LMFDB - Embedded newform 756.2.ck.a.605.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.3
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63320 - 0.576754i) q^{3} +(0.109190 + 0.619249i) q^{5} +(-2.49443 - 0.881937i) q^{7} +(2.33471 + 1.88391i) q^{9} +O(q^{10})$	\(q+(-1.63320 - 0.576754i) q^{3} +(0.109190 + 0.619249i) q^{5} +(-2.49443 - 0.881937i) q^{7} +(2.33471 + 1.88391i) q^{9} +(-1.84753 - 0.325769i) q^{11} +(0.235703 + 0.280900i) q^{13} +(0.178824 - 1.07434i) q^{15} +3.97503 q^{17} +1.40905i q^{19} +(3.56525 + 2.87906i) q^{21} +(3.12882 + 3.72878i) q^{23} +(4.32692 - 1.57487i) q^{25} +(-2.72650 - 4.42337i) q^{27} +(2.85223 - 3.39915i) q^{29} +(-3.24035 + 8.90279i) q^{31} +(2.82950 + 1.59762i) q^{33} +(0.273771 - 1.64097i) q^{35} +(-0.196473 + 0.340302i) q^{37} +(-0.222941 - 0.594710i) q^{39} +(-0.337003 + 0.282779i) q^{41} +(8.15803 - 2.96928i) q^{43} +(-0.911684 + 1.65147i) q^{45} +(9.21115 - 3.35258i) q^{47} +(5.44437 + 4.39986i) q^{49} +(-6.49203 - 2.29261i) q^{51} +(8.64238 + 4.98968i) q^{53} -1.17965i q^{55} +(0.812676 - 2.30127i) q^{57} +(0.442479 - 0.371284i) q^{59} +(1.99861 + 5.49113i) q^{61} +(-4.16228 - 6.75836i) q^{63} +(-0.148210 + 0.176630i) q^{65} +(0.618194 + 3.50595i) q^{67} +(-2.95941 - 7.89443i) q^{69} +(12.2893 - 7.09525i) q^{71} +(-5.51091 + 3.18172i) q^{73} +(-7.97505 + 0.0765143i) q^{75} +(4.32122 + 2.44201i) q^{77} +(-1.75512 + 9.95378i) q^{79} +(1.90173 + 8.79678i) q^{81} +(-3.38160 - 2.83750i) q^{83} +(0.434034 + 2.46153i) q^{85} +(-6.61875 + 3.90648i) q^{87} -6.22400 q^{89} +(-0.340209 - 0.908561i) q^{91} +(10.4269 - 12.6712i) q^{93} +(-0.872552 + 0.153855i) q^{95} +(2.12529 + 5.83919i) q^{97} +(-3.69972 - 4.24116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−1.63320	−	0.576754i	−0.942931	−	0.332989i
$3$	−1.63320	−	0.576754i	−0.942931	−	0.332989i
$4$		0			0
$5$	0.109190	+	0.619249i	0.0488314	+	0.276936i	0.999440	−	0.0334549i	$-0.0106510\pi$
$5$	0.109190	+	0.619249i	0.0488314	+	0.276936i	−0.950609	+	0.310391i	$0.899540\pi$
$6$		0			0
$7$	−2.49443	−	0.881937i	−0.942806	−	0.333341i
$7$	−2.49443	−	0.881937i	−0.942806	−	0.333341i
$8$		0			0
$9$	2.33471	+	1.88391i	0.778236	+	0.627971i
$10$		0			0
$11$	−1.84753	−	0.325769i	−0.557050	−	0.0982230i	−0.111967	−	0.993712i	$-0.535715\pi$
$11$	−1.84753	−	0.325769i	−0.557050	−	0.0982230i	−0.445084	+	0.895489i	$0.646826\pi$
$12$		0			0
$13$	0.235703	+	0.280900i	0.0653723	+	0.0779077i	0.797740	−	0.603002i	$-0.206029\pi$
$13$	0.235703	+	0.280900i	0.0653723	+	0.0779077i	−0.732367	+	0.680910i	$0.761585\pi$
$14$		0			0
$15$	0.178824	−	1.07434i	0.0461722	−	0.277392i
$16$		0			0
$17$	3.97503			0.964086			0.482043	−	0.876148i	$-0.339895\pi$
$17$	3.97503			0.964086			0.482043	+	0.876148i	$0.339895\pi$
$18$		0			0
$19$			1.40905i			0.323258i	0.986852	+	0.161629i	$0.0516748\pi$
$19$			1.40905i			0.323258i	−0.986852	+	0.161629i	$0.948325\pi$
$20$		0			0
$21$	3.56525	+	2.87906i	0.778002	+	0.628262i
$22$		0			0
$23$	3.12882	+	3.72878i	0.652404	+	0.777505i	0.986275	−	0.165114i	$-0.0527991\pi$
$23$	3.12882	+	3.72878i	0.652404	+	0.777505i	−0.333870	+	0.942619i	$0.608355\pi$
$24$		0			0
$25$	4.32692	−	1.57487i	0.865383	−	0.314974i
$26$		0			0
$27$	−2.72650	−	4.42337i	−0.524715	−	0.851278i
$28$		0			0
$29$	2.85223	−	3.39915i	0.529646	−	0.631207i	−0.433188	−	0.901304i	$-0.642611\pi$
$29$	2.85223	−	3.39915i	0.529646	−	0.631207i	0.962833	+	0.270097i	$0.0870557\pi$
$30$		0			0
$31$	−3.24035	+	8.90279i	−0.581984	+	1.59899i	0.202801	+	0.979220i	$0.434996\pi$
$31$	−3.24035	+	8.90279i	−0.581984	+	1.59899i	−0.784785	+	0.619768i	$0.787227\pi$
$32$		0			0
$33$	2.82950	+	1.59762i	0.492553	+	0.278109i
$34$		0			0
$35$	0.273771	−	1.64097i	0.0462757	−	0.277375i
$36$		0			0
$37$	−0.196473	+	0.340302i	−0.0323000	+	0.0559452i	−0.881724	−	0.471766i	$-0.843617\pi$
$37$	−0.196473	+	0.340302i	−0.0323000	+	0.0559452i	0.849424	+	0.527712i	$0.176950\pi$
$38$		0			0
$39$	−0.222941	−	0.594710i	−0.0356991	−	0.0952298i
$40$		0			0
$41$	−0.337003	+	0.282779i	−0.0526311	+	0.0441627i	−0.668724	−	0.743511i	$-0.733159\pi$
$41$	−0.337003	+	0.282779i	−0.0526311	+	0.0441627i	0.616093	+	0.787674i	$0.288715\pi$
$42$		0			0
$43$	8.15803	−	2.96928i	1.24409	−	0.452811i	0.365688	−	0.930737i	$-0.380834\pi$
$43$	8.15803	−	2.96928i	1.24409	−	0.452811i	0.878400	+	0.477926i	$0.158611\pi$
$44$		0			0
$45$	−0.911684	+	1.65147i	−0.135906	+	0.246187i
$46$		0			0
$47$	9.21115	−	3.35258i	1.34358	−	0.489024i	0.432644	−	0.901565i	$-0.357581\pi$
$47$	9.21115	−	3.35258i	1.34358	−	0.489024i	0.910939	+	0.412540i	$0.135358\pi$
$48$		0			0
$49$	5.44437	+	4.39986i	0.777768	+	0.628552i
$50$		0			0
$51$	−6.49203	−	2.29261i	−0.909066	−	0.321030i
$52$		0			0
$53$	8.64238	+	4.98968i	1.18712	+	0.685385i	0.957651	−	0.287930i	$-0.0929671\pi$
$53$	8.64238	+	4.98968i	1.18712	+	0.685385i	0.229471	+	0.973316i	$0.426300\pi$
$54$		0			0
$55$		−	1.17965i		−	0.159064i
$56$		0			0
$57$	0.812676	−	2.30127i	0.107642	−	0.304810i
$58$		0			0
$59$	0.442479	−	0.371284i	0.0576058	−	0.0483370i	−0.613530	−	0.789671i	$-0.710251\pi$
$59$	0.442479	−	0.371284i	0.0576058	−	0.0483370i	0.671136	+	0.741334i	$0.265807\pi$
$60$		0			0
$61$	1.99861	+	5.49113i	0.255895	+	0.703067i	0.999410	+	0.0343471i	$0.0109352\pi$
$61$	1.99861	+	5.49113i	0.255895	+	0.703067i	−0.743515	+	0.668720i	$0.766843\pi$
$62$		0			0
$63$	−4.16228	−	6.75836i	−0.524398	−	0.851473i
$64$		0			0
$65$	−0.148210	+	0.176630i	−0.0183832	+	0.0219083i
$66$		0			0
$67$	0.618194	+	3.50595i	0.0755244	+	0.428320i	0.999002	+	0.0446676i	$0.0142229\pi$
$67$	0.618194	+	3.50595i	0.0755244	+	0.428320i	−0.923477	+	0.383653i	$0.874666\pi$
$68$		0			0
$69$	−2.95941	−	7.89443i	−0.356271	−	0.950377i
$70$		0			0
$71$	12.2893	−	7.09525i	1.45848	−	0.842051i	0.459539	−	0.888157i	$-0.348014\pi$
$71$	12.2893	−	7.09525i	1.45848	−	0.842051i	0.998937	+	0.0461059i	$0.0146812\pi$
$72$		0			0
$73$	−5.51091	+	3.18172i	−0.645003	+	0.372392i	−0.786539	−	0.617541i	$-0.788129\pi$
$73$	−5.51091	+	3.18172i	−0.645003	+	0.372392i	0.141536	+	0.989933i	$0.454796\pi$
$74$		0			0
$75$	−7.97505	+	0.0765143i	−0.920879	+	0.00883511i
$76$		0			0
$77$	4.32122	+	2.44201i	0.492449	+	0.278293i
$78$		0			0
$79$	−1.75512	+	9.95378i	−0.197466	+	1.11989i	0.711396	+	0.702791i	$0.248063\pi$
$79$	−1.75512	+	9.95378i	−0.197466	+	1.11989i	−0.908862	+	0.417096i	$0.863048\pi$
$80$		0			0
$81$	1.90173	+	8.79678i	0.211304	+	0.977420i
$82$		0			0
$83$	−3.38160	−	2.83750i	−0.371178	−	0.311456i	0.438049	−	0.898951i	$-0.355670\pi$
$83$	−3.38160	−	2.83750i	−0.371178	−	0.311456i	−0.809228	+	0.587495i	$0.800114\pi$
$84$		0			0
$85$	0.434034	+	2.46153i	0.0470776	+	0.266990i
$86$		0			0
$87$	−6.61875	+	3.90648i	−0.709604	+	0.418818i
$88$		0			0
$89$	−6.22400			−0.659742			−0.329871	−	0.944026i	$-0.607005\pi$
$89$	−6.22400			−0.659742			−0.329871	+	0.944026i	$0.607005\pi$
$90$		0			0
$91$	−0.340209	−	0.908561i	−0.0356636	−	0.0952431i
$92$		0			0
$93$	10.4269	−	12.6712i	1.08122	−	1.31394i
$94$		0			0
$95$	−0.872552	+	0.153855i	−0.0895220	+	0.0157851i
$96$		0			0
$97$	2.12529	+	5.83919i	0.215791	+	0.592880i	0.999605	−	0.0281157i	$-0.00895069\pi$
$97$	2.12529	+	5.83919i	0.215791	+	0.592880i	−0.783814	+	0.620996i	$0.786728\pi$
$98$		0			0
$99$	−3.69972	−	4.24116i	−0.371836	−	0.426252i
$100$		0			0
$101$	−12.8654	−	10.7953i	−1.28015	−	1.07418i	−0.993223	−	0.116224i	$-0.962921\pi$
$101$	−12.8654	−	10.7953i	−1.28015	−	1.07418i	−0.286930	−	0.957952i	$-0.592635\pi$
$102$		0			0
$103$	−3.84869	+	0.678628i	−0.379223	+	0.0668672i	−0.360011	−	0.932948i	$-0.617227\pi$
$103$	−3.84869	+	0.678628i	−0.379223	+	0.0668672i	−0.0192122	+	0.999815i	$0.506116\pi$
$104$		0			0
$105$	−1.39356	+	2.52214i	−0.135998	+	0.246136i
$106$		0			0
$107$	10.8698	−	6.27569i	1.05082	−	0.606693i	0.127944	−	0.991781i	$-0.459162\pi$
$107$	10.8698	−	6.27569i	1.05082	−	0.606693i	0.922880	+	0.385088i	$0.125829\pi$
$108$		0			0
$109$	−0.894424	+	1.54919i	−0.0856703	+	0.148385i	−0.905677	−	0.423969i	$-0.860636\pi$
$109$	−0.894424	+	1.54919i	−0.0856703	+	0.148385i	0.820006	+	0.572354i	$0.193970\pi$
$110$		0			0
$111$	0.517151	−	0.442465i	0.0490858	−	0.0419969i
$112$		0			0
$113$	3.18174	−	8.74175i	0.299313	−	0.822355i	−0.695302	−	0.718717i	$-0.744730\pi$
$113$	3.18174	−	8.74175i	0.299313	−	0.822355i	0.994615	−	0.103638i	$-0.0330483\pi$
$114$		0			0
$115$	−1.96741	+	2.34467i	−0.183462	+	0.218641i
$116$		0			0
$117$	0.0211066	+	1.09986i	0.00195131	+	0.101683i
$118$		0			0
$119$	−9.91543	−	3.50572i	−0.908946	−	0.321369i
$120$		0			0
$121$	−7.02939	−	2.55849i	−0.639035	−	0.232590i
$122$		0			0
$123$	0.713489	−	0.267468i	0.0643331	−	0.0241168i
$124$		0			0
$125$	3.01970	+	5.23027i	0.270090	+	0.467809i
$126$		0			0
$127$	−1.10888	+	1.92063i	−0.0983971	+	0.170429i	−0.911021	−	0.412359i	$-0.864705\pi$
$127$	−1.10888	+	1.92063i	−0.0983971	+	0.170429i	0.812624	+	0.582788i	$0.198038\pi$
$128$		0			0
$129$	−15.0363	+	0.144261i	−1.32387	+	0.0127015i
$130$		0			0
$131$	2.30973	−	1.93809i	0.201802	−	0.169332i	−0.536286	−	0.844036i	$-0.680173\pi$
$131$	2.30973	−	1.93809i	0.201802	−	0.169332i	0.738088	+	0.674704i	$0.235729\pi$
$132$		0			0
$133$	1.24269	−	3.51478i	0.107755	−	0.304770i
$134$		0			0
$135$	2.44146	−	2.17137i	0.210127	−	0.186882i
$136$		0			0
$137$	4.52151	+	12.4228i	0.386299	+	1.06135i	0.968654	+	0.248413i	$0.0799090\pi$
$137$	4.52151	+	12.4228i	0.386299	+	1.06135i	−0.582355	+	0.812934i	$0.697869\pi$
$138$		0			0
$139$	−21.1007	+	3.72062i	−1.78974	+	0.315579i	−0.967367	−	0.253378i	$-0.918459\pi$
$139$	−21.1007	+	3.72062i	−1.78974	+	0.315579i	−0.822368	+	0.568956i	$0.807347\pi$
$140$		0			0
$141$	−16.9773	+	0.162884i	−1.42975	+	0.0137173i
$142$		0			0
$143$	−0.343959	−	0.595755i	−0.0287633	−	0.0498196i
$144$		0			0
$145$	2.41636	+	1.39508i	0.200668	+	0.115855i
$146$		0			0
$147$	−6.35413	−	10.3259i	−0.524080	−	0.851669i
$148$		0			0
$149$	−5.55270	+	15.2559i	−0.454895	+	1.24981i	0.474346	+	0.880339i	$0.342685\pi$
$149$	−5.55270	+	15.2559i	−0.454895	+	1.24981i	−0.929241	+	0.369475i	$0.879538\pi$
$150$		0			0
$151$	−2.53282	+	14.3643i	−0.206118	+	1.16895i	0.689553	+	0.724235i	$0.257807\pi$
$151$	−2.53282	+	14.3643i	−0.206118	+	1.16895i	−0.895671	+	0.444717i	$0.853304\pi$
$152$		0			0
$153$	9.28053	+	7.48861i	0.750287	+	0.605418i
$154$		0			0
$155$	−5.86686	−	1.03448i	−0.471237	−	0.0830918i
$156$		0			0
$157$	4.78689	+	5.70479i	0.382035	+	0.455292i	0.922455	−	0.386103i	$-0.126179\pi$
$157$	4.78689	+	5.70479i	0.382035	+	0.455292i	−0.540420	+	0.841395i	$0.681735\pi$
$158$		0			0
$159$	−11.2369	−	13.1337i	−0.891148	−	1.04157i
$160$		0			0
$161$	−4.51608	−	12.0606i	−0.355917	−	0.950510i
$162$		0			0
$163$	−10.6878	−	18.5118i	−0.837134	−	1.44996i	−0.892281	−	0.451481i	$-0.850896\pi$
$163$	−10.6878	−	18.5118i	−0.837134	−	1.44996i	0.0551466	−	0.998478i	$-0.482437\pi$
$164$		0			0
$165$	−0.680368	+	1.92661i	−0.0529666	+	0.149986i
$166$		0			0
$167$	3.47846	+	1.26606i	0.269172	+	0.0979704i	0.473080	−	0.881020i	$-0.343142\pi$
$167$	3.47846	+	1.26606i	0.269172	+	0.0979704i	−0.203908	+	0.978990i	$0.565364\pi$
$168$		0			0
$169$	2.23408	−	12.6701i	0.171852	−	0.974622i
$170$		0			0
$171$	−2.65453	+	3.28972i	−0.202997	+	0.251571i
$172$		0			0
$173$	−0.900056	−	0.755236i	−0.0684300	−	0.0574196i	0.607931	−	0.793990i	$-0.292000\pi$
$173$	−0.900056	−	0.755236i	−0.0684300	−	0.0574196i	−0.676361	+	0.736570i	$0.736444\pi$
$174$		0			0
$175$	−12.1821	+	0.112334i	−0.920883	+	0.00849168i
$176$		0			0
$177$	−0.936798	+	0.351181i	−0.0704140	+	0.0263964i
$178$		0			0
$179$			4.19541i			0.313579i	0.987632	+	0.156790i	$0.0501145\pi$
$179$			4.19541i			0.313579i	−0.987632	+	0.156790i	$0.949886\pi$
$180$		0			0
$181$	−1.69261	−	0.977228i	−0.125811	−	0.0726368i	0.435774	−	0.900056i	$-0.356475\pi$
$181$	−1.69261	−	0.977228i	−0.125811	−	0.0726368i	−0.561585	+	0.827419i	$0.689808\pi$
$182$		0			0
$183$	−0.0971014	−	10.1208i	−0.00717794	−	0.748154i
$184$		0			0
$185$	−0.232184	−	0.0845082i	−0.0170705	−	0.00621316i
$186$		0			0
$187$	−7.34397	−	1.29494i	−0.537044	−	0.0946954i
$188$		0			0
$189$	2.89993	+	13.4384i	0.210939	+	0.977499i
$190$		0			0
$191$	1.09300	+	0.192725i	0.0790864	+	0.0139451i	0.213051	−	0.977041i	$-0.431660\pi$
$191$	1.09300	+	0.192725i	0.0790864	+	0.0139451i	−0.133965	+	0.990986i	$0.542771\pi$
$192$		0			0
$193$	2.16408	+	0.787661i	0.155774	+	0.0566971i	0.418730	−	0.908111i	$-0.362475\pi$
$193$	2.16408	+	0.787661i	0.155774	+	0.0566971i	−0.262956	+	0.964808i	$0.584698\pi$
$194$		0			0
$195$	0.343930	−	0.202992i	0.0246294	−	0.0145366i
$196$		0			0
$197$	−16.4656	−	9.50640i	−1.17312	−	0.677303i	−0.218709	−	0.975790i	$-0.570185\pi$
$197$	−16.4656	−	9.50640i	−1.17312	−	0.677303i	−0.954414	+	0.298488i	$0.903518\pi$
$198$		0			0
$199$		−	3.52524i		−	0.249897i	−0.992163	−	0.124949i	$-0.960123\pi$
$199$		−	3.52524i		−	0.249897i	0.992163	−	0.124949i	$-0.0398766\pi$
$200$		0			0
$201$	1.01244	−	6.08248i	0.0714117	−	0.429025i
$202$		0			0
$203$	−10.1125	+	5.96347i	−0.709760	+	0.418554i
$204$		0			0
$205$	−0.211908	−	0.177812i	−0.0148003	−	0.0124189i
$206$		0			0
$207$	0.280178	+	14.6001i	0.0194737	+	1.01477i
$208$		0			0
$209$	0.459025	−	2.60326i	0.0317514	−	0.180071i
$210$		0			0
$211$	9.65706	+	3.51488i	0.664820	+	0.241975i	0.652316	−	0.757947i	$-0.273798\pi$
$211$	9.65706	+	3.51488i	0.664820	+	0.241975i	0.0125038	+	0.999922i	$0.496020\pi$
$212$		0			0
$213$	−24.1632	+	4.50007i	−1.65564	+	0.308339i
$214$		0			0
$215$	2.72950	+	4.72763i	0.186150	+	0.322422i
$216$		0			0
$217$	15.9345	−	19.3496i	1.08171	−	1.31354i
$218$		0			0
$219$	10.8355	−	2.01796i	0.732195	−	0.136361i
$220$		0			0
$221$	0.936926	+	1.11659i	0.0630245	+	0.0751097i
$222$		0			0
$223$	27.8071	+	4.90315i	1.86210	+	0.328339i	0.987638	−	0.156749i	$-0.0501013\pi$
$223$	27.8071	+	4.90315i	1.86210	+	0.328339i	0.874465	+	0.485088i	$0.161212\pi$
$224$		0			0
$225$	13.0690	+	4.47468i	0.871267	+	0.298312i
$226$		0			0
$227$	−1.30132	+	7.38017i	−0.0863718	+	0.489839i	0.910680	+	0.413112i	$0.135558\pi$
$227$	−1.30132	+	7.38017i	−0.0863718	+	0.489839i	−0.997052	+	0.0767270i	$0.975553\pi$
$228$		0			0
$229$	0.533350	−	1.46537i	0.0352448	−	0.0968342i	−0.920822	−	0.389983i	$-0.872481\pi$
$229$	0.533350	−	1.46537i	0.0352448	−	0.0968342i	0.956067	+	0.293149i	$0.0947031\pi$
$230$		0			0
$231$	−5.64900	−	6.48058i	−0.371677	−	0.426391i
$232$		0			0
$233$	11.5533	+	6.67028i	0.756879	+	0.436984i	0.828174	−	0.560471i	$-0.189380\pi$
$233$	11.5533	+	6.67028i	0.756879	+	0.436984i	−0.0712949	+	0.997455i	$0.522713\pi$
$234$		0			0
$235$	3.08185	+	5.33792i	0.201038	+	0.348208i
$236$		0			0
$237$	8.60735	−	15.2443i	0.559107	−	0.990222i
$238$		0			0
$239$	8.46669	−	1.49291i	0.547665	−	0.0965680i	0.107032	−	0.994256i	$-0.465865\pi$
$239$	8.46669	−	1.49291i	0.547665	−	0.0965680i	0.440633	+	0.897688i	$0.354754\pi$
$240$		0			0
$241$	3.63407	+	9.98452i	0.234091	+	0.643160i	1.00000		0.000210696i	$6.70668e-5\pi$
$241$	3.63407	+	9.98452i	0.234091	+	0.643160i	−0.765909	+	0.642949i	$0.777711\pi$
$242$		0			0
$243$	1.96766	−	15.4638i	0.126226	−	0.992002i
$244$		0			0
$245$	−2.13014	+	3.85184i	−0.136089	+	0.246085i
$246$		0			0
$247$	−0.395802	+	0.332118i	−0.0251843	+	0.0211321i
$248$		0			0
$249$	3.88630	+	6.58456i	0.246284	+	0.417280i
$250$		0			0
$251$	11.6262	−	20.1372i	0.733839	−	1.27105i	−0.221391	−	0.975185i	$-0.571060\pi$
$251$	11.6262	−	20.1372i	0.733839	−	1.27105i	0.955231	−	0.295862i	$-0.0956068\pi$
$252$		0			0
$253$	−4.56586	−	7.90830i	−0.287053	−	0.497191i
$254$		0			0
$255$	0.710832	−	4.27051i	0.0445140	−	0.267430i
$256$		0			0
$257$	11.3456	+	4.12947i	0.707721	+	0.257589i	0.670704	−	0.741725i	$-0.265992\pi$
$257$	11.3456	+	4.12947i	0.707721	+	0.257589i	0.0370171	+	0.999315i	$0.488214\pi$
$258$		0			0
$259$	0.790214	−	0.675582i	0.0491015	−	0.0419786i
$260$		0			0
$261$	13.0628	−	2.56268i	0.808570	−	0.158626i
$262$		0			0
$263$	16.0766	−	19.1593i	0.991325	−	1.18142i	0.00792406	−	0.999969i	$-0.497478\pi$
$263$	16.0766	−	19.1593i	0.991325	−	1.18142i	0.983401	−	0.181446i	$-0.0580779\pi$
$264$		0			0
$265$	−2.14619	+	5.89661i	−0.131839	+	0.362226i
$266$		0			0
$267$	10.1651	+	3.58972i	0.622091	+	0.219687i
$268$		0			0
$269$	7.62612	−	13.2088i	0.464973	−	0.805356i	−0.534228	−	0.845341i	$-0.679397\pi$
$269$	7.62612	−	13.2088i	0.464973	−	0.805356i	0.999200	+	0.0399844i	$0.0127308\pi$
$270$		0			0
$271$	−18.4322	+	10.6418i	−1.11967	+	0.646444i	−0.941318	−	0.337522i	$-0.890411\pi$
$271$	−18.4322	+	10.6418i	−1.11967	+	0.646444i	−0.178356	+	0.983966i	$0.557078\pi$
$272$		0			0
$273$	0.0316143	+	1.68008i	0.00191339	+	0.101683i
$274$		0			0
$275$	−8.50714	+	1.50004i	−0.513000	+	0.0904557i
$276$		0			0
$277$	−0.961066	−	0.806430i	−0.0577449	−	0.0484537i	0.613458	−	0.789727i	$-0.289778\pi$
$277$	−0.961066	−	0.806430i	−0.0577449	−	0.0484537i	−0.671203	+	0.741273i	$0.734222\pi$
$278$		0			0
$279$	−24.3374	+	14.6809i	−1.45704	+	0.878921i
$280$		0			0
$281$	3.55922	+	9.77886i	0.212325	+	0.583358i	0.999440	−	0.0334475i	$-0.0106487\pi$
$281$	3.55922	+	9.77886i	0.212325	+	0.583358i	−0.787115	+	0.616806i	$0.788426\pi$
$282$		0			0
$283$	−9.41503	+	1.66012i	−0.559665	+	0.0986841i	−0.446323	−	0.894872i	$-0.647267\pi$
$283$	−9.41503	+	1.66012i	−0.559665	+	0.0986841i	−0.113342	+	0.993556i	$0.536156\pi$
$284$		0			0
$285$	1.51379	+	0.251972i	0.0896693	+	0.0149256i
$286$		0			0
$287$	1.09002	−	0.408158i	0.0643421	−	0.0240928i
$288$		0			0
$289$	−1.19916			−0.0705388
$290$		0			0
$291$	−0.103256	−	10.7624i	−0.00605299	−	0.630901i
$292$		0			0
$293$	3.33317	+	18.9033i	0.194726	+	1.10435i	0.912809	+	0.408388i	$0.133909\pi$
$293$	3.33317	+	18.9033i	0.194726	+	1.10435i	−0.718083	+	0.695958i	$0.754980\pi$
$294$		0			0
$295$	0.278231	+	0.233464i	0.0161993	+	0.0135928i
$296$		0			0
$297$	3.59629	+	9.06050i	0.208678	+	0.525744i
$298$		0			0
$299$	−0.309943	+	1.75777i	−0.0179244	+	0.101655i
$300$		0			0
$301$	−22.9684	+	0.211797i	−1.32387	+	0.0122078i
$302$		0			0
$303$	14.7855	+	25.0511i	0.849407	+	1.43915i
$304$		0			0
$305$	−3.18215	+	1.83721i	−0.182209	+	0.105198i
$306$		0			0
$307$	21.9964	−	12.6996i	1.25540	−	0.724807i	0.283225	−	0.959053i	$-0.408596\pi$
$307$	21.9964	−	12.6996i	1.25540	−	0.724807i	0.972177	+	0.234246i	$0.0752622\pi$
$308$		0			0
$309$	6.67710	+	1.11141i	0.379847	+	0.0632259i
$310$		0			0
$311$	2.27297	+	12.8907i	0.128888	+	0.730962i	0.978922	+	0.204234i	$0.0654703\pi$
$311$	2.27297	+	12.8907i	0.128888	+	0.730962i	−0.850034	+	0.526728i	$0.823419\pi$
$312$		0			0
$313$	−3.81819	+	4.55034i	−0.215817	+	0.257200i	−0.863081	−	0.505065i	$-0.831468\pi$
$313$	−3.81819	+	4.55034i	−0.215817	+	0.257200i	0.647264	+	0.762266i	$0.275913\pi$
$314$		0			0
$315$	3.73063	−	3.31543i	0.210197	−	0.186803i
$316$		0			0
$317$	−10.5297	−	28.9300i	−0.591404	−	1.62487i	−0.767901	−	0.640569i	$-0.778699\pi$
$317$	−10.5297	−	28.9300i	−0.591404	−	1.62487i	0.176497	−	0.984301i	$-0.443524\pi$
$318$		0			0
$319$	−6.37691	+	5.35086i	−0.357038	+	0.299591i
$320$		0			0
$321$	−21.3721	+	3.98027i	−1.19288	+	0.222157i
$322$		0			0
$323$			5.60101i			0.311649i
$324$		0			0
$325$	1.46225	+	0.844230i	0.0811110	+	0.0468294i
$326$		0			0
$327$	2.35428	−	2.01428i	0.130192	−	0.111390i
$328$		0			0
$329$	−25.9333	+	0.239138i	−1.42975	+	0.0131841i
$330$		0			0
$331$	16.0263	−	5.83309i	0.880885	−	0.320616i	0.138318	−	0.990388i	$-0.455830\pi$
$331$	16.0263	−	5.83309i	0.880885	−	0.320616i	0.742567	+	0.669772i	$0.233608\pi$
$332$		0			0
$333$	−1.09981	+	0.424367i	−0.0602691	+	0.0232551i
$334$		0			0
$335$	−2.10356	+	0.765631i	−0.114929	+	0.0418309i
$336$		0			0
$337$	13.1848	−	11.0634i	0.718221	−	0.602659i	−0.208671	−	0.977986i	$-0.566914\pi$
$337$	13.1848	−	11.0634i	0.718221	−	0.602659i	0.926893	+	0.375327i	$0.122469\pi$
$338$		0			0
$339$	−10.2383	+	12.4420i	−0.556067	+	0.675756i
$340$		0			0
$341$	8.88689	−	15.3925i	0.481252	−	0.833553i
$342$		0			0
$343$	−9.70022	−	15.7767i	−0.523762	−	0.851864i
$344$		0			0
$345$	4.56547	−	2.69461i	0.245797	−	0.145073i
$346$		0			0
$347$	−0.845241	+	2.32228i	−0.0453749	+	0.124667i	−0.960310	−	0.278934i	$-0.910019\pi$
$347$	−0.845241	+	2.32228i	−0.0453749	+	0.124667i	0.914935	+	0.403600i	$0.132241\pi$
$348$		0			0
$349$	−9.60242	+	11.4437i	−0.514006	+	0.612568i	−0.959153	−	0.282889i	$-0.908707\pi$
$349$	−9.60242	+	11.4437i	−0.514006	+	0.612568i	0.445147	+	0.895458i	$0.353152\pi$
$350$		0			0
$351$	0.599880	−	1.80848i	0.0320192	−	0.0965293i
$352$		0			0
$353$	−22.6470	+	8.24284i	−1.20538	+	0.438722i	−0.865099	−	0.501602i	$-0.832744\pi$
$353$	−22.6470	+	8.24284i	−1.20538	+	0.438722i	−0.340281	+	0.940324i	$0.610522\pi$
$354$		0			0
$355$	5.73560	+	6.83542i	0.304414	+	0.362787i
$356$		0			0
$357$	14.1720	+	11.4443i	0.750061	+	0.605698i
$358$		0			0
$359$			27.6871i			1.46127i	0.682768	+	0.730635i	$0.260776\pi$
$359$			27.6871i			1.46127i	−0.682768	+	0.730635i	$0.739224\pi$
$360$		0			0
$361$	17.0146			0.895504
$362$		0			0
$363$	10.0048	+	8.23276i	0.525116	+	0.432108i
$364$		0			0
$365$	−2.57201	−	3.06521i	−0.134625	−	0.160440i
$366$		0			0
$367$	30.1123	+	5.30961i	1.57185	+	0.277159i	0.890564	−	0.454859i	$-0.150310\pi$
$367$	30.1123	+	5.30961i	1.57185	+	0.277159i	0.681285	+	0.732018i	$0.261421\pi$
$368$		0			0
$369$	−1.31954	+	0.0253221i	−0.0686923	+	0.00131822i
$370$		0			0
$371$	−17.1572	−	20.0684i	−0.890760	−	1.04190i
$372$		0			0
$373$	−0.955166	−	5.41701i	−0.0494566	−	0.280482i	0.950043	−	0.312120i	$-0.101039\pi$
$373$	−0.955166	−	5.41701i	−0.0494566	−	0.280482i	−0.999499	+	0.0316373i	$0.989928\pi$
$374$		0			0
$375$	−1.91520	−	10.2837i	−0.0989005	−	0.531049i
$376$		0			0
$377$	1.62710			0.0838000
$378$		0			0
$379$	−20.4096			−1.04837			−0.524185	−	0.851604i	$-0.675630\pi$
$379$	−20.4096			−1.04837			−0.524185	+	0.851604i	$0.675630\pi$
$380$		0			0
$381$	2.91876	−	2.49724i	0.149533	−	0.127937i
$382$		0			0
$383$	2.82778	+	16.0371i	0.144493	+	0.819459i	0.967773	+	0.251824i	$0.0810304\pi$
$383$	2.82778	+	16.0371i	0.144493	+	0.819459i	−0.823280	+	0.567635i	$0.807859\pi$
$384$		0			0
$385$	−1.04038	+	2.94255i	−0.0530225	+	0.149966i
$386$		0			0
$387$	24.6405	+	8.43663i	1.25255	+	0.428858i
$388$		0			0
$389$	−16.0873	−	2.83663i	−0.815661	−	0.143823i	−0.249772	−	0.968305i	$-0.580356\pi$
$389$	−16.0873	−	2.83663i	−0.815661	−	0.143823i	−0.565889	+	0.824482i	$0.691467\pi$
$390$		0			0
$391$	12.4372	+	14.8220i	0.628974	+	0.749582i
$392$		0			0
$393$	−4.89005	+	1.83315i	−0.246671	+	0.0924703i
$394$		0			0
$395$	−6.35550			−0.319780
$396$		0			0
$397$		−	9.16393i		−	0.459924i	−0.973200	−	0.229962i	$-0.926140\pi$
$397$		−	9.16393i		−	0.459924i	0.973200	−	0.229962i	$-0.0738603\pi$
$398$		0			0
$399$	−4.05674	+	5.02362i	−0.203091	+	0.251496i
$400$		0			0
$401$	12.5976	+	15.0132i	0.629092	+	0.749722i	0.982605	−	0.185707i	$-0.0594576\pi$
$401$	12.5976	+	15.0132i	0.629092	+	0.749722i	−0.353513	+	0.935429i	$0.615013\pi$
$402$		0			0
$403$	−3.26456	+	1.18820i	−0.162619	+	0.0591885i
$404$		0			0
$405$	−5.23975	+	2.13817i	−0.260365	+	0.106246i
$406$		0			0
$407$	0.473849	−	0.564712i	0.0234878	−	0.0279917i
$408$		0			0
$409$	5.57617	−	15.3204i	0.275724	−	0.757544i	−0.722111	−	0.691777i	$-0.756828\pi$
$409$	5.57617	−	15.3204i	0.275724	−	0.757544i	0.997835	−	0.0657676i	$-0.0209496\pi$
$410$		0			0
$411$	−0.219676	−	22.8967i	−0.0108358	−	1.12941i
$412$		0			0
$413$	−1.43118	+	0.535904i	−0.0704239	+	0.0263701i
$414$		0			0
$415$	1.38788	−	2.40388i	0.0681283	−	0.118002i
$416$		0			0
$417$	36.6076	+	6.09337i	1.79268	+	0.298394i
$418$		0			0
$419$	6.43393	−	5.39871i	0.314318	−	0.263744i	−0.471956	−	0.881622i	$-0.656452\pi$
$419$	6.43393	−	5.39871i	0.314318	−	0.263744i	0.786274	+	0.617878i	$0.212007\pi$
$420$		0			0
$421$	20.1286	−	7.32622i	0.981009	−	0.357058i	0.198777	−	0.980045i	$-0.436303\pi$
$421$	20.1286	−	7.32622i	0.981009	−	0.357058i	0.782232	+	0.622987i	$0.214081\pi$
$422$		0			0
$423$	27.8213	+	9.52570i	1.35272	+	0.463156i
$424$		0			0
$425$	17.1996	−	6.26015i	0.834304	−	0.303662i
$426$		0			0
$427$	−0.142559	−	15.4599i	−0.00689893	−	0.748156i
$428$		0			0
$429$	0.218152	+	1.17137i	0.0105325	+	0.0565543i
$430$		0			0
$431$	23.7130	+	13.6907i	1.14222	+	0.659459i	0.946978	−	0.321297i	$-0.104119\pi$
$431$	23.7130	+	13.6907i	1.14222	+	0.659459i	0.195237	+	0.980756i	$0.437452\pi$
$432$		0			0
$433$		−	9.79725i		−	0.470826i	−0.971895	−	0.235413i	$-0.924356\pi$
$433$		−	9.79725i		−	0.470826i	0.971895	−	0.235413i	$-0.0756443\pi$
$434$		0			0
$435$	−3.14178	−	3.67210i	−0.150637	−	0.176064i
$436$		0			0
$437$	−5.25404	+	4.40867i	−0.251335	+	0.210895i
$438$		0			0
$439$	−8.14845	−	22.3877i	−0.388904	−	1.06851i	−0.967495	−	0.252888i	$-0.918619\pi$
$439$	−8.14845	−	22.3877i	−0.388904	−	1.06851i	0.578591	−	0.815618i	$-0.303603\pi$
$440$		0			0
$441$	4.42207	+	20.5291i	0.210575	+	0.977578i
$442$		0			0
$443$	−20.8243	+	24.8175i	−0.989394	+	1.17911i	−0.00556848	+	0.999984i	$0.501773\pi$
$443$	−20.8243	+	24.8175i	−0.989394	+	1.17911i	−0.983826	+	0.179129i	$0.942672\pi$
$444$		0			0
$445$	−0.679600	−	3.85420i	−0.0322161	−	0.182707i
$446$		0			0
$447$	17.8676	−	21.7135i	0.845109	−	1.02701i
$448$		0			0
$449$	−27.4242	+	15.8334i	−1.29423	+	0.747223i	−0.979401	−	0.201927i	$-0.935280\pi$
$449$	−27.4242	+	15.8334i	−1.29423	+	0.747223i	−0.314827	+	0.949149i	$0.601946\pi$
$450$		0			0
$451$	0.714743	−	0.412657i	0.0336559	−	0.0194313i
$452$		0			0
$453$	12.4213	−	21.9990i	0.583603	−	1.03361i
$454$		0			0
$455$	0.525478	−	0.309880i	0.0246348	−	0.0145274i
$456$		0			0
$457$	6.17622	−	35.0271i	0.288911	−	1.63850i	−0.402059	−	0.915614i	$-0.631705\pi$
$457$	6.17622	−	35.0271i	0.288911	−	1.63850i	0.690970	−	0.722883i	$-0.257184\pi$
$458$		0			0
$459$	−10.8379	−	17.5830i	−0.505870	−	0.820705i
$460$		0			0
$461$	20.6320	+	17.3123i	0.960927	+	0.806313i	0.981104	−	0.193483i	$-0.0619784\pi$
$461$	20.6320	+	17.3123i	0.960927	+	0.806313i	−0.0201766	+	0.999796i	$0.506423\pi$
$462$		0			0
$463$	5.46034	+	30.9671i	0.253763	+	1.43916i	0.799227	+	0.601029i	$0.205242\pi$
$463$	5.46034	+	30.9671i	0.253763	+	1.43916i	−0.545464	+	0.838134i	$0.683647\pi$
$464$		0			0
$465$	8.98513	+	5.07326i	0.416675	+	0.235267i
$466$		0			0
$467$	36.1290			1.67185			0.835926	−	0.548841i	$-0.184931\pi$
$467$	36.1290			1.67185			0.835926	+	0.548841i	$0.184931\pi$
$468$		0			0
$469$	1.54999	−	9.29056i	0.0715717	−	0.428998i
$470$		0			0
$471$	−4.52770	−	12.0779i	−0.208625	−	0.556522i
$472$		0			0
$473$	−16.0395	+	2.82819i	−0.737496	+	0.130040i
$474$		0			0
$475$	2.21907	+	6.09684i	0.101818	+	0.279742i
$476$		0			0
$477$	10.7773	+	27.9310i	0.493459	+	1.27887i
$478$		0			0
$479$	−7.55786	−	6.34179i	−0.345327	−	0.289764i	0.453583	−	0.891214i	$-0.350145\pi$
$479$	−7.55786	−	6.34179i	−0.345327	−	0.289764i	−0.798910	+	0.601450i	$0.794590\pi$
$480$		0			0
$481$	−0.141900	+	0.0250208i	−0.00647009	+	0.00114085i
$482$		0			0
$483$	0.419662	+	22.3021i	0.0190953	+	1.01478i
$484$		0			0
$485$	−3.38385	+	1.95367i	−0.153653	+	0.0887114i
$486$		0			0
$487$	−5.29343	+	9.16849i	−0.239868	+	0.415464i	−0.960676	−	0.277671i	$-0.910438\pi$
$487$	−5.29343	+	9.16849i	−0.239868	+	0.415464i	0.720808	+	0.693135i	$0.243771\pi$
$488$		0			0
$489$	6.77860	+	36.3978i	0.306539	+	1.64597i
$490$		0			0
$491$	1.98343	−	5.44942i	0.0895107	−	0.245929i	−0.886857	−	0.462044i	$-0.847116\pi$
$491$	1.98343	−	5.44942i	0.0895107	−	0.245929i	0.976368	+	0.216115i	$0.0693386\pi$
$492$		0			0
$493$	11.3377	−	13.5117i	0.510624	−	0.608538i
$494$		0			0
$495$	2.22236	−	2.75414i	0.0998876	−	0.123789i
$496$		0			0
$497$	−36.9125	+	6.86020i	−1.65575	+	0.307722i
$498$		0			0
$499$	−19.0968	−	6.95065i	−0.854888	−	0.311154i	−0.122856	−	0.992424i	$-0.539205\pi$
$499$	−19.0968	−	6.95065i	−0.854888	−	0.311154i	−0.732032	+	0.681271i	$0.761428\pi$
$500$		0			0
$501$	−4.95084	−	4.07395i	−0.221187	−	0.182011i
$502$		0			0
$503$	−6.84793	−	11.8610i	−0.305334	−	0.528854i	0.672001	−	0.740550i	$-0.265435\pi$
$503$	−6.84793	−	11.8610i	−0.305334	−	0.528854i	−0.977336	+	0.211695i	$0.932102\pi$
$504$		0			0
$505$	5.28022	−	9.14561i	0.234967	−	0.406974i
$506$		0			0
$507$	−10.9562	+	19.4043i	−0.486583	+	0.861776i
$508$		0			0
$509$	3.01278	−	2.52802i	0.133539	−	0.112053i	−0.573572	−	0.819155i	$-0.694443\pi$
$509$	3.01278	−	2.52802i	0.133539	−	0.112053i	0.707111	+	0.707103i	$0.249998\pi$
$510$		0			0
$511$	16.5527	−	3.07632i	0.732246	−	0.136088i
$512$		0			0
$513$	6.23275	−	3.84178i	0.275183	−	0.169619i
$514$		0			0
$515$	−0.840479	−	2.30920i	−0.0370359	−	0.101755i
$516$		0			0
$517$	−18.1100	+	3.19328i	−0.796477	+	0.140440i
$518$		0			0
$519$	1.03439	+	1.75257i	0.0454046	+	0.0769291i
$520$		0			0
$521$	−19.2670	−	33.3713i	−0.844100	−	1.46202i	−0.886400	−	0.462920i	$-0.846802\pi$
$521$	−19.2670	−	33.3713i	−0.844100	−	1.46202i	0.0422996	−	0.999105i	$-0.486532\pi$
$522$		0			0
$523$	−24.8394	−	14.3410i	−1.08615	−	0.627090i	−0.153602	−	0.988133i	$-0.549088\pi$
$523$	−24.8394	−	14.3410i	−1.08615	−	0.627090i	−0.932549	+	0.361043i	$0.882421\pi$
$524$		0			0
$525$	19.9607	+	6.84263i	0.871156	+	0.298637i
$526$		0			0
$527$	−12.8805	+	35.3888i	−0.561083	+	1.54156i
$528$		0			0
$529$	−0.120400	+	0.682823i	−0.00523479	+	0.0296880i
$530$		0			0
$531$	1.73253	−	0.0332475i	0.0751853	−	0.00144282i
$532$		0			0
$533$	−0.158865	−	0.0280123i	−0.00688122	−	0.00121335i
$534$		0			0
$535$	5.07309	+	6.04587i	0.219329	+	0.261386i
$536$		0			0
$537$	2.41972	−	6.85195i	0.104419	−	0.295684i
$538$		0			0
$539$	−8.62529	−	9.90247i	−0.371518	−	0.426530i
$540$		0			0
$541$	−6.07663	−	10.5250i	−0.261255	−	0.452507i	0.705321	−	0.708888i	$-0.250803\pi$
$541$	−6.07663	−	10.5250i	−0.261255	−	0.452507i	−0.966576	+	0.256382i	$0.917470\pi$
$542$		0			0
$543$	2.20076	+	2.57223i	0.0944434	+	0.110385i
$544$		0			0
$545$	−1.05699	−	0.384715i	−0.0452767	−	0.0164794i
$546$		0			0
$547$	0.380983	−	2.16066i	0.0162897	−	0.0923832i	−0.975579	−	0.219649i	$-0.929509\pi$
$547$	0.380983	−	2.16066i	0.0162897	−	0.0923832i	0.991869	+	0.127265i	$0.0406200\pi$
$548$		0			0
$549$	−5.67865	+	16.5854i	−0.242359	+	0.707847i
$550$		0			0
$551$	4.78958	+	4.01893i	0.204043	+	0.171212i
$552$		0			0
$553$	13.1566	−	23.2811i	0.559477	−	0.990013i
$554$		0			0
$555$	0.330464	+	0.271932i	0.0140274	+	0.0115429i
$556$		0			0
$557$			21.0683i			0.892694i	0.894860	+	0.446347i	$0.147275\pi$
$557$			21.0683i			0.892694i	−0.894860	+	0.446347i	$0.852725\pi$
$558$		0			0
$559$	2.75694	+	1.59172i	0.116606	+	0.0673227i
$560$		0			0
$561$	11.2473	+	6.35057i	0.474863	+	0.268121i
$562$		0			0
$563$	−39.4456	−	14.3570i	−1.66243	−	0.605076i	−0.671691	−	0.740832i	$-0.734432\pi$
$563$	−39.4456	−	14.3570i	−1.66243	−	0.605076i	−0.990742	+	0.135756i	$0.956654\pi$
$564$		0			0
$565$	5.76073	+	1.01577i	0.242356	+	0.0427339i
$566$		0			0
$567$	3.01447	−	23.6202i	0.126596	−	0.991954i
$568$		0			0
$569$	−16.1479	−	2.84732i	−0.676957	−	0.119366i	−0.175409	−	0.984496i	$-0.556125\pi$
$569$	−16.1479	−	2.84732i	−0.676957	−	0.119366i	−0.501548	+	0.865130i	$0.667236\pi$
$570$		0			0
$571$	15.3637	+	5.59193i	0.642951	+	0.234015i	0.642858	−	0.765985i	$-0.277748\pi$
$571$	15.3637	+	5.59193i	0.642951	+	0.234015i	9.25327e−5		1.00000i	$0.499971\pi$
$572$		0			0
$573$	−1.67393	−	0.945149i	−0.0699295	−	0.0394842i
$574$		0			0
$575$	19.4105	+	11.2067i	0.809474	+	0.467350i
$576$		0			0
$577$		−	3.58396i		−	0.149202i	−0.997213	−	0.0746011i	$-0.976232\pi$
$577$		−	3.58396i		−	0.149202i	0.997213	−	0.0746011i	$-0.0237683\pi$
$578$		0			0
$579$	−3.08010	−	2.53455i	−0.128004	−	0.105332i
$580$		0			0
$581$	5.93267	+	10.0603i	0.246129	+	0.417371i
$582$		0			0
$583$	−14.3416	−	12.0340i	−0.593966	−	0.498397i
$584$		0			0
$585$	−0.678785	+	0.133165i	−0.0280643	+	0.00550568i
$586$		0			0
$587$	6.72409	−	38.1342i	0.277533	−	1.57397i	−0.453266	−	0.891375i	$-0.649741\pi$
$587$	6.72409	−	38.1342i	0.277533	−	1.57397i	0.730799	−	0.682593i	$-0.239148\pi$
$588$		0			0
$589$	−12.5445	−	4.56582i	−0.516886	−	0.188131i
$590$		0			0
$591$	21.4088	+	25.0225i	0.880639	+	1.02929i
$592$		0			0
$593$	3.48794	+	6.04130i	0.143233	+	0.248086i	0.928712	−	0.370801i	$-0.120917\pi$
$593$	3.48794	+	6.04130i	0.143233	+	0.248086i	−0.785479	+	0.618888i	$0.787584\pi$
$594$		0			0
$595$	1.08825	−	6.52291i	0.0446137	−	0.267413i
$596$		0			0
$597$	−2.03320	+	5.75743i	−0.0832131	+	0.235636i
$598$		0			0
$599$	4.57709	+	5.45477i	0.187015	+	0.222876i	0.851403	−	0.524512i	$-0.175752\pi$
$599$	4.57709	+	5.45477i	0.187015	+	0.222876i	−0.664388	+	0.747388i	$0.731308\pi$
$600$		0			0
$601$	17.0560	+	3.00744i	0.695730	+	0.122676i	0.510319	−	0.859985i	$-0.329527\pi$
$601$	17.0560	+	3.00744i	0.695730	+	0.122676i	0.185411	+	0.982661i	$0.440638\pi$
$602$		0			0
$603$	−5.16161	+	9.35000i	−0.210197	+	0.380762i
$604$		0			0
$605$	0.816800	−	4.63230i	0.0332076	−	0.188330i
$606$		0			0
$607$	−14.4488	+	39.6977i	−0.586457	+	1.61128i	0.190474	+	0.981692i	$0.438998\pi$
$607$	−14.4488	+	39.6977i	−0.586457	+	1.61128i	−0.776931	+	0.629586i	$0.783225\pi$
$608$		0			0
$609$	19.9553	−	3.90712i	0.808629	−	0.158324i
$610$		0			0
$611$	3.11284	+	1.79720i	0.125932	+	0.0727068i
$612$		0			0
$613$	−1.48185	−	2.56665i	−0.0598515	−	0.103666i	0.834547	−	0.550937i	$-0.185729\pi$
$613$	−1.48185	−	2.56665i	−0.0598515	−	0.103666i	−0.894399	+	0.447271i	$0.852396\pi$
$614$		0			0
$615$	0.243535	+	0.412622i	0.00982029	+	0.0166385i
$616$		0			0
$617$	−22.7707	+	4.01508i	−0.916713	+	0.161641i	−0.612050	−	0.790819i	$-0.709655\pi$
$617$	−22.7707	+	4.01508i	−0.916713	+	0.161641i	−0.304663	+	0.952460i	$0.598544\pi$
$618$		0			0
$619$	0.908965	+	2.49736i	0.0365344	+	0.100377i	0.956619	−	0.291343i	$-0.0941022\pi$
$619$	0.908965	+	2.49736i	0.0365344	+	0.100377i	−0.920084	+	0.391721i	$0.871880\pi$
$620$		0			0
$621$	7.96306	−	24.0065i	0.319547	−	0.963346i
$622$		0			0
$623$	15.5253	+	5.48917i	0.622009	+	0.219919i
$624$		0			0
$625$	14.7276	−	12.3579i	0.589102	−	0.494316i
$626$		0			0
$627$	−2.25112	+	3.98691i	−0.0899011	+	0.159222i
$628$		0			0
$629$	−0.780987	+	1.35271i	−0.0311400	+	0.0539360i
$630$		0			0
$631$	−10.8636	−	18.8163i	−0.432473	−	0.749065i	0.564613	−	0.825356i	$-0.309026\pi$
$631$	−10.8636	−	18.8163i	−0.432473	−	0.749065i	−0.997086	+	0.0762910i	$0.975692\pi$
$632$		0			0
$633$	−13.7447	−	11.3103i	−0.546304	−	0.449543i
$634$		0			0
$635$	−1.31043	−	0.476957i	−0.0520028	−	0.0189275i
$636$		0			0
$637$	0.0473346	+	2.56639i	0.00187546	+	0.101684i
$638$		0			0
$639$	42.0589	+	6.58671i	1.66382	+	0.260566i
$640$		0			0
$641$	10.3126	−	12.2900i	0.407321	−	0.485427i	−0.522916	−	0.852384i	$-0.675156\pi$
$641$	10.3126	−	12.2900i	0.407321	−	0.485427i	0.930238	+	0.366957i	$0.119600\pi$
$642$		0			0
$643$	−6.32054	+	17.3655i	−0.249258	+	0.684830i	0.750456	+	0.660920i	$0.229834\pi$
$643$	−6.32054	+	17.3655i	−0.249258	+	0.684830i	−0.999714	+	0.0239099i	$0.992389\pi$
$644$		0			0
$645$	−1.73115	−	9.29544i	−0.0681639	−	0.366008i
$646$		0			0
$647$	12.7137	−	22.0208i	0.499828	−	0.865727i	−0.500172	−	0.865926i	$-0.666730\pi$
$647$	12.7137	−	22.0208i	0.499828	−	0.865727i	1.00000		0.000199058i	$6.33620e-5\pi$
$648$		0			0
$649$	−0.938445	+	0.541811i	−0.0368372	+	0.0212680i
$650$		0			0
$651$	−37.1843	+	22.4116i	−1.45737	+	0.878378i
$652$		0			0
$653$	−15.8052	+	2.78688i	−0.618505	+	0.109059i	−0.474117	−	0.880462i	$-0.657233\pi$
$653$	−15.8052	+	2.78688i	−0.618505	+	0.109059i	−0.144388	+	0.989521i	$0.546121\pi$
$654$		0			0
$655$	1.45236	+	1.21867i	0.0567484	+	0.0476175i
$656$		0			0
$657$	−18.8605	−	2.95368i	−0.735816	−	0.115234i
$658$		0			0
$659$	−2.85356	−	7.84009i	−0.111159	−	0.305407i	0.871623	−	0.490177i	$-0.163068\pi$
$659$	−2.85356	−	7.84009i	−0.111159	−	0.305407i	−0.982782	+	0.184771i	$0.940846\pi$
$660$		0			0
$661$	18.6628	−	3.29075i	0.725898	−	0.127995i	0.201524	−	0.979484i	$-0.435411\pi$
$661$	18.6628	−	3.29075i	0.725898	−	0.127995i	0.524374	+	0.851488i	$0.324299\pi$
$662$		0			0
$663$	−0.886196	−	2.36399i	−0.0344170	−	0.0918097i
$664$		0			0
$665$	2.31221	+	0.385757i	0.0896637	+	0.0149590i
$666$		0			0
$667$	21.5988			0.836310
$668$		0			0
$669$	−42.5868	−	24.0457i	−1.64650	−	0.929662i
$670$		0			0
$671$	−1.90364	−	10.7961i	−0.0734893	−	0.416779i
$672$		0			0
$673$	−29.7861	−	24.9935i	−1.14817	−	0.963428i	−0.148493	−	0.988913i	$-0.547442\pi$
$673$	−29.7861	−	24.9935i	−1.14817	−	0.963428i	−0.999675	+	0.0254859i	$0.991887\pi$
$674$		0			0
$675$	−18.7636	−	14.8457i	−0.722210	−	0.571410i
$676$		0			0
$677$	−6.83083	+	38.7396i	−0.262530	+	1.48888i	0.513447	+	0.858121i	$0.328368\pi$
$677$	−6.83083	+	38.7396i	−0.262530	+	1.48888i	−0.775977	+	0.630761i	$0.782743\pi$
$678$		0			0
$679$	−0.151596	−	16.4398i	−0.00581771	−	0.630903i
$680$		0			0
$681$	6.38187	−	11.3028i	0.244554	−	0.433123i
$682$		0			0
$683$	13.4133	−	7.74417i	0.513246	−	0.296323i	−0.220921	−	0.975292i	$-0.570906\pi$
$683$	13.4133	−	7.74417i	0.513246	−	0.296323i	0.734167	+	0.678969i	$0.237573\pi$
$684$		0			0
$685$	−7.19907	+	4.15638i	−0.275062	+	0.158807i
$686$		0			0
$687$	−1.71623	+	2.08563i	−0.0654781	+	0.0795718i
$688$		0			0
$689$	0.635435	+	3.60373i	0.0242081	+	0.137291i
$690$		0			0
$691$	−25.3848	+	30.2524i	−0.965683	+	1.15086i	0.0228327	+	0.999739i	$0.492731\pi$
$691$	−25.3848	+	30.2524i	−0.965683	+	1.15086i	−0.988516	+	0.151117i	$0.951713\pi$
$692$		0			0
$693$	5.48826	+	13.8422i	0.208482	+	0.525822i
$694$		0			0
$695$	−4.60797	−	12.6603i	−0.174790	−	0.480233i
$696$		0			0
$697$	−1.33960	+	1.12406i	−0.0507408	+	0.0425766i
$698$		0			0
$699$	−15.0217	−	17.5573i	−0.568174	−	0.664079i
$700$		0			0
$701$		−	17.7766i		−	0.671415i	−0.941966	−	0.335707i	$-0.891025\pi$
$701$		−	17.7766i		−	0.671415i	0.941966	−	0.335707i	$-0.108975\pi$
$702$		0			0
$703$	−0.479502	−	0.276841i	−0.0180848	−	0.0104412i
$704$		0			0
$705$	−1.95462	−	10.4954i	−0.0736153	−	0.395279i
$706$		0			0
$707$	22.5710	+	38.2747i	0.848870	+	1.43947i
$708$		0			0
$709$	−44.5363	+	16.2099i	−1.67260	+	0.608775i	−0.992266	−	0.124130i	$-0.960386\pi$
$709$	−44.5363	+	16.2099i	−1.67260	+	0.608775i	−0.680331	+	0.732905i	$0.738164\pi$
$710$		0			0
$711$	−22.8498	+	19.9327i	−0.856933	+	0.747534i
$712$		0			0
$713$	−43.3351	+	15.7727i	−1.62291	+	0.590691i
$714$		0			0
$715$	0.331364	−	0.278047i	0.0123923	−	0.0103984i
$716$		0			0
$717$	−14.6889	−	2.44498i	−0.548566	−	0.0913094i
$718$		0			0
$719$	−23.7545	+	41.1440i	−0.885894	+	1.53441i	−0.0412079	+	0.999151i	$0.513121\pi$
$719$	−23.7545	+	41.1440i	−0.885894	+	1.53441i	−0.844686	+	0.535262i	$0.820213\pi$
$720$		0			0
$721$	10.1988	+	1.70151i	0.379823	+	0.0633676i
$722$		0			0
$723$	−0.176560	−	18.4027i	−0.00656632	−	0.684405i
$724$		0			0
$725$	6.98814	−	19.1997i	0.259533	−	0.713061i
$726$		0			0
$727$	8.50270	−	10.1331i	0.315348	−	0.375817i	−0.584966	−	0.811057i	$-0.698892\pi$
$727$	8.50270	−	10.1331i	0.315348	−	0.375817i	0.900314	+	0.435241i	$0.143337\pi$
$728$		0			0
$729$	−12.1324	+	24.1206i	−0.449348	+	0.893357i
$730$		0			0
$731$	32.4284	−	11.8030i	1.19941	−	0.436549i
$732$		0			0
$733$	−13.9826	−	16.6638i	−0.516458	−	0.615491i	0.443281	−	0.896382i	$-0.353814\pi$
$733$	−13.9826	−	16.6638i	−0.516458	−	0.615491i	−0.959739	+	0.280892i	$0.909370\pi$
$734$		0			0
$735$	5.70051	−	5.06228i	0.210267	−	0.186725i
$736$		0			0
$737$		−	6.67873i		−	0.246014i
$738$		0			0
$739$	−8.14348			−0.299563			−0.149781	−	0.988719i	$-0.547857\pi$
$739$	−8.14348			−0.299563			−0.149781	+	0.988719i	$0.547857\pi$
$740$		0			0
$741$	0.837976	−	0.314135i	0.0307838	−	0.0115400i
$742$		0			0
$743$	−20.7786	−	24.7630i	−0.762294	−	0.908466i	0.235697	−	0.971827i	$-0.424263\pi$
$743$	−20.7786	−	24.7630i	−0.762294	−	0.908466i	−0.997991	+	0.0633603i	$0.979818\pi$
$744$		0			0
$745$	−10.0535	−	1.77270i	−0.368332	−	0.0649469i
$746$		0			0
$747$	−2.54944	−	12.9954i	−0.0932793	−	0.475476i
$748$		0			0
$749$	−32.6487	+	6.06778i	−1.19296	+	0.221712i
$750$		0			0
$751$	−2.29857	−	13.0358i	−0.0838759	−	0.475684i	−0.997594	−	0.0693340i	$-0.977913\pi$
$751$	−2.29857	−	13.0358i	−0.0838759	−	0.475684i	0.913718	−	0.406350i	$-0.133199\pi$
$752$		0			0
$753$	−30.6022	+	26.1826i	−1.11520	+	0.954148i
$754$		0			0
$755$	−9.17164			−0.333790
$756$		0			0
$757$	−11.8523			−0.430780			−0.215390	−	0.976528i	$-0.569102\pi$
$757$	−11.8523			−0.430780			−0.215390	+	0.976528i	$0.569102\pi$
$758$		0			0
$759$	2.89583	+	15.5493i	0.105112	+	0.564402i
$760$		0			0
$761$	−6.93204	−	39.3135i	−0.251286	−	1.42511i	−0.805428	−	0.592693i	$-0.798065\pi$
$761$	−6.93204	−	39.3135i	−0.251286	−	1.42511i	0.554142	−	0.832422i	$-0.313046\pi$
$762$		0			0
$763$	3.59736	−	3.07552i	0.130233	−	0.111341i
$764$		0			0
$765$	−3.62397	+	6.56464i	−0.131025	+	0.237345i
$766$		0			0
$767$	0.208587	+	0.0367796i	0.00753165	+	0.00132803i
$768$		0			0
$769$	−14.9148	−	17.7747i	−0.537840	−	0.640973i	0.426862	−	0.904317i	$-0.359619\pi$
$769$	−14.9148	−	17.7747i	−0.537840	−	0.640973i	−0.964702	+	0.263344i	$0.915175\pi$
$770$		0			0
$771$	−16.1480	−	13.2879i	−0.581557	−	0.478552i
$772$		0			0
$773$	17.4609			0.628024			0.314012	−	0.949419i	$-0.398327\pi$
$773$	17.4609			0.628024			0.314012	+	0.949419i	$0.398327\pi$
$774$		0			0
$775$			43.6248i			1.56705i
$776$		0			0
$777$	−1.68022	+	0.647604i	−0.0602777	+	0.0232327i
$778$		0			0
$779$	−0.398450	−	0.474854i	−0.0142760	−	0.0170134i
$780$		0			0
$781$	−25.0163	+	9.10519i	−0.895153	+	0.325809i
$782$		0			0
$783$	−22.8123	−	3.34867i	−0.815246	−	0.119672i
$784$		0			0
$785$	−3.01000	+	3.58718i	−0.107432	+	0.128032i
$786$		0			0
$787$	3.84537	−	10.5651i	0.137073	−	0.376604i	−0.852096	−	0.523385i	$-0.824669\pi$
$787$	3.84537	−	10.5651i	0.137073	−	0.376604i	0.989169	+	0.146781i	$0.0468912\pi$
$788$		0			0
$789$	−37.3066	+	22.0189i	−1.32815	+	0.783892i
$790$		0			0
$791$	−15.6463	+	18.9996i	−0.556319	+	0.675548i
$792$		0			0
$793$	−1.07138	+	1.85569i	−0.0380458	+	0.0658973i
$794$		0			0
$795$	6.90606	−	8.39254i	0.244933	−	0.297653i
$796$		0			0
$797$	37.0264	−	31.0688i	1.31154	−	1.10051i	0.323517	−	0.946222i	$-0.395135\pi$
$797$	37.0264	−	31.0688i	1.31154	−	1.10051i	0.988025	−	0.154292i	$-0.0493098\pi$
$798$		0			0
$799$	36.6146	−	13.3266i	1.29533	−	0.471462i
$800$		0			0
$801$	−14.5312	−	11.7255i	−0.513436	−	0.414299i
$802$		0			0
$803$	11.2181	−	4.08304i	0.395877	−	0.144087i
$804$		0			0
$805$	6.97541	−	4.11348i	0.245851	−	0.144981i
$806$		0			0
$807$	−20.0733	+	17.1743i	−0.706612	+	0.604564i
$808$		0			0
$809$	−40.4168	−	23.3346i	−1.42098	−	0.820402i	−0.424596	−	0.905383i	$-0.639584\pi$
$809$	−40.4168	−	23.3346i	−1.42098	−	0.820402i	−0.996383	+	0.0849808i	$0.972917\pi$
$810$		0			0
$811$		−	21.4580i		−	0.753491i	−0.926317	−	0.376746i	$-0.877043\pi$
$811$		−	21.4580i		−	0.753491i	0.926317	−	0.376746i	$-0.122957\pi$
$812$		0			0
$813$	36.2412	−	6.74942i	1.27103	−	0.236713i
$814$		0			0
$815$	10.2964	−	8.63973i	0.360668	−	0.302636i
$816$		0			0
$817$	4.18387	+	11.4951i	0.146375	+	0.402162i
$818$		0			0
$819$	0.917362	−	2.76215i	0.0320552	−	0.0965174i
$820$		0			0
$821$	−18.7859	+	22.3881i	−0.655632	+	0.781352i	−0.986752	−	0.162237i	$-0.948129\pi$
$821$	−18.7859	+	22.3881i	−0.655632	+	0.781352i	0.331120	+	0.943589i	$0.392574\pi$
$822$		0			0
$823$	−0.194528	−	1.10323i	−0.00678083	−	0.0384560i	0.981230	−	0.192843i	$-0.0617708\pi$
$823$	−0.194528	−	1.10323i	−0.00678083	−	0.0384560i	−0.988010	+	0.154387i	$0.950660\pi$
$824$		0			0
$825$	14.7590	+	2.45666i	0.513844	+	0.0855299i
$826$		0			0
$827$	−31.2630	+	18.0497i	−1.08712	+	0.627650i	−0.932809	−	0.360372i	$-0.882650\pi$
$827$	−31.2630	+	18.0497i	−1.08712	+	0.627650i	−0.154313	+	0.988022i	$0.549316\pi$
$828$		0			0
$829$	14.9177	−	8.61274i	0.518113	−	0.299133i	−0.218049	−	0.975938i	$-0.569969\pi$
$829$	14.9177	−	8.61274i	0.518113	−	0.299133i	0.736162	+	0.676805i	$0.236636\pi$
$830$		0			0
$831$	1.10450	+	1.87136i	0.0383149	+	0.0649169i
$832$		0			0
$833$	21.6415	+	17.4896i	0.749835	+	0.605978i
$834$		0			0
$835$	−0.404190	+	2.29227i	−0.0139876	+	0.0793274i
$836$		0			0
$837$	48.2151	−	9.94019i	1.66656	−	0.343583i
$838$		0			0
$839$	27.8026	+	23.3291i	0.959851	+	0.805411i	0.980929	−	0.194367i	$-0.0622653\pi$
$839$	27.8026	+	23.3291i	0.959851	+	0.805411i	−0.0210778	+	0.999778i	$0.506710\pi$
$840$		0			0
$841$	1.61676	+	9.16909i	0.0557503	+	0.316176i
$842$		0			0
$843$	−0.172923	−	18.0237i	−0.00595578	−	0.620768i
$844$		0			0
$845$	8.08987			0.278300
$846$		0			0
$847$	15.2779	+	12.5814i	0.524955	+	0.432304i
$848$		0			0
$849$	16.3341	+	2.71884i	0.560586	+	0.0933103i
$850$		0			0
$851$	−1.88364	+	0.332137i	−0.0645704	+	0.0113855i
$852$		0			0
$853$	12.7651	+	35.0719i	0.437069	+	1.20084i	0.941390	+	0.337321i	$0.109521\pi$
$853$	12.7651	+	35.0719i	0.437069	+	1.20084i	−0.504320	+	0.863517i	$0.668257\pi$
$854$		0			0
$855$	−2.32700	−	1.28461i	−0.0795819	−	0.0439327i
$856$		0			0
$857$	−26.6548	−	22.3660i	−0.910511	−	0.764009i	0.0617051	−	0.998094i	$-0.480346\pi$
$857$	−26.6548	−	22.3660i	−0.910511	−	0.764009i	−0.972216	+	0.234085i	$0.924791\pi$
$858$		0			0
$859$	−38.3088	+	6.75488i	−1.30708	+	0.230473i	−0.783441	−	0.621467i	$-0.786537\pi$
$859$	−38.3088	+	6.75488i	−1.30708	+	0.230473i	−0.523639	+	0.851940i	$0.675426\pi$
$860$		0			0
$861$	−2.01564	+	0.0379285i	−0.0686928	+	0.00129260i
$862$		0			0
$863$	−11.7694	+	6.79505i	−0.400634	+	0.231306i	−0.686758	−	0.726886i	$-0.740967\pi$
$863$	−11.7694	+	6.79505i	−0.400634	+	0.231306i	0.286123	+	0.958193i	$0.407633\pi$
$864$		0			0
$865$	0.369402	−	0.639823i	0.0125600	−	0.0217546i
$866$		0			0
$867$	1.95847	+	0.691620i	0.0665132	+	0.0234887i
$868$		0			0
$869$	6.48526	−	17.8181i	0.219997	−	0.604438i
$870$		0			0
$871$	−0.839112	+	1.00001i	−0.0284322	+	0.0338842i
$872$		0			0
$873$	−6.03860	+	17.6367i	−0.204376	+	0.596911i
$874$		0			0
$875$	−2.91966	−	15.7097i	−0.0987025	−	0.531086i
$876$		0			0
$877$	−24.9631	−	9.08582i	−0.842943	−	0.306806i	−0.115783	−	0.993274i	$-0.536938\pi$
$877$	−24.9631	−	9.08582i	−0.842943	−	0.306806i	−0.727160	+	0.686468i	$0.759160\pi$
$878$		0			0
$879$	5.45884	−	32.7954i	0.184122	−	1.10616i
$880$		0			0
$881$	−22.4911	−	38.9557i	−0.757744	−	1.31245i	−0.943999	−	0.329949i	$-0.892968\pi$
$881$	−22.4911	−	38.9557i	−0.757744	−	1.31245i	0.186255	−	0.982501i	$-0.440365\pi$
$882$		0			0
$883$	−19.4761	+	33.7336i	−0.655423	+	1.13523i	0.326365	+	0.945244i	$0.394176\pi$
$883$	−19.4761	+	33.7336i	−0.655423	+	1.13523i	−0.981788	+	0.189982i	$0.939157\pi$
$884$		0			0
$885$	−0.319757	−	0.541765i	−0.0107485	−	0.0182112i
$886$		0			0
$887$	2.88696	−	2.42245i	0.0969346	−	0.0813377i	−0.593032	−	0.805179i	$-0.702069\pi$
$887$	2.88696	−	2.42245i	0.0969346	−	0.0813377i	0.689967	+	0.723841i	$0.257625\pi$
$888$		0			0
$889$	4.45990	−	3.81293i	0.149580	−	0.127882i
$890$		0			0
$891$	−0.647785	−	16.8718i	−0.0217016	−	0.565227i
$892$		0			0
$893$	4.72396	+	12.9790i	0.158081	+	0.434325i
$894$		0			0
$895$	−2.59800	+	0.458097i	−0.0868415	+	0.0153125i
$896$		0			0
$897$	1.52000	−	2.69204i	0.0507514	−	0.0898846i
$898$		0			0
$899$	21.0197	+	36.4072i	0.701047	+	1.21425i
$900$		0			0
$901$	34.3537	+	19.8341i	1.14449	+	0.660770i
$902$		0			0
$903$	37.6342	+	12.9012i	1.25239	+	0.429325i
$904$		0			0
$905$	0.420331	−	1.15485i	0.0139723	−	0.0383885i
$906$		0			0
$907$	5.92834	−	33.6213i	0.196847	−	1.11638i	−0.712916	−	0.701250i	$-0.752626\pi$
$907$	5.92834	−	33.6213i	0.196847	−	1.11638i	0.909763	−	0.415128i	$-0.136263\pi$
$908$		0			0
$909$	−9.69943	−	49.4412i	−0.321710	−	1.63986i
$910$		0			0
$911$	50.5872	+	8.91989i	1.67603	+	0.295529i	0.929225	−	0.369515i	$-0.120476\pi$
$911$	50.5872	+	8.91989i	1.67603	+	0.295529i	0.746804	+	0.665044i	$0.231587\pi$
$912$		0			0
$913$	5.32322	+	6.34397i	0.176173	+	0.209955i
$914$		0			0
$915$	6.25671	−	1.16523i	0.206840	−	0.0385212i
$916$		0			0
$917$	−7.47072	+	2.79740i	−0.246705	+	0.0923783i
$918$		0			0
$919$	21.6545	+	37.5066i	0.714315	+	1.23723i	0.963223	+	0.268703i	$0.0865949\pi$
$919$	21.6545	+	37.5066i	0.714315	+	1.23723i	−0.248908	+	0.968527i	$0.580072\pi$
$920$		0			0
$921$	−43.2492	+	8.05457i	−1.42511	+	0.265407i
$922$		0			0
$923$	4.88969	+	1.77970i	0.160946	+	0.0585796i
$924$		0			0
$925$	−0.314193	+	1.78188i	−0.0103306	+	0.0585877i
$926$		0			0
$927$	−10.2640	−	5.66620i	−0.337116	−	0.186103i
$928$		0			0
$929$	18.5363	+	15.5538i	0.608156	+	0.510303i	0.894056	−	0.447956i	$-0.147848\pi$
$929$	18.5363	+	15.5538i	0.608156	+	0.510303i	−0.285900	+	0.958260i	$0.592292\pi$
$930$		0			0
$931$	−6.19963	+	7.67140i	−0.203185	+	0.251420i
$932$		0			0
$933$	3.72252	−	22.3640i	0.121870	−	0.732165i
$934$		0			0
$935$		−	4.68914i		−	0.153351i
$936$		0			0
$937$	−37.1975	−	21.4760i	−1.21519	−	0.701590i	−0.251304	−	0.967908i	$-0.580859\pi$
$937$	−37.1975	−	21.4760i	−1.21519	−	0.701590i	−0.963885	+	0.266318i	$0.914193\pi$
$938$		0			0
$939$	8.86031	−	5.22948i	0.289145	−	0.170658i
$940$		0			0
$941$	34.3360	+	12.4973i	1.11932	+	0.407400i	0.834404	−	0.551153i	$-0.185812\pi$
$941$	34.3360	+	12.4973i	1.11932	+	0.407400i	0.284917	+	0.958552i	$0.408034\pi$
$942$		0			0
$943$	−2.10885	−	0.371846i	−0.0686735	−	0.0121090i
$944$		0			0
$945$	−8.00506	+	3.26312i	−0.260405	+	0.106149i
$946$		0			0
$947$	50.9510	+	8.98404i	1.65569	+	0.291942i	0.921897	−	0.387435i	$-0.126639\pi$
$947$	50.9510	+	8.98404i	1.65569	+	0.291942i	0.733789	+	0.679377i	$0.237750\pi$
$948$		0			0
$949$	−2.19268	−	0.798072i	−0.0711775	−	0.0259065i
$950$		0			0
$951$	0.511578	+	53.3216i	0.0165891	+	1.72907i
$952$		0			0
$953$	−26.8149	−	15.4816i	−0.868620	−	0.501498i	−0.00173046	−	0.999999i	$-0.500551\pi$
$953$	−26.8149	−	15.4816i	−0.868620	−	0.501498i	−0.866889	+	0.498501i	$0.833884\pi$
$954$		0			0
$955$			0.697880i			0.0225829i
$956$		0			0
$957$	13.5009	−	5.06114i	0.436423	−	0.163603i
$958$		0			0
$959$	−0.322517	−	34.9754i	−0.0104146	−	1.12941i
$960$		0			0
$961$	−45.0124	−	37.7699i	−1.45201	−	1.21838i
$962$		0			0
$963$	37.2007	+	5.82588i	1.19878	+	0.187736i
$964$		0			0
$965$	−0.251461	+	1.42611i	−0.00809483	+	0.0459081i
$966$		0			0
$967$	42.8851	+	15.6089i	1.37909	+	0.501948i	0.921903	−	0.387421i	$-0.126634\pi$
$967$	42.8851	+	15.6089i	1.37909	+	0.501948i	0.457189	+	0.889369i	$0.348856\pi$
$968$		0			0
$969$	3.23041	−	9.14759i	0.103776	−	0.293863i
$970$		0			0
$971$	8.12697	+	14.0763i	0.260807	+	0.451731i	0.966457	−	0.256830i	$-0.0826781\pi$
$971$	8.12697	+	14.0763i	0.260807	+	0.451731i	−0.705650	+	0.708561i	$0.749345\pi$
$972$		0			0
$973$	55.9155	+	9.32864i	1.79257	+	0.299062i
$974$		0			0
$975$	−1.90124	−	2.22216i	−0.0608883	−	0.0711660i
$976$		0			0
$977$	1.52839	+	1.82147i	0.0488976	+	0.0582739i	0.789939	−	0.613186i	$-0.210112\pi$
$977$	1.52839	+	1.82147i	0.0488976	+	0.0582739i	−0.741041	+	0.671459i	$0.765668\pi$
$978$		0			0
$979$	11.4990	+	2.02758i	0.367510	+	0.0648019i
$980$		0			0
$981$	−5.00676	+	1.93188i	−0.159853	+	0.0616803i
$982$		0			0
$983$	5.20954	−	29.5448i	0.166158	−	0.942332i	−0.781703	−	0.623650i	$-0.785649\pi$
$983$	5.20954	−	29.5448i	0.166158	−	0.942332i	0.947862	−	0.318681i	$-0.103240\pi$
$984$		0			0
$985$	4.08894	−	11.2343i	0.130285	−	0.357954i
$986$		0			0
$987$	42.4923	+	14.5666i	1.35255	+	0.463660i
$988$		0			0
$989$	36.5968	+	21.1292i	1.16371	+	0.671869i
$990$		0			0
$991$	−14.3559	−	24.8651i	−0.456029	−	0.789866i	0.542718	−	0.839915i	$-0.317395\pi$
$991$	−14.3559	−	24.8651i	−0.456029	−	0.789866i	−0.998747	+	0.0500496i	$0.984062\pi$
$992$		0			0
$993$	−29.5385	+	0.283398i	−0.937375	+	0.00899337i
$994$		0			0
$995$	2.18300	−	0.384921i	0.0692057	−	0.0122028i
$996$		0			0
$997$	13.0156	+	35.7600i	0.412207	+	1.13253i	0.956015	+	0.293319i	$0.0947599\pi$
$997$	13.0156	+	35.7600i	0.412207	+	1.13253i	−0.543808	+	0.839210i	$0.683018\pi$
$998$		0			0
$999$	2.04096	−	0.0587587i	0.0645733	−	0.00185904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.3	yes	144
7.5	odd	6		756.2.ca.a.173.6	✓	144
27.5	odd	18		756.2.ca.a.437.6	yes	144
189.5	even	18	inner	756.2.ck.a.5.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.6	✓	144	7.5	odd	6
756.2.ca.a.437.6	yes	144	27.5	odd	18
756.2.ck.a.5.3	yes	144	189.5	even	18	inner
756.2.ck.a.605.3	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63320 - 0.576754i) q^{3} +(0.109190 + 0.619249i) q^{5} +(-2.49443 - 0.881937i) q^{7} +(2.33471 + 1.88391i) q^{9} +O(q^{10})\)	\(q+(-1.63320 - 0.576754i) q^{3} +(0.109190 + 0.619249i) q^{5} +(-2.49443 - 0.881937i) q^{7} +(2.33471 + 1.88391i) q^{9} +(-1.84753 - 0.325769i) q^{11} +(0.235703 + 0.280900i) q^{13} +(0.178824 - 1.07434i) q^{15} +3.97503 q^{17} +1.40905i q^{19} +(3.56525 + 2.87906i) q^{21} +(3.12882 + 3.72878i) q^{23} +(4.32692 - 1.57487i) q^{25} +(-2.72650 - 4.42337i) q^{27} +(2.85223 - 3.39915i) q^{29} +(-3.24035 + 8.90279i) q^{31} +(2.82950 + 1.59762i) q^{33} +(0.273771 - 1.64097i) q^{35} +(-0.196473 + 0.340302i) q^{37} +(-0.222941 - 0.594710i) q^{39} +(-0.337003 + 0.282779i) q^{41} +(8.15803 - 2.96928i) q^{43} +(-0.911684 + 1.65147i) q^{45} +(9.21115 - 3.35258i) q^{47} +(5.44437 + 4.39986i) q^{49} +(-6.49203 - 2.29261i) q^{51} +(8.64238 + 4.98968i) q^{53} -1.17965i q^{55} +(0.812676 - 2.30127i) q^{57} +(0.442479 - 0.371284i) q^{59} +(1.99861 + 5.49113i) q^{61} +(-4.16228 - 6.75836i) q^{63} +(-0.148210 + 0.176630i) q^{65} +(0.618194 + 3.50595i) q^{67} +(-2.95941 - 7.89443i) q^{69} +(12.2893 - 7.09525i) q^{71} +(-5.51091 + 3.18172i) q^{73} +(-7.97505 + 0.0765143i) q^{75} +(4.32122 + 2.44201i) q^{77} +(-1.75512 + 9.95378i) q^{79} +(1.90173 + 8.79678i) q^{81} +(-3.38160 - 2.83750i) q^{83} +(0.434034 + 2.46153i) q^{85} +(-6.61875 + 3.90648i) q^{87} -6.22400 q^{89} +(-0.340209 - 0.908561i) q^{91} +(10.4269 - 12.6712i) q^{93} +(-0.872552 + 0.153855i) q^{95} +(2.12529 + 5.83919i) q^{97} +(-3.69972 - 4.24116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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