LMFDB - Embedded newform 3150.2.bf.f.1151.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.8
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.f.1601.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.29693 - 2.30608i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.29693 - 2.30608i) q^{7} +1.00000i q^{8} +(-1.11120 - 0.641550i) q^{11} -6.14864i q^{13} +(0.0298666 + 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.26128 + 5.64871i) q^{17} +(-5.22868 + 3.01878i) q^{19} +1.28310 q^{22} +(2.49343 - 1.43958i) q^{23} +(3.07432 + 5.32488i) q^{26} +(-1.34866 - 2.27621i) q^{28} -1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(0.866025 + 0.500000i) q^{32} -6.52257i q^{34} +(4.76690 + 8.25652i) q^{37} +(3.01878 - 5.22868i) q^{38} -8.71759 q^{41} -5.35859 q^{43} +(-1.11120 + 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(-0.403086 - 0.698165i) q^{47} +(-3.63597 - 5.98162i) q^{49} +(-5.32488 - 3.07432i) q^{52} +(5.77488 + 3.33413i) q^{53} +(2.30608 + 1.29693i) q^{56} +(0.675260 + 1.16959i) q^{58} +(-0.798110 + 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} +8.65515 q^{62} -1.00000 q^{64} +(-2.69731 + 4.67188i) q^{67} +(3.26128 + 5.64871i) q^{68} +15.6787i q^{71} +(10.7532 + 6.20837i) q^{73} +(-8.25652 - 4.76690i) q^{74} +6.03756i q^{76} +(-2.92060 + 1.73046i) q^{77} +(5.59093 + 9.68377i) q^{79} +(7.54966 - 4.35880i) q^{82} -3.74493 q^{83} +(4.64067 - 2.67929i) q^{86} +(0.641550 - 1.11120i) q^{88} +(1.81971 + 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} -2.87917i q^{92} +(0.698165 + 0.403086i) q^{94} -8.76818i q^{97} +(6.13965 + 3.36225i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.29693	−	2.30608i	0.490192	−	0.871614i
$7$	1.29693	−	2.30608i	0.490192	−	0.871614i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	−1.11120	−	0.641550i	−0.335038	−	0.193435i	0.323037	−	0.946386i	$-0.395296\pi$
$11$	−1.11120	−	0.641550i	−0.335038	−	0.193435i	−0.658076	+	0.752952i	$0.728629\pi$
$12$		0			0
$13$		−	6.14864i		−	1.70533i	−0.522462	−	0.852663i	$-0.674986\pi$
$13$		−	6.14864i		−	1.70533i	0.522462	−	0.852663i	$-0.325014\pi$
$14$	0.0298666	+	2.64558i	0.00798219	+	0.707062i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.26128	+	5.64871i	−0.790977	+	1.37001i	0.134385	+	0.990929i	$0.457094\pi$
$17$	−3.26128	+	5.64871i	−0.790977	+	1.37001i	−0.925362	+	0.379084i	$0.876239\pi$
$18$		0			0
$19$	−5.22868	+	3.01878i	−1.19954	+	0.692555i	−0.960453	−	0.278443i	$-0.910182\pi$
$19$	−5.22868	+	3.01878i	−1.19954	+	0.692555i	−0.239088	+	0.970998i	$0.576848\pi$
$20$		0			0
$21$		0			0
$22$	1.28310			0.273558
$23$	2.49343	−	1.43958i	0.519917	−	0.300174i	−0.216984	−	0.976175i	$-0.569622\pi$
$23$	2.49343	−	1.43958i	0.519917	−	0.300174i	0.736901	+	0.676001i	$0.236289\pi$
$24$		0			0
$25$		0			0
$26$	3.07432	+	5.32488i	0.602923	+	1.04429i
$27$		0			0
$28$	−1.34866	−	2.27621i	−0.254872	−	0.430163i
$29$		−	1.35052i		−	0.250785i	−0.992107	−	0.125393i	$-0.959981\pi$
$29$		−	1.35052i		−	0.250785i	0.992107	−	0.125393i	$-0.0400191\pi$
$30$		0			0
$31$	−7.49558	−	4.32758i	−1.34625	−	0.777255i	−0.358530	−	0.933518i	$-0.616722\pi$
$31$	−7.49558	−	4.32758i	−1.34625	−	0.777255i	−0.987716	+	0.156263i	$0.950055\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	6.52257i		−	1.11861i
$35$		0			0
$36$		0			0
$37$	4.76690	+	8.25652i	0.783674	+	1.35736i	0.929788	+	0.368095i	$0.119990\pi$
$37$	4.76690	+	8.25652i	0.783674	+	1.35736i	−0.146114	+	0.989268i	$0.546677\pi$
$38$	3.01878	−	5.22868i	0.489710	−	0.848203i
$39$		0			0
$40$		0			0
$41$	−8.71759			−1.36146			−0.680730	−	0.732535i	$-0.738337\pi$
$41$	−8.71759			−1.36146			−0.680730	+	0.732535i	$0.738337\pi$
$42$		0			0
$43$	−5.35859			−0.817177			−0.408588	−	0.912719i	$-0.633979\pi$
$43$	−5.35859			−0.817177			−0.408588	+	0.912719i	$0.633979\pi$
$44$	−1.11120	+	0.641550i	−0.167519	+	0.0967173i
$45$		0			0
$46$	−1.43958	+	2.49343i	−0.212255	+	0.367637i
$47$	−0.403086	−	0.698165i	−0.0587961	−	0.101838i	0.835129	−	0.550054i	$-0.185393\pi$
$47$	−0.403086	−	0.698165i	−0.0587961	−	0.101838i	−0.893925	+	0.448216i	$0.852060\pi$
$48$		0			0
$49$	−3.63597	−	5.98162i	−0.519424	−	0.854517i
$50$		0			0
$51$		0			0
$52$	−5.32488	−	3.07432i	−0.738427	−	0.426331i
$53$	5.77488	+	3.33413i	0.793241	+	0.457978i	0.841102	−	0.540876i	$-0.181907\pi$
$53$	5.77488	+	3.33413i	0.793241	+	0.457978i	−0.0478611	+	0.998854i	$0.515240\pi$
$54$		0			0
$55$		0			0
$56$	2.30608	+	1.29693i	0.308162	+	0.173309i
$57$		0			0
$58$	0.675260	+	1.16959i	0.0886660	+	0.153574i
$59$	−0.798110	+	1.38237i	−0.103905	+	0.179969i	−0.913290	−	0.407309i	$-0.866467\pi$
$59$	−0.798110	+	1.38237i	−0.103905	+	0.179969i	0.809385	+	0.587278i	$0.199800\pi$
$60$		0			0
$61$	−5.50239	+	3.17681i	−0.704509	+	0.406748i	−0.809025	−	0.587775i	$-0.800004\pi$
$61$	−5.50239	+	3.17681i	−0.704509	+	0.406748i	0.104516	+	0.994523i	$0.466671\pi$
$62$	8.65515			1.09921
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−2.69731	+	4.67188i	−0.329529	+	0.570761i	−0.982418	−	0.186692i	$-0.940223\pi$
$67$	−2.69731	+	4.67188i	−0.329529	+	0.570761i	0.652889	+	0.757453i	$0.273557\pi$
$68$	3.26128	+	5.64871i	0.395489	+	0.685006i
$69$		0			0
$70$		0			0
$71$			15.6787i			1.86072i	0.366650	+	0.930359i	$0.380505\pi$
$71$			15.6787i			1.86072i	−0.366650	+	0.930359i	$0.619495\pi$
$72$		0			0
$73$	10.7532	+	6.20837i	1.25857	+	0.726635i	0.972796	−	0.231663i	$-0.0744166\pi$
$73$	10.7532	+	6.20837i	1.25857	+	0.726635i	0.285772	+	0.958298i	$0.407750\pi$
$74$	−8.25652	−	4.76690i	−0.959801	−	0.554141i
$75$		0			0
$76$			6.03756i			0.692555i
$77$	−2.92060	+	1.73046i	−0.332834	+	0.197204i
$78$		0			0
$79$	5.59093	+	9.68377i	0.629028	+	1.08951i	0.987747	+	0.156064i	$0.0498805\pi$
$79$	5.59093	+	9.68377i	0.629028	+	1.08951i	−0.358719	+	0.933446i	$0.616786\pi$
$80$		0			0
$81$		0			0
$82$	7.54966	−	4.35880i	0.833720	−	0.481349i
$83$	−3.74493			−0.411059			−0.205530	−	0.978651i	$-0.565892\pi$
$83$	−3.74493			−0.411059			−0.205530	+	0.978651i	$0.565892\pi$
$84$		0			0
$85$		0			0
$86$	4.64067	−	2.67929i	0.500417	−	0.288916i
$87$		0			0
$88$	0.641550	−	1.11120i	0.0683894	−	0.118454i
$89$	1.81971	+	3.15183i	0.192889	+	0.334093i	0.946206	−	0.323564i	$-0.104881\pi$
$89$	1.81971	+	3.15183i	0.192889	+	0.334093i	−0.753318	+	0.657657i	$0.771548\pi$
$90$		0			0
$91$	−14.1792	−	7.97433i	−1.48639	−	0.835937i
$92$		−	2.87917i		−	0.300174i
$93$		0			0
$94$	0.698165	+	0.403086i	0.0720102	+	0.0415751i
$95$		0			0
$96$		0			0
$97$		−	8.76818i		−	0.890274i	−0.895463	−	0.445137i	$-0.853155\pi$
$97$		−	8.76818i		−	0.890274i	0.895463	−	0.445137i	$-0.146845\pi$
$98$	6.13965	+	3.36225i	0.620198	+	0.339639i
$99$		0			0
$100$		0			0
$101$	−0.853270	+	1.47791i	−0.0849035	+	0.147057i	−0.905350	−	0.424666i	$-0.860392\pi$
$101$	−0.853270	+	1.47791i	−0.0849035	+	0.147057i	0.820447	+	0.571723i	$0.193725\pi$
$102$		0			0
$103$	8.97583	−	5.18220i	0.884415	−	0.510617i	0.0123035	−	0.999924i	$-0.496084\pi$
$103$	8.97583	−	5.18220i	0.884415	−	0.510617i	0.872112	+	0.489307i	$0.162750\pi$
$104$	6.14864			0.602923
$105$		0			0
$106$	−6.66826			−0.647679
$107$	9.97106	−	5.75680i	0.963939	−	0.556531i	0.0665560	−	0.997783i	$-0.478799\pi$
$107$	9.97106	−	5.75680i	0.963939	−	0.556531i	0.897383	+	0.441252i	$0.145466\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$		0			0
$112$	−2.64558	+	0.0298666i	−0.249984	+	0.00282213i
$113$			13.3875i			1.25939i	0.776843	+	0.629695i	$0.216820\pi$
$113$			13.3875i			1.25939i	−0.776843	+	0.629695i	$0.783180\pi$
$114$		0			0
$115$		0			0
$116$	−1.16959	−	0.675260i	−0.108593	−	0.0626963i
$117$		0			0
$118$		−	1.59622i		−	0.146944i
$119$	8.79670	+	14.8467i	0.806392	+	1.36100i
$120$		0			0
$121$	−4.67683	−	8.10050i	−0.425166	−	0.736409i
$122$	3.17681	−	5.50239i	0.287615	−	0.498163i
$123$		0			0
$124$	−7.49558	+	4.32758i	−0.673123	+	0.388628i
$125$		0			0
$126$		0			0
$127$	−5.65313			−0.501634			−0.250817	−	0.968035i	$-0.580699\pi$
$127$	−5.65313			−0.501634			−0.250817	+	0.968035i	$0.580699\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	6.23366	+	10.7970i	0.544638	+	0.943340i	0.998630	+	0.0523344i	$0.0166662\pi$
$131$	6.23366	+	10.7970i	0.544638	+	0.943340i	−0.453992	+	0.891006i	$0.650001\pi$
$132$		0			0
$133$	0.180321	+	15.9729i	0.0156358	+	1.38502i
$134$		−	5.39463i		−	0.466025i
$135$		0			0
$136$	−5.64871	−	3.26128i	−0.484373	−	0.279653i
$137$	−0.0441401	−	0.0254843i	−0.00377114	−	0.00217727i	0.498113	−	0.867112i	$-0.334026\pi$
$137$	−0.0441401	−	0.0254843i	−0.00377114	−	0.00217727i	−0.501884	+	0.864935i	$0.667360\pi$
$138$		0			0
$139$		−	1.05069i		−	0.0891184i	−0.999007	−	0.0445592i	$-0.985812\pi$
$139$		−	1.05069i		−	0.0891184i	0.999007	−	0.0445592i	$-0.0141883\pi$
$140$		0			0
$141$		0			0
$142$	−7.83934	−	13.5781i	−0.657863	−	1.13945i
$143$	−3.94466	+	6.83235i	−0.329869	+	0.571350i
$144$		0			0
$145$		0			0
$146$	−12.4167			−1.02762
$147$		0			0
$148$	9.53381			0.783674
$149$	−7.12137	+	4.11153i	−0.583406	+	0.336829i	−0.762486	−	0.647005i	$-0.776021\pi$
$149$	−7.12137	+	4.11153i	−0.583406	+	0.336829i	0.179080	+	0.983835i	$0.442688\pi$
$150$		0			0
$151$	2.13357	−	3.69546i	0.173628	−	0.300732i	−0.766058	−	0.642772i	$-0.777784\pi$
$151$	2.13357	−	3.69546i	0.173628	−	0.300732i	0.939686	+	0.342040i	$0.111118\pi$
$152$	−3.01878	−	5.22868i	−0.244855	−	0.424102i
$153$		0			0
$154$	1.66409	−	2.95892i	0.134096	−	0.238437i
$155$		0			0
$156$		0			0
$157$	4.18466	+	2.41601i	0.333972	+	0.192819i	0.657603	−	0.753364i	$-0.271570\pi$
$157$	4.18466	+	2.41601i	0.333972	+	0.192819i	−0.323631	+	0.946183i	$0.604904\pi$
$158$	−9.68377	−	5.59093i	−0.770399	−	0.444790i
$159$		0			0
$160$		0			0
$161$	−0.0859910	−	7.61708i	−0.00677704	−	0.600310i
$162$		0			0
$163$	−5.37661	−	9.31256i	−0.421128	−	0.729416i	0.574922	−	0.818208i	$-0.305032\pi$
$163$	−5.37661	−	9.31256i	−0.421128	−	0.729416i	−0.996050	+	0.0887927i	$0.971699\pi$
$164$	−4.35880	+	7.54966i	−0.340365	+	0.589529i
$165$		0			0
$166$	3.24320	−	1.87246i	0.251721	−	0.145331i
$167$	−18.9267			−1.46459			−0.732295	−	0.680988i	$-0.761551\pi$
$167$	−18.9267			−1.46459			−0.732295	+	0.680988i	$0.761551\pi$
$168$		0			0
$169$	−24.8057			−1.90813
$170$		0			0
$171$		0			0
$172$	−2.67929	+	4.64067i	−0.204294	+	0.353848i
$173$	−5.92176	−	10.2568i	−0.450223	−	0.779810i	0.548176	−	0.836363i	$-0.315322\pi$
$173$	−5.92176	−	10.2568i	−0.450223	−	0.779810i	−0.998400	+	0.0565531i	$0.981989\pi$
$174$		0			0
$175$		0			0
$176$			1.28310i			0.0967173i
$177$		0			0
$178$	−3.15183	−	1.81971i	−0.236239	−	0.136393i
$179$	−3.27843	−	1.89280i	−0.245041	−	0.141475i	0.372450	−	0.928052i	$-0.378518\pi$
$179$	−3.27843	−	1.89280i	−0.245041	−	0.141475i	−0.617492	+	0.786577i	$0.711851\pi$
$180$		0			0
$181$			19.0033i			1.41251i	0.707960	+	0.706253i	$0.249616\pi$
$181$			19.0033i			1.41251i	−0.707960	+	0.706253i	$0.750384\pi$
$182$	16.2667	−	0.183639i	1.20577	−	0.0136122i
$183$		0			0
$184$	1.43958	+	2.49343i	0.106128	+	0.183818i
$185$		0			0
$186$		0			0
$187$	7.24785	−	4.18455i	0.530016	−	0.306005i
$188$	−0.806172			−0.0587961
$189$		0			0
$190$		0			0
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	−0.408756	−	0.912644i	$-0.634037\pi$
$191$	2.44949	−	1.41421i	0.177239	−	0.102329i	0.585995	+	0.810315i	$0.300704\pi$
$192$		0			0
$193$	1.76946	−	3.06479i	0.127368	−	0.220608i	−0.795288	−	0.606232i	$-0.792680\pi$
$193$	1.76946	−	3.06479i	0.127368	−	0.220608i	0.922656	+	0.385623i	$0.126014\pi$
$194$	4.38409	+	7.59347i	0.314759	+	0.545179i
$195$		0			0
$196$	−6.99822	+	0.158029i	−0.499873	+	0.0112878i
$197$			2.36728i			0.168662i	0.996438	+	0.0843308i	$0.0268752\pi$
$197$			2.36728i			0.168662i	−0.996438	+	0.0843308i	$0.973125\pi$
$198$		0			0
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	3.00000	+	1.73205i	0.212664	+	0.122782i	−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$		0			0
$202$		−	1.70654i		−	0.120072i
$203$	−3.11440	−	1.75153i	−0.218588	−	0.122933i
$204$		0			0
$205$		0			0
$206$	−5.18220	+	8.97583i	−0.361061	+	0.625376i
$207$		0			0
$208$	−5.32488	+	3.07432i	−0.369214	+	0.213166i
$209$	7.74679			0.535856
$210$		0			0
$211$	−14.3620			−0.988721			−0.494361	−	0.869257i	$-0.664598\pi$
$211$	−14.3620			−0.988721			−0.494361	+	0.869257i	$0.664598\pi$
$212$	5.77488	−	3.33413i	0.396621	−	0.228989i
$213$		0			0
$214$	−5.75680	+	9.97106i	−0.393527	+	0.681608i
$215$		0			0
$216$		0			0
$217$	−19.7009	+	11.6728i	−1.33739	+	0.792403i
$218$			2.00000i			0.135457i
$219$		0			0
$220$		0			0
$221$	34.7319	+	20.0524i	2.33632	+	1.34887i
$222$		0			0
$223$			13.5975i			0.910557i	0.890349	+	0.455279i	$0.150460\pi$
$223$			13.5975i			0.910557i	−0.890349	+	0.455279i	$0.849540\pi$
$224$	2.27621	−	1.34866i	0.152086	−	0.0901109i
$225$		0			0
$226$	−6.69375	−	11.5939i	−0.445261	−	0.771215i
$227$	−6.17797	+	10.7006i	−0.410046	+	0.710221i	−0.994894	−	0.100922i	$-0.967821\pi$
$227$	−6.17797	+	10.7006i	−0.410046	+	0.710221i	0.584848	+	0.811143i	$0.301154\pi$
$228$		0			0
$229$	2.09008	−	1.20671i	0.138116	−	0.0797414i	−0.429350	−	0.903138i	$-0.641257\pi$
$229$	2.09008	−	1.20671i	0.138116	−	0.0797414i	0.567466	+	0.823397i	$0.307924\pi$
$230$		0			0
$231$		0			0
$232$	1.35052			0.0886660
$233$	−11.1506	+	6.43780i	−0.730500	+	0.421754i	−0.818605	−	0.574357i	$-0.805252\pi$
$233$	−11.1506	+	6.43780i	−0.730500	+	0.421754i	0.0881051	+	0.996111i	$0.471919\pi$
$234$		0			0
$235$		0			0
$236$	0.798110	+	1.38237i	0.0519525	+	0.0899844i
$237$		0			0
$238$	−15.0415	−	8.45929i	−0.974997	−	0.548334i
$239$		−	27.2546i		−	1.76296i	−0.472226	−	0.881478i	$-0.656549\pi$
$239$		−	27.2546i		−	1.76296i	0.472226	−	0.881478i	$-0.343451\pi$
$240$		0			0
$241$	2.26690	+	1.30880i	0.146024	+	0.0843070i	0.571232	−	0.820789i	$-0.306466\pi$
$241$	2.26690	+	1.30880i	0.146024	+	0.0843070i	−0.425208	+	0.905096i	$0.639799\pi$
$242$	8.10050	+	4.67683i	0.520720	+	0.300638i
$243$		0			0
$244$			6.35361i			0.406748i
$245$		0			0
$246$		0			0
$247$	18.5614	+	32.1492i	1.18103	+	2.04561i
$248$	4.32758	−	7.49558i	0.274801	−	0.475970i
$249$		0			0
$250$		0			0
$251$	−26.7173			−1.68638			−0.843190	−	0.537615i	$-0.819325\pi$
$251$	−26.7173			−1.68638			−0.843190	+	0.537615i	$0.819325\pi$
$252$		0			0
$253$	−3.69426			−0.232256
$254$	4.89575	−	2.82656i	0.307187	−	0.177354i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.28063	−	9.14632i	−0.329397	−	0.570532i	0.652996	−	0.757362i	$-0.273512\pi$
$257$	−5.28063	−	9.14632i	−0.329397	−	0.570532i	−0.982392	+	0.186830i	$0.940179\pi$
$258$		0			0
$259$	25.2225	−	0.284743i	1.56725	−	0.0176930i
$260$		0			0
$261$		0			0
$262$	−10.7970	−	6.23366i	−0.667042	−	0.385117i
$263$	7.21550	+	4.16587i	0.444927	+	0.256879i	0.705685	−	0.708526i	$-0.250639\pi$
$263$	7.21550	+	4.16587i	0.444927	+	0.256879i	−0.260759	+	0.965404i	$0.583973\pi$
$264$		0			0
$265$		0			0
$266$	−8.14259	−	13.7427i	−0.499254	−	0.842621i
$267$		0			0
$268$	2.69731	+	4.67188i	0.164765	+	0.285381i
$269$	−7.14171	+	12.3698i	−0.435438	+	0.754201i	−0.997331	−	0.0730091i	$-0.976740\pi$
$269$	−7.14171	+	12.3698i	−0.435438	+	0.754201i	0.561893	+	0.827210i	$0.310073\pi$
$270$		0			0
$271$	−6.58566	+	3.80223i	−0.400050	+	0.230969i	−0.686506	−	0.727125i	$-0.740856\pi$
$271$	−6.58566	+	3.80223i	−0.400050	+	0.230969i	0.286456	+	0.958094i	$0.407523\pi$
$272$	6.52257			0.395489
$273$		0			0
$274$	0.0509686			0.00307912
$275$		0			0
$276$		0			0
$277$	6.02002	−	10.4270i	0.361708	−	0.626497i	−0.626534	−	0.779394i	$-0.715527\pi$
$277$	6.02002	−	10.4270i	0.361708	−	0.626497i	0.988242	+	0.152897i	$0.0488604\pi$
$278$	0.525345	+	0.909924i	0.0315081	+	0.0545736i
$279$		0			0
$280$		0			0
$281$		−	12.7879i		−	0.762861i	−0.924397	−	0.381431i	$-0.875431\pi$
$281$		−	12.7879i		−	0.762861i	0.924397	−	0.381431i	$-0.124569\pi$
$282$		0			0
$283$	−13.4685	−	7.77607i	−0.800622	−	0.462239i	0.0430666	−	0.999072i	$-0.486287\pi$
$283$	−13.4685	−	7.77607i	−0.800622	−	0.462239i	−0.843689	+	0.536833i	$0.819621\pi$
$284$	13.5781	+	7.83934i	0.805715	+	0.465180i
$285$		0			0
$286$		−	7.88931i		−	0.466505i
$287$	−11.3061	+	20.1034i	−0.667376	+	1.18667i
$288$		0			0
$289$	−12.7719	−	22.1216i	−0.751290	−	1.30127i
$290$		0			0
$291$		0			0
$292$	10.7532	−	6.20837i	0.629284	−	0.363317i
$293$	−11.5536			−0.674967			−0.337483	−	0.941331i	$-0.609576\pi$
$293$	−11.5536			−0.674967			−0.337483	+	0.941331i	$0.609576\pi$
$294$		0			0
$295$		0			0
$296$	−8.25652	+	4.76690i	−0.479900	+	0.277071i
$297$		0			0
$298$	4.11153	−	7.12137i	0.238174	−	0.412530i
$299$	−8.85148	−	15.3312i	−0.511894	−	0.886627i
$300$		0			0
$301$	−6.94969	+	12.3573i	−0.400573	+	0.712263i
$302$			4.26715i			0.245547i
$303$		0			0
$304$	5.22868	+	3.01878i	0.299885	+	0.173139i
$305$		0			0
$306$		0			0
$307$		−	2.57617i		−	0.147030i	−0.997294	−	0.0735150i	$-0.976578\pi$
$307$		−	2.57617i		−	0.147030i	0.997294	−	0.0735150i	$-0.0234217\pi$
$308$	0.0383219	+	3.39455i	0.00218359	+	0.193422i
$309$		0			0
$310$		0			0
$311$	−12.3570	+	21.4030i	−0.700702	+	1.21365i	0.267519	+	0.963553i	$0.413796\pi$
$311$	−12.3570	+	21.4030i	−0.700702	+	1.21365i	−0.968220	+	0.250098i	$0.919537\pi$
$312$		0			0
$313$	7.79573	−	4.50087i	0.440641	−	0.254404i	−0.263229	−	0.964733i	$-0.584787\pi$
$313$	7.79573	−	4.50087i	0.440641	−	0.254404i	0.703869	+	0.710329i	$0.251454\pi$
$314$	−4.83203			−0.272687
$315$		0			0
$316$	11.1819			0.629028
$317$	−20.7031	+	11.9529i	−1.16280	+	0.671344i	−0.951974	−	0.306180i	$-0.900949\pi$
$317$	−20.7031	+	11.9529i	−1.16280	+	0.671344i	−0.210828	+	0.977523i	$0.567616\pi$
$318$		0			0
$319$	−0.866426	+	1.50069i	−0.0485106	+	0.0840227i
$320$		0			0
$321$		0			0
$322$	3.88301	+	6.55359i	0.216392	+	0.365217i
$323$		−	39.3804i		−	2.19118i
$324$		0			0
$325$		0			0
$326$	9.31256	+	5.37661i	0.515775	+	0.297783i
$327$		0			0
$328$		−	8.71759i		−	0.481349i
$329$	−2.13279	+	0.0240776i	−0.117585	+	0.00132744i
$330$		0			0
$331$	−2.18364	−	3.78217i	−0.120024	−	0.207887i	0.799753	−	0.600329i	$-0.204964\pi$
$331$	−2.18364	−	3.78217i	−0.120024	−	0.207887i	−0.919777	+	0.392442i	$0.871630\pi$
$332$	−1.87246	+	3.24320i	−0.102765	+	0.177994i
$333$		0			0
$334$	16.3910	−	9.46334i	0.896874	−	0.517811i
$335$		0			0
$336$		0			0
$337$	19.5159			1.06310			0.531549	−	0.847028i	$-0.321610\pi$
$337$	19.5159			1.06310			0.531549	+	0.847028i	$0.321610\pi$
$338$	21.4824	−	12.4029i	1.16849	−	0.674627i
$339$		0			0
$340$		0			0
$341$	5.55271	+	9.61758i	0.300696	+	0.520821i
$342$		0			0
$343$	−18.5096	+	0.627092i	−0.999427	+	0.0338598i
$344$		−	5.35859i		−	0.288916i
$345$		0			0
$346$	10.2568	+	5.92176i	0.551409	+	0.318356i
$347$	−23.3088	−	13.4574i	−1.25128	−	0.722429i	−0.279919	−	0.960024i	$-0.590308\pi$
$347$	−23.3088	−	13.4574i	−1.25128	−	0.722429i	−0.971364	+	0.237595i	$0.923641\pi$
$348$		0			0
$349$		−	10.3821i		−	0.555741i	−0.960619	−	0.277870i	$-0.910371\pi$
$349$		−	10.3821i		−	0.555741i	0.960619	−	0.277870i	$-0.0896286\pi$
$350$		0			0
$351$		0			0
$352$	−0.641550	−	1.11120i	−0.0341947	−	0.0592270i
$353$	0.0844756	−	0.146316i	0.00449618	−	0.00778761i	−0.863769	−	0.503889i	$-0.831902\pi$
$353$	0.0844756	−	0.146316i	0.00449618	−	0.00778761i	0.868265	+	0.496101i	$0.165235\pi$
$354$		0			0
$355$		0			0
$356$	3.63941			0.192889
$357$		0			0
$358$	3.78561			0.200075
$359$	−32.6198	+	18.8330i	−1.72161	+	0.993970i	−0.805975	+	0.591949i	$0.798359\pi$
$359$	−32.6198	+	18.8330i	−1.72161	+	0.993970i	−0.915631	+	0.402021i	$0.868308\pi$
$360$		0			0
$361$	8.72604	−	15.1139i	0.459265	−	0.795471i
$362$	−9.50166	−	16.4574i	−0.499396	−	0.864979i
$363$		0			0
$364$	−13.9956	+	8.29240i	−0.733568	+	0.434640i
$365$		0			0
$366$		0			0
$367$	−13.1253	−	7.57787i	−0.685133	−	0.395562i	0.116653	−	0.993173i	$-0.462783\pi$
$367$	−13.1253	−	7.57787i	−0.685133	−	0.395562i	−0.801786	+	0.597611i	$0.796117\pi$
$368$	−2.49343	−	1.43958i	−0.129979	−	0.0750435i
$369$		0			0
$370$		0			0
$371$	15.1784	−	8.99319i	0.788021	−	0.466903i
$372$		0			0
$373$	6.02002	+	10.4270i	0.311705	+	0.539889i	0.978732	−	0.205145i	$-0.0657667\pi$
$373$	6.02002	+	10.4270i	0.311705	+	0.539889i	−0.667027	+	0.745034i	$0.732433\pi$
$374$	−4.18455	+	7.24785i	−0.216378	+	0.374778i
$375$		0			0
$376$	0.698165	−	0.403086i	0.0360051	−	0.0207876i
$377$	−8.30386			−0.427671
$378$		0			0
$379$	−18.0918			−0.929312			−0.464656	−	0.885491i	$-0.653822\pi$
$379$	−18.0918			−0.929312			−0.464656	+	0.885491i	$0.653822\pi$
$380$		0			0
$381$		0			0
$382$	−1.41421	+	2.44949i	−0.0723575	+	0.125327i
$383$	−14.5769	−	25.2480i	−0.744846	−	1.29011i	−0.950267	−	0.311437i	$-0.899190\pi$
$383$	−14.5769	−	25.2480i	−0.744846	−	1.29011i	0.205421	−	0.978674i	$-0.434144\pi$
$384$		0			0
$385$		0			0
$386$			3.53892i			0.180126i
$387$		0			0
$388$	−7.59347	−	4.38409i	−0.385500	−	0.222568i
$389$	17.0297	+	9.83207i	0.863438	+	0.498506i	0.865162	−	0.501493i	$-0.167216\pi$
$389$	17.0297	+	9.83207i	0.863438	+	0.498506i	−0.00172432	+	0.999999i	$0.500549\pi$
$390$		0			0
$391$			18.7796i			0.949723i
$392$	5.98162	−	3.63597i	0.302117	−	0.183644i
$393$		0			0
$394$	−1.18364	−	2.05012i	−0.0596309	−	0.103284i
$395$		0			0
$396$		0			0
$397$	−4.92295	+	2.84227i	−0.247076	+	0.142649i	−0.618425	−	0.785844i	$-0.712229\pi$
$397$	−4.92295	+	2.84227i	−0.247076	+	0.142649i	0.371349	+	0.928493i	$0.378895\pi$
$398$	−3.46410			−0.173640
$399$		0			0
$400$		0			0
$401$	8.84787	−	5.10832i	0.441842	−	0.255097i	−0.262537	−	0.964922i	$-0.584559\pi$
$401$	8.84787	−	5.10832i	0.441842	−	0.255097i	0.704378	+	0.709825i	$0.251226\pi$
$402$		0			0
$403$	−26.6087	+	46.0876i	−1.32547	+	2.29579i
$404$	0.853270	+	1.47791i	0.0424518	+	0.0735286i
$405$		0			0
$406$	3.57291	−	0.0403355i	0.177321	−	0.00200182i
$407$		−	12.2328i		−	0.606359i
$408$		0			0
$409$	−12.0969	−	6.98414i	−0.598153	−	0.345344i	0.170162	−	0.985416i	$-0.445571\pi$
$409$	−12.0969	−	6.98414i	−0.598153	−	0.345344i	−0.768314	+	0.640073i	$0.778904\pi$
$410$		0			0
$411$		0			0
$412$		−	10.3644i		−	0.510617i
$413$	2.15275	+	3.63333i	0.105930	+	0.178784i
$414$		0			0
$415$		0			0
$416$	3.07432	−	5.32488i	0.150731	−	0.261074i
$417$		0			0
$418$	−6.70891	+	3.87339i	−0.328144	+	0.189454i
$419$	11.3181			0.552924			0.276462	−	0.961025i	$-0.410838\pi$
$419$	11.3181			0.552924			0.276462	+	0.961025i	$0.410838\pi$
$420$		0			0
$421$	−13.9099			−0.677928			−0.338964	−	0.940799i	$-0.610077\pi$
$421$	−13.9099			−0.677928			−0.338964	+	0.940799i	$0.610077\pi$
$422$	12.4379	−	7.18100i	0.605466	−	0.349566i
$423$		0			0
$424$	−3.33413	+	5.77488i	−0.161920	+	0.280453i
$425$		0			0
$426$		0			0
$427$	0.189761	+	16.8090i	0.00918318	+	0.813445i
$428$		−	11.5136i		−	0.556531i
$429$		0			0
$430$		0			0
$431$	−22.5947	−	13.0451i	−1.08835	−	0.628359i	−0.155213	−	0.987881i	$-0.549606\pi$
$431$	−22.5947	−	13.0451i	−1.08835	−	0.628359i	−0.933137	+	0.359522i	$0.882940\pi$
$432$		0			0
$433$		−	8.42614i		−	0.404935i	−0.979289	−	0.202467i	$-0.935104\pi$
$433$		−	8.42614i		−	0.404935i	0.979289	−	0.202467i	$-0.0648960\pi$
$434$	11.2251	−	19.9594i	0.538822	−	0.958083i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−8.69157	+	15.0542i	−0.415774	+	0.720142i
$438$		0			0
$439$	23.9529	−	13.8292i	1.14321	−	0.660033i	0.195987	−	0.980606i	$-0.437209\pi$
$439$	23.9529	−	13.8292i	1.14321	−	0.660033i	0.947224	+	0.320573i	$0.103875\pi$
$440$		0			0
$441$		0			0
$442$	−40.1049			−1.90759
$443$	2.04142	−	1.17861i	0.0969906	−	0.0559975i	−0.450720	−	0.892665i	$-0.648833\pi$
$443$	2.04142	−	1.17861i	0.0969906	−	0.0559975i	0.547711	+	0.836668i	$0.315499\pi$
$444$		0			0
$445$		0			0
$446$	−6.79876	−	11.7758i	−0.321931	−	0.557600i
$447$		0			0
$448$	−1.29693	+	2.30608i	−0.0612740	+	0.108952i
$449$			12.8021i			0.604169i	0.953281	+	0.302084i	$0.0976824\pi$
$449$			12.8021i			0.604169i	−0.953281	+	0.302084i	$0.902318\pi$
$450$		0			0
$451$	9.68696	+	5.59277i	0.456141	+	0.263353i
$452$	11.5939	+	6.69375i	0.545332	+	0.314847i
$453$		0			0
$454$		−	12.3559i		−	0.579893i
$455$		0			0
$456$		0			0
$457$	17.2621	+	29.8989i	0.807488	+	1.39861i	0.914599	+	0.404363i	$0.132507\pi$
$457$	17.2621	+	29.8989i	0.807488	+	1.39861i	−0.107111	+	0.994247i	$0.534160\pi$
$458$	−1.20671	+	2.09008i	−0.0563857	+	0.0976628i
$459$		0			0
$460$		0			0
$461$	−20.2692			−0.944032			−0.472016	−	0.881590i	$-0.656474\pi$
$461$	−20.2692			−0.944032			−0.472016	+	0.881590i	$0.656474\pi$
$462$		0			0
$463$	13.1246			0.609952			0.304976	−	0.952360i	$-0.401352\pi$
$463$	13.1246			0.609952			0.304976	+	0.952360i	$0.401352\pi$
$464$	−1.16959	+	0.675260i	−0.0542966	+	0.0313482i
$465$		0			0
$466$	6.43780	−	11.1506i	0.298225	−	0.516541i
$467$	−0.765836	−	1.32647i	−0.0354387	−	0.0613816i	0.847762	−	0.530377i	$-0.177950\pi$
$467$	−0.765836	−	1.32647i	−0.0354387	−	0.0613816i	−0.883201	+	0.468995i	$0.844616\pi$
$468$		0			0
$469$	7.27550	+	12.2793i	0.335951	+	0.567005i
$470$		0			0
$471$		0			0
$472$	−1.38237	−	0.798110i	−0.0636286	−	0.0367360i
$473$	5.95444	+	3.43780i	0.273786	+	0.158070i
$474$		0			0
$475$		0			0
$476$	17.2560	−	0.194807i	0.790927	−	0.00892896i
$477$		0			0
$478$	13.6273	+	23.6032i	0.623299	+	1.07959i
$479$	14.6585	−	25.3893i	0.669764	−	1.16007i	−0.308205	−	0.951320i	$-0.599728\pi$
$479$	14.6585	−	25.3893i	0.669764	−	1.16007i	0.977970	−	0.208746i	$-0.0669382\pi$
$480$		0			0
$481$	50.7663	−	29.3100i	2.31475	−	1.33642i
$482$	−2.61759			−0.119228
$483$		0			0
$484$	−9.35366			−0.425166
$485$		0			0
$486$		0			0
$487$	4.09770	−	7.09743i	0.185685	−	0.321615i	−0.758122	−	0.652112i	$-0.773883\pi$
$487$	4.09770	−	7.09743i	0.185685	−	0.321615i	0.943807	+	0.330497i	$0.107216\pi$
$488$	−3.17681	−	5.50239i	−0.143807	−	0.249082i
$489$		0			0
$490$		0			0
$491$		−	40.4383i		−	1.82495i	−0.409129	−	0.912477i	$-0.634167\pi$
$491$		−	40.4383i		−	1.82495i	0.409129	−	0.912477i	$-0.365833\pi$
$492$		0			0
$493$	7.62869	+	4.40443i	0.343579	+	0.198366i
$494$	−32.1492	−	18.5614i	−1.44646	−	0.835116i
$495$		0			0
$496$			8.65515i			0.388628i
$497$	36.1562	+	20.3341i	1.62183	+	0.912109i
$498$		0			0
$499$	8.72450	+	15.1113i	0.390562	+	0.676474i	0.992524	−	0.122051i	$-0.0389473\pi$
$499$	8.72450	+	15.1113i	0.390562	+	0.676474i	−0.601961	+	0.798525i	$0.705614\pi$
$500$		0			0
$501$		0			0
$502$	23.1379	−	13.3586i	1.03269	−	0.596226i
$503$	−1.91949			−0.0855860			−0.0427930	−	0.999084i	$-0.513626\pi$
$503$	−1.91949			−0.0855860			−0.0427930	+	0.999084i	$0.513626\pi$
$504$		0			0
$505$		0			0
$506$	3.19932	−	1.84713i	0.142227	−	0.0821149i
$507$		0			0
$508$	−2.82656	+	4.89575i	−0.125408	+	0.217214i
$509$	−5.54549	−	9.60508i	−0.245800	−	0.425737i	0.716556	−	0.697529i	$-0.245717\pi$
$509$	−5.54549	−	9.60508i	−0.245800	−	0.425737i	−0.962356	+	0.271792i	$0.912384\pi$
$510$		0			0
$511$	28.2631	−	16.7459i	1.25029	−	0.740796i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	9.14632	+	5.28063i	0.403427	+	0.232919i
$515$		0			0
$516$		0			0
$517$			1.03440i			0.0454928i
$518$	−21.7009	+	12.8578i	−0.953484	+	0.564941i
$519$		0			0
$520$		0			0
$521$	19.8706	−	34.4168i	0.870546	−	1.50783i	0.00911254	−	0.999958i	$-0.497099\pi$
$521$	19.8706	−	34.4168i	0.870546	−	1.50783i	0.861433	−	0.507871i	$-0.169567\pi$
$522$		0			0
$523$	27.0900	−	15.6404i	1.18456	−	0.683907i	0.227496	−	0.973779i	$-0.426946\pi$
$523$	27.0900	−	15.6404i	1.18456	−	0.683907i	0.957065	+	0.289872i	$0.0936129\pi$
$524$	12.4673			0.544638
$525$		0			0
$526$	−8.33174			−0.363281
$527$	48.8904	−	28.2269i	2.12970	−	1.22958i
$528$		0			0
$529$	−7.35519	+	12.7396i	−0.319791	+	0.553894i
$530$		0			0
$531$		0			0
$532$	13.9231	+	7.83026i	0.603641	+	0.339485i
$533$			53.6013i			2.32173i
$534$		0			0
$535$		0			0
$536$	−4.67188	−	2.69731i	−0.201795	−	0.116506i
$537$		0			0
$538$		−	14.2834i		−	0.615802i
$539$	0.202767	+	8.97941i	0.00873380	+	0.386771i
$540$		0			0
$541$	12.3987	+	21.4752i	0.533061	+	0.923290i	0.999254	+	0.0386065i	$0.0122919\pi$
$541$	12.3987	+	21.4752i	0.533061	+	0.923290i	−0.466193	+	0.884683i	$0.654375\pi$
$542$	3.80223	−	6.58566i	0.163320	−	0.282878i
$543$		0			0
$544$	−5.64871	+	3.26128i	−0.242186	+	0.139826i
$545$		0			0
$546$		0			0
$547$	−40.5380			−1.73328			−0.866640	−	0.498934i	$-0.833725\pi$
$547$	−40.5380			−1.73328			−0.866640	+	0.498934i	$0.833725\pi$
$548$	−0.0441401	+	0.0254843i	−0.00188557	+	0.00108863i
$549$		0			0
$550$		0			0
$551$	4.07692	+	7.06144i	0.173683	+	0.300827i
$552$		0			0
$553$	29.5825	−	0.333964i	1.25798	−	0.0142016i
$554$			12.0400i			0.511532i
$555$		0			0
$556$	−0.909924	−	0.525345i	−0.0385894	−	0.0222796i
$557$	−20.5650	−	11.8732i	−0.871367	−	0.503084i	−0.00356477	−	0.999994i	$-0.501135\pi$
$557$	−20.5650	−	11.8732i	−0.871367	−	0.503084i	−0.867802	+	0.496910i	$0.834468\pi$
$558$		0			0
$559$			32.9480i			1.39355i
$560$		0			0
$561$		0			0
$562$	6.39394	+	11.0746i	0.269712	+	0.467155i
$563$	−4.21434	+	7.29944i	−0.177613	+	0.307635i	−0.941062	−	0.338233i	$-0.890171\pi$
$563$	−4.21434	+	7.29944i	−0.177613	+	0.307635i	0.763449	+	0.645868i	$0.223504\pi$
$564$		0			0
$565$		0			0
$566$	15.5521			0.653705
$567$		0			0
$568$	−15.6787			−0.657863
$569$	20.3139	−	11.7283i	0.851605	−	0.491674i	−0.00958727	−	0.999954i	$-0.503052\pi$
$569$	20.3139	−	11.7283i	0.851605	−	0.491674i	0.861192	+	0.508280i	$0.169718\pi$
$570$		0			0
$571$	−7.67946	+	13.3012i	−0.321376	+	0.556639i	−0.980772	−	0.195157i	$-0.937479\pi$
$571$	−7.67946	+	13.3012i	−0.321376	+	0.556639i	0.659397	+	0.751795i	$0.270812\pi$
$572$	3.94466	+	6.83235i	0.164934	+	0.285675i
$573$		0			0
$574$	−0.260365	−	23.0631i	−0.0108674	−	0.962636i
$575$		0			0
$576$		0			0
$577$	−12.3329	−	7.12041i	−0.513426	−	0.296426i	0.220815	−	0.975316i	$-0.429128\pi$
$577$	−12.3329	−	7.12041i	−0.513426	−	0.296426i	−0.734241	+	0.678889i	$0.762462\pi$
$578$	22.1216	+	12.7719i	0.920139	+	0.531242i
$579$		0			0
$580$		0			0
$581$	−4.85690	+	8.63609i	−0.201498	+	0.358285i
$582$		0			0
$583$	−4.27802	−	7.40975i	−0.177178	−	0.306881i
$584$	−6.20837	+	10.7532i	−0.256904	+	0.444971i
$585$		0			0
$586$	10.0057	−	5.77679i	0.413331	−	0.238637i
$587$	−12.5249			−0.516958			−0.258479	−	0.966017i	$-0.583221\pi$
$587$	−12.5249			−0.516958			−0.258479	+	0.966017i	$0.583221\pi$
$588$		0			0
$589$	52.2560			2.15317
$590$		0			0
$591$		0			0
$592$	4.76690	−	8.25652i	0.195919	−	0.339341i
$593$	7.35750	+	12.7436i	0.302136	+	0.523316i	0.976620	−	0.214975i	$-0.0689669\pi$
$593$	7.35750	+	12.7436i	0.302136	+	0.523316i	−0.674483	+	0.738290i	$0.735634\pi$
$594$		0			0
$595$		0			0
$596$			8.22305i			0.336829i
$597$		0			0
$598$	15.3312	+	8.85148i	0.626940	+	0.361964i
$599$	23.9304	+	13.8162i	0.977769	+	0.564515i	0.901596	−	0.432579i	$-0.142396\pi$
$599$	23.9304	+	13.8162i	0.977769	+	0.564515i	0.0761732	+	0.997095i	$0.475730\pi$
$600$		0			0
$601$			8.82137i			0.359831i	0.983682	+	0.179916i	$0.0575825\pi$
$601$			8.82137i			0.359831i	−0.983682	+	0.179916i	$0.942418\pi$
$602$	−0.160043	−	14.1766i	−0.00652286	−	0.577794i
$603$		0			0
$604$	−2.13357	−	3.69546i	−0.0868139	−	0.150366i
$605$		0			0
$606$		0			0
$607$	22.9803	−	13.2677i	0.932743	−	0.538519i	0.0450649	−	0.998984i	$-0.485651\pi$
$607$	22.9803	−	13.2677i	0.932743	−	0.538519i	0.887678	+	0.460465i	$0.152317\pi$
$608$	−6.03756			−0.244855
$609$		0			0
$610$		0			0
$611$	−4.29276	+	2.47843i	−0.173667	+	0.100266i
$612$		0			0
$613$	0.456842	−	0.791273i	0.0184517	−	0.0319592i	−0.856652	−	0.515894i	$-0.827460\pi$
$613$	0.456842	−	0.791273i	0.0184517	−	0.0319592i	0.875104	+	0.483935i	$0.160793\pi$
$614$	1.28809	+	2.23103i	0.0519830	+	0.0900371i
$615$		0			0
$616$	−1.73046	−	2.92060i	−0.0697223	−	0.117674i
$617$			35.0558i			1.41129i	0.708565	+	0.705646i	$0.249343\pi$
$617$			35.0558i			1.41129i	−0.708565	+	0.705646i	$0.750657\pi$
$618$		0			0
$619$	−16.5382	−	9.54835i	−0.664727	−	0.383781i	0.129348	−	0.991599i	$-0.458711\pi$
$619$	−16.5382	−	9.54835i	−0.664727	−	0.383781i	−0.794076	+	0.607819i	$0.792045\pi$
$620$		0			0
$621$		0			0
$622$		−	24.7140i		−	0.990942i
$623$	9.62837	−	0.108697i	0.385753	−	0.00435485i
$624$		0			0
$625$		0			0
$626$	−4.50087	+	7.79573i	−0.179891	+	0.311580i
$627$		0			0
$628$	4.18466	−	2.41601i	0.166986	−	0.0964095i
$629$	−62.1849			−2.47947
$630$		0			0
$631$	21.5350			0.857296			0.428648	−	0.903472i	$-0.358990\pi$
$631$	21.5350			0.857296			0.428648	+	0.903472i	$0.358990\pi$
$632$	−9.68377	+	5.59093i	−0.385200	+	0.222395i
$633$		0			0
$634$	11.9529	−	20.7031i	0.474712	−	0.822225i
$635$		0			0
$636$		0			0
$637$	−36.7788	+	22.3562i	−1.45723	+	0.885786i
$638$		−	1.73285i		−	0.0686043i
$639$		0			0
$640$		0			0
$641$	−28.6767	−	16.5565i	−1.13266	−	0.653943i	−0.188060	−	0.982158i	$-0.560220\pi$
$641$	−28.6767	−	16.5565i	−1.13266	−	0.653943i	−0.944603	+	0.328214i	$0.893553\pi$
$642$		0			0
$643$			3.31191i			0.130609i	0.997865	+	0.0653044i	$0.0208018\pi$
$643$			3.31191i			0.130609i	−0.997865	+	0.0653044i	$0.979198\pi$
$644$	−6.63958	−	3.73407i	−0.261636	−	0.147143i
$645$		0			0
$646$	19.6902	+	34.1044i	0.774700	+	1.34182i
$647$	11.6669	−	20.2077i	0.458674	−	0.794447i	−0.540217	−	0.841526i	$-0.681658\pi$
$647$	11.6669	−	20.2077i	0.458674	−	0.794447i	0.998891	+	0.0470789i	$0.0149912\pi$
$648$		0			0
$649$	1.77371	−	1.02405i	0.0696244	−	0.0401977i
$650$		0			0
$651$		0			0
$652$	−10.7532			−0.421128
$653$	−15.1211	+	8.73019i	−0.591735	+	0.341639i	−0.765783	−	0.643099i	$-0.777649\pi$
$653$	−15.1211	+	8.73019i	−0.591735	+	0.341639i	0.174048	+	0.984737i	$0.444315\pi$
$654$		0			0
$655$		0			0
$656$	4.35880	+	7.54966i	0.170182	+	0.294765i
$657$		0			0
$658$	1.83501	−	1.08725i	0.0715363	−	0.0423854i
$659$		−	1.29864i		−	0.0505877i	−0.999680	−	0.0252939i	$-0.991948\pi$
$659$		−	1.29864i		−	0.0505877i	0.999680	−	0.0252939i	$-0.00805215\pi$
$660$		0			0
$661$	4.39869	+	2.53959i	0.171089	+	0.0987785i	0.583099	−	0.812401i	$-0.301840\pi$
$661$	4.39869	+	2.53959i	0.171089	+	0.0987785i	−0.412010	+	0.911179i	$0.635173\pi$
$662$	3.78217	+	2.18364i	0.146998	+	0.0848695i
$663$		0			0
$664$		−	3.74493i		−	0.145331i
$665$		0			0
$666$		0			0
$667$	−1.94419	−	3.36743i	−0.0752793	−	0.130387i
$668$	−9.46334	+	16.3910i	−0.366147	+	0.634186i
$669$		0			0
$670$		0			0
$671$	8.15232			0.314717
$672$		0			0
$673$	−18.4124			−0.709747			−0.354873	−	0.934914i	$-0.615476\pi$
$673$	−18.4124			−0.709747			−0.354873	+	0.934914i	$0.615476\pi$
$674$	−16.9012	+	9.75794i	−0.651012	+	0.375862i
$675$		0			0
$676$	−12.4029	+	21.4824i	−0.477033	+	0.826246i
$677$	−20.6397	−	35.7491i	−0.793250	−	1.37395i	−0.923945	−	0.382526i	$-0.875054\pi$
$677$	−20.6397	−	35.7491i	−0.793250	−	1.37395i	0.130695	−	0.991423i	$-0.458279\pi$
$678$		0			0
$679$	−20.2201	−	11.3717i	−0.775976	−	0.436405i
$680$		0			0
$681$		0			0
$682$	−9.61758	−	5.55271i	−0.368276	−	0.212624i
$683$	−19.9007	−	11.4896i	−0.761477	−	0.439639i	0.0683485	−	0.997662i	$-0.478227\pi$
$683$	−19.9007	−	11.4896i	−0.761477	−	0.439639i	−0.829826	+	0.558022i	$0.811560\pi$
$684$		0			0
$685$		0			0
$686$	15.7163	−	9.79790i	0.600050	−	0.374085i
$687$		0			0
$688$	2.67929	+	4.64067i	0.102147	+	0.176924i
$689$	20.5004	−	35.5077i	0.781001	−	1.35273i
$690$		0			0
$691$	11.0048	−	6.35361i	0.418642	−	0.241703i	−0.275854	−	0.961199i	$-0.588961\pi$
$691$	11.0048	−	6.35361i	0.418642	−	0.241703i	0.694496	+	0.719497i	$0.255627\pi$
$692$	−11.8435			−0.450223
$693$		0			0
$694$	26.9147			1.02167
$695$		0			0
$696$		0			0
$697$	28.4305	−	49.2431i	1.07688	−	1.86522i
$698$	5.19105	+	8.99116i	0.196484	+	0.340320i
$699$		0			0
$700$		0			0
$701$		−	26.5441i		−	1.00256i	−0.865286	−	0.501279i	$-0.832863\pi$
$701$		−	26.5441i		−	1.00256i	0.865286	−	0.501279i	$-0.167137\pi$
$702$		0			0
$703$	−49.8492	−	28.7804i	−1.88010	−	1.08548i
$704$	1.11120	+	0.641550i	0.0418798	+	0.0241793i
$705$		0			0
$706$			0.168951i			0.00635856i
$707$	2.30154	+	3.88444i	0.0865582	+	0.146089i
$708$		0			0
$709$	21.1766	+	36.6789i	0.795303	+	1.37751i	0.922646	+	0.385647i	$0.126022\pi$
$709$	21.1766	+	36.6789i	0.795303	+	1.37751i	−0.127343	+	0.991859i	$0.540645\pi$
$710$		0			0
$711$		0			0
$712$	−3.15183	+	1.81971i	−0.118120	+	0.0681964i
$713$	−24.9196			−0.933248
$714$		0			0
$715$		0			0
$716$	−3.27843	+	1.89280i	−0.122521	+	0.0707374i
$717$		0			0
$718$	18.8330	−	32.6198i	0.702843	−	1.21736i
$719$	11.9507	+	20.6992i	0.445686	+	0.771951i	0.998100	−	0.0616189i	$-0.0196263\pi$
$719$	11.9507	+	20.6992i	0.445686	+	0.771951i	−0.552413	+	0.833570i	$0.686293\pi$
$720$		0			0
$721$	−0.309550	−	27.4199i	−0.0115282	−	1.02117i
$722$			17.4521i			0.649499i
$723$		0			0
$724$	16.4574	+	9.50166i	0.611633	+	0.353126i
$725$		0			0
$726$		0			0
$727$		−	22.4529i		−	0.832731i	−0.909197	−	0.416365i	$-0.863304\pi$
$727$		−	22.4529i		−	0.832731i	0.909197	−	0.416365i	$-0.136696\pi$
$728$	7.97433	−	14.1792i	0.295548	−	0.525517i
$729$		0			0
$730$		0			0
$731$	17.4759	−	30.2691i	0.646368	−	1.11954i
$732$		0			0
$733$	23.8547	−	13.7725i	0.881094	−	0.508700i	0.0100750	−	0.999949i	$-0.496793\pi$
$733$	23.8547	−	13.7725i	0.881094	−	0.508700i	0.871019	+	0.491249i	$0.163460\pi$
$734$	15.1557			0.559409
$735$		0			0
$736$	2.87917			0.106128
$737$	5.99449	−	3.46092i	0.220810	−	0.127485i
$738$		0			0
$739$	15.5456	−	26.9258i	0.571856	−	0.990483i	−0.424520	−	0.905419i	$-0.639557\pi$
$739$	15.5456	−	26.9258i	0.571856	−	0.990483i	0.996375	−	0.0850646i	$-0.0271097\pi$
$740$		0			0
$741$		0			0
$742$	−8.64824	+	15.3775i	−0.317487	+	0.564526i
$743$			1.12610i			0.0413127i	0.999787	+	0.0206564i	$0.00657559\pi$
$743$			1.12610i			0.0413127i	−0.999787	+	0.0206564i	$0.993424\pi$
$744$		0			0
$745$		0			0
$746$	−10.4270	−	6.02002i	−0.381759	−	0.220409i
$747$		0			0
$748$		−	8.36910i		−	0.306005i
$749$	−0.343872	−	30.4602i	−0.0125648	−	1.11299i
$750$		0			0
$751$	4.77108	+	8.26375i	0.174099	+	0.301549i	0.939849	−	0.341590i	$-0.110965\pi$
$751$	4.77108	+	8.26375i	0.174099	+	0.301549i	−0.765750	+	0.643138i	$0.777632\pi$
$752$	−0.403086	+	0.698165i	−0.0146990	+	0.0254595i
$753$		0			0
$754$	7.19135	−	4.15193i	0.261894	−	0.151204i
$755$		0			0
$756$		0			0
$757$	33.1687			1.20554			0.602768	−	0.797917i	$-0.294065\pi$
$757$	33.1687			1.20554			0.602768	+	0.797917i	$0.294065\pi$
$758$	15.6679	−	9.04589i	0.569085	−	0.328562i
$759$		0			0
$760$		0			0
$761$	2.17122	+	3.76067i	0.0787068	+	0.136324i	0.902692	−	0.430287i	$-0.141588\pi$
$761$	2.17122	+	3.76067i	0.0787068	+	0.136324i	−0.823985	+	0.566611i	$0.808254\pi$
$762$		0			0
$763$	−2.69731	−	4.55242i	−0.0976493	−	0.164809i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$	25.2480	+	14.5769i	0.912246	+	0.526685i
$767$	8.49967	+	4.90729i	0.306905	+	0.177192i
$768$		0			0
$769$			46.1795i			1.66528i	0.553818	+	0.832638i	$0.313170\pi$
$769$			46.1795i			1.66528i	−0.553818	+	0.832638i	$0.686830\pi$
$770$		0			0
$771$		0			0
$772$	−1.76946	−	3.06479i	−0.0636842	−	0.110304i
$773$	−8.98723	+	15.5663i	−0.323248	+	0.559883i	−0.981156	−	0.193216i	$-0.938108\pi$
$773$	−8.98723	+	15.5663i	−0.323248	+	0.559883i	0.657908	+	0.753098i	$0.271442\pi$
$774$		0			0
$775$		0			0
$776$	8.76818			0.314759
$777$		0			0
$778$	−19.6641			−0.704994
$779$	45.5815	−	26.3165i	1.63313	−	0.942886i
$780$		0			0
$781$	10.0587	−	17.4221i	0.359927	−	0.623412i
$782$	−9.38978	−	16.2636i	−0.335778	−	0.581584i
$783$		0			0
$784$	−3.36225	+	6.13965i	−0.120080	+	0.219273i
$785$		0			0
$786$		0			0
$787$	−11.9873	−	6.92087i	−0.427301	−	0.246702i	0.270895	−	0.962609i	$-0.412680\pi$
$787$	−11.9873	−	6.92087i	−0.427301	−	0.246702i	−0.698196	+	0.715907i	$0.746014\pi$
$788$	2.05012	+	1.18364i	0.0730326	+	0.0421654i
$789$		0			0
$790$		0			0
$791$	30.8726	+	17.3626i	1.09770	+	0.617342i
$792$		0			0
$793$	19.5330	+	33.8322i	0.693638	+	1.20142i
$794$	2.84227	−	4.92295i	0.100868	−	0.174709i
$795$		0			0
$796$	3.00000	−	1.73205i	0.106332	−	0.0613909i
$797$	7.46138			0.264296			0.132148	−	0.991230i	$-0.457813\pi$
$797$	7.46138			0.264296			0.132148	+	0.991230i	$0.457813\pi$
$798$		0			0
$799$	5.25831			0.186026
$800$		0			0
$801$		0			0
$802$	−5.10832	+	8.84787i	−0.180381	+	0.312429i
$803$	−7.96596	−	13.7974i	−0.281113	−	0.486901i
$804$		0			0
$805$		0			0
$806$		−	53.2174i		−	1.87450i
$807$		0			0
$808$	−1.47791	−	0.853270i	−0.0519926	−	0.0300179i
$809$	1.28750	+	0.743340i	0.0452662	+	0.0261344i	0.522462	−	0.852662i	$-0.325014\pi$
$809$	1.28750	+	0.743340i	0.0452662	+	0.0261344i	−0.477196	+	0.878797i	$0.658347\pi$
$810$		0			0
$811$		−	31.5494i		−	1.10785i	−0.832567	−	0.553925i	$-0.813129\pi$
$811$		−	31.5494i		−	1.10785i	0.832567	−	0.553925i	$-0.186871\pi$
$812$	−3.07407	+	1.82139i	−0.107879	+	0.0639182i
$813$		0			0
$814$	6.11641	+	10.5939i	0.214380	+	0.371317i
$815$		0			0
$816$		0			0
$817$	28.0183	−	16.1764i	0.980237	−	0.565940i
$818$	13.9683			0.488390
$819$		0			0
$820$		0			0
$821$	−27.5430	+	15.9020i	−0.961257	+	0.554982i	−0.896560	−	0.442923i	$-0.853942\pi$
$821$	−27.5430	+	15.9020i	−0.961257	+	0.554982i	−0.0646976	+	0.997905i	$0.520608\pi$
$822$		0			0
$823$	18.3186	−	31.7287i	0.638545	−	1.10599i	−0.347207	−	0.937788i	$-0.612870\pi$
$823$	18.3186	−	31.7287i	0.638545	−	1.10599i	0.985752	−	0.168204i	$-0.0537967\pi$
$824$	5.18220	+	8.97583i	0.180530	+	0.312688i
$825$		0			0
$826$	−3.68100	−	2.07018i	−0.128078	−	0.0720308i
$827$			21.9864i			0.764541i	0.924050	+	0.382271i	$0.124858\pi$
$827$			21.9864i			0.764541i	−0.924050	+	0.382271i	$0.875142\pi$
$828$		0			0
$829$	21.0498	+	12.1531i	0.731090	+	0.422095i	0.818821	−	0.574049i	$-0.194628\pi$
$829$	21.0498	+	12.1531i	0.731090	+	0.422095i	−0.0877305	+	0.996144i	$0.527961\pi$
$830$		0			0
$831$		0			0
$832$			6.14864i			0.213166i
$833$	45.6463	−	1.03076i	1.58155	−	0.0357136i
$834$		0			0
$835$		0			0
$836$	3.87339	−	6.70891i	0.133964	−	0.232033i
$837$		0			0
$838$	−9.80175	+	5.65904i	−0.338596	+	0.195488i
$839$	−27.3914			−0.945655			−0.472827	−	0.881155i	$-0.656767\pi$
$839$	−27.3914			−0.945655			−0.472827	+	0.881155i	$0.656767\pi$
$840$		0			0
$841$	27.1761			0.937107
$842$	12.0463	−	6.95496i	0.415145	−	0.239684i
$843$		0			0
$844$	−7.18100	+	12.4379i	−0.247180	+	0.428129i
$845$		0			0
$846$		0			0
$847$	−24.7459	+	0.279362i	−0.850278	+	0.00959899i
$848$		−	6.66826i		−	0.228989i
$849$		0			0
$850$		0			0
$851$	23.7719	+	13.7247i	0.814890	+	0.470477i
$852$		0			0
$853$		−	22.6073i		−	0.774060i	−0.922067	−	0.387030i	$-0.873501\pi$
$853$		−	22.6073i		−	0.774060i	0.922067	−	0.387030i	$-0.126499\pi$
$854$	−8.56884	−	14.4622i	−0.293220	−	0.494885i
$855$		0			0
$856$	5.75680	+	9.97106i	0.196763	+	0.340804i
$857$	−23.9289	+	41.4461i	−0.817396	+	1.41577i	0.0901984	+	0.995924i	$0.471250\pi$
$857$	−23.9289	+	41.4461i	−0.817396	+	1.41577i	−0.907595	+	0.419848i	$0.862083\pi$
$858$		0			0
$859$	−41.5770	+	24.0045i	−1.41859	+	0.819022i	−0.996175	−	0.0873810i	$-0.972150\pi$
$859$	−41.5770	+	24.0045i	−1.41859	+	0.819022i	−0.422413	+	0.906403i	$0.638817\pi$
$860$		0			0
$861$		0			0
$862$	26.0901			0.888634
$863$	41.1855	−	23.7785i	1.40197	−	0.809428i	0.407376	−	0.913260i	$-0.366444\pi$
$863$	41.1855	−	23.7785i	1.40197	−	0.809428i	0.994595	+	0.103832i	$0.0331104\pi$
$864$		0			0
$865$		0			0
$866$	4.21307	+	7.29726i	0.143166	+	0.247971i
$867$		0			0
$868$	0.258500	+	22.8979i	0.00877406	+	0.777206i
$869$		−	14.3474i		−	0.486703i
$870$		0			0
$871$	28.7257	+	16.5848i	0.973334	+	0.561955i
$872$	1.73205	+	1.00000i	0.0586546	+	0.0338643i
$873$		0			0
$874$		−	17.3831i		−	0.587993i
$875$		0			0
$876$		0			0
$877$	18.5002	+	32.0433i	0.624707	+	1.08202i	0.988597	+	0.150583i	$0.0481151\pi$
$877$	18.5002	+	32.0433i	0.624707	+	1.08202i	−0.363890	+	0.931442i	$0.618552\pi$
$878$	−13.8292	+	23.9529i	−0.466714	+	0.808372i
$879$		0			0
$880$		0			0
$881$	−5.97213			−0.201206			−0.100603	−	0.994927i	$-0.532077\pi$
$881$	−5.97213			−0.201206			−0.100603	+	0.994927i	$0.532077\pi$
$882$		0			0
$883$	11.0589			0.372163			0.186081	−	0.982534i	$-0.440421\pi$
$883$	11.0589			0.372163			0.186081	+	0.982534i	$0.440421\pi$
$884$	34.7319	−	20.0524i	1.16816	−	0.674437i
$885$		0			0
$886$	−1.17861	+	2.04142i	−0.0395962	+	0.0685827i
$887$	2.97535	+	5.15346i	0.0999026	+	0.173036i	0.911644	−	0.410980i	$-0.134814\pi$
$887$	2.97535	+	5.15346i	0.0999026	+	0.173036i	−0.811742	+	0.584017i	$0.801480\pi$
$888$		0			0
$889$	−7.33169	+	13.0365i	−0.245897	+	0.437231i
$890$		0			0
$891$		0			0
$892$	11.7758	+	6.79876i	0.394283	+	0.227639i
$893$	4.21521	+	2.43365i	0.141057	+	0.0814391i
$894$		0			0
$895$		0			0
$896$	−0.0298666	−	2.64558i	−0.000997774	−	0.0883827i
$897$		0			0
$898$	−6.40105	−	11.0869i	−0.213606	−	0.369976i
$899$	−5.84448	+	10.1229i	−0.194924	+	0.337619i
$900$		0			0
$901$	−37.6671	+	21.7471i	−1.25487	+	0.724500i
$902$	−11.1855			−0.372438
$903$		0			0
$904$	−13.3875			−0.445261
$905$		0			0
$906$		0			0
$907$	−27.6572	+	47.9037i	−0.918343	+	1.59062i	−0.116411	+	0.993201i	$0.537139\pi$
$907$	−27.6572	+	47.9037i	−0.918343	+	1.59062i	−0.801932	+	0.597415i	$0.796195\pi$
$908$	6.17797	+	10.7006i	0.205023	+	0.355110i
$909$		0			0
$910$		0			0
$911$		−	35.2080i		−	1.16649i	−0.812295	−	0.583246i	$-0.801782\pi$
$911$		−	35.2080i		−	1.16649i	0.812295	−	0.583246i	$-0.198218\pi$
$912$		0			0
$913$	4.16135	+	2.40256i	0.137721	+	0.0795131i
$914$	−29.8989	−	17.2621i	−0.988966	−	0.570980i
$915$		0			0
$916$		−	2.41341i		−	0.0797414i
$917$	32.9833	−	0.372357i	1.08921	−	0.0122963i
$918$		0			0
$919$	−25.4437	−	44.0698i	−0.839311	−	1.45373i	−0.890471	−	0.455039i	$-0.849625\pi$
$919$	−25.4437	−	44.0698i	−0.839311	−	1.45373i	0.0511601	−	0.998690i	$-0.483708\pi$
$920$		0			0
$921$		0			0
$922$	17.5537	−	10.1346i	0.578099	−	0.333766i
$923$	96.4026			3.17313
$924$		0			0
$925$		0			0
$926$	−11.3662	+	6.56230i	−0.373518	+	0.215651i
$927$		0			0
$928$	0.675260	−	1.16959i	0.0221665	−	0.0383935i
$929$	29.8405	+	51.6853i	0.979036	+	1.69574i	0.665918	+	0.746025i	$0.268040\pi$
$929$	29.8405	+	51.6853i	0.979036	+	1.69574i	0.313118	+	0.949714i	$0.398627\pi$
$930$		0			0
$931$	37.0685	+	20.2998i	1.21487	+	0.665298i
$932$			12.8756i			0.421754i
$933$		0			0
$934$	1.32647	+	0.765836i	0.0434033	+	0.0250589i
$935$		0			0
$936$		0			0
$937$			24.2579i			0.792471i	0.918149	+	0.396235i	$0.129684\pi$
$937$			24.2579i			0.792471i	−0.918149	+	0.396235i	$0.870316\pi$
$938$	−12.4404	−	6.99643i	−0.406194	−	0.228442i
$939$		0			0
$940$		0			0
$941$	−15.0539	+	26.0742i	−0.490744	+	0.849994i	−0.999943	−	0.0106549i	$-0.996608\pi$
$941$	−15.0539	+	26.0742i	−0.490744	+	0.849994i	0.509199	+	0.860649i	$0.329942\pi$
$942$		0			0
$943$	−21.7367	+	12.5497i	−0.707845	+	0.408675i
$944$	1.59622			0.0519525
$945$		0			0
$946$	−6.87560			−0.223545
$947$	39.9779	−	23.0812i	1.29911	−	0.750039i	0.318857	−	0.947803i	$-0.396701\pi$
$947$	39.9779	−	23.0812i	1.29911	−	0.750039i	0.980250	+	0.197764i	$0.0633678\pi$
$948$		0			0
$949$	38.1730	−	66.1176i	1.23915	−	2.14627i
$950$		0			0
$951$		0			0
$952$	−14.8467	+	8.79670i	−0.481185	+	0.285103i
$953$			23.7121i			0.768110i	0.923310	+	0.384055i	$0.125473\pi$
$953$			23.7121i			0.768110i	−0.923310	+	0.384055i	$0.874527\pi$
$954$		0			0
$955$		0			0
$956$	−23.6032	−	13.6273i	−0.763382	−	0.440739i
$957$		0			0
$958$			29.3170i			0.947190i
$959$	−0.116015	+	0.0687391i	−0.00374632	+	0.00221970i
$960$		0			0
$961$	21.9558	+	38.0286i	0.708252	+	1.22673i
$962$	−29.3100	+	50.7663i	−0.944991	+	1.63677i
$963$		0			0
$964$	2.26690	−	1.30880i	0.0730120	−	0.0421535i
$965$		0			0
$966$		0			0
$967$	0.0922780			0.00296746			0.00148373	−	0.999999i	$-0.499528\pi$
$967$	0.0922780			0.00296746			0.00148373	+	0.999999i	$0.499528\pi$
$968$	8.10050	−	4.67683i	0.260360	−	0.150319i
$969$		0			0
$970$		0			0
$971$	−19.8502	−	34.3816i	−0.637024	−	1.10336i	−0.986082	−	0.166257i	$-0.946832\pi$
$971$	−19.8502	−	34.3816i	−0.637024	−	1.10336i	0.349058	−	0.937101i	$-0.386502\pi$
$972$		0			0
$973$	−2.42297	−	1.36267i	−0.0776769	−	0.0436851i
$974$			8.19540i			0.262598i
$975$		0			0
$976$	5.50239	+	3.17681i	0.176127	+	0.101687i
$977$	31.8758	+	18.4035i	1.01980	+	0.588779i	0.914045	−	0.405613i	$-0.132942\pi$
$977$	31.8758	+	18.4035i	1.01980	+	0.588779i	0.105751	+	0.994393i	$0.466275\pi$
$978$		0			0
$979$		−	4.66973i		−	0.149245i
$980$		0			0
$981$		0			0
$982$	20.2191	+	35.0206i	0.645218	+	1.11755i
$983$	31.2865	−	54.1899i	0.997885	−	1.72839i	0.442650	−	0.896694i	$-0.354038\pi$
$983$	31.2865	−	54.1899i	0.997885	−	1.72839i	0.555235	−	0.831693i	$-0.312628\pi$
$984$		0			0
$985$		0			0
$986$	−8.80886			−0.280531
$987$		0			0
$988$	37.1227			1.18103
$989$	−13.3613	+	7.71414i	−0.424864	+	0.245295i
$990$		0			0
$991$	17.4019	−	30.1410i	0.552791	−	0.957462i	−0.445281	−	0.895391i	$-0.646896\pi$
$991$	17.4019	−	30.1410i	0.552791	−	0.957462i	0.998072	−	0.0620708i	$-0.0197704\pi$
$992$	−4.32758	−	7.49558i	−0.137401	−	0.237985i
$993$		0			0
$994$	−41.4793	+	0.468269i	−1.31564	+	0.0148526i
$995$		0			0
$996$		0			0
$997$	−42.3167	−	24.4316i	−1.34018	−	0.773755i	−0.353349	−	0.935492i	$-0.614957\pi$
$997$	−42.3167	−	24.4316i	−1.34018	−	0.773755i	−0.986834	+	0.161736i	$0.948291\pi$
$998$	−15.1113	−	8.72450i	−0.478339	−	0.276169i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.f.1151.8		32
3.2	odd	2	inner	3150.2.bf.f.1151.10		32
5.2	odd	4		630.2.bo.a.269.1	yes	16
5.3	odd	4		630.2.bo.b.269.6	yes	16
5.4	even	2	inner	3150.2.bf.f.1151.9		32
7.5	odd	6	inner	3150.2.bf.f.1601.10		32
15.2	even	4		630.2.bo.b.269.8	yes	16
15.8	even	4		630.2.bo.a.269.3	yes	16
15.14	odd	2	inner	3150.2.bf.f.1151.7		32
21.5	even	6	inner	3150.2.bf.f.1601.8		32
35.3	even	12		4410.2.d.a.4409.7		16
35.12	even	12		630.2.bo.a.89.3	yes	16
35.17	even	12		4410.2.d.b.4409.8		16
35.18	odd	12		4410.2.d.a.4409.10		16
35.19	odd	6	inner	3150.2.bf.f.1601.7		32
35.32	odd	12		4410.2.d.b.4409.9		16
35.33	even	12		630.2.bo.b.89.8	yes	16
105.17	odd	12		4410.2.d.a.4409.9		16
105.32	even	12		4410.2.d.a.4409.8		16
105.38	odd	12		4410.2.d.b.4409.10		16
105.47	odd	12		630.2.bo.b.89.6	yes	16
105.53	even	12		4410.2.d.b.4409.7		16
105.68	odd	12		630.2.bo.a.89.1	✓	16
105.89	even	6	inner	3150.2.bf.f.1601.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.1	✓	16	105.68	odd	12
630.2.bo.a.89.3	yes	16	35.12	even	12
630.2.bo.a.269.1	yes	16	5.2	odd	4
630.2.bo.a.269.3	yes	16	15.8	even	4
630.2.bo.b.89.6	yes	16	105.47	odd	12
630.2.bo.b.89.8	yes	16	35.33	even	12
630.2.bo.b.269.6	yes	16	5.3	odd	4
630.2.bo.b.269.8	yes	16	15.2	even	4
3150.2.bf.f.1151.7		32	15.14	odd	2	inner
3150.2.bf.f.1151.8		32	1.1	even	1	trivial
3150.2.bf.f.1151.9		32	5.4	even	2	inner
3150.2.bf.f.1151.10		32	3.2	odd	2	inner
3150.2.bf.f.1601.7		32	35.19	odd	6	inner
3150.2.bf.f.1601.8		32	21.5	even	6	inner
3150.2.bf.f.1601.9		32	105.89	even	6	inner
3150.2.bf.f.1601.10		32	7.5	odd	6	inner
4410.2.d.a.4409.7		16	35.3	even	12
4410.2.d.a.4409.8		16	105.32	even	12
4410.2.d.a.4409.9		16	105.17	odd	12
4410.2.d.a.4409.10		16	35.18	odd	12
4410.2.d.b.4409.7		16	105.53	even	12
4410.2.d.b.4409.8		16	35.17	even	12
4410.2.d.b.4409.9		16	35.32	odd	12
4410.2.d.b.4409.10		16	105.38	odd	12

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.29693 - 2.30608i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.29693 - 2.30608i) q^{7} +1.00000i q^{8} +(-1.11120 - 0.641550i) q^{11} -6.14864i q^{13} +(0.0298666 + 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.26128 + 5.64871i) q^{17} +(-5.22868 + 3.01878i) q^{19} +1.28310 q^{22} +(2.49343 - 1.43958i) q^{23} +(3.07432 + 5.32488i) q^{26} +(-1.34866 - 2.27621i) q^{28} -1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(0.866025 + 0.500000i) q^{32} -6.52257i q^{34} +(4.76690 + 8.25652i) q^{37} +(3.01878 - 5.22868i) q^{38} -8.71759 q^{41} -5.35859 q^{43} +(-1.11120 + 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(-0.403086 - 0.698165i) q^{47} +(-3.63597 - 5.98162i) q^{49} +(-5.32488 - 3.07432i) q^{52} +(5.77488 + 3.33413i) q^{53} +(2.30608 + 1.29693i) q^{56} +(0.675260 + 1.16959i) q^{58} +(-0.798110 + 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} +8.65515 q^{62} -1.00000 q^{64} +(-2.69731 + 4.67188i) q^{67} +(3.26128 + 5.64871i) q^{68} +15.6787i q^{71} +(10.7532 + 6.20837i) q^{73} +(-8.25652 - 4.76690i) q^{74} +6.03756i q^{76} +(-2.92060 + 1.73046i) q^{77} +(5.59093 + 9.68377i) q^{79} +(7.54966 - 4.35880i) q^{82} -3.74493 q^{83} +(4.64067 - 2.67929i) q^{86} +(0.641550 - 1.11120i) q^{88} +(1.81971 + 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} -2.87917i q^{92} +(0.698165 + 0.403086i) q^{94} -8.76818i q^{97} +(6.13965 + 3.36225i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 48 q^{19} + 24 q^{31} - 16 q^{46} + 56 q^{49} + 48 q^{61} - 32 q^{64} - 8 q^{79} - 56 q^{91} + 120 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 48 * q^19 + 24 * q^31 - 16 * q^46 + 56 * q^49 + 48 * q^61 - 32 * q^64 - 8 * q^79 - 56 * q^91 + 120 * q^94

Introduction

L-functions

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Database

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