LMFDB - Embedded newform 900.3.c.u.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:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.4
Root			$1.40906 - 0.120653i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.u.451.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438172 + 1.95141i) q^{2} +(-3.61601 + 1.71011i) q^{4} -6.33166i q^{7} +(-4.92155 - 6.30701i) q^{8} +O(q^{10})$	\(q+(0.438172 + 1.95141i) q^{2} +(-3.61601 + 1.71011i) q^{4} -6.33166i q^{7} +(-4.92155 - 6.30701i) q^{8} +9.27963i q^{11} -18.5674 q^{13} +(12.3557 - 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} +13.9110 q^{17} +17.2468i q^{19} +(-18.1084 + 4.06607i) q^{22} -33.7148i q^{23} +(-8.13571 - 36.2327i) q^{26} +(10.8278 + 22.8954i) q^{28} +28.6177 q^{29} -23.4939i q^{31} +(28.5820 + 14.3898i) q^{32} +(6.09542 + 27.1461i) q^{34} +67.3338 q^{37} +(-33.6556 + 7.55706i) q^{38} +44.0791 q^{41} -50.2937i q^{43} +(-15.8691 - 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} -31.1594i q^{47} +8.91003 q^{49} +(67.1400 - 31.7522i) q^{52} +81.6070 q^{53} +(-39.9338 + 31.1616i) q^{56} +(12.5395 + 55.8449i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(45.8462 - 10.2943i) q^{62} +(-15.5566 + 62.0805i) q^{64} +4.49911i q^{67} +(-50.3025 + 23.7893i) q^{68} +13.3360i q^{71} -40.8904 q^{73} +(29.5037 + 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} +58.7555 q^{77} -141.309i q^{79} +(19.3142 + 86.0164i) q^{82} +69.8503i q^{83} +(98.1438 - 22.0373i) q^{86} +(58.5266 - 45.6702i) q^{88} +46.3079 q^{89} +117.563i q^{91} +(57.6559 + 121.913i) q^{92} +(60.8049 - 13.6532i) q^{94} -68.5543 q^{97} +(3.90412 + 17.3871i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * 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 $

$2$	0.438172	+	1.95141i	0.219086	+	0.975706i
$2$	0.438172	+	1.95141i	0.219086	+	0.975706i
$3$		0			0
$3$		0			0
$4$	−3.61601	+	1.71011i	−0.904003	+	0.427526i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	6.33166i		−	0.904523i	−0.891885	−	0.452262i	$-0.850617\pi$
$7$		−	6.33166i		−	0.904523i	0.891885	−	0.452262i	$-0.149383\pi$
$8$	−4.92155	−	6.30701i	−0.615194	−	0.788376i
$9$		0			0
$10$		0			0
$11$			9.27963i			0.843602i	0.906688	+	0.421801i	$0.138602\pi$
$11$			9.27963i			0.843602i	−0.906688	+	0.421801i	$0.861398\pi$
$12$		0			0
$13$	−18.5674			−1.42826			−0.714131	−	0.700012i	$-0.753178\pi$
$13$	−18.5674			−1.42826			−0.714131	+	0.700012i	$0.753178\pi$
$14$	12.3557	−	2.77436i	0.882549	−	0.198168i
$15$		0			0
$16$	10.1511	−	12.3675i	0.634442	−	0.772970i
$17$	13.9110			0.818296			0.409148	−	0.912468i	$-0.365826\pi$
$17$	13.9110			0.818296			0.409148	+	0.912468i	$0.365826\pi$
$18$		0			0
$19$			17.2468i			0.907727i	0.891071	+	0.453864i	$0.149955\pi$
$19$			17.2468i			0.907727i	−0.891071	+	0.453864i	$0.850045\pi$
$20$		0			0
$21$		0			0
$22$	−18.1084	+	4.06607i	−0.823108	+	0.184821i
$23$		−	33.7148i		−	1.46586i	−0.680303	−	0.732931i	$-0.738152\pi$
$23$		−	33.7148i		−	1.46586i	0.680303	−	0.732931i	$-0.261848\pi$
$24$		0			0
$25$		0			0
$26$	−8.13571	−	36.2327i	−0.312912	−	1.39356i
$27$		0			0
$28$	10.8278	+	22.8954i	0.386708	+	0.817692i
$29$	28.6177			0.986817			0.493409	−	0.869798i	$-0.335751\pi$
$29$	28.6177			0.986817			0.493409	+	0.869798i	$0.335751\pi$
$30$		0			0
$31$		−	23.4939i		−	0.757866i	−0.925424	−	0.378933i	$-0.876291\pi$
$31$		−	23.4939i		−	0.757866i	0.925424	−	0.378933i	$-0.123709\pi$
$32$	28.5820	+	14.3898i	0.893189	+	0.449682i
$33$		0			0
$34$	6.09542	+	27.1461i	0.179277	+	0.798416i
$35$		0			0
$36$		0			0
$37$	67.3338			1.81983			0.909916	−	0.414793i	$-0.136146\pi$
$37$	67.3338			1.81983			0.909916	+	0.414793i	$0.136146\pi$
$38$	−33.6556	+	7.55706i	−0.885674	+	0.198870i
$39$		0			0
$40$		0			0
$41$	44.0791			1.07510			0.537550	−	0.843232i	$-0.319350\pi$
$41$	44.0791			1.07510			0.537550	+	0.843232i	$0.319350\pi$
$42$		0			0
$43$		−	50.2937i		−	1.16962i	−0.811170	−	0.584811i	$-0.801169\pi$
$43$		−	50.2937i		−	1.16962i	0.811170	−	0.584811i	$-0.198831\pi$
$44$	−15.8691	−	33.5552i	−0.360662	−	0.762619i
$45$		0			0
$46$	65.7915	−	14.7729i	1.43025	−	0.321150i
$47$		−	31.1594i		−	0.662967i	−0.943461	−	0.331483i	$-0.892451\pi$
$47$		−	31.1594i		−	0.662967i	0.943461	−	0.331483i	$-0.107549\pi$
$48$		0			0
$49$	8.91003			0.181837
$50$		0			0
$51$		0			0
$52$	67.1400	−	31.7522i	1.29115	−	0.610620i
$53$	81.6070			1.53975			0.769877	−	0.638192i	$-0.220318\pi$
$53$	81.6070			1.53975			0.769877	+	0.638192i	$0.220318\pi$
$54$		0			0
$55$		0			0
$56$	−39.9338	+	31.1616i	−0.713104	+	0.556457i
$57$		0			0
$58$	12.5395	+	55.8449i	0.216198	+	0.962843i
$59$			19.2751i			0.326697i	0.986568	+	0.163349i	$0.0522296\pi$
$59$			19.2751i			0.326697i	−0.986568	+	0.163349i	$0.947770\pi$
$60$		0			0
$61$	−53.1563			−0.871415			−0.435707	−	0.900088i	$-0.643502\pi$
$61$	−53.1563			−0.871415			−0.435707	+	0.900088i	$0.643502\pi$
$62$	45.8462	−	10.2943i	0.739455	−	0.166038i
$63$		0			0
$64$	−15.5566	+	62.0805i	−0.243072	+	0.970008i
$65$		0			0
$66$		0			0
$67$			4.49911i			0.0671509i	0.999436	+	0.0335754i	$0.0106894\pi$
$67$			4.49911i			0.0671509i	−0.999436	+	0.0335754i	$0.989311\pi$
$68$	−50.3025	+	23.7893i	−0.739742	+	0.349843i
$69$		0			0
$70$		0			0
$71$			13.3360i			0.187832i	0.995580	+	0.0939158i	$0.0299385\pi$
$71$			13.3360i			0.187832i	−0.995580	+	0.0939158i	$0.970062\pi$
$72$		0			0
$73$	−40.8904			−0.560143			−0.280071	−	0.959979i	$-0.590358\pi$
$73$	−40.8904			−0.560143			−0.280071	+	0.959979i	$0.590358\pi$
$74$	29.5037	+	131.396i	0.398699	+	1.77562i
$75$		0			0
$76$	−29.4939	−	62.3647i	−0.388077	−	0.820588i
$77$	58.7555			0.763058
$78$		0			0
$79$		−	141.309i		−	1.78872i	−0.447352	−	0.894358i	$-0.647633\pi$
$79$		−	141.309i		−	1.78872i	0.447352	−	0.894358i	$-0.352367\pi$
$80$		0			0
$81$		0			0
$82$	19.3142	+	86.0164i	0.235539	+	1.04898i
$83$			69.8503i			0.841570i	0.907160	+	0.420785i	$0.138245\pi$
$83$			69.8503i			0.841570i	−0.907160	+	0.420785i	$0.861755\pi$
$84$		0			0
$85$		0			0
$86$	98.1438	−	22.0373i	1.14121	−	0.256248i
$87$		0			0
$88$	58.5266	−	45.6702i	0.665076	−	0.518979i
$89$	46.3079			0.520313			0.260157	−	0.965566i	$-0.416226\pi$
$89$	46.3079			0.520313			0.260157	+	0.965566i	$0.416226\pi$
$90$		0			0
$91$			117.563i			1.29190i
$92$	57.6559	+	121.913i	0.626695	+	1.32514i
$93$		0			0
$94$	60.8049	−	13.6532i	0.646860	−	0.145247i
$95$		0			0
$96$		0			0
$97$	−68.5543			−0.706745			−0.353373	−	0.935483i	$-0.614965\pi$
$97$	−68.5543			−0.706745			−0.353373	+	0.935483i	$0.614965\pi$
$98$	3.90412	+	17.3871i	0.0398380	+	0.177420i
$99$		0			0
$100$		0			0
$101$	43.3949			0.429653			0.214826	−	0.976652i	$-0.431081\pi$
$101$	43.3949			0.429653			0.214826	+	0.976652i	$0.431081\pi$
$102$		0			0
$103$		−	85.7919i		−	0.832931i	−0.909152	−	0.416465i	$-0.863269\pi$
$103$		−	85.7919i		−	0.832931i	0.909152	−	0.416465i	$-0.136731\pi$
$104$	91.3805	+	117.105i	0.878659	+	1.12601i
$105$		0			0
$106$	35.7579	+	159.249i	0.337338	+	1.50235i
$107$			183.075i			1.71098i	0.517818	+	0.855491i	$0.326745\pi$
$107$			183.075i			1.71098i	−0.517818	+	0.855491i	$0.673255\pi$
$108$		0			0
$109$	81.4798			0.747521			0.373761	−	0.927525i	$-0.378068\pi$
$109$	81.4798			0.747521			0.373761	+	0.927525i	$0.378068\pi$
$110$		0			0
$111$		0			0
$112$	−78.3070	−	64.2732i	−0.699170	−	0.573868i
$113$	−172.814			−1.52933			−0.764664	−	0.644429i	$-0.777095\pi$
$113$	−172.814			−1.52933			−0.764664	+	0.644429i	$0.777095\pi$
$114$		0			0
$115$		0			0
$116$	−103.482	+	48.9393i	−0.892086	+	0.421891i
$117$		0			0
$118$	−37.6137	+	8.44582i	−0.318760	+	0.0715748i
$119$		−	88.0800i		−	0.740168i
$120$		0			0
$121$	34.8885			0.288335
$122$	−23.2916	−	103.730i	−0.190915	−	0.850244i
$123$		0			0
$124$	40.1770	+	84.9541i	0.324008	+	0.685113i
$125$		0			0
$126$		0			0
$127$			22.3785i			0.176208i	0.996111	+	0.0881041i	$0.0280808\pi$
$127$			22.3785i			0.176208i	−0.996111	+	0.0881041i	$0.971919\pi$
$128$	−127.961	−	3.15546i	−0.999696	−	0.0246520i
$129$		0			0
$130$		0			0
$131$		−	1.75315i		−	0.0133828i	−0.999978	−	0.00669141i	$-0.997870\pi$
$131$		−	1.75315i		−	0.0133828i	0.999978	−	0.00669141i	$-0.00212996\pi$
$132$		0			0
$133$	109.201			0.821060
$134$	−8.77961	+	1.97138i	−0.0655195	+	0.0147118i
$135$		0			0
$136$	−68.4639	−	87.7370i	−0.503411	−	0.645125i
$137$	−19.5084			−0.142397			−0.0711987	−	0.997462i	$-0.522682\pi$
$137$	−19.5084			−0.142397			−0.0711987	+	0.997462i	$0.522682\pi$
$138$		0			0
$139$		−	257.370i		−	1.85158i	−0.378038	−	0.925790i	$-0.623401\pi$
$139$		−	257.370i		−	1.85158i	0.378038	−	0.925790i	$-0.376599\pi$
$140$		0			0
$141$		0			0
$142$	−26.0241	+	5.84348i	−0.183268	+	0.0411512i
$143$		−	172.299i		−	1.20489i
$144$		0			0
$145$		0			0
$146$	−17.9170	−	79.7940i	−0.122719	−	0.546534i
$147$		0			0
$148$	−243.480	+	115.148i	−1.64513	+	0.778026i
$149$	111.673			0.749486			0.374743	−	0.927129i	$-0.377731\pi$
$149$	111.673			0.749486			0.374743	+	0.927129i	$0.377731\pi$
$150$		0			0
$151$		−	6.45275i		−	0.0427335i	−0.999772	−	0.0213667i	$-0.993198\pi$
$151$		−	6.45275i		−	0.0427335i	0.999772	−	0.0213667i	$-0.00680176\pi$
$152$	108.776	−	84.8811i	0.715630	−	0.558428i
$153$		0			0
$154$	25.7450	+	114.656i	0.167175	+	0.744520i
$155$		0			0
$156$		0			0
$157$	75.9075			0.483488			0.241744	−	0.970340i	$-0.422281\pi$
$157$	75.9075			0.483488			0.241744	+	0.970340i	$0.422281\pi$
$158$	275.751	−	61.9174i	1.74526	−	0.391882i
$159$		0			0
$160$		0			0
$161$	−213.471			−1.32591
$162$		0			0
$163$		−	249.298i		−	1.52944i	−0.644364	−	0.764719i	$-0.722878\pi$
$163$		−	249.298i		−	1.52944i	0.644364	−	0.764719i	$-0.277122\pi$
$164$	−159.391	+	75.3799i	−0.971893	+	0.459634i
$165$		0			0
$166$	−136.307	+	30.6064i	−0.821124	+	0.184376i
$167$		−	79.1883i		−	0.474182i	−0.971487	−	0.237091i	$-0.923806\pi$
$167$		−	79.1883i		−	0.474182i	0.971487	−	0.237091i	$-0.0761939\pi$
$168$		0			0
$169$	175.749			1.03993
$170$		0			0
$171$		0			0
$172$	86.0076	+	181.863i	0.500044	+	1.05734i
$173$	−27.7204			−0.160234			−0.0801168	−	0.996785i	$-0.525529\pi$
$173$	−27.7204			−0.160234			−0.0801168	+	0.996785i	$0.525529\pi$
$174$		0			0
$175$		0			0
$176$	114.766	+	94.1982i	0.652080	+	0.535217i
$177$		0			0
$178$	20.2908	+	90.3657i	0.113993	+	0.507673i
$179$		−	204.324i		−	1.14147i	−0.821133	−	0.570737i	$-0.806658\pi$
$179$		−	204.324i		−	1.14147i	0.821133	−	0.570737i	$-0.193342\pi$
$180$		0			0
$181$	−49.8262			−0.275283			−0.137641	−	0.990482i	$-0.543952\pi$
$181$	−49.8262			−0.275283			−0.137641	+	0.990482i	$0.543952\pi$
$182$	−229.413	+	51.5126i	−1.26051	+	0.283036i
$183$		0			0
$184$	−212.640	+	165.929i	−1.15565	+	0.901790i
$185$		0			0
$186$		0			0
$187$			129.089i			0.690317i
$188$	53.2859	+	112.673i	0.283436	+	0.599324i
$189$		0			0
$190$		0			0
$191$			1.13703i			0.00595301i	0.999996	+	0.00297651i	$0.000947453\pi$
$191$			1.13703i			0.00595301i	−0.999996	+	0.00297651i	$0.999053\pi$
$192$		0			0
$193$	76.6452			0.397126			0.198563	−	0.980088i	$-0.436373\pi$
$193$	76.6452			0.397126			0.198563	+	0.980088i	$0.436373\pi$
$194$	−30.0385	−	133.778i	−0.154838	−	0.689575i
$195$		0			0
$196$	−32.2188	+	15.2371i	−0.164382	+	0.0777403i
$197$	134.496			0.682719			0.341359	−	0.939933i	$-0.389113\pi$
$197$	134.496			0.682719			0.341359	+	0.939933i	$0.389113\pi$
$198$		0			0
$199$			176.014i			0.884491i	0.896894	+	0.442245i	$0.145818\pi$
$199$			176.014i			0.884491i	−0.896894	+	0.442245i	$0.854182\pi$
$200$		0			0
$201$		0			0
$202$	19.0144	+	84.6813i	0.0941308	+	0.419214i
$203$		−	181.198i		−	0.892599i
$204$		0			0
$205$		0			0
$206$	167.415	−	37.5916i	0.812695	−	0.182483i
$207$		0			0
$208$	−188.479	+	229.633i	−0.906150	+	1.10400i
$209$	−160.044			−0.765761
$210$		0			0
$211$			218.087i			1.03359i	0.856110	+	0.516793i	$0.172874\pi$
$211$			218.087i			1.03359i	−0.856110	+	0.516793i	$0.827126\pi$
$212$	−295.092	+	139.557i	−1.39194	+	0.658286i
$213$		0			0
$214$	−357.255	+	80.2183i	−1.66941	+	0.374852i
$215$		0			0
$216$		0			0
$217$	−148.755			−0.685508
$218$	35.7021	+	159.001i	0.163771	+	0.729361i
$219$		0			0
$220$		0			0
$221$	−258.292			−1.16874
$222$		0			0
$223$			328.579i			1.47345i	0.676193	+	0.736724i	$0.263628\pi$
$223$			328.579i			1.47345i	−0.676193	+	0.736724i	$0.736372\pi$
$224$	91.1115	−	180.972i	0.406748	−	0.807910i
$225$		0			0
$226$	−75.7222	−	337.231i	−0.335054	−	1.49217i
$227$		−	157.649i		−	0.694491i	−0.937774	−	0.347245i	$-0.887117\pi$
$227$		−	157.649i		−	0.694491i	0.937774	−	0.347245i	$-0.112883\pi$
$228$		0			0
$229$	−273.148			−1.19279			−0.596393	−	0.802692i	$-0.703400\pi$
$229$	−273.148			−1.19279			−0.596393	+	0.802692i	$0.703400\pi$
$230$		0			0
$231$		0			0
$232$	−140.844	−	180.492i	−0.607084	−	0.777983i
$233$	108.746			0.466720			0.233360	−	0.972390i	$-0.425028\pi$
$233$	108.746			0.466720			0.233360	+	0.972390i	$0.425028\pi$
$234$		0			0
$235$		0			0
$236$	−32.9625	−	69.6992i	−0.139672	−	0.295335i
$237$		0			0
$238$	171.880	−	38.5942i	0.722186	−	0.162160i
$239$		−	178.994i		−	0.748927i	−0.927242	−	0.374464i	$-0.877827\pi$
$239$		−	178.994i		−	0.748927i	0.927242	−	0.374464i	$-0.122173\pi$
$240$		0			0
$241$	358.623			1.48806			0.744032	−	0.668144i	$-0.232911\pi$
$241$	358.623			1.48806			0.744032	+	0.668144i	$0.232911\pi$
$242$	15.2872	+	68.0819i	0.0631701	+	0.281330i
$243$		0			0
$244$	192.214	−	90.9029i	0.787762	−	0.372553i
$245$		0			0
$246$		0			0
$247$		−	320.229i		−	1.29647i
$248$	−148.176	+	115.626i	−0.597483	+	0.466235i
$249$		0			0
$250$		0			0
$251$			306.220i			1.22000i	0.792401	+	0.610000i	$0.208831\pi$
$251$			306.220i			1.22000i	−0.792401	+	0.610000i	$0.791169\pi$
$252$		0			0
$253$	312.861			1.23660
$254$	−43.6696	+	9.80560i	−0.171927	+	0.0386047i
$255$		0			0
$256$	−49.9113	−	251.087i	−0.194966	−	0.980810i
$257$	−251.062			−0.976895			−0.488447	−	0.872593i	$-0.662437\pi$
$257$	−251.062			−0.976895			−0.488447	+	0.872593i	$0.662437\pi$
$258$		0			0
$259$		−	426.335i		−	1.64608i
$260$		0			0
$261$		0			0
$262$	3.42112	−	0.768181i	0.0130577	−	0.00293199i
$263$		−	48.7645i		−	0.185416i	−0.995693	−	0.0927082i	$-0.970448\pi$
$263$		−	48.7645i		−	0.185416i	0.995693	−	0.0927082i	$-0.0295524\pi$
$264$		0			0
$265$		0			0
$266$	47.8488	+	213.096i	0.179883	+	0.801113i
$267$		0			0
$268$	−7.69395	−	16.2688i	−0.0287088	−	0.0607046i
$269$	−148.696			−0.552772			−0.276386	−	0.961047i	$-0.589137\pi$
$269$	−148.696			−0.552772			−0.276386	+	0.961047i	$0.589137\pi$
$270$		0			0
$271$			83.3415i			0.307533i	0.988107	+	0.153767i	$0.0491404\pi$
$271$			83.3415i			0.307533i	−0.988107	+	0.153767i	$0.950860\pi$
$272$	141.212	−	172.045i	0.519162	−	0.632519i
$273$		0			0
$274$	−8.54805	−	38.0690i	−0.0311972	−	0.138938i
$275$		0			0
$276$		0			0
$277$	−144.080			−0.520146			−0.260073	−	0.965589i	$-0.583747\pi$
$277$	−144.080			−0.520146			−0.260073	+	0.965589i	$0.583747\pi$
$278$	502.234	−	112.772i	1.80660	−	0.405655i
$279$		0			0
$280$		0			0
$281$	343.671			1.22303			0.611514	−	0.791233i	$-0.290561\pi$
$281$	343.671			1.22303			0.611514	+	0.791233i	$0.290561\pi$
$282$		0			0
$283$		−	314.955i		−	1.11292i	−0.830876	−	0.556458i	$-0.812160\pi$
$283$		−	314.955i		−	1.11292i	0.830876	−	0.556458i	$-0.187840\pi$
$284$	−22.8061	−	48.2233i	−0.0803030	−	0.169800i
$285$		0			0
$286$	336.225	−	75.4964i	1.17561	−	0.263973i
$287$		−	279.094i		−	0.972453i
$288$		0			0
$289$	−95.4831			−0.330391
$290$		0			0
$291$		0			0
$292$	147.860	−	69.9269i	0.506371	−	0.239476i
$293$	−6.55421			−0.0223693			−0.0111847	−	0.999937i	$-0.503560\pi$
$293$	−6.55421			−0.0223693			−0.0111847	+	0.999937i	$0.503560\pi$
$294$		0			0
$295$		0			0
$296$	−331.387	−	424.674i	−1.11955	−	1.43471i
$297$		0			0
$298$	48.9321	+	217.921i	0.164202	+	0.731278i
$299$			625.997i			2.09364i
$300$		0			0
$301$	−318.443			−1.05795
$302$	12.5920	−	2.82741i	0.0416953	−	0.00936229i
$303$		0			0
$304$	213.300	+	175.074i	0.701646	+	0.575900i
$305$		0			0
$306$		0			0
$307$		−	354.559i		−	1.15492i	−0.816420	−	0.577458i	$-0.804045\pi$
$307$		−	354.559i		−	1.15492i	0.816420	−	0.577458i	$-0.195955\pi$
$308$	−212.460	+	100.478i	−0.689807	+	0.326228i
$309$		0			0
$310$		0			0
$311$		−	193.387i		−	0.621823i	−0.950439	−	0.310912i	$-0.899366\pi$
$311$		−	193.387i		−	0.621823i	0.950439	−	0.310912i	$-0.100634\pi$
$312$		0			0
$313$	23.5224			0.0751514			0.0375757	−	0.999294i	$-0.488036\pi$
$313$	23.5224			0.0751514			0.0375757	+	0.999294i	$0.488036\pi$
$314$	33.2605	+	148.127i	0.105925	+	0.471742i
$315$		0			0
$316$	241.653	+	510.973i	0.764724	+	1.61700i
$317$	−214.004			−0.675092			−0.337546	−	0.941309i	$-0.609597\pi$
$317$	−214.004			−0.675092			−0.337546	+	0.941309i	$0.609597\pi$
$318$		0			0
$319$			265.562i			0.832481i
$320$		0			0
$321$		0			0
$322$	−93.5369	−	416.570i	−0.290487	−	1.29369i
$323$			239.921i			0.742790i
$324$		0			0
$325$		0			0
$326$	486.483	−	109.235i	1.49228	−	0.335078i
$327$		0			0
$328$	−216.938	−	278.007i	−0.661395	−	0.847583i
$329$	−197.291			−0.599669
$330$		0			0
$331$		−	412.454i		−	1.24609i	−0.782188	−	0.623043i	$-0.785896\pi$
$331$		−	412.454i		−	1.24609i	0.782188	−	0.623043i	$-0.214104\pi$
$332$	−119.451	−	252.579i	−0.359793	−	0.760782i
$333$		0			0
$334$	154.529	−	34.6981i	0.462662	−	0.103886i
$335$		0			0
$336$		0			0
$337$	−103.268			−0.306433			−0.153216	−	0.988193i	$-0.548963\pi$
$337$	−103.268			−0.306433			−0.153216	+	0.988193i	$0.548963\pi$
$338$	77.0081	+	342.958i	0.227835	+	1.01467i
$339$		0			0
$340$		0			0
$341$	218.014			0.639338
$342$		0			0
$343$		−	366.667i		−	1.06900i
$344$	−317.203	+	247.523i	−0.922102	+	0.719545i
$345$		0			0
$346$	−12.1463	−	54.0939i	−0.0351049	−	0.156341i
$347$		−	153.211i		−	0.441531i	−0.975327	−	0.220766i	$-0.929144\pi$
$347$		−	153.211i		−	0.441531i	0.975327	−	0.220766i	$-0.0708556\pi$
$348$		0			0
$349$	−84.7317			−0.242784			−0.121392	−	0.992605i	$-0.538736\pi$
$349$	−84.7317			−0.242784			−0.121392	+	0.992605i	$0.538736\pi$
$350$		0			0
$351$		0			0
$352$	−133.532	+	265.231i	−0.379353	+	0.753496i
$353$	256.065			0.725396			0.362698	−	0.931907i	$-0.381856\pi$
$353$	256.065			0.725396			0.362698	+	0.931907i	$0.381856\pi$
$354$		0			0
$355$		0			0
$356$	−167.450	+	79.1914i	−0.470365	+	0.222448i
$357$		0			0
$358$	398.720	−	89.5289i	1.11374	−	0.250081i
$359$		−	667.258i		−	1.85866i	−0.369253	−	0.929329i	$-0.620386\pi$
$359$		−	667.258i		−	1.85866i	0.369253	−	0.929329i	$-0.379614\pi$
$360$		0			0
$361$	63.5473			0.176031
$362$	−21.8324	−	97.2314i	−0.0603106	−	0.268595i
$363$		0			0
$364$	−201.044	−	425.108i	−0.552320	−	1.16788i
$365$		0			0
$366$		0			0
$367$			245.301i			0.668396i	0.942503	+	0.334198i	$0.108465\pi$
$367$			245.301i			0.668396i	−0.942503	+	0.334198i	$0.891535\pi$
$368$	−416.969	−	342.242i	−1.13307	−	0.930005i
$369$		0			0
$370$		0			0
$371$		−	516.708i		−	1.39274i
$372$		0			0
$373$	−698.787			−1.87342			−0.936712	−	0.350101i	$-0.886147\pi$
$373$	−698.787			−1.87342			−0.936712	+	0.350101i	$0.886147\pi$
$374$	−251.906	+	56.5632i	−0.673546	+	0.151239i
$375$		0			0
$376$	−196.523	+	153.353i	−0.522667	+	0.407853i
$377$	−531.357			−1.40943
$378$		0			0
$379$		−	208.691i		−	0.550636i	−0.961353	−	0.275318i	$-0.911217\pi$
$379$		−	208.691i		−	0.550636i	0.961353	−	0.275318i	$-0.0887831\pi$
$380$		0			0
$381$		0			0
$382$	−2.21880	+	0.498212i	−0.00580839	+	0.00130422i
$383$			156.524i			0.408680i	0.978900	+	0.204340i	$0.0655048\pi$
$383$			156.524i			0.408680i	−0.978900	+	0.204340i	$0.934495\pi$
$384$		0			0
$385$		0			0
$386$	33.5838	+	149.566i	0.0870046	+	0.387478i
$387$		0			0
$388$	247.893	−	117.235i	0.638900	−	0.302152i
$389$	−386.588			−0.993801			−0.496900	−	0.867808i	$-0.665529\pi$
$389$	−386.588			−0.993801			−0.496900	+	0.867808i	$0.665529\pi$
$390$		0			0
$391$		−	469.008i		−	1.19951i
$392$	−43.8512	−	56.1956i	−0.111865	−	0.143356i
$393$		0			0
$394$	58.9322	+	262.456i	0.149574	+	0.666133i
$395$		0			0
$396$		0			0
$397$	561.155			1.41349			0.706744	−	0.707470i	$-0.250163\pi$
$397$	561.155			1.41349			0.706744	+	0.707470i	$0.250163\pi$
$398$	−343.475	+	77.1242i	−0.863002	+	0.193779i
$399$		0			0
$400$		0			0
$401$	−16.9333			−0.0422276			−0.0211138	−	0.999777i	$-0.506721\pi$
$401$	−16.9333			−0.0422276			−0.0211138	+	0.999777i	$0.506721\pi$
$402$		0			0
$403$			436.220i			1.08243i
$404$	−156.917	+	74.2099i	−0.388407	+	0.183688i
$405$		0			0
$406$	353.591	−	79.3957i	0.870914	−	0.195556i
$407$			624.832i			1.53521i
$408$		0			0
$409$	258.490			0.632006			0.316003	−	0.948758i	$-0.397659\pi$
$409$	258.490			0.632006			0.316003	+	0.948758i	$0.397659\pi$
$410$		0			0
$411$		0			0
$412$	146.713	+	310.224i	0.356100	+	0.752972i
$413$	122.044			0.295505
$414$		0			0
$415$		0			0
$416$	−530.694	−	267.182i	−1.27571	−	0.642264i
$417$		0			0
$418$	−70.1267	−	312.312i	−0.167767	−	0.747157i
$419$			258.917i			0.617941i	0.951072	+	0.308970i	$0.0999844\pi$
$419$			258.917i			0.617941i	−0.951072	+	0.308970i	$0.900016\pi$
$420$		0			0
$421$	97.4654			0.231509			0.115755	−	0.993278i	$-0.463071\pi$
$421$	97.4654			0.231509			0.115755	+	0.993278i	$0.463071\pi$
$422$	−425.577	+	95.5594i	−1.00848	+	0.226444i
$423$		0			0
$424$	−401.633	−	514.696i	−0.947248	−	1.21390i
$425$		0			0
$426$		0			0
$427$			336.568i			0.788215i
$428$	−313.078	−	662.002i	−0.731490	−	1.54673i
$429$		0			0
$430$		0			0
$431$			389.968i			0.904799i	0.891815	+	0.452399i	$0.149432\pi$
$431$			389.968i			0.904799i	−0.891815	+	0.452399i	$0.850568\pi$
$432$		0			0
$433$	−275.893			−0.637166			−0.318583	−	0.947895i	$-0.603207\pi$
$433$	−275.893			−0.637166			−0.318583	+	0.947895i	$0.603207\pi$
$434$	−65.1803	−	290.283i	−0.150185	−	0.668854i
$435$		0			0
$436$	−294.632	+	139.339i	−0.675761	+	0.319585i
$437$	581.473			1.33060
$438$		0			0
$439$			446.143i			1.01627i	0.861277	+	0.508136i	$0.169665\pi$
$439$			446.143i			1.01627i	−0.861277	+	0.508136i	$0.830335\pi$
$440$		0			0
$441$		0			0
$442$	−113.176	−	504.034i	−0.256055	−	1.14035i
$443$			794.679i			1.79386i	0.442174	+	0.896929i	$0.354207\pi$
$443$			794.679i			1.79386i	−0.442174	+	0.896929i	$0.645793\pi$
$444$		0			0
$445$		0			0
$446$	−641.193	+	143.974i	−1.43765	+	0.322812i
$447$		0			0
$448$	393.073	+	98.4993i	0.877395	+	0.219865i
$449$	750.226			1.67088			0.835441	−	0.549581i	$-0.185212\pi$
$449$	750.226			1.67088			0.835441	+	0.549581i	$0.185212\pi$
$450$		0			0
$451$			409.037i			0.906957i
$452$	624.898	−	295.530i	1.38252	−	0.653828i
$453$		0			0
$454$	307.639	−	69.0775i	0.677619	−	0.152153i
$455$		0			0
$456$		0			0
$457$	−101.092			−0.221209			−0.110604	−	0.993865i	$-0.535279\pi$
$457$	−101.092			−0.221209			−0.110604	+	0.993865i	$0.535279\pi$
$458$	−119.686	−	533.024i	−0.261323	−	1.16381i
$459$		0			0
$460$		0			0
$461$	4.48690			0.00973297			0.00486648	−	0.999988i	$-0.498451\pi$
$461$	4.48690			0.00973297			0.00486648	+	0.999988i	$0.498451\pi$
$462$		0			0
$463$			515.108i			1.11254i	0.831000	+	0.556272i	$0.187769\pi$
$463$			515.108i			1.11254i	−0.831000	+	0.556272i	$0.812231\pi$
$464$	290.500	−	353.930i	0.626079	−	0.762780i
$465$		0			0
$466$	47.6493	+	212.208i	0.102252	+	0.455382i
$467$			295.498i			0.632758i	0.948633	+	0.316379i	$0.102467\pi$
$467$			295.498i			0.632758i	−0.948633	+	0.316379i	$0.897533\pi$
$468$		0			0
$469$	28.4869			0.0607396
$470$		0			0
$471$		0			0
$472$	121.568	−	94.8637i	0.257560	−	0.200982i
$473$	466.707			0.986696
$474$		0			0
$475$		0			0
$476$	150.626	+	318.498i	0.316441	+	0.669114i
$477$		0			0
$478$	349.290	−	78.4299i	0.730732	−	0.164079i
$479$			273.155i			0.570260i	0.958489	+	0.285130i	$0.0920368\pi$
$479$			273.155i			0.570260i	−0.958489	+	0.285130i	$0.907963\pi$
$480$		0			0
$481$	−1250.21			−2.59920
$482$	157.139	+	699.822i	0.326014	+	1.45191i
$483$		0			0
$484$	−126.157	+	59.6631i	−0.260656	+	0.123271i
$485$		0			0
$486$		0			0
$487$			357.751i			0.734601i	0.930102	+	0.367301i	$0.119718\pi$
$487$			357.751i			0.734601i	−0.930102	+	0.367301i	$0.880282\pi$
$488$	261.612	+	335.257i	0.536089	+	0.687002i
$489$		0			0
$490$		0			0
$491$		−	422.379i		−	0.860242i	−0.902771	−	0.430121i	$-0.858471\pi$
$491$		−	422.379i		−	0.860242i	0.902771	−	0.430121i	$-0.141529\pi$
$492$		0			0
$493$	398.102			0.807509
$494$	624.898	−	140.315i	1.26498	−	0.284039i
$495$		0			0
$496$	−290.561	−	238.488i	−0.585808	−	0.480822i
$497$	84.4394			0.169898
$498$		0			0
$499$			207.096i			0.415021i	0.978233	+	0.207511i	$0.0665362\pi$
$499$			207.096i			0.415021i	−0.978233	+	0.207511i	$0.933464\pi$
$500$		0			0
$501$		0			0
$502$	−597.562	+	134.177i	−1.19036	+	0.267285i
$503$		−	702.853i		−	1.39732i	−0.715452	−	0.698661i	$-0.753779\pi$
$503$		−	702.853i		−	1.39732i	0.715452	−	0.698661i	$-0.246221\pi$
$504$		0			0
$505$		0			0
$506$	137.087	+	610.520i	0.270923	+	1.20656i
$507$		0			0
$508$	−38.2695	−	80.9207i	−0.0753337	−	0.159293i
$509$	389.029			0.764300			0.382150	−	0.924100i	$-0.375184\pi$
$509$	389.029			0.764300			0.382150	+	0.924100i	$0.375184\pi$
$510$		0			0
$511$			258.904i			0.506662i
$512$	468.105	−	207.417i	0.914267	−	0.405111i
$513$		0			0
$514$	−110.008	−	489.925i	−0.214024	−	0.953162i
$515$		0			0
$516$		0			0
$517$	289.148			0.559280
$518$	831.954	−	186.808i	1.60609	−	0.360633i
$519$		0			0
$520$		0			0
$521$	151.753			0.291273			0.145637	−	0.989338i	$-0.453477\pi$
$521$	151.753			0.291273			0.145637	+	0.989338i	$0.453477\pi$
$522$		0			0
$523$			557.762i			1.06647i	0.845968	+	0.533234i	$0.179023\pi$
$523$			557.762i			1.06647i	−0.845968	+	0.533234i	$0.820977\pi$
$524$	2.99807	+	6.33941i	0.00572151	+	0.0120981i
$525$		0			0
$526$	95.1596	−	21.3672i	0.180912	−	0.0406221i
$527$		−	326.824i		−	0.620159i
$528$		0			0
$529$	−607.689			−1.14875
$530$		0			0
$531$		0			0
$532$	−394.872	+	186.745i	−0.742241	+	0.351025i
$533$	−818.435			−1.53552
$534$		0			0
$535$		0			0
$536$	28.3759	−	22.1426i	0.0529401	−	0.0413108i
$537$		0			0
$538$	−65.1542	−	290.166i	−0.121104	−	0.539342i
$539$			82.6818i			0.153398i
$540$		0			0
$541$	340.979			0.630275			0.315137	−	0.949046i	$-0.397949\pi$
$541$	340.979			0.630275			0.315137	+	0.949046i	$0.397949\pi$
$542$	−162.633	+	36.5179i	−0.300062	+	0.0673761i
$543$		0			0
$544$	397.606	+	200.177i	0.730893	+	0.367973i
$545$		0			0
$546$		0			0
$547$		−	113.651i		−	0.207771i	−0.994589	−	0.103885i	$-0.966872\pi$
$547$		−	113.651i		−	0.207771i	0.994589	−	0.103885i	$-0.0331275\pi$
$548$	70.5428	−	33.3615i	0.128728	−	0.0608787i
$549$		0			0
$550$		0			0
$551$			493.564i			0.895761i
$552$		0			0
$553$	−894.718			−1.61794
$554$	−63.1319	−	281.160i	−0.113957	−	0.507509i
$555$		0			0
$556$	440.129	+	930.651i	0.791599	+	1.67383i
$557$	233.232			0.418728			0.209364	−	0.977838i	$-0.432861\pi$
$557$	233.232			0.418728			0.209364	+	0.977838i	$0.432861\pi$
$558$		0			0
$559$			933.825i			1.67053i
$560$		0			0
$561$		0			0
$562$	150.587	+	670.644i	0.267948	+	1.19332i
$563$			167.786i			0.298021i	0.988836	+	0.149011i	$0.0476088\pi$
$563$			167.786i			0.298021i	−0.988836	+	0.149011i	$0.952391\pi$
$564$		0			0
$565$		0			0
$566$	614.607	−	138.004i	1.08588	−	0.243824i
$567$		0			0
$568$	84.1105	−	65.6341i	0.148082	−	0.115553i
$569$	−381.089			−0.669752			−0.334876	−	0.942262i	$-0.608694\pi$
$569$	−381.089			−0.669752			−0.334876	+	0.942262i	$0.608694\pi$
$570$		0			0
$571$		−	453.871i		−	0.794870i	−0.917630	−	0.397435i	$-0.869900\pi$
$571$		−	453.871i		−	0.794870i	0.917630	−	0.397435i	$-0.130100\pi$
$572$	294.649	+	623.034i	0.515120	+	1.08922i
$573$		0			0
$574$	544.627	−	122.291i	0.948828	−	0.213051i
$575$		0			0
$576$		0			0
$577$	−688.294			−1.19288			−0.596442	−	0.802656i	$-0.703419\pi$
$577$	−688.294			−1.19288			−0.596442	+	0.802656i	$0.703419\pi$
$578$	−41.8380	−	186.327i	−0.0723841	−	0.322365i
$579$		0			0
$580$		0			0
$581$	442.269			0.761220
$582$		0			0
$583$			757.282i			1.29894i
$584$	201.244	+	257.896i	0.344597	+	0.441603i
$585$		0			0
$586$	−2.87187	−	12.7900i	−0.00490080	−	0.0218259i
$587$		−	249.163i		−	0.424468i	−0.977219	−	0.212234i	$-0.931926\pi$
$587$		−	249.163i		−	0.424468i	0.977219	−	0.212234i	$-0.0680739\pi$
$588$		0			0
$589$	405.194			0.687936
$590$		0			0
$591$		0			0
$592$	683.510	−	832.752i	1.15458	−	1.40668i
$593$	−163.937			−0.276454			−0.138227	−	0.990401i	$-0.544140\pi$
$593$	−163.937			−0.276454			−0.138227	+	0.990401i	$0.544140\pi$
$594$		0			0
$595$		0			0
$596$	−403.812	+	190.973i	−0.677538	+	0.320425i
$597$		0			0
$598$	−1221.58	+	274.294i	−2.04277	+	0.458686i
$599$			170.412i			0.284494i	0.989831	+	0.142247i	$0.0454327\pi$
$599$			170.412i			0.284494i	−0.989831	+	0.142247i	$0.954567\pi$
$600$		0			0
$601$	1119.87			1.86335			0.931674	−	0.363295i	$-0.118348\pi$
$601$	1119.87			1.86335			0.931674	+	0.363295i	$0.118348\pi$
$602$	−139.533	−	621.413i	−0.231782	−	1.03225i
$603$		0			0
$604$	11.0349	+	23.3332i	0.0182697	+	0.0386312i
$605$		0			0
$606$		0			0
$607$			660.957i			1.08889i	0.838796	+	0.544445i	$0.183260\pi$
$607$			660.957i			1.08889i	−0.838796	+	0.544445i	$0.816740\pi$
$608$	−248.179	+	492.949i	−0.408189	+	0.810772i
$609$		0			0
$610$		0			0
$611$			578.550i			0.946890i
$612$		0			0
$613$	179.315			0.292520			0.146260	−	0.989246i	$-0.453276\pi$
$613$	179.315			0.292520			0.146260	+	0.989246i	$0.453276\pi$
$614$	691.891	−	155.358i	1.12686	−	0.253026i
$615$		0			0
$616$	−289.168	−	370.571i	−0.469429	−	0.601576i
$617$	−63.6752			−0.103201			−0.0516007	−	0.998668i	$-0.516432\pi$
$617$	−63.6752			−0.103201			−0.0516007	+	0.998668i	$0.516432\pi$
$618$		0			0
$619$			872.350i			1.40929i	0.709561	+	0.704644i	$0.248893\pi$
$619$			872.350i			1.40929i	−0.709561	+	0.704644i	$0.751107\pi$
$620$		0			0
$621$		0			0
$622$	377.378	−	84.7367i	0.606716	−	0.136233i
$623$		−	293.206i		−	0.470636i
$624$		0			0
$625$		0			0
$626$	10.3068	+	45.9019i	0.0164646	+	0.0733257i
$627$		0			0
$628$	−274.483	+	129.810i	−0.437074	+	0.206704i
$629$	936.682			1.48916
$630$		0			0
$631$		−	340.783i		−	0.540068i	−0.962851	−	0.270034i	$-0.912965\pi$
$631$		−	340.783i		−	0.540068i	0.962851	−	0.270034i	$-0.0870349\pi$
$632$	−891.234	+	695.458i	−1.41018	+	1.10041i
$633$		0			0
$634$	−93.7705	−	417.610i	−0.147903	−	0.658691i
$635$		0			0
$636$		0			0
$637$	−165.436			−0.259712
$638$	−518.220	+	116.362i	−0.812257	+	0.182385i
$639$		0			0
$640$		0			0
$641$	−766.210			−1.19534			−0.597668	−	0.801744i	$-0.703906\pi$
$641$	−766.210			−1.19534			−0.597668	+	0.801744i	$0.703906\pi$
$642$		0			0
$643$		−	1163.47i		−	1.80943i	−0.426014	−	0.904717i	$-0.640083\pi$
$643$		−	1163.47i		−	1.80943i	0.426014	−	0.904717i	$-0.359917\pi$
$644$	771.913	−	365.058i	1.19862	−	0.566860i
$645$		0			0
$646$	−468.185	+	105.127i	−0.724744	+	0.162735i
$647$			740.530i			1.14456i	0.820059	+	0.572279i	$0.193941\pi$
$647$			740.530i			1.14456i	−0.820059	+	0.572279i	$0.806059\pi$
$648$		0			0
$649$	−178.866			−0.275603
$650$		0			0
$651$		0			0
$652$	426.326	+	901.465i	0.653875	+	1.38262i
$653$	109.569			0.167793			0.0838967	−	0.996474i	$-0.473263\pi$
$653$	109.569			0.167793			0.0838967	+	0.996474i	$0.473263\pi$
$654$		0			0
$655$		0			0
$656$	447.450	−	545.149i	0.682089	−	0.831020i
$657$		0			0
$658$	−86.4473	−	384.996i	−0.131379	−	0.585100i
$659$			723.214i			1.09744i	0.836006	+	0.548721i	$0.184885\pi$
$659$			723.214i			1.09744i	−0.836006	+	0.548721i	$0.815115\pi$
$660$		0			0
$661$	700.333			1.05951			0.529753	−	0.848152i	$-0.322285\pi$
$661$	700.333			1.05951			0.529753	+	0.848152i	$0.322285\pi$
$662$	804.868	−	180.726i	1.21581	−	0.273000i
$663$		0			0
$664$	440.546	−	343.772i	0.663473	−	0.517729i
$665$		0			0
$666$		0			0
$667$		−	964.841i		−	1.44654i
$668$	135.420	+	286.346i	0.202725	+	0.428662i
$669$		0			0
$670$		0			0
$671$		−	493.271i		−	0.735128i
$672$		0			0
$673$	1221.18			1.81454			0.907269	−	0.420552i	$-0.138163\pi$
$673$	1221.18			1.81454			0.907269	+	0.420552i	$0.138163\pi$
$674$	−45.2490	−	201.518i	−0.0671350	−	0.298988i
$675$		0			0
$676$	−635.509	+	300.549i	−0.940103	+	0.444599i
$677$	989.373			1.46141			0.730704	−	0.682695i	$-0.239192\pi$
$677$	989.373			1.46141			0.730704	+	0.682695i	$0.239192\pi$
$678$		0			0
$679$			434.063i			0.639268i
$680$		0			0
$681$		0			0
$682$	95.5276	+	425.435i	0.140070	+	0.623806i
$683$			307.312i			0.449945i	0.974365	+	0.224972i	$0.0722292\pi$
$683$			307.312i			0.449945i	−0.974365	+	0.224972i	$0.927771\pi$
$684$		0			0
$685$		0			0
$686$	715.518	−	160.663i	1.04303	−	0.234203i
$687$		0			0
$688$	−622.009	−	510.536i	−0.904083	−	0.742058i
$689$	−1515.23			−2.19917
$690$		0			0
$691$			893.378i			1.29288i	0.762966	+	0.646438i	$0.223742\pi$
$691$			893.378i			1.29288i	−0.762966	+	0.646438i	$0.776258\pi$
$692$	100.237	−	47.4048i	0.144852	−	0.0685041i
$693$		0			0
$694$	298.978	−	67.1329i	0.430805	−	0.0967332i
$695$		0			0
$696$		0			0
$697$	613.186			0.879750
$698$	−37.1270	−	165.346i	−0.0531906	−	0.236886i
$699$		0			0
$700$		0			0
$701$	−1127.42			−1.60830			−0.804149	−	0.594428i	$-0.797378\pi$
$701$	−1127.42			−1.60830			−0.804149	+	0.594428i	$0.797378\pi$
$702$		0			0
$703$			1161.29i			1.65191i
$704$	−576.084	−	144.360i	−0.818301	−	0.205056i
$705$		0			0
$706$	112.200	+	499.688i	0.158924	+	0.707773i
$707$		−	274.762i		−	0.388631i
$708$		0			0
$709$	1093.27			1.54199			0.770997	−	0.636839i	$-0.219758\pi$
$709$	1093.27			1.54199			0.770997	+	0.636839i	$0.219758\pi$
$710$		0			0
$711$		0			0
$712$	−227.907	−	292.064i	−0.320094	−	0.410202i
$713$	−792.091			−1.11093
$714$		0			0
$715$		0			0
$716$	349.415	+	738.837i	0.488010	+	1.03190i
$717$		0			0
$718$	1302.10	−	292.374i	1.81350	−	0.407206i
$719$			769.690i			1.07050i	0.844693	+	0.535251i	$0.179783\pi$
$719$			769.690i			1.07050i	−0.844693	+	0.535251i	$0.820217\pi$
$720$		0			0
$721$	−543.205			−0.753405
$722$	27.8446	+	124.007i	0.0385660	+	0.171755i
$723$		0			0
$724$	180.172	−	85.2081i	0.248857	−	0.117691i
$725$		0			0
$726$		0			0
$727$		−	295.050i		−	0.405846i	−0.979195	−	0.202923i	$-0.934956\pi$
$727$		−	295.050i		−	0.405846i	0.979195	−	0.202923i	$-0.0650441\pi$
$728$	741.468	−	578.591i	1.01850	−	0.794767i
$729$		0			0
$730$		0			0
$731$		−	699.638i		−	0.957097i
$732$		0			0
$733$	−261.200			−0.356344			−0.178172	−	0.983999i	$-0.557018\pi$
$733$	−261.200			−0.356344			−0.178172	+	0.983999i	$0.557018\pi$
$734$	−478.684	+	107.484i	−0.652158	+	0.146436i
$735$		0			0
$736$	485.150	−	963.638i	0.659172	−	1.30929i
$737$	−41.7501			−0.0566487
$738$		0			0
$739$		−	482.679i		−	0.653151i	−0.945171	−	0.326576i	$-0.894105\pi$
$739$		−	482.679i		−	0.653151i	0.945171	−	0.326576i	$-0.105895\pi$
$740$		0			0
$741$		0			0
$742$	1008.31	−	226.407i	1.35891	−	0.305130i
$743$		−	23.7067i		−	0.0319067i	−0.999873	−	0.0159534i	$-0.994922\pi$
$743$		−	23.7067i		−	0.0319067i	0.999873	−	0.0159534i	$-0.00507833\pi$
$744$		0			0
$745$		0			0
$746$	−306.189	−	1363.62i	−0.410441	−	1.82791i
$747$		0			0
$748$	−220.756	−	466.788i	−0.295129	−	0.624048i
$749$	1159.17			1.54762
$750$		0			0
$751$		−	395.508i		−	0.526642i	−0.964708	−	0.263321i	$-0.915182\pi$
$751$		−	395.508i		−	0.526642i	0.964708	−	0.263321i	$-0.0848179\pi$
$752$	−385.365	−	316.302i	−0.512453	−	0.420614i
$753$		0			0
$754$	−232.825	−	1036.90i	−0.308787	−	1.37519i
$755$		0			0
$756$		0			0
$757$	−393.940			−0.520396			−0.260198	−	0.965555i	$-0.583788\pi$
$757$	−393.940			−0.520396			−0.260198	+	0.965555i	$0.583788\pi$
$758$	407.242	−	91.4425i	0.537259	−	0.120637i
$759$		0			0
$760$		0			0
$761$	369.354			0.485354			0.242677	−	0.970107i	$-0.421975\pi$
$761$	369.354			0.485354			0.242677	+	0.970107i	$0.421975\pi$
$762$		0			0
$763$		−	515.903i		−	0.676150i
$764$	−1.94443	−	4.11150i	−0.00254507	−	0.00538154i
$765$		0			0
$766$	−305.444	+	68.5846i	−0.398751	+	0.0895360i
$767$		−	357.890i		−	0.466610i
$768$		0			0
$769$	−873.491			−1.13588			−0.567940	−	0.823070i	$-0.692259\pi$
$769$	−873.491			−1.13588			−0.567940	+	0.823070i	$0.692259\pi$
$770$		0			0
$771$		0			0
$772$	−277.150	+	131.071i	−0.359003	+	0.169782i
$773$	−1176.93			−1.52254			−0.761272	−	0.648432i	$-0.775425\pi$
$773$	−1176.93			−1.52254			−0.761272	+	0.648432i	$0.775425\pi$
$774$		0			0
$775$		0			0
$776$	337.394	+	432.372i	0.434786	+	0.557181i
$777$		0			0
$778$	−169.392	−	754.393i	−0.217728	−	0.969657i
$779$			760.224i			0.975897i
$780$		0			0
$781$	−123.754			−0.158455
$782$	915.228	−	205.506i	1.17037	−	0.262795i
$783$		0			0
$784$	90.4464	−	110.195i	0.115365	−	0.140555i
$785$		0			0
$786$		0			0
$787$			603.482i			0.766814i	0.923580	+	0.383407i	$0.125249\pi$
$787$			603.482i			0.766814i	−0.923580	+	0.383407i	$0.874751\pi$
$788$	−486.338	+	230.002i	−0.617180	+	0.291880i
$789$		0			0
$790$		0			0
$791$			1094.20i			1.38331i
$792$		0			0
$793$	986.975			1.24461
$794$	245.882	+	1095.04i	0.309675	+	1.37915i
$795$		0			0
$796$	−301.002	−	636.467i	−0.378143	−	0.799582i
$797$	860.121			1.07920			0.539599	−	0.841922i	$-0.318576\pi$
$797$	860.121			1.07920			0.539599	+	0.841922i	$0.318576\pi$
$798$		0			0
$799$		−	433.460i		−	0.542503i
$800$		0			0
$801$		0			0
$802$	−7.41967	−	33.0437i	−0.00925146	−	0.0412017i
$803$		−	379.448i		−	0.472538i
$804$		0			0
$805$		0			0
$806$	−851.245	+	191.139i	−1.05614	+	0.237145i
$807$		0			0
$808$	−213.570	−	273.692i	−0.264320	−	0.338728i
$809$	−941.012			−1.16318			−0.581589	−	0.813483i	$-0.697569\pi$
$809$	−941.012			−1.16318			−0.581589	+	0.813483i	$0.697569\pi$
$810$		0			0
$811$		−	1105.29i		−	1.36287i	−0.731878	−	0.681436i	$-0.761356\pi$
$811$		−	1105.29i		−	1.36287i	0.731878	−	0.681436i	$-0.238644\pi$
$812$	309.867	+	655.213i	0.381610	+	0.806912i
$813$		0			0
$814$	−1219.30	+	273.784i	−1.49792	+	0.336344i
$815$		0			0
$816$		0			0
$817$	867.407			1.06170
$818$	113.263	+	504.421i	0.138463	+	0.616652i
$819$		0			0
$820$		0			0
$821$	193.170			0.235286			0.117643	−	0.993056i	$-0.462466\pi$
$821$	193.170			0.235286			0.117643	+	0.993056i	$0.462466\pi$
$822$		0			0
$823$			178.778i			0.217227i	0.994084	+	0.108614i	$0.0346411\pi$
$823$			178.778i			0.217227i	−0.994084	+	0.108614i	$0.965359\pi$
$824$	−541.090	+	422.229i	−0.656662	+	0.512414i
$825$		0			0
$826$	53.4761	+	238.158i	0.0647410	+	0.288326i
$827$			1558.61i			1.88465i	0.334697	+	0.942326i	$0.391366\pi$
$827$			1558.61i			1.88465i	−0.334697	+	0.942326i	$0.608634\pi$
$828$		0			0
$829$	−565.477			−0.682119			−0.341059	−	0.940042i	$-0.610786\pi$
$829$	−565.477			−0.682119			−0.341059	+	0.940042i	$0.610786\pi$
$830$		0			0
$831$		0			0
$832$	288.846	−	1152.67i	0.347171	−	1.38543i
$833$	123.948			0.148797
$834$		0			0
$835$		0			0
$836$	578.721	−	273.692i	0.692250	−	0.327383i
$837$		0			0
$838$	−505.254	+	113.450i	−0.602928	+	0.135382i
$839$		−	1280.25i		−	1.52592i	−0.646443	−	0.762962i	$-0.723744\pi$
$839$		−	1280.25i		−	1.52592i	0.646443	−	0.762962i	$-0.276256\pi$
$840$		0			0
$841$	−22.0271			−0.0261915
$842$	42.7066	+	190.195i	0.0507204	+	0.225885i
$843$		0			0
$844$	−372.952	−	788.604i	−0.441886	−	0.934365i
$845$		0			0
$846$		0			0
$847$		−	220.903i		−	0.260806i
$848$	828.398	−	1009.28i	0.976885	−	1.19018i
$849$		0			0
$850$		0			0
$851$		−	2270.15i		−	2.66762i
$852$		0			0
$853$	−120.366			−0.141109			−0.0705546	−	0.997508i	$-0.522477\pi$
$853$	−120.366			−0.141109			−0.0705546	+	0.997508i	$0.522477\pi$
$854$	−656.782	+	147.474i	−0.769066	+	0.172687i
$855$		0			0
$856$	1154.66	−	901.014i	1.34890	−	1.05259i
$857$	−717.784			−0.837554			−0.418777	−	0.908089i	$-0.637541\pi$
$857$	−717.784			−0.837554			−0.418777	+	0.908089i	$0.637541\pi$
$858$		0			0
$859$			252.894i			0.294405i	0.989106	+	0.147203i	$0.0470269\pi$
$859$			252.894i			0.294405i	−0.989106	+	0.147203i	$0.952973\pi$
$860$		0			0
$861$		0			0
$862$	−760.989	+	170.873i	−0.882817	+	0.198229i
$863$			1234.73i			1.43075i	0.698743	+	0.715373i	$0.253743\pi$
$863$			1234.73i			1.43075i	−0.698743	+	0.715373i	$0.746257\pi$
$864$		0			0
$865$		0			0
$866$	−120.888	−	538.381i	−0.139594	−	0.621687i
$867$		0			0
$868$	537.901	−	254.387i	0.619701	−	0.293073i
$869$	1311.29			1.50897
$870$		0			0
$871$		−	83.5368i		−	0.0959091i
$872$	−401.007	−	513.894i	−0.459871	−	0.589327i
$873$		0			0
$874$	254.785	+	1134.69i	0.291516	+	1.29828i
$875$		0			0
$876$		0			0
$877$	685.723			0.781896			0.390948	−	0.920413i	$-0.372147\pi$
$877$	685.723			0.781896			0.390948	+	0.920413i	$0.372147\pi$
$878$	−870.609	+	195.487i	−0.991582	+	0.222651i
$879$		0			0
$880$		0			0
$881$	458.454			0.520379			0.260189	−	0.965558i	$-0.416215\pi$
$881$	458.454			0.520379			0.260189	+	0.965558i	$0.416215\pi$
$882$		0			0
$883$			771.505i			0.873732i	0.899527	+	0.436866i	$0.143912\pi$
$883$			771.505i			0.873732i	−0.899527	+	0.436866i	$0.856088\pi$
$884$	933.986	−	441.707i	1.05655	−	0.499668i
$885$		0			0
$886$	−1550.75	+	348.206i	−1.75028	+	0.393009i
$887$		−	1161.05i		−	1.30896i	−0.756080	−	0.654480i	$-0.772888\pi$
$887$		−	1161.05i		−	1.30896i	0.756080	−	0.654480i	$-0.227112\pi$
$888$		0			0
$889$	141.693			0.159385
$890$		0			0
$891$		0			0
$892$	−561.905	−	1188.15i	−0.629938	−	1.33200i
$893$	537.401			0.601793
$894$		0			0
$895$		0			0
$896$	−19.9793	+	810.207i	−0.0222983	+	0.904248i
$897$		0			0
$898$	328.728	+	1464.00i	0.366066	+	1.63029i
$899$		−	672.340i		−	0.747876i
$900$		0			0
$901$	1135.24			1.25997
$902$	−798.200	+	179.229i	−0.884923	+	0.198701i
$903$		0			0
$904$	850.514	+	1089.94i	0.940834	+	1.20569i
$905$		0			0
$906$		0			0
$907$		−	392.544i		−	0.432793i	−0.976306	−	0.216397i	$-0.930570\pi$
$907$		−	392.544i		−	0.432793i	0.976306	−	0.216397i	$-0.0694304\pi$
$908$	269.597	+	570.062i	0.296913	+	0.627822i
$909$		0			0
$910$		0			0
$911$		−	1013.40i		−	1.11240i	−0.831048	−	0.556201i	$-0.812259\pi$
$911$		−	1013.40i		−	1.11240i	0.831048	−	0.556201i	$-0.187741\pi$
$912$		0			0
$913$	−648.185			−0.709950
$914$	−44.2958	−	197.273i	−0.0484637	−	0.215835i
$915$		0			0
$916$	987.707	−	467.112i	1.07828	−	0.509948i
$917$	−11.1004			−0.0121051
$918$		0			0
$919$		−	970.018i		−	1.05551i	−0.849395	−	0.527757i	$-0.823033\pi$
$919$		−	970.018i		−	1.05551i	0.849395	−	0.527757i	$-0.176967\pi$
$920$		0			0
$921$		0			0
$922$	1.96603	+	8.75578i	0.00213236	+	0.00949651i
$923$		−	247.616i		−	0.268273i
$924$		0			0
$925$		0			0
$926$	−1005.19	+	225.706i	−1.08552	+	0.243743i
$927$		0			0
$928$	817.952	+	411.804i	0.881414	+	0.443754i
$929$	−980.857			−1.05582			−0.527910	−	0.849300i	$-0.677024\pi$
$929$	−980.857			−1.05582			−0.527910	+	0.849300i	$0.677024\pi$
$930$		0			0
$931$			153.670i			0.165059i
$932$	−393.226	+	185.967i	−0.421917	+	0.199535i
$933$		0			0
$934$	−576.638	+	129.479i	−0.617386	+	0.138628i
$935$		0			0
$936$		0			0
$937$	−964.666			−1.02953			−0.514763	−	0.857333i	$-0.672120\pi$
$937$	−964.666			−1.02953			−0.514763	+	0.857333i	$0.672120\pi$
$938$	12.4821	+	55.5896i	0.0133072	+	0.0592639i
$939$		0			0
$940$		0			0
$941$	1581.10			1.68023			0.840117	−	0.542405i	$-0.182486\pi$
$941$	1581.10			1.68023			0.840117	+	0.542405i	$0.182486\pi$
$942$		0			0
$943$		−	1486.12i		−	1.57595i
$944$	238.386	+	195.663i	0.252527	+	0.207271i
$945$		0			0
$946$	204.498	+	910.738i	0.216171	+	0.962725i
$947$		−	1245.27i		−	1.31497i	−0.753469	−	0.657483i	$-0.771621\pi$
$947$		−	1245.27i		−	1.31497i	0.753469	−	0.657483i	$-0.228379\pi$
$948$		0			0
$949$	759.229			0.800031
$950$		0			0
$951$		0			0
$952$	−555.521	+	433.490i	−0.583530	+	0.455347i
$953$	1106.52			1.16109			0.580546	−	0.814228i	$-0.302839\pi$
$953$	1106.52			1.16109			0.580546	+	0.814228i	$0.302839\pi$
$954$		0			0
$955$		0			0
$956$	306.098	+	647.243i	0.320186	+	0.677032i
$957$		0			0
$958$	−533.037	+	119.689i	−0.556406	+	0.124936i
$959$			123.521i			0.128802i
$960$		0			0
$961$	409.039			0.425638
$962$	−547.808	−	2439.68i	−0.569447	−	2.53605i
$963$		0			0
$964$	−1296.79	+	613.284i	−1.34521	+	0.636187i
$965$		0			0
$966$		0			0
$967$		−	406.453i		−	0.420324i	−0.977667	−	0.210162i	$-0.932601\pi$
$967$		−	406.453i		−	0.420324i	0.977667	−	0.210162i	$-0.0673992\pi$
$968$	−171.706	−	220.042i	−0.177382	−	0.227316i
$969$		0			0
$970$		0			0
$971$			1815.22i			1.86943i	0.355393	+	0.934717i	$0.384347\pi$
$971$			1815.22i			1.86943i	−0.355393	+	0.934717i	$0.615653\pi$
$972$		0			0
$973$	−1629.58			−1.67480
$974$	−698.119	+	156.756i	−0.716754	+	0.160941i
$975$		0			0
$976$	−539.594	+	657.412i	−0.552862	+	0.673578i
$977$	−1457.74			−1.49205			−0.746027	−	0.665916i	$-0.768041\pi$
$977$	−1457.74			−1.49205			−0.746027	+	0.665916i	$0.768041\pi$
$978$		0			0
$979$			429.720i			0.438938i
$980$		0			0
$981$		0			0
$982$	824.235	−	185.074i	0.839343	−	0.188467i
$983$			19.9496i			0.0202946i	0.999949	+	0.0101473i	$0.00323004\pi$
$983$			19.9496i			0.0202946i	−0.999949	+	0.0101473i	$0.996770\pi$
$984$		0			0
$985$		0			0
$986$	174.437	+	776.860i	0.176914	+	0.787891i
$987$		0			0
$988$	547.625	+	1157.95i	0.554276	+	1.17201i
$989$	−1695.65			−1.71450
$990$		0			0
$991$			605.720i			0.611221i	0.952157	+	0.305611i	$0.0988605\pi$
$991$			605.720i			0.611221i	−0.952157	+	0.305611i	$0.901139\pi$
$992$	338.073	−	671.502i	0.340799	−	0.676918i
$993$		0			0
$994$	36.9989	+	164.776i	0.0372223	+	0.165771i
$995$		0			0
$996$		0			0
$997$	−1238.47			−1.24220			−0.621099	−	0.783732i	$-0.713314\pi$
$997$	−1238.47			−1.24220			−0.621099	+	0.783732i	$0.713314\pi$
$998$	−404.129	+	90.7434i	−0.404939	+	0.0909253i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.u.451.4		8
3.2	odd	2		300.3.c.d.151.5		8
4.3	odd	2	inner	900.3.c.u.451.3		8
5.2	odd	4		900.3.f.f.199.2		16
5.3	odd	4		900.3.f.f.199.15		16
5.4	even	2		180.3.c.b.91.5		8
12.11	even	2		300.3.c.d.151.6		8
15.2	even	4		300.3.f.b.199.15		16
15.8	even	4		300.3.f.b.199.2		16
15.14	odd	2		60.3.c.a.31.4	yes	8
20.3	even	4		900.3.f.f.199.1		16
20.7	even	4		900.3.f.f.199.16		16
20.19	odd	2		180.3.c.b.91.6		8
40.19	odd	2		2880.3.e.j.2431.5		8
40.29	even	2		2880.3.e.j.2431.8		8
60.23	odd	4		300.3.f.b.199.16		16
60.47	odd	4		300.3.f.b.199.1		16
60.59	even	2		60.3.c.a.31.3	✓	8
120.29	odd	2		960.3.e.c.511.2		8
120.59	even	2		960.3.e.c.511.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.3	✓	8	60.59	even	2
60.3.c.a.31.4	yes	8	15.14	odd	2
180.3.c.b.91.5		8	5.4	even	2
180.3.c.b.91.6		8	20.19	odd	2
300.3.c.d.151.5		8	3.2	odd	2
300.3.c.d.151.6		8	12.11	even	2
300.3.f.b.199.1		16	60.47	odd	4
300.3.f.b.199.2		16	15.8	even	4
300.3.f.b.199.15		16	15.2	even	4
300.3.f.b.199.16		16	60.23	odd	4
900.3.c.u.451.3		8	4.3	odd	2	inner
900.3.c.u.451.4		8	1.1	even	1	trivial
900.3.f.f.199.1		16	20.3	even	4
900.3.f.f.199.2		16	5.2	odd	4
900.3.f.f.199.15		16	5.3	odd	4
900.3.f.f.199.16		16	20.7	even	4
960.3.e.c.511.2		8	120.29	odd	2
960.3.e.c.511.5		8	120.59	even	2
2880.3.e.j.2431.5		8	40.19	odd	2
2880.3.e.j.2431.8		8	40.29	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.438172 + 1.95141i) q^{2} +(-3.61601 + 1.71011i) q^{4} -6.33166i q^{7} +(-4.92155 - 6.30701i) q^{8} +O(q^{10})\)	\(q+(0.438172 + 1.95141i) q^{2} +(-3.61601 + 1.71011i) q^{4} -6.33166i q^{7} +(-4.92155 - 6.30701i) q^{8} +9.27963i q^{11} -18.5674 q^{13} +(12.3557 - 2.77436i) q^{14} +(10.1511 - 12.3675i) q^{16} +13.9110 q^{17} +17.2468i q^{19} +(-18.1084 + 4.06607i) q^{22} -33.7148i q^{23} +(-8.13571 - 36.2327i) q^{26} +(10.8278 + 22.8954i) q^{28} +28.6177 q^{29} -23.4939i q^{31} +(28.5820 + 14.3898i) q^{32} +(6.09542 + 27.1461i) q^{34} +67.3338 q^{37} +(-33.6556 + 7.55706i) q^{38} +44.0791 q^{41} -50.2937i q^{43} +(-15.8691 - 33.5552i) q^{44} +(65.7915 - 14.7729i) q^{46} -31.1594i q^{47} +8.91003 q^{49} +(67.1400 - 31.7522i) q^{52} +81.6070 q^{53} +(-39.9338 + 31.1616i) q^{56} +(12.5395 + 55.8449i) q^{58} +19.2751i q^{59} -53.1563 q^{61} +(45.8462 - 10.2943i) q^{62} +(-15.5566 + 62.0805i) q^{64} +4.49911i q^{67} +(-50.3025 + 23.7893i) q^{68} +13.3360i q^{71} -40.8904 q^{73} +(29.5037 + 131.396i) q^{74} +(-29.4939 - 62.3647i) q^{76} +58.7555 q^{77} -141.309i q^{79} +(19.3142 + 86.0164i) q^{82} +69.8503i q^{83} +(98.1438 - 22.0373i) q^{86} +(58.5266 - 45.6702i) q^{88} +46.3079 q^{89} +117.563i q^{91} +(57.6559 + 121.913i) q^{92} +(60.8049 - 13.6532i) q^{94} -68.5543 q^{97} +(3.90412 + 17.3871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more