LMFDB - Embedded newform 354.5.d.a.235.5

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			235.5
Character	$\chi$	$=$	354.235
Dual form			354.5.d.a.235.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.141718 q^{5} +14.6969i q^{6} -89.1589 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})$	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.141718 q^{5} +14.6969i q^{6} -89.1589 q^{7} +22.6274i q^{8} +27.0000 q^{9} -0.400839i q^{10} +153.350i q^{11} +41.5692 q^{12} +17.2883i q^{13} +252.179i q^{14} -0.736387 q^{15} +64.0000 q^{16} +317.986 q^{17} -76.3675i q^{18} -445.688 q^{19} -1.13374 q^{20} +463.283 q^{21} +433.739 q^{22} +279.113i q^{23} -117.576i q^{24} -624.980 q^{25} +48.8986 q^{26} -140.296 q^{27} +713.271 q^{28} +307.051 q^{29} +2.08282i q^{30} -1292.41i q^{31} -181.019i q^{32} -796.829i q^{33} -899.399i q^{34} -12.6354 q^{35} -216.000 q^{36} +1869.21i q^{37} +1260.59i q^{38} -89.8325i q^{39} +3.20671i q^{40} +718.037 q^{41} -1310.36i q^{42} -2323.57i q^{43} -1226.80i q^{44} +3.82638 q^{45} +789.450 q^{46} -662.549i q^{47} -332.554 q^{48} +5548.31 q^{49} +1767.71i q^{50} -1652.30 q^{51} -138.306i q^{52} +1410.50 q^{53} +396.817i q^{54} +21.7324i q^{55} -2017.44i q^{56} +2315.86 q^{57} -868.471i q^{58} +(-3480.35 + 67.4691i) q^{59} +5.89110 q^{60} -1563.16i q^{61} -3655.49 q^{62} -2407.29 q^{63} -512.000 q^{64} +2.45006i q^{65} -2253.77 q^{66} -6675.03i q^{67} -2543.88 q^{68} -1450.31i q^{69} +35.7383i q^{70} +2263.33 q^{71} +610.940i q^{72} +407.793i q^{73} +5286.92 q^{74} +3247.49 q^{75} +3565.50 q^{76} -13672.5i q^{77} -254.085 q^{78} -1336.33 q^{79} +9.06994 q^{80} +729.000 q^{81} -2030.92i q^{82} -10010.1i q^{83} -3706.27 q^{84} +45.0642 q^{85} -6572.05 q^{86} -1595.48 q^{87} -3469.91 q^{88} -509.616i q^{89} -10.8226i q^{90} -1541.40i q^{91} -2232.90i q^{92} +6715.57i q^{93} -1873.97 q^{94} -63.1619 q^{95} +940.604i q^{96} -4566.49i q^{97} -15693.0i q^{98} +4140.44i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.141718			0.00566871			0.00283436	−	0.999996i	$-0.499098\pi$
$5$	0.141718			0.00566871			0.00283436	+	0.999996i	$0.499098\pi$
$6$			14.6969i			0.408248i
$7$	−89.1589			−1.81957			−0.909785	−	0.415080i	$-0.863754\pi$
$7$	−89.1589			−1.81957			−0.909785	+	0.415080i	$0.863754\pi$
$8$			22.6274i			0.353553i
$9$	27.0000			0.333333
$10$		−	0.400839i		−	0.00400839i
$11$			153.350i			1.26735i	0.773598	+	0.633677i	$0.218455\pi$
$11$			153.350i			1.26735i	−0.773598	+	0.633677i	$0.781545\pi$
$12$	41.5692			0.288675
$13$			17.2883i			0.102297i	0.998691	+	0.0511487i	$0.0162882\pi$
$13$			17.2883i			0.102297i	−0.998691	+	0.0511487i	$0.983712\pi$
$14$			252.179i			1.28663i
$15$	−0.736387			−0.00327283
$16$	64.0000			0.250000
$17$	317.986			1.10030			0.550148	−	0.835067i	$-0.314571\pi$
$17$	317.986			1.10030			0.550148	+	0.835067i	$0.314571\pi$
$18$		−	76.3675i		−	0.235702i
$19$	−445.688			−1.23459			−0.617296	−	0.786731i	$-0.711772\pi$
$19$	−445.688			−1.23459			−0.617296	+	0.786731i	$0.711772\pi$
$20$	−1.13374			−0.00283436
$21$	463.283			1.05053
$22$	433.739			0.896154
$23$			279.113i			0.527623i	0.964574	+	0.263812i	$0.0849797\pi$
$23$			279.113i			0.527623i	−0.964574	+	0.263812i	$0.915020\pi$
$24$		−	117.576i		−	0.204124i
$25$	−624.980			−0.999968
$26$	48.8986			0.0723352
$27$	−140.296			−0.192450
$28$	713.271			0.909785
$29$	307.051			0.365102			0.182551	−	0.983196i	$-0.441565\pi$
$29$	307.051			0.365102			0.182551	+	0.983196i	$0.441565\pi$
$30$			2.08282i			0.00231424i
$31$		−	1292.41i		−	1.34486i	−0.740160	−	0.672430i	$-0.765250\pi$
$31$		−	1292.41i		−	1.34486i	0.740160	−	0.672430i	$-0.234750\pi$
$32$		−	181.019i		−	0.176777i
$33$		−	796.829i		−	0.731707i
$34$		−	899.399i		−	0.778027i
$35$	−12.6354			−0.0103146
$36$	−216.000			−0.166667
$37$			1869.21i			1.36538i	0.730707	+	0.682692i	$0.239191\pi$
$37$			1869.21i			1.36538i	−0.730707	+	0.682692i	$0.760809\pi$
$38$			1260.59i			0.872988i
$39$		−	89.8325i		−	0.0590614i
$40$			3.20671i			0.00200419i
$41$	718.037			0.427149			0.213574	−	0.976927i	$-0.431489\pi$
$41$	718.037			0.427149			0.213574	+	0.976927i	$0.431489\pi$
$42$		−	1310.36i		−	0.742836i
$43$		−	2323.57i		−	1.25666i	−0.777946	−	0.628331i	$-0.783738\pi$
$43$		−	2323.57i		−	1.25666i	0.777946	−	0.628331i	$-0.216262\pi$
$44$		−	1226.80i		−	0.633677i
$45$	3.82638			0.00188957
$46$	789.450			0.373086
$47$		−	662.549i		−	0.299932i	−0.988691	−	0.149966i	$-0.952084\pi$
$47$		−	662.549i		−	0.299932i	0.988691	−	0.149966i	$-0.0479164\pi$
$48$	−332.554			−0.144338
$49$	5548.31			2.31083
$50$			1767.71i			0.707084i
$51$	−1652.30			−0.635256
$52$		−	138.306i		−	0.0511487i
$53$	1410.50			0.502136			0.251068	−	0.967969i	$-0.419218\pi$
$53$	1410.50			0.502136			0.251068	+	0.967969i	$0.419218\pi$
$54$			396.817i			0.136083i
$55$			21.7324i			0.00718426i
$56$		−	2017.44i		−	0.643315i
$57$	2315.86			0.712792
$58$		−	868.471i		−	0.258166i
$59$	−3480.35	+	67.4691i	−0.999812	+	0.0193821i
$59$	−3480.35	+	67.4691i	−0.999812	+	0.0193821i
$60$	5.89110			0.00163642
$61$		−	1563.16i		−	0.420091i	−0.977692	−	0.210046i	$-0.932639\pi$
$61$		−	1563.16i		−	0.420091i	0.977692	−	0.210046i	$-0.0673612\pi$
$62$	−3655.49			−0.950960
$63$	−2407.29			−0.606523
$64$	−512.000			−0.125000
$65$			2.45006i			0.000579895i
$66$	−2253.77			−0.517395
$67$		−	6675.03i		−	1.48697i	−0.668750	−	0.743487i	$-0.733170\pi$
$67$		−	6675.03i		−	1.48697i	0.668750	−	0.743487i	$-0.266830\pi$
$68$	−2543.88			−0.550148
$69$		−	1450.31i		−	0.304623i
$70$			35.7383i			0.00729354i
$71$	2263.33			0.448985			0.224492	−	0.974476i	$-0.427928\pi$
$71$	2263.33			0.448985			0.224492	+	0.974476i	$0.427928\pi$
$72$			610.940i			0.117851i
$73$			407.793i			0.0765234i	0.999268	+	0.0382617i	$0.0121821\pi$
$73$			407.793i			0.0765234i	−0.999268	+	0.0382617i	$0.987818\pi$
$74$	5286.92			0.965472
$75$	3247.49			0.577332
$76$	3565.50			0.617296
$77$		−	13672.5i		−	2.30604i
$78$	−254.085			−0.0417628
$79$	−1336.33			−0.214122			−0.107061	−	0.994252i	$-0.534144\pi$
$79$	−1336.33			−0.214122			−0.107061	+	0.994252i	$0.534144\pi$
$80$	9.06994			0.00141718
$81$	729.000			0.111111
$82$		−	2030.92i		−	0.302040i
$83$		−	10010.1i		−	1.45306i	−0.687136	−	0.726529i	$-0.741132\pi$
$83$		−	10010.1i		−	1.45306i	0.687136	−	0.726529i	$-0.258868\pi$
$84$	−3706.27			−0.525265
$85$	45.0642			0.00623726
$86$	−6572.05			−0.888595
$87$	−1595.48			−0.210792
$88$	−3469.91			−0.448077
$89$		−	509.616i		−	0.0643373i	−0.999482	−	0.0321687i	$-0.989759\pi$
$89$		−	509.616i		−	0.0643373i	0.999482	−	0.0321687i	$-0.0102414\pi$
$90$		−	10.8226i		−	0.00133613i
$91$		−	1541.40i		−	0.186137i
$92$		−	2232.90i		−	0.263812i
$93$			6715.57i			0.776456i
$94$	−1873.97			−0.212084
$95$	−63.1619			−0.00699854
$96$			940.604i			0.102062i
$97$		−	4566.49i		−	0.485333i	−0.970110	−	0.242666i	$-0.921978\pi$
$97$		−	4566.49i		−	0.485333i	0.970110	−	0.242666i	$-0.0780220\pi$
$98$		−	15693.0i		−	1.63401i
$99$			4140.44i			0.422451i
$100$	4999.84			0.499984
$101$		−	13652.8i		−	1.33838i	−0.743093	−	0.669188i	$-0.766642\pi$
$101$		−	13652.8i		−	1.33838i	0.743093	−	0.669188i	$-0.233358\pi$
$102$			4673.41i			0.449194i
$103$			12122.8i			1.14269i	0.820712	+	0.571343i	$0.193577\pi$
$103$			12122.8i			1.14269i	−0.820712	+	0.571343i	$0.806423\pi$
$104$	−391.189			−0.0361676
$105$	65.6555			0.00595515
$106$		−	3989.50i		−	0.355064i
$107$	9728.94			0.849763			0.424882	−	0.905249i	$-0.360316\pi$
$107$	9728.94			0.849763			0.424882	+	0.905249i	$0.360316\pi$
$108$	1122.37			0.0962250
$109$			10146.8i			0.854035i	0.904243	+	0.427017i	$0.140436\pi$
$109$			10146.8i			0.854035i	−0.904243	+	0.427017i	$0.859564\pi$
$110$	61.4685			0.00508004
$111$		−	9712.70i		−	0.788304i
$112$	−5706.17			−0.454892
$113$			12488.4i			0.978027i	0.872276	+	0.489014i	$0.162643\pi$
$113$			12488.4i			0.978027i	−0.872276	+	0.489014i	$0.837357\pi$
$114$		−	6550.24i		−	0.504020i
$115$			39.5552i			0.00299094i
$116$	−2456.41			−0.182551
$117$			466.783i			0.0340991i
$118$	190.831	+	9843.91i	0.0137052	+	0.706974i
$119$	−28351.3			−2.00207
$120$		−	16.6625i		−	0.00115712i
$121$	−8875.15			−0.606185
$122$	−4421.28			−0.297049
$123$	−3731.03			−0.246614
$124$			10339.3i			0.672430i
$125$	−177.144			−0.0113372
$126$			6808.85i			0.428877i
$127$	−3128.55			−0.193970			−0.0969851	−	0.995286i	$-0.530920\pi$
$127$	−3128.55			−0.193970			−0.0969851	+	0.995286i	$0.530920\pi$
$128$			1448.15i			0.0883883i
$129$			12073.6i			0.725535i
$130$	6.92980			0.000410047
$131$			10688.4i			0.622833i	0.950274	+	0.311416i	$0.100803\pi$
$131$			10688.4i			0.622833i	−0.950274	+	0.311416i	$0.899197\pi$
$132$			6374.63i			0.365853i
$133$	39737.0			2.24643
$134$	−18879.8			−1.05145
$135$	−19.8825			−0.00109094
$136$			7195.19i			0.389013i
$137$	31594.3			1.68332			0.841661	−	0.540006i	$-0.181578\pi$
$137$	31594.3			1.68332			0.841661	+	0.540006i	$0.181578\pi$
$138$	−4102.10			−0.215401
$139$	9555.91			0.494587			0.247293	−	0.968941i	$-0.420459\pi$
$139$	9555.91			0.494587			0.247293	+	0.968941i	$0.420459\pi$
$140$	101.083			0.00515731
$141$			3442.70i			0.173166i
$142$		−	6401.67i		−	0.317480i
$143$	−2651.15			−0.129647
$144$	1728.00			0.0833333
$145$	43.5146			0.00206966
$146$	1153.41			0.0541102
$147$	−28829.9			−1.33416
$148$		−	14953.7i		−	0.682692i
$149$		−	22919.0i		−	1.03234i	−0.856485	−	0.516171i	$-0.827357\pi$
$149$		−	22919.0i		−	1.03234i	0.856485	−	0.516171i	$-0.172643\pi$
$150$		−	9185.29i		−	0.408235i
$151$		−	1712.80i		−	0.0751197i	−0.999294	−	0.0375599i	$-0.988042\pi$
$151$		−	1712.80i		−	0.0751197i	0.999294	−	0.0375599i	$-0.0119585\pi$
$152$		−	10084.8i		−	0.436494i
$153$	8585.61			0.366765
$154$	−38671.7			−1.63061
$155$		−	183.158i		−	0.00762363i
$156$			718.660i			0.0295307i
$157$		−	13119.4i		−	0.532250i	−0.963939	−	0.266125i	$-0.914257\pi$
$157$		−	13119.4i		−	0.532250i	0.963939	−	0.266125i	$-0.0857433\pi$
$158$			3779.72i			0.151407i
$159$	−7329.18			−0.289909
$160$		−	25.6537i		−	0.00100210i
$161$		−	24885.4i		−	0.960047i
$162$		−	2061.92i		−	0.0785674i
$163$	41702.7			1.56960			0.784799	−	0.619750i	$-0.212766\pi$
$163$	41702.7			1.56960			0.784799	+	0.619750i	$0.212766\pi$
$164$	−5744.30			−0.213574
$165$		−	112.925i		−	0.00414784i
$166$	−28312.9			−1.02747
$167$	5986.02			0.214637			0.107319	−	0.994225i	$-0.465774\pi$
$167$	5986.02			0.214637			0.107319	+	0.994225i	$0.465774\pi$
$168$			10482.9i			0.371418i
$169$	28262.1			0.989535
$170$		−	127.461i		−	0.00441041i
$171$	−12033.6			−0.411531
$172$			18588.6i			0.628331i
$173$			28616.4i			0.956144i	0.878321	+	0.478072i	$0.158664\pi$
$173$			28616.4i			0.956144i	−0.878321	+	0.478072i	$0.841336\pi$
$174$			4512.71i			0.149052i
$175$	55722.5			1.81951
$176$			9814.38i			0.316838i
$177$	18084.4	−	350.580i	0.577242	−	0.0111903i
$178$	−1441.41			−0.0454934
$179$			9263.66i			0.289119i	0.989496	+	0.144560i	$0.0461765\pi$
$179$			9263.66i			0.289119i	−0.989496	+	0.144560i	$0.953823\pi$
$180$	−30.6110			−0.000944785
$181$	12290.4			0.375153			0.187576	−	0.982250i	$-0.439937\pi$
$181$	12290.4			0.375153			0.187576	+	0.982250i	$0.439937\pi$
$182$	−4359.75			−0.131619
$183$			8122.41i			0.242540i
$184$	−6315.60			−0.186543
$185$			264.900i			0.00773997i
$186$	18994.5			0.549037
$187$			48763.0i			1.39446i
$188$			5300.39i			0.149966i
$189$	12508.6			0.350176
$190$			178.649i			0.00494872i
$191$		−	34272.7i		−	0.939466i	−0.882809	−	0.469733i	$-0.844350\pi$
$191$		−	34272.7i		−	0.939466i	0.882809	−	0.469733i	$-0.155650\pi$
$192$	2660.43			0.0721688
$193$	−13375.9			−0.359095			−0.179547	−	0.983749i	$-0.557463\pi$
$193$	−13375.9			−0.359095			−0.179547	+	0.983749i	$0.557463\pi$
$194$	−12916.0			−0.343182
$195$		−	12.7309i		−	0.000334802i
$196$	−44386.5			−1.15542
$197$	51898.6			1.33728			0.668641	−	0.743585i	$-0.266876\pi$
$197$	51898.6			1.33728			0.668641	+	0.743585i	$0.266876\pi$
$198$	11710.9			0.298718
$199$	19304.7			0.487480			0.243740	−	0.969841i	$-0.421626\pi$
$199$	19304.7			0.487480			0.243740	+	0.969841i	$0.421626\pi$
$200$		−	14141.7i		−	0.353542i
$201$			34684.5i			0.858505i
$202$	−38615.9			−0.946374
$203$	−27376.3			−0.664329
$204$	13218.4			0.317628
$205$	101.759			0.00242138
$206$	34288.3			0.808001
$207$			7536.04i			0.175874i
$208$			1106.45i			0.0255744i
$209$		−	68346.1i		−	1.56466i
$210$		−	185.702i		−	0.00421092i
$211$			77223.7i			1.73455i	0.497833	+	0.867273i	$0.334129\pi$
$211$			77223.7i			1.73455i	−0.497833	+	0.867273i	$0.665871\pi$
$212$	−11284.0			−0.251068
$213$	−11760.6			−0.259222
$214$		−	27517.6i		−	0.600873i
$215$		−	329.291i		−	0.00712366i
$216$		−	3174.54i		−	0.0680414i
$217$			115230.i			2.44707i
$218$	28699.4			0.603894
$219$		−	2118.96i		−	0.0441808i
$220$		−	173.859i		−	0.00359213i
$221$			5497.42i			0.112557i
$222$	−27471.7			−0.557415
$223$	33182.1			0.667259			0.333629	−	0.942704i	$-0.391727\pi$
$223$	33182.1			0.667259			0.333629	+	0.942704i	$0.391727\pi$
$224$			16139.5i			0.321658i
$225$	−16874.5			−0.333323
$226$	35322.6			0.691570
$227$			11503.1i			0.223235i	0.993751	+	0.111617i	$0.0356031\pi$
$227$			11503.1i			0.223235i	−0.993751	+	0.111617i	$0.964397\pi$
$228$	−18526.9			−0.356396
$229$			31043.5i			0.591971i	0.955193	+	0.295985i	$0.0956479\pi$
$229$			31043.5i			0.591971i	−0.955193	+	0.295985i	$0.904352\pi$
$230$	111.879			0.00211492
$231$			71044.4i			1.33139i
$232$			6947.77i			0.129083i
$233$			30210.5i			0.556476i	0.960512	+	0.278238i	$0.0897504\pi$
$233$			30210.5i			0.556476i	−0.960512	+	0.278238i	$0.910250\pi$
$234$	1320.26			0.0241117
$235$		−	93.8950i		−	0.00170023i
$236$	27842.8	−	539.753i	0.499906	−	0.00969105i
$237$	6943.79			0.123623
$238$			80189.4i			1.41567i
$239$	−8313.22			−0.145537			−0.0727685	−	0.997349i	$-0.523183\pi$
$239$	−8313.22			−0.145537			−0.0727685	+	0.997349i	$0.523183\pi$
$240$	−47.1288			−0.000818208
$241$	−85002.9			−1.46352			−0.731761	−	0.681561i	$-0.761301\pi$
$241$	−85002.9			−1.46352			−0.731761	+	0.681561i	$0.761301\pi$
$242$			25102.7i			0.428637i
$243$	−3788.00			−0.0641500
$244$			12505.3i			0.210046i
$245$	786.295			0.0130995
$246$			10552.9i			0.174383i
$247$		−	7705.16i		−	0.126296i
$248$	29243.9			0.475480
$249$			52014.1i			0.838924i
$250$			501.040i			0.00801664i
$251$	−96883.8			−1.53781			−0.768907	−	0.639361i	$-0.779199\pi$
$251$	−96883.8			−1.53781			−0.768907	+	0.639361i	$0.779199\pi$
$252$	19258.3			0.303262
$253$	−42801.9			−0.668685
$254$			8848.86i			0.137158i
$255$	−234.161			−0.00360109
$256$	4096.00			0.0625000
$257$	−36163.6			−0.547528			−0.273764	−	0.961797i	$-0.588269\pi$
$257$	−36163.6			−0.547528			−0.273764	+	0.961797i	$0.588269\pi$
$258$	34149.4			0.513030
$259$		−	166657.i		−	2.48441i
$260$		−	19.6004i		−	0.000289947i
$261$	8290.37			0.121701
$262$	30231.5			0.440409
$263$	98674.7			1.42657			0.713287	−	0.700872i	$-0.247206\pi$
$263$	98674.7			1.42657			0.713287	+	0.700872i	$0.247206\pi$
$264$	18030.2			0.258697
$265$	199.893			0.00284647
$266$		−	112393.i		−	1.58846i
$267$			2648.04i			0.0371452i
$268$			53400.2i			0.743487i
$269$		−	141006.i		−	1.94865i	−0.225152	−	0.974324i	$-0.572288\pi$
$269$		−	141006.i		−	1.94865i	0.225152	−	0.974324i	$-0.427712\pi$
$270$			56.2361i			0.000771414i
$271$	50037.7			0.681332			0.340666	−	0.940184i	$-0.389348\pi$
$271$	50037.7			0.681332			0.340666	+	0.940184i	$0.389348\pi$
$272$	20351.1			0.275074
$273$			8009.36i			0.107466i
$274$		−	89362.1i		−	1.19029i
$275$		−	95840.5i		−	1.26731i
$276$			11602.5i			0.152312i
$277$	−68916.0			−0.898175			−0.449087	−	0.893488i	$-0.648251\pi$
$277$	−68916.0			−0.898175			−0.449087	+	0.893488i	$0.648251\pi$
$278$		−	27028.2i		−	0.349726i
$279$		−	34895.1i		−	0.448287i
$280$		−	285.907i		−	0.00364677i
$281$	−137775.			−1.74484			−0.872422	−	0.488754i	$-0.837452\pi$
$281$	−137775.			−1.74484			−0.872422	+	0.488754i	$0.837452\pi$
$282$	9737.44			0.122447
$283$			66293.1i			0.827743i	0.910335	+	0.413872i	$0.135824\pi$
$283$			66293.1i			0.827743i	−0.910335	+	0.413872i	$0.864176\pi$
$284$	−18106.7			−0.224492
$285$	328.199			0.00404061
$286$			7498.59i			0.0916743i
$287$	−64019.4			−0.777227
$288$		−	4887.52i		−	0.0589256i
$289$	17593.8			0.210652
$290$		−	123.078i		−	0.00146347i
$291$			23728.2i			0.280207i
$292$		−	3262.35i		−	0.0382617i
$293$	154306.			1.79741			0.898706	−	0.438551i	$-0.144508\pi$
$293$	154306.			1.79741			0.898706	+	0.438551i	$0.144508\pi$
$294$			81543.2i			0.943394i
$295$	−493.227	+	9.56157i	−0.00566765	+	0.000109872i
$296$	−42295.4			−0.482736
$297$		−	21514.4i		−	0.243902i
$298$	−64824.8			−0.729977
$299$	−4825.38			−0.0539745
$300$	−25979.9			−0.288666
$301$			207167.i			2.28659i
$302$	−4844.54			−0.0531177
$303$			70941.9i			0.772711i
$304$	−28524.0			−0.308648
$305$		−	221.527i		−	0.00238138i
$306$		−	24283.8i		−	0.259342i
$307$	−163960.			−1.73964			−0.869821	−	0.493367i	$-0.835766\pi$
$307$	−163960.			−1.73964			−0.869821	+	0.493367i	$0.835766\pi$
$308$			109380.i			1.15302i
$309$		−	62991.7i		−	0.659730i
$310$	−518.048			−0.00539072
$311$	130860.			1.35296			0.676481	−	0.736460i	$-0.263504\pi$
$311$	130860.			1.35296			0.676481	+	0.736460i	$0.263504\pi$
$312$	2032.68			0.0208814
$313$		−	124479.i		−	1.27059i	−0.772268	−	0.635297i	$-0.780878\pi$
$313$		−	124479.i		−	1.27059i	0.772268	−	0.635297i	$-0.219122\pi$
$314$	−37107.3			−0.376357
$315$	−341.156			−0.00343821
$316$	10690.7			0.107061
$317$	30612.0			0.304630			0.152315	−	0.988332i	$-0.451327\pi$
$317$	30612.0			0.304630			0.152315	+	0.988332i	$0.451327\pi$
$318$			20730.1i			0.204996i
$319$			47086.2i			0.462713i
$320$	−72.5595			−0.000708589
$321$	−50553.0			−0.490611
$322$	−70386.5			−0.678856
$323$	−141722.			−1.35842
$324$	−5832.00			−0.0555556
$325$		−	10804.8i		−	0.102294i
$326$		−	117953.i		−	1.10987i
$327$		−	52724.2i		−	0.493077i
$328$			16247.3i			0.151020i
$329$			59072.1i			0.545746i
$330$	−319.400			−0.00293296
$331$	100240.			0.914924			0.457462	−	0.889229i	$-0.348759\pi$
$331$	100240.			0.914924			0.457462	+	0.889229i	$0.348759\pi$
$332$			80080.9i			0.726529i
$333$			50468.7i			0.455128i
$334$		−	16931.0i		−	0.151771i
$335$		−	945.971i		−	0.00842923i
$336$	29650.1			0.262632
$337$			87358.7i			0.769212i	0.923081	+	0.384606i	$0.125663\pi$
$337$			87358.7i			0.769212i	−0.923081	+	0.384606i	$0.874337\pi$
$338$		−	79937.3i		−	0.699707i
$339$		−	64891.8i		−	0.564664i
$340$	−360.514			−0.00311863
$341$	198191.			1.70441
$342$			34036.1i			0.290996i
$343$	−280611.			−2.38515
$344$	52576.4			0.444297
$345$		−	205.535i		−	0.00172682i
$346$	80939.5			0.676096
$347$		−	66248.2i		−	0.550193i	−0.961417	−	0.275096i	$-0.911290\pi$
$347$		−	66248.2i		−	0.550193i	0.961417	−	0.275096i	$-0.0887098\pi$
$348$	12763.9			0.105396
$349$		−	190128.i		−	1.56097i	−0.625174	−	0.780485i	$-0.714972\pi$
$349$		−	190128.i		−	1.56097i	0.625174	−	0.780485i	$-0.285028\pi$
$350$		−	157607.i		−	1.28659i
$351$		−	2425.48i		−	0.0196871i
$352$	27759.3			0.224039
$353$			123820.i			0.993664i	0.867847	+	0.496832i	$0.165504\pi$
$353$			123820.i			0.993664i	−0.867847	+	0.496832i	$0.834496\pi$
$354$	−991.589	−	51150.4i	−0.00791271	−	0.408172i
$355$	320.755			0.00254517
$356$			4076.93i			0.0321687i
$357$	147317.			1.15589
$358$	26201.6			0.204438
$359$	−119958.			−0.930765			−0.465382	−	0.885110i	$-0.654083\pi$
$359$	−119958.			−0.930765			−0.465382	+	0.885110i	$0.654083\pi$
$360$			86.5811i			0.000668064i
$361$	68316.4			0.524216
$362$		−	34762.4i		−	0.265273i
$363$	46116.6			0.349981
$364$			12331.2i			0.0930686i
$365$			57.7916i			0.000433789i
$366$	22973.7			0.171501
$367$		−	204596.i		−	1.51902i	−0.650493	−	0.759512i	$-0.725438\pi$
$367$		−	204596.i		−	1.51902i	0.650493	−	0.759512i	$-0.274562\pi$
$368$			17863.2i			0.131906i
$369$	19387.0			0.142383
$370$	749.251			0.00547298
$371$	−125759.			−0.913672
$372$		−	53724.5i		−	0.388228i
$373$	148994.			1.07091			0.535453	−	0.844565i	$-0.320141\pi$
$373$	148994.			1.07091			0.535453	+	0.844565i	$0.320141\pi$
$374$	137923.			0.986035
$375$	920.469			0.00654556
$376$	14991.8			0.106042
$377$			5308.38i			0.0373490i
$378$		−	35379.8i		−	0.247612i
$379$	68812.0			0.479056			0.239528	−	0.970890i	$-0.423007\pi$
$379$	68812.0			0.479056			0.239528	+	0.970890i	$0.423007\pi$
$380$	505.295			0.00349927
$381$	16256.4			0.111989
$382$	−96937.7			−0.664303
$383$	−63017.5			−0.429599			−0.214800	−	0.976658i	$-0.568910\pi$
$383$	−63017.5			−0.429599			−0.214800	+	0.976658i	$0.568910\pi$
$384$		−	7524.83i		−	0.0510310i
$385$		−	1937.64i		−	0.0130723i
$386$			37832.8i			0.253918i
$387$		−	62736.4i		−	0.418888i
$388$			36532.0i			0.242666i
$389$	66876.2			0.441949			0.220975	−	0.975280i	$-0.429076\pi$
$389$	66876.2			0.441949			0.220975	+	0.975280i	$0.429076\pi$
$390$	−36.0083			−0.000236741
$391$			88753.8i			0.580542i
$392$			125544.i			0.817003i
$393$		−	55538.7i		−	0.359593i
$394$		−	146791.i		−	0.945601i
$395$	−189.382			−0.00121379
$396$		−	33123.5i		−	0.211226i
$397$		−	205628.i		−	1.30467i	−0.757929	−	0.652337i	$-0.773789\pi$
$397$		−	205628.i		−	1.30467i	0.757929	−	0.652337i	$-0.226211\pi$
$398$		−	54602.0i		−	0.344701i
$399$	−206480.			−1.29697
$400$	−39998.7			−0.249992
$401$		−	152584.i		−	0.948897i	−0.880283	−	0.474448i	$-0.842648\pi$
$401$		−	152584.i		−	0.948897i	0.880283	−	0.474448i	$-0.157352\pi$
$402$	98102.5			0.607055
$403$	22343.6			0.137576
$404$			109222.i			0.669188i
$405$	103.312			0.000629857
$406$			77431.9i			0.469751i
$407$	−286643.			−1.73042
$408$		−	37387.3i		−	0.224597i
$409$		−	298256.i		−	1.78296i	−0.453057	−	0.891482i	$-0.649666\pi$
$409$		−	298256.i		−	1.78296i	0.453057	−	0.891482i	$-0.350334\pi$
$410$		−	287.817i		−	0.00171218i
$411$	−164169.			−0.971867
$412$		−	96982.0i		−	0.571343i
$413$	310304.	−	6015.47i	1.81923	−	0.0352671i
$414$	21315.2			0.124362
$415$		−	1418.61i		−	0.00823697i
$416$	3129.51			0.0180838
$417$	−49654.0			−0.285550
$418$	−193312.			−1.10638
$419$			56659.4i			0.322733i	0.986895	+	0.161367i	$0.0515901\pi$
$419$			56659.4i			0.322733i	−0.986895	+	0.161367i	$0.948410\pi$
$420$	−525.244			−0.00297757
$421$		−	306014.i		−	1.72654i	−0.504739	−	0.863272i	$-0.668411\pi$
$421$		−	306014.i		−	1.72654i	0.504739	−	0.863272i	$-0.331589\pi$
$422$	218422.			1.22651
$423$		−	17888.8i		−	0.0999772i
$424$			31916.0i			0.177532i
$425$	−198735.			−1.10026
$426$			33264.1i			0.183297i
$427$			139370.i			0.764385i
$428$	−77831.5			−0.424882
$429$	13775.8			0.0748517
$430$	−931.376			−0.00503719
$431$		−	245207.i		−	1.32002i	−0.751259	−	0.660008i	$-0.770553\pi$
$431$		−	245207.i		−	1.32002i	0.751259	−	0.660008i	$-0.229447\pi$
$432$	−8978.95			−0.0481125
$433$	65342.4			0.348513			0.174257	−	0.984700i	$-0.444248\pi$
$433$	65342.4			0.348513			0.174257	+	0.984700i	$0.444248\pi$
$434$	325920.			1.73034
$435$	−226.108			−0.00119492
$436$		−	81174.3i		−	0.427017i
$437$		−	124397.i		−	0.651399i
$438$	−5993.32			−0.0312406
$439$	−14493.6			−0.0752049			−0.0376024	−	0.999293i	$-0.511972\pi$
$439$	−14493.6			−0.0752049			−0.0376024	+	0.999293i	$0.511972\pi$
$440$	−491.748			−0.00254002
$441$	149804.			0.770278
$442$	15549.1			0.0795902
$443$		−	28672.8i		−	0.146104i	−0.997328	−	0.0730522i	$-0.976726\pi$
$443$		−	28672.8i		−	0.146104i	0.997328	−	0.0730522i	$-0.0232740\pi$
$444$			77701.6i			0.394152i
$445$		−	72.2217i		−	0.000364710i
$446$		−	93853.2i		−	0.471823i
$447$			119091.i			0.596023i
$448$	45649.4			0.227446
$449$	−100054.			−0.496297			−0.248148	−	0.968722i	$-0.579822\pi$
$449$	−100054.			−0.496297			−0.248148	+	0.968722i	$0.579822\pi$
$450$			47728.2i			0.235695i
$451$			110111.i			0.541348i
$452$		−	99907.5i		−	0.489014i
$453$			8899.99i			0.0433704i
$454$	32535.6			0.157851
$455$		−	218.444i		−	0.00105516i
$456$			52401.9i			0.252010i
$457$			220235.i			1.05452i	0.849704	+	0.527260i	$0.176781\pi$
$457$			220235.i			1.05452i	−0.849704	+	0.527260i	$0.823219\pi$
$458$	87804.3			0.418586
$459$	−44612.1			−0.211752
$460$		−	316.442i		−	0.00149547i
$461$	−233164.			−1.09714			−0.548568	−	0.836106i	$-0.684827\pi$
$461$	−233164.			−1.09714			−0.548568	+	0.836106i	$0.684827\pi$
$462$	200944.			0.941436
$463$			113985.i			0.531724i	0.964011	+	0.265862i	$0.0856565\pi$
$463$			113985.i			0.531724i	−0.964011	+	0.265862i	$0.914343\pi$
$464$	19651.3			0.0912755
$465$			951.715i			0.00440150i
$466$	85448.3			0.393488
$467$		−	416986.i		−	1.91200i	−0.293369	−	0.955999i	$-0.594776\pi$
$467$		−	416986.i		−	1.91200i	0.293369	−	0.955999i	$-0.405224\pi$
$468$		−	3734.27i		−	0.0170496i
$469$			595138.i			2.70565i
$470$	−265.575			−0.00120224
$471$			68170.5i			0.307294i
$472$	−1526.65	−	78751.2i	−0.00685261	−	0.353487i
$473$	356319.			1.59264
$474$		−	19640.0i		−	0.0874148i
$475$	278546.			1.23455
$476$	226810.			1.00103
$477$	38083.5			0.167379
$478$			23513.3i			0.102910i
$479$	−287635.			−1.25363			−0.626816	−	0.779167i	$-0.715642\pi$
$479$	−287635.			−1.25363			−0.626816	+	0.779167i	$0.715642\pi$
$480$			133.300i			0.000578561i
$481$	−32315.4			−0.139675
$482$			240424.i			1.03487i
$483$			129308.i			0.554284i
$484$	71001.2			0.303092
$485$		−	647.154i		−	0.00275121i
$486$			10714.1i			0.0453609i
$487$	274773.			1.15855			0.579277	−	0.815131i	$-0.303335\pi$
$487$	274773.			1.15855			0.579277	+	0.815131i	$0.303335\pi$
$488$	35370.3			0.148525
$489$	−216693.			−0.906208
$490$		−	2223.98i		−	0.00926271i
$491$	58684.5			0.243422			0.121711	−	0.992566i	$-0.461162\pi$
$491$	58684.5			0.243422			0.121711	+	0.992566i	$0.461162\pi$
$492$	29848.2			0.123307
$493$	97637.8			0.401720
$494$	−21793.5			−0.0893044
$495$			586.775i			0.00239475i
$496$		−	82714.3i		−	0.336215i
$497$	−201796.			−0.816959
$498$	147118.			0.593209
$499$	−285742.			−1.14755			−0.573776	−	0.819012i	$-0.694522\pi$
$499$	−285742.			−1.14755			−0.573776	+	0.819012i	$0.694522\pi$
$500$	1417.16			0.00566862
$501$	−31104.3			−0.123921
$502$			274029.i			1.08740i
$503$			464741.i			1.83685i	0.395590	+	0.918427i	$0.370540\pi$
$503$			464741.i			1.83685i	−0.395590	+	0.918427i	$0.629460\pi$
$504$		−	54470.8i		−	0.214438i
$505$		−	1934.84i		−	0.00758687i
$506$			121062.i			0.472832i
$507$	−146854.			−0.571308
$508$	25028.4			0.0969851
$509$			141408.i			0.545804i	0.962042	+	0.272902i	$0.0879835\pi$
$509$			141408.i			0.545804i	−0.962042	+	0.272902i	$0.912016\pi$
$510$			662.306i			0.00254635i
$511$		−	36358.4i		−	0.139240i
$512$		−	11585.2i		−	0.0441942i
$513$	62528.2			0.237597
$514$			102286.i			0.387160i
$515$			1718.01i			0.00647756i
$516$		−	96589.0i		−	0.362767i
$517$	101602.			0.380119
$518$	−471376.			−1.75674
$519$		−	148695.i		−	0.552030i
$520$	−55.4384			−0.000205024
$521$	62659.7			0.230841			0.115420	−	0.993317i	$-0.463178\pi$
$521$	62659.7			0.230841			0.115420	+	0.993317i	$0.463178\pi$
$522$		−	23448.7i		−	0.0860554i
$523$	401872.			1.46921			0.734606	−	0.678494i	$-0.237367\pi$
$523$	401872.			1.46921			0.734606	+	0.678494i	$0.237367\pi$
$524$		−	85507.5i		−	0.311416i
$525$	−289543.			−1.05050
$526$		−	279094.i		−	1.00874i
$527$		−	410968.i		−	1.47975i
$528$		−	50997.0i		−	0.182927i
$529$	201937.			0.721614
$530$		−	565.383i		−	0.00201276i
$531$	−93969.3	+	1821.67i	−0.333271	+	0.00646070i
$532$	−317896.			−1.12321
$533$			12413.6i			0.0436962i
$534$	7489.79			0.0262656
$535$	1378.76			0.00481706
$536$	151039.			0.525725
$537$		−	48135.4i		−	0.166923i
$538$	−398825.			−1.37790
$539$			850832.i			2.92864i
$540$	159.060			0.000545472
$541$		−	331335.i		−	1.13207i	−0.824382	−	0.566034i	$-0.808477\pi$
$541$		−	331335.i		−	1.13207i	0.824382	−	0.566034i	$-0.191523\pi$
$542$		−	141528.i		−	0.481774i
$543$	−63862.7			−0.216595
$544$		−	57561.5i		−	0.194507i
$545$			1437.98i			0.00484128i
$546$	22653.9			0.0759902
$547$	−322316.			−1.07723			−0.538613	−	0.842553i	$-0.681052\pi$
$547$	−322316.			−1.07723			−0.538613	+	0.842553i	$0.681052\pi$
$548$	−252754.			−0.841661
$549$		−	42205.3i		−	0.140030i
$550$	−271078.			−0.896125
$551$	−136849.			−0.450752
$552$	32816.8			0.107701
$553$	119146.			0.389609
$554$			194924.i			0.635105i
$555$		−	1376.46i		−	0.00446867i
$556$	−76447.3			−0.247293
$557$	−272295.			−0.877665			−0.438832	−	0.898569i	$-0.644608\pi$
$557$	−272295.			−0.877665			−0.438832	+	0.898569i	$0.644608\pi$
$558$	−98698.3			−0.316987
$559$	40170.5			0.128553
$560$	−808.666			−0.00257865
$561$		−	253380.i		−	0.805094i
$562$			389685.i			1.23379i
$563$			390792.i			1.23290i	0.787393	+	0.616451i	$0.211430\pi$
$563$			390792.i			1.23290i	−0.787393	+	0.616451i	$0.788570\pi$
$564$		−	27541.6i		−	0.0865828i
$565$			1769.83i			0.00554416i
$566$	187505.			0.585303
$567$	−64996.8			−0.202174
$568$			51213.4i			0.158740i
$569$			192985.i			0.596073i	0.954555	+	0.298036i	$0.0963317\pi$
$569$			192985.i			0.596073i	−0.954555	+	0.298036i	$0.903668\pi$
$570$		−	928.286i		−	0.00285714i
$571$		−	622999.i		−	1.91080i	−0.295315	−	0.955400i	$-0.595424\pi$
$571$		−	622999.i		−	1.91080i	0.295315	−	0.955400i	$-0.404576\pi$
$572$	21209.2			0.0648235
$573$			178086.i			0.542401i
$574$			181074.i			0.549582i
$575$		−	174440.i		−	0.527606i
$576$	−13824.0			−0.0416667
$577$	425350.			1.27760			0.638800	−	0.769373i	$-0.279431\pi$
$577$	425350.			1.27760			0.638800	+	0.769373i	$0.279431\pi$
$578$		−	49762.9i		−	0.148953i
$579$	69503.4			0.207324
$580$	−348.117			−0.00103483
$581$			892491.i			2.64394i
$582$	67113.5			0.198136
$583$			216300.i			0.636384i
$584$	−9227.31			−0.0270551
$585$			66.1515i			0.000193298i
$586$		−	436443.i		−	1.27096i
$587$		−	190373.i		−	0.552495i	−0.961086	−	0.276248i	$-0.910909\pi$
$587$		−	190373.i		−	0.552495i	0.961086	−	0.276248i	$-0.0890910\pi$
$588$	230639.			0.667080
$589$			576012.i			1.66035i
$590$	27.0442	+	1395.06i	7.76909e−5	+	0.00400763i
$591$	−269673.			−0.772080
$592$			119629.i			0.341346i
$593$	−387212.			−1.10113			−0.550566	−	0.834792i	$-0.685588\pi$
$593$	−387212.			−1.10113			−0.550566	+	0.834792i	$0.685588\pi$
$594$	−60851.8			−0.172465
$595$	−4017.88			−0.0113491
$596$			183352.i			0.516171i
$597$	−100310.			−0.281447
$598$			13648.2i			0.0381657i
$599$	−418635.			−1.16676			−0.583381	−	0.812199i	$-0.698271\pi$
$599$	−418635.			−1.16676			−0.583381	+	0.812199i	$0.698271\pi$
$600$			73482.3i			0.204118i
$601$			102580.i			0.283996i	0.989867	+	0.141998i	$0.0453526\pi$
$601$			102580.i			0.283996i	−0.989867	+	0.141998i	$0.954647\pi$
$602$	585957.			1.61686
$603$		−	180226.i		−	0.495658i
$604$			13702.4i			0.0375599i
$605$	−1257.77			−0.00343629
$606$	200654.			0.546389
$607$	504166.			1.36835			0.684173	−	0.729319i	$-0.260163\pi$
$607$	504166.			1.36835			0.684173	+	0.729319i	$0.260163\pi$
$608$			80678.1i			0.218247i
$609$	142252.			0.383550
$610$	−626.574			−0.00168389
$611$	11454.3			0.0306822
$612$	−68684.9			−0.183383
$613$		−	451674.i		−	1.20200i	−0.799249	−	0.601000i	$-0.794769\pi$
$613$		−	451674.i		−	1.20200i	0.799249	−	0.601000i	$-0.205231\pi$
$614$			463748.i			1.23011i
$615$	−528.753			−0.00139799
$616$	309373.			0.815307
$617$	149230.			0.392000			0.196000	−	0.980604i	$-0.437205\pi$
$617$	149230.			0.392000			0.196000	+	0.980604i	$0.437205\pi$
$618$	−178167.			−0.466499
$619$	−324745.			−0.847542			−0.423771	−	0.905769i	$-0.639294\pi$
$619$	−324745.			−0.847542			−0.423771	+	0.905769i	$0.639294\pi$
$620$			1465.26i			0.00381182i
$621$		−	39158.4i		−	0.101541i
$622$		−	370127.i		−	0.956688i
$623$			45436.8i			0.117066i
$624$		−	5749.28i		−	0.0147654i
$625$	390587.			0.999904
$626$	−352079.			−0.898446
$627$			355137.i			0.903359i
$628$			104955.i			0.266125i
$629$			594382.i			1.50233i
$630$			964.935i			0.00243118i
$631$	−81746.8			−0.205311			−0.102655	−	0.994717i	$-0.532734\pi$
$631$	−81746.8			−0.205311			−0.102655	+	0.994717i	$0.532734\pi$
$632$		−	30237.8i		−	0.0757034i
$633$		−	401266.i		−	1.00144i
$634$		−	86583.7i		−	0.215406i
$635$	−443.371			−0.00109956
$636$	58633.4			0.144954
$637$			95920.7i			0.236392i
$638$	133180.			0.327188
$639$	61110.0			0.149662
$640$			205.229i			0.000501048i
$641$	−463888.			−1.12901			−0.564505	−	0.825430i	$-0.690933\pi$
$641$	−463888.			−1.12901			−0.564505	+	0.825430i	$0.690933\pi$
$642$			142986.i			0.346914i
$643$	−624059.			−1.50940			−0.754699	−	0.656071i	$-0.772217\pi$
$643$	−624059.			−1.50940			−0.754699	+	0.656071i	$0.772217\pi$
$644$			199083.i			0.480024i
$645$			1711.05i			0.00411285i
$646$			400851.i			0.960545i
$647$	250236.			0.597779			0.298889	−	0.954288i	$-0.403384\pi$
$647$	250236.			0.597779			0.298889	+	0.954288i	$0.403384\pi$
$648$			16495.4i			0.0392837i
$649$	−10346.4	−	533710.i	−0.0245640	−	1.26712i
$650$	−30560.6			−0.0723329
$651$		−	598753.i		−	1.41282i
$652$	−333621.			−0.784799
$653$	153928.			0.360986			0.180493	−	0.983576i	$-0.442231\pi$
$653$	153928.			0.360986			0.180493	+	0.983576i	$0.442231\pi$
$654$	−149127.			−0.348658
$655$			1514.74i			0.00353066i
$656$	45954.4			0.106787
$657$			11010.4i			0.0255078i
$658$	167081.			0.385901
$659$			787734.i			1.81388i	0.421260	+	0.906940i	$0.361588\pi$
$659$			787734.i			1.81388i	−0.421260	+	0.906940i	$0.638412\pi$
$660$			903.399i			0.00207392i
$661$	−74406.3			−0.170297			−0.0851484	−	0.996368i	$-0.527136\pi$
$661$	−74406.3			−0.170297			−0.0851484	+	0.996368i	$0.527136\pi$
$662$		−	283521.i		−	0.646949i
$663$		−	28565.4i		−	0.0649851i
$664$	226503.			0.513734
$665$	5631.44			0.0127343
$666$	142747.			0.321824
$667$			85701.8i			0.192636i
$668$	−47888.2			−0.107319
$669$	−172419.			−0.385242
$670$	−2675.61			−0.00596037
$671$	239710.			0.532404
$672$		−	83863.2i		−	0.185709i
$673$			664641.i			1.46743i	0.679458	+	0.733714i	$0.262215\pi$
$673$			664641.i			1.46743i	−0.679458	+	0.733714i	$0.737785\pi$
$674$	247088.			0.543915
$675$	87682.3			0.192444
$676$	−226097.			−0.494768
$677$	33702.5			0.0735333			0.0367667	−	0.999324i	$-0.488294\pi$
$677$	33702.5			0.0735333			0.0367667	+	0.999324i	$0.488294\pi$
$678$	−183542.			−0.399278
$679$			407144.i			0.883097i
$680$			1019.69i			0.00220521i
$681$		−	59771.7i		−	0.128885i
$682$		−	560569.i		−	1.20520i
$683$			17408.2i			0.0373176i	0.999826	+	0.0186588i	$0.00593962\pi$
$683$			17408.2i			0.0373176i	−0.999826	+	0.0186588i	$0.994060\pi$
$684$	96268.5			0.205765
$685$	4477.47			0.00954227
$686$			793687.i			1.68656i
$687$		−	161307.i		−	0.341774i
$688$		−	148708.i		−	0.314166i
$689$			24385.1i			0.0513673i
$690$	−581.341			−0.00122105
$691$			143317.i			0.300153i	0.988674	+	0.150076i	$0.0479520\pi$
$691$			143317.i			0.300153i	−0.988674	+	0.150076i	$0.952048\pi$
$692$		−	228931.i		−	0.478072i
$693$		−	369157.i		−	0.768679i
$694$	−187378.			−0.389045
$695$	1354.24			0.00280367
$696$		−	36101.7i		−	0.0745262i
$697$	228325.			0.469990
$698$	−537762.			−1.10377
$699$		−	156979.i		−	0.321282i
$700$	−445780.			−0.909756
$701$			724797.i			1.47496i	0.675369	+	0.737480i	$0.263984\pi$
$701$			724797.i			1.47496i	−0.675369	+	0.737480i	$0.736016\pi$
$702$	−6860.28			−0.0139209
$703$		−	833083.i		−	1.68569i
$704$		−	78515.1i		−	0.158419i
$705$			487.893i			0.000981626i
$706$	350214.			0.702627
$707$			1.21727e6i			2.43527i
$708$	−144675.	+	2804.64i	−0.288621	+	0.00559513i
$709$	412172.			0.819948			0.409974	−	0.912097i	$-0.365538\pi$
$709$	412172.			0.819948			0.409974	+	0.912097i	$0.365538\pi$
$710$		−	907.231i		−	0.00179970i
$711$	−36081.0			−0.0713739
$712$	11531.3			0.0227467
$713$	360728.			0.709580
$714$		−	416677.i		−	0.817340i
$715$	−375.715			−0.000734932
$716$		−	74109.3i		−	0.144560i
$717$	43196.8			0.0840258
$718$			339292.i			0.658150i
$719$			259293.i			0.501571i	0.968043	+	0.250786i	$0.0806889\pi$
$719$			259293.i			0.501571i	−0.968043	+	0.250786i	$0.919311\pi$
$720$	244.888			0.000472393
$721$		−	1.08085e6i		−	2.07920i
$722$		−	193228.i		−	0.370677i
$723$	441688.			0.844965
$724$	−98323.0			−0.187576
$725$	−191901.			−0.365090
$726$		−	130438.i		−	0.247474i
$727$	359129.			0.679487			0.339744	−	0.940518i	$-0.389660\pi$
$727$	359129.			0.679487			0.339744	+	0.940518i	$0.389660\pi$
$728$	34878.0			0.0658095
$729$	19683.0			0.0370370
$730$	163.459			0.000306735
$731$		−	738862.i		−	1.38270i
$732$		−	64979.3i		−	0.121270i
$733$	448431.			0.834618			0.417309	−	0.908765i	$-0.362973\pi$
$733$	448431.			0.834618			0.417309	+	0.908765i	$0.362973\pi$
$734$	−578684.			−1.07411
$735$	−4085.71			−0.00756297
$736$	50524.8			0.0932715
$737$	1.02361e6			1.88452
$738$		−	54834.7i		−	0.100680i
$739$		−	954219.i		−	1.74727i	−0.486585	−	0.873633i	$-0.661758\pi$
$739$		−	954219.i		−	1.74727i	0.486585	−	0.873633i	$-0.338242\pi$
$740$		−	2119.20i		−	0.00386998i
$741$			40037.2i			0.0729168i
$742$			355699.i			0.646064i
$743$	670112.			1.21386			0.606932	−	0.794754i	$-0.292400\pi$
$743$	670112.			1.21386			0.606932	+	0.794754i	$0.292400\pi$
$744$	−151956.			−0.274519
$745$		−	3248.04i		−	0.00585205i
$746$		−	421419.i		−	0.757244i
$747$		−	270273.i		−	0.484353i
$748$		−	390104.i		−	0.697232i
$749$	−867422.			−1.54620
$750$		−	2603.48i		−	0.00462841i
$751$			473613.i			0.839738i	0.907585	+	0.419869i	$0.137924\pi$
$751$			473613.i			0.839738i	−0.907585	+	0.419869i	$0.862076\pi$
$752$		−	42403.1i		−	0.0749829i
$753$	503423.			0.887857
$754$	15014.4			0.0264097
$755$		−	242.735i		−	0.000425832i
$756$	−100069.			−0.175088
$757$	−310856.			−0.542460			−0.271230	−	0.962515i	$-0.587430\pi$
$757$	−310856.			−0.542460			−0.271230	+	0.962515i	$0.587430\pi$
$758$		−	194630.i		−	0.338743i
$759$	222405.			0.386066
$760$		−	1429.19i		−	0.00247436i
$761$	892312.			1.54080			0.770402	−	0.637559i	$-0.220056\pi$
$761$	892312.			1.54080			0.770402	+	0.637559i	$0.220056\pi$
$762$		−	45980.0i		−	0.0791880i
$763$		−	904676.i		−	1.55398i
$764$			274181.i			0.469733i
$765$	1216.73			0.00207909
$766$			178240.i			0.303772i
$767$	−1166.42	−	60169.1i	−0.00198274	−	0.102278i
$768$	−21283.4			−0.0360844
$769$		−	113622.i		−	0.192136i	−0.995375	−	0.0960682i	$-0.969373\pi$
$769$		−	113622.i		−	0.192136i	0.995375	−	0.0960682i	$-0.0306267\pi$
$770$	−5480.46			−0.00924349
$771$	187912.			0.316115
$772$	107007.			0.179547
$773$		−	113583.i		−	0.190088i	−0.995473	−	0.0950442i	$-0.969701\pi$
$773$		−	113583.i		−	0.190088i	0.995473	−	0.0950442i	$-0.0302992\pi$
$774$	−177445.			−0.296198
$775$			807731.i			1.34482i
$776$	103328.			0.171591
$777$			865974.i			1.43437i
$778$		−	189154.i		−	0.312505i
$779$	−320020.			−0.527354
$780$			101.847i			0.000167401i
$781$			347082.i			0.569023i
$782$	251034.			0.410505
$783$	−43078.0			−0.0702639
$784$	355092.			0.577708
$785$		−	1859.26i		−	0.00301717i
$786$	−157087.			−0.254270
$787$	−255189.			−0.412014			−0.206007	−	0.978551i	$-0.566047\pi$
$787$	−255189.			−0.412014			−0.206007	+	0.978551i	$0.566047\pi$
$788$	−415189.			−0.668641
$789$	−512729.			−0.823633
$790$			535.654i			0.000858282i
$791$		−	1.11346e6i		−	1.77959i
$792$	−93687.5			−0.149359
$793$	27024.3			0.0429742
$794$	−581605.			−0.922544
$795$	−1038.68			−0.00164341
$796$	−154438.			−0.243740
$797$		−	976515.i		−	1.53731i	−0.639662	−	0.768656i	$-0.720926\pi$
$797$		−	976515.i		−	1.53731i	0.639662	−	0.768656i	$-0.279074\pi$
$798$			584012.i			0.917099i
$799$		−	210681.i		−	0.330014i
$800$			113133.i			0.176771i
$801$		−	13759.6i		−	0.0214458i
$802$	−431571.			−0.670971
$803$	−62535.0			−0.0969822
$804$		−	277476.i		−	0.429253i
$805$		−	3526.70i		−	0.00544223i
$806$		−	63197.1i		−	0.0972808i
$807$			732689.i			1.12505i
$808$	308927.			0.473187
$809$		−	749933.i		−	1.14584i	−0.819610	−	0.572922i	$-0.805810\pi$
$809$		−	749933.i		−	1.14584i	0.819610	−	0.572922i	$-0.194190\pi$
$810$		−	292.211i		−	0.000445376i
$811$			237245.i			0.360707i	0.983602	+	0.180354i	$0.0577242\pi$
$811$			237245.i			0.360707i	−0.983602	+	0.180354i	$0.942276\pi$
$812$	219011.			0.332164
$813$	−260003.			−0.393367
$814$			810748.i			1.22359i
$815$	5910.01			0.00889760
$816$	−105747.			−0.158814
$817$			1.03559e6i			1.55147i
$818$	−843595.			−1.26075
$819$		−	41617.9i		−	0.0620458i
$820$	−814.069			−0.00121069
$821$		−	1.31531e6i		−	1.95139i	−0.219142	−	0.975693i	$-0.570326\pi$
$821$		−	1.31531e6i		−	1.95139i	0.219142	−	0.975693i	$-0.429674\pi$
$822$			464339.i			0.687213i
$823$			610152.i			0.900820i	0.892822	+	0.450410i	$0.148722\pi$
$823$			610152.i			0.900820i	−0.892822	+	0.450410i	$0.851278\pi$
$824$	−274307.			−0.404000
$825$			498002.i			0.731683i
$826$	−17014.3	−	877672.i	−0.0249376	−	1.28639i
$827$	938440.			1.37213			0.686065	−	0.727540i	$-0.259336\pi$
$827$	938440.			1.37213			0.686065	+	0.727540i	$0.259336\pi$
$828$		−	60288.4i		−	0.0879372i
$829$	156068.			0.227094			0.113547	−	0.993533i	$-0.463779\pi$
$829$	156068.			0.227094			0.113547	+	0.993533i	$0.463779\pi$
$830$	−4012.44			−0.00582442
$831$	358098.			0.518561
$832$		−	8851.59i		−	0.0127872i
$833$	1.76428e6			2.54260
$834$			140443.i			0.201914i
$835$	848.326			0.00121672
$836$			546769.i			0.782332i
$837$			181320.i			0.258819i
$838$	160257.			0.228207
$839$			475667.i			0.675739i	0.941193	+	0.337869i	$0.109706\pi$
$839$			475667.i			0.675739i	−0.941193	+	0.337869i	$0.890294\pi$
$840$			1485.61i			0.00210546i
$841$	−613001.			−0.866700
$842$	−865540.			−1.22085
$843$	715898.			1.00739
$844$		−	617790.i		−	0.867273i
$845$	4005.25			0.00560939
$846$	−50597.2			−0.0706945
$847$	791299.			1.10300
$848$	90272.1			0.125534
$849$		−	344469.i		−	0.477898i
$850$			562106.i			0.778002i
$851$	−521720.			−0.720408
$852$	94085.0			0.129611
$853$	1.04833e6			1.44078			0.720391	−	0.693568i	$-0.243962\pi$
$853$	1.04833e6			1.44078			0.720391	+	0.693568i	$0.243962\pi$
$854$	394197.			0.540502
$855$	−1705.37			−0.00233285
$856$			220141.i			0.300437i
$857$			40916.3i			0.0557102i	0.999612	+	0.0278551i	$0.00886770\pi$
$857$			40916.3i			0.0557102i	−0.999612	+	0.0278551i	$0.991132\pi$
$858$		−	38963.8i		−	0.0529282i
$859$		−	213006.i		−	0.288672i	−0.989529	−	0.144336i	$-0.953895\pi$
$859$		−	213006.i		−	0.288672i	0.989529	−	0.144336i	$-0.0461046\pi$
$860$			2634.33i			0.00356183i
$861$	332655.			0.448732
$862$	−693551.			−0.933392
$863$			645270.i			0.866404i	0.901297	+	0.433202i	$0.142616\pi$
$863$			645270.i			0.866404i	−0.901297	+	0.433202i	$0.857384\pi$
$864$			25396.3i			0.0340207i
$865$			4055.46i			0.00542011i
$866$		−	184816.i		−	0.246436i
$867$	−91420.3			−0.121620
$868$		−	921840.i		−	1.22353i
$869$		−	204926.i		−	0.271368i
$870$			639.531i			0.000844935i
$871$	115400.			0.152114
$872$	−229596.			−0.301947
$873$		−	123295.i		−	0.161778i
$874$	−351848.			−0.460609
$875$	15794.0			0.0206289
$876$			16951.7i			0.0220904i
$877$	−530994.			−0.690384			−0.345192	−	0.938532i	$-0.612186\pi$
$877$	−530994.			−0.690384			−0.345192	+	0.938532i	$0.612186\pi$
$878$			40994.0i			0.0531779i
$879$	−801798.			−1.03774
$880$			1390.87i			0.00179607i
$881$		−	687431.i		−	0.885680i	−0.896601	−	0.442840i	$-0.853971\pi$
$881$		−	687431.i		−	0.885680i	0.896601	−	0.442840i	$-0.146029\pi$
$882$		−	423711.i		−	0.544669i
$883$	−1.42459e6			−1.82713			−0.913563	−	0.406698i	$-0.866680\pi$
$883$	−1.42459e6			−1.82713			−0.913563	+	0.406698i	$0.866680\pi$
$884$		−	43979.4i		−	0.0562787i
$885$	2562.88	−	49.6834i	0.00327222	−	6.34344e-5i
$886$	−81099.0			−0.103311
$887$		−	919991.i		−	1.16933i	−0.811276	−	0.584664i	$-0.801226\pi$
$887$		−	919991.i		−	1.16933i	0.811276	−	0.584664i	$-0.198774\pi$
$888$	219773.			0.278708
$889$	278938.			0.352942
$890$	−204.274			−0.000257889
$891$			111792.i			0.140817i
$892$	−265457.			−0.333629
$893$			295290.i			0.370293i
$894$	336840.			0.421452
$895$			1312.83i			0.00163893i
$896$		−	129116.i		−	0.160829i
$897$	25073.4			0.0311622
$898$			282995.i			0.350935i
$899$		−	396836.i		−	0.491012i
$900$	134996.			0.166661
$901$	448519.			0.552499
$902$	311440.			0.382791
$903$		−	1.07647e6i		−	1.32016i
$904$	−282581.			−0.345785
$905$	1741.77			0.00212663
$906$	25173.0			0.0306675
$907$	−1.08390e6			−1.31757			−0.658786	−	0.752331i	$-0.728930\pi$
$907$	−1.08390e6			−1.31757			−0.658786	+	0.752331i	$0.728930\pi$
$908$		−	92024.6i		−	0.111617i
$909$		−	368625.i		−	0.446125i
$910$	−617.854			−0.000746110
$911$	150420.			0.181246			0.0906231	−	0.995885i	$-0.471114\pi$
$911$	150420.			0.181246			0.0906231	+	0.995885i	$0.471114\pi$
$912$	148215.			0.178198
$913$	1.53505e6			1.84154
$914$	622920.			0.745658
$915$			1151.09i			0.00137489i
$916$		−	248348.i		−	0.295985i
$917$		−	952969.i		−	1.13329i
$918$			126182.i			0.149731i
$919$			33694.3i			0.0398956i	0.999801	+	0.0199478i	$0.00635001\pi$
$919$			33694.3i			0.0398956i	−0.999801	+	0.0199478i	$0.993650\pi$
$920$	−895.033			−0.00105746
$921$	851959.			1.00438
$922$			659489.i			0.775792i
$923$			39129.1i			0.0459300i
$924$		−	568355.i		−	0.665696i
$925$		−	1.16822e6i		−	1.36534i
$926$	322399.			0.375986
$927$			327314.i			0.380895i
$928$		−	55582.1i		−	0.0645415i
$929$			1.71637e6i			1.98874i	0.105957	+	0.994371i	$0.466210\pi$
$929$			1.71637e6i			1.98874i	−0.105957	+	0.994371i	$0.533790\pi$
$930$	2691.86			0.00311233
$931$	−2.47281e6			−2.85294
$932$		−	241684.i		−	0.278238i
$933$	−679968.			−0.781133
$934$	−1.17941e6			−1.35199
$935$			6910.59i			0.00790482i
$936$	−10562.1			−0.0120559
$937$		−	1.27855e6i		−	1.45626i	−0.685438	−	0.728131i	$-0.740389\pi$
$937$		−	1.27855e6i		−	1.45626i	0.685438	−	0.728131i	$-0.259611\pi$
$938$	1.68331e6			1.91319
$939$			646811.i			0.733578i
$940$			751.160i			0.000850113i
$941$		−	1.17567e6i		−	1.32772i	−0.747855	−	0.663862i	$-0.768916\pi$
$941$		−	1.17567e6i		−	1.32772i	0.747855	−	0.663862i	$-0.231084\pi$
$942$	192815.			0.217290
$943$			200413.i			0.225374i
$944$	−222742.	+	4318.02i	−0.249953	+	0.00484552i
$945$	1772.70			0.00198505
$946$		−	1.00782e6i		−	1.12616i
$947$	−786404.			−0.876891			−0.438446	−	0.898758i	$-0.644471\pi$
$947$	−786404.			−0.876891			−0.438446	+	0.898758i	$0.644471\pi$
$948$	−55550.3			−0.0618116
$949$	−7050.04			−0.00782815
$950$		−	787846.i		−	0.872960i
$951$	−159064.			−0.175878
$952$		−	641516.i		−	0.707837i
$953$	260783.			0.287140			0.143570	−	0.989640i	$-0.454142\pi$
$953$	260783.			0.287140			0.143570	+	0.989640i	$0.454142\pi$
$954$		−	107717.i		−	0.118355i
$955$		−	4857.05i		−	0.00532556i
$956$	66505.8			0.0727685
$957$		−	244667.i		−	0.267148i
$958$			813554.i			0.886452i
$959$	−2.81691e6			−3.06292
$960$	377.030			0.000409104
$961$	−746806.			−0.808651
$962$			91401.7i			0.0987653i
$963$	262681.			0.283254
$964$	680023.			0.731761
$965$	−1895.61			−0.00203561
$966$	365739.			0.391938
$967$		−	483157.i		−	0.516696i	−0.966052	−	0.258348i	$-0.916822\pi$
$967$		−	483157.i		−	0.516696i	0.966052	−	0.258348i	$-0.0831782\pi$
$968$		−	200822.i		−	0.214319i
$969$	736410.			0.784282
$970$	−1830.43			−0.00194540
$971$	226095.			0.239802			0.119901	−	0.992786i	$-0.461742\pi$
$971$	226095.			0.239802			0.119901	+	0.992786i	$0.461742\pi$
$972$	30304.0			0.0320750
$973$	−851994.			−0.899935
$974$		−	777176.i		−	0.819222i
$975$			56143.5i			0.0590595i
$976$		−	100042.i		−	0.105023i
$977$		−	301208.i		−	0.315556i	−0.987475	−	0.157778i	$-0.949567\pi$
$977$		−	301208.i		−	0.315556i	0.987475	−	0.157778i	$-0.0504331\pi$
$978$			612902.i			0.640786i
$979$	78149.5			0.0815381
$980$	−6290.36			−0.00654973
$981$			273963.i			0.284678i
$982$		−	165985.i		−	0.172126i
$983$		−	1.05343e6i		−	1.09018i	−0.838377	−	0.545091i	$-0.816495\pi$
$983$		−	1.05343e6i		−	1.09018i	0.838377	−	0.545091i	$-0.183505\pi$
$984$		−	84423.6i		−	0.0871914i
$985$	7354.95			0.00758067
$986$		−	276161.i		−	0.284059i
$987$		−	306948.i		−	0.315087i
$988$			61641.3i			0.0631478i
$989$	648538.			0.663045
$990$	1659.65			0.00169335
$991$		−	1.37122e6i		−	1.39624i	−0.715983	−	0.698118i	$-0.754021\pi$
$991$		−	1.37122e6i		−	1.39624i	0.715983	−	0.698118i	$-0.245979\pi$
$992$	−233951.			−0.237740
$993$	−520862.			−0.528231
$994$			570766.i			0.577678i
$995$	2735.82			0.00276339
$996$		−	416113.i		−	0.419462i
$997$	−1.45309e6			−1.46185			−0.730924	−	0.682459i	$-0.760911\pi$
$997$	−1.45309e6			−1.46185			−0.730924	+	0.682459i	$0.760911\pi$
$998$			808199.i			0.811442i
$999$		−	262243.i		−	0.262768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.d.a.235.5	✓	40
3.2	odd	2		1062.5.d.b.235.34		40
59.58	odd	2	inner	354.5.d.a.235.6	yes	40
177.176	even	2		1062.5.d.b.235.33		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.d.a.235.5	✓	40	1.1	even	1	trivial
354.5.d.a.235.6	yes	40	59.58	odd	2	inner
1062.5.d.b.235.33		40	177.176	even	2
1062.5.d.b.235.34		40	3.2	odd	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)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.141718 q^{5} +14.6969i q^{6} -89.1589 q^{7} +22.6274i q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} -5.19615 q^{3} -8.00000 q^{4} +0.141718 q^{5} +14.6969i q^{6} -89.1589 q^{7} +22.6274i q^{8} +27.0000 q^{9} -0.400839i q^{10} +153.350i q^{11} +41.5692 q^{12} +17.2883i q^{13} +252.179i q^{14} -0.736387 q^{15} +64.0000 q^{16} +317.986 q^{17} -76.3675i q^{18} -445.688 q^{19} -1.13374 q^{20} +463.283 q^{21} +433.739 q^{22} +279.113i q^{23} -117.576i q^{24} -624.980 q^{25} +48.8986 q^{26} -140.296 q^{27} +713.271 q^{28} +307.051 q^{29} +2.08282i q^{30} -1292.41i q^{31} -181.019i q^{32} -796.829i q^{33} -899.399i q^{34} -12.6354 q^{35} -216.000 q^{36} +1869.21i q^{37} +1260.59i q^{38} -89.8325i q^{39} +3.20671i q^{40} +718.037 q^{41} -1310.36i q^{42} -2323.57i q^{43} -1226.80i q^{44} +3.82638 q^{45} +789.450 q^{46} -662.549i q^{47} -332.554 q^{48} +5548.31 q^{49} +1767.71i q^{50} -1652.30 q^{51} -138.306i q^{52} +1410.50 q^{53} +396.817i q^{54} +21.7324i q^{55} -2017.44i q^{56} +2315.86 q^{57} -868.471i q^{58} +(-3480.35 + 67.4691i) q^{59} +5.89110 q^{60} -1563.16i q^{61} -3655.49 q^{62} -2407.29 q^{63} -512.000 q^{64} +2.45006i q^{65} -2253.77 q^{66} -6675.03i q^{67} -2543.88 q^{68} -1450.31i q^{69} +35.7383i q^{70} +2263.33 q^{71} +610.940i q^{72} +407.793i q^{73} +5286.92 q^{74} +3247.49 q^{75} +3565.50 q^{76} -13672.5i q^{77} -254.085 q^{78} -1336.33 q^{79} +9.06994 q^{80} +729.000 q^{81} -2030.92i q^{82} -10010.1i q^{83} -3706.27 q^{84} +45.0642 q^{85} -6572.05 q^{86} -1595.48 q^{87} -3469.91 q^{88} -509.616i q^{89} -10.8226i q^{90} -1541.40i q^{91} -2232.90i q^{92} +6715.57i q^{93} -1873.97 q^{94} -63.1619 q^{95} +940.604i q^{96} -4566.49i q^{97} -15693.0i q^{98} +4140.44i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 320 q^{4} - 80 q^{7} + 1080 q^{9}+O(q^{10}) \) 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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