LMFDB - Embedded newform 354.5.d.a.235.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,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, 5, names="a")

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.8
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -8.58312 q^{5} -14.6969i q^{6} +95.1629 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -8.58312 q^{5} -14.6969i q^{6} +95.1629 q^{7} -22.6274i q^{8} +27.0000 q^{9} -24.2767i q^{10} +131.932i q^{11} +41.5692 q^{12} -273.586i q^{13} +269.161i q^{14} +44.5992 q^{15} +64.0000 q^{16} -52.4071 q^{17} +76.3675i q^{18} -545.702 q^{19} +68.6650 q^{20} -494.481 q^{21} -373.160 q^{22} -456.661i q^{23} +117.576i q^{24} -551.330 q^{25} +773.818 q^{26} -140.296 q^{27} -761.303 q^{28} +1257.37 q^{29} +126.146i q^{30} -1294.22i q^{31} +181.019i q^{32} -685.539i q^{33} -148.230i q^{34} -816.795 q^{35} -216.000 q^{36} +1292.32i q^{37} -1543.48i q^{38} +1421.59i q^{39} +194.214i q^{40} -410.070 q^{41} -1398.60i q^{42} -1101.32i q^{43} -1055.46i q^{44} -231.744 q^{45} +1291.63 q^{46} -21.4964i q^{47} -332.554 q^{48} +6654.98 q^{49} -1559.40i q^{50} +272.315 q^{51} +2188.69i q^{52} +5039.67 q^{53} -396.817i q^{54} -1132.39i q^{55} -2153.29i q^{56} +2835.55 q^{57} +3556.39i q^{58} +(899.512 - 3362.77i) q^{59} -356.794 q^{60} -5229.91i q^{61} +3660.60 q^{62} +2569.40 q^{63} -512.000 q^{64} +2348.22i q^{65} +1939.00 q^{66} +4921.99i q^{67} +419.257 q^{68} +2372.88i q^{69} -2310.24i q^{70} -367.053 q^{71} -610.940i q^{72} -7394.47i q^{73} -3655.23 q^{74} +2864.80 q^{75} +4365.61 q^{76} +12555.0i q^{77} -4020.87 q^{78} -5329.52 q^{79} -549.320 q^{80} +729.000 q^{81} -1159.85i q^{82} +2810.66i q^{83} +3955.85 q^{84} +449.816 q^{85} +3115.01 q^{86} -6533.50 q^{87} +2985.28 q^{88} -10299.9i q^{89} -655.472i q^{90} -26035.2i q^{91} +3653.28i q^{92} +6724.95i q^{93} +60.8010 q^{94} +4683.82 q^{95} -940.604i q^{96} +1028.81i q^{97} +18823.1i q^{98} +3562.17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	$ 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) $ 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * 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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−8.00000			−0.500000
$5$	−8.58312			−0.343325			−0.171662	−	0.985156i	$-0.554914\pi$
$5$	−8.58312			−0.343325			−0.171662	+	0.985156i	$0.554914\pi$
$6$		−	14.6969i		−	0.408248i
$7$	95.1629			1.94210			0.971050	−	0.238875i	$-0.0767786\pi$
$7$	95.1629			1.94210			0.971050	+	0.238875i	$0.0767786\pi$
$8$		−	22.6274i		−	0.353553i
$9$	27.0000			0.333333
$10$		−	24.2767i		−	0.242767i
$11$			131.932i			1.09035i	0.838323	+	0.545174i	$0.183536\pi$
$11$			131.932i			1.09035i	−0.838323	+	0.545174i	$0.816464\pi$
$12$	41.5692			0.288675
$13$		−	273.586i		−	1.61885i	−0.587222	−	0.809426i	$-0.699779\pi$
$13$		−	273.586i		−	1.61885i	0.587222	−	0.809426i	$-0.300221\pi$
$14$			269.161i			1.37327i
$15$	44.5992			0.198219
$16$	64.0000			0.250000
$17$	−52.4071			−0.181339			−0.0906697	−	0.995881i	$-0.528901\pi$
$17$	−52.4071			−0.181339			−0.0906697	+	0.995881i	$0.528901\pi$
$18$			76.3675i			0.235702i
$19$	−545.702			−1.51164			−0.755820	−	0.654780i	$-0.772761\pi$
$19$	−545.702			−1.51164			−0.755820	+	0.654780i	$0.772761\pi$
$20$	68.6650			0.171662
$21$	−494.481			−1.12127
$22$	−373.160			−0.770993
$23$		−	456.661i		−	0.863252i	−0.902053	−	0.431626i	$-0.857940\pi$
$23$		−	456.661i		−	0.863252i	0.902053	−	0.431626i	$-0.142060\pi$
$24$			117.576i			0.204124i
$25$	−551.330			−0.882128
$26$	773.818			1.14470
$27$	−140.296			−0.192450
$28$	−761.303			−0.971050
$29$	1257.37			1.49509			0.747546	−	0.664210i	$-0.231232\pi$
$29$	1257.37			1.49509			0.747546	+	0.664210i	$0.231232\pi$
$30$			126.146i			0.140162i
$31$		−	1294.22i		−	1.34674i	−0.739306	−	0.673370i	$-0.764846\pi$
$31$		−	1294.22i		−	1.34674i	0.739306	−	0.673370i	$-0.235154\pi$
$32$			181.019i			0.176777i
$33$		−	685.539i		−	0.629513i
$34$		−	148.230i		−	0.128226i
$35$	−816.795			−0.666771
$36$	−216.000			−0.166667
$37$			1292.32i			0.943988i	0.881602	+	0.471994i	$0.156466\pi$
$37$			1292.32i			0.943988i	−0.881602	+	0.471994i	$0.843534\pi$
$38$		−	1543.48i		−	1.06889i
$39$			1421.59i			0.934644i
$40$			194.214i			0.121384i
$41$	−410.070			−0.243944			−0.121972	−	0.992534i	$-0.538922\pi$
$41$	−410.070			−0.243944			−0.121972	+	0.992534i	$0.538922\pi$
$42$		−	1398.60i		−	0.792859i
$43$		−	1101.32i		−	0.595631i	−0.954623	−	0.297815i	$-0.903742\pi$
$43$		−	1101.32i		−	0.595631i	0.954623	−	0.297815i	$-0.0962580\pi$
$44$		−	1055.46i		−	0.545174i
$45$	−231.744			−0.114442
$46$	1291.63			0.610412
$47$		−	21.4964i		−	0.00973129i	−0.999988	−	0.00486564i	$-0.998451\pi$
$47$		−	21.4964i		−	0.00973129i	0.999988	−	0.00486564i	$-0.00154879\pi$
$48$	−332.554			−0.144338
$49$	6654.98			2.77176
$50$		−	1559.40i		−	0.623759i
$51$	272.315			0.104696
$52$			2188.69i			0.809426i
$53$	5039.67			1.79412			0.897058	−	0.441913i	$-0.145700\pi$
$53$	5039.67			1.79412			0.897058	+	0.441913i	$0.145700\pi$
$54$		−	396.817i		−	0.136083i
$55$		−	1132.39i		−	0.374344i
$56$		−	2153.29i		−	0.686636i
$57$	2835.55			0.872745
$58$			3556.39i			1.05719i
$59$	899.512	−	3362.77i	0.258406	−	0.966036i
$59$	899.512	−	3362.77i	0.258406	−	0.966036i
$60$	−356.794			−0.0991093
$61$		−	5229.91i		−	1.40551i	−0.711431	−	0.702756i	$-0.751953\pi$
$61$		−	5229.91i		−	1.40551i	0.711431	−	0.702756i	$-0.248047\pi$
$62$	3660.60			0.952289
$63$	2569.40			0.647367
$64$	−512.000			−0.125000
$65$			2348.22i			0.555792i
$66$	1939.00			0.445133
$67$			4921.99i			1.09646i	0.836329	+	0.548228i	$0.184697\pi$
$67$			4921.99i			1.09646i	−0.836329	+	0.548228i	$0.815303\pi$
$68$	419.257			0.0906697
$69$			2372.88i			0.498399i
$70$		−	2310.24i		−	0.471479i
$71$	−367.053			−0.0728134			−0.0364067	−	0.999337i	$-0.511591\pi$
$71$	−367.053			−0.0728134			−0.0364067	+	0.999337i	$0.511591\pi$
$72$		−	610.940i		−	0.117851i
$73$		−	7394.47i		−	1.38759i	−0.720172	−	0.693795i	$-0.755937\pi$
$73$		−	7394.47i		−	1.38759i	0.720172	−	0.693795i	$-0.244063\pi$
$74$	−3655.23			−0.667500
$75$	2864.80			0.509297
$76$	4365.61			0.755820
$77$			12555.0i			2.11757i
$78$	−4020.87			−0.660893
$79$	−5329.52			−0.853953			−0.426976	−	0.904263i	$-0.640421\pi$
$79$	−5329.52			−0.853953			−0.426976	+	0.904263i	$0.640421\pi$
$80$	−549.320			−0.0858312
$81$	729.000			0.111111
$82$		−	1159.85i		−	0.172495i
$83$			2810.66i			0.407993i	0.978972	+	0.203996i	$0.0653931\pi$
$83$			2810.66i			0.407993i	−0.978972	+	0.203996i	$0.934607\pi$
$84$	3955.85			0.560636
$85$	449.816			0.0622583
$86$	3115.01			0.421175
$87$	−6533.50			−0.863192
$88$	2985.28			0.385496
$89$		−	10299.9i		−	1.30033i	−0.759792	−	0.650166i	$-0.774699\pi$
$89$		−	10299.9i		−	1.30033i	0.759792	−	0.650166i	$-0.225301\pi$
$90$		−	655.472i		−	0.0809224i
$91$		−	26035.2i		−	3.14397i
$92$			3653.28i			0.431626i
$93$			6724.95i			0.777541i
$94$	60.8010			0.00688106
$95$	4683.82			0.518983
$96$		−	940.604i		−	0.102062i
$97$			1028.81i			0.109343i	0.998504	+	0.0546717i	$0.0174112\pi$
$97$			1028.81i			0.109343i	−0.998504	+	0.0546717i	$0.982589\pi$
$98$			18823.1i			1.95993i
$99$			3562.17i			0.363449i
$100$	4410.64			0.441064
$101$			12468.5i			1.22228i	0.791522	+	0.611140i	$0.209289\pi$
$101$			12468.5i			1.22228i	−0.791522	+	0.611140i	$0.790711\pi$
$102$			770.224i			0.0740315i
$103$		−	4502.00i		−	0.424356i	−0.977231	−	0.212178i	$-0.931944\pi$
$103$		−	4502.00i		−	0.424356i	0.977231	−	0.212178i	$-0.0680557\pi$
$104$	−6190.54			−0.572350
$105$	4244.19			0.384961
$106$			14254.3i			1.26863i
$107$	10435.7			0.911493			0.455747	−	0.890110i	$-0.349372\pi$
$107$	10435.7			0.911493			0.455747	+	0.890110i	$0.349372\pi$
$108$	1122.37			0.0962250
$109$		−	506.543i		−	0.0426347i	−0.999773	−	0.0213174i	$-0.993214\pi$
$109$		−	506.543i		−	0.0426347i	0.999773	−	0.0213174i	$-0.00678604\pi$
$110$	3202.88			0.264701
$111$		−	6715.09i		−	0.545011i
$112$	6090.43			0.485525
$113$		−	15400.8i		−	1.20611i	−0.797699	−	0.603056i	$-0.793949\pi$
$113$		−	15400.8i		−	1.20611i	0.797699	−	0.603056i	$-0.206051\pi$
$114$			8020.15i			0.617124i
$115$			3919.57i			0.296376i
$116$	−10059.0			−0.747546
$117$		−	7386.82i		−	0.539617i
$118$	9511.36	+	2544.21i	0.683091	+	0.182721i
$119$	−4987.21			−0.352179
$120$		−	1009.16i		−	0.0700809i
$121$	−2765.09			−0.188859
$122$	14792.4			0.993847
$123$	2130.79			0.140841
$124$			10353.7i			0.673370i
$125$	10096.6			0.646181
$126$			7267.36i			0.457758i
$127$	27110.8			1.68088			0.840438	−	0.541908i	$-0.182298\pi$
$127$	27110.8			1.68088			0.840438	+	0.541908i	$0.182298\pi$
$128$		−	1448.15i		−	0.0883883i
$129$			5722.63i			0.343888i
$130$	−6641.77			−0.393004
$131$		−	23150.8i		−	1.34904i	−0.738259	−	0.674518i	$-0.764352\pi$
$131$		−	23150.8i		−	1.34904i	0.738259	−	0.674518i	$-0.235648\pi$
$132$			5484.32i			0.314756i
$133$	−51930.6			−2.93576
$134$	−13921.5			−0.775312
$135$	1204.18			0.0660729
$136$			1185.84i			0.0641132i
$137$	18148.8			0.966959			0.483479	−	0.875356i	$-0.339373\pi$
$137$	18148.8			0.966959			0.483479	+	0.875356i	$0.339373\pi$
$138$	−6711.51			−0.352421
$139$	16684.5			0.863542			0.431771	−	0.901983i	$-0.357889\pi$
$139$	16684.5			0.863542			0.431771	+	0.901983i	$0.357889\pi$
$140$	6534.36			0.333386
$141$			111.699i			0.00561836i
$142$		−	1038.18i		−	0.0514869i
$143$	36094.8			1.76511
$144$	1728.00			0.0833333
$145$	−10792.2			−0.513302
$146$	20914.7			0.981174
$147$	−34580.3			−1.60027
$148$		−	10338.6i		−	0.471994i
$149$		−	411.005i		−	0.0185129i	−0.999957	−	0.00925646i	$-0.997054\pi$
$149$		−	411.005i		−	0.0185129i	0.999957	−	0.00925646i	$-0.00294646\pi$
$150$			8102.86i			0.360127i
$151$			53.0397i			0.00232620i	0.999999	+	0.00116310i	$0.000370227\pi$
$151$			53.0397i			0.00232620i	−0.999999	+	0.00116310i	$0.999630\pi$
$152$			12347.8i			0.534445i
$153$	−1414.99			−0.0604465
$154$	−35511.0			−1.49735
$155$			11108.4i			0.462369i
$156$		−	11372.8i		−	0.467322i
$157$			2381.02i			0.0965972i	0.998833	+	0.0482986i	$0.0153799\pi$
$157$			2381.02i			0.0965972i	−0.998833	+	0.0482986i	$0.984620\pi$
$158$		−	15074.2i		−	0.603836i
$159$	−26186.9			−1.03583
$160$		−	1553.71i		−	0.0606918i
$161$		−	43457.2i		−	1.67652i
$162$			2061.92i			0.0785674i
$163$	23710.8			0.892425			0.446213	−	0.894927i	$-0.352773\pi$
$163$	23710.8			0.892425			0.446213	+	0.894927i	$0.352773\pi$
$164$	3280.56			0.121972
$165$			5884.07i			0.216127i
$166$	−7949.75			−0.288494
$167$	−37806.5			−1.35561			−0.677803	−	0.735243i	$-0.737068\pi$
$167$	−37806.5			−1.35561			−0.677803	+	0.735243i	$0.737068\pi$
$168$			11188.8i			0.396430i
$169$	−46288.2			−1.62068
$170$			1272.27i			0.0440233i
$171$	−14734.0			−0.503880
$172$			8810.57i			0.297815i
$173$			25970.2i			0.867726i	0.900979	+	0.433863i	$0.142850\pi$
$173$			25970.2i			0.867726i	−0.900979	+	0.433863i	$0.857150\pi$
$174$		−	18479.5i		−	0.610369i
$175$	−52466.2			−1.71318
$176$			8443.66i			0.272587i
$177$	−4674.00	+	17473.5i	−0.149191	+	0.557741i
$178$	29132.6			0.919473
$179$			4265.61i			0.133130i	0.997782	+	0.0665649i	$0.0212039\pi$
$179$			4265.61i			0.133130i	−0.997782	+	0.0665649i	$0.978796\pi$
$180$	1853.95			0.0572208
$181$	−12314.3			−0.375883			−0.187941	−	0.982180i	$-0.560182\pi$
$181$	−12314.3			−0.375883			−0.187941	+	0.982180i	$0.560182\pi$
$182$	73638.8			2.22312
$183$			27175.4i			0.811473i
$184$	−10333.0			−0.305206
$185$		−	11092.1i		−	0.324094i
$186$	−19021.0			−0.549804
$187$		−	6914.18i		−	0.197723i
$188$			171.971i			0.00486564i
$189$	−13351.0			−0.373757
$190$			13247.9i			0.366977i
$191$		−	26041.6i		−	0.713839i	−0.934135	−	0.356920i	$-0.883827\pi$
$191$		−	26041.6i		−	0.713839i	0.934135	−	0.356920i	$-0.116173\pi$
$192$	2660.43			0.0721688
$193$	37989.9			1.01989			0.509946	−	0.860207i	$-0.329666\pi$
$193$	37989.9			1.01989			0.509946	+	0.860207i	$0.329666\pi$
$194$	−2909.92			−0.0773175
$195$		−	12201.7i		−	0.320887i
$196$	−53239.9			−1.38588
$197$	−22213.8			−0.572388			−0.286194	−	0.958172i	$-0.592390\pi$
$197$	−22213.8			−0.572388			−0.286194	+	0.958172i	$0.592390\pi$
$198$	−10075.3			−0.256998
$199$	−30281.6			−0.764668			−0.382334	−	0.924024i	$-0.624880\pi$
$199$	−30281.6			−0.764668			−0.382334	+	0.924024i	$0.624880\pi$
$200$			12475.2i			0.311879i
$201$		−	25575.4i		−	0.633039i
$202$	−35266.2			−0.864283
$203$	119655.			2.90362
$204$	−2178.52			−0.0523482
$205$	3519.68			0.0837521
$206$	12733.6			0.300065
$207$		−	12329.8i		−	0.287751i
$208$		−	17509.5i		−	0.404713i
$209$		−	71995.6i		−	1.64821i
$210$			12004.4i			0.272208i
$211$			31773.1i			0.713666i	0.934168	+	0.356833i	$0.116143\pi$
$211$			31773.1i			0.713666i	−0.934168	+	0.356833i	$0.883857\pi$
$212$	−40317.4			−0.897058
$213$	1907.26			0.0420389
$214$			29516.6i			0.644523i
$215$			9452.77i			0.204495i
$216$			3174.54i			0.0680414i
$217$		−	123161.i		−	2.61550i
$218$	1432.72			0.0301473
$219$			38422.8i			0.801126i
$220$			9059.11i			0.187172i
$221$			14337.8i			0.293562i
$222$	18993.1			0.385381
$223$	−87090.0			−1.75129			−0.875646	−	0.482954i	$-0.839564\pi$
$223$	−87090.0			−1.75129			−0.875646	+	0.482954i	$0.839564\pi$
$224$			17226.3i			0.343318i
$225$	−14885.9			−0.294043
$226$	43560.2			0.852850
$227$			84408.6i			1.63808i	0.573737	+	0.819040i	$0.305493\pi$
$227$			84408.6i			1.63808i	−0.573737	+	0.819040i	$0.694507\pi$
$228$	−22684.4			−0.436373
$229$		−	99672.5i		−	1.90066i	−0.311246	−	0.950329i	$-0.600746\pi$
$229$		−	99672.5i		−	1.90066i	0.311246	−	0.950329i	$-0.399254\pi$
$230$	−11086.2			−0.209569
$231$		−	65237.9i		−	1.22258i
$232$		−	28451.1i		−	0.528595i
$233$		−	53625.0i		−	0.987768i	−0.869528	−	0.493884i	$-0.835577\pi$
$233$		−	53625.0i		−	0.987768i	0.869528	−	0.493884i	$-0.164423\pi$
$234$	20893.1			0.381567
$235$			184.506i			0.00334099i
$236$	−7196.10	+	26902.2i	−0.129203	+	0.483018i
$237$	27693.0			0.493030
$238$		−	14106.0i		−	0.249028i
$239$	−21269.8			−0.372364			−0.186182	−	0.982515i	$-0.559611\pi$
$239$	−21269.8			−0.372364			−0.186182	+	0.982515i	$0.559611\pi$
$240$	2854.35			0.0495547
$241$	8327.41			0.143376			0.0716879	−	0.997427i	$-0.477161\pi$
$241$	8327.41			0.143376			0.0716879	+	0.997427i	$0.477161\pi$
$242$		−	7820.85i		−	0.133544i
$243$	−3788.00			−0.0641500
$244$			41839.3i			0.702756i
$245$	−57120.5			−0.951612
$246$			6026.78i			0.0995898i
$247$			149296.i			2.44712i
$248$	−29284.8			−0.476144
$249$		−	14604.6i		−	0.235555i
$250$			28557.4i			0.456919i
$251$	19842.1			0.314950			0.157475	−	0.987523i	$-0.449665\pi$
$251$	19842.1			0.314950			0.157475	+	0.987523i	$0.449665\pi$
$252$	−20555.2			−0.323683
$253$	60248.2			0.941246
$254$			76681.0i			1.18856i
$255$	−2337.31			−0.0359449
$256$	4096.00			0.0625000
$257$	−98630.3			−1.49329			−0.746645	−	0.665223i	$-0.768337\pi$
$257$	−98630.3			−1.49329			−0.746645	+	0.665223i	$0.768337\pi$
$258$	−16186.1			−0.243165
$259$			122981.i			1.83332i
$260$		−	18785.8i		−	0.277896i
$261$	33949.1			0.498364
$262$	65480.3			0.953912
$263$	−62308.2			−0.900811			−0.450406	−	0.892824i	$-0.648721\pi$
$263$	−62308.2			−0.900811			−0.450406	+	0.892824i	$0.648721\pi$
$264$	−15512.0			−0.222566
$265$	−43256.1			−0.615965
$266$		−	146882.i		−	2.07589i
$267$			53520.0i			0.750747i
$268$		−	39375.9i		−	0.548228i
$269$			64567.1i			0.892291i	0.894960	+	0.446145i	$0.147204\pi$
$269$			64567.1i			0.892291i	−0.894960	+	0.446145i	$0.852796\pi$
$270$			3405.93i			0.0467206i
$271$	−12450.9			−0.169536			−0.0847679	−	0.996401i	$-0.527015\pi$
$271$	−12450.9			−0.169536			−0.0847679	+	0.996401i	$0.527015\pi$
$272$	−3354.05			−0.0453349
$273$			135283.i			1.81517i
$274$			51332.7i			0.683743i
$275$		−	72738.2i		−	0.961827i
$276$		−	18983.0i		−	0.249200i
$277$	−71095.1			−0.926575			−0.463287	−	0.886208i	$-0.653330\pi$
$277$	−71095.1			−0.926575			−0.463287	+	0.886208i	$0.653330\pi$
$278$			47190.9i			0.610616i
$279$		−	34943.9i		−	0.448913i
$280$			18482.0i			0.235739i
$281$	125076.			1.58402			0.792011	−	0.610507i	$-0.209034\pi$
$281$	125076.			1.58402			0.792011	+	0.610507i	$0.209034\pi$
$282$	−315.931			−0.00397278
$283$			17962.7i			0.224284i	0.993692	+	0.112142i	$0.0357712\pi$
$283$			17962.7i			0.224284i	−0.993692	+	0.112142i	$0.964229\pi$
$284$	2936.42			0.0364067
$285$	−24337.9			−0.299635
$286$			102091.i			1.24812i
$287$	−39023.5			−0.473764
$288$			4887.52i			0.0589256i
$289$	−80774.5			−0.967116
$290$		−	30524.9i		−	0.362959i
$291$		−	5345.87i		−	0.0631295i
$292$			59155.7i			0.693795i
$293$	115222.			1.34215			0.671073	−	0.741391i	$-0.265833\pi$
$293$	115222.			1.34215			0.671073	+	0.741391i	$0.265833\pi$
$294$		−	97807.9i		−	1.13156i
$295$	−7720.62	+	28863.1i	−0.0887173	+	0.331664i
$296$	29241.8			0.333750
$297$		−	18509.6i		−	0.209838i
$298$	1162.50			0.0130906
$299$	−124936.			−1.39748
$300$	−22918.4			−0.254648
$301$		−	104805.i		−	1.15677i
$302$	−150.019			−0.00164487
$303$		−	64788.1i		−	0.705684i
$304$	−34924.9			−0.377910
$305$			44888.9i			0.482547i
$306$		−	4002.20i		−	0.0427421i
$307$	20644.3			0.219040			0.109520	−	0.993985i	$-0.465069\pi$
$307$	20644.3			0.219040			0.109520	+	0.993985i	$0.465069\pi$
$308$		−	100440.i		−	1.05878i
$309$			23393.1i			0.245002i
$310$	−31419.4			−0.326944
$311$	177337.			1.83349			0.916746	−	0.399471i	$-0.130806\pi$
$311$	177337.			1.83349			0.916746	+	0.399471i	$0.130806\pi$
$312$	32167.0			0.330447
$313$		−	163758.i		−	1.67153i	−0.549085	−	0.835767i	$-0.685024\pi$
$313$		−	163758.i		−	1.67153i	0.549085	−	0.835767i	$-0.314976\pi$
$314$	−6734.55			−0.0683045
$315$	−22053.5			−0.222257
$316$	42636.1			0.426976
$317$	27031.8			0.269002			0.134501	−	0.990913i	$-0.457057\pi$
$317$	27031.8			0.269002			0.134501	+	0.990913i	$0.457057\pi$
$318$		−	74067.8i		−	0.732445i
$319$			165888.i			1.63017i
$320$	4394.56			0.0429156
$321$	−54225.4			−0.526251
$322$	122915.			1.18548
$323$	28598.7			0.274120
$324$	−5832.00			−0.0555556
$325$			150836.i			1.42803i
$326$			67064.4i			0.631040i
$327$			2632.07i			0.0246152i
$328$			9278.83i			0.0862473i
$329$		−	2045.66i		−	0.0188991i
$330$	−16642.7			−0.152825
$331$	−92586.9			−0.845071			−0.422536	−	0.906346i	$-0.638860\pi$
$331$	−92586.9			−0.845071			−0.422536	+	0.906346i	$0.638860\pi$
$332$		−	22485.3i		−	0.203996i
$333$			34892.6i			0.314663i
$334$		−	106933.i		−	0.958559i
$335$		−	42246.1i		−	0.376441i
$336$	−31646.8			−0.280318
$337$		−	148036.i		−	1.30349i	−0.758437	−	0.651746i	$-0.774037\pi$
$337$		−	148036.i		−	1.30349i	0.758437	−	0.651746i	$-0.225963\pi$
$338$		−	130923.i		−	1.14599i
$339$			80025.2i			0.696349i
$340$	−3598.53			−0.0311292
$341$	170749.			1.46842
$342$		−	41673.9i		−	0.356297i
$343$	404822.			3.44093
$344$	−24920.1			−0.210587
$345$		−	20366.7i		−	0.171113i
$346$	−73454.7			−0.613575
$347$			218482.i			1.81450i	0.420597	+	0.907248i	$0.361821\pi$
$347$			218482.i			1.81450i	−0.420597	+	0.907248i	$0.638179\pi$
$348$	52268.0			0.431596
$349$			31922.6i			0.262089i	0.991377	+	0.131044i	$0.0418330\pi$
$349$			31922.6i			0.262089i	−0.991377	+	0.131044i	$0.958167\pi$
$350$		−	148397.i		−	1.21140i
$351$			38383.0i			0.311548i
$352$	−23882.3			−0.192748
$353$			177507.i			1.42451i	0.701919	+	0.712257i	$0.252327\pi$
$353$			177507.i			1.42451i	−0.701919	+	0.712257i	$0.747673\pi$
$354$	−49422.5	−	13220.1i	−0.394383	−	0.105494i
$355$	3150.46			0.0249987
$356$			82399.4i			0.650166i
$357$	25914.3			0.203331
$358$	−12065.0			−0.0941370
$359$	161699.			1.25464			0.627319	−	0.778762i	$-0.284152\pi$
$359$	161699.			1.25464			0.627319	+	0.778762i	$0.284152\pi$
$360$			5243.77i			0.0404612i
$361$	167470.			1.28505
$362$		−	34830.1i		−	0.265789i
$363$	14367.8			0.109038
$364$			208282.i			1.57199i
$365$			63467.6i			0.476394i
$366$	−76863.7			−0.573798
$367$			41054.2i			0.304807i	0.988318	+	0.152404i	$0.0487013\pi$
$367$			41054.2i			0.304807i	−0.988318	+	0.152404i	$0.951299\pi$
$368$		−	29226.3i		−	0.215813i
$369$	−11071.9			−0.0813148
$370$	31373.3			0.229169
$371$	479590.			3.48435
$372$		−	53799.6i		−	0.388770i
$373$	−92005.2			−0.661294			−0.330647	−	0.943754i	$-0.607267\pi$
$373$	−92005.2			−0.661294			−0.330647	+	0.943754i	$0.607267\pi$
$374$	19556.3			0.139811
$375$	−52463.4			−0.373073
$376$	−486.408			−0.00344053
$377$		−	343999.i		−	2.42033i
$378$		−	37762.3i		−	0.264286i
$379$	11581.7			0.0806294			0.0403147	−	0.999187i	$-0.487164\pi$
$379$	11581.7			0.0806294			0.0403147	+	0.999187i	$0.487164\pi$
$380$	−37470.6			−0.259492
$381$	−140872.			−0.970454
$382$	73656.7			0.504761
$383$	−147773.			−1.00739			−0.503693	−	0.863882i	$-0.668026\pi$
$383$	−147773.			−1.00739			−0.503693	+	0.863882i	$0.668026\pi$
$384$			7524.83i			0.0510310i
$385$		−	107761.i		−	0.727013i
$386$			107452.i			0.721172i
$387$		−	29735.7i		−	0.198544i
$388$		−	8230.50i		−	0.0546717i
$389$	−64660.1			−0.427304			−0.213652	−	0.976910i	$-0.568536\pi$
$389$	−64660.1			−0.427304			−0.213652	+	0.976910i	$0.568536\pi$
$390$	34511.6			0.226901
$391$			23932.3i			0.156542i
$392$		−	150585.i		−	0.979963i
$393$			120295.i			0.778866i
$394$		−	62830.1i		−	0.404739i
$395$	45743.9			0.293183
$396$		−	28497.3i		−	0.181725i
$397$		−	154170.i		−	0.978177i	−0.872234	−	0.489089i	$-0.837329\pi$
$397$		−	154170.i		−	0.978177i	0.872234	−	0.489089i	$-0.162671\pi$
$398$		−	85649.4i		−	0.540702i
$399$	269839.			1.69496
$400$	−35285.1			−0.220532
$401$			143098.i			0.889909i	0.895553	+	0.444954i	$0.146780\pi$
$401$			143098.i			0.889909i	−0.895553	+	0.444954i	$0.853220\pi$
$402$	72338.2			0.447626
$403$	−354079.			−2.18017
$404$		−	99747.8i		−	0.611140i
$405$	−6257.09			−0.0381472
$406$			338436.i			2.05317i
$407$	−170498.			−1.02928
$408$		−	6161.79i		−	0.0370158i
$409$		−	307880.i		−	1.84050i	−0.391333	−	0.920249i	$-0.627986\pi$
$409$		−	307880.i		−	1.84050i	0.391333	−	0.920249i	$-0.372014\pi$
$410$			9955.17i			0.0592217i
$411$	−94304.2			−0.558274
$412$			36016.0i			0.212178i
$413$	85600.2	−	320011.i	0.501851	−	1.87614i
$414$	34874.0			0.203471
$415$		−	24124.2i		−	0.140074i
$416$	49524.3			0.286175
$417$	−86695.2			−0.498566
$418$	203634.			1.16546
$419$			157109.i			0.894896i	0.894310	+	0.447448i	$0.147667\pi$
$419$			157109.i			0.894896i	−0.894310	+	0.447448i	$0.852333\pi$
$420$	−33953.5			−0.192480
$421$			290700.i			1.64014i	0.572262	+	0.820071i	$0.306066\pi$
$421$			290700.i			1.64014i	−0.572262	+	0.820071i	$0.693934\pi$
$422$	−89868.0			−0.504638
$423$		−	580.403i		−	0.00324376i
$424$		−	114035.i		−	0.634316i
$425$	28893.6			0.159965
$426$			5394.55i			0.0297260i
$427$		−	497694.i		−	2.72965i
$428$	−83485.5			−0.455747
$429$	−187554.			−1.01909
$430$	−26736.5			−0.144600
$431$		−	27648.3i		−	0.148838i	−0.997227	−	0.0744191i	$-0.976290\pi$
$431$		−	27648.3i		−	0.148838i	0.997227	−	0.0744191i	$-0.0237103\pi$
$432$	−8978.95			−0.0481125
$433$	25924.5			0.138272			0.0691360	−	0.997607i	$-0.477976\pi$
$433$	25924.5			0.138272			0.0691360	+	0.997607i	$0.477976\pi$
$434$	348353.			1.84944
$435$	56077.8			0.296355
$436$			4052.34i			0.0213174i
$437$			249201.i			1.30493i
$438$	−108676.			−0.566481
$439$	88484.8			0.459134			0.229567	−	0.973293i	$-0.426269\pi$
$439$	88484.8			0.459134			0.229567	+	0.973293i	$0.426269\pi$
$440$	−25623.0			−0.132350
$441$	179685.			0.923918
$442$	−40553.5			−0.207579
$443$		−	249080.i		−	1.26920i	−0.772839	−	0.634602i	$-0.781164\pi$
$443$		−	249080.i		−	1.26920i	0.772839	−	0.634602i	$-0.218836\pi$
$444$			53720.7i			0.272506i
$445$			88405.5i			0.446436i
$446$		−	246328.i		−	1.23835i
$447$			2135.65i			0.0106884i
$448$	−48723.4			−0.242763
$449$	−118296.			−0.586783			−0.293391	−	0.955992i	$-0.594784\pi$
$449$	−118296.			−0.586783			−0.293391	+	0.955992i	$0.594784\pi$
$450$		−	42103.7i		−	0.207920i
$451$		−	54101.5i		−	0.265984i
$452$			123207.i			0.603056i
$453$		−	275.602i		−	0.00134303i
$454$	−238744.			−1.15830
$455$			223464.i			1.07940i
$456$		−	64161.2i		−	0.308562i
$457$			37204.6i			0.178141i	0.996025	+	0.0890706i	$0.0283897\pi$
$457$			37204.6i			0.178141i	−0.996025	+	0.0890706i	$0.971610\pi$
$458$	281916.			1.34397
$459$	7352.51			0.0348988
$460$		−	31356.6i		−	0.148188i
$461$	−101602.			−0.478079			−0.239039	−	0.971010i	$-0.576832\pi$
$461$	−101602.			−0.478079			−0.239039	+	0.971010i	$0.576832\pi$
$462$	184521.			0.864493
$463$			13014.3i			0.0607098i	0.999539	+	0.0303549i	$0.00966376\pi$
$463$			13014.3i			0.0607098i	−0.999539	+	0.0303549i	$0.990336\pi$
$464$	80471.8			0.373773
$465$		−	57721.0i		−	0.266949i
$466$	151674.			0.698458
$467$		−	92547.0i		−	0.424354i	−0.977231	−	0.212177i	$-0.931945\pi$
$467$		−	92547.0i		−	0.424354i	0.977231	−	0.212177i	$-0.0680554\pi$
$468$			59094.5i			0.269809i
$469$			468391.i			2.12943i
$470$	−521.863			−0.00236244
$471$		−	12372.2i		−	0.0557704i
$472$	−76090.9	−	20353.6i	−0.341545	−	0.0913604i
$473$	145300.			0.649445
$474$			78327.6i			0.348625i
$475$	300862.			1.33346
$476$	39897.7			0.176090
$477$	136071.			0.598039
$478$		−	60160.0i		−	0.263301i
$479$	−100019.			−0.435924			−0.217962	−	0.975957i	$-0.569941\pi$
$479$	−100019.			−0.435924			−0.217962	+	0.975957i	$0.569941\pi$
$480$			8073.32i			0.0350404i
$481$	353560.			1.52818
$482$			23553.5i			0.101382i
$483$			225810.i			0.967941i
$484$	22120.7			0.0944296
$485$		−	8830.42i		−	0.0375403i
$486$		−	10714.1i		−	0.0453609i
$487$	168177.			0.709103			0.354552	−	0.935036i	$-0.384633\pi$
$487$	168177.			0.709103			0.354552	+	0.935036i	$0.384633\pi$
$488$	−118339.			−0.496924
$489$	−123205.			−0.515242
$490$		−	161561.i		−	0.672891i
$491$	−354250.			−1.46942			−0.734711	−	0.678381i	$-0.762682\pi$
$491$	−354250.			−1.46942			−0.734711	+	0.678381i	$0.762682\pi$
$492$	−17046.3			−0.0704206
$493$	−65895.2			−0.271119
$494$	−422274.			−1.73037
$495$		−	30574.5i		−	0.124781i
$496$		−	82829.9i		−	0.336685i
$497$	−34929.8			−0.141411
$498$	41308.1			0.166562
$499$	7890.04			0.0316868			0.0158434	−	0.999874i	$-0.494957\pi$
$499$	7890.04			0.0316868			0.0158434	+	0.999874i	$0.494957\pi$
$500$	−80772.7			−0.323091
$501$	196448.			0.782660
$502$			56122.0i			0.222703i
$503$			142867.i			0.564673i	0.959315	+	0.282337i	$0.0911095\pi$
$503$			142867.i			0.564673i	−0.959315	+	0.282337i	$0.908890\pi$
$504$		−	58138.9i		−	0.228879i
$505$		−	107018.i		−	0.419639i
$506$			170408.i			0.665561i
$507$	240521.			0.935700
$508$	−216887.			−0.840438
$509$		−	247130.i		−	0.953872i	−0.878938	−	0.476936i	$-0.841747\pi$
$509$		−	247130.i		−	0.953872i	0.878938	−	0.476936i	$-0.158253\pi$
$510$		−	6610.92i		−	0.0254169i
$511$		−	703679.i		−	2.69484i
$512$			11585.2i			0.0441942i
$513$	76559.9			0.290915
$514$		−	278969.i		−	1.05592i
$515$			38641.2i			0.145692i
$516$		−	45781.1i		−	0.171944i
$517$	2836.07			0.0106105
$518$	−347842.			−1.29635
$519$		−	134945.i		−	0.500982i
$520$	53134.2			0.196502
$521$	−462172.			−1.70266			−0.851330	−	0.524631i	$-0.824203\pi$
$521$	−462172.			−1.70266			−0.851330	+	0.524631i	$0.824203\pi$
$522$			96022.4i			0.352397i
$523$	−320393.			−1.17133			−0.585666	−	0.810552i	$-0.699167\pi$
$523$	−320393.			−1.17133			−0.585666	+	0.810552i	$0.699167\pi$
$524$			185206.i			0.674518i
$525$	272622.			0.989106
$526$		−	176234.i		−	0.636970i
$527$			67826.2i			0.244217i
$528$		−	43874.5i		−	0.157378i
$529$	71302.1			0.254795
$530$		−	122347.i		−	0.435553i
$531$	24286.8	−	90794.9i	0.0861354	−	0.322012i
$532$	415445.			1.46788
$533$			112189.i			0.394909i
$534$	−151377.			−0.530858
$535$	−89570.7			−0.312938
$536$	111372.			0.387656
$537$		−	22164.8i		−	0.0768625i
$538$	−182623.			−0.630945
$539$			878006.i			3.02218i
$540$	−9633.43			−0.0330364
$541$			350231.i			1.19663i	0.801261	+	0.598315i	$0.204163\pi$
$541$			350231.i			1.19663i	−0.801261	+	0.598315i	$0.795837\pi$
$542$		−	35216.4i		−	0.119880i
$543$	63987.0			0.217016
$544$		−	9486.70i		−	0.0320566i
$545$			4347.72i			0.0146376i
$546$	−382638.			−1.28352
$547$	−89105.8			−0.297805			−0.148902	−	0.988852i	$-0.547574\pi$
$547$	−89105.8			−0.297805			−0.148902	+	0.988852i	$0.547574\pi$
$548$	−145191.			−0.483479
$549$		−	141208.i		−	0.468504i
$550$	205735.			0.680114
$551$	−686151.			−2.26004
$552$	53692.1			0.176211
$553$	−507173.			−1.65846
$554$		−	201087.i		−	0.655187i
$555$			57636.4i			0.187116i
$556$	−133476.			−0.431771
$557$	310857.			1.00196			0.500981	−	0.865459i	$-0.332973\pi$
$557$	310857.			1.00196			0.500981	+	0.865459i	$0.332973\pi$
$558$	98836.2			0.317430
$559$	−301306.			−0.964238
$560$	−52274.9			−0.166693
$561$			35927.1i			0.114156i
$562$			353768.i			1.12007i
$563$			326868.i			1.03123i	0.856820	+	0.515616i	$0.172437\pi$
$563$			326868.i			1.03123i	−0.856820	+	0.515616i	$0.827563\pi$
$564$		−	893.589i		−	0.00280918i
$565$			132187.i			0.414088i
$566$	−50806.2			−0.158593
$567$	69373.8			0.215789
$568$			8305.45i			0.0257434i
$569$		−	31535.5i		−	0.0974037i	−0.998813	−	0.0487018i	$-0.984492\pi$
$569$		−	31535.5i		−	0.0974037i	0.998813	−	0.0487018i	$-0.0155084\pi$
$570$		−	68837.9i		−	0.211874i
$571$		−	10858.0i		−	0.0333027i	−0.999861	−	0.0166513i	$-0.994699\pi$
$571$		−	10858.0i		−	0.0333027i	0.999861	−	0.0166513i	$-0.00530053\pi$
$572$	−288758.			−0.882556
$573$			135316.i			0.412135i
$574$		−	110375.i		−	0.335002i
$575$			251771.i			0.761499i
$576$	−13824.0			−0.0416667
$577$	−46919.3			−0.140929			−0.0704644	−	0.997514i	$-0.522448\pi$
$577$	−46919.3			−0.140929			−0.0704644	+	0.997514i	$0.522448\pi$
$578$		−	228465.i		−	0.683854i
$579$	−197401.			−0.588834
$580$	86337.4			0.256651
$581$			267471.i			0.792363i
$582$	15120.4			0.0446393
$583$			664895.i			1.95621i
$584$	−167318.			−0.490587
$585$			63401.9i			0.185264i
$586$			325897.i			0.949041i
$587$			613348.i			1.78004i	0.455918	+	0.890022i	$0.349311\pi$
$587$			613348.i			1.78004i	−0.455918	+	0.890022i	$0.650689\pi$
$588$	276643.			0.800137
$589$			706257.i			2.03579i
$590$	−81637.1	−	21837.2i	−0.234522	−	0.0627326i
$591$	115426.			0.330468
$592$			82708.4i			0.235997i
$593$	−410553.			−1.16751			−0.583754	−	0.811930i	$-0.698417\pi$
$593$	−410553.			−1.16751			−0.583754	+	0.811930i	$0.698417\pi$
$594$	52353.0			0.148378
$595$	42805.8			0.120912
$596$			3288.04i			0.00925646i
$597$	157348.			0.441481
$598$		−	353372.i		−	0.988166i
$599$	329676.			0.918827			0.459413	−	0.888223i	$-0.348060\pi$
$599$	329676.			0.918827			0.459413	+	0.888223i	$0.348060\pi$
$600$		−	64822.9i		−	0.180064i
$601$		−	42340.1i		−	0.117220i	−0.998281	−	0.0586102i	$-0.981333\pi$
$601$		−	42340.1i		−	0.117220i	0.998281	−	0.0586102i	$-0.0186669\pi$
$602$	296433.			0.817963
$603$			132894.i			0.365486i
$604$		−	424.318i		−	0.00116310i
$605$	23733.1			0.0648400
$606$	183248.			0.498994
$607$	−130815.			−0.355041			−0.177521	−	0.984117i	$-0.556808\pi$
$607$	−130815.			−0.355041			−0.177521	+	0.984117i	$0.556808\pi$
$608$		−	98782.6i		−	0.267223i
$609$	−621747.			−1.67641
$610$	−126965.			−0.341212
$611$	−5881.11			−0.0157535
$612$	11319.9			0.0302232
$613$		−	553042.i		−	1.47176i	−0.677111	−	0.735881i	$-0.736768\pi$
$613$		−	553042.i		−	1.47176i	0.677111	−	0.735881i	$-0.263232\pi$
$614$			58390.8i			0.154885i
$615$	−18288.8			−0.0483543
$616$	284088.			0.748673
$617$	−261401.			−0.686652			−0.343326	−	0.939216i	$-0.611554\pi$
$617$	−261401.			−0.686652			−0.343326	+	0.939216i	$0.611554\pi$
$618$	−66165.6			−0.173243
$619$	−257764.			−0.672731			−0.336366	−	0.941731i	$-0.609198\pi$
$619$	−257764.			−0.672731			−0.336366	+	0.941731i	$0.609198\pi$
$620$		−	88867.4i		−	0.231185i
$621$			64067.7i			0.166133i
$622$			501585.i			1.29647i
$623$		−	980171.i		−	2.52538i
$624$			90982.0i			0.233661i
$625$	257921.			0.660278
$626$	463179.			1.18195
$627$			374100.i			0.951596i
$628$		−	19048.2i		−	0.0482986i
$629$		−	67726.7i		−	0.171182i
$630$		−	62376.6i		−	0.157160i
$631$	317014.			0.796195			0.398098	−	0.917343i	$-0.369671\pi$
$631$	317014.			0.796195			0.398098	+	0.917343i	$0.369671\pi$
$632$			120593.i			0.301918i
$633$		−	165098.i		−	0.412035i
$634$			76457.4i			0.190213i
$635$	−232696.			−0.577086
$636$	209495.			0.517917
$637$		−	1.82071e6i		−	4.48706i
$638$	−469202.			−1.15271
$639$	−9910.42			−0.0242711
$640$			12429.7i			0.0303459i
$641$	870.284			0.00211809			0.00105905	−	0.999999i	$-0.499663\pi$
$641$	870.284			0.00211809			0.00105905	+	0.999999i	$0.499663\pi$
$642$		−	153373.i		−	0.372115i
$643$	80727.9			0.195255			0.0976274	−	0.995223i	$-0.468875\pi$
$643$	80727.9			0.195255			0.0976274	+	0.995223i	$0.468875\pi$
$644$			347657.i			0.838262i
$645$		−	49118.0i		−	0.118065i
$646$			80889.2i			0.193832i
$647$	−58846.1			−0.140575			−0.0702877	−	0.997527i	$-0.522392\pi$
$647$	−58846.1			−0.140575			−0.0702877	+	0.997527i	$0.522392\pi$
$648$		−	16495.4i		−	0.0392837i
$649$	443658.	+	118675.i	1.05332	+	0.281753i
$650$	−426629.			−1.00977
$651$			639966.i			1.51006i
$652$	−189687.			−0.446213
$653$	−152585.			−0.357836			−0.178918	−	0.983864i	$-0.557260\pi$
$653$	−152585.			−0.357836			−0.178918	+	0.983864i	$0.557260\pi$
$654$	−7444.63			−0.0174055
$655$			198706.i			0.463157i
$656$	−26244.5			−0.0609861
$657$		−	199651.i		−	0.462530i
$658$	5786.01			0.0133637
$659$		−	412632.i		−	0.950149i	−0.879945	−	0.475075i	$-0.842421\pi$
$659$		−	412632.i		−	0.950149i	0.879945	−	0.475075i	$-0.157579\pi$
$660$		−	47072.5i		−	0.108064i
$661$	−576494.			−1.31945			−0.659724	−	0.751508i	$-0.729327\pi$
$661$	−576494.			−1.31945			−0.659724	+	0.751508i	$0.729327\pi$
$662$		−	261875.i		−	0.597556i
$663$		−	74501.6i		−	0.169488i
$664$	63598.0			0.144247
$665$	445726.			1.00792
$666$	−98691.2			−0.222500
$667$		−	574192.i		−	1.29064i
$668$	302452.			0.677803
$669$	452533.			1.01111
$670$	119490.			0.266184
$671$	689993.			1.53250
$672$		−	89510.6i		−	0.198215i
$673$		−	195316.i		−	0.431228i	−0.976479	−	0.215614i	$-0.930825\pi$
$673$		−	195316.i		−	0.431228i	0.976479	−	0.215614i	$-0.0691753\pi$
$674$	418710.			0.921708
$675$	77349.5			0.169766
$676$	370306.			0.810340
$677$	−518777.			−1.13189			−0.565944	−	0.824444i	$-0.691488\pi$
$677$	−518777.			−1.13189			−0.565944	+	0.824444i	$0.691488\pi$
$678$	−226345.			−0.492393
$679$			97904.8i			0.212356i
$680$		−	10178.2i		−	0.0220116i
$681$		−	438600.i		−	0.945745i
$682$			482951.i			1.03833i
$683$			145446.i			0.311788i	0.987774	+	0.155894i	$0.0498258\pi$
$683$			145446.i			0.311788i	−0.987774	+	0.155894i	$0.950174\pi$
$684$	117872.			0.251940
$685$	−155774.			−0.331981
$686$			1.14501e6i			2.43310i
$687$			517913.i			1.09735i
$688$		−	70484.6i		−	0.148908i
$689$		−	1.37878e6i		−	2.90441i
$690$	57605.7			0.120995
$691$		−	339098.i		−	0.710182i	−0.934832	−	0.355091i	$-0.884450\pi$
$691$		−	339098.i		−	0.710182i	0.934832	−	0.355091i	$-0.115550\pi$
$692$		−	207761.i		−	0.433863i
$693$			338986.i			0.705855i
$694$	−617959.			−1.28304
$695$	−143205.			−0.296475
$696$			147836.i			0.305184i
$697$	21490.6			0.0442367
$698$	−90290.9			−0.185325
$699$			278643.i			0.570288i
$700$	419729.			0.856591
$701$		−	387493.i		−	0.788548i	−0.918993	−	0.394274i	$-0.870996\pi$
$701$		−	387493.i		−	0.788548i	0.918993	−	0.394274i	$-0.129004\pi$
$702$	−108564.			−0.220298
$703$		−	705221.i		−	1.42697i
$704$		−	67549.3i		−	0.136294i
$705$		−	958.723i		−	0.00192892i
$706$	−502066.			−1.00728
$707$			1.18654e6i			2.37379i
$708$	37392.0	−	139788.i	0.0745955	−	0.278871i
$709$	630837.			1.25494			0.627472	−	0.778639i	$-0.284090\pi$
$709$	630837.			1.25494			0.627472	+	0.778639i	$0.284090\pi$
$710$			8910.83i			0.0176767i
$711$	−143897.			−0.284651
$712$	−233061.			−0.459737
$713$	−591018.			−1.16258
$714$			73296.8i			0.143777i
$715$	−309806.			−0.606007
$716$		−	34124.9i		−	0.0665649i
$717$	110521.			0.214984
$718$			457354.i			0.887163i
$719$			940850.i			1.81996i	0.414649	+	0.909982i	$0.363904\pi$
$719$			940850.i			1.81996i	−0.414649	+	0.909982i	$0.636096\pi$
$720$	−14831.6			−0.0286104
$721$		−	428423.i		−	0.824143i
$722$			473675.i			0.908670i
$723$	−43270.5			−0.0827781
$724$	98514.4			0.187941
$725$	−693227.			−1.31886
$726$			40638.3i			0.0771014i
$727$	888716.			1.68149			0.840744	−	0.541432i	$-0.182118\pi$
$727$	888716.			1.68149			0.840744	+	0.541432i	$0.182118\pi$
$728$	−589110.			−1.11156
$729$	19683.0			0.0370370
$730$	−179513.			−0.336862
$731$			57717.1i			0.108011i
$732$		−	217403.i		−	0.405736i
$733$	−399087.			−0.742779			−0.371389	−	0.928477i	$-0.621119\pi$
$733$	−399087.			−0.742779			−0.371389	+	0.928477i	$0.621119\pi$
$734$	−116119.			−0.215531
$735$	296807.			0.549414
$736$	82664.4			0.152603
$737$	−649369.			−1.19552
$738$		−	31316.1i		−	0.0574982i
$739$		−	217002.i		−	0.397351i	−0.980065	−	0.198676i	$-0.936336\pi$
$739$		−	217002.i		−	0.397351i	0.980065	−	0.198676i	$-0.0636641\pi$
$740$			88737.0i			0.162047i
$741$		−	775766.i		−	1.41285i
$742$			1.35649e6i			2.46381i
$743$	−522972.			−0.947330			−0.473665	−	0.880705i	$-0.657069\pi$
$743$	−522972.			−0.947330			−0.473665	+	0.880705i	$0.657069\pi$
$744$	152168.			0.274902
$745$			3527.71i			0.00635594i
$746$		−	260230.i		−	0.467606i
$747$			75887.8i			0.135998i
$748$			55313.4i			0.0988616i
$749$	993090.			1.77021
$750$		−	148389.i		−	0.263802i
$751$		−	701840.i		−	1.24440i	−0.782860	−	0.622198i	$-0.786240\pi$
$751$		−	701840.i		−	1.24440i	0.782860	−	0.622198i	$-0.213760\pi$
$752$		−	1375.77i		−	0.00243282i
$753$	−103103.			−0.181836
$754$	972977.			1.71143
$755$		−	455.246i		−	0.000798643i
$756$	106808.			0.186879
$757$	232474.			0.405679			0.202839	−	0.979212i	$-0.434983\pi$
$757$	232474.			0.405679			0.202839	+	0.979212i	$0.434983\pi$
$758$			32758.0i			0.0570136i
$759$	−313059.			−0.543429
$760$		−	105983.i		−	0.183488i
$761$	−308114.			−0.532038			−0.266019	−	0.963968i	$-0.585708\pi$
$761$	−308114.			−0.532038			−0.266019	+	0.963968i	$0.585708\pi$
$762$		−	398446.i		−	0.686214i
$763$		−	48204.1i		−	0.0828009i
$764$			208333.i			0.356920i
$765$	12145.0			0.0207528
$766$		−	417964.i		−	0.712330i
$767$	−920007.	−	246094.i	−1.56387	−	0.418321i
$768$	−21283.4			−0.0360844
$769$			174340.i			0.294811i	0.989076	+	0.147405i	$0.0470922\pi$
$769$			174340.i			0.294811i	−0.989076	+	0.147405i	$0.952908\pi$
$770$	304796.			0.514076
$771$	512498.			0.862151
$772$	−303919.			−0.509946
$773$			1.07357e6i			1.79668i	0.439301	+	0.898340i	$0.355226\pi$
$773$			1.07357e6i			1.79668i	−0.439301	+	0.898340i	$0.644774\pi$
$774$	84105.2			0.140392
$775$			713541.i			1.18800i
$776$	23279.4			0.0386588
$777$		−	639027.i		−	1.05847i
$778$		−	182886.i		−	0.302149i
$779$	223776.			0.368756
$780$			97613.7i			0.160443i
$781$		−	48426.0i		−	0.0793920i
$782$	−67690.6			−0.110692
$783$	−176404.			−0.287731
$784$	425919.			0.692939
$785$		−	20436.6i		−	0.0331642i
$786$	−340246.			−0.550741
$787$	990825.			1.59973			0.799866	−	0.600178i	$-0.204904\pi$
$787$	990825.			1.59973			0.799866	+	0.600178i	$0.204904\pi$
$788$	177710.			0.286194
$789$	323763.			0.520084
$790$			129383.i			0.207312i
$791$		−	1.46559e6i		−	2.34239i
$792$	80602.7			0.128499
$793$	−1.43083e6			−2.27531
$794$	436057.			0.691676
$795$	224765.			0.355627
$796$	242253.			0.382334
$797$		−	835080.i		−	1.31465i	−0.753605	−	0.657327i	$-0.771687\pi$
$797$		−	835080.i		−	1.31465i	0.753605	−	0.657327i	$-0.228313\pi$
$798$			763221.i			1.19852i
$799$			1126.56i			0.00176467i
$800$		−	99801.4i		−	0.155940i
$801$		−	278098.i		−	0.433444i
$802$	−404743.			−0.629260
$803$	975568.			1.51296
$804$			204603.i			0.316520i
$805$			372998.i			0.575592i
$806$		−	1.00149e6i		−	1.54161i
$807$		−	335500.i		−	0.515164i
$808$	282130.			0.432141
$809$		−	395497.i		−	0.604291i	−0.953262	−	0.302145i	$-0.902297\pi$
$809$		−	395497.i		−	0.604291i	0.953262	−	0.302145i	$-0.0977028\pi$
$810$		−	17697.7i		−	0.0269741i
$811$		−	1.14679e6i		−	1.74358i	−0.489876	−	0.871792i	$-0.662958\pi$
$811$		−	1.14679e6i		−	1.74358i	0.489876	−	0.871792i	$-0.337042\pi$
$812$	−957242.			−1.45181
$813$	64696.7			0.0978816
$814$		−	482242.i		−	0.727807i
$815$	−203513.			−0.306392
$816$	17428.2			0.0261741
$817$			600993.i			0.900379i
$818$	870817.			1.30143
$819$		−	702951.i		−	1.04799i
$820$	−28157.5			−0.0418761
$821$		−	360529.i		−	0.534877i	−0.963575	−	0.267438i	$-0.913823\pi$
$821$		−	360529.i		−	0.534877i	0.963575	−	0.267438i	$-0.0861772\pi$
$822$		−	266732.i		−	0.394759i
$823$			534265.i			0.788782i	0.918943	+	0.394391i	$0.129045\pi$
$823$			534265.i			0.788782i	−0.918943	+	0.394391i	$0.870955\pi$
$824$	−101869.			−0.150033
$825$			377959.i			0.555311i
$826$	905129.	+	242114.i	1.32663	+	0.354862i
$827$	−833438.			−1.21860			−0.609301	−	0.792939i	$-0.708550\pi$
$827$	−833438.			−1.21860			−0.609301	+	0.792939i	$0.708550\pi$
$828$			98638.7i			0.143875i
$829$	−740165.			−1.07701			−0.538505	−	0.842622i	$-0.681011\pi$
$829$	−740165.			−1.07701			−0.538505	+	0.842622i	$0.681011\pi$
$830$	68233.6			0.0990472
$831$	369421.			0.534958
$832$			140076.i			0.202356i
$833$	−348768.			−0.502629
$834$		−	245211.i		−	0.352539i
$835$	324498.			0.465413
$836$			575965.i			0.824107i
$837$			181574.i			0.259180i
$838$	−444371.			−0.632787
$839$			694451.i			0.986547i	0.869874	+	0.493273i	$0.164200\pi$
$839$			694451.i			0.986547i	−0.869874	+	0.493273i	$0.835800\pi$
$840$		−	96035.1i		−	0.136104i
$841$	873705.			1.23530
$842$	−822225.			−1.15976
$843$	−649913.			−0.914535
$844$		−	254185.i		−	0.356833i
$845$	397297.			0.556419
$846$	1641.63			0.00229369
$847$	−263134.			−0.366784
$848$	322539.			0.448529
$849$		−	93337.0i		−	0.129491i
$850$			81723.5i			0.113112i
$851$	590151.			0.814900
$852$	−15258.1			−0.0210194
$853$	91717.8			0.126054			0.0630269	−	0.998012i	$-0.479925\pi$
$853$	91717.8			0.126054			0.0630269	+	0.998012i	$0.479925\pi$
$854$	1.40769e6			1.93015
$855$	126463.			0.172994
$856$		−	236133.i		−	0.322261i
$857$			590534.i			0.804050i	0.915629	+	0.402025i	$0.131693\pi$
$857$			590534.i			0.804050i	−0.915629	+	0.402025i	$0.868307\pi$
$858$		−	530483.i		−	0.720604i
$859$			787470.i			1.06720i	0.845736	+	0.533602i	$0.179162\pi$
$859$			787470.i			1.06720i	−0.845736	+	0.533602i	$0.820838\pi$
$860$		−	75622.2i		−	0.102247i
$861$	202772.			0.273528
$862$	78201.3			0.105245
$863$		−	89579.0i		−	0.120278i	−0.998190	−	0.0601388i	$-0.980846\pi$
$863$		−	89579.0i		−	0.120278i	0.998190	−	0.0601388i	$-0.0191543\pi$
$864$		−	25396.3i		−	0.0340207i
$865$		−	222905.i		−	0.297912i
$866$			73325.5i			0.0977731i
$867$	419717.			0.558365
$868$			985292.i			1.30775i
$869$		−	703135.i		−	0.931106i
$870$			158612.i			0.209555i
$871$	1.34659e6			1.77500
$872$	−11461.8			−0.0150736
$873$			27777.9i			0.0364478i
$874$	−704846.			−0.922722
$875$	960820.			1.25495
$876$		−	307382.i		−	0.400563i
$877$	299782.			0.389768			0.194884	−	0.980826i	$-0.437567\pi$
$877$	299782.			0.389768			0.194884	+	0.980826i	$0.437567\pi$
$878$			250273.i			0.324657i
$879$	−598711.			−0.774889
$880$		−	72472.9i		−	0.0935859i
$881$			23395.4i			0.0301424i	0.999886	+	0.0150712i	$0.00479750\pi$
$881$			23395.4i			0.0301424i	−0.999886	+	0.0150712i	$0.995202\pi$
$882$			508225.i			0.653309i
$883$	218850.			0.280689			0.140344	−	0.990103i	$-0.455179\pi$
$883$	218850.			0.280689			0.140344	+	0.990103i	$0.455179\pi$
$884$		−	114703.i		−	0.146781i
$885$	40117.5	−	149977.i	0.0512210	−	0.191486i
$886$	704505.			0.897463
$887$			978920.i			1.24423i	0.782927	+	0.622114i	$0.213726\pi$
$887$			978920.i			1.24423i	−0.782927	+	0.622114i	$0.786274\pi$
$888$	−151945.			−0.192691
$889$	2.57995e6			3.26443
$890$	−250049.			−0.315678
$891$			96178.5i			0.121150i
$892$	696720.			0.875646
$893$			11730.6i			0.0147102i
$894$	−6040.52			−0.00755787
$895$		−	36612.2i		−	0.0457068i
$896$		−	137811.i		−	0.171659i
$897$	649186.			0.806834
$898$		−	334592.i		−	0.414918i
$899$		−	1.62731e6i		−	2.01350i
$900$	119087.			0.147021
$901$	−264115.			−0.325344
$902$	153022.			0.188079
$903$			544583.i			0.667864i
$904$	−348481.			−0.426425
$905$	105695.			0.129050
$906$	779.522			0.000949668
$907$	−38646.2			−0.0469778			−0.0234889	−	0.999724i	$-0.507477\pi$
$907$	−38646.2			−0.0469778			−0.0234889	+	0.999724i	$0.507477\pi$
$908$		−	675269.i		−	0.819040i
$909$			336649.i			0.407427i
$910$	−632050.			−0.763254
$911$	229839.			0.276941			0.138470	−	0.990367i	$-0.455781\pi$
$911$	229839.			0.276941			0.138470	+	0.990367i	$0.455781\pi$
$912$	181475.			0.218186
$913$	−370816.			−0.444854
$914$	−105231.			−0.125965
$915$		−	233250.i		−	0.278599i
$916$			797380.i			0.950329i
$917$		−	2.20310e6i		−	2.61996i
$918$			20796.0i			0.0246772i
$919$			753554.i			0.892243i	0.894972	+	0.446122i	$0.147195\pi$
$919$			753554.i			0.892243i	−0.894972	+	0.446122i	$0.852805\pi$
$920$	88689.8			0.104785
$921$	−107271.			−0.126463
$922$		−	287373.i		−	0.338053i
$923$			100420.i			0.117874i
$924$			521904.i			0.611289i
$925$		−	712494.i		−	0.832718i
$926$	−36810.0			−0.0429283
$927$		−	121554.i		−	0.141452i
$928$			227609.i			0.264297i
$929$			1.07850e6i			1.24966i	0.780763	+	0.624828i	$0.214831\pi$
$929$			1.07850e6i			1.24966i	−0.780763	+	0.624828i	$0.785169\pi$
$930$	163260.			0.188761
$931$	−3.63164e6			−4.18989
$932$			429000.i			0.493884i
$933$	−921471.			−1.05857
$934$	261762.			0.300064
$935$			59345.2i			0.0678833i
$936$	−167145.			−0.190783
$937$			1.54993e6i			1.76536i	0.469977	+	0.882679i	$0.344262\pi$
$937$			1.54993e6i			1.76536i	−0.469977	+	0.882679i	$0.655738\pi$
$938$	−1.32481e6			−1.50573
$939$			850914.i			0.965060i
$940$		−	1476.05i		−	0.00167050i
$941$		−	42164.0i		−	0.0476171i	−0.999717	−	0.0238085i	$-0.992421\pi$
$941$		−	42164.0i		−	0.0476171i	0.999717	−	0.0238085i	$-0.00757921\pi$
$942$	34993.8			0.0394356
$943$			187263.i			0.210585i
$944$	57568.8	−	215217.i	0.0646016	−	0.241509i
$945$	114593.			0.128320
$946$			410970.i			0.459227i
$947$	1.44514e6			1.61143			0.805715	−	0.592304i	$-0.201782\pi$
$947$	1.44514e6			1.61143			0.805715	+	0.592304i	$0.201782\pi$
$948$	−221544.			−0.246515
$949$	−2.02302e6			−2.24630
$950$			850966.i			0.942898i
$951$	−140461.			−0.155309
$952$			112848.i			0.124514i
$953$	708673.			0.780297			0.390148	−	0.920752i	$-0.372424\pi$
$953$	708673.			0.780297			0.390148	+	0.920752i	$0.372424\pi$
$954$			384867.i			0.422877i
$955$			223518.i			0.245079i
$956$	170158.			0.186182
$957$		−	861979.i		−	0.941180i
$958$		−	282896.i		−	0.308245i
$959$	1.72710e6			1.87793
$960$	−22834.8			−0.0247773
$961$	−751477.			−0.813708
$962$			1.00002e6i			1.08058i
$963$	281763.			0.303831
$964$	−66619.3			−0.0716879
$965$	−326072.			−0.350154
$966$	−638687.			−0.684438
$967$		−	955580.i		−	1.02191i	−0.859606	−	0.510957i	$-0.829291\pi$
$967$		−	955580.i		−	1.02191i	0.859606	−	0.510957i	$-0.170709\pi$
$968$			62566.8i			0.0667718i
$969$	−148603.			−0.158263
$970$	24976.2			0.0265450
$971$	−152116.			−0.161338			−0.0806688	−	0.996741i	$-0.525706\pi$
$971$	−152116.			−0.161338			−0.0806688	+	0.996741i	$0.525706\pi$
$972$	30304.0			0.0320750
$973$	1.58775e6			1.67709
$974$			475677.i			0.501412i
$975$		−	783767.i		−	0.824476i
$976$		−	334714.i		−	0.351378i
$977$		−	1.51924e6i		−	1.59161i	−0.605551	−	0.795806i	$-0.707047\pi$
$977$		−	1.51924e6i		−	1.59161i	0.605551	−	0.795806i	$-0.292953\pi$
$978$		−	348477.i		−	0.364331i
$979$	1.35889e6			1.41781
$980$	456964.			0.475806
$981$		−	13676.7i		−	0.0142116i
$982$		−	1.00197e6i		−	1.03904i
$983$			1.41964e6i			1.46916i	0.678520	+	0.734582i	$0.262622\pi$
$983$			1.41964e6i			1.46916i	−0.678520	+	0.734582i	$0.737378\pi$
$984$		−	48214.2i		−	0.0497949i
$985$	190664.			0.196515
$986$		−	186380.i		−	0.191710i
$987$			10629.6i			0.0109114i
$988$		−	1.19437e6i		−	1.22356i
$989$	−502930.			−0.514180
$990$	86477.8			0.0882336
$991$			597852.i			0.608761i	0.952551	+	0.304380i	$0.0984494\pi$
$991$			597852.i			0.608761i	−0.952551	+	0.304380i	$0.901551\pi$
$992$	234278.			0.238072
$993$	481095.			0.487902
$994$		−	98796.4i		−	0.0999927i
$995$	259911.			0.262530
$996$			116837.i			0.117777i
$997$	1.73155e6			1.74198			0.870991	−	0.491299i	$-0.163478\pi$
$997$	1.73155e6			1.74198			0.870991	+	0.491299i	$0.163478\pi$
$998$			22316.4i			0.0224059i
$999$		−	181307.i		−	0.181670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.8	yes	40
3.2	odd	2		1062.5.d.b.235.31		40
59.58	odd	2	inner	354.5.d.a.235.7	✓	40
177.176	even	2		1062.5.d.b.235.32		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.7	✓	40	59.58	odd	2	inner
354.5.d.a.235.8	yes	40	1.1	even	1	trivial
1062.5.d.b.235.31		40	3.2	odd	2
1062.5.d.b.235.32		40	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -8.58312 q^{5} -14.6969i q^{6} +95.1629 q^{7} -22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} -8.58312 q^{5} -14.6969i q^{6} +95.1629 q^{7} -22.6274i q^{8} +27.0000 q^{9} -24.2767i q^{10} +131.932i q^{11} +41.5692 q^{12} -273.586i q^{13} +269.161i q^{14} +44.5992 q^{15} +64.0000 q^{16} -52.4071 q^{17} +76.3675i q^{18} -545.702 q^{19} +68.6650 q^{20} -494.481 q^{21} -373.160 q^{22} -456.661i q^{23} +117.576i q^{24} -551.330 q^{25} +773.818 q^{26} -140.296 q^{27} -761.303 q^{28} +1257.37 q^{29} +126.146i q^{30} -1294.22i q^{31} +181.019i q^{32} -685.539i q^{33} -148.230i q^{34} -816.795 q^{35} -216.000 q^{36} +1292.32i q^{37} -1543.48i q^{38} +1421.59i q^{39} +194.214i q^{40} -410.070 q^{41} -1398.60i q^{42} -1101.32i q^{43} -1055.46i q^{44} -231.744 q^{45} +1291.63 q^{46} -21.4964i q^{47} -332.554 q^{48} +6654.98 q^{49} -1559.40i q^{50} +272.315 q^{51} +2188.69i q^{52} +5039.67 q^{53} -396.817i q^{54} -1132.39i q^{55} -2153.29i q^{56} +2835.55 q^{57} +3556.39i q^{58} +(899.512 - 3362.77i) q^{59} -356.794 q^{60} -5229.91i q^{61} +3660.60 q^{62} +2569.40 q^{63} -512.000 q^{64} +2348.22i q^{65} +1939.00 q^{66} +4921.99i q^{67} +419.257 q^{68} +2372.88i q^{69} -2310.24i q^{70} -367.053 q^{71} -610.940i q^{72} -7394.47i q^{73} -3655.23 q^{74} +2864.80 q^{75} +4365.61 q^{76} +12555.0i q^{77} -4020.87 q^{78} -5329.52 q^{79} -549.320 q^{80} +729.000 q^{81} -1159.85i q^{82} +2810.66i q^{83} +3955.85 q^{84} +449.816 q^{85} +3115.01 q^{86} -6533.50 q^{87} +2985.28 q^{88} -10299.9i q^{89} -655.472i q^{90} -26035.2i q^{91} +3653.28i q^{92} +6724.95i q^{93} +60.8010 q^{94} +4683.82 q^{95} -940.604i q^{96} +1028.81i q^{97} +18823.1i q^{98} +3562.17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9} - 144 q^{15} + 2560 q^{16} + 480 q^{17} - 792 q^{19} - 1024 q^{22} + 3400 q^{25} + 768 q^{26} + 640 q^{28} + 1608 q^{29} - 5760 q^{35} - 8640 q^{36} + 6264 q^{41} + 7040 q^{46} + 17912 q^{49} + 1296 q^{51} - 1104 q^{53} + 5040 q^{57} + 13584 q^{59} + 1152 q^{60} - 12288 q^{62} - 2160 q^{63} - 20480 q^{64} + 1152 q^{66} - 3840 q^{68} + 35352 q^{71} + 4608 q^{74} + 3168 q^{75} + 6336 q^{76} - 12672 q^{78} - 15720 q^{79} + 29160 q^{81} - 26872 q^{85} + 18432 q^{86} + 7776 q^{87} + 8192 q^{88} - 18432 q^{94} - 19128 q^{95}+O(q^{100}) \) 40 * q - 320 * q^4 - 80 * q^7 + 1080 * q^9 - 144 * q^15 + 2560 * q^16 + 480 * q^17 - 792 * q^19 - 1024 * q^22 + 3400 * q^25 + 768 * q^26 + 640 * q^28 + 1608 * q^29 - 5760 * q^35 - 8640 * q^36 + 6264 * q^41 + 7040 * q^46 + 17912 * q^49 + 1296 * q^51 - 1104 * q^53 + 5040 * q^57 + 13584 * q^59 + 1152 * q^60 - 12288 * q^62 - 2160 * q^63 - 20480 * q^64 + 1152 * q^66 - 3840 * q^68 + 35352 * q^71 + 4608 * q^74 + 3168 * q^75 + 6336 * q^76 - 12672 * q^78 - 15720 * q^79 + 29160 * q^81 - 26872 * q^85 + 18432 * q^86 + 7776 * q^87 + 8192 * q^88 - 18432 * q^94 - 19128 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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