LMFDB - Embedded newform 475.3.d.c.474.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(474,475)]

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([1, 1]))

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

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

chi := DirichletCharacter("475.474");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.d (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:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			474.13
Character	$\chi$	$=$	475.474
Dual form			475.3.d.c.474.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.151673 q^{2} +5.10387 q^{3} -3.97700 q^{4} +0.774118 q^{6} -6.35478i q^{7} -1.20989 q^{8} +17.0495 q^{9} +O(q^{10})$	\(q+0.151673 q^{2} +5.10387 q^{3} -3.97700 q^{4} +0.774118 q^{6} -6.35478i q^{7} -1.20989 q^{8} +17.0495 q^{9} +10.0445 q^{11} -20.2981 q^{12} +3.79583 q^{13} -0.963848i q^{14} +15.7245 q^{16} -13.4309i q^{17} +2.58594 q^{18} +(-2.99005 + 18.7633i) q^{19} -32.4340i q^{21} +1.52348 q^{22} -16.7800i q^{23} -6.17514 q^{24} +0.575725 q^{26} +41.0834 q^{27} +25.2729i q^{28} -24.9494i q^{29} -46.3492i q^{31} +7.22455 q^{32} +51.2658 q^{33} -2.03710i q^{34} -67.8056 q^{36} +68.4543 q^{37} +(-0.453510 + 2.84588i) q^{38} +19.3734 q^{39} +47.5852i q^{41} -4.91935i q^{42} -43.4186i q^{43} -39.9469 q^{44} -2.54507i q^{46} +37.4512i q^{47} +80.2556 q^{48} +8.61675 q^{49} -68.5494i q^{51} -15.0960 q^{52} +9.48017 q^{53} +6.23123 q^{54} +7.68861i q^{56} +(-15.2608 + 95.7651i) q^{57} -3.78414i q^{58} +87.7096i q^{59} -95.9399 q^{61} -7.02991i q^{62} -108.346i q^{63} -61.8021 q^{64} +7.77563 q^{66} -75.1263 q^{67} +53.4146i q^{68} -85.6428i q^{69} +77.6831i q^{71} -20.6280 q^{72} +120.344i q^{73} +10.3827 q^{74} +(11.8914 - 74.6214i) q^{76} -63.8306i q^{77} +2.93842 q^{78} -12.8248i q^{79} +56.2390 q^{81} +7.21738i q^{82} +108.761i q^{83} +128.990i q^{84} -6.58543i q^{86} -127.338i q^{87} -12.1528 q^{88} -156.732i q^{89} -24.1217i q^{91} +66.7339i q^{92} -236.560i q^{93} +5.68033i q^{94} +36.8731 q^{96} +56.1983 q^{97} +1.30693 q^{98} +171.253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9	$ 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9} + 64 q^{11} - 88 q^{16} - 16 q^{19} - 200 q^{24} + 216 q^{26} - 160 q^{36} - 152 q^{39} + 512 q^{44} - 144 q^{49} + 152 q^{54} - 592 q^{61} - 376 q^{64} + 304 q^{66} - 272 q^{74} + 496 q^{76} - 744 q^{81} - 88 q^{96} + 624 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9 + 64 * q^11 - 88 * q^16 - 16 * q^19 - 200 * q^24 + 216 * q^26 - 160 * q^36 - 152 * q^39 + 512 * q^44 - 144 * q^49 + 152 * q^54 - 592 * q^61 - 376 * q^64 + 304 * q^66 - 272 * q^74 + 496 * q^76 - 744 * q^81 - 88 * q^96 + 624 * 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 $

$2$	0.151673			0.0758364			0.0379182	−	0.999281i	$-0.487927\pi$
$2$	0.151673			0.0758364			0.0379182	+	0.999281i	$0.487927\pi$
$3$	5.10387			1.70129			0.850645	−	0.525741i	$-0.176212\pi$
$3$	5.10387			1.70129			0.850645	+	0.525741i	$0.176212\pi$
$4$	−3.97700			−0.994249
$5$		0			0
$5$		0			0
$6$	0.774118			0.129020
$7$		−	6.35478i		−	0.907826i	−0.891046	−	0.453913i	$-0.850028\pi$
$7$		−	6.35478i		−	0.907826i	0.891046	−	0.453913i	$-0.149972\pi$
$8$	−1.20989			−0.151237
$9$	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	$0.349078\pi$
$12$	−20.2981			−1.69150
$13$	3.79583			0.291987			0.145994	−	0.989286i	$-0.453362\pi$
$13$	3.79583			0.291987			0.145994	+	0.989286i	$0.453362\pi$
$14$		−	0.963848i		−	0.0688463i
$15$		0			0
$16$	15.7245			0.982780
$17$		−	13.4309i		−	0.790052i	−0.918670	−	0.395026i	$-0.870736\pi$
$17$		−	13.4309i		−	0.790052i	0.918670	−	0.395026i	$-0.129264\pi$
$18$	2.58594			0.143663
$19$	−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
$22$	1.52348			0.0692490
$23$		−	16.7800i		−	0.729564i	−0.931093	−	0.364782i	$-0.881144\pi$
$23$		−	16.7800i		−	0.729564i	0.931093	−	0.364782i	$-0.118856\pi$
$24$	−6.17514			−0.257297
$25$		0			0
$26$	0.575725			0.0221433
$27$	41.0834			1.52161
$28$			25.2729i			0.902605i
$29$		−	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	$-0.731222\pi$
$31$		−	46.3492i		−	1.49513i	0.664186	−	0.747567i	$-0.268778\pi$
$32$	7.22455			0.225767
$33$	51.2658			1.55351
$34$		−	2.03710i		−	0.0599147i
$35$		0			0
$36$	−67.8056			−1.88349
$37$	68.4543			1.85012			0.925058	−	0.379825i	$-0.124016\pi$
$37$	68.4543			1.85012			0.925058	+	0.379825i	$0.124016\pi$
$38$	−0.453510	+	2.84588i	−0.0119345	+	0.0748915i
$39$	19.3734			0.496755
$40$		0			0
$41$			47.5852i			1.16061i	0.814398	+	0.580307i	$0.197068\pi$
$41$			47.5852i			1.16061i	−0.814398	+	0.580307i	$0.802932\pi$
$42$		−	4.91935i		−	0.117127i
$43$		−	43.4186i		−	1.00974i	−0.863197	−	0.504868i	$-0.831541\pi$
$43$		−	43.4186i		−	1.00974i	0.863197	−	0.504868i	$-0.168459\pi$
$44$	−39.9469			−0.907884
$45$		0			0
$46$		−	2.54507i		−	0.0553275i
$47$			37.4512i			0.796834i	0.917204	+	0.398417i	$0.130440\pi$
$47$			37.4512i			0.796834i	−0.917204	+	0.398417i	$0.869560\pi$
$48$	80.2556			1.67199
$49$	8.61675			0.175852
$50$		0			0
$51$		−	68.5494i		−	1.34411i
$52$	−15.0960			−0.290308
$53$	9.48017			0.178871			0.0894356	−	0.995993i	$-0.471494\pi$
$53$	9.48017			0.178871			0.0894356	+	0.995993i	$0.471494\pi$
$54$	6.23123			0.115393
$55$		0			0
$56$			7.68861i			0.137297i
$57$	−15.2608	+	95.7651i	−0.267734	+	1.68009i
$58$		−	3.78414i		−	0.0652438i
$59$			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	$0.788054\pi$
$62$		−	7.02991i		−	0.113386i
$63$		−	108.346i		−	1.71977i
$64$	−61.8021			−0.965658
$65$		0			0
$66$	7.77563			0.117813
$67$	−75.1263			−1.12129			−0.560644	−	0.828057i	$-0.689446\pi$
$67$	−75.1263			−1.12129			−0.560644	+	0.828057i	$0.689446\pi$
$68$			53.4146i			0.785508i
$69$		−	85.6428i		−	1.24120i
$70$		0			0
$71$			77.6831i			1.09413i	0.837091	+	0.547064i	$0.184255\pi$
$71$			77.6831i			1.09413i	−0.837091	+	0.547064i	$0.815745\pi$
$72$	−20.6280			−0.286500
$73$			120.344i			1.64854i	0.566193	+	0.824272i	$0.308416\pi$
$73$			120.344i			1.64854i	−0.566193	+	0.824272i	$0.691584\pi$
$74$	10.3827			0.140306
$75$		0			0
$76$	11.8914	−	74.6214i	0.156466	−	0.981860i
$77$		−	63.8306i		−	0.828969i
$78$	2.93842			0.0376721
$79$		−	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
$82$			7.21738i			0.0880169i
$83$			108.761i			1.31037i	0.755467	+	0.655186i	$0.227410\pi$
$83$			108.761i			1.31037i	−0.755467	+	0.655186i	$0.772590\pi$
$84$			128.990i			1.53559i
$85$		0			0
$86$		−	6.58543i		−	0.0765748i
$87$		−	127.338i		−	1.46366i
$88$	−12.1528			−0.138100
$89$		−	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
$92$			66.7339i			0.725368i
$93$		−	236.560i		−	2.54366i
$94$			5.68033i			0.0604290i
$95$		0			0
$96$	36.8731			0.384095
$97$	56.1983			0.579364			0.289682	−	0.957123i	$-0.406450\pi$
$97$	56.1983			0.579364			0.289682	+	0.957123i	$0.406450\pi$
$98$	1.30693			0.0133360
$99$	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	$0.543401\pi$
$102$		−	10.3971i		−	0.101932i
$103$	20.2246			0.196355			0.0981777	−	0.995169i	$-0.468699\pi$
$103$	20.2246			0.196355			0.0981777	+	0.995169i	$0.468699\pi$
$104$	−4.59256			−0.0441592
$105$		0			0
$106$	1.43788			0.0135649
$107$	29.0356			0.271361			0.135680	−	0.990753i	$-0.456678\pi$
$107$	29.0356			0.271361			0.135680	+	0.990753i	$0.456678\pi$
$108$	−163.388			−1.51286
$109$			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
$112$		−	99.9256i		−	0.892193i
$113$	−130.480			−1.15469			−0.577346	−	0.816500i	$-0.695912\pi$
$113$	−130.480			−1.15469			−0.577346	+	0.816500i	$0.695912\pi$
$114$	−2.31465	+	14.5250i	−0.0203040	+	0.127412i
$115$		0			0
$116$			99.2235i			0.855375i
$117$	64.7169			0.553136
$118$			13.3032i			0.112739i
$119$	−85.3503			−0.717230
$120$		0			0
$121$	−20.1081			−0.166182
$122$	−14.5515			−0.119274
$123$			242.868i			1.97454i
$124$			184.330i			1.48654i
$125$		0			0
$126$		−	16.4331i		−	0.130421i
$127$	−51.2735			−0.403728			−0.201864	−	0.979414i	$-0.564700\pi$
$127$	−51.2735			−0.403728			−0.201864	+	0.979414i	$0.564700\pi$
$128$	−38.2719			−0.298999
$129$		−	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	$0.639878\pi$
$132$	−203.884			−1.54457
$133$	119.236	+	19.0011i	0.896514	+	0.142866i
$134$	−11.3946			−0.0850345
$135$		0			0
$136$			16.2499i			0.119485i
$137$		−	103.250i		−	0.753646i	−0.926285	−	0.376823i	$-0.877016\pi$
$137$		−	103.250i		−	0.753646i	0.926285	−	0.376823i	$-0.122984\pi$
$138$		−	12.9897i		−	0.0941281i
$139$	−12.1509			−0.0874164			−0.0437082	−	0.999044i	$-0.513917\pi$
$139$	−12.1509			−0.0874164			−0.0437082	+	0.999044i	$0.513917\pi$
$140$		0			0
$141$			191.146i			1.35564i
$142$			11.7824i			0.0829748i
$143$	38.1272			0.266624
$144$	268.094			1.86176
$145$		0			0
$146$			18.2529i			0.125020i
$147$	43.9787			0.299175
$148$	−272.242			−1.83948
$149$	−247.081			−1.65826			−0.829130	−	0.559056i	$-0.811164\pi$
$149$	−247.081			−1.65826			−0.829130	+	0.559056i	$0.811164\pi$
$150$		0			0
$151$		−	61.9073i		−	0.409982i	−0.978764	−	0.204991i	$-0.934283\pi$
$151$		−	61.9073i		−	0.409982i	0.978764	−	0.204991i	$-0.0657165\pi$
$152$	3.61765	−	22.7015i	0.0238003	−	0.149352i
$153$		−	228.989i		−	1.49666i
$154$		−	9.68137i		−	0.0628660i
$155$		0			0
$156$	−77.0481			−0.493898
$157$			74.5130i			0.474605i	0.971436	+	0.237303i	$0.0762633\pi$
$157$			74.5130i			0.474605i	−0.971436	+	0.237303i	$0.923737\pi$
$158$		−	1.94517i		−	0.0123112i
$159$	48.3855			0.304311
$160$		0			0
$161$	−106.633			−0.662317
$162$	8.52992			0.0526538
$163$			67.2648i			0.412667i	0.978482	+	0.206334i	$0.0661532\pi$
$163$			67.2648i			0.412667i	−0.978482	+	0.206334i	$0.933847\pi$
$164$		−	189.246i		−	1.15394i
$165$		0			0
$166$			16.4961i			0.0993740i
$167$	165.664			0.992001			0.496001	−	0.868322i	$-0.334801\pi$
$167$	165.664			0.992001			0.496001	+	0.868322i	$0.334801\pi$
$168$			39.2416i			0.233581i
$169$	−154.592			−0.914743
$170$		0			0
$171$	−50.9788	+	319.903i	−0.298122	+	1.87078i
$172$			172.676i			1.00393i
$173$	309.445			1.78870			0.894349	−	0.447370i	$-0.147639\pi$
$173$	309.445			1.78870			0.894349	+	0.447370i	$0.147639\pi$
$174$		−	19.3138i		−	0.110999i
$175$		0			0
$176$	157.944			0.897411
$177$			447.658i			2.52914i
$178$		−	23.7720i		−	0.133550i
$179$		−	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	$0.0901089\pi$
$181$			101.114i			0.558639i	−0.960198	+	0.279319i	$0.909891\pi$
$182$		−	3.65861i		−	0.0201022i
$183$	−489.665			−2.67576
$184$			20.3020i			0.110337i
$185$		0			0
$186$		−	35.8797i		−	0.192902i
$187$		−	134.906i		−	0.721425i
$188$		−	148.943i		−	0.792251i
$189$		−	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	$0.547844\pi$
$192$	−315.430			−1.64286
$193$	−156.431			−0.810524			−0.405262	−	0.914201i	$-0.632820\pi$
$193$	−156.431			−0.810524			−0.405262	+	0.914201i	$0.632820\pi$
$194$	8.52376			0.0439369
$195$		0			0
$196$	−34.2688			−0.174841
$197$			168.534i			0.855503i	0.903896	+	0.427751i	$0.140694\pi$
$197$			168.534i			0.855503i	−0.903896	+	0.427751i	$0.859306\pi$
$198$	25.9745			0.131184
$199$	−40.9710			−0.205885			−0.102942	−	0.994687i	$-0.532826\pi$
$199$	−40.9710			−0.205885			−0.102942	+	0.994687i	$0.532826\pi$
$200$		0			0
$201$	−383.435			−1.90764
$202$	−4.16446			−0.0206161
$203$	−158.548			−0.781023
$204$			272.621i			1.33638i
$205$		0			0
$206$	3.06752			0.0148909
$207$		−	286.089i		−	1.38207i
$208$	59.6875			0.286959
$209$	−30.0336	+	188.467i	−0.143701	+	0.901758i
$210$		0			0
$211$			264.352i			1.25285i	0.779481	+	0.626426i	$0.215483\pi$
$211$			264.352i			1.25285i	−0.779481	+	0.626426i	$0.784517\pi$
$212$	−37.7026			−0.177842
$213$			396.484i			1.86143i
$214$	4.40391			0.0205790
$215$		0			0
$216$	−49.7065			−0.230123
$217$	−294.539			−1.35732
$218$			15.6334i			0.0717130i
$219$			614.219i			2.80465i
$220$		0			0
$221$		−	50.9814i		−	0.230685i
$222$	52.9917			0.238701
$223$	220.658			0.989498			0.494749	−	0.869036i	$-0.335260\pi$
$223$	220.658			0.989498			0.494749	+	0.869036i	$0.335260\pi$
$224$		−	45.9104i		−	0.204957i
$225$		0			0
$226$	−19.7903			−0.0875677
$227$	156.019			0.687308			0.343654	−	0.939096i	$-0.388335\pi$
$227$	156.019			0.687308			0.343654	+	0.939096i	$0.388335\pi$
$228$	60.6923	−	380.858i	0.266194	−	1.67043i
$229$	−259.477			−1.13309			−0.566545	−	0.824031i	$-0.691720\pi$
$229$	−259.477			−1.13309			−0.566545	+	0.824031i	$0.691720\pi$
$230$		0			0
$231$		−	325.783i		−	1.41032i
$232$			30.1861i			0.130112i
$233$			353.499i			1.51716i	0.651578	+	0.758582i	$0.274107\pi$
$233$			353.499i			1.51716i	−0.651578	+	0.758582i	$0.725893\pi$
$234$	9.81580			0.0419479
$235$		0			0
$236$		−	348.821i		−	1.47805i
$237$		−	65.4558i		−	0.276185i
$238$	−12.9453			−0.0543921
$239$	176.322			0.737750			0.368875	−	0.929479i	$-0.379743\pi$
$239$	176.322			0.737750			0.368875	+	0.929479i	$0.379743\pi$
$240$		0			0
$241$			35.4360i			0.147037i	0.997294	+	0.0735187i	$0.0234229\pi$
$241$			35.4360i			0.147037i	−0.997294	+	0.0735187i	$0.976577\pi$
$242$	−3.04985			−0.0126027
$243$	−82.7142			−0.340388
$244$	381.553			1.56374
$245$		0			0
$246$			36.8366i			0.149742i
$247$	−11.3497	+	71.2222i	−0.0459504	+	0.288349i
$248$			56.0776i			0.226119i
$249$			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	$0.292067\pi$
$252$			430.890i			1.70988i
$253$		−	168.546i		−	0.666191i
$254$	−7.77680			−0.0306173
$255$		0			0
$256$	241.404			0.942983
$257$	294.709			1.14673			0.573364	−	0.819300i	$-0.305638\pi$
$257$	294.709			1.14673			0.573364	+	0.819300i	$0.305638\pi$
$258$		−	33.6112i		−	0.130276i
$259$		−	435.012i		−	1.67958i
$260$		0			0
$261$		−	425.373i		−	1.62978i
$262$	−16.9060			−0.0645267
$263$		−	339.127i		−	1.28946i	−0.764412	−	0.644728i	$-0.776971\pi$
$263$		−	339.127i		−	1.28946i	0.764412	−	0.644728i	$-0.223029\pi$
$264$	−62.0261			−0.234948
$265$		0			0
$266$	18.0849	+	2.88196i	0.0679884	+	0.0108344i
$267$		−	799.939i		−	2.99603i
$268$	298.777			1.11484
$269$			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	$0.251584\pi$
$272$		−	211.194i		−	0.776447i
$273$		−	123.114i		−	0.450967i
$274$		−	15.6602i		−	0.0571538i
$275$		0			0
$276$			340.601i			1.23406i
$277$			33.7216i			0.121739i	0.998146	+	0.0608694i	$0.0193873\pi$
$277$			33.7216i			0.121739i	−0.998146	+	0.0608694i	$0.980613\pi$
$278$	−1.84296			−0.00662935
$279$		−	790.228i		−	2.83236i
$280$		0			0
$281$		−	209.260i		−	0.744699i	−0.928093	−	0.372349i	$-0.878552\pi$
$281$		−	209.260i		−	0.744699i	0.928093	−	0.372349i	$-0.121448\pi$
$282$			28.9916i			0.102807i
$283$			341.019i			1.20501i	0.798114	+	0.602506i	$0.205831\pi$
$283$			341.019i			1.20501i	−0.798114	+	0.602506i	$0.794169\pi$
$284$		−	308.945i		−	1.08784i
$285$		0			0
$286$	5.78287			0.0202198
$287$	302.394			1.05364
$288$	123.175			0.427690
$289$	108.611			0.375818
$290$		0			0
$291$	286.829			0.985666
$292$		−	478.607i		−	1.63906i
$293$	409.506			1.39763			0.698815	−	0.715303i	$-0.253711\pi$
$293$	409.506			1.39763			0.698815	+	0.715303i	$0.253711\pi$
$294$	6.67038			0.0226884
$295$		0			0
$296$	−82.8224			−0.279806
$297$	412.662			1.38943
$298$	−37.4754			−0.125756
$299$		−	63.6940i		−	0.213023i
$300$		0			0
$301$	−275.916			−0.916665
$302$		−	9.38966i		−	0.0310916i
$303$	−140.136			−0.462496
$304$	−47.0170	+	295.042i	−0.154661	+	0.970534i
$305$		0			0
$306$		−	34.7315i		−	0.113502i
$307$	−235.337			−0.766571			−0.383286	−	0.923630i	$-0.625207\pi$
$307$	−235.337			−0.766571			−0.383286	+	0.923630i	$0.625207\pi$
$308$			253.854i			0.824201i
$309$	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	$0.602601\pi$
$312$	−23.4398			−0.0751276
$313$			27.8992i			0.0891348i	0.999006	+	0.0445674i	$0.0141909\pi$
$313$			27.8992i			0.0891348i	−0.999006	+	0.0445674i	$0.985809\pi$
$314$			11.3016i			0.0359924i
$315$		0			0
$316$			51.0040i			0.161405i
$317$	372.696			1.17570			0.587848	−	0.808971i	$-0.299975\pi$
$317$	372.696			1.17570			0.587848	+	0.808971i	$0.299975\pi$
$318$	7.33877			0.0230779
$319$		−	250.604i		−	0.785592i
$320$		0			0
$321$	148.194			0.461663
$322$	−16.1733			−0.0502278
$323$	252.007	+	40.1591i	0.780207	+	0.124331i
$324$	−223.662			−0.690315
$325$		0			0
$326$			10.2022i			0.0312952i
$327$			526.073i			1.60879i
$328$		−	57.5730i		−	0.175528i
$329$	237.994			0.723386
$330$		0			0
$331$		−	3.74805i		−	0.0113234i	−0.999984	−	0.00566170i	$-0.998198\pi$
$331$		−	3.74805i		−	0.0113234i	0.999984	−	0.00566170i	$-0.00180219\pi$
$332$		−	432.542i		−	1.30284i
$333$	1167.11			3.50483
$334$	25.1268			0.0752298
$335$		0			0
$336$		−	510.007i		−	1.51788i
$337$	−410.554			−1.21826			−0.609131	−	0.793070i	$-0.708482\pi$
$337$	−410.554			−1.21826			−0.609131	+	0.793070i	$0.708482\pi$
$338$	−23.4474			−0.0693709
$339$	−665.953			−1.96446
$340$		0			0
$341$		−	465.554i		−	1.36526i
$342$	−7.73210	+	48.5206i	−0.0226085	+	0.141873i
$343$		−	366.142i		−	1.06747i
$344$			52.5320i			0.152709i
$345$		0			0
$346$	46.9344			0.135648
$347$			210.073i			0.605399i	0.953086	+	0.302700i	$0.0978879\pi$
$347$			210.073i			0.605399i	−0.953086	+	0.302700i	$0.902112\pi$
$348$			506.424i			1.45524i
$349$	308.461			0.883843			0.441921	−	0.897054i	$-0.354297\pi$
$349$	308.461			0.883843			0.441921	+	0.897054i	$0.354297\pi$
$350$		0			0
$351$	155.946			0.444290
$352$	72.5670			0.206156
$353$		−	556.817i		−	1.57739i	−0.614787	−	0.788693i	$-0.710758\pi$
$353$		−	556.817i		−	1.57739i	0.614787	−	0.788693i	$-0.289242\pi$
$354$			67.8976i			0.191801i
$355$		0			0
$356$			623.322i			1.75090i
$357$	−435.617			−1.22021
$358$		−	32.1400i		−	0.0897766i
$359$	−118.795			−0.330904			−0.165452	−	0.986218i	$-0.552908\pi$
$359$	−118.795			−0.330904			−0.165452	+	0.986218i	$0.552908\pi$
$360$		0			0
$361$	−343.119	−	112.206i	−0.950469	−	0.310821i
$362$			15.3362i			0.0423652i
$363$	−102.629			−0.282724
$364$			95.9319i			0.263549i
$365$		0			0
$366$	−74.2689			−0.202920
$367$			378.940i			1.03253i	0.856428	+	0.516267i	$0.172679\pi$
$367$			378.940i			1.03253i	−0.856428	+	0.516267i	$0.827321\pi$
$368$		−	263.856i		−	0.717001i
$369$			811.302i			2.19865i
$370$		0			0
$371$		−	60.2444i		−	0.162384i
$372$			940.798i			2.52903i
$373$	−201.901			−0.541290			−0.270645	−	0.962679i	$-0.587237\pi$
$373$	−201.901			−0.541290			−0.270645	+	0.962679i	$0.587237\pi$
$374$		−	20.4616i		−	0.0547103i
$375$		0			0
$376$		−	45.3120i		−	0.120511i
$377$		−	94.7036i		−	0.251203i
$378$		−	39.5981i		−	0.104757i
$379$			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
$382$	−8.67582			−0.0227116
$383$	146.990			0.383785			0.191893	−	0.981416i	$-0.438537\pi$
$383$	146.990			0.383785			0.191893	+	0.981416i	$0.438537\pi$
$384$	−195.335			−0.508684
$385$		0			0
$386$	−23.7264			−0.0614672
$387$		−	740.265i		−	1.91283i
$388$	−223.500			−0.576032
$389$	187.901			0.483035			0.241518	−	0.970396i	$-0.422355\pi$
$389$	187.901			0.483035			0.241518	+	0.970396i	$0.422355\pi$
$390$		0			0
$391$	−225.370			−0.576393
$392$	−10.4254			−0.0265953
$393$	−568.896			−1.44757
$394$			25.5620i			0.0648783i
$395$		0			0
$396$	−681.073			−1.71988
$397$			26.5137i			0.0667852i	0.999442	+	0.0333926i	$0.0106312\pi$
$397$			26.5137i			0.0667852i	−0.999442	+	0.0333926i	$0.989369\pi$
$398$	−6.21419			−0.0156136
$399$	608.567	+	96.9793i	1.52523	+	0.243056i
$400$		0			0
$401$			38.9717i			0.0971864i	0.998819	+	0.0485932i	$0.0154738\pi$
$401$			38.9717i			0.0971864i	−0.998819	+	0.0485932i	$0.984526\pi$
$402$	−58.1566			−0.144668
$403$		−	175.934i		−	0.436560i
$404$	109.196			0.270287
$405$		0			0
$406$	−24.0474			−0.0592300
$407$	687.589			1.68941
$408$			82.9375i			0.203278i
$409$		−	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
$412$	−80.4331			−0.195226
$413$	557.375			1.34958
$414$		−	43.3920i		−	0.104812i
$415$		0			0
$416$	27.4232			0.0659211
$417$	−62.0165			−0.148721
$418$	−4.55528	+	28.5854i	−0.0108978	+	0.0683861i
$419$	−207.979			−0.496370			−0.248185	−	0.968713i	$-0.579834\pi$
$419$	−207.979			−0.496370			−0.248185	+	0.968713i	$0.579834\pi$
$420$		0			0
$421$			182.812i			0.434232i	0.976146	+	0.217116i	$0.0696650\pi$
$421$			182.812i			0.434232i	−0.976146	+	0.217116i	$0.930335\pi$
$422$			40.0950i			0.0950118i
$423$			638.523i			1.50951i
$424$	−11.4700			−0.0270519
$425$		0			0
$426$			60.1359i			0.141164i
$427$			609.677i			1.42782i
$428$	−115.474			−0.269800
$429$	194.596			0.453605
$430$		0			0
$431$			175.672i			0.407592i	0.979013	+	0.203796i	$0.0653279\pi$
$431$			175.672i			0.407592i	−0.979013	+	0.203796i	$0.934672\pi$
$432$	646.014			1.49540
$433$	−343.766			−0.793918			−0.396959	−	0.917836i	$-0.629934\pi$
$433$	−343.766			−0.793918			−0.396959	+	0.917836i	$0.629934\pi$
$434$	−44.6735			−0.102934
$435$		0			0
$436$		−	409.922i		−	0.940189i
$437$	314.847	+	50.1730i	0.720473	+	0.114812i
$438$			93.1603i			0.212695i
$439$			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
$442$		−	7.73250i		−	0.0174943i
$443$			193.700i			0.437246i	0.975809	+	0.218623i	$0.0701565\pi$
$443$			193.700i			0.437246i	−0.975809	+	0.218623i	$0.929843\pi$
$444$	−1389.49			−3.12948
$445$		0			0
$446$	33.4678			0.0750400
$447$	−1261.07			−2.82118
$448$			392.739i			0.876650i
$449$		−	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
$452$	518.919			1.14805
$453$		−	315.967i		−	0.697498i
$454$	23.6638			0.0521230
$455$		0			0
$456$	18.4640	−	115.866i	0.0404912	−	0.254091i
$457$		−	213.763i		−	0.467753i	−0.972266	−	0.233876i	$-0.924859\pi$
$457$		−	213.763i		−	0.467753i	0.972266	−	0.233876i	$-0.0751411\pi$
$458$	−39.3557			−0.0859295
$459$		−	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	$0.754259\pi$
$462$		−	49.4124i		−	0.106953i
$463$		−	481.283i		−	1.03949i	−0.854322	−	0.519744i	$-0.826027\pi$
$463$		−	481.283i		−	1.03949i	0.854322	−	0.519744i	$-0.173973\pi$
$464$		−	392.316i		−	0.845508i
$465$		0			0
$466$			53.6162i			0.115056i
$467$			420.429i			0.900277i	0.892959	+	0.450139i	$0.148625\pi$
$467$			420.429i			0.900277i	−0.892959	+	0.450139i	$0.851375\pi$
$468$	−257.379			−0.549955
$469$			477.411i			1.01793i
$470$		0			0
$471$			380.305i			0.807441i
$472$		−	106.119i		−	0.224829i
$473$		−	436.118i		−	0.922026i
$474$		−	9.92787i		−	0.0209449i
$475$		0			0
$476$	339.438			0.713105
$477$	161.632			0.338851
$478$	26.7433			0.0559483
$479$	124.589			0.260101			0.130051	−	0.991507i	$-0.458486\pi$
$479$	124.589			0.260101			0.130051	+	0.991507i	$0.458486\pi$
$480$		0			0
$481$	259.841			0.540210
$482$			5.37468i			0.0111508i
$483$	−544.241			−1.12679
$484$	79.9697			0.165227
$485$		0			0
$486$	−12.5455			−0.0258138
$487$	−770.701			−1.58255			−0.791274	−	0.611462i	$-0.790582\pi$
$487$	−770.701			−1.58255			−0.791274	+	0.611462i	$0.790582\pi$
$488$	116.077			0.237863
$489$			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	$0.482389\pi$
$492$		−	965.887i		−	1.96318i
$493$	−335.092			−0.679700
$494$	−1.72145	+	10.8025i	−0.00348471	+	0.0218674i
$495$		0			0
$496$		−	728.816i		−	1.46939i
$497$	493.659			0.993278
$498$			84.1938i			0.169064i
$499$	192.861			0.386495			0.193247	−	0.981150i	$-0.438098\pi$
$499$	192.861			0.386495			0.193247	+	0.981150i	$0.438098\pi$
$500$		0			0
$501$	845.528			1.68768
$502$	46.2750			0.0921813
$503$		−	544.862i		−	1.08322i	−0.840629	−	0.541612i	$-0.817814\pi$
$503$		−	544.862i		−	1.08322i	0.840629	−	0.541612i	$-0.182186\pi$
$504$			131.087i			0.260093i
$505$		0			0
$506$		−	25.5639i		−	0.0505216i
$507$	−789.015			−1.55624
$508$	203.914			0.401406
$509$		−	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
$512$	189.702			0.370512
$513$	−122.841	+	770.858i	−0.239457	+	1.50265i
$514$	44.6994			0.0869638
$515$		0			0
$516$			881.314i			1.70797i
$517$			376.178i			0.727618i
$518$		−	65.9795i		−	0.127374i
$519$	1579.36			3.04309
$520$		0			0
$521$			535.499i			1.02783i	0.857841	+	0.513915i	$0.171805\pi$
$521$			535.499i			1.02783i	−0.857841	+	0.513915i	$0.828195\pi$
$522$		−	64.5176i		−	0.123597i
$523$	−693.075			−1.32519			−0.662595	−	0.748978i	$-0.730545\pi$
$523$	−693.075			−1.32519			−0.662595	+	0.748978i	$0.730545\pi$
$524$	443.290			0.845974
$525$		0			0
$526$		−	51.4363i		−	0.0977877i
$527$	−622.510			−1.18123
$528$	806.127			1.52676
$529$	247.432			0.467736
$530$		0			0
$531$			1495.40i			2.81620i
$532$	−474.202	−	75.5674i	−0.891358	−	0.142044i
$533$			180.626i			0.338885i
$534$		−	121.329i		−	0.227208i
$535$		0			0
$536$	90.8949			0.169580
$537$		−	1081.53i		−	2.01402i
$538$			5.04480i			0.00937695i
$539$	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	$0.435621\pi$
$542$	57.8389			0.106714
$543$			516.071i			0.950406i
$544$		−	97.0321i		−	0.178368i
$545$		0			0
$546$		−	18.6730i		−	0.0341997i
$547$	288.990			0.528318			0.264159	−	0.964479i	$-0.414906\pi$
$547$	288.990			0.528318			0.264159	+	0.964479i	$0.414906\pi$
$548$			410.623i			0.749312i
$549$	−1635.72			−2.97946
$550$		0			0
$551$	468.131	+	74.5999i	0.849603	+	0.135390i
$552$			103.619i			0.187715i
$553$	−81.4985			−0.147375
$554$			5.11466i			0.00923223i
$555$		0			0
$556$	48.3240			0.0869137
$557$			216.252i			0.388245i	0.980977	+	0.194122i	$0.0621859\pi$
$557$			216.252i			0.388245i	−0.980977	+	0.194122i	$0.937814\pi$
$558$		−	119.856i		−	0.214796i
$559$		−	164.810i		−	0.294830i
$560$		0			0
$561$		−	688.545i		−	1.22735i
$562$		−	31.7391i		−	0.0564753i
$563$	132.093			0.234624			0.117312	−	0.993095i	$-0.462572\pi$
$563$	132.093			0.234624			0.117312	+	0.993095i	$0.462572\pi$
$564$		−	760.186i		−	1.34785i
$565$		0			0
$566$			51.7233i			0.0913839i
$567$		−	357.386i		−	0.630311i
$568$		−	93.9883i		−	0.165472i
$569$			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	$0.548622\pi$
$572$	−151.632			−0.265091
$573$	−291.945			−0.509503
$574$	45.8649			0.0799040
$575$		0			0
$576$	−1053.69			−1.82933
$577$		−	252.461i		−	0.437541i	−0.975776	−	0.218770i	$-0.929795\pi$
$577$		−	252.461i		−	0.437541i	0.975776	−	0.218770i	$-0.0702046\pi$
$578$	16.4734			0.0285007
$579$	−798.404			−1.37894
$580$		0			0
$581$	691.152			1.18959
$582$	43.5041			0.0747494
$583$	95.2235			0.163334
$584$		−	145.603i		−	0.249321i
$585$		0			0
$586$	62.1109			0.105991
$587$		−	378.687i		−	0.645123i	−0.946548	−	0.322562i	$-0.895456\pi$
$587$		−	378.687i		−	0.645123i	0.946548	−	0.322562i	$-0.104544\pi$
$588$	−174.903			−0.297455
$589$	869.661	+	138.586i	1.47650	+	0.235291i
$590$		0			0
$591$			860.175i			1.45546i
$592$	1076.41			1.81826
$593$		−	501.502i		−	0.845704i	−0.906199	−	0.422852i	$-0.861029\pi$
$593$		−	501.502i		−	0.845704i	0.906199	−	0.422852i	$-0.138971\pi$
$594$	62.5896			0.105370
$595$		0			0
$596$	982.639			1.64872
$597$	−209.111			−0.350269
$598$		−	9.66065i		−	0.0161549i
$599$		−	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	$0.0157183\pi$
$601$			59.3311i			0.0987206i	−0.998781	+	0.0493603i	$0.984282\pi$
$602$	−41.8490			−0.0695166
$603$	−1280.86			−2.12415
$604$			246.205i			0.407624i
$605$		0			0
$606$	−21.2549			−0.0350740
$607$	95.8823			0.157961			0.0789805	−	0.996876i	$-0.474834\pi$
$607$	95.8823			0.157961			0.0789805	+	0.996876i	$0.474834\pi$
$608$	−21.6018	+	135.556i	−0.0355293	+	0.222954i
$609$	−809.207			−1.32875
$610$		0			0
$611$			142.158i			0.232665i
$612$			910.689i			1.48805i
$613$		−	740.997i		−	1.20880i	−0.796679	−	0.604402i	$-0.793412\pi$
$613$		−	740.997i		−	1.20880i	0.796679	−	0.604402i	$-0.206588\pi$
$614$	−35.6943			−0.0581340
$615$		0			0
$616$			77.2282i			0.125370i
$617$		−	274.604i		−	0.445064i	−0.974925	−	0.222532i	$-0.928568\pi$
$617$		−	274.604i		−	0.445064i	0.974925	−	0.222532i	$-0.0714321\pi$
$618$	15.6562			0.0253337
$619$	−610.524			−0.986307			−0.493153	−	0.869942i	$-0.664156\pi$
$619$	−610.524			−0.986307			−0.493153	+	0.869942i	$0.664156\pi$
$620$		0			0
$621$		−	689.378i		−	1.11011i
$622$	−29.8851			−0.0480468
$623$	−995.997			−1.59871
$624$	304.637			0.488200
$625$		0			0
$626$			4.23155i			0.00675967i
$627$	−153.287	+	961.913i	−0.244478	+	1.53415i
$628$		−	296.338i		−	0.471876i
$629$		−	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	$0.724821\pi$
$632$			15.5166i			0.0245516i
$633$			1349.22i			2.13146i
$634$	56.5278			0.0891606
$635$		0			0
$636$	−192.429			−0.302561
$637$	32.7078			0.0513465
$638$		−	38.0098i		−	0.0595765i
$639$			1324.45i			2.07270i
$640$		0			0
$641$		−	1110.13i		−	1.73187i	−0.500152	−	0.865937i	$-0.666723\pi$
$641$		−	1110.13i		−	1.73187i	0.500152	−	0.865937i	$-0.333277\pi$
$642$	22.4770			0.0350109
$643$			346.176i			0.538376i	0.963088	+	0.269188i	$0.0867553\pi$
$643$			346.176i			0.538376i	−0.963088	+	0.269188i	$0.913245\pi$
$644$	424.079			0.658508
$645$		0			0
$646$	38.2226	+	6.09104i	0.0591682	+	0.00942885i
$647$		−	708.711i		−	1.09538i	−0.836681	−	0.547690i	$-0.815507\pi$
$647$		−	708.711i		−	1.09538i	0.836681	−	0.547690i	$-0.184493\pi$
$648$	−68.0432			−0.105005
$649$			880.999i			1.35747i
$650$		0			0
$651$	−1503.29			−2.30920
$652$		−	267.512i		−	0.410294i
$653$			628.097i			0.961864i	0.876758	+	0.480932i	$0.159702\pi$
$653$			628.097i			0.961864i	−0.876758	+	0.480932i	$0.840298\pi$
$654$			79.7910i			0.122005i
$655$		0			0
$656$			748.252i			1.14063i
$657$			2051.80i			3.12298i
$658$	36.0972			0.0548590
$659$			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	$-0.893199\pi$
$661$		−	435.287i		−	0.658528i	0.944238	−	0.329264i	$-0.106801\pi$
$662$		−	0.568477i		−	0.000858727i
$663$		−	260.202i		−	0.392462i
$664$		−	131.589i		−	0.198176i
$665$		0			0
$666$	177.019			0.265794
$667$	−418.650			−0.627661
$668$	−658.846			−0.986296
$669$	1126.21			1.68342
$670$		0			0
$671$	−963.668			−1.43617
$672$		−	234.321i		−	0.348692i
$673$	428.742			0.637061			0.318530	−	0.947913i	$-0.396811\pi$
$673$	428.742			0.637061			0.318530	+	0.947913i	$0.396811\pi$
$674$	−62.2700			−0.0923887
$675$		0			0
$676$	614.810			0.909483
$677$	−162.012			−0.239309			−0.119654	−	0.992816i	$-0.538179\pi$
$677$	−162.012			−0.239309			−0.119654	+	0.992816i	$0.538179\pi$
$678$	−101.007			−0.148978
$679$		−	357.128i		−	0.525962i
$680$		0			0
$681$	796.300			1.16931
$682$		−	70.6119i		−	0.103537i
$683$	884.714			1.29533			0.647667	−	0.761923i	$-0.275745\pi$
$683$	884.714			1.29533			0.647667	+	0.761923i	$0.275745\pi$
$684$	202.742	−	1272.25i	0.296407	−	1.86002i
$685$		0			0
$686$		−	55.5338i		−	0.0809530i
$687$	−1324.34			−1.92771
$688$		−	682.735i		−	0.992348i
$689$	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	$0.771956\pi$
$692$	−1230.66			−1.77841
$693$		−	1088.28i		−	1.57039i
$694$			31.8624i			0.0459113i
$695$		0			0
$696$			154.066i			0.221359i
$697$	639.111			0.916946
$698$	46.7852			0.0670275
$699$			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	$0.670028\pi$
$702$	23.6527			0.0336933
$703$	−204.682	+	1284.43i	−0.291155	+	1.82706i
$704$	−620.771			−0.881777
$705$		0			0
$706$		−	84.4541i		−	0.119623i
$707$			174.482i			0.246793i
$708$		−	1780.33i		−	2.51460i
$709$	227.442			0.320792			0.160396	−	0.987053i	$-0.448723\pi$
$709$	227.442			0.320792			0.160396	+	0.987053i	$0.448723\pi$
$710$		0			0
$711$		−	218.655i		−	0.307532i
$712$			189.629i			0.266333i
$713$	−777.738			−1.09080
$714$	−66.0712			−0.0925367
$715$		0			0
$716$			842.739i			1.17701i
$717$	899.926			1.25513
$718$	−18.0179			−0.0250946
$719$	−413.703			−0.575386			−0.287693	−	0.957723i	$-0.592888\pi$
$719$	−413.703			−0.575386			−0.287693	+	0.957723i	$0.592888\pi$
$720$		0			0
$721$		−	128.523i		−	0.178256i
$722$	−52.0419	−	17.0186i	−0.0720801	−	0.0235715i
$723$			180.861i			0.250153i
$724$		−	402.129i		−	0.555426i
$725$		0			0
$726$	−15.5660			−0.0214408
$727$		−	297.592i		−	0.409342i	−0.978831	−	0.204671i	$-0.934388\pi$
$727$		−	297.592i		−	0.409342i	0.978831	−	0.204671i	$-0.0656124\pi$
$728$			29.1847i			0.0400889i
$729$	−928.313			−1.27341
$730$		0			0
$731$	−583.151			−0.797744
$732$	1947.39			2.66037
$733$			772.246i			1.05354i	0.850007	+	0.526771i	$0.176597\pi$
$733$			772.246i			1.05354i	−0.850007	+	0.526771i	$0.823403\pi$
$734$			57.4749i			0.0783037i
$735$		0			0
$736$		−	121.228i		−	0.164712i
$737$	−754.606			−1.02389
$738$			123.052i			0.166738i
$739$	−1209.35			−1.63646			−0.818231	−	0.574889i	$-0.805045\pi$
$739$	−1209.35			−1.63646			−0.818231	+	0.574889i	$0.805045\pi$
$740$		0			0
$741$	−57.9276	+	363.509i	−0.0781749	+	0.490565i
$742$		−	9.13744i		−	0.0123146i
$743$	−62.2804			−0.0838229			−0.0419114	−	0.999121i	$-0.513345\pi$
$743$	−62.2804			−0.0838229			−0.0419114	+	0.999121i	$0.513345\pi$
$744$			286.212i			0.384694i
$745$		0			0
$746$	−30.6229			−0.0410495
$747$			1854.31i			2.48235i
$748$			536.522i			0.717276i
$749$		−	184.515i		−	0.246348i
$750$		0			0
$751$		−	1440.03i		−	1.91748i	−0.284285	−	0.958740i	$-0.591756\pi$
$751$		−	1440.03i		−	1.91748i	0.284285	−	0.958740i	$-0.408244\pi$
$752$			588.900i			0.783112i
$753$	1557.18			2.06796
$754$		−	14.3640i		−	0.0190504i
$755$		0			0
$756$			1038.30i			1.37341i
$757$		−	513.483i		−	0.678313i	−0.940730	−	0.339157i	$-0.889858\pi$
$757$		−	513.483i		−	0.678313i	0.940730	−	0.339157i	$-0.110142\pi$
$758$			40.5401i			0.0534829i
$759$		−	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	$0.471868\pi$
$762$	−39.6917			−0.0520889
$763$	655.009			0.858465
$764$	227.487			0.297758
$765$		0			0
$766$	22.2944			0.0291049
$767$			332.931i			0.434069i
$768$	1232.09			1.60429
$769$	103.497			0.134586			0.0672932	−	0.997733i	$-0.478564\pi$
$769$	103.497			0.134586			0.0672932	+	0.997733i	$0.478564\pi$
$770$		0			0
$771$	1504.16			1.95092
$772$	622.126			0.805862
$773$	1361.14			1.76086			0.880429	−	0.474177i	$-0.157254\pi$
$773$	1361.14			1.76086			0.880429	+	0.474177i	$0.157254\pi$
$774$		−	112.278i		−	0.145062i
$775$		0			0
$776$	−67.9940			−0.0876211
$777$		−	2220.24i		−	2.85746i
$778$	28.4994			0.0366317
$779$	−892.853	−	142.282i	−1.14615	−	0.182647i
$780$		0			0
$781$			780.288i			0.999088i
$782$	−34.1825			−0.0437116
$783$		−	1025.00i		−	1.30907i
$784$	135.494			0.172824
$785$		0			0
$786$	−86.2860			−0.109779
$787$	945.437			1.20132			0.600659	−	0.799506i	$-0.294905\pi$
$787$	945.437			1.20132			0.600659	+	0.799506i	$0.294905\pi$
$788$		−	670.259i		−	0.850582i
$789$		−	1730.86i		−	2.19374i
$790$		0			0
$791$			829.173i			1.04826i
$792$	−207.198			−0.261614
$793$	−364.172			−0.459233
$794$			4.02141i			0.00506475i
$795$		0			0
$796$	162.942			0.204701
$797$	−642.975			−0.806745			−0.403372	−	0.915036i	$-0.632162\pi$
$797$	−642.975			−0.806745			−0.403372	+	0.915036i	$0.632162\pi$
$798$	92.3030	+	14.7091i	0.115668	+	0.0184325i
$799$	503.002			0.629540
$800$		0			0
$801$		−	2672.19i		−	3.33607i
$802$			5.91095i			0.00737027i
$803$			1208.79i			1.50535i
$804$	1524.92			1.89666
$805$		0			0
$806$		−	26.6844i		−	0.0331072i
$807$			169.760i			0.210359i
$808$	33.2199			0.0411137
$809$	1206.61			1.49148			0.745740	−	0.666238i	$-0.232096\pi$
$809$	1206.61			1.49148			0.745740	+	0.666238i	$0.232096\pi$
$810$		0			0
$811$			1322.86i			1.63115i	0.578651	+	0.815575i	$0.303579\pi$
$811$			1322.86i			1.63115i	−0.578651	+	0.815575i	$0.696421\pi$
$812$	630.544			0.776532
$813$	1946.31			2.39398
$814$	104.289			0.128119
$815$		0			0
$816$		−	1077.90i		−	1.32096i
$817$	814.675	+	129.824i	0.997154	+	0.158903i
$818$		−	16.9742i		−	0.0207508i
$819$		−	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	$0.556280\pi$
$822$		−	79.9273i		−	0.0972352i
$823$		−	1068.46i		−	1.29825i	−0.760684	−	0.649123i	$-0.775136\pi$
$823$		−	1068.46i		−	1.29825i	0.760684	−	0.649123i	$-0.224864\pi$
$824$	−24.4696			−0.0296961
$825$		0			0
$826$	84.5387			0.102347
$827$	393.538			0.475862			0.237931	−	0.971282i	$-0.423531\pi$
$827$	393.538			0.475862			0.237931	+	0.971282i	$0.423531\pi$
$828$			1137.78i			1.37413i
$829$			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
$832$	−234.591			−0.281960
$833$		−	115.731i		−	0.138932i
$834$	−9.40622			−0.0112784
$835$		0			0
$836$	119.443	−	749.534i	0.142875	−	0.896572i
$837$		−	1904.18i		−	2.27501i
$838$	−31.5447			−0.0376429
$839$		−	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
$842$			27.7276i			0.0329306i
$843$		−	1068.04i		−	1.26695i
$844$		−	1051.32i		−	1.24565i
$845$		0			0
$846$			96.8465i			0.114476i
$847$			127.782i			0.150865i
$848$	149.071			0.175791
$849$			1740.51i			2.05008i
$850$		0			0
$851$		−	1148.66i		−	1.34978i
$852$		−	1576.82i		−	1.85072i
$853$		−	719.082i		−	0.843003i	−0.906828	−	0.421502i	$-0.861503\pi$
$853$		−	719.082i		−	0.843003i	0.906828	−	0.421502i	$-0.138497\pi$
$854$			92.4715i			0.108280i
$855$		0			0
$856$	−35.1300			−0.0410397
$857$	153.486			0.179097			0.0895485	−	0.995982i	$-0.471458\pi$
$857$	153.486			0.179097			0.0895485	+	0.995982i	$0.471458\pi$
$858$	29.5150			0.0343998
$859$	−914.298			−1.06438			−0.532188	−	0.846627i	$-0.678630\pi$
$859$	−914.298			−1.06438			−0.532188	+	0.846627i	$0.678630\pi$
$860$		0			0
$861$	1543.38			1.79254
$862$			26.6447i			0.0309103i
$863$	−1647.58			−1.90914			−0.954568	−	0.297992i	$-0.903683\pi$
$863$	−1647.58			−1.90914			−0.954568	+	0.297992i	$0.903683\pi$
$864$	296.809			0.343529
$865$		0			0
$866$	−52.1400			−0.0602079
$867$	554.338			0.639375
$868$	1171.38			1.34952
$869$		−	128.818i		−	0.148237i
$870$		0			0
$871$	−285.167			−0.327402
$872$		−	124.708i		−	0.143014i
$873$	958.151			1.09754
$874$	47.7537	+	7.60989i	0.0546381	+	0.00870696i
$875$		0			0
$876$		−	2442.74i		−	2.78852i
$877$	−819.184			−0.934076			−0.467038	−	0.884237i	$-0.654679\pi$
$877$	−819.184			−0.934076			−0.467038	+	0.884237i	$0.654679\pi$
$878$			67.9599i			0.0774031i
$879$	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	$0.329430\pi$
$882$	22.2824			0.0252635
$883$			1007.40i			1.14088i	0.821338	+	0.570442i	$0.193228\pi$
$883$			1007.40i			1.14088i	−0.821338	+	0.570442i	$0.806772\pi$
$884$			202.753i			0.229358i
$885$		0			0
$886$			29.3790i			0.0331592i
$887$	668.366			0.753513			0.376756	−	0.926312i	$-0.377039\pi$
$887$	668.366			0.753513			0.376756	+	0.926312i	$0.377039\pi$
$888$	−422.715			−0.476030
$889$			325.832i			0.366515i
$890$		0			0
$891$	564.892			0.633998
$892$	−877.556			−0.983807
$893$	−702.706	−	111.981i	−0.786905	−	0.125399i
$894$	−191.270			−0.213948
$895$		0			0
$896$			243.210i			0.271439i
$897$		−	325.086i		−	0.362414i
$898$		−	114.494i		−	0.127499i
$899$	−1156.38			−1.28630
$900$		0			0
$901$		−	127.327i		−	0.141317i
$902$			72.4950i			0.0803714i
$903$	−1408.24			−1.55951
$904$	157.867			0.174632
$905$		0			0
$906$		−	47.9236i		−	0.0528958i
$907$	−1186.27			−1.30791			−0.653954	−	0.756534i	$-0.726891\pi$
$907$	−1186.27			−1.30791			−0.653954	+	0.756534i	$0.726891\pi$
$908$	−620.486			−0.683355
$909$	−468.125			−0.514989
$910$		0			0
$911$		−	526.830i		−	0.578298i	−0.957284	−	0.289149i	$-0.906628\pi$
$911$		−	526.830i		−	0.578298i	0.957284	−	0.289149i	$-0.0933724\pi$
$912$	−239.969	+	1505.86i	−0.263123	+	1.65116i
$913$			1092.45i			1.19655i
$914$		−	32.4220i		−	0.0354727i
$915$		0			0
$916$	1031.94			1.12657
$917$			708.327i			0.772439i
$918$		−	83.6910i		−	0.0911666i
$919$	−959.827			−1.04443			−0.522213	−	0.852815i	$-0.674893\pi$
$919$	−959.827			−1.04443			−0.522213	+	0.852815i	$0.674893\pi$
$920$		0			0
$921$	−1201.13			−1.30416
$922$	−100.198			−0.108674
$923$			294.872i			0.319471i
$924$			1295.64i			1.40220i
$925$		0			0
$926$		−	72.9975i		−	0.0788310i
$927$	344.818			0.371972
$928$		−	180.248i		−	0.194233i
$929$	288.443			0.310488			0.155244	−	0.987876i	$-0.450384\pi$
$929$	288.443			0.310488			0.155244	+	0.987876i	$0.450384\pi$
$930$		0			0
$931$	−25.7645	+	161.678i	−0.0276740	+	0.173661i
$932$		−	1405.86i		−	1.50844i
$933$	−1005.65			−1.07786
$934$			63.7677i			0.0682738i
$935$		0			0
$936$	−78.3006			−0.0836545
$937$			1072.58i			1.14470i	0.820009	+	0.572350i	$0.193968\pi$
$937$			1072.58i			1.14470i	−0.820009	+	0.572350i	$0.806032\pi$
$938$			72.4103i			0.0771965i
$939$			142.394i			0.151644i
$940$		0			0
$941$		−	250.856i		−	0.266585i	−0.991077	−	0.133293i	$-0.957445\pi$
$941$		−	250.856i		−	0.266585i	0.991077	−	0.133293i	$-0.0425550\pi$
$942$			57.6819i			0.0612334i
$943$	798.478			0.846743
$944$			1379.19i			1.46100i
$945$		0			0
$946$		−	66.1473i		−	0.0699232i
$947$		−	346.018i		−	0.365383i	−0.983170	−	0.182692i	$-0.941519\pi$
$947$		−	346.018i		−	0.365383i	0.983170	−	0.182692i	$-0.0584810\pi$
$948$			260.318i			0.274597i
$949$			456.805i			0.481354i
$950$		0			0
$951$	1902.19			2.00020
$952$	103.265			0.108471
$953$	1194.91			1.25384			0.626920	−	0.779084i	$-0.284315\pi$
$953$	1194.91			1.25384			0.626920	+	0.779084i	$0.284315\pi$
$954$	24.5152			0.0256972
$955$		0			0
$956$	−701.233			−0.733507
$957$		−	1279.05i		−	1.33652i
$958$	18.8967			0.0197252
$959$	−656.128			−0.684180
$960$		0			0
$961$	−1187.24			−1.23543
$962$	39.4109			0.0409676
$963$	495.042			0.514062
$964$		−	140.929i		−	0.146192i
$965$		0			0
$966$	−82.5466			−0.0854520
$967$			1235.74i			1.27791i	0.769244	+	0.638955i	$0.220633\pi$
$967$			1235.74i			1.27791i	−0.769244	+	0.638955i	$0.779367\pi$
$968$	24.3286			0.0251329
$969$	1286.21	+	204.966i	1.32736	+	0.211524i
$970$		0			0
$971$			882.995i			0.909367i	0.890653	+	0.454683i	$0.150248\pi$
$971$			882.995i			0.909367i	−0.890653	+	0.454683i	$0.849752\pi$
$972$	328.954			0.338430
$973$			77.2162i			0.0793589i
$974$	−116.894			−0.120015
$975$		0			0
$976$	−1508.61			−1.54570
$977$	254.773			0.260771			0.130385	−	0.991463i	$-0.458379\pi$
$977$	254.773			0.260771			0.130385	+	0.991463i	$0.458379\pi$
$978$			52.0709i			0.0532422i
$979$		−	1574.29i		−	1.60806i
$980$		0			0
$981$			1757.35i			1.79138i
$982$	8.23625			0.00838722
$983$	966.862			0.983583			0.491791	−	0.870713i	$-0.336342\pi$
$983$	966.862			0.983583			0.491791	+	0.870713i	$0.336342\pi$
$984$		−	293.845i		−	0.298623i
$985$		0			0
$986$	−50.8244			−0.0515460
$987$	1214.69			1.23069
$988$	45.1379	−	283.250i	0.0456861	−	0.286691i
$989$	−728.564			−0.736667
$990$		0			0
$991$			1440.50i			1.45358i	0.686857	+	0.726792i	$0.258990\pi$
$991$			1440.50i			1.45358i	−0.686857	+	0.726792i	$0.741010\pi$
$992$		−	334.852i		−	0.337552i
$993$		−	19.1295i		−	0.0192644i
$994$	74.8747			0.0753267
$995$		0			0
$996$		−	2207.64i		−	2.21650i
$997$		−	1340.38i		−	1.34441i	−0.740363	−	0.672207i	$-0.765346\pi$
$997$		−	1340.38i		−	1.34441i	0.740363	−	0.672207i	$-0.234654\pi$
$998$	29.2518			0.0293104
$999$	2812.33			2.81515

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.c.a.56.6	✓	12	5.3	odd	4
95.3.c.a.56.7	yes	12	95.18	even	4
475.3.c.g.151.6		12	95.37	even	4
475.3.c.g.151.7		12	5.2	odd	4
475.3.d.c.474.11		24	19.18	odd	2	inner
475.3.d.c.474.12		24	5.4	even	2	inner
475.3.d.c.474.13		24	1.1	even	1	trivial
475.3.d.c.474.14		24	95.94	odd	2	inner
855.3.e.a.721.6		12	285.113	odd	4
855.3.e.a.721.7		12	15.8	even	4
1520.3.h.a.721.1		12	20.3	even	4
1520.3.h.a.721.12		12	380.303	odd	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.151673 q^{2} +5.10387 q^{3} -3.97700 q^{4} +0.774118 q^{6} -6.35478i q^{7} -1.20989 q^{8} +17.0495 q^{9} +O(q^{10})\)	\(q+0.151673 q^{2} +5.10387 q^{3} -3.97700 q^{4} +0.774118 q^{6} -6.35478i q^{7} -1.20989 q^{8} +17.0495 q^{9} +10.0445 q^{11} -20.2981 q^{12} +3.79583 q^{13} -0.963848i q^{14} +15.7245 q^{16} -13.4309i q^{17} +2.58594 q^{18} +(-2.99005 + 18.7633i) q^{19} -32.4340i q^{21} +1.52348 q^{22} -16.7800i q^{23} -6.17514 q^{24} +0.575725 q^{26} +41.0834 q^{27} +25.2729i q^{28} -24.9494i q^{29} -46.3492i q^{31} +7.22455 q^{32} +51.2658 q^{33} -2.03710i q^{34} -67.8056 q^{36} +68.4543 q^{37} +(-0.453510 + 2.84588i) q^{38} +19.3734 q^{39} +47.5852i q^{41} -4.91935i q^{42} -43.4186i q^{43} -39.9469 q^{44} -2.54507i q^{46} +37.4512i q^{47} +80.2556 q^{48} +8.61675 q^{49} -68.5494i q^{51} -15.0960 q^{52} +9.48017 q^{53} +6.23123 q^{54} +7.68861i q^{56} +(-15.2608 + 95.7651i) q^{57} -3.78414i q^{58} +87.7096i q^{59} -95.9399 q^{61} -7.02991i q^{62} -108.346i q^{63} -61.8021 q^{64} +7.77563 q^{66} -75.1263 q^{67} +53.4146i q^{68} -85.6428i q^{69} +77.6831i q^{71} -20.6280 q^{72} +120.344i q^{73} +10.3827 q^{74} +(11.8914 - 74.6214i) q^{76} -63.8306i q^{77} +2.93842 q^{78} -12.8248i q^{79} +56.2390 q^{81} +7.21738i q^{82} +108.761i q^{83} +128.990i q^{84} -6.58543i q^{86} -127.338i q^{87} -12.1528 q^{88} -156.732i q^{89} -24.1217i q^{91} +66.7339i q^{92} -236.560i q^{93} +5.68033i q^{94} +36.8731 q^{96} +56.1983 q^{97} +1.30693 q^{98} +171.253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9	\( 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9} + 64 q^{11} - 88 q^{16} - 16 q^{19} - 200 q^{24} + 216 q^{26} - 160 q^{36} - 152 q^{39} + 512 q^{44} - 144 q^{49} + 152 q^{54} - 592 q^{61} - 376 q^{64} + 304 q^{66} - 272 q^{74} + 496 q^{76} - 744 q^{81} - 88 q^{96} + 624 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9 + 64 * q^11 - 88 * q^16 - 16 * q^19 - 200 * q^24 + 216 * q^26 - 160 * q^36 - 152 * q^39 + 512 * q^44 - 144 * q^49 + 152 * q^54 - 592 * q^61 - 376 * q^64 + 304 * q^66 - 272 * q^74 + 496 * q^76 - 744 * q^81 - 88 * q^96 + 624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more