LMFDB - Embedded newform 315.3.ca.b.298.7

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			298.7
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.901161 - 0.241465i) q^{2} +(-2.71032 - 1.56480i) q^{4} +(-2.44472 + 4.36158i) q^{5} +(5.41162 - 4.44009i) q^{7} +(4.70337 + 4.70337i) q^{8} +O(q^{10})$	\(q+(-0.901161 - 0.241465i) q^{2} +(-2.71032 - 1.56480i) q^{4} +(-2.44472 + 4.36158i) q^{5} +(5.41162 - 4.44009i) q^{7} +(4.70337 + 4.70337i) q^{8} +(3.25625 - 3.34017i) q^{10} +(-3.17246 + 5.49486i) q^{11} +(-5.74921 - 5.74921i) q^{13} +(-5.94887 + 2.69452i) q^{14} +(3.15641 + 5.46707i) q^{16} +(-0.226953 - 0.847000i) q^{17} +(5.02493 - 2.90114i) q^{19} +(13.4510 - 7.99576i) q^{20} +(4.18571 - 4.18571i) q^{22} +(9.99491 - 37.3015i) q^{23} +(-13.0467 - 21.3256i) q^{25} +(3.79273 + 6.56920i) q^{26} +(-21.6151 + 3.56594i) q^{28} -28.7187i q^{29} +(30.5551 - 52.9230i) q^{31} +(-8.41054 - 31.3886i) q^{32} +0.818085i q^{34} +(6.13593 + 34.4580i) q^{35} +(-11.3239 - 3.03422i) q^{37} +(-5.22880 + 1.40105i) q^{38} +(-32.0125 + 9.01571i) q^{40} -21.6632 q^{41} +(45.3759 + 45.3759i) q^{43} +(17.1967 - 9.92854i) q^{44} +(-18.0141 + 31.2013i) q^{46} +(-49.7271 - 13.3243i) q^{47} +(9.57121 - 48.0561i) q^{49} +(6.60780 + 22.3682i) q^{50} +(6.58580 + 24.5786i) q^{52} +(43.5401 - 11.6665i) q^{53} +(-16.2105 - 27.2703i) q^{55} +(46.3362 + 4.56946i) q^{56} +(-6.93457 + 25.8802i) q^{58} +(-50.4665 - 29.1369i) q^{59} +(-14.0159 - 24.2763i) q^{61} +(-40.3141 + 40.3141i) q^{62} +5.06570i q^{64} +(39.1308 - 11.0204i) q^{65} +(9.00447 + 33.6051i) q^{67} +(-0.710272 + 2.65077i) q^{68} +(2.79094 - 32.5338i) q^{70} -22.2152 q^{71} +(22.4783 - 6.02304i) q^{73} +(9.47198 + 5.46865i) q^{74} -18.1589 q^{76} +(7.22953 + 43.8221i) q^{77} +(127.568 - 73.6514i) q^{79} +(-31.5616 + 0.401515i) q^{80} +(19.5220 + 5.23091i) q^{82} +(86.8716 + 86.8716i) q^{83} +(4.24909 + 1.08080i) q^{85} +(-29.9343 - 51.8478i) q^{86} +(-40.7656 + 10.9231i) q^{88} +(47.6858 - 27.5314i) q^{89} +(-56.6395 - 5.58552i) q^{91} +(-85.4588 + 85.4588i) q^{92} +(41.5948 + 24.0148i) q^{94} +(0.369043 + 29.0091i) q^{95} +(-114.461 + 114.461i) q^{97} +(-20.2291 + 40.9952i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.901161	−	0.241465i	−0.450581	−	0.120733i	0.0263905	−	0.999652i	$-0.491599\pi$
$2$	−0.901161	−	0.241465i	−0.450581	−	0.120733i	−0.476971	+	0.878919i	$0.658265\pi$
$3$		0			0
$3$		0			0
$4$	−2.71032	−	1.56480i	−0.677579	−	0.391200i
$5$	−2.44472	+	4.36158i	−0.488943	+	0.872316i
$5$	−2.44472	+	4.36158i	−0.488943	+	0.872316i
$6$		0			0
$7$	5.41162	−	4.44009i	0.773088	−	0.634298i
$7$	5.41162	−	4.44009i	0.773088	−	0.634298i
$8$	4.70337	+	4.70337i	0.587921	+	0.587921i
$9$		0			0
$10$	3.25625	−	3.34017i	0.325625	−	0.334017i
$11$	−3.17246	+	5.49486i	−0.288405	+	0.499533i	−0.973429	−	0.228988i	$-0.926458\pi$
$11$	−3.17246	+	5.49486i	−0.288405	+	0.499533i	0.685024	+	0.728521i	$0.259792\pi$
$12$		0			0
$13$	−5.74921	−	5.74921i	−0.442247	−	0.442247i	0.450520	−	0.892767i	$-0.351239\pi$
$13$	−5.74921	−	5.74921i	−0.442247	−	0.442247i	−0.892767	+	0.450520i	$0.851239\pi$
$14$	−5.94887	+	2.69452i	−0.424919	+	0.192466i
$15$		0			0
$16$	3.15641	+	5.46707i	0.197276	+	0.341692i
$17$	−0.226953	−	0.847000i	−0.0133502	−	0.0498235i	0.958929	−	0.283645i	$-0.0915436\pi$
$17$	−0.226953	−	0.847000i	−0.0133502	−	0.0498235i	−0.972280	+	0.233821i	$0.924877\pi$
$18$		0			0
$19$	5.02493	−	2.90114i	0.264470	−	0.152692i	−0.361902	−	0.932216i	$-0.617872\pi$
$19$	5.02493	−	2.90114i	0.264470	−	0.152692i	0.626372	+	0.779524i	$0.284539\pi$
$20$	13.4510	−	7.99576i	0.672548	−	0.399788i
$21$		0			0
$22$	4.18571	−	4.18571i	0.190260	−	0.190260i
$23$	9.99491	−	37.3015i	0.434561	−	1.62181i	−0.307552	−	0.951531i	$-0.599510\pi$
$23$	9.99491	−	37.3015i	0.434561	−	1.62181i	0.742114	−	0.670274i	$-0.233823\pi$
$24$		0			0
$25$	−13.0467	−	21.3256i	−0.521869	−	0.853026i
$26$	3.79273	+	6.56920i	0.145874	+	0.252662i
$27$		0			0
$28$	−21.6151	+	3.56594i	−0.771966	+	0.127355i
$29$		−	28.7187i		−	0.990300i	−0.868808	−	0.495150i	$-0.835113\pi$
$29$		−	28.7187i		−	0.990300i	0.868808	−	0.495150i	$-0.164887\pi$
$30$		0			0
$31$	30.5551	−	52.9230i	0.985648	−	1.70719i	0.346626	−	0.938003i	$-0.387327\pi$
$31$	30.5551	−	52.9230i	0.985648	−	1.70719i	0.639022	−	0.769189i	$-0.279339\pi$
$32$	−8.41054	−	31.3886i	−0.262829	−	0.980893i
$33$		0			0
$34$			0.818085i			0.0240613i
$35$	6.13593	+	34.4580i	0.175312	+	0.984513i
$36$		0			0
$37$	−11.3239	−	3.03422i	−0.306051	−	0.0820061i	0.102525	−	0.994730i	$-0.467308\pi$
$37$	−11.3239	−	3.03422i	−0.306051	−	0.0820061i	−0.408576	+	0.912724i	$0.633974\pi$
$38$	−5.22880	+	1.40105i	−0.137600	+	0.0368698i
$39$		0			0
$40$	−32.0125	+	9.01571i	−0.800313	+	0.225393i
$41$	−21.6632			−0.528370			−0.264185	−	0.964472i	$-0.585103\pi$
$41$	−21.6632			−0.528370			−0.264185	+	0.964472i	$0.585103\pi$
$42$		0			0
$43$	45.3759	+	45.3759i	1.05525	+	1.05525i	0.998381	+	0.0568731i	$0.0181131\pi$
$43$	45.3759	+	45.3759i	1.05525	+	1.05525i	0.0568731	+	0.998381i	$0.481887\pi$
$44$	17.1967	−	9.92854i	0.390835	−	0.225649i
$45$		0			0
$46$	−18.0141	+	31.2013i	−0.391610	+	0.678288i
$47$	−49.7271	−	13.3243i	−1.05802	−	0.283497i	−0.312460	−	0.949931i	$-0.601153\pi$
$47$	−49.7271	−	13.3243i	−1.05802	−	0.283497i	−0.745564	+	0.666434i	$0.767820\pi$
$48$		0			0
$49$	9.57121	−	48.0561i	0.195331	−	0.980737i
$50$	6.60780	+	22.3682i	0.132156	+	0.447363i
$51$		0			0
$52$	6.58580	+	24.5786i	0.126650	+	0.472664i
$53$	43.5401	−	11.6665i	0.821511	−	0.220123i	0.176504	−	0.984300i	$-0.443521\pi$
$53$	43.5401	−	11.6665i	0.821511	−	0.220123i	0.645007	+	0.764177i	$0.276854\pi$
$54$		0			0
$55$	−16.2105	−	27.2703i	−0.294736	−	0.495824i
$56$	46.3362	+	4.56946i	0.827432	+	0.0815974i
$57$		0			0
$58$	−6.93457	+	25.8802i	−0.119562	+	0.446210i
$59$	−50.4665	−	29.1369i	−0.855365	−	0.493845i	0.00709232	−	0.999975i	$-0.497742\pi$
$59$	−50.4665	−	29.1369i	−0.855365	−	0.493845i	−0.862457	+	0.506130i	$0.831076\pi$
$60$		0			0
$61$	−14.0159	−	24.2763i	−0.229770	−	0.397973i	0.727970	−	0.685609i	$-0.240464\pi$
$61$	−14.0159	−	24.2763i	−0.229770	−	0.397973i	−0.957740	+	0.287636i	$0.907131\pi$
$62$	−40.3141	+	40.3141i	−0.650228	+	0.650228i
$63$		0			0
$64$			5.06570i			0.0791516i
$65$	39.1308	−	11.0204i	0.602013	−	0.169545i
$66$		0			0
$67$	9.00447	+	33.6051i	0.134395	+	0.501569i	1.00000		0.000841087i	$0.000267726\pi$
$67$	9.00447	+	33.6051i	0.134395	+	0.501569i	−0.865605	+	0.500728i	$0.833066\pi$
$68$	−0.710272	+	2.65077i	−0.0104452	+	0.0389820i
$69$		0			0
$70$	2.79094	−	32.5338i	0.0398706	−	0.464768i
$71$	−22.2152			−0.312890			−0.156445	−	0.987687i	$-0.550003\pi$
$71$	−22.2152			−0.312890			−0.156445	+	0.987687i	$0.550003\pi$
$72$		0			0
$73$	22.4783	−	6.02304i	0.307922	−	0.0825074i	−0.101549	−	0.994831i	$-0.532380\pi$
$73$	22.4783	−	6.02304i	0.307922	−	0.0825074i	0.409471	+	0.912323i	$0.365713\pi$
$74$	9.47198	+	5.46865i	0.128000	+	0.0739007i
$75$		0			0
$76$	−18.1589			−0.238932
$77$	7.22953	+	43.8221i	0.0938900	+	0.569118i
$78$		0			0
$79$	127.568	−	73.6514i	1.61479	−	0.932297i	0.626546	−	0.779385i	$-0.284468\pi$
$79$	127.568	−	73.6514i	1.61479	−	0.932297i	0.988240	−	0.152912i	$-0.0488651\pi$
$80$	−31.5616	+	0.401515i	−0.394520	+	0.00501894i
$81$		0			0
$82$	19.5220	+	5.23091i	0.238073	+	0.0637915i
$83$	86.8716	+	86.8716i	1.04665	+	1.04665i	0.998857	+	0.0477883i	$0.0152173\pi$
$83$	86.8716	+	86.8716i	1.04665	+	1.04665i	0.0477883	+	0.998857i	$0.484783\pi$
$84$		0			0
$85$	4.24909	+	1.08080i	0.0499893	+	0.0127153i
$86$	−29.9343	−	51.8478i	−0.348073	−	0.602881i
$87$		0			0
$88$	−40.7656	+	10.9231i	−0.463245	+	0.124126i
$89$	47.6858	−	27.5314i	0.535795	−	0.309342i	−0.207578	−	0.978219i	$-0.566558\pi$
$89$	47.6858	−	27.5314i	0.535795	−	0.309342i	0.743373	+	0.668877i	$0.233225\pi$
$90$		0			0
$91$	−56.6395	−	5.58552i	−0.622413	−	0.0613794i
$92$	−85.4588	+	85.4588i	−0.928900	+	0.928900i
$93$		0			0
$94$	41.5948	+	24.0148i	0.442498	+	0.255476i
$95$	0.369043	+	29.0091i	0.00388466	+	0.305359i
$96$		0			0
$97$	−114.461	+	114.461i	−1.18001	+	1.18001i	−0.200267	+	0.979741i	$0.564181\pi$
$97$	−114.461	+	114.461i	−1.18001	+	1.18001i	−0.979741	+	0.200267i	$0.935819\pi$
$98$	−20.2291	+	40.9952i	−0.206419	+	0.418318i
$99$		0			0
$100$	1.99036	+	78.2148i	0.0199036	+	0.782148i
$101$	−19.8817	+	34.4360i	−0.196848	+	0.340951i	−0.947505	−	0.319742i	$-0.896404\pi$
$101$	−19.8817	+	34.4360i	−0.196848	+	0.340951i	0.750657	+	0.660692i	$0.229737\pi$
$102$		0			0
$103$	−5.25895	+	19.6267i	−0.0510578	+	0.190550i	−0.986744	−	0.162282i	$-0.948115\pi$
$103$	−5.25895	+	19.6267i	−0.0510578	+	0.190550i	0.935687	+	0.352832i	$0.114781\pi$
$104$		−	54.0813i		−	0.520013i
$105$		0			0
$106$	−42.0537			−0.396733
$107$	92.6228	+	24.8182i	0.865633	+	0.231946i	0.664199	−	0.747556i	$-0.268773\pi$
$107$	92.6228	+	24.8182i	0.865633	+	0.231946i	0.201435	+	0.979502i	$0.435440\pi$
$108$		0			0
$109$	−89.8337	−	51.8655i	−0.824163	−	0.475830i	0.0276872	−	0.999617i	$-0.491186\pi$
$109$	−89.8337	−	51.8655i	−0.824163	−	0.475830i	−0.851850	+	0.523786i	$0.824519\pi$
$110$	8.02344	+	28.4892i	0.0729404	+	0.258993i
$111$		0			0
$112$	41.3556	+	15.5709i	0.369246	+	0.139026i
$113$	−87.9948	−	87.9948i	−0.778715	−	0.778715i	0.200897	−	0.979612i	$-0.435614\pi$
$113$	−87.9948	−	87.9948i	−0.778715	−	0.778715i	−0.979612	+	0.200897i	$0.935614\pi$
$114$		0			0
$115$	138.259	+	134.785i	1.20225	+	1.17205i
$116$	−44.9390	+	77.8367i	−0.387406	+	0.671006i
$117$		0			0
$118$	38.4429	+	38.4429i	0.325788	+	0.325788i
$119$	−4.98894	−	3.57595i	−0.0419238	−	0.0300500i
$120$		0			0
$121$	40.3710	+	69.9246i	0.333645	+	0.577890i
$122$	6.76873	+	25.2612i	0.0554814	+	0.207059i
$123$		0			0
$124$	−165.628	+	95.6253i	−1.33571	+	0.771172i
$125$	124.909	−	4.76920i	0.999272	−	0.0381536i
$126$		0			0
$127$	−105.877	+	105.877i	−0.833679	+	0.833679i	−0.988018	−	0.154339i	$-0.950675\pi$
$127$	−105.877	+	105.877i	−0.833679	+	0.833679i	0.154339	+	0.988018i	$0.450675\pi$
$128$	−32.4190	+	120.989i	−0.253273	+	0.945228i
$129$		0			0
$130$	−37.9242	+	0.482458i	−0.291725	+	0.00371122i
$131$	−77.5089	−	134.249i	−0.591671	−	1.02480i	−0.994007	−	0.109312i	$-0.965135\pi$
$131$	−77.5089	−	134.249i	−0.591671	−	1.02480i	0.402337	−	0.915492i	$-0.368198\pi$
$132$		0			0
$133$	14.3117	−	38.0110i	0.107606	−	0.285797i
$134$		−	32.4579i		−	0.242223i
$135$		0			0
$136$	2.91631	−	5.05120i	0.0214434	−	0.0371411i
$137$	−25.2465	−	94.2214i	−0.184281	−	0.687747i	−0.994783	−	0.102011i	$-0.967472\pi$
$137$	−25.2465	−	94.2214i	−0.184281	−	0.687747i	0.810502	−	0.585736i	$-0.199194\pi$
$138$		0			0
$139$			124.815i			0.897952i	0.893544	+	0.448976i	$0.148211\pi$
$139$			124.815i			0.897952i	−0.893544	+	0.448976i	$0.851789\pi$
$140$	37.2895	−	102.993i	0.266354	−	0.735667i
$141$		0			0
$142$	20.0195	+	5.36420i	0.140982	+	0.0377761i
$143$	49.8302	−	13.3520i	0.348463	−	0.0933704i
$144$		0			0
$145$	125.259	+	70.2090i	0.863854	+	0.484200i
$146$	−21.7109			−0.148705
$147$		0			0
$148$	25.9433	+	25.9433i	0.175293	+	0.175293i
$149$	193.793	−	111.886i	1.30062	−	0.750915i	0.320112	−	0.947380i	$-0.396279\pi$
$149$	193.793	−	111.886i	1.30062	−	0.750915i	0.980511	+	0.196465i	$0.0629461\pi$
$150$		0			0
$151$	28.9470	−	50.1377i	0.191702	−	0.332037i	−0.754112	−	0.656745i	$-0.771933\pi$
$151$	28.9470	−	50.1377i	0.191702	−	0.332037i	0.945814	+	0.324708i	$0.105266\pi$
$152$	37.2792	+	9.98894i	0.245258	+	0.0657167i
$153$		0			0
$154$	4.06654	−	41.2364i	0.0264061	−	0.267769i
$155$	156.129	+	262.650i	1.00728	+	1.69452i
$156$		0			0
$157$	−19.9364	−	74.4038i	−0.126984	−	0.473910i	0.872919	−	0.487865i	$-0.162224\pi$
$157$	−19.9364	−	74.4038i	−0.126984	−	0.473910i	−0.999903	+	0.0139557i	$0.995558\pi$
$158$	−132.744	+	35.5686i	−0.840150	+	0.225117i
$159$		0			0
$160$	157.465	+	40.0529i	0.984156	+	0.250331i
$161$	−111.533	−	246.240i	−0.692754	−	1.52944i
$162$		0			0
$163$	82.4159	−	307.581i	0.505619	−	1.88700i	0.0458718	−	0.998947i	$-0.485393\pi$
$163$	82.4159	−	307.581i	0.505619	−	1.88700i	0.459748	−	0.888050i	$-0.347940\pi$
$164$	58.7140	+	33.8986i	0.358012	+	0.206699i
$165$		0			0
$166$	−57.3088	−	99.2618i	−0.345234	−	0.597963i
$167$	−125.538	+	125.538i	−0.751723	+	0.751723i	−0.974801	−	0.223077i	$-0.928390\pi$
$167$	−125.538	+	125.538i	−0.751723	+	0.751723i	0.223077	+	0.974801i	$0.428390\pi$
$168$		0			0
$169$		−	102.893i		−	0.608835i
$170$	−3.56814	−	1.99998i	−0.0209891	−	0.0117646i
$171$		0			0
$172$	−51.9788	−	193.987i	−0.302202	−	1.12783i
$173$	−46.2175	+	172.486i	−0.267153	+	0.997029i	0.693766	+	0.720200i	$0.255950\pi$
$173$	−46.2175	+	172.486i	−0.267153	+	0.997029i	−0.960919	+	0.276829i	$0.910717\pi$
$174$		0			0
$175$	−165.292	−	57.4776i	−0.944524	−	0.328443i
$176$	−40.0544			−0.227582
$177$		0			0
$178$	−49.6205	+	13.2958i	−0.278767	+	0.0746953i
$179$	−107.202	−	61.8932i	−0.598895	−	0.345772i	0.169712	−	0.985494i	$-0.445716\pi$
$179$	−107.202	−	61.8932i	−0.598895	−	0.345772i	−0.768607	+	0.639722i	$0.779050\pi$
$180$		0			0
$181$	173.845			0.960472			0.480236	−	0.877139i	$-0.340551\pi$
$181$	173.845			0.960472			0.480236	+	0.877139i	$0.340551\pi$
$182$	49.6927	+	18.7099i	0.273037	+	0.102802i
$183$		0			0
$184$	222.453	−	128.433i	1.20898	−	0.698006i
$185$	40.9177	−	41.9722i	0.221177	−	0.226877i
$186$		0			0
$187$	5.37414	+	1.44000i	0.0287387	+	0.00770052i
$188$	113.926	+	113.926i	0.605991	+	0.605991i
$189$		0			0
$190$	6.67212	−	26.2310i	0.0351164	−	0.138058i
$191$	−14.8999	−	25.8073i	−0.0780097	−	0.135117i	0.824381	−	0.566035i	$-0.191523\pi$
$191$	−14.8999	−	25.8073i	−0.0780097	−	0.135117i	−0.902391	+	0.430918i	$0.858190\pi$
$192$		0			0
$193$	−85.9499	+	23.0302i	−0.445336	+	0.119327i	−0.474516	−	0.880247i	$-0.657377\pi$
$193$	−85.9499	+	23.0302i	−0.445336	+	0.119327i	0.0291802	+	0.999574i	$0.490710\pi$
$194$	130.786	−	75.5093i	0.674154	−	0.389223i
$195$		0			0
$196$	−101.139	+	115.270i	−0.516017	+	0.588113i
$197$	15.1895	−	15.1895i	0.0771040	−	0.0771040i	−0.667503	−	0.744607i	$-0.732637\pi$
$197$	15.1895	−	15.1895i	0.0771040	−	0.0771040i	0.744607	+	0.667503i	$0.232637\pi$
$198$		0			0
$199$	−190.662	−	110.079i	−0.958101	−	0.553160i	−0.0625127	−	0.998044i	$-0.519911\pi$
$199$	−190.662	−	110.079i	−0.958101	−	0.553160i	−0.895588	+	0.444885i	$0.853245\pi$
$200$	38.9388	−	161.666i	0.194694	−	0.808330i
$201$		0			0
$202$	26.2317	−	26.2317i	0.129860	−	0.129860i
$203$	−127.514	−	155.415i	−0.628146	−	0.765589i
$204$		0			0
$205$	52.9603	−	94.4856i	0.258343	−	0.460905i
$206$	9.47833	−	16.4169i	0.0460113	−	0.0796939i
$207$		0			0
$208$	13.2844	−	49.5782i	0.0638675	−	0.238357i
$209$			36.8150i			0.176148i
$210$		0			0
$211$	−265.998			−1.26065			−0.630326	−	0.776330i	$-0.717079\pi$
$211$	−265.998			−1.26065			−0.630326	+	0.776330i	$0.717079\pi$
$212$	−136.263	−	36.5116i	−0.642751	−	0.172225i
$213$		0			0
$214$	−77.4753	−	44.7304i	−0.362034	−	0.209021i
$215$	−308.842	+	86.9794i	−1.43647	+	0.404556i
$216$		0			0
$217$	−69.6302	−	422.066i	−0.320877	−	1.94501i
$218$	68.4309	+	68.4309i	0.313903	+	0.313903i
$219$		0			0
$220$	1.26297	+	99.2773i	0.00574077	+	0.451261i
$221$	−3.56478	+	6.17438i	−0.0161302	+	0.0279384i
$222$		0			0
$223$	153.429	+	153.429i	0.688020	+	0.688020i	0.961794	−	0.273774i	$-0.0882719\pi$
$223$	153.429	+	153.429i	0.688020	+	0.688020i	−0.273774	+	0.961794i	$0.588272\pi$
$224$	−184.883	−	132.519i	−0.825369	−	0.591604i
$225$		0			0
$226$	58.0498	+	100.545i	0.256858	+	0.444890i
$227$	−31.4644	−	117.427i	−0.138610	−	0.517298i	−0.999957	−	0.00928178i	$-0.997045\pi$
$227$	−31.4644	−	117.427i	−0.138610	−	0.517298i	0.861347	−	0.508017i	$-0.169621\pi$
$228$		0			0
$229$	−25.0201	+	14.4454i	−0.109258	+	0.0630802i	−0.553633	−	0.832761i	$-0.686759\pi$
$229$	−25.0201	+	14.4454i	−0.109258	+	0.0630802i	0.444375	+	0.895841i	$0.353426\pi$
$230$	−92.0475	−	154.848i	−0.400206	−	0.673252i
$231$		0			0
$232$	135.075	−	135.075i	0.582218	−	0.582218i
$233$	−57.6663	+	215.214i	−0.247495	+	0.923663i	0.724618	+	0.689151i	$0.242016\pi$
$233$	−57.6663	+	215.214i	−0.247495	+	0.923663i	−0.972113	+	0.234513i	$0.924651\pi$
$234$		0			0
$235$	179.684	−	184.314i	0.764612	−	0.784317i
$236$	91.1868	+	157.940i	0.386385	+	0.669238i
$237$		0			0
$238$	3.63237	+	4.42716i	0.0152621	+	0.0186015i
$239$		−	372.324i		−	1.55784i	−0.627124	−	0.778920i	$-0.715768\pi$
$239$		−	372.324i		−	1.55784i	0.627124	−	0.778920i	$-0.284232\pi$
$240$		0			0
$241$	19.9134	−	34.4910i	0.0826282	−	0.143116i	−0.821750	−	0.569848i	$-0.807002\pi$
$241$	19.9134	−	34.4910i	0.0826282	−	0.143116i	0.904378	+	0.426732i	$0.140335\pi$
$242$	−19.4964	−	72.7616i	−0.0805637	−	0.300668i
$243$		0			0
$244$			87.7287i			0.359544i
$245$	186.202	+	159.229i	0.760007	+	0.649915i
$246$		0			0
$247$	−45.5687	−	12.2101i	−0.184489	−	0.0494336i
$248$	392.628	−	105.204i	1.58318	−	0.424211i
$249$		0			0
$250$	−113.715	−	25.8634i	−0.454859	−	0.103454i
$251$	16.5512			0.0659409			0.0329705	−	0.999456i	$-0.489503\pi$
$251$	16.5512			0.0659409			0.0329705	+	0.999456i	$0.489503\pi$
$252$		0			0
$253$	173.258	+	173.258i	0.684815	+	0.684815i
$254$	120.978	−	69.8468i	0.476292	−	0.274987i
$255$		0			0
$256$	68.5608	−	118.751i	0.267816	−	0.463870i
$257$	112.862	+	30.2413i	0.439152	+	0.117670i	0.471619	−	0.881802i	$-0.343670\pi$
$257$	112.862	+	30.2413i	0.439152	+	0.117670i	−0.0324673	+	0.999473i	$0.510336\pi$
$258$		0			0
$259$	−74.7527	+	33.8590i	−0.288621	+	0.130730i
$260$	−123.302	−	31.3631i	−0.474237	−	0.120627i
$261$		0			0
$262$	37.4314	+	139.696i	0.142868	+	0.533191i
$263$	−102.374	+	27.4309i	−0.389253	+	0.104300i	−0.448137	−	0.893965i	$-0.647912\pi$
$263$	−102.374	+	27.4309i	−0.389253	+	0.104300i	0.0588842	+	0.998265i	$0.481246\pi$
$264$		0			0
$265$	−55.5586	+	218.425i	−0.209655	+	0.824245i
$266$	−22.0755	+	30.7983i	−0.0829904	+	0.115783i
$267$		0			0
$268$	28.1804	−	105.171i	0.105151	−	0.392428i
$269$	372.354	+	214.979i	1.38421	+	0.799177i	0.992655	−	0.120976i	$-0.0386024\pi$
$269$	372.354	+	214.979i	1.38421	+	0.799177i	0.391559	+	0.920153i	$0.371936\pi$
$270$		0			0
$271$	120.424	+	208.581i	0.444370	+	0.769671i	0.998008	−	0.0630859i	$-0.0200942\pi$
$271$	120.424	+	208.581i	0.444370	+	0.769671i	−0.553638	+	0.832757i	$0.686761\pi$
$272$	3.91425	−	3.91425i	0.0143906	−	0.0143906i
$273$		0			0
$274$			91.0048i			0.332134i
$275$	158.572	−	4.03523i	0.576624	−	0.0146736i
$276$		0			0
$277$	22.3512	+	83.4157i	0.0806901	+	0.301140i	0.994463	−	0.105085i	$-0.0335116\pi$
$277$	22.3512	+	83.4157i	0.0806901	+	0.301140i	−0.913773	+	0.406225i	$0.866845\pi$
$278$	30.1386	−	112.479i	0.108412	−	0.404600i
$279$		0			0
$280$	−133.209	+	190.928i	−0.475746	+	0.681886i
$281$	369.537			1.31508			0.657539	−	0.753420i	$-0.271597\pi$
$281$	369.537			1.31508			0.657539	+	0.753420i	$0.271597\pi$
$282$		0			0
$283$	−296.803	+	79.5280i	−1.04877	+	0.281018i	−0.741744	−	0.670683i	$-0.766001\pi$
$283$	−296.803	+	79.5280i	−1.04877	+	0.281018i	−0.307028	+	0.951700i	$0.599335\pi$
$284$	60.2102	+	34.7624i	0.212008	+	0.122403i
$285$		0			0
$286$	−48.1291			−0.168284
$287$	−117.233	+	96.1864i	−0.408477	+	0.335144i
$288$		0			0
$289$	249.615	−	144.116i	0.863721	−	0.498670i
$290$	−95.9253	−	93.5153i	−0.330777	−	0.322467i
$291$		0			0
$292$	−70.3481	−	18.8497i	−0.240918	−	0.0645539i
$293$	−296.489	−	296.489i	−1.01191	−	1.01191i	−0.999928	−	0.0119781i	$-0.996187\pi$
$293$	−296.489	−	296.489i	−1.01191	−	1.01191i	−0.0119781	−	0.999928i	$-0.503813\pi$
$294$		0			0
$295$	250.459	−	148.882i	0.849014	−	0.504686i
$296$	−38.9893	−	67.5315i	−0.131721	−	0.228147i
$297$		0			0
$298$	−201.655	+	54.0334i	−0.676695	+	0.181320i
$299$	−271.917	+	156.991i	−0.909422	+	0.525055i
$300$		0			0
$301$	447.031	+	44.0840i	1.48515	+	0.146459i
$302$	−38.1924	+	38.1924i	−0.126465	+	0.126465i
$303$		0			0
$304$	31.7215	+	18.3144i	0.104347	+	0.0602448i
$305$	140.148	−	1.78291i	0.459502	−	0.00584562i
$306$		0			0
$307$	−373.720	+	373.720i	−1.21733	+	1.21733i	−0.248766	+	0.968564i	$0.580025\pi$
$307$	−373.720	+	373.720i	−1.21733	+	1.21733i	−0.968564	+	0.248766i	$0.919975\pi$
$308$	48.9785	−	130.084i	0.159021	−	0.422352i
$309$		0			0
$310$	−77.2766	−	274.390i	−0.249279	−	0.885128i
$311$	−241.180	+	417.737i	−0.775499	+	1.34320i	0.159014	+	0.987276i	$0.449169\pi$
$311$	−241.180	+	417.737i	−0.775499	+	1.34320i	−0.934513	+	0.355928i	$0.884165\pi$
$312$		0			0
$313$	−35.4941	+	132.466i	−0.113400	+	0.423213i	−0.999162	−	0.0409254i	$-0.986969\pi$
$313$	−35.4941	+	132.466i	−0.113400	+	0.423213i	0.885763	+	0.464139i	$0.153636\pi$
$314$			71.8638i			0.228866i
$315$		0			0
$316$	−461.000			−1.45886
$317$	153.392	+	41.1012i	0.483886	+	0.129657i	0.492512	−	0.870306i	$-0.336079\pi$
$317$	153.392	+	41.1012i	0.483886	+	0.129657i	−0.00862536	+	0.999963i	$0.502746\pi$
$318$		0			0
$319$	157.805	+	91.1089i	0.494687	+	0.285608i
$320$	−22.0944	−	12.3842i	−0.0690451	−	0.0387006i
$321$		0			0
$322$	41.0512	+	248.833i	0.127488	+	0.772774i
$323$	−3.59769	−	3.59769i	−0.0111384	−	0.0111384i
$324$		0			0
$325$	−47.5972	+	197.614i	−0.146453	+	0.608043i
$326$	−148.540	+	257.279i	−0.455645	+	0.789199i
$327$		0			0
$328$	−101.890	−	101.890i	−0.310640	−	0.310640i
$329$	−328.265	+	148.687i	−0.997767	+	0.451935i
$330$		0			0
$331$	−114.201	−	197.802i	−0.345018	−	0.597589i	0.640339	−	0.768093i	$-0.278794\pi$
$331$	−114.201	−	197.802i	−0.345018	−	0.597589i	−0.985357	+	0.170503i	$0.945461\pi$
$332$	−99.5127	−	371.386i	−0.299737	−	1.11863i
$333$		0			0
$334$	143.443	−	82.8167i	0.429469	−	0.247954i
$335$	−168.585	−	42.8813i	−0.503238	−	0.128004i
$336$		0			0
$337$	234.580	−	234.580i	0.696082	−	0.696082i	−0.267481	−	0.963563i	$-0.586191\pi$
$337$	234.580	−	234.580i	0.696082	−	0.696082i	0.963563	+	0.267481i	$0.0861912\pi$
$338$	−24.8451	+	92.7233i	−0.0735063	+	0.274329i
$339$		0			0
$340$	−9.82514	−	9.57830i	−0.0288975	−	0.0281715i
$341$	193.869	+	335.792i	0.568532	+	0.984727i
$342$		0			0
$343$	−161.578	−	302.558i	−0.471072	−	0.882095i
$344$			426.840i			1.24081i
$345$		0			0
$346$	83.2988	−	144.278i	0.240748	−	0.416988i
$347$	−7.80239	−	29.1189i	−0.0224853	−	0.0839161i	0.953771	−	0.300533i	$-0.0971645\pi$
$347$	−7.80239	−	29.1189i	−0.0224853	−	0.0839161i	−0.976257	+	0.216617i	$0.930498\pi$
$348$		0			0
$349$		−	292.832i		−	0.839062i	−0.907741	−	0.419531i	$-0.862195\pi$
$349$		−	292.832i		−	0.839062i	0.907741	−	0.419531i	$-0.137805\pi$
$350$	135.076	+	91.7088i	0.385930	+	0.262025i
$351$		0			0
$352$	199.158	+	53.3642i	0.565789	+	0.151603i
$353$	219.306	−	58.7627i	0.621262	−	0.166467i	0.0655606	−	0.997849i	$-0.479116\pi$
$353$	219.306	−	58.7627i	0.621262	−	0.166467i	0.555701	+	0.831382i	$0.312450\pi$
$354$		0			0
$355$	54.3099	−	96.8934i	0.152986	−	0.272939i
$356$	−172.325			−0.484058
$357$		0			0
$358$	81.6613	+	81.6613i	0.228104	+	0.228104i
$359$	−341.968	+	197.435i	−0.952557	+	0.549959i	−0.893874	−	0.448317i	$-0.852023\pi$
$359$	−341.968	+	197.435i	−0.952557	+	0.549959i	−0.0586830	+	0.998277i	$0.518690\pi$
$360$		0			0
$361$	−163.667	+	283.479i	−0.453370	+	0.785261i
$362$	−156.663	−	41.9777i	−0.432770	−	0.115960i
$363$		0			0
$364$	144.771	+	103.768i	0.397722	+	0.285077i
$365$	−28.6831	+	112.765i	−0.0785838	+	0.308947i
$366$		0			0
$367$	62.2669	+	232.383i	0.169665	+	0.633197i	0.997399	+	0.0720767i	$0.0229626\pi$
$367$	62.2669	+	232.383i	0.169665	+	0.633197i	−0.827735	+	0.561120i	$0.810371\pi$
$368$	235.478	−	63.0961i	0.639886	−	0.171457i
$369$		0			0
$370$	−47.0083	+	27.9435i	−0.127049	+	0.0755229i
$371$	183.822	−	256.457i	0.495477	−	0.691258i
$372$		0			0
$373$	−70.5913	+	263.450i	−0.189253	+	0.706301i	0.804427	+	0.594051i	$0.202472\pi$
$373$	−70.5913	+	263.450i	−0.189253	+	0.706301i	−0.993680	+	0.112250i	$0.964194\pi$
$374$	−4.49526	−	2.59534i	−0.0120194	−	0.00693941i
$375$		0			0
$376$	−171.216	−	296.554i	−0.455361	−	0.788708i
$377$	−165.110	+	165.110i	−0.437957	+	0.437957i
$378$		0			0
$379$			492.386i			1.29917i	0.760289	+	0.649585i	$0.225058\pi$
$379$			492.386i			1.29917i	−0.760289	+	0.649585i	$0.774942\pi$
$380$	44.3932	−	79.2013i	0.116824	−	0.208424i
$381$		0			0
$382$	7.19560	+	26.8543i	0.0188366	+	0.0702993i
$383$	179.594	−	670.253i	0.468913	−	1.75001i	−0.174666	−	0.984628i	$-0.555885\pi$
$383$	179.594	−	670.253i	0.468913	−	1.75001i	0.643579	−	0.765379i	$-0.277449\pi$
$384$		0			0
$385$	−208.808	−	75.6004i	−0.542357	−	0.196365i
$386$	83.0157			0.215067
$387$		0			0
$388$	489.333	−	131.116i	1.26117	−	0.337929i
$389$	46.6270	+	26.9201i	0.119864	+	0.0692034i	0.558733	−	0.829347i	$-0.311288\pi$
$389$	46.6270	+	26.9201i	0.119864	+	0.0692034i	−0.438869	+	0.898551i	$0.644621\pi$
$390$		0			0
$391$	−33.8627			−0.0866055
$392$	271.043	−	181.009i	0.691435	−	0.461757i
$393$		0			0
$394$	−17.3559	+	10.0204i	−0.0440506	+	0.0254326i
$395$	9.36891	+	736.455i	0.0237188	+	1.86444i
$396$		0			0
$397$	370.697	+	99.3280i	0.933746	+	0.250196i	0.693451	−	0.720504i	$-0.256089\pi$
$397$	370.697	+	99.3280i	0.933746	+	0.250196i	0.240294	+	0.970700i	$0.422756\pi$
$398$	145.237	+	145.237i	0.364917	+	0.364917i
$399$		0			0
$400$	75.4079	−	138.640i	0.188520	−	0.346600i
$401$	−277.288	−	480.277i	−0.691491	−	1.19770i	−0.971349	−	0.237657i	$-0.923621\pi$
$401$	−277.288	−	480.277i	−0.691491	−	1.19770i	0.279858	−	0.960041i	$-0.409713\pi$
$402$		0			0
$403$	−479.933	+	128.598i	−1.19090	+	0.319101i
$404$	107.771	−	62.2217i	0.266760	−	0.154014i
$405$		0			0
$406$	77.3830	+	170.844i	0.190599	+	0.420797i
$407$	52.5972	−	52.5972i	0.129231	−	0.129231i
$408$		0			0
$409$	230.537	+	133.100i	0.563659	+	0.325429i	0.754613	−	0.656170i	$-0.227825\pi$
$409$	230.537	+	133.100i	0.563659	+	0.325429i	−0.190954	+	0.981599i	$0.561158\pi$
$410$	−70.5408	+	72.3587i	−0.172051	+	0.176485i
$411$		0			0
$412$	44.9653	−	44.9653i	0.109139	−	0.109139i
$413$	−402.476	+	66.3983i	−0.974518	+	0.160771i
$414$		0			0
$415$	−591.274	+	166.521i	−1.42476	+	0.401255i
$416$	−132.105	+	228.813i	−0.317561	+	0.550032i
$417$		0			0
$418$	8.88956	−	33.1763i	0.0212669	−	0.0793691i
$419$			426.729i			1.01845i	0.860635	+	0.509223i	$0.170067\pi$
$419$			426.729i			1.01845i	−0.860635	+	0.509223i	$0.829933\pi$
$420$		0			0
$421$	−115.529			−0.274415			−0.137207	−	0.990542i	$-0.543813\pi$
$421$	−115.529			−0.274415			−0.137207	+	0.990542i	$0.543813\pi$
$422$	239.707	+	64.2292i	0.568026	+	0.152202i
$423$		0			0
$424$	259.657	+	149.913i	0.612399	+	0.353569i
$425$	−15.1018	+	15.8905i	−0.0355337	+	0.0373894i
$426$		0			0
$427$	−183.638	−	69.1421i	−0.430065	−	0.161925i
$428$	−212.201	−	212.201i	−0.495798	−	0.495798i
$429$		0			0
$430$	299.319	−	3.80783i	0.696091	−	0.00885541i
$431$	180.772	−	313.107i	0.419425	−	0.726466i	−0.576456	−	0.817128i	$-0.695565\pi$
$431$	180.772	−	313.107i	0.419425	−	0.726466i	0.995882	+	0.0906620i	$0.0288983\pi$
$432$		0			0
$433$	−132.541	−	132.541i	−0.306098	−	0.306098i	0.537296	−	0.843394i	$-0.319446\pi$
$433$	−132.541	−	132.541i	−0.306098	−	0.306098i	−0.843394	+	0.537296i	$0.819446\pi$
$434$	−39.1663	+	397.163i	−0.0902450	+	0.915122i
$435$		0			0
$436$	162.318	+	281.144i	0.372290	+	0.644825i
$437$	−57.9934	−	216.434i	−0.132708	−	0.495273i
$438$		0			0
$439$	−694.152	+	400.769i	−1.58121	+	0.912913i	−0.586529	+	0.809929i	$0.699506\pi$
$439$	−694.152	+	400.769i	−1.58121	+	0.912913i	−0.994683	+	0.102984i	$0.967161\pi$
$440$	52.0183	−	204.506i	0.118223	−	0.464787i
$441$		0			0
$442$	4.70334	−	4.70334i	0.0106410	−	0.0106410i
$443$	−58.8515	+	219.637i	−0.132848	+	0.495794i	−0.999997	−	0.00225336i	$-0.999283\pi$
$443$	−58.8515	+	219.637i	−0.132848	+	0.495794i	0.867150	+	0.498047i	$0.165949\pi$
$444$		0			0
$445$	3.50216	+	275.292i	0.00787003	+	0.618633i
$446$	−101.216	−	175.312i	−0.226942	−	0.393075i
$447$		0			0
$448$	22.4922	+	27.4136i	0.0502057	+	0.0611911i
$449$		−	662.413i		−	1.47531i	−0.675179	−	0.737654i	$-0.735934\pi$
$449$		−	662.413i		−	1.47531i	0.675179	−	0.737654i	$-0.264066\pi$
$450$		0			0
$451$	68.7255	−	119.036i	0.152385	−	0.263938i
$452$	100.799	+	376.188i	0.223007	+	0.832275i
$453$		0			0
$454$			113.418i			0.249819i
$455$	162.829	−	233.383i	0.357867	−	0.512929i
$456$		0			0
$457$	297.859	+	79.8111i	0.651770	+	0.174641i	0.569529	−	0.821971i	$-0.307126\pi$
$457$	297.859	+	79.8111i	0.651770	+	0.174641i	0.0822410	+	0.996612i	$0.473792\pi$
$458$	26.0352	−	6.97611i	0.0568454	−	0.0152317i
$459$		0			0
$460$	−163.813	−	581.658i	−0.356115	−	1.26447i
$461$	684.929			1.48575			0.742873	−	0.669432i	$-0.233463\pi$
$461$	684.929			1.48575			0.742873	+	0.669432i	$0.233463\pi$
$462$		0			0
$463$	201.578	+	201.578i	0.435375	+	0.435375i	0.890452	−	0.455077i	$-0.150388\pi$
$463$	201.578	+	201.578i	0.435375	+	0.435375i	−0.455077	+	0.890452i	$0.650388\pi$
$464$	157.007	−	90.6481i	0.338377	−	0.195362i
$465$		0			0
$466$	103.933	−	180.018i	0.223033	−	0.386304i
$467$	795.026	+	213.027i	1.70241	+	0.456160i	0.973545	−	0.228496i	$-0.0733808\pi$
$467$	795.026	+	213.027i	1.70241	+	0.456160i	0.728866	+	0.684656i	$0.240047\pi$
$468$		0			0
$469$	197.939	+	141.878i	0.422044	+	0.302511i
$470$	−206.430	+	122.710i	−0.439212	+	0.261084i
$471$		0			0
$472$	−100.321	−	374.404i	−0.212545	−	0.793229i
$473$	−393.288	+	105.381i	−0.831475	+	0.222793i
$474$		0			0
$475$	−127.428	−	69.3094i	−0.268269	−	0.145914i
$476$	7.92595	+	17.4986i	0.0166511	+	0.0367619i
$477$		0			0
$478$	−89.9033	+	335.524i	−0.188082	+	0.701932i
$479$	−686.937	−	396.603i	−1.43411	−	0.827982i	−0.436675	−	0.899619i	$-0.643844\pi$
$479$	−686.937	−	396.603i	−1.43411	−	0.827982i	−0.997431	+	0.0716375i	$0.977178\pi$
$480$		0			0
$481$	47.6590	+	82.5478i	0.0990831	+	0.171617i
$482$	−26.2736	+	26.2736i	−0.0545095	+	0.0545095i
$483$		0			0
$484$		−	252.690i		−	0.522088i
$485$	−219.406	−	779.054i	−0.452383	−	1.60630i
$486$		0			0
$487$	80.1179	+	299.004i	0.164513	+	0.613971i	0.998102	+	0.0615857i	$0.0196158\pi$
$487$	80.1179	+	299.004i	0.164513	+	0.613971i	−0.833589	+	0.552386i	$0.813718\pi$
$488$	48.2584	−	180.103i	0.0988901	−	0.369063i
$489$		0			0
$490$	−129.349	−	188.452i	−0.263978	−	0.384597i
$491$	566.849			1.15448			0.577239	−	0.816575i	$-0.304130\pi$
$491$	566.849			1.15448			0.577239	+	0.816575i	$0.304130\pi$
$492$		0			0
$493$	−24.3247	+	6.51779i	−0.0493402	+	0.0132207i
$494$	38.1164	+	22.0065i	0.0771587	+	0.0445476i
$495$		0			0
$496$	385.778			0.777778
$497$	−120.220	+	98.6375i	−0.241892	+	0.198466i
$498$		0			0
$499$	−426.256	+	246.099i	−0.854220	+	0.493184i	−0.862073	−	0.506785i	$-0.830834\pi$
$499$	−426.256	+	246.099i	−0.854220	+	0.493184i	0.00785223	+	0.999969i	$0.497501\pi$
$500$	−346.006	−	182.532i	−0.692011	−	0.365063i
$501$		0			0
$502$	−14.9153	−	3.99653i	−0.0297117	−	0.00796122i
$503$	113.182	+	113.182i	0.225015	+	0.225015i	0.810606	−	0.585591i	$-0.199138\pi$
$503$	113.182	+	113.182i	0.225015	+	0.225015i	−0.585591	+	0.810606i	$0.699138\pi$
$504$		0			0
$505$	−101.590	−	170.902i	−0.201169	−	0.338419i
$506$	−114.298	−	197.969i	−0.225885	−	0.391244i
$507$		0			0
$508$	452.638	−	121.284i	0.891019	−	0.238748i
$509$	−599.580	+	346.168i	−1.17796	+	0.680094i	−0.955541	−	0.294858i	$-0.904728\pi$
$509$	−599.580	+	346.168i	−1.17796	+	0.680094i	−0.222416	+	0.974952i	$0.571394\pi$
$510$		0			0
$511$	94.9011	−	132.400i	0.185716	−	0.259100i
$512$	263.822	−	263.822i	0.515278	−	0.515278i
$513$		0			0
$514$	−94.4046	−	54.5045i	−0.183667	−	0.106040i
$515$	−72.7466	−	70.9190i	−0.141256	−	0.137707i
$516$		0			0
$517$	230.973	−	230.973i	0.446755	−	0.446755i
$518$	75.5400	−	12.4622i	0.145830	−	0.0240583i
$519$		0			0
$520$	235.880	+	132.213i	0.453615	+	0.254257i
$521$	−216.865	+	375.621i	−0.416248	+	0.720963i	−0.995559	−	0.0941443i	$-0.969988\pi$
$521$	−216.865	+	375.621i	−0.416248	+	0.720963i	0.579311	+	0.815107i	$0.303322\pi$
$522$		0			0
$523$	−46.4148	+	173.222i	−0.0887471	+	0.331209i	−0.995997	−	0.0893824i	$-0.971511\pi$
$523$	−46.4148	+	173.222i	−0.0887471	+	0.331209i	0.907250	+	0.420591i	$0.138177\pi$
$524$			485.144i			0.925847i
$525$		0			0
$526$	98.8787			0.187982
$527$	−51.7603	−	13.8691i	−0.0982169	−	0.0263171i
$528$		0			0
$529$	−833.378	−	481.151i	−1.57538	−	0.909548i
$530$	102.809	−	183.420i	0.193980	−	0.346076i
$531$		0			0
$532$	−98.2688	+	80.6269i	−0.184716	+	0.151554i
$533$	124.546	+	124.546i	0.233670	+	0.233670i
$534$		0			0
$535$	−334.683	+	343.308i	−0.625575	+	0.641697i
$536$	−115.706	+	200.409i	−0.215869	+	0.373897i
$537$		0			0
$538$	−283.641	−	283.641i	−0.527214	−	0.527214i
$539$	233.697	+	205.049i	0.433576	+	0.380424i
$540$		0			0
$541$	−112.946	−	195.629i	−0.208773	−	0.361606i	0.742555	−	0.669785i	$-0.233614\pi$
$541$	−112.946	−	195.629i	−0.208773	−	0.361606i	−0.951328	+	0.308179i	$0.900280\pi$
$542$	−58.1566	−	217.043i	−0.107300	−	0.400449i
$543$		0			0
$544$	−24.6773	+	14.2474i	−0.0453627	+	0.0261902i
$545$	445.833	−	265.020i	0.818043	−	0.486276i
$546$		0			0
$547$	204.480	−	204.480i	0.373821	−	0.373821i	−0.495046	−	0.868867i	$-0.664849\pi$
$547$	204.480	−	204.480i	0.373821	−	0.373821i	0.868867	+	0.495046i	$0.164849\pi$
$548$	−79.0116	+	294.875i	−0.144182	+	0.538094i
$549$		0			0
$550$	−143.873	−	34.6532i	−0.261587	−	0.0630057i
$551$	−83.3170	−	144.309i	−0.151211	−	0.261904i
$552$		0			0
$553$	363.331	−	964.987i	0.657017	−	1.74500i
$554$		−	80.5680i		−	0.145430i
$555$		0			0
$556$	195.311	−	338.289i	0.351279	−	0.608433i
$557$	18.0213	+	67.2563i	0.0323542	+	0.120747i	0.980214	−	0.197939i	$-0.0634249\pi$
$557$	18.0213	+	67.2563i	0.0323542	+	0.120747i	−0.947860	+	0.318687i	$0.896758\pi$
$558$		0			0
$559$		−	521.752i		−	0.933366i
$560$	−169.016	+	142.309i	−0.301815	+	0.254123i
$561$		0			0
$562$	−333.012	−	89.2304i	−0.592549	−	0.158773i
$563$	70.3730	−	18.8564i	0.124996	−	0.0334927i	−0.195778	−	0.980648i	$-0.562723\pi$
$563$	70.3730	−	18.8564i	0.124996	−	0.0334927i	0.320775	+	0.947155i	$0.396057\pi$
$564$		0			0
$565$	598.919	−	168.674i	1.06003	−	0.298538i
$566$	286.670			0.506484
$567$		0			0
$568$	−104.486	−	104.486i	−0.183955	−	0.183955i
$569$	1.86123	−	1.07458i	0.00327105	−	0.00188854i	−0.498364	−	0.866968i	$-0.666066\pi$
$569$	1.86123	−	1.07458i	0.00327105	−	0.00188854i	0.501635	+	0.865080i	$0.332732\pi$
$570$		0			0
$571$	59.6097	−	103.247i	0.104395	−	0.180818i	−0.809096	−	0.587677i	$-0.800043\pi$
$571$	59.6097	−	103.247i	0.104395	−	0.180818i	0.913491	+	0.406859i	$0.133376\pi$
$572$	−155.949	−	41.7864i	−0.272638	−	0.0730531i
$573$		0			0
$574$	128.871	−	58.3718i	0.224515	−	0.101693i
$575$	−925.880	+	273.515i	−1.61023	+	0.475678i
$576$		0			0
$577$	−129.489	−	483.261i	−0.224418	−	0.837540i	−0.982637	−	0.185540i	$-0.940597\pi$
$577$	−129.489	−	483.261i	−0.224418	−	0.837540i	0.758219	−	0.652000i	$-0.226070\pi$
$578$	−259.743	+	69.5978i	−0.449382	+	0.120411i
$579$		0			0
$580$	−229.628	−	386.294i	−0.395910	−	0.666024i
$581$	855.834	+	84.3982i	1.47304	+	0.145264i
$582$		0			0
$583$	−74.0232	+	276.258i	−0.126969	+	0.473856i
$584$	134.052	+	77.3951i	0.229542	+	0.132526i
$585$		0			0
$586$	195.592	+	338.776i	0.333775	+	0.578116i
$587$	201.820	−	201.820i	0.343817	−	0.343817i	−0.513983	−	0.857800i	$-0.671831\pi$
$587$	201.820	−	201.820i	0.343817	−	0.343817i	0.857800	+	0.513983i	$0.171831\pi$
$588$		0			0
$589$		−	354.579i		−	0.602001i
$590$	−261.654	+	73.6898i	−0.443481	+	0.124898i
$591$		0			0
$592$	−19.1545	−	71.4857i	−0.0323556	−	0.120753i
$593$	−167.591	+	625.460i	−0.282616	+	1.05474i	0.667948	+	0.744208i	$0.267173\pi$
$593$	−167.591	+	625.460i	−0.282616	+	1.05474i	−0.950564	+	0.310529i	$0.899494\pi$
$594$		0			0
$595$	27.7933	−	13.0175i	0.0467114	−	0.0218781i
$596$	−700.320			−1.17503
$597$		0			0
$598$	282.949	−	75.8160i	0.473159	−	0.126783i
$599$	710.555	+	410.239i	1.18624	+	0.684873i	0.957449	−	0.288604i	$-0.0931910\pi$
$599$	710.555	+	410.239i	1.18624	+	0.684873i	0.228786	+	0.973477i	$0.426524\pi$
$600$		0			0
$601$	622.468			1.03572			0.517860	−	0.855465i	$-0.326729\pi$
$601$	622.468			1.03572			0.517860	+	0.855465i	$0.326729\pi$
$602$	−392.202	−	147.669i	−0.651498	−	0.245298i
$603$		0			0
$604$	−156.911	+	90.5926i	−0.259786	+	0.149988i
$605$	−403.677	+	5.13544i	−0.667236	+	0.00848833i
$606$		0			0
$607$	518.474	+	138.925i	0.854158	+	0.228871i	0.659225	−	0.751946i	$-0.270884\pi$
$607$	518.474	+	138.925i	0.854158	+	0.228871i	0.194933	+	0.980817i	$0.437551\pi$
$608$	−133.325	−	133.325i	−0.219285	−	0.219285i
$609$		0			0
$610$	−126.727	−	32.2342i	−0.207748	−	0.0528430i
$611$	209.287	+	362.496i	0.342532	+	0.593283i
$612$		0			0
$613$	749.051	−	200.708i	1.22194	−	0.327419i	0.410506	−	0.911858i	$-0.365352\pi$
$613$	749.051	−	200.708i	1.22194	−	0.327419i	0.811437	+	0.584439i	$0.198686\pi$
$614$	427.023	−	246.542i	0.695477	−	0.401534i
$615$		0			0
$616$	−172.108	+	240.115i	−0.279396	+	0.389796i
$617$	−40.4359	+	40.4359i	−0.0655363	+	0.0655363i	−0.739115	−	0.673579i	$-0.764756\pi$
$617$	−40.4359	+	40.4359i	−0.0655363	+	0.0655363i	0.673579	+	0.739115i	$0.264756\pi$
$618$		0			0
$619$	−228.173	−	131.736i	−0.368616	−	0.212821i	0.304238	−	0.952596i	$-0.401598\pi$
$619$	−228.173	−	131.736i	−0.368616	−	0.212821i	−0.672854	+	0.739776i	$0.734932\pi$
$620$	−12.1641	−	956.175i	−0.0196195	−	1.54222i
$621$		0			0
$622$	318.211	−	318.211i	0.511594	−	0.511594i
$623$	135.815	−	360.719i	0.218002	−	0.579003i
$624$		0			0
$625$	−284.566	+	556.460i	−0.455305	+	0.890335i
$626$	63.9718	−	110.802i	0.102191	−	0.177001i
$627$		0			0
$628$	−62.3931	+	232.854i	−0.0993521	+	0.370787i
$629$			10.2800i			0.0163433i
$630$		0			0
$631$	827.879			1.31201			0.656006	−	0.754756i	$-0.272245\pi$
$631$	827.879			1.31201			0.656006	+	0.754756i	$0.272245\pi$
$632$	946.410	+	253.590i	1.49748	+	0.401249i
$633$		0			0
$634$	−128.306	−	74.0777i	−0.202376	−	0.116842i
$635$	−202.952	−	720.632i	−0.319610	−	1.13485i
$636$		0			0
$637$	−331.312	+	221.258i	−0.520113	+	0.347344i
$638$	−120.208	−	120.208i	−0.188414	−	0.188414i
$639$		0			0
$640$	−448.449	−	437.182i	−0.700701	−	0.683097i
$641$	425.709	−	737.350i	0.664133	−	1.15031i	−0.315386	−	0.948963i	$-0.602134\pi$
$641$	425.709	−	737.350i	0.664133	−	1.15031i	0.979520	−	0.201349i	$-0.0645326\pi$
$642$		0			0
$643$	−746.802	−	746.802i	−1.16143	−	1.16143i	−0.984162	−	0.177271i	$-0.943273\pi$
$643$	−746.802	−	746.802i	−1.16143	−	1.16143i	−0.177271	−	0.984162i	$-0.556727\pi$
$644$	−83.0257	+	841.915i	−0.128922	+	1.30732i
$645$		0			0
$646$	2.37338	+	4.11082i	0.00367396	+	0.00636349i
$647$	−12.8027	−	47.7805i	−0.0197879	−	0.0738493i	0.955326	−	0.295555i	$-0.0955044\pi$
$647$	−12.8027	−	47.7805i	−0.0197879	−	0.0738493i	−0.975114	+	0.221705i	$0.928838\pi$
$648$		0			0
$649$	320.206	−	184.871i	0.493384	−	0.284855i
$650$	90.6097	−	166.589i	0.139400	−	0.256291i
$651$		0			0
$652$	−704.676	+	704.676i	−1.08079	+	1.08079i
$653$	−156.550	+	584.252i	−0.239739	+	0.894719i	0.736216	+	0.676747i	$0.236611\pi$
$653$	−156.550	+	584.252i	−0.239739	+	0.894719i	−0.975955	+	0.217972i	$0.930056\pi$
$654$		0			0
$655$	775.026	−	9.85960i	1.18325	−	0.0150528i
$656$	−68.3779	−	118.434i	−0.104235	−	0.180540i
$657$		0			0
$658$	331.723	−	54.7258i	0.504138	−	0.0831700i
$659$		−	388.703i		−	0.589837i	−0.955522	−	0.294919i	$-0.904707\pi$
$659$		−	388.703i		−	0.589837i	0.955522	−	0.294919i	$-0.0952926\pi$
$660$		0			0
$661$	−202.057	+	349.973i	−0.305684	+	0.529460i	−0.977413	−	0.211337i	$-0.932218\pi$
$661$	−202.057	+	349.973i	−0.305684	+	0.529460i	0.671730	+	0.740796i	$0.265552\pi$
$662$	55.1512	+	205.827i	0.0833100	+	0.310917i
$663$		0			0
$664$			817.178i			1.23069i
$665$	130.800	+	155.348i	0.196692	+	0.233605i
$666$		0			0
$667$	−1071.25	−	287.041i	−1.60607	−	0.430346i
$668$	536.689	−	143.805i	0.803426	−	0.215277i
$669$		0			0
$670$	141.568	+	79.3504i	0.211295	+	0.118433i
$671$	177.860			0.265067
$672$		0			0
$673$	141.994	+	141.994i	0.210987	+	0.210987i	0.804687	−	0.593700i	$-0.202333\pi$
$673$	141.994	+	141.994i	0.210987	+	0.210987i	−0.593700	+	0.804687i	$0.702333\pi$
$674$	−268.037	+	154.751i	−0.397681	+	0.229601i
$675$		0			0
$676$	−161.007	+	278.873i	−0.238177	+	0.412534i
$677$	−129.601	−	34.7265i	−0.191434	−	0.0512947i	0.161828	−	0.986819i	$-0.448261\pi$
$677$	−129.601	−	34.7265i	−0.191434	−	0.0512947i	−0.353262	+	0.935524i	$0.614928\pi$
$678$		0			0
$679$	−111.202	+	1127.63i	−0.163773	+	1.66073i
$680$	14.9016	+	25.0684i	0.0219142	+	0.0368654i
$681$		0			0
$682$	−93.6255	−	349.415i	−0.137281	−	0.512339i
$683$	429.989	−	115.215i	0.629560	−	0.168690i	0.0700897	−	0.997541i	$-0.477671\pi$
$683$	429.989	−	115.215i	0.629560	−	0.168690i	0.559470	+	0.828851i	$0.311005\pi$
$684$		0			0
$685$	472.674	+	120.230i	0.690036	+	0.175518i
$686$	72.5502	+	311.669i	0.105758	+	0.454329i
$687$		0			0
$688$	−104.848	+	391.299i	−0.152396	+	0.568748i
$689$	−317.394	−	183.248i	−0.460660	−	0.265962i
$690$		0			0
$691$	−257.093	−	445.297i	−0.372059	−	0.644424i	0.617823	−	0.786317i	$-0.288015\pi$
$691$	−257.093	−	445.297i	−0.372059	−	0.644424i	−0.989882	+	0.141892i	$0.954681\pi$
$692$	395.170	−	395.170i	0.571055	−	0.571055i
$693$		0			0
$694$			28.1248i			0.0405257i
$695$	−544.392	−	305.138i	−0.783297	−	0.439047i
$696$		0			0
$697$	4.91652	+	18.3487i	0.00705383	+	0.0263252i
$698$	−70.7089	+	263.889i	−0.101302	+	0.378065i
$699$		0			0
$700$	358.052	+	414.431i	0.511502	+	0.592044i
$701$	−441.593			−0.629947			−0.314973	−	0.949100i	$-0.601996\pi$
$701$	−441.593			−0.629947			−0.314973	+	0.949100i	$0.601996\pi$
$702$		0			0
$703$	−65.7044	+	17.6054i	−0.0934629	+	0.0250433i
$704$	−27.8353	−	16.0707i	−0.0395388	−	0.0228277i
$705$		0			0
$706$	−211.819			−0.300027
$707$	45.3072	+	274.631i	0.0640837	+	0.388446i
$708$		0			0
$709$	−182.944	+	105.623i	−0.258031	+	0.148974i	−0.623436	−	0.781874i	$-0.714264\pi$
$709$	−182.944	+	105.623i	−0.258031	+	0.148974i	0.365405	+	0.930849i	$0.380931\pi$
$710$	−72.3383	+	74.2026i	−0.101885	+	0.104511i
$711$		0			0
$712$	353.774	+	94.7935i	0.496874	+	0.133137i
$713$	−1668.71	−	1668.71i	−2.34041	−	2.34041i
$714$		0			0
$715$	−63.5851	+	249.980i	−0.0889302	+	0.349623i
$716$	193.701	+	335.500i	0.270532	+	0.468576i
$717$		0			0
$718$	355.842	−	95.3476i	0.495602	−	0.132796i
$719$	149.598	−	86.3704i	0.208064	−	0.120126i	−0.392347	−	0.919817i	$-0.628337\pi$
$719$	149.598	−	86.3704i	0.208064	−	0.120126i	0.600411	+	0.799691i	$0.295004\pi$
$720$		0			0
$721$	58.6848	+	129.562i	0.0813936	+	0.179698i
$722$	215.940	−	215.940i	0.299087	−	0.299087i
$723$		0			0
$724$	−471.176	−	272.034i	−0.650796	−	0.375737i
$725$	−612.444	+	374.685i	−0.844751	+	0.516807i
$726$		0			0
$727$	81.3739	−	81.3739i	0.111931	−	0.111931i	−0.648923	−	0.760854i	$-0.724780\pi$
$727$	81.3739	−	81.3739i	0.111931	−	0.111931i	0.760854	+	0.648923i	$0.224780\pi$
$728$	−240.126	−	292.667i	−0.329843	−	0.402016i
$729$		0			0
$730$	53.0770	−	94.6939i	0.0727083	−	0.129718i
$731$	28.1352	−	48.7316i	0.0384887	−	0.0666643i
$732$		0			0
$733$	162.793	−	607.551i	0.222091	−	0.828856i	−0.761458	−	0.648214i	$-0.775516\pi$
$733$	162.793	−	607.551i	0.222091	−	0.828856i	0.983549	−	0.180641i	$-0.0578173\pi$
$734$		−	224.450i		−	0.305790i
$735$		0			0
$736$	−1254.90			−1.70503
$737$	−213.222	−	57.1326i	−0.289311	−	0.0775205i
$738$		0			0
$739$	879.807	+	507.957i	1.19054	+	0.687357i	0.958429	−	0.285333i	$-0.0921041\pi$
$739$	879.807	+	507.957i	1.19054	+	0.687357i	0.232109	+	0.972690i	$0.425437\pi$
$740$	−176.578	+	49.7298i	−0.238619	+	0.0672024i
$741$		0			0
$742$	−227.579	+	186.722i	−0.306710	+	0.251647i
$743$	827.334	+	827.334i	1.11351	+	1.11351i	0.992673	+	0.120832i	$0.0385562\pi$
$743$	827.334	+	827.334i	1.11351	+	1.11351i	0.120832	+	0.992673i	$0.461444\pi$
$744$		0			0
$745$	14.2326	+	1118.77i	0.0191042	+	1.50171i
$746$	127.228	−	220.366i	0.170547	−	0.295397i
$747$		0			0
$748$	−12.3123	−	12.3123i	−0.0164603	−	0.0164603i
$749$	611.434	−	276.947i	0.816334	−	0.369755i
$750$		0			0
$751$	−36.7464	−	63.6466i	−0.0489299	−	0.0847491i	0.840523	−	0.541776i	$-0.182248\pi$
$751$	−36.7464	−	63.6466i	−0.0489299	−	0.0847491i	−0.889453	+	0.457027i	$0.848914\pi$
$752$	−84.1143	−	313.919i	−0.111854	−	0.417445i
$753$		0			0
$754$	188.659	−	108.922i	0.250211	−	0.144459i
$755$	147.912	+	248.827i	0.195910	+	0.329572i
$756$		0			0
$757$	270.218	−	270.218i	0.356958	−	0.356958i	−0.505732	−	0.862691i	$-0.668778\pi$
$757$	270.218	−	270.218i	0.356958	−	0.356958i	0.862691	+	0.505732i	$0.168778\pi$
$758$	118.894	−	443.719i	0.156852	−	0.585381i
$759$		0			0
$760$	−134.705	+	138.176i	−0.177243	+	0.181811i
$761$	461.228	+	798.870i	0.606082	+	1.04976i	0.991880	+	0.127181i	$0.0405928\pi$
$761$	461.228	+	798.870i	0.606082	+	1.04976i	−0.385798	+	0.922583i	$0.626074\pi$
$762$		0			0
$763$	−716.433	+	118.193i	−0.938969	+	0.154906i
$764$			93.2612i			0.122070i
$765$		0			0
$766$	−323.686	+	560.640i	−0.422566	+	0.731906i
$767$	122.629	+	457.657i	0.159881	+	0.596684i
$768$		0			0
$769$		−	638.346i		−	0.830099i	−0.909799	−	0.415050i	$-0.863764\pi$
$769$		−	638.346i		−	0.830099i	0.909799	−	0.415050i	$-0.136236\pi$
$770$	169.914	+	118.548i	0.220668	+	0.153958i
$771$		0			0
$772$	268.989	+	72.0754i	0.348431	+	0.0933619i
$773$	610.759	−	163.652i	0.790115	−	0.211711i	0.158876	−	0.987299i	$-0.449213\pi$
$773$	610.759	−	163.652i	0.790115	−	0.211711i	0.631240	+	0.775588i	$0.282546\pi$
$774$		0			0
$775$	−1527.26	+	38.8648i	−1.97066	+	0.0501481i
$776$	−1076.70			−1.38750
$777$		0			0
$778$	−35.5182	−	35.5182i	−0.0456532	−	0.0456532i
$779$	−108.856	+	62.8480i	−0.139738	+	0.0806778i
$780$		0			0
$781$	70.4768	−	122.069i	0.0902392	−	0.156299i
$782$	30.5158	+	8.17668i	0.0390228	+	0.0104561i
$783$		0			0
$784$	292.937	−	99.3585i	0.373644	−	0.126733i
$785$	373.257	+	94.9418i	0.475487	+	0.120945i
$786$		0			0
$787$	66.9318	+	249.793i	0.0850468	+	0.317399i	0.995323	−	0.0966025i	$-0.0307975\pi$
$787$	66.9318	+	249.793i	0.0850468	+	0.317399i	−0.910276	+	0.414001i	$0.864131\pi$
$788$	−64.9369	+	17.3998i	−0.0824072	+	0.0220809i
$789$		0			0
$790$	169.385	−	665.927i	0.214412	−	0.842945i
$791$	−866.899	−	85.4895i	−1.09595	−	0.108078i
$792$		0			0
$793$	−58.9891	+	220.150i	−0.0743873	+	0.277617i
$794$	−310.073	−	179.021i	−0.390521	−	0.225467i
$795$		0			0
$796$	344.503	+	596.696i	0.432793	+	0.749619i
$797$	−406.066	+	406.066i	−0.509493	+	0.509493i	−0.914371	−	0.404878i	$-0.867314\pi$
$797$	−406.066	+	406.066i	−0.509493	+	0.509493i	0.404878	+	0.914371i	$0.367314\pi$
$798$		0			0
$799$			45.1428i			0.0564992i
$800$	−559.651	+	588.878i	−0.699564	+	0.736098i
$801$		0			0
$802$	133.911	+	499.762i	0.166971	+	0.623145i
$803$	−38.2157	+	142.623i	−0.0475912	+	0.177613i
$804$		0			0
$805$	1346.66	+	115.525i	1.67287	+	0.143509i
$806$	463.549			0.575123
$807$		0			0
$808$	−255.476	+	68.4546i	−0.316183	+	0.0847211i
$809$	577.593	+	333.474i	0.713959	+	0.412205i	0.812525	−	0.582926i	$-0.198092\pi$
$809$	577.593	+	333.474i	0.713959	+	0.412205i	−0.0985659	+	0.995131i	$0.531426\pi$
$810$		0			0
$811$	−1163.00			−1.43403			−0.717013	−	0.697060i	$-0.754491\pi$
$811$	−1163.00			−1.43403			−0.717013	+	0.697060i	$0.754491\pi$
$812$	102.409	+	620.756i	0.126119	+	0.764478i
$813$		0			0
$814$	−60.0989	+	34.6981i	−0.0738316	+	0.0426267i
$815$	1140.05	+	1111.41i	1.39884	+	1.36369i
$816$		0			0
$817$	359.653	+	96.3687i	0.440212	+	0.117954i
$818$	−175.611	−	175.611i	−0.214684	−	0.214684i
$819$		0			0
$820$	−291.390	+	173.213i	−0.355354	+	0.211236i
$821$	−240.295	−	416.202i	−0.292685	−	0.506946i	0.681758	−	0.731577i	$-0.261215\pi$
$821$	−240.295	−	416.202i	−0.292685	−	0.506946i	−0.974444	+	0.224632i	$0.927882\pi$
$822$		0			0
$823$	863.634	−	231.410i	1.04937	−	0.281179i	0.307380	−	0.951587i	$-0.400548\pi$
$823$	863.634	−	231.410i	1.04937	−	0.281179i	0.741993	+	0.670408i	$0.233881\pi$
$824$	−117.046	+	67.5767i	−0.142046	+	0.0820106i
$825$		0			0
$826$	378.729	+	37.3484i	0.458509	+	0.0452160i
$827$	−563.481	+	563.481i	−0.681356	+	0.681356i	−0.960306	−	0.278950i	$-0.910014\pi$
$827$	−563.481	+	563.481i	−0.681356	+	0.681356i	0.278950	+	0.960306i	$0.410014\pi$
$828$		0			0
$829$	−81.3692	−	46.9785i	−0.0981534	−	0.0566689i	0.450120	−	0.892968i	$-0.351381\pi$
$829$	−81.3692	−	46.9785i	−0.0981534	−	0.0566689i	−0.548273	+	0.836299i	$0.684715\pi$
$830$	573.042	−	7.29003i	0.690412	−	0.00878317i
$831$		0			0
$832$	29.1238	−	29.1238i	0.0350045	−	0.0350045i
$833$	−42.8757	+	2.79966i	−0.0514715	+	0.00336094i
$834$		0			0
$835$	−240.639	−	854.447i	−0.288190	−	1.02329i
$836$	57.6082	−	99.7804i	0.0689094	−	0.119355i
$837$		0			0
$838$	103.040	−	384.551i	0.122960	−	0.458892i
$839$		−	65.5829i		−	0.0781679i	−0.999236	−	0.0390840i	$-0.987556\pi$
$839$		−	65.5829i		−	0.0781679i	0.999236	−	0.0390840i	$-0.0124440\pi$
$840$		0			0
$841$	16.2369			0.0193066
$842$	104.110	+	27.8962i	0.123646	+	0.0331308i
$843$		0			0
$844$	720.938	+	416.234i	0.854192	+	0.493168i
$845$	448.776	+	251.544i	0.531096	+	0.297686i
$846$		0			0
$847$	528.944	+	199.155i	0.624491	+	0.235129i
$848$	201.212	+	201.212i	0.237279	+	0.237279i
$849$		0			0
$850$	17.4462	−	10.6733i	0.0205249	−	0.0125569i
$851$	−226.362	+	392.071i	−0.265996	+	0.460718i
$852$		0			0
$853$	368.911	+	368.911i	0.432486	+	0.432486i	0.889473	−	0.456987i	$-0.151072\pi$
$853$	368.911	+	368.911i	0.432486	+	0.432486i	−0.456987	+	0.889473i	$0.651072\pi$
$854$	148.792	+	106.650i	0.174229	+	0.124883i
$855$		0			0
$856$	318.910	+	552.368i	0.372558	+	0.645290i
$857$	−158.199	−	590.408i	−0.184597	−	0.688924i	−0.994717	−	0.102660i	$-0.967265\pi$
$857$	−158.199	−	590.408i	−0.184597	−	0.688924i	0.810120	−	0.586264i	$-0.199402\pi$
$858$		0			0
$859$	494.728	−	285.631i	0.575934	−	0.332516i	−0.183582	−	0.983004i	$-0.558769\pi$
$859$	494.728	−	285.631i	0.575934	−	0.332516i	0.759516	+	0.650489i	$0.225436\pi$
$860$	973.165	+	247.535i	1.13159	+	0.287831i
$861$		0			0
$862$	−238.509	+	238.509i	−0.276693	+	0.276693i
$863$	−232.269	+	866.839i	−0.269141	+	1.00445i	0.690525	+	0.723308i	$0.257379\pi$
$863$	−232.269	+	866.839i	−0.269141	+	1.00445i	−0.959667	+	0.281141i	$0.909287\pi$
$864$		0			0
$865$	−639.323	−	623.261i	−0.739101	−	0.720532i
$866$	87.4365	+	151.444i	0.100966	+	0.174878i
$867$		0			0
$868$	−471.730	+	1252.89i	−0.543468	+	1.44342i
$869$			934.625i			1.07552i
$870$		0			0
$871$	141.434	−	244.972i	0.162382	−	0.281253i
$872$	−178.578	−	666.464i	−0.204792	−	0.764293i
$873$		0			0
$874$			209.045i			0.239182i
$875$	654.784	−	580.416i	0.748325	−	0.663333i
$876$		0			0
$877$	853.633	+	228.730i	0.973355	+	0.260810i	0.710244	−	0.703956i	$-0.248585\pi$
$877$	853.633	+	228.730i	0.973355	+	0.260810i	0.263111	+	0.964765i	$0.415251\pi$
$878$	722.315	−	193.544i	0.822682	−	0.220437i
$879$		0			0
$880$	97.9215	−	174.700i	0.111274	−	0.198523i
$881$	−492.018			−0.558476			−0.279238	−	0.960222i	$-0.590082\pi$
$881$	−492.018			−0.558476			−0.279238	+	0.960222i	$0.590082\pi$
$882$		0			0
$883$	−645.402	−	645.402i	−0.730919	−	0.730919i	0.239882	−	0.970802i	$-0.422891\pi$
$883$	−645.402	−	645.402i	−0.730919	−	0.730919i	−0.970802	+	0.239882i	$0.922891\pi$
$884$	19.3234	−	11.1563i	0.0218590	−	0.0126203i
$885$		0			0
$886$	106.069	−	183.717i	0.119717	−	0.207356i
$887$	−356.023	−	95.3960i	−0.401379	−	0.107549i	0.0524818	−	0.998622i	$-0.483287\pi$
$887$	−356.023	−	95.3960i	−0.401379	−	0.107549i	−0.453860	+	0.891073i	$0.649954\pi$
$888$		0			0
$889$	−102.863	+	1043.07i	−0.115706	+	1.17331i
$890$	63.3174	−	248.928i	0.0711432	−	0.279694i
$891$		0			0
$892$	−175.755	−	655.925i	−0.197034	−	0.735342i
$893$	−288.531	+	77.3117i	−0.323103	+	0.0865752i
$894$		0			0
$895$	532.031	−	316.259i	0.594448	−	0.353362i
$896$	361.764	+	798.691i	0.403754	+	0.891396i
$897$		0			0
$898$	−159.950	+	596.941i	−0.178118	+	0.664745i
$899$	−1519.88	−	877.502i	−1.69063	−	0.976087i
$900$		0			0
$901$	−19.7631	−	34.2307i	−0.0219346	−	0.0379919i
$902$	−90.6758	+	90.6758i	−0.100528	+	0.100528i
$903$		0			0
$904$		−	827.744i		−	0.915646i
$905$	−425.003	+	758.240i	−0.469616	+	0.837835i
$906$		0			0
$907$	313.795	+	1171.10i	0.345971	+	1.29118i	0.891474	+	0.453071i	$0.149672\pi$
$907$	313.795	+	1171.10i	0.345971	+	1.29118i	−0.545504	+	0.838108i	$0.683662\pi$
$908$	−98.4711	+	367.499i	−0.108448	+	0.404735i
$909$		0			0
$910$	−203.089	+	170.998i	−0.223175	+	0.187910i
$911$	−897.922			−0.985644			−0.492822	−	0.870130i	$-0.664035\pi$
$911$	−897.922			−0.985644			−0.492822	+	0.870130i	$0.664035\pi$
$912$		0			0
$913$	−752.944	+	201.751i	−0.824692	+	0.220976i
$914$	−249.147	−	143.845i	−0.272590	−	0.157380i
$915$		0			0
$916$	90.4165			0.0987080
$917$	−1015.53	−	382.360i	−1.10745	−	0.416968i
$918$		0			0
$919$	1425.32	−	822.906i	1.55094	−	0.895437i	0.552877	−	0.833263i	$-0.313530\pi$
$919$	1425.32	−	822.906i	1.55094	−	0.895437i	0.998065	−	0.0621736i	$-0.0198032\pi$
$920$	16.3375	+	1284.23i	0.0177581	+	1.39590i
$921$		0			0
$922$	−617.231	−	165.387i	−0.669448	−	0.179378i
$923$	127.720	+	127.720i	0.138375	+	0.138375i
$924$		0			0
$925$	83.0328	+	281.076i	0.0897652	+	0.303866i
$926$	−132.980	−	230.329i	−0.143607	−	0.248735i
$927$		0			0
$928$	−901.438	+	241.540i	−0.971378	+	0.260280i
$929$	801.774	−	462.904i	0.863051	−	0.498282i	−0.00198210	−	0.999998i	$-0.500631\pi$
$929$	801.774	−	462.904i	0.863051	−	0.498282i	0.865033	+	0.501716i	$0.167298\pi$
$930$		0			0
$931$	−91.3231	−	269.246i	−0.0980914	−	0.289201i
$932$	493.060	−	493.060i	0.529035	−	0.529035i
$933$		0			0
$934$	−665.008	−	383.943i	−0.712000	−	0.411073i
$935$	−19.4189	+	19.9194i	−0.0207689	+	0.0213041i
$936$		0			0
$937$	−77.9145	+	77.9145i	−0.0831531	+	0.0831531i	−0.747460	−	0.664307i	$-0.768727\pi$
$937$	−77.9145	+	77.9145i	−0.0831531	+	0.0831531i	0.664307	+	0.747460i	$0.268727\pi$
$938$	−144.116	−	175.650i	−0.153642	−	0.187260i
$939$		0			0
$940$	−775.415	+	218.381i	−0.824910	+	0.232320i
$941$	656.896	−	1137.78i	0.698083	−	1.20912i	−0.271047	−	0.962566i	$-0.587370\pi$
$941$	656.896	−	1137.78i	0.698083	−	1.20912i	0.969130	−	0.246550i	$-0.0792968\pi$
$942$		0			0
$943$	−216.521	+	808.069i	−0.229609	+	0.856913i
$944$		−	367.872i		−	0.389695i
$945$		0			0
$946$	379.862			0.401545
$947$	−296.162	−	79.3565i	−0.312738	−	0.0837978i	0.0990364	−	0.995084i	$-0.468424\pi$
$947$	−296.162	−	79.3565i	−0.312738	−	0.0837978i	−0.411774	+	0.911286i	$0.635091\pi$
$948$		0			0
$949$	−163.860	−	94.6047i	−0.172666	−	0.0996889i
$950$	98.0970	+	93.2283i	0.103260	+	0.0981350i
$951$		0			0
$952$	−6.64581	−	40.2838i	−0.00698089	−	0.0423149i
$953$	266.647	+	266.647i	0.279797	+	0.279797i	0.833028	−	0.553231i	$-0.186605\pi$
$953$	266.647	+	266.647i	0.279797	+	0.279797i	−0.553231	+	0.833028i	$0.686605\pi$
$954$		0			0
$955$	148.986	−	1.89535i	0.156007	−	0.00198466i
$956$	−582.612	+	1009.11i	−0.609427	+	1.05556i
$957$		0			0
$958$	523.275	+	523.275i	0.546216	+	0.546216i
$959$	−554.976	−	397.793i	−0.578703	−	0.414800i
$960$		0			0
$961$	−1386.73	−	2401.88i	−1.44300	−	2.49936i
$962$	−23.0160	−	85.8969i	−0.0239251	−	0.0892899i
$963$		0			0
$964$	−107.943	+	62.3210i	−0.111974	+	0.0646484i
$965$	109.675	−	431.179i	0.113653	−	0.446818i
$966$		0			0
$967$	273.152	−	273.152i	0.282474	−	0.282474i	−0.551621	−	0.834095i	$-0.685990\pi$
$967$	273.152	−	273.152i	0.282474	−	0.282474i	0.834095	+	0.551621i	$0.185990\pi$
$968$	−139.002	+	518.761i	−0.143597	+	0.535910i
$969$		0			0
$970$	9.60524	+	755.032i	0.00990231	+	0.778383i
$971$	22.8872	+	39.6418i	0.0235707	+	0.0408257i	0.877570	−	0.479448i	$-0.159163\pi$
$971$	22.8872	+	39.6418i	0.0235707	+	0.0408257i	−0.853999	+	0.520274i	$0.825830\pi$
$972$		0			0
$973$	554.191	+	675.453i	0.569569	+	0.694196i
$974$		−	288.797i		−	0.296506i
$975$		0			0
$976$	88.4802	−	153.252i	0.0906560	−	0.157021i
$977$	391.814	+	1462.27i	0.401038	+	1.49669i	0.811248	+	0.584702i	$0.198788\pi$
$977$	391.814	+	1462.27i	0.401038	+	1.49669i	−0.410211	+	0.911991i	$0.634545\pi$
$978$		0			0
$979$			349.369i			0.356863i
$980$	−255.503	−	722.930i	−0.260718	−	0.737684i
$981$		0			0
$982$	−510.822	−	136.874i	−0.520186	−	0.139383i
$983$	629.846	−	168.767i	0.640739	−	0.171685i	0.0762007	−	0.997093i	$-0.475721\pi$
$983$	629.846	−	168.767i	0.640739	−	0.171685i	0.564538	+	0.825407i	$0.309054\pi$
$984$		0			0
$985$	29.1162	+	103.384i	0.0295596	+	0.104959i
$986$	23.4943			0.0238279
$987$		0			0
$988$	104.399	+	104.399i	0.105667	+	0.105667i
$989$	2146.12	−	1239.06i	2.16999	−	1.25284i
$990$		0			0
$991$	−35.1066	+	60.8064i	−0.0354254	+	0.0613586i	−0.883195	−	0.469007i	$-0.844612\pi$
$991$	−35.1066	+	60.8064i	−0.0354254	+	0.0613586i	0.847769	+	0.530365i	$0.177945\pi$
$992$	−1918.16	−	513.969i	−1.93363	−	0.518114i
$993$		0			0
$994$	132.155	−	59.8593i	0.132953	−	0.0602206i
$995$	946.232	−	562.476i	0.950987	−	0.565303i
$996$		0			0
$997$	−205.022	−	765.152i	−0.205639	−	0.767454i	−0.989254	−	0.146208i	$-0.953293\pi$
$997$	−205.022	−	765.152i	−0.205639	−	0.767454i	0.783615	−	0.621247i	$-0.213373\pi$
$998$	443.550	−	118.849i	0.444439	−	0.119087i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.298.7		64
3.2	odd	2		105.3.v.a.88.10	yes	64
5.2	odd	4	inner	315.3.ca.b.172.10		64
7.2	even	3	inner	315.3.ca.b.163.10		64
15.2	even	4		105.3.v.a.67.7	yes	64
21.2	odd	6		105.3.v.a.58.7	yes	64
35.2	odd	12	inner	315.3.ca.b.37.7		64
105.2	even	12		105.3.v.a.37.10	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.10	✓	64	105.2	even	12
105.3.v.a.58.7	yes	64	21.2	odd	6
105.3.v.a.67.7	yes	64	15.2	even	4
105.3.v.a.88.10	yes	64	3.2	odd	2
315.3.ca.b.37.7		64	35.2	odd	12	inner
315.3.ca.b.163.10		64	7.2	even	3	inner
315.3.ca.b.172.10		64	5.2	odd	4	inner
315.3.ca.b.298.7		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)

\(f(q)\)	\(=\)	\(q+(-0.901161 - 0.241465i) q^{2} +(-2.71032 - 1.56480i) q^{4} +(-2.44472 + 4.36158i) q^{5} +(5.41162 - 4.44009i) q^{7} +(4.70337 + 4.70337i) q^{8} +O(q^{10})\)	\(q+(-0.901161 - 0.241465i) q^{2} +(-2.71032 - 1.56480i) q^{4} +(-2.44472 + 4.36158i) q^{5} +(5.41162 - 4.44009i) q^{7} +(4.70337 + 4.70337i) q^{8} +(3.25625 - 3.34017i) q^{10} +(-3.17246 + 5.49486i) q^{11} +(-5.74921 - 5.74921i) q^{13} +(-5.94887 + 2.69452i) q^{14} +(3.15641 + 5.46707i) q^{16} +(-0.226953 - 0.847000i) q^{17} +(5.02493 - 2.90114i) q^{19} +(13.4510 - 7.99576i) q^{20} +(4.18571 - 4.18571i) q^{22} +(9.99491 - 37.3015i) q^{23} +(-13.0467 - 21.3256i) q^{25} +(3.79273 + 6.56920i) q^{26} +(-21.6151 + 3.56594i) q^{28} -28.7187i q^{29} +(30.5551 - 52.9230i) q^{31} +(-8.41054 - 31.3886i) q^{32} +0.818085i q^{34} +(6.13593 + 34.4580i) q^{35} +(-11.3239 - 3.03422i) q^{37} +(-5.22880 + 1.40105i) q^{38} +(-32.0125 + 9.01571i) q^{40} -21.6632 q^{41} +(45.3759 + 45.3759i) q^{43} +(17.1967 - 9.92854i) q^{44} +(-18.0141 + 31.2013i) q^{46} +(-49.7271 - 13.3243i) q^{47} +(9.57121 - 48.0561i) q^{49} +(6.60780 + 22.3682i) q^{50} +(6.58580 + 24.5786i) q^{52} +(43.5401 - 11.6665i) q^{53} +(-16.2105 - 27.2703i) q^{55} +(46.3362 + 4.56946i) q^{56} +(-6.93457 + 25.8802i) q^{58} +(-50.4665 - 29.1369i) q^{59} +(-14.0159 - 24.2763i) q^{61} +(-40.3141 + 40.3141i) q^{62} +5.06570i q^{64} +(39.1308 - 11.0204i) q^{65} +(9.00447 + 33.6051i) q^{67} +(-0.710272 + 2.65077i) q^{68} +(2.79094 - 32.5338i) q^{70} -22.2152 q^{71} +(22.4783 - 6.02304i) q^{73} +(9.47198 + 5.46865i) q^{74} -18.1589 q^{76} +(7.22953 + 43.8221i) q^{77} +(127.568 - 73.6514i) q^{79} +(-31.5616 + 0.401515i) q^{80} +(19.5220 + 5.23091i) q^{82} +(86.8716 + 86.8716i) q^{83} +(4.24909 + 1.08080i) q^{85} +(-29.9343 - 51.8478i) q^{86} +(-40.7656 + 10.9231i) q^{88} +(47.6858 - 27.5314i) q^{89} +(-56.6395 - 5.58552i) q^{91} +(-85.4588 + 85.4588i) q^{92} +(41.5948 + 24.0148i) q^{94} +(0.369043 + 29.0091i) q^{95} +(-114.461 + 114.461i) q^{97} +(-20.2291 + 40.9952i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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