LMFDB - Embedded newform 225.4.k.c.124.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 $ x^12 - 23x^10 + 198x^8 - 719x^6 + 886x^4 + 585*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.2
Root			$-0.0378788 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.4.k.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +O(q^{10})$	\(q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +(10.4166 - 18.0422i) q^{11} +(-31.0869 - 4.73733i) q^{12} +(-51.9018 + 29.9655i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} -74.0460i q^{17} +(-30.1471 + 96.6172i) q^{18} +63.8390 q^{19} +(-151.731 + 59.2655i) q^{21} +(-67.6322 + 39.0475i) q^{22} +(28.4484 - 16.4247i) q^{23} +(-29.6307 - 23.7087i) q^{24} +224.655 q^{26} +(126.104 + 61.4884i) q^{27} +189.717i q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-195.444 + 112.840i) q^{32} +(39.3853 + 100.834i) q^{33} +(-138.783 + 240.379i) q^{34} +(120.139 - 110.748i) q^{36} +215.365i q^{37} +(-207.244 - 119.652i) q^{38} +(46.9143 - 307.857i) q^{39} +(-70.8407 - 122.700i) q^{41} +(603.654 + 91.9908i) q^{42} +(119.430 + 68.9529i) q^{43} +126.078 q^{44} -123.138 q^{46} +(-29.0803 - 16.7895i) q^{47} +(143.281 + 366.829i) q^{48} +(319.885 + 554.058i) q^{49} +(300.422 + 240.379i) q^{51} +(-314.096 - 181.344i) q^{52} +41.9914i q^{53} +(-294.131 - 435.967i) q^{54} +(-114.474 + 198.275i) q^{56} +(-207.244 + 259.010i) q^{57} +(519.445 - 299.902i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} -953.535i q^{62} +(252.119 - 808.007i) q^{63} +239.652 q^{64} +(61.1331 - 401.162i) q^{66} +(-742.646 + 428.767i) q^{67} +(388.072 - 224.054i) q^{68} +(-25.7146 + 168.742i) q^{69} +588.665 q^{71} +(192.384 - 43.2522i) q^{72} +618.191i q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(565.607 - 326.553i) q^{77} +(-729.311 + 911.481i) q^{78} +(-172.644 + 299.029i) q^{79} +(-658.851 + 312.021i) q^{81} +531.102i q^{82} +(-946.711 - 546.584i) q^{83} +(-769.728 - 615.889i) q^{84} +(-258.474 - 447.691i) q^{86} +(-302.496 - 774.450i) q^{87} +(131.765 + 76.0746i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(172.162 + 99.3979i) q^{92} +(-1306.68 - 199.125i) q^{93} +(62.9366 + 109.009i) q^{94} +(176.663 - 1159.28i) q^{96} +(174.427 + 100.705i) q^{97} -2398.22i q^{98} +(-536.967 - 167.547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−3.24635	−	1.87428i	−1.14776	−	0.662659i	−0.199419	−	0.979914i	$-0.563905\pi$
$2$	−3.24635	−	1.87428i	−1.14776	−	0.662659i	−0.948340	+	0.317255i	$0.897239\pi$
$3$	−3.24635	+	4.05724i	−0.624761	+	0.780816i
$3$	−3.24635	+	4.05724i	−0.624761	+	0.780816i
$4$	3.02587	+	5.24096i	0.378234	+	0.655120i
$5$		0			0
$5$		0			0
$6$	18.1432	−	7.08665i	1.23449	−	0.482185i
$7$	27.1492	+	15.6746i	1.46592	+	0.846348i	0.999274	−	0.0380969i	$-0.0121296\pi$
$7$	27.1492	+	15.6746i	1.46592	+	0.846348i	0.466644	+	0.884445i	$0.345463\pi$
$8$			7.30318i			0.322758i
$9$	−5.92239	−	26.3425i	−0.219348	−	0.975647i
$10$		0			0
$11$	10.4166	−	18.0422i	0.285522	−	0.494538i	−0.687214	−	0.726455i	$-0.741166\pi$
$11$	10.4166	−	18.0422i	0.285522	−	0.494538i	0.972736	+	0.231917i	$0.0744998\pi$
$12$	−31.0869	−	4.73733i	−0.747834	−	0.113962i
$13$	−51.9018	+	29.9655i	−1.10731	+	0.639303i	−0.938130	−	0.346283i	$-0.887444\pi$
$13$	−51.9018	+	29.9655i	−1.10731	+	0.639303i	−0.169175	+	0.985586i	$0.554110\pi$
$14$	−58.7572	−	101.770i	−1.12168	−	1.94281i
$15$		0			0
$16$	37.8952	−	65.6364i	0.592112	−	1.02557i
$17$		−	74.0460i		−	1.05640i	−0.849120	−	0.528200i	$-0.822867\pi$
$17$		−	74.0460i		−	1.05640i	0.849120	−	0.528200i	$-0.177133\pi$
$18$	−30.1471	+	96.6172i	−0.394763	+	1.26516i
$19$	63.8390			0.770825			0.385413	−	0.922744i	$-0.374059\pi$
$19$	63.8390			0.770825			0.385413	+	0.922744i	$0.374059\pi$
$20$		0			0
$21$	−151.731	+	59.2655i	−1.57669	+	0.615847i
$22$	−67.6322	+	39.0475i	−0.655420	+	0.378407i
$23$	28.4484	−	16.4247i	0.257909	−	0.148904i	−0.365472	−	0.930823i	$-0.619092\pi$
$23$	28.4484	−	16.4247i	0.257909	−	0.148904i	0.623380	+	0.781919i	$0.285759\pi$
$24$	−29.6307	−	23.7087i	−0.252015	−	0.201646i
$25$		0			0
$26$	224.655			1.69456
$27$	126.104	+	61.4884i	0.898841	+	0.438276i
$28$			189.717i			1.28047i
$29$	−80.0044	+	138.572i	−0.512291	+	0.887314i	0.487607	+	0.873063i	$0.337870\pi$
$29$	−80.0044	+	138.572i	−0.512291	+	0.887314i	−0.999898	+	0.0142513i	$0.995464\pi$
$30$		0			0
$31$	127.187	+	220.294i	0.736884	+	1.27632i	0.953892	+	0.300151i	$0.0970371\pi$
$31$	127.187	+	220.294i	0.736884	+	1.27632i	−0.217007	+	0.976170i	$0.569630\pi$
$32$	−195.444	+	112.840i	−1.07969	+	0.623358i
$33$	39.3853	+	100.834i	0.207760	+	0.531908i
$34$	−138.783	+	240.379i	−0.700033	+	1.21249i
$35$		0			0
$36$	120.139	−	110.748i	0.556201	−	0.512722i
$37$			215.365i			0.956914i	0.878111	+	0.478457i	$0.158804\pi$
$37$			215.365i			0.956914i	−0.878111	+	0.478457i	$0.841196\pi$
$38$	−207.244	−	119.652i	−0.884722	−	0.510794i
$39$	46.9143	−	307.857i	0.192623	−	1.26401i
$40$		0			0
$41$	−70.8407	−	122.700i	−0.269841	−	0.467377i	0.698980	−	0.715141i	$-0.253638\pi$
$41$	−70.8407	−	122.700i	−0.269841	−	0.467377i	−0.968820	+	0.247764i	$0.920304\pi$
$42$	603.654	+	91.9908i	2.21776	+	0.337964i
$43$	119.430	+	68.9529i	0.423556	+	0.244540i	0.696597	−	0.717462i	$-0.254696\pi$
$43$	119.430	+	68.9529i	0.423556	+	0.244540i	−0.273042	+	0.962002i	$0.588030\pi$
$44$	126.078			0.431976
$45$		0			0
$46$	−123.138			−0.394689
$47$	−29.0803	−	16.7895i	−0.0902509	−	0.0521064i	0.454195	−	0.890902i	$-0.349927\pi$
$47$	−29.0803	−	16.7895i	−0.0902509	−	0.0521064i	−0.544446	+	0.838796i	$0.683260\pi$
$48$	143.281	+	366.829i	0.430852	+	1.10307i
$49$	319.885	+	554.058i	0.932611	+	1.61533i
$50$		0			0
$51$	300.422	+	240.379i	0.824854	+	0.659997i
$52$	−314.096	−	181.344i	−0.837641	−	0.483612i
$53$			41.9914i			0.108829i	0.998518	+	0.0544147i	$0.0173293\pi$
$53$			41.9914i			0.108829i	−0.998518	+	0.0544147i	$0.982671\pi$
$54$	−294.131	−	435.967i	−0.741225	−	1.09866i
$55$		0			0
$56$	−114.474	+	198.275i	−0.273166	+	0.473137i
$57$	−207.244	+	259.010i	−0.481581	+	0.601873i
$58$	519.445	−	299.902i	1.17597	−	0.678949i
$59$	307.571	+	532.728i	0.678683	+	1.17551i	0.975378	+	0.220541i	$0.0707824\pi$
$59$	307.571	+	532.728i	0.678683	+	1.17551i	−0.296694	+	0.954973i	$0.595884\pi$
$60$		0			0
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	−0.786903	−	0.617077i	$-0.788317\pi$
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	0.927856	+	0.372939i	$0.121650\pi$
$62$		−	953.535i		−	1.95321i
$63$	252.119	−	808.007i	0.504191	−	1.61586i
$64$	239.652			0.468071
$65$		0			0
$66$	61.1331	−	401.162i	0.114015	−	0.748176i
$67$	−742.646	+	428.767i	−1.35416	+	0.781824i	−0.988829	−	0.149055i	$-0.952377\pi$
$67$	−742.646	+	428.767i	−1.35416	+	0.781824i	−0.365329	+	0.930878i	$0.619044\pi$
$68$	388.072	−	224.054i	0.692069	−	0.399566i
$69$	−25.7146	+	168.742i	−0.0448649	+	0.294408i
$70$		0			0
$71$	588.665			0.983968			0.491984	−	0.870604i	$-0.336272\pi$
$71$	588.665			0.983968			0.491984	+	0.870604i	$0.336272\pi$
$72$	192.384	−	43.2522i	0.314898	−	0.0707962i
$73$			618.191i			0.991148i	0.868566	+	0.495574i	$0.165042\pi$
$73$			618.191i			0.991148i	−0.868566	+	0.495574i	$0.834958\pi$
$74$	403.655	−	699.152i	0.634108	−	1.09831i
$75$		0			0
$76$	193.169	+	334.578i	0.291552	+	0.504983i
$77$	565.607	−	326.553i	0.837103	−	0.483301i
$78$	−729.311	+	911.481i	−1.05869	+	1.32314i
$79$	−172.644	+	299.029i	−0.245873	+	0.425865i	−0.962377	−	0.271718i	$-0.912408\pi$
$79$	−172.644	+	299.029i	−0.245873	+	0.425865i	0.716503	+	0.697584i	$0.245741\pi$
$80$		0			0
$81$	−658.851	+	312.021i	−0.903773	+	0.428012i
$82$			531.102i			0.715249i
$83$	−946.711	−	546.584i	−1.25199	−	0.722836i	−0.280484	−	0.959859i	$-0.590495\pi$
$83$	−946.711	−	546.584i	−1.25199	−	0.722836i	−0.971504	+	0.237023i	$0.923828\pi$
$84$	−769.728	−	615.889i	−0.999812	−	0.799988i
$85$		0			0
$86$	−258.474	−	447.691i	−0.324093	−	0.561346i
$87$	−302.496	−	774.450i	−0.372770	−	0.954365i
$88$	131.765	+	76.0746i	0.159616	+	0.0921543i
$89$	−414.849			−0.494089			−0.247045	−	0.969004i	$-0.579459\pi$
$89$	−414.849			−0.494089			−0.247045	+	0.969004i	$0.579459\pi$
$90$		0			0
$91$	−1878.79			−2.16429
$92$	172.162	+	99.3979i	0.195100	+	0.112641i
$93$	−1306.68	−	199.125i	−1.45695	−	0.222024i
$94$	62.9366	+	109.009i	0.0690576	+	0.119611i
$95$		0			0
$96$	176.663	−	1159.28i	0.187819	−	1.23249i
$97$	174.427	+	100.705i	0.182581	+	0.105413i	0.588505	−	0.808494i	$-0.299717\pi$
$97$	174.427	+	100.705i	0.182581	+	0.105413i	−0.405924	+	0.913907i	$0.633050\pi$
$98$		−	2398.22i		−	2.47201i
$99$	−536.967	−	167.547i	−0.545123	−	0.170092i
$100$		0			0
$101$	−132.691	+	229.828i	−0.130726	+	0.226424i	−0.923957	−	0.382498i	$-0.875064\pi$
$101$	−132.691	+	229.828i	−0.130726	+	0.226424i	0.793231	+	0.608921i	$0.208397\pi$
$102$	−524.738	−	1343.43i	−0.509380	−	1.30411i
$103$	456.931	−	263.809i	0.437114	−	0.252368i	−0.265259	−	0.964177i	$-0.585457\pi$
$103$	456.931	−	263.809i	0.437114	−	0.252368i	0.702373	+	0.711810i	$0.252124\pi$
$104$	−218.843	−	379.048i	−0.206340	−	0.357391i
$105$		0			0
$106$	78.7038	−	136.319i	0.0721168	−	0.124910i
$107$			2084.24i			1.88310i	0.336877	+	0.941549i	$0.390629\pi$
$107$			2084.24i			1.88310i	−0.336877	+	0.941549i	$0.609371\pi$
$108$	59.3157	+	846.961i	0.0528487	+	0.754619i
$109$	−925.651			−0.813406			−0.406703	−	0.913560i	$-0.633322\pi$
$109$	−925.651			−0.813406			−0.406703	+	0.913560i	$0.633322\pi$
$110$		0			0
$111$	−873.788	−	699.152i	−0.747174	−	0.597843i
$112$	2057.65	−	1187.98i	1.73598	−	1.00227i
$113$	−472.866	+	273.009i	−0.393659	+	0.227279i	−0.683745	−	0.729721i	$-0.739650\pi$
$113$	−472.866	+	273.009i	−0.393659	+	0.227279i	0.290085	+	0.957001i	$0.406316\pi$
$114$	1158.25	−	452.405i	0.951576	−	0.371681i
$115$		0			0
$116$	−968.332			−0.775063
$117$	1096.75	+	1189.75i	0.866619	+	0.940109i
$118$		−	2305.90i		−	1.79894i
$119$	1160.64	−	2010.29i	0.894082	−	1.54860i
$120$		0			0
$121$	448.487	+	776.802i	0.336955	+	0.583623i
$122$	−436.008	+	251.729i	−0.323560	+	0.186807i
$123$	727.796	+	110.909i	0.533522	+	0.0813033i
$124$	−769.701	+	1333.16i	−0.557429	+	0.965495i
$125$		0			0
$126$	−2332.90	+	2150.53i	−1.64946	+	1.52051i
$127$		−	975.972i		−	0.681918i	−0.940078	−	0.340959i	$-0.889248\pi$
$127$		−	975.972i		−	0.681918i	0.940078	−	0.340959i	$-0.110752\pi$
$128$	785.559	+	453.543i	0.542455	+	0.313187i
$129$	−667.470	+	260.710i	−0.455562	+	0.177940i
$130$		0			0
$131$	814.614	+	1410.95i	0.543307	+	0.941035i	0.998711	+	0.0507502i	$0.0161612\pi$
$131$	814.614	+	1410.95i	0.543307	+	0.941035i	−0.455405	+	0.890285i	$0.650505\pi$
$132$	−409.293	+	511.528i	−0.269882	+	0.337294i
$133$	1733.18	+	1000.65i	1.12997	+	0.652387i
$134$	3214.52			2.07233
$135$		0			0
$136$	540.771			0.340961
$137$	−572.833	−	330.725i	−0.357229	−	0.206246i	0.310635	−	0.950529i	$-0.399458\pi$
$137$	−572.833	−	330.725i	−0.357229	−	0.206246i	−0.667865	+	0.744283i	$0.732792\pi$
$138$	399.749	−	499.600i	0.246586	−	0.308180i
$139$	691.495	+	1197.70i	0.421955	+	0.730848i	0.996131	−	0.0878842i	$-0.0280105\pi$
$139$	691.495	+	1197.70i	0.421955	+	0.730848i	−0.574175	+	0.818732i	$0.694677\pi$
$140$		0			0
$141$	162.524	−	63.4810i	0.0970708	−	0.0379153i
$142$	−1911.02	−	1103.33i	−1.12936	−	0.652035i
$143$			1248.56i			0.730139i
$144$	−1953.45	−	609.528i	−1.13047	−	0.352736i
$145$		0			0
$146$	1158.66	−	2006.87i	0.656793	−	1.13760i
$147$	−3286.41	−	500.815i	−1.84393	−	0.280997i
$148$	−1128.72	+	651.667i	−0.626894	+	0.361937i
$149$	1581.75	+	2739.66i	0.869676	+	1.50632i	0.862328	+	0.506349i	$0.169005\pi$
$149$	1581.75	+	2739.66i	0.869676	+	1.50632i	0.00734719	+	0.999973i	$0.497661\pi$
$150$		0			0
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	−0.282488	−	0.959271i	$-0.591160\pi$
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	0.971997	−	0.234994i	$-0.0755071\pi$
$152$			466.228i			0.248790i
$153$	−1950.55	+	438.529i	−1.03067	+	0.231719i
$154$	−2448.21			−1.28106
$155$		0			0
$156$	1755.42	−	685.659i	0.900937	−	0.351901i
$157$	3031.92	−	1750.48i	1.54123	−	0.889832i	0.542474	−	0.840073i	$-0.317488\pi$
$157$	3031.92	−	1750.48i	1.54123	−	0.889832i	0.998761	−	0.0497594i	$-0.0158454\pi$
$158$	1120.93	−	647.168i	0.564407	−	0.325860i
$159$	−170.369	−	136.319i	−0.0849758	−	0.0679924i
$160$		0			0
$161$	1029.80			0.504097
$162$	2723.68	+	221.943i	1.32094	+	0.107639i
$163$		−	263.950i		−	0.126835i	−0.997987	−	0.0634176i	$-0.979800\pi$
$163$		−	263.950i		−	0.126835i	0.997987	−	0.0634176i	$-0.0202000\pi$
$164$	428.710	−	742.547i	0.204126	−	0.353556i
$165$		0			0
$166$	2048.90	+	3548.81i	0.957987	+	1.65928i
$167$	−3108.21	+	1794.53i	−1.44024	+	0.831524i	−0.997865	−	0.0653054i	$-0.979198\pi$
$167$	−3108.21	+	1794.53i	−1.44024	+	0.831524i	−0.442377	+	0.896829i	$0.645865\pi$
$168$	−432.826	−	1108.12i	−0.198770	−	0.508889i
$169$	697.365	−	1207.87i	0.317417	−	0.549782i
$170$		0			0
$171$	−378.080	−	1681.68i	−0.169079	−	0.752053i
$172$			834.570i			0.369973i
$173$	320.824	+	185.228i	0.140993	+	0.0814024i	0.568837	−	0.822450i	$-0.307393\pi$
$173$	320.824	+	185.228i	0.140993	+	0.0814024i	−0.427844	+	0.903853i	$0.640727\pi$
$174$	−469.529	+	3081.10i	−0.204568	+	1.34240i
$175$		0			0
$176$	−789.482	−	1367.42i	−0.338122	−	0.585644i
$177$	−3159.89	−	481.535i	−1.34188	−	0.204488i
$178$	1346.75	+	777.545i	0.567095	+	0.327413i
$179$	−446.898			−0.186607			−0.0933036	−	0.995638i	$-0.529743\pi$
$179$	−446.898			−0.186607			−0.0933036	+	0.995638i	$0.529743\pi$
$180$		0			0
$181$	−904.046			−0.371255			−0.185628	−	0.982620i	$-0.559432\pi$
$181$	−904.046			−0.371255			−0.185628	+	0.982620i	$0.559432\pi$
$182$	6099.21	+	3521.38i	2.48409	+	1.43419i
$183$	253.907	+	650.051i	0.102565	+	0.262586i
$184$	119.952	+	207.764i	0.0480598	+	0.0832420i
$185$		0			0
$186$	3868.72	+	3095.51i	1.52510	+	1.22029i
$187$	−1335.95	−	771.311i	−0.522430	−	0.301625i
$188$		−	203.211i		−	0.0788336i
$189$	2459.81	+	3645.99i	0.946693	+	1.40321i
$190$		0			0
$191$	299.793	−	519.257i	0.113572	−	0.196713i	−0.803636	−	0.595121i	$-0.797104\pi$
$191$	299.793	−	519.257i	0.113572	−	0.196713i	0.917208	+	0.398409i	$0.130437\pi$
$192$	−777.995	+	972.326i	−0.292432	+	0.365477i
$193$	3822.40	−	2206.87i	1.42561	−	0.823076i	0.428839	−	0.903381i	$-0.358923\pi$
$193$	3822.40	−	2206.87i	1.42561	−	0.823076i	0.996770	+	0.0803048i	$0.0255894\pi$
$194$	−377.500	−	653.850i	−0.139706	−	0.241978i
$195$		0			0
$196$	−1935.86	+	3353.01i	−0.705490	+	1.22194i
$197$		−	4807.15i		−	1.73855i	−0.494325	−	0.869277i	$-0.664585\pi$
$197$		−	4807.15i		−	1.73855i	0.494325	−	0.869277i	$-0.335415\pi$
$198$	1429.15	+	1550.35i	0.512956	+	0.556456i
$199$	−313.833			−0.111794			−0.0558970	−	0.998437i	$-0.517802\pi$
$199$	−313.833			−0.111794			−0.0558970	+	0.998437i	$0.517802\pi$
$200$		0			0
$201$	671.281	−	4405.02i	0.235565	−	1.54580i
$202$	861.527	−	497.403i	0.300083	−	0.173253i
$203$	−4344.11	+	2508.07i	−1.50195	+	0.867153i
$204$	−350.780	+	2301.86i	−0.120390	+	0.790012i
$205$		0			0
$206$	−1977.81			−0.668935
$207$	−601.149	−	652.127i	−0.201849	−	0.218966i
$208$			4542.20i			1.51416i
$209$	664.989	−	1151.79i	0.220087	−	0.381202i
$210$		0			0
$211$	−1219.41	−	2112.08i	−0.397856	−	0.689106i	0.595605	−	0.803277i	$-0.296912\pi$
$211$	−1219.41	−	2112.08i	−0.397856	−	0.689106i	−0.993461	+	0.114171i	$0.963579\pi$
$212$	−220.075	+	127.061i	−0.0712964	+	0.0411630i
$213$	−1911.02	+	2388.36i	−0.614745	+	0.768298i
$214$	3906.46	−	6766.19i	1.24785	−	2.16134i
$215$		0			0
$216$	−449.060	+	920.959i	−0.141457	+	0.290108i
$217$			7974.40i			2.49464i
$218$	3004.99	+	1734.93i	0.933594	+	0.539011i
$219$	−2508.15	−	2006.87i	−0.773904	−	0.619230i
$220$		0			0
$221$	2218.83	+	3843.12i	0.675360	+	1.16976i
$222$	1526.22	+	3907.42i	0.461410	+	1.18130i
$223$	−2020.79	−	1166.71i	−0.606827	−	0.350352i	0.164896	−	0.986311i	$-0.447271\pi$
$223$	−2020.79	−	1166.71i	−0.606827	−	0.350352i	−0.771722	+	0.635959i	$0.780605\pi$
$224$	−7074.87			−2.11031
$225$		0			0
$226$	2046.79			0.602435
$227$	2358.79	+	1361.85i	0.689684	+	0.398189i	0.803494	−	0.595313i	$-0.202972\pi$
$227$	2358.79	+	1361.85i	0.689684	+	0.398189i	−0.113810	+	0.993503i	$0.536305\pi$
$228$	−1984.56	−	302.426i	−0.576449	−	0.0878451i
$229$	−1657.08	−	2870.15i	−0.478179	−	0.828230i	0.521508	−	0.853246i	$-0.325370\pi$
$229$	−1657.08	−	2870.15i	−0.478179	−	0.828230i	−0.999687	+	0.0250162i	$0.992036\pi$
$230$		0			0
$231$	−511.255	+	3354.91i	−0.145619	+	0.955571i
$232$	−1012.01	−	584.286i	−0.286388	−	0.165346i
$233$			3175.44i			0.892833i	0.894825	+	0.446416i	$0.147300\pi$
$233$			3175.44i			0.892833i	−0.894825	+	0.446416i	$0.852700\pi$
$234$	−1330.50	−	5917.98i	−0.371698	−	1.65329i
$235$		0			0
$236$	−1861.34	+	3223.93i	−0.513402	+	0.889238i
$237$	−652.767	−	1671.21i	−0.178910	−	0.458046i
$238$	−7535.70	+	4350.74i	−2.05238	+	1.18494i
$239$	−123.062	−	213.150i	−0.0333064	−	0.0576884i	0.848892	−	0.528567i	$-0.177270\pi$
$239$	−123.062	−	213.150i	−0.0333064	−	0.0576884i	−0.882198	+	0.470878i	$0.843937\pi$
$240$		0			0
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	−0.259421	−	0.965764i	$-0.583532\pi$
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	0.966087	−	0.258217i	$-0.0831349\pi$
$242$		−	3362.36i		−	0.893144i
$243$	872.919	−	3686.04i	0.230444	−	0.973086i
$244$	812.791			0.213252
$245$		0			0
$246$	−2154.81	−	1724.14i	−0.558478	−	0.446860i
$247$	−3313.36	+	1912.97i	−0.853539	+	0.492791i
$248$	−1608.84	+	928.867i	−0.411943	+	0.237835i
$249$	5290.98	−	2066.63i	1.34659	−	0.525973i
$250$		0			0
$251$	2821.23			0.709459			0.354730	−	0.934969i	$-0.384573\pi$
$251$	2821.23			0.709459			0.354730	+	0.934969i	$0.384573\pi$
$252$	4997.62	−	1123.58i	1.24929	−	0.280868i
$253$		−	684.361i		−	0.170061i
$254$	−1829.25	+	3168.35i	−0.451879	+	0.782677i
$255$		0			0
$256$	−2658.74	−	4605.08i	−0.649107	−	1.12429i
$257$	−1631.76	+	942.096i	−0.396056	+	0.228663i	−0.684781	−	0.728749i	$-0.740102\pi$
$257$	−1631.76	+	942.096i	−0.396056	+	0.228663i	0.288725	+	0.957412i	$0.406769\pi$
$258$	2655.49	+	404.670i	0.640789	+	0.0976497i
$259$	−3375.76	+	5846.99i	−0.809883	+	1.40276i
$260$		0			0
$261$	4124.14	+	1286.84i	0.978075	+	0.305185i
$262$		−	6107.27i		−	1.44011i
$263$	478.922	+	276.506i	0.112287	+	0.0648292i	0.555092	−	0.831789i	$-0.312683\pi$
$263$	478.922	+	276.506i	0.112287	+	0.0648292i	−0.442804	+	0.896618i	$0.646016\pi$
$264$	−736.409	+	287.638i	−0.171677	+	0.0670563i
$265$		0			0
$266$	−3751.00	−	6496.93i	−0.864620	−	1.49757i
$267$	1346.75	−	1683.14i	0.308688	−	0.385793i
$268$	−4494.30	−	2594.78i	−1.02438	−	0.591424i
$269$	−3363.48			−0.762361			−0.381180	−	0.924501i	$-0.624482\pi$
$269$	−3363.48			−0.762361			−0.381180	+	0.924501i	$0.624482\pi$
$270$		0			0
$271$	−3333.85			−0.747295			−0.373648	−	0.927571i	$-0.621893\pi$
$271$	−3333.85			−0.747295			−0.373648	+	0.927571i	$0.621893\pi$
$272$	−4860.11	−	2805.99i	−1.08341	−	0.625507i
$273$	6099.21	−	7622.70i	1.35217	−	1.68991i
$274$	1239.75	+	2147.30i	0.273342	+	0.473443i
$275$		0			0
$276$	−962.181	+	375.823i	−0.209842	+	0.0819633i
$277$	4665.50	+	2693.63i	1.01199	+	0.584275i	0.911775	−	0.410690i	$-0.134712\pi$
$277$	4665.50	+	2693.63i	1.01199	+	0.584275i	0.100220	+	0.994965i	$0.468045\pi$
$278$		−	5184.23i		−	1.11845i
$279$	5049.83	−	4655.08i	1.08360	−	0.998897i
$280$		0			0
$281$	−1858.35	+	3218.76i	−0.394519	+	0.683327i	−0.993040	−	0.117781i	$-0.962422\pi$
$281$	−1858.35	+	3218.76i	−0.394519	+	0.683327i	0.598521	+	0.801107i	$0.295755\pi$
$282$	−646.591	−	98.5340i	−0.136539	−	0.0208071i
$283$	−2397.81	+	1384.38i	−0.503658	+	0.290787i	−0.730223	−	0.683209i	$-0.760584\pi$
$283$	−2397.81	+	1384.38i	−0.503658	+	0.290787i	0.226565	+	0.973996i	$0.427250\pi$
$284$	1781.23	+	3085.17i	0.372170	+	0.644617i
$285$		0			0
$286$	2340.16	−	4053.27i	0.483833	−	0.838024i
$287$		−	4441.60i		−	0.913516i
$288$	4129.98	+	4480.20i	0.845004	+	0.916662i
$289$	−569.810			−0.115980
$290$		0			0
$291$	−974.836	+	380.766i	−0.196378	+	0.0767041i
$292$	−3239.91	+	1870.57i	−0.649321	+	0.374886i
$293$	3013.76	−	1740.00i	0.600907	−	0.346934i	−0.168491	−	0.985703i	$-0.553890\pi$
$293$	3013.76	−	1740.00i	0.600907	−	0.346934i	0.769398	+	0.638769i	$0.220556\pi$
$294$	9730.17	+	7785.48i	1.93019	+	1.54442i
$295$		0			0
$296$	−1572.85			−0.308852
$297$	2422.96	−	1634.68i	0.473382	−	0.319374i
$298$		−	11858.6i		−	2.30519i
$299$	−984.348	+	1704.94i	−0.190389	+	0.329764i
$300$		0			0
$301$	2161.62	+	3744.03i	0.413932	+	0.716951i
$302$	−8306.75	+	4795.91i	−1.58278	+	0.913819i
$303$	−501.705	−	1284.47i	−0.0951229	−	0.243533i
$304$	2419.19	−	4190.16i	0.456415	−	0.790534i
$305$		0			0
$306$	7154.11	+	2232.27i	1.33651	+	0.417027i
$307$		−	1810.36i		−	0.336555i	−0.985740	−	0.168278i	$-0.946179\pi$
$307$		−	1810.36i		−	0.336555i	0.985740	−	0.168278i	$-0.0538205\pi$
$308$	3422.91	+	1976.22i	0.633241	+	0.365602i
$309$	−413.021	+	2710.29i	−0.0760387	+	0.498975i
$310$		0			0
$311$	443.649	+	768.422i	0.0808907	+	0.140107i	0.903633	−	0.428308i	$-0.140890\pi$
$311$	443.649	+	768.422i	0.0808907	+	0.140107i	−0.822742	+	0.568415i	$0.807557\pi$
$312$	2248.33	+	342.623i	0.407970	+	0.0621706i
$313$	−1918.36	−	1107.57i	−0.346429	−	0.200011i	0.316682	−	0.948532i	$-0.397431\pi$
$313$	−1918.36	−	1107.57i	−0.346429	−	0.200011i	−0.663111	+	0.748521i	$0.730764\pi$
$314$	−13123.6			−2.35862
$315$		0			0
$316$	−2089.60			−0.371990
$317$	569.884	+	329.023i	0.100971	+	0.0582958i	0.549635	−	0.835405i	$-0.314767\pi$
$317$	569.884	+	329.023i	0.100971	+	0.0582958i	−0.448664	+	0.893700i	$0.648100\pi$
$318$	297.578	+	761.859i	0.0524760	+	0.134349i
$319$	1666.76	+	2886.91i	0.292540	+	0.506695i
$320$		0			0
$321$	−8456.28	−	6766.19i	−1.47035	−	1.17649i
$322$	−3343.10	−	1930.14i	−0.578582	−	0.334045i
$323$		−	4727.03i		−	0.814299i
$324$	−3628.88	−	2508.88i	−0.622237	−	0.430192i
$325$		0			0
$326$	−494.717	+	856.875i	−0.0840485	+	0.145576i
$327$	3004.99	−	3755.59i	0.508184	−	0.635121i
$328$	896.098	−	517.362i	0.150850	−	0.0870931i
$329$	−526.337	−	911.643i	−0.0882003	−	0.152767i
$330$		0			0
$331$	−2638.22	+	4569.53i	−0.438096	+	0.758804i	−0.997543	−	0.0700619i	$-0.977680\pi$
$331$	−2638.22	+	4569.53i	−0.438096	+	0.758804i	0.559447	+	0.828866i	$0.311014\pi$
$332$		−	6615.57i		−	1.09360i
$333$	5673.25	−	1275.48i	0.933610	−	0.209897i
$334$	13453.8			2.20407
$335$		0			0
$336$	−1859.92	+	12205.0i	−0.301984	+	1.98165i
$337$	−2910.95	+	1680.64i	−0.470532	+	0.271662i	−0.716462	−	0.697626i	$-0.754240\pi$
$337$	−2910.95	+	1680.64i	−0.470532	+	0.271662i	0.245930	+	0.969288i	$0.420907\pi$
$338$	−4527.78	+	2614.12i	−0.728636	+	0.420678i
$339$	427.426	−	2804.82i	0.0684796	−	0.449371i
$340$		0			0
$341$	5299.44			0.841586
$342$	−1924.56	+	6167.95i	−0.304293	+	0.975217i
$343$			9303.52i			1.46456i
$344$	−503.575	+	872.218i	−0.0789272	+	0.136706i
$345$		0			0
$346$	−694.339	−	1202.63i	−0.107884	−	0.186861i
$347$	8102.13	−	4677.77i	1.25344	−	0.723677i	0.281653	−	0.959516i	$-0.409117\pi$
$347$	8102.13	−	4677.77i	1.25344	−	0.723677i	0.971792	+	0.235840i	$0.0757841\pi$
$348$	3143.55	−	3928.75i	0.484229	−	0.605182i
$349$	3519.65	−	6096.22i	0.539836	−	0.935023i	−0.459077	−	0.888397i	$-0.651820\pi$
$349$	3519.65	−	6096.22i	0.539836	−	0.935023i	0.998912	−	0.0466263i	$-0.0148470\pi$
$350$		0			0
$351$	−8387.55	+	587.410i	−1.27548	+	0.0893266i
$352$			4701.65i			0.711929i
$353$	3639.19	+	2101.09i	0.548710	+	0.316798i	0.748602	−	0.663020i	$-0.230726\pi$
$353$	3639.19	+	2101.09i	0.548710	+	0.316798i	−0.199891	+	0.979818i	$0.564059\pi$
$354$	9355.58	+	7485.76i	1.40464	+	1.12391i
$355$		0			0
$356$	−1255.28	−	2174.21i	−0.186881	−	0.323688i
$357$	4388.37	+	11235.1i	0.650581	+	1.66562i
$358$	1450.79	+	837.612i	0.214180	+	0.123657i
$359$	−588.013			−0.0864461			−0.0432230	−	0.999065i	$-0.513763\pi$
$359$	−588.013			−0.0864461			−0.0432230	+	0.999065i	$0.513763\pi$
$360$		0			0
$361$	−2783.58			−0.405828
$362$	2934.85	+	1694.44i	0.426112	+	0.246016i
$363$	−4607.62	−	702.155i	−0.666218	−	0.101525i
$364$	−5684.97	−	9846.66i	−0.818608	−	1.41787i
$365$		0			0
$366$	394.109	−	2586.19i	0.0562853	−	0.369350i
$367$	6742.10	+	3892.55i	0.958950	+	0.553650i	0.895850	−	0.444357i	$-0.146568\pi$
$367$	6742.10	+	3892.55i	0.958950	+	0.553650i	0.0631004	+	0.998007i	$0.479901\pi$
$368$		−	2489.67i		−	0.352671i
$369$	−2812.67	+	2592.79i	−0.396806	+	0.365787i
$370$		0			0
$371$	−658.198	+	1140.03i	−0.0921077	+	0.159535i
$372$	−2910.23	−	7450.77i	−0.405615	−	1.03845i
$373$	6775.81	−	3912.02i	0.940585	−	0.543047i	0.0504412	−	0.998727i	$-0.483937\pi$
$373$	6775.81	−	3912.02i	0.940585	−	0.543047i	0.890144	+	0.455680i	$0.150604\pi$
$374$	2891.31	+	5007.90i	0.399749	+	0.692385i
$375$		0			0
$376$	122.617	−	212.378i	0.0168177	−	0.0291292i
$377$		−	9589.49i		−	1.31004i
$378$	−1151.81	−	16446.5i	−0.156727	−	2.23788i
$379$	4679.90			0.634275			0.317138	−	0.948379i	$-0.397278\pi$
$379$	4679.90			0.634275			0.317138	+	0.948379i	$0.397278\pi$
$380$		0			0
$381$	3959.75	+	3168.35i	0.532452	+	0.426036i
$382$	−1946.47	+	1123.79i	−0.260707	+	0.150519i
$383$	5826.31	−	3363.82i	0.777313	−	0.448782i	−0.0581644	−	0.998307i	$-0.518525\pi$
$383$	5826.31	−	3363.82i	0.777313	−	0.448782i	0.835477	+	0.549525i	$0.185191\pi$
$384$	−4390.33	+	1714.84i	−0.583446	+	0.227891i
$385$		0			0
$386$	−16545.2			−2.18167
$387$	1109.08	−	3554.44i	0.145679	−	0.466880i
$388$			1218.89i			0.159483i
$389$	−2386.44	+	4133.43i	−0.311047	+	0.538749i	−0.978589	−	0.205823i	$-0.934013\pi$
$389$	−2386.44	+	4133.43i	−0.311047	+	0.538749i	0.667542	+	0.744572i	$0.267346\pi$
$390$		0			0
$391$	−1216.18	−	2106.49i	−0.157302	−	0.272455i
$392$	−4046.38	+	2336.18i	−0.521360	+	0.301007i
$393$	−8369.10	−	1275.37i	−1.07421	−	0.163699i
$394$	−9009.95	+	15605.7i	−1.15207	+	1.99544i
$395$		0			0
$396$	−746.681	−	3321.20i	−0.0947529	−	0.421456i
$397$		−	4688.95i		−	0.592775i	−0.955068	−	0.296388i	$-0.904218\pi$
$397$		−	4688.95i		−	0.592775i	0.955068	−	0.296388i	$-0.0957820\pi$
$398$	1018.81	+	588.211i	0.128313	+	0.0740813i
$399$	−9686.39	+	3783.45i	−1.21535	+	0.474711i
$400$		0			0
$401$	−766.916	−	1328.34i	−0.0955061	−	0.165421i	0.814314	−	0.580425i	$-0.197114\pi$
$401$	−766.916	−	1328.34i	−0.0955061	−	0.165421i	−0.909820	+	0.415004i	$0.863780\pi$
$402$	−10435.5	+	13042.1i	−1.29471	+	1.61811i
$403$	−13202.4	−	7622.43i	−1.63191	−	0.942185i
$404$	−1606.03			−0.197780
$405$		0			0
$406$	18803.3			2.29851
$407$	3885.66	+	2243.38i	0.473230	+	0.273220i
$408$	−1755.53	+	2194.04i	−0.213019	+	0.266228i
$409$	−4389.41	−	7602.68i	−0.530666	−	0.919140i	−0.999360	−	0.0357796i	$-0.988609\pi$
$409$	−4389.41	−	7602.68i	−0.530666	−	0.919140i	0.468694	−	0.883361i	$-0.344725\pi$
$410$		0			0
$411$	3201.45	−	1250.47i	0.384224	−	0.150076i
$412$	2765.23	+	1596.50i	0.330662	+	0.190908i
$413$			19284.2i			2.29761i
$414$	729.271	+	3243.76i	0.0865742	+	0.385077i
$415$		0			0
$416$	6762.61	−	11713.2i	0.797029	−	1.38050i
$417$	−7104.21	−	1082.61i	−0.834279	−	0.127136i
$418$	−4317.58	+	2492.75i	−0.505214	+	0.291686i
$419$	−2138.02	−	3703.17i	−0.249282	−	0.431770i	0.714044	−	0.700100i	$-0.246861\pi$
$419$	−2138.02	−	3703.17i	−0.249282	−	0.431770i	−0.963327	+	0.268330i	$0.913528\pi$
$420$		0			0
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	0.0550823	+	0.998482i	$0.482458\pi$
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	−0.892252	+	0.451538i	$0.850875\pi$
$422$			9142.07i			1.05457i
$423$	−270.052	+	865.480i	−0.0310411	+	0.0994825i
$424$	−306.671			−0.0351256
$425$		0			0
$426$	10680.3	−	4171.66i	1.21470	−	0.474455i
$427$	3646.32	−	2105.21i	0.413250	−	0.238590i
$428$	−10923.4	+	6306.65i	−1.23366	+	0.712251i
$429$	−5065.71	−	4053.27i	−0.570105	−	0.456163i
$430$		0			0
$431$	−2208.11			−0.246777			−0.123389	−	0.992358i	$-0.539376\pi$
$431$	−2208.11			−0.246777			−0.123389	+	0.992358i	$0.539376\pi$
$432$	8814.60	−	5946.89i	0.981696	−	0.662314i
$433$			10062.3i			1.11677i	0.829581	+	0.558386i	$0.188579\pi$
$433$			10062.3i			1.11677i	−0.829581	+	0.558386i	$0.811421\pi$
$434$	14946.3	−	25887.7i	1.65310	−	2.86325i
$435$		0			0
$436$	−2800.90	−	4851.30i	−0.307658	−	0.532879i
$437$	1816.12	−	1048.54i	0.198803	−	0.114779i
$438$	4380.90	+	11216.0i	0.477917	+	1.22356i
$439$	6658.62	−	11533.1i	0.723915	−	1.25386i	−0.235504	−	0.971873i	$-0.575674\pi$
$439$	6658.62	−	11533.1i	0.723915	−	1.25386i	0.959419	−	0.281984i	$-0.0909925\pi$
$440$		0			0
$441$	12700.8	−	11707.9i	1.37142	−	1.26422i
$442$		−	16634.8i		−	1.79013i
$443$	−12362.6	−	7137.55i	−1.32588	−	0.765497i	−0.341220	−	0.939983i	$-0.610840\pi$
$443$	−12362.6	−	7137.55i	−1.32588	−	0.765497i	−0.984660	+	0.174486i	$0.944174\pi$
$444$	1020.26	−	6695.03i	0.109052	−	0.715613i
$445$		0			0
$446$	4373.47	+	7575.08i	0.464327	+	0.804238i
$447$	−16250.4	−	2476.39i	−1.71950	−	0.262034i
$448$	6506.36	+	3756.45i	0.686153	+	0.396151i
$449$	1690.02			0.177632			0.0888162	−	0.996048i	$-0.471692\pi$
$449$	1690.02			0.177632			0.0888162	+	0.996048i	$0.471692\pi$
$450$		0			0
$451$	−2951.69			−0.308181
$452$	−2861.66	−	1652.18i	−0.297791	−	0.171929i
$453$	4837.39	+	12384.7i	0.501723	+	1.28451i
$454$	−5104.97	−	8842.07i	−0.527727	−	0.914051i
$455$		0			0
$456$	−1891.60	−	1513.54i	−0.194259	−	0.155434i
$457$	5771.53	+	3332.19i	0.590767	+	0.341080i	0.765401	−	0.643554i	$-0.222541\pi$
$457$	5771.53	+	3332.19i	0.590767	+	0.341080i	−0.174633	+	0.984634i	$0.555874\pi$
$458$			12423.3i			1.26748i
$459$	4552.97	−	9337.49i	0.462994	−	0.949535i
$460$		0			0
$461$	−833.712	+	1444.03i	−0.0842295	+	0.145890i	−0.905063	−	0.425278i	$-0.860176\pi$
$461$	−833.712	+	1444.03i	−0.0842295	+	0.145890i	0.820833	+	0.571168i	$0.193510\pi$
$462$	7947.76	−	9932.99i	0.800354	−	1.00027i
$463$	5050.68	−	2916.01i	0.506966	−	0.292697i	−0.224620	−	0.974446i	$-0.572114\pi$
$463$	5050.68	−	2916.01i	0.506966	−	0.292697i	0.731585	+	0.681750i	$0.238781\pi$
$464$	6063.56	+	10502.4i	0.606668	+	1.05078i
$465$		0			0
$466$	5951.67	−	10308.6i	0.591644	−	1.02476i
$467$			17410.6i			1.72519i	0.505892	+	0.862597i	$0.331163\pi$
$467$			17410.6i			1.72519i	−0.505892	+	0.862597i	$0.668837\pi$
$468$	−2916.84	+	9348.06i	−0.288100	+	0.923321i
$469$	−26883.0			−2.64678
$470$		0			0
$471$	−2740.57	+	17983.9i	−0.268108	+	1.75935i
$472$	−3890.61	+	2246.24i	−0.379406	+	0.219050i
$473$	2488.12	−	1436.52i	0.241869	−	0.139643i
$474$	−1013.21	+	6648.81i	−0.0981822	+	0.644283i
$475$		0			0
$476$	14047.8			1.35269
$477$	1106.16	−	248.689i	0.106179	−	0.0238715i
$478$			922.614i			0.0882832i
$479$	−1639.67	+	2839.99i	−0.156406	+	0.270903i	−0.933570	−	0.358395i	$-0.883324\pi$
$479$	−1639.67	+	2839.99i	−0.156406	+	0.270903i	0.777164	+	0.629298i	$0.216657\pi$
$480$		0			0
$481$	−6453.53	−	11177.8i	−0.611758	−	1.05960i
$482$	−17165.9	+	9910.71i	−1.62216	+	0.936557i
$483$	−3343.10	+	4178.15i	−0.314940	+	0.393607i
$484$	−2714.13	+	4701.00i	−0.254895	+	0.441492i
$485$		0			0
$486$	−9742.49	+	10330.1i	−0.909318	+	0.964162i
$487$		−	10506.7i		−	0.977624i	−0.872389	−	0.488812i	$-0.837430\pi$
$487$		−	10506.7i		−	0.977624i	0.872389	−	0.488812i	$-0.162570\pi$
$488$	849.456	+	490.433i	0.0787972	+	0.0454936i
$489$	1070.91	+	856.875i	0.0990350	+	0.0792417i
$490$		0			0
$491$	7132.25	+	12353.4i	0.655548	+	1.13544i	0.981756	+	0.190144i	$0.0608956\pi$
$491$	7132.25	+	12353.4i	0.655548	+	1.13544i	−0.326208	+	0.945298i	$0.605771\pi$
$492$	1620.95	+	4149.95i	0.148532	+	0.380272i
$493$	10260.7	+	5924.01i	0.937359	+	0.541184i
$494$	14341.8			1.30621
$495$		0			0
$496$	19279.1			1.74527
$497$	15981.8	+	9227.09i	1.44242	+	0.832780i
$498$	−21049.8	−	3207.78i	−1.89411	−	0.288643i
$499$	4723.70	+	8181.68i	0.423771	+	0.733993i	0.996305	−	0.0858882i	$-0.0273728\pi$
$499$	4723.70	+	8181.68i	0.423771	+	0.733993i	−0.572534	+	0.819881i	$0.694039\pi$
$500$		0			0
$501$	2809.52	−	18436.4i	0.250539	−	1.64407i
$502$	−9158.70	−	5287.78i	−0.814288	−	0.470130i
$503$		−	14579.2i		−	1.29235i	−0.763188	−	0.646177i	$-0.776367\pi$
$503$		−	14579.2i		−	1.29235i	0.763188	−	0.646177i	$-0.223633\pi$
$504$	5901.02	+	1841.27i	0.521532	+	0.162732i
$505$		0			0
$506$	−1282.69	+	2221.68i	−0.112692	+	0.195189i
$507$	2636.73	+	6750.55i	0.230969	+	0.591327i
$508$	5115.03	−	2953.17i	0.446738	−	0.257924i
$509$	4205.32	+	7283.83i	0.366204	+	0.634283i	0.988969	−	0.148126i	$-0.0473240\pi$
$509$	4205.32	+	7283.83i	0.366204	+	0.634283i	−0.622765	+	0.782409i	$0.713991\pi$
$510$		0			0
$511$	−9689.89	+	16783.4i	−0.838856	+	1.45294i
$512$			12676.3i			1.09417i
$513$	8050.35	+	3925.36i	0.692849	+	0.337834i
$514$	7063.02			0.606102
$515$		0			0
$516$	−3386.05	−	2709.31i	−0.288881	−	0.231145i
$517$	−605.838	+	349.781i	−0.0515372	+	0.0297550i
$518$	21917.8	−	12654.3i	1.85910	−	1.07335i
$519$	−1793.02	+	700.345i	−0.151647	+	0.0592327i
$520$		0			0
$521$	10058.1			0.845781			0.422890	−	0.906181i	$-0.361016\pi$
$521$	10058.1			0.845781			0.422890	+	0.906181i	$0.361016\pi$
$522$	−10976.5	−	11907.3i	−0.920361	−	0.998409i
$523$		−	20006.3i		−	1.67269i	−0.548205	−	0.836344i	$-0.684688\pi$
$523$		−	20006.3i		−	1.67269i	0.548205	−	0.836344i	$-0.315312\pi$
$524$	−4929.83	+	8538.72i	−0.410994	+	0.711862i
$525$		0			0
$526$	−1036.50	−	1795.27i	−0.0859192	−	0.148817i
$527$	16311.9	−	9417.67i	1.34830	−	0.778444i
$528$	8110.90	+	1236.02i	0.668525	+	0.101877i
$529$	−5543.96	+	9602.42i	−0.455655	+	0.789218i
$530$		0			0
$531$	12211.8	−	11257.2i	0.998019	−	0.920001i
$532$			12111.4i			0.987019i
$533$	7353.52	+	4245.56i	0.597592	+	0.345020i
$534$	−7526.70	+	2939.89i	−0.609948	+	0.238243i
$535$		0			0
$536$	−3131.36	−	5423.67i	−0.252340	−	0.437065i
$537$	1450.79	−	1813.17i	0.116585	−	0.145706i
$538$	10919.0	+	6304.11i	0.875006	+	0.505185i
$539$	13328.5			1.06512
$540$		0			0
$541$	−1884.15			−0.149734			−0.0748668	−	0.997194i	$-0.523853\pi$
$541$	−1884.15			−0.149734			−0.0748668	+	0.997194i	$0.523853\pi$
$542$	10822.9	+	6248.58i	0.857715	+	0.495202i
$543$	2934.85	−	3667.93i	0.231946	−	0.289882i
$544$	8355.34	+	14471.9i	0.658515	+	1.14058i
$545$		0			0
$546$	−34087.3	+	13314.3i	−2.67180	+	1.04359i
$547$	15585.4	+	8998.24i	1.21825	+	0.703358i	0.964544	−	0.263922i	$-0.0850163\pi$
$547$	15585.4	+	8998.24i	1.21825	+	0.703358i	0.253708	+	0.967281i	$0.418350\pi$
$548$		−	4002.93i		−	0.312038i
$549$	−3461.68	−	1080.14i	−0.269109	−	0.0839691i
$550$		0			0
$551$	−5107.40	+	8846.28i	−0.394887	+	0.683964i
$552$	−1232.35	−	187.798i	−0.0950226	−	0.0144805i
$553$	−9374.30	+	5412.25i	−0.720860	+	0.416189i
$554$	−10097.2	−	17488.9i	−0.774351	−	1.34121i
$555$		0			0
$556$	−4184.75	+	7248.19i	−0.319196	+	0.552863i
$557$		−	3615.76i		−	0.275054i	−0.990498	−	0.137527i	$-0.956085\pi$
$557$		−	3615.76i		−	0.275054i	0.990498	−	0.137527i	$-0.0439153\pi$
$558$	−25118.5	+	5647.21i	−1.90564	+	0.428433i
$559$	−8264.84			−0.625341
$560$		0			0
$561$	7466.36	−	2916.32i	0.561907	−	0.219478i
$562$	12065.7	−	6966.14i	0.905625	−	0.522863i
$563$	−12836.1	+	7410.91i	−0.960881	+	0.554765i	−0.896444	−	0.443157i	$-0.853858\pi$
$563$	−12836.1	+	7410.91i	−0.960881	+	0.554765i	−0.0644370	+	0.997922i	$0.520525\pi$
$564$	824.478	+	659.696i	0.0615546	+	0.0492522i
$565$		0			0
$566$	10378.9			0.770771
$567$	−22778.1	−	1856.11i	−1.68710	−	0.137477i
$568$			4299.13i			0.317583i
$569$	11224.7	−	19441.8i	0.827005	−	1.43241i	−0.0733726	−	0.997305i	$-0.523376\pi$
$569$	11224.7	−	19441.8i	0.827005	−	1.43241i	0.900377	−	0.435110i	$-0.143290\pi$
$570$		0			0
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	0.994646	+	0.103338i	$0.0329523\pi$
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	−0.407830	+	0.913058i	$0.633714\pi$
$572$	−6543.66	+	3777.98i	−0.478329	+	0.276163i
$573$	1133.52	+	2902.03i	0.0826410	+	0.211577i
$574$	−8324.81	+	14419.0i	−0.605350	+	1.04850i
$575$		0			0
$576$	−1419.31	−	6313.03i	−0.102670	−	0.456672i
$577$			3096.97i			0.223446i	0.993739	+	0.111723i	$0.0356370\pi$
$577$			3096.97i			0.223446i	−0.993739	+	0.111723i	$0.964363\pi$
$578$	1849.81	+	1067.99i	0.133117	+	0.0768553i
$579$	−3455.09	+	22672.7i	−0.247994	+	1.62736i
$580$		0			0
$581$	−17135.0	−	29678.6i	−1.22354	−	2.11924i
$582$	3878.33	+	591.018i	0.276223	+	0.0420936i
$583$	757.616	+	437.410i	0.0538203	+	0.0310732i
$584$	−4514.76			−0.319901
$585$		0			0
$586$	−13045.0			−0.919595
$587$	−21325.7	−	12312.4i	−1.49950	−	0.865734i	−0.499496	−	0.866316i	$-0.666481\pi$
$587$	−21325.7	−	12312.4i	−1.49950	−	0.865734i	−1.00000		0.000582275i	$0.999815\pi$
$588$	−7319.49	−	18739.3i	−0.513351	−	1.31428i
$589$	8119.48	+	14063.3i	0.568009	+	0.983820i
$590$		0			0
$591$	19503.8	+	15605.7i	1.35749	+	1.08618i
$592$	14135.8	+	8161.30i	0.981381	+	0.566601i
$593$		−	27128.8i		−	1.87866i	−0.343014	−	0.939330i	$-0.611448\pi$
$593$		−	27128.8i		−	1.87866i	0.343014	−	0.939330i	$-0.388552\pi$
$594$	−10929.7	+	765.442i	−0.754965	+	0.0528729i
$595$		0			0
$596$	−9572.32	+	16579.7i	−0.657881	+	1.13948i
$597$	1018.81	−	1273.29i	0.0698445	−	0.0872906i
$598$	6391.08	−	3689.89i	0.437042	−	0.252326i
$599$	2815.87	+	4877.24i	0.192076	+	0.332685i	0.945938	−	0.324347i	$-0.105145\pi$
$599$	2815.87	+	4877.24i	0.192076	+	0.332685i	−0.753862	+	0.657033i	$0.771811\pi$
$600$		0			0
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	−0.499387	−	0.866379i	$-0.666441\pi$
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	1.00000		0.000707853i	$-0.000225317\pi$
$602$		−	16205.9i		−	1.09718i
$603$	15693.0	+	17023.8i	1.05982	+	1.14969i
$604$	15485.2			1.04318
$605$		0			0
$606$	−778.738	+	5110.16i	−0.0522014	+	0.342552i
$607$	−12801.7	+	7391.04i	−0.856018	+	0.494222i	−0.862677	−	0.505756i	$-0.831214\pi$
$607$	−12801.7	+	7391.04i	−0.856018	+	0.494222i	0.00665872	+	0.999978i	$0.497880\pi$
$608$	−12477.0	+	7203.59i	−0.832251	+	0.480500i
$609$	3926.66	−	25767.2i	0.261275	−	1.71451i
$610$		0			0
$611$	2012.43			0.133247
$612$	−8200.44	−	8895.85i	−0.541639	−	0.587571i
$613$		−	4947.28i		−	0.325969i	−0.986629	−	0.162984i	$-0.947888\pi$
$613$		−	4947.28i		−	0.325969i	0.986629	−	0.162984i	$-0.0521120\pi$
$614$	−3393.12	+	5877.06i	−0.223021	+	0.386284i
$615$		0			0
$616$	2384.88	+	4130.73i	0.155989	+	0.270181i
$617$	−3242.09	+	1871.82i	−0.211543	+	0.122134i	−0.602028	−	0.798475i	$-0.705640\pi$
$617$	−3242.09	+	1871.82i	−0.211543	+	0.122134i	0.390485	+	0.920609i	$0.372307\pi$
$618$	6420.67	−	8024.45i	0.417924	−	0.522315i
$619$	3069.37	−	5316.30i	0.199303	−	0.345202i	−0.749000	−	0.662570i	$-0.769466\pi$
$619$	3069.37	−	5316.30i	0.199303	−	0.345202i	0.948303	+	0.317368i	$0.102799\pi$
$620$		0			0
$621$	4597.38	−	321.971i	0.297080	−	0.0208055i
$622$		−	3326.09i		−	0.214412i
$623$	−11262.8	−	6502.59i	−0.724294	−	0.418171i
$624$	−18428.8	−	14745.6i	−1.18228	−	0.945986i
$625$		0			0
$626$	4151.79	+	7191.11i	0.265078	+	0.459128i
$627$	2514.32	+	6437.15i	0.160147	+	0.410008i
$628$	18348.4	+	10593.5i	1.16589	+	0.673129i
$629$	15946.9			1.01088
$630$		0			0
$631$	−5548.00			−0.350019			−0.175010	−	0.984567i	$-0.555996\pi$
$631$	−5548.00			−0.350019			−0.175010	+	0.984567i	$0.555996\pi$
$632$	−2183.86	−	1260.85i	−0.137451	−	0.0793575i
$633$	12527.8	+	1909.12i	0.786630	+	0.119874i
$634$	−1233.36	−	2136.25i	−0.0772605	−	0.133819i
$635$		0			0
$636$	198.927	−	1305.38i	0.0124025	−	0.0813864i
$637$	−33205.3	−	19171.1i	−2.06537	−	1.19244i
$638$		−	12495.9i		−	0.775418i
$639$	−3486.31	−	15506.9i	−0.215831	−	0.960005i
$640$		0			0
$641$	5804.05	−	10052.9i	0.357639	−	0.619448i	−0.629927	−	0.776654i	$-0.716915\pi$
$641$	5804.05	−	10052.9i	0.357639	−	0.619448i	0.987566	+	0.157206i	$0.0502487\pi$
$642$	14770.3	+	37814.9i	0.908002	+	2.32466i
$643$	11017.3	−	6360.85i	0.675708	−	0.390120i	−0.122528	−	0.992465i	$-0.539100\pi$
$643$	11017.3	−	6360.85i	0.675708	−	0.390120i	0.798236	+	0.602345i	$0.205767\pi$
$644$	3116.04	+	5397.15i	0.190667	+	0.330244i
$645$		0			0
$646$	−8859.78	+	15345.6i	−0.539603	+	0.934620i
$647$		−	28203.7i		−	1.71376i	−0.515518	−	0.856879i	$-0.672400\pi$
$647$		−	28203.7i		−	1.71376i	0.515518	−	0.856879i	$-0.327600\pi$
$648$	−2278.74	−	4811.70i	−0.138144	−	0.291700i
$649$	12815.4			0.775115
$650$		0			0
$651$	−32354.0	−	25887.7i	−1.94786	−	1.55856i
$652$	1383.35	−	798.678i	0.0830924	−	0.0479734i
$653$	19652.5	−	11346.4i	1.17774	−	0.679966i	0.222247	−	0.974991i	$-0.428661\pi$
$653$	19652.5	−	11346.4i	1.17774	−	0.679966i	0.955490	+	0.295024i	$0.0953277\pi$
$654$	−16794.3	+	6559.76i	−1.00414	+	0.392213i
$655$		0			0
$656$	−10738.1			−0.639103
$657$	16284.7	−	3661.17i	0.967010	−	0.217406i
$658$			3946.02i			0.233787i
$659$	3002.00	−	5199.61i	0.177453	−	0.307357i	−0.763555	−	0.645743i	$-0.776548\pi$
$659$	3002.00	−	5199.61i	0.177453	−	0.307357i	0.941007	+	0.338386i	$0.109881\pi$
$660$		0			0
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	0.635755	−	0.771891i	$-0.280689\pi$
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	−0.986355	+	0.164635i	$0.947356\pi$
$662$	17129.2	−	9889.54i	1.00566	−	0.580616i
$663$	−22795.6	−	3473.81i	−1.33530	−	0.203487i
$664$	3991.80	−	6914.00i	0.233301	−	0.404089i
$665$		0			0
$666$	−20808.0	−	6492.63i	−1.21065	−	0.377754i
$667$			5256.19i			0.305128i
$668$	−18810.1	−	10860.0i	−1.08950	−	0.629021i
$669$	11293.8	−	4411.31i	0.652682	−	0.254934i
$670$		0			0
$671$	−1399.03	−	2423.19i	−0.0804901	−	0.139413i
$672$	22967.5	−	28704.5i	1.31844	−	1.64777i
$673$	−13885.6	−	8016.85i	−0.795319	−	0.459178i	0.0465125	−	0.998918i	$-0.485189\pi$
$673$	−13885.6	−	8016.85i	−0.795319	−	0.459178i	−0.841832	+	0.539740i	$0.818523\pi$
$674$	12599.9			0.720077
$675$		0			0
$676$	8440.54			0.480231
$677$	−9796.38	−	5655.94i	−0.556138	−	0.321086i	0.195456	−	0.980712i	$-0.437381\pi$
$677$	−9796.38	−	5655.94i	−0.556138	−	0.321086i	−0.751594	+	0.659626i	$0.770715\pi$
$678$	−6644.59	+	8304.31i	−0.376378	+	0.470391i
$679$	3157.03	+	5468.14i	0.178432	+	0.309054i
$680$		0			0
$681$	−13182.8	+	5149.13i	−0.741800	+	0.289743i
$682$	−17203.8	−	9932.64i	−0.965937	−	0.557684i
$683$			652.395i			0.0365493i	0.999833	+	0.0182747i	$0.00581733\pi$
$683$			652.395i			0.0365493i	−0.999833	+	0.0182747i	$0.994183\pi$
$684$	7669.59	−	7070.04i	0.428734	−	0.395219i
$685$		0			0
$686$	17437.4	−	30202.5i	0.970502	−	1.68096i
$687$	17024.3	+	2594.34i	0.945443	+	0.144076i
$688$	9051.64	−	5225.96i	0.501585	−	0.289590i
$689$	−1258.29	−	2179.43i	−0.0695750	−	0.120507i
$690$		0			0
$691$	−6268.93	+	10858.1i	−0.345125	+	0.597774i	−0.985376	−	0.170392i	$-0.945497\pi$
$691$	−6268.93	+	10858.1i	−0.345125	+	0.597774i	0.640252	+	0.768165i	$0.278830\pi$
$692$			2241.90i			0.123157i
$693$	−11952.0	−	12965.5i	−0.655148	−	0.710705i
$694$	−35069.8			−1.91820
$695$		0			0
$696$	5655.94	−	2209.18i	0.308029	−	0.120314i
$697$	−9085.42	+	5245.47i	−0.493737	+	0.285059i
$698$	−22852.1	+	13193.6i	−1.23920	+	0.715454i
$699$	−12883.5	−	10308.6i	−0.697138	−	0.557807i
$700$		0			0
$701$	5880.60			0.316844			0.158422	−	0.987372i	$-0.449359\pi$
$701$	5880.60			0.316844			0.158422	+	0.987372i	$0.449359\pi$
$702$	28329.9	+	13813.7i	1.52314	+	0.742684i
$703$			13748.7i			0.737614i
$704$	2496.37	−	4323.84i	0.133644	−	0.231479i
$705$		0			0
$706$	−7876.07	−	13641.8i	−0.419858	−	0.727216i
$707$	−7204.93	+	4159.77i	−0.383266	+	0.221279i
$708$	−7037.71	−	18017.9i	−0.373578	−	0.956434i
$709$	3203.33	−	5548.33i	0.169681	−	0.293895i	−0.768627	−	0.639697i	$-0.779060\pi$
$709$	3203.33	−	5548.33i	0.169681	−	0.293895i	0.938308	+	0.345802i	$0.112393\pi$
$710$		0			0
$711$	8899.62	+	2776.91i	0.469426	+	0.146473i
$712$		−	3029.72i		−	0.159471i
$713$	7236.52	+	4178.00i	0.380098	+	0.219449i
$714$	6811.55	−	44698.2i	0.357025	−	2.34284i
$715$		0			0
$716$	−1352.25	−	2342.17i	−0.0705812	−	0.122250i
$717$	1264.30	+	192.667i	0.0658526	+	0.0100353i
$718$	1908.90	+	1102.10i	0.0992193	+	0.0572843i
$719$	−21907.0			−1.13629			−0.568144	−	0.822929i	$-0.692338\pi$
$719$	−21907.0			−1.13629			−0.568144	+	0.822929i	$0.692338\pi$
$720$		0			0
$721$	16540.4			0.854364
$722$	9036.47	+	5217.21i	0.465793	+	0.268926i
$723$	9996.44	+	25592.9i	0.514207	+	1.31647i
$724$	−2735.53	−	4738.07i	−0.140421	−	0.243217i
$725$		0			0
$726$	13641.9	+	10915.4i	0.697382	+	0.558002i
$727$	−11579.6	−	6685.46i	−0.590732	−	0.341059i	0.174655	−	0.984630i	$-0.444119\pi$
$727$	−11579.6	−	6685.46i	−0.590732	−	0.341059i	−0.765387	+	0.643571i	$0.777452\pi$
$728$		−	13721.1i		−	0.698542i
$729$	12121.4	+	15507.8i	0.615829	+	0.787880i
$730$		0			0
$731$	5105.69	−	8843.31i	0.258332	−	0.447444i
$732$	−2638.61	+	3297.69i	−0.133232	+	0.166511i
$733$	−26146.2	+	15095.5i	−1.31751	+	0.760663i	−0.983327	−	0.181846i	$-0.941793\pi$
$733$	−26146.2	+	15095.5i	−1.31751	+	0.760663i	−0.334181	+	0.942509i	$0.608460\pi$
$734$	−14591.5	−	25273.2i	−0.733762	−	1.27091i
$735$		0			0
$736$	−3706.72	+	6420.22i	−0.185641	+	0.321539i
$737$			17865.2i			0.892910i
$738$	13990.5	−	3145.39i	0.697830	−	0.156888i
$739$	11624.7			0.578650			0.289325	−	0.957231i	$-0.406569\pi$
$739$	11624.7			0.578650			0.289325	+	0.957231i	$0.406569\pi$
$740$		0			0
$741$	2994.96	−	19653.3i	0.148479	−	0.974334i
$742$	4273.49	−	2467.30i	0.211435	−	0.122072i
$743$	4550.42	−	2627.19i	0.224682	−	0.129720i	−0.383434	−	0.923568i	$-0.625259\pi$
$743$	4550.42	−	2627.19i	0.224682	−	0.129720i	0.608116	+	0.793848i	$0.291925\pi$
$744$	1454.24	−	9542.90i	0.0716601	−	0.470241i
$745$		0			0
$746$	−29328.9			−1.43942
$747$	−8791.57	+	28175.8i	−0.430612	+	1.38005i
$748$		−	9335.55i		−	0.456339i
$749$	−32669.7	+	56585.5i	−1.59376	+	2.76047i
$750$		0			0
$751$	14614.4	+	25312.9i	0.710102	+	1.22993i	0.964819	+	0.262917i	$0.0846844\pi$
$751$	14614.4	+	25312.9i	0.710102	+	1.22993i	−0.254717	+	0.967016i	$0.581982\pi$
$752$	−2204.00	+	1272.48i	−0.106877	+	0.0617057i
$753$	−9158.70	+	11446.4i	−0.443242	+	0.553957i
$754$	−17973.4	+	31130.9i	−0.868108	+	1.50361i
$755$		0			0
$756$	−11665.4	+	23924.1i	−0.561199	+	1.15094i
$757$			32885.9i			1.57894i	0.613789	+	0.789470i	$0.289645\pi$
$757$			32885.9i			1.57894i	−0.613789	+	0.789470i	$0.710355\pi$
$758$	−15192.6	−	8771.46i	−0.727995	−	0.420308i
$759$	2776.62	+	2221.68i	0.132786	+	0.106247i
$760$		0			0
$761$	6634.11	+	11490.6i	0.316014	+	0.547352i	0.979652	−	0.200702i	$-0.0643221\pi$
$761$	6634.11	+	11490.6i	0.316014	+	0.547352i	−0.663639	+	0.748053i	$0.730989\pi$
$762$	−6916.37	−	17707.3i	−0.328811	−	0.841820i
$763$	−25130.7	−	14509.2i	−1.19239	−	0.688425i
$764$	3628.54			0.171827
$765$		0			0
$766$	−25219.0			−1.18956
$767$	−31927.0	−	18433.0i	−1.50302	−	0.867769i
$768$	27315.1	+	4162.55i	1.28340	+	0.195577i
$769$	17142.9	+	29692.4i	0.803887	+	1.39237i	0.917040	+	0.398796i	$0.130572\pi$
$769$	17142.9	+	29692.4i	0.803887	+	1.39237i	−0.113153	+	0.993578i	$0.536095\pi$
$770$		0			0
$771$	1474.95	−	9678.81i	0.0688964	−	0.452106i
$772$	23132.2	+	13355.4i	1.07843	+	0.622630i
$773$			27987.1i			1.30223i	0.758978	+	0.651117i	$0.225699\pi$
$773$			27987.1i			1.30223i	−0.758978	+	0.651117i	$0.774301\pi$
$774$	−10262.5	+	9460.25i	−0.476586	+	0.439330i
$775$		0			0
$776$	−735.469	+	1273.87i	−0.0340229	+	0.0589294i
$777$	−12763.7	−	32677.7i	−0.589313	−	1.50876i
$778$	15494.4	−	8945.72i	0.714014	−	0.412236i
$779$	−4522.40	−	7833.03i	−0.208000	−	0.360266i
$780$		0			0
$781$	6131.92	−	10620.8i	0.280944	−	0.486610i
$782$			9117.88i			0.416950i
$783$	−18609.4	+	12555.1i	−0.849356	+	0.573029i
$784$	48488.5			2.20884
$785$		0			0
$786$	24778.7	+	19826.3i	1.12446	+	0.899723i
$787$	307.265	−	177.400i	0.0139172	−	0.00803509i	−0.493025	−	0.870015i	$-0.664109\pi$
$787$	307.265	−	177.400i	0.0139172	−	0.00803509i	0.506942	+	0.861980i	$0.330776\pi$
$788$	25194.1	−	14545.8i	1.13896	−	0.657580i
$789$	−2676.60	+	1045.47i	−0.120772	+	0.0471731i
$790$		0			0
$791$	−17117.2			−0.769430
$792$	1223.63	−	3921.56i	0.0548987	−	0.175943i
$793$			8049.15i			0.360446i
$794$	−8788.42	+	15222.0i	−0.392808	+	0.680363i
$795$		0			0
$796$	−949.617	−	1644.78i	−0.0422843	−	0.0732385i
$797$	11086.2	−	6400.65i	0.492717	−	0.284470i	−0.232984	−	0.972481i	$-0.574849\pi$
$797$	11086.2	−	6400.65i	0.492717	−	0.284470i	0.725701	+	0.688011i	$0.241516\pi$
$798$	38536.7	+	5872.60i	1.70950	+	0.260511i
$799$	−1243.20	+	2153.28i	−0.0550452	+	0.0953411i
$800$		0			0
$801$	2456.90	+	10928.2i	0.108377	+	0.482056i
$802$			5749.67i			0.253152i
$803$	11153.5	+	6439.48i	0.490160	+	0.282994i
$804$	25117.7	−	9810.86i	1.10178	−	0.430351i
$805$		0			0
$806$	28573.2	+	49490.2i	1.24869	+	2.16280i
$807$	10919.0	−	13646.4i	0.476293	−	0.595264i
$808$	−1678.48	−	969.069i	−0.0730800	−	0.0421927i
$809$	16374.9			0.711632			0.355816	−	0.934556i	$-0.384203\pi$
$809$	16374.9			0.711632			0.355816	+	0.934556i	$0.384203\pi$
$810$		0			0
$811$	−35518.2			−1.53787			−0.768936	−	0.639326i	$-0.779214\pi$
$811$	−35518.2			−1.53787			−0.768936	+	0.639326i	$0.779214\pi$
$812$	−26289.4	−	15178.2i	−1.13618	−	0.655974i
$813$	10822.9	−	13526.2i	0.466881	−	0.583500i
$814$	−8409.47	−	14565.6i	−0.362103	−	0.627181i
$815$		0			0
$816$	27162.2	−	10609.4i	1.16528	−	0.455152i
$817$	7624.29	+	4401.89i	0.326487	+	0.188498i
$818$			32908.0i			1.40660i
$819$	11126.9	+	49491.9i	0.474733	+	2.11158i
$820$		0			0
$821$	−21471.9	+	37190.5i	−0.912760	+	1.58095i	−0.102612	+	0.994721i	$0.532720\pi$
$821$	−21471.9	+	37190.5i	−0.912760	+	1.58095i	−0.810148	+	0.586226i	$0.800613\pi$
$822$	−12736.8	−	1940.96i	−0.540445	−	0.0823584i
$823$	6856.26	−	3958.46i	0.290394	−	0.167659i	−0.347726	−	0.937596i	$-0.613046\pi$
$823$	6856.26	−	3958.46i	0.290394	−	0.167659i	0.638119	+	0.769937i	$0.279713\pi$
$824$	1926.64	+	3337.04i	0.0814536	+	0.141082i
$825$		0			0
$826$	36144.0	−	62603.3i	1.52253	−	2.63710i
$827$			18774.4i			0.789421i	0.918806	+	0.394710i	$0.129155\pi$
$827$			18774.4i			0.789421i	−0.918806	+	0.394710i	$0.870845\pi$
$828$	1598.77	−	5123.85i	0.0671030	−	0.215056i
$829$	−22166.1			−0.928661			−0.464330	−	0.885662i	$-0.653705\pi$
$829$	−22166.1			−0.928661			−0.464330	+	0.885662i	$0.653705\pi$
$830$		0			0
$831$	−26074.5	+	10184.6i	−1.08847	+	0.425149i
$832$	−12438.4	+	7181.30i	−0.518297	+	0.299239i
$833$	41025.8	−	23686.2i	1.70643	−	0.985210i
$834$	21033.6	+	16829.8i	0.873304	+	0.698764i
$835$		0			0
$836$	8048.68			0.332978
$837$	2493.22	+	35600.4i	0.102961	+	1.47017i
$838$			16029.1i			0.660757i
$839$	21295.4	−	36884.7i	0.876279	−	1.51776i	0.0208849	−	0.999782i	$-0.493352\pi$
$839$	21295.4	−	36884.7i	0.876279	−	1.51776i	0.855394	−	0.517978i	$-0.173315\pi$
$840$		0			0
$841$	−606.908	−	1051.20i	−0.0248845	−	0.0431012i
$842$	46952.9	−	27108.3i	1.92174	−	1.10952i
$843$	−7026.40	−	17989.0i	−0.287073	−	0.734963i
$844$	7379.55	−	12781.7i	0.300965	−	0.521287i
$845$		0			0
$846$	2498.84	−	2303.50i	0.101551	−	0.0936122i
$847$			28119.4i			1.14072i
$848$	2756.16	+	1591.27i	0.111612	+	0.0644393i
$849$	2167.39	−	14222.7i	0.0876145	−	0.574937i
$850$		0			0
$851$	3537.31	+	6126.79i	0.142488	+	0.246796i
$852$	−18299.8	−	2788.70i	−0.735845	−	0.112135i
$853$	22916.0	+	13230.6i	0.919847	+	0.531074i	0.883586	−	0.468269i	$-0.155122\pi$
$853$	22916.0	+	13230.6i	0.919847	+	0.531074i	0.0362605	+	0.999342i	$0.488455\pi$
$854$	−15783.0			−0.632416
$855$		0			0
$856$	−15221.6			−0.607784
$857$	17328.3	+	10004.5i	0.690693	+	0.398772i	0.803871	−	0.594803i	$-0.202770\pi$
$857$	17328.3	+	10004.5i	0.690693	+	0.398772i	−0.113179	+	0.993575i	$0.536103\pi$
$858$	8848.12	+	22652.9i	0.352063	+	0.901350i
$859$	−8909.03	−	15430.9i	−0.353868	−	0.612917i	0.633056	−	0.774106i	$-0.281800\pi$
$859$	−8909.03	−	15430.9i	−0.353868	−	0.612917i	−0.986923	+	0.161189i	$0.948467\pi$
$860$		0			0
$861$	18020.6	+	14419.0i	0.713288	+	0.570729i
$862$	7168.31	+	4138.63i	0.283241	+	0.163529i
$863$		−	12769.5i		−	0.503683i	−0.967769	−	0.251841i	$-0.918964\pi$
$863$		−	12769.5i		−	0.503683i	0.967769	−	0.251841i	$-0.0810361\pi$
$864$	−31584.6	+	2211.98i	−1.24367	+	0.0870986i
$865$		0			0
$866$	18859.6	−	32665.7i	0.740039	−	1.28179i
$867$	1849.81	−	2311.86i	0.0724598	−	0.0905592i
$868$	−41793.5	+	24129.5i	−1.63429	+	0.943558i
$869$	3596.75	+	6229.75i	0.140404	+	0.243187i
$870$		0			0
$871$	25696.4	−	44507.5i	0.999644	−	1.73144i
$872$		−	6760.19i		−	0.262533i
$873$	1619.80	−	5191.25i	0.0627973	−	0.201257i
$874$	−7861.01			−0.304236
$875$		0			0
$876$	2928.57	−	19217.6i	0.112954	−	0.741214i
$877$	23796.0	−	13738.6i	0.916231	−	0.528986i	0.0338003	−	0.999429i	$-0.489239\pi$
$877$	23796.0	−	13738.6i	0.916231	−	0.528986i	0.882431	+	0.470442i	$0.155906\pi$
$878$	−43232.5	+	24960.3i	−1.66176	+	0.959417i
$879$	−2724.15	+	17876.2i	−0.104532	+	0.685948i
$880$		0			0
$881$	31509.1			1.20496			0.602480	−	0.798134i	$-0.294179\pi$
$881$	31509.1			1.20496			0.602480	+	0.798134i	$0.294179\pi$
$882$	−63175.1	+	14203.2i	−2.41181	+	0.542230i
$883$		−	5271.46i		−	0.200905i	−0.994942	−	0.100452i	$-0.967971\pi$
$883$		−	5271.46i		−	0.200905i	0.994942	−	0.100452i	$-0.0320290\pi$
$884$	−13427.8	+	23257.6i	−0.510888	+	0.884883i
$885$		0			0
$886$	26755.6	+	46342.0i	1.01453	+	1.75721i
$887$	9035.91	−	5216.89i	0.342048	−	0.197481i	−0.319130	−	0.947711i	$-0.603391\pi$
$887$	9035.91	−	5216.89i	0.342048	−	0.197481i	0.661177	+	0.750230i	$0.270057\pi$
$888$	5106.03	−	6381.43i	0.192958	−	0.241156i
$889$	15298.0	−	26496.9i	0.577140	−	0.999636i
$890$		0			0
$891$	−1233.49	+	15137.3i	−0.0463787	+	0.569157i
$892$		−	14121.2i		−	0.530059i
$893$	−1856.46	−	1071.83i	−0.0695677	−	0.0401649i
$894$	48113.0	+	38497.1i	1.79993	+	1.44019i
$895$		0			0
$896$	14218.2	+	24626.6i	0.530130	+	0.918212i
$897$	−3721.81	−	9528.58i	−0.138537	−	0.354682i
$898$	−5486.40	−	3167.57i	−0.203879	−	0.117710i
$899$	−40702.0			−1.51000
$900$		0			0
$901$	3109.30			0.114967
$902$	9582.23	+	5532.30i	0.353718	+	0.204219i
$903$	−22207.8	−	3384.24i	−0.818415	−	0.124718i
$904$	−1993.84	−	3453.43i	−0.0733562	−	0.127057i
$905$		0			0
$906$	7508.51	−	49271.7i	0.275335	−	1.80678i
$907$	−17915.1	−	10343.3i	−0.655856	−	0.378659i	0.134840	−	0.990867i	$-0.456948\pi$
$907$	−17915.1	−	10343.3i	−0.655856	−	0.378659i	−0.790696	+	0.612209i	$0.790281\pi$
$908$			16483.1i			0.602434i
$909$	6840.10	+	2134.29i	0.249584	+	0.0778766i
$910$		0			0
$911$	11820.0	−	20472.9i	0.429874	−	0.744563i	−0.566988	−	0.823726i	$-0.691891\pi$
$911$	11820.0	−	20472.9i	0.429874	−	0.744563i	0.996862	+	0.0791627i	$0.0252247\pi$
$912$	9146.95	+	23418.0i	0.332111	+	0.850271i
$913$	−19723.1	+	11387.1i	−0.714939	+	0.412770i
$914$	−12490.9	−	21635.0i	−0.452039	−	0.782955i
$915$		0			0
$916$	10028.2	−	17369.4i	0.361727	−	0.626529i
$917$			51075.0i			1.83931i
$918$	−32281.6	+	21779.2i	−1.16062	+	0.783030i
$919$	−27335.2			−0.981180			−0.490590	−	0.871390i	$-0.663219\pi$
$919$	−27335.2			−0.981180			−0.490590	+	0.871390i	$0.663219\pi$
$920$		0			0
$921$	7345.05	+	5877.06i	0.262788	+	0.210267i
$922$	5413.04	−	3125.22i	0.193350	−	0.111631i
$923$	−30552.8	+	17639.7i	−1.08955	+	0.629054i
$924$	−19129.9	+	7472.06i	−0.681092	+	0.266031i
$925$		0			0
$926$	−21861.7			−0.775832
$927$	−9655.50	−	10474.3i	−0.342102	−	0.371112i
$928$		−	36110.7i		−	1.27736i
$929$	−6614.28	+	11456.3i	−0.233593	+	0.404594i	−0.958863	−	0.283870i	$-0.908382\pi$
$929$	−6614.28	+	11456.3i	−0.233593	+	0.404594i	0.725270	+	0.688464i	$0.241715\pi$
$930$		0			0
$931$	20421.2	+	35370.5i	0.718880	+	1.24514i
$932$	−16642.4	+	9608.47i	−0.584913	+	0.337700i
$933$	−4557.91	−	694.580i	−0.159935	−	0.0243725i
$934$	32632.3	−	56520.9i	1.14321	−	1.98011i
$935$		0			0
$936$	−8688.98	+	8009.75i	−0.303428	+	0.279708i
$937$		−	18740.4i		−	0.653387i	−0.945130	−	0.326693i	$-0.894066\pi$
$937$		−	18740.4i		−	0.653387i	0.945130	−	0.326693i	$-0.105934\pi$
$938$	87271.6	+	50386.3i	3.03787	+	1.75391i
$939$	10721.3	−	4187.70i	0.372607	−	0.145538i
$940$		0			0
$941$	−27244.5	−	47188.9i	−0.943832	−	1.63476i	−0.758074	−	0.652169i	$-0.773859\pi$
$941$	−27244.5	−	47188.9i	−0.943832	−	1.63476i	−0.185758	−	0.982596i	$-0.559474\pi$
$942$	42603.8	−	53245.6i	1.47357	−	1.84165i
$943$	−4030.61	−	2327.07i	−0.139188	−	0.0803605i
$944$	46621.8			1.60743
$945$		0			0
$946$	−10769.7			−0.370142
$947$	9771.11	+	5641.35i	0.335289	+	0.193579i	0.658187	−	0.752855i	$-0.271324\pi$
$947$	9771.11	+	5641.35i	0.335289	+	0.193579i	−0.322898	+	0.946434i	$0.604657\pi$
$948$	6783.57	−	8477.99i	0.232405	−	0.290456i
$949$	−18524.4	−	32085.2i	−0.633644	−	1.09750i
$950$		0			0
$951$	−3184.97	+	1244.03i	−0.108601	+	0.0424191i
$952$	14681.5	+	8476.36i	0.499821	+	0.288572i
$953$			51190.0i			1.73999i	0.493063	+	0.869994i	$0.335877\pi$
$953$			51190.0i			1.73999i	−0.493063	+	0.869994i	$0.664123\pi$
$954$	−4057.09	−	1265.92i	−0.137687	−	0.0429618i
$955$		0			0
$956$	744.741	−	1289.93i	0.0251952	−	0.0436394i
$957$	−17123.7	−	2609.49i	−0.578403	−	0.0881428i
$958$	10645.9	−	6146.41i	0.359033	−	0.207288i
$959$	−10368.0	−	17957.8i	−0.349113	−	0.604681i
$960$		0			0
$961$	−17457.4	+	30237.2i	−0.585997	+	1.01498i
$962$			48383.0i			1.62155i
$963$	54904.1	−	12343.7i	1.83724	−	0.413053i
$964$	32000.0			1.06914
$965$		0			0
$966$	18683.9	−	7297.84i	0.622303	−	0.243068i
$967$	20042.9	−	11571.8i	0.666530	−	0.384822i	−0.128230	−	0.991744i	$-0.540930\pi$
$967$	20042.9	−	11571.8i	0.666530	−	0.384822i	0.794761	+	0.606923i	$0.207596\pi$
$968$	−5673.12	+	3275.38i	−0.188369	+	0.108755i
$969$	19178.7	+	15345.6i	0.635818	+	0.508742i
$970$		0			0
$971$	−34124.5			−1.12782			−0.563908	−	0.825838i	$-0.690703\pi$
$971$	−34124.5			−1.12782			−0.563908	+	0.825838i	$0.690703\pi$
$972$	21959.8	−	6578.56i	0.724650	−	0.217086i
$973$			43355.6i			1.42848i
$974$	−19692.5	+	34108.4i	−0.647831	+	1.12208i
$975$		0			0
$976$	−5089.58	−	8815.42i	−0.166920	−	0.289113i
$977$	−31578.5	+	18231.8i	−1.03407	+	0.597020i	−0.918148	−	0.396239i	$-0.870315\pi$
$977$	−31578.5	+	18231.8i	−1.03407	+	0.597020i	−0.115921	+	0.993258i	$0.536982\pi$
$978$	−1870.52	−	4788.90i	−0.0611581	−	0.156577i
$979$	−4321.34	+	7484.78i	−0.141073	+	0.244346i
$980$		0			0
$981$	5482.06	+	24383.9i	0.178419	+	0.793597i
$982$		−	53471.4i		−	1.73762i
$983$	−44636.3	−	25770.8i	−1.44830	−	0.836176i	−0.449918	−	0.893070i	$-0.648547\pi$
$983$	−44636.3	−	25770.8i	−1.44830	−	0.836176i	−0.998380	+	0.0568941i	$0.981880\pi$
$984$	−809.986	+	5315.22i	−0.0262413	+	0.172198i
$985$		0			0
$986$	−22206.5	−	38462.8i	−0.717241	−	1.24230i
$987$	5407.43	+	824.038i	0.174387	+	0.0265749i
$988$	−20051.6	−	11576.8i	−0.645675	−	0.372780i
$989$	4530.12			0.145652
$990$		0			0
$991$	34299.1			1.09944			0.549721	−	0.835348i	$-0.314734\pi$
$991$	34299.1			1.09944			0.549721	+	0.835348i	$0.314734\pi$
$992$	−49715.9	−	28703.5i	−1.59121	−	0.918685i
$993$	−9975.10	−	25538.2i	−0.318782	−	0.816144i
$994$	−34588.3	−	59908.8i	−1.10370	−	1.91166i
$995$		0			0
$996$	26840.9	+	21476.5i	0.853903	+	0.683241i
$997$	−18443.7	−	10648.5i	−0.585877	−	0.338256i	0.177589	−	0.984105i	$-0.443170\pi$
$997$	−18443.7	−	10648.5i	−0.585877	−	0.338256i	−0.763465	+	0.645849i	$0.776504\pi$
$998$		−	35414.2i		−	1.12326i
$999$	−13242.5	+	27158.4i	−0.419392	+	0.860113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.c.124.2		12
5.2	odd	4		225.4.e.c.151.3		6
5.3	odd	4		45.4.e.b.16.1	✓	6
5.4	even	2	inner	225.4.k.c.124.5		12
9.4	even	3	inner	225.4.k.c.49.5		12
15.8	even	4		135.4.e.b.46.3		6
45.2	even	12		2025.4.a.q.1.3		3
45.4	even	6	inner	225.4.k.c.49.2		12
45.7	odd	12		2025.4.a.s.1.1		3
45.13	odd	12		45.4.e.b.31.1	yes	6
45.22	odd	12		225.4.e.c.76.3		6
45.23	even	12		135.4.e.b.91.3		6
45.38	even	12		405.4.a.j.1.1		3
45.43	odd	12		405.4.a.h.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.1	✓	6	5.3	odd	4
45.4.e.b.31.1	yes	6	45.13	odd	12
135.4.e.b.46.3		6	15.8	even	4
135.4.e.b.91.3		6	45.23	even	12
225.4.e.c.76.3		6	45.22	odd	12
225.4.e.c.151.3		6	5.2	odd	4
225.4.k.c.49.2		12	45.4	even	6	inner
225.4.k.c.49.5		12	9.4	even	3	inner
225.4.k.c.124.2		12	1.1	even	1	trivial
225.4.k.c.124.5		12	5.4	even	2	inner
405.4.a.h.1.3		3	45.43	odd	12
405.4.a.j.1.1		3	45.38	even	12
2025.4.a.q.1.3		3	45.2	even	12
2025.4.a.s.1.1		3	45.7	odd	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +O(q^{10})\)	\(q+(-3.24635 - 1.87428i) q^{2} +(-3.24635 + 4.05724i) q^{3} +(3.02587 + 5.24096i) q^{4} +(18.1432 - 7.08665i) q^{6} +(27.1492 + 15.6746i) q^{7} +7.30318i q^{8} +(-5.92239 - 26.3425i) q^{9} +(10.4166 - 18.0422i) q^{11} +(-31.0869 - 4.73733i) q^{12} +(-51.9018 + 29.9655i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} -74.0460i q^{17} +(-30.1471 + 96.6172i) q^{18} +63.8390 q^{19} +(-151.731 + 59.2655i) q^{21} +(-67.6322 + 39.0475i) q^{22} +(28.4484 - 16.4247i) q^{23} +(-29.6307 - 23.7087i) q^{24} +224.655 q^{26} +(126.104 + 61.4884i) q^{27} +189.717i q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-195.444 + 112.840i) q^{32} +(39.3853 + 100.834i) q^{33} +(-138.783 + 240.379i) q^{34} +(120.139 - 110.748i) q^{36} +215.365i q^{37} +(-207.244 - 119.652i) q^{38} +(46.9143 - 307.857i) q^{39} +(-70.8407 - 122.700i) q^{41} +(603.654 + 91.9908i) q^{42} +(119.430 + 68.9529i) q^{43} +126.078 q^{44} -123.138 q^{46} +(-29.0803 - 16.7895i) q^{47} +(143.281 + 366.829i) q^{48} +(319.885 + 554.058i) q^{49} +(300.422 + 240.379i) q^{51} +(-314.096 - 181.344i) q^{52} +41.9914i q^{53} +(-294.131 - 435.967i) q^{54} +(-114.474 + 198.275i) q^{56} +(-207.244 + 259.010i) q^{57} +(519.445 - 299.902i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} -953.535i q^{62} +(252.119 - 808.007i) q^{63} +239.652 q^{64} +(61.1331 - 401.162i) q^{66} +(-742.646 + 428.767i) q^{67} +(388.072 - 224.054i) q^{68} +(-25.7146 + 168.742i) q^{69} +588.665 q^{71} +(192.384 - 43.2522i) q^{72} +618.191i q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(565.607 - 326.553i) q^{77} +(-729.311 + 911.481i) q^{78} +(-172.644 + 299.029i) q^{79} +(-658.851 + 312.021i) q^{81} +531.102i q^{82} +(-946.711 - 546.584i) q^{83} +(-769.728 - 615.889i) q^{84} +(-258.474 - 447.691i) q^{86} +(-302.496 - 774.450i) q^{87} +(131.765 + 76.0746i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(172.162 + 99.3979i) q^{92} +(-1306.68 - 199.125i) q^{93} +(62.9366 + 109.009i) q^{94} +(176.663 - 1159.28i) q^{96} +(174.427 + 100.705i) q^{97} -2398.22i q^{98} +(-536.967 - 167.547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Introduction

L-functions

Modular forms

Varieties

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