LMFDB - Embedded newform 3150.2.bf.f.1601.6

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			1601.6
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.f.1151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +(-1.37897 + 0.796151i) q^{11} -0.925091i q^{13} +(-1.24501 - 2.33451i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.97883 + 3.42743i) q^{17} +(-0.541679 - 0.312739i) q^{19} +1.59230 q^{22} +(-6.74256 - 3.89282i) q^{23} +(-0.462546 + 0.801153i) q^{26} +(-0.0890445 + 2.64425i) q^{28} -9.34805i q^{29} +(8.94618 - 5.16508i) q^{31} +(0.866025 - 0.500000i) q^{32} -3.95765i q^{34} +(0.213192 - 0.369259i) q^{37} +(0.312739 + 0.541679i) q^{38} +8.35463 q^{41} +6.27133 q^{43} +(-1.37897 - 0.796151i) q^{44} +(3.89282 + 6.74256i) q^{46} +(-1.39065 + 2.40868i) q^{47} +(3.08425 + 6.28390i) q^{49} +(0.801153 - 0.462546i) q^{52} +(-2.90217 + 1.67557i) q^{53} +(1.39924 - 2.24547i) q^{56} +(-4.67403 + 8.09565i) q^{58} +(3.10680 + 5.38113i) q^{59} +(9.52671 + 5.50025i) q^{61} -10.3302 q^{62} -1.00000 q^{64} +(-0.178089 - 0.308459i) q^{67} +(-1.97883 + 3.42743i) q^{68} -9.07975i q^{71} +(-5.91515 + 3.41511i) q^{73} +(-0.369259 + 0.213192i) q^{74} -0.625477i q^{76} +(-4.21045 - 0.141786i) q^{77} +(4.52582 - 7.83895i) q^{79} +(-7.23532 - 4.17731i) q^{82} +0.809898 q^{83} +(-5.43113 - 3.13566i) q^{86} +(0.796151 + 1.37897i) q^{88} +(2.00721 - 3.47659i) q^{89} +(1.29443 - 2.07726i) q^{91} -7.78564i q^{92} +(2.40868 - 1.39065i) q^{94} +7.87721i q^{97} +(0.470912 - 6.98414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	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
$7$	2.24547	+	1.39924i	0.848707	+	0.528863i
$7$	2.24547	+	1.39924i	0.848707	+	0.528863i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	−1.37897	+	0.796151i	−0.415776	+	0.240049i	−0.693269	−	0.720679i	$-0.743830\pi$
$11$	−1.37897	+	0.796151i	−0.415776	+	0.240049i	0.277492	+	0.960728i	$0.410497\pi$
$12$		0			0
$13$		−	0.925091i		−	0.256574i	−0.991737	−	0.128287i	$-0.959052\pi$
$13$		−	0.925091i		−	0.256574i	0.991737	−	0.128287i	$-0.0409479\pi$
$14$	−1.24501	−	2.33451i	−0.332743	−	0.623925i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.97883	+	3.42743i	0.479936	+	0.831273i	0.999735	−	0.0230153i	$-0.00732664\pi$
$17$	1.97883	+	3.42743i	0.479936	+	0.831273i	−0.519799	+	0.854288i	$0.673993\pi$
$18$		0			0
$19$	−0.541679	−	0.312739i	−0.124270	−	0.0717472i	0.436577	−	0.899667i	$-0.356191\pi$
$19$	−0.541679	−	0.312739i	−0.124270	−	0.0717472i	−0.560846	+	0.827920i	$0.689524\pi$
$20$		0			0
$21$		0			0
$22$	1.59230			0.339480
$23$	−6.74256	−	3.89282i	−1.40592	−	0.811709i	−0.410930	−	0.911667i	$-0.634796\pi$
$23$	−6.74256	−	3.89282i	−1.40592	−	0.811709i	−0.994992	+	0.0999578i	$0.968129\pi$
$24$		0			0
$25$		0			0
$26$	−0.462546	+	0.801153i	−0.0907127	+	0.157119i
$27$		0			0
$28$	−0.0890445	+	2.64425i	−0.0168278	+	0.499717i
$29$		−	9.34805i		−	1.73589i	−0.496661	−	0.867945i	$-0.665441\pi$
$29$		−	9.34805i		−	1.73589i	0.496661	−	0.867945i	$-0.334559\pi$
$30$		0			0
$31$	8.94618	−	5.16508i	1.60678	−	0.927675i	0.616696	−	0.787201i	$-0.288471\pi$
$31$	8.94618	−	5.16508i	1.60678	−	0.927675i	0.990084	−	0.140474i	$-0.0448626\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	3.95765i		−	0.678732i
$35$		0			0
$36$		0			0
$37$	0.213192	−	0.369259i	0.0350485	−	0.0607058i	−0.847969	−	0.530046i	$-0.822175\pi$
$37$	0.213192	−	0.369259i	0.0350485	−	0.0607058i	0.883018	+	0.469340i	$0.155508\pi$
$38$	0.312739	+	0.541679i	0.0507329	+	0.0878720i
$39$		0			0
$40$		0			0
$41$	8.35463			1.30477			0.652387	−	0.757886i	$-0.273768\pi$
$41$	8.35463			1.30477			0.652387	+	0.757886i	$0.273768\pi$
$42$		0			0
$43$	6.27133			0.956369			0.478184	−	0.878259i	$-0.341295\pi$
$43$	6.27133			0.956369			0.478184	+	0.878259i	$0.341295\pi$
$44$	−1.37897	−	0.796151i	−0.207888	−	0.120024i
$45$		0			0
$46$	3.89282	+	6.74256i	0.573965	+	0.994137i
$47$	−1.39065	+	2.40868i	−0.202847	+	0.351342i	−0.949445	−	0.313934i	$-0.898353\pi$
$47$	−1.39065	+	2.40868i	−0.202847	+	0.351342i	0.746597	+	0.665276i	$0.231686\pi$
$48$		0			0
$49$	3.08425	+	6.28390i	0.440607	+	0.897700i
$50$		0			0
$51$		0			0
$52$	0.801153	−	0.462546i	0.111100	−	0.0641435i
$53$	−2.90217	+	1.67557i	−0.398644	+	0.230157i	−0.685899	−	0.727697i	$-0.740591\pi$
$53$	−2.90217	+	1.67557i	−0.398644	+	0.230157i	0.287255	+	0.957854i	$0.407257\pi$
$54$		0			0
$55$		0			0
$56$	1.39924	−	2.24547i	0.186981	−	0.300063i
$57$		0			0
$58$	−4.67403	+	8.09565i	−0.613730	+	1.06301i
$59$	3.10680	+	5.38113i	0.404471	+	0.700564i	0.994260	−	0.106994i	$-0.0341224\pi$
$59$	3.10680	+	5.38113i	0.404471	+	0.700564i	−0.589789	+	0.807557i	$0.700789\pi$
$60$		0			0
$61$	9.52671	+	5.50025i	1.21977	+	0.704235i	0.964869	−	0.262732i	$-0.0846236\pi$
$61$	9.52671	+	5.50025i	1.21977	+	0.704235i	0.254902	+	0.966967i	$0.417957\pi$
$62$	−10.3302			−1.31193
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−0.178089	−	0.308459i	−0.0217570	−	0.0376843i	0.854942	−	0.518724i	$-0.173593\pi$
$67$	−0.178089	−	0.308459i	−0.0217570	−	0.0376843i	−0.876699	+	0.481039i	$0.840259\pi$
$68$	−1.97883	+	3.42743i	−0.239968	+	0.415637i
$69$		0			0
$70$		0			0
$71$		−	9.07975i		−	1.07757i	−0.842444	−	0.538784i	$-0.818884\pi$
$71$		−	9.07975i		−	1.07757i	0.842444	−	0.538784i	$-0.181116\pi$
$72$		0			0
$73$	−5.91515	+	3.41511i	−0.692316	+	0.399709i	−0.804479	−	0.593981i	$-0.797555\pi$
$73$	−5.91515	+	3.41511i	−0.692316	+	0.399709i	0.112163	+	0.993690i	$0.464222\pi$
$74$	−0.369259	+	0.213192i	−0.0429255	+	0.0247830i
$75$		0			0
$76$		−	0.625477i		−	0.0717472i
$77$	−4.21045	−	0.141786i	−0.479825	−	0.0161580i
$78$		0			0
$79$	4.52582	−	7.83895i	0.509195	−	0.881951i	−0.490749	−	0.871301i	$-0.663277\pi$
$79$	4.52582	−	7.83895i	0.509195	−	0.881951i	0.999943	−	0.0106498i	$-0.00339001\pi$
$80$		0			0
$81$		0			0
$82$	−7.23532	−	4.17731i	−0.799007	−	0.461307i
$83$	0.809898			0.0888978			0.0444489	−	0.999012i	$-0.485847\pi$
$83$	0.809898			0.0888978			0.0444489	+	0.999012i	$0.485847\pi$
$84$		0			0
$85$		0			0
$86$	−5.43113	−	3.13566i	−0.585654	−	0.338127i
$87$		0			0
$88$	0.796151	+	1.37897i	0.0848700	+	0.146999i
$89$	2.00721	−	3.47659i	0.212764	−	0.368518i	−0.739815	−	0.672811i	$-0.765087\pi$
$89$	2.00721	−	3.47659i	0.212764	−	0.368518i	0.952579	+	0.304293i	$0.0984201\pi$
$90$		0			0
$91$	1.29443	−	2.07726i	0.135693	−	0.217756i
$92$		−	7.78564i		−	0.811709i
$93$		0			0
$94$	2.40868	−	1.39065i	0.248436	−	0.143435i
$95$		0			0
$96$		0			0
$97$			7.87721i			0.799809i	0.916557	+	0.399905i	$0.130957\pi$
$97$			7.87721i			0.799809i	−0.916557	+	0.399905i	$0.869043\pi$
$98$	0.470912	−	6.98414i	0.0475693	−	0.705505i
$99$		0			0
$100$		0			0
$101$	−3.76411	−	6.51962i	−0.374543	−	0.648727i	0.615716	−	0.787968i	$-0.288867\pi$
$101$	−3.76411	−	6.51962i	−0.374543	−	0.648727i	−0.990258	+	0.139241i	$0.955534\pi$
$102$		0			0
$103$	1.44073	+	0.831805i	0.141959	+	0.0819601i	0.569297	−	0.822132i	$-0.307215\pi$
$103$	1.44073	+	0.831805i	0.141959	+	0.0819601i	−0.427338	+	0.904092i	$0.640549\pi$
$104$	−0.925091			−0.0907127
$105$		0			0
$106$	3.35114			0.325492
$107$	16.8033	+	9.70139i	1.62444	+	0.937869i	0.985713	+	0.168433i	$0.0538706\pi$
$107$	16.8033	+	9.70139i	1.62444	+	0.937869i	0.638724	+	0.769436i	$0.279463\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$		0			0
$112$	−2.33451	+	1.24501i	−0.220591	+	0.117643i
$113$			16.0750i			1.51221i	0.654451	+	0.756104i	$0.272900\pi$
$113$			16.0750i			1.51221i	−0.654451	+	0.756104i	$0.727100\pi$
$114$		0			0
$115$		0			0
$116$	8.09565	−	4.67403i	0.751662	−	0.433972i
$117$		0			0
$118$		−	6.21360i		−	0.572008i
$119$	−0.352407	+	10.4650i	−0.0323051	+	0.959328i
$120$		0			0
$121$	−4.23229	+	7.33053i	−0.384753	+	0.666412i
$122$	−5.50025	−	9.52671i	−0.497969	−	0.862508i
$123$		0			0
$124$	8.94618	+	5.16508i	0.803390	+	0.463838i
$125$		0			0
$126$		0			0
$127$	−13.2173			−1.17285			−0.586424	−	0.810004i	$-0.699465\pi$
$127$	−13.2173			−1.17285			−0.586424	+	0.810004i	$0.699465\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	4.70080	−	8.14203i	0.410711	−	0.711372i	−0.584257	−	0.811569i	$-0.698614\pi$
$131$	4.70080	−	8.14203i	0.410711	−	0.711372i	0.994968	+	0.100197i	$0.0319472\pi$
$132$		0			0
$133$	−0.778726	−	1.46018i	−0.0675241	−	0.126614i
$134$			0.356178i			0.0307691i
$135$		0			0
$136$	3.42743	−	1.97883i	0.293899	−	0.169683i
$137$	8.11701	−	4.68636i	0.693483	−	0.400382i	−0.111433	−	0.993772i	$-0.535544\pi$
$137$	8.11701	−	4.68636i	0.693483	−	0.400382i	0.804915	+	0.593390i	$0.202211\pi$
$138$		0			0
$139$			14.1106i			1.19685i	0.801180	+	0.598423i	$0.204206\pi$
$139$			14.1106i			1.19685i	−0.801180	+	0.598423i	$0.795794\pi$
$140$		0			0
$141$		0			0
$142$	−4.53988	+	7.86330i	−0.380978	+	0.659873i
$143$	0.736513	+	1.27568i	0.0615903	+	0.106678i
$144$		0			0
$145$		0			0
$146$	6.83023			0.565274
$147$		0			0
$148$	0.426383			0.0350485
$149$	2.14103	+	1.23612i	0.175400	+	0.101267i	0.585130	−	0.810940i	$-0.301044\pi$
$149$	2.14103	+	1.23612i	0.175400	+	0.101267i	−0.409730	+	0.912207i	$0.634377\pi$
$150$		0			0
$151$	10.4425	+	18.0869i	0.849796	+	1.47189i	0.881391	+	0.472388i	$0.156608\pi$
$151$	10.4425	+	18.0869i	0.849796	+	1.47189i	−0.0315949	+	0.999501i	$0.510059\pi$
$152$	−0.312739	+	0.541679i	−0.0253664	+	0.0439360i
$153$		0			0
$154$	3.57546	+	2.22802i	0.288119	+	0.179539i
$155$		0			0
$156$		0			0
$157$	21.1722	−	12.2238i	1.68972	−	0.975563i	0.735002	−	0.678065i	$-0.237181\pi$
$157$	21.1722	−	12.2238i	1.68972	−	0.975563i	0.954723	−	0.297498i	$-0.0961521\pi$
$158$	−7.83895	+	4.52582i	−0.623634	+	0.360055i
$159$		0			0
$160$		0			0
$161$	−9.69321	−	18.1757i	−0.763932	−	1.43244i
$162$		0			0
$163$	2.95758	−	5.12267i	0.231655	−	0.401239i	−0.726640	−	0.687018i	$-0.758919\pi$
$163$	2.95758	−	5.12267i	0.231655	−	0.401239i	0.958295	+	0.285780i	$0.0922526\pi$
$164$	4.17731	+	7.23532i	0.326193	+	0.564983i
$165$		0			0
$166$	−0.701392	−	0.404949i	−0.0544386	−	0.0314301i
$167$	−12.1440			−0.939733			−0.469867	−	0.882737i	$-0.655698\pi$
$167$	−12.1440			−0.939733			−0.469867	+	0.882737i	$0.655698\pi$
$168$		0			0
$169$	12.1442			0.934170
$170$		0			0
$171$		0			0
$172$	3.13566	+	5.43113i	0.239092	+	0.414120i
$173$	−8.19918	+	14.2014i	−0.623372	+	1.07971i	0.365481	+	0.930819i	$0.380904\pi$
$173$	−8.19918	+	14.2014i	−0.623372	+	1.07971i	−0.988853	+	0.148893i	$0.952429\pi$
$174$		0			0
$175$		0			0
$176$		−	1.59230i		−	0.120024i
$177$		0			0
$178$	−3.47659	+	2.00721i	−0.260581	+	0.150447i
$179$	2.73398	−	1.57846i	0.204347	−	0.117980i	−0.394334	−	0.918967i	$-0.629025\pi$
$179$	2.73398	−	1.57846i	0.204347	−	0.117980i	0.598682	+	0.800987i	$0.295691\pi$
$180$		0			0
$181$		−	8.17916i		−	0.607952i	−0.952680	−	0.303976i	$-0.901686\pi$
$181$		−	8.17916i		−	0.607952i	0.952680	−	0.303976i	$-0.0983143\pi$
$182$	−2.15964	+	1.15175i	−0.160083	+	0.0853733i
$183$		0			0
$184$	−3.89282	+	6.74256i	−0.286983	+	0.497068i
$185$		0			0
$186$		0			0
$187$	−5.45750	−	3.15089i	−0.399092	−	0.230416i
$188$	−2.78130			−0.202847
$189$		0			0
$190$		0			0
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	0.408756	−	0.912644i	$-0.365963\pi$
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	−0.585995	+	0.810315i	$0.699296\pi$
$192$		0			0
$193$	8.85772	+	15.3420i	0.637593	+	1.10434i	0.985959	+	0.166985i	$0.0534031\pi$
$193$	8.85772	+	15.3420i	0.637593	+	1.10434i	−0.348367	+	0.937358i	$0.613264\pi$
$194$	3.93860	−	6.82186i	0.282775	−	0.489781i
$195$		0			0
$196$	−3.89989	+	5.81299i	−0.278564	+	0.415213i
$197$		−	4.30350i		−	0.306612i	−0.988179	−	0.153306i	$-0.951008\pi$
$197$		−	4.30350i		−	0.306612i	0.988179	−	0.153306i	$-0.0489919\pi$
$198$		0			0
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	3.00000	−	1.73205i	0.212664	−	0.122782i	0.602549	+	0.798082i	$0.294152\pi$
$200$		0			0
$201$		0			0
$202$			7.52821i			0.529683i
$203$	13.0802	−	20.9907i	0.918048	−	1.47326i
$204$		0			0
$205$		0			0
$206$	−0.831805	−	1.44073i	−0.0579546	−	0.100380i
$207$		0			0
$208$	0.801153	+	0.462546i	0.0555499	+	0.0320718i
$209$	0.995949			0.0688912
$210$		0			0
$211$	10.3886			0.715183			0.357592	−	0.933878i	$-0.383598\pi$
$211$	10.3886			0.715183			0.357592	+	0.933878i	$0.383598\pi$
$212$	−2.90217	−	1.67557i	−0.199322	−	0.115079i
$213$		0			0
$214$	−9.70139	−	16.8033i	−0.663173	−	1.14865i
$215$		0			0
$216$		0			0
$217$	27.3155	+	0.919844i	1.85430	+	0.0624431i
$218$		−	2.00000i		−	0.135457i
$219$		0			0
$220$		0			0
$221$	3.17068	−	1.83059i	0.213283	−	0.123139i
$222$		0			0
$223$		−	18.3555i		−	1.22918i	−0.788848	−	0.614589i	$-0.789322\pi$
$223$		−	18.3555i		−	1.22918i	0.788848	−	0.614589i	$-0.210678\pi$
$224$	2.64425	+	0.0890445i	0.176677	+	0.00594954i
$225$		0			0
$226$	8.03750	−	13.9214i	0.534646	−	0.926035i
$227$	1.51152	+	2.61803i	0.100323	+	0.173765i	0.911818	−	0.410595i	$-0.134679\pi$
$227$	1.51152	+	2.61803i	0.100323	+	0.173765i	−0.811495	+	0.584360i	$0.801346\pi$
$228$		0			0
$229$	−9.22014	−	5.32325i	−0.609284	−	0.351770i	0.163401	−	0.986560i	$-0.447754\pi$
$229$	−9.22014	−	5.32325i	−0.609284	−	0.351770i	−0.772685	+	0.634789i	$0.781087\pi$
$230$		0			0
$231$		0			0
$232$	−9.34805			−0.613730
$233$	3.45185	+	1.99293i	0.226138	+	0.130561i	0.608789	−	0.793332i	$-0.291655\pi$
$233$	3.45185	+	1.99293i	0.226138	+	0.130561i	−0.382651	+	0.923893i	$0.624989\pi$
$234$		0			0
$235$		0			0
$236$	−3.10680	+	5.38113i	−0.202235	+	0.350282i
$237$		0			0
$238$	5.53771	−	8.88678i	0.358956	−	0.576044i
$239$		−	8.24699i		−	0.533453i	−0.963772	−	0.266727i	$-0.914058\pi$
$239$		−	8.24699i		−	0.533453i	0.963772	−	0.266727i	$-0.0859421\pi$
$240$		0			0
$241$	−9.48785	+	5.47782i	−0.611166	+	0.352857i	−0.773422	−	0.633892i	$-0.781456\pi$
$241$	−9.48785	+	5.47782i	−0.611166	+	0.352857i	0.162255	+	0.986749i	$0.448123\pi$
$242$	7.33053	−	4.23229i	0.471225	−	0.272062i
$243$		0			0
$244$			11.0005i			0.704235i
$245$		0			0
$246$		0			0
$247$	−0.289312	+	0.501103i	−0.0184085	+	0.0318844i
$248$	−5.16508	−	8.94618i	−0.327983	−	0.568083i
$249$		0			0
$250$		0			0
$251$	21.7369			1.37202			0.686012	−	0.727590i	$-0.259360\pi$
$251$	21.7369			1.37202			0.686012	+	0.727590i	$0.259360\pi$
$252$		0			0
$253$	12.3971			0.779399
$254$	11.4465	+	6.60867i	0.718220	+	0.414665i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.71758	+	15.0993i	−0.543787	+	0.941868i	0.454895	+	0.890545i	$0.349677\pi$
$257$	−8.71758	+	15.0993i	−0.543787	+	0.941868i	−0.998682	+	0.0513223i	$0.983656\pi$
$258$		0			0
$259$	0.995397	−	0.530852i	0.0618510	−	0.0329856i
$260$		0			0
$261$		0			0
$262$	−8.14203	+	4.70080i	−0.503016	+	0.290417i
$263$	15.8926	−	9.17557i	0.979977	−	0.565790i	0.0777137	−	0.996976i	$-0.475238\pi$
$263$	15.8926	−	9.17557i	0.979977	−	0.565790i	0.902263	+	0.431186i	$0.141905\pi$
$264$		0			0
$265$		0			0
$266$	−0.0556953	+	1.65392i	−0.00341490	+	0.101408i
$267$		0			0
$268$	0.178089	−	0.308459i	0.0108785	−	0.0188422i
$269$	−12.4185	−	21.5095i	−0.757171	−	1.31146i	−0.944288	−	0.329121i	$-0.893248\pi$
$269$	−12.4185	−	21.5095i	−0.757171	−	1.31146i	0.187117	−	0.982338i	$-0.440086\pi$
$270$		0			0
$271$	21.1663	+	12.2204i	1.28576	+	0.742335i	0.977895	−	0.209094i	$-0.0670516\pi$
$271$	21.1663	+	12.2204i	1.28576	+	0.742335i	0.307867	+	0.951430i	$0.400385\pi$
$272$	−3.95765			−0.239968
$273$		0			0
$274$	−9.37271			−0.566226
$275$		0			0
$276$		0			0
$277$	−11.5985	−	20.0892i	−0.696888	−	1.20704i	−0.969540	−	0.244932i	$-0.921234\pi$
$277$	−11.5985	−	20.0892i	−0.696888	−	1.20704i	0.272653	−	0.962113i	$-0.412099\pi$
$278$	7.05530	−	12.2201i	0.423149	−	0.732915i
$279$		0			0
$280$		0			0
$281$			14.0801i			0.839949i	0.907536	+	0.419974i	$0.137961\pi$
$281$			14.0801i			0.839949i	−0.907536	+	0.419974i	$0.862039\pi$
$282$		0			0
$283$	2.42331	−	1.39910i	0.144051	−	0.0831677i	−0.426242	−	0.904609i	$-0.640163\pi$
$283$	2.42331	−	1.39910i	0.144051	−	0.0831677i	0.570293	+	0.821441i	$0.306830\pi$
$284$	7.86330	−	4.53988i	0.466601	−	0.269392i
$285$		0			0
$286$		−	1.47303i		−	0.0871018i
$287$	18.7600	+	11.6901i	1.10737	+	0.690047i
$288$		0			0
$289$	0.668498	−	1.15787i	0.0393234	−	0.0681101i
$290$		0			0
$291$		0			0
$292$	−5.91515	−	3.41511i	−0.346158	−	0.199854i
$293$	25.5598			1.49322			0.746609	−	0.665263i	$-0.231681\pi$
$293$	25.5598			1.49322			0.746609	+	0.665263i	$0.231681\pi$
$294$		0			0
$295$		0			0
$296$	−0.369259	−	0.213192i	−0.0214627	−	0.0123915i
$297$		0			0
$298$	−1.23612	−	2.14103i	−0.0716068	−	0.124027i
$299$	−3.60121	+	6.23749i	−0.208264	+	0.360723i
$300$		0			0
$301$	14.0821	+	8.77510i	0.811677	+	0.505788i
$302$		−	20.8849i		−	1.20179i
$303$		0			0
$304$	0.541679	−	0.312739i	0.0310674	−	0.0179368i
$305$		0			0
$306$		0			0
$307$		−	34.2860i		−	1.95681i	−0.206704	−	0.978403i	$-0.566274\pi$
$307$		−	34.2860i		−	1.95681i	0.206704	−	0.978403i	$-0.433726\pi$
$308$	−1.98243	−	3.71725i	−0.112960	−	0.211810i
$309$		0			0
$310$		0			0
$311$	4.34021	+	7.51746i	0.246110	+	0.426276i	0.962443	−	0.271483i	$-0.0875141\pi$
$311$	4.34021	+	7.51746i	0.246110	+	0.426276i	−0.716333	+	0.697759i	$0.754181\pi$
$312$		0			0
$313$	−25.9992	−	15.0106i	−1.46956	−	0.848452i	−0.470145	−	0.882589i	$-0.655798\pi$
$313$	−25.9992	−	15.0106i	−1.46956	−	0.848452i	−0.999417	+	0.0341376i	$0.989132\pi$
$314$	−24.4475			−1.37965
$315$		0			0
$316$	9.05164			0.509195
$317$	24.0111	+	13.8628i	1.34860	+	0.778613i	0.988051	−	0.154128i	$-0.0492567\pi$
$317$	24.0111	+	13.8628i	1.34860	+	0.778613i	0.360547	+	0.932741i	$0.382590\pi$
$318$		0			0
$319$	7.44246	+	12.8907i	0.416698	+	0.721742i
$320$		0			0
$321$		0			0
$322$	−0.693269	+	20.5872i	−0.0386344	+	1.14728i
$323$		−	2.47542i		−	0.137736i
$324$		0			0
$325$		0			0
$326$	−5.12267	+	2.95758i	−0.283719	+	0.163805i
$327$		0			0
$328$		−	8.35463i		−	0.461307i
$329$	−6.49298	+	3.46275i	−0.357970	+	0.190908i
$330$		0			0
$331$	−3.15175	+	5.45899i	−0.173236	+	0.300053i	−0.939549	−	0.342414i	$-0.888756\pi$
$331$	−3.15175	+	5.45899i	−0.173236	+	0.300053i	0.766314	+	0.642467i	$0.222089\pi$
$332$	0.404949	+	0.701392i	0.0222245	+	0.0384939i
$333$		0			0
$334$	10.5170	+	6.07201i	0.575467	+	0.332246i
$335$		0			0
$336$		0			0
$337$	27.4097			1.49310			0.746550	−	0.665329i	$-0.231709\pi$
$337$	27.4097			1.49310			0.746550	+	0.665329i	$0.231709\pi$
$338$	−10.5172	−	6.07210i	−0.572060	−	0.330279i
$339$		0			0
$340$		0			0
$341$	−8.22437	+	14.2450i	−0.445374	+	0.771411i
$342$		0			0
$343$	−1.86711	+	18.4259i	−0.100815	+	0.994905i
$344$		−	6.27133i		−	0.338127i
$345$		0			0
$346$	14.2014	−	8.19918i	0.763472	−	0.440791i
$347$	−7.07258	+	4.08336i	−0.379676	+	0.219206i	−0.677677	−	0.735359i	$-0.737013\pi$
$347$	−7.07258	+	4.08336i	−0.379676	+	0.219206i	0.298001	+	0.954566i	$0.403680\pi$
$348$		0			0
$349$		−	27.5885i		−	1.47678i	−0.674374	−	0.738390i	$-0.735587\pi$
$349$		−	27.5885i		−	1.47678i	0.674374	−	0.738390i	$-0.264413\pi$
$350$		0			0
$351$		0			0
$352$	−0.796151	+	1.37897i	−0.0424350	+	0.0734996i
$353$	3.52142	+	6.09929i	0.187426	+	0.324632i	0.944391	−	0.328823i	$-0.106652\pi$
$353$	3.52142	+	6.09929i	0.187426	+	0.324632i	−0.756965	+	0.653455i	$0.773319\pi$
$354$		0			0
$355$		0			0
$356$	4.01442			0.212764
$357$		0			0
$358$	−3.15693			−0.166849
$359$	−14.1545	−	8.17213i	−0.747048	−	0.431308i	0.0775782	−	0.996986i	$-0.475281\pi$
$359$	−14.1545	−	8.17213i	−0.747048	−	0.431308i	−0.824626	+	0.565678i	$0.808615\pi$
$360$		0			0
$361$	−9.30439	−	16.1157i	−0.489705	−	0.848193i
$362$	−4.08958	+	7.08336i	−0.214943	+	0.372293i
$363$		0			0
$364$	2.44618	+	0.0823743i	0.128214	+	0.00431759i
$365$		0			0
$366$		0			0
$367$	2.60498	−	1.50399i	0.135979	−	0.0785076i	−0.430467	−	0.902606i	$-0.641651\pi$
$367$	2.60498	−	1.50399i	0.135979	−	0.0785076i	0.566446	+	0.824099i	$0.308318\pi$
$368$	6.74256	−	3.89282i	0.351480	−	0.202927i
$369$		0			0
$370$		0			0
$371$	−8.86126	−	0.298401i	−0.460054	−	0.0154922i
$372$		0			0
$373$	−11.5985	+	20.0892i	−0.600549	+	1.04018i	0.392189	+	0.919884i	$0.371718\pi$
$373$	−11.5985	+	20.0892i	−0.600549	+	1.04018i	−0.992738	+	0.120296i	$0.961616\pi$
$374$	3.15089	+	5.45750i	0.162929	+	0.282201i
$375$		0			0
$376$	2.40868	+	1.39065i	0.124218	+	0.0717174i
$377$	−8.64780			−0.445384
$378$		0			0
$379$	−27.2718			−1.40086			−0.700429	−	0.713722i	$-0.747008\pi$
$379$	−27.2718			−1.40086			−0.700429	+	0.713722i	$0.747008\pi$
$380$		0			0
$381$		0			0
$382$	1.41421	+	2.44949i	0.0723575	+	0.125327i
$383$	2.13098	−	3.69096i	0.108888	−	0.188599i	−0.806432	−	0.591327i	$-0.798604\pi$
$383$	2.13098	−	3.69096i	0.108888	−	0.188599i	0.915320	+	0.402727i	$0.131938\pi$
$384$		0			0
$385$		0			0
$386$		−	17.7154i		−	0.901692i
$387$		0			0
$388$	−6.82186	+	3.93860i	−0.346327	+	0.199952i
$389$	1.80282	−	1.04086i	0.0914066	−	0.0527736i	−0.453600	−	0.891205i	$-0.649860\pi$
$389$	1.80282	−	1.04086i	0.0914066	−	0.0527736i	0.545007	+	0.838432i	$0.316527\pi$
$390$		0			0
$391$		−	30.8129i		−	1.55827i
$392$	6.28390	−	3.08425i	0.317385	−	0.155778i
$393$		0			0
$394$	−2.15175	+	3.72694i	−0.108404	+	0.187760i
$395$		0			0
$396$		0			0
$397$	−19.3791	−	11.1885i	−0.972610	−	0.561537i	−0.0725790	−	0.997363i	$-0.523123\pi$
$397$	−19.3791	−	11.1885i	−0.972610	−	0.561537i	−0.900031	+	0.435826i	$0.856456\pi$
$398$	−3.46410			−0.173640
$399$		0			0
$400$		0			0
$401$	17.0295	+	9.83196i	0.850411	+	0.490985i	0.860789	−	0.508961i	$-0.169970\pi$
$401$	17.0295	+	9.83196i	0.850411	+	0.490985i	−0.0103787	+	0.999946i	$0.503304\pi$
$402$		0			0
$403$	−4.77817	−	8.27603i	−0.238017	−	0.412258i
$404$	3.76411	−	6.51962i	0.187271	−	0.324363i
$405$		0			0
$406$	−21.8231	+	11.6384i	−1.08306	+	0.577606i
$407$			0.678932i			0.0336534i
$408$		0			0
$409$	−2.19932	+	1.26978i	−0.108750	+	0.0627866i	−0.553388	−	0.832923i	$-0.686665\pi$
$409$	−2.19932	+	1.26978i	−0.108750	+	0.0627866i	0.444639	+	0.895710i	$0.353332\pi$
$410$		0			0
$411$		0			0
$412$			1.66361i			0.0819601i
$413$	−0.553287	+	16.4303i	−0.0272255	+	0.808483i
$414$		0			0
$415$		0			0
$416$	−0.462546	−	0.801153i	−0.0226782	−	0.0392797i
$417$		0			0
$418$	−0.862517	−	0.497974i	−0.0421871	−	0.0243567i
$419$	32.0568			1.56608			0.783039	−	0.621973i	$-0.213669\pi$
$419$	32.0568			1.56608			0.783039	+	0.621973i	$0.213669\pi$
$420$		0			0
$421$	−25.2201			−1.22915			−0.614577	−	0.788857i	$-0.710673\pi$
$421$	−25.2201			−1.22915			−0.614577	+	0.788857i	$0.710673\pi$
$422$	−8.99682	−	5.19432i	−0.437959	−	0.252855i
$423$		0			0
$424$	1.67557	+	2.90217i	0.0813729	+	0.140942i
$425$		0			0
$426$		0			0
$427$	13.6957	+	25.6808i	0.662784	+	1.24278i
$428$			19.4028i			0.937869i
$429$		0			0
$430$		0			0
$431$	−29.1599	+	16.8355i	−1.40458	+	0.810937i	−0.994859	−	0.101271i	$-0.967709\pi$
$431$	−29.1599	+	16.8355i	−1.40458	+	0.810937i	−0.409726	+	0.912209i	$0.634376\pi$
$432$		0			0
$433$		−	22.7610i		−	1.09382i	−0.837190	−	0.546912i	$-0.815803\pi$
$433$		−	22.7610i		−	1.09382i	0.837190	−	0.546912i	$-0.184197\pi$
$434$	−23.1960	−	14.4544i	−1.11344	−	0.693832i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	2.43487	+	4.21732i	0.116476	+	0.201742i
$438$		0			0
$439$	−1.86282	−	1.07550i	−0.0889074	−	0.0513307i	0.454887	−	0.890549i	$-0.349680\pi$
$439$	−1.86282	−	1.07550i	−0.0889074	−	0.0513307i	−0.543795	+	0.839218i	$0.683013\pi$
$440$		0			0
$441$		0			0
$442$	−3.66119			−0.174145
$443$	6.63790	+	3.83239i	0.315376	+	0.182082i	0.649330	−	0.760507i	$-0.275050\pi$
$443$	6.63790	+	3.83239i	0.315376	+	0.182082i	−0.333954	+	0.942590i	$0.608383\pi$
$444$		0			0
$445$		0			0
$446$	−9.17777	+	15.8964i	−0.434580	+	0.752715i
$447$		0			0
$448$	−2.24547	−	1.39924i	−0.106088	−	0.0661079i
$449$		−	18.8337i		−	0.888817i	−0.895824	−	0.444408i	$-0.853414\pi$
$449$		−	18.8337i		−	0.888817i	0.895824	−	0.444408i	$-0.146586\pi$
$450$		0			0
$451$	−11.5208	+	6.65155i	−0.542494	+	0.313209i
$452$	−13.9214	+	8.03750i	−0.654805	+	0.378052i
$453$		0			0
$454$		−	3.02304i		−	0.141879i
$455$		0			0
$456$		0			0
$457$	−14.6325	+	25.3442i	−0.684478	+	1.18555i	0.289123	+	0.957292i	$0.406636\pi$
$457$	−14.6325	+	25.3442i	−0.684478	+	1.18555i	−0.973601	+	0.228258i	$0.926697\pi$
$458$	5.32325	+	9.22014i	0.248739	+	0.430829i
$459$		0			0
$460$		0			0
$461$	14.1963			0.661188			0.330594	−	0.943773i	$-0.392751\pi$
$461$	14.1963			0.661188			0.330594	+	0.943773i	$0.392751\pi$
$462$		0			0
$463$	−7.65787			−0.355891			−0.177946	−	0.984040i	$-0.556945\pi$
$463$	−7.65787			−0.355891			−0.177946	+	0.984040i	$0.556945\pi$
$464$	8.09565	+	4.67403i	0.375831	+	0.216986i
$465$		0			0
$466$	−1.99293	−	3.45185i	−0.0923206	−	0.159904i
$467$	8.85713	−	15.3410i	0.409859	−	0.709897i	−0.585015	−	0.811023i	$-0.698911\pi$
$467$	8.85713	−	15.3410i	0.409859	−	0.709897i	0.994874	+	0.101126i	$0.0322446\pi$
$468$		0			0
$469$	0.0317157	−	0.941825i	0.00146450	−	0.0434894i
$470$		0			0
$471$		0			0
$472$	5.38113	−	3.10680i	0.247687	−	0.143002i
$473$	−8.64800	+	4.99293i	−0.397636	+	0.229575i
$474$		0			0
$475$		0			0
$476$	−9.23918	+	4.92732i	−0.423477	+	0.225843i
$477$		0			0
$478$	−4.12349	+	7.14210i	−0.188604	+	0.326672i
$479$	6.41996	+	11.1197i	0.293336	+	0.508072i	0.974596	−	0.223969i	$-0.0719013\pi$
$479$	6.41996	+	11.1197i	0.293336	+	0.508072i	−0.681261	+	0.732041i	$0.738568\pi$
$480$		0			0
$481$	−0.341598	−	0.197222i	−0.0155755	−	0.00899254i
$482$	10.9556			0.499015
$483$		0			0
$484$	−8.46457			−0.384753
$485$		0			0
$486$		0			0
$487$	−1.88929	−	3.27235i	−0.0856119	−	0.148284i	0.820040	−	0.572306i	$-0.193951\pi$
$487$	−1.88929	−	3.27235i	−0.0856119	−	0.148284i	−0.905652	+	0.424022i	$0.860618\pi$
$488$	5.50025	−	9.52671i	0.248985	−	0.431254i
$489$		0			0
$490$		0			0
$491$		−	32.1664i		−	1.45165i	−0.687880	−	0.725824i	$-0.741459\pi$
$491$		−	32.1664i		−	1.45165i	0.687880	−	0.725824i	$-0.258541\pi$
$492$		0			0
$493$	32.0398	−	18.4982i	1.44300	−	0.833115i
$494$	0.501103	−	0.289312i	0.0225457	−	0.0130168i
$495$		0			0
$496$			10.3302i			0.463838i
$497$	12.7048	−	20.3883i	0.569886	−	0.914540i
$498$		0			0
$499$	15.9683	−	27.6579i	0.714839	−	1.23814i	−0.248183	−	0.968713i	$-0.579833\pi$
$499$	15.9683	−	27.6579i	0.714839	−	1.23814i	0.963022	−	0.269424i	$-0.0868332\pi$
$500$		0			0
$501$		0			0
$502$	−18.8247	−	10.8685i	−0.840190	−	0.485084i
$503$	5.29834			0.236241			0.118121	−	0.992999i	$-0.462313\pi$
$503$	5.29834			0.236241			0.118121	+	0.992999i	$0.462313\pi$
$504$		0			0
$505$		0			0
$506$	−10.7362	−	6.19855i	−0.477282	−	0.275559i
$507$		0			0
$508$	−6.60867	−	11.4465i	−0.293212	−	0.507858i
$509$	−18.6321	+	32.2718i	−0.825854	+	1.43042i	0.0754100	+	0.997153i	$0.475973\pi$
$509$	−18.6321	+	32.2718i	−0.825854	+	1.43042i	−0.901265	+	0.433269i	$0.857360\pi$
$510$		0			0
$511$	−18.0608	−	0.608195i	−0.798965	−	0.0269049i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	15.0993	−	8.71758i	0.666001	−	0.384516i
$515$		0			0
$516$		0			0
$517$		−	4.42867i		−	0.194773i
$518$	−1.12747	−	0.0379671i	−0.0495380	−	0.00166818i
$519$		0			0
$520$		0			0
$521$	6.00676	+	10.4040i	0.263161	+	0.455808i	0.967080	−	0.254472i	$-0.0819017\pi$
$521$	6.00676	+	10.4040i	0.263161	+	0.455808i	−0.703919	+	0.710280i	$0.748568\pi$
$522$		0			0
$523$	−23.4136	−	13.5178i	−1.02380	−	0.591093i	−0.108600	−	0.994085i	$-0.534637\pi$
$523$	−23.4136	−	13.5178i	−1.02380	−	0.591093i	−0.915203	+	0.402992i	$0.867970\pi$
$524$	9.40160			0.410711
$525$		0			0
$526$	−18.3511			−0.800148
$527$	35.4058	+	20.4416i	1.54230	+	0.890449i
$528$		0			0
$529$	18.8081	+	32.5766i	0.817744	+	1.41637i
$530$		0			0
$531$		0			0
$532$	0.875193	−	1.40449i	0.0379444	−	0.0608923i
$533$		−	7.72879i		−	0.334771i
$534$		0			0
$535$		0			0
$536$	−0.308459	+	0.178089i	−0.0133234	+	0.00769228i
$537$		0			0
$538$			24.8371i			1.07080i
$539$	−9.25604	−	6.20981i	−0.398686	−	0.267475i
$540$		0			0
$541$	5.85450	−	10.1403i	0.251705	−	0.435965i	−0.712291	−	0.701885i	$-0.752342\pi$
$541$	5.85450	−	10.1403i	0.251705	−	0.435965i	0.963995	+	0.265919i	$0.0856755\pi$
$542$	−12.2204	−	21.1663i	−0.524910	−	0.909171i
$543$		0			0
$544$	3.42743	+	1.97883i	0.146950	+	0.0848415i
$545$		0			0
$546$		0			0
$547$	17.6050			0.752737			0.376369	−	0.926470i	$-0.377173\pi$
$547$	17.6050			0.752737			0.376369	+	0.926470i	$0.377173\pi$
$548$	8.11701	+	4.68636i	0.346741	+	0.200191i
$549$		0			0
$550$		0			0
$551$	−2.92350	+	5.06364i	−0.124545	+	0.215718i
$552$		0			0
$553$	21.1312	−	11.2694i	0.898589	−	0.479224i
$554$			23.1970i			0.985548i
$555$		0			0
$556$	−12.2201	+	7.05530i	−0.518249	+	0.299211i
$557$	−17.3913	+	10.0409i	−0.736892	+	0.425445i	−0.820938	−	0.571017i	$-0.806549\pi$
$557$	−17.3913	+	10.0409i	−0.736892	+	0.425445i	0.0840462	+	0.996462i	$0.473216\pi$
$558$		0			0
$559$		−	5.80155i		−	0.245380i
$560$		0			0
$561$		0			0
$562$	7.04005	−	12.1937i	0.296967	−	0.514361i
$563$	−11.9038	−	20.6180i	−0.501687	−	0.868947i	−0.999998	−	0.00194851i	$-0.999380\pi$
$563$	−11.9038	−	20.6180i	−0.501687	−	0.868947i	0.498312	−	0.866998i	$-0.333954\pi$
$564$		0			0
$565$		0			0
$566$	−2.79820			−0.117617
$567$		0			0
$568$	−9.07975			−0.380978
$569$	35.8766	+	20.7134i	1.50403	+	0.868350i	0.999989	+	0.00466765i	$0.00148577\pi$
$569$	35.8766	+	20.7134i	1.50403	+	0.868350i	0.504037	+	0.863682i	$0.331848\pi$
$570$		0			0
$571$	−20.5784	−	35.6428i	−0.861177	−	1.49160i	−0.870793	−	0.491649i	$-0.836394\pi$
$571$	−20.5784	−	35.6428i	−0.861177	−	1.49160i	0.00961607	−	0.999954i	$-0.496939\pi$
$572$	−0.736513	+	1.27568i	−0.0307951	+	0.0533388i
$573$		0			0
$574$	−10.4016	−	19.5040i	−0.434155	−	0.814080i
$575$		0			0
$576$		0			0
$577$	10.7532	−	6.20835i	0.447661	−	0.258457i	−0.259181	−	0.965829i	$-0.583453\pi$
$577$	10.7532	−	6.20835i	0.447661	−	0.258457i	0.706842	+	0.707372i	$0.250119\pi$
$578$	−1.15787	+	0.668498i	−0.0481611	+	0.0278058i
$579$		0			0
$580$		0			0
$581$	1.81860	+	1.13324i	0.0754482	+	0.0470148i
$582$		0			0
$583$	2.66802	−	4.62114i	0.110498	−	0.191388i
$584$	3.41511	+	5.91515i	0.141318	+	0.244771i
$585$		0			0
$586$	−22.1354	−	12.7799i	−0.914406	−	0.527932i
$587$	−4.01980			−0.165915			−0.0829575	−	0.996553i	$-0.526437\pi$
$587$	−4.01980			−0.165915			−0.0829575	+	0.996553i	$0.526437\pi$
$588$		0			0
$589$	−6.46127			−0.266232
$590$		0			0
$591$		0			0
$592$	0.213192	+	0.369259i	0.00876213	+	0.0151764i
$593$	−21.7667	+	37.7010i	−0.893850	+	1.54819i	−0.0586292	+	0.998280i	$0.518673\pi$
$593$	−21.7667	+	37.7010i	−0.893850	+	1.54819i	−0.835221	+	0.549914i	$0.814660\pi$
$594$		0			0
$595$		0			0
$596$			2.47225i			0.101267i
$597$		0			0
$598$	6.23749	−	3.60121i	0.255070	−	0.147265i
$599$	−27.8218	+	16.0629i	−1.13677	+	0.656314i	−0.945629	−	0.325249i	$-0.894552\pi$
$599$	−27.8218	+	16.0629i	−1.13677	+	0.656314i	−0.191141	+	0.981563i	$0.561219\pi$
$600$		0			0
$601$		−	8.21681i		−	0.335171i	−0.985858	−	0.167585i	$-0.946403\pi$
$601$		−	8.21681i		−	0.335171i	0.985858	−	0.167585i	$-0.0535970\pi$
$602$	−7.80788	−	14.6405i	−0.318225	−	0.596702i
$603$		0			0
$604$	−10.4425	+	18.0869i	−0.424898	+	0.735945i
$605$		0			0
$606$		0			0
$607$	−24.4532	−	14.1180i	−0.992523	−	0.573034i	−0.0864957	−	0.996252i	$-0.527567\pi$
$607$	−24.4532	−	14.1180i	−0.992523	−	0.573034i	−0.906028	+	0.423219i	$0.860900\pi$
$608$	−0.625477			−0.0253664
$609$		0			0
$610$		0			0
$611$	2.22825	+	1.28648i	0.0901452	+	0.0520454i
$612$		0			0
$613$	15.3962	+	26.6670i	0.621846	+	1.07707i	0.989142	+	0.146965i	$0.0469504\pi$
$613$	15.3962	+	26.6670i	0.621846	+	1.07707i	−0.367296	+	0.930104i	$0.619716\pi$
$614$	−17.1430	+	29.6926i	−0.691836	+	1.19829i
$615$		0			0
$616$	−0.141786	+	4.21045i	−0.00571272	+	0.169644i
$617$			4.42613i			0.178189i	0.996023	+	0.0890947i	$0.0283974\pi$
$617$			4.42613i			0.178189i	−0.996023	+	0.0890947i	$0.971603\pi$
$618$		0			0
$619$	−9.47047	+	5.46778i	−0.380650	+	0.219768i	−0.678101	−	0.734969i	$-0.737197\pi$
$619$	−9.47047	+	5.46778i	−0.380650	+	0.219768i	0.297451	+	0.954737i	$0.403864\pi$
$620$		0			0
$621$		0			0
$622$		−	8.68041i		−	0.348053i
$623$	9.37171	−	4.99800i	0.375470	−	0.200241i
$624$		0			0
$625$		0			0
$626$	15.0106	+	25.9992i	0.599946	+	1.03914i
$627$		0			0
$628$	21.1722	+	12.2238i	0.844862	+	0.487781i
$629$	1.68748			0.0672841
$630$		0			0
$631$	−38.2293			−1.52189			−0.760943	−	0.648819i	$-0.775263\pi$
$631$	−38.2293			−1.52189			−0.760943	+	0.648819i	$0.775263\pi$
$632$	−7.83895	−	4.52582i	−0.311817	−	0.180028i
$633$		0			0
$634$	−13.8628	−	24.0111i	−0.550563	−	0.953603i
$635$		0			0
$636$		0			0
$637$	5.81318	−	2.85321i	0.230327	−	0.113048i
$638$		−	14.8849i		−	0.589300i
$639$		0			0
$640$		0			0
$641$	−29.0339	+	16.7627i	−1.14677	+	0.662088i	−0.948098	−	0.317979i	$-0.896996\pi$
$641$	−29.0339	+	16.7627i	−1.14677	+	0.662088i	−0.198671	+	0.980066i	$0.563663\pi$
$642$		0			0
$643$			17.4072i			0.686474i	0.939249	+	0.343237i	$0.111523\pi$
$643$			17.4072i			0.686474i	−0.939249	+	0.343237i	$0.888477\pi$
$644$	10.8940	−	17.4824i	0.429283	−	0.688903i
$645$		0			0
$646$	−1.23771	+	2.14378i	−0.0486971	+	0.0843458i
$647$	−19.1301	−	33.1343i	−0.752082	−	1.30264i	−0.946812	−	0.321787i	$-0.895716\pi$
$647$	−19.1301	−	33.1343i	−0.752082	−	1.30264i	0.194730	−	0.980857i	$-0.437617\pi$
$648$		0			0
$649$	−8.56839	−	4.94696i	−0.336339	−	0.194185i
$650$		0			0
$651$		0			0
$652$	5.91515			0.231655
$653$	28.0023	+	16.1671i	1.09581	+	0.632669i	0.935119	−	0.354335i	$-0.115293\pi$
$653$	28.0023	+	16.1671i	1.09581	+	0.632669i	0.160696	+	0.987004i	$0.448626\pi$
$654$		0			0
$655$		0			0
$656$	−4.17731	+	7.23532i	−0.163097	+	0.282492i
$657$		0			0
$658$	7.35446	+	0.247660i	0.286707	+	0.00965478i
$659$			16.4516i			0.640865i	0.947271	+	0.320433i	$0.103828\pi$
$659$			16.4516i			0.640865i	−0.947271	+	0.320433i	$0.896172\pi$
$660$		0			0
$661$	−2.14550	+	1.23870i	−0.0834502	+	0.0481800i	−0.541144	−	0.840930i	$-0.682009\pi$
$661$	−2.14550	+	1.23870i	−0.0834502	+	0.0481800i	0.457694	+	0.889110i	$0.348675\pi$
$662$	5.45899	−	3.15175i	0.212170	−	0.122496i
$663$		0			0
$664$		−	0.809898i		−	0.0314301i
$665$		0			0
$666$		0			0
$667$	−36.3903	+	63.0298i	−1.40904	+	2.44052i
$668$	−6.07201	−	10.5170i	−0.234933	−	0.406916i
$669$		0			0
$670$		0			0
$671$	−17.5161			−0.676202
$672$		0			0
$673$	17.0784			0.658326			0.329163	−	0.944273i	$-0.393233\pi$
$673$	17.0784			0.658326			0.329163	+	0.944273i	$0.393233\pi$
$674$	−23.7375	−	13.7048i	−0.914333	−	0.527891i
$675$		0			0
$676$	6.07210	+	10.5172i	0.233542	+	0.404507i
$677$	−23.3041	+	40.3639i	−0.895650	+	1.55131i	−0.0626524	+	0.998035i	$0.519956\pi$
$677$	−23.3041	+	40.3639i	−0.895650	+	1.55131i	−0.832998	+	0.553276i	$0.813377\pi$
$678$		0			0
$679$	−11.0221	+	17.6880i	−0.422990	+	0.678803i
$680$		0			0
$681$		0			0
$682$	14.2450	−	8.22437i	0.545470	−	0.314927i
$683$	2.04994	−	1.18353i	0.0784388	−	0.0452867i	−0.460268	−	0.887780i	$-0.652247\pi$
$683$	2.04994	−	1.18353i	0.0784388	−	0.0452867i	0.538706	+	0.842494i	$0.318913\pi$
$684$		0			0
$685$		0			0
$686$	10.8299	−	15.0237i	0.413488	−	0.573609i
$687$		0			0
$688$	−3.13566	+	5.43113i	−0.119546	+	0.207060i
$689$	1.55006	+	2.68478i	0.0590524	+	0.102282i
$690$		0			0
$691$	−19.0534	−	11.0005i	−0.724826	−	0.418479i	0.0917001	−	0.995787i	$-0.470770\pi$
$691$	−19.0534	−	11.0005i	−0.724826	−	0.418479i	−0.816527	+	0.577308i	$0.804103\pi$
$692$	−16.3984			−0.623372
$693$		0			0
$694$	8.16672			0.310004
$695$		0			0
$696$		0			0
$697$	16.5323	+	28.6349i	0.626207	+	1.08462i
$698$	−13.7943	+	23.8924i	−0.522120	+	0.904339i
$699$		0			0
$700$		0			0
$701$		−	28.7909i		−	1.08742i	−0.839274	−	0.543708i	$-0.817020\pi$
$701$		−	28.7909i		−	1.08742i	0.839274	−	0.543708i	$-0.182980\pi$
$702$		0			0
$703$	−0.230963	+	0.133347i	−0.00871094	+	0.00502926i
$704$	1.37897	−	0.796151i	0.0519721	−	0.0300061i
$705$		0			0
$706$		−	7.04285i		−	0.265061i
$707$	0.670346	−	19.9065i	0.0252110	−	0.748661i
$708$		0			0
$709$	−7.64049	+	13.2337i	−0.286945	+	0.497003i	−0.973079	−	0.230472i	$-0.925973\pi$
$709$	−7.64049	+	13.2337i	−0.286945	+	0.497003i	0.686134	+	0.727475i	$0.259306\pi$
$710$		0			0
$711$		0			0
$712$	−3.47659	−	2.00721i	−0.130291	−	0.0752234i
$713$	−80.4269			−3.01201
$714$		0			0
$715$		0			0
$716$	2.73398	+	1.57846i	0.102174	+	0.0589900i
$717$		0			0
$718$	8.17213	+	14.1545i	0.304981	+	0.528243i
$719$	8.33730	−	14.4406i	0.310929	−	0.538545i	−0.667635	−	0.744489i	$-0.732693\pi$
$719$	8.33730	−	14.4406i	0.310929	−	0.538545i	0.978564	+	0.205944i	$0.0660266\pi$
$720$		0			0
$721$	2.07121	+	3.88372i	0.0771360	+	0.144637i
$722$			18.6088i			0.692547i
$723$		0			0
$724$	7.08336	−	4.08958i	0.263251	−	0.151988i
$725$		0			0
$726$		0			0
$727$		−	32.4228i		−	1.20250i	−0.799062	−	0.601248i	$-0.794670\pi$
$727$		−	32.4228i		−	1.20250i	0.799062	−	0.601248i	$-0.205330\pi$
$728$	−2.07726	−	1.29443i	−0.0769885	−	0.0479746i
$729$		0			0
$730$		0			0
$731$	12.4099	+	21.4945i	0.458996	+	0.795004i
$732$		0			0
$733$	40.1207	+	23.1637i	1.48189	+	0.855570i	0.999789	−	0.0205452i	$-0.00654019\pi$
$733$	40.1207	+	23.1637i	1.48189	+	0.855570i	0.482102	+	0.876115i	$0.339874\pi$
$734$	−3.00798			−0.111026
$735$		0			0
$736$	−7.78564			−0.286983
$737$	0.491161	+	0.283572i	0.0180921	+	0.0104455i
$738$		0			0
$739$	−8.23689	−	14.2667i	−0.302999	−	0.524809i	0.673815	−	0.738900i	$-0.264655\pi$
$739$	−8.23689	−	14.2667i	−0.302999	−	0.524809i	−0.976814	+	0.214091i	$0.931321\pi$
$740$		0			0
$741$		0			0
$742$	7.52488	+	4.68905i	0.276247	+	0.172141i
$743$		−	38.4778i		−	1.41161i	−0.708405	−	0.705806i	$-0.750585\pi$
$743$		−	38.4778i		−	1.41161i	0.708405	−	0.705806i	$-0.249415\pi$
$744$		0			0
$745$		0			0
$746$	20.0892	−	11.5985i	0.735519	−	0.424652i
$747$		0			0
$748$		−	6.30178i		−	0.230416i
$749$	24.1567	+	45.2960i	0.882666	+	1.65508i
$750$		0			0
$751$	−18.9145	+	32.7608i	−0.690198	+	1.19546i	0.281574	+	0.959539i	$0.409143\pi$
$751$	−18.9145	+	32.7608i	−0.690198	+	1.19546i	−0.971773	+	0.235919i	$0.924190\pi$
$752$	−1.39065	−	2.40868i	−0.0507118	−	0.0878355i
$753$		0			0
$754$	7.48922	+	4.32390i	0.272741	+	0.157467i
$755$		0			0
$756$		0			0
$757$	−11.1485			−0.405197			−0.202599	−	0.979262i	$-0.564939\pi$
$757$	−11.1485			−0.405197			−0.202599	+	0.979262i	$0.564939\pi$
$758$	23.6181	+	13.6359i	0.857846	+	0.495278i
$759$		0			0
$760$		0			0
$761$	−14.6239	+	25.3294i	−0.530117	+	0.918189i	0.469266	+	0.883057i	$0.344519\pi$
$761$	−14.6239	+	25.3294i	−0.530117	+	0.918189i	−0.999383	+	0.0351321i	$0.988815\pi$
$762$		0			0
$763$	−0.178089	+	5.28850i	−0.00644726	+	0.191457i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$	−3.69096	+	2.13098i	−0.133360	+	0.0769953i
$767$	4.97804	−	2.87407i	0.179747	−	0.103777i
$768$		0			0
$769$			0.892823i			0.0321960i	0.999870	+	0.0160980i	$0.00512438\pi$
$769$			0.892823i			0.0321960i	−0.999870	+	0.0160980i	$0.994876\pi$
$770$		0			0
$771$		0			0
$772$	−8.85772	+	15.3420i	−0.318796	+	0.552172i
$773$	−9.89011	−	17.1302i	−0.355723	−	0.616130i	0.631519	−	0.775361i	$-0.282432\pi$
$773$	−9.89011	−	17.1302i	−0.355723	−	0.616130i	−0.987241	+	0.159231i	$0.949099\pi$
$774$		0			0
$775$		0			0
$776$	7.87721			0.282775
$777$		0			0
$778$	−2.08172			−0.0746332
$779$	−4.52553	−	2.61281i	−0.162144	−	0.0936138i
$780$		0			0
$781$	7.22886	+	12.5207i	0.258669	+	0.448028i
$782$	−15.4064	+	26.6847i	−0.550933	+	0.954243i
$783$		0			0
$784$	−6.98414	−	0.470912i	−0.249434	−	0.0168183i
$785$		0			0
$786$		0			0
$787$	23.0325	−	13.2978i	0.821021	−	0.474017i	−0.0297473	−	0.999557i	$-0.509470\pi$
$787$	23.0325	−	13.2978i	0.821021	−	0.474017i	0.850769	+	0.525541i	$0.176137\pi$
$788$	3.72694	−	2.15175i	0.132767	−	0.0766529i
$789$		0			0
$790$		0			0
$791$	−22.4928	+	36.0959i	−0.799752	+	1.28342i
$792$		0			0
$793$	5.08823	−	8.81308i	0.180688	−	0.312962i
$794$	11.1885	+	19.3791i	0.397066	+	0.687739i
$795$		0			0
$796$	3.00000	+	1.73205i	0.106332	+	0.0613909i
$797$	21.4698			0.760499			0.380250	−	0.924884i	$-0.375838\pi$
$797$	21.4698			0.760499			0.380250	+	0.924884i	$0.375838\pi$
$798$		0			0
$799$	−11.0074			−0.389415
$800$		0			0
$801$		0			0
$802$	−9.83196	−	17.0295i	−0.347179	−	0.601331i
$803$	5.43790	−	9.41871i	0.191899	−	0.332379i
$804$		0			0
$805$		0			0
$806$			9.55634i			0.336608i
$807$		0			0
$808$	−6.51962	+	3.76411i	−0.229360	+	0.132421i
$809$	−18.2930	+	10.5615i	−0.643149	+	0.371322i	−0.785827	−	0.618447i	$-0.787762\pi$
$809$	−18.2930	+	10.5615i	−0.643149	+	0.371322i	0.142677	+	0.989769i	$0.454429\pi$
$810$		0			0
$811$		−	13.3784i		−	0.469779i	−0.972022	−	0.234889i	$-0.924527\pi$
$811$		−	13.3784i		−	0.469779i	0.972022	−	0.234889i	$-0.0754728\pi$
$812$	24.7186	+	0.832393i	0.867453	+	0.0292113i
$813$		0			0
$814$	0.339466	−	0.587972i	0.0118983	−	0.0206084i
$815$		0			0
$816$		0			0
$817$	−3.39705	−	1.96129i	−0.118848	−	0.0686167i
$818$	2.53956			0.0887936
$819$		0			0
$820$		0			0
$821$	5.67591	+	3.27699i	0.198091	+	0.114368i	0.595765	−	0.803159i	$-0.296849\pi$
$821$	5.67591	+	3.27699i	0.198091	+	0.114368i	−0.397674	+	0.917527i	$0.630182\pi$
$822$		0			0
$823$	−21.9344	−	37.9915i	−0.764585	−	1.32430i	−0.940466	−	0.339889i	$-0.889611\pi$
$823$	−21.9344	−	37.9915i	−0.764585	−	1.32430i	0.175880	−	0.984412i	$-0.443723\pi$
$824$	0.831805	−	1.44073i	0.0289773	−	0.0501901i
$825$		0			0
$826$	8.69432	−	13.9524i	0.302514	−	0.485467i
$827$		−	19.1611i		−	0.666296i	−0.942875	−	0.333148i	$-0.891889\pi$
$827$		−	19.1611i		−	0.666296i	0.942875	−	0.333148i	$-0.108111\pi$
$828$		0			0
$829$	−14.6635	+	8.46597i	−0.509284	+	0.294035i	−0.732539	−	0.680725i	$-0.761665\pi$
$829$	−14.6635	+	8.46597i	−0.509284	+	0.294035i	0.223255	+	0.974760i	$0.428332\pi$
$830$		0			0
$831$		0			0
$832$			0.925091i			0.0320718i
$833$	−15.4344	+	23.0058i	−0.534771	+	0.797103i
$834$		0			0
$835$		0			0
$836$	0.497974	+	0.862517i	0.0172228	+	0.0298308i
$837$		0			0
$838$	−27.7620	−	16.0284i	−0.959023	−	0.553692i
$839$	10.5028			0.362596			0.181298	−	0.983428i	$-0.441970\pi$
$839$	10.5028			0.362596			0.181298	+	0.983428i	$0.441970\pi$
$840$		0			0
$841$	−58.3861			−2.01331
$842$	21.8413	+	12.6101i	0.752700	+	0.434572i
$843$		0			0
$844$	5.19432	+	8.99682i	0.178796	+	0.309683i
$845$		0			0
$846$		0			0
$847$	−19.7606	+	10.5385i	−0.678984	+	0.362107i
$848$		−	3.35114i		−	0.115079i
$849$		0			0
$850$		0			0
$851$	−2.87492	+	1.65983i	−0.0985509	+	0.0568984i
$852$		0			0
$853$			30.2419i			1.03546i	0.855544	+	0.517731i	$0.173223\pi$
$853$			30.2419i			1.03546i	−0.855544	+	0.517731i	$0.826777\pi$
$854$	0.979534	−	29.0881i	0.0335190	−	0.995374i
$855$		0			0
$856$	9.70139	−	16.8033i	0.331587	−	0.574325i
$857$	−11.1322	−	19.2816i	−0.380270	−	0.658646i	0.610831	−	0.791761i	$-0.290835\pi$
$857$	−11.1322	−	19.2816i	−0.380270	−	0.658646i	−0.991101	+	0.133115i	$0.957502\pi$
$858$		0			0
$859$	−26.7059	−	15.4187i	−0.911195	−	0.526078i	−0.0303793	−	0.999538i	$-0.509672\pi$
$859$	−26.7059	−	15.4187i	−0.911195	−	0.526078i	−0.880815	+	0.473460i	$0.843005\pi$
$860$		0			0
$861$		0			0
$862$	33.6710			1.14684
$863$	−20.0190	−	11.5580i	−0.681454	−	0.393437i	0.118949	−	0.992900i	$-0.462048\pi$
$863$	−20.0190	−	11.5580i	−0.681454	−	0.393437i	−0.800403	+	0.599463i	$0.795381\pi$
$864$		0			0
$865$		0			0
$866$	−11.3805	+	19.7116i	−0.386725	+	0.669828i
$867$		0			0
$868$	12.8612	+	24.1159i	0.436536	+	0.818546i
$869$			14.4130i			0.488926i
$870$		0			0
$871$	−0.285353	+	0.164749i	−0.00966882	+	0.00558230i
$872$	1.73205	−	1.00000i	0.0586546	−	0.0338643i
$873$		0			0
$874$		−	4.86974i		−	0.164721i
$875$		0			0
$876$		0			0
$877$	−12.6074	+	21.8366i	−0.425720	+	0.737369i	−0.996487	−	0.0837427i	$-0.973313\pi$
$877$	−12.6074	+	21.8366i	−0.425720	+	0.737369i	0.570767	+	0.821112i	$0.306646\pi$
$878$	1.07550	+	1.86282i	0.0362963	+	0.0628670i
$879$		0			0
$880$		0			0
$881$	−20.5142			−0.691140			−0.345570	−	0.938393i	$-0.612314\pi$
$881$	−20.5142			−0.691140			−0.345570	+	0.938393i	$0.612314\pi$
$882$		0			0
$883$	−43.0491			−1.44872			−0.724358	−	0.689424i	$-0.757864\pi$
$883$	−43.0491			−1.44872			−0.724358	+	0.689424i	$0.757864\pi$
$884$	3.17068	+	1.83059i	0.106642	+	0.0615696i
$885$		0			0
$886$	−3.83239	−	6.63790i	−0.128752	−	0.223005i
$887$	−16.6952	+	28.9170i	−0.560571	+	0.970938i	0.436876	+	0.899522i	$0.356085\pi$
$887$	−16.6952	+	28.9170i	−0.560571	+	0.970938i	−0.997447	+	0.0714156i	$0.977248\pi$
$888$		0			0
$889$	−29.6791	−	18.4942i	−0.995405	−	0.620277i
$890$		0			0
$891$		0			0
$892$	15.8964	−	9.17777i	0.532250	−	0.307294i
$893$	1.50657	−	0.869820i	0.0504156	−	0.0291074i
$894$		0			0
$895$		0			0
$896$	1.24501	+	2.33451i	0.0415929	+	0.0779906i
$897$		0			0
$898$	−9.41684	+	16.3104i	−0.314244	+	0.544287i
$899$	−48.2834	−	83.6293i	−1.61034	−	2.78919i
$900$		0			0
$901$	−11.4858	−	6.63132i	−0.382647	−	0.220921i
$902$	13.3031			0.442945
$903$		0			0
$904$	16.0750			0.534646
$905$		0			0
$906$		0			0
$907$	−13.6898	−	23.7115i	−0.454563	−	0.787327i	0.544100	−	0.839021i	$-0.316871\pi$
$907$	−13.6898	−	23.7115i	−0.454563	−	0.787327i	−0.998663	+	0.0516937i	$0.983538\pi$
$908$	−1.51152	+	2.61803i	−0.0501616	+	0.0868825i
$909$		0			0
$910$		0			0
$911$			33.0422i			1.09474i	0.836892	+	0.547368i	$0.184370\pi$
$911$			33.0422i			1.09474i	−0.836892	+	0.547368i	$0.815630\pi$
$912$		0			0
$913$	−1.11683	+	0.644801i	−0.0369616	+	0.0213398i
$914$	25.3442	−	14.6325i	0.838311	−	0.483999i
$915$		0			0
$916$		−	10.6465i		−	0.351770i
$917$	21.9482	−	11.7051i	0.724792	−	0.386537i
$918$		0			0
$919$	−13.2444	+	22.9400i	−0.436893	+	0.756722i	−0.997448	−	0.0713958i	$-0.977255\pi$
$919$	−13.2444	+	22.9400i	−0.436893	+	0.756722i	0.560555	+	0.828117i	$0.310588\pi$
$920$		0			0
$921$		0			0
$922$	−12.2944	−	7.09815i	−0.404893	−	0.233765i
$923$	−8.39960			−0.276476
$924$		0			0
$925$		0			0
$926$	6.63191	+	3.82893i	0.217938	+	0.125827i
$927$		0			0
$928$	−4.67403	−	8.09565i	−0.153432	−	0.265753i
$929$	15.5952	−	27.0117i	0.511663	−	0.886226i	−0.488246	−	0.872706i	$-0.662363\pi$
$929$	15.5952	−	27.0117i	0.511663	−	0.886226i	0.999909	−	0.0135196i	$-0.00430354\pi$
$930$		0			0
$931$	0.294545	−	4.36842i	0.00965332	−	0.143169i
$932$			3.98585i			0.130561i
$933$		0			0
$934$	−15.3410	+	8.85713i	−0.501973	+	0.289814i
$935$		0			0
$936$		0			0
$937$			6.40017i			0.209084i	0.994520	+	0.104542i	$0.0333377\pi$
$937$			6.40017i			0.209084i	−0.994520	+	0.104542i	$0.966662\pi$
$938$	−0.498379	+	0.799787i	−0.0162727	+	0.0261140i
$939$		0			0
$940$		0			0
$941$	−2.56243	−	4.43825i	−0.0835327	−	0.144683i	0.821232	−	0.570594i	$-0.193287\pi$
$941$	−2.56243	−	4.43825i	−0.0835327	−	0.144683i	−0.904765	+	0.425911i	$0.859954\pi$
$942$		0			0
$943$	−56.3316	−	32.5231i	−1.83441	−	1.05910i
$944$	−6.21360			−0.202235
$945$		0			0
$946$	9.98585			0.324668
$947$	−36.5679	−	21.1125i	−1.18830	−	0.686064i	−0.230378	−	0.973101i	$-0.573996\pi$
$947$	−36.5679	−	21.1125i	−1.18830	−	0.686064i	−0.957919	+	0.287037i	$0.907330\pi$
$948$		0			0
$949$	3.15929	+	5.47206i	0.102555	+	0.177630i
$950$		0			0
$951$		0			0
$952$	10.4650	+	0.352407i	0.339174	+	0.0114216i
$953$			8.12428i			0.263171i	0.991305	+	0.131586i	$0.0420068\pi$
$953$			8.12428i			0.263171i	−0.991305	+	0.131586i	$0.957993\pi$
$954$		0			0
$955$		0			0
$956$	7.14210	−	4.12349i	0.230992	−	0.133363i
$957$		0			0
$958$		−	12.8399i		−	0.414839i
$959$	24.7838	+	0.834589i	0.800311	+	0.0269503i
$960$		0			0
$961$	37.8560	−	65.5686i	1.22116	−	2.11512i
$962$	0.197222	+	0.341598i	0.00635869	+	0.0110136i
$963$		0			0
$964$	−9.48785	−	5.47782i	−0.305583	−	0.176429i
$965$		0			0
$966$		0			0
$967$	52.3097			1.68217			0.841084	−	0.540905i	$-0.181918\pi$
$967$	52.3097			1.68217			0.841084	+	0.540905i	$0.181918\pi$
$968$	7.33053	+	4.23229i	0.235612	+	0.136031i
$969$		0			0
$970$		0			0
$971$	8.55280	−	14.8139i	0.274473	−	0.475400i	−0.695529	−	0.718498i	$-0.744830\pi$
$971$	8.55280	−	14.8139i	0.274473	−	0.475400i	0.970002	+	0.243097i	$0.0781634\pi$
$972$		0			0
$973$	−19.7441	+	31.6849i	−0.632968	+	1.01577i
$974$			3.77858i			0.121073i
$975$		0			0
$976$	−9.52671	+	5.50025i	−0.304943	+	0.176059i
$977$	−31.5215	+	18.1989i	−1.00846	+	0.582235i	−0.910741	−	0.412979i	$-0.864488\pi$
$977$	−31.5215	+	18.1989i	−1.00846	+	0.582235i	−0.0977201	+	0.995214i	$0.531155\pi$
$978$		0			0
$979$			6.39217i			0.204295i
$980$		0			0
$981$		0			0
$982$	−16.0832	+	27.8569i	−0.513235	+	0.888950i
$983$	12.8641	+	22.2813i	0.410302	+	0.710664i	0.994923	−	0.100643i	$-0.0320900\pi$
$983$	12.8641	+	22.2813i	0.410302	+	0.710664i	−0.584621	+	0.811307i	$0.698757\pi$
$984$		0			0
$985$		0			0
$986$	−36.9963			−1.17820
$987$		0			0
$988$	−0.578623			−0.0184085
$989$	−42.2848	−	24.4132i	−1.34458	−	0.776293i
$990$		0			0
$991$	6.07375	+	10.5200i	0.192939	+	0.334180i	0.946223	−	0.323515i	$-0.104865\pi$
$991$	6.07375	+	10.5200i	0.192939	+	0.334180i	−0.753284	+	0.657696i	$0.771531\pi$
$992$	5.16508	−	8.94618i	0.163991	−	0.284041i
$993$		0			0
$994$	−21.1968	+	11.3044i	−0.672321	+	0.358554i
$995$		0			0
$996$		0			0
$997$	14.8552	−	8.57663i	0.470468	−	0.271625i	−0.245968	−	0.969278i	$-0.579106\pi$
$997$	14.8552	−	8.57663i	0.470468	−	0.271625i	0.716435	+	0.697653i	$0.245772\pi$
$998$	−27.6579	+	15.9683i	−0.875495	+	0.505467i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.f.1601.6		32
3.2	odd	2	inner	3150.2.bf.f.1601.14		32
5.2	odd	4		630.2.bo.b.89.4	yes	16
5.3	odd	4		630.2.bo.a.89.2	✓	16
5.4	even	2	inner	3150.2.bf.f.1601.13		32
7.3	odd	6	inner	3150.2.bf.f.1151.16		32
15.2	even	4		630.2.bo.a.89.5	yes	16
15.8	even	4		630.2.bo.b.89.7	yes	16
15.14	odd	2	inner	3150.2.bf.f.1601.5		32
21.17	even	6	inner	3150.2.bf.f.1151.6		32
35.2	odd	12		4410.2.d.a.4409.13		16
35.3	even	12		630.2.bo.a.269.5	yes	16
35.12	even	12		4410.2.d.a.4409.4		16
35.17	even	12		630.2.bo.b.269.7	yes	16
35.23	odd	12		4410.2.d.b.4409.14		16
35.24	odd	6	inner	3150.2.bf.f.1151.5		32
35.33	even	12		4410.2.d.b.4409.3		16
105.2	even	12		4410.2.d.b.4409.4		16
105.17	odd	12		630.2.bo.a.269.2	yes	16
105.23	even	12		4410.2.d.a.4409.3		16
105.38	odd	12		630.2.bo.b.269.4	yes	16
105.47	odd	12		4410.2.d.b.4409.13		16
105.59	even	6	inner	3150.2.bf.f.1151.15		32
105.68	odd	12		4410.2.d.a.4409.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.2	✓	16	5.3	odd	4
630.2.bo.a.89.5	yes	16	15.2	even	4
630.2.bo.a.269.2	yes	16	105.17	odd	12
630.2.bo.a.269.5	yes	16	35.3	even	12
630.2.bo.b.89.4	yes	16	5.2	odd	4
630.2.bo.b.89.7	yes	16	15.8	even	4
630.2.bo.b.269.4	yes	16	105.38	odd	12
630.2.bo.b.269.7	yes	16	35.17	even	12
3150.2.bf.f.1151.5		32	35.24	odd	6	inner
3150.2.bf.f.1151.6		32	21.17	even	6	inner
3150.2.bf.f.1151.15		32	105.59	even	6	inner
3150.2.bf.f.1151.16		32	7.3	odd	6	inner
3150.2.bf.f.1601.5		32	15.14	odd	2	inner
3150.2.bf.f.1601.6		32	1.1	even	1	trivial
3150.2.bf.f.1601.13		32	5.4	even	2	inner
3150.2.bf.f.1601.14		32	3.2	odd	2	inner
4410.2.d.a.4409.3		16	105.23	even	12
4410.2.d.a.4409.4		16	35.12	even	12
4410.2.d.a.4409.13		16	35.2	odd	12
4410.2.d.a.4409.14		16	105.68	odd	12
4410.2.d.b.4409.3		16	35.33	even	12
4410.2.d.b.4409.4		16	105.2	even	12
4410.2.d.b.4409.13		16	105.47	odd	12
4410.2.d.b.4409.14		16	35.23	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.24547 + 1.39924i) q^{7} -1.00000i q^{8} +(-1.37897 + 0.796151i) q^{11} -0.925091i q^{13} +(-1.24501 - 2.33451i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.97883 + 3.42743i) q^{17} +(-0.541679 - 0.312739i) q^{19} +1.59230 q^{22} +(-6.74256 - 3.89282i) q^{23} +(-0.462546 + 0.801153i) q^{26} +(-0.0890445 + 2.64425i) q^{28} -9.34805i q^{29} +(8.94618 - 5.16508i) q^{31} +(0.866025 - 0.500000i) q^{32} -3.95765i q^{34} +(0.213192 - 0.369259i) q^{37} +(0.312739 + 0.541679i) q^{38} +8.35463 q^{41} +6.27133 q^{43} +(-1.37897 - 0.796151i) q^{44} +(3.89282 + 6.74256i) q^{46} +(-1.39065 + 2.40868i) q^{47} +(3.08425 + 6.28390i) q^{49} +(0.801153 - 0.462546i) q^{52} +(-2.90217 + 1.67557i) q^{53} +(1.39924 - 2.24547i) q^{56} +(-4.67403 + 8.09565i) q^{58} +(3.10680 + 5.38113i) q^{59} +(9.52671 + 5.50025i) q^{61} -10.3302 q^{62} -1.00000 q^{64} +(-0.178089 - 0.308459i) q^{67} +(-1.97883 + 3.42743i) q^{68} -9.07975i q^{71} +(-5.91515 + 3.41511i) q^{73} +(-0.369259 + 0.213192i) q^{74} -0.625477i q^{76} +(-4.21045 - 0.141786i) q^{77} +(4.52582 - 7.83895i) q^{79} +(-7.23532 - 4.17731i) q^{82} +0.809898 q^{83} +(-5.43113 - 3.13566i) q^{86} +(0.796151 + 1.37897i) q^{88} +(2.00721 - 3.47659i) q^{89} +(1.29443 - 2.07726i) q^{91} -7.78564i q^{92} +(2.40868 - 1.39065i) q^{94} +7.87721i q^{97} +(0.470912 - 6.98414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 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

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