LMFDB - Embedded newform 3150.2.bf.f.1151.7

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			1151.7
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.f.1601.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	0.658076	−	0.752952i	$-0.271371\pi$
$11$	1.11120	+	0.641550i	0.335038	+	0.193435i	−0.323037	+	0.946386i	$0.604704\pi$
$12$		0			0
$13$			6.14864i			1.70533i	0.522462	+	0.852663i	$0.325014\pi$
$13$			6.14864i			1.70533i	−0.522462	+	0.852663i	$0.674986\pi$
$14$	−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	$0.0400191\pi$
$29$			1.35052i			0.250785i	−0.992107	+	0.125393i	$0.959981\pi$
$30$		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	$-0.880010\pi$
$37$	−4.76690	−	8.25652i	−0.783674	−	1.35736i	0.146114	−	0.989268i	$-0.453323\pi$
$38$	3.01878	−	5.22868i	0.489710	−	0.848203i
$39$		0			0
$40$		0			0
$41$	8.71759			1.36146			0.680730	−	0.732535i	$-0.261663\pi$
$41$	8.71759			1.36146			0.680730	+	0.732535i	$0.261663\pi$
$42$		0			0
$43$	5.35859			0.817177			0.408588	−	0.912719i	$-0.366021\pi$
$43$	5.35859			0.817177			0.408588	+	0.912719i	$0.366021\pi$
$44$	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	−0.809385	−	0.587278i	$-0.800200\pi$
$59$	0.798110	−	1.38237i	0.103905	−	0.179969i	0.913290	+	0.407309i	$0.133533\pi$
$60$		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	−0.652889	−	0.757453i	$-0.726443\pi$
$67$	2.69731	−	4.67188i	0.329529	−	0.570761i	0.982418	+	0.186692i	$0.0597766\pi$
$68$	3.26128	+	5.64871i	0.395489	+	0.685006i
$69$		0			0
$70$		0			0
$71$		−	15.6787i		−	1.86072i	−0.366650	−	0.930359i	$-0.619495\pi$
$71$		−	15.6787i		−	1.86072i	0.366650	−	0.930359i	$-0.380505\pi$
$72$		0			0
$73$	−10.7532	−	6.20837i	−1.25857	−	0.726635i	−0.285772	−	0.958298i	$-0.592250\pi$
$73$	−10.7532	−	6.20837i	−1.25857	−	0.726635i	−0.972796	+	0.231663i	$0.925583\pi$
$74$	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	0.753318	−	0.657657i	$-0.228452\pi$
$89$	−1.81971	−	3.15183i	−0.192889	−	0.334093i	−0.946206	+	0.323564i	$0.895119\pi$
$90$		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	$0.146845\pi$
$97$			8.76818i			0.890274i	−0.895463	+	0.445137i	$0.853155\pi$
$98$	6.13965	+	3.36225i	0.620198	+	0.339639i
$99$		0			0
$100$		0			0
$101$	0.853270	−	1.47791i	0.0849035	−	0.147057i	−0.820447	−	0.571723i	$-0.806275\pi$
$101$	0.853270	−	1.47791i	0.0849035	−	0.147057i	0.905350	+	0.424666i	$0.139608\pi$
$102$		0			0
$103$	−8.97583	+	5.18220i	−0.884415	+	0.510617i	−0.872112	−	0.489307i	$-0.837250\pi$
$103$	−8.97583	+	5.18220i	−0.884415	+	0.510617i	−0.0123035	+	0.999924i	$0.503916\pi$
$104$	−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	$-0.419301\pi$
$127$	5.65313			0.501634			0.250817	+	0.968035i	$0.419301\pi$
$128$	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	$-0.983334\pi$
$131$	−6.23366	−	10.7970i	−0.544638	−	0.943340i	0.453992	−	0.891006i	$-0.349999\pi$
$132$		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	−0.179080	−	0.983835i	$-0.557312\pi$
$149$	7.12137	−	4.11153i	0.583406	−	0.336829i	0.762486	+	0.647005i	$0.223979\pi$
$150$		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	0.323631	−	0.946183i	$-0.395096\pi$
$157$	−4.18466	−	2.41601i	−0.333972	−	0.192819i	−0.657603	+	0.753364i	$0.728430\pi$
$158$	−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	0.996050	−	0.0887927i	$-0.0283009\pi$
$163$	5.37661	+	9.31256i	0.421128	+	0.729416i	−0.574922	+	0.818208i	$0.694968\pi$
$164$	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	0.617492	−	0.786577i	$-0.288149\pi$
$179$	3.27843	+	1.89280i	0.245041	+	0.141475i	−0.372450	+	0.928052i	$0.621482\pi$
$180$		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	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	−1.76946	+	3.06479i	−0.127368	+	0.220608i	−0.922656	−	0.385623i	$-0.873986\pi$
$193$	−1.76946	+	3.06479i	−0.127368	+	0.220608i	0.795288	+	0.606232i	$0.207320\pi$
$194$	−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	$-0.849540\pi$
$223$		−	13.5975i		−	0.910557i	0.890349	−	0.455279i	$-0.150460\pi$
$224$	−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	$0.343451\pi$
$239$			27.2546i			1.76296i	−0.472226	+	0.881478i	$0.656549\pi$
$240$		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	$-0.180675\pi$
$251$	26.7173			1.68638			0.843190	+	0.537615i	$0.180675\pi$
$252$		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	−0.561893	−	0.827210i	$-0.689927\pi$
$269$	7.14171	−	12.3698i	0.435438	−	0.754201i	0.997331	+	0.0730091i	$0.0232602\pi$
$270$		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	−0.988242	−	0.152897i	$-0.951140\pi$
$277$	−6.02002	+	10.4270i	−0.361708	+	0.626497i	0.626534	+	0.779394i	$0.284473\pi$
$278$	0.525345	+	0.909924i	0.0315081	+	0.0545736i
$279$		0			0
$280$		0			0
$281$			12.7879i			0.762861i	0.924397	+	0.381431i	$0.124569\pi$
$281$			12.7879i			0.762861i	−0.924397	+	0.381431i	$0.875431\pi$
$282$		0			0
$283$	13.4685	+	7.77607i	0.800622	+	0.462239i	0.843689	−	0.536833i	$-0.180379\pi$
$283$	13.4685	+	7.77607i	0.800622	+	0.462239i	−0.0430666	+	0.999072i	$0.513713\pi$
$284$	−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	$0.0234217\pi$
$307$			2.57617i			0.147030i	−0.997294	+	0.0735150i	$0.976578\pi$
$308$	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	$-0.586204\pi$
$311$	12.3570	−	21.4030i	0.700702	−	1.21365i	0.968220	−	0.250098i	$-0.0804629\pi$
$312$		0			0
$313$	−7.79573	+	4.50087i	−0.440641	+	0.254404i	−0.703869	−	0.710329i	$-0.748546\pi$
$313$	−7.79573	+	4.50087i	−0.440641	+	0.254404i	0.263229	+	0.964733i	$0.415213\pi$
$314$	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	$-0.678390\pi$
$337$	−19.5159			−1.06310			−0.531549	+	0.847028i	$0.678390\pi$
$338$	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	$-0.201641\pi$
$359$	32.6198	−	18.8330i	1.72161	−	0.993970i	0.915631	−	0.402021i	$-0.131692\pi$
$360$		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	0.801786	−	0.597611i	$-0.203883\pi$
$367$	13.1253	+	7.57787i	0.685133	+	0.395562i	−0.116653	+	0.993173i	$0.537217\pi$
$368$	−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	0.667027	−	0.745034i	$-0.267567\pi$
$373$	−6.02002	−	10.4270i	−0.311705	−	0.539889i	−0.978732	+	0.205145i	$0.934233\pi$
$374$	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	0.00172432	−	0.999999i	$-0.499451\pi$
$389$	−17.0297	−	9.83207i	−0.863438	−	0.498506i	−0.865162	+	0.501493i	$0.832784\pi$
$390$		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	−0.371349	−	0.928493i	$-0.621105\pi$
$397$	4.92295	−	2.84227i	0.247076	−	0.142649i	0.618425	+	0.785844i	$0.287771\pi$
$398$	−3.46410			−0.173640
$399$		0			0
$400$		0			0
$401$	−8.84787	+	5.10832i	−0.441842	+	0.255097i	−0.704378	−	0.709825i	$-0.748774\pi$
$401$	−8.84787	+	5.10832i	−0.441842	+	0.255097i	0.262537	+	0.964922i	$0.415441\pi$
$402$		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	$-0.589162\pi$
$419$	−11.3181			−0.552924			−0.276462	+	0.961025i	$0.589162\pi$
$420$		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	0.933137	−	0.359522i	$-0.117060\pi$
$431$	22.5947	+	13.0451i	1.08835	+	0.628359i	0.155213	+	0.987881i	$0.450394\pi$
$432$		0			0
$433$			8.42614i			0.404935i	0.979289	+	0.202467i	$0.0648960\pi$
$433$			8.42614i			0.404935i	−0.979289	+	0.202467i	$0.935104\pi$
$434$	−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	$-0.902318\pi$
$449$		−	12.8021i		−	0.604169i	0.953281	−	0.302084i	$-0.0976824\pi$
$450$		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	$-0.867493\pi$
$457$	−17.2621	−	29.8989i	−0.807488	−	1.39861i	0.107111	−	0.994247i	$-0.465840\pi$
$458$	−1.20671	+	2.09008i	−0.0563857	+	0.0976628i
$459$		0			0
$460$		0			0
$461$	20.2692			0.944032			0.472016	−	0.881590i	$-0.343526\pi$
$461$	20.2692			0.944032			0.472016	+	0.881590i	$0.343526\pi$
$462$		0			0
$463$	−13.1246			−0.609952			−0.304976	−	0.952360i	$-0.598648\pi$
$463$	−13.1246			−0.609952			−0.304976	+	0.952360i	$0.598648\pi$
$464$	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	$0.400272\pi$
$479$	−14.6585	+	25.3893i	−0.669764	+	1.16007i	−0.977970	+	0.208746i	$0.933062\pi$
$480$		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	−0.943807	−	0.330497i	$-0.892784\pi$
$487$	−4.09770	+	7.09743i	−0.185685	+	0.321615i	0.758122	+	0.652112i	$0.226117\pi$
$488$	−3.17681	−	5.50239i	−0.143807	−	0.249082i
$489$		0			0
$490$		0			0
$491$			40.4383i			1.82495i	0.409129	+	0.912477i	$0.365833\pi$
$491$			40.4383i			1.82495i	−0.409129	+	0.912477i	$0.634167\pi$
$492$		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	0.962356	−	0.271792i	$-0.0876161\pi$
$509$	5.54549	+	9.60508i	0.245800	+	0.425737i	−0.716556	+	0.697529i	$0.754283\pi$
$510$		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	$0.502901\pi$
$521$	−19.8706	+	34.4168i	−0.870546	+	1.50783i	−0.861433	+	0.507871i	$0.830433\pi$
$522$		0			0
$523$	−27.0900	+	15.6404i	−1.18456	+	0.683907i	−0.957065	−	0.289872i	$-0.906387\pi$
$523$	−27.0900	+	15.6404i	−1.18456	+	0.683907i	−0.227496	+	0.973779i	$0.573054\pi$
$524$	−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	$-0.166275\pi$
$547$	40.5380			1.73328			0.866640	+	0.498934i	$0.166275\pi$
$548$	−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	−0.861192	−	0.508280i	$-0.830282\pi$
$569$	−20.3139	+	11.7283i	−0.851605	+	0.491674i	0.00958727	+	0.999954i	$0.496948\pi$
$570$		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	0.734241	−	0.678889i	$-0.237538\pi$
$577$	12.3329	+	7.12041i	0.513426	+	0.296426i	−0.220815	+	0.975316i	$0.570872\pi$
$578$	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	−0.0761732	−	0.997095i	$-0.524270\pi$
$599$	−23.9304	−	13.8162i	−0.977769	−	0.564515i	−0.901596	+	0.432579i	$0.857604\pi$
$600$		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	−0.887678	−	0.460465i	$-0.847683\pi$
$607$	−22.9803	+	13.2677i	−0.932743	+	0.538519i	−0.0450649	+	0.998984i	$0.514349\pi$
$608$	−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	−0.875104	−	0.483935i	$-0.839207\pi$
$613$	−0.456842	+	0.791273i	−0.0184517	+	0.0319592i	0.856652	+	0.515894i	$0.172540\pi$
$614$	−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	0.944603	−	0.328214i	$-0.106447\pi$
$641$	28.6767	+	16.5565i	1.13266	+	0.653943i	0.188060	+	0.982158i	$0.439780\pi$
$642$		0			0
$643$		−	3.31191i		−	0.130609i	−0.997865	−	0.0653044i	$-0.979198\pi$
$643$		−	3.31191i		−	0.130609i	0.997865	−	0.0653044i	$-0.0208018\pi$
$644$	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	$0.00805215\pi$
$659$			1.29864i			0.0505877i	−0.999680	+	0.0252939i	$0.991948\pi$
$660$		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	$-0.384524\pi$
$673$	18.4124			0.709747			0.354873	+	0.934914i	$0.384524\pi$
$674$	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	$0.167137\pi$
$701$			26.5441i			1.00256i	−0.865286	+	0.501279i	$0.832863\pi$
$702$		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	0.552413	−	0.833570i	$-0.313707\pi$
$719$	−11.9507	−	20.6992i	−0.445686	−	0.771951i	−0.998100	+	0.0616189i	$0.980374\pi$
$720$		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	$0.136696\pi$
$727$			22.4529i			0.832731i	−0.909197	+	0.416365i	$0.863304\pi$
$728$	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	−0.871019	−	0.491249i	$-0.836540\pi$
$733$	−23.8547	+	13.7725i	−0.881094	+	0.508700i	−0.0100750	+	0.999949i	$0.503207\pi$
$734$	−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	$-0.705935\pi$
$757$	−33.1687			−1.20554			−0.602768	+	0.797917i	$0.705935\pi$
$758$	15.6679	−	9.04589i	0.569085	−	0.328562i
$759$		0			0
$760$		0			0
$761$	−2.17122	−	3.76067i	−0.0787068	−	0.136324i	0.823985	−	0.566611i	$-0.191746\pi$
$761$	−2.17122	−	3.76067i	−0.0787068	−	0.136324i	−0.902692	+	0.430287i	$0.858412\pi$
$762$		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	0.698196	−	0.715907i	$-0.253986\pi$
$787$	11.9873	+	6.92087i	0.427301	+	0.246702i	−0.270895	+	0.962609i	$0.587320\pi$
$788$	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	0.477196	−	0.878797i	$-0.341653\pi$
$809$	−1.28750	−	0.743340i	−0.0452662	−	0.0261344i	−0.522462	+	0.852662i	$0.674986\pi$
$810$		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	0.0646976	−	0.997905i	$-0.479392\pi$
$821$	27.5430	−	15.9020i	0.961257	−	0.554982i	0.896560	+	0.442923i	$0.146058\pi$
$822$		0			0
$823$	−18.3186	+	31.7287i	−0.638545	+	1.10599i	0.347207	+	0.937788i	$0.387130\pi$
$823$	−18.3186	+	31.7287i	−0.638545	+	1.10599i	−0.985752	+	0.168204i	$0.946203\pi$
$824$	−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	$-0.343233\pi$
$839$	27.3914			0.945655			0.472827	+	0.881155i	$0.343233\pi$
$840$		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	$0.126499\pi$
$853$			22.6073i			0.774060i	−0.922067	+	0.387030i	$0.873501\pi$
$854$	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	$-0.951885\pi$
$877$	−18.5002	−	32.0433i	−0.624707	−	1.08202i	0.363890	−	0.931442i	$-0.381448\pi$
$878$	−13.8292	+	23.9529i	−0.466714	+	0.808372i
$879$		0			0
$880$		0			0
$881$	5.97213			0.201206			0.100603	−	0.994927i	$-0.467923\pi$
$881$	5.97213			0.201206			0.100603	+	0.994927i	$0.467923\pi$
$882$		0			0
$883$	−11.0589			−0.372163			−0.186081	−	0.982534i	$-0.559579\pi$
$883$	−11.0589			−0.372163			−0.186081	+	0.982534i	$0.559579\pi$
$884$	−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	$-0.462861\pi$
$907$	27.6572	−	47.9037i	0.918343	−	1.59062i	0.801932	−	0.597415i	$-0.203805\pi$
$908$	6.17797	+	10.7006i	0.205023	+	0.355110i
$909$		0			0
$910$		0			0
$911$			35.2080i			1.16649i	0.812295	+	0.583246i	$0.198218\pi$
$911$			35.2080i			1.16649i	−0.812295	+	0.583246i	$0.801782\pi$
$912$		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	$-0.731960\pi$
$929$	−29.8405	−	51.6853i	−0.979036	−	1.69574i	−0.313118	−	0.949714i	$-0.601373\pi$
$930$		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	$-0.870316\pi$
$937$		−	24.2579i		−	0.792471i	0.918149	−	0.396235i	$-0.129684\pi$
$938$	−12.4404	−	6.99643i	−0.406194	−	0.228442i
$939$		0			0
$940$		0			0
$941$	15.0539	−	26.0742i	0.490744	−	0.849994i	−0.509199	−	0.860649i	$-0.670058\pi$
$941$	15.0539	−	26.0742i	0.490744	−	0.849994i	0.999943	+	0.0106549i	$0.00339164\pi$
$942$		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	$-0.500472\pi$
$967$	−0.0922780			−0.00296746			−0.00148373	+	0.999999i	$0.500472\pi$
$968$	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	$0.0531683\pi$
$971$	19.8502	+	34.3816i	0.637024	+	1.10336i	−0.349058	+	0.937101i	$0.613498\pi$
$972$		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	0.986834	−	0.161736i	$-0.0517094\pi$
$997$	42.3167	+	24.4316i	1.34018	+	0.773755i	0.353349	+	0.935492i	$0.385043\pi$
$998$	−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.1151.7		32
3.2	odd	2	inner	3150.2.bf.f.1151.9		32
5.2	odd	4		630.2.bo.a.269.3	yes	16
5.3	odd	4		630.2.bo.b.269.8	yes	16
5.4	even	2	inner	3150.2.bf.f.1151.10		32
7.5	odd	6	inner	3150.2.bf.f.1601.9		32
15.2	even	4		630.2.bo.b.269.6	yes	16
15.8	even	4		630.2.bo.a.269.1	yes	16
15.14	odd	2	inner	3150.2.bf.f.1151.8		32
21.5	even	6	inner	3150.2.bf.f.1601.7		32
35.3	even	12		4410.2.d.a.4409.9		16
35.12	even	12		630.2.bo.a.89.1	✓	16
35.17	even	12		4410.2.d.b.4409.10		16
35.18	odd	12		4410.2.d.a.4409.8		16
35.19	odd	6	inner	3150.2.bf.f.1601.8		32
35.32	odd	12		4410.2.d.b.4409.7		16
35.33	even	12		630.2.bo.b.89.6	yes	16
105.17	odd	12		4410.2.d.a.4409.7		16
105.32	even	12		4410.2.d.a.4409.10		16
105.38	odd	12		4410.2.d.b.4409.8		16
105.47	odd	12		630.2.bo.b.89.8	yes	16
105.53	even	12		4410.2.d.b.4409.9		16
105.68	odd	12		630.2.bo.a.89.3	yes	16
105.89	even	6	inner	3150.2.bf.f.1601.10		32

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

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

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