LMFDB - Embedded newform 175.5.c.d.174.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,5,Mod(174,175)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("175.174");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	175.c (of order $2$, degree $1$, not 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:	$18.0897435397$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			174.7
Character	$\chi$	$=$	175.174
Dual form			175.5.c.d.174.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.50299i q^{2} +5.52807 q^{3} -26.2889 q^{4} -35.9490i q^{6} +(44.7373 + 19.9894i) q^{7} +66.9085i q^{8} -50.4404 q^{9} +O(q^{10})$	\(q-6.50299i q^{2} +5.52807 q^{3} -26.2889 q^{4} -35.9490i q^{6} +(44.7373 + 19.9894i) q^{7} +66.9085i q^{8} -50.4404 q^{9} -105.424 q^{11} -145.327 q^{12} -234.089 q^{13} +(129.991 - 290.926i) q^{14} +14.4831 q^{16} -375.251 q^{17} +328.014i q^{18} -45.1673i q^{19} +(247.311 + 110.503i) q^{21} +685.571i q^{22} +46.3674i q^{23} +369.875i q^{24} +1522.28i q^{26} -726.612 q^{27} +(-1176.09 - 525.500i) q^{28} +257.421 q^{29} -194.899i q^{31} +976.352i q^{32} -582.791 q^{33} +2440.26i q^{34} +1326.02 q^{36} -2523.02i q^{37} -293.723 q^{38} -1294.06 q^{39} -2504.06i q^{41} +(718.600 - 1608.26i) q^{42} +2288.24i q^{43} +2771.48 q^{44} +301.527 q^{46} +2624.74 q^{47} +80.0637 q^{48} +(1601.84 + 1788.55i) q^{49} -2074.42 q^{51} +6153.94 q^{52} -358.663i q^{53} +4725.15i q^{54} +(-1337.46 + 2993.30i) q^{56} -249.688i q^{57} -1674.01i q^{58} -854.723i q^{59} -2085.25i q^{61} -1267.43 q^{62} +(-2256.57 - 1008.28i) q^{63} +6580.94 q^{64} +3789.89i q^{66} +7558.23i q^{67} +9864.94 q^{68} +256.322i q^{69} -282.660 q^{71} -3374.89i q^{72} -9190.85 q^{73} -16407.2 q^{74} +1187.40i q^{76} +(-4716.38 - 2107.37i) q^{77} +8415.27i q^{78} +7184.60 q^{79} +68.9152 q^{81} -16283.9 q^{82} +5064.74 q^{83} +(-6501.52 - 2905.00i) q^{84} +14880.4 q^{86} +1423.04 q^{87} -7053.76i q^{88} -10243.7i q^{89} +(-10472.5 - 4679.31i) q^{91} -1218.95i q^{92} -1077.42i q^{93} -17068.6i q^{94} +5397.34i q^{96} -608.860 q^{97} +(11630.9 - 10416.8i) q^{98} +5317.63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 244 q^{4} + 868 q^{9}+O(q^{10}) $ 24 * q - 244 * q^4 + 868 * q^9	$ 24 q - 244 q^{4} + 868 q^{9} + 252 q^{11} - 156 q^{14} + 1156 q^{16} - 1284 q^{21} + 4380 q^{29} - 7164 q^{36} - 17268 q^{39} + 22392 q^{44} + 15688 q^{46} + 17592 q^{49} + 14412 q^{51} - 13212 q^{56} - 40292 q^{64} - 11328 q^{71} - 35208 q^{74} + 3180 q^{79} - 23824 q^{81} + 86256 q^{84} + 35208 q^{86} - 14364 q^{91} - 46168 q^{99}+O(q^{100}) $ 24 * q - 244 * q^4 + 868 * q^9 + 252 * q^11 - 156 * q^14 + 1156 * q^16 - 1284 * q^21 + 4380 * q^29 - 7164 * q^36 - 17268 * q^39 + 22392 * q^44 + 15688 * q^46 + 17592 * q^49 + 14412 * q^51 - 13212 * q^56 - 40292 * q^64 - 11328 * q^71 - 35208 * q^74 + 3180 * q^79 - 23824 * q^81 + 86256 * q^84 + 35208 * q^86 - 14364 * q^91 - 46168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	6.50299i		−	1.62575i	−0.582440	−	0.812874i	$-0.697902\pi$
$2$		−	6.50299i		−	1.62575i	0.582440	−	0.812874i	$-0.302098\pi$
$3$	5.52807			0.614230			0.307115	−	0.951672i	$-0.400636\pi$
$3$	5.52807			0.614230			0.307115	+	0.951672i	$0.400636\pi$
$4$	−26.2889			−1.64305
$5$		0			0
$5$		0			0
$6$		−	35.9490i		−	0.998583i
$7$	44.7373	+	19.9894i	0.913005	+	0.407948i
$7$	44.7373	+	19.9894i	0.913005	+	0.407948i
$8$			66.9085i			1.04545i
$9$	−50.4404			−0.622722
$10$		0			0
$11$	−105.424			−0.871273			−0.435636	−	0.900123i	$-0.643477\pi$
$11$	−105.424			−0.871273			−0.435636	+	0.900123i	$0.643477\pi$
$12$	−145.327			−1.00921
$13$	−234.089			−1.38514			−0.692571	−	0.721349i	$-0.743522\pi$
$13$	−234.089			−1.38514			−0.692571	+	0.721349i	$0.743522\pi$
$14$	129.991	−	290.926i	0.663220	−	1.48432i
$15$		0			0
$16$	14.4831			0.0565747
$17$	−375.251			−1.29845			−0.649224	−	0.760597i	$-0.724906\pi$
$17$	−375.251			−1.29845			−0.649224	+	0.760597i	$0.724906\pi$
$18$			328.014i			1.01239i
$19$		−	45.1673i		−	0.125117i	−0.998041	−	0.0625586i	$-0.980074\pi$
$19$		−	45.1673i		−	0.125117i	0.998041	−	0.0625586i	$-0.0199260\pi$
$20$		0			0
$21$	247.311	+	110.503i	0.560795	+	0.250574i
$22$			685.571i			1.41647i
$23$			46.3674i			0.0876510i	0.999039	+	0.0438255i	$0.0139546\pi$
$23$			46.3674i			0.0876510i	−0.999039	+	0.0438255i	$0.986045\pi$
$24$			369.875i			0.642144i
$25$		0			0
$26$			1522.28i			2.25189i
$27$	−726.612			−0.996724
$28$	−1176.09	−	525.500i	−1.50012	−	0.670280i
$29$	257.421			0.306089			0.153045	−	0.988219i	$-0.451092\pi$
$29$	257.421			0.306089			0.153045	+	0.988219i	$0.451092\pi$
$30$		0			0
$31$		−	194.899i		−	0.202809i	−0.994845	−	0.101404i	$-0.967666\pi$
$31$		−	194.899i		−	0.202809i	0.994845	−	0.101404i	$-0.0323336\pi$
$32$			976.352i			0.953469i
$33$	−582.791			−0.535162
$34$			2440.26i			2.11095i
$35$		0			0
$36$	1326.02			1.02317
$37$		−	2523.02i		−	1.84296i	−0.388421	−	0.921482i	$-0.626979\pi$
$37$		−	2523.02i		−	1.84296i	0.388421	−	0.921482i	$-0.373021\pi$
$38$	−293.723			−0.203409
$39$	−1294.06			−0.850796
$40$		0			0
$41$		−	2504.06i		−	1.48963i	−0.667274	−	0.744813i	$-0.732539\pi$
$41$		−	2504.06i		−	1.48963i	0.667274	−	0.744813i	$-0.267461\pi$
$42$	718.600	−	1608.26i	0.407370	−	0.911711i
$43$			2288.24i			1.23756i	0.785565	+	0.618779i	$0.212372\pi$
$43$			2288.24i			1.23756i	−0.785565	+	0.618779i	$0.787628\pi$
$44$	2771.48			1.43155
$45$		0			0
$46$	301.527			0.142498
$47$	2624.74			1.18820			0.594101	−	0.804391i	$-0.297508\pi$
$47$	2624.74			1.18820			0.594101	+	0.804391i	$0.297508\pi$
$48$	80.0637			0.0347499
$49$	1601.84	+	1788.55i	0.667157	+	0.744917i
$50$		0			0
$51$	−2074.42			−0.797545
$52$	6153.94			2.27587
$53$		−	358.663i		−	0.127683i	−0.997960	−	0.0638417i	$-0.979665\pi$
$53$		−	358.663i		−	0.127683i	0.997960	−	0.0638417i	$-0.0203353\pi$
$54$			4725.15i			1.62042i
$55$		0			0
$56$	−1337.46	+	2993.30i	−0.426487	+	0.954497i
$57$		−	249.688i		−	0.0768508i
$58$		−	1674.01i		−	0.497624i
$59$		−	854.723i		−	0.245540i	−0.992435	−	0.122770i	$-0.960822\pi$
$59$		−	854.723i		−	0.245540i	0.992435	−	0.122770i	$-0.0391777\pi$
$60$		0			0
$61$		−	2085.25i		−	0.560400i	−0.959942	−	0.280200i	$-0.909599\pi$
$61$		−	2085.25i		−	0.560400i	0.959942	−	0.280200i	$-0.0904007\pi$
$62$	−1267.43			−0.329716
$63$	−2256.57	−	1008.28i	−0.568548	−	0.254038i
$64$	6580.94			1.60667
$65$		0			0
$66$			3789.89i			0.870038i
$67$			7558.23i			1.68372i	0.539693	+	0.841862i	$0.318540\pi$
$67$			7558.23i			1.68372i	−0.539693	+	0.841862i	$0.681460\pi$
$68$	9864.94			2.13342
$69$			256.322i			0.0538379i
$70$		0			0
$71$	−282.660			−0.0560722			−0.0280361	−	0.999607i	$-0.508925\pi$
$71$	−282.660			−0.0560722			−0.0280361	+	0.999607i	$0.508925\pi$
$72$		−	3374.89i		−	0.651021i
$73$	−9190.85			−1.72469			−0.862343	−	0.506325i	$-0.831004\pi$
$73$	−9190.85			−1.72469			−0.862343	+	0.506325i	$0.831004\pi$
$74$	−16407.2			−2.99619
$75$		0			0
$76$			1187.40i			0.205575i
$77$	−4716.38	−	2107.37i	−0.795477	−	0.355434i
$78$			8415.27i			1.38318i
$79$	7184.60			1.15119			0.575597	−	0.817734i	$-0.304770\pi$
$79$	7184.60			1.15119			0.575597	+	0.817734i	$0.304770\pi$
$80$		0			0
$81$	68.9152			0.0105038
$82$	−16283.9			−2.42175
$83$	5064.74			0.735192			0.367596	−	0.929986i	$-0.380181\pi$
$83$	5064.74			0.735192			0.367596	+	0.929986i	$0.380181\pi$
$84$	−6501.52	−	2905.00i	−0.921417	−	0.411706i
$85$		0			0
$86$	14880.4			2.01196
$87$	1423.04			0.188009
$88$		−	7053.76i		−	0.910868i
$89$		−	10243.7i		−	1.29323i	−0.762817	−	0.646614i	$-0.776184\pi$
$89$		−	10243.7i		−	1.29323i	0.762817	−	0.646614i	$-0.223816\pi$
$90$		0			0
$91$	−10472.5	−	4679.31i	−1.26464	−	0.565066i
$92$		−	1218.95i		−	0.144015i
$93$		−	1077.42i		−	0.124571i
$94$		−	17068.6i		−	1.93172i
$95$		0			0
$96$			5397.34i			0.585649i
$97$	−608.860			−0.0647104			−0.0323552	−	0.999476i	$-0.510301\pi$
$97$	−608.860			−0.0647104			−0.0323552	+	0.999476i	$0.510301\pi$
$98$	11630.9	−	10416.8i	1.21105	−	1.08463i
$99$	5317.63			0.542560
$100$		0			0
$101$		−	14966.3i		−	1.46714i	−0.679616	−	0.733568i	$-0.737854\pi$
$101$		−	14966.3i		−	1.46714i	0.679616	−	0.733568i	$-0.262146\pi$
$102$			13489.9i			1.29661i
$103$	−18840.1			−1.77586			−0.887930	−	0.459979i	$-0.847857\pi$
$103$	−18840.1			−1.77586			−0.887930	+	0.459979i	$0.847857\pi$
$104$		−	15662.5i		−	1.44809i
$105$		0			0
$106$	−2332.38			−0.207581
$107$		−	3903.78i		−	0.340971i	−0.985360	−	0.170485i	$-0.945466\pi$
$107$		−	3903.78i		−	0.340971i	0.985360	−	0.170485i	$-0.0545336\pi$
$108$	19101.8			1.63767
$109$	−16429.7			−1.38285			−0.691427	−	0.722447i	$-0.743018\pi$
$109$	−16429.7			−1.38285			−0.691427	+	0.722447i	$0.743018\pi$
$110$		0			0
$111$		−	13947.4i		−	1.13200i
$112$	647.935	+	289.510i	0.0516530	+	0.0230795i
$113$			19430.8i			1.52172i	0.648918	+	0.760858i	$0.275222\pi$
$113$			19430.8i			1.52172i	−0.648918	+	0.760858i	$0.724778\pi$
$114$	−1623.72			−0.124940
$115$		0			0
$116$	−6767.31			−0.502922
$117$	11807.6			0.862558
$118$	−5558.26			−0.399185
$119$	−16787.7	−	7501.06i	−1.18549	−	0.529699i
$120$		0			0
$121$	−3526.78			−0.240884
$122$	−13560.3			−0.911068
$123$		−	13842.6i		−	0.914972i
$124$			5123.68i			0.333226i
$125$		0			0
$126$	−6556.81	+	14674.4i	−0.413001	+	0.924316i
$127$			3473.63i			0.215365i	0.994185	+	0.107683i	$0.0343431\pi$
$127$			3473.63i			0.215365i	−0.994185	+	0.107683i	$0.965657\pi$
$128$		−	27174.1i		−	1.65858i
$129$			12649.6i			0.760145i
$130$		0			0
$131$			5214.48i			0.303856i	0.988392	+	0.151928i	$0.0485482\pi$
$131$			5214.48i			0.303856i	−0.988392	+	0.151928i	$0.951452\pi$
$132$	15320.9			0.879300
$133$	902.870	−	2020.66i	0.0510413	−	0.114233i
$134$	49151.1			2.73731
$135$		0			0
$136$		−	25107.5i		−	1.35746i
$137$		−	25017.6i		−	1.33292i	−0.745540	−	0.666461i	$-0.767808\pi$
$137$		−	25017.6i		−	1.33292i	0.745540	−	0.666461i	$-0.232192\pi$
$138$	1666.86			0.0875268
$139$			9723.25i			0.503248i	0.967825	+	0.251624i	$0.0809646\pi$
$139$			9723.25i			0.503248i	−0.967825	+	0.251624i	$0.919035\pi$
$140$		0			0
$141$	14509.7			0.729829
$142$			1838.14i			0.0911593i
$143$	24678.6			1.20684
$144$	−730.535			−0.0352303
$145$		0			0
$146$			59768.0i			2.80390i
$147$	8855.11	+	9887.20i	0.409788	+	0.457550i
$148$			66327.3i			3.02809i
$149$	−4969.64			−0.223847			−0.111924	−	0.993717i	$-0.535701\pi$
$149$	−4969.64			−0.223847			−0.111924	+	0.993717i	$0.535701\pi$
$150$		0			0
$151$	−15572.0			−0.682954			−0.341477	−	0.939890i	$-0.610927\pi$
$151$	−15572.0			−0.682954			−0.341477	+	0.939890i	$0.610927\pi$
$152$	3022.08			0.130803
$153$	18927.8			0.808571
$154$	−13704.2	+	30670.6i	−0.577845	+	1.29324i
$155$		0			0
$156$	34019.4			1.39790
$157$	−2245.97			−0.0911180			−0.0455590	−	0.998962i	$-0.514507\pi$
$157$	−2245.97			−0.0911180			−0.0455590	+	0.998962i	$0.514507\pi$
$158$		−	46721.4i		−	1.87155i
$159$		−	1982.71i		−	0.0784270i
$160$		0			0
$161$	−926.858	+	2074.35i	−0.0357570	+	0.0800259i
$162$		−	448.155i		−	0.0170765i
$163$			27048.4i			1.01804i	0.860754	+	0.509021i	$0.169993\pi$
$163$			27048.4i			1.01804i	−0.860754	+	0.509021i	$0.830007\pi$
$164$			65828.9i			2.44754i
$165$		0			0
$166$		−	32936.0i		−	1.19524i
$167$	36693.5			1.31570			0.657849	−	0.753149i	$-0.271466\pi$
$167$	36693.5			1.31570			0.657849	+	0.753149i	$0.271466\pi$
$168$	−7393.59	+	16547.2i	−0.261961	+	0.586281i
$169$	26236.7			0.918620
$170$		0			0
$171$			2278.26i			0.0779132i
$172$		−	60155.4i		−	2.03338i
$173$	−3132.59			−0.104667			−0.0523337	−	0.998630i	$-0.516666\pi$
$173$	−3132.59			−0.104667			−0.0523337	+	0.998630i	$0.516666\pi$
$174$		−	9254.03i		−	0.305656i
$175$		0			0
$176$	−1526.87			−0.0492920
$177$		−	4724.97i		−	0.150818i
$178$	−66614.4			−2.10246
$179$	25816.5			0.805732			0.402866	−	0.915259i	$-0.368014\pi$
$179$	25816.5			0.805732			0.402866	+	0.915259i	$0.368014\pi$
$180$		0			0
$181$		−	31614.4i		−	0.965002i	−0.875895	−	0.482501i	$-0.839728\pi$
$181$		−	31614.4i		−	0.965002i	0.875895	−	0.482501i	$-0.160272\pi$
$182$	−30429.5	+	68102.6i	−0.918654	+	2.05599i
$183$		−	11527.4i		−	0.344214i
$184$	−3102.37			−0.0916343
$185$		0			0
$186$	−7006.43			−0.202521
$187$	39560.5			1.13130
$188$	−69001.4			−1.95228
$189$	−32506.6	−	14524.6i	−0.910014	−	0.406611i
$190$		0			0
$191$	−4727.49			−0.129588			−0.0647938	−	0.997899i	$-0.520639\pi$
$191$	−4727.49			−0.129588			−0.0647938	+	0.997899i	$0.520639\pi$
$192$	36379.9			0.986867
$193$		−	36953.1i		−	0.992057i	−0.868306	−	0.496028i	$-0.834791\pi$
$193$		−	36953.1i		−	0.992057i	0.868306	−	0.496028i	$-0.165209\pi$
$194$			3959.41i			0.105203i
$195$		0			0
$196$	−42110.7	−	47018.8i	−1.09618	−	1.22394i
$197$			3222.40i			0.0830322i	0.999138	+	0.0415161i	$0.0132188\pi$
$197$			3222.40i			0.0830322i	−0.999138	+	0.0415161i	$0.986781\pi$
$198$		−	34580.5i		−	0.882066i
$199$		−	51984.5i		−	1.31271i	−0.754453	−	0.656354i	$-0.772098\pi$
$199$		−	51984.5i		−	1.31271i	0.754453	−	0.656354i	$-0.227902\pi$
$200$		0			0
$201$			41782.4i			1.03419i
$202$	−97325.4			−2.38519
$203$	11516.3	+	5145.70i	0.279461	+	0.124868i
$204$	54534.1			1.31041
$205$		0			0
$206$			122517.i			2.88710i
$207$		−	2338.79i		−	0.0545822i
$208$	−3390.34			−0.0783641
$209$			4761.72i			0.109011i
$210$		0			0
$211$	−15750.2			−0.353770			−0.176885	−	0.984232i	$-0.556602\pi$
$211$	−15750.2			−0.353770			−0.176885	+	0.984232i	$0.556602\pi$
$212$			9428.84i			0.209791i
$213$	−1562.56			−0.0344412
$214$	−25386.2			−0.554333
$215$		0			0
$216$		−	48616.5i		−	1.04202i
$217$	3895.93	−	8719.26i	0.0827354	−	0.185165i
$218$			106842.i			2.24817i
$219$	−50807.7			−1.05935
$220$		0			0
$221$	87842.3			1.79854
$222$	−90699.9			−1.84035
$223$	−11942.3			−0.240148			−0.120074	−	0.992765i	$-0.538313\pi$
$223$	−11942.3			−0.240148			−0.120074	+	0.992765i	$0.538313\pi$
$224$	−19516.7	+	43679.3i	−0.388965	+	0.870522i
$225$		0			0
$226$	126358.			2.47393
$227$	−79946.4			−1.55148			−0.775742	−	0.631051i	$-0.782624\pi$
$227$	−79946.4			−1.55148			−0.775742	+	0.631051i	$0.782624\pi$
$228$			6564.02i			0.126270i
$229$			40487.1i			0.772050i	0.922488	+	0.386025i	$0.126152\pi$
$229$			40487.1i			0.772050i	−0.922488	+	0.386025i	$0.873848\pi$
$230$		0			0
$231$	−26072.5	−	11649.7i	−0.488606	−	0.218318i
$232$			17223.7i			0.320000i
$233$		−	40236.2i		−	0.741148i	−0.928803	−	0.370574i	$-0.879161\pi$
$233$		−	40236.2i		−	0.741148i	0.928803	−	0.370574i	$-0.120839\pi$
$234$		−	76784.4i		−	1.40230i
$235$		0			0
$236$			22469.7i			0.403435i
$237$	39717.0			0.707097
$238$	−48779.3	+	109170.i	−0.861156	+	1.92731i
$239$	12346.0			0.216137			0.108069	−	0.994143i	$-0.465533\pi$
$239$	12346.0			0.216137			0.108069	+	0.994143i	$0.465533\pi$
$240$		0			0
$241$		−	20969.2i		−	0.361034i	−0.983572	−	0.180517i	$-0.942223\pi$
$241$		−	20969.2i		−	0.361034i	0.983572	−	0.180517i	$-0.0577771\pi$
$242$			22934.6i			0.391616i
$243$	59236.5			1.00318
$244$			54818.8i			0.920767i
$245$		0			0
$246$	−90018.4			−1.48751
$247$			10573.2i			0.173305i
$248$	13040.4			0.212025
$249$	27998.2			0.451577
$250$		0			0
$251$			82331.2i			1.30682i	0.757003	+	0.653411i	$0.226663\pi$
$251$			82331.2i			1.30682i	−0.757003	+	0.653411i	$0.773337\pi$
$252$	59322.6	+	26506.4i	0.934156	+	0.417398i
$253$		−	4888.24i		−	0.0763680i
$254$	22589.0			0.350130
$255$		0			0
$256$	−71418.2			−1.08975
$257$	6751.23			0.102216			0.0511078	−	0.998693i	$-0.483725\pi$
$257$	6751.23			0.102216			0.0511078	+	0.998693i	$0.483725\pi$
$258$	82260.0			1.23580
$259$	50433.7	−	112873.i	0.751833	−	1.68264i
$260$		0			0
$261$	−12984.4			−0.190608
$262$	33909.7			0.493994
$263$			23786.1i			0.343884i	0.985107	+	0.171942i	$0.0550042\pi$
$263$			23786.1i			0.343884i	−0.985107	+	0.171942i	$0.944996\pi$
$264$		−	38993.7i		−	0.559482i
$265$		0			0
$266$	−13140.4	−	5871.35i	−0.185714	−	0.0829803i
$267$		−	56627.7i		−	0.794340i
$268$		−	198697.i		−	2.76645i
$269$			74052.1i			1.02337i	0.859173	+	0.511685i	$0.170979\pi$
$269$			74052.1i			1.02337i	−0.859173	+	0.511685i	$0.829021\pi$
$270$		0			0
$271$		−	61472.9i		−	0.837037i	−0.908208	−	0.418519i	$-0.862549\pi$
$271$		−	61472.9i		−	0.837037i	0.908208	−	0.418519i	$-0.137451\pi$
$272$	−5434.81			−0.0734593
$273$	−57892.7	−	25867.5i	−0.776781	−	0.347080i
$274$	−162689.			−2.16699
$275$		0			0
$276$		−	6738.42i		−	0.0884586i
$277$			73318.6i			0.955552i	0.878482	+	0.477776i	$0.158557\pi$
$277$			73318.6i			0.955552i	−0.878482	+	0.477776i	$0.841443\pi$
$278$	63230.2			0.818154
$279$			9830.80i			0.126293i
$280$		0			0
$281$	−63569.9			−0.805080			−0.402540	−	0.915403i	$-0.631872\pi$
$281$	−63569.9			−0.805080			−0.402540	+	0.915403i	$0.631872\pi$
$282$		−	94356.6i		−	1.18652i
$283$	99674.3			1.24454			0.622272	−	0.782801i	$-0.286210\pi$
$283$	99674.3			1.24454			0.622272	+	0.782801i	$0.286210\pi$
$284$	7430.82			0.0921298
$285$		0			0
$286$		−	160485.i		−	1.96201i
$287$	50054.7	−	112025.i	0.607689	−	1.36004i
$288$		−	49247.6i		−	0.593746i
$289$	57292.6			0.685967
$290$		0			0
$291$	−3365.82			−0.0397471
$292$	241617.			2.83375
$293$	33390.9			0.388949			0.194475	−	0.980908i	$-0.437700\pi$
$293$	33390.9			0.388949			0.194475	+	0.980908i	$0.437700\pi$
$294$	64296.4	−	57584.7i	0.743861	−	0.666212i
$295$		0			0
$296$	168811.			1.92672
$297$	76602.3			0.868419
$298$			32317.5i			0.363919i
$299$		−	10854.1i		−	0.121409i
$300$		0			0
$301$	−45740.7	+	102370.i	−0.504859	+	1.12990i
$302$			101265.i			1.11031i
$303$		−	82734.5i		−	0.901159i
$304$		−	654.164i		−	0.00707847i
$305$		0			0
$306$		−	123088.i		−	1.31453i
$307$	−81081.7			−0.860292			−0.430146	−	0.902759i	$-0.641538\pi$
$307$	−81081.7			−0.860292			−0.430146	+	0.902759i	$0.641538\pi$
$308$	123988.	+	55400.3i	1.30701	+	0.583997i
$309$	−104149.			−1.09079
$310$		0			0
$311$		−	58811.2i		−	0.608050i	−0.952664	−	0.304025i	$-0.901669\pi$
$311$		−	58811.2i		−	0.608050i	0.952664	−	0.304025i	$-0.0983306\pi$
$312$		−	86583.7i		−	0.889461i
$313$	−146677.			−1.49718			−0.748590	−	0.663033i	$-0.769269\pi$
$313$	−146677.			−1.49718			−0.748590	+	0.663033i	$0.769269\pi$
$314$			14605.5i			0.148135i
$315$		0			0
$316$	−188875.			−1.89147
$317$		−	106159.i		−	1.05642i	−0.849114	−	0.528210i	$-0.822863\pi$
$317$		−	106159.i		−	1.05642i	0.849114	−	0.528210i	$-0.177137\pi$
$318$	−12893.6			−0.127502
$319$	−27138.4			−0.266687
$320$		0			0
$321$		−	21580.3i		−	0.209435i
$322$	13489.5	+	6027.35i	0.130102	+	0.0581319i
$323$			16949.1i			0.162458i
$324$	−1811.70			−0.0172583
$325$		0			0
$326$	175895.			1.65508
$327$	−90824.4			−0.849390
$328$	167543.			1.55732
$329$	117424.	+	52467.0i	1.08483	+	0.484724i
$330$		0			0
$331$	−24297.3			−0.221769			−0.110885	−	0.993833i	$-0.535368\pi$
$331$	−24297.3			−0.221769			−0.110885	+	0.993833i	$0.535368\pi$
$332$	−133146.			−1.20796
$333$			127262.i			1.14765i
$334$		−	238618.i		−	2.13899i
$335$		0			0
$336$	3581.83	+	1600.43i	0.0317268	+	0.0141761i
$337$			170981.i			1.50553i	0.658292	+	0.752763i	$0.271279\pi$
$337$			170981.i			1.50553i	−0.658292	+	0.752763i	$0.728721\pi$
$338$		−	170617.i		−	1.49344i
$339$			107415.i			0.934684i
$340$		0			0
$341$			20547.1i			0.176702i
$342$	14815.5			0.126667
$343$	35910.1	+	112035.i	0.305231	+	0.952278i
$344$	−153103.			−1.29380
$345$		0			0
$346$			20371.2i			0.170163i
$347$			202470.i			1.68152i	0.541406	+	0.840761i	$0.317892\pi$
$347$			202470.i			1.68152i	−0.541406	+	0.840761i	$0.682108\pi$
$348$	−37410.2			−0.308910
$349$		−	90133.9i		−	0.740009i	−0.929030	−	0.370005i	$-0.879356\pi$
$349$		−	90133.9i		−	0.740009i	0.929030	−	0.370005i	$-0.120644\pi$
$350$		0			0
$351$	170092.			1.38061
$352$		−	102931.i		−	0.830732i
$353$	−118178.			−0.948388			−0.474194	−	0.880420i	$-0.657261\pi$
$353$	−118178.			−0.948388			−0.474194	+	0.880420i	$0.657261\pi$
$354$	−30726.4			−0.245192
$355$		0			0
$356$			269294.i			2.12485i
$357$	−92803.7	−	41466.4i	−0.728163	−	0.325357i
$358$		−	167884.i		−	1.30992i
$359$	−194552.			−1.50955			−0.754774	−	0.655985i	$-0.772253\pi$
$359$	−194552.			−1.50955			−0.754774	+	0.655985i	$0.772253\pi$
$360$		0			0
$361$	128281.			0.984346
$362$	−205588.			−1.56885
$363$	−19496.3			−0.147958
$364$	275310.	+	123014.i	2.07788	+	0.928434i
$365$		0			0
$366$	−74962.5			−0.559605
$367$	−105692.			−0.784710			−0.392355	−	0.919814i	$-0.628339\pi$
$367$	−105692.			−0.784710			−0.392355	+	0.919814i	$0.628339\pi$
$368$			671.545i			0.00495883i
$369$			126306.i			0.927622i
$370$		0			0
$371$	7169.46	−	16045.6i	0.0520881	−	0.116576i
$372$			28324.1i			0.204677i
$373$			66392.5i			0.477201i	0.971118	+	0.238600i	$0.0766886\pi$
$373$			66392.5i			0.477201i	−0.971118	+	0.238600i	$0.923311\pi$
$374$		−	257262.i		−	1.83921i
$375$		0			0
$376$			175617.i			1.24220i
$377$	−60259.5			−0.423978
$378$	−94453.1	+	211390.i	−0.661047	+	1.47945i
$379$	−175353.			−1.22077			−0.610387	−	0.792103i	$-0.708986\pi$
$379$	−175353.			−1.22077			−0.610387	+	0.792103i	$0.708986\pi$
$380$		0			0
$381$			19202.5i			0.132284i
$382$			30742.8i			0.210677i
$383$	−4098.21			−0.0279381			−0.0139690	−	0.999902i	$-0.504447\pi$
$383$	−4098.21			−0.0279381			−0.0139690	+	0.999902i	$0.504447\pi$
$384$		−	150221.i		−	1.01875i
$385$		0			0
$386$	−240306.			−1.61283
$387$		−	115420.i		−	0.770654i
$388$	16006.2			0.106323
$389$	207427.			1.37077			0.685387	−	0.728179i	$-0.259633\pi$
$389$	207427.			1.37077			0.685387	+	0.728179i	$0.259633\pi$
$390$		0			0
$391$		−	17399.4i		−	0.113810i
$392$	−119669.	+	107177.i	−0.778770	+	0.697476i
$393$			28826.0i			0.186638i
$394$	20955.2			0.134989
$395$		0			0
$396$	−139795.			−0.891457
$397$	−115680.			−0.733968			−0.366984	−	0.930227i	$-0.619610\pi$
$397$	−115680.			−0.733968			−0.366984	+	0.930227i	$0.619610\pi$
$398$	−338055.			−2.13413
$399$	4991.13	−	11170.4i	0.0313511	−	0.0701652i
$400$		0			0
$401$	−198641.			−1.23532			−0.617661	−	0.786444i	$-0.711920\pi$
$401$	−198641.			−1.23532			−0.617661	+	0.786444i	$0.711920\pi$
$402$	271711.			1.68134
$403$			45623.8i			0.280919i
$404$			393446.i			2.41059i
$405$		0			0
$406$	33462.5	−	74890.5i	0.203005	−	0.454333i
$407$			265987.i			1.60572i
$408$		−	138796.i		−	0.833790i
$409$		−	39642.8i		−	0.236983i	−0.992955	−	0.118492i	$-0.962194\pi$
$409$		−	39642.8i		−	0.236983i	0.992955	−	0.118492i	$-0.0378059\pi$
$410$		0			0
$411$		−	138299.i		−	0.818720i
$412$	495285.			2.91783
$413$	17085.4	−	38238.0i	0.100167	−	0.224179i
$414$	−15209.1			−0.0887369
$415$		0			0
$416$		−	228553.i		−	1.32069i
$417$			53750.8i			0.309110i
$418$	30965.4			0.177225
$419$		−	157716.i		−	0.898354i	−0.893443	−	0.449177i	$-0.851717\pi$
$419$		−	157716.i		−	0.898354i	0.893443	−	0.449177i	$-0.148283\pi$
$420$		0			0
$421$	9811.94			0.0553593			0.0276797	−	0.999617i	$-0.491188\pi$
$421$	9811.94			0.0553593			0.0276797	+	0.999617i	$0.491188\pi$
$422$			102423.i			0.575141i
$423$	−132393.			−0.739919
$424$	23997.6			0.133486
$425$		0			0
$426$			10161.3i			0.0559928i
$427$	41682.9	−	93288.2i	0.228614	−	0.511648i
$428$			102626.i			0.560234i
$429$	136425.			0.741276
$430$		0			0
$431$	223189.			1.20149			0.600743	−	0.799442i	$-0.294872\pi$
$431$	223189.			1.20149			0.600743	+	0.799442i	$0.294872\pi$
$432$	−10523.6			−0.0563894
$433$	−112634.			−0.600748			−0.300374	−	0.953821i	$-0.597112\pi$
$433$	−112634.			−0.600748			−0.300374	+	0.953821i	$0.597112\pi$
$434$	−56701.2	−	25335.2i	−0.301032	−	0.134507i
$435$		0			0
$436$	431918.			2.27210
$437$	2094.29			0.0109667
$438$			330402.i			1.72224i
$439$			73105.8i			0.379335i	0.981848	+	0.189667i	$0.0607410\pi$
$439$			73105.8i			0.379335i	−0.981848	+	0.189667i	$0.939259\pi$
$440$		0			0
$441$	−80797.8	−	90215.0i	−0.415453	−	0.463876i
$442$		−	571237.i		−	2.92396i
$443$			50089.8i			0.255236i	0.991823	+	0.127618i	$0.0407331\pi$
$443$			50089.8i			0.255236i	−0.991823	+	0.127618i	$0.959267\pi$
$444$			366662.i			1.85994i
$445$		0			0
$446$			77660.9i			0.390421i
$447$	−27472.5			−0.137494
$448$	294413.	+	131549.i	1.46690	+	0.655439i
$449$	5042.02			0.0250099			0.0125049	−	0.999922i	$-0.496019\pi$
$449$	5042.02			0.0250099			0.0125049	+	0.999922i	$0.496019\pi$
$450$		0			0
$451$			263988.i			1.29787i
$452$		−	510814.i		−	2.50026i
$453$	−86083.3			−0.419491
$454$			519891.i			2.52232i
$455$		0			0
$456$	16706.3			0.0803433
$457$			38281.4i			0.183297i	0.995791	+	0.0916486i	$0.0292136\pi$
$457$			38281.4i			0.183297i	−0.995791	+	0.0916486i	$0.970786\pi$
$458$	263287.			1.25516
$459$	272662.			1.29419
$460$		0			0
$461$		−	37749.3i		−	0.177626i	−0.996048	−	0.0888132i	$-0.971693\pi$
$461$		−	37749.3i		−	0.177626i	0.996048	−	0.0888132i	$-0.0283074\pi$
$462$	−75757.7	+	169549.i	−0.354930	+	0.794349i
$463$		−	343927.i		−	1.60437i	−0.597075	−	0.802185i	$-0.703671\pi$
$463$		−	343927.i		−	1.60437i	0.597075	−	0.802185i	$-0.296329\pi$
$464$	3728.26			0.0173169
$465$		0			0
$466$	−261656.			−1.20492
$467$	96841.6			0.444046			0.222023	−	0.975041i	$-0.428734\pi$
$467$	96841.6			0.444046			0.222023	+	0.975041i	$0.428734\pi$
$468$	−310408.			−1.41723
$469$	−151085.	+	338135.i	−0.686871	+	1.53725i
$470$		0			0
$471$	−12415.9			−0.0559674
$472$	57188.2			0.256698
$473$		−	241236.i		−	1.07825i
$474$		−	258279.i		−	1.14956i
$475$		0			0
$476$	441330.	+	197195.i	1.94782	+	0.870324i
$477$			18091.1i			0.0795112i
$478$		−	80285.7i		−	0.351384i
$479$			41421.1i			0.180530i	0.995918	+	0.0902652i	$0.0287715\pi$
$479$			41421.1i			0.180530i	−0.995918	+	0.0902652i	$0.971229\pi$
$480$		0			0
$481$			590611.i			2.55277i
$482$	−136363.			−0.586951
$483$	−5123.74	+	11467.2i	−0.0219630	+	0.0491543i
$484$	92715.0			0.395785
$485$		0			0
$486$		−	385215.i		−	1.63091i
$487$			29470.2i			0.124258i	0.998068	+	0.0621290i	$0.0197890\pi$
$487$			29470.2i			0.124258i	−0.998068	+	0.0621290i	$0.980211\pi$
$488$	139521.			0.585867
$489$			149525.i			0.625312i
$490$		0			0
$491$	−198756.			−0.824437			−0.412218	−	0.911085i	$-0.635246\pi$
$491$	−198756.			−0.824437			−0.412218	+	0.911085i	$0.635246\pi$
$492$			363907.i			1.50335i
$493$	−96597.7			−0.397441
$494$	68757.3			0.281751
$495$		0			0
$496$		−	2822.75i		−	0.0114738i
$497$	−12645.4	−	5650.22i	−0.0511942	−	0.0228745i
$498$		−	182072.i		−	0.734150i
$499$	−62009.6			−0.249034			−0.124517	−	0.992218i	$-0.539738\pi$
$499$	−62009.6			−0.249034			−0.124517	+	0.992218i	$0.539738\pi$
$500$		0			0
$501$	202844.			0.808142
$502$	535399.			2.12456
$503$	335191.			1.32482			0.662409	−	0.749143i	$-0.269534\pi$
$503$	335191.			1.32482			0.662409	+	0.749143i	$0.269534\pi$
$504$	67462.2	−	150984.i	0.265583	−	0.594386i
$505$		0			0
$506$	−31788.2			−0.124155
$507$	145038.			0.564244
$508$		−	91317.8i		−	0.353857i
$509$		−	27607.7i		−	0.106560i	−0.998580	−	0.0532800i	$-0.983032\pi$
$509$		−	27607.7i		−	0.106560i	0.998580	−	0.0532800i	$-0.0169676\pi$
$510$		0			0
$511$	−411173.	−	183720.i	−1.57465	−	0.703581i
$512$			29645.3i			0.113088i
$513$			32819.1i			0.124707i
$514$		−	43903.2i		−	0.166177i
$515$		0			0
$516$		−	332543.i		−	1.24896i
$517$	−276710.			−1.03525
$518$	−734011.	−	327970.i	−2.73554	−	1.22229i
$519$	−17317.2			−0.0642899
$520$		0			0
$521$			73225.7i			0.269767i	0.990861	+	0.134883i	$0.0430660\pi$
$521$			73225.7i			0.269767i	−0.990861	+	0.134883i	$0.956934\pi$
$522$			84437.7i			0.309881i
$523$	208338.			0.761668			0.380834	−	0.924643i	$-0.375637\pi$
$523$	208338.			0.761668			0.380834	+	0.924643i	$0.375637\pi$
$524$		−	137083.i		−	0.499253i
$525$		0			0
$526$	154681.			0.559069
$527$			73136.2i			0.263337i
$528$	−8440.64			−0.0302766
$529$	277691.			0.992317
$530$		0			0
$531$			43112.6i			0.152903i
$532$	−23735.4	+	53121.0i	−0.0838637	+	0.187691i
$533$			586173.i			2.06334i
$534$	−368249.			−1.29140
$535$		0			0
$536$	−505710.			−1.76024
$537$	142715.			0.494905
$538$	481560.			1.66374
$539$	−168873.	−	188556.i	−0.581276	−	0.649026i
$540$		0			0
$541$	71741.5			0.245118			0.122559	−	0.992461i	$-0.460890\pi$
$541$	71741.5			0.245118			0.122559	+	0.992461i	$0.460890\pi$
$542$	−399757.			−1.36081
$543$		−	174767.i		−	0.592733i
$544$		−	366377.i		−	1.23803i
$545$		0			0
$546$	−168216.	+	376476.i	−0.564265	+	1.26285i
$547$		−	184265.i		−	0.615839i	−0.951412	−	0.307919i	$-0.900367\pi$
$547$		−	184265.i		−	0.615839i	0.951412	−	0.307919i	$-0.0996327\pi$
$548$			657685.i			2.19006i
$549$			105181.i			0.348973i
$550$		0			0
$551$		−	11627.0i		−	0.0382971i
$552$	−17150.1			−0.0562846
$553$	321419.	+	143616.i	1.05105	+	0.469627i
$554$	476790.			1.55349
$555$		0			0
$556$		−	255613.i		−	0.826864i
$557$		−	386198.i		−	1.24480i	−0.782700	−	0.622399i	$-0.786158\pi$
$557$		−	386198.i		−	1.24480i	0.782700	−	0.622399i	$-0.213842\pi$
$558$	63929.6			0.205321
$559$		−	535653.i		−	1.71419i
$560$		0			0
$561$	218693.			0.694880
$562$			413394.i			1.30886i
$563$	352409.			1.11181			0.555904	−	0.831246i	$-0.312372\pi$
$563$	352409.			1.11181			0.555904	+	0.831246i	$0.312372\pi$
$564$	−381445.			−1.19915
$565$		0			0
$566$		−	648181.i		−	2.02332i
$567$	3083.08	+	1377.58i	0.00958999	+	0.00428498i
$568$		−	18912.4i		−	0.0586204i
$569$	−265786.			−0.820932			−0.410466	−	0.911876i	$-0.634634\pi$
$569$	−265786.			−0.820932			−0.410466	+	0.911876i	$0.634634\pi$
$570$		0			0
$571$	455939.			1.39841			0.699205	−	0.714921i	$-0.253537\pi$
$571$	455939.			1.39841			0.699205	+	0.714921i	$0.253537\pi$
$572$	−648773.			−1.98290
$573$	−26133.9			−0.0795966
$574$	−728496.	−	325505.i	−2.21107	−	0.987949i
$575$		0			0
$576$	−331945.			−1.00051
$577$	211395.			0.634956			0.317478	−	0.948266i	$-0.397164\pi$
$577$	211395.			0.634956			0.317478	+	0.948266i	$0.397164\pi$
$578$		−	372573.i		−	1.11521i
$579$		−	204279.i		−	0.609351i
$580$		0			0
$581$	226583.	+	101241.i	0.671234	+	0.299920i
$582$			21887.9i			0.0646187i
$583$			37811.7i			0.111247i
$584$		−	614946.i		−	1.80306i
$585$		0			0
$586$		−	217141.i		−	0.632333i
$587$	−158002.			−0.458550			−0.229275	−	0.973362i	$-0.573635\pi$
$587$	−158002.			−0.458550			−0.229275	+	0.973362i	$0.573635\pi$
$588$	−232791.	−	259923.i	−0.673304	−	0.751780i
$589$	−8803.08			−0.0253749
$590$		0			0
$591$			17813.6i			0.0510009i
$592$		−	36541.2i		−	0.104265i
$593$	−239670.			−0.681561			−0.340780	−	0.940143i	$-0.610691\pi$
$593$	−239670.			−0.681561			−0.340780	+	0.940143i	$0.610691\pi$
$594$		−	498144.i		−	1.41183i
$595$		0			0
$596$	130646.			0.367794
$597$		−	287374.i		−	0.806304i
$598$	−70584.1			−0.197381
$599$	−183572.			−0.511626			−0.255813	−	0.966726i	$-0.582343\pi$
$599$	−183572.			−0.511626			−0.255813	+	0.966726i	$0.582343\pi$
$600$		0			0
$601$		−	14783.5i		−	0.0409287i	−0.999791	−	0.0204643i	$-0.993486\pi$
$601$		−	14783.5i		−	0.0409287i	0.999791	−	0.0204643i	$-0.00651446\pi$
$602$	665710.	+	297451.i	1.83693	+	0.820773i
$603$		−	381241.i		−	1.04849i
$604$	409371.			1.12213
$605$		0			0
$606$	−538022.			−1.46506
$607$	−591265.			−1.60474			−0.802370	−	0.596827i	$-0.796428\pi$
$607$	−591265.			−1.60474			−0.802370	+	0.596827i	$0.796428\pi$
$608$	44099.2			0.119295
$609$	63663.0	+	28445.8i	0.171653	+	0.0766979i
$610$		0			0
$611$	−614422.			−1.64583
$612$	−497592.			−1.32853
$613$		−	90639.8i		−	0.241212i	−0.992700	−	0.120606i	$-0.961516\pi$
$613$		−	90639.8i		−	0.241212i	0.992700	−	0.120606i	$-0.0384837\pi$
$614$			527273.i			1.39862i
$615$		0			0
$616$	141001.	−	315566.i	0.371586	−	0.831627i
$617$			504471.i			1.32515i	0.748995	+	0.662576i	$0.230537\pi$
$617$			504471.i			1.32515i	−0.748995	+	0.662576i	$0.769463\pi$
$618$			677282.i			1.77334i
$619$		−	732305.i		−	1.91122i	−0.294634	−	0.955610i	$-0.595198\pi$
$619$		−	732305.i		−	1.91122i	0.294634	−	0.955610i	$-0.404802\pi$
$620$		0			0
$621$		−	33691.1i		−	0.0873639i
$622$	−382448.			−0.988535
$623$	204765.	−	458273.i	0.527569	−	1.18072i
$624$	−18742.1			−0.0481336
$625$		0			0
$626$			953841.i			2.43404i
$627$			26323.1i			0.0669580i
$628$	59044.0			0.149712
$629$			946766.i			2.39299i
$630$		0			0
$631$	537983.			1.35117			0.675585	−	0.737282i	$-0.263891\pi$
$631$	537983.			1.35117			0.675585	+	0.737282i	$0.263891\pi$
$632$			480711.i			1.20351i
$633$	−87068.1			−0.217296
$634$	−690348.			−1.71747
$635$		0			0
$636$			52123.3i			0.128860i
$637$	−374974.	−	418679.i	−0.924108	−	1.03182i
$638$			176481.i			0.433566i
$639$	14257.5			0.0349174
$640$		0			0
$641$	226234.			0.550608			0.275304	−	0.961357i	$-0.411221\pi$
$641$	226234.			0.550608			0.275304	+	0.961357i	$0.411221\pi$
$642$	−140337.			−0.340488
$643$	−186548.			−0.451199			−0.225599	−	0.974220i	$-0.572434\pi$
$643$	−186548.			−0.451199			−0.225599	+	0.974220i	$0.572434\pi$
$644$	24366.1	−	54532.3i	0.0587508	−	0.131487i
$645$		0			0
$646$	110220.			0.264116
$647$	580904.			1.38770			0.693850	−	0.720120i	$-0.255913\pi$
$647$	580904.			1.38770			0.693850	+	0.720120i	$0.255913\pi$
$648$			4611.01i			0.0109811i
$649$			90108.4i			0.213932i
$650$		0			0
$651$	21536.9	−	48200.7i	0.0508185	−	0.113734i
$652$		−	711072.i		−	1.67270i
$653$			242502.i			0.568707i	0.958720	+	0.284354i	$0.0917789\pi$
$653$			242502.i			0.568707i	−0.958720	+	0.284354i	$0.908221\pi$
$654$			590630.i			1.38089i
$655$		0			0
$656$		−	36266.6i		−	0.0842751i
$657$	463591.			1.07400
$658$	341192.	−	763604.i	0.788039	−	1.76367i
$659$	377939.			0.870265			0.435132	−	0.900367i	$-0.356702\pi$
$659$	377939.			0.870265			0.435132	+	0.900367i	$0.356702\pi$
$660$		0			0
$661$			377336.i			0.863625i	0.901963	+	0.431812i	$0.142126\pi$
$661$			377336.i			0.863625i	−0.901963	+	0.431812i	$0.857874\pi$
$662$			158005.i			0.360541i
$663$	485598.			1.10471
$664$			338874.i			0.768603i
$665$		0			0
$666$	827584.			1.86579
$667$			11936.0i			0.0268291i
$668$	−964632.			−2.16177
$669$	−66018.1			−0.147506
$670$		0			0
$671$			219835.i			0.488261i
$672$	−107890.	+	241462.i	−0.238914	+	0.534701i
$673$			334342.i			0.738177i	0.929394	+	0.369088i	$0.120330\pi$
$673$			334342.i			0.738177i	−0.929394	+	0.369088i	$0.879670\pi$
$674$	1.11189e6			2.44760
$675$		0			0
$676$	−689734.			−1.50934
$677$	823510.			1.79677			0.898383	−	0.439212i	$-0.144742\pi$
$677$	823510.			1.79677			0.898383	+	0.439212i	$0.144742\pi$
$678$	698517.			1.51956
$679$	−27238.7	−	12170.8i	−0.0590809	−	0.0263984i
$680$		0			0
$681$	−441949.			−0.952967
$682$	133617.			0.287272
$683$		−	821787.i		−	1.76164i	−0.473448	−	0.880822i	$-0.656991\pi$
$683$		−	821787.i		−	1.76164i	0.473448	−	0.880822i	$-0.343009\pi$
$684$		−	59892.9i		−	0.128016i
$685$		0			0
$686$	728560.	−	233523.i	1.54816	−	0.496229i
$687$			223815.i			0.474216i
$688$			33140.9i			0.0700145i
$689$			83959.0i			0.176860i
$690$		0			0
$691$		−	744548.i		−	1.55933i	−0.626200	−	0.779663i	$-0.715391\pi$
$691$		−	744548.i		−	1.55933i	0.626200	−	0.779663i	$-0.284609\pi$
$692$	82352.3			0.171974
$693$	237896.	+	106297.i	0.495361	+	0.221336i
$694$	1.31666e6			2.73373
$695$		0			0
$696$			95213.6i			0.196553i
$697$			939652.i			1.93420i
$698$	−586140.			−1.20307
$699$		−	222428.i		−	0.455235i
$700$		0			0
$701$	318730.			0.648616			0.324308	−	0.945952i	$-0.394869\pi$
$701$	318730.			0.648616			0.324308	+	0.945952i	$0.394869\pi$
$702$		−	1.10611e6i		−	2.24452i
$703$	−113958.			−0.230587
$704$	−693789.			−1.39985
$705$		0			0
$706$			768509.i			1.54184i
$707$	299167.	−	669549.i	0.598515	−	1.33950i
$708$			124214.i			0.247802i
$709$	−150036.			−0.298471			−0.149235	−	0.988802i	$-0.547681\pi$
$709$	−150036.			−0.298471			−0.149235	+	0.988802i	$0.547681\pi$
$710$		0			0
$711$	−362394.			−0.716873
$712$	685388.			1.35200
$713$	9036.97			0.0177764
$714$	−269656.	+	603501.i	−0.528948	+	1.18381i
$715$		0			0
$716$	−678686.			−1.32386
$717$	68249.4			0.132758
$718$			1.26517e6i			2.45414i
$719$			124427.i			0.240690i	0.992732	+	0.120345i	$0.0384001\pi$
$719$			124427.i			0.240690i	−0.992732	+	0.120345i	$0.961600\pi$
$720$		0			0
$721$	−842854.	−	376603.i	−1.62137	−	0.724458i
$722$		−	834209.i		−	1.60030i
$723$		−	115919.i		−	0.221758i
$724$			831108.i			1.58555i
$725$		0			0
$726$			126784.i			0.240542i
$727$	534357.			1.01103			0.505513	−	0.862819i	$-0.331303\pi$
$727$	534357.			1.01103			0.505513	+	0.862819i	$0.331303\pi$
$728$	313085.	−	700700.i	0.590745	−	1.32211i
$729$	321882.			0.605677
$730$		0			0
$731$		−	858667.i		−	1.60690i
$732$			303042.i			0.565563i
$733$	−638734.			−1.18881			−0.594404	−	0.804166i	$-0.702612\pi$
$733$	−638734.			−1.18881			−0.594404	+	0.804166i	$0.702612\pi$
$734$			687312.i			1.27574i
$735$		0			0
$736$	−45270.9			−0.0835725
$737$		−	796819.i		−	1.46698i
$738$	821366.			1.50808
$739$	−198812.			−0.364044			−0.182022	−	0.983295i	$-0.558264\pi$
$739$	−198812.			−0.364044			−0.182022	+	0.983295i	$0.558264\pi$
$740$		0			0
$741$			58449.3i			0.106449i
$742$	−104344.	−	46623.0i	−0.189523	−	0.0846822i
$743$			865398.i			1.56761i	0.621006	+	0.783806i	$0.286724\pi$
$743$			865398.i			1.56761i	−0.621006	+	0.783806i	$0.713276\pi$
$744$	72088.3			0.130232
$745$		0			0
$746$	431750.			0.775808
$747$	−255468.			−0.457820
$748$	−1.04000e6			−1.85879
$749$	78034.3	−	174644.i	0.139098	−	0.311308i
$750$		0			0
$751$	−18813.0			−0.0333564			−0.0166782	−	0.999861i	$-0.505309\pi$
$751$	−18813.0			−0.0333564			−0.0166782	+	0.999861i	$0.505309\pi$
$752$	38014.4			0.0672222
$753$			455132.i			0.802690i
$754$			391867.i			0.689280i
$755$		0			0
$756$	854563.	+	381834.i	1.49520	+	0.668085i
$757$			247909.i			0.432614i	0.976325	+	0.216307i	$0.0694012\pi$
$757$			247909.i			0.432614i	−0.976325	+	0.216307i	$0.930599\pi$
$758$			1.14032e6i			1.98467i
$759$		−	27022.5i		−	0.0469075i
$760$		0			0
$761$		−	882187.i		−	1.52332i	−0.647976	−	0.761661i	$-0.724384\pi$
$761$		−	882187.i		−	1.52332i	0.647976	−	0.761661i	$-0.275616\pi$
$762$	124873.			0.215060
$763$	−735019.	−	328420.i	−1.26255	−	0.564132i
$764$	124280.			0.212920
$765$		0			0
$766$			26650.6i			0.0454202i
$767$			200081.i			0.340107i
$768$	−394805.			−0.669360
$769$			10006.5i			0.0169212i	0.999964	+	0.00846060i	$0.00269312\pi$
$769$			10006.5i			0.0169212i	−0.999964	+	0.00846060i	$0.997307\pi$
$770$		0			0
$771$	37321.3			0.0627838
$772$			971456.i			1.63000i
$773$	−148529.			−0.248573			−0.124286	−	0.992246i	$-0.539664\pi$
$773$	−148529.			−0.248573			−0.124286	+	0.992246i	$0.539664\pi$
$774$	−750575.			−1.25289
$775$		0			0
$776$		−	40737.9i		−	0.0676511i
$777$	278801.	−	623969.i	0.461798	−	1.03353i
$778$		−	1.34889e6i		−	2.22853i
$779$	−113102.			−0.186378
$780$		0			0
$781$	29799.2			0.0488542
$782$	−113148.			−0.185027
$783$	−187045.			−0.305087
$784$	23199.7	+	25903.7i	0.0377442	+	0.0421435i
$785$		0			0
$786$	187455.			0.303426
$787$	−954103.			−1.54044			−0.770222	−	0.637776i	$-0.779855\pi$
$787$	−954103.			−1.54044			−0.770222	+	0.637776i	$0.779855\pi$
$788$		−	84713.2i		−	0.136426i
$789$			131491.i			0.211224i
$790$		0			0
$791$	−388411.	+	869281.i	−0.620781	+	1.38934i
$792$			355795.i			0.567217i
$793$			488134.i			0.776233i
$794$			752266.i			1.19325i
$795$		0			0
$796$			1.36662e6i			2.15685i
$797$	−105180.			−0.165583			−0.0827914	−	0.996567i	$-0.526384\pi$
$797$	−105180.			−0.165583			−0.0827914	+	0.996567i	$0.526384\pi$
$798$	−72640.8	−	32457.2i	−0.114071	−	0.0509690i
$799$	−984936.			−1.54282
$800$		0			0
$801$			516695.i			0.805321i
$802$			1.29176e6i			2.00832i
$803$	968936.			1.50267
$804$		−	1.09841e6i		−	1.69924i
$805$		0			0
$806$	296691.			0.456704
$807$			409365.i			0.628585i
$808$	1.00137e6			1.53381
$809$	−13264.8			−0.0202677			−0.0101338	−	0.999949i	$-0.503226\pi$
$809$	−13264.8			−0.0202677			−0.0101338	+	0.999949i	$0.503226\pi$
$810$		0			0
$811$			68424.4i			0.104033i	0.998646	+	0.0520163i	$0.0165648\pi$
$811$			68424.4i			0.104033i	−0.998646	+	0.0520163i	$0.983435\pi$
$812$	−302751.	−	135275.i	−0.459170	−	0.205166i
$813$		−	339826.i		−	0.514133i
$814$	1.72971e6			2.61050
$815$		0			0
$816$	−30044.0			−0.0451209
$817$	103354.			0.154840
$818$	−257797.			−0.385275
$819$	528238.	+	236026.i	0.787520	+	0.351879i
$820$		0			0
$821$	23666.0			0.0351107			0.0175553	−	0.999846i	$-0.494412\pi$
$821$	23666.0			0.0351107			0.0175553	+	0.999846i	$0.494412\pi$
$822$	−899357.			−1.33103
$823$			541429.i			0.799358i	0.916655	+	0.399679i	$0.130878\pi$
$823$			541429.i			0.799358i	−0.916655	+	0.399679i	$0.869122\pi$
$824$		−	1.26056e6i		−	1.85656i
$825$		0			0
$826$	−248661.	−	111106.i	−0.364458	−	0.162847i
$827$			486140.i			0.710805i	0.934713	+	0.355402i	$0.115656\pi$
$827$			486140.i			0.710805i	−0.934713	+	0.355402i	$0.884344\pi$
$828$			61484.2i			0.0896815i
$829$			199179.i			0.289824i	0.989445	+	0.144912i	$0.0462900\pi$
$829$			199179.i			0.289824i	−0.989445	+	0.144912i	$0.953710\pi$
$830$		0			0
$831$			405310.i			0.586929i
$832$	−1.54053e6			−2.22547
$833$	−601095.	−	671154.i	−0.866269	−	0.967236i
$834$	349541.			0.502535
$835$		0			0
$836$		−	125180.i		−	0.179112i
$837$			141616.i			0.202144i
$838$	−1.02562e6			−1.46050
$839$		−	1.05803e6i		−	1.50306i	−0.659701	−	0.751528i	$-0.729317\pi$
$839$		−	1.05803e6i		−	1.50306i	0.659701	−	0.751528i	$-0.270683\pi$
$840$		0			0
$841$	−641015.			−0.906309
$842$		−	63806.9i		−	0.0900003i
$843$	−351419.			−0.494504
$844$	414055.			0.581263
$845$		0			0
$846$			860950.i			1.20292i
$847$	−157778.	−	70498.3i	−0.219928	−	0.0982679i
$848$		−	5194.56i		−	0.00722365i
$849$	551007.			0.764436
$850$		0			0
$851$	116986.			0.161538
$852$	41078.1			0.0565889
$853$	−659921.			−0.906972			−0.453486	−	0.891263i	$-0.649820\pi$
$853$	−659921.			−0.906972			−0.453486	+	0.891263i	$0.649820\pi$
$854$	−606652.	−	271064.i	−0.831810	−	0.371668i
$855$		0			0
$856$	261196.			0.356466
$857$	−776880.			−1.05777			−0.528886	−	0.848693i	$-0.677390\pi$
$857$	−776880.			−1.05777			−0.528886	+	0.848693i	$0.677390\pi$
$858$		−	887171.i		−	1.20513i
$859$		−	31227.0i		−	0.0423198i	−0.999776	−	0.0211599i	$-0.993264\pi$
$859$		−	31227.0i		−	0.0423198i	0.999776	−	0.0211599i	$-0.00673591\pi$
$860$		0			0
$861$	276706.	−	619281.i	0.373261	−	0.835375i
$862$		−	1.45140e6i		−	1.95331i
$863$			197197.i			0.264776i	0.991198	+	0.132388i	$0.0422645\pi$
$863$			197197.i			0.264776i	−0.991198	+	0.132388i	$0.957736\pi$
$864$		−	709429.i		−	0.950345i
$865$		0			0
$866$			732456.i			0.976665i
$867$	316718.			0.421341
$868$	−102420.	+	229220.i	−0.135939	+	0.304237i
$869$	−757429.			−1.00300
$870$		0			0
$871$		−	1.76930e6i		−	2.33220i
$872$		−	1.09929e6i		−	1.44570i
$873$	30711.2			0.0402965
$874$		−	13619.2i		−	0.0178290i
$875$		0			0
$876$	1.33568e6			1.74058
$877$			1.22846e6i			1.59720i	0.601860	+	0.798602i	$0.294427\pi$
$877$			1.22846e6i			1.59720i	−0.601860	+	0.798602i	$0.705573\pi$
$878$	475406.			0.616703
$879$	184587.			0.238904
$880$		0			0
$881$		−	1.23726e6i		−	1.59408i	−0.603927	−	0.797040i	$-0.706398\pi$
$881$		−	1.23726e6i		−	1.59408i	0.603927	−	0.797040i	$-0.293602\pi$
$882$	−586667.	+	525427.i	−0.754145	+	0.675422i
$883$			708608.i			0.908835i	0.890789	+	0.454417i	$0.150152\pi$
$883$			708608.i			0.908835i	−0.890789	+	0.454417i	$0.849848\pi$
$884$	−2.30927e6			−2.95509
$885$		0			0
$886$	325733.			0.414949
$887$	−48621.1			−0.0617984			−0.0308992	−	0.999523i	$-0.509837\pi$
$887$	−48621.1			−0.0617984			−0.0308992	+	0.999523i	$0.509837\pi$
$888$	933201.			1.18345
$889$	−69435.9	+	155401.i	−0.0878578	+	0.196630i
$890$		0			0
$891$	−7265.31			−0.00915164
$892$	313951.			0.394577
$893$		−	118552.i		−	0.148665i
$894$			178653.i			0.223530i
$895$		0			0
$896$	543196.	−	1.21570e6i	0.676613	−	1.51429i
$897$		−	60002.2i		−	0.0745732i
$898$		−	32788.2i		−	0.0406597i
$899$		−	50171.2i		−	0.0620776i
$900$		0			0
$901$			134589.i			0.165790i
$902$	1.71671e6			2.11001
$903$	−252858.	+	565907.i	−0.310099	+	0.694016i
$904$	−1.30009e6			−1.59087
$905$		0			0
$906$			559799.i			0.681986i
$907$		−	1.42767e6i		−	1.73546i	−0.497036	−	0.867730i	$-0.665578\pi$
$907$		−	1.42767e6i		−	1.73546i	0.497036	−	0.867730i	$-0.334422\pi$
$908$	2.10170e6			2.54917
$909$			754905.i			0.913617i
$910$		0			0
$911$	−583391.			−0.702947			−0.351474	−	0.936198i	$-0.614319\pi$
$911$	−583391.			−0.702947			−0.351474	+	0.936198i	$0.614319\pi$
$912$		−	3616.27i		−	0.00434781i
$913$	−533945.			−0.640553
$914$	248944.			0.297995
$915$		0			0
$916$		−	1.06436e6i		−	1.26852i
$917$	−104234.	+	233281.i	−0.123957	+	0.277422i
$918$		−	1.77312e6i		−	2.10403i
$919$	−911636.			−1.07942			−0.539710	−	0.841851i	$-0.681466\pi$
$919$	−911636.			−1.07942			−0.539710	+	0.841851i	$0.681466\pi$
$920$		0			0
$921$	−448225.			−0.528417
$922$	−245484.			−0.288776
$923$	66167.7			0.0776681
$924$	685416.	+	306257.i	0.802806	+	0.358709i
$925$		0			0
$926$	−2.23656e6			−2.60830
$927$	950303.			1.10587
$928$			251334.i			0.291847i
$929$		−	1.18209e6i		−	1.36968i	−0.728696	−	0.684838i	$-0.759873\pi$
$929$		−	1.18209e6i		−	1.36968i	0.728696	−	0.684838i	$-0.240127\pi$
$930$		0			0
$931$	80783.8	−	72351.1i	0.0932020	−	0.0834729i
$932$			1.05776e6i			1.21775i
$933$		−	325112.i		−	0.373482i
$934$		−	629760.i		−	0.721907i
$935$		0			0
$936$			790026.i			0.901757i
$937$	648753.			0.738925			0.369463	−	0.929246i	$-0.379542\pi$
$937$	648753.			0.738925			0.369463	+	0.929246i	$0.379542\pi$
$938$	2.19889e6	+	982503.i	2.49918	+	1.11668i
$939$	−810842.			−0.919613
$940$		0			0
$941$			539679.i			0.609475i	0.952436	+	0.304738i	$0.0985688\pi$
$941$			539679.i			0.609475i	−0.952436	+	0.304738i	$0.901431\pi$
$942$			80740.3i			0.0909889i
$943$	116107.			0.130567
$944$		−	12379.1i		−	0.0138913i
$945$		0			0
$946$	−1.56875e6			−1.75296
$947$		−	380310.i		−	0.424071i	−0.977262	−	0.212035i	$-0.931991\pi$
$947$		−	380310.i		−	0.424071i	0.977262	−	0.212035i	$-0.0680092\pi$
$948$	−1.04411e6			−1.16180
$949$	2.15148e6			2.38894
$950$		0			0
$951$		−	586852.i		−	0.648884i
$952$	501885.	−	1.12324e6i	0.553771	−	1.23936i
$953$		−	1.51323e6i		−	1.66617i	−0.553147	−	0.833084i	$-0.686573\pi$
$953$		−	1.51323e6i		−	1.66617i	0.553147	−	0.833084i	$-0.313427\pi$
$954$	117646.			0.129265
$955$		0			0
$956$	−324562.			−0.355125
$957$	−150023.			−0.163807
$958$	269361.			0.293497
$959$	500088.	−	1.11922e6i	0.543762	−	1.21696i
$960$		0			0
$961$	885535.			0.958869
$962$	3.84074e6			4.15016
$963$			196908.i			0.212330i
$964$			551258.i			0.593199i
$965$		0			0
$966$	74570.8	+	33319.6i	0.0799125	+	0.0357064i
$967$			393218.i			0.420514i	0.977646	+	0.210257i	$0.0674300\pi$
$967$			393218.i			0.420514i	−0.977646	+	0.210257i	$0.932570\pi$
$968$		−	235971.i		−	0.251831i
$969$			93695.8i			0.0997867i
$970$		0			0
$971$		−	957332.i		−	1.01537i	−0.861543	−	0.507685i	$-0.830502\pi$
$971$		−	957332.i		−	1.01537i	0.861543	−	0.507685i	$-0.169498\pi$
$972$	−1.55726e6			−1.64827
$973$	−194362.	+	434992.i	−0.205299	+	0.459468i
$974$	191644.			0.202012
$975$		0			0
$976$		−	30200.9i		−	0.0317044i
$977$		−	1.33928e6i		−	1.40308i	−0.712631	−	0.701539i	$-0.752497\pi$
$977$		−	1.33928e6i		−	1.40308i	0.712631	−	0.701539i	$-0.247503\pi$
$978$	972362.			1.01660
$979$			1.07993e6i			1.12675i
$980$		0			0
$981$	828721.			0.861133
$982$			1.29251e6i			1.34033i
$983$	1.72782e6			1.78810			0.894050	−	0.447968i	$-0.147852\pi$
$983$	1.72782e6			1.78810			0.894050	+	0.447968i	$0.147852\pi$
$984$	926188.			0.956553
$985$		0			0
$986$			628174.i			0.646139i
$987$	649126.	+	290041.i	0.666338	+	0.297732i
$988$		−	277957.i		−	0.284750i
$989$	−106100.			−0.108473
$990$		0			0
$991$	946703.			0.963977			0.481988	−	0.876178i	$-0.339915\pi$
$991$	946703.			0.963977			0.481988	+	0.876178i	$0.339915\pi$
$992$	190290.			0.193372
$993$	−134317.			−0.136217
$994$	−36743.3	+	82233.2i	−0.0371882	+	0.0832289i
$995$		0			0
$996$	−736042.			−0.741966
$997$	−552328.			−0.555657			−0.277829	−	0.960631i	$-0.589615\pi$
$997$	−552328.			−0.555657			−0.277829	+	0.960631i	$0.589615\pi$
$998$			403248.i			0.404866i
$999$			1.83325e6i			1.83693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.5.c.d.174.7		24
5.2	odd	4		35.5.d.a.6.11	✓	12
5.3	odd	4		175.5.d.i.76.2		12
5.4	even	2	inner	175.5.c.d.174.18		24
7.6	odd	2	inner	175.5.c.d.174.17		24
15.2	even	4		315.5.h.a.181.2		12
20.7	even	4		560.5.f.b.321.8		12
35.13	even	4		175.5.d.i.76.1		12
35.27	even	4		35.5.d.a.6.12	yes	12
35.34	odd	2	inner	175.5.c.d.174.8		24
105.62	odd	4		315.5.h.a.181.1		12
140.27	odd	4		560.5.f.b.321.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.d.a.6.11	✓	12	5.2	odd	4
35.5.d.a.6.12	yes	12	35.27	even	4
175.5.c.d.174.7		24	1.1	even	1	trivial
175.5.c.d.174.8		24	35.34	odd	2	inner
175.5.c.d.174.17		24	7.6	odd	2	inner
175.5.c.d.174.18		24	5.4	even	2	inner
175.5.d.i.76.1		12	35.13	even	4
175.5.d.i.76.2		12	5.3	odd	4
315.5.h.a.181.1		12	105.62	odd	4
315.5.h.a.181.2		12	15.2	even	4
560.5.f.b.321.5		12	140.27	odd	4
560.5.f.b.321.8		12	20.7	even	4

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-6.50299i q^{2} +5.52807 q^{3} -26.2889 q^{4} -35.9490i q^{6} +(44.7373 + 19.9894i) q^{7} +66.9085i q^{8} -50.4404 q^{9} +O(q^{10})\)	\(q-6.50299i q^{2} +5.52807 q^{3} -26.2889 q^{4} -35.9490i q^{6} +(44.7373 + 19.9894i) q^{7} +66.9085i q^{8} -50.4404 q^{9} -105.424 q^{11} -145.327 q^{12} -234.089 q^{13} +(129.991 - 290.926i) q^{14} +14.4831 q^{16} -375.251 q^{17} +328.014i q^{18} -45.1673i q^{19} +(247.311 + 110.503i) q^{21} +685.571i q^{22} +46.3674i q^{23} +369.875i q^{24} +1522.28i q^{26} -726.612 q^{27} +(-1176.09 - 525.500i) q^{28} +257.421 q^{29} -194.899i q^{31} +976.352i q^{32} -582.791 q^{33} +2440.26i q^{34} +1326.02 q^{36} -2523.02i q^{37} -293.723 q^{38} -1294.06 q^{39} -2504.06i q^{41} +(718.600 - 1608.26i) q^{42} +2288.24i q^{43} +2771.48 q^{44} +301.527 q^{46} +2624.74 q^{47} +80.0637 q^{48} +(1601.84 + 1788.55i) q^{49} -2074.42 q^{51} +6153.94 q^{52} -358.663i q^{53} +4725.15i q^{54} +(-1337.46 + 2993.30i) q^{56} -249.688i q^{57} -1674.01i q^{58} -854.723i q^{59} -2085.25i q^{61} -1267.43 q^{62} +(-2256.57 - 1008.28i) q^{63} +6580.94 q^{64} +3789.89i q^{66} +7558.23i q^{67} +9864.94 q^{68} +256.322i q^{69} -282.660 q^{71} -3374.89i q^{72} -9190.85 q^{73} -16407.2 q^{74} +1187.40i q^{76} +(-4716.38 - 2107.37i) q^{77} +8415.27i q^{78} +7184.60 q^{79} +68.9152 q^{81} -16283.9 q^{82} +5064.74 q^{83} +(-6501.52 - 2905.00i) q^{84} +14880.4 q^{86} +1423.04 q^{87} -7053.76i q^{88} -10243.7i q^{89} +(-10472.5 - 4679.31i) q^{91} -1218.95i q^{92} -1077.42i q^{93} -17068.6i q^{94} +5397.34i q^{96} -608.860 q^{97} +(11630.9 - 10416.8i) q^{98} +5317.63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 244 q^{4} + 868 q^{9}+O(q^{10}) \) 24 * q - 244 * q^4 + 868 * q^9	\( 24 q - 244 q^{4} + 868 q^{9} + 252 q^{11} - 156 q^{14} + 1156 q^{16} - 1284 q^{21} + 4380 q^{29} - 7164 q^{36} - 17268 q^{39} + 22392 q^{44} + 15688 q^{46} + 17592 q^{49} + 14412 q^{51} - 13212 q^{56} - 40292 q^{64} - 11328 q^{71} - 35208 q^{74} + 3180 q^{79} - 23824 q^{81} + 86256 q^{84} + 35208 q^{86} - 14364 q^{91} - 46168 q^{99}+O(q^{100}) \) 24 * q - 244 * q^4 + 868 * q^9 + 252 * q^11 - 156 * q^14 + 1156 * q^16 - 1284 * q^21 + 4380 * q^29 - 7164 * q^36 - 17268 * q^39 + 22392 * q^44 + 15688 * q^46 + 17592 * q^49 + 14412 * q^51 - 13212 * q^56 - 40292 * q^64 - 11328 * q^71 - 35208 * q^74 + 3180 * q^79 - 23824 * q^81 + 86256 * q^84 + 35208 * q^86 - 14364 * q^91 - 46168 * q^99

Introduction

L-functions

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