LMFDB - Embedded newform 354.3.d.a.235.15

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			235.15
Root			$7.71614 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +7.71614 q^{5} -2.44949i q^{6} -7.56506 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +7.71614 q^{5} -2.44949i q^{6} -7.56506 q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.9123i q^{10} -2.42694i q^{11} +3.46410 q^{12} +20.7553i q^{13} -10.6986i q^{14} -13.3647 q^{15} +4.00000 q^{16} +31.7647 q^{17} +4.24264i q^{18} -4.95867 q^{19} -15.4323 q^{20} +13.1031 q^{21} +3.43222 q^{22} +31.3139i q^{23} +4.89898i q^{24} +34.5388 q^{25} -29.3524 q^{26} -5.19615 q^{27} +15.1301 q^{28} -11.8424 q^{29} -18.9006i q^{30} +8.07558i q^{31} +5.65685i q^{32} +4.20359i q^{33} +44.9220i q^{34} -58.3731 q^{35} -6.00000 q^{36} +41.8766i q^{37} -7.01262i q^{38} -35.9493i q^{39} -21.8245i q^{40} -44.4010 q^{41} +18.5305i q^{42} +6.57752i q^{43} +4.85389i q^{44} +23.1484 q^{45} -44.2845 q^{46} +92.7318i q^{47} -6.92820 q^{48} +8.23017 q^{49} +48.8452i q^{50} -55.0180 q^{51} -41.5106i q^{52} +45.1599 q^{53} -7.34847i q^{54} -18.7266i q^{55} +21.3972i q^{56} +8.58867 q^{57} -16.7477i q^{58} +(55.8007 - 19.1647i) q^{59} +26.7295 q^{60} +42.6199i q^{61} -11.4206 q^{62} -22.6952 q^{63} -8.00000 q^{64} +160.151i q^{65} -5.94477 q^{66} -76.9923i q^{67} -63.5293 q^{68} -54.2372i q^{69} -82.5520i q^{70} -32.2995 q^{71} -8.48528i q^{72} -119.215i q^{73} -59.2224 q^{74} -59.8230 q^{75} +9.91734 q^{76} +18.3600i q^{77} +50.8399 q^{78} +94.3895 q^{79} +30.8646 q^{80} +9.00000 q^{81} -62.7925i q^{82} -108.087i q^{83} -26.2061 q^{84} +245.101 q^{85} -9.30201 q^{86} +20.5117 q^{87} -6.86443 q^{88} -58.7505i q^{89} +32.7368i q^{90} -157.015i q^{91} -62.6277i q^{92} -13.9873i q^{93} -131.143 q^{94} -38.2618 q^{95} -9.79796i q^{96} -21.2762i q^{97} +11.6392i q^{98} -7.28083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	7.71614			1.54323			0.771614	−	0.636091i	$-0.219450\pi$
$5$	7.71614			1.54323			0.771614	+	0.636091i	$0.219450\pi$
$6$		−	2.44949i		−	0.408248i
$7$	−7.56506			−1.08072			−0.540362	−	0.841433i	$-0.681713\pi$
$7$	−7.56506			−1.08072			−0.540362	+	0.841433i	$0.681713\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$			10.9123i			1.09123i
$11$		−	2.42694i		−	0.220631i	−0.993897	−	0.110316i	$-0.964814\pi$
$11$		−	2.42694i		−	0.220631i	0.993897	−	0.110316i	$-0.0351862\pi$
$12$	3.46410			0.288675
$13$			20.7553i			1.59656i	0.602285	+	0.798281i	$0.294257\pi$
$13$			20.7553i			1.59656i	−0.602285	+	0.798281i	$0.705743\pi$
$14$		−	10.6986i		−	0.764187i
$15$	−13.3647			−0.890983
$16$	4.00000			0.250000
$17$	31.7647			1.86851			0.934255	−	0.356606i	$-0.116066\pi$
$17$	31.7647			1.86851			0.934255	+	0.356606i	$0.116066\pi$
$18$			4.24264i			0.235702i
$19$	−4.95867			−0.260983			−0.130491	−	0.991449i	$-0.541655\pi$
$19$	−4.95867			−0.260983			−0.130491	+	0.991449i	$0.541655\pi$
$20$	−15.4323			−0.771614
$21$	13.1031			0.623956
$22$	3.43222			0.156010
$23$			31.3139i			1.36147i	0.732529	+	0.680736i	$0.238340\pi$
$23$			31.3139i			1.36147i	−0.732529	+	0.680736i	$0.761660\pi$
$24$			4.89898i			0.204124i
$25$	34.5388			1.38155
$26$	−29.3524			−1.12894
$27$	−5.19615			−0.192450
$28$	15.1301			0.540362
$29$	−11.8424			−0.408359			−0.204180	−	0.978933i	$-0.565453\pi$
$29$	−11.8424			−0.408359			−0.204180	+	0.978933i	$0.565453\pi$
$30$		−	18.9006i		−	0.630020i
$31$			8.07558i			0.260503i	0.991481	+	0.130251i	$0.0415784\pi$
$31$			8.07558i			0.260503i	−0.991481	+	0.130251i	$0.958422\pi$
$32$			5.65685i			0.176777i
$33$			4.20359i			0.127382i
$34$			44.9220i			1.32124i
$35$	−58.3731			−1.66780
$36$	−6.00000			−0.166667
$37$			41.8766i			1.13180i	0.824474	+	0.565900i	$0.191471\pi$
$37$			41.8766i			1.13180i	−0.824474	+	0.565900i	$0.808529\pi$
$38$		−	7.01262i		−	0.184543i
$39$		−	35.9493i		−	0.921776i
$40$		−	21.8245i		−	0.545613i
$41$	−44.4010			−1.08295			−0.541476	−	0.840716i	$-0.682134\pi$
$41$	−44.4010			−1.08295			−0.541476	+	0.840716i	$0.682134\pi$
$42$			18.5305i			0.441203i
$43$			6.57752i			0.152966i	0.997071	+	0.0764828i	$0.0243690\pi$
$43$			6.57752i			0.152966i	−0.997071	+	0.0764828i	$0.975631\pi$
$44$			4.85389i			0.110316i
$45$	23.1484			0.514409
$46$	−44.2845			−0.962706
$47$			92.7318i			1.97302i	0.163710	+	0.986509i	$0.447654\pi$
$47$			92.7318i			1.97302i	−0.163710	+	0.986509i	$0.552346\pi$
$48$	−6.92820			−0.144338
$49$	8.23017			0.167963
$50$			48.8452i			0.976905i
$51$	−55.0180			−1.07878
$52$		−	41.5106i		−	0.798281i
$53$	45.1599			0.852074			0.426037	−	0.904706i	$-0.359909\pi$
$53$	45.1599			0.852074			0.426037	+	0.904706i	$0.359909\pi$
$54$		−	7.34847i		−	0.136083i
$55$		−	18.7266i		−	0.340484i
$56$			21.3972i			0.382093i
$57$	8.58867			0.150678
$58$		−	16.7477i		−	0.288754i
$59$	55.8007	−	19.1647i	0.945774	−	0.324826i
$59$	55.8007	−	19.1647i	0.945774	−	0.324826i
$60$	26.7295			0.445491
$61$			42.6199i			0.698687i	0.936995	+	0.349343i	$0.113595\pi$
$61$			42.6199i			0.698687i	−0.936995	+	0.349343i	$0.886405\pi$
$62$	−11.4206			−0.184203
$63$	−22.6952			−0.360241
$64$	−8.00000			−0.125000
$65$			160.151i			2.46386i
$66$	−5.94477			−0.0900723
$67$		−	76.9923i		−	1.14914i	−0.818456	−	0.574570i	$-0.805169\pi$
$67$		−	76.9923i		−	1.14914i	0.818456	−	0.574570i	$-0.194831\pi$
$68$	−63.5293			−0.934255
$69$		−	54.2372i		−	0.786046i
$70$		−	82.5520i		−	1.17931i
$71$	−32.2995			−0.454923			−0.227461	−	0.973787i	$-0.573043\pi$
$71$	−32.2995			−0.454923			−0.227461	+	0.973787i	$0.573043\pi$
$72$		−	8.48528i		−	0.117851i
$73$		−	119.215i		−	1.63309i	−0.577284	−	0.816543i	$-0.695888\pi$
$73$		−	119.215i		−	1.63309i	0.577284	−	0.816543i	$-0.304112\pi$
$74$	−59.2224			−0.800303
$75$	−59.8230			−0.797639
$76$	9.91734			0.130491
$77$			18.3600i			0.238441i
$78$	50.8399			0.651794
$79$	94.3895			1.19480			0.597402	−	0.801942i	$-0.296200\pi$
$79$	94.3895			1.19480			0.597402	+	0.801942i	$0.296200\pi$
$80$	30.8646			0.385807
$81$	9.00000			0.111111
$82$		−	62.7925i		−	0.765763i
$83$		−	108.087i		−	1.30225i	−0.758969	−	0.651127i	$-0.774296\pi$
$83$		−	108.087i		−	1.30225i	0.758969	−	0.651127i	$-0.225704\pi$
$84$	−26.2061			−0.311978
$85$	245.101			2.88354
$86$	−9.30201			−0.108163
$87$	20.5117			0.235766
$88$	−6.86443			−0.0780049
$89$		−	58.7505i		−	0.660118i	−0.943960	−	0.330059i	$-0.892931\pi$
$89$		−	58.7505i		−	0.660118i	0.943960	−	0.330059i	$-0.107069\pi$
$90$			32.7368i			0.363742i
$91$		−	157.015i		−	1.72544i
$92$		−	62.6277i		−	0.680736i
$93$		−	13.9873i		−	0.150401i
$94$	−131.143			−1.39513
$95$	−38.2618			−0.402756
$96$		−	9.79796i		−	0.102062i
$97$		−	21.2762i		−	0.219343i	−0.993968	−	0.109671i	$-0.965020\pi$
$97$		−	21.2762i		−	0.219343i	0.993968	−	0.109671i	$-0.0349798\pi$
$98$			11.6392i			0.118767i
$99$		−	7.28083i		−	0.0735438i
$100$	−69.0776			−0.690776
$101$			68.9296i			0.682471i	0.939978	+	0.341235i	$0.110845\pi$
$101$			68.9296i			0.682471i	−0.939978	+	0.341235i	$0.889155\pi$
$102$		−	77.8072i		−	0.762816i
$103$		−	91.3137i		−	0.886540i	−0.896388	−	0.443270i	$-0.853818\pi$
$103$		−	91.3137i		−	0.886540i	0.896388	−	0.443270i	$-0.146182\pi$
$104$	58.7049			0.564470
$105$	101.105			0.962906
$106$			63.8658i			0.602508i
$107$	138.265			1.29219			0.646096	−	0.763256i	$-0.276400\pi$
$107$	138.265			1.29219			0.646096	+	0.763256i	$0.276400\pi$
$108$	10.3923			0.0962250
$109$			122.018i			1.11943i	0.828685	+	0.559715i	$0.189090\pi$
$109$			122.018i			1.11943i	−0.828685	+	0.559715i	$0.810910\pi$
$110$	26.4835			0.240759
$111$		−	72.5324i		−	0.653445i
$112$	−30.2602			−0.270181
$113$		−	25.8859i		−	0.229079i	−0.993419	−	0.114539i	$-0.963461\pi$
$113$		−	25.8859i		−	0.229079i	0.993419	−	0.114539i	$-0.0365392\pi$
$114$			12.1462i			0.106546i
$115$			241.622i			2.10106i
$116$	23.6848			0.204180
$117$			62.2659i			0.532188i
$118$	27.1030	+	78.9140i	0.229687	+	0.668763i
$119$	−240.302			−2.01934
$120$			37.8012i			0.315010i
$121$	115.110			0.951322
$122$	−60.2736			−0.494046
$123$	76.9048			0.625243
$124$		−	16.1512i		−	0.130251i
$125$	73.6027			0.588821
$126$		−	32.0958i		−	0.254729i
$127$	114.217			0.899348			0.449674	−	0.893193i	$-0.351540\pi$
$127$	114.217			0.899348			0.449674	+	0.893193i	$0.351540\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	11.3926i		−	0.0883147i
$130$	−226.488			−1.74221
$131$			197.744i			1.50949i	0.656017	+	0.754746i	$0.272240\pi$
$131$			197.744i			1.50949i	−0.656017	+	0.754746i	$0.727760\pi$
$132$		−	8.40718i		−	0.0636908i
$133$	37.5127			0.282050
$134$	108.884			0.812564
$135$	−40.0942			−0.296994
$136$		−	89.8440i		−	0.660618i
$137$	−163.072			−1.19031			−0.595154	−	0.803612i	$-0.702909\pi$
$137$	−163.072			−1.19031			−0.595154	+	0.803612i	$0.702909\pi$
$138$	76.7030			0.555819
$139$	−77.3221			−0.556274			−0.278137	−	0.960541i	$-0.589717\pi$
$139$	−77.3221			−0.556274			−0.278137	+	0.960541i	$0.589717\pi$
$140$	116.746			0.833901
$141$		−	160.616i		−	1.13912i
$142$		−	45.6784i		−	0.321679i
$143$	50.3720			0.352252
$144$	12.0000			0.0833333
$145$	−91.3777			−0.630191
$146$	168.596			1.15477
$147$	−14.2551			−0.0969732
$148$		−	83.7532i		−	0.565900i
$149$		−	12.7571i		−	0.0856183i	−0.999083	−	0.0428092i	$-0.986369\pi$
$149$		−	12.7571i		−	0.0856183i	0.999083	−	0.0428092i	$-0.0136307\pi$
$150$		−	84.6024i		−	0.564016i
$151$			124.275i			0.823011i	0.911407	+	0.411506i	$0.134997\pi$
$151$			124.275i			0.823011i	−0.911407	+	0.411506i	$0.865003\pi$
$152$			14.0252i			0.0922713i
$153$	95.2940			0.622836
$154$	−25.9649			−0.168603
$155$			62.3123i			0.402015i
$156$			71.8985i			0.460888i
$157$		−	273.654i		−	1.74302i	−0.490381	−	0.871508i	$-0.663142\pi$
$157$		−	273.654i		−	1.74302i	0.490381	−	0.871508i	$-0.336858\pi$
$158$			133.487i			0.844854i
$159$	−78.2193			−0.491945
$160$			43.6491i			0.272807i
$161$		−	236.891i		−	1.47137i
$162$			12.7279i			0.0785674i
$163$	210.141			1.28921			0.644605	−	0.764516i	$-0.277022\pi$
$163$	210.141			1.28921			0.644605	+	0.764516i	$0.277022\pi$
$164$	88.8021			0.541476
$165$			32.4355i			0.196579i
$166$	152.858			0.920833
$167$	−169.518			−1.01508			−0.507539	−	0.861629i	$-0.669445\pi$
$167$	−169.518			−1.01508			−0.507539	+	0.861629i	$0.669445\pi$
$168$		−	37.0611i		−	0.220602i
$169$	−261.783			−1.54901
$170$			346.624i			2.03897i
$171$	−14.8760			−0.0869942
$172$		−	13.1550i		−	0.0764828i
$173$		−	317.891i		−	1.83752i	−0.394814	−	0.918761i	$-0.629191\pi$
$173$		−	317.891i		−	1.83752i	0.394814	−	0.918761i	$-0.370809\pi$
$174$			29.0079i			0.166712i
$175$	−261.288			−1.49308
$176$		−	9.70778i		−	0.0551578i
$177$	−96.6496	+	33.1943i	−0.546043	+	0.187538i
$178$	83.0858			0.466774
$179$		−	257.362i		−	1.43778i	−0.695125	−	0.718889i	$-0.744651\pi$
$179$		−	257.362i		−	1.43778i	0.695125	−	0.718889i	$-0.255349\pi$
$180$	−46.2968			−0.257205
$181$	25.3182			0.139879			0.0699397	−	0.997551i	$-0.477719\pi$
$181$	25.3182			0.139879			0.0699397	+	0.997551i	$0.477719\pi$
$182$	222.053			1.22007
$183$		−	73.8198i		−	0.403387i
$184$	88.5690			0.481353
$185$			323.126i			1.74662i
$186$	19.7811			0.106350
$187$		−	77.0910i		−	0.412252i
$188$		−	185.464i		−	0.986509i
$189$	39.3092			0.207985
$190$		−	54.1103i		−	0.284791i
$191$		−	221.080i		−	1.15749i	−0.815510	−	0.578743i	$-0.803543\pi$
$191$		−	221.080i		−	1.15749i	0.815510	−	0.578743i	$-0.196457\pi$
$192$	13.8564			0.0721688
$193$	57.6741			0.298830			0.149415	−	0.988775i	$-0.452261\pi$
$193$	57.6741			0.298830			0.149415	+	0.988775i	$0.452261\pi$
$194$	30.0891			0.155099
$195$		−	277.389i		−	1.42251i
$196$	−16.4603			−0.0839813
$197$	−308.022			−1.56356			−0.781782	−	0.623551i	$-0.785689\pi$
$197$	−308.022			−1.56356			−0.781782	+	0.623551i	$0.785689\pi$
$198$	10.2967			0.0520033
$199$	−73.8733			−0.371223			−0.185611	−	0.982623i	$-0.559427\pi$
$199$	−73.8733			−0.371223			−0.185611	+	0.982623i	$0.559427\pi$
$200$		−	97.6905i		−	0.488452i
$201$			133.355i			0.663456i
$202$	−97.4811			−0.482580
$203$	89.5886			0.441323
$204$	110.036			0.539392
$205$	−342.604			−1.67124
$206$	129.137			0.626879
$207$			93.9416i			0.453824i
$208$			83.0213i			0.399141i
$209$			12.0344i			0.0575809i
$210$			142.984i			0.680877i
$211$		−	6.70616i		−	0.0317828i	−0.999874	−	0.0158914i	$-0.994941\pi$
$211$		−	6.70616i		−	0.0317828i	0.999874	−	0.0158914i	$-0.00505860\pi$
$212$	−90.3199			−0.426037
$213$	55.9444			0.262650
$214$			195.536i			0.913718i
$215$			50.7530i			0.236061i
$216$			14.6969i			0.0680414i
$217$		−	61.0923i		−	0.281531i
$218$	−172.559			−0.791557
$219$			206.487i			0.942863i
$220$			37.4533i			0.170242i
$221$			659.286i			2.98319i
$222$	102.576			0.462055
$223$	−38.3888			−0.172147			−0.0860735	−	0.996289i	$-0.527432\pi$
$223$	−38.3888			−0.172147			−0.0860735	+	0.996289i	$0.527432\pi$
$224$		−	42.7945i		−	0.191047i
$225$	103.616			0.460517
$226$	36.6082			0.161983
$227$			198.932i			0.876354i	0.898889	+	0.438177i	$0.144376\pi$
$227$			198.932i			0.876354i	−0.898889	+	0.438177i	$0.855624\pi$
$228$	−17.1773			−0.0753392
$229$			176.710i			0.771659i	0.922570	+	0.385830i	$0.126085\pi$
$229$			176.710i			0.771659i	−0.922570	+	0.385830i	$0.873915\pi$
$230$	−341.705			−1.48568
$231$		−	31.8004i		−	0.137664i
$232$			33.4954i			0.144377i
$233$		−	41.0416i		−	0.176144i	−0.996114	−	0.0880720i	$-0.971929\pi$
$233$		−	41.0416i		−	0.176144i	0.996114	−	0.0880720i	$-0.0280706\pi$
$234$	−88.0573			−0.376313
$235$			715.531i			3.04481i
$236$	−111.601	+	38.3295i	−0.472887	+	0.162413i
$237$	−163.487			−0.689820
$238$		−	339.838i		−	1.42789i
$239$	8.01774			0.0335470			0.0167735	−	0.999859i	$-0.494661\pi$
$239$	8.01774			0.0335470			0.0167735	+	0.999859i	$0.494661\pi$
$240$	−53.4590			−0.222746
$241$	−95.3184			−0.395512			−0.197756	−	0.980251i	$-0.563365\pi$
$241$	−95.3184			−0.395512			−0.197756	+	0.980251i	$0.563365\pi$
$242$			162.790i			0.672686i
$243$	−15.5885			−0.0641500
$244$		−	85.2398i		−	0.349343i
$245$	63.5051			0.259205
$246$			108.760i			0.442113i
$247$		−	102.919i		−	0.416675i
$248$	22.8412			0.0921016
$249$			187.212i			0.751857i
$250$			104.090i			0.416360i
$251$	58.2290			0.231988			0.115994	−	0.993250i	$-0.462995\pi$
$251$	58.2290			0.231988			0.115994	+	0.993250i	$0.462995\pi$
$252$	45.3904			0.180121
$253$	75.9970			0.300383
$254$			161.527i			0.635935i
$255$	−424.527			−1.66481
$256$	16.0000			0.0625000
$257$	277.153			1.07841			0.539207	−	0.842173i	$-0.318724\pi$
$257$	277.153			1.07841			0.539207	+	0.842173i	$0.318724\pi$
$258$	16.1116			0.0624479
$259$		−	316.799i		−	1.22316i
$260$		−	320.302i		−	1.23193i
$261$	−35.5273			−0.136120
$262$	−279.652			−1.06737
$263$	−250.510			−0.952510			−0.476255	−	0.879307i	$-0.658006\pi$
$263$	−250.510			−0.952510			−0.476255	+	0.879307i	$0.658006\pi$
$264$	11.8895			0.0450362
$265$	348.460			1.31494
$266$			53.0509i			0.199439i
$267$			101.759i			0.381119i
$268$			153.985i			0.574570i
$269$		−	475.178i		−	1.76646i	−0.468939	−	0.883231i	$-0.655363\pi$
$269$		−	475.178i		−	1.76646i	0.468939	−	0.883231i	$-0.344637\pi$
$270$		−	56.7018i		−	0.210007i
$271$	−224.434			−0.828171			−0.414085	−	0.910238i	$-0.635899\pi$
$271$	−224.434			−0.828171			−0.414085	+	0.910238i	$0.635899\pi$
$272$	127.059			0.467127
$273$			271.958i			0.996185i
$274$		−	230.619i		−	0.841675i
$275$		−	83.8237i		−	0.304814i
$276$			108.474i			0.393023i
$277$	−232.425			−0.839079			−0.419539	−	0.907737i	$-0.637808\pi$
$277$	−232.425			−0.839079			−0.419539	+	0.907737i	$0.637808\pi$
$278$		−	109.350i		−	0.393345i
$279$			24.2268i			0.0868342i
$280$			165.104i			0.589657i
$281$	46.3684			0.165012			0.0825060	−	0.996591i	$-0.473708\pi$
$281$	46.3684			0.165012			0.0825060	+	0.996591i	$0.473708\pi$
$282$	227.146			0.805481
$283$		−	190.008i		−	0.671407i	−0.941968	−	0.335703i	$-0.891026\pi$
$283$		−	190.008i		−	0.671407i	0.941968	−	0.335703i	$-0.108974\pi$
$284$	64.5990			0.227461
$285$	66.2714			0.232531
$286$			71.2367i			0.249080i
$287$	335.897			1.17037
$288$			16.9706i			0.0589256i
$289$	719.994			2.49133
$290$		−	129.228i		−	0.445613i
$291$			36.8515i			0.126638i
$292$			238.431i			0.816543i
$293$	380.760			1.29952			0.649761	−	0.760139i	$-0.274869\pi$
$293$	380.760			1.29952			0.649761	+	0.760139i	$0.274869\pi$
$294$		−	20.1597i		−	0.0685704i
$295$	430.566	−	147.878i	1.45954	−	0.501281i
$296$	118.445			0.400152
$297$			12.6108i			0.0424605i
$298$	18.0413			0.0605413
$299$	−649.929			−2.17368
$300$	119.646			0.398820
$301$		−	49.7593i		−	0.165313i
$302$	−175.751			−0.581957
$303$		−	119.389i		−	0.394025i
$304$	−19.8347			−0.0652457
$305$			328.861i			1.07823i
$306$			134.766i			0.440412i
$307$	−67.6965			−0.220510			−0.110255	−	0.993903i	$-0.535167\pi$
$307$	−67.6965			−0.220510			−0.110255	+	0.993903i	$0.535167\pi$
$308$		−	36.7200i		−	0.119221i
$309$			158.160i			0.511844i
$310$	−88.1229			−0.284268
$311$	143.194			0.460430			0.230215	−	0.973140i	$-0.426057\pi$
$311$	143.194			0.460430			0.230215	+	0.973140i	$0.426057\pi$
$312$	−101.680			−0.325897
$313$			233.140i			0.744857i	0.928061	+	0.372428i	$0.121475\pi$
$313$			233.140i			0.744857i	−0.928061	+	0.372428i	$0.878525\pi$
$314$	387.005			1.23250
$315$	−175.119			−0.555934
$316$	−188.779			−0.597402
$317$	141.408			0.446083			0.223042	−	0.974809i	$-0.428401\pi$
$317$	141.408			0.446083			0.223042	+	0.974809i	$0.428401\pi$
$318$		−	110.619i		−	0.347858i
$319$			28.7409i			0.0900968i
$320$	−61.7291			−0.192903
$321$	−239.481			−0.746048
$322$	335.015			1.04042
$323$	−157.510			−0.487649
$324$	−18.0000			−0.0555556
$325$			716.864i			2.20573i
$326$			297.185i			0.911609i
$327$		−	211.341i		−	0.646304i
$328$			125.585i			0.382881i
$329$		−	701.522i		−	2.13229i
$330$	−45.8707			−0.139002
$331$	−239.335			−0.723067			−0.361533	−	0.932359i	$-0.617747\pi$
$331$	−239.335			−0.723067			−0.361533	+	0.932359i	$0.617747\pi$
$332$			216.174i			0.651127i
$333$			125.630i			0.377267i
$334$		−	239.735i		−	0.717769i
$335$		−	594.084i		−	1.77338i
$336$	52.4123			0.155989
$337$		−	89.3149i		−	0.265029i	−0.991181	−	0.132515i	$-0.957695\pi$
$337$		−	89.3149i		−	0.265029i	0.991181	−	0.132515i	$-0.0423052\pi$
$338$		−	370.217i		−	1.09532i
$339$			44.8357i			0.132259i
$340$	−490.201			−1.44177
$341$	19.5990			0.0574750
$342$		−	21.0379i		−	0.0615142i
$343$	308.426			0.899202
$344$	18.6040			0.0540815
$345$		−	418.502i		−	1.21305i
$346$	449.566			1.29932
$347$			243.475i			0.701657i	0.936440	+	0.350829i	$0.114100\pi$
$347$			243.475i			0.701657i	−0.936440	+	0.350829i	$0.885900\pi$
$348$	−41.0233			−0.117883
$349$		−	179.758i		−	0.515065i	−0.966270	−	0.257533i	$-0.917090\pi$
$349$		−	179.758i		−	0.515065i	0.966270	−	0.257533i	$-0.0829095\pi$
$350$		−	369.517i		−	1.05576i
$351$		−	107.848i		−	0.307259i
$352$	13.7289			0.0390025
$353$			562.170i			1.59255i	0.604935	+	0.796275i	$0.293199\pi$
$353$			562.170i			1.59255i	−0.604935	+	0.796275i	$0.706801\pi$
$354$	−46.9438	−	136.683i	−0.132610	−	0.386111i
$355$	−249.227			−0.702049
$356$			117.501i			0.330059i
$357$	416.215			1.16587
$358$	363.965			1.01666
$359$	−458.013			−1.27580			−0.637901	−	0.770118i	$-0.720197\pi$
$359$	−458.013			−1.27580			−0.637901	+	0.770118i	$0.720197\pi$
$360$		−	65.4736i		−	0.181871i
$361$	−336.412			−0.931888
$362$			35.8053i			0.0989097i
$363$	−199.376			−0.549246
$364$			314.031i			0.862721i
$365$		−	919.882i		−	2.52022i
$366$	104.397			0.285238
$367$			320.619i			0.873622i	0.899553	+	0.436811i	$0.143892\pi$
$367$			320.619i			0.873622i	−0.899553	+	0.436811i	$0.856108\pi$
$368$			125.255i			0.340368i
$369$	−133.203			−0.360984
$370$	−456.969			−1.23505
$371$	−341.638			−0.920856
$372$			27.9746i			0.0752007i
$373$	517.511			1.38743			0.693714	−	0.720250i	$-0.255973\pi$
$373$	517.511			1.38743			0.693714	+	0.720250i	$0.255973\pi$
$374$	109.023			0.291506
$375$	−127.484			−0.339956
$376$	262.285			0.697567
$377$		−	245.793i		−	0.651971i
$378$			55.5916i			0.147068i
$379$	−130.956			−0.345530			−0.172765	−	0.984963i	$-0.555270\pi$
$379$	−130.956			−0.345530			−0.172765	+	0.984963i	$0.555270\pi$
$380$	76.5236			0.201378
$381$	−197.830			−0.519239
$382$	312.654			0.818466
$383$	380.323			0.993011			0.496505	−	0.868034i	$-0.334616\pi$
$383$	380.323			0.993011			0.496505	+	0.868034i	$0.334616\pi$
$384$			19.5959i			0.0510310i
$385$			141.668i			0.367969i
$386$			81.5635i			0.211304i
$387$			19.7325i			0.0509885i
$388$			42.5525i			0.109671i
$389$	−432.621			−1.11214			−0.556068	−	0.831137i	$-0.687691\pi$
$389$	−432.621			−1.11214			−0.556068	+	0.831137i	$0.687691\pi$
$390$	392.288			1.00587
$391$			994.674i			2.54392i
$392$		−	23.2784i		−	0.0593837i
$393$		−	342.502i		−	0.871506i
$394$		−	435.609i		−	1.10561i
$395$	728.323			1.84385
$396$			14.5617i			0.0367719i
$397$			438.440i			1.10438i	0.833717	+	0.552191i	$0.186208\pi$
$397$			438.440i			1.10438i	−0.833717	+	0.552191i	$0.813792\pi$
$398$		−	104.473i		−	0.262494i
$399$	−64.9738			−0.162842
$400$	138.155			0.345388
$401$			177.376i			0.442334i	0.975236	+	0.221167i	$0.0709867\pi$
$401$			177.376i			0.442334i	−0.975236	+	0.221167i	$0.929013\pi$
$402$	−188.592			−0.469134
$403$	−167.611			−0.415909
$404$		−	137.859i		−	0.341235i
$405$	69.4452			0.171470
$406$			126.697i			0.312063i
$407$	101.632			0.249710
$408$			155.614i			0.381408i
$409$		−	598.274i		−	1.46277i	−0.681963	−	0.731387i	$-0.738874\pi$
$409$		−	598.274i		−	1.46277i	0.681963	−	0.731387i	$-0.261126\pi$
$410$		−	484.516i		−	1.18175i
$411$	282.449			0.687225
$412$			182.627i			0.443270i
$413$	−422.135	+	144.982i	−1.02212	+	0.351047i
$414$	−132.853			−0.320902
$415$		−	834.015i		−	2.00968i
$416$	−117.410			−0.282235
$417$	133.926			0.321165
$418$	−17.0192			−0.0407159
$419$		−	415.349i		−	0.991287i	−0.868526	−	0.495643i	$-0.834932\pi$
$419$		−	415.349i		−	0.991287i	0.868526	−	0.495643i	$-0.165068\pi$
$420$	−202.210			−0.481453
$421$		−	102.071i		−	0.242448i	−0.992625	−	0.121224i	$-0.961318\pi$
$421$		−	102.071i		−	0.242448i	0.992625	−	0.121224i	$-0.0386819\pi$
$422$	9.48395			0.0224738
$423$			278.195i			0.657672i
$424$		−	127.732i		−	0.301254i
$425$	1097.11			2.58144
$426$			79.1173i			0.185721i
$427$		−	322.422i		−	0.755087i
$428$	−276.529			−0.646096
$429$	−87.2468			−0.203373
$430$	−71.7756			−0.166920
$431$			541.413i			1.25618i	0.778141	+	0.628090i	$0.216163\pi$
$431$			541.413i			1.25618i	−0.778141	+	0.628090i	$0.783837\pi$
$432$	−20.7846			−0.0481125
$433$	569.163			1.31446			0.657232	−	0.753688i	$-0.271727\pi$
$433$	569.163			1.31446			0.657232	+	0.753688i	$0.271727\pi$
$434$	86.3976			0.199073
$435$	158.271			0.363841
$436$		−	244.036i		−	0.559715i
$437$		−	155.275i		−	0.355321i
$438$	−292.017			−0.666705
$439$	30.3026			0.0690263			0.0345132	−	0.999404i	$-0.489012\pi$
$439$	30.3026			0.0690263			0.0345132	+	0.999404i	$0.489012\pi$
$440$	−52.9669			−0.120379
$441$	24.6905			0.0559875
$442$	−932.371			−2.10944
$443$		−	765.726i		−	1.72850i	−0.503061	−	0.864251i	$-0.667793\pi$
$443$		−	765.726i		−	1.72850i	0.503061	−	0.864251i	$-0.332207\pi$
$444$			145.065i			0.326722i
$445$		−	453.327i		−	1.01871i
$446$		−	54.2899i		−	0.121726i
$447$			22.0960i			0.0494318i
$448$	60.5205			0.135090
$449$	801.900			1.78597			0.892985	−	0.450087i	$-0.148607\pi$
$449$	801.900			1.78597			0.892985	+	0.450087i	$0.148607\pi$
$450$			146.536i			0.325635i
$451$			107.759i			0.238933i
$452$			51.7718i			0.114539i
$453$		−	215.250i		−	0.475166i
$454$	−281.333			−0.619676
$455$		−	1211.55i		−	2.66275i
$456$		−	24.2924i		−	0.0532729i
$457$			25.7788i			0.0564087i	0.999602	+	0.0282043i	$0.00897891\pi$
$457$			25.7788i			0.0564087i	−0.999602	+	0.0282043i	$0.991021\pi$
$458$	−249.906			−0.545645
$459$	−165.054			−0.359595
$460$		−	483.244i		−	1.05053i
$461$	−589.030			−1.27772			−0.638861	−	0.769322i	$-0.720594\pi$
$461$	−589.030			−1.27772			−0.638861	+	0.769322i	$0.720594\pi$
$462$	44.9726			0.0973433
$463$		−	668.771i		−	1.44443i	−0.691669	−	0.722215i	$-0.743124\pi$
$463$		−	668.771i		−	1.44443i	0.691669	−	0.722215i	$-0.256876\pi$
$464$	−47.3697			−0.102090
$465$		−	107.928i		−	0.232103i
$466$	58.0415			0.124553
$467$			294.089i			0.629741i	0.949135	+	0.314871i	$0.101961\pi$
$467$			294.089i			0.629741i	−0.949135	+	0.314871i	$0.898039\pi$
$468$		−	124.532i		−	0.266094i
$469$			582.452i			1.24190i
$470$	−1011.91			−2.15301
$471$			473.982i			1.00633i
$472$	−54.2061	−	157.828i	−0.114843	−	0.334382i
$473$	15.9633			0.0337490
$474$		−	231.206i		−	0.487777i
$475$	−171.267			−0.360561
$476$	480.603			1.00967
$477$	135.480			0.284025
$478$			11.3388i			0.0237213i
$479$	−24.8902			−0.0519629			−0.0259814	−	0.999662i	$-0.508271\pi$
$479$	−24.8902			−0.0519629			−0.0259814	+	0.999662i	$0.508271\pi$
$480$		−	75.6024i		−	0.157505i
$481$	−869.162			−1.80699
$482$		−	134.801i		−	0.279669i
$483$			410.308i			0.849499i
$484$	−230.220			−0.475661
$485$		−	164.170i		−	0.338496i
$486$		−	22.0454i		−	0.0453609i
$487$	745.105			1.52999			0.764995	−	0.644037i	$-0.222742\pi$
$487$	745.105			1.52999			0.764995	+	0.644037i	$0.222742\pi$
$488$	120.547			0.247023
$489$	−363.975			−0.744326
$490$			89.8098i			0.183285i
$491$	−896.795			−1.82647			−0.913233	−	0.407437i	$-0.866423\pi$
$491$	−896.795			−1.82647			−0.913233	+	0.407437i	$0.866423\pi$
$492$	−153.810			−0.312621
$493$	−376.170			−0.763023
$494$	145.549			0.294634
$495$		−	56.1799i		−	0.113495i
$496$			32.3023i			0.0651257i
$497$	244.348			0.491645
$498$	−264.758			−0.531643
$499$	844.318			1.69202			0.846010	−	0.533167i	$-0.178998\pi$
$499$	844.318			1.69202			0.846010	+	0.533167i	$0.178998\pi$
$500$	−147.205			−0.294411
$501$	293.614			0.586056
$502$			82.3482i			0.164040i
$503$			456.901i			0.908352i	0.890912	+	0.454176i	$0.150066\pi$
$503$			456.901i			0.908352i	−0.890912	+	0.454176i	$0.849934\pi$
$504$			64.1917i			0.127364i
$505$			531.870i			1.05321i
$506$			107.476i			0.212403i
$507$	453.422			0.894323
$508$	−228.434			−0.449674
$509$			369.383i			0.725704i	0.931847	+	0.362852i	$0.118197\pi$
$509$			369.383i			0.725704i	−0.931847	+	0.362852i	$0.881803\pi$
$510$		−	600.371i		−	1.17720i
$511$			901.871i			1.76491i
$512$			22.6274i			0.0441942i
$513$	25.7660			0.0502261
$514$			391.953i			0.762555i
$515$		−	704.589i		−	1.36813i
$516$			22.7852i			0.0441573i
$517$	225.055			0.435309
$518$	448.021			0.864906
$519$			550.604i			1.06089i
$520$	452.975			0.871106
$521$	700.980			1.34545			0.672725	−	0.739892i	$-0.265124\pi$
$521$	700.980			1.34545			0.672725	+	0.739892i	$0.265124\pi$
$522$		−	50.2431i		−	0.0962512i
$523$	65.5084			0.125255			0.0626275	−	0.998037i	$-0.480052\pi$
$523$	65.5084			0.125255			0.0626275	+	0.998037i	$0.480052\pi$
$524$		−	395.487i		−	0.754746i
$525$	452.564			0.862027
$526$		−	354.275i		−	0.673526i
$527$			256.518i			0.486752i
$528$			16.8144i			0.0318454i
$529$	−451.558			−0.853607
$530$			492.797i			0.929806i
$531$	167.402	−	57.4942i	0.315258	−	0.108275i
$532$	−75.0253			−0.141025
$533$		−	921.557i		−	1.72900i
$534$	−143.909			−0.269492
$535$	1066.87			1.99415
$536$	−217.767			−0.406282
$537$			445.764i			0.830101i
$538$	672.003			1.24908
$539$		−	19.9742i		−	0.0370578i
$540$	80.1885			0.148497
$541$		−	664.599i		−	1.22846i	−0.789126	−	0.614232i	$-0.789466\pi$
$541$		−	664.599i		−	1.22846i	0.789126	−	0.614232i	$-0.210534\pi$
$542$		−	317.398i		−	0.585605i
$543$	−43.8524			−0.0807594
$544$			179.688i			0.330309i
$545$			941.507i			1.72754i
$546$	−384.607			−0.704409
$547$	−202.532			−0.370260			−0.185130	−	0.982714i	$-0.559271\pi$
$547$	−202.532			−0.370260			−0.185130	+	0.982714i	$0.559271\pi$
$548$	326.144			0.595154
$549$			127.860i			0.232896i
$550$	118.545			0.215536
$551$	58.7227			0.106575
$552$	−153.406			−0.277909
$553$	−714.063			−1.29125
$554$		−	328.698i		−	0.593318i
$555$		−	559.670i		−	1.00841i
$556$	154.644			0.278137
$557$	−805.762			−1.44661			−0.723305	−	0.690529i	$-0.757378\pi$
$557$	−805.762			−1.44661			−0.723305	+	0.690529i	$0.757378\pi$
$558$	−34.2618			−0.0614011
$559$	−136.518			−0.244219
$560$	−233.492			−0.416950
$561$			133.526i			0.238014i
$562$			65.5748i			0.116681i
$563$			36.2162i			0.0643272i	0.999483	+	0.0321636i	$0.0102398\pi$
$563$			36.2162i			0.0643272i	−0.999483	+	0.0321636i	$0.989760\pi$
$564$			321.232i			0.569561i
$565$		−	199.739i		−	0.353521i
$566$	268.712			0.474756
$567$	−68.0856			−0.120080
$568$			91.3568i			0.160839i
$569$			657.898i			1.15624i	0.815953	+	0.578118i	$0.196213\pi$
$569$			657.898i			1.15624i	−0.815953	+	0.578118i	$0.803787\pi$
$570$			93.7219i			0.164424i
$571$		−	594.370i		−	1.04093i	−0.853884	−	0.520464i	$-0.825759\pi$
$571$		−	594.370i		−	1.04093i	0.853884	−	0.520464i	$-0.174241\pi$
$572$	−100.744			−0.176126
$573$			382.921i			0.668275i
$574$			475.029i			0.827577i
$575$			1081.54i			1.88094i
$576$	−24.0000			−0.0416667
$577$	−842.498			−1.46014			−0.730068	−	0.683375i	$-0.760512\pi$
$577$	−842.498			−1.46014			−0.730068	+	0.683375i	$0.760512\pi$
$578$			1018.22i			1.76163i
$579$	−99.8945			−0.172529
$580$	182.755			0.315096
$581$			817.686i			1.40738i
$582$	−52.1159			−0.0895462
$583$		−	109.601i		−	0.187994i
$584$	−337.192			−0.577383
$585$			480.453i			0.821287i
$586$			538.476i			0.918901i
$587$			917.410i			1.56288i	0.623981	+	0.781439i	$0.285514\pi$
$587$			917.410i			1.56288i	−0.623981	+	0.781439i	$0.714486\pi$
$588$	28.5101			0.0484866
$589$		−	40.0442i		−	0.0679867i
$590$	209.131	+	608.912i	0.354459	+	1.03205i
$591$	533.510			0.902724
$592$			167.506i			0.282950i
$593$	721.800			1.21720			0.608600	−	0.793477i	$-0.291731\pi$
$593$	721.800			1.21720			0.608600	+	0.793477i	$0.291731\pi$
$594$	−17.8343			−0.0300241
$595$	−1854.20			−3.11630
$596$			25.5143i			0.0428092i
$597$	127.952			0.214325
$598$		−	919.139i		−	1.53702i
$599$	−439.404			−0.733562			−0.366781	−	0.930307i	$-0.619540\pi$
$599$	−439.404			−0.733562			−0.366781	+	0.930307i	$0.619540\pi$
$600$			169.205i			0.282008i
$601$		−	657.294i		−	1.09367i	−0.837241	−	0.546834i	$-0.815833\pi$
$601$		−	657.294i		−	1.09367i	0.837241	−	0.546834i	$-0.184167\pi$
$602$	70.3703			0.116894
$603$		−	230.977i		−	0.383046i
$604$		−	248.549i		−	0.411506i
$605$	888.204			1.46811
$606$	168.842			0.278618
$607$	1173.83			1.93383			0.966913	−	0.255108i	$-0.0821110\pi$
$607$	1173.83			1.93383			0.966913	+	0.255108i	$0.0821110\pi$
$608$		−	28.0505i		−	0.0461357i
$609$	−155.172			−0.254798
$610$	−465.080			−0.762426
$611$	−1924.68			−3.15005
$612$	−190.588			−0.311418
$613$		−	872.138i		−	1.42274i	−0.702819	−	0.711369i	$-0.748076\pi$
$613$		−	872.138i		−	1.42274i	0.702819	−	0.711369i	$-0.251924\pi$
$614$		−	95.7373i		−	0.155924i
$615$	593.408			0.964892
$616$	51.9299			0.0843017
$617$	668.521			1.08350			0.541751	−	0.840539i	$-0.317762\pi$
$617$	668.521			1.08350			0.541751	+	0.840539i	$0.317762\pi$
$618$	−223.672			−0.361929
$619$	268.471			0.433717			0.216858	−	0.976203i	$-0.430419\pi$
$619$	268.471			0.433717			0.216858	+	0.976203i	$0.430419\pi$
$620$		−	124.625i		−	0.201008i
$621$		−	162.712i		−	0.262015i
$622$			202.506i			0.325573i
$623$			444.451i			0.713405i
$624$		−	143.797i		−	0.230444i
$625$	−295.541			−0.472866
$626$	−329.710			−0.526693
$627$		−	20.8442i		−	0.0332444i
$628$			547.307i			0.871508i
$629$			1330.20i			2.11478i
$630$		−	247.656i		−	0.393105i
$631$	754.307			1.19542			0.597708	−	0.801714i	$-0.296078\pi$
$631$	754.307			1.19542			0.597708	+	0.801714i	$0.296078\pi$
$632$		−	266.974i		−	0.422427i
$633$			11.6154i			0.0183498i
$634$			199.982i			0.315429i
$635$	881.315			1.38790
$636$	156.439			0.245973
$637$			170.820i			0.268163i
$638$	−40.6457			−0.0637081
$639$	−96.8985			−0.151641
$640$		−	87.2981i		−	0.136403i
$641$	969.139			1.51192			0.755958	−	0.654620i	$-0.227171\pi$
$641$	969.139			1.51192			0.755958	+	0.654620i	$0.227171\pi$
$642$		−	338.678i		−	0.527535i
$643$	−487.180			−0.757667			−0.378833	−	0.925465i	$-0.623675\pi$
$643$	−487.180			−0.757667			−0.378833	+	0.925465i	$0.623675\pi$
$644$			473.783i			0.735687i
$645$		−	87.9068i		−	0.136290i
$646$		−	222.753i		−	0.344820i
$647$	−54.3687			−0.0840321			−0.0420160	−	0.999117i	$-0.513378\pi$
$647$	−54.3687			−0.0840321			−0.0420160	+	0.999117i	$0.513378\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	−46.5118	−	135.425i	−0.0716668	−	0.208667i
$650$	−1013.80			−1.55969
$651$			105.815i			0.162542i
$652$	−420.282			−0.644605
$653$	367.514			0.562809			0.281404	−	0.959589i	$-0.409200\pi$
$653$	367.514			0.562809			0.281404	+	0.959589i	$0.409200\pi$
$654$	298.882			0.457006
$655$			1525.82i			2.32949i
$656$	−177.604			−0.270738
$657$		−	357.646i		−	0.544362i
$658$	992.102			1.50775
$659$		−	581.630i		−	0.882595i	−0.897361	−	0.441297i	$-0.854518\pi$
$659$		−	581.630i		−	0.882595i	0.897361	−	0.441297i	$-0.145482\pi$
$660$		−	64.8710i		−	0.0982893i
$661$	199.768			0.302222			0.151111	−	0.988517i	$-0.451715\pi$
$661$	199.768			0.302222			0.151111	+	0.988517i	$0.451715\pi$
$662$		−	338.471i		−	0.511285i
$663$		−	1141.92i		−	1.72235i
$664$	−305.717			−0.460417
$665$	289.453			0.435267
$666$	−177.667			−0.266768
$667$		−	370.832i		−	0.555970i
$668$	339.036			0.507539
$669$	66.4913			0.0993891
$670$	840.161			1.25397
$671$	103.436			0.154152
$672$			74.1222i			0.110301i
$673$			103.561i			0.153880i	0.997036	+	0.0769400i	$0.0245150\pi$
$673$			103.561i			0.153880i	−0.997036	+	0.0769400i	$0.975485\pi$
$674$	126.310			0.187404
$675$	−179.469			−0.265880
$676$	523.566			0.774506
$677$	−452.064			−0.667746			−0.333873	−	0.942618i	$-0.608356\pi$
$677$	−452.064			−0.667746			−0.333873	+	0.942618i	$0.608356\pi$
$678$	−63.4073			−0.0935211
$679$			160.956i			0.237049i
$680$		−	693.249i		−	1.01948i
$681$		−	344.561i		−	0.505963i
$682$			27.7172i			0.0406410i
$683$			604.103i			0.884485i	0.896895	+	0.442243i	$0.145817\pi$
$683$			604.103i			0.884485i	−0.896895	+	0.442243i	$0.854183\pi$
$684$	29.7520			0.0434971
$685$	−1258.29			−1.83692
$686$			436.181i			0.635832i
$687$		−	306.071i		−	0.445518i
$688$			26.3101i			0.0382414i
$689$			937.309i			1.36039i
$690$	591.851			0.857755
$691$			146.347i			0.211790i	0.994377	+	0.105895i	$0.0337707\pi$
$691$			146.347i			0.211790i	−0.994377	+	0.105895i	$0.966229\pi$
$692$			635.783i			0.918761i
$693$			55.0799i			0.0794804i
$694$	−344.326			−0.496147
$695$	−596.628			−0.858458
$696$		−	58.0158i		−	0.0833560i
$697$	−1410.38			−2.02351
$698$	254.216			0.364206
$699$			71.0861i			0.101697i
$700$	522.576			0.746538
$701$		−	429.224i		−	0.612302i	−0.951983	−	0.306151i	$-0.900959\pi$
$701$		−	429.224i		−	0.612302i	0.951983	−	0.306151i	$-0.0990413\pi$
$702$	152.520			0.217265
$703$		−	207.652i		−	0.295380i
$704$			19.4156i			0.0275789i
$705$		−	1239.34i		−	1.75792i
$706$	−795.028			−1.12610
$707$		−	521.456i		−	0.737562i
$708$	193.299	−	66.3886i	0.273021	−	0.0937692i
$709$	−948.196			−1.33737			−0.668686	−	0.743545i	$-0.733143\pi$
$709$	−948.196			−1.33737			−0.668686	+	0.743545i	$0.733143\pi$
$710$		−	352.461i		−	0.496424i
$711$	283.169			0.398268
$712$	−166.172			−0.233387
$713$	−252.878			−0.354667
$714$			588.616i			0.824393i
$715$	388.677			0.543604
$716$			514.724i			0.718889i
$717$	−13.8871			−0.0193684
$718$		−	647.728i		−	0.902129i
$719$		−	841.219i		−	1.16998i	−0.811039	−	0.584992i	$-0.801098\pi$
$719$		−	841.219i		−	1.16998i	0.811039	−	0.584992i	$-0.198902\pi$
$720$	92.5937			0.128602
$721$			690.794i			0.958105i
$722$		−	475.758i		−	0.658944i
$723$	165.096			0.228349
$724$	−50.6363			−0.0699397
$725$	−409.023			−0.564169
$726$		−	281.961i		−	0.388376i
$727$	1330.58			1.83023			0.915116	−	0.403190i	$-0.132099\pi$
$727$	1330.58			1.83023			0.915116	+	0.403190i	$0.132099\pi$
$728$	−444.106			−0.610036
$729$	27.0000			0.0370370
$730$	1300.91			1.78207
$731$			208.933i			0.285817i
$732$			147.640i			0.201693i
$733$	−908.813			−1.23985			−0.619927	−	0.784660i	$-0.712838\pi$
$733$	−908.813			−1.23985			−0.619927	+	0.784660i	$0.712838\pi$
$734$	−453.424			−0.617744
$735$	−109.994			−0.149652
$736$	−177.138			−0.240677
$737$	−186.856			−0.253536
$738$		−	188.378i		−	0.255254i
$739$		−	91.6635i		−	0.124037i	−0.998075	−	0.0620186i	$-0.980246\pi$
$739$		−	91.6635i		−	0.124037i	0.998075	−	0.0620186i	$-0.0197538\pi$
$740$		−	646.251i		−	0.873312i
$741$			178.261i			0.240568i
$742$		−	483.149i		−	0.651144i
$743$	342.901			0.461509			0.230754	−	0.973012i	$-0.425881\pi$
$743$	342.901			0.461509			0.230754	+	0.973012i	$0.425881\pi$
$744$	−39.5621			−0.0531749
$745$		−	98.4358i		−	0.132129i
$746$			731.871i			0.981060i
$747$		−	324.261i		−	0.434085i
$748$			154.182i			0.206126i
$749$	−1045.98			−1.39650
$750$		−	180.289i		−	0.240385i
$751$			395.722i			0.526927i	0.964669	+	0.263463i	$0.0848648\pi$
$751$			395.722i			0.526927i	−0.964669	+	0.263463i	$0.915135\pi$
$752$			370.927i			0.493254i
$753$	−100.856			−0.133938
$754$	347.604			0.461013
$755$			958.921i			1.27009i
$756$	−78.6184			−0.103993
$757$	271.976			0.359282			0.179641	−	0.983732i	$-0.442506\pi$
$757$	271.976			0.359282			0.179641	+	0.983732i	$0.442506\pi$
$758$		−	185.200i		−	0.244327i
$759$	−131.631			−0.173426
$760$			108.221i			0.142396i
$761$	−239.313			−0.314472			−0.157236	−	0.987561i	$-0.550258\pi$
$761$	−239.313			−0.314472			−0.157236	+	0.987561i	$0.550258\pi$
$762$		−	279.774i		−	0.367157i
$763$		−	923.073i		−	1.20979i
$764$			442.160i			0.578743i
$765$	735.302			0.961179
$766$			537.858i			0.702165i
$767$	397.770	+	1158.16i	0.518605	+	1.50999i
$768$	−27.7128			−0.0360844
$769$		−	901.993i		−	1.17294i	−0.809970	−	0.586472i	$-0.800517\pi$
$769$		−	901.993i		−	1.17294i	0.809970	−	0.586472i	$-0.199483\pi$
$770$	−200.349			−0.260194
$771$	−480.042			−0.622623
$772$	−115.348			−0.149415
$773$			267.398i			0.345923i	0.984929	+	0.172961i	$0.0553336\pi$
$773$			267.398i			0.345923i	−0.984929	+	0.172961i	$0.944666\pi$
$774$	−27.9060			−0.0360543
$775$			278.921i			0.359898i
$776$	−60.1783			−0.0775493
$777$			548.712i			0.706193i
$778$		−	611.819i		−	0.786399i
$779$	220.170			0.282632
$780$			554.779i			0.711255i
$781$			78.3891i			0.100370i
$782$	−1406.68			−1.79883
$783$	61.5350			0.0785888
$784$	32.9207			0.0419906
$785$		−	2111.55i		−	2.68987i
$786$	484.371			0.616248
$787$	129.107			0.164050			0.0820249	−	0.996630i	$-0.473861\pi$
$787$	129.107			0.164050			0.0820249	+	0.996630i	$0.473861\pi$
$788$	616.044			0.781782
$789$	433.896			0.549932
$790$			1030.00i			1.30380i
$791$			195.829i			0.247571i
$792$	−20.5933			−0.0260016
$793$	−884.589			−1.11550
$794$	−620.048			−0.780917
$795$	−603.551			−0.759184
$796$	147.747			0.185611
$797$		−	268.793i		−	0.337256i	−0.985680	−	0.168628i	$-0.946066\pi$
$797$		−	268.793i		−	0.337256i	0.985680	−	0.168628i	$-0.0539337\pi$
$798$		−	91.8869i		−	0.115146i
$799$			2945.59i			3.68660i
$800$			195.381i			0.244226i
$801$		−	176.252i		−	0.220039i
$802$	−250.848			−0.312778
$803$	−289.329			−0.360310
$804$		−	266.709i		−	0.331728i
$805$		−	1827.89i		−	2.27067i
$806$		−	237.038i		−	0.294092i
$807$			823.033i			1.01987i
$808$	194.962			0.241290
$809$		−	344.470i		−	0.425797i	−0.977074	−	0.212899i	$-0.931710\pi$
$809$		−	344.470i		−	0.425797i	0.977074	−	0.212899i	$-0.0682904\pi$
$810$			98.2104i			0.121247i
$811$		−	86.1187i		−	0.106188i	−0.998590	−	0.0530942i	$-0.983092\pi$
$811$		−	86.1187i		−	0.106188i	0.998590	−	0.0530942i	$-0.0169083\pi$
$812$	−179.177			−0.220662
$813$	388.732			0.478145
$814$			143.730i			0.176572i
$815$	1621.48			1.98954
$816$	−220.072			−0.269696
$817$		−	32.6157i		−	0.0399213i
$818$	846.088			1.03434
$819$		−	471.046i		−	0.575147i
$820$	685.209			0.835621
$821$			1450.65i			1.76693i	0.468500	+	0.883463i	$0.344794\pi$
$821$			1450.65i			1.76693i	−0.468500	+	0.883463i	$0.655206\pi$
$822$			399.444i			0.485941i
$823$		−	1600.34i		−	1.94451i	−0.233915	−	0.972257i	$-0.575154\pi$
$823$		−	1600.34i		−	1.94451i	0.233915	−	0.972257i	$-0.424846\pi$
$824$	−258.274			−0.313439
$825$			145.187i			0.175984i
$826$	−205.036	−	596.990i	−0.248228	−	0.722748i
$827$	140.513			0.169907			0.0849535	−	0.996385i	$-0.472926\pi$
$827$	140.513			0.169907			0.0849535	+	0.996385i	$0.472926\pi$
$828$		−	187.883i		−	0.226912i
$829$	1350.26			1.62878			0.814392	−	0.580315i	$-0.197071\pi$
$829$	1350.26			1.62878			0.814392	+	0.580315i	$0.197071\pi$
$830$	1179.48			1.42106
$831$	402.572			0.484442
$832$		−	166.043i		−	0.199570i
$833$	261.428			0.313840
$834$			189.400i			0.227098i
$835$	−1308.03			−1.56650
$836$		−	24.0688i		−	0.0287905i
$837$		−	41.9620i		−	0.0501338i
$838$	587.392			0.700946
$839$		−	102.717i		−	0.122428i	−0.998125	−	0.0612142i	$-0.980503\pi$
$839$		−	102.717i		−	0.122428i	0.998125	−	0.0612142i	$-0.0194973\pi$
$840$		−	285.968i		−	0.340439i
$841$	−700.757			−0.833243
$842$	144.350			0.171437
$843$	−80.3124			−0.0952698
$844$			13.4123i			0.0158914i
$845$	−2019.95			−2.39048
$846$	−393.428			−0.465045
$847$	−870.814			−1.02812
$848$	180.640			0.213019
$849$			329.104i			0.387637i
$850$			1551.55i			1.82536i
$851$	−1311.32			−1.54091
$852$	−111.889			−0.131325
$853$	−582.081			−0.682393			−0.341197	−	0.939992i	$-0.610832\pi$
$853$	−582.081			−0.682393			−0.341197	+	0.939992i	$0.610832\pi$
$854$	455.974			0.533927
$855$	−114.785			−0.134252
$856$		−	391.071i		−	0.456859i
$857$			781.711i			0.912148i	0.889942	+	0.456074i	$0.150745\pi$
$857$			781.711i			0.912148i	−0.889942	+	0.456074i	$0.849255\pi$
$858$		−	123.386i		−	0.143806i
$859$			1068.99i			1.24446i	0.782834	+	0.622231i	$0.213773\pi$
$859$			1068.99i			1.24446i	−0.782834	+	0.622231i	$0.786227\pi$
$860$		−	101.506i		−	0.118030i
$861$	−581.790			−0.675714
$862$	−765.674			−0.888253
$863$		−	987.568i		−	1.14434i	−0.820134	−	0.572172i	$-0.806101\pi$
$863$		−	987.568i		−	1.14434i	0.820134	−	0.572172i	$-0.193899\pi$
$864$		−	29.3939i		−	0.0340207i
$865$		−	2452.89i		−	2.83571i
$866$			804.918i			0.929467i
$867$	−1247.07			−1.43837
$868$			122.185i			0.140766i
$869$		−	229.078i		−	0.263611i
$870$			223.829i			0.257275i
$871$	1598.00			1.83467
$872$	345.119			0.395779
$873$		−	63.8287i		−	0.0731142i
$874$	219.592			0.251250
$875$	−556.809			−0.636353
$876$		−	412.974i		−	0.471431i
$877$	−518.873			−0.591645			−0.295823	−	0.955243i	$-0.595594\pi$
$877$	−518.873			−0.591645			−0.295823	+	0.955243i	$0.595594\pi$
$878$			42.8543i			0.0488090i
$879$	−659.495			−0.750279
$880$		−	74.9065i		−	0.0851211i
$881$			638.669i			0.724937i	0.931996	+	0.362468i	$0.118066\pi$
$881$			638.669i			0.724937i	−0.931996	+	0.362468i	$0.881934\pi$
$882$			34.9176i			0.0395892i
$883$	1237.73			1.40173			0.700866	−	0.713293i	$-0.252797\pi$
$883$	1237.73			1.40173			0.700866	+	0.713293i	$0.252797\pi$
$884$		−	1318.57i		−	1.49160i
$885$	−745.761	+	256.132i	−0.842668	+	0.289415i
$886$	1082.90			1.22224
$887$		−	756.022i		−	0.852336i	−0.904644	−	0.426168i	$-0.859863\pi$
$887$		−	756.022i		−	0.852336i	0.904644	−	0.426168i	$-0.140137\pi$
$888$	−205.153			−0.231028
$889$	−864.060			−0.971946
$890$	641.101			0.720338
$891$		−	21.8425i		−	0.0245146i
$892$	76.7775			0.0860735
$893$		−	459.827i		−	0.514923i
$894$	−31.2485			−0.0349535
$895$		−	1985.84i		−	2.21882i
$896$			85.5889i			0.0955233i
$897$	1125.71			1.25497
$898$			1134.06i			1.26287i
$899$		−	95.6344i		−	0.106379i
$900$	−207.233			−0.230259
$901$	1434.49			1.59211
$902$	−152.394			−0.168951
$903$			86.1857i			0.0954437i
$904$	−73.2164			−0.0809916
$905$	195.359			0.215866
$906$	304.410			0.335993
$907$	−810.443			−0.893542			−0.446771	−	0.894648i	$-0.647426\pi$
$907$	−810.443			−0.893542			−0.446771	+	0.894648i	$0.647426\pi$
$908$		−	397.865i		−	0.438177i
$909$			206.789i			0.227490i
$910$	1713.39			1.88285
$911$	1138.70			1.24995			0.624974	−	0.780646i	$-0.285110\pi$
$911$	1138.70			1.24995			0.624974	+	0.780646i	$0.285110\pi$
$912$	34.3547			0.0376696
$913$	−262.321			−0.287318
$914$	−36.4567			−0.0398870
$915$		−	569.604i		−	0.622518i
$916$		−	353.420i		−	0.385830i
$917$		−	1495.94i		−	1.63134i
$918$		−	233.422i		−	0.254272i
$919$		−	237.117i		−	0.258016i	−0.991644	−	0.129008i	$-0.958821\pi$
$919$		−	237.117i		−	0.258016i	0.991644	−	0.129008i	$-0.0411793\pi$
$920$	683.411			0.742838
$921$	117.254			0.127311
$922$		−	833.014i		−	0.903486i
$923$		−	670.386i		−	0.726312i
$924$			63.6008i			0.0688321i
$925$			1446.37i			1.56364i
$926$	945.785			1.02137
$927$		−	273.941i		−	0.295513i
$928$		−	66.9908i		−	0.0721884i
$929$		−	259.206i		−	0.279016i	−0.990221	−	0.139508i	$-0.955448\pi$
$929$		−	259.206i		−	0.279016i	0.990221	−	0.139508i	$-0.0445521\pi$
$930$	152.633			0.164122
$931$	−40.8107			−0.0438353
$932$			82.0831i			0.0880720i
$933$	−248.019			−0.265829
$934$	−415.905			−0.445294
$935$		−	594.845i		−	0.636198i
$936$	176.115			0.188157
$937$			324.007i			0.345792i	0.984940	+	0.172896i	$0.0553124\pi$
$937$			324.007i			0.345792i	−0.984940	+	0.172896i	$0.944688\pi$
$938$	−823.711			−0.878157
$939$		−	403.811i		−	0.430043i
$940$		−	1431.06i		−	1.52241i
$941$		−	299.570i		−	0.318353i	−0.987250	−	0.159176i	$-0.949116\pi$
$941$		−	299.570i		−	0.318353i	0.987250	−	0.159176i	$-0.0508838\pi$
$942$	−670.312			−0.711583
$943$		−	1390.37i		−	1.47441i
$944$	223.203	−	76.6590i	0.236443	−	0.0812065i
$945$	303.315			0.320969
$946$			22.5755i			0.0238641i
$947$	1191.15			1.25782			0.628909	−	0.777479i	$-0.283502\pi$
$947$	1191.15			1.25782			0.628909	+	0.777479i	$0.283502\pi$
$948$	326.975			0.344910
$949$	2474.35			2.60732
$950$		−	242.207i		−	0.254955i
$951$	−244.927			−0.257546
$952$			679.676i			0.713945i
$953$	−342.984			−0.359899			−0.179950	−	0.983676i	$-0.557593\pi$
$953$	−342.984			−0.359899			−0.179950	+	0.983676i	$0.557593\pi$
$954$			191.597i			0.200836i
$955$		−	1705.88i		−	1.78626i
$956$	−16.0355			−0.0167735
$957$		−	49.7807i		−	0.0520174i
$958$		−	35.2001i		−	0.0367433i
$959$	1233.65			1.28639
$960$	106.918			0.111373
$961$	895.785			0.932138
$962$		−	1229.18i		−	1.27773i
$963$	414.794			0.430731
$964$	190.637			0.197756
$965$	445.022			0.461162
$966$	−580.263			−0.600686
$967$			826.131i			0.854324i	0.904175	+	0.427162i	$0.140487\pi$
$967$			826.131i			0.854324i	−0.904175	+	0.427162i	$0.859513\pi$
$968$		−	325.580i		−	0.336343i
$969$	272.816			0.281544
$970$	232.172			0.239353
$971$	−124.784			−0.128511			−0.0642555	−	0.997933i	$-0.520467\pi$
$971$	−124.784			−0.128511			−0.0642555	+	0.997933i	$0.520467\pi$
$972$	31.1769			0.0320750
$973$	584.947			0.601178
$974$			1053.74i			1.08187i
$975$		−	1241.64i		−	1.27348i
$976$			170.480i			0.174672i
$977$			980.254i			1.00333i	0.865062	+	0.501665i	$0.167279\pi$
$977$			980.254i			1.00333i	−0.865062	+	0.501665i	$0.832721\pi$
$978$		−	514.739i		−	0.526318i
$979$	−142.584			−0.145643
$980$	−127.010			−0.129602
$981$			366.054i			0.373144i
$982$		−	1268.26i		−	1.29151i
$983$			1676.08i			1.70507i	0.522673	+	0.852533i	$0.324935\pi$
$983$			1676.08i			1.70507i	−0.522673	+	0.852533i	$0.675065\pi$
$984$		−	217.520i		−	0.221057i
$985$	−2376.74			−2.41294
$986$		−	531.985i		−	0.539539i
$987$			1215.07i			1.23108i
$988$			205.838i			0.208338i
$989$	−205.967			−0.208258
$990$	79.4504			0.0802529
$991$			122.726i			0.123840i	0.998081	+	0.0619201i	$0.0197224\pi$
$991$			122.726i			0.123840i	−0.998081	+	0.0619201i	$0.980278\pi$
$992$	−45.6824			−0.0460508
$993$	414.540			0.417463
$994$			345.560i			0.347646i
$995$	−570.017			−0.572881
$996$		−	374.425i		−	0.375929i
$997$	833.148			0.835655			0.417828	−	0.908526i	$-0.362792\pi$
$997$	833.148			0.835655			0.417828	+	0.908526i	$0.362792\pi$
$998$			1194.05i			1.19644i
$999$		−	217.597i		−	0.217815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.15	yes	20
3.2	odd	2		1062.3.d.f.235.2		20
59.58	odd	2	inner	354.3.d.a.235.5	✓	20
177.176	even	2		1062.3.d.f.235.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.5	✓	20	59.58	odd	2	inner
354.3.d.a.235.15	yes	20	1.1	even	1	trivial
1062.3.d.f.235.2		20	3.2	odd	2
1062.3.d.f.235.12		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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +7.71614 q^{5} -2.44949i q^{6} -7.56506 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205 q^{3} -2.00000 q^{4} +7.71614 q^{5} -2.44949i q^{6} -7.56506 q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.9123i q^{10} -2.42694i q^{11} +3.46410 q^{12} +20.7553i q^{13} -10.6986i q^{14} -13.3647 q^{15} +4.00000 q^{16} +31.7647 q^{17} +4.24264i q^{18} -4.95867 q^{19} -15.4323 q^{20} +13.1031 q^{21} +3.43222 q^{22} +31.3139i q^{23} +4.89898i q^{24} +34.5388 q^{25} -29.3524 q^{26} -5.19615 q^{27} +15.1301 q^{28} -11.8424 q^{29} -18.9006i q^{30} +8.07558i q^{31} +5.65685i q^{32} +4.20359i q^{33} +44.9220i q^{34} -58.3731 q^{35} -6.00000 q^{36} +41.8766i q^{37} -7.01262i q^{38} -35.9493i q^{39} -21.8245i q^{40} -44.4010 q^{41} +18.5305i q^{42} +6.57752i q^{43} +4.85389i q^{44} +23.1484 q^{45} -44.2845 q^{46} +92.7318i q^{47} -6.92820 q^{48} +8.23017 q^{49} +48.8452i q^{50} -55.0180 q^{51} -41.5106i q^{52} +45.1599 q^{53} -7.34847i q^{54} -18.7266i q^{55} +21.3972i q^{56} +8.58867 q^{57} -16.7477i q^{58} +(55.8007 - 19.1647i) q^{59} +26.7295 q^{60} +42.6199i q^{61} -11.4206 q^{62} -22.6952 q^{63} -8.00000 q^{64} +160.151i q^{65} -5.94477 q^{66} -76.9923i q^{67} -63.5293 q^{68} -54.2372i q^{69} -82.5520i q^{70} -32.2995 q^{71} -8.48528i q^{72} -119.215i q^{73} -59.2224 q^{74} -59.8230 q^{75} +9.91734 q^{76} +18.3600i q^{77} +50.8399 q^{78} +94.3895 q^{79} +30.8646 q^{80} +9.00000 q^{81} -62.7925i q^{82} -108.087i q^{83} -26.2061 q^{84} +245.101 q^{85} -9.30201 q^{86} +20.5117 q^{87} -6.86443 q^{88} -58.7505i q^{89} +32.7368i q^{90} -157.015i q^{91} -62.6277i q^{92} -13.9873i q^{93} -131.143 q^{94} -38.2618 q^{95} -9.79796i q^{96} -21.2762i q^{97} +11.6392i q^{98} -7.28083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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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