LMFDB - Embedded newform 315.3.ca.b.298.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, 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:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.6
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984292 - 0.263740i) q^{2} +(-2.56483 - 1.48081i) q^{4} +(4.04958 - 2.93273i) q^{5} +(-5.81621 - 3.89508i) q^{7} +(5.01620 + 5.01620i) q^{8} +O(q^{10})$	\(q+(-0.984292 - 0.263740i) q^{2} +(-2.56483 - 1.48081i) q^{4} +(4.04958 - 2.93273i) q^{5} +(-5.81621 - 3.89508i) q^{7} +(5.01620 + 5.01620i) q^{8} +(-4.75945 + 1.81862i) q^{10} +(2.58885 - 4.48403i) q^{11} +(-3.12416 - 3.12416i) q^{13} +(4.69756 + 5.36787i) q^{14} +(2.30879 + 3.99894i) q^{16} +(-4.02869 - 15.0353i) q^{17} +(-17.1897 + 9.92450i) q^{19} +(-14.7293 + 1.52531i) q^{20} +(-3.73081 + 3.73081i) q^{22} +(-9.71406 + 36.2534i) q^{23} +(7.79821 - 23.7526i) q^{25} +(2.25112 + 3.89905i) q^{26} +(9.14974 + 18.6029i) q^{28} -11.8306i q^{29} +(-9.02952 + 15.6396i) q^{31} +(-8.56207 - 31.9541i) q^{32} +15.8616i q^{34} +(-34.9764 + 1.28394i) q^{35} +(-70.9224 - 19.0036i) q^{37} +(19.5372 - 5.23498i) q^{38} +(35.0247 + 5.60235i) q^{40} -60.6872 q^{41} +(-33.1804 - 33.1804i) q^{43} +(-13.2799 + 7.66718i) q^{44} +(19.1229 - 33.1219i) q^{46} +(19.9094 + 5.33470i) q^{47} +(18.6567 + 45.3092i) q^{49} +(-13.9402 + 21.3228i) q^{50} +(3.38666 + 12.6392i) q^{52} +(6.28105 - 1.68300i) q^{53} +(-2.66666 - 25.7508i) q^{55} +(-9.63679 - 48.7138i) q^{56} +(-3.12020 + 11.6447i) q^{58} +(32.2232 + 18.6041i) q^{59} +(-6.88336 - 11.9223i) q^{61} +(13.0125 - 13.0125i) q^{62} +15.2400i q^{64} +(-21.8138 - 3.48922i) q^{65} +(-0.969242 - 3.61726i) q^{67} +(-11.9314 + 44.5287i) q^{68} +(34.7657 + 7.96093i) q^{70} +77.9344 q^{71} +(-123.630 + 33.1265i) q^{73} +(64.7964 + 37.4102i) q^{74} +58.7850 q^{76} +(-32.5230 + 15.9963i) q^{77} +(73.5670 - 42.4739i) q^{79} +(21.0774 + 9.42297i) q^{80} +(59.7339 + 16.0057i) q^{82} +(10.0091 + 10.0091i) q^{83} +(-60.4089 - 49.0715i) q^{85} +(23.9082 + 41.4102i) q^{86} +(35.4790 - 9.50657i) q^{88} +(95.4344 - 55.0991i) q^{89} +(6.00193 + 30.3396i) q^{91} +(78.5990 - 78.5990i) q^{92} +(-18.1897 - 10.5018i) q^{94} +(-40.5054 + 90.6029i) q^{95} +(30.0049 - 30.0049i) q^{97} +(-6.41377 - 49.5181i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.984292	−	0.263740i	−0.492146	−	0.131870i	0.00420656	−	0.999991i	$-0.498661\pi$
$2$	−0.984292	−	0.263740i	−0.492146	−	0.131870i	−0.496353	+	0.868121i	$0.665328\pi$
$3$		0			0
$3$		0			0
$4$	−2.56483	−	1.48081i	−0.641207	−	0.370201i
$5$	4.04958	−	2.93273i	0.809916	−	0.586546i
$5$	4.04958	−	2.93273i	0.809916	−	0.586546i
$6$		0			0
$7$	−5.81621	−	3.89508i	−0.830888	−	0.556440i
$7$	−5.81621	−	3.89508i	−0.830888	−	0.556440i
$8$	5.01620	+	5.01620i	0.627025	+	0.627025i
$9$		0			0
$10$	−4.75945	+	1.81862i	−0.475945	+	0.181862i
$11$	2.58885	−	4.48403i	0.235350	−	0.407639i	−0.724024	−	0.689775i	$-0.757710\pi$
$11$	2.58885	−	4.48403i	0.235350	−	0.407639i	0.959374	+	0.282136i	$0.0910429\pi$
$12$		0			0
$13$	−3.12416	−	3.12416i	−0.240320	−	0.240320i	0.576663	−	0.816982i	$-0.304355\pi$
$13$	−3.12416	−	3.12416i	−0.240320	−	0.240320i	−0.816982	+	0.576663i	$0.804355\pi$
$14$	4.69756	+	5.36787i	0.335540	+	0.383419i
$15$		0			0
$16$	2.30879	+	3.99894i	0.144299	+	0.249934i
$17$	−4.02869	−	15.0353i	−0.236982	−	0.884429i	−0.977245	−	0.212112i	$-0.931966\pi$
$17$	−4.02869	−	15.0353i	−0.236982	−	0.884429i	0.740263	−	0.672317i	$-0.234701\pi$
$18$		0			0
$19$	−17.1897	+	9.92450i	−0.904723	+	0.522342i	−0.878730	−	0.477320i	$-0.841608\pi$
$19$	−17.1897	+	9.92450i	−0.904723	+	0.522342i	−0.0259936	+	0.999662i	$0.508275\pi$
$20$	−14.7293	+	1.52531i	−0.736464	+	0.0762655i
$21$		0			0
$22$	−3.73081	+	3.73081i	−0.169582	+	0.169582i
$23$	−9.71406	+	36.2534i	−0.422350	+	1.57623i	0.347292	+	0.937757i	$0.387101\pi$
$23$	−9.71406	+	36.2534i	−0.422350	+	1.57623i	−0.769642	+	0.638476i	$0.779565\pi$
$24$		0			0
$25$	7.79821	−	23.7526i	0.311928	−	0.950106i
$26$	2.25112	+	3.89905i	0.0865814	+	0.149963i
$27$		0			0
$28$	9.14974	+	18.6029i	0.326777	+	0.664389i
$29$		−	11.8306i		−	0.407951i	−0.978976	−	0.203975i	$-0.934614\pi$
$29$		−	11.8306i		−	0.407951i	0.978976	−	0.203975i	$-0.0653863\pi$
$30$		0			0
$31$	−9.02952	+	15.6396i	−0.291275	+	0.504503i	−0.974111	−	0.226068i	$-0.927413\pi$
$31$	−9.02952	+	15.6396i	−0.291275	+	0.504503i	0.682837	+	0.730571i	$0.260746\pi$
$32$	−8.56207	−	31.9541i	−0.267565	−	0.998565i
$33$		0			0
$34$			15.8616i			0.466519i
$35$	−34.9764	+	1.28394i	−0.999327	+	0.0366839i
$36$		0			0
$37$	−70.9224	−	19.0036i	−1.91682	−	0.513611i	−0.990633	−	0.136552i	$-0.956398\pi$
$37$	−70.9224	−	19.0036i	−1.91682	−	0.513611i	−0.926189	−	0.377059i	$-0.876935\pi$
$38$	19.5372	−	5.23498i	0.514137	−	0.137763i
$39$		0			0
$40$	35.0247	+	5.60235i	0.875617	+	0.140059i
$41$	−60.6872			−1.48018			−0.740088	−	0.672510i	$-0.765216\pi$
$41$	−60.6872			−1.48018			−0.740088	+	0.672510i	$0.765216\pi$
$42$		0			0
$43$	−33.1804	−	33.1804i	−0.771637	−	0.771637i	0.206756	−	0.978393i	$-0.433709\pi$
$43$	−33.1804	−	33.1804i	−0.771637	−	0.771637i	−0.978393	+	0.206756i	$0.933709\pi$
$44$	−13.2799	+	7.66718i	−0.301817	+	0.174254i
$45$		0			0
$46$	19.1229	−	33.1219i	0.415716	−	0.720041i
$47$	19.9094	+	5.33470i	0.423604	+	0.113504i	0.464322	−	0.885666i	$-0.346298\pi$
$47$	19.9094	+	5.33470i	0.423604	+	0.113504i	−0.0407183	+	0.999171i	$0.512965\pi$
$48$		0			0
$49$	18.6567	+	45.3092i	0.380749	+	0.924678i
$50$	−13.9402	+	21.3228i	−0.278805	+	0.426457i
$51$		0			0
$52$	3.38666	+	12.6392i	0.0651281	+	0.243062i
$53$	6.28105	−	1.68300i	0.118510	−	0.0317547i	−0.199076	−	0.979984i	$-0.563794\pi$
$53$	6.28105	−	1.68300i	0.118510	−	0.0317547i	0.317587	+	0.948229i	$0.397128\pi$
$54$		0			0
$55$	−2.66666	−	25.7508i	−0.0484847	−	0.468197i
$56$	−9.63679	−	48.7138i	−0.172086	−	0.869889i
$57$		0			0
$58$	−3.12020	+	11.6447i	−0.0537965	+	0.200771i
$59$	32.2232	+	18.6041i	0.546155	+	0.315323i	0.747570	−	0.664183i	$-0.231221\pi$
$59$	32.2232	+	18.6041i	0.546155	+	0.315323i	−0.201415	+	0.979506i	$0.564554\pi$
$60$		0			0
$61$	−6.88336	−	11.9223i	−0.112842	−	0.195448i	0.804073	−	0.594530i	$-0.202662\pi$
$61$	−6.88336	−	11.9223i	−0.112842	−	0.195448i	−0.916915	+	0.399082i	$0.869329\pi$
$62$	13.0125	−	13.0125i	0.209879	−	0.209879i
$63$		0			0
$64$			15.2400i			0.238125i
$65$	−21.8138	−	3.48922i	−0.335597	−	0.0536803i
$66$		0			0
$67$	−0.969242	−	3.61726i	−0.0144663	−	0.0539889i	0.958315	−	0.285712i	$-0.0922302\pi$
$67$	−0.969242	−	3.61726i	−0.0144663	−	0.0539889i	−0.972782	+	0.231723i	$0.925564\pi$
$68$	−11.9314	+	44.5287i	−0.175462	+	0.654833i
$69$		0			0
$70$	34.7657	+	7.96093i	0.496652	+	0.113728i
$71$	77.9344			1.09767			0.548834	−	0.835932i	$-0.315072\pi$
$71$	77.9344			1.09767			0.548834	+	0.835932i	$0.315072\pi$
$72$		0			0
$73$	−123.630	+	33.1265i	−1.69356	+	0.453788i	−0.971305	−	0.237838i	$-0.923561\pi$
$73$	−123.630	+	33.1265i	−1.69356	+	0.453788i	−0.722256	+	0.691626i	$0.756895\pi$
$74$	64.7964	+	37.4102i	0.875626	+	0.505543i
$75$		0			0
$76$	58.7850			0.773487
$77$	−32.5230	+	15.9963i	−0.422376	+	0.207744i
$78$		0			0
$79$	73.5670	−	42.4739i	0.931227	−	0.537644i	0.0440278	−	0.999030i	$-0.485981\pi$
$79$	73.5670	−	42.4739i	0.931227	−	0.537644i	0.887200	+	0.461386i	$0.152648\pi$
$80$	21.0774	+	9.42297i	0.263468	+	0.117787i
$81$		0			0
$82$	59.7339	+	16.0057i	0.728463	+	0.195191i
$83$	10.0091	+	10.0091i	0.120591	+	0.120591i	0.764827	−	0.644236i	$-0.222824\pi$
$83$	10.0091	+	10.0091i	0.120591	+	0.120591i	−0.644236	+	0.764827i	$0.722824\pi$
$84$		0			0
$85$	−60.4089	−	49.0715i	−0.710693	−	0.577312i
$86$	23.9082	+	41.4102i	0.278002	+	0.481514i
$87$		0			0
$88$	35.4790	−	9.50657i	0.403170	−	0.108029i
$89$	95.4344	−	55.0991i	1.07230	−	0.619091i	0.143489	−	0.989652i	$-0.454168\pi$
$89$	95.4344	−	55.0991i	1.07230	−	0.619091i	0.928808	+	0.370561i	$0.120835\pi$
$90$		0			0
$91$	6.00193	+	30.3396i	0.0659552	+	0.333402i
$92$	78.5990	−	78.5990i	0.854337	−	0.854337i
$93$		0			0
$94$	−18.1897	−	10.5018i	−0.193507	−	0.111721i
$95$	−40.5054	+	90.6029i	−0.426372	+	0.953715i
$96$		0			0
$97$	30.0049	−	30.0049i	0.309328	−	0.309328i	−0.535321	−	0.844649i	$-0.679809\pi$
$97$	30.0049	−	30.0049i	0.309328	−	0.309328i	0.844649	+	0.535321i	$0.179809\pi$
$98$	−6.41377	−	49.5181i	−0.0654466	−	0.505286i
$99$		0			0
$100$	−55.1741	+	49.3739i	−0.551741	+	0.493739i
$101$	34.2964	−	59.4032i	0.339569	−	0.588150i	−0.644783	−	0.764366i	$-0.723052\pi$
$101$	34.2964	−	59.4032i	0.339569	−	0.588150i	0.984352	+	0.176215i	$0.0563855\pi$
$102$		0			0
$103$	33.3675	−	124.529i	0.323956	−	1.20902i	−0.591401	−	0.806378i	$-0.701425\pi$
$103$	33.3675	−	124.529i	0.323956	−	1.20902i	0.915357	−	0.402643i	$-0.131908\pi$
$104$		−	31.3428i		−	0.301373i
$105$		0			0
$106$	−6.62626			−0.0625119
$107$	−22.9093	−	6.13854i	−0.214106	−	0.0573695i	0.150172	−	0.988660i	$-0.452017\pi$
$107$	−22.9093	−	6.13854i	−0.214106	−	0.0573695i	−0.364278	+	0.931290i	$0.618684\pi$
$108$		0			0
$109$	167.284	+	96.5816i	1.53472	+	0.886070i	0.999135	+	0.0415874i	$0.0132415\pi$
$109$	167.284	+	96.5816i	1.53472	+	0.886070i	0.535583	+	0.844482i	$0.320092\pi$
$110$	−4.16676	+	26.0497i	−0.0378796	+	0.236815i
$111$		0			0
$112$	2.14778	−	32.2516i	0.0191766	−	0.287961i
$113$	−129.366	−	129.366i	−1.14483	−	1.14483i	−0.987555	−	0.157275i	$-0.949729\pi$
$113$	−129.366	−	129.366i	−1.14483	−	1.14483i	−0.157275	−	0.987555i	$-0.550271\pi$
$114$		0			0
$115$	66.9834	+	175.300i	0.582464	+	1.52434i
$116$	−17.5188	+	30.3434i	−0.151024	+	0.261581i
$117$		0			0
$118$	−26.8104	−	26.8104i	−0.227206	−	0.227206i
$119$	−35.1319	+	103.141i	−0.295226	+	0.866727i
$120$		0			0
$121$	47.0957	+	81.5721i	0.389220	+	0.674149i
$122$	3.63084	+	13.5505i	0.0297610	+	0.111069i
$123$		0			0
$124$	46.3184	−	26.7419i	0.373535	−	0.215661i
$125$	−38.0806	−	119.058i	−0.304645	−	0.952466i
$126$		0			0
$127$	54.2797	−	54.2797i	0.427400	−	0.427400i	−0.460342	−	0.887742i	$-0.652273\pi$
$127$	54.2797	−	54.2797i	0.427400	−	0.427400i	0.887742	+	0.460342i	$0.152273\pi$
$128$	−30.2289	+	112.816i	−0.236163	+	0.881373i
$129$		0			0
$130$	20.5509	+	9.18760i	0.158084	+	0.0706738i
$131$	9.27972	+	16.0730i	0.0708376	+	0.122694i	0.899269	−	0.437397i	$-0.144099\pi$
$131$	9.27972	+	16.0730i	0.0708376	+	0.122694i	−0.828431	+	0.560091i	$0.810766\pi$
$132$		0			0
$133$	138.636	+	9.23239i	1.04238	+	0.0694165i
$134$			3.81607i			0.0284781i
$135$		0			0
$136$	55.2113	−	95.6288i	0.405965	−	0.703153i
$137$	−27.9757	−	104.407i	−0.204202	−	0.762094i	−0.989691	−	0.143218i	$-0.954255\pi$
$137$	−27.9757	−	104.407i	−0.204202	−	0.762094i	0.785489	−	0.618876i	$-0.212412\pi$
$138$		0			0
$139$		−	135.516i		−	0.974938i	−0.873140	−	0.487469i	$-0.837920\pi$
$139$		−	135.516i		−	0.974938i	0.873140	−	0.487469i	$-0.162080\pi$
$140$	91.6099	+	48.5002i	0.654356	+	0.346430i
$141$		0			0
$142$	−76.7102	−	20.5544i	−0.540213	−	0.144750i
$143$	−22.0968	+	5.92082i	−0.154523	+	0.0414043i
$144$		0			0
$145$	−34.6959	−	47.9089i	−0.239282	−	0.330406i
$146$	130.425			0.893320
$147$		0			0
$148$	153.763	+	153.763i	1.03894	+	1.03894i
$149$	−34.6086	+	19.9813i	−0.232273	+	0.134103i	−0.611620	−	0.791152i	$-0.709482\pi$
$149$	−34.6086	+	19.9813i	−0.232273	+	0.134103i	0.379347	+	0.925254i	$0.376149\pi$
$150$		0			0
$151$	−20.0625	+	34.7493i	−0.132864	+	0.230128i	−0.924780	−	0.380503i	$-0.875751\pi$
$151$	−20.0625	+	34.7493i	−0.132864	+	0.230128i	0.791915	+	0.610631i	$0.209084\pi$
$152$	−136.010	−	36.4439i	−0.894806	−	0.239762i
$153$		0			0
$154$	36.2310	−	7.16738i	0.235266	−	0.0465414i
$155$	9.30090	+	89.8149i	0.0600058	+	0.579451i
$156$		0			0
$157$	−39.9568	−	149.121i	−0.254502	−	0.949813i	−0.968367	−	0.249530i	$-0.919724\pi$
$157$	−39.9568	−	149.121i	−0.254502	−	0.949813i	0.713865	−	0.700283i	$-0.246943\pi$
$158$	−83.6134	+	22.4042i	−0.529199	+	0.141798i
$159$		0			0
$160$	−128.385	−	104.290i	−0.802409	−	0.651815i
$161$	197.709	−	173.020i	1.22800	−	1.07466i
$162$		0			0
$163$	−56.0733	+	209.268i	−0.344008	+	1.28386i	0.549759	+	0.835324i	$0.314720\pi$
$163$	−56.0733	+	209.268i	−0.344008	+	1.28386i	−0.893767	+	0.448532i	$0.851947\pi$
$164$	155.652	+	89.8659i	0.949100	+	0.547963i
$165$		0			0
$166$	−7.21206	−	12.4917i	−0.0434461	−	0.0752509i
$167$	−66.5271	+	66.5271i	−0.398366	+	0.398366i	−0.877656	−	0.479290i	$-0.840894\pi$
$167$	−66.5271	+	66.5271i	−0.398366	+	0.398366i	0.479290	+	0.877656i	$0.340894\pi$
$168$		0			0
$169$		−	149.479i		−	0.884493i
$170$	46.5179	+	64.2330i	0.273635	+	0.377841i
$171$		0			0
$172$	35.9684	+	134.236i	0.209118	+	0.780440i
$173$	55.0739	−	205.539i	0.318346	−	1.18808i	−0.602487	−	0.798129i	$-0.705824\pi$
$173$	55.0739	−	205.539i	0.318346	−	1.18808i	0.920833	−	0.389956i	$-0.127510\pi$
$174$		0			0
$175$	−137.874	+	107.776i	−0.787854	+	0.615862i
$176$	23.9085			0.135844
$177$		0			0
$178$	−108.467	+	29.0637i	−0.609366	+	0.163279i
$179$	254.711	+	147.057i	1.42296	+	0.821549i	0.996551	−	0.0829801i	$-0.0264438\pi$
$179$	254.711	+	147.057i	1.42296	+	0.821549i	0.426413	+	0.904529i	$0.359777\pi$
$180$		0			0
$181$	−160.740			−0.888065			−0.444032	−	0.896011i	$-0.646452\pi$
$181$	−160.740			−0.888065			−0.444032	+	0.896011i	$0.646452\pi$
$182$	2.09413	−	31.4460i	0.0115062	−	0.172780i
$183$		0			0
$184$	−230.582	+	133.126i	−1.25316	+	0.723513i
$185$	−342.938	+	131.040i	−1.85372	+	0.708322i
$186$		0			0
$187$	−77.8483	−	20.8594i	−0.416301	−	0.111548i
$188$	−43.1645	−	43.1645i	−0.229599	−	0.229599i
$189$		0			0
$190$	63.7647	−	78.4968i	0.335604	−	0.413141i
$191$	−73.6284	−	127.528i	−0.385489	−	0.667686i	0.606348	−	0.795199i	$-0.292634\pi$
$191$	−73.6284	−	127.528i	−0.385489	−	0.667686i	−0.991837	+	0.127513i	$0.959300\pi$
$192$		0			0
$193$	−96.7332	+	25.9196i	−0.501208	+	0.134298i	−0.500561	−	0.865702i	$-0.666873\pi$
$193$	−96.7332	+	25.9196i	−0.501208	+	0.134298i	−0.000647439		1.00000i	$0.500206\pi$
$194$	−37.4470	+	21.6200i	−0.193026	+	0.111444i
$195$		0			0
$196$	19.2429	−	143.837i	0.0981781	−	0.733864i
$197$	−130.900	+	130.900i	−0.664467	+	0.664467i	−0.956430	−	0.291963i	$-0.905692\pi$
$197$	−130.900	+	130.900i	−0.664467	+	0.664467i	0.291963	+	0.956430i	$0.405692\pi$
$198$		0			0
$199$	−113.445	−	65.4975i	−0.570076	−	0.329133i	0.187104	−	0.982340i	$-0.440090\pi$
$199$	−113.445	−	65.4975i	−0.570076	−	0.329133i	−0.757180	+	0.653207i	$0.773423\pi$
$200$	158.265	−	80.0306i	0.791327	−	0.400153i
$201$		0			0
$202$	−49.4247	+	49.4247i	−0.244677	+	0.244677i
$203$	−46.0811	+	68.8092i	−0.227000	+	0.338961i
$204$		0			0
$205$	−245.758	+	177.979i	−1.19882	+	0.868191i
$206$	−65.6867	+	113.773i	−0.318867	+	0.552295i
$207$		0			0
$208$	5.28030	−	19.7063i	0.0253860	−	0.0947420i
$209$			102.772i			0.491734i
$210$		0			0
$211$	−284.859			−1.35004			−0.675021	−	0.737798i	$-0.735866\pi$
$211$	−284.859			−1.35004			−0.675021	+	0.737798i	$0.735866\pi$
$212$	−18.6020	−	4.98439i	−0.0877453	−	0.0235113i
$213$		0			0
$214$	20.9305	+	12.0842i	0.0978061	+	0.0564684i
$215$	−231.676	−	37.0576i	−1.07756	−	0.172361i
$216$		0			0
$217$	113.435	−	55.7925i	0.522742	−	0.257108i
$218$	−139.184	−	139.184i	−0.638459	−	0.638459i
$219$		0			0
$220$	−31.2924	+	69.9953i	−0.142238	+	0.318161i
$221$	−34.3863	+	59.5589i	−0.155594	+	0.269497i
$222$		0			0
$223$	−163.068	−	163.068i	−0.731248	−	0.731248i	0.239619	−	0.970867i	$-0.422977\pi$
$223$	−163.068	−	163.068i	−0.731248	−	0.731248i	−0.970867	+	0.239619i	$0.922977\pi$
$224$	−74.6649	+	219.202i	−0.333325	+	0.978579i
$225$		0			0
$226$	93.2148	+	161.453i	0.412455	+	0.714393i
$227$	−87.4422	−	326.339i	−0.385208	−	1.43762i	−0.837839	−	0.545918i	$-0.816181\pi$
$227$	−87.4422	−	326.339i	−0.385208	−	1.43762i	0.452631	−	0.891698i	$-0.350486\pi$
$228$		0			0
$229$	−196.388	+	113.385i	−0.857590	+	0.495130i	−0.863205	−	0.504854i	$-0.831546\pi$
$229$	−196.388	+	113.385i	−0.857590	+	0.495130i	0.00561424	+	0.999984i	$0.498213\pi$
$230$	−19.6977	−	190.212i	−0.0856420	−	0.827009i
$231$		0			0
$232$	59.3446	−	59.3446i	0.255795	−	0.255795i
$233$	−41.7928	+	155.973i	−0.179368	+	0.669411i	0.816398	+	0.577489i	$0.195968\pi$
$233$	−41.7928	+	155.973i	−0.179368	+	0.669411i	−0.995766	+	0.0919215i	$0.970699\pi$
$234$		0			0
$235$	96.2699	−	36.7855i	0.409659	−	0.156534i
$236$	−55.0979	−	95.4324i	−0.233466	−	0.404375i
$237$		0			0
$238$	61.7824	−	92.2547i	0.259590	−	0.387625i
$239$		−	62.1386i		−	0.259994i	−0.991514	−	0.129997i	$-0.958503\pi$
$239$		−	62.1386i		−	0.259994i	0.991514	−	0.129997i	$-0.0414968\pi$
$240$		0			0
$241$	204.217	−	353.714i	0.847373	−	1.46769i	−0.0361717	−	0.999346i	$-0.511516\pi$
$241$	204.217	−	353.714i	0.847373	−	1.46769i	0.883545	−	0.468347i	$-0.155150\pi$
$242$	−24.8420	−	92.7118i	−0.102653	−	0.383107i
$243$		0			0
$244$			40.7717i			0.167097i
$245$	208.432	+	128.768i	0.850741	+	0.525585i
$246$		0			0
$247$	84.7092	+	22.6978i	0.342952	+	0.0918937i
$248$	−123.745	+	33.1574i	−0.498973	+	0.133699i
$249$		0			0
$250$	6.08196	+	127.231i	0.0243278	+	0.508926i
$251$	106.431			0.424030			0.212015	−	0.977266i	$-0.431997\pi$
$251$	106.431			0.424030			0.212015	+	0.977266i	$0.431997\pi$
$252$		0			0
$253$	137.413	+	137.413i	0.543133	+	0.543133i
$254$	−67.7429	+	39.1114i	−0.266704	+	0.153982i
$255$		0			0
$256$	89.9881	−	155.864i	0.351516	−	0.608843i
$257$	377.542	+	101.162i	1.46904	+	0.393627i	0.902600	−	0.430480i	$-0.141656\pi$
$257$	377.542	+	101.162i	1.46904	+	0.393627i	0.566435	+	0.824107i	$0.308322\pi$
$258$		0			0
$259$	338.479	+	386.778i	1.30687	+	1.49335i
$260$	50.7819	+	41.2513i	0.195315	+	0.158659i
$261$		0			0
$262$	−4.89487	−	18.2679i	−0.0186827	−	0.0697249i
$263$	302.308	−	81.0033i	1.14946	−	0.307997i	0.366712	−	0.930335i	$-0.380483\pi$
$263$	302.308	−	81.0033i	1.14946	−	0.307997i	0.782749	+	0.622337i	$0.213817\pi$
$264$		0			0
$265$	20.4998	−	25.2361i	0.0773578	−	0.0952304i
$266$	−134.023	−	45.6512i	−0.503847	−	0.171621i
$267$		0			0
$268$	−2.87052	+	10.7129i	−0.0107109	+	0.0399736i
$269$	−218.161	−	125.955i	−0.811007	−	0.468235i	0.0362986	−	0.999341i	$-0.488443\pi$
$269$	−218.161	−	125.955i	−0.811007	−	0.468235i	−0.847305	+	0.531106i	$0.821777\pi$
$270$		0			0
$271$	−146.480	−	253.711i	−0.540517	−	0.936203i	−0.998874	−	0.0474352i	$-0.984895\pi$
$271$	−146.480	−	253.711i	−0.540517	−	0.936203i	0.458357	−	0.888768i	$-0.348438\pi$
$272$	50.8238	−	50.8238i	0.186852	−	0.186852i
$273$		0			0
$274$			110.145i			0.401990i
$275$	−86.3191	−	96.4595i	−0.313888	−	0.350762i
$276$		0			0
$277$	−35.8623	−	133.840i	−0.129467	−	0.483177i	0.870493	−	0.492182i	$-0.163800\pi$
$277$	−35.8623	−	133.840i	−0.129467	−	0.483177i	−0.999959	+	0.00900462i	$0.997134\pi$
$278$	−35.7411	+	133.388i	−0.128565	+	0.479812i
$279$		0			0
$280$	−181.889	−	169.008i	−0.649605	−	0.603601i
$281$	127.812			0.454848			0.227424	−	0.973796i	$-0.426970\pi$
$281$	127.812			0.454848			0.227424	+	0.973796i	$0.426970\pi$
$282$		0			0
$283$	242.594	−	65.0029i	0.857223	−	0.229692i	0.196668	−	0.980470i	$-0.436988\pi$
$283$	242.594	−	65.0029i	0.857223	−	0.229692i	0.660555	+	0.750778i	$0.270321\pi$
$284$	−199.888	−	115.406i	−0.703832	−	0.406358i
$285$		0			0
$286$	23.3113			0.0815079
$287$	352.970	+	236.382i	1.22986	+	0.823629i
$288$		0			0
$289$	40.4518	−	23.3549i	0.139972	−	0.0808127i
$290$	21.5154	+	56.3070i	0.0741909	+	0.194162i
$291$		0			0
$292$	366.144	+	98.1079i	1.25392	+	0.335986i
$293$	21.9976	+	21.9976i	0.0750770	+	0.0750770i	0.743648	−	0.668571i	$-0.233094\pi$
$293$	21.9976	+	21.9976i	0.0750770	+	0.0750770i	−0.668571	+	0.743648i	$0.733094\pi$
$294$		0			0
$295$	185.051	−	19.1632i	0.627291	−	0.0649599i
$296$	−260.435	−	451.087i	−0.879849	−	1.52394i
$297$		0			0
$298$	39.3349	−	10.5397i	0.131996	−	0.0353683i
$299$	143.609	−	82.9129i	0.480299	−	0.277301i
$300$		0			0
$301$	63.7440	+	322.225i	0.211774	+	1.07051i
$302$	28.9121	−	28.9121i	0.0957356	−	0.0957356i
$303$		0			0
$304$	−79.3749	−	45.8271i	−0.261102	−	0.150747i
$305$	−62.8397	−	28.0934i	−0.206032	−	0.0921095i
$306$		0			0
$307$	−121.636	+	121.636i	−0.396210	+	0.396210i	−0.876894	−	0.480684i	$-0.840388\pi$
$307$	−121.636	+	121.636i	−0.396210	+	0.396210i	0.480684	+	0.876894i	$0.340388\pi$
$308$	107.103	+	7.13249i	0.347738	+	0.0231574i
$309$		0			0
$310$	14.5330	−	90.8571i	0.0468807	−	0.293087i
$311$	−301.676	+	522.518i	−0.970020	+	1.68012i	−0.274542	+	0.961575i	$0.588526\pi$
$311$	−301.676	+	522.518i	−0.970020	+	1.68012i	−0.695477	+	0.718548i	$0.744807\pi$
$312$		0			0
$313$	−56.5067	+	210.886i	−0.180533	+	0.673757i	0.815010	+	0.579447i	$0.196731\pi$
$313$	−56.5067	+	210.886i	−0.180533	+	0.673757i	−0.995543	+	0.0943104i	$0.969935\pi$
$314$			157.316i			0.501008i
$315$		0			0
$316$	−251.582			−0.796146
$317$	9.46959	+	2.53737i	0.0298725	+	0.00800432i	0.273724	−	0.961808i	$-0.411744\pi$
$317$	9.46959	+	2.53737i	0.0298725	+	0.00800432i	−0.243852	+	0.969812i	$0.578411\pi$
$318$		0			0
$319$	−53.0486	−	30.6276i	−0.166297	−	0.0960114i
$320$	44.6948	+	61.7156i	0.139671	+	0.192861i
$321$		0			0
$322$	−240.236	+	118.159i	−0.746073	+	0.366952i
$323$	218.470	+	218.470i	0.676377	+	0.676377i
$324$		0			0
$325$	−98.5698	+	49.8442i	−0.303292	+	0.153367i
$326$	110.385	−	191.193i	0.338604	−	0.586480i
$327$		0			0
$328$	−304.419	−	304.419i	−0.928107	−	0.928107i
$329$	−95.0181	−	108.576i	−0.288809	−	0.330020i
$330$		0			0
$331$	229.481	+	397.473i	0.693296	+	1.20082i	0.970752	+	0.240086i	$0.0771756\pi$
$331$	229.481	+	397.473i	0.693296	+	1.20082i	−0.277455	+	0.960738i	$0.589491\pi$
$332$	−10.8501	−	40.4931i	−0.0326810	−	0.121967i
$333$		0			0
$334$	83.0280	−	47.9362i	0.248587	−	0.143522i
$335$	−14.5335	−	11.8059i	−0.0433835	−	0.0352414i
$336$		0			0
$337$	75.1343	−	75.1343i	0.222951	−	0.222951i	−0.586789	−	0.809740i	$-0.699608\pi$
$337$	75.1343	−	75.1343i	0.222951	−	0.222951i	0.809740	+	0.586789i	$0.199608\pi$
$338$	−39.4237	+	147.131i	−0.116638	+	0.435300i
$339$		0			0
$340$	82.2732	+	215.314i	0.241980	+	0.633277i
$341$	46.7522	+	80.9772i	0.137103	+	0.237470i
$342$		0			0
$343$	67.9718	−	336.198i	0.198168	−	0.980168i
$344$		−	332.879i		−	0.967671i
$345$		0			0
$346$	−108.418	+	187.785i	−0.313346	+	0.542731i
$347$	−2.16426	−	8.07713i	−0.00623706	−	0.0232770i	0.962737	−	0.270439i	$-0.0871688\pi$
$347$	−2.16426	−	8.07713i	−0.00623706	−	0.0232770i	−0.968974	+	0.247162i	$0.920502\pi$
$348$		0			0
$349$		−	571.222i		−	1.63674i	−0.574693	−	0.818369i	$-0.694878\pi$
$349$		−	571.222i		−	1.63674i	0.574693	−	0.818369i	$-0.305122\pi$
$350$	164.134	−	69.7198i	0.468953	−	0.199199i
$351$		0			0
$352$	−165.449	−	44.3319i	−0.470025	−	0.125943i
$353$	645.496	−	172.960i	1.82860	−	0.489972i	0.830818	−	0.556544i	$-0.187873\pi$
$353$	645.496	−	172.960i	1.82860	−	0.489972i	0.997782	+	0.0665723i	$0.0212063\pi$
$354$		0			0
$355$	315.602	−	228.560i	0.889018	−	0.643832i
$356$	−326.364			−0.916753
$357$		0			0
$358$	−211.925	−	211.925i	−0.591968	−	0.591968i
$359$	395.711	−	228.464i	1.10226	−	0.636390i	0.165446	−	0.986219i	$-0.447094\pi$
$359$	395.711	−	228.464i	1.10226	−	0.636390i	0.936814	+	0.349829i	$0.113760\pi$
$360$		0			0
$361$	16.4914	−	28.5640i	0.0456826	−	0.0791246i
$362$	158.215	+	42.3935i	0.437057	+	0.117109i
$363$		0			0
$364$	29.5331	−	86.7036i	0.0811350	−	0.238197i
$365$	−403.498	+	496.722i	−1.10547	+	1.36088i
$366$		0			0
$367$	24.7429	+	92.3418i	0.0674194	+	0.251613i	0.991408	−	0.130808i	$-0.0417572\pi$
$367$	24.7429	+	92.3418i	0.0674194	+	0.251613i	−0.923988	+	0.382421i	$0.875091\pi$
$368$	−167.403	+	44.8554i	−0.454898	+	0.121890i
$369$		0			0
$370$	372.112	−	38.5345i	1.00571	−	0.104147i
$371$	−43.0873	−	14.6765i	−0.116138	−	0.0395593i
$372$		0			0
$373$	34.6037	−	129.143i	0.0927713	−	0.346227i	−0.903901	−	0.427742i	$-0.859309\pi$
$373$	34.6037	−	129.143i	0.0927713	−	0.346227i	0.996672	+	0.0815149i	$0.0259758\pi$
$374$	71.1240	+	41.0635i	0.190171	+	0.109795i
$375$		0			0
$376$	73.1095	+	126.629i	0.194440	+	0.336780i
$377$	−36.9606	+	36.9606i	−0.0980387	+	0.0980387i
$378$		0			0
$379$			407.491i			1.07517i	0.843208	+	0.537587i	$0.180664\pi$
$379$			407.491i			1.07517i	−0.843208	+	0.537587i	$0.819336\pi$
$380$	238.055	−	172.400i	0.626460	−	0.453685i
$381$		0			0
$382$	38.8375	+	144.944i	0.101669	+	0.379434i
$383$	52.0748	−	194.346i	0.135966	−	0.507430i	−0.864026	−	0.503446i	$-0.832065\pi$
$383$	52.0748	−	194.346i	0.135966	−	0.507430i	0.999992	−	0.00398411i	$-0.00126818\pi$
$384$		0			0
$385$	−84.7917	+	160.159i	−0.220238	+	0.415998i
$386$	102.050			0.264377
$387$		0			0
$388$	−121.389	+	32.5260i	−0.312857	+	0.0838299i
$389$	−184.186	−	106.340i	−0.473487	−	0.273368i	0.244211	−	0.969722i	$-0.421471\pi$
$389$	−184.186	−	106.340i	−0.473487	−	0.273368i	−0.717698	+	0.696354i	$0.754804\pi$
$390$		0			0
$391$	584.215			1.49415
$392$	−133.695	+	320.866i	−0.341057	+	0.818536i
$393$		0			0
$394$	163.367	−	94.3202i	0.414638	−	0.239391i
$395$	173.351	−	387.753i	0.438863	−	0.981654i
$396$		0			0
$397$	211.533	+	56.6800i	0.532828	+	0.142771i	0.515194	−	0.857074i	$-0.327720\pi$
$397$	211.533	+	56.6800i	0.532828	+	0.142771i	0.0176340	+	0.999845i	$0.494387\pi$
$398$	94.3887	+	94.3887i	0.237158	+	0.237158i
$399$		0			0
$400$	112.990	−	23.6553i	0.282474	−	0.0591382i
$401$	248.520	+	430.449i	0.619750	+	1.07344i	0.989531	+	0.144319i	$0.0460992\pi$
$401$	248.520	+	430.449i	0.619750	+	1.07344i	−0.369782	+	0.929119i	$0.620567\pi$
$402$		0			0
$403$	77.0702	−	20.6509i	0.191241	−	0.0512429i
$404$	−175.929	+	101.573i	−0.435468	+	0.251418i
$405$		0			0
$406$	63.5050	−	55.5749i	0.156416	−	0.136884i
$407$	−268.820	+	268.820i	−0.660493	+	0.660493i
$408$		0			0
$409$	−113.088	−	65.2914i	−0.276499	−	0.159637i	0.355339	−	0.934738i	$-0.384366\pi$
$409$	−113.088	−	65.2914i	−0.276499	−	0.159637i	−0.631837	+	0.775101i	$0.717699\pi$
$410$	288.838	−	110.367i	0.704482	−	0.269188i
$411$		0			0
$412$	−269.985	+	269.985i	−0.655304	+	0.655304i
$413$	−114.953	−	233.717i	−0.278335	−	0.565901i
$414$		0			0
$415$	69.8865	+	11.1787i	0.168401	+	0.0269365i
$416$	−73.0803	+	126.579i	−0.175674	+	0.304276i
$417$		0			0
$418$	27.1052	−	101.158i	0.0648450	−	0.242005i
$419$		−	467.512i		−	1.11578i	−0.829915	−	0.557890i	$-0.811611\pi$
$419$		−	467.512i		−	1.11578i	0.829915	−	0.557890i	$-0.188389\pi$
$420$		0			0
$421$	−403.062			−0.957391			−0.478696	−	0.877981i	$-0.658890\pi$
$421$	−403.062			−0.957391			−0.478696	+	0.877981i	$0.658890\pi$
$422$	280.384	+	75.1288i	0.664418	+	0.178030i
$423$		0			0
$424$	39.9493	+	23.0647i	0.0942200	+	0.0543979i
$425$	−388.544	−	21.5562i	−0.914222	−	0.0507204i
$426$		0			0
$427$	−6.40333	+	96.1541i	−0.0149961	+	0.225185i
$428$	49.6686	+	49.6686i	0.116048	+	0.116048i
$429$		0			0
$430$	218.263	+	97.5777i	0.507588	+	0.226925i
$431$	−185.222	+	320.815i	−0.429750	+	0.744350i	−0.996851	−	0.0792991i	$-0.974732\pi$
$431$	−185.222	+	320.815i	−0.429750	+	0.744350i	0.567100	+	0.823649i	$0.308065\pi$
$432$		0			0
$433$	116.395	+	116.395i	0.268810	+	0.268810i	0.828621	−	0.559811i	$-0.189126\pi$
$433$	116.395	+	116.395i	0.268810	+	0.268810i	−0.559811	+	0.828621i	$0.689126\pi$
$434$	−126.368	+	24.9987i	−0.291170	+	0.0576007i
$435$		0			0
$436$	−286.037	−	495.431i	−0.656048	−	1.13631i
$437$	−192.814	−	719.593i	−0.441223	−	1.64667i
$438$		0			0
$439$	−238.473	+	137.683i	−0.543219	+	0.313628i	−0.746383	−	0.665517i	$-0.768211\pi$
$439$	−238.473	+	137.683i	−0.543219	+	0.313628i	0.203163	+	0.979145i	$0.434878\pi$
$440$	115.795	−	142.548i	0.263170	−	0.323972i
$441$		0			0
$442$	49.5543	−	49.5543i	0.112114	−	0.112114i
$443$	−201.380	+	751.559i	−0.454581	+	1.69652i	0.234734	+	0.972060i	$0.424578\pi$
$443$	−201.380	+	751.559i	−0.454581	+	1.69652i	−0.689315	+	0.724461i	$0.742089\pi$
$444$		0			0
$445$	224.879	−	503.011i	0.505345	−	1.13036i
$446$	117.499	+	203.515i	0.263451	+	0.456311i
$447$		0			0
$448$	59.3610	−	88.6391i	0.132502	−	0.197855i
$449$		−	437.111i		−	0.973521i	−0.873536	−	0.486760i	$-0.838178\pi$
$449$		−	437.111i		−	0.973521i	0.873536	−	0.486760i	$-0.161822\pi$
$450$		0			0
$451$	−157.110	+	272.123i	−0.348360	+	0.603377i
$452$	140.236	+	523.367i	0.310256	+	1.15789i
$453$		0			0
$454$			344.275i			0.758315i
$455$	113.283	+	105.261i	0.248974	+	0.231342i
$456$		0			0
$457$	161.133	+	43.1755i	0.352589	+	0.0944760i	0.430766	−	0.902463i	$-0.358243\pi$
$457$	161.133	+	43.1755i	0.352589	+	0.0944760i	−0.0781772	+	0.996939i	$0.524910\pi$
$458$	223.207	−	59.8083i	0.487353	−	0.130586i
$459$		0			0
$460$	87.7835	−	548.803i	0.190834	−	1.19305i
$461$	350.553			0.760418			0.380209	−	0.924901i	$-0.375852\pi$
$461$	350.553			0.760418			0.380209	+	0.924901i	$0.375852\pi$
$462$		0			0
$463$	394.302	+	394.302i	0.851623	+	0.851623i	0.990333	−	0.138710i	$-0.0442955\pi$
$463$	394.302	+	394.302i	0.851623	+	0.851623i	−0.138710	+	0.990333i	$0.544295\pi$
$464$	47.3098	−	27.3143i	0.101961	−	0.0588670i
$465$		0			0
$466$	82.2726	−	142.500i	0.176551	−	0.305795i
$467$	−148.947	−	39.9101i	−0.318944	−	0.0854607i	0.0957955	−	0.995401i	$-0.469461\pi$
$467$	−148.947	−	39.9101i	−0.318944	−	0.0854607i	−0.414739	+	0.909940i	$0.636127\pi$
$468$		0			0
$469$	−8.45220	+	24.8140i	−0.0180217	+	0.0529084i
$470$	−104.460	+	10.8174i	−0.222254	+	0.0230158i
$471$		0			0
$472$	68.3162	+	254.959i	0.144738	+	0.540168i
$473$	−234.681	+	62.8826i	−0.496154	+	0.132944i
$474$		0			0
$475$	101.684	+	485.695i	0.214072	+	1.02252i
$476$	242.838	−	212.514i	0.510165	−	0.446459i
$477$		0			0
$478$	−16.3885	+	61.1626i	−0.0342855	+	0.127955i
$479$	−24.0342	−	13.8762i	−0.0501758	−	0.0289690i	0.474702	−	0.880146i	$-0.342556\pi$
$479$	−24.0342	−	13.8762i	−0.0501758	−	0.0289690i	−0.524878	+	0.851177i	$0.675889\pi$
$480$		0			0
$481$	162.203	+	280.943i	0.337219	+	0.584081i
$482$	−294.298	+	294.298i	−0.610576	+	0.610576i
$483$		0			0
$484$		−	278.958i		−	0.576360i
$485$	33.5110	−	209.503i	0.0690948	−	0.431965i
$486$		0			0
$487$	7.42611	+	27.7146i	0.0152487	+	0.0569089i	0.973131	−	0.230252i	$-0.0739551\pi$
$487$	7.42611	+	27.7146i	0.0152487	+	0.0569089i	−0.957882	+	0.287161i	$0.907288\pi$
$488$	25.2765	−	94.3331i	0.0517961	−	0.193306i
$489$		0			0
$490$	−171.196	−	181.718i	−0.349380	−	0.370852i
$491$	−220.188			−0.448449			−0.224224	−	0.974538i	$-0.571985\pi$
$491$	−220.188			−0.448449			−0.224224	+	0.974538i	$0.571985\pi$
$492$		0			0
$493$	−177.876	+	47.6618i	−0.360804	+	0.0966770i
$494$	−77.3922	−	44.6824i	−0.156664	−	0.0904503i
$495$		0			0
$496$	−83.3890			−0.168123
$497$	−453.283	−	303.561i	−0.912038	−	0.610786i
$498$		0			0
$499$	523.463	−	302.222i	1.04902	−	0.605654i	0.126648	−	0.991948i	$-0.459578\pi$
$499$	523.463	−	302.222i	1.04902	−	0.605654i	0.922376	+	0.386293i	$0.126245\pi$
$500$	−78.6319	+	361.754i	−0.157264	+	0.723508i
$501$		0			0
$502$	−104.760	−	28.0703i	−0.208684	−	0.0559168i
$503$	−597.944	−	597.944i	−1.18876	−	1.18876i	−0.977412	−	0.211343i	$-0.932216\pi$
$503$	−597.944	−	597.944i	−1.18876	−	1.18876i	−0.211343	−	0.977412i	$-0.567784\pi$
$504$		0			0
$505$	−35.3272	−	341.140i	−0.0699549	−	0.675525i
$506$	−99.0130	−	171.496i	−0.195678	−	0.338924i
$507$		0			0
$508$	−219.596	+	58.8406i	−0.432276	+	0.115828i
$509$	−578.494	+	333.993i	−1.13653	+	0.656176i	−0.945569	−	0.325422i	$-0.894494\pi$
$509$	−578.494	+	333.993i	−1.13653	+	0.656176i	−0.190961	+	0.981598i	$0.561160\pi$
$510$		0			0
$511$	848.089	+	288.877i	1.65966	+	0.565318i
$512$	200.665	−	200.665i	0.391924	−	0.391924i
$513$		0			0
$514$	−344.931	−	199.146i	−0.671072	−	0.387444i
$515$	−230.086	−	602.148i	−0.446769	−	1.16922i
$516$		0			0
$517$	75.4635	−	75.4635i	0.145964	−	0.145964i
$518$	−231.154	−	469.973i	−0.446243	−	0.907283i
$519$		0			0
$520$	−91.9199	−	126.925i	−0.176769	−	0.244087i
$521$	−66.0241	+	114.357i	−0.126726	+	0.219495i	−0.922406	−	0.386221i	$-0.873780\pi$
$521$	−66.0241	+	114.357i	−0.126726	+	0.219495i	0.795681	+	0.605717i	$0.207113\pi$
$522$		0			0
$523$	−9.74425	+	36.3660i	−0.0186314	+	0.0695335i	−0.974616	−	0.223885i	$-0.928126\pi$
$523$	−9.74425	+	36.3660i	−0.0186314	+	0.0695335i	0.955984	+	0.293418i	$0.0947928\pi$
$524$		−	54.9659i		−	0.104897i
$525$		0			0
$526$	−318.923			−0.606318
$527$	271.523	+	72.7543i	0.515224	+	0.138054i
$528$		0			0
$529$	−761.815	−	439.834i	−1.44010	−	0.831445i
$530$	−26.8336	+	19.4330i	−0.0506294	+	0.0366661i
$531$		0			0
$532$	−341.906	−	228.972i	−0.642681	−	0.430399i
$533$	189.596	+	189.596i	0.355716	+	0.355716i
$534$		0			0
$535$	−110.776	+	42.3284i	−0.207058	+	0.0791185i
$536$	13.2830	−	23.0068i	0.0247817	−	0.0429232i
$537$		0			0
$538$	181.515	+	181.515i	0.337388	+	0.337388i
$539$	251.467	+	33.6419i	0.466544	+	0.0624154i
$540$		0			0
$541$	−272.705	−	472.340i	−0.504077	−	0.873086i	−0.999989	−	0.00471373i	$-0.998500\pi$
$541$	−272.705	−	472.340i	−0.504077	−	0.873086i	0.495912	−	0.868373i	$-0.334834\pi$
$542$	77.2654	+	288.359i	0.142556	+	0.532027i
$543$		0			0
$544$	−445.945	+	257.466i	−0.819751	+	0.473284i
$545$	960.679	−	99.4843i	1.76271	−	0.182540i
$546$		0			0
$547$	−470.178	+	470.178i	−0.859558	+	0.859558i	−0.991286	−	0.131728i	$-0.957948\pi$
$547$	−470.178	+	470.178i	−0.859558	+	0.859558i	0.131728	+	0.991286i	$0.457948\pi$
$548$	−82.8532	+	309.212i	−0.151192	+	0.564256i
$549$		0			0
$550$	59.5229	+	117.710i	0.108223	+	0.214018i
$551$	117.413	+	203.365i	0.213090	+	0.369083i
$552$		0			0
$553$	−593.320	−	39.5119i	−1.07291	−	0.0714501i
$554$			141.196i			0.254866i
$555$		0			0
$556$	−200.673	+	347.576i	−0.360923	+	0.625137i
$557$	169.860	+	633.927i	0.304955	+	1.13811i	0.932984	+	0.359918i	$0.117195\pi$
$557$	169.860	+	633.927i	0.304955	+	1.13811i	−0.628028	+	0.778190i	$0.716138\pi$
$558$		0			0
$559$			207.322i			0.370879i
$560$	−85.8876	−	136.904i	−0.153371	−	0.244472i
$561$		0			0
$562$	−125.805	−	33.7092i	−0.223851	−	0.0599808i
$563$	1076.55	−	288.461i	1.91217	−	0.512364i	0.919233	−	0.393713i	$-0.128810\pi$
$563$	1076.55	−	288.461i	1.91217	−	0.512364i	0.992936	−	0.118651i	$-0.0378570\pi$
$564$		0			0
$565$	−903.272	−	144.482i	−1.59871	−	0.255721i
$566$	−255.927			−0.452168
$567$		0			0
$568$	390.934	+	390.934i	0.688265	+	0.688265i
$569$	−401.795	+	231.976i	−0.706142	+	0.407691i	−0.809631	−	0.586939i	$-0.800333\pi$
$569$	−401.795	+	231.976i	−0.706142	+	0.407691i	0.103489	+	0.994631i	$0.466999\pi$
$570$		0			0
$571$	−457.777	+	792.892i	−0.801710	+	1.38860i	0.116779	+	0.993158i	$0.462743\pi$
$571$	−457.777	+	792.892i	−0.801710	+	1.38860i	−0.918490	+	0.395445i	$0.870590\pi$
$572$	65.4421	+	17.5352i	0.114409	+	0.0306559i
$573$		0			0
$574$	−285.082	−	325.761i	−0.496659	−	0.567528i
$575$	785.361	+	513.446i	1.36584	+	0.892949i
$576$		0			0
$577$	−127.163	−	474.579i	−0.220387	−	0.822495i	−0.984200	−	0.177058i	$-0.943342\pi$
$577$	−127.163	−	474.579i	−0.220387	−	0.822495i	0.763814	−	0.645437i	$-0.223325\pi$
$578$	−45.9760	+	12.3192i	−0.0795433	+	0.0213136i
$579$		0			0
$580$	18.0453	+	174.256i	0.0311126	+	0.300441i
$581$	−19.2288	−	97.2011i	−0.0330960	−	0.167300i
$582$		0			0
$583$	8.71409	−	32.5214i	0.0149470	−	0.0557829i
$584$	−786.322	−	453.983i	−1.34644	−	0.777368i
$585$		0			0
$586$	−15.8504	−	27.4537i	−0.0270484	−	0.0468492i
$587$	−379.329	+	379.329i	−0.646217	+	0.646217i	−0.952077	−	0.305860i	$-0.901056\pi$
$587$	−379.329	+	379.329i	−0.646217	+	0.646217i	0.305860	+	0.952077i	$0.401056\pi$
$588$		0			0
$589$		−	358.454i		−	0.608580i
$590$	−187.198	−	29.9432i	−0.317285	−	0.0507512i
$591$		0			0
$592$	−87.7506	−	327.490i	−0.148227	−	0.553192i
$593$	125.542	−	468.530i	0.211707	−	0.790101i	−0.775593	−	0.631233i	$-0.782549\pi$
$593$	125.542	−	468.530i	0.211707	−	0.790101i	0.987300	−	0.158868i	$-0.0507843\pi$
$594$		0			0
$595$	160.214	+	520.708i	0.269267	+	0.875140i
$596$	118.354			0.198580
$597$		0			0
$598$	−163.221	+	43.7350i	−0.272945	+	0.0731354i
$599$	63.6790	+	36.7651i	0.106309	+	0.0613774i	0.552212	−	0.833704i	$-0.313784\pi$
$599$	63.6790	+	36.7651i	0.106309	+	0.0613774i	−0.445903	+	0.895081i	$0.647117\pi$
$600$		0			0
$601$	491.594			0.817960			0.408980	−	0.912543i	$-0.365885\pi$
$601$	491.594			0.817960			0.408980	+	0.912543i	$0.365885\pi$
$602$	22.2409	−	333.975i	0.0369450	−	0.554776i
$603$		0			0
$604$	102.914	−	59.4173i	0.170387	−	0.0983730i
$605$	429.946	+	192.214i	0.710655	+	0.317709i
$606$		0			0
$607$	−664.790	−	178.130i	−1.09521	−	0.293459i	−0.334395	−	0.942433i	$-0.608532\pi$
$607$	−664.790	−	178.130i	−1.09521	−	0.293459i	−0.760811	+	0.648974i	$0.775199\pi$
$608$	464.308	+	464.308i	0.763664	+	0.763664i
$609$		0			0
$610$	54.4432	+	44.2255i	0.0892512	+	0.0725008i
$611$	−45.5336	−	78.8665i	−0.0745231	−	0.129078i
$612$		0			0
$613$	349.460	−	93.6376i	0.570082	−	0.152753i	0.0377478	−	0.999287i	$-0.487982\pi$
$613$	349.460	−	93.6376i	0.570082	−	0.152753i	0.532334	+	0.846534i	$0.321315\pi$
$614$	151.806	−	87.6453i	0.247241	−	0.142745i
$615$		0			0
$616$	−243.382	−	82.9013i	−0.395101	−	0.134580i
$617$	−201.236	+	201.236i	−0.326153	+	0.326153i	−0.851121	−	0.524969i	$-0.824077\pi$
$617$	−201.236	+	201.236i	−0.326153	+	0.326153i	0.524969	+	0.851121i	$0.324077\pi$
$618$		0			0
$619$	339.835	+	196.204i	0.549006	+	0.316969i	0.748721	−	0.662885i	$-0.230668\pi$
$619$	339.835	+	196.204i	0.549006	+	0.316969i	−0.199715	+	0.979854i	$0.564002\pi$
$620$	109.143	−	244.133i	0.176037	−	0.393762i
$621$		0			0
$622$	434.746	−	434.746i	0.698949	−	0.698949i
$623$	−769.682	−	51.2566i	−1.23545	−	0.0822739i
$624$		0			0
$625$	−503.376	−	370.456i	−0.805402	−	0.592730i
$626$	111.238	−	192.670i	0.177697	−	0.307780i
$627$		0			0
$628$	−118.336	+	441.637i	−0.188434	+	0.703244i
$629$			1142.90i			1.81701i
$630$		0			0
$631$	−478.217			−0.757872			−0.378936	−	0.925423i	$-0.623710\pi$
$631$	−478.217			−0.757872			−0.378936	+	0.925423i	$0.623710\pi$
$632$	582.084	+	155.969i	0.921019	+	0.246786i
$633$		0			0
$634$	−8.65163	−	4.99502i	−0.0136461	−	0.00787858i
$635$	60.6224	−	378.998i	0.0954684	−	0.596847i
$636$		0			0
$637$	83.2668	−	199.840i	0.130717	−	0.313720i
$638$	44.1376	+	44.1376i	0.0691812	+	0.0691812i
$639$		0			0
$640$	208.444	+	545.509i	0.325693	+	0.852358i
$641$	−321.732	+	557.257i	−0.501922	+	0.869355i	0.498075	+	0.867134i	$0.334040\pi$
$641$	−321.732	+	557.257i	−0.501922	+	0.869355i	−0.999998	+	0.00222115i	$0.999293\pi$
$642$		0			0
$643$	687.066	+	687.066i	1.06853	+	1.06853i	0.997472	+	0.0710604i	$0.0226383\pi$
$643$	687.066	+	687.066i	1.06853	+	1.06853i	0.0710604	+	0.997472i	$0.477362\pi$
$644$	−763.299	+	150.999i	−1.18525	+	0.234471i
$645$		0			0
$646$	−157.419	−	272.658i	−0.243682	−	0.422070i
$647$	55.6541	+	207.704i	0.0860187	+	0.321026i	0.995505	−	0.0947073i	$-0.0301915\pi$
$647$	55.6541	+	207.704i	0.0860187	+	0.321026i	−0.909486	+	0.415734i	$0.863525\pi$
$648$		0			0
$649$	166.842	−	96.3264i	0.257076	−	0.148423i
$650$	110.167	−	23.0644i	0.169488	−	0.0354837i
$651$		0			0
$652$	453.704	−	453.704i	0.695866	−	0.695866i
$653$	165.462	−	617.511i	0.253387	−	0.945652i	−0.715594	−	0.698516i	$-0.753844\pi$
$653$	165.462	−	617.511i	0.253387	−	0.945652i	0.968981	−	0.247136i	$-0.0794894\pi$
$654$		0			0
$655$	84.7166	+	37.8738i	0.129338	+	0.0578226i
$656$	−140.114	−	242.684i	−0.213588	−	0.369946i
$657$		0			0
$658$	64.8896	+	131.931i	0.0986165	+	0.200503i
$659$		−	929.680i		−	1.41074i	−0.708837	−	0.705372i	$-0.750780\pi$
$659$		−	929.680i		−	1.41074i	0.708837	−	0.705372i	$-0.249220\pi$
$660$		0			0
$661$	573.316	−	993.012i	0.867346	−	1.50229i	0.00264699	−	0.999996i	$-0.499157\pi$
$661$	573.316	−	993.012i	0.867346	−	1.50229i	0.864699	−	0.502291i	$-0.167509\pi$
$662$	−121.047	−	451.753i	−0.182850	−	0.682406i
$663$		0			0
$664$			100.415i			0.151228i
$665$	588.494	−	369.194i	0.884953	−	0.555179i
$666$		0			0
$667$	428.898	+	114.923i	0.643026	+	0.172298i
$668$	269.144	−	72.1170i	0.402911	−	0.107960i
$669$		0			0
$670$	11.1915	+	15.4535i	0.0167037	+	0.0230649i
$671$	−71.2801			−0.106230
$672$		0			0
$673$	−171.530	−	171.530i	−0.254874	−	0.254874i	0.568091	−	0.822966i	$-0.307682\pi$
$673$	−171.530	−	171.530i	−0.254874	−	0.254874i	−0.822966	+	0.568091i	$0.807682\pi$
$674$	−93.7701	+	54.1382i	−0.139125	+	0.0803237i
$675$		0			0
$676$	−221.350	+	383.389i	−0.327440	+	0.567143i
$677$	−244.926	−	65.6278i	−0.361782	−	0.0969391i	0.0733492	−	0.997306i	$-0.476631\pi$
$677$	−244.926	−	65.6278i	−0.361782	−	0.0969391i	−0.435131	+	0.900367i	$0.643298\pi$
$678$		0			0
$679$	−291.386	+	57.6433i	−0.429140	+	0.0848945i
$680$	−56.8706	−	549.176i	−0.0836333	−	0.807612i
$681$		0			0
$682$	−24.6609	−	92.0357i	−0.0361597	−	0.134950i
$683$	−900.620	+	241.320i	−1.31862	+	0.353324i	−0.848462	−	0.529256i	$-0.822471\pi$
$683$	−900.620	+	241.320i	−1.31862	+	0.353324i	−0.470162	+	0.882580i	$0.655804\pi$
$684$		0			0
$685$	−419.487	−	340.759i	−0.612390	−	0.497458i
$686$	−155.573	+	312.990i	−0.226783	+	0.456253i
$687$		0			0
$688$	56.0798	−	209.293i	0.0815114	−	0.304205i
$689$	−24.8809	−	14.3650i	−0.0361117	−	0.0208491i
$690$		0			0
$691$	−112.934	−	195.607i	−0.163435	−	0.283078i	0.772663	−	0.634816i	$-0.218924\pi$
$691$	−112.934	−	195.607i	−0.163435	−	0.283078i	−0.936098	+	0.351738i	$0.885591\pi$
$692$	−445.618	+	445.618i	−0.643956	+	0.643956i
$693$		0			0
$694$			8.52106i			0.0122782i
$695$	−397.433	−	548.784i	−0.571846	−	0.789618i
$696$		0			0
$697$	244.490	+	912.450i	0.350775	+	1.30911i
$698$	−150.654	+	562.249i	−0.215837	+	0.805514i
$699$		0			0
$700$	513.220	−	72.2614i	0.733171	−	0.103231i
$701$	−36.9618			−0.0527273			−0.0263636	−	0.999652i	$-0.508393\pi$
$701$	−36.9618			−0.0527273			−0.0263636	+	0.999652i	$0.508393\pi$
$702$		0			0
$703$	1407.74	−	377.203i	2.00247	−	0.536561i
$704$	68.3366	+	39.4541i	0.0970690	+	0.0560428i
$705$		0			0
$706$	−680.973			−0.964551
$707$	−430.856	+	211.914i	−0.609414	+	0.299737i
$708$		0			0
$709$	903.894	−	521.863i	1.27489	−	0.736055i	0.298982	−	0.954259i	$-0.403353\pi$
$709$	903.894	−	521.863i	1.27489	−	0.736055i	0.975903	+	0.218204i	$0.0700197\pi$
$710$	−370.925	+	141.733i	−0.522429	+	0.199624i
$711$		0			0
$712$	755.106	+	202.330i	1.06054	+	0.284172i
$713$	−479.274	−	479.274i	−0.672194	−	0.672194i
$714$		0			0
$715$	−72.1186	+	88.7807i	−0.100865	+	0.124169i
$716$	−435.526	−	754.353i	−0.608277	−	1.05357i
$717$		0			0
$718$	−449.751	+	120.510i	−0.626393	+	0.167842i
$719$	122.057	−	70.4696i	0.169759	−	0.0980106i	−0.412713	−	0.910861i	$-0.635419\pi$
$719$	122.057	−	70.4696i	0.169759	−	0.0980106i	0.582472	+	0.812851i	$0.302085\pi$
$720$		0			0
$721$	−679.123	+	594.319i	−0.941919	+	0.824298i
$722$	−23.7659	+	23.7659i	−0.0329167	+	0.0329167i
$723$		0			0
$724$	412.270	+	238.024i	0.569434	+	0.328763i
$725$	−281.007	−	92.2573i	−0.387597	−	0.127251i
$726$		0			0
$727$	−596.540	+	596.540i	−0.820551	+	0.820551i	−0.986187	−	0.165636i	$-0.947032\pi$
$727$	−596.540	+	596.540i	−0.820551	+	0.820551i	0.165636	+	0.986187i	$0.447032\pi$
$728$	−122.083	+	182.296i	−0.167696	+	0.250407i
$729$		0			0
$730$	528.165	−	382.500i	0.723514	−	0.523973i
$731$	−365.203	+	632.550i	−0.499594	+	0.865322i
$732$		0			0
$733$	−88.6776	+	330.949i	−0.120979	+	0.451500i	−0.999665	−	0.0259012i	$-0.991754\pi$
$733$	−88.6776	+	330.949i	−0.120979	+	0.451500i	0.878685	+	0.477401i	$0.158421\pi$
$734$		−	97.4170i		−	0.132721i
$735$		0			0
$736$	1241.61			1.68698
$737$	−18.7291	−	5.01845i	−0.0254126	−	0.00680930i
$738$		0			0
$739$	−781.571	−	451.241i	−1.05761	−	0.610610i	−0.132838	−	0.991138i	$-0.542409\pi$
$739$	−781.571	−	451.241i	−1.05761	−	0.610610i	−0.924769	+	0.380528i	$0.875742\pi$
$740$	1073.62	+	171.731i	1.45084	+	0.232069i
$741$		0			0
$742$	38.5397	+	25.8098i	0.0519404	+	0.0347841i
$743$	554.070	+	554.070i	0.745721	+	0.745721i	0.973672	−	0.227952i	$-0.0732029\pi$
$743$	554.070	+	554.070i	0.745721	+	0.745721i	−0.227952	+	0.973672i	$0.573203\pi$
$744$		0			0
$745$	−81.5507	+	182.414i	−0.109464	+	0.244850i
$746$	−68.1203	+	117.988i	−0.0913140	+	0.158161i
$747$		0			0
$748$	168.779	+	168.779i	0.225640	+	0.225640i
$749$	109.336	+	124.937i	0.145975	+	0.166805i
$750$		0			0
$751$	1.48979	+	2.58040i	0.00198375	+	0.00343595i	0.867016	−	0.498281i	$-0.166035\pi$
$751$	1.48979	+	2.58040i	0.00198375	+	0.00343595i	−0.865032	+	0.501717i	$0.832702\pi$
$752$	24.6334	+	91.9331i	0.0327572	+	0.122251i
$753$		0			0
$754$	46.1280	−	26.6320i	0.0611777	−	0.0353210i
$755$	20.6655	+	199.558i	0.0273715	+	0.264315i
$756$		0			0
$757$	−334.049	+	334.049i	−0.441280	+	0.441280i	−0.892442	−	0.451162i	$-0.851010\pi$
$757$	−334.049	+	334.049i	−0.441280	+	0.441280i	0.451162	+	0.892442i	$0.351010\pi$
$758$	107.472	−	401.090i	0.141783	−	0.529143i
$759$		0			0
$760$	−657.665	+	251.299i	−0.865349	+	0.330657i
$761$	381.045	+	659.989i	0.500716	+	0.867266i	1.00000		0.000827175i	$0.000263298\pi$
$761$	381.045	+	659.989i	0.500716	+	0.867266i	−0.499283	+	0.866439i	$0.666403\pi$
$762$		0			0
$763$	−596.768	−	1213.33i	−0.782134	−	1.59020i
$764$			436.117i			0.570834i
$765$		0			0
$766$	−102.514	+	177.559i	−0.133830	+	0.231800i
$767$	−42.5482	−	158.792i	−0.0554736	−	0.207030i
$768$		0			0
$769$			903.265i			1.17460i	0.809370	+	0.587299i	$0.199809\pi$
$769$			903.265i			1.17460i	−0.809370	+	0.587299i	$0.800191\pi$
$770$	125.700	−	135.280i	0.163247	−	0.175689i
$771$		0			0
$772$	286.486	+	76.7637i	0.371096	+	0.0994348i
$773$	264.358	−	70.8344i	0.341989	−	0.0916358i	−0.0837366	−	0.996488i	$-0.526685\pi$
$773$	264.358	−	70.8344i	0.341989	−	0.0916358i	0.425726	+	0.904852i	$0.360019\pi$
$774$		0			0
$775$	301.067	+	336.436i	0.388474	+	0.434111i
$776$	301.021			0.387913
$777$		0			0
$778$	153.247	+	153.247i	0.196976	+	0.196976i
$779$	1043.20	−	602.290i	1.33915	−	0.773158i
$780$		0			0
$781$	201.761	−	349.460i	0.258336	−	0.447452i
$782$	−575.038	−	154.081i	−0.735342	−	0.197034i
$783$		0			0
$784$	−138.115	+	179.216i	−0.176166	+	0.228592i
$785$	−599.139	−	486.694i	−0.763234	−	0.619992i
$786$		0			0
$787$	−88.1411	−	328.947i	−0.111996	−	0.417976i	0.887048	−	0.461677i	$-0.152752\pi$
$787$	−88.1411	−	328.947i	−0.111996	−	0.417976i	−0.999045	+	0.0437006i	$0.986085\pi$
$788$	529.574	−	141.899i	0.672048	−	0.180075i
$789$		0			0
$790$	−272.894	+	335.943i	−0.345436	+	0.425244i
$791$	248.529	+	1256.31i	0.314196	+	1.58825i
$792$		0			0
$793$	−15.7425	+	58.7519i	−0.0198519	+	0.0740882i
$794$	−193.261	−	111.579i	−0.243402	−	0.140528i
$795$		0			0
$796$	193.978	+	335.980i	0.243691	+	0.422085i
$797$	648.529	−	648.529i	0.813713	−	0.813713i	−0.171476	−	0.985188i	$-0.554854\pi$
$797$	648.529	−	648.529i	0.813713	−	0.813713i	0.985188	+	0.171476i	$0.0548535\pi$
$798$		0			0
$799$		−	320.835i		−	0.401546i
$800$	−825.762	−	45.8127i	−1.03220	−	0.0572659i
$801$		0			0
$802$	−131.089	−	489.232i	−0.163453	−	0.610015i
$803$	−171.520	+	640.120i	−0.213598	+	0.797160i
$804$		0			0
$805$	293.216	−	1280.49i	0.364244	−	1.59067i
$806$	−81.3060			−0.100876
$807$		0			0
$808$	470.016	−	125.940i	0.581703	−	0.155867i
$809$	702.763	+	405.741i	0.868682	+	0.501534i	0.866910	−	0.498465i	$-0.166103\pi$
$809$	702.763	+	405.741i	0.868682	+	0.501534i	0.00177173	+	0.999998i	$0.499436\pi$
$810$		0			0
$811$	−435.248			−0.536681			−0.268340	−	0.963324i	$-0.586475\pi$
$811$	−435.248			−0.536681			−0.268340	+	0.963324i	$0.586475\pi$
$812$	220.083	−	108.247i	0.271038	−	0.133309i
$813$		0			0
$814$	335.497	−	193.699i	0.412158	−	0.237960i
$815$	386.654	+	1011.90i	0.474422	+	1.24159i
$816$		0			0
$817$	899.661	+	241.063i	1.10118	+	0.295059i
$818$	94.0916	+	94.0916i	0.115026	+	0.115026i
$819$		0			0
$820$	893.879	−	92.5668i	1.09010	−	0.112886i
$821$	39.3171	+	68.0993i	0.0478893	+	0.0829468i	0.888976	−	0.457953i	$-0.151417\pi$
$821$	39.3171	+	68.0993i	0.0478893	+	0.0829468i	−0.841087	+	0.540900i	$0.818084\pi$
$822$		0			0
$823$	−550.402	+	147.480i	−0.668775	+	0.179198i	−0.577203	−	0.816601i	$-0.695856\pi$
$823$	−550.402	+	147.480i	−0.668775	+	0.179198i	−0.0915721	+	0.995798i	$0.529189\pi$
$824$	792.041	−	457.285i	0.961215	−	0.554958i
$825$		0			0
$826$	51.5063	+	260.363i	0.0623563	+	0.315210i
$827$	776.861	−	776.861i	0.939373	−	0.939373i	−0.0588915	−	0.998264i	$-0.518757\pi$
$827$	776.861	−	776.861i	0.939373	−	0.939373i	0.998264	+	0.0588915i	$0.0187566\pi$
$828$		0			0
$829$	340.924	+	196.833i	0.411247	+	0.237434i	0.691325	−	0.722543i	$-0.257027\pi$
$829$	340.924	+	196.833i	0.411247	+	0.237434i	−0.280078	+	0.959977i	$0.590360\pi$
$830$	−65.8404	−	29.4349i	−0.0793258	−	0.0354638i
$831$		0			0
$832$	47.6122	−	47.6122i	0.0572262	−	0.0572262i
$833$	606.075	−	463.046i	0.727582	−	0.555877i
$834$		0			0
$835$	−74.3010	+	464.513i	−0.0889832	+	0.556303i
$836$	152.186	−	263.594i	0.182040	−	0.315303i
$837$		0			0
$838$	−123.302	+	460.168i	−0.147138	+	0.549126i
$839$			773.632i			0.922088i	0.887377	+	0.461044i	$0.152525\pi$
$839$			773.632i			0.922088i	−0.887377	+	0.461044i	$0.847475\pi$
$840$		0			0
$841$	701.037			0.833576
$842$	396.730	+	106.304i	0.471176	+	0.126251i
$843$		0			0
$844$	730.615	+	421.821i	0.865657	+	0.499787i
$845$	−438.382	−	605.328i	−0.518795	−	0.716365i
$846$		0			0
$847$	43.8113	−	657.882i	0.0517253	−	0.776720i
$848$	21.2318	+	21.2318i	0.0250375	+	0.0250375i
$849$		0			0
$850$	376.756	+	123.692i	0.443242	+	0.145520i
$851$	1377.89	−	2386.57i	1.61914	−	2.80443i
$852$		0			0
$853$	−1071.79	−	1071.79i	−1.25650	−	1.25650i	−0.952755	−	0.303741i	$-0.901764\pi$
$853$	−1071.79	−	1071.79i	−1.25650	−	1.25650i	−0.303741	−	0.952755i	$-0.598236\pi$
$854$	31.6624	−	92.9549i	0.0370755	−	0.108846i
$855$		0			0
$856$	−84.1257	−	145.710i	−0.0982777	−	0.170222i
$857$	−123.785	−	461.973i	−0.144440	−	0.539059i	−0.999780	−	0.0209905i	$-0.993318\pi$
$857$	−123.785	−	461.973i	−0.144440	−	0.539059i	0.855339	−	0.518068i	$-0.173349\pi$
$858$		0			0
$859$	310.128	−	179.053i	0.361034	−	0.208443i	−0.308500	−	0.951224i	$-0.599827\pi$
$859$	310.128	−	179.053i	0.361034	−	0.208443i	0.669534	+	0.742781i	$0.266494\pi$
$860$	539.334	+	438.113i	0.627132	+	0.509434i
$861$		0			0
$862$	266.925	−	266.925i	0.309657	−	0.309657i
$863$	56.2825	−	210.049i	0.0652173	−	0.243394i	−0.925620	−	0.378454i	$-0.876456\pi$
$863$	56.2825	−	210.049i	0.0652173	−	0.243394i	0.990837	+	0.135060i	$0.0431226\pi$
$864$		0			0
$865$	−379.763	−	993.862i	−0.439032	−	1.14897i
$866$	−83.8684	−	145.264i	−0.0968458	−	0.167742i
$867$		0			0
$868$	−373.559	−	24.8770i	−0.430368	−	0.0286601i
$869$		−	439.835i		−	0.506139i
$870$		0			0
$871$	−8.27283	+	14.3290i	−0.00949808	+	0.0164512i
$872$	354.659	+	1323.60i	0.406719	+	1.51789i
$873$		0			0
$874$			759.142i			0.868584i
$875$	−242.257	+	840.795i	−0.276865	+	0.960909i
$876$		0			0
$877$	403.957	+	108.240i	0.460613	+	0.123421i	0.481661	−	0.876358i	$-0.340034\pi$
$877$	403.957	+	108.240i	0.460613	+	0.123421i	−0.0210482	+	0.999778i	$0.506700\pi$
$878$	271.040	−	72.6249i	0.308701	−	0.0827163i
$879$		0			0
$880$	96.8193	−	70.1170i	0.110022	−	0.0796784i
$881$	218.930			0.248501			0.124251	−	0.992251i	$-0.460347\pi$
$881$	218.930			0.248501			0.124251	+	0.992251i	$0.460347\pi$
$882$		0			0
$883$	−322.254	−	322.254i	−0.364954	−	0.364954i	0.500679	−	0.865633i	$-0.333084\pi$
$883$	−322.254	−	322.254i	−0.364954	−	0.364954i	−0.865633	+	0.500679i	$0.833084\pi$
$884$	176.390	−	101.839i	0.199536	−	0.115202i
$885$		0			0
$886$	396.433	−	686.641i	0.447441	−	0.774990i
$887$	494.995	+	132.633i	0.558055	+	0.149530i	0.526813	−	0.849981i	$-0.323387\pi$
$887$	494.995	+	132.633i	0.558055	+	0.149530i	0.0312425	+	0.999512i	$0.490054\pi$
$888$		0			0
$889$	−527.127	+	104.279i	−0.592943	+	0.117299i
$890$	−354.011	+	435.801i	−0.397765	+	0.489664i
$891$		0			0
$892$	176.770	+	659.715i	0.198173	+	0.739591i
$893$	−395.181	+	105.889i	−0.442532	+	0.118576i
$894$		0			0
$895$	1462.75	−	151.477i	1.63436	−	0.169248i
$896$	615.244	−	538.416i	0.686656	−	0.600911i
$897$		0			0
$898$	−115.284	+	430.245i	−0.128378	+	0.479114i
$899$	185.025	+	106.824i	0.205812	+	0.118826i
$900$		0			0
$901$	−50.6088	−	87.6570i	−0.0561696	−	0.0972886i
$902$	226.412	−	226.412i	0.251011	−	0.251011i
$903$		0			0
$904$		−	1297.85i		−	1.43567i
$905$	−650.928	+	471.406i	−0.719258	+	0.520891i
$906$		0			0
$907$	231.181	+	862.781i	0.254886	+	0.951246i	0.968154	+	0.250355i	$0.0805474\pi$
$907$	231.181	+	862.781i	0.254886	+	0.951246i	−0.713268	+	0.700891i	$0.752786\pi$
$908$	−258.970	+	966.489i	−0.285209	+	1.06441i
$909$		0			0
$910$	−83.7422	−	133.485i	−0.0920244	−	0.146686i
$911$	−1570.35			−1.72377			−0.861884	−	0.507106i	$-0.830715\pi$
$911$	−1570.35			−1.72377			−0.861884	+	0.507106i	$0.830715\pi$
$912$		0			0
$913$	70.7930	−	18.9689i	0.0775389	−	0.0207765i
$914$	−147.215	−	84.9947i	−0.161067	−	0.0929920i
$915$		0			0
$916$	671.603			0.733191
$917$	8.63258	−	129.629i	0.00941394	−	0.141362i
$918$		0			0
$919$	−254.283	+	146.810i	−0.276695	+	0.159750i	−0.631926	−	0.775029i	$-0.717735\pi$
$919$	−254.283	+	146.810i	−0.276695	+	0.159750i	0.355231	+	0.934778i	$0.384402\pi$
$920$	−543.336	+	1215.34i	−0.590582	+	1.32102i
$921$		0			0
$922$	−345.046	−	92.4548i	−0.374237	−	0.100276i
$923$	−243.479	−	243.479i	−0.263791	−	0.263791i
$924$		0			0
$925$	−1004.45	+	1536.40i	−1.08590	+	1.66097i
$926$	−284.115	−	492.101i	−0.306819	−	0.531427i
$927$		0			0
$928$	−378.035	+	101.294i	−0.407365	+	0.109153i
$929$	−365.315	+	210.915i	−0.393235	+	0.227034i	−0.683561	−	0.729894i	$-0.739570\pi$
$929$	−365.315	+	210.915i	−0.393235	+	0.227034i	0.290326	+	0.956928i	$0.406236\pi$
$930$		0			0
$931$	−770.375	−	593.696i	−0.827471	−	0.637697i
$932$	338.157	−	338.157i	0.362829	−	0.362829i
$933$		0			0
$934$	136.081	+	78.5665i	0.145697	+	0.0841183i
$935$	−376.428	+	143.836i	−0.402597	+	0.153836i
$936$		0			0
$937$	−339.016	+	339.016i	−0.361810	+	0.361810i	−0.864479	−	0.502669i	$-0.832352\pi$
$937$	−339.016	+	339.016i	−0.361810	+	0.361810i	0.502669	+	0.864479i	$0.332352\pi$
$938$	14.8639	−	22.1951i	0.0158464	−	0.0236621i
$939$		0			0
$940$	−301.388	−	48.2084i	−0.320626	−	0.0512855i
$941$	16.4292	−	28.4562i	0.0174593	−	0.0302404i	−0.857164	−	0.515044i	$-0.827776\pi$
$941$	16.4292	−	28.4562i	0.0174593	−	0.0302404i	0.874623	+	0.484804i	$0.161109\pi$
$942$		0			0
$943$	589.519	−	2200.11i	0.625153	−	2.33310i
$944$			171.811i			0.182003i
$945$		0			0
$946$	247.579			0.261712
$947$	297.523	+	79.7211i	0.314174	+	0.0841828i	0.412461	−	0.910975i	$-0.364669\pi$
$947$	297.523	+	79.7211i	0.314174	+	0.0841828i	−0.0982863	+	0.995158i	$0.531336\pi$
$948$		0			0
$949$	489.732	+	282.747i	0.516050	+	0.297942i
$950$	28.0106	−	504.884i	0.0294848	−	0.531457i
$951$		0			0
$952$	−693.602	+	341.145i	−0.728574	+	0.358346i
$953$	−311.252	−	311.252i	−0.326602	−	0.326602i	0.524691	−	0.851293i	$-0.324181\pi$
$953$	−311.252	−	311.252i	−0.326602	−	0.326602i	−0.851293	+	0.524691i	$0.824181\pi$
$954$		0			0
$955$	−672.169	−	300.503i	−0.703842	−	0.314663i
$956$	−92.0152	+	159.375i	−0.0962502	+	0.166710i
$957$		0			0
$958$	19.9970	+	19.9970i	0.0208737	+	0.0208737i
$959$	−243.960	+	716.220i	−0.254390	+	0.746841i
$960$		0			0
$961$	317.436	+	549.814i	0.330318	+	0.572127i
$962$	−85.5587	−	319.309i	−0.0889384	−	0.331922i
$963$		0			0
$964$	−1047.56	+	604.811i	−1.08668	+	0.627397i
$965$	−315.714	+	388.655i	−0.327164	+	0.402752i
$966$		0			0
$967$	−886.120	+	886.120i	−0.916360	+	0.916360i	−0.996762	−	0.0804023i	$-0.974379\pi$
$967$	−886.120	+	886.120i	−0.916360	+	0.916360i	0.0804023	+	0.996762i	$0.474379\pi$
$968$	−172.941	+	645.423i	−0.178658	+	0.666760i
$969$		0			0
$970$	−88.2390	+	197.374i	−0.0909680	+	0.203478i
$971$	−553.141	−	958.068i	−0.569661	−	0.986682i	−0.996599	−	0.0824012i	$-0.973741\pi$
$971$	−553.141	−	958.068i	−0.569661	−	0.986682i	0.426938	−	0.904281i	$-0.359592\pi$
$972$		0			0
$973$	−527.847	+	788.192i	−0.542494	+	0.810064i
$974$		−	29.2378i		−	0.0300183i
$975$		0			0
$976$	31.7844	−	55.0523i	0.0325660	−	0.0564060i
$977$	−430.663	−	1607.26i	−0.440802	−	1.64509i	−0.726788	−	0.686861i	$-0.758988\pi$
$977$	−430.663	−	1607.26i	−0.440802	−	1.64509i	0.285987	−	0.958234i	$-0.407679\pi$
$978$		0			0
$979$		−	570.574i		−	0.582813i
$980$	−343.910	−	638.915i	−0.350929	−	0.651955i
$981$		0			0
$982$	216.730	+	58.0726i	0.220702	+	0.0591370i
$983$	−637.114	+	170.714i	−0.648132	+	0.173666i	−0.567884	−	0.823108i	$-0.692238\pi$
$983$	−637.114	+	170.714i	−0.648132	+	0.173666i	−0.0802479	+	0.996775i	$0.525571\pi$
$984$		0			0
$985$	−146.196	+	913.984i	−0.148422	+	0.927903i
$986$	187.652			0.190317
$987$		0			0
$988$	−183.654	−	183.654i	−0.185884	−	0.185884i
$989$	1525.22	−	880.584i	1.54218	−	0.890378i
$990$		0			0
$991$	52.1749	−	90.3696i	0.0526487	−	0.0911903i	−0.838500	−	0.544902i	$-0.816567\pi$
$991$	52.1749	−	90.3696i	0.0526487	−	0.0911903i	0.891149	+	0.453711i	$0.149900\pi$
$992$	577.060	+	154.623i	0.581714	+	0.155870i
$993$		0			0
$994$	366.102	+	418.341i	0.368312	+	0.420867i
$995$	−651.491	+	67.4660i	−0.654765	+	0.0678050i
$996$		0			0
$997$	−348.936	−	1302.25i	−0.349986	−	1.30616i	−0.886679	−	0.462386i	$-0.846993\pi$
$997$	−348.936	−	1302.25i	−0.349986	−	1.30616i	0.536693	−	0.843778i	$-0.319673\pi$
$998$	−594.949	+	159.416i	−0.596141	+	0.159735i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.298.6		64
3.2	odd	2		105.3.v.a.88.11	yes	64
5.2	odd	4	inner	315.3.ca.b.172.11		64
7.2	even	3	inner	315.3.ca.b.163.11		64
15.2	even	4		105.3.v.a.67.6	yes	64
21.2	odd	6		105.3.v.a.58.6	yes	64
35.2	odd	12	inner	315.3.ca.b.37.6		64
105.2	even	12		105.3.v.a.37.11	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.11	✓	64	105.2	even	12
105.3.v.a.58.6	yes	64	21.2	odd	6
105.3.v.a.67.6	yes	64	15.2	even	4
105.3.v.a.88.11	yes	64	3.2	odd	2
315.3.ca.b.37.6		64	35.2	odd	12	inner
315.3.ca.b.163.11		64	7.2	even	3	inner
315.3.ca.b.172.11		64	5.2	odd	4	inner
315.3.ca.b.298.6		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984292 - 0.263740i) q^{2} +(-2.56483 - 1.48081i) q^{4} +(4.04958 - 2.93273i) q^{5} +(-5.81621 - 3.89508i) q^{7} +(5.01620 + 5.01620i) q^{8} +O(q^{10})\)	\(q+(-0.984292 - 0.263740i) q^{2} +(-2.56483 - 1.48081i) q^{4} +(4.04958 - 2.93273i) q^{5} +(-5.81621 - 3.89508i) q^{7} +(5.01620 + 5.01620i) q^{8} +(-4.75945 + 1.81862i) q^{10} +(2.58885 - 4.48403i) q^{11} +(-3.12416 - 3.12416i) q^{13} +(4.69756 + 5.36787i) q^{14} +(2.30879 + 3.99894i) q^{16} +(-4.02869 - 15.0353i) q^{17} +(-17.1897 + 9.92450i) q^{19} +(-14.7293 + 1.52531i) q^{20} +(-3.73081 + 3.73081i) q^{22} +(-9.71406 + 36.2534i) q^{23} +(7.79821 - 23.7526i) q^{25} +(2.25112 + 3.89905i) q^{26} +(9.14974 + 18.6029i) q^{28} -11.8306i q^{29} +(-9.02952 + 15.6396i) q^{31} +(-8.56207 - 31.9541i) q^{32} +15.8616i q^{34} +(-34.9764 + 1.28394i) q^{35} +(-70.9224 - 19.0036i) q^{37} +(19.5372 - 5.23498i) q^{38} +(35.0247 + 5.60235i) q^{40} -60.6872 q^{41} +(-33.1804 - 33.1804i) q^{43} +(-13.2799 + 7.66718i) q^{44} +(19.1229 - 33.1219i) q^{46} +(19.9094 + 5.33470i) q^{47} +(18.6567 + 45.3092i) q^{49} +(-13.9402 + 21.3228i) q^{50} +(3.38666 + 12.6392i) q^{52} +(6.28105 - 1.68300i) q^{53} +(-2.66666 - 25.7508i) q^{55} +(-9.63679 - 48.7138i) q^{56} +(-3.12020 + 11.6447i) q^{58} +(32.2232 + 18.6041i) q^{59} +(-6.88336 - 11.9223i) q^{61} +(13.0125 - 13.0125i) q^{62} +15.2400i q^{64} +(-21.8138 - 3.48922i) q^{65} +(-0.969242 - 3.61726i) q^{67} +(-11.9314 + 44.5287i) q^{68} +(34.7657 + 7.96093i) q^{70} +77.9344 q^{71} +(-123.630 + 33.1265i) q^{73} +(64.7964 + 37.4102i) q^{74} +58.7850 q^{76} +(-32.5230 + 15.9963i) q^{77} +(73.5670 - 42.4739i) q^{79} +(21.0774 + 9.42297i) q^{80} +(59.7339 + 16.0057i) q^{82} +(10.0091 + 10.0091i) q^{83} +(-60.4089 - 49.0715i) q^{85} +(23.9082 + 41.4102i) q^{86} +(35.4790 - 9.50657i) q^{88} +(95.4344 - 55.0991i) q^{89} +(6.00193 + 30.3396i) q^{91} +(78.5990 - 78.5990i) q^{92} +(-18.1897 - 10.5018i) q^{94} +(-40.5054 + 90.6029i) q^{95} +(30.0049 - 30.0049i) q^{97} +(-6.41377 - 49.5181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) \) 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

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