LMFDB - Embedded newform 900.3.c.t.451.8

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			451.8
Root			$1.65359 + 0.954702i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.t.451.7

$q$-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	$-0.618542\pi$
$11$		−	20.4920i		−	1.86291i	0.363861	−	0.931453i	$-0.381458\pi$
$12$		0			0
$13$	−0.416712			−0.0320548			−0.0160274	−	0.999872i	$-0.505102\pi$
$13$	−0.416712			−0.0320548			−0.0160274	+	0.999872i	$0.505102\pi$
$14$	−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	$-0.315877\pi$
$17$	18.5884			1.09343			0.546717	+	0.837317i	$0.315877\pi$
$18$		0			0
$19$		−	12.4503i		−	0.655281i	−0.944803	−	0.327640i	$-0.893747\pi$
$19$		−	12.4503i		−	0.655281i	0.944803	−	0.327640i	$-0.106253\pi$
$20$		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	$0.237005\pi$
$31$			42.0148i			1.35532i	−0.735377	+	0.677658i	$0.762995\pi$
$32$	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	$-0.258250\pi$
$37$	50.9523			1.37709			0.688545	+	0.725194i	$0.258250\pi$
$38$	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	$-0.408744\pi$
$53$	29.9744			0.565554			0.282777	+	0.959186i	$0.408744\pi$
$54$		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	$0.0661083\pi$
$59$			24.3311i			0.412391i	−0.978511	+	0.206196i	$0.933892\pi$
$60$		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	$0.0892150\pi$
$71$			39.2803i			0.553244i	−0.960979	+	0.276622i	$0.910785\pi$
$72$		0			0
$73$	−46.5814			−0.638101			−0.319051	−	0.947738i	$-0.603364\pi$
$73$	−46.5814			−0.638101			−0.319051	+	0.947738i	$0.603364\pi$
$74$	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	$-0.776832\pi$
$79$		−	101.920i		−	1.29012i	0.764131	−	0.645062i	$-0.223168\pi$
$80$		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	$-0.336086\pi$
$97$	95.5437			0.984987			0.492494	+	0.870316i	$0.336086\pi$
$98$	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	$-0.356100\pi$
$113$	98.7245			0.873668			0.436834	+	0.899542i	$0.356100\pi$
$114$		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	$-0.994583\pi$
$131$		−	4.45811i		−	0.0340314i	0.999855	−	0.0170157i	$-0.00541653\pi$
$132$		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	$-0.269224\pi$
$137$	181.700			1.32628			0.663139	+	0.748496i	$0.269224\pi$
$138$		0			0
$139$			223.419i			1.60733i	0.595083	+	0.803664i	$0.297119\pi$
$139$			223.419i			1.60733i	−0.595083	+	0.803664i	$0.702881\pi$
$140$		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	$-0.918920\pi$
$151$		−	76.0961i		−	0.503948i	0.967734	−	0.251974i	$-0.0810797\pi$
$152$	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	$-0.465166\pi$
$157$	34.2940			0.218433			0.109217	+	0.994018i	$0.465166\pi$
$158$	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	$-0.688244\pi$
$173$	−192.900			−1.11503			−0.557513	+	0.830168i	$0.688244\pi$
$174$		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	$-0.890311\pi$
$179$		−	120.939i		−	0.675637i	0.941211	−	0.337819i	$-0.109689\pi$
$180$		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	$0.261513\pi$
$191$			279.706i			1.46443i	−0.681075	+	0.732214i	$0.738487\pi$
$192$		0			0
$193$	−102.534			−0.531263			−0.265632	−	0.964075i	$-0.585580\pi$
$193$	−102.534			−0.531263			−0.265632	+	0.964075i	$0.585580\pi$
$194$	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	$-0.531530\pi$
$197$	−38.9632			−0.197783			−0.0988913	+	0.995098i	$0.531530\pi$
$198$		0			0
$199$			147.646i			0.741940i	0.928645	+	0.370970i	$0.120975\pi$
$199$			147.646i			0.741940i	−0.928645	+	0.370970i	$0.879025\pi$
$200$		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	$0.186490\pi$
$211$			233.336i			1.10586i	−0.833229	+	0.552928i	$0.813510\pi$
$212$	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	$-0.594708\pi$
$233$	−136.615			−0.586329			−0.293164	+	0.956062i	$0.594708\pi$
$234$		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	$-0.962312\pi$
$239$		−	56.4632i		−	0.236248i	0.992999	−	0.118124i	$-0.0376880\pi$
$240$		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	$-0.710877\pi$
$251$		−	395.809i		−	1.57693i	0.615081	−	0.788464i	$-0.289123\pi$
$252$		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	$-0.568511\pi$
$257$	−109.778			−0.427151			−0.213576	+	0.976927i	$0.568511\pi$
$258$		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	$-0.791874\pi$
$271$		−	329.669i		−	1.21649i	0.793750	−	0.608245i	$-0.208126\pi$
$272$	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	$-0.315024\pi$
$277$	304.124			1.09792			0.548960	+	0.835849i	$0.315024\pi$
$278$	−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	$-0.732041\pi$
$293$	−390.339			−1.33222			−0.666108	+	0.745855i	$0.732041\pi$
$294$		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	$0.0548205\pi$
$311$			106.594i			0.342747i	−0.985206	+	0.171373i	$0.945180\pi$
$312$		0			0
$313$	−46.2243			−0.147682			−0.0738408	−	0.997270i	$-0.523526\pi$
$313$	−46.2243			−0.147682			−0.0738408	+	0.997270i	$0.523526\pi$
$314$	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	$-0.495799\pi$
$317$	8.36780			0.0263969			0.0131984	+	0.999913i	$0.495799\pi$
$318$		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	$0.0536605\pi$
$331$			111.072i			0.335564i	−0.985824	+	0.167782i	$0.946339\pi$
$332$	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	$-0.611780\pi$
$337$	−231.853			−0.687990			−0.343995	+	0.938972i	$0.611780\pi$
$338$	−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	$-0.580128\pi$
$353$	−175.851			−0.498161			−0.249081	+	0.968483i	$0.580128\pi$
$354$		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	$0.159863\pi$
$359$			345.628i			0.962753i	−0.876514	+	0.481377i	$0.840137\pi$
$360$		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	$-0.519929\pi$
$373$	−46.6749			−0.125134			−0.0625668	+	0.998041i	$0.519929\pi$
$374$	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	$-0.950403\pi$
$379$		−	117.629i		−	0.310368i	0.987886	−	0.155184i	$-0.0495970\pi$
$380$		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	$-0.541740\pi$
$397$	−103.819			−0.261508			−0.130754	+	0.991415i	$0.541740\pi$
$398$	−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	$0.0642572\pi$
$419$			168.020i			0.401003i	−0.979693	+	0.200502i	$0.935743\pi$
$420$		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	$0.0494643\pi$
$431$			133.413i			0.309544i	−0.987950	+	0.154772i	$0.950536\pi$
$432$		0			0
$433$	706.716			1.63214			0.816069	−	0.577954i	$-0.196149\pi$
$433$	706.716			1.63214			0.816069	+	0.577954i	$0.196149\pi$
$434$	−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	$0.196169\pi$
$439$			507.488i			1.15601i	−0.816033	+	0.578005i	$0.803831\pi$
$440$		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	$-0.326912\pi$
$457$	472.873			1.03473			0.517367	+	0.855764i	$0.326912\pi$
$458$	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	$0.194101\pi$
$479$			548.640i			1.14539i	−0.819770	+	0.572693i	$0.805899\pi$
$480$		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	$-0.719916\pi$
$491$		−	756.810i		−	1.54136i	0.637220	−	0.770682i	$-0.280084\pi$
$492$		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	$-0.749430\pi$
$499$		−	706.956i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$500$		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	$-0.509103\pi$
$557$	−31.8538			−0.0571882			−0.0285941	+	0.999591i	$0.509103\pi$
$558$		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	$0.0747995\pi$
$571$			265.895i			0.465666i	−0.972517	+	0.232833i	$0.925200\pi$
$572$	−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	$-0.461817\pi$
$577$	138.097			0.239336			0.119668	+	0.992814i	$0.461817\pi$
$578$	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	$-0.404534\pi$
$593$	350.392			0.590880			0.295440	+	0.955361i	$0.404534\pi$
$594$		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	$-0.925798\pi$
$599$		−	276.745i		−	0.462012i	0.972952	−	0.231006i	$-0.0742017\pi$
$600$		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	$-0.194050\pi$
$613$	1005.15			1.63972			0.819862	+	0.572561i	$0.194050\pi$
$614$	−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	$-0.642247\pi$
$617$	−533.282			−0.864314			−0.432157	+	0.901798i	$0.642247\pi$
$618$		0			0
$619$			1136.85i			1.83659i	0.395900	+	0.918294i	$0.370433\pi$
$619$			1136.85i			1.83659i	−0.395900	+	0.918294i	$0.629567\pi$
$620$		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	$-0.733752\pi$
$631$		−	936.738i		−	1.48453i	0.670107	−	0.742265i	$-0.266248\pi$
$632$	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	$-0.370606\pi$
$653$	516.391			0.790797			0.395399	+	0.918510i	$0.370606\pi$
$654$		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	$-0.930592\pi$
$659$		−	285.118i		−	0.432653i	0.976321	−	0.216326i	$-0.0694076\pi$
$660$		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	$-0.142375\pi$
$673$	1213.59			1.80325			0.901626	+	0.432517i	$0.142375\pi$
$674$	−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	$-0.440443\pi$
$677$	251.863			0.372028			0.186014	+	0.982547i	$0.440443\pi$
$678$		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	$-0.842998\pi$
$691$		−	654.347i		−	0.946957i	0.880805	−	0.473479i	$-0.157002\pi$
$692$	−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	$-0.986628\pi$
$719$		−	60.3910i		−	0.0839930i	0.999118	−	0.0419965i	$-0.0133718\pi$
$720$		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	$-0.793311\pi$
$733$	−1167.65			−1.59298			−0.796488	+	0.604654i	$0.793311\pi$
$734$	−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	$-0.982765\pi$
$739$		−	79.9863i		−	0.108236i	0.998535	−	0.0541179i	$-0.0172347\pi$
$740$		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	$-0.987547\pi$
$751$		−	58.7486i		−	0.0782271i	0.999235	−	0.0391136i	$-0.0124534\pi$
$752$	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	$-0.258699\pi$
$757$	1040.91			1.37504			0.687522	+	0.726164i	$0.258699\pi$
$758$	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	$-0.709926\pi$
$773$	−947.271			−1.22545			−0.612724	+	0.790297i	$0.709926\pi$
$774$		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	$-0.662811\pi$
$797$	−780.220			−0.978946			−0.489473	+	0.872018i	$0.662811\pi$
$798$		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	$-0.938940\pi$
$811$		−	309.236i		−	0.381302i	0.981658	−	0.190651i	$-0.0610599\pi$
$812$	−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	$-0.776643\pi$
$839$		−	1083.17i		−	1.29103i	0.763748	−	0.645514i	$-0.223357\pi$
$840$		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	$-0.753096\pi$
$853$	−1218.00			−1.42790			−0.713951	+	0.700196i	$0.753096\pi$
$854$	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	$-0.538547\pi$
$857$	−207.055			−0.241604			−0.120802	+	0.992677i	$0.538547\pi$
$858$		0			0
$859$			1186.36i			1.38109i	0.723290	+	0.690544i	$0.242629\pi$
$859$			1186.36i			1.38109i	−0.723290	+	0.690544i	$0.757371\pi$
$860$		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	$-0.619541\pi$
$877$	−643.339			−0.733567			−0.366784	+	0.930306i	$0.619541\pi$
$878$	−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	$-0.775713\pi$
$911$		−	1180.19i		−	1.29549i	0.761858	−	0.647744i	$-0.224287\pi$
$912$		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	$0.00944761\pi$
$919$			54.5449i			0.0593524i	−0.999560	+	0.0296762i	$0.990552\pi$
$920$		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	$-0.557274\pi$
$937$	−335.374			−0.357923			−0.178962	+	0.983856i	$0.557274\pi$
$938$	−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	$-0.772141\pi$
$953$	−1438.16			−1.50908			−0.754542	+	0.656251i	$0.772141\pi$
$954$		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	$-0.890899\pi$
$971$		−	652.667i		−	0.672159i	0.941834	−	0.336080i	$-0.109101\pi$
$972$		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	$-0.576862\pi$
$977$	−467.260			−0.478260			−0.239130	+	0.970988i	$0.576862\pi$
$978$		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	$0.329999\pi$
$991$			1705.99i			1.72148i	−0.509044	+	0.860740i	$0.670001\pi$
$992$	−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	$-0.281815\pi$
$997$	1262.24			1.26604			0.633020	+	0.774136i	$0.281815\pi$
$998$	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.t.451.8		8
3.2	odd	2		300.3.c.e.151.1	✓	8
4.3	odd	2	inner	900.3.c.t.451.7		8
5.2	odd	4		900.3.f.h.199.8		16
5.3	odd	4		900.3.f.h.199.9		16
5.4	even	2		900.3.c.n.451.1		8
12.11	even	2		300.3.c.e.151.2	yes	8
15.2	even	4		300.3.f.c.199.9		16
15.8	even	4		300.3.f.c.199.8		16
15.14	odd	2		300.3.c.g.151.8	yes	8
20.3	even	4		900.3.f.h.199.7		16
20.7	even	4		900.3.f.h.199.10		16
20.19	odd	2		900.3.c.n.451.2		8
60.23	odd	4		300.3.f.c.199.10		16
60.47	odd	4		300.3.f.c.199.7		16
60.59	even	2		300.3.c.g.151.7	yes	8

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