LMFDB - Embedded newform 354.3.d.a.235.16

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			235.16
Root			$-8.79591 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -8.79591 q^{5} +2.44949i q^{6} +6.82395 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -8.79591 q^{5} +2.44949i q^{6} +6.82395 q^{7} -2.82843i q^{8} +3.00000 q^{9} -12.4393i q^{10} -12.5045i q^{11} -3.46410 q^{12} -10.7852i q^{13} +9.65053i q^{14} -15.2350 q^{15} +4.00000 q^{16} -16.2358 q^{17} +4.24264i q^{18} +12.1286 q^{19} +17.5918 q^{20} +11.8194 q^{21} +17.6840 q^{22} -20.1807i q^{23} -4.89898i q^{24} +52.3681 q^{25} +15.2526 q^{26} +5.19615 q^{27} -13.6479 q^{28} +47.7216 q^{29} -21.5455i q^{30} -48.4812i q^{31} +5.65685i q^{32} -21.6584i q^{33} -22.9609i q^{34} -60.0229 q^{35} -6.00000 q^{36} +59.1761i q^{37} +17.1525i q^{38} -18.6805i q^{39} +24.8786i q^{40} -11.8824 q^{41} +16.7152i q^{42} -42.8539i q^{43} +25.0090i q^{44} -26.3877 q^{45} +28.5398 q^{46} -83.4628i q^{47} +6.92820 q^{48} -2.43364 q^{49} +74.0596i q^{50} -28.1212 q^{51} +21.5704i q^{52} -67.9676 q^{53} +7.34847i q^{54} +109.988i q^{55} -19.3011i q^{56} +21.0074 q^{57} +67.4885i q^{58} +(35.7260 - 46.9537i) q^{59} +30.4699 q^{60} -1.03956i q^{61} +68.5628 q^{62} +20.4719 q^{63} -8.00000 q^{64} +94.8656i q^{65} +30.6296 q^{66} +77.6236i q^{67} +32.4716 q^{68} -34.9539i q^{69} -84.8852i q^{70} -78.3585 q^{71} -8.48528i q^{72} -52.1492i q^{73} -83.6877 q^{74} +90.7041 q^{75} -24.2572 q^{76} -85.3300i q^{77} +26.4182 q^{78} -82.7400 q^{79} -35.1836 q^{80} +9.00000 q^{81} -16.8043i q^{82} +5.82457i q^{83} -23.6389 q^{84} +142.809 q^{85} +60.6046 q^{86} +82.6562 q^{87} -35.3680 q^{88} +123.453i q^{89} -37.3179i q^{90} -73.5977i q^{91} +40.3613i q^{92} -83.9720i q^{93} +118.034 q^{94} -106.682 q^{95} +9.79796i q^{96} -61.9735i q^{97} -3.44169i q^{98} -37.5134i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−8.79591			−1.75918			−0.879591	−	0.475730i	$-0.842184\pi$
$5$	−8.79591			−1.75918			−0.879591	+	0.475730i	$0.842184\pi$
$6$			2.44949i			0.408248i
$7$	6.82395			0.974851			0.487425	−	0.873165i	$-0.337936\pi$
$7$	6.82395			0.974851			0.487425	+	0.873165i	$0.337936\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$		−	12.4393i		−	1.24393i
$11$		−	12.5045i		−	1.13677i	−0.822762	−	0.568385i	$-0.807568\pi$
$11$		−	12.5045i		−	1.13677i	0.822762	−	0.568385i	$-0.192432\pi$
$12$	−3.46410			−0.288675
$13$		−	10.7852i		−	0.829630i	−0.909906	−	0.414815i	$-0.863846\pi$
$13$		−	10.7852i		−	0.829630i	0.909906	−	0.414815i	$-0.136154\pi$
$14$			9.65053i			0.689324i
$15$	−15.2350			−1.01566
$16$	4.00000			0.250000
$17$	−16.2358			−0.955047			−0.477523	−	0.878619i	$-0.658465\pi$
$17$	−16.2358			−0.955047			−0.477523	+	0.878619i	$0.658465\pi$
$18$			4.24264i			0.235702i
$19$	12.1286			0.638348			0.319174	−	0.947696i	$-0.396594\pi$
$19$	12.1286			0.638348			0.319174	+	0.947696i	$0.396594\pi$
$20$	17.5918			0.879591
$21$	11.8194			0.562830
$22$	17.6840			0.803818
$23$		−	20.1807i		−	0.877420i	−0.898629	−	0.438710i	$-0.855436\pi$
$23$		−	20.1807i		−	0.877420i	0.898629	−	0.438710i	$-0.144564\pi$
$24$		−	4.89898i		−	0.204124i
$25$	52.3681			2.09472
$26$	15.2526			0.586637
$27$	5.19615			0.192450
$28$	−13.6479			−0.487425
$29$	47.7216			1.64557			0.822786	−	0.568352i	$-0.192419\pi$
$29$	47.7216			1.64557			0.822786	+	0.568352i	$0.192419\pi$
$30$		−	21.5455i		−	0.718183i
$31$		−	48.4812i		−	1.56391i	−0.623334	−	0.781956i	$-0.714222\pi$
$31$		−	48.4812i		−	1.56391i	0.623334	−	0.781956i	$-0.285778\pi$
$32$			5.65685i			0.176777i
$33$		−	21.6584i		−	0.656315i
$34$		−	22.9609i		−	0.675320i
$35$	−60.0229			−1.71494
$36$	−6.00000			−0.166667
$37$			59.1761i			1.59935i	0.600430	+	0.799677i	$0.294996\pi$
$37$			59.1761i			1.59935i	−0.600430	+	0.799677i	$0.705004\pi$
$38$			17.1525i			0.451381i
$39$		−	18.6805i		−	0.478987i
$40$			24.8786i			0.621965i
$41$	−11.8824			−0.289815			−0.144907	−	0.989445i	$-0.546288\pi$
$41$	−11.8824			−0.289815			−0.144907	+	0.989445i	$0.546288\pi$
$42$			16.7152i			0.397981i
$43$		−	42.8539i		−	0.996602i	−0.867004	−	0.498301i	$-0.833957\pi$
$43$		−	42.8539i		−	0.996602i	0.867004	−	0.498301i	$-0.166043\pi$
$44$			25.0090i			0.568385i
$45$	−26.3877			−0.586394
$46$	28.5398			0.620430
$47$		−	83.4628i		−	1.77580i	−0.460033	−	0.887902i	$-0.652162\pi$
$47$		−	83.4628i		−	1.77580i	0.460033	−	0.887902i	$-0.347838\pi$
$48$	6.92820			0.144338
$49$	−2.43364			−0.0496662
$50$			74.0596i			1.48119i
$51$	−28.1212			−0.551397
$52$			21.5704i			0.414815i
$53$	−67.9676			−1.28241			−0.641204	−	0.767371i	$-0.721565\pi$
$53$	−67.9676			−1.28241			−0.641204	+	0.767371i	$0.721565\pi$
$54$			7.34847i			0.136083i
$55$			109.988i			1.99979i
$56$		−	19.3011i		−	0.344662i
$57$	21.0074			0.368551
$58$			67.4885i			1.16359i
$59$	35.7260	−	46.9537i	0.605526	−	0.795826i
$59$	35.7260	−	46.9537i	0.605526	−	0.795826i
$60$	30.4699			0.507832
$61$		−	1.03956i		−	0.0170420i	−0.999964	−	0.00852098i	$-0.997288\pi$
$61$		−	1.03956i		−	0.0170420i	0.999964	−	0.00852098i	$-0.00271235\pi$
$62$	68.5628			1.10585
$63$	20.4719			0.324950
$64$	−8.00000			−0.125000
$65$			94.8656i			1.45947i
$66$	30.6296			0.464085
$67$			77.6236i			1.15856i	0.815128	+	0.579280i	$0.196666\pi$
$67$			77.6236i			1.15856i	−0.815128	+	0.579280i	$0.803334\pi$
$68$	32.4716			0.477523
$69$		−	34.9539i		−	0.506579i
$70$		−	84.8852i		−	1.21265i
$71$	−78.3585			−1.10364			−0.551820	−	0.833963i	$-0.686067\pi$
$71$	−78.3585			−1.10364			−0.551820	+	0.833963i	$0.686067\pi$
$72$		−	8.48528i		−	0.117851i
$73$		−	52.1492i		−	0.714372i	−0.934033	−	0.357186i	$-0.883736\pi$
$73$		−	52.1492i		−	0.714372i	0.934033	−	0.357186i	$-0.116264\pi$
$74$	−83.6877			−1.13091
$75$	90.7041			1.20939
$76$	−24.2572			−0.319174
$77$		−	85.3300i		−	1.10818i
$78$	26.4182			0.338695
$79$	−82.7400			−1.04734			−0.523671	−	0.851921i	$-0.675438\pi$
$79$	−82.7400			−1.04734			−0.523671	+	0.851921i	$0.675438\pi$
$80$	−35.1836			−0.439796
$81$	9.00000			0.111111
$82$		−	16.8043i		−	0.204930i
$83$			5.82457i			0.0701756i	0.999384	+	0.0350878i	$0.0111711\pi$
$83$			5.82457i			0.0701756i	−0.999384	+	0.0350878i	$0.988829\pi$
$84$	−23.6389			−0.281415
$85$	142.809			1.68010
$86$	60.6046			0.704704
$87$	82.6562			0.950071
$88$	−35.3680			−0.401909
$89$			123.453i			1.38711i	0.720402	+	0.693557i	$0.243957\pi$
$89$			123.453i			1.38711i	−0.720402	+	0.693557i	$0.756043\pi$
$90$		−	37.3179i		−	0.414643i
$91$		−	73.5977i		−	0.808766i
$92$			40.3613i			0.438710i
$93$		−	83.9720i		−	0.902924i
$94$	118.034			1.25568
$95$	−106.682			−1.12297
$96$			9.79796i			0.102062i
$97$		−	61.9735i		−	0.638902i	−0.947603	−	0.319451i	$-0.896501\pi$
$97$		−	61.9735i		−	0.638902i	0.947603	−	0.319451i	$-0.103499\pi$
$98$		−	3.44169i		−	0.0351193i
$99$		−	37.5134i		−	0.378924i
$100$	−104.736			−1.04736
$101$			69.2834i			0.685974i	0.939340	+	0.342987i	$0.111439\pi$
$101$			69.2834i			0.685974i	−0.939340	+	0.342987i	$0.888561\pi$
$102$		−	39.7694i		−	0.389896i
$103$		−	62.0626i		−	0.602549i	−0.953537	−	0.301275i	$-0.902588\pi$
$103$		−	62.0626i		−	0.602549i	0.953537	−	0.301275i	$-0.0974121\pi$
$104$	−30.5051			−0.293319
$105$	−103.963			−0.990121
$106$		−	96.1207i		−	0.906799i
$107$	60.8234			0.568443			0.284222	−	0.958759i	$-0.408265\pi$
$107$	60.8234			0.568443			0.284222	+	0.958759i	$0.408265\pi$
$108$	−10.3923			−0.0962250
$109$		−	13.6463i		−	0.125195i	−0.998039	−	0.0625977i	$-0.980061\pi$
$109$		−	13.6463i		−	0.125195i	0.998039	−	0.0625977i	$-0.0199385\pi$
$110$	−155.547			−1.41406
$111$			102.496i			0.923388i
$112$	27.2958			0.243713
$113$			163.841i			1.44992i	0.688788	+	0.724962i	$0.258143\pi$
$113$			163.841i			1.44992i	−0.688788	+	0.724962i	$0.741857\pi$
$114$			29.7089i			0.260605i
$115$			177.507i			1.54354i
$116$	−95.4431			−0.822786
$117$		−	32.3556i		−	0.276543i
$118$	66.4026	+	50.5242i	0.562734	+	0.428171i
$119$	−110.792			−0.931028
$120$			43.0910i			0.359092i
$121$	−35.3620			−0.292248
$122$	1.47016			0.0120505
$123$	−20.5809			−0.167325
$124$			96.9625i			0.781956i
$125$	−240.727			−1.92582
$126$			28.9516i			0.229775i
$127$	−105.637			−0.831784			−0.415892	−	0.909414i	$-0.636531\pi$
$127$	−105.637			−0.831784			−0.415892	+	0.909414i	$0.636531\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	74.2251i		−	0.575389i
$130$	−134.160			−1.03200
$131$			115.230i			0.879618i	0.898091	+	0.439809i	$0.144954\pi$
$131$			115.230i			0.879618i	−0.898091	+	0.439809i	$0.855046\pi$
$132$			43.3168i			0.328157i
$133$	82.7652			0.622294
$134$	−109.776			−0.819226
$135$	−45.7049			−0.338555
$136$			45.9218i			0.337660i
$137$	−13.4796			−0.0983915			−0.0491958	−	0.998789i	$-0.515666\pi$
$137$	−13.4796			−0.0983915			−0.0491958	+	0.998789i	$0.515666\pi$
$138$	49.4323			0.358205
$139$	142.673			1.02642			0.513211	−	0.858263i	$-0.328456\pi$
$139$	142.673			1.02642			0.513211	+	0.858263i	$0.328456\pi$
$140$	120.046			0.857470
$141$		−	144.562i		−	1.02526i
$142$		−	110.816i		−	0.780392i
$143$	−134.863			−0.943100
$144$	12.0000			0.0833333
$145$	−419.755			−2.89486
$146$	73.7501			0.505137
$147$	−4.21519			−0.0286748
$148$		−	118.352i		−	0.799677i
$149$			70.0275i			0.469983i	0.971997	+	0.234992i	$0.0755063\pi$
$149$			70.0275i			0.469983i	−0.971997	+	0.234992i	$0.924494\pi$
$150$			128.275i			0.855167i
$151$		−	101.346i		−	0.671168i	−0.942010	−	0.335584i	$-0.891066\pi$
$151$		−	101.346i		−	0.671168i	0.942010	−	0.335584i	$-0.108934\pi$
$152$		−	34.3049i		−	0.225690i
$153$	−48.7074			−0.318349
$154$	120.675			0.783603
$155$			426.437i			2.75120i
$156$			37.3610i			0.239494i
$157$		−	200.517i		−	1.27718i	−0.769547	−	0.638590i	$-0.779518\pi$
$157$		−	200.517i		−	1.27718i	0.769547	−	0.638590i	$-0.220482\pi$
$158$		−	117.012i		−	0.740583i
$159$	−117.723			−0.740398
$160$		−	49.7572i		−	0.310982i
$161$		−	137.712i		−	0.855354i
$162$			12.7279i			0.0785674i
$163$	266.681			1.63608			0.818040	−	0.575161i	$-0.195061\pi$
$163$	266.681			1.63608			0.818040	+	0.575161i	$0.195061\pi$
$164$	23.7648			0.144907
$165$			190.505i			1.15458i
$166$	−8.23719			−0.0496216
$167$	159.778			0.956753			0.478377	−	0.878155i	$-0.341225\pi$
$167$	159.778			0.956753			0.478377	+	0.878155i	$0.341225\pi$
$168$		−	33.4304i		−	0.198991i
$169$	52.6796			0.311714
$170$			201.962i			1.18801i
$171$	36.3859			0.212783
$172$			85.7078i			0.498301i
$173$		−	224.389i		−	1.29705i	−0.761195	−	0.648523i	$-0.775387\pi$
$173$		−	224.389i		−	1.29705i	0.761195	−	0.648523i	$-0.224613\pi$
$174$			116.893i			0.671802i
$175$	357.357			2.04204
$176$		−	50.0179i		−	0.284193i
$177$	61.8793	−	81.3262i	0.349600	−	0.459470i
$178$	−174.589			−0.980837
$179$			153.878i			0.859653i	0.902911	+	0.429827i	$0.141425\pi$
$179$			153.878i			0.859653i	−0.902911	+	0.429827i	$0.858575\pi$
$180$	52.7755			0.293197
$181$	−78.4933			−0.433664			−0.216832	−	0.976209i	$-0.569572\pi$
$181$	−78.4933			−0.433664			−0.216832	+	0.976209i	$0.569572\pi$
$182$	104.083			0.571884
$183$		−	1.80057i		−	0.00983918i
$184$	−57.0795			−0.310215
$185$		−	520.508i		−	2.81356i
$186$	118.754			0.638464
$187$			203.020i			1.08567i
$188$			166.926i			0.887902i
$189$	35.4583			0.187610
$190$		−	150.872i		−	0.794061i
$191$		−	308.445i		−	1.61490i	−0.589938	−	0.807449i	$-0.700848\pi$
$191$		−	308.445i		−	1.61490i	0.589938	−	0.807449i	$-0.299152\pi$
$192$	−13.8564			−0.0721688
$193$	−319.363			−1.65473			−0.827366	−	0.561664i	$-0.810162\pi$
$193$	−319.363			−1.65473			−0.827366	+	0.561664i	$0.810162\pi$
$194$	87.6438			0.451772
$195$			164.312i			0.842626i
$196$	4.86729			0.0248331
$197$	265.224			1.34631			0.673156	−	0.739500i	$-0.264938\pi$
$197$	265.224			1.34631			0.673156	+	0.739500i	$0.264938\pi$
$198$	53.0520			0.267939
$199$	136.838			0.687626			0.343813	−	0.939038i	$-0.388281\pi$
$199$	136.838			0.687626			0.343813	+	0.939038i	$0.388281\pi$
$200$		−	148.119i		−	0.740596i
$201$			134.448i			0.668895i
$202$	−97.9815			−0.485057
$203$	325.650			1.60419
$204$	56.2424			0.275698
$205$	104.517			0.509837
$206$	87.7697			0.426067
$207$		−	60.5420i		−	0.292473i
$208$		−	43.1408i		−	0.207408i
$209$		−	151.662i		−	0.725656i
$210$		−	147.025i		−	0.700121i
$211$			23.2317i			0.110103i	0.998484	+	0.0550515i	$0.0175323\pi$
$211$			23.2317i			0.110103i	−0.998484	+	0.0550515i	$0.982468\pi$
$212$	135.935			0.641204
$213$	−135.721			−0.637187
$214$			86.0173i			0.401950i
$215$			376.939i			1.75321i
$216$		−	14.6969i		−	0.0680414i
$217$		−	330.834i		−	1.52458i
$218$	19.2988			0.0885265
$219$		−	90.3250i		−	0.412443i
$220$		−	219.977i		−	0.999894i
$221$			175.106i			0.792336i
$222$	−144.951			−0.652934
$223$	323.720			1.45166			0.725829	−	0.687875i	$-0.241456\pi$
$223$	323.720			1.45166			0.725829	+	0.687875i	$0.241456\pi$
$224$			38.6021i			0.172331i
$225$	157.104			0.698241
$226$	−231.707			−1.02525
$227$		−	355.671i		−	1.56683i	−0.621497	−	0.783417i	$-0.713475\pi$
$227$		−	355.671i		−	1.56683i	0.621497	−	0.783417i	$-0.286525\pi$
$228$	−42.0148			−0.184275
$229$			356.754i			1.55788i	0.627101	+	0.778938i	$0.284241\pi$
$229$			356.754i			1.55788i	−0.627101	+	0.778938i	$0.715759\pi$
$230$	−251.033			−1.09145
$231$		−	147.796i		−	0.639809i
$232$		−	134.977i		−	0.581797i
$233$			329.651i			1.41481i	0.706807	+	0.707406i	$0.250135\pi$
$233$			329.651i			1.41481i	−0.706807	+	0.707406i	$0.749865\pi$
$234$	45.7577			0.195546
$235$			734.131i			3.12396i
$236$	−71.4520	+	93.9075i	−0.302763	+	0.397913i
$237$	−143.310			−0.604683
$238$		−	156.684i		−	0.658336i
$239$	38.0585			0.159241			0.0796204	−	0.996825i	$-0.474629\pi$
$239$	38.0585			0.159241			0.0796204	+	0.996825i	$0.474629\pi$
$240$	−60.9399			−0.253916
$241$	−29.6107			−0.122866			−0.0614330	−	0.998111i	$-0.519567\pi$
$241$	−29.6107			−0.122866			−0.0614330	+	0.998111i	$0.519567\pi$
$242$		−	50.0094i		−	0.206651i
$243$	15.5885			0.0641500
$244$			2.07912i			0.00852098i
$245$	21.4061			0.0873719
$246$		−	29.1058i		−	0.118316i
$247$		−	130.810i		−	0.529593i
$248$	−137.126			−0.552926
$249$			10.0885i			0.0405159i
$250$		−	340.439i		−	1.36176i
$251$	384.372			1.53136			0.765682	−	0.643219i	$-0.222402\pi$
$251$	384.372			1.53136			0.765682	+	0.643219i	$0.222402\pi$
$252$	−40.9437			−0.162475
$253$	−252.349			−0.997426
$254$		−	149.393i		−	0.588160i
$255$	247.352			0.970007
$256$	16.0000			0.0625000
$257$	193.398			0.752522			0.376261	−	0.926514i	$-0.377210\pi$
$257$	193.398			0.752522			0.376261	+	0.926514i	$0.377210\pi$
$258$	104.970			0.406861
$259$			403.815i			1.55913i
$260$		−	189.731i		−	0.729735i
$261$	143.165			0.548524
$262$	−162.960			−0.621984
$263$	−100.681			−0.382816			−0.191408	−	0.981511i	$-0.561305\pi$
$263$	−100.681			−0.382816			−0.191408	+	0.981511i	$0.561305\pi$
$264$	−61.2592			−0.232042
$265$	597.837			2.25599
$266$			117.048i			0.440029i
$267$			213.827i			0.800850i
$268$		−	155.247i		−	0.579280i
$269$			91.4655i			0.340021i	0.985442	+	0.170010i	$0.0543801\pi$
$269$			91.4655i			0.340021i	−0.985442	+	0.170010i	$0.945620\pi$
$270$		−	64.6365i		−	0.239394i
$271$	−104.003			−0.383774			−0.191887	−	0.981417i	$-0.561461\pi$
$271$	−104.003			−0.383774			−0.191887	+	0.981417i	$0.561461\pi$
$272$	−64.9432			−0.238762
$273$		−	127.475i		−	0.466941i
$274$		−	19.0631i		−	0.0695733i
$275$		−	654.835i		−	2.38122i
$276$			69.9079i			0.253289i
$277$	−174.421			−0.629678			−0.314839	−	0.949145i	$-0.601951\pi$
$277$	−174.421			−0.629678			−0.314839	+	0.949145i	$0.601951\pi$
$278$			201.770i			0.725790i
$279$		−	145.444i		−	0.521304i
$280$			169.770i			0.606323i
$281$	110.896			0.394647			0.197323	−	0.980338i	$-0.436775\pi$
$281$	110.896			0.394647			0.197323	+	0.980338i	$0.436775\pi$
$282$	204.441			0.724969
$283$			312.265i			1.10341i	0.834039	+	0.551706i	$0.186023\pi$
$283$			312.265i			1.10341i	−0.834039	+	0.551706i	$0.813977\pi$
$284$	156.717			0.551820
$285$	−184.779			−0.648348
$286$		−	190.725i		−	0.666872i
$287$	−81.0850			−0.282526
$288$			16.9706i			0.0589256i
$289$	−25.3989			−0.0878855
$290$		−	593.623i		−	2.04698i
$291$		−	107.341i		−	0.368870i
$292$			104.298i			0.357186i
$293$	285.595			0.974726			0.487363	−	0.873200i	$-0.337959\pi$
$293$	285.595			0.974726			0.487363	+	0.873200i	$0.337959\pi$
$294$		−	5.96118i		−	0.0202761i
$295$	−314.243	+	413.001i	−1.06523	+	1.40000i
$296$	167.375			0.565457
$297$		−	64.9752i		−	0.218772i
$298$	−99.0339			−0.332328
$299$	−217.652			−0.727934
$300$	−181.408			−0.604694
$301$		−	292.433i		−	0.971539i
$302$	143.325			0.474588
$303$			120.002i			0.396047i
$304$	48.5145			0.159587
$305$			9.14387i			0.0299799i
$306$		−	68.8827i		−	0.225107i
$307$	323.523			1.05382			0.526910	−	0.849921i	$-0.323351\pi$
$307$	323.523			1.05382			0.526910	+	0.849921i	$0.323351\pi$
$308$			170.660i			0.554091i
$309$		−	107.496i		−	0.347882i
$310$	−603.073			−1.94540
$311$	−161.881			−0.520517			−0.260259	−	0.965539i	$-0.583808\pi$
$311$	−161.881			−0.520517			−0.260259	+	0.965539i	$0.583808\pi$
$312$	−52.8364			−0.169348
$313$			367.526i			1.17420i	0.809513	+	0.587102i	$0.199731\pi$
$313$			367.526i			1.17420i	−0.809513	+	0.587102i	$0.800269\pi$
$314$	283.574			0.903102
$315$	−180.069			−0.571647
$316$	165.480			0.523671
$317$	56.5322			0.178335			0.0891675	−	0.996017i	$-0.471579\pi$
$317$	56.5322			0.178335			0.0891675	+	0.996017i	$0.471579\pi$
$318$		−	166.486i		−	0.523541i
$319$		−	596.733i		−	1.87064i
$320$	70.3673			0.219898
$321$	105.349			0.328191
$322$	194.754			0.604826
$323$	−196.918			−0.609653
$324$	−18.0000			−0.0555556
$325$		−	564.800i		−	1.73785i
$326$			377.144i			1.15688i
$327$		−	23.6361i		−	0.0722816i
$328$			33.6085i			0.102465i
$329$		−	569.546i		−	1.73114i
$330$	−269.415			−0.816410
$331$	196.297			0.593043			0.296521	−	0.955026i	$-0.404173\pi$
$331$	196.297			0.593043			0.296521	+	0.955026i	$0.404173\pi$
$332$		−	11.6491i		−	0.0350878i
$333$			177.528i			0.533118i
$334$			225.960i			0.676527i
$335$		−	682.770i		−	2.03812i
$336$	47.2777			0.140708
$337$		−	242.771i		−	0.720390i	−0.932877	−	0.360195i	$-0.882710\pi$
$337$		−	242.771i		−	0.720390i	0.932877	−	0.360195i	$-0.117290\pi$
$338$			74.5002i			0.220415i
$339$			283.782i			0.837114i
$340$	−285.617			−0.840051
$341$	−606.233			−1.77781
$342$			51.4574i			0.150460i
$343$	−350.981			−1.02327
$344$	−121.209			−0.352352
$345$			307.452i			0.891164i
$346$	317.334			0.917150
$347$			488.413i			1.40753i	0.710433	+	0.703765i	$0.248499\pi$
$347$			488.413i			1.40753i	−0.710433	+	0.703765i	$0.751501\pi$
$348$	−165.312			−0.475036
$349$		−	174.367i		−	0.499619i	−0.968295	−	0.249810i	$-0.919632\pi$
$349$		−	174.367i		−	0.499619i	0.968295	−	0.249810i	$-0.0803680\pi$
$350$			505.379i			1.44394i
$351$		−	56.0415i		−	0.159662i
$352$	70.7360			0.200955
$353$			233.386i			0.661151i	0.943779	+	0.330576i	$0.107243\pi$
$353$			233.386i			0.661151i	−0.943779	+	0.330576i	$0.892757\pi$
$354$	115.013	+	87.5105i	0.324895	+	0.247205i
$355$	689.234			1.94150
$356$		−	246.906i		−	0.693557i
$357$	−191.898			−0.537529
$358$	−217.616			−0.607867
$359$	−36.1082			−0.100580			−0.0502900	−	0.998735i	$-0.516015\pi$
$359$	−36.1082			−0.100580			−0.0502900	+	0.998735i	$0.516015\pi$
$360$			74.6358i			0.207322i
$361$	−213.897			−0.592511
$362$		−	111.006i		−	0.306647i
$363$	−61.2488			−0.168729
$364$			147.195i			0.404383i
$365$			458.699i			1.25671i
$366$	2.54639			0.00695735
$367$			218.491i			0.595343i	0.954668	+	0.297672i	$0.0962100\pi$
$367$			218.491i			0.595343i	−0.954668	+	0.297672i	$0.903790\pi$
$368$		−	80.7227i		−	0.219355i
$369$	−35.6472			−0.0966050
$370$	736.109			1.98948
$371$	−463.808			−1.25016
$372$			167.944i			0.451462i
$373$	−571.861			−1.53314			−0.766570	−	0.642161i	$-0.778038\pi$
$373$	−571.861			−1.53314			−0.766570	+	0.642161i	$0.778038\pi$
$374$	−287.114			−0.767684
$375$	−416.951			−1.11187
$376$	−236.068			−0.627841
$377$		−	514.686i		−	1.36522i
$378$			50.1456i			0.132660i
$379$	35.9912			0.0949636			0.0474818	−	0.998872i	$-0.484880\pi$
$379$	35.9912			0.0949636			0.0474818	+	0.998872i	$0.484880\pi$
$380$	213.365			0.561486
$381$	−182.968			−0.480231
$382$	436.208			1.14190
$383$	−621.047			−1.62153			−0.810766	−	0.585370i	$-0.800949\pi$
$383$	−621.047			−1.62153			−0.810766	+	0.585370i	$0.800949\pi$
$384$		−	19.5959i		−	0.0510310i
$385$			750.555i			1.94949i
$386$		−	451.648i		−	1.17007i
$387$		−	128.562i		−	0.332201i
$388$			123.947i			0.319451i
$389$	599.598			1.54138			0.770692	−	0.637208i	$-0.219911\pi$
$389$	599.598			1.54138			0.770692	+	0.637208i	$0.219911\pi$
$390$	−232.372			−0.595827
$391$			327.649i			0.837977i
$392$			6.88338i			0.0175596i
$393$			199.584i			0.507848i
$394$			375.083i			0.951987i
$395$	727.774			1.84247
$396$			75.0269i			0.189462i
$397$		−	448.731i		−	1.13030i	−0.824987	−	0.565152i	$-0.808817\pi$
$397$		−	448.731i		−	1.13030i	0.824987	−	0.565152i	$-0.191183\pi$
$398$			193.518i			0.486225i
$399$	143.353			0.359282
$400$	209.472			0.523681
$401$		−	242.158i		−	0.603885i	−0.953326	−	0.301943i	$-0.902365\pi$
$401$		−	242.158i		−	0.603885i	0.953326	−	0.301943i	$-0.0976351\pi$
$402$	−190.138			−0.472980
$403$	−522.880			−1.29747
$404$		−	138.567i		−	0.342987i
$405$	−79.1632			−0.195465
$406$			460.538i			1.13433i
$407$	739.966			1.81810
$408$			79.5388i			0.194948i
$409$			144.111i			0.352350i	0.984359	+	0.176175i	$0.0563724\pi$
$409$			144.111i			0.352350i	−0.984359	+	0.176175i	$0.943628\pi$
$410$			147.809i			0.360509i
$411$	−23.3474			−0.0568064
$412$			124.125i			0.301275i
$413$	243.793	−	320.410i	0.590297	−	0.775811i
$414$	85.6193			0.206810
$415$		−	51.2324i		−	0.123452i
$416$	61.0103			0.146659
$417$	247.116			0.592605
$418$	214.483			0.513116
$419$			53.4061i			0.127461i	0.997967	+	0.0637304i	$0.0202998\pi$
$419$			53.4061i			0.127461i	−0.997967	+	0.0637304i	$0.979700\pi$
$420$	207.925			0.495061
$421$			287.533i			0.682977i	0.939886	+	0.341488i	$0.110931\pi$
$421$			287.533i			0.682977i	−0.939886	+	0.341488i	$0.889069\pi$
$422$	−32.8546			−0.0778546
$423$		−	250.388i		−	0.591935i
$424$			192.241i			0.453399i
$425$	−850.237			−2.00056
$426$		−	191.938i		−	0.450559i
$427$		−	7.09391i		−	0.0166134i
$428$	−121.647			−0.284222
$429$	−233.590			−0.544499
$430$	−533.072			−1.23970
$431$			436.097i			1.01182i	0.862585	+	0.505912i	$0.168844\pi$
$431$			436.097i			1.01182i	−0.862585	+	0.505912i	$0.831156\pi$
$432$	20.7846			0.0481125
$433$	139.256			0.321608			0.160804	−	0.986986i	$-0.448591\pi$
$433$	139.256			0.321608			0.160804	+	0.986986i	$0.448591\pi$
$434$	467.870			1.07804
$435$	−727.036			−1.67135
$436$			27.2926i			0.0625977i
$437$		−	244.764i		−	0.560100i
$438$	127.739			0.291641
$439$	−347.407			−0.791360			−0.395680	−	0.918388i	$-0.629491\pi$
$439$	−347.407			−0.791360			−0.395680	+	0.918388i	$0.629491\pi$
$440$	311.094			0.707032
$441$	−7.30093			−0.0165554
$442$	−247.638			−0.560266
$443$		−	123.421i		−	0.278602i	−0.990250	−	0.139301i	$-0.955514\pi$
$443$		−	123.421i		−	0.278602i	0.990250	−	0.139301i	$-0.0444856\pi$
$444$		−	204.992i		−	0.461694i
$445$		−	1085.88i		−	2.44018i
$446$			457.809i			1.02648i
$447$			121.291i			0.271345i
$448$	−54.5916			−0.121856
$449$	600.978			1.33848			0.669240	−	0.743046i	$-0.266620\pi$
$449$	600.978			1.33848			0.669240	+	0.743046i	$0.266620\pi$
$450$			222.179i			0.493731i
$451$			148.583i			0.329453i
$452$		−	327.683i		−	0.724962i
$453$		−	175.537i		−	0.387499i
$454$	502.995			1.10792
$455$			647.359i			1.42277i
$456$		−	59.4179i		−	0.130302i
$457$			866.610i			1.89630i	0.317821	+	0.948151i	$0.397049\pi$
$457$			866.610i			1.89630i	−0.317821	+	0.948151i	$0.602951\pi$
$458$	−504.526			−1.10158
$459$	−84.3637			−0.183799
$460$		−	355.015i		−	0.771771i
$461$	−364.465			−0.790597			−0.395299	−	0.918553i	$-0.629359\pi$
$461$	−364.465			−0.790597			−0.395299	+	0.918553i	$0.629359\pi$
$462$	209.015			0.452413
$463$		−	259.618i		−	0.560731i	−0.959893	−	0.280365i	$-0.909544\pi$
$463$		−	259.618i		−	0.560731i	0.959893	−	0.280365i	$-0.0904556\pi$
$464$	190.886			0.411393
$465$			738.610i			1.58841i
$466$	−466.198			−1.00042
$467$		−	463.287i		−	0.992049i	−0.868309	−	0.496025i	$-0.834793\pi$
$467$		−	463.287i		−	0.992049i	0.868309	−	0.496025i	$-0.165207\pi$
$468$			64.7112i			0.138272i
$469$			529.700i			1.12942i
$470$	−1038.22			−2.20898
$471$		−	347.306i		−	0.737380i
$472$	−132.805	−	101.048i	−0.281367	−	0.214086i
$473$	−535.866			−1.13291
$474$		−	202.671i		−	0.427576i
$475$	635.152			1.33716
$476$	221.585			0.465514
$477$	−203.903			−0.427469
$478$			53.8229i			0.112600i
$479$	532.837			1.11240			0.556198	−	0.831050i	$-0.312260\pi$
$479$	532.837			1.11240			0.556198	+	0.831050i	$0.312260\pi$
$480$		−	86.1820i		−	0.179546i
$481$	638.226			1.32687
$482$		−	41.8759i		−	0.0868794i
$483$		−	238.524i		−	0.493839i
$484$	70.7240			0.146124
$485$			545.114i			1.12395i
$486$			22.0454i			0.0453609i
$487$	91.1420			0.187150			0.0935749	−	0.995612i	$-0.470171\pi$
$487$	91.1420			0.187150			0.0935749	+	0.995612i	$0.470171\pi$
$488$	−2.94032			−0.00602524
$489$	461.905			0.944591
$490$			30.2728i			0.0617812i
$491$	269.260			0.548391			0.274195	−	0.961674i	$-0.411589\pi$
$491$	269.260			0.548391			0.274195	+	0.961674i	$0.411589\pi$
$492$	41.1619			0.0836623
$493$	−774.798			−1.57160
$494$	184.993			0.374479
$495$			329.965i			0.666596i
$496$		−	193.925i		−	0.390978i
$497$	−534.715			−1.07588
$498$	−14.2672			−0.0286491
$499$	−136.296			−0.273138			−0.136569	−	0.990631i	$-0.543608\pi$
$499$	−136.296			−0.273138			−0.136569	+	0.990631i	$0.543608\pi$
$500$	481.454			0.962908
$501$	276.743			0.552382
$502$			543.585i			1.08284i
$503$		−	631.840i		−	1.25614i	−0.778155	−	0.628072i	$-0.783844\pi$
$503$		−	631.840i		−	1.25614i	0.778155	−	0.628072i	$-0.216156\pi$
$504$		−	57.9032i		−	0.114887i
$505$		−	609.410i		−	1.20675i
$506$		−	356.875i		−	0.705286i
$507$	91.2437			0.179968
$508$	211.273			0.415892
$509$			664.787i			1.30606i	0.757330	+	0.653032i	$0.226504\pi$
$509$			664.787i			1.30606i	−0.757330	+	0.653032i	$0.773496\pi$
$510$			349.808i			0.685899i
$511$		−	355.864i		−	0.696406i
$512$			22.6274i			0.0441942i
$513$	63.0222			0.122850
$514$			273.506i			0.532113i
$515$			545.897i			1.05999i
$516$			148.450i			0.287694i
$517$	−1043.66			−2.01868
$518$	−571.081			−1.10247
$519$		−	388.653i		−	0.748850i
$520$	268.320			0.516001
$521$	824.550			1.58263			0.791315	−	0.611408i	$-0.209397\pi$
$521$	824.550			1.58263			0.791315	+	0.611408i	$0.209397\pi$
$522$			202.465i			0.387865i
$523$	−545.495			−1.04301			−0.521505	−	0.853248i	$-0.674629\pi$
$523$	−545.495			−1.04301			−0.521505	+	0.853248i	$0.674629\pi$
$524$		−	230.460i		−	0.439809i
$525$	618.961			1.17897
$526$		−	142.384i		−	0.270692i
$527$			787.132i			1.49361i
$528$		−	86.6336i		−	0.164079i
$529$	121.741			0.230134
$530$			845.469i			1.59522i
$531$	107.178	−	140.861i	0.201842	−	0.265275i
$532$	−165.530			−0.311147
$533$			128.154i			0.240439i
$534$	−302.397			−0.566287
$535$	−534.997			−0.999995
$536$	219.553			0.409613
$537$			266.524i			0.496321i
$538$	−129.352			−0.240431
$539$			30.4314i			0.0564591i
$540$	91.4098			0.169277
$541$		−	84.6286i		−	0.156430i	−0.996937	−	0.0782149i	$-0.975078\pi$
$541$		−	84.6286i		−	0.156430i	0.996937	−	0.0782149i	$-0.0249220\pi$
$542$		−	147.082i		−	0.271369i
$543$	−135.954			−0.250376
$544$		−	91.8435i		−	0.168830i
$545$			120.032i			0.220242i
$546$	180.277			0.330177
$547$	−422.728			−0.772812			−0.386406	−	0.922329i	$-0.626284\pi$
$547$	−422.728			−0.772812			−0.386406	+	0.922329i	$0.626284\pi$
$548$	26.9593			0.0491958
$549$		−	3.11868i		−	0.00568065i
$550$	926.077			1.68378
$551$	578.797			1.05045
$552$	−98.8647			−0.179103
$553$	−564.614			−1.02100
$554$		−	246.668i		−	0.445250i
$555$		−	901.546i		−	1.62441i
$556$	−285.345			−0.513211
$557$	459.594			0.825124			0.412562	−	0.910930i	$-0.364634\pi$
$557$	459.594			0.825124			0.412562	+	0.910930i	$0.364634\pi$
$558$	205.688			0.368617
$559$	−462.188			−0.826812
$560$	−240.092			−0.428735
$561$			351.641i			0.626812i
$562$			156.830i			0.279057i
$563$		−	656.382i		−	1.16587i	−0.812520	−	0.582933i	$-0.801905\pi$
$563$		−	656.382i		−	1.16587i	0.812520	−	0.582933i	$-0.198095\pi$
$564$			289.124i			0.512630i
$565$		−	1441.14i		−	2.55068i
$566$	−441.610			−0.780230
$567$	61.4156			0.108317
$568$			221.631i			0.390196i
$569$		−	419.159i		−	0.736659i	−0.929695	−	0.368329i	$-0.879930\pi$
$569$		−	419.159i		−	0.736659i	0.929695	−	0.368329i	$-0.120070\pi$
$570$		−	261.317i		−	0.458451i
$571$			310.065i			0.543020i	0.962436	+	0.271510i	$0.0875230\pi$
$571$			310.065i			0.543020i	−0.962436	+	0.271510i	$0.912477\pi$
$572$	269.726			0.471550
$573$		−	534.243i		−	0.932361i
$574$		−	114.672i		−	0.199776i
$575$		−	1056.82i		−	1.83795i
$576$	−24.0000			−0.0416667
$577$	−141.733			−0.245637			−0.122819	−	0.992429i	$-0.539193\pi$
$577$	−141.733			−0.245637			−0.122819	+	0.992429i	$0.539193\pi$
$578$		−	35.9195i		−	0.0621444i
$579$	−553.153			−0.955360
$580$	839.509			1.44743
$581$			39.7466i			0.0684107i
$582$	151.803			0.260831
$583$			849.899i			1.45780i
$584$	−147.500			−0.252569
$585$			284.597i			0.486490i
$586$			403.892i			0.689235i
$587$		−	26.7719i		−	0.0456079i	−0.999740	−	0.0228040i	$-0.992741\pi$
$587$		−	26.7719i		−	0.0456079i	0.999740	−	0.0228040i	$-0.00725936\pi$
$588$	8.43039			0.0143374
$589$		−	588.011i		−	0.998320i
$590$	−584.071	−	444.406i	−0.989951	−	0.753231i
$591$	459.381			0.777294
$592$			236.704i			0.399839i
$593$	−848.696			−1.43119			−0.715595	−	0.698515i	$-0.753844\pi$
$593$	−848.696			−1.43119			−0.715595	+	0.698515i	$0.753844\pi$
$594$	91.8888			0.154695
$595$	974.520			1.63785
$596$		−	140.055i		−	0.234992i
$597$	237.010			0.397001
$598$		−	307.807i		−	0.514727i
$599$	−683.508			−1.14108			−0.570541	−	0.821269i	$-0.693266\pi$
$599$	−683.508			−1.14108			−0.570541	+	0.821269i	$0.693266\pi$
$600$		−	256.550i		−	0.427583i
$601$		−	832.145i		−	1.38460i	−0.721609	−	0.692301i	$-0.756597\pi$
$601$		−	832.145i		−	1.38460i	0.721609	−	0.692301i	$-0.243403\pi$
$602$	413.563			0.686981
$603$			232.871i			0.386187i
$604$			202.693i			0.335584i
$605$	311.041			0.514118
$606$	−169.709			−0.280048
$607$	85.9959			0.141674			0.0708368	−	0.997488i	$-0.477433\pi$
$607$	85.9959			0.141674			0.0708368	+	0.997488i	$0.477433\pi$
$608$			68.6098i			0.112845i
$609$	564.042			0.926177
$610$	−12.9314			−0.0211990
$611$	−900.162			−1.47326
$612$	97.4148			0.159174
$613$			262.356i			0.427986i	0.976835	+	0.213993i	$0.0686470\pi$
$613$			262.356i			0.427986i	−0.976835	+	0.213993i	$0.931353\pi$
$614$			457.530i			0.745163i
$615$	181.028			0.294355
$616$	−241.350			−0.391801
$617$	−170.571			−0.276452			−0.138226	−	0.990401i	$-0.544140\pi$
$617$	−170.571			−0.276452			−0.138226	+	0.990401i	$0.544140\pi$
$618$	152.022			0.245990
$619$	−650.889			−1.05152			−0.525759	−	0.850634i	$-0.676218\pi$
$619$	−650.889			−1.05152			−0.525759	+	0.850634i	$0.676218\pi$
$620$		−	852.873i		−	1.37560i
$621$		−	104.862i		−	0.168860i
$622$		−	228.934i		−	0.368061i
$623$			842.438i			1.35223i
$624$		−	74.7220i		−	0.119747i
$625$	808.212			1.29314
$626$	−519.760			−0.830288
$627$		−	262.686i		−	0.418958i
$628$			401.034i			0.638590i
$629$		−	960.771i		−	1.52746i
$630$		−	254.656i		−	0.404215i
$631$	1052.91			1.66864			0.834318	−	0.551283i	$-0.185862\pi$
$631$	1052.91			1.66864			0.834318	+	0.551283i	$0.185862\pi$
$632$			234.024i			0.370291i
$633$			40.2385i			0.0635680i
$634$			79.9486i			0.126102i
$635$	929.170			1.46326
$636$	235.447			0.370199
$637$			26.2473i			0.0412046i
$638$	843.908			1.32274
$639$	−235.075			−0.367880
$640$			99.5144i			0.155491i
$641$	670.936			1.04670			0.523351	−	0.852117i	$-0.324682\pi$
$641$	670.936			1.04670			0.523351	+	0.852117i	$0.324682\pi$
$642$			148.986i			0.232066i
$643$	471.735			0.733647			0.366823	−	0.930291i	$-0.380445\pi$
$643$	471.735			0.733647			0.366823	+	0.930291i	$0.380445\pi$
$644$			275.424i			0.427677i
$645$			652.878i			1.01221i
$646$		−	278.484i		−	0.431090i
$647$	1063.06			1.64305			0.821527	−	0.570169i	$-0.193122\pi$
$647$	1063.06			1.64305			0.821527	+	0.570169i	$0.193122\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	−587.132	−	446.735i	−0.904672	−	0.688344i
$650$	798.747			1.22884
$651$		−	573.021i		−	0.880217i
$652$	−533.362			−0.818040
$653$	−864.569			−1.32400			−0.661998	−	0.749506i	$-0.730291\pi$
$653$	−864.569			−1.32400			−0.661998	+	0.749506i	$0.730291\pi$
$654$	33.4265			0.0511108
$655$		−	1013.55i		−	1.54741i
$656$	−47.5296			−0.0724537
$657$		−	156.448i		−	0.238124i
$658$	805.460			1.22410
$659$			828.217i			1.25678i	0.777899	+	0.628389i	$0.216285\pi$
$659$			828.217i			1.25678i	−0.777899	+	0.628389i	$0.783715\pi$
$660$		−	381.011i		−	0.577289i
$661$	1241.82			1.87869			0.939346	−	0.342971i	$-0.111433\pi$
$661$	1241.82			1.87869			0.939346	+	0.342971i	$0.111433\pi$
$662$			277.606i			0.419345i
$663$			303.293i			0.457455i
$664$	16.4744			0.0248108
$665$	−727.995			−1.09473
$666$	−251.063			−0.376971
$667$		−	963.053i		−	1.44386i
$668$	−319.556			−0.478377
$669$	560.699			0.838115
$670$	965.583			1.44117
$671$	−12.9992			−0.0193728
$672$			66.8608i			0.0994953i
$673$		−	303.565i		−	0.451063i	−0.974236	−	0.225531i	$-0.927588\pi$
$673$		−	303.565i		−	0.451063i	0.974236	−	0.225531i	$-0.0724119\pi$
$674$	343.331			0.509393
$675$	272.112			0.403130
$676$	−105.359			−0.155857
$677$	−1025.70			−1.51506			−0.757532	−	0.652798i	$-0.773595\pi$
$677$	−1025.70			−1.51506			−0.757532	+	0.652798i	$0.773595\pi$
$678$	−401.328			−0.591929
$679$		−	422.904i		−	0.622834i
$680$		−	403.924i		−	0.594006i
$681$		−	616.041i		−	0.904612i
$682$		−	857.343i		−	1.25710i
$683$		−	592.992i		−	0.868217i	−0.900861	−	0.434108i	$-0.857064\pi$
$683$		−	592.992i		−	0.868217i	0.900861	−	0.434108i	$-0.142936\pi$
$684$	−72.7717			−0.106391
$685$	118.566			0.173089
$686$		−	496.362i		−	0.723560i
$687$			617.915i			0.899440i
$688$		−	171.416i		−	0.249151i
$689$			733.044i			1.06392i
$690$	−434.802			−0.630148
$691$		−	151.805i		−	0.219689i	−0.993949	−	0.109845i	$-0.964965\pi$
$691$		−	151.805i		−	0.219689i	0.993949	−	0.109845i	$-0.0350353\pi$
$692$			448.778i			0.648523i
$693$		−	255.990i		−	0.369394i
$694$	−690.720			−0.995274
$695$	−1254.94			−1.80566
$696$		−	233.787i		−	0.335901i
$697$	192.920			0.276787
$698$	246.592			0.353284
$699$			570.973i			0.816843i
$700$	−714.715			−1.02102
$701$			468.735i			0.668667i	0.942455	+	0.334333i	$0.108511\pi$
$701$			468.735i			0.668667i	−0.942455	+	0.334333i	$0.891489\pi$
$702$	79.2547			0.112898
$703$			717.725i			1.02095i
$704$			100.036i			0.142096i
$705$			1271.55i			1.80362i
$706$	−330.058			−0.467505
$707$			472.787i			0.668722i
$708$	−123.759	+	162.652i	−0.174800	+	0.229735i
$709$	737.452			1.04013			0.520065	−	0.854127i	$-0.325908\pi$
$709$	737.452			1.04013			0.520065	+	0.854127i	$0.325908\pi$
$710$			974.724i			1.37285i
$711$	−248.220			−0.349114
$712$	349.178			0.490419
$713$	−978.384			−1.37221
$714$		−	271.385i		−	0.380091i
$715$	1186.25			1.65908
$716$		−	307.756i		−	0.429827i
$717$	65.9193			0.0919377
$718$		−	51.0648i		−	0.0711208i
$719$		−	756.166i		−	1.05169i	−0.850580	−	0.525846i	$-0.823749\pi$
$719$		−	756.166i		−	1.05169i	0.850580	−	0.525846i	$-0.176251\pi$
$720$	−105.551			−0.146599
$721$		−	423.512i		−	0.587396i
$722$		−	302.495i		−	0.418969i
$723$	−51.2872			−0.0709367
$724$	156.987			0.216832
$725$	2499.09			3.44701
$726$		−	86.6189i		−	0.119310i
$727$	−255.179			−0.351003			−0.175501	−	0.984479i	$-0.556155\pi$
$727$	−255.179			−0.351003			−0.175501	+	0.984479i	$0.556155\pi$
$728$	−208.166			−0.285942
$729$	27.0000			0.0370370
$730$	−648.699			−0.888629
$731$			695.767i			0.951802i
$732$			3.60114i			0.00491959i
$733$	740.541			1.01029			0.505144	−	0.863035i	$-0.331439\pi$
$733$	740.541			1.01029			0.505144	+	0.863035i	$0.331439\pi$
$734$	−308.993			−0.420971
$735$	37.0765			0.0504442
$736$	114.159			0.155107
$737$	970.642			1.31702
$738$		−	50.4128i		−	0.0683100i
$739$			454.886i			0.615543i	0.951460	+	0.307771i	$0.0995832\pi$
$739$			454.886i			0.615543i	−0.951460	+	0.307771i	$0.900417\pi$
$740$			1041.02i			1.40678i
$741$		−	226.569i		−	0.305761i
$742$		−	655.923i		−	0.883994i
$743$	−257.942			−0.347162			−0.173581	−	0.984820i	$-0.555534\pi$
$743$	−257.942			−0.347162			−0.173581	+	0.984820i	$0.555534\pi$
$744$	−237.509			−0.319232
$745$		−	615.956i		−	0.826787i
$746$		−	808.733i		−	1.08409i
$747$			17.4737i			0.0233919i
$748$		−	406.040i		−	0.542835i
$749$	415.056			0.554147
$750$		−	589.658i		−	0.786211i
$751$		−	793.937i		−	1.05717i	−0.848879	−	0.528587i	$-0.822722\pi$
$751$		−	793.937i		−	1.05717i	0.848879	−	0.528587i	$-0.177278\pi$
$752$		−	333.851i		−	0.443951i
$753$	665.753			0.884134
$754$	727.876			0.965353
$755$			891.434i			1.18071i
$756$	−70.9166			−0.0938050
$757$	−1339.58			−1.76959			−0.884793	−	0.465985i	$-0.845700\pi$
$757$	−1339.58			−1.76959			−0.884793	+	0.465985i	$0.845700\pi$
$758$			50.8993i			0.0671494i
$759$	−437.081			−0.575864
$760$			301.743i			0.397030i
$761$	−381.945			−0.501899			−0.250949	−	0.968000i	$-0.580743\pi$
$761$	−381.945			−0.501899			−0.250949	+	0.968000i	$0.580743\pi$
$762$		−	258.756i		−	0.339574i
$763$		−	93.1217i		−	0.122047i
$764$			616.891i			0.807449i
$765$	428.426			0.560034
$766$		−	878.293i		−	1.14660i
$767$	−506.405	−	385.312i	−0.660241	−	0.502362i
$768$	27.7128			0.0360844
$769$			881.768i			1.14664i	0.819331	+	0.573321i	$0.194345\pi$
$769$			881.768i			1.14664i	−0.819331	+	0.573321i	$0.805655\pi$
$770$	−1061.45			−1.37850
$771$	334.975			0.434469
$772$	638.726			0.827366
$773$			1047.05i			1.35453i	0.735740	+	0.677264i	$0.236835\pi$
$773$			1047.05i			1.35453i	−0.735740	+	0.677264i	$0.763165\pi$
$774$	181.814			0.234901
$775$		−	2538.87i		−	3.27596i
$776$	−175.288			−0.225886
$777$			699.428i			0.900165i
$778$			847.960i			1.08992i
$779$	−144.117			−0.185003
$780$		−	328.624i		−	0.421313i
$781$			979.832i			1.25459i
$782$	−463.366			−0.592540
$783$	247.969			0.316690
$784$	−9.73457			−0.0124165
$785$			1763.73i			2.24679i
$786$	−282.255			−0.359103
$787$	−916.014			−1.16393			−0.581966	−	0.813213i	$-0.697716\pi$
$787$	−916.014			−1.16393			−0.581966	+	0.813213i	$0.697716\pi$
$788$	−530.447			−0.673156
$789$	−174.384			−0.221019
$790$			1029.23i			1.30282i
$791$			1118.05i			1.41346i
$792$	−106.104			−0.133970
$793$	−11.2119			−0.0141385
$794$	634.601			0.799246
$795$	1035.48			1.30250
$796$	−273.675			−0.343813
$797$			1232.99i			1.54703i	0.633775	+	0.773517i	$0.281505\pi$
$797$			1232.99i			1.54703i	−0.633775	+	0.773517i	$0.718495\pi$
$798$			202.732i			0.254051i
$799$			1355.08i			1.69598i
$800$			296.238i			0.370298i
$801$			370.359i			0.462371i
$802$	342.463			0.427011
$803$	−652.098			−0.812078
$804$		−	268.896i		−	0.334448i
$805$			1211.30i			1.50472i
$806$		−	739.463i		−	0.917448i
$807$			158.423i			0.196311i
$808$	195.963			0.242528
$809$			658.726i			0.814247i	0.913373	+	0.407124i	$0.133468\pi$
$809$			658.726i			0.814247i	−0.913373	+	0.407124i	$0.866532\pi$
$810$		−	111.954i		−	0.138214i
$811$			756.962i			0.933368i	0.884424	+	0.466684i	$0.154552\pi$
$811$			756.962i			0.933368i	−0.884424	+	0.466684i	$0.845448\pi$
$812$	−651.300			−0.802093
$813$	−180.138			−0.221572
$814$			1046.47i			1.28559i
$815$	−2345.70			−2.87816
$816$	−112.485			−0.137849
$817$		−	519.759i		−	0.636180i
$818$	−203.804			−0.249149
$819$		−	220.793i		−	0.269589i
$820$	−209.033			−0.254919
$821$		−	1114.46i		−	1.35744i	−0.734395	−	0.678722i	$-0.762534\pi$
$821$		−	1114.46i		−	1.35744i	0.734395	−	0.678722i	$-0.237466\pi$
$822$		−	33.0182i		−	0.0401682i
$823$			824.336i			1.00162i	0.865556	+	0.500812i	$0.166965\pi$
$823$			824.336i			1.00162i	−0.865556	+	0.500812i	$0.833035\pi$
$824$	−175.539			−0.213033
$825$		−	1134.21i		−	1.37480i
$826$	453.128	+	344.775i	0.548582	+	0.417403i
$827$	407.228			0.492416			0.246208	−	0.969217i	$-0.420815\pi$
$827$	407.228			0.492416			0.246208	+	0.969217i	$0.420815\pi$
$828$			121.084i			0.146237i
$829$	−1039.10			−1.25343			−0.626717	−	0.779247i	$-0.715602\pi$
$829$	−1039.10			−1.25343			−0.626717	+	0.779247i	$0.715602\pi$
$830$	72.4536			0.0872935
$831$	−302.106			−0.363545
$832$			86.2815i			0.103704i
$833$	39.5121			0.0474335
$834$			349.475i			0.419035i
$835$	−1405.39			−1.68310
$836$			303.324i			0.362828i
$837$		−	251.916i		−	0.300975i
$838$	−75.5276			−0.0901284
$839$		−	379.127i		−	0.451879i	−0.974141	−	0.225940i	$-0.927455\pi$
$839$		−	379.127i		−	0.451879i	0.974141	−	0.225940i	$-0.0725452\pi$
$840$			294.051i			0.350061i
$841$	1436.35			1.70790
$842$	−406.633			−0.482937
$843$	192.077			0.227849
$844$		−	46.4635i		−	0.0550515i
$845$	−463.365			−0.548361
$846$	354.103			0.418561
$847$	−241.309			−0.284898
$848$	−271.870			−0.320602
$849$			540.860i			0.637055i
$850$		−	1202.42i		−	1.41461i
$851$	1194.21			1.40331
$852$	271.442			0.318594
$853$	−1176.59			−1.37936			−0.689679	−	0.724115i	$-0.742248\pi$
$853$	−1176.59			−1.37936			−0.689679	+	0.724115i	$0.742248\pi$
$854$	10.0323			0.0117474
$855$	−320.047			−0.374324
$856$		−	172.035i		−	0.200975i
$857$		−	1567.20i		−	1.82870i	−0.404921	−	0.914352i	$-0.632701\pi$
$857$		−	1567.20i		−	1.82870i	0.404921	−	0.914352i	$-0.367299\pi$
$858$		−	330.346i		−	0.385019i
$859$		−	1165.81i		−	1.35717i	−0.734522	−	0.678585i	$-0.762593\pi$
$859$		−	1165.81i		−	1.35717i	0.734522	−	0.678585i	$-0.237407\pi$
$860$		−	753.878i		−	0.876603i
$861$	−140.443			−0.163117
$862$	−616.734			−0.715468
$863$		−	824.885i		−	0.955835i	−0.878405	−	0.477917i	$-0.841392\pi$
$863$		−	824.885i		−	0.955835i	0.878405	−	0.477917i	$-0.158608\pi$
$864$			29.3939i			0.0340207i
$865$			1973.71i			2.28174i
$866$			196.938i			0.227411i
$867$	−43.9922			−0.0507407
$868$			661.668i			0.762290i
$869$			1034.62i			1.19059i
$870$		−	1028.18i		−	1.18182i
$871$	837.185			0.961177
$872$	−38.5976			−0.0442633
$873$		−	185.921i		−	0.212967i
$874$	346.148			0.396050
$875$	−1642.71			−1.87738
$876$			180.650i			0.206221i
$877$	745.919			0.850534			0.425267	−	0.905068i	$-0.360180\pi$
$877$	745.919			0.850534			0.425267	+	0.905068i	$0.360180\pi$
$878$		−	491.308i		−	0.559576i
$879$	494.664			0.562758
$880$			439.953i			0.499947i
$881$			870.811i			0.988435i	0.869338	+	0.494217i	$0.164545\pi$
$881$			870.811i			0.988435i	−0.869338	+	0.494217i	$0.835455\pi$
$882$		−	10.3251i		−	0.0117064i
$883$	1336.01			1.51303			0.756515	−	0.653976i	$-0.226900\pi$
$883$	1336.01			1.51303			0.756515	+	0.653976i	$0.226900\pi$
$884$		−	350.212i		−	0.396168i
$885$	−544.284	+	715.338i	−0.615011	+	0.808292i
$886$	174.543			0.197002
$887$			802.902i			0.905188i	0.891717	+	0.452594i	$0.149501\pi$
$887$			802.902i			0.905188i	−0.891717	+	0.452594i	$0.850499\pi$
$888$	289.903			0.326467
$889$	−720.859			−0.810865
$890$	1535.67			1.72547
$891$		−	112.540i		−	0.126308i
$892$	−647.439			−0.725829
$893$		−	1012.29i		−	1.13358i
$894$	−171.532			−0.191870
$895$		−	1353.50i		−	1.51229i
$896$		−	77.2042i		−	0.0861654i
$897$	−376.985			−0.420273
$898$			849.911i			0.946448i
$899$		−	2313.60i		−	2.57353i
$900$	−314.208			−0.349120
$901$	1103.51			1.22476
$902$	−210.129			−0.232959
$903$		−	506.509i		−	0.560918i
$904$	463.414			0.512626
$905$	690.420			0.762895
$906$	248.247			0.274003
$907$	−737.743			−0.813388			−0.406694	−	0.913565i	$-0.633318\pi$
$907$	−737.743			−0.813388			−0.406694	+	0.913565i	$0.633318\pi$
$908$			711.342i			0.783417i
$909$			207.850i			0.228658i
$910$	−915.503			−1.00605
$911$	340.971			0.374282			0.187141	−	0.982333i	$-0.440078\pi$
$911$	340.971			0.374282			0.187141	+	0.982333i	$0.440078\pi$
$912$	84.0296			0.0921377
$913$	72.8333			0.0797736
$914$	−1225.57			−1.34089
$915$			15.8377i			0.0173089i
$916$		−	713.507i		−	0.778938i
$917$			786.324i			0.857497i
$918$		−	119.308i		−	0.129965i
$919$		−	319.034i		−	0.347153i	−0.984820	−	0.173577i	$-0.944468\pi$
$919$		−	319.034i		−	0.347153i	0.984820	−	0.173577i	$-0.0555324\pi$
$920$	502.067			0.545725
$921$	560.358			0.608423
$922$		−	515.432i		−	0.559037i
$923$			845.111i			0.915614i
$924$			295.592i			0.319905i
$925$			3098.94i			3.35020i
$926$	367.156			0.396497
$927$		−	186.188i		−	0.200850i
$928$			269.954i			0.290899i
$929$		−	1600.95i		−	1.72331i	−0.507495	−	0.861655i	$-0.669428\pi$
$929$		−	1600.95i		−	1.72331i	0.507495	−	0.861655i	$-0.330572\pi$
$930$	−1044.55			−1.12317
$931$	−29.5167			−0.0317043
$932$		−	659.303i		−	0.707406i
$933$	−280.386			−0.300521
$934$	655.187			0.701485
$935$		−	1785.75i		−	1.90989i
$936$	−91.5154			−0.0977729
$937$		−	711.821i		−	0.759681i	−0.925052	−	0.379840i	$-0.875979\pi$
$937$		−	711.821i		−	0.759681i	0.925052	−	0.379840i	$-0.124021\pi$
$938$	−749.108			−0.798623
$939$			636.573i			0.677927i
$940$		−	1468.26i		−	1.56198i
$941$		−	1198.04i		−	1.27315i	−0.771214	−	0.636576i	$-0.780350\pi$
$941$		−	1198.04i		−	1.27315i	0.771214	−	0.636576i	$-0.219650\pi$
$942$	491.165			0.521406
$943$			239.795i			0.254289i
$944$	142.904	−	187.815i	0.151381	−	0.198956i
$945$	−311.888			−0.330040
$946$		−	757.829i		−	0.801087i
$947$	268.079			0.283082			0.141541	−	0.989932i	$-0.454794\pi$
$947$	268.079			0.283082			0.141541	+	0.989932i	$0.454794\pi$
$948$	286.620			0.302342
$949$	−562.439			−0.592665
$950$			898.241i			0.945517i
$951$	97.9166			0.102962
$952$			313.368i			0.329168i
$953$	798.095			0.837455			0.418728	−	0.908112i	$-0.362476\pi$
$953$	798.095			0.837455			0.418728	+	0.908112i	$0.362476\pi$
$954$		−	288.362i		−	0.302266i
$955$			2713.06i			2.84090i
$956$	−76.1171			−0.0796204
$957$		−	1033.57i		−	1.08001i
$958$			753.546i			0.786582i
$959$	−91.9844			−0.0959170
$960$	121.880			0.126958
$961$	−1389.43			−1.44582
$962$			902.588i			0.938241i
$963$	182.470			0.189481
$964$	59.2214			0.0614330
$965$	2809.09			2.91097
$966$	337.324			0.349197
$967$		−	153.711i		−	0.158956i	−0.996837	−	0.0794781i	$-0.974675\pi$
$967$		−	153.711i		−	0.158956i	0.996837	−	0.0794781i	$-0.0253254\pi$
$968$			100.019i			0.103325i
$969$	−341.072			−0.351983
$970$	−770.907			−0.794750
$971$	−1229.75			−1.26647			−0.633237	−	0.773958i	$-0.718274\pi$
$971$	−1229.75			−1.26647			−0.633237	+	0.773958i	$0.718274\pi$
$972$	−31.1769			−0.0320750
$973$	973.592			1.00061
$974$			128.894i			0.132335i
$975$		−	978.262i		−	1.00335i
$976$		−	4.15824i		−	0.00426049i
$977$			793.806i			0.812493i	0.913764	+	0.406247i	$0.133163\pi$
$977$			793.806i			0.812493i	−0.913764	+	0.406247i	$0.866837\pi$
$978$			653.232i			0.667927i
$979$	1543.72			1.57683
$980$	−42.8122			−0.0436859
$981$		−	40.9389i		−	0.0417318i
$982$			380.791i			0.387771i
$983$		−	228.801i		−	0.232758i	−0.993205	−	0.116379i	$-0.962871\pi$
$983$		−	228.801i		−	0.232758i	0.993205	−	0.116379i	$-0.0371287\pi$
$984$			58.2117i			0.0591582i
$985$	−2332.88			−2.36841
$986$		−	1095.73i		−	1.11129i
$987$		−	986.483i		−	0.999476i
$988$			261.619i			0.264797i
$989$	−864.820			−0.874439
$990$	−466.641			−0.471354
$991$		−	3.71799i		−	0.00375175i	−0.999998	−	0.00187588i	$-0.999403\pi$
$991$		−	3.71799i		−	0.00375175i	0.999998	−	0.00187588i	$-0.000597110\pi$
$992$	274.251			0.276463
$993$	339.997			0.342393
$994$		−	756.201i		−	0.760765i
$995$	−1203.61			−1.20966
$996$		−	20.1769i		−	0.0202579i
$997$	1195.55			1.19915			0.599574	−	0.800319i	$-0.295337\pi$
$997$	1195.55			1.19915			0.599574	+	0.800319i	$0.295337\pi$
$998$		−	192.751i		−	0.193138i
$999$			307.488i			0.307796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.16	yes	20
3.2	odd	2		1062.3.d.f.235.10		20
59.58	odd	2	inner	354.3.d.a.235.6	✓	20
177.176	even	2		1062.3.d.f.235.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.6	✓	20	59.58	odd	2	inner
354.3.d.a.235.16	yes	20	1.1	even	1	trivial
1062.3.d.f.235.10		20	3.2	odd	2
1062.3.d.f.235.20		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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -8.79591 q^{5} +2.44949i q^{6} +6.82395 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} -8.79591 q^{5} +2.44949i q^{6} +6.82395 q^{7} -2.82843i q^{8} +3.00000 q^{9} -12.4393i q^{10} -12.5045i q^{11} -3.46410 q^{12} -10.7852i q^{13} +9.65053i q^{14} -15.2350 q^{15} +4.00000 q^{16} -16.2358 q^{17} +4.24264i q^{18} +12.1286 q^{19} +17.5918 q^{20} +11.8194 q^{21} +17.6840 q^{22} -20.1807i q^{23} -4.89898i q^{24} +52.3681 q^{25} +15.2526 q^{26} +5.19615 q^{27} -13.6479 q^{28} +47.7216 q^{29} -21.5455i q^{30} -48.4812i q^{31} +5.65685i q^{32} -21.6584i q^{33} -22.9609i q^{34} -60.0229 q^{35} -6.00000 q^{36} +59.1761i q^{37} +17.1525i q^{38} -18.6805i q^{39} +24.8786i q^{40} -11.8824 q^{41} +16.7152i q^{42} -42.8539i q^{43} +25.0090i q^{44} -26.3877 q^{45} +28.5398 q^{46} -83.4628i q^{47} +6.92820 q^{48} -2.43364 q^{49} +74.0596i q^{50} -28.1212 q^{51} +21.5704i q^{52} -67.9676 q^{53} +7.34847i q^{54} +109.988i q^{55} -19.3011i q^{56} +21.0074 q^{57} +67.4885i q^{58} +(35.7260 - 46.9537i) q^{59} +30.4699 q^{60} -1.03956i q^{61} +68.5628 q^{62} +20.4719 q^{63} -8.00000 q^{64} +94.8656i q^{65} +30.6296 q^{66} +77.6236i q^{67} +32.4716 q^{68} -34.9539i q^{69} -84.8852i q^{70} -78.3585 q^{71} -8.48528i q^{72} -52.1492i q^{73} -83.6877 q^{74} +90.7041 q^{75} -24.2572 q^{76} -85.3300i q^{77} +26.4182 q^{78} -82.7400 q^{79} -35.1836 q^{80} +9.00000 q^{81} -16.8043i q^{82} +5.82457i q^{83} -23.6389 q^{84} +142.809 q^{85} +60.6046 q^{86} +82.6562 q^{87} -35.3680 q^{88} +123.453i q^{89} -37.3179i q^{90} -73.5977i q^{91} +40.3613i q^{92} -83.9720i q^{93} +118.034 q^{94} -106.682 q^{95} +9.79796i q^{96} -61.9735i q^{97} -3.44169i q^{98} -37.5134i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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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