LMFDB - Embedded newform 315.3.ca.b.298.2

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			298.2
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.41166 - 0.914152i) q^{2} +(7.33966 + 4.23756i) q^{4} +(4.98672 + 0.364163i) q^{5} +(-6.35750 + 2.92953i) q^{7} +(-11.1766 - 11.1766i) q^{8} +O(q^{10})$	\(q+(-3.41166 - 0.914152i) q^{2} +(7.33966 + 4.23756i) q^{4} +(4.98672 + 0.364163i) q^{5} +(-6.35750 + 2.92953i) q^{7} +(-11.1766 - 11.1766i) q^{8} +(-16.6801 - 5.80102i) q^{10} +(-8.72135 + 15.1058i) q^{11} +(-8.72144 - 8.72144i) q^{13} +(24.3677 - 4.18286i) q^{14} +(10.9636 + 18.9894i) q^{16} +(-3.02215 - 11.2788i) q^{17} +(-3.12903 + 1.80655i) q^{19} +(35.0577 + 23.8044i) q^{20} +(43.5633 - 43.5633i) q^{22} +(6.21349 - 23.1890i) q^{23} +(24.7348 + 3.63196i) q^{25} +(21.7819 + 37.7273i) q^{26} +(-59.0760 - 5.43848i) q^{28} -46.5831i q^{29} +(-1.10507 + 1.91403i) q^{31} +(-3.68097 - 13.7376i) q^{32} +41.2423i q^{34} +(-32.7699 + 12.2936i) q^{35} +(-29.3791 - 7.87211i) q^{37} +(12.3266 - 3.30292i) q^{38} +(-51.6647 - 59.8049i) q^{40} -29.9435 q^{41} +(-19.6771 - 19.6771i) q^{43} +(-128.024 + 73.9145i) q^{44} +(-42.3966 + 73.4331i) q^{46} +(-79.1503 - 21.2083i) q^{47} +(31.8357 - 37.2490i) q^{49} +(-81.0665 - 35.0024i) q^{50} +(-27.0549 - 100.970i) q^{52} +(-1.63190 + 0.437265i) q^{53} +(-48.9919 + 72.1526i) q^{55} +(103.798 + 38.3132i) q^{56} +(-42.5841 + 158.926i) q^{58} +(76.5567 + 44.2000i) q^{59} +(-23.4309 - 40.5836i) q^{61} +(5.51984 - 5.51984i) q^{62} -37.4755i q^{64} +(-40.3154 - 46.6674i) q^{65} +(3.01836 + 11.2647i) q^{67} +(25.6131 - 95.5894i) q^{68} +(123.038 - 11.9849i) q^{70} -67.1402 q^{71} +(-17.6525 + 4.72997i) q^{73} +(93.0353 + 53.7140i) q^{74} -30.6214 q^{76} +(11.1930 - 121.585i) q^{77} +(19.4021 - 11.2018i) q^{79} +(47.7569 + 98.6876i) q^{80} +(102.157 + 27.3729i) q^{82} +(-52.4430 - 52.4430i) q^{83} +(-10.9633 - 57.3450i) q^{85} +(49.1438 + 85.1196i) q^{86} +(266.308 - 71.3570i) q^{88} +(-44.2757 + 25.5626i) q^{89} +(80.9964 + 29.8968i) q^{91} +(143.870 - 143.870i) q^{92} +(250.647 + 144.711i) q^{94} +(-16.2615 + 7.86926i) q^{95} +(9.15031 - 9.15031i) q^{97} +(-142.664 + 97.9785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.41166	−	0.914152i	−1.70583	−	0.457076i	−0.731435	−	0.681912i	$-0.761149\pi$
$2$	−3.41166	−	0.914152i	−1.70583	−	0.457076i	−0.974397	+	0.224836i	$0.927815\pi$
$3$		0			0
$3$		0			0
$4$	7.33966	+	4.23756i	1.83492	+	1.05939i
$5$	4.98672	+	0.364163i	0.997344	+	0.0728326i
$5$	4.98672	+	0.364163i	0.997344	+	0.0728326i
$6$		0			0
$7$	−6.35750	+	2.92953i	−0.908215	+	0.418505i
$7$	−6.35750	+	2.92953i	−0.908215	+	0.418505i
$8$	−11.1766	−	11.1766i	−1.39708	−	1.39708i
$9$		0			0
$10$	−16.6801	−	5.80102i	−1.66801	−	0.580102i
$11$	−8.72135	+	15.1058i	−0.792850	+	1.37326i	0.131345	+	0.991337i	$0.458070\pi$
$11$	−8.72135	+	15.1058i	−0.792850	+	1.37326i	−0.924195	+	0.381920i	$0.875263\pi$
$12$		0			0
$13$	−8.72144	−	8.72144i	−0.670880	−	0.670880i	0.287039	−	0.957919i	$-0.407329\pi$
$13$	−8.72144	−	8.72144i	−0.670880	−	0.670880i	−0.957919	+	0.287039i	$0.907329\pi$
$14$	24.3677	−	4.18286i	1.74055	−	0.298776i
$15$		0			0
$16$	10.9636	+	18.9894i	0.685222	+	1.18684i
$17$	−3.02215	−	11.2788i	−0.177774	−	0.663461i	−0.996063	−	0.0886535i	$-0.971744\pi$
$17$	−3.02215	−	11.2788i	−0.177774	−	0.663461i	0.818289	−	0.574807i	$-0.194923\pi$
$18$		0			0
$19$	−3.12903	+	1.80655i	−0.164686	+	0.0950814i	−0.580078	−	0.814561i	$-0.696978\pi$
$19$	−3.12903	+	1.80655i	−0.164686	+	0.0950814i	0.415392	+	0.909643i	$0.363644\pi$
$20$	35.0577	+	23.8044i	1.75288	+	1.19022i
$21$		0			0
$22$	43.5633	−	43.5633i	1.98015	−	1.98015i
$23$	6.21349	−	23.1890i	0.270152	−	1.00822i	−0.688870	−	0.724885i	$-0.741893\pi$
$23$	6.21349	−	23.1890i	0.270152	−	1.00822i	0.959021	−	0.283334i	$-0.0914406\pi$
$24$		0			0
$25$	24.7348	+	3.63196i	0.989391	+	0.145278i
$26$	21.7819	+	37.7273i	0.837765	+	1.45105i
$27$		0			0
$28$	−59.0760	−	5.43848i	−2.10986	−	0.194231i
$29$		−	46.5831i		−	1.60631i	−0.595767	−	0.803157i	$-0.703152\pi$
$29$		−	46.5831i		−	1.60631i	0.595767	−	0.803157i	$-0.296848\pi$
$30$		0			0
$31$	−1.10507	+	1.91403i	−0.0356474	+	0.0617430i	−0.883299	−	0.468811i	$-0.844683\pi$
$31$	−1.10507	+	1.91403i	−0.0356474	+	0.0617430i	0.847651	+	0.530554i	$0.178016\pi$
$32$	−3.68097	−	13.7376i	−0.115030	−	0.429300i
$33$		0			0
$34$			41.2423i			1.21301i
$35$	−32.7699	+	12.2936i	−0.936283	+	0.351246i
$36$		0			0
$37$	−29.3791	−	7.87211i	−0.794030	−	0.212760i	−0.161069	−	0.986943i	$-0.551494\pi$
$37$	−29.3791	−	7.87211i	−0.794030	−	0.212760i	−0.632961	+	0.774183i	$0.718161\pi$
$38$	12.3266	−	3.30292i	0.324386	−	0.0869188i
$39$		0			0
$40$	−51.6647	−	59.8049i	−1.29162	−	1.49512i
$41$	−29.9435			−0.730329			−0.365165	−	0.930943i	$-0.618987\pi$
$41$	−29.9435			−0.730329			−0.365165	+	0.930943i	$0.618987\pi$
$42$		0			0
$43$	−19.6771	−	19.6771i	−0.457608	−	0.457608i	0.440262	−	0.897869i	$-0.354886\pi$
$43$	−19.6771	−	19.6771i	−0.457608	−	0.457608i	−0.897869	+	0.440262i	$0.854886\pi$
$44$	−128.024	+	73.9145i	−2.90963	+	1.67987i
$45$		0			0
$46$	−42.3966	+	73.4331i	−0.921666	+	1.59637i
$47$	−79.1503	−	21.2083i	−1.68405	−	0.451240i	−0.715206	−	0.698913i	$-0.753667\pi$
$47$	−79.1503	−	21.2083i	−1.68405	−	0.451240i	−0.968844	+	0.247674i	$0.920334\pi$
$48$		0			0
$49$	31.8357	−	37.2490i	0.649707	−	0.760185i
$50$	−81.0665	−	35.0024i	−1.62133	−	0.700047i
$51$		0			0
$52$	−27.0549	−	100.970i	−0.520286	−	1.94173i
$53$	−1.63190	+	0.437265i	−0.0307905	+	0.00825028i	−0.274181	−	0.961678i	$-0.588407\pi$
$53$	−1.63190	+	0.437265i	−0.0307905	+	0.00825028i	0.243391	+	0.969928i	$0.421740\pi$
$54$		0			0
$55$	−48.9919	+	72.1526i	−0.890763	+	1.31186i
$56$	103.798	+	38.3132i	1.85353	+	0.684164i
$57$		0			0
$58$	−42.5841	+	158.926i	−0.734208	+	2.74010i
$59$	76.5567	+	44.2000i	1.29757	+	0.749153i	0.979984	−	0.199076i	$-0.0637941\pi$
$59$	76.5567	+	44.2000i	1.29757	+	0.749153i	0.317587	+	0.948229i	$0.397127\pi$
$60$		0			0
$61$	−23.4309	−	40.5836i	−0.384114	−	0.665305i	0.607532	−	0.794295i	$-0.292160\pi$
$61$	−23.4309	−	40.5836i	−0.384114	−	0.665305i	−0.991646	+	0.128990i	$0.958826\pi$
$62$	5.51984	−	5.51984i	0.0890296	−	0.0890296i
$63$		0			0
$64$		−	37.4755i		−	0.585554i
$65$	−40.3154	−	46.6674i	−0.620236	−	0.717960i
$66$		0			0
$67$	3.01836	+	11.2647i	0.0450501	+	0.168129i	0.984786	−	0.173772i	$-0.0555957\pi$
$67$	3.01836	+	11.2647i	0.0450501	+	0.168129i	−0.939736	+	0.341902i	$0.888929\pi$
$68$	25.6131	−	95.5894i	0.376663	−	1.40573i
$69$		0			0
$70$	123.038	−	11.9849i	1.75769	−	0.171213i
$71$	−67.1402			−0.945636			−0.472818	−	0.881160i	$-0.656763\pi$
$71$	−67.1402			−0.945636			−0.472818	+	0.881160i	$0.656763\pi$
$72$		0			0
$73$	−17.6525	+	4.72997i	−0.241815	+	0.0647941i	−0.377691	−	0.925932i	$-0.623282\pi$
$73$	−17.6525	+	4.72997i	−0.241815	+	0.0647941i	0.135876	+	0.990726i	$0.456615\pi$
$74$	93.0353	+	53.7140i	1.25723	+	0.725865i
$75$		0			0
$76$	−30.6214			−0.402913
$77$	11.1930	−	121.585i	0.145363	−	1.57902i
$78$		0			0
$79$	19.4021	−	11.2018i	0.245596	−	0.141795i	−0.372150	−	0.928173i	$-0.621379\pi$
$79$	19.4021	−	11.2018i	0.245596	−	0.141795i	0.617746	+	0.786378i	$0.288046\pi$
$80$	47.7569	+	98.6876i	0.596962	+	1.23359i
$81$		0			0
$82$	102.157	+	27.3729i	1.24582	+	0.333816i
$83$	−52.4430	−	52.4430i	−0.631844	−	0.631844i	0.316686	−	0.948530i	$-0.397430\pi$
$83$	−52.4430	−	52.4430i	−0.631844	−	0.631844i	−0.948530	+	0.316686i	$0.897430\pi$
$84$		0			0
$85$	−10.9633	−	57.3450i	−0.128980	−	0.674647i
$86$	49.1438	+	85.1196i	0.571440	+	0.989763i
$87$		0			0
$88$	266.308	−	71.3570i	3.02623	−	0.810875i
$89$	−44.2757	+	25.5626i	−0.497480	+	0.287220i	−0.727672	−	0.685925i	$-0.759398\pi$
$89$	−44.2757	+	25.5626i	−0.497480	+	0.287220i	0.230192	+	0.973145i	$0.426065\pi$
$90$		0			0
$91$	80.9964	+	29.8968i	0.890070	+	0.328536i
$92$	143.870	−	143.870i	1.56380	−	1.56380i
$93$		0			0
$94$	250.647	+	144.711i	2.66645	+	1.53948i
$95$	−16.2615	+	7.86926i	−0.171173	+	0.0828343i
$96$		0			0
$97$	9.15031	−	9.15031i	0.0943331	−	0.0943331i	−0.658365	−	0.752698i	$-0.728752\pi$
$97$	9.15031	−	9.15031i	0.0943331	−	0.0943331i	0.752698	+	0.658365i	$0.228752\pi$
$98$	−142.664	+	97.9785i	−1.45575	+	0.999781i
$99$		0			0
$100$	166.154	+	131.472i	1.66154	+	1.31472i
$101$	−42.1642	+	73.0305i	−0.417467	+	0.723074i	−0.995684	−	0.0928089i	$-0.970415\pi$
$101$	−42.1642	+	73.0305i	−0.417467	+	0.723074i	0.578217	+	0.815883i	$0.303749\pi$
$102$		0			0
$103$	−30.3411	+	113.235i	−0.294574	+	1.09937i	0.646981	+	0.762506i	$0.276031\pi$
$103$	−30.3411	+	113.235i	−0.294574	+	1.09937i	−0.941555	+	0.336859i	$0.890635\pi$
$104$			194.953i			1.87455i
$105$		0			0
$106$	5.96720			0.0562944
$107$	138.045	+	36.9890i	1.29014	+	0.345691i	0.837713	−	0.546111i	$-0.183892\pi$
$107$	138.045	+	36.9890i	1.29014	+	0.345691i	0.452425	+	0.891802i	$0.350559\pi$
$108$		0			0
$109$	−140.724	−	81.2472i	−1.29105	−	0.745387i	−0.312208	−	0.950014i	$-0.601069\pi$
$109$	−140.724	−	81.2472i	−1.29105	−	0.745387i	−0.978840	+	0.204627i	$0.934402\pi$
$110$	233.102	−	201.374i	2.11911	−	1.83067i
$111$		0			0
$112$	−125.331	−	88.6073i	−1.11903	−	0.791136i
$113$	3.09464	+	3.09464i	0.0273862	+	0.0273862i	0.720667	−	0.693281i	$-0.243836\pi$
$113$	3.09464	+	3.09464i	0.0273862	+	0.0273862i	−0.693281	+	0.720667i	$0.743836\pi$
$114$		0			0
$115$	39.4295	−	113.375i	0.342865	−	0.985866i
$116$	197.399	−	341.904i	1.70171	−	2.94745i
$117$		0			0
$118$	−220.780	−	220.780i	−1.87102	−	1.87102i
$119$	52.2551	+	62.8517i	0.439118	+	0.528166i
$120$		0			0
$121$	−91.6240	−	158.697i	−0.757223	−	1.31155i
$122$	42.8389	+	159.877i	0.351139	+	1.31047i
$123$		0			0
$124$	−16.2217	+	9.36558i	−0.130820	+	0.0755289i
$125$	122.023	+	27.1191i	0.976182	+	0.216953i
$126$		0			0
$127$	−117.674	+	117.674i	−0.926571	+	0.926571i	−0.997483	−	0.0709120i	$-0.977409\pi$
$127$	−117.674	+	117.674i	−0.926571	+	0.926571i	0.0709120	+	0.997483i	$0.477409\pi$
$128$	−48.9822	+	182.804i	−0.382673	+	1.42816i
$129$		0			0
$130$	94.8813	+	196.068i	0.729856	+	1.50821i
$131$	−81.6255	−	141.379i	−0.623095	−	1.07923i	−0.988906	−	0.148543i	$-0.952542\pi$
$131$	−81.6255	−	141.379i	−0.623095	−	1.07923i	0.365811	−	0.930689i	$-0.380792\pi$
$132$		0			0
$133$	14.6005	−	20.6517i	0.109778	−	0.155276i
$134$		−	41.1905i		−	0.307392i
$135$		0			0
$136$	−92.2820	+	159.837i	−0.678544	+	1.17527i
$137$	38.2623	+	142.797i	0.279287	+	1.04231i	0.952914	+	0.303241i	$0.0980688\pi$
$137$	38.2623	+	142.797i	0.279287	+	1.04231i	−0.673627	+	0.739072i	$0.735265\pi$
$138$		0			0
$139$			101.553i			0.730596i	0.930891	+	0.365298i	$0.119033\pi$
$139$			101.553i			0.730596i	−0.930891	+	0.365298i	$0.880967\pi$
$140$	−292.615	−	48.6335i	−2.09011	−	0.347382i
$141$		0			0
$142$	229.060	+	61.3763i	1.61310	+	0.432228i
$143$	207.807	−	55.6818i	1.45320	−	0.389383i
$144$		0			0
$145$	16.9639	−	232.297i	0.116992	−	1.60205i
$146$	64.5483			0.442112
$147$		0			0
$148$	−182.274	−	182.274i	−1.23158	−	1.23158i
$149$	−91.7653	+	52.9807i	−0.615874	+	0.355575i	−0.775261	−	0.631641i	$-0.782382\pi$
$149$	−91.7653	+	52.9807i	−0.615874	+	0.355575i	0.159387	+	0.987216i	$0.449048\pi$
$150$		0			0
$151$	80.5845	−	139.576i	0.533672	−	0.924347i	−0.465554	−	0.885019i	$-0.654145\pi$
$151$	80.5845	−	139.576i	0.533672	−	0.924347i	0.999226	−	0.0393279i	$-0.0125217\pi$
$152$	55.1632	+	14.7809i	0.362916	+	0.0972429i
$153$		0			0
$154$	−149.334	+	404.574i	−0.969699	+	2.62711i
$155$	−6.20769	+	9.14233i	−0.0400496	+	0.0589828i
$156$		0			0
$157$	−35.5563	−	132.698i	−0.226473	−	0.845210i	−0.981809	−	0.189872i	$-0.939193\pi$
$157$	−35.5563	−	132.698i	−0.226473	−	0.845210i	0.755336	−	0.655338i	$-0.227474\pi$
$158$	−76.4335	+	20.4803i	−0.483756	+	0.129622i
$159$		0			0
$160$	−13.3533	−	69.8460i	−0.0834579	−	0.436537i
$161$	28.4309	+	165.627i	0.176589	+	1.02874i
$162$		0			0
$163$	−48.8824	+	182.431i	−0.299892	+	1.11921i	0.637362	+	0.770564i	$0.280025\pi$
$163$	−48.8824	+	182.431i	−0.299892	+	1.11921i	−0.937254	+	0.348647i	$0.886641\pi$
$164$	−219.775	−	126.887i	−1.34009	−	0.773703i
$165$		0			0
$166$	130.977	+	226.859i	0.789018	+	1.36662i
$167$	114.153	−	114.153i	0.683552	−	0.683552i	−0.277247	−	0.960799i	$-0.589422\pi$
$167$	114.153	−	114.153i	0.683552	−	0.683552i	0.960799	+	0.277247i	$0.0894220\pi$
$168$		0			0
$169$		−	16.8729i		−	0.0998396i
$170$	−15.0189	+	205.664i	−0.0883466	+	1.20979i
$171$		0			0
$172$	−61.0406	−	227.807i	−0.354887	−	1.32446i
$173$	−53.9511	+	201.348i	−0.311856	+	1.16386i	0.615025	+	0.788508i	$0.289146\pi$
$173$	−53.9511	+	201.348i	−0.311856	+	1.16386i	−0.926881	+	0.375355i	$0.877521\pi$
$174$		0			0
$175$	−167.891	+	49.3712i	−0.959379	+	0.282121i
$176$	−382.468			−2.17312
$177$		0			0
$178$	174.422	−	46.7362i	0.979899	−	0.262563i
$179$	102.967	+	59.4481i	0.575235	+	0.332112i	0.759238	−	0.650814i	$-0.225572\pi$
$179$	102.967	+	59.4481i	0.575235	+	0.332112i	−0.184002	+	0.982926i	$0.558905\pi$
$180$		0			0
$181$	−2.13381			−0.0117890			−0.00589449	−	0.999983i	$-0.501876\pi$
$181$	−2.13381			−0.0117890			−0.00589449	+	0.999983i	$0.501876\pi$
$182$	−249.002	−	176.041i	−1.36814	−	0.967257i
$183$		0			0
$184$	−328.622	+	189.730i	−1.78599	+	1.03114i
$185$	−143.639	−	49.9548i	−0.776426	−	0.270026i
$186$		0			0
$187$	196.733	+	52.7146i	1.05205	+	0.281896i
$188$	−491.066	−	491.066i	−2.61205	−	2.61205i
$189$		0			0
$190$	62.6724	−	11.9818i	0.329855	−	0.0630621i
$191$	−85.4671	−	148.033i	−0.447472	−	0.775044i	0.550749	−	0.834671i	$-0.314342\pi$
$191$	−85.4671	−	148.033i	−0.447472	−	0.775044i	−0.998221	+	0.0596272i	$0.981009\pi$
$192$		0			0
$193$	80.0626	−	21.4527i	0.414832	−	0.111154i	−0.0453656	−	0.998970i	$-0.514445\pi$
$193$	80.0626	−	21.4527i	0.414832	−	0.111154i	0.460197	+	0.887817i	$0.347779\pi$
$194$	−39.5825	+	22.8530i	−0.204034	+	0.117799i
$195$		0			0
$196$	391.508	−	138.490i	1.99749	−	0.706582i
$197$	−32.0391	+	32.0391i	−0.162635	+	0.162635i	−0.783733	−	0.621098i	$-0.786687\pi$
$197$	−32.0391	+	32.0391i	−0.162635	+	0.162635i	0.621098	+	0.783733i	$0.286687\pi$
$198$		0			0
$199$	22.0307	+	12.7194i	0.110707	+	0.0639167i	0.554331	−	0.832296i	$-0.312974\pi$
$199$	22.0307	+	12.7194i	0.110707	+	0.0639167i	−0.443624	+	0.896213i	$0.646307\pi$
$200$	−235.859	−	317.045i	−1.17929	−	1.58522i
$201$		0			0
$202$	210.611	−	210.611i	1.04263	−	1.04263i
$203$	136.467	+	296.152i	0.672250	+	1.45888i
$204$		0			0
$205$	−149.320	−	10.9043i	−0.728390	−	0.0531918i
$206$	207.027	−	358.582i	1.00499	−	1.74069i
$207$		0			0
$208$	69.9973	−	261.233i	0.336525	−	1.25593i
$209$		−	63.0221i		−	0.301541i
$210$		0			0
$211$	139.996			0.663487			0.331744	−	0.943370i	$-0.392363\pi$
$211$	139.996			0.663487			0.331744	+	0.943370i	$0.392363\pi$
$212$	−13.8305	−	3.70587i	−0.0652382	−	0.0174805i
$213$		0			0
$214$	−437.148	−	252.388i	−2.04275	−	1.17938i
$215$	−90.9587	−	105.290i	−0.423064	−	0.489721i
$216$		0			0
$217$	1.41824	−	15.4058i	0.00653568	−	0.0709945i
$218$	405.831	+	405.831i	1.86161	+	1.86161i
$219$		0			0
$220$	−665.335	+	321.969i	−3.02425	+	1.46350i
$221$	−72.0102	+	124.725i	−0.325838	+	0.564368i
$222$		0			0
$223$	132.643	+	132.643i	0.594809	+	0.594809i	0.938927	−	0.344117i	$-0.111822\pi$
$223$	132.643	+	132.643i	0.594809	+	0.594809i	−0.344117	+	0.938927i	$0.611822\pi$
$224$	63.6465	+	76.5532i	0.284136	+	0.341755i
$225$		0			0
$226$	−7.72888	−	13.3868i	−0.0341986	−	0.0592337i
$227$	−63.5422	−	237.143i	−0.279922	−	1.04468i	−0.952471	−	0.304629i	$-0.901467\pi$
$227$	−63.5422	−	237.143i	−0.279922	−	1.04468i	0.672549	−	0.740052i	$-0.265199\pi$
$228$		0			0
$229$	217.561	−	125.609i	0.950047	−	0.548510i	0.0569516	−	0.998377i	$-0.481862\pi$
$229$	217.561	−	125.609i	0.950047	−	0.548510i	0.893096	+	0.449867i	$0.148529\pi$
$230$	−238.162	+	350.751i	−1.03549	+	1.52501i
$231$		0			0
$232$	−520.643	+	520.643i	−2.24415	+	2.24415i
$233$	76.4808	−	285.430i	0.328244	−	1.22502i	−0.582767	−	0.812640i	$-0.698030\pi$
$233$	76.4808	−	285.430i	0.328244	−	1.22502i	0.911010	−	0.412383i	$-0.135304\pi$
$234$		0			0
$235$	−386.977	−	134.583i	−1.64671	−	0.572695i
$236$	374.600	+	648.827i	1.58729	+	2.74927i
$237$		0			0
$238$	−120.821	−	262.198i	−0.507650	−	1.10167i
$239$		−	100.831i		−	0.421885i	−0.977498	−	0.210943i	$-0.932347\pi$
$239$		−	100.831i		−	0.421885i	0.977498	−	0.210943i	$-0.0676533\pi$
$240$		0			0
$241$	−179.672	+	311.201i	−0.745527	+	1.29129i	0.204421	+	0.978883i	$0.434469\pi$
$241$	−179.672	+	311.201i	−0.745527	+	1.29129i	−0.949948	+	0.312408i	$0.898865\pi$
$242$	167.517	+	625.181i	0.692217	+	2.58339i
$243$		0			0
$244$		−	397.160i		−	1.62770i
$245$	172.320	−	174.157i	0.703348	−	0.710846i
$246$		0			0
$247$	43.0453	+	11.5340i	0.174273	+	0.0466962i
$248$	33.7434	−	9.04153i	0.136062	−	0.0364578i
$249$		0			0
$250$	−391.510	−	204.068i	−1.56604	−	0.816274i
$251$	−17.4715			−0.0696075			−0.0348038	−	0.999394i	$-0.511081\pi$
$251$	−17.4715			−0.0696075			−0.0348038	+	0.999394i	$0.511081\pi$
$252$		0			0
$253$	296.100	+	296.100i	1.17035	+	1.17035i
$254$	509.038	−	293.893i	2.00409	−	1.15706i
$255$		0			0
$256$	259.270	−	449.070i	1.01278	−	1.75418i
$257$	−77.1706	−	20.6778i	−0.300275	−	0.0804583i	0.105536	−	0.994415i	$-0.466344\pi$
$257$	−77.1706	−	20.6778i	−0.300275	−	0.0804583i	−0.405811	+	0.913957i	$0.633011\pi$
$258$		0			0
$259$	209.839	−	36.0202i	0.810191	−	0.139074i
$260$	−98.1454	−	513.362i	−0.377482	−	1.97447i
$261$		0			0
$262$	149.236	+	556.957i	0.569604	+	2.12579i
$263$	−167.452	+	44.8686i	−0.636699	+	0.170603i	−0.562708	−	0.826656i	$-0.690240\pi$
$263$	−167.452	+	44.8686i	−0.636699	+	0.170603i	−0.0739911	+	0.997259i	$0.523574\pi$
$264$		0			0
$265$	−8.29704	+	1.58624i	−0.0313096	+	0.00598582i
$266$	−68.6907	+	57.1096i	−0.258236	+	0.214698i
$267$		0			0
$268$	−25.5809	+	95.4694i	−0.0954513	+	0.356229i
$269$	160.485	+	92.6559i	0.596597	+	0.344446i	0.767702	−	0.640807i	$-0.221400\pi$
$269$	160.485	+	92.6559i	0.596597	+	0.344446i	−0.171104	+	0.985253i	$0.554734\pi$
$270$		0			0
$271$	−182.223	−	315.620i	−0.672410	−	1.16465i	−0.977219	−	0.212235i	$-0.931926\pi$
$271$	−182.223	−	315.620i	−0.672410	−	1.16465i	0.304808	−	0.952414i	$-0.401408\pi$
$272$	181.045	−	181.045i	0.665607	−	0.665607i
$273$		0			0
$274$		−	522.152i		−	1.90567i
$275$	−270.584	+	341.964i	−0.983943	+	1.24350i
$276$		0			0
$277$	125.143	+	467.038i	0.451778	+	1.68606i	0.697391	+	0.716691i	$0.254344\pi$
$277$	125.143	+	467.038i	0.451778	+	1.68606i	−0.245613	+	0.969368i	$0.578989\pi$
$278$	92.8347	−	346.464i	0.333938	−	1.24627i
$279$		0			0
$280$	503.659	+	228.856i	1.79878	+	0.817345i
$281$	472.914			1.68297			0.841484	−	0.540282i	$-0.181682\pi$
$281$	472.914			1.68297			0.841484	+	0.540282i	$0.181682\pi$
$282$		0			0
$283$	−239.837	+	64.2640i	−0.847479	+	0.227081i	−0.656324	−	0.754479i	$-0.727890\pi$
$283$	−239.837	+	64.2640i	−0.847479	+	0.227081i	−0.191154	+	0.981560i	$0.561223\pi$
$284$	−492.786	−	284.510i	−1.73516	−	1.00180i
$285$		0			0
$286$	−759.870			−2.65689
$287$	190.366	−	87.7205i	0.663296	−	0.305646i
$288$		0			0
$289$	132.203	−	76.3272i	0.457449	−	0.264108i
$290$	−270.230	+	777.011i	−0.931827	+	2.67935i
$291$		0			0
$292$	−149.607	−	40.0871i	−0.512353	−	0.137284i
$293$	−61.1515	−	61.1515i	−0.208708	−	0.208708i	0.595010	−	0.803718i	$-0.297148\pi$
$293$	−61.1515	−	61.1515i	−0.208708	−	0.208708i	−0.803718	+	0.595010i	$0.797148\pi$
$294$		0			0
$295$	365.671	+	248.292i	1.23956	+	0.841669i
$296$	240.376	+	416.344i	0.812082	+	1.40657i
$297$		0			0
$298$	361.505	−	96.8649i	1.21310	−	0.325050i
$299$	−256.433	+	148.051i	−0.857634	+	0.495155i
$300$		0			0
$301$	182.742	+	67.4526i	0.607117	+	0.224095i
$302$	−402.521	+	402.521i	−1.33285	+	1.33285i
$303$		0			0
$304$	−68.6106	−	39.6123i	−0.225693	−	0.130304i
$305$	−102.065	−	210.912i	−0.334638	−	0.691514i
$306$		0			0
$307$	−36.7448	+	36.7448i	−0.119690	+	0.119690i	−0.764415	−	0.644725i	$-0.776972\pi$
$307$	−36.7448	+	36.7448i	−0.119690	+	0.119690i	0.644725	+	0.764415i	$0.276972\pi$
$308$	597.375	−	844.961i	1.93953	−	2.74338i
$309$		0			0
$310$	29.5360	−	25.5158i	0.0952775	−	0.0823089i
$311$	44.4761	−	77.0348i	0.143010	−	0.247700i	−0.785619	−	0.618711i	$-0.787655\pi$
$311$	44.4761	−	77.0348i	0.143010	−	0.247700i	0.928629	+	0.371010i	$0.120989\pi$
$312$		0			0
$313$	47.5609	−	177.500i	0.151952	−	0.567092i	−0.847395	−	0.530962i	$-0.821831\pi$
$313$	47.5609	−	177.500i	0.151952	−	0.567092i	0.999347	−	0.0361293i	$-0.0115028\pi$
$314$			485.224i			1.54530i
$315$		0			0
$316$	189.873			0.600864
$317$	356.038	+	95.4002i	1.12315	+	0.300947i	0.772157	−	0.635431i	$-0.219178\pi$
$317$	356.038	+	95.4002i	1.12315	+	0.300947i	0.350992	+	0.936378i	$0.385844\pi$
$318$		0			0
$319$	703.676	+	406.268i	2.20588	+	1.27357i
$320$	13.6472	−	186.880i	0.0426475	−	0.583999i
$321$		0			0
$322$	54.4118	−	591.054i	0.168981	−	1.83557i
$323$	29.8321	+	29.8321i	0.0923596	+	0.0923596i
$324$		0			0
$325$	−184.047	−	247.399i	−0.566298	−	0.761227i
$326$	333.540	−	577.709i	1.02313	−	1.77211i
$327$		0			0
$328$	334.668	+	334.668i	1.02033	+	1.02033i
$329$	565.329	−	97.0420i	1.71832	−	0.294961i
$330$		0			0
$331$	224.992	+	389.697i	0.679734	+	1.17733i	0.975061	+	0.221937i	$0.0712381\pi$
$331$	224.992	+	389.697i	0.679734	+	1.17733i	−0.295327	+	0.955396i	$0.595429\pi$
$332$	−162.684	−	607.145i	−0.490012	−	1.82875i
$333$		0			0
$334$	−493.805	+	285.099i	−1.47846	+	0.853589i
$335$	10.9495	+	57.2729i	0.0326852	+	0.170964i
$336$		0			0
$337$	−9.37231	+	9.37231i	−0.0278110	+	0.0278110i	−0.720876	−	0.693065i	$-0.756260\pi$
$337$	−9.37231	+	9.37231i	−0.0278110	+	0.0278110i	0.693065	+	0.720876i	$0.256260\pi$
$338$	−15.4244	+	57.5646i	−0.0456343	+	0.170309i
$339$		0			0
$340$	162.536	−	467.350i	0.478046	−	1.37456i
$341$	−19.2754	−	33.3859i	−0.0565260	−	0.0979060i
$342$		0			0
$343$	−93.2729	+	330.074i	−0.271933	+	0.962316i
$344$			439.849i			1.27863i
$345$		0			0
$346$	368.126	−	637.613i	1.06395	−	1.84281i
$347$	101.459	+	378.650i	0.292389	+	1.09121i	0.943269	+	0.332029i	$0.107733\pi$
$347$	101.459	+	378.650i	0.292389	+	1.09121i	−0.650880	+	0.759180i	$0.725600\pi$
$348$		0			0
$349$		−	480.726i		−	1.37744i	−0.725028	−	0.688720i	$-0.758173\pi$
$349$		−	480.726i		−	1.37744i	0.725028	−	0.688720i	$-0.241827\pi$
$350$	617.921	−	14.9596i	1.76549	−	0.0427416i
$351$		0			0
$352$	239.621	+	64.2062i	0.680741	+	0.182404i
$353$	−535.395	+	143.459i	−1.51670	+	0.406398i	−0.918654	−	0.395064i	$-0.870722\pi$
$353$	−535.395	+	143.459i	−1.51670	+	0.406398i	−0.598045	+	0.801462i	$0.704056\pi$
$354$		0			0
$355$	−334.809	−	24.4500i	−0.943125	−	0.0688732i
$356$	−433.292			−1.21711
$357$		0			0
$358$	−296.944	−	296.944i	−0.829454	−	0.829454i
$359$	87.7247	−	50.6479i	0.244359	−	0.141080i	−0.372820	−	0.927904i	$-0.621609\pi$
$359$	87.7247	−	50.6479i	0.244359	−	0.141080i	0.617178	+	0.786823i	$0.288276\pi$
$360$		0			0
$361$	−173.973	+	301.330i	−0.481919	+	0.834708i
$362$	7.27983	+	1.95062i	0.0201100	+	0.00538846i
$363$		0			0
$364$	467.797	+	562.659i	1.28516	+	1.54577i
$365$	−89.7506	+	17.1587i	−0.245892	+	0.0470100i
$366$		0			0
$367$	−78.8661	−	294.332i	−0.214894	−	0.801996i	−0.986204	−	0.165536i	$-0.947065\pi$
$367$	−78.8661	−	294.332i	−0.214894	−	0.801996i	0.771310	−	0.636460i	$-0.219602\pi$
$368$	508.469	−	136.244i	1.38171	−	0.370228i
$369$		0			0
$370$	444.381	+	301.737i	1.20103	+	0.815505i
$371$	9.09379	−	7.56061i	0.0245116	−	0.0203790i
$372$		0			0
$373$	27.7530	−	103.576i	0.0744048	−	0.277682i	−0.918693	−	0.394973i	$-0.870754\pi$
$373$	27.7530	−	103.576i	0.0744048	−	0.277682i	0.993098	+	0.117290i	$0.0374208\pi$
$374$	−622.999	−	359.689i	−1.66577	−	0.961734i
$375$		0			0
$376$	647.598	+	1121.67i	1.72234	+	2.98317i
$377$	−406.272	+	406.272i	−1.07764	+	1.07764i
$378$		0			0
$379$		0	5.00789e-5i		0	1.32134e-7i	−1.00000		6.60672e-8i	$-1.00000\pi$
$379$		0	5.00789e-5i		0	1.32134e-7i	1.00000		6.60672e-8i	$-2.10298e-8\pi$
$380$	−152.700	−	11.1512i	−0.401843	−	0.0293452i
$381$		0			0
$382$	156.260	+	583.170i	0.409057	+	1.52662i
$383$	−48.7638	+	181.989i	−0.127321	+	0.475167i	−0.999912	−	0.0132843i	$-0.995771\pi$
$383$	−48.7638	+	181.989i	−0.127321	+	0.475167i	0.872591	+	0.488451i	$0.162438\pi$
$384$		0			0
$385$	100.093	−	602.234i	0.259982	−	1.56424i
$386$	−292.757			−0.758439
$387$		0			0
$388$	105.935	−	28.3852i	0.273029	−	0.0731578i
$389$	−182.547	−	105.394i	−0.469273	−	0.270935i	0.246662	−	0.969102i	$-0.420666\pi$
$389$	−182.547	−	105.394i	−0.469273	−	0.270935i	−0.715935	+	0.698166i	$0.754000\pi$
$390$		0			0
$391$	−280.324			−0.716940
$392$	−772.135	+	60.5035i	−1.96973	+	0.154346i
$393$		0			0
$394$	138.595	−	80.0181i	0.351765	−	0.203092i
$395$	100.832	−	48.7947i	0.255271	−	0.123531i
$396$		0			0
$397$	−242.295	−	64.9229i	−0.610316	−	0.163534i	−0.0595944	−	0.998223i	$-0.518981\pi$
$397$	−242.295	−	64.9229i	−0.610316	−	0.163534i	−0.550722	+	0.834689i	$0.685647\pi$
$398$	−63.5338	−	63.5338i	−0.159633	−	0.159633i
$399$		0			0
$400$	202.212	+	509.519i	0.505530	+	1.27380i
$401$	−172.876	−	299.430i	−0.431113	−	0.746709i	0.565857	−	0.824503i	$-0.308545\pi$
$401$	−172.876	−	299.430i	−0.431113	−	0.746709i	−0.996969	+	0.0777947i	$0.975212\pi$
$402$		0			0
$403$	26.3309	−	7.05535i	0.0653373	−	0.0175071i
$404$	−618.942	+	357.346i	−1.53203	+	0.884520i
$405$		0			0
$406$	−194.851	−	1135.12i	−0.479928	−	2.79587i
$407$	375.141	−	375.141i	0.921721	−	0.921721i
$408$		0			0
$409$	−98.4923	−	56.8646i	−0.240812	−	0.139033i	0.374738	−	0.927131i	$-0.377733\pi$
$409$	−98.4923	−	56.8646i	−0.240812	−	0.139033i	−0.615550	+	0.788098i	$0.711066\pi$
$410$	499.461	+	173.703i	1.21820	+	0.423666i
$411$		0			0
$412$	−702.532	+	702.532i	−1.70518	+	1.70518i
$413$	−616.195	−	56.7263i	−1.49200	−	0.137352i
$414$		0			0
$415$	−242.421	−	280.617i	−0.584147	−	0.676185i
$416$	−87.7081	+	151.915i	−0.210837	+	0.365180i
$417$		0			0
$418$	−57.6118	+	215.010i	−0.137827	+	0.514378i
$419$		−	220.394i		−	0.526000i	−0.964796	−	0.263000i	$-0.915288\pi$
$419$		−	220.394i		−	0.526000i	0.964796	−	0.263000i	$-0.0847120\pi$
$420$		0			0
$421$	−611.981			−1.45364			−0.726818	−	0.686830i	$-0.759002\pi$
$421$	−611.981			−1.45364			−0.726818	+	0.686830i	$0.759002\pi$
$422$	−477.618	−	127.977i	−1.13180	−	0.303264i
$423$		0			0
$424$	23.1263	+	13.3520i	0.0545431	+	0.0314905i
$425$	−33.7880	−	289.956i	−0.0795012	−	0.682249i
$426$		0			0
$427$	267.853	+	189.368i	0.627291	+	0.443486i
$428$	856.459	+	856.459i	2.00107	+	2.00107i
$429$		0			0
$430$	214.069	+	442.364i	0.497835	+	1.02875i
$431$	−362.392	+	627.681i	−0.840816	+	1.45634i	0.0483893	+	0.998829i	$0.484591\pi$
$431$	−362.392	+	627.681i	−0.840816	+	1.45634i	−0.889206	+	0.457508i	$0.848742\pi$
$432$		0			0
$433$	−152.433	−	152.433i	−0.352038	−	0.352038i	0.508829	−	0.860867i	$-0.330078\pi$
$433$	−152.433	−	152.433i	−0.352038	−	0.352038i	−0.860867	+	0.508829i	$0.830078\pi$
$434$	−18.9218	+	51.2629i	−0.0435987	+	0.118117i
$435$		0			0
$436$	−688.579	−	1192.65i	−1.57931	−	2.73545i
$437$	22.4499	+	83.7842i	0.0513728	+	0.191726i
$438$		0			0
$439$	−719.426	+	415.361i	−1.63878	+	0.946152i	−0.657530	+	0.753428i	$0.728399\pi$
$439$	−719.426	+	415.361i	−1.63878	+	0.946152i	−0.981253	+	0.192723i	$0.938268\pi$
$440$	1353.99	−	258.858i	3.07725	−	0.588313i
$441$		0			0
$442$	359.692	−	359.692i	0.813783	−	0.813783i
$443$	86.1258	−	321.426i	0.194415	−	0.725566i	−0.798003	−	0.602654i	$-0.794110\pi$
$443$	86.1258	−	321.426i	0.194415	−	0.725566i	0.992418	−	0.122912i	$-0.0392234\pi$
$444$		0			0
$445$	−230.100	+	111.350i	−0.517078	+	0.250225i
$446$	−331.276	−	573.787i	−0.742771	−	1.28652i
$447$		0			0
$448$	109.786	+	238.250i	0.245057	+	0.531809i
$449$			20.5616i			0.0457943i	0.999738	+	0.0228971i	$0.00728902\pi$
$449$			20.5616i			0.0457943i	−0.999738	+	0.0228971i	$0.992711\pi$
$450$		0			0
$451$	261.148	−	452.321i	0.579042	−	1.00293i
$452$	9.59989	+	35.8273i	0.0212387	+	0.0792639i
$453$		0			0
$454$			867.138i			1.91000i
$455$	393.019	+	178.583i	0.863778	+	0.392490i
$456$		0			0
$457$	521.445	+	139.721i	1.14102	+	0.305734i	0.779360	−	0.626577i	$-0.215545\pi$
$457$	521.445	+	139.721i	1.14102	+	0.305734i	0.361657	+	0.932311i	$0.382211\pi$
$458$	−857.070	+	229.651i	−1.87133	+	0.501422i
$459$		0			0
$460$	769.831	−	665.047i	1.67355	−	1.44575i
$461$	−650.544			−1.41116			−0.705579	−	0.708632i	$-0.749313\pi$
$461$	−650.544			−1.41116			−0.705579	+	0.708632i	$0.749313\pi$
$462$		0			0
$463$	229.971	+	229.971i	0.496697	+	0.496697i	0.910408	−	0.413711i	$-0.135768\pi$
$463$	229.971	+	229.971i	0.496697	+	0.496697i	−0.413711	+	0.910408i	$0.635768\pi$
$464$	884.587	−	510.717i	1.90644	−	1.10068i
$465$		0			0
$466$	−521.854	+	903.877i	−1.11986	+	1.93965i
$467$	−564.037	−	151.133i	−1.20779	−	0.323626i	−0.401895	−	0.915686i	$-0.631648\pi$
$467$	−564.037	−	151.133i	−1.20779	−	0.323626i	−0.805894	+	0.592060i	$0.798315\pi$
$468$		0			0
$469$	−52.1895	−	62.7728i	−0.111278	−	0.133844i
$470$	1197.21	+	812.909i	2.54725	+	1.72959i
$471$		0			0
$472$	−361.639	−	1349.66i	−0.766184	−	2.85944i
$473$	468.851	−	125.628i	0.991228	−	0.265599i
$474$		0			0
$475$	−83.9571	+	33.3200i	−0.176752	+	0.0701473i
$476$	117.197	+	682.744i	0.246212	+	1.43434i
$477$		0			0
$478$	−92.1745	+	344.000i	−0.192834	+	0.719665i
$479$	−255.740	−	147.651i	−0.533904	−	0.308249i	0.208701	−	0.977980i	$-0.433076\pi$
$479$	−255.740	−	147.651i	−0.533904	−	0.308249i	−0.742605	+	0.669730i	$0.766410\pi$
$480$		0			0
$481$	187.572	+	324.885i	0.389963	+	0.675436i
$482$	897.465	−	897.465i	1.86196	−	1.86196i
$483$		0			0
$484$		−	1553.05i		−	3.20878i
$485$	48.9622	−	42.2978i	0.100953	−	0.0872120i
$486$		0			0
$487$	−8.56814	−	31.9767i	−0.0175937	−	0.0656606i	0.956571	−	0.291500i	$-0.0941543\pi$
$487$	−8.56814	−	31.9767i	−0.0175937	−	0.0656606i	−0.974165	+	0.225839i	$0.927488\pi$
$488$	−191.709	+	715.468i	−0.392846	+	1.46612i
$489$		0			0
$490$	−747.105	+	436.639i	−1.52470	+	0.891099i
$491$	−602.433			−1.22695			−0.613476	−	0.789713i	$-0.710229\pi$
$491$	−602.433			−1.22695			−0.613476	+	0.789713i	$0.710229\pi$
$492$		0			0
$493$	−525.403	+	140.781i	−1.06573	+	0.285561i
$494$	−136.312	−	78.7000i	−0.275936	−	0.159312i
$495$		0			0
$496$	−48.4619			−0.0977055
$497$	426.844	−	196.689i	0.858841	−	0.395754i
$498$		0			0
$499$	712.187	−	411.181i	1.42723	−	0.824010i	0.430326	−	0.902673i	$-0.358398\pi$
$499$	712.187	−	411.181i	1.42723	−	0.824010i	0.996901	+	0.0786631i	$0.0250651\pi$
$500$	780.688	+	716.123i	1.56138	+	1.43225i
$501$		0			0
$502$	59.6068	+	15.9716i	0.118739	+	0.0318159i
$503$	494.995	+	494.995i	0.984086	+	0.984086i	0.999875	−	0.0157893i	$-0.00502609\pi$
$503$	494.995	+	494.995i	0.984086	+	0.984086i	−0.0157893	+	0.999875i	$0.505026\pi$
$504$		0			0
$505$	−236.856	+	348.828i	−0.469022	+	0.690749i
$506$	−739.512	−	1280.87i	−1.46149	−	2.53137i
$507$		0			0
$508$	−1362.34	+	365.039i	−2.68178	+	0.718580i
$509$	503.114	−	290.473i	0.988437	−	0.570674i	0.0836299	−	0.996497i	$-0.473349\pi$
$509$	503.114	−	290.473i	0.988437	−	0.570674i	0.904807	+	0.425823i	$0.140015\pi$
$510$		0			0
$511$	98.3692	−	81.7844i	0.192503	−	0.160048i
$512$	−759.774	+	759.774i	−1.48393	+	1.48393i
$513$		0			0
$514$	244.377	+	141.091i	0.475442	+	0.274497i
$515$	−192.539	+	553.621i	−0.373861	+	1.07499i
$516$		0			0
$517$	1010.67	−	1010.67i	1.95487	−	1.95487i
$518$	−748.829	−	68.9365i	−1.44562	−	0.133082i
$519$		0			0
$520$	−70.9947	+	972.176i	−0.136528	+	1.86957i
$521$	274.035	−	474.643i	0.525979	−	0.911023i	−0.473563	−	0.880760i	$-0.657032\pi$
$521$	274.035	−	474.643i	0.525979	−	0.911023i	0.999542	−	0.0302629i	$-0.00963445\pi$
$522$		0			0
$523$	60.8889	−	227.240i	0.116422	−	0.434494i	−0.882967	−	0.469435i	$-0.844458\pi$
$523$	60.8889	−	227.240i	0.116422	−	0.434494i	0.999389	+	0.0349409i	$0.0111243\pi$
$524$		−	1383.57i		−	2.64040i
$525$		0			0
$526$	612.306			1.16408
$527$	24.9278	+	6.67937i	0.0473013	+	0.0126743i
$528$		0			0
$529$	−40.9971	−	23.6697i	−0.0774992	−	0.0447442i
$530$	29.7568	+	2.17304i	0.0561449	+	0.00410007i
$531$		0			0
$532$	194.675	−	89.7064i	0.365931	−	0.168621i
$533$	261.151	+	261.151i	0.489964	+	0.489964i
$534$		0			0
$535$	674.921	+	234.725i	1.26153	+	0.438737i
$536$	92.1661	−	159.636i	0.171952	−	0.297829i
$537$		0			0
$538$	−462.818	−	462.818i	−0.860256	−	0.860256i
$539$	285.028	+	805.766i	0.528808	+	1.49493i
$540$		0			0
$541$	261.735	+	453.339i	0.483799	+	0.837965i	0.999827	−	0.0186072i	$-0.00592319\pi$
$541$	261.735	+	453.339i	0.483799	+	0.837965i	−0.516028	+	0.856572i	$0.672590\pi$
$542$	333.159	+	1243.37i	0.614685	+	2.29404i
$543$		0			0
$544$	−143.819	+	83.0342i	−0.264374	+	0.152636i
$545$	−672.165	−	456.404i	−1.23333	−	0.837438i
$546$		0			0
$547$	−201.681	+	201.681i	−0.368703	+	0.368703i	−0.867004	−	0.498301i	$-0.833958\pi$
$547$	−201.681	+	201.681i	−0.368703	+	0.368703i	0.498301	+	0.867004i	$0.333958\pi$
$548$	−324.277	+	1210.22i	−0.591747	+	2.20843i
$549$		0			0
$550$	1235.75	−	919.309i	2.24682	−	1.67147i
$551$	84.1545	+	145.760i	0.152731	+	0.264537i
$552$		0			0
$553$	−90.5327	+	128.054i	−0.163712	+	0.231563i
$554$		−	1707.78i		−	3.08263i
$555$		0			0
$556$	−430.336	+	745.364i	−0.773985	+	1.34058i
$557$	−178.472	−	666.065i	−0.320416	−	1.19581i	−0.918841	−	0.394629i	$-0.870873\pi$
$557$	−178.472	−	666.065i	−0.320416	−	1.19581i	0.598425	−	0.801179i	$-0.295793\pi$
$558$		0			0
$559$			343.226i			0.614000i
$560$	−592.723	−	487.501i	−1.05843	−	0.870537i
$561$		0			0
$562$	−1613.42	−	432.315i	−2.87086	−	0.769244i
$563$	739.166	−	198.059i	1.31291	−	0.351792i	0.466590	−	0.884474i	$-0.345483\pi$
$563$	739.166	−	198.059i	1.31291	−	0.351792i	0.846315	+	0.532682i	$0.178816\pi$
$564$		0			0
$565$	14.3051	+	16.5590i	0.0253188	+	0.0293080i
$566$	876.988			1.54945
$567$		0			0
$568$	750.402	+	750.402i	1.32113	+	1.32113i
$569$	116.121	−	67.0425i	0.204079	−	0.117825i	−0.394478	−	0.918906i	$-0.629074\pi$
$569$	116.121	−	67.0425i	0.204079	−	0.117825i	0.598557	+	0.801080i	$0.295741\pi$
$570$		0			0
$571$	−286.520	+	496.267i	−0.501786	+	0.869119i	0.498212	+	0.867055i	$0.333990\pi$
$571$	−286.520	+	496.267i	−0.501786	+	0.869119i	−0.999998	+	0.00206333i	$0.999343\pi$
$572$	1761.19	+	471.910i	3.07901	+	0.825017i
$573$		0			0
$574$	−729.654	+	125.249i	−1.27117	+	0.218205i
$575$	237.911	−	551.009i	0.413758	−	0.958276i
$576$		0			0
$577$	−178.653	−	666.742i	−0.309624	−	1.15553i	−0.928891	−	0.370352i	$-0.879237\pi$
$577$	−178.653	−	666.742i	−0.309624	−	1.15553i	0.619268	−	0.785180i	$-0.287430\pi$
$578$	−520.805	+	139.549i	−0.901048	+	0.241435i
$579$		0			0
$580$	1108.88	−	1633.10i	1.91186	−	2.81568i
$581$	487.040	+	179.773i	0.838280	+	0.309420i
$582$		0			0
$583$	7.62709	−	28.4647i	0.0130825	−	0.0488245i
$584$	250.161	+	144.430i	0.428358	+	0.247312i
$585$		0			0
$586$	152.726	+	264.530i	0.260625	+	0.451416i
$587$	−688.633	+	688.633i	−1.17314	+	1.17314i	−0.191682	+	0.981457i	$0.561394\pi$
$587$	−688.633	+	688.633i	−1.17314	+	1.17314i	−0.981457	+	0.191682i	$0.938606\pi$
$588$		0			0
$589$		−	7.98542i		−	0.0135576i
$590$	−1020.57	−	1181.37i	−1.72978	−	2.00232i
$591$		0			0
$592$	−172.613	−	644.199i	−0.291576	−	1.08817i
$593$	100.681	−	375.748i	0.169783	−	0.633640i	−0.827598	−	0.561321i	$-0.810293\pi$
$593$	100.681	−	375.748i	0.169783	−	0.633640i	0.997382	−	0.0723188i	$-0.0230399\pi$
$594$		0			0
$595$	237.693	+	332.453i	0.399484	+	0.558745i
$596$	−898.035			−1.50677
$597$		0			0
$598$	1010.20	−	270.683i	1.68930	−	0.452647i
$599$	−223.139	−	128.830i	−0.372520	−	0.215074i	0.302039	−	0.953296i	$-0.402333\pi$
$599$	−223.139	−	128.830i	−0.372520	−	0.215074i	−0.674559	+	0.738221i	$0.735666\pi$
$600$		0			0
$601$	91.8404			0.152813			0.0764064	−	0.997077i	$-0.475655\pi$
$601$	91.8404			0.152813			0.0764064	+	0.997077i	$0.475655\pi$
$602$	−561.793	−	397.180i	−0.933211	−	0.659767i
$603$		0			0
$604$	1182.93	−	682.963i	1.95849	−	1.13073i
$605$	−399.112	−	824.746i	−0.659689	−	1.36322i
$606$		0			0
$607$	759.412	+	203.484i	1.25109	+	0.335229i	0.822757	−	0.568393i	$-0.192435\pi$
$607$	759.412	+	203.484i	1.25109	+	0.335229i	0.428333	+	0.903621i	$0.359101\pi$
$608$	36.3355	+	36.3355i	0.0597623	+	0.0597623i
$609$		0			0
$610$	155.404	+	812.862i	0.254761	+	1.33256i
$611$	505.338	+	875.272i	0.827068	+	1.43252i
$612$		0			0
$613$	407.928	−	109.304i	0.665461	−	0.178310i	0.0897518	−	0.995964i	$-0.471393\pi$
$613$	407.928	−	109.304i	0.665461	−	0.178310i	0.575709	+	0.817654i	$0.304726\pi$
$614$	158.951	−	91.7706i	0.258878	−	0.149464i
$615$		0			0
$616$	−1484.01	+	1233.81i	−2.40911	+	2.00294i
$617$	−174.640	+	174.640i	−0.283047	+	0.283047i	−0.834323	−	0.551276i	$-0.814141\pi$
$617$	−174.640	+	174.640i	−0.283047	+	0.283047i	0.551276	+	0.834323i	$0.314141\pi$
$618$		0			0
$619$	408.198	+	235.673i	0.659448	+	0.380732i	0.792066	−	0.610435i	$-0.209005\pi$
$619$	408.198	+	235.673i	0.659448	+	0.380732i	−0.132619	+	0.991167i	$0.542339\pi$
$620$	−84.3035	+	40.7962i	−0.135973	+	0.0658003i
$621$		0			0
$622$	−222.159	+	222.159i	−0.357169	+	0.357169i
$623$	206.597	−	292.222i	0.331616	−	0.469056i
$624$		0			0
$625$	598.618	+	179.671i	0.957788	+	0.287474i
$626$	−324.524	+	562.091i	−0.518408	+	0.897909i
$627$		0			0
$628$	301.344	−	1124.63i	0.479847	−	1.79081i
$629$			355.153i			0.564631i
$630$		0			0
$631$	−670.413			−1.06246			−0.531230	−	0.847227i	$-0.678270\pi$
$631$	−670.413			−1.06246			−0.531230	+	0.847227i	$0.678270\pi$
$632$	−342.049	−	91.6516i	−0.541216	−	0.145018i
$633$		0			0
$634$	−1127.47	−	650.947i	−1.77835	−	1.02673i
$635$	−629.662	+	543.957i	−0.991594	+	0.856625i
$636$		0			0
$637$	−602.518	+	47.2125i	−0.945868	+	0.0741170i
$638$	−2029.32	−	2029.32i	−3.18075	−	3.18075i
$639$		0			0
$640$	−310.831	+	893.755i	−0.485673	+	1.39649i
$641$	−617.665	+	1069.83i	−0.963596	+	1.66900i	−0.250256	+	0.968180i	$0.580515\pi$
$641$	−617.665	+	1069.83i	−0.963596	+	1.66900i	−0.713341	+	0.700818i	$0.752819\pi$
$642$		0			0
$643$	−504.796	−	504.796i	−0.785064	−	0.785064i	0.195617	−	0.980680i	$-0.437329\pi$
$643$	−504.796	−	504.796i	−0.785064	−	0.785064i	−0.980680	+	0.195617i	$0.937329\pi$
$644$	−493.181	+	1336.12i	−0.765809	+	2.07473i
$645$		0			0
$646$	−74.5061	−	129.048i	−0.115334	−	0.199765i
$647$	−27.8251	−	103.845i	−0.0430064	−	0.160502i	0.941083	−	0.338175i	$-0.109810\pi$
$647$	−27.8251	−	103.845i	−0.0430064	−	0.160502i	−0.984090	+	0.177673i	$0.943143\pi$
$648$		0			0
$649$	−1335.36	+	770.968i	−2.05756	+	1.18793i
$650$	401.746	+	1012.29i	0.618071	+	1.55737i
$651$		0			0
$652$	−1131.84	+	1131.84i	−1.73596	+	1.73596i
$653$	−79.6877	+	297.399i	−0.122033	+	0.455434i	−0.999717	−	0.0238067i	$-0.992421\pi$
$653$	−79.6877	+	297.399i	−0.122033	+	0.455434i	0.877683	+	0.479241i	$0.159088\pi$
$654$		0			0
$655$	−355.558	−	734.745i	−0.542837	−	1.12175i
$656$	−328.287	−	568.610i	−0.500438	−	0.866784i
$657$		0			0
$658$	−2017.42	−	185.722i	−3.06599	−	0.282252i
$659$			590.013i			0.895315i	0.894205	+	0.447658i	$0.147742\pi$
$659$			590.013i			0.895315i	−0.894205	+	0.447658i	$0.852258\pi$
$660$		0			0
$661$	−1.19346	+	2.06714i	−0.00180554	+	0.00312729i	−0.866927	−	0.498436i	$-0.833908\pi$
$661$	−1.19346	+	2.06714i	−0.00180554	+	0.00312729i	0.865121	+	0.501563i	$0.167241\pi$
$662$	−411.354	−	1535.19i	−0.621380	−	2.31902i
$663$		0			0
$664$			1172.27i			1.76547i
$665$	80.3291	−	97.6674i	0.120796	−	0.146868i
$666$		0			0
$667$	−1080.22	−	289.444i	−1.61952	−	0.433948i
$668$	1321.58	−	354.115i	1.97841	−	0.530113i
$669$		0			0
$670$	15.0001	−	205.405i	0.0223882	−	0.306575i
$671$	817.398			1.21818
$672$		0			0
$673$	−50.3354	−	50.3354i	−0.0747925	−	0.0747925i	0.668721	−	0.743513i	$-0.266842\pi$
$673$	−50.3354	−	50.3354i	−0.0747925	−	0.0747925i	−0.743513	+	0.668721i	$0.766842\pi$
$674$	40.5429	−	23.4075i	0.0601527	−	0.0347292i
$675$		0			0
$676$	71.4998	−	123.841i	0.105769	−	0.183197i
$677$	500.800	+	134.189i	0.739734	+	0.198211i	0.608960	−	0.793201i	$-0.291587\pi$
$677$	500.800	+	134.189i	0.739734	+	0.198211i	0.130774	+	0.991412i	$0.458254\pi$
$678$		0			0
$679$	−31.3670	+	84.9793i	−0.0461958	+	0.125154i
$680$	−518.391	+	763.457i	−0.762340	+	1.12273i
$681$		0			0
$682$	35.2413	+	131.522i	0.0516734	+	0.192848i
$683$	97.0866	−	26.0143i	0.142147	−	0.0380883i	−0.187044	−	0.982352i	$-0.559891\pi$
$683$	97.0866	−	26.0143i	0.142147	−	0.0380883i	0.329191	+	0.944263i	$0.393224\pi$
$684$		0			0
$685$	138.802	+	726.022i	0.202631	+	1.05989i
$686$	619.954	−	1040.84i	0.903723	−	1.51726i
$687$		0			0
$688$	157.926	−	589.389i	0.229544	−	0.856670i
$689$	18.0461	+	10.4189i	0.0261917	+	0.0151218i
$690$		0			0
$691$	0.723424	+	1.25301i	0.00104692	+	0.00181332i	0.866548	−	0.499093i	$-0.166333\pi$
$691$	0.723424	+	1.25301i	0.00104692	+	0.00181332i	−0.865501	+	0.500906i	$0.833000\pi$
$692$	−1249.21	+	1249.21i	−1.80521	+	1.80521i
$693$		0			0
$694$		−	1384.57i		−	1.99506i
$695$	−36.9818	+	506.416i	−0.0532112	+	0.728655i
$696$		0			0
$697$	90.4939	+	337.728i	0.129833	+	0.484545i
$698$	−439.457	+	1640.08i	−0.629595	+	2.34968i
$699$		0			0
$700$	−1441.48	−	349.081i	−2.05926	−	0.498687i
$701$	230.081			0.328218			0.164109	−	0.986442i	$-0.447525\pi$
$701$	230.081			0.328218			0.164109	+	0.986442i	$0.447525\pi$
$702$		0			0
$703$	106.149	−	28.4427i	0.150995	−	0.0404590i
$704$	566.098	+	326.837i	0.804117	+	0.464257i
$705$		0			0
$706$	1957.73			2.77299
$707$	54.1135	−	587.813i	0.0765396	−	0.831419i
$708$		0			0
$709$	383.431	−	221.374i	0.540805	−	0.312234i	−0.204600	−	0.978846i	$-0.565589\pi$
$709$	383.431	−	221.374i	0.540805	−	0.312234i	0.745405	+	0.666612i	$0.232256\pi$
$710$	1119.91	+	389.482i	1.57733	+	0.548566i
$711$		0			0
$712$	780.559	+	209.150i	1.09629	+	0.293750i
$713$	37.5183	+	37.5183i	0.0526203	+	0.0526203i
$714$		0			0
$715$	1056.55	−	201.994i	1.47770	−	0.282509i
$716$	503.829	+	872.658i	0.703672	+	1.21880i
$717$		0			0
$718$	−345.587	+	92.5998i	−0.481319	+	0.128969i
$719$	446.525	−	257.801i	0.621036	−	0.358555i	−0.156236	−	0.987720i	$-0.549936\pi$
$719$	446.525	−	257.801i	0.621036	−	0.358555i	0.777272	+	0.629164i	$0.216603\pi$
$720$		0			0
$721$	−138.831	−	808.775i	−0.192553	−	1.12174i
$722$	868.998	−	868.998i	1.20360	−	1.20360i
$723$		0			0
$724$	−15.6614	−	9.04213i	−0.0216318	−	0.0124891i
$725$	169.188	−	1152.22i	0.233363	−	1.58927i
$726$		0			0
$727$	−829.146	+	829.146i	−1.14050	+	1.14050i	−0.152145	+	0.988358i	$0.548618\pi$
$727$	−829.146	+	829.146i	−1.14050	+	1.14050i	−0.988358	+	0.152145i	$0.951382\pi$
$728$	−571.121	−	1239.41i	−0.784507	−	1.70249i
$729$		0			0
$730$	321.884	+	23.5061i	0.440937	+	0.0322001i
$731$	−162.468	+	281.402i	−0.222254	+	0.384956i
$732$		0			0
$733$	266.886	−	996.034i	0.364102	−	1.35885i	−0.504533	−	0.863392i	$-0.668335\pi$
$733$	266.886	−	996.034i	0.364102	−	1.35885i	0.868635	−	0.495453i	$-0.164998\pi$
$734$			1076.26i			1.46629i
$735$		0			0
$736$	−341.433			−0.463904
$737$	−196.486	−	52.6484i	−0.266603	−	0.0714360i
$738$		0			0
$739$	−287.660	−	166.081i	−0.389256	−	0.224737i	0.292582	−	0.956241i	$-0.405486\pi$
$739$	−287.660	−	166.081i	−0.389256	−	0.224737i	−0.681838	+	0.731503i	$0.738819\pi$
$740$	−842.574	−	975.329i	−1.13861	−	1.31801i
$741$		0			0
$742$	−37.9365	+	17.4811i	−0.0511274	+	0.0235595i
$743$	764.980	+	764.980i	1.02958	+	1.02958i	0.999549	+	0.0300340i	$0.00956155\pi$
$743$	764.980	+	764.980i	1.02958	+	1.02958i	0.0300340	+	0.999549i	$0.490438\pi$
$744$		0			0
$745$	−476.902	+	230.783i	−0.640136	+	0.309775i
$746$	−189.368	+	327.994i	−0.253844	+	0.439671i
$747$		0			0
$748$	1220.58	+	1220.58i	1.63179	+	1.63179i
$749$	−985.980	+	169.249i	−1.31640	+	0.225967i
$750$		0			0
$751$	−66.3561	−	114.932i	−0.0883570	−	0.153039i	0.818460	−	0.574564i	$-0.194828\pi$
$751$	−66.3561	−	114.932i	−0.0883570	−	0.153039i	−0.906817	+	0.421525i	$0.861495\pi$
$752$	−465.036	−	1735.54i	−0.618399	−	2.30790i
$753$		0			0
$754$	1757.46	−	1014.67i	2.33084	−	1.34571i
$755$	452.681	−	666.683i	0.599577	−	0.883024i
$756$		0			0
$757$	705.876	−	705.876i	0.932465	−	0.932465i	−0.0653945	−	0.997859i	$-0.520831\pi$
$757$	705.876	−	705.876i	0.932465	−	0.932465i	0.997859	+	0.0653945i	$0.0208306\pi$
$758$	−4.57797e−5	0	0.000170852i	−6.03954e−8	0	2.25399e-7i
$759$		0			0
$760$	269.701	+	93.7968i	0.354869	+	0.123417i
$761$	21.9538	+	38.0250i	0.0288486	+	0.0499672i	0.880089	−	0.474808i	$-0.157483\pi$
$761$	21.9538	+	38.0250i	0.0288486	+	0.0499672i	−0.851241	+	0.524776i	$0.824149\pi$
$762$		0			0
$763$	1132.67	+	104.273i	1.48450	+	0.136661i
$764$		−	1448.69i		−	1.89619i
$765$		0			0
$766$	332.731	−	576.308i	0.434375	−	0.752360i
$767$	−282.197	−	1053.17i	−0.367923	−	1.37311i
$768$		0			0
$769$		−	317.954i		−	0.413464i	−0.978398	−	0.206732i	$-0.933717\pi$
$769$		−	317.954i		−	0.413464i	0.978398	−	0.206732i	$-0.0662829\pi$
$770$	−892.017	+	1963.12i	−1.15846	+	2.54950i
$771$		0			0
$772$	678.539	+	181.814i	0.878937	+	0.235510i
$773$	681.538	−	182.617i	0.881679	−	0.236245i	0.210547	−	0.977584i	$-0.432475\pi$
$773$	681.538	−	182.617i	0.881679	−	0.236245i	0.671131	+	0.741339i	$0.265809\pi$
$774$		0			0
$775$	−34.2853	+	43.3296i	−0.0442391	+	0.0559092i
$776$	−204.540			−0.263582
$777$		0			0
$778$	526.444	+	526.444i	0.676663	+	0.676663i
$779$	93.6941	−	54.0943i	0.120275	−	0.0694407i
$780$		0			0
$781$	585.553	−	1014.21i	0.749748	−	1.29860i
$782$	956.369	+	256.258i	1.22298	+	0.327696i
$783$		0			0
$784$	1056.37	+	196.159i	1.34741	+	0.250203i
$785$	−128.986	−	674.676i	−0.164313	−	0.859460i
$786$		0			0
$787$	−81.4498	−	303.975i	−0.103494	−	0.386245i	0.894676	−	0.446716i	$-0.147406\pi$
$787$	−81.4498	−	303.975i	−0.103494	−	0.386245i	−0.998170	+	0.0604708i	$0.980740\pi$
$788$	−370.924	+	99.3888i	−0.470716	+	0.126128i
$789$		0			0
$790$	−388.611	+	74.2952i	−0.491912	+	0.0940446i
$791$	−28.7400	−	10.6083i	−0.0363337	−	0.0134113i
$792$		0			0
$793$	−149.596	+	558.299i	−0.188645	+	0.704034i
$794$	767.281	+	442.990i	0.966349	+	0.557922i
$795$		0			0
$796$	107.799	+	186.713i	0.135425	+	0.234564i
$797$	−298.666	+	298.666i	−0.374738	+	0.374738i	−0.869200	−	0.494461i	$-0.835365\pi$
$797$	−298.666	+	298.666i	−0.374738	+	0.374738i	0.494461	+	0.869200i	$0.335365\pi$
$798$		0			0
$799$			956.818i			1.19752i
$800$	−41.1537	−	353.165i	−0.0514421	−	0.441456i
$801$		0			0
$802$	316.070	+	1179.59i	0.394102	+	1.47081i
$803$	82.5035	−	307.907i	0.102744	−	0.383446i
$804$		0			0
$805$	81.4615	+	836.289i	0.101194	+	1.03887i
$806$	−96.2819			−0.119456
$807$		0			0
$808$	1287.49	−	344.982i	1.59343	−	0.426958i
$809$	1146.88	+	662.154i	1.41766	+	0.818485i	0.996093	−	0.0883137i	$-0.0281478\pi$
$809$	1146.88	+	662.154i	1.41766	+	0.818485i	0.421564	+	0.906798i	$0.361481\pi$
$810$		0			0
$811$	238.488			0.294067			0.147033	−	0.989132i	$-0.453028\pi$
$811$	238.488			0.294067			0.147033	+	0.989132i	$0.453028\pi$
$812$	−253.341	+	2751.94i	−0.311997	+	3.38909i
$813$		0			0
$814$	−1622.79	+	936.917i	−1.99360	+	1.15100i
$815$	−310.197	+	891.933i	−0.380610	+	1.09440i
$816$		0			0
$817$	97.1180	+	26.0227i	0.118871	+	0.0318515i
$818$	284.040	+	284.040i	0.347237	+	0.347237i
$819$		0			0
$820$	−1049.75	−	712.786i	−1.28018	−	0.869251i
$821$	−276.005	−	478.055i	−0.336182	−	0.582284i	0.647529	−	0.762041i	$-0.275802\pi$
$821$	−276.005	−	478.055i	−0.336182	−	0.582284i	−0.983711	+	0.179756i	$0.942469\pi$
$822$		0			0
$823$	−700.442	+	187.683i	−0.851084	+	0.228047i	−0.657891	−	0.753113i	$-0.728551\pi$
$823$	−700.442	+	187.683i	−0.851084	+	0.228047i	−0.193194	+	0.981161i	$0.561885\pi$
$824$	1604.70	−	926.472i	1.94745	−	1.12436i
$825$		0			0
$826$	2050.39	+	756.827i	2.48231	+	0.916255i
$827$	−403.921	+	403.921i	−0.488417	+	0.488417i	−0.907807	−	0.419389i	$-0.862244\pi$
$827$	−403.921	+	403.921i	−0.488417	+	0.488417i	0.419389	+	0.907807i	$0.362244\pi$
$828$		0			0
$829$	292.544	+	168.900i	0.352887	+	0.203740i	0.665956	−	0.745991i	$-0.268024\pi$
$829$	292.544	+	168.900i	0.352887	+	0.203740i	−0.313069	+	0.949730i	$0.601357\pi$
$830$	570.532	+	1178.98i	0.687388	+	1.42046i
$831$		0			0
$832$	−326.840	+	326.840i	−0.392837	+	0.392837i
$833$	−516.338	−	246.497i	−0.619854	−	0.295914i
$834$		0			0
$835$	610.820	−	527.679i	0.731521	−	0.631951i
$836$	267.060	−	462.561i	0.319449	−	0.553303i
$837$		0			0
$838$	−201.474	+	751.910i	−0.240422	+	0.897268i
$839$		−	1419.09i		−	1.69141i	−0.533649	−	0.845706i	$-0.679180\pi$
$839$		−	1419.09i		−	1.69141i	0.533649	−	0.845706i	$-0.320820\pi$
$840$		0			0
$841$	−1328.99			−1.58025
$842$	2087.87	+	559.444i	2.47966	+	0.664423i
$843$		0			0
$844$	1027.52	+	593.240i	1.21744	+	0.702891i
$845$	6.14448	−	84.1404i	0.00727158	−	0.0995744i
$846$		0			0
$847$	1047.41	+	740.504i	1.23661	+	0.874266i
$848$	−26.1948	−	26.1948i	−0.0308901	−	0.0308901i
$849$		0			0
$850$	−149.790	+	1020.12i	−0.176224	+	1.20014i
$851$	−365.094	+	632.361i	−0.429017	+	0.743080i
$852$		0			0
$853$	−104.379	−	104.379i	−0.122367	−	0.122367i	0.643271	−	0.765638i	$-0.277577\pi$
$853$	−104.379	−	104.379i	−0.122367	−	0.122367i	−0.765638	+	0.643271i	$0.777577\pi$
$854$	−740.713	−	890.920i	−0.867346	−	1.04323i
$855$		0			0
$856$	−1129.46	−	1956.29i	−1.31947	−	2.28539i
$857$	−306.801	−	1145.00i	−0.357995	−	1.33605i	−0.876674	−	0.481085i	$-0.840243\pi$
$857$	−306.801	−	1145.00i	−0.357995	−	1.33605i	0.518679	−	0.854969i	$-0.326424\pi$
$858$		0			0
$859$	−70.8786	+	40.9218i	−0.0825129	+	0.0476388i	−0.540689	−	0.841223i	$-0.681836\pi$
$859$	−70.8786	+	40.9218i	−0.0825129	+	0.0476388i	0.458176	+	0.888862i	$0.348503\pi$
$860$	−221.434	−	1158.24i	−0.257481	−	1.34679i
$861$		0			0
$862$	1810.15	−	1810.15i	2.09995	−	2.09995i
$863$	148.450	−	554.024i	0.172016	−	0.641974i	−0.825024	−	0.565097i	$-0.808839\pi$
$863$	148.450	−	554.024i	0.172016	−	0.641974i	0.997041	−	0.0768766i	$-0.0244948\pi$
$864$		0			0
$865$	−342.363	+	984.420i	−0.395795	+	1.13806i
$866$	380.702	+	659.395i	0.439609	+	0.761426i
$867$		0			0
$868$	75.6924	−	107.064i	0.0872033	−	0.123345i
$869$			390.779i			0.449688i
$870$		0			0
$871$	71.9197	−	124.569i	0.0825714	−	0.143018i
$872$	664.754	+	2480.90i	0.762333	+	2.84506i
$873$		0			0
$874$		−	306.366i		−	0.350533i
$875$	−855.206	+	185.060i	−0.977379	+	0.211498i
$876$		0			0
$877$	−1061.54	−	284.440i	−1.21043	−	0.324333i	−0.403497	−	0.914981i	$-0.632206\pi$
$877$	−1061.54	−	284.440i	−1.21043	−	0.324333i	−0.806929	+	0.590648i	$0.798872\pi$
$878$	2834.14	−	759.406i	3.22795	−	0.864927i
$879$		0			0
$880$	−1907.26	−	139.281i	−2.16734	−	0.158274i
$881$	791.292			0.898175			0.449087	−	0.893488i	$-0.351749\pi$
$881$	791.292			0.898175			0.449087	+	0.893488i	$0.351749\pi$
$882$		0			0
$883$	−364.152	−	364.152i	−0.412403	−	0.412403i	0.470172	−	0.882575i	$-0.344192\pi$
$883$	−364.152	−	364.152i	−0.412403	−	0.412403i	−0.882575	+	0.470172i	$0.844192\pi$
$884$	−1057.06	+	610.294i	−1.19577	+	0.690378i
$885$		0			0
$886$	−587.664	+	1017.86i	−0.663278	+	1.14883i
$887$	−651.280	−	174.510i	−0.734250	−	0.196742i	−0.127729	−	0.991809i	$-0.540769\pi$
$887$	−651.280	−	174.510i	−0.734250	−	0.196742i	−0.606521	+	0.795067i	$0.707435\pi$
$888$		0			0
$889$	403.384	−	1092.85i	0.453751	−	1.22930i
$890$	886.813	−	169.542i	0.996420	−	0.190497i
$891$		0			0
$892$	411.471	+	1535.63i	0.461291	+	1.72156i
$893$	285.977	−	76.6274i	0.320243	−	0.0858090i
$894$		0			0
$895$	491.819	+	333.948i	0.549519	+	0.373126i
$896$	−224.126	−	1305.67i	−0.250141	−	1.45722i
$897$		0			0
$898$	18.7965	−	70.1493i	0.0209315	−	0.0781173i
$899$	89.1617	+	51.4775i	0.0991787	+	0.0572609i
$900$		0			0
$901$	9.86368	+	17.0844i	0.0109475	+	0.0189616i
$902$	−1304.44	+	1304.44i	−1.44616	+	1.44616i
$903$		0			0
$904$		−	69.1753i		−	0.0765213i
$905$	−10.6407	−	0.777054i	−0.0117577	−	0.000858623i
$906$		0			0
$907$	−254.987	−	951.626i	−0.281133	−	1.04920i	−0.951619	−	0.307280i	$-0.900581\pi$
$907$	−254.987	−	951.626i	−0.281133	−	1.04920i	0.670486	−	0.741922i	$-0.266086\pi$
$908$	538.528	−	2009.81i	0.593092	−	2.21345i
$909$		0			0
$910$	−1177.60	−	968.544i	−1.29406	−	1.06433i
$911$	−395.990			−0.434676			−0.217338	−	0.976096i	$-0.569737\pi$
$911$	−395.990			−0.434676			−0.217338	+	0.976096i	$0.569737\pi$
$912$		0			0
$913$	1249.57	−	334.821i	1.36864	−	0.366726i
$914$	−1651.27	−	953.359i	−1.80664	−	1.04306i
$915$		0			0
$916$	2129.10			2.32434
$917$	933.110	+	659.696i	1.01757	+	0.719406i
$918$		0			0
$919$	−967.833	+	558.779i	−1.05314	+	0.608029i	−0.923526	−	0.383536i	$-0.874706\pi$
$919$	−967.833	+	558.779i	−1.05314	+	0.608029i	−0.129612	+	0.991565i	$0.541373\pi$
$920$	−1707.84	+	826.458i	−1.85634	+	0.898324i
$921$		0			0
$922$	2219.43	+	594.696i	2.40720	+	0.645006i
$923$	585.559	+	585.559i	0.634409	+	0.634409i
$924$		0			0
$925$	−698.095	−	301.419i	−0.754697	−	0.325858i
$926$	−574.354	−	994.811i	−0.620253	−	1.07431i
$927$		0			0
$928$	−639.939	+	171.471i	−0.689590	+	0.184775i
$929$	−724.522	+	418.303i	−0.779894	+	0.450272i	−0.836393	−	0.548131i	$-0.815340\pi$
$929$	−724.522	+	418.303i	−0.779894	+	0.450272i	0.0564987	+	0.998403i	$0.482006\pi$
$930$		0			0
$931$	−32.3226	+	174.066i	−0.0347181	+	0.186967i
$932$	1770.87	−	1770.87i	1.90008	−	1.90008i
$933$		0			0
$934$	1786.15	+	1031.23i	1.91236	+	1.10410i
$935$	961.858	+	334.516i	1.02873	+	0.357771i
$936$		0			0
$937$	−406.918	+	406.918i	−0.434277	+	0.434277i	−0.890081	−	0.455803i	$-0.849352\pi$
$937$	−406.918	+	406.918i	−0.434277	+	0.434277i	0.455803	+	0.890081i	$0.349352\pi$
$938$	120.669	+	261.869i	0.128645	+	0.279178i
$939$		0			0
$940$	−2269.98	−	2627.64i	−2.41487	−	2.79536i
$941$	−75.9717	+	131.587i	−0.0807350	+	0.139837i	−0.903566	−	0.428449i	$-0.859060\pi$
$941$	−75.9717	+	131.587i	−0.0807350	+	0.139837i	0.822831	+	0.568286i	$0.192393\pi$
$942$		0			0
$943$	−186.054	+	694.361i	−0.197300	+	0.736332i
$944$			1938.36i			2.05335i
$945$		0			0
$946$	−1714.40			−1.81227
$947$	−532.138	−	142.586i	−0.561920	−	0.150566i	−0.0333318	−	0.999444i	$-0.510612\pi$
$947$	−532.138	−	142.586i	−0.561920	−	0.150566i	−0.528588	+	0.848878i	$0.677278\pi$
$948$		0			0
$949$	195.207	+	112.703i	0.205698	+	0.118760i
$950$	316.893	−	36.9270i	0.333571	−	0.0388705i
$951$		0			0
$952$	118.435	−	1286.51i	0.124406	−	1.35137i
$953$	−12.6759	−	12.6759i	−0.0133010	−	0.0133010i	0.700425	−	0.713726i	$-0.252994\pi$
$953$	−12.6759	−	12.6759i	−0.0133010	−	0.0133010i	−0.713726	+	0.700425i	$0.752994\pi$
$954$		0			0
$955$	−372.292	−	769.325i	−0.389835	−	0.805576i
$956$	427.275	−	740.063i	0.446941	−	0.774124i
$957$		0			0
$958$	737.522	+	737.522i	0.769856	+	0.769856i
$959$	−661.581	−	795.741i	−0.689865	−	0.829761i
$960$		0			0
$961$	478.058	+	828.020i	0.497459	+	0.861623i
$962$	−342.939	−	1279.87i	−0.356485	−	1.33042i
$963$		0			0
$964$	−2637.46	+	1522.74i	−2.73596	+	1.57961i
$965$	407.062	−	77.8228i	0.421826	−	0.0806454i
$966$		0			0
$967$	−674.724	+	674.724i	−0.697750	+	0.697750i	−0.963925	−	0.266175i	$-0.914240\pi$
$967$	−674.724	+	674.724i	−0.697750	+	0.697750i	0.266175	+	0.963925i	$0.414240\pi$
$968$	−749.656	+	2797.75i	−0.774438	+	2.89024i
$969$		0			0
$970$	−205.709	+	99.5470i	−0.212071	+	0.102626i
$971$	−876.594	−	1518.30i	−0.902774	−	1.56365i	−0.823878	−	0.566768i	$-0.808194\pi$
$971$	−876.594	−	1518.30i	−0.902774	−	1.56365i	−0.0788965	−	0.996883i	$-0.525140\pi$
$972$		0			0
$973$	−297.502	−	645.622i	−0.305758	−	0.663538i
$974$			116.926i			0.120048i
$975$		0			0
$976$	513.773	−	889.881i	0.526407	−	0.911763i
$977$	320.764	+	1197.11i	0.328315	+	1.22529i	0.910937	+	0.412546i	$0.135360\pi$
$977$	320.764	+	1197.11i	0.328315	+	1.22529i	−0.582621	+	0.812744i	$0.697973\pi$
$978$		0			0
$979$		−	891.762i		−	0.910891i
$980$	2002.77	−	548.038i	2.04365	−	0.559223i
$981$		0			0
$982$	2055.30	+	550.716i	2.09297	+	0.560810i
$983$	−1036.06	+	277.611i	−1.05398	+	0.282412i	−0.743894	−	0.668297i	$-0.767023\pi$
$983$	−1036.06	+	277.611i	−1.05398	+	0.282412i	−0.310083	+	0.950710i	$0.600357\pi$
$984$		0			0
$985$	−171.438	+	148.103i	−0.174048	+	0.150358i
$986$	1921.19			1.94847
$987$		0			0
$988$	267.062	+	267.062i	0.270306	+	0.270306i
$989$	−578.558	+	334.030i	−0.584992	+	0.337746i
$990$		0			0
$991$	128.143	−	221.951i	0.129307	−	0.223966i	−0.794101	−	0.607785i	$-0.792058\pi$
$991$	128.143	−	221.951i	0.129307	−	0.223966i	0.923408	+	0.383819i	$0.125391\pi$
$992$	30.3619	+	8.13546i	0.0306068	+	0.00820106i
$993$		0			0
$994$	−1636.05	+	280.838i	−1.64593	+	0.282533i
$995$	105.229	+	71.4510i	0.105758	+	0.0718101i
$996$		0			0
$997$	−374.016	−	1395.85i	−0.375141	−	1.40005i	−0.853138	−	0.521685i	$-0.825304\pi$
$997$	−374.016	−	1395.85i	−0.375141	−	1.40005i	0.477997	−	0.878362i	$-0.341363\pi$
$998$	−2805.62	+	751.764i	−2.81124	+	0.753271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.298.2		64
3.2	odd	2		105.3.v.a.88.15	yes	64
5.2	odd	4	inner	315.3.ca.b.172.15		64
7.2	even	3	inner	315.3.ca.b.163.15		64
15.2	even	4		105.3.v.a.67.2	yes	64
21.2	odd	6		105.3.v.a.58.2	yes	64
35.2	odd	12	inner	315.3.ca.b.37.2		64
105.2	even	12		105.3.v.a.37.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.15	✓	64	105.2	even	12
105.3.v.a.58.2	yes	64	21.2	odd	6
105.3.v.a.67.2	yes	64	15.2	even	4
105.3.v.a.88.15	yes	64	3.2	odd	2
315.3.ca.b.37.2		64	35.2	odd	12	inner
315.3.ca.b.163.15		64	7.2	even	3	inner
315.3.ca.b.172.15		64	5.2	odd	4	inner
315.3.ca.b.298.2		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)

\(f(q)\)	\(=\)	\(q+(-3.41166 - 0.914152i) q^{2} +(7.33966 + 4.23756i) q^{4} +(4.98672 + 0.364163i) q^{5} +(-6.35750 + 2.92953i) q^{7} +(-11.1766 - 11.1766i) q^{8} +O(q^{10})\)	\(q+(-3.41166 - 0.914152i) q^{2} +(7.33966 + 4.23756i) q^{4} +(4.98672 + 0.364163i) q^{5} +(-6.35750 + 2.92953i) q^{7} +(-11.1766 - 11.1766i) q^{8} +(-16.6801 - 5.80102i) q^{10} +(-8.72135 + 15.1058i) q^{11} +(-8.72144 - 8.72144i) q^{13} +(24.3677 - 4.18286i) q^{14} +(10.9636 + 18.9894i) q^{16} +(-3.02215 - 11.2788i) q^{17} +(-3.12903 + 1.80655i) q^{19} +(35.0577 + 23.8044i) q^{20} +(43.5633 - 43.5633i) q^{22} +(6.21349 - 23.1890i) q^{23} +(24.7348 + 3.63196i) q^{25} +(21.7819 + 37.7273i) q^{26} +(-59.0760 - 5.43848i) q^{28} -46.5831i q^{29} +(-1.10507 + 1.91403i) q^{31} +(-3.68097 - 13.7376i) q^{32} +41.2423i q^{34} +(-32.7699 + 12.2936i) q^{35} +(-29.3791 - 7.87211i) q^{37} +(12.3266 - 3.30292i) q^{38} +(-51.6647 - 59.8049i) q^{40} -29.9435 q^{41} +(-19.6771 - 19.6771i) q^{43} +(-128.024 + 73.9145i) q^{44} +(-42.3966 + 73.4331i) q^{46} +(-79.1503 - 21.2083i) q^{47} +(31.8357 - 37.2490i) q^{49} +(-81.0665 - 35.0024i) q^{50} +(-27.0549 - 100.970i) q^{52} +(-1.63190 + 0.437265i) q^{53} +(-48.9919 + 72.1526i) q^{55} +(103.798 + 38.3132i) q^{56} +(-42.5841 + 158.926i) q^{58} +(76.5567 + 44.2000i) q^{59} +(-23.4309 - 40.5836i) q^{61} +(5.51984 - 5.51984i) q^{62} -37.4755i q^{64} +(-40.3154 - 46.6674i) q^{65} +(3.01836 + 11.2647i) q^{67} +(25.6131 - 95.5894i) q^{68} +(123.038 - 11.9849i) q^{70} -67.1402 q^{71} +(-17.6525 + 4.72997i) q^{73} +(93.0353 + 53.7140i) q^{74} -30.6214 q^{76} +(11.1930 - 121.585i) q^{77} +(19.4021 - 11.2018i) q^{79} +(47.7569 + 98.6876i) q^{80} +(102.157 + 27.3729i) q^{82} +(-52.4430 - 52.4430i) q^{83} +(-10.9633 - 57.3450i) q^{85} +(49.1438 + 85.1196i) q^{86} +(266.308 - 71.3570i) q^{88} +(-44.2757 + 25.5626i) q^{89} +(80.9964 + 29.8968i) q^{91} +(143.870 - 143.870i) q^{92} +(250.647 + 144.711i) q^{94} +(-16.2615 + 7.86926i) q^{95} +(9.15031 - 9.15031i) q^{97} +(-142.664 + 97.9785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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