LMFDB - Embedded newform 900.3.c.n.451.2

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			451.2
Root			$1.65359 + 0.954702i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.n.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97650 + 0.305673i) q^{2} +(3.81313 - 1.20833i) q^{4} +0.329898i q^{7} +(-7.16731 + 3.55383i) q^{8} +O(q^{10})$	\(q+(-1.97650 + 0.305673i) q^{2} +(3.81313 - 1.20833i) q^{4} +0.329898i q^{7} +(-7.16731 + 3.55383i) q^{8} +20.4920i q^{11} +0.416712 q^{13} +(-0.100841 - 0.652044i) q^{14} +(13.0799 - 9.21501i) q^{16} -18.5884 q^{17} +12.4503i q^{19} +(-6.26384 - 40.5024i) q^{22} -23.2304i q^{23} +(-0.823633 + 0.127378i) q^{26} +(0.398624 + 1.25794i) q^{28} +23.9166 q^{29} -42.0148i q^{31} +(-23.0357 + 22.2117i) q^{32} +(36.7400 - 5.68197i) q^{34} -50.9523 q^{37} +(-3.80573 - 24.6081i) q^{38} -46.7073 q^{41} +55.5866i q^{43} +(24.7610 + 78.1385i) q^{44} +(7.10090 + 45.9149i) q^{46} -81.7616i q^{47} +48.8912 q^{49} +(1.58898 - 0.503524i) q^{52} -29.9744 q^{53} +(-1.17240 - 2.36448i) q^{56} +(-47.2713 + 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(12.8428 + 83.0424i) q^{62} +(38.7406 - 50.9428i) q^{64} +72.8008i q^{67} +(-70.8799 + 22.4608i) q^{68} -39.2803i q^{71} +46.5814 q^{73} +(100.707 - 15.5747i) q^{74} +(15.0441 + 47.4747i) q^{76} -6.76026 q^{77} +101.920i q^{79} +(92.3170 - 14.2771i) q^{82} -5.88913i q^{83} +(-16.9913 - 109.867i) q^{86} +(-72.8250 - 146.872i) q^{88} +61.0100 q^{89} +0.137472i q^{91} +(-28.0699 - 88.5804i) q^{92} +(24.9923 + 161.602i) q^{94} -95.5437 q^{97} +(-96.6335 + 14.9447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.97650	+	0.305673i	−0.988251	+	0.152836i
$2$	−1.97650	+	0.305673i	−0.988251	+	0.152836i
$3$		0			0
$3$		0			0
$4$	3.81313	−	1.20833i	0.953282	−	0.302082i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.329898i			0.0471283i	0.999722	+	0.0235641i	$0.00750139\pi$
$7$			0.329898i			0.0471283i	−0.999722	+	0.0235641i	$0.992499\pi$
$8$	−7.16731	+	3.55383i	−0.895913	+	0.444229i
$9$		0			0
$10$		0			0
$11$			20.4920i			1.86291i	0.363861	+	0.931453i	$0.381458\pi$
$11$			20.4920i			1.86291i	−0.363861	+	0.931453i	$0.618542\pi$
$12$		0			0
$13$	0.416712			0.0320548			0.0160274	−	0.999872i	$-0.494898\pi$
$13$	0.416712			0.0320548			0.0160274	+	0.999872i	$0.494898\pi$
$14$	−0.100841	−	0.652044i	−0.00720292	−	0.0465746i
$15$		0			0
$16$	13.0799	−	9.21501i	0.817493	−	0.575938i
$17$	−18.5884			−1.09343			−0.546717	−	0.837317i	$-0.684123\pi$
$17$	−18.5884			−1.09343			−0.546717	+	0.837317i	$0.684123\pi$
$18$		0			0
$19$			12.4503i			0.655281i	0.944803	+	0.327640i	$0.106253\pi$
$19$			12.4503i			0.655281i	−0.944803	+	0.327640i	$0.893747\pi$
$20$		0			0
$21$		0			0
$22$	−6.26384	−	40.5024i	−0.284720	−	1.84102i
$23$		−	23.2304i		−	1.01002i	−0.863114	−	0.505008i	$-0.831489\pi$
$23$		−	23.2304i		−	1.01002i	0.863114	−	0.505008i	$-0.168511\pi$
$24$		0			0
$25$		0			0
$26$	−0.823633	+	0.127378i	−0.0316782	+	0.00489914i
$27$		0			0
$28$	0.398624	+	1.25794i	0.0142366	+	0.0449265i
$29$	23.9166			0.824712			0.412356	−	0.911023i	$-0.364706\pi$
$29$	23.9166			0.824712			0.412356	+	0.911023i	$0.364706\pi$
$30$		0			0
$31$		−	42.0148i		−	1.35532i	−0.735377	−	0.677658i	$-0.762995\pi$
$31$		−	42.0148i		−	1.35532i	0.735377	−	0.677658i	$-0.237005\pi$
$32$	−23.0357	+	22.2117i	−0.719865	+	0.694115i
$33$		0			0
$34$	36.7400	−	5.68197i	1.08059	−	0.167117i
$35$		0			0
$36$		0			0
$37$	−50.9523			−1.37709			−0.688545	−	0.725194i	$-0.741750\pi$
$37$	−50.9523			−1.37709			−0.688545	+	0.725194i	$0.741750\pi$
$38$	−3.80573	−	24.6081i	−0.100151	−	0.647582i
$39$		0			0
$40$		0			0
$41$	−46.7073			−1.13920			−0.569601	−	0.821921i	$-0.692902\pi$
$41$	−46.7073			−1.13920			−0.569601	+	0.821921i	$0.692902\pi$
$42$		0			0
$43$			55.5866i			1.29271i	0.763036	+	0.646356i	$0.223708\pi$
$43$			55.5866i			1.29271i	−0.763036	+	0.646356i	$0.776292\pi$
$44$	24.7610	+	78.1385i	0.562750	+	1.77588i
$45$		0			0
$46$	7.10090	+	45.9149i	0.154367	+	0.998151i
$47$		−	81.7616i		−	1.73961i	−0.493397	−	0.869804i	$-0.664245\pi$
$47$		−	81.7616i		−	1.73961i	0.493397	−	0.869804i	$-0.335755\pi$
$48$		0			0
$49$	48.8912			0.997779
$50$		0			0
$51$		0			0
$52$	1.58898	−	0.503524i	0.0305572	−	0.00968316i
$53$	−29.9744			−0.565554			−0.282777	−	0.959186i	$-0.591256\pi$
$53$	−29.9744			−0.565554			−0.282777	+	0.959186i	$0.591256\pi$
$54$		0			0
$55$		0			0
$56$	−1.17240	−	2.36448i	−0.0209357	−	0.0422228i
$57$		0			0
$58$	−47.2713	+	7.31067i	−0.815023	+	0.126046i
$59$		−	24.3311i		−	0.412391i	−0.978511	−	0.206196i	$-0.933892\pi$
$59$		−	24.3311i		−	0.412391i	0.978511	−	0.206196i	$-0.0661083\pi$
$60$		0			0
$61$	−74.8416			−1.22691			−0.613456	−	0.789729i	$-0.710221\pi$
$61$	−74.8416			−1.22691			−0.613456	+	0.789729i	$0.710221\pi$
$62$	12.8428	+	83.0424i	0.207142	+	1.33939i
$63$		0			0
$64$	38.7406	−	50.9428i	0.605321	−	0.795981i
$65$		0			0
$66$		0			0
$67$			72.8008i			1.08658i	0.839545	+	0.543290i	$0.182822\pi$
$67$			72.8008i			1.08658i	−0.839545	+	0.543290i	$0.817178\pi$
$68$	−70.8799	+	22.4608i	−1.04235	+	0.330307i
$69$		0			0
$70$		0			0
$71$		−	39.2803i		−	0.553244i	−0.960979	−	0.276622i	$-0.910785\pi$
$71$		−	39.2803i		−	0.553244i	0.960979	−	0.276622i	$-0.0892150\pi$
$72$		0			0
$73$	46.5814			0.638101			0.319051	−	0.947738i	$-0.396636\pi$
$73$	46.5814			0.638101			0.319051	+	0.947738i	$0.396636\pi$
$74$	100.707	−	15.5747i	1.36091	−	0.210469i
$75$		0			0
$76$	15.0441	+	47.4747i	0.197948	+	0.624667i
$77$	−6.76026			−0.0877955
$78$		0			0
$79$			101.920i			1.29012i	0.764131	+	0.645062i	$0.223168\pi$
$79$			101.920i			1.29012i	−0.764131	+	0.645062i	$0.776832\pi$
$80$		0			0
$81$		0			0
$82$	92.3170	−	14.2771i	1.12582	−	0.174112i
$83$		−	5.88913i		−	0.0709534i	−0.999371	−	0.0354767i	$-0.988705\pi$
$83$		−	5.88913i		−	0.0709534i	0.999371	−	0.0354767i	$-0.0112950\pi$
$84$		0			0
$85$		0			0
$86$	−16.9913	−	109.867i	−0.197574	−	1.27752i
$87$		0			0
$88$	−72.8250	−	146.872i	−0.827557	−	1.66900i
$89$	61.0100			0.685506			0.342753	−	0.939426i	$-0.388641\pi$
$89$	61.0100			0.685506			0.342753	+	0.939426i	$0.388641\pi$
$90$		0			0
$91$			0.137472i			0.00151069i
$92$	−28.0699	−	88.5804i	−0.305108	−	0.962831i
$93$		0			0
$94$	24.9923	+	161.602i	0.265876	+	1.71917i
$95$		0			0
$96$		0			0
$97$	−95.5437			−0.984987			−0.492494	−	0.870316i	$-0.663914\pi$
$97$	−95.5437			−0.984987			−0.492494	+	0.870316i	$0.663914\pi$
$98$	−96.6335	+	14.9447i	−0.986057	+	0.152497i
$99$		0			0
$100$		0			0
$101$	−162.675			−1.61064			−0.805322	−	0.592838i	$-0.798008\pi$
$101$	−162.675			−1.61064			−0.805322	+	0.592838i	$0.798008\pi$
$102$		0			0
$103$		−	158.196i		−	1.53588i	−0.640521	−	0.767941i	$-0.721282\pi$
$103$		−	158.196i		−	1.53588i	0.640521	−	0.767941i	$-0.278718\pi$
$104$	−2.98670	+	1.48092i	−0.0287183	+	0.0142397i
$105$		0			0
$106$	59.2445	−	9.16236i	0.558910	−	0.0864373i
$107$			18.1827i			0.169932i	0.996384	+	0.0849660i	$0.0270782\pi$
$107$			18.1827i			0.169932i	−0.996384	+	0.0849660i	$0.972922\pi$
$108$		0			0
$109$	−156.842			−1.43891			−0.719457	−	0.694537i	$-0.755609\pi$
$109$	−156.842			−1.43891			−0.719457	+	0.694537i	$0.755609\pi$
$110$		0			0
$111$		0			0
$112$	3.04001	+	4.31503i	0.0271430	+	0.0385270i
$113$	−98.7245			−0.873668			−0.436834	−	0.899542i	$-0.643900\pi$
$113$	−98.7245			−0.873668			−0.436834	+	0.899542i	$0.643900\pi$
$114$		0			0
$115$		0			0
$116$	91.1972	−	28.8991i	0.786183	−	0.249130i
$117$		0			0
$118$	7.43735	+	48.0904i	0.0630284	+	0.407546i
$119$		−	6.13227i		−	0.0515317i
$120$		0			0
$121$	−298.921			−2.47042
$122$	147.925	−	22.8770i	1.21250	−	0.187517i
$123$		0			0
$124$	−50.7676	−	160.208i	−0.409416	−	1.29200i
$125$		0			0
$126$		0			0
$127$		−	27.0938i		−	0.213337i	−0.994295	−	0.106669i	$-0.965982\pi$
$127$		−	27.0938i		−	0.213337i	0.994295	−	0.106669i	$-0.0340184\pi$
$128$	−60.9990	+	112.531i	−0.476555	+	0.879145i
$129$		0			0
$130$		0			0
$131$			4.45811i			0.0340314i	0.999855	+	0.0170157i	$0.00541653\pi$
$131$			4.45811i			0.0340314i	−0.999855	+	0.0170157i	$0.994583\pi$
$132$		0			0
$133$	−4.10734			−0.0308822
$134$	−22.2533	−	143.891i	−0.166069	−	1.07381i
$135$		0			0
$136$	133.229	−	66.0600i	0.979622	−	0.485735i
$137$	−181.700			−1.32628			−0.663139	−	0.748496i	$-0.730776\pi$
$137$	−181.700			−1.32628			−0.663139	+	0.748496i	$0.730776\pi$
$138$		0			0
$139$		−	223.419i		−	1.60733i	−0.595083	−	0.803664i	$-0.702881\pi$
$139$		−	223.419i		−	1.60733i	0.595083	−	0.803664i	$-0.297119\pi$
$140$		0			0
$141$		0			0
$142$	12.0069	+	77.6377i	0.0845559	+	0.546744i
$143$			8.53925i			0.0597151i
$144$		0			0
$145$		0			0
$146$	−92.0683	+	14.2387i	−0.630604	+	0.0975251i
$147$		0			0
$148$	−194.288	+	61.5670i	−1.31275	+	0.415994i
$149$	−123.867			−0.831324			−0.415662	−	0.909519i	$-0.636450\pi$
$149$	−123.867			−0.831324			−0.415662	+	0.909519i	$0.636450\pi$
$150$		0			0
$151$			76.0961i			0.503948i	0.967734	+	0.251974i	$0.0810797\pi$
$151$			76.0961i			0.503948i	−0.967734	+	0.251974i	$0.918920\pi$
$152$	−44.2464	−	89.2353i	−0.291095	−	0.587075i
$153$		0			0
$154$	13.3617	−	2.06643i	0.0867641	−	0.0134184i
$155$		0			0
$156$		0			0
$157$	−34.2940			−0.218433			−0.109217	−	0.994018i	$-0.534834\pi$
$157$	−34.2940			−0.218433			−0.109217	+	0.994018i	$0.534834\pi$
$158$	−31.1541	−	201.445i	−0.197178	−	1.27497i
$159$		0			0
$160$		0			0
$161$	7.66365			0.0476003
$162$		0			0
$163$			165.538i			1.01557i	0.861483	+	0.507786i	$0.169536\pi$
$163$			165.538i			1.01557i	−0.861483	+	0.507786i	$0.830464\pi$
$164$	−178.101	+	56.4377i	−1.08598	+	0.344132i
$165$		0			0
$166$	1.80015	+	11.6399i	0.0108443	+	0.0701198i
$167$			83.6064i			0.500637i	0.968164	+	0.250319i	$0.0805353\pi$
$167$			83.6064i			0.500637i	−0.968164	+	0.250319i	$0.919465\pi$
$168$		0			0
$169$	−168.826			−0.998972
$170$		0			0
$171$		0			0
$172$	67.1668	+	211.959i	0.390505	+	1.23232i
$173$	192.900			1.11503			0.557513	−	0.830168i	$-0.311756\pi$
$173$	192.900			1.11503			0.557513	+	0.830168i	$0.311756\pi$
$174$		0			0
$175$		0			0
$176$	188.834	+	268.033i	1.07292	+	1.52291i
$177$		0			0
$178$	−120.587	+	18.6491i	−0.677452	+	0.104770i
$179$			120.939i			0.675637i	0.941211	+	0.337819i	$0.109689\pi$
$179$			120.939i			0.675637i	−0.941211	+	0.337819i	$0.890311\pi$
$180$		0			0
$181$	−107.583			−0.594381			−0.297191	−	0.954818i	$-0.596050\pi$
$181$	−107.583			−0.594381			−0.297191	+	0.954818i	$0.596050\pi$
$182$	−0.0420216	−	0.271715i	−0.000230888	−	0.00149294i
$183$		0			0
$184$	82.5569	+	166.499i	0.448679	+	0.904887i
$185$		0			0
$186$		0			0
$187$		−	380.913i		−	2.03697i
$188$	−98.7947	−	311.767i	−0.525504	−	1.65834i
$189$		0			0
$190$		0			0
$191$		−	279.706i		−	1.46443i	−0.681075	−	0.732214i	$-0.738487\pi$
$191$		−	279.706i		−	1.46443i	0.681075	−	0.732214i	$-0.261513\pi$
$192$		0			0
$193$	102.534			0.531263			0.265632	−	0.964075i	$-0.414420\pi$
$193$	102.534			0.531263			0.265632	+	0.964075i	$0.414420\pi$
$194$	188.842	−	29.2051i	0.973415	−	0.150542i
$195$		0			0
$196$	186.428	−	59.0765i	0.951165	−	0.301411i
$197$	38.9632			0.197783			0.0988913	−	0.995098i	$-0.468470\pi$
$197$	38.9632			0.197783			0.0988913	+	0.995098i	$0.468470\pi$
$198$		0			0
$199$		−	147.646i		−	0.741940i	−0.928645	−	0.370970i	$-0.879025\pi$
$199$		−	147.646i		−	0.741940i	0.928645	−	0.370970i	$-0.120975\pi$
$200$		0			0
$201$		0			0
$202$	321.528	−	49.7254i	1.59172	−	0.246165i
$203$			7.89005i			0.0388672i
$204$		0			0
$205$		0			0
$206$	48.3562	+	312.674i	0.234739	+	1.51784i
$207$		0			0
$208$	5.45055	−	3.84001i	0.0262046	−	0.0184616i
$209$	−255.132			−1.22073
$210$		0			0
$211$		−	233.336i		−	1.10586i	−0.833229	−	0.552928i	$-0.813510\pi$
$211$		−	233.336i		−	1.10586i	0.833229	−	0.552928i	$-0.186490\pi$
$212$	−114.296	+	36.2189i	−0.539133	+	0.170844i
$213$		0			0
$214$	−5.55797	−	35.9382i	−0.0259718	−	0.167936i
$215$		0			0
$216$		0			0
$217$	13.8606			0.0638737
$218$	309.998	−	47.9422i	1.42201	−	0.219918i
$219$		0			0
$220$		0			0
$221$	−7.74600			−0.0350498
$222$		0			0
$223$		−	82.7105i		−	0.370899i	−0.982654	−	0.185450i	$-0.940626\pi$
$223$		−	82.7105i		−	0.370899i	0.982654	−	0.185450i	$-0.0593741\pi$
$224$	−7.32758	−	7.59941i	−0.0327124	−	0.0339260i
$225$		0			0
$226$	195.129	−	30.1774i	0.863403	−	0.133528i
$227$			361.534i			1.59266i	0.604862	+	0.796330i	$0.293228\pi$
$227$			361.534i			1.59266i	−0.604862	+	0.796330i	$0.706772\pi$
$228$		0			0
$229$	121.818			0.531955			0.265977	−	0.963979i	$-0.414305\pi$
$229$	121.818			0.531955			0.265977	+	0.963979i	$0.414305\pi$
$230$		0			0
$231$		0			0
$232$	−171.418	+	84.9957i	−0.738870	+	0.366361i
$233$	136.615			0.586329			0.293164	−	0.956062i	$-0.405292\pi$
$233$	136.615			0.586329			0.293164	+	0.956062i	$0.405292\pi$
$234$		0			0
$235$		0			0
$236$	−29.3999	−	92.7775i	−0.124576	−	0.393125i
$237$		0			0
$238$	1.87447	+	12.1204i	0.00787592	+	0.0509262i
$239$			56.4632i			0.236248i	0.992999	+	0.118124i	$0.0376880\pi$
$239$			56.4632i			0.236248i	−0.992999	+	0.118124i	$0.962312\pi$
$240$		0			0
$241$	−2.24158			−0.00930117			−0.00465059	−	0.999989i	$-0.501480\pi$
$241$	−2.24158			−0.00930117			−0.00465059	+	0.999989i	$0.501480\pi$
$242$	590.818	−	91.3720i	2.44140	−	0.377570i
$243$		0			0
$244$	−285.381	+	90.4331i	−1.16959	+	0.370627i
$245$		0			0
$246$		0			0
$247$			5.18820i			0.0210049i
$248$	149.314	+	301.133i	0.602071	+	1.21425i
$249$		0			0
$250$		0			0
$251$			395.809i			1.57693i	0.615081	+	0.788464i	$0.289123\pi$
$251$			395.809i			1.57693i	−0.615081	+	0.788464i	$0.710877\pi$
$252$		0			0
$253$	476.036			1.88157
$254$	8.28184	+	53.5510i	0.0326057	+	0.210831i
$255$		0			0
$256$	86.1671	−	241.063i	0.336590	−	0.941651i
$257$	109.778			0.427151			0.213576	−	0.976927i	$-0.431489\pi$
$257$	109.778			0.427151			0.213576	+	0.976927i	$0.431489\pi$
$258$		0			0
$259$		−	16.8091i		−	0.0648998i
$260$		0			0
$261$		0			0
$262$	−1.36272	−	8.81147i	−0.00520124	−	0.0336316i
$263$			327.702i			1.24601i	0.782216	+	0.623007i	$0.214089\pi$
$263$			327.702i			1.24601i	−0.782216	+	0.623007i	$0.785911\pi$
$264$		0			0
$265$		0			0
$266$	8.11816	−	1.25550i	0.0305194	−	0.00471993i
$267$		0			0
$268$	87.9672	+	277.599i	0.328236	+	1.03582i
$269$	130.032			0.483392			0.241696	−	0.970352i	$-0.422296\pi$
$269$	130.032			0.483392			0.241696	+	0.970352i	$0.422296\pi$
$270$		0			0
$271$			329.669i			1.21649i	0.793750	+	0.608245i	$0.208126\pi$
$271$			329.669i			1.21649i	−0.793750	+	0.608245i	$0.791874\pi$
$272$	−243.134	+	171.292i	−0.893875	+	0.629751i
$273$		0			0
$274$	359.131	−	55.5408i	1.31070	−	0.202704i
$275$		0			0
$276$		0			0
$277$	−304.124			−1.09792			−0.548960	−	0.835849i	$-0.684976\pi$
$277$	−304.124			−1.09792			−0.548960	+	0.835849i	$0.684976\pi$
$278$	68.2930	+	441.588i	0.245658	+	1.58844i
$279$		0			0
$280$		0			0
$281$	−240.099			−0.854446			−0.427223	−	0.904146i	$-0.640508\pi$
$281$	−240.099			−0.854446			−0.427223	+	0.904146i	$0.640508\pi$
$282$		0			0
$283$			86.6730i			0.306265i	0.988206	+	0.153133i	$0.0489362\pi$
$283$			86.6730i			0.306265i	−0.988206	+	0.153133i	$0.951064\pi$
$284$	−47.4635	−	149.781i	−0.167125	−	0.527398i
$285$		0			0
$286$	−2.61022	−	16.8779i	−0.00912664	−	0.0590135i
$287$		−	15.4086i		−	0.0536886i
$288$		0			0
$289$	56.5280			0.195599
$290$		0			0
$291$		0			0
$292$	177.621	−	56.2856i	0.608290	−	0.192759i
$293$	390.339			1.33222			0.666108	−	0.745855i	$-0.267959\pi$
$293$	390.339			1.33222			0.666108	+	0.745855i	$0.267959\pi$
$294$		0			0
$295$		0			0
$296$	365.191	−	181.076i	1.23375	−	0.611743i
$297$		0			0
$298$	244.824	−	37.8629i	0.821557	−	0.127057i
$299$		−	9.68038i		−	0.0323759i
$300$		0			0
$301$	−18.3379			−0.0609233
$302$	−23.2605	−	150.404i	−0.0770216	−	0.498027i
$303$		0			0
$304$	114.730	+	162.849i	0.377401	+	0.535687i
$305$		0			0
$306$		0			0
$307$			60.2318i			0.196195i	0.995177	+	0.0980973i	$0.0312757\pi$
$307$			60.2318i			0.196195i	−0.995177	+	0.0980973i	$0.968724\pi$
$308$	−25.7777	+	8.16860i	−0.0836939	+	0.0265214i
$309$		0			0
$310$		0			0
$311$		−	106.594i		−	0.342747i	−0.985206	−	0.171373i	$-0.945180\pi$
$311$		−	106.594i		−	0.342747i	0.985206	−	0.171373i	$-0.0548205\pi$
$312$		0			0
$313$	46.2243			0.147682			0.0738408	−	0.997270i	$-0.476474\pi$
$313$	46.2243			0.147682			0.0738408	+	0.997270i	$0.476474\pi$
$314$	67.7823	−	10.4828i	0.215867	−	0.0333846i
$315$		0			0
$316$	123.152	+	388.633i	0.389723	+	1.22985i
$317$	−8.36780			−0.0263969			−0.0131984	−	0.999913i	$-0.504201\pi$
$317$	−8.36780			−0.0263969			−0.0131984	+	0.999913i	$0.504201\pi$
$318$		0			0
$319$			490.099i			1.53636i
$320$		0			0
$321$		0			0
$322$	−15.1472	+	2.34257i	−0.0470411	+	0.00727507i
$323$		−	231.432i		−	0.716506i
$324$		0			0
$325$		0			0
$326$	−50.6006	−	327.187i	−0.155217	−	1.00364i
$327$		0			0
$328$	334.765	−	165.990i	1.02063	−	0.506066i
$329$	26.9730			0.0819847
$330$		0			0
$331$		−	111.072i		−	0.335564i	−0.985824	−	0.167782i	$-0.946339\pi$
$331$		−	111.072i		−	0.335564i	0.985824	−	0.167782i	$-0.0536605\pi$
$332$	−7.11600	−	22.4560i	−0.0214337	−	0.0676386i
$333$		0			0
$334$	−25.5562	−	165.248i	−0.0765156	−	0.494755i
$335$		0			0
$336$		0			0
$337$	231.853			0.687990			0.343995	−	0.938972i	$-0.388220\pi$
$337$	231.853			0.687990			0.343995	+	0.938972i	$0.388220\pi$
$338$	333.686	−	51.6057i	0.987236	−	0.152679i
$339$		0			0
$340$		0			0
$341$	860.966			2.52483
$342$		0			0
$343$			32.2941i			0.0941518i
$344$	−197.546	−	398.406i	−0.574260	−	1.15816i
$345$		0			0
$346$	−381.266	+	58.9642i	−1.10193	+	0.170417i
$347$		−	402.088i		−	1.15875i	−0.815059	−	0.579377i	$-0.803296\pi$
$347$		−	402.088i		−	1.15875i	0.815059	−	0.579377i	$-0.196704\pi$
$348$		0			0
$349$	−163.284			−0.467864			−0.233932	−	0.972253i	$-0.575159\pi$
$349$	−163.284			−0.467864			−0.233932	+	0.972253i	$0.575159\pi$
$350$		0			0
$351$		0			0
$352$	−455.161	−	472.046i	−1.29307	−	1.34104i
$353$	175.851			0.498161			0.249081	−	0.968483i	$-0.419872\pi$
$353$	175.851			0.498161			0.249081	+	0.968483i	$0.419872\pi$
$354$		0			0
$355$		0			0
$356$	232.639	−	73.7201i	0.653481	−	0.207079i
$357$		0			0
$358$	−36.9678	−	239.037i	−0.103262	−	0.667700i
$359$		−	345.628i		−	0.962753i	−0.876514	−	0.481377i	$-0.840137\pi$
$359$		−	345.628i		−	0.962753i	0.876514	−	0.481377i	$-0.159863\pi$
$360$		0			0
$361$	205.989			0.570607
$362$	212.638	−	32.8852i	0.587398	−	0.0908431i
$363$		0			0
$364$	0.166112	+	0.524200i	0.000456351	+	0.00144011i
$365$		0			0
$366$		0			0
$367$			728.998i			1.98637i	0.116546	+	0.993185i	$0.462818\pi$
$367$			728.998i			1.98637i	−0.116546	+	0.993185i	$0.537182\pi$
$368$	−214.068	−	303.851i	−0.581707	−	0.825682i
$369$		0			0
$370$		0			0
$371$		−	9.88848i		−	0.0266536i
$372$		0			0
$373$	46.6749			0.125134			0.0625668	−	0.998041i	$-0.480071\pi$
$373$	46.6749			0.125134			0.0625668	+	0.998041i	$0.480071\pi$
$374$	116.435	+	752.875i	0.311323	+	2.01303i
$375$		0			0
$376$	290.567	+	586.010i	0.772784	+	1.55854i
$377$	9.96635			0.0264360
$378$		0			0
$379$			117.629i			0.310368i	0.987886	+	0.155184i	$0.0495970\pi$
$379$			117.629i			0.310368i	−0.987886	+	0.155184i	$0.950403\pi$
$380$		0			0
$381$		0			0
$382$	85.4985	+	552.839i	0.223818	+	1.44722i
$383$			251.669i			0.657100i	0.944487	+	0.328550i	$0.106560\pi$
$383$			251.669i			0.657100i	−0.944487	+	0.328550i	$0.893440\pi$
$384$		0			0
$385$		0			0
$386$	−202.658	+	31.3418i	−0.525022	+	0.0811964i
$387$		0			0
$388$	−364.321	+	115.448i	−0.938970	+	0.297547i
$389$	−356.890			−0.917454			−0.458727	−	0.888577i	$-0.651694\pi$
$389$	−356.890			−0.917454			−0.458727	+	0.888577i	$0.651694\pi$
$390$		0			0
$391$			431.815i			1.10439i
$392$	−350.418	+	173.751i	−0.893923	+	0.443242i
$393$		0			0
$394$	−77.0108	+	11.9100i	−0.195459	+	0.0302284i
$395$		0			0
$396$		0			0
$397$	103.819			0.261508			0.130754	−	0.991415i	$-0.458260\pi$
$397$	103.819			0.261508			0.130754	+	0.991415i	$0.458260\pi$
$398$	45.1314	+	291.823i	0.113396	+	0.733224i
$399$		0			0
$400$		0			0
$401$	121.598			0.303237			0.151618	−	0.988439i	$-0.451551\pi$
$401$	121.598			0.303237			0.151618	+	0.988439i	$0.451551\pi$
$402$		0			0
$403$		−	17.5081i		−	0.0434444i
$404$	−620.301	+	196.565i	−1.53540	+	0.486546i
$405$		0			0
$406$	−2.41177	−	15.5947i	−0.00594033	−	0.0384106i
$407$		−	1044.11i		−	2.56539i
$408$		0			0
$409$	182.788			0.446915			0.223457	−	0.974714i	$-0.428266\pi$
$409$	182.788			0.446915			0.223457	+	0.974714i	$0.428266\pi$
$410$		0			0
$411$		0			0
$412$	−191.152	−	603.221i	−0.463962	−	1.46413i
$413$	8.02677			0.0194353
$414$		0			0
$415$		0			0
$416$	−9.59924	+	9.25587i	−0.0230751	+	0.0222497i
$417$		0			0
$418$	504.269	−	77.9869i	1.20638	−	0.186572i
$419$		−	168.020i		−	0.401003i	−0.979693	−	0.200502i	$-0.935743\pi$
$419$		−	168.020i		−	0.401003i	0.979693	−	0.200502i	$-0.0642572\pi$
$420$		0			0
$421$	625.291			1.48525			0.742626	−	0.669706i	$-0.233580\pi$
$421$	625.291			1.48525			0.742626	+	0.669706i	$0.233580\pi$
$422$	71.3244	+	461.189i	0.169015	+	1.09286i
$423$		0			0
$424$	214.836	−	106.524i	0.506688	−	0.251236i
$425$		0			0
$426$		0			0
$427$		−	24.6901i		−	0.0578222i
$428$	21.9707	+	69.3331i	0.0513334	+	0.161993i
$429$		0			0
$430$		0			0
$431$		−	133.413i		−	0.309544i	−0.987950	−	0.154772i	$-0.950536\pi$
$431$		−	133.413i		−	0.309544i	0.987950	−	0.154772i	$-0.0494643\pi$
$432$		0			0
$433$	−706.716			−1.63214			−0.816069	−	0.577954i	$-0.803851\pi$
$433$	−706.716			−1.63214			−0.816069	+	0.577954i	$0.803851\pi$
$434$	−27.3955	+	4.23681i	−0.0631233	+	0.00976223i
$435$		0			0
$436$	−598.057	+	189.516i	−1.37169	+	0.434670i
$437$	289.226			0.661844
$438$		0			0
$439$		−	507.488i		−	1.15601i	−0.816033	−	0.578005i	$-0.803831\pi$
$439$		−	507.488i		−	1.15601i	0.816033	−	0.578005i	$-0.196169\pi$
$440$		0			0
$441$		0			0
$442$	15.3100	−	2.36774i	0.0346380	−	0.00535689i
$443$		−	412.172i		−	0.930410i	−0.885203	−	0.465205i	$-0.845981\pi$
$443$		−	412.172i		−	0.930410i	0.885203	−	0.465205i	$-0.154019\pi$
$444$		0			0
$445$		0			0
$446$	25.2824	+	163.478i	0.0566869	+	0.366542i
$447$		0			0
$448$	16.8059	+	12.7804i	0.0375132	+	0.0285277i
$449$	808.617			1.80093			0.900465	−	0.434929i	$-0.143227\pi$
$449$	808.617			1.80093			0.900465	+	0.434929i	$0.143227\pi$
$450$		0			0
$451$		−	957.124i		−	2.12223i
$452$	−376.449	+	119.291i	−0.832852	+	0.263919i
$453$		0			0
$454$	−110.511	−	714.573i	−0.243417	−	1.57395i
$455$		0			0
$456$		0			0
$457$	−472.873			−1.03473			−0.517367	−	0.855764i	$-0.673088\pi$
$457$	−472.873			−1.03473			−0.517367	+	0.855764i	$0.673088\pi$
$458$	−240.773	+	37.2364i	−0.525705	+	0.0813021i
$459$		0			0
$460$		0			0
$461$	−433.776			−0.940946			−0.470473	−	0.882414i	$-0.655917\pi$
$461$	−433.776			−0.940946			−0.470473	+	0.882414i	$0.655917\pi$
$462$		0			0
$463$			530.624i			1.14606i	0.819536	+	0.573028i	$0.194231\pi$
$463$			530.624i			1.14606i	−0.819536	+	0.573028i	$0.805769\pi$
$464$	312.827	−	220.392i	0.674196	−	0.474983i
$465$		0			0
$466$	−270.019	+	41.7594i	−0.579440	+	0.0896124i
$467$			355.266i			0.760741i	0.924834	+	0.380370i	$0.124203\pi$
$467$			355.266i			0.760741i	−0.924834	+	0.380370i	$0.875797\pi$
$468$		0			0
$469$	−24.0168			−0.0512086
$470$		0			0
$471$		0			0
$472$	86.4686	+	174.388i	0.183196	+	0.369467i
$473$	−1139.08			−2.40820
$474$		0			0
$475$		0			0
$476$	−7.40978	−	23.3831i	−0.0155668	−	0.0491242i
$477$		0			0
$478$	−17.2593	−	111.600i	−0.0361072	−	0.233472i
$479$		−	548.640i		−	1.14539i	−0.819770	−	0.572693i	$-0.805899\pi$
$479$		−	548.640i		−	1.14539i	0.819770	−	0.572693i	$-0.194101\pi$
$480$		0			0
$481$	−21.2324			−0.0441423
$482$	4.43050	−	0.685191i	0.00919190	−	0.00142156i
$483$		0			0
$484$	−1139.82	+	361.194i	−2.35501	+	0.746269i
$485$		0			0
$486$		0			0
$487$			134.618i			0.276422i	0.990403	+	0.138211i	$0.0441352\pi$
$487$			134.618i			0.276422i	−0.990403	+	0.138211i	$0.955865\pi$
$488$	536.412	−	265.974i	1.09921	−	0.545029i
$489$		0			0
$490$		0			0
$491$			756.810i			1.54136i	0.637220	+	0.770682i	$0.280084\pi$
$491$			756.810i			1.54136i	−0.637220	+	0.770682i	$0.719916\pi$
$492$		0			0
$493$	−444.572			−0.901768
$494$	−1.58589	−	10.2545i	−0.00321031	−	0.0207581i
$495$		0			0
$496$	−387.167	−	549.549i	−0.780579	−	1.10796i
$497$	12.9585			0.0260734
$498$		0			0
$499$			706.956i			1.41675i	0.705838	+	0.708373i	$0.250570\pi$
$499$			706.956i			1.41675i	−0.705838	+	0.708373i	$0.749430\pi$
$500$		0			0
$501$		0			0
$502$	−120.988	−	782.318i	−0.241012	−	1.55840i
$503$			100.567i			0.199935i	0.994991	+	0.0999673i	$0.0318738\pi$
$503$			100.567i			0.199935i	−0.994991	+	0.0999673i	$0.968126\pi$
$504$		0			0
$505$		0			0
$506$	−940.887	+	145.511i	−1.85946	+	0.287572i
$507$		0			0
$508$	−32.7382	−	103.312i	−0.0644452	−	0.203370i
$509$	−753.185			−1.47973			−0.739867	−	0.672753i	$-0.765112\pi$
$509$	−753.185			−1.47973			−0.739867	+	0.672753i	$0.765112\pi$
$510$		0			0
$511$			15.3671i			0.0300726i
$512$	−96.6232	+	502.800i	−0.188717	+	0.982031i
$513$		0			0
$514$	−216.976	+	33.5561i	−0.422133	+	0.0652843i
$515$		0			0
$516$		0			0
$517$	1675.46			3.24073
$518$	5.13807	+	33.2231i	0.00991906	+	0.0641373i
$519$		0			0
$520$		0			0
$521$	−117.708			−0.225926			−0.112963	−	0.993599i	$-0.536034\pi$
$521$	−117.708			−0.225926			−0.112963	+	0.993599i	$0.536034\pi$
$522$		0			0
$523$		−	617.411i		−	1.18052i	−0.807214	−	0.590259i	$-0.799026\pi$
$523$		−	617.411i		−	1.18052i	0.807214	−	0.590259i	$-0.200974\pi$
$524$	5.38686	+	16.9994i	0.0102803	+	0.0324415i
$525$		0			0
$526$	−100.170	−	647.704i	−0.190437	−	1.23138i
$527$			780.988i			1.48195i
$528$		0			0
$529$	−10.6508			−0.0201338
$530$		0			0
$531$		0			0
$532$	−15.6618	+	4.96301i	−0.0294395	+	0.00932896i
$533$	−19.4635			−0.0365169
$534$		0			0
$535$		0			0
$536$	−258.722	−	521.786i	−0.482690	−	0.973481i
$537$		0			0
$538$	−257.009	+	39.7474i	−0.477713	+	0.0738799i
$539$			1001.88i			1.85877i
$540$		0			0
$541$	352.762			0.652056			0.326028	−	0.945360i	$-0.394290\pi$
$541$	352.762			0.652056			0.326028	+	0.945360i	$0.394290\pi$
$542$	−100.771	−	651.591i	−0.185924	−	1.20220i
$543$		0			0
$544$	428.196	−	412.879i	0.787125	−	0.758969i
$545$		0			0
$546$		0			0
$547$		−	295.110i		−	0.539507i	−0.962929	−	0.269753i	$-0.913058\pi$
$547$		−	295.110i		−	0.539507i	0.962929	−	0.269753i	$-0.0869422\pi$
$548$	−692.846	+	219.553i	−1.26432	+	0.400644i
$549$		0			0
$550$		0			0
$551$			297.770i			0.540418i
$552$		0			0
$553$	−33.6231			−0.0608013
$554$	601.102	−	92.9624i	1.08502	−	0.167802i
$555$		0			0
$556$	−269.963	−	851.924i	−0.485545	−	1.53224i
$557$	31.8538			0.0571882			0.0285941	−	0.999591i	$-0.490897\pi$
$557$	31.8538			0.0571882			0.0285941	+	0.999591i	$0.490897\pi$
$558$		0			0
$559$			23.1636i			0.0414376i
$560$		0			0
$561$		0			0
$562$	474.557	−	73.3919i	0.844408	−	0.130591i
$563$		−	906.668i		−	1.61042i	−0.592988	−	0.805211i	$-0.702052\pi$
$563$		−	906.668i		−	1.61042i	0.592988	−	0.805211i	$-0.297948\pi$
$564$		0			0
$565$		0			0
$566$	−26.4936	−	171.310i	−0.0468085	−	0.302667i
$567$		0			0
$568$	139.596	+	281.534i	0.245767	+	0.495659i
$569$	465.009			0.817239			0.408620	−	0.912705i	$-0.366010\pi$
$569$	465.009			0.817239			0.408620	+	0.912705i	$0.366010\pi$
$570$		0			0
$571$		−	265.895i		−	0.465666i	−0.972517	−	0.232833i	$-0.925200\pi$
$571$		−	265.895i		−	0.465666i	0.972517	−	0.232833i	$-0.0747995\pi$
$572$	10.3182	+	32.5613i	0.0180388	+	0.0569253i
$573$		0			0
$574$	4.71000	+	30.4552i	0.00820557	+	0.0530578i
$575$		0			0
$576$		0			0
$577$	−138.097			−0.239336			−0.119668	−	0.992814i	$-0.538183\pi$
$577$	−138.097			−0.239336			−0.119668	+	0.992814i	$0.538183\pi$
$578$	−111.728	+	17.2791i	−0.193301	+	0.0298946i
$579$		0			0
$580$		0			0
$581$	1.94281			0.00334391
$582$		0			0
$583$		−	614.234i		−	1.05358i
$584$	−333.863	+	165.542i	−0.571683	+	0.283463i
$585$		0			0
$586$	−771.507	+	119.316i	−1.31656	+	0.203611i
$587$			648.473i			1.10472i	0.833604	+	0.552362i	$0.186273\pi$
$587$			648.473i			1.10472i	−0.833604	+	0.552362i	$0.813727\pi$
$588$		0			0
$589$	523.098			0.888113
$590$		0			0
$591$		0			0
$592$	−666.451	+	469.526i	−1.12576	+	0.793118i
$593$	−350.392			−0.590880			−0.295440	−	0.955361i	$-0.595466\pi$
$593$	−350.392			−0.590880			−0.295440	+	0.955361i	$0.595466\pi$
$594$		0			0
$595$		0			0
$596$	−472.322	+	149.672i	−0.792486	+	0.251128i
$597$		0			0
$598$	2.95903	+	19.1333i	0.00494821	+	0.0319955i
$599$			276.745i			0.462012i	0.972952	+	0.231006i	$0.0742017\pi$
$599$			276.745i			0.462012i	−0.972952	+	0.231006i	$0.925798\pi$
$600$		0			0
$601$	815.487			1.35688			0.678442	−	0.734654i	$-0.262656\pi$
$601$	815.487			1.35688			0.678442	+	0.734654i	$0.262656\pi$
$602$	36.2449	−	5.60540i	0.0602075	−	0.00931130i
$603$		0			0
$604$	91.9490	+	290.164i	0.152233	+	0.480405i
$605$		0			0
$606$		0			0
$607$			247.049i			0.407001i	0.979075	+	0.203500i	$0.0652318\pi$
$607$			247.049i			0.407001i	−0.979075	+	0.203500i	$0.934768\pi$
$608$	−276.543	−	286.802i	−0.454840	−	0.471713i
$609$		0			0
$610$		0			0
$611$		−	34.0710i		−	0.0557627i
$612$		0			0
$613$	−1005.15			−1.63972			−0.819862	−	0.572561i	$-0.805950\pi$
$613$	−1005.15			−1.63972			−0.819862	+	0.572561i	$0.805950\pi$
$614$	−18.4112	−	119.048i	−0.0299857	−	0.193890i
$615$		0			0
$616$	48.4528	−	24.0248i	0.0786572	−	0.0390013i
$617$	533.282			0.864314			0.432157	−	0.901798i	$-0.357753\pi$
$617$	533.282			0.864314			0.432157	+	0.901798i	$0.357753\pi$
$618$		0			0
$619$		−	1136.85i		−	1.83659i	−0.395900	−	0.918294i	$-0.629567\pi$
$619$		−	1136.85i		−	1.83659i	0.395900	−	0.918294i	$-0.370433\pi$
$620$		0			0
$621$		0			0
$622$	32.5830	+	210.684i	0.0523842	+	0.338720i
$623$			20.1271i			0.0323067i
$624$		0			0
$625$		0			0
$626$	−91.3625	+	14.1295i	−0.145946	+	0.0225711i
$627$		0			0
$628$	−130.768	+	41.4384i	−0.208229	+	0.0659847i
$629$	947.121			1.50576
$630$		0			0
$631$			936.738i			1.48453i	0.670107	+	0.742265i	$0.266248\pi$
$631$			936.738i			1.48453i	−0.670107	+	0.742265i	$0.733752\pi$
$632$	−362.206	−	730.490i	−0.573110	−	1.15584i
$633$		0			0
$634$	16.5390	−	2.55781i	0.0260867	−	0.00403440i
$635$		0			0
$636$		0			0
$637$	20.3735			0.0319836
$638$	−149.810	−	968.682i	−0.234812	−	1.51831i
$639$		0			0
$640$		0			0
$641$	−214.558			−0.334723			−0.167362	−	0.985896i	$-0.553525\pi$
$641$	−214.558			−0.334723			−0.167362	+	0.985896i	$0.553525\pi$
$642$		0			0
$643$			786.394i			1.22301i	0.791241	+	0.611504i	$0.209435\pi$
$643$			786.394i			1.22301i	−0.791241	+	0.611504i	$0.790565\pi$
$644$	29.2225	−	9.26020i	0.0453765	−	0.0143792i
$645$		0			0
$646$	70.7424	+	457.425i	0.109508	+	0.708088i
$647$		−	316.550i		−	0.489258i	−0.969617	−	0.244629i	$-0.921334\pi$
$647$		−	316.550i		−	0.489258i	0.969617	−	0.244629i	$-0.0786661\pi$
$648$		0			0
$649$	498.592			0.768246
$650$		0			0
$651$		0			0
$652$	200.024	+	631.219i	0.306786	+	0.968127i
$653$	−516.391			−0.790797			−0.395399	−	0.918510i	$-0.629394\pi$
$653$	−516.391			−0.790797			−0.395399	+	0.918510i	$0.629394\pi$
$654$		0			0
$655$		0			0
$656$	−610.926	+	430.408i	−0.931290	+	0.656110i
$657$		0			0
$658$	−53.3121	+	8.24491i	−0.0810215	+	0.0125303i
$659$			285.118i			0.432653i	0.976321	+	0.216326i	$0.0694076\pi$
$659$			285.118i			0.432653i	−0.976321	+	0.216326i	$0.930592\pi$
$660$		0			0
$661$	−391.847			−0.592809			−0.296405	−	0.955062i	$-0.595788\pi$
$661$	−391.847			−0.592809			−0.296405	+	0.955062i	$0.595788\pi$
$662$	33.9516	+	219.534i	0.0512865	+	0.331622i
$663$		0			0
$664$	20.9290	+	42.2092i	0.0315196	+	0.0635681i
$665$		0			0
$666$		0			0
$667$		−	555.593i		−	0.832973i
$668$	101.024	+	318.802i	0.151233	+	0.477248i
$669$		0			0
$670$		0			0
$671$		−	1533.65i		−	2.28562i
$672$		0			0
$673$	−1213.59			−1.80325			−0.901626	−	0.432517i	$-0.857625\pi$
$673$	−1213.59			−1.80325			−0.901626	+	0.432517i	$0.857625\pi$
$674$	−458.257	+	70.8711i	−0.679907	+	0.105150i
$675$		0			0
$676$	−643.756	+	203.997i	−0.952303	+	0.301771i
$677$	−251.863			−0.372028			−0.186014	−	0.982547i	$-0.559557\pi$
$677$	−251.863			−0.372028			−0.186014	+	0.982547i	$0.559557\pi$
$678$		0			0
$679$		−	31.5197i		−	0.0464207i
$680$		0			0
$681$		0			0
$682$	−1701.70	+	263.174i	−2.49517	+	0.385886i
$683$			664.793i			0.973342i	0.873585	+	0.486671i	$0.161789\pi$
$683$			664.793i			0.973342i	−0.873585	+	0.486671i	$0.838211\pi$
$684$		0			0
$685$		0			0
$686$	−9.87143	−	63.8293i	−0.0143898	−	0.0930457i
$687$		0			0
$688$	512.231	+	727.067i	0.744522	+	1.05678i
$689$	−12.4907			−0.0181287
$690$		0			0
$691$			654.347i			0.946957i	0.880805	+	0.473479i	$0.157002\pi$
$691$			654.347i			0.946957i	−0.880805	+	0.473479i	$0.842998\pi$
$692$	735.551	−	233.086i	1.06293	−	0.336829i
$693$		0			0
$694$	122.907	+	794.728i	0.177100	+	1.14514i
$695$		0			0
$696$		0			0
$697$	868.213			1.24564
$698$	322.732	−	49.9117i	0.462367	−	0.0715067i
$699$		0			0
$700$		0			0
$701$	1266.25			1.80635			0.903174	−	0.429275i	$-0.141231\pi$
$701$	1266.25			1.80635			0.903174	+	0.429275i	$0.141231\pi$
$702$		0			0
$703$		−	634.373i		−	0.902380i
$704$	1043.92	+	793.870i	1.48284	+	1.12766i
$705$		0			0
$706$	−347.570	+	53.7529i	−0.492309	+	0.0761372i
$707$		−	53.6661i		−	0.0759068i
$708$		0			0
$709$	−493.220			−0.695656			−0.347828	−	0.937558i	$-0.613081\pi$
$709$	−493.220			−0.695656			−0.347828	+	0.937558i	$0.613081\pi$
$710$		0			0
$711$		0			0
$712$	−437.278	+	216.819i	−0.614154	+	0.304522i
$713$	−976.020			−1.36889
$714$		0			0
$715$		0			0
$716$	146.134	+	461.156i	0.204098	+	0.644073i
$717$		0			0
$718$	105.649	+	683.135i	0.147144	+	0.951442i
$719$			60.3910i			0.0839930i	0.999118	+	0.0419965i	$0.0133718\pi$
$719$			60.3910i			0.0839930i	−0.999118	+	0.0419965i	$0.986628\pi$
$720$		0			0
$721$	52.1884			0.0723834
$722$	−407.138	+	62.9653i	−0.563904	+	0.0872096i
$723$		0			0
$724$	−410.228	+	129.995i	−0.566613	+	0.179552i
$725$		0			0
$726$		0			0
$727$		−	994.690i		−	1.36821i	−0.729383	−	0.684106i	$-0.760193\pi$
$727$		−	994.690i		−	1.36821i	0.729383	−	0.684106i	$-0.239807\pi$
$728$	−0.488554	−	0.985307i	−0.000671090	−	0.00135344i
$729$		0			0
$730$		0			0
$731$		−	1033.27i		−	1.41350i
$732$		0			0
$733$	1167.65			1.59298			0.796488	−	0.604654i	$-0.206689\pi$
$733$	1167.65			1.59298			0.796488	+	0.604654i	$0.206689\pi$
$734$	−222.835	−	1440.87i	−0.303590	−	1.96303i
$735$		0			0
$736$	515.986	+	535.127i	0.701067	+	0.727075i
$737$	−1491.83			−2.02420
$738$		0			0
$739$			79.9863i			0.108236i	0.998535	+	0.0541179i	$0.0172347\pi$
$739$			79.9863i			0.108236i	−0.998535	+	0.0541179i	$0.982765\pi$
$740$		0			0
$741$		0			0
$742$	3.02264	+	19.5446i	0.00407364	+	0.0263405i
$743$			402.122i			0.541214i	0.962690	+	0.270607i	$0.0872244\pi$
$743$			402.122i			0.541214i	−0.962690	+	0.270607i	$0.912776\pi$
$744$		0			0
$745$		0			0
$746$	−92.2530	+	14.2672i	−0.123664	+	0.0191250i
$747$		0			0
$748$	−460.267	−	1452.47i	−0.615330	−	1.94180i
$749$	−5.99844			−0.00800860
$750$		0			0
$751$			58.7486i			0.0782271i	0.999235	+	0.0391136i	$0.0124534\pi$
$751$			58.7486i			0.0782271i	−0.999235	+	0.0391136i	$0.987547\pi$
$752$	−753.434	−	1069.43i	−1.00191	−	1.42212i
$753$		0			0
$754$	−19.6985	+	3.04644i	−0.0261254	+	0.00404038i
$755$		0			0
$756$		0			0
$757$	−1040.91			−1.37504			−0.687522	−	0.726164i	$-0.741301\pi$
$757$	−1040.91			−1.37504			−0.687522	+	0.726164i	$0.741301\pi$
$758$	−35.9561	−	232.495i	−0.0474355	−	0.306721i
$759$		0			0
$760$		0			0
$761$	−750.095			−0.985670			−0.492835	−	0.870123i	$-0.664039\pi$
$761$	−750.095			−0.985670			−0.492835	+	0.870123i	$0.664039\pi$
$762$		0			0
$763$		−	51.7417i		−	0.0678135i
$764$	−337.976	−	1066.55i	−0.442377	−	1.39601i
$765$		0			0
$766$	−76.9285	−	497.425i	−0.100429	−	0.649380i
$767$		−	10.1391i		−	0.0132191i
$768$		0			0
$769$	1065.98			1.38619			0.693094	−	0.720847i	$-0.256247\pi$
$769$	1065.98			1.38619			0.693094	+	0.720847i	$0.256247\pi$
$770$		0			0
$771$		0			0
$772$	390.975	−	123.894i	0.506444	−	0.160485i
$773$	947.271			1.22545			0.612724	−	0.790297i	$-0.290074\pi$
$773$	947.271			1.22545			0.612724	+	0.790297i	$0.290074\pi$
$774$		0			0
$775$		0			0
$776$	684.791	−	339.546i	0.882463	−	0.437560i
$777$		0			0
$778$	705.393	−	109.092i	0.906675	−	0.140220i
$779$		−	581.521i		−	0.746497i
$780$		0			0
$781$	804.931			1.03064
$782$	−131.994	−	853.484i	−0.168791	−	1.09141i
$783$		0			0
$784$	639.491	−	450.533i	0.815678	−	0.574659i
$785$		0			0
$786$		0			0
$787$			11.5874i			0.0147236i	0.999973	+	0.00736178i	$0.00234335\pi$
$787$			11.5874i			0.0147236i	−0.999973	+	0.00736178i	$0.997657\pi$
$788$	148.572	−	47.0803i	0.188543	−	0.0597465i
$789$		0			0
$790$		0			0
$791$		−	32.5690i		−	0.0411744i
$792$		0			0
$793$	−31.1874			−0.0393284
$794$	−205.198	+	31.7345i	−0.258436	+	0.0399679i
$795$		0			0
$796$	−178.405	−	562.994i	−0.224127	−	0.707278i
$797$	780.220			0.978946			0.489473	−	0.872018i	$-0.337189\pi$
$797$	780.220			0.978946			0.489473	+	0.872018i	$0.337189\pi$
$798$		0			0
$799$			1519.82i			1.90215i
$800$		0			0
$801$		0			0
$802$	−240.339	+	37.1692i	−0.299674	+	0.0463457i
$803$			954.545i			1.18872i
$804$		0			0
$805$		0			0
$806$	5.35175	+	34.6048i	0.00663989	+	0.0429340i
$807$		0			0
$808$	1165.94	−	578.120i	1.44300	−	0.715495i
$809$	1061.80			1.31249			0.656243	−	0.754549i	$-0.272145\pi$
$809$	1061.80			1.31249			0.656243	+	0.754549i	$0.272145\pi$
$810$		0			0
$811$			309.236i			0.381302i	0.981658	+	0.190651i	$0.0610599\pi$
$811$			309.236i			0.381302i	−0.981658	+	0.190651i	$0.938940\pi$
$812$	9.53376	+	30.0858i	0.0117411	+	0.0370514i
$813$		0			0
$814$	319.157	+	2063.69i	0.392085	+	2.53525i
$815$		0			0
$816$		0			0
$817$	−692.072			−0.847089
$818$	−361.281	+	55.8734i	−0.441664	+	0.0683049i
$819$		0			0
$820$		0			0
$821$	1156.76			1.40897			0.704483	−	0.709721i	$-0.251179\pi$
$821$	1156.76			1.40897			0.704483	+	0.709721i	$0.251179\pi$
$822$		0			0
$823$		−	1441.89i		−	1.75200i	−0.482314	−	0.875998i	$-0.660204\pi$
$823$		−	1441.89i		−	1.75200i	0.482314	−	0.875998i	$-0.339796\pi$
$824$	562.201	+	1133.84i	0.682283	+	1.37602i
$825$		0			0
$826$	−15.8649	+	2.45357i	−0.0192069	+	0.00297042i
$827$		−	367.599i		−	0.444497i	−0.974990	−	0.222249i	$-0.928660\pi$
$827$		−	367.599i		−	0.444497i	0.974990	−	0.222249i	$-0.0713397\pi$
$828$		0			0
$829$	172.743			0.208375			0.104188	−	0.994558i	$-0.466776\pi$
$829$	172.743			0.208375			0.104188	+	0.994558i	$0.466776\pi$
$830$		0			0
$831$		0			0
$832$	16.1437	−	21.2285i	0.0194034	−	0.0255150i
$833$	−908.808			−1.09101
$834$		0			0
$835$		0			0
$836$	−972.850	+	308.283i	−1.16370	+	0.368759i
$837$		0			0
$838$	51.3593	+	332.093i	0.0612879	+	0.396292i
$839$			1083.17i			1.29103i	0.763748	+	0.645514i	$0.223357\pi$
$839$			1083.17i			1.29103i	−0.763748	+	0.645514i	$0.776643\pi$
$840$		0			0
$841$	−268.994			−0.319850
$842$	−1235.89	+	191.135i	−1.46780	+	0.227001i
$843$		0			0
$844$	−281.946	−	889.739i	−0.334059	−	1.05419i
$845$		0			0
$846$		0			0
$847$		−	98.6133i		−	0.116427i
$848$	−392.062	+	276.214i	−0.462337	+	0.325724i
$849$		0			0
$850$		0			0
$851$			1183.64i			1.39088i
$852$		0			0
$853$	1218.00			1.42790			0.713951	−	0.700196i	$-0.246904\pi$
$853$	1218.00			1.42790			0.713951	+	0.700196i	$0.246904\pi$
$854$	7.54709	+	48.8000i	0.00883734	+	0.0571429i
$855$		0			0
$856$	−64.6184	−	130.321i	−0.0754888	−	0.152244i
$857$	207.055			0.241604			0.120802	−	0.992677i	$-0.461453\pi$
$857$	207.055			0.241604			0.120802	+	0.992677i	$0.461453\pi$
$858$		0			0
$859$		−	1186.36i		−	1.38109i	−0.723290	−	0.690544i	$-0.757371\pi$
$859$		−	1186.36i		−	1.38109i	0.723290	−	0.690544i	$-0.242629\pi$
$860$		0			0
$861$		0			0
$862$	40.7809	+	263.692i	0.0473096	+	0.305907i
$863$		−	885.953i		−	1.02660i	−0.858210	−	0.513298i	$-0.828423\pi$
$863$		−	885.953i		−	1.02660i	0.858210	−	0.513298i	$-0.171577\pi$
$864$		0			0
$865$		0			0
$866$	1396.83	−	216.024i	1.61296	−	0.249450i
$867$		0			0
$868$	52.8522	−	16.7481i	0.0608897	−	0.0192951i
$869$	−2088.54			−2.40338
$870$		0			0
$871$			30.3370i			0.0348301i
$872$	1124.13	−	557.389i	1.28914	−	0.639207i
$873$		0			0
$874$	−571.656	+	88.4086i	−0.654069	+	0.101154i
$875$		0			0
$876$		0			0
$877$	643.339			0.733567			0.366784	−	0.930306i	$-0.380459\pi$
$877$	643.339			0.733567			0.366784	+	0.930306i	$0.380459\pi$
$878$	155.125	+	1003.05i	0.176680	+	1.14243i
$879$		0			0
$880$		0			0
$881$	−353.918			−0.401723			−0.200861	−	0.979620i	$-0.564374\pi$
$881$	−353.918			−0.401723			−0.200861	+	0.979620i	$0.564374\pi$
$882$		0			0
$883$			1093.51i			1.23840i	0.785233	+	0.619200i	$0.212543\pi$
$883$			1093.51i			1.23840i	−0.785233	+	0.619200i	$0.787457\pi$
$884$	−29.5365	+	9.35971i	−0.0334123	+	0.0105879i
$885$		0			0
$886$	125.990	+	814.659i	0.142201	+	0.919479i
$887$			520.234i			0.586510i	0.956034	+	0.293255i	$0.0947384\pi$
$887$			520.234i			0.586510i	−0.956034	+	0.293255i	$0.905262\pi$
$888$		0			0
$889$	8.93819			0.0100542
$890$		0			0
$891$		0			0
$892$	−99.9413	−	315.386i	−0.112042	−	0.353571i
$893$	1017.96			1.13993
$894$		0			0
$895$		0			0
$896$	−37.1236	−	20.1234i	−0.0414326	−	0.0224592i
$897$		0			0
$898$	−1598.23	+	247.172i	−1.77977	+	0.275248i
$899$		−	1004.85i		−	1.11775i
$900$		0			0
$901$	557.175			0.618397
$902$	292.567	+	1891.76i	0.324354	+	2.09729i
$903$		0			0
$904$	707.588	−	350.850i	0.782730	−	0.388109i
$905$		0			0
$906$		0			0
$907$			567.834i			0.626057i	0.949744	+	0.313029i	$0.101344\pi$
$907$			567.834i			0.626057i	−0.949744	+	0.313029i	$0.898656\pi$
$908$	436.851	+	1378.58i	0.481114	+	1.51825i
$909$		0			0
$910$		0			0
$911$			1180.19i			1.29549i	0.761858	+	0.647744i	$0.224287\pi$
$911$			1180.19i			1.29549i	−0.761858	+	0.647744i	$0.775713\pi$
$912$		0			0
$913$	120.680			0.132180
$914$	934.635	−	144.545i	1.02258	−	0.158145i
$915$		0			0
$916$	464.506	−	147.196i	0.507103	−	0.160694i
$917$	−1.47072			−0.00160384
$918$		0			0
$919$		−	54.5449i		−	0.0593524i	−0.999560	−	0.0296762i	$-0.990552\pi$
$919$		−	54.5449i		−	0.0593524i	0.999560	−	0.0296762i	$-0.00944761\pi$
$920$		0			0
$921$		0			0
$922$	857.360	−	132.594i	0.929892	−	0.143811i
$923$		−	16.3686i		−	0.0177341i
$924$		0			0
$925$		0			0
$926$	−162.197	−	1048.78i	−0.175159	−	1.13259i
$927$		0			0
$928$	−550.936	+	531.228i	−0.593681	+	0.572444i
$929$	−175.428			−0.188835			−0.0944175	−	0.995533i	$-0.530099\pi$
$929$	−175.428			−0.188835			−0.0944175	+	0.995533i	$0.530099\pi$
$930$		0			0
$931$			608.711i			0.653825i
$932$	520.929	−	165.075i	0.558937	−	0.177119i
$933$		0			0
$934$	−108.595	−	702.184i	−0.116269	−	0.751803i
$935$		0			0
$936$		0			0
$937$	335.374			0.357923			0.178962	−	0.983856i	$-0.442726\pi$
$937$	335.374			0.357923			0.178962	+	0.983856i	$0.442726\pi$
$938$	47.4694	−	7.34130i	0.0506070	−	0.00782654i
$939$		0			0
$940$		0			0
$941$	−709.182			−0.753647			−0.376823	−	0.926285i	$-0.622984\pi$
$941$	−709.182			−0.753647			−0.376823	+	0.926285i	$0.622984\pi$
$942$		0			0
$943$			1085.03i			1.15061i
$944$	−224.211	−	318.248i	−0.237512	−	0.337127i
$945$		0			0
$946$	2251.39	−	348.186i	2.37991	−	0.368061i
$947$			992.486i			1.04803i	0.851708	+	0.524016i	$0.175567\pi$
$947$			992.486i			1.04803i	−0.851708	+	0.524016i	$0.824433\pi$
$948$		0			0
$949$	19.4110			0.0204542
$950$		0			0
$951$		0			0
$952$	21.7930	+	43.9518i	0.0228919	+	0.0461679i
$953$	1438.16			1.50908			0.754542	−	0.656251i	$-0.227859\pi$
$953$	1438.16			1.50908			0.754542	+	0.656251i	$0.227859\pi$
$954$		0			0
$955$		0			0
$956$	68.2260	+	215.301i	0.0713661	+	0.225211i
$957$		0			0
$958$	167.704	+	1084.39i	0.175057	+	1.13193i
$959$		−	59.9425i		−	0.0625052i
$960$		0			0
$961$	−804.245			−0.836883
$962$	41.9660	−	6.49018i	0.0436237	−	0.00674655i
$963$		0			0
$964$	−8.54744	+	2.70857i	−0.00886664	+	0.00280971i
$965$		0			0
$966$		0			0
$967$			1376.32i			1.42329i	0.702539	+	0.711646i	$0.252050\pi$
$967$			1376.32i			1.42329i	−0.702539	+	0.711646i	$0.747950\pi$
$968$	2142.46	−	1062.31i	2.21328	−	1.09743i
$969$		0			0
$970$		0			0
$971$			652.667i			0.672159i	0.941834	+	0.336080i	$0.109101\pi$
$971$			652.667i			0.672159i	−0.941834	+	0.336080i	$0.890899\pi$
$972$		0			0
$973$	73.7053			0.0757506
$974$	−41.1490	−	266.072i	−0.0422474	−	0.273175i
$975$		0			0
$976$	−978.920	+	689.666i	−1.00299	+	0.706625i
$977$	467.260			0.478260			0.239130	−	0.970988i	$-0.423138\pi$
$977$	467.260			0.478260			0.239130	+	0.970988i	$0.423138\pi$
$978$		0			0
$979$			1250.22i			1.27703i
$980$		0			0
$981$		0			0
$982$	−231.336	−	1495.84i	−0.235577	−	1.52326i
$983$		−	1044.27i		−	1.06233i	−0.847268	−	0.531165i	$-0.821754\pi$
$983$		−	1044.27i		−	1.06233i	0.847268	−	0.531165i	$-0.178246\pi$
$984$		0			0
$985$		0			0
$986$	878.697	−	135.894i	0.891174	−	0.137823i
$987$		0			0
$988$	6.26905	+	19.7833i	0.00634519	+	0.0200236i
$989$	1291.30			1.30566
$990$		0			0
$991$		−	1705.99i		−	1.72148i	−0.509044	−	0.860740i	$-0.670001\pi$
$991$		−	1705.99i		−	1.72148i	0.509044	−	0.860740i	$-0.329999\pi$
$992$	933.219	+	967.839i	0.940745	+	0.975644i
$993$		0			0
$994$	−25.6125	+	3.96106i	−0.0257671	+	0.00398497i
$995$		0			0
$996$		0			0
$997$	−1262.24			−1.26604			−0.633020	−	0.774136i	$-0.718185\pi$
$997$	−1262.24			−1.26604			−0.633020	+	0.774136i	$0.718185\pi$
$998$	−216.097	−	1397.30i	−0.216530	−	1.40010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.n.451.2		8
3.2	odd	2		300.3.c.g.151.7	yes	8
4.3	odd	2	inner	900.3.c.n.451.1		8
5.2	odd	4		900.3.f.h.199.7		16
5.3	odd	4		900.3.f.h.199.10		16
5.4	even	2		900.3.c.t.451.7		8
12.11	even	2		300.3.c.g.151.8	yes	8
15.2	even	4		300.3.f.c.199.10		16
15.8	even	4		300.3.f.c.199.7		16
15.14	odd	2		300.3.c.e.151.2	yes	8
20.3	even	4		900.3.f.h.199.8		16
20.7	even	4		900.3.f.h.199.9		16
20.19	odd	2		900.3.c.t.451.8		8
60.23	odd	4		300.3.f.c.199.9		16
60.47	odd	4		300.3.f.c.199.8		16
60.59	even	2		300.3.c.e.151.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.1	✓	8	60.59	even	2
300.3.c.e.151.2	yes	8	15.14	odd	2
300.3.c.g.151.7	yes	8	3.2	odd	2
300.3.c.g.151.8	yes	8	12.11	even	2
300.3.f.c.199.7		16	15.8	even	4
300.3.f.c.199.8		16	60.47	odd	4
300.3.f.c.199.9		16	60.23	odd	4
300.3.f.c.199.10		16	15.2	even	4
900.3.c.n.451.1		8	4.3	odd	2	inner
900.3.c.n.451.2		8	1.1	even	1	trivial
900.3.c.t.451.7		8	5.4	even	2
900.3.c.t.451.8		8	20.19	odd	2
900.3.f.h.199.7		16	5.2	odd	4
900.3.f.h.199.8		16	20.3	even	4
900.3.f.h.199.9		16	20.7	even	4
900.3.f.h.199.10		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)

\(f(q)\)	\(=\)	\(q+(-1.97650 + 0.305673i) q^{2} +(3.81313 - 1.20833i) q^{4} +0.329898i q^{7} +(-7.16731 + 3.55383i) q^{8} +O(q^{10})\)	\(q+(-1.97650 + 0.305673i) q^{2} +(3.81313 - 1.20833i) q^{4} +0.329898i q^{7} +(-7.16731 + 3.55383i) q^{8} +20.4920i q^{11} +0.416712 q^{13} +(-0.100841 - 0.652044i) q^{14} +(13.0799 - 9.21501i) q^{16} -18.5884 q^{17} +12.4503i q^{19} +(-6.26384 - 40.5024i) q^{22} -23.2304i q^{23} +(-0.823633 + 0.127378i) q^{26} +(0.398624 + 1.25794i) q^{28} +23.9166 q^{29} -42.0148i q^{31} +(-23.0357 + 22.2117i) q^{32} +(36.7400 - 5.68197i) q^{34} -50.9523 q^{37} +(-3.80573 - 24.6081i) q^{38} -46.7073 q^{41} +55.5866i q^{43} +(24.7610 + 78.1385i) q^{44} +(7.10090 + 45.9149i) q^{46} -81.7616i q^{47} +48.8912 q^{49} +(1.58898 - 0.503524i) q^{52} -29.9744 q^{53} +(-1.17240 - 2.36448i) q^{56} +(-47.2713 + 7.31067i) q^{58} -24.3311i q^{59} -74.8416 q^{61} +(12.8428 + 83.0424i) q^{62} +(38.7406 - 50.9428i) q^{64} +72.8008i q^{67} +(-70.8799 + 22.4608i) q^{68} -39.2803i q^{71} +46.5814 q^{73} +(100.707 - 15.5747i) q^{74} +(15.0441 + 47.4747i) q^{76} -6.76026 q^{77} +101.920i q^{79} +(92.3170 - 14.2771i) q^{82} -5.88913i q^{83} +(-16.9913 - 109.867i) q^{86} +(-72.8250 - 146.872i) q^{88} +61.0100 q^{89} +0.137472i q^{91} +(-28.0699 - 88.5804i) q^{92} +(24.9923 + 161.602i) q^{94} -95.5437 q^{97} +(-96.6335 + 14.9447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{4} - 20 q^{8}+O(q^{10}) \) 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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