LMFDB - Embedded newform 675.3.g.j.82.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,3,Mod(82,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.82"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	675.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-16,0,0,0,0,0,-40,0,0,-152,0,0,0,0,0,136,0,0,0, 0,0,112,0,0,200] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(31)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.3924178443$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 286x^{12} + 16269x^{8} + 85684x^{4} + 62500 $ x^16 + 286x^12 + 16269x^8 + 85684*x^4 + 62500
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			82.5
Root			$0.683187 + 0.683187i$ of defining polynomial
Character	$\chi$	$=$	675.82
Dual form			675.3.g.j.568.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.683187 + 0.683187i) q^{2} -3.06651i q^{4} +(-1.91393 - 1.91393i) q^{7} +(4.82775 - 4.82775i) q^{8} -16.0422 q^{11} +(-0.607722 + 0.607722i) q^{13} -2.61514i q^{14} -5.66955 q^{16} +(7.56049 + 7.56049i) q^{17} -21.0707i q^{19} +(-10.9598 - 10.9598i) q^{22} +(-25.2822 + 25.2822i) q^{23} -0.830376 q^{26} +(-5.86908 + 5.86908i) q^{28} +13.4595i q^{29} -39.2058 q^{31} +(-23.1843 - 23.1843i) q^{32} +10.3305i q^{34} +(-5.47784 - 5.47784i) q^{37} +(14.3952 - 14.3952i) q^{38} +69.4260 q^{41} +(-55.6177 + 55.6177i) q^{43} +49.1937i q^{44} -34.5449 q^{46} +(-13.7120 - 13.7120i) q^{47} -41.6738i q^{49} +(1.86359 + 1.86359i) q^{52} +(-34.8894 + 34.8894i) q^{53} -18.4799 q^{56} +(-9.19538 + 9.19538i) q^{58} -62.0004i q^{59} -67.2121 q^{61} +(-26.7849 - 26.7849i) q^{62} -9.00028i q^{64} +(-29.2919 - 29.2919i) q^{67} +(23.1843 - 23.1843i) q^{68} -71.3882 q^{71} +(23.5751 - 23.5751i) q^{73} -7.48478i q^{74} -64.6135 q^{76} +(30.7037 + 30.7037i) q^{77} -5.61768i q^{79} +(47.4309 + 47.4309i) q^{82} +(26.0960 - 26.0960i) q^{83} -75.9945 q^{86} +(-77.4479 + 77.4479i) q^{88} -23.2369i q^{89} +2.32627 q^{91} +(77.5282 + 77.5282i) q^{92} -18.7357i q^{94} +(-97.3193 - 97.3193i) q^{97} +(28.4710 - 28.4710i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{7} - 40 q^{13} - 152 q^{16} + 136 q^{22} + 112 q^{28} + 200 q^{31} - 16 q^{37} - 136 q^{43} + 152 q^{46} - 640 q^{52} - 48 q^{58} - 280 q^{61} + 344 q^{67} + 776 q^{73} + 144 q^{76} + 880 q^{82}+ \cdots - 448 q^{97}+O(q^{100}) $ 16 * q - 16 * q^7 - 40 * q^13 - 152 * q^16 + 136 * q^22 + 112 * q^28 + 200 * q^31 - 16 * q^37 - 136 * q^43 + 152 * q^46 - 640 * q^52 - 48 * q^58 - 280 * q^61 + 344 * q^67 + 776 * q^73 + 144 * q^76 + 880 * q^82 - 1200 * q^88 + 152 * q^91 - 448 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.683187	+	0.683187i	0.341593	+	0.341593i	0.856966	−	0.515373i	$-0.172347\pi$
$2$	0.683187	+	0.683187i	0.341593	+	0.341593i	−0.515373	+	0.856966i	$0.672347\pi$
$3$		0			0
$3$		0			0
$4$		−	3.06651i		−	0.766628i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.91393	−	1.91393i	−0.273418	−	0.273418i	0.557056	−	0.830475i	$-0.311931\pi$
$7$	−1.91393	−	1.91393i	−0.273418	−	0.273418i	−0.830475	+	0.557056i	$0.811931\pi$
$8$	4.82775	−	4.82775i	0.603468	−	0.603468i
$9$		0			0
$10$		0			0
$11$	−16.0422			−1.45839			−0.729193	−	0.684308i	$-0.760104\pi$
$11$	−16.0422			−1.45839			−0.729193	+	0.684308i	$0.760104\pi$
$12$		0			0
$13$	−0.607722	+	0.607722i	−0.0467479	+	0.0467479i	−0.730094	−	0.683346i	$-0.760524\pi$
$13$	−0.607722	+	0.607722i	−0.0467479	+	0.0467479i	0.683346	+	0.730094i	$0.260524\pi$
$14$		−	2.61514i		−	0.186796i
$15$		0			0
$16$	−5.66955			−0.354347
$17$	7.56049	+	7.56049i	0.444735	+	0.444735i	0.893600	−	0.448865i	$-0.148172\pi$
$17$	7.56049	+	7.56049i	0.444735	+	0.444735i	−0.448865	+	0.893600i	$0.648172\pi$
$18$		0			0
$19$		−	21.0707i		−	1.10898i	−0.832189	−	0.554492i	$-0.812913\pi$
$19$		−	21.0707i		−	1.10898i	0.832189	−	0.554492i	$-0.187087\pi$
$20$		0			0
$21$		0			0
$22$	−10.9598	−	10.9598i	−0.498175	−	0.498175i
$23$	−25.2822	+	25.2822i	−1.09923	+	1.09923i	−0.104725	+	0.994501i	$0.533396\pi$
$23$	−25.2822	+	25.2822i	−1.09923	+	1.09923i	−0.994501	+	0.104725i	$0.966604\pi$
$24$		0			0
$25$		0			0
$26$	−0.830376			−0.0319375
$27$		0			0
$28$	−5.86908	+	5.86908i	−0.209610	+	0.209610i
$29$			13.4595i			0.464122i	0.972701	+	0.232061i	$0.0745469\pi$
$29$			13.4595i			0.464122i	−0.972701	+	0.232061i	$0.925453\pi$
$30$		0			0
$31$	−39.2058			−1.26470			−0.632352	−	0.774681i	$-0.717910\pi$
$31$	−39.2058			−1.26470			−0.632352	+	0.774681i	$0.717910\pi$
$32$	−23.1843	−	23.1843i	−0.724511	−	0.724511i
$33$		0			0
$34$			10.3305i			0.303837i
$35$		0			0
$36$		0			0
$37$	−5.47784	−	5.47784i	−0.148050	−	0.148050i	0.629196	−	0.777246i	$-0.283384\pi$
$37$	−5.47784	−	5.47784i	−0.148050	−	0.148050i	−0.777246	+	0.629196i	$0.783384\pi$
$38$	14.3952	−	14.3952i	0.378821	−	0.378821i
$39$		0			0
$40$		0			0
$41$	69.4260			1.69332			0.846658	−	0.532137i	$-0.178611\pi$
$41$	69.4260			1.69332			0.846658	+	0.532137i	$0.178611\pi$
$42$		0			0
$43$	−55.6177	+	55.6177i	−1.29343	+	1.29343i	−0.360785	+	0.932649i	$0.617491\pi$
$43$	−55.6177	+	55.6177i	−1.29343	+	1.29343i	−0.932649	+	0.360785i	$0.882509\pi$
$44$			49.1937i			1.11804i
$45$		0			0
$46$	−34.5449			−0.750976
$47$	−13.7120	−	13.7120i	−0.291745	−	0.291745i	0.546024	−	0.837769i	$-0.316141\pi$
$47$	−13.7120	−	13.7120i	−0.291745	−	0.291745i	−0.837769	+	0.546024i	$0.816141\pi$
$48$		0			0
$49$		−	41.6738i		−	0.850485i
$50$		0			0
$51$		0			0
$52$	1.86359	+	1.86359i	0.0358382	+	0.0358382i
$53$	−34.8894	+	34.8894i	−0.658290	+	0.658290i	−0.954975	−	0.296685i	$-0.904119\pi$
$53$	−34.8894	+	34.8894i	−0.658290	+	0.658290i	0.296685	+	0.954975i	$0.404119\pi$
$54$		0			0
$55$		0			0
$56$	−18.4799			−0.329998
$57$		0			0
$58$	−9.19538	+	9.19538i	−0.158541	+	0.158541i
$59$		−	62.0004i		−	1.05085i	−0.850839	−	0.525427i	$-0.823906\pi$
$59$		−	62.0004i		−	1.05085i	0.850839	−	0.525427i	$-0.176094\pi$
$60$		0			0
$61$	−67.2121			−1.10184			−0.550919	−	0.834559i	$-0.685723\pi$
$61$	−67.2121			−1.10184			−0.550919	+	0.834559i	$0.685723\pi$
$62$	−26.7849	−	26.7849i	−0.432014	−	0.432014i
$63$		0			0
$64$		−	9.00028i		−	0.140629i
$65$		0			0
$66$		0			0
$67$	−29.2919	−	29.2919i	−0.437192	−	0.437192i	0.453874	−	0.891066i	$-0.350042\pi$
$67$	−29.2919	−	29.2919i	−0.437192	−	0.437192i	−0.891066	+	0.453874i	$0.850042\pi$
$68$	23.1843	−	23.1843i	0.340946	−	0.340946i
$69$		0			0
$70$		0			0
$71$	−71.3882			−1.00547			−0.502734	−	0.864441i	$-0.667672\pi$
$71$	−71.3882			−1.00547			−0.502734	+	0.864441i	$0.667672\pi$
$72$		0			0
$73$	23.5751	−	23.5751i	0.322947	−	0.322947i	−0.526950	−	0.849896i	$-0.676664\pi$
$73$	23.5751	−	23.5751i	0.322947	−	0.322947i	0.849896	+	0.526950i	$0.176664\pi$
$74$		−	7.48478i		−	0.101146i
$75$		0			0
$76$	−64.6135			−0.850178
$77$	30.7037	+	30.7037i	0.398749	+	0.398749i
$78$		0			0
$79$		−	5.61768i		−	0.0711099i	−0.999368	−	0.0355550i	$-0.988680\pi$
$79$		−	5.61768i		−	0.0711099i	0.999368	−	0.0355550i	$-0.0113199\pi$
$80$		0			0
$81$		0			0
$82$	47.4309	+	47.4309i	0.578425	+	0.578425i
$83$	26.0960	−	26.0960i	0.314410	−	0.314410i	−0.532206	−	0.846615i	$-0.678637\pi$
$83$	26.0960	−	26.0960i	0.314410	−	0.314410i	0.846615	+	0.532206i	$0.178637\pi$
$84$		0			0
$85$		0			0
$86$	−75.9945			−0.883657
$87$		0			0
$88$	−77.4479	+	77.4479i	−0.880089	+	0.880089i
$89$		−	23.2369i		−	0.261089i	−0.991442	−	0.130545i	$-0.958327\pi$
$89$		−	23.2369i		−	0.261089i	0.991442	−	0.130545i	$-0.0416726\pi$
$90$		0			0
$91$	2.32627			0.0255634
$92$	77.5282	+	77.5282i	0.842698	+	0.842698i
$93$		0			0
$94$		−	18.7357i		−	0.199316i
$95$		0			0
$96$		0			0
$97$	−97.3193	−	97.3193i	−1.00329	−	1.00329i	−0.999995	−	0.00329707i	$-0.998951\pi$
$97$	−97.3193	−	97.3193i	−1.00329	−	1.00329i	−0.00329707	−	0.999995i	$-0.501049\pi$
$98$	28.4710	−	28.4710i	0.290520	−	0.290520i
$99$		0			0
$100$		0			0
$101$	122.375			1.21163			0.605815	−	0.795606i	$-0.292847\pi$
$101$	122.375			1.21163			0.605815	+	0.795606i	$0.292847\pi$
$102$		0			0
$103$	14.4661	−	14.4661i	0.140447	−	0.140447i	−0.633387	−	0.773835i	$-0.718336\pi$
$103$	14.4661	−	14.4661i	0.140447	−	0.140447i	0.773835	+	0.633387i	$0.218336\pi$
$104$			5.86786i			0.0564217i
$105$		0			0
$106$	−47.6719			−0.449735
$107$	133.967	+	133.967i	1.25203	+	1.25203i	0.954809	+	0.297221i	$0.0960599\pi$
$107$	133.967	+	133.967i	1.25203	+	1.25203i	0.297221	+	0.954809i	$0.403940\pi$
$108$		0			0
$109$		−	162.075i		−	1.48692i	−0.668778	−	0.743462i	$-0.733183\pi$
$109$		−	162.075i		−	1.48692i	0.668778	−	0.743462i	$-0.266817\pi$
$110$		0			0
$111$		0			0
$112$	10.8511	+	10.8511i	0.0968848	+	0.0968848i
$113$	93.7017	−	93.7017i	0.829219	−	0.829219i	−0.158190	−	0.987409i	$-0.550566\pi$
$113$	93.7017	−	93.7017i	0.829219	−	0.829219i	0.987409	+	0.158190i	$0.0505658\pi$
$114$		0			0
$115$		0			0
$116$	41.2738			0.355809
$117$		0			0
$118$	42.3578	−	42.3578i	0.358965	−	0.358965i
$119$		−	28.9405i		−	0.243197i
$120$		0			0
$121$	136.353			1.12689
$122$	−45.9184	−	45.9184i	−0.376380	−	0.376380i
$123$		0			0
$124$			120.225i			0.969558i
$125$		0			0
$126$		0			0
$127$	−24.9948	−	24.9948i	−0.196810	−	0.196810i	0.601821	−	0.798631i	$-0.294442\pi$
$127$	−24.9948	−	24.9948i	−0.196810	−	0.196810i	−0.798631	+	0.601821i	$0.794442\pi$
$128$	−86.5885	+	86.5885i	−0.676473	+	0.676473i
$129$		0			0
$130$		0			0
$131$	−80.1902			−0.612139			−0.306069	−	0.952009i	$-0.599014\pi$
$131$	−80.1902			−0.612139			−0.306069	+	0.952009i	$0.599014\pi$
$132$		0			0
$133$	−40.3278	+	40.3278i	−0.303216	+	0.303216i
$134$		−	40.0237i		−	0.298684i
$135$		0			0
$136$	73.0003			0.536767
$137$	−156.457	−	156.457i	−1.14202	−	1.14202i	−0.988080	−	0.153940i	$-0.950804\pi$
$137$	−156.457	−	156.457i	−1.14202	−	1.14202i	−0.153940	−	0.988080i	$-0.549196\pi$
$138$		0			0
$139$		−	63.5449i		−	0.457158i	−0.973525	−	0.228579i	$-0.926592\pi$
$139$		−	63.5449i		−	0.457158i	0.973525	−	0.228579i	$-0.0734079\pi$
$140$		0			0
$141$		0			0
$142$	−48.7715	−	48.7715i	−0.343461	−	0.343461i
$143$	9.74923	−	9.74923i	0.0681764	−	0.0681764i
$144$		0			0
$145$		0			0
$146$	32.2124			0.220633
$147$		0			0
$148$	−16.7979	+	16.7979i	−0.113499	+	0.113499i
$149$			148.160i			0.994360i	0.867647	+	0.497180i	$0.165631\pi$
$149$			148.160i			0.994360i	−0.867647	+	0.497180i	$0.834369\pi$
$150$		0			0
$151$	−37.1721			−0.246173			−0.123086	−	0.992396i	$-0.539279\pi$
$151$	−37.1721			−0.246173			−0.123086	+	0.992396i	$0.539279\pi$
$152$	−101.724	−	101.724i	−0.669237	−	0.669237i
$153$		0			0
$154$			41.9527i			0.272420i
$155$		0			0
$156$		0			0
$157$	135.379	+	135.379i	0.862285	+	0.862285i	0.991603	−	0.129318i	$-0.0412788\pi$
$157$	135.379	+	135.379i	0.862285	+	0.862285i	−0.129318	+	0.991603i	$0.541279\pi$
$158$	3.83793	−	3.83793i	0.0242907	−	0.0242907i
$159$		0			0
$160$		0			0
$161$	96.7766			0.601097
$162$		0			0
$163$	202.426	−	202.426i	1.24188	−	1.24188i	0.282654	−	0.959222i	$-0.408785\pi$
$163$	202.426	−	202.426i	1.24188	−	1.24188i	0.959222	−	0.282654i	$-0.0912147\pi$
$164$		−	212.896i		−	1.29814i
$165$		0			0
$166$	35.6569			0.214800
$167$	15.4478	+	15.4478i	0.0925018	+	0.0925018i	0.751843	−	0.659342i	$-0.229165\pi$
$167$	15.4478	+	15.4478i	0.0925018	+	0.0925018i	−0.659342	+	0.751843i	$0.729165\pi$
$168$		0			0
$169$			168.261i			0.995629i
$170$		0			0
$171$		0			0
$172$	170.552	+	170.552i	0.991583	+	0.991583i
$173$	−102.849	+	102.849i	−0.594501	+	0.594501i	−0.938844	−	0.344343i	$-0.888102\pi$
$173$	−102.849	+	102.849i	−0.594501	+	0.594501i	0.344343	+	0.938844i	$0.388102\pi$
$174$		0			0
$175$		0			0
$176$	90.9522			0.516774
$177$		0			0
$178$	15.8752	−	15.8752i	0.0891863	−	0.0891863i
$179$			159.775i			0.892599i	0.894884	+	0.446299i	$0.147258\pi$
$179$			159.775i			0.892599i	−0.894884	+	0.446299i	$0.852742\pi$
$180$		0			0
$181$	204.918			1.13214			0.566070	−	0.824357i	$-0.308463\pi$
$181$	204.918			1.13214			0.566070	+	0.824357i	$0.308463\pi$
$182$	1.58928	+	1.58928i	0.00873230	+	0.00873230i
$183$		0			0
$184$			244.112i			1.32670i
$185$		0			0
$186$		0			0
$187$	−121.287	−	121.287i	−0.648595	−	0.648595i
$188$	−42.0481	+	42.0481i	−0.223660	+	0.223660i
$189$		0			0
$190$		0			0
$191$	−57.2319			−0.299644			−0.149822	−	0.988713i	$-0.547870\pi$
$191$	−57.2319			−0.299644			−0.149822	+	0.988713i	$0.547870\pi$
$192$		0			0
$193$	94.2729	−	94.2729i	0.488461	−	0.488461i	−0.419359	−	0.907820i	$-0.637745\pi$
$193$	94.2729	−	94.2729i	0.488461	−	0.488461i	0.907820	+	0.419359i	$0.137745\pi$
$194$		−	132.974i		−	0.685435i
$195$		0			0
$196$	−127.793			−0.652006
$197$	−45.0889	−	45.0889i	−0.228878	−	0.228878i	0.583346	−	0.812224i	$-0.301743\pi$
$197$	−45.0889	−	45.0889i	−0.228878	−	0.228878i	−0.812224	+	0.583346i	$0.801743\pi$
$198$		0			0
$199$		−	158.275i		−	0.795352i	−0.917526	−	0.397676i	$-0.869817\pi$
$199$		−	158.275i		−	0.795352i	0.917526	−	0.397676i	$-0.130183\pi$
$200$		0			0
$201$		0			0
$202$	83.6047	+	83.6047i	0.413885	+	0.413885i
$203$	25.7606	−	25.7606i	0.126899	−	0.126899i
$204$		0			0
$205$		0			0
$206$	19.7661			0.0959518
$207$		0			0
$208$	3.44551	−	3.44551i	0.0165650	−	0.0165650i
$209$			338.021i			1.61733i
$210$		0			0
$211$	261.703			1.24030			0.620150	−	0.784484i	$-0.287072\pi$
$211$	261.703			1.24030			0.620150	+	0.784484i	$0.287072\pi$
$212$	106.989	+	106.989i	0.504664	+	0.504664i
$213$		0			0
$214$			183.049i			0.855370i
$215$		0			0
$216$		0			0
$217$	75.0371	+	75.0371i	0.345793	+	0.345793i
$218$	110.727	−	110.727i	0.507923	−	0.507923i
$219$		0			0
$220$		0			0
$221$	−9.18936			−0.0415808
$222$		0			0
$223$	−180.063	+	180.063i	−0.807458	+	0.807458i	−0.984249	−	0.176790i	$-0.943428\pi$
$223$	−180.063	+	180.063i	−0.807458	+	0.807458i	0.176790	+	0.984249i	$0.443428\pi$
$224$			88.7463i			0.396189i
$225$		0			0
$226$	128.032			0.566511
$227$	187.888	+	187.888i	0.827699	+	0.827699i	0.987198	−	0.159499i	$-0.0509880\pi$
$227$	187.888	+	187.888i	0.827699	+	0.827699i	−0.159499	+	0.987198i	$0.550988\pi$
$228$		0			0
$229$			132.747i			0.579679i	0.957075	+	0.289840i	$0.0936020\pi$
$229$			132.747i			0.579679i	−0.957075	+	0.289840i	$0.906398\pi$
$230$		0			0
$231$		0			0
$232$	64.9792	+	64.9792i	0.280083	+	0.280083i
$233$	−53.9875	+	53.9875i	−0.231706	+	0.231706i	−0.813404	−	0.581699i	$-0.802388\pi$
$233$	−53.9875	+	53.9875i	−0.231706	+	0.231706i	0.581699	+	0.813404i	$0.302388\pi$
$234$		0			0
$235$		0			0
$236$	−190.125			−0.805614
$237$		0			0
$238$	19.7717	−	19.7717i	0.0830745	−	0.0830745i
$239$		−	103.767i		−	0.434171i	−0.976153	−	0.217085i	$-0.930345\pi$
$239$		−	103.767i		−	0.434171i	0.976153	−	0.217085i	$-0.0696550\pi$
$240$		0			0
$241$	281.196			1.16679			0.583395	−	0.812188i	$-0.301724\pi$
$241$	281.196			1.16679			0.583395	+	0.812188i	$0.301724\pi$
$242$	93.1549	+	93.1549i	0.384938	+	0.384938i
$243$		0			0
$244$			206.107i			0.844699i
$245$		0			0
$246$		0			0
$247$	12.8051	+	12.8051i	0.0518426	+	0.0518426i
$248$	−189.276	+	189.276i	−0.763209	+	0.763209i
$249$		0			0
$250$		0			0
$251$	−313.354			−1.24842			−0.624212	−	0.781255i	$-0.714580\pi$
$251$	−313.354			−1.24842			−0.624212	+	0.781255i	$0.714580\pi$
$252$		0			0
$253$	405.583	−	405.583i	1.60310	−	1.60310i
$254$		−	34.1523i		−	0.134458i
$255$		0			0
$256$	−154.313			−0.602786
$257$	−141.763	−	141.763i	−0.551609	−	0.551609i	0.375296	−	0.926905i	$-0.377541\pi$
$257$	−141.763	−	141.763i	−0.551609	−	0.551609i	−0.926905	+	0.375296i	$0.877541\pi$
$258$		0			0
$259$			20.9684i			0.0809590i
$260$		0			0
$261$		0			0
$262$	−54.7849	−	54.7849i	−0.209103	−	0.209103i
$263$	170.260	−	170.260i	0.647375	−	0.647375i	−0.304983	−	0.952358i	$-0.598651\pi$
$263$	170.260	−	170.260i	0.647375	−	0.647375i	0.952358	+	0.304983i	$0.0986507\pi$
$264$		0			0
$265$		0			0
$266$	−55.1028			−0.207153
$267$		0			0
$268$	−89.8240	+	89.8240i	−0.335164	+	0.335164i
$269$		−	476.960i		−	1.77309i	−0.462646	−	0.886543i	$-0.653100\pi$
$269$		−	476.960i		−	1.77309i	0.462646	−	0.886543i	$-0.346900\pi$
$270$		0			0
$271$	105.987			0.391095			0.195548	−	0.980694i	$-0.437352\pi$
$271$	105.987			0.391095			0.195548	+	0.980694i	$0.437352\pi$
$272$	−42.8646	−	42.8646i	−0.157590	−	0.157590i
$273$		0			0
$274$		−	213.778i		−	0.780213i
$275$		0			0
$276$		0			0
$277$	−2.45621	−	2.45621i	−0.00886718	−	0.00886718i	0.702659	−	0.711526i	$-0.251996\pi$
$277$	−2.45621	−	2.45621i	−0.00886718	−	0.00886718i	−0.711526	+	0.702659i	$0.751996\pi$
$278$	43.4130	−	43.4130i	0.156162	−	0.156162i
$279$		0			0
$280$		0			0
$281$	−206.625			−0.735321			−0.367660	−	0.929960i	$-0.619841\pi$
$281$	−206.625			−0.735321			−0.367660	+	0.929960i	$0.619841\pi$
$282$		0			0
$283$	40.8251	−	40.8251i	0.144258	−	0.144258i	−0.631289	−	0.775547i	$-0.717474\pi$
$283$	40.8251	−	40.8251i	0.144258	−	0.144258i	0.775547	+	0.631289i	$0.217474\pi$
$284$			218.913i			0.770820i
$285$		0			0
$286$	13.3211			0.0465772
$287$	−132.876	−	132.876i	−0.462984	−	0.462984i
$288$		0			0
$289$		−	174.678i		−	0.604422i
$290$		0			0
$291$		0			0
$292$	−72.2934	−	72.2934i	−0.247580	−	0.247580i
$293$	−212.663	+	212.663i	−0.725811	+	0.725811i	−0.969782	−	0.243971i	$-0.921550\pi$
$293$	−212.663	+	212.663i	−0.725811	+	0.725811i	0.243971	+	0.969782i	$0.421550\pi$
$294$		0			0
$295$		0			0
$296$	−52.8913			−0.178687
$297$		0			0
$298$	−101.221	+	101.221i	−0.339667	+	0.339667i
$299$		−	30.7291i		−	0.102773i
$300$		0			0
$301$	212.896			0.707297
$302$	−25.3955	−	25.3955i	−0.0840910	−	0.0840910i
$303$		0			0
$304$			119.461i			0.392965i
$305$		0			0
$306$		0			0
$307$	−6.45878	−	6.45878i	−0.0210384	−	0.0210384i	0.696509	−	0.717548i	$-0.254735\pi$
$307$	−6.45878	−	6.45878i	−0.0210384	−	0.0210384i	−0.717548	+	0.696509i	$0.754735\pi$
$308$	94.1532	−	94.1532i	0.305692	−	0.305692i
$309$		0			0
$310$		0			0
$311$	429.168			1.37996			0.689980	−	0.723828i	$-0.257619\pi$
$311$	429.168			1.37996			0.689980	+	0.723828i	$0.257619\pi$
$312$		0			0
$313$	91.6067	−	91.6067i	0.292673	−	0.292673i	−0.545462	−	0.838135i	$-0.683646\pi$
$313$	91.6067	−	91.6067i	0.292673	−	0.292673i	0.838135	+	0.545462i	$0.183646\pi$
$314$			184.978i			0.589102i
$315$		0			0
$316$	−17.2267			−0.0545148
$317$	−101.368	−	101.368i	−0.319771	−	0.319771i	0.528908	−	0.848679i	$-0.322602\pi$
$317$	−101.368	−	101.368i	−0.319771	−	0.319771i	−0.848679	+	0.528908i	$0.822602\pi$
$318$		0			0
$319$		−	215.921i		−	0.676869i
$320$		0			0
$321$		0			0
$322$	66.1165	+	66.1165i	0.205331	+	0.205331i
$323$	159.305	−	159.305i	0.493204	−	0.493204i
$324$		0			0
$325$		0			0
$326$	276.589			0.848433
$327$		0			0
$328$	335.171	−	335.171i	1.02186	−	1.02186i
$329$			52.4877i			0.159537i
$330$		0			0
$331$	−40.7620			−0.123148			−0.0615741	−	0.998103i	$-0.519612\pi$
$331$	−40.7620			−0.123148			−0.0615741	+	0.998103i	$0.519612\pi$
$332$	−80.0237	−	80.0237i	−0.241035	−	0.241035i
$333$		0			0
$334$			21.1075i			0.0631960i
$335$		0			0
$336$		0			0
$337$	−251.752	−	251.752i	−0.747038	−	0.747038i	0.226884	−	0.973922i	$-0.427146\pi$
$337$	−251.752	−	251.752i	−0.747038	−	0.747038i	−0.973922	+	0.226884i	$0.927146\pi$
$338$	−114.954	+	114.954i	−0.340100	+	0.340100i
$339$		0			0
$340$		0			0
$341$	628.949			1.84443
$342$		0			0
$343$	−173.543	+	173.543i	−0.505956	+	0.505956i
$344$			537.016i			1.56109i
$345$		0			0
$346$	−140.530			−0.406155
$347$	119.157	+	119.157i	0.343392	+	0.343392i	0.857641	−	0.514249i	$-0.171929\pi$
$347$	119.157	+	119.157i	0.343392	+	0.343392i	−0.514249	+	0.857641i	$0.671929\pi$
$348$		0			0
$349$			16.0231i			0.0459116i	0.999736	+	0.0229558i	$0.00730770\pi$
$349$			16.0231i			0.0459116i	−0.999736	+	0.0229558i	$0.992692\pi$
$350$		0			0
$351$		0			0
$352$	371.929	+	371.929i	1.05662	+	1.05662i
$353$	−147.916	+	147.916i	−0.419025	+	0.419025i	−0.884868	−	0.465842i	$-0.845751\pi$
$353$	−147.916	+	147.916i	−0.419025	+	0.419025i	0.465842	+	0.884868i	$0.345751\pi$
$354$		0			0
$355$		0			0
$356$	−71.2563			−0.200158
$357$		0			0
$358$	−109.156	+	109.156i	−0.304906	+	0.304906i
$359$		−	160.120i		−	0.446018i	−0.974816	−	0.223009i	$-0.928412\pi$
$359$		−	160.120i		−	0.446018i	0.974816	−	0.223009i	$-0.0715879\pi$
$360$		0			0
$361$	−82.9741			−0.229845
$362$	139.997	+	139.997i	0.386732	+	0.386732i
$363$		0			0
$364$		−	7.13355i		−	0.0195977i
$365$		0			0
$366$		0			0
$367$	−146.732	−	146.732i	−0.399814	−	0.399814i	0.478353	−	0.878168i	$-0.341234\pi$
$367$	−146.732	−	146.732i	−0.399814	−	0.399814i	−0.878168	+	0.478353i	$0.841234\pi$
$368$	143.339	−	143.339i	0.389507	−	0.389507i
$369$		0			0
$370$		0			0
$371$	133.552			0.359977
$372$		0			0
$373$	−275.593	+	275.593i	−0.738854	+	0.738854i	−0.972356	−	0.233502i	$-0.924981\pi$
$373$	−275.593	+	275.593i	−0.738854	+	0.738854i	0.233502	+	0.972356i	$0.424981\pi$
$374$		−	165.724i		−	0.443111i
$375$		0			0
$376$	−132.396			−0.352118
$377$	−8.17966	−	8.17966i	−0.0216967	−	0.0216967i
$378$		0			0
$379$		−	276.991i		−	0.730846i	−0.930842	−	0.365423i	$-0.880924\pi$
$379$		−	276.991i		−	0.730846i	0.930842	−	0.365423i	$-0.119076\pi$
$380$		0			0
$381$		0			0
$382$	−39.1001	−	39.1001i	−0.102356	−	0.102356i
$383$	−29.6395	+	29.6395i	−0.0773876	+	0.0773876i	−0.744741	−	0.667353i	$-0.767427\pi$
$383$	−29.6395	+	29.6395i	−0.0773876	+	0.0773876i	0.667353	+	0.744741i	$0.267427\pi$
$384$		0			0
$385$		0			0
$386$	128.812			0.333710
$387$		0			0
$388$	−298.431	+	298.431i	−0.769152	+	0.769152i
$389$		−	609.728i		−	1.56742i	−0.621124	−	0.783712i	$-0.713324\pi$
$389$		−	609.728i		−	1.56742i	0.621124	−	0.783712i	$-0.286676\pi$
$390$		0			0
$391$	−382.292			−0.977728
$392$	−201.190	−	201.190i	−0.513241	−	0.513241i
$393$		0			0
$394$		−	61.6083i		−	0.156366i
$395$		0			0
$396$		0			0
$397$	−353.820	−	353.820i	−0.891235	−	0.891235i	0.103404	−	0.994639i	$-0.467026\pi$
$397$	−353.820	−	353.820i	−0.891235	−	0.891235i	−0.994639	+	0.103404i	$0.967026\pi$
$398$	108.131	−	108.131i	0.271687	−	0.271687i
$399$		0			0
$400$		0			0
$401$	−510.979			−1.27426			−0.637131	−	0.770756i	$-0.719879\pi$
$401$	−510.979			−1.27426			−0.637131	+	0.770756i	$0.719879\pi$
$402$		0			0
$403$	23.8263	−	23.8263i	0.0591222	−	0.0591222i
$404$		−	375.263i		−	0.928869i
$405$		0			0
$406$	35.1986			0.0866960
$407$	87.8769	+	87.8769i	0.215914	+	0.215914i
$408$		0			0
$409$		−	129.175i		−	0.315831i	−0.987453	−	0.157916i	$-0.949523\pi$
$409$		−	129.175i		−	0.315831i	0.987453	−	0.157916i	$-0.0504774\pi$
$410$		0			0
$411$		0			0
$412$	−44.3604	−	44.3604i	−0.107671	−	0.107671i
$413$	−118.664	+	118.664i	−0.287323	+	0.287323i
$414$		0			0
$415$		0			0
$416$	28.1793			0.0677387
$417$		0			0
$418$	−230.931	+	230.931i	−0.552468	+	0.552468i
$419$			359.249i			0.857396i	0.903448	+	0.428698i	$0.141028\pi$
$419$			359.249i			0.857396i	−0.903448	+	0.428698i	$0.858972\pi$
$420$		0			0
$421$	−105.532			−0.250669			−0.125335	−	0.992115i	$-0.540000\pi$
$421$	−105.532			−0.250669			−0.125335	+	0.992115i	$0.540000\pi$
$422$	178.792	+	178.792i	0.423678	+	0.423678i
$423$		0			0
$424$			336.874i			0.794515i
$425$		0			0
$426$		0			0
$427$	128.639	+	128.639i	0.301262	+	0.301262i
$428$	410.812	−	410.812i	0.959841	−	0.959841i
$429$		0			0
$430$		0			0
$431$	−402.361			−0.933551			−0.466776	−	0.884376i	$-0.654584\pi$
$431$	−402.361			−0.933551			−0.466776	+	0.884376i	$0.654584\pi$
$432$		0			0
$433$	−36.1598	+	36.1598i	−0.0835098	+	0.0835098i	−0.747628	−	0.664118i	$-0.768807\pi$
$433$	−36.1598	+	36.1598i	−0.0835098	+	0.0835098i	0.664118	+	0.747628i	$0.268807\pi$
$434$			102.529i			0.236241i
$435$		0			0
$436$	−497.004			−1.13992
$437$	532.713	+	532.713i	1.21902	+	1.21902i
$438$		0			0
$439$		−	172.795i		−	0.393611i	−0.980443	−	0.196805i	$-0.936943\pi$
$439$		−	172.795i		−	0.393611i	0.980443	−	0.196805i	$-0.0630567\pi$
$440$		0			0
$441$		0			0
$442$	−6.27805	−	6.27805i	−0.0142037	−	0.0142037i
$443$	−238.409	+	238.409i	−0.538170	+	0.538170i	−0.922991	−	0.384821i	$-0.874263\pi$
$443$	−238.409	+	238.409i	−0.538170	+	0.538170i	0.384821	+	0.922991i	$0.374263\pi$
$444$		0			0
$445$		0			0
$446$	−246.033			−0.551644
$447$		0			0
$448$	−17.2259	+	17.2259i	−0.0384506	+	0.0384506i
$449$			272.621i			0.607174i	0.952804	+	0.303587i	$0.0981843\pi$
$449$			272.621i			0.607174i	−0.952804	+	0.303587i	$0.901816\pi$
$450$		0			0
$451$	−1113.75			−2.46951
$452$	−287.338	−	287.338i	−0.635703	−	0.635703i
$453$		0			0
$454$			256.725i			0.565473i
$455$		0			0
$456$		0			0
$457$	583.277	+	583.277i	1.27632	+	1.27632i	0.942713	+	0.333605i	$0.108265\pi$
$457$	583.277	+	583.277i	1.27632	+	1.27632i	0.333605	+	0.942713i	$0.391735\pi$
$458$	−90.6907	+	90.6907i	−0.198015	+	0.198015i
$459$		0			0
$460$		0			0
$461$	−506.067			−1.09776			−0.548879	−	0.835902i	$-0.684945\pi$
$461$	−506.067			−1.09776			−0.548879	+	0.835902i	$0.684945\pi$
$462$		0			0
$463$	−129.301	+	129.301i	−0.279267	+	0.279267i	−0.832816	−	0.553549i	$-0.813273\pi$
$463$	−129.301	+	129.301i	−0.279267	+	0.279267i	0.553549	+	0.832816i	$0.313273\pi$
$464$		−	76.3095i		−	0.164460i
$465$		0			0
$466$	−73.7670			−0.158298
$467$	−160.498	−	160.498i	−0.343679	−	0.343679i	0.514070	−	0.857748i	$-0.328137\pi$
$467$	−160.498	−	160.498i	−0.343679	−	0.343679i	−0.857748	+	0.514070i	$0.828137\pi$
$468$		0			0
$469$			112.125i			0.239073i
$470$		0			0
$471$		0			0
$472$	−299.322	−	299.322i	−0.634157	−	0.634157i
$473$	892.232	−	892.232i	1.88633	−	1.88633i
$474$		0			0
$475$		0			0
$476$	−88.7463			−0.186442
$477$		0			0
$478$	70.8921	−	70.8921i	0.148310	−	0.148310i
$479$		−	779.221i		−	1.62677i	−0.581729	−	0.813383i	$-0.697624\pi$
$479$		−	779.221i		−	1.62677i	0.581729	−	0.813383i	$-0.302376\pi$
$480$		0			0
$481$	6.65801			0.0138420
$482$	192.110	+	192.110i	0.398568	+	0.398568i
$483$		0			0
$484$		−	418.130i		−	0.863904i
$485$		0			0
$486$		0			0
$487$	−523.288	−	523.288i	−1.07451	−	1.07451i	−0.996991	−	0.0775227i	$-0.975299\pi$
$487$	−523.288	−	523.288i	−1.07451	−	1.07451i	−0.0775227	−	0.996991i	$-0.524701\pi$
$488$	−324.483	+	324.483i	−0.664924	+	0.664924i
$489$		0			0
$490$		0			0
$491$	160.638			0.327166			0.163583	−	0.986530i	$-0.447695\pi$
$491$	160.638			0.327166			0.163583	+	0.986530i	$0.447695\pi$
$492$		0			0
$493$	−101.761	+	101.761i	−0.206411	+	0.206411i
$494$			17.4966i			0.0354182i
$495$		0			0
$496$	222.279			0.448144
$497$	136.632	+	136.632i	0.274913	+	0.274913i
$498$		0			0
$499$		−	192.018i		−	0.384806i	−0.981316	−	0.192403i	$-0.938372\pi$
$499$		−	192.018i		−	0.384806i	0.981316	−	0.192403i	$-0.0616280\pi$
$500$		0			0
$501$		0			0
$502$	−214.079	−	214.079i	−0.426453	−	0.426453i
$503$	179.873	−	179.873i	0.357600	−	0.357600i	−0.505328	−	0.862928i	$-0.668628\pi$
$503$	179.873	−	179.873i	0.357600	−	0.357600i	0.862928	+	0.505328i	$0.168628\pi$
$504$		0			0
$505$		0			0
$506$	554.178			1.09521
$507$		0			0
$508$	−76.6470	+	76.6470i	−0.150880	+	0.150880i
$509$			45.1629i			0.0887286i	0.999015	+	0.0443643i	$0.0141262\pi$
$509$			45.1629i			0.0887286i	−0.999015	+	0.0443643i	$0.985874\pi$
$510$		0			0
$511$	−90.2421			−0.176599
$512$	240.929	+	240.929i	0.470565	+	0.470565i
$513$		0			0
$514$		−	193.702i		−	0.376852i
$515$		0			0
$516$		0			0
$517$	219.972	+	219.972i	0.425477	+	0.425477i
$518$	−14.3253	+	14.3253i	−0.0276551	+	0.0276551i
$519$		0			0
$520$		0			0
$521$	284.623			0.546301			0.273150	−	0.961971i	$-0.411934\pi$
$521$	284.623			0.546301			0.273150	+	0.961971i	$0.411934\pi$
$522$		0			0
$523$	−451.674	+	451.674i	−0.863621	+	0.863621i	−0.991757	−	0.128135i	$-0.959101\pi$
$523$	−451.674	+	451.674i	−0.863621	+	0.863621i	0.128135	+	0.991757i	$0.459101\pi$
$524$			245.904i			0.469283i
$525$		0			0
$526$	232.638			0.442278
$527$	−296.415	−	296.415i	−0.562458	−	0.562458i
$528$		0			0
$529$		−	749.379i		−	1.41660i
$530$		0			0
$531$		0			0
$532$	123.666	+	123.666i	0.232454	+	0.232454i
$533$	−42.1917	+	42.1917i	−0.0791589	+	0.0791589i
$534$		0			0
$535$		0			0
$536$	−282.828			−0.527664
$537$		0			0
$538$	325.853	−	325.853i	0.605674	−	0.605674i
$539$			668.541i			1.24033i
$540$		0			0
$541$	88.5229			0.163628			0.0818142	−	0.996648i	$-0.473929\pi$
$541$	88.5229			0.163628			0.0818142	+	0.996648i	$0.473929\pi$
$542$	72.4088	+	72.4088i	0.133595	+	0.133595i
$543$		0			0
$544$		−	350.570i		−	0.644430i
$545$		0			0
$546$		0			0
$547$	−183.312	−	183.312i	−0.335123	−	0.335123i	0.519405	−	0.854528i	$-0.326154\pi$
$547$	−183.312	−	183.312i	−0.335123	−	0.335123i	−0.854528	+	0.519405i	$0.826154\pi$
$548$	−479.776	+	479.776i	−0.875505	+	0.875505i
$549$		0			0
$550$		0			0
$551$	283.602			0.514704
$552$		0			0
$553$	−10.7518	+	10.7518i	−0.0194427	+	0.0194427i
$554$		−	3.35610i		−	0.00605794i
$555$		0			0
$556$	−194.861			−0.350470
$557$	−372.533	−	372.533i	−0.668821	−	0.668821i	0.288622	−	0.957443i	$-0.406803\pi$
$557$	−372.533	−	372.533i	−0.668821	−	0.668821i	−0.957443	+	0.288622i	$0.906803\pi$
$558$		0			0
$559$		−	67.6002i		−	0.120931i
$560$		0			0
$561$		0			0
$562$	−141.163	−	141.163i	−0.251181	−	0.251181i
$563$	−727.111	+	727.111i	−1.29149	+	1.29149i	−0.357630	+	0.933863i	$0.616415\pi$
$563$	−727.111	+	727.111i	−1.29149	+	1.29149i	−0.933863	+	0.357630i	$0.883585\pi$
$564$		0			0
$565$		0			0
$566$	55.7823			0.0985553
$567$		0			0
$568$	−344.644	+	344.644i	−0.606768	+	0.606768i
$569$			407.776i			0.716653i	0.933596	+	0.358327i	$0.116653\pi$
$569$			407.776i			0.716653i	−0.933596	+	0.358327i	$0.883347\pi$
$570$		0			0
$571$	−107.205			−0.187750			−0.0938748	−	0.995584i	$-0.529925\pi$
$571$	−107.205			−0.187750			−0.0938748	+	0.995584i	$0.529925\pi$
$572$	−29.8961	−	29.8961i	−0.0522660	−	0.0522660i
$573$		0			0
$574$		−	181.559i		−	0.316304i
$575$		0			0
$576$		0			0
$577$	−539.921	−	539.921i	−0.935738	−	0.935738i	0.0623179	−	0.998056i	$-0.480151\pi$
$577$	−539.921	−	539.921i	−0.935738	−	0.935738i	−0.998056	+	0.0623179i	$0.980151\pi$
$578$	119.338	−	119.338i	0.206466	−	0.206466i
$579$		0			0
$580$		0			0
$581$	−99.8917			−0.171931
$582$		0			0
$583$	559.704	−	559.704i	0.960041	−	0.960041i
$584$		−	227.629i		−	0.389776i
$585$		0			0
$586$	−290.577			−0.495864
$587$	−523.572	−	523.572i	−0.891946	−	0.891946i	0.102760	−	0.994706i	$-0.467233\pi$
$587$	−523.572	−	523.572i	−0.891946	−	0.891946i	−0.994706	+	0.102760i	$0.967233\pi$
$588$		0			0
$589$			826.094i			1.40254i
$590$		0			0
$591$		0			0
$592$	31.0569	+	31.0569i	0.0524609	+	0.0524609i
$593$	−43.9329	+	43.9329i	−0.0740858	+	0.0740858i	−0.743179	−	0.669093i	$-0.766683\pi$
$593$	−43.9329	+	43.9329i	−0.0740858	+	0.0740858i	0.669093	+	0.743179i	$0.266683\pi$
$594$		0			0
$595$		0			0
$596$	454.333			0.762304
$597$		0			0
$598$	20.9937	−	20.9937i	0.0351066	−	0.0351066i
$599$			110.244i			0.184047i	0.995757	+	0.0920237i	$0.0293336\pi$
$599$			110.244i			0.184047i	−0.995757	+	0.0920237i	$0.970666\pi$
$600$		0			0
$601$	614.730			1.02284			0.511422	−	0.859329i	$-0.329119\pi$
$601$	614.730			1.02284			0.511422	+	0.859329i	$0.329119\pi$
$602$	145.448	+	145.448i	0.241608	+	0.241608i
$603$		0			0
$604$			113.989i			0.188723i
$605$		0			0
$606$		0			0
$607$	643.427	+	643.427i	1.06001	+	1.06001i	0.998080	+	0.0619314i	$0.0197260\pi$
$607$	643.427	+	643.427i	1.06001	+	1.06001i	0.0619314	+	0.998080i	$0.480274\pi$
$608$	−488.510	+	488.510i	−0.803471	+	0.803471i
$609$		0			0
$610$		0			0
$611$	16.6662			0.0272769
$612$		0			0
$613$	−60.7205	+	60.7205i	−0.0990546	+	0.0990546i	−0.754897	−	0.655843i	$-0.772313\pi$
$613$	−60.7205	+	60.7205i	−0.0990546	+	0.0990546i	0.655843	+	0.754897i	$0.272313\pi$
$614$		−	8.82511i		−	0.0143731i
$615$		0			0
$616$	296.459			0.481265
$617$	−627.123	−	627.123i	−1.01641	−	1.01641i	−0.999863	−	0.0165444i	$-0.994734\pi$
$617$	−627.123	−	627.123i	−1.01641	−	1.01641i	−0.0165444	−	0.999863i	$-0.505266\pi$
$618$		0			0
$619$		−	587.816i		−	0.949622i	−0.880088	−	0.474811i	$-0.842516\pi$
$619$		−	587.816i		−	0.949622i	0.880088	−	0.474811i	$-0.157484\pi$
$620$		0			0
$621$		0			0
$622$	293.201	+	293.201i	0.471385	+	0.471385i
$623$	−44.4738	+	44.4738i	−0.0713865	+	0.0713865i
$624$		0			0
$625$		0			0
$626$	125.169			0.199950
$627$		0			0
$628$	415.141	−	415.141i	0.661052	−	0.661052i
$629$		−	82.8304i		−	0.131686i
$630$		0			0
$631$	−347.806			−0.551197			−0.275599	−	0.961273i	$-0.588876\pi$
$631$	−347.806			−0.551197			−0.275599	+	0.961273i	$0.588876\pi$
$632$	−27.1207	−	27.1207i	−0.0429126	−	0.0429126i
$633$		0			0
$634$		−	138.506i		−	0.218464i
$635$		0			0
$636$		0			0
$637$	25.3261	+	25.3261i	0.0397584	+	0.0397584i
$638$	147.514	−	147.514i	0.231214	−	0.231214i
$639$		0			0
$640$		0			0
$641$	−532.992			−0.831500			−0.415750	−	0.909479i	$-0.636481\pi$
$641$	−532.992			−0.831500			−0.415750	+	0.909479i	$0.636481\pi$
$642$		0			0
$643$	−717.465	+	717.465i	−1.11581	+	1.11581i	−0.123460	+	0.992350i	$0.539399\pi$
$643$	−717.465	+	717.465i	−1.11581	+	1.11581i	−0.992350	+	0.123460i	$0.960601\pi$
$644$		−	296.767i		−	0.460818i
$645$		0			0
$646$	217.670			0.336950
$647$	−28.7251	−	28.7251i	−0.0443973	−	0.0443973i	0.684560	−	0.728957i	$-0.259995\pi$
$647$	−28.7251	−	28.7251i	−0.0443973	−	0.0443973i	−0.728957	+	0.684560i	$0.759995\pi$
$648$		0			0
$649$			994.625i			1.53255i
$650$		0			0
$651$		0			0
$652$	−620.741	−	620.741i	−0.952057	−	0.952057i
$653$	18.3291	−	18.3291i	0.0280690	−	0.0280690i	−0.692933	−	0.721002i	$-0.743682\pi$
$653$	18.3291	−	18.3291i	0.0280690	−	0.0280690i	0.721002	+	0.692933i	$0.243682\pi$
$654$		0			0
$655$		0			0
$656$	−393.614			−0.600021
$657$		0			0
$658$	−35.8589	+	35.8589i	−0.0544968	+	0.0544968i
$659$			698.827i			1.06043i	0.847862	+	0.530217i	$0.177890\pi$
$659$			698.827i			1.06043i	−0.847862	+	0.530217i	$0.822110\pi$
$660$		0			0
$661$	229.808			0.347667			0.173833	−	0.984775i	$-0.444385\pi$
$661$	229.808			0.347667			0.173833	+	0.984775i	$0.444385\pi$
$662$	−27.8481	−	27.8481i	−0.0420666	−	0.0420666i
$663$		0			0
$664$		−	251.970i		−	0.379472i
$665$		0			0
$666$		0			0
$667$	−340.287	−	340.287i	−0.510175	−	0.510175i
$668$	47.3709	−	47.3709i	0.0709145	−	0.0709145i
$669$		0			0
$670$		0			0
$671$	1078.23			1.60690
$672$		0			0
$673$	739.046	−	739.046i	1.09814	−	1.09814i	0.103509	−	0.994629i	$-0.466993\pi$
$673$	739.046	−	739.046i	1.09814	−	1.09814i	0.994629	−	0.103509i	$-0.0330069\pi$
$674$		−	343.987i		−	0.510366i
$675$		0			0
$676$	515.975			0.763277
$677$	671.650	+	671.650i	0.992098	+	0.992098i	0.999969	−	0.00787098i	$-0.00250544\pi$
$677$	671.650	+	671.650i	0.992098	+	0.992098i	−0.00787098	+	0.999969i	$0.502505\pi$
$678$		0			0
$679$			372.524i			0.548636i
$680$		0			0
$681$		0			0
$682$	429.690	+	429.690i	0.630044	+	0.630044i
$683$	293.612	−	293.612i	0.429885	−	0.429885i	−0.458704	−	0.888589i	$-0.651686\pi$
$683$	293.612	−	293.612i	0.429885	−	0.429885i	0.888589	+	0.458704i	$0.151686\pi$
$684$		0			0
$685$		0			0
$686$	−237.125			−0.345663
$687$		0			0
$688$	315.327	−	315.327i	0.458324	−	0.458324i
$689$		−	42.4061i		−	0.0615474i
$690$		0			0
$691$	−566.147			−0.819316			−0.409658	−	0.912239i	$-0.634352\pi$
$691$	−566.147			−0.819316			−0.409658	+	0.912239i	$0.634352\pi$
$692$	315.387	+	315.387i	0.455761	+	0.455761i
$693$		0			0
$694$			162.813i			0.234601i
$695$		0			0
$696$		0			0
$697$	524.895	+	524.895i	0.753077	+	0.753077i
$698$	−10.9468	+	10.9468i	−0.0156831	+	0.0156831i
$699$		0			0
$700$		0			0
$701$	−660.345			−0.942004			−0.471002	−	0.882132i	$-0.656108\pi$
$701$	−660.345			−0.942004			−0.471002	+	0.882132i	$0.656108\pi$
$702$		0			0
$703$	−115.422	+	115.422i	−0.164185	+	0.164185i
$704$			144.385i			0.205092i
$705$		0			0
$706$	−202.108			−0.286272
$707$	−234.216	−	234.216i	−0.331282	−	0.331282i
$708$		0			0
$709$			1216.32i			1.71554i	0.514034	+	0.857770i	$0.328151\pi$
$709$			1216.32i			1.71554i	−0.514034	+	0.857770i	$0.671849\pi$
$710$		0			0
$711$		0			0
$712$	−112.182	−	112.182i	−0.157559	−	0.157559i
$713$	991.209	−	991.209i	1.39020	−	1.39020i
$714$		0			0
$715$		0			0
$716$	489.953			0.684291
$717$		0			0
$718$	109.392	−	109.392i	0.152357	−	0.152357i
$719$			376.633i			0.523829i	0.965091	+	0.261914i	$0.0843538\pi$
$719$			376.633i			0.523829i	−0.965091	+	0.261914i	$0.915646\pi$
$720$		0			0
$721$	−55.3741			−0.0768018
$722$	−56.6868	−	56.6868i	−0.0785135	−	0.0785135i
$723$		0			0
$724$		−	628.382i		−	0.867931i
$725$		0			0
$726$		0			0
$727$	562.754	+	562.754i	0.774077	+	0.774077i	0.978816	−	0.204740i	$-0.0656348\pi$
$727$	562.754	+	562.754i	0.774077	+	0.774077i	−0.204740	+	0.978816i	$0.565635\pi$
$728$	11.2307	−	11.2307i	0.0154267	−	0.0154267i
$729$		0			0
$730$		0			0
$731$	−840.994			−1.15047
$732$		0			0
$733$	316.775	−	316.775i	0.432163	−	0.432163i	−0.457201	−	0.889364i	$-0.651148\pi$
$733$	316.775	−	316.775i	0.432163	−	0.432163i	0.889364	+	0.457201i	$0.151148\pi$
$734$		−	200.491i		−	0.273148i
$735$		0			0
$736$	1172.30			1.59280
$737$	469.908	+	469.908i	0.637595	+	0.637595i
$738$		0			0
$739$			322.406i			0.436273i	0.975918	+	0.218137i	$0.0699979\pi$
$739$			322.406i			0.436273i	−0.975918	+	0.218137i	$0.930002\pi$
$740$		0			0
$741$		0			0
$742$	91.2406	+	91.2406i	0.122966	+	0.122966i
$743$	33.6619	−	33.6619i	0.0453054	−	0.0453054i	−0.684091	−	0.729397i	$-0.739801\pi$
$743$	33.6619	−	33.6619i	0.0453054	−	0.0453054i	0.729397	+	0.684091i	$0.239801\pi$
$744$		0			0
$745$		0			0
$746$	−376.562			−0.504775
$747$		0			0
$748$	−371.929	+	371.929i	−0.497231	+	0.497231i
$749$		−	512.807i		−	0.684656i
$750$		0			0
$751$	1008.00			1.34221			0.671106	−	0.741362i	$-0.265820\pi$
$751$	1008.00			1.34221			0.671106	+	0.741362i	$0.265820\pi$
$752$	77.7410	+	77.7410i	0.103379	+	0.103379i
$753$		0			0
$754$		−	11.1765i		−	0.0148229i
$755$		0			0
$756$		0			0
$757$	839.534	+	839.534i	1.10903	+	1.10903i	0.993278	+	0.115750i	$0.0369272\pi$
$757$	839.534	+	839.534i	1.10903	+	1.10903i	0.115750	+	0.993278i	$0.463073\pi$
$758$	189.236	−	189.236i	0.249652	−	0.249652i
$759$		0			0
$760$		0			0
$761$	−233.272			−0.306534			−0.153267	−	0.988185i	$-0.548979\pi$
$761$	−233.272			−0.306534			−0.153267	+	0.988185i	$0.548979\pi$
$762$		0			0
$763$	−310.199	+	310.199i	−0.406552	+	0.406552i
$764$			175.502i			0.229715i
$765$		0			0
$766$	−40.4986			−0.0528702
$767$	37.6790	+	37.6790i	0.0491252	+	0.0491252i
$768$		0			0
$769$			1059.42i			1.37766i	0.724922	+	0.688831i	$0.241876\pi$
$769$			1059.42i			1.37766i	−0.724922	+	0.688831i	$0.758124\pi$
$770$		0			0
$771$		0			0
$772$	−289.089	−	289.089i	−0.374468	−	0.374468i
$773$	−672.938	+	672.938i	−0.870554	+	0.870554i	−0.992533	−	0.121979i	$-0.961076\pi$
$773$	−672.938	+	672.938i	−0.870554	+	0.870554i	0.121979	+	0.992533i	$0.461076\pi$
$774$		0			0
$775$		0			0
$776$	−939.666			−1.21091
$777$		0			0
$778$	416.558	−	416.558i	0.535421	−	0.535421i
$779$		−	1462.85i		−	1.87786i
$780$		0			0
$781$	1145.23			1.46636
$782$	−261.177	−	261.177i	−0.333985	−	0.333985i
$783$		0			0
$784$			236.271i			0.301366i
$785$		0			0
$786$		0			0
$787$	−441.897	−	441.897i	−0.561496	−	0.561496i	0.368236	−	0.929732i	$-0.379962\pi$
$787$	−441.897	−	441.897i	−0.561496	−	0.561496i	−0.929732	+	0.368236i	$0.879962\pi$
$788$	−138.266	+	138.266i	−0.175464	+	0.175464i
$789$		0			0
$790$		0			0
$791$	−358.677			−0.453447
$792$		0			0
$793$	40.8463	−	40.8463i	0.0515086	−	0.0515086i
$794$		−	483.451i		−	0.608880i
$795$		0			0
$796$	−485.352			−0.609739
$797$	880.801	+	880.801i	1.10515	+	1.10515i	0.993779	+	0.111366i	$0.0355227\pi$
$797$	880.801	+	880.801i	1.10515	+	1.10515i	0.111366	+	0.993779i	$0.464477\pi$
$798$		0			0
$799$		−	207.339i		−	0.259499i
$800$		0			0
$801$		0			0
$802$	−349.094	−	349.094i	−0.435279	−	0.435279i
$803$	−378.198	+	378.198i	−0.470981	+	0.470981i
$804$		0			0
$805$		0			0
$806$	32.5556			0.0403915
$807$		0			0
$808$	590.793	−	590.793i	0.731180	−	0.731180i
$809$			1201.69i			1.48540i	0.669623	+	0.742701i	$0.266456\pi$
$809$			1201.69i			1.48540i	−0.669623	+	0.742701i	$0.733544\pi$
$810$		0			0
$811$	−214.518			−0.264511			−0.132255	−	0.991216i	$-0.542222\pi$
$811$	−214.518			−0.264511			−0.132255	+	0.991216i	$0.542222\pi$
$812$	−78.9952	−	78.9952i	−0.0972847	−	0.0972847i
$813$		0			0
$814$			120.073i			0.147509i
$815$		0			0
$816$		0			0
$817$	1171.90	+	1171.90i	1.43440	+	1.43440i
$818$	88.2506	−	88.2506i	0.107886	−	0.107886i
$819$		0			0
$820$		0			0
$821$	1242.79			1.51375			0.756877	−	0.653557i	$-0.226724\pi$
$821$	1242.79			1.51375			0.756877	+	0.653557i	$0.226724\pi$
$822$		0			0
$823$	76.3353	−	76.3353i	0.0927525	−	0.0927525i	−0.659208	−	0.751961i	$-0.729108\pi$
$823$	76.3353	−	76.3353i	0.0927525	−	0.0927525i	0.751961	+	0.659208i	$0.229108\pi$
$824$		−	139.677i		−	0.169511i
$825$		0			0
$826$	−162.140			−0.196295
$827$	323.536	+	323.536i	0.391216	+	0.391216i	0.875121	−	0.483905i	$-0.160782\pi$
$827$	323.536	+	323.536i	0.391216	+	0.391216i	−0.483905	+	0.875121i	$0.660782\pi$
$828$		0			0
$829$			361.865i			0.436507i	0.975892	+	0.218254i	$0.0700360\pi$
$829$			361.865i			0.436507i	−0.975892	+	0.218254i	$0.929964\pi$
$830$		0			0
$831$		0			0
$832$	5.46967	+	5.46967i	0.00657412	+	0.00657412i
$833$	315.074	−	315.074i	0.378240	−	0.378240i
$834$		0			0
$835$		0			0
$836$	1036.55			1.23989
$837$		0			0
$838$	−245.434	+	245.434i	−0.292881	+	0.292881i
$839$		−	35.4295i		−	0.0422283i	−0.999777	−	0.0211141i	$-0.993279\pi$
$839$		−	35.4295i		−	0.0422283i	0.999777	−	0.0211141i	$-0.00672134\pi$
$840$		0			0
$841$	659.841			0.784591
$842$	−72.0979	−	72.0979i	−0.0856270	−	0.0856270i
$843$		0			0
$844$		−	802.516i		−	0.950848i
$845$		0			0
$846$		0			0
$847$	−260.971	−	260.971i	−0.308112	−	0.308112i
$848$	197.807	−	197.807i	0.233263	−	0.233263i
$849$		0			0
$850$		0			0
$851$	276.984			0.325480
$852$		0			0
$853$	996.367	−	996.367i	1.16807	−	1.16807i	0.185414	−	0.982661i	$-0.440638\pi$
$853$	996.367	−	996.367i	1.16807	−	1.16807i	0.982661	−	0.185414i	$-0.0593625\pi$
$854$			175.769i			0.205818i
$855$		0			0
$856$	1293.52			1.51112
$857$	613.451	+	613.451i	0.715812	+	0.715812i	0.967745	−	0.251932i	$-0.0810661\pi$
$857$	613.451	+	613.451i	0.715812	+	0.715812i	−0.251932	+	0.967745i	$0.581066\pi$
$858$		0			0
$859$			199.954i			0.232776i	0.993204	+	0.116388i	$0.0371316\pi$
$859$			199.954i			0.232776i	−0.993204	+	0.116388i	$0.962868\pi$
$860$		0			0
$861$		0			0
$862$	−274.887	−	274.887i	−0.318895	−	0.318895i
$863$	290.842	−	290.842i	0.337013	−	0.337013i	−0.518229	−	0.855242i	$-0.673409\pi$
$863$	290.842	−	290.842i	0.337013	−	0.337013i	0.855242	+	0.518229i	$0.173409\pi$
$864$		0			0
$865$		0			0
$866$	−49.4077			−0.0570528
$867$		0			0
$868$	230.102	−	230.102i	0.265095	−	0.265095i
$869$			90.1202i			0.103706i
$870$		0			0
$871$	35.6027			0.0408756
$872$	−782.455	−	782.455i	−0.897311	−	0.897311i
$873$		0			0
$874$			727.885i			0.832821i
$875$		0			0
$876$		0			0
$877$	−57.7576	−	57.7576i	−0.0658582	−	0.0658582i	0.673411	−	0.739269i	$-0.264829\pi$
$877$	−57.7576	−	57.7576i	−0.0658582	−	0.0658582i	−0.739269	+	0.673411i	$0.764829\pi$
$878$	118.051	−	118.051i	0.134455	−	0.134455i
$879$		0			0
$880$		0			0
$881$	673.852			0.764872			0.382436	−	0.923982i	$-0.375085\pi$
$881$	673.852			0.764872			0.382436	+	0.923982i	$0.375085\pi$
$882$		0			0
$883$	701.206	−	701.206i	0.794118	−	0.794118i	−0.188043	−	0.982161i	$-0.560214\pi$
$883$	701.206	−	701.206i	0.794118	−	0.794118i	0.982161	+	0.188043i	$0.0602144\pi$
$884$			28.1793i			0.0318770i
$885$		0			0
$886$	−325.756			−0.367671
$887$	−713.261	−	713.261i	−0.804128	−	0.804128i	0.179610	−	0.983738i	$-0.442516\pi$
$887$	−713.261	−	713.261i	−0.804128	−	0.804128i	−0.983738	+	0.179610i	$0.942516\pi$
$888$		0			0
$889$			95.6766i			0.107623i
$890$		0			0
$891$		0			0
$892$	552.166	+	552.166i	0.619020	+	0.619020i
$893$	−288.922	+	288.922i	−0.323541	+	0.323541i
$894$		0			0
$895$		0			0
$896$	331.448			0.369920
$897$		0			0
$898$	−186.251	+	186.251i	−0.207407	+	0.207407i
$899$		−	527.692i		−	0.586977i
$900$		0			0
$901$	−527.562			−0.585529
$902$	−760.898	−	760.898i	−0.843567	−	0.843567i
$903$		0			0
$904$		−	904.736i		−	1.00081i
$905$		0			0
$906$		0			0
$907$	−10.7160	−	10.7160i	−0.0118148	−	0.0118148i	0.701175	−	0.712990i	$-0.252659\pi$
$907$	−10.7160	−	10.7160i	−0.0118148	−	0.0118148i	−0.712990	+	0.701175i	$0.752659\pi$
$908$	576.160	−	576.160i	0.634537	−	0.634537i
$909$		0			0
$910$		0			0
$911$	952.181			1.04520			0.522602	−	0.852577i	$-0.324961\pi$
$911$	952.181			1.04520			0.522602	+	0.852577i	$0.324961\pi$
$912$		0			0
$913$	−418.638	+	418.638i	−0.458530	+	0.458530i
$914$			796.975i			0.871963i
$915$		0			0
$916$	407.069			0.444398
$917$	153.478	+	153.478i	0.167370	+	0.167370i
$918$		0			0
$919$			605.183i			0.658523i	0.944239	+	0.329262i	$0.106800\pi$
$919$			605.183i			0.658523i	−0.944239	+	0.329262i	$0.893200\pi$
$920$		0			0
$921$		0			0
$922$	−345.738	−	345.738i	−0.374987	−	0.374987i
$923$	43.3842	−	43.3842i	0.0470035	−	0.0470035i
$924$		0			0
$925$		0			0
$926$	−176.673			−0.190791
$927$		0			0
$928$	312.051	−	312.051i	0.336261	−	0.336261i
$929$			278.073i			0.299325i	0.988737	+	0.149663i	$0.0478188\pi$
$929$			278.073i			0.299325i	−0.988737	+	0.149663i	$0.952181\pi$
$930$		0			0
$931$	−878.095			−0.943174
$932$	165.553	+	165.553i	0.177632	+	0.177632i
$933$		0			0
$934$		−	219.300i		−	0.234797i
$935$		0			0
$936$		0			0
$937$	−896.938	−	896.938i	−0.957244	−	0.957244i	0.0418787	−	0.999123i	$-0.486666\pi$
$937$	−896.938	−	896.938i	−0.957244	−	0.957244i	−0.999123	+	0.0418787i	$0.986666\pi$
$938$	−76.6024	+	76.6024i	−0.0816657	+	0.0816657i
$939$		0			0
$940$		0			0
$941$	−360.668			−0.383282			−0.191641	−	0.981465i	$-0.561381\pi$
$941$	−360.668			−0.383282			−0.191641	+	0.981465i	$0.561381\pi$
$942$		0			0
$943$	−1755.24	+	1755.24i	−1.86134	+	1.86134i
$944$			351.514i			0.372366i
$945$		0			0
$946$	1219.12			1.28871
$947$	−934.038	−	934.038i	−0.986313	−	0.986313i	0.0135946	−	0.999908i	$-0.495673\pi$
$947$	−934.038	−	934.038i	−0.986313	−	0.986313i	−0.999908	+	0.0135946i	$0.995673\pi$
$948$		0			0
$949$			28.6542i			0.0301941i
$950$		0			0
$951$		0			0
$952$	−139.717	−	139.717i	−0.146762	−	0.146762i
$953$	−546.187	+	546.187i	−0.573124	+	0.573124i	−0.933000	−	0.359876i	$-0.882819\pi$
$953$	−546.187	+	546.187i	−0.573124	+	0.573124i	0.359876	+	0.933000i	$0.382819\pi$
$954$		0			0
$955$		0			0
$956$	−318.202			−0.332847
$957$		0			0
$958$	532.353	−	532.353i	0.555692	−	0.555692i
$959$			598.894i			0.624498i
$960$		0			0
$961$	576.097			0.599476
$962$	4.54867	+	4.54867i	0.00472834	+	0.00472834i
$963$		0			0
$964$		−	862.292i		−	0.894494i
$965$		0			0
$966$		0			0
$967$	760.948	+	760.948i	0.786916	+	0.786916i	0.980987	−	0.194072i	$-0.0621694\pi$
$967$	760.948	+	760.948i	0.786916	+	0.786916i	−0.194072	+	0.980987i	$0.562169\pi$
$968$	658.280	−	658.280i	0.680041	−	0.680041i
$969$		0			0
$970$		0			0
$971$	892.281			0.918930			0.459465	−	0.888196i	$-0.348041\pi$
$971$	892.281			0.918930			0.459465	+	0.888196i	$0.348041\pi$
$972$		0			0
$973$	−121.620	+	121.620i	−0.124995	+	0.124995i
$974$		−	715.007i		−	0.734093i
$975$		0			0
$976$	381.062			0.390432
$977$	−263.487	−	263.487i	−0.269690	−	0.269690i	0.559285	−	0.828975i	$-0.311076\pi$
$977$	−263.487	−	263.487i	−0.269690	−	0.269690i	−0.828975	+	0.559285i	$0.811076\pi$
$978$		0			0
$979$			372.773i			0.380769i
$980$		0			0
$981$		0			0
$982$	109.746	+	109.746i	0.111758	+	0.111758i
$983$	−917.630	+	917.630i	−0.933499	+	0.933499i	−0.997923	−	0.0644232i	$-0.979479\pi$
$983$	−917.630	+	917.630i	−0.933499	+	0.933499i	0.0644232	+	0.997923i	$0.479479\pi$
$984$		0			0
$985$		0			0
$986$	−139.043			−0.141017
$987$		0			0
$988$	39.2671	−	39.2671i	0.0397440	−	0.0397440i
$989$		−	2812.27i		−	2.84355i
$990$		0			0
$991$	−1393.97			−1.40663			−0.703315	−	0.710878i	$-0.748298\pi$
$991$	−1393.97			−1.40663			−0.703315	+	0.710878i	$0.748298\pi$
$992$	908.961	+	908.961i	0.916292	+	0.916292i
$993$		0			0
$994$			186.690i			0.187817i
$995$		0			0
$996$		0			0
$997$	243.100	+	243.100i	0.243831	+	0.243831i	0.818433	−	0.574602i	$-0.194843\pi$
$997$	243.100	+	243.100i	0.243831	+	0.243831i	−0.574602	+	0.818433i	$0.694843\pi$
$998$	131.184	−	131.184i	0.131447	−	0.131447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.3.g.j.82.5		16
3.2	odd	2	inner	675.3.g.j.82.4		16
5.2	odd	4		135.3.g.b.28.4	✓	16
5.3	odd	4	inner	675.3.g.j.568.5		16
5.4	even	2		135.3.g.b.82.4	yes	16
15.2	even	4		135.3.g.b.28.5	yes	16
15.8	even	4	inner	675.3.g.j.568.4		16
15.14	odd	2		135.3.g.b.82.5	yes	16
45.2	even	12		405.3.l.n.28.4		32
45.4	even	6		405.3.l.n.217.5		32
45.7	odd	12		405.3.l.n.28.5		32
45.14	odd	6		405.3.l.n.217.4		32
45.22	odd	12		405.3.l.n.298.4		32
45.29	odd	6		405.3.l.n.352.5		32
45.32	even	12		405.3.l.n.298.5		32
45.34	even	6		405.3.l.n.352.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.4	✓	16	5.2	odd	4
135.3.g.b.28.5	yes	16	15.2	even	4
135.3.g.b.82.4	yes	16	5.4	even	2
135.3.g.b.82.5	yes	16	15.14	odd	2
405.3.l.n.28.4		32	45.2	even	12
405.3.l.n.28.5		32	45.7	odd	12
405.3.l.n.217.4		32	45.14	odd	6
405.3.l.n.217.5		32	45.4	even	6
405.3.l.n.298.4		32	45.22	odd	12
405.3.l.n.298.5		32	45.32	even	12
405.3.l.n.352.4		32	45.34	even	6
405.3.l.n.352.5		32	45.29	odd	6
675.3.g.j.82.4		16	3.2	odd	2	inner
675.3.g.j.82.5		16	1.1	even	1	trivial
675.3.g.j.568.4		16	15.8	even	4	inner
675.3.g.j.568.5		16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	675.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.683187 + 0.683187i) q^{2} -3.06651i q^{4} +(-1.91393 - 1.91393i) q^{7} +(4.82775 - 4.82775i) q^{8} -16.0422 q^{11} +(-0.607722 + 0.607722i) q^{13} -2.61514i q^{14} -5.66955 q^{16} +(7.56049 + 7.56049i) q^{17} -21.0707i q^{19} +(-10.9598 - 10.9598i) q^{22} +(-25.2822 + 25.2822i) q^{23} -0.830376 q^{26} +(-5.86908 + 5.86908i) q^{28} +13.4595i q^{29} -39.2058 q^{31} +(-23.1843 - 23.1843i) q^{32} +10.3305i q^{34} +(-5.47784 - 5.47784i) q^{37} +(14.3952 - 14.3952i) q^{38} +69.4260 q^{41} +(-55.6177 + 55.6177i) q^{43} +49.1937i q^{44} -34.5449 q^{46} +(-13.7120 - 13.7120i) q^{47} -41.6738i q^{49} +(1.86359 + 1.86359i) q^{52} +(-34.8894 + 34.8894i) q^{53} -18.4799 q^{56} +(-9.19538 + 9.19538i) q^{58} -62.0004i q^{59} -67.2121 q^{61} +(-26.7849 - 26.7849i) q^{62} -9.00028i q^{64} +(-29.2919 - 29.2919i) q^{67} +(23.1843 - 23.1843i) q^{68} -71.3882 q^{71} +(23.5751 - 23.5751i) q^{73} -7.48478i q^{74} -64.6135 q^{76} +(30.7037 + 30.7037i) q^{77} -5.61768i q^{79} +(47.4309 + 47.4309i) q^{82} +(26.0960 - 26.0960i) q^{83} -75.9945 q^{86} +(-77.4479 + 77.4479i) q^{88} -23.2369i q^{89} +2.32627 q^{91} +(77.5282 + 77.5282i) q^{92} -18.7357i q^{94} +(-97.3193 - 97.3193i) q^{97} +(28.4710 - 28.4710i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{7} - 40 q^{13} - 152 q^{16} + 136 q^{22} + 112 q^{28} + 200 q^{31} - 16 q^{37} - 136 q^{43} + 152 q^{46} - 640 q^{52} - 48 q^{58} - 280 q^{61} + 344 q^{67} + 776 q^{73} + 144 q^{76} + 880 q^{82}+ \cdots - 448 q^{97}+O(q^{100}) \) 16 * q - 16 * q^7 - 40 * q^13 - 152 * q^16 + 136 * q^22 + 112 * q^28 + 200 * q^31 - 16 * q^37 - 136 * q^43 + 152 * q^46 - 640 * q^52 - 48 * q^58 - 280 * q^61 + 344 * q^67 + 776 * q^73 + 144 * q^76 + 880 * q^82 - 1200 * q^88 + 152 * q^91 - 448 * q^97

Introduction

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