LMFDB - Embedded newform 920.2.bv.a.217.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.34
Character	$\chi$	$=$	920.217
Dual form			920.2.bv.a.513.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73970 - 0.595986i) q^{3} +(1.99839 + 1.00322i) q^{5} +(-1.14188 + 0.623512i) q^{7} +(4.42188 - 2.01940i) q^{9} +O(q^{10})$	\(q+(2.73970 - 0.595986i) q^{3} +(1.99839 + 1.00322i) q^{5} +(-1.14188 + 0.623512i) q^{7} +(4.42188 - 2.01940i) q^{9} +(2.43481 + 2.10978i) q^{11} +(-1.67321 + 3.06426i) q^{13} +(6.07289 + 1.55751i) q^{15} +(-0.304897 - 0.228243i) q^{17} +(0.396025 - 2.75441i) q^{19} +(-2.75680 + 2.38878i) q^{21} +(-4.58843 - 1.39509i) q^{23} +(2.98711 + 4.00963i) q^{25} +(4.17748 - 3.12722i) q^{27} +(2.99218 - 0.430210i) q^{29} +(1.66799 - 1.07195i) q^{31} +(7.92806 + 4.32905i) q^{33} +(-2.90743 + 0.100469i) q^{35} +(-6.69865 - 2.49847i) q^{37} +(-2.75785 + 9.39237i) q^{39} +(4.50294 - 9.86007i) q^{41} +(-1.46410 - 6.73035i) q^{43} +(10.8625 + 0.400551i) q^{45} +(0.151151 + 0.151151i) q^{47} +(-2.86937 + 4.46482i) q^{49} +(-0.971358 - 0.443604i) q^{51} +(3.80580 + 6.96980i) q^{53} +(2.74913 + 6.65880i) q^{55} +(-0.556601 - 7.78230i) q^{57} +(0.0148351 + 0.0505239i) q^{59} +(-6.54157 - 10.1789i) q^{61} +(-3.79012 + 5.06301i) q^{63} +(-6.41784 + 4.44498i) q^{65} +(-5.17522 - 0.370139i) q^{67} +(-13.4024 - 1.08749i) q^{69} +(-6.49309 - 7.49342i) q^{71} +(4.43451 + 5.92381i) q^{73} +(10.5735 + 9.20493i) q^{75} +(-4.09573 - 0.890971i) q^{77} +(-4.14460 + 1.21697i) q^{79} +(0.0310959 - 0.0358866i) q^{81} +(5.65402 - 15.1590i) q^{83} +(-0.380326 - 0.761997i) q^{85} +(7.94128 - 2.96194i) q^{87} +(-3.42133 - 2.19875i) q^{89} -4.54228i q^{91} +(3.93092 - 3.93092i) q^{93} +(3.55469 - 5.10709i) q^{95} +(1.72985 + 4.63790i) q^{97} +(15.0269 + 4.41230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	2.73970	−	0.595986i	1.58177	−	0.344093i	0.666048	−	0.745909i	$-0.267985\pi$
$3$	2.73970	−	0.595986i	1.58177	−	0.344093i	0.915720	+	0.401816i	$0.131621\pi$
$4$		0			0
$5$	1.99839	+	1.00322i	0.893706	+	0.448652i
$5$	1.99839	+	1.00322i	0.893706	+	0.448652i
$6$		0			0
$7$	−1.14188	+	0.623512i	−0.431589	+	0.235666i	−0.680332	−	0.732904i	$-0.738164\pi$
$7$	−1.14188	+	0.623512i	−0.431589	+	0.235666i	0.248743	+	0.968570i	$0.419983\pi$
$8$		0			0
$9$	4.42188	−	2.01940i	1.47396	−	0.673135i
$10$		0			0
$11$	2.43481	+	2.10978i	0.734123	+	0.636121i	0.939495	−	0.342563i	$-0.111295\pi$
$11$	2.43481	+	2.10978i	0.734123	+	0.636121i	−0.205372	+	0.978684i	$0.565840\pi$
$12$		0			0
$13$	−1.67321	+	3.06426i	−0.464065	+	0.849872i	0.535919	+	0.844269i	$0.319965\pi$
$13$	−1.67321	+	3.06426i	−0.464065	+	0.849872i	−0.999984	+	0.00560291i	$0.998217\pi$
$14$		0			0
$15$	6.07289	+	1.55751i	1.56801	+	0.402146i
$16$		0			0
$17$	−0.304897	−	0.228243i	−0.0739484	−	0.0553571i	0.561664	−	0.827365i	$-0.310161\pi$
$17$	−0.304897	−	0.228243i	−0.0739484	−	0.0553571i	−0.635612	+	0.772008i	$0.719252\pi$
$18$		0			0
$19$	0.396025	−	2.75441i	0.0908543	−	0.631906i	−0.892614	−	0.450823i	$-0.851131\pi$
$19$	0.396025	−	2.75441i	0.0908543	−	0.631906i	0.983468	−	0.181083i	$-0.0579602\pi$
$20$		0			0
$21$	−2.75680	+	2.38878i	−0.601583	+	0.521275i
$22$		0			0
$23$	−4.58843	−	1.39509i	−0.956755	−	0.290896i
$23$	−4.58843	−	1.39509i	−0.956755	−	0.290896i
$24$		0			0
$25$	2.98711	+	4.00963i	0.597422	+	0.801927i
$26$		0			0
$27$	4.17748	−	3.12722i	0.803956	−	0.601834i
$28$		0			0
$29$	2.99218	−	0.430210i	0.555633	−	0.0798880i	0.141222	−	0.989978i	$-0.454897\pi$
$29$	2.99218	−	0.430210i	0.555633	−	0.0798880i	0.414411	+	0.910090i	$0.363988\pi$
$30$		0			0
$31$	1.66799	−	1.07195i	0.299579	−	0.192528i	−0.382212	−	0.924075i	$-0.624838\pi$
$31$	1.66799	−	1.07195i	0.299579	−	0.192528i	0.681791	+	0.731547i	$0.261201\pi$
$32$		0			0
$33$	7.92806	+	4.32905i	1.38010	+	0.753590i
$34$		0			0
$35$	−2.90743	+	0.100469i	−0.491446	+	0.0169823i
$36$		0			0
$37$	−6.69865	−	2.49847i	−1.10125	−	0.410745i	−0.267876	−	0.963453i	$-0.586322\pi$
$37$	−6.69865	−	2.49847i	−1.10125	−	0.410745i	−0.833375	+	0.552708i	$0.813595\pi$
$38$		0			0
$39$	−2.75785	+	9.39237i	−0.441609	+	1.50398i
$40$		0			0
$41$	4.50294	−	9.86007i	0.703241	−	1.53988i	−0.132755	−	0.991149i	$-0.542382\pi$
$41$	4.50294	−	9.86007i	0.703241	−	1.53988i	0.835997	−	0.548735i	$-0.184890\pi$
$42$		0			0
$43$	−1.46410	−	6.73035i	−0.223273	−	1.02637i	−0.943176	−	0.332294i	$-0.892177\pi$
$43$	−1.46410	−	6.73035i	−0.223273	−	1.02637i	0.719903	−	0.694075i	$-0.244186\pi$
$44$		0			0
$45$	10.8625	+	0.400551i	1.61929	+	0.0597106i
$46$		0			0
$47$	0.151151	+	0.151151i	0.0220477	+	0.0220477i	0.718045	−	0.695997i	$-0.245037\pi$
$47$	0.151151	+	0.151151i	0.0220477	+	0.0220477i	−0.695997	+	0.718045i	$0.745037\pi$
$48$		0			0
$49$	−2.86937	+	4.46482i	−0.409910	+	0.637832i
$50$		0			0
$51$	−0.971358	−	0.443604i	−0.136017	−	0.0621170i
$52$		0			0
$53$	3.80580	+	6.96980i	0.522766	+	0.957375i	0.997032	+	0.0769932i	$0.0245320\pi$
$53$	3.80580	+	6.96980i	0.522766	+	0.957375i	−0.474265	+	0.880382i	$0.657286\pi$
$54$		0			0
$55$	2.74913	+	6.65880i	0.370693	+	0.897872i
$56$		0			0
$57$	−0.556601	−	7.78230i	−0.0737236	−	1.03079i
$58$		0			0
$59$	0.0148351	+	0.0505239i	0.00193137	+	0.00657765i	0.960453	−	0.278442i	$-0.0898180\pi$
$59$	0.0148351	+	0.0505239i	0.00193137	+	0.00657765i	−0.958522	+	0.285020i	$0.908000\pi$
$60$		0			0
$61$	−6.54157	−	10.1789i	−0.837563	−	1.30327i	−0.950832	−	0.309708i	$-0.899769\pi$
$61$	−6.54157	−	10.1789i	−0.837563	−	1.30327i	0.113269	−	0.993564i	$-0.463868\pi$
$62$		0			0
$63$	−3.79012	+	5.06301i	−0.477510	+	0.637879i
$64$		0			0
$65$	−6.41784	+	4.44498i	−0.796035	+	0.551332i
$66$		0			0
$67$	−5.17522	−	0.370139i	−0.632253	−	0.0452197i	−0.248465	−	0.968641i	$-0.579926\pi$
$67$	−5.17522	−	0.370139i	−0.632253	−	0.0452197i	−0.383788	+	0.923421i	$0.625381\pi$
$68$		0			0
$69$	−13.4024	−	1.08749i	−1.61346	−	0.130918i
$70$		0			0
$71$	−6.49309	−	7.49342i	−0.770588	−	0.889306i	0.225804	−	0.974173i	$-0.427499\pi$
$71$	−6.49309	−	7.49342i	−0.770588	−	0.889306i	−0.996392	+	0.0848668i	$0.972954\pi$
$72$		0			0
$73$	4.43451	+	5.92381i	0.519020	+	0.693330i	0.981098	−	0.193509i	$-0.0619870\pi$
$73$	4.43451	+	5.92381i	0.519020	+	0.693330i	−0.462078	+	0.886839i	$0.652896\pi$
$74$		0			0
$75$	10.5735	+	9.20493i	1.22092	+	1.06289i
$76$		0			0
$77$	−4.09573	−	0.890971i	−0.466752	−	0.101536i
$78$		0			0
$79$	−4.14460	+	1.21697i	−0.466304	+	0.136919i	−0.506440	−	0.862275i	$-0.669039\pi$
$79$	−4.14460	+	1.21697i	−0.466304	+	0.136919i	0.0401362	+	0.999194i	$0.487221\pi$
$80$		0			0
$81$	0.0310959	−	0.0358866i	0.00345510	−	0.00398740i
$82$		0			0
$83$	5.65402	−	15.1590i	0.620610	−	1.66392i	−0.120646	−	0.992696i	$-0.538496\pi$
$83$	5.65402	−	15.1590i	0.620610	−	1.66392i	0.741255	−	0.671223i	$-0.234231\pi$
$84$		0			0
$85$	−0.380326	−	0.761997i	−0.0412521	−	0.0826501i
$86$		0			0
$87$	7.94128	−	2.96194i	0.851394	−	0.317554i
$88$		0			0
$89$	−3.42133	−	2.19875i	−0.362660	−	0.233067i	0.346602	−	0.938012i	$-0.387335\pi$
$89$	−3.42133	−	2.19875i	−0.362660	−	0.233067i	−0.709262	+	0.704945i	$0.750972\pi$
$90$		0			0
$91$		−	4.54228i		−	0.476160i
$92$		0			0
$93$	3.93092	−	3.93092i	0.407617	−	0.407617i
$94$		0			0
$95$	3.55469	−	5.10709i	0.364703	−	0.523976i
$96$		0			0
$97$	1.72985	+	4.63790i	0.175639	+	0.470908i	0.994702	−	0.102796i	$-0.0327789\pi$
$97$	1.72985	+	4.63790i	0.175639	+	0.470908i	−0.819063	+	0.573704i	$0.805506\pi$
$98$		0			0
$99$	15.0269	+	4.41230i	1.51026	+	0.443453i
$100$		0			0
$101$	3.13989	+	6.87540i	0.312431	+	0.684128i	0.999081	−	0.0428599i	$-0.0136469\pi$
$101$	3.13989	+	6.87540i	0.312431	+	0.684128i	−0.686650	+	0.726988i	$0.740920\pi$
$102$		0			0
$103$	−0.0109417		0.000782568i	−0.00107812		7.71087e-5i	−0.0718782	−	0.997413i	$-0.522899\pi$
$103$	−0.0109417		0.000782568i	−0.00107812		7.71087e-5i	0.0708001	+	0.997491i	$0.477445\pi$
$104$		0			0
$105$	−7.90563	+	2.00804i	−0.771510	+	0.195965i
$106$		0			0
$107$	3.84176	−	17.6603i	0.371397	−	1.70728i	−0.289813	−	0.957083i	$-0.593593\pi$
$107$	3.84176	−	17.6603i	0.371397	−	1.70728i	0.661210	−	0.750201i	$-0.270043\pi$
$108$		0			0
$109$	0.505077	+	3.51289i	0.0483776	+	0.336474i	0.999608	+	0.0279928i	$0.00891156\pi$
$109$	0.505077	+	3.51289i	0.0483776	+	0.336474i	−0.951230	+	0.308481i	$0.900179\pi$
$110$		0			0
$111$	−19.8414	−	2.85276i	−1.88326	−	0.270772i
$112$		0			0
$113$	−0.830369	+	11.6101i	−0.0781145	+	1.09218i	0.795625	+	0.605790i	$0.207143\pi$
$113$	−0.830369	+	11.6101i	−0.0781145	+	1.09218i	−0.873739	+	0.486394i	$0.838312\pi$
$114$		0			0
$115$	−7.76990	−	7.39112i	−0.724546	−	0.689226i
$116$		0			0
$117$	−1.21076	+	16.9287i	−0.111935	+	1.56506i
$118$		0			0
$119$	0.490468	+	0.0705186i	0.0449611	+	0.00646443i
$120$		0			0
$121$	−0.0883120	−	0.614223i	−0.00802836	−	0.0558385i
$122$		0			0
$123$	6.46026	−	29.6973i	0.582502	−	2.67772i
$124$		0			0
$125$	1.94687	+	11.0095i	0.174134	+	0.984722i
$126$		0			0
$127$	8.12055	−	0.580793i	0.720582	−	0.0515371i	0.293769	−	0.955877i	$-0.405091\pi$
$127$	8.12055	−	0.580793i	0.720582	−	0.0515371i	0.426814	+	0.904340i	$0.359636\pi$
$128$		0			0
$129$	−8.02239	−	17.5666i	−0.706332	−	1.54665i
$130$		0			0
$131$	8.99115	+	2.64004i	0.785560	+	0.230661i	0.649825	−	0.760084i	$-0.274842\pi$
$131$	8.99115	+	2.64004i	0.785560	+	0.230661i	0.135735	+	0.990745i	$0.456660\pi$
$132$		0			0
$133$	1.26520	+	3.39213i	0.109707	+	0.294135i
$134$		0			0
$135$	11.4855	−	2.05848i	0.988515	−	0.177166i
$136$		0			0
$137$	−14.0931	+	14.0931i	−1.20405	+	1.20405i	−0.231130	+	0.972923i	$0.574242\pi$
$137$	−14.0931	+	14.0931i	−1.20405	+	1.20405i	−0.972923	+	0.231130i	$0.925758\pi$
$138$		0			0
$139$			1.57034i			0.133194i	0.997780	+	0.0665971i	$0.0212142\pi$
$139$			1.57034i			0.133194i	−0.997780	+	0.0665971i	$0.978786\pi$
$140$		0			0
$141$	0.504193	+	0.324025i	0.0424607	+	0.0272879i
$142$		0			0
$143$	−10.5389	+	3.93079i	−0.881303	+	0.328709i
$144$		0			0
$145$	6.41113	+	2.14208i	0.532415	+	0.177890i
$146$		0			0
$147$	−5.20025	+	13.9424i	−0.428909	+	1.14995i
$148$		0			0
$149$	−11.7950	+	13.6121i	−0.966284	+	1.11515i	0.0270221	+	0.999635i	$0.491398\pi$
$149$	−11.7950	+	13.6121i	−0.966284	+	1.11515i	−0.993306	+	0.115516i	$0.963148\pi$
$150$		0			0
$151$	16.2605	−	4.77453i	1.32326	−	0.388546i	0.457595	−	0.889161i	$-0.348711\pi$
$151$	16.2605	−	4.77453i	1.32326	−	0.388546i	0.865670	+	0.500615i	$0.166893\pi$
$152$		0			0
$153$	−1.80913	−	0.393553i	−0.146260	−	0.0318169i
$154$		0			0
$155$	4.40868	−	0.468819i	0.354114	−	0.0376565i
$156$		0			0
$157$	8.98863	+	12.0074i	0.717371	+	0.958295i	1.00000		0.000934051i	$-0.000297318\pi$
$157$	8.98863	+	12.0074i	0.717371	+	0.958295i	−0.282629	+	0.959229i	$0.591206\pi$
$158$		0			0
$159$	14.5807	+	16.8270i	1.15632	+	1.33447i
$160$		0			0
$161$	6.10929	−	1.26792i	0.481479	−	0.0999265i
$162$		0			0
$163$	7.93406	+	0.567455i	0.621443	+	0.0444465i	0.378511	−	0.925597i	$-0.376436\pi$
$163$	7.93406	+	0.567455i	0.621443	+	0.0444465i	0.242932	+	0.970043i	$0.421891\pi$
$164$		0			0
$165$	11.5004	+	16.6047i	0.895302	+	1.29267i
$166$		0			0
$167$	−14.5329	+	19.4137i	−1.12459	+	1.50228i	−0.285423	+	0.958402i	$0.592134\pi$
$167$	−14.5329	+	19.4137i	−1.12459	+	1.50228i	−0.839167	+	0.543874i	$0.816957\pi$
$168$		0			0
$169$	0.438288	+	0.681989i	0.0337144	+	0.0524607i
$170$		0			0
$171$	−3.81110	−	12.9794i	−0.291442	−	0.992561i
$172$		0			0
$173$	−0.490018	−	6.85135i	−0.0372554	−	0.520899i	−0.981476	−	0.191585i	$-0.938637\pi$
$173$	−0.490018	−	6.85135i	−0.0372554	−	0.520899i	0.944221	−	0.329314i	$-0.106817\pi$
$174$		0			0
$175$	−5.91097	−	2.71601i	−0.446828	−	0.205311i
$176$		0			0
$177$	0.0707554	+	0.129579i	0.00531830	+	0.00973975i
$178$		0			0
$179$	−11.9480	−	5.45646i	−0.893034	−	0.407835i	−0.0845951	−	0.996415i	$-0.526960\pi$
$179$	−11.9480	−	5.45646i	−0.893034	−	0.407835i	−0.808439	+	0.588581i	$0.799687\pi$
$180$		0			0
$181$	7.11331	−	11.0685i	0.528728	−	0.822717i	−0.469456	−	0.882956i	$-0.655550\pi$
$181$	7.11331	−	11.0685i	0.528728	−	0.822717i	0.998184	+	0.0602389i	$0.0191863\pi$
$182$		0			0
$183$	−23.9884	−	23.9884i	−1.77328	−	1.77328i
$184$		0			0
$185$	−10.8800	−	11.7131i	−0.799913	−	0.861165i
$186$		0			0
$187$	−0.260825	−	1.19899i	−0.0190734	−	0.0876791i
$188$		0			0
$189$	−2.82031	+	6.17561i	−0.205147	+	0.449210i
$190$		0			0
$191$	−0.388994	+	1.32479i	−0.0281466	+	0.0958586i	−0.972368	−	0.233452i	$-0.924998\pi$
$191$	−0.388994	+	1.32479i	−0.0281466	+	0.0958586i	0.944222	+	0.329310i	$0.106816\pi$
$192$		0			0
$193$	7.85851	+	2.93107i	0.565668	+	0.210983i	0.615996	−	0.787750i	$-0.288754\pi$
$193$	7.85851	+	2.93107i	0.565668	+	0.210983i	−0.0503278	+	0.998733i	$0.516027\pi$
$194$		0			0
$195$	−14.9338	+	16.0029i	−1.06943	+	1.14599i
$196$		0			0
$197$	−19.0593	−	10.4072i	−1.35792	−	0.741480i	−0.375263	−	0.926918i	$-0.622448\pi$
$197$	−19.0593	−	10.4072i	−1.35792	−	0.741480i	−0.982656	+	0.185438i	$0.940629\pi$
$198$		0			0
$199$	1.24499	−	0.800107i	0.0882551	−	0.0567181i	−0.495769	−	0.868454i	$-0.665114\pi$
$199$	1.24499	−	0.800107i	0.0882551	−	0.0567181i	0.584024	+	0.811736i	$0.301477\pi$
$200$		0			0
$201$	−14.3992	+	2.07029i	−1.01564	+	0.146027i
$202$		0			0
$203$	−3.14846	+	2.35691i	−0.220979	+	0.165422i
$204$		0			0
$205$	18.8904	−	15.1868i	1.31936	−	1.06069i
$206$		0			0
$207$	−23.1067	+	3.09699i	−1.60603	+	0.215256i
$208$		0			0
$209$	6.77544	−	5.87095i	0.468667	−	0.406102i
$210$		0			0
$211$	1.66835	−	11.6036i	0.114854	−	0.798826i	−0.848231	−	0.529627i	$-0.822332\pi$
$211$	1.66835	−	11.6036i	0.114854	−	0.798826i	0.963085	−	0.269199i	$-0.0867590\pi$
$212$		0			0
$213$	−22.2551	−	16.6600i	−1.52490	−	1.14152i
$214$		0			0
$215$	3.82617	−	14.9187i	0.260943	−	1.01744i
$216$		0			0
$217$	−1.23626	+	2.26405i	−0.0839229	+	0.153693i
$218$		0			0
$219$	15.6797	+	13.5866i	1.05954	+	0.918096i
$220$		0			0
$221$	1.20955	−	0.552385i	0.0813634	−	0.0371574i
$222$		0			0
$223$	−8.64543	+	4.72076i	−0.578941	+	0.316125i	−0.741903	−	0.670507i	$-0.766077\pi$
$223$	−8.64543	+	4.72076i	−0.578941	+	0.316125i	0.162963	+	0.986632i	$0.447895\pi$
$224$		0			0
$225$	21.3057	+	11.6979i	1.42038	+	0.779862i
$226$		0			0
$227$	−18.2313	+	3.96597i	−1.21005	+	0.263231i	−0.771943	−	0.635692i	$-0.780715\pi$
$227$	−18.2313	+	3.96597i	−1.21005	+	0.263231i	−0.438108	+	0.898922i	$0.644351\pi$
$228$		0			0
$229$	−8.39180			−0.554546			−0.277273	−	0.960791i	$-0.589431\pi$
$229$	−8.39180			−0.554546			−0.277273	+	0.960791i	$0.589431\pi$
$230$		0			0
$231$	−11.7521			−0.773231
$232$		0			0
$233$	−20.7812	+	4.52068i	−1.36142	+	0.296159i	−0.833212	−	0.552954i	$-0.813501\pi$
$233$	−20.7812	+	4.52068i	−1.36142	+	0.296159i	−0.528211	+	0.849113i	$0.677137\pi$
$234$		0			0
$235$	0.150421	+	0.453696i	0.00981240	+	0.0295959i
$236$		0			0
$237$	−10.6297	+	5.80425i	−0.690472	+	0.377026i
$238$		0			0
$239$	23.4574	−	10.7126i	1.51733	−	0.692943i	0.529478	−	0.848323i	$-0.322388\pi$
$239$	23.4574	−	10.7126i	1.51733	−	0.692943i	0.987855	+	0.155381i	$0.0496604\pi$
$240$		0			0
$241$	−11.9934	−	10.3924i	−0.772565	−	0.669431i	0.176575	−	0.984287i	$-0.443498\pi$
$241$	−11.9934	−	10.3924i	−0.772565	−	0.669431i	−0.949139	+	0.314856i	$0.898044\pi$
$242$		0			0
$243$	−7.43881	+	13.6232i	−0.477200	+	0.873927i
$244$		0			0
$245$	−10.2133	+	6.04385i	−0.652504	+	0.386128i
$246$		0			0
$247$	7.77760	+	5.82224i	0.494877	+	0.370460i
$248$		0			0
$249$	6.45578	−	44.9009i	0.409118	−	2.84548i
$250$		0			0
$251$	−16.8014	+	14.5585i	−1.06049	+	0.918923i	−0.996871	−	0.0790511i	$-0.974811\pi$
$251$	−16.8014	+	14.5585i	−1.06049	+	0.918923i	−0.0636230	+	0.997974i	$0.520266\pi$
$252$		0			0
$253$	−8.22865	−	13.0773i	−0.517331	−	0.822166i
$254$		0			0
$255$	−1.49612	−	1.86098i	−0.0936906	−	0.116539i
$256$		0			0
$257$	15.9615	−	11.9486i	0.995651	−	0.745335i	0.0285148	−	0.999593i	$-0.490922\pi$
$257$	15.9615	−	11.9486i	0.995651	−	0.745335i	0.967136	+	0.254258i	$0.0818313\pi$
$258$		0			0
$259$	9.20686	−	1.32375i	0.572087	−	0.0822536i
$260$		0			0
$261$	12.3623	−	7.94475i	0.765206	−	0.491768i
$262$		0			0
$263$	−17.9967	−	9.82694i	−1.10972	−	0.605955i	−0.183534	−	0.983013i	$-0.558754\pi$
$263$	−17.9967	−	9.82694i	−1.10972	−	0.605955i	−0.926189	+	0.377058i	$0.876936\pi$
$264$		0			0
$265$	0.613240	+	17.7464i	0.0376710	+	1.09015i
$266$		0			0
$267$	−10.6838	−	3.98487i	−0.653840	−	0.243870i
$268$		0			0
$269$	−4.97906	+	16.9571i	−0.303579	+	1.03389i	0.656538	+	0.754293i	$0.272020\pi$
$269$	−4.97906	+	16.9571i	−0.303579	+	1.03389i	−0.960116	+	0.279601i	$0.909798\pi$
$270$		0			0
$271$	1.57268	−	3.44369i	0.0955335	−	0.209189i	−0.855832	−	0.517254i	$-0.826954\pi$
$271$	1.57268	−	3.44369i	0.0955335	−	0.209189i	0.951365	+	0.308065i	$0.0996814\pi$
$272$		0			0
$273$	−2.70713	−	12.4445i	−0.163843	−	0.753175i
$274$		0			0
$275$	−1.18638	+	16.0648i	−0.0715414	+	0.968746i
$276$		0			0
$277$	17.5998	+	17.5998i	1.05747	+	1.05747i	0.998245	+	0.0592262i	$0.0188633\pi$
$277$	17.5998	+	17.5998i	1.05747	+	1.05747i	0.0592262	+	0.998245i	$0.481137\pi$
$278$		0			0
$279$	5.21093	−	8.10837i	0.311970	−	0.485435i
$280$		0			0
$281$	23.6831	+	10.8157i	1.41281	+	0.645210i	0.968123	−	0.250474i	$-0.0805864\pi$
$281$	23.6831	+	10.8157i	1.41281	+	0.645210i	0.444690	+	0.895684i	$0.353314\pi$
$282$		0			0
$283$	−1.75185	−	3.20828i	−0.104137	−	0.190712i	0.820415	−	0.571768i	$-0.193742\pi$
$283$	−1.75185	−	3.20828i	−0.104137	−	0.190712i	−0.924552	+	0.381056i	$0.875561\pi$
$284$		0			0
$285$	6.69503	−	16.1104i	0.396579	−	0.954300i
$286$		0			0
$287$	1.00607	+	14.0666i	0.0593862	+	0.830327i
$288$		0			0
$289$	−4.74859	−	16.1722i	−0.279329	−	0.951306i
$290$		0			0
$291$	7.50340	+	11.6755i	0.439857	+	0.684431i
$292$		0			0
$293$	−18.5493	+	24.7790i	−1.08366	+	1.44760i	−0.199813	+	0.979834i	$0.564034\pi$
$293$	−18.5493	+	24.7790i	−1.08366	+	1.44760i	−0.883850	+	0.467771i	$0.845057\pi$
$294$		0			0
$295$	−0.0210400	+	0.115849i	−0.00122500	+	0.00674500i
$296$		0			0
$297$	16.7691	+	1.19935i	0.973042	+	0.0695934i
$298$		0			0
$299$	11.9523	−	11.7259i	0.691221	−	0.678125i
$300$		0			0
$301$	5.86828	+	6.77236i	0.338242	+	0.390352i
$302$		0			0
$303$	12.7000	+	16.9652i	0.729597	+	0.974627i
$304$		0			0
$305$	−2.86097	−	26.9040i	−0.163819	−	1.54052i
$306$		0			0
$307$	−13.1208	−	2.85426i	−0.748844	−	0.162901i	−0.178081	−	0.984016i	$-0.556989\pi$
$307$	−13.1208	−	2.85426i	−0.748844	−	0.162901i	−0.570763	+	0.821115i	$0.693353\pi$
$308$		0			0
$309$	−0.0295107	+	0.00866512i	−0.00167880	+	0.000492942i
$310$		0			0
$311$	0.948327	−	1.09443i	0.0537747	−	0.0620593i	−0.728225	−	0.685338i	$-0.759654\pi$
$311$	0.948327	−	1.09443i	0.0537747	−	0.0620593i	0.782000	+	0.623279i	$0.214200\pi$
$312$		0			0
$313$	2.58045	−	6.91845i	0.145855	−	0.391054i	−0.843393	−	0.537297i	$-0.819445\pi$
$313$	2.58045	−	6.91845i	0.145855	−	0.391054i	0.989249	+	0.146243i	$0.0467182\pi$
$314$		0			0
$315$	−12.6534	+	6.31554i	−0.712940	+	0.355841i
$316$		0			0
$317$	−13.2000	+	4.92334i	−0.741386	+	0.276522i	−0.691643	−	0.722240i	$-0.743113\pi$
$317$	−13.2000	+	4.92334i	−0.741386	+	0.276522i	−0.0497425	+	0.998762i	$0.515840\pi$
$318$		0			0
$319$	8.19303	+	5.26534i	0.458722	+	0.294803i
$320$		0			0
$321$		−	50.6736i		−	2.82832i
$322$		0			0
$323$	−0.749423	+	0.749423i	−0.0416990	+	0.0416990i
$324$		0			0
$325$	−17.2846	+	2.44431i	−0.958779	+	0.135586i
$326$		0			0
$327$	3.47740	+	9.32326i	0.192300	+	0.515577i
$328$		0			0
$329$	−0.266841	−	0.0783515i	−0.0147114	−	0.00431966i
$330$		0			0
$331$	9.63376	+	21.0950i	0.529520	+	1.15949i	0.965708	+	0.259631i	$0.0836008\pi$
$331$	9.63376	+	21.0950i	0.529520	+	1.15949i	−0.436188	+	0.899855i	$0.643672\pi$
$332$		0			0
$333$	−34.6660	+	2.47936i	−1.89969	+	0.135868i
$334$		0			0
$335$	−9.97076	−	5.93155i	−0.544761	−	0.324075i
$336$		0			0
$337$	2.38047	−	10.9428i	0.129672	−	0.596094i	−0.865747	−	0.500483i	$-0.833156\pi$
$337$	2.38047	−	10.9428i	0.129672	−	0.596094i	0.995419	−	0.0956110i	$-0.0304805\pi$
$338$		0			0
$339$	4.64448	+	32.3030i	0.252253	+	1.75446i
$340$		0			0
$341$	6.32280	+	0.909082i	0.342399	+	0.0492295i
$342$		0			0
$343$	1.14229	−	15.9713i	0.0616779	−	0.862369i
$344$		0			0
$345$	−25.6922	−	15.6187i	−1.38322	−	0.840885i
$346$		0			0
$347$	−0.259937	+	3.63440i	−0.0139542	+	0.195105i	0.985693	+	0.168550i	$0.0539083\pi$
$347$	−0.259937	+	3.63440i	−0.0139542	+	0.195105i	−0.999647	+	0.0265552i	$0.991546\pi$
$348$		0			0
$349$	26.6246	+	3.82804i	1.42518	+	0.204910i	0.811366	−	0.584539i	$-0.198724\pi$
$349$	26.6246	+	3.82804i	1.42518	+	0.204910i	0.613816	+	0.789449i	$0.289634\pi$
$350$		0			0
$351$	2.59281	+	18.0334i	0.138394	+	0.962550i
$352$		0			0
$353$	−1.70659	+	7.84508i	−0.0908328	+	0.417552i	0.909167	+	0.416433i	$0.136720\pi$
$353$	−1.70659	+	7.84508i	−0.0908328	+	0.417552i	−0.999999	+	0.00111896i	$0.999644\pi$
$354$		0			0
$355$	−5.45818	−	21.4887i	−0.289690	−	1.14050i
$356$		0			0
$357$	1.38576	−	0.0991118i	0.0733424	−	0.00524555i
$358$		0			0
$359$	−2.81170	−	6.15676i	−0.148396	−	0.324941i	0.820807	−	0.571206i	$-0.193524\pi$
$359$	−2.81170	−	6.15676i	−0.148396	−	0.324941i	−0.969203	+	0.246264i	$0.920797\pi$
$360$		0			0
$361$	10.8004	+	3.17129i	0.568443	+	0.166910i
$362$		0			0
$363$	−0.608017	−	1.63016i	−0.0319126	−	0.0855611i
$364$		0			0
$365$	2.91900	+	16.2869i	0.152788	+	0.852493i
$366$		0			0
$367$	−15.0717	+	15.0717i	−0.786737	+	0.786737i	−0.980958	−	0.194221i	$-0.937782\pi$
$367$	−15.0717	+	15.0717i	−0.786737	+	0.786737i	0.194221	+	0.980958i	$0.437782\pi$
$368$		0			0
$369$		−	52.6933i		−	2.74310i
$370$		0			0
$371$	−8.69151	−	5.58569i	−0.451241	−	0.289995i
$372$		0			0
$373$	−7.66715	+	2.85970i	−0.396990	+	0.148070i	−0.540027	−	0.841648i	$-0.681586\pi$
$373$	−7.66715	+	2.85970i	−0.396990	+	0.148070i	0.143037	+	0.989717i	$0.454313\pi$
$374$		0			0
$375$	11.8954	+	29.0025i	0.614275	+	1.49768i
$376$		0			0
$377$	−3.68827	+	9.88864i	−0.189956	+	0.509291i
$378$		0			0
$379$	−23.0227	+	26.5696i	−1.18260	+	1.36479i	−0.266499	+	0.963835i	$0.585867\pi$
$379$	−23.0227	+	26.5696i	−1.18260	+	1.36479i	−0.916098	+	0.400955i	$0.868678\pi$
$380$		0			0
$381$	21.9018	−	6.43094i	1.12206	−	0.329467i
$382$		0			0
$383$	31.8297	+	6.92413i	1.62642	+	0.353807i	0.931064	−	0.364856i	$-0.118882\pi$
$383$	31.8297	+	6.92413i	1.62642	+	0.353807i	0.695359	+	0.718663i	$0.255246\pi$
$384$		0			0
$385$	−7.29102	−	5.88941i	−0.371585	−	0.300152i
$386$		0			0
$387$	−20.0654	−	26.8042i	−1.01998	−	1.36253i
$388$		0			0
$389$	2.26378	+	2.61254i	0.114778	+	0.132461i	0.810231	−	0.586111i	$-0.199342\pi$
$389$	2.26378	+	2.61254i	0.114778	+	0.132461i	−0.695453	+	0.718572i	$0.744796\pi$
$390$		0			0
$391$	1.08058	+	1.47264i	0.0546473	+	0.0744745i
$392$		0			0
$393$	26.2065	+	1.87433i	1.32194	+	0.0945472i
$394$		0			0
$395$	−9.50340	−	1.72597i	−0.478168	−	0.0868429i
$396$		0			0
$397$	17.6095	−	23.5235i	0.883796	−	1.18061i	−0.0988469	−	0.995103i	$-0.531515\pi$
$397$	17.6095	−	23.5235i	0.883796	−	1.18061i	0.982642	−	0.185510i	$-0.0593937\pi$
$398$		0			0
$399$	5.48793	+	8.53939i	0.274740	+	0.427504i
$400$		0			0
$401$	−4.65966	−	15.8693i	−0.232692	−	0.792477i	−0.990201	−	0.139652i	$-0.955402\pi$
$401$	−4.65966	−	15.8693i	−0.232692	−	0.792477i	0.757508	−	0.652826i	$-0.226417\pi$
$402$		0			0
$403$	0.493837	+	6.90474i	0.0245998	+	0.343950i
$404$		0			0
$405$	0.0981437	−	0.0405194i	0.00487680	−	0.00201342i
$406$		0			0
$407$	−11.0387	−	20.2159i	−0.547170	−	1.00207i
$408$		0			0
$409$	32.6934	+	14.9306i	1.61658	+	0.738269i	0.998842	−	0.0481133i	$-0.0153209\pi$
$409$	32.6934	+	14.9306i	1.61658	+	0.738269i	0.617741	+	0.786382i	$0.288048\pi$
$410$		0			0
$411$	−30.2116	+	47.0101i	−1.49023	+	2.31884i
$412$		0			0
$413$	−0.0484422	−	0.0484422i	−0.00238368	−	0.00238368i
$414$		0			0
$415$	26.5067	−	24.6214i	1.30116	−	1.20862i
$416$		0			0
$417$	0.935899	+	4.30226i	0.0458311	+	0.210682i
$418$		0			0
$419$	13.2916	−	29.1045i	0.649337	−	1.42185i	−0.242797	−	0.970077i	$-0.578065\pi$
$419$	13.2916	−	29.1045i	0.649337	−	1.42185i	0.892134	−	0.451772i	$-0.149208\pi$
$420$		0			0
$421$	0.703128	−	2.39464i	0.0342684	−	0.116707i	−0.940583	−	0.339565i	$-0.889720\pi$
$421$	0.703128	−	2.39464i	0.0342684	−	0.116707i	0.974851	+	0.222857i	$0.0715384\pi$
$422$		0			0
$423$	0.973608	+	0.363137i	0.0473384	+	0.0176563i
$424$		0			0
$425$	0.00441009	−	1.90431i	0.000213921	−	0.0923728i
$426$		0			0
$427$	13.8163	+	7.54429i	0.668620	+	0.365094i
$428$		0			0
$429$	−26.5306	+	17.0502i	−1.28091	+	0.823192i
$430$		0			0
$431$	−27.1975	+	3.91041i	−1.31006	+	0.188358i	−0.761724	−	0.647902i	$-0.775647\pi$
$431$	−27.1975	+	3.91041i	−1.31006	+	0.188358i	−0.548333	+	0.836260i	$0.684738\pi$
$432$		0			0
$433$	14.0675	−	10.5308i	0.676041	−	0.506078i	−0.205215	−	0.978717i	$-0.565789\pi$
$433$	14.0675	−	10.5308i	0.676041	−	0.506078i	0.881256	+	0.472639i	$0.156698\pi$
$434$		0			0
$435$	18.8412	+	2.04771i	0.903368	+	0.0981803i
$436$		0			0
$437$	−5.65978	+	12.0860i	−0.270744	+	0.578149i
$438$		0			0
$439$	8.01002	−	6.94072i	0.382297	−	0.331262i	−0.442420	−	0.896808i	$-0.645880\pi$
$439$	8.01002	−	6.94072i	0.382297	−	0.331262i	0.824717	+	0.565546i	$0.191334\pi$
$440$		0			0
$441$	−3.67171	+	25.5373i	−0.174844	+	1.21606i
$442$		0			0
$443$	21.0819	+	15.7817i	1.00163	+	0.749810i	0.968340	−	0.249636i	$-0.0803108\pi$
$443$	21.0819	+	15.7817i	1.00163	+	0.749810i	0.0332893	+	0.999446i	$0.489402\pi$
$444$		0			0
$445$	−4.63131	−	7.82629i	−0.219545	−	0.371002i
$446$		0			0
$447$	−24.2021	+	44.3229i	−1.14472	+	2.09640i
$448$		0			0
$449$	18.3088	+	15.8647i	0.864047	+	0.748701i	0.969336	−	0.245741i	$-0.0790311\pi$
$449$	18.3088	+	15.8647i	0.864047	+	0.748701i	−0.105289	+	0.994442i	$0.533577\pi$
$450$		0			0
$451$	31.7663	−	14.5072i	1.49582	−	0.683117i
$452$		0			0
$453$	41.7035	−	22.7718i	1.95940	−	1.06991i
$454$		0			0
$455$	4.55689	−	9.07723i	0.213630	−	0.425547i
$456$		0			0
$457$	−6.63583	+	1.44354i	−0.310411	+	0.0675258i	−0.365072	−	0.930979i	$-0.618956\pi$
$457$	−6.63583	+	1.44354i	−0.310411	+	0.0675258i	0.0546612	+	0.998505i	$0.482592\pi$
$458$		0			0
$459$	−1.98747			−0.0927671
$460$		0			0
$461$	7.34969			0.342309			0.171154	−	0.985244i	$-0.445250\pi$
$461$	7.34969			0.342309			0.171154	+	0.985244i	$0.445250\pi$
$462$		0			0
$463$	0.982041	−	0.213630i	0.0456393	−	0.00992822i	−0.189688	−	0.981844i	$-0.560748\pi$
$463$	0.982041	−	0.213630i	0.0456393	−	0.00992822i	0.235327	+	0.971916i	$0.424384\pi$
$464$		0			0
$465$	11.7991	−	3.91194i	0.547169	−	0.181412i
$466$		0			0
$467$	3.53646	−	1.93105i	0.163648	−	0.0893584i	−0.395338	−	0.918536i	$-0.629372\pi$
$467$	3.53646	−	1.93105i	0.163648	−	0.0893584i	0.558986	+	0.829177i	$0.311191\pi$
$468$		0			0
$469$	6.14025	−	2.80416i	0.283530	−	0.129484i
$470$		0			0
$471$	31.7824	+	27.5396i	1.46446	+	1.26896i
$472$		0			0
$473$	10.6347	−	19.4761i	0.488986	−	0.895510i
$474$		0			0
$475$	12.2272	−	6.63982i	0.561021	−	0.304656i
$476$		0			0
$477$	30.9036	+	23.1342i	1.41498	+	1.05924i
$478$		0			0
$479$	−0.959278	+	6.67193i	−0.0438305	+	0.304848i	0.956100	+	0.293041i	$0.0946674\pi$
$479$	−0.959278	+	6.67193i	−0.0438305	+	0.304848i	−0.999930	+	0.0118067i	$0.996242\pi$
$480$		0			0
$481$	18.8642	−	16.3459i	0.860134	−	0.745310i
$482$		0			0
$483$	15.9820	−	7.11479i	0.727205	−	0.323734i
$484$		0			0
$485$	−1.19592	+	11.0037i	−0.0543037	+	0.499654i
$486$		0			0
$487$	15.8285	−	11.8491i	0.717259	−	0.536933i	−0.177150	−	0.984184i	$-0.556688\pi$
$487$	15.8285	−	11.8491i	0.717259	−	0.536933i	0.894409	+	0.447251i	$0.147597\pi$
$488$		0			0
$489$	22.0752	−	3.17393i	0.998273	−	0.143530i
$490$		0			0
$491$	11.5391	−	7.41573i	0.520752	−	0.334667i	−0.253717	−	0.967278i	$-0.581653\pi$
$491$	11.5391	−	7.41573i	0.520752	−	0.334667i	0.774470	+	0.632611i	$0.218017\pi$
$492$		0			0
$493$	−1.01050	−	0.551774i	−0.0455106	−	0.0248507i
$494$		0			0
$495$	25.6031	+	23.8928i	1.15078	+	1.07390i
$496$		0			0
$497$	12.0866	+	4.50805i	0.542156	+	0.202214i
$498$		0			0
$499$	−7.97019	+	27.1440i	−0.356795	+	1.21513i	0.564227	+	0.825620i	$0.309174\pi$
$499$	−7.97019	+	27.1440i	−0.356795	+	1.21513i	−0.921021	+	0.389512i	$0.872644\pi$
$500$		0			0
$501$	−28.2456	+	61.8491i	−1.26192	+	2.76322i
$502$		0			0
$503$	5.41031	+	24.8708i	0.241234	+	1.10893i	0.925218	+	0.379436i	$0.123882\pi$
$503$	5.41031	+	24.8708i	0.241234	+	1.10893i	−0.683984	+	0.729497i	$0.739754\pi$
$504$		0			0
$505$	−0.622800	+	16.8897i	−0.0277142	+	0.751582i
$506$		0			0
$507$	1.60723	+	1.60723i	0.0713798	+	0.0713798i
$508$		0			0
$509$	19.8560	−	30.8965i	0.880102	−	1.36946i	−0.0486710	−	0.998815i	$-0.515499\pi$
$509$	19.8560	−	30.8965i	0.880102	−	1.36946i	0.928773	−	0.370650i	$-0.120865\pi$
$510$		0			0
$511$	−8.75724	−	3.99930i	−0.387397	−	0.176918i
$512$		0			0
$513$	−6.95927	−	12.7450i	−0.307259	−	0.562704i
$514$		0			0
$515$	−0.0226509	−	0.00941306i	−0.000998118	−	0.000414789i
$516$		0			0
$517$	0.0491295	+	0.686920i	0.00216071	+	0.0302107i
$518$		0			0
$519$	−5.42581	−	18.4786i	−0.238167	−	0.811121i
$520$		0			0
$521$	−4.44640	−	6.91873i	−0.194800	−	0.303115i	0.730089	−	0.683352i	$-0.239479\pi$
$521$	−4.44640	−	6.91873i	−0.194800	−	0.303115i	−0.924889	+	0.380237i	$0.875842\pi$
$522$		0			0
$523$	−3.00678	+	4.01659i	−0.131477	+	0.175633i	−0.861449	−	0.507844i	$-0.830442\pi$
$523$	−3.00678	+	4.01659i	−0.131477	+	0.175633i	0.729971	+	0.683478i	$0.239533\pi$
$524$		0			0
$525$	−17.8130	−	3.91821i	−0.777424	−	0.171005i
$526$		0			0
$527$	−0.753229	−	0.0538720i	−0.0328112	−	0.00234670i
$528$		0			0
$529$	19.1075	+	12.8025i	0.830759	+	0.556632i
$530$		0			0
$531$	0.167627	+	0.193452i	0.00727441	+	0.00839511i
$532$		0			0
$533$	22.6794	+	30.2962i	0.982355	+	1.31227i
$534$		0			0
$535$	25.3944	−	31.4380i	1.09790	−	1.35918i
$536$		0			0
$537$	−35.9859	−	7.82825i	−1.55291	−	0.337814i
$538$		0			0
$539$	−16.4062	+	4.81728i	−0.706663	+	0.207495i
$540$		0			0
$541$	15.4514	−	17.8319i	0.664307	−	0.766651i	−0.319167	−	0.947698i	$-0.603403\pi$
$541$	15.4514	−	17.8319i	0.664307	−	0.766651i	0.983474	+	0.181047i	$0.0579487\pi$
$542$		0			0
$543$	12.8917	−	34.5639i	0.553235	−	1.48328i
$544$		0			0
$545$	−2.51485	+	7.52682i	−0.107724	+	0.322414i
$546$		0			0
$547$	34.3245	−	12.8024i	1.46761	−	0.547389i	0.516510	−	0.856281i	$-0.327231\pi$
$547$	34.3245	−	12.8024i	1.46761	−	0.547389i	0.951097	+	0.308891i	$0.0999580\pi$
$548$		0			0
$549$	−49.4813	−	31.7997i	−2.11181	−	1.35718i
$550$		0			0
$551$		−	8.41207i		−	0.358366i
$552$		0			0
$553$	3.97384	−	3.97384i	0.168985	−	0.168985i
$554$		0			0
$555$	−36.7888	−	25.6061i	−1.56160	−	1.08692i
$556$		0			0
$557$	15.1354	+	40.5796i	0.641307	+	1.71941i	0.693186	+	0.720759i	$0.256206\pi$
$557$	15.1354	+	40.5796i	0.641307	+	1.71941i	−0.0518787	+	0.998653i	$0.516521\pi$
$558$		0			0
$559$	23.0733	+	6.77493i	0.975896	+	0.286549i
$560$		0			0
$561$	−1.42917	−	3.12944i	−0.0603395	−	0.132125i
$562$		0			0
$563$	9.73428	−	0.696209i	0.410251	−	0.0293417i	0.135311	−	0.990803i	$-0.456797\pi$
$563$	9.73428	−	0.696209i	0.410251	−	0.0293417i	0.274940	+	0.961461i	$0.411342\pi$
$564$		0			0
$565$	−13.3068	+	22.3684i	−0.559822	+	0.941046i
$566$		0			0
$567$	−0.0131320	+	0.0603668i	−0.000551492	+	0.00253517i
$568$		0			0
$569$	1.17274	+	8.15660i	0.0491639	+	0.341942i	0.999526	+	0.0307954i	$0.00980402\pi$
$569$	1.17274	+	8.15660i	0.0491639	+	0.341942i	−0.950362	+	0.311147i	$0.899287\pi$
$570$		0			0
$571$	12.7056	+	1.82680i	0.531715	+	0.0764490i	0.402943	−	0.915225i	$-0.367987\pi$
$571$	12.7056	+	1.82680i	0.531715	+	0.0764490i	0.128772	+	0.991674i	$0.458896\pi$
$572$		0			0
$573$	−0.276171	+	3.86137i	−0.0115372	+	0.161311i
$574$		0			0
$575$	−8.11236	−	22.5652i	−0.338309	−	0.941035i
$576$		0			0
$577$	1.00479	−	14.0488i	0.0418299	−	0.584858i	−0.932708	−	0.360634i	$-0.882560\pi$
$577$	1.00479	−	14.0488i	0.0418299	−	0.584858i	0.974537	−	0.224225i	$-0.0719850\pi$
$578$		0			0
$579$	23.2769	+	3.34671i	0.967353	+	0.139084i
$580$		0			0
$581$	2.99564	+	20.8351i	0.124280	+	0.864386i
$582$		0			0
$583$	−5.43831	+	24.9995i	−0.225232	+	1.03537i
$584$		0			0
$585$	−19.4027	+	32.6154i	−0.802203	+	1.34848i
$586$		0			0
$587$	−32.2007	+	2.30304i	−1.32906	+	0.0950565i	−0.717733	−	0.696319i	$-0.754820\pi$
$587$	−32.2007	+	2.30304i	−1.32906	+	0.0950565i	−0.611331	+	0.791375i	$0.709365\pi$
$588$		0			0
$589$	−2.29203	−	5.01884i	−0.0944413	−	0.206798i
$590$		0			0
$591$	−58.4194	−	17.1535i	−2.40305	−	0.705600i
$592$		0			0
$593$	11.0235	+	29.5552i	0.452681	+	1.21368i	0.940215	+	0.340581i	$0.110624\pi$
$593$	11.0235	+	29.5552i	0.452681	+	1.21368i	−0.487534	+	0.873104i	$0.662104\pi$
$594$		0			0
$595$	0.909400	+	0.632969i	0.0372817	+	0.0259492i
$596$		0			0
$597$	2.93405	−	2.93405i	0.120083	−	0.120083i
$598$		0			0
$599$		−	44.6540i		−	1.82451i	−0.409621	−	0.912256i	$-0.634339\pi$
$599$		−	44.6540i		−	1.82451i	0.409621	−	0.912256i	$-0.365661\pi$
$600$		0			0
$601$	−11.0045	−	7.07216i	−0.448883	−	0.288479i	0.296603	−	0.955001i	$-0.404146\pi$
$601$	−11.0045	−	7.07216i	−0.448883	−	0.288479i	−0.745486	+	0.666521i	$0.767782\pi$
$602$		0			0
$603$	−23.6316	+	8.81415i	−0.962355	+	0.358940i
$604$		0			0
$605$	0.439718	−	1.31605i	0.0178771	−	0.0535052i
$606$		0			0
$607$	6.27015	−	16.8109i	0.254498	−	0.682334i	−0.745379	−	0.666641i	$-0.767732\pi$
$607$	6.27015	−	16.8109i	0.254498	−	0.682334i	0.999877	−	0.0156937i	$-0.00499566\pi$
$608$		0			0
$609$	−7.22116	+	8.33366i	−0.292616	+	0.337697i
$610$		0			0
$611$	−0.716074	+	0.210258i	−0.0289693	+	0.00850614i
$612$		0			0
$613$	3.98643	+	0.867194i	0.161010	+	0.0350256i	0.292348	−	0.956312i	$-0.405564\pi$
$613$	3.98643	+	0.867194i	0.161010	+	0.0350256i	−0.131338	+	0.991338i	$0.541927\pi$
$614$		0			0
$615$	42.7030	−	52.8658i	1.72195	−	2.13175i
$616$		0			0
$617$	−8.74742	−	11.6852i	−0.352158	−	0.470428i	0.589127	−	0.808040i	$-0.299472\pi$
$617$	−8.74742	−	11.6852i	−0.352158	−	0.470428i	−0.941285	+	0.337612i	$0.890381\pi$
$618$		0			0
$619$	25.2073	+	29.0908i	1.01317	+	1.16926i	0.985506	+	0.169640i	$0.0542605\pi$
$619$	25.2073	+	29.0908i	1.01317	+	1.16926i	0.0276613	+	0.999617i	$0.491194\pi$
$620$		0			0
$621$	−23.5308	+	8.52109i	−0.944260	+	0.341940i
$622$		0			0
$623$	5.27768	+	0.377467i	0.211446	+	0.0151229i
$624$		0			0
$625$	−7.15434	+	23.9544i	−0.286174	+	0.958178i
$626$		0			0
$627$	15.0637	−	20.1227i	0.601586	−	0.803625i
$628$		0			0
$629$	1.47214	+	2.29070i	0.0586981	+	0.0913361i
$630$		0			0
$631$	−5.60999	−	19.1059i	−0.223330	−	0.760592i	−0.992575	−	0.121638i	$-0.961185\pi$
$631$	−5.60999	−	19.1059i	−0.223330	−	0.760592i	0.769245	−	0.638955i	$-0.220633\pi$
$632$		0			0
$633$	−2.34481	−	32.7848i	−0.0931980	−	1.30308i
$634$		0			0
$635$	16.8107	+	6.98603i	0.667111	+	0.277232i
$636$		0			0
$637$	−8.88032	−	16.2631i	−0.351851	−	0.644367i
$638$		0			0
$639$	−43.8439	−	20.0228i	−1.73444	−	0.792091i
$640$		0			0
$641$	13.7159	−	21.3424i	0.541747	−	0.842975i	−0.457176	−	0.889376i	$-0.651139\pi$
$641$	13.7159	−	21.3424i	0.541747	−	0.842975i	0.998923	+	0.0464015i	$0.0147754\pi$
$642$		0			0
$643$	19.8060	+	19.8060i	0.781070	+	0.781070i	0.980011	−	0.198941i	$-0.0637502\pi$
$643$	19.8060	+	19.8060i	0.781070	+	0.781070i	−0.198941	+	0.980011i	$0.563750\pi$
$644$		0			0
$645$	1.59125	−	43.1531i	0.0626554	−	1.69915i
$646$		0			0
$647$	−3.27887	−	15.0727i	−0.128906	−	0.592570i	−0.995598	−	0.0937270i	$-0.970122\pi$
$647$	−3.27887	−	15.0727i	−0.128906	−	0.592570i	0.866692	−	0.498843i	$-0.166242\pi$
$648$		0			0
$649$	−0.0704733	+	0.154315i	−0.00276632	+	0.00605739i
$650$		0			0
$651$	−2.03765	+	6.93961i	−0.0798619	+	0.271985i
$652$		0			0
$653$	−18.3637	−	6.84929i	−0.718626	−	0.268033i	−0.0365672	−	0.999331i	$-0.511642\pi$
$653$	−18.3637	−	6.84929i	−0.718626	−	0.268033i	−0.682058	+	0.731298i	$0.738915\pi$
$654$		0			0
$655$	15.3193	+	14.2959i	0.598573	+	0.558587i
$656$		0			0
$657$	31.5714	+	17.2393i	1.23172	+	0.672569i
$658$		0			0
$659$	−12.3362	+	7.92797i	−0.480549	+	0.308830i	−0.758395	−	0.651796i	$-0.774016\pi$
$659$	−12.3362	+	7.92797i	−0.480549	+	0.308830i	0.277846	+	0.960626i	$0.410380\pi$
$660$		0			0
$661$	−0.865419	+	0.124428i	−0.0336609	+	0.00483970i	−0.159125	−	0.987258i	$-0.550867\pi$
$661$	−0.865419	+	0.124428i	−0.0336609	+	0.00483970i	0.125464	+	0.992098i	$0.459958\pi$
$662$		0			0
$663$	2.98460	−	2.23425i	0.115912	−	0.0867710i
$664$		0			0
$665$	−0.874684	+	8.04806i	−0.0339188	+	0.312090i
$666$		0			0
$667$	−14.3296	−	2.20036i	−0.554844	−	0.0851984i
$668$		0			0
$669$	−20.8724	+	18.0860i	−0.806973	+	0.699247i
$670$		0			0
$671$	5.54767	−	38.5849i	0.214166	−	1.48955i
$672$		0			0
$673$	−10.3905	−	7.77823i	−0.400524	−	0.299829i	0.379961	−	0.925002i	$-0.375937\pi$
$673$	−10.3905	−	7.77823i	−0.400524	−	0.299829i	−0.780486	+	0.625174i	$0.785028\pi$
$674$		0			0
$675$	25.0176	+	7.40881i	0.962928	+	0.285165i
$676$		0			0
$677$	20.0825	−	36.7784i	0.771834	−	1.41351i	−0.134486	−	0.990916i	$-0.542938\pi$
$677$	20.0825	−	36.7784i	0.771834	−	1.41351i	0.906320	−	0.422593i	$-0.138880\pi$
$678$		0			0
$679$	−4.86707	−	4.21734i	−0.186781	−	0.161847i
$680$		0			0
$681$	−47.5846	+	21.7312i	−1.82345	+	0.832740i
$682$		0			0
$683$	−44.3938	+	24.2409i	−1.69868	+	0.927551i	−0.728544	+	0.684999i	$0.759803\pi$
$683$	−44.3938	+	24.2409i	−1.69868	+	0.927551i	−0.970138	+	0.242552i	$0.922015\pi$
$684$		0			0
$685$	−42.3019	+	14.0250i	−1.61627	+	0.535869i
$686$		0			0
$687$	−22.9910	+	5.00140i	−0.877163	+	0.190815i
$688$		0			0
$689$	−27.7252			−1.05624
$690$		0			0
$691$	−32.8985			−1.25152			−0.625759	−	0.780017i	$-0.715210\pi$
$691$	−32.8985			−1.25152			−0.625759	+	0.780017i	$0.715210\pi$
$692$		0			0
$693$	−19.9100	+	4.33117i	−0.756320	+	0.164527i
$694$		0			0
$695$	−1.57539	+	3.13814i	−0.0597579	+	0.119037i
$696$		0			0
$697$	−3.62343	+	1.97854i	−0.137247	+	0.0749426i
$698$		0			0
$699$	−54.2401	+	24.7706i	−2.05155	+	0.936911i
$700$		0			0
$701$	0.899247	+	0.779202i	0.0339641	+	0.0294300i	0.671677	−	0.740844i	$-0.265574\pi$
$701$	0.899247	+	0.779202i	0.0339641	+	0.0294300i	−0.637713	+	0.770274i	$0.720120\pi$
$702$		0			0
$703$	−9.53464	+	17.4614i	−0.359606	+	0.658569i
$704$		0			0
$705$	0.682506	+	1.15334i	0.0257047	+	0.0434375i
$706$		0			0
$707$	−7.87227	−	5.89311i	−0.296067	−	0.221633i
$708$		0			0
$709$	−1.47746	+	10.2760i	−0.0554871	+	0.385921i	0.943087	+	0.332545i	$0.107907\pi$
$709$	−1.47746	+	10.2760i	−0.0554871	+	0.385921i	−0.998574	+	0.0533763i	$0.983002\pi$
$710$		0			0
$711$	−15.8694	+	13.7509i	−0.595148	+	0.515699i
$712$		0			0
$713$	−9.14891	+	2.59158i	−0.342629	+	0.0970555i
$714$		0			0
$715$	−25.0042	−	2.71752i	−0.935102	−	0.101629i
$716$		0			0
$717$	57.8817	−	43.3297i	2.16163	−	1.61818i
$718$		0			0
$719$	16.1631	−	2.32390i	0.602782	−	0.0866670i	0.165834	−	0.986154i	$-0.446968\pi$
$719$	16.1631	−	2.32390i	0.602782	−	0.0866670i	0.436948	+	0.899487i	$0.356059\pi$
$720$		0			0
$721$	0.0120062	−	0.00771590i	0.000447133	−	0.000287355i
$722$		0			0
$723$	−39.0521	−	21.3241i	−1.45236	−	0.793051i
$724$		0			0
$725$	10.6629	+	10.7125i	0.396012	+	0.397850i
$726$		0			0
$727$	43.0873	+	16.0707i	1.59802	+	0.596031i	0.981526	−	0.191328i	$-0.0612795\pi$
$727$	43.0873	+	16.0707i	1.59802	+	0.596031i	0.616495	+	0.787359i	$0.288552\pi$
$728$		0			0
$729$	−12.3011	+	41.8936i	−0.455595	+	1.55161i
$730$		0			0
$731$	−1.08976	+	2.38624i	−0.0403061	+	0.0882582i
$732$		0			0
$733$	−7.00174	−	32.1865i	−0.258615	−	1.18884i	−0.904861	−	0.425706i	$-0.860026\pi$
$733$	−7.00174	−	32.1865i	−0.258615	−	1.18884i	0.646246	−	0.763129i	$-0.276338\pi$
$734$		0			0
$735$	−24.3794	+	22.6453i	−0.899246	+	0.835286i
$736$		0			0
$737$	−11.8198	−	11.8198i	−0.435387	−	0.435387i
$738$		0			0
$739$	−21.8082	+	33.9342i	−0.802228	+	1.24829i	0.162934	+	0.986637i	$0.447904\pi$
$739$	−21.8082	+	33.9342i	−0.802228	+	1.24829i	−0.965162	+	0.261654i	$0.915732\pi$
$740$		0			0
$741$	24.7783	+	11.3159i	0.910253	+	0.415699i
$742$		0			0
$743$	−1.09801	−	2.01085i	−0.0402820	−	0.0737709i	0.856763	−	0.515711i	$-0.172472\pi$
$743$	−1.09801	−	2.01085i	−0.0402820	−	0.0737709i	−0.897045	+	0.441940i	$0.854290\pi$
$744$		0			0
$745$	−37.2269	+	15.3694i	−1.36389	+	0.563092i
$746$		0			0
$747$	−5.61079	−	78.4491i	−0.205288	−	2.87030i
$748$		0			0
$749$	6.62459	+	22.5613i	0.242057	+	0.824371i
$750$		0			0
$751$	−8.37309	−	13.0288i	−0.305538	−	0.475427i	0.654200	−	0.756321i	$-0.273005\pi$
$751$	−8.37309	−	13.0288i	−0.305538	−	0.475427i	−0.959739	+	0.280894i	$0.909369\pi$
$752$		0			0
$753$	−37.3541	+	49.8993i	−1.36126	+	1.81843i
$754$		0			0
$755$	37.2848	+	6.77150i	1.35693	+	0.246440i
$756$		0			0
$757$	20.9019	+	1.49493i	0.759692	+	0.0543342i	0.445810	−	0.895128i	$-0.352916\pi$
$757$	20.9019	+	1.49493i	0.759692	+	0.0543342i	0.313882	+	0.949462i	$0.398370\pi$
$758$		0			0
$759$	−30.3380	−	30.9239i	−1.10120	−	1.12247i
$760$		0			0
$761$	−4.50767	−	5.20212i	−0.163403	−	0.188577i	0.668143	−	0.744033i	$-0.267089\pi$
$761$	−4.50767	−	5.20212i	−0.163403	−	0.188577i	−0.831546	+	0.555456i	$0.812544\pi$
$762$		0			0
$763$	−2.76707	−	3.69637i	−0.100175	−	0.133818i
$764$		0			0
$765$	−3.22053	−	2.60143i	−0.116439	−	0.0940547i
$766$		0			0
$767$	−0.179641	−	0.0390784i	−0.00648645	−	0.00141104i
$768$		0			0
$769$	22.1894	−	6.51540i	0.800171	−	0.234951i	0.144014	−	0.989576i	$-0.453999\pi$
$769$	22.1894	−	6.51540i	0.800171	−	0.234951i	0.656157	+	0.754624i	$0.272181\pi$
$770$		0			0
$771$	36.6086	−	42.2485i	1.31843	−	1.52154i
$772$		0			0
$773$	−3.24389	+	8.69721i	−0.116675	+	0.312817i	−0.982140	−	0.188152i	$-0.939750\pi$
$773$	−3.24389	+	8.69721i	−0.116675	+	0.312817i	0.865465	+	0.500969i	$0.167023\pi$
$774$		0			0
$775$	9.28058	+	3.48598i	0.333368	+	0.125220i
$776$		0			0
$777$	24.4351	−	9.11384i	0.876606	−	0.326957i
$778$		0			0
$779$	−25.3754	−	16.3078i	−0.909169	−	0.584287i
$780$		0			0
$781$		−	31.9440i		−	1.14305i
$782$		0			0
$783$	11.1544	−	11.1544i	0.398625	−	0.398625i
$784$		0			0
$785$	5.91674	+	33.0130i	0.211177	+	1.17828i
$786$		0			0
$787$	9.76854	+	26.1905i	0.348211	+	0.933589i	0.986495	+	0.163789i	$0.0523715\pi$
$787$	9.76854	+	26.1905i	0.348211	+	0.933589i	−0.638285	+	0.769800i	$0.720356\pi$
$788$		0			0
$789$	−55.1623	−	16.1971i	−1.96383	−	0.576633i
$790$		0			0
$791$	−6.29085	−	13.7750i	−0.223677	−	0.489784i
$792$		0			0
$793$	42.1362	−	3.01364i	1.49630	−	0.107017i
$794$		0			0
$795$	12.2567	+	48.2544i	0.434700	+	1.71141i
$796$		0			0
$797$	8.25168	−	37.9323i	0.292289	−	1.34363i	−0.563418	−	0.826172i	$-0.690514\pi$
$797$	8.25168	−	37.9323i	0.292289	−	1.34363i	0.855707	−	0.517460i	$-0.173123\pi$
$798$		0			0
$799$	−0.0115863	−	0.0805848i	−0.000409895	−	0.00285089i
$800$		0			0
$801$	−19.5689	−	2.81358i	−0.691431	−	0.0994128i
$802$		0			0
$803$	−1.70072	+	23.7792i	−0.0600171	+	0.839149i
$804$		0			0
$805$	13.4807	+	3.59513i	0.475133	+	0.126712i
$806$		0			0
$807$	−3.53494	+	49.4249i	−0.124436	+	1.73984i
$808$		0			0
$809$	−16.0091	−	2.30176i	−0.562851	−	0.0809257i	−0.144984	−	0.989434i	$-0.546313\pi$
$809$	−16.0091	−	2.30176i	−0.562851	−	0.0809257i	−0.417867	+	0.908508i	$0.637222\pi$
$810$		0			0
$811$	2.14373	+	14.9100i	0.0752767	+	0.523561i	0.992215	+	0.124533i	$0.0397432\pi$
$811$	2.14373	+	14.9100i	0.0752767	+	0.523561i	−0.916939	+	0.399028i	$0.869348\pi$
$812$		0			0
$813$	2.25629	−	10.3720i	0.0791314	−	0.363761i
$814$		0			0
$815$	15.2860	+	9.09358i	0.535447	+	0.318534i
$816$		0			0
$817$	−19.1180	+	1.36735i	−0.668854	+	0.0478374i
$818$		0			0
$819$	−9.17269	−	20.0854i	−0.320520	−	0.701841i
$820$		0			0
$821$	26.4709	+	7.77257i	0.923842	+	0.271264i	0.708856	−	0.705353i	$-0.249211\pi$
$821$	26.4709	+	7.77257i	0.923842	+	0.271264i	0.214985	+	0.976617i	$0.431030\pi$
$822$		0			0
$823$	−14.5345	−	38.9685i	−0.506641	−	1.35836i	−0.898760	−	0.438442i	$-0.855531\pi$
$823$	−14.5345	−	38.9685i	−0.506641	−	1.35836i	0.392119	−	0.919915i	$-0.371742\pi$
$824$		0			0
$825$	6.32409	+	44.7200i	0.220177	+	1.55695i
$826$		0			0
$827$	0.443269	−	0.443269i	0.0154140	−	0.0154140i	−0.699358	−	0.714772i	$-0.746531\pi$
$827$	0.443269	−	0.443269i	0.0154140	−	0.0154140i	0.714772	+	0.699358i	$0.246531\pi$
$828$		0			0
$829$		−	52.5605i		−	1.82550i	−0.408516	−	0.912751i	$-0.633953\pi$
$829$		−	52.5605i		−	1.82550i	0.408516	−	0.912751i	$-0.366047\pi$
$830$		0			0
$831$	58.7075	+	37.7290i	2.03654	+	1.30881i
$832$		0			0
$833$	1.89393	−	0.706399i	0.0656207	−	0.0244753i
$834$		0			0
$835$	−48.5185	+	24.2164i	−1.67905	+	0.838044i
$836$		0			0
$837$	3.61575	−	9.69421i	0.124979	−	0.335081i
$838$		0			0
$839$	9.18903	−	10.6047i	0.317240	−	0.366115i	−0.574624	−	0.818417i	$-0.694852\pi$
$839$	9.18903	−	10.6047i	0.317240	−	0.366115i	0.891865	+	0.452302i	$0.149397\pi$
$840$		0			0
$841$	−19.0573	+	5.59571i	−0.657147	+	0.192956i
$842$		0			0
$843$	71.3306	+	15.5170i	2.45676	+	0.534435i
$844$		0			0
$845$	0.191686	+	1.80258i	0.00659420	+	0.0620105i
$846$		0			0
$847$	0.483817	+	0.646304i	0.0166242	+	0.0222073i
$848$		0			0
$849$	−6.71165	−	7.74566i	−0.230343	−	0.265830i
$850$		0			0
$851$	27.2507	+	20.8093i	0.934143	+	0.713332i
$852$		0			0
$853$	−27.6438	−	1.97712i	−0.946504	−	0.0676953i	−0.410454	−	0.911881i	$-0.634630\pi$
$853$	−27.6438	−	1.97712i	−0.946504	−	0.0676953i	−0.536050	+	0.844186i	$0.680084\pi$
$854$		0			0
$855$	5.40511	−	29.7613i	0.184851	−	1.01781i
$856$		0			0
$857$	6.35846	−	8.49391i	0.217201	−	0.290146i	−0.678686	−	0.734429i	$-0.737450\pi$
$857$	6.35846	−	8.49391i	0.217201	−	0.290146i	0.895887	+	0.444282i	$0.146541\pi$
$858$		0			0
$859$	13.0347	+	20.2823i	0.444737	+	0.692024i	0.989169	−	0.146781i	$-0.0468912\pi$
$859$	13.0347	+	20.2823i	0.444737	+	0.692024i	−0.544432	+	0.838805i	$0.683255\pi$
$860$		0			0
$861$	11.1398	+	37.9388i	0.379645	+	1.29295i
$862$		0			0
$863$	1.86653	+	26.0976i	0.0635376	+	0.888372i	0.924859	+	0.380311i	$0.124183\pi$
$863$	1.86653	+	26.0976i	0.0635376	+	0.888372i	−0.861321	+	0.508061i	$0.830363\pi$
$864$		0			0
$865$	5.89415	−	14.1833i	0.200407	−	0.482245i
$866$		0			0
$867$	−22.6481	−	41.4769i	−0.769170	−	1.40863i
$868$		0			0
$869$	−12.6588	−	5.78110i	−0.429422	−	0.196110i
$870$		0			0
$871$	9.79344	−	15.2389i	0.331838	−	0.516350i
$872$		0			0
$873$	17.0150	+	17.0150i	0.575870	+	0.575870i
$874$		0			0
$875$	−9.08767	−	11.3576i	−0.307219	−	0.383958i
$876$		0			0
$877$	−7.76644	−	35.7017i	−0.262254	−	1.20556i	−0.900198	−	0.435480i	$-0.856579\pi$
$877$	−7.76644	−	35.7017i	−0.262254	−	1.20556i	0.637944	−	0.770082i	$-0.279785\pi$
$878$		0			0
$879$	−36.0517	+	78.9422i	−1.21599	+	2.66266i
$880$		0			0
$881$	4.95414	−	16.8723i	0.166909	−	0.568441i	−0.832976	−	0.553309i	$-0.813365\pi$
$881$	4.95414	−	16.8723i	0.166909	−	0.568441i	0.999886	−	0.0151319i	$-0.00481682\pi$
$882$		0			0
$883$	50.6483	+	18.8908i	1.70445	+	0.635727i	0.997442	−	0.0714788i	$-0.0227718\pi$
$883$	50.6483	+	18.8908i	1.70445	+	0.635727i	0.707008	+	0.707206i	$0.250045\pi$
$884$		0			0
$885$	0.0114010	+	0.329932i	0.000383242	+	0.0110905i
$886$		0			0
$887$	−8.86097	−	4.83846i	−0.297522	−	0.162460i	0.323554	−	0.946210i	$-0.395122\pi$
$887$	−8.86097	−	4.83846i	−0.297522	−	0.162460i	−0.621076	+	0.783750i	$0.713304\pi$
$888$		0			0
$889$	−8.91054	+	5.72646i	−0.298850	+	0.192059i
$890$		0			0
$891$	0.151425	−	0.0217717i	0.00507294	−	0.000729379i
$892$		0			0
$893$	0.476192	−	0.356473i	0.0159352	−	0.0119289i
$894$		0			0
$895$	−18.4027	−	22.8905i	−0.615134	−	0.765146i
$896$		0			0
$897$	25.7574	−	39.2488i	0.860014	−	1.31048i
$898$		0			0
$899$	4.52975	−	3.92505i	0.151075	−	0.130908i
$900$		0			0
$901$	0.430432	−	2.99372i	0.0143398	−	0.0997352i
$902$		0			0
$903$	20.1136	+	15.0568i	0.669338	+	0.501060i
$904$		0			0
$905$	25.3193	−	14.9830i	0.841642	−	0.498052i
$906$		0			0
$907$	−24.5834	+	45.0212i	−0.816279	+	1.49490i	0.0518994	+	0.998652i	$0.483472\pi$
$907$	−24.5834	+	45.0212i	−0.816279	+	1.49490i	−0.868179	+	0.496252i	$0.834709\pi$
$908$		0			0
$909$	27.7684	+	24.0615i	0.921021	+	0.798069i
$910$		0			0
$911$	−12.3807	+	5.65406i	−0.410190	+	0.187327i	−0.609813	−	0.792545i	$-0.708755\pi$
$911$	−12.3807	+	5.65406i	−0.410190	+	0.187327i	0.199623	+	0.979873i	$0.436028\pi$
$912$		0			0
$913$	45.7486	−	24.9806i	1.51406	−	0.826738i
$914$		0			0
$915$	−23.8726	−	72.0038i	−0.789204	−	2.38037i
$916$		0			0
$917$	−11.9129	+	2.59149i	−0.393398	+	0.0855785i
$918$		0			0
$919$	6.14454			0.202690			0.101345	−	0.994851i	$-0.467685\pi$
$919$	6.14454			0.202690			0.101345	+	0.994851i	$0.467685\pi$
$920$		0			0
$921$	−37.6482			−1.24055
$922$		0			0
$923$	33.8261	−	7.35842i	1.11340	−	0.242205i
$924$		0			0
$925$	−9.99167	−	34.3223i	−0.328524	−	1.12851i
$926$		0			0
$927$	−0.0468027	+	0.0255562i	−0.00153720	+	0.000839376i
$928$		0			0
$929$	−32.5825	+	14.8799i	−1.06900	+	0.488195i	−0.870633	−	0.491933i	$-0.836291\pi$
$929$	−32.5825	+	14.8799i	−1.06900	+	0.488195i	−0.198365	+	0.980128i	$0.563563\pi$
$930$		0			0
$931$	11.1616	+	9.67161i	0.365808	+	0.316974i
$932$		0			0
$933$	1.94587	−	3.56360i	0.0637049	−	0.116667i
$934$		0			0
$935$	0.681621	−	2.65772i	0.0222914	−	0.0869167i
$936$		0			0
$937$	17.8594	+	13.3694i	0.583440	+	0.436758i	0.849792	−	0.527118i	$-0.176727\pi$
$937$	17.8594	+	13.3694i	0.583440	+	0.436758i	−0.266352	+	0.963876i	$0.585818\pi$
$938$		0			0
$939$	2.94636	−	20.4924i	0.0961509	−	0.668744i
$940$		0			0
$941$	13.5728	−	11.7609i	0.442460	−	0.383393i	−0.404945	−	0.914341i	$-0.632709\pi$
$941$	13.5728	−	11.7609i	0.442460	−	0.383393i	0.847405	+	0.530948i	$0.178164\pi$
$942$		0			0
$943$	−34.4171	+	38.9603i	−1.12078	+	1.26872i
$944$		0			0
$945$	−11.8316	+	9.51189i	−0.384880	+	0.309422i
$946$		0			0
$947$	16.8858	−	12.6405i	0.548715	−	0.410763i	−0.288628	−	0.957441i	$-0.593199\pi$
$947$	16.8858	−	12.6405i	0.548715	−	0.410763i	0.837342	+	0.546679i	$0.184108\pi$
$948$		0			0
$949$	−25.5720	+	3.67669i	−0.830101	+	0.119351i
$950$		0			0
$951$	−33.2298	+	21.3555i	−1.07755	+	0.692500i
$952$		0			0
$953$	−7.41602	−	4.04945i	−0.240228	−	0.131175i	0.354626	−	0.935008i	$-0.384608\pi$
$953$	−7.41602	−	4.04945i	−0.240228	−	0.131175i	−0.594854	+	0.803834i	$0.702790\pi$
$954$		0			0
$955$	−2.10641	+	2.25720i	−0.0681620	+	0.0730414i
$956$		0			0
$957$	25.5846	+	9.54254i	0.827031	+	0.308467i
$958$		0			0
$959$	7.30536	−	24.8798i	0.235902	−	0.803410i
$960$		0			0
$961$	−11.2448	+	24.6226i	−0.362734	+	0.794277i
$962$		0			0
$963$	−18.6755	−	85.8497i	−0.601808	−	2.76647i
$964$		0			0
$965$	12.7638	+	13.7412i	0.410883	+	0.442345i
$966$		0			0
$967$	17.4266	+	17.4266i	0.560401	+	0.560401i	0.929421	−	0.369020i	$-0.120307\pi$
$967$	17.4266	+	17.4266i	0.560401	+	0.560401i	−0.369020	+	0.929421i	$0.620307\pi$
$968$		0			0
$969$	−1.60655	+	2.49984i	−0.0516098	+	0.0803065i
$970$		0			0
$971$	−7.78857	−	3.55692i	−0.249947	−	0.114147i	0.286502	−	0.958080i	$-0.407507\pi$
$971$	−7.78857	−	3.55692i	−0.249947	−	0.114147i	−0.536449	+	0.843933i	$0.680235\pi$
$972$		0			0
$973$	−0.979124	−	1.79313i	−0.0313893	−	0.0574852i
$974$		0			0
$975$	−45.8980	+	16.9981i	−1.46991	+	0.544374i
$976$		0			0
$977$	−1.52422	−	21.3114i	−0.0487641	−	0.681812i	−0.961769	−	0.273863i	$-0.911699\pi$
$977$	−1.52422	−	21.3114i	−0.0487641	−	0.681812i	0.913005	−	0.407949i	$-0.133756\pi$
$978$		0			0
$979$	−3.69141	−	12.5718i	−0.117978	−	0.401796i
$980$		0			0
$981$	9.32734	+	14.5136i	0.297799	+	0.463384i
$982$		0			0
$983$	−6.51718	+	8.70593i	−0.207866	+	0.277676i	−0.892343	−	0.451358i	$-0.850940\pi$
$983$	−6.51718	+	8.70593i	−0.207866	+	0.277676i	0.684477	+	0.729034i	$0.260031\pi$
$984$		0			0
$985$	−27.6472	−	39.9182i	−0.880914	−	1.27190i
$986$		0			0
$987$	−0.777761	−	0.0556266i	−0.0247564	−	0.00177061i
$988$		0			0
$989$	−2.67152	+	32.9243i	−0.0849494	+	1.04693i
$990$		0			0
$991$	−27.5169	−	31.7562i	−0.874103	−	1.00877i	−0.999860	−	0.0167077i	$-0.994682\pi$
$991$	−27.5169	−	31.7562i	−0.874103	−	1.00877i	0.125757	−	0.992061i	$-0.459864\pi$
$992$		0			0
$993$	38.9660	+	52.0525i	1.23655	+	1.65183i
$994$		0			0
$995$	3.29066	−	0.349928i	0.104321	−	0.0110935i
$996$		0			0
$997$	−44.9066	−	9.76883i	−1.42221	−	0.309382i	−0.565313	−	0.824877i	$-0.691244\pi$
$997$	−44.9066	−	9.76883i	−1.42221	−	0.309382i	−0.856893	+	0.515495i	$0.827608\pi$
$998$		0			0
$999$	−35.7967	+	10.5109i	−1.13256	+	0.332549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.217.34	yes	720
5.3	odd	4	inner	920.2.bv.a.33.34	✓	720
23.7	odd	22	inner	920.2.bv.a.697.34	yes	720
115.53	even	44	inner	920.2.bv.a.513.34	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.33.34	✓	720	5.3	odd	4	inner
920.2.bv.a.217.34	yes	720	1.1	even	1	trivial
920.2.bv.a.513.34	yes	720	115.53	even	44	inner
920.2.bv.a.697.34	yes	720	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73970 - 0.595986i) q^{3} +(1.99839 + 1.00322i) q^{5} +(-1.14188 + 0.623512i) q^{7} +(4.42188 - 2.01940i) q^{9} +O(q^{10})\)	\(q+(2.73970 - 0.595986i) q^{3} +(1.99839 + 1.00322i) q^{5} +(-1.14188 + 0.623512i) q^{7} +(4.42188 - 2.01940i) q^{9} +(2.43481 + 2.10978i) q^{11} +(-1.67321 + 3.06426i) q^{13} +(6.07289 + 1.55751i) q^{15} +(-0.304897 - 0.228243i) q^{17} +(0.396025 - 2.75441i) q^{19} +(-2.75680 + 2.38878i) q^{21} +(-4.58843 - 1.39509i) q^{23} +(2.98711 + 4.00963i) q^{25} +(4.17748 - 3.12722i) q^{27} +(2.99218 - 0.430210i) q^{29} +(1.66799 - 1.07195i) q^{31} +(7.92806 + 4.32905i) q^{33} +(-2.90743 + 0.100469i) q^{35} +(-6.69865 - 2.49847i) q^{37} +(-2.75785 + 9.39237i) q^{39} +(4.50294 - 9.86007i) q^{41} +(-1.46410 - 6.73035i) q^{43} +(10.8625 + 0.400551i) q^{45} +(0.151151 + 0.151151i) q^{47} +(-2.86937 + 4.46482i) q^{49} +(-0.971358 - 0.443604i) q^{51} +(3.80580 + 6.96980i) q^{53} +(2.74913 + 6.65880i) q^{55} +(-0.556601 - 7.78230i) q^{57} +(0.0148351 + 0.0505239i) q^{59} +(-6.54157 - 10.1789i) q^{61} +(-3.79012 + 5.06301i) q^{63} +(-6.41784 + 4.44498i) q^{65} +(-5.17522 - 0.370139i) q^{67} +(-13.4024 - 1.08749i) q^{69} +(-6.49309 - 7.49342i) q^{71} +(4.43451 + 5.92381i) q^{73} +(10.5735 + 9.20493i) q^{75} +(-4.09573 - 0.890971i) q^{77} +(-4.14460 + 1.21697i) q^{79} +(0.0310959 - 0.0358866i) q^{81} +(5.65402 - 15.1590i) q^{83} +(-0.380326 - 0.761997i) q^{85} +(7.94128 - 2.96194i) q^{87} +(-3.42133 - 2.19875i) q^{89} -4.54228i q^{91} +(3.93092 - 3.93092i) q^{93} +(3.55469 - 5.10709i) q^{95} +(1.72985 + 4.63790i) q^{97} +(15.0269 + 4.41230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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