LMFDB - Embedded newform 175.4.k.d.74.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(74,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 75 x^{18} + 3638 x^{16} - 105775 x^{14} + 2246038 x^{12} - 30934571 x^{10} + 307864753 x^{8} + \cdots + 16777216 $ x^20 - 75x^18 + 3638x^16 - 105775x^14 + 2246038x^12 - 30934571x^10 + 307864753x^8 - 1719258496x^6 + 6352449536x^4 - 328728576*x^2 + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			74.5
Root			$-0.197018 - 0.113749i$ of defining polynomial
Character	$\chi$	$=$	175.74
Dual form			175.4.k.d.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.197018 + 0.113749i) q^{2} +(-1.56628 - 0.904291i) q^{3} +(-3.97412 + 6.88338i) q^{4} +0.411448 q^{6} +(16.6030 + 8.20612i) q^{7} -3.62818i q^{8} +(-11.8645 - 20.5499i) q^{9} +O(q^{10})$	\(q+(-0.197018 + 0.113749i) q^{2} +(-1.56628 - 0.904291i) q^{3} +(-3.97412 + 6.88338i) q^{4} +0.411448 q^{6} +(16.6030 + 8.20612i) q^{7} -3.62818i q^{8} +(-11.8645 - 20.5499i) q^{9} +(-8.85094 + 15.3303i) q^{11} +(12.4492 - 7.18753i) q^{12} +62.3178i q^{13} +(-4.20453 + 0.271811i) q^{14} +(-31.3803 - 54.3522i) q^{16} +(-75.4848 - 43.5812i) q^{17} +(4.67506 + 2.69914i) q^{18} +(-50.8618 - 88.0952i) q^{19} +(-18.5842 - 27.8670i) q^{21} -4.02713i q^{22} +(-81.0943 + 46.8198i) q^{23} +(-3.28093 + 5.68274i) q^{24} +(-7.08856 - 12.2777i) q^{26} +91.7477i q^{27} +(-122.468 + 81.6726i) q^{28} -297.385 q^{29} +(-45.6389 + 79.0490i) q^{31} +(37.5018 + 21.6517i) q^{32} +(27.7261 - 16.0077i) q^{33} +19.8292 q^{34} +188.604 q^{36} +(243.535 - 140.605i) q^{37} +(20.0414 + 11.5709i) q^{38} +(56.3534 - 97.6070i) q^{39} -271.754 q^{41} +(6.83126 + 3.37639i) q^{42} +7.81066i q^{43} +(-70.3495 - 121.849i) q^{44} +(10.6514 - 18.4487i) q^{46} +(-80.0661 + 46.2262i) q^{47} +113.508i q^{48} +(208.319 + 272.493i) q^{49} +(78.8201 + 136.520i) q^{51} +(-428.957 - 247.658i) q^{52} +(156.148 + 90.1519i) q^{53} +(-10.4362 - 18.0760i) q^{54} +(29.7733 - 60.2387i) q^{56} +183.975i q^{57} +(58.5904 - 33.8272i) q^{58} +(-49.8506 + 86.3437i) q^{59} +(-217.109 - 376.044i) q^{61} -20.7655i q^{62} +(-28.3511 - 438.552i) q^{63} +492.233 q^{64} +(-3.64170 + 6.30761i) q^{66} +(399.718 + 230.777i) q^{67} +(599.972 - 346.394i) q^{68} +169.355 q^{69} +518.417 q^{71} +(-74.5589 + 43.0466i) q^{72} +(-470.136 - 271.433i) q^{73} +(-31.9872 + 55.4035i) q^{74} +808.524 q^{76} +(-272.754 + 181.897i) q^{77} +25.6405i q^{78} +(119.851 + 207.587i) q^{79} +(-237.375 + 411.146i) q^{81} +(53.5405 - 30.9116i) q^{82} -299.184i q^{83} +(265.675 - 17.1751i) q^{84} +(-0.888452 - 1.53884i) q^{86} +(465.789 + 268.923i) q^{87} +(55.6211 + 32.1128i) q^{88} +(527.180 + 913.102i) q^{89} +(-511.387 + 1034.66i) q^{91} -744.271i q^{92} +(142.967 - 82.5418i) q^{93} +(10.5163 - 18.2148i) q^{94} +(-39.1588 - 67.8251i) q^{96} +288.854i q^{97} +(-72.0383 - 29.9900i) q^{98} +420.049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9}+O(q^{10}) $ 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9	$ 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41} + 2182 q^{44} - 674 q^{46} - 1996 q^{49} - 1464 q^{51} - 1548 q^{54} - 2676 q^{56} + 1416 q^{59} - 3888 q^{61} + 500 q^{64} - 2964 q^{66} - 1496 q^{69} + 3456 q^{71} - 6570 q^{74} + 2764 q^{76} + 436 q^{79} + 910 q^{81} + 1468 q^{84} + 8528 q^{86} + 4644 q^{89} + 1048 q^{91} - 5354 q^{94} - 9184 q^{96} - 140 q^{99}+O(q^{100}) $ 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.197018	+	0.113749i	−0.0696565	+	0.0402162i	−0.534424	−	0.845217i	$-0.679471\pi$
$2$	−0.197018	+	0.113749i	−0.0696565	+	0.0402162i	0.464767	+	0.885433i	$0.346138\pi$
$3$	−1.56628	−	0.904291i	−0.301430	−	0.174031i	0.341655	−	0.939825i	$-0.389013\pi$
$3$	−1.56628	−	0.904291i	−0.301430	−	0.174031i	−0.643085	+	0.765795i	$0.722346\pi$
$4$	−3.97412	+	6.88338i	−0.496765	+	0.860423i
$5$		0			0
$5$		0			0
$6$	0.411448			0.0279955
$7$	16.6030	+	8.20612i	0.896478	+	0.443089i
$7$	16.6030	+	8.20612i	0.896478	+	0.443089i
$8$		−	3.62818i		−	0.160345i
$9$	−11.8645	−	20.5499i	−0.439426	−	0.761109i
$10$		0			0
$11$	−8.85094	+	15.3303i	−0.242605	+	0.420205i	−0.961456	−	0.274960i	$-0.911335\pi$
$11$	−8.85094	+	15.3303i	−0.242605	+	0.420205i	0.718850	+	0.695165i	$0.244669\pi$
$12$	12.4492	−	7.18753i	0.299480	−	0.172905i
$13$			62.3178i			1.32953i	0.747054	+	0.664763i	$0.231467\pi$
$13$			62.3178i			1.32953i	−0.747054	+	0.664763i	$0.768533\pi$
$14$	−4.20453	+	0.271811i	−0.0802649	+	0.00518889i
$15$		0			0
$16$	−31.3803	−	54.3522i	−0.490317	−	0.849254i
$17$	−75.4848	−	43.5812i	−1.07693	−	0.621764i	−0.146861	−	0.989157i	$-0.546917\pi$
$17$	−75.4848	−	43.5812i	−1.07693	−	0.621764i	−0.930066	+	0.367393i	$0.880250\pi$
$18$	4.67506	+	2.69914i	0.0612178	+	0.0353441i
$19$	−50.8618	−	88.0952i	−0.614131	−	1.06371i	−0.990536	−	0.137251i	$-0.956173\pi$
$19$	−50.8618	−	88.0952i	−0.614131	−	1.06371i	0.376405	−	0.926455i	$-0.377160\pi$
$20$		0			0
$21$	−18.5842	−	27.8670i	−0.193114	−	0.289575i
$22$		−	4.02713i		−	0.0390267i
$23$	−81.0943	+	46.8198i	−0.735188	+	0.424461i	−0.820317	−	0.571909i	$-0.806203\pi$
$23$	−81.0943	+	46.8198i	−0.735188	+	0.424461i	0.0851289	+	0.996370i	$0.472870\pi$
$24$	−3.28093	+	5.68274i	−0.0279049	+	0.0483327i
$25$		0			0
$26$	−7.08856	−	12.2777i	−0.0534685	−	0.0926102i
$27$			91.7477i			0.653957i
$28$	−122.468	+	81.6726i	−0.826583	+	0.551238i
$29$	−297.385			−1.90424			−0.952122	−	0.305718i	$-0.901104\pi$
$29$	−297.385			−1.90424			−0.952122	+	0.305718i	$0.901104\pi$
$30$		0			0
$31$	−45.6389	+	79.0490i	−0.264419	+	0.457987i	−0.967411	−	0.253210i	$-0.918514\pi$
$31$	−45.6389	+	79.0490i	−0.264419	+	0.457987i	0.702992	+	0.711198i	$0.251847\pi$
$32$	37.5018	+	21.6517i	0.207170	+	0.119610i
$33$	27.7261	−	16.0077i	0.146257	−	0.0844417i
$34$	19.8292			0.100020
$35$		0			0
$36$	188.604			0.873167
$37$	243.535	−	140.605i	1.08208	−	0.624738i	0.150621	−	0.988592i	$-0.451873\pi$
$37$	243.535	−	140.605i	1.08208	−	0.624738i	0.931456	+	0.363854i	$0.118539\pi$
$38$	20.0414	+	11.5709i	0.0855565	+	0.0493961i
$39$	56.3534	−	97.6070i	0.231379	−	0.400760i
$40$		0			0
$41$	−271.754			−1.03514			−0.517570	−	0.855641i	$-0.673163\pi$
$41$	−271.754			−1.03514			−0.517570	+	0.855641i	$0.673163\pi$
$42$	6.83126	+	3.37639i	0.0250973	+	0.0124045i
$43$			7.81066i			0.0277003i	0.999904	+	0.0138502i	$0.00440879\pi$
$43$			7.81066i			0.0277003i	−0.999904	+	0.0138502i	$0.995591\pi$
$44$	−70.3495	−	121.849i	−0.241036	−	0.417486i
$45$		0			0
$46$	10.6514	−	18.4487i	0.0341404	−	0.0591330i
$47$	−80.0661	+	46.2262i	−0.248486	+	0.143464i	−0.619071	−	0.785335i	$-0.712491\pi$
$47$	−80.0661	+	46.2262i	−0.248486	+	0.143464i	0.370585	+	0.928799i	$0.379157\pi$
$48$			113.508i			0.341321i
$49$	208.319	+	272.493i	0.607344	+	0.794439i
$50$		0			0
$51$	78.8201	+	136.520i	0.216412	+	0.374837i
$52$	−428.957	−	247.658i	−1.14395	−	0.660462i
$53$	156.148	+	90.1519i	0.404689	+	0.233648i	0.688505	−	0.725231i	$-0.258267\pi$
$53$	156.148	+	90.1519i	0.404689	+	0.233648i	−0.283816	+	0.958879i	$0.591600\pi$
$54$	−10.4362	−	18.0760i	−0.0262997	−	0.0455524i
$55$		0			0
$56$	29.7733	−	60.2387i	0.0710469	−	0.143745i
$57$			183.975i			0.427511i
$58$	58.5904	−	33.8272i	0.132643	−	0.0765815i
$59$	−49.8506	+	86.3437i	−0.110000	+	0.190525i	−0.915770	−	0.401703i	$-0.868418\pi$
$59$	−49.8506	+	86.3437i	−0.110000	+	0.190525i	0.805770	+	0.592228i	$0.201752\pi$
$60$		0			0
$61$	−217.109	−	376.044i	−0.455704	−	0.789303i	0.543024	−	0.839717i	$-0.317279\pi$
$61$	−217.109	−	376.044i	−0.455704	−	0.789303i	−0.998728	+	0.0504143i	$0.983946\pi$
$62$		−	20.7655i		−	0.0425358i
$63$	−28.3511	−	438.552i	−0.0566969	−	0.877022i
$64$	492.233			0.961393
$65$		0			0
$66$	−3.64170	+	6.30761i	−0.00679185	+	0.0117638i
$67$	399.718	+	230.777i	0.728855	+	0.420805i	0.818003	−	0.575214i	$-0.195081\pi$
$67$	399.718	+	230.777i	0.728855	+	0.420805i	−0.0891481	+	0.996018i	$0.528414\pi$
$68$	599.972	−	346.394i	1.06996	−	0.617741i
$69$	169.355			0.295478
$70$		0			0
$71$	518.417			0.866546			0.433273	−	0.901263i	$-0.357359\pi$
$71$	518.417			0.866546			0.433273	+	0.901263i	$0.357359\pi$
$72$	−74.5589	+	43.0466i	−0.122040	+	0.0704596i
$73$	−470.136	−	271.433i	−0.753771	−	0.435190i	0.0732839	−	0.997311i	$-0.476652\pi$
$73$	−470.136	−	271.433i	−0.753771	−	0.435190i	−0.827055	+	0.562121i	$0.809985\pi$
$74$	−31.9872	+	55.4035i	−0.0502492	+	0.0870341i
$75$		0			0
$76$	808.524			1.22032
$77$	−272.754	+	181.897i	−0.403679	+	0.269208i
$78$			25.6405i			0.0372207i
$79$	119.851	+	207.587i	0.170687	+	0.295638i	0.938660	−	0.344844i	$-0.112068\pi$
$79$	119.851	+	207.587i	0.170687	+	0.295638i	−0.767973	+	0.640482i	$0.778735\pi$
$80$		0			0
$81$	−237.375	+	411.146i	−0.325618	+	0.563986i
$82$	53.5405	−	30.9116i	0.0721043	−	0.0416294i
$83$		−	299.184i		−	0.395660i	−0.980236	−	0.197830i	$-0.936611\pi$
$83$		−	299.184i		−	0.395660i	0.980236	−	0.197830i	$-0.0633894\pi$
$84$	265.675	−	17.1751i	0.345090	−	0.0223090i
$85$		0			0
$86$	−0.888452	−	1.53884i	−0.00111400	−	0.00192951i
$87$	465.789	+	268.923i	0.573997	+	0.331398i
$88$	55.6211	+	32.1128i	0.0673776	+	0.0389004i
$89$	527.180	+	913.102i	0.627876	+	1.08751i	0.987977	+	0.154599i	$0.0494087\pi$
$89$	527.180	+	913.102i	0.627876	+	1.08751i	−0.360102	+	0.932913i	$0.617258\pi$
$90$		0			0
$91$	−511.387	+	1034.66i	−0.589098	+	1.19189i
$92$		−	744.271i		−	0.843430i
$93$	142.967	−	82.5418i	0.159408	−	0.0920343i
$94$	10.5163	−	18.2148i	0.0115391	−	0.0199863i
$95$		0			0
$96$	−39.1588	−	67.8251i	−0.0416316	−	0.0721080i
$97$			288.854i			0.302358i	0.988506	+	0.151179i	$0.0483069\pi$
$97$			288.854i			0.302358i	−0.988506	+	0.151179i	$0.951693\pi$
$98$	−72.0383	−	29.9900i	−0.0742548	−	0.0309128i
$99$	420.049			0.426429
$100$		0			0
$101$	−177.419	+	307.300i	−0.174791	+	0.302747i	−0.940089	−	0.340929i	$-0.889258\pi$
$101$	−177.419	+	307.300i	−0.174791	+	0.302747i	0.765298	+	0.643676i	$0.222592\pi$
$102$	−31.0580	−	17.9314i	−0.0301491	−	0.0174066i
$103$	921.578	−	532.073i	0.881609	−	0.508997i	0.0104207	−	0.999946i	$-0.496683\pi$
$103$	921.578	−	532.073i	0.881609	−	0.508997i	0.871189	+	0.490948i	$0.163350\pi$
$104$	226.100			0.213182
$105$		0			0
$106$	−41.0186			−0.0375857
$107$	−1206.98	+	696.853i	−1.09050	+	0.629601i	−0.933710	−	0.358031i	$-0.883448\pi$
$107$	−1206.98	+	696.853i	−1.09050	+	0.629601i	−0.156791	+	0.987632i	$0.550115\pi$
$108$	−631.534	−	364.616i	−0.562680	−	0.324863i
$109$	−72.2419	+	125.127i	−0.0634818	+	0.109954i	−0.896020	−	0.444015i	$-0.853554\pi$
$109$	−72.2419	+	125.127i	−0.0634818	+	0.109954i	0.832538	+	0.553968i	$0.186887\pi$
$110$		0			0
$111$	−508.591			−0.434895
$112$	−74.9854	−	1159.92i	−0.0632630	−	0.978591i
$113$			2023.91i			1.68489i	0.538780	+	0.842447i	$0.318886\pi$
$113$			2023.91i			1.68489i	−0.538780	+	0.842447i	$0.681114\pi$
$114$	−20.9270	−	36.2466i	−0.0171929	−	0.0297790i
$115$		0			0
$116$	1181.85	−	2047.02i	0.945963	−	1.63846i
$117$	1280.63	−	739.370i	1.01191	−	0.584229i
$118$		−	22.6817i		−	0.0176951i
$119$	−895.641	−	1343.02i	−0.689944	−	1.03457i
$120$		0			0
$121$	508.822	+	881.305i	0.382285	+	0.662137i
$122$	85.5489	+	49.3917i	0.0634855	+	0.0366534i
$123$	425.642	+	245.744i	0.312023	+	0.180147i
$124$	−362.749	−	628.300i	−0.262709	−	0.455025i
$125$		0			0
$126$	55.4704	+	83.1780i	0.0392198	+	0.0588102i
$127$			1606.56i			1.12252i	0.827641	+	0.561258i	$0.189682\pi$
$127$			1606.56i			1.12252i	−0.827641	+	0.561258i	$0.810318\pi$
$128$	−396.993	+	229.204i	−0.274137	+	0.158273i
$129$	7.06311	−	12.2337i	0.00482072	−	0.00834973i
$130$		0			0
$131$	−1424.16	−	2466.72i	−0.949843	−	1.64518i	−0.745750	−	0.666226i	$-0.767909\pi$
$131$	−1424.16	−	2466.72i	−0.949843	−	1.64518i	−0.204093	−	0.978951i	$-0.565425\pi$
$132$			254.466i			0.167791i
$133$	−121.538	−	1880.02i	−0.0792381	−	1.22570i
$134$	−105.002			−0.0676927
$135$		0			0
$136$	−158.120	+	273.873i	−0.0996964	+	0.172679i
$137$	−728.948	−	420.859i	−0.454586	−	0.262455i	0.255179	−	0.966894i	$-0.417866\pi$
$137$	−728.948	−	420.859i	−0.454586	−	0.262455i	−0.709765	+	0.704439i	$0.751199\pi$
$138$	−33.3661	+	19.2639i	−0.0205819	+	0.0118830i
$139$	−2429.10			−1.48226			−0.741128	−	0.671363i	$-0.765709\pi$
$139$	−2429.10			−1.48226			−0.741128	+	0.671363i	$0.765709\pi$
$140$		0			0
$141$	167.208			0.0998684
$142$	−102.138	+	58.9692i	−0.0603606	+	0.0348492i
$143$	−955.349	−	551.571i	−0.558673	−	0.322550i
$144$	−744.624	+	1289.73i	−0.430916	+	0.746369i
$145$		0			0
$146$	123.501			0.0700067
$147$	−79.8730	−	615.180i	−0.0448151	−	0.345165i
$148$			2235.12i			1.24139i
$149$	−288.974	−	500.517i	−0.158884	−	0.275194i	0.775583	−	0.631246i	$-0.217456\pi$
$149$	−288.974	−	500.517i	−0.158884	−	0.275194i	−0.934466	+	0.356051i	$0.884123\pi$
$150$		0			0
$151$	−391.808	+	678.632i	−0.211158	+	0.365737i	−0.952077	−	0.305858i	$-0.901057\pi$
$151$	−391.808	+	678.632i	−0.211158	+	0.365737i	0.740919	+	0.671594i	$0.234390\pi$
$152$	−319.625	+	184.536i	−0.170559	+	0.0984726i
$153$			2068.28i			1.09288i
$154$	33.0471	−	66.8624i	0.0172923	−	0.0349865i
$155$		0			0
$156$	447.911	+	775.804i	0.229882	+	0.398167i
$157$	1188.54	+	686.202i	0.604176	+	0.348821i	0.770683	−	0.637219i	$-0.219915\pi$
$157$	1188.54	+	686.202i	0.604176	+	0.348821i	−0.166507	+	0.986040i	$0.553249\pi$
$158$	−47.2255	−	27.2657i	−0.0237789	−	0.0137287i
$159$	−163.047	−	282.406i	−0.0813238	−	0.140857i
$160$		0			0
$161$	−1730.62	+	111.879i	−0.847154	+	0.0547660i
$162$		−	108.004i		−	0.0523804i
$163$	−3251.74	+	1877.39i	−1.56255	+	0.902139i	−0.565553	+	0.824712i	$0.691337\pi$
$163$	−3251.74	+	1877.39i	−1.56255	+	0.902139i	−0.996998	+	0.0774270i	$0.975330\pi$
$164$	1079.98	−	1870.58i	0.514222	−	0.890659i
$165$		0			0
$166$	34.0318	+	58.9448i	0.0159119	+	0.0275603i
$167$		−	1945.55i		−	0.901505i	−0.892649	−	0.450752i	$-0.851156\pi$
$167$		−	1945.55i		−	0.901505i	0.892649	−	0.450752i	$-0.148844\pi$
$168$	−101.107	+	67.4268i	−0.0464318	+	0.0309648i
$169$	−1686.50			−0.767639
$170$		0			0
$171$	−1206.90	+	2090.41i	−0.539731	+	0.934841i
$172$	−53.7638	−	31.0405i	−0.0238340	−	0.0137606i
$173$	1790.37	−	1033.67i	0.786817	−	0.454269i	−0.0520235	−	0.998646i	$-0.516567\pi$
$173$	1790.37	−	1033.67i	0.786817	−	0.454269i	0.838841	+	0.544377i	$0.183234\pi$
$174$	−122.359			−0.0533102
$175$		0			0
$176$	1110.98			0.475814
$177$	156.160	−	90.1589i	0.0663146	−	0.0382868i
$178$	−207.728	−	119.932i	−0.0874713	−	0.0505016i
$179$	1197.96	−	2074.93i	0.500222	−	0.866409i	−0.499778	−	0.866153i	$-0.666585\pi$
$179$	1197.96	−	2074.93i	0.500222	−	0.866409i	1.00000		0.000255918i	$-8.14612e-5\pi$
$180$		0			0
$181$	1319.40			0.541826			0.270913	−	0.962604i	$-0.412674\pi$
$181$	1319.40			0.541826			0.270913	+	0.962604i	$0.412674\pi$
$182$	−16.9386	−	262.017i	−0.00689876	−	0.106714i
$183$			785.319i			0.317227i
$184$	169.871	+	294.225i	0.0680600	+	0.117883i
$185$		0			0
$186$	−18.7780	+	32.5245i	−0.00740254	+	0.0128216i
$187$	1336.22	−	771.469i	0.522536	−	0.301687i
$188$		−	734.834i		−	0.285071i
$189$	−752.893	+	1523.29i	−0.289761	+	0.586258i
$190$		0			0
$191$	−1054.04	−	1825.64i	−0.399306	−	0.691617i	0.594335	−	0.804218i	$-0.297415\pi$
$191$	−1054.04	−	1825.64i	−0.399306	−	0.691617i	−0.993640	+	0.112600i	$0.964082\pi$
$192$	−770.974	−	445.122i	−0.289793	−	0.167312i
$193$	3145.07	+	1815.81i	1.17299	+	0.677227i	0.954383	−	0.298585i	$-0.0965148\pi$
$193$	3145.07	+	1815.81i	1.17299	+	0.677227i	0.218609	+	0.975813i	$0.429848\pi$
$194$	−32.8568	−	56.9096i	−0.0121597	−	0.0210612i
$195$		0			0
$196$	−2703.56	+	351.021i	−0.985261	+	0.127923i
$197$			3280.46i			1.18641i	0.805051	+	0.593206i	$0.202138\pi$
$197$			3280.46i			1.18641i	−0.805051	+	0.593206i	$0.797862\pi$
$198$	−82.7573	+	47.7799i	−0.0297036	+	0.0171494i
$199$	−324.367	+	561.819i	−0.115546	+	0.200132i	−0.917998	−	0.396585i	$-0.870195\pi$
$199$	−324.367	+	561.819i	−0.115546	+	0.200132i	0.802452	+	0.596717i	$0.203529\pi$
$200$		0			0
$201$	−417.380	−	722.923i	−0.146466	−	0.253687i
$202$		−	80.7249i		−	0.0281177i
$203$	−4937.49	−	2440.38i	−1.70711	−	0.843750i
$204$	−1252.96			−0.430024
$205$		0			0
$206$	−121.045	+	209.656i	−0.0409399	+	0.0709100i
$207$	1924.29	+	1110.99i	0.646122	+	0.373039i
$208$	3387.11	−	1955.55i	1.12910	−	0.651889i
$209$	1800.70			0.595966
$210$		0			0
$211$	5072.33			1.65495			0.827474	−	0.561504i	$-0.189777\pi$
$211$	5072.33			1.65495			0.827474	+	0.561504i	$0.189777\pi$
$212$	−1241.10	+	716.550i	−0.402071	+	0.232136i
$213$	−811.986	−	468.800i	−0.261203	−	0.150806i
$214$	158.532	−	274.586i	0.0506404	−	0.0877117i
$215$		0			0
$216$	332.877			0.104858
$217$	−1406.43	+	937.931i	−0.439975	+	0.293414i
$218$		−	32.8697i		−	0.0102120i
$219$	490.910	+	850.280i	0.151473	+	0.262359i
$220$		0			0
$221$	2715.88	−	4704.04i	0.826651	−	1.43180i
$222$	100.202	−	57.8515i	0.0302933	−	0.0174898i
$223$			163.717i			0.0491629i	0.999698	+	0.0245814i	$0.00782530\pi$
$223$			163.717i			0.0491629i	−0.999698	+	0.0245814i	$0.992175\pi$
$224$	444.966	+	667.227i	0.132725	+	0.199022i
$225$		0			0
$226$	−230.216	−	398.747i	−0.0677600	−	0.117364i
$227$	−5479.02	−	3163.31i	−1.60201	−	0.924918i	−0.991086	−	0.133225i	$-0.957467\pi$
$227$	−5479.02	−	3163.31i	−1.60201	−	0.924918i	−0.610920	−	0.791693i	$-0.709200\pi$
$228$	−1266.37	−	731.141i	−0.367841	−	0.212373i
$229$	1742.23	+	3017.64i	0.502752	+	0.870791i	0.999995	+	0.00318013i	$0.00101227\pi$
$229$	1742.23	+	3017.64i	0.502752	+	0.870791i	−0.497243	+	0.867611i	$0.665654\pi$
$230$		0			0
$231$	591.697	−	38.2515i	0.168532	−	0.0108951i
$232$			1078.97i			0.305335i
$233$	3893.76	−	2248.06i	1.09480	−	0.632084i	0.159951	−	0.987125i	$-0.448866\pi$
$233$	3893.76	−	2248.06i	1.09480	−	0.632084i	0.934851	+	0.355041i	$0.115533\pi$
$234$	−168.205	+	291.339i	−0.0469909	+	0.0813907i
$235$		0			0
$236$	−396.224	−	686.281i	−0.109288	−	0.189293i
$237$		−	433.519i		−	0.118819i
$238$	329.224	+	162.721i	0.0896656	+	0.0443177i
$239$	1529.73			0.414016			0.207008	−	0.978339i	$-0.433627\pi$
$239$	1529.73			0.414016			0.207008	+	0.978339i	$0.433627\pi$
$240$		0			0
$241$	−2286.20	+	3959.82i	−0.611067	+	1.05840i	0.379994	+	0.924989i	$0.375926\pi$
$241$	−2286.20	+	3959.82i	−0.611067	+	1.05840i	−0.991061	+	0.133410i	$0.957407\pi$
$242$	−200.494	−	115.756i	−0.0532573	−	0.0307481i
$243$	2888.90	−	1667.91i	0.762646	−	0.440314i
$244$	3451.27			0.905512
$245$		0			0
$246$	−111.812			−0.0289793
$247$	5489.89	−	3169.59i	1.41423	−	0.816503i
$248$	286.804	+	165.586i	0.0734358	+	0.0423982i
$249$	−270.550	+	468.606i	−0.0688571	+	0.119264i
$250$		0			0
$251$	−537.143			−0.135076			−0.0675382	−	0.997717i	$-0.521514\pi$
$251$	−537.143			−0.135076			−0.0675382	+	0.997717i	$0.521514\pi$
$252$	3131.39	+	1547.71i	0.782775	+	0.386891i
$253$		−	1657.60i		−	0.411906i
$254$	−182.744	−	316.523i	−0.0451433	−	0.0781905i
$255$		0			0
$256$	−1916.79	+	3319.98i	−0.467966	+	0.810541i
$257$	−760.850	+	439.277i	−0.184671	+	0.106620i	−0.589486	−	0.807779i	$-0.700669\pi$
$257$	−760.850	+	439.277i	−0.184671	+	0.106620i	0.404814	+	0.914399i	$0.367336\pi$
$258$			3.21368i			0.000775484i
$259$	5197.23	−	335.985i	1.24687	−	0.0806066i
$260$		0			0
$261$	3528.33	+	6111.25i	0.836775	+	1.44934i
$262$	561.172	+	323.993i	0.132326	+	0.0763982i
$263$	3216.44	+	1857.01i	0.754123	+	0.435393i	0.827182	−	0.561935i	$-0.189943\pi$
$263$	3216.44	+	1857.01i	0.754123	+	0.435393i	−0.0730589	+	0.997328i	$0.523276\pi$
$264$	−58.0787	−	100.595i	−0.0135398	−	0.0234516i
$265$		0			0
$266$	237.795	+	356.574i	0.0548126	+	0.0821916i
$267$		−	1906.90i		−	0.437079i
$268$	−3177.05	+	1834.27i	−0.724140	+	0.418082i
$269$	−77.2299	+	133.766i	−0.0175048	+	0.0303192i	−0.874645	−	0.484764i	$-0.838906\pi$
$269$	−77.2299	+	133.766i	−0.0175048	+	0.0303192i	0.857140	+	0.515083i	$0.172239\pi$
$270$		0			0
$271$	−1203.15	−	2083.92i	−0.269691	−	0.467118i	0.699091	−	0.715033i	$-0.253588\pi$
$271$	−1203.15	−	2083.92i	−0.269691	−	0.467118i	−0.968782	+	0.247914i	$0.920255\pi$
$272$			5470.36i			1.21944i
$273$	1736.61	−	1158.13i	0.384998	−	0.256751i
$274$	191.488			0.0422198
$275$		0			0
$276$	−673.038	+	1165.74i	−0.146783	+	0.254236i
$277$	−1255.53	−	724.878i	−0.272337	−	0.157234i	0.357612	−	0.933870i	$-0.383591\pi$
$277$	−1255.53	−	724.878i	−0.272337	−	0.157234i	−0.629949	+	0.776636i	$0.716924\pi$
$278$	478.578	−	276.307i	0.103249	−	0.0596108i
$279$	2165.94			0.464771
$280$		0			0
$281$	2037.07			0.432460			0.216230	−	0.976342i	$-0.430624\pi$
$281$	2037.07			0.432460			0.216230	+	0.976342i	$0.430624\pi$
$282$	−32.9430	+	19.0197i	−0.00695648	+	0.00401633i
$283$	−6379.33	−	3683.11i	−1.33997	−	0.773633i	−0.353169	−	0.935560i	$-0.614896\pi$
$283$	−6379.33	−	3683.11i	−1.33997	−	0.773633i	−0.986803	+	0.161927i	$0.948229\pi$
$284$	−2060.25	+	3568.46i	−0.430470	+	0.745596i
$285$		0			0
$286$	250.962			0.0518870
$287$	−4511.92	−	2230.04i	−0.927981	−	0.458660i
$288$		−	1027.55i		−	0.210239i
$289$	1342.13	+	2324.65i	0.273180	+	0.473162i
$290$		0			0
$291$	261.208	−	452.426i	0.0526196	−	0.0911398i
$292$	3736.76	−	2157.42i	0.748894	−	0.432374i
$293$			542.935i			0.108255i	0.998534	+	0.0541273i	$0.0172377\pi$
$293$			542.935i			0.108255i	−0.998534	+	0.0541273i	$0.982762\pi$
$294$	85.7124	+	112.116i	0.0170029	+	0.0222407i
$295$		0			0
$296$	−510.140	−	883.588i	−0.100173	−	0.173505i
$297$	−1406.52	−	812.053i	−0.274796	−	0.158654i
$298$	113.866	+	65.7407i	0.0221346	+	0.0127794i
$299$	−2917.71	−	5053.62i	−0.564332	−	0.977452i
$300$		0			0
$301$	−64.0953	+	129.680i	−0.0122737	+	0.0248327i
$302$		−	178.271i		−	0.0339679i
$303$	555.777	−	320.878i	0.105375	−	0.0608381i
$304$	−3192.11	+	5528.90i	−0.602238	+	1.04311i
$305$		0			0
$306$	−235.264	−	407.489i	−0.0439514	−	0.0761261i
$307$			5314.23i			0.987945i	0.869478	+	0.493972i	$0.164456\pi$
$307$			5314.23i			0.987945i	−0.869478	+	0.493972i	$0.835544\pi$
$308$	−168.105	−	2600.35i	−0.0310996	−	0.481068i
$309$	−1924.60			−0.354325
$310$		0			0
$311$	4420.00	−	7655.66i	0.805901	−	1.39586i	−0.109781	−	0.993956i	$-0.535015\pi$
$311$	4420.00	−	7655.66i	0.805901	−	1.39586i	0.915681	−	0.401905i	$-0.131652\pi$
$312$	−354.136	−	204.460i	−0.0642596	−	0.0371003i
$313$	1642.28	−	948.172i	0.296573	−	0.171226i	−0.344329	−	0.938849i	$-0.611894\pi$
$313$	1642.28	−	948.172i	0.296573	−	0.171226i	0.640902	+	0.767623i	$0.278560\pi$
$314$	−312.218			−0.0561130
$315$		0			0
$316$	−1905.20			−0.339165
$317$	−5259.20	+	3036.40i	−0.931818	+	0.537985i	−0.887386	−	0.461027i	$-0.847481\pi$
$317$	−5259.20	+	3036.40i	−0.931818	+	0.537985i	−0.0444320	+	0.999012i	$0.514148\pi$
$318$	64.2466	+	37.0928i	0.0113295	+	0.00654107i
$319$	2632.14	−	4559.00i	0.461980	−	0.800173i
$320$		0			0
$321$	2520.63			0.438280
$322$	328.237	−	218.898i	0.0568073	−	0.0378841i
$323$			8866.46i			1.52738i
$324$	−1886.72	−	3267.89i	−0.323511	−	0.560338i
$325$		0			0
$326$	427.101	−	739.761i	0.0725612	−	0.125680i
$327$	226.302	−	130.656i	0.0382707	−	0.0220956i
$328$			985.971i			0.165979i
$329$	−1708.68	+	110.461i	−0.286329	+	0.0185103i
$330$		0			0
$331$	−1670.89	−	2894.07i	−0.277463	−	0.480581i	0.693290	−	0.720658i	$-0.256160\pi$
$331$	−1670.89	−	2894.07i	−0.277463	−	0.480581i	−0.970754	+	0.240078i	$0.922827\pi$
$332$	2059.40	+	1189.00i	0.340435	+	0.196550i
$333$	−5778.84	−	3336.42i	−0.950987	−	0.549052i
$334$	221.304	+	383.309i	0.0362551	+	0.0627957i
$335$		0			0
$336$	−931.458	+	1884.57i	−0.151236	+	0.305987i
$337$		−	8568.87i		−	1.38509i	−0.721373	−	0.692547i	$-0.756489\pi$
$337$		−	8568.87i		−	1.38509i	0.721373	−	0.692547i	$-0.243511\pi$
$338$	332.272	−	191.837i	0.0534711	−	0.0308715i
$339$	1830.20	−	3170.00i	0.293224	−	0.507878i
$340$		0			0
$341$	−807.895	−	1399.32i	−0.128299	−	0.222220i
$342$		−	549.133i		−	0.0868237i
$343$	1222.61	+	6233.68i	0.192463	+	0.981304i
$344$	28.3385			0.00444160
$345$		0			0
$346$	−235.157	+	407.305i	−0.0365380	+	0.0632856i
$347$	5409.83	+	3123.36i	0.836930	+	0.483202i	0.856220	−	0.516612i	$-0.172807\pi$
$347$	5409.83	+	3123.36i	0.836930	+	0.483202i	−0.0192895	+	0.999814i	$0.506140\pi$
$348$	−3702.20	+	2137.47i	−0.570284	+	0.329254i
$349$	−7091.01			−1.08760			−0.543801	−	0.839214i	$-0.683015\pi$
$349$	−7091.01			−1.08760			−0.543801	+	0.839214i	$0.683015\pi$
$350$		0			0
$351$	−5717.51			−0.869453
$352$	−663.852	+	383.275i	−0.100521	+	0.0580359i
$353$	6312.65	+	3644.61i	0.951809	+	0.549527i	0.893642	−	0.448780i	$-0.148141\pi$
$353$	6312.65	+	3644.61i	0.951809	+	0.549527i	0.0581667	+	0.998307i	$0.481475\pi$
$354$	−20.5109	+	35.5259i	−0.00307950	+	0.00533384i
$355$		0			0
$356$	−8380.31			−1.24763
$357$	188.346	+	2913.46i	0.0279225	+	0.431923i
$358$			545.065i			0.0804681i
$359$	−4334.11	−	7506.89i	−0.637174	−	1.10362i	−0.986050	−	0.166448i	$-0.946770\pi$
$359$	−4334.11	−	7506.89i	−0.637174	−	1.10362i	0.348876	−	0.937169i	$-0.386563\pi$
$360$		0			0
$361$	−1744.34	+	3021.29i	−0.254314	+	0.440485i
$362$	−259.947	+	150.080i	−0.0377417	+	0.0217902i
$363$		−	1840.49i		−	0.266118i
$364$	−5089.66	−	7631.95i	−0.732886	−	1.09896i
$365$		0			0
$366$	−89.3290	−	154.722i	−0.0127576	−	0.0220969i
$367$	3271.51	+	1888.81i	0.465317	+	0.268651i	0.714277	−	0.699863i	$-0.246755\pi$
$367$	3271.51	+	1888.81i	0.465317	+	0.268651i	−0.248960	+	0.968514i	$0.580089\pi$
$368$	5089.52	+	2938.44i	0.720950	+	0.416241i
$369$	3224.22	+	5584.52i	0.454868	+	0.787855i
$370$		0			0
$371$	1852.72	+	2778.16i	0.259268	+	0.388773i
$372$			1312.12i			0.182878i
$373$	1508.73	−	871.066i	0.209435	−	0.120917i	−0.391614	−	0.920130i	$-0.628083\pi$
$373$	1508.73	−	871.066i	0.209435	−	0.120917i	0.601049	+	0.799212i	$0.294750\pi$
$374$	−175.507	+	303.987i	−0.0242654	+	0.0420289i
$375$		0			0
$376$	167.717	+	290.495i	0.0230036	+	0.0398434i
$377$		−	18532.4i		−	2.53174i
$378$	−24.9380	−	385.756i	−0.00339331	−	0.0524898i
$379$	3471.30			0.470471			0.235236	−	0.971938i	$-0.424414\pi$
$379$	3471.30			0.470471			0.235236	+	0.971938i	$0.424414\pi$
$380$		0			0
$381$	1452.80	−	2516.33i	0.195352	−	0.338360i
$382$	415.329	+	239.790i	0.0556285	+	0.0321171i
$383$	−12509.8	+	7222.55i	−1.66899	+	0.963591i	−0.700803	+	0.713355i	$0.747175\pi$
$383$	−12509.8	+	7222.55i	−1.66899	+	0.963591i	−0.968185	+	0.250236i	$0.919492\pi$
$384$	829.069			0.110178
$385$		0			0
$386$	−826.183			−0.108942
$387$	160.509	−	92.6697i	0.0210830	−	0.0121723i
$388$	−1988.29	−	1147.94i	−0.260155	−	0.150201i
$389$	−3864.78	+	6693.99i	−0.503733	+	0.872491i	0.496258	+	0.868175i	$0.334707\pi$
$389$	−3864.78	+	6693.99i	−0.503733	+	0.872491i	−0.999991	+	0.00431550i	$0.998626\pi$
$390$		0			0
$391$	8161.85			1.05566
$392$	988.653	−	755.819i	0.127384	−	0.0973843i
$393$			5151.43i			0.661209i
$394$	−373.148	−	646.311i	−0.0477130	−	0.0826414i
$395$		0			0
$396$	−1669.32	+	2891.35i	−0.211835	+	0.366909i
$397$	−8720.55	+	5034.81i	−1.10245	+	0.636499i	−0.936863	−	0.349697i	$-0.886285\pi$
$397$	−8720.55	+	5034.81i	−1.10245	+	0.636499i	−0.165585	+	0.986195i	$0.552951\pi$
$398$		−	147.585i		−	0.0185874i
$399$	−1509.73	+	3054.54i	−0.189426	+	0.383254i
$400$		0			0
$401$	−751.587	−	1301.79i	−0.0935972	−	0.162115i	0.815425	−	0.578863i	$-0.196503\pi$
$401$	−751.587	−	1301.79i	−0.0935972	−	0.162115i	−0.909022	+	0.416748i	$0.863170\pi$
$402$	164.463	+	94.9527i	0.0204046	+	0.0117806i
$403$	−4926.15	−	2844.12i	−0.608906	−	0.351552i
$404$	−1410.17	−	2442.49i	−0.173660	−	0.300788i
$405$		0			0
$406$	1250.37	−	80.8325i	0.152844	−	0.00988091i
$407$			4977.94i			0.606259i
$408$	495.321	−	285.974i	0.0601031	−	0.0347005i
$409$	−306.691	+	531.204i	−0.0370779	+	0.0642209i	−0.883969	−	0.467546i	$-0.845138\pi$
$409$	−306.691	+	531.204i	−0.0370779	+	0.0642209i	0.846891	+	0.531767i	$0.178472\pi$
$410$		0			0
$411$	761.158	+	1318.36i	0.0913507	+	0.158224i
$412$			8458.10i			1.01141i
$413$	−1536.22	+	1024.48i	−0.183032	+	0.122062i
$414$	−505.494			−0.0600089
$415$		0			0
$416$	−1349.28	+	2337.03i	−0.159024	+	0.275438i
$417$	3804.65	+	2196.62i	0.446797	+	0.257959i
$418$	−354.771	+	204.827i	−0.0415129	+	0.0239675i
$419$	−12334.4			−1.43813			−0.719065	−	0.694943i	$-0.755429\pi$
$419$	−12334.4			−1.43813			−0.719065	+	0.694943i	$0.755429\pi$
$420$		0			0
$421$	−2432.22			−0.281566			−0.140783	−	0.990040i	$-0.544962\pi$
$421$	−2432.22			−0.281566			−0.140783	+	0.990040i	$0.544962\pi$
$422$	−999.343	+	576.971i	−0.115278	+	0.0665557i
$423$	1899.89	+	1096.90i	0.218383	+	0.126083i
$424$	327.088	−	566.532i	0.0374641	−	0.0648897i
$425$		0			0
$426$	213.301			0.0242594
$427$	−518.797	−	8025.08i	−0.0587971	−	0.909510i
$428$		−	11077.5i		−	1.25106i
$429$	997.562	+	1727.83i	0.112267	+	0.194453i
$430$		0			0
$431$	655.240	−	1134.91i	0.0732292	−	0.126837i	−0.827086	−	0.562076i	$-0.810003\pi$
$431$	655.240	−	1134.91i	0.0732292	−	0.126837i	0.900315	+	0.435239i	$0.143336\pi$
$432$	4986.69	−	2879.07i	0.555376	−	0.320646i
$433$		−	4954.86i		−	0.549920i	−0.961456	−	0.274960i	$-0.911335\pi$
$433$		−	4954.86i		−	0.549920i	0.961456	−	0.274960i	$-0.0886646\pi$
$434$	170.404	−	344.769i	0.0188471	−	0.0381323i
$435$		0			0
$436$	−574.197	−	994.538i	−0.0630712	−	0.109242i
$437$	8249.20	+	4762.68i	0.903004	+	0.521350i
$438$	−193.436	−	111.681i	−0.0211022	−	0.0121833i
$439$	−4097.67	−	7097.37i	−0.445492	−	0.771615i	0.552594	−	0.833450i	$-0.313638\pi$
$439$	−4097.67	−	7097.37i	−0.445492	−	0.771615i	−0.998086	+	0.0618354i	$0.980305\pi$
$440$		0			0
$441$	3128.10	−	7513.94i	0.337771	−	0.811352i
$442$			1235.71i			0.132979i
$443$	−2560.58	+	1478.35i	−0.274621	+	0.158552i	−0.630986	−	0.775795i	$-0.717349\pi$
$443$	−2560.58	+	1478.35i	−0.274621	+	0.158552i	0.356365	+	0.934347i	$0.384016\pi$
$444$	2021.20	−	3500.83i	0.216041	−	0.374193i
$445$		0			0
$446$	−18.6226	−	32.2553i	−0.00197714	−	0.00342451i
$447$			1045.27i			0.110603i
$448$	8172.54	+	4039.33i	0.861867	+	0.425983i
$449$	10453.5			1.09873			0.549364	−	0.835583i	$-0.314870\pi$
$449$	10453.5			1.09873			0.549364	+	0.835583i	$0.314870\pi$
$450$		0			0
$451$	2405.28	−	4166.06i	0.251131	−	0.434971i
$452$	−13931.3	−	8043.25i	−1.44972	−	0.836997i
$453$	1227.36	−	708.617i	0.127299	−	0.0734961i
$454$	1439.29			0.148787
$455$		0			0
$456$	667.497			0.0685491
$457$	1944.39	−	1122.60i	0.199026	−	0.114908i	−0.397175	−	0.917743i	$-0.630009\pi$
$457$	1944.39	−	1122.60i	0.199026	−	0.114908i	0.596201	+	0.802835i	$0.296676\pi$
$458$	−686.505	−	396.354i	−0.0700399	−	0.0404375i
$459$	3998.47	−	6925.55i	0.406607	−	0.704264i
$460$		0			0
$461$	−12441.1			−1.25692			−0.628459	−	0.777842i	$-0.716314\pi$
$461$	−12441.1			−1.25692			−0.628459	+	0.777842i	$0.716314\pi$
$462$	−112.224	+	74.8410i	−0.0113012	+	0.00753662i
$463$		−	17086.0i		−	1.71502i	−0.514468	−	0.857510i	$-0.672010\pi$
$463$		−	17086.0i		−	1.71502i	0.514468	−	0.857510i	$-0.327990\pi$
$464$	9332.04	+	16163.6i	0.933683	+	1.61719i
$465$		0			0
$466$	−511.429	+	885.820i	−0.0508401	+	0.0880576i
$467$	−10140.4	+	5854.55i	−1.00480	+	0.580121i	−0.909665	−	0.415344i	$-0.863661\pi$
$467$	−10140.4	+	5854.55i	−1.00480	+	0.580121i	−0.0951340	+	0.995464i	$0.530328\pi$
$468$			11753.4i			1.16090i
$469$	4742.73	+	7111.73i	0.466948	+	0.700190i
$470$		0			0
$471$	−1241.05	−	2149.57i	−0.121411	−	0.210291i
$472$	313.271	+	180.867i	0.0305497	+	0.0176379i
$473$	−119.740	−	69.1317i	−0.0116398	−	0.00672025i
$474$	49.3122	+	85.4113i	0.00477845	+	0.00827652i
$475$		0			0
$476$	12803.9	−	827.733i	1.23291	−	0.0797039i
$477$		−	4278.44i		−	0.410684i
$478$	−301.385	+	174.005i	−0.0288389	+	0.0166502i
$479$	5845.99	−	10125.5i	0.557641	−	0.965862i	−0.440052	−	0.897972i	$-0.645040\pi$
$479$	5845.99	−	10125.5i	0.557641	−	0.965862i	0.997693	−	0.0678900i	$-0.0216267\pi$
$480$		0			0
$481$	8762.18	+	15176.5i	0.830605	+	1.43865i
$482$		−	1040.21i		−	0.0982992i
$483$	2811.80	+	1389.75i	0.264889	+	0.130923i
$484$	−8088.48			−0.759624
$485$		0			0
$486$	−379.444	+	657.216i	−0.0354155	+	0.0613414i
$487$	−6173.76	−	3564.42i	−0.574455	−	0.331662i	0.184472	−	0.982838i	$-0.440943\pi$
$487$	−6173.76	−	3564.42i	−0.574455	−	0.331662i	−0.758927	+	0.651176i	$0.774276\pi$
$488$	−1364.35	+	787.711i	−0.126560	+	0.0730696i
$489$	6790.84			0.628001
$490$		0			0
$491$	−4330.34			−0.398015			−0.199008	−	0.979998i	$-0.563772\pi$
$491$	−4330.34			−0.398015			−0.199008	+	0.979998i	$0.563772\pi$
$492$	−3383.11	+	1953.24i	−0.310004	+	0.178981i
$493$	22448.1	+	12960.4i	2.05073	+	1.18399i
$494$	−721.074	+	1248.94i	−0.0656733	+	0.113750i
$495$		0			0
$496$	5728.65			0.518597
$497$	8607.28	+	4254.20i	0.776839	+	0.383957i
$498$		−	123.099i		−	0.0110767i
$499$	4817.84	+	8344.74i	0.432216	+	0.748621i	0.997064	−	0.0765745i	$-0.0243983\pi$
$499$	4817.84	+	8344.74i	0.432216	+	0.748621i	−0.564847	+	0.825195i	$0.691065\pi$
$500$		0			0
$501$	−1759.35	+	3047.28i	−0.156890	+	0.271741i
$502$	105.827	−	61.0993i	0.00940895	−	0.00543226i
$503$		−	18763.3i		−	1.66325i	−0.555335	−	0.831626i	$-0.687410\pi$
$503$		−	18763.3i		−	1.66325i	0.555335	−	0.831626i	$-0.312590\pi$
$504$	−1591.15	+	102.863i	−0.140626	+	0.00909103i
$505$		0			0
$506$	188.550	+	326.577i	0.0165653	+	0.0286920i
$507$	2641.53	+	1525.09i	0.231390	+	0.133593i
$508$	−11058.6	−	6384.68i	−0.965838	−	0.557627i
$509$	7902.27	+	13687.1i	0.688137	+	1.19189i	0.972440	+	0.233154i	$0.0749047\pi$
$509$	7902.27	+	13687.1i	0.688137	+	1.19189i	−0.284302	+	0.958735i	$0.591762\pi$
$510$		0			0
$511$	−5578.25	−	8364.60i	−0.482911	−	0.724126i
$512$		−	4539.39i		−	0.391826i
$513$	8082.53	−	4666.45i	0.695618	−	0.401615i
$514$	99.9343	−	173.091i	0.00857570	−	0.0148536i
$515$		0			0
$516$	56.1394	+	97.2362i	0.00478953	+	0.00829571i
$517$		−	1636.58i		−	0.139220i
$518$	−985.731	+	657.373i	−0.0836111	+	0.0557593i
$519$	−3738.96			−0.316228
$520$		0			0
$521$	−4725.82	+	8185.36i	−0.397393	+	0.688305i	−0.993403	−	0.114672i	$-0.963418\pi$
$521$	−4725.82	+	8185.36i	−0.397393	+	0.688305i	0.596010	+	0.802977i	$0.296752\pi$
$522$	−1390.29	−	802.686i	−0.116574	−	0.0673039i
$523$	−2342.24	+	1352.29i	−0.195830	+	0.113062i	−0.594709	−	0.803941i	$-0.702733\pi$
$523$	−2342.24	+	1352.29i	−0.195830	+	0.113062i	0.398879	+	0.917004i	$0.369399\pi$
$524$	22639.2			1.88740
$525$		0			0
$526$	−844.931			−0.0700394
$527$	6890.09	−	3978.00i	0.569520	−	0.328813i
$528$	−1740.10	−	1004.65i	−0.143425	−	0.0828064i
$529$	−1699.31	+	2943.29i	−0.139665	+	0.241908i
$530$		0			0
$531$	2365.81			0.193347
$532$	13423.9	+	6634.85i	1.09399	+	0.540709i
$533$		−	16935.1i		−	1.37625i
$534$	216.907	+	375.694i	0.0175777	+	0.0304454i
$535$		0			0
$536$	837.301	−	1450.25i	0.0674737	−	0.116868i
$537$	−3752.68	+	2166.61i	−0.301564	+	0.174108i
$538$		−	35.1392i		−	0.00281591i
$539$	−6021.21	+	781.774i	−0.481172	+	0.0624738i
$540$		0			0
$541$	−30.3818	−	52.6228i	−0.00241445	−	0.00418194i	0.864816	−	0.502090i	$-0.167435\pi$
$541$	−30.3818	−	52.6228i	−0.00241445	−	0.00418194i	−0.867230	+	0.497908i	$0.834102\pi$
$542$	474.086	+	273.713i	0.0375714	+	0.0216919i
$543$	−2066.55	−	1193.13i	−0.163323	−	0.0942945i
$544$	−1887.21	−	3268.74i	−0.148738	−	0.257622i
$545$		0			0
$546$	−210.409	+	425.709i	−0.0164921	+	0.0333675i
$547$			14267.4i			1.11523i	0.830100	+	0.557614i	$0.188283\pi$
$547$			14267.4i			1.11523i	−0.830100	+	0.557614i	$0.811717\pi$
$548$	5793.86	−	3345.09i	0.451645	−	0.260757i
$549$	−5151.78	+	8923.15i	−0.400497	+	0.693681i
$550$		0			0
$551$	15125.6	+	26198.2i	1.16946	+	2.02556i
$552$		−	614.451i		−	0.0473782i
$553$	286.392	+	4430.08i	0.0220228	+	0.340662i
$554$	329.816			0.0252934
$555$		0			0
$556$	9653.55	−	16720.4i	0.736334	−	1.27537i
$557$	16975.6	+	9800.88i	1.29135	+	0.745559i	0.978893	−	0.204374i	$-0.0655158\pi$
$557$	16975.6	+	9800.88i	1.29135	+	0.745559i	0.312454	+	0.949933i	$0.398849\pi$
$558$	−426.729	+	246.372i	−0.0323743	+	0.0186913i
$559$	−486.743			−0.0368283
$560$		0			0
$561$	−2790.53			−0.210011
$562$	−401.340	+	231.714i	−0.0301236	+	0.0173919i
$563$	6132.48	+	3540.59i	0.459064	+	0.265041i	0.711651	−	0.702533i	$-0.247948\pi$
$563$	6132.48	+	3540.59i	0.459064	+	0.265041i	−0.252586	+	0.967574i	$0.581281\pi$
$564$	−664.505	+	1150.96i	−0.0496112	+	0.0859290i
$565$		0			0
$566$	1675.79			0.124450
$567$	−7315.06	+	4878.32i	−0.541805	+	0.361323i
$568$		−	1880.91i		−	0.138946i
$569$	−6017.28	−	10422.2i	−0.443334	−	0.767878i	0.554600	−	0.832117i	$-0.312871\pi$
$569$	−6017.28	−	10422.2i	−0.443334	−	0.767878i	−0.997935	+	0.0642392i	$0.979538\pi$
$570$		0			0
$571$	−2089.69	+	3619.45i	−0.153154	+	0.265270i	−0.932385	−	0.361466i	$-0.882276\pi$
$571$	−2089.69	+	3619.45i	−0.153154	+	0.265270i	0.779231	+	0.626736i	$0.215610\pi$
$572$	7593.35	−	4384.02i	0.555059	−	0.320464i
$573$			3812.62i			0.277966i
$574$	1142.60	−	73.8655i	0.0830855	−	0.00537123i
$575$		0			0
$576$	−5840.11	−	10115.4i	−0.422461	−	0.731725i
$577$	−14455.4	−	8345.82i	−1.04296	−	0.602151i	−0.122287	−	0.992495i	$-0.539023\pi$
$577$	−14455.4	−	8345.82i	−1.04296	−	0.602151i	−0.920669	+	0.390344i	$0.872356\pi$
$578$	−528.850	−	305.332i	−0.0380576	−	0.0219726i
$579$	−3284.04	−	5688.13i	−0.235717	−	0.408274i
$580$		0			0
$581$	2455.15	−	4967.36i	0.175313	−	0.354700i
$582$			118.848i			0.00846465i
$583$	−2764.11	+	1595.86i	−0.196360	+	0.113368i
$584$	−984.809	+	1705.74i	−0.0697803	+	0.120863i
$585$		0			0
$586$	−61.7581	−	106.968i	−0.00435359	−	0.00754064i
$587$		−	8878.89i		−	0.624311i	−0.950031	−	0.312156i	$-0.898949\pi$
$587$		−	8878.89i		−	0.624311i	0.950031	−	0.312156i	$-0.101051\pi$
$588$	4551.95	+	1895.01i	0.319250	+	0.132906i
$589$	9285.11			0.649552
$590$		0			0
$591$	2966.49	−	5138.12i	0.206472	−	0.357621i
$592$	−15284.4	−	8824.44i	−1.06112	−	0.612639i
$593$	−20591.6	+	11888.5i	−1.42596	+	0.823278i	−0.996799	−	0.0799505i	$-0.974524\pi$
$593$	−20591.6	+	11888.5i	−1.42596	+	0.823278i	−0.429160	+	0.903228i	$0.641190\pi$
$594$	369.480			0.0255218
$595$		0			0
$596$	4593.67			0.315711
$597$	1016.10	−	586.644i	0.0696584	−	0.0402173i
$598$	1149.68	+	663.770i	0.0786188	+	0.0453906i
$599$	6354.72	−	11006.7i	0.433467	−	0.750787i	−0.563702	−	0.825978i	$-0.690623\pi$
$599$	6354.72	−	11006.7i	0.433467	−	0.750787i	0.997169	+	0.0751912i	$0.0239567\pi$
$600$		0			0
$601$	−13296.4			−0.902446			−0.451223	−	0.892411i	$-0.649012\pi$
$601$	−13296.4			−0.902446			−0.451223	+	0.892411i	$0.649012\pi$
$602$	−2.12302	−	32.8402i	−0.000143734	−	0.00222336i
$603$		−	10952.2i		−	0.739651i
$604$	−3114.19	−	5393.93i	−0.209792	−	0.363371i
$605$		0			0
$606$	−72.9988	+	126.438i	−0.00489336	+	0.00847554i
$607$	−5056.27	+	2919.24i	−0.338102	+	0.195203i	−0.659432	−	0.751764i	$-0.729203\pi$
$607$	−5056.27	+	2919.24i	−0.338102	+	0.195203i	0.321330	+	0.946967i	$0.395870\pi$
$608$		−	4404.97i		−	0.293824i
$609$	5526.67	+	8287.25i	0.367737	+	0.551422i
$610$		0			0
$611$	−2880.71	−	4989.54i	−0.190738	−	0.330369i
$612$	−14236.7	−	8219.59i	−0.940337	−	0.542904i
$613$	3698.20	+	2135.16i	0.243669	+	0.140682i	0.616862	−	0.787072i	$-0.288404\pi$
$613$	3698.20	+	2135.16i	0.243669	+	0.140682i	−0.373193	+	0.927754i	$0.621737\pi$
$614$	−604.486	−	1047.00i	−0.0397314	−	0.0688168i
$615$		0			0
$616$	659.954	+	989.603i	0.0431661	+	0.0647276i
$617$		−	2869.54i		−	0.187234i	−0.995608	−	0.0936168i	$-0.970157\pi$
$617$		−	2869.54i		−	0.187234i	0.995608	−	0.0936168i	$-0.0298429\pi$
$618$	379.181	−	218.920i	0.0246811	−	0.0142496i
$619$	−3441.03	+	5960.04i	−0.223436	+	0.387002i	−0.955849	−	0.293858i	$-0.905061\pi$
$619$	−3441.03	+	5960.04i	−0.223436	+	0.387002i	0.732413	+	0.680860i	$0.238394\pi$
$620$		0			0
$621$	−4295.61	−	7440.21i	−0.277579	−	0.480782i
$622$			2011.07i			0.129641i
$623$	1259.73	+	19486.3i	0.0810115	+	1.25314i
$624$	−7073.54			−0.453796
$625$		0			0
$626$	−215.707	+	373.615i	−0.0137722	+	0.0238541i
$627$	−2820.40	−	1628.36i	−0.179642	−	0.103717i
$628$	−9446.78	+	5454.10i	−0.600267	+	0.346564i
$629$	−24510.9			−1.55376
$630$		0			0
$631$	−28101.9			−1.77293			−0.886467	−	0.462793i	$-0.846847\pi$
$631$	−28101.9			−1.77293			−0.886467	+	0.462793i	$0.846847\pi$
$632$	753.164	−	434.840i	0.0474039	−	0.0273687i
$633$	−7944.69	−	4586.87i	−0.498852	−	0.288012i
$634$	690.773	−	1196.45i	0.0432715	−	0.0749484i
$635$		0			0
$636$	2591.88			0.161595
$637$	−16981.1	+	12982.0i	−1.05623	+	0.807480i
$638$			1197.61i			0.0743164i
$639$	−6150.77	−	10653.4i	−0.380783	−	0.659536i
$640$		0			0
$641$	−6838.90	+	11845.3i	−0.421404	+	0.729894i	−0.996077	−	0.0884896i	$-0.971796\pi$
$641$	−6838.90	+	11845.3i	−0.421404	+	0.729894i	0.574673	+	0.818383i	$0.305129\pi$
$642$	−496.611	+	286.719i	−0.0305291	+	0.0176260i
$643$			17919.1i			1.09901i	0.835492	+	0.549503i	$0.185183\pi$
$643$			17919.1i			1.09901i	−0.835492	+	0.549503i	$0.814817\pi$
$644$	6107.58	−	12357.1i	0.373715	−	0.756116i
$645$		0			0
$646$	−1008.55	−	1746.86i	−0.0614254	−	0.106392i
$647$	27269.6	+	15744.1i	1.65700	+	0.956669i	0.974088	+	0.226169i	$0.0726201\pi$
$647$	27269.6	+	15744.1i	1.65700	+	0.956669i	0.682912	+	0.730501i	$0.260713\pi$
$648$	1491.71	+	861.241i	0.0904321	+	0.0522110i
$649$	−882.449	−	1528.45i	−0.0533731	−	0.0924449i
$650$		0			0
$651$	3051.02	−	197.240i	0.183685	−	0.0118747i
$652$		−	29843.9i		−	1.79261i
$653$	961.687	−	555.230i	0.0576320	−	0.0332739i	−0.470907	−	0.882183i	$-0.656073\pi$
$653$	961.687	−	555.230i	0.0576320	−	0.0332739i	0.528539	+	0.848909i	$0.322740\pi$
$654$	−29.7238	+	51.4831i	−0.00177720	+	0.00307821i
$655$		0			0
$656$	8527.70	+	14770.4i	0.507547	+	0.879097i
$657$			12881.7i			0.764936i
$658$	324.076	−	216.122i	0.0192003	−	0.0128044i
$659$	−12793.3			−0.756230			−0.378115	−	0.925759i	$-0.623428\pi$
$659$	−12793.3			−0.756230			−0.378115	+	0.925759i	$0.623428\pi$
$660$		0			0
$661$	1019.80	−	1766.35i	0.0600086	−	0.103938i	−0.834460	−	0.551068i	$-0.814221\pi$
$661$	1019.80	−	1766.35i	0.0600086	−	0.103938i	0.894469	+	0.447130i	$0.147554\pi$
$662$	658.392	+	380.123i	0.0386543	+	0.0223171i
$663$	−8507.65	+	4911.89i	−0.498356	+	0.287726i
$664$	−1085.50			−0.0634419
$665$		0			0
$666$	1518.05			0.0883232
$667$	24116.3	−	13923.5i	1.39998	−	0.808278i
$668$	13392.0	+	7731.86i	0.775675	+	0.447836i
$669$	148.048	−	256.427i	0.00855586	−	0.0148192i
$670$		0			0
$671$	7686.48			0.442225
$672$	−93.5728	−	1447.44i	−0.00537150	−	0.0830897i
$673$			4039.94i			0.231394i	0.993285	+	0.115697i	$0.0369102\pi$
$673$			4039.94i			0.231394i	−0.993285	+	0.115697i	$0.963090\pi$
$674$	974.698	+	1688.23i	0.0557032	+	0.0964808i
$675$		0			0
$676$	6702.37	−	11608.8i	0.381337	−	0.660494i
$677$	971.291	−	560.775i	0.0551399	−	0.0318351i	−0.472177	−	0.881504i	$-0.656532\pi$
$677$	971.291	−	560.775i	0.0551399	−	0.0318351i	0.527317	+	0.849669i	$0.323198\pi$
$678$			832.731i			0.0471694i
$679$	−2370.37	+	4795.85i	−0.133971	+	0.271057i
$680$		0			0
$681$	5721.11	+	9909.26i	0.321929	+	0.557597i
$682$	318.340	+	183.794i	0.0178737	+	0.0103194i
$683$	−8861.19	−	5116.01i	−0.496434	−	0.286616i	0.230806	−	0.973000i	$-0.425864\pi$
$683$	−8861.19	−	5116.01i	−0.496434	−	0.286616i	−0.727240	+	0.686384i	$0.759197\pi$
$684$	−9592.74	−	16615.1i	−0.536239	−	0.928794i
$685$		0			0
$686$	−949.950	−	1089.08i	−0.0528707	−	0.0606141i
$687$		−	6301.95i		−	0.349977i
$688$	424.527	−	245.101i	0.0235246	−	0.0135819i
$689$	−5618.07	+	9730.78i	−0.310640	+	0.538045i
$690$		0			0
$691$	−11257.3	−	19498.2i	−0.619750	−	1.07344i	−0.989531	−	0.144320i	$-0.953901\pi$
$691$	−11257.3	−	19498.2i	−0.619750	−	1.07344i	0.369781	−	0.929119i	$-0.379433\pi$
$692$			16431.7i			0.902661i
$693$	6974.06	+	3446.97i	0.382284	+	0.188946i
$694$	−1421.11			−0.0777302
$695$		0			0
$696$	975.702	−	1689.97i	0.0531378	−	0.0920373i
$697$	20513.3	+	11843.3i	1.11477	+	0.643613i
$698$	1397.06	−	806.593i	0.0757586	−	0.0437392i
$699$	−8131.62			−0.440009
$700$		0			0
$701$	−19172.5			−1.03300			−0.516501	−	0.856287i	$-0.672766\pi$
$701$	−19172.5			−1.03300			−0.516501	+	0.856287i	$0.672766\pi$
$702$	1126.45	−	650.359i	0.0605631	−	0.0349661i
$703$	−24773.2	−	14302.8i	−1.32907	−	0.767342i
$704$	−4356.73	+	7546.07i	−0.233239	+	0.403982i
$705$		0			0
$706$	−1658.28			−0.0883996
$707$	−5467.43	+	3646.17i	−0.290840	+	0.193958i
$708$			1433.21i			0.0760781i
$709$	−13166.6	−	22805.2i	−0.697437	−	1.20800i	−0.969352	−	0.245675i	$-0.920990\pi$
$709$	−13166.6	−	22805.2i	−0.697437	−	1.20800i	0.271916	−	0.962321i	$-0.412343\pi$
$710$		0			0
$711$	2843.94	−	4925.84i	0.150008	−	0.259822i
$712$	3312.90	−	1912.70i	0.174377	−	0.100676i
$713$		−	8547.23i		−	0.448943i
$714$	−368.509	−	552.581i	−0.0193153	−	0.0289633i
$715$		0			0
$716$	9521.67	+	16492.0i	0.496985	+	0.860804i
$717$	−2395.98	−	1383.32i	−0.124797	−	0.0720517i
$718$	1707.80	+	985.997i	0.0887666	+	0.0512494i
$719$	8523.86	+	14763.8i	0.442123	+	0.765779i	0.997847	−	0.0655877i	$-0.0208922\pi$
$719$	8523.86	+	14763.8i	0.442123	+	0.765779i	−0.555724	+	0.831367i	$0.687559\pi$
$720$		0			0
$721$	19667.2	−	1271.43i	1.01587	−	0.0656733i
$722$		−	793.666i		−	0.0409102i
$723$	7161.66	−	4134.78i	0.368388	−	0.212689i
$724$	−5243.47	+	9081.96i	−0.269160	+	0.466199i
$725$		0			0
$726$	209.353	+	362.611i	0.0107023	+	0.0185368i
$727$		−	16021.2i		−	0.817325i	−0.912686	−	0.408662i	$-0.865995\pi$
$727$		−	16021.2i		−	0.817325i	0.912686	−	0.408662i	$-0.134005\pi$
$728$	3753.94	+	1855.41i	0.191113	+	0.0944587i
$729$	6785.17			0.344722
$730$		0			0
$731$	340.398	−	589.586i	0.0172231	−	0.0298312i
$732$	−5405.65	−	3120.95i	−0.272949	−	0.157587i
$733$	−6533.44	+	3772.08i	−0.329220	+	0.190075i	−0.655495	−	0.755200i	$-0.727540\pi$
$733$	−6533.44	+	3772.08i	−0.329220	+	0.190075i	0.326275	+	0.945275i	$0.394206\pi$
$734$	−859.397			−0.0432165
$735$		0			0
$736$	−4054.91			−0.203079
$737$	−7075.76	+	4085.19i	−0.353648	+	0.204179i
$738$	−1270.46	−	733.502i	−0.0633691	−	0.0365862i
$739$	8771.94	−	15193.4i	0.436645	−	0.756292i	−0.560783	−	0.827963i	$-0.689500\pi$
$739$	8771.94	−	15193.4i	0.436645	−	0.756292i	0.997428	+	0.0716708i	$0.0228331\pi$
$740$		0			0
$741$	−11464.9			−0.568387
$742$	−681.032	−	336.604i	−0.0336947	−	0.0166538i
$743$			26595.9i			1.31320i	0.754239	+	0.656600i	$0.228006\pi$
$743$			26595.9i			1.31320i	−0.754239	+	0.656600i	$0.771994\pi$
$744$	−299.477	−	518.709i	−0.0147572	−	0.0255602i
$745$		0			0
$746$	−198.165	+	343.232i	−0.00972565	+	0.0168453i
$747$	−6148.22	+	3549.68i	−0.301140	+	0.173863i
$748$			12263.6i			0.599470i
$749$	−25758.0	+	1665.18i	−1.25658	+	0.0812341i
$750$		0			0
$751$	−4808.03	−	8327.76i	−0.233619	−	0.404639i	0.725252	−	0.688484i	$-0.241723\pi$
$751$	−4808.03	−	8327.76i	−0.233619	−	0.404639i	−0.958870	+	0.283844i	$0.908390\pi$
$752$	5025.00	+	2901.18i	0.243674	+	0.140685i
$753$	841.316	+	485.734i	0.0407161	+	0.0235075i
$754$	2108.03	+	3651.22i	0.101817	+	0.176352i
$755$		0			0
$756$	−7493.27	−	11236.2i	−0.360486	−	0.540550i
$757$			8519.83i			0.409060i	0.978860	+	0.204530i	$0.0655666\pi$
$757$			8519.83i			0.409060i	−0.978860	+	0.204530i	$0.934433\pi$
$758$	−683.910	+	394.855i	−0.0327714	+	0.0189206i
$759$	−1498.95	+	2596.26i	−0.0716845	+	0.124161i
$760$		0			0
$761$	2114.23	+	3661.95i	0.100710	+	0.174436i	0.911978	−	0.410240i	$-0.134555\pi$
$761$	2114.23	+	3661.95i	0.100710	+	0.174436i	−0.811267	+	0.584676i	$0.801222\pi$
$762$			661.017i			0.0314253i
$763$	−2226.24	+	1484.65i	−0.105629	+	0.0704430i
$764$	16755.5			0.793444
$765$		0			0
$766$	1643.11	−	2845.95i	0.0775039	−	0.134241i
$767$	−5380.75	−	3106.58i	−0.253308	−	0.146248i
$768$	6004.45	−	3466.67i	0.282118	−	0.162881i
$769$	25293.4			1.18609			0.593046	−	0.805169i	$-0.297925\pi$
$769$	25293.4			1.18609			0.593046	+	0.805169i	$0.297925\pi$
$770$		0			0
$771$	1588.94			0.0742207
$772$	−24997.8	+	14432.5i	−1.16540	+	0.672846i
$773$	13247.4	+	7648.39i	0.616398	+	0.355878i	0.775465	−	0.631390i	$-0.217515\pi$
$773$	13247.4	+	7648.39i	0.616398	+	0.355878i	−0.159067	+	0.987268i	$0.550849\pi$
$774$	−21.0821	+	36.5153i	−0.000979044	+	0.00169575i
$775$		0			0
$776$	1048.02			0.0484814
$777$	−8444.13	−	4173.56i	−0.389873	−	0.192697i
$778$		−	1758.45i		−	0.0810329i
$779$	13821.9	+	23940.2i	0.635712	+	1.10109i
$780$		0			0
$781$	−4588.48	+	7947.48i	−0.210229	+	0.364127i
$782$	−1608.03	+	928.399i	−0.0735335	+	0.0424546i
$783$		−	27284.4i		−	1.24529i
$784$	8273.47	−	19873.5i	0.376889	−	0.905316i
$785$		0			0
$786$	−585.968	−	1014.93i	−0.0265913	−	0.0460575i
$787$	−14540.4	−	8394.92i	−0.658590	−	0.380237i	0.133150	−	0.991096i	$-0.457491\pi$
$787$	−14540.4	−	8394.92i	−0.658590	−	0.380237i	−0.791739	+	0.610859i	$0.790824\pi$
$788$	−22580.7	−	13037.0i	−1.02082	−	0.589368i
$789$	−3358.56	−	5817.20i	−0.151544	−	0.262481i
$790$		0			0
$791$	−16608.4	+	33602.9i	−0.746558	+	1.51047i
$792$		−	1524.01i		−	0.0683755i
$793$	23434.2	−	13529.7i	1.04940	−	0.605870i
$794$	1145.41	−	1983.90i	0.0511951	−	0.0886726i
$795$		0			0
$796$	−2578.14	−	4465.48i	−0.114799	−	0.198838i
$797$		−	18124.8i		−	0.805537i	−0.915302	−	0.402768i	$-0.868048\pi$
$797$		−	18124.8i		−	0.805537i	0.915302	−	0.402768i	$-0.131952\pi$
$798$	−50.0065	−	773.531i	−0.00221831	−	0.0343141i
$799$	8058.37			0.356802
$800$		0			0
$801$	12509.5	−	21667.0i	0.551810	−	0.955764i
$802$	296.153	+	170.984i	0.0130393	+	0.00752825i
$803$	8322.30	−	4804.88i	0.365738	−	0.211159i
$804$	6634.87			0.291037
$805$		0			0
$806$	1294.06			0.0565524
$807$	241.927	−	139.677i	0.0105530	−	0.00609275i
$808$	1114.94	+	643.710i	0.0485438	+	0.0280268i
$809$	−5388.96	+	9333.95i	−0.234197	+	0.405642i	−0.959039	−	0.283274i	$-0.908580\pi$
$809$	−5388.96	+	9333.95i	−0.234197	+	0.405642i	0.724842	+	0.688915i	$0.241913\pi$
$810$		0			0
$811$	11986.8			0.519007			0.259503	−	0.965742i	$-0.416441\pi$
$811$	11986.8			0.519007			0.259503	+	0.965742i	$0.416441\pi$
$812$	36420.3	−	24288.3i	1.57402	−	1.04969i
$813$			4352.00i			0.187738i
$814$	−566.234	−	980.746i	−0.0243814	−	0.0422299i
$815$		0			0
$816$	4946.80	−	8568.10i	0.212221	−	0.367578i
$817$	688.082	−	397.264i	0.0294650	−	0.0170116i
$818$		−	139.543i		−	0.00596454i
$819$	27329.6	−	1766.78i	1.16602	−	0.0753800i
$820$		0			0
$821$	−5370.22	−	9301.50i	−0.228285	−	0.395401i	0.729015	−	0.684498i	$-0.239978\pi$
$821$	−5370.22	−	9301.50i	−0.228285	−	0.395401i	−0.957300	+	0.289097i	$0.906645\pi$
$822$	−299.924	−	173.161i	−0.0127263	−	0.00734756i
$823$	28060.0	+	16200.4i	1.18847	+	0.686163i	0.957958	−	0.286907i	$-0.0926270\pi$
$823$	28060.0	+	16200.4i	1.18847	+	0.686163i	0.230511	+	0.973070i	$0.425960\pi$
$824$	−1930.46	−	3343.65i	−0.0816149	−	0.141361i
$825$		0			0
$826$	186.129	−	376.585i	0.00784051	−	0.0158633i
$827$			3825.30i			0.160845i	0.996761	+	0.0804225i	$0.0256269\pi$
$827$			3825.30i			0.160845i	−0.996761	+	0.0804225i	$0.974373\pi$
$828$	−15294.7	+	8830.41i	−0.641942	+	0.370626i
$829$	15918.2	−	27571.0i	0.666900	−	1.15511i	−0.311866	−	0.950126i	$-0.600954\pi$
$829$	15918.2	−	27571.0i	0.666900	−	1.15511i	0.978766	−	0.204979i	$-0.0657126\pi$
$830$		0			0
$831$	1311.00	+	2270.72i	0.0547271	+	0.0947900i
$832$			30674.9i			1.27820i
$833$	−3849.38	−	29647.8i	−0.160112	−	1.23318i
$834$	−999.448			−0.0414965
$835$		0			0
$836$	−7156.20	+	12394.9i	−0.296055	+	0.512783i
$837$	−7252.56	−	4187.27i	−0.299504	−	0.172919i
$838$	2430.11	−	1403.02i	0.100175	−	0.0578361i
$839$	−6354.36			−0.261474			−0.130737	−	0.991417i	$-0.541734\pi$
$839$	−6354.36			−0.261474			−0.130737	+	0.991417i	$0.541734\pi$
$840$		0			0
$841$	64049.1			2.62615
$842$	479.192	−	276.662i	0.0196129	−	0.0113235i
$843$	−3190.61	−	1842.10i	−0.130357	−	0.0752614i
$844$	−20158.1	+	34914.8i	−0.822121	+	1.42395i
$845$		0			0
$846$	−499.085			−0.0202824
$847$	1215.87	+	18807.8i	0.0493243	+	0.762978i
$848$		−	11316.0i		−	0.458245i
$849$	6661.21	+	11537.6i	0.269272	+	0.466393i
$850$		0			0
$851$	−13166.2	+	22804.5i	−0.530354	+	0.918600i
$852$	6453.86	−	3726.14i	0.259514	−	0.149830i
$853$		−	16620.2i		−	0.667135i	−0.942726	−	0.333568i	$-0.891747\pi$
$853$		−	16620.2i		−	0.667135i	0.942726	−	0.333568i	$-0.108253\pi$
$854$	1015.05	+	1522.08i	0.0406726	+	0.0609887i
$855$		0			0
$856$	2528.31	+	4379.16i	0.100953	+	0.174856i
$857$	29826.3	+	17220.2i	1.18885	+	0.686385i	0.958046	−	0.286614i	$-0.0925298\pi$
$857$	29826.3	+	17220.2i	1.18885	+	0.686385i	0.230808	+	0.972999i	$0.425863\pi$
$858$	−393.076	−	226.943i	−0.0156403	−	0.00902994i
$859$	14596.3	+	25281.5i	0.579765	+	1.00418i	0.995506	+	0.0946994i	$0.0301890\pi$
$859$	14596.3	+	25281.5i	0.579765	+	1.00418i	−0.415741	+	0.909483i	$0.636478\pi$
$860$		0			0
$861$	5050.32	+	7572.96i	0.199901	+	0.299751i
$862$			298.130i			0.0117800i
$863$	−22570.7	+	13031.2i	−0.890285	+	0.514006i	−0.874036	−	0.485862i	$-0.838506\pi$
$863$	−22570.7	+	13031.2i	−0.890285	+	0.514006i	−0.0162495	+	0.999868i	$0.505173\pi$
$864$	−1986.49	+	3440.70i	−0.0782196	+	0.135480i
$865$		0			0
$866$	563.609	+	976.199i	0.0221157	+	0.0383055i
$867$		−	4854.72i		−	0.190167i
$868$	−866.816	−	13408.4i	−0.0338959	−	0.524323i
$869$	−4243.16			−0.165638
$870$		0			0
$871$	−14381.5	+	24909.5i	−0.559471	+	0.969032i
$872$	453.982	+	262.107i	0.0176305	+	0.0101790i
$873$	5935.94	−	3427.11i	0.230127	−	0.132864i
$874$	−2166.99			−0.0838668
$875$		0			0
$876$	−7803.74			−0.300986
$877$	−25156.8	+	14524.3i	−0.968625	+	0.559236i	−0.898817	−	0.438325i	$-0.855572\pi$
$877$	−25156.8	+	14524.3i	−0.968625	+	0.559236i	−0.0698080	+	0.997560i	$0.522239\pi$
$878$	1614.63	+	932.208i	0.0620629	+	0.0358320i
$879$	490.972	−	850.388i	0.0188397	−	0.0326312i
$880$		0			0
$881$	24440.9			0.934660			0.467330	−	0.884083i	$-0.345216\pi$
$881$	24440.9			0.934660			0.467330	+	0.884083i	$0.345216\pi$
$882$	238.406	+	1836.20i	0.00910154	+	0.0700999i
$883$		−	38951.9i		−	1.48453i	−0.670108	−	0.742264i	$-0.733752\pi$
$883$		−	38951.9i		−	1.48453i	0.670108	−	0.742264i	$-0.266248\pi$
$884$	21586.5	+	37388.9i	0.821303	+	1.42254i
$885$		0			0
$886$	336.321	−	582.525i	0.0127527	−	0.0220884i
$887$	2722.64	−	1571.91i	0.103063	−	0.0595036i	−0.447582	−	0.894243i	$-0.647715\pi$
$887$	2722.64	−	1571.91i	0.103063	−	0.0595036i	0.550646	+	0.834739i	$0.314382\pi$
$888$			1845.26i			0.0697330i
$889$	−13183.7	+	26673.8i	−0.497374	+	1.00631i
$890$		0			0
$891$	−4201.99	−	7278.06i	−0.157993	−	0.273652i
$892$	−1126.93	−	650.632i	−0.0423008	−	0.0244224i
$893$	8144.61	+	4702.29i	0.305206	+	0.176211i
$894$	−118.898	−	205.937i	−0.00444802	−	0.00770420i
$895$		0			0
$896$	−8472.15	+	547.700i	−0.315887	+	0.0204212i
$897$			10553.8i			0.392845i
$898$	−2059.52	+	1189.07i	−0.0765336	+	0.0441867i
$899$	13572.4	−	23508.0i	0.503519	−	0.872120i
$900$		0			0
$901$	−7857.85	−	13610.2i	−0.290547	−	0.503242i
$902$			1094.39i			0.0403981i
$903$	217.660	−	145.155i	0.00802134	−	0.00534934i
$904$	7343.10			0.270163
$905$		0			0
$906$	−161.209	+	279.221i	−0.00591147	+	0.0102390i
$907$	11119.4	+	6419.77i	0.407070	+	0.235022i	0.689530	−	0.724257i	$-0.257817\pi$
$907$	11119.4	+	6419.77i	0.407070	+	0.235022i	−0.282460	+	0.959279i	$0.591150\pi$
$908$	43548.6	−	25142.8i	1.59164	−	0.918935i
$909$	8419.98			0.307231
$910$		0			0
$911$	17451.4			0.634678			0.317339	−	0.948312i	$-0.397211\pi$
$911$	17451.4			0.634678			0.317339	+	0.948312i	$0.397211\pi$
$912$	9999.48	−	5773.20i	0.363066	−	0.209616i
$913$	4586.58	+	2648.06i	0.166258	+	0.0959892i
$914$	−255.388	+	442.344i	−0.00924231	+	0.0160082i
$915$		0			0
$916$	−27695.4			−0.998998
$917$	−3403.13	−	52641.8i	−0.122553	−	1.89573i
$918$			1819.28i			0.0654088i
$919$	−3968.83	−	6874.21i	−0.142459	−	0.246746i	0.785963	−	0.618273i	$-0.212167\pi$
$919$	−3968.83	−	6874.21i	−0.142459	−	0.246746i	−0.928422	+	0.371527i	$0.878834\pi$
$920$		0			0
$921$	4805.61	−	8323.56i	0.171933	−	0.297797i
$922$	2451.12	−	1415.16i	0.0875526	−	0.0505485i
$923$			32306.6i			1.15210i
$924$	−2088.18	+	4224.89i	−0.0743463	+	0.150421i
$925$		0			0
$926$	1943.51	+	3366.26i	0.0689716	+	0.119462i
$927$	−21868.1	−	12625.6i	−0.774805	−	0.447334i
$928$	−11152.5	−	6438.89i	−0.394502	−	0.227766i
$929$	−890.701	−	1542.74i	−0.0314563	−	0.0544840i	0.849869	−	0.526995i	$-0.176681\pi$
$929$	−890.701	−	1542.74i	−0.0314563	−	0.0544840i	−0.881325	+	0.472511i	$0.843348\pi$
$930$		0			0
$931$	13409.8	−	32211.4i	0.472061	−	1.13393i
$932$			35736.3i			1.25599i
$933$	−13845.9	+	7993.93i	−0.485846	+	0.280503i
$934$	1331.89	−	2306.91i	0.0466605	−	0.0808184i
$935$		0			0
$936$	−2682.57	−	4646.35i	−0.0936779	−	0.162255i
$937$		−	46363.0i		−	1.61645i	−0.588874	−	0.808225i	$-0.700429\pi$
$937$		−	46363.0i		−	1.61645i	0.588874	−	0.808225i	$-0.299571\pi$
$938$	−1743.35	−	861.662i	−0.0606850	−	0.0299939i
$939$	−3429.70			−0.119195
$940$		0			0
$941$	−8267.66	+	14320.0i	−0.286416	+	0.496088i	−0.972952	−	0.231009i	$-0.925797\pi$
$941$	−8267.66	+	14320.0i	−0.286416	+	0.496088i	0.686535	+	0.727097i	$0.259131\pi$
$942$	489.021	+	282.336i	0.0169142	+	0.00976541i
$943$	22037.7	−	12723.5i	0.761024	−	0.439377i
$944$	6257.30			0.215739
$945$		0			0
$946$	31.4545			0.00108105
$947$	−2367.98	+	1367.15i	−0.0812555	+	0.0469129i	−0.540077	−	0.841615i	$-0.681605\pi$
$947$	−2367.98	+	1367.15i	−0.0812555	+	0.0469129i	0.458822	+	0.888528i	$0.348272\pi$
$948$	2984.08	+	1722.86i	0.102235	+	0.0590252i
$949$	16915.1	−	29297.8i	0.578596	−	1.00216i
$950$		0			0
$951$	10983.2			0.374505
$952$	−4872.70	+	3249.55i	−0.165888	+	0.110629i
$953$			35524.6i			1.20751i	0.797171	+	0.603754i	$0.206329\pi$
$953$			35524.6i			1.20751i	−0.797171	+	0.603754i	$0.793671\pi$
$954$	486.666	+	842.931i	0.0165161	+	0.0286068i
$955$		0			0
$956$	−6079.33	+	10529.7i	−0.205669	+	0.356229i
$957$	−8245.33	+	4760.45i	−0.278510	+	0.160798i
$958$			2659.89i			0.0897048i
$959$	−8649.11	−	12969.4i	−0.291235	−	0.436707i
$960$		0			0
$961$	10729.7	+	18584.3i	0.360165	+	0.623824i
$962$	−3452.62	−	1993.37i	−0.115714	−	0.0668076i
$963$	28640.6	+	16535.6i	0.958390	+	0.553327i
$964$	−18171.3	−	31473.6i	−0.607114	−	1.05155i
$965$		0			0
$966$	−712.059	+	46.0325i	−0.0237165	+	0.00153320i
$967$			9328.92i			0.310236i	0.987896	+	0.155118i	$0.0495757\pi$
$967$			9328.92i			0.310236i	−0.987896	+	0.155118i	$0.950424\pi$
$968$	3197.53	−	1846.10i	0.106170	−	0.0612973i
$969$	8017.86	−	13887.3i	0.265811	−	0.460398i
$970$		0			0
$971$	−24569.1	−	42554.8i	−0.812007	−	1.40644i	−0.911457	−	0.411394i	$-0.865042\pi$
$971$	−24569.1	−	42554.8i	−0.812007	−	1.40644i	0.0994509	−	0.995042i	$-0.468291\pi$
$972$			26513.9i			0.874930i
$973$	−40330.4	−	19933.5i	−1.32881	−	0.656772i
$974$	1621.79			0.0533527
$975$		0			0
$976$	−13625.9	+	23600.7i	−0.446879	+	0.774017i
$977$	−12792.4	−	7385.67i	−0.418898	−	0.241851i	0.275708	−	0.961242i	$-0.411088\pi$
$977$	−12792.4	−	7385.67i	−0.418898	−	0.241851i	−0.694606	+	0.719391i	$0.744421\pi$
$978$	−1337.92	+	772.448i	−0.0437443	+	0.0252558i
$979$	−18664.1			−0.609304
$980$		0			0
$981$	3428.46			0.111582
$982$	853.157	−	492.570i	0.0277244	−	0.0160067i
$983$	−17884.3	−	10325.5i	−0.580284	−	0.335027i	0.180962	−	0.983490i	$-0.442079\pi$
$983$	−17884.3	−	10325.5i	−0.580284	−	0.335027i	−0.761246	+	0.648463i	$0.775412\pi$
$984$	891.606	−	1544.31i	0.0288855	−	0.0500312i
$985$		0			0
$986$	−5896.91			−0.190462
$987$	2776.15	+	1372.13i	0.0895298	+	0.0442506i
$988$			50385.4i			1.62244i
$989$	−365.694	−	633.400i	−0.0117577	−	0.0203650i
$990$		0			0
$991$	22970.7	−	39786.4i	0.736315	−	1.27534i	−0.217829	−	0.975987i	$-0.569897\pi$
$991$	22970.7	−	39786.4i	0.736315	−	1.27534i	0.954144	−	0.299348i	$-0.0967692\pi$
$992$	−3423.08	+	1976.32i	−0.109559	+	0.0632542i
$993$			6043.88i			0.193149i
$994$	−2179.70	+	140.911i	−0.0695532	+	0.00449641i
$995$		0			0
$996$	−2150.40	−	3724.60i	−0.0684116	−	0.118492i
$997$	−7815.94	−	4512.54i	−0.248278	−	0.143344i	0.370697	−	0.928754i	$-0.379119\pi$
$997$	−7815.94	−	4512.54i	−0.248278	−	0.143344i	−0.618976	+	0.785410i	$0.712452\pi$
$998$	−1898.41	−	1096.04i	−0.0602134	−	0.0347642i
$999$	12900.2	+	22343.7i	0.408552	+	0.707632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.k.d.74.5		20
5.2	odd	4		175.4.e.d.151.3		10
5.3	odd	4		35.4.e.c.11.3	✓	10
5.4	even	2	inner	175.4.k.d.74.6		20
7.2	even	3	inner	175.4.k.d.149.6		20
15.8	even	4		315.4.j.g.46.3		10
20.3	even	4		560.4.q.n.81.3		10
35.2	odd	12		175.4.e.d.51.3		10
35.3	even	12		245.4.a.n.1.3		5
35.9	even	6	inner	175.4.k.d.149.5		20
35.13	even	4		245.4.e.o.116.3		10
35.17	even	12		1225.4.a.bf.1.3		5
35.18	odd	12		245.4.a.m.1.3		5
35.23	odd	12		35.4.e.c.16.3	yes	10
35.32	odd	12		1225.4.a.bg.1.3		5
35.33	even	12		245.4.e.o.226.3		10
105.23	even	12		315.4.j.g.226.3		10
105.38	odd	12		2205.4.a.bt.1.3		5
105.53	even	12		2205.4.a.bu.1.3		5
140.23	even	12		560.4.q.n.401.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.c.11.3	✓	10	5.3	odd	4
35.4.e.c.16.3	yes	10	35.23	odd	12
175.4.e.d.51.3		10	35.2	odd	12
175.4.e.d.151.3		10	5.2	odd	4
175.4.k.d.74.5		20	1.1	even	1	trivial
175.4.k.d.74.6		20	5.4	even	2	inner
175.4.k.d.149.5		20	35.9	even	6	inner
175.4.k.d.149.6		20	7.2	even	3	inner
245.4.a.m.1.3		5	35.18	odd	12
245.4.a.n.1.3		5	35.3	even	12
245.4.e.o.116.3		10	35.13	even	4
245.4.e.o.226.3		10	35.33	even	12
315.4.j.g.46.3		10	15.8	even	4
315.4.j.g.226.3		10	105.23	even	12
560.4.q.n.81.3		10	20.3	even	4
560.4.q.n.401.3		10	140.23	even	12
1225.4.a.bf.1.3		5	35.17	even	12
1225.4.a.bg.1.3		5	35.32	odd	12
2205.4.a.bt.1.3		5	105.38	odd	12
2205.4.a.bu.1.3		5	105.53	even	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.197018 + 0.113749i) q^{2} +(-1.56628 - 0.904291i) q^{3} +(-3.97412 + 6.88338i) q^{4} +0.411448 q^{6} +(16.6030 + 8.20612i) q^{7} -3.62818i q^{8} +(-11.8645 - 20.5499i) q^{9} +O(q^{10})\)	\(q+(-0.197018 + 0.113749i) q^{2} +(-1.56628 - 0.904291i) q^{3} +(-3.97412 + 6.88338i) q^{4} +0.411448 q^{6} +(16.6030 + 8.20612i) q^{7} -3.62818i q^{8} +(-11.8645 - 20.5499i) q^{9} +(-8.85094 + 15.3303i) q^{11} +(12.4492 - 7.18753i) q^{12} +62.3178i q^{13} +(-4.20453 + 0.271811i) q^{14} +(-31.3803 - 54.3522i) q^{16} +(-75.4848 - 43.5812i) q^{17} +(4.67506 + 2.69914i) q^{18} +(-50.8618 - 88.0952i) q^{19} +(-18.5842 - 27.8670i) q^{21} -4.02713i q^{22} +(-81.0943 + 46.8198i) q^{23} +(-3.28093 + 5.68274i) q^{24} +(-7.08856 - 12.2777i) q^{26} +91.7477i q^{27} +(-122.468 + 81.6726i) q^{28} -297.385 q^{29} +(-45.6389 + 79.0490i) q^{31} +(37.5018 + 21.6517i) q^{32} +(27.7261 - 16.0077i) q^{33} +19.8292 q^{34} +188.604 q^{36} +(243.535 - 140.605i) q^{37} +(20.0414 + 11.5709i) q^{38} +(56.3534 - 97.6070i) q^{39} -271.754 q^{41} +(6.83126 + 3.37639i) q^{42} +7.81066i q^{43} +(-70.3495 - 121.849i) q^{44} +(10.6514 - 18.4487i) q^{46} +(-80.0661 + 46.2262i) q^{47} +113.508i q^{48} +(208.319 + 272.493i) q^{49} +(78.8201 + 136.520i) q^{51} +(-428.957 - 247.658i) q^{52} +(156.148 + 90.1519i) q^{53} +(-10.4362 - 18.0760i) q^{54} +(29.7733 - 60.2387i) q^{56} +183.975i q^{57} +(58.5904 - 33.8272i) q^{58} +(-49.8506 + 86.3437i) q^{59} +(-217.109 - 376.044i) q^{61} -20.7655i q^{62} +(-28.3511 - 438.552i) q^{63} +492.233 q^{64} +(-3.64170 + 6.30761i) q^{66} +(399.718 + 230.777i) q^{67} +(599.972 - 346.394i) q^{68} +169.355 q^{69} +518.417 q^{71} +(-74.5589 + 43.0466i) q^{72} +(-470.136 - 271.433i) q^{73} +(-31.9872 + 55.4035i) q^{74} +808.524 q^{76} +(-272.754 + 181.897i) q^{77} +25.6405i q^{78} +(119.851 + 207.587i) q^{79} +(-237.375 + 411.146i) q^{81} +(53.5405 - 30.9116i) q^{82} -299.184i q^{83} +(265.675 - 17.1751i) q^{84} +(-0.888452 - 1.53884i) q^{86} +(465.789 + 268.923i) q^{87} +(55.6211 + 32.1128i) q^{88} +(527.180 + 913.102i) q^{89} +(-511.387 + 1034.66i) q^{91} -744.271i q^{92} +(142.967 - 82.5418i) q^{93} +(10.5163 - 18.2148i) q^{94} +(-39.1588 - 67.8251i) q^{96} +288.854i q^{97} +(-72.0383 - 29.9900i) q^{98} +420.049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9}+O(q^{10}) \) 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9	\( 20 q + 70 q^{4} + 64 q^{6} + 162 q^{9} - 94 q^{11} - 14 q^{14} - 342 q^{16} - 42 q^{19} + 356 q^{21} + 1696 q^{24} + 94 q^{26} - 760 q^{29} - 776 q^{31} - 520 q^{34} + 4916 q^{36} + 28 q^{39} - 1124 q^{41} + 2182 q^{44} - 674 q^{46} - 1996 q^{49} - 1464 q^{51} - 1548 q^{54} - 2676 q^{56} + 1416 q^{59} - 3888 q^{61} + 500 q^{64} - 2964 q^{66} - 1496 q^{69} + 3456 q^{71} - 6570 q^{74} + 2764 q^{76} + 436 q^{79} + 910 q^{81} + 1468 q^{84} + 8528 q^{86} + 4644 q^{89} + 1048 q^{91} - 5354 q^{94} - 9184 q^{96} - 140 q^{99}+O(q^{100}) \) 20 * q + 70 * q^4 + 64 * q^6 + 162 * q^9 - 94 * q^11 - 14 * q^14 - 342 * q^16 - 42 * q^19 + 356 * q^21 + 1696 * q^24 + 94 * q^26 - 760 * q^29 - 776 * q^31 - 520 * q^34 + 4916 * q^36 + 28 * q^39 - 1124 * q^41 + 2182 * q^44 - 674 * q^46 - 1996 * q^49 - 1464 * q^51 - 1548 * q^54 - 2676 * q^56 + 1416 * q^59 - 3888 * q^61 + 500 * q^64 - 2964 * q^66 - 1496 * q^69 + 3456 * q^71 - 6570 * q^74 + 2764 * q^76 + 436 * q^79 + 910 * q^81 + 1468 * q^84 + 8528 * q^86 + 4644 * q^89 + 1048 * q^91 - 5354 * q^94 - 9184 * q^96 - 140 * q^99

Introduction

L-functions

Modular forms

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