LMFDB - Embedded newform 1224.2.h.c.611.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(611,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1224.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			611.18
Character	$\chi$	$=$	1224.611
Dual form			1224.2.h.c.611.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933778 - 1.06210i) q^{2} +(-0.256118 + 1.98353i) q^{4} -3.62179i q^{5} +1.18114 q^{7} +(2.34587 - 1.58016i) q^{8} +O(q^{10})$	\(q+(-0.933778 - 1.06210i) q^{2} +(-0.256118 + 1.98353i) q^{4} -3.62179i q^{5} +1.18114 q^{7} +(2.34587 - 1.58016i) q^{8} +(-3.84671 + 3.38195i) q^{10} -5.34326 q^{11} +6.66295i q^{13} +(-1.10292 - 1.25449i) q^{14} +(-3.86881 - 1.01604i) q^{16} +(-1.54823 + 3.82139i) q^{17} +0.692491 q^{19} +(7.18395 + 0.927607i) q^{20} +(4.98942 + 5.67509i) q^{22} +5.64119i q^{23} -8.11740 q^{25} +(7.07673 - 6.22172i) q^{26} +(-0.302511 + 2.34283i) q^{28} +1.90843i q^{29} +8.08929 q^{31} +(2.53347 + 5.05782i) q^{32} +(5.50440 - 1.92395i) q^{34} -4.27785i q^{35} -8.32659 q^{37} +(-0.646633 - 0.735496i) q^{38} +(-5.72300 - 8.49626i) q^{40} -3.42928 q^{41} -6.89610 q^{43} +(1.36851 - 10.5985i) q^{44} +(5.99151 - 5.26762i) q^{46} +9.04763 q^{47} -5.60491 q^{49} +(7.57985 + 8.62150i) q^{50} +(-13.2162 - 1.70650i) q^{52} -6.65539 q^{53} +19.3522i q^{55} +(2.77080 - 1.86639i) q^{56} +(2.02695 - 1.78205i) q^{58} +1.66078i q^{59} +4.88629 q^{61} +(-7.55360 - 8.59165i) q^{62} +(3.00622 - 7.41368i) q^{64} +24.1318 q^{65} +8.55229 q^{67} +(-7.18332 - 4.04969i) q^{68} +(-4.54351 + 3.99456i) q^{70} -1.73403i q^{71} -8.99143i q^{73} +(7.77519 + 8.84368i) q^{74} +(-0.177360 + 1.37358i) q^{76} -6.31114 q^{77} +6.44027 q^{79} +(-3.67988 + 14.0120i) q^{80} +(3.20219 + 3.64224i) q^{82} +11.3835i q^{83} +(13.8403 + 5.60736i) q^{85} +(6.43942 + 7.32435i) q^{86} +(-12.5346 + 8.44319i) q^{88} +8.13825i q^{89} +7.86988i q^{91} +(-11.1895 - 1.44481i) q^{92} +(-8.44848 - 9.60950i) q^{94} -2.50806i q^{95} +6.89086i q^{97} +(5.23374 + 5.95298i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 24 q^{4}+O(q^{10}) $ 56 * q + 24 * q^4	$ 56 q + 24 q^{4} - 56 q^{16} - 32 q^{19} + 8 q^{25} - 4 q^{34} - 40 q^{49} - 56 q^{52} + 72 q^{64} - 56 q^{70} + 8 q^{76} - 40 q^{94}+O(q^{100}) $ 56 * q + 24 * q^4 - 56 * q^16 - 32 * q^19 + 8 * q^25 - 4 * q^34 - 40 * q^49 - 56 * q^52 + 72 * q^64 - 56 * q^70 + 8 * q^76 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.933778	−	1.06210i	−0.660281	−	0.751019i
$2$	−0.933778	−	1.06210i	−0.660281	−	0.751019i
$3$		0			0
$3$		0			0
$4$	−0.256118	+	1.98353i	−0.128059	+	0.991767i
$5$		−	3.62179i		−	1.61972i	−0.586626	−	0.809858i	$-0.699544\pi$
$5$		−	3.62179i		−	1.61972i	0.586626	−	0.809858i	$-0.300456\pi$
$6$		0			0
$7$	1.18114			0.446429			0.223215	−	0.974769i	$-0.428345\pi$
$7$	1.18114			0.446429			0.223215	+	0.974769i	$0.428345\pi$
$8$	2.34587	−	1.58016i	0.829390	−	0.558669i
$9$		0			0
$10$	−3.84671	+	3.38195i	−1.21644	+	1.06947i
$11$	−5.34326			−1.61105			−0.805527	−	0.592559i	$-0.798118\pi$
$11$	−5.34326			−1.61105			−0.805527	+	0.592559i	$0.798118\pi$
$12$		0			0
$13$			6.66295i			1.84797i	0.382428	+	0.923985i	$0.375088\pi$
$13$			6.66295i			1.84797i	−0.382428	+	0.923985i	$0.624912\pi$
$14$	−1.10292	−	1.25449i	−0.294768	−	0.335277i
$15$		0			0
$16$	−3.86881	−	1.01604i	−0.967202	−	0.254009i
$17$	−1.54823	+	3.82139i	−0.375500	+	0.926822i
$17$	−1.54823	+	3.82139i	−0.375500	+	0.926822i
$18$		0			0
$19$	0.692491			0.158868			0.0794342	−	0.996840i	$-0.474689\pi$
$19$	0.692491			0.158868			0.0794342	+	0.996840i	$0.474689\pi$
$20$	7.18395	+	0.927607i	1.60638	+	0.207419i
$21$		0			0
$22$	4.98942	+	5.67509i	1.06375	+	1.20993i
$23$			5.64119i			1.17627i	0.808763	+	0.588134i	$0.200137\pi$
$23$			5.64119i			1.17627i	−0.808763	+	0.588134i	$0.799863\pi$
$24$		0			0
$25$	−8.11740			−1.62348
$26$	7.07673	−	6.22172i	1.38786	−	1.22018i
$27$		0			0
$28$	−0.302511	+	2.34283i	−0.0571693	+	0.442753i
$29$			1.90843i			0.354387i	0.984176	+	0.177194i	$0.0567019\pi$
$29$			1.90843i			0.354387i	−0.984176	+	0.177194i	$0.943298\pi$
$30$		0			0
$31$	8.08929			1.45288			0.726440	−	0.687230i	$-0.241173\pi$
$31$	8.08929			1.45288			0.726440	+	0.687230i	$0.241173\pi$
$32$	2.53347	+	5.05782i	0.447859	+	0.894104i
$33$		0			0
$34$	5.50440	−	1.92395i	0.943997	−	0.329955i
$35$		−	4.27785i		−	0.723088i
$36$		0			0
$37$	−8.32659			−1.36888			−0.684442	−	0.729068i	$-0.739954\pi$
$37$	−8.32659			−1.36888			−0.684442	+	0.729068i	$0.739954\pi$
$38$	−0.646633	−	0.735496i	−0.104898	−	0.119313i
$39$		0			0
$40$	−5.72300	−	8.49626i	−0.904886	−	1.34338i
$41$	−3.42928			−0.535564			−0.267782	−	0.963480i	$-0.586291\pi$
$41$	−3.42928			−0.535564			−0.267782	+	0.963480i	$0.586291\pi$
$42$		0			0
$43$	−6.89610			−1.05164			−0.525822	−	0.850594i	$-0.676242\pi$
$43$	−6.89610			−1.05164			−0.525822	+	0.850594i	$0.676242\pi$
$44$	1.36851	−	10.5985i	0.206310	−	1.59779i
$45$		0			0
$46$	5.99151	−	5.26762i	0.883400	−	0.776668i
$47$	9.04763			1.31973			0.659867	−	0.751383i	$-0.270613\pi$
$47$	9.04763			1.31973			0.659867	+	0.751383i	$0.270613\pi$
$48$		0			0
$49$	−5.60491			−0.800701
$50$	7.57985	+	8.62150i	1.07195	+	1.21926i
$51$		0			0
$52$	−13.2162	−	1.70650i	−1.83276	−	0.236649i
$53$	−6.65539			−0.914188			−0.457094	−	0.889418i	$-0.651110\pi$
$53$	−6.65539			−0.914188			−0.457094	+	0.889418i	$0.651110\pi$
$54$		0			0
$55$			19.3522i			2.60945i
$56$	2.77080	−	1.86639i	0.370264	−	0.249406i
$57$		0			0
$58$	2.02695	−	1.78205i	0.266152	−	0.233995i
$59$			1.66078i			0.216214i	0.994139	+	0.108107i	$0.0344790\pi$
$59$			1.66078i			0.216214i	−0.994139	+	0.108107i	$0.965521\pi$
$60$		0			0
$61$	4.88629			0.625626			0.312813	−	0.949815i	$-0.398729\pi$
$61$	4.88629			0.625626			0.312813	+	0.949815i	$0.398729\pi$
$62$	−7.55360	−	8.59165i	−0.959309	−	1.09114i
$63$		0			0
$64$	3.00622	−	7.41368i	0.375777	−	0.926710i
$65$	24.1318			2.99319
$66$		0			0
$67$	8.55229			1.04483			0.522415	−	0.852692i	$-0.325031\pi$
$67$	8.55229			1.04483			0.522415	+	0.852692i	$0.325031\pi$
$68$	−7.18332	−	4.04969i	−0.871105	−	0.491097i
$69$		0			0
$70$	−4.54351	+	3.99456i	−0.543053	+	0.477441i
$71$		−	1.73403i		−	0.205791i	−0.994692	−	0.102896i	$-0.967189\pi$
$71$		−	1.73403i		−	0.205791i	0.994692	−	0.102896i	$-0.0328108\pi$
$72$		0			0
$73$		−	8.99143i		−	1.05237i	−0.850371	−	0.526184i	$-0.823622\pi$
$73$		−	8.99143i		−	1.05237i	0.850371	−	0.526184i	$-0.176378\pi$
$74$	7.77519	+	8.84368i	0.903847	+	1.02806i
$75$		0			0
$76$	−0.177360	+	1.37358i	−0.0203445	+	0.157560i
$77$	−6.31114			−0.719222
$78$		0			0
$79$	6.44027			0.724587			0.362294	−	0.932064i	$-0.381994\pi$
$79$	6.44027			0.724587			0.362294	+	0.932064i	$0.381994\pi$
$80$	−3.67988	+	14.0120i	−0.411423	+	1.56659i
$81$		0			0
$82$	3.20219	+	3.64224i	0.353622	+	0.402219i
$83$			11.3835i			1.24950i	0.780823	+	0.624752i	$0.214800\pi$
$83$			11.3835i			1.24950i	−0.780823	+	0.624752i	$0.785200\pi$
$84$		0			0
$85$	13.8403	+	5.60736i	1.50119	+	0.608204i
$86$	6.43942	+	7.32435i	0.694381	+	0.789805i
$87$		0			0
$88$	−12.5346	+	8.44319i	−1.33619	+	0.900047i
$89$			8.13825i			0.862653i	0.902196	+	0.431326i	$0.141954\pi$
$89$			8.13825i			0.862653i	−0.902196	+	0.431326i	$0.858046\pi$
$90$		0			0
$91$			7.86988i			0.824988i
$92$	−11.1895	−	1.44481i	−1.16658	−	0.150632i
$93$		0			0
$94$	−8.44848	−	9.60950i	−0.871394	−	0.991145i
$95$		−	2.50806i		−	0.257322i
$96$		0			0
$97$			6.89086i			0.699661i	0.936813	+	0.349831i	$0.113761\pi$
$97$			6.89086i			0.699661i	−0.936813	+	0.349831i	$0.886239\pi$
$98$	5.23374	+	5.95298i	0.528687	+	0.601342i
$99$		0			0
$100$	2.07901	−	16.1011i	0.207901	−	1.61011i
$101$	−7.21896			−0.718313			−0.359157	−	0.933277i	$-0.616936\pi$
$101$	−7.21896			−0.718313			−0.359157	+	0.933277i	$0.616936\pi$
$102$		0			0
$103$			8.72196i			0.859400i	0.902972	+	0.429700i	$0.141381\pi$
$103$			8.72196i			0.859400i	−0.902972	+	0.429700i	$0.858619\pi$
$104$	10.5285	+	15.6304i	1.03240	+	1.53269i
$105$		0			0
$106$	6.21466	+	7.06870i	0.603621	+	0.686573i
$107$	13.6474			1.31934			0.659671	−	0.751554i	$-0.270696\pi$
$107$	13.6474			1.31934			0.659671	+	0.751554i	$0.270696\pi$
$108$		0			0
$109$	−12.9038			−1.23596			−0.617982	−	0.786192i	$-0.712049\pi$
$109$	−12.9038			−1.23596			−0.617982	+	0.786192i	$0.712049\pi$
$110$	20.5540	−	18.0707i	1.95975	−	1.72297i
$111$		0			0
$112$	−4.56960	−	1.20008i	−0.431787	−	0.113397i
$113$	−3.28872			−0.309377			−0.154688	−	0.987963i	$-0.549437\pi$
$113$	−3.28872			−0.309377			−0.154688	+	0.987963i	$0.549437\pi$
$114$		0			0
$115$	20.4312			1.90522
$116$	−3.78544	−	0.488785i	−0.351470	−	0.0453825i
$117$		0			0
$118$	1.76391	−	1.55079i	0.162381	−	0.142762i
$119$	−1.82867	+	4.51359i	−0.167634	+	0.413760i
$120$		0			0
$121$	17.5505			1.59550
$122$	−4.56271	−	5.18974i	−0.413089	−	0.469857i
$123$		0			0
$124$	−2.07181	+	16.0454i	−0.186054	+	1.44092i
$125$			11.2906i			1.00986i
$126$		0			0
$127$		−	5.07890i		−	0.450680i	−0.974280	−	0.225340i	$-0.927651\pi$
$127$		−	5.07890i		−	0.450680i	0.974280	−	0.225340i	$-0.0723492\pi$
$128$	−10.6812	+	3.72983i	−0.944095	+	0.329673i
$129$		0			0
$130$	−22.5338	−	25.6305i	−1.97634	−	2.24794i
$131$	−10.6767			−0.932830			−0.466415	−	0.884566i	$-0.654455\pi$
$131$	−10.6767			−0.932830			−0.466415	+	0.884566i	$0.654455\pi$
$132$		0			0
$133$	0.817930			0.0709235
$134$	−7.98594	−	9.08340i	−0.689880	−	0.784686i
$135$		0			0
$136$	2.40644	+	11.4109i	0.206351	+	0.978478i
$137$			0.0369638i			0.00315803i	0.999999	+	0.00157901i	$0.000502616\pi$
$137$			0.0369638i			0.00315803i	−0.999999	+	0.00157901i	$0.999497\pi$
$138$		0			0
$139$			18.5586i			1.57412i	0.616874	+	0.787062i	$0.288399\pi$
$139$			18.5586i			1.57412i	−0.616874	+	0.787062i	$0.711601\pi$
$140$	8.48525	+	1.09563i	0.717135	+	0.0925980i
$141$		0			0
$142$	−1.84172	+	1.61920i	−0.154553	+	0.135880i
$143$		−	35.6019i		−	2.97718i
$144$		0			0
$145$	6.91196			0.574007
$146$	−9.54981	+	8.39600i	−0.790348	+	0.694858i
$147$		0			0
$148$	2.13259	−	16.5161i	0.175298	−	1.35761i
$149$	−4.85767			−0.397956			−0.198978	−	0.980004i	$-0.563762\pi$
$149$	−4.85767			−0.397956			−0.198978	+	0.980004i	$0.563762\pi$
$150$		0			0
$151$			14.8039i			1.20473i	0.798222	+	0.602363i	$0.205774\pi$
$151$			14.8039i			1.20473i	−0.798222	+	0.602363i	$0.794226\pi$
$152$	1.62450	−	1.09424i	0.131764	−	0.0887549i
$153$		0			0
$154$	5.89321	+	6.70307i	0.474888	+	0.540149i
$155$		−	29.2978i		−	2.35325i
$156$		0			0
$157$		−	9.35906i		−	0.746934i	−0.927643	−	0.373467i	$-0.878169\pi$
$157$		−	9.35906i		−	0.746934i	0.927643	−	0.373467i	$-0.121831\pi$
$158$	−6.01378	−	6.84022i	−0.478431	−	0.544179i
$159$		0			0
$160$	18.3184	−	9.17571i	1.44819	−	0.725404i
$161$			6.66303i			0.525121i
$162$		0			0
$163$		−	16.9278i		−	1.32589i	−0.748668	−	0.662945i	$-0.769306\pi$
$163$		−	16.9278i		−	1.32589i	0.748668	−	0.662945i	$-0.230694\pi$
$164$	0.878301	−	6.80209i	0.0685838	−	0.531154i
$165$		0			0
$166$	12.0905	−	10.6297i	0.938401	−	0.825023i
$167$			9.17661i			0.710108i	0.934846	+	0.355054i	$0.115537\pi$
$167$			9.17661i			0.710108i	−0.934846	+	0.355054i	$0.884463\pi$
$168$		0			0
$169$	−31.3949			−2.41499
$170$	−6.96815	−	19.9358i	−0.534433	−	1.52901i
$171$		0			0
$172$	1.76621	−	13.6786i	0.134673	−	1.04299i
$173$			3.40214i			0.258660i	0.991602	+	0.129330i	$0.0412827\pi$
$173$			3.40214i			0.258660i	−0.991602	+	0.129330i	$0.958717\pi$
$174$		0			0
$175$	−9.58779			−0.724768
$176$	20.6721	+	5.42896i	1.55821	+	0.409223i
$177$		0			0
$178$	8.64364	−	7.59932i	0.647869	−	0.569593i
$179$		−	25.9810i		−	1.94191i	−0.239264	−	0.970955i	$-0.576906\pi$
$179$		−	25.9810i		−	1.94191i	0.239264	−	0.970955i	$-0.423094\pi$
$180$		0			0
$181$	18.3228			1.36192			0.680960	−	0.732321i	$-0.261563\pi$
$181$	18.3228			1.36192			0.680960	+	0.732321i	$0.261563\pi$
$182$	8.35861	−	7.34872i	0.619581	−	0.544723i
$183$		0			0
$184$	8.91396	+	13.2335i	0.657146	+	0.975586i
$185$			30.1572i			2.21720i
$186$		0			0
$187$	8.27259	−	20.4187i	0.604952	−	1.49316i
$188$	−2.31726	+	17.9463i	−0.169004	+	1.30887i
$189$		0			0
$190$	−2.66382	+	2.34197i	−0.193253	+	0.169905i
$191$	−5.00973			−0.362491			−0.181246	−	0.983438i	$-0.558013\pi$
$191$	−5.00973			−0.362491			−0.181246	+	0.983438i	$0.558013\pi$
$192$		0			0
$193$			24.7563i			1.78199i	0.454009	+	0.890997i	$0.349993\pi$
$193$			24.7563i			1.78199i	−0.454009	+	0.890997i	$0.650007\pi$
$194$	7.31880	−	6.43454i	0.525459	−	0.461973i
$195$		0			0
$196$	1.43552	−	11.1175i	0.102537	−	0.794109i
$197$			17.2594i			1.22968i	0.788650	+	0.614842i	$0.210780\pi$
$197$			17.2594i			1.22968i	−0.788650	+	0.614842i	$0.789220\pi$
$198$		0			0
$199$	−2.16648			−0.153578			−0.0767889	−	0.997047i	$-0.524467\pi$
$199$	−2.16648			−0.153578			−0.0767889	+	0.997047i	$0.524467\pi$
$200$	−19.0424	+	12.8268i	−1.34650	+	0.906988i
$201$		0			0
$202$	6.74090	+	7.66727i	0.474288	+	0.539467i
$203$			2.25413i			0.158209i
$204$		0			0
$205$			12.4202i			0.867461i
$206$	9.26361	−	8.14437i	0.645426	−	0.567445i
$207$		0			0
$208$	6.76981	−	25.7777i	0.469402	−	1.78736i
$209$	−3.70016			−0.255946
$210$		0			0
$211$		−	16.7291i		−	1.15168i	−0.817564	−	0.575838i	$-0.804676\pi$
$211$		−	16.7291i		−	1.15168i	0.817564	−	0.575838i	$-0.195324\pi$
$212$	1.70457	−	13.2012i	0.117070	−	0.906662i
$213$		0			0
$214$	−12.7436	−	14.4949i	−0.871136	−	0.990851i
$215$			24.9762i			1.70337i
$216$		0			0
$217$	9.55459			0.648608
$218$	12.0493	+	13.7052i	0.816083	+	0.928232i
$219$		0			0
$220$	−38.3857	−	4.95645i	−2.58797	−	0.334164i
$221$	−25.4617	−	10.3158i	−1.71274	−	0.693914i
$222$		0			0
$223$			1.53097i			0.102521i	0.998685	+	0.0512605i	$0.0163239\pi$
$223$			1.53097i			0.102521i	−0.998685	+	0.0512605i	$0.983676\pi$
$224$	2.99239	+	5.97399i	0.199937	+	0.399154i
$225$		0			0
$226$	3.07093	+	3.49295i	0.204275	+	0.232348i
$227$	−16.6745			−1.10673			−0.553364	−	0.832940i	$-0.686656\pi$
$227$	−16.6745			−1.10673			−0.553364	+	0.832940i	$0.686656\pi$
$228$		0			0
$229$			2.69611i			0.178164i	0.996024	+	0.0890819i	$0.0283933\pi$
$229$			2.69611i			0.178164i	−0.996024	+	0.0890819i	$0.971607\pi$
$230$	−19.0782	−	21.7000i	−1.25798	−	1.43086i
$231$		0			0
$232$	3.01562	+	4.47694i	0.197985	+	0.293926i
$233$	−26.8316			−1.75780			−0.878899	−	0.477008i	$-0.841721\pi$
$233$	−26.8316			−1.75780			−0.878899	+	0.477008i	$0.841721\pi$
$234$		0			0
$235$		−	32.7687i		−	2.13759i
$236$	−3.29420	−	0.425355i	−0.214434	−	0.0276882i
$237$		0			0
$238$	6.50147	−	2.27246i	0.421428	−	0.147301i
$239$	−8.76006			−0.566641			−0.283321	−	0.959025i	$-0.591436\pi$
$239$	−8.76006			−0.566641			−0.283321	+	0.959025i	$0.591436\pi$
$240$		0			0
$241$		−	2.75236i		−	0.177295i	−0.996063	−	0.0886476i	$-0.971745\pi$
$241$		−	2.75236i		−	0.177295i	0.996063	−	0.0886476i	$-0.0282545\pi$
$242$	−16.3882	−	18.6404i	−1.05348	−	1.19825i
$243$		0			0
$244$	−1.25147	+	9.69213i	−0.0801170	+	0.620475i
$245$			20.2998i			1.29691i
$246$		0			0
$247$			4.61404i			0.293584i
$248$	18.9764	−	12.7823i	1.20500	−	0.811680i
$249$		0			0
$250$	11.9917	−	10.5429i	0.758424	−	0.666791i
$251$		−	2.61985i		−	0.165364i	−0.996576	−	0.0826818i	$-0.973651\pi$
$251$		−	2.61985i		−	0.165364i	0.996576	−	0.0826818i	$-0.0263485\pi$
$252$		0			0
$253$		−	30.1424i		−	1.89503i
$254$	−5.39431	+	4.74257i	−0.338469	+	0.297575i
$255$		0			0
$256$	13.9353	+	7.86171i	0.870958	+	0.491357i
$257$			3.00640i			0.187534i	0.995594	+	0.0937669i	$0.0298908\pi$
$257$			3.00640i			0.187534i	−0.995594	+	0.0937669i	$0.970109\pi$
$258$		0			0
$259$	−9.83487			−0.611109
$260$	−6.18060	+	47.8663i	−0.383305	+	2.96854i
$261$		0			0
$262$	9.96969	+	11.3398i	0.615930	+	0.700573i
$263$	16.1476			0.995703			0.497852	−	0.867262i	$-0.334122\pi$
$263$	16.1476			0.995703			0.497852	+	0.867262i	$0.334122\pi$
$264$		0			0
$265$			24.1045i			1.48073i
$266$	−0.763764	−	0.868724i	−0.0468294	−	0.0532649i
$267$		0			0
$268$	−2.19040	+	16.9638i	−0.133800	+	1.03623i
$269$			11.8650i			0.723423i	0.932290	+	0.361711i	$0.117807\pi$
$269$			11.8650i			0.723423i	−0.932290	+	0.361711i	$0.882193\pi$
$270$		0			0
$271$		−	1.12428i		−	0.0682950i	−0.999417	−	0.0341475i	$-0.989128\pi$
$271$		−	1.12428i		−	0.0682950i	0.999417	−	0.0341475i	$-0.0108716\pi$
$272$	9.87247	−	13.2111i	0.598606	−	0.801043i
$273$		0			0
$274$	0.0392592	−	0.0345159i	0.00237174	−	0.00208518i
$275$	43.3734			2.61551
$276$		0			0
$277$	−16.3663			−0.983358			−0.491679	−	0.870777i	$-0.663617\pi$
$277$	−16.3663			−0.983358			−0.491679	+	0.870777i	$0.663617\pi$
$278$	19.7112	−	17.3297i	1.18220	−	1.03936i
$279$		0			0
$280$	−6.75967	−	10.0353i	−0.403967	−	0.599722i
$281$		−	0.186718i		−	0.0111387i	−0.999984	−	0.00556934i	$-0.998227\pi$
$281$		−	0.186718i		−	0.0111387i	0.999984	−	0.00556934i	$-0.00177279\pi$
$282$		0			0
$283$			15.4116i			0.916125i	0.888920	+	0.458063i	$0.151456\pi$
$283$			15.4116i			0.916125i	−0.888920	+	0.458063i	$0.848544\pi$
$284$	3.43951	+	0.444116i	0.204097	+	0.0263535i
$285$		0			0
$286$	−37.8128	+	33.2443i	−2.23592	+	1.96577i
$287$	−4.05046			−0.239091
$288$		0			0
$289$	−12.2060	−	11.8328i	−0.717999	−	0.696044i
$290$	−6.45423	−	7.34120i	−0.379006	−	0.431090i
$291$		0			0
$292$	17.8348	+	2.30287i	1.04370	+	0.134765i
$293$	17.2373			1.00701			0.503507	−	0.863991i	$-0.332043\pi$
$293$	17.2373			1.00701			0.503507	+	0.863991i	$0.332043\pi$
$294$		0			0
$295$	6.01499			0.350206
$296$	−19.5331	+	13.1573i	−1.13534	+	0.764753i
$297$		0			0
$298$	4.53599	+	5.15934i	0.262763	+	0.298872i
$299$	−37.5870			−2.17371
$300$		0			0
$301$	−8.14526			−0.469485
$302$	15.7233	−	13.8236i	0.904772	−	0.795457i
$303$		0			0
$304$	−2.67912	−	0.703597i	−0.153658	−	0.0403541i
$305$		−	17.6972i		−	1.01334i
$306$		0			0
$307$	11.0720			0.631911			0.315955	−	0.948774i	$-0.397675\pi$
$307$	11.0720			0.631911			0.315955	+	0.948774i	$0.397675\pi$
$308$	1.61640	−	12.5184i	0.0921028	−	0.713300i
$309$		0			0
$310$	−31.1172	+	27.3576i	−1.76734	+	1.55381i
$311$		−	0.535200i		−	0.0303484i	−0.999885	−	0.0151742i	$-0.995170\pi$
$311$		−	0.535200i		−	0.0303484i	0.999885	−	0.0151742i	$-0.00483029\pi$
$312$		0			0
$313$		−	28.9542i		−	1.63659i	−0.574800	−	0.818294i	$-0.694920\pi$
$313$		−	28.9542i		−	1.63659i	0.574800	−	0.818294i	$-0.305080\pi$
$314$	−9.94027	+	8.73928i	−0.560962	+	0.493186i
$315$		0			0
$316$	−1.64947	+	12.7745i	−0.0927900	+	0.718622i
$317$		−	32.4690i		−	1.82364i	−0.410588	−	0.911821i	$-0.634676\pi$
$317$		−	32.4690i		−	1.82364i	0.410588	−	0.911821i	$-0.365324\pi$
$318$		0			0
$319$		−	10.1973i		−	0.570937i
$320$	−26.8508	−	10.8879i	−1.50101	−	0.608652i
$321$		0			0
$322$	7.07682	−	6.22179i	0.394376	−	0.346727i
$323$	−1.07213	+	2.64628i	−0.0596552	+	0.147243i
$324$		0			0
$325$		−	54.0858i		−	3.00014i
$326$	−17.9791	+	15.8068i	−0.995769	+	0.875460i
$327$		0			0
$328$	−8.04465	+	5.41880i	−0.444192	+	0.299203i
$329$	10.6865			0.589167
$330$		0			0
$331$	−10.5963			−0.582428			−0.291214	−	0.956658i	$-0.594059\pi$
$331$	−10.5963			−0.582428			−0.291214	+	0.956658i	$0.594059\pi$
$332$	−22.5796	−	2.91553i	−1.23922	−	0.160010i
$333$		0			0
$334$	9.74649	−	8.56892i	0.533304	−	0.468870i
$335$		−	30.9747i		−	1.69233i
$336$		0			0
$337$			2.48046i			0.135119i	0.997715	+	0.0675596i	$0.0215213\pi$
$337$			2.48046i			0.135119i	−0.997715	+	0.0675596i	$0.978479\pi$
$338$	29.3159	+	33.3446i	1.59457	+	1.81371i
$339$		0			0
$340$	−14.6671	+	26.0165i	−0.795437	+	1.41094i
$341$	−43.2232			−2.34067
$342$		0			0
$343$	−14.8882			−0.803885
$344$	−16.1773	+	10.8969i	−0.872224	+	0.587522i
$345$		0			0
$346$	3.61342	−	3.17684i	0.194259	−	0.170788i
$347$	−4.66781			−0.250581			−0.125291	−	0.992120i	$-0.539986\pi$
$347$	−4.66781			−0.250581			−0.125291	+	0.992120i	$0.539986\pi$
$348$		0			0
$349$			17.8707i			0.956597i	0.878197	+	0.478298i	$0.158746\pi$
$349$			17.8707i			0.956597i	−0.878197	+	0.478298i	$0.841254\pi$
$350$	8.95286	+	10.1832i	0.478551	+	0.544315i
$351$		0			0
$352$	−13.5370	−	27.0253i	−0.721525	−	1.44045i
$353$			4.04601i			0.215347i	0.994186	+	0.107674i	$0.0343401\pi$
$353$			4.04601i			0.215347i	−0.994186	+	0.107674i	$0.965660\pi$
$354$		0			0
$355$	−6.28030			−0.333324
$356$	−16.1425	−	2.08435i	−0.855550	−	0.110470i
$357$		0			0
$358$	−27.5944	+	24.2605i	−1.45841	+	1.28221i
$359$	−23.4791			−1.23918			−0.619590	−	0.784926i	$-0.712701\pi$
$359$	−23.4791			−1.23918			−0.619590	+	0.784926i	$0.712701\pi$
$360$		0			0
$361$	−18.5205			−0.974761
$362$	−17.1094	−	19.4606i	−0.899249	−	1.02283i
$363$		0			0
$364$	−15.6102	−	2.01562i	−0.818195	−	0.105647i
$365$	−32.5651			−1.70454
$366$		0			0
$367$	13.1347			0.685627			0.342813	−	0.939404i	$-0.388620\pi$
$367$	13.1347			0.685627			0.342813	+	0.939404i	$0.388620\pi$
$368$	5.73166	−	21.8247i	0.298783	−	1.13769i
$369$		0			0
$370$	32.0300	−	28.1601i	1.66516	−	1.46398i
$371$	−7.86095			−0.408120
$372$		0			0
$373$			7.51304i			0.389011i	0.980901	+	0.194505i	$0.0623101\pi$
$373$			7.51304i			0.389011i	−0.980901	+	0.194505i	$0.937690\pi$
$374$	−29.4115	+	10.2802i	−1.52083	+	0.531575i
$375$		0			0
$376$	21.2246	−	14.2967i	1.09457	−	0.737295i
$377$	−12.7158			−0.654897
$378$		0			0
$379$			9.69855i			0.498181i	0.968480	+	0.249090i	$0.0801317\pi$
$379$			9.69855i			0.498181i	−0.968480	+	0.249090i	$0.919868\pi$
$380$	4.97482	+	0.642360i	0.255203	+	0.0329524i
$381$		0			0
$382$	4.67797	+	5.32084i	0.239346	+	0.272238i
$383$	26.7791			1.36835			0.684175	−	0.729318i	$-0.260162\pi$
$383$	26.7791			1.36835			0.684175	+	0.729318i	$0.260162\pi$
$384$		0			0
$385$			22.8577i			1.16493i
$386$	26.2937	−	23.1168i	1.33831	−	1.17662i
$387$		0			0
$388$	−13.6683	−	1.76488i	−0.693901	−	0.0895980i
$389$	23.0611			1.16924			0.584621	−	0.811306i	$-0.301243\pi$
$389$	23.0611			1.16924			0.584621	+	0.811306i	$0.301243\pi$
$390$		0			0
$391$	−21.5572	−	8.73384i	−1.09019	−	0.441689i
$392$	−13.1484	+	8.85663i	−0.664094	+	0.447327i
$393$		0			0
$394$	18.3313	−	16.1165i	0.923516	−	0.811937i
$395$		−	23.3253i		−	1.17363i
$396$		0			0
$397$	−12.9301			−0.648944			−0.324472	−	0.945895i	$-0.605187\pi$
$397$	−12.9301			−0.648944			−0.324472	+	0.945895i	$0.605187\pi$
$398$	2.02301	+	2.30102i	0.101404	+	0.115340i
$399$		0			0
$400$	31.4046	+	8.24758i	1.57023	+	0.412379i
$401$	21.9768			1.09747			0.548734	−	0.835997i	$-0.315110\pi$
$401$	21.9768			1.09747			0.548734	+	0.835997i	$0.315110\pi$
$402$		0			0
$403$			53.8986i			2.68488i
$404$	1.84891	−	14.3190i	0.0919865	−	0.712399i
$405$		0			0
$406$	2.39411	−	2.10486i	0.118818	−	0.104462i
$407$	44.4912			2.20535
$408$		0			0
$409$	−14.7032			−0.727026			−0.363513	−	0.931589i	$-0.618423\pi$
$409$	−14.7032			−0.727026			−0.363513	+	0.931589i	$0.618423\pi$
$410$	13.1915	−	11.5977i	0.651480	−	0.572768i
$411$		0			0
$412$	−17.3003	−	2.23385i	−0.852325	−	0.110054i
$413$			1.96161i			0.0965244i
$414$		0			0
$415$	41.2288			2.02384
$416$	−33.7000	+	16.8804i	−1.65228	+	0.827630i
$417$		0			0
$418$	3.45513	+	3.92995i	0.168996	+	0.192220i
$419$	−28.4797			−1.39132			−0.695662	−	0.718370i	$-0.744889\pi$
$419$	−28.4797			−1.39132			−0.695662	+	0.718370i	$0.744889\pi$
$420$		0			0
$421$		−	15.5326i		−	0.757013i	−0.925599	−	0.378506i	$-0.876438\pi$
$421$		−	15.5326i		−	0.757013i	0.925599	−	0.378506i	$-0.123562\pi$
$422$	−17.7679	+	15.6212i	−0.864930	+	0.760429i
$423$		0			0
$424$	−15.6127	+	10.5166i	−0.758219	+	0.510729i
$425$	12.5676	−	31.0197i	0.609617	−	1.50468i
$426$		0			0
$427$	5.77140			0.279298
$428$	−3.49534	+	27.0700i	−0.168954	+	1.30848i
$429$		0			0
$430$	26.5273	−	23.3223i	1.27926	−	1.12470i
$431$		−	10.4813i		−	0.504867i	−0.967614	−	0.252434i	$-0.918769\pi$
$431$		−	10.4813i		−	0.504867i	0.967614	−	0.252434i	$-0.0812309\pi$
$432$		0			0
$433$	7.96586			0.382815			0.191407	−	0.981511i	$-0.438695\pi$
$433$	7.96586			0.382815			0.191407	+	0.981511i	$0.438695\pi$
$434$	−8.92187	−	10.1479i	−0.428263	−	0.487117i
$435$		0			0
$436$	3.30491	−	25.5952i	0.158276	−	1.22579i
$437$			3.90647i			0.186872i
$438$		0			0
$439$	−31.7122			−1.51354			−0.756770	−	0.653681i	$-0.773224\pi$
$439$	−31.7122			−1.51354			−0.756770	+	0.653681i	$0.773224\pi$
$440$	30.5795	+	45.3978i	1.45782	+	2.16425i
$441$		0			0
$442$	12.8192	+	36.6755i	0.609747	+	1.74448i
$443$			13.3688i			0.635171i	0.948230	+	0.317586i	$0.102872\pi$
$443$			13.3688i			0.635171i	−0.948230	+	0.317586i	$0.897128\pi$
$444$		0			0
$445$	29.4751			1.39725
$446$	1.62604	−	1.42958i	0.0769952	−	0.0676926i
$447$		0			0
$448$	3.55076	−	8.75660i	0.167758	−	0.413710i
$449$	2.01452			0.0950712			0.0475356	−	0.998870i	$-0.484863\pi$
$449$	2.01452			0.0950712			0.0475356	+	0.998870i	$0.484863\pi$
$450$		0			0
$451$	18.3236			0.862823
$452$	0.842301	−	6.52329i	0.0396185	−	0.306830i
$453$		0			0
$454$	15.5703	+	17.7100i	0.730751	+	0.831174i
$455$	28.5031			1.33625
$456$		0			0
$457$	26.3281			1.23158			0.615788	−	0.787912i	$-0.288838\pi$
$457$	26.3281			1.23158			0.615788	+	0.787912i	$0.288838\pi$
$458$	2.86354	−	2.51757i	0.133804	−	0.117638i
$459$		0			0
$460$	−5.23281	+	40.5260i	−0.243981	+	1.88953i
$461$	19.3286			0.900225			0.450112	−	0.892972i	$-0.351384\pi$
$461$	19.3286			0.900225			0.450112	+	0.892972i	$0.351384\pi$
$462$		0			0
$463$			22.3567i			1.03901i	0.854469	+	0.519503i	$0.173883\pi$
$463$			22.3567i			1.03901i	−0.854469	+	0.519503i	$0.826117\pi$
$464$	1.93904	−	7.38337i	0.0900177	−	0.342764i
$465$		0			0
$466$	25.0548	+	28.4979i	1.16064	+	1.32014i
$467$		−	19.0174i		−	0.880022i	−0.897992	−	0.440011i	$-0.854975\pi$
$467$		−	19.0174i		−	0.880022i	0.897992	−	0.440011i	$-0.145025\pi$
$468$		0			0
$469$	10.1015			0.466442
$470$	−34.8037	+	30.5987i	−1.60537	+	1.41141i
$471$		0			0
$472$	2.62428	+	3.89596i	0.120792	+	0.179326i
$473$	36.8477			1.69426
$474$		0			0
$475$	−5.62123			−0.257920
$476$	−8.48450	−	4.78325i	−0.388887	−	0.219240i
$477$		0			0
$478$	8.17995	+	9.30407i	0.374142	+	0.425558i
$479$			8.69335i			0.397209i	0.980080	+	0.198605i	$0.0636409\pi$
$479$			8.69335i			0.397209i	−0.980080	+	0.198605i	$0.936359\pi$
$480$		0			0
$481$		−	55.4797i		−	2.52966i
$482$	−2.92329	+	2.57009i	−0.133152	+	0.117065i
$483$		0			0
$484$	−4.49499	+	34.8119i	−0.204318	+	1.58236i
$485$	24.9573			1.13325
$486$		0			0
$487$	−12.7910			−0.579616			−0.289808	−	0.957085i	$-0.593591\pi$
$487$	−12.7910			−0.579616			−0.289808	+	0.957085i	$0.593591\pi$
$488$	11.4626	−	7.72111i	0.518888	−	0.349518i
$489$		0			0
$490$	21.5605	−	18.9555i	0.974003	−	0.856323i
$491$		−	5.78080i		−	0.260884i	−0.991456	−	0.130442i	$-0.958360\pi$
$491$		−	5.78080i		−	0.260884i	0.991456	−	0.130442i	$-0.0416396\pi$
$492$		0			0
$493$	−7.29287	−	2.95469i	−0.328454	−	0.133073i
$494$	4.90057	−	4.30849i	0.220487	−	0.193848i
$495$		0			0
$496$	−31.2959	−	8.21903i	−1.40523	−	0.369045i
$497$		−	2.04813i		−	0.0918713i
$498$		0			0
$499$			13.8967i			0.622100i	0.950394	+	0.311050i	$0.100681\pi$
$499$			13.8967i			0.622100i	−0.950394	+	0.311050i	$0.899319\pi$
$500$	−22.3952	−	2.89172i	−1.00155	−	0.129322i
$501$		0			0
$502$	−2.78255	+	2.44636i	−0.124191	+	0.109186i
$503$			23.3528i			1.04125i	0.853785	+	0.520625i	$0.174301\pi$
$503$			23.3528i			1.04125i	−0.853785	+	0.520625i	$0.825699\pi$
$504$		0			0
$505$			26.1456i			1.16346i
$506$	−32.0142	+	28.1463i	−1.42321	+	1.25125i
$507$		0			0
$508$	10.0742	+	1.30080i	0.446969	+	0.0577136i
$509$	31.6573			1.40319			0.701593	−	0.712578i	$-0.252473\pi$
$509$	31.6573			1.40319			0.701593	+	0.712578i	$0.252473\pi$
$510$		0			0
$511$		−	10.6201i		−	0.469808i
$512$	−4.66258	−	22.1418i	−0.206059	−	0.978540i
$513$		0			0
$514$	3.19310	−	2.80730i	0.140841	−	0.123825i
$515$	31.5892			1.39198
$516$		0			0
$517$	−48.3439			−2.12616
$518$	9.18359	+	10.4456i	0.403504	+	0.458955i
$519$		0			0
$520$	56.6102	−	38.1321i	2.48252	−	1.67220i
$521$	26.9722			1.18167			0.590836	−	0.806791i	$-0.298798\pi$
$521$	26.9722			1.18167			0.590836	+	0.806791i	$0.298798\pi$
$522$		0			0
$523$	25.9078			1.13287			0.566434	−	0.824107i	$-0.308323\pi$
$523$	25.9078			1.13287			0.566434	+	0.824107i	$0.308323\pi$
$524$	2.73450	−	21.1776i	0.119457	−	0.925150i
$525$		0			0
$526$	−15.0783	−	17.1504i	−0.657443	−	0.747792i
$527$	−12.5241	+	30.9123i	−0.545557	+	1.34656i
$528$		0			0
$529$	−8.82300			−0.383609
$530$	25.6014	−	22.5082i	1.11205	−	0.977694i
$531$		0			0
$532$	−0.209487	+	1.62239i	−0.00908239	+	0.0703395i
$533$		−	22.8491i		−	0.989706i
$534$		0			0
$535$		−	49.4280i		−	2.13696i
$536$	20.0626	−	13.5140i	0.866571	−	0.583714i
$537$		0			0
$538$	12.6018	−	11.0793i	0.543304	−	0.477662i
$539$	29.9485			1.28997
$540$		0			0
$541$	−24.8418			−1.06803			−0.534017	−	0.845474i	$-0.679318\pi$
$541$	−24.8418			−1.06803			−0.534017	+	0.845474i	$0.679318\pi$
$542$	−1.19410	+	1.04983i	−0.0512909	+	0.0450939i
$543$		0			0
$544$	−23.2503	+	1.85072i	−0.996847	+	0.0793489i
$545$			46.7351i			2.00191i
$546$		0			0
$547$		−	39.4825i		−	1.68815i	−0.536227	−	0.844074i	$-0.680151\pi$
$547$		−	39.4825i		−	1.68815i	0.536227	−	0.844074i	$-0.319849\pi$
$548$	−0.0733188	−	0.00946709i	−0.00313203	−	0.000404414i
$549$		0			0
$550$	−40.5011	−	46.0669i	−1.72697	−	1.96430i
$551$			1.32157i			0.0563010i
$552$		0			0
$553$	7.60687			0.323477
$554$	15.2825	+	17.3827i	0.649292	+	0.738521i
$555$		0			0
$556$	−36.8117	−	4.75321i	−1.56116	−	0.201581i
$557$	30.3318			1.28520			0.642599	−	0.766203i	$-0.277856\pi$
$557$	30.3318			1.28520			0.642599	+	0.766203i	$0.277856\pi$
$558$		0			0
$559$		−	45.9484i		−	1.94341i
$560$	−4.34645	+	16.5502i	−0.183671	+	0.699372i
$561$		0			0
$562$	−0.198314	+	0.174353i	−0.00836536	+	0.00735466i
$563$			38.1522i			1.60792i	0.594681	+	0.803962i	$0.297279\pi$
$563$			38.1522i			1.60792i	−0.594681	+	0.803962i	$0.702721\pi$
$564$		0			0
$565$			11.9111i			0.501102i
$566$	16.3687	−	14.3910i	0.688027	−	0.604900i
$567$		0			0
$568$	−2.74004	−	4.06781i	−0.114969	−	0.170681i
$569$		−	3.84130i		−	0.161036i	−0.996753	−	0.0805179i	$-0.974343\pi$
$569$		−	3.84130i		−	0.161036i	0.996753	−	0.0805179i	$-0.0256574\pi$
$570$		0			0
$571$			15.9874i			0.669051i	0.942387	+	0.334526i	$0.108576\pi$
$571$			15.9874i			0.669051i	−0.942387	+	0.334526i	$0.891424\pi$
$572$	70.6176	+	9.11829i	2.95267	+	0.381255i
$573$		0			0
$574$	3.78223	+	4.30200i	0.157867	+	0.179562i
$575$		−	45.7918i		−	1.90965i
$576$		0			0
$577$	−24.9708			−1.03955			−0.519774	−	0.854304i	$-0.673984\pi$
$577$	−24.9708			−1.03955			−0.519774	+	0.854304i	$0.673984\pi$
$578$	−1.16991	+	24.0131i	−0.0486617	+	0.998815i
$579$		0			0
$580$	−1.77028	+	13.7101i	−0.0735068	+	0.569281i
$581$			13.4455i			0.557815i
$582$		0			0
$583$	35.5615			1.47281
$584$	−14.2079	−	21.0927i	−0.587926	−	0.872824i
$585$		0			0
$586$	−16.0958	−	18.3078i	−0.664912	−	0.756287i
$587$		−	28.2425i		−	1.16569i	−0.812582	−	0.582847i	$-0.801939\pi$
$587$		−	28.2425i		−	1.16569i	0.812582	−	0.582847i	$-0.198061\pi$
$588$		0			0
$589$	5.60177			0.230817
$590$	−5.61666	−	6.38852i	−0.231234	−	0.263011i
$591$		0			0
$592$	32.2140	+	8.46013i	1.32399	+	0.347709i
$593$			20.5555i			0.844115i	0.906569	+	0.422057i	$0.138692\pi$
$593$			20.5555i			0.844115i	−0.906569	+	0.422057i	$0.861308\pi$
$594$		0			0
$595$	16.3473	+	6.62308i	0.670174	+	0.271520i
$596$	1.24414	−	9.63535i	0.0509619	−	0.394679i
$597$		0			0
$598$	35.0979	+	39.9212i	1.43526	+	1.63250i
$599$	−13.8198			−0.564661			−0.282330	−	0.959317i	$-0.591107\pi$
$599$	−13.8198			−0.564661			−0.282330	+	0.959317i	$0.591107\pi$
$600$		0			0
$601$		−	5.46980i		−	0.223118i	−0.993758	−	0.111559i	$-0.964416\pi$
$601$		−	5.46980i		−	0.223118i	0.993758	−	0.111559i	$-0.0355844\pi$
$602$	7.60586	+	8.65109i	0.309992	+	0.352592i
$603$		0			0
$604$	−29.3641	−	3.79155i	−1.19481	−	0.154276i
$605$		−	63.5642i		−	2.58425i
$606$		0			0
$607$	35.9372			1.45864			0.729322	−	0.684170i	$-0.239836\pi$
$607$	35.9372			1.45864			0.729322	+	0.684170i	$0.239836\pi$
$608$	1.75441	+	3.50250i	0.0711506	+	0.142045i
$609$		0			0
$610$	−18.7962	+	16.5252i	−0.761035	+	0.669086i
$611$			60.2840i			2.43883i
$612$		0			0
$613$			16.6849i			0.673899i	0.941523	+	0.336949i	$0.109395\pi$
$613$			16.6849i			0.673899i	−0.941523	+	0.336949i	$0.890605\pi$
$614$	−10.3388	−	11.7596i	−0.417238	−	0.474577i
$615$		0			0
$616$	−14.8051	+	9.97259i	−0.596515	+	0.401807i
$617$	−28.5025			−1.14747			−0.573734	−	0.819042i	$-0.694506\pi$
$617$	−28.5025			−1.14747			−0.573734	+	0.819042i	$0.694506\pi$
$618$		0			0
$619$			26.1142i			1.04962i	0.851219	+	0.524810i	$0.175864\pi$
$619$			26.1142i			1.04962i	−0.851219	+	0.524810i	$0.824136\pi$
$620$	58.1131	+	7.50369i	2.33388	+	0.301355i
$621$		0			0
$622$	−0.568437	+	0.499758i	−0.0227922	+	0.0200385i
$623$			9.61241i			0.385113i
$624$		0			0
$625$	0.305155			0.0122062
$626$	−30.7523	+	27.0368i	−1.22911	+	1.08061i
$627$		0			0
$628$	18.5640	+	2.39702i	0.740785	+	0.0956517i
$629$	12.8915	−	31.8191i	0.514016	−	1.26871i
$630$		0			0
$631$		−	25.2773i		−	1.00627i	−0.864207	−	0.503136i	$-0.832180\pi$
$631$		−	25.2773i		−	1.00627i	0.864207	−	0.503136i	$-0.167820\pi$
$632$	15.1080	−	10.1766i	0.600966	−	0.404805i
$633$		0			0
$634$	−34.4854	+	30.3189i	−1.36959	+	1.20412i
$635$	−18.3947			−0.729973
$636$		0			0
$637$		−	37.3452i		−	1.47967i
$638$	−10.8305	+	9.52198i	−0.428785	+	0.376979i
$639$		0			0
$640$	13.5087	+	38.6852i	0.533977	+	1.52917i
$641$	−33.8918			−1.33864			−0.669322	−	0.742972i	$-0.733415\pi$
$641$	−33.8918			−1.33864			−0.669322	+	0.742972i	$0.733415\pi$
$642$		0			0
$643$		−	26.7558i		−	1.05514i	−0.849510	−	0.527572i	$-0.823103\pi$
$643$		−	26.7558i		−	1.05514i	0.849510	−	0.527572i	$-0.176897\pi$
$644$	−13.2163	−	1.70652i	−0.520797	−	0.0672465i
$645$		0			0
$646$	3.81175	−	1.33232i	0.149971	−	0.0524194i
$647$	14.6489			0.575907			0.287954	−	0.957644i	$-0.407025\pi$
$647$	14.6489			0.575907			0.287954	+	0.957644i	$0.407025\pi$
$648$		0			0
$649$		−	8.87396i		−	0.348333i
$650$	−57.4446	+	50.5041i	−2.25316	+	1.98094i
$651$		0			0
$652$	33.5769	+	4.33553i	1.31497	+	0.169792i
$653$			39.0328i			1.52747i	0.645528	+	0.763736i	$0.276637\pi$
$653$			39.0328i			1.52747i	−0.645528	+	0.763736i	$0.723363\pi$
$654$		0			0
$655$			38.6689i			1.51092i
$656$	13.2672	+	3.48428i	0.517998	+	0.136038i
$657$		0			0
$658$	−9.97884	−	11.3502i	−0.389016	−	0.442476i
$659$			36.4228i			1.41883i	0.704790	+	0.709416i	$0.251041\pi$
$659$			36.4228i			1.41883i	−0.704790	+	0.709416i	$0.748959\pi$
$660$		0			0
$661$			29.8077i			1.15938i	0.814835	+	0.579692i	$0.196827\pi$
$661$			29.8077i			1.15938i	−0.814835	+	0.579692i	$0.803173\pi$
$662$	9.89464	+	11.2544i	0.384566	+	0.437415i
$663$		0			0
$664$	17.9877	+	26.7043i	0.698060	+	1.03633i
$665$		−	2.96237i		−	0.114876i
$666$		0			0
$667$	−10.7658			−0.416855
$668$	−18.2021	−	2.35030i	−0.704261	−	0.0909357i
$669$		0			0
$670$	−32.8982	+	28.9234i	−1.27097	+	1.11741i
$671$	−26.1088			−1.00792
$672$		0			0
$673$		−	1.12932i		−	0.0435321i	−0.999763	−	0.0217661i	$-0.993071\pi$
$673$		−	1.12932i		−	0.0435321i	0.999763	−	0.0217661i	$-0.00692890\pi$
$674$	2.63450	−	2.31620i	0.101477	−	0.0892166i
$675$		0			0
$676$	8.04081	−	62.2729i	0.309262	−	2.39511i
$677$		−	18.5385i		−	0.712493i	−0.934392	−	0.356247i	$-0.884056\pi$
$677$		−	18.5385i		−	0.712493i	0.934392	−	0.356247i	$-0.115944\pi$
$678$		0			0
$679$			8.13908i			0.312349i
$680$	41.3280	−	8.71564i	1.58486	−	0.334230i
$681$		0			0
$682$	40.3609	+	45.9074i	1.54550	+	1.75789i
$683$	−32.0323			−1.22568			−0.612841	−	0.790206i	$-0.709974\pi$
$683$	−32.0323			−1.22568			−0.612841	+	0.790206i	$0.709974\pi$
$684$		0			0
$685$	0.133875			0.00511511
$686$	13.9022	+	15.8127i	0.530790	+	0.603733i
$687$		0			0
$688$	26.6797	+	7.00669i	1.01715	+	0.267128i
$689$		−	44.3446i		−	1.68939i
$690$		0			0
$691$		−	19.8752i		−	0.756087i	−0.925788	−	0.378043i	$-0.876597\pi$
$691$		−	19.8752i		−	0.756087i	0.925788	−	0.378043i	$-0.123403\pi$
$692$	−6.74826	−	0.871350i	−0.256530	−	0.0331238i
$693$		0			0
$694$	4.35870	+	4.95769i	0.165454	+	0.188191i
$695$	67.2156			2.54963
$696$		0			0
$697$	5.30931	−	13.1046i	0.201104	−	0.496373i
$698$	18.9805	−	16.6873i	0.718422	−	0.631622i
$699$		0			0
$700$	2.45561	−	19.0177i	0.0928132	−	0.718801i
$701$	10.8001			0.407915			0.203958	−	0.978980i	$-0.434620\pi$
$701$	10.8001			0.407915			0.203958	+	0.978980i	$0.434620\pi$
$702$		0			0
$703$	−5.76609			−0.217472
$704$	−16.0630	+	39.6132i	−0.605397	+	1.49298i
$705$		0			0
$706$	4.29727	−	3.77807i	0.161730	−	0.142190i
$707$	−8.52661			−0.320676
$708$		0			0
$709$	−15.6286			−0.586945			−0.293473	−	0.955968i	$-0.594811\pi$
$709$	−15.6286			−0.586945			−0.293473	+	0.955968i	$0.594811\pi$
$710$	5.86440	+	6.67031i	0.220087	+	0.250332i
$711$		0			0
$712$	12.8597	+	19.0913i	0.481938	+	0.715476i
$713$			45.6332i			1.70898i
$714$		0			0
$715$	−128.943			−4.82219
$716$	51.5341	+	6.65420i	1.92592	+	0.248679i
$717$		0			0
$718$	21.9243	+	24.9372i	0.818206	+	0.930647i
$719$			1.93732i			0.0722499i	0.999347	+	0.0361250i	$0.0115014\pi$
$719$			1.93732i			0.0722499i	−0.999347	+	0.0361250i	$0.988499\pi$
$720$		0			0
$721$			10.3019i			0.383661i
$722$	17.2940	+	19.6706i	0.643616	+	0.732064i
$723$		0			0
$724$	−4.69279	+	36.3438i	−0.174406	+	1.35071i
$725$		−	15.4915i		−	0.575341i
$726$		0			0
$727$		−	28.5491i		−	1.05883i	−0.848363	−	0.529414i	$-0.822412\pi$
$727$		−	28.5491i		−	1.05883i	0.848363	−	0.529414i	$-0.177588\pi$
$728$	12.4356	+	18.4617i	0.460895	+	0.684237i
$729$		0			0
$730$	30.4086	+	34.5875i	1.12547	+	1.28014i
$731$	10.6767	−	26.3526i	0.394893	−	0.974688i
$732$		0			0
$733$		−	11.4163i		−	0.421671i	−0.977522	−	0.210836i	$-0.932382\pi$
$733$		−	11.4163i		−	0.421671i	0.977522	−	0.210836i	$-0.0676185\pi$
$734$	−12.2649	−	13.9504i	−0.452706	−	0.514919i
$735$		0			0
$736$	−28.5321	+	14.2918i	−1.05171	+	0.526802i
$737$	−45.6972			−1.68328
$738$		0			0
$739$	38.0328			1.39906			0.699529	−	0.714604i	$-0.253393\pi$
$739$	38.0328			1.39906			0.699529	+	0.714604i	$0.253393\pi$
$740$	−59.8178	−	7.72381i	−2.19895	−	0.283933i
$741$		0			0
$742$	7.34038	+	8.34913i	0.269474	+	0.306506i
$743$		−	20.6846i		−	0.758844i	−0.925224	−	0.379422i	$-0.876123\pi$
$743$		−	20.6846i		−	0.758844i	0.925224	−	0.379422i	$-0.123877\pi$
$744$		0			0
$745$			17.5935i			0.644576i
$746$	7.97961	−	7.01551i	0.292154	−	0.256856i
$747$		0			0
$748$	38.3823	+	21.6385i	1.40340	+	0.791184i
$749$	16.1195			0.588993
$750$		0			0
$751$	8.04847			0.293693			0.146846	−	0.989159i	$-0.453088\pi$
$751$	8.04847			0.293693			0.146846	+	0.989159i	$0.453088\pi$
$752$	−35.0036	−	9.19274i	−1.27645	−	0.335225i
$753$		0			0
$754$	11.8737	+	13.5055i	0.432416	+	0.491840i
$755$	53.6168			1.95131
$756$		0			0
$757$			16.6017i			0.603399i	0.953403	+	0.301700i	$0.0975539\pi$
$757$			16.6017i			0.603399i	−0.953403	+	0.301700i	$0.902446\pi$
$758$	10.3008	−	9.05629i	0.374143	−	0.328939i
$759$		0			0
$760$	−3.96313	−	5.88359i	−0.143758	−	0.213420i
$761$		−	20.8942i		−	0.757415i	−0.925516	−	0.378708i	$-0.876369\pi$
$761$		−	20.8942i		−	0.757415i	0.925516	−	0.378708i	$-0.123631\pi$
$762$		0			0
$763$	−15.2412			−0.551770
$764$	1.28308	−	9.93696i	0.0464203	−	0.359507i
$765$		0			0
$766$	−25.0058	−	28.4422i	−0.903495	−	1.02766i
$767$	−11.0657			−0.399558
$768$		0			0
$769$	12.0767			0.435496			0.217748	−	0.976005i	$-0.430129\pi$
$769$	12.0767			0.435496			0.217748	+	0.976005i	$0.430129\pi$
$770$	24.2772	−	21.3440i	0.874888	−	0.769184i
$771$		0			0
$772$	−49.1049	−	6.34053i	−1.76732	−	0.228201i
$773$	8.74673			0.314598			0.157299	−	0.987551i	$-0.449721\pi$
$773$	8.74673			0.314598			0.157299	+	0.987551i	$0.449721\pi$
$774$		0			0
$775$	−65.6640			−2.35872
$776$	10.8886	+	16.1651i	0.390879	+	0.580292i
$777$		0			0
$778$	−21.5339	−	24.4932i	−0.772028	−	0.878123i
$779$	−2.37475			−0.0850842
$780$		0			0
$781$			9.26538i			0.331541i
$782$	10.8534	+	31.0514i	0.388116	+	1.11039i
$783$		0			0
$784$	21.6843	+	5.69480i	0.774439	+	0.203386i
$785$	−33.8966			−1.20982
$786$		0			0
$787$		−	2.83239i		−	0.100964i	−0.998725	−	0.0504819i	$-0.983924\pi$
$787$		−	2.83239i		−	0.100964i	0.998725	−	0.0504819i	$-0.0160757\pi$
$788$	−34.2347	−	4.42046i	−1.21956	−	0.157472i
$789$		0			0
$790$	−24.7739	+	21.7807i	−0.881415	+	0.774922i
$791$	−3.88444			−0.138115
$792$		0			0
$793$			32.5571i			1.15614i
$794$	12.0739	+	13.7331i	0.428485	+	0.487369i
$795$		0			0
$796$	0.554875	−	4.29729i	0.0196670	−	0.152313i
$797$	−4.90753			−0.173834			−0.0869168	−	0.996216i	$-0.527701\pi$
$797$	−4.90753			−0.173834			−0.0869168	+	0.996216i	$0.527701\pi$
$798$		0			0
$799$	−14.0078	+	34.5745i	−0.495560	+	1.22316i
$800$	−20.5652	−	41.0563i	−0.727089	−	1.45156i
$801$		0			0
$802$	−20.5214	−	23.3415i	−0.724636	−	0.824219i
$803$			48.0436i			1.69542i
$804$		0			0
$805$	24.1321			0.850546
$806$	57.2458	−	50.3293i	2.01640	−	1.77277i
$807$		0			0
$808$	−16.9347	+	11.4071i	−0.595762	+	0.401300i
$809$	9.49156			0.333705			0.166853	−	0.985982i	$-0.446640\pi$
$809$	9.49156			0.333705			0.166853	+	0.985982i	$0.446640\pi$
$810$		0			0
$811$		−	8.48311i		−	0.297882i	−0.988846	−	0.148941i	$-0.952414\pi$
$811$		−	8.48311i		−	0.297882i	0.988846	−	0.148941i	$-0.0475865\pi$
$812$	−4.47114	−	0.577323i	−0.156906	−	0.0202601i
$813$		0			0
$814$	−41.5449	−	47.2541i	−1.45615	−	1.65626i
$815$	−61.3092			−2.14757
$816$		0			0
$817$	−4.77549			−0.167073
$818$	13.7295	+	15.6163i	0.480041	+	0.546010i
$819$		0			0
$820$	−24.6358	−	3.18103i	−0.860319	−	0.111086i
$821$			8.83437i			0.308322i	0.988046	+	0.154161i	$0.0492674\pi$
$821$			8.83437i			0.308322i	−0.988046	+	0.154161i	$0.950733\pi$
$822$		0			0
$823$	5.67818			0.197929			0.0989644	−	0.995091i	$-0.468447\pi$
$823$	5.67818			0.197929			0.0989644	+	0.995091i	$0.468447\pi$
$824$	13.7821	+	20.4606i	0.480121	+	0.712778i
$825$		0			0
$826$	2.08343	−	1.83171i	0.0724917	−	0.0637332i
$827$	−13.2629			−0.461195			−0.230597	−	0.973049i	$-0.574068\pi$
$827$	−13.2629			−0.461195			−0.230597	+	0.973049i	$0.574068\pi$
$828$		0			0
$829$			2.07928i			0.0722165i	0.999348	+	0.0361083i	$0.0114961\pi$
$829$			2.07928i			0.0722165i	−0.999348	+	0.0361083i	$0.988504\pi$
$830$	−38.4985	−	43.7892i	−1.33630	−	1.51994i
$831$		0			0
$832$	49.3970	+	20.0303i	1.71253	+	0.694425i
$833$	8.67767	−	21.4185i	0.300664	−	0.742108i
$834$		0			0
$835$	33.2358			1.15017
$836$	0.947679	−	7.33940i	0.0327762	−	0.253838i
$837$		0			0
$838$	26.5937	+	30.2483i	0.918664	+	1.04491i
$839$			15.0806i			0.520641i	0.965522	+	0.260321i	$0.0838283\pi$
$839$			15.0806i			0.520641i	−0.965522	+	0.260321i	$0.916172\pi$
$840$		0			0
$841$	25.3579			0.874410
$842$	−16.4972	+	14.5040i	−0.568531	+	0.499841i
$843$		0			0
$844$	33.1826	+	4.28461i	1.14219	+	0.147482i
$845$			113.706i			3.91160i
$846$		0			0
$847$	20.7296			0.712276
$848$	25.7484	+	6.76213i	0.884205	+	0.232212i
$849$		0			0
$850$	−44.6814	+	15.6175i	−1.53256	+	0.535675i
$851$		−	46.9719i		−	1.61017i
$852$		0			0
$853$	13.3284			0.456356			0.228178	−	0.973619i	$-0.426723\pi$
$853$	13.3284			0.456356			0.228178	+	0.973619i	$0.426723\pi$
$854$	−5.38920	−	6.12981i	−0.184415	−	0.209758i
$855$		0			0
$856$	32.0150	−	21.5650i	1.09425	−	0.737076i
$857$	17.5303			0.598825			0.299412	−	0.954124i	$-0.403209\pi$
$857$	17.5303			0.598825			0.299412	+	0.954124i	$0.403209\pi$
$858$		0			0
$859$	−50.7587			−1.73187			−0.865933	−	0.500160i	$-0.833274\pi$
$859$	−50.7587			−1.73187			−0.865933	+	0.500160i	$0.833274\pi$
$860$	−49.5412	−	6.39687i	−1.68934	−	0.218131i
$861$		0			0
$862$	−11.1322	+	9.78722i	−0.379165	+	0.333354i
$863$	48.9159			1.66512			0.832558	−	0.553938i	$-0.186875\pi$
$863$	48.9159			1.66512			0.832558	+	0.553938i	$0.186875\pi$
$864$		0			0
$865$	12.3219			0.418956
$866$	−7.43835	−	8.46055i	−0.252765	−	0.287501i
$867$		0			0
$868$	−2.44710	+	18.9519i	−0.0830601	+	0.643268i
$869$	−34.4121			−1.16735
$870$		0			0
$871$			56.9835i			1.93081i
$872$	−30.2707	+	20.3901i	−1.02510	+	0.690495i
$873$		0			0
$874$	4.14907	−	3.64778i	0.140344	−	0.123388i
$875$			13.3358i			0.450831i
$876$		0			0
$877$	−5.26891			−0.177919			−0.0889593	−	0.996035i	$-0.528354\pi$
$877$	−5.26891			−0.177919			−0.0889593	+	0.996035i	$0.528354\pi$
$878$	29.6121	+	33.6816i	0.999361	+	1.13670i
$879$		0			0
$880$	19.6626	−	74.8699i	0.662825	−	2.52387i
$881$	−37.7030			−1.27025			−0.635123	−	0.772411i	$-0.719050\pi$
$881$	−37.7030			−1.27025			−0.635123	+	0.772411i	$0.719050\pi$
$882$		0			0
$883$	−17.8547			−0.600857			−0.300428	−	0.953804i	$-0.597130\pi$
$883$	−17.8547			−0.600857			−0.300428	+	0.953804i	$0.597130\pi$
$884$	26.9829	−	47.8621i	0.907532	−	1.60978i
$885$		0			0
$886$	14.1990	−	12.4835i	0.477026	−	0.419391i
$887$		−	39.8319i		−	1.33743i	−0.743521	−	0.668713i	$-0.766846\pi$
$887$		−	39.8319i		−	1.33743i	0.743521	−	0.668713i	$-0.233154\pi$
$888$		0			0
$889$		−	5.99890i		−	0.201196i
$890$	−27.5232	−	31.3055i	−0.922579	−	1.04936i
$891$		0			0
$892$	−3.03672	−	0.392108i	−0.101677	−	0.0131287i
$893$	6.26541			0.209664
$894$		0			0
$895$	−94.0978			−3.14534
$896$	−12.6160	+	4.40545i	−0.421472	+	0.147176i
$897$		0			0
$898$	−1.88112	−	2.13963i	−0.0627736	−	0.0714002i
$899$			15.4379i			0.514883i
$900$		0			0
$901$	10.3041	−	25.4328i	0.343278	−	0.847290i
$902$	−17.1101	−	19.4615i	−0.569705	−	0.647996i
$903$		0			0
$904$	−7.71491	+	5.19669i	−0.256594	+	0.172839i
$905$		−	66.3613i		−	2.20592i
$906$		0			0
$907$			9.27025i			0.307814i	0.988085	+	0.153907i	$0.0491856\pi$
$907$			9.27025i			0.307814i	−0.988085	+	0.153907i	$0.950814\pi$
$908$	4.27065	−	33.0745i	0.141726	−	1.09762i
$909$		0			0
$910$	−26.6156	−	30.2732i	−0.882297	−	1.00355i
$911$			13.7439i			0.455356i	0.973737	+	0.227678i	$0.0731133\pi$
$911$			13.7439i			0.455356i	−0.973737	+	0.227678i	$0.926887\pi$
$912$		0			0
$913$		−	60.8252i		−	2.01302i
$914$	−24.5846	−	27.9631i	−0.813186	−	0.924938i
$915$		0			0
$916$	−5.34782	−	0.690522i	−0.176697	−	0.0228155i
$917$	−12.6107			−0.416442
$918$		0			0
$919$		−	5.85281i		−	0.193066i	−0.995330	−	0.0965332i	$-0.969225\pi$
$919$		−	5.85281i		−	0.193066i	0.995330	−	0.0965332i	$-0.0307754\pi$
$920$	47.9290	−	32.2845i	1.58017	−	1.06439i
$921$		0			0
$922$	−18.0487	−	20.5290i	−0.594401	−	0.676086i
$923$	11.5538			0.380297
$924$		0			0
$925$	67.5903			2.22235
$926$	23.7451	−	20.8762i	0.780312	−	0.686035i
$927$		0			0
$928$	−9.65252	+	4.83497i	−0.316859	+	0.158716i
$929$	23.8045			0.780999			0.390500	−	0.920603i	$-0.372302\pi$
$929$	23.8045			0.780999			0.390500	+	0.920603i	$0.372302\pi$
$930$		0			0
$931$	−3.88135			−0.127206
$932$	6.87206	−	53.2214i	0.225102	−	1.74332i
$933$		0			0
$934$	−20.1984	+	17.7581i	−0.660913	+	0.581061i
$935$	−73.9522	−	29.9616i	−2.41850	−	0.979850i
$936$		0			0
$937$	−26.7531			−0.873986			−0.436993	−	0.899465i	$-0.643956\pi$
$937$	−26.7531			−0.873986			−0.436993	+	0.899465i	$0.643956\pi$
$938$	−9.43252	−	10.7288i	−0.307983	−	0.350307i
$939$		0			0
$940$	64.9978	+	8.39265i	2.11999	+	0.273738i
$941$		−	3.36287i		−	0.109627i	−0.998497	−	0.0548133i	$-0.982544\pi$
$941$		−	3.36287i		−	0.109627i	0.998497	−	0.0548133i	$-0.0174564\pi$
$942$		0			0
$943$		−	19.3452i		−	0.629967i
$944$	1.68741	−	6.42522i	0.0549205	−	0.209123i
$945$		0			0
$946$	−34.4075	−	39.1359i	−1.11868	−	1.27242i
$947$	45.7558			1.48686			0.743432	−	0.668812i	$-0.233197\pi$
$947$	45.7558			1.48686			0.743432	+	0.668812i	$0.233197\pi$
$948$		0			0
$949$	59.9095			1.94474
$950$	5.24898	+	5.97031i	0.170299	+	0.193703i
$951$		0			0
$952$	2.84235	+	13.4779i	0.0921210	+	0.436821i
$953$		−	22.5083i		−	0.729115i	−0.931181	−	0.364557i	$-0.881220\pi$
$953$		−	22.5083i		−	0.729115i	0.931181	−	0.364557i	$-0.118780\pi$
$954$		0			0
$955$			18.1442i			0.587133i
$956$	2.24361	−	17.3759i	0.0725636	−	0.561976i
$957$		0			0
$958$	9.23321	−	8.11765i	0.298312	−	0.262269i
$959$			0.0436594i			0.00140983i
$960$		0			0
$961$	34.4367			1.11086
$962$	−58.9250	+	51.8057i	−1.89982	+	1.67028i
$963$		0			0
$964$	5.45940	+	0.704930i	0.175836	+	0.0227043i
$965$	89.6621			2.88632
$966$		0			0
$967$		−	27.3288i		−	0.878834i	−0.898283	−	0.439417i	$-0.855185\pi$
$967$		−	27.3288i		−	0.878834i	0.898283	−	0.439417i	$-0.144815\pi$
$968$	41.1711	−	27.7325i	1.32329	−	0.891355i
$969$		0			0
$970$	−23.3046	−	26.5072i	−0.748265	−	0.851094i
$971$			49.4412i			1.58664i	0.608803	+	0.793321i	$0.291650\pi$
$971$			49.4412i			1.58664i	−0.608803	+	0.793321i	$0.708350\pi$
$972$		0			0
$973$			21.9204i			0.702735i
$974$	11.9440	+	13.5854i	0.382709	+	0.435303i
$975$		0			0
$976$	−18.9041	−	4.96466i	−0.605106	−	0.158915i
$977$		−	9.91996i		−	0.317368i	−0.987329	−	0.158684i	$-0.949275\pi$
$977$		−	9.91996i		−	0.317368i	0.987329	−	0.158684i	$-0.0507251\pi$
$978$		0			0
$979$		−	43.4848i		−	1.38978i
$980$	−40.2654	−	5.19915i	−1.28623	−	0.166081i
$981$		0			0
$982$	−6.13979	+	5.39798i	−0.195929	+	0.172256i
$983$			34.8952i			1.11298i	0.830853	+	0.556491i	$0.187853\pi$
$983$			34.8952i			1.11298i	−0.830853	+	0.556491i	$0.812147\pi$
$984$		0			0
$985$	62.5102			1.99174
$986$	3.67173	+	10.5048i	0.116932	+	0.334541i
$987$		0			0
$988$	−9.15209	−	1.18174i	−0.291167	−	0.0375961i
$989$		−	38.9022i		−	1.23702i
$990$		0			0
$991$	11.1366			0.353766			0.176883	−	0.984232i	$-0.443399\pi$
$991$	11.1366			0.353766			0.176883	+	0.984232i	$0.443399\pi$
$992$	20.4940	+	40.9142i	0.650685	+	1.29903i
$993$		0			0
$994$	−2.17532	+	1.91250i	−0.0689971	+	0.0606608i
$995$			7.84656i			0.248753i
$996$		0			0
$997$	−14.5272			−0.460082			−0.230041	−	0.973181i	$-0.573886\pi$
$997$	−14.5272			−0.460082			−0.230041	+	0.973181i	$0.573886\pi$
$998$	14.7597	−	12.9764i	0.467209	−	0.410761i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.h.c.611.18	yes	56
3.2	odd	2	inner	1224.2.h.c.611.39	yes	56
4.3	odd	2		4896.2.h.c.2447.47		56
8.3	odd	2	inner	1224.2.h.c.611.38	yes	56
8.5	even	2		4896.2.h.c.2447.52		56
12.11	even	2		4896.2.h.c.2447.6		56
17.16	even	2	inner	1224.2.h.c.611.17	✓	56
24.5	odd	2		4896.2.h.c.2447.9		56
24.11	even	2	inner	1224.2.h.c.611.19	yes	56
51.50	odd	2	inner	1224.2.h.c.611.40	yes	56
68.67	odd	2		4896.2.h.c.2447.10		56
136.67	odd	2	inner	1224.2.h.c.611.37	yes	56
136.101	even	2		4896.2.h.c.2447.5		56
204.203	even	2		4896.2.h.c.2447.51		56
408.101	odd	2		4896.2.h.c.2447.48		56
408.203	even	2	inner	1224.2.h.c.611.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1224.2.h.c.611.17	✓	56	17.16	even	2	inner
1224.2.h.c.611.18	yes	56	1.1	even	1	trivial
1224.2.h.c.611.19	yes	56	24.11	even	2	inner
1224.2.h.c.611.20	yes	56	408.203	even	2	inner
1224.2.h.c.611.37	yes	56	136.67	odd	2	inner
1224.2.h.c.611.38	yes	56	8.3	odd	2	inner
1224.2.h.c.611.39	yes	56	3.2	odd	2	inner
1224.2.h.c.611.40	yes	56	51.50	odd	2	inner
4896.2.h.c.2447.5		56	136.101	even	2
4896.2.h.c.2447.6		56	12.11	even	2
4896.2.h.c.2447.9		56	24.5	odd	2
4896.2.h.c.2447.10		56	68.67	odd	2
4896.2.h.c.2447.47		56	4.3	odd	2
4896.2.h.c.2447.48		56	408.101	odd	2
4896.2.h.c.2447.51		56	204.203	even	2
4896.2.h.c.2447.52		56	8.5	even	2

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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933778 - 1.06210i) q^{2} +(-0.256118 + 1.98353i) q^{4} -3.62179i q^{5} +1.18114 q^{7} +(2.34587 - 1.58016i) q^{8} +O(q^{10})\)	\(q+(-0.933778 - 1.06210i) q^{2} +(-0.256118 + 1.98353i) q^{4} -3.62179i q^{5} +1.18114 q^{7} +(2.34587 - 1.58016i) q^{8} +(-3.84671 + 3.38195i) q^{10} -5.34326 q^{11} +6.66295i q^{13} +(-1.10292 - 1.25449i) q^{14} +(-3.86881 - 1.01604i) q^{16} +(-1.54823 + 3.82139i) q^{17} +0.692491 q^{19} +(7.18395 + 0.927607i) q^{20} +(4.98942 + 5.67509i) q^{22} +5.64119i q^{23} -8.11740 q^{25} +(7.07673 - 6.22172i) q^{26} +(-0.302511 + 2.34283i) q^{28} +1.90843i q^{29} +8.08929 q^{31} +(2.53347 + 5.05782i) q^{32} +(5.50440 - 1.92395i) q^{34} -4.27785i q^{35} -8.32659 q^{37} +(-0.646633 - 0.735496i) q^{38} +(-5.72300 - 8.49626i) q^{40} -3.42928 q^{41} -6.89610 q^{43} +(1.36851 - 10.5985i) q^{44} +(5.99151 - 5.26762i) q^{46} +9.04763 q^{47} -5.60491 q^{49} +(7.57985 + 8.62150i) q^{50} +(-13.2162 - 1.70650i) q^{52} -6.65539 q^{53} +19.3522i q^{55} +(2.77080 - 1.86639i) q^{56} +(2.02695 - 1.78205i) q^{58} +1.66078i q^{59} +4.88629 q^{61} +(-7.55360 - 8.59165i) q^{62} +(3.00622 - 7.41368i) q^{64} +24.1318 q^{65} +8.55229 q^{67} +(-7.18332 - 4.04969i) q^{68} +(-4.54351 + 3.99456i) q^{70} -1.73403i q^{71} -8.99143i q^{73} +(7.77519 + 8.84368i) q^{74} +(-0.177360 + 1.37358i) q^{76} -6.31114 q^{77} +6.44027 q^{79} +(-3.67988 + 14.0120i) q^{80} +(3.20219 + 3.64224i) q^{82} +11.3835i q^{83} +(13.8403 + 5.60736i) q^{85} +(6.43942 + 7.32435i) q^{86} +(-12.5346 + 8.44319i) q^{88} +8.13825i q^{89} +7.86988i q^{91} +(-11.1895 - 1.44481i) q^{92} +(-8.44848 - 9.60950i) q^{94} -2.50806i q^{95} +6.89086i q^{97} +(5.23374 + 5.95298i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 24 q^{4}+O(q^{10}) \) 56 * q + 24 * q^4	\( 56 q + 24 q^{4} - 56 q^{16} - 32 q^{19} + 8 q^{25} - 4 q^{34} - 40 q^{49} - 56 q^{52} + 72 q^{64} - 56 q^{70} + 8 q^{76} - 40 q^{94}+O(q^{100}) \) 56 * q + 24 * q^4 - 56 * q^16 - 32 * q^19 + 8 * q^25 - 4 * q^34 - 40 * q^49 - 56 * q^52 + 72 * q^64 - 56 * q^70 + 8 * q^76 - 40 * q^94

Introduction

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