LMFDB - Embedded newform 225.3.g.a.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,3,Mod(82,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("225.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	225.g (of order $4$, 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:	$6.13080594811$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	225.118
Dual form			225.3.g.a.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.224745 - 0.224745i) q^{2} +3.89898i q^{4} +(-3.44949 + 3.44949i) q^{7} +(1.77526 + 1.77526i) q^{8} -11.3485 q^{11} +(5.55051 + 5.55051i) q^{13} +1.55051i q^{14} -14.7980 q^{16} +(-17.3485 + 17.3485i) q^{17} -8.69694i q^{19} +(-2.55051 + 2.55051i) q^{22} +(11.5505 + 11.5505i) q^{23} +2.49490 q^{26} +(-13.4495 - 13.4495i) q^{28} +35.1464i q^{29} +10.6969 q^{31} +(-10.4268 + 10.4268i) q^{32} +7.79796i q^{34} +(6.04541 - 6.04541i) q^{37} +(-1.95459 - 1.95459i) q^{38} -0.696938 q^{41} +(26.4949 + 26.4949i) q^{43} -44.2474i q^{44} +5.19184 q^{46} +(44.2474 - 44.2474i) q^{47} +25.2020i q^{49} +(-21.6413 + 21.6413i) q^{52} +(-0.696938 - 0.696938i) q^{53} -12.2474 q^{56} +(7.89898 + 7.89898i) q^{58} -39.9342i q^{59} +5.90918 q^{61} +(2.40408 - 2.40408i) q^{62} -54.5051i q^{64} +(45.1010 - 45.1010i) q^{67} +(-67.6413 - 67.6413i) q^{68} +68.0000 q^{71} +(-77.7878 - 77.7878i) q^{73} -2.71735i q^{74} +33.9092 q^{76} +(39.1464 - 39.1464i) q^{77} +24.4949i q^{79} +(-0.156633 + 0.156633i) q^{82} +(13.1464 + 13.1464i) q^{83} +11.9092 q^{86} +(-20.1464 - 20.1464i) q^{88} +82.1816i q^{89} -38.2929 q^{91} +(-45.0352 + 45.0352i) q^{92} -19.8888i q^{94} +(24.5959 - 24.5959i) q^{97} +(5.66403 + 5.66403i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8} - 16 q^{11} + 32 q^{13} - 20 q^{16} - 40 q^{17} - 20 q^{22} + 56 q^{23} - 88 q^{26} - 44 q^{28} - 16 q^{31} - 76 q^{32} - 64 q^{37} - 96 q^{38} + 56 q^{41} + 8 q^{43}+ \cdots - 188 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8 - 16 * q^11 + 32 * q^13 - 20 * q^16 - 40 * q^17 - 20 * q^22 + 56 * q^23 - 88 * q^26 - 44 * q^28 - 16 * q^31 - 76 * q^32 - 64 * q^37 - 96 * q^38 + 56 * q^41 + 8 * q^43 - 136 * q^46 + 128 * q^47 + 80 * q^52 + 56 * q^53 + 12 * q^58 + 200 * q^61 + 88 * q^62 + 200 * q^67 - 104 * q^68 + 272 * q^71 - 76 * q^73 + 312 * q^76 + 88 * q^77 - 128 * q^82 - 16 * q^83 + 224 * q^86 - 12 * q^88 - 16 * q^91 + 104 * q^92 + 20 * q^97 - 188 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.224745	−	0.224745i	0.112372	−	0.112372i	−0.648685	−	0.761057i	$-0.724681\pi$
$2$	0.224745	−	0.224745i	0.112372	−	0.112372i	0.761057	+	0.648685i	$0.224681\pi$
$3$		0			0
$3$		0			0
$4$			3.89898i			0.974745i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.44949	+	3.44949i	−0.492784	+	0.492784i	−0.909182	−	0.416398i	$-0.863292\pi$
$7$	−3.44949	+	3.44949i	−0.492784	+	0.492784i	0.416398	+	0.909182i	$0.363292\pi$
$8$	1.77526	+	1.77526i	0.221907	+	0.221907i
$9$		0			0
$10$		0			0
$11$	−11.3485			−1.03168			−0.515840	−	0.856685i	$-0.672520\pi$
$11$	−11.3485			−1.03168			−0.515840	+	0.856685i	$0.672520\pi$
$12$		0			0
$13$	5.55051	+	5.55051i	0.426962	+	0.426962i	0.887592	−	0.460630i	$-0.152376\pi$
$13$	5.55051	+	5.55051i	0.426962	+	0.426962i	−0.460630	+	0.887592i	$0.652376\pi$
$14$			1.55051i			0.110751i
$15$		0			0
$16$	−14.7980			−0.924872
$17$	−17.3485	+	17.3485i	−1.02050	+	1.02050i	−0.0207127	+	0.999785i	$0.506594\pi$
$17$	−17.3485	+	17.3485i	−1.02050	+	1.02050i	−0.999785	+	0.0207127i	$0.993406\pi$
$18$		0			0
$19$		−	8.69694i		−	0.457734i	−0.973458	−	0.228867i	$-0.926498\pi$
$19$		−	8.69694i		−	0.457734i	0.973458	−	0.228867i	$-0.0735020\pi$
$20$		0			0
$21$		0			0
$22$	−2.55051	+	2.55051i	−0.115932	+	0.115932i
$23$	11.5505	+	11.5505i	0.502196	+	0.502196i	0.912120	−	0.409924i	$-0.134445\pi$
$23$	11.5505	+	11.5505i	0.502196	+	0.502196i	−0.409924	+	0.912120i	$0.634445\pi$
$24$		0			0
$25$		0			0
$26$	2.49490			0.0959576
$27$		0			0
$28$	−13.4495	−	13.4495i	−0.480339	−	0.480339i
$29$			35.1464i			1.21195i	0.795485	+	0.605973i	$0.207216\pi$
$29$			35.1464i			1.21195i	−0.795485	+	0.605973i	$0.792784\pi$
$30$		0			0
$31$	10.6969			0.345063			0.172531	−	0.985004i	$-0.444805\pi$
$31$	10.6969			0.345063			0.172531	+	0.985004i	$0.444805\pi$
$32$	−10.4268	+	10.4268i	−0.325837	+	0.325837i
$33$		0			0
$34$			7.79796i			0.229352i
$35$		0			0
$36$		0			0
$37$	6.04541	−	6.04541i	0.163389	−	0.163389i	−0.620677	−	0.784066i	$-0.713142\pi$
$37$	6.04541	−	6.04541i	0.163389	−	0.163389i	0.784066	+	0.620677i	$0.213142\pi$
$38$	−1.95459	−	1.95459i	−0.0514366	−	0.0514366i
$39$		0			0
$40$		0			0
$41$	−0.696938			−0.0169985			−0.00849925	−	0.999964i	$-0.502705\pi$
$41$	−0.696938			−0.0169985			−0.00849925	+	0.999964i	$0.502705\pi$
$42$		0			0
$43$	26.4949	+	26.4949i	0.616160	+	0.616160i	0.944544	−	0.328384i	$-0.106504\pi$
$43$	26.4949	+	26.4949i	0.616160	+	0.616160i	−0.328384	+	0.944544i	$0.606504\pi$
$44$		−	44.2474i		−	1.00562i
$45$		0			0
$46$	5.19184			0.112866
$47$	44.2474	−	44.2474i	0.941435	−	0.941435i	−0.0569424	−	0.998377i	$-0.518135\pi$
$47$	44.2474	−	44.2474i	0.941435	−	0.941435i	0.998377	+	0.0569424i	$0.0181351\pi$
$48$		0			0
$49$			25.2020i			0.514327i
$50$		0			0
$51$		0			0
$52$	−21.6413	+	21.6413i	−0.416179	+	0.416179i
$53$	−0.696938	−	0.696938i	−0.0131498	−	0.0131498i	0.700501	−	0.713651i	$-0.252960\pi$
$53$	−0.696938	−	0.696938i	−0.0131498	−	0.0131498i	−0.713651	+	0.700501i	$0.752960\pi$
$54$		0			0
$55$		0			0
$56$	−12.2474			−0.218704
$57$		0			0
$58$	7.89898	+	7.89898i	0.136189	+	0.136189i
$59$		−	39.9342i		−	0.676851i	−0.940993	−	0.338425i	$-0.890106\pi$
$59$		−	39.9342i		−	0.676851i	0.940993	−	0.338425i	$-0.109894\pi$
$60$		0			0
$61$	5.90918			0.0968719			0.0484359	−	0.998826i	$-0.484576\pi$
$61$	5.90918			0.0968719			0.0484359	+	0.998826i	$0.484576\pi$
$62$	2.40408	−	2.40408i	0.0387755	−	0.0387755i
$63$		0			0
$64$		−	54.5051i		−	0.851642i
$65$		0			0
$66$		0			0
$67$	45.1010	−	45.1010i	0.673150	−	0.673150i	−0.285291	−	0.958441i	$-0.592090\pi$
$67$	45.1010	−	45.1010i	0.673150	−	0.673150i	0.958441	+	0.285291i	$0.0920903\pi$
$68$	−67.6413	−	67.6413i	−0.994725	−	0.994725i
$69$		0			0
$70$		0			0
$71$	68.0000			0.957746			0.478873	−	0.877884i	$-0.341045\pi$
$71$	68.0000			0.957746			0.478873	+	0.877884i	$0.341045\pi$
$72$		0			0
$73$	−77.7878	−	77.7878i	−1.06559	−	1.06559i	−0.997693	−	0.0678931i	$-0.978372\pi$
$73$	−77.7878	−	77.7878i	−1.06559	−	1.06559i	−0.0678931	−	0.997693i	$-0.521628\pi$
$74$		−	2.71735i		−	0.0367209i
$75$		0			0
$76$	33.9092			0.446173
$77$	39.1464	−	39.1464i	0.508395	−	0.508395i
$78$		0			0
$79$			24.4949i			0.310062i	0.987910	+	0.155031i	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$		0			0
$81$		0			0
$82$	−0.156633	+	0.156633i	−0.00191016	+	0.00191016i
$83$	13.1464	+	13.1464i	0.158391	+	0.158391i	0.781853	−	0.623463i	$-0.214275\pi$
$83$	13.1464	+	13.1464i	0.158391	+	0.158391i	−0.623463	+	0.781853i	$0.714275\pi$
$84$		0			0
$85$		0			0
$86$	11.9092			0.138479
$87$		0			0
$88$	−20.1464	−	20.1464i	−0.228937	−	0.228937i
$89$			82.1816i			0.923389i	0.887039	+	0.461695i	$0.152758\pi$
$89$			82.1816i			0.923389i	−0.887039	+	0.461695i	$0.847242\pi$
$90$		0			0
$91$	−38.2929			−0.420801
$92$	−45.0352	+	45.0352i	−0.489513	+	0.489513i
$93$		0			0
$94$		−	19.8888i		−	0.211583i
$95$		0			0
$96$		0			0
$97$	24.5959	−	24.5959i	0.253566	−	0.253566i	−0.568865	−	0.822431i	$-0.692617\pi$
$97$	24.5959	−	24.5959i	0.253566	−	0.253566i	0.822431	+	0.568865i	$0.192617\pi$
$98$	5.66403	+	5.66403i	0.0577962	+	0.0577962i
$99$		0			0
$100$		0			0
$101$	105.621			1.04575			0.522876	−	0.852409i	$-0.324859\pi$
$101$	105.621			1.04575			0.522876	+	0.852409i	$0.324859\pi$
$102$		0			0
$103$	89.2474	+	89.2474i	0.866480	+	0.866480i	0.992081	−	0.125601i	$-0.0400858\pi$
$103$	89.2474	+	89.2474i	0.866480	+	0.866480i	−0.125601	+	0.992081i	$0.540086\pi$
$104$			19.7071i			0.189492i
$105$		0			0
$106$	−0.313267			−0.00295535
$107$	68.7423	−	68.7423i	0.642452	−	0.642452i	−0.308706	−	0.951158i	$-0.599896\pi$
$107$	68.7423	−	68.7423i	0.642452	−	0.642452i	0.951158	+	0.308706i	$0.0998958\pi$
$108$		0			0
$109$		−	68.6969i		−	0.630247i	−0.949051	−	0.315124i	$-0.897954\pi$
$109$		−	68.6969i		−	0.630247i	0.949051	−	0.315124i	$-0.102046\pi$
$110$		0			0
$111$		0			0
$112$	51.0454	−	51.0454i	0.455763	−	0.455763i
$113$	97.6413	+	97.6413i	0.864083	+	0.864083i	0.991809	−	0.127727i	$-0.0407681\pi$
$113$	97.6413	+	97.6413i	0.864083	+	0.864083i	−0.127727	+	0.991809i	$0.540768\pi$
$114$		0			0
$115$		0			0
$116$	−137.035			−1.18134
$117$		0			0
$118$	−8.97500	−	8.97500i	−0.0760593	−	0.0760593i
$119$		−	119.687i		−	1.00577i
$120$		0			0
$121$	7.78775			0.0643616
$122$	1.32806	−	1.32806i	0.0108857	−	0.0108857i
$123$		0			0
$124$			41.7071i			0.336348i
$125$		0			0
$126$		0			0
$127$	−164.621	+	164.621i	−1.29623	+	1.29623i	−0.365362	+	0.930865i	$0.619055\pi$
$127$	−164.621	+	164.621i	−1.29623	+	1.29623i	−0.930865	+	0.365362i	$0.880945\pi$
$128$	−53.9569	−	53.9569i	−0.421538	−	0.421538i
$129$		0			0
$130$		0			0
$131$	−106.136			−0.810200			−0.405100	−	0.914272i	$-0.632763\pi$
$131$	−106.136			−0.810200			−0.405100	+	0.914272i	$0.632763\pi$
$132$		0			0
$133$	30.0000	+	30.0000i	0.225564	+	0.225564i
$134$		−	20.2724i		−	0.151287i
$135$		0			0
$136$	−61.5959			−0.452911
$137$	−166.631	+	166.631i	−1.21629	+	1.21629i	−0.247363	+	0.968923i	$0.579564\pi$
$137$	−166.631	+	166.631i	−1.21629	+	1.21629i	−0.968923	+	0.247363i	$0.920436\pi$
$138$		0			0
$139$			191.171i			1.37533i	0.726026	+	0.687667i	$0.241365\pi$
$139$			191.171i			1.37533i	−0.726026	+	0.687667i	$0.758635\pi$
$140$		0			0
$141$		0			0
$142$	15.2827	−	15.2827i	0.107624	−	0.107624i
$143$	−62.9898	−	62.9898i	−0.440488	−	0.440488i
$144$		0			0
$145$		0			0
$146$	−34.9648			−0.239485
$147$		0			0
$148$	23.5709	+	23.5709i	0.159263	+	0.159263i
$149$			84.8536i			0.569487i	0.958604	+	0.284744i	$0.0919084\pi$
$149$			84.8536i			0.569487i	−0.958604	+	0.284744i	$0.908092\pi$
$150$		0			0
$151$	148.969			0.986552			0.493276	−	0.869873i	$-0.335799\pi$
$151$	148.969			0.986552			0.493276	+	0.869873i	$0.335799\pi$
$152$	15.4393	−	15.4393i	0.101574	−	0.101574i
$153$		0			0
$154$		−	17.5959i		−	0.114259i
$155$		0			0
$156$		0			0
$157$	−16.8536	+	16.8536i	−0.107348	+	0.107348i	−0.758741	−	0.651393i	$-0.774185\pi$
$157$	−16.8536	+	16.8536i	−0.107348	+	0.107348i	0.651393	+	0.758741i	$0.274185\pi$
$158$	5.50510	+	5.50510i	0.0348424	+	0.0348424i
$159$		0			0
$160$		0			0
$161$	−79.6867			−0.494949
$162$		0			0
$163$	−130.606	−	130.606i	−0.801265	−	0.801265i	0.182029	−	0.983293i	$-0.441734\pi$
$163$	−130.606	−	130.606i	−0.801265	−	0.801265i	−0.983293	+	0.182029i	$0.941734\pi$
$164$		−	2.71735i		−	0.0165692i
$165$		0			0
$166$	5.90918			0.0355975
$167$	−45.0352	+	45.0352i	−0.269672	+	0.269672i	−0.828968	−	0.559296i	$-0.811071\pi$
$167$	−45.0352	+	45.0352i	−0.269672	+	0.269672i	0.559296	+	0.828968i	$0.311071\pi$
$168$		0			0
$169$		−	107.384i		−	0.635406i
$170$		0			0
$171$		0			0
$172$	−103.303	+	103.303i	−0.600599	+	0.600599i
$173$	146.631	+	146.631i	0.847579	+	0.847579i	0.989831	−	0.142252i	$-0.0454343\pi$
$173$	146.631	+	146.631i	0.847579	+	0.847579i	−0.142252	+	0.989831i	$0.545434\pi$
$174$		0			0
$175$		0			0
$176$	167.934			0.954171
$177$		0			0
$178$	18.4699	+	18.4699i	0.103763	+	0.103763i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$		0			0
$181$	−286.272			−1.58162			−0.790808	−	0.612064i	$-0.790339\pi$
$181$	−286.272			−1.58162			−0.790808	+	0.612064i	$0.790339\pi$
$182$	−8.60612	+	8.60612i	−0.0472864	+	0.0472864i
$183$		0			0
$184$			41.0102i			0.222882i
$185$		0			0
$186$		0			0
$187$	196.879	−	196.879i	1.05283	−	1.05283i
$188$	172.520	+	172.520i	0.917659	+	0.917659i
$189$		0			0
$190$		0			0
$191$	−48.0908			−0.251784			−0.125892	−	0.992044i	$-0.540179\pi$
$191$	−48.0908			−0.251784			−0.125892	+	0.992044i	$0.540179\pi$
$192$		0			0
$193$	255.565	+	255.565i	1.32417	+	1.32417i	0.910364	+	0.413809i	$0.135802\pi$
$193$	255.565	+	255.565i	1.32417	+	1.32417i	0.413809	+	0.910364i	$0.364198\pi$
$194$		−	11.0556i		−	0.0569877i
$195$		0			0
$196$	−98.2622			−0.501338
$197$	−96.6969	+	96.6969i	−0.490847	+	0.490847i	−0.908573	−	0.417726i	$-0.862827\pi$
$197$	−96.6969	+	96.6969i	−0.490847	+	0.490847i	0.417726	+	0.908573i	$0.362827\pi$
$198$		0			0
$199$		−	192.606i		−	0.967870i	−0.875104	−	0.483935i	$-0.839207\pi$
$199$		−	192.606i		−	0.967870i	0.875104	−	0.483935i	$-0.160793\pi$
$200$		0			0
$201$		0			0
$202$	23.7378	−	23.7378i	0.117514	−	0.117514i
$203$	−121.237	−	121.237i	−0.597228	−	0.597228i
$204$		0			0
$205$		0			0
$206$	40.1158			0.194737
$207$		0			0
$208$	−82.1362	−	82.1362i	−0.394886	−	0.394886i
$209$			98.6969i			0.472234i
$210$		0			0
$211$	147.212			0.697688			0.348844	−	0.937181i	$-0.386574\pi$
$211$	147.212			0.697688			0.348844	+	0.937181i	$0.386574\pi$
$212$	2.71735	−	2.71735i	0.0128177	−	0.0128177i
$213$		0			0
$214$		−	30.8990i		−	0.144388i
$215$		0			0
$216$		0			0
$217$	−36.8990	+	36.8990i	−0.170041	+	0.170041i
$218$	−15.4393	−	15.4393i	−0.0708224	−	0.0708224i
$219$		0			0
$220$		0			0
$221$	−192.586			−0.871429
$222$		0			0
$223$	−167.429	−	167.429i	−0.750803	−	0.750803i	0.223826	−	0.974629i	$-0.428145\pi$
$223$	−167.429	−	167.429i	−0.750803	−	0.750803i	−0.974629	+	0.223826i	$0.928145\pi$
$224$		−	71.9342i		−	0.321135i
$225$		0			0
$226$	43.8888			0.194198
$227$	253.171	−	253.171i	1.11529	−	1.11529i	0.122870	−	0.992423i	$-0.460790\pi$
$227$	253.171	−	253.171i	1.11529	−	1.11529i	0.992423	−	0.122870i	$-0.0392098\pi$
$228$		0			0
$229$			224.202i			0.979048i	0.871990	+	0.489524i	$0.162829\pi$
$229$			224.202i			0.979048i	−0.871990	+	0.489524i	$0.837171\pi$
$230$		0			0
$231$		0			0
$232$	−62.3939	+	62.3939i	−0.268939	+	0.268939i
$233$	−205.712	−	205.712i	−0.882883	−	0.882883i	0.110944	−	0.993827i	$-0.464613\pi$
$233$	−205.712	−	205.712i	−0.882883	−	0.882883i	−0.993827	+	0.110944i	$0.964613\pi$
$234$		0			0
$235$		0			0
$236$	155.703			0.659757
$237$		0			0
$238$	−26.8990	−	26.8990i	−0.113021	−	0.113021i
$239$		−	345.798i		−	1.44685i	−0.690401	−	0.723427i	$-0.742566\pi$
$239$		−	345.798i		−	1.44685i	0.690401	−	0.723427i	$-0.257434\pi$
$240$		0			0
$241$	101.576			0.421475			0.210738	−	0.977543i	$-0.432413\pi$
$241$	101.576			0.421475			0.210738	+	0.977543i	$0.432413\pi$
$242$	1.75026	−	1.75026i	0.00723247	−	0.00723247i
$243$		0			0
$244$			23.0398i			0.0944254i
$245$		0			0
$246$		0			0
$247$	48.2724	−	48.2724i	0.195435	−	0.195435i
$248$	18.9898	+	18.9898i	0.0765718	+	0.0765718i
$249$		0			0
$250$		0			0
$251$	331.258			1.31975			0.659876	−	0.751375i	$-0.270609\pi$
$251$	331.258			1.31975			0.659876	+	0.751375i	$0.270609\pi$
$252$		0			0
$253$	−131.081	−	131.081i	−0.518105	−	0.518105i
$254$			73.9954i			0.291321i
$255$		0			0
$256$	193.767			0.756904
$257$	33.2372	−	33.2372i	0.129328	−	0.129328i	−0.639480	−	0.768808i	$-0.720850\pi$
$257$	33.2372	−	33.2372i	0.129328	−	0.129328i	0.768808	+	0.639480i	$0.220850\pi$
$258$		0			0
$259$			41.7071i			0.161031i
$260$		0			0
$261$		0			0
$262$	−23.8536	+	23.8536i	−0.0910442	+	0.0910442i
$263$	−278.157	−	278.157i	−1.05763	−	1.05763i	−0.998235	−	0.0593952i	$-0.981083\pi$
$263$	−278.157	−	278.157i	−1.05763	−	1.05763i	−0.0593952	−	0.998235i	$-0.518917\pi$
$264$		0			0
$265$		0			0
$266$	13.4847			0.0506943
$267$		0			0
$268$	175.848	+	175.848i	0.656149	+	0.656149i
$269$		−	488.499i		−	1.81598i	−0.418988	−	0.907992i	$-0.637615\pi$
$269$		−	488.499i		−	1.81598i	0.418988	−	0.907992i	$-0.362385\pi$
$270$		0			0
$271$	131.576			0.485518			0.242759	−	0.970087i	$-0.421947\pi$
$271$	131.576			0.485518			0.242759	+	0.970087i	$0.421947\pi$
$272$	256.722	−	256.722i	0.943831	−	0.943831i
$273$		0			0
$274$			74.8990i			0.273354i
$275$		0			0
$276$		0			0
$277$	−101.510	+	101.510i	−0.366461	+	0.366461i	−0.866185	−	0.499724i	$-0.833435\pi$
$277$	−101.510	+	101.510i	−0.366461	+	0.366461i	0.499724	+	0.866185i	$0.333435\pi$
$278$	42.9648	+	42.9648i	0.154550	+	0.154550i
$279$		0			0
$280$		0			0
$281$	−343.303			−1.22172			−0.610860	−	0.791739i	$-0.709176\pi$
$281$	−343.303			−1.22172			−0.610860	+	0.791739i	$0.709176\pi$
$282$		0			0
$283$	−1.19184	−	1.19184i	−0.00421143	−	0.00421143i	0.704998	−	0.709209i	$-0.250948\pi$
$283$	−1.19184	−	1.19184i	−0.00421143	−	0.00421143i	−0.709209	+	0.704998i	$0.750948\pi$
$284$			265.131i			0.933558i
$285$		0			0
$286$	−28.3133			−0.0989974
$287$	2.40408	−	2.40408i	0.00837659	−	0.00837659i
$288$		0			0
$289$		−	312.939i		−	1.08283i
$290$		0			0
$291$		0			0
$292$	303.293	−	303.293i	1.03867	−	1.03867i
$293$	96.5653	+	96.5653i	0.329574	+	0.329574i	0.852425	−	0.522850i	$-0.175131\pi$
$293$	96.5653	+	96.5653i	0.329574	+	0.329574i	−0.522850	+	0.852425i	$0.675131\pi$
$294$		0			0
$295$		0			0
$296$	21.4643			0.0725145
$297$		0			0
$298$	19.0704	+	19.0704i	0.0639946	+	0.0639946i
$299$			128.222i			0.428838i
$300$		0			0
$301$	−182.788			−0.607268
$302$	33.4801	−	33.4801i	0.110861	−	0.110861i
$303$		0			0
$304$			128.697i			0.423345i
$305$		0			0
$306$		0			0
$307$	124.969	−	124.969i	0.407066	−	0.407066i	−0.473648	−	0.880714i	$-0.657063\pi$
$307$	124.969	−	124.969i	0.407066	−	0.407066i	0.880714	+	0.473648i	$0.157063\pi$
$308$	152.631	+	152.631i	0.495556	+	0.495556i
$309$		0			0
$310$		0			0
$311$	586.302			1.88522			0.942608	−	0.333902i	$-0.108365\pi$
$311$	586.302			1.88522			0.942608	+	0.333902i	$0.108365\pi$
$312$		0			0
$313$	102.373	+	102.373i	0.327072	+	0.327072i	0.851472	−	0.524400i	$-0.175710\pi$
$313$	102.373	+	102.373i	0.327072	+	0.327072i	−0.524400	+	0.851472i	$0.675710\pi$
$314$			7.57551i			0.0241258i
$315$		0			0
$316$	−95.5051			−0.302231
$317$	−108.783	+	108.783i	−0.343165	+	0.343165i	−0.857556	−	0.514391i	$-0.828018\pi$
$317$	−108.783	+	108.783i	−0.343165	+	0.343165i	0.514391	+	0.857556i	$0.328018\pi$
$318$		0			0
$319$		−	398.858i		−	1.25034i
$320$		0			0
$321$		0			0
$322$	−17.9092	+	17.9092i	−0.0556186	+	0.0556186i
$323$	150.879	+	150.879i	0.467116	+	0.467116i
$324$		0			0
$325$		0			0
$326$	−58.7061			−0.180080
$327$		0			0
$328$	−1.23724	−	1.23724i	−0.00377208	−	0.00377208i
$329$			305.262i			0.927849i
$330$		0			0
$331$	−245.423			−0.741461			−0.370730	−	0.928741i	$-0.620893\pi$
$331$	−245.423			−0.741461			−0.370730	+	0.928741i	$0.620893\pi$
$332$	−51.2577	+	51.2577i	−0.154391	+	0.154391i
$333$		0			0
$334$			20.2429i			0.0606074i
$335$		0			0
$336$		0			0
$337$	−213.808	+	213.808i	−0.634446	+	0.634446i	−0.949180	−	0.314734i	$-0.898085\pi$
$337$	−213.808	+	213.808i	−0.634446	+	0.634446i	0.314734	+	0.949180i	$0.398085\pi$
$338$	−24.1339	−	24.1339i	−0.0714022	−	0.0714022i
$339$		0			0
$340$		0			0
$341$	−121.394			−0.355994
$342$		0			0
$343$	−255.959	−	255.959i	−0.746237	−	0.746237i
$344$			94.0704i			0.273460i
$345$		0			0
$346$	65.9092			0.190489
$347$	−160.050	+	160.050i	−0.461239	+	0.461239i	−0.899062	−	0.437822i	$-0.855750\pi$
$347$	−160.050	+	160.050i	−0.461239	+	0.461239i	0.437822	+	0.899062i	$0.355750\pi$
$348$		0			0
$349$			298.009i			0.853894i	0.904277	+	0.426947i	$0.140411\pi$
$349$			298.009i			0.853894i	−0.904277	+	0.426947i	$0.859589\pi$
$350$		0			0
$351$		0			0
$352$	118.328	−	118.328i	0.336159	−	0.336159i
$353$	−22.5199	−	22.5199i	−0.0637957	−	0.0637957i	0.674489	−	0.738285i	$-0.264364\pi$
$353$	−22.5199	−	22.5199i	−0.0637957	−	0.0637957i	−0.738285	+	0.674489i	$0.764364\pi$
$354$		0			0
$355$		0			0
$356$	−320.424			−0.900069
$357$		0			0
$358$	41.2883	+	41.2883i	0.115330	+	0.115330i
$359$			48.2724i			0.134464i	0.997737	+	0.0672318i	$0.0214167\pi$
$359$			48.2724i			0.134464i	−0.997737	+	0.0672318i	$0.978583\pi$
$360$		0			0
$361$	285.363			0.790480
$362$	−64.3383	+	64.3383i	−0.177730	+	0.177730i
$363$		0			0
$364$		−	149.303i		−	0.410173i
$365$		0			0
$366$		0			0
$367$	−146.510	+	146.510i	−0.399209	+	0.399209i	−0.877954	−	0.478745i	$-0.841092\pi$
$367$	−146.510	+	146.510i	−0.399209	+	0.399209i	0.478745	+	0.877954i	$0.341092\pi$
$368$	−170.924	−	170.924i	−0.464467	−	0.464467i
$369$		0			0
$370$		0			0
$371$	4.80816			0.0129600
$372$		0			0
$373$	−86.2066	−	86.2066i	−0.231117	−	0.231117i	0.582042	−	0.813159i	$-0.302254\pi$
$373$	−86.2066	−	86.2066i	−0.231117	−	0.231117i	−0.813159	+	0.582042i	$0.802254\pi$
$374$		−	88.4949i		−	0.236617i
$375$		0			0
$376$	157.101			0.417822
$377$	−195.081	+	195.081i	−0.517455	+	0.517455i
$378$		0			0
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$		0			0
$381$		0			0
$382$	−10.8082	+	10.8082i	−0.0282936	+	0.0282936i
$383$	−10.6311	−	10.6311i	−0.0277575	−	0.0277575i	0.693092	−	0.720849i	$-0.256248\pi$
$383$	−10.6311	−	10.6311i	−0.0277575	−	0.0277575i	−0.720849	+	0.693092i	$0.756248\pi$
$384$		0			0
$385$		0			0
$386$	114.874			0.297601
$387$		0			0
$388$	95.8990	+	95.8990i	0.247162	+	0.247162i
$389$		−	535.337i		−	1.37619i	−0.725621	−	0.688094i	$-0.758448\pi$
$389$		−	535.337i		−	1.37619i	0.725621	−	0.688094i	$-0.241552\pi$
$390$		0			0
$391$	−400.767			−1.02498
$392$	−44.7401	+	44.7401i	−0.114133	+	0.114133i
$393$		0			0
$394$			43.4643i			0.110315i
$395$		0			0
$396$		0			0
$397$	−118.742	+	118.742i	−0.299099	+	0.299099i	−0.840661	−	0.541562i	$-0.817833\pi$
$397$	−118.742	+	118.742i	−0.299099	+	0.299099i	0.541562	+	0.840661i	$0.317833\pi$
$398$	−43.2872	−	43.2872i	−0.108762	−	0.108762i
$399$		0			0
$400$		0			0
$401$	−420.302			−1.04813			−0.524067	−	0.851677i	$-0.675586\pi$
$401$	−420.302			−1.04813			−0.524067	+	0.851677i	$0.675586\pi$
$402$		0			0
$403$	59.3735	+	59.3735i	0.147329	+	0.147329i
$404$			411.814i			1.01934i
$405$		0			0
$406$	−54.4949			−0.134224
$407$	−68.6061	+	68.6061i	−0.168565	+	0.168565i
$408$		0			0
$409$			515.110i			1.25944i	0.776823	+	0.629719i	$0.216830\pi$
$409$			515.110i			1.25944i	−0.776823	+	0.629719i	$0.783170\pi$
$410$		0			0
$411$		0			0
$412$	−347.974	+	347.974i	−0.844597	+	0.844597i
$413$	137.753	+	137.753i	0.333541	+	0.333541i
$414$		0			0
$415$		0			0
$416$	−115.748			−0.278240
$417$		0			0
$418$	22.1816	+	22.1816i	0.0530661	+	0.0530661i
$419$		−	88.6015i		−	0.211460i	−0.994395	−	0.105730i	$-0.966282\pi$
$419$		−	88.6015i		−	0.211460i	0.994395	−	0.105730i	$-0.0337178\pi$
$420$		0			0
$421$	−257.151			−0.610810			−0.305405	−	0.952223i	$-0.598792\pi$
$421$	−257.151			−0.610810			−0.305405	+	0.952223i	$0.598792\pi$
$422$	33.0852	−	33.0852i	0.0784009	−	0.0784009i
$423$		0			0
$424$		−	2.47449i		−	0.00583605i
$425$		0			0
$426$		0			0
$427$	−20.3837	+	20.3837i	−0.0477369	+	0.0477369i
$428$	268.025	+	268.025i	0.626227	+	0.626227i
$429$		0			0
$430$		0			0
$431$	−804.636			−1.86690			−0.933452	−	0.358702i	$-0.883219\pi$
$431$	−804.636			−1.86690			−0.933452	+	0.358702i	$0.883219\pi$
$432$		0			0
$433$	344.848	+	344.848i	0.796416	+	0.796416i	0.982528	−	0.186113i	$-0.0595890\pi$
$433$	344.848	+	344.848i	0.796416	+	0.796416i	−0.186113	+	0.982528i	$0.559589\pi$
$434$			16.5857i			0.0382159i
$435$		0			0
$436$	267.848			0.614330
$437$	100.454	−	100.454i	0.229872	−	0.229872i
$438$		0			0
$439$		−	432.929i		−	0.986170i	−0.869981	−	0.493085i	$-0.835869\pi$
$439$		−	432.929i		−	0.986170i	0.869981	−	0.493085i	$-0.164131\pi$
$440$		0			0
$441$		0			0
$442$	−43.2827	+	43.2827i	−0.0979246	+	0.0979246i
$443$	245.131	+	245.131i	0.553342	+	0.553342i	0.927404	−	0.374062i	$-0.122035\pi$
$443$	245.131	+	245.131i	0.553342	+	0.553342i	−0.374062	+	0.927404i	$0.622035\pi$
$444$		0			0
$445$		0			0
$446$	−75.2577			−0.168739
$447$		0			0
$448$	188.015	+	188.015i	0.419676	+	0.419676i
$449$			386.091i			0.859890i	0.902855	+	0.429945i	$0.141467\pi$
$449$			386.091i			0.859890i	−0.902855	+	0.429945i	$0.858533\pi$
$450$		0			0
$451$	7.90918			0.0175370
$452$	−380.702	+	380.702i	−0.842260	+	0.842260i
$453$		0			0
$454$		−	113.798i		−	0.250656i
$455$		0			0
$456$		0			0
$457$	223.747	−	223.747i	0.489599	−	0.489599i	−0.418580	−	0.908180i	$-0.637472\pi$
$457$	223.747	−	223.747i	0.489599	−	0.489599i	0.908180	+	0.418580i	$0.137472\pi$
$458$	50.3883	+	50.3883i	0.110018	+	0.110018i
$459$		0			0
$460$		0			0
$461$	722.620			1.56751			0.783753	−	0.621073i	$-0.213303\pi$
$461$	722.620			1.56751			0.783753	+	0.621073i	$0.213303\pi$
$462$		0			0
$463$	129.702	+	129.702i	0.280133	+	0.280133i	0.833162	−	0.553029i	$-0.186528\pi$
$463$	129.702	+	129.702i	0.280133	+	0.280133i	−0.553029	+	0.833162i	$0.686528\pi$
$464$		−	520.095i		−	1.12090i
$465$		0			0
$466$	−92.4653			−0.198423
$467$	415.258	−	415.258i	0.889203	−	0.889203i	−0.105244	−	0.994446i	$-0.533562\pi$
$467$	415.258	−	415.258i	0.889203	−	0.889203i	0.994446	+	0.105244i	$0.0335623\pi$
$468$		0			0
$469$			311.151i			0.663435i
$470$		0			0
$471$		0			0
$472$	70.8934	−	70.8934i	0.150198	−	0.150198i
$473$	−300.677	−	300.677i	−0.635680	−	0.635680i
$474$		0			0
$475$		0			0
$476$	466.656			0.980370
$477$		0			0
$478$	−77.7163	−	77.7163i	−0.162586	−	0.162586i
$479$			304.949i			0.636637i	0.947984	+	0.318318i	$0.103118\pi$
$479$			304.949i			0.636637i	−0.947984	+	0.318318i	$0.896882\pi$
$480$		0			0
$481$	67.1102			0.139522
$482$	22.8286	−	22.8286i	0.0473622	−	0.0473622i
$483$		0			0
$484$			30.3643i			0.0627361i
$485$		0			0
$486$		0			0
$487$	429.318	−	429.318i	0.881556	−	0.881556i	−0.112137	−	0.993693i	$-0.535769\pi$
$487$	429.318	−	429.318i	0.881556	−	0.881556i	0.993693	+	0.112137i	$0.0357694\pi$
$488$	10.4903	+	10.4903i	0.0214965	+	0.0214965i
$489$		0			0
$490$		0			0
$491$	414.318			0.843825			0.421912	−	0.906637i	$-0.361359\pi$
$491$	414.318			0.843825			0.421912	+	0.906637i	$0.361359\pi$
$492$		0			0
$493$	−609.737	−	609.737i	−1.23679	−	1.23679i
$494$		−	21.6980i		−	0.0439230i
$495$		0			0
$496$	−158.293			−0.319139
$497$	−234.565	+	234.565i	−0.471962	+	0.471962i
$498$		0			0
$499$		−	367.585i		−	0.736643i	−0.929699	−	0.368321i	$-0.879933\pi$
$499$		−	367.585i		−	0.736643i	0.929699	−	0.368321i	$-0.120067\pi$
$500$		0			0
$501$		0			0
$502$	74.4485	−	74.4485i	0.148304	−	0.148304i
$503$	−9.59133	−	9.59133i	−0.0190683	−	0.0190683i	0.697508	−	0.716577i	$-0.254292\pi$
$503$	−9.59133	−	9.59133i	−0.0190683	−	0.0190683i	−0.716577	+	0.697508i	$0.754292\pi$
$504$		0			0
$505$		0			0
$506$	−58.9194			−0.116441
$507$		0			0
$508$	−641.854	−	641.854i	−1.26349	−	1.26349i
$509$			777.489i			1.52748i	0.645522	+	0.763742i	$0.276640\pi$
$509$			777.489i			1.52748i	−0.645522	+	0.763742i	$0.723360\pi$
$510$		0			0
$511$	536.656			1.05021
$512$	259.376	−	259.376i	0.506593	−	0.506593i
$513$		0			0
$514$		−	14.9398i		−	0.0290658i
$515$		0			0
$516$		0			0
$517$	−502.141	+	502.141i	−0.971259	+	0.971259i
$518$	9.37347	+	9.37347i	0.0180955	+	0.0180955i
$519$		0			0
$520$		0			0
$521$	−321.605			−0.617284			−0.308642	−	0.951178i	$-0.599875\pi$
$521$	−321.605			−0.617284			−0.308642	+	0.951178i	$0.599875\pi$
$522$		0			0
$523$	582.454	+	582.454i	1.11368	+	1.11368i	0.992649	+	0.121030i	$0.0386198\pi$
$523$	582.454	+	582.454i	1.11368	+	1.11368i	0.121030	+	0.992649i	$0.461380\pi$
$524$		−	413.823i		−	0.789738i
$525$		0			0
$526$	−125.029			−0.237697
$527$	−185.576	+	185.576i	−0.352136	+	0.352136i
$528$		0			0
$529$		−	262.171i		−	0.495598i
$530$		0			0
$531$		0			0
$532$	−116.969	+	116.969i	−0.219867	+	0.219867i
$533$	−3.86836	−	3.86836i	−0.00725772	−	0.00725772i
$534$		0			0
$535$		0			0
$536$	160.132			0.298753
$537$		0			0
$538$	−109.788	−	109.788i	−0.204066	−	0.204066i
$539$		−	286.005i		−	0.530621i
$540$		0			0
$541$	460.697			0.851566			0.425783	−	0.904825i	$-0.359999\pi$
$541$	460.697			0.851566			0.425783	+	0.904825i	$0.359999\pi$
$542$	29.5709	−	29.5709i	0.0545589	−	0.0545589i
$543$		0			0
$544$		−	361.778i		−	0.665032i
$545$		0			0
$546$		0			0
$547$	661.778	−	661.778i	1.20983	−	1.20983i	0.238750	−	0.971081i	$-0.423262\pi$
$547$	661.778	−	661.778i	1.20983	−	1.20983i	0.971081	−	0.238750i	$-0.0767376\pi$
$548$	−649.691	−	649.691i	−1.18557	−	1.18557i
$549$		0			0
$550$		0			0
$551$	305.666			0.554748
$552$		0			0
$553$	−84.4949	−	84.4949i	−0.152794	−	0.152794i
$554$			45.6276i			0.0823602i
$555$		0			0
$556$	−745.373			−1.34060
$557$	125.909	−	125.909i	0.226049	−	0.226049i	−0.584991	−	0.811040i	$-0.698902\pi$
$557$	125.909	−	125.909i	0.226049	−	0.226049i	0.811040	+	0.584991i	$0.198902\pi$
$558$		0			0
$559$			294.120i			0.526155i
$560$		0			0
$561$		0			0
$562$	−77.1556	+	77.1556i	−0.137288	+	0.137288i
$563$	−200.009	−	200.009i	−0.355256	−	0.355256i	0.506805	−	0.862061i	$-0.330826\pi$
$563$	−200.009	−	200.009i	−0.355256	−	0.355256i	−0.862061	+	0.506805i	$0.830826\pi$
$564$		0			0
$565$		0			0
$566$	−0.535718			−0.000946498
$567$		0			0
$568$	120.717	+	120.717i	0.212531	+	0.212531i
$569$		−	599.839i		−	1.05420i	−0.849804	−	0.527099i	$-0.823280\pi$
$569$		−	599.839i		−	1.05420i	0.849804	−	0.527099i	$-0.176720\pi$
$570$		0			0
$571$	−247.970			−0.434274			−0.217137	−	0.976141i	$-0.569672\pi$
$571$	−247.970			−0.434274			−0.217137	+	0.976141i	$0.569672\pi$
$572$	245.596	−	245.596i	0.429363	−	0.429363i
$573$		0			0
$574$		−	1.08061i		−	0.00188260i
$575$		0			0
$576$		0			0
$577$	292.121	−	292.121i	0.506276	−	0.506276i	−0.407105	−	0.913381i	$-0.633462\pi$
$577$	292.121	−	292.121i	0.506276	−	0.506276i	0.913381	+	0.407105i	$0.133462\pi$
$578$	−70.3314	−	70.3314i	−0.121681	−	0.121681i
$579$		0			0
$580$		0			0
$581$	−90.6969			−0.156105
$582$		0			0
$583$	7.90918	+	7.90918i	0.0135664	+	0.0135664i
$584$		−	276.186i		−	0.472922i
$585$		0			0
$586$	43.4051			0.0740702
$587$	611.217	−	611.217i	1.04126	−	1.04126i	0.0421437	−	0.999112i	$-0.486581\pi$
$587$	611.217	−	611.217i	1.04126	−	1.04126i	0.999112	−	0.0421437i	$-0.0134187\pi$
$588$		0			0
$589$		−	93.0306i		−	0.157947i
$590$		0			0
$591$		0			0
$592$	−89.4597	+	89.4597i	−0.151114	+	0.151114i
$593$	524.742	+	524.742i	0.884894	+	0.884894i	0.994027	−	0.109133i	$-0.0348074\pi$
$593$	524.742	+	524.742i	0.884894	+	0.884894i	−0.109133	+	0.994027i	$0.534807\pi$
$594$		0			0
$595$		0			0
$596$	−330.842			−0.555105
$597$		0			0
$598$	28.8173	+	28.8173i	0.0481895	+	0.0481895i
$599$		−	368.858i		−	0.615790i	−0.951420	−	0.307895i	$-0.900375\pi$
$599$		−	368.858i		−	0.615790i	0.951420	−	0.307895i	$-0.0996245\pi$
$600$		0			0
$601$	932.484			1.55155			0.775777	−	0.631007i	$-0.217358\pi$
$601$	932.484			1.55155			0.775777	+	0.631007i	$0.217358\pi$
$602$	−41.0806	+	41.0806i	−0.0682402	+	0.0682402i
$603$		0			0
$604$			580.829i			0.961637i
$605$		0			0
$606$		0			0
$607$	−513.611	+	513.611i	−0.846146	+	0.846146i	−0.989650	−	0.143504i	$-0.954163\pi$
$607$	−513.611	+	513.611i	−0.846146	+	0.846146i	0.143504	+	0.989650i	$0.454163\pi$
$608$	90.6811	+	90.6811i	0.149147	+	0.149147i
$609$		0			0
$610$		0			0
$611$	491.192			0.803915
$612$		0			0
$613$	615.287	+	615.287i	1.00373	+	1.00373i	0.999993	+	0.00373821i	$0.00118991\pi$
$613$	615.287	+	615.287i	1.00373	+	1.00373i	0.00373821	+	0.999993i	$0.498810\pi$
$614$		−	56.1725i		−	0.0914861i
$615$		0			0
$616$	138.990			0.225633
$617$	546.752	−	546.752i	0.886145	−	0.886145i	−0.108005	−	0.994150i	$-0.534446\pi$
$617$	546.752	−	546.752i	0.886145	−	0.886145i	0.994150	+	0.108005i	$0.0344463\pi$
$618$		0			0
$619$		−	152.869i		−	0.246962i	−0.992347	−	0.123481i	$-0.960594\pi$
$619$		−	152.869i		−	0.246962i	0.992347	−	0.123481i	$-0.0394058\pi$
$620$		0			0
$621$		0			0
$622$	131.768	−	131.768i	0.211846	−	0.211846i
$623$	−283.485	−	283.485i	−0.455032	−	0.455032i
$624$		0			0
$625$		0			0
$626$	46.0158			0.0735077
$627$		0			0
$628$	−65.7117	−	65.7117i	−0.104637	−	0.104637i
$629$			209.757i			0.333477i
$630$		0			0
$631$	−41.4847			−0.0657444			−0.0328722	−	0.999460i	$-0.510465\pi$
$631$	−41.4847			−0.0657444			−0.0328722	+	0.999460i	$0.510465\pi$
$632$	−43.4847	+	43.4847i	−0.0688049	+	0.0688049i
$633$		0			0
$634$			48.8969i			0.0771245i
$635$		0			0
$636$		0			0
$637$	−139.884	+	139.884i	−0.219598	+	0.219598i
$638$	−89.6413	−	89.6413i	−0.140504	−	0.140504i
$639$		0			0
$640$		0			0
$641$	−47.2122			−0.0736541			−0.0368270	−	0.999322i	$-0.511725\pi$
$641$	−47.2122			−0.0736541			−0.0368270	+	0.999322i	$0.511725\pi$
$642$		0			0
$643$	−460.372	−	460.372i	−0.715976	−	0.715976i	0.251803	−	0.967779i	$-0.418977\pi$
$643$	−460.372	−	460.372i	−0.715976	−	0.715976i	−0.967779	+	0.251803i	$0.918977\pi$
$644$		−	310.697i		−	0.482449i
$645$		0			0
$646$	67.8184			0.104982
$647$	−281.287	+	281.287i	−0.434756	+	0.434756i	−0.890243	−	0.455487i	$-0.849465\pi$
$647$	−281.287	+	281.287i	−0.434756	+	0.434756i	0.455487	+	0.890243i	$0.349465\pi$
$648$		0			0
$649$			453.192i			0.698293i
$650$		0			0
$651$		0			0
$652$	509.231	−	509.231i	0.781029	−	0.781029i
$653$	89.8230	+	89.8230i	0.137554	+	0.137554i	0.772531	−	0.634977i	$-0.218990\pi$
$653$	89.8230	+	89.8230i	0.137554	+	0.137554i	−0.634977	+	0.772531i	$0.718990\pi$
$654$		0			0
$655$		0			0
$656$	10.3133			0.0157214
$657$		0			0
$658$	68.6061	+	68.6061i	0.104265	+	0.104265i
$659$			1081.24i			1.64072i	0.571844	+	0.820362i	$0.306228\pi$
$659$			1081.24i			1.64072i	−0.571844	+	0.820362i	$0.693772\pi$
$660$		0			0
$661$	−632.393			−0.956721			−0.478361	−	0.878163i	$-0.658769\pi$
$661$	−632.393			−0.956721			−0.478361	+	0.878163i	$0.658769\pi$
$662$	−55.1577	+	55.1577i	−0.0833197	+	0.0833197i
$663$		0			0
$664$			46.6765i			0.0702960i
$665$		0			0
$666$		0			0
$667$	−405.959	+	405.959i	−0.608634	+	0.608634i
$668$	−175.591	−	175.591i	−0.262861	−	0.262861i
$669$		0			0
$670$		0			0
$671$	−67.0602			−0.0999407
$672$		0			0
$673$	−233.293	−	233.293i	−0.346646	−	0.346646i	0.512213	−	0.858859i	$-0.328826\pi$
$673$	−233.293	−	233.293i	−0.346646	−	0.346646i	−0.858859	+	0.512213i	$0.828826\pi$
$674$			96.1046i			0.142588i
$675$		0			0
$676$	418.687			0.619359
$677$	−48.3883	+	48.3883i	−0.0714745	+	0.0714745i	−0.741940	−	0.670466i	$-0.766094\pi$
$677$	−48.3883	+	48.3883i	−0.0714745	+	0.0714745i	0.670466	+	0.741940i	$0.266094\pi$
$678$		0			0
$679$			169.687i			0.249907i
$680$		0			0
$681$		0			0
$682$	−27.2827	+	27.2827i	−0.0400039	+	0.0400039i
$683$	213.410	+	213.410i	0.312459	+	0.312459i	0.845862	−	0.533402i	$-0.179087\pi$
$683$	213.410	+	213.410i	0.312459	+	0.312459i	−0.533402	+	0.845862i	$0.679087\pi$
$684$		0			0
$685$		0			0
$686$	−115.051			−0.167713
$687$		0			0
$688$	−392.070	−	392.070i	−0.569870	−	0.569870i
$689$		−	7.73673i		−	0.0112289i
$690$		0			0
$691$	151.121			0.218700			0.109350	−	0.994003i	$-0.465123\pi$
$691$	151.121			0.218700			0.109350	+	0.994003i	$0.465123\pi$
$692$	−571.712	+	571.712i	−0.826173	+	0.826173i
$693$		0			0
$694$			71.9408i			0.103661i
$695$		0			0
$696$		0			0
$697$	12.0908	−	12.0908i	0.0173469	−	0.0173469i
$698$	66.9760	+	66.9760i	0.0959542	+	0.0959542i
$699$		0			0
$700$		0			0
$701$	745.680			1.06374			0.531869	−	0.846827i	$-0.321490\pi$
$701$	745.680			1.06374			0.531869	+	0.846827i	$0.321490\pi$
$702$		0			0
$703$	−52.5765	−	52.5765i	−0.0747888	−	0.0747888i
$704$			618.549i			0.878621i
$705$		0			0
$706$	−10.1225			−0.0143378
$707$	−364.338	+	364.338i	−0.515330	+	0.515330i
$708$		0			0
$709$		−	719.049i		−	1.01417i	−0.861895	−	0.507087i	$-0.830722\pi$
$709$		−	719.049i		−	1.01417i	0.861895	−	0.507087i	$-0.169278\pi$
$710$		0			0
$711$		0			0
$712$	−145.893	+	145.893i	−0.204906	+	0.204906i
$713$	123.555	+	123.555i	0.173289	+	0.173289i
$714$		0			0
$715$		0			0
$716$	−716.288			−1.00040
$717$		0			0
$718$	10.8490	+	10.8490i	0.0151100	+	0.0151100i
$719$		−	605.271i		−	0.841824i	−0.907101	−	0.420912i	$-0.861710\pi$
$719$		−	605.271i		−	0.841824i	0.907101	−	0.420912i	$-0.138290\pi$
$720$		0			0
$721$	−615.716			−0.853975
$722$	64.1339	−	64.1339i	0.0888282	−	0.0888282i
$723$		0			0
$724$		−	1116.17i		−	1.54167i
$725$		0			0
$726$		0			0
$727$	246.126	−	246.126i	0.338550	−	0.338550i	−0.517271	−	0.855821i	$-0.673052\pi$
$727$	246.126	−	246.126i	0.338550	−	0.338550i	0.855821	+	0.517271i	$0.173052\pi$
$728$	−67.9796	−	67.9796i	−0.0933786	−	0.0933786i
$729$		0			0
$730$		0			0
$731$	−919.292			−1.25758
$732$		0			0
$733$	270.763	+	270.763i	0.369390	+	0.369390i	0.867255	−	0.497865i	$-0.165882\pi$
$733$	270.763	+	270.763i	0.369390	+	0.369390i	−0.497865	+	0.867255i	$0.665882\pi$
$734$			65.8546i			0.0897202i
$735$		0			0
$736$	−240.869			−0.327268
$737$	−511.828	+	511.828i	−0.694474	+	0.694474i
$738$		0			0
$739$			515.666i			0.697789i	0.937162	+	0.348895i	$0.113443\pi$
$739$			515.666i			0.697789i	−0.937162	+	0.348895i	$0.886557\pi$
$740$		0			0
$741$		0			0
$742$	1.08061	−	1.08061i	0.00145635	−	0.00145635i
$743$	420.702	+	420.702i	0.566220	+	0.566220i	0.931067	−	0.364847i	$-0.118879\pi$
$743$	420.702	+	420.702i	0.566220	+	0.566220i	−0.364847	+	0.931067i	$0.618879\pi$
$744$		0			0
$745$		0			0
$746$	−38.7490			−0.0519424
$747$		0			0
$748$	767.626	+	767.626i	1.02624	+	1.02624i
$749$			474.252i			0.633180i
$750$		0			0
$751$	−859.787			−1.14486			−0.572428	−	0.819955i	$-0.693998\pi$
$751$	−859.787			−1.14486			−0.572428	+	0.819955i	$0.693998\pi$
$752$	−654.772	+	654.772i	−0.870707	+	0.870707i
$753$		0			0
$754$			87.6867i			0.116295i
$755$		0			0
$756$		0			0
$757$	956.075	−	956.075i	1.26298	−	1.26298i	0.313337	−	0.949642i	$-0.398553\pi$
$757$	956.075	−	956.075i	1.26298	−	1.26298i	0.949642	−	0.313337i	$-0.101447\pi$
$758$	47.1964	+	47.1964i	0.0622644	+	0.0622644i
$759$		0			0
$760$		0			0
$761$	322.758			0.424124			0.212062	−	0.977256i	$-0.431982\pi$
$761$	322.758			0.424124			0.212062	+	0.977256i	$0.431982\pi$
$762$		0			0
$763$	236.969	+	236.969i	0.310576	+	0.310576i
$764$		−	187.505i		−	0.245426i
$765$		0			0
$766$	−4.77858			−0.00623835
$767$	221.655	−	221.655i	0.288990	−	0.288990i
$768$		0			0
$769$		−	692.402i		−	0.900393i	−0.892930	−	0.450196i	$-0.851354\pi$
$769$		−	692.402i		−	0.900393i	0.892930	−	0.450196i	$-0.148646\pi$
$770$		0			0
$771$		0			0
$772$	−996.444	+	996.444i	−1.29073	+	1.29073i
$773$	375.226	+	375.226i	0.485415	+	0.485415i	0.906856	−	0.421441i	$-0.138475\pi$
$773$	375.226	+	375.226i	0.485415	+	0.485415i	−0.421441	+	0.906856i	$0.638475\pi$
$774$		0			0
$775$		0			0
$776$	87.3281			0.112536
$777$		0			0
$778$	−120.314	−	120.314i	−0.154646	−	0.154646i
$779$			6.06123i			0.00778078i
$780$		0			0
$781$	−771.696			−0.988087
$782$	−90.0704	+	90.0704i	−0.115180	+	0.115180i
$783$		0			0
$784$		−	372.939i		−	0.475687i
$785$		0			0
$786$		0			0
$787$	−910.990	+	910.990i	−1.15755	+	1.15755i	−0.172546	+	0.985001i	$0.555199\pi$
$787$	−910.990	+	910.990i	−1.15755	+	1.15755i	−0.985001	+	0.172546i	$0.944801\pi$
$788$	−377.019	−	377.019i	−0.478451	−	0.478451i
$789$		0			0
$790$		0			0
$791$	−673.626			−0.851613
$792$		0			0
$793$	32.7990	+	32.7990i	0.0413606	+	0.0413606i
$794$			53.3735i			0.0672210i
$795$		0			0
$796$	750.967			0.943426
$797$	−7.21683	+	7.21683i	−0.00905500	+	0.00905500i	−0.711620	−	0.702565i	$-0.752038\pi$
$797$	−7.21683	+	7.21683i	−0.00905500	+	0.00905500i	0.702565	+	0.711620i	$0.252038\pi$
$798$		0			0
$799$			1535.25i			1.92147i
$800$		0			0
$801$		0			0
$802$	−94.4607	+	94.4607i	−0.117781	+	0.117781i
$803$	882.772	+	882.772i	1.09934	+	1.09934i
$804$		0			0
$805$		0			0
$806$	26.6878			0.0331114
$807$		0			0
$808$	187.504	+	187.504i	0.232059	+	0.232059i
$809$		−	150.000i		−	0.185414i	−0.995693	−	0.0927070i	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$		0			0
$811$	1336.85			1.64839			0.824197	−	0.566304i	$-0.191627\pi$
$811$	1336.85			1.64839			0.824197	+	0.566304i	$0.191627\pi$
$812$	472.702	−	472.702i	0.582145	−	0.582145i
$813$		0			0
$814$			30.8377i			0.0378842i
$815$		0			0
$816$		0			0
$817$	230.424	−	230.424i	0.282037	−	0.282037i
$818$	115.768	+	115.768i	0.141526	+	0.141526i
$819$		0			0
$820$		0			0
$821$	33.8934			0.0412830			0.0206415	−	0.999787i	$-0.493429\pi$
$821$	33.8934			0.0412830			0.0206415	+	0.999787i	$0.493429\pi$
$822$		0			0
$823$	−481.631	−	481.631i	−0.585214	−	0.585214i	0.351117	−	0.936331i	$-0.385802\pi$
$823$	−481.631	−	481.631i	−0.585214	−	0.585214i	−0.936331	+	0.351117i	$0.885802\pi$
$824$			316.874i			0.384556i
$825$		0			0
$826$	61.9184			0.0749617
$827$	350.756	−	350.756i	0.424131	−	0.424131i	−0.462492	−	0.886623i	$-0.653045\pi$
$827$	350.756	−	350.756i	0.424131	−	0.424131i	0.886623	+	0.462492i	$0.153045\pi$
$828$		0			0
$829$			697.423i			0.841283i	0.907227	+	0.420641i	$0.138195\pi$
$829$			697.423i			0.841283i	−0.907227	+	0.420641i	$0.861805\pi$
$830$		0			0
$831$		0			0
$832$	302.531	−	302.531i	0.363619	−	0.363619i
$833$	−437.217	−	437.217i	−0.524870	−	0.524870i
$834$		0			0
$835$		0			0
$836$	−384.817			−0.460308
$837$		0			0
$838$	−19.9127	−	19.9127i	−0.0237622	−	0.0237622i
$839$			72.3724i			0.0862604i	0.999069	+	0.0431302i	$0.0137330\pi$
$839$			72.3724i			0.0862604i	−0.999069	+	0.0431302i	$0.986267\pi$
$840$		0			0
$841$	−394.271			−0.468813
$842$	−57.7934	+	57.7934i	−0.0686382	+	0.0686382i
$843$		0			0
$844$			573.978i			0.680068i
$845$		0			0
$846$		0			0
$847$	−26.8638	+	26.8638i	−0.0317164	+	0.0317164i
$848$	10.3133	+	10.3133i	0.0121619	+	0.0121619i
$849$		0			0
$850$		0			0
$851$	139.655			0.164107
$852$		0			0
$853$	74.5699	+	74.5699i	0.0874207	+	0.0874207i	0.749465	−	0.662044i	$-0.230311\pi$
$853$	74.5699	+	74.5699i	0.0874207	+	0.0874207i	−0.662044	+	0.749465i	$0.730311\pi$
$854$			9.16225i			0.0107286i
$855$		0			0
$856$	244.070			0.285129
$857$	−293.176	+	293.176i	−0.342096	+	0.342096i	−0.857155	−	0.515059i	$-0.827770\pi$
$857$	−293.176	+	293.176i	−0.342096	+	0.342096i	0.515059	+	0.857155i	$0.327770\pi$
$858$		0			0
$859$			786.867i			0.916027i	0.888945	+	0.458014i	$0.151439\pi$
$859$			786.867i			0.916027i	−0.888945	+	0.458014i	$0.848561\pi$
$860$		0			0
$861$		0			0
$862$	−180.838	+	180.838i	−0.209789	+	0.209789i
$863$	−1072.68	−	1072.68i	−1.24297	−	1.24297i	−0.958764	−	0.284204i	$-0.908271\pi$
$863$	−1072.68	−	1072.68i	−1.24297	−	1.24297i	−0.284204	−	0.958764i	$-0.591729\pi$
$864$		0			0
$865$		0			0
$866$	155.006			0.178990
$867$		0			0
$868$	−143.868	−	143.868i	−0.165747	−	0.165747i
$869$		−	277.980i		−	0.319884i
$870$		0			0
$871$	500.667			0.574819
$872$	121.955	−	121.955i	0.139856	−	0.139856i
$873$		0			0
$874$		−	45.1531i		−	0.0516626i
$875$		0			0
$876$		0			0
$877$	−239.460	+	239.460i	−0.273044	+	0.273044i	−0.830324	−	0.557280i	$-0.811845\pi$
$877$	−239.460	+	239.460i	−0.273044	+	0.273044i	0.557280	+	0.830324i	$0.311845\pi$
$878$	−97.2985	−	97.2985i	−0.110818	−	0.110818i
$879$		0			0
$880$		0			0
$881$	−62.8490			−0.0713382			−0.0356691	−	0.999364i	$-0.511356\pi$
$881$	−62.8490			−0.0713382			−0.0356691	+	0.999364i	$0.511356\pi$
$882$		0			0
$883$	158.061	+	158.061i	0.179005	+	0.179005i	0.790922	−	0.611917i	$-0.209601\pi$
$883$	158.061	+	158.061i	0.179005	+	0.179005i	−0.611917	+	0.790922i	$0.709601\pi$
$884$		−	750.888i		−	0.849421i
$885$		0			0
$886$	110.184			0.124361
$887$	30.2066	−	30.2066i	0.0340548	−	0.0340548i	−0.689874	−	0.723929i	$-0.742334\pi$
$887$	30.2066	−	30.2066i	0.0340548	−	0.0340548i	0.723929	+	0.689874i	$0.242334\pi$
$888$		0			0
$889$		−	1135.72i		−	1.27752i
$890$		0			0
$891$		0			0
$892$	652.803	−	652.803i	0.731841	−	0.731841i
$893$	−384.817	−	384.817i	−0.430926	−	0.430926i
$894$		0			0
$895$		0			0
$896$	372.247			0.415455
$897$		0			0
$898$	86.7719	+	86.7719i	0.0966280	+	0.0966280i
$899$			375.959i			0.418197i
$900$		0			0
$901$	24.1816			0.0268387
$902$	1.77755	−	1.77755i	0.00197067	−	0.00197067i
$903$		0			0
$904$			346.677i			0.383492i
$905$		0			0
$906$		0			0
$907$	−571.342	+	571.342i	−0.629925	+	0.629925i	−0.948049	−	0.318124i	$-0.896947\pi$
$907$	−571.342	+	571.342i	−0.629925	+	0.629925i	0.318124	+	0.948049i	$0.396947\pi$
$908$	987.110	+	987.110i	1.08713	+	1.08713i
$909$		0			0
$910$		0			0
$911$	−173.362			−0.190299			−0.0951494	−	0.995463i	$-0.530333\pi$
$911$	−173.362			−0.190299			−0.0951494	+	0.995463i	$0.530333\pi$
$912$		0			0
$913$	−149.192	−	149.192i	−0.163408	−	0.163408i
$914$		−	100.572i		−	0.110035i
$915$		0			0
$916$	−874.159			−0.954322
$917$	366.116	−	366.116i	0.399254	−	0.399254i
$918$		0			0
$919$		−	1147.42i		−	1.24856i	−0.781202	−	0.624278i	$-0.785393\pi$
$919$		−	1147.42i		−	1.24856i	0.781202	−	0.624278i	$-0.214607\pi$
$920$		0			0
$921$		0			0
$922$	162.405	−	162.405i	0.176144	−	0.176144i
$923$	377.435	+	377.435i	0.408922	+	0.408922i
$924$		0			0
$925$		0			0
$926$	58.2995			0.0629584
$927$		0			0
$928$	−366.464	−	366.464i	−0.394897	−	0.394897i
$929$		−	220.293i		−	0.237129i	−0.992946	−	0.118565i	$-0.962171\pi$
$929$		−	220.293i		−	0.237129i	0.992946	−	0.118565i	$-0.0378292\pi$
$930$		0			0
$931$	219.181			0.235425
$932$	802.066	−	802.066i	0.860586	−	0.860586i
$933$		0			0
$934$		−	186.654i		−	0.199844i
$935$		0			0
$936$		0			0
$937$	396.090	−	396.090i	0.422721	−	0.422721i	−0.463418	−	0.886140i	$-0.653377\pi$
$937$	396.090	−	396.090i	0.422721	−	0.422721i	0.886140	+	0.463418i	$0.153377\pi$
$938$	69.9296	+	69.9296i	0.0745518	+	0.0745518i
$939$		0			0
$940$		0			0
$941$	−185.771			−0.197419			−0.0987093	−	0.995116i	$-0.531471\pi$
$941$	−185.771			−0.197419			−0.0987093	+	0.995116i	$0.531471\pi$
$942$		0			0
$943$	−8.04999	−	8.04999i	−0.00853658	−	0.00853658i
$944$			590.944i			0.626000i
$945$		0			0
$946$	−135.151			−0.142866
$947$	−845.190	+	845.190i	−0.892492	+	0.892492i	−0.994757	−	0.102265i	$-0.967391\pi$
$947$	−845.190	+	845.190i	−0.892492	+	0.892492i	0.102265	+	0.994757i	$0.467391\pi$
$948$		0			0
$949$		−	863.523i		−	0.909930i
$950$		0			0
$951$		0			0
$952$	212.474	−	212.474i	0.223187	−	0.223187i
$953$	−630.499	−	630.499i	−0.661594	−	0.661594i	0.294161	−	0.955756i	$-0.404960\pi$
$953$	−630.499	−	630.499i	−0.661594	−	0.661594i	−0.955756	+	0.294161i	$0.904960\pi$
$954$		0			0
$955$		0			0
$956$	1348.26			1.41031
$957$		0			0
$958$	68.5357	+	68.5357i	0.0715404	+	0.0715404i
$959$		−	1149.58i		−	1.19873i
$960$		0			0
$961$	−846.576			−0.880932
$962$	15.0827	−	15.0827i	0.0156785	−	0.0156785i
$963$		0			0
$964$			396.041i			0.410831i
$965$		0			0
$966$		0			0
$967$	381.690	−	381.690i	0.394716	−	0.394716i	−0.481649	−	0.876364i	$-0.659962\pi$
$967$	381.690	−	381.690i	0.394716	−	0.394716i	0.876364	+	0.481649i	$0.159962\pi$
$968$	13.8252	+	13.8252i	0.0142823	+	0.0142823i
$969$		0			0
$970$		0			0
$971$	1000.44			1.03032			0.515159	−	0.857095i	$-0.327733\pi$
$971$	1000.44			1.03032			0.515159	+	0.857095i	$0.327733\pi$
$972$		0			0
$973$	−659.444	−	659.444i	−0.677743	−	0.677743i
$974$		−	192.974i		−	0.198125i
$975$		0			0
$976$	−87.4439			−0.0895941
$977$	593.662	−	593.662i	0.607637	−	0.607637i	−0.334691	−	0.942328i	$-0.608632\pi$
$977$	593.662	−	593.662i	0.607637	−	0.607637i	0.942328	+	0.334691i	$0.108632\pi$
$978$		0			0
$979$		−	932.636i		−	0.952641i
$980$		0			0
$981$		0			0
$982$	93.1158	−	93.1158i	0.0948226	−	0.0948226i
$983$	−1217.34	−	1217.34i	−1.23839	−	1.23839i	−0.960659	−	0.277731i	$-0.910418\pi$
$983$	−1217.34	−	1217.34i	−1.23839	−	1.23839i	−0.277731	−	0.960659i	$-0.589582\pi$
$984$		0			0
$985$		0			0
$986$	−274.070			−0.277962
$987$		0			0
$988$	188.213	+	188.213i	0.190499	+	0.190499i
$989$			612.059i			0.618867i
$990$		0			0
$991$	−544.061			−0.549002			−0.274501	−	0.961587i	$-0.588513\pi$
$991$	−544.061			−0.549002			−0.274501	+	0.961587i	$0.588513\pi$
$992$	−111.535	+	111.535i	−0.112434	+	0.112434i
$993$		0			0
$994$			105.435i			0.106071i
$995$		0			0
$996$		0			0
$997$	316.733	−	316.733i	0.317686	−	0.317686i	−0.530192	−	0.847878i	$-0.677880\pi$
$997$	316.733	−	316.733i	0.317686	−	0.317686i	0.847878	+	0.530192i	$0.177880\pi$
$998$	−82.6128	−	82.6128i	−0.0827783	−	0.0827783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.3.g.a.118.2		4
3.2	odd	2		75.3.f.c.43.1		4
5.2	odd	4	inner	225.3.g.a.82.2		4
5.3	odd	4		45.3.g.b.37.1		4
5.4	even	2		45.3.g.b.28.1		4
12.11	even	2		1200.3.bg.k.193.1		4
15.2	even	4		75.3.f.c.7.1		4
15.8	even	4		15.3.f.a.7.2	✓	4
15.14	odd	2		15.3.f.a.13.2	yes	4
20.3	even	4		720.3.bh.k.577.2		4
20.19	odd	2		720.3.bh.k.433.2		4
45.4	even	6		405.3.l.f.298.1		8
45.13	odd	12		405.3.l.f.217.2		8
45.14	odd	6		405.3.l.h.298.2		8
45.23	even	12		405.3.l.h.217.1		8
45.29	odd	6		405.3.l.h.28.1		8
45.34	even	6		405.3.l.f.28.2		8
45.38	even	12		405.3.l.h.352.2		8
45.43	odd	12		405.3.l.f.352.1		8
60.23	odd	4		240.3.bg.a.97.2		4
60.47	odd	4		1200.3.bg.k.1057.1		4
60.59	even	2		240.3.bg.a.193.2		4
120.29	odd	2		960.3.bg.i.193.2		4
120.53	even	4		960.3.bg.i.577.2		4
120.59	even	2		960.3.bg.h.193.1		4
120.83	odd	4		960.3.bg.h.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.2	✓	4	15.8	even	4
15.3.f.a.13.2	yes	4	15.14	odd	2
45.3.g.b.28.1		4	5.4	even	2
45.3.g.b.37.1		4	5.3	odd	4
75.3.f.c.7.1		4	15.2	even	4
75.3.f.c.43.1		4	3.2	odd	2
225.3.g.a.82.2		4	5.2	odd	4	inner
225.3.g.a.118.2		4	1.1	even	1	trivial
240.3.bg.a.97.2		4	60.23	odd	4
240.3.bg.a.193.2		4	60.59	even	2
405.3.l.f.28.2		8	45.34	even	6
405.3.l.f.217.2		8	45.13	odd	12
405.3.l.f.298.1		8	45.4	even	6
405.3.l.f.352.1		8	45.43	odd	12
405.3.l.h.28.1		8	45.29	odd	6
405.3.l.h.217.1		8	45.23	even	12
405.3.l.h.298.2		8	45.14	odd	6
405.3.l.h.352.2		8	45.38	even	12
720.3.bh.k.433.2		4	20.19	odd	2
720.3.bh.k.577.2		4	20.3	even	4
960.3.bg.h.193.1		4	120.59	even	2
960.3.bg.h.577.1		4	120.83	odd	4
960.3.bg.i.193.2		4	120.29	odd	2
960.3.bg.i.577.2		4	120.53	even	4
1200.3.bg.k.193.1		4	12.11	even	2
1200.3.bg.k.1057.1		4	60.47	odd	4

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	225.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.224745 - 0.224745i) q^{2} +3.89898i q^{4} +(-3.44949 + 3.44949i) q^{7} +(1.77526 + 1.77526i) q^{8} -11.3485 q^{11} +(5.55051 + 5.55051i) q^{13} +1.55051i q^{14} -14.7980 q^{16} +(-17.3485 + 17.3485i) q^{17} -8.69694i q^{19} +(-2.55051 + 2.55051i) q^{22} +(11.5505 + 11.5505i) q^{23} +2.49490 q^{26} +(-13.4495 - 13.4495i) q^{28} +35.1464i q^{29} +10.6969 q^{31} +(-10.4268 + 10.4268i) q^{32} +7.79796i q^{34} +(6.04541 - 6.04541i) q^{37} +(-1.95459 - 1.95459i) q^{38} -0.696938 q^{41} +(26.4949 + 26.4949i) q^{43} -44.2474i q^{44} +5.19184 q^{46} +(44.2474 - 44.2474i) q^{47} +25.2020i q^{49} +(-21.6413 + 21.6413i) q^{52} +(-0.696938 - 0.696938i) q^{53} -12.2474 q^{56} +(7.89898 + 7.89898i) q^{58} -39.9342i q^{59} +5.90918 q^{61} +(2.40408 - 2.40408i) q^{62} -54.5051i q^{64} +(45.1010 - 45.1010i) q^{67} +(-67.6413 - 67.6413i) q^{68} +68.0000 q^{71} +(-77.7878 - 77.7878i) q^{73} -2.71735i q^{74} +33.9092 q^{76} +(39.1464 - 39.1464i) q^{77} +24.4949i q^{79} +(-0.156633 + 0.156633i) q^{82} +(13.1464 + 13.1464i) q^{83} +11.9092 q^{86} +(-20.1464 - 20.1464i) q^{88} +82.1816i q^{89} -38.2929 q^{91} +(-45.0352 + 45.0352i) q^{92} -19.8888i q^{94} +(24.5959 - 24.5959i) q^{97} +(5.66403 + 5.66403i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{7} + 12 q^{8} - 16 q^{11} + 32 q^{13} - 20 q^{16} - 40 q^{17} - 20 q^{22} + 56 q^{23} - 88 q^{26} - 44 q^{28} - 16 q^{31} - 76 q^{32} - 64 q^{37} - 96 q^{38} + 56 q^{41} + 8 q^{43}+ \cdots - 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^7 + 12 * q^8 - 16 * q^11 + 32 * q^13 - 20 * q^16 - 40 * q^17 - 20 * q^22 + 56 * q^23 - 88 * q^26 - 44 * q^28 - 16 * q^31 - 76 * q^32 - 64 * q^37 - 96 * q^38 + 56 * q^41 + 8 * q^43 - 136 * q^46 + 128 * q^47 + 80 * q^52 + 56 * q^53 + 12 * q^58 + 200 * q^61 + 88 * q^62 + 200 * q^67 - 104 * q^68 + 272 * q^71 - 76 * q^73 + 312 * q^76 + 88 * q^77 - 128 * q^82 - 16 * q^83 + 224 * q^86 - 12 * q^88 - 16 * q^91 + 104 * q^92 + 20 * q^97 - 188 * q^98

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