LMFDB - Embedded newform 315.3.o.b.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (of order $4$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	315.127
Dual form			315.3.o.b.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08980 - 2.08980i) q^{2} +4.73454i q^{4} +(-0.137153 - 4.99812i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} +O(q^{10})$	\(q+(-2.08980 - 2.08980i) q^{2} +4.73454i q^{4} +(-0.137153 - 4.99812i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} +(-10.1585 + 10.7317i) q^{10} -2.70159 q^{11} +(-2.37916 + 2.37916i) q^{13} +7.81932i q^{14} +12.5223 q^{16} +(-16.3715 - 16.3715i) q^{17} -9.18722i q^{19} +(23.6638 - 0.649359i) q^{20} +(5.64579 + 5.64579i) q^{22} +(-21.4530 + 21.4530i) q^{23} +(-24.9624 + 1.37102i) q^{25} +9.94394 q^{26} +(8.85752 - 8.85752i) q^{28} +52.3515i q^{29} -5.01849 q^{31} +(-32.3093 - 32.3093i) q^{32} +68.4262i q^{34} +(-9.09403 + 9.60721i) q^{35} +(23.2257 + 23.2257i) q^{37} +(-19.1995 + 19.1995i) q^{38} +(-7.88291 - 7.46184i) q^{40} +60.5336 q^{41} +(-8.78639 + 8.78639i) q^{43} -12.7908i q^{44} +89.6651 q^{46} +(-2.24235 - 2.24235i) q^{47} +7.00000i q^{49} +(55.0316 + 49.3013i) q^{50} +(-11.2642 - 11.2642i) q^{52} +(25.6733 - 25.6733i) q^{53} +(0.370533 + 13.5029i) q^{55} -5.74364 q^{56} +(109.404 - 109.404i) q^{58} +100.980i q^{59} -82.1567 q^{61} +(10.4877 + 10.4877i) q^{62} +84.9509i q^{64} +(12.2176 + 11.5650i) q^{65} +(-65.1606 - 65.1606i) q^{67} +(77.5114 - 77.5114i) q^{68} +(39.0819 - 1.07245i) q^{70} +22.8905 q^{71} +(-5.38609 + 5.38609i) q^{73} -97.0741i q^{74} +43.4973 q^{76} +(5.05422 + 5.05422i) q^{77} +117.836i q^{79} +(-1.71747 - 62.5878i) q^{80} +(-126.503 - 126.503i) q^{82} +(-85.5086 + 85.5086i) q^{83} +(-79.5811 + 84.0719i) q^{85} +36.7236 q^{86} +(-4.14709 + 4.14709i) q^{88} -119.010i q^{89} +8.90199 q^{91} +(-101.570 - 101.570i) q^{92} +9.37213i q^{94} +(-45.9188 + 1.26006i) q^{95} +(-55.1059 - 55.1059i) q^{97} +(14.6286 - 14.6286i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.08980	−	2.08980i	−1.04490	−	1.04490i	−0.998943	−	0.0459576i	$-0.985366\pi$
$2$	−2.08980	−	2.08980i	−1.04490	−	1.04490i	−0.0459576	−	0.998943i	$-0.514634\pi$
$3$		0			0
$3$		0			0
$4$			4.73454i			1.18364i
$5$	−0.137153	−	4.99812i	−0.0274307	−	0.999624i
$5$	−0.137153	−	4.99812i	−0.0274307	−	0.999624i
$6$		0			0
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	1.53505	−	1.53505i	0.191882	−	0.191882i
$9$		0			0
$10$	−10.1585	+	10.7317i	−1.01585	+	1.07317i
$11$	−2.70159			−0.245599			−0.122800	−	0.992431i	$-0.539187\pi$
$11$	−2.70159			−0.245599			−0.122800	+	0.992431i	$0.539187\pi$
$12$		0			0
$13$	−2.37916	+	2.37916i	−0.183012	+	0.183012i	−0.792667	−	0.609655i	$-0.791308\pi$
$13$	−2.37916	+	2.37916i	−0.183012	+	0.183012i	0.609655	+	0.792667i	$0.291308\pi$
$14$			7.81932i			0.558523i
$15$		0			0
$16$	12.5223			0.782642
$17$	−16.3715	−	16.3715i	−0.963027	−	0.963027i	0.0363138	−	0.999340i	$-0.488438\pi$
$17$	−16.3715	−	16.3715i	−0.963027	−	0.963027i	−0.999340	+	0.0363138i	$0.988438\pi$
$18$		0			0
$19$		−	9.18722i		−	0.483538i	−0.970334	−	0.241769i	$-0.922272\pi$
$19$		−	9.18722i		−	0.483538i	0.970334	−	0.241769i	$-0.0777276\pi$
$20$	23.6638	−	0.649359i	1.18319	−	0.0324679i
$21$		0			0
$22$	5.64579	+	5.64579i	0.256627	+	0.256627i
$23$	−21.4530	+	21.4530i	−0.932740	+	0.932740i	−0.997876	−	0.0651365i	$-0.979252\pi$
$23$	−21.4530	+	21.4530i	−0.932740	+	0.932740i	0.0651365	+	0.997876i	$0.479252\pi$
$24$		0			0
$25$	−24.9624	+	1.37102i	−0.998495	+	0.0548407i
$26$	9.94394			0.382459
$27$		0			0
$28$	8.85752	−	8.85752i	0.316340	−	0.316340i
$29$			52.3515i			1.80523i	0.430453	+	0.902613i	$0.358354\pi$
$29$			52.3515i			1.80523i	−0.430453	+	0.902613i	$0.641646\pi$
$30$		0			0
$31$	−5.01849			−0.161887			−0.0809434	−	0.996719i	$-0.525793\pi$
$31$	−5.01849			−0.161887			−0.0809434	+	0.996719i	$0.525793\pi$
$32$	−32.3093	−	32.3093i	−1.00966	−	1.00966i
$33$		0			0
$34$			68.4262i			2.01253i
$35$	−9.09403	+	9.60721i	−0.259830	+	0.274492i
$36$		0			0
$37$	23.2257	+	23.2257i	0.627721	+	0.627721i	0.947494	−	0.319773i	$-0.103607\pi$
$37$	23.2257	+	23.2257i	0.627721	+	0.627721i	−0.319773	+	0.947494i	$0.603607\pi$
$38$	−19.1995	+	19.1995i	−0.505249	+	0.505249i
$39$		0			0
$40$	−7.88291	−	7.46184i	−0.197073	−	0.186546i
$41$	60.5336			1.47643			0.738215	−	0.674566i	$-0.235669\pi$
$41$	60.5336			1.47643			0.738215	+	0.674566i	$0.235669\pi$
$42$		0			0
$43$	−8.78639	+	8.78639i	−0.204335	+	0.204335i	−0.801854	−	0.597520i	$-0.796153\pi$
$43$	−8.78639	+	8.78639i	−0.204335	+	0.204335i	0.597520	+	0.801854i	$0.296153\pi$
$44$		−	12.7908i		−	0.290700i
$45$		0			0
$46$	89.6651			1.94924
$47$	−2.24235	−	2.24235i	−0.0477096	−	0.0477096i	0.682850	−	0.730559i	$-0.260740\pi$
$47$	−2.24235	−	2.24235i	−0.0477096	−	0.0477096i	−0.730559	+	0.682850i	$0.760740\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	55.0316	+	49.3013i	1.10063	+	0.986025i
$51$		0			0
$52$	−11.2642	−	11.2642i	−0.216620	−	0.216620i
$53$	25.6733	−	25.6733i	0.484401	−	0.484401i	−0.422133	−	0.906534i	$-0.638718\pi$
$53$	25.6733	−	25.6733i	0.484401	−	0.484401i	0.906534	+	0.422133i	$0.138718\pi$
$54$		0			0
$55$	0.370533	+	13.5029i	0.00673696	+	0.245507i
$56$	−5.74364			−0.102565
$57$		0			0
$58$	109.404	−	109.404i	1.88628	−	1.88628i
$59$			100.980i			1.71152i	0.517374	+	0.855759i	$0.326909\pi$
$59$			100.980i			1.71152i	−0.517374	+	0.855759i	$0.673091\pi$
$60$		0			0
$61$	−82.1567			−1.34683			−0.673415	−	0.739264i	$-0.735173\pi$
$61$	−82.1567			−1.34683			−0.673415	+	0.739264i	$0.735173\pi$
$62$	10.4877	+	10.4877i	0.169156	+	0.169156i
$63$		0			0
$64$			84.9509i			1.32736i
$65$	12.2176	+	11.5650i	0.187963	+	0.177923i
$66$		0			0
$67$	−65.1606	−	65.1606i	−0.972546	−	0.972546i	0.0270874	−	0.999633i	$-0.491377\pi$
$67$	−65.1606	−	65.1606i	−0.972546	−	0.972546i	−0.999633	+	0.0270874i	$0.991377\pi$
$68$	77.5114	−	77.5114i	1.13987	−	1.13987i
$69$		0			0
$70$	39.0819	−	1.07245i	0.558313	−	0.0153207i
$71$	22.8905			0.322402			0.161201	−	0.986922i	$-0.448463\pi$
$71$	22.8905			0.322402			0.161201	+	0.986922i	$0.448463\pi$
$72$		0			0
$73$	−5.38609	+	5.38609i	−0.0737820	+	0.0737820i	−0.743035	−	0.669253i	$-0.766614\pi$
$73$	−5.38609	+	5.38609i	−0.0737820	+	0.0737820i	0.669253	+	0.743035i	$0.266614\pi$
$74$		−	97.0741i		−	1.31181i
$75$		0			0
$76$	43.4973			0.572333
$77$	5.05422	+	5.05422i	0.0656392	+	0.0656392i
$78$		0			0
$79$			117.836i			1.49159i	0.666175	+	0.745795i	$0.267930\pi$
$79$			117.836i			1.49159i	−0.666175	+	0.745795i	$0.732070\pi$
$80$	−1.71747	−	62.5878i	−0.0214684	−	0.782347i
$81$		0			0
$82$	−126.503	−	126.503i	−1.54272	−	1.54272i
$83$	−85.5086	+	85.5086i	−1.03022	+	1.03022i	−0.0306951	+	0.999529i	$0.509772\pi$
$83$	−85.5086	+	85.5086i	−1.03022	+	1.03022i	−0.999529	+	0.0306951i	$0.990228\pi$
$84$		0			0
$85$	−79.5811	+	84.0719i	−0.936248	+	0.989081i
$86$	36.7236			0.427019
$87$		0			0
$88$	−4.14709	+	4.14709i	−0.0471260	+	0.0471260i
$89$		−	119.010i		−	1.33719i	−0.743629	−	0.668593i	$-0.766897\pi$
$89$		−	119.010i		−	1.33719i	0.743629	−	0.668593i	$-0.233103\pi$
$90$		0			0
$91$	8.90199			0.0978241
$92$	−101.570	−	101.570i	−1.10402	−	1.10402i
$93$		0			0
$94$			9.37213i			0.0997035i
$95$	−45.9188	+	1.26006i	−0.483356	+	0.0132638i
$96$		0			0
$97$	−55.1059	−	55.1059i	−0.568102	−	0.568102i	0.363494	−	0.931596i	$-0.381584\pi$
$97$	−55.1059	−	55.1059i	−0.568102	−	0.568102i	−0.931596	+	0.363494i	$0.881584\pi$
$98$	14.6286	−	14.6286i	0.149272	−	0.149272i
$99$		0			0
$100$	−6.49114	−	118.185i	−0.0649114	−	1.18185i
$101$	−128.322			−1.27052			−0.635259	−	0.772299i	$-0.719107\pi$
$101$	−128.322			−1.27052			−0.635259	+	0.772299i	$0.719107\pi$
$102$		0			0
$103$	10.5985	−	10.5985i	0.102898	−	0.102898i	−0.653783	−	0.756682i	$-0.726819\pi$
$103$	10.5985	−	10.5985i	0.102898	−	0.102898i	0.756682	+	0.653783i	$0.226819\pi$
$104$			7.30426i			0.0702333i
$105$		0			0
$106$	−107.304			−1.01230
$107$	−138.356	−	138.356i	−1.29305	−	1.29305i	−0.932894	−	0.360151i	$-0.882725\pi$
$107$	−138.356	−	138.356i	−1.29305	−	1.29305i	−0.360151	−	0.932894i	$-0.617275\pi$
$108$		0			0
$109$		−	161.387i		−	1.48061i	−0.672271	−	0.740305i	$-0.734681\pi$
$109$		−	161.387i		−	1.48061i	0.672271	−	0.740305i	$-0.265319\pi$
$110$	27.4440	−	28.9927i	0.249491	−	0.263570i
$111$		0			0
$112$	−23.4270	−	23.4270i	−0.209170	−	0.209170i
$113$	34.2178	−	34.2178i	0.302812	−	0.302812i	−0.539301	−	0.842113i	$-0.681311\pi$
$113$	34.2178	−	34.2178i	0.302812	−	0.302812i	0.842113	+	0.539301i	$0.181311\pi$
$114$		0			0
$115$	110.167	+	104.282i	0.957975	+	0.906803i
$116$	−247.861			−2.13673
$117$		0			0
$118$	211.027	−	211.027i	1.78837	−	1.78837i
$119$			61.2564i			0.514759i
$120$		0			0
$121$	−113.701			−0.939681
$122$	171.691	+	171.691i	1.40730	+	1.40730i
$123$		0			0
$124$		−	23.7603i		−	0.191615i
$125$	10.2762	+	124.577i	0.0822095	+	0.996615i
$126$		0			0
$127$	−13.3778	−	13.3778i	−0.105337	−	0.105337i	0.652474	−	0.757811i	$-0.273731\pi$
$127$	−13.3778	−	13.3778i	−0.105337	−	0.105337i	−0.757811	+	0.652474i	$0.773731\pi$
$128$	48.2934	−	48.2934i	0.377292	−	0.377292i
$129$		0			0
$130$	−1.36384	−	49.7010i	−0.0104911	−	0.382315i
$131$	−27.9162			−0.213101			−0.106550	−	0.994307i	$-0.533981\pi$
$131$	−27.9162			−0.213101			−0.106550	+	0.994307i	$0.533981\pi$
$132$		0			0
$133$	−17.1877	+	17.1877i	−0.129231	+	0.129231i
$134$			272.345i			2.03243i
$135$		0			0
$136$	−50.2621			−0.369574
$137$	−69.2726	−	69.2726i	−0.505639	−	0.505639i	0.407546	−	0.913185i	$-0.366385\pi$
$137$	−69.2726	−	69.2726i	−0.505639	−	0.505639i	−0.913185	+	0.407546i	$0.866385\pi$
$138$		0			0
$139$		−	233.891i		−	1.68267i	−0.540513	−	0.841335i	$-0.681770\pi$
$139$		−	233.891i		−	1.68267i	0.540513	−	0.841335i	$-0.318230\pi$
$140$	−45.4858	−	43.0561i	−0.324898	−	0.307544i
$141$		0			0
$142$	−47.8367	−	47.8367i	−0.336878	−	0.336878i
$143$	6.42751	−	6.42751i	0.0449477	−	0.0449477i
$144$		0			0
$145$	261.659	−	7.18019i	1.80455	−	0.0495186i
$146$	22.5117			0.154190
$147$		0			0
$148$	−109.963	+	109.963i	−0.742993	+	0.742993i
$149$		−	127.594i		−	0.856336i	−0.903699	−	0.428168i	$-0.859159\pi$
$149$		−	127.594i		−	0.856336i	0.903699	−	0.428168i	$-0.140841\pi$
$150$		0			0
$151$	49.1914			0.325771			0.162886	−	0.986645i	$-0.447920\pi$
$151$	49.1914			0.325771			0.162886	+	0.986645i	$0.447920\pi$
$152$	−14.1029	−	14.1029i	−0.0927821	−	0.0927821i
$153$		0			0
$154$		−	21.1246i		−	0.137173i
$155$	0.688303	+	25.0830i	0.00444067	+	0.161826i
$156$		0			0
$157$	130.828	+	130.828i	0.833301	+	0.833301i	0.987967	−	0.154666i	$-0.0494302\pi$
$157$	130.828	+	130.828i	0.833301	+	0.833301i	−0.154666	+	0.987967i	$0.549430\pi$
$158$	246.253	−	246.253i	1.55856	−	1.55856i
$159$		0			0
$160$	−157.054	+	165.917i	−0.981589	+	1.03698i
$161$	80.2698			0.498570
$162$		0			0
$163$	−35.5824	+	35.5824i	−0.218297	+	0.218297i	−0.807780	−	0.589483i	$-0.799331\pi$
$163$	−35.5824	+	35.5824i	−0.218297	+	0.218297i	0.589483	+	0.807780i	$0.299331\pi$
$164$			286.599i			1.74756i
$165$		0			0
$166$	357.392			2.15296
$167$	−27.7479	−	27.7479i	−0.166155	−	0.166155i	0.619132	−	0.785287i	$-0.287485\pi$
$167$	−27.7479	−	27.7479i	−0.166155	−	0.166155i	−0.785287	+	0.619132i	$0.787485\pi$
$168$		0			0
$169$			157.679i			0.933013i
$170$	342.002	−	9.38488i	2.01178	−	0.0552052i
$171$		0			0
$172$	−41.5995	−	41.5995i	−0.241858	−	0.241858i
$173$	190.785	−	190.785i	1.10280	−	1.10280i	0.108732	−	0.994071i	$-0.465321\pi$
$173$	190.785	−	190.785i	1.10280	−	1.10280i	0.994071	−	0.108732i	$-0.0346790\pi$
$174$		0			0
$175$	49.2653	+	44.1354i	0.281516	+	0.252202i
$176$	−33.8301			−0.192216
$177$		0			0
$178$	−248.706	+	248.706i	−1.39723	+	1.39723i
$179$			180.379i			1.00770i	0.863791	+	0.503851i	$0.168084\pi$
$179$			180.379i			1.00770i	−0.863791	+	0.503851i	$0.831916\pi$
$180$		0			0
$181$	−20.8061			−0.114951			−0.0574754	−	0.998347i	$-0.518305\pi$
$181$	−20.8061			−0.114951			−0.0574754	+	0.998347i	$0.518305\pi$
$182$	−18.6034	−	18.6034i	−0.102217	−	0.102217i
$183$		0			0
$184$			65.8630i			0.357951i
$185$	112.899	−	119.270i	0.610266	−	0.644704i
$186$		0			0
$187$	44.2290	+	44.2290i	0.236519	+	0.236519i
$188$	10.6165	−	10.6165i	0.0564708	−	0.0564708i
$189$		0			0
$190$	98.5946	+	93.3280i	0.518919	+	0.491200i
$191$	−221.603			−1.16022			−0.580112	−	0.814536i	$-0.696991\pi$
$191$	−221.603			−1.16022			−0.580112	+	0.814536i	$0.696991\pi$
$192$		0			0
$193$	−188.688	+	188.688i	−0.977659	+	0.977659i	−0.999756	−	0.0220973i	$-0.992966\pi$
$193$	−188.688	+	188.688i	−0.977659	+	0.977659i	0.0220973	+	0.999756i	$0.492966\pi$
$194$			230.321i			1.18722i
$195$		0			0
$196$	−33.1418			−0.169091
$197$	−85.7353	−	85.7353i	−0.435205	−	0.435205i	0.455190	−	0.890394i	$-0.349571\pi$
$197$	−85.7353	−	85.7353i	−0.435205	−	0.435205i	−0.890394	+	0.455190i	$0.849571\pi$
$198$		0			0
$199$		−	106.621i		−	0.535783i	−0.963449	−	0.267892i	$-0.913673\pi$
$199$		−	106.621i		−	0.535783i	0.963449	−	0.267892i	$-0.0863269\pi$
$200$	−36.2140	+	40.4231i	−0.181070	+	0.202116i
$201$		0			0
$202$	268.168	+	268.168i	1.32756	+	1.32756i
$203$	97.9408	−	97.9408i	0.482467	−	0.482467i
$204$		0			0
$205$	−8.30239	−	302.554i	−0.0404995	−	1.47587i
$206$	−44.2976			−0.215037
$207$		0			0
$208$	−29.7924	+	29.7924i	−0.143233	+	0.143233i
$209$			24.8201i			0.118757i
$210$		0			0
$211$	−210.119			−0.995827			−0.497913	−	0.867227i	$-0.665900\pi$
$211$	−210.119			−0.995827			−0.497913	+	0.867227i	$0.665900\pi$
$212$	121.551	+	121.551i	0.573355	+	0.573355i
$213$		0			0
$214$			578.273i			2.70221i
$215$	45.1205	+	42.7103i	0.209863	+	0.198653i
$216$		0			0
$217$	9.38874	+	9.38874i	0.0432661	+	0.0432661i
$218$	−337.266	+	337.266i	−1.54709	+	1.54709i
$219$		0			0
$220$	−63.9300	+	1.75430i	−0.290591	+	0.00797410i
$221$	77.9005			0.352491
$222$		0			0
$223$	−138.303	+	138.303i	−0.620191	+	0.620191i	−0.945580	−	0.325389i	$-0.894505\pi$
$223$	−138.303	+	138.303i	−0.620191	+	0.620191i	0.325389	+	0.945580i	$0.394505\pi$
$224$			120.890i			0.539688i
$225$		0			0
$226$	−143.017			−0.632818
$227$	286.401	+	286.401i	1.26168	+	1.26168i	0.950280	+	0.311397i	$0.100797\pi$
$227$	286.401	+	286.401i	1.26168	+	1.26168i	0.311397	+	0.950280i	$0.399203\pi$
$228$		0			0
$229$		−	210.860i		−	0.920787i	−0.887715	−	0.460394i	$-0.847708\pi$
$229$		−	210.860i		−	0.920787i	0.887715	−	0.460394i	$-0.152292\pi$
$230$	−12.2979	−	448.157i	−0.0534690	−	1.94851i
$231$		0			0
$232$	80.3624	+	80.3624i	0.346389	+	0.346389i
$233$	−217.881	+	217.881i	−0.935112	+	0.935112i	−0.998019	−	0.0629077i	$-0.979963\pi$
$233$	−217.881	+	217.881i	−0.935112	+	0.935112i	0.0629077	+	0.998019i	$0.479963\pi$
$234$		0			0
$235$	−10.9000	+	11.5151i	−0.0463829	+	0.0490003i
$236$	−478.092			−2.02581
$237$		0			0
$238$	128.014	−	128.014i	0.537873	−	0.537873i
$239$		−	103.424i		−	0.432737i	−0.976312	−	0.216369i	$-0.930579\pi$
$239$		−	103.424i		−	0.432737i	0.976312	−	0.216369i	$-0.0694213\pi$
$240$		0			0
$241$	−13.3346			−0.0553304			−0.0276652	−	0.999617i	$-0.508807\pi$
$241$	−13.3346			−0.0553304			−0.0276652	+	0.999617i	$0.508807\pi$
$242$	237.613	+	237.613i	0.981874	+	0.981874i
$243$		0			0
$244$		−	388.974i		−	1.59416i
$245$	34.9868	−	0.960074i	0.142803	−	0.00391867i
$246$		0			0
$247$	21.8579	+	21.8579i	0.0884934	+	0.0884934i
$248$	−7.70365	+	7.70365i	−0.0310631	+	0.0310631i
$249$		0			0
$250$	238.866	−	281.816i	0.955463	−	1.12726i
$251$	324.833			1.29416			0.647078	−	0.762424i	$-0.275991\pi$
$251$	324.833			1.29416			0.647078	+	0.762424i	$0.275991\pi$
$252$		0			0
$253$	57.9573	−	57.9573i	0.229080	−	0.229080i
$254$			55.9141i			0.220134i
$255$		0			0
$256$	137.956			0.538891
$257$	−45.5488	−	45.5488i	−0.177233	−	0.177233i	0.612916	−	0.790148i	$-0.289997\pi$
$257$	−45.5488	−	45.5488i	−0.177233	−	0.177233i	−0.790148	+	0.612916i	$0.789997\pi$
$258$		0			0
$259$		−	86.9025i		−	0.335531i
$260$	−54.7550	+	57.8449i	−0.210596	+	0.222480i
$261$		0			0
$262$	58.3393	+	58.3393i	0.222669	+	0.222669i
$263$	186.483	−	186.483i	0.709062	−	0.709062i	−0.257276	−	0.966338i	$-0.582825\pi$
$263$	186.483	−	186.483i	0.709062	−	0.709062i	0.966338	+	0.257276i	$0.0828250\pi$
$264$		0			0
$265$	−131.839	−	124.797i	−0.497506	−	0.470931i
$266$	71.8379			0.270067
$267$		0			0
$268$	308.506	−	308.506i	1.15114	−	1.15114i
$269$		−	489.403i		−	1.81934i	−0.415330	−	0.909671i	$-0.636334\pi$
$269$		−	489.403i		−	1.81934i	0.415330	−	0.909671i	$-0.363666\pi$
$270$		0			0
$271$	35.3651			0.130499			0.0652493	−	0.997869i	$-0.479216\pi$
$271$	35.3651			0.130499			0.0652493	+	0.997869i	$0.479216\pi$
$272$	−205.008	−	205.008i	−0.753705	−	0.753705i
$273$		0			0
$274$			289.532i			1.05669i
$275$	67.4382	−	3.70393i	0.245230	−	0.0134688i
$276$		0			0
$277$	−88.7149	−	88.7149i	−0.320270	−	0.320270i	0.528600	−	0.848871i	$-0.322717\pi$
$277$	−88.7149	−	88.7149i	−0.320270	−	0.320270i	−0.848871	+	0.528600i	$0.822717\pi$
$278$	−488.786	+	488.786i	−1.75822	+	1.75822i
$279$		0			0
$280$	0.787760	+	28.7074i	0.00281343	+	0.102526i
$281$	31.7224			0.112891			0.0564456	−	0.998406i	$-0.482023\pi$
$281$	31.7224			0.112891			0.0564456	+	0.998406i	$0.482023\pi$
$282$		0			0
$283$	−111.462	+	111.462i	−0.393859	+	0.393859i	−0.876060	−	0.482202i	$-0.839837\pi$
$283$	−111.462	+	111.462i	−0.393859	+	0.393859i	0.482202	+	0.876060i	$0.339837\pi$
$284$			108.376i			0.381607i
$285$		0			0
$286$	−26.8645			−0.0939317
$287$	−113.248	−	113.248i	−0.394593	−	0.394593i
$288$		0			0
$289$			247.049i			0.854841i
$290$	−561.821	−	531.811i	−1.93731	−	1.83383i
$291$		0			0
$292$	−25.5007	−	25.5007i	−0.0873311	−	0.0873311i
$293$	−10.3345	+	10.3345i	−0.0352712	+	0.0352712i	−0.724522	−	0.689251i	$-0.757940\pi$
$293$	−10.3345	+	10.3345i	−0.0352712	+	0.0352712i	0.689251	+	0.724522i	$0.257940\pi$
$294$		0			0
$295$	504.708	−	13.8497i	1.71087	−	0.0469481i
$296$	71.3053			0.240896
$297$		0			0
$298$	−266.646	+	266.646i	−0.894786	+	0.894786i
$299$		−	102.080i		−	0.341405i
$300$		0			0
$301$	32.8756			0.109221
$302$	−102.800	−	102.800i	−0.340399	−	0.340399i
$303$		0			0
$304$		−	115.045i		−	0.378437i
$305$	11.2681	+	410.629i	0.0369445	+	1.34632i
$306$		0			0
$307$	296.667	+	296.667i	0.966341	+	0.966341i	0.999452	−	0.0331110i	$-0.0105415\pi$
$307$	296.667	+	296.667i	0.966341	+	0.966341i	−0.0331110	+	0.999452i	$0.510541\pi$
$308$	−23.9294	+	23.9294i	−0.0776929	+	0.0776929i
$309$		0			0
$310$	50.9801	−	53.8570i	0.164452	−	0.173732i
$311$	36.8400			0.118457			0.0592284	−	0.998244i	$-0.481136\pi$
$311$	36.8400			0.118457			0.0592284	+	0.998244i	$0.481136\pi$
$312$		0			0
$313$	−90.5345	+	90.5345i	−0.289248	+	0.289248i	−0.836783	−	0.547535i	$-0.815566\pi$
$313$	−90.5345	+	90.5345i	−0.289248	+	0.289248i	0.547535	+	0.836783i	$0.315566\pi$
$314$		−	546.810i		−	1.74143i
$315$		0			0
$316$	−557.898			−1.76550
$317$	−2.40123	−	2.40123i	−0.00757485	−	0.00757485i	0.703309	−	0.710884i	$-0.251705\pi$
$317$	−2.40123	−	2.40123i	−0.00757485	−	0.00757485i	−0.710884	+	0.703309i	$0.751705\pi$
$318$		0			0
$319$		−	141.433i		−	0.443362i
$320$	424.595	−	11.6513i	1.32686	−	0.0364103i
$321$		0			0
$322$	−167.748	−	167.748i	−0.520957	−	0.520957i
$323$	−150.408	+	150.408i	−0.465660	+	0.465660i
$324$		0			0
$325$	56.1276	−	62.6513i	0.172700	−	0.192773i
$326$	148.720			0.456198
$327$		0			0
$328$	92.9223	−	92.9223i	0.283300	−	0.283300i
$329$			8.39010i			0.0255018i
$330$		0			0
$331$	−288.021			−0.870154			−0.435077	−	0.900393i	$-0.643279\pi$
$331$	−288.021			−0.870154			−0.435077	+	0.900393i	$0.643279\pi$
$332$	−404.844	−	404.844i	−1.21941	−	1.21941i
$333$		0			0
$334$			115.975i			0.347232i
$335$	−316.743	+	334.617i	−0.945502	+	0.998857i
$336$		0			0
$337$	−354.146	−	354.146i	−1.05088	−	1.05088i	−0.998634	−	0.0522432i	$-0.983363\pi$
$337$	−354.146	−	354.146i	−1.05088	−	1.05088i	−0.0522432	−	0.998634i	$-0.516637\pi$
$338$	329.518	−	329.518i	0.974906	−	0.974906i
$339$		0			0
$340$	−398.042	−	376.780i	−1.17071	−	1.10818i
$341$	13.5579			0.0397593
$342$		0			0
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			26.9751i			0.0784161i
$345$		0			0
$346$	−797.405			−2.30464
$347$	440.033	+	440.033i	1.26811	+	1.26811i	0.947064	+	0.321044i	$0.104034\pi$
$347$	440.033	+	440.033i	1.26811	+	1.26811i	0.321044	+	0.947064i	$0.395966\pi$
$348$		0			0
$349$		−	429.577i		−	1.23088i	−0.788184	−	0.615440i	$-0.788978\pi$
$349$		−	429.577i		−	1.23088i	0.788184	−	0.615440i	$-0.211022\pi$
$350$	−10.7204	−	195.189i	−0.0306298	−	0.557683i
$351$		0			0
$352$	87.2865	+	87.2865i	0.247973	+	0.247973i
$353$	−240.557	+	240.557i	−0.681463	+	0.681463i	−0.960330	−	0.278867i	$-0.910041\pi$
$353$	−240.557	+	240.557i	−0.681463	+	0.681463i	0.278867	+	0.960330i	$0.410041\pi$
$354$		0			0
$355$	−3.13952	−	114.410i	−0.00884371	−	0.322281i
$356$	563.456			1.58274
$357$		0			0
$358$	376.956	−	376.956i	1.05295	−	1.05295i
$359$			53.5007i			0.149027i	0.997220	+	0.0745135i	$0.0237404\pi$
$359$			53.5007i			0.149027i	−0.997220	+	0.0745135i	$0.976260\pi$
$360$		0			0
$361$	276.595			0.766191
$362$	43.4806	+	43.4806i	0.120112	+	0.120112i
$363$		0			0
$364$			42.1469i			0.115788i
$365$	27.6590	+	26.1816i	0.0757781	+	0.0717304i
$366$		0			0
$367$	1.26172	+	1.26172i	0.00343792	+	0.00343792i	0.708824	−	0.705386i	$-0.249226\pi$
$367$	1.26172	+	1.26172i	0.00343792	+	0.00343792i	−0.705386	+	0.708824i	$0.749226\pi$
$368$	−268.640	+	268.640i	−0.730001	+	0.730001i
$369$		0			0
$370$	−485.188	+	13.3140i	−1.31132	+	0.0359839i
$371$	−96.0606			−0.258923
$372$		0			0
$373$	−48.6449	+	48.6449i	−0.130415	+	0.130415i	−0.769301	−	0.638886i	$-0.779396\pi$
$373$	−48.6449	+	48.6449i	−0.130415	+	0.130415i	0.638886	+	0.769301i	$0.279396\pi$
$374$		−	184.860i		−	0.494277i
$375$		0			0
$376$	−6.88425			−0.0183092
$377$	−124.553	−	124.553i	−0.330378	−	0.330378i
$378$		0			0
$379$			482.025i			1.27183i	0.771758	+	0.635917i	$0.219378\pi$
$379$			482.025i			1.27183i	−0.771758	+	0.635917i	$0.780622\pi$
$380$	−5.96581	−	217.405i	−0.0156995	−	0.572118i
$381$		0			0
$382$	463.106	+	463.106i	1.21232	+	1.21232i
$383$	75.2958	−	75.2958i	0.196595	−	0.196595i	−0.601944	−	0.798539i	$-0.705607\pi$
$383$	75.2958	−	75.2958i	0.196595	−	0.196595i	0.798539	+	0.601944i	$0.205607\pi$
$384$		0			0
$385$	24.5684	−	25.9548i	0.0638139	−	0.0674150i
$386$	788.641			2.04311
$387$		0			0
$388$	260.901	−	260.901i	0.672426	−	0.672426i
$389$		−	270.881i		−	0.696353i	−0.937429	−	0.348176i	$-0.886801\pi$
$389$		−	270.881i		−	0.696353i	0.937429	−	0.348176i	$-0.113199\pi$
$390$		0			0
$391$	702.434			1.79651
$392$	10.7454	+	10.7454i	0.0274117	+	0.0274117i
$393$		0			0
$394$			358.340i			0.909492i
$395$	588.957	−	16.1616i	1.49103	−	0.0409153i
$396$		0			0
$397$	−62.2126	−	62.2126i	−0.156707	−	0.156707i	0.624399	−	0.781106i	$-0.285344\pi$
$397$	−62.2126	−	62.2126i	−0.156707	−	0.156707i	−0.781106	+	0.624399i	$0.785344\pi$
$398$	−222.817	+	222.817i	−0.559841	+	0.559841i
$399$		0			0
$400$	−312.586	+	17.1683i	−0.781464	+	0.0429206i
$401$	−520.801			−1.29876			−0.649378	−	0.760466i	$-0.724971\pi$
$401$	−520.801			−1.29876			−0.649378	+	0.760466i	$0.724971\pi$
$402$		0			0
$403$	11.9398	−	11.9398i	0.0296273	−	0.0296273i
$404$		−	607.547i		−	1.50383i
$405$		0			0
$406$	−409.354			−1.00826
$407$	−62.7463	−	62.7463i	−0.154168	−	0.154168i
$408$		0			0
$409$		−	575.516i		−	1.40713i	−0.710631	−	0.703564i	$-0.751591\pi$
$409$		−	575.516i		−	1.40713i	0.710631	−	0.703564i	$-0.248409\pi$
$410$	−614.928	+	649.629i	−1.49982	+	1.58446i
$411$		0			0
$412$	50.1791	+	50.1791i	0.121794	+	0.121794i
$413$	188.916	−	188.916i	0.457423	−	0.457423i
$414$		0			0
$415$	439.110	+	415.654i	1.05810	+	1.00158i
$416$	153.738			0.369562
$417$		0			0
$418$	51.8692	−	51.8692i	0.124089	−	0.124089i
$419$			113.474i			0.270822i	0.990790	+	0.135411i	$0.0432355\pi$
$419$			113.474i			0.270822i	−0.990790	+	0.135411i	$0.956765\pi$
$420$		0			0
$421$	737.737			1.75234			0.876172	−	0.481999i	$-0.160089\pi$
$421$	737.737			1.75234			0.876172	+	0.481999i	$0.160089\pi$
$422$	439.108	+	439.108i	1.04054	+	1.04054i
$423$		0			0
$424$		−	78.8196i		−	0.185895i
$425$	431.116	+	386.225i	1.01439	+	0.908764i
$426$		0			0
$427$	153.701	+	153.701i	0.359956	+	0.359956i
$428$	655.052	−	655.052i	1.53049	−	1.53049i
$429$		0			0
$430$	−5.03677	−	183.549i	−0.0117134	−	0.426858i
$431$	−626.096			−1.45266			−0.726329	−	0.687347i	$-0.758775\pi$
$431$	−626.096			−1.45266			−0.726329	+	0.687347i	$0.758775\pi$
$432$		0			0
$433$	99.3139	−	99.3139i	0.229362	−	0.229362i	−0.583064	−	0.812426i	$-0.698146\pi$
$433$	99.3139	−	99.3139i	0.229362	−	0.229362i	0.812426	+	0.583064i	$0.198146\pi$
$434$		−	39.2412i		−	0.0904176i
$435$		0			0
$436$	764.092			1.75250
$437$	197.094	+	197.094i	0.451015	+	0.451015i
$438$		0			0
$439$			249.762i			0.568933i	0.958686	+	0.284467i	$0.0918165\pi$
$439$			249.762i			0.568933i	−0.958686	+	0.284467i	$0.908183\pi$
$440$	21.2964	+	20.1588i	0.0484009	+	0.0458155i
$441$		0			0
$442$	−162.797	−	162.797i	−0.368318	−	0.368318i
$443$	213.838	−	213.838i	0.482704	−	0.482704i	−0.423290	−	0.905994i	$-0.639125\pi$
$443$	213.838	−	213.838i	0.482704	−	0.482704i	0.905994	+	0.423290i	$0.139125\pi$
$444$		0			0
$445$	−594.824	+	16.3226i	−1.33668	+	0.0366799i
$446$	578.050			1.29608
$447$		0			0
$448$	158.929	−	158.929i	0.354751	−	0.354751i
$449$		−	540.540i		−	1.20387i	−0.798544	−	0.601937i	$-0.794396\pi$
$449$		−	540.540i		−	1.20387i	0.798544	−	0.601937i	$-0.205604\pi$
$450$		0			0
$451$	−163.537			−0.362610
$452$	162.006	+	162.006i	0.358420	+	0.358420i
$453$		0			0
$454$		−	1197.04i		−	2.63666i
$455$	−1.22094	−	44.4932i	−0.00268338	−	0.0977873i
$456$		0			0
$457$	−236.212	−	236.212i	−0.516876	−	0.516876i	0.399749	−	0.916625i	$-0.369097\pi$
$457$	−236.212	−	236.212i	−0.516876	−	0.516876i	−0.916625	+	0.399749i	$0.869097\pi$
$458$	−440.656	+	440.656i	−0.962131	+	0.962131i
$459$		0			0
$460$	−493.729	+	521.591i	−1.07332	+	1.13389i
$461$	−156.987			−0.340536			−0.170268	−	0.985398i	$-0.554463\pi$
$461$	−156.987			−0.340536			−0.170268	+	0.985398i	$0.554463\pi$
$462$		0			0
$463$	−269.161	+	269.161i	−0.581342	+	0.581342i	−0.935272	−	0.353930i	$-0.884845\pi$
$463$	−269.161	+	269.161i	−0.581342	+	0.581342i	0.353930	+	0.935272i	$0.384845\pi$
$464$			655.560i			1.41284i
$465$		0			0
$466$	910.656			1.95420
$467$	−114.700	−	114.700i	−0.245610	−	0.245610i	0.573556	−	0.819166i	$-0.305564\pi$
$467$	−114.700	−	114.700i	−0.245610	−	0.245610i	−0.819166	+	0.573556i	$0.805564\pi$
$468$		0			0
$469$			243.808i			0.519848i
$470$	46.8430	−	1.28542i	0.0996660	−	0.00273494i
$471$		0			0
$472$	155.009	+	155.009i	0.328409	+	0.328409i
$473$	23.7372	−	23.7372i	0.0501844	−	0.0501844i
$474$		0			0
$475$	12.5958	+	229.335i	0.0265176	+	0.482810i
$476$	−290.021			−0.609288
$477$		0			0
$478$	−216.136	+	216.136i	−0.452168	+	0.452168i
$479$			158.331i			0.330546i	0.986248	+	0.165273i	$0.0528505\pi$
$479$			158.331i			0.330546i	−0.986248	+	0.165273i	$0.947149\pi$
$480$		0			0
$481$	−110.515			−0.229761
$482$	27.8667	+	27.8667i	0.0578148	+	0.0578148i
$483$		0			0
$484$		−	538.324i		−	1.11224i
$485$	−267.868	+	282.984i	−0.552305	+	0.583472i
$486$		0			0
$487$	220.865	+	220.865i	0.453521	+	0.453521i	0.896521	−	0.443000i	$-0.146086\pi$
$487$	220.865	+	220.865i	0.453521	+	0.453521i	−0.443000	+	0.896521i	$0.646086\pi$
$488$	−126.115	+	126.115i	−0.258432	+	0.258432i
$489$		0			0
$490$	−75.1219	−	71.1092i	−0.153310	−	0.145121i
$491$	−925.802			−1.88554			−0.942772	−	0.333439i	$-0.891791\pi$
$491$	−925.802			−1.88554			−0.942772	+	0.333439i	$0.891791\pi$
$492$		0			0
$493$	857.071	−	857.071i	1.73848	−	1.73848i
$494$		−	91.3572i		−	0.184934i
$495$		0			0
$496$	−62.8429			−0.126699
$497$	−42.8243	−	42.8243i	−0.0861656	−	0.0861656i
$498$		0			0
$499$		−	114.955i		−	0.230370i	−0.993344	−	0.115185i	$-0.963254\pi$
$499$		−	114.955i		−	0.230370i	0.993344	−	0.115185i	$-0.0367461\pi$
$500$	−589.815	+	48.6531i	−1.17963	+	0.0973061i
$501$		0			0
$502$	−678.837	−	678.837i	−1.35226	−	1.35226i
$503$	46.4397	−	46.4397i	0.0923254	−	0.0923254i	−0.659436	−	0.751761i	$-0.729205\pi$
$503$	46.4397	−	46.4397i	0.0923254	−	0.0923254i	0.751761	+	0.659436i	$0.229205\pi$
$504$		0			0
$505$	17.5998	+	641.370i	0.0348512	+	1.27004i
$506$	−242.239			−0.478732
$507$		0			0
$508$	63.3380	−	63.3380i	0.124681	−	0.124681i
$509$			185.083i			0.363621i	0.983334	+	0.181811i	$0.0581958\pi$
$509$			185.083i			0.363621i	−0.983334	+	0.181811i	$0.941804\pi$
$510$		0			0
$511$	20.1529			0.0394381
$512$	−481.475	−	481.475i	−0.940380	−	0.940380i
$513$		0			0
$514$			190.376i			0.370381i
$515$	−54.4262	−	51.5190i	−0.105682	−	0.100037i
$516$		0			0
$517$	6.05791	+	6.05791i	0.0117174	+	0.0117174i
$518$	−181.609	+	181.609i	−0.350597	+	0.350597i
$519$		0			0
$520$	36.5076	−	1.00180i	0.0702069	−	0.00192655i
$521$	275.217			0.528248			0.264124	−	0.964489i	$-0.414917\pi$
$521$	275.217			0.528248			0.264124	+	0.964489i	$0.414917\pi$
$522$		0			0
$523$	−424.281	+	424.281i	−0.811245	+	0.811245i	−0.984821	−	0.173576i	$-0.944468\pi$
$523$	−424.281	+	424.281i	−0.811245	+	0.811245i	0.173576	+	0.984821i	$0.444468\pi$
$524$		−	132.170i		−	0.252233i
$525$		0			0
$526$	−779.426			−1.48180
$527$	82.1600	+	82.1600i	0.155901	+	0.155901i
$528$		0			0
$529$		−	391.464i		−	0.740007i
$530$	14.7171	+	536.318i	0.0277681	+	1.01192i
$531$		0			0
$532$	−81.3760	−	81.3760i	−0.152962	−	0.152962i
$533$	−144.019	+	144.019i	−0.270205	+	0.270205i
$534$		0			0
$535$	−672.543	+	710.495i	−1.25709	+	1.32803i
$536$	−200.050			−0.373227
$537$		0			0
$538$	−1022.76	+	1022.76i	−1.90103	+	1.90103i
$539$		−	18.9111i		−	0.0350856i
$540$		0			0
$541$	−484.593			−0.895735			−0.447868	−	0.894100i	$-0.647816\pi$
$541$	−484.593			−0.895735			−0.447868	+	0.894100i	$0.647816\pi$
$542$	−73.9061	−	73.9061i	−0.136358	−	0.136358i
$543$		0			0
$544$			1057.90i			1.94467i
$545$	−806.629	+	22.1347i	−1.48005	+	0.0406142i
$546$		0			0
$547$	−367.275	−	367.275i	−0.671436	−	0.671436i	0.286611	−	0.958047i	$-0.407471\pi$
$547$	−367.275	−	367.275i	−0.671436	−	0.671436i	−0.958047	+	0.286611i	$0.907471\pi$
$548$	327.974	−	327.974i	0.598493	−	0.598493i
$549$		0			0
$550$	−148.673	−	133.192i	−0.270314	−	0.242167i
$551$	480.965			0.872895
$552$		0			0
$553$	220.450	−	220.450i	0.398644	−	0.398644i
$554$			370.793i			0.669302i
$555$		0			0
$556$	1107.37			1.99167
$557$	−532.387	−	532.387i	−0.955811	−	0.955811i	0.0432528	−	0.999064i	$-0.486228\pi$
$557$	−532.387	−	532.387i	−0.955811	−	0.955811i	−0.999064	+	0.0432528i	$0.986228\pi$
$558$		0			0
$559$		−	41.8084i		−	0.0747914i
$560$	−113.878	+	120.304i	−0.203353	+	0.214829i
$561$		0			0
$562$	−66.2936	−	66.2936i	−0.117960	−	0.117960i
$563$	724.535	−	724.535i	1.28692	−	1.28692i	0.350268	−	0.936649i	$-0.386090\pi$
$563$	724.535	−	724.535i	1.28692	−	1.28692i	0.936649	−	0.350268i	$-0.113910\pi$
$564$		0			0
$565$	−175.718	−	166.332i	−0.311005	−	0.294392i
$566$	465.867			0.823087
$567$		0			0
$568$	35.1382	−	35.1382i	0.0618630	−	0.0618630i
$569$			63.5327i			0.111657i	0.998440	+	0.0558284i	$0.0177800\pi$
$569$			63.5327i			0.111657i	−0.998440	+	0.0558284i	$0.982220\pi$
$570$		0			0
$571$	186.947			0.327403			0.163701	−	0.986510i	$-0.447657\pi$
$571$	186.947			0.327403			0.163701	+	0.986510i	$0.447657\pi$
$572$	30.4314	+	30.4314i	0.0532017	+	0.0532017i
$573$		0			0
$574$			473.332i			0.824620i
$575$	506.106	−	564.931i	0.880184	−	0.982488i
$576$		0			0
$577$	650.925	+	650.925i	1.12812	+	1.12812i	0.990483	+	0.137637i	$0.0439506\pi$
$577$	650.925	+	650.925i	1.12812	+	1.12812i	0.137637	+	0.990483i	$0.456049\pi$
$578$	516.283	−	516.283i	0.893224	−	0.893224i
$579$		0			0
$580$	33.9949	+	1238.84i	0.0586120	+	2.13593i
$581$	319.944			0.550678
$582$		0			0
$583$	−69.3587	+	69.3587i	−0.118969	+	0.118969i
$584$			16.5359i			0.0283148i
$585$		0			0
$586$	43.1939			0.0737098
$587$	451.044	+	451.044i	0.768389	+	0.768389i	0.977823	−	0.209434i	$-0.0671621\pi$
$587$	451.044	+	451.044i	0.768389	+	0.768389i	−0.209434	+	0.977823i	$0.567162\pi$
$588$		0			0
$589$			46.1060i			0.0782785i
$590$	−1083.68	−	1025.80i	−1.83675	−	1.73864i
$591$		0			0
$592$	290.838	+	290.838i	0.491281	+	0.491281i
$593$	−459.882	+	459.882i	−0.775518	+	0.775518i	−0.979065	−	0.203547i	$-0.934753\pi$
$593$	−459.882	+	459.882i	−0.775518	+	0.775518i	0.203547	+	0.979065i	$0.434753\pi$
$594$		0			0
$595$	306.167	−	8.40152i	0.514566	−	0.0141202i
$596$	604.100			1.01359
$597$		0			0
$598$	−213.327	+	213.327i	−0.356735	+	0.356735i
$599$		−	415.835i		−	0.694216i	−0.937825	−	0.347108i	$-0.887164\pi$
$599$		−	415.835i		−	0.694216i	0.937825	−	0.347108i	$-0.112836\pi$
$600$		0			0
$601$	−693.471			−1.15386			−0.576931	−	0.816793i	$-0.695750\pi$
$601$	−693.471			−1.15386			−0.576931	+	0.816793i	$0.695750\pi$
$602$	−68.7036	−	68.7036i	−0.114126	−	0.114126i
$603$		0			0
$604$			232.899i			0.385594i
$605$	15.5945	+	568.293i	0.0257761	+	0.939327i
$606$		0			0
$607$	247.205	+	247.205i	0.407257	+	0.407257i	0.880781	−	0.473524i	$-0.157018\pi$
$607$	247.205	+	247.205i	0.407257	+	0.407257i	−0.473524	+	0.880781i	$0.657018\pi$
$608$	−296.833	+	296.833i	−0.488211	+	0.488211i
$609$		0			0
$610$	834.585	−	881.681i	1.36817	−	1.44538i
$611$	10.6698			0.0174629
$612$		0			0
$613$	512.566	−	512.566i	0.836159	−	0.836159i	−0.152192	−	0.988351i	$-0.548633\pi$
$613$	512.566	−	512.566i	0.836159	−	0.836159i	0.988351	+	0.152192i	$0.0486331\pi$
$614$		−	1239.95i		−	2.01946i
$615$		0			0
$616$	15.5170			0.0251899
$617$	700.942	+	700.942i	1.13605	+	1.13605i	0.989152	+	0.146897i	$0.0469284\pi$
$617$	700.942	+	700.942i	1.13605	+	1.13605i	0.146897	+	0.989152i	$0.453072\pi$
$618$		0			0
$619$			354.521i			0.572732i	0.958120	+	0.286366i	$0.0924473\pi$
$619$			354.521i			0.572732i	−0.958120	+	0.286366i	$0.907553\pi$
$620$	−118.757	+	3.25880i	−0.191543	+	0.00525613i
$621$		0			0
$622$	−76.9884	−	76.9884i	−0.123776	−	0.123776i
$623$	−222.646	+	222.646i	−0.357378	+	0.357378i
$624$		0			0
$625$	621.241	−	68.4477i	0.993985	−	0.109516i
$626$	378.398			0.604470
$627$		0			0
$628$	−619.412	+	619.412i	−0.986325	+	0.986325i
$629$		−	760.476i		−	1.20902i
$630$		0			0
$631$	930.684			1.47494			0.737468	−	0.675383i	$-0.236021\pi$
$631$	930.684			1.47494			0.737468	+	0.675383i	$0.236021\pi$
$632$	180.884	+	180.884i	0.286209	+	0.286209i
$633$		0			0
$634$			10.0362i			0.0158299i
$635$	−65.0292	+	68.6989i	−0.102408	+	0.108187i
$636$		0			0
$637$	−16.6541	−	16.6541i	−0.0261446	−	0.0261446i
$638$	−295.566	+	295.566i	−0.463270	+	0.463270i
$639$		0			0
$640$	−248.000	−	234.753i	−0.387500	−	0.366801i
$641$	499.986			0.780009			0.390005	−	0.920813i	$-0.372473\pi$
$641$	499.986			0.780009			0.390005	+	0.920813i	$0.372473\pi$
$642$		0			0
$643$	−385.589	+	385.589i	−0.599672	+	0.599672i	−0.940225	−	0.340554i	$-0.889386\pi$
$643$	−385.589	+	385.589i	−0.599672	+	0.599672i	0.340554	+	0.940225i	$0.389386\pi$
$644$			380.041i			0.590126i
$645$		0			0
$646$	628.647			0.973137
$647$	84.6226	+	84.6226i	0.130792	+	0.130792i	0.769472	−	0.638680i	$-0.220519\pi$
$647$	84.6226	+	84.6226i	0.130792	+	0.130792i	−0.638680	+	0.769472i	$0.720519\pi$
$648$		0			0
$649$		−	272.806i		−	0.420348i
$650$	−248.224	+	13.6333i	−0.381884	+	0.0209743i
$651$		0			0
$652$	−168.467	−	168.467i	−0.258384	−	0.258384i
$653$	132.499	−	132.499i	0.202907	−	0.202907i	−0.598337	−	0.801244i	$-0.704172\pi$
$653$	132.499	−	132.499i	0.202907	−	0.202907i	0.801244	+	0.598337i	$0.204172\pi$
$654$		0			0
$655$	3.82880	+	139.528i	0.00584549	+	0.213020i
$656$	758.018			1.15552
$657$		0			0
$658$	17.5337	−	17.5337i	0.0266469	−	0.0266469i
$659$			921.339i			1.39809i	0.715080	+	0.699043i	$0.246390\pi$
$659$			921.339i			1.39809i	−0.715080	+	0.699043i	$0.753610\pi$
$660$		0			0
$661$	705.918			1.06795			0.533977	−	0.845499i	$-0.320697\pi$
$661$	705.918			1.06795			0.533977	+	0.845499i	$0.320697\pi$
$662$	601.907	+	601.907i	0.909224	+	0.909224i
$663$		0			0
$664$			262.520i			0.395362i
$665$	88.2636	+	83.5489i	0.132727	+	0.125637i
$666$		0			0
$667$	−1123.10	−	1123.10i	−1.68381	−	1.68381i
$668$	131.374	−	131.374i	0.196667	−	0.196667i
$669$		0			0
$670$	1361.21	−	37.3531i	2.03166	−	0.0557509i
$671$	221.954			0.330781
$672$		0			0
$673$	480.376	−	480.376i	0.713783	−	0.713783i	−0.253542	−	0.967324i	$-0.581595\pi$
$673$	480.376	−	480.376i	0.713783	−	0.713783i	0.967324	+	0.253542i	$0.0815955\pi$
$674$			1480.19i			2.19613i
$675$		0			0
$676$	−746.539			−1.10435
$677$	−146.784	−	146.784i	−0.216815	−	0.216815i	0.590340	−	0.807155i	$-0.298994\pi$
$677$	−146.784	−	146.784i	−0.216815	−	0.216815i	−0.807155	+	0.590340i	$0.798994\pi$
$678$		0			0
$679$			206.187i			0.303663i
$680$	6.89361	+	251.216i	0.0101377	+	0.369435i
$681$		0			0
$682$	−28.3334	−	28.3334i	−0.0415445	−	0.0415445i
$683$	88.7069	−	88.7069i	0.129878	−	0.129878i	−0.639179	−	0.769058i	$-0.720726\pi$
$683$	88.7069	−	88.7069i	0.129878	−	0.129878i	0.769058	+	0.639179i	$0.220726\pi$
$684$		0			0
$685$	−336.731	+	355.733i	−0.491579	+	0.519319i
$686$	−54.7353			−0.0797890
$687$		0			0
$688$	−110.025	+	110.025i	−0.159921	+	0.159921i
$689$			122.161i			0.177303i
$690$		0			0
$691$	−664.952			−0.962304			−0.481152	−	0.876637i	$-0.659781\pi$
$691$	−664.952			−0.962304			−0.481152	+	0.876637i	$0.659781\pi$
$692$	903.280	+	903.280i	1.30532	+	1.30532i
$693$		0			0
$694$		−	1839.17i		−	2.65009i
$695$	−1169.02	+	32.0790i	−1.68204	+	0.0461568i
$696$		0			0
$697$	−991.023	−	991.023i	−1.42184	−	1.42184i
$698$	−897.731	+	897.731i	−1.28615	+	1.28615i
$699$		0			0
$700$	−208.961	+	233.249i	−0.298516	+	0.333212i
$701$	137.923			0.196751			0.0983757	−	0.995149i	$-0.468635\pi$
$701$	137.923			0.196751			0.0983757	+	0.995149i	$0.468635\pi$
$702$		0			0
$703$	213.380	−	213.380i	0.303527	−	0.303527i
$704$		−	229.503i		−	0.325998i
$705$		0			0
$706$	1005.43			1.42412
$707$	240.069	+	240.069i	0.339560	+	0.339560i
$708$		0			0
$709$			371.525i			0.524013i	0.965066	+	0.262006i	$0.0843842\pi$
$709$			371.525i			0.524013i	−0.965066	+	0.262006i	$0.915616\pi$
$710$	−232.533	+	245.655i	−0.327511	+	0.345992i
$711$		0			0
$712$	−182.686	−	182.686i	−0.256581	−	0.256581i
$713$	107.662	−	107.662i	0.150998	−	0.150998i
$714$		0			0
$715$	−33.0070	−	31.2439i	−0.0461637	−	0.0436978i
$716$	−854.010			−1.19275
$717$		0			0
$718$	111.806	−	111.806i	0.155718	−	0.155718i
$719$		−	85.5943i		−	0.119046i	−0.998227	−	0.0595232i	$-0.981042\pi$
$719$		−	85.5943i		−	0.119046i	0.998227	−	0.0595232i	$-0.0189580\pi$
$720$		0			0
$721$	−39.6560			−0.0550014
$722$	−578.029	−	578.029i	−0.800594	−	0.800594i
$723$		0			0
$724$		−	98.5073i		−	0.136060i
$725$	−71.7749	−	1306.82i	−0.0989999	−	1.80251i
$726$		0			0
$727$	589.673	+	589.673i	0.811104	+	0.811104i	0.984799	−	0.173695i	$-0.0555707\pi$
$727$	589.673	+	589.673i	0.811104	+	0.811104i	−0.173695	+	0.984799i	$0.555571\pi$
$728$	13.6650	−	13.6650i	0.0187706	−	0.0187706i
$729$		0			0
$730$	−3.08756	−	112.516i	−0.00422953	−	0.154132i
$731$	287.692			0.393559
$732$		0			0
$733$	1019.17	−	1019.17i	1.39040	−	1.39040i	0.565992	−	0.824411i	$-0.308493\pi$
$733$	1019.17	−	1019.17i	1.39040	−	1.39040i	0.824411	−	0.565992i	$-0.191507\pi$
$734$		−	5.27347i		−	0.00718457i
$735$		0			0
$736$	1386.26			1.88351
$737$	176.037	+	176.037i	0.238857	+	0.238857i
$738$		0			0
$739$			54.4746i			0.0737139i	0.999321	+	0.0368570i	$0.0117346\pi$
$739$			54.4746i			0.0737139i	−0.999321	+	0.0368570i	$0.988265\pi$
$740$	564.690	+	534.526i	0.763094	+	0.722333i
$741$		0			0
$742$	200.748	+	200.748i	0.270549	+	0.270549i
$743$	−247.895	+	247.895i	−0.333641	+	0.333641i	−0.853968	−	0.520326i	$-0.825810\pi$
$743$	−247.895	+	247.895i	−0.333641	+	0.333641i	0.520326	+	0.853968i	$0.325810\pi$
$744$		0			0
$745$	−637.730	+	17.5000i	−0.856014	+	0.0234899i
$746$	203.316			0.272542
$747$		0			0
$748$	−209.404	+	209.404i	−0.279952	+	0.279952i
$749$			517.680i			0.691162i
$750$		0			0
$751$	−1361.29			−1.81263			−0.906316	−	0.422600i	$-0.861117\pi$
$751$	−1361.29			−1.81263			−0.906316	+	0.422600i	$0.861117\pi$
$752$	−28.0793	−	28.0793i	−0.0373395	−	0.0373395i
$753$		0			0
$754$			520.580i			0.690425i
$755$	−6.74677	−	245.865i	−0.00893612	−	0.325648i
$756$		0			0
$757$	178.475	+	178.475i	0.235767	+	0.235767i	0.815095	−	0.579328i	$-0.196685\pi$
$757$	178.475	+	178.475i	0.235767	+	0.235767i	−0.579328	+	0.815095i	$0.696685\pi$
$758$	1007.34	−	1007.34i	1.32894	−	1.32894i
$759$		0			0
$760$	−68.5536	+	72.4221i	−0.0902021	+	0.0952922i
$761$	−815.185			−1.07120			−0.535601	−	0.844471i	$-0.679915\pi$
$761$	−815.185			−1.07120			−0.535601	+	0.844471i	$0.679915\pi$
$762$		0			0
$763$	−301.927	+	301.927i	−0.395710	+	0.395710i
$764$		−	1049.19i		−	1.37328i
$765$		0			0
$766$	−314.707			−0.410844
$767$	−240.246	−	240.246i	−0.313229	−	0.313229i
$768$		0			0
$769$			327.202i			0.425490i	0.977108	+	0.212745i	$0.0682403\pi$
$769$			327.202i			0.425490i	−0.977108	+	0.212745i	$0.931760\pi$
$770$	−105.583	+	2.89731i	−0.137121	+	0.00376274i
$771$		0			0
$772$	−893.352	−	893.352i	−1.15719	−	1.15719i
$773$	−224.127	+	224.127i	−0.289944	+	0.289944i	−0.837058	−	0.547114i	$-0.815726\pi$
$773$	−224.127	+	224.127i	−0.289944	+	0.289944i	0.547114	+	0.837058i	$0.315726\pi$
$774$		0			0
$775$	125.274	−	6.88044i	0.161643	−	0.00887799i
$776$	−169.181			−0.218017
$777$		0			0
$778$	−566.088	+	566.088i	−0.727620	+	0.727620i
$779$		−	556.136i		−	0.713910i
$780$		0			0
$781$	−61.8409			−0.0791817
$782$	−1467.95	−	1467.95i	−1.87717	−	1.87717i
$783$		0			0
$784$			87.6559i			0.111806i
$785$	635.951	−	671.838i	0.810129	−	0.855845i
$786$		0			0
$787$	−309.705	−	309.705i	−0.393526	−	0.393526i	0.482416	−	0.875942i	$-0.339759\pi$
$787$	−309.705	−	309.705i	−0.393526	−	0.393526i	−0.875942	+	0.482416i	$0.839759\pi$
$788$	405.918	−	405.918i	0.515124	−	0.515124i
$789$		0			0
$790$	−1264.58	−	1197.03i	−1.60073	−	1.51523i
$791$	−128.031			−0.161860
$792$		0			0
$793$	195.464	−	195.464i	0.246486	−	0.246486i
$794$			260.024i			0.327486i
$795$		0			0
$796$	504.801			0.634173
$797$	138.230	+	138.230i	0.173438	+	0.173438i	0.788488	−	0.615050i	$-0.210864\pi$
$797$	138.230	+	138.230i	0.173438	+	0.173438i	−0.615050	+	0.788488i	$0.710864\pi$
$798$		0			0
$799$			73.4210i			0.0918911i
$800$	850.813	+	762.220i	1.06352	+	0.952774i
$801$		0			0
$802$	1088.37	+	1088.37i	1.35707	+	1.35707i
$803$	14.5510	−	14.5510i	0.0181208	−	0.0181208i
$804$		0			0
$805$	−11.0093	−	401.198i	−0.0136761	−	0.498383i
$806$	−49.9036			−0.0619151
$807$		0			0
$808$	−196.981	+	196.981i	−0.243789	+	0.243789i
$809$		−	814.512i		−	1.00681i	−0.864050	−	0.503407i	$-0.832080\pi$
$809$		−	814.512i		−	1.00681i	0.864050	−	0.503407i	$-0.167920\pi$
$810$		0			0
$811$	255.277			0.314769			0.157384	−	0.987537i	$-0.449694\pi$
$811$	255.277			0.314769			0.157384	+	0.987537i	$0.449694\pi$
$812$	463.705	+	463.705i	0.571065	+	0.571065i
$813$		0			0
$814$			262.255i			0.322180i
$815$	182.725	+	172.965i	0.224203	+	0.212227i
$816$		0			0
$817$	80.7225	+	80.7225i	0.0988036	+	0.0988036i
$818$	−1202.71	+	1202.71i	−1.47031	+	1.47031i
$819$		0			0
$820$	1432.46	−	39.3080i	1.74690	−	0.0479366i
$821$	340.619			0.414883			0.207441	−	0.978247i	$-0.433486\pi$
$821$	340.619			0.414883			0.207441	+	0.978247i	$0.433486\pi$
$822$		0			0
$823$	−109.226	+	109.226i	−0.132717	+	0.132717i	−0.770345	−	0.637628i	$-0.779916\pi$
$823$	−109.226	+	109.226i	−0.132717	+	0.132717i	0.637628	+	0.770345i	$0.279916\pi$
$824$		−	32.5385i		−	0.0394885i
$825$		0			0
$826$	−789.592			−0.955922
$827$	543.650	+	543.650i	0.657376	+	0.657376i	0.954758	−	0.297383i	$-0.0961137\pi$
$827$	543.650	+	543.650i	0.657376	+	0.657376i	−0.297383	+	0.954758i	$0.596114\pi$
$828$		0			0
$829$		−	419.953i		−	0.506578i	−0.967391	−	0.253289i	$-0.918488\pi$
$829$		−	419.953i		−	0.506578i	0.967391	−	0.253289i	$-0.0815123\pi$
$830$	−49.0175	−	1786.29i	−0.0590573	−	2.15215i
$831$		0			0
$832$	−202.112	−	202.112i	−0.242923	−	0.242923i
$833$	114.600	−	114.600i	0.137575	−	0.137575i
$834$		0			0
$835$	−134.882	+	142.493i	−0.161535	+	0.170650i
$836$	−117.512			−0.140565
$837$		0			0
$838$	237.139	−	237.139i	0.282982	−	0.282982i
$839$			762.801i			0.909178i	0.890701	+	0.454589i	$0.150214\pi$
$839$			762.801i			0.909178i	−0.890701	+	0.454589i	$0.849786\pi$
$840$		0			0
$841$	−1899.68			−2.25884
$842$	−1541.72	−	1541.72i	−1.83103	−	1.83103i
$843$		0			0
$844$		−	994.820i		−	1.17870i
$845$	788.099	−	21.6262i	0.932662	−	0.0255932i
$846$		0			0
$847$	212.716	+	212.716i	0.251140	+	0.251140i
$848$	321.487	−	321.487i	0.379113	−	0.379113i
$849$		0			0
$850$	−93.8135	−	1708.08i	−0.110369	−	2.00951i
$851$	−996.522			−1.17100
$852$		0			0
$853$	−594.088	+	594.088i	−0.696469	+	0.696469i	−0.963647	−	0.267178i	$-0.913909\pi$
$853$	−594.088	+	594.088i	−0.696469	+	0.696469i	0.267178	+	0.963647i	$0.413909\pi$
$854$		−	642.410i		−	0.752236i
$855$		0			0
$856$	−424.767			−0.496223
$857$	−346.747	−	346.747i	−0.404605	−	0.404605i	0.475247	−	0.879852i	$-0.342359\pi$
$857$	−346.747	−	346.747i	−0.404605	−	0.404605i	−0.879852	+	0.475247i	$0.842359\pi$
$858$		0			0
$859$		−	1031.74i		−	1.20110i	−0.799588	−	0.600549i	$-0.794949\pi$
$859$		−	1031.74i		−	1.20110i	0.799588	−	0.600549i	$-0.205051\pi$
$860$	−202.214	+	213.625i	−0.235132	+	0.248401i
$861$		0			0
$862$	1308.42	+	1308.42i	1.51788	+	1.51788i
$863$	695.429	−	695.429i	0.805828	−	0.805828i	−0.178172	−	0.983999i	$-0.557018\pi$
$863$	695.429	−	695.429i	0.805828	−	0.805828i	0.983999	+	0.178172i	$0.0570182\pi$
$864$		0			0
$865$	−979.732	−	927.399i	−1.13264	−	1.07214i
$866$	−415.093			−0.479322
$867$		0			0
$868$	−44.4514	+	44.4514i	−0.0512113	+	0.0512113i
$869$		−	318.344i		−	0.366334i
$870$		0			0
$871$	310.055			0.355975
$872$	−247.737	−	247.737i	−0.284102	−	0.284102i
$873$		0			0
$874$		−	823.774i		−	0.942533i
$875$	213.837	−	252.287i	0.244385	−	0.288328i
$876$		0			0
$877$	1168.49	+	1168.49i	1.33237	+	1.33237i	0.903247	+	0.429121i	$0.141177\pi$
$877$	1168.49	+	1168.49i	1.33237	+	1.33237i	0.429121	+	0.903247i	$0.358823\pi$
$878$	521.953	−	521.953i	0.594479	−	0.594479i
$879$		0			0
$880$	4.63991	+	169.087i	0.00527262	+	0.192144i
$881$	303.523			0.344522			0.172261	−	0.985051i	$-0.444893\pi$
$881$	303.523			0.344522			0.172261	+	0.985051i	$0.444893\pi$
$882$		0			0
$883$	720.863	−	720.863i	0.816379	−	0.816379i	−0.169202	−	0.985581i	$-0.554119\pi$
$883$	720.863	−	720.863i	0.816379	−	0.816379i	0.985581	+	0.169202i	$0.0541190\pi$
$884$			368.824i			0.417221i
$885$		0			0
$886$	−893.757			−1.00876
$887$	−975.650	−	975.650i	−1.09994	−	1.09994i	−0.994416	−	0.105527i	$-0.966347\pi$
$887$	−975.650	−	975.650i	−1.09994	−	1.09994i	−0.105527	−	0.994416i	$-0.533653\pi$
$888$		0			0
$889$			50.0553i			0.0563052i
$890$	1277.17	+	1208.95i	1.43503	+	1.35837i
$891$		0			0
$892$	−654.799	−	654.799i	−0.734080	−	0.734080i
$893$	−20.6010	+	20.6010i	−0.0230694	+	0.0230694i
$894$		0			0
$895$	901.554	−	24.7395i	1.00732	−	0.0276419i
$896$	−180.697			−0.201671
$897$		0			0
$898$	−1129.62	+	1129.62i	−1.25793	+	1.25793i
$899$		−	262.726i		−	0.292242i
$900$		0			0
$901$	−840.617			−0.932983
$902$	341.760	+	341.760i	0.378892	+	0.378892i
$903$		0			0
$904$		−	105.052i		−	0.116208i
$905$	2.85362	+	103.991i	0.00315318	+	0.114907i
$906$		0			0
$907$	−265.891	−	265.891i	−0.293155	−	0.293155i	0.545171	−	0.838325i	$-0.316465\pi$
$907$	−265.891	−	265.891i	−0.293155	−	0.293155i	−0.838325	+	0.545171i	$0.816465\pi$
$908$	−1355.98	+	1355.98i	−1.49337	+	1.49337i
$909$		0			0
$910$	−90.4305	+	95.5335i	−0.0993742	+	0.104982i
$911$	−916.932			−1.00651			−0.503256	−	0.864138i	$-0.667865\pi$
$911$	−916.932			−1.00651			−0.503256	+	0.864138i	$0.667865\pi$
$912$		0			0
$913$	231.009	−	231.009i	0.253022	−	0.253022i
$914$			987.274i			1.08017i
$915$		0			0
$916$	998.327			1.08988
$917$	52.2264	+	52.2264i	0.0569535	+	0.0569535i
$918$		0			0
$919$		−	421.767i		−	0.458941i	−0.973316	−	0.229470i	$-0.926301\pi$
$919$		−	421.767i		−	0.458941i	0.973316	−	0.229470i	$-0.0736994\pi$
$920$	329.191	−	9.03334i	0.357816	−	0.00981884i
$921$		0			0
$922$	328.072	+	328.072i	0.355827	+	0.355827i
$923$	−54.4602	+	54.4602i	−0.0590035	+	0.0590035i
$924$		0			0
$925$	−611.611	−	547.925i	−0.661201	−	0.592352i
$926$	1124.99			1.21489
$927$		0			0
$928$	1691.44	−	1691.44i	1.82267	−	1.82267i
$929$		−	416.476i		−	0.448305i	−0.974554	−	0.224153i	$-0.928039\pi$
$929$		−	416.476i		−	0.448305i	0.974554	−	0.224153i	$-0.0719614\pi$
$930$		0			0
$931$	64.3106			0.0690769
$932$	−1031.57	−	1031.57i	−1.10683	−	1.10683i
$933$		0			0
$934$			479.401i			0.513277i
$935$	214.996	−	227.128i	0.229942	−	0.242918i
$936$		0			0
$937$	877.123	+	877.123i	0.936097	+	0.936097i	0.998077	−	0.0619806i	$-0.0197417\pi$
$937$	877.123	+	877.123i	0.936097	+	0.936097i	−0.0619806	+	0.998077i	$0.519742\pi$
$938$	509.511	−	509.511i	0.543189	−	0.543189i
$939$		0			0
$940$	−54.5186	−	51.6064i	−0.0579985	−	0.0549005i
$941$	−1322.22			−1.40513			−0.702563	−	0.711621i	$-0.747961\pi$
$941$	−1322.22			−1.40513			−0.702563	+	0.711621i	$0.747961\pi$
$942$		0			0
$943$	−1298.63	+	1298.63i	−1.37713	+	1.37713i
$944$			1264.49i			1.33951i
$945$		0			0
$946$	−99.2122			−0.104876
$947$	445.898	+	445.898i	0.470853	+	0.470853i	0.902191	−	0.431338i	$-0.141958\pi$
$947$	445.898	+	445.898i	0.470853	+	0.470853i	−0.431338	+	0.902191i	$0.641958\pi$
$948$		0			0
$949$		−	25.6287i		−	0.0270060i
$950$	452.942	−	505.588i	0.476781	−	0.532197i
$951$		0			0
$952$	94.0317	+	94.0317i	0.0987728	+	0.0987728i
$953$	−568.485	+	568.485i	−0.596521	+	0.596521i	−0.939385	−	0.342864i	$-0.888603\pi$
$953$	−568.485	+	568.485i	−0.596521	+	0.596521i	0.342864	+	0.939385i	$0.388603\pi$
$954$		0			0
$955$	30.3936	+	1107.60i	0.0318257	+	1.15979i
$956$	489.667			0.512204
$957$		0			0
$958$	330.881	−	330.881i	0.345388	−	0.345388i
$959$			259.194i			0.270275i
$960$		0			0
$961$	−935.815			−0.973793
$962$	230.955	+	230.955i	0.240078	+	0.240078i
$963$		0			0
$964$		−	63.1334i		−	0.0654911i
$965$	968.965	+	917.206i	1.00411	+	0.950473i
$966$		0			0
$967$	−721.223	−	721.223i	−0.745836	−	0.745836i	0.227858	−	0.973694i	$-0.426828\pi$
$967$	−721.223	−	721.223i	−0.745836	−	0.745836i	−0.973694	+	0.227858i	$0.926828\pi$
$968$	−174.538	+	174.538i	−0.180307	+	0.180307i
$969$		0			0
$970$	1151.17	−	31.5893i	1.18677	−	0.0325663i
$971$	−670.576			−0.690604			−0.345302	−	0.938492i	$-0.612223\pi$
$971$	−670.576			−0.690604			−0.345302	+	0.938492i	$0.612223\pi$
$972$		0			0
$973$	−437.570	+	437.570i	−0.449713	+	0.449713i
$974$		−	923.127i		−	0.947769i
$975$		0			0
$976$	−1028.79			−1.05409
$977$	787.654	+	787.654i	0.806196	+	0.806196i	0.984056	−	0.177860i	$-0.0569173\pi$
$977$	787.654	+	787.654i	0.806196	+	0.806196i	−0.177860	+	0.984056i	$0.556917\pi$
$978$		0			0
$979$			321.515i			0.328412i
$980$	4.54551	+	165.647i	0.00463828	+	0.169027i
$981$		0			0
$982$	1934.74	+	1934.74i	1.97021	+	1.97021i
$983$	585.387	−	585.387i	0.595510	−	0.595510i	−0.343604	−	0.939115i	$-0.611648\pi$
$983$	585.387	−	585.387i	0.595510	−	0.595510i	0.939115	+	0.343604i	$0.111648\pi$
$984$		0			0
$985$	−416.756	+	440.274i	−0.423103	+	0.446979i
$986$	−3582.22			−3.63308
$987$		0			0
$988$	−103.487	+	103.487i	−0.104744	+	0.104744i
$989$		−	376.989i		−	0.381182i
$990$		0			0
$991$	−1406.48			−1.41925			−0.709627	−	0.704577i	$-0.751137\pi$
$991$	−1406.48			−1.41925			−0.709627	+	0.704577i	$0.751137\pi$
$992$	162.144	+	162.144i	0.163451	+	0.163451i
$993$		0			0
$994$			178.989i			0.180069i
$995$	−532.904	+	14.6234i	−0.535582	+	0.0146969i
$996$		0			0
$997$	718.536	+	718.536i	0.720698	+	0.720698i	0.968747	−	0.248049i	$-0.0797894\pi$
$997$	718.536	+	718.536i	0.720698	+	0.720698i	−0.248049	+	0.968747i	$0.579789\pi$
$998$	−240.232	+	240.232i	−0.240714	+	0.240714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.127.4		24
3.2	odd	2		105.3.l.a.22.9	✓	24
5.3	odd	4	inner	315.3.o.b.253.4		24
15.2	even	4		525.3.l.e.43.4		24
15.8	even	4		105.3.l.a.43.9	yes	24
15.14	odd	2		525.3.l.e.232.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.9	✓	24	3.2	odd	2
105.3.l.a.43.9	yes	24	15.8	even	4
315.3.o.b.127.4		24	1.1	even	1	trivial
315.3.o.b.253.4		24	5.3	odd	4	inner
525.3.l.e.43.4		24	15.2	even	4
525.3.l.e.232.4		24	15.14	odd	2

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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08980 - 2.08980i) q^{2} +4.73454i q^{4} +(-0.137153 - 4.99812i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} +O(q^{10})\)	\(q+(-2.08980 - 2.08980i) q^{2} +4.73454i q^{4} +(-0.137153 - 4.99812i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(1.53505 - 1.53505i) q^{8} +(-10.1585 + 10.7317i) q^{10} -2.70159 q^{11} +(-2.37916 + 2.37916i) q^{13} +7.81932i q^{14} +12.5223 q^{16} +(-16.3715 - 16.3715i) q^{17} -9.18722i q^{19} +(23.6638 - 0.649359i) q^{20} +(5.64579 + 5.64579i) q^{22} +(-21.4530 + 21.4530i) q^{23} +(-24.9624 + 1.37102i) q^{25} +9.94394 q^{26} +(8.85752 - 8.85752i) q^{28} +52.3515i q^{29} -5.01849 q^{31} +(-32.3093 - 32.3093i) q^{32} +68.4262i q^{34} +(-9.09403 + 9.60721i) q^{35} +(23.2257 + 23.2257i) q^{37} +(-19.1995 + 19.1995i) q^{38} +(-7.88291 - 7.46184i) q^{40} +60.5336 q^{41} +(-8.78639 + 8.78639i) q^{43} -12.7908i q^{44} +89.6651 q^{46} +(-2.24235 - 2.24235i) q^{47} +7.00000i q^{49} +(55.0316 + 49.3013i) q^{50} +(-11.2642 - 11.2642i) q^{52} +(25.6733 - 25.6733i) q^{53} +(0.370533 + 13.5029i) q^{55} -5.74364 q^{56} +(109.404 - 109.404i) q^{58} +100.980i q^{59} -82.1567 q^{61} +(10.4877 + 10.4877i) q^{62} +84.9509i q^{64} +(12.2176 + 11.5650i) q^{65} +(-65.1606 - 65.1606i) q^{67} +(77.5114 - 77.5114i) q^{68} +(39.0819 - 1.07245i) q^{70} +22.8905 q^{71} +(-5.38609 + 5.38609i) q^{73} -97.0741i q^{74} +43.4973 q^{76} +(5.05422 + 5.05422i) q^{77} +117.836i q^{79} +(-1.71747 - 62.5878i) q^{80} +(-126.503 - 126.503i) q^{82} +(-85.5086 + 85.5086i) q^{83} +(-79.5811 + 84.0719i) q^{85} +36.7236 q^{86} +(-4.14709 + 4.14709i) q^{88} -119.010i q^{89} +8.90199 q^{91} +(-101.570 - 101.570i) q^{92} +9.37213i q^{94} +(-45.9188 + 1.26006i) q^{95} +(-55.1059 - 55.1059i) q^{97} +(14.6286 - 14.6286i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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Database

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