LMFDB - Embedded newform 354.3.d.a.235.20

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			235.20
Root			$7.74549 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	354.235
Dual form			354.3.d.a.235.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +7.74549 q^{5} +2.44949i q^{6} +7.40466 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +7.74549 q^{5} +2.44949i q^{6} +7.40466 q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.9538i q^{10} -4.00447i q^{11} -3.46410 q^{12} -19.5586i q^{13} +10.4718i q^{14} +13.4156 q^{15} +4.00000 q^{16} +8.82813 q^{17} +4.24264i q^{18} -29.4750 q^{19} -15.4910 q^{20} +12.8252 q^{21} +5.66318 q^{22} -1.24447i q^{23} -4.89898i q^{24} +34.9926 q^{25} +27.6601 q^{26} +5.19615 q^{27} -14.8093 q^{28} -25.5288 q^{29} +18.9725i q^{30} -4.73284i q^{31} +5.65685i q^{32} -6.93595i q^{33} +12.4849i q^{34} +57.3527 q^{35} -6.00000 q^{36} +58.2356i q^{37} -41.6840i q^{38} -33.8765i q^{39} -21.9075i q^{40} +31.1751 q^{41} +18.1376i q^{42} +80.6621i q^{43} +8.00894i q^{44} +23.2365 q^{45} +1.75994 q^{46} +34.4873i q^{47} +6.92820 q^{48} +5.82899 q^{49} +49.4869i q^{50} +15.2908 q^{51} +39.1172i q^{52} -44.0290 q^{53} +7.34847i q^{54} -31.0166i q^{55} -20.9435i q^{56} -51.0522 q^{57} -36.1031i q^{58} +(-33.7393 - 48.4011i) q^{59} -26.8312 q^{60} +37.8344i q^{61} +6.69325 q^{62} +22.2140 q^{63} -8.00000 q^{64} -151.491i q^{65} +9.80891 q^{66} +32.0552i q^{67} -17.6563 q^{68} -2.15548i q^{69} +81.1090i q^{70} -117.363 q^{71} -8.48528i q^{72} +24.0627i q^{73} -82.3576 q^{74} +60.6089 q^{75} +58.9501 q^{76} -29.6518i q^{77} +47.9086 q^{78} +112.119 q^{79} +30.9819 q^{80} +9.00000 q^{81} +44.0883i q^{82} +151.334i q^{83} -25.6505 q^{84} +68.3782 q^{85} -114.073 q^{86} -44.2171 q^{87} -11.3264 q^{88} -66.5946i q^{89} +32.8613i q^{90} -144.825i q^{91} +2.48893i q^{92} -8.19753i q^{93} -48.7724 q^{94} -228.298 q^{95} +9.79796i q^{96} -97.4651i q^{97} +8.24343i q^{98} -12.0134i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	7.74549			1.54910			0.774549	−	0.632514i	$-0.217977\pi$
$5$	7.74549			1.54910			0.774549	+	0.632514i	$0.217977\pi$
$6$			2.44949i			0.408248i
$7$	7.40466			1.05781			0.528904	−	0.848681i	$-0.322603\pi$
$7$	7.40466			1.05781			0.528904	+	0.848681i	$0.322603\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000			0.333333
$10$			10.9538i			1.09538i
$11$		−	4.00447i		−	0.364043i	−0.983295	−	0.182021i	$-0.941736\pi$
$11$		−	4.00447i		−	0.364043i	0.983295	−	0.182021i	$-0.0582640\pi$
$12$	−3.46410			−0.288675
$13$		−	19.5586i		−	1.50451i	−0.658872	−	0.752255i	$-0.728966\pi$
$13$		−	19.5586i		−	1.50451i	0.658872	−	0.752255i	$-0.271034\pi$
$14$			10.4718i			0.747984i
$15$	13.4156			0.894372
$16$	4.00000			0.250000
$17$	8.82813			0.519302			0.259651	−	0.965703i	$-0.416393\pi$
$17$	8.82813			0.519302			0.259651	+	0.965703i	$0.416393\pi$
$18$			4.24264i			0.235702i
$19$	−29.4750			−1.55132			−0.775659	−	0.631153i	$-0.782582\pi$
$19$	−29.4750			−1.55132			−0.775659	+	0.631153i	$0.782582\pi$
$20$	−15.4910			−0.774549
$21$	12.8252			0.610726
$22$	5.66318			0.257417
$23$		−	1.24447i		−	0.0541072i	−0.999634	−	0.0270536i	$-0.991388\pi$
$23$		−	1.24447i		−	0.0541072i	0.999634	−	0.0270536i	$-0.00861249\pi$
$24$		−	4.89898i		−	0.204124i
$25$	34.9926			1.39970
$26$	27.6601			1.06385
$27$	5.19615			0.192450
$28$	−14.8093			−0.528904
$29$	−25.5288			−0.880303			−0.440151	−	0.897924i	$-0.645075\pi$
$29$	−25.5288			−0.880303			−0.440151	+	0.897924i	$0.645075\pi$
$30$			18.9725i			0.632416i
$31$		−	4.73284i		−	0.152672i	−0.997082	−	0.0763362i	$-0.975678\pi$
$31$		−	4.73284i		−	0.152672i	0.997082	−	0.0763362i	$-0.0243222\pi$
$32$			5.65685i			0.176777i
$33$		−	6.93595i		−	0.210180i
$34$			12.4849i			0.367202i
$35$	57.3527			1.63865
$36$	−6.00000			−0.166667
$37$			58.2356i			1.57394i	0.616994	+	0.786968i	$0.288350\pi$
$37$			58.2356i			1.57394i	−0.616994	+	0.786968i	$0.711650\pi$
$38$		−	41.6840i		−	1.09695i
$39$		−	33.8765i		−	0.868629i
$40$		−	21.9075i		−	0.547689i
$41$	31.1751			0.760368			0.380184	−	0.924911i	$-0.375861\pi$
$41$	31.1751			0.760368			0.380184	+	0.924911i	$0.375861\pi$
$42$			18.1376i			0.431849i
$43$			80.6621i			1.87586i	0.346821	+	0.937931i	$0.387261\pi$
$43$			80.6621i			1.87586i	−0.346821	+	0.937931i	$0.612739\pi$
$44$			8.00894i			0.182021i
$45$	23.2365			0.516366
$46$	1.75994			0.0382596
$47$			34.4873i			0.733772i	0.930266	+	0.366886i	$0.119576\pi$
$47$			34.4873i			0.733772i	−0.930266	+	0.366886i	$0.880424\pi$
$48$	6.92820			0.144338
$49$	5.82899			0.118959
$50$			49.4869i			0.989739i
$51$	15.2908			0.299819
$52$			39.1172i			0.752255i
$53$	−44.0290			−0.830737			−0.415368	−	0.909653i	$-0.636347\pi$
$53$	−44.0290			−0.830737			−0.415368	+	0.909653i	$0.636347\pi$
$54$			7.34847i			0.136083i
$55$		−	31.0166i		−	0.563938i
$56$		−	20.9435i		−	0.373992i
$57$	−51.0522			−0.895653
$58$		−	36.1031i		−	0.622468i
$59$	−33.7393	−	48.4011i	−0.571852	−	0.820357i
$59$	−33.7393	−	48.4011i	−0.571852	−	0.820357i
$60$	−26.8312			−0.447186
$61$			37.8344i			0.620236i	0.950698	+	0.310118i	$0.100369\pi$
$61$			37.8344i			0.620236i	−0.950698	+	0.310118i	$0.899631\pi$
$62$	6.69325			0.107956
$63$	22.2140			0.352603
$64$	−8.00000			−0.125000
$65$		−	151.491i		−	2.33063i
$66$	9.80891			0.148620
$67$			32.0552i			0.478436i	0.970966	+	0.239218i	$0.0768911\pi$
$67$			32.0552i			0.478436i	−0.970966	+	0.239218i	$0.923109\pi$
$68$	−17.6563			−0.259651
$69$		−	2.15548i		−	0.0312388i
$70$			81.1090i			1.15870i
$71$	−117.363			−1.65300			−0.826499	−	0.562938i	$-0.809671\pi$
$71$	−117.363			−1.65300			−0.826499	+	0.562938i	$0.809671\pi$
$72$		−	8.48528i		−	0.117851i
$73$			24.0627i			0.329626i	0.986325	+	0.164813i	$0.0527020\pi$
$73$			24.0627i			0.329626i	−0.986325	+	0.164813i	$0.947298\pi$
$74$	−82.3576			−1.11294
$75$	60.6089			0.808118
$76$	58.9501			0.775659
$77$		−	29.6518i		−	0.385088i
$78$	47.9086			0.614213
$79$	112.119			1.41923			0.709614	−	0.704590i	$-0.248869\pi$
$79$	112.119			1.41923			0.709614	+	0.704590i	$0.248869\pi$
$80$	30.9819			0.387274
$81$	9.00000			0.111111
$82$			44.0883i			0.537662i
$83$			151.334i			1.82330i	0.410968	+	0.911650i	$0.365191\pi$
$83$			151.334i			1.82330i	−0.410968	+	0.911650i	$0.634809\pi$
$84$	−25.6505			−0.305363
$85$	68.3782			0.804449
$86$	−114.073			−1.32644
$87$	−44.2171			−0.508243
$88$	−11.3264			−0.128709
$89$		−	66.5946i		−	0.748253i	−0.927378	−	0.374127i	$-0.877942\pi$
$89$		−	66.5946i		−	0.748253i	0.927378	−	0.374127i	$-0.122058\pi$
$90$			32.8613i			0.365126i
$91$		−	144.825i		−	1.59148i
$92$			2.48893i			0.0270536i
$93$		−	8.19753i		−	0.0881455i
$94$	−48.7724			−0.518855
$95$	−228.298			−2.40314
$96$			9.79796i			0.102062i
$97$		−	97.4651i		−	1.00479i	−0.864637	−	0.502397i	$-0.832452\pi$
$97$		−	97.4651i		−	1.00479i	0.864637	−	0.502397i	$-0.167548\pi$
$98$			8.24343i			0.0841167i
$99$		−	12.0134i		−	0.121348i
$100$	−69.9851			−0.699851
$101$		−	98.6578i		−	0.976810i	−0.872617	−	0.488405i	$-0.837579\pi$
$101$		−	98.6578i		−	0.976810i	0.872617	−	0.488405i	$-0.162421\pi$
$102$			21.6244i			0.212004i
$103$			7.05381i			0.0684836i	0.999414	+	0.0342418i	$0.0109016\pi$
$103$			7.05381i			0.0684836i	−0.999414	+	0.0342418i	$0.989098\pi$
$104$	−55.3201			−0.531924
$105$	99.3378			0.946074
$106$		−	62.2665i		−	0.587419i
$107$	57.4186			0.536622			0.268311	−	0.963332i	$-0.413534\pi$
$107$	57.4186			0.536622			0.268311	+	0.963332i	$0.413534\pi$
$108$	−10.3923			−0.0962250
$109$			138.622i			1.27176i	0.771788	+	0.635880i	$0.219363\pi$
$109$			138.622i			1.27176i	−0.771788	+	0.635880i	$0.780637\pi$
$110$	43.8641			0.398764
$111$			100.867i			0.908713i
$112$	29.6186			0.264452
$113$		−	209.920i		−	1.85770i	−0.370462	−	0.928848i	$-0.620801\pi$
$113$		−	209.920i		−	1.85770i	0.370462	−	0.928848i	$-0.379199\pi$
$114$		−	72.1988i		−	0.633323i
$115$		−	9.63900i		−	0.0838174i
$116$	51.0576			0.440151
$117$		−	58.6759i		−	0.501503i
$118$	68.4494	−	47.7145i	0.580080	−	0.404360i
$119$	65.3693			0.549322
$120$		−	37.9450i		−	0.316208i
$121$	104.964			0.867473
$122$	−53.5059			−0.438573
$123$	53.9969			0.438999
$124$			9.46569i			0.0763362i
$125$	77.3972			0.619177
$126$			31.4153i			0.249328i
$127$	−190.451			−1.49961			−0.749807	−	0.661657i	$-0.769854\pi$
$127$	−190.451			−1.49961			−0.749807	+	0.661657i	$0.769854\pi$
$128$		−	11.3137i		−	0.0883883i
$129$			139.711i			1.08303i
$130$	214.241			1.64801
$131$		−	235.226i		−	1.79562i	−0.440383	−	0.897810i	$-0.645157\pi$
$131$		−	235.226i		−	1.79562i	0.440383	−	0.897810i	$-0.354843\pi$
$132$			13.8719i			0.105090i
$133$	−218.253			−1.64100
$134$	−45.3329			−0.338305
$135$	40.2467			0.298124
$136$		−	24.9697i		−	0.183601i
$137$	2.22930			0.0162723			0.00813614	−	0.999967i	$-0.497410\pi$
$137$	2.22930			0.0162723			0.00813614	+	0.999967i	$0.497410\pi$
$138$	3.04831			0.0220892
$139$	−113.790			−0.818631			−0.409316	−	0.912393i	$-0.634232\pi$
$139$	−113.790			−0.818631			−0.409316	+	0.912393i	$0.634232\pi$
$140$	−114.705			−0.819324
$141$			59.7337i			0.423643i
$142$		−	165.976i		−	1.16885i
$143$	−78.3220			−0.547706
$144$	12.0000			0.0833333
$145$	−197.733			−1.36367
$146$	−34.0297			−0.233080
$147$	10.0961			0.0686810
$148$		−	116.471i		−	0.786968i
$149$		−	57.5687i		−	0.386367i	−0.981163	−	0.193184i	$-0.938119\pi$
$149$		−	57.5687i		−	0.386367i	0.981163	−	0.193184i	$-0.0618813\pi$
$150$			85.7139i			0.571426i
$151$		−	24.9883i		−	0.165485i	−0.996571	−	0.0827426i	$-0.973632\pi$
$151$		−	24.9883i		−	0.165485i	0.996571	−	0.0827426i	$-0.0263679\pi$
$152$			83.3680i			0.548473i
$153$	26.4844			0.173101
$154$	41.9339			0.272298
$155$		−	36.6582i		−	0.236504i
$156$			67.7531i			0.434314i
$157$			114.433i			0.728872i	0.931228	+	0.364436i	$0.118738\pi$
$157$			114.433i			0.728872i	−0.931228	+	0.364436i	$0.881262\pi$
$158$			158.560i			1.00355i
$159$	−76.2605			−0.479626
$160$			43.8151i			0.273844i
$161$		−	9.21485i		−	0.0572351i
$162$			12.7279i			0.0785674i
$163$	115.726			0.709977			0.354989	−	0.934871i	$-0.384485\pi$
$163$	115.726			0.709977			0.354989	+	0.934871i	$0.384485\pi$
$164$	−62.3502			−0.380184
$165$		−	53.7223i		−	0.325590i
$166$	−214.018			−1.28927
$167$	10.5436			0.0631356			0.0315678	−	0.999502i	$-0.489950\pi$
$167$	10.5436			0.0631356			0.0315678	+	0.999502i	$0.489950\pi$
$168$		−	36.2753i		−	0.215924i
$169$	−213.540			−1.26355
$170$			96.7013i			0.568831i
$171$	−88.4251			−0.517106
$172$		−	161.324i		−	0.937931i
$173$		−	68.9417i		−	0.398507i	−0.979948	−	0.199253i	$-0.936148\pi$
$173$		−	68.9417i		−	0.398507i	0.979948	−	0.199253i	$-0.0638517\pi$
$174$		−	62.5325i		−	0.359382i
$175$	259.108			1.48062
$176$		−	16.0179i		−	0.0910107i
$177$	−58.4381	−	83.8331i	−0.330159	−	0.473633i
$178$	94.1789			0.529095
$179$			152.087i			0.849649i	0.905276	+	0.424825i	$0.139664\pi$
$179$			152.087i			0.849649i	−0.905276	+	0.424825i	$0.860336\pi$
$180$	−46.4729			−0.258183
$181$	−81.1957			−0.448595			−0.224297	−	0.974521i	$-0.572009\pi$
$181$	−81.1957			−0.448595			−0.224297	+	0.974521i	$0.572009\pi$
$182$	204.813			1.12535
$183$			65.5311i			0.358093i
$184$	−3.51988			−0.0191298
$185$			451.063i			2.43818i
$186$	11.5931			0.0623283
$187$		−	35.3520i		−	0.189048i
$188$		−	68.9745i		−	0.366886i
$189$	38.4757			0.203575
$190$		−	322.863i		−	1.69928i
$191$			13.5994i			0.0712012i	0.999366	+	0.0356006i	$0.0113344\pi$
$191$			13.5994i			0.0712012i	−0.999366	+	0.0356006i	$0.988666\pi$
$192$	−13.8564			−0.0721688
$193$	216.667			1.12263			0.561314	−	0.827603i	$-0.310296\pi$
$193$	216.667			1.12263			0.561314	+	0.827603i	$0.310296\pi$
$194$	137.836			0.710497
$195$		−	262.390i		−	1.34559i
$196$	−11.6580			−0.0594795
$197$	265.328			1.34684			0.673422	−	0.739258i	$-0.264824\pi$
$197$	265.328			1.34684			0.673422	+	0.739258i	$0.264824\pi$
$198$	16.9895			0.0858057
$199$	−131.448			−0.660544			−0.330272	−	0.943886i	$-0.607140\pi$
$199$	−131.448			−0.660544			−0.330272	+	0.943886i	$0.607140\pi$
$200$		−	98.9739i		−	0.494869i
$201$			55.5213i			0.276225i
$202$	139.523			0.690709
$203$	−189.032			−0.931192
$204$	−30.5815			−0.149910
$205$	241.466			1.17788
$206$	−9.97559			−0.0484252
$207$		−	3.73340i		−	0.0180357i
$208$		−	78.2345i		−	0.376127i
$209$			118.032i			0.564746i
$210$			140.485i			0.668975i
$211$			362.962i			1.72020i	0.510124	+	0.860101i	$0.329599\pi$
$211$			362.962i			1.72020i	−0.510124	+	0.860101i	$0.670401\pi$
$212$	88.0581			0.415368
$213$	−203.278			−0.954359
$214$			81.2022i			0.379449i
$215$			624.767i			2.90589i
$216$		−	14.6969i		−	0.0680414i
$217$		−	35.0451i		−	0.161498i
$218$	−196.041			−0.899270
$219$			41.6778i			0.190309i
$220$			62.0332i			0.281969i
$221$		−	172.666i		−	0.781295i
$222$	−142.648			−0.642557
$223$	−69.0199			−0.309506			−0.154753	−	0.987953i	$-0.549458\pi$
$223$	−69.0199			−0.309506			−0.154753	+	0.987953i	$0.549458\pi$
$224$			41.8871i			0.186996i
$225$	104.978			0.466567
$226$	296.871			1.31359
$227$		−	134.615i		−	0.593020i	−0.955030	−	0.296510i	$-0.904177\pi$
$227$		−	134.615i		−	0.593020i	0.955030	−	0.296510i	$-0.0958227\pi$
$228$	102.104			0.447827
$229$		−	321.197i		−	1.40261i	−0.712864	−	0.701303i	$-0.752602\pi$
$229$		−	321.197i		−	1.40261i	0.712864	−	0.701303i	$-0.247398\pi$
$230$	13.6316			0.0592678
$231$		−	51.3583i		−	0.222330i
$232$			72.2063i			0.311234i
$233$			141.218i			0.606085i	0.952977	+	0.303042i	$0.0980024\pi$
$233$			141.218i			0.606085i	−0.952977	+	0.303042i	$0.901998\pi$
$234$	82.9802			0.354616
$235$			267.121i			1.13668i
$236$	67.4785	+	96.8021i	0.285926	+	0.410178i
$237$	194.196			0.819392
$238$			92.4462i			0.388429i
$239$	42.8513			0.179294			0.0896471	−	0.995974i	$-0.471426\pi$
$239$	42.8513			0.179294			0.0896471	+	0.995974i	$0.471426\pi$
$240$	53.6623			0.223593
$241$	167.621			0.695523			0.347761	−	0.937583i	$-0.386942\pi$
$241$	167.621			0.695523			0.347761	+	0.937583i	$0.386942\pi$
$242$			148.442i			0.613396i
$243$	15.5885			0.0641500
$244$		−	75.6688i		−	0.310118i
$245$	45.1483			0.184279
$246$			76.3631i			0.310419i
$247$			576.491i			2.33397i
$248$	−13.3865			−0.0539778
$249$			262.118i			1.05268i
$250$			109.456i			0.437825i
$251$	80.1349			0.319263			0.159631	−	0.987177i	$-0.448969\pi$
$251$	80.1349			0.319263			0.159631	+	0.987177i	$0.448969\pi$
$252$	−44.4280			−0.176301
$253$	−4.98343			−0.0196974
$254$		−	269.338i		−	1.06039i
$255$	118.434			0.464449
$256$	16.0000			0.0625000
$257$	163.633			0.636704			0.318352	−	0.947973i	$-0.396871\pi$
$257$	163.633			0.636704			0.318352	+	0.947973i	$0.396871\pi$
$258$	−197.581			−0.765818
$259$			431.215i			1.66492i
$260$			302.982i			1.16532i
$261$	−76.5863			−0.293434
$262$	332.660			1.26970
$263$	105.069			0.399502			0.199751	−	0.979847i	$-0.435987\pi$
$263$	105.069			0.399502			0.199751	+	0.979847i	$0.435987\pi$
$264$	−19.6178			−0.0743099
$265$	−341.026			−1.28689
$266$		−	308.656i		−	1.16036i
$267$		−	115.345i		−	0.432004i
$268$		−	64.1104i		−	0.239218i
$269$		−	469.581i		−	1.74565i	−0.488029	−	0.872827i	$-0.662284\pi$
$269$		−	469.581i		−	1.74565i	0.488029	−	0.872827i	$-0.337716\pi$
$270$			56.9175i			0.210805i
$271$	185.388			0.684087			0.342044	−	0.939684i	$-0.388881\pi$
$271$	185.388			0.684087			0.342044	+	0.939684i	$0.388881\pi$
$272$	35.3125			0.129825
$273$		−	250.844i		−	0.918843i
$274$			3.15271i			0.0115062i
$275$		−	140.127i		−	0.509552i
$276$			4.31096i			0.0156194i
$277$	470.537			1.69869			0.849345	−	0.527839i	$-0.176997\pi$
$277$	470.537			1.69869			0.849345	+	0.527839i	$0.176997\pi$
$278$		−	160.923i		−	0.578860i
$279$		−	14.1985i		−	0.0508908i
$280$		−	162.218i		−	0.579350i
$281$	−111.017			−0.395077			−0.197539	−	0.980295i	$-0.563295\pi$
$281$	−111.017			−0.395077			−0.197539	+	0.980295i	$0.563295\pi$
$282$	−84.4762			−0.299561
$283$			81.8102i			0.289082i	0.989499	+	0.144541i	$0.0461706\pi$
$283$			81.8102i			0.289082i	−0.989499	+	0.144541i	$0.953829\pi$
$284$	234.726			0.826499
$285$	−395.424			−1.38745
$286$		−	110.764i		−	0.387287i
$287$	230.841			0.804324
$288$			16.9706i			0.0589256i
$289$	−211.064			−0.730326
$290$		−	279.636i		−	0.964263i
$291$		−	168.814i		−	0.580118i
$292$		−	48.1253i		−	0.164813i
$293$	−209.795			−0.716026			−0.358013	−	0.933717i	$-0.616546\pi$
$293$	−209.795			−0.716026			−0.358013	+	0.933717i	$0.616546\pi$
$294$			14.2780i			0.0485648i
$295$	−261.327	−	374.890i	−0.885854	−	1.27081i
$296$	164.715			0.556471
$297$		−	20.8078i		−	0.0700601i
$298$	81.4144			0.273203
$299$	−24.3401			−0.0814049
$300$	−121.218			−0.404059
$301$			597.275i			1.98430i
$302$	35.3387			0.117016
$303$		−	170.880i		−	0.563961i
$304$	−117.900			−0.387829
$305$			293.046i			0.960806i
$306$			37.4546i			0.122401i
$307$	−241.024			−0.785094			−0.392547	−	0.919732i	$-0.628406\pi$
$307$	−241.024			−0.785094			−0.392547	+	0.919732i	$0.628406\pi$
$308$			59.3035i			0.192544i
$309$			12.2176i			0.0395390i
$310$	51.8425			0.167234
$311$	−4.50483			−0.0144850			−0.00724249	−	0.999974i	$-0.502305\pi$
$311$	−4.50483			−0.0144850			−0.00724249	+	0.999974i	$0.502305\pi$
$312$	−95.8173			−0.307107
$313$		−	489.847i		−	1.56501i	−0.622647	−	0.782503i	$-0.713943\pi$
$313$		−	489.847i		−	1.56501i	0.622647	−	0.782503i	$-0.286057\pi$
$314$	−161.833			−0.515390
$315$	172.058			0.546216
$316$	−224.238			−0.709614
$317$	499.798			1.57665			0.788325	−	0.615259i	$-0.210948\pi$
$317$	499.798			1.57665			0.788325	+	0.615259i	$0.210948\pi$
$318$		−	107.849i		−	0.339147i
$319$			102.229i			0.320468i
$320$	−61.9639			−0.193637
$321$	99.4519			0.309819
$322$	13.0318			0.0404713
$323$	−260.209			−0.805602
$324$	−18.0000			−0.0555556
$325$		−	684.406i		−	2.10587i
$326$			163.662i			0.502030i
$327$			240.100i			0.734251i
$328$		−	88.1765i		−	0.268831i
$329$			255.366i			0.776190i
$330$	75.9748			0.230227
$331$	−375.117			−1.13328			−0.566641	−	0.823965i	$-0.691758\pi$
$331$	−375.117			−1.13328			−0.566641	+	0.823965i	$0.691758\pi$
$332$		−	302.668i		−	0.911650i
$333$			174.707i			0.524645i
$334$			14.9110i			0.0446436i
$335$			248.283i			0.741144i
$336$	51.3010			0.152682
$337$		−	381.288i		−	1.13142i	−0.824605	−	0.565710i	$-0.808602\pi$
$337$		−	381.288i		−	1.13142i	0.824605	−	0.565710i	$-0.191398\pi$
$338$		−	301.991i		−	0.893464i
$339$		−	363.591i		−	1.07254i
$340$	−136.756			−0.402225
$341$	−18.9525			−0.0555793
$342$		−	125.052i		−	0.365649i
$343$	−319.667			−0.931973
$344$	228.147			0.663218
$345$		−	16.6952i		−	0.0483920i
$346$	97.4982			0.281787
$347$			355.001i			1.02306i	0.859266	+	0.511528i	$0.170920\pi$
$347$			355.001i			1.02306i	−0.859266	+	0.511528i	$0.829080\pi$
$348$	88.4343			0.254122
$349$			5.79204i			0.0165961i	0.999966	+	0.00829805i	$0.00264138\pi$
$349$			5.79204i			0.0165961i	−0.999966	+	0.00829805i	$0.997359\pi$
$350$			366.434i			1.04695i
$351$		−	101.630i		−	0.289543i
$352$	22.6527			0.0643543
$353$		−	477.888i		−	1.35379i	−0.736079	−	0.676895i	$-0.763325\pi$
$353$		−	477.888i		−	1.35379i	0.736079	−	0.676895i	$-0.236675\pi$
$354$	118.558	−	82.6440i	0.334909	−	0.233458i
$355$	−909.032			−2.56065
$356$			133.189i			0.374127i
$357$	113.223			0.317151
$358$	−215.084			−0.600793
$359$	−332.764			−0.926919			−0.463459	−	0.886118i	$-0.653392\pi$
$359$	−332.764			−0.926919			−0.463459	+	0.886118i	$0.653392\pi$
$360$		−	65.7226i		−	0.182563i
$361$	507.777			1.40659
$362$		−	114.828i		−	0.317205i
$363$	181.803			0.500836
$364$			289.650i			0.795742i
$365$			186.377i			0.510622i
$366$	−92.6749			−0.253210
$367$		−	492.687i		−	1.34247i	−0.741244	−	0.671235i	$-0.765764\pi$
$367$		−	492.687i		−	1.34247i	0.741244	−	0.671235i	$-0.234236\pi$
$368$		−	4.97787i		−	0.0135268i
$369$	93.5253			0.253456
$370$	−637.900			−1.72405
$371$	−326.020			−0.878760
$372$			16.3951i			0.0440727i
$373$	367.073			0.984110			0.492055	−	0.870564i	$-0.336246\pi$
$373$	367.073			0.984110			0.492055	+	0.870564i	$0.336246\pi$
$374$	49.9953			0.133677
$375$	134.056			0.357482
$376$	97.5447			0.259427
$377$			499.308i			1.32442i
$378$			54.4129i			0.143950i
$379$	347.845			0.917798			0.458899	−	0.888489i	$-0.348244\pi$
$379$	347.845			0.917798			0.458899	+	0.888489i	$0.348244\pi$
$380$	456.597			1.20157
$381$	−329.871			−0.865802
$382$	−19.2325			−0.0503468
$383$	320.942			0.837969			0.418985	−	0.907993i	$-0.362386\pi$
$383$	320.942			0.837969			0.418985	+	0.907993i	$0.362386\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		−	229.667i		−	0.596538i
$386$			306.414i			0.793817i
$387$			241.986i			0.625288i
$388$			194.930i			0.502397i
$389$	344.325			0.885154			0.442577	−	0.896731i	$-0.354064\pi$
$389$	344.325			0.885154			0.442577	+	0.896731i	$0.354064\pi$
$390$	371.076			0.951476
$391$		−	10.9863i		−	0.0280980i
$392$		−	16.4869i		−	0.0420583i
$393$		−	407.424i		−	1.03670i
$394$			375.231i			0.952363i
$395$	868.417			2.19852
$396$			24.0268i			0.0606738i
$397$			339.996i			0.856414i	0.903681	+	0.428207i	$0.140855\pi$
$397$			339.996i			0.856414i	−0.903681	+	0.428207i	$0.859145\pi$
$398$		−	185.896i		−	0.467075i
$399$	−378.025			−0.947430
$400$	139.970			0.349926
$401$		−	33.6512i		−	0.0839183i	−0.999119	−	0.0419591i	$-0.986640\pi$
$401$		−	33.6512i		−	0.0839183i	0.999119	−	0.0419591i	$-0.0133599\pi$
$402$	−78.5189			−0.195321
$403$	−92.5679			−0.229697
$404$			197.316i			0.488405i
$405$	69.7094			0.172122
$406$		−	267.332i		−	0.658452i
$407$	233.203			0.572980
$408$		−	43.2488i		−	0.106002i
$409$			37.6215i			0.0919842i	0.998942	+	0.0459921i	$0.0146449\pi$
$409$			37.6215i			0.0919842i	−0.998942	+	0.0459921i	$0.985355\pi$
$410$			341.485i			0.832890i
$411$	3.86126			0.00939480
$412$		−	14.1076i		−	0.0342418i
$413$	−249.828	−	358.393i	−0.604910	−	0.867780i
$414$	5.27983			0.0127532
$415$			1172.15i			2.82447i
$416$	110.640			0.265962
$417$	−197.090			−0.472637
$418$	−166.922			−0.399336
$419$			408.607i			0.975196i	0.873068	+	0.487598i	$0.162127\pi$
$419$			408.607i			0.975196i	−0.873068	+	0.487598i	$0.837873\pi$
$420$	−198.676			−0.473037
$421$		−	645.164i		−	1.53246i	−0.642569	−	0.766228i	$-0.722131\pi$
$421$		−	645.164i		−	1.53246i	0.642569	−	0.766228i	$-0.277869\pi$
$422$	−513.306			−1.21637
$423$			103.462i			0.244591i
$424$			124.533i			0.293710i
$425$	308.919			0.726868
$426$		−	287.479i		−	0.674834i
$427$			280.151i			0.656091i
$428$	−114.837			−0.268311
$429$	−135.658			−0.316218
$430$	−883.554			−2.05478
$431$		−	308.175i		−	0.715023i	−0.933909	−	0.357512i	$-0.883625\pi$
$431$		−	308.175i		−	0.715023i	0.933909	−	0.357512i	$-0.116375\pi$
$432$	20.7846			0.0481125
$433$	−784.573			−1.81195			−0.905973	−	0.423335i	$-0.860859\pi$
$433$	−784.573			−1.81195			−0.905973	+	0.423335i	$0.860859\pi$
$434$	49.5613			0.114196
$435$	−342.483			−0.787318
$436$		−	277.244i		−	0.635880i
$437$			36.6807i			0.0839375i
$438$	−58.9413			−0.134569
$439$	−362.248			−0.825167			−0.412583	−	0.910920i	$-0.635373\pi$
$439$	−362.248			−0.825167			−0.412583	+	0.910920i	$0.635373\pi$
$440$	−87.7281			−0.199382
$441$	17.4870			0.0396530
$442$	244.187			0.552459
$443$		−	49.2729i		−	0.111226i	−0.998452	−	0.0556128i	$-0.982289\pi$
$443$		−	49.2729i		−	0.111226i	0.998452	−	0.0556128i	$-0.0177112\pi$
$444$		−	201.734i		−	0.454356i
$445$		−	515.807i		−	1.15912i
$446$		−	97.6089i		−	0.218854i
$447$		−	99.7119i		−	0.223069i
$448$	−59.2373			−0.132226
$449$	384.700			0.856792			0.428396	−	0.903591i	$-0.359079\pi$
$449$	384.700			0.856792			0.428396	+	0.903591i	$0.359079\pi$
$450$			148.461i			0.329913i
$451$		−	124.840i		−	0.276807i
$452$			419.839i			0.928848i
$453$		−	43.2809i		−	0.0955429i
$454$	190.375			0.419328
$455$		−	1121.74i		−	2.46536i
$456$			144.398i			0.316661i
$457$		−	416.205i		−	0.910733i	−0.890304	−	0.455366i	$-0.849508\pi$
$457$		−	416.205i		−	0.910733i	0.890304	−	0.455366i	$-0.150492\pi$
$458$	454.241			0.991792
$459$	45.8723			0.0999397
$460$			19.2780i			0.0419087i
$461$	−222.765			−0.483222			−0.241611	−	0.970373i	$-0.577676\pi$
$461$	−222.765			−0.483222			−0.241611	+	0.970373i	$0.577676\pi$
$462$	72.6317			0.157211
$463$		−	145.299i		−	0.313821i	−0.987613	−	0.156911i	$-0.949847\pi$
$463$		−	145.299i		−	0.313821i	0.987613	−	0.156911i	$-0.0501535\pi$
$464$	−102.115			−0.220076
$465$		−	63.4938i		−	0.136546i
$466$	−199.712			−0.428567
$467$			387.905i			0.830631i	0.909677	+	0.415315i	$0.136329\pi$
$467$			387.905i			0.830631i	−0.909677	+	0.415315i	$0.863671\pi$
$468$			117.352i			0.250752i
$469$			237.358i			0.506094i
$470$	−377.766			−0.803757
$471$			198.204i			0.420815i
$472$	−136.899	+	95.4291i	−0.290040	+	0.202180i
$473$	323.009			0.682894
$474$			274.634i			0.579398i
$475$	−1031.41			−2.17138
$476$	−130.739			−0.274661
$477$	−132.087			−0.276912
$478$			60.6009i			0.126780i
$479$	−727.357			−1.51849			−0.759245	−	0.650805i	$-0.774432\pi$
$479$	−727.357			−1.51849			−0.759245	+	0.650805i	$0.774432\pi$
$480$			75.8900i			0.158104i
$481$	1139.01			2.36800
$482$			237.052i			0.491809i
$483$		−	15.9606i		−	0.0330447i
$484$	−209.928			−0.433736
$485$		−	754.914i		−	1.55652i
$486$			22.0454i			0.0453609i
$487$	−491.586			−1.00942			−0.504709	−	0.863290i	$-0.668400\pi$
$487$	−491.586			−1.00942			−0.504709	+	0.863290i	$0.668400\pi$
$488$	107.012			0.219287
$489$	200.444			0.409906
$490$			63.8494i			0.130305i
$491$	726.370			1.47937			0.739684	−	0.672954i	$-0.234975\pi$
$491$	726.370			1.47937			0.739684	+	0.672954i	$0.234975\pi$
$492$	−107.994			−0.219499
$493$	−225.371			−0.457143
$494$	−815.281			−1.65037
$495$		−	93.0497i		−	0.187979i
$496$		−	18.9314i		−	0.0381681i
$497$	−869.032			−1.74856
$498$	−370.691			−0.744359
$499$	621.595			1.24568			0.622840	−	0.782349i	$-0.285979\pi$
$499$	621.595			1.24568			0.622840	+	0.782349i	$0.285979\pi$
$500$	−154.794			−0.309589
$501$	18.2621			0.0364514
$502$			113.328i			0.225753i
$503$		−	878.744i		−	1.74701i	−0.486818	−	0.873503i	$-0.661843\pi$
$503$		−	878.744i		−	1.74701i	0.486818	−	0.873503i	$-0.338157\pi$
$504$		−	62.8306i		−	0.124664i
$505$		−	764.153i		−	1.51317i
$506$		−	7.04764i		−	0.0139281i
$507$	−369.862			−0.729510
$508$	380.902			0.749807
$509$		−	182.390i		−	0.358329i	−0.983819	−	0.179165i	$-0.942661\pi$
$509$		−	182.390i		−	0.358329i	0.983819	−	0.179165i	$-0.0573395\pi$
$510$			167.492i			0.328415i
$511$			178.176i			0.348681i
$512$			22.6274i			0.0441942i
$513$	−153.157			−0.298551
$514$			231.412i			0.450218i
$515$			54.6352i			0.106088i
$516$		−	279.422i		−	0.541515i
$517$	138.103			0.267124
$518$	−609.830			−1.17728
$519$		−	119.410i		−	0.230078i
$520$	−428.481			−0.824003
$521$	−980.540			−1.88203			−0.941017	−	0.338360i	$-0.890128\pi$
$521$	−980.540			−1.88203			−0.941017	+	0.338360i	$0.890128\pi$
$522$		−	108.309i		−	0.207489i
$523$	−536.582			−1.02597			−0.512985	−	0.858398i	$-0.671460\pi$
$523$	−536.582			−1.02597			−0.512985	+	0.858398i	$0.671460\pi$
$524$			470.453i			0.897810i
$525$	448.788			0.854835
$526$			148.590i			0.282490i
$527$		−	41.7822i		−	0.0792831i
$528$		−	27.7438i		−	0.0525451i
$529$	527.451			0.997072
$530$		−	482.284i		−	0.909970i
$531$	−101.218	−	145.203i	−0.190617	−	0.273452i
$532$	436.505			0.820498
$533$		−	609.742i		−	1.14398i
$534$	163.123			0.305473
$535$	444.735			0.831280
$536$	90.6658			0.169153
$537$			263.423i			0.490545i
$538$	664.088			1.23436
$539$		−	23.3420i		−	0.0433062i
$540$	−80.4935			−0.149062
$541$			513.326i			0.948847i	0.880297	+	0.474424i	$0.157344\pi$
$541$			513.326i			0.948847i	−0.880297	+	0.474424i	$0.842656\pi$
$542$			262.178i			0.483723i
$543$	−140.635			−0.258996
$544$			49.9395i			0.0918005i
$545$			1073.69i			1.97008i
$546$	354.747			0.649720
$547$	−27.4285			−0.0501435			−0.0250718	−	0.999686i	$-0.507981\pi$
$547$	−27.4285			−0.0501435			−0.0250718	+	0.999686i	$0.507981\pi$
$548$	−4.45860			−0.00813614
$549$			113.503i			0.206745i
$550$	198.169			0.360307
$551$	752.461			1.36563
$552$	−6.09662			−0.0110446
$553$	830.204			1.50127
$554$			665.440i			1.20115i
$555$			781.265i			1.40768i
$556$	227.579			0.409316
$557$	24.2247			0.0434914			0.0217457	−	0.999764i	$-0.493078\pi$
$557$	24.2247			0.0434914			0.0217457	+	0.999764i	$0.493078\pi$
$558$	20.0798			0.0359852
$559$	1577.64			2.82225
$560$	229.411			0.409662
$561$		−	61.2315i		−	0.109147i
$562$		−	157.001i		−	0.279362i
$563$		−	137.830i		−	0.244814i	−0.992480	−	0.122407i	$-0.960939\pi$
$563$		−	137.830i		−	0.244814i	0.992480	−	0.122407i	$-0.0390614\pi$
$564$		−	119.467i		−	0.211822i
$565$		−	1625.93i		−	2.87775i
$566$	−115.697			−0.204412
$567$	66.6419			0.117534
$568$			331.952i			0.584423i
$569$			691.407i			1.21513i	0.794271	+	0.607563i	$0.207853\pi$
$569$			691.407i			1.21513i	−0.794271	+	0.607563i	$0.792147\pi$
$570$		−	559.215i		−	0.981078i
$571$			584.297i			1.02329i	0.859198	+	0.511644i	$0.170963\pi$
$571$			584.297i			1.02329i	−0.859198	+	0.511644i	$0.829037\pi$
$572$	156.644			0.273853
$573$			23.5549i			0.0411080i
$574$			326.459i			0.568743i
$575$		−	43.5471i		−	0.0757340i
$576$	−24.0000			−0.0416667
$577$	339.647			0.588644			0.294322	−	0.955706i	$-0.404906\pi$
$577$	339.647			0.588644			0.294322	+	0.955706i	$0.404906\pi$
$578$		−	298.490i		−	0.516418i
$579$	375.278			0.648149
$580$	395.466			0.681837
$581$			1120.58i			1.92870i
$582$	238.740			0.410206
$583$			176.313i			0.302424i
$584$	68.0595			0.116540
$585$		−	454.473i		−	0.776877i
$586$		−	296.696i		−	0.506307i
$587$		−	91.6472i		−	0.156128i	−0.996948	−	0.0780641i	$-0.975126\pi$
$587$		−	91.6472i		−	0.156128i	0.996948	−	0.0780641i	$-0.0248739\pi$
$588$	−20.1922			−0.0343405
$589$			139.501i			0.236843i
$590$	530.174	−	369.572i	0.898600	−	0.626394i
$591$	459.562			0.777601
$592$			232.943i			0.393484i
$593$	−1151.07			−1.94109			−0.970547	−	0.240913i	$-0.922553\pi$
$593$	−1151.07			−1.94109			−0.970547	+	0.240913i	$0.922553\pi$
$594$	29.4267			0.0495400
$595$	506.317			0.850953
$596$			115.137i			0.193184i
$597$	−227.675			−0.381365
$598$		−	34.4220i		−	0.0575619i
$599$	1042.38			1.74019			0.870096	−	0.492882i	$-0.164057\pi$
$599$	1042.38			1.74019			0.870096	+	0.492882i	$0.164057\pi$
$600$		−	171.428i		−	0.285713i
$601$			1054.03i			1.75379i	0.480685	+	0.876893i	$0.340388\pi$
$601$			1054.03i			1.75379i	−0.480685	+	0.876893i	$0.659612\pi$
$602$	−844.675			−1.40311
$603$			96.1657i			0.159479i
$604$			49.9765i			0.0827426i
$605$	812.999			1.34380
$606$	241.661			0.398781
$607$	369.407			0.608578			0.304289	−	0.952580i	$-0.401581\pi$
$607$	369.407			0.608578			0.304289	+	0.952580i	$0.401581\pi$
$608$		−	166.736i		−	0.274237i
$609$	−327.413			−0.537624
$610$	−414.429			−0.679392
$611$	674.523			1.10397
$612$	−52.9688			−0.0865503
$613$			417.526i			0.681120i	0.940223	+	0.340560i	$0.110617\pi$
$613$			417.526i			0.681120i	−0.940223	+	0.340560i	$0.889383\pi$
$614$		−	340.859i		−	0.555145i
$615$	418.232			0.680052
$616$	−83.8678			−0.136149
$617$	−86.3926			−0.140020			−0.0700102	−	0.997546i	$-0.522303\pi$
$617$	−86.3926			−0.140020			−0.0700102	+	0.997546i	$0.522303\pi$
$618$	−17.2782			−0.0279583
$619$	−390.327			−0.630576			−0.315288	−	0.948996i	$-0.602101\pi$
$619$	−390.327			−0.630576			−0.315288	+	0.948996i	$0.602101\pi$
$620$			73.3164i			0.118252i
$621$		−	6.46644i		−	0.0104129i
$622$		−	6.37079i		−	0.0102424i
$623$		−	493.110i		−	0.791509i
$624$		−	135.506i		−	0.217157i
$625$	−275.335			−0.440536
$626$	692.748			1.10663
$627$			204.437i			0.326056i
$628$		−	228.866i		−	0.364436i
$629$			514.112i			0.817348i
$630$			243.327i			0.386233i
$631$	−632.550			−1.00246			−0.501228	−	0.865315i	$-0.667118\pi$
$631$	−632.550			−1.00246			−0.501228	+	0.865315i	$0.667118\pi$
$632$		−	317.121i		−	0.501773i
$633$			628.669i			0.993159i
$634$			706.821i			1.11486i
$635$	−1475.14			−2.32305
$636$	152.521			0.239813
$637$		−	114.007i		−	0.178975i
$638$	−144.574			−0.226605
$639$	−352.089			−0.550999
$640$		−	87.6302i		−	0.136922i
$641$	−231.847			−0.361696			−0.180848	−	0.983511i	$-0.557884\pi$
$641$	−231.847			−0.361696			−0.180848	+	0.983511i	$0.557884\pi$
$642$			140.646i			0.219075i
$643$	987.623			1.53596			0.767981	−	0.640473i	$-0.221262\pi$
$643$	987.623			1.53596			0.767981	+	0.640473i	$0.221262\pi$
$644$			18.4297i			0.0286176i
$645$			1082.13i			1.67772i
$646$		−	367.992i		−	0.569647i
$647$	796.971			1.23179			0.615897	−	0.787827i	$-0.288794\pi$
$647$	796.971			1.23179			0.615897	+	0.787827i	$0.288794\pi$
$648$		−	25.4558i		−	0.0392837i
$649$	−193.821	+	135.108i	−0.298645	+	0.208179i
$650$	967.897			1.48907
$651$		−	60.6999i		−	0.0932410i
$652$	−231.453			−0.354989
$653$	−151.955			−0.232703			−0.116352	−	0.993208i	$-0.537120\pi$
$653$	−151.955			−0.232703			−0.116352	+	0.993208i	$0.537120\pi$
$654$	−339.553			−0.519194
$655$		−	1821.94i		−	2.78159i
$656$	124.700			0.190092
$657$			72.1880i			0.109875i
$658$	−361.143			−0.548849
$659$		−	1159.62i		−	1.75967i	−0.475282	−	0.879834i	$-0.657654\pi$
$659$		−	1159.62i		−	1.75967i	0.475282	−	0.879834i	$-0.342346\pi$
$660$			107.445i			0.162795i
$661$	801.056			1.21188			0.605942	−	0.795509i	$-0.292796\pi$
$661$	801.056			1.21188			0.605942	+	0.795509i	$0.292796\pi$
$662$		−	530.495i		−	0.801352i
$663$		−	299.066i		−	0.451081i
$664$	428.037			0.644634
$665$	−1690.47			−2.54206
$666$	−247.073			−0.370980
$667$			31.7697i			0.0476308i
$668$	−21.0873			−0.0315678
$669$	−119.546			−0.178694
$670$	−351.126			−0.524068
$671$	151.507			0.225792
$672$			72.5506i			0.107962i
$673$			697.466i			1.03635i	0.855273	+	0.518177i	$0.173389\pi$
$673$			697.466i			1.03635i	−0.855273	+	0.518177i	$0.826611\pi$
$674$	539.223			0.800034
$675$	181.827			0.269373
$676$	427.080			0.631774
$677$	626.963			0.926090			0.463045	−	0.886335i	$-0.346757\pi$
$677$	626.963			0.926090			0.463045	+	0.886335i	$0.346757\pi$
$678$	514.196			0.758401
$679$		−	721.696i		−	1.06288i
$680$		−	193.403i		−	0.284416i
$681$		−	233.161i		−	0.342380i
$682$		−	26.8029i		−	0.0393005i
$683$			550.936i			0.806641i	0.915059	+	0.403321i	$0.132144\pi$
$683$			550.936i			0.806641i	−0.915059	+	0.403321i	$0.867856\pi$
$684$	176.850			0.258553
$685$	17.2670			0.0252073
$686$		−	452.077i		−	0.659004i
$687$		−	556.329i		−	0.809794i
$688$			322.648i			0.468966i
$689$			861.147i			1.24985i
$690$	23.6106			0.0342183
$691$			1267.62i			1.83448i	0.398337	+	0.917239i	$0.369588\pi$
$691$			1267.62i			1.83448i	−0.398337	+	0.917239i	$0.630412\pi$
$692$			137.883i			0.199253i
$693$		−	88.9553i		−	0.128363i
$694$	−502.047			−0.723410
$695$	−881.357			−1.26814
$696$			125.065i			0.179691i
$697$	275.218			0.394861
$698$	−8.19118			−0.0117352
$699$			244.596i			0.349923i
$700$	−518.216			−0.740308
$701$			1267.37i			1.80794i	0.427595	+	0.903970i	$0.359361\pi$
$701$			1267.37i			1.80794i	−0.427595	+	0.903970i	$0.640639\pi$
$702$	143.726			0.204738
$703$		−	1716.50i		−	2.44167i
$704$			32.0358i			0.0455054i
$705$			462.666i			0.656264i
$706$	675.836			0.957274
$707$		−	730.528i		−	1.03328i
$708$	116.876	+	167.666i	0.165079	+	0.236817i
$709$	−501.357			−0.707132			−0.353566	−	0.935410i	$-0.615031\pi$
$709$	−501.357			−0.707132			−0.353566	+	0.935410i	$0.615031\pi$
$710$		−	1285.57i		−	1.81066i
$711$	336.357			0.473076
$712$	−188.358			−0.264548
$713$	−5.88987			−0.00826068
$714$			160.121i			0.224260i
$715$	−606.642			−0.848450
$716$		−	304.174i		−	0.424825i
$717$	74.2206			0.103516
$718$		−	470.599i		−	0.655431i
$719$		−	561.681i		−	0.781198i	−0.920561	−	0.390599i	$-0.872268\pi$
$719$		−	561.681i		−	0.781198i	0.920561	−	0.390599i	$-0.127732\pi$
$720$	92.9458			0.129091
$721$			52.2310i			0.0724425i
$722$			718.106i			0.994606i
$723$	290.328			0.401560
$724$	162.391			0.224297
$725$	−893.317			−1.23216
$726$			257.109i			0.354144i
$727$	1053.55			1.44918			0.724589	−	0.689181i	$-0.242030\pi$
$727$	1053.55			1.44918			0.724589	+	0.689181i	$0.242030\pi$
$728$	−409.627			−0.562674
$729$	27.0000			0.0370370
$730$	−263.577			−0.361064
$731$			712.096i			0.974139i
$732$		−	131.062i		−	0.179047i
$733$	−1122.48			−1.53136			−0.765678	−	0.643223i	$-0.777597\pi$
$733$	−1122.48			−1.53136			−0.765678	+	0.643223i	$0.777597\pi$
$734$	696.764			0.949270
$735$	78.1992			0.106394
$736$	7.03977			0.00956490
$737$	128.364			0.174171
$738$			132.265i			0.179221i
$739$			140.089i			0.189566i	0.995498	+	0.0947831i	$0.0302158\pi$
$739$			140.089i			0.189566i	−0.995498	+	0.0947831i	$0.969784\pi$
$740$		−	902.127i		−	1.21909i
$741$			998.512i			1.34752i
$742$		−	461.062i		−	0.621377i
$743$	174.473			0.234822			0.117411	−	0.993083i	$-0.462540\pi$
$743$	174.473			0.234822			0.117411	+	0.993083i	$0.462540\pi$
$744$	−23.1861			−0.0311641
$745$		−	445.898i		−	0.598520i
$746$			519.119i			0.695871i
$747$			454.002i			0.607767i
$748$			70.7040i			0.0945241i
$749$	425.165			0.567644
$750$			189.584i			0.252778i
$751$		−	391.697i		−	0.521567i	−0.965397	−	0.260783i	$-0.916019\pi$
$751$		−	391.697i		−	0.521567i	0.965397	−	0.260783i	$-0.0839809\pi$
$752$			137.949i			0.183443i
$753$	138.798			0.184326
$754$	−706.128			−0.936509
$755$		−	193.546i		−	0.256353i
$756$	−76.9515			−0.101788
$757$	382.403			0.505156			0.252578	−	0.967576i	$-0.418722\pi$
$757$	382.403			0.505156			0.252578	+	0.967576i	$0.418722\pi$
$758$			491.928i			0.648981i
$759$	−8.63156			−0.0113723
$760$			645.725i			0.849639i
$761$	−943.577			−1.23992			−0.619959	−	0.784634i	$-0.712851\pi$
$761$	−943.577			−1.23992			−0.619959	+	0.784634i	$0.712851\pi$
$762$		−	466.508i		−	0.612215i
$763$			1026.45i			1.34528i
$764$		−	27.1988i		−	0.0356006i
$765$	205.134			0.268150
$766$			453.881i			0.592534i
$767$	−946.658	+	659.894i	−1.23423	+	0.860357i
$768$	27.7128			0.0360844
$769$			148.742i			0.193423i	0.995312	+	0.0967114i	$0.0308324\pi$
$769$			148.742i			0.193423i	−0.995312	+	0.0967114i	$0.969168\pi$
$770$	324.798			0.421816
$771$	283.420			0.367601
$772$	−433.334			−0.561314
$773$		−	585.587i		−	0.757551i	−0.925489	−	0.378776i	$-0.876345\pi$
$773$		−	585.587i		−	0.757551i	0.925489	−	0.378776i	$-0.123655\pi$
$774$	−342.220			−0.442145
$775$		−	165.614i		−	0.213696i
$776$	−275.673			−0.355248
$777$			746.887i			0.961244i
$778$			486.949i			0.625898i
$779$	−918.887			−1.17957
$780$			524.780i			0.672795i
$781$			469.976i			0.601762i
$782$	15.5370			0.0198683
$783$	−132.651			−0.169414
$784$	23.3160			0.0297397
$785$			886.339i			1.12909i
$786$	576.184			0.733059
$787$	1136.37			1.44392			0.721962	−	0.691932i	$-0.243240\pi$
$787$	1136.37			1.44392			0.721962	+	0.691932i	$0.243240\pi$
$788$	−530.657			−0.673422
$789$	181.985			0.230652
$790$			1228.13i			1.55459i
$791$		−	1554.38i		−	1.96509i
$792$	−33.9791			−0.0429029
$793$	739.989			0.933151
$794$	−480.827			−0.605576
$795$	−590.675			−0.742987
$796$	262.897			0.330272
$797$			394.545i			0.495038i	0.968883	+	0.247519i	$0.0796152\pi$
$797$			394.545i			0.495038i	−0.968883	+	0.247519i	$0.920385\pi$
$798$		−	534.607i		−	0.669934i
$799$			304.458i			0.381049i
$800$			197.948i			0.247435i
$801$		−	199.784i		−	0.249418i
$802$	47.5900			0.0593392
$803$	96.3583			0.119998
$804$		−	111.043i		−	0.138113i
$805$		−	71.3735i		−	0.0886627i
$806$		−	130.911i		−	0.162420i
$807$		−	813.338i		−	1.00785i
$808$	−279.046			−0.345354
$809$			1246.53i			1.54083i	0.637545	+	0.770413i	$0.279950\pi$
$809$			1246.53i			1.54083i	−0.637545	+	0.770413i	$0.720050\pi$
$810$			98.5839i			0.121709i
$811$			468.351i			0.577499i	0.957405	+	0.288749i	$0.0932394\pi$
$811$			468.351i			0.577499i	−0.957405	+	0.288749i	$0.906761\pi$
$812$	378.064			0.465596
$813$	321.101			0.394958
$814$			329.799i			0.405158i
$815$	896.356			1.09982
$816$	61.1631			0.0749548
$817$		−	2377.52i		−	2.91006i
$818$	−53.2049			−0.0650427
$819$		−	434.475i		−	0.530494i
$820$	−482.933			−0.588942
$821$		−	77.0645i		−	0.0938666i	−0.998898	−	0.0469333i	$-0.985055\pi$
$821$		−	77.0645i		−	0.0938666i	0.998898	−	0.0469333i	$-0.0149448\pi$
$822$			5.46065i			0.00664313i
$823$		−	332.546i		−	0.404066i	−0.979379	−	0.202033i	$-0.935245\pi$
$823$		−	332.546i		−	0.404066i	0.979379	−	0.202033i	$-0.0647548\pi$
$824$	19.9512			0.0242126
$825$		−	242.707i		−	0.294190i
$826$	506.845	−	353.310i	0.613613	−	0.427736i
$827$	−1240.44			−1.49993			−0.749964	−	0.661478i	$-0.769929\pi$
$827$	−1240.44			−1.49993			−0.749964	+	0.661478i	$0.769929\pi$
$828$			7.46680i			0.00901787i
$829$	228.732			0.275913			0.137957	−	0.990438i	$-0.455947\pi$
$829$	228.732			0.275913			0.137957	+	0.990438i	$0.455947\pi$
$830$	−1657.68			−1.99720
$831$	814.994			0.980739
$832$			156.469i			0.188064i
$833$	51.4591			0.0617756
$834$		−	278.727i		−	0.334205i
$835$	81.6657			0.0978032
$836$		−	236.064i		−	0.282373i
$837$		−	24.5926i		−	0.0293818i
$838$	−577.857			−0.689567
$839$		−	752.073i		−	0.896392i	−0.893935	−	0.448196i	$-0.852067\pi$
$839$		−	752.073i		−	0.896392i	0.893935	−	0.448196i	$-0.147933\pi$
$840$		−	280.970i		−	0.334488i
$841$	−189.281			−0.225067
$842$	912.400			1.08361
$843$	−192.286			−0.228098
$844$		−	725.925i		−	0.860101i
$845$	−1653.97			−1.95736
$846$	−146.317			−0.172952
$847$	777.224			0.917620
$848$	−176.116			−0.207684
$849$			141.699i			0.166902i
$850$			436.877i			0.513973i
$851$	72.4723			0.0851614
$852$	406.557			0.477179
$853$	−713.731			−0.836731			−0.418365	−	0.908279i	$-0.637397\pi$
$853$	−713.731			−0.836731			−0.418365	+	0.908279i	$0.637397\pi$
$854$	−396.193			−0.463926
$855$	−684.895			−0.801047
$856$		−	162.404i		−	0.189725i
$857$			572.158i			0.667629i	0.942639	+	0.333815i	$0.108336\pi$
$857$			572.158i			0.667629i	−0.942639	+	0.333815i	$0.891664\pi$
$858$		−	191.849i		−	0.223600i
$859$			604.917i			0.704211i	0.935960	+	0.352105i	$0.114534\pi$
$859$			604.917i			0.704211i	−0.935960	+	0.352105i	$0.885466\pi$
$860$		−	1249.53i		−	1.45295i
$861$	399.828			0.464377
$862$	435.825			0.505598
$863$		−	588.590i		−	0.682028i	−0.940058	−	0.341014i	$-0.889230\pi$
$863$		−	588.590i		−	0.682028i	0.940058	−	0.341014i	$-0.110770\pi$
$864$			29.3939i			0.0340207i
$865$		−	533.987i		−	0.617326i
$866$		−	1109.55i		−	1.28124i
$867$	−365.574			−0.421654
$868$			70.0902i			0.0807491i
$869$		−	448.978i		−	0.516660i
$870$		−	484.344i		−	0.556718i
$871$	626.956			0.719812
$872$	392.082			0.449635
$873$		−	292.395i		−	0.334931i
$874$	−51.8743			−0.0593528
$875$	573.100			0.654971
$876$		−	83.3555i		−	0.0951547i
$877$	−1654.43			−1.88646			−0.943232	−	0.332136i	$-0.892231\pi$
$877$	−1654.43			−1.88646			−0.943232	+	0.332136i	$0.892231\pi$
$878$		−	512.296i		−	0.583481i
$879$	−363.376			−0.413398
$880$		−	124.066i		−	0.140984i
$881$		−	82.6260i		−	0.0937866i	−0.998900	−	0.0468933i	$-0.985068\pi$
$881$		−	82.6260i		−	0.0937866i	0.998900	−	0.0468933i	$-0.0149321\pi$
$882$			24.7303i			0.0280389i
$883$	−1094.98			−1.24007			−0.620035	−	0.784574i	$-0.712882\pi$
$883$	−1094.98			−1.24007			−0.620035	+	0.784574i	$0.712882\pi$
$884$			345.332i			0.390647i
$885$	−452.632	−	649.328i	−0.511448	−	0.733704i
$886$	69.6825			0.0786484
$887$			91.1653i			0.102779i	0.998679	+	0.0513897i	$0.0163651\pi$
$887$			91.1653i			0.102779i	−0.998679	+	0.0513897i	$0.983635\pi$
$888$	285.295			0.321278
$889$	−1410.22			−1.58630
$890$	729.462			0.819620
$891$		−	36.0402i		−	0.0404492i
$892$	138.040			0.154753
$893$		−	1016.51i		−	1.13831i
$894$	141.014			0.157734
$895$			1177.99i			1.31619i
$896$		−	83.7742i		−	0.0934980i
$897$	−42.1582			−0.0469991
$898$			544.047i			0.605843i
$899$			120.824i			0.134398i
$900$	−209.955			−0.233284
$901$	−388.694			−0.431403
$902$	176.550			0.195732
$903$			1034.51i			1.14564i
$904$	−593.742			−0.656794
$905$	−628.900			−0.694917
$906$	61.2085			0.0675590
$907$	−926.857			−1.02189			−0.510947	−	0.859612i	$-0.670705\pi$
$907$	−926.857			−1.02189			−0.510947	+	0.859612i	$0.670705\pi$
$908$			269.231i			0.296510i
$909$		−	295.973i		−	0.325603i
$910$	1586.38			1.74327
$911$	118.777			0.130380			0.0651902	−	0.997873i	$-0.479235\pi$
$911$	118.777			0.130380			0.0651902	+	0.997873i	$0.479235\pi$
$912$	−204.209			−0.223913
$913$	606.012			0.663759
$914$	588.603			0.643985
$915$			507.570i			0.554721i
$916$			642.393i			0.701303i
$917$		−	1741.77i		−	1.89942i
$918$			64.8732i			0.0706680i
$919$		−	1249.99i		−	1.36016i	−0.733137	−	0.680081i	$-0.761944\pi$
$919$		−	1249.99i		−	1.36016i	0.733137	−	0.680081i	$-0.238056\pi$
$920$	−27.2632			−0.0296339
$921$	−417.465			−0.453274
$922$		−	315.038i		−	0.341689i
$923$			2295.46i			2.48695i
$924$			102.717i			0.111165i
$925$			2037.81i			2.20304i
$926$	205.484			0.221905
$927$			21.1614i			0.0228279i
$928$		−	144.413i		−	0.155617i
$929$		−	1432.06i		−	1.54151i	−0.637133	−	0.770754i	$-0.719880\pi$
$929$		−	1432.06i		−	1.54151i	0.637133	−	0.770754i	$-0.280120\pi$
$930$	89.7938			0.0965525
$931$	−171.810			−0.184543
$932$		−	282.435i		−	0.303042i
$933$	−7.80259			−0.00836291
$934$	−548.580			−0.587345
$935$		−	273.818i		−	0.292854i
$936$	−165.960			−0.177308
$937$			331.956i			0.354276i	0.984186	+	0.177138i	$0.0566838\pi$
$937$			331.956i			0.354276i	−0.984186	+	0.177138i	$0.943316\pi$
$938$	−335.675			−0.357862
$939$		−	848.440i		−	0.903557i
$940$		−	534.241i		−	0.568342i
$941$			1114.80i			1.18470i	0.805682	+	0.592349i	$0.201799\pi$
$941$			1114.80i			1.18470i	−0.805682	+	0.592349i	$0.798201\pi$
$942$	−280.302			−0.297561
$943$		−	38.7964i		−	0.0411414i
$944$	−134.957	−	193.604i	−0.142963	−	0.205089i
$945$	298.013			0.315358
$946$			456.804i			0.482879i
$947$	−1671.37			−1.76491			−0.882457	−	0.470393i	$-0.844112\pi$
$947$	−1671.37			−1.76491			−0.882457	+	0.470393i	$0.844112\pi$
$948$	−388.392			−0.409696
$949$	470.633			0.495925
$950$		−	1458.63i		−	1.53540i
$951$	865.676			0.910280
$952$		−	184.892i		−	0.194215i
$953$	212.089			0.222549			0.111275	−	0.993790i	$-0.464507\pi$
$953$	212.089			0.222549			0.111275	+	0.993790i	$0.464507\pi$
$954$		−	186.799i		−	0.195806i
$955$			105.334i			0.110298i
$956$	−85.7026			−0.0896471
$957$			177.066i			0.185022i
$958$		−	1028.64i		−	1.07374i
$959$	16.5072			0.0172130
$960$	−107.325			−0.111796
$961$	938.600			0.976691
$962$			1610.80i			1.67443i
$963$	172.256			0.178874
$964$	−335.242			−0.347761
$965$	1678.19			1.73906
$966$	22.5717			0.0233661
$967$			1471.95i			1.52218i	0.648648	+	0.761088i	$0.275335\pi$
$967$			1471.95i			1.52218i	−0.648648	+	0.761088i	$0.724665\pi$
$968$		−	296.884i		−	0.306698i
$969$	−450.696			−0.465114
$970$	1067.61			1.10063
$971$	−594.572			−0.612330			−0.306165	−	0.951979i	$-0.599046\pi$
$971$	−594.572			−0.612330			−0.306165	+	0.951979i	$0.599046\pi$
$972$	−31.1769			−0.0320750
$973$	−842.574			−0.865955
$974$		−	695.208i		−	0.713766i
$975$		−	1185.43i		−	1.21582i
$976$			151.338i			0.155059i
$977$			370.295i			0.379012i	0.981880	+	0.189506i	$0.0606887\pi$
$977$			370.295i			0.379012i	−0.981880	+	0.189506i	$0.939311\pi$
$978$			283.470i			0.289847i
$979$	−266.676			−0.272396
$980$	−90.2967			−0.0921395
$981$			415.865i			0.423920i
$982$			1027.24i			1.04607i
$983$		−	632.522i		−	0.643461i	−0.946831	−	0.321730i	$-0.895736\pi$
$983$		−	632.522i		−	0.643461i	0.946831	−	0.321730i	$-0.104264\pi$
$984$		−	152.726i		−	0.155210i
$985$	2055.10			2.08639
$986$		−	318.723i		−	0.323249i
$987$			442.308i			0.448133i
$988$		−	1152.98i		−	1.16699i
$989$	100.381			0.101498
$990$	131.592			0.132921
$991$			897.086i			0.905233i	0.891705	+	0.452616i	$0.149509\pi$
$991$			897.086i			0.905233i	−0.891705	+	0.452616i	$0.850491\pi$
$992$	26.7730			0.0269889
$993$	−649.721			−0.654301
$994$		−	1229.00i		−	1.23642i
$995$	−1018.13			−1.02325
$996$		−	524.236i		−	0.526341i
$997$	−178.238			−0.178774			−0.0893871	−	0.995997i	$-0.528491\pi$
$997$	−178.238			−0.178774			−0.0893871	+	0.995997i	$0.528491\pi$
$998$			879.068i			0.880829i
$999$			302.601i			0.302904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.d.a.235.20	yes	20
3.2	odd	2		1062.3.d.f.235.1		20
59.58	odd	2	inner	354.3.d.a.235.10	✓	20
177.176	even	2		1062.3.d.f.235.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.d.a.235.10	✓	20	59.58	odd	2	inner
354.3.d.a.235.20	yes	20	1.1	even	1	trivial
1062.3.d.f.235.1		20	3.2	odd	2
1062.3.d.f.235.11		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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +7.74549 q^{5} +2.44949i q^{6} +7.40466 q^{7} -2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +1.73205 q^{3} -2.00000 q^{4} +7.74549 q^{5} +2.44949i q^{6} +7.40466 q^{7} -2.82843i q^{8} +3.00000 q^{9} +10.9538i q^{10} -4.00447i q^{11} -3.46410 q^{12} -19.5586i q^{13} +10.4718i q^{14} +13.4156 q^{15} +4.00000 q^{16} +8.82813 q^{17} +4.24264i q^{18} -29.4750 q^{19} -15.4910 q^{20} +12.8252 q^{21} +5.66318 q^{22} -1.24447i q^{23} -4.89898i q^{24} +34.9926 q^{25} +27.6601 q^{26} +5.19615 q^{27} -14.8093 q^{28} -25.5288 q^{29} +18.9725i q^{30} -4.73284i q^{31} +5.65685i q^{32} -6.93595i q^{33} +12.4849i q^{34} +57.3527 q^{35} -6.00000 q^{36} +58.2356i q^{37} -41.6840i q^{38} -33.8765i q^{39} -21.9075i q^{40} +31.1751 q^{41} +18.1376i q^{42} +80.6621i q^{43} +8.00894i q^{44} +23.2365 q^{45} +1.75994 q^{46} +34.4873i q^{47} +6.92820 q^{48} +5.82899 q^{49} +49.4869i q^{50} +15.2908 q^{51} +39.1172i q^{52} -44.0290 q^{53} +7.34847i q^{54} -31.0166i q^{55} -20.9435i q^{56} -51.0522 q^{57} -36.1031i q^{58} +(-33.7393 - 48.4011i) q^{59} -26.8312 q^{60} +37.8344i q^{61} +6.69325 q^{62} +22.2140 q^{63} -8.00000 q^{64} -151.491i q^{65} +9.80891 q^{66} +32.0552i q^{67} -17.6563 q^{68} -2.15548i q^{69} +81.1090i q^{70} -117.363 q^{71} -8.48528i q^{72} +24.0627i q^{73} -82.3576 q^{74} +60.6089 q^{75} +58.9501 q^{76} -29.6518i q^{77} +47.9086 q^{78} +112.119 q^{79} +30.9819 q^{80} +9.00000 q^{81} +44.0883i q^{82} +151.334i q^{83} -25.6505 q^{84} +68.3782 q^{85} -114.073 q^{86} -44.2171 q^{87} -11.3264 q^{88} -66.5946i q^{89} +32.8613i q^{90} -144.825i q^{91} +2.48893i q^{92} -8.19753i q^{93} -48.7724 q^{94} -228.298 q^{95} +9.79796i q^{96} -97.4651i q^{97} +8.24343i q^{98} -12.0134i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} + 8 q^{7} + 60 q^{9}+O(q^{10}) \) 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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