LMFDB - Embedded newform 900.3.c.n.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("900.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.c (of order $2$, degree $1$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.4069419264.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 $ x^8 - 7x^6 + 50x^4 - 84x^3 + 55x^2 - 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.4
Root			$-2.65095 - 1.53053i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.n.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.534079 + 1.92737i) q^{2} +(-3.42952 - 2.05874i) q^{4} +11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} +O(q^{10})$	\(q+(-0.534079 + 1.92737i) q^{2} +(-3.42952 - 2.05874i) q^{4} +11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} -14.5382i q^{11} -22.4802 q^{13} +(-23.0738 - 6.39379i) q^{14} +(7.52322 + 14.1209i) q^{16} +12.6890 q^{17} -8.76336i q^{19} +(28.0205 + 7.76455i) q^{22} +4.99653i q^{23} +(12.0062 - 43.3278i) q^{26} +(24.6464 - 41.0570i) q^{28} -2.74712 q^{29} -16.3466i q^{31} +(-31.2343 + 6.95833i) q^{32} +(-6.77695 + 24.4565i) q^{34} -32.4872 q^{37} +(16.8902 + 4.68032i) q^{38} -42.7586 q^{41} -16.5435i q^{43} +(-29.9303 + 49.8591i) q^{44} +(-9.63018 - 2.66854i) q^{46} -48.5912i q^{47} -94.3200 q^{49} +(77.0964 + 46.2809i) q^{52} +94.1066 q^{53} +(65.9689 + 69.4305i) q^{56} +(1.46718 - 5.29471i) q^{58} -43.2650i q^{59} +56.7678 q^{61} +(31.5060 + 8.73038i) q^{62} +(3.27028 - 63.9164i) q^{64} -61.1106i q^{67} +(-43.5173 - 26.1234i) q^{68} -39.6643i q^{71} +99.5452 q^{73} +(17.3507 - 62.6149i) q^{74} +(-18.0414 + 30.0541i) q^{76} +174.046 q^{77} -10.7780i q^{79} +(22.8365 - 82.4118i) q^{82} -140.263i q^{83} +(31.8855 + 8.83554i) q^{86} +(-80.1118 - 84.3156i) q^{88} -54.8723 q^{89} -269.125i q^{91} +(10.2865 - 17.1357i) q^{92} +(93.6533 + 25.9515i) q^{94} -14.1601 q^{97} +(50.3743 - 181.790i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{4} - 20 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^4 - 20 * q^8	$ 8 q - 2 q^{2} - 8 q^{4} - 20 q^{8} + 8 q^{13} - 22 q^{14} + 40 q^{16} + 4 q^{22} + 66 q^{26} + 104 q^{28} + 32 q^{29} - 112 q^{32} + 124 q^{34} - 176 q^{37} + 170 q^{38} + 16 q^{41} - 40 q^{44} - 76 q^{46} + 16 q^{49} + 56 q^{52} + 304 q^{53} + 172 q^{56} - 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 88 q^{68} + 240 q^{73} + 108 q^{74} + 120 q^{76} + 384 q^{77} + 320 q^{82} - 214 q^{86} - 200 q^{88} - 128 q^{89} - 312 q^{92} + 12 q^{94} + 216 q^{97} - 60 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^4 - 20 * q^8 + 8 * q^13 - 22 * q^14 + 40 * q^16 + 4 * q^22 + 66 * q^26 + 104 * q^28 + 32 * q^29 - 112 * q^32 + 124 * q^34 - 176 * q^37 + 170 * q^38 + 16 * q^41 - 40 * q^44 - 76 * q^46 + 16 * q^49 + 56 * q^52 + 304 * q^53 + 172 * q^56 - 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 88 * q^68 + 240 * q^73 + 108 * q^74 + 120 * q^76 + 384 * q^77 + 320 * q^82 - 214 * q^86 - 200 * q^88 - 128 * q^89 - 312 * q^92 + 12 * q^94 + 216 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.534079	+	1.92737i	−0.267039	+	0.963686i
$2$	−0.534079	+	1.92737i	−0.267039	+	0.963686i
$3$		0			0
$3$		0			0
$4$	−3.42952	−	2.05874i	−0.857380	−	0.514684i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			11.9716i			1.71023i	0.518436	+	0.855117i	$0.326515\pi$
$7$			11.9716i			1.71023i	−0.518436	+	0.855117i	$0.673485\pi$
$8$	5.79958	−	5.51043i	0.724948	−	0.688804i
$9$		0			0
$10$		0			0
$11$		−	14.5382i		−	1.32166i	−0.750537	−	0.660828i	$-0.770205\pi$
$11$		−	14.5382i		−	1.32166i	0.750537	−	0.660828i	$-0.229795\pi$
$12$		0			0
$13$	−22.4802			−1.72925			−0.864625	−	0.502418i	$-0.832444\pi$
$13$	−22.4802			−1.72925			−0.864625	+	0.502418i	$0.832444\pi$
$14$	−23.0738	−	6.39379i	−1.64813	−	0.456699i
$15$		0			0
$16$	7.52322	+	14.1209i	0.470201	+	0.882559i
$17$	12.6890			0.746414			0.373207	−	0.927748i	$-0.378258\pi$
$17$	12.6890			0.746414			0.373207	+	0.927748i	$0.378258\pi$
$18$		0			0
$19$		−	8.76336i		−	0.461229i	−0.973045	−	0.230615i	$-0.925926\pi$
$19$		−	8.76336i		−	0.461229i	0.973045	−	0.230615i	$-0.0740737\pi$
$20$		0			0
$21$		0			0
$22$	28.0205	+	7.76455i	1.27366	+	0.352934i
$23$			4.99653i			0.217241i	0.994083	+	0.108620i	$0.0346433\pi$
$23$			4.99653i			0.217241i	−0.994083	+	0.108620i	$0.965357\pi$
$24$		0			0
$25$		0			0
$26$	12.0062	−	43.3278i	0.461778	−	1.66645i
$27$		0			0
$28$	24.6464	−	41.0570i	0.880229	−	1.46632i
$29$	−2.74712			−0.0947282			−0.0473641	−	0.998878i	$-0.515082\pi$
$29$	−2.74712			−0.0947282			−0.0473641	+	0.998878i	$0.515082\pi$
$30$		0			0
$31$		−	16.3466i		−	0.527310i	−0.964617	−	0.263655i	$-0.915072\pi$
$31$		−	16.3466i		−	0.527310i	0.964617	−	0.263655i	$-0.0849281\pi$
$32$	−31.2343	+	6.95833i	−0.976072	+	0.217448i
$33$		0			0
$34$	−6.77695	+	24.4565i	−0.199322	+	0.719309i
$35$		0			0
$36$		0			0
$37$	−32.4872			−0.878032			−0.439016	−	0.898479i	$-0.644673\pi$
$37$	−32.4872			−0.878032			−0.439016	+	0.898479i	$0.644673\pi$
$38$	16.8902	+	4.68032i	0.444480	+	0.123166i
$39$		0			0
$40$		0			0
$41$	−42.7586			−1.04289			−0.521447	−	0.853284i	$-0.674607\pi$
$41$	−42.7586			−1.04289			−0.521447	+	0.853284i	$0.674607\pi$
$42$		0			0
$43$		−	16.5435i		−	0.384733i	−0.981323	−	0.192367i	$-0.938384\pi$
$43$		−	16.5435i		−	0.384733i	0.981323	−	0.192367i	$-0.0616163\pi$
$44$	−29.9303	+	49.8591i	−0.680235	+	1.13316i
$45$		0			0
$46$	−9.63018	−	2.66854i	−0.209352	−	0.0580118i
$47$		−	48.5912i		−	1.03386i	−0.856029	−	0.516928i	$-0.827076\pi$
$47$		−	48.5912i		−	1.03386i	0.856029	−	0.516928i	$-0.172924\pi$
$48$		0			0
$49$	−94.3200			−1.92490
$50$		0			0
$51$		0			0
$52$	77.0964	+	46.2809i	1.48262	+	0.890017i
$53$	94.1066			1.77560			0.887798	−	0.460233i	$-0.152234\pi$
$53$	94.1066			1.77560			0.887798	+	0.460233i	$0.152234\pi$
$54$		0			0
$55$		0			0
$56$	65.9689	+	69.4305i	1.17802	+	1.23983i
$57$		0			0
$58$	1.46718	−	5.29471i	0.0252961	−	0.0912882i
$59$		−	43.2650i		−	0.733305i	−0.930358	−	0.366653i	$-0.880504\pi$
$59$		−	43.2650i		−	0.733305i	0.930358	−	0.366653i	$-0.119496\pi$
$60$		0			0
$61$	56.7678			0.930620			0.465310	−	0.885148i	$-0.345943\pi$
$61$	56.7678			0.930620			0.465310	+	0.885148i	$0.345943\pi$
$62$	31.5060	+	8.73038i	0.508161	+	0.140813i
$63$		0			0
$64$	3.27028	−	63.9164i	0.0510981	−	0.998694i
$65$		0			0
$66$		0			0
$67$		−	61.1106i		−	0.912098i	−0.889955	−	0.456049i	$-0.849264\pi$
$67$		−	61.1106i		−	0.912098i	0.889955	−	0.456049i	$-0.150736\pi$
$68$	−43.5173	−	26.1234i	−0.639961	−	0.384167i
$69$		0			0
$70$		0			0
$71$		−	39.6643i		−	0.558652i	−0.960196	−	0.279326i	$-0.909889\pi$
$71$		−	39.6643i		−	0.558652i	0.960196	−	0.279326i	$-0.0901110\pi$
$72$		0			0
$73$	99.5452			1.36363			0.681817	−	0.731523i	$-0.261190\pi$
$73$	99.5452			1.36363			0.681817	+	0.731523i	$0.261190\pi$
$74$	17.3507	−	62.6149i	0.234469	−	0.846147i
$75$		0			0
$76$	−18.0414	+	30.0541i	−0.237387	+	0.395449i
$77$	174.046			2.26034
$78$		0			0
$79$		−	10.7780i		−	0.136430i	−0.997671	−	0.0682151i	$-0.978270\pi$
$79$		−	10.7780i		−	0.136430i	0.997671	−	0.0682151i	$-0.0217304\pi$
$80$		0			0
$81$		0			0
$82$	22.8365	−	82.4118i	0.278494	−	1.00502i
$83$		−	140.263i		−	1.68991i	−0.534837	−	0.844955i	$-0.679627\pi$
$83$		−	140.263i		−	1.68991i	0.534837	−	0.844955i	$-0.320373\pi$
$84$		0			0
$85$		0			0
$86$	31.8855	+	8.83554i	0.370762	+	0.102739i
$87$		0			0
$88$	−80.1118	−	84.3156i	−0.910362	−	0.958131i
$89$	−54.8723			−0.616543			−0.308271	−	0.951298i	$-0.599751\pi$
$89$	−54.8723			−0.616543			−0.308271	+	0.951298i	$0.599751\pi$
$90$		0			0
$91$		−	269.125i		−	2.95742i
$92$	10.2865	−	17.1357i	0.111810	−	0.186258i
$93$		0			0
$94$	93.6533	+	25.9515i	0.996312	+	0.276080i
$95$		0			0
$96$		0			0
$97$	−14.1601			−0.145980			−0.0729902	−	0.997333i	$-0.523254\pi$
$97$	−14.1601			−0.145980			−0.0729902	+	0.997333i	$0.523254\pi$
$98$	50.3743	−	181.790i	0.514023	−	1.85500i
$99$		0			0
$100$		0			0
$101$	163.410			1.61792			0.808962	−	0.587861i	$-0.200030\pi$
$101$	163.410			1.61792			0.808962	+	0.587861i	$0.200030\pi$
$102$		0			0
$103$			169.591i			1.64651i	0.567672	+	0.823255i	$0.307844\pi$
$103$			169.591i			1.64651i	−0.567672	+	0.823255i	$0.692156\pi$
$104$	−130.376	+	123.876i	−1.25362	+	1.19111i
$105$		0			0
$106$	−50.2603	+	181.378i	−0.474154	+	1.71112i
$107$		−	8.14840i		−	0.0761532i	−0.999275	−	0.0380766i	$-0.987877\pi$
$107$		−	8.14840i		−	0.0761532i	0.999275	−	0.0380766i	$-0.0121231\pi$
$108$		0			0
$109$	−25.2322			−0.231488			−0.115744	−	0.993279i	$-0.536925\pi$
$109$	−25.2322			−0.231488			−0.115744	+	0.993279i	$0.536925\pi$
$110$		0			0
$111$		0			0
$112$	−169.051	+	90.0652i	−1.50938	+	0.804153i
$113$	97.8142			0.865613			0.432806	−	0.901487i	$-0.357523\pi$
$113$	97.8142			0.865613			0.432806	+	0.901487i	$0.357523\pi$
$114$		0			0
$115$		0			0
$116$	9.42129	+	5.65559i	0.0812180	+	0.0487551i
$117$		0			0
$118$	83.3877	+	23.1069i	0.706676	+	0.195821i
$119$			151.909i			1.27654i
$120$		0			0
$121$	−90.3597			−0.746774
$122$	−30.3185	+	109.413i	−0.248512	+	0.896825i
$123$		0			0
$124$	−33.6534	+	56.0611i	−0.271398	+	0.452105i
$125$		0			0
$126$		0			0
$127$		−	167.563i		−	1.31939i	−0.751533	−	0.659695i	$-0.770685\pi$
$127$		−	167.563i		−	1.31939i	0.751533	−	0.659695i	$-0.229315\pi$
$128$	121.444	+	40.4394i	0.948782	+	0.315933i
$129$		0			0
$130$		0			0
$131$		−	82.0465i		−	0.626309i	−0.949702	−	0.313155i	$-0.898614\pi$
$131$		−	82.0465i		−	0.626309i	0.949702	−	0.313155i	$-0.101386\pi$
$132$		0			0
$133$	104.912			0.788810
$134$	117.783	+	32.6378i	0.878976	+	0.243566i
$135$		0			0
$136$	73.5911	−	69.9221i	0.541111	−	0.514133i
$137$	−254.459			−1.85737			−0.928683	−	0.370874i	$-0.879058\pi$
$137$	−254.459			−1.85737			−0.928683	+	0.370874i	$0.879058\pi$
$138$		0			0
$139$		−	78.9483i		−	0.567974i	−0.958828	−	0.283987i	$-0.908343\pi$
$139$		−	78.9483i		−	0.567974i	0.958828	−	0.283987i	$-0.0916572\pi$
$140$		0			0
$141$		0			0
$142$	76.4478	+	21.1838i	0.538365	+	0.149182i
$143$			326.823i			2.28547i
$144$		0			0
$145$		0			0
$146$	−53.1650	+	191.861i	−0.364144	+	1.31411i
$147$		0			0
$148$	111.415	+	66.8825i	0.752807	+	0.451909i
$149$	32.3433			0.217069			0.108534	−	0.994093i	$-0.465384\pi$
$149$	32.3433			0.217069			0.108534	+	0.994093i	$0.465384\pi$
$150$		0			0
$151$			38.7953i			0.256922i	0.991715	+	0.128461i	$0.0410038\pi$
$151$			38.7953i			0.256922i	−0.991715	+	0.128461i	$0.958996\pi$
$152$	−48.2899	−	50.8238i	−0.317697	−	0.334367i
$153$		0			0
$154$	−92.9543	+	335.452i	−0.603600	+	2.17826i
$155$		0			0
$156$		0			0
$157$	−44.2021			−0.281542			−0.140771	−	0.990042i	$-0.544958\pi$
$157$	−44.2021			−0.281542			−0.140771	+	0.990042i	$0.544958\pi$
$158$	20.7732	+	5.75629i	0.131476	+	0.0364322i
$159$		0			0
$160$		0			0
$161$	−59.8167			−0.371532
$162$		0			0
$163$			52.9366i			0.324764i	0.986728	+	0.162382i	$0.0519177\pi$
$163$			52.9366i			0.324764i	−0.986728	+	0.162382i	$0.948082\pi$
$164$	146.642	+	88.0287i	0.894156	+	0.536760i
$165$		0			0
$166$	270.338	+	74.9112i	1.62854	+	0.451272i
$167$		−	179.273i		−	1.07349i	−0.843744	−	0.536745i	$-0.819654\pi$
$167$		−	179.273i		−	1.07349i	0.843744	−	0.536745i	$-0.180346\pi$
$168$		0			0
$169$	336.361			1.99030
$170$		0			0
$171$		0			0
$172$	−34.0587	+	56.7364i	−0.198016	+	0.329863i
$173$	−177.276			−1.02471			−0.512357	−	0.858772i	$-0.671228\pi$
$173$	−177.276			−1.02471			−0.512357	+	0.858772i	$0.671228\pi$
$174$		0			0
$175$		0			0
$176$	205.293	−	109.374i	1.16644	−	0.621444i
$177$		0			0
$178$	29.3061	−	105.759i	0.164641	−	0.594154i
$179$		−	102.849i		−	0.574573i	−0.957845	−	0.287286i	$-0.907247\pi$
$179$		−	102.849i		−	0.574573i	0.957845	−	0.287286i	$-0.0927532\pi$
$180$		0			0
$181$	−115.413			−0.637640			−0.318820	−	0.947815i	$-0.603286\pi$
$181$	−115.413			−0.637640			−0.318820	+	0.947815i	$0.603286\pi$
$182$	518.704	+	143.734i	2.85002	+	0.789747i
$183$		0			0
$184$	27.5331	+	28.9778i	0.149636	+	0.157488i
$185$		0			0
$186$		0			0
$187$		−	184.476i		−	0.986503i
$188$	−100.036	+	166.645i	−0.532109	+	0.886407i
$189$		0			0
$190$		0			0
$191$		−	191.305i		−	1.00160i	−0.865563	−	0.500799i	$-0.833040\pi$
$191$		−	191.305i		−	1.00160i	0.865563	−	0.500799i	$-0.166960\pi$
$192$		0			0
$193$	−160.332			−0.830734			−0.415367	−	0.909654i	$-0.636347\pi$
$193$	−160.332			−0.830734			−0.415367	+	0.909654i	$0.636347\pi$
$194$	7.56261	−	27.2918i	0.0389825	−	0.140679i
$195$		0			0
$196$	323.472	+	194.180i	1.65037	+	0.990714i
$197$	−355.081			−1.80244			−0.901220	−	0.433362i	$-0.857327\pi$
$197$	−355.081			−1.80244			−0.901220	+	0.433362i	$0.857327\pi$
$198$		0			0
$199$			88.2032i			0.443232i	0.975134	+	0.221616i	$0.0711332\pi$
$199$			88.2032i			0.443232i	−0.975134	+	0.221616i	$0.928867\pi$
$200$		0			0
$201$		0			0
$202$	−87.2740	+	314.952i	−0.432049	+	1.55917i
$203$		−	32.8875i		−	0.162007i
$204$		0			0
$205$		0			0
$206$	−326.864	−	90.5747i	−1.58672	−	0.439683i
$207$		0			0
$208$	−169.124	−	317.442i	−0.813095	−	1.52617i
$209$	−127.404			−0.609586
$210$		0			0
$211$		−	190.584i		−	0.903243i	−0.892210	−	0.451622i	$-0.850846\pi$
$211$		−	190.584i		−	0.903243i	0.892210	−	0.451622i	$-0.149154\pi$
$212$	−322.741	−	193.741i	−1.52236	−	0.913871i
$213$		0			0
$214$	15.7050	+	4.35188i	0.0733878	+	0.0203359i
$215$		0			0
$216$		0			0
$217$	195.696			0.901824
$218$	13.4760	−	48.6318i	0.0618164	−	0.223082i
$219$		0			0
$220$		0			0
$221$	−285.253			−1.29074
$222$		0			0
$223$			79.2869i			0.355547i	0.984071	+	0.177773i	$0.0568894\pi$
$223$			79.2869i			0.355547i	−0.984071	+	0.177773i	$0.943111\pi$
$224$	−83.3026	−	373.926i	−0.371887	−	1.66931i
$225$		0			0
$226$	−52.2405	+	188.524i	−0.231153	+	0.834178i
$227$			353.645i			1.55791i	0.627082	+	0.778953i	$0.284249\pi$
$227$			353.645i			1.55791i	−0.627082	+	0.778953i	$0.715751\pi$
$228$		0			0
$229$	−22.7911			−0.0995244			−0.0497622	−	0.998761i	$-0.515846\pi$
$229$	−22.7911			−0.0995244			−0.0497622	+	0.998761i	$0.515846\pi$
$230$		0			0
$231$		0			0
$232$	−15.9321	+	15.1378i	−0.0686730	+	0.0652491i
$233$	−189.710			−0.814205			−0.407103	−	0.913382i	$-0.633461\pi$
$233$	−189.710			−0.814205			−0.407103	+	0.913382i	$0.633461\pi$
$234$		0			0
$235$		0			0
$236$	−89.0712	+	148.378i	−0.377420	+	0.628721i
$237$		0			0
$238$	−292.784	−	81.1311i	−1.23019	−	0.340887i
$239$		−	267.778i		−	1.12041i	−0.828355	−	0.560204i	$-0.810723\pi$
$239$		−	267.778i		−	1.12041i	0.828355	−	0.560204i	$-0.189277\pi$
$240$		0			0
$241$	−301.663			−1.25171			−0.625857	−	0.779938i	$-0.715251\pi$
$241$	−301.663			−1.25171			−0.625857	+	0.779938i	$0.715251\pi$
$242$	48.2592	−	174.157i	0.199418	−	0.719656i
$243$		0			0
$244$	−194.686	−	116.870i	−0.797895	−	0.478975i
$245$		0			0
$246$		0			0
$247$			197.002i			0.797580i
$248$	−90.0769	−	94.8035i	−0.363213	−	0.382272i
$249$		0			0
$250$		0			0
$251$		−	63.1891i		−	0.251749i	−0.992046	−	0.125875i	$-0.959826\pi$
$251$		−	63.1891i		−	0.251749i	0.992046	−	0.125875i	$-0.0401737\pi$
$252$		0			0
$253$	72.6407			0.287117
$254$	322.955	+	89.4916i	1.27148	+	0.352329i
$255$		0			0
$256$	−142.802	+	212.470i	−0.557822	+	0.829961i
$257$	150.719			0.586456			0.293228	−	0.956043i	$-0.405271\pi$
$257$	150.719			0.586456			0.293228	+	0.956043i	$0.405271\pi$
$258$		0			0
$259$		−	388.925i		−	1.50164i
$260$		0			0
$261$		0			0
$262$	158.134	+	43.8193i	0.603565	+	0.167249i
$263$			203.755i			0.774735i	0.921925	+	0.387368i	$0.126616\pi$
$263$			203.755i			0.774735i	−0.921925	+	0.387368i	$0.873384\pi$
$264$		0			0
$265$		0			0
$266$	−56.0311	+	202.204i	−0.210643	+	0.760165i
$267$		0			0
$268$	−125.810	+	209.580i	−0.469442	+	0.782014i
$269$	−76.3986			−0.284010			−0.142005	−	0.989866i	$-0.545355\pi$
$269$	−76.3986			−0.284010			−0.142005	+	0.989866i	$0.545355\pi$
$270$		0			0
$271$			169.216i			0.624414i	0.950014	+	0.312207i	$0.101068\pi$
$271$			169.216i			0.624414i	−0.950014	+	0.312207i	$0.898932\pi$
$272$	95.4624	+	179.181i	0.350965	+	0.658755i
$273$		0			0
$274$	135.901	−	490.437i	0.495990	−	1.78992i
$275$		0			0
$276$		0			0
$277$	273.891			0.988774			0.494387	−	0.869242i	$-0.335393\pi$
$277$	273.891			0.988774			0.494387	+	0.869242i	$0.335393\pi$
$278$	152.163	+	42.1646i	0.547348	+	0.151671i
$279$		0			0
$280$		0			0
$281$	311.672			1.10915			0.554577	−	0.832133i	$-0.312880\pi$
$281$	311.672			1.10915			0.554577	+	0.832133i	$0.312880\pi$
$282$		0			0
$283$			264.566i			0.934861i	0.884030	+	0.467431i	$0.154820\pi$
$283$			264.566i			0.934861i	−0.884030	+	0.467431i	$0.845180\pi$
$284$	−81.6583	+	136.029i	−0.287529	+	0.478977i
$285$		0			0
$286$	−629.909	−	174.549i	−2.20248	−	0.610311i
$287$		−	511.891i		−	1.78359i
$288$		0			0
$289$	−127.988			−0.442866
$290$		0			0
$291$		0			0
$292$	−341.392	−	204.937i	−1.16915	−	0.701840i
$293$	121.281			0.413927			0.206964	−	0.978349i	$-0.433642\pi$
$293$	121.281			0.413927			0.206964	+	0.978349i	$0.433642\pi$
$294$		0			0
$295$		0			0
$296$	−188.412	+	179.018i	−0.636527	+	0.604792i
$297$		0			0
$298$	−17.2739	+	62.3375i	−0.0579659	+	0.209186i
$299$		−	112.323i		−	0.375663i
$300$		0			0
$301$	198.053			0.657984
$302$	−74.7729	−	20.7197i	−0.247592	−	0.0686083i
$303$		0			0
$304$	123.747	−	65.9286i	0.407062	−	0.216870i
$305$		0			0
$306$		0			0
$307$		−	161.768i		−	0.526932i	−0.964669	−	0.263466i	$-0.915134\pi$
$307$		−	161.768i		−	0.526932i	0.964669	−	0.263466i	$-0.0848656\pi$
$308$	−596.895	−	358.315i	−1.93797	−	1.16336i
$309$		0			0
$310$		0			0
$311$			26.3813i			0.0848273i	0.999100	+	0.0424137i	$0.0135047\pi$
$311$			26.3813i			0.0848273i	−0.999100	+	0.0424137i	$0.986495\pi$
$312$		0			0
$313$	−5.39902			−0.0172493			−0.00862463	−	0.999963i	$-0.502745\pi$
$313$	−5.39902			−0.0172493			−0.00862463	+	0.999963i	$0.502745\pi$
$314$	23.6074	−	85.1938i	0.0751827	−	0.271318i
$315$		0			0
$316$	−22.1890	+	36.9633i	−0.0702184	+	0.116972i
$317$	270.157			0.852231			0.426116	−	0.904669i	$-0.359882\pi$
$317$	270.157			0.852231			0.426116	+	0.904669i	$0.359882\pi$
$318$		0			0
$319$			39.9382i			0.125198i
$320$		0			0
$321$		0			0
$322$	31.9468	−	115.289i	0.0992137	−	0.358040i
$323$		−	111.199i		−	0.344268i
$324$		0			0
$325$		0			0
$326$	−102.028	−	28.2723i	−0.312971	−	0.0867248i
$327$		0			0
$328$	−247.982	+	235.619i	−0.756043	+	0.718349i
$329$	581.716			1.76813
$330$		0			0
$331$		−	480.728i		−	1.45235i	−0.687510	−	0.726174i	$-0.741296\pi$
$331$		−	480.728i		−	1.45235i	0.687510	−	0.726174i	$-0.258704\pi$
$332$	−288.763	+	481.033i	−0.869770	+	1.44890i
$333$		0			0
$334$	345.526	+	95.7459i	1.03451	+	0.286664i
$335$		0			0
$336$		0			0
$337$	−568.382			−1.68659			−0.843297	−	0.537448i	$-0.819388\pi$
$337$	−568.382			−1.68659			−0.843297	+	0.537448i	$0.819388\pi$
$338$	−179.643	+	648.293i	−0.531489	+	1.91803i
$339$		0			0
$340$		0			0
$341$	−237.651			−0.696923
$342$		0			0
$343$		−	542.554i		−	1.58179i
$344$	−91.1620	−	95.9455i	−0.265006	−	0.278911i
$345$		0			0
$346$	94.6791	−	341.676i	0.273639	−	0.987503i
$347$			370.184i			1.06681i	0.845859	+	0.533406i	$0.179088\pi$
$347$			370.184i			1.06681i	−0.845859	+	0.533406i	$0.820912\pi$
$348$		0			0
$349$	−488.570			−1.39991			−0.699957	−	0.714185i	$-0.746797\pi$
$349$	−488.570			−1.39991			−0.699957	+	0.714185i	$0.746797\pi$
$350$		0			0
$351$		0			0
$352$	101.162	+	454.091i	0.287391	+	1.29003i
$353$	−649.728			−1.84059			−0.920295	−	0.391226i	$-0.872051\pi$
$353$	−649.728			−1.84059			−0.920295	+	0.391226i	$0.872051\pi$
$354$		0			0
$355$		0			0
$356$	188.186	+	112.968i	0.528612	+	0.317325i
$357$		0			0
$358$	198.227	+	54.9292i	0.553708	+	0.153434i
$359$			405.910i			1.13067i	0.824862	+	0.565334i	$0.191253\pi$
$359$			405.910i			1.13067i	−0.824862	+	0.565334i	$0.808747\pi$
$360$		0			0
$361$	284.204			0.787268
$362$	61.6395	−	222.443i	0.170275	−	0.614484i
$363$		0			0
$364$	−554.058	+	922.970i	−1.52214	+	2.53563i
$365$		0			0
$366$		0			0
$367$		−	46.2347i		−	0.125980i	−0.998014	−	0.0629900i	$-0.979936\pi$
$367$		−	46.2347i		−	0.125980i	0.998014	−	0.0629900i	$-0.0200636\pi$
$368$	−70.5558	+	37.5900i	−0.191728	+	0.102147i
$369$		0			0
$370$		0			0
$371$			1126.61i			3.03668i
$372$		0			0
$373$	−138.262			−0.370676			−0.185338	−	0.982675i	$-0.559338\pi$
$373$	−138.262			−0.370676			−0.185338	+	0.982675i	$0.559338\pi$
$374$	355.554	+	98.5247i	0.950679	+	0.263435i
$375$		0			0
$376$	−267.759	−	281.809i	−0.712124	−	0.749491i
$377$	61.7559			0.163809
$378$		0			0
$379$		−	254.516i		−	0.671546i	−0.941943	−	0.335773i	$-0.891002\pi$
$379$		−	254.516i		−	0.671546i	0.941943	−	0.335773i	$-0.108998\pi$
$380$		0			0
$381$		0			0
$382$	368.716	+	102.172i	0.965226	+	0.267466i
$383$		−	62.7205i		−	0.163761i	−0.996642	−	0.0818805i	$-0.973907\pi$
$383$		−	62.7205i		−	0.163761i	0.996642	−	0.0818805i	$-0.0260926\pi$
$384$		0			0
$385$		0			0
$386$	85.6298	−	309.019i	0.221839	−	0.800567i
$387$		0			0
$388$	48.5623	+	29.1519i	0.125161	+	0.0751338i
$389$	−110.130			−0.283112			−0.141556	−	0.989930i	$-0.545210\pi$
$389$	−110.130			−0.283112			−0.141556	+	0.989930i	$0.545210\pi$
$390$		0			0
$391$			63.4012i			0.162152i
$392$	−547.016	+	519.744i	−1.39545	+	1.32588i
$393$		0			0
$394$	189.641	−	684.372i	0.481322	−	1.73698i
$395$		0			0
$396$		0			0
$397$	−292.953			−0.737916			−0.368958	−	0.929446i	$-0.620285\pi$
$397$	−292.953			−0.737916			−0.368958	+	0.929446i	$0.620285\pi$
$398$	−170.000	−	47.1074i	−0.427136	−	0.118360i
$399$		0			0
$400$		0			0
$401$	−518.103			−1.29203			−0.646014	−	0.763325i	$-0.723565\pi$
$401$	−518.103			−1.29203			−0.646014	+	0.763325i	$0.723565\pi$
$402$		0			0
$403$			367.476i			0.911851i
$404$	−560.419	−	336.419i	−1.38718	−	0.832720i
$405$		0			0
$406$	63.3864	+	17.5645i	0.156124	+	0.0432623i
$407$			472.306i			1.16046i
$408$		0			0
$409$	−181.984			−0.444948			−0.222474	−	0.974939i	$-0.571413\pi$
$409$	−181.984			−0.444948			−0.222474	+	0.974939i	$0.571413\pi$
$410$		0			0
$411$		0			0
$412$	349.142	−	581.614i	0.847432	−	1.41168i
$413$	517.953			1.25412
$414$		0			0
$415$		0			0
$416$	702.155	−	156.425i	1.68787	−	0.376022i
$417$		0			0
$418$	68.0435	−	245.554i	0.162784	−	0.587450i
$419$		−	163.347i		−	0.389849i	−0.980818	−	0.194925i	$-0.937554\pi$
$419$		−	163.347i		−	0.389849i	0.980818	−	0.194925i	$-0.0624462\pi$
$420$		0			0
$421$	−467.206			−1.10975			−0.554876	−	0.831933i	$-0.687234\pi$
$421$	−467.206			−1.10975			−0.554876	+	0.831933i	$0.687234\pi$
$422$	367.327	+	101.787i	0.870442	+	0.241201i
$423$		0			0
$424$	545.779	−	518.568i	1.28721	−	1.22304i
$425$		0			0
$426$		0			0
$427$			679.603i			1.59158i
$428$	−16.7754	+	27.9451i	−0.0391948	+	0.0652923i
$429$		0			0
$430$		0			0
$431$		−	685.527i		−	1.59055i	−0.606248	−	0.795275i	$-0.707326\pi$
$431$		−	685.527i		−	1.59055i	0.606248	−	0.795275i	$-0.292674\pi$
$432$		0			0
$433$	−592.777			−1.36900			−0.684500	−	0.729013i	$-0.739979\pi$
$433$	−592.777			−1.36900			−0.684500	+	0.729013i	$0.739979\pi$
$434$	−104.517	+	377.178i	−0.240822	+	0.869074i
$435$		0			0
$436$	86.5343	+	51.9464i	0.198473	+	0.119143i
$437$	43.7864			0.100198
$438$		0			0
$439$			464.439i			1.05795i	0.848638	+	0.528974i	$0.177423\pi$
$439$			464.439i			1.05795i	−0.848638	+	0.528974i	$0.822577\pi$
$440$		0			0
$441$		0			0
$442$	152.347	−	549.788i	0.344677	−	1.24386i
$443$		−	54.2868i		−	0.122544i	−0.998121	−	0.0612718i	$-0.980484\pi$
$443$		−	54.2868i		−	0.122544i	0.998121	−	0.0612718i	$-0.0195156\pi$
$444$		0			0
$445$		0			0
$446$	−152.815	−	42.3454i	−0.342635	−	0.0949449i
$447$		0			0
$448$	765.184	+	39.1506i	1.70800	+	0.0873897i
$449$	428.051			0.953343			0.476671	−	0.879082i	$-0.341843\pi$
$449$	428.051			0.953343			0.476671	+	0.879082i	$0.341843\pi$
$450$		0			0
$451$			621.634i			1.37835i
$452$	−335.456	−	201.374i	−0.742159	−	0.445517i
$453$		0			0
$454$	−681.605	−	188.874i	−1.50133	−	0.416022i
$455$		0			0
$456$		0			0
$457$	66.5848			0.145700			0.0728498	−	0.997343i	$-0.476791\pi$
$457$	66.5848			0.145700			0.0728498	+	0.997343i	$0.476791\pi$
$458$	12.1722	−	43.9269i	0.0265769	−	0.0959103i
$459$		0			0
$460$		0			0
$461$	238.626			0.517627			0.258814	−	0.965927i	$-0.416668\pi$
$461$	238.626			0.517627			0.258814	+	0.965927i	$0.416668\pi$
$462$		0			0
$463$		−	386.958i		−	0.835762i	−0.908502	−	0.417881i	$-0.862773\pi$
$463$		−	386.958i		−	0.835762i	0.908502	−	0.417881i	$-0.137227\pi$
$464$	−20.6672	−	38.7919i	−0.0445413	−	0.0836032i
$465$		0			0
$466$	101.320	−	365.641i	0.217425	−	0.784638i
$467$		−	235.964i		−	0.505276i	−0.967561	−	0.252638i	$-0.918702\pi$
$467$		−	235.964i		−	0.505276i	0.967561	−	0.252638i	$-0.0812981\pi$
$468$		0			0
$469$	731.593			1.55990
$470$		0			0
$471$		0			0
$472$	−238.409	−	250.919i	−0.505104	−	0.531608i
$473$	−240.513			−0.508485
$474$		0			0
$475$		0			0
$476$	312.740	−	520.974i	0.657016	−	1.09448i
$477$		0			0
$478$	516.107	+	143.014i	1.07972	+	0.299193i
$479$		−	529.496i		−	1.10542i	−0.833374	−	0.552710i	$-0.813594\pi$
$479$		−	529.496i		−	1.10542i	0.833374	−	0.552710i	$-0.186406\pi$
$480$		0			0
$481$	730.320			1.51834
$482$	161.112	−	581.417i	0.334257	−	1.20626i
$483$		0			0
$484$	309.890	+	186.027i	0.640270	+	0.384353i
$485$		0			0
$486$		0			0
$487$			880.801i			1.80863i	0.426869	+	0.904314i	$0.359617\pi$
$487$			880.801i			1.80863i	−0.426869	+	0.904314i	$0.640383\pi$
$488$	329.230	−	312.815i	0.674651	−	0.641015i
$489$		0			0
$490$		0			0
$491$		−	86.4466i		−	0.176062i	−0.996118	−	0.0880312i	$-0.971942\pi$
$491$		−	86.4466i		−	0.176062i	0.996118	−	0.0880312i	$-0.0280575\pi$
$492$		0			0
$493$	−34.8583			−0.0707065
$494$	−379.697	−	105.215i	−0.768617	−	0.212985i
$495$		0			0
$496$	230.830	−	122.979i	0.465383	−	0.247942i
$497$	474.846			0.955425
$498$		0			0
$499$			874.536i			1.75258i	0.481786	+	0.876289i	$0.339988\pi$
$499$			874.536i			1.75258i	−0.481786	+	0.876289i	$0.660012\pi$
$500$		0			0
$501$		0			0
$502$	121.789	+	33.7479i	0.242607	+	0.0672269i
$503$			17.5479i			0.0348865i	0.999848	+	0.0174433i	$0.00555265\pi$
$503$			17.5479i			0.0348865i	−0.999848	+	0.0174433i	$0.994447\pi$
$504$		0			0
$505$		0			0
$506$	−38.7958	+	140.006i	−0.0766716	+	0.276691i
$507$		0			0
$508$	−344.967	+	574.659i	−0.679069	+	1.13122i
$509$	−609.132			−1.19672			−0.598362	−	0.801226i	$-0.704181\pi$
$509$	−609.132			−1.19672			−0.598362	+	0.801226i	$0.704181\pi$
$510$		0			0
$511$			1191.72i			2.33213i
$512$	−333.241	−	388.709i	−0.650861	−	0.759197i
$513$		0			0
$514$	−80.4959	+	290.492i	−0.156607	+	0.565159i
$515$		0			0
$516$		0			0
$517$	−706.430			−1.36640
$518$	749.602	+	207.716i	1.44711	+	0.400997i
$519$		0			0
$520$		0			0
$521$	−433.724			−0.832484			−0.416242	−	0.909254i	$-0.636653\pi$
$521$	−433.724			−0.832484			−0.416242	+	0.909254i	$0.636653\pi$
$522$		0			0
$523$			473.223i			0.904823i	0.891809	+	0.452412i	$0.149436\pi$
$523$			473.223i			0.904823i	−0.891809	+	0.452412i	$0.850564\pi$
$524$	−168.912	+	281.380i	−0.322351	+	0.536985i
$525$		0			0
$526$	−392.712	−	108.821i	−0.746601	−	0.206885i
$527$		−	207.423i		−	0.393592i
$528$		0			0
$529$	504.035			0.952807
$530$		0			0
$531$		0			0
$532$	−359.797	−	215.985i	−0.676310	−	0.405988i
$533$	961.224			1.80342
$534$		0			0
$535$		0			0
$536$	−336.746	−	354.416i	−0.628257	−	0.661223i
$537$		0			0
$538$	40.8029	−	147.249i	0.0758418	−	0.273696i
$539$			1371.24i			2.54405i
$540$		0			0
$541$	294.889			0.545081			0.272540	−	0.962144i	$-0.412136\pi$
$541$	294.889			0.545081			0.272540	+	0.962144i	$0.412136\pi$
$542$	−326.142	−	90.3747i	−0.601739	−	0.166743i
$543$		0			0
$544$	−396.333	+	88.2946i	−0.728554	+	0.162306i
$545$		0			0
$546$		0			0
$547$		−	966.695i		−	1.76727i	−0.468179	−	0.883634i	$-0.655090\pi$
$547$		−	966.695i		−	1.76727i	0.468179	−	0.883634i	$-0.344910\pi$
$548$	872.673	+	523.864i	1.59247	+	0.955956i
$549$		0			0
$550$		0			0
$551$			24.0740i			0.0436914i
$552$		0			0
$553$	129.030			0.233327
$554$	−146.279	+	527.889i	−0.264042	+	0.952868i
$555$		0			0
$556$	−162.534	+	270.755i	−0.292327	+	0.486969i
$557$	74.2603			0.133322			0.0666609	−	0.997776i	$-0.478765\pi$
$557$	74.2603			0.133322			0.0666609	+	0.997776i	$0.478765\pi$
$558$		0			0
$559$			371.903i			0.665300i
$560$		0			0
$561$		0			0
$562$	−166.457	+	600.708i	−0.296187	+	1.06887i
$563$		−	663.688i		−	1.17884i	−0.807826	−	0.589421i	$-0.799356\pi$
$563$		−	663.688i		−	1.17884i	0.807826	−	0.589421i	$-0.200644\pi$
$564$		0			0
$565$		0			0
$566$	−509.916	−	141.299i	−0.900912	−	0.249645i
$567$		0			0
$568$	−218.567	−	230.036i	−0.384802	−	0.404993i
$569$	667.450			1.17302			0.586511	−	0.809941i	$-0.300501\pi$
$569$	667.450			1.17302			0.586511	+	0.809941i	$0.300501\pi$
$570$		0			0
$571$			185.898i			0.325565i	0.986662	+	0.162782i	$0.0520469\pi$
$571$			185.898i			0.325565i	−0.986662	+	0.162782i	$0.947953\pi$
$572$	672.841	−	1120.84i	1.17630	−	1.95952i
$573$		0			0
$574$	986.603	+	273.390i	1.71882	+	0.476289i
$575$		0			0
$576$		0			0
$577$	664.331			1.15135			0.575676	−	0.817678i	$-0.304739\pi$
$577$	664.331			1.15135			0.575676	+	0.817678i	$0.304739\pi$
$578$	68.3557	−	246.681i	0.118263	−	0.426783i
$579$		0			0
$580$		0			0
$581$	1679.17			2.89014
$582$		0			0
$583$		−	1368.14i		−	2.34673i
$584$	577.321	−	548.537i	0.988563	−	0.939276i
$585$		0			0
$586$	−64.7734	+	233.753i	−0.110535	+	0.398896i
$587$		−	763.083i		−	1.29997i	−0.759946	−	0.649986i	$-0.774775\pi$
$587$		−	763.083i		−	1.29997i	0.759946	−	0.649986i	$-0.225225\pi$
$588$		0			0
$589$	−143.251			−0.243211
$590$		0			0
$591$		0			0
$592$	−244.408	−	458.750i	−0.412852	−	0.774915i
$593$	286.193			0.482618			0.241309	−	0.970448i	$-0.422423\pi$
$593$	286.193			0.482618			0.241309	+	0.970448i	$0.422423\pi$
$594$		0			0
$595$		0			0
$596$	−110.922	−	66.5862i	−0.186111	−	0.111722i
$597$		0			0
$598$	216.489	+	59.9895i	0.362021	+	0.100317i
$599$		−	604.151i		−	1.00860i	−0.863529	−	0.504300i	$-0.831751\pi$
$599$		−	604.151i		−	1.00860i	0.863529	−	0.504300i	$-0.168249\pi$
$600$		0			0
$601$	275.562			0.458505			0.229253	−	0.973367i	$-0.426372\pi$
$601$	275.562			0.458505			0.229253	+	0.973367i	$0.426372\pi$
$602$	−105.776	+	381.722i	−0.175707	+	0.634089i
$603$		0			0
$604$	79.8692	−	133.049i	0.132234	−	0.220280i
$605$		0			0
$606$		0			0
$607$			52.1487i			0.0859121i	0.999077	+	0.0429561i	$0.0136775\pi$
$607$			52.1487i			0.0859121i	−0.999077	+	0.0429561i	$0.986322\pi$
$608$	60.9784	+	273.717i	0.100293	+	0.450193i
$609$		0			0
$610$		0			0
$611$			1092.34i			1.78779i
$612$		0			0
$613$	898.128			1.46513			0.732567	−	0.680695i	$-0.238322\pi$
$613$	898.128			1.46513			0.732567	+	0.680695i	$0.238322\pi$
$614$	311.787	+	86.3968i	0.507796	+	0.140711i
$615$		0			0
$616$	1009.39	−	959.070i	1.63863	−	1.55693i
$617$	−636.868			−1.03220			−0.516101	−	0.856528i	$-0.672617\pi$
$617$	−636.868			−1.03220			−0.516101	+	0.856528i	$0.672617\pi$
$618$		0			0
$619$		−	190.559i		−	0.307849i	−0.988083	−	0.153925i	$-0.950809\pi$
$619$		−	190.559i		−	0.307849i	0.988083	−	0.153925i	$-0.0491913\pi$
$620$		0			0
$621$		0			0
$622$	−50.8466	−	14.0897i	−0.0817469	−	0.0226522i
$623$		−	656.911i		−	1.05443i
$624$		0			0
$625$		0			0
$626$	2.88350	−	10.4059i	0.00460623	−	0.0166229i
$627$		0			0
$628$	151.592	+	91.0004i	0.241388	+	0.144905i
$629$	−412.231			−0.655376
$630$		0			0
$631$			578.160i			0.916261i	0.888885	+	0.458130i	$0.151481\pi$
$631$			578.160i			0.916261i	−0.888885	+	0.458130i	$0.848519\pi$
$632$	−59.3913	−	62.5078i	−0.0939736	−	0.0989047i
$633$		0			0
$634$	−144.285	+	520.693i	−0.227579	+	0.821283i
$635$		0			0
$636$		0			0
$637$	2120.34			3.32863
$638$	−76.9757	−	21.3301i	−0.120652	−	0.0334328i
$639$		0			0
$640$		0			0
$641$	35.3085			0.0550834			0.0275417	−	0.999621i	$-0.491232\pi$
$641$	35.3085			0.0550834			0.0275417	+	0.999621i	$0.491232\pi$
$642$		0			0
$643$		−	1045.67i		−	1.62623i	−0.582100	−	0.813117i	$-0.697769\pi$
$643$		−	1045.67i		−	1.62623i	0.582100	−	0.813117i	$-0.302231\pi$
$644$	205.143	+	123.147i	0.318544	+	0.191222i
$645$		0			0
$646$	214.321	+	59.3888i	0.331766	+	0.0919331i
$647$			2.71164i			0.00419110i	0.999998	+	0.00209555i	$0.000667035\pi$
$647$			2.71164i			0.00419110i	−0.999998	+	0.00209555i	$0.999333\pi$
$648$		0			0
$649$	−628.996			−0.969177
$650$		0			0
$651$		0			0
$652$	108.982	−	181.547i	0.167151	−	0.278446i
$653$	−206.765			−0.316639			−0.158319	−	0.987388i	$-0.550608\pi$
$653$	−206.765			−0.316639			−0.158319	+	0.987388i	$0.550608\pi$
$654$		0			0
$655$		0			0
$656$	−321.682	−	603.792i	−0.490370	−	0.920415i
$657$		0			0
$658$	−310.682	+	1121.18i	−0.472161	+	1.70393i
$659$			708.330i			1.07486i	0.843309	+	0.537428i	$0.180604\pi$
$659$			708.330i			1.07486i	−0.843309	+	0.537428i	$0.819396\pi$
$660$		0			0
$661$	1229.66			1.86031			0.930155	−	0.367167i	$-0.119672\pi$
$661$	1229.66			1.86031			0.930155	+	0.367167i	$0.119672\pi$
$662$	926.540	+	256.746i	1.39961	+	0.387834i
$663$		0			0
$664$	−772.907	−	813.464i	−1.16402	−	1.22510i
$665$		0			0
$666$		0			0
$667$		−	13.7261i		−	0.0205788i
$668$	−369.076	+	614.820i	−0.552508	+	0.920390i
$669$		0			0
$670$		0			0
$671$		−	825.303i		−	1.22996i
$672$		0			0
$673$	753.492			1.11960			0.559801	−	0.828627i	$-0.310878\pi$
$673$	753.492			1.11960			0.559801	+	0.828627i	$0.310878\pi$
$674$	303.561	−	1095.48i	0.450387	−	1.62535i
$675$		0			0
$676$	−1153.56	−	692.479i	−1.70645	−	1.02438i
$677$	332.246			0.490762			0.245381	−	0.969427i	$-0.421087\pi$
$677$	332.246			0.490762			0.245381	+	0.969427i	$0.421087\pi$
$678$		0			0
$679$		−	169.520i		−	0.249661i
$680$		0			0
$681$		0			0
$682$	126.924	−	458.041i	0.186106	−	0.671615i
$683$			1120.62i			1.64074i	0.571835	+	0.820368i	$0.306232\pi$
$683$			1120.62i			1.64074i	−0.571835	+	0.820368i	$0.693768\pi$
$684$		0			0
$685$		0			0
$686$	1045.70	+	289.767i	1.52435	+	0.422400i
$687$		0			0
$688$	233.610	−	124.461i	0.339550	−	0.180902i
$689$	−2115.54			−3.07045
$690$		0			0
$691$			331.115i			0.479182i	0.970874	+	0.239591i	$0.0770134\pi$
$691$			331.115i			0.479182i	−0.970874	+	0.239591i	$0.922987\pi$
$692$	607.970	+	364.964i	0.878570	+	0.527404i
$693$		0			0
$694$	−713.482	−	197.707i	−1.02807	−	0.284881i
$695$		0			0
$696$		0			0
$697$	−542.566			−0.778431
$698$	260.935	−	941.655i	0.373832	−	1.34908i
$699$		0			0
$700$		0			0
$701$	564.971			0.805949			0.402975	−	0.915211i	$-0.367976\pi$
$701$	564.971			0.805949			0.402975	+	0.915211i	$0.367976\pi$
$702$		0			0
$703$			284.697i			0.404974i
$704$	−929.230	−	47.5440i	−1.31993	−	0.0675341i
$705$		0			0
$706$	347.006	−	1252.27i	0.491510	−	1.77375i
$707$			1956.29i			2.76703i
$708$		0			0
$709$	1.56083			0.00220146			0.00110073	−	0.999999i	$-0.499650\pi$
$709$	1.56083			0.00220146			0.00110073	+	0.999999i	$0.499650\pi$
$710$		0			0
$711$		0			0
$712$	−318.236	+	302.370i	−0.446961	+	0.424677i
$713$	81.6765			0.114553
$714$		0			0
$715$		0			0
$716$	−211.738	+	352.721i	−0.295723	+	0.492627i
$717$		0			0
$718$	−782.339	−	216.788i	−1.08961	−	0.301933i
$719$		−	75.0325i		−	0.104357i	−0.998638	−	0.0521784i	$-0.983384\pi$
$719$		−	75.0325i		−	0.104357i	0.998638	−	0.0521784i	$-0.0166164\pi$
$720$		0			0
$721$	−2030.28			−2.81592
$722$	−151.787	+	547.766i	−0.210231	+	0.758678i
$723$		0			0
$724$	395.810	+	237.604i	0.546699	+	0.328183i
$725$		0			0
$726$		0			0
$727$			1229.26i			1.69087i	0.534082	+	0.845433i	$0.320657\pi$
$727$			1229.26i			1.69087i	−0.534082	+	0.845433i	$0.679343\pi$
$728$	−1483.00	−	1560.81i	−2.03708	−	2.14397i
$729$		0			0
$730$		0			0
$731$		−	209.922i		−	0.287170i
$732$		0			0
$733$	691.736			0.943705			0.471852	−	0.881678i	$-0.343586\pi$
$733$	691.736			0.943705			0.471852	+	0.881678i	$0.343586\pi$
$734$	89.1114	+	24.6930i	0.121405	+	0.0336416i
$735$		0			0
$736$	−34.7676	−	156.063i	−0.0472385	−	0.212042i
$737$	−888.438			−1.20548
$738$		0			0
$739$			71.4311i			0.0966591i	0.998831	+	0.0483296i	$0.0153898\pi$
$739$			71.4311i			0.0966591i	−0.998831	+	0.0483296i	$0.984610\pi$
$740$		0			0
$741$		0			0
$742$	−2171.40	−	601.698i	−2.92641	−	0.810914i
$743$		−	1006.92i		−	1.35521i	−0.735426	−	0.677605i	$-0.763018\pi$
$743$		−	1006.92i		−	1.35521i	0.735426	−	0.677605i	$-0.236982\pi$
$744$		0			0
$745$		0			0
$746$	73.8428	−	266.482i	0.0989850	−	0.357215i
$747$		0			0
$748$	−379.787	+	632.664i	−0.507737	+	0.845808i
$749$	97.5496			0.130240
$750$		0			0
$751$		−	1110.14i		−	1.47822i	−0.673587	−	0.739108i	$-0.735247\pi$
$751$		−	1110.14i		−	1.47822i	0.673587	−	0.739108i	$-0.264753\pi$
$752$	686.154	−	365.562i	0.912439	−	0.486120i
$753$		0			0
$754$	−32.9825	+	119.026i	−0.0437433	+	0.157860i
$755$		0			0
$756$		0			0
$757$	326.752			0.431641			0.215821	−	0.976433i	$-0.430757\pi$
$757$	326.752			0.431641			0.215821	+	0.976433i	$0.430757\pi$
$758$	490.547	+	135.932i	0.647160	+	0.179329i
$759$		0			0
$760$		0			0
$761$	−162.162			−0.213091			−0.106546	−	0.994308i	$-0.533979\pi$
$761$	−162.162			−0.213091			−0.106546	+	0.994308i	$0.533979\pi$
$762$		0			0
$763$		−	302.070i		−	0.395898i
$764$	−393.847	+	656.085i	−0.515507	+	0.858750i
$765$		0			0
$766$	120.886	+	33.4977i	0.157814	+	0.0437306i
$767$			972.608i			1.26807i
$768$		0			0
$769$	−154.694			−0.201162			−0.100581	−	0.994929i	$-0.532070\pi$
$769$	−154.694			−0.201162			−0.100581	+	0.994929i	$0.532070\pi$
$770$		0			0
$771$		0			0
$772$	549.861	+	330.081i	0.712255	+	0.427566i
$773$	208.302			0.269472			0.134736	−	0.990882i	$-0.456981\pi$
$773$	208.302			0.269472			0.134736	+	0.990882i	$0.456981\pi$
$774$		0			0
$775$		0			0
$776$	−82.1226	+	78.0283i	−0.105828	+	0.100552i
$777$		0			0
$778$	58.8183	−	212.262i	0.0756019	−	0.272831i
$779$			374.709i			0.481013i
$780$		0			0
$781$	−576.648			−0.738346
$782$	−122.198	−	33.8612i	−0.156263	−	0.0433008i
$783$		0			0
$784$	−709.590	−	1331.89i	−0.905089	−	1.69884i
$785$		0			0
$786$		0			0
$787$			377.158i			0.479235i	0.970867	+	0.239617i	$0.0770220\pi$
$787$			377.158i			0.479235i	−0.970867	+	0.239617i	$0.922978\pi$
$788$	1217.76	+	731.017i	1.54538	+	0.927687i
$789$		0			0
$790$		0			0
$791$			1171.00i			1.48040i
$792$		0			0
$793$	−1276.15			−1.60927
$794$	156.460	−	564.629i	0.197053	−	0.711119i
$795$		0			0
$796$	181.587	−	302.495i	0.228124	−	0.380018i
$797$	−321.141			−0.402937			−0.201468	−	0.979495i	$-0.564571\pi$
$797$	−321.141			−0.402937			−0.201468	+	0.979495i	$0.564571\pi$
$798$		0			0
$799$		−	616.576i		−	0.771685i
$800$		0			0
$801$		0			0
$802$	276.708	−	998.577i	0.345022	−	1.24511i
$803$		−	1447.21i		−	1.80225i
$804$		0			0
$805$		0			0
$806$	−708.263	−	196.261i	−0.878738	−	0.243500i
$807$		0			0
$808$	947.712	−	900.462i	1.17291	−	1.11443i
$809$	861.938			1.06544			0.532718	−	0.846293i	$-0.321171\pi$
$809$	861.938			1.06544			0.532718	+	0.846293i	$0.321171\pi$
$810$		0			0
$811$		−	1011.44i		−	1.24715i	−0.781765	−	0.623574i	$-0.785680\pi$
$811$		−	1011.44i		−	1.24715i	0.781765	−	0.623574i	$-0.214320\pi$
$812$	−67.7066	+	112.788i	−0.0833825	+	0.138902i
$813$		0			0
$814$	−910.308	−	252.248i	−1.11832	−	0.309887i
$815$		0			0
$816$		0			0
$817$	−144.977			−0.177450
$818$	97.1935	−	350.750i	0.118818	−	0.428790i
$819$		0			0
$820$		0			0
$821$	−68.0368			−0.0828707			−0.0414353	−	0.999141i	$-0.513193\pi$
$821$	−68.0368			−0.0828707			−0.0414353	+	0.999141i	$0.513193\pi$
$822$		0			0
$823$			980.340i			1.19118i	0.803289	+	0.595589i	$0.203081\pi$
$823$			980.340i			1.19118i	−0.803289	+	0.595589i	$0.796919\pi$
$824$	934.517	+	983.554i	1.13412	+	1.19363i
$825$		0			0
$826$	−276.628	+	998.288i	−0.334900	+	1.20858i
$827$		−	1183.88i		−	1.43153i	−0.698341	−	0.715766i	$-0.746078\pi$
$827$		−	1183.88i		−	1.43153i	0.698341	−	0.715766i	$-0.253922\pi$
$828$		0			0
$829$	98.7892			0.119167			0.0595833	−	0.998223i	$-0.481023\pi$
$829$	98.7892			0.119167			0.0595833	+	0.998223i	$0.481023\pi$
$830$		0			0
$831$		0			0
$832$	−73.5167	+	1436.86i	−0.0883614	+	1.72699i
$833$	−1196.83			−1.43677
$834$		0			0
$835$		0			0
$836$	436.933	+	262.290i	0.522647	+	0.313744i
$837$		0			0
$838$	314.830	+	87.2401i	0.375692	+	0.104105i
$839$			407.965i			0.486251i	0.969995	+	0.243125i	$0.0781727\pi$
$839$			407.965i			0.486251i	−0.969995	+	0.243125i	$0.921827\pi$
$840$		0			0
$841$	−833.453			−0.991027
$842$	249.525	−	900.479i	0.296347	−	1.06945i
$843$		0			0
$844$	−392.363	+	653.613i	−0.464885	+	0.774423i
$845$		0			0
$846$		0			0
$847$		−	1081.75i		−	1.27716i
$848$	707.984	+	1328.87i	0.834887	+	1.56707i
$849$		0			0
$850$		0			0
$851$		−	162.323i		−	0.190744i
$852$		0			0
$853$	−907.020			−1.06333			−0.531665	−	0.846955i	$-0.678433\pi$
$853$	−907.020			−1.06333			−0.531665	+	0.846955i	$0.678433\pi$
$854$	−1309.85	−	362.962i	−1.53378	−	0.425014i
$855$		0			0
$856$	−44.9012	−	47.2573i	−0.0524546	−	0.0552071i
$857$	693.549			0.809275			0.404638	−	0.914477i	$-0.367398\pi$
$857$	693.549			0.809275			0.404638	+	0.914477i	$0.367398\pi$
$858$		0			0
$859$			397.401i			0.462632i	0.972879	+	0.231316i	$0.0743031\pi$
$859$			397.401i			0.462632i	−0.972879	+	0.231316i	$0.925697\pi$
$860$		0			0
$861$		0			0
$862$	1321.27	+	366.126i	1.53279	+	0.424740i
$863$			1193.06i			1.38246i	0.722636	+	0.691229i	$0.242930\pi$
$863$			1193.06i			1.38246i	−0.722636	+	0.691229i	$0.757070\pi$
$864$		0			0
$865$		0			0
$866$	316.590	−	1142.50i	0.365577	−	1.31929i
$867$		0			0
$868$	−671.142	−	402.886i	−0.773206	−	0.464154i
$869$	−156.693			−0.180314
$870$		0			0
$871$			1373.78i			1.57724i
$872$	−146.336	+	139.040i	−0.167817	+	0.159450i
$873$		0			0
$874$	−23.3854	+	84.3927i	−0.0267567	+	0.0965591i
$875$		0			0
$876$		0			0
$877$	−136.545			−0.155695			−0.0778477	−	0.996965i	$-0.524805\pi$
$877$	−136.545			−0.155695			−0.0778477	+	0.996965i	$0.524805\pi$
$878$	−895.146	−	248.047i	−1.01953	−	0.282514i
$879$		0			0
$880$		0			0
$881$	836.578			0.949578			0.474789	−	0.880100i	$-0.342524\pi$
$881$	836.578			0.949578			0.474789	+	0.880100i	$0.342524\pi$
$882$		0			0
$883$			632.625i			0.716450i	0.933635	+	0.358225i	$0.116618\pi$
$883$			632.625i			0.716450i	−0.933635	+	0.358225i	$0.883382\pi$
$884$	978.280	+	587.260i	1.10665	+	0.664321i
$885$		0			0
$886$	104.631	+	28.9934i	0.118093	+	0.0327239i
$887$			290.957i			0.328024i	0.986458	+	0.164012i	$0.0524435\pi$
$887$			290.957i			0.328024i	−0.986458	+	0.164012i	$0.947556\pi$
$888$		0			0
$889$	2006.00			2.25646
$890$		0			0
$891$		0			0
$892$	163.231	−	271.916i	0.182994	−	0.304838i
$893$	−425.822			−0.476844
$894$		0			0
$895$		0			0
$896$	−484.126	+	1453.88i	−0.540319	+	1.62264i
$897$		0			0
$898$	−228.613	+	825.013i	−0.254580	+	0.918723i
$899$			44.9061i			0.0499511i
$900$		0			0
$901$	1194.12			1.32533
$902$	−1198.12	−	332.001i	−1.32829	−	0.368073i
$903$		0			0
$904$	567.282	−	538.999i	0.627524	−	0.596237i
$905$		0			0
$906$		0			0
$907$		−	473.341i		−	0.521875i	−0.965356	−	0.260938i	$-0.915968\pi$
$907$		−	473.341i		−	0.521875i	0.965356	−	0.260938i	$-0.0840317\pi$
$908$	728.061	−	1212.83i	0.801830	−	1.33572i
$909$		0			0
$910$		0			0
$911$		−	1176.67i		−	1.29163i	−0.763495	−	0.645813i	$-0.776518\pi$
$911$		−	1176.67i		−	1.29163i	0.763495	−	0.645813i	$-0.223482\pi$
$912$		0			0
$913$	−2039.17			−2.23348
$914$	−35.5615	+	128.334i	−0.0389075	+	0.140409i
$915$		0			0
$916$	78.1625	+	46.9208i	0.0853303	+	0.0512236i
$917$	982.230			1.07113
$918$		0			0
$919$		−	1491.24i		−	1.62267i	−0.584580	−	0.811336i	$-0.698741\pi$
$919$		−	1491.24i		−	1.62267i	0.584580	−	0.811336i	$-0.301259\pi$
$920$		0			0
$921$		0			0
$922$	−127.445	+	459.921i	−0.138227	+	0.498830i
$923$			891.663i			0.966048i
$924$		0			0
$925$		0			0
$926$	745.812	+	206.666i	0.805412	+	0.223181i
$927$		0			0
$928$	85.8043	−	19.1154i	0.0924615	−	0.0205984i
$929$	1217.24			1.31027			0.655134	−	0.755513i	$-0.272612\pi$
$929$	1217.24			1.31027			0.655134	+	0.755513i	$0.272612\pi$
$930$		0			0
$931$			826.560i			0.887819i
$932$	650.613	+	390.562i	0.698083	+	0.419058i
$933$		0			0
$934$	454.790	+	126.023i	0.486927	+	0.134928i
$935$		0			0
$936$		0			0
$937$	−468.840			−0.500363			−0.250182	−	0.968199i	$-0.580490\pi$
$937$	−468.840			−0.500363			−0.250182	+	0.968199i	$0.580490\pi$
$938$	−390.728	+	1410.05i	−0.416555	+	1.50325i
$939$		0			0
$940$		0			0
$941$	−358.033			−0.380481			−0.190241	−	0.981737i	$-0.560927\pi$
$941$	−358.033			−0.380481			−0.190241	+	0.981737i	$0.560927\pi$
$942$		0			0
$943$		−	213.645i		−	0.226559i
$944$	610.943	−	325.492i	0.647185	−	0.344801i
$945$		0			0
$946$	128.453	−	463.559i	0.135785	−	0.490020i
$947$		−	1148.77i		−	1.21306i	−0.795059	−	0.606532i	$-0.792560\pi$
$947$		−	1148.77i		−	1.21306i	0.795059	−	0.606532i	$-0.207440\pi$
$948$		0			0
$949$	−2237.80			−2.35806
$950$		0			0
$951$		0			0
$952$	837.082	+	881.006i	0.879288	+	0.925427i
$953$	−911.785			−0.956753			−0.478376	−	0.878155i	$-0.658774\pi$
$953$	−911.785			−0.956753			−0.478376	+	0.878155i	$0.658774\pi$
$954$		0			0
$955$		0			0
$956$	−551.283	+	918.348i	−0.576656	+	0.960615i
$957$		0			0
$958$	1020.54	+	282.792i	1.06528	+	0.295190i
$959$		−	3046.29i		−	3.17653i
$960$		0			0
$961$	693.788			0.721944
$962$	−390.048	+	1407.60i	−0.405455	+	1.46320i
$963$		0			0
$964$	1034.56	+	621.045i	1.07320	+	0.644237i
$965$		0			0
$966$		0			0
$967$			311.565i			0.322197i	0.986938	+	0.161099i	$0.0515037\pi$
$967$			311.565i			0.322197i	−0.986938	+	0.161099i	$0.948496\pi$
$968$	−524.048	+	497.921i	−0.541372	+	0.514381i
$969$		0			0
$970$		0			0
$971$			370.530i			0.381596i	0.981629	+	0.190798i	$0.0611075\pi$
$971$			370.530i			0.381596i	−0.981629	+	0.190798i	$0.938892\pi$
$972$		0			0
$973$	945.141			0.971368
$974$	−1697.63	−	470.417i	−1.74295	−	0.482974i
$975$		0			0
$976$	427.077	+	801.615i	0.437578	+	0.821327i
$977$	−1402.53			−1.43555			−0.717773	−	0.696278i	$-0.754838\pi$
$977$	−1402.53			−1.43555			−0.717773	+	0.696278i	$0.754838\pi$
$978$		0			0
$979$			797.746i			0.814858i
$980$		0			0
$981$		0			0
$982$	166.615	+	46.1693i	0.169669	+	0.0470156i
$983$			988.944i			1.00605i	0.864273	+	0.503023i	$0.167779\pi$
$983$			988.944i			1.00605i	−0.864273	+	0.503023i	$0.832221\pi$
$984$		0			0
$985$		0			0
$986$	18.6171	−	67.1849i	0.0188814	−	0.0681388i
$987$		0			0
$988$	405.576	−	675.624i	0.410502	−	0.683830i
$989$	82.6603			0.0835797
$990$		0			0
$991$			90.1483i			0.0909670i	0.998965	+	0.0454835i	$0.0144828\pi$
$991$			90.1483i			0.0909670i	−0.998965	+	0.0454835i	$0.985517\pi$
$992$	113.745	+	510.575i	0.114663	+	0.514693i
$993$		0			0
$994$	−253.605	+	915.205i	−0.255136	+	0.920729i
$995$		0			0
$996$		0			0
$997$	−655.605			−0.657578			−0.328789	−	0.944403i	$-0.606640\pi$
$997$	−655.605			−0.657578			−0.328789	+	0.944403i	$0.606640\pi$
$998$	−1685.56	−	467.071i	−1.68893	−	0.468007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.n.451.4		8
3.2	odd	2		300.3.c.g.151.5	yes	8
4.3	odd	2	inner	900.3.c.n.451.3		8
5.2	odd	4		900.3.f.h.199.3		16
5.3	odd	4		900.3.f.h.199.14		16
5.4	even	2		900.3.c.t.451.5		8
12.11	even	2		300.3.c.g.151.6	yes	8
15.2	even	4		300.3.f.c.199.14		16
15.8	even	4		300.3.f.c.199.3		16
15.14	odd	2		300.3.c.e.151.4	yes	8
20.3	even	4		900.3.f.h.199.4		16
20.7	even	4		900.3.f.h.199.13		16
20.19	odd	2		900.3.c.t.451.6		8
60.23	odd	4		300.3.f.c.199.13		16
60.47	odd	4		300.3.f.c.199.4		16
60.59	even	2		300.3.c.e.151.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.3	✓	8	60.59	even	2
300.3.c.e.151.4	yes	8	15.14	odd	2
300.3.c.g.151.5	yes	8	3.2	odd	2
300.3.c.g.151.6	yes	8	12.11	even	2
300.3.f.c.199.3		16	15.8	even	4
300.3.f.c.199.4		16	60.47	odd	4
300.3.f.c.199.13		16	60.23	odd	4
300.3.f.c.199.14		16	15.2	even	4
900.3.c.n.451.3		8	4.3	odd	2	inner
900.3.c.n.451.4		8	1.1	even	1	trivial
900.3.c.t.451.5		8	5.4	even	2
900.3.c.t.451.6		8	20.19	odd	2
900.3.f.h.199.3		16	5.2	odd	4
900.3.f.h.199.4		16	20.3	even	4
900.3.f.h.199.13		16	20.7	even	4
900.3.f.h.199.14		16	5.3	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.534079 + 1.92737i) q^{2} +(-3.42952 - 2.05874i) q^{4} +11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} +O(q^{10})\)	\(q+(-0.534079 + 1.92737i) q^{2} +(-3.42952 - 2.05874i) q^{4} +11.9716i q^{7} +(5.79958 - 5.51043i) q^{8} -14.5382i q^{11} -22.4802 q^{13} +(-23.0738 - 6.39379i) q^{14} +(7.52322 + 14.1209i) q^{16} +12.6890 q^{17} -8.76336i q^{19} +(28.0205 + 7.76455i) q^{22} +4.99653i q^{23} +(12.0062 - 43.3278i) q^{26} +(24.6464 - 41.0570i) q^{28} -2.74712 q^{29} -16.3466i q^{31} +(-31.2343 + 6.95833i) q^{32} +(-6.77695 + 24.4565i) q^{34} -32.4872 q^{37} +(16.8902 + 4.68032i) q^{38} -42.7586 q^{41} -16.5435i q^{43} +(-29.9303 + 49.8591i) q^{44} +(-9.63018 - 2.66854i) q^{46} -48.5912i q^{47} -94.3200 q^{49} +(77.0964 + 46.2809i) q^{52} +94.1066 q^{53} +(65.9689 + 69.4305i) q^{56} +(1.46718 - 5.29471i) q^{58} -43.2650i q^{59} +56.7678 q^{61} +(31.5060 + 8.73038i) q^{62} +(3.27028 - 63.9164i) q^{64} -61.1106i q^{67} +(-43.5173 - 26.1234i) q^{68} -39.6643i q^{71} +99.5452 q^{73} +(17.3507 - 62.6149i) q^{74} +(-18.0414 + 30.0541i) q^{76} +174.046 q^{77} -10.7780i q^{79} +(22.8365 - 82.4118i) q^{82} -140.263i q^{83} +(31.8855 + 8.83554i) q^{86} +(-80.1118 - 84.3156i) q^{88} -54.8723 q^{89} -269.125i q^{91} +(10.2865 - 17.1357i) q^{92} +(93.6533 + 25.9515i) q^{94} -14.1601 q^{97} +(50.3743 - 181.790i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{4} - 20 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^4 - 20 * q^8	\( 8 q - 2 q^{2} - 8 q^{4} - 20 q^{8} + 8 q^{13} - 22 q^{14} + 40 q^{16} + 4 q^{22} + 66 q^{26} + 104 q^{28} + 32 q^{29} - 112 q^{32} + 124 q^{34} - 176 q^{37} + 170 q^{38} + 16 q^{41} - 40 q^{44} - 76 q^{46} + 16 q^{49} + 56 q^{52} + 304 q^{53} + 172 q^{56} - 12 q^{58} + 136 q^{61} + 238 q^{62} + 16 q^{64} - 88 q^{68} + 240 q^{73} + 108 q^{74} + 120 q^{76} + 384 q^{77} + 320 q^{82} - 214 q^{86} - 200 q^{88} - 128 q^{89} - 312 q^{92} + 12 q^{94} + 216 q^{97} - 60 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^4 - 20 * q^8 + 8 * q^13 - 22 * q^14 + 40 * q^16 + 4 * q^22 + 66 * q^26 + 104 * q^28 + 32 * q^29 - 112 * q^32 + 124 * q^34 - 176 * q^37 + 170 * q^38 + 16 * q^41 - 40 * q^44 - 76 * q^46 + 16 * q^49 + 56 * q^52 + 304 * q^53 + 172 * q^56 - 12 * q^58 + 136 * q^61 + 238 * q^62 + 16 * q^64 - 88 * q^68 + 240 * q^73 + 108 * q^74 + 120 * q^76 + 384 * q^77 + 320 * q^82 - 214 * q^86 - 200 * q^88 - 128 * q^89 - 312 * q^92 + 12 * q^94 + 216 * q^97 - 60 * q^98

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