	−0.778465	+	0.449447i	−0.835886	−	0.548903i	$-0.815046\pi$
$859$	−22.8158	+	13.1727i	−0.778465	+	0.449447i	0.0574212	+	0.998350i	$0.481712\pi$
$860$		0			0
$861$	−6.78645	+	30.3883i	−0.231282	+	1.03563i
$862$		0			0
$863$	−16.7057	−	9.64502i	−0.568668	−	0.328320i	0.187949	−	0.982179i	$-0.439816\pi$
$863$	−16.7057	−	9.64502i	−0.568668	−	0.328320i	−0.756617	+	0.653858i	$0.773149\pi$
$864$		0			0
$865$	−17.9225	−	31.0426i	−0.609382	−	1.05548i
$866$		0			0
$867$	−12.9092	−	25.9507i	−0.438421	−	0.881333i
$868$		0			0
$869$	−34.3633	−	19.8397i	−1.16570	−	0.673015i
$870$		0			0
$871$	0.422510	+	0.243936i	0.0143162	+	0.00826546i
$872$		0			0
$873$	−6.88297	−	5.20626i	−0.232953	−	0.176205i
$874$		0			0
$875$	22.3613	+	18.1318i	0.755951	+	0.612968i
$876$		0			0
$877$	−1.03512	−	1.79288i	−0.0349535	−	0.0605413i	0.848019	−	0.529965i	$-0.177795\pi$
$877$	−1.03512	−	1.79288i	−0.0349535	−	0.0605413i	−0.882973	+	0.469424i	$0.844462\pi$
$878$		0			0
$879$	14.5268	+	29.2024i	0.489977	+	0.984973i
$880$		0			0
$881$	51.2438			1.72645			0.863224	−	0.504822i	$-0.168442\pi$
$881$	51.2438			1.72645			0.863224	+	0.504822i	$0.168442\pi$
$882$		0			0
$883$	−17.3129			−0.582626			−0.291313	−	0.956628i	$-0.594092\pi$
$883$	−17.3129			−0.582626			−0.291313	+	0.956628i	$0.594092\pi$
$884$		0			0
$885$	−59.9783	−	3.72293i	−2.01615	−	0.125145i
$886$		0			0
$887$	−12.7982	−	22.1672i	−0.429723	−	0.744302i	0.567125	−	0.823631i	$-0.308055\pi$
$887$	−12.7982	−	22.1672i	−0.429723	−	0.744302i	−0.996848	+	0.0793293i	$0.974722\pi$
$888$		0			0
$889$	31.1320	+	25.2436i	1.04413	+	0.846642i
$890$		0			0
$891$	43.0358	−	12.1718i	1.44175	−	0.407772i
$892$		0			0
$893$	19.6156	+	11.3251i	0.656410	+	0.378979i
$894$		0			0
$895$	9.43944	+	5.44987i	0.315526	+	0.182169i
$896$		0			0
$897$	−1.01669	+	1.53304i	−0.0339464	+	0.0511867i
$898$		0			0
$899$	12.6643	+	21.9352i	0.422377	+	0.731578i
$900$		0			0
$901$	3.55146	+	2.05044i	0.118316	+	0.0683100i
$902$		0			0
$903$	−34.2141	−	31.4494i	−1.13858	−	1.04657i
$904$		0			0
$905$	−42.7587	+	24.6868i	−1.42135	+	0.820616i
$906$		0			0
$907$	−20.2723	+	35.1127i	−0.673132	+	1.16590i	0.303880	+	0.952710i	$0.401718\pi$
$907$	−20.2723	+	35.1127i	−0.673132	+	1.16590i	−0.977011	+	0.213188i	$0.931615\pi$
$908$		0			0
$909$	−3.64292	−	0.453991i	−0.120828	−	0.0150579i
$910$		0			0
$911$	−33.7855	+	19.5061i	−1.11936	+	0.646265i	−0.941238	−	0.337743i	$-0.890336\pi$
$911$	−33.7855	+	19.5061i	−1.11936	+	0.646265i	−0.178125	+	0.984008i	$0.557003\pi$
$912$		0			0
$913$		−	48.3373i		−	1.59973i
$914$		0			0
$915$	0.268025	−	4.31801i	0.00886063	−	0.142749i
$916$		0			0
$917$	−0.275146	+	1.72995i	−0.00908611	+	0.0571280i
$918$		0			0
$919$	2.62491	−	4.54648i	0.0865878	−	0.149975i	−0.819479	−	0.573109i	$-0.805737\pi$
$919$	2.62491	−	4.54648i	0.0865878	−	0.149975i	0.906067	+	0.423135i	$0.139070\pi$
$920$		0			0
$921$	9.57314	+	6.34879i	0.315446	+	0.209200i
$922$		0			0
$923$	−1.34198	+	2.32437i	−0.0441717	+	0.0765076i
$924$		0			0
$925$	32.8626	+	56.9197i	1.08052	+	1.87151i
$926$		0			0
$927$	−3.38264	−	2.55862i	−0.111101	−	0.0840360i
$928$		0			0
$929$	−35.7977			−1.17449			−0.587243	−	0.809411i	$-0.699787\pi$
$929$	−35.7977			−1.17449			−0.587243	+	0.809411i	$0.699787\pi$
$930$		0			0
$931$	−4.25498	+	13.0380i	−0.139451	+	0.427303i
$932$		0			0
$933$	11.2801	−	17.0089i	0.369294	−	0.556847i
$934$		0			0
$935$	−8.00645	+	4.62253i	−0.261839	+	0.151173i
$936$		0			0
$937$			53.7334i			1.75540i	0.479215	+	0.877698i	$0.340921\pi$
$937$			53.7334i			1.75540i	−0.479215	+	0.877698i	$0.659079\pi$
$938$		0			0
$939$	−40.7642	−	27.0343i	−1.33029	−	0.882232i
$940$		0			0
$941$	35.4300			1.15498			0.577492	−	0.816396i	$-0.304031\pi$
$941$	35.4300			1.15498			0.577492	+	0.816396i	$0.304031\pi$
$942$		0			0
$943$			37.3432i			1.21606i
$944$		0			0
$945$	−16.7135	+	46.6978i	−0.543692	+	1.51908i
$946$		0			0
$947$		−	26.3688i		−	0.856871i	−0.903572	−	0.428435i	$-0.859065\pi$
$947$		−	26.3688i		−	0.856871i	0.903572	−	0.428435i	$-0.140935\pi$
$948$		0			0
$949$	−1.22611			−0.0398012
$950$		0			0
$951$	−4.46218	−	2.95926i	−0.144696	−	0.0959607i
$952$		0			0
$953$		−	5.92765i		−	0.192015i	−0.995381	−	0.0960076i	$-0.969393\pi$
$953$		−	5.92765i		−	0.192015i	0.995381	−	0.0960076i	$-0.0306073\pi$
$954$		0			0
$955$	−43.3961	+	25.0547i	−1.40426	+	0.810752i
$956$		0			0
$957$	37.4309	−	56.4409i	1.20997	−	1.82447i
$958$		0			0
$959$	−2.89634	−	7.55985i	−0.0935277	−	0.244120i
$960$		0			0
$961$	20.6381			0.665744
$962$		0			0
$963$	−1.17593	+	9.43592i	−0.0378939	+	0.304068i
$964$		0			0
$965$	35.1319	+	60.8502i	1.13093	+	1.95884i
$966$		0			0
$967$	−21.9191	+	37.9649i	−0.704869	+	1.22087i	0.261870	+	0.965103i	$0.415661\pi$
$967$	−21.9191	+	37.9649i	−0.704869	+	1.22087i	−0.966739	+	0.255766i	$0.917672\pi$
$968$		0			0
$969$	1.45837	+	0.967176i	0.0468497	+	0.0310702i
$970$		0			0
$971$	−8.84354	+	15.3175i	−0.283803	+	0.491561i	−0.972318	−	0.233661i	$-0.924929\pi$
$971$	−8.84354	+	15.3175i	−0.283803	+	0.491561i	0.688515	+	0.725222i	$0.258263\pi$
$972$		0			0
$973$	−1.01023	−	2.63685i	−0.0323866	−	0.0845336i
$974$		0			0
$975$	0.166217	−	2.67784i	0.00532321	−	0.0857596i
$976$		0			0
$977$		−	44.4914i		−	1.42341i	−0.702480	−	0.711704i	$-0.747924\pi$
$977$		−	44.4914i		−	1.42341i	0.702480	−	0.711704i	$-0.252076\pi$
$978$		0			0
$979$	38.0545	−	21.9708i	1.21623	−	0.702189i
$980$		0			0
$981$	36.0117	−	47.6096i	1.14977	−	1.52006i
$982$		0			0
$983$	7.29121	−	12.6288i	0.232554	−	0.402795i	−0.726005	−	0.687689i	$-0.758625\pi$
$983$	7.29121	−	12.6288i	0.232554	−	0.402795i	0.958559	+	0.284894i	$0.0919586\pi$
$984$		0			0
$985$	81.8082	−	47.2320i	2.60663	−	1.50494i
$986$		0			0
$987$	50.5501	−	15.8521i	1.60903	−	0.504579i
$988$		0			0
$989$	−48.2682	−	27.8676i	−1.53484	−	0.886140i
$990$		0			0
$991$	−5.58041	−	9.66556i	−0.177268	−	0.307037i	0.763676	−	0.645600i	$-0.223392\pi$
$991$	−5.58041	−	9.66556i	−0.177268	−	0.307037i	−0.940944	+	0.338563i	$0.890059\pi$
$992$		0			0
$993$	−0.0659323	+	0.0994172i	−0.00209230	+	0.00315491i
$994$		0			0
$995$	2.09260	+	1.20816i	0.0663399	+	0.0383014i
$996$		0			0
$997$	−48.0254	−	27.7275i	−1.52098	−	0.878138i	−0.999694	−	0.0247555i	$-0.992119\pi$
$997$	−48.0254	−	27.7275i	−1.52098	−	0.878138i	−0.521286	−	0.853382i	$-0.674547\pi$
$998$		0			0
$999$	−27.7572	+	32.3214i	−0.878200	+	1.02260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.18	✓	48
3.2	odd	2		1512.2.bs.a.1097.22		48
4.3	odd	2		1008.2.ca.e.257.7		48
7.3	odd	6		504.2.cx.a.185.23	yes	48
9.2	odd	6		504.2.cx.a.425.23	yes	48
9.7	even	3		1512.2.cx.a.89.22		48
12.11	even	2		3024.2.ca.e.2609.22		48
21.17	even	6		1512.2.cx.a.17.22		48
28.3	even	6		1008.2.df.e.689.2		48
36.7	odd	6		3024.2.df.e.1601.22		48
36.11	even	6		1008.2.df.e.929.2		48
63.38	even	6	inner	504.2.bs.a.353.18	yes	48
63.52	odd	6		1512.2.bs.a.521.22		48
84.59	odd	6		3024.2.df.e.17.22		48
252.115	even	6		3024.2.ca.e.2033.22		48
252.227	odd	6		1008.2.ca.e.353.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.18	✓	48	1.1	even	1	trivial
504.2.bs.a.353.18	yes	48	63.38	even	6	inner
504.2.cx.a.185.23	yes	48	7.3	odd	6
504.2.cx.a.425.23	yes	48	9.2	odd	6
1008.2.ca.e.257.7		48	4.3	odd	2
1008.2.ca.e.353.7		48	252.227	odd	6
1008.2.df.e.689.2		48	28.3	even	6
1008.2.df.e.929.2		48	36.11	even	6
1512.2.bs.a.521.22		48	63.52	odd	6
1512.2.bs.a.1097.22		48	3.2	odd	2
1512.2.cx.a.17.22		48	21.17	even	6
1512.2.cx.a.89.22		48	9.7	even	3
3024.2.ca.e.2033.22		48	252.115	even	6
3024.2.ca.e.2609.22		48	12.11	even	2
3024.2.df.e.17.22		48	84.59	odd	6
3024.2.df.e.1601.22		48	36.7	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.957290 - 1.44347i) q^{3} +(-1.80389 - 3.12442i) q^{5} +(2.05506 + 1.66636i) q^{7} +(-1.16719 - 2.76363i) q^{9} +O(q^{10})\)	\(q+(0.957290 - 1.44347i) q^{3} +(-1.80389 - 3.12442i) q^{5} +(2.05506 + 1.66636i) q^{7} +(-1.16719 - 2.76363i) q^{9} +(-4.30356 - 2.48466i) q^{11} +(-0.167352 - 0.0966208i) q^{13} +(-6.23684 - 0.387129i) q^{15} +(0.257836 + 0.446584i) q^{17} +(1.69676 + 0.979624i) q^{19} +(4.37261 - 1.37122i) q^{21} +(4.75967 - 2.74800i) q^{23} +(-4.00801 + 6.94208i) q^{25} +(-5.10655 - 0.960796i) q^{27} +(-6.81428 + 3.93423i) q^{29} -3.21900i q^{31} +(-7.70629 + 3.83351i) q^{33} +(1.49931 - 9.42678i) q^{35} +(4.09961 - 7.10074i) q^{37} +(-0.299673 + 0.149073i) q^{39} +(-3.39731 + 5.88431i) q^{41} +(-5.07054 - 8.78243i) q^{43} +(-6.52928 + 8.63208i) q^{45} +11.5606 q^{47} +(1.44651 + 6.84891i) q^{49} +(0.891453 + 0.0553337i) q^{51} +(6.88707 - 3.97625i) q^{53} +17.9282i q^{55} +(3.03834 - 1.51143i) q^{57} +9.61678 q^{59} +0.692340i q^{61} +(2.20655 - 7.62438i) q^{63} +0.697172i q^{65} -2.52467 q^{67} +(0.589743 - 9.50105i) q^{69} -13.8891i q^{71} +(5.49489 - 3.17248i) q^{73} +(6.18383 + 12.4310i) q^{75} +(-4.70373 - 12.2774i) q^{77} +7.98485 q^{79} +(-6.27533 + 6.45138i) q^{81} +(4.86357 + 8.42395i) q^{83} +(0.930212 - 1.61117i) q^{85} +(-0.844318 + 13.6024i) q^{87} +(-4.42128 + 7.65787i) q^{89} +(-0.182913 - 0.477429i) q^{91} +(-4.64651 - 3.08151i) q^{93} -7.06852i q^{95} +(2.49132 - 1.43837i) q^{97} +(-1.84361 + 14.7935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

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