LMFDB - Embedded newform 354.3.d.a.235.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.d (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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 $ x^20 - 300x^18 - 88x^17 + 37952x^16 + 27000x^15 - 2574056x^14 - 3295208x^13 + 98138134x^12 + 195465720x^11 - 1935828112x^10 - 5590976152x^9 + 12661641204x^8 + 55962519336x^7 + 75365256136x^6 + 219349710792x^5 + 570681930321x^4 + 614778274152x^3 + 1559028888924x^2 + 534075251472x + 2455573689828
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.18
Root			$-0.662289 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -0.662289 q^{5} +2.44949i q^{6} -11.5463 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -0.662289 q^{5} +2.44949i q^{6} -11.5463 q^{7} -2.82843i q^{8} +3.00000 q^{9} -0.936618i q^{10} -14.0682i q^{11} -3.46410 q^{12} -13.5651i q^{13} -16.3289i q^{14} -1.14712 q^{15} +4.00000 q^{16} +13.5553 q^{17} +4.24264i q^{18} +26.5624 q^{19} +1.32458 q^{20} -19.9987 q^{21} +19.8954 q^{22} -22.7826i q^{23} -4.89898i q^{24} -24.5614 q^{25} +19.1840 q^{26} +5.19615 q^{27} +23.0926 q^{28} -42.2715 q^{29} -1.62227i q^{30} -8.50302i q^{31} +5.65685i q^{32} -24.3668i q^{33} +19.1701i q^{34} +7.64697 q^{35} -6.00000 q^{36} -67.3408i q^{37} +37.5649i q^{38} -23.4955i q^{39} +1.87324i q^{40} -43.0303 q^{41} -28.2825i q^{42} +40.9913i q^{43} +28.1364i q^{44} -1.98687 q^{45} +32.2195 q^{46} +58.7751i q^{47} +6.92820 q^{48} +84.3166 q^{49} -34.7350i q^{50} +23.4785 q^{51} +27.1303i q^{52} -47.0214 q^{53} +7.34847i q^{54} +9.31721i q^{55} +32.6578i q^{56} +46.0075 q^{57} -59.7809i q^{58} +(52.1855 - 27.5259i) q^{59} +2.29424 q^{60} -9.71992i q^{61} +12.0251 q^{62} -34.6388 q^{63} -8.00000 q^{64} +8.98404i q^{65} +34.4599 q^{66} -101.799i q^{67} -27.1106 q^{68} -39.4607i q^{69} +10.8144i q^{70} -85.3891 q^{71} -8.48528i q^{72} +41.2625i q^{73} +95.2342 q^{74} -42.5415 q^{75} -53.1248 q^{76} +162.435i q^{77} +33.2277 q^{78} +119.379 q^{79} -2.64915 q^{80} +9.00000 q^{81} -60.8541i q^{82} -13.8927i q^{83} +39.9975 q^{84} -8.97753 q^{85} -57.9704 q^{86} -73.2163 q^{87} -39.7909 q^{88} +28.7153i q^{89} -2.80985i q^{90} +156.627i q^{91} +45.5652i q^{92} -14.7277i q^{93} -83.1206 q^{94} -17.5920 q^{95} +9.79796i q^{96} +109.955i q^{97} +119.242i q^{98} -42.2046i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	$ 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) $ 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−2.00000			−0.500000
$5$	−0.662289			−0.132458			−0.0662289	−	0.997804i	$-0.521097\pi$
$5$	−0.662289			−0.132458			−0.0662289	+	0.997804i	$0.521097\pi$
$6$			2.44949i			0.408248i
$7$	−11.5463			−1.64947			−0.824734	−	0.565520i	$-0.808675\pi$
$7$	−11.5463			−1.64947			−0.824734	+	0.565520i	$0.808675\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		−	0.936618i		−	0.0936618i
$11$		−	14.0682i		−	1.27893i	−0.768822	−	0.639463i	$-0.779157\pi$
$11$		−	14.0682i		−	1.27893i	0.768822	−	0.639463i	$-0.220843\pi$
$12$	−3.46410			−0.288675
$13$		−	13.5651i		−	1.04347i	−0.853107	−	0.521736i	$-0.825284\pi$
$13$		−	13.5651i		−	1.04347i	0.853107	−	0.521736i	$-0.174716\pi$
$14$		−	16.3289i		−	1.16635i
$15$	−1.14712			−0.0764745
$16$	4.00000			0.250000
$17$	13.5553			0.797372			0.398686	−	0.917088i	$-0.369466\pi$
$17$	13.5553			0.797372			0.398686	+	0.917088i	$0.369466\pi$
$18$			4.24264i			0.235702i
$19$	26.5624			1.39802			0.699011	−	0.715111i	$-0.253624\pi$
$19$	26.5624			1.39802			0.699011	+	0.715111i	$0.253624\pi$
$20$	1.32458			0.0662289
$21$	−19.9987			−0.952321
$22$	19.8954			0.904338
$23$		−	22.7826i		−	0.990549i	−0.868737	−	0.495274i	$-0.835068\pi$
$23$		−	22.7826i		−	0.990549i	0.868737	−	0.495274i	$-0.164932\pi$
$24$		−	4.89898i		−	0.204124i
$25$	−24.5614			−0.982455
$26$	19.1840			0.737847
$27$	5.19615			0.192450
$28$	23.0926			0.824734
$29$	−42.2715			−1.45764			−0.728819	−	0.684707i	$-0.759930\pi$
$29$	−42.2715			−1.45764			−0.728819	+	0.684707i	$0.759930\pi$
$30$		−	1.62227i		−	0.0540756i
$31$		−	8.50302i		−	0.274291i	−0.990551	−	0.137146i	$-0.956207\pi$
$31$		−	8.50302i		−	0.274291i	0.990551	−	0.137146i	$-0.0437928\pi$
$32$			5.65685i			0.176777i
$33$		−	24.3668i		−	0.738389i
$34$			19.1701i			0.563827i
$35$	7.64697			0.218485
$36$	−6.00000			−0.166667
$37$		−	67.3408i		−	1.82002i	−0.414585	−	0.910010i	$-0.636073\pi$
$37$		−	67.3408i		−	1.82002i	0.414585	−	0.910010i	$-0.363927\pi$
$38$			37.5649i			0.988551i
$39$		−	23.4955i		−	0.602449i
$40$			1.87324i			0.0468309i
$41$	−43.0303			−1.04952			−0.524760	−	0.851250i	$-0.675845\pi$
$41$	−43.0303			−1.04952			−0.524760	+	0.851250i	$0.675845\pi$
$42$		−	28.2825i		−	0.673393i
$43$			40.9913i			0.953286i	0.879097	+	0.476643i	$0.158147\pi$
$43$			40.9913i			0.953286i	−0.879097	+	0.476643i	$0.841853\pi$
$44$			28.1364i			0.639463i
$45$	−1.98687			−0.0441526
$46$	32.2195			0.700424
$47$			58.7751i			1.25053i	0.780411	+	0.625267i	$0.215010\pi$
$47$			58.7751i			1.25053i	−0.780411	+	0.625267i	$0.784990\pi$
$48$	6.92820			0.144338
$49$	84.3166			1.72075
$50$		−	34.7350i		−	0.694701i
$51$	23.4785			0.460363
$52$			27.1303i			0.521736i
$53$	−47.0214			−0.887195			−0.443598	−	0.896226i	$-0.646298\pi$
$53$	−47.0214			−0.887195			−0.443598	+	0.896226i	$0.646298\pi$
$54$			7.34847i			0.136083i
$55$			9.31721i			0.169404i
$56$			32.6578i			0.583175i
$57$	46.0075			0.807148
$58$		−	59.7809i		−	1.03071i
$59$	52.1855	−	27.5259i	0.884500	−	0.466540i
$59$	52.1855	−	27.5259i	0.884500	−	0.466540i
$60$	2.29424			0.0382373
$61$		−	9.71992i		−	0.159343i	−0.996821	−	0.0796715i	$-0.974613\pi$
$61$		−	9.71992i		−	0.159343i	0.996821	−	0.0796715i	$-0.0253871\pi$
$62$	12.0251			0.193953
$63$	−34.6388			−0.549823
$64$	−8.00000			−0.125000
$65$			8.98404i			0.138216i
$66$	34.4599			0.522120
$67$		−	101.799i		−	1.51939i	−0.650282	−	0.759693i	$-0.725349\pi$
$67$		−	101.799i		−	1.51939i	0.650282	−	0.759693i	$-0.274651\pi$
$68$	−27.1106			−0.398686
$69$		−	39.4607i		−	0.571894i
$70$			10.8144i			0.154492i
$71$	−85.3891			−1.20266			−0.601332	−	0.798999i	$-0.705363\pi$
$71$	−85.3891			−1.20266			−0.601332	+	0.798999i	$0.705363\pi$
$72$		−	8.48528i		−	0.117851i
$73$			41.2625i			0.565240i	0.959232	+	0.282620i	$0.0912035\pi$
$73$			41.2625i			0.565240i	−0.959232	+	0.282620i	$0.908797\pi$
$74$	95.2342			1.28695
$75$	−42.5415			−0.567221
$76$	−53.1248			−0.699011
$77$			162.435i			2.10955i
$78$	33.2277			0.425996
$79$	119.379			1.51113			0.755563	−	0.655076i	$-0.227364\pi$
$79$	119.379			1.51113			0.755563	+	0.655076i	$0.227364\pi$
$80$	−2.64915			−0.0331144
$81$	9.00000			0.111111
$82$		−	60.8541i		−	0.742123i
$83$		−	13.8927i		−	0.167382i	−0.996492	−	0.0836910i	$-0.973329\pi$
$83$		−	13.8927i		−	0.167382i	0.996492	−	0.0836910i	$-0.0266709\pi$
$84$	39.9975			0.476161
$85$	−8.97753			−0.105618
$86$	−57.9704			−0.674075
$87$	−73.2163			−0.841567
$88$	−39.7909			−0.452169
$89$			28.7153i			0.322643i	0.986902	+	0.161322i	$0.0515757\pi$
$89$			28.7153i			0.322643i	−0.986902	+	0.161322i	$0.948424\pi$
$90$		−	2.80985i		−	0.0312206i
$91$			156.627i			1.72118i
$92$			45.5652i			0.495274i
$93$		−	14.7277i		−	0.158362i
$94$	−83.1206			−0.884261
$95$	−17.5920			−0.185179
$96$			9.79796i			0.102062i
$97$			109.955i			1.13356i	0.823870	+	0.566778i	$0.191810\pi$
$97$			109.955i			1.13356i	−0.823870	+	0.566778i	$0.808190\pi$
$98$			119.242i			1.21675i
$99$		−	42.2046i		−	0.426309i
$100$	49.1227			0.491227
$101$		−	125.062i		−	1.23824i	−0.785296	−	0.619120i	$-0.787489\pi$
$101$		−	125.062i		−	1.23824i	0.785296	−	0.619120i	$-0.212511\pi$
$102$			33.2036i			0.325526i
$103$			32.9708i			0.320104i	0.987109	+	0.160052i	$0.0511663\pi$
$103$			32.9708i			0.320104i	−0.987109	+	0.160052i	$0.948834\pi$
$104$	−38.3680			−0.368923
$105$	13.2449			0.126142
$106$		−	66.4982i		−	0.627342i
$107$	−126.104			−1.17854			−0.589272	−	0.807935i	$-0.700585\pi$
$107$	−126.104			−1.17854			−0.589272	+	0.807935i	$0.700585\pi$
$108$	−10.3923			−0.0962250
$109$		−	206.195i		−	1.89169i	−0.324612	−	0.945847i	$-0.605234\pi$
$109$		−	206.195i		−	1.89169i	0.324612	−	0.945847i	$-0.394766\pi$
$110$	−13.1765			−0.119787
$111$		−	116.638i		−	1.05079i
$112$	−46.1851			−0.412367
$113$			92.8673i			0.821834i	0.911673	+	0.410917i	$0.134791\pi$
$113$			92.8673i			0.821834i	−0.911673	+	0.410917i	$0.865209\pi$
$114$			65.0644i			0.570740i
$115$			15.0887i			0.131206i
$116$	84.5429			0.728819
$117$		−	40.6954i		−	0.347824i
$118$	38.9275	+	73.8014i	0.329894	+	0.625436i
$119$	−156.514			−1.31524
$120$			3.24454i			0.0270378i
$121$	−76.9141			−0.635654
$122$	13.7460			0.112673
$123$	−74.5307			−0.605941
$124$			17.0060i			0.137146i
$125$	32.8239			0.262591
$126$		−	48.9867i		−	0.388783i
$127$	62.8376			0.494785			0.247392	−	0.968915i	$-0.420426\pi$
$127$	62.8376			0.494785			0.247392	+	0.968915i	$0.420426\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			70.9990i			0.550380i
$130$	−12.7054			−0.0977335
$131$			142.643i			1.08888i	0.838801	+	0.544439i	$0.183257\pi$
$131$			142.643i			1.08888i	−0.838801	+	0.544439i	$0.816743\pi$
$132$			48.7337i			0.369194i
$133$	−306.697			−2.30599
$134$	143.965			1.07437
$135$	−3.44135			−0.0254915
$136$		−	38.3402i		−	0.281913i
$137$	−1.42140			−0.0103752			−0.00518759	−	0.999987i	$-0.501651\pi$
$137$	−1.42140			−0.0103752			−0.00518759	+	0.999987i	$0.501651\pi$
$138$	55.8058			0.404390
$139$	191.419			1.37712			0.688559	−	0.725181i	$-0.258244\pi$
$139$	191.419			1.37712			0.688559	+	0.725181i	$0.258244\pi$
$140$	−15.2939			−0.109242
$141$			101.801i			0.721996i
$142$		−	120.758i		−	0.850412i
$143$	−190.837			−1.33453
$144$	12.0000			0.0833333
$145$	27.9959			0.193075
$146$	−58.3540			−0.399685
$147$	146.041			0.993474
$148$			134.682i			0.910010i
$149$		−	136.589i		−	0.916706i	−0.888770	−	0.458353i	$-0.848439\pi$
$149$		−	136.589i		−	0.916706i	0.888770	−	0.458353i	$-0.151561\pi$
$150$		−	60.1628i		−	0.401086i
$151$			281.766i			1.86600i	0.359876	+	0.933000i	$0.382819\pi$
$151$			281.766i			1.86600i	−0.359876	+	0.933000i	$0.617181\pi$
$152$		−	75.1299i		−	0.494275i
$153$	40.6660			0.265791
$154$	−229.718			−1.49168
$155$			5.63146i			0.0363320i
$156$			46.9911i			0.301225i
$157$		−	212.519i		−	1.35363i	−0.736155	−	0.676813i	$-0.763361\pi$
$157$		−	212.519i		−	1.35363i	0.736155	−	0.676813i	$-0.236639\pi$
$158$			168.827i			1.06853i
$159$	−81.4434			−0.512222
$160$		−	3.74647i		−	0.0234154i
$161$			263.055i			1.63388i
$162$			12.7279i			0.0785674i
$163$	−140.068			−0.859312			−0.429656	−	0.902993i	$-0.641365\pi$
$163$	−140.068			−0.859312			−0.429656	+	0.902993i	$0.641365\pi$
$164$	86.0607			0.524760
$165$			16.1379i			0.0978053i
$166$	19.6473			0.118357
$167$	73.5681			0.440528			0.220264	−	0.975440i	$-0.429308\pi$
$167$	73.5681			0.440528			0.220264	+	0.975440i	$0.429308\pi$
$168$			56.5650i			0.336696i
$169$	−15.0132			−0.0888358
$170$		−	12.6962i		−	0.0746832i
$171$	79.6872			0.466007
$172$		−	81.9826i		−	0.476643i
$173$			277.998i			1.60693i	0.595354	+	0.803463i	$0.297012\pi$
$173$			277.998i			1.60693i	−0.595354	+	0.803463i	$0.702988\pi$
$174$		−	103.544i		−	0.595078i
$175$	283.593			1.62053
$176$		−	56.2728i		−	0.319732i
$177$	90.3879	−	47.6762i	0.510666	−	0.269357i
$178$	−40.6095			−0.228143
$179$			165.095i			0.922317i	0.887318	+	0.461158i	$0.152566\pi$
$179$			165.095i			0.922317i	−0.887318	+	0.461158i	$0.847434\pi$
$180$	3.97373			0.0220763
$181$	−48.7732			−0.269465			−0.134733	−	0.990882i	$-0.543018\pi$
$181$	−48.7732			−0.269465			−0.134733	+	0.990882i	$0.543018\pi$
$182$	−221.504			−1.21706
$183$		−	16.8354i		−	0.0919967i
$184$	−64.4390			−0.350212
$185$			44.5990i			0.241076i
$186$	20.8281			0.111979
$187$		−	190.699i		−	1.01978i
$188$		−	117.550i		−	0.625267i
$189$	−59.9962			−0.317440
$190$		−	24.8788i		−	0.130941i
$191$		−	67.7608i		−	0.354769i	−0.984142	−	0.177384i	$-0.943236\pi$
$191$		−	67.7608i		−	0.354769i	0.984142	−	0.177384i	$-0.0567636\pi$
$192$	−13.8564			−0.0721688
$193$	1.63999			0.00849736			0.00424868	−	0.999991i	$-0.498648\pi$
$193$	1.63999			0.00849736			0.00424868	+	0.999991i	$0.498648\pi$
$194$	−155.500			−0.801546
$195$			15.5608i			0.0797991i
$196$	−168.633			−0.860373
$197$	155.152			0.787574			0.393787	−	0.919202i	$-0.371165\pi$
$197$	155.152			0.787574			0.393787	+	0.919202i	$0.371165\pi$
$198$	59.6863			0.301446
$199$	251.026			1.26144			0.630718	−	0.776012i	$-0.282761\pi$
$199$	251.026			1.26144			0.630718	+	0.776012i	$0.282761\pi$
$200$			69.4701i			0.347350i
$201$		−	176.321i		−	0.877217i
$202$	176.865			0.875568
$203$	488.078			2.40433
$204$	−46.9570			−0.230181
$205$	28.4985			0.139017
$206$	−46.6277			−0.226348
$207$		−	68.3479i		−	0.330183i
$208$		−	54.2606i		−	0.260868i
$209$		−	373.685i		−	1.78797i
$210$			18.7312i			0.0891961i
$211$		−	249.153i		−	1.18082i	−0.807104	−	0.590409i	$-0.798966\pi$
$211$		−	249.153i		−	1.18082i	0.807104	−	0.590409i	$-0.201034\pi$
$212$	94.0427			0.443598
$213$	−147.898			−0.694358
$214$		−	178.338i		−	0.833357i
$215$		−	27.1481i		−	0.126270i
$216$		−	14.6969i		−	0.0680414i
$217$			98.1783i			0.452434i
$218$	291.603			1.33763
$219$			71.4687i			0.326341i
$220$		−	18.6344i		−	0.0847019i
$221$		−	183.880i		−	0.832036i
$222$	164.951			0.743020
$223$	214.338			0.961158			0.480579	−	0.876951i	$-0.340427\pi$
$223$	214.338			0.961158			0.480579	+	0.876951i	$0.340427\pi$
$224$		−	65.3156i		−	0.291588i
$225$	−73.6841			−0.327485
$226$	−131.334			−0.581124
$227$		−	341.465i		−	1.50425i	−0.659021	−	0.752125i	$-0.729029\pi$
$227$		−	341.465i		−	1.50425i	0.659021	−	0.752125i	$-0.270971\pi$
$228$	−92.0149			−0.403574
$229$			284.636i			1.24295i	0.783433	+	0.621477i	$0.213467\pi$
$229$			284.636i			1.24295i	−0.783433	+	0.621477i	$0.786533\pi$
$230$	−21.3386			−0.0927765
$231$			281.346i			1.21795i
$232$			119.562i			0.515353i
$233$		−	377.861i		−	1.62172i	−0.585241	−	0.810860i	$-0.699000\pi$
$233$		−	377.861i		−	1.62172i	0.585241	−	0.810860i	$-0.301000\pi$
$234$	57.5520			0.245949
$235$		−	38.9261i		−	0.165643i
$236$	−104.371	+	55.0518i	−0.442250	+	0.233270i
$237$	206.770			0.872449
$238$		−	221.344i		−	0.930015i
$239$	313.718			1.31263			0.656314	−	0.754488i	$-0.272115\pi$
$239$	313.718			1.31263			0.656314	+	0.754488i	$0.272115\pi$
$240$	−4.58847			−0.0191186
$241$	70.8960			0.294174			0.147087	−	0.989124i	$-0.453010\pi$
$241$	70.8960			0.294174			0.147087	+	0.989124i	$0.453010\pi$
$242$		−	108.773i		−	0.449475i
$243$	15.5885			0.0641500
$244$			19.4398i			0.0796715i
$245$	−55.8419			−0.227926
$246$		−	105.402i		−	0.428465i
$247$		−	360.323i		−	1.45880i
$248$	−24.0502			−0.0969765
$249$		−	24.0629i		−	0.0966381i
$250$			46.4201i			0.185680i
$251$	244.796			0.975283			0.487642	−	0.873044i	$-0.337857\pi$
$251$	244.796			0.975283			0.487642	+	0.873044i	$0.337857\pi$
$252$	69.2777			0.274911
$253$	−320.510			−1.26684
$254$			88.8658i			0.349866i
$255$	−15.5495			−0.0609786
$256$	16.0000			0.0625000
$257$	134.668			0.524002			0.262001	−	0.965068i	$-0.415618\pi$
$257$	134.668			0.524002			0.262001	+	0.965068i	$0.415618\pi$
$258$	−100.408			−0.389177
$259$			777.535i			3.00207i
$260$		−	17.9681i		−	0.0691080i
$261$	−126.814			−0.485879
$262$	−201.728			−0.769953
$263$	−264.351			−1.00514			−0.502568	−	0.864538i	$-0.667611\pi$
$263$	−264.351			−1.00514			−0.502568	+	0.864538i	$0.667611\pi$
$264$	−68.9198			−0.261060
$265$	31.1417			0.117516
$266$		−	433.735i		−	1.63058i
$267$			49.7363i			0.186278i
$268$			203.598i			0.759693i
$269$		−	301.901i		−	1.12231i	−0.827711	−	0.561155i	$-0.810357\pi$
$269$		−	301.901i		−	1.12231i	0.827711	−	0.561155i	$-0.189643\pi$
$270$		−	4.86681i		−	0.0180252i
$271$	392.633			1.44883			0.724415	−	0.689364i	$-0.242110\pi$
$271$	392.633			1.44883			0.724415	+	0.689364i	$0.242110\pi$
$272$	54.2213			0.199343
$273$			271.286i			0.993721i
$274$		−	2.01016i		−	0.00733637i
$275$			345.534i			1.25649i
$276$			78.9213i			0.285947i
$277$	−173.219			−0.625341			−0.312670	−	0.949862i	$-0.601224\pi$
$277$	−173.219			−0.625341			−0.312670	+	0.949862i	$0.601224\pi$
$278$			270.708i			0.973769i
$279$		−	25.5091i		−	0.0914303i
$280$		−	21.6289i		−	0.0772461i
$281$	−67.8065			−0.241304			−0.120652	−	0.992695i	$-0.538499\pi$
$281$	−67.8065			−0.241304			−0.120652	+	0.992695i	$0.538499\pi$
$282$	−143.969			−0.510528
$283$		−	28.6790i		−	0.101339i	−0.998715	−	0.0506697i	$-0.983864\pi$
$283$		−	28.6790i		−	0.101339i	0.998715	−	0.0506697i	$-0.0161356\pi$
$284$	170.778			0.601332
$285$	−30.4702			−0.106913
$286$		−	269.884i		−	0.943652i
$287$	496.840			1.73115
$288$			16.9706i			0.0589256i
$289$	−105.253			−0.364198
$290$			39.5922i			0.136525i
$291$			190.448i			0.654459i
$292$		−	82.5250i		−	0.282620i
$293$	−244.828			−0.835589			−0.417794	−	0.908542i	$-0.637197\pi$
$293$	−244.828			−0.835589			−0.417794	+	0.908542i	$0.637197\pi$
$294$			206.533i			0.702492i
$295$	−34.5619	+	18.2301i	−0.117159	+	0.0617969i
$296$	−190.468			−0.643475
$297$		−	73.1005i		−	0.246130i
$298$	193.166			0.648209
$299$	−309.050			−1.03361
$300$	85.0831			0.283610
$301$		−	473.297i		−	1.57242i
$302$	−398.477			−1.31946
$303$		−	216.614i		−	0.714899i
$304$	106.250			0.349505
$305$			6.43740i			0.0211062i
$306$			57.5103i			0.187942i
$307$	97.4532			0.317437			0.158719	−	0.987324i	$-0.449264\pi$
$307$	97.4532			0.317437			0.158719	+	0.987324i	$0.449264\pi$
$308$		−	324.871i		−	1.05477i
$309$			57.1070i			0.184812i
$310$	−7.96408			−0.0256906
$311$	−386.814			−1.24377			−0.621887	−	0.783107i	$-0.713634\pi$
$311$	−386.814			−1.24377			−0.621887	+	0.783107i	$0.713634\pi$
$312$	−66.4554			−0.212998
$313$			44.0812i			0.140834i	0.997518	+	0.0704172i	$0.0224331\pi$
$313$			44.0812i			0.140834i	−0.997518	+	0.0704172i	$0.977567\pi$
$314$	300.547			0.957157
$315$	22.9409			0.0728283
$316$	−238.758			−0.755563
$317$	−384.370			−1.21252			−0.606262	−	0.795265i	$-0.707332\pi$
$317$	−384.370			−1.21252			−0.606262	+	0.795265i	$0.707332\pi$
$318$		−	115.178i		−	0.362196i
$319$			594.683i			1.86421i
$320$	5.29831			0.0165572
$321$	−218.419			−0.680433
$322$	−372.015			−1.15533
$323$	360.062			1.11474
$324$	−18.0000			−0.0555556
$325$			333.179i			1.02517i
$326$		−	198.086i		−	0.607625i
$327$		−	357.140i		−	1.09217i
$328$			121.708i			0.371062i
$329$		−	678.634i		−	2.06272i
$330$	−22.8224			−0.0691588
$331$	540.941			1.63426			0.817132	−	0.576451i	$-0.195563\pi$
$331$	540.941			1.63426			0.817132	+	0.576451i	$0.195563\pi$
$332$			27.7854i			0.0836910i
$333$		−	202.022i		−	0.606674i
$334$			104.041i			0.311500i
$335$			67.4202i			0.201254i
$336$	−79.9950			−0.238080
$337$		−	66.9358i		−	0.198622i	−0.995056	−	0.0993112i	$-0.968336\pi$
$337$		−	66.9358i		−	0.198622i	0.995056	−	0.0993112i	$-0.0316639\pi$
$338$		−	21.2319i		−	0.0628164i
$339$			160.851i			0.474486i
$340$	17.9551			0.0528090
$341$	−119.622			−0.350798
$342$			112.695i			0.329517i
$343$	−407.775			−1.18885
$344$	115.941			0.337037
$345$			26.1343i			0.0757517i
$346$	−393.149			−1.13627
$347$			209.650i			0.604179i	0.953280	+	0.302089i	$0.0976841\pi$
$347$			209.650i			0.604179i	−0.953280	+	0.302089i	$0.902316\pi$
$348$	146.433			0.420784
$349$			104.485i			0.299385i	0.988733	+	0.149692i	$0.0478283\pi$
$349$			104.485i			0.299385i	−0.988733	+	0.149692i	$0.952172\pi$
$350$			401.060i			1.14589i
$351$		−	70.4866i		−	0.200816i
$352$	79.5817			0.226084
$353$		−	477.203i		−	1.35185i	−0.736970	−	0.675925i	$-0.763744\pi$
$353$		−	477.203i		−	1.35185i	0.736970	−	0.675925i	$-0.236256\pi$
$354$	67.4244	+	127.828i	0.190464	+	0.361096i
$355$	56.5522			0.159302
$356$		−	57.4305i		−	0.161322i
$357$	−271.089			−0.759354
$358$	−233.479			−0.652176
$359$	357.746			0.996506			0.498253	−	0.867032i	$-0.333975\pi$
$359$	357.746			0.996506			0.498253	+	0.867032i	$0.333975\pi$
$360$			5.61971i			0.0156103i
$361$	344.562			0.954465
$362$		−	68.9758i		−	0.190541i
$363$	−133.219			−0.366995
$364$		−	313.254i		−	0.860588i
$365$		−	27.3277i		−	0.0748704i
$366$	23.8089			0.0650515
$367$			294.878i			0.803483i	0.915753	+	0.401742i	$0.131595\pi$
$367$			294.878i			0.803483i	−0.915753	+	0.401742i	$0.868405\pi$
$368$		−	91.1305i		−	0.247637i
$369$	−129.091			−0.349840
$370$	−63.0726			−0.170466
$371$	542.922			1.46340
$372$			29.4553i			0.0791810i
$373$	572.972			1.53612			0.768059	−	0.640380i	$-0.221223\pi$
$373$	572.972			1.53612			0.768059	+	0.640380i	$0.221223\pi$
$374$	269.689			0.721093
$375$	56.8527			0.151607
$376$	166.241			0.442131
$377$			573.419i			1.52100i
$378$		−	84.8475i		−	0.224464i
$379$	−162.404			−0.428507			−0.214254	−	0.976778i	$-0.568732\pi$
$379$	−162.404			−0.428507			−0.214254	+	0.976778i	$0.568732\pi$
$380$	35.1840			0.0925894
$381$	108.838			0.285664
$382$	95.8283			0.250859
$383$	−141.726			−0.370041			−0.185020	−	0.982735i	$-0.559235\pi$
$383$	−141.726			−0.370041			−0.185020	+	0.982735i	$0.559235\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		−	107.579i		−	0.279426i
$386$			2.31930i			0.00600854i
$387$			122.974i			0.317762i
$388$		−	219.910i		−	0.566778i
$389$	−187.633			−0.482347			−0.241174	−	0.970482i	$-0.577532\pi$
$389$	−187.633			−0.482347			−0.241174	+	0.970482i	$0.577532\pi$
$390$	−22.0063			−0.0564265
$391$		−	308.826i		−	0.789835i
$392$		−	238.483i		−	0.608376i
$393$			247.065i			0.628664i
$394$			219.418i			0.556899i
$395$	−79.0633			−0.200160
$396$			84.4092i			0.213154i
$397$			339.828i			0.855990i	0.903781	+	0.427995i	$0.140780\pi$
$397$			339.828i			0.855990i	−0.903781	+	0.427995i	$0.859220\pi$
$398$			355.004i			0.891969i
$399$	−531.215			−1.33137
$400$	−98.2455			−0.245614
$401$			644.909i			1.60825i	0.594459	+	0.804126i	$0.297366\pi$
$401$			644.909i			1.60825i	−0.594459	+	0.804126i	$0.702634\pi$
$402$	249.355			0.620286
$403$	−115.345			−0.286215
$404$			250.125i			0.619120i
$405$	−5.96060			−0.0147175
$406$			690.247i			1.70012i
$407$	−947.363			−2.32767
$408$		−	66.4072i		−	0.162763i
$409$		−	63.1537i		−	0.154410i	−0.997015	−	0.0772050i	$-0.975400\pi$
$409$		−	63.1537i		−	0.154410i	0.997015	−	0.0772050i	$-0.0245996\pi$
$410$			40.3030i			0.0982999i
$411$	−2.46194			−0.00599012
$412$		−	65.9415i		−	0.160052i
$413$	−602.548	+	317.822i	−1.45895	+	0.769544i
$414$	96.6585			0.233475
$415$			9.20099i			0.0221710i
$416$	76.7361			0.184462
$417$	331.548			0.795079
$418$	528.471			1.26428
$419$		−	193.020i		−	0.460668i	−0.973112	−	0.230334i	$-0.926018\pi$
$419$		−	193.020i		−	0.460668i	0.973112	−	0.230334i	$-0.0739819\pi$
$420$	−26.4899			−0.0630712
$421$		−	308.586i		−	0.732983i	−0.930421	−	0.366492i	$-0.880559\pi$
$421$		−	308.586i		−	0.732983i	0.930421	−	0.366492i	$-0.119441\pi$
$422$	352.355			0.834964
$423$			176.325i			0.416845i
$424$			132.996i			0.313671i
$425$	−332.937			−0.783382
$426$		−	209.160i		−	0.490985i
$427$			112.229i			0.262831i
$428$	252.208			0.589272
$429$	−330.540			−0.770489
$430$	38.3932			0.0892864
$431$		−	209.079i		−	0.485103i	−0.970139	−	0.242551i	$-0.922016\pi$
$431$		−	209.079i		−	0.485103i	0.970139	−	0.242551i	$-0.0779843\pi$
$432$	20.7846			0.0481125
$433$	−570.111			−1.31665			−0.658327	−	0.752732i	$-0.728736\pi$
$433$	−570.111			−1.31665			−0.658327	+	0.752732i	$0.728736\pi$
$434$	−138.845			−0.319919
$435$	48.4904			0.111472
$436$			412.389i			0.945847i
$437$		−	605.161i		−	1.38481i
$438$	−101.072			−0.230758
$439$	52.8591			0.120408			0.0602040	−	0.998186i	$-0.480825\pi$
$439$	52.8591			0.120408			0.0602040	+	0.998186i	$0.480825\pi$
$440$	26.3530			0.0598933
$441$	252.950			0.573582
$442$	260.045			0.588338
$443$		−	286.588i		−	0.646925i	−0.946241	−	0.323462i	$-0.895153\pi$
$443$		−	286.588i		−	0.646925i	0.946241	−	0.323462i	$-0.104847\pi$
$444$			233.275i			0.525395i
$445$		−	19.0178i		−	0.0427366i
$446$			303.120i			0.679641i
$447$		−	236.580i		−	0.529261i
$448$	92.3702			0.206184
$449$	7.01555			0.0156248			0.00781241	−	0.999969i	$-0.497513\pi$
$449$	7.01555			0.0156248			0.00781241	+	0.999969i	$0.497513\pi$
$450$		−	104.205i		−	0.231567i
$451$			605.359i			1.34226i
$452$		−	185.735i		−	0.410917i
$453$			488.033i			1.07734i
$454$	482.904			1.06366
$455$		−	103.732i		−	0.227983i
$456$		−	130.129i		−	0.285370i
$457$		−	734.014i		−	1.60616i	−0.595873	−	0.803079i	$-0.703194\pi$
$457$		−	734.014i		−	1.60616i	0.595873	−	0.803079i	$-0.296806\pi$
$458$	−402.537			−0.878901
$459$	70.4355			0.153454
$460$		−	30.1773i		−	0.0656029i
$461$	685.811			1.48766			0.743830	−	0.668369i	$-0.233007\pi$
$461$	685.811			1.48766			0.743830	+	0.668369i	$0.233007\pi$
$462$	−397.884			−0.861220
$463$			52.8967i			0.114248i	0.998367	+	0.0571239i	$0.0181930\pi$
$463$			52.8967i			0.114248i	−0.998367	+	0.0571239i	$0.981807\pi$
$464$	−169.086			−0.364409
$465$			9.75397i			0.0209763i
$466$	534.376			1.14673
$467$		−	268.196i		−	0.574295i	−0.957886	−	0.287147i	$-0.907293\pi$
$467$		−	268.196i		−	0.574295i	0.957886	−	0.287147i	$-0.0927070\pi$
$468$			81.3909i			0.173912i
$469$			1175.40i			2.50618i
$470$	55.0498			0.117127
$471$		−	368.094i		−	0.781516i
$472$	−77.8550	−	147.603i	−0.164947	−	0.312718i
$473$	576.674			1.21918
$474$			292.417i			0.616914i
$475$	−652.409			−1.37349
$476$	313.027			0.657620
$477$	−141.064			−0.295732
$478$			443.665i			0.928169i
$479$	39.3804			0.0822138			0.0411069	−	0.999155i	$-0.486912\pi$
$479$	39.3804			0.0822138			0.0411069	+	0.999155i	$0.486912\pi$
$480$		−	6.48908i		−	0.0135189i
$481$	−913.488			−1.89914
$482$			100.262i			0.208013i
$483$			455.624i			0.943320i
$484$	153.828			0.317827
$485$		−	72.8220i		−	0.150148i
$486$			22.0454i			0.0453609i
$487$	−324.530			−0.666386			−0.333193	−	0.942859i	$-0.608126\pi$
$487$	−324.530			−0.666386			−0.333193	+	0.942859i	$0.608126\pi$
$488$	−27.4921			−0.0563363
$489$	−242.605			−0.496124
$490$		−	78.9724i		−	0.161168i
$491$	270.286			0.550481			0.275241	−	0.961375i	$-0.411242\pi$
$491$	270.286			0.550481			0.275241	+	0.961375i	$0.411242\pi$
$492$	149.061			0.302970
$493$	−573.003			−1.16228
$494$	509.574			1.03153
$495$			27.9516i			0.0564679i
$496$		−	34.0121i		−	0.0685728i
$497$	985.927			1.98376
$498$	34.0301			0.0683334
$499$	45.3667			0.0909153			0.0454576	−	0.998966i	$-0.485525\pi$
$499$	45.3667			0.0909153			0.0454576	+	0.998966i	$0.485525\pi$
$500$	−65.6479			−0.131296
$501$	127.424			0.254339
$502$			346.194i			0.689629i
$503$		−	9.26063i		−	0.0184108i	−0.999958	−	0.00920540i	$-0.997070\pi$
$503$		−	9.26063i		−	0.0184108i	0.999958	−	0.00920540i	$-0.00293021\pi$
$504$			97.9734i			0.194392i
$505$			82.8273i			0.164015i
$506$		−	453.270i		−	0.895791i
$507$	−26.0037			−0.0512894
$508$	−125.675			−0.247392
$509$			238.440i			0.468448i	0.972183	+	0.234224i	$0.0752549\pi$
$509$			238.440i			0.468448i	−0.972183	+	0.234224i	$0.924745\pi$
$510$		−	21.9904i		−	0.0431184i
$511$		−	476.428i		−	0.932345i
$512$			22.6274i			0.0441942i
$513$	138.022			0.269049
$514$			190.450i			0.370525i
$515$		−	21.8362i		−	0.0424003i
$516$		−	141.998i		−	0.275190i
$517$	826.860			1.59934
$518$	−1099.60			−2.12278
$519$			481.507i			0.927760i
$520$	25.4107			0.0488668
$521$	−246.531			−0.473188			−0.236594	−	0.971609i	$-0.576031\pi$
$521$	−246.531			−0.473188			−0.236594	+	0.971609i	$0.576031\pi$
$522$		−	179.343i		−	0.343568i
$523$	−153.732			−0.293943			−0.146971	−	0.989141i	$-0.546953\pi$
$523$	−153.732			−0.293943			−0.146971	+	0.989141i	$0.546953\pi$
$524$		−	285.286i		−	0.544439i
$525$	491.197			0.935613
$526$		−	373.848i		−	0.710738i
$527$		−	115.261i		−	0.218712i
$528$		−	97.4673i		−	0.184597i
$529$	9.95227			0.0188134
$530$			44.0410i			0.0830963i
$531$	156.556	−	82.5776i	0.294833	−	0.155513i
$532$	613.394			1.15300
$533$			583.713i			1.09515i
$534$	−70.3377			−0.131719
$535$	83.5174			0.156107
$536$	−287.931			−0.537184
$537$			285.952i			0.532500i
$538$	426.953			0.793593
$539$		−	1186.18i		−	2.20071i
$540$	6.88271			0.0127458
$541$		−	615.997i		−	1.13863i	−0.822120	−	0.569314i	$-0.807209\pi$
$541$		−	615.997i		−	1.13863i	0.822120	−	0.569314i	$-0.192791\pi$
$542$			555.267i			1.02448i
$543$	−84.4777			−0.155576
$544$			76.6805i			0.140957i
$545$			136.560i			0.250570i
$546$	−383.656			−0.702667
$547$	−548.762			−1.00322			−0.501611	−	0.865093i	$-0.667259\pi$
$547$	−548.762			−1.00322			−0.501611	+	0.865093i	$0.667259\pi$
$548$	2.84280			0.00518759
$549$		−	29.1598i		−	0.0531143i
$550$	−488.659			−0.888471
$551$	−1122.83			−2.03781
$552$	−111.612			−0.202195
$553$	−1378.38			−2.49255
$554$		−	244.969i		−	0.442183i
$555$			77.2478i			0.139185i
$556$	−382.839			−0.688559
$557$	912.310			1.63790			0.818949	−	0.573866i	$-0.194557\pi$
$557$	912.310			1.63790			0.818949	+	0.573866i	$0.194557\pi$
$558$	36.0753			0.0646510
$559$	556.053			0.994728
$560$	30.5879			0.0546212
$561$		−	330.300i		−	0.588770i
$562$		−	95.8929i		−	0.170628i
$563$		−	33.3081i		−	0.0591618i	−0.999562	−	0.0295809i	$-0.990583\pi$
$563$		−	33.3081i		−	0.0591618i	0.999562	−	0.0295809i	$-0.00941726\pi$
$564$		−	203.603i		−	0.360998i
$565$		−	61.5049i		−	0.108858i
$566$	40.5583			0.0716577
$567$	−103.917			−0.183274
$568$			241.517i			0.425206i
$569$			794.495i			1.39630i	0.715951	+	0.698150i	$0.245993\pi$
$569$			794.495i			1.39630i	−0.715951	+	0.698150i	$0.754007\pi$
$570$		−	43.0914i		−	0.0755989i
$571$		−	1061.81i		−	1.85956i	−0.368113	−	0.929781i	$-0.619996\pi$
$571$		−	1061.81i		−	1.85956i	0.368113	−	0.929781i	$-0.380004\pi$
$572$	381.674			0.667263
$573$		−	117.365i		−	0.204826i
$574$			702.638i			1.22411i
$575$			559.572i			0.973169i
$576$	−24.0000			−0.0416667
$577$	−278.793			−0.483176			−0.241588	−	0.970379i	$-0.577668\pi$
$577$	−278.793			−0.483176			−0.241588	+	0.970379i	$0.577668\pi$
$578$		−	148.851i		−	0.257527i
$579$	2.84055			0.00490595
$580$	−55.9918			−0.0965377
$581$			160.409i			0.276091i
$582$	−269.334			−0.462773
$583$			661.506i			1.13466i
$584$	116.708			0.199842
$585$			26.9521i			0.0460720i
$586$		−	346.238i		−	0.590851i
$587$			62.0253i			0.105665i	0.998603	+	0.0528324i	$0.0168249\pi$
$587$			62.0253i			0.105665i	−0.998603	+	0.0528324i	$0.983175\pi$
$588$	−292.081			−0.496737
$589$		−	225.861i		−	0.383465i
$590$	−25.7812	−	48.8779i	−0.0436970	−	0.0828438i
$591$	268.731			0.454706
$592$		−	269.363i		−	0.455005i
$593$	−913.976			−1.54127			−0.770637	−	0.637274i	$-0.780062\pi$
$593$	−913.976			−1.54127			−0.770637	+	0.637274i	$0.780062\pi$
$594$	103.380			0.174040
$595$	103.657			0.174214
$596$			273.179i			0.458353i
$597$	434.789			0.728290
$598$		−	437.062i		−	0.730873i
$599$	300.317			0.501365			0.250682	−	0.968069i	$-0.419345\pi$
$599$	300.317			0.501365			0.250682	+	0.968069i	$0.419345\pi$
$600$			120.326i			0.200543i
$601$		−	368.321i		−	0.612847i	−0.951895	−	0.306424i	$-0.900868\pi$
$601$		−	368.321i		−	0.612847i	0.951895	−	0.306424i	$-0.0991324\pi$
$602$	669.343			1.11187
$603$		−	305.396i		−	0.506462i
$604$		−	563.532i		−	0.933000i
$605$	50.9393			0.0841972
$606$	306.339			0.505510
$607$	−799.754			−1.31755			−0.658776	−	0.752339i	$-0.728925\pi$
$607$	−799.754			−1.31755			−0.658776	+	0.752339i	$0.728925\pi$
$608$			150.260i			0.247138i
$609$	845.376			1.38814
$610$	−9.10385			−0.0149243
$611$	797.293			1.30490
$612$	−81.3319			−0.132895
$613$		−	706.350i		−	1.15228i	−0.817350	−	0.576142i	$-0.804558\pi$
$613$		−	706.350i		−	1.15228i	0.817350	−	0.576142i	$-0.195442\pi$
$614$			137.820i			0.224462i
$615$	49.3609			0.0802616
$616$	459.436			0.745838
$617$	556.713			0.902290			0.451145	−	0.892451i	$-0.351016\pi$
$617$	556.713			0.902290			0.451145	+	0.892451i	$0.351016\pi$
$618$	−80.7615			−0.130682
$619$	1029.05			1.66244			0.831220	−	0.555944i	$-0.187643\pi$
$619$	1029.05			1.66244			0.831220	+	0.555944i	$0.187643\pi$
$620$		−	11.2629i		−	0.0181660i
$621$		−	118.382i		−	0.190631i
$622$		−	547.037i		−	0.879481i
$623$		−	331.555i		−	0.532190i
$624$		−	93.9821i		−	0.150612i
$625$	592.295			0.947673
$626$	−62.3402			−0.0995849
$627$		−	647.242i		−	1.03228i
$628$			425.038i			0.676813i
$629$		−	912.826i		−	1.45123i
$630$			32.4433i			0.0514974i
$631$	254.460			0.403265			0.201632	−	0.979461i	$-0.435375\pi$
$631$	254.460			0.403265			0.201632	+	0.979461i	$0.435375\pi$
$632$		−	337.654i		−	0.534263i
$633$		−	431.545i		−	0.681746i
$634$		−	543.582i		−	0.857384i
$635$	−41.6167			−0.0655380
$636$	162.887			0.256111
$637$		−	1143.77i		−	1.79555i
$638$	−841.009			−1.31820
$639$	−256.167			−0.400888
$640$			7.49294i			0.0117077i
$641$	161.317			0.251665			0.125832	−	0.992052i	$-0.459840\pi$
$641$	161.317			0.251665			0.125832	+	0.992052i	$0.459840\pi$
$642$		−	308.891i		−	0.481139i
$643$	620.678			0.965284			0.482642	−	0.875818i	$-0.339677\pi$
$643$	620.678			0.965284			0.482642	+	0.875818i	$0.339677\pi$
$644$		−	526.109i		−	0.816939i
$645$		−	47.0218i		−	0.0729021i
$646$			509.205i			0.788242i
$647$	−1035.04			−1.59975			−0.799874	−	0.600168i	$-0.795100\pi$
$647$	−1035.04			−1.59975			−0.799874	+	0.600168i	$0.795100\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	−387.239	−	734.156i	−0.596671	−	1.13121i
$650$	−471.186			−0.724901
$651$			170.050i			0.261213i
$652$	280.136			0.429656
$653$	−1223.00			−1.87290			−0.936449	−	0.350804i	$-0.885908\pi$
$653$	−1223.00			−1.87290			−0.936449	+	0.350804i	$0.885908\pi$
$654$	505.072			0.772281
$655$		−	94.4708i		−	0.144230i
$656$	−172.121			−0.262380
$657$			123.787i			0.188413i
$658$	959.733			1.45856
$659$			556.041i			0.843765i	0.906650	+	0.421883i	$0.138631\pi$
$659$			556.041i			0.843765i	−0.906650	+	0.421883i	$0.861369\pi$
$660$		−	32.2757i		−	0.0489026i
$661$	−334.843			−0.506570			−0.253285	−	0.967392i	$-0.581511\pi$
$661$	−334.843			−0.506570			−0.253285	+	0.967392i	$0.581511\pi$
$662$			765.006i			1.15560i
$663$		−	318.489i		−	0.480376i
$664$	−39.2945			−0.0591785
$665$	203.122			0.305447
$666$	285.703			0.428983
$667$			963.055i			1.44386i
$668$	−147.136			−0.220264
$669$	371.245			0.554925
$670$	−95.3466			−0.142308
$671$	−136.742			−0.203788
$672$		−	113.130i		−	0.168348i
$673$			391.264i			0.581372i	0.956818	+	0.290686i	$0.0938836\pi$
$673$			391.264i			0.581372i	−0.956818	+	0.290686i	$0.906116\pi$
$674$	94.6615			0.140447
$675$	−127.625			−0.189074
$676$	30.0265			0.0444179
$677$	327.699			0.484045			0.242023	−	0.970271i	$-0.422189\pi$
$677$	327.699			0.484045			0.242023	+	0.970271i	$0.422189\pi$
$678$	−227.477			−0.335512
$679$		−	1269.57i		−	1.86977i
$680$			25.3923i			0.0373416i
$681$		−	591.434i		−	0.868479i
$682$		−	169.171i		−	0.248052i
$683$			310.923i			0.455231i	0.973751	+	0.227615i	$0.0730929\pi$
$683$			310.923i			0.455231i	−0.973751	+	0.227615i	$0.926907\pi$
$684$	−159.374			−0.233004
$685$	0.941378			0.00137427
$686$		−	576.681i		−	0.840643i
$687$			493.005i			0.717620i
$688$			163.965i			0.238321i
$689$			637.852i			0.925764i
$690$	−36.9595			−0.0535646
$691$		−	426.522i		−	0.617254i	−0.951183	−	0.308627i	$-0.900131\pi$
$691$		−	426.522i		−	0.617254i	0.951183	−	0.308627i	$-0.0998694\pi$
$692$		−	555.997i		−	0.803463i
$693$			487.306i			0.703183i
$694$	−296.490			−0.427219
$695$	−126.775			−0.182410
$696$			207.087i			0.297539i
$697$	−583.290			−0.836858
$698$	−147.764			−0.211697
$699$		−	654.474i		−	0.936300i
$700$	−567.185			−0.810264
$701$			713.727i			1.01816i	0.860720	+	0.509078i	$0.170014\pi$
$701$			713.727i			1.01816i	−0.860720	+	0.509078i	$0.829986\pi$
$702$	99.6831			0.141999
$703$		−	1788.73i		−	2.54443i
$704$			112.546i			0.159866i
$705$		−	67.4220i		−	0.0956340i
$706$	674.867			0.955902
$707$			1444.00i			2.04244i
$708$	−180.776	+	95.3525i	−0.255333	+	0.134679i
$709$	−304.713			−0.429779			−0.214890	−	0.976638i	$-0.568939\pi$
$709$	−304.713			−0.429779			−0.214890	+	0.976638i	$0.568939\pi$
$710$			79.9769i			0.112644i
$711$	358.137			0.503708
$712$	81.2190			0.114072
$713$	−193.721			−0.271699
$714$		−	383.378i		−	0.536944i
$715$	126.389			0.176768
$716$		−	330.189i		−	0.461158i
$717$	543.376			0.757847
$718$			505.929i			0.704636i
$719$			871.582i			1.21221i	0.795383	+	0.606107i	$0.207270\pi$
$719$			871.582i			1.21221i	−0.795383	+	0.606107i	$0.792730\pi$
$720$	−7.94746			−0.0110381
$721$		−	380.690i		−	0.528002i
$722$			487.284i			0.674909i
$723$	122.796			0.169842
$724$	97.5465			0.134733
$725$	1038.25			1.43206
$726$		−	188.400i		−	0.259505i
$727$	−395.811			−0.544444			−0.272222	−	0.962234i	$-0.587759\pi$
$727$	−395.811			−0.544444			−0.272222	+	0.962234i	$0.587759\pi$
$728$	443.008			0.608528
$729$	27.0000			0.0370370
$730$	38.6472			0.0529413
$731$			555.650i			0.760123i
$732$			33.6708i			0.0459984i
$733$	1119.11			1.52676			0.763379	−	0.645951i	$-0.223539\pi$
$733$	1119.11			1.52676			0.763379	+	0.645951i	$0.223539\pi$
$734$	−417.021			−0.568148
$735$	−96.7210			−0.131593
$736$	128.878			0.175106
$737$	−1432.13			−1.94318
$738$		−	182.562i		−	0.247374i
$739$		−	523.185i		−	0.707963i	−0.935252	−	0.353982i	$-0.884828\pi$
$739$		−	523.185i		−	0.707963i	0.935252	−	0.353982i	$-0.115172\pi$
$740$		−	89.1981i		−	0.120538i
$741$		−	624.098i		−	0.842237i
$742$			767.807i			1.03478i
$743$	143.939			0.193727			0.0968633	−	0.995298i	$-0.469119\pi$
$743$	143.939			0.193727			0.0968633	+	0.995298i	$0.469119\pi$
$744$	−41.6561			−0.0559894
$745$			90.4615i			0.121425i
$746$			810.304i			1.08620i
$747$		−	41.6781i		−	0.0557940i
$748$			381.398i			0.509890i
$749$	1456.03			1.94397
$750$			80.4019i			0.107203i
$751$			398.466i			0.530580i	0.964169	+	0.265290i	$0.0854677\pi$
$751$			398.466i			0.530580i	−0.964169	+	0.265290i	$0.914532\pi$
$752$			235.100i			0.312634i
$753$	423.999			0.563080
$754$	−810.937			−1.07551
$755$		−	186.610i		−	0.247166i
$756$	119.992			0.158720
$757$	452.438			0.597672			0.298836	−	0.954304i	$-0.403402\pi$
$757$	452.438			0.597672			0.298836	+	0.954304i	$0.403402\pi$
$758$		−	229.674i		−	0.303000i
$759$	−555.140			−0.731410
$760$			49.7577i			0.0654706i
$761$	1044.23			1.37218			0.686088	−	0.727518i	$-0.259326\pi$
$761$	1044.23			1.37218			0.686088	+	0.727518i	$0.259326\pi$
$762$			153.920i			0.201995i
$763$			2380.78i			3.12029i
$764$			135.522i			0.177384i
$765$	−26.9326			−0.0352060
$766$		−	200.430i		−	0.261658i
$767$	−373.393	−	707.904i	−0.486822	−	0.922952i
$768$	27.7128			0.0360844
$769$		−	722.516i		−	0.939553i	−0.882785	−	0.469776i	$-0.844335\pi$
$769$		−	722.516i		−	0.939553i	0.882785	−	0.469776i	$-0.155665\pi$
$770$	152.140			0.197584
$771$	233.253			0.302532
$772$	−3.27998			−0.00424868
$773$			1489.64i			1.92710i	0.267536	+	0.963548i	$0.413791\pi$
$773$			1489.64i			1.92710i	−0.267536	+	0.963548i	$0.586209\pi$
$774$	−173.911			−0.224692
$775$			208.846i			0.269479i
$776$	311.000			0.400773
$777$			1346.73i			1.73324i
$778$		−	265.353i		−	0.341071i
$779$	−1142.99			−1.46725
$780$		−	31.1216i		−	0.0398995i
$781$			1201.27i			1.53812i
$782$	436.745			0.558498
$783$	−219.649			−0.280522
$784$	337.266			0.430187
$785$			140.749i			0.179298i
$786$	−349.402			−0.444532
$787$	620.277			0.788153			0.394077	−	0.919078i	$-0.371064\pi$
$787$	620.277			0.788153			0.394077	+	0.919078i	$0.371064\pi$
$788$	−310.304			−0.393787
$789$	−457.869			−0.580315
$790$		−	111.812i		−	0.141535i
$791$		−	1072.27i		−	1.35559i
$792$	−119.373			−0.150723
$793$	−131.852			−0.166270
$794$	−480.589			−0.605276
$795$	53.9390			0.0678478
$796$	−502.051			−0.630718
$797$		−	24.4815i		−	0.0307171i	−0.999882	−	0.0153585i	$-0.995111\pi$
$797$		−	24.4815i		−	0.0307171i	0.999882	−	0.0153585i	$-0.00488897\pi$
$798$		−	751.251i		−	0.941418i
$799$			796.715i			0.997141i
$800$		−	138.940i		−	0.173675i
$801$			86.1458i			0.107548i
$802$	−912.039			−1.13721
$803$	580.489			0.722900
$804$			352.641i			0.438609i
$805$		−	174.218i		−	0.216420i
$806$		−	163.122i		−	0.202385i
$807$		−	522.908i		−	0.647966i
$808$	−353.730			−0.437784
$809$			432.252i			0.534304i	0.963654	+	0.267152i	$0.0860826\pi$
$809$			432.252i			0.534304i	−0.963654	+	0.267152i	$0.913917\pi$
$810$		−	8.42956i		−	0.0104069i
$811$		−	1214.04i		−	1.49697i	−0.663153	−	0.748484i	$-0.730782\pi$
$811$		−	1214.04i		−	1.49697i	0.663153	−	0.748484i	$-0.269218\pi$
$812$	−976.157			−1.20216
$813$	680.061			0.836483
$814$		−	1339.77i		−	1.64591i
$815$	92.7654			0.113823
$816$	93.9140			0.115091
$817$			1088.83i			1.33271i
$818$	89.3128			0.109184
$819$			469.881i			0.573725i
$820$	−56.9970			−0.0695086
$821$			609.672i			0.742597i	0.928513	+	0.371299i	$0.121087\pi$
$821$			609.672i			0.742597i	−0.928513	+	0.371299i	$0.878913\pi$
$822$		−	3.48171i		−	0.00423565i
$823$			1461.44i			1.77574i	0.460092	+	0.887871i	$0.347817\pi$
$823$			1461.44i			1.77574i	−0.460092	+	0.887871i	$0.652183\pi$
$824$	93.2554			0.113174
$825$			598.483i			0.725434i
$826$	−449.468	−	852.132i	−0.544150	−	1.03164i
$827$	636.218			0.769308			0.384654	−	0.923061i	$-0.374321\pi$
$827$	636.218			0.769308			0.384654	+	0.923061i	$0.374321\pi$
$828$			136.696i			0.165091i
$829$	−737.463			−0.889582			−0.444791	−	0.895635i	$-0.646722\pi$
$829$	−737.463			−0.889582			−0.444791	+	0.895635i	$0.646722\pi$
$830$	−13.0122			−0.0156773
$831$	−300.025			−0.361041
$832$			108.521i			0.130434i
$833$	1142.94			1.37207
$834$			468.880i			0.562206i
$835$	−48.7233			−0.0583513
$836$			747.370i			0.893984i
$837$		−	44.1830i		−	0.0527873i
$838$	272.972			0.325742
$839$		−	994.791i		−	1.18569i	−0.805318	−	0.592843i	$-0.798005\pi$
$839$		−	994.791i		−	1.18569i	0.805318	−	0.592843i	$-0.201995\pi$
$840$		−	37.4624i		−	0.0445980i
$841$	945.878			1.12471
$842$	436.406			0.518297
$843$	−117.444			−0.139317
$844$			498.305i			0.590409i
$845$	9.94310			0.0117670
$846$	−249.362			−0.294754
$847$	888.072			1.04849
$848$	−188.085			−0.221799
$849$		−	49.6735i		−	0.0585083i
$850$		−	470.844i		−	0.553935i
$851$	−1534.20			−1.80282
$852$	295.797			0.347179
$853$	283.892			0.332816			0.166408	−	0.986057i	$-0.446783\pi$
$853$	283.892			0.332816			0.166408	+	0.986057i	$0.446783\pi$
$854$	−158.716			−0.185850
$855$	−52.7760			−0.0617263
$856$			356.677i			0.416678i
$857$			213.800i			0.249475i	0.992190	+	0.124737i	$0.0398088\pi$
$857$			213.800i			0.249475i	−0.992190	+	0.124737i	$0.960191\pi$
$858$		−	467.454i		−	0.544818i
$859$		−	959.719i		−	1.11725i	−0.829420	−	0.558626i	$-0.811329\pi$
$859$		−	959.719i		−	1.11725i	0.829420	−	0.558626i	$-0.188671\pi$
$860$			54.2961i			0.0631351i
$861$	860.553			0.999481
$862$	295.683			0.343020
$863$			64.3712i			0.0745900i	0.999304	+	0.0372950i	$0.0118741\pi$
$863$			64.3712i			0.0745900i	−0.999304	+	0.0372950i	$0.988126\pi$
$864$			29.3939i			0.0340207i
$865$		−	184.115i		−	0.212850i
$866$		−	806.259i		−	0.931015i
$867$	−182.304			−0.210270
$868$		−	196.357i		−	0.226217i
$869$		−	1679.45i		−	1.93262i
$870$			68.5757i			0.0788227i
$871$	−1380.92			−1.58544
$872$	−583.207			−0.668815
$873$			329.865i			0.377852i
$874$	855.827			0.979208
$875$	−378.994			−0.433136
$876$		−	142.937i		−	0.163171i
$877$	−656.983			−0.749125			−0.374563	−	0.927202i	$-0.622207\pi$
$877$	−656.983			−0.749125			−0.374563	+	0.927202i	$0.622207\pi$
$878$			74.7541i			0.0851413i
$879$	−424.054			−0.482427
$880$			37.2688i			0.0423509i
$881$		−	700.120i		−	0.794688i	−0.917670	−	0.397344i	$-0.869932\pi$
$881$		−	700.120i		−	0.794688i	0.917670	−	0.397344i	$-0.130068\pi$
$882$			357.725i			0.405584i
$883$	790.761			0.895539			0.447770	−	0.894149i	$-0.352218\pi$
$883$	790.761			0.895539			0.447770	+	0.894149i	$0.352218\pi$
$884$			367.760i			0.416018i
$885$	−59.8629	+	31.5754i	−0.0676417	+	0.0356784i
$886$	405.296			0.457445
$887$			426.151i			0.480441i	0.970718	+	0.240221i	$0.0772198\pi$
$887$			426.151i			0.480441i	−0.970718	+	0.240221i	$0.922780\pi$
$888$	−329.901			−0.371510
$889$	−725.541			−0.816132
$890$	26.8952			0.0302194
$891$		−	126.614i		−	0.142103i
$892$	−428.676			−0.480579
$893$			1561.21i			1.74827i
$894$	334.574			0.374244
$895$		−	109.340i		−	0.122168i
$896$			130.631i			0.145794i
$897$	−535.290			−0.596755
$898$			9.92148i			0.0110484i
$899$			359.435i			0.399817i
$900$	147.368			0.163742
$901$	−637.389			−0.707424
$902$	−856.107			−0.949121
$903$		−	819.774i		−	0.907834i
$904$	262.668			0.290562
$905$	32.3020			0.0356928
$906$	−690.183			−0.761791
$907$	−104.375			−0.115077			−0.0575387	−	0.998343i	$-0.518325\pi$
$907$	−104.375			−0.115077			−0.0575387	+	0.998343i	$0.518325\pi$
$908$			682.929i			0.752125i
$909$		−	375.187i		−	0.412747i
$910$	146.700			0.161208
$911$	648.989			0.712392			0.356196	−	0.934411i	$-0.384074\pi$
$911$	648.989			0.712392			0.356196	+	0.934411i	$0.384074\pi$
$912$	184.030			0.201787
$913$	−195.445			−0.214069
$914$	1038.05			1.13572
$915$			11.1499i			0.0121857i
$916$		−	569.273i		−	0.621477i
$917$		−	1647.00i		−	1.79607i
$918$			99.6108i			0.108509i
$919$			721.317i			0.784893i	0.919775	+	0.392447i	$0.128371\pi$
$919$			721.317i			0.784893i	−0.919775	+	0.392447i	$0.871629\pi$
$920$	42.6772			0.0463883
$921$	168.794			0.183272
$922$			969.883i			1.05193i
$923$			1158.32i			1.25495i
$924$		−	562.692i		−	0.608974i
$925$			1653.98i			1.78809i
$926$	−74.8072			−0.0807853
$927$			98.9123i			0.106701i
$928$		−	239.124i		−	0.257676i
$929$		−	594.411i		−	0.639839i	−0.947445	−	0.319920i	$-0.896344\pi$
$929$		−	594.411i		−	0.639839i	0.947445	−	0.319920i	$-0.103656\pi$
$930$	−13.7942			−0.0148325
$931$	2239.65			2.40564
$932$			755.721i			0.810860i
$933$	−669.981			−0.718093
$934$	379.286			0.406088
$935$			126.298i			0.135078i
$936$	−115.104			−0.122974
$937$			1506.68i			1.60799i	0.594639	+	0.803993i	$0.297295\pi$
$937$			1506.68i			1.60799i	−0.594639	+	0.803993i	$0.702705\pi$
$938$	−1662.26			−1.77214
$939$			76.3508i			0.0813108i
$940$			77.8522i			0.0828215i
$941$			325.309i			0.345706i	0.984948	+	0.172853i	$0.0552985\pi$
$941$			325.309i			0.345706i	−0.984948	+	0.172853i	$0.944701\pi$
$942$	520.563			0.552615
$943$			980.344i			1.03960i
$944$	208.742	−	110.104i	0.221125	−	0.116635i
$945$	39.7348			0.0420474
$946$			815.540i			0.862092i
$947$	−1373.34			−1.45020			−0.725101	−	0.688643i	$-0.758207\pi$
$947$	−1373.34			−1.45020			−0.725101	+	0.688643i	$0.758207\pi$
$948$	−413.541			−0.436224
$949$	559.732			0.589812
$950$		−	922.646i		−	0.971207i
$951$	−665.749			−0.700051
$952$			442.687i			0.465007i
$953$	−1225.99			−1.28645			−0.643227	−	0.765676i	$-0.722405\pi$
$953$	−1225.99			−1.28645			−0.643227	+	0.765676i	$0.722405\pi$
$954$		−	199.495i		−	0.209114i
$955$			44.8772i			0.0469919i
$956$	−627.437			−0.656314
$957$			1030.02i			1.07630i
$958$			55.6923i			0.0581339i
$959$	16.4119			0.0171135
$960$	9.17694			0.00955931
$961$	888.699			0.924764
$962$		−	1291.87i		−	1.34290i
$963$	−378.313			−0.392848
$964$	−141.792			−0.147087
$965$	−1.08615			−0.00112554
$966$	−644.349			−0.667028
$967$		−	494.584i		−	0.511462i	−0.966748	−	0.255731i	$-0.917684\pi$
$967$		−	494.584i		−	0.511462i	0.966748	−	0.255731i	$-0.0823161\pi$
$968$			217.546i			0.224738i
$969$	623.646			0.643597
$970$	102.986			0.106171
$971$	−1226.03			−1.26265			−0.631323	−	0.775520i	$-0.717488\pi$
$971$	−1226.03			−1.26265			−0.631323	+	0.775520i	$0.717488\pi$
$972$	−31.1769			−0.0320750
$973$	−2210.18			−2.27151
$974$		−	458.955i		−	0.471206i
$975$			577.082i			0.591879i
$976$		−	38.8797i		−	0.0398358i
$977$			326.352i			0.334034i	0.985954	+	0.167017i	$0.0534135\pi$
$977$			326.352i			0.334034i	−0.985954	+	0.167017i	$0.946586\pi$
$978$		−	343.095i		−	0.350813i
$979$	403.972			0.412637
$980$	111.684			0.113963
$981$		−	618.584i		−	0.630565i
$982$			382.243i			0.389249i
$983$		−	1474.48i		−	1.49998i	−0.661446	−	0.749992i	$-0.730057\pi$
$983$		−	1474.48i		−	1.49998i	0.661446	−	0.749992i	$-0.269943\pi$
$984$			210.805i			0.214232i
$985$	−102.756			−0.104320
$986$		−	810.349i		−	0.821855i
$987$		−	1175.43i		−	1.19091i
$988$			720.646i			0.729399i
$989$	933.889			0.944276
$990$	−39.5296			−0.0399288
$991$		−	1286.17i		−	1.29785i	−0.760851	−	0.648926i	$-0.775218\pi$
$991$		−	1286.17i		−	1.29785i	0.760851	−	0.648926i	$-0.224782\pi$
$992$	48.1004			0.0484883
$993$	936.938			0.943543
$994$			1394.31i			1.40273i
$995$	−166.251			−0.167087
$996$			48.1258i			0.0483190i
$997$	−1105.38			−1.10870			−0.554351	−	0.832283i	$-0.687033\pi$
$997$	−1105.38			−1.10870			−0.554351	+	0.832283i	$0.687033\pi$
$998$			64.1582i			0.0642868i
$999$		−	349.913i		−	0.350263i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.18	yes	20
3.2	odd	2		1062.3.d.f.235.6		20
59.58	odd	2	inner	354.3.d.a.235.8	✓	20
177.176	even	2		1062.3.d.f.235.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.8	✓	20	59.58	odd	2	inner
354.3.d.a.235.18	yes	20	1.1	even	1	trivial
1062.3.d.f.235.6		20	3.2	odd	2
1062.3.d.f.235.16		20	177.176	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -0.662289 q^{5} +2.44949i q^{6} -11.5463 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -0.662289 q^{5} +2.44949i q^{6} -11.5463 q^{7} -2.82843i q^{8} +3.00000 q^{9} -0.936618i q^{10} -14.0682i q^{11} -3.46410 q^{12} -13.5651i q^{13} -16.3289i q^{14} -1.14712 q^{15} +4.00000 q^{16} +13.5553 q^{17} +4.24264i q^{18} +26.5624 q^{19} +1.32458 q^{20} -19.9987 q^{21} +19.8954 q^{22} -22.7826i q^{23} -4.89898i q^{24} -24.5614 q^{25} +19.1840 q^{26} +5.19615 q^{27} +23.0926 q^{28} -42.2715 q^{29} -1.62227i q^{30} -8.50302i q^{31} +5.65685i q^{32} -24.3668i q^{33} +19.1701i q^{34} +7.64697 q^{35} -6.00000 q^{36} -67.3408i q^{37} +37.5649i q^{38} -23.4955i q^{39} +1.87324i q^{40} -43.0303 q^{41} -28.2825i q^{42} +40.9913i q^{43} +28.1364i q^{44} -1.98687 q^{45} +32.2195 q^{46} +58.7751i q^{47} +6.92820 q^{48} +84.3166 q^{49} -34.7350i q^{50} +23.4785 q^{51} +27.1303i q^{52} -47.0214 q^{53} +7.34847i q^{54} +9.31721i q^{55} +32.6578i q^{56} +46.0075 q^{57} -59.7809i q^{58} +(52.1855 - 27.5259i) q^{59} +2.29424 q^{60} -9.71992i q^{61} +12.0251 q^{62} -34.6388 q^{63} -8.00000 q^{64} +8.98404i q^{65} +34.4599 q^{66} -101.799i q^{67} -27.1106 q^{68} -39.4607i q^{69} +10.8144i q^{70} -85.3891 q^{71} -8.48528i q^{72} +41.2625i q^{73} +95.2342 q^{74} -42.5415 q^{75} -53.1248 q^{76} +162.435i q^{77} +33.2277 q^{78} +119.379 q^{79} -2.64915 q^{80} +9.00000 q^{81} -60.8541i q^{82} -13.8927i q^{83} +39.9975 q^{84} -8.97753 q^{85} -57.9704 q^{86} -73.2163 q^{87} -39.7909 q^{88} +28.7153i q^{89} -2.80985i q^{90} +156.627i q^{91} +45.5652i q^{92} -14.7277i q^{93} -83.1206 q^{94} -17.5920 q^{95} +9.79796i q^{96} +109.955i q^{97} +119.242i q^{98} -42.2046i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9} - 24 q^{15} + 80 q^{16} + 72 q^{19} + 16 q^{22} + 140 q^{25} + 64 q^{26} - 16 q^{28} + 56 q^{29} - 80 q^{35} - 120 q^{36} - 8 q^{41} + 16 q^{46} + 52 q^{49} + 32 q^{53} - 48 q^{57} + 192 q^{59} + 48 q^{60} - 16 q^{62} + 24 q^{63} - 160 q^{64} + 96 q^{66} - 568 q^{71} - 288 q^{74} - 96 q^{75} - 144 q^{76} + 192 q^{78} + 528 q^{79} + 180 q^{81} + 568 q^{85} - 416 q^{86} - 216 q^{87} - 32 q^{88} - 480 q^{94} - 456 q^{95}+O(q^{100}) \) 20 * q - 40 * q^4 + 8 * q^7 + 60 * q^9 - 24 * q^15 + 80 * q^16 + 72 * q^19 + 16 * q^22 + 140 * q^25 + 64 * q^26 - 16 * q^28 + 56 * q^29 - 80 * q^35 - 120 * q^36 - 8 * q^41 + 16 * q^46 + 52 * q^49 + 32 * q^53 - 48 * q^57 + 192 * q^59 + 48 * q^60 - 16 * q^62 + 24 * q^63 - 160 * q^64 + 96 * q^66 - 568 * q^71 - 288 * q^74 - 96 * q^75 - 144 * q^76 + 192 * q^78 + 528 * q^79 + 180 * q^81 + 568 * q^85 - 416 * q^86 - 216 * q^87 - 32 * q^88 - 480 * q^94 - 456 * q^95

Introduction

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