LMFDB - Embedded newform 950.3.d.b.949.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,3,Mod(949,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("950.949");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	950.d (of order $2$, degree $1$, not 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:	$25.8856251142$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			949.18
Character	$\chi$	$=$	950.949
Dual form			950.3.d.b.949.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -1.89288 q^{3} +2.00000 q^{4} -2.67694 q^{6} +1.68650i q^{7} +2.82843 q^{8} -5.41699 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -1.89288 q^{3} +2.00000 q^{4} -2.67694 q^{6} +1.68650i q^{7} +2.82843 q^{8} -5.41699 q^{9} +1.04411 q^{11} -3.78577 q^{12} +6.02294 q^{13} +2.38506i q^{14} +4.00000 q^{16} -21.6652i q^{17} -7.66078 q^{18} +(17.3019 - 7.85143i) q^{19} -3.19234i q^{21} +1.47660 q^{22} +39.8186i q^{23} -5.35389 q^{24} +8.51772 q^{26} +27.2897 q^{27} +3.37299i q^{28} -0.278403i q^{29} -19.8410i q^{31} +5.65685 q^{32} -1.97638 q^{33} -30.6392i q^{34} -10.8340 q^{36} +68.3424 q^{37} +(24.4686 - 11.1036i) q^{38} -11.4007 q^{39} -3.84932i q^{41} -4.51465i q^{42} +65.0642i q^{43} +2.08822 q^{44} +56.3120i q^{46} -9.61045i q^{47} -7.57154 q^{48} +46.1557 q^{49} +41.0097i q^{51} +12.0459 q^{52} +62.0602 q^{53} +38.5935 q^{54} +4.77013i q^{56} +(-32.7505 + 14.8618i) q^{57} -0.393722i q^{58} -94.0807i q^{59} -19.4070 q^{61} -28.0595i q^{62} -9.13572i q^{63} +8.00000 q^{64} -2.79503 q^{66} +62.2388 q^{67} -43.3304i q^{68} -75.3720i q^{69} +41.4101i q^{71} -15.3216 q^{72} -3.25235i q^{73} +96.6507 q^{74} +(34.6038 - 15.7029i) q^{76} +1.76089i q^{77} -16.1231 q^{78} -84.1379i q^{79} -2.90334 q^{81} -5.44376i q^{82} +5.58177i q^{83} -6.38468i q^{84} +92.0147i q^{86} +0.526985i q^{87} +2.95319 q^{88} +84.3407i q^{89} +10.1577i q^{91} +79.6372i q^{92} +37.5568i q^{93} -13.5912i q^{94} -10.7078 q^{96} -1.89498 q^{97} +65.2741 q^{98} -5.65594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9}+O(q^{10}) $ 24 * q + 48 * q^4 - 16 * q^6 + 56 * q^9	$ 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9} + 8 q^{11} + 96 q^{16} + 24 q^{19} - 32 q^{24} - 32 q^{26} + 112 q^{36} - 200 q^{39} + 16 q^{44} + 216 q^{49} - 224 q^{54} - 152 q^{61} + 192 q^{64} + 16 q^{66} - 144 q^{74} + 48 q^{76} - 264 q^{81} - 64 q^{96} - 256 q^{99}+O(q^{100}) $ 24 * q + 48 * q^4 - 16 * q^6 + 56 * q^9 + 8 * q^11 + 96 * q^16 + 24 * q^19 - 32 * q^24 - 32 * q^26 + 112 * q^36 - 200 * q^39 + 16 * q^44 + 216 * q^49 - 224 * q^54 - 152 * q^61 + 192 * q^64 + 16 * q^66 - 144 * q^74 + 48 * q^76 - 264 * q^81 - 64 * q^96 - 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	−1.89288			−0.630961			−0.315481	−	0.948932i	$-0.602166\pi$
$3$	−1.89288			−0.630961			−0.315481	+	0.948932i	$0.602166\pi$
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−2.67694			−0.446157
$7$			1.68650i			0.240928i	0.992718	+	0.120464i	$0.0384382\pi$
$7$			1.68650i			0.240928i	−0.992718	+	0.120464i	$0.961562\pi$
$8$	2.82843			0.353553
$9$	−5.41699			−0.601888
$10$		0			0
$11$	1.04411			0.0949193			0.0474596	−	0.998873i	$-0.484887\pi$
$11$	1.04411			0.0949193			0.0474596	+	0.998873i	$0.484887\pi$
$12$	−3.78577			−0.315481
$13$	6.02294			0.463303			0.231652	−	0.972799i	$-0.425587\pi$
$13$	6.02294			0.463303			0.231652	+	0.972799i	$0.425587\pi$
$14$			2.38506i			0.170362i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	21.6652i		−	1.27442i	−0.770689	−	0.637212i	$-0.780088\pi$
$17$		−	21.6652i		−	1.27442i	0.770689	−	0.637212i	$-0.219912\pi$
$18$	−7.66078			−0.425599
$19$	17.3019	−	7.85143i	0.910625	−	0.413233i
$19$	17.3019	−	7.85143i	0.910625	−	0.413233i
$20$		0			0
$21$		−	3.19234i		−	0.152016i
$22$	1.47660			0.0671181
$23$			39.8186i			1.73124i	0.500698	+	0.865622i	$0.333077\pi$
$23$			39.8186i			1.73124i	−0.500698	+	0.865622i	$0.666923\pi$
$24$	−5.35389			−0.223079
$25$		0			0
$26$	8.51772			0.327605
$27$	27.2897			1.01073
$28$			3.37299i			0.120464i
$29$		−	0.278403i		−	0.00960011i	−0.999988	−	0.00480006i	$-0.998472\pi$
$29$		−	0.278403i		−	0.00960011i	0.999988	−	0.00480006i	$-0.00152791\pi$
$30$		0			0
$31$		−	19.8410i		−	0.640034i	−0.947412	−	0.320017i	$-0.896311\pi$
$31$		−	19.8410i		−	0.640034i	0.947412	−	0.320017i	$-0.103689\pi$
$32$	5.65685			0.176777
$33$	−1.97638			−0.0598904
$34$		−	30.6392i		−	0.901154i
$35$		0			0
$36$	−10.8340			−0.300944
$37$	68.3424			1.84709			0.923546	−	0.383488i	$-0.125277\pi$
$37$	68.3424			1.84709			0.923546	+	0.383488i	$0.125277\pi$
$38$	24.4686	−	11.1036i	0.643909	−	0.292200i
$39$	−11.4007			−0.292326
$40$		0			0
$41$		−	3.84932i		−	0.0938858i	−0.998898	−	0.0469429i	$-0.985052\pi$
$41$		−	3.84932i		−	0.0938858i	0.998898	−	0.0469429i	$-0.0149479\pi$
$42$		−	4.51465i		−	0.107492i
$43$			65.0642i			1.51312i	0.653924	+	0.756561i	$0.273122\pi$
$43$			65.0642i			1.51312i	−0.653924	+	0.756561i	$0.726878\pi$
$44$	2.08822			0.0474596
$45$		0			0
$46$			56.3120i			1.22417i
$47$		−	9.61045i		−	0.204478i	−0.994760	−	0.102239i	$-0.967399\pi$
$47$		−	9.61045i		−	0.204478i	0.994760	−	0.102239i	$-0.0326006\pi$
$48$	−7.57154			−0.157740
$49$	46.1557			0.941954
$50$		0			0
$51$			41.0097i			0.804112i
$52$	12.0459			0.231652
$53$	62.0602			1.17095			0.585474	−	0.810691i	$-0.300909\pi$
$53$	62.0602			1.17095			0.585474	+	0.810691i	$0.300909\pi$
$54$	38.5935			0.714694
$55$		0			0
$56$			4.77013i			0.0851809i
$57$	−32.7505	+	14.8618i	−0.574569	+	0.260734i
$58$		−	0.393722i		−	0.00678830i
$59$		−	94.0807i		−	1.59459i	−0.603591	−	0.797294i	$-0.706264\pi$
$59$		−	94.0807i		−	1.59459i	0.603591	−	0.797294i	$-0.293736\pi$
$60$		0			0
$61$	−19.4070			−0.318148			−0.159074	−	0.987267i	$-0.550851\pi$
$61$	−19.4070			−0.318148			−0.159074	+	0.987267i	$0.550851\pi$
$62$		−	28.0595i		−	0.452572i
$63$		−	9.13572i		−	0.145012i
$64$	8.00000			0.125000
$65$		0			0
$66$	−2.79503			−0.0423489
$67$	62.2388			0.928937			0.464469	−	0.885590i	$-0.346245\pi$
$67$	62.2388			0.928937			0.464469	+	0.885590i	$0.346245\pi$
$68$		−	43.3304i		−	0.637212i
$69$		−	75.3720i		−	1.09235i
$70$		0			0
$71$			41.4101i			0.583241i	0.956534	+	0.291621i	$0.0941945\pi$
$71$			41.4101i			0.583241i	−0.956534	+	0.291621i	$0.905805\pi$
$72$	−15.3216			−0.212799
$73$		−	3.25235i		−	0.0445527i	−0.999752	−	0.0222763i	$-0.992909\pi$
$73$		−	3.25235i		−	0.0445527i	0.999752	−	0.0222763i	$-0.00709137\pi$
$74$	96.6507			1.30609
$75$		0			0
$76$	34.6038	−	15.7029i	0.455313	−	0.206617i
$77$			1.76089i			0.0228687i
$78$	−16.1231			−0.206706
$79$		−	84.1379i		−	1.06504i	−0.846418	−	0.532519i	$-0.821246\pi$
$79$		−	84.1379i		−	1.06504i	0.846418	−	0.532519i	$-0.178754\pi$
$80$		0			0
$81$	−2.90334			−0.0358437
$82$		−	5.44376i		−	0.0663873i
$83$			5.58177i			0.0672503i	0.999435	+	0.0336251i	$0.0107052\pi$
$83$			5.58177i			0.0672503i	−0.999435	+	0.0336251i	$0.989295\pi$
$84$		−	6.38468i		−	0.0760081i
$85$		0			0
$86$			92.0147i			1.06994i
$87$			0.526985i			0.00605730i
$88$	2.95319			0.0335590
$89$			84.3407i			0.947648i	0.880619	+	0.473824i	$0.157127\pi$
$89$			84.3407i			0.947648i	−0.880619	+	0.473824i	$0.842873\pi$
$90$		0			0
$91$			10.1577i			0.111623i
$92$			79.6372i			0.865622i
$93$			37.5568i			0.403837i
$94$		−	13.5912i		−	0.144588i
$95$		0			0
$96$	−10.7078			−0.111539
$97$	−1.89498			−0.0195359			−0.00976795	−	0.999952i	$-0.503109\pi$
$97$	−1.89498			−0.0195359			−0.00976795	+	0.999952i	$0.503109\pi$
$98$	65.2741			0.666062
$99$	−5.65594			−0.0571307
$100$		0			0
$101$	15.0979			0.149484			0.0747418	−	0.997203i	$-0.476187\pi$
$101$	15.0979			0.149484			0.0747418	+	0.997203i	$0.476187\pi$
$102$			57.9965i			0.568593i
$103$	143.352			1.39177			0.695883	−	0.718155i	$-0.255013\pi$
$103$	143.352			1.39177			0.695883	+	0.718155i	$0.255013\pi$
$104$	17.0354			0.163802
$105$		0			0
$106$	87.7664			0.827985
$107$	118.658			1.10895			0.554475	−	0.832200i	$-0.312919\pi$
$107$	118.658			1.10895			0.554475	+	0.832200i	$0.312919\pi$
$108$	54.5794			0.505365
$109$		−	62.2344i		−	0.570957i	−0.958385	−	0.285479i	$-0.907847\pi$
$109$		−	62.2344i		−	0.570957i	0.958385	−	0.285479i	$-0.0921526\pi$
$110$		0			0
$111$	−129.364			−1.16544
$112$			6.74598i			0.0602320i
$113$	−88.8122			−0.785949			−0.392974	−	0.919549i	$-0.628554\pi$
$113$	−88.8122			−0.785949			−0.392974	+	0.919549i	$0.628554\pi$
$114$	−46.3161	+	21.0178i	−0.406282	+	0.184367i
$115$		0			0
$116$		−	0.556806i		−	0.00480006i
$117$	−32.6262			−0.278856
$118$		−	133.050i		−	1.12754i
$119$	36.5383			0.307044
$120$		0			0
$121$	−119.910			−0.990990
$122$	−27.4456			−0.224964
$123$			7.28632i			0.0592383i
$124$		−	39.6821i		−	0.320017i
$125$		0			0
$126$		−	12.9199i		−	0.102539i
$127$	9.31099			0.0733149			0.0366574	−	0.999328i	$-0.488329\pi$
$127$	9.31099			0.0733149			0.0366574	+	0.999328i	$0.488329\pi$
$128$	11.3137			0.0883883
$129$		−	123.159i		−	0.954721i
$130$		0			0
$131$	147.708			1.12754			0.563769	−	0.825932i	$-0.309351\pi$
$131$	147.708			1.12754			0.563769	+	0.825932i	$0.309351\pi$
$132$	−3.95277			−0.0299452
$133$	13.2414	+	29.1795i	0.0995594	+	0.219395i
$134$	88.0189			0.656858
$135$		0			0
$136$		−	61.2785i		−	0.450577i
$137$			147.080i			1.07358i	0.843716	+	0.536789i	$0.180363\pi$
$137$			147.080i			1.07358i	−0.843716	+	0.536789i	$0.819637\pi$
$138$		−	106.592i		−	0.772407i
$139$	78.4626			0.564479			0.282240	−	0.959344i	$-0.408923\pi$
$139$	78.4626			0.564479			0.282240	+	0.959344i	$0.408923\pi$
$140$		0			0
$141$			18.1915i			0.129018i
$142$			58.5628i			0.412414i
$143$	6.28862			0.0439764
$144$	−21.6680			−0.150472
$145$		0			0
$146$		−	4.59951i		−	0.0315035i
$147$	−87.3675			−0.594337
$148$	136.685			0.923546
$149$	−135.184			−0.907273			−0.453637	−	0.891187i	$-0.649874\pi$
$149$	−135.184			−0.907273			−0.453637	+	0.891187i	$0.649874\pi$
$150$		0			0
$151$		−	168.771i		−	1.11769i	−0.829272	−	0.558846i	$-0.811244\pi$
$151$		−	168.771i		−	1.11769i	0.829272	−	0.558846i	$-0.188756\pi$
$152$	48.9371	−	22.2072i	0.321955	−	0.146100i
$153$			117.360i			0.767060i
$154$			2.49027i			0.0161706i
$155$		0			0
$156$	−22.8015			−0.146163
$157$			4.58432i			0.0291995i	0.999893	+	0.0145998i	$0.00464741\pi$
$157$			4.58432i			0.0291995i	−0.999893	+	0.0145998i	$0.995353\pi$
$158$		−	118.989i		−	0.753095i
$159$	−117.473			−0.738823
$160$		0			0
$161$	−67.1539			−0.417105
$162$	−4.10594			−0.0253453
$163$			187.644i			1.15119i	0.817734	+	0.575596i	$0.195230\pi$
$163$			187.644i			1.15119i	−0.817734	+	0.575596i	$0.804770\pi$
$164$		−	7.69864i		−	0.0469429i
$165$		0			0
$166$			7.89382i			0.0475531i
$167$	108.235			0.648112			0.324056	−	0.946038i	$-0.394953\pi$
$167$	108.235			0.648112			0.324056	+	0.946038i	$0.394953\pi$
$168$		−	9.02930i		−	0.0537458i
$169$	−132.724			−0.785350
$170$		0			0
$171$	−93.7241	+	42.5311i	−0.548094	+	0.248720i
$172$			130.128i			0.756561i
$173$	−102.097			−0.590155			−0.295078	−	0.955473i	$-0.595345\pi$
$173$	−102.097			−0.590155			−0.295078	+	0.955473i	$0.595345\pi$
$174$			0.745270i			0.00428316i
$175$		0			0
$176$	4.17645			0.0237298
$177$			178.084i			1.00612i
$178$			119.276i			0.670089i
$179$		−	121.752i		−	0.680181i	−0.940393	−	0.340090i	$-0.889542\pi$
$179$		−	121.752i		−	0.680181i	0.940393	−	0.340090i	$-0.110458\pi$
$180$		0			0
$181$		−	40.3187i		−	0.222755i	−0.993778	−	0.111378i	$-0.964474\pi$
$181$		−	40.3187i		−	0.222755i	0.993778	−	0.111378i	$-0.0355263\pi$
$182$			14.3651i			0.0789291i
$183$	36.7352			0.200739
$184$			112.624i			0.612087i
$185$		0			0
$186$			53.1133i			0.285556i
$187$		−	22.6209i		−	0.120967i
$188$		−	19.2209i		−	0.102239i
$189$			46.0239i			0.243513i
$190$		0			0
$191$	−226.244			−1.18452			−0.592261	−	0.805746i	$-0.701765\pi$
$191$	−226.244			−1.18452			−0.592261	+	0.805746i	$0.701765\pi$
$192$	−15.1431			−0.0788702
$193$	−6.91887			−0.0358491			−0.0179245	−	0.999839i	$-0.505706\pi$
$193$	−6.91887			−0.0358491			−0.0179245	+	0.999839i	$0.505706\pi$
$194$	−2.67991			−0.0138140
$195$		0			0
$196$	92.3115			0.470977
$197$		−	235.124i		−	1.19352i	−0.802419	−	0.596762i	$-0.796454\pi$
$197$		−	235.124i		−	1.19352i	0.802419	−	0.596762i	$-0.203546\pi$
$198$	−7.99871			−0.0403975
$199$	−39.9542			−0.200775			−0.100388	−	0.994948i	$-0.532008\pi$
$199$	−39.9542			−0.200775			−0.100388	+	0.994948i	$0.532008\pi$
$200$		0			0
$201$	−117.811			−0.586124
$202$	21.3516			0.105701
$203$	0.469526			0.00231293
$204$			82.0195i			0.402056i
$205$		0			0
$206$	202.730			0.984128
$207$		−	215.697i		−	1.04201i
$208$	24.0918			0.115826
$209$	18.0651	−	8.19777i	0.0864359	−	0.0392238i
$210$		0			0
$211$			244.243i			1.15755i	0.815487	+	0.578776i	$0.196469\pi$
$211$			244.243i			1.15755i	−0.815487	+	0.578776i	$0.803531\pi$
$212$	124.120			0.585474
$213$		−	78.3846i		−	0.368003i
$214$	167.807			0.784146
$215$		0			0
$216$	77.1869			0.357347
$217$	33.4618			0.154202
$218$		−	88.0127i		−	0.403728i
$219$			6.15632i			0.0281110i
$220$		0			0
$221$		−	130.488i		−	0.590444i
$222$	−182.949			−0.824093
$223$	−336.370			−1.50839			−0.754193	−	0.656653i	$-0.771972\pi$
$223$	−336.370			−1.50839			−0.754193	+	0.656653i	$0.771972\pi$
$224$			9.54026i			0.0425904i
$225$		0			0
$226$	−125.599			−0.555750
$227$	−288.533			−1.27107			−0.635536	−	0.772071i	$-0.719221\pi$
$227$	−288.533			−1.27107			−0.635536	+	0.772071i	$0.719221\pi$
$228$	−65.5009	+	29.7237i	−0.287285	+	0.130367i
$229$	−412.489			−1.80126			−0.900632	−	0.434583i	$-0.856896\pi$
$229$	−412.489			−1.80126			−0.900632	+	0.434583i	$0.856896\pi$
$230$		0			0
$231$		−	3.33316i		−	0.0144293i
$232$		−	0.787443i		−	0.00339415i
$233$			33.7493i			0.144847i	0.997374	+	0.0724234i	$0.0230733\pi$
$233$			33.7493i			0.144847i	−0.997374	+	0.0724234i	$0.976927\pi$
$234$	−46.1404			−0.197181
$235$		0			0
$236$		−	188.161i		−	0.797294i
$237$			159.263i			0.671998i
$238$	51.6729			0.217113
$239$	197.741			0.827368			0.413684	−	0.910421i	$-0.364242\pi$
$239$	197.741			0.827368			0.413684	+	0.910421i	$0.364242\pi$
$240$		0			0
$241$		−	348.779i		−	1.44722i	−0.690211	−	0.723608i	$-0.742482\pi$
$241$		−	348.779i		−	1.44722i	0.690211	−	0.723608i	$-0.257518\pi$
$242$	−169.578			−0.700736
$243$	−240.112			−0.988113
$244$	−38.8140			−0.159074
$245$		0			0
$246$			10.3044i			0.0418878i
$247$	104.208	−	47.2887i	0.421895	−	0.191452i
$248$		−	56.1189i		−	0.226286i
$249$		−	10.5657i		−	0.0424323i
$250$		0			0
$251$	70.8555			0.282293			0.141146	−	0.989989i	$-0.454921\pi$
$251$	70.8555			0.282293			0.141146	+	0.989989i	$0.454921\pi$
$252$		−	18.2714i		−	0.0725058i
$253$			41.5751i			0.164328i
$254$	13.1677			0.0518414
$255$		0			0
$256$	16.0000			0.0625000
$257$	−513.143			−1.99667			−0.998333	−	0.0577124i	$-0.981619\pi$
$257$	−513.143			−1.99667			−0.998333	+	0.0577124i	$0.981619\pi$
$258$		−	174.173i		−	0.675090i
$259$			115.259i			0.445016i
$260$		0			0
$261$			1.50811i			0.00577819i
$262$	208.890			0.797290
$263$			39.7483i			0.151134i	0.997141	+	0.0755670i	$0.0240767\pi$
$263$			39.7483i			0.151134i	−0.997141	+	0.0755670i	$0.975923\pi$
$264$	−5.59006			−0.0211745
$265$		0			0
$266$	18.7262	+	41.2661i	0.0703991	+	0.155136i
$267$		−	159.647i		−	0.597930i
$268$	124.478			0.464469
$269$			516.941i			1.92172i	0.277043	+	0.960858i	$0.410646\pi$
$269$			516.941i			1.92172i	−0.277043	+	0.960858i	$0.589354\pi$
$270$		0			0
$271$	147.956			0.545963			0.272982	−	0.962019i	$-0.411990\pi$
$271$	147.956			0.545963			0.272982	+	0.962019i	$0.411990\pi$
$272$		−	86.6608i		−	0.318606i
$273$		−	19.2273i		−	0.0704296i
$274$			208.003i			0.759135i
$275$		0			0
$276$		−	150.744i		−	0.546174i
$277$		−	400.546i		−	1.44601i	−0.690840	−	0.723007i	$-0.742759\pi$
$277$		−	400.546i		−	1.44601i	0.690840	−	0.723007i	$-0.257241\pi$
$278$	110.963			0.399147
$279$			107.479i			0.385228i
$280$		0			0
$281$			251.143i			0.893748i	0.894597	+	0.446874i	$0.147463\pi$
$281$			251.143i			0.893748i	−0.894597	+	0.446874i	$0.852537\pi$
$282$			25.7266i			0.0912292i
$283$			420.587i			1.48617i	0.669195	+	0.743087i	$0.266639\pi$
$283$			420.587i			1.48617i	−0.669195	+	0.743087i	$0.733361\pi$
$284$			82.8203i			0.291621i
$285$		0			0
$286$	8.89346			0.0310960
$287$	6.49186			0.0226197
$288$	−30.6431			−0.106400
$289$	−180.381			−0.624156
$290$		0			0
$291$	3.58698			0.0123264
$292$		−	6.50469i		−	0.0222763i
$293$	−335.367			−1.14460			−0.572299	−	0.820045i	$-0.693948\pi$
$293$	−335.367			−1.14460			−0.572299	+	0.820045i	$0.693948\pi$
$294$	−123.556			−0.420259
$295$		0			0
$296$	193.301			0.653046
$297$	28.4935			0.0959377
$298$	−191.179			−0.641539
$299$			239.825i			0.802091i
$300$		0			0
$301$	−109.730			−0.364553
$302$		−	238.679i		−	0.790327i
$303$	−28.5785			−0.0943185
$304$	69.2075	−	31.4057i	0.227656	−	0.103308i
$305$		0			0
$306$			165.972i			0.542393i
$307$	311.594			1.01497			0.507483	−	0.861662i	$-0.330576\pi$
$307$	311.594			1.01497			0.507483	+	0.861662i	$0.330576\pi$
$308$			3.52178i			0.0114343i
$309$	−271.349			−0.878151
$310$		0			0
$311$	288.128			0.926457			0.463228	−	0.886239i	$-0.346691\pi$
$311$	288.128			0.926457			0.463228	+	0.886239i	$0.346691\pi$
$312$	−32.2461			−0.103353
$313$		−	137.897i		−	0.440567i	−0.975436	−	0.220284i	$-0.929302\pi$
$313$		−	137.897i		−	0.440567i	0.975436	−	0.220284i	$-0.0706983\pi$
$314$			6.48321i			0.0206472i
$315$		0			0
$316$		−	168.276i		−	0.532519i
$317$	−288.819			−0.911101			−0.455551	−	0.890210i	$-0.650558\pi$
$317$	−288.819			−0.911101			−0.455551	+	0.890210i	$0.650558\pi$
$318$	−166.132			−0.522426
$319$		−	0.290684i		−	0.000911236i
$320$		0			0
$321$	−224.605			−0.699705
$322$	−94.9700			−0.294938
$323$	−170.103	−	374.849i	−0.526634	−	1.16052i
$324$	−5.80668			−0.0179218
$325$		0			0
$326$			265.369i			0.814016i
$327$			117.802i			0.360252i
$328$		−	10.8875i		−	0.0331937i
$329$	16.2080			0.0492644
$330$		0			0
$331$		−	114.877i		−	0.347060i	−0.984829	−	0.173530i	$-0.944483\pi$
$331$		−	114.877i		−	0.347060i	0.984829	−	0.173530i	$-0.0555173\pi$
$332$			11.1635i			0.0336251i
$333$	−370.210			−1.11174
$334$	153.067			0.458284
$335$		0			0
$336$		−	12.7694i		−	0.0380041i
$337$	11.1235			0.0330075			0.0165038	−	0.999864i	$-0.494746\pi$
$337$	11.1235			0.0330075			0.0165038	+	0.999864i	$0.494746\pi$
$338$	−187.700			−0.555327
$339$	168.111			0.495903
$340$		0			0
$341$		−	20.7163i		−	0.0607515i
$342$	−132.546	+	60.1481i	−0.387561	+	0.175872i
$343$			160.480i			0.467871i
$344$			184.029i			0.534969i
$345$		0			0
$346$	−144.387			−0.417303
$347$		−	258.149i		−	0.743944i	−0.928244	−	0.371972i	$-0.878682\pi$
$347$		−	258.149i		−	0.743944i	0.928244	−	0.371972i	$-0.121318\pi$
$348$			1.05397i			0.00302865i
$349$	465.062			1.33256			0.666278	−	0.745703i	$-0.267886\pi$
$349$	465.062			1.33256			0.666278	+	0.745703i	$0.267886\pi$
$350$		0			0
$351$	164.364			0.468274
$352$	5.90639			0.0167795
$353$		−	506.379i		−	1.43450i	−0.696815	−	0.717251i	$-0.745400\pi$
$353$		−	506.379i		−	1.43450i	0.696815	−	0.717251i	$-0.254600\pi$
$354$			251.849i			0.711437i
$355$		0			0
$356$			168.681i			0.473824i
$357$	−69.1627			−0.193733
$358$		−	172.184i		−	0.480960i
$359$	2.91049			0.00810722			0.00405361	−	0.999992i	$-0.498710\pi$
$359$	2.91049			0.00810722			0.00405361	+	0.999992i	$0.498710\pi$
$360$		0			0
$361$	237.710	−	271.689i	0.658477	−	0.752601i
$362$		−	57.0192i		−	0.157512i
$363$	226.975			0.625277
$364$			20.3153i			0.0558113i
$365$		0			0
$366$	51.9514			0.141944
$367$		−	382.586i		−	1.04247i	−0.853414	−	0.521234i	$-0.825472\pi$
$367$		−	382.586i		−	1.04247i	0.853414	−	0.521234i	$-0.174528\pi$
$368$			159.274i			0.432811i
$369$			20.8517i			0.0565087i
$370$		0			0
$371$			104.664i			0.282114i
$372$			75.1136i			0.201918i
$373$	394.786			1.05841			0.529204	−	0.848495i	$-0.322491\pi$
$373$	394.786			1.05841			0.529204	+	0.848495i	$0.322491\pi$
$374$		−	31.9908i		−	0.0855368i
$375$		0			0
$376$		−	27.1825i		−	0.0722938i
$377$		−	1.67681i		−	0.00444776i
$378$			65.0877i			0.172190i
$379$			614.957i			1.62258i	0.584645	+	0.811289i	$0.301234\pi$
$379$			614.957i			1.62258i	−0.584645	+	0.811289i	$0.698766\pi$
$380$		0			0
$381$	−17.6246			−0.0462589
$382$	−319.957			−0.837584
$383$	445.383			1.16288			0.581440	−	0.813589i	$-0.302489\pi$
$383$	445.383			1.16288			0.581440	+	0.813589i	$0.302489\pi$
$384$	−21.4155			−0.0557696
$385$		0			0
$386$	−9.78477			−0.0253491
$387$		−	352.452i		−	0.910729i
$388$	−3.78996			−0.00976795
$389$	−116.462			−0.299387			−0.149694	−	0.988732i	$-0.547829\pi$
$389$	−116.462			−0.299387			−0.149694	+	0.988732i	$0.547829\pi$
$390$		0			0
$391$	862.679			2.20634
$392$	130.548			0.333031
$393$	−279.593			−0.711433
$394$		−	332.516i		−	0.843948i
$395$		0			0
$396$	−11.3119			−0.0285654
$397$			310.718i			0.782665i	0.920249	+	0.391332i	$0.127986\pi$
$397$			310.718i			0.782665i	−0.920249	+	0.391332i	$0.872014\pi$
$398$	−56.5038			−0.141969
$399$	−25.0644	−	55.2335i	−0.0628181	−	0.138430i
$400$		0			0
$401$			462.347i			1.15299i	0.817102	+	0.576493i	$0.195579\pi$
$401$			462.347i			1.15299i	−0.817102	+	0.576493i	$0.804421\pi$
$402$	−166.610			−0.414452
$403$		−	119.501i		−	0.296530i
$404$	30.1957			0.0747418
$405$		0			0
$406$	0.664010			0.00163549
$407$	71.3571			0.175325
$408$			115.993i			0.284297i
$409$			552.392i			1.35059i	0.737547	+	0.675296i	$0.235984\pi$
$409$			552.392i			1.35059i	−0.737547	+	0.675296i	$0.764016\pi$
$410$		0			0
$411$		−	278.406i		−	0.677387i
$412$	286.704			0.695883
$413$	158.667			0.384181
$414$		−	305.042i		−	0.736816i
$415$		0			0
$416$	34.0709			0.0819012
$417$	−148.521			−0.356165
$418$	25.5479	−	11.5934i	0.0611194	−	0.0277354i
$419$	35.7864			0.0854090			0.0427045	−	0.999088i	$-0.486403\pi$
$419$	35.7864			0.0854090			0.0427045	+	0.999088i	$0.486403\pi$
$420$		0			0
$421$		−	669.640i		−	1.59059i	−0.606221	−	0.795297i	$-0.707315\pi$
$421$		−	669.640i		−	1.59059i	0.606221	−	0.795297i	$-0.292685\pi$
$422$			345.412i			0.818513i
$423$			52.0597i			0.123073i
$424$	175.533			0.413992
$425$		0			0
$426$		−	110.853i		−	0.260217i
$427$		−	32.7298i		−	0.0766506i
$428$	237.315			0.554475
$429$	−11.9036			−0.0277474
$430$		0			0
$431$			174.646i			0.405212i	0.979260	+	0.202606i	$0.0649411\pi$
$431$			174.646i			0.405212i	−0.979260	+	0.202606i	$0.935059\pi$
$432$	109.159			0.252682
$433$	111.608			0.257755			0.128877	−	0.991661i	$-0.458863\pi$
$433$	111.608			0.257755			0.128877	+	0.991661i	$0.458863\pi$
$434$	47.3222			0.109037
$435$		0			0
$436$		−	124.469i		−	0.285479i
$437$	312.633	+	688.937i	0.715408	+	1.57651i
$438$			8.70634i			0.0198775i
$439$		−	93.1300i		−	0.212141i	−0.994359	−	0.106071i	$-0.966173\pi$
$439$		−	93.1300i		−	0.212141i	0.994359	−	0.106071i	$-0.0338270\pi$
$440$		0			0
$441$	−250.025			−0.566950
$442$		−	184.538i		−	0.417507i
$443$		−	796.123i		−	1.79712i	−0.438854	−	0.898558i	$-0.644616\pi$
$443$		−	796.123i		−	1.79712i	0.438854	−	0.898558i	$-0.355384\pi$
$444$	−258.729			−0.582722
$445$		0			0
$446$	−475.699			−1.06659
$447$	255.887			0.572454
$448$			13.4920i			0.0301160i
$449$			186.109i			0.414496i	0.978288	+	0.207248i	$0.0664508\pi$
$449$			186.109i			0.414496i	−0.978288	+	0.207248i	$0.933549\pi$
$450$		0			0
$451$		−	4.01912i		−	0.00891157i
$452$	−177.624			−0.392974
$453$			319.465i			0.705220i
$454$	−408.048			−0.898784
$455$		0			0
$456$	−92.6323	+	42.0357i	−0.203141	+	0.0921834i
$457$			576.986i			1.26255i	0.775558	+	0.631276i	$0.217468\pi$
$457$			576.986i			1.26255i	−0.775558	+	0.631276i	$0.782532\pi$
$458$	−583.348			−1.27369
$459$		−	591.237i		−	1.28810i
$460$		0			0
$461$	223.865			0.485608			0.242804	−	0.970075i	$-0.421933\pi$
$461$	223.865			0.485608			0.242804	+	0.970075i	$0.421933\pi$
$462$		−	4.71380i		−	0.0102030i
$463$			452.579i			0.977492i	0.872426	+	0.488746i	$0.162545\pi$
$463$			452.579i			0.977492i	−0.872426	+	0.488746i	$0.837455\pi$
$464$		−	1.11361i		−	0.00240003i
$465$		0			0
$466$			47.7287i			0.102422i
$467$			69.9506i			0.149787i	0.997192	+	0.0748936i	$0.0238617\pi$
$467$			69.9506i			0.149787i	−0.997192	+	0.0748936i	$0.976138\pi$
$468$	−65.2524			−0.139428
$469$			104.965i			0.223807i
$470$		0			0
$471$		−	8.67760i		−	0.0184238i
$472$		−	266.100i		−	0.563772i
$473$			67.9343i			0.143624i
$474$			225.232i			0.475174i
$475$		0			0
$476$	73.0765			0.153522
$477$	−336.179			−0.704779
$478$	279.648			0.585037
$479$	137.500			0.287055			0.143528	−	0.989646i	$-0.454155\pi$
$479$	137.500			0.287055			0.143528	+	0.989646i	$0.454155\pi$
$480$		0			0
$481$	411.622			0.855763
$482$		−	493.248i		−	1.02334i
$483$	127.115			0.263177
$484$	−239.820			−0.495495
$485$		0			0
$486$	−339.569			−0.698702
$487$	329.190			0.675954			0.337977	−	0.941154i	$-0.390257\pi$
$487$	329.190			0.675954			0.337977	+	0.941154i	$0.390257\pi$
$488$	−54.8913			−0.112482
$489$		−	355.189i		−	0.726358i
$490$		0			0
$491$	−438.255			−0.892576			−0.446288	−	0.894889i	$-0.647254\pi$
$491$	−438.255			−0.892576			−0.446288	+	0.894889i	$0.647254\pi$
$492$			14.5726i			0.0296192i
$493$	−6.03166			−0.0122346
$494$	147.373	−	66.8763i	0.298325	−	0.135377i
$495$		0			0
$496$		−	79.3642i		−	0.160008i
$497$	−69.8380			−0.140519
$498$		−	14.9421i		−	0.0300042i
$499$	695.692			1.39417			0.697086	−	0.716988i	$-0.254480\pi$
$499$	695.692			1.39417			0.697086	+	0.716988i	$0.254480\pi$
$500$		0			0
$501$	−204.876			−0.408934
$502$	100.205			0.199611
$503$			34.2415i			0.0680746i	0.999421	+	0.0340373i	$0.0108365\pi$
$503$			34.2415i			0.0680746i	−0.999421	+	0.0340373i	$0.989163\pi$
$504$		−	25.8397i		−	0.0512693i
$505$		0			0
$506$			58.7961i			0.116198i
$507$	251.232			0.495526
$508$	18.6220			0.0366574
$509$		−	391.055i		−	0.768281i	−0.923275	−	0.384140i	$-0.874498\pi$
$509$		−	391.055i		−	0.768281i	0.923275	−	0.384140i	$-0.125502\pi$
$510$		0			0
$511$	5.48507			0.0107340
$512$	22.6274			0.0441942
$513$	472.163	−	214.263i	0.920396	−	0.417667i
$514$	−725.694			−1.41186
$515$		0			0
$516$		−	246.318i		−	0.477361i
$517$		−	10.0344i		−	0.0194089i
$518$			163.001i			0.314674i
$519$	193.258			0.372365
$520$		0			0
$521$		−	423.418i		−	0.812702i	−0.913717	−	0.406351i	$-0.866801\pi$
$521$		−	423.418i		−	0.812702i	0.913717	−	0.406351i	$-0.133199\pi$
$522$			2.13279i			0.00408580i
$523$	−277.177			−0.529976			−0.264988	−	0.964252i	$-0.585368\pi$
$523$	−277.177			−0.529976			−0.264988	+	0.964252i	$0.585368\pi$
$524$	295.415			0.563769
$525$		0			0
$526$			56.2125i			0.106868i
$527$	−429.860			−0.815674
$528$	−7.90553			−0.0149726
$529$	−1056.52			−1.99721
$530$		0			0
$531$			509.634i			0.959762i
$532$	26.4828	+	58.3591i	0.0497797	+	0.109698i
$533$		−	23.1842i		−	0.0434976i
$534$		−	225.775i		−	0.422800i
$535$		0			0
$536$	176.038			0.328429
$537$			230.463i			0.429168i
$538$			731.066i			1.35886i
$539$	48.1918			0.0894096
$540$		0			0
$541$	−562.342			−1.03945			−0.519725	−	0.854334i	$-0.673965\pi$
$541$	−562.342			−1.03945			−0.519725	+	0.854334i	$0.673965\pi$
$542$	209.241			0.386054
$543$			76.3186i			0.140550i
$544$		−	122.557i		−	0.225288i
$545$		0			0
$546$		−	27.1915i		−	0.0498012i
$547$	−727.214			−1.32946			−0.664729	−	0.747084i	$-0.731453\pi$
$547$	−727.214			−1.32946			−0.664729	+	0.747084i	$0.731453\pi$
$548$			294.161i			0.536789i
$549$	105.128			0.191489
$550$		0			0
$551$	−2.18586	−	4.81690i	−0.00396708	−	0.00874210i
$552$		−	213.184i		−	0.386204i
$553$	141.898			0.256597
$554$		−	566.458i		−	1.02249i
$555$		0			0
$556$	156.925			0.282240
$557$			692.987i			1.24414i	0.782961	+	0.622071i	$0.213709\pi$
$557$			692.987i			1.24414i	−0.782961	+	0.622071i	$0.786291\pi$
$558$			151.998i			0.272398i
$559$			391.878i			0.701034i
$560$		0			0
$561$			42.8187i			0.0763257i
$562$			355.170i			0.631975i
$563$	285.285			0.506723			0.253362	−	0.967372i	$-0.418464\pi$
$563$	285.285			0.506723			0.253362	+	0.967372i	$0.418464\pi$
$564$			36.3829i			0.0645088i
$565$		0			0
$566$			594.800i			1.05088i
$567$		−	4.89647i		−	0.00863574i
$568$			117.126i			0.206207i
$569$		−	843.131i		−	1.48178i	−0.671628	−	0.740888i	$-0.734405\pi$
$569$		−	843.131i		−	1.48178i	0.671628	−	0.740888i	$-0.265595\pi$
$570$		0			0
$571$	−798.131			−1.39778			−0.698889	−	0.715230i	$-0.746322\pi$
$571$	−798.131			−1.39778			−0.698889	+	0.715230i	$0.746322\pi$
$572$	12.5772			0.0219882
$573$	428.253			0.747388
$574$	9.18087			0.0159946
$575$		0			0
$576$	−43.3359			−0.0752360
$577$			28.4942i			0.0493834i	0.999695	+	0.0246917i	$0.00786041\pi$
$577$			28.4942i			0.0493834i	−0.999695	+	0.0246917i	$0.992140\pi$
$578$	−255.097			−0.441345
$579$	13.0966			0.0226194
$580$		0			0
$581$	−9.41364			−0.0162025
$582$	5.07276			0.00871608
$583$	64.7978			0.111145
$584$		−	9.19902i		−	0.0157518i
$585$		0			0
$586$	−474.281			−0.809352
$587$		−	546.088i		−	0.930303i	−0.885231	−	0.465151i	$-0.846000\pi$
$587$		−	546.088i		−	0.930303i	0.885231	−	0.465151i	$-0.154000\pi$
$588$	−174.735			−0.297168
$589$	−155.781	−	343.287i	−0.264483	−	0.582831i
$590$		0			0
$591$			445.063i			0.753067i
$592$	273.370			0.461773
$593$		−	1058.29i		−	1.78464i	−0.451407	−	0.892318i	$-0.649078\pi$
$593$		−	1058.29i		−	1.78464i	0.451407	−	0.892318i	$-0.350922\pi$
$594$	40.2959			0.0678382
$595$		0			0
$596$	−270.367			−0.453637
$597$	75.6288			0.126681
$598$			339.164i			0.567164i
$599$			554.840i			0.926278i	0.886286	+	0.463139i	$0.153277\pi$
$599$			554.840i			0.926278i	−0.886286	+	0.463139i	$0.846723\pi$
$600$		0			0
$601$		−	662.009i		−	1.10151i	−0.834666	−	0.550756i	$-0.814339\pi$
$601$		−	662.009i		−	1.10151i	0.834666	−	0.550756i	$-0.185661\pi$
$602$	−155.182			−0.257778
$603$	−337.147			−0.559116
$604$		−	337.543i		−	0.558846i
$605$		0			0
$606$	−40.4161			−0.0666932
$607$	895.503			1.47529			0.737646	−	0.675187i	$-0.235937\pi$
$607$	895.503			1.47529			0.737646	+	0.675187i	$0.235937\pi$
$608$	97.8742	−	44.4144i	0.160977	−	0.0730500i
$609$	−0.888758			−0.00145937
$610$		0			0
$611$		−	57.8832i		−	0.0947351i
$612$			234.720i			0.383530i
$613$		−	548.725i		−	0.895146i	−0.894247	−	0.447573i	$-0.852288\pi$
$613$		−	548.725i		−	0.895146i	0.894247	−	0.447573i	$-0.147712\pi$
$614$	440.661			0.717689
$615$		0			0
$616$			4.98055i			0.00808531i
$617$			763.924i			1.23813i	0.785341	+	0.619063i	$0.212487\pi$
$617$			763.924i			1.23813i	−0.785341	+	0.619063i	$0.787513\pi$
$618$	−383.745			−0.620947
$619$	508.039			0.820741			0.410370	−	0.911919i	$-0.365399\pi$
$619$	508.039			0.820741			0.410370	+	0.911919i	$0.365399\pi$
$620$		0			0
$621$			1086.64i			1.74982i
$622$	407.475			0.655104
$623$	−142.240			−0.228315
$624$	−45.6029			−0.0730816
$625$		0			0
$626$		−	195.016i		−	0.311528i
$627$	−34.1951	+	15.5174i	−0.0545377	+	0.0247487i
$628$			9.16865i			0.0145998i
$629$		−	1480.65i		−	2.35398i
$630$		0			0
$631$	673.489			1.06734			0.533668	−	0.845694i	$-0.320813\pi$
$631$	673.489			1.06734			0.533668	+	0.845694i	$0.320813\pi$
$632$		−	237.978i		−	0.376548i
$633$		−	462.325i		−	0.730371i
$634$	−408.452			−0.644246
$635$		0			0
$636$	−234.946			−0.369411
$637$	277.993			0.436410
$638$		−	0.411089i		−	0.000644341i
$639$		−	224.318i		−	0.351046i
$640$		0			0
$641$			1084.01i			1.69112i	0.533878	+	0.845562i	$0.320734\pi$
$641$			1084.01i			1.69112i	−0.533878	+	0.845562i	$0.679266\pi$
$642$	−317.640			−0.494766
$643$			579.940i			0.901929i	0.892542	+	0.450964i	$0.148920\pi$
$643$			579.940i			0.901929i	−0.892542	+	0.450964i	$0.851080\pi$
$644$	−134.308			−0.208553
$645$		0			0
$646$	−240.562	−	530.116i	−0.372387	−	0.820613i
$647$			585.847i			0.905482i	0.891642	+	0.452741i	$0.149554\pi$
$647$			585.847i			0.905482i	−0.891642	+	0.452741i	$0.850446\pi$
$648$	−8.21188			−0.0126727
$649$		−	98.2307i		−	0.151357i
$650$		0			0
$651$	−63.3394			−0.0972955
$652$			375.289i			0.575596i
$653$			715.361i			1.09550i	0.836642	+	0.547749i	$0.184515\pi$
$653$			715.361i			1.09550i	−0.836642	+	0.547749i	$0.815485\pi$
$654$			166.598i			0.254737i
$655$		0			0
$656$		−	15.3973i		−	0.0234715i
$657$			17.6179i			0.0268157i
$658$	22.9215			0.0348352
$659$		−	669.081i		−	1.01530i	−0.861564	−	0.507649i	$-0.830515\pi$
$659$		−	669.081i		−	1.01530i	0.861564	−	0.507649i	$-0.169485\pi$
$660$		0			0
$661$			291.273i			0.440655i	0.975426	+	0.220327i	$0.0707126\pi$
$661$			291.273i			0.440655i	−0.975426	+	0.220327i	$0.929287\pi$
$662$		−	162.460i		−	0.245408i
$663$			246.999i			0.372548i
$664$			15.7876i			0.0237766i
$665$		0			0
$666$	−523.556			−0.786120
$667$	11.0856			0.0166201
$668$	216.469			0.324056
$669$	636.710			0.951734
$670$		0			0
$671$	−20.2631			−0.0301983
$672$		−	18.0586i		−	0.0268729i
$673$	1212.39			1.80147			0.900734	−	0.434372i	$-0.143030\pi$
$673$	1212.39			1.80147			0.900734	+	0.434372i	$0.143030\pi$
$674$	15.7311			0.0233398
$675$		0			0
$676$	−265.448			−0.392675
$677$	158.703			0.234421			0.117211	−	0.993107i	$-0.462605\pi$
$677$	158.703			0.234421			0.117211	+	0.993107i	$0.462605\pi$
$678$	237.745			0.350657
$679$		−	3.19588i		−	0.00470674i
$680$		0			0
$681$	546.160			0.801998
$682$		−	29.2972i		−	0.0429578i
$683$	−109.346			−0.160097			−0.0800483	−	0.996791i	$-0.525507\pi$
$683$	−109.346			−0.160097			−0.0800483	+	0.996791i	$0.525507\pi$
$684$	−187.448	+	85.0622i	−0.274047	+	0.124360i
$685$		0			0
$686$			226.953i			0.330835i
$687$	780.795			1.13653
$688$			260.257i			0.378280i
$689$	373.785			0.542503
$690$		0			0
$691$	487.341			0.705269			0.352634	−	0.935761i	$-0.385286\pi$
$691$	487.341			0.705269			0.352634	+	0.935761i	$0.385286\pi$
$692$	−204.194			−0.295078
$693$		−	9.53872i		−	0.0137644i
$694$		−	365.077i		−	0.526048i
$695$		0			0
$696$			1.49054i			0.00214158i
$697$	−83.3963			−0.119650
$698$	657.697			0.942259
$699$		−	63.8835i		−	0.0913927i
$700$		0			0
$701$	−925.556			−1.32034			−0.660168	−	0.751118i	$-0.729515\pi$
$701$	−925.556			−1.32034			−0.660168	+	0.751118i	$0.729515\pi$
$702$	232.446			0.331120
$703$	1182.45	−	536.585i	1.68201	−	0.763279i
$704$	8.35290			0.0118649
$705$		0			0
$706$		−	716.128i		−	1.01435i
$707$			25.4625i			0.0360148i
$708$			356.168i			0.503062i
$709$	181.394			0.255845			0.127923	−	0.991784i	$-0.459169\pi$
$709$	181.394			0.255845			0.127923	+	0.991784i	$0.459169\pi$
$710$		0			0
$711$			455.774i			0.641033i
$712$			238.552i			0.335044i
$713$	790.043			1.10805
$714$	−97.8108			−0.136990
$715$		0			0
$716$		−	243.505i		−	0.340090i
$717$	−374.301			−0.522037
$718$	4.11606			0.00573267
$719$	783.075			1.08912			0.544559	−	0.838723i	$-0.316697\pi$
$719$	783.075			1.08912			0.544559	+	0.838723i	$0.316697\pi$
$720$		0			0
$721$			241.762i			0.335315i
$722$	336.173	−	384.226i	0.465613	−	0.532169i
$723$			660.199i			0.913138i
$724$		−	80.6374i		−	0.111378i
$725$		0			0
$726$	320.992			0.442137
$727$		−	790.679i		−	1.08759i	−0.839217	−	0.543796i	$-0.816987\pi$
$727$		−	790.679i		−	1.08759i	0.839217	−	0.543796i	$-0.183013\pi$
$728$			28.7302i			0.0394646i
$729$	480.633			0.659305
$730$		0			0
$731$	1409.63			1.92836
$732$	73.4704			0.100369
$733$		−	820.219i		−	1.11899i	−0.828834	−	0.559494i	$-0.810995\pi$
$733$		−	820.219i		−	1.11899i	0.828834	−	0.559494i	$-0.189005\pi$
$734$		−	541.058i		−	0.737136i
$735$		0			0
$736$			225.248i			0.306044i
$737$	64.9843			0.0881740
$738$			29.4888i			0.0399577i
$739$	−19.5055			−0.0263944			−0.0131972	−	0.999913i	$-0.504201\pi$
$739$	−19.5055			−0.0263944			−0.0131972	+	0.999913i	$0.504201\pi$
$740$		0			0
$741$	−197.254	+	89.5120i	−0.266200	+	0.120799i
$742$			148.018i			0.199485i
$743$	−1204.63			−1.62131			−0.810653	−	0.585527i	$-0.800887\pi$
$743$	−1204.63			−1.62131			−0.810653	+	0.585527i	$0.800887\pi$
$744$			106.227i			0.142778i
$745$		0			0
$746$	558.312			0.748407
$747$		−	30.2364i		−	0.0404771i
$748$		−	45.2418i		−	0.0604837i
$749$			200.116i			0.267177i
$750$		0			0
$751$		−	1442.98i		−	1.92141i	−0.277575	−	0.960704i	$-0.589531\pi$
$751$		−	1442.98i		−	1.92141i	0.277575	−	0.960704i	$-0.410469\pi$
$752$		−	38.4418i		−	0.0511194i
$753$	−134.121			−0.178116
$754$		−	2.37136i		−	0.00314504i
$755$		0			0
$756$			92.0479i			0.121756i
$757$			947.346i			1.25145i	0.780044	+	0.625724i	$0.215196\pi$
$757$			947.346i			1.25145i	−0.780044	+	0.625724i	$0.784804\pi$
$758$			869.681i			1.14734i
$759$		−	78.6969i		−	0.103685i
$760$		0			0
$761$	−892.677			−1.17303			−0.586516	−	0.809938i	$-0.699501\pi$
$761$	−892.677			−1.17303			−0.586516	+	0.809938i	$0.699501\pi$
$762$	−24.9250			−0.0327099
$763$	104.958			0.137560
$764$	−452.487			−0.592261
$765$		0			0
$766$	629.867			0.822281
$767$		−	566.642i		−	0.738777i
$768$	−30.2862			−0.0394351
$769$	629.290			0.818322			0.409161	−	0.912462i	$-0.365821\pi$
$769$	629.290			0.818322			0.409161	+	0.912462i	$0.365821\pi$
$770$		0			0
$771$	971.321			1.25982
$772$	−13.8377			−0.0179245
$773$	291.337			0.376892			0.188446	−	0.982084i	$-0.439655\pi$
$773$	291.337			0.376892			0.188446	+	0.982084i	$0.439655\pi$
$774$		−	498.442i		−	0.643983i
$775$		0			0
$776$	−5.35982			−0.00690698
$777$		−	218.172i		−	0.280788i
$778$	−164.702			−0.211699
$779$	−30.2227	−	66.6005i	−0.0387967	−	0.0854948i
$780$		0			0
$781$			43.2368i			0.0553609i
$782$	1220.01			1.56012
$783$		−	7.59754i		−	0.00970311i
$784$	184.623			0.235488
$785$		0			0
$786$	−395.405			−0.503059
$787$	889.115			1.12975			0.564876	−	0.825176i	$-0.308924\pi$
$787$	889.115			1.12975			0.564876	+	0.825176i	$0.308924\pi$
$788$		−	470.248i		−	0.596762i
$789$		−	75.2388i		−	0.0953598i
$790$		0			0
$791$		−	149.781i		−	0.189357i
$792$	−15.9974			−0.0201988
$793$	−116.887			−0.147399
$794$			439.421i			0.553427i
$795$		0			0
$796$	−79.9085			−0.100388
$797$	−800.716			−1.00466			−0.502331	−	0.864675i	$-0.667524\pi$
$797$	−800.716			−1.00466			−0.502331	+	0.864675i	$0.667524\pi$
$798$	−35.4465	−	78.1120i	−0.0444191	−	0.0978847i
$799$	−208.212			−0.260591
$800$		0			0
$801$		−	456.873i		−	0.570378i
$802$			653.858i			0.815284i
$803$		−	3.39581i		−	0.00422891i
$804$	−235.622			−0.293062
$805$		0			0
$806$		−	169.000i		−	0.209678i
$807$		−	978.510i		−	1.21253i
$808$	42.7032			0.0528505
$809$	327.560			0.404894			0.202447	−	0.979293i	$-0.435111\pi$
$809$	327.560			0.404894			0.202447	+	0.979293i	$0.435111\pi$
$810$		0			0
$811$			414.555i			0.511166i	0.966787	+	0.255583i	$0.0822673\pi$
$811$			414.555i			0.511166i	−0.966787	+	0.255583i	$0.917733\pi$
$812$	0.939051			0.00115647
$813$	−280.064			−0.344482
$814$	100.914			0.123973
$815$		0			0
$816$			164.039i			0.201028i
$817$	510.847	+	1125.73i	0.625272	+	1.37789i
$818$			781.201i			0.955013i
$819$		−	55.0239i		−	0.0671843i
$820$		0			0
$821$	−594.805			−0.724489			−0.362244	−	0.932083i	$-0.617989\pi$
$821$	−594.805			−0.724489			−0.362244	+	0.932083i	$0.617989\pi$
$822$		−	393.726i		−	0.478985i
$823$		−	704.177i		−	0.855622i	−0.903868	−	0.427811i	$-0.859285\pi$
$823$		−	704.177i		−	0.855622i	0.903868	−	0.427811i	$-0.140715\pi$
$824$	405.461			0.492064
$825$		0			0
$826$	224.388			0.271657
$827$	−829.642			−1.00319			−0.501597	−	0.865101i	$-0.667254\pi$
$827$	−829.642			−1.00319			−0.501597	+	0.865101i	$0.667254\pi$
$828$		−	431.394i		−	0.521007i
$829$			693.036i			0.835990i	0.908449	+	0.417995i	$0.137267\pi$
$829$			693.036i			0.835990i	−0.908449	+	0.417995i	$0.862733\pi$
$830$		0			0
$831$			758.188i			0.912380i
$832$	48.1835			0.0579129
$833$		−	999.973i		−	1.20045i
$834$	−210.040			−0.251846
$835$		0			0
$836$	36.1302	−	16.3955i	0.0432179	−	0.0196119i
$837$		−	541.456i		−	0.646901i
$838$	50.6096			0.0603933
$839$			1482.55i			1.76704i	0.468391	+	0.883521i	$0.344834\pi$
$839$			1482.55i			1.76704i	−0.468391	+	0.883521i	$0.655166\pi$
$840$		0			0
$841$	840.922			0.999908
$842$		−	947.014i		−	1.12472i
$843$		−	475.385i		−	0.563921i
$844$			488.487i			0.578776i
$845$		0			0
$846$			73.6235i			0.0870254i
$847$		−	202.227i		−	0.238757i
$848$	248.241			0.292737
$849$		−	796.123i		−	0.937718i
$850$		0			0
$851$			2721.30i			3.19777i
$852$		−	156.769i		−	0.184001i
$853$			1327.68i			1.55648i	0.627966	+	0.778240i	$0.283888\pi$
$853$			1327.68i			1.55648i	−0.627966	+	0.778240i	$0.716112\pi$
$854$		−	46.2870i		−	0.0542002i
$855$		0			0
$856$	335.615			0.392073
$857$	274.944			0.320822			0.160411	−	0.987050i	$-0.448718\pi$
$857$	274.944			0.320822			0.160411	+	0.987050i	$0.448718\pi$
$858$	−16.8343			−0.0196204
$859$	182.211			0.212120			0.106060	−	0.994360i	$-0.466176\pi$
$859$	182.211			0.212120			0.106060	+	0.994360i	$0.466176\pi$
$860$		0			0
$861$	−12.2883			−0.0142722
$862$			246.987i			0.286528i
$863$	173.434			0.200966			0.100483	−	0.994939i	$-0.467961\pi$
$863$	173.434			0.200966			0.100483	+	0.994939i	$0.467961\pi$
$864$	154.374			0.178673
$865$		0			0
$866$	157.837			0.182260
$867$	341.441			0.393818
$868$	66.9236			0.0771010
$869$		−	87.8494i		−	0.101093i
$870$		0			0
$871$	374.860			0.430379
$872$		−	176.025i		−	0.201864i
$873$	10.2651			0.0117584
$874$	442.130	+	974.304i	0.505869	+	1.11476i
$875$		0			0
$876$			12.3126i			0.0140555i
$877$	708.930			0.808358			0.404179	−	0.914680i	$-0.367557\pi$
$877$	708.930			0.808358			0.404179	+	0.914680i	$0.367557\pi$
$878$		−	131.706i		−	0.150006i
$879$	634.811			0.722197
$880$		0			0
$881$	−188.482			−0.213941			−0.106970	−	0.994262i	$-0.534115\pi$
$881$	−188.482			−0.213941			−0.106970	+	0.994262i	$0.534115\pi$
$882$	−353.589			−0.400894
$883$			227.812i			0.257998i	0.991645	+	0.128999i	$0.0411764\pi$
$883$			227.812i			0.257998i	−0.991645	+	0.128999i	$0.958824\pi$
$884$		−	260.976i		−	0.295222i
$885$		0			0
$886$		−	1125.89i		−	1.27075i
$887$	−799.124			−0.900928			−0.450464	−	0.892794i	$-0.648742\pi$
$887$	−799.124			−0.900928			−0.450464	+	0.892794i	$0.648742\pi$
$888$	−365.897			−0.412047
$889$			15.7029i			0.0176636i
$890$		0			0
$891$	−3.03141			−0.00340226
$892$	−672.740			−0.754193
$893$	−75.4558	−	166.279i	−0.0844969	−	0.186203i
$894$	361.879			0.404786
$895$		0			0
$896$			19.0805i			0.0212952i
$897$		−	453.961i		−	0.506088i
$898$			263.198i			0.293093i
$899$	−5.52381			−0.00614439
$900$		0			0
$901$		−	1344.55i		−	1.49228i
$902$		−	5.68389i		−	0.00630143i
$903$	207.707			0.230019
$904$	−251.199			−0.277875
$905$		0			0
$906$			451.791i			0.498666i
$907$	−182.629			−0.201355			−0.100677	−	0.994919i	$-0.532101\pi$
$907$	−182.629			−0.201355			−0.100677	+	0.994919i	$0.532101\pi$
$908$	−577.067			−0.635536
$909$	−81.7849			−0.0899724
$910$		0			0
$911$		−	1124.39i		−	1.23423i	−0.786872	−	0.617116i	$-0.788301\pi$
$911$		−	1124.39i		−	1.23423i	0.786872	−	0.617116i	$-0.211699\pi$
$912$	−131.002	+	59.4474i	−0.143642	+	0.0651835i
$913$			5.82800i			0.00638335i
$914$			815.982i			0.892759i
$915$		0			0
$916$	−824.979			−0.900632
$917$			249.108i			0.271656i
$918$		−	836.135i		−	0.910823i
$919$	−985.231			−1.07207			−0.536034	−	0.844196i	$-0.680078\pi$
$919$	−985.231			−1.07207			−0.536034	+	0.844196i	$0.680078\pi$
$920$		0			0
$921$	−589.812			−0.640404
$922$	316.593			0.343377
$923$			249.411i			0.270218i
$924$		−	6.66632i		−	0.00721463i
$925$		0			0
$926$			640.043i			0.691191i
$927$	−776.536			−0.837687
$928$		−	1.57489i		−	0.00169708i
$929$	−842.513			−0.906903			−0.453452	−	0.891281i	$-0.649807\pi$
$929$	−842.513			−0.906903			−0.453452	+	0.891281i	$0.649807\pi$
$930$		0			0
$931$	798.581	−	362.388i	0.857767	−	0.389246i
$932$			67.4986i			0.0724234i
$933$	−545.393			−0.584559
$934$			98.9251i			0.105916i
$935$		0			0
$936$	−92.2808			−0.0985906
$937$			612.166i			0.653326i	0.945141	+	0.326663i	$0.105924\pi$
$937$			612.166i			0.653326i	−0.945141	+	0.326663i	$0.894076\pi$
$938$			148.444i			0.158255i
$939$			261.024i			0.277981i
$940$		0			0
$941$		−	760.768i		−	0.808467i	−0.914656	−	0.404234i	$-0.867538\pi$
$941$		−	760.768i		−	0.808467i	0.914656	−	0.404234i	$-0.132462\pi$
$942$		−	12.2720i		−	0.0130276i
$943$	153.275			0.162539
$944$		−	376.323i		−	0.398647i
$945$		0			0
$946$			96.0736i			0.101558i
$947$		−	23.9008i		−	0.0252384i	−0.999920	−	0.0126192i	$-0.995983\pi$
$947$		−	23.9008i		−	0.0252384i	0.999920	−	0.0126192i	$-0.00401693\pi$
$948$			318.527i			0.335999i
$949$		−	19.5887i		−	0.0206414i
$950$		0			0
$951$	546.701			0.574870
$952$	103.346			0.108557
$953$	−52.0625			−0.0546301			−0.0273150	−	0.999627i	$-0.508696\pi$
$953$	−52.0625			−0.0546301			−0.0273150	+	0.999627i	$0.508696\pi$
$954$	−475.429			−0.498354
$955$		0			0
$956$	395.482			0.413684
$957$			0.550231i			0.000574955i
$958$	194.454			0.202979
$959$	−248.050			−0.258655
$960$		0			0
$961$	567.333			0.590357
$962$	582.122			0.605116
$963$	−642.767			−0.667463
$964$		−	697.558i		−	0.723608i
$965$		0			0
$966$	179.767			0.186094
$967$		−	987.119i		−	1.02081i	−0.859935	−	0.510403i	$-0.829496\pi$
$967$		−	987.119i		−	1.02081i	0.859935	−	0.510403i	$-0.170504\pi$
$968$	−339.156			−0.350368
$969$	321.985	+	709.545i	0.332286	+	0.732245i
$970$		0			0
$971$			1204.48i			1.24045i	0.784422	+	0.620227i	$0.212960\pi$
$971$			1204.48i			1.24045i	−0.784422	+	0.620227i	$0.787040\pi$
$972$	−480.223			−0.494057
$973$			132.327i			0.135999i
$974$	465.544			0.477972
$975$		0			0
$976$	−77.6280			−0.0795369
$977$	−556.615			−0.569719			−0.284859	−	0.958569i	$-0.591947\pi$
$977$	−556.615			−0.569719			−0.284859	+	0.958569i	$0.591947\pi$
$978$		−	502.313i		−	0.513613i
$979$			88.0611i			0.0899501i
$980$		0			0
$981$			337.123i			0.343652i
$982$	−619.786			−0.631146
$983$	−462.624			−0.470625			−0.235312	−	0.971920i	$-0.575611\pi$
$983$	−462.624			−0.470625			−0.235312	+	0.971920i	$0.575611\pi$
$984$			20.6088i			0.0209439i
$985$		0			0
$986$	−8.53006			−0.00865118
$987$	−30.6798			−0.0310839
$988$	208.416	−	94.5774i	0.210948	−	0.0957261i
$989$	−2590.77			−2.61958
$990$		0			0
$991$		−	1691.69i		−	1.70706i	−0.521046	−	0.853528i	$-0.674458\pi$
$991$		−	1691.69i		−	1.70706i	0.521046	−	0.853528i	$-0.325542\pi$
$992$		−	112.238i		−	0.113143i
$993$			217.448i			0.218981i
$994$	−98.7659			−0.0993620
$995$		0			0
$996$		−	21.1313i		−	0.0212162i
$997$		−	742.809i		−	0.745044i	−0.928023	−	0.372522i	$-0.878493\pi$
$997$		−	742.809i		−	0.745044i	0.928023	−	0.372522i	$-0.121507\pi$
$998$	983.857			0.985828
$999$	1865.04			1.86691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.3.d.b.949.18		24
5.2	odd	4		950.3.c.c.151.10	yes	12
5.3	odd	4		950.3.c.b.151.3	✓	12
5.4	even	2	inner	950.3.d.b.949.7		24
19.18	odd	2	inner	950.3.d.b.949.6		24
95.18	even	4		950.3.c.b.151.10	yes	12
95.37	even	4		950.3.c.c.151.3	yes	12
95.94	odd	2	inner	950.3.d.b.949.19		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.3.c.b.151.3	✓	12	5.3	odd	4
950.3.c.b.151.10	yes	12	95.18	even	4
950.3.c.c.151.3	yes	12	95.37	even	4
950.3.c.c.151.10	yes	12	5.2	odd	4
950.3.d.b.949.6		24	19.18	odd	2	inner
950.3.d.b.949.7		24	5.4	even	2	inner
950.3.d.b.949.18		24	1.1	even	1	trivial
950.3.d.b.949.19		24	95.94	odd	2	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	950.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -1.89288 q^{3} +2.00000 q^{4} -2.67694 q^{6} +1.68650i q^{7} +2.82843 q^{8} -5.41699 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -1.89288 q^{3} +2.00000 q^{4} -2.67694 q^{6} +1.68650i q^{7} +2.82843 q^{8} -5.41699 q^{9} +1.04411 q^{11} -3.78577 q^{12} +6.02294 q^{13} +2.38506i q^{14} +4.00000 q^{16} -21.6652i q^{17} -7.66078 q^{18} +(17.3019 - 7.85143i) q^{19} -3.19234i q^{21} +1.47660 q^{22} +39.8186i q^{23} -5.35389 q^{24} +8.51772 q^{26} +27.2897 q^{27} +3.37299i q^{28} -0.278403i q^{29} -19.8410i q^{31} +5.65685 q^{32} -1.97638 q^{33} -30.6392i q^{34} -10.8340 q^{36} +68.3424 q^{37} +(24.4686 - 11.1036i) q^{38} -11.4007 q^{39} -3.84932i q^{41} -4.51465i q^{42} +65.0642i q^{43} +2.08822 q^{44} +56.3120i q^{46} -9.61045i q^{47} -7.57154 q^{48} +46.1557 q^{49} +41.0097i q^{51} +12.0459 q^{52} +62.0602 q^{53} +38.5935 q^{54} +4.77013i q^{56} +(-32.7505 + 14.8618i) q^{57} -0.393722i q^{58} -94.0807i q^{59} -19.4070 q^{61} -28.0595i q^{62} -9.13572i q^{63} +8.00000 q^{64} -2.79503 q^{66} +62.2388 q^{67} -43.3304i q^{68} -75.3720i q^{69} +41.4101i q^{71} -15.3216 q^{72} -3.25235i q^{73} +96.6507 q^{74} +(34.6038 - 15.7029i) q^{76} +1.76089i q^{77} -16.1231 q^{78} -84.1379i q^{79} -2.90334 q^{81} -5.44376i q^{82} +5.58177i q^{83} -6.38468i q^{84} +92.0147i q^{86} +0.526985i q^{87} +2.95319 q^{88} +84.3407i q^{89} +10.1577i q^{91} +79.6372i q^{92} +37.5568i q^{93} -13.5912i q^{94} -10.7078 q^{96} -1.89498 q^{97} +65.2741 q^{98} -5.65594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9}+O(q^{10}) \) 24 * q + 48 * q^4 - 16 * q^6 + 56 * q^9	\( 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9} + 8 q^{11} + 96 q^{16} + 24 q^{19} - 32 q^{24} - 32 q^{26} + 112 q^{36} - 200 q^{39} + 16 q^{44} + 216 q^{49} - 224 q^{54} - 152 q^{61} + 192 q^{64} + 16 q^{66} - 144 q^{74} + 48 q^{76} - 264 q^{81} - 64 q^{96} - 256 q^{99}+O(q^{100}) \) 24 * q + 48 * q^4 - 16 * q^6 + 56 * q^9 + 8 * q^11 + 96 * q^16 + 24 * q^19 - 32 * q^24 - 32 * q^26 + 112 * q^36 - 200 * q^39 + 16 * q^44 + 216 * q^49 - 224 * q^54 - 152 * q^61 + 192 * q^64 + 16 * q^66 - 144 * q^74 + 48 * q^76 - 264 * q^81 - 64 * q^96 - 256 * q^99

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