LMFDB - Embedded newform 315.3.ca.b.37.13

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			37.13
Character	$\chi$	$=$	315.37
Dual form			315.3.ca.b.298.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +O(q^{10})$	\(q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +(-4.34532 + 11.5293i) q^{10} +(-4.95365 - 8.57997i) q^{11} +(-14.1612 + 14.1612i) q^{13} +(-6.57942 + 15.9453i) q^{14} +(-9.99739 + 17.3160i) q^{16} +(4.22139 - 15.7544i) q^{17} +(23.3583 + 13.4859i) q^{19} +(-1.02028 + 10.3110i) q^{20} +(-17.2630 - 17.2630i) q^{22} +(-1.79608 - 6.70305i) q^{23} +(-8.01443 - 23.6806i) q^{25} +(-24.6752 + 42.7387i) q^{26} +(-1.87388 + 14.3844i) q^{28} +18.5702i q^{29} +(19.6183 + 33.9798i) q^{31} +(-7.83442 + 29.2385i) q^{32} -40.1915i q^{34} +(-10.1902 - 33.4837i) q^{35} +(42.8463 - 11.4806i) q^{37} +(64.1994 + 17.2022i) q^{38} +(-3.85835 - 23.4360i) q^{40} +55.1266 q^{41} +(-36.0471 + 36.0471i) q^{43} +(-17.7800 - 10.2653i) q^{44} +(-8.55017 - 14.8093i) q^{46} +(-24.5013 + 6.56509i) q^{47} +(-12.8106 - 47.2958i) q^{49} +(-34.1792 - 51.2538i) q^{50} +(-10.7413 + 40.0872i) q^{52} +(-15.4837 - 4.14884i) q^{53} +(49.2957 + 4.87786i) q^{55} +(-4.38501 - 32.9617i) q^{56} +(11.8437 + 44.2013i) q^{58} +(36.0497 - 20.8133i) q^{59} +(-51.6108 + 89.3925i) q^{61} +(68.3677 + 68.3677i) q^{62} -5.38813i q^{64} +(-16.2665 - 98.8047i) q^{65} +(1.98123 - 7.39406i) q^{67} +(-8.74787 - 32.6475i) q^{68} +(-45.6103 - 73.2000i) q^{70} -58.5591 q^{71} +(-19.6506 - 5.26536i) q^{73} +(94.6621 - 54.6532i) q^{74} +55.8931 q^{76} +(68.7699 + 8.95880i) q^{77} +(-47.2373 - 27.2725i) q^{79} +(-41.2185 - 91.0814i) q^{80} +(131.214 - 35.1587i) q^{82} +(-40.8378 + 40.8378i) q^{83} +(51.7067 + 63.0633i) q^{85} +(-62.8103 + 108.791i) q^{86} +(45.4590 + 12.1807i) q^{88} +(49.6991 + 28.6938i) q^{89} +(-18.4869 - 138.964i) q^{91} +(-10.1686 - 10.1686i) q^{92} +(-54.1316 + 31.2529i) q^{94} +(-122.864 + 55.6015i) q^{95} +(37.4558 + 37.4558i) q^{97} +(-60.6565 - 104.405i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.38023	−	0.637781i	1.19012	−	0.318891i	0.391184	−	0.920312i	$-0.372065\pi$
$2$	2.38023	−	0.637781i	1.19012	−	0.318891i	0.798932	+	0.601422i	$0.205399\pi$
$3$		0			0
$3$		0			0
$4$	1.79464	−	1.03614i	0.448660	−	0.259034i
$5$	−2.91424	+	4.06291i	−0.582848	+	0.812581i
$5$	−2.91424	+	4.06291i	−0.582848	+	0.812581i
$6$		0			0
$7$	−4.25379	+	5.55925i	−0.607684	+	0.794179i
$7$	−4.25379	+	5.55925i	−0.607684	+	0.794179i
$8$	−3.35897	+	3.35897i	−0.419871	+	0.419871i
$9$		0			0
$10$	−4.34532	+	11.5293i	−0.434532	+	1.15293i
$11$	−4.95365	−	8.57997i	−0.450331	−	0.779997i	0.548075	−	0.836429i	$-0.315361\pi$
$11$	−4.95365	−	8.57997i	−0.450331	−	0.779997i	−0.998406	+	0.0564323i	$0.982027\pi$
$12$		0			0
$13$	−14.1612	+	14.1612i	−1.08932	+	1.08932i	−0.0937246	+	0.995598i	$0.529877\pi$
$13$	−14.1612	+	14.1612i	−1.08932	+	1.08932i	−0.995598	+	0.0937246i	$0.970123\pi$
$14$	−6.57942	+	15.9453i	−0.469959	+	1.13895i
$15$		0			0
$16$	−9.99739	+	17.3160i	−0.624837	+	1.08225i
$17$	4.22139	−	15.7544i	0.248317	−	0.926731i	−0.723370	−	0.690460i	$-0.757408\pi$
$17$	4.22139	−	15.7544i	0.248317	−	0.926731i	0.971687	−	0.236271i	$-0.0759253\pi$
$18$		0			0
$19$	23.3583	+	13.4859i	1.22939	+	0.709787i	0.966902	−	0.255150i	$-0.0821247\pi$
$19$	23.3583	+	13.4859i	1.22939	+	0.709787i	0.262485	+	0.964936i	$0.415458\pi$
$20$	−1.02028	+	10.3110i	−0.0510142	+	0.515550i
$21$		0			0
$22$	−17.2630	−	17.2630i	−0.784680	−	0.784680i
$23$	−1.79608	−	6.70305i	−0.0780903	−	0.291437i	0.915826	−	0.401575i	$-0.131537\pi$
$23$	−1.79608	−	6.70305i	−0.0780903	−	0.291437i	−0.993916	+	0.110138i	$0.964871\pi$
$24$		0			0
$25$	−8.01443	−	23.6806i	−0.320577	−	0.947222i
$26$	−24.6752	+	42.7387i	−0.949046	+	1.64380i
$27$		0			0
$28$	−1.87388	+	14.3844i	−0.0669243	+	0.513727i
$29$			18.5702i			0.640350i	0.947358	+	0.320175i	$0.103742\pi$
$29$			18.5702i			0.640350i	−0.947358	+	0.320175i	$0.896258\pi$
$30$		0			0
$31$	19.6183	+	33.9798i	0.632847	+	1.09612i	0.986967	+	0.160923i	$0.0514470\pi$
$31$	19.6183	+	33.9798i	0.632847	+	1.09612i	−0.354120	+	0.935200i	$0.615220\pi$
$32$	−7.83442	+	29.2385i	−0.244826	+	0.913702i
$33$		0			0
$34$		−	40.1915i		−	1.18210i
$35$	−10.1902	−	33.4837i	−0.291148	−	0.956678i
$36$		0			0
$37$	42.8463	−	11.4806i	1.15801	−	0.310288i	0.371839	−	0.928297i	$-0.378727\pi$
$37$	42.8463	−	11.4806i	1.15801	−	0.310288i	0.786170	+	0.618010i	$0.212061\pi$
$38$	64.1994	+	17.2022i	1.68946	+	0.452689i
$39$		0			0
$40$	−3.85835	−	23.4360i	−0.0964587	−	0.585901i
$41$	55.1266			1.34455			0.672275	−	0.740301i	$-0.265317\pi$
$41$	55.1266			1.34455			0.672275	+	0.740301i	$0.265317\pi$
$42$		0			0
$43$	−36.0471	+	36.0471i	−0.838304	+	0.838304i	−0.988636	−	0.150331i	$-0.951966\pi$
$43$	−36.0471	+	36.0471i	−0.838304	+	0.838304i	0.150331	+	0.988636i	$0.451966\pi$
$44$	−17.7800	−	10.2653i	−0.404091	−	0.233302i
$45$		0			0
$46$	−8.55017	−	14.8093i	−0.185873	−	0.321942i
$47$	−24.5013	+	6.56509i	−0.521303	+	0.139683i	−0.509869	−	0.860252i	$-0.670306\pi$
$47$	−24.5013	+	6.56509i	−0.521303	+	0.139683i	−0.0114339	+	0.999935i	$0.503640\pi$
$48$		0			0
$49$	−12.8106	−	47.2958i	−0.261440	−	0.965220i
$50$	−34.1792	−	51.2538i	−0.683585	−	1.02508i
$51$		0			0
$52$	−10.7413	+	40.0872i	−0.206564	+	0.770907i
$53$	−15.4837	−	4.14884i	−0.292145	−	0.0782800i	0.109770	−	0.993957i	$-0.464989\pi$
$53$	−15.4837	−	4.14884i	−0.292145	−	0.0782800i	−0.401915	+	0.915677i	$0.631655\pi$
$54$		0			0
$55$	49.2957	+	4.87786i	0.896286	+	0.0886884i
$56$	−4.38501	−	32.9617i	−0.0783038	−	0.588602i
$57$		0			0
$58$	11.8437	+	44.2013i	0.204202	+	0.762091i
$59$	36.0497	−	20.8133i	0.611011	−	0.352767i	−0.162350	−	0.986733i	$-0.551907\pi$
$59$	36.0497	−	20.8133i	0.611011	−	0.352767i	0.773361	+	0.633966i	$0.218574\pi$
$60$		0			0
$61$	−51.6108	+	89.3925i	−0.846078	+	1.46545i	0.0386035	+	0.999255i	$0.487709\pi$
$61$	−51.6108	+	89.3925i	−0.846078	+	1.46545i	−0.884682	+	0.466196i	$0.845624\pi$
$62$	68.3677	+	68.3677i	1.10270	+	1.10270i
$63$		0			0
$64$		−	5.38813i		−	0.0841895i
$65$	−16.2665	−	98.8047i	−0.250254	−	1.52007i
$66$		0			0
$67$	1.98123	−	7.39406i	0.0295706	−	0.110359i	−0.949563	−	0.313576i	$-0.898473\pi$
$67$	1.98123	−	7.39406i	0.0295706	−	0.110359i	0.979134	+	0.203217i	$0.0651396\pi$
$68$	−8.74787	−	32.6475i	−0.128645	−	0.480110i
$69$		0			0
$70$	−45.6103	−	73.2000i	−0.651575	−	1.04571i
$71$	−58.5591			−0.824776			−0.412388	−	0.911008i	$-0.635305\pi$
$71$	−58.5591			−0.824776			−0.412388	+	0.911008i	$0.635305\pi$
$72$		0			0
$73$	−19.6506	−	5.26536i	−0.269186	−	0.0721282i	0.121701	−	0.992567i	$-0.461165\pi$
$73$	−19.6506	−	5.26536i	−0.269186	−	0.0721282i	−0.390887	+	0.920439i	$0.627832\pi$
$74$	94.6621	−	54.6532i	1.27922	−	0.738557i
$75$		0			0
$76$	55.8931			0.735435
$77$	68.7699	+	8.95880i	0.893116	+	0.116348i
$78$		0			0
$79$	−47.2373	−	27.2725i	−0.597940	−	0.345221i	0.170291	−	0.985394i	$-0.445529\pi$
$79$	−47.2373	−	27.2725i	−0.597940	−	0.345221i	−0.768231	+	0.640173i	$0.778863\pi$
$80$	−41.2185	−	91.0814i	−0.515231	−	1.13852i
$81$		0			0
$82$	131.214	−	35.1587i	1.60017	−	0.428765i
$83$	−40.8378	+	40.8378i	−0.492022	+	0.492022i	−0.908943	−	0.416921i	$-0.863109\pi$
$83$	−40.8378	+	40.8378i	−0.492022	+	0.492022i	0.416921	+	0.908943i	$0.363109\pi$
$84$		0			0
$85$	51.7067	+	63.0633i	0.608314	+	0.741921i
$86$	−62.8103	+	108.791i	−0.730352	+	1.26501i
$87$		0			0
$88$	45.4590	+	12.1807i	0.516580	+	0.138417i
$89$	49.6991	+	28.6938i	0.558416	+	0.322402i	0.752510	−	0.658581i	$-0.228843\pi$
$89$	49.6991	+	28.6938i	0.558416	+	0.322402i	−0.194093	+	0.980983i	$0.562176\pi$
$90$		0			0
$91$	−18.4869	−	138.964i	−0.203153	−	1.52708i
$92$	−10.1686	−	10.1686i	−0.110528	−	0.110528i
$93$		0			0
$94$	−54.1316	+	31.2529i	−0.575868	+	0.332478i
$95$	−122.864	+	55.6015i	−1.29330	+	0.585279i
$96$		0			0
$97$	37.4558	+	37.4558i	0.386142	+	0.386142i	0.873309	−	0.487167i	$-0.161970\pi$
$97$	37.4558	+	37.4558i	0.386142	+	0.386142i	−0.487167	+	0.873309i	$0.661970\pi$
$98$	−60.6565	−	104.405i	−0.618944	−	1.06535i
$99$		0			0
$100$	−38.9193	−	34.1940i	−0.389193	−	0.341940i
$101$	63.1499	+	109.379i	0.625247	+	1.08296i	0.988493	+	0.151266i	$0.0483350\pi$
$101$	63.1499	+	109.379i	0.625247	+	1.08296i	−0.363246	+	0.931693i	$0.618332\pi$
$102$		0			0
$103$	−27.2007	−	101.514i	−0.264085	−	0.985578i	−0.962808	−	0.270186i	$-0.912915\pi$
$103$	−27.2007	−	101.514i	−0.264085	−	0.985578i	0.698724	−	0.715392i	$-0.253752\pi$
$104$		−	95.1341i		−	0.914751i
$105$		0			0
$106$	−39.5008			−0.372649
$107$	−32.6136	+	8.73879i	−0.304800	+	0.0816709i	−0.407977	−	0.912992i	$-0.633766\pi$
$107$	−32.6136	+	8.73879i	−0.304800	+	0.0816709i	0.103177	+	0.994663i	$0.467099\pi$
$108$		0			0
$109$	35.1577	−	20.2983i	0.322548	−	0.186223i	−0.329980	−	0.943988i	$-0.607042\pi$
$109$	35.1577	−	20.2983i	0.322548	−	0.186223i	0.652528	+	0.757765i	$0.273709\pi$
$110$	120.446	−	19.8294i	1.09497	−	0.180268i
$111$		0			0
$112$	−53.7371	−	129.237i	−0.479796	−	1.15390i
$113$	−106.341	+	106.341i	−0.941068	+	0.941068i	−0.998358	−	0.0572893i	$-0.981754\pi$
$113$	−106.341	+	106.341i	−0.941068	+	0.941068i	0.0572893	+	0.998358i	$0.481754\pi$
$114$		0			0
$115$	32.4681	+	12.2370i	0.282331	+	0.106409i
$116$	19.2412	+	33.3268i	0.165873	+	0.287300i
$117$		0			0
$118$	72.5323	−	72.5323i	0.614680	−	0.614680i
$119$	69.6260	+	90.4838i	0.585092	+	0.760368i
$120$		0			0
$121$	11.4228	−	19.7849i	0.0944033	−	0.163511i
$122$	−65.8328	+	245.691i	−0.539613	+	2.01386i
$123$		0			0
$124$	70.4154	+	40.6544i	0.567866	+	0.327858i
$125$	119.568	+	36.4489i	0.956543	+	0.291591i
$126$		0			0
$127$	128.619	+	128.619i	1.01275	+	1.01275i	0.999918	+	0.0128332i	$0.00408505\pi$
$127$	128.619	+	128.619i	1.01275	+	1.01275i	0.0128332	+	0.999918i	$0.495915\pi$
$128$	−34.7741	−	129.779i	−0.271673	−	1.01390i
$129$		0			0
$130$	−101.734	−	224.804i	−0.782569	−	1.72926i
$131$	59.4366	−	102.947i	0.453715	−	0.785857i	−0.544899	−	0.838502i	$-0.683432\pi$
$131$	59.4366	−	102.947i	0.453715	−	0.785857i	0.998613	+	0.0526451i	$0.0167652\pi$
$132$		0			0
$133$	−174.333	+	72.4885i	−1.31078	+	0.545027i
$134$		−	18.8632i		−	0.140770i
$135$		0			0
$136$	38.7392	+	67.0982i	0.284847	+	0.493369i
$137$	30.9311	−	115.436i	0.225774	−	0.842600i	−0.756319	−	0.654203i	$-0.773004\pi$
$137$	30.9311	−	115.436i	0.225774	−	0.842600i	0.982093	−	0.188397i	$-0.0603292\pi$
$138$		0			0
$139$			141.309i			1.01661i	0.861176	+	0.508307i	$0.169729\pi$
$139$			141.309i			1.01661i	−0.861176	+	0.508307i	$0.830271\pi$
$140$	−52.9814	−	49.5329i	−0.378439	−	0.353806i
$141$		0			0
$142$	−139.384	+	37.3479i	−0.981580	+	0.263013i
$143$	191.652	+	51.3530i	1.34022	+	0.359112i
$144$		0			0
$145$	−75.4488	−	54.1179i	−0.520337	−	0.373227i
$146$	−50.1311			−0.343364
$147$		0			0
$148$	64.9983	−	64.9983i	0.439177	−	0.439177i
$149$	−138.446	−	79.9316i	−0.929165	−	0.536453i	−0.0426173	−	0.999091i	$-0.513570\pi$
$149$	−138.446	−	79.9316i	−0.929165	−	0.536453i	−0.886547	+	0.462638i	$0.846903\pi$
$150$		0			0
$151$	36.6513	+	63.4819i	0.242724	+	0.420410i	0.961489	−	0.274843i	$-0.0886258\pi$
$151$	36.6513	+	63.4819i	0.242724	+	0.420410i	−0.718765	+	0.695253i	$0.755292\pi$
$152$	−123.759	+	33.1611i	−0.814203	+	0.218165i
$153$		0			0
$154$	169.402	−	22.5362i	1.10001	−	0.146339i
$155$	−195.229	−	19.3181i	−1.25954	−	0.124633i
$156$		0			0
$157$	−21.2192	+	79.1910i	−0.135154	+	0.504401i	0.864843	+	0.502042i	$0.167418\pi$
$157$	−21.2192	+	79.1910i	−0.135154	+	0.504401i	−0.999997	+	0.00235945i	$0.999249\pi$
$158$	−129.830	−	34.7877i	−0.821706	−	0.220175i
$159$		0			0
$160$	−95.9618	−	117.038i	−0.599761	−	0.731490i
$161$	44.9041	+	18.5285i	0.278907	+	0.115084i
$162$		0			0
$163$	−11.9897	−	44.7462i	−0.0735564	−	0.274516i	0.919346	−	0.393451i	$-0.128719\pi$
$163$	−11.9897	−	44.7462i	−0.0735564	−	0.274516i	−0.992902	+	0.118934i	$0.962052\pi$
$164$	98.9324	−	57.1187i	0.603246	−	0.348284i
$165$		0			0
$166$	−71.1579	+	123.249i	−0.428662	+	0.742464i
$167$	−60.5283	−	60.5283i	−0.362445	−	0.362445i	0.502267	−	0.864712i	$-0.332499\pi$
$167$	−60.5283	−	60.5283i	−0.362445	−	0.362445i	−0.864712	+	0.502267i	$0.832499\pi$
$168$		0			0
$169$		−	232.079i		−	1.37325i
$170$	163.295	+	117.128i	0.960556	+	0.688987i
$171$		0			0
$172$	−27.3419	+	102.041i	−0.158964	+	0.593263i
$173$	28.2921	+	105.588i	0.163538	+	0.610333i	0.998222	+	0.0596036i	$0.0189837\pi$
$173$	28.2921	+	105.588i	0.163538	+	0.610333i	−0.834684	+	0.550729i	$0.814350\pi$
$174$		0			0
$175$	165.738	+	56.1778i	0.947074	+	0.321016i
$176$	198.094			1.12553
$177$		0			0
$178$	136.596	+	36.6007i	0.767391	+	0.205622i
$179$	218.631	−	126.227i	1.22140	−	0.705177i	0.256185	−	0.966628i	$-0.417534\pi$
$179$	218.631	−	126.227i	1.22140	−	0.705177i	0.965217	+	0.261451i	$0.0842010\pi$
$180$		0			0
$181$	119.101			0.658017			0.329008	−	0.944327i	$-0.393286\pi$
$181$	119.101			0.658017			0.329008	+	0.944327i	$0.393286\pi$
$182$	−132.632	−	318.977i	−0.728748	−	1.75262i
$183$		0			0
$184$	28.5483	+	16.4824i	0.155154	+	0.0895782i
$185$	−78.2196	+	207.538i	−0.422809	+	1.12183i
$186$		0			0
$187$	−156.084	+	41.8225i	−0.834673	+	0.223650i
$188$	−37.1686	+	37.1686i	−0.197705	+	0.197705i
$189$		0			0
$190$	−256.983	+	210.705i	−1.35254	+	1.10897i
$191$	−26.3773	+	45.6869i	−0.138101	+	0.239198i	−0.926778	−	0.375610i	$-0.877433\pi$
$191$	−26.3773	+	45.6869i	−0.138101	+	0.239198i	0.788677	+	0.614808i	$0.210767\pi$
$192$		0			0
$193$	177.369	+	47.5259i	0.919010	+	0.246248i	0.687162	−	0.726504i	$-0.258856\pi$
$193$	177.369	+	47.5259i	0.919010	+	0.246248i	0.231848	+	0.972752i	$0.425523\pi$
$194$	113.042	+	65.2649i	0.582692	+	0.336417i
$195$		0			0
$196$	−71.9952	−	71.6054i	−0.367322	−	0.365334i
$197$	121.992	+	121.992i	0.619251	+	0.619251i	0.945339	−	0.326088i	$-0.105731\pi$
$197$	121.992	+	121.992i	0.619251	+	0.619251i	−0.326088	+	0.945339i	$0.605731\pi$
$198$		0			0
$199$	80.9671	−	46.7464i	0.406870	−	0.234906i	−0.282574	−	0.959245i	$-0.591188\pi$
$199$	80.9671	−	46.7464i	0.406870	−	0.234906i	0.689444	+	0.724339i	$0.257855\pi$
$200$	106.463	+	52.6221i	0.532313	+	0.263110i
$201$		0			0
$202$	220.071	+	220.071i	1.08946	+	1.08946i
$203$	−103.236	−	78.9935i	−0.508553	−	0.389131i
$204$		0			0
$205$	−160.652	+	223.974i	−0.783668	+	1.09256i
$206$	−129.488	−	224.280i	−0.628583	−	1.08874i
$207$		0			0
$208$	−103.640	−	386.790i	−0.498270	−	1.85957i
$209$		−	267.218i		−	1.27856i
$210$		0			0
$211$	21.8880			0.103735			0.0518674	−	0.998654i	$-0.483483\pi$
$211$	21.8880			0.103735			0.0518674	+	0.998654i	$0.483483\pi$
$212$	−32.0864	+	8.59753i	−0.151351	+	0.0405544i
$213$		0			0
$214$	−72.0545	+	41.6007i	−0.336703	+	0.194396i
$215$	−41.4062	−	251.506i	−0.192587	−	1.16979i
$216$		0			0
$217$	−272.354	−	35.4801i	−1.25509	−	0.163503i
$218$	70.7377	−	70.7377i	0.324485	−	0.324485i
$219$		0			0
$220$	93.5222	−	42.3231i	0.425101	−	0.192378i
$221$	163.322	+	282.882i	0.739012	+	1.28001i
$222$		0			0
$223$	−88.4889	+	88.4889i	−0.396811	+	0.396811i	−0.877107	−	0.480295i	$-0.840529\pi$
$223$	−88.4889	+	88.4889i	−0.396811	+	0.396811i	0.480295	+	0.877107i	$0.340529\pi$
$224$	−129.218	−	167.928i	−0.576866	−	0.749677i
$225$		0			0
$226$	−185.294	+	320.938i	−0.819883	+	1.42008i
$227$	−4.21650	+	15.7362i	−0.0185749	+	0.0693225i	−0.974591	−	0.223991i	$-0.928091\pi$
$227$	−4.21650	+	15.7362i	−0.0185749	+	0.0693225i	0.956016	+	0.293314i	$0.0947580\pi$
$228$		0			0
$229$	345.781	+	199.637i	1.50996	+	0.871776i	0.999933	+	0.0116184i	$0.00369834\pi$
$229$	345.781	+	199.637i	1.50996	+	0.871776i	0.510028	+	0.860158i	$0.329635\pi$
$230$	85.0861	+	8.41936i	0.369940	+	0.0366059i
$231$		0			0
$232$	−62.3766	−	62.3766i	−0.268865	−	0.268865i
$233$	46.2513	+	172.612i	0.198503	+	0.740825i	0.991332	+	0.131380i	$0.0419408\pi$
$233$	46.2513	+	172.612i	0.198503	+	0.740825i	−0.792829	+	0.609445i	$0.791393\pi$
$234$		0			0
$235$	44.7291	−	118.679i	0.190337	−	0.505015i
$236$	43.1308	−	74.7047i	0.182758	−	0.316545i
$237$		0			0
$238$	223.435	+	170.966i	0.938802	+	0.718346i
$239$			372.693i			1.55938i	0.626164	+	0.779692i	$0.284624\pi$
$239$			372.693i			1.55938i	−0.626164	+	0.779692i	$0.715376\pi$
$240$		0			0
$241$	0.499495	+	0.865151i	0.00207259	+	0.00358984i	0.867060	−	0.498204i	$-0.166007\pi$
$241$	0.499495	+	0.865151i	0.00207259	+	0.00358984i	−0.864987	+	0.501794i	$0.832674\pi$
$242$	14.5705	−	54.3778i	0.0602087	−	0.224702i
$243$		0			0
$244$			213.903i			0.876652i
$245$	229.491	+	85.7830i	0.936699	+	0.350135i
$246$		0			0
$247$	−521.759	+	139.805i	−2.11239	+	0.566012i
$248$	−180.034	−	48.2401i	−0.725945	−	0.194516i
$249$		0			0
$250$	307.846	+	10.4987i	1.23138	+	0.0419946i
$251$	40.4760			0.161259			0.0806296	−	0.996744i	$-0.474307\pi$
$251$	40.4760			0.161259			0.0806296	+	0.996744i	$0.474307\pi$
$252$		0			0
$253$	−48.6148	+	48.6148i	−0.192153	+	0.192153i
$254$	388.175	+	224.113i	1.52825	+	0.882334i
$255$		0			0
$256$	−154.765	−	268.060i	−0.604550	−	1.04711i
$257$	−485.965	+	130.214i	−1.89091	+	0.506669i	−0.892457	+	0.451133i	$0.851020\pi$
$257$	−485.965	+	130.214i	−1.89091	+	0.506669i	−0.998457	+	0.0555353i	$0.982313\pi$
$258$		0			0
$259$	−118.435	+	287.030i	−0.457280	+	1.10822i
$260$	−131.568	−	160.465i	−0.506030	−	0.617172i
$261$		0			0
$262$	75.8151	−	282.946i	0.289371	−	1.07995i
$263$	−302.228	−	80.9818i	−1.14916	−	0.307916i	−0.366530	−	0.930406i	$-0.619454\pi$
$263$	−302.228	−	80.9818i	−1.14916	−	0.307916i	−0.782627	+	0.622491i	$0.786121\pi$
$264$		0			0
$265$	61.9795	−	50.8180i	0.233885	−	0.191766i
$266$	−368.722	+	283.726i	−1.38617	+	1.06664i
$267$		0			0
$268$	−4.10565	−	15.3225i	−0.0153196	−	0.0571735i
$269$	−274.266	+	158.348i	−1.01958	+	0.588653i	−0.913981	−	0.405756i	$-0.867008\pi$
$269$	−274.266	+	158.348i	−1.01958	+	0.588653i	−0.105596	+	0.994409i	$0.533675\pi$
$270$		0			0
$271$	83.6427	−	144.873i	0.308645	−	0.534588i	−0.669421	−	0.742883i	$-0.733458\pi$
$271$	83.6427	−	144.873i	0.308645	−	0.534588i	0.978066	+	0.208295i	$0.0667913\pi$
$272$	230.601	+	230.601i	0.847797	+	0.847797i
$273$		0			0
$274$		−	294.492i		−	1.07479i
$275$	−163.478	+	186.069i	−0.594464	+	0.676613i
$276$		0			0
$277$	67.5940	−	252.264i	0.244022	−	0.910701i	−0.729851	−	0.683606i	$-0.760411\pi$
$277$	67.5940	−	252.264i	0.244022	−	0.910701i	0.973873	−	0.227095i	$-0.0729227\pi$
$278$	90.1245	+	336.349i	0.324189	+	1.20989i
$279$		0			0
$280$	146.699	+	78.2424i	0.523926	+	0.279437i
$281$	288.113			1.02531			0.512657	−	0.858594i	$-0.328661\pi$
$281$	288.113			1.02531			0.512657	+	0.858594i	$0.328661\pi$
$282$		0			0
$283$	−311.860	−	83.5625i	−1.10198	−	0.295274i	−0.338408	−	0.941000i	$-0.609888\pi$
$283$	−311.860	−	83.5625i	−1.10198	−	0.295274i	−0.763570	+	0.645726i	$0.776555\pi$
$284$	−105.093	+	60.6752i	−0.370044	+	0.213645i
$285$		0			0
$286$	488.929			1.70954
$287$	−234.497	+	306.463i	−0.817062	+	1.06781i
$288$		0			0
$289$	19.8992	+	11.4888i	0.0688555	+	0.0397538i
$290$	−214.101	−	80.6932i	−0.738280	−	0.278253i
$291$		0			0
$292$	−40.7214	+	10.9113i	−0.139457	+	0.0373673i
$293$	−98.1765	+	98.1765i	−0.335074	+	0.335074i	−0.854509	−	0.519436i	$-0.826142\pi$
$293$	−98.1765	+	98.1765i	−0.335074	+	0.335074i	0.519436	+	0.854509i	$0.326142\pi$
$294$		0			0
$295$	−20.4949	+	207.121i	−0.0694741	+	0.702106i
$296$	−105.356	+	182.483i	−0.355934	+	0.616496i
$297$		0			0
$298$	−380.511	−	101.958i	−1.27688	−	0.342140i
$299$	120.358	+	69.4886i	0.402535	+	0.232403i
$300$		0			0
$301$	−47.0581	−	353.731i	−0.156339	−	1.17519i
$302$	127.726	+	127.726i	0.422934	+	0.422934i
$303$		0			0
$304$	−467.045	+	269.648i	−1.53633	+	0.887001i
$305$	−212.787	−	470.201i	−0.697663	−	1.54164i
$306$		0			0
$307$	−38.0161	−	38.0161i	−0.123831	−	0.123831i	0.642475	−	0.766306i	$-0.277907\pi$
$307$	−38.0161	−	38.0161i	−0.123831	−	0.123831i	−0.766306	+	0.642475i	$0.777907\pi$
$308$	132.700	−	55.1772i	0.430844	−	0.179147i
$309$		0			0
$310$	−477.011	+	78.5319i	−1.53875	+	0.253329i
$311$	−182.194	−	315.569i	−0.585832	−	1.01469i	−0.994771	−	0.102129i	$-0.967434\pi$
$311$	−182.194	−	315.569i	−0.585832	−	1.01469i	0.408939	−	0.912562i	$-0.365899\pi$
$312$		0			0
$313$	61.0959	+	228.013i	0.195195	+	0.728476i	0.992216	+	0.124526i	$0.0397409\pi$
$313$	61.0959	+	228.013i	0.195195	+	0.728476i	−0.797022	+	0.603951i	$0.793592\pi$
$314$			202.026i			0.643396i
$315$		0			0
$316$	−113.032			−0.357696
$317$	306.481	−	82.1214i	0.966818	−	0.259058i	0.259334	−	0.965788i	$-0.416497\pi$
$317$	306.481	−	82.1214i	0.966818	−	0.259058i	0.707484	+	0.706730i	$0.249830\pi$
$318$		0			0
$319$	159.331	−	91.9900i	0.499471	−	0.288370i
$320$	21.8915	+	15.7023i	0.0684108	+	0.0490696i
$321$		0			0
$322$	118.699	+	15.4632i	0.368632	+	0.0480224i
$323$	311.068	−	311.068i	0.963059	−	0.963059i
$324$		0			0
$325$	448.839	+	221.851i	1.38104	+	0.682619i
$326$	−57.0765	−	98.8595i	−0.175081	−	0.303250i
$327$		0			0
$328$	−185.169	+	185.169i	−0.564539	+	0.564539i
$329$	67.7262	−	164.135i	0.205855	−	0.498891i
$330$		0			0
$331$	258.974	−	448.556i	0.782399	−	1.35515i	−0.148142	−	0.988966i	$-0.547329\pi$
$331$	258.974	−	448.556i	0.782399	−	1.35515i	0.930541	−	0.366189i	$-0.119338\pi$
$332$	−30.9756	+	115.603i	−0.0933001	+	0.348201i
$333$		0			0
$334$	−182.675	−	105.468i	−0.546932	−	0.315771i
$335$	24.2676	+	29.5976i	0.0724406	+	0.0883511i
$336$		0			0
$337$	153.115	+	153.115i	0.454348	+	0.454348i	0.896795	−	0.442447i	$-0.145889\pi$
$337$	153.115	+	153.115i	0.454348	+	0.454348i	−0.442447	+	0.896795i	$0.645889\pi$
$338$	−148.016	−	552.402i	−0.437916	−	1.63432i
$339$		0			0
$340$	158.137	+	59.6008i	0.465109	+	0.175296i
$341$	194.364	−	336.648i	0.569982	−	0.987237i
$342$		0			0
$343$	317.422	+	129.969i	0.925430	+	0.378919i
$344$		−	242.162i		−	0.703960i
$345$		0			0
$346$	134.684	+	233.279i	0.389259	+	0.674216i
$347$	106.451	−	397.282i	0.306777	−	1.14491i	−0.624629	−	0.780922i	$-0.714750\pi$
$347$	106.451	−	397.282i	0.306777	−	1.14491i	0.931405	−	0.363984i	$-0.118584\pi$
$348$		0			0
$349$		−	338.935i		−	0.971160i	−0.874192	−	0.485580i	$-0.838609\pi$
$349$		−	338.935i		−	0.971160i	0.874192	−	0.485580i	$-0.161391\pi$
$350$	430.324	+	28.0118i	1.22950	+	0.0800337i
$351$		0			0
$352$	289.674	−	77.6179i	0.822937	−	0.220505i
$353$	452.404	+	121.221i	1.28160	+	0.343403i	0.834464	−	0.551063i	$-0.185778\pi$
$353$	452.404	+	121.221i	1.28160	+	0.343403i	0.447135	+	0.894466i	$0.352444\pi$
$354$		0			0
$355$	170.655	−	237.920i	0.480719	−	0.670198i
$356$	118.923			0.334052
$357$		0			0
$358$	439.887	−	439.887i	1.22874	−	1.22874i
$359$	−303.691	−	175.336i	−0.845935	−	0.488401i	0.0133422	−	0.999911i	$-0.495753\pi$
$359$	−303.691	−	175.336i	−0.845935	−	0.488401i	−0.859277	+	0.511510i	$0.829086\pi$
$360$		0			0
$361$	183.241	+	317.383i	0.507594	+	0.879178i
$362$	283.488	−	75.9604i	0.783116	−	0.209835i
$363$		0			0
$364$	−177.163	−	230.236i	−0.486713	−	0.632517i
$365$	78.6591	−	64.4940i	0.215504	−	0.176696i
$366$		0			0
$367$	104.910	−	391.530i	0.285859	−	1.06684i	−0.662351	−	0.749194i	$-0.730441\pi$
$367$	104.910	−	391.530i	0.285859	−	1.06684i	0.948210	−	0.317645i	$-0.102892\pi$
$368$	134.026	+	35.9122i	0.364201	+	0.0975874i
$369$		0			0
$370$	−53.8170	+	543.876i	−0.145451	+	1.46993i
$371$	88.9287	−	68.4294i	0.239700	−	0.184446i
$372$		0			0
$373$	19.7292	+	73.6304i	0.0528933	+	0.197401i	0.987317	−	0.158764i	$-0.0507509\pi$
$373$	19.7292	+	73.6304i	0.0528933	+	0.197401i	−0.934423	+	0.356165i	$0.884084\pi$
$374$	−344.842	+	199.095i	−0.922038	+	0.532339i
$375$		0			0
$376$	60.2471	−	104.351i	0.160232	−	0.277529i
$377$	−262.976	−	262.976i	−0.697548	−	0.697548i
$378$		0			0
$379$		−	503.251i		−	1.32784i	−0.747804	−	0.663919i	$-0.768892\pi$
$379$		−	503.251i		−	1.32784i	0.747804	−	0.663919i	$-0.231108\pi$
$380$	−162.886	+	227.088i	−0.428647	+	0.597601i
$381$		0			0
$382$	−33.6459	+	125.568i	−0.0880784	+	0.328713i
$383$	−193.815	−	723.327i	−0.506044	−	1.88858i	−0.456311	−	0.889820i	$-0.650830\pi$
$383$	−193.815	−	723.327i	−0.506044	−	1.88858i	−0.0497332	−	0.998763i	$-0.515837\pi$
$384$		0			0
$385$	−236.811	+	253.298i	−0.615093	+	0.657917i
$386$	452.490			1.17226
$387$		0			0
$388$	106.029	+	28.4104i	0.273271	+	0.0732227i
$389$	385.145	−	222.364i	0.990091	−	0.571629i	0.0847892	−	0.996399i	$-0.472978\pi$
$389$	385.145	−	222.364i	0.990091	−	0.571629i	0.905301	+	0.424770i	$0.139645\pi$
$390$		0			0
$391$	−113.185			−0.289475
$392$	201.895	+	115.835i	0.515039	+	0.295497i
$393$		0			0
$394$	368.175	+	212.566i	0.934454	+	0.539507i
$395$	248.466	−	112.442i	0.629028	−	0.284664i
$396$		0			0
$397$	−652.508	+	174.839i	−1.64360	+	0.440400i	−0.957810	−	0.287403i	$-0.907208\pi$
$397$	−652.508	+	174.839i	−1.64360	+	0.440400i	−0.685786	+	0.727803i	$0.740542\pi$
$398$	162.906	−	162.906i	0.409313	−	0.409313i
$399$		0			0
$400$	490.176	+	97.9659i	1.22544	+	0.244915i
$401$	−195.581	+	338.757i	−0.487734	+	0.844780i	−0.999901	−	0.0141063i	$-0.995510\pi$
$401$	−195.581	+	338.757i	−0.487734	+	0.844780i	0.512167	+	0.858886i	$0.328843\pi$
$402$		0			0
$403$	−759.013	−	203.377i	−1.88341	−	0.504657i
$404$	226.663	+	130.864i	0.561047	+	0.323920i
$405$		0			0
$406$	−296.107	−	122.181i	−0.729327	−	0.300938i
$407$	−310.749	−	310.749i	−0.763511	−	0.763511i
$408$		0			0
$409$	−150.958	+	87.1558i	−0.369091	+	0.213095i	−0.673061	−	0.739587i	$-0.735021\pi$
$409$	−150.958	+	87.1558i	−0.369091	+	0.213095i	0.303970	+	0.952682i	$0.401688\pi$
$410$	−239.543	+	635.572i	−0.584250	+	1.55017i
$411$		0			0
$412$	−153.998	−	153.998i	−0.373782	−	0.373782i
$413$	−37.6414	+	288.944i	−0.0911414	+	0.699623i
$414$		0			0
$415$	−46.9091	−	284.931i	−0.113034	−	0.686581i
$416$	−303.107	−	524.996i	−0.728622	−	1.26201i
$417$		0			0
$418$	−170.427	−	636.042i	−0.407720	−	1.52163i
$419$			190.392i			0.454396i	0.973849	+	0.227198i	$0.0729564\pi$
$419$			190.392i			0.454396i	−0.973849	+	0.227198i	$0.927044\pi$
$420$		0			0
$421$	581.913			1.38222			0.691108	−	0.722751i	$-0.257123\pi$
$421$	581.913			1.38222			0.691108	+	0.722751i	$0.257123\pi$
$422$	52.0986	−	13.9598i	0.123456	−	0.0330800i
$423$		0			0
$424$	65.9451	−	38.0734i	0.155531	−	0.0897958i
$425$	−406.906	+	26.2980i	−0.957426	+	0.0618777i
$426$		0			0
$427$	−277.414	−	667.174i	−0.649681	−	1.56247i
$428$	−49.4751	+	49.4751i	−0.115596	+	0.115596i
$429$		0			0
$430$	−258.962	−	572.234i	−0.602237	−	1.33078i
$431$	−286.895	−	496.916i	−0.665649	−	1.15294i	−0.979109	−	0.203336i	$-0.934822\pi$
$431$	−286.895	−	496.916i	−0.665649	−	1.15294i	0.313460	−	0.949601i	$-0.398512\pi$
$432$		0			0
$433$	267.818	−	267.818i	0.618518	−	0.618518i	−0.326633	−	0.945151i	$-0.605914\pi$
$433$	267.818	−	267.818i	0.618518	−	0.618518i	0.945151	+	0.326633i	$0.105914\pi$
$434$	−670.895	+	89.2515i	−1.54584	+	0.205649i
$435$		0			0
$436$	42.0637	−	72.8564i	0.0964763	−	0.167102i
$437$	48.4436	−	180.794i	0.110855	−	0.413716i
$438$		0			0
$439$	334.556	+	193.156i	0.762086	+	0.439991i	0.830044	−	0.557698i	$-0.188315\pi$
$439$	334.556	+	193.156i	0.762086	+	0.439991i	−0.0679581	+	0.997688i	$0.521648\pi$
$440$	−181.967	+	149.198i	−0.413562	+	0.339087i
$441$		0			0
$442$	569.160	+	569.160i	1.28769	+	1.28769i
$443$	125.217	+	467.317i	0.282657	+	1.05489i	0.950534	+	0.310619i	$0.100536\pi$
$443$	125.217	+	467.317i	0.282657	+	1.05489i	−0.667877	+	0.744271i	$0.732797\pi$
$444$		0			0
$445$	−261.415	+	118.302i	−0.587449	+	0.265848i
$446$	−154.188	+	267.061i	−0.345712	+	0.598791i
$447$		0			0
$448$	29.9540	+	22.9200i	0.0668615	+	0.0511606i
$449$			213.080i			0.474566i	0.971441	+	0.237283i	$0.0762569\pi$
$449$			213.080i			0.474566i	−0.971441	+	0.237283i	$0.923743\pi$
$450$		0			0
$451$	−273.078	−	472.984i	−0.605494	−	1.04875i
$452$	−80.6599	+	301.027i	−0.178451	+	0.665989i
$453$		0			0
$454$			40.1450i			0.0884252i
$455$	618.475	+	329.865i	1.35929	+	0.724977i
$456$		0			0
$457$	740.545	−	198.429i	1.62045	−	0.434198i	0.669316	−	0.742978i	$-0.266587\pi$
$457$	740.545	−	198.429i	1.62045	−	0.434198i	0.951134	+	0.308780i	$0.0999206\pi$
$458$	950.364	+	254.649i	2.07503	+	0.556003i
$459$		0			0
$460$	70.9477	−	11.6803i	0.154234	−	0.0253921i
$461$	−332.527			−0.721317			−0.360659	−	0.932698i	$-0.617448\pi$
$461$	−332.527			−0.721317			−0.360659	+	0.932698i	$0.617448\pi$
$462$		0			0
$463$	−394.630	+	394.630i	−0.852332	+	0.852332i	−0.990420	−	0.138088i	$-0.955904\pi$
$463$	−394.630	+	394.630i	−0.852332	+	0.852332i	0.138088	+	0.990420i	$0.455904\pi$
$464$	−321.561	−	185.653i	−0.693018	−	0.400114i
$465$		0			0
$466$	220.178	+	381.359i	0.472484	+	0.818367i
$467$	594.918	−	159.408i	1.27392	−	0.341345i	0.442386	−	0.896825i	$-0.354132\pi$
$467$	594.918	−	159.408i	1.27392	−	0.341345i	0.831530	+	0.555480i	$0.187466\pi$
$468$		0			0
$469$	32.6777	+	42.4670i	0.0696753	+	0.0905479i
$470$	30.7747	−	311.010i	0.0654782	−	0.661723i
$471$		0			0
$472$	−51.1786	+	191.001i	−0.108429	+	0.404663i
$473$	487.847	+	130.718i	1.03139	+	0.276360i
$474$		0			0
$475$	132.151	−	661.221i	0.278212	−	1.39204i
$476$	218.707	+	90.2439i	0.459469	+	0.189588i
$477$		0			0
$478$	237.696	+	887.095i	0.497273	+	1.85585i
$479$	−219.614	+	126.794i	−0.458484	+	0.264706i	−0.711407	−	0.702781i	$-0.751942\pi$
$479$	−219.614	+	126.794i	−0.458484	+	0.264706i	0.252923	+	0.967487i	$0.418608\pi$
$480$		0			0
$481$	−444.176	+	769.335i	−0.923442	+	1.59945i
$482$	1.74069	+	1.74069i	0.00361139	+	0.00361139i
$483$		0			0
$484$		−	47.3423i		−	0.0978147i
$485$	−261.335	+	43.0244i	−0.538834	+	0.0887100i
$486$		0			0
$487$	107.670	−	401.832i	0.221089	−	0.825116i	−0.762845	−	0.646582i	$-0.776198\pi$
$487$	107.670	−	401.832i	0.221089	−	0.825116i	0.983934	−	0.178534i	$-0.0571355\pi$
$488$	−126.908	−	473.626i	−0.260057	−	0.970545i
$489$		0			0
$490$	600.954	+	57.8182i	1.22644	+	0.117996i
$491$	283.991			0.578392			0.289196	−	0.957270i	$-0.406612\pi$
$491$	283.991			0.578392			0.289196	+	0.957270i	$0.406612\pi$
$492$		0			0
$493$	292.562	+	78.3918i	0.593433	+	0.159010i
$494$	−1152.74	+	665.537i	−2.33349	+	1.34724i
$495$		0			0
$496$	−784.525			−1.58170
$497$	249.098	−	325.545i	0.501203	−	0.655020i
$498$		0			0
$499$	−716.123	−	413.454i	−1.43512	−	0.828565i	−0.437612	−	0.899164i	$-0.644176\pi$
$499$	−716.123	−	413.454i	−1.43512	−	0.828565i	−0.997505	+	0.0705988i	$0.977509\pi$
$500$	252.347	−	58.4760i	0.504695	−	0.116952i
$501$		0			0
$502$	96.3424	−	25.8149i	0.191917	−	0.0514240i
$503$	−118.670	+	118.670i	−0.235924	+	0.235924i	−0.815160	−	0.579236i	$-0.803351\pi$
$503$	−118.670	+	118.670i	−0.235924	+	0.235924i	0.579236	+	0.815160i	$0.303351\pi$
$504$		0			0
$505$	−628.430	−	62.1838i	−1.24442	−	0.123136i
$506$	−84.7090	+	146.720i	−0.167409	+	0.289961i
$507$		0			0
$508$	364.093	+	97.5583i	0.716718	+	0.192044i
$509$	154.005	+	88.9151i	0.302565	+	0.174686i	0.643594	−	0.765367i	$-0.277442\pi$
$509$	154.005	+	88.9151i	0.302565	+	0.174686i	−0.341030	+	0.940052i	$0.610776\pi$
$510$		0			0
$511$	112.861	−	86.8448i	0.220863	−	0.169951i
$512$	−159.321	−	159.321i	−0.311175	−	0.311175i
$513$		0			0
$514$	−1073.66	+	619.879i	−2.08883	+	1.20599i
$515$	491.713	+	185.323i	0.954783	+	0.359851i
$516$		0			0
$517$	177.699	+	177.699i	0.343711	+	0.343711i
$518$	−98.8418	+	758.734i	−0.190814	+	1.46474i
$519$		0			0
$520$	386.521	+	277.243i	0.743310	+	0.533160i
$521$	−376.277	−	651.731i	−0.722221	−	1.25092i	−0.960108	−	0.279631i	$-0.909788\pi$
$521$	−376.277	−	651.731i	−0.722221	−	1.25092i	0.237887	−	0.971293i	$-0.423545\pi$
$522$		0			0
$523$	141.063	+	526.453i	0.269718	+	1.00660i	0.959299	+	0.282393i	$0.0911284\pi$
$523$	141.063	+	526.453i	0.269718	+	1.00660i	−0.689580	+	0.724209i	$0.742205\pi$
$524$		−	246.338i		−	0.470110i
$525$		0			0
$526$	−771.022			−1.46582
$527$	618.149	−	165.633i	1.17296	−	0.314293i
$528$		0			0
$529$	416.422	−	240.422i	0.787188	−	0.454483i
$530$	115.115	−	160.488i	0.217198	−	0.302808i
$531$		0			0
$532$	−237.757	+	310.724i	−0.446912	+	0.584067i
$533$	−780.658	+	780.658i	−1.46465	+	1.46465i
$534$		0			0
$535$	59.5389	−	157.973i	0.111288	−	0.295277i
$536$	18.1815	+	31.4913i	0.0339208	+	0.0587525i
$537$		0			0
$538$	−551.826	+	551.826i	−1.02570	+	1.02570i
$539$	−342.337	+	344.201i	−0.635134	+	0.638591i
$540$		0			0
$541$	−30.4507	+	52.7421i	−0.0562859	+	0.0974901i	−0.892795	−	0.450462i	$-0.851259\pi$
$541$	−30.4507	+	52.7421i	−0.0562859	+	0.0974901i	0.836510	+	0.547952i	$0.184593\pi$
$542$	106.692	−	398.178i	0.196848	−	0.734646i
$543$		0			0
$544$	427.563	+	246.854i	0.785962	+	0.453775i
$545$	−19.9878	+	201.997i	−0.0366748	+	0.370636i
$546$		0			0
$547$	219.616	+	219.616i	0.401492	+	0.401492i	0.878759	−	0.477266i	$-0.158372\pi$
$547$	219.616	+	219.616i	0.401492	+	0.401492i	−0.477266	+	0.878759i	$0.658372\pi$
$548$	−64.0976	−	239.215i	−0.116966	−	0.436524i
$549$		0			0
$550$	−270.444	+	547.150i	−0.491716	+	0.994818i
$551$	−250.436	+	433.768i	−0.454512	+	0.787238i
$552$		0			0
$553$	352.552	−	146.593i	0.637526	−	0.265086i
$554$		−	643.557i		−	1.16166i
$555$		0			0
$556$	146.416	+	253.600i	0.263338	+	0.456115i
$557$	−257.028	+	959.243i	−0.461451	+	1.72216i	0.206943	+	0.978353i	$0.433648\pi$
$557$	−257.028	+	959.243i	−0.461451	+	1.72216i	−0.668395	+	0.743807i	$0.733018\pi$
$558$		0			0
$559$		−	1020.94i		−	1.82637i
$560$	681.679	+	158.297i	1.21728	+	0.282673i
$561$		0			0
$562$	685.776	−	183.753i	1.22024	−	0.326963i
$563$	−275.338	−	73.7765i	−0.489055	−	0.131042i	0.00586099	−	0.999983i	$-0.498134\pi$
$563$	−275.338	−	73.7765i	−0.489055	−	0.131042i	−0.494916	+	0.868941i	$0.664801\pi$
$564$		0			0
$565$	−122.150	−	741.955i	−0.216195	−	1.31319i
$566$	−795.593			−1.40564
$567$		0			0
$568$	196.698	−	196.698i	0.346300	−	0.346300i
$569$	−231.224	−	133.497i	−0.406368	−	0.234617i	0.282860	−	0.959161i	$-0.408717\pi$
$569$	−231.224	−	133.497i	−0.406368	−	0.234617i	−0.689228	+	0.724544i	$0.742050\pi$
$570$		0			0
$571$	104.149	+	180.391i	0.182397	+	0.315921i	0.942696	−	0.333652i	$-0.108281\pi$
$571$	104.149	+	180.391i	0.182397	+	0.315921i	−0.760299	+	0.649573i	$0.774948\pi$
$572$	397.155	−	106.417i	0.694328	−	0.186045i
$573$		0			0
$574$	−362.701	+	879.010i	−0.631883	+	1.53138i
$575$	−144.338	+	96.2533i	−0.251022	+	0.167397i
$576$		0			0
$577$	−41.0956	+	153.371i	−0.0712228	+	0.265807i	−0.992350	−	0.123454i	$-0.960603\pi$
$577$	−41.0956	+	153.371i	−0.0712228	+	0.265807i	0.921128	+	0.389261i	$0.127270\pi$
$578$	54.6922	+	14.6547i	0.0946232	+	0.0253542i
$579$		0			0
$580$	−191.477	−	18.9468i	−0.330133	−	0.0326670i
$581$	−53.3122	−	400.743i	−0.0917594	−	0.689747i
$582$		0			0
$583$	41.1038	+	153.401i	0.0705039	+	0.263124i
$584$	83.6919	−	48.3196i	0.143308	−	0.0827390i
$585$		0			0
$586$	−171.068	+	296.298i	−0.291925	+	0.505628i
$587$	−20.2654	−	20.2654i	−0.0345236	−	0.0345236i	0.689634	−	0.724158i	$-0.257771\pi$
$587$	−20.2654	−	20.2654i	−0.0345236	−	0.0345236i	−0.724158	+	0.689634i	$0.757771\pi$
$588$		0			0
$589$			1058.28i			1.79674i
$590$	83.3156	+	506.068i	0.141213	+	0.857743i
$591$		0			0
$592$	−229.553	+	856.703i	−0.387758	+	1.44713i
$593$	189.157	+	705.944i	0.318983	+	1.19046i	0.920223	+	0.391393i	$0.128007\pi$
$593$	189.157	+	705.944i	0.318983	+	1.19046i	−0.601240	+	0.799068i	$0.705327\pi$
$594$		0			0
$595$	−570.534	+	19.1926i	−0.958881	+	0.0322564i
$596$	−331.280			−0.555839
$597$		0			0
$598$	330.798	+	88.6371i	0.553174	+	0.148223i
$599$	728.928	−	420.847i	1.21691	−	0.702583i	0.252653	−	0.967557i	$-0.418697\pi$
$599$	728.928	−	420.847i	1.21691	−	0.702583i	0.964256	+	0.264974i	$0.0853634\pi$
$600$		0			0
$601$	−374.471			−0.623079			−0.311540	−	0.950233i	$-0.600845\pi$
$601$	−374.471			−0.623079			−0.311540	+	0.950233i	$0.600845\pi$
$602$	−337.613	−	811.950i	−0.560818	−	1.34875i
$603$		0			0
$604$	131.552	+	75.9515i	0.217801	+	0.125747i
$605$	47.0953	+	104.068i	0.0778435	+	0.172013i
$606$		0			0
$607$	488.562	−	130.910i	0.804880	−	0.215667i	0.167155	−	0.985931i	$-0.446542\pi$
$607$	488.562	−	130.910i	0.804880	−	0.215667i	0.637725	+	0.770264i	$0.279875\pi$
$608$	−577.307	+	577.307i	−0.949519	+	0.949519i
$609$		0			0
$610$	−806.368	−	983.475i	−1.32192	−	1.61225i
$611$	253.997	−	439.937i	0.415708	−	0.720027i
$612$		0			0
$613$	660.473	+	176.973i	1.07744	+	0.288700i	0.753548	−	0.657393i	$-0.228341\pi$
$613$	660.473	+	176.973i	1.07744	+	0.288700i	0.323896	+	0.946093i	$0.395007\pi$
$614$	−114.733	−	66.2412i	−0.186862	−	0.107885i
$615$		0			0
$616$	−261.089	+	200.904i	−0.423845	+	0.326143i
$617$	−5.21905	−	5.21905i	−0.00845875	−	0.00845875i	0.702865	−	0.711324i	$-0.251904\pi$
$617$	−5.21905	−	5.21905i	−0.00845875	−	0.00845875i	−0.711324	+	0.702865i	$0.751904\pi$
$618$		0			0
$619$	−803.223	+	463.741i	−1.29761	+	0.749178i	−0.979991	−	0.199040i	$-0.936218\pi$
$619$	−803.223	+	463.741i	−1.29761	+	0.749178i	−0.317622	+	0.948217i	$0.602884\pi$
$620$	−370.382	+	167.615i	−0.597391	+	0.270347i
$621$		0			0
$622$	−634.928	−	634.928i	−1.02078	−	1.02078i
$623$	−370.925	+	154.232i	−0.595386	+	0.247564i
$624$		0			0
$625$	−496.538	+	379.573i	−0.794460	+	0.607316i
$626$	290.845	+	503.758i	0.464609	+	0.804726i
$627$		0			0
$628$	43.9719	+	164.105i	0.0700189	+	0.261314i
$629$		−	723.484i		−	1.15021i
$630$		0			0
$631$	−659.617			−1.04535			−0.522676	−	0.852531i	$-0.675066\pi$
$631$	−659.617			−1.04535			−0.522676	+	0.852531i	$0.675066\pi$
$632$	250.276	−	67.0613i	0.396006	−	0.106110i
$633$		0			0
$634$	677.121	−	390.936i	1.06801	−	0.616619i
$635$	−897.396	+	147.741i	−1.41322	+	0.232663i
$636$		0			0
$637$	851.177	+	488.352i	1.33623	+	0.766643i
$638$	320.576	−	320.576i	0.502470	−	0.502470i
$639$		0			0
$640$	628.619	+	236.922i	0.982218	+	0.370191i
$641$	115.909	+	200.760i	0.180825	+	0.313198i	0.942162	−	0.335159i	$-0.108790\pi$
$641$	115.909	+	200.760i	0.180825	+	0.313198i	−0.761337	+	0.648357i	$0.775457\pi$
$642$		0			0
$643$	−207.642	+	207.642i	−0.322927	+	0.322927i	−0.849889	−	0.526962i	$-0.823331\pi$
$643$	−207.642	+	207.642i	−0.322927	+	0.322927i	0.526962	+	0.849889i	$0.323331\pi$
$644$	99.7848	−	13.2747i	0.154945	−	0.0206129i
$645$		0			0
$646$	542.021	−	938.808i	0.839042	−	1.45326i
$647$	−119.193	+	444.834i	−0.184224	+	0.687534i	0.810571	+	0.585640i	$0.199157\pi$
$647$	−119.193	+	444.834i	−0.184224	+	0.687534i	−0.994795	+	0.101894i	$0.967510\pi$
$648$		0			0
$649$	−357.154	−	206.203i	−0.550315	−	0.317725i
$650$	1209.83	+	241.796i	1.86128	+	0.371994i
$651$		0			0
$652$	−67.8803	−	67.8803i	−0.104111	−	0.104111i
$653$	−211.888	−	790.779i	−0.324485	−	1.21099i	−0.914829	−	0.403842i	$-0.867675\pi$
$653$	−211.888	−	790.779i	−0.324485	−	1.21099i	0.590344	−	0.807152i	$-0.298992\pi$
$654$		0			0
$655$	245.053	+	541.498i	0.374126	+	0.826715i
$656$	−551.122	+	954.571i	−0.840125	+	1.45514i
$657$		0			0
$658$	56.5217	−	433.874i	0.0858992	−	0.659383i
$659$			472.040i			0.716297i	0.933665	+	0.358149i	$0.116592\pi$
$659$			472.040i			0.716297i	−0.933665	+	0.358149i	$0.883408\pi$
$660$		0			0
$661$	20.0334	+	34.6989i	0.0303078	+	0.0524946i	0.880781	−	0.473523i	$-0.157018\pi$
$661$	20.0334	+	34.6989i	0.0303078	+	0.0524946i	−0.850474	+	0.526018i	$0.823685\pi$
$662$	330.338	−	1232.84i	0.499000	−	1.86229i
$663$		0			0
$664$		−	274.346i		−	0.413172i
$665$	213.534	−	919.549i	0.321104	−	1.38278i
$666$		0			0
$667$	124.477	−	33.3534i	0.186622	−	0.0500052i
$668$	−171.342	−	45.9110i	−0.256500	−	0.0687291i
$669$		0			0
$670$	76.6394	+	54.9718i	0.114387	+	0.0820475i
$671$	1022.65			1.52406
$672$		0			0
$673$	−170.430	+	170.430i	−0.253239	+	0.253239i	−0.822297	−	0.569059i	$-0.807308\pi$
$673$	−170.430	+	170.430i	−0.253239	+	0.253239i	0.569059	+	0.822297i	$0.307308\pi$
$674$	462.104	+	266.796i	0.685614	+	0.395839i
$675$		0			0
$676$	−240.465	−	416.498i	−0.355718	−	0.616122i
$677$	−873.260	+	233.989i	−1.28990	+	0.345627i	−0.837621	−	0.546251i	$-0.816054\pi$
$677$	−873.260	+	233.989i	−1.28990	+	0.345627i	−0.452276	+	0.891878i	$0.649388\pi$
$678$		0			0
$679$	−367.555	+	48.8972i	−0.541319	+	0.0720135i
$680$	−385.509	−	38.1465i	−0.566925	−	0.0560978i
$681$		0			0
$682$	247.923	−	925.262i	0.363524	−	1.35669i
$683$	370.963	+	99.3993i	0.543138	+	0.145533i	0.519948	−	0.854198i	$-0.325951\pi$
$683$	370.963	+	99.3993i	0.543138	+	0.145533i	0.0231896	+	0.999731i	$0.492618\pi$
$684$		0			0
$685$	378.866	+	462.079i	0.553090	+	0.674568i
$686$	838.431	+	106.911i	1.22220	+	0.155846i
$687$		0			0
$688$	−263.814	−	984.567i	−0.383451	−	1.43106i
$689$	278.020	−	160.515i	0.403512	−	0.232968i
$690$		0			0
$691$	−143.113	+	247.880i	−0.207111	+	0.358726i	−0.950803	−	0.309796i	$-0.899739\pi$
$691$	−143.113	+	247.880i	−0.207111	+	0.358726i	0.743693	+	0.668522i	$0.233073\pi$
$692$	160.177	+	160.177i	0.231470	+	0.231470i
$693$		0			0
$694$		−	1013.52i		−	1.46040i
$695$	−574.127	−	411.809i	−0.826082	−	0.592531i
$696$		0			0
$697$	232.711	−	868.488i	0.333875	−	1.24604i
$698$	−216.166	−	806.743i	−0.309694	−	1.15579i
$699$		0			0
$700$	355.648	−	70.9080i	0.508068	−	0.101297i
$701$	737.080			1.05147			0.525735	−	0.850648i	$-0.323790\pi$
$701$	737.080			1.05147			0.525735	+	0.850648i	$0.323790\pi$
$702$		0			0
$703$	1155.65	+	309.655i	1.64388	+	0.440476i
$704$	−46.2299	+	26.6909i	−0.0656675	+	0.0379132i
$705$		0			0
$706$	1154.14			1.63476
$707$	−876.691	−	114.208i	−1.24002	−	0.161539i
$708$		0			0
$709$	777.250	+	448.745i	1.09626	+	0.632927i	0.935237	−	0.354023i	$-0.115187\pi$
$709$	777.250	+	448.745i	1.09626	+	0.632927i	0.161025	+	0.986950i	$0.448520\pi$
$710$	254.458	−	675.146i	0.358391	−	0.950910i
$711$		0			0
$712$	−263.319	+	70.5562i	−0.369830	+	0.0990958i
$713$	192.533	−	192.533i	0.270032	−	0.270032i
$714$		0			0
$715$	−767.162	+	629.010i	−1.07295	+	0.879734i
$716$	261.576	−	453.063i	0.365330	−	0.632769i
$717$		0			0
$718$	−834.680	−	223.652i	−1.16251	−	0.311493i
$719$	−86.3910	−	49.8778i	−0.120154	−	0.0693711i	0.438718	−	0.898625i	$-0.355433\pi$
$719$	−86.3910	−	49.8778i	−0.120154	−	0.0693711i	−0.558873	+	0.829254i	$0.688766\pi$
$720$		0			0
$721$	680.051	+	280.606i	0.943205	+	0.389189i
$722$	638.578	+	638.578i	0.884457	+	0.884457i
$723$		0			0
$724$	213.744	−	123.405i	0.295226	−	0.170449i
$725$	439.752	−	148.829i	0.606554	−	0.205282i
$726$		0			0
$727$	−794.241	−	794.241i	−1.09249	−	1.09249i	−0.995262	−	0.0972298i	$-0.969002\pi$
$727$	−794.241	−	794.241i	−1.09249	−	1.09249i	−0.0972298	−	0.995262i	$-0.530998\pi$
$728$	528.874	+	404.680i	0.726476	+	0.555880i
$729$		0			0
$730$	146.094	−	203.678i	0.200129	−	0.279011i
$731$	415.733	+	720.070i	0.568718	+	0.985048i
$732$		0			0
$733$	−100.435	−	374.828i	−0.137019	−	0.511362i	−0.999981	−	0.00609363i	$-0.998060\pi$
$733$	−100.435	−	374.828i	−0.137019	−	0.511362i	0.862963	−	0.505268i	$-0.168606\pi$
$734$		−	998.842i		−	1.36082i
$735$		0			0
$736$	210.058			0.285405
$737$	−73.2551	+	19.6287i	−0.0993964	+	0.0266332i
$738$		0			0
$739$	−994.736	+	574.311i	−1.34606	+	0.777147i	−0.987689	−	0.156433i	$-0.950000\pi$
$739$	−994.736	+	574.311i	−1.34606	+	0.777147i	−0.358369	+	0.933580i	$0.616667\pi$
$740$	74.6615	+	453.502i	0.100894	+	0.612841i
$741$		0			0
$742$	168.028	−	219.595i	0.226453	−	0.295950i
$743$	−720.519	+	720.519i	−0.969743	+	0.969743i	−0.999556	−	0.0298125i	$-0.990509\pi$
$743$	−720.519	+	720.519i	−0.969743	+	0.969743i	0.0298125	+	0.999556i	$0.490509\pi$
$744$		0			0
$745$	728.218	−	329.552i	0.977473	−	0.442351i
$746$	93.9202	+	162.675i	0.125898	+	0.218062i
$747$		0			0
$748$	−236.780	+	236.780i	−0.316551	+	0.316551i
$749$	90.1503	−	218.480i	0.120361	−	0.291696i
$750$		0			0
$751$	301.457	−	522.139i	0.401407	−	0.695258i	−0.592489	−	0.805579i	$-0.701854\pi$
$751$	301.457	−	522.139i	0.401407	−	0.695258i	0.993896	+	0.110321i	$0.0351878\pi$
$752$	131.268	−	489.897i	0.174558	−	0.651459i
$753$		0			0
$754$	−793.664	−	458.222i	−1.05260	−	0.607722i
$755$	−364.732	−	36.0906i	−0.483088	−	0.0478021i
$756$		0			0
$757$	590.863	+	590.863i	0.780532	+	0.780532i	0.979921	−	0.199389i	$-0.0638956\pi$
$757$	590.863	+	590.863i	0.780532	+	0.780532i	−0.199389	+	0.979921i	$0.563896\pi$
$758$	−320.964	−	1197.85i	−0.423435	−	1.58028i
$759$		0			0
$760$	225.932	−	599.460i	0.297280	−	0.788764i
$761$	104.936	−	181.755i	0.137892	−	0.238837i	−0.788806	−	0.614642i	$-0.789301\pi$
$761$	104.936	−	181.755i	0.137892	−	0.238837i	0.926699	+	0.375805i	$0.122634\pi$
$762$		0			0
$763$	−36.7101	+	281.796i	−0.0481128	+	0.369326i
$764$			109.322i			0.143092i
$765$		0			0
$766$	−922.649	−	1598.08i	−1.20450	−	2.08626i
$767$	−215.765	+	805.247i	−0.281311	+	1.04987i
$768$		0			0
$769$			864.088i			1.12365i	0.827256	+	0.561826i	$0.189901\pi$
$769$			864.088i			1.12365i	−0.827256	+	0.561826i	$0.810099\pi$
$770$	−402.116	+	753.941i	−0.522229	+	0.979145i
$771$		0			0
$772$	367.557	−	98.4865i	0.476110	−	0.127573i
$773$	1017.55	+	272.652i	1.31637	+	0.352719i	0.847615	−	0.530612i	$-0.178038\pi$
$773$	1017.55	+	272.652i	1.31637	+	0.352719i	0.468750	+	0.883331i	$0.344704\pi$
$774$		0			0
$775$	647.432	−	736.900i	0.835396	−	0.950839i
$776$	−251.626			−0.324260
$777$		0			0
$778$	774.916	−	774.916i	0.996036	−	0.996036i
$779$	1287.67	+	743.434i	1.65297	+	0.954344i
$780$		0			0
$781$	290.081	+	502.435i	0.371423	+	0.643323i
$782$	−269.406	+	72.1871i	−0.344509	+	0.0923109i
$783$		0			0
$784$	947.045	+	251.007i	1.20797	+	0.320162i
$785$	−259.908	−	316.993i	−0.331093	−	0.403813i
$786$		0			0
$787$	−194.583	+	726.193i	−0.247246	+	0.922736i	0.724995	+	0.688754i	$0.241842\pi$
$787$	−194.583	+	726.193i	−0.247246	+	0.922736i	−0.972241	+	0.233981i	$0.924825\pi$
$788$	345.333	+	92.5318i	0.438240	+	0.117426i
$789$		0			0
$790$	519.694	−	426.106i	0.657840	−	0.539374i
$791$	−138.824	−	1043.53i	−0.175504	−	1.31925i
$792$		0			0
$793$	−535.034	−	1996.77i	−0.674696	−	2.51800i
$794$	−1441.61	+	832.315i	−1.81563	+	1.04826i
$795$		0			0
$796$	96.8712	−	167.786i	0.121697	−	0.210786i
$797$	−545.785	−	545.785i	−0.684799	−	0.684799i	0.276278	−	0.961078i	$-0.410899\pi$
$797$	−545.785	−	545.785i	−0.684799	−	0.684799i	−0.961078	+	0.276278i	$0.910899\pi$
$798$		0			0
$799$			413.717i			0.517794i
$800$	755.171	−	48.8062i	0.943964	−	0.0610077i
$801$		0			0
$802$	−249.476	+	931.058i	−0.311068	+	1.16092i
$803$	52.1654	+	194.684i	0.0649632	+	0.242446i
$804$		0			0
$805$	−206.141	+	128.445i	−0.256076	+	0.159559i
$806$	−1936.34			−2.40240
$807$		0			0
$808$	−579.519	−	155.282i	−0.717227	−	0.192180i
$809$	−1039.15	+	599.951i	−1.28448	+	0.741596i	−0.977664	−	0.210172i	$-0.932598\pi$
$809$	−1039.15	+	599.951i	−1.28448	+	0.741596i	−0.306818	+	0.951768i	$0.599264\pi$
$810$		0			0
$811$	−205.108			−0.252907			−0.126454	−	0.991973i	$-0.540359\pi$
$811$	−205.108			−0.252907			−0.126454	+	0.991973i	$0.540359\pi$
$812$	−267.120	−	34.7982i	−0.328965	−	0.0428550i
$813$		0			0
$814$	−937.845	−	541.465i	−1.15214	−	0.665190i
$815$	216.740	+	81.6879i	0.265939	+	0.100231i
$816$		0			0
$817$	−1328.13	+	355.871i	−1.62562	+	0.435583i
$818$	−303.729	+	303.729i	−0.371307	+	0.371307i
$819$		0			0
$820$	−56.2448	+	568.411i	−0.0685912	+	0.693184i
$821$	565.065	−	978.721i	0.688264	−	1.19211i	−0.284134	−	0.958784i	$-0.591706\pi$
$821$	565.065	−	978.721i	0.688264	−	1.19211i	0.972399	−	0.233325i	$-0.0749604\pi$
$822$		0			0
$823$	241.324	+	64.6626i	0.293225	+	0.0785694i	0.402433	−	0.915450i	$-0.368165\pi$
$823$	241.324	+	64.6626i	0.293225	+	0.0785694i	−0.109208	+	0.994019i	$0.534831\pi$
$824$	432.351	+	249.618i	0.524697	+	0.302934i
$825$		0			0
$826$	94.6882	+	711.762i	0.114635	+	0.861697i
$827$	−89.4358	−	89.4358i	−0.108145	−	0.108145i	0.650964	−	0.759109i	$-0.274365\pi$
$827$	−89.4358	−	89.4358i	−0.108145	−	0.108145i	−0.759109	+	0.650964i	$0.774365\pi$
$828$		0			0
$829$	1109.73	−	640.705i	1.33864	−	0.772865i	0.352035	−	0.935987i	$-0.385490\pi$
$829$	1109.73	−	640.705i	1.33864	−	0.772865i	0.986606	+	0.163122i	$0.0521565\pi$
$830$	−293.379	−	648.285i	−0.353468	−	0.781066i
$831$		0			0
$832$	76.3023	+	76.3023i	0.0917095	+	0.0917095i
$833$	−799.196	+	2.16932i	−0.959419	+	0.00260423i
$834$		0			0
$835$	422.315	−	69.5270i	0.505766	−	0.0832659i
$836$	−276.875	−	479.561i	−0.331190	−	0.573637i
$837$		0			0
$838$	121.428	+	453.177i	0.144903	+	0.540784i
$839$			778.113i			0.927429i	0.885985	+	0.463715i	$0.153484\pi$
$839$			778.113i			0.927429i	−0.885985	+	0.463715i	$0.846516\pi$
$840$		0			0
$841$	496.149			0.589952
$842$	1385.09	−	371.133i	1.64500	−	0.440776i
$843$		0			0
$844$	39.2811	−	22.6790i	0.0465416	−	0.0268708i
$845$	942.915	+	676.333i	1.11588	+	0.800394i
$846$		0			0
$847$	61.3989	+	147.663i	0.0724898	+	0.174336i
$848$	226.638	−	226.638i	0.267261	−	0.267261i
$849$		0			0
$850$	−951.758	+	322.112i	−1.11972	+	0.378956i
$851$	−153.911	−	266.581i	−0.180859	−	0.313256i
$852$		0			0
$853$	−108.028	+	108.028i	−0.126645	+	0.126645i	−0.767588	−	0.640943i	$-0.778543\pi$
$853$	−108.028	+	108.028i	−0.126645	+	0.126645i	0.640943	+	0.767588i	$0.278543\pi$
$854$	−1085.82	−	1411.10i	−1.27145	−	1.65234i
$855$		0			0
$856$	80.1948	−	138.901i	0.0936855	−	0.162268i
$857$	−212.132	+	791.688i	−0.247529	+	0.923790i	0.724567	+	0.689205i	$0.242040\pi$
$857$	−212.132	+	791.688i	−0.247529	+	0.923790i	−0.972096	+	0.234585i	$0.924627\pi$
$858$		0			0
$859$	1179.22	+	680.823i	1.37278	+	0.792577i	0.991278	−	0.131790i	$-0.0420724\pi$
$859$	1179.22	+	680.823i	1.37278	+	0.792577i	0.381505	+	0.924367i	$0.375406\pi$
$860$	−334.903	−	408.460i	−0.389423	−	0.474953i
$861$		0			0
$862$	−999.800	−	999.800i	−1.15986	−	1.15986i
$863$	−277.178	−	1034.44i	−0.321180	−	1.19866i	−0.918097	−	0.396356i	$-0.870275\pi$
$863$	−277.178	−	1034.44i	−0.321180	−	1.19866i	0.596917	−	0.802303i	$-0.296392\pi$
$864$		0			0
$865$	−511.443	−	192.759i	−0.591263	−	0.222843i
$866$	466.660	−	808.279i	0.538868	−	0.933348i
$867$		0			0
$868$	−525.540	+	218.522i	−0.605461	+	0.251753i
$869$			540.392i			0.621855i
$870$		0			0
$871$	76.6521	+	132.765i	0.0880047	+	0.152429i
$872$	−49.9123	+	186.275i	−0.0572389	+	0.213619i
$873$		0			0
$874$		−	461.228i		−	0.527721i
$875$	−711.245	+	509.662i	−0.812852	+	0.582471i
$876$		0			0
$877$	−465.705	+	124.785i	−0.531021	+	0.142287i	−0.514360	−	0.857575i	$-0.671970\pi$
$877$	−465.705	+	124.785i	−0.531021	+	0.142287i	−0.0166612	+	0.999861i	$0.505304\pi$
$878$	919.512	+	246.382i	1.04728	+	0.280618i
$879$		0			0
$880$	−577.293	+	804.838i	−0.656015	+	0.914588i
$881$	1420.89			1.61281			0.806407	−	0.591361i	$-0.201409\pi$
$881$	1420.89			1.61281			0.806407	+	0.591361i	$0.201409\pi$
$882$		0			0
$883$	−429.653	+	429.653i	−0.486583	+	0.486583i	−0.907226	−	0.420643i	$-0.861804\pi$
$883$	−429.653	+	429.653i	−0.486583	+	0.486583i	0.420643	+	0.907226i	$0.361804\pi$
$884$	586.208	+	338.447i	0.663131	+	0.382859i
$885$		0			0
$886$	596.092	+	1032.46i	0.672790	+	1.16531i
$887$	622.797	−	166.878i	0.702139	−	0.188137i	0.109950	−	0.993937i	$-0.464931\pi$
$887$	622.797	−	166.878i	0.702139	−	0.188137i	0.592188	+	0.805800i	$0.298264\pi$
$888$		0			0
$889$	−1262.15	+	167.908i	−1.41974	+	0.188873i
$890$	−546.778	+	448.312i	−0.614357	+	0.503722i
$891$		0			0
$892$	−67.1192	+	250.492i	−0.0752458	+	0.280821i
$893$	−660.845	−	177.073i	−0.740028	−	0.198290i
$894$		0			0
$895$	−124.295	+	1256.13i	−0.138878	+	1.40350i
$896$	869.395	+	358.734i	0.970307	+	0.400372i
$897$		0			0
$898$	135.899	+	507.181i	0.151335	+	0.564789i
$899$	−631.010	+	364.314i	−0.701903	+	0.405244i
$900$		0			0
$901$	−130.725	+	226.423i	−0.145089	+	0.251302i
$902$	−951.649	−	951.649i	−1.05504	−	1.05504i
$903$		0			0
$904$		−	714.391i		−	0.790255i
$905$	−347.089	+	483.896i	−0.383524	+	0.534692i
$906$		0			0
$907$	−291.651	+	1088.45i	−0.321555	+	1.20006i	0.596174	+	0.802855i	$0.296687\pi$
$907$	−291.651	+	1088.45i	−0.321555	+	1.20006i	−0.917730	+	0.397206i	$0.869980\pi$
$908$	8.73774	+	32.6097i	0.00962306	+	0.0359138i
$909$		0			0
$910$	1682.50	+	390.703i	1.84890	+	0.429344i
$911$	−1735.25			−1.90477			−0.952386	−	0.304894i	$-0.901379\pi$
$911$	−1735.25			−1.90477			−0.952386	+	0.304894i	$0.901379\pi$
$912$		0			0
$913$	552.683	+	148.091i	0.605348	+	0.162203i
$914$	1636.12	−	944.612i	1.79006	−	1.03349i
$915$		0			0
$916$	827.403			0.903279
$917$	319.479	+	768.339i	0.348396	+	0.837883i
$918$		0			0
$919$	1173.78	+	677.685i	1.27724	+	0.737415i	0.976340	−	0.216240i	$-0.0693794\pi$
$919$	1173.78	+	677.685i	1.27724	+	0.737415i	0.300901	+	0.953655i	$0.402713\pi$
$920$	−150.163	+	67.9556i	−0.163221	+	0.0738648i
$921$		0			0
$922$	−791.492	+	212.080i	−0.858451	+	0.230021i
$923$	829.267	−	829.267i	0.898448	−	0.898448i
$924$		0			0
$925$	−615.257	−	922.614i	−0.665143	−	0.997421i
$926$	−687.623	+	1191.00i	−0.742573	+	1.28617i
$927$		0			0
$928$	−542.963	−	145.486i	−0.585089	−	0.156774i
$929$	537.999	+	310.614i	0.579117	+	0.334353i	0.760782	−	0.649007i	$-0.224815\pi$
$929$	537.999	+	310.614i	0.579117	+	0.334353i	−0.181666	+	0.983360i	$0.558149\pi$
$930$		0			0
$931$	338.595	−	1277.51i	0.363689	−	1.37219i
$932$	261.854	+	261.854i	0.280959	+	0.280959i
$933$		0			0
$934$	1314.38	−	758.856i	1.40726	−	0.812480i
$935$	284.944	−	756.035i	0.304753	−	0.808593i
$936$		0			0
$937$	601.415	+	601.415i	0.641852	+	0.641852i	0.951011	−	0.309158i	$-0.100047\pi$
$937$	601.415	+	601.415i	0.641852	+	0.641852i	−0.309158	+	0.951011i	$0.600047\pi$
$938$	104.865	+	80.2400i	0.111797	+	0.0855437i
$939$		0			0
$940$	−42.6944	−	259.331i	−0.0454196	−	0.275884i
$941$	−413.011	−	715.356i	−0.438906	−	0.760208i	0.558699	−	0.829370i	$-0.311301\pi$
$941$	−413.011	−	715.356i	−0.438906	−	0.760208i	−0.997605	+	0.0691625i	$0.977967\pi$
$942$		0			0
$943$	−99.0116	−	369.516i	−0.104996	−	0.391852i
$944$			832.314i			0.881688i
$945$		0			0
$946$	1244.56			1.31560
$947$	310.097	−	83.0902i	0.327452	−	0.0877405i	−0.0913479	−	0.995819i	$-0.529118\pi$
$947$	310.097	−	83.0902i	0.327452	−	0.0877405i	0.418800	+	0.908079i	$0.362451\pi$
$948$		0			0
$949$	352.839	−	203.712i	0.371801	−	0.214660i
$950$	−107.165	−	1658.14i	−0.112805	−	1.74541i
$951$		0			0
$952$	−537.804	−	70.0608i	−0.564920	−	0.0735933i
$953$	949.142	−	949.142i	0.995951	−	0.995951i	−0.00404058	−	0.999992i	$-0.501286\pi$
$953$	949.142	−	949.142i	0.995951	−	0.995951i	0.999992	+	0.00404058i	$0.00128616\pi$
$954$		0			0
$955$	−108.752	−	240.311i	−0.113876	−	0.251635i
$956$	386.160	+	668.849i	0.403933	+	0.699633i
$957$		0			0
$958$	−441.865	+	441.865i	−0.461237	+	0.461237i
$959$	510.165	+	662.995i	0.531976	+	0.691340i
$960$		0			0
$961$	−289.252	+	500.998i	−0.300990	+	0.521330i
$962$	−566.574	+	2114.48i	−0.588954	+	2.19801i
$963$		0			0
$964$	1.79283	+	1.03509i	0.00185978	+	0.00107374i
$965$	−709.989	+	582.132i	−0.735739	+	0.603245i
$966$		0			0
$967$	−767.779	−	767.779i	−0.793980	−	0.793980i	0.188158	−	0.982139i	$-0.439748\pi$
$967$	−767.779	−	767.779i	−0.793980	−	0.793980i	−0.982139	+	0.188158i	$0.939748\pi$
$968$	28.0879	+	104.826i	0.0290165	+	0.108291i
$969$		0			0
$970$	−594.597	+	269.082i	−0.612987	+	0.277405i
$971$	−302.931	+	524.692i	−0.311978	+	0.540362i	−0.978791	−	0.204864i	$-0.934325\pi$
$971$	−302.931	+	524.692i	−0.311978	+	0.540362i	0.666812	+	0.745226i	$0.267658\pi$
$972$		0			0
$973$	−785.575	−	601.101i	−0.807374	−	0.617781i
$974$		−	1025.12i		−	1.05249i
$975$		0			0
$976$	−1031.95	−	1787.38i	−1.05732	−	1.83133i
$977$	−210.757	+	786.557i	−0.215719	+	0.805074i	0.770193	+	0.637811i	$0.220160\pi$
$977$	−210.757	+	786.557i	−0.215719	+	0.805074i	−0.985912	+	0.167263i	$0.946507\pi$
$978$		0			0
$979$		−	568.555i		−	0.580751i
$980$	500.737	−	83.8346i	0.510956	−	0.0855455i
$981$		0			0
$982$	675.964	−	181.124i	0.688354	−	0.184444i
$983$	372.638	+	99.8479i	0.379082	+	0.101575i	0.443328	−	0.896359i	$-0.353798\pi$
$983$	372.638	+	99.8479i	0.379082	+	0.101575i	−0.0642463	+	0.997934i	$0.520464\pi$
$984$		0			0
$985$	−851.159	+	140.129i	−0.864121	+	0.142263i
$986$	746.363			0.756961
$987$		0			0
$988$	−791.513	+	791.513i	−0.801127	+	0.801127i
$989$	306.369	+	176.882i	0.309776	+	0.178849i
$990$		0			0
$991$	−89.1517	−	154.415i	−0.0899614	−	0.155818i	0.817533	−	0.575881i	$-0.195341\pi$
$991$	−89.1517	−	154.415i	−0.0899614	−	0.155818i	−0.907495	+	0.420064i	$0.862008\pi$
$992$	−1147.21	+	307.395i	−1.15647	+	0.309874i
$993$		0			0
$994$	385.285	−	933.743i	0.387611	−	0.939379i
$995$	−46.0312	+	465.192i	−0.0462625	+	0.467529i
$996$		0			0
$997$	84.9412	−	317.005i	0.0851968	−	0.317959i	−0.910155	−	0.414269i	$-0.864037\pi$
$997$	84.9412	−	317.005i	0.0851968	−	0.317959i	0.995351	+	0.0963100i	$0.0307040\pi$
$998$	−1968.23	−	527.387i	−1.97218	−	0.528443i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.37.13		64
3.2	odd	2		105.3.v.a.37.4	✓	64
5.3	odd	4	inner	315.3.ca.b.163.4		64
7.4	even	3	inner	315.3.ca.b.172.4		64
15.8	even	4		105.3.v.a.58.13	yes	64
21.11	odd	6		105.3.v.a.67.13	yes	64
35.18	odd	12	inner	315.3.ca.b.298.13		64
105.53	even	12		105.3.v.a.88.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.4	✓	64	3.2	odd	2
105.3.v.a.58.13	yes	64	15.8	even	4
105.3.v.a.67.13	yes	64	21.11	odd	6
105.3.v.a.88.4	yes	64	105.53	even	12
315.3.ca.b.37.13		64	1.1	even	1	trivial
315.3.ca.b.163.4		64	5.3	odd	4	inner
315.3.ca.b.172.4		64	7.4	even	3	inner
315.3.ca.b.298.13		64	35.18	odd	12	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)

\(f(q)\)	\(=\)	\(q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +O(q^{10})\)	\(q+(2.38023 - 0.637781i) q^{2} +(1.79464 - 1.03614i) q^{4} +(-2.91424 + 4.06291i) q^{5} +(-4.25379 + 5.55925i) q^{7} +(-3.35897 + 3.35897i) q^{8} +(-4.34532 + 11.5293i) q^{10} +(-4.95365 - 8.57997i) q^{11} +(-14.1612 + 14.1612i) q^{13} +(-6.57942 + 15.9453i) q^{14} +(-9.99739 + 17.3160i) q^{16} +(4.22139 - 15.7544i) q^{17} +(23.3583 + 13.4859i) q^{19} +(-1.02028 + 10.3110i) q^{20} +(-17.2630 - 17.2630i) q^{22} +(-1.79608 - 6.70305i) q^{23} +(-8.01443 - 23.6806i) q^{25} +(-24.6752 + 42.7387i) q^{26} +(-1.87388 + 14.3844i) q^{28} +18.5702i q^{29} +(19.6183 + 33.9798i) q^{31} +(-7.83442 + 29.2385i) q^{32} -40.1915i q^{34} +(-10.1902 - 33.4837i) q^{35} +(42.8463 - 11.4806i) q^{37} +(64.1994 + 17.2022i) q^{38} +(-3.85835 - 23.4360i) q^{40} +55.1266 q^{41} +(-36.0471 + 36.0471i) q^{43} +(-17.7800 - 10.2653i) q^{44} +(-8.55017 - 14.8093i) q^{46} +(-24.5013 + 6.56509i) q^{47} +(-12.8106 - 47.2958i) q^{49} +(-34.1792 - 51.2538i) q^{50} +(-10.7413 + 40.0872i) q^{52} +(-15.4837 - 4.14884i) q^{53} +(49.2957 + 4.87786i) q^{55} +(-4.38501 - 32.9617i) q^{56} +(11.8437 + 44.2013i) q^{58} +(36.0497 - 20.8133i) q^{59} +(-51.6108 + 89.3925i) q^{61} +(68.3677 + 68.3677i) q^{62} -5.38813i q^{64} +(-16.2665 - 98.8047i) q^{65} +(1.98123 - 7.39406i) q^{67} +(-8.74787 - 32.6475i) q^{68} +(-45.6103 - 73.2000i) q^{70} -58.5591 q^{71} +(-19.6506 - 5.26536i) q^{73} +(94.6621 - 54.6532i) q^{74} +55.8931 q^{76} +(68.7699 + 8.95880i) q^{77} +(-47.2373 - 27.2725i) q^{79} +(-41.2185 - 91.0814i) q^{80} +(131.214 - 35.1587i) q^{82} +(-40.8378 + 40.8378i) q^{83} +(51.7067 + 63.0633i) q^{85} +(-62.8103 + 108.791i) q^{86} +(45.4590 + 12.1807i) q^{88} +(49.6991 + 28.6938i) q^{89} +(-18.4869 - 138.964i) q^{91} +(-10.1686 - 10.1686i) q^{92} +(-54.1316 + 31.2529i) q^{94} +(-122.864 + 55.6015i) q^{95} +(37.4558 + 37.4558i) q^{97} +(-60.6565 - 104.405i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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