LMFDB - Embedded newform 475.3.c.g.151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(151,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("475.151");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.c (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:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 30x^{10} + 329x^{8} + 1620x^{6} + 3479x^{4} + 2470x^{2} + 55 $ x^12 + 30x^10 + 329x^8 + 1620x^6 + 3479x^4 + 2470*x^2 + 55
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.6
Root			$-0.151673i$ of defining polynomial
Character	$\chi$	$=$	475.151
Dual form			475.3.c.g.151.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.151673i q^{2} +5.10387i q^{3} +3.97700 q^{4} +0.774118 q^{6} +6.35478 q^{7} -1.20989i q^{8} -17.0495 q^{9} +O(q^{10})$	\(q-0.151673i q^{2} +5.10387i q^{3} +3.97700 q^{4} +0.774118 q^{6} +6.35478 q^{7} -1.20989i q^{8} -17.0495 q^{9} +10.0445 q^{11} +20.2981i q^{12} +3.79583i q^{13} -0.963848i q^{14} +15.7245 q^{16} +13.4309 q^{17} +2.58594i q^{18} +(2.99005 + 18.7633i) q^{19} +32.4340i q^{21} -1.52348i q^{22} -16.7800 q^{23} +6.17514 q^{24} +0.575725 q^{26} -41.0834i q^{27} +25.2729 q^{28} -24.9494i q^{29} +46.3492i q^{31} -7.22455i q^{32} +51.2658i q^{33} -2.03710i q^{34} -67.8056 q^{36} -68.4543i q^{37} +(2.84588 - 0.453510i) q^{38} -19.3734 q^{39} -47.5852i q^{41} +4.91935 q^{42} -43.4186 q^{43} +39.9469 q^{44} +2.54507i q^{46} -37.4512 q^{47} +80.2556i q^{48} -8.61675 q^{49} +68.5494i q^{51} +15.0960i q^{52} +9.48017i q^{53} -6.23123 q^{54} -7.68861i q^{56} +(-95.7651 + 15.2608i) q^{57} -3.78414 q^{58} +87.7096i q^{59} -95.9399 q^{61} +7.02991 q^{62} -108.346 q^{63} +61.8021 q^{64} +7.77563 q^{66} +75.1263i q^{67} +53.4146 q^{68} -85.6428i q^{69} -77.6831i q^{71} +20.6280i q^{72} +120.344 q^{73} -10.3827 q^{74} +(11.8914 + 74.6214i) q^{76} +63.8306 q^{77} +2.93842i q^{78} -12.8248i q^{79} +56.2390 q^{81} -7.21738 q^{82} +108.761 q^{83} +128.990i q^{84} +6.58543i q^{86} +127.338 q^{87} -12.1528i q^{88} -156.732i q^{89} +24.1217i q^{91} -66.7339 q^{92} -236.560 q^{93} +5.68033i q^{94} +36.8731 q^{96} -56.1983i q^{97} +1.30693i q^{98} -171.253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	$ 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	0.151673i		−	0.0758364i	−0.999281	−	0.0379182i	$-0.987927\pi$
$2$		−	0.151673i		−	0.0758364i	0.999281	−	0.0379182i	$-0.0120726\pi$
$3$			5.10387i			1.70129i	0.525741	+	0.850645i	$0.323788\pi$
$3$			5.10387i			1.70129i	−0.525741	+	0.850645i	$0.676212\pi$
$4$	3.97700			0.994249
$5$		0			0
$5$		0			0
$6$	0.774118			0.129020
$7$	6.35478			0.907826			0.453913	−	0.891046i	$-0.350028\pi$
$7$	6.35478			0.907826			0.453913	+	0.891046i	$0.350028\pi$
$8$		−	1.20989i		−	0.151237i
$9$	−17.0495			−1.89438
$10$		0			0
$11$	10.0445			0.913136			0.456568	−	0.889688i	$-0.349078\pi$
$11$	10.0445			0.913136			0.456568	+	0.889688i	$0.349078\pi$
$12$			20.2981i			1.69150i
$13$			3.79583i			0.291987i	0.989286	+	0.145994i	$0.0466379\pi$
$13$			3.79583i			0.291987i	−0.989286	+	0.145994i	$0.953362\pi$
$14$		−	0.963848i		−	0.0688463i
$15$		0			0
$16$	15.7245			0.982780
$17$	13.4309			0.790052			0.395026	−	0.918670i	$-0.370736\pi$
$17$	13.4309			0.790052			0.395026	+	0.918670i	$0.370736\pi$
$18$			2.58594i			0.143663i
$19$	2.99005	+	18.7633i	0.157371	+	0.987540i
$19$	2.99005	+	18.7633i	0.157371	+	0.987540i
$20$		0			0
$21$			32.4340i			1.54447i
$22$		−	1.52348i		−	0.0692490i
$23$	−16.7800			−0.729564			−0.364782	−	0.931093i	$-0.618856\pi$
$23$	−16.7800			−0.729564			−0.364782	+	0.931093i	$0.618856\pi$
$24$	6.17514			0.257297
$25$		0			0
$26$	0.575725			0.0221433
$27$		−	41.0834i		−	1.52161i
$28$	25.2729			0.902605
$29$		−	24.9494i		−	0.860323i	−0.902752	−	0.430161i	$-0.858457\pi$
$29$		−	24.9494i		−	0.860323i	0.902752	−	0.430161i	$-0.141543\pi$
$30$		0			0
$31$			46.3492i			1.49513i	0.664186	+	0.747567i	$0.268778\pi$
$31$			46.3492i			1.49513i	−0.664186	+	0.747567i	$0.731222\pi$
$32$		−	7.22455i		−	0.225767i
$33$			51.2658i			1.55351i
$34$		−	2.03710i		−	0.0599147i
$35$		0			0
$36$	−67.8056			−1.88349
$37$		−	68.4543i		−	1.85012i	−0.379825	−	0.925058i	$-0.624016\pi$
$37$		−	68.4543i		−	1.85012i	0.379825	−	0.925058i	$-0.375984\pi$
$38$	2.84588	−	0.453510i	0.0748915	−	0.0119345i
$39$	−19.3734			−0.496755
$40$		0			0
$41$		−	47.5852i		−	1.16061i	−0.814398	−	0.580307i	$-0.802932\pi$
$41$		−	47.5852i		−	1.16061i	0.814398	−	0.580307i	$-0.197068\pi$
$42$	4.91935			0.117127
$43$	−43.4186			−1.00974			−0.504868	−	0.863197i	$-0.668459\pi$
$43$	−43.4186			−1.00974			−0.504868	+	0.863197i	$0.668459\pi$
$44$	39.9469			0.907884
$45$		0			0
$46$			2.54507i			0.0553275i
$47$	−37.4512			−0.796834			−0.398417	−	0.917204i	$-0.630440\pi$
$47$	−37.4512			−0.796834			−0.398417	+	0.917204i	$0.630440\pi$
$48$			80.2556i			1.67199i
$49$	−8.61675			−0.175852
$50$		0			0
$51$			68.5494i			1.34411i
$52$			15.0960i			0.290308i
$53$			9.48017i			0.178871i	0.995993	+	0.0894356i	$0.0285063\pi$
$53$			9.48017i			0.178871i	−0.995993	+	0.0894356i	$0.971494\pi$
$54$	−6.23123			−0.115393
$55$		0			0
$56$		−	7.68861i		−	0.137297i
$57$	−95.7651	+	15.2608i	−1.68009	+	0.267734i
$58$	−3.78414			−0.0652438
$59$			87.7096i			1.48660i	0.668956	+	0.743302i	$0.266741\pi$
$59$			87.7096i			1.48660i	−0.668956	+	0.743302i	$0.733259\pi$
$60$		0			0
$61$	−95.9399			−1.57279			−0.786393	−	0.617727i	$-0.788054\pi$
$61$	−95.9399			−1.57279			−0.786393	+	0.617727i	$0.788054\pi$
$62$	7.02991			0.113386
$63$	−108.346			−1.71977
$64$	61.8021			0.965658
$65$		0			0
$66$	7.77563			0.117813
$67$			75.1263i			1.12129i	0.828057	+	0.560644i	$0.189446\pi$
$67$			75.1263i			1.12129i	−0.828057	+	0.560644i	$0.810554\pi$
$68$	53.4146			0.785508
$69$		−	85.6428i		−	1.24120i
$70$		0			0
$71$		−	77.6831i		−	1.09413i	−0.837091	−	0.547064i	$-0.815745\pi$
$71$		−	77.6831i		−	1.09413i	0.837091	−	0.547064i	$-0.184255\pi$
$72$			20.6280i			0.286500i
$73$	120.344			1.64854			0.824272	−	0.566193i	$-0.191584\pi$
$73$	120.344			1.64854			0.824272	+	0.566193i	$0.191584\pi$
$74$	−10.3827			−0.140306
$75$		0			0
$76$	11.8914	+	74.6214i	0.156466	+	0.981860i
$77$	63.8306			0.828969
$78$			2.93842i			0.0376721i
$79$		−	12.8248i		−	0.162339i	−0.996700	−	0.0811693i	$-0.974135\pi$
$79$		−	12.8248i		−	0.162339i	0.996700	−	0.0811693i	$-0.0258655\pi$
$80$		0			0
$81$	56.2390			0.694308
$82$	−7.21738			−0.0880169
$83$	108.761			1.31037			0.655186	−	0.755467i	$-0.272590\pi$
$83$	108.761			1.31037			0.655186	+	0.755467i	$0.272590\pi$
$84$			128.990i			1.53559i
$85$		0			0
$86$			6.58543i			0.0765748i
$87$	127.338			1.46366
$88$		−	12.1528i		−	0.138100i
$89$		−	156.732i		−	1.76103i	−0.474016	−	0.880516i	$-0.657196\pi$
$89$		−	156.732i		−	1.76103i	0.474016	−	0.880516i	$-0.342804\pi$
$90$		0			0
$91$			24.1217i			0.265074i
$92$	−66.7339			−0.725368
$93$	−236.560			−2.54366
$94$			5.68033i			0.0604290i
$95$		0			0
$96$	36.8731			0.384095
$97$		−	56.1983i		−	0.579364i	−0.957123	−	0.289682i	$-0.906450\pi$
$97$		−	56.1983i		−	0.579364i	0.957123	−	0.289682i	$-0.0935496\pi$
$98$			1.30693i			0.0133360i
$99$	−171.253			−1.72983
$100$		0			0
$101$	−27.4569			−0.271850			−0.135925	−	0.990719i	$-0.543401\pi$
$101$	−27.4569			−0.271850			−0.135925	+	0.990719i	$0.543401\pi$
$102$	10.3971			0.101932
$103$			20.2246i			0.196355i	0.995169	+	0.0981777i	$0.0313013\pi$
$103$			20.2246i			0.196355i	−0.995169	+	0.0981777i	$0.968699\pi$
$104$	4.59256			0.0441592
$105$		0			0
$106$	1.43788			0.0135649
$107$		−	29.0356i		−	0.271361i	−0.990753	−	0.135680i	$-0.956678\pi$
$107$		−	29.0356i		−	0.271361i	0.990753	−	0.135680i	$-0.0433220\pi$
$108$		−	163.388i		−	1.51286i
$109$			103.073i			0.945627i	0.881162	+	0.472814i	$0.156762\pi$
$109$			103.073i			0.945627i	−0.881162	+	0.472814i	$0.843238\pi$
$110$		0			0
$111$	349.382			3.14758
$112$	99.9256			0.892193
$113$		−	130.480i		−	1.15469i	−0.816500	−	0.577346i	$-0.804088\pi$
$113$		−	130.480i		−	1.15469i	0.816500	−	0.577346i	$-0.195912\pi$
$114$	2.31465	+	14.5250i	0.0203040	+	0.127412i
$115$		0			0
$116$		−	99.2235i		−	0.855375i
$117$		−	64.7169i		−	0.553136i
$118$	13.3032			0.112739
$119$	85.3503			0.717230
$120$		0			0
$121$	−20.1081			−0.166182
$122$			14.5515i			0.119274i
$123$	242.868			1.97454
$124$			184.330i			1.48654i
$125$		0			0
$126$			16.4331i			0.130421i
$127$			51.2735i			0.403728i	0.979414	+	0.201864i	$0.0646999\pi$
$127$			51.2735i			0.403728i	−0.979414	+	0.201864i	$0.935300\pi$
$128$		−	38.2719i		−	0.298999i
$129$		−	221.603i		−	1.71785i
$130$		0			0
$131$	−111.464			−0.850867			−0.425434	−	0.904990i	$-0.639878\pi$
$131$	−111.464			−0.850867			−0.425434	+	0.904990i	$0.639878\pi$
$132$			203.884i			1.54457i
$133$	19.0011	+	119.236i	0.142866	+	0.896514i
$134$	11.3946			0.0850345
$135$		0			0
$136$		−	16.2499i		−	0.119485i
$137$	103.250			0.753646			0.376823	−	0.926285i	$-0.377016\pi$
$137$	103.250			0.753646			0.376823	+	0.926285i	$0.377016\pi$
$138$	−12.9897			−0.0941281
$139$	12.1509			0.0874164			0.0437082	−	0.999044i	$-0.486083\pi$
$139$	12.1509			0.0874164			0.0437082	+	0.999044i	$0.486083\pi$
$140$		0			0
$141$		−	191.146i		−	1.35564i
$142$	−11.7824			−0.0829748
$143$			38.1272i			0.266624i
$144$	−268.094			−1.86176
$145$		0			0
$146$		−	18.2529i		−	0.125020i
$147$		−	43.9787i		−	0.299175i
$148$		−	272.242i		−	1.83948i
$149$	247.081			1.65826			0.829130	−	0.559056i	$-0.188836\pi$
$149$	247.081			1.65826			0.829130	+	0.559056i	$0.188836\pi$
$150$		0			0
$151$			61.9073i			0.409982i	0.978764	+	0.204991i	$0.0657165\pi$
$151$			61.9073i			0.409982i	−0.978764	+	0.204991i	$0.934283\pi$
$152$	22.7015	−	3.61765i	0.149352	−	0.0238003i
$153$	−228.989			−1.49666
$154$		−	9.68137i		−	0.0628660i
$155$		0			0
$156$	−77.0481			−0.493898
$157$	−74.5130			−0.474605			−0.237303	−	0.971436i	$-0.576263\pi$
$157$	−74.5130			−0.474605			−0.237303	+	0.971436i	$0.576263\pi$
$158$	−1.94517			−0.0123112
$159$	−48.3855			−0.304311
$160$		0			0
$161$	−106.633			−0.662317
$162$		−	8.52992i		−	0.0526538i
$163$	67.2648			0.412667			0.206334	−	0.978482i	$-0.433847\pi$
$163$	67.2648			0.412667			0.206334	+	0.978482i	$0.433847\pi$
$164$		−	189.246i		−	1.15394i
$165$		0			0
$166$		−	16.4961i		−	0.0993740i
$167$		−	165.664i		−	0.992001i	−0.868322	−	0.496001i	$-0.834801\pi$
$167$		−	165.664i		−	0.992001i	0.868322	−	0.496001i	$-0.165199\pi$
$168$	39.2416			0.233581
$169$	154.592			0.914743
$170$		0			0
$171$	−50.9788	−	319.903i	−0.298122	−	1.87078i
$172$	−172.676			−1.00393
$173$			309.445i			1.78870i	0.447370	+	0.894349i	$0.352361\pi$
$173$			309.445i			1.78870i	−0.447370	+	0.894349i	$0.647639\pi$
$174$		−	19.3138i		−	0.110999i
$175$		0			0
$176$	157.944			0.897411
$177$	−447.658			−2.52914
$178$	−23.7720			−0.133550
$179$		−	211.904i		−	1.18382i	−0.806005	−	0.591909i	$-0.798374\pi$
$179$		−	211.904i		−	1.18382i	0.806005	−	0.591909i	$-0.201626\pi$
$180$		0			0
$181$		−	101.114i		−	0.558639i	−0.960198	−	0.279319i	$-0.909891\pi$
$181$		−	101.114i		−	0.558639i	0.960198	−	0.279319i	$-0.0901089\pi$
$182$	3.65861			0.0201022
$183$		−	489.665i		−	2.67576i
$184$			20.3020i			0.110337i
$185$		0			0
$186$			35.8797i			0.192902i
$187$	134.906			0.721425
$188$	−148.943			−0.792251
$189$		−	261.076i		−	1.38135i
$190$		0			0
$191$	−57.2008			−0.299481			−0.149740	−	0.988725i	$-0.547844\pi$
$191$	−57.2008			−0.299481			−0.149740	+	0.988725i	$0.547844\pi$
$192$			315.430i			1.64286i
$193$		−	156.431i		−	0.810524i	−0.914201	−	0.405262i	$-0.867180\pi$
$193$		−	156.431i		−	0.810524i	0.914201	−	0.405262i	$-0.132820\pi$
$194$	−8.52376			−0.0439369
$195$		0			0
$196$	−34.2688			−0.174841
$197$	−168.534			−0.855503			−0.427751	−	0.903896i	$-0.640694\pi$
$197$	−168.534			−0.855503			−0.427751	+	0.903896i	$0.640694\pi$
$198$			25.9745i			0.131184i
$199$	40.9710			0.205885			0.102942	−	0.994687i	$-0.467174\pi$
$199$	40.9710			0.205885			0.102942	+	0.994687i	$0.467174\pi$
$200$		0			0
$201$	−383.435			−1.90764
$202$			4.16446i			0.0206161i
$203$		−	158.548i		−	0.781023i
$204$			272.621i			1.33638i
$205$		0			0
$206$	3.06752			0.0148909
$207$	286.089			1.38207
$208$			59.6875i			0.286959i
$209$	30.0336	+	188.467i	0.143701	+	0.901758i
$210$		0			0
$211$		−	264.352i		−	1.25285i	−0.779481	−	0.626426i	$-0.784517\pi$
$211$		−	264.352i		−	1.25285i	0.779481	−	0.626426i	$-0.215483\pi$
$212$			37.7026i			0.177842i
$213$	396.484			1.86143
$214$	−4.40391			−0.0205790
$215$		0			0
$216$	−49.7065			−0.230123
$217$			294.539i			1.35732i
$218$	15.6334			0.0717130
$219$			614.219i			2.80465i
$220$		0			0
$221$			50.9814i			0.230685i
$222$		−	52.9917i		−	0.238701i
$223$			220.658i			0.989498i	0.869036	+	0.494749i	$0.164740\pi$
$223$			220.658i			0.989498i	−0.869036	+	0.494749i	$0.835260\pi$
$224$		−	45.9104i		−	0.204957i
$225$		0			0
$226$	−19.7903			−0.0875677
$227$		−	156.019i		−	0.687308i	−0.939096	−	0.343654i	$-0.888335\pi$
$227$		−	156.019i		−	0.687308i	0.939096	−	0.343654i	$-0.111665\pi$
$228$	−380.858	+	60.6923i	−1.67043	+	0.266194i
$229$	259.477			1.13309			0.566545	−	0.824031i	$-0.308280\pi$
$229$	259.477			1.13309			0.566545	+	0.824031i	$0.308280\pi$
$230$		0			0
$231$			325.783i			1.41032i
$232$	−30.1861			−0.130112
$233$	353.499			1.51716			0.758582	−	0.651578i	$-0.225893\pi$
$233$	353.499			1.51716			0.758582	+	0.651578i	$0.225893\pi$
$234$	−9.81580			−0.0419479
$235$		0			0
$236$			348.821i			1.47805i
$237$	65.4558			0.276185
$238$		−	12.9453i		−	0.0543921i
$239$	−176.322			−0.737750			−0.368875	−	0.929479i	$-0.620257\pi$
$239$	−176.322			−0.737750			−0.368875	+	0.929479i	$0.620257\pi$
$240$		0			0
$241$		−	35.4360i		−	0.147037i	−0.997294	−	0.0735187i	$-0.976577\pi$
$241$		−	35.4360i		−	0.147037i	0.997294	−	0.0735187i	$-0.0234229\pi$
$242$			3.04985i			0.0126027i
$243$		−	82.7142i		−	0.340388i
$244$	−381.553			−1.56374
$245$		0			0
$246$		−	36.8366i		−	0.149742i
$247$	−71.2222	+	11.3497i	−0.288349	+	0.0459504i
$248$	56.0776			0.226119
$249$			555.101i			2.22932i
$250$		0			0
$251$	305.098			1.21553			0.607764	−	0.794118i	$-0.292067\pi$
$251$	305.098			1.21553			0.607764	+	0.794118i	$0.292067\pi$
$252$	−430.890			−1.70988
$253$	−168.546			−0.666191
$254$	7.77680			0.0306173
$255$		0			0
$256$	241.404			0.942983
$257$		−	294.709i		−	1.14673i	−0.819300	−	0.573364i	$-0.805638\pi$
$257$		−	294.709i		−	1.14673i	0.819300	−	0.573364i	$-0.194362\pi$
$258$	−33.6112			−0.130276
$259$		−	435.012i		−	1.67958i
$260$		0			0
$261$			425.373i			1.62978i
$262$			16.9060i			0.0645267i
$263$	−339.127			−1.28946			−0.644728	−	0.764412i	$-0.723029\pi$
$263$	−339.127			−1.28946			−0.644728	+	0.764412i	$0.723029\pi$
$264$	62.0261			0.234948
$265$		0			0
$266$	18.0849	−	2.88196i	0.0679884	−	0.0108344i
$267$	799.939			2.99603
$268$			298.777i			1.11484i
$269$			33.2611i			0.123647i	0.998087	+	0.0618235i	$0.0196916\pi$
$269$			33.2611i			0.123647i	−0.998087	+	0.0618235i	$0.980308\pi$
$270$		0			0
$271$	381.340			1.40716			0.703579	−	0.710618i	$-0.251584\pi$
$271$	381.340			1.40716			0.703579	+	0.710618i	$0.251584\pi$
$272$	211.194			0.776447
$273$	−123.114			−0.450967
$274$		−	15.6602i		−	0.0571538i
$275$		0			0
$276$		−	340.601i		−	1.23406i
$277$	−33.7216			−0.121739			−0.0608694	−	0.998146i	$-0.519387\pi$
$277$	−33.7216			−0.121739			−0.0608694	+	0.998146i	$0.519387\pi$
$278$		−	1.84296i		−	0.00662935i
$279$		−	790.228i		−	2.83236i
$280$		0			0
$281$			209.260i			0.744699i	0.928093	+	0.372349i	$0.121448\pi$
$281$			209.260i			0.744699i	−0.928093	+	0.372349i	$0.878552\pi$
$282$	−28.9916			−0.102807
$283$	341.019			1.20501			0.602506	−	0.798114i	$-0.294169\pi$
$283$	341.019			1.20501			0.602506	+	0.798114i	$0.294169\pi$
$284$		−	308.945i		−	1.08784i
$285$		0			0
$286$	5.78287			0.0202198
$287$		−	302.394i		−	1.05364i
$288$			123.175i			0.427690i
$289$	−108.611			−0.375818
$290$		0			0
$291$	286.829			0.985666
$292$	478.607			1.63906
$293$			409.506i			1.39763i	0.715303	+	0.698815i	$0.246289\pi$
$293$			409.506i			1.39763i	−0.715303	+	0.698815i	$0.753711\pi$
$294$	−6.67038			−0.0226884
$295$		0			0
$296$	−82.8224			−0.279806
$297$		−	412.662i		−	1.38943i
$298$		−	37.4754i		−	0.125756i
$299$		−	63.6940i		−	0.213023i
$300$		0			0
$301$	−275.916			−0.916665
$302$	9.38966			0.0310916
$303$		−	140.136i		−	0.462496i
$304$	47.0170	+	295.042i	0.154661	+	0.970534i
$305$		0			0
$306$			34.7315i			0.113502i
$307$			235.337i			0.766571i	0.923630	+	0.383286i	$0.125207\pi$
$307$			235.337i			0.766571i	−0.923630	+	0.383286i	$0.874793\pi$
$308$	253.854			0.824201
$309$	−103.224			−0.334057
$310$		0			0
$311$	−197.036			−0.633558			−0.316779	−	0.948499i	$-0.602601\pi$
$311$	−197.036			−0.633558			−0.316779	+	0.948499i	$0.602601\pi$
$312$			23.4398i			0.0751276i
$313$	27.8992			0.0891348			0.0445674	−	0.999006i	$-0.485809\pi$
$313$	27.8992			0.0891348			0.0445674	+	0.999006i	$0.485809\pi$
$314$			11.3016i			0.0359924i
$315$		0			0
$316$		−	51.0040i		−	0.161405i
$317$		−	372.696i		−	1.17570i	−0.808971	−	0.587848i	$-0.799975\pi$
$317$		−	372.696i		−	1.17570i	0.808971	−	0.587848i	$-0.200025\pi$
$318$			7.33877i			0.0230779i
$319$		−	250.604i		−	0.785592i
$320$		0			0
$321$	148.194			0.461663
$322$			16.1733i			0.0502278i
$323$	40.1591	+	252.007i	0.124331	+	0.780207i
$324$	223.662			0.690315
$325$		0			0
$326$		−	10.2022i		−	0.0312952i
$327$	−526.073			−1.60879
$328$	−57.5730			−0.175528
$329$	−237.994			−0.723386
$330$		0			0
$331$			3.74805i			0.0113234i	0.999984	+	0.00566170i	$0.00180219\pi$
$331$			3.74805i			0.0113234i	−0.999984	+	0.00566170i	$0.998198\pi$
$332$	432.542			1.30284
$333$			1167.11i			3.50483i
$334$	−25.1268			−0.0752298
$335$		0			0
$336$			510.007i			1.51788i
$337$			410.554i			1.21826i	0.793070	+	0.609131i	$0.208482\pi$
$337$			410.554i			1.21826i	−0.793070	+	0.609131i	$0.791518\pi$
$338$		−	23.4474i		−	0.0693709i
$339$	665.953			1.96446
$340$		0			0
$341$			465.554i			1.36526i
$342$	−48.5206	+	7.73210i	−0.141873	+	0.0226085i
$343$	−366.142			−1.06747
$344$			52.5320i			0.152709i
$345$		0			0
$346$	46.9344			0.135648
$347$	−210.073			−0.605399			−0.302700	−	0.953086i	$-0.597888\pi$
$347$	−210.073			−0.605399			−0.302700	+	0.953086i	$0.597888\pi$
$348$	506.424			1.45524
$349$	−308.461			−0.883843			−0.441921	−	0.897054i	$-0.645703\pi$
$349$	−308.461			−0.883843			−0.441921	+	0.897054i	$0.645703\pi$
$350$		0			0
$351$	155.946			0.444290
$352$		−	72.5670i		−	0.206156i
$353$	−556.817			−1.57739			−0.788693	−	0.614787i	$-0.789242\pi$
$353$	−556.817			−1.57739			−0.788693	+	0.614787i	$0.789242\pi$
$354$			67.8976i			0.191801i
$355$		0			0
$356$		−	623.322i		−	1.75090i
$357$			435.617i			1.22021i
$358$	−32.1400			−0.0897766
$359$	118.795			0.330904			0.165452	−	0.986218i	$-0.447092\pi$
$359$	118.795			0.330904			0.165452	+	0.986218i	$0.447092\pi$
$360$		0			0
$361$	−343.119	+	112.206i	−0.950469	+	0.310821i
$362$	−15.3362			−0.0423652
$363$		−	102.629i		−	0.282724i
$364$			95.9319i			0.263549i
$365$		0			0
$366$	−74.2689			−0.202920
$367$	−378.940			−1.03253			−0.516267	−	0.856428i	$-0.672679\pi$
$367$	−378.940			−1.03253			−0.516267	+	0.856428i	$0.672679\pi$
$368$	−263.856			−0.717001
$369$			811.302i			2.19865i
$370$		0			0
$371$			60.2444i			0.162384i
$372$	−940.798			−2.52903
$373$		−	201.901i		−	0.541290i	−0.962679	−	0.270645i	$-0.912763\pi$
$373$		−	201.901i		−	0.541290i	0.962679	−	0.270645i	$-0.0872369\pi$
$374$		−	20.4616i		−	0.0547103i
$375$		0			0
$376$			45.3120i			0.120511i
$377$	94.7036			0.251203
$378$	−39.5981			−0.104757
$379$			267.286i			0.705241i	0.935766	+	0.352620i	$0.114709\pi$
$379$			267.286i			0.705241i	−0.935766	+	0.352620i	$0.885291\pi$
$380$		0			0
$381$	−261.693			−0.686858
$382$			8.67582i			0.0227116i
$383$			146.990i			0.383785i	0.981416	+	0.191893i	$0.0614626\pi$
$383$			146.990i			0.383785i	−0.981416	+	0.191893i	$0.938537\pi$
$384$	195.335			0.508684
$385$		0			0
$386$	−23.7264			−0.0614672
$387$	740.265			1.91283
$388$		−	223.500i		−	0.576032i
$389$	−187.901			−0.483035			−0.241518	−	0.970396i	$-0.577645\pi$
$389$	−187.901			−0.483035			−0.241518	+	0.970396i	$0.577645\pi$
$390$		0			0
$391$	−225.370			−0.576393
$392$			10.4254i			0.0265953i
$393$		−	568.896i		−	1.44757i
$394$			25.5620i			0.0648783i
$395$		0			0
$396$	−681.073			−1.71988
$397$	−26.5137			−0.0667852			−0.0333926	−	0.999442i	$-0.510631\pi$
$397$	−26.5137			−0.0667852			−0.0333926	+	0.999442i	$0.510631\pi$
$398$		−	6.21419i		−	0.0156136i
$399$	−608.567	+	96.9793i	−1.52523	+	0.243056i
$400$		0			0
$401$		−	38.9717i		−	0.0971864i	−0.998819	−	0.0485932i	$-0.984526\pi$
$401$		−	38.9717i		−	0.0971864i	0.998819	−	0.0485932i	$-0.0154738\pi$
$402$			58.1566i			0.144668i
$403$	−175.934			−0.436560
$404$	−109.196			−0.270287
$405$		0			0
$406$	−24.0474			−0.0592300
$407$		−	687.589i		−	1.68941i
$408$	82.9375			0.203278
$409$		−	111.913i		−	0.273626i	−0.990597	−	0.136813i	$-0.956314\pi$
$409$		−	111.913i		−	0.273626i	0.990597	−	0.136813i	$-0.0436860\pi$
$410$		0			0
$411$			526.972i			1.28217i
$412$			80.4331i			0.195226i
$413$			557.375i			1.34958i
$414$		−	43.3920i		−	0.104812i
$415$		0			0
$416$	27.4232			0.0659211
$417$			62.0165i			0.148721i
$418$	28.5854	−	4.55528i	0.0683861	−	0.0108978i
$419$	207.979			0.496370			0.248185	−	0.968713i	$-0.420166\pi$
$419$	207.979			0.496370			0.248185	+	0.968713i	$0.420166\pi$
$420$		0			0
$421$		−	182.812i		−	0.434232i	−0.976146	−	0.217116i	$-0.930335\pi$
$421$		−	182.812i		−	0.434232i	0.976146	−	0.217116i	$-0.0696650\pi$
$422$	−40.0950			−0.0950118
$423$	638.523			1.50951
$424$	11.4700			0.0270519
$425$		0			0
$426$		−	60.1359i		−	0.141164i
$427$	−609.677			−1.42782
$428$		−	115.474i		−	0.269800i
$429$	−194.596			−0.453605
$430$		0			0
$431$		−	175.672i		−	0.407592i	−0.979013	−	0.203796i	$-0.934672\pi$
$431$		−	175.672i		−	0.407592i	0.979013	−	0.203796i	$-0.0653279\pi$
$432$		−	646.014i		−	1.49540i
$433$		−	343.766i		−	0.793918i	−0.917836	−	0.396959i	$-0.870066\pi$
$433$		−	343.766i		−	0.793918i	0.917836	−	0.396959i	$-0.129934\pi$
$434$	44.6735			0.102934
$435$		0			0
$436$			409.922i			0.940189i
$437$	−50.1730	−	314.847i	−0.114812	−	0.720473i
$438$	93.1603			0.212695
$439$			448.069i			1.02066i	0.859979	+	0.510329i	$0.170476\pi$
$439$			448.069i			1.02066i	−0.859979	+	0.510329i	$0.829524\pi$
$440$		0			0
$441$	146.911			0.333131
$442$	7.73250			0.0174943
$443$	193.700			0.437246			0.218623	−	0.975809i	$-0.429843\pi$
$443$	193.700			0.437246			0.218623	+	0.975809i	$0.429843\pi$
$444$	1389.49			3.12948
$445$		0			0
$446$	33.4678			0.0750400
$447$			1261.07i			2.82118i
$448$	392.739			0.876650
$449$		−	754.877i		−	1.68124i	−0.541625	−	0.840621i	$-0.682191\pi$
$449$		−	754.877i		−	1.68124i	0.541625	−	0.840621i	$-0.317809\pi$
$450$		0			0
$451$		−	477.969i		−	1.05980i
$452$		−	518.919i		−	1.14805i
$453$	−315.967			−0.697498
$454$	−23.6638			−0.0521230
$455$		0			0
$456$	18.4640	+	115.866i	0.0404912	+	0.254091i
$457$	213.763			0.467753			0.233876	−	0.972266i	$-0.424859\pi$
$457$	213.763			0.467753			0.233876	+	0.972266i	$0.424859\pi$
$458$		−	39.3557i		−	0.0859295i
$459$		−	551.786i		−	1.20215i
$460$		0			0
$461$	−660.616			−1.43301			−0.716504	−	0.697583i	$-0.754259\pi$
$461$	−660.616			−1.43301			−0.716504	+	0.697583i	$0.754259\pi$
$462$	49.4124			0.106953
$463$	−481.283			−1.03949			−0.519744	−	0.854322i	$-0.673973\pi$
$463$	−481.283			−1.03949			−0.519744	+	0.854322i	$0.673973\pi$
$464$		−	392.316i		−	0.845508i
$465$		0			0
$466$		−	53.6162i		−	0.115056i
$467$	−420.429			−0.900277			−0.450139	−	0.892959i	$-0.648625\pi$
$467$	−420.429			−0.900277			−0.450139	+	0.892959i	$0.648625\pi$
$468$		−	257.379i		−	0.549955i
$469$			477.411i			1.01793i
$470$		0			0
$471$		−	380.305i		−	0.807441i
$472$	106.119			0.224829
$473$	−436.118			−0.922026
$474$		−	9.92787i		−	0.0209449i
$475$		0			0
$476$	339.438			0.713105
$477$		−	161.632i		−	0.338851i
$478$			26.7433i			0.0559483i
$479$	−124.589			−0.260101			−0.130051	−	0.991507i	$-0.541514\pi$
$479$	−124.589			−0.260101			−0.130051	+	0.991507i	$0.541514\pi$
$480$		0			0
$481$	259.841			0.540210
$482$	−5.37468			−0.0111508
$483$		−	544.241i		−	1.12679i
$484$	−79.9697			−0.165227
$485$		0			0
$486$	−12.5455			−0.0258138
$487$			770.701i			1.58255i	0.611462	+	0.791274i	$0.290582\pi$
$487$			770.701i			1.58255i	−0.611462	+	0.791274i	$0.709418\pi$
$488$			116.077i			0.237863i
$489$			343.311i			0.702067i
$490$		0			0
$491$	54.3027			0.110596			0.0552981	−	0.998470i	$-0.482389\pi$
$491$	54.3027			0.110596			0.0552981	+	0.998470i	$0.482389\pi$
$492$	965.887			1.96318
$493$		−	335.092i		−	0.679700i
$494$	1.72145	+	10.8025i	0.00348471	+	0.0218674i
$495$		0			0
$496$			728.816i			1.46939i
$497$		−	493.659i		−	0.993278i
$498$	84.1938			0.169064
$499$	−192.861			−0.386495			−0.193247	−	0.981150i	$-0.561902\pi$
$499$	−192.861			−0.386495			−0.193247	+	0.981150i	$0.561902\pi$
$500$		0			0
$501$	845.528			1.68768
$502$		−	46.2750i		−	0.0921813i
$503$	−544.862			−1.08322			−0.541612	−	0.840629i	$-0.682186\pi$
$503$	−544.862			−1.08322			−0.541612	+	0.840629i	$0.682186\pi$
$504$			131.087i			0.260093i
$505$		0			0
$506$			25.5639i			0.0505216i
$507$			789.015i			1.55624i
$508$			203.914i			0.401406i
$509$		−	629.472i		−	1.23668i	−0.785909	−	0.618342i	$-0.787805\pi$
$509$		−	629.472i		−	1.23668i	0.785909	−	0.618342i	$-0.212195\pi$
$510$		0			0
$511$	764.758			1.49659
$512$		−	189.702i		−	0.370512i
$513$	770.858	−	122.841i	1.50265	−	0.239457i
$514$	−44.6994			−0.0869638
$515$		0			0
$516$		−	881.314i		−	1.70797i
$517$	−376.178			−0.727618
$518$	−65.9795			−0.127374
$519$	−1579.36			−3.04309
$520$		0			0
$521$		−	535.499i		−	1.02783i	−0.857841	−	0.513915i	$-0.828195\pi$
$521$		−	535.499i		−	1.02783i	0.857841	−	0.513915i	$-0.171805\pi$
$522$	64.5176			0.123597
$523$		−	693.075i		−	1.32519i	−0.748978	−	0.662595i	$-0.769455\pi$
$523$		−	693.075i		−	1.32519i	0.748978	−	0.662595i	$-0.230545\pi$
$524$	−443.290			−0.845974
$525$		0			0
$526$			51.4363i			0.0977877i
$527$			622.510i			1.18123i
$528$			806.127i			1.52676i
$529$	−247.432			−0.467736
$530$		0			0
$531$		−	1495.40i		−	2.81620i
$532$	75.5674	+	474.202i	0.142044	+	0.891358i
$533$	180.626			0.338885
$534$		−	121.329i		−	0.227208i
$535$		0			0
$536$	90.8949			0.169580
$537$	1081.53			2.01402
$538$	5.04480			0.00937695
$539$	−86.5509			−0.160577
$540$		0			0
$541$	217.348			0.401752			0.200876	−	0.979617i	$-0.435621\pi$
$541$	217.348			0.401752			0.200876	+	0.979617i	$0.435621\pi$
$542$		−	57.8389i		−	0.106714i
$543$	516.071			0.950406
$544$		−	97.0321i		−	0.178368i
$545$		0			0
$546$			18.6730i			0.0341997i
$547$		−	288.990i		−	0.528318i	−0.964479	−	0.264159i	$-0.914906\pi$
$547$		−	288.990i		−	0.528318i	0.964479	−	0.264159i	$-0.0850944\pi$
$548$	410.623			0.749312
$549$	1635.72			2.97946
$550$		0			0
$551$	468.131	−	74.5999i	0.849603	−	0.135390i
$552$	−103.619			−0.187715
$553$		−	81.4985i		−	0.147375i
$554$			5.11466i			0.00923223i
$555$		0			0
$556$	48.3240			0.0869137
$557$	−216.252			−0.388245			−0.194122	−	0.980977i	$-0.562186\pi$
$557$	−216.252			−0.388245			−0.194122	+	0.980977i	$0.562186\pi$
$558$	−119.856			−0.214796
$559$		−	164.810i		−	0.294830i
$560$		0			0
$561$			688.545i			1.22735i
$562$	31.7391			0.0564753
$563$			132.093i			0.234624i	0.993095	+	0.117312i	$0.0374277\pi$
$563$			132.093i			0.234624i	−0.993095	+	0.117312i	$0.962572\pi$
$564$		−	760.186i		−	1.34785i
$565$		0			0
$566$		−	51.7233i		−	0.0913839i
$567$	357.386			0.630311
$568$	−93.9883			−0.165472
$569$			540.812i			0.950460i	0.879861	+	0.475230i	$0.157635\pi$
$569$			540.812i			0.950460i	−0.879861	+	0.475230i	$0.842365\pi$
$570$		0			0
$571$	−173.764			−0.304316			−0.152158	−	0.988356i	$-0.548622\pi$
$571$	−173.764			−0.304316			−0.152158	+	0.988356i	$0.548622\pi$
$572$			151.632i			0.265091i
$573$		−	291.945i		−	0.509503i
$574$	−45.8649			−0.0799040
$575$		0			0
$576$	−1053.69			−1.82933
$577$	252.461			0.437541			0.218770	−	0.975776i	$-0.429795\pi$
$577$	252.461			0.437541			0.218770	+	0.975776i	$0.429795\pi$
$578$			16.4734i			0.0285007i
$579$	798.404			1.37894
$580$		0			0
$581$	691.152			1.18959
$582$		−	43.5041i		−	0.0747494i
$583$			95.2235i			0.163334i
$584$		−	145.603i		−	0.249321i
$585$		0			0
$586$	62.1109			0.105991
$587$	378.687			0.645123			0.322562	−	0.946548i	$-0.395456\pi$
$587$	378.687			0.645123			0.322562	+	0.946548i	$0.395456\pi$
$588$		−	174.903i		−	0.297455i
$589$	−869.661	+	138.586i	−1.47650	+	0.235291i
$590$		0			0
$591$		−	860.175i		−	1.45546i
$592$		−	1076.41i		−	1.81826i
$593$	−501.502			−0.845704			−0.422852	−	0.906199i	$-0.638971\pi$
$593$	−501.502			−0.845704			−0.422852	+	0.906199i	$0.638971\pi$
$594$	−62.5896			−0.105370
$595$		0			0
$596$	982.639			1.64872
$597$			209.111i			0.350269i
$598$	−9.66065			−0.0161549
$599$		−	52.0491i		−	0.0868933i	−0.999056	−	0.0434467i	$-0.986166\pi$
$599$		−	52.0491i		−	0.0868933i	0.999056	−	0.0434467i	$-0.0138339\pi$
$600$		0			0
$601$		−	59.3311i		−	0.0987206i	−0.998781	−	0.0493603i	$-0.984282\pi$
$601$		−	59.3311i		−	0.0987206i	0.998781	−	0.0493603i	$-0.0157183\pi$
$602$			41.8490i			0.0695166i
$603$		−	1280.86i		−	2.12415i
$604$			246.205i			0.407624i
$605$		0			0
$606$	−21.2549			−0.0350740
$607$		−	95.8823i		−	0.157961i	−0.996876	−	0.0789805i	$-0.974834\pi$
$607$		−	95.8823i		−	0.157961i	0.996876	−	0.0789805i	$-0.0251665\pi$
$608$	135.556	−	21.6018i	0.222954	−	0.0355293i
$609$	809.207			1.32875
$610$		0			0
$611$		−	142.158i		−	0.232665i
$612$	−910.689			−1.48805
$613$	−740.997			−1.20880			−0.604402	−	0.796679i	$-0.706588\pi$
$613$	−740.997			−1.20880			−0.604402	+	0.796679i	$0.706588\pi$
$614$	35.6943			0.0581340
$615$		0			0
$616$		−	77.2282i		−	0.125370i
$617$	274.604			0.445064			0.222532	−	0.974925i	$-0.428568\pi$
$617$	274.604			0.445064			0.222532	+	0.974925i	$0.428568\pi$
$618$			15.6562i			0.0253337i
$619$	610.524			0.986307			0.493153	−	0.869942i	$-0.335844\pi$
$619$	610.524			0.986307			0.493153	+	0.869942i	$0.335844\pi$
$620$		0			0
$621$			689.378i			1.11011i
$622$			29.8851i			0.0480468i
$623$		−	995.997i		−	1.59871i
$624$	−304.637			−0.488200
$625$		0			0
$626$		−	4.23155i		−	0.00675967i
$627$	−961.913	+	153.287i	−1.53415	+	0.244478i
$628$	−296.338			−0.471876
$629$		−	919.402i		−	1.46169i
$630$		0			0
$631$	−819.064			−1.29804			−0.649021	−	0.760771i	$-0.724821\pi$
$631$	−819.064			−1.29804			−0.649021	+	0.760771i	$0.724821\pi$
$632$	−15.5166			−0.0245516
$633$	1349.22			2.13146
$634$	−56.5278			−0.0891606
$635$		0			0
$636$	−192.429			−0.302561
$637$		−	32.7078i		−	0.0513465i
$638$	−38.0098			−0.0595765
$639$			1324.45i			2.07270i
$640$		0			0
$641$			1110.13i			1.73187i	0.500152	+	0.865937i	$0.333277\pi$
$641$			1110.13i			1.73187i	−0.500152	+	0.865937i	$0.666723\pi$
$642$		−	22.4770i		−	0.0350109i
$643$	346.176			0.538376			0.269188	−	0.963088i	$-0.413245\pi$
$643$	346.176			0.538376			0.269188	+	0.963088i	$0.413245\pi$
$644$	−424.079			−0.658508
$645$		0			0
$646$	38.2226	−	6.09104i	0.0591682	−	0.00942885i
$647$	708.711			1.09538			0.547690	−	0.836681i	$-0.315507\pi$
$647$	708.711			1.09538			0.547690	+	0.836681i	$0.315507\pi$
$648$		−	68.0432i		−	0.105005i
$649$			880.999i			1.35747i
$650$		0			0
$651$	−1503.29			−2.30920
$652$	267.512			0.410294
$653$	628.097			0.961864			0.480932	−	0.876758i	$-0.340298\pi$
$653$	628.097			0.961864			0.480932	+	0.876758i	$0.340298\pi$
$654$			79.7910i			0.122005i
$655$		0			0
$656$		−	748.252i		−	1.14063i
$657$	−2051.80			−3.12298
$658$			36.0972i			0.0548590i
$659$			635.622i			0.964525i	0.876027	+	0.482262i	$0.160185\pi$
$659$			635.622i			0.964525i	−0.876027	+	0.482262i	$0.839815\pi$
$660$		0			0
$661$			435.287i			0.658528i	0.944238	+	0.329264i	$0.106801\pi$
$661$			435.287i			0.658528i	−0.944238	+	0.329264i	$0.893199\pi$
$662$	0.568477			0.000858727
$663$	−260.202			−0.392462
$664$		−	131.589i		−	0.198176i
$665$		0			0
$666$	177.019			0.265794
$667$			418.650i			0.627661i
$668$		−	658.846i		−	0.986296i
$669$	−1126.21			−1.68342
$670$		0			0
$671$	−963.668			−1.43617
$672$	234.321			0.348692
$673$			428.742i			0.637061i	0.947913	+	0.318530i	$0.103189\pi$
$673$			428.742i			0.637061i	−0.947913	+	0.318530i	$0.896811\pi$
$674$	62.2700			0.0923887
$675$		0			0
$676$	614.810			0.909483
$677$			162.012i			0.239309i	0.992816	+	0.119654i	$0.0381786\pi$
$677$			162.012i			0.239309i	−0.992816	+	0.119654i	$0.961821\pi$
$678$		−	101.007i		−	0.148978i
$679$		−	357.128i		−	0.525962i
$680$		0			0
$681$	796.300			1.16931
$682$	70.6119			0.103537
$683$			884.714i			1.29533i	0.761923	+	0.647667i	$0.224255\pi$
$683$			884.714i			1.29533i	−0.761923	+	0.647667i	$0.775745\pi$
$684$	−202.742	−	1272.25i	−0.296407	−	1.86002i
$685$		0			0
$686$			55.5338i			0.0809530i
$687$			1324.34i			1.92771i
$688$	−682.735			−0.992348
$689$	−35.9852			−0.0522281
$690$		0			0
$691$	−1042.25			−1.50832			−0.754160	−	0.656691i	$-0.771956\pi$
$691$	−1042.25			−1.50832			−0.754160	+	0.656691i	$0.771956\pi$
$692$			1230.66i			1.77841i
$693$	−1088.28			−1.57039
$694$			31.8624i			0.0459113i
$695$		0			0
$696$		−	154.066i		−	0.221359i
$697$		−	639.111i		−	0.916946i
$698$			46.7852i			0.0670275i
$699$			1804.21i			2.58113i
$700$		0			0
$701$	−713.782			−1.01823			−0.509117	−	0.860697i	$-0.670028\pi$
$701$	−713.782			−1.01823			−0.509117	+	0.860697i	$0.670028\pi$
$702$		−	23.6527i		−	0.0336933i
$703$	1284.43	−	204.682i	1.82706	−	0.291155i
$704$	620.771			0.881777
$705$		0			0
$706$			84.4541i			0.119623i
$707$	−174.482			−0.246793
$708$	−1780.33			−2.51460
$709$	−227.442			−0.320792			−0.160396	−	0.987053i	$-0.551277\pi$
$709$	−227.442			−0.320792			−0.160396	+	0.987053i	$0.551277\pi$
$710$		0			0
$711$			218.655i			0.307532i
$712$	−189.629			−0.266333
$713$		−	777.738i		−	1.09080i
$714$	66.0712			0.0925367
$715$		0			0
$716$		−	842.739i		−	1.17701i
$717$		−	899.926i		−	1.25513i
$718$		−	18.0179i		−	0.0250946i
$719$	413.703			0.575386			0.287693	−	0.957723i	$-0.407112\pi$
$719$	413.703			0.575386			0.287693	+	0.957723i	$0.407112\pi$
$720$		0			0
$721$			128.523i			0.178256i
$722$	17.0186	+	52.0419i	0.0235715	+	0.0720801i
$723$	180.861			0.250153
$724$		−	402.129i		−	0.555426i
$725$		0			0
$726$	−15.5660			−0.0214408
$727$	297.592			0.409342			0.204671	−	0.978831i	$-0.434388\pi$
$727$	297.592			0.409342			0.204671	+	0.978831i	$0.434388\pi$
$728$	29.1847			0.0400889
$729$	928.313			1.27341
$730$		0			0
$731$	−583.151			−0.797744
$732$		−	1947.39i		−	2.66037i
$733$	772.246			1.05354			0.526771	−	0.850007i	$-0.323403\pi$
$733$	772.246			1.05354			0.526771	+	0.850007i	$0.323403\pi$
$734$			57.4749i			0.0783037i
$735$		0			0
$736$			121.228i			0.164712i
$737$			754.606i			1.02389i
$738$	123.052			0.166738
$739$	1209.35			1.63646			0.818231	−	0.574889i	$-0.194955\pi$
$739$	1209.35			1.63646			0.818231	+	0.574889i	$0.194955\pi$
$740$		0			0
$741$	−57.9276	−	363.509i	−0.0781749	−	0.490565i
$742$	9.13744			0.0123146
$743$		−	62.2804i		−	0.0838229i	−0.999121	−	0.0419114i	$-0.986655\pi$
$743$		−	62.2804i		−	0.0838229i	0.999121	−	0.0419114i	$-0.0133447\pi$
$744$			286.212i			0.384694i
$745$		0			0
$746$	−30.6229			−0.0410495
$747$	−1854.31			−2.48235
$748$	536.522			0.717276
$749$		−	184.515i		−	0.246348i
$750$		0			0
$751$			1440.03i			1.91748i	0.284285	+	0.958740i	$0.408244\pi$
$751$			1440.03i			1.91748i	−0.284285	+	0.958740i	$0.591756\pi$
$752$	−588.900			−0.783112
$753$			1557.18i			2.06796i
$754$		−	14.3640i		−	0.0190504i
$755$		0			0
$756$		−	1038.30i		−	1.37341i
$757$	513.483			0.678313			0.339157	−	0.940730i	$-0.389858\pi$
$757$	513.483			0.678313			0.339157	+	0.940730i	$0.389858\pi$
$758$	40.5401			0.0534829
$759$		−	860.238i		−	1.13338i
$760$		0			0
$761$	134.340			0.176531			0.0882654	−	0.996097i	$-0.471868\pi$
$761$	134.340			0.176531			0.0882654	+	0.996097i	$0.471868\pi$
$762$			39.6917i			0.0520889i
$763$			655.009i			0.858465i
$764$	−227.487			−0.297758
$765$		0			0
$766$	22.2944			0.0291049
$767$	−332.931			−0.434069
$768$			1232.09i			1.60429i
$769$	−103.497			−0.134586			−0.0672932	−	0.997733i	$-0.521436\pi$
$769$	−103.497			−0.134586			−0.0672932	+	0.997733i	$0.521436\pi$
$770$		0			0
$771$	1504.16			1.95092
$772$		−	622.126i		−	0.805862i
$773$			1361.14i			1.76086i	0.474177	+	0.880429i	$0.342746\pi$
$773$			1361.14i			1.76086i	−0.474177	+	0.880429i	$0.657254\pi$
$774$		−	112.278i		−	0.145062i
$775$		0			0
$776$	−67.9940			−0.0876211
$777$	2220.24			2.85746
$778$			28.4994i			0.0366317i
$779$	892.853	−	142.282i	1.14615	−	0.182647i
$780$		0			0
$781$		−	780.288i		−	0.999088i
$782$			34.1825i			0.0437116i
$783$	−1025.00			−1.30907
$784$	−135.494			−0.172824
$785$		0			0
$786$	−86.2860			−0.109779
$787$		−	945.437i		−	1.20132i	−0.799506	−	0.600659i	$-0.794905\pi$
$787$		−	945.437i		−	1.20132i	0.799506	−	0.600659i	$-0.205095\pi$
$788$	−670.259			−0.850582
$789$		−	1730.86i		−	2.19374i
$790$		0			0
$791$		−	829.173i		−	1.04826i
$792$			207.198i			0.261614i
$793$		−	364.172i		−	0.459233i
$794$			4.02141i			0.00506475i
$795$		0			0
$796$	162.942			0.204701
$797$			642.975i			0.806745i	0.915036	+	0.403372i	$0.132162\pi$
$797$			642.975i			0.806745i	−0.915036	+	0.403372i	$0.867838\pi$
$798$	14.7091	+	92.3030i	0.0184325	+	0.115668i
$799$	−503.002			−0.629540
$800$		0			0
$801$			2672.19i			3.33607i
$802$	−5.91095			−0.00737027
$803$	1208.79			1.50535
$804$	−1524.92			−1.89666
$805$		0			0
$806$			26.6844i			0.0331072i
$807$	−169.760			−0.210359
$808$			33.2199i			0.0411137i
$809$	−1206.61			−1.49148			−0.745740	−	0.666238i	$-0.767904\pi$
$809$	−1206.61			−1.49148			−0.745740	+	0.666238i	$0.767904\pi$
$810$		0			0
$811$		−	1322.86i		−	1.63115i	−0.578651	−	0.815575i	$-0.696421\pi$
$811$		−	1322.86i		−	1.63115i	0.578651	−	0.815575i	$-0.303579\pi$
$812$		−	630.544i		−	0.776532i
$813$			1946.31i			2.39398i
$814$	−104.289			−0.128119
$815$		0			0
$816$			1077.90i			1.32096i
$817$	−129.824	−	814.675i	−0.158903	−	0.997154i
$818$	−16.9742			−0.0207508
$819$		−	411.262i		−	0.502151i
$820$		0			0
$821$	−288.808			−0.351776			−0.175888	−	0.984410i	$-0.556280\pi$
$821$	−288.808			−0.351776			−0.175888	+	0.984410i	$0.556280\pi$
$822$	79.9273			0.0972352
$823$	−1068.46			−1.29825			−0.649123	−	0.760684i	$-0.724864\pi$
$823$	−1068.46			−1.29825			−0.649123	+	0.760684i	$0.724864\pi$
$824$	24.4696			0.0296961
$825$		0			0
$826$	84.5387			0.102347
$827$		−	393.538i		−	0.475862i	−0.971282	−	0.237931i	$-0.923531\pi$
$827$		−	393.538i		−	0.475862i	0.971282	−	0.237931i	$-0.0764692\pi$
$828$	1137.78			1.37413
$829$			814.069i			0.981989i	0.871163	+	0.490995i	$0.163367\pi$
$829$			814.069i			0.981989i	−0.871163	+	0.490995i	$0.836633\pi$
$830$		0			0
$831$		−	172.111i		−	0.207113i
$832$			234.591i			0.281960i
$833$	−115.731			−0.138932
$834$	9.40622			0.0112784
$835$		0			0
$836$	119.443	+	749.534i	0.142875	+	0.896572i
$837$	1904.18			2.27501
$838$		−	31.5447i		−	0.0376429i
$839$		−	219.914i		−	0.262115i	−0.991375	−	0.131057i	$-0.958163\pi$
$839$		−	219.914i		−	0.262115i	0.991375	−	0.131057i	$-0.0418372\pi$
$840$		0			0
$841$	218.529			0.259845
$842$	−27.7276			−0.0329306
$843$	−1068.04			−1.26695
$844$		−	1051.32i		−	1.24565i
$845$		0			0
$846$		−	96.8465i		−	0.114476i
$847$	−127.782			−0.150865
$848$			149.071i			0.175791i
$849$			1740.51i			2.05008i
$850$		0			0
$851$			1148.66i			1.34978i
$852$	1576.82			1.85072
$853$	−719.082			−0.843003			−0.421502	−	0.906828i	$-0.638497\pi$
$853$	−719.082			−0.843003			−0.421502	+	0.906828i	$0.638497\pi$
$854$			92.4715i			0.108280i
$855$		0			0
$856$	−35.1300			−0.0410397
$857$		−	153.486i		−	0.179097i	−0.995982	−	0.0895485i	$-0.971458\pi$
$857$		−	153.486i		−	0.179097i	0.995982	−	0.0895485i	$-0.0285424\pi$
$858$			29.5150i			0.0343998i
$859$	914.298			1.06438			0.532188	−	0.846627i	$-0.321370\pi$
$859$	914.298			1.06438			0.532188	+	0.846627i	$0.321370\pi$
$860$		0			0
$861$	1543.38			1.79254
$862$	−26.6447			−0.0309103
$863$		−	1647.58i		−	1.90914i	−0.297992	−	0.954568i	$-0.596317\pi$
$863$		−	1647.58i		−	1.90914i	0.297992	−	0.954568i	$-0.403683\pi$
$864$	−296.809			−0.343529
$865$		0			0
$866$	−52.1400			−0.0602079
$867$		−	554.338i		−	0.639375i
$868$			1171.38i			1.34952i
$869$		−	128.818i		−	0.148237i
$870$		0			0
$871$	−285.167			−0.327402
$872$	124.708			0.143014
$873$			958.151i			1.09754i
$874$	−47.7537	+	7.60989i	−0.0546381	+	0.00870696i
$875$		0			0
$876$			2442.74i			2.78852i
$877$			819.184i			0.934076i	0.884237	+	0.467038i	$0.154679\pi$
$877$			819.184i			0.934076i	−0.884237	+	0.467038i	$0.845321\pi$
$878$	67.9599			0.0774031
$879$	−2090.06			−2.37777
$880$		0			0
$881$	899.647			1.02117			0.510583	−	0.859829i	$-0.329430\pi$
$881$	899.647			1.02117			0.510583	+	0.859829i	$0.329430\pi$
$882$		−	22.2824i		−	0.0252635i
$883$	1007.40			1.14088			0.570442	−	0.821338i	$-0.306772\pi$
$883$	1007.40			1.14088			0.570442	+	0.821338i	$0.306772\pi$
$884$			202.753i			0.229358i
$885$		0			0
$886$		−	29.3790i		−	0.0331592i
$887$		−	668.366i		−	0.753513i	−0.926312	−	0.376756i	$-0.877039\pi$
$887$		−	668.366i		−	0.753513i	0.926312	−	0.376756i	$-0.122961\pi$
$888$		−	422.715i		−	0.476030i
$889$			325.832i			0.366515i
$890$		0			0
$891$	564.892			0.633998
$892$			877.556i			0.983807i
$893$	−111.981	−	702.706i	−0.125399	−	0.786905i
$894$	191.270			0.213948
$895$		0			0
$896$		−	243.210i		−	0.271439i
$897$	325.086			0.362414
$898$	−114.494			−0.127499
$899$	1156.38			1.28630
$900$		0			0
$901$			127.327i			0.141317i
$902$	−72.4950			−0.0803714
$903$		−	1408.24i		−	1.55951i
$904$	−157.867			−0.174632
$905$		0			0
$906$			47.9236i			0.0528958i
$907$			1186.27i			1.30791i	0.756534	+	0.653954i	$0.226891\pi$
$907$			1186.27i			1.30791i	−0.756534	+	0.653954i	$0.773109\pi$
$908$		−	620.486i		−	0.683355i
$909$	468.125			0.514989
$910$		0			0
$911$			526.830i			0.578298i	0.957284	+	0.289149i	$0.0933724\pi$
$911$			526.830i			0.578298i	−0.957284	+	0.289149i	$0.906628\pi$
$912$	−1505.86	+	239.969i	−1.65116	+	0.263123i
$913$	1092.45			1.19655
$914$		−	32.4220i		−	0.0354727i
$915$		0			0
$916$	1031.94			1.12657
$917$	−708.327			−0.772439
$918$	−83.6910			−0.0911666
$919$	959.827			1.04443			0.522213	−	0.852815i	$-0.325107\pi$
$919$	959.827			1.04443			0.522213	+	0.852815i	$0.325107\pi$
$920$		0			0
$921$	−1201.13			−1.30416
$922$			100.198i			0.108674i
$923$	294.872			0.319471
$924$			1295.64i			1.40220i
$925$		0			0
$926$			72.9975i			0.0788310i
$927$		−	344.818i		−	0.371972i
$928$	−180.248			−0.194233
$929$	−288.443			−0.310488			−0.155244	−	0.987876i	$-0.549616\pi$
$929$	−288.443			−0.310488			−0.155244	+	0.987876i	$0.549616\pi$
$930$		0			0
$931$	−25.7645	−	161.678i	−0.0276740	−	0.173661i
$932$	1405.86			1.50844
$933$		−	1005.65i		−	1.07786i
$934$			63.7677i			0.0682738i
$935$		0			0
$936$	−78.3006			−0.0836545
$937$	−1072.58			−1.14470			−0.572350	−	0.820009i	$-0.693968\pi$
$937$	−1072.58			−1.14470			−0.572350	+	0.820009i	$0.693968\pi$
$938$	72.4103			0.0771965
$939$			142.394i			0.151644i
$940$		0			0
$941$			250.856i			0.266585i	0.991077	+	0.133293i	$0.0425550\pi$
$941$			250.856i			0.266585i	−0.991077	+	0.133293i	$0.957445\pi$
$942$	−57.6819			−0.0612334
$943$			798.478i			0.846743i
$944$			1379.19i			1.46100i
$945$		0			0
$946$			66.1473i			0.0699232i
$947$	346.018			0.365383			0.182692	−	0.983170i	$-0.441519\pi$
$947$	346.018			0.365383			0.182692	+	0.983170i	$0.441519\pi$
$948$	260.318			0.274597
$949$			456.805i			0.481354i
$950$		0			0
$951$	1902.19			2.00020
$952$		−	103.265i		−	0.108471i
$953$			1194.91i			1.25384i	0.779084	+	0.626920i	$0.215685\pi$
$953$			1194.91i			1.25384i	−0.779084	+	0.626920i	$0.784315\pi$
$954$	−24.5152			−0.0256972
$955$		0			0
$956$	−701.233			−0.733507
$957$	1279.05			1.33652
$958$			18.8967i			0.0197252i
$959$	656.128			0.684180
$960$		0			0
$961$	−1187.24			−1.23543
$962$		−	39.4109i		−	0.0409676i
$963$			495.042i			0.514062i
$964$		−	140.929i		−	0.146192i
$965$		0			0
$966$	−82.5466			−0.0854520
$967$	−1235.74			−1.27791			−0.638955	−	0.769244i	$-0.720633\pi$
$967$	−1235.74			−1.27791			−0.638955	+	0.769244i	$0.720633\pi$
$968$			24.3286i			0.0251329i
$969$	−1286.21	+	204.966i	−1.32736	+	0.211524i
$970$		0			0
$971$		−	882.995i		−	0.909367i	−0.890653	−	0.454683i	$-0.849752\pi$
$971$		−	882.995i		−	0.909367i	0.890653	−	0.454683i	$-0.150248\pi$
$972$		−	328.954i		−	0.338430i
$973$	77.2162			0.0793589
$974$	116.894			0.120015
$975$		0			0
$976$	−1508.61			−1.54570
$977$		−	254.773i		−	0.260771i	−0.991463	−	0.130385i	$-0.958379\pi$
$977$		−	254.773i		−	0.260771i	0.991463	−	0.130385i	$-0.0416214\pi$
$978$	52.0709			0.0532422
$979$		−	1574.29i		−	1.60806i
$980$		0			0
$981$		−	1757.35i		−	1.79138i
$982$		−	8.23625i		−	0.00838722i
$983$			966.862i			0.983583i	0.870713	+	0.491791i	$0.163658\pi$
$983$			966.862i			0.983583i	−0.870713	+	0.491791i	$0.836342\pi$
$984$		−	293.845i		−	0.298623i
$985$		0			0
$986$	−50.8244			−0.0515460
$987$		−	1214.69i		−	1.23069i
$988$	−283.250	+	45.1379i	−0.286691	+	0.0456861i
$989$	728.564			0.736667
$990$		0			0
$991$		−	1440.50i		−	1.45358i	−0.686857	−	0.726792i	$-0.741010\pi$
$991$		−	1440.50i		−	1.45358i	0.686857	−	0.726792i	$-0.258990\pi$
$992$	334.852			0.337552
$993$	−19.1295			−0.0192644
$994$	−74.8747			−0.0753267
$995$		0			0
$996$			2207.64i			2.21650i
$997$	1340.38			1.34441			0.672207	−	0.740363i	$-0.265346\pi$
$997$	1340.38			1.34441			0.672207	+	0.740363i	$0.265346\pi$
$998$			29.2518i			0.0293104i
$999$	−2812.33			−2.81515

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.c.g.151.6		12
5.2	odd	4		475.3.d.c.474.14		24
5.3	odd	4		475.3.d.c.474.11		24
5.4	even	2		95.3.c.a.56.7	yes	12
15.14	odd	2		855.3.e.a.721.6		12
19.18	odd	2	inner	475.3.c.g.151.7		12
20.19	odd	2		1520.3.h.a.721.12		12
95.18	even	4		475.3.d.c.474.13		24
95.37	even	4		475.3.d.c.474.12		24
95.94	odd	2		95.3.c.a.56.6	✓	12
285.284	even	2		855.3.e.a.721.7		12
380.379	even	2		1520.3.h.a.721.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.c.a.56.6	✓	12	95.94	odd	2
95.3.c.a.56.7	yes	12	5.4	even	2
475.3.c.g.151.6		12	1.1	even	1	trivial
475.3.c.g.151.7		12	19.18	odd	2	inner
475.3.d.c.474.11		24	5.3	odd	4
475.3.d.c.474.12		24	95.37	even	4
475.3.d.c.474.13		24	95.18	even	4
475.3.d.c.474.14		24	5.2	odd	4
855.3.e.a.721.6		12	15.14	odd	2
855.3.e.a.721.7		12	285.284	even	2
1520.3.h.a.721.1		12	380.379	even	2
1520.3.h.a.721.12		12	20.19	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.151673i q^{2} +5.10387i q^{3} +3.97700 q^{4} +0.774118 q^{6} +6.35478 q^{7} -1.20989i q^{8} -17.0495 q^{9} +O(q^{10})\)	\(q-0.151673i q^{2} +5.10387i q^{3} +3.97700 q^{4} +0.774118 q^{6} +6.35478 q^{7} -1.20989i q^{8} -17.0495 q^{9} +10.0445 q^{11} +20.2981i q^{12} +3.79583i q^{13} -0.963848i q^{14} +15.7245 q^{16} +13.4309 q^{17} +2.58594i q^{18} +(2.99005 + 18.7633i) q^{19} +32.4340i q^{21} -1.52348i q^{22} -16.7800 q^{23} +6.17514 q^{24} +0.575725 q^{26} -41.0834i q^{27} +25.2729 q^{28} -24.9494i q^{29} +46.3492i q^{31} -7.22455i q^{32} +51.2658i q^{33} -2.03710i q^{34} -67.8056 q^{36} -68.4543i q^{37} +(2.84588 - 0.453510i) q^{38} -19.3734 q^{39} -47.5852i q^{41} +4.91935 q^{42} -43.4186 q^{43} +39.9469 q^{44} +2.54507i q^{46} -37.4512 q^{47} +80.2556i q^{48} -8.61675 q^{49} +68.5494i q^{51} +15.0960i q^{52} +9.48017i q^{53} -6.23123 q^{54} -7.68861i q^{56} +(-95.7651 + 15.2608i) q^{57} -3.78414 q^{58} +87.7096i q^{59} -95.9399 q^{61} +7.02991 q^{62} -108.346 q^{63} +61.8021 q^{64} +7.77563 q^{66} +75.1263i q^{67} +53.4146 q^{68} -85.6428i q^{69} -77.6831i q^{71} +20.6280i q^{72} +120.344 q^{73} -10.3827 q^{74} +(11.8914 + 74.6214i) q^{76} +63.8306 q^{77} +2.93842i q^{78} -12.8248i q^{79} +56.2390 q^{81} -7.21738 q^{82} +108.761 q^{83} +128.990i q^{84} +6.58543i q^{86} +127.338 q^{87} -12.1528i q^{88} -156.732i q^{89} +24.1217i q^{91} -66.7339 q^{92} -236.560 q^{93} +5.68033i q^{94} +36.8731 q^{96} -56.1983i q^{97} +1.30693i q^{98} -171.253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9}+O(q^{10}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9	\( 12 q - 12 q^{4} - 28 q^{6} - 20 q^{7} - 48 q^{9} + 32 q^{11} - 44 q^{16} + 44 q^{17} + 8 q^{19} - 36 q^{23} + 100 q^{24} + 108 q^{26} + 36 q^{28} - 80 q^{36} + 44 q^{38} + 76 q^{39} - 100 q^{42} - 320 q^{43} - 256 q^{44} + 56 q^{47} + 72 q^{49} - 76 q^{54} - 60 q^{57} - 68 q^{58} - 296 q^{61} + 376 q^{62} + 96 q^{63} + 188 q^{64} + 152 q^{66} + 340 q^{68} + 244 q^{73} + 136 q^{74} + 248 q^{76} + 200 q^{77} - 372 q^{81} - 424 q^{82} + 160 q^{83} - 444 q^{87} - 716 q^{92} - 296 q^{93} - 44 q^{96} - 312 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 28 * q^6 - 20 * q^7 - 48 * q^9 + 32 * q^11 - 44 * q^16 + 44 * q^17 + 8 * q^19 - 36 * q^23 + 100 * q^24 + 108 * q^26 + 36 * q^28 - 80 * q^36 + 44 * q^38 + 76 * q^39 - 100 * q^42 - 320 * q^43 - 256 * q^44 + 56 * q^47 + 72 * q^49 - 76 * q^54 - 60 * q^57 - 68 * q^58 - 296 * q^61 + 376 * q^62 + 96 * q^63 + 188 * q^64 + 152 * q^66 + 340 * q^68 + 244 * q^73 + 136 * q^74 + 248 * q^76 + 200 * q^77 - 372 * q^81 - 424 * q^82 + 160 * q^83 - 444 * q^87 - 716 * q^92 - 296 * q^93 - 44 * q^96 - 312 * q^99

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