LMFDB - Embedded newform 804.2.s.b.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +O(q^{10})$	\(q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +(1.09908 - 0.322720i) q^{11} +(-1.75990 - 2.73846i) q^{13} +(1.04390 + 0.144638i) q^{15} +(6.02227 + 0.865872i) q^{17} +(-3.63947 - 4.20017i) q^{19} +(0.931865 + 2.01316i) q^{21} +(-8.45963 + 3.86338i) q^{23} +(-3.89482 + 2.50305i) q^{25} +(-1.54033 - 4.96260i) q^{27} -1.03707i q^{29} +(-4.67082 + 7.26794i) q^{31} +(-1.96526 - 0.272298i) q^{33} +(0.708870 + 0.323730i) q^{35} -7.68565 q^{37} +(0.830965 + 5.57663i) q^{39} +(-0.975368 + 6.78383i) q^{41} +(6.37193 + 0.916145i) q^{43} +(-1.54562 - 0.971087i) q^{45} +(1.82570 - 0.833771i) q^{47} +(-0.762752 - 5.30506i) q^{49} +(-8.89431 - 5.65188i) q^{51} +(0.719704 + 5.00565i) q^{53} +(-0.586331 + 0.376812i) q^{55} +(2.75924 + 9.22215i) q^{57} +(-4.32558 + 6.73073i) q^{59} +(-2.70183 + 9.20160i) q^{61} +(-0.0393469 - 3.84213i) q^{63} +(1.49687 + 1.29705i) q^{65} +(-6.99330 - 4.25368i) q^{67} +(16.1080 - 0.0824778i) q^{69} +(-12.4132 + 1.78475i) q^{71} +(-2.27484 - 0.667954i) q^{73} +(7.93145 - 1.18185i) q^{75} +(-1.33453 - 0.609459i) q^{77} +(-8.54411 - 13.2949i) q^{79} +(-1.09812 + 8.93276i) q^{81} +(-3.58147 - 12.1974i) q^{83} +(-3.66427 + 0.526843i) q^{85} +(-0.737815 + 1.63773i) q^{87} +(1.31786 + 0.601845i) q^{89} +(-0.593340 + 4.12677i) q^{91} +(12.5468 - 8.15445i) q^{93} +(2.84474 + 1.82820i) q^{95} -10.2951i q^{97} +(2.90980 + 1.82818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.57919	−	0.711443i	−0.911747	−	0.410752i
$3$	−1.57919	−	0.711443i	−0.911747	−	0.410752i
$4$		0			0
$5$	−0.583807	+	0.171421i	−0.261086	+	0.0766618i	−0.409656	−	0.912240i	$-0.634351\pi$
$5$	−0.583807	+	0.171421i	−0.261086	+	0.0766618i	0.148570	+	0.988902i	$0.452533\pi$
$6$		0			0
$7$	−0.967947	−	0.838730i	−0.365849	−	0.317010i	0.452464	−	0.891783i	$-0.350545\pi$
$7$	−0.967947	−	0.838730i	−0.365849	−	0.317010i	−0.818313	+	0.574772i	$0.805091\pi$
$8$		0			0
$9$	1.98770	+	2.24701i	0.662566	+	0.749004i
$10$		0			0
$11$	1.09908	−	0.322720i	0.331386	−	0.0973037i	−0.111807	−	0.993730i	$-0.535664\pi$
$11$	1.09908	−	0.322720i	0.331386	−	0.0973037i	0.443193	+	0.896426i	$0.353846\pi$
$12$		0			0
$13$	−1.75990	−	2.73846i	−0.488109	−	0.759513i	0.506607	−	0.862177i	$-0.330900\pi$
$13$	−1.75990	−	2.73846i	−0.488109	−	0.759513i	−0.994716	+	0.102664i	$0.967263\pi$
$14$		0			0
$15$	1.04390	+	0.144638i	0.269534	+	0.0373455i
$16$		0			0
$17$	6.02227	+	0.865872i	1.46062	+	0.210005i	0.826370	−	0.563127i	$-0.190402\pi$
$17$	6.02227	+	0.865872i	1.46062	+	0.210005i	0.634245	+	0.773132i	$0.281311\pi$
$18$		0			0
$19$	−3.63947	−	4.20017i	−0.834951	−	0.963585i	0.164790	−	0.986329i	$-0.447305\pi$
$19$	−3.63947	−	4.20017i	−0.834951	−	0.963585i	−0.999741	+	0.0227439i	$0.992760\pi$
$20$		0			0
$21$	0.931865	+	2.01316i	0.203350	+	0.439307i
$22$		0			0
$23$	−8.45963	+	3.86338i	−1.76395	+	0.805571i	−0.780323	+	0.625377i	$0.784945\pi$
$23$	−8.45963	+	3.86338i	−1.76395	+	0.805571i	−0.983631	+	0.180194i	$0.942327\pi$
$24$		0			0
$25$	−3.89482	+	2.50305i	−0.778965	+	0.500610i
$26$		0			0
$27$	−1.54033	−	4.96260i	−0.296437	−	0.955052i
$28$		0			0
$29$		−	1.03707i		−	0.192579i	−0.995353	−	0.0962894i	$-0.969303\pi$
$29$		−	1.03707i		−	0.192579i	0.995353	−	0.0962894i	$-0.0306974\pi$
$30$		0			0
$31$	−4.67082	+	7.26794i	−0.838904	+	1.30536i	0.111318	+	0.993785i	$0.464493\pi$
$31$	−4.67082	+	7.26794i	−0.838904	+	1.30536i	−0.950222	+	0.311575i	$0.899143\pi$
$32$		0			0
$33$	−1.96526	−	0.272298i	−0.342108	−	0.0474011i
$34$		0			0
$35$	0.708870	+	0.323730i	0.119821	+	0.0547203i
$36$		0			0
$37$	−7.68565			−1.26351			−0.631756	−	0.775167i	$-0.717666\pi$
$37$	−7.68565			−1.26351			−0.631756	+	0.775167i	$0.717666\pi$
$38$		0			0
$39$	0.830965	+	5.57663i	0.133061	+	0.892976i
$40$		0			0
$41$	−0.975368	+	6.78383i	−0.152327	+	1.05946i	0.759979	+	0.649947i	$0.225209\pi$
$41$	−0.975368	+	6.78383i	−0.152327	+	1.05946i	−0.912306	+	0.409509i	$0.865700\pi$
$42$		0			0
$43$	6.37193	+	0.916145i	0.971710	+	0.139711i	0.609846	−	0.792520i	$-0.291231\pi$
$43$	6.37193	+	0.916145i	0.971710	+	0.139711i	0.361864	+	0.932231i	$0.382140\pi$
$44$		0			0
$45$	−1.54562	−	0.971087i	−0.230407	−	0.144761i
$46$		0			0
$47$	1.82570	−	0.833771i	0.266306	−	0.121618i	−0.277787	−	0.960643i	$-0.589601\pi$
$47$	1.82570	−	0.833771i	0.266306	−	0.121618i	0.544093	+	0.839025i	$0.316874\pi$
$48$		0			0
$49$	−0.762752	−	5.30506i	−0.108965	−	0.757865i
$50$		0			0
$51$	−8.89431	−	5.65188i	−1.24545	−	0.791422i
$52$		0			0
$53$	0.719704	+	5.00565i	0.0988589	+	0.687579i	0.977630	+	0.210334i	$0.0674552\pi$
$53$	0.719704	+	5.00565i	0.0988589	+	0.687579i	−0.878771	+	0.477244i	$0.841636\pi$
$54$		0			0
$55$	−0.586331	+	0.376812i	−0.0790608	+	0.0508093i
$56$		0			0
$57$	2.75924	+	9.22215i	0.365470	+	1.22150i
$58$		0			0
$59$	−4.32558	+	6.73073i	−0.563142	+	0.876266i	−0.999726	−	0.0233972i	$-0.992552\pi$
$59$	−4.32558	+	6.73073i	−0.563142	+	0.876266i	0.436584	+	0.899663i	$0.356188\pi$
$60$		0			0
$61$	−2.70183	+	9.20160i	−0.345934	+	1.17814i	0.584410	+	0.811458i	$0.301326\pi$
$61$	−2.70183	+	9.20160i	−0.345934	+	1.17814i	−0.930345	+	0.366686i	$0.880492\pi$
$62$		0			0
$63$	−0.0393469	−	3.84213i	−0.00495724	−	0.484063i
$64$		0			0
$65$	1.49687	+	1.29705i	0.185664	+	0.160879i
$66$		0			0
$67$	−6.99330	−	4.25368i	−0.854367	−	0.519669i
$67$	−6.99330	−	4.25368i	−0.854367	−	0.519669i
$68$		0			0
$69$	16.1080	−	0.0824778i	1.93917	−	0.00992916i
$70$		0			0
$71$	−12.4132	+	1.78475i	−1.47318	+	0.211811i	−0.831656	−	0.555291i	$-0.812607\pi$
$71$	−12.4132	+	1.78475i	−1.47318	+	0.211811i	−0.641524	+	0.767103i	$0.721698\pi$
$72$		0			0
$73$	−2.27484	−	0.667954i	−0.266250	−	0.0781781i	0.145883	−	0.989302i	$-0.453398\pi$
$73$	−2.27484	−	0.667954i	−0.266250	−	0.0781781i	−0.412133	+	0.911124i	$0.635216\pi$
$74$		0			0
$75$	7.93145	−	1.18185i	0.915845	−	0.136469i
$76$		0			0
$77$	−1.33453	−	0.609459i	−0.152084	−	0.0694542i
$78$		0			0
$79$	−8.54411	−	13.2949i	−0.961288	−	1.49579i	−0.865817	−	0.500361i	$-0.833201\pi$
$79$	−8.54411	−	13.2949i	−0.961288	−	1.49579i	−0.0954710	−	0.995432i	$-0.530436\pi$
$80$		0			0
$81$	−1.09812	+	8.93276i	−0.122014	+	0.992528i
$82$		0			0
$83$	−3.58147	−	12.1974i	−0.393118	−	1.33884i	−0.883950	−	0.467582i	$-0.845125\pi$
$83$	−3.58147	−	12.1974i	−0.393118	−	1.33884i	0.490832	−	0.871254i	$-0.336693\pi$
$84$		0			0
$85$	−3.66427	+	0.526843i	−0.397446	+	0.0571441i
$86$		0			0
$87$	−0.737815	+	1.63773i	−0.0791021	+	0.175583i
$88$		0			0
$89$	1.31786	+	0.601845i	0.139692	+	0.0637954i	0.484035	−	0.875049i	$-0.339171\pi$
$89$	1.31786	+	0.601845i	0.139692	+	0.0637954i	−0.344342	+	0.938844i	$0.611898\pi$
$90$		0			0
$91$	−0.593340	+	4.12677i	−0.0621989	+	0.432603i
$92$		0			0
$93$	12.5468	−	8.15445i	1.30105	−	0.845577i
$94$		0			0
$95$	2.84474	+	1.82820i	0.291864	+	0.187570i
$96$		0			0
$97$		−	10.2951i		−	1.04531i	−0.852545	−	0.522654i	$-0.824942\pi$
$97$		−	10.2951i		−	1.04531i	0.852545	−	0.522654i	$-0.175058\pi$
$98$		0			0
$99$	2.90980	+	1.82818i	0.292446	+	0.183739i
$100$		0			0
$101$	11.0980	+	12.8078i	1.10430	+	1.27443i	0.958494	+	0.285113i	$0.0920311\pi$
$101$	11.0980	+	12.8078i	1.10430	+	1.27443i	0.145803	+	0.989314i	$0.453423\pi$
$102$		0			0
$103$	6.87710	+	4.41965i	0.677621	+	0.435481i	0.833666	−	0.552269i	$-0.186238\pi$
$103$	6.87710	+	4.41965i	0.677621	+	0.435481i	−0.156045	+	0.987750i	$0.549874\pi$
$104$		0			0
$105$	−0.889126	−	1.01555i	−0.0867698	−	0.0991078i
$106$		0			0
$107$	4.41018	−	15.0197i	0.426348	−	1.45201i	−0.414158	−	0.910205i	$-0.635924\pi$
$107$	4.41018	−	15.0197i	0.426348	−	1.45201i	0.840506	−	0.541802i	$-0.182258\pi$
$108$		0			0
$109$	4.47433	+	6.96219i	0.428563	+	0.666857i	0.986637	−	0.162934i	$-0.0520959\pi$
$109$	4.47433	+	6.96219i	0.428563	+	0.666857i	−0.558074	+	0.829791i	$0.688460\pi$
$110$		0			0
$111$	12.1371	+	5.46790i	1.15200	+	0.518990i
$112$		0			0
$113$	−8.56513	−	2.51495i	−0.805740	−	0.236587i	−0.147175	−	0.989110i	$-0.547018\pi$
$113$	−8.56513	−	2.51495i	−0.805740	−	0.236587i	−0.658565	+	0.752524i	$0.728836\pi$
$114$		0			0
$115$	4.27652	−	3.70563i	0.398788	−	0.345551i
$116$		0			0
$117$	2.65521	−	9.39776i	0.245474	−	0.868823i
$118$		0			0
$119$	−5.10300	−	5.88918i	−0.467792	−	0.539860i
$120$		0			0
$121$	−8.14995	+	5.23766i	−0.740905	+	0.476151i
$122$		0			0
$123$	6.36660	−	10.0191i	0.574057	−	0.903388i
$124$		0			0
$125$	3.83701	−	4.42814i	0.343192	−	0.396065i
$126$		0			0
$127$	−11.6912	+	13.4924i	−1.03743	+	1.19725i	−0.0574060	+	0.998351i	$0.518283\pi$
$127$	−11.6912	+	13.4924i	−1.03743	+	1.19725i	−0.980019	+	0.198902i	$0.936262\pi$
$128$		0			0
$129$	−9.41071	−	5.98003i	−0.828567	−	0.526513i
$130$		0			0
$131$	12.8076	−	5.84904i	1.11901	−	0.511033i	0.231966	−	0.972724i	$-0.425484\pi$
$131$	12.8076	−	5.84904i	1.11901	−	0.511033i	0.887041	+	0.461691i	$0.152757\pi$
$132$		0			0
$133$			7.11807i			0.617215i
$134$		0			0
$135$	1.74995	+	2.63315i	0.150612	+	0.226626i
$136$		0			0
$137$	−2.05122	−	4.49155i	−0.175248	−	0.383739i	0.801542	−	0.597938i	$-0.204013\pi$
$137$	−2.05122	−	4.49155i	−0.175248	−	0.383739i	−0.976790	+	0.214199i	$0.931286\pi$
$138$		0			0
$139$	4.82451	+	16.4308i	0.409210	+	1.39364i	0.864202	+	0.503145i	$0.167824\pi$
$139$	4.82451	+	16.4308i	0.409210	+	1.39364i	−0.454992	+	0.890496i	$0.650358\pi$
$140$		0			0
$141$	−3.47632	+	0.0177998i	−0.292759	+	0.00149902i
$142$		0			0
$143$	−2.81804	−	2.44184i	−0.235656	−	0.204197i
$144$		0			0
$145$	0.177775	+	0.605447i	0.0147634	+	0.0502797i
$146$		0			0
$147$	−2.56972	+	8.92036i	−0.211947	+	0.735739i
$148$		0			0
$149$	7.26172	−	6.29231i	0.594903	−	0.515486i	−0.304554	−	0.952495i	$-0.598508\pi$
$149$	7.26172	−	6.29231i	0.594903	−	0.515486i	0.899457	+	0.437009i	$0.143962\pi$
$150$		0			0
$151$	2.84904	−	19.8155i	0.231852	−	1.61256i	−0.458231	−	0.888833i	$-0.651517\pi$
$151$	2.84904	−	19.8155i	0.231852	−	1.61256i	0.690082	−	0.723731i	$-0.257574\pi$
$152$		0			0
$153$	10.0248	+	15.2532i	0.810459	+	1.23315i
$154$		0			0
$155$	1.48098	−	5.04375i	0.118955	−	0.405123i
$156$		0			0
$157$	−2.80627	−	6.14488i	−0.223965	−	0.490414i	0.763976	−	0.645244i	$-0.223244\pi$
$157$	−2.80627	−	6.14488i	−0.223965	−	0.490414i	−0.987941	+	0.154830i	$0.950517\pi$
$158$		0			0
$159$	2.42468	−	8.41691i	0.192290	−	0.667504i
$160$		0			0
$161$	11.4288	+	3.35580i	0.900716	+	0.264474i
$162$		0			0
$163$	0.764311			0.0598654			0.0299327	−	0.999552i	$-0.490471\pi$
$163$	0.764311			0.0598654			0.0299327	+	0.999552i	$0.490471\pi$
$164$		0			0
$165$	1.19401	−	0.177917i	0.0929535	−	0.0138508i
$166$		0			0
$167$	12.8888	−	11.1682i	0.997362	−	0.864219i	0.00661997	−	0.999978i	$-0.497893\pi$
$167$	12.8888	−	11.1682i	0.997362	−	0.864219i	0.990742	+	0.135759i	$0.0433473\pi$
$168$		0			0
$169$	0.998474	−	2.18635i	0.0768057	−	0.168181i
$170$		0			0
$171$	2.20367	−	16.5266i	0.168519	−	1.26382i
$172$		0			0
$173$	4.09433	−	6.37090i	0.311286	−	0.484371i	−0.649996	−	0.759938i	$-0.725229\pi$
$173$	4.09433	−	6.37090i	0.311286	−	0.484371i	0.961282	+	0.275567i	$0.0888657\pi$
$174$		0			0
$175$	5.86937	+	0.843887i	0.443682	+	0.0637919i
$176$		0			0
$177$	11.6194	−	7.55171i	0.873371	−	0.567621i
$178$		0			0
$179$	−2.25923	+	4.94702i	−0.168863	+	0.369758i	−0.975077	−	0.221865i	$-0.928785\pi$
$179$	−2.25923	+	4.94702i	−0.168863	+	0.369758i	0.806214	+	0.591623i	$0.201513\pi$
$180$		0			0
$181$	−4.41394	−	9.66518i	−0.328085	−	0.718407i	0.671662	−	0.740857i	$-0.265581\pi$
$181$	−4.41394	−	9.66518i	−0.328085	−	0.718407i	−0.999748	+	0.0224503i	$0.992853\pi$
$182$		0			0
$183$	10.8131	−	12.6089i	0.799330	−	0.932077i
$184$		0			0
$185$	4.48693	−	1.31748i	0.329886	−	0.0968632i
$186$		0			0
$187$	6.89841	−	0.991841i	0.504462	−	0.0725306i
$188$		0			0
$189$	−2.67132	+	6.09545i	−0.194310	+	0.443379i
$190$		0			0
$191$	−10.4922	+	22.9746i	−0.759185	+	1.66238i	−0.0100657	+	0.999949i	$0.503204\pi$
$191$	−10.4922	+	22.9746i	−0.759185	+	1.66238i	−0.749120	+	0.662435i	$0.769523\pi$
$192$		0			0
$193$	13.0421	+	8.38163i	0.938789	+	0.603323i	0.918051	−	0.396462i	$-0.129762\pi$
$193$	13.0421	+	8.38163i	0.938789	+	0.603323i	0.0207378	+	0.999785i	$0.493398\pi$
$194$		0			0
$195$	−1.44107	−	3.11323i	−0.103198	−	0.222943i
$196$		0			0
$197$	−2.51254	−	17.4751i	−0.179011	−	1.24505i	−0.859056	−	0.511881i	$-0.828949\pi$
$197$	−2.51254	−	17.4751i	−0.179011	−	1.24505i	0.680045	−	0.733170i	$-0.261960\pi$
$198$		0			0
$199$	−2.27947	+	2.63064i	−0.161587	+	0.186481i	−0.830769	−	0.556617i	$-0.812099\pi$
$199$	−2.27947	+	2.63064i	−0.161587	+	0.186481i	0.669182	+	0.743098i	$0.266645\pi$
$200$		0			0
$201$	8.01751	+	11.6927i	0.565512	+	0.824740i
$202$		0			0
$203$	−0.869821	+	1.00383i	−0.0610494	+	0.0704548i
$204$		0			0
$205$	−0.593465	−	4.12764i	−0.0414494	−	0.288287i
$206$		0			0
$207$	−25.4962	−	11.3296i	−1.77211	−	0.787465i
$208$		0			0
$209$	−5.35555	−	3.44180i	−0.370451	−	0.238075i
$210$		0			0
$211$	0.718721	−	1.57378i	0.0494788	−	0.108343i	−0.883278	−	0.468849i	$-0.844669\pi$
$211$	0.718721	−	1.57378i	0.0494788	−	0.108343i	0.932757	+	0.360506i	$0.117396\pi$
$212$		0			0
$213$	20.8726	+	6.01285i	1.43017	+	0.411993i
$214$		0			0
$215$	−3.87702	+	0.557431i	−0.264411	+	0.0380165i
$216$		0			0
$217$	10.6169	−	3.11742i	0.720725	−	0.211624i
$218$		0			0
$219$	3.11720	+	2.67325i	0.210641	+	0.180642i
$220$		0			0
$221$	−8.22746	−	18.0156i	−0.553439	−	1.21186i
$222$		0			0
$223$	1.72185	−	3.77033i	0.115304	−	0.252480i	−0.843178	−	0.537635i	$-0.819318\pi$
$223$	1.72185	−	3.77033i	0.115304	−	0.252480i	0.958481	+	0.285155i	$0.0920451\pi$
$224$		0			0
$225$	−13.3661	−	3.77641i	−0.891074	−	0.251760i
$226$		0			0
$227$	−18.7033	−	2.68913i	−1.24138	−	0.178484i	−0.509833	−	0.860273i	$-0.670293\pi$
$227$	−18.7033	−	2.68913i	−1.24138	−	0.178484i	−0.731548	+	0.681789i	$0.761202\pi$
$228$		0			0
$229$	−5.93670	+	9.23768i	−0.392308	+	0.610443i	−0.980085	−	0.198580i	$-0.936367\pi$
$229$	−5.93670	+	9.23768i	−0.392308	+	0.610443i	0.587777	+	0.809023i	$0.300003\pi$
$230$		0			0
$231$	1.67388	+	1.91189i	0.110133	+	0.125793i
$232$		0			0
$233$	0.376373	−	0.824142i	0.0246570	−	0.0539913i	−0.896903	−	0.442228i	$-0.854188\pi$
$233$	0.376373	−	0.824142i	0.0246570	−	0.0539913i	0.921560	+	0.388236i	$0.126916\pi$
$234$		0			0
$235$	−0.922932	+	0.799725i	−0.0602054	+	0.0521683i
$236$		0			0
$237$	4.03423	+	27.0739i	0.262051	+	1.75864i
$238$		0			0
$239$	4.03610			0.261074			0.130537	−	0.991443i	$-0.458330\pi$
$239$	4.03610			0.261074			0.130537	+	0.991443i	$0.458330\pi$
$240$		0			0
$241$	−4.39067	−	1.28922i	−0.282828	−	0.0830458i	0.137242	−	0.990538i	$-0.456176\pi$
$241$	−4.39067	−	1.28922i	−0.282828	−	0.0830458i	−0.420070	+	0.907492i	$0.637994\pi$
$242$		0			0
$243$	8.08930	−	13.3253i	0.518929	−	0.854817i
$244$		0			0
$245$	1.35470	+	2.96638i	0.0865485	+	0.189515i
$246$		0			0
$247$	−5.09690	+	17.3584i	−0.324308	+	1.10449i
$248$		0			0
$249$	−3.02191	+	21.8100i	−0.191506	+	1.38215i
$250$		0			0
$251$	−3.39552	+	23.6163i	−0.214323	+	1.49065i	0.544173	+	0.838973i	$0.316843\pi$
$251$	−3.39552	+	23.6163i	−0.214323	+	1.49065i	−0.758496	+	0.651677i	$0.774066\pi$
$252$		0			0
$253$	−8.05104	+	6.97626i	−0.506164	+	0.438594i
$254$		0			0
$255$	6.16141	+	1.77494i	0.385842	+	0.111151i
$256$		0			0
$257$	5.18032	+	17.6425i	0.323139	+	1.10051i	0.947601	+	0.319456i	$0.103500\pi$
$257$	5.18032	+	17.6425i	0.323139	+	1.10051i	−0.624462	+	0.781055i	$0.714682\pi$
$258$		0			0
$259$	7.43930	+	6.44619i	0.462255	+	0.400547i
$260$		0			0
$261$	2.33030	−	2.06138i	0.144242	−	0.127596i
$262$		0			0
$263$	2.34820	+	7.99724i	0.144796	+	0.493131i	0.999670	−	0.0257060i	$-0.00818338\pi$
$263$	2.34820	+	7.99724i	0.144796	+	0.493131i	−0.854873	+	0.518837i	$0.826365\pi$
$264$		0			0
$265$	−1.27824	−	2.79896i	−0.0785217	−	0.171939i
$266$		0			0
$267$	−1.65297	−	1.88801i	−0.101160	−	0.115544i
$268$		0			0
$269$			11.6474i			0.710157i	0.934837	+	0.355078i	$0.115546\pi$
$269$			11.6474i			0.710157i	−0.934837	+	0.355078i	$0.884454\pi$
$270$		0			0
$271$	9.86330	−	4.50442i	0.599153	−	0.273624i	−0.0926633	−	0.995697i	$-0.529538\pi$
$271$	9.86330	−	4.50442i	0.599153	−	0.273624i	0.691816	+	0.722073i	$0.256811\pi$
$272$		0			0
$273$	3.87296	−	6.09484i	0.234402	−	0.368876i
$274$		0			0
$275$	−3.47295	+	4.00800i	−0.209427	+	0.241691i
$276$		0			0
$277$	−1.64801	+	1.90191i	−0.0990196	+	0.114275i	−0.803096	−	0.595849i	$-0.796816\pi$
$277$	−1.64801	+	1.90191i	−0.0990196	+	0.114275i	0.704077	+	0.710124i	$0.251361\pi$
$278$		0			0
$279$	−25.6153	+	3.95107i	−1.53355	+	0.236544i
$280$		0			0
$281$	7.41890	−	4.76784i	0.442574	−	0.284425i	−0.300314	−	0.953840i	$-0.597092\pi$
$281$	7.41890	−	4.76784i	0.442574	−	0.284425i	0.742889	+	0.669415i	$0.233455\pi$
$282$		0			0
$283$	−9.32066	−	10.7566i	−0.554056	−	0.639415i	0.407767	−	0.913086i	$-0.366307\pi$
$283$	−9.32066	−	10.7566i	−0.554056	−	0.639415i	−0.961823	+	0.273671i	$0.911762\pi$
$284$		0			0
$285$	−3.19173	−	4.91096i	−0.189062	−	0.290900i
$286$		0			0
$287$	6.63391	−	5.74831i	0.391587	−	0.339312i
$288$		0			0
$289$	19.2066	+	5.63958i	1.12980	+	0.331740i
$290$		0			0
$291$	−7.32437	+	16.2579i	−0.429362	+	0.953057i
$292$		0			0
$293$	−10.1776	−	15.8366i	−0.594582	−	0.925187i	−0.999939	−	0.0110287i	$-0.996489\pi$
$293$	−10.1776	−	15.8366i	−0.594582	−	0.925187i	0.405358	−	0.914158i	$-0.367147\pi$
$294$		0			0
$295$	1.37151	−	4.67094i	0.0798525	−	0.271953i
$296$		0			0
$297$	−3.29448	−	4.95721i	−0.191165	−	0.287646i
$298$		0			0
$299$	25.4679	+	16.3672i	1.47284	+	0.946539i
$300$		0			0
$301$	−5.39929	−	6.23111i	−0.311210	−	0.359155i
$302$		0			0
$303$	−8.41390	−	28.1217i	−0.483366	−	1.61555i
$304$		0			0
$305$		−	5.83511i		−	0.334117i
$306$		0			0
$307$	−1.02503	−	0.658746i	−0.0585015	−	0.0375966i	0.511063	−	0.859543i	$-0.329252\pi$
$307$	−1.02503	−	0.658746i	−0.0585015	−	0.0375966i	−0.569565	+	0.821947i	$0.692888\pi$
$308$		0			0
$309$	−7.71594	−	11.8721i	−0.438945	−	0.675382i
$310$		0			0
$311$	−0.910675	+	6.33389i	−0.0516397	+	0.359162i	0.947575	+	0.319534i	$0.103526\pi$
$311$	−0.910675	+	6.33389i	−0.0516397	+	0.359162i	−0.999215	+	0.0396278i	$0.987383\pi$
$312$		0			0
$313$	−18.0740	−	8.25412i	−1.02160	−	0.466550i	−0.167068	−	0.985945i	$-0.553430\pi$
$313$	−18.0740	−	8.25412i	−1.02160	−	0.466550i	−0.854534	+	0.519395i	$0.826157\pi$
$314$		0			0
$315$	0.681593	+	2.23632i	0.0384034	+	0.126002i
$316$		0			0
$317$	−7.47147	+	1.07423i	−0.419639	+	0.0603350i	−0.348900	−	0.937160i	$-0.613445\pi$
$317$	−7.47147	+	1.07423i	−0.419639	+	0.0603350i	−0.0707391	+	0.997495i	$0.522536\pi$
$318$		0			0
$319$	−0.334682	−	1.13982i	−0.0187386	−	0.0638179i
$320$		0			0
$321$	−17.6502	+	20.5814i	−0.985136	+	1.14874i
$322$		0			0
$323$	−18.2810	−	28.4459i	−1.01718	−	1.58277i
$324$		0			0
$325$	13.7090	+	6.26070i	0.760440	+	0.347281i
$326$		0			0
$327$	−2.11262	−	14.1779i	−0.116828	−	0.784038i
$328$		0			0
$329$	−2.46649	−	0.724228i	−0.135982	−	0.0399280i
$330$		0			0
$331$	20.9135	−	3.00691i	1.14951	−	0.165275i	0.458891	−	0.888493i	$-0.348247\pi$
$331$	20.9135	−	3.00691i	1.14951	−	0.165275i	0.690620	+	0.723218i	$0.257338\pi$
$332$		0			0
$333$	−15.2767	−	17.2697i	−0.837160	−	0.946376i
$334$		0			0
$335$	4.81190	+	1.28453i	0.262902	+	0.0701812i
$336$		0			0
$337$	−8.27804	−	7.17296i	−0.450934	−	0.390736i	0.399572	−	0.916702i	$-0.369159\pi$
$337$	−8.27804	−	7.17296i	−0.450934	−	0.390736i	−0.850506	+	0.525966i	$0.823704\pi$
$338$		0			0
$339$	11.7367	+	10.0652i	0.637453	+	0.546666i
$340$		0			0
$341$	−2.78811	+	9.49543i	−0.150985	+	0.514206i
$342$		0			0
$343$	−8.55829	+	13.3170i	−0.462104	+	0.719048i
$344$		0			0
$345$	−9.38979	+	2.80939i	−0.505529	+	0.151253i
$346$		0			0
$347$	8.52778	−	5.48047i	0.457795	−	0.294207i	−0.291346	−	0.956618i	$-0.594103\pi$
$347$	8.52778	−	5.48047i	0.457795	−	0.294207i	0.749141	+	0.662411i	$0.230467\pi$
$348$		0			0
$349$	−3.83309	−	26.6597i	−0.205181	−	1.42706i	−0.788608	−	0.614897i	$-0.789198\pi$
$349$	−3.83309	−	26.6597i	−0.205181	−	1.42706i	0.583427	−	0.812166i	$-0.301711\pi$
$350$		0			0
$351$	−10.8791	+	12.9518i	−0.580681	+	0.691318i
$352$		0			0
$353$	4.00838	+	27.8789i	0.213344	+	1.48384i	0.761882	+	0.647716i	$0.224276\pi$
$353$	4.00838	+	27.8789i	0.213344	+	1.48384i	−0.548537	+	0.836126i	$0.684815\pi$
$354$		0			0
$355$	6.94098	−	3.16984i	0.368389	−	0.168238i
$356$		0			0
$357$	3.86881	+	12.9306i	0.204759	+	0.684362i
$358$		0			0
$359$	13.9546	+	2.00637i	0.736496	+	0.105892i	0.500347	−	0.865825i	$-0.333206\pi$
$359$	13.9546	+	2.00637i	0.736496	+	0.105892i	0.236149	+	0.971717i	$0.424115\pi$
$360$		0			0
$361$	−1.69171	+	11.7661i	−0.0890376	+	0.619270i
$362$		0			0
$363$	16.5966	−	2.47304i	0.871098	−	0.129801i
$364$		0			0
$365$	1.44257			0.0755076
$366$		0			0
$367$	10.4511	+	4.77287i	0.545544	+	0.249142i	0.669070	−	0.743200i	$-0.266693\pi$
$367$	10.4511	+	4.77287i	0.545544	+	0.249142i	−0.123526	+	0.992341i	$0.539420\pi$
$368$		0			0
$369$	−17.1821	+	11.2925i	−0.894463	+	0.587866i
$370$		0			0
$371$	3.50175	−	5.44884i	0.181802	−	0.282890i
$372$		0			0
$373$		−	12.8632i		−	0.666030i	−0.942922	−	0.333015i	$-0.891934\pi$
$373$		−	12.8632i		−	0.666030i	0.942922	−	0.333015i	$-0.108066\pi$
$374$		0			0
$375$	−9.20975	+	4.26308i	−0.475589	+	0.220144i
$376$		0			0
$377$	−2.83997	+	1.82514i	−0.146266	+	0.0939995i
$378$		0			0
$379$	−16.1756	+	7.38714i	−0.830884	+	0.379452i	−0.785001	−	0.619495i	$-0.787337\pi$
$379$	−16.1756	+	7.38714i	−0.830884	+	0.379452i	−0.0458831	+	0.998947i	$0.514610\pi$
$380$		0			0
$381$	28.0617	−	12.9894i	1.43764	−	0.665467i
$382$		0			0
$383$	9.24502	+	10.6693i	0.472398	+	0.545177i	0.941077	−	0.338192i	$-0.109815\pi$
$383$	9.24502	+	10.6693i	0.472398	+	0.545177i	−0.468679	+	0.883369i	$0.655270\pi$
$384$		0			0
$385$	0.883580	+	0.127040i	0.0450314	+	0.00647454i
$386$		0			0
$387$	10.6069	+	16.1388i	0.539178	+	0.820382i
$388$		0			0
$389$	−20.1160	−	31.3011i	−1.01992	−	1.58703i	−0.789322	−	0.613979i	$-0.789568\pi$
$389$	−20.1160	−	31.3011i	−1.01992	−	1.58703i	−0.230599	−	0.973049i	$-0.574068\pi$
$390$		0			0
$391$	−54.2914	+	15.9414i	−2.74563	+	0.806190i
$392$		0			0
$393$	−24.3870	+	0.124869i	−1.23016	+	0.00629880i
$394$		0			0
$395$	7.26714	+	6.29701i	0.365649	+	0.316837i
$396$		0			0
$397$	0.849895	−	0.249552i	0.0426550	−	0.0125246i	−0.260335	−	0.965518i	$-0.583833\pi$
$397$	0.849895	−	0.249552i	0.0426550	−	0.0125246i	0.302990	+	0.952994i	$0.402015\pi$
$398$		0			0
$399$	5.06410	−	11.2408i	0.253522	−	0.562744i
$400$		0			0
$401$	−30.6446			−1.53032			−0.765160	−	0.643840i	$-0.777340\pi$
$401$	−30.6446			−1.53032			−0.765160	+	0.643840i	$0.777340\pi$
$402$		0			0
$403$	28.1232			1.40091
$404$		0			0
$405$	−0.890170	−	5.40324i	−0.0442329	−	0.268489i
$406$		0			0
$407$	−8.44716	+	2.48031i	−0.418710	+	0.122944i
$408$		0			0
$409$	−3.99205	−	3.45913i	−0.197394	−	0.171043i	0.550555	−	0.834799i	$-0.314416\pi$
$409$	−3.99205	−	3.45913i	−0.197394	−	0.171043i	−0.747949	+	0.663756i	$0.768961\pi$
$410$		0			0
$411$	0.0437907	+	8.55235i	0.00216004	+	0.421856i
$412$		0			0
$413$	9.83219	−	2.88699i	0.483811	−	0.142060i
$414$		0			0
$415$	4.18178	+	6.50697i	0.205275	+	0.319415i
$416$		0			0
$417$	4.07074	−	29.3797i	0.199345	−	1.43873i
$418$		0			0
$419$	−31.2307	−	4.49030i	−1.52572	−	0.219366i	−0.672179	−	0.740389i	$-0.734641\pi$
$419$	−31.2307	−	4.49030i	−1.52572	−	0.219366i	−0.853543	+	0.521023i	$0.825551\pi$
$420$		0			0
$421$	−9.84377	−	11.3603i	−0.479756	−	0.553668i	0.463343	−	0.886179i	$-0.346650\pi$
$421$	−9.84377	−	11.3603i	−0.479756	−	0.553668i	−0.943099	+	0.332511i	$0.892104\pi$
$422$		0			0
$423$	5.50244	+	2.44509i	0.267538	+	0.118885i
$424$		0			0
$425$	−25.6230	+	11.7016i	−1.24290	+	0.567613i
$426$		0			0
$427$	10.3329	−	6.64055i	0.500044	−	0.321359i
$428$		0			0
$429$	2.71299	+	5.86101i	0.130984	+	0.282972i
$430$		0			0
$431$			34.5012i			1.66187i	0.556373	+	0.830933i	$0.312192\pi$
$431$			34.5012i			1.66187i	−0.556373	+	0.830933i	$0.687808\pi$
$432$		0			0
$433$	8.95964	−	13.9415i	0.430573	−	0.669985i	−0.556392	−	0.830920i	$-0.687815\pi$
$433$	8.95964	−	13.9415i	0.430573	−	0.669985i	0.986965	+	0.160935i	$0.0514510\pi$
$434$		0			0
$435$	0.150000	−	1.08259i	0.00719195	−	0.0519064i
$436$		0			0
$437$	47.0154	+	21.4712i	2.24905	+	1.02711i
$438$		0			0
$439$	−0.732575			−0.0349639			−0.0174819	−	0.999847i	$-0.505565\pi$
$439$	−0.732575			−0.0349639			−0.0174819	+	0.999847i	$0.505565\pi$
$440$		0			0
$441$	10.4044	−	12.2588i	0.495448	−	0.583750i
$442$		0			0
$443$	5.09060	−	35.4059i	0.241862	−	1.68218i	−0.400903	−	0.916120i	$-0.631304\pi$
$443$	5.09060	−	35.4059i	0.241862	−	1.68218i	0.642765	−	0.766064i	$-0.277787\pi$
$444$		0			0
$445$	−0.872542	−	0.125453i	−0.0413624	−	0.00594702i
$446$		0			0
$447$	−15.9443	+	4.77047i	−0.754138	+	0.225636i
$448$		0			0
$449$	0.701077	−	0.320171i	0.0330859	−	0.0151098i	−0.398803	−	0.917036i	$-0.630574\pi$
$449$	0.701077	−	0.320171i	0.0330859	−	0.0151098i	0.431889	+	0.901927i	$0.357847\pi$
$450$		0			0
$451$	1.11727	+	7.77076i	0.0526100	+	0.365911i
$452$		0			0
$453$	−18.5968	+	29.2656i	−0.873754	+	1.37502i
$454$		0			0
$455$	−0.361020	−	2.51095i	−0.0169249	−	0.117715i
$456$		0			0
$457$	22.2164	−	14.2776i	1.03924	−	0.667879i	0.0944416	−	0.995530i	$-0.469893\pi$
$457$	22.2164	−	14.2776i	1.03924	−	0.667879i	0.944799	+	0.327651i	$0.106257\pi$
$458$		0			0
$459$	−4.97933	−	31.2198i	−0.232415	−	1.45722i
$460$		0			0
$461$	−13.8050	+	21.4810i	−0.642964	+	1.00047i	0.354885	+	0.934910i	$0.384520\pi$
$461$	−13.8050	+	21.4810i	−0.642964	+	1.00047i	−0.997849	+	0.0655610i	$0.979116\pi$
$462$		0			0
$463$	−2.08357	+	7.09599i	−0.0968317	+	0.329779i	−0.993635	−	0.112652i	$-0.964065\pi$
$463$	−2.08357	+	7.09599i	−0.0968317	+	0.329779i	0.896803	+	0.442431i	$0.145884\pi$
$464$		0			0
$465$	−5.92709	+	6.91141i	−0.274862	+	0.320509i
$466$		0			0
$467$	−8.29179	−	7.18487i	−0.383698	−	0.332476i	0.441560	−	0.897232i	$-0.354425\pi$
$467$	−8.29179	−	7.18487i	−0.383698	−	0.332476i	−0.825258	+	0.564755i	$0.808971\pi$
$468$		0			0
$469$	3.20145	+	9.98283i	0.147829	+	0.460964i
$470$		0			0
$471$	0.0599100	+	11.7004i	0.00276051	+	0.539128i
$472$		0			0
$473$	7.29893	−	1.04943i	0.335605	−	0.0482528i
$474$		0			0
$475$	24.6883	+	7.24914i	1.13278	+	0.332613i
$476$		0			0
$477$	−9.81720	+	11.5669i	−0.449499	+	0.529612i
$478$		0			0
$479$	26.7907	+	12.2349i	1.22410	+	0.559027i	0.919363	−	0.393409i	$-0.128704\pi$
$479$	26.7907	+	12.2349i	1.22410	+	0.559027i	0.304736	+	0.952437i	$0.401432\pi$
$480$		0			0
$481$	13.5260	+	21.0469i	0.616732	+	0.959654i
$482$		0			0
$483$	−15.6608	−	13.4304i	−0.712592	−	0.611104i
$484$		0			0
$485$	1.76480	+	6.01034i	0.0801352	+	0.272916i
$486$		0			0
$487$	−21.4636	+	3.08600i	−0.972607	+	0.139840i	−0.610258	−	0.792203i	$-0.708934\pi$
$487$	−21.4636	+	3.08600i	−0.972607	+	0.139840i	−0.362349	+	0.932042i	$0.618025\pi$
$488$		0			0
$489$	−1.20699	−	0.543764i	−0.0545821	−	0.0245898i
$490$		0			0
$491$	−10.3451	−	4.72447i	−0.466870	−	0.213212i	0.168068	−	0.985775i	$-0.446247\pi$
$491$	−10.3451	−	4.72447i	−0.466870	−	0.213212i	−0.634938	+	0.772563i	$0.718974\pi$
$492$		0			0
$493$	0.897968	−	6.24551i	0.0404425	−	0.281283i
$494$		0			0
$495$	−2.01215	−	0.568504i	−0.0904393	−	0.0255524i
$496$		0			0
$497$	13.5123	+	8.68381i	0.606108	+	0.389522i
$498$		0			0
$499$		−	33.0070i		−	1.47760i	−0.673927	−	0.738798i	$-0.735394\pi$
$499$		−	33.0070i		−	1.47760i	0.673927	−	0.738798i	$-0.264606\pi$
$500$		0			0
$501$	−28.2993	+	8.46707i	−1.26432	+	0.378281i
$502$		0			0
$503$	−14.5907	−	16.8386i	−0.650567	−	0.750795i	0.330639	−	0.943757i	$-0.392736\pi$
$503$	−14.5907	−	16.8386i	−0.650567	−	0.750795i	−0.981206	+	0.192963i	$0.938190\pi$
$504$		0			0
$505$	−8.67464	−	5.57485i	−0.386017	−	0.248078i
$506$		0			0
$507$	−3.13225	+	2.74231i	−0.139108	+	0.121790i
$508$		0			0
$509$	−0.629879	+	2.14517i	−0.0279189	+	0.0950831i	−0.972274	−	0.233845i	$-0.924869\pi$
$509$	−0.629879	+	2.14517i	−0.0279189	+	0.0950831i	0.944355	+	0.328928i	$0.106687\pi$
$510$		0			0
$511$	1.64169	+	2.55453i	0.0726242	+	0.113006i
$512$		0			0
$513$	−15.2378	+	24.5309i	−0.672763	+	1.08306i
$514$		0			0
$515$	−4.77252	−	1.40134i	−0.210302	−	0.0617503i
$516$		0			0
$517$	1.73752	−	1.50557i	0.0764163	−	0.0662151i
$518$		0			0
$519$	−10.9983	+	7.14799i	−0.482770	+	0.313762i
$520$		0			0
$521$	12.0476	+	13.9037i	0.527817	+	0.609133i	0.955571	−	0.294762i	$-0.0952404\pi$
$521$	12.0476	+	13.9037i	0.527817	+	0.609133i	−0.427754	+	0.903895i	$0.640695\pi$
$522$		0			0
$523$	−5.28647	+	3.39741i	−0.231161	+	0.148558i	−0.651094	−	0.758997i	$-0.725690\pi$
$523$	−5.28647	+	3.39741i	−0.231161	+	0.148558i	0.419933	+	0.907555i	$0.362053\pi$
$524$		0			0
$525$	−8.66848	−	5.50838i	−0.378323	−	0.240405i
$526$		0			0
$527$	−34.4220	+	39.7252i	−1.49945	+	1.73046i
$528$		0			0
$529$	41.5778	−	47.9833i	1.80773	−	2.08623i
$530$		0			0
$531$	−23.7220	+	3.65902i	−1.02945	+	0.158788i
$532$		0			0
$533$	20.2938	−	9.26788i	0.879023	−	0.401436i
$534$		0			0
$535$			9.52458i			0.411784i
$536$		0			0
$537$	7.08729	−	6.20499i	0.305839	−	0.267765i
$538$		0			0
$539$	−2.55037	−	5.58454i	−0.109852	−	0.240543i
$540$		0			0
$541$	−7.79124	−	26.5345i	−0.334972	−	1.14081i	−0.939020	−	0.343861i	$-0.888265\pi$
$541$	−7.79124	−	26.5345i	−0.334972	−	1.14081i	0.604049	−	0.796947i	$-0.293553\pi$
$542$		0			0
$543$	0.0942314	+	18.4034i	0.00404386	+	0.789767i
$544$		0			0
$545$	−3.80561	−	3.29758i	−0.163014	−	0.141253i
$546$		0			0
$547$	9.77075	+	33.2761i	0.417767	+	1.42278i	0.852737	+	0.522340i	$0.174941\pi$
$547$	9.77075	+	33.2761i	0.417767	+	1.42278i	−0.434970	+	0.900445i	$0.643241\pi$
$548$		0			0
$549$	−26.0465	+	12.2189i	−1.11164	+	0.521492i
$550$		0			0
$551$	−4.35586	+	3.77437i	−0.185566	+	0.160794i
$552$		0			0
$553$	−2.88059	+	20.0350i	−0.122495	+	0.851973i
$554$		0			0
$555$	−8.02304	−	1.11164i	−0.340559	−	0.0471865i
$556$		0			0
$557$	−3.66286	+	12.4745i	−0.155200	+	0.528563i	−0.999979	−	0.00655314i	$-0.997914\pi$
$557$	−3.66286	+	12.4745i	−0.155200	+	0.528563i	0.844778	+	0.535116i	$0.179732\pi$
$558$		0			0
$559$	−8.70515	−	19.0616i	−0.368189	−	0.806220i
$560$		0			0
$561$	−11.5996	−	3.34152i	−0.489733	−	0.141079i
$562$		0			0
$563$	7.56202	+	2.22041i	0.318701	+	0.0935791i	0.437171	−	0.899379i	$-0.355981\pi$
$563$	7.56202	+	2.22041i	0.318701	+	0.0935791i	−0.118469	+	0.992958i	$0.537799\pi$
$564$		0			0
$565$	5.43150			0.228505
$566$		0			0
$567$	8.55510	−	7.72540i	0.359280	−	0.324436i
$568$		0			0
$569$	24.4567	−	21.1919i	1.02528	−	0.888409i	0.0314691	−	0.999505i	$-0.489981\pi$
$569$	24.4567	−	21.1919i	1.02528	−	0.888409i	0.993810	+	0.111096i	$0.0354360\pi$
$570$		0			0
$571$	−11.7884	+	25.8130i	−0.493330	+	1.08024i	0.485250	+	0.874376i	$0.338729\pi$
$571$	−11.7884	+	25.8130i	−0.493330	+	1.08024i	−0.978580	+	0.205867i	$0.933999\pi$
$572$		0			0
$573$	32.9143	−	28.8167i	1.37501	−	1.20384i
$574$		0			0
$575$	23.2785	−	36.2221i	0.970781	−	1.51056i
$576$		0			0
$577$	−13.5436	−	1.94728i	−0.563828	−	0.0810663i	−0.145494	−	0.989359i	$-0.546477\pi$
$577$	−13.5436	−	1.94728i	−0.563828	−	0.0810663i	−0.418335	+	0.908293i	$0.637386\pi$
$578$		0			0
$579$	−14.6329	−	22.5149i	−0.608122	−	0.935688i
$580$		0			0
$581$	−6.76364	+	14.8103i	−0.280603	+	0.614435i
$582$		0			0
$583$	2.40643	+	5.26936i	0.0996644	+	0.218234i
$584$		0			0
$585$	0.0608476	+	5.94163i	0.00251574	+	0.245656i
$586$		0			0
$587$	15.3714	−	4.51344i	0.634444	−	0.186290i	0.0513323	−	0.998682i	$-0.483653\pi$
$587$	15.3714	−	4.51344i	0.634444	−	0.186290i	0.583112	+	0.812392i	$0.301835\pi$
$588$		0			0
$589$	47.5258	−	6.83319i	1.95827	−	0.281556i
$590$		0			0
$591$	−8.46477	+	29.3841i	−0.348194	+	1.20870i
$592$		0			0
$593$	−0.420135	+	0.919968i	−0.0172529	+	0.0377786i	−0.918062	−	0.396436i	$-0.870247\pi$
$593$	−0.420135	+	0.919968i	−0.0172529	+	0.0377786i	0.900809	+	0.434215i	$0.142974\pi$
$594$		0			0
$595$	3.98870	+	2.56338i	0.163521	+	0.105088i
$596$		0			0
$597$	5.47127	−	2.53258i	0.223924	−	0.103652i
$598$		0			0
$599$	1.01345	+	7.04867i	0.0414083	+	0.288001i	0.999995	+	0.00319963i	$0.00101847\pi$
$599$	1.01345	+	7.04867i	0.0414083	+	0.288001i	−0.958587	+	0.284801i	$0.908072\pi$
$600$		0			0
$601$	9.23676	−	10.6598i	0.376775	−	0.434822i	−0.535415	−	0.844589i	$-0.679845\pi$
$601$	9.23676	−	10.6598i	0.376775	−	0.434822i	0.912190	+	0.409767i	$0.134390\pi$
$602$		0			0
$603$	−4.34249	−	24.1690i	−0.176840	−	0.984240i
$604$		0			0
$605$	3.86015	−	4.45485i	0.156937	−	0.181116i
$606$		0			0
$607$	2.12560	+	14.7839i	0.0862754	+	0.600059i	0.986392	+	0.164410i	$0.0525720\pi$
$607$	2.12560	+	14.7839i	0.0862754	+	0.600059i	−0.900117	+	0.435649i	$0.856519\pi$
$608$		0			0
$609$	2.08778	−	0.966407i	0.0846011	−	0.0391608i
$610$		0			0
$611$	−5.49631	−	3.53227i	−0.222357	−	0.142900i
$612$		0			0
$613$	−1.00616	+	2.20318i	−0.0406384	+	0.0889857i	−0.928862	−	0.370425i	$-0.879212\pi$
$613$	−1.00616	+	2.20318i	−0.0406384	+	0.0889857i	0.888224	+	0.459411i	$0.151939\pi$
$614$		0			0
$615$	−1.99939	+	6.94056i	−0.0806231	+	0.279870i
$616$		0			0
$617$	−33.8862	+	4.87210i	−1.36421	+	0.196144i	−0.785232	−	0.619201i	$-0.787456\pi$
$617$	−33.8862	+	4.87210i	−1.36421	+	0.196144i	−0.578976	+	0.815345i	$0.696547\pi$
$618$		0			0
$619$	18.7221	−	5.49730i	0.752504	−	0.220955i	0.117084	−	0.993122i	$-0.462645\pi$
$619$	18.7221	−	5.49730i	0.752504	−	0.220955i	0.635420	+	0.772167i	$0.280827\pi$
$620$		0			0
$621$	32.2031	+	36.0308i	1.29226	+	1.44587i
$622$		0			0
$623$	−0.770829	−	1.68788i	−0.0308826	−	0.0676235i
$624$		0			0
$625$	8.13542	−	17.8141i	0.325417	−	0.712563i
$626$		0			0
$627$	6.00880	+	9.24544i	0.239968	+	0.369227i
$628$		0			0
$629$	−46.2851	−	6.65479i	−1.84551	−	0.265344i
$630$		0			0
$631$	18.6285	−	28.9865i	0.741589	−	1.15394i	−0.241427	−	0.970419i	$-0.577616\pi$
$631$	18.6285	−	28.9865i	0.741589	−	1.15394i	0.983017	−	0.183517i	$-0.0587481\pi$
$632$		0			0
$633$	−2.25465	+	1.97397i	−0.0896144	+	0.0784583i
$634$		0			0
$635$	4.51252	−	9.88104i	0.179074	−	0.392117i
$636$		0			0
$637$	−13.1853	+	11.4252i	−0.522422	+	0.452681i
$638$		0			0
$639$	−28.6841	−	24.3451i	−1.13473	−	0.963079i
$640$		0			0
$641$	−39.9842			−1.57928			−0.789641	−	0.613570i	$-0.789733\pi$
$641$	−39.9842			−1.57928			−0.789641	+	0.613570i	$0.789733\pi$
$642$		0			0
$643$	35.2776	+	10.3584i	1.39121	+	0.408497i	0.889658	−	0.456628i	$-0.150943\pi$
$643$	35.2776	+	10.3584i	1.39121	+	0.408497i	0.501556	+	0.865125i	$0.332761\pi$
$644$		0			0
$645$	6.51914	+	1.87799i	0.256691	+	0.0739457i
$646$		0			0
$647$	6.01849	+	13.1787i	0.236611	+	0.518106i	0.990270	−	0.139160i	$-0.0444401\pi$
$647$	6.01849	+	13.1787i	0.236611	+	0.518106i	−0.753659	+	0.657266i	$0.771713\pi$
$648$		0			0
$649$	−2.58203	+	8.79357i	−0.101353	+	0.345178i
$650$		0			0
$651$	−18.9841	−	2.63036i	−0.744044	−	0.103092i
$652$		0			0
$653$	0.548182	−	3.81269i	0.0214520	−	0.149202i	−0.976280	−	0.216511i	$-0.930532\pi$
$653$	0.548182	−	3.81269i	0.0214520	−	0.149202i	0.997732	+	0.0673090i	$0.0214413\pi$
$654$		0			0
$655$	−6.47452	+	5.61021i	−0.252981	+	0.219209i
$656$		0			0
$657$	−3.02080	−	6.43929i	−0.117853	−	0.251221i
$658$		0			0
$659$	−1.69144	−	5.76053i	−0.0658893	−	0.224398i	0.919966	−	0.391999i	$-0.128216\pi$
$659$	−1.69144	−	5.76053i	−0.0658893	−	0.224398i	−0.985855	+	0.167601i	$0.946398\pi$
$660$		0			0
$661$	−9.68627	−	8.39320i	−0.376752	−	0.326458i	0.445815	−	0.895125i	$-0.352914\pi$
$661$	−9.68627	−	8.39320i	−0.376752	−	0.326458i	−0.822568	+	0.568667i	$0.807459\pi$
$662$		0			0
$663$	0.175645	+	34.3035i	0.00682148	+	1.33224i
$664$		0			0
$665$	−1.22019	−	4.15558i	−0.0473168	−	0.161146i
$666$		0			0
$667$	4.00659	+	8.77321i	0.155136	+	0.339700i
$668$		0			0
$669$	−5.40151	+	4.72907i	−0.208834	+	0.182836i
$670$		0			0
$671$			10.9853i			0.424081i
$672$		0			0
$673$	32.8059	−	14.9819i	1.26457	−	0.577511i	0.333640	−	0.942701i	$-0.391723\pi$
$673$	32.8059	−	14.9819i	1.26457	−	0.577511i	0.930933	+	0.365190i	$0.118996\pi$
$674$		0			0
$675$	18.4210	+	15.4729i	0.709023	+	0.595552i
$676$		0			0
$677$	−6.41707	+	7.40570i	−0.246628	+	0.284624i	−0.865544	−	0.500834i	$-0.833027\pi$
$677$	−6.41707	+	7.40570i	−0.246628	+	0.284624i	0.618915	+	0.785458i	$0.287572\pi$
$678$		0			0
$679$	−8.63481	+	9.96510i	−0.331373	+	0.382425i
$680$		0			0
$681$	27.6229	+	17.5530i	1.05851	+	0.672632i
$682$		0			0
$683$	−13.6651	+	8.78203i	−0.522881	+	0.336035i	−0.775311	−	0.631580i	$-0.782407\pi$
$683$	−13.6651	+	8.78203i	−0.522881	+	0.336035i	0.252430	+	0.967615i	$0.418770\pi$
$684$		0			0
$685$	1.96746	+	2.27057i	0.0751729	+	0.0867542i
$686$		0			0
$687$	15.9473	−	10.3644i	0.608426	−	0.395428i
$688$		0			0
$689$	12.4412	−	10.7803i	0.473971	−	0.410698i
$690$		0			0
$691$	−5.07491	−	1.49013i	−0.193059	−	0.0566872i	0.183774	−	0.982969i	$-0.441169\pi$
$691$	−5.07491	−	1.49013i	−0.193059	−	0.0566872i	−0.376833	+	0.926281i	$0.622987\pi$
$692$		0			0
$693$	−1.28318	−	4.21012i	−0.0487438	−	0.159929i
$694$		0			0
$695$	−5.63317	−	8.76538i	−0.213678	−	0.332490i
$696$		0			0
$697$	−11.7479	+	40.0095i	−0.444982	+	1.51547i
$698$		0			0
$699$	−1.18070	+	1.03371i	−0.0446580	+	0.0390985i
$700$		0			0
$701$	18.4569	+	11.8615i	0.697108	+	0.448004i	0.840606	−	0.541647i	$-0.182199\pi$
$701$	18.4569	+	11.8615i	0.697108	+	0.448004i	−0.143499	+	0.989651i	$0.545835\pi$
$702$		0			0
$703$	27.9717	+	32.2810i	1.05497	+	1.21750i
$704$		0			0
$705$	2.02645	−	0.606306i	0.0763204	−	0.0228348i
$706$		0			0
$707$		−	21.7056i		−	0.816322i
$708$		0			0
$709$	−16.7714	−	10.7783i	−0.629865	−	0.404789i	0.186395	−	0.982475i	$-0.440320\pi$
$709$	−16.7714	−	10.7783i	−0.629865	−	0.404789i	−0.816259	+	0.577686i	$0.803956\pi$
$710$		0			0
$711$	12.8907	−	45.6250i	0.483439	−	1.71107i
$712$		0			0
$713$	11.4346	−	79.5292i	0.428228	−	2.97839i
$714$		0			0
$715$	2.06377	+	0.942492i	0.0771806	+	0.0352472i
$716$		0			0
$717$	−6.37379	−	2.87146i	−0.238033	−	0.107237i
$718$		0			0
$719$	20.6253	−	2.96548i	0.769195	−	0.110594i	0.253465	−	0.967345i	$-0.418430\pi$
$719$	20.6253	−	2.96548i	0.769195	−	0.110594i	0.515730	+	0.856751i	$0.327521\pi$
$720$		0			0
$721$	−2.94978	−	10.0460i	−0.109855	−	0.374133i
$722$		0			0
$723$	6.01651	+	5.15964i	0.223756	+	0.191889i
$724$		0			0
$725$	2.59583	+	4.03920i	0.0964069	+	0.150012i
$726$		0			0
$727$	14.7024	+	6.71435i	0.545281	+	0.249021i	0.668957	−	0.743301i	$-0.266741\pi$
$727$	14.7024	+	6.71435i	0.545281	+	0.249021i	−0.123676	+	0.992323i	$0.539468\pi$
$728$		0			0
$729$	−22.2547	+	15.2881i	−0.824250	+	0.566226i
$730$		0			0
$731$	37.5802	+	11.0345i	1.38995	+	0.408127i
$732$		0			0
$733$	−6.02305	+	0.865984i	−0.222467	+	0.0319859i	−0.252647	−	0.967559i	$-0.581301\pi$
$733$	−6.02305	+	0.865984i	−0.222467	+	0.0319859i	0.0301801	+	0.999544i	$0.490392\pi$
$734$		0			0
$735$	−0.0289209	−	5.64827i	−0.00106676	−	0.208340i
$736$		0			0
$737$	−9.05896	−	2.41827i	−0.333691	−	0.0890780i
$738$		0			0
$739$	16.3473	+	14.1650i	0.601345	+	0.521068i	0.901476	−	0.432830i	$-0.142485\pi$
$739$	16.3473	+	14.1650i	0.601345	+	0.521068i	−0.300131	+	0.953898i	$0.597030\pi$
$740$		0			0
$741$	20.3985	−	23.7862i	0.749359	−	0.873806i
$742$		0			0
$743$	2.90477	−	9.89274i	0.106566	−	0.362929i	−0.888894	−	0.458113i	$-0.848526\pi$
$743$	2.90477	−	9.89274i	0.106566	−	0.362929i	0.995460	+	0.0951835i	$0.0303438\pi$
$744$		0			0
$745$	−3.16080	+	4.91830i	−0.115803	+	0.180193i
$746$		0			0
$747$	20.2888	−	32.2923i	0.742328	−	1.18151i
$748$		0			0
$749$	−16.8663	+	10.8393i	−0.616280	+	0.396059i
$750$		0			0
$751$	5.38440	+	37.4493i	0.196480	+	1.36654i	0.814400	+	0.580304i	$0.197066\pi$
$751$	5.38440	+	37.4493i	0.196480	+	1.36654i	−0.617920	+	0.786241i	$0.712025\pi$
$752$		0			0
$753$	22.1639	−	34.8790i	0.807696	−	1.27106i
$754$		0			0
$755$	1.73351	+	12.0568i	0.0630888	+	0.438792i
$756$		0			0
$757$	−34.1999	+	15.6186i	−1.24302	+	0.567667i	−0.924837	−	0.380363i	$-0.875799\pi$
$757$	−34.1999	+	15.6186i	−1.24302	+	0.567667i	−0.318180	+	0.948030i	$0.603072\pi$
$758$		0			0
$759$	17.6774	−	5.28900i	0.641647	−	0.191979i
$760$		0			0
$761$	36.7723	+	5.28706i	1.33300	+	0.191656i	0.771714	−	0.635969i	$-0.219400\pi$
$761$	36.7723	+	5.28706i	1.33300	+	0.191656i	0.561281	+	0.827625i	$0.310309\pi$
$762$		0			0
$763$	1.50849	−	10.4918i	0.0546110	−	0.379828i
$764$		0			0
$765$	−8.46728	−	7.18646i	−0.306135	−	0.259827i
$766$		0			0
$767$	26.0445			0.940411
$768$		0			0
$769$	−24.3703	−	11.1296i	−0.878817	−	0.401342i	−0.0756767	−	0.997132i	$-0.524112\pi$
$769$	−24.3703	−	11.1296i	−0.878817	−	0.401342i	−0.803140	+	0.595790i	$0.796839\pi$
$770$		0			0
$771$	4.37095	−	31.5465i	0.157416	−	1.13612i
$772$		0			0
$773$	13.4086	−	20.8642i	0.482273	−	0.750432i	−0.511805	−	0.859102i	$-0.671023\pi$
$773$	13.4086	−	20.8642i	0.482273	−	0.750432i	0.994078	+	0.108670i	$0.0346592\pi$
$774$		0			0
$775$		−	39.9986i		−	1.43679i
$776$		0			0
$777$	−7.16198	−	15.4724i	−0.256935	−	0.555070i
$778$		0			0
$779$	32.0430	−	20.5928i	1.14806	−	0.737814i
$780$		0			0
$781$	−13.0672	+	5.96759i	−0.467581	+	0.213537i
$782$		0			0
$783$	−5.14655	+	1.59743i	−0.183923	+	0.0570875i
$784$		0			0
$785$	2.69168	+	3.10636i	0.0960702	+	0.110871i
$786$		0			0
$787$	20.3595	+	2.92726i	0.725738	+	0.104345i	0.495276	−	0.868736i	$-0.335067\pi$
$787$	20.3595	+	2.92726i	0.725738	+	0.104345i	0.230462	+	0.973081i	$0.425976\pi$
$788$		0			0
$789$	1.98132	−	14.2998i	0.0705369	−	0.509086i
$790$		0			0
$791$	6.18123	+	9.61817i	0.219779	+	0.341983i
$792$		0			0
$793$	29.9532	−	8.79506i	1.06367	−	0.312322i
$794$		0			0
$795$	0.0272887	+	5.32949i	0.000967829	+	0.189017i
$796$		0			0
$797$	−7.71803	−	6.68771i	−0.273387	−	0.236891i	0.507367	−	0.861730i	$-0.330619\pi$
$797$	−7.71803	−	6.68771i	−0.273387	−	0.236891i	−0.780753	+	0.624839i	$0.785164\pi$
$798$		0			0
$799$	11.7168	−	3.44037i	0.414511	−	0.121712i
$800$		0			0
$801$	1.26715	+	4.15752i	0.0447724	+	0.146899i
$802$		0			0
$803$	−2.71580			−0.0958386
$804$		0			0
$805$	−7.24746			−0.255440
$806$		0			0
$807$	8.28649	−	18.3935i	0.291698	−	0.647483i
$808$		0			0
$809$	34.0046	−	9.98466i	1.19554	−	0.351042i	0.377394	−	0.926053i	$-0.376820\pi$
$809$	34.0046	−	9.98466i	1.19554	−	0.351042i	0.818146	+	0.575011i	$0.195002\pi$
$810$		0			0
$811$	−4.44647	−	3.85289i	−0.156137	−	0.135293i	0.573289	−	0.819353i	$-0.305667\pi$
$811$	−4.44647	−	3.85289i	−0.156137	−	0.135293i	−0.729426	+	0.684060i	$0.760213\pi$
$812$		0			0
$813$	−18.7807	+	0.0961631i	−0.658668	+	0.00337259i
$814$		0			0
$815$	−0.446210	+	0.131019i	−0.0156300	+	0.00458939i
$816$		0			0
$817$	−19.3425	−	30.0974i	−0.676707	−	1.05298i
$818$		0			0
$819$	−10.4523	+	6.86953i	−0.365232	+	0.240041i
$820$		0			0
$821$	7.00706	+	1.00746i	0.244548	+	0.0351607i	0.263499	−	0.964660i	$-0.415123\pi$
$821$	7.00706	+	1.00746i	0.244548	+	0.0351607i	−0.0189507	+	0.999820i	$0.506033\pi$
$822$		0			0
$823$	5.19952	+	6.00056i	0.181244	+	0.209167i	0.839100	−	0.543977i	$-0.183082\pi$
$823$	5.19952	+	6.00056i	0.181244	+	0.209167i	−0.657856	+	0.753143i	$0.728537\pi$
$824$		0			0
$825$	8.33591	−	3.85859i	0.290219	−	0.134339i
$826$		0			0
$827$	−28.6400	+	13.0795i	−0.995911	+	0.454817i	−0.845598	−	0.533821i	$-0.820756\pi$
$827$	−28.6400	+	13.0795i	−0.995911	+	0.454817i	−0.150314	+	0.988638i	$0.548028\pi$
$828$		0			0
$829$	11.0313	−	7.08936i	0.383131	−	0.246224i	−0.334871	−	0.942264i	$-0.608693\pi$
$829$	11.0313	−	7.08936i	0.383131	−	0.246224i	0.718003	+	0.696040i	$0.245056\pi$
$830$		0			0
$831$	3.95563	−	1.83101i	0.137219	−	0.0635171i
$832$		0			0
$833$		−	32.6089i		−	1.12983i
$834$		0			0
$835$	−5.61008	+	8.72945i	−0.194145	+	0.302095i
$836$		0			0
$837$	43.2625	+	11.9843i	1.49537	+	0.414240i
$838$		0			0
$839$	−15.6423	−	7.14361i	−0.540033	−	0.246625i	0.126674	−	0.991944i	$-0.459570\pi$
$839$	−15.6423	−	7.14361i	−0.540033	−	0.246625i	−0.666707	+	0.745319i	$0.732297\pi$
$840$		0			0
$841$	27.9245			0.962913
$842$		0			0
$843$	−15.1079	+	2.25120i	−0.520344	+	0.0775356i
$844$		0			0
$845$	−0.208129	+	1.44757i	−0.00715984	+	0.0497978i
$846$		0			0
$847$	12.2817	+	1.76584i	0.422004	+	0.0606751i
$848$		0			0
$849$	7.06639	+	23.6179i	0.242518	+	0.810564i
$850$		0			0
$851$	65.0177	−	29.6926i	2.22878	−	1.01785i
$852$		0			0
$853$	−0.134668	−	0.936635i	−0.00461094	−	0.0320698i	0.987386	−	0.158331i	$-0.0506113\pi$
$853$	−0.134668	−	0.936635i	−0.00461094	−	0.0320698i	−0.991997	+	0.126261i	$0.959702\pi$
$854$		0			0
$855$	1.54649	+	10.0261i	0.0528887	+	0.342885i
$856$		0			0
$857$	−1.72713	−	12.0125i	−0.0589976	−	0.410338i	−0.997823	−	0.0659447i	$-0.978994\pi$
$857$	−1.72713	−	12.0125i	−0.0589976	−	0.410338i	0.938826	−	0.344393i	$-0.111915\pi$
$858$		0			0
$859$	−36.6716	+	23.5674i	−1.25122	+	0.804109i	−0.987057	−	0.160370i	$-0.948731\pi$
$859$	−36.6716	+	23.5674i	−1.25122	+	0.804109i	−0.264160	+	0.964479i	$0.585095\pi$
$860$		0			0
$861$	−14.5658	+	4.35804i	−0.496402	+	0.148522i
$862$		0			0
$863$	−3.46860	+	5.39725i	−0.118073	+	0.183725i	−0.895259	−	0.445546i	$-0.853010\pi$
$863$	−3.46860	+	5.39725i	−0.118073	+	0.183725i	0.777187	+	0.629270i	$0.216646\pi$
$864$		0			0
$865$	−1.29819	+	4.42123i	−0.0441398	+	0.150326i
$866$		0			0
$867$	−26.3187	−	22.5704i	−0.893831	−	0.766532i
$868$		0			0
$869$	−13.6812	−	11.8548i	−0.464103	−	0.402148i
$870$		0			0
$871$	0.658990	+	26.6370i	0.0223290	+	0.902559i
$872$		0			0
$873$	23.1332	−	20.4635i	0.782940	−	0.692585i
$874$		0			0
$875$	−7.42804	+	1.06799i	−0.251113	+	0.0361047i
$876$		0			0
$877$	3.11686	+	0.915192i	0.105249	+	0.0309038i	0.333933	−	0.942597i	$-0.391624\pi$
$877$	3.11686	+	0.915192i	0.105249	+	0.0309038i	−0.228684	+	0.973501i	$0.573442\pi$
$878$		0			0
$879$	4.80550	+	32.2499i	0.162086	+	1.08776i
$880$		0			0
$881$	−13.5673	−	6.19597i	−0.457093	−	0.208748i	0.173542	−	0.984826i	$-0.444479\pi$
$881$	−13.5673	−	6.19597i	−0.457093	−	0.208748i	−0.630636	+	0.776079i	$0.717206\pi$
$882$		0			0
$883$	−0.529588	−	0.824054i	−0.0178220	−	0.0277316i	0.832228	−	0.554433i	$-0.187065\pi$
$883$	−0.529588	−	0.824054i	−0.0178220	−	0.0277316i	−0.850050	+	0.526702i	$0.823429\pi$
$884$		0			0
$885$	−5.48899	+	6.40056i	−0.184510	+	0.215152i
$886$		0			0
$887$	−7.52995	−	25.6447i	−0.252831	−	0.861063i	−0.983894	−	0.178753i	$-0.942794\pi$
$887$	−7.52995	−	25.6447i	−0.252831	−	0.861063i	0.731063	−	0.682310i	$-0.239025\pi$
$888$		0			0
$889$	22.6329	−	3.25412i	0.759083	−	0.109140i
$890$		0			0
$891$	1.67585	+	10.1722i	0.0561430	+	0.340782i
$892$		0			0
$893$	−10.1466	−	4.63378i	−0.339542	−	0.155064i
$894$		0			0
$895$	0.470929	−	3.27539i	0.0157414	−	0.109484i
$896$		0			0
$897$	−28.5743	−	43.9659i	−0.954068	−	1.46798i
$898$		0			0
$899$	7.53735	+	4.84396i	0.251385	+	0.161555i
$900$		0			0
$901$			30.7685i			1.02505i
$902$		0			0
$903$	4.09343	+	13.6814i	0.136221	+	0.455289i
$904$		0			0
$905$	4.23370	+	4.88595i	0.140733	+	0.162415i
$906$		0			0
$907$	14.7658	+	9.48942i	0.490291	+	0.315091i	0.762323	−	0.647197i	$-0.224059\pi$
$907$	14.7658	+	9.48942i	0.490291	+	0.315091i	−0.272031	+	0.962288i	$0.587695\pi$
$908$		0			0
$909$	−6.71979	+	50.3955i	−0.222881	+	1.67151i
$910$		0			0
$911$	−9.19977	+	31.3315i	−0.304802	+	1.03806i	0.654590	+	0.755984i	$0.272841\pi$
$911$	−9.19977	+	31.3315i	−0.304802	+	1.03806i	−0.959392	+	0.282076i	$0.908977\pi$
$912$		0			0
$913$	−7.87267	−	12.2501i	−0.260547	−	0.405420i
$914$		0			0
$915$	−4.15135	+	9.21476i	−0.137239	+	0.304630i
$916$		0			0
$917$	−17.3029	−	5.08058i	−0.571391	−	0.167775i
$918$		0			0
$919$	13.5238	−	11.7184i	0.446108	−	0.386554i	−0.402635	−	0.915361i	$-0.631906\pi$
$919$	13.5238	−	11.7184i	0.446108	−	0.386554i	0.848743	+	0.528806i	$0.177360\pi$
$920$		0			0
$921$	1.15006	+	1.76954i	0.0378957	+	0.0583082i
$922$		0			0
$923$	26.7336	+	30.8522i	0.879947	+	1.01551i
$924$		0			0
$925$	29.9342	−	19.2376i	0.984232	−	0.632527i
$926$		0			0
$927$	3.73860	+	24.2378i	0.122792	+	0.796075i
$928$		0			0
$929$	0.123089	−	0.142052i	0.00403842	−	0.00466058i	−0.753727	−	0.657188i	$-0.771746\pi$
$929$	0.123089	−	0.142052i	0.00403842	−	0.00466058i	0.757765	+	0.652527i	$0.226291\pi$
$930$		0			0
$931$	−19.5061	+	22.5113i	−0.639287	+	0.737777i
$932$		0			0
$933$	5.94433	−	9.35453i	0.194609	−	0.306254i
$934$		0			0
$935$	−3.85731	+	1.76158i	−0.126148	+	0.0576097i
$936$		0			0
$937$		−	56.5535i		−	1.84752i	−0.382970	−	0.923761i	$-0.625099\pi$
$937$		−	56.5535i		−	1.84752i	0.382970	−	0.923761i	$-0.374901\pi$
$938$		0			0
$939$	22.6700	+	25.8935i	0.739807	+	0.845001i
$940$		0			0
$941$	−18.3483	−	40.1772i	−0.598139	−	1.30974i	−0.930397	−	0.366553i	$-0.880538\pi$
$941$	−18.3483	−	40.1772i	−0.598139	−	1.30974i	0.332259	−	0.943188i	$-0.392189\pi$
$942$		0			0
$943$	−17.9573	−	61.1569i	−0.584770	−	1.99154i
$944$		0			0
$945$	0.514646	−	4.01649i	0.0167414	−	0.130656i
$946$		0			0
$947$	2.19087	+	1.89840i	0.0711938	+	0.0616898i	0.689731	−	0.724066i	$-0.257729\pi$
$947$	2.19087	+	1.89840i	0.0711938	+	0.0616898i	−0.618537	+	0.785756i	$0.712274\pi$
$948$		0			0
$949$	2.17434	+	7.40511i	0.0705820	+	0.240380i
$950$		0			0
$951$	12.5631	+	3.61910i	0.407388	+	0.117357i
$952$		0			0
$953$	−11.8130	+	10.2360i	−0.382659	+	0.331576i	−0.824857	−	0.565341i	$-0.808744\pi$
$953$	−11.8130	+	10.2360i	−0.382659	+	0.331576i	0.442198	+	0.896918i	$0.354199\pi$
$954$		0			0
$955$	2.18705	−	15.2113i	0.0707714	−	0.492226i
$956$		0			0
$957$	−0.282392	+	2.03811i	−0.00912844	+	0.0658827i
$958$		0			0
$959$	−1.78173	+	6.06800i	−0.0575350	+	0.195946i
$960$		0			0
$961$	−18.1285	−	39.6958i	−0.584790	−	1.28051i
$962$		0			0
$963$	42.5155	−	19.9448i	1.37004	−	0.642714i
$964$		0			0
$965$	−9.05084	−	2.65757i	−0.291357	−	0.0855501i
$966$		0			0
$967$	−1.44665			−0.0465211			−0.0232605	−	0.999729i	$-0.507405\pi$
$967$	−1.44665			−0.0465211			−0.0232605	+	0.999729i	$0.507405\pi$
$968$		0			0
$969$	8.63167	+	57.9274i	0.277289	+	1.86090i
$970$		0			0
$971$	32.5255	−	28.1835i	1.04379	−	0.904451i	0.0482559	−	0.998835i	$-0.484634\pi$
$971$	32.5255	−	28.1835i	1.04379	−	0.904451i	0.995536	+	0.0943843i	$0.0300882\pi$
$972$		0			0
$973$	9.11113	−	19.9506i	0.292089	−	0.639587i
$974$		0			0
$975$	−17.1951	−	19.6400i	−0.550682	−	0.628985i
$976$		0			0
$977$	−31.7663	+	49.4294i	−1.01630	+	1.58139i	−0.220899	+	0.975297i	$0.570899\pi$
$977$	−31.7663	+	49.4294i	−1.01630	+	1.58139i	−0.795396	+	0.606090i	$0.792737\pi$
$978$		0			0
$979$	1.64266	+	0.236179i	0.0524996	+	0.00754831i
$980$		0			0
$981$	−6.75052	+	23.8926i	−0.215527	+	0.762832i
$982$		0			0
$983$	−19.0818	+	41.7833i	−0.608614	+	1.33268i	0.314904	+	0.949124i	$0.398028\pi$
$983$	−19.0818	+	41.7833i	−0.608614	+	1.33268i	−0.923518	+	0.383555i	$0.874700\pi$
$984$		0			0
$985$	4.46244	+	9.77139i	0.142185	+	0.311342i
$986$		0			0
$987$	3.37982	+	2.89846i	0.107581	+	0.0922592i
$988$		0			0
$989$	−57.4435	+	16.8669i	−1.82660	+	0.536338i
$990$		0			0
$991$	−56.8347	+	8.17159i	−1.80541	+	0.259579i	−0.961086	−	0.276249i	$-0.910908\pi$
$991$	−56.8347	+	8.17159i	−1.80541	+	0.259579i	−0.844327	+	0.535828i	$0.819999\pi$
$992$		0			0
$993$	−35.1657	−	10.1303i	−1.11595	−	0.321475i
$994$		0			0
$995$	0.879820	−	1.92654i	0.0278922	−	0.0610753i
$996$		0			0
$997$	15.1288	+	9.72267i	0.479133	+	0.307920i	0.757822	−	0.652461i	$-0.226264\pi$
$997$	15.1288	+	9.72267i	0.479133	+	0.307920i	−0.278689	+	0.960381i	$0.589900\pi$
$998$		0			0
$999$	11.8385	+	38.1408i	0.374552	+	1.20672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.3	✓	200
3.2	odd	2	inner	804.2.s.b.5.9	yes	200
67.27	odd	22	inner	804.2.s.b.161.9	yes	200
201.161	even	22	inner	804.2.s.b.161.3	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.3	✓	200	1.1	even	1	trivial
804.2.s.b.5.9	yes	200	3.2	odd	2	inner
804.2.s.b.161.3	yes	200	201.161	even	22	inner
804.2.s.b.161.9	yes	200	67.27	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +O(q^{10})\)	\(q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +(1.09908 - 0.322720i) q^{11} +(-1.75990 - 2.73846i) q^{13} +(1.04390 + 0.144638i) q^{15} +(6.02227 + 0.865872i) q^{17} +(-3.63947 - 4.20017i) q^{19} +(0.931865 + 2.01316i) q^{21} +(-8.45963 + 3.86338i) q^{23} +(-3.89482 + 2.50305i) q^{25} +(-1.54033 - 4.96260i) q^{27} -1.03707i q^{29} +(-4.67082 + 7.26794i) q^{31} +(-1.96526 - 0.272298i) q^{33} +(0.708870 + 0.323730i) q^{35} -7.68565 q^{37} +(0.830965 + 5.57663i) q^{39} +(-0.975368 + 6.78383i) q^{41} +(6.37193 + 0.916145i) q^{43} +(-1.54562 - 0.971087i) q^{45} +(1.82570 - 0.833771i) q^{47} +(-0.762752 - 5.30506i) q^{49} +(-8.89431 - 5.65188i) q^{51} +(0.719704 + 5.00565i) q^{53} +(-0.586331 + 0.376812i) q^{55} +(2.75924 + 9.22215i) q^{57} +(-4.32558 + 6.73073i) q^{59} +(-2.70183 + 9.20160i) q^{61} +(-0.0393469 - 3.84213i) q^{63} +(1.49687 + 1.29705i) q^{65} +(-6.99330 - 4.25368i) q^{67} +(16.1080 - 0.0824778i) q^{69} +(-12.4132 + 1.78475i) q^{71} +(-2.27484 - 0.667954i) q^{73} +(7.93145 - 1.18185i) q^{75} +(-1.33453 - 0.609459i) q^{77} +(-8.54411 - 13.2949i) q^{79} +(-1.09812 + 8.93276i) q^{81} +(-3.58147 - 12.1974i) q^{83} +(-3.66427 + 0.526843i) q^{85} +(-0.737815 + 1.63773i) q^{87} +(1.31786 + 0.601845i) q^{89} +(-0.593340 + 4.12677i) q^{91} +(12.5468 - 8.15445i) q^{93} +(2.84474 + 1.82820i) q^{95} -10.2951i q^{97} +(2.90980 + 1.82818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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