LMFDB - Embedded newform 315.3.ca.b.163.3

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			163.3
Character	$\chi$	$=$	315.163
Dual form			315.3.ca.b.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +O(q^{10})$	\(q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +(1.09812 - 14.8351i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 + 7.79302i) q^{13} +(9.99344 + 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(-25.8415 - 6.92421i) q^{17} +(-28.5616 - 16.4901i) q^{19} +(-23.8300 + 4.53140i) q^{20} +(-29.2893 + 29.2893i) q^{22} +(-20.4773 + 5.48688i) q^{23} +(19.5742 + 15.5516i) q^{25} +(16.3944 - 28.3960i) q^{26} +(24.5616 - 23.4519i) q^{28} -18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(43.8970 + 11.7622i) q^{32} +79.5940i q^{34} +(-34.8355 - 3.38952i) q^{35} +(5.40117 + 20.1574i) q^{37} +(-25.3954 + 94.7768i) q^{38} +(5.50557 + 11.4058i) q^{40} +1.69819 q^{41} +(26.7992 + 26.7992i) q^{43} +(58.4946 + 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(-2.75524 - 10.2827i) q^{47} +(43.5218 - 22.5134i) q^{49} +(29.6188 - 68.2264i) q^{50} +(-51.6453 - 13.8383i) q^{52} +(-11.5451 + 43.0869i) q^{53} +(-13.0042 - 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(-52.1677 + 13.9783i) q^{58} +(9.04603 - 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 + 48.7105i) q^{62} -87.7280i q^{64} +(23.9544 + 49.6260i) q^{65} +(-40.9029 - 10.9599i) q^{67} +(125.367 - 33.5921i) q^{68} +(17.0834 + 102.719i) q^{70} +20.1105 q^{71} +(-1.68295 + 6.28085i) q^{73} +(53.7685 - 31.0433i) q^{74} +160.000 q^{76} +(67.3023 + 70.4869i) q^{77} +(-10.5341 - 6.08184i) q^{79} +(-44.9486 + 38.7528i) q^{80} +(-1.30764 - 4.88019i) q^{82} +(-20.6649 - 20.6649i) q^{83} +(-110.591 - 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(9.12749 - 34.0643i) q^{88} +(-145.002 - 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 - 72.7245i) q^{92} +(-27.4284 + 15.8358i) q^{94} +(-107.677 - 124.892i) q^{95} +(-66.3082 + 66.3082i) q^{97} +(-98.2105 - 107.735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.770020	−	2.87375i	−0.385010	−	1.43688i	−0.838151	−	0.545438i	$-0.816363\pi$
$2$	−0.770020	−	2.87375i	−0.385010	−	1.43688i	0.453141	−	0.891439i	$-0.350303\pi$
$3$		0			0
$3$		0			0
$4$	−4.20143	+	2.42570i	−1.05036	+	0.606424i
$5$	4.72092	+	1.64709i	0.944184	+	0.329418i
$5$	4.72092	+	1.64709i	0.944184	+	0.329418i
$6$		0			0
$7$	−6.80154	+	1.65502i	−0.971648	+	0.236431i
$7$	−6.80154	+	1.65502i	−0.971648	+	0.236431i
$8$	1.79111	+	1.79111i	0.223889	+	0.223889i
$9$		0			0
$10$	1.09812	−	14.8351i	0.109812	−	1.48351i
$11$	−6.96127	−	12.0573i	−0.632842	−	1.09612i	−0.986968	−	0.160917i	$-0.948555\pi$
$11$	−6.96127	−	12.0573i	−0.632842	−	1.09612i	0.354126	−	0.935198i	$-0.384779\pi$
$12$		0			0
$13$	7.79302	+	7.79302i	0.599463	+	0.599463i	0.940170	−	0.340707i	$-0.110666\pi$
$13$	7.79302	+	7.79302i	0.599463	+	0.599463i	−0.340707	+	0.940170i	$0.610666\pi$
$14$	9.99344	+	18.2715i	0.713817	+	1.30511i
$15$		0			0
$16$	−5.93477	+	10.2793i	−0.370923	+	0.642458i
$17$	−25.8415	−	6.92421i	−1.52009	−	0.407307i	−0.600318	−	0.799761i	$-0.704959\pi$
$17$	−25.8415	−	6.92421i	−1.52009	−	0.407307i	−0.919771	+	0.392455i	$0.871626\pi$
$18$		0			0
$19$	−28.5616	−	16.4901i	−1.50324	−	0.867898i	−0.999993	−	0.00375778i	$-0.998804\pi$
$19$	−28.5616	−	16.4901i	−1.50324	−	0.867898i	−0.503251	−	0.864140i	$-0.667863\pi$
$20$	−23.8300	+	4.53140i	−1.19150	+	0.226570i
$21$		0			0
$22$	−29.2893	+	29.2893i	−1.33133	+	1.33133i
$23$	−20.4773	+	5.48688i	−0.890318	+	0.238560i	−0.674854	−	0.737952i	$-0.735793\pi$
$23$	−20.4773	+	5.48688i	−0.890318	+	0.238560i	−0.215464	+	0.976512i	$0.569127\pi$
$24$		0			0
$25$	19.5742	+	15.5516i	0.782968	+	0.622062i
$26$	16.3944	−	28.3960i	0.630555	−	1.09215i
$27$		0			0
$28$	24.5616	−	23.4519i	0.877201	−	0.837569i
$29$		−	18.1531i		−	0.625971i	−0.949758	−	0.312985i	$-0.898671\pi$
$29$		−	18.1531i		−	0.625971i	0.949758	−	0.312985i	$-0.101329\pi$
$30$		0			0
$31$	−11.5772	−	20.0522i	−0.373457	−	0.646846i	0.616638	−	0.787247i	$-0.288494\pi$
$31$	−11.5772	−	20.0522i	−0.373457	−	0.646846i	−0.990095	+	0.140401i	$0.955161\pi$
$32$	43.8970	+	11.7622i	1.37178	+	0.367567i
$33$		0			0
$34$			79.5940i			2.34100i
$35$	−34.8355	−	3.38952i	−0.995300	−	0.0968434i
$36$		0			0
$37$	5.40117	+	20.1574i	0.145978	+	0.544796i	0.999710	+	0.0240837i	$0.00766681\pi$
$37$	5.40117	+	20.1574i	0.145978	+	0.544796i	−0.853732	+	0.520712i	$0.825667\pi$
$38$	−25.3954	+	94.7768i	−0.668299	+	2.49413i
$39$		0			0
$40$	5.50557	+	11.4058i	0.137639	+	0.285145i
$41$	1.69819			0.0414193			0.0207097	−	0.999786i	$-0.493407\pi$
$41$	1.69819			0.0414193			0.0207097	+	0.999786i	$0.493407\pi$
$42$		0			0
$43$	26.7992	+	26.7992i	0.623236	+	0.623236i	0.946358	−	0.323121i	$-0.104732\pi$
$43$	26.7992	+	26.7992i	0.623236	+	0.623236i	−0.323121	+	0.946358i	$0.604732\pi$
$44$	58.4946	+	33.7719i	1.32942	+	0.767542i
$45$		0			0
$46$	31.5359	+	54.6218i	0.685563	+	1.18743i
$47$	−2.75524	−	10.2827i	−0.0586222	−	0.218781i	0.930401	−	0.366544i	$-0.119459\pi$
$47$	−2.75524	−	10.2827i	−0.0586222	−	0.218781i	−0.989023	+	0.147763i	$0.952793\pi$
$48$		0			0
$49$	43.5218	−	22.5134i	0.888200	−	0.459456i
$50$	29.6188	−	68.2264i	0.592376	−	1.36453i
$51$		0			0
$52$	−51.6453	−	13.8383i	−0.993179	−	0.266122i
$53$	−11.5451	+	43.0869i	−0.217832	+	0.812961i	0.767318	+	0.641267i	$0.221591\pi$
$53$	−11.5451	+	43.0869i	−0.217832	+	0.812961i	−0.985150	+	0.171694i	$0.945076\pi$
$54$		0			0
$55$	−13.0042	−	68.3872i	−0.236440	−	1.24340i
$56$	−15.1466	−	9.21797i	−0.270475	−	0.164607i
$57$		0			0
$58$	−52.1677	+	13.9783i	−0.899443	+	0.241005i
$59$	9.04603	−	5.22273i	0.153323	−	0.0885208i	−0.421376	−	0.906886i	$-0.638453\pi$
$59$	9.04603	−	5.22273i	0.153323	−	0.0885208i	0.574698	+	0.818365i	$0.305119\pi$
$60$		0			0
$61$	40.5827	−	70.2914i	0.665291	−	1.15232i	−0.313915	−	0.949451i	$-0.601641\pi$
$61$	40.5827	−	70.2914i	0.665291	−	1.15232i	0.979206	−	0.202867i	$-0.0650258\pi$
$62$	−48.7105	+	48.7105i	−0.785654	+	0.785654i
$63$		0			0
$64$		−	87.7280i		−	1.37075i
$65$	23.9544	+	49.6260i	0.368530	+	0.763477i
$66$		0			0
$67$	−40.9029	−	10.9599i	−0.610491	−	0.163581i	−0.0596898	−	0.998217i	$-0.519011\pi$
$67$	−40.9029	−	10.9599i	−0.610491	−	0.163581i	−0.550801	+	0.834636i	$0.685678\pi$
$68$	125.367	−	33.5921i	1.84364	−	0.494001i
$69$		0			0
$70$	17.0834	+	102.719i	0.244048	+	1.46741i
$71$	20.1105			0.283247			0.141623	−	0.989921i	$-0.454768\pi$
$71$	20.1105			0.283247			0.141623	+	0.989921i	$0.454768\pi$
$72$		0			0
$73$	−1.68295	+	6.28085i	−0.0230541	+	0.0860390i	−0.976494	−	0.215543i	$-0.930848\pi$
$73$	−1.68295	+	6.28085i	−0.0230541	+	0.0860390i	0.953440	+	0.301582i	$0.0975146\pi$
$74$	53.7685	−	31.0433i	0.726602	−	0.419504i
$75$		0			0
$76$	160.000			2.10526
$77$	67.3023	+	70.4869i	0.874056	+	0.915415i
$78$		0			0
$79$	−10.5341	−	6.08184i	−0.133342	−	0.0769853i	0.431845	−	0.901948i	$-0.357863\pi$
$79$	−10.5341	−	6.08184i	−0.133342	−	0.0769853i	−0.565187	+	0.824963i	$0.691196\pi$
$80$	−44.9486	+	38.7528i	−0.561857	+	0.484410i
$81$		0			0
$82$	−1.30764	−	4.88019i	−0.0159469	−	0.0595145i
$83$	−20.6649	−	20.6649i	−0.248975	−	0.248975i	0.571575	−	0.820550i	$-0.306333\pi$
$83$	−20.6649	−	20.6649i	−0.248975	−	0.248975i	−0.820550	+	0.571575i	$0.806333\pi$
$84$		0			0
$85$	−110.591	−	75.2519i	−1.30107	−	0.885317i
$86$	56.3783	−	97.6501i	0.655562	−	1.13547i
$87$		0			0
$88$	9.12749	−	34.0643i	0.103721	−	0.387094i
$89$	−145.002	−	83.7168i	−1.62923	−	0.940638i	−0.984322	−	0.176381i	$-0.943561\pi$
$89$	−145.002	−	83.7168i	−1.62923	−	0.940638i	−0.644911	−	0.764257i	$-0.723106\pi$
$90$		0			0
$91$	−65.9021	−	40.1069i	−0.724199	−	0.440735i
$92$	72.7245	−	72.7245i	0.790484	−	0.790484i
$93$		0			0
$94$	−27.4284	+	15.8358i	−0.291791	+	0.168466i
$95$	−107.677	−	124.892i	−1.13344	−	1.31465i
$96$		0			0
$97$	−66.3082	+	66.3082i	−0.683589	+	0.683589i	−0.960807	−	0.277218i	$-0.910588\pi$
$97$	−66.3082	+	66.3082i	−0.683589	+	0.683589i	0.277218	+	0.960807i	$0.410588\pi$
$98$	−98.2105	−	107.735i	−1.00215	−	1.09934i
$99$		0			0
$100$	−119.963	−	17.8577i	−1.19963	−	0.178577i
$101$	22.9150	+	39.6899i	0.226881	+	0.392969i	0.956882	−	0.290477i	$-0.0938138\pi$
$101$	22.9150	+	39.6899i	0.226881	+	0.392969i	−0.730001	+	0.683446i	$0.760481\pi$
$102$		0			0
$103$	−21.1782	+	5.67468i	−0.205614	+	0.0550940i	−0.360156	−	0.932892i	$-0.617276\pi$
$103$	−21.1782	+	5.67468i	−0.205614	+	0.0550940i	0.154542	+	0.987986i	$0.450610\pi$
$104$			27.9163i			0.268426i
$105$		0			0
$106$	132.711			1.25199
$107$	−26.1382	−	97.5490i	−0.244282	−	0.911673i	−0.973743	−	0.227650i	$-0.926896\pi$
$107$	−26.1382	−	97.5490i	−0.244282	−	0.911673i	0.729461	−	0.684022i	$-0.239771\pi$
$108$		0			0
$109$	109.890	−	63.4449i	1.00816	−	0.582064i	0.0975104	−	0.995235i	$-0.468912\pi$
$109$	109.890	−	63.4449i	1.00816	−	0.582064i	0.910654	+	0.413171i	$0.135579\pi$
$110$	−186.515	+	90.0304i	−1.69559	+	0.818458i
$111$		0			0
$112$	23.3531	−	79.7374i	0.208510	−	0.711941i
$113$	10.2422	+	10.2422i	0.0906391	+	0.0906391i	0.750973	−	0.660333i	$-0.229585\pi$
$113$	10.2422	+	10.2422i	0.0906391	+	0.0906391i	−0.660333	+	0.750973i	$0.729585\pi$
$114$		0			0
$115$	−105.709	−	7.82482i	−0.919210	−	0.0680419i
$116$	44.0340	+	76.2692i	0.379604	+	0.657493i
$117$		0			0
$118$	−21.9745	−	21.9745i	−0.186224	−	0.186224i
$119$	187.222	+	4.32709i	1.57329	+	0.0363621i
$120$		0			0
$121$	−36.4184	+	63.0786i	−0.300979	+	0.521311i
$122$	−233.250	−	62.4991i	−1.91188	−	0.512287i
$123$		0			0
$124$	97.2812	+	56.1654i	0.784526	+	0.452946i
$125$	66.7935	+	105.658i	0.534348	+	0.845265i
$126$		0			0
$127$	138.223	−	138.223i	1.08837	−	1.08837i	0.0926732	−	0.995697i	$-0.470459\pi$
$127$	138.223	−	138.223i	1.08837	−	1.08837i	0.995697	−	0.0926732i	$-0.0295412\pi$
$128$	−76.5208	+	20.5037i	−0.597819	+	0.160185i
$129$		0			0
$130$	124.168	−	107.052i	0.955135	−	0.823478i
$131$	−11.0263	+	19.0981i	−0.0841704	+	0.145787i	−0.905037	−	0.425332i	$-0.860157\pi$
$131$	−11.0263	+	19.0981i	−0.0841704	+	0.145787i	0.820867	+	0.571119i	$0.193491\pi$
$132$		0			0
$133$	221.554	+	64.8877i	1.66582	+	0.487878i
$134$			125.984i			0.940181i
$135$		0			0
$136$	−33.8829	−	58.6870i	−0.249139	−	0.431522i
$137$	−207.089	−	55.4894i	−1.51160	−	0.405032i	−0.594634	−	0.803997i	$-0.702703\pi$
$137$	−207.089	−	55.4894i	−1.51160	−	0.405032i	−0.916966	+	0.398965i	$0.869370\pi$
$138$		0			0
$139$			203.695i			1.46543i	0.680534	+	0.732716i	$0.261748\pi$
$139$			203.695i			1.46543i	−0.680534	+	0.732716i	$0.738252\pi$
$140$	154.581	−	70.2595i	1.10415	−	0.501854i
$141$		0			0
$142$	−15.4855	−	57.7926i	−0.109053	−	0.406990i
$143$	39.7132	−	148.212i	0.277715	−	1.03645i
$144$		0			0
$145$	29.8998	−	85.6996i	0.206206	−	0.591032i
$146$	19.3455			0.132504
$147$		0			0
$148$	−71.5885	−	71.5885i	−0.483706	−	0.483706i
$149$	106.635	+	61.5658i	0.715672	+	0.413193i	0.813157	−	0.582044i	$-0.197747\pi$
$149$	106.635	+	61.5658i	0.715672	+	0.413193i	−0.0974859	+	0.995237i	$0.531080\pi$
$150$		0			0
$151$	−50.6434	−	87.7170i	−0.335387	−	0.580907i	0.648172	−	0.761494i	$-0.275534\pi$
$151$	−50.6434	−	87.7170i	−0.335387	−	0.580907i	−0.983559	+	0.180587i	$0.942200\pi$
$152$	−21.6215	−	80.6925i	−0.142247	−	0.530872i
$153$		0			0
$154$	150.738	−	247.687i	0.978818	−	1.60836i
$155$	−21.6271	−	113.734i	−0.139529	−	0.733765i
$156$		0			0
$157$	70.0141	+	18.7602i	0.445950	+	0.119492i	0.474804	−	0.880092i	$-0.342519\pi$
$157$	70.0141	+	18.7602i	0.445950	+	0.119492i	−0.0288540	+	0.999584i	$0.509186\pi$
$158$	−9.36628	+	34.9554i	−0.0592802	+	0.221237i
$159$		0			0
$160$	187.861	+	127.830i	1.17413	+	0.798940i
$161$	130.196	−	71.2096i	0.808673	−	0.442295i
$162$		0			0
$163$	−175.917	+	47.1369i	−1.07925	+	0.289183i	−0.754287	−	0.656545i	$-0.772017\pi$
$163$	−175.917	+	47.1369i	−1.07925	+	0.289183i	−0.324960	+	0.945728i	$0.605351\pi$
$164$	−7.13484	+	4.11930i	−0.0435051	+	0.0251177i
$165$		0			0
$166$	−43.4735	+	75.2984i	−0.261889	+	0.453605i
$167$	188.951	−	188.951i	1.13144	−	1.13144i	0.141505	−	0.989938i	$-0.454806\pi$
$167$	188.951	−	188.951i	1.13144	−	1.13144i	0.989938	−	0.141505i	$-0.0451940\pi$
$168$		0			0
$169$		−	47.5377i		−	0.281288i
$170$	−131.098	+	375.757i	−0.771167	+	2.21033i
$171$		0			0
$172$	−177.601	−	47.5882i	−1.03257	−	0.276675i
$173$	−8.81487	+	2.36194i	−0.0509530	+	0.0136528i	−0.284206	−	0.958763i	$-0.591730\pi$
$173$	−8.81487	+	2.36194i	−0.0509530	+	0.0136528i	0.233253	+	0.972416i	$0.425063\pi$
$174$		0			0
$175$	−158.873	−	73.3788i	−0.907844	−	0.419307i
$176$	165.254			0.938944
$177$		0			0
$178$	−128.927	+	481.163i	−0.724310	+	2.70316i
$179$	232.008	−	133.950i	1.29613	−	0.748322i	0.316398	−	0.948626i	$-0.397526\pi$
$179$	232.008	−	133.950i	1.29613	−	0.748322i	0.979734	+	0.200304i	$0.0641931\pi$
$180$		0			0
$181$	−226.975			−1.25401			−0.627004	−	0.779016i	$-0.715719\pi$
$181$	−226.975			−1.25401			−0.627004	+	0.779016i	$0.715719\pi$
$182$	−64.5115	+	220.270i	−0.354459	+	1.21027i
$183$		0			0
$184$	−46.5047	−	26.8495i	−0.252743	−	0.145921i
$185$	−7.70259	+	104.058i	−0.0416356	+	0.562475i
$186$		0			0
$187$	96.4026	+	359.779i	0.515522	+	1.92395i
$188$	36.5187	+	36.5187i	0.194248	+	0.194248i
$189$		0			0
$190$	−275.995	+	405.605i	−1.45261	+	2.13477i
$191$	−77.8090	+	134.769i	−0.407377	+	0.705597i	−0.994595	−	0.103831i	$-0.966890\pi$
$191$	−77.8090	+	134.769i	−0.407377	+	0.705597i	0.587218	+	0.809429i	$0.300223\pi$
$192$		0			0
$193$	54.4390	−	203.169i	0.282067	−	1.05269i	−0.668889	−	0.743363i	$-0.733230\pi$
$193$	54.4390	−	203.169i	0.282067	−	1.05269i	0.950956	−	0.309327i	$-0.100104\pi$
$194$	241.612	+	139.495i	1.24542	+	0.719045i
$195$		0			0
$196$	−128.243	+	200.159i	−0.654303	+	1.02122i
$197$	98.6199	−	98.6199i	0.500609	−	0.500609i	−0.411018	−	0.911627i	$-0.634827\pi$
$197$	98.6199	−	98.6199i	0.500609	−	0.500609i	0.911627	+	0.411018i	$0.134827\pi$
$198$		0			0
$199$	35.8210	−	20.6813i	0.180005	−	0.103926i	−0.407290	−	0.913299i	$-0.633526\pi$
$199$	35.8210	−	20.6813i	0.180005	−	0.103926i	0.587295	+	0.809373i	$0.300193\pi$
$200$	7.20499	+	62.9140i	0.0360250	+	0.314570i
$201$		0			0
$202$	96.4140	−	96.4140i	0.477297	−	0.477297i
$203$	30.0438	+	123.469i	0.147999	+	0.608223i
$204$		0			0
$205$	8.01703	+	2.79707i	0.0391075	+	0.0136443i
$206$	32.6153	+	56.4913i	0.158327	+	0.274230i
$207$		0			0
$208$	−126.357	+	33.8572i	−0.607485	+	0.162775i
$209$			459.167i			2.19697i
$210$		0			0
$211$	326.483			1.54731			0.773655	−	0.633607i	$-0.218426\pi$
$211$	326.483			1.54731			0.773655	+	0.633607i	$0.218426\pi$
$212$	−56.0099	−	209.032i	−0.264198	−	0.985999i
$213$		0			0
$214$	−260.205	+	150.229i	−1.21591	+	0.702006i
$215$	82.3761	+	170.657i	0.383145	+	0.793755i
$216$		0			0
$217$	111.929	+	117.226i	0.515803	+	0.540210i
$218$	−266.943	−	266.943i	−1.22451	−	1.22451i
$219$		0			0
$220$	220.523	+	255.780i	1.00238	+	1.16264i
$221$	−147.423	−	255.344i	−0.667072	−	1.15540i
$222$		0			0
$223$	−39.2007	−	39.2007i	−0.175788	−	0.175788i	0.613729	−	0.789517i	$-0.289669\pi$
$223$	−39.2007	−	39.2007i	−0.175788	−	0.175788i	−0.789517	+	0.613729i	$0.789669\pi$
$224$	−318.033	−	7.35042i	−1.41979	−	0.0328144i
$225$		0			0
$226$	21.5469	−	37.3203i	0.0953403	−	0.165134i
$227$	3.48231	+	0.933082i	0.0153406	+	0.00411049i	0.266481	−	0.963840i	$-0.414139\pi$
$227$	3.48231	+	0.933082i	0.0153406	+	0.00411049i	−0.251141	+	0.967951i	$0.580806\pi$
$228$		0			0
$229$	46.0053	+	26.5612i	0.200896	+	0.115988i	0.597074	−	0.802186i	$-0.296330\pi$
$229$	46.0053	+	26.5612i	0.200896	+	0.115988i	−0.396177	+	0.918174i	$0.629663\pi$
$230$	58.9116	+	309.807i	0.256137	+	1.34699i
$231$		0			0
$232$	32.5143	−	32.5143i	0.140148	−	0.140148i
$233$	−124.839	+	33.4506i	−0.535791	+	0.143565i	−0.516561	−	0.856250i	$-0.672788\pi$
$233$	−124.839	+	33.4506i	−0.535791	+	0.143565i	−0.0192298	+	0.999815i	$0.506121\pi$
$234$		0			0
$235$	3.92924	−	53.0820i	0.0167202	−	0.225881i
$236$	−25.3375	+	43.8859i	−0.107362	+	0.185957i
$237$		0			0
$238$	−131.730	−	541.361i	−0.553485	−	2.27463i
$239$			365.148i			1.52782i	0.645325	+	0.763908i	$0.276722\pi$
$239$			365.148i			1.52782i	−0.645325	+	0.763908i	$0.723278\pi$
$240$		0			0
$241$	−196.782	−	340.837i	−0.816525	−	1.41426i	−0.908228	−	0.418476i	$-0.862564\pi$
$241$	−196.782	−	340.837i	−0.816525	−	1.41426i	0.0917031	−	0.995786i	$-0.470769\pi$
$242$	209.315	+	56.0859i	0.864939	+	0.231760i
$243$		0			0
$244$			393.766i			1.61379i
$245$	242.545	−	34.5995i	0.989978	−	0.141222i
$246$		0			0
$247$	−94.0739	−	351.089i	−0.380866	−	1.42141i
$248$	15.1798	−	56.6516i	0.0612087	−	0.228434i
$249$		0			0
$250$	252.203	−	273.307i	1.00881	−	1.09323i
$251$	−353.349			−1.40777			−0.703883	−	0.710316i	$-0.748552\pi$
$251$	−353.349			−1.40777			−0.703883	+	0.710316i	$0.748552\pi$
$252$		0			0
$253$	208.705	+	208.705i	0.824920	+	0.824920i
$254$	−503.653	−	290.784i	−1.98289	−	1.14482i
$255$		0			0
$256$	−57.6108	−	99.7848i	−0.225042	−	0.389784i
$257$	14.5977	+	54.4792i	0.0568002	+	0.211981i	0.988493	−	0.151266i	$-0.0483348\pi$
$257$	14.5977	+	54.4792i	0.0568002	+	0.211981i	−0.931693	+	0.363247i	$0.881668\pi$
$258$		0			0
$259$	−70.0972	−	128.163i	−0.270646	−	0.494836i
$260$	−221.021	−	150.394i	−0.850079	−	0.578439i
$261$		0			0
$262$	63.3739	+	16.9810i	0.241885	+	0.0648129i
$263$	−73.5553	+	274.512i	−0.279678	+	1.04377i	0.672963	+	0.739676i	$0.265021\pi$
$263$	−73.5553	+	274.512i	−0.279678	+	1.04377i	−0.952641	+	0.304097i	$0.901645\pi$
$264$		0			0
$265$	−125.472	+	184.394i	−0.473477	+	0.695827i
$266$	15.8701	−	686.658i	0.0596620	−	2.58142i
$267$		0			0
$268$	198.436	−	53.1708i	0.740433	−	0.198399i
$269$	228.544	−	131.950i	0.849607	−	0.490521i	−0.0109111	−	0.999940i	$-0.503473\pi$
$269$	228.544	−	131.950i	0.849607	−	0.490521i	0.860518	+	0.509419i	$0.170140\pi$
$270$		0			0
$271$	50.4495	−	87.3810i	0.186160	−	0.322439i	−0.757807	−	0.652479i	$-0.773729\pi$
$271$	50.4495	−	87.3810i	0.186160	−	0.322439i	0.943967	+	0.330040i	$0.107062\pi$
$272$	224.540	−	224.540i	0.825514	−	0.825514i
$273$		0			0
$274$			637.851i			2.32792i
$275$	51.2480	−	344.270i	0.186356	−	1.25189i
$276$		0			0
$277$	253.335	+	67.8808i	0.914566	+	0.245057i	0.685261	−	0.728297i	$-0.259688\pi$
$277$	253.335	+	67.8808i	0.914566	+	0.245057i	0.229305	+	0.973355i	$0.426355\pi$
$278$	585.370	−	156.849i	2.10565	−	0.564206i
$279$		0			0
$280$	−56.3231	−	68.4651i	−0.201154	−	0.244518i
$281$	−394.591			−1.40424			−0.702119	−	0.712060i	$-0.747762\pi$
$281$	−394.591			−1.40424			−0.702119	+	0.712060i	$0.747762\pi$
$282$		0			0
$283$	−79.1013	+	295.210i	−0.279510	+	1.04315i	0.673249	+	0.739416i	$0.264898\pi$
$283$	−79.1013	+	295.210i	−0.279510	+	1.04315i	−0.952758	+	0.303729i	$0.901768\pi$
$284$	−84.4929	+	48.7820i	−0.297510	+	0.171768i
$285$		0			0
$286$	−456.504			−1.59617
$287$	−11.5503	+	2.81054i	−0.0402450	+	0.00979282i
$288$		0			0
$289$	369.558	+	213.364i	1.27875	+	0.738285i
$290$	−269.303	−	19.9344i	−0.928631	−	0.0687393i
$291$		0			0
$292$	−8.16464	−	30.4709i	−0.0279611	−	0.104352i
$293$	−232.731	−	232.731i	−0.794304	−	0.794304i	0.187887	−	0.982191i	$-0.439836\pi$
$293$	−232.731	−	232.731i	−0.794304	−	0.794304i	−0.982191	+	0.187887i	$0.939836\pi$
$294$		0			0
$295$	51.3079	−	9.75647i	0.173925	−	0.0330728i
$296$	−26.4301	+	45.7782i	−0.0892908	+	0.154656i
$297$		0			0
$298$	94.8138	−	353.850i	0.318167	−	1.18742i
$299$	−202.339	−	116.821i	−0.676720	−	0.390705i
$300$		0			0
$301$	−226.629	−	137.922i	−0.752919	−	0.458214i
$302$	−213.081	+	213.081i	−0.705565	+	0.705565i
$303$		0			0
$304$	339.014	−	195.730i	1.11518	−	0.643847i
$305$	307.364	−	264.997i	1.00775	−	0.868842i
$306$		0			0
$307$	192.175	−	192.175i	0.625976	−	0.625976i	−0.321077	−	0.947053i	$-0.604045\pi$
$307$	192.175	−	192.175i	0.625976	−	0.625976i	0.947053	+	0.321077i	$0.104045\pi$
$308$	−453.746	−	132.891i	−1.47320	−	0.431464i
$309$		0			0
$310$	−310.189	+	149.728i	−1.00061	+	0.482993i
$311$	−69.8332	−	120.955i	−0.224544	−	0.388922i	0.731638	−	0.681693i	$-0.238756\pi$
$311$	−69.8332	−	120.955i	−0.224544	−	0.388922i	−0.956183	+	0.292771i	$0.905423\pi$
$312$		0			0
$313$	−47.2333	+	12.6561i	−0.150905	+	0.0404349i	−0.333481	−	0.942757i	$-0.608223\pi$
$313$	−47.2333	+	12.6561i	−0.150905	+	0.0404349i	0.182576	+	0.983192i	$0.441557\pi$
$314$		−	215.649i		−	0.686780i
$315$		0			0
$316$	59.0108			0.186743
$317$	77.1789	+	288.036i	0.243467	+	0.908630i	0.974148	+	0.225911i	$0.0725359\pi$
$317$	77.1789	+	288.036i	0.243467	+	0.908630i	−0.730681	+	0.682719i	$0.760797\pi$
$318$		0			0
$319$	−218.877	+	126.369i	−0.686136	+	0.396141i
$320$	144.496	−	414.157i	0.451549	−	1.29424i
$321$		0			0
$322$	−304.893	−	319.319i	−0.946871	−	0.991675i
$323$	623.895	+	623.895i	1.93156	+	1.93156i
$324$		0			0
$325$	31.3485	+	273.736i	0.0964571	+	0.842263i
$326$	270.920	+	469.247i	0.831042	+	1.43941i
$327$		0			0
$328$	3.04165	+	3.04165i	0.00927331	+	0.00927331i
$329$	35.7580	+	65.3782i	0.108687	+	0.198718i
$330$		0			0
$331$	−43.7659	+	75.8048i	−0.132223	+	0.229018i	−0.924533	−	0.381101i	$-0.875545\pi$
$331$	−43.7659	+	75.8048i	−0.132223	+	0.229018i	0.792310	+	0.610119i	$0.208878\pi$
$332$	136.949	+	36.6954i	0.412498	+	0.110528i
$333$		0			0
$334$	−688.494	−	397.502i	−2.06136	−	1.19013i
$335$	−175.047	−	119.112i	−0.522530	−	0.355557i
$336$		0			0
$337$	170.978	−	170.978i	0.507354	−	0.507354i	−0.406359	−	0.913713i	$-0.633202\pi$
$337$	170.978	−	170.978i	0.507354	−	0.507354i	0.913713	+	0.406359i	$0.133202\pi$
$338$	−136.612	+	36.6050i	−0.404177	+	0.108299i
$339$		0			0
$340$	647.179	+	47.9056i	1.90347	+	0.140899i
$341$	−161.183	+	279.178i	−0.472678	+	0.818703i
$342$		0			0
$343$	−258.755	+	225.155i	−0.754389	+	0.656428i
$344$			96.0004i			0.279071i
$345$		0			0
$346$	13.5753	+	23.5130i	0.0392348	+	0.0679567i
$347$	−64.4278	−	17.2634i	−0.185671	−	0.0497504i	0.164785	−	0.986329i	$-0.447307\pi$
$347$	−64.4278	−	17.2634i	−0.185671	−	0.0497504i	−0.350456	+	0.936579i	$0.613974\pi$
$348$		0			0
$349$		−	445.265i		−	1.27583i	−0.770106	−	0.637915i	$-0.779797\pi$
$349$		−	445.265i		−	1.27583i	0.770106	−	0.637915i	$-0.220203\pi$
$350$	−88.5374	+	513.064i	−0.252964	+	1.46590i
$351$		0			0
$352$	−163.759	−	611.157i	−0.465224	−	1.73624i
$353$	−95.8678	+	357.784i	−0.271580	+	1.01355i	0.686518	+	0.727112i	$0.259138\pi$
$353$	−95.8678	+	357.784i	−0.271580	+	1.01355i	−0.958099	+	0.286439i	$0.907529\pi$
$354$		0			0
$355$	94.9401	+	33.1238i	0.267437	+	0.0933064i
$356$	812.287			2.28170
$357$		0			0
$358$	−563.589	−	563.589i	−1.57427	−	1.57427i
$359$	−507.313	−	292.897i	−1.41313	−	0.815870i	−0.417446	−	0.908702i	$-0.637075\pi$
$359$	−507.313	−	292.897i	−1.41313	−	0.815870i	−0.995682	+	0.0928320i	$0.970408\pi$
$360$		0			0
$361$	363.345	+	629.331i	1.00649	+	1.74330i
$362$	174.776	+	652.272i	0.482806	+	1.80186i
$363$		0			0
$364$	374.170	+	8.64786i	1.02794	+	0.0237579i
$365$	−18.2902	+	26.8794i	−0.0501101	+	0.0736422i
$366$		0			0
$367$	−291.219	−	78.0318i	−0.793511	−	0.212621i	−0.160778	−	0.986991i	$-0.551400\pi$
$367$	−291.219	−	78.0318i	−0.793511	−	0.212621i	−0.632733	+	0.774370i	$0.718067\pi$
$368$	65.1268	−	243.056i	0.176975	−	0.660479i
$369$		0			0
$370$	304.968	−	57.9913i	0.824238	−	0.156733i
$371$	7.21478	−	312.165i	0.0194469	−	0.841414i
$372$		0			0
$373$	−510.035	+	136.663i	−1.36739	+	0.366390i	−0.866523	−	0.499137i	$-0.833650\pi$
$373$	−510.035	+	136.663i	−1.36739	+	0.366390i	−0.500862	+	0.865527i	$0.666984\pi$
$374$	959.686	−	554.075i	2.56600	−	1.48148i
$375$		0			0
$376$	13.4825	−	23.3524i	0.0358577	−	0.0621074i
$377$	141.468	−	141.468i	0.375246	−	0.375246i
$378$		0			0
$379$		−	177.062i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$379$		−	177.062i		−	0.467182i	0.972335	−	0.233591i	$-0.0750476\pi$
$380$	755.346	+	263.534i	1.98775	+	0.693509i
$381$		0			0
$382$	447.208	+	119.829i	1.17070	+	0.313688i
$383$	−260.649	+	69.8407i	−0.680545	+	0.182352i	−0.582500	−	0.812830i	$-0.697926\pi$
$383$	−260.649	+	69.8407i	−0.680545	+	0.182352i	−0.0980450	+	0.995182i	$0.531259\pi$
$384$		0			0
$385$	201.631	+	443.616i	0.523716	+	1.15225i
$386$	−625.777			−1.62118
$387$		0			0
$388$	117.746	−	439.433i	0.303468	−	1.13256i
$389$	161.408	−	93.1891i	0.414931	−	0.239561i	−0.277975	−	0.960588i	$-0.589663\pi$
$389$	161.408	−	93.1891i	0.414931	−	0.239561i	0.692906	+	0.721028i	$0.256330\pi$
$390$		0			0
$391$	567.157			1.45053
$392$	118.276	+	37.6284i	0.301725	+	0.0959909i
$393$		0			0
$394$	−359.349	−	207.470i	−0.912053	−	0.526574i
$395$	−39.7131	−	46.0624i	−0.100540	−	0.116614i
$396$		0			0
$397$	176.603	+	659.091i	0.444844	+	1.66018i	0.716349	+	0.697742i	$0.245812\pi$
$397$	176.603	+	659.091i	0.444844	+	1.66018i	−0.271506	+	0.962437i	$0.587522\pi$
$398$	−87.0158	−	87.0158i	−0.218633	−	0.218633i
$399$		0			0
$400$	−276.028	+	108.915i	−0.690070	+	0.272287i
$401$	−63.9305	+	110.731i	−0.159428	+	0.276137i	−0.934662	−	0.355536i	$-0.884298\pi$
$401$	−63.9305	+	110.731i	−0.159428	+	0.276137i	0.775235	+	0.631673i	$0.217632\pi$
$402$		0			0
$403$	66.0463	−	246.488i	0.163887	−	0.611634i
$404$	−192.551	−	111.170i	−0.476612	−	0.275172i
$405$		0			0
$406$	331.686	−	181.412i	0.816961	−	0.446829i
$407$	205.445	−	205.445i	0.504778	−	0.504778i
$408$		0			0
$409$	−67.5742	+	39.0140i	−0.165218	+	0.0953887i	−0.580329	−	0.814382i	$-0.697076\pi$
$409$	−67.5742	+	39.0140i	−0.165218	+	0.0953887i	0.415111	+	0.909771i	$0.363743\pi$
$410$	1.86482	−	25.1928i	0.00454835	−	0.0614458i
$411$		0			0
$412$	75.2137	−	75.2137i	0.182558	−	0.182558i
$413$	−52.8832	+	50.4939i	−0.128046	+	0.122261i
$414$		0			0
$415$	−63.5206	−	131.595i	−0.153062	−	0.317095i
$416$	250.427	+	433.752i	0.601988	+	1.04267i
$417$		0			0
$418$	1319.53	−	353.568i	3.15678	−	0.845856i
$419$		−	38.0855i		−	0.0908962i	−0.998967	−	0.0454481i	$-0.985528\pi$
$419$		−	38.0855i		−	0.0908962i	0.998967	−	0.0454481i	$-0.0144716\pi$
$420$		0			0
$421$	−151.613			−0.360126			−0.180063	−	0.983655i	$-0.557630\pi$
$421$	−151.613			−0.360126			−0.180063	+	0.983655i	$0.557630\pi$
$422$	−251.398	−	938.231i	−0.595730	−	2.22330i
$423$		0			0
$424$	−97.8519	+	56.4948i	−0.230783	+	0.133242i
$425$	−398.145	−	537.412i	−0.936811	−	1.26450i
$426$		0			0
$427$	−159.691	+	545.255i	−0.373985	+	1.27694i
$428$	346.442	+	346.442i	0.809444	+	0.809444i
$429$		0			0
$430$	426.996	−	368.138i	0.993014	−	0.856136i
$431$	268.299	+	464.707i	0.622503	+	1.07821i	0.989018	+	0.147795i	$0.0472175\pi$
$431$	268.299	+	464.707i	0.622503	+	1.07821i	−0.366515	+	0.930412i	$0.619449\pi$
$432$		0			0
$433$	421.429	+	421.429i	0.973278	+	0.973278i	0.999652	−	0.0263739i	$-0.00839605\pi$
$433$	421.429	+	421.429i	0.973278	+	0.973278i	−0.0263739	+	0.999652i	$0.508396\pi$
$434$	250.690	−	411.923i	0.577626	−	0.949132i
$435$		0			0
$436$	−307.796	+	533.119i	−0.705955	+	1.22275i
$437$	675.344	+	180.958i	1.54541	+	0.414092i
$438$		0			0
$439$	−411.292	−	237.460i	−0.936884	−	0.540910i	−0.0479017	−	0.998852i	$-0.515253\pi$
$439$	−411.292	−	237.460i	−0.936884	−	0.540910i	−0.888982	+	0.457942i	$0.848587\pi$
$440$	99.1970	−	145.781i	0.225448	−	0.331320i
$441$		0			0
$442$	−620.277	+	620.277i	−1.40334	+	1.40334i
$443$	90.9998	−	24.3833i	0.205417	−	0.0550414i	−0.154643	−	0.987970i	$-0.549423\pi$
$443$	90.9998	−	24.3833i	0.205417	−	0.0550414i	0.360060	+	0.932929i	$0.382756\pi$
$444$		0			0
$445$	−546.653	−	634.051i	−1.22843	−	1.42483i
$446$	−82.4678	+	142.839i	−0.184905	+	0.320266i
$447$		0			0
$448$	145.192	+	596.685i	0.324088	+	1.33189i
$449$			521.631i			1.16176i	0.813989	+	0.580881i	$0.197292\pi$
$449$			521.631i			1.16176i	−0.813989	+	0.580881i	$0.802708\pi$
$450$		0			0
$451$	−11.8216	−	20.4756i	−0.0262119	−	0.0454003i
$452$	−67.8765	−	18.1875i	−0.150169	−	0.0402377i
$453$		0			0
$454$		−	10.7258i		−	0.0236251i
$455$	−245.059	−	297.888i	−0.538591	−	0.654699i
$456$		0			0
$457$	−107.539	−	401.339i	−0.235314	−	0.878204i	−0.978007	−	0.208572i	$-0.933118\pi$
$457$	−107.539	−	401.339i	−0.235314	−	0.878204i	0.742693	−	0.669632i	$-0.233548\pi$
$458$	40.9053	−	152.661i	0.0893128	−	0.333320i
$459$		0			0
$460$	463.110	−	223.543i	1.00676	−	0.485963i
$461$	−280.539			−0.608544			−0.304272	−	0.952585i	$-0.598413\pi$
$461$	−280.539			−0.608544			−0.304272	+	0.952585i	$0.598413\pi$
$462$		0			0
$463$	−326.436	−	326.436i	−0.705045	−	0.705045i	0.260444	−	0.965489i	$-0.416131\pi$
$463$	−326.436	−	326.436i	−0.705045	−	0.705045i	−0.965489	+	0.260444i	$0.916131\pi$
$464$	186.602	+	107.735i	0.402160	+	0.232187i
$465$		0			0
$466$	192.257	+	333.000i	0.412570	+	0.714592i
$467$	−109.999	−	410.520i	−0.235543	−	0.879058i	−0.977903	−	0.209057i	$-0.932960\pi$
$467$	−109.999	−	410.520i	−0.235543	−	0.879058i	0.742360	−	0.670001i	$-0.233706\pi$
$468$		0			0
$469$	296.342	+	6.84907i	0.631858	+	0.0146036i
$470$	−155.570	+	29.5825i	−0.331000	+	0.0629415i
$471$		0			0
$472$	25.5569	+	6.84795i	0.0541459	+	0.0145084i
$473$	136.569	−	509.681i	0.288728	−	1.07755i
$474$		0			0
$475$	−302.625	−	766.958i	−0.637105	−	1.61465i
$476$	−797.096	+	435.963i	−1.67457	+	0.915889i
$477$		0			0
$478$	1049.35	−	281.171i	2.19529	−	0.588225i
$479$	−183.280	+	105.817i	−0.382630	+	0.220912i	−0.678962	−	0.734173i	$-0.737570\pi$
$479$	−183.280	+	105.817i	−0.382630	+	0.220912i	0.296332	+	0.955085i	$0.404237\pi$
$480$		0			0
$481$	−114.996	+	199.179i	−0.239077	+	0.414093i
$482$	−827.956	+	827.956i	−1.71775	+	1.71775i
$483$		0			0
$484$		−	353.361i		−	0.730084i
$485$	−422.251	+	203.820i	−0.870621	+	0.420248i
$486$		0			0
$487$	−46.3134	−	12.4096i	−0.0950993	−	0.0254818i	0.210956	−	0.977496i	$-0.432342\pi$
$487$	−46.3134	−	12.4096i	−0.0950993	−	0.0254818i	−0.306055	+	0.952014i	$0.599009\pi$
$488$	198.588	−	53.2114i	0.406942	−	0.109040i
$489$		0			0
$490$	−286.195	−	670.371i	−0.584071	−	1.36810i
$491$	784.457			1.59767			0.798836	−	0.601549i	$-0.205449\pi$
$491$	784.457			1.59767			0.798836	+	0.601549i	$0.205449\pi$
$492$		0			0
$493$	−125.696	+	469.105i	−0.254962	+	0.951531i
$494$	−936.504	+	540.691i	−1.89576	+	1.09452i
$495$		0			0
$496$	274.831			0.554095
$497$	−136.782	+	33.2833i	−0.275216	+	0.0669684i
$498$		0			0
$499$	50.6730	+	29.2561i	0.101549	+	0.0586294i	0.549914	−	0.835221i	$-0.314660\pi$
$499$	50.6730	+	29.2561i	0.101549	+	0.0586294i	−0.448365	+	0.893850i	$0.647994\pi$
$500$	−536.923	−	281.894i	−1.07385	−	0.563789i
$501$		0			0
$502$	272.086	+	1015.44i	0.542004	+	2.02279i
$503$	−144.269	−	144.269i	−0.286816	−	0.286816i	0.549004	−	0.835820i	$-0.315007\pi$
$503$	−144.269	−	144.269i	−0.286816	−	0.286816i	−0.835820	+	0.549004i	$0.815007\pi$
$504$		0			0
$505$	42.8070	+	225.116i	0.0847664	+	0.445774i
$506$	439.059	−	760.473i	0.867706	−	1.50291i
$507$		0			0
$508$	−245.447	+	916.021i	−0.483164	+	1.80319i
$509$	−38.7059	−	22.3469i	−0.0760431	−	0.0439035i	0.461496	−	0.887142i	$-0.347313\pi$
$509$	−38.7059	−	22.3469i	−0.0760431	−	0.0439035i	−0.537539	+	0.843239i	$0.680646\pi$
$510$		0			0
$511$	1.05171	−	45.5047i	0.00205814	−	0.0890503i
$512$	−466.464	+	466.464i	−0.911063	+	0.911063i
$513$		0			0
$514$	145.319	−	83.9001i	0.282722	−	0.163230i
$515$	−109.327	−	8.09265i	−0.212286	−	0.0157139i
$516$		0			0
$517$	−104.801	+	104.801i	−0.202711	+	0.202711i
$518$	−314.331	+	300.130i	−0.606817	+	0.579401i
$519$		0			0
$520$	−45.9806	+	131.791i	−0.0884242	+	0.253443i
$521$	−139.872	−	242.266i	−0.268469	−	0.465001i	0.699998	−	0.714145i	$-0.253184\pi$
$521$	−139.872	−	242.266i	−0.268469	−	0.465001i	−0.968467	+	0.249143i	$0.919851\pi$
$522$		0			0
$523$	−238.051	+	63.7856i	−0.455165	+	0.121961i	−0.479115	−	0.877752i	$-0.659042\pi$
$523$	−238.051	+	63.7856i	−0.455165	+	0.121961i	0.0239502	+	0.999713i	$0.492376\pi$
$524$		−	106.986i		−	0.204172i
$525$		0			0
$526$	845.520			1.60745
$527$	160.325	+	598.343i	0.304223	+	1.13537i
$528$		0			0
$529$	−68.9129	+	39.7869i	−0.130270	+	0.0752115i
$530$	626.519	+	218.587i	1.18211	+	0.412429i
$531$		0			0
$532$	−1088.24	+	264.802i	−2.04557	+	0.497749i
$533$	13.2340	+	13.2340i	0.0248293	+	0.0248293i
$534$		0			0
$535$	37.2756	−	503.573i	0.0696740	−	0.941258i
$536$	−53.6312	−	92.8919i	−0.100058	−	0.173306i
$537$		0			0
$538$	−555.176	−	555.176i	−1.03193	−	1.03193i
$539$	−574.416	−	368.033i	−1.06571	−	0.682807i
$540$		0			0
$541$	−391.651	+	678.360i	−0.723939	+	1.25390i	0.235470	+	0.971882i	$0.424337\pi$
$541$	−391.651	+	678.360i	−0.723939	+	1.25390i	−0.959409	+	0.282018i	$0.908996\pi$
$542$	−289.959	−	77.6942i	−0.534979	−	0.143347i
$543$		0			0
$544$	−1052.92	−	607.904i	−1.93552	−	1.11747i
$545$	623.281	−	118.520i	1.14363	−	0.217468i
$546$		0			0
$547$	−32.2224	+	32.2224i	−0.0589074	+	0.0589074i	−0.735947	−	0.677039i	$-0.763263\pi$
$547$	−32.2224	+	32.2224i	−0.0589074	+	0.0589074i	0.677039	+	0.735947i	$0.263263\pi$
$548$	1004.67	−	269.201i	1.83334	−	0.491243i
$549$		0			0
$550$	−1028.81	+	117.820i	−1.87056	+	0.214219i
$551$	−299.347	+	518.484i	−0.543279	+	0.940986i
$552$		0			0
$553$	81.7133	+	23.9318i	0.147764	+	0.0432763i
$554$		−	780.291i		−	1.40847i
$555$		0			0
$556$	−494.103	−	855.811i	−0.888674	−	1.53923i
$557$	−805.560	−	215.849i	−1.44625	−	0.387521i	−0.551531	−	0.834155i	$-0.685956\pi$
$557$	−805.560	−	215.849i	−1.44625	−	0.387521i	−0.894717	+	0.446634i	$0.852623\pi$
$558$		0			0
$559$			417.693i			0.747214i
$560$	241.583	−	337.969i	0.431398	−	0.603517i
$561$		0			0
$562$	303.843	+	1133.96i	0.540646	+	2.01772i
$563$	−217.180	+	810.525i	−0.385754	+	1.43965i	0.451221	+	0.892412i	$0.350989\pi$
$563$	−217.180	+	810.525i	−0.385754	+	1.43965i	−0.836975	+	0.547241i	$0.815678\pi$
$564$		0			0
$565$	31.4829	+	65.2226i	0.0557219	+	0.115438i
$566$	909.271			1.60649
$567$		0			0
$568$	36.0201	+	36.0201i	0.0634157	+	0.0634157i
$569$	663.998	+	383.359i	1.16696	+	0.673742i	0.952961	−	0.303093i	$-0.0980191\pi$
$569$	663.998	+	383.359i	1.16696	+	0.673742i	0.213995	+	0.976835i	$0.431352\pi$
$570$		0			0
$571$	−525.520	−	910.227i	−0.920350	−	1.59409i	−0.798874	−	0.601498i	$-0.794571\pi$
$571$	−525.520	−	910.227i	−0.920350	−	1.59409i	−0.121476	−	0.992594i	$-0.538763\pi$
$572$	192.665	+	719.034i	0.336826	+	1.25705i
$573$		0			0
$574$	16.9708	+	31.0286i	0.0295658	+	0.0540568i
$575$	−486.156	−	211.053i	−0.845490	−	0.367048i
$576$		0			0
$577$	−191.449	−	51.2986i	−0.331801	−	0.0889058i	0.0890726	−	0.996025i	$-0.471610\pi$
$577$	−191.449	−	51.2986i	−0.331801	−	0.0889058i	−0.420873	+	0.907119i	$0.638276\pi$
$578$	328.590	−	1226.31i	0.568494	−	2.12165i
$579$		0			0
$580$	82.2591	+	432.589i	0.141826	+	0.745843i
$581$	174.754	+	106.352i	0.300782	+	0.183051i
$582$		0			0
$583$	599.879	−	160.737i	1.02895	−	0.275707i
$584$	−14.2640	+	8.23534i	−0.0244247	+	0.0141016i
$585$		0			0
$586$	−489.604	+	848.019i	−0.835502	+	1.44713i
$587$	−425.592	+	425.592i	−0.725029	+	0.725029i	−0.969625	−	0.244596i	$-0.921345\pi$
$587$	−425.592	+	425.592i	−0.725029	+	0.725029i	0.244596	+	0.969625i	$0.421345\pi$
$588$		0			0
$589$			763.632i			1.29649i
$590$	−67.5458	−	139.934i	−0.114484	−	0.237176i
$591$		0			0
$592$	−239.260	−	64.1094i	−0.404155	−	0.108293i
$593$	521.131	−	139.637i	0.878805	−	0.235475i	0.208914	−	0.977934i	$-0.433007\pi$
$593$	521.131	−	139.637i	0.878805	−	0.235475i	0.669892	+	0.742459i	$0.266341\pi$
$594$		0			0
$595$	876.732	+	328.799i	1.47350	+	0.552603i
$596$	−597.360			−1.00228
$597$		0			0
$598$	−179.909	+	671.428i	−0.300851	+	1.12279i
$599$	−329.578	+	190.282i	−0.550213	+	0.317666i	−0.749208	−	0.662335i	$-0.769566\pi$
$599$	−329.578	+	190.282i	−0.550213	+	0.317666i	0.198995	+	0.980001i	$0.436232\pi$
$600$		0			0
$601$	−566.492			−0.942582			−0.471291	−	0.881978i	$-0.656212\pi$
$601$	−566.492			−0.942582			−0.471291	+	0.881978i	$0.656212\pi$
$602$	−221.846	+	757.478i	−0.368516	+	1.25827i
$603$		0			0
$604$	425.550	+	245.691i	0.704552	+	0.406773i
$605$	−275.825	+	237.805i	−0.455909	+	0.393066i
$606$		0			0
$607$	−278.422	−	1039.09i	−0.458685	−	1.71184i	−0.677021	−	0.735963i	$-0.736730\pi$
$607$	−278.422	−	1039.09i	−0.458685	−	1.71184i	0.218336	−	0.975874i	$-0.429937\pi$
$608$	−1059.81	−	1059.81i	−1.74311	−	1.74311i
$609$		0			0
$610$	−998.212	−	679.236i	−1.63641	−	1.11350i
$611$	58.6616	−	101.605i	0.0960092	−	0.166293i
$612$		0			0
$613$	−108.584	+	405.242i	−0.177136	+	0.661079i	0.819042	+	0.573733i	$0.194505\pi$
$613$	−108.584	+	405.242i	−0.177136	+	0.661079i	−0.996178	+	0.0873463i	$0.972161\pi$
$614$	−700.241	−	404.284i	−1.14046	−	0.658444i
$615$		0			0
$616$	−5.70396	+	246.795i	−0.00925968	+	0.400642i
$617$	504.052	−	504.052i	0.816940	−	0.816940i	−0.168724	−	0.985663i	$-0.553965\pi$
$617$	504.052	−	504.052i	0.816940	−	0.816940i	0.985663	+	0.168724i	$0.0539645\pi$
$618$		0			0
$619$	210.689	−	121.641i	0.340369	−	0.196512i	−0.320066	−	0.947395i	$-0.603705\pi$
$619$	210.689	−	121.641i	0.340369	−	0.196512i	0.660435	+	0.750883i	$0.270372\pi$
$620$	366.748	+	425.383i	0.591529	+	0.686102i
$621$		0			0
$622$	−293.821	+	293.821i	−0.472381	+	0.472381i
$623$	1124.79	+	329.422i	1.80544	+	0.528768i
$624$		0			0
$625$	141.298	+	608.818i	0.226077	+	0.974109i
$626$	72.7413	+	125.992i	0.116200	+	0.201264i
$627$		0			0
$628$	−339.666	+	91.0132i	−0.540869	+	0.144926i
$629$		−	558.298i		−	0.887596i
$630$		0			0
$631$	912.593			1.44626			0.723132	−	0.690710i	$-0.242702\pi$
$631$	912.593			1.44626			0.723132	+	0.690710i	$0.242702\pi$
$632$	−7.97440	−	29.7609i	−0.0126177	−	0.0470900i
$633$		0			0
$634$	768.315	−	443.587i	1.21185	−	0.699663i
$635$	880.205	−	424.874i	1.38615	−	0.669093i
$636$		0			0
$637$	514.613	+	163.719i	0.807870	+	0.257016i
$638$	531.693	+	531.693i	0.833375	+	0.833375i
$639$		0			0
$640$	−395.020	−	29.2403i	−0.617219	−	0.0456879i
$641$	−114.103	−	197.632i	−0.178007	−	0.308318i	0.763191	−	0.646173i	$-0.223632\pi$
$641$	−114.103	−	197.632i	−0.178007	−	0.308318i	−0.941198	+	0.337856i	$0.890298\pi$
$642$		0			0
$643$	434.914	+	434.914i	0.676382	+	0.676382i	0.959180	−	0.282797i	$-0.0912624\pi$
$643$	434.914	+	434.914i	0.676382	+	0.676382i	−0.282797	+	0.959180i	$0.591262\pi$
$644$	−374.278	+	614.999i	−0.581177	+	0.954967i
$645$		0			0
$646$	1312.51	−	2273.33i	2.03175	−	3.51909i
$647$	345.598	+	92.6027i	0.534155	+	0.143126i	0.515806	−	0.856705i	$-0.327492\pi$
$647$	345.598	+	92.6027i	0.534155	+	0.143126i	0.0183485	+	0.999832i	$0.494159\pi$
$648$		0			0
$649$	−125.944	−	72.7136i	−0.194058	−	0.112039i
$650$	762.510	−	300.870i	1.17309	−	0.462877i
$651$		0			0
$652$	624.764	−	624.764i	0.958228	−	0.958228i
$653$	663.599	−	177.811i	1.01623	−	0.272298i	0.288000	−	0.957630i	$-0.407010\pi$
$653$	663.599	−	177.811i	1.01623	−	0.272298i	0.728231	+	0.685332i	$0.240343\pi$
$654$		0			0
$655$	−83.5107	+	71.9995i	−0.127497	+	0.109923i
$656$	−10.0784	+	17.4563i	−0.0153634	+	0.0266102i
$657$		0			0
$658$	160.347	−	153.102i	0.243688	−	0.232678i
$659$		−	619.112i		−	0.939471i	−0.882807	−	0.469736i	$-0.844349\pi$
$659$		−	619.112i		−	0.939471i	0.882807	−	0.469736i	$-0.155651\pi$
$660$		0			0
$661$	−249.541	−	432.217i	−0.377520	−	0.653884i	0.613181	−	0.789943i	$-0.289890\pi$
$661$	−249.541	−	432.217i	−0.377520	−	0.653884i	−0.990701	+	0.136059i	$0.956556\pi$
$662$	251.545	+	67.4013i	0.379978	+	0.101815i
$663$		0			0
$664$		−	74.0263i		−	0.111485i
$665$	939.065	+	671.250i	1.41213	+	1.00940i
$666$		0			0
$667$	99.6041	+	371.728i	0.149332	+	0.557313i
$668$	−335.526	+	1252.20i	−0.502285	+	1.87455i
$669$		0			0
$670$	−207.507	+	594.762i	−0.309712	+	0.887704i
$671$	−1130.03			−1.68410
$672$		0			0
$673$	588.355	+	588.355i	0.874227	+	0.874227i	0.992930	−	0.118703i	$-0.0378735\pi$
$673$	588.355	+	588.355i	0.874227	+	0.874227i	−0.118703	+	0.992930i	$0.537874\pi$
$674$	−623.006	−	359.693i	−0.924341	−	0.533669i
$675$		0			0
$676$	115.312	+	199.727i	0.170580	+	0.295454i
$677$	221.070	+	825.046i	0.326544	+	1.21868i	0.912750	+	0.408518i	$0.133954\pi$
$677$	221.070	+	825.046i	0.326544	+	1.21868i	−0.586206	+	0.810162i	$0.699379\pi$
$678$		0			0
$679$	341.256	−	560.739i	0.502586	−	0.825830i
$680$	−63.2961	−	332.865i	−0.0930824	−	0.489507i
$681$		0			0
$682$	926.403	+	248.229i	1.35836	+	0.363972i
$683$	77.6050	−	289.626i	0.113624	−	0.424050i	−0.885557	−	0.464532i	$-0.846223\pi$
$683$	77.6050	−	289.626i	0.113624	−	0.424050i	0.999180	+	0.0404821i	$0.0128894\pi$
$684$		0			0
$685$	−886.256	−	603.055i	−1.29380	−	0.880373i
$686$	846.287	+	570.225i	1.23365	+	0.831232i
$687$		0			0
$688$	−434.524	+	116.430i	−0.631576	+	0.169230i
$689$	−425.748	+	245.806i	−0.617922	+	0.356758i
$690$		0			0
$691$	−422.621	+	732.000i	−0.611607	+	1.05933i	0.379363	+	0.925248i	$0.376143\pi$
$691$	−422.621	+	732.000i	−0.611607	+	1.05933i	−0.990970	+	0.134086i	$0.957190\pi$
$692$	31.3057	−	31.3057i	0.0452395	−	0.0452395i
$693$		0			0
$694$			198.443i			0.285941i
$695$	−335.504	+	961.629i	−0.482740	+	1.38364i
$696$		0			0
$697$	−43.8839	−	11.7586i	−0.0629611	−	0.0168704i
$698$	−1279.58	+	342.863i	−1.83321	+	0.491208i
$699$		0			0
$700$	845.488	−	77.0813i	1.20784	−	0.110116i
$701$	177.525			0.253245			0.126623	−	0.991951i	$-0.459586\pi$
$701$	177.525			0.253245			0.126623	+	0.991951i	$0.459586\pi$
$702$		0			0
$703$	178.131	−	664.795i	0.253387	−	0.945654i
$704$	−1057.76	+	610.698i	−1.50250	+	0.867469i
$705$		0			0
$706$	1102.00			1.56091
$707$	−221.545	−	232.028i	−0.313359	−	0.328186i
$708$		0			0
$709$	488.278	+	281.907i	0.688685	+	0.397613i	0.803119	−	0.595818i	$-0.203172\pi$
$709$	488.278	+	281.907i	0.688685	+	0.397613i	−0.114434	+	0.993431i	$0.536505\pi$
$710$	22.0838	−	298.341i	0.0311040	−	0.420198i
$711$		0			0
$712$	−109.768	−	409.660i	−0.154169	−	0.575365i
$713$	347.093	+	347.093i	0.486807	+	0.486807i
$714$		0			0
$715$	431.601	−	634.285i	0.603638	−	0.887112i
$716$	−649.843	+	1125.56i	−0.907602	+	1.57201i
$717$		0			0
$718$	−451.074	+	1683.43i	−0.628236	+	2.34461i
$719$	−340.465	−	196.567i	−0.473525	−	0.273390i	0.244189	−	0.969728i	$-0.421478\pi$
$719$	−340.465	−	196.567i	−0.473525	−	0.273390i	−0.717714	+	0.696338i	$0.754812\pi$
$720$		0			0
$721$	134.653	−	73.6469i	0.186758	−	0.102146i
$722$	1528.76	−	1528.76i	2.11740	−	2.11740i
$723$		0			0
$724$	953.622	−	550.574i	1.31716	−	0.760461i
$725$	282.310	−	355.333i	0.389393	−	0.490115i
$726$		0			0
$727$	−110.762	+	110.762i	−0.152356	+	0.152356i	−0.779169	−	0.626814i	$-0.784359\pi$
$727$	−110.762	+	110.762i	−0.152356	+	0.152356i	0.626814	+	0.779169i	$0.284359\pi$
$728$	−46.2020	−	189.874i	−0.0634643	−	0.260815i
$729$		0			0
$730$	91.3287	+	31.8638i	0.125108	+	0.0436490i
$731$	−506.968	−	878.094i	−0.693527	−	1.20122i
$732$		0			0
$733$	673.766	−	180.535i	0.919190	−	0.246296i	0.231951	−	0.972727i	$-0.425489\pi$
$733$	673.766	−	180.535i	0.919190	−	0.246296i	0.687239	+	0.726431i	$0.258822\pi$
$734$			896.977i			1.22204i
$735$		0			0
$736$	−963.429			−1.30901
$737$	152.590	+	569.472i	0.207042	+	0.772689i
$738$		0			0
$739$	−701.070	+	404.763i	−0.948675	+	0.547717i	−0.892669	−	0.450713i	$-0.851170\pi$
$739$	−701.070	+	404.763i	−0.948675	+	0.547717i	−0.0560056	+	0.998430i	$0.517836\pi$
$740$	−220.051	−	455.876i	−0.297366	−	0.616049i
$741$		0			0
$742$	−902.640	+	219.640i	−1.21650	+	0.296010i
$743$	−615.379	−	615.379i	−0.828235	−	0.828235i	0.159037	−	0.987273i	$-0.449161\pi$
$743$	−615.379	−	615.379i	−0.828235	−	0.828235i	−0.987273	+	0.159037i	$0.949161\pi$
$744$		0			0
$745$	402.011	+	466.285i	0.539613	+	0.625885i
$746$	785.474	+	1360.48i	1.05291	+	1.82370i
$747$		0			0
$748$	−1277.74	−	1277.74i	−1.70821	−	1.70821i
$749$	339.225	+	620.224i	0.452904	+	0.828069i
$750$		0			0
$751$	−666.673	+	1154.71i	−0.887713	+	1.53756i	−0.0451417	+	0.998981i	$0.514374\pi$
$751$	−666.673	+	1154.71i	−0.887713	+	1.53756i	−0.842572	+	0.538584i	$0.818959\pi$
$752$	122.051	+	32.7035i	0.162302	+	0.0434887i
$753$		0			0
$754$	−515.477	−	297.611i	−0.683656	−	0.394709i
$755$	−94.6059	−	497.519i	−0.125306	−	0.658966i
$756$		0			0
$757$	897.927	−	897.927i	1.18617	−	1.18617i	0.208047	−	0.978119i	$-0.433289\pi$
$757$	897.927	−	897.927i	1.18617	−	1.18617i	0.978119	−	0.208047i	$-0.0667106\pi$
$758$	−508.832	+	136.341i	−0.671283	+	0.179870i
$759$		0			0
$760$	30.8343	−	416.555i	0.0405715	−	0.548099i
$761$	19.9063	−	34.4788i	0.0261581	−	0.0453072i	−0.852650	−	0.522483i	$-0.825006\pi$
$761$	19.9063	−	34.4788i	0.0261581	−	0.0453072i	0.878808	+	0.477175i	$0.158339\pi$
$762$		0			0
$763$	−642.417	+	613.393i	−0.841963	+	0.803923i
$764$		−	754.964i		−	0.988173i
$765$		0			0
$766$	401.410	+	695.262i	0.524034	+	0.907653i
$767$	111.197	+	29.7951i	0.144976	+	0.0388462i
$768$		0			0
$769$		−	246.046i		−	0.319956i	−0.987121	−	0.159978i	$-0.948858\pi$
$769$		−	246.046i		−	0.319956i	0.987121	−	0.159978i	$-0.0511424\pi$
$770$	1119.58	−	921.031i	1.45401	−	1.19614i
$771$		0			0
$772$	264.105	+	985.653i	0.342105	+	1.27675i
$773$	203.881	−	760.894i	0.263753	−	0.984339i	−0.699257	−	0.714871i	$-0.746485\pi$
$773$	203.881	−	760.894i	0.263753	−	0.984339i	0.963009	−	0.269468i	$-0.0868479\pi$
$774$		0			0
$775$	85.2297	−	572.549i	0.109974	−	0.738773i
$776$	−237.530			−0.306096
$777$		0			0
$778$	−392.090	−	392.090i	−0.503972	−	0.503972i
$779$	−48.5031	−	28.0033i	−0.0622633	−	0.0359477i
$780$		0			0
$781$	−139.995	−	242.478i	−0.179250	−	0.310471i
$782$	−436.722	−	1629.87i	−0.558469	−	2.08423i
$783$		0			0
$784$	−26.8700	+	580.987i	−0.0342730	+	0.741055i
$785$	299.631	+	203.885i	0.381696	+	0.259726i
$786$		0			0
$787$	−831.602	−	222.827i	−1.05667	−	0.283135i	−0.311667	−	0.950192i	$-0.600887\pi$
$787$	−831.602	−	222.827i	−1.05667	−	0.283135i	−0.745007	+	0.667057i	$0.767554\pi$
$788$	−175.123	+	653.567i	−0.222237	+	0.829400i
$789$		0			0
$790$	−101.792	+	149.595i	−0.128851	+	0.189360i
$791$	−86.6139	−	52.7118i	−0.109499	−	0.0666394i
$792$		0			0
$793$	864.044	−	231.520i	1.08959	−	0.291954i
$794$	1758.08	−	1015.03i	2.21420	−	1.27837i
$795$		0			0
$796$	−100.333	+	173.782i	−0.126046	+	0.218319i
$797$	−710.464	+	710.464i	−0.891423	+	0.891423i	−0.994657	−	0.103234i	$-0.967081\pi$
$797$	−710.464	+	710.464i	−0.891423	+	0.891423i	0.103234	+	0.994657i	$0.467081\pi$
$798$		0			0
$799$			284.799i			0.356444i
$800$	676.328	+	912.901i	0.845410	+	1.14113i
$801$		0			0
$802$	367.441	+	98.4556i	0.458156	+	0.122763i
$803$	87.4453	−	23.4309i	0.108898	−	0.0291792i
$804$		0			0
$805$	731.935	−	121.730i	0.909236	−	0.151217i
$806$	−759.204			−0.941940
$807$		0			0
$808$	−30.0457	+	112.132i	−0.0371853	+	0.138777i
$809$	836.414	−	482.904i	1.03389	−	0.596914i	0.115790	−	0.993274i	$-0.463060\pi$
$809$	836.414	−	482.904i	1.03389	−	0.596914i	0.918095	+	0.396359i	$0.129727\pi$
$810$		0			0
$811$	−632.087			−0.779392			−0.389696	−	0.920944i	$-0.627420\pi$
$811$	−632.087			−0.779392			−0.389696	+	0.920944i	$0.627420\pi$
$812$	−425.726	−	445.871i	−0.524293	−	0.549102i
$813$		0			0
$814$	−748.594	−	432.201i	−0.919649	−	0.530959i
$815$	−908.130	−	67.2218i	−1.11427	−	0.0824807i
$816$		0			0
$817$	−323.508	−	1207.35i	−0.395970	−	1.47778i
$818$	164.150	+	164.150i	0.200673	+	0.200673i
$819$		0			0
$820$	−40.4679	+	7.69518i	−0.0493510	+	0.00938437i
$821$	518.747	−	898.496i	0.631848	−	1.09439i	−0.355326	−	0.934742i	$-0.615630\pi$
$821$	518.747	−	898.496i	0.631848	−	1.09439i	0.987174	−	0.159650i	$-0.0510365\pi$
$822$		0			0
$823$	384.072	−	1433.38i	0.466673	−	1.74165i	−0.184607	−	0.982812i	$-0.559101\pi$
$823$	384.072	−	1433.38i	0.466673	−	1.74165i	0.651281	−	0.758837i	$-0.274232\pi$
$824$	−48.0964	−	27.7685i	−0.0583695	−	0.0336996i
$825$		0			0
$826$	185.828	+	113.092i	0.224974	+	0.136915i
$827$	896.076	−	896.076i	1.08353	−	1.08353i	0.0873480	−	0.996178i	$-0.472161\pi$
$827$	896.076	−	896.076i	1.08353	−	1.08353i	0.996178	−	0.0873480i	$-0.0278392\pi$
$828$		0			0
$829$	566.312	−	326.960i	0.683127	−	0.394403i	−0.117905	−	0.993025i	$-0.537618\pi$
$829$	566.312	−	326.960i	0.683127	−	0.394403i	0.801032	+	0.598621i	$0.204285\pi$
$830$	−329.258	+	283.873i	−0.396697	+	0.342016i
$831$		0			0
$832$	683.666	−	683.666i	0.821714	−	0.821714i
$833$	−1280.56	+	280.425i	−1.53728	+	0.336644i
$834$		0			0
$835$	1203.24	−	580.803i	1.44101	−	0.695573i
$836$	−1113.80	−	1929.16i	−1.33230	−	2.30761i
$837$		0			0
$838$	−109.448	+	29.3266i	−0.130607	+	0.0349959i
$839$			1045.69i			1.24636i	0.782079	+	0.623179i	$0.214159\pi$
$839$			1045.69i			1.24636i	−0.782079	+	0.623179i	$0.785841\pi$
$840$		0			0
$841$	511.463			0.608161
$842$	116.745	+	435.699i	0.138652	+	0.517457i
$843$		0			0
$844$	−1371.69	+	791.948i	−1.62523	+	0.938327i
$845$	78.2989	−	224.422i	0.0926614	−	0.265588i
$846$		0			0
$847$	143.305	−	489.305i	0.169191	−	0.577692i
$848$	−374.387	−	374.387i	−0.441494	−	0.441494i
$849$		0			0
$850$	−1237.81	+	1557.99i	−1.45625	+	1.83293i
$851$	−221.203	−	383.135i	−0.259933	−	0.450217i
$852$		0			0
$853$	−707.639	−	707.639i	−0.829588	−	0.829588i	0.157871	−	0.987460i	$-0.449537\pi$
$853$	−707.639	−	707.639i	−0.829588	−	0.829588i	−0.987460	+	0.157871i	$0.949537\pi$
$854$	1689.89	+	39.0570i	1.97880	+	0.0457342i
$855$		0			0
$856$	127.904	−	221.537i	0.149421	−	0.258805i
$857$	−1189.25	−	318.658i	−1.38769	−	0.371829i	−0.513779	−	0.857923i	$-0.671755\pi$
$857$	−1189.25	−	318.658i	−1.38769	−	0.371829i	−0.873907	+	0.486093i	$0.838421\pi$
$858$		0			0
$859$	−268.193	−	154.841i	−0.312215	−	0.180258i	0.335702	−	0.941968i	$-0.391026\pi$
$859$	−268.193	−	154.841i	−0.312215	−	0.180258i	−0.647917	+	0.761711i	$0.724360\pi$
$860$	−760.061	−	517.185i	−0.883792	−	0.601378i
$861$		0			0
$862$	1128.86	−	1128.86i	1.30958	−	1.30958i
$863$	1355.42	−	363.183i	1.57059	−	0.420837i	0.634590	−	0.772849i	$-0.281169\pi$
$863$	1355.42	−	363.183i	1.57059	−	0.420837i	0.935996	+	0.352011i	$0.114502\pi$
$864$		0			0
$865$	−45.5046	−	3.36835i	−0.0526065	−	0.00389405i
$866$	886.576	−	1535.59i	1.02376	−	1.77320i
$867$		0			0
$868$	−754.617	−	221.008i	−0.869374	−	0.254618i
$869$			169.349i			0.194878i
$870$		0			0
$871$	−233.346	−	404.168i	−0.267906	−	0.464027i
$872$	310.461	+	83.1879i	0.356034	+	0.0953990i
$873$		0			0
$874$		−	2080.12i		−	2.37999i
$875$	−629.164	−	608.093i	−0.719045	−	0.694963i
$876$		0			0
$877$	−164.653	−	614.493i	−0.187746	−	0.700676i	−0.994026	−	0.109143i	$-0.965189\pi$
$877$	−164.653	−	614.493i	−0.187746	−	0.700676i	0.806281	−	0.591533i	$-0.201477\pi$
$878$	−365.697	+	1364.80i	−0.416512	+	1.55444i
$879$		0			0
$880$	780.152	+	272.188i	0.886536	+	0.309305i
$881$	947.178			1.07512			0.537559	−	0.843226i	$-0.319347\pi$
$881$	947.178			1.07512			0.537559	+	0.843226i	$0.319347\pi$
$882$		0			0
$883$	−1152.12	−	1152.12i	−1.30478	−	1.30478i	−0.925132	−	0.379646i	$-0.876046\pi$
$883$	−1152.12	−	1152.12i	−1.30478	−	1.30478i	−0.379646	−	0.925132i	$-0.623954\pi$
$884$	1238.77	+	715.207i	1.40133	+	0.809057i
$885$		0			0
$886$	−140.143	−	242.735i	−0.158175	−	0.273968i
$887$	10.7496	+	40.1181i	0.0121191	+	0.0452290i	0.971721	−	0.236134i	$-0.0758803\pi$
$887$	10.7496	+	40.1181i	0.0121191	+	0.0452290i	−0.959602	+	0.281363i	$0.909214\pi$
$888$		0			0
$889$	−711.367	+	1168.89i	−0.800188	+	1.31484i
$890$	−1401.17	+	2059.18i	−1.57435	+	2.31368i
$891$		0			0
$892$	259.788	+	69.6100i	0.291242	+	0.0780381i
$893$	−90.8683	+	339.125i	−0.101756	+	0.379759i
$894$		0			0
$895$	1315.92	−	250.229i	1.47030	−	0.279585i
$896$	486.525	−	266.100i	0.542997	−	0.296987i
$897$		0			0
$898$	1499.04	−	401.666i	1.66931	−	0.447290i
$899$	−364.011	+	210.162i	−0.404907	+	0.233773i
$900$		0			0
$901$	596.686	−	1033.49i	0.662249	−	1.14705i
$902$	−49.7389	+	49.7389i	−0.0551429	+	0.0551429i
$903$		0			0
$904$			36.6899i			0.0405861i
$905$	−1071.53	−	373.849i	−1.18401	−	0.413093i
$906$		0			0
$907$	1521.13	+	407.585i	1.67710	+	0.449377i	0.967011	−	0.254735i	$-0.0819883\pi$
$907$	1521.13	+	407.585i	1.67710	+	0.449377i	0.710088	+	0.704112i	$0.248655\pi$
$908$	−16.8941	+	4.52675i	−0.0186058	+	0.00498541i
$909$		0			0
$910$	−667.357	+	933.619i	−0.733359	+	1.02596i
$911$	1032.26			1.13311			0.566556	−	0.824023i	$-0.308276\pi$
$911$	1032.26			1.13311			0.566556	+	0.824023i	$0.308276\pi$
$912$		0			0
$913$	−105.309	+	393.017i	−0.115343	+	0.430468i
$914$	−1070.54	+	618.079i	−1.17127	+	0.676235i
$915$		0			0
$916$	−257.717			−0.281351
$917$	43.3881	−	148.145i	0.0473153	−	0.161555i
$918$		0			0
$919$	181.801	+	104.963i	0.197824	+	0.114214i	0.595640	−	0.803251i	$-0.296898\pi$
$919$	181.801	+	104.963i	0.197824	+	0.114214i	−0.397816	+	0.917465i	$0.630232\pi$
$920$	−175.321	−	203.352i	−0.190567	−	0.221034i
$921$		0			0
$922$	216.020	+	806.199i	0.234295	+	0.874403i
$923$	156.722	+	156.722i	0.169796	+	0.169796i
$924$		0			0
$925$	−207.756	+	478.562i	−0.224601	+	0.517365i
$926$	−686.735	+	1189.46i	−0.741614	+	1.28451i
$927$		0			0
$928$	213.520	−	796.868i	0.230086	−	0.858694i
$929$	194.809	+	112.473i	0.209698	+	0.121069i	0.601171	−	0.799121i	$-0.294701\pi$
$929$	194.809	+	112.473i	0.209698	+	0.121069i	−0.391473	+	0.920189i	$0.628034\pi$
$930$		0			0
$931$	−1614.30	−	74.6596i	−1.73394	−	0.0801930i
$932$	443.363	−	443.363i	0.475711	−	0.475711i
$933$		0			0
$934$	−1095.03	+	632.218i	−1.17241	+	0.676893i
$935$	−137.479	+	1857.27i	−0.147037	+	1.98639i
$936$		0			0
$937$	−650.762	+	650.762i	−0.694516	+	0.694516i	−0.963222	−	0.268706i	$-0.913404\pi$
$937$	−650.762	+	650.762i	−0.694516	+	0.694516i	0.268706	+	0.963222i	$0.413404\pi$
$938$	−208.506	−	856.887i	−0.222288	−	0.913525i
$939$		0			0
$940$	112.252	+	232.551i	0.119417	+	0.247395i
$941$	−175.589	−	304.130i	−0.186599	−	0.323199i	0.757515	−	0.652817i	$-0.226413\pi$
$941$	−175.589	−	304.130i	−0.186599	−	0.323199i	−0.944114	+	0.329619i	$0.893080\pi$
$942$		0			0
$943$	−34.7744	+	9.31777i	−0.0368764	+	0.00988099i
$944$			123.983i			0.131338i
$945$		0			0
$946$	−1569.86			−1.65947
$947$	−100.521	−	375.151i	−0.106147	−	0.396147i	0.892326	−	0.451392i	$-0.149073\pi$
$947$	−100.521	−	375.151i	−0.106147	−	0.396147i	−0.998473	+	0.0552454i	$0.982406\pi$
$948$		0			0
$949$	−62.0620	+	35.8315i	−0.0653973	+	0.0377571i
$950$	−1971.02	+	1460.24i	−2.07476	+	1.53710i
$951$		0			0
$952$	327.584	+	343.085i	0.344101	+	0.360383i
$953$	−413.158	−	413.158i	−0.433535	−	0.433535i	0.456294	−	0.889829i	$-0.349176\pi$
$953$	−413.158	−	413.158i	−0.433535	−	0.433535i	−0.889829	+	0.456294i	$0.849176\pi$
$954$		0			0
$955$	−589.307	+	508.076i	−0.617075	+	0.532017i
$956$	−885.739	−	1534.15i	−0.926505	−	1.60475i
$957$		0			0
$958$	445.221	+	445.221i	0.464740	+	0.464740i
$959$	1500.36	+	34.6765i	1.56451	+	0.0361590i
$960$		0			0
$961$	212.439	−	367.955i	0.221060	−	0.382888i
$962$	660.940	+	177.098i	0.687048	+	0.184094i
$963$		0			0
$964$	1653.54	+	954.669i	1.71529	+	0.990321i
$965$	591.640	−	869.479i	0.613098	−	0.901015i
$966$		0			0
$967$	−967.834	+	967.834i	−1.00086	+	1.00086i	−0.000862358		1.00000i	$0.500274\pi$
$967$	−967.834	+	967.834i	−1.00086	+	1.00086i	−1.00000		0.000862358i	$0.999726\pi$
$968$	−178.210	+	47.7512i	−0.184101	+	0.0493298i
$969$		0			0
$970$	910.871	+	1056.50i	0.939042	+	1.08918i
$971$	−540.722	+	936.558i	−0.556871	+	0.964529i	0.440884	+	0.897564i	$0.354665\pi$
$971$	−540.722	+	936.558i	−0.556871	+	0.964529i	−0.997755	+	0.0669653i	$0.978668\pi$
$972$		0			0
$973$	−337.119	−	1385.44i	−0.346474	−	1.42389i
$974$			142.649i			0.146457i
$975$		0			0
$976$	481.699	+	834.327i	0.493544	+	0.854843i
$977$	314.733	+	84.3325i	0.322143	+	0.0863178i	0.416266	−	0.909243i	$-0.363338\pi$
$977$	314.733	+	84.3325i	0.322143	+	0.0863178i	−0.0941240	+	0.995560i	$0.530005\pi$
$978$		0			0
$979$			2331.10i			2.38110i
$980$	−935.107	+	733.707i	−0.954190	+	0.748681i
$981$		0			0
$982$	−604.048	−	2254.34i	−0.615120	−	2.29566i
$983$	258.858	−	966.073i	0.263335	−	0.982780i	−0.699926	−	0.714215i	$-0.746784\pi$
$983$	258.858	−	966.073i	0.263335	−	0.982780i	0.963261	−	0.268565i	$-0.0865495\pi$
$984$		0			0
$985$	628.013	−	303.141i	0.637576	−	0.307757i
$986$	1444.88			1.46540
$987$		0			0
$988$	1246.88	+	1246.88i	1.26202	+	1.26202i
$989$	−695.819	−	401.731i	−0.703558	−	0.406199i
$990$		0			0
$991$	770.884	+	1335.21i	0.777885	+	1.34734i	0.933158	+	0.359465i	$0.117041\pi$
$991$	770.884	+	1335.21i	0.777885	+	1.34734i	−0.155273	+	0.987872i	$0.549626\pi$
$992$	−272.345	−	1016.40i	−0.274541	−	1.02460i
$993$		0			0
$994$	200.973	+	367.450i	0.202186	+	0.369668i
$995$	203.172	−	38.6343i	0.204193	−	0.0388284i
$996$		0			0
$997$	−840.254	−	225.145i	−0.842782	−	0.225823i	−0.188500	−	0.982073i	$-0.560363\pi$
$997$	−840.254	−	225.145i	−0.842782	−	0.225823i	−0.654282	+	0.756250i	$0.727029\pi$
$998$	45.0555	−	168.150i	0.0451458	−	0.168486i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.163.3		64
3.2	odd	2		105.3.v.a.58.14	yes	64
5.2	odd	4	inner	315.3.ca.b.37.14		64
7.4	even	3	inner	315.3.ca.b.298.14		64
15.2	even	4		105.3.v.a.37.3	✓	64
21.11	odd	6		105.3.v.a.88.3	yes	64
35.32	odd	12	inner	315.3.ca.b.172.3		64
105.32	even	12		105.3.v.a.67.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.3	✓	64	15.2	even	4
105.3.v.a.58.14	yes	64	3.2	odd	2
105.3.v.a.67.14	yes	64	105.32	even	12
105.3.v.a.88.3	yes	64	21.11	odd	6
315.3.ca.b.37.14		64	5.2	odd	4	inner
315.3.ca.b.163.3		64	1.1	even	1	trivial
315.3.ca.b.172.3		64	35.32	odd	12	inner
315.3.ca.b.298.14		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)

\(f(q)\)	\(=\)	\(q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +O(q^{10})\)	\(q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +(1.09812 - 14.8351i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 + 7.79302i) q^{13} +(9.99344 + 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(-25.8415 - 6.92421i) q^{17} +(-28.5616 - 16.4901i) q^{19} +(-23.8300 + 4.53140i) q^{20} +(-29.2893 + 29.2893i) q^{22} +(-20.4773 + 5.48688i) q^{23} +(19.5742 + 15.5516i) q^{25} +(16.3944 - 28.3960i) q^{26} +(24.5616 - 23.4519i) q^{28} -18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(43.8970 + 11.7622i) q^{32} +79.5940i q^{34} +(-34.8355 - 3.38952i) q^{35} +(5.40117 + 20.1574i) q^{37} +(-25.3954 + 94.7768i) q^{38} +(5.50557 + 11.4058i) q^{40} +1.69819 q^{41} +(26.7992 + 26.7992i) q^{43} +(58.4946 + 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(-2.75524 - 10.2827i) q^{47} +(43.5218 - 22.5134i) q^{49} +(29.6188 - 68.2264i) q^{50} +(-51.6453 - 13.8383i) q^{52} +(-11.5451 + 43.0869i) q^{53} +(-13.0042 - 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(-52.1677 + 13.9783i) q^{58} +(9.04603 - 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 + 48.7105i) q^{62} -87.7280i q^{64} +(23.9544 + 49.6260i) q^{65} +(-40.9029 - 10.9599i) q^{67} +(125.367 - 33.5921i) q^{68} +(17.0834 + 102.719i) q^{70} +20.1105 q^{71} +(-1.68295 + 6.28085i) q^{73} +(53.7685 - 31.0433i) q^{74} +160.000 q^{76} +(67.3023 + 70.4869i) q^{77} +(-10.5341 - 6.08184i) q^{79} +(-44.9486 + 38.7528i) q^{80} +(-1.30764 - 4.88019i) q^{82} +(-20.6649 - 20.6649i) q^{83} +(-110.591 - 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(9.12749 - 34.0643i) q^{88} +(-145.002 - 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 - 72.7245i) q^{92} +(-27.4284 + 15.8358i) q^{94} +(-107.677 - 124.892i) q^{95} +(-66.3082 + 66.3082i) q^{97} +(-98.2105 - 107.735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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