LMFDB - Embedded newform 315.3.ca.b.163.2

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			163.2
Character	$\chi$	$=$	315.163
Dual form			315.3.ca.b.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.853412 - 3.18498i) q^{2} +(-5.95167 + 3.43620i) q^{4} +(-1.64838 - 4.72047i) q^{5} +(4.89410 - 5.00478i) q^{7} +(6.69718 + 6.69718i) q^{8} +O(q^{10})$	\(q+(-0.853412 - 3.18498i) q^{2} +(-5.95167 + 3.43620i) q^{4} +(-1.64838 - 4.72047i) q^{5} +(4.89410 - 5.00478i) q^{7} +(6.69718 + 6.69718i) q^{8} +(-13.6279 + 9.27855i) q^{10} +(0.581984 + 1.00803i) q^{11} +(-14.6930 - 14.6930i) q^{13} +(-20.1168 - 11.3165i) q^{14} +(1.87012 - 3.23914i) q^{16} +(-26.0209 - 6.97229i) q^{17} +(24.9464 + 14.4028i) q^{19} +(26.0311 + 22.4305i) q^{20} +(2.71387 - 2.71387i) q^{22} +(11.9268 - 3.19577i) q^{23} +(-19.5657 + 15.5622i) q^{25} +(-34.2576 + 59.3359i) q^{26} +(-11.9307 + 46.6039i) q^{28} +12.5542i q^{29} +(8.24013 + 14.2723i) q^{31} +(24.6815 + 6.61339i) q^{32} +88.8263i q^{34} +(-31.6922 - 14.8527i) q^{35} +(-3.66129 - 13.6641i) q^{37} +(24.5830 - 91.7452i) q^{38} +(20.5744 - 42.6533i) q^{40} -48.3009 q^{41} +(-0.357576 - 0.357576i) q^{43} +(-6.92755 - 3.99962i) q^{44} +(-20.3569 - 35.2592i) q^{46} +(7.33258 + 27.3656i) q^{47} +(-1.09559 - 48.9878i) q^{49} +(66.2630 + 49.0354i) q^{50} +(137.936 + 36.9597i) q^{52} +(-12.2029 + 45.5418i) q^{53} +(3.79903 - 4.40884i) q^{55} +(66.2945 - 0.741234i) q^{56} +(39.9849 - 10.7139i) q^{58} +(49.5210 - 28.5910i) q^{59} +(6.30786 - 10.9255i) q^{61} +(38.4248 - 38.4248i) q^{62} -99.2149i q^{64} +(-45.1382 + 93.5772i) q^{65} +(-44.9851 - 12.0537i) q^{67} +(178.826 - 47.9163i) q^{68} +(-20.2590 + 113.615i) q^{70} -19.0442 q^{71} +(31.7865 - 118.629i) q^{73} +(-40.3953 + 23.3222i) q^{74} -197.963 q^{76} +(7.89323 + 2.02068i) q^{77} +(-74.1583 - 42.8153i) q^{79} +(-18.3729 - 3.48852i) q^{80} +(41.2206 + 153.837i) q^{82} +(-18.0900 - 18.0900i) q^{83} +(9.97979 + 134.324i) q^{85} +(-0.833713 + 1.44403i) q^{86} +(-2.85328 + 10.6486i) q^{88} +(-78.1616 - 45.1266i) q^{89} +(-145.444 + 1.62620i) q^{91} +(-60.0029 + 60.0029i) q^{92} +(80.9010 - 46.7082i) q^{94} +(26.8670 - 141.500i) q^{95} +(84.2362 - 84.2362i) q^{97} +(-155.090 + 45.2962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.853412	−	3.18498i	−0.426706	−	1.59249i	−0.760169	−	0.649726i	$-0.774884\pi$
$2$	−0.853412	−	3.18498i	−0.426706	−	1.59249i	0.333463	−	0.942763i	$-0.391783\pi$
$3$		0			0
$3$		0			0
$4$	−5.95167	+	3.43620i	−1.48792	+	0.859049i
$5$	−1.64838	−	4.72047i	−0.329675	−	0.944094i
$5$	−1.64838	−	4.72047i	−0.329675	−	0.944094i
$6$		0			0
$7$	4.89410	−	5.00478i	0.699157	−	0.714968i
$7$	4.89410	−	5.00478i	0.699157	−	0.714968i
$8$	6.69718	+	6.69718i	0.837147	+	0.837147i
$9$		0			0
$10$	−13.6279	+	9.27855i	−1.36279	+	0.927855i
$11$	0.581984	+	1.00803i	0.0529076	+	0.0916387i	0.891266	−	0.453480i	$-0.149818\pi$
$11$	0.581984	+	1.00803i	0.0529076	+	0.0916387i	−0.838359	+	0.545119i	$0.816484\pi$
$12$		0			0
$13$	−14.6930	−	14.6930i	−1.13023	−	1.13023i	−0.990139	−	0.140089i	$-0.955261\pi$
$13$	−14.6930	−	14.6930i	−1.13023	−	1.13023i	−0.140089	−	0.990139i	$-0.544739\pi$
$14$	−20.1168	−	11.3165i	−1.43691	−	0.808318i
$15$		0			0
$16$	1.87012	−	3.23914i	0.116882	−	0.202446i
$17$	−26.0209	−	6.97229i	−1.53064	−	0.410135i	−0.607414	−	0.794385i	$-0.707793\pi$
$17$	−26.0209	−	6.97229i	−1.53064	−	0.410135i	−0.923229	+	0.384251i	$0.874460\pi$
$18$		0			0
$19$	24.9464	+	14.4028i	1.31297	+	0.758042i	0.982586	−	0.185806i	$-0.0594895\pi$
$19$	24.9464	+	14.4028i	1.31297	+	0.758042i	0.330381	+	0.943848i	$0.392823\pi$
$20$	26.0311	+	22.4305i	1.30155	+	1.12153i
$21$		0			0
$22$	2.71387	−	2.71387i	0.123358	−	0.123358i
$23$	11.9268	−	3.19577i	0.518555	−	0.138946i	0.00995696	−	0.999950i	$-0.496831\pi$
$23$	11.9268	−	3.19577i	0.518555	−	0.138946i	0.508598	+	0.861004i	$0.330164\pi$
$24$		0			0
$25$	−19.5657	+	15.5622i	−0.782629	+	0.622489i
$26$	−34.2576	+	59.3359i	−1.31760	+	2.28215i
$27$		0			0
$28$	−11.9307	+	46.6039i	−0.426095	+	1.66442i
$29$			12.5542i			0.432905i	0.976293	+	0.216452i	$0.0694486\pi$
$29$			12.5542i			0.432905i	−0.976293	+	0.216452i	$0.930551\pi$
$30$		0			0
$31$	8.24013	+	14.2723i	0.265811	+	0.460398i	0.967776	−	0.251814i	$-0.0810271\pi$
$31$	8.24013	+	14.2723i	0.265811	+	0.460398i	−0.701965	+	0.712211i	$0.747694\pi$
$32$	24.6815	+	6.61339i	0.771297	+	0.206668i
$33$		0			0
$34$			88.8263i			2.61254i
$35$	−31.6922	−	14.8527i	−0.905492	−	0.424363i
$36$		0			0
$37$	−3.66129	−	13.6641i	−0.0989538	−	0.369300i	0.898635	−	0.438696i	$-0.144560\pi$
$37$	−3.66129	−	13.6641i	−0.0989538	−	0.369300i	−0.997589	+	0.0693957i	$0.977893\pi$
$38$	24.5830	−	91.7452i	0.646922	−	2.41435i
$39$		0			0
$40$	20.5744	−	42.6533i	0.514359	−	1.06633i
$41$	−48.3009			−1.17807			−0.589036	−	0.808107i	$-0.700492\pi$
$41$	−48.3009			−1.17807			−0.589036	+	0.808107i	$0.700492\pi$
$42$		0			0
$43$	−0.357576	−	0.357576i	−0.00831573	−	0.00831573i	0.702937	−	0.711252i	$-0.251872\pi$
$43$	−0.357576	−	0.357576i	−0.00831573	−	0.00831573i	−0.711252	+	0.702937i	$0.751872\pi$
$44$	−6.92755	−	3.99962i	−0.157444	−	0.0909005i
$45$		0			0
$46$	−20.3569	−	35.2592i	−0.442541	−	0.766504i
$47$	7.33258	+	27.3656i	0.156012	+	0.582246i	0.999017	+	0.0443391i	$0.0141182\pi$
$47$	7.33258	+	27.3656i	0.156012	+	0.582246i	−0.843004	+	0.537907i	$0.819215\pi$
$48$		0			0
$49$	−1.09559	−	48.9878i	−0.0223590	−	0.999750i
$50$	66.2630	+	49.0354i	1.32526	+	0.980707i
$51$		0			0
$52$	137.936	+	36.9597i	2.65261	+	0.710764i
$53$	−12.2029	+	45.5418i	−0.230243	+	0.859280i	0.749992	+	0.661447i	$0.230057\pi$
$53$	−12.2029	+	45.5418i	−0.230243	+	0.859280i	−0.980236	+	0.197834i	$0.936609\pi$
$54$		0			0
$55$	3.79903	−	4.40884i	0.0690732	−	0.0801608i
$56$	66.2945	−	0.741234i	1.18383	−	0.0132363i
$57$		0			0
$58$	39.9849	−	10.7139i	0.689396	−	0.184723i
$59$	49.5210	−	28.5910i	0.839340	−	0.484593i	−0.0177000	−	0.999843i	$-0.505634\pi$
$59$	49.5210	−	28.5910i	0.839340	−	0.484593i	0.857040	+	0.515250i	$0.172301\pi$
$60$		0			0
$61$	6.30786	−	10.9255i	0.103408	−	0.179107i	−0.809679	−	0.586873i	$-0.800359\pi$
$61$	6.30786	−	10.9255i	0.103408	−	0.179107i	0.913086	+	0.407766i	$0.133692\pi$
$62$	38.4248	−	38.4248i	0.619755	−	0.619755i
$63$		0			0
$64$		−	99.2149i		−	1.55023i
$65$	−45.1382	+	93.5772i	−0.694434	+	1.43965i
$66$		0			0
$67$	−44.9851	−	12.0537i	−0.671419	−	0.179906i	−0.0930251	−	0.995664i	$-0.529654\pi$
$67$	−44.9851	−	12.0537i	−0.671419	−	0.179906i	−0.578394	+	0.815758i	$0.696320\pi$
$68$	178.826	−	47.9163i	2.62980	−	0.704652i
$69$		0			0
$70$	−20.2590	+	113.615i	−0.289414	+	1.62306i
$71$	−19.0442			−0.268228			−0.134114	−	0.990966i	$-0.542819\pi$
$71$	−19.0442			−0.268228			−0.134114	+	0.990966i	$0.542819\pi$
$72$		0			0
$73$	31.7865	−	118.629i	0.435432	−	1.62505i	−0.304599	−	0.952481i	$-0.598523\pi$
$73$	31.7865	−	118.629i	0.435432	−	1.62505i	0.740031	−	0.672573i	$-0.234811\pi$
$74$	−40.3953	+	23.3222i	−0.545883	+	0.315165i
$75$		0			0
$76$	−197.963			−2.60478
$77$	7.89323	+	2.02068i	0.102509	+	0.0262426i
$78$		0			0
$79$	−74.1583	−	42.8153i	−0.938712	−	0.541966i	−0.0491557	−	0.998791i	$-0.515653\pi$
$79$	−74.1583	−	42.8153i	−0.938712	−	0.541966i	−0.889556	+	0.456825i	$0.848986\pi$
$80$	−18.3729	−	3.48852i	−0.229662	−	0.0436065i
$81$		0			0
$82$	41.2206	+	153.837i	0.502690	+	1.87607i
$83$	−18.0900	−	18.0900i	−0.217952	−	0.217952i	0.589683	−	0.807635i	$-0.299253\pi$
$83$	−18.0900	−	18.0900i	−0.217952	−	0.217952i	−0.807635	+	0.589683i	$0.799253\pi$
$84$		0			0
$85$	9.97979	+	134.324i	0.117409	+	1.58028i
$86$	−0.833713	+	1.44403i	−0.00969433	+	0.0167911i
$87$		0			0
$88$	−2.85328	+	10.6486i	−0.0324236	+	0.121007i
$89$	−78.1616	−	45.1266i	−0.878220	−	0.507041i	−0.00814896	−	0.999967i	$-0.502594\pi$
$89$	−78.1616	−	45.1266i	−0.878220	−	0.507041i	−0.870071	+	0.492926i	$0.835927\pi$
$90$		0			0
$91$	−145.444	+	1.62620i	−1.59828	+	0.0178703i
$92$	−60.0029	+	60.0029i	−0.652205	+	0.652205i
$93$		0			0
$94$	80.9010	−	46.7082i	0.860649	−	0.496896i
$95$	26.8670	−	141.500i	0.282810	−	1.48947i
$96$		0			0
$97$	84.2362	−	84.2362i	0.868414	−	0.868414i	−0.123883	−	0.992297i	$-0.539535\pi$
$97$	84.2362	−	84.2362i	0.868414	−	0.868414i	0.992297	+	0.123883i	$0.0395347\pi$
$98$	−155.090	+	45.2962i	−1.58255	+	0.462206i
$99$		0			0
$100$	62.9738	−	159.853i	0.629738	−	1.59853i
$101$	−37.0883	−	64.2388i	−0.367211	−	0.636028i	0.621917	−	0.783083i	$-0.286354\pi$
$101$	−37.0883	−	64.2388i	−0.367211	−	0.636028i	−0.989128	+	0.147055i	$0.953021\pi$
$102$		0			0
$103$	−92.6702	+	24.8309i	−0.899711	+	0.241077i	−0.678892	−	0.734238i	$-0.737540\pi$
$103$	−92.6702	+	24.8309i	−0.899711	+	0.241077i	−0.220819	+	0.975315i	$0.570873\pi$
$104$		−	196.803i		−	1.89233i
$105$		0			0
$106$	155.464			1.46664
$107$	−11.4367	−	42.6823i	−0.106885	−	0.398900i	0.891667	−	0.452692i	$-0.149536\pi$
$107$	−11.4367	−	42.6823i	−0.106885	−	0.398900i	−0.998552	+	0.0537912i	$0.982869\pi$
$108$		0			0
$109$	−117.615	+	67.9052i	−1.07904	+	0.622984i	−0.930637	−	0.365943i	$-0.880746\pi$
$109$	−117.615	+	67.9052i	−1.07904	+	0.622984i	−0.148403	+	0.988927i	$0.547413\pi$
$110$	−17.2842	−	8.33726i	−0.157129	−	0.0757933i
$111$		0			0
$112$	−7.05863	−	25.2122i	−0.0630235	−	0.225109i
$113$	4.59841	+	4.59841i	0.0406939	+	0.0406939i	0.727161	−	0.686467i	$-0.240839\pi$
$113$	4.59841	+	4.59841i	0.0406939	+	0.0406939i	−0.686467	+	0.727161i	$0.740839\pi$
$114$		0			0
$115$	−34.7453	−	51.0322i	−0.302133	−	0.443758i
$116$	−43.1388	−	74.7186i	−0.371886	−	0.644126i
$117$		0			0
$118$	−133.324	−	133.324i	−1.12986	−	1.12986i
$119$	−162.244	+	96.1059i	−1.36339	+	0.807613i
$120$		0			0
$121$	59.8226	−	103.616i	0.494402	−	0.856329i
$122$	−40.1808	−	10.7664i	−0.329351	−	0.0882492i
$123$		0			0
$124$	−98.0851	−	56.6294i	−0.791009	−	0.456689i
$125$	105.713	+	66.7070i	0.845702	+	0.533656i
$126$		0			0
$127$	16.6949	−	16.6949i	0.131456	−	0.131456i	−0.638317	−	0.769773i	$-0.720369\pi$
$127$	16.6949	−	16.6949i	0.131456	−	0.131456i	0.769773	+	0.638317i	$0.220369\pi$
$128$	−217.271	+	58.2177i	−1.69743	+	0.454825i
$129$		0			0
$130$	336.563	+	63.9042i	2.58895	+	0.491571i
$131$	63.4004	−	109.813i	0.483973	−	0.838266i	−0.515858	−	0.856674i	$-0.672527\pi$
$131$	63.4004	−	109.813i	0.483973	−	0.838266i	0.999831	+	0.0184088i	$0.00586002\pi$
$132$		0			0
$133$	194.173	−	54.3623i	1.45995	−	0.408739i
$134$			153.563i			1.14599i
$135$		0			0
$136$	−127.572	−	220.961i	−0.938031	−	1.62472i
$137$	156.100	+	41.8269i	1.13942	+	0.305306i	0.778716	−	0.627377i	$-0.215871\pi$
$137$	156.100	+	41.8269i	1.13942	+	0.305306i	0.360700	+	0.932682i	$0.382538\pi$
$138$		0			0
$139$		−	92.5186i		−	0.665601i	−0.942997	−	0.332801i	$-0.892006\pi$
$139$		−	92.5186i		−	0.665601i	0.942997	−	0.332801i	$-0.107994\pi$
$140$	239.658	−	20.5024i	1.71185	−	0.146446i
$141$		0			0
$142$	16.2525	+	60.6552i	0.114454	+	0.427149i
$143$	6.25981	−	23.3619i	0.0437749	−	0.163370i
$144$		0			0
$145$	59.2619	−	20.6941i	0.408703	−	0.142718i
$146$	−404.957			−2.77368
$147$		0			0
$148$	68.7434	+	68.7434i	0.464482	+	0.464482i
$149$	−140.299	−	81.0014i	−0.941601	−	0.543634i	−0.0511394	−	0.998692i	$-0.516285\pi$
$149$	−140.299	−	81.0014i	−0.941601	−	0.543634i	−0.890462	+	0.455058i	$0.849619\pi$
$150$		0			0
$151$	143.434	+	248.435i	0.949893	+	1.64526i	0.745645	+	0.666344i	$0.232142\pi$
$151$	143.434	+	248.435i	0.949893	+	1.64526i	0.204248	+	0.978919i	$0.434525\pi$
$152$	70.6122	+	263.528i	0.464554	+	1.73374i
$153$		0			0
$154$	−0.300367	−	26.8642i	−0.00195043	−	0.174443i
$155$	53.7893	−	62.4235i	0.347028	−	0.402732i
$156$		0			0
$157$	−276.357	−	74.0497i	−1.76024	−	0.471654i	−0.773474	−	0.633828i	$-0.781483\pi$
$157$	−276.357	−	74.0497i	−1.76024	−	0.471654i	−0.986762	+	0.162174i	$0.948149\pi$
$158$	−73.0782	+	272.731i	−0.462520	+	1.72615i
$159$		0			0
$160$	−9.46607	−	127.410i	−0.0591630	−	0.796310i
$161$	42.3767	−	75.3312i	0.263209	−	0.467896i
$162$		0			0
$163$	9.84068	−	2.63680i	0.0603722	−	0.0161767i	−0.228507	−	0.973542i	$-0.573384\pi$
$163$	9.84068	−	2.63680i	0.0603722	−	0.0161767i	0.288879	+	0.957366i	$0.406718\pi$
$164$	287.471	−	165.972i	1.75287	−	1.01202i
$165$		0			0
$166$	−42.1781	+	73.0547i	−0.254085	+	0.440088i
$167$	71.1342	−	71.1342i	0.425954	−	0.425954i	−0.461294	−	0.887247i	$-0.652615\pi$
$167$	71.1342	−	71.1342i	0.425954	−	0.425954i	0.887247	+	0.461294i	$0.152615\pi$
$168$		0			0
$169$			262.766i			1.55483i
$170$	419.302	−	146.419i	2.46648	−	0.861289i
$171$		0			0
$172$	3.35688	+	0.899473i	0.0195167	+	0.00522949i
$173$	289.128	−	77.4717i	1.67126	−	0.447813i	0.705811	−	0.708401i	$-0.250583\pi$
$173$	289.128	−	77.4717i	1.67126	−	0.447813i	0.965450	+	0.260588i	$0.0839163\pi$
$174$		0			0
$175$	−17.8711	+	174.085i	−0.102120	+	0.994772i
$176$	4.35351			0.0247359
$177$		0			0
$178$	−77.0232	+	287.455i	−0.432715	+	1.61491i
$179$	280.191	−	161.768i	1.56531	−	0.903733i	0.568608	−	0.822609i	$-0.307482\pi$
$179$	280.191	−	161.768i	1.56531	−	0.903733i	0.996704	−	0.0811241i	$-0.0258510\pi$
$180$		0			0
$181$	43.2716			0.239069			0.119535	−	0.992830i	$-0.461860\pi$
$181$	43.2716			0.239069			0.119535	+	0.992830i	$0.461860\pi$
$182$	129.303	+	461.847i	0.710456	+	2.53762i
$183$		0			0
$184$	101.278	+	58.4731i	0.550426	+	0.317788i
$185$	−58.4659	+	39.8066i	−0.316032	+	0.215171i
$186$		0			0
$187$	−8.11552	−	30.2875i	−0.0433985	−	0.161965i
$188$	−137.675	−	137.675i	−0.732312	−	0.732312i
$189$		0			0
$190$	−473.603	+	35.1870i	−2.49265	+	0.185195i
$191$	19.2949	−	33.4198i	0.101021	−	0.174973i	−0.811085	−	0.584929i	$-0.801123\pi$
$191$	19.2949	−	33.4198i	0.101021	−	0.174973i	0.912105	+	0.409956i	$0.134456\pi$
$192$		0			0
$193$	62.4940	−	233.231i	0.323803	−	1.20845i	−0.591706	−	0.806154i	$-0.701545\pi$
$193$	62.4940	−	233.231i	0.323803	−	1.20845i	0.915509	−	0.402296i	$-0.131788\pi$
$194$	−340.178	−	196.402i	−1.75350	−	1.01238i
$195$		0			0
$196$	174.852	+	287.794i	0.892103	+	1.46834i
$197$	−217.403	+	217.403i	−1.10357	+	1.10357i	−0.109594	+	0.993976i	$0.534955\pi$
$197$	−217.403	+	217.403i	−1.10357	+	1.10357i	−0.993976	+	0.109594i	$0.965045\pi$
$198$		0			0
$199$	168.448	−	97.2533i	0.846470	−	0.488710i	−0.0129880	−	0.999916i	$-0.504134\pi$
$199$	168.448	−	97.2533i	0.846470	−	0.488710i	0.859458	+	0.511206i	$0.170801\pi$
$200$	−235.258	−	26.8121i	−1.17629	−	0.134060i
$201$		0			0
$202$	−172.948	+	172.948i	−0.856177	+	0.856177i
$203$	62.8311	+	61.4416i	0.309513	+	0.302668i
$204$		0			0
$205$	79.6181	+	228.003i	0.388381	+	1.11221i
$206$	158.172	+	273.962i	0.767824	+	1.32991i
$207$		0			0
$208$	−75.0701	+	20.1150i	−0.360914	+	0.0967066i
$209$			33.5288i			0.160425i
$210$		0			0
$211$	−67.4406			−0.319624			−0.159812	−	0.987147i	$-0.551089\pi$
$211$	−67.4406			−0.319624			−0.159812	+	0.987147i	$0.551089\pi$
$212$	−83.8632	−	312.982i	−0.395581	−	1.47633i
$213$		0			0
$214$	−126.182	+	72.8513i	−0.589636	+	0.340426i
$215$	−1.09851	+	2.27735i	−0.00510934	+	0.0105923i
$216$		0			0
$217$	111.758	+	28.6101i	0.515013	+	0.131844i
$218$	316.651	+	316.651i	1.45253	+	1.45253i
$219$		0			0
$220$	−7.46090	+	39.2942i	−0.0339132	+	0.178610i
$221$	279.881	+	484.768i	1.26643	+	2.19352i
$222$		0			0
$223$	17.6765	+	17.6765i	0.0792670	+	0.0792670i	0.745629	−	0.666362i	$-0.232149\pi$
$223$	17.6765	+	17.6765i	0.0792670	+	0.0792670i	−0.666362	+	0.745629i	$0.732149\pi$
$224$	153.892	−	91.1588i	0.687019	−	0.406959i
$225$		0			0
$226$	10.7215	−	18.5702i	0.0474402	−	0.0821689i
$227$	−309.764	−	83.0011i	−1.36460	−	0.365644i	−0.499097	−	0.866546i	$-0.666335\pi$
$227$	−309.764	−	83.0011i	−1.36460	−	0.365644i	−0.865504	+	0.500903i	$0.833001\pi$
$228$		0			0
$229$	−290.289	−	167.598i	−1.26764	−	0.731870i	−0.293096	−	0.956083i	$-0.594685\pi$
$229$	−290.289	−	167.598i	−1.26764	−	0.731870i	−0.974540	+	0.224213i	$0.928019\pi$
$230$	−132.884	+	154.215i	−0.577757	+	0.670498i
$231$		0			0
$232$	−84.0779	+	84.0779i	−0.362405	+	0.362405i
$233$	267.882	−	71.7786i	1.14971	−	0.308063i	0.366859	−	0.930277i	$-0.380433\pi$
$233$	267.882	−	71.7786i	1.14971	−	0.308063i	0.782847	+	0.622214i	$0.213767\pi$
$234$		0			0
$235$	117.092	−	79.7220i	0.498262	−	0.339243i
$236$	−196.489	+	340.328i	−0.832579	+	1.44207i
$237$		0			0
$238$	444.556	+	434.725i	1.86788	+	1.82657i
$239$			57.1966i			0.239316i	0.992815	+	0.119658i	$0.0381799\pi$
$239$			57.1966i			0.239316i	−0.992815	+	0.119658i	$0.961820\pi$
$240$		0			0
$241$	−4.95051	−	8.57453i	−0.0205415	−	0.0355790i	0.855572	−	0.517684i	$-0.173206\pi$
$241$	−4.95051	−	8.57453i	−0.0205415	−	0.0355790i	−0.876113	+	0.482105i	$0.839872\pi$
$242$	−381.067	−	102.107i	−1.57466	−	0.421928i
$243$		0			0
$244$			86.7002i			0.355329i
$245$	−229.439	+	85.9219i	−0.936487	+	0.350702i
$246$		0			0
$247$	−154.916	−	578.156i	−0.627192	−	2.34071i
$248$	−40.3987	+	150.770i	−0.162898	+	0.607943i
$249$		0			0
$250$	122.244	−	393.621i	0.488975	−	1.57448i
$251$	187.727			0.747915			0.373957	−	0.927446i	$-0.378001\pi$
$251$	187.727			0.747915			0.373957	+	0.927446i	$0.378001\pi$
$252$		0			0
$253$	10.1626	+	10.1626i	0.0401684	+	0.0401684i
$254$	−67.4206	−	38.9253i	−0.265436	−	0.153249i
$255$		0			0
$256$	172.414	+	298.630i	0.673493	+	1.16652i
$257$	−32.0914	−	119.767i	−0.124869	−	0.466018i	0.874966	−	0.484185i	$-0.160884\pi$
$257$	−32.0914	−	119.767i	−0.124869	−	0.466018i	−0.999835	+	0.0181666i	$0.994217\pi$
$258$		0			0
$259$	−86.3046	−	48.5496i	−0.333222	−	0.187450i
$260$	−52.9023	−	712.044i	−0.203470	−	2.73863i
$261$		0			0
$262$	−403.858	−	108.213i	−1.54144	−	0.413028i
$263$	3.17875	−	11.8632i	0.0120865	−	0.0451074i	−0.959619	−	0.281302i	$-0.909234\pi$
$263$	3.17875	−	11.8632i	0.0120865	−	0.0451074i	0.971706	+	0.236195i	$0.0759003\pi$
$264$		0			0
$265$	235.094	−	17.4666i	0.887147	−	0.0659118i
$266$	−338.852	−	572.043i	−1.27388	−	2.15054i
$267$		0			0
$268$	309.155	−	82.8379i	1.15356	−	0.309097i
$269$	16.4548	−	9.50018i	0.0611703	−	0.0353167i	−0.469103	−	0.883143i	$-0.655423\pi$
$269$	16.4548	−	9.50018i	0.0611703	−	0.0353167i	0.530273	+	0.847827i	$0.322089\pi$
$270$		0			0
$271$	49.9304	−	86.4820i	0.184245	−	0.319122i	−0.759077	−	0.651001i	$-0.774349\pi$
$271$	49.9304	−	86.4820i	0.184245	−	0.319122i	0.943322	+	0.331879i	$0.107683\pi$
$272$	−71.2465	+	71.2465i	−0.261935	+	0.261935i
$273$		0			0
$274$		−	532.870i		−	1.94478i
$275$	−27.0740	−	10.6658i	−0.0984511	−	0.0387846i
$276$		0			0
$277$	−68.7510	−	18.4218i	−0.248199	−	0.0665046i	0.132575	−	0.991173i	$-0.457676\pi$
$277$	−68.7510	−	18.4218i	−0.248199	−	0.0665046i	−0.380773	+	0.924668i	$0.624342\pi$
$278$	−294.670	+	78.9565i	−1.05996	+	0.284016i
$279$		0			0
$280$	−112.777	−	311.720i	−0.402776	−	1.11328i
$281$	121.502			0.432393			0.216196	−	0.976350i	$-0.430635\pi$
$281$	121.502			0.432393			0.216196	+	0.976350i	$0.430635\pi$
$282$		0			0
$283$	−68.4910	+	255.612i	−0.242018	+	0.903223i	0.732841	+	0.680400i	$0.238194\pi$
$283$	−68.4910	+	255.612i	−0.242018	+	0.903223i	−0.974859	+	0.222823i	$0.928473\pi$
$284$	113.345	−	65.4395i	0.399100	−	0.230421i
$285$		0			0
$286$	−79.7495			−0.278844
$287$	−236.390	+	241.735i	−0.823657	+	0.842284i
$288$		0			0
$289$	378.195	+	218.351i	1.30863	+	0.755539i
$290$	−116.485	−	171.087i	−0.401673	−	0.589956i
$291$		0			0
$292$	218.449	+	815.265i	0.748115	+	2.79200i
$293$	−59.1809	−	59.1809i	−0.201983	−	0.201983i	0.598866	−	0.800849i	$-0.295618\pi$
$293$	−59.1809	−	59.1809i	−0.201983	−	0.201983i	−0.800849	+	0.598866i	$0.795618\pi$
$294$		0			0
$295$	−216.592	−	186.634i	−0.734211	−	0.632658i
$296$	66.9907	−	116.031i	0.226320	−	0.391998i
$297$		0			0
$298$	−138.255	+	515.976i	−0.463944	+	1.73146i
$299$	−222.195	−	128.284i	−0.743127	−	0.429044i
$300$		0			0
$301$	−3.53960	+	0.0395760i	−0.0117595	+	0.000131482i
$302$	668.851	−	668.851i	2.21474	−	2.21474i
$303$		0			0
$304$	93.3054	−	53.8699i	0.306926	−	0.177204i
$305$	−61.9714	−	11.7667i	−0.203185	−	0.0385793i
$306$		0			0
$307$	−100.076	+	100.076i	−0.325979	+	0.325979i	−0.851055	−	0.525076i	$-0.824037\pi$
$307$	−100.076	+	100.076i	−0.325979	+	0.325979i	0.525076	+	0.851055i	$0.324037\pi$
$308$	−53.9213	+	15.0963i	−0.175069	+	0.0490139i
$309$		0			0
$310$	−244.722	−	118.045i	−0.789425	−	0.380789i
$311$	141.092	+	244.378i	0.453671	+	0.785781i	0.998611	−	0.0526944i	$-0.0167809\pi$
$311$	141.092	+	244.378i	0.453671	+	0.785781i	−0.544940	+	0.838475i	$0.683448\pi$
$312$		0			0
$313$	190.794	−	51.1230i	0.609564	−	0.163332i	0.0591850	−	0.998247i	$-0.481150\pi$
$313$	190.794	−	51.1230i	0.609564	−	0.163332i	0.550379	+	0.834915i	$0.314483\pi$
$314$			943.386i			3.00441i
$315$		0			0
$316$	588.487			1.86230
$317$	40.5648	+	151.390i	0.127965	+	0.477571i	0.999928	−	0.0120003i	$-0.00381989\pi$
$317$	40.5648	+	151.390i	0.127965	+	0.477571i	−0.871963	+	0.489571i	$0.837153\pi$
$318$		0			0
$319$	−12.6550	+	7.30636i	−0.0396708	+	0.0229039i
$320$	−468.341	+	163.543i	−1.46357	+	0.511073i
$321$		0			0
$322$	−276.093	−	70.6802i	−0.857432	−	0.219504i
$323$	−548.708	−	548.708i	−1.69878	−	1.69878i
$324$		0			0
$325$	516.133	+	58.8231i	1.58810	+	0.180994i
$326$	−16.7963	−	29.0921i	−0.0515224	−	0.0892394i
$327$		0			0
$328$	−323.480	−	323.480i	−0.986219	−	0.986219i
$329$	172.845	+	97.2319i	0.525365	+	0.295538i
$330$		0			0
$331$	−245.598	+	425.389i	−0.741989	+	1.28516i	0.209599	+	0.977787i	$0.432784\pi$
$331$	−245.598	+	425.389i	−0.741989	+	1.28516i	−0.951588	+	0.307375i	$0.900549\pi$
$332$	169.827	+	45.5050i	0.511527	+	0.137063i
$333$		0			0
$334$	−287.268	−	165.854i	−0.860083	−	0.496569i
$335$	17.2531	+	232.220i	0.0515018	+	0.693194i
$336$		0			0
$337$	−250.219	+	250.219i	−0.742489	+	0.742489i	−0.973056	−	0.230567i	$-0.925942\pi$
$337$	−250.219	+	250.219i	−0.742489	+	0.742489i	0.230567	+	0.973056i	$0.425942\pi$
$338$	836.904	−	224.248i	2.47605	−	0.663455i
$339$		0			0
$340$	−520.960	−	765.160i	−1.53224	−	2.25047i
$341$	−9.59124	+	16.6125i	−0.0281268	+	0.0487171i
$342$		0			0
$343$	−250.535	−	234.268i	−0.730422	−	0.682996i
$344$		−	4.78951i		−	0.0139230i
$345$		0			0
$346$	−493.491	−	854.751i	−1.42627	−	2.47038i
$347$	−599.530	−	160.644i	−1.72775	−	0.462950i	−0.748089	−	0.663598i	$-0.769028\pi$
$347$	−599.530	−	160.644i	−1.72775	−	0.462950i	−0.979663	+	0.200649i	$0.935695\pi$
$348$		0			0
$349$		−	69.6374i		−	0.199534i	−0.995011	−	0.0997671i	$-0.968190\pi$
$349$		−	69.6374i		−	0.199534i	0.995011	−	0.0997671i	$-0.0318098\pi$
$350$	569.709	−	91.6474i	1.62774	−	0.261850i
$351$		0			0
$352$	7.69777	+	28.7285i	0.0218687	+	0.0816149i
$353$	−14.7407	+	55.0131i	−0.0417584	+	0.155845i	−0.983657	−	0.180053i	$-0.942373\pi$
$353$	−14.7407	+	55.0131i	−0.0417584	+	0.155845i	0.941898	+	0.335898i	$0.109040\pi$
$354$		0			0
$355$	31.3919	+	89.8974i	0.0884280	+	0.253232i
$356$	620.256			1.74229
$357$		0			0
$358$	−754.346	−	754.346i	−2.10711	−	2.10711i
$359$	52.7945	+	30.4809i	0.147060	+	0.0849051i	0.571725	−	0.820446i	$-0.306275\pi$
$359$	52.7945	+	30.4809i	0.147060	+	0.0849051i	−0.424665	+	0.905351i	$0.639608\pi$
$360$		0			0
$361$	234.381	+	405.960i	0.649255	+	1.12454i
$362$	−36.9285	−	137.819i	−0.102012	−	0.380715i
$363$		0			0
$364$	860.045	−	509.452i	2.36276	−	1.39959i
$365$	−612.380	+	45.4976i	−1.67775	+	0.124651i
$366$		0			0
$367$	348.106	+	93.2748i	0.948519	+	0.254155i	0.699734	−	0.714404i	$-0.253302\pi$
$367$	348.106	+	93.2748i	0.948519	+	0.254155i	0.248785	+	0.968559i	$0.419969\pi$
$368$	11.9529	−	44.6089i	0.0324808	−	0.121220i
$369$		0			0
$370$	176.679	+	152.241i	0.477510	+	0.411463i
$371$	168.205	+	283.959i	0.453382	+	0.765388i
$372$		0			0
$373$	17.3999	−	4.66229i	0.0466485	−	0.0124994i	−0.235419	−	0.971894i	$-0.575646\pi$
$373$	17.3999	−	4.66229i	0.0466485	−	0.0124994i	0.282068	+	0.959394i	$0.408980\pi$
$374$	−89.5392	+	51.6955i	−0.239410	+	0.138223i
$375$		0			0
$376$	−134.164	+	232.380i	−0.356820	+	0.618031i
$377$	184.459	−	184.459i	0.489281	−	0.489281i
$378$		0			0
$379$			93.7813i			0.247444i	0.992317	+	0.123722i	$0.0394831\pi$
$379$			93.7813i			0.247444i	−0.992317	+	0.123722i	$0.960517\pi$
$380$	326.318	+	934.481i	0.858732	+	2.45916i
$381$		0			0
$382$	−122.908	−	32.9330i	−0.321748	−	0.0862122i
$383$	399.952	−	107.167i	1.04426	−	0.279809i	0.304382	−	0.952550i	$-0.401550\pi$
$383$	399.952	−	107.167i	1.04426	−	0.279809i	0.739878	+	0.672741i	$0.234883\pi$
$384$		0			0
$385$	−3.47246	−	40.5906i	−0.00901937	−	0.105430i
$386$	−796.168			−2.06261
$387$		0			0
$388$	−211.894	+	790.798i	−0.546118	+	2.03814i
$389$	142.385	−	82.2062i	0.366029	−	0.211327i	−0.305693	−	0.952130i	$-0.598888\pi$
$389$	142.385	−	82.2062i	0.366029	−	0.211327i	0.671722	+	0.740803i	$0.265555\pi$
$390$		0			0
$391$	−332.627			−0.850710
$392$	320.742	−	335.417i	0.818220	−	0.855656i
$393$		0			0
$394$	877.960	+	506.890i	2.22832	+	1.28652i
$395$	−79.8677	+	420.638i	−0.202197	+	1.06491i
$396$		0			0
$397$	151.277	+	564.572i	0.381050	+	1.42210i	0.844301	+	0.535870i	$0.180016\pi$
$397$	151.277	+	564.572i	0.381050	+	1.42210i	−0.463251	+	0.886227i	$0.653317\pi$
$398$	−453.505	−	453.505i	−1.13946	−	1.13946i
$399$		0			0
$400$	13.8180	+	92.4793i	0.0345451	+	0.231198i
$401$	80.2339	−	138.969i	0.200084	−	0.346556i	−0.748471	−	0.663168i	$-0.769212\pi$
$401$	80.2339	−	138.969i	0.200084	−	0.346556i	0.948555	+	0.316611i	$0.102545\pi$
$402$		0			0
$403$	88.6308	−	330.775i	0.219928	−	0.820781i
$404$	441.475	+	254.886i	1.09276	+	0.630905i
$405$		0			0
$406$	142.069	−	252.551i	0.349925	−	0.622046i
$407$	11.6430	−	11.6430i	0.0286068	−	0.0286068i
$408$		0			0
$409$	143.273	−	82.7185i	0.350300	−	0.202246i	−0.314518	−	0.949252i	$-0.601843\pi$
$409$	143.273	−	82.7185i	0.350300	−	0.202246i	0.664817	+	0.747006i	$0.268509\pi$
$410$	658.238	−	448.163i	1.60546	−	1.09308i
$411$		0			0
$412$	466.219	−	466.219i	1.13160	−	1.13160i
$413$	99.2694	−	387.769i	0.240362	−	0.938908i
$414$		0			0
$415$	−55.5744	+	115.213i	−0.133914	+	0.277621i
$416$	−265.474	−	459.814i	−0.638159	−	1.10532i
$417$		0			0
$418$	106.788	−	28.6139i	0.255475	−	0.0684542i
$419$		−	572.116i		−	1.36543i	−0.730684	−	0.682716i	$-0.760799\pi$
$419$		−	572.116i		−	1.36543i	0.730684	−	0.682716i	$-0.239201\pi$
$420$		0			0
$421$	259.398			0.616148			0.308074	−	0.951362i	$-0.400316\pi$
$421$	259.398			0.616148			0.308074	+	0.951362i	$0.400316\pi$
$422$	57.5546	+	214.797i	0.136385	+	0.508997i
$423$		0			0
$424$	−386.727	+	223.277i	−0.912092	+	0.526596i
$425$	617.622	−	268.526i	1.45323	−	0.631825i
$426$		0			0
$427$	−23.8086	−	85.0401i	−0.0557578	−	0.199157i
$428$	214.732	+	214.732i	0.501711	+	0.501711i
$429$		0			0
$430$	8.19079	+	1.55521i	0.0190483	+	0.00361676i
$431$	310.336	+	537.517i	0.720036	+	1.24714i	0.960985	+	0.276602i	$0.0892082\pi$
$431$	310.336	+	537.517i	0.720036	+	1.24714i	−0.240948	+	0.970538i	$0.577458\pi$
$432$		0			0
$433$	334.651	+	334.651i	0.772865	+	0.772865i	0.978606	−	0.205741i	$-0.0659605\pi$
$433$	334.651	+	334.651i	0.772865	+	0.772865i	−0.205741	+	0.978606i	$0.565961\pi$
$434$	−4.25280	−	380.362i	−0.00979908	−	0.876411i
$435$		0			0
$436$	466.672	−	808.299i	1.07035	−	1.85390i
$437$	343.558	+	92.0560i	0.786173	+	0.210654i
$438$		0			0
$439$	−568.777	−	328.383i	−1.29562	−	0.748026i	−0.315975	−	0.948768i	$-0.602332\pi$
$439$	−568.777	−	328.383i	−1.29562	−	0.748026i	−0.979644	+	0.200741i	$0.935665\pi$
$440$	54.9696	−	4.08404i	0.124931	−	0.00928191i
$441$		0			0
$442$	1305.12	−	1305.12i	2.95276	−	2.95276i
$443$	−576.431	+	154.454i	−1.30120	+	0.348655i	−0.841904	−	0.539628i	$-0.818565\pi$
$443$	−576.431	+	154.454i	−1.30120	+	0.348655i	−0.459296	+	0.888283i	$0.651898\pi$
$444$		0			0
$445$	−84.1792	+	443.345i	−0.189167	+	0.996281i
$446$	41.2140	−	71.3847i	0.0924081	−	0.160055i
$447$		0			0
$448$	−496.548	−	485.567i	−1.10837	−	1.08386i
$449$		−	162.638i		−	0.362223i	−0.983463	−	0.181111i	$-0.942031\pi$
$449$		−	162.638i		−	0.362223i	0.983463	−	0.181111i	$-0.0579694\pi$
$450$		0			0
$451$	−28.1104	−	48.6886i	−0.0623290	−	0.107957i
$452$	−43.1693	−	11.5672i	−0.0955072	−	0.0255911i
$453$		0			0
$454$			1057.43i			2.32913i
$455$	247.422	+	683.883i	0.543786	+	1.50304i
$456$		0			0
$457$	−130.445	−	486.828i	−0.285438	−	1.06527i	−0.948519	−	0.316721i	$-0.897418\pi$
$457$	−130.445	−	486.828i	−0.285438	−	1.06527i	0.663081	−	0.748548i	$-0.269249\pi$
$458$	−286.061	+	1067.59i	−0.624587	+	2.33099i
$459$		0			0
$460$	382.149	+	184.335i	0.830759	+	0.400727i
$461$	−323.423			−0.701568			−0.350784	−	0.936456i	$-0.614085\pi$
$461$	−323.423			−0.701568			−0.350784	+	0.936456i	$0.614085\pi$
$462$		0			0
$463$	108.492	+	108.492i	0.234324	+	0.234324i	0.814495	−	0.580171i	$-0.197014\pi$
$463$	108.492	+	108.492i	0.234324	+	0.234324i	−0.580171	+	0.814495i	$0.697014\pi$
$464$	40.6649	+	23.4779i	0.0876399	+	0.0505989i
$465$		0			0
$466$	−457.227	−	791.940i	−0.981173	−	1.69944i
$467$	121.774	+	454.466i	0.260758	+	0.973161i	0.964796	+	0.262999i	$0.0847116\pi$
$467$	121.774	+	454.466i	0.260758	+	0.973161i	−0.704038	+	0.710162i	$0.748622\pi$
$468$		0			0
$469$	−280.488	+	166.148i	−0.598055	+	0.354261i
$470$	−353.840	−	304.898i	−0.752851	−	0.648720i
$471$		0			0
$472$	523.130	+	140.172i	1.10833	+	0.296975i
$473$	0.152342	−	0.568550i	0.000322077	−	0.00120201i
$474$		0			0
$475$	−712.233	+	106.420i	−1.49944	+	0.224042i
$476$	635.382	−	1129.49i	1.33484	−	2.37288i
$477$		0			0
$478$	182.170	−	48.8123i	0.381109	−	0.102118i
$479$	−79.9576	+	46.1636i	−0.166926	+	0.0963749i	−0.581136	−	0.813807i	$-0.697391\pi$
$479$	−79.9576	+	46.1636i	−0.166926	+	0.0963749i	0.414209	+	0.910182i	$0.364058\pi$
$480$		0			0
$481$	−146.971	+	254.561i	−0.305553	+	0.529234i
$482$	−23.0849	+	23.0849i	−0.0478939	+	0.0478939i
$483$		0			0
$484$			822.249i			1.69886i
$485$	−536.487	−	258.782i	−1.10616	−	0.533570i
$486$		0			0
$487$	770.171	+	206.367i	1.58146	+	0.423751i	0.939378	−	0.342884i	$-0.111404\pi$
$487$	770.171	+	206.367i	1.58146	+	0.423751i	0.642083	+	0.766635i	$0.278071\pi$
$488$	115.415	−	30.9254i	0.236506	−	0.0633717i
$489$		0			0
$490$	469.466	+	657.432i	0.958094	+	1.34170i
$491$	−442.461			−0.901143			−0.450572	−	0.892740i	$-0.648780\pi$
$491$	−442.461			−0.901143			−0.450572	+	0.892740i	$0.648780\pi$
$492$		0			0
$493$	87.5317	−	326.673i	0.177549	−	0.662622i
$494$	−1709.21	+	986.810i	−3.45993	+	1.99759i
$495$		0			0
$496$	61.6401			0.124274
$497$	−93.2040	+	95.3118i	−0.187533	+	0.191774i
$498$		0			0
$499$	−59.9751	−	34.6267i	−0.120191	−	0.0693921i	0.438699	−	0.898634i	$-0.355439\pi$
$499$	−59.9751	−	34.6267i	−0.120191	−	0.0693921i	−0.558890	+	0.829242i	$0.688773\pi$
$500$	−858.385	−	33.7683i	−1.71677	−	0.0675366i
$501$		0			0
$502$	−160.208	−	597.905i	−0.319140	−	1.19105i
$503$	−570.214	−	570.214i	−1.13363	−	1.13363i	−0.989569	−	0.144057i	$-0.953985\pi$
$503$	−570.214	−	570.214i	−1.13363	−	1.13363i	−0.144057	−	0.989569i	$-0.546015\pi$
$504$		0			0
$505$	−242.102	+	280.964i	−0.479410	+	0.556365i
$506$	23.6948	−	41.0405i	0.0468276	−	0.0811078i
$507$		0			0
$508$	−41.9956	+	156.730i	−0.0826685	+	0.308523i
$509$	−252.827	−	145.970i	−0.496713	−	0.286778i	0.230642	−	0.973039i	$-0.425917\pi$
$509$	−252.827	−	145.970i	−0.496713	−	0.286778i	−0.727355	+	0.686261i	$0.759251\pi$
$510$		0			0
$511$	−438.145	−	739.666i	−0.857426	−	1.44749i
$512$	167.775	−	167.775i	0.327686	−	0.327686i
$513$		0			0
$514$	−354.067	+	204.421i	−0.688846	+	0.397706i
$515$	269.969	+	396.517i	0.524212	+	0.769935i
$516$		0			0
$517$	−23.3177	+	23.3177i	−0.0451020	+	0.0451020i
$518$	−80.9760	+	316.311i	−0.156324	+	0.610639i
$519$		0			0
$520$	−929.002	+	324.405i	−1.78654	+	0.623856i
$521$	−204.719	−	354.584i	−0.392935	−	0.680583i	0.599900	−	0.800075i	$-0.295207\pi$
$521$	−204.719	−	354.584i	−0.392935	−	0.680583i	−0.992835	+	0.119491i	$0.961874\pi$
$522$		0			0
$523$	138.251	−	37.0443i	0.264343	−	0.0708305i	−0.124213	−	0.992256i	$-0.539641\pi$
$523$	138.251	−	37.0443i	0.264343	−	0.0708305i	0.388556	+	0.921425i	$0.372974\pi$
$524$			871.426i			1.66303i
$525$		0			0
$526$	−40.4970			−0.0769904
$527$	−114.905	−	428.832i	−0.218036	−	0.813723i
$528$		0			0
$529$	−326.093	+	188.270i	−0.616432	+	0.355897i
$530$	−256.263	−	733.863i	−0.483515	−	1.38465i
$531$		0			0
$532$	−968.853	+	990.763i	−1.82115	+	1.86234i
$533$	709.684	+	709.684i	1.33149	+	1.33149i
$534$		0			0
$535$	−182.629	+	124.343i	−0.341362	+	0.232417i
$536$	−220.547	−	381.999i	−0.411469	−	0.712685i
$537$		0			0
$538$	−44.3006	−	44.3006i	−0.0823431	−	0.0823431i
$539$	48.7433	−	29.6145i	0.0904328	−	0.0549433i
$540$		0			0
$541$	−97.2826	+	168.498i	−0.179820	+	0.311457i	−0.941819	−	0.336121i	$-0.890885\pi$
$541$	−97.2826	+	168.498i	−0.179820	+	0.311457i	0.761999	+	0.647578i	$0.224218\pi$
$542$	−318.054	−	85.2224i	−0.586816	−	0.157237i
$543$		0			0
$544$	−596.125	−	344.173i	−1.09582	−	0.632671i
$545$	514.419	+	443.267i	0.943888	+	0.813333i
$546$		0			0
$547$	−170.750	+	170.750i	−0.312158	+	0.312158i	−0.845745	−	0.533587i	$-0.820844\pi$
$547$	−170.750	+	170.750i	−0.312158	+	0.312158i	0.533587	+	0.845745i	$0.320844\pi$
$548$	−1072.78	+	287.451i	−1.95763	+	0.524545i
$549$		0			0
$550$	−10.8649	+	95.3325i	−0.0197544	+	0.173332i
$551$	−180.816	+	313.183i	−0.328160	+	0.568389i
$552$		0			0
$553$	−577.219	+	161.603i	−1.04380	+	0.292230i
$554$			234.692i			0.423631i
$555$		0			0
$556$	317.912	+	550.640i	0.571785	+	0.990360i
$557$	562.331	+	150.676i	1.00957	+	0.270514i	0.725450	−	0.688275i	$-0.241632\pi$
$557$	562.331	+	150.676i	1.00957	+	0.270514i	0.284121	+	0.958789i	$0.408298\pi$
$558$		0			0
$559$			10.5077i			0.0187973i
$560$	−107.378	+	74.8793i	−0.191747	+	0.133713i
$561$		0			0
$562$	−103.692	−	386.982i	−0.184505	−	0.688581i
$563$	108.207	−	403.835i	0.192197	−	0.717291i	−0.800777	−	0.598963i	$-0.795580\pi$
$563$	108.207	−	403.835i	0.192197	−	0.717291i	0.992975	−	0.118328i	$-0.0377535\pi$
$564$		0			0
$565$	14.1268	−	29.2866i	0.0250031	−	0.0518346i
$566$	872.570			1.54164
$567$		0			0
$568$	−127.542	−	127.542i	−0.224546	−	0.224546i
$569$	424.932	+	245.335i	0.746806	+	0.431168i	0.824539	−	0.565806i	$-0.191435\pi$
$569$	424.932	+	245.335i	0.746806	+	0.431168i	−0.0777329	+	0.996974i	$0.524768\pi$
$570$		0			0
$571$	105.483	+	182.702i	0.184734	+	0.319969i	0.943487	−	0.331410i	$-0.107524\pi$
$571$	105.483	+	182.702i	0.184734	+	0.319969i	−0.758753	+	0.651379i	$0.774191\pi$
$572$	43.0199	+	160.553i	0.0752096	+	0.280686i
$573$		0			0
$574$	971.660	+	546.595i	1.69279	+	0.952257i
$575$	−183.622	+	248.135i	−0.319343	+	0.431538i
$576$		0			0
$577$	−68.3580	−	18.3165i	−0.118471	−	0.0317443i	0.199096	−	0.979980i	$-0.436199\pi$
$577$	−68.3580	−	18.3165i	−0.118471	−	0.0317443i	−0.317568	+	0.948236i	$0.602866\pi$
$578$	372.687	−	1390.89i	0.644787	−	2.40638i
$579$		0			0
$580$	−281.598	+	326.800i	−0.485514	+	0.563448i
$581$	−179.071	+	2.00218i	−0.308212	+	0.00344609i
$582$		0			0
$583$	−53.0092	+	14.2038i	−0.0909249	+	0.0243633i
$584$	1007.36	−	581.599i	1.72493	−	0.995888i
$585$		0			0
$586$	−137.984	+	238.996i	−0.235468	+	0.407842i
$587$	716.384	−	716.384i	1.22042	−	1.22042i	0.252932	−	0.967484i	$-0.418605\pi$
$587$	716.384	−	716.384i	1.22042	−	1.22042i	0.967484	−	0.252932i	$-0.0813949\pi$
$588$		0			0
$589$			474.724i			0.805982i
$590$	−409.583	+	849.117i	−0.694208	+	1.43918i
$591$		0			0
$592$	−51.1070	−	13.6941i	−0.0863294	−	0.0231319i
$593$	−676.921	+	181.380i	−1.14152	+	0.305869i	−0.779562	−	0.626325i	$-0.784558\pi$
$593$	−676.921	+	181.380i	−1.14152	+	0.305869i	−0.361958	+	0.932194i	$0.617892\pi$
$594$		0			0
$595$	721.104	+	607.449i	1.21194	+	1.02092i
$596$	1113.35			1.86803
$597$		0			0
$598$	−218.959	+	817.165i	−0.366152	+	1.36650i
$599$	39.4905	−	22.7998i	0.0659273	−	0.0380632i	−0.466674	−	0.884429i	$-0.654548\pi$
$599$	39.4905	−	22.7998i	0.0659273	−	0.0380632i	0.532601	+	0.846366i	$0.321215\pi$
$600$		0			0
$601$	1084.31			1.80418			0.902092	−	0.431544i	$-0.142031\pi$
$601$	1084.31			1.80418			0.902092	+	0.431544i	$0.142031\pi$
$602$	3.14679	+	11.2398i	0.00522723	+	0.0186707i
$603$		0			0
$604$	−1707.34	−	985.734i	−2.82672	−	1.63201i
$605$	−587.725	−	111.593i	−0.971447	−	0.184451i
$606$		0			0
$607$	−109.843	−	409.938i	−0.180960	−	0.675351i	−0.995459	−	0.0951869i	$-0.969655\pi$
$607$	−109.843	−	409.938i	−0.180960	−	0.675351i	0.814500	−	0.580164i	$-0.197012\pi$
$608$	520.462	+	520.462i	0.856024	+	0.856024i
$609$		0			0
$610$	15.4105	+	207.419i	0.0252631	+	0.340032i
$611$	294.344	−	509.819i	0.481741	−	0.834400i
$612$		0			0
$613$	149.542	−	558.097i	0.243950	−	0.910435i	−0.729958	−	0.683492i	$-0.760460\pi$
$613$	149.542	−	558.097i	0.243950	−	0.910435i	0.973908	−	0.226943i	$-0.0728731\pi$
$614$	404.144	+	233.333i	0.658215	+	0.380021i
$615$		0			0
$616$	39.3295	+	66.3952i	0.0638466	+	0.107784i
$617$	−23.3244	+	23.3244i	−0.0378030	+	0.0378030i	−0.725756	−	0.687953i	$-0.758510\pi$
$617$	−23.3244	+	23.3244i	−0.0378030	+	0.0378030i	0.687953	+	0.725756i	$0.258510\pi$
$618$		0			0
$619$	534.066	−	308.343i	0.862788	−	0.498131i	−0.00215709	−	0.999998i	$-0.500687\pi$
$619$	534.066	−	308.343i	0.862788	−	0.498131i	0.864945	+	0.501867i	$0.167353\pi$
$620$	−105.637	+	556.354i	−0.170382	+	0.897346i
$621$		0			0
$622$	657.928	−	657.928i	1.05776	−	1.05776i
$623$	−608.379	+	170.327i	−0.976532	+	0.273398i
$624$		0			0
$625$	140.634	−	608.972i	0.225015	−	0.974355i
$626$	−325.651	−	564.044i	−0.520210	−	0.901029i
$627$		0			0
$628$	1899.24	−	508.899i	3.02426	−	0.810348i
$629$			381.081i			0.605852i
$630$		0			0
$631$	524.168			0.830695			0.415347	−	0.909663i	$-0.363660\pi$
$631$	524.168			0.830695			0.415347	+	0.909663i	$0.363660\pi$
$632$	−209.909	−	783.393i	−0.332135	−	1.23955i
$633$		0			0
$634$	447.555	−	258.396i	0.705923	−	0.407565i
$635$	−106.327	−	51.2884i	−0.167445	−	0.0807692i
$636$		0			0
$637$	−703.678	+	735.873i	−1.10467	+	1.15522i
$638$	34.0705	+	34.0705i	0.0534020	+	0.0534020i
$639$		0			0
$640$	632.959	+	929.658i	0.988999	+	1.45259i
$641$	−29.7943	−	51.6052i	−0.0464809	−	0.0805074i	0.841849	−	0.539713i	$-0.181467\pi$
$641$	−29.7943	−	51.6052i	−0.0464809	−	0.0805074i	−0.888330	+	0.459206i	$0.848134\pi$
$642$		0			0
$643$	−282.054	−	282.054i	−0.438653	−	0.438653i	0.452906	−	0.891558i	$-0.350387\pi$
$643$	−282.054	−	282.054i	−0.438653	−	0.438653i	−0.891558	+	0.452906i	$0.850387\pi$
$644$	6.64103	+	593.961i	0.0103122	+	0.922300i
$645$		0			0
$646$	−1279.35	+	2215.89i	−1.98041	+	3.43018i
$647$	422.913	+	113.319i	0.653652	+	0.175145i	0.570379	−	0.821381i	$-0.306796\pi$
$647$	422.913	+	113.319i	0.653652	+	0.175145i	0.0832724	+	0.996527i	$0.473463\pi$
$648$		0			0
$649$	57.6409	+	33.2790i	0.0888149	+	0.0512773i
$650$	−253.124	−	1694.07i	−0.389422	−	2.60627i
$651$		0			0
$652$	−49.5079	+	49.5079i	−0.0759323	+	0.0759323i
$653$	454.660	−	121.826i	0.696263	−	0.186563i	0.106707	−	0.994291i	$-0.465969\pi$
$653$	454.660	−	121.826i	0.696263	−	0.186563i	0.589556	+	0.807727i	$0.299303\pi$
$654$		0			0
$655$	−622.876	−	118.267i	−0.950956	−	0.180561i
$656$	−90.3285	+	156.454i	−0.137696	+	0.238496i
$657$		0			0
$658$	162.173	−	633.486i	0.246464	−	0.962745i
$659$			1076.98i			1.63426i	0.576454	+	0.817129i	$0.304436\pi$
$659$			1076.98i			1.63426i	−0.576454	+	0.817129i	$0.695564\pi$
$660$		0			0
$661$	−36.2193	−	62.7337i	−0.0547948	−	0.0949073i	0.837327	−	0.546702i	$-0.184117\pi$
$661$	−36.2193	−	62.7337i	−0.0547948	−	0.0949073i	−0.892122	+	0.451795i	$0.850784\pi$
$662$	1564.45	+	419.193i	2.36322	+	0.633222i
$663$		0			0
$664$		−	242.305i		−	0.364916i
$665$	−576.686	−	826.978i	−0.867197	−	1.24358i
$666$		0			0
$667$	40.1204	+	149.731i	0.0601505	+	0.224485i
$668$	−178.936	+	667.799i	−0.267868	+	0.999699i
$669$		0			0
$670$	724.891	−	253.130i	1.08193	−	0.377806i
$671$	14.6843			0.0218842
$672$		0			0
$673$	−217.067	−	217.067i	−0.322537	−	0.322537i	0.527203	−	0.849740i	$-0.323241\pi$
$673$	−217.067	−	217.067i	−0.322537	−	0.322537i	−0.849740	+	0.527203i	$0.823241\pi$
$674$	1010.48	+	583.402i	1.49923	+	0.865581i
$675$		0			0
$676$	−902.916	−	1563.90i	−1.33568	−	2.31346i
$677$	−190.851	−	712.265i	−0.281907	−	1.05209i	−0.951070	−	0.308975i	$-0.900014\pi$
$677$	−190.851	−	712.265i	−0.281907	−	1.05209i	0.669164	−	0.743115i	$-0.266652\pi$
$678$		0			0
$679$	−9.32314	−	833.843i	−0.0137307	−	1.22805i
$680$	−832.756	+	966.428i	−1.22464	+	1.42122i
$681$		0			0
$682$	61.0958	+	16.3706i	0.0895833	+	0.0240038i
$683$	119.977	−	447.760i	0.175662	−	0.655579i	−0.820776	−	0.571250i	$-0.806459\pi$
$683$	119.977	−	447.760i	0.175662	−	0.655579i	0.996438	−	0.0843288i	$-0.0268746\pi$
$684$		0			0
$685$	−59.8689	−	805.812i	−0.0873998	−	1.17637i
$686$	−532.328	+	997.874i	−0.775988	+	1.45463i
$687$		0			0
$688$	−1.82695	+	0.489530i	−0.00265545	+	0.000711526i
$689$	848.441	−	489.848i	1.23141	−	0.710955i
$690$		0			0
$691$	206.290	−	357.305i	0.298538	−	0.517084i	−0.677263	−	0.735741i	$-0.736834\pi$
$691$	206.290	−	357.305i	0.298538	−	0.517084i	0.975802	+	0.218657i	$0.0701676\pi$
$692$	−1454.59	+	1454.59i	−2.10200	+	2.10200i
$693$		0			0
$694$			2046.58i			2.94897i
$695$	−436.731	+	152.505i	−0.628391	+	0.219432i
$696$		0			0
$697$	1256.84	+	336.768i	1.80321	+	0.483168i
$698$	−221.794	+	59.4294i	−0.317756	+	0.0851424i
$699$		0			0
$700$	−491.828	−	1097.51i	−0.702612	−	1.56786i
$701$	946.008			1.34951			0.674756	−	0.738041i	$-0.264249\pi$
$701$	946.008			1.34951			0.674756	+	0.738041i	$0.264249\pi$
$702$		0			0
$703$	105.466	−	393.603i	0.150022	−	0.559890i
$704$	100.011	−	57.7415i	0.142061	−	0.0820191i
$705$		0			0
$706$	187.795			0.265999
$707$	−503.015	−	128.772i	−0.711478	−	0.182139i
$708$		0			0
$709$	66.1749	+	38.2061i	0.0933355	+	0.0538873i	0.545941	−	0.837823i	$-0.316172\pi$
$709$	66.1749	+	38.2061i	0.0933355	+	0.0538873i	−0.452606	+	0.891711i	$0.649505\pi$
$710$	259.531	−	176.702i	0.365537	−	0.248876i
$711$		0			0
$712$	−221.241	−	825.683i	−0.310732	−	1.15967i
$713$	143.889	+	143.889i	0.201808	+	0.201808i
$714$		0			0
$715$	−120.598	+	8.95999i	−0.168668	+	0.0125315i
$716$	−1111.74	+	1925.58i	−1.55270	+	2.68936i
$717$		0			0
$718$	52.0256	−	194.162i	0.0724591	−	0.270421i
$719$	726.346	+	419.356i	1.01022	+	0.583249i	0.911255	−	0.411842i	$-0.135114\pi$
$719$	726.346	+	419.356i	1.01022	+	0.583249i	0.0989618	+	0.995091i	$0.468448\pi$
$720$		0			0
$721$	−329.264	+	585.319i	−0.456677	+	0.811815i
$722$	1092.95	−	1092.95i	1.51378	−	1.51378i
$723$		0			0
$724$	−257.538	+	148.690i	−0.355715	+	0.205372i
$725$	−195.372	−	245.632i	−0.269478	−	0.338803i
$726$		0			0
$727$	325.814	−	325.814i	0.448162	−	0.448162i	−0.446581	−	0.894743i	$-0.647359\pi$
$727$	325.814	−	325.814i	0.448162	−	0.448162i	0.894743	+	0.446581i	$0.147359\pi$
$728$	−984.954	−	963.172i	−1.35296	−	1.32304i
$729$		0			0
$730$	667.522	+	1911.59i	0.914414	+	2.61862i
$731$	6.81135	+	11.7976i	0.00931785	+	0.0161390i
$732$		0			0
$733$	657.430	−	176.158i	0.896903	−	0.240324i	0.219217	−	0.975676i	$-0.429650\pi$
$733$	657.430	−	176.158i	0.896903	−	0.240324i	0.677686	+	0.735352i	$0.262983\pi$
$734$		−	1188.31i		−	1.61896i
$735$		0			0
$736$	315.505			0.428676
$737$	−14.0301	−	52.3612i	−0.0190368	−	0.0710464i
$738$		0			0
$739$	1219.14	−	703.869i	1.64971	−	0.952461i	0.672526	−	0.740074i	$-0.265209\pi$
$739$	1219.14	−	703.869i	1.64971	−	0.952461i	0.977185	−	0.212388i	$-0.0681240\pi$
$740$	211.186	−	437.816i	0.285387	−	0.591643i
$741$		0			0
$742$	760.856	−	778.062i	1.02541	−	1.04860i
$743$	431.433	+	431.433i	0.580664	+	0.580664i	0.935086	−	0.354422i	$-0.115322\pi$
$743$	431.433	+	431.433i	0.580664	+	0.580664i	−0.354422	+	0.935086i	$0.615322\pi$
$744$		0			0
$745$	−151.100	+	795.796i	−0.202819	+	1.06818i
$746$	−29.6986	−	51.4394i	−0.0398104	−	0.0689537i
$747$		0			0
$748$	152.375	+	152.375i	0.203710	+	0.203710i
$749$	−269.588	−	151.653i	−0.359931	−	0.202475i
$750$		0			0
$751$	98.6211	−	170.817i	0.131320	−	0.227452i	−0.792866	−	0.609396i	$-0.791412\pi$
$751$	98.6211	−	170.817i	0.131320	−	0.227452i	0.924186	+	0.381944i	$0.124745\pi$
$752$	102.354	+	27.4256i	0.136109	+	0.0364702i
$753$		0			0
$754$	−744.917	−	430.078i	−0.987953	−	0.570395i
$755$	936.296	−	1086.59i	1.24013	−	1.43919i
$756$		0			0
$757$	−925.874	+	925.874i	−1.22308	+	1.22308i	−0.256553	+	0.966530i	$0.582587\pi$
$757$	−925.874	+	925.874i	−1.22308	+	1.22308i	−0.966530	+	0.256553i	$0.917413\pi$
$758$	298.691	−	80.0341i	0.394052	−	0.105586i
$759$		0			0
$760$	1127.58	−	767.717i	1.48366	−	1.01015i
$761$	−148.294	+	256.852i	−0.194867	+	0.337519i	−0.946857	−	0.321655i	$-0.895761\pi$
$761$	−148.294	+	256.852i	−0.194867	+	0.337519i	0.751990	+	0.659174i	$0.229094\pi$
$762$		0			0
$763$	−235.770	+	920.973i	−0.309004	+	1.20704i
$764$			265.205i			0.347127i
$765$		0			0
$766$	−682.647	−	1182.38i	−0.891184	−	1.54358i
$767$	−1147.70	−	307.524i	−1.49635	−	0.400945i
$768$		0			0
$769$			483.085i			0.628199i	0.949390	+	0.314099i	$0.101703\pi$
$769$			483.085i			0.628199i	−0.949390	+	0.314099i	$0.898297\pi$
$770$	−126.317	+	45.7002i	−0.164048	+	0.0593509i
$771$		0			0
$772$	429.484	+	1602.85i	0.556326	+	2.07624i
$773$	82.9229	−	309.472i	0.107274	−	0.400353i	−0.891319	−	0.453376i	$-0.850219\pi$
$773$	82.9229	−	309.472i	0.107274	−	0.400353i	0.998593	+	0.0530240i	$0.0168860\pi$
$774$		0			0
$775$	−383.333	−	151.013i	−0.494623	−	0.194856i
$776$	1128.29			1.45398
$777$		0			0
$778$	−383.338	−	383.338i	−0.492723	−	0.492723i
$779$	−1204.93	−	695.669i	−1.54677	−	0.893028i
$780$		0			0
$781$	−11.0834	−	19.1970i	−0.0141913	−	0.0245800i
$782$	283.868	+	1059.41i	0.363003	+	1.35475i
$783$		0			0
$784$	−160.727	−	88.0641i	−0.205009	−	0.112327i
$785$	105.991	+	1426.60i	0.135020	+	1.81732i
$786$		0			0
$787$	−817.557	−	219.064i	−1.03883	−	0.278353i	−0.301200	−	0.953561i	$-0.597387\pi$
$787$	−817.557	−	219.064i	−1.03883	−	0.278353i	−0.737627	+	0.675208i	$0.764054\pi$
$788$	546.872	−	2040.95i	0.694000	−	2.59004i
$789$		0			0
$790$	1407.88	−	104.600i	1.78213	−	0.132406i
$791$	45.5191	−	0.508945i	0.0575463	−	0.000643420i
$792$		0			0
$793$	−253.209	+	67.8473i	−0.319306	+	0.0855577i
$794$	1669.05	−	963.626i	2.10208	−	1.21363i
$795$		0			0
$796$	−668.363	+	1157.64i	−0.839652	+	1.45432i
$797$	−1003.28	+	1003.28i	−1.25882	+	1.25882i	−0.307160	+	0.951658i	$0.599379\pi$
$797$	−1003.28	+	1003.28i	−1.25882	+	1.25882i	−0.951658	+	0.307160i	$0.900621\pi$
$798$		0			0
$799$		−	763.203i		−	0.955197i
$800$	−585.830	+	254.703i	−0.732287	+	0.318379i
$801$		0			0
$802$	−511.086	−	136.945i	−0.637265	−	0.170755i
$803$	138.080	−	36.9985i	0.171955	−	0.0460753i
$804$		0			0
$805$	−425.452	−	75.8637i	−0.528511	−	0.0942407i
$806$	−1129.15			−1.40093
$807$		0			0
$808$	181.832	−	678.606i	0.225040	−	0.839859i
$809$	331.791	−	191.559i	0.410124	−	0.236785i	−0.280719	−	0.959790i	$-0.590573\pi$
$809$	331.791	−	191.559i	0.410124	−	0.236785i	0.690843	+	0.723005i	$0.257240\pi$
$810$		0			0
$811$	537.982			0.663357			0.331678	−	0.943393i	$-0.392385\pi$
$811$	537.982			0.663357			0.331678	+	0.943393i	$0.392385\pi$
$812$	−585.076	−	149.780i	−0.720537	−	0.184458i
$813$		0			0
$814$	−47.0188	−	27.1463i	−0.0577627	−	0.0333493i
$815$	−28.6681	−	42.1062i	−0.0351756	−	0.0516640i
$816$		0			0
$817$	−3.77013	−	14.0703i	−0.00461461	−	0.0172220i
$818$	−385.727	−	385.727i	−0.471549	−	0.471549i
$819$		0			0
$820$	−1257.32	−	1083.42i	−1.53332	−	1.32124i
$821$	192.500	−	333.419i	0.234470	−	0.406114i	−0.724649	−	0.689119i	$-0.757998\pi$
$821$	192.500	−	333.419i	0.234470	−	0.406114i	0.959118	+	0.283005i	$0.0913312\pi$
$822$		0			0
$823$	−57.6069	+	214.992i	−0.0699963	+	0.261230i	−0.992052	−	0.125827i	$-0.959842\pi$
$823$	−57.6069	+	214.992i	−0.0699963	+	0.261230i	0.922056	+	0.387057i	$0.126508\pi$
$824$	−786.926	−	454.332i	−0.955007	−	0.551374i
$825$		0			0
$826$	−1319.75	+	14.7561i	−1.59776	+	0.0178645i
$827$	542.598	−	542.598i	0.656104	−	0.656104i	−0.298352	−	0.954456i	$-0.596437\pi$
$827$	542.598	−	542.598i	0.656104	−	0.656104i	0.954456	+	0.298352i	$0.0964370\pi$
$828$		0			0
$829$	968.472	−	559.148i	1.16824	−	0.674485i	0.214976	−	0.976619i	$-0.431033\pi$
$829$	968.472	−	559.148i	1.16824	−	0.674485i	0.953265	+	0.302135i	$0.0976992\pi$
$830$	414.378	+	78.6791i	0.499250	+	0.0947941i
$831$		0			0
$832$	−1457.76	+	1457.76i	−1.75212	+	1.75212i
$833$	−313.048	+	1282.35i	−0.375808	+	1.53943i
$834$		0			0
$835$	−453.043	−	218.531i	−0.542567	−	0.261714i
$836$	−115.212	−	199.552i	−0.137813	−	0.238699i
$837$		0			0
$838$	−1822.18	+	488.251i	−2.17444	+	0.582638i
$839$			866.690i			1.03300i	0.856286	+	0.516502i	$0.172766\pi$
$839$			866.690i			1.03300i	−0.856286	+	0.516502i	$0.827234\pi$
$840$		0			0
$841$	683.391			0.812594
$842$	−221.374	−	826.177i	−0.262914	−	0.981208i
$843$		0			0
$844$	401.384	−	231.739i	0.475574	−	0.274573i
$845$	1240.38	−	433.137i	1.46791	−	0.512589i
$846$		0			0
$847$	−225.796	−	806.505i	−0.266583	−	0.952190i
$848$	124.696	+	124.696i	0.147047	+	0.147047i
$849$		0			0
$850$	−1382.34	−	1737.95i	−1.62628	−	2.04465i
$851$	−87.3347	−	151.268i	−0.102626	−	0.177753i
$852$		0			0
$853$	846.282	+	846.282i	0.992124	+	0.992124i	0.999969	−	0.00784512i	$-0.00249721\pi$
$853$	846.282	+	846.282i	0.992124	+	0.992124i	−0.00784512	+	0.999969i	$0.502497\pi$
$854$	−250.532	+	148.404i	−0.293363	+	0.173775i
$855$		0			0
$856$	209.258	−	362.445i	0.244460	−	0.423417i
$857$	940.421	+	251.985i	1.09734	+	0.294032i	0.761681	−	0.647952i	$-0.224374\pi$
$857$	940.421	+	251.985i	1.09734	+	0.294032i	0.335659	+	0.941983i	$0.391041\pi$
$858$		0			0
$859$	1270.34	+	733.431i	1.47886	+	0.853819i	0.999714	−	0.0239168i	$-0.00761368\pi$
$859$	1270.34	+	733.431i	1.47886	+	0.853819i	0.479144	+	0.877736i	$0.340947\pi$
$860$	−1.28746	−	17.3287i	−0.00149705	−	0.0201497i
$861$		0			0
$862$	1447.14	−	1447.14i	1.67881	−	1.67881i
$863$	805.996	−	215.966i	0.933946	−	0.250250i	0.240410	−	0.970672i	$-0.422718\pi$
$863$	805.996	−	215.966i	0.933946	−	0.250250i	0.693537	+	0.720421i	$0.256052\pi$
$864$		0			0
$865$	−842.295	−	1237.12i	−0.973751	−	1.43020i
$866$	780.260	−	1351.45i	0.900993	−	1.56057i
$867$		0			0
$868$	−763.456	+	213.744i	−0.879557	+	0.246249i
$869$		−	99.6712i		−	0.114696i
$870$		0			0
$871$	483.859	+	838.069i	0.555521	+	0.962191i
$872$	−1242.46	−	332.917i	−1.42484	−	0.381786i
$873$		0			0
$874$		−	1172.79i		−	1.34186i
$875$	851.222	−	202.598i	0.972825	−	0.231540i
$876$		0			0
$877$	−389.839	−	1454.90i	−0.444514	−	1.65895i	−0.717215	−	0.696852i	$-0.754584\pi$
$877$	−389.839	−	1454.90i	−0.444514	−	1.65895i	0.272701	−	0.962099i	$-0.412083\pi$
$878$	−560.493	+	2091.79i	−0.638375	+	2.38245i
$879$		0			0
$880$	−7.17623	−	20.5506i	−0.00815481	−	0.0233530i
$881$	−381.409			−0.432928			−0.216464	−	0.976291i	$-0.569452\pi$
$881$	−381.409			−0.432928			−0.216464	+	0.976291i	$0.569452\pi$
$882$		0			0
$883$	523.721	+	523.721i	0.593115	+	0.593115i	0.938472	−	0.345356i	$-0.112242\pi$
$883$	523.721	+	523.721i	0.593115	+	0.593115i	−0.345356	+	0.938472i	$0.612242\pi$
$884$	−3331.52	−	1923.45i	−3.76869	−	2.17585i
$885$		0			0
$886$	983.867	+	1704.11i	1.11046	+	1.92337i
$887$	−286.223	−	1068.20i	−0.322686	−	1.20428i	−0.916617	−	0.399766i	$-0.869091\pi$
$887$	−286.223	−	1068.20i	−0.322686	−	1.20428i	0.593931	−	0.804516i	$-0.297575\pi$
$888$		0			0
$889$	−1.84777	−	165.261i	−0.00207848	−	0.185895i
$890$	1483.88	−	110.247i	1.66729	−	0.123873i
$891$		0			0
$892$	−165.945	−	44.4648i	−0.186037	−	0.0498485i
$893$	−211.219	+	788.281i	−0.236528	+	0.882734i
$894$		0			0
$895$	−1225.48	−	1055.98i	−1.36925	−	1.17986i
$896$	−771.981	+	1372.32i	−0.861585	+	1.53160i
$897$		0			0
$898$	−517.998	+	138.797i	−0.576835	+	0.154563i
$899$	−179.178	+	103.448i	−0.199308	+	0.115071i
$900$		0			0
$901$	635.062	−	1099.96i	0.704841	−	1.22082i
$902$	−131.082	+	131.082i	−0.145324	+	0.145324i
$903$		0			0
$904$			61.5927i			0.0681336i
$905$	−71.3278	−	204.262i	−0.0788152	−	0.225704i
$906$		0			0
$907$	−881.400	−	236.171i	−0.971776	−	0.260386i	−0.262198	−	0.965014i	$-0.584447\pi$
$907$	−881.400	−	236.171i	−0.971776	−	0.260386i	−0.709577	+	0.704628i	$0.751114\pi$
$908$	2128.82	−	570.416i	2.34452	−	0.628212i
$909$		0			0
$910$	1967.00	−	1371.67i	2.16154	−	1.50733i
$911$	−269.276			−0.295583			−0.147791	−	0.989019i	$-0.547216\pi$
$911$	−269.276			−0.295583			−0.147791	+	0.989019i	$0.547216\pi$
$912$		0			0
$913$	7.70711	−	28.7633i	0.00844153	−	0.0315042i
$914$	−1439.21	+	830.930i	−1.57463	+	0.909113i
$915$		0			0
$916$	2303.60			2.51485
$917$	−239.301	−	854.740i	−0.260960	−	0.932104i
$918$		0			0
$919$	−723.603	−	417.773i	−0.787381	−	0.454595i	0.0516585	−	0.998665i	$-0.483549\pi$
$919$	−723.603	−	417.773i	−0.787381	−	0.454595i	−0.839040	+	0.544070i	$0.816883\pi$
$920$	109.076	−	574.467i	0.118561	−	0.624421i
$921$		0			0
$922$	276.013	+	1030.09i	0.299363	+	1.11724i
$923$	279.815	+	279.815i	0.303158	+	0.303158i
$924$		0			0
$925$	284.280	+	210.370i	0.307329	+	0.227427i
$926$	252.956	−	438.132i	0.273170	−	0.473145i
$927$		0			0
$928$	−83.0260	+	309.857i	−0.0894676	+	0.333898i
$929$	−1433.61	−	827.695i	−1.54318	−	0.890953i	−0.998636	−	0.0522181i	$-0.983371\pi$
$929$	−1433.61	−	827.695i	−1.54318	−	0.890953i	−0.544540	−	0.838735i	$-0.683296\pi$
$930$		0			0
$931$	678.230	−	1237.85i	0.728496	−	1.32959i
$932$	−1347.70	+	1347.70i	−1.44603	+	1.44603i
$933$		0			0
$934$	1343.54	−	775.694i	1.43848	−	0.830507i
$935$	−129.594	+	88.2343i	−0.138603	+	0.0943682i
$936$		0			0
$937$	−260.635	+	260.635i	−0.278159	+	0.278159i	−0.832374	−	0.554215i	$-0.813019\pi$
$937$	−260.635	+	260.635i	−0.278159	+	0.278159i	0.554215	+	0.832374i	$0.313019\pi$
$938$	768.550	+	751.554i	0.819350	+	0.801230i
$939$		0			0
$940$	−422.950	+	876.829i	−0.449946	+	0.932796i
$941$	398.010	+	689.374i	0.422965	+	0.732597i	0.996228	−	0.0867746i	$-0.0276560\pi$
$941$	398.010	+	689.374i	0.422965	+	0.732597i	−0.573263	+	0.819371i	$0.694323\pi$
$942$		0			0
$943$	−576.074	+	154.359i	−0.610895	+	0.163689i
$944$		−	213.874i		−	0.226562i
$945$		0			0
$946$	−1.94083			−0.00205162
$947$	419.263	+	1564.71i	0.442727	+	1.65228i	0.721869	+	0.692030i	$0.243283\pi$
$947$	419.263	+	1564.71i	0.442727	+	1.65228i	−0.279142	+	0.960250i	$0.590050\pi$
$948$		0			0
$949$	−2210.05	+	1275.97i	−2.32882	+	1.34454i
$950$	946.774	+	2177.63i	0.996604	+	2.29224i
$951$		0			0
$952$	−1730.21	−	442.937i	−1.81745	−	0.465270i
$953$	−935.909	−	935.909i	−0.982066	−	0.982066i	0.0177757	−	0.999842i	$-0.494342\pi$
$953$	−935.909	−	935.909i	−0.982066	−	0.982066i	−0.999842	+	0.0177757i	$0.994342\pi$
$954$		0			0
$955$	−189.562	−	35.9928i	−0.198495	−	0.0376888i
$956$	−196.539	−	340.415i	−0.205585	−	0.356083i
$957$		0			0
$958$	215.267	+	215.267i	0.224704	+	0.224704i
$959$	973.303	−	576.541i	1.01491	−	0.601190i
$960$		0			0
$961$	344.701	−	597.039i	0.358689	−	0.621268i
$962$	936.200	+	250.854i	0.973180	+	0.260763i
$963$		0			0
$964$	58.9276	+	34.0218i	0.0611282	+	0.0352924i
$965$	−1203.97	+	89.4509i	−1.24764	+	0.0926952i
$966$		0			0
$967$	−469.949	+	469.949i	−0.485987	+	0.485987i	−0.907037	−	0.421050i	$-0.861662\pi$
$967$	−469.949	+	469.949i	−0.485987	+	0.485987i	0.421050	+	0.907037i	$0.361662\pi$
$968$	1094.58	−	293.291i	1.13076	−	0.302986i
$969$		0			0
$970$	−366.369	+	1929.55i	−0.377700	+	1.98922i
$971$	−313.617	+	543.200i	−0.322983	+	0.559424i	−0.981102	−	0.193490i	$-0.938019\pi$
$971$	−313.617	+	543.200i	−0.322983	+	0.559424i	0.658119	+	0.752914i	$0.271352\pi$
$972$		0			0
$973$	−463.035	−	452.795i	−0.475884	−	0.465360i
$974$		−	2629.09i		−	2.69928i
$975$		0			0
$976$	−23.5929	−	40.8641i	−0.0241730	−	0.0418689i
$977$	918.098	+	246.004i	0.939712	+	0.251795i	0.695991	−	0.718050i	$-0.254965\pi$
$977$	918.098	+	246.004i	0.939712	+	0.251795i	0.243721	+	0.969845i	$0.421632\pi$
$978$		0			0
$979$		−	105.052i		−	0.107305i
$980$	1070.30	−	1299.78i	1.09215	−	1.32630i
$981$		0			0
$982$	377.602	+	1409.23i	0.384523	+	1.43506i
$983$	295.733	−	1103.69i	0.300847	−	1.12278i	−0.635614	−	0.772007i	$-0.719253\pi$
$983$	295.733	−	1103.69i	0.300847	−	1.12278i	0.936462	−	0.350770i	$-0.114080\pi$
$984$		0			0
$985$	1384.61	+	667.884i	1.40569	+	0.678055i
$986$	−1115.15			−1.13098
$987$		0			0
$988$	2908.67	+	2908.67i	2.94400	+	2.94400i
$989$	−5.40746	−	3.12200i	−0.00546761	−	0.00315672i
$990$		0			0
$991$	−430.389	−	745.456i	−0.434298	−	0.752226i	0.562940	−	0.826498i	$-0.309670\pi$
$991$	−430.389	−	745.456i	−0.434298	−	0.752226i	−0.997238	+	0.0742715i	$0.976337\pi$
$992$	108.990	+	406.757i	0.109869	+	0.410038i
$993$		0			0
$994$	383.107	+	215.512i	0.385420	+	0.216813i
$995$	−736.746	−	634.842i	−0.740449	−	0.638032i
$996$		0			0
$997$	−344.942	−	92.4269i	−0.345980	−	0.0927050i	0.0816447	−	0.996661i	$-0.473983\pi$
$997$	−344.942	−	92.4269i	−0.345980	−	0.0927050i	−0.427624	+	0.903957i	$0.640649\pi$
$998$	−59.1016	+	220.570i	−0.0592201	+	0.221012i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.163.2		64
3.2	odd	2		105.3.v.a.58.15	yes	64
5.2	odd	4	inner	315.3.ca.b.37.15		64
7.4	even	3	inner	315.3.ca.b.298.15		64
15.2	even	4		105.3.v.a.37.2	✓	64
21.11	odd	6		105.3.v.a.88.2	yes	64
35.32	odd	12	inner	315.3.ca.b.172.2		64
105.32	even	12		105.3.v.a.67.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.2	✓	64	15.2	even	4
105.3.v.a.58.15	yes	64	3.2	odd	2
105.3.v.a.67.15	yes	64	105.32	even	12
105.3.v.a.88.2	yes	64	21.11	odd	6
315.3.ca.b.37.15		64	5.2	odd	4	inner
315.3.ca.b.163.2		64	1.1	even	1	trivial
315.3.ca.b.172.2		64	35.32	odd	12	inner
315.3.ca.b.298.15		64	7.4	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.853412 - 3.18498i) q^{2} +(-5.95167 + 3.43620i) q^{4} +(-1.64838 - 4.72047i) q^{5} +(4.89410 - 5.00478i) q^{7} +(6.69718 + 6.69718i) q^{8} +O(q^{10})\)	\(q+(-0.853412 - 3.18498i) q^{2} +(-5.95167 + 3.43620i) q^{4} +(-1.64838 - 4.72047i) q^{5} +(4.89410 - 5.00478i) q^{7} +(6.69718 + 6.69718i) q^{8} +(-13.6279 + 9.27855i) q^{10} +(0.581984 + 1.00803i) q^{11} +(-14.6930 - 14.6930i) q^{13} +(-20.1168 - 11.3165i) q^{14} +(1.87012 - 3.23914i) q^{16} +(-26.0209 - 6.97229i) q^{17} +(24.9464 + 14.4028i) q^{19} +(26.0311 + 22.4305i) q^{20} +(2.71387 - 2.71387i) q^{22} +(11.9268 - 3.19577i) q^{23} +(-19.5657 + 15.5622i) q^{25} +(-34.2576 + 59.3359i) q^{26} +(-11.9307 + 46.6039i) q^{28} +12.5542i q^{29} +(8.24013 + 14.2723i) q^{31} +(24.6815 + 6.61339i) q^{32} +88.8263i q^{34} +(-31.6922 - 14.8527i) q^{35} +(-3.66129 - 13.6641i) q^{37} +(24.5830 - 91.7452i) q^{38} +(20.5744 - 42.6533i) q^{40} -48.3009 q^{41} +(-0.357576 - 0.357576i) q^{43} +(-6.92755 - 3.99962i) q^{44} +(-20.3569 - 35.2592i) q^{46} +(7.33258 + 27.3656i) q^{47} +(-1.09559 - 48.9878i) q^{49} +(66.2630 + 49.0354i) q^{50} +(137.936 + 36.9597i) q^{52} +(-12.2029 + 45.5418i) q^{53} +(3.79903 - 4.40884i) q^{55} +(66.2945 - 0.741234i) q^{56} +(39.9849 - 10.7139i) q^{58} +(49.5210 - 28.5910i) q^{59} +(6.30786 - 10.9255i) q^{61} +(38.4248 - 38.4248i) q^{62} -99.2149i q^{64} +(-45.1382 + 93.5772i) q^{65} +(-44.9851 - 12.0537i) q^{67} +(178.826 - 47.9163i) q^{68} +(-20.2590 + 113.615i) q^{70} -19.0442 q^{71} +(31.7865 - 118.629i) q^{73} +(-40.3953 + 23.3222i) q^{74} -197.963 q^{76} +(7.89323 + 2.02068i) q^{77} +(-74.1583 - 42.8153i) q^{79} +(-18.3729 - 3.48852i) q^{80} +(41.2206 + 153.837i) q^{82} +(-18.0900 - 18.0900i) q^{83} +(9.97979 + 134.324i) q^{85} +(-0.833713 + 1.44403i) q^{86} +(-2.85328 + 10.6486i) q^{88} +(-78.1616 - 45.1266i) q^{89} +(-145.444 + 1.62620i) q^{91} +(-60.0029 + 60.0029i) q^{92} +(80.9010 - 46.7082i) q^{94} +(26.8670 - 141.500i) q^{95} +(84.2362 - 84.2362i) q^{97} +(-155.090 + 45.2962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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