LMFDB - Embedded newform 756.2.ck.a.5.3

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			5.3
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.3

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.950609	−	0.310391i	$-0.899540\pi$
$5$	0.109190	−	0.619249i	0.0488314	−	0.276936i	0.999440	+	0.0334549i	$0.0106510\pi$
$6$		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	−0.445084	−	0.895489i	$-0.646826\pi$
$11$	−1.84753	+	0.325769i	−0.557050	+	0.0982230i	−0.111967	+	0.993712i	$0.535715\pi$
$12$		0			0
$13$	0.235703	−	0.280900i	0.0653723	−	0.0779077i	−0.732367	−	0.680910i	$-0.761585\pi$
$13$	0.235703	−	0.280900i	0.0653723	−	0.0779077i	0.797740	+	0.603002i	$0.206029\pi$
$14$		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	$-0.948325\pi$
$19$		−	1.40905i		−	0.323258i	0.986852	−	0.161629i	$-0.0516748\pi$
$20$		0			0
$21$	3.56525	−	2.87906i	0.778002	−	0.628262i
$22$		0			0
$23$	3.12882	−	3.72878i	0.652404	−	0.777505i	−0.333870	−	0.942619i	$-0.608355\pi$
$23$	3.12882	−	3.72878i	0.652404	−	0.777505i	0.986275	+	0.165114i	$0.0527991\pi$
$24$		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	0.962833	−	0.270097i	$-0.0870557\pi$
$29$	2.85223	+	3.39915i	0.529646	+	0.631207i	−0.433188	+	0.901304i	$0.642611\pi$
$30$		0			0
$31$	−3.24035	−	8.90279i	−0.581984	−	1.59899i	−0.784785	−	0.619768i	$-0.787227\pi$
$31$	−3.24035	−	8.90279i	−0.581984	−	1.59899i	0.202801	−	0.979220i	$-0.434996\pi$
$32$		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	0.849424	−	0.527712i	$-0.176950\pi$
$37$	−0.196473	−	0.340302i	−0.0323000	−	0.0559452i	−0.881724	+	0.471766i	$0.843617\pi$
$38$		0			0
$39$	−0.222941	+	0.594710i	−0.0356991	+	0.0952298i
$40$		0			0
$41$	−0.337003	−	0.282779i	−0.0526311	−	0.0441627i	0.616093	−	0.787674i	$-0.288715\pi$
$41$	−0.337003	−	0.282779i	−0.0526311	−	0.0441627i	−0.668724	+	0.743511i	$0.733159\pi$
$42$		0			0
$43$	8.15803	+	2.96928i	1.24409	+	0.452811i	0.878400	−	0.477926i	$-0.158611\pi$
$43$	8.15803	+	2.96928i	1.24409	+	0.452811i	0.365688	+	0.930737i	$0.380834\pi$
$44$		0			0
$45$	−0.911684	−	1.65147i	−0.135906	−	0.246187i
$46$		0			0
$47$	9.21115	+	3.35258i	1.34358	+	0.489024i	0.910939	−	0.412540i	$-0.135358\pi$
$47$	9.21115	+	3.35258i	1.34358	+	0.489024i	0.432644	+	0.901565i	$0.357581\pi$
$48$		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	0.229471	−	0.973316i	$-0.426300\pi$
$53$	8.64238	−	4.98968i	1.18712	−	0.685385i	0.957651	+	0.287930i	$0.0929671\pi$
$54$		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	0.671136	−	0.741334i	$-0.265807\pi$
$59$	0.442479	+	0.371284i	0.0576058	+	0.0483370i	−0.613530	+	0.789671i	$0.710251\pi$
$60$		0			0
$61$	1.99861	−	5.49113i	0.255895	−	0.703067i	−0.743515	−	0.668720i	$-0.766843\pi$
$61$	1.99861	−	5.49113i	0.255895	−	0.703067i	0.999410	−	0.0343471i	$-0.0109352\pi$
$62$		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	−0.923477	−	0.383653i	$-0.874666\pi$
$67$	0.618194	−	3.50595i	0.0755244	−	0.428320i	0.999002	−	0.0446676i	$-0.0142229\pi$
$68$		0			0
$69$	−2.95941	+	7.89443i	−0.356271	+	0.950377i
$70$		0			0
$71$	12.2893	+	7.09525i	1.45848	+	0.842051i	0.998937	−	0.0461059i	$-0.0146812\pi$
$71$	12.2893	+	7.09525i	1.45848	+	0.842051i	0.459539	+	0.888157i	$0.348014\pi$
$72$		0			0
$73$	−5.51091	−	3.18172i	−0.645003	−	0.372392i	0.141536	−	0.989933i	$-0.454796\pi$
$73$	−5.51091	−	3.18172i	−0.645003	−	0.372392i	−0.786539	+	0.617541i	$0.788129\pi$
$74$		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	−0.908862	−	0.417096i	$-0.863048\pi$
$79$	−1.75512	−	9.95378i	−0.197466	−	1.11989i	0.711396	−	0.702791i	$-0.248063\pi$
$80$		0			0
$81$	1.90173	−	8.79678i	0.211304	−	0.977420i
$82$		0			0
$83$	−3.38160	+	2.83750i	−0.371178	+	0.311456i	−0.809228	−	0.587495i	$-0.800114\pi$
$83$	−3.38160	+	2.83750i	−0.371178	+	0.311456i	0.438049	+	0.898951i	$0.355670\pi$
$84$		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	−0.783814	−	0.620996i	$-0.786728\pi$
$97$	2.12529	−	5.83919i	0.215791	−	0.592880i	0.999605	+	0.0281157i	$0.00895069\pi$
$98$		0			0
$99$	−3.69972	+	4.24116i	−0.371836	+	0.426252i
$100$		0			0
$101$	−12.8654	+	10.7953i	−1.28015	+	1.07418i	−0.286930	+	0.957952i	$0.592635\pi$
$101$	−12.8654	+	10.7953i	−1.28015	+	1.07418i	−0.993223	+	0.116224i	$0.962921\pi$
$102$		0			0
$103$	−3.84869	−	0.678628i	−0.379223	−	0.0668672i	−0.0192122	−	0.999815i	$-0.506116\pi$
$103$	−3.84869	−	0.678628i	−0.379223	−	0.0668672i	−0.360011	+	0.932948i	$0.617227\pi$
$104$		0			0
$105$	−1.39356	−	2.52214i	−0.135998	−	0.246136i
$106$		0			0
$107$	10.8698	+	6.27569i	1.05082	+	0.606693i	0.922880	−	0.385088i	$-0.125829\pi$
$107$	10.8698	+	6.27569i	1.05082	+	0.606693i	0.127944	+	0.991781i	$0.459162\pi$
$108$		0			0
$109$	−0.894424	−	1.54919i	−0.0856703	−	0.148385i	0.820006	−	0.572354i	$-0.193970\pi$
$109$	−0.894424	−	1.54919i	−0.0856703	−	0.148385i	−0.905677	+	0.423969i	$0.860636\pi$
$110$		0			0
$111$	0.517151	+	0.442465i	0.0490858	+	0.0419969i
$112$		0			0
$113$	3.18174	+	8.74175i	0.299313	+	0.822355i	0.994615	+	0.103638i	$0.0330483\pi$
$113$	3.18174	+	8.74175i	0.299313	+	0.822355i	−0.695302	+	0.718717i	$0.744730\pi$
$114$		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	0.812624	−	0.582788i	$-0.198038\pi$
$127$	−1.10888	−	1.92063i	−0.0983971	−	0.170429i	−0.911021	+	0.412359i	$0.864705\pi$
$128$		0			0
$129$	−15.0363	−	0.144261i	−1.32387	−	0.0127015i
$130$		0			0
$131$	2.30973	+	1.93809i	0.201802	+	0.169332i	0.738088	−	0.674704i	$-0.235729\pi$
$131$	2.30973	+	1.93809i	0.201802	+	0.169332i	−0.536286	+	0.844036i	$0.680173\pi$
$132$		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	−0.582355	−	0.812934i	$-0.697869\pi$
$137$	4.52151	−	12.4228i	0.386299	−	1.06135i	0.968654	−	0.248413i	$-0.0799090\pi$
$138$		0			0
$139$	−21.1007	−	3.72062i	−1.78974	−	0.315579i	−0.822368	−	0.568956i	$-0.807347\pi$
$139$	−21.1007	−	3.72062i	−1.78974	−	0.315579i	−0.967367	+	0.253378i	$0.918459\pi$
$140$		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	−0.929241	−	0.369475i	$-0.879538\pi$
$149$	−5.55270	−	15.2559i	−0.454895	−	1.24981i	0.474346	−	0.880339i	$-0.342685\pi$
$150$		0			0
$151$	−2.53282	−	14.3643i	−0.206118	−	1.16895i	−0.895671	−	0.444717i	$-0.853304\pi$
$151$	−2.53282	−	14.3643i	−0.206118	−	1.16895i	0.689553	−	0.724235i	$-0.257807\pi$
$152$		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	−0.540420	−	0.841395i	$-0.681735\pi$
$157$	4.78689	−	5.70479i	0.382035	−	0.455292i	0.922455	+	0.386103i	$0.126179\pi$
$158$		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	0.0551466	+	0.998478i	$0.482437\pi$
$163$	−10.6878	+	18.5118i	−0.837134	+	1.44996i	−0.892281	+	0.451481i	$0.850896\pi$
$164$		0			0
$165$	−0.680368	−	1.92661i	−0.0529666	−	0.149986i
$166$		0			0
$167$	3.47846	−	1.26606i	0.269172	−	0.0979704i	−0.203908	−	0.978990i	$-0.565364\pi$
$167$	3.47846	−	1.26606i	0.269172	−	0.0979704i	0.473080	+	0.881020i	$0.343142\pi$
$168$		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	−0.676361	−	0.736570i	$-0.736444\pi$
$173$	−0.900056	+	0.755236i	−0.0684300	+	0.0574196i	0.607931	+	0.793990i	$0.292000\pi$
$174$		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	$-0.949886\pi$
$179$		−	4.19541i		−	0.313579i	0.987632	−	0.156790i	$-0.0501145\pi$
$180$		0			0
$181$	−1.69261	+	0.977228i	−0.125811	+	0.0726368i	−0.561585	−	0.827419i	$-0.689808\pi$
$181$	−1.69261	+	0.977228i	−0.125811	+	0.0726368i	0.435774	+	0.900056i	$0.356475\pi$
$182$		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	−0.133965	−	0.990986i	$-0.542771\pi$
$191$	1.09300	−	0.192725i	0.0790864	−	0.0139451i	0.213051	+	0.977041i	$0.431660\pi$
$192$		0			0
$193$	2.16408	−	0.787661i	0.155774	−	0.0566971i	−0.262956	−	0.964808i	$-0.584698\pi$
$193$	2.16408	−	0.787661i	0.155774	−	0.0566971i	0.418730	+	0.908111i	$0.362475\pi$
$194$		0			0
$195$	0.343930	+	0.202992i	0.0246294	+	0.0145366i
$196$		0			0
$197$	−16.4656	+	9.50640i	−1.17312	+	0.677303i	−0.954414	−	0.298488i	$-0.903518\pi$
$197$	−16.4656	+	9.50640i	−1.17312	+	0.677303i	−0.218709	+	0.975790i	$0.570185\pi$
$198$		0			0
$199$			3.52524i			0.249897i	0.992163	+	0.124949i	$0.0398766\pi$
$199$			3.52524i			0.249897i	−0.992163	+	0.124949i	$0.960123\pi$
$200$		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	0.0125038	−	0.999922i	$-0.496020\pi$
$211$	9.65706	−	3.51488i	0.664820	−	0.241975i	0.652316	+	0.757947i	$0.273798\pi$
$212$		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	0.874465	−	0.485088i	$-0.161212\pi$
$223$	27.8071	−	4.90315i	1.86210	−	0.328339i	0.987638	+	0.156749i	$0.0501013\pi$
$224$		0			0
$225$	13.0690	−	4.47468i	0.871267	−	0.298312i
$226$		0			0
$227$	−1.30132	−	7.38017i	−0.0863718	−	0.489839i	−0.997052	−	0.0767270i	$-0.975553\pi$
$227$	−1.30132	−	7.38017i	−0.0863718	−	0.489839i	0.910680	−	0.413112i	$-0.135558\pi$
$228$		0			0
$229$	0.533350	+	1.46537i	0.0352448	+	0.0968342i	0.956067	−	0.293149i	$-0.0947031\pi$
$229$	0.533350	+	1.46537i	0.0352448	+	0.0968342i	−0.920822	+	0.389983i	$0.872481\pi$
$230$		0			0
$231$	−5.64900	+	6.48058i	−0.371677	+	0.426391i
$232$		0			0
$233$	11.5533	−	6.67028i	0.756879	−	0.436984i	−0.0712949	−	0.997455i	$-0.522713\pi$
$233$	11.5533	−	6.67028i	0.756879	−	0.436984i	0.828174	+	0.560471i	$0.189380\pi$
$234$		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	0.440633	−	0.897688i	$-0.354754\pi$
$239$	8.46669	+	1.49291i	0.547665	+	0.0965680i	0.107032	+	0.994256i	$0.465865\pi$
$240$		0			0
$241$	3.63407	−	9.98452i	0.234091	−	0.643160i	−0.765909	−	0.642949i	$-0.777711\pi$
$241$	3.63407	−	9.98452i	0.234091	−	0.643160i	1.00000		0.000210696i	$-6.70668e-5\pi$
$242$		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	0.955231	+	0.295862i	$0.0956068\pi$
$251$	11.6262	+	20.1372i	0.733839	+	1.27105i	−0.221391	+	0.975185i	$0.571060\pi$
$252$		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	0.0370171	−	0.999315i	$-0.488214\pi$
$257$	11.3456	−	4.12947i	0.707721	−	0.257589i	0.670704	+	0.741725i	$0.265992\pi$
$258$		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	0.983401	+	0.181446i	$0.0580779\pi$
$263$	16.0766	+	19.1593i	0.991325	+	1.18142i	0.00792406	+	0.999969i	$0.497478\pi$
$264$		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	0.999200	−	0.0399844i	$-0.0127308\pi$
$269$	7.62612	+	13.2088i	0.464973	+	0.805356i	−0.534228	+	0.845341i	$0.679397\pi$
$270$		0			0
$271$	−18.4322	−	10.6418i	−1.11967	−	0.646444i	−0.178356	−	0.983966i	$-0.557078\pi$
$271$	−18.4322	−	10.6418i	−1.11967	−	0.646444i	−0.941318	+	0.337522i	$0.890411\pi$
$272$		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	−0.671203	−	0.741273i	$-0.734222\pi$
$277$	−0.961066	+	0.806430i	−0.0577449	+	0.0484537i	0.613458	+	0.789727i	$0.289778\pi$
$278$		0			0
$279$	−24.3374	−	14.6809i	−1.45704	−	0.878921i
$280$		0			0
$281$	3.55922	−	9.77886i	0.212325	−	0.583358i	−0.787115	−	0.616806i	$-0.788426\pi$
$281$	3.55922	−	9.77886i	0.212325	−	0.583358i	0.999440	+	0.0334475i	$0.0106487\pi$
$282$		0			0
$283$	−9.41503	−	1.66012i	−0.559665	−	0.0986841i	−0.113342	−	0.993556i	$-0.536156\pi$
$283$	−9.41503	−	1.66012i	−0.559665	−	0.0986841i	−0.446323	+	0.894872i	$0.647267\pi$
$284$		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	−0.718083	−	0.695958i	$-0.754980\pi$
$293$	3.33317	−	18.9033i	0.194726	−	1.10435i	0.912809	−	0.408388i	$-0.133909\pi$
$294$		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	0.972177	−	0.234246i	$-0.0752622\pi$
$307$	21.9964	+	12.6996i	1.25540	+	0.724807i	0.283225	+	0.959053i	$0.408596\pi$
$308$		0			0
$309$	6.67710	−	1.11141i	0.379847	−	0.0632259i
$310$		0			0
$311$	2.27297	−	12.8907i	0.128888	−	0.730962i	−0.850034	−	0.526728i	$-0.823419\pi$
$311$	2.27297	−	12.8907i	0.128888	−	0.730962i	0.978922	−	0.204234i	$-0.0654703\pi$
$312$		0			0
$313$	−3.81819	−	4.55034i	−0.215817	−	0.257200i	0.647264	−	0.762266i	$-0.275913\pi$
$313$	−3.81819	−	4.55034i	−0.215817	−	0.257200i	−0.863081	+	0.505065i	$0.831468\pi$
$314$		0			0
$315$	3.73063	+	3.31543i	0.210197	+	0.186803i
$316$		0			0
$317$	−10.5297	+	28.9300i	−0.591404	+	1.62487i	0.176497	+	0.984301i	$0.443524\pi$
$317$	−10.5297	+	28.9300i	−0.591404	+	1.62487i	−0.767901	+	0.640569i	$0.778699\pi$
$318$		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	0.742567	−	0.669772i	$-0.233608\pi$
$331$	16.0263	+	5.83309i	0.880885	+	0.320616i	0.138318	+	0.990388i	$0.455830\pi$
$332$		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	0.926893	−	0.375327i	$-0.122469\pi$
$337$	13.1848	+	11.0634i	0.718221	+	0.602659i	−0.208671	+	0.977986i	$0.566914\pi$
$338$		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	0.914935	−	0.403600i	$-0.132241\pi$
$347$	−0.845241	−	2.32228i	−0.0453749	−	0.124667i	−0.960310	+	0.278934i	$0.910019\pi$
$348$		0			0
$349$	−9.60242	−	11.4437i	−0.514006	−	0.612568i	0.445147	−	0.895458i	$-0.353152\pi$
$349$	−9.60242	−	11.4437i	−0.514006	−	0.612568i	−0.959153	+	0.282889i	$0.908707\pi$
$350$		0			0
$351$	0.599880	+	1.80848i	0.0320192	+	0.0965293i
$352$		0			0
$353$	−22.6470	−	8.24284i	−1.20538	−	0.438722i	−0.340281	−	0.940324i	$-0.610522\pi$
$353$	−22.6470	−	8.24284i	−1.20538	−	0.438722i	−0.865099	+	0.501602i	$0.832744\pi$
$354$		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	$-0.739224\pi$
$359$		−	27.6871i		−	1.46127i	0.682768	−	0.730635i	$-0.260776\pi$
$360$		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	0.681285	−	0.732018i	$-0.261421\pi$
$367$	30.1123	−	5.30961i	1.57185	−	0.277159i	0.890564	+	0.454859i	$0.150310\pi$
$368$		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	−0.999499	−	0.0316373i	$-0.989928\pi$
$373$	−0.955166	+	5.41701i	−0.0494566	+	0.280482i	0.950043	+	0.312120i	$0.101039\pi$
$374$		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	−0.823280	−	0.567635i	$-0.807859\pi$
$383$	2.82778	−	16.0371i	0.144493	−	0.819459i	0.967773	−	0.251824i	$-0.0810304\pi$
$384$		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	−0.565889	−	0.824482i	$-0.691467\pi$
$389$	−16.0873	+	2.83663i	−0.815661	+	0.143823i	−0.249772	+	0.968305i	$0.580356\pi$
$390$		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	$0.0738603\pi$
$397$			9.16393i			0.459924i	−0.973200	+	0.229962i	$0.926140\pi$
$398$		0			0
$399$	−4.05674	−	5.02362i	−0.203091	−	0.251496i
$400$		0			0
$401$	12.5976	−	15.0132i	0.629092	−	0.749722i	−0.353513	−	0.935429i	$-0.615013\pi$
$401$	12.5976	−	15.0132i	0.629092	−	0.749722i	0.982605	+	0.185707i	$0.0594576\pi$
$402$		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	0.997835	+	0.0657676i	$0.0209496\pi$
$409$	5.57617	+	15.3204i	0.275724	+	0.757544i	−0.722111	+	0.691777i	$0.756828\pi$
$410$		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	0.786274	−	0.617878i	$-0.212007\pi$
$419$	6.43393	+	5.39871i	0.314318	+	0.263744i	−0.471956	+	0.881622i	$0.656452\pi$
$420$		0			0
$421$	20.1286	+	7.32622i	0.981009	+	0.357058i	0.782232	−	0.622987i	$-0.214081\pi$
$421$	20.1286	+	7.32622i	0.981009	+	0.357058i	0.198777	+	0.980045i	$0.436303\pi$
$422$		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	0.195237	−	0.980756i	$-0.437452\pi$
$431$	23.7130	−	13.6907i	1.14222	−	0.659459i	0.946978	+	0.321297i	$0.104119\pi$
$432$		0			0
$433$			9.79725i			0.470826i	0.971895	+	0.235413i	$0.0756443\pi$
$433$			9.79725i			0.470826i	−0.971895	+	0.235413i	$0.924356\pi$
$434$		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	0.578591	+	0.815618i	$0.303603\pi$
$439$	−8.14845	+	22.3877i	−0.388904	+	1.06851i	−0.967495	+	0.252888i	$0.918619\pi$
$440$		0			0
$441$	4.42207	−	20.5291i	0.210575	−	0.977578i
$442$		0			0
$443$	−20.8243	−	24.8175i	−0.989394	−	1.17911i	−0.983826	−	0.179129i	$-0.942672\pi$
$443$	−20.8243	−	24.8175i	−0.989394	−	1.17911i	−0.00556848	−	0.999984i	$-0.501773\pi$
$444$		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	−0.314827	−	0.949149i	$-0.601946\pi$
$449$	−27.4242	−	15.8334i	−1.29423	−	0.747223i	−0.979401	+	0.201927i	$0.935280\pi$
$450$		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	0.690970	+	0.722883i	$0.257184\pi$
$457$	6.17622	+	35.0271i	0.288911	+	1.63850i	−0.402059	+	0.915614i	$0.631705\pi$
$458$		0			0
$459$	−10.8379	+	17.5830i	−0.505870	+	0.820705i
$460$		0			0
$461$	20.6320	−	17.3123i	0.960927	−	0.806313i	−0.0201766	−	0.999796i	$-0.506423\pi$
$461$	20.6320	−	17.3123i	0.960927	−	0.806313i	0.981104	+	0.193483i	$0.0619784\pi$
$462$		0			0
$463$	5.46034	−	30.9671i	0.253763	−	1.43916i	−0.545464	−	0.838134i	$-0.683647\pi$
$463$	5.46034	−	30.9671i	0.253763	−	1.43916i	0.799227	−	0.601029i	$-0.205242\pi$
$464$		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	−0.798910	−	0.601450i	$-0.794590\pi$
$479$	−7.55786	+	6.34179i	−0.345327	+	0.289764i	0.453583	+	0.891214i	$0.350145\pi$
$480$		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	0.720808	−	0.693135i	$-0.243771\pi$
$487$	−5.29343	−	9.16849i	−0.239868	−	0.415464i	−0.960676	+	0.277671i	$0.910438\pi$
$488$		0			0
$489$	6.77860	−	36.3978i	0.306539	−	1.64597i
$490$		0			0
$491$	1.98343	+	5.44942i	0.0895107	+	0.245929i	0.976368	−	0.216115i	$-0.0693386\pi$
$491$	1.98343	+	5.44942i	0.0895107	+	0.245929i	−0.886857	+	0.462044i	$0.847116\pi$
$492$		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	−0.732032	−	0.681271i	$-0.761428\pi$
$499$	−19.0968	+	6.95065i	−0.854888	+	0.311154i	−0.122856	+	0.992424i	$0.539205\pi$
$500$		0			0
$501$	−4.95084	+	4.07395i	−0.221187	+	0.182011i
$502$		0			0
$503$	−6.84793	+	11.8610i	−0.305334	+	0.528854i	−0.977336	−	0.211695i	$-0.932102\pi$
$503$	−6.84793	+	11.8610i	−0.305334	+	0.528854i	0.672001	+	0.740550i	$0.265435\pi$
$504$		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	0.707111	−	0.707103i	$-0.249998\pi$
$509$	3.01278	+	2.52802i	0.133539	+	0.112053i	−0.573572	+	0.819155i	$0.694443\pi$
$510$		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	0.0422996	+	0.999105i	$0.486532\pi$
$521$	−19.2670	+	33.3713i	−0.844100	+	1.46202i	−0.886400	+	0.462920i	$0.846802\pi$
$522$		0			0
$523$	−24.8394	+	14.3410i	−1.08615	+	0.627090i	−0.932549	−	0.361043i	$-0.882421\pi$
$523$	−24.8394	+	14.3410i	−1.08615	+	0.627090i	−0.153602	+	0.988133i	$0.549088\pi$
$524$		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	−0.966576	−	0.256382i	$-0.917470\pi$
$541$	−6.07663	+	10.5250i	−0.261255	+	0.452507i	0.705321	+	0.708888i	$0.250803\pi$
$542$		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	0.991869	−	0.127265i	$-0.0406200\pi$
$547$	0.380983	+	2.16066i	0.0162897	+	0.0923832i	−0.975579	+	0.219649i	$0.929509\pi$
$548$		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	$-0.852725\pi$
$557$		−	21.0683i		−	0.892694i	0.894860	−	0.446347i	$-0.147275\pi$
$558$		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	−0.990742	−	0.135756i	$-0.956654\pi$
$563$	−39.4456	+	14.3570i	−1.66243	+	0.605076i	−0.671691	+	0.740832i	$0.734432\pi$
$564$		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	−0.501548	−	0.865130i	$-0.667236\pi$
$569$	−16.1479	+	2.84732i	−0.676957	+	0.119366i	−0.175409	+	0.984496i	$0.556125\pi$
$570$		0			0
$571$	15.3637	−	5.59193i	0.642951	−	0.234015i	9.25327e−5	−	1.00000i	$-0.499971\pi$
$571$	15.3637	−	5.59193i	0.642951	−	0.234015i	0.642858	+	0.765985i	$0.277748\pi$
$572$		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	$0.0237683\pi$
$577$			3.58396i			0.149202i	−0.997213	+	0.0746011i	$0.976232\pi$
$578$		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	0.730799	+	0.682593i	$0.239148\pi$
$587$	6.72409	+	38.1342i	0.277533	+	1.57397i	−0.453266	+	0.891375i	$0.649741\pi$
$588$		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	−0.785479	−	0.618888i	$-0.787584\pi$
$593$	3.48794	−	6.04130i	0.143233	−	0.248086i	0.928712	+	0.370801i	$0.120917\pi$
$594$		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	−0.664388	−	0.747388i	$-0.731308\pi$
$599$	4.57709	−	5.45477i	0.187015	−	0.222876i	0.851403	+	0.524512i	$0.175752\pi$
$600$		0			0
$601$	17.0560	−	3.00744i	0.695730	−	0.122676i	0.185411	−	0.982661i	$-0.440638\pi$
$601$	17.0560	−	3.00744i	0.695730	−	0.122676i	0.510319	+	0.859985i	$0.329527\pi$
$602$		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	−0.776931	−	0.629586i	$-0.783225\pi$
$607$	−14.4488	−	39.6977i	−0.586457	−	1.61128i	0.190474	−	0.981692i	$-0.438998\pi$
$608$		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	−0.894399	−	0.447271i	$-0.852396\pi$
$613$	−1.48185	+	2.56665i	−0.0598515	+	0.103666i	0.834547	+	0.550937i	$0.185729\pi$
$614$		0			0
$615$	0.243535	−	0.412622i	0.00982029	−	0.0166385i
$616$		0			0
$617$	−22.7707	−	4.01508i	−0.916713	−	0.161641i	−0.304663	−	0.952460i	$-0.598544\pi$
$617$	−22.7707	−	4.01508i	−0.916713	−	0.161641i	−0.612050	+	0.790819i	$0.709655\pi$
$618$		0			0
$619$	0.908965	−	2.49736i	0.0365344	−	0.100377i	−0.920084	−	0.391721i	$-0.871880\pi$
$619$	0.908965	−	2.49736i	0.0365344	−	0.100377i	0.956619	+	0.291343i	$0.0941022\pi$
$620$		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	−0.997086	−	0.0762910i	$-0.975692\pi$
$631$	−10.8636	+	18.8163i	−0.432473	+	0.749065i	0.564613	+	0.825356i	$0.309026\pi$
$632$		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	0.930238	−	0.366957i	$-0.119600\pi$
$641$	10.3126	+	12.2900i	0.407321	+	0.485427i	−0.522916	+	0.852384i	$0.675156\pi$
$642$		0			0
$643$	−6.32054	−	17.3655i	−0.249258	−	0.684830i	−0.999714	−	0.0239099i	$-0.992389\pi$
$643$	−6.32054	−	17.3655i	−0.249258	−	0.684830i	0.750456	−	0.660920i	$-0.229834\pi$
$644$		0			0
$645$	−1.73115	+	9.29544i	−0.0681639	+	0.366008i
$646$		0			0
$647$	12.7137	+	22.0208i	0.499828	+	0.865727i	1.00000		0.000199058i	$-6.33620e-5\pi$
$647$	12.7137	+	22.0208i	0.499828	+	0.865727i	−0.500172	+	0.865926i	$0.666730\pi$
$648$		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	−0.144388	−	0.989521i	$-0.546121\pi$
$653$	−15.8052	−	2.78688i	−0.618505	−	0.109059i	−0.474117	+	0.880462i	$0.657233\pi$
$654$		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	−0.982782	−	0.184771i	$-0.940846\pi$
$659$	−2.85356	+	7.84009i	−0.111159	+	0.305407i	0.871623	+	0.490177i	$0.163068\pi$
$660$		0			0
$661$	18.6628	+	3.29075i	0.725898	+	0.127995i	0.524374	−	0.851488i	$-0.324299\pi$
$661$	18.6628	+	3.29075i	0.725898	+	0.127995i	0.201524	+	0.979484i	$0.435411\pi$
$662$		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	−0.999675	−	0.0254859i	$-0.991887\pi$
$673$	−29.7861	+	24.9935i	−1.14817	+	0.963428i	−0.148493	+	0.988913i	$0.547442\pi$
$674$		0			0
$675$	−18.7636	+	14.8457i	−0.722210	+	0.571410i
$676$		0			0
$677$	−6.83083	−	38.7396i	−0.262530	−	1.48888i	−0.775977	−	0.630761i	$-0.782743\pi$
$677$	−6.83083	−	38.7396i	−0.262530	−	1.48888i	0.513447	−	0.858121i	$-0.328368\pi$
$678$		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	0.734167	−	0.678969i	$-0.237573\pi$
$683$	13.4133	+	7.74417i	0.513246	+	0.296323i	−0.220921	+	0.975292i	$0.570906\pi$
$684$		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	−0.988516	−	0.151117i	$-0.951713\pi$
$691$	−25.3848	−	30.2524i	−0.965683	−	1.15086i	0.0228327	−	0.999739i	$-0.492731\pi$
$692$		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	$0.108975\pi$
$701$			17.7766i			0.671415i	−0.941966	+	0.335707i	$0.891025\pi$
$702$		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	−0.680331	−	0.732905i	$-0.738164\pi$
$709$	−44.5363	−	16.2099i	−1.67260	−	0.608775i	−0.992266	+	0.124130i	$0.960386\pi$
$710$		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	−0.844686	−	0.535262i	$-0.820213\pi$
$719$	−23.7545	−	41.1440i	−0.885894	−	1.53441i	−0.0412079	−	0.999151i	$-0.513121\pi$
$720$		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	0.900314	−	0.435241i	$-0.143337\pi$
$727$	8.50270	+	10.1331i	0.315348	+	0.375817i	−0.584966	+	0.811057i	$0.698892\pi$
$728$		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	−0.959739	−	0.280892i	$-0.909370\pi$
$733$	−13.9826	+	16.6638i	−0.516458	+	0.615491i	0.443281	+	0.896382i	$0.353814\pi$
$734$		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	−0.997991	−	0.0633603i	$-0.979818\pi$
$743$	−20.7786	+	24.7630i	−0.762294	+	0.908466i	0.235697	+	0.971827i	$0.424263\pi$
$744$		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	0.913718	+	0.406350i	$0.133199\pi$
$751$	−2.29857	+	13.0358i	−0.0838759	+	0.475684i	−0.997594	+	0.0693340i	$0.977913\pi$
$752$		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	0.554142	+	0.832422i	$0.313046\pi$
$761$	−6.93204	+	39.3135i	−0.251286	+	1.42511i	−0.805428	+	0.592693i	$0.798065\pi$
$762$		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	−0.964702	−	0.263344i	$-0.915175\pi$
$769$	−14.9148	+	17.7747i	−0.537840	+	0.640973i	0.426862	+	0.904317i	$0.359619\pi$
$770$		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	0.989169	−	0.146781i	$-0.0468912\pi$
$787$	3.84537	+	10.5651i	0.137073	+	0.376604i	−0.852096	+	0.523385i	$0.824669\pi$
$788$		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	0.988025	+	0.154292i	$0.0493098\pi$
$797$	37.0264	+	31.0688i	1.31154	+	1.10051i	0.323517	+	0.946222i	$0.395135\pi$
$798$		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	−0.996383	−	0.0849808i	$-0.972917\pi$
$809$	−40.4168	+	23.3346i	−1.42098	+	0.820402i	−0.424596	+	0.905383i	$0.639584\pi$
$810$		0			0
$811$			21.4580i			0.753491i	0.926317	+	0.376746i	$0.122957\pi$
$811$			21.4580i			0.753491i	−0.926317	+	0.376746i	$0.877043\pi$
$812$		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	0.331120	−	0.943589i	$-0.392574\pi$
$821$	−18.7859	−	22.3881i	−0.655632	−	0.781352i	−0.986752	+	0.162237i	$0.948129\pi$
$822$		0			0
$823$	−0.194528	+	1.10323i	−0.00678083	+	0.0384560i	−0.988010	−	0.154387i	$-0.950660\pi$
$823$	−0.194528	+	1.10323i	−0.00678083	+	0.0384560i	0.981230	+	0.192843i	$0.0617708\pi$
$824$		0			0
$825$	14.7590	−	2.45666i	0.513844	−	0.0855299i
$826$		0			0
$827$	−31.2630	−	18.0497i	−1.08712	−	0.627650i	−0.154313	−	0.988022i	$-0.549316\pi$
$827$	−31.2630	−	18.0497i	−1.08712	−	0.627650i	−0.932809	+	0.360372i	$0.882650\pi$
$828$		0			0
$829$	14.9177	+	8.61274i	0.518113	+	0.299133i	0.736162	−	0.676805i	$-0.236636\pi$
$829$	14.9177	+	8.61274i	0.518113	+	0.299133i	−0.218049	+	0.975938i	$0.569969\pi$
$830$		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	−0.0210778	−	0.999778i	$-0.506710\pi$
$839$	27.8026	−	23.3291i	0.959851	−	0.805411i	0.980929	+	0.194367i	$0.0622653\pi$
$840$		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	−0.504320	−	0.863517i	$-0.668257\pi$
$853$	12.7651	−	35.0719i	0.437069	−	1.20084i	0.941390	−	0.337321i	$-0.109521\pi$
$854$		0			0
$855$	−2.32700	+	1.28461i	−0.0795819	+	0.0439327i
$856$		0			0
$857$	−26.6548	+	22.3660i	−0.910511	+	0.764009i	−0.972216	−	0.234085i	$-0.924791\pi$
$857$	−26.6548	+	22.3660i	−0.910511	+	0.764009i	0.0617051	+	0.998094i	$0.480346\pi$
$858$		0			0
$859$	−38.3088	−	6.75488i	−1.30708	−	0.230473i	−0.523639	−	0.851940i	$-0.675426\pi$
$859$	−38.3088	−	6.75488i	−1.30708	−	0.230473i	−0.783441	+	0.621467i	$0.786537\pi$
$860$		0			0
$861$	−2.01564	−	0.0379285i	−0.0686928	−	0.00129260i
$862$		0			0
$863$	−11.7694	−	6.79505i	−0.400634	−	0.231306i	0.286123	−	0.958193i	$-0.407633\pi$
$863$	−11.7694	−	6.79505i	−0.400634	−	0.231306i	−0.686758	+	0.726886i	$0.740967\pi$
$864$		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	−0.727160	−	0.686468i	$-0.759160\pi$
$877$	−24.9631	+	9.08582i	−0.842943	+	0.306806i	−0.115783	+	0.993274i	$0.536938\pi$
$878$		0			0
$879$	5.45884	+	32.7954i	0.184122	+	1.10616i
$880$		0			0
$881$	−22.4911	+	38.9557i	−0.757744	+	1.31245i	0.186255	+	0.982501i	$0.440365\pi$
$881$	−22.4911	+	38.9557i	−0.757744	+	1.31245i	−0.943999	+	0.329949i	$0.892968\pi$
$882$		0			0
$883$	−19.4761	−	33.7336i	−0.655423	−	1.13523i	−0.981788	−	0.189982i	$-0.939157\pi$
$883$	−19.4761	−	33.7336i	−0.655423	−	1.13523i	0.326365	−	0.945244i	$-0.394176\pi$
$884$		0			0
$885$	−0.319757	+	0.541765i	−0.0107485	+	0.0182112i
$886$		0			0
$887$	2.88696	+	2.42245i	0.0969346	+	0.0813377i	0.689967	−	0.723841i	$-0.257625\pi$
$887$	2.88696	+	2.42245i	0.0969346	+	0.0813377i	−0.593032	+	0.805179i	$0.702069\pi$
$888$		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	0.909763	+	0.415128i	$0.136263\pi$
$907$	5.92834	+	33.6213i	0.196847	+	1.11638i	−0.712916	+	0.701250i	$0.752626\pi$
$908$		0			0
$909$	−9.69943	+	49.4412i	−0.321710	+	1.63986i
$910$		0			0
$911$	50.5872	−	8.91989i	1.67603	−	0.295529i	0.746804	−	0.665044i	$-0.231587\pi$
$911$	50.5872	−	8.91989i	1.67603	−	0.295529i	0.929225	+	0.369515i	$0.120476\pi$
$912$		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	−0.248908	−	0.968527i	$-0.580072\pi$
$919$	21.6545	−	37.5066i	0.714315	−	1.23723i	0.963223	−	0.268703i	$-0.0865949\pi$
$920$		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	−0.285900	−	0.958260i	$-0.592292\pi$
$929$	18.5363	−	15.5538i	0.608156	−	0.510303i	0.894056	+	0.447956i	$0.147848\pi$
$930$		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	−0.963885	−	0.266318i	$-0.914193\pi$
$937$	−37.1975	+	21.4760i	−1.21519	+	0.701590i	−0.251304	+	0.967908i	$0.580859\pi$
$938$		0			0
$939$	8.86031	+	5.22948i	0.289145	+	0.170658i
$940$		0			0
$941$	34.3360	−	12.4973i	1.11932	−	0.407400i	0.284917	−	0.958552i	$-0.408034\pi$
$941$	34.3360	−	12.4973i	1.11932	−	0.407400i	0.834404	+	0.551153i	$0.185812\pi$
$942$		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	0.733789	−	0.679377i	$-0.237750\pi$
$947$	50.9510	−	8.98404i	1.65569	−	0.291942i	0.921897	+	0.387435i	$0.126639\pi$
$948$		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	−0.866889	−	0.498501i	$-0.833884\pi$
$953$	−26.8149	+	15.4816i	−0.868620	+	0.501498i	−0.00173046	+	0.999999i	$0.500551\pi$
$954$		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	0.457189	−	0.889369i	$-0.348856\pi$
$967$	42.8851	−	15.6089i	1.37909	−	0.501948i	0.921903	+	0.387421i	$0.126634\pi$
$968$		0			0
$969$	3.23041	+	9.14759i	0.103776	+	0.293863i
$970$		0			0
$971$	8.12697	−	14.0763i	0.260807	−	0.451731i	−0.705650	−	0.708561i	$-0.749345\pi$
$971$	8.12697	−	14.0763i	0.260807	−	0.451731i	0.966457	+	0.256830i	$0.0826781\pi$
$972$		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	−0.741041	−	0.671459i	$-0.765668\pi$
$977$	1.52839	−	1.82147i	0.0488976	−	0.0582739i	0.789939	+	0.613186i	$0.210112\pi$
$978$		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	0.947862	+	0.318681i	$0.103240\pi$
$983$	5.20954	+	29.5448i	0.166158	+	0.942332i	−0.781703	+	0.623650i	$0.785649\pi$
$984$		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	−0.998747	−	0.0500496i	$-0.984062\pi$
$991$	−14.3559	+	24.8651i	−0.456029	+	0.789866i	0.542718	+	0.839915i	$0.317395\pi$
$992$		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	−0.543808	−	0.839210i	$-0.683018\pi$
$997$	13.0156	−	35.7600i	0.412207	−	1.13253i	0.956015	−	0.293319i	$-0.0947599\pi$
$998$		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.5.3	yes	144
7.3	odd	6		756.2.ca.a.437.6	yes	144
27.11	odd	18		756.2.ca.a.173.6	✓	144
189.38	even	18	inner	756.2.ck.a.605.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.6	✓	144	27.11	odd	18
756.2.ca.a.437.6	yes	144	7.3	odd	6
756.2.ck.a.5.3	yes	144	1.1	even	1	trivial
756.2.ck.a.605.3	yes	144	189.38	even	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
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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