LMFDB - Embedded newform 315.3.ca.b.298.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(37,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.ca (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			298.3
Character	$\chi$	$=$	315.298
Dual form			315.3.ca.b.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.88660 - 0.773463i) q^{2} +(4.27013 + 2.46536i) q^{4} +(-0.160937 - 4.99741i) q^{5} +(5.19830 + 4.68804i) q^{7} +(-1.96674 - 1.96674i) q^{8} +O(q^{10})$	\(q+(-2.88660 - 0.773463i) q^{2} +(4.27013 + 2.46536i) q^{4} +(-0.160937 - 4.99741i) q^{5} +(5.19830 + 4.68804i) q^{7} +(-1.96674 - 1.96674i) q^{8} +(-3.40075 + 14.5500i) q^{10} +(-6.71313 + 11.6275i) q^{11} +(-3.94411 - 3.94411i) q^{13} +(-11.3794 - 17.5532i) q^{14} +(-5.70544 - 9.88212i) q^{16} +(2.53643 + 9.46609i) q^{17} +(-4.57992 + 2.64422i) q^{19} +(11.6332 - 21.7363i) q^{20} +(28.3716 - 28.3716i) q^{22} +(1.98091 - 7.39285i) q^{23} +(-24.9482 + 1.60854i) q^{25} +(8.33445 + 14.4357i) q^{26} +(10.6397 + 32.8342i) q^{28} +36.7188i q^{29} +(-9.71723 + 16.8307i) q^{31} +(11.7054 + 43.6852i) q^{32} -29.2867i q^{34} +(22.5914 - 26.7325i) q^{35} +(43.7832 + 11.7317i) q^{37} +(15.2656 - 4.09041i) q^{38} +(-9.51208 + 10.1451i) q^{40} -57.9301 q^{41} +(46.3359 + 46.3359i) q^{43} +(-57.3319 + 33.1006i) q^{44} +(-11.4362 + 19.8080i) q^{46} +(61.3721 + 16.4446i) q^{47} +(5.04463 + 48.7396i) q^{49} +(73.2597 + 14.6533i) q^{50} +(-7.11820 - 26.5655i) q^{52} +(38.8830 - 10.4187i) q^{53} +(59.1877 + 31.6770i) q^{55} +(-1.00355 - 19.4438i) q^{56} +(28.4006 - 105.992i) q^{58} +(60.4517 + 34.9018i) q^{59} +(-39.4523 - 68.3334i) q^{61} +(41.0677 - 41.0677i) q^{62} -89.5118i q^{64} +(-19.0756 + 20.3451i) q^{65} +(28.7353 + 107.241i) q^{67} +(-12.5064 + 46.6746i) q^{68} +(-85.8891 + 59.6925i) q^{70} +121.479 q^{71} +(4.70119 - 1.25968i) q^{73} +(-117.311 - 67.7293i) q^{74} -26.0758 q^{76} +(-89.4070 + 28.9718i) q^{77} +(-116.005 + 66.9753i) q^{79} +(-48.4668 + 30.1028i) q^{80} +(167.221 + 44.8068i) q^{82} +(-99.6896 - 99.6896i) q^{83} +(46.8977 - 14.1990i) q^{85} +(-97.9142 - 169.592i) q^{86} +(36.0712 - 9.66526i) q^{88} +(20.5641 - 11.8727i) q^{89} +(-2.01253 - 38.9928i) q^{91} +(26.6847 - 26.6847i) q^{92} +(-164.438 - 94.9381i) q^{94} +(13.9513 + 22.4622i) q^{95} +(-40.9086 + 40.9086i) q^{97} +(23.1364 - 144.594i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8	$ 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8} - 16 q^{10} - 16 q^{11} + 80 q^{16} - 56 q^{17} - 96 q^{22} - 72 q^{23} - 4 q^{25} + 288 q^{26} - 380 q^{28} - 136 q^{31} + 48 q^{32} - 76 q^{35} - 28 q^{37} + 68 q^{38} + 164 q^{40} - 128 q^{41} + 344 q^{43} + 240 q^{46} - 412 q^{47} + 72 q^{50} + 388 q^{52} + 40 q^{53} - 8 q^{55} + 864 q^{56} + 56 q^{58} - 216 q^{61} + 912 q^{62} - 20 q^{65} - 368 q^{67} + 492 q^{68} + 416 q^{70} - 784 q^{71} - 316 q^{73} - 32 q^{76} - 844 q^{77} - 908 q^{80} + 556 q^{82} - 1408 q^{83} - 536 q^{85} - 1024 q^{86} + 372 q^{88} - 1064 q^{91} + 1704 q^{92} - 260 q^{95} + 352 q^{97} - 272 q^{98}+O(q^{100}) $ 64 * q - 4 * q^5 - 4 * q^7 - 24 * q^8 - 16 * q^10 - 16 * q^11 + 80 * q^16 - 56 * q^17 - 96 * q^22 - 72 * q^23 - 4 * q^25 + 288 * q^26 - 380 * q^28 - 136 * q^31 + 48 * q^32 - 76 * q^35 - 28 * q^37 + 68 * q^38 + 164 * q^40 - 128 * q^41 + 344 * q^43 + 240 * q^46 - 412 * q^47 + 72 * q^50 + 388 * q^52 + 40 * q^53 - 8 * q^55 + 864 * q^56 + 56 * q^58 - 216 * q^61 + 912 * q^62 - 20 * q^65 - 368 * q^67 + 492 * q^68 + 416 * q^70 - 784 * q^71 - 316 * q^73 - 32 * q^76 - 844 * q^77 - 908 * q^80 + 556 * q^82 - 1408 * q^83 - 536 * q^85 - 1024 * q^86 + 372 * q^88 - 1064 * q^91 + 1704 * q^92 - 260 * q^95 + 352 * q^97 - 272 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.88660	−	0.773463i	−1.44330	−	0.386731i	−0.549613	−	0.835419i	$-0.685225\pi$
$2$	−2.88660	−	0.773463i	−1.44330	−	0.386731i	−0.893688	+	0.448688i	$0.851891\pi$
$3$		0			0
$3$		0			0
$4$	4.27013	+	2.46536i	1.06753	+	0.616340i
$5$	−0.160937	−	4.99741i	−0.0321874	−	0.999482i
$5$	−0.160937	−	4.99741i	−0.0321874	−	0.999482i
$6$		0			0
$7$	5.19830	+	4.68804i	0.742614	+	0.669719i
$7$	5.19830	+	4.68804i	0.742614	+	0.669719i
$8$	−1.96674	−	1.96674i	−0.245842	−	0.245842i
$9$		0			0
$10$	−3.40075	+	14.5500i	−0.340075	+	1.45500i
$11$	−6.71313	+	11.6275i	−0.610285	+	1.05704i	0.380907	+	0.924613i	$0.375612\pi$
$11$	−6.71313	+	11.6275i	−0.610285	+	1.05704i	−0.991192	+	0.132431i	$0.957722\pi$
$12$		0			0
$13$	−3.94411	−	3.94411i	−0.303393	−	0.303393i	0.538947	−	0.842340i	$-0.318822\pi$
$13$	−3.94411	−	3.94411i	−0.303393	−	0.303393i	−0.842340	+	0.538947i	$0.818822\pi$
$14$	−11.3794	−	17.5532i	−0.812814	−	1.25380i
$15$		0			0
$16$	−5.70544	−	9.88212i	−0.356590	−	0.617632i
$17$	2.53643	+	9.46609i	0.149202	+	0.556829i	0.999532	+	0.0305799i	$0.00973539\pi$
$17$	2.53643	+	9.46609i	0.149202	+	0.556829i	−0.850330	+	0.526249i	$0.823598\pi$
$18$		0			0
$19$	−4.57992	+	2.64422i	−0.241049	+	0.139169i	−0.615659	−	0.788013i	$-0.711110\pi$
$19$	−4.57992	+	2.64422i	−0.241049	+	0.139169i	0.374610	+	0.927182i	$0.377777\pi$
$20$	11.6332	−	21.7363i	0.581659	−	1.08682i
$21$		0			0
$22$	28.3716	−	28.3716i	1.28962	−	1.28962i
$23$	1.98091	−	7.39285i	0.0861264	−	0.321428i	−0.909399	−	0.415925i	$-0.863458\pi$
$23$	1.98091	−	7.39285i	0.0861264	−	0.321428i	0.995525	+	0.0944974i	$0.0301244\pi$
$24$		0			0
$25$	−24.9482	+	1.60854i	−0.997928	+	0.0643415i
$26$	8.33445	+	14.4357i	0.320556	+	0.555219i
$27$		0			0
$28$	10.6397	+	32.8342i	0.379990	+	1.17265i
$29$			36.7188i			1.26616i	0.774085	+	0.633082i	$0.218211\pi$
$29$			36.7188i			1.26616i	−0.774085	+	0.633082i	$0.781789\pi$
$30$		0			0
$31$	−9.71723	+	16.8307i	−0.313459	+	0.542927i	−0.979109	−	0.203337i	$-0.934821\pi$
$31$	−9.71723	+	16.8307i	−0.313459	+	0.542927i	0.665650	+	0.746264i	$0.268155\pi$
$32$	11.7054	+	43.6852i	0.365794	+	1.36516i
$33$		0			0
$34$		−	29.2867i		−	0.861373i
$35$	22.5914	−	26.7325i	0.645470	−	0.763786i
$36$		0			0
$37$	43.7832	+	11.7317i	1.18333	+	0.317072i	0.796246	−	0.604973i	$-0.206816\pi$
$37$	43.7832	+	11.7317i	1.18333	+	0.317072i	0.387083	+	0.922045i	$0.373483\pi$
$38$	15.2656	−	4.09041i	0.401727	−	0.107642i
$39$		0			0
$40$	−9.51208	+	10.1451i	−0.237802	+	0.253628i
$41$	−57.9301			−1.41293			−0.706464	−	0.707749i	$-0.749711\pi$
$41$	−57.9301			−1.41293			−0.706464	+	0.707749i	$0.749711\pi$
$42$		0			0
$43$	46.3359	+	46.3359i	1.07758	+	1.07758i	0.996726	+	0.0808525i	$0.0257643\pi$
$43$	46.3359	+	46.3359i	1.07758	+	1.07758i	0.0808525	+	0.996726i	$0.474236\pi$
$44$	−57.3319	+	33.1006i	−1.30300	+	0.752286i
$45$		0			0
$46$	−11.4362	+	19.8080i	−0.248613	+	0.430610i
$47$	61.3721	+	16.4446i	1.30579	+	0.349885i	0.843636	−	0.536915i	$-0.180410\pi$
$47$	61.3721	+	16.4446i	1.30579	+	0.349885i	0.462153	+	0.886800i	$0.347077\pi$
$48$		0			0
$49$	5.04463	+	48.7396i	0.102952	+	0.994686i
$50$	73.2597	+	14.6533i	1.46519	+	0.293066i
$51$		0			0
$52$	−7.11820	−	26.5655i	−0.136889	−	0.510875i
$53$	38.8830	−	10.4187i	0.733641	−	0.196578i	0.127391	−	0.991853i	$-0.459340\pi$
$53$	38.8830	−	10.4187i	0.733641	−	0.196578i	0.606250	+	0.795274i	$0.292673\pi$
$54$		0			0
$55$	59.1877	+	31.6770i	1.07614	+	0.575945i
$56$	−1.00355	−	19.4438i	−0.0179206	−	0.347212i
$57$		0			0
$58$	28.4006	−	105.992i	0.489666	−	1.82746i
$59$	60.4517	+	34.9018i	1.02461	+	0.591556i	0.915434	−	0.402467i	$-0.131847\pi$
$59$	60.4517	+	34.9018i	1.02461	+	0.591556i	0.109171	+	0.994023i	$0.465181\pi$
$60$		0			0
$61$	−39.4523	−	68.3334i	−0.646759	−	1.12022i	−0.983892	−	0.178763i	$-0.942790\pi$
$61$	−39.4523	−	68.3334i	−0.646759	−	1.12022i	0.337133	−	0.941457i	$-0.390543\pi$
$62$	41.0677	−	41.0677i	0.662383	−	0.662383i
$63$		0			0
$64$		−	89.5118i		−	1.39862i
$65$	−19.0756	+	20.3451i	−0.293470	+	0.313001i
$66$		0			0
$67$	28.7353	+	107.241i	0.428885	+	1.60062i	0.755291	+	0.655389i	$0.227495\pi$
$67$	28.7353	+	107.241i	0.428885	+	1.60062i	−0.326407	+	0.945229i	$0.605838\pi$
$68$	−12.5064	+	46.6746i	−0.183918	+	0.686392i
$69$		0			0
$70$	−85.8891	+	59.6925i	−1.22699	+	0.852750i
$71$	121.479			1.71097			0.855486	−	0.517826i	$-0.173259\pi$
$71$	121.479			1.71097			0.855486	+	0.517826i	$0.173259\pi$
$72$		0			0
$73$	4.70119	−	1.25968i	0.0643998	−	0.0172559i	−0.226475	−	0.974017i	$-0.572720\pi$
$73$	4.70119	−	1.25968i	0.0643998	−	0.0172559i	0.290875	+	0.956761i	$0.406054\pi$
$74$	−117.311	−	67.7293i	−1.58528	−	0.915261i
$75$		0			0
$76$	−26.0758			−0.343103
$77$	−89.4070	+	28.9718i	−1.16113	+	0.376257i
$78$		0			0
$79$	−116.005	+	66.9753i	−1.46841	+	0.847788i	−0.999374	−	0.0353889i	$-0.988733\pi$
$79$	−116.005	+	66.9753i	−1.46841	+	0.847788i	−0.469039	+	0.883177i	$0.655400\pi$
$80$	−48.4668	+	30.1028i	−0.605835	+	0.376285i
$81$		0			0
$82$	167.221	+	44.8068i	2.03928	+	0.546424i
$83$	−99.6896	−	99.6896i	−1.20108	−	1.20108i	−0.973838	−	0.227242i	$-0.927029\pi$
$83$	−99.6896	−	99.6896i	−1.20108	−	1.20108i	−0.227242	−	0.973838i	$-0.572971\pi$
$84$		0			0
$85$	46.8977	−	14.1990i	0.551738	−	0.167047i
$86$	−97.9142	−	169.592i	−1.13854	−	1.97200i
$87$		0			0
$88$	36.0712	−	9.66526i	0.409900	−	0.109832i
$89$	20.5641	−	11.8727i	0.231058	−	0.133401i	−0.380002	−	0.924986i	$-0.624077\pi$
$89$	20.5641	−	11.8727i	0.231058	−	0.133401i	0.611060	+	0.791584i	$0.290743\pi$
$90$		0			0
$91$	−2.01253	−	38.9928i	−0.0221158	−	0.428492i
$92$	26.6847	−	26.6847i	0.290052	−	0.290052i
$93$		0			0
$94$	−164.438	−	94.9381i	−1.74934	−	1.00998i
$95$	13.9513	+	22.4622i	0.146856	+	0.236444i
$96$		0			0
$97$	−40.9086	+	40.9086i	−0.421738	+	0.421738i	−0.885802	−	0.464064i	$-0.846391\pi$
$97$	−40.9086	+	40.9086i	−0.421738	+	0.421738i	0.464064	+	0.885802i	$0.346391\pi$
$98$	23.1364	−	144.594i	0.236086	−	1.47545i
$99$		0			0
$100$	−110.498	−	54.6376i	−1.10498	−	0.546376i
$101$	−34.1609	+	59.1683i	−0.338226	+	0.585825i	−0.984099	−	0.177620i	$-0.943160\pi$
$101$	−34.1609	+	59.1683i	−0.338226	+	0.585825i	0.645873	+	0.763445i	$0.276494\pi$
$102$		0			0
$103$	32.8404	−	122.562i	0.318839	−	1.18992i	−0.601524	−	0.798855i	$-0.705439\pi$
$103$	32.8404	−	122.562i	0.318839	−	1.18992i	0.920362	−	0.391067i	$-0.127894\pi$
$104$			15.5141i			0.149174i
$105$		0			0
$106$	−120.298			−1.13489
$107$	−58.6252	−	15.7086i	−0.547899	−	0.146809i	−0.0257581	−	0.999668i	$-0.508200\pi$
$107$	−58.6252	−	15.7086i	−0.547899	−	0.146809i	−0.522141	+	0.852859i	$0.674867\pi$
$108$		0			0
$109$	18.6575	+	10.7719i	0.171170	+	0.0988251i	0.583137	−	0.812374i	$-0.301825\pi$
$109$	18.6575	+	10.7719i	0.171170	+	0.0988251i	−0.411967	+	0.911199i	$0.635158\pi$
$110$	−146.350	−	137.218i	−1.33046	−	1.24744i
$111$		0			0
$112$	16.6691	−	78.1175i	0.148831	−	0.697478i
$113$	−12.3946	−	12.3946i	−0.109686	−	0.109686i	0.650134	−	0.759820i	$-0.274713\pi$
$113$	−12.3946	−	12.3946i	−0.109686	−	0.109686i	−0.759820	+	0.650134i	$0.774713\pi$
$114$		0			0
$115$	−37.2639	−	8.70962i	−0.324034	−	0.0757358i
$116$	−90.5250	+	156.794i	−0.780388	+	1.35167i
$117$		0			0
$118$	−147.505	−	147.505i	−1.25004	−	1.25004i
$119$	−31.1923	+	61.0985i	−0.262120	+	0.513432i
$120$		0			0
$121$	−29.6323	−	51.3247i	−0.244895	−	0.424171i
$122$	61.0298	+	227.766i	0.500244	+	1.86694i
$123$		0			0
$124$	−82.9877	+	47.9129i	−0.669255	+	0.386395i
$125$	12.0536	+	124.417i	0.0964288	+	0.995340i
$126$		0			0
$127$	−21.0785	+	21.0785i	−0.165973	+	0.165973i	−0.785207	−	0.619234i	$-0.787443\pi$
$127$	−21.0785	+	21.0785i	−0.165973	+	0.165973i	0.619234	+	0.785207i	$0.287443\pi$
$128$	−22.4125	+	83.6445i	−0.175097	+	0.653472i
$129$		0			0
$130$	70.7998	−	43.9739i	0.544614	−	0.338261i
$131$	62.6091	+	108.442i	0.477932	+	0.827803i	0.999680	−	0.0252971i	$-0.00805318\pi$
$131$	62.6091	+	108.442i	0.477932	+	0.827803i	−0.521748	+	0.853100i	$0.674720\pi$
$132$		0			0
$133$	−36.2040	−	7.72540i	−0.272211	−	0.0580857i
$134$		−	331.789i		−	2.47604i
$135$		0			0
$136$	13.6288	−	23.6058i	0.100212	−	0.173572i
$137$	9.48345	+	35.3927i	0.0692222	+	0.258341i	0.991861	−	0.127324i	$-0.0406388\pi$
$137$	9.48345	+	35.3927i	0.0692222	+	0.258341i	−0.922639	+	0.385665i	$0.873972\pi$
$138$		0			0
$139$			84.6491i			0.608986i	0.952515	+	0.304493i	$0.0984870\pi$
$139$			84.6491i			0.608986i	−0.952515	+	0.304493i	$0.901513\pi$
$140$	162.374	−	58.4552i	1.15981	−	0.417537i
$141$		0			0
$142$	−350.662	−	93.9595i	−2.46945	−	0.661687i
$143$	72.3374	−	19.3828i	0.505856	−	0.135544i
$144$		0			0
$145$	183.499	−	5.90941i	1.26551	−	0.0407546i
$146$	−14.5448			−0.0996217
$147$		0			0
$148$	158.037	+	158.037i	1.06782	+	1.06782i
$149$	−28.2589	+	16.3153i	−0.189657	+	0.109499i	−0.591822	−	0.806069i	$-0.701591\pi$
$149$	−28.2589	+	16.3153i	−0.189657	+	0.109499i	0.402165	+	0.915567i	$0.368258\pi$
$150$		0			0
$151$	78.0454	−	135.179i	0.516857	−	0.895223i	−0.482951	−	0.875647i	$-0.660435\pi$
$151$	78.0454	−	135.179i	0.516857	−	0.895223i	0.999808	−	0.0195756i	$-0.00623149\pi$
$152$	14.2080	+	3.80702i	0.0934737	+	0.0250462i
$153$		0			0
$154$	280.491	−	14.4770i	1.82137	−	0.0940063i
$155$	85.6740	+	45.8523i	0.552735	+	0.295821i
$156$		0			0
$157$	17.2166	+	64.2534i	0.109660	+	0.409257i	0.998832	−	0.0483159i	$-0.0153854\pi$
$157$	17.2166	+	64.2534i	0.109660	+	0.409257i	−0.889172	+	0.457573i	$0.848719\pi$
$158$	386.662	−	103.606i	2.44723	−	0.655733i
$159$		0			0
$160$	216.429	−	65.5272i	1.35268	−	0.409545i
$161$	44.9553	−	29.1437i	0.279225	−	0.181017i
$162$		0			0
$163$	−15.1289	+	56.4617i	−0.0928152	+	0.346391i	−0.996679	−	0.0814289i	$-0.974052\pi$
$163$	−15.1289	+	56.4617i	−0.0928152	+	0.346391i	0.903864	+	0.427820i	$0.140718\pi$
$164$	−247.369	−	142.818i	−1.50835	−	0.870844i
$165$		0			0
$166$	210.658	+	364.871i	1.26902	+	2.19802i
$167$	93.0212	−	93.0212i	0.557013	−	0.557013i	−0.371443	−	0.928456i	$-0.621137\pi$
$167$	93.0212	−	93.0212i	0.557013	−	0.557013i	0.928456	+	0.371443i	$0.121137\pi$
$168$		0			0
$169$		−	137.888i		−	0.815905i
$170$	−146.358	+	4.71331i	−0.860927	+	0.0277254i
$171$		0			0
$172$	83.6255	+	312.095i	0.486195	+	1.81450i
$173$	−62.6748	+	233.906i	−0.362282	+	1.35206i	0.508786	+	0.860893i	$0.330094\pi$
$173$	−62.6748	+	233.906i	−0.362282	+	1.35206i	−0.871068	+	0.491162i	$0.836572\pi$
$174$		0			0
$175$	−137.229	−	108.596i	−0.784166	−	0.620551i
$176$	153.206			0.870486
$177$		0			0
$178$	−68.5435	+	18.3662i	−0.385076	+	0.103181i
$179$	−228.989	−	132.207i	−1.27927	−	0.738585i	−0.302553	−	0.953133i	$-0.597839\pi$
$179$	−228.989	−	132.207i	−1.27927	−	0.738585i	−0.976713	+	0.214548i	$0.931172\pi$
$180$		0			0
$181$	286.020			1.58022			0.790110	−	0.612965i	$-0.210023\pi$
$181$	286.020			1.58022			0.790110	+	0.612965i	$0.210023\pi$
$182$	−24.3501	+	114.113i	−0.133792	+	0.626996i
$183$		0			0
$184$	−18.4357	+	10.6439i	−0.100194	+	0.0578471i
$185$	51.5816	−	220.690i	0.278819	−	1.19292i
$186$		0			0
$187$	−127.094	−	34.0548i	−0.679649	−	0.182111i
$188$	221.525	+	221.525i	1.17832	+	1.17832i
$189$		0			0
$190$	−22.8983	−	75.6303i	−0.120517	−	0.398054i
$191$	−38.1037	−	65.9976i	−0.199496	−	0.345537i	0.748869	−	0.662718i	$-0.230597\pi$
$191$	−38.1037	−	65.9976i	−0.199496	−	0.345537i	−0.948365	+	0.317181i	$0.897264\pi$
$192$		0			0
$193$	−236.585	+	63.3927i	−1.22583	+	0.328459i	−0.812953	−	0.582329i	$-0.802142\pi$
$193$	−236.585	+	63.3927i	−1.22583	+	0.328459i	−0.412874	+	0.910788i	$0.635475\pi$
$194$	149.728	−	86.4456i	0.771795	−	0.445596i
$195$		0			0
$196$	−98.6195	+	220.561i	−0.503161	+	1.12531i
$197$	−136.078	+	136.078i	−0.690750	+	0.690750i	−0.962397	−	0.271647i	$-0.912432\pi$
$197$	−136.078	+	136.078i	−0.690750	+	0.690750i	0.271647	+	0.962397i	$0.412432\pi$
$198$		0			0
$199$	107.888	+	62.2892i	0.542151	+	0.313011i	0.745950	−	0.666002i	$-0.231996\pi$
$199$	107.888	+	62.2892i	0.542151	+	0.313011i	−0.203799	+	0.979013i	$0.565329\pi$
$200$	52.2302	+	45.9030i	0.261151	+	0.229515i
$201$		0			0
$202$	144.373	−	144.373i	0.714720	−	0.714720i
$203$	−172.139	+	190.875i	−0.847975	+	0.940272i
$204$		0			0
$205$	9.32309	+	289.500i	0.0454785	+	1.41220i
$206$	−189.594	+	328.387i	−0.920360	+	1.59411i
$207$		0			0
$208$	−16.4733	+	61.4790i	−0.0791984	+	0.295572i
$209$		−	71.0040i		−	0.339732i
$210$		0			0
$211$	−25.5567			−0.121122			−0.0605610	−	0.998164i	$-0.519289\pi$
$211$	−25.5567			−0.121122			−0.0605610	+	0.998164i	$0.519289\pi$
$212$	191.721	+	51.3715i	0.904344	+	0.242318i
$213$		0			0
$214$	157.078	+	90.6889i	0.734008	+	0.423780i
$215$	224.102	−	239.017i	1.04234	−	1.11170i
$216$		0			0
$217$	−129.416	+	41.9365i	−0.596388	+	0.193256i
$218$	−45.5252	−	45.5252i	−0.208831	−	0.208831i
$219$		0			0
$220$	174.644	+	281.184i	0.793836	+	1.27811i
$221$	27.3313	−	47.3393i	0.123671	−	0.214205i
$222$		0			0
$223$	−58.9789	−	58.9789i	−0.264479	−	0.264479i	0.562392	−	0.826871i	$-0.309881\pi$
$223$	−58.9789	−	58.9789i	−0.264479	−	0.264479i	−0.826871	+	0.562392i	$0.809881\pi$
$224$	−143.949	+	281.964i	−0.642631	+	1.25877i
$225$		0			0
$226$	26.1914	+	45.3649i	0.115891	+	0.200730i
$227$	−106.629	−	397.945i	−0.469732	−	1.75306i	−0.640704	−	0.767788i	$-0.721358\pi$
$227$	−106.629	−	397.945i	−0.469732	−	1.75306i	0.170972	−	0.985276i	$-0.445309\pi$
$228$		0			0
$229$	−325.569	+	187.967i	−1.42170	+	0.820818i	−0.996444	−	0.0842553i	$-0.973149\pi$
$229$	−325.569	+	187.967i	−1.42170	+	0.820818i	−0.425255	+	0.905074i	$0.639816\pi$
$230$	100.829	+	53.9634i	0.438389	+	0.234624i
$231$		0			0
$232$	72.2163	−	72.2163i	0.311277	−	0.311277i
$233$	−6.28523	+	23.4568i	−0.0269752	+	0.100673i	−0.978101	−	0.208131i	$-0.933262\pi$
$233$	−6.28523	+	23.4568i	−0.0269752	+	0.100673i	0.951126	+	0.308804i	$0.0999287\pi$
$234$		0			0
$235$	72.3034	−	309.348i	0.307674	−	1.31638i
$236$	172.091	+	298.070i	0.729199	+	1.26301i
$237$		0			0
$238$	137.297	−	152.241i	0.576878	−	0.639668i
$239$			50.6675i			0.211998i	0.994366	+	0.105999i	$0.0338040\pi$
$239$			50.6675i			0.211998i	−0.994366	+	0.105999i	$0.966196\pi$
$240$		0			0
$241$	58.3080	−	100.992i	0.241942	−	0.419055i	−0.719326	−	0.694673i	$-0.755549\pi$
$241$	58.3080	−	100.992i	0.241942	−	0.419055i	0.961267	+	0.275618i	$0.0888824\pi$
$242$	45.8390	+	171.074i	0.189417	+	0.706916i
$243$		0			0
$244$		−	389.057i		−	1.59449i
$245$	242.760	−	33.0541i	0.990857	−	0.134915i
$246$		0			0
$247$	28.4928	+	7.63463i	0.115356	+	0.0309094i
$248$	52.2129	−	13.9904i	0.210536	−	0.0564130i
$249$		0			0
$250$	61.4383	−	368.467i	0.245753	−	1.47387i
$251$	−320.629			−1.27741			−0.638704	−	0.769452i	$-0.720529\pi$
$251$	−320.629			−1.27741			−0.638704	+	0.769452i	$0.720529\pi$
$252$		0			0
$253$	72.6621	+	72.6621i	0.287202	+	0.287202i
$254$	77.1488	−	44.5419i	0.303736	−	0.175362i
$255$		0			0
$256$	−49.6319	+	85.9650i	−0.193875	+	0.335801i
$257$	191.876	+	51.4131i	0.746600	+	0.200051i	0.612009	−	0.790850i	$-0.290361\pi$
$257$	191.876	+	51.4131i	0.746600	+	0.200051i	0.134591	+	0.990901i	$0.457028\pi$
$258$		0			0
$259$	172.600	+	266.242i	0.666407	+	1.02796i
$260$	−131.613	+	39.8480i	−0.506204	+	0.153261i
$261$		0			0
$262$	−96.8516	−	361.455i	−0.369663	−	1.37960i
$263$	15.3255	−	4.10646i	0.0582720	−	0.0156139i	−0.229565	−	0.973293i	$-0.573730\pi$
$263$	15.3255	−	4.10646i	0.0582720	−	0.0156139i	0.287837	+	0.957679i	$0.407064\pi$
$264$		0			0
$265$	−58.3240	−	192.637i	−0.220091	−	0.726933i
$266$	98.5313	+	50.3026i	0.370418	+	0.189108i
$267$		0			0
$268$	−141.686	+	528.778i	−0.528677	+	1.97305i
$269$	89.8942	+	51.9004i	0.334179	+	0.192938i	0.657695	−	0.753284i	$-0.271532\pi$
$269$	89.8942	+	51.9004i	0.334179	+	0.192938i	−0.323516	+	0.946223i	$0.604865\pi$
$270$		0			0
$271$	78.5571	+	136.065i	0.289878	+	0.502084i	0.973781	−	0.227490i	$-0.0730518\pi$
$271$	78.5571	+	136.065i	0.289878	+	0.502084i	−0.683902	+	0.729574i	$0.739718\pi$
$272$	79.0736	−	79.0736i	0.290712	−	0.290712i
$273$		0			0
$274$		−	109.500i		−	0.399634i
$275$	148.777	−	300.883i	0.541009	−	1.09412i
$276$		0			0
$277$	54.1211	+	201.983i	0.195383	+	0.729179i	0.992167	+	0.124916i	$0.0398660\pi$
$277$	54.1211	+	201.983i	0.195383	+	0.729179i	−0.796784	+	0.604264i	$0.793467\pi$
$278$	65.4729	−	244.348i	0.235514	−	0.878950i
$279$		0			0
$280$	−97.0073	+	8.14441i	−0.346455	+	0.0290872i
$281$	−454.909			−1.61889			−0.809446	−	0.587194i	$-0.800232\pi$
$281$	−454.909			−1.61889			−0.809446	+	0.587194i	$0.800232\pi$
$282$		0			0
$283$	99.1636	−	26.5708i	0.350401	−	0.0938898i	−0.0793253	−	0.996849i	$-0.525277\pi$
$283$	99.1636	−	26.5708i	0.350401	−	0.0938898i	0.429727	+	0.902959i	$0.358610\pi$
$284$	518.731	+	299.489i	1.82652	+	1.05454i
$285$		0			0
$286$	−223.801			−0.782522
$287$	−301.138	−	271.578i	−1.04926	−	0.946266i
$288$		0			0
$289$	167.108	−	96.4798i	0.578228	−	0.333840i
$290$	−534.259	−	124.871i	−1.84227	−	0.430591i
$291$		0			0
$292$	23.1802	+	6.21112i	0.0793843	+	0.0212710i
$293$	−102.346	−	102.346i	−0.349302	−	0.349302i	0.510547	−	0.859850i	$-0.329443\pi$
$293$	−102.346	−	102.346i	−0.349302	−	0.349302i	−0.859850	+	0.510547i	$0.829443\pi$
$294$		0			0
$295$	164.690	−	307.719i	0.558270	−	1.04311i
$296$	−63.0369	−	109.183i	−0.212963	−	0.368862i
$297$		0			0
$298$	94.1914	−	25.2385i	0.316079	−	0.0846930i
$299$	−36.9711	+	21.3453i	−0.123649	+	0.0713889i
$300$		0			0
$301$	23.6435	+	458.092i	0.0785498	+	1.52190i
$302$	−329.842	+	329.842i	−1.09219	+	1.09219i
$303$		0			0
$304$	52.2610	+	30.1729i	0.171911	+	0.0992529i
$305$	−335.141	+	208.157i	−1.09882	+	0.682481i
$306$		0			0
$307$	29.1999	−	29.1999i	0.0951137	−	0.0951137i	−0.657949	−	0.753063i	$-0.728576\pi$
$307$	29.1999	−	29.1999i	0.0951137	−	0.0951137i	0.753063	+	0.657949i	$0.228576\pi$
$308$	−453.205	−	96.7072i	−1.47144	−	0.313985i
$309$		0			0
$310$	−211.842	−	198.623i	−0.683360	−	0.640719i
$311$	201.089	−	348.297i	0.646589	−	1.11992i	−0.337343	−	0.941382i	$-0.609528\pi$
$311$	201.089	−	348.297i	0.646589	−	1.11992i	0.983932	−	0.178543i	$-0.0571384\pi$
$312$		0			0
$313$	74.2751	−	277.198i	0.237301	−	0.885618i	−0.739798	−	0.672829i	$-0.765079\pi$
$313$	74.2751	−	277.198i	0.237301	−	0.885618i	0.977098	−	0.212788i	$-0.0682545\pi$
$314$		−	198.790i		−	0.633091i
$315$		0			0
$316$	−660.473			−2.09010
$317$	335.924	+	90.0106i	1.05970	+	0.283945i	0.746254	−	0.665662i	$-0.231851\pi$
$317$	335.924	+	90.0106i	1.05970	+	0.283945i	0.313444	+	0.949607i	$0.398517\pi$
$318$		0			0
$319$	−426.947	−	246.498i	−1.33839	−	0.772721i
$320$	−447.327	+	14.4058i	−1.39790	+	0.0450180i
$321$		0			0
$322$	−152.310	+	49.3549i	−0.473011	+	0.153276i
$323$	−36.6471	−	36.6471i	−0.113458	−	0.113458i
$324$		0			0
$325$	104.743	+	92.0542i	0.322285	+	0.283244i
$326$	87.3421	−	151.281i	0.267921	−	0.464052i
$327$		0			0
$328$	113.933	+	113.933i	0.347358	+	0.347358i
$329$	241.938	+	373.199i	0.735373	+	1.13434i
$330$		0			0
$331$	−36.2176	−	62.7307i	−0.109419	−	0.189519i	0.806116	−	0.591757i	$-0.201566\pi$
$331$	−36.2176	−	62.7307i	−0.109419	−	0.189519i	−0.915535	+	0.402239i	$0.868232\pi$
$332$	−179.917	−	671.458i	−0.541918	−	2.02246i
$333$		0			0
$334$	−340.464	+	196.567i	−1.01935	+	0.588523i
$335$	531.305	−	160.861i	1.58598	−	0.480182i
$336$		0			0
$337$	−255.737	+	255.737i	−0.758865	+	0.758865i	−0.976116	−	0.217251i	$-0.930291\pi$
$337$	−255.737	+	255.737i	−0.758865	+	0.758865i	0.217251	+	0.976116i	$0.430291\pi$
$338$	−106.651	+	398.028i	−0.315536	+	1.17760i
$339$		0			0
$340$	235.265	+	54.9881i	0.691956	+	0.161730i
$341$	−130.466	−	225.974i	−0.382599	−	0.662680i
$342$		0			0
$343$	−202.270	+	277.013i	−0.589707	+	0.807617i
$344$		−	182.261i		−	0.529829i
$345$		0			0
$346$	361.835	−	626.716i	1.04576	−	1.81132i
$347$	74.6974	+	278.775i	0.215266	+	0.803385i	0.986073	+	0.166315i	$0.0531869\pi$
$347$	74.6974	+	278.775i	0.215266	+	0.803385i	−0.770806	+	0.637070i	$0.780146\pi$
$348$		0			0
$349$		−	480.492i		−	1.37677i	−0.725347	−	0.688384i	$-0.758320\pi$
$349$		−	480.492i		−	1.37677i	0.725347	−	0.688384i	$-0.241680\pi$
$350$	312.131	+	419.616i	0.891802	+	1.19890i
$351$		0			0
$352$	−586.529	−	157.160i	−1.66627	−	0.446477i
$353$	93.2268	−	24.9800i	0.264098	−	0.0707650i	−0.124340	−	0.992240i	$-0.539681\pi$
$353$	93.2268	−	24.9800i	0.264098	−	0.0707650i	0.388438	+	0.921475i	$0.373015\pi$
$354$		0			0
$355$	−19.5505	−	607.080i	−0.0550718	−	1.71009i
$356$	117.082			0.328882
$357$		0			0
$358$	558.742	+	558.742i	1.56073	+	1.56073i
$359$	−280.865	+	162.157i	−0.782353	+	0.451692i	−0.837264	−	0.546799i	$-0.815846\pi$
$359$	−280.865	+	162.157i	−0.782353	+	0.451692i	0.0549104	+	0.998491i	$0.482513\pi$
$360$		0			0
$361$	−166.516	+	288.415i	−0.461264	+	0.798932i
$362$	−825.626	−	221.226i	−2.28073	−	0.611121i
$363$		0			0
$364$	87.5375	−	171.466i	0.240488	−	0.471060i
$365$	−7.05173	−	23.2910i	−0.0193198	−	0.0638110i
$366$		0			0
$367$	−66.7783	−	249.220i	−0.181957	−	0.679074i	−0.995261	−	0.0972351i	$-0.969000\pi$
$367$	−66.7783	−	249.220i	−0.181957	−	0.679074i	0.813304	−	0.581839i	$-0.197667\pi$
$368$	−84.3589	+	22.6039i	−0.229236	+	0.0614237i
$369$		0			0
$370$	−319.591	+	597.149i	−0.863760	+	1.61392i
$371$	250.968	+	128.125i	0.676464	+	0.345352i
$372$		0			0
$373$	127.015	−	474.026i	0.340523	−	1.27085i	−0.557234	−	0.830356i	$-0.688137\pi$
$373$	127.015	−	474.026i	0.340523	−	1.27085i	0.897756	−	0.440492i	$-0.145196\pi$
$374$	340.531	+	196.605i	0.910510	+	0.525683i
$375$		0			0
$376$	−88.3607	−	153.045i	−0.235002	−	0.407035i
$377$	144.823	−	144.823i	0.384145	−	0.384145i
$378$		0			0
$379$			177.802i			0.469134i	0.972100	+	0.234567i	$0.0753672\pi$
$379$			177.802i			0.469134i	−0.972100	+	0.234567i	$0.924633\pi$
$380$	4.19656	+	130.312i	0.0110436	+	0.342925i
$381$		0			0
$382$	58.9436	+	219.981i	0.154303	+	0.575866i
$383$	119.288	−	445.189i	0.311457	−	1.16237i	−0.615786	−	0.787913i	$-0.711162\pi$
$383$	119.288	−	445.189i	0.311457	−	1.16237i	0.927243	−	0.374460i	$-0.122172\pi$
$384$		0			0
$385$	159.173	+	442.141i	0.413435	+	1.14842i
$386$	731.958			1.89626
$387$		0			0
$388$	−275.540	+	73.8306i	−0.710153	+	0.190285i
$389$	−258.574	−	149.288i	−0.664714	−	0.383773i	0.129357	−	0.991598i	$-0.458709\pi$
$389$	−258.574	−	149.288i	−0.664714	−	0.383773i	−0.794071	+	0.607825i	$0.792042\pi$
$390$		0			0
$391$	75.0058			0.191831
$392$	85.9367	−	105.780i	0.219226	−	0.269846i
$393$		0			0
$394$	498.053	−	287.551i	1.26409	−	0.729825i
$395$	353.372	+	568.944i	0.894614	+	1.44036i
$396$		0			0
$397$	86.8147	+	23.2619i	0.218677	+	0.0585943i	0.366494	−	0.930420i	$-0.380558\pi$
$397$	86.8147	+	23.2619i	0.218677	+	0.0585943i	−0.147817	+	0.989015i	$0.547225\pi$
$398$	−263.252	−	263.252i	−0.661436	−	0.661436i
$399$		0			0
$400$	158.236	+	237.364i	0.395591	+	0.593409i
$401$	48.6620	+	84.2851i	0.121352	+	0.210187i	0.920301	−	0.391211i	$-0.127944\pi$
$401$	48.6620	+	84.2851i	0.121352	+	0.210187i	−0.798949	+	0.601398i	$0.794610\pi$
$402$		0			0
$403$	104.708	−	28.0565i	0.259822	−	0.0696190i
$404$	−291.743	+	168.438i	−0.722135	+	0.416925i
$405$		0			0
$406$	644.532	−	417.838i	1.58752	−	1.02916i
$407$	−430.332	+	430.332i	−1.05733	+	1.05733i
$408$		0			0
$409$	232.510	+	134.240i	0.568485	+	0.328215i	0.756544	−	0.653943i	$-0.226886\pi$
$409$	232.510	+	134.240i	0.568485	+	0.328215i	−0.188059	+	0.982158i	$0.560220\pi$
$410$	197.006	−	842.883i	0.480502	−	2.05581i
$411$		0			0
$412$	442.392	−	442.392i	1.07377	−	1.07377i
$413$	150.625	+	464.830i	0.364710	+	1.12550i
$414$		0			0
$415$	−482.146	+	514.234i	−1.16180	+	1.23912i
$416$	126.132	−	218.466i	0.303201	−	0.525160i
$417$		0			0
$418$	−54.9190	+	204.960i	−0.131385	+	0.490336i
$419$			515.863i			1.23118i	0.788068	+	0.615588i	$0.211081\pi$
$419$			515.863i			1.23118i	−0.788068	+	0.615588i	$0.788919\pi$
$420$		0			0
$421$	−470.236			−1.11695			−0.558475	−	0.829521i	$-0.688613\pi$
$421$	−470.236			−1.11695			−0.558475	+	0.829521i	$0.688613\pi$
$422$	73.7721	+	19.7672i	0.174815	+	0.0468417i
$423$		0			0
$424$	−96.9634	−	55.9819i	−0.228687	−	0.132033i
$425$	−78.5060	−	232.082i	−0.184720	−	0.546075i
$426$		0			0
$427$	115.265	−	540.172i	0.269941	−	1.26504i
$428$	−211.610	−	211.610i	−0.494416	−	0.494416i
$429$		0			0
$430$	−831.764	+	516.611i	−1.93434	+	1.20142i
$431$	135.577	−	234.827i	0.314564	−	0.544841i	−0.664781	−	0.747039i	$-0.731475\pi$
$431$	135.577	−	234.827i	0.314564	−	0.544841i	0.979345	+	0.202198i	$0.0648083\pi$
$432$		0			0
$433$	−135.694	−	135.694i	−0.313381	−	0.313381i	0.532837	−	0.846218i	$-0.321126\pi$
$433$	−135.694	−	135.694i	−0.313381	−	0.313381i	−0.846218	+	0.532837i	$0.821126\pi$
$434$	406.009	−	20.9554i	0.935506	−	0.0482842i
$435$		0			0
$436$	53.1134	+	91.9950i	0.121820	+	0.210998i
$437$	10.4759	+	39.0966i	0.0239723	+	0.0894660i
$438$		0			0
$439$	406.331	−	234.596i	0.925584	−	0.534386i	0.0401720	−	0.999193i	$-0.487209\pi$
$439$	406.331	−	234.596i	0.925584	−	0.534386i	0.885412	+	0.464806i	$0.153876\pi$
$440$	−54.1064	−	178.707i	−0.122969	−	0.406153i
$441$		0			0
$442$	−115.510	+	115.510i	−0.261335	+	0.261335i
$443$	−79.5993	+	297.069i	−0.179682	+	0.670584i	0.816024	+	0.578018i	$0.196174\pi$
$443$	−79.5993	+	297.069i	−0.179682	+	0.670584i	−0.995707	+	0.0925661i	$0.970493\pi$
$444$		0			0
$445$	−62.6423	−	100.857i	−0.140769	−	0.226644i
$446$	124.631	+	215.867i	0.279441	+	0.484006i
$447$		0			0
$448$	419.635	−	465.309i	0.936685	−	1.03864i
$449$		−	556.174i		−	1.23870i	−0.785117	−	0.619348i	$-0.787397\pi$
$449$		−	556.174i		−	1.23870i	0.785117	−	0.619348i	$-0.212603\pi$
$450$		0			0
$451$	388.892	−	673.581i	0.862289	−	1.49353i
$452$	−22.3693	−	83.4834i	−0.0494896	−	0.184698i
$453$		0			0
$454$			1231.18i			2.71186i
$455$	−194.539	+	16.3328i	−0.427558	+	0.0358964i
$456$		0			0
$457$	496.047	+	132.915i	1.08544	+	0.290843i	0.756823	−	0.653620i	$-0.226750\pi$
$457$	496.047	+	132.915i	1.08544	+	0.290843i	0.328618	+	0.944463i	$0.393417\pi$
$458$	1085.17	−	290.772i	2.36938	−	0.634872i
$459$		0			0
$460$	−137.649	−	129.060i	−0.299237	−	0.280565i
$461$	140.261			0.304254			0.152127	−	0.988361i	$-0.451388\pi$
$461$	140.261			0.304254			0.152127	+	0.988361i	$0.451388\pi$
$462$		0			0
$463$	−440.572	−	440.572i	−0.951560	−	0.951560i	0.0473198	−	0.998880i	$-0.484932\pi$
$463$	−440.572	−	440.572i	−0.951560	−	0.951560i	−0.998880	+	0.0473198i	$0.984932\pi$
$464$	362.859	−	209.497i	0.782024	−	0.451502i
$465$		0			0
$466$	36.2859	−	62.8490i	0.0778667	−	0.134869i
$467$	428.655	+	114.858i	0.917892	+	0.245948i	0.686684	−	0.726956i	$-0.259066\pi$
$467$	428.655	+	114.858i	0.917892	+	0.245948i	0.231208	+	0.972904i	$0.425732\pi$
$468$		0			0
$469$	−353.377	+	692.185i	−0.753470	+	1.47587i
$470$	−447.980	+	837.041i	−0.953150	+	1.78094i
$471$		0			0
$472$	−50.2500	−	187.535i	−0.106462	−	0.397321i
$473$	−849.829	+	227.711i	−1.79668	+	0.481419i
$474$		0			0
$475$	110.008	−	73.3355i	0.231595	−	0.154391i
$476$	−283.825	+	183.998i	−0.596270	+	0.386551i
$477$		0			0
$478$	39.1894	−	146.257i	0.0819862	−	0.305977i
$479$	190.500	+	109.985i	0.397703	+	0.229614i	0.685492	−	0.728080i	$-0.259587\pi$
$479$	190.500	+	109.985i	0.397703	+	0.229614i	−0.287789	+	0.957694i	$0.592920\pi$
$480$		0			0
$481$	−126.415	−	218.957i	−0.262816	−	0.455211i
$482$	−246.426	+	246.426i	−0.511257	+	0.511257i
$483$		0			0
$484$		−	292.217i		−	0.603755i
$485$	211.021	+	197.853i	0.435095	+	0.407945i
$486$		0			0
$487$	−100.187	−	373.904i	−0.205723	−	0.767770i	−0.989228	−	0.146384i	$-0.953237\pi$
$487$	−100.187	−	373.904i	−0.205723	−	0.767770i	0.783504	−	0.621386i	$-0.213430\pi$
$488$	−56.8016	+	211.987i	−0.116397	+	0.434399i
$489$		0			0
$490$	−726.318	−	92.3518i	−1.48228	−	0.188473i
$491$	−285.045			−0.580539			−0.290269	−	0.956945i	$-0.593745\pi$
$491$	−285.045			−0.580539			−0.290269	+	0.956945i	$0.593745\pi$
$492$		0			0
$493$	−347.583	+	93.1347i	−0.705037	+	0.188914i
$494$	−76.3423	−	44.0763i	−0.154539	−	0.0892232i
$495$		0			0
$496$	221.764			0.447106
$497$	631.484	+	569.498i	1.27059	+	1.14587i
$498$		0			0
$499$	439.080	−	253.503i	0.879920	−	0.508022i	0.00928793	−	0.999957i	$-0.497044\pi$
$499$	439.080	−	253.503i	0.879920	−	0.508022i	0.870632	+	0.491935i	$0.163710\pi$
$500$	−255.263	+	560.995i	−0.510527	+	1.12199i
$501$		0			0
$502$	925.530	+	247.995i	1.84368	+	0.494014i
$503$	−261.451	−	261.451i	−0.519784	−	0.519784i	0.397722	−	0.917506i	$-0.369801\pi$
$503$	−261.451	−	261.451i	−0.519784	−	0.519784i	−0.917506	+	0.397722i	$0.869801\pi$
$504$		0			0
$505$	301.186	+	161.193i	0.596408	+	0.319195i
$506$	−153.545	−	265.948i	−0.303449	−	0.525589i
$507$		0			0
$508$	−141.974	+	38.0419i	−0.279477	+	0.0748856i
$509$	−9.46947	+	5.46720i	−0.0186041	+	0.0107411i	−0.509273	−	0.860605i	$-0.670086\pi$
$509$	−9.46947	+	5.46720i	−0.0186041	+	0.0107411i	0.490669	+	0.871346i	$0.336752\pi$
$510$		0			0
$511$	30.3436	+	15.4911i	0.0593808	+	0.0303153i
$512$	454.686	−	454.686i	0.888059	−	0.888059i
$513$		0			0
$514$	−514.104	−	296.818i	−1.00020	−	0.577467i
$515$	−617.777	−	144.392i	−1.19957	−	0.280373i
$516$		0			0
$517$	−603.209	+	603.209i	−1.16675	+	1.16675i
$518$	−292.298	−	902.033i	−0.564282	−	1.74138i
$519$		0			0
$520$	77.5302	−	2.49679i	0.149096	−	0.00480152i
$521$	−71.2494	+	123.408i	−0.136755	+	0.236867i	−0.926267	−	0.376869i	$-0.877001\pi$
$521$	−71.2494	+	123.408i	−0.136755	+	0.236867i	0.789511	+	0.613736i	$0.210334\pi$
$522$		0			0
$523$	8.25954	−	30.8250i	0.0157926	−	0.0589389i	−0.957580	−	0.288168i	$-0.906954\pi$
$523$	8.25954	−	30.8250i	0.0157926	−	0.0589389i	0.973372	+	0.229229i	$0.0736205\pi$
$524$			617.416i			1.17827i
$525$		0			0
$526$	−47.4149			−0.0901424
$527$	−183.968	−	49.2942i	−0.349086	−	0.0935374i
$528$		0			0
$529$	407.397	+	235.211i	0.770127	+	0.444633i
$530$	19.3604	+	601.179i	0.0365291	+	1.13430i
$531$		0			0
$532$	−135.550	−	122.244i	−0.254793	−	0.229783i
$533$	228.483	+	228.483i	0.428673	+	0.428673i
$534$		0			0
$535$	−69.0672	+	295.502i	−0.129098	+	0.552341i
$536$	154.401	−	267.431i	0.288062	−	0.498938i
$537$		0			0
$538$	−219.346	−	219.346i	−0.407706	−	0.407706i
$539$	−600.585	−	268.539i	−1.11426	−	0.498218i
$540$		0			0
$541$	−86.8285	−	150.391i	−0.160496	−	0.277988i	0.774551	−	0.632512i	$-0.217976\pi$
$541$	−86.8285	−	150.391i	−0.160496	−	0.277988i	−0.935047	+	0.354524i	$0.884643\pi$
$542$	−121.522	−	453.526i	−0.224210	−	0.836764i
$543$		0			0
$544$	−383.838	+	221.609i	−0.705584	+	0.407369i
$545$	50.8291	−	94.9729i	0.0932643	−	0.174262i
$546$		0			0
$547$	95.8716	−	95.8716i	0.175268	−	0.175268i	−0.614021	−	0.789289i	$-0.710449\pi$
$547$	95.8716	−	95.8716i	0.175268	−	0.175268i	0.789289	+	0.614021i	$0.210449\pi$
$548$	−46.7602	+	174.511i	−0.0853289	+	0.318452i
$549$		0			0
$550$	−662.183	+	753.457i	−1.20397	+	1.36992i
$551$	−97.0925	−	168.169i	−0.176211	−	0.305207i
$552$		0			0
$553$	−917.009	−	195.676i	−1.65824	−	0.353845i
$554$		−	624.904i		−	1.12799i
$555$		0			0
$556$	−208.690	+	361.462i	−0.375342	+	0.650112i
$557$	−12.5270	−	46.7512i	−0.0224900	−	0.0839340i	0.953769	−	0.300542i	$-0.0971674\pi$
$557$	−12.5270	−	46.7512i	−0.0224900	−	0.0839340i	−0.976259	+	0.216608i	$0.930501\pi$
$558$		0			0
$559$		−	365.508i		−	0.653860i
$560$	−393.068	−	70.7304i	−0.701907	−	0.126304i
$561$		0			0
$562$	1313.14	+	351.855i	2.33655	+	0.626076i
$563$	−272.294	+	72.9609i	−0.483648	+	0.129593i	−0.492401	−	0.870369i	$-0.663881\pi$
$563$	−272.294	+	72.9609i	−0.483648	+	0.129593i	0.00875281	+	0.999962i	$0.497214\pi$
$564$		0			0
$565$	−59.9460	+	63.9355i	−0.106099	+	0.113160i
$566$	−306.797			−0.542045
$567$		0			0
$568$	−238.918	−	238.918i	−0.420629	−	0.420629i
$569$	466.721	−	269.461i	0.820247	−	0.473570i	−0.0302544	−	0.999542i	$-0.509632\pi$
$569$	466.721	−	269.461i	0.820247	−	0.473570i	0.850502	+	0.525972i	$0.176298\pi$
$570$		0			0
$571$	150.339	−	260.394i	0.263290	−	0.456032i	−0.703824	−	0.710374i	$-0.748526\pi$
$571$	150.339	−	260.394i	0.263290	−	0.456032i	0.967114	+	0.254342i	$0.0818590\pi$
$572$	356.676	+	95.5709i	0.623559	+	0.167082i
$573$		0			0
$574$	659.210	+	1016.86i	1.14845	+	1.77153i
$575$	−37.5284	+	187.625i	−0.0652668	+	0.326304i
$576$		0			0
$577$	72.3090	+	269.861i	0.125319	+	0.467697i	0.999851	−	0.0172714i	$-0.00549794\pi$
$577$	72.3090	+	269.861i	0.125319	+	0.467697i	−0.874532	+	0.484968i	$0.838831\pi$
$578$	−556.998	+	149.247i	−0.963664	+	0.258213i
$579$		0			0
$580$	798.132	+	427.156i	1.37609	+	0.736477i
$581$	−50.8680	−	985.565i	−0.0875524	−	1.69633i
$582$		0			0
$583$	−139.884	+	522.053i	−0.239938	+	0.895460i
$584$	−11.7235	−	6.76855i	−0.0200744	−	0.0115900i
$585$		0			0
$586$	216.271	+	374.592i	0.369062	+	0.639235i
$587$	210.055	−	210.055i	0.357845	−	0.357845i	−0.505173	−	0.863018i	$-0.668571\pi$
$587$	210.055	−	210.055i	0.357845	−	0.357845i	0.863018	+	0.505173i	$0.168571\pi$
$588$		0			0
$589$		−	102.778i		−	0.174496i
$590$	−713.403	+	760.881i	−1.20916	+	1.28963i
$591$		0			0
$592$	−133.869	−	499.605i	−0.226129	−	0.843927i
$593$	271.762	−	1014.23i	0.458284	−	1.71034i	−0.219966	−	0.975508i	$-0.570595\pi$
$593$	271.762	−	1014.23i	0.458284	−	1.71034i	0.678250	−	0.734831i	$-0.262739\pi$
$594$		0			0
$595$	310.354	+	146.047i	0.521603	+	0.245458i
$596$	−160.892			−0.269953
$597$		0			0
$598$	123.231	−	33.0196i	0.206071	−	0.0552167i
$599$	516.500	+	298.201i	0.862270	+	0.497832i	0.864772	−	0.502165i	$-0.167463\pi$
$599$	516.500	+	298.201i	0.862270	+	0.497832i	−0.00250190	+	0.999997i	$0.500796\pi$
$600$		0			0
$601$	−480.552			−0.799588			−0.399794	−	0.916605i	$-0.630918\pi$
$601$	−480.552			−0.799588			−0.399794	+	0.916605i	$0.630918\pi$
$602$	286.068	−	1340.62i	0.475196	−	2.22694i
$603$		0			0
$604$	666.528	−	384.820i	1.10352	−	0.637119i
$605$	−251.722	+	156.345i	−0.416069	+	0.258421i
$606$		0			0
$607$	822.130	+	220.289i	1.35441	+	0.362914i	0.861762	−	0.507312i	$-0.169361\pi$
$607$	822.130	+	220.289i	1.35441	+	0.362914i	0.492652	+	0.870226i	$0.336028\pi$
$608$	−169.123	−	169.123i	−0.278163	−	0.278163i
$609$		0			0
$610$	1128.42	−	341.647i	1.84987	−	0.560077i
$611$	−177.199	−	306.918i	−0.290015	−	0.502320i
$612$		0			0
$613$	1030.27	−	276.060i	1.68070	−	0.450343i	0.712737	−	0.701431i	$-0.247455\pi$
$613$	1030.27	−	276.060i	1.68070	−	0.450343i	0.967964	+	0.251089i	$0.0807885\pi$
$614$	−106.874	+	61.7035i	−0.174061	+	0.100494i
$615$		0			0
$616$	232.820	+	118.860i	0.377955	+	0.192955i
$617$	270.729	−	270.729i	0.438783	−	0.438783i	−0.452819	−	0.891602i	$-0.649582\pi$
$617$	270.729	−	270.729i	0.438783	−	0.438783i	0.891602	+	0.452819i	$0.149582\pi$
$618$		0			0
$619$	136.247	+	78.6625i	0.220109	+	0.127080i	0.606001	−	0.795464i	$-0.292773\pi$
$619$	136.247	+	78.6625i	0.220109	+	0.127080i	−0.385892	+	0.922544i	$0.626106\pi$
$620$	252.796	+	407.012i	0.407736	+	0.656471i
$621$		0			0
$622$	−849.859	+	849.859i	−1.36633	+	1.36633i
$623$	162.558	+	34.6875i	0.260928	+	0.0556782i
$624$		0			0
$625$	619.825	−	80.2602i	0.991720	−	0.128416i
$626$	−428.805	+	742.712i	−0.684992	+	1.18644i
$627$		0			0
$628$	−84.8905	+	316.816i	−0.135176	+	0.504483i
$629$			444.212i			0.706219i
$630$		0			0
$631$	−131.406			−0.208250			−0.104125	−	0.994564i	$-0.533204\pi$
$631$	−131.406			−0.208250			−0.104125	+	0.994564i	$0.533204\pi$
$632$	359.874	+	96.4279i	0.569421	+	0.152576i
$633$		0			0
$634$	−900.060	−	519.650i	−1.41965	−	0.819637i
$635$	108.730	+	101.946i	0.171229	+	0.160545i
$636$		0			0
$637$	172.338	−	212.131i	0.270546	−	0.333016i
$638$	1041.77	+	1041.77i	1.63287	+	1.63287i
$639$		0			0
$640$	421.613	+	98.5428i	0.658770	+	0.153973i
$641$	128.958	−	223.362i	0.201182	−	0.348458i	−0.747727	−	0.664006i	$-0.768855\pi$
$641$	128.958	−	223.362i	0.201182	−	0.348458i	0.948910	+	0.315548i	$0.102188\pi$
$642$		0			0
$643$	778.940	+	778.940i	1.21142	+	1.21142i	0.970561	+	0.240854i	$0.0774274\pi$
$643$	778.940	+	778.940i	1.21142	+	1.21142i	0.240854	+	0.970561i	$0.422573\pi$
$644$	263.814	−	13.6162i	0.409650	−	0.0211432i
$645$		0			0
$646$	77.4404	+	134.131i	0.119877	+	0.207633i
$647$	−98.6974	−	368.344i	−0.152546	−	0.569310i	−0.999303	−	0.0373301i	$-0.988115\pi$
$647$	−98.6974	−	368.344i	−0.152546	−	0.569310i	0.846757	−	0.531980i	$-0.178552\pi$
$648$		0			0
$649$	−811.641	+	468.601i	−1.25060	+	0.722035i
$650$	−231.150	−	346.738i	−0.355615	−	0.533444i
$651$		0			0
$652$	−203.801	+	203.801i	−0.312578	+	0.312578i
$653$	−291.908	+	1089.41i	−0.447026	+	1.66832i	0.263506	+	0.964658i	$0.415121\pi$
$653$	−291.908	+	1089.41i	−0.447026	+	1.66832i	−0.710532	+	0.703665i	$0.751546\pi$
$654$		0			0
$655$	531.854	−	330.336i	0.811990	−	0.504329i
$656$	330.517	+	572.472i	0.503836	+	0.872670i
$657$		0			0
$658$	−409.723	−	1264.41i	−0.622679	−	1.92159i
$659$			737.560i			1.11921i	0.828759	+	0.559605i	$0.189047\pi$
$659$			737.560i			1.11921i	−0.828759	+	0.559605i	$0.810953\pi$
$660$		0			0
$661$	−166.939	+	289.147i	−0.252555	+	0.437439i	−0.964229	−	0.265072i	$-0.914604\pi$
$661$	−166.939	+	289.147i	−0.252555	+	0.437439i	0.711673	+	0.702511i	$0.247938\pi$
$662$	56.0259	+	209.092i	0.0846313	+	0.315848i
$663$		0			0
$664$			392.127i			0.590553i
$665$	−32.7804	+	182.170i	−0.0492939	+	0.273939i
$666$		0			0
$667$	271.456	+	72.7365i	0.406981	+	0.109050i
$668$	626.543	−	167.882i	0.937939	−	0.251320i
$669$		0			0
$670$	−1658.09	+	53.3972i	−2.47476	+	0.0796973i
$671$	1059.40			1.57883
$672$		0			0
$673$	−183.139	−	183.139i	−0.272123	−	0.272123i	0.557831	−	0.829954i	$-0.311634\pi$
$673$	−183.139	−	183.139i	−0.272123	−	0.272123i	−0.829954	+	0.557831i	$0.811634\pi$
$674$	936.016	−	540.409i	1.38875	−	0.801794i
$675$		0			0
$676$	339.943	−	588.799i	0.502875	−	0.871005i
$677$	806.946	+	216.220i	1.19194	+	0.319380i	0.799654	−	0.600461i	$-0.205016\pi$
$677$	806.946	+	216.220i	1.19194	+	0.319380i	0.392290	+	0.919842i	$0.371683\pi$
$678$		0			0
$679$	−404.436	+	20.8742i	−0.595635	+	0.0307425i
$680$	−120.161	−	64.3098i	−0.176708	−	0.0945733i
$681$		0			0
$682$	201.821	+	753.208i	0.295926	+	1.10441i
$683$	909.178	−	243.613i	1.33115	−	0.356681i	0.478008	−	0.878355i	$-0.341359\pi$
$683$	909.178	−	243.613i	1.33115	−	0.356681i	0.853145	+	0.521674i	$0.174692\pi$
$684$		0			0
$685$	175.346	−	53.0887i	0.255979	−	0.0775017i
$686$	798.131	−	643.177i	1.16346	−	0.937576i
$687$		0			0
$688$	193.530	−	722.263i	0.281293	−	1.04980i
$689$	−194.451	−	112.266i	−0.282222	−	0.162941i
$690$		0			0
$691$	−409.191	−	708.740i	−0.592172	−	1.02567i	−0.993939	−	0.109931i	$-0.964937\pi$
$691$	−409.191	−	708.740i	−0.592172	−	1.02567i	0.401767	−	0.915742i	$-0.368396\pi$
$692$	−844.291	+	844.291i	−1.22007	+	1.22007i
$693$		0			0
$694$		−	862.487i		−	1.24278i
$695$	423.026	−	13.6232i	0.608670	−	0.0196017i
$696$		0			0
$697$	−146.936	−	548.371i	−0.210812	−	0.786760i
$698$	−371.643	+	1386.99i	−0.532439	+	1.98709i
$699$		0			0
$700$	−318.257	−	802.040i	−0.454652	−	1.14577i
$701$	−480.047			−0.684803			−0.342402	−	0.939554i	$-0.611240\pi$
$701$	−480.047			−0.684803			−0.342402	+	0.939554i	$0.611240\pi$
$702$		0			0
$703$	−231.545	+	62.0422i	−0.329366	+	0.0882535i
$704$	1040.80	+	600.905i	1.47841	+	0.853558i
$705$		0			0
$706$	−288.430			−0.408541
$707$	−454.962	+	147.427i	−0.643510	+	0.208525i
$708$		0			0
$709$	−1211.17	+	699.271i	−1.70828	+	0.986278i	−0.771597	+	0.636112i	$0.780542\pi$
$709$	−1211.17	+	699.271i	−1.70828	+	0.986278i	−0.936688	+	0.350166i	$0.886125\pi$
$710$	−413.120	+	1767.52i	−0.581859	+	2.48947i
$711$		0			0
$712$	−63.7948	−	17.0938i	−0.0895994	−	0.0240081i
$713$	105.178	+	105.178i	0.147515	+	0.147515i
$714$		0			0
$715$	−108.505	−	358.380i	−0.151756	−	0.501231i
$716$	−651.874	−	1129.08i	−0.910438	−	1.57693i
$717$		0			0
$718$	936.168	−	250.845i	1.30385	−	0.349367i
$719$	−742.957	+	428.946i	−1.03332	+	0.596587i	−0.917934	−	0.396734i	$-0.870144\pi$
$719$	−742.957	+	428.946i	−1.03332	+	0.596587i	−0.115386	+	0.993321i	$0.536810\pi$
$720$		0			0
$721$	745.289	−	483.157i	1.03369	−	0.670120i
$722$	703.744	−	703.744i	0.974715	−	0.974715i
$723$		0			0
$724$	1221.34	+	705.142i	1.68694	+	0.973953i
$725$	−59.0635	−	916.067i	−0.0814669	−	1.26354i
$726$		0			0
$727$	8.47406	−	8.47406i	0.0116562	−	0.0116562i	−0.701255	−	0.712911i	$-0.747376\pi$
$727$	8.47406	−	8.47406i	0.0116562	−	0.0116562i	0.712911	+	0.701255i	$0.247376\pi$
$728$	−72.7305	+	80.6468i	−0.0999046	+	0.110779i
$729$		0			0
$730$	2.34079	+	72.6862i	0.00320656	+	0.0995701i
$731$	−321.092	+	556.147i	−0.439250	+	0.760804i
$732$		0			0
$733$	−288.580	+	1076.99i	−0.393697	+	1.46930i	0.430292	+	0.902690i	$0.358411\pi$
$733$	−288.580	+	1076.99i	−0.393697	+	1.46930i	−0.823989	+	0.566606i	$0.808256\pi$
$734$			771.050i			1.05048i
$735$		0			0
$736$	346.145			0.470306
$737$	−1439.85	−	385.807i	−1.95367	−	0.523483i
$738$		0			0
$739$	−635.156	−	366.708i	−0.859481	−	0.496221i	0.00435760	−	0.999991i	$-0.498613\pi$
$739$	−635.156	−	366.708i	−0.859481	−	0.496221i	−0.863838	+	0.503769i	$0.831946\pi$
$740$	764.341	−	815.209i	1.03289	−	1.10163i
$741$		0			0
$742$	−625.345	−	563.962i	−0.842784	−	0.760056i
$743$	342.256	+	342.256i	0.460641	+	0.460641i	0.898865	−	0.438225i	$-0.144393\pi$
$743$	342.256	+	342.256i	0.460641	+	0.460641i	−0.438225	+	0.898865i	$0.644393\pi$
$744$		0			0
$745$	86.0820	+	138.595i	0.115546	+	0.186034i
$746$	−733.284	+	1270.08i	−0.982954	+	1.70253i
$747$		0			0
$748$	−458.752	−	458.752i	−0.613304	−	0.613304i
$749$	−231.109	−	356.495i	−0.308557	−	0.475961i
$750$		0			0
$751$	−217.704	−	377.075i	−0.289886	−	0.502097i	0.683897	−	0.729579i	$-0.260284\pi$
$751$	−217.704	−	377.075i	−0.289886	−	0.502097i	−0.973782	+	0.227482i	$0.926951\pi$
$752$	−187.648	−	700.310i	−0.249531	−	0.931264i
$753$		0			0
$754$	−530.061	+	306.031i	−0.702999	+	0.405877i
$755$	−688.103	−	368.270i	−0.911395	−	0.487774i
$756$		0			0
$757$	136.675	−	136.675i	0.180548	−	0.180548i	−0.611047	−	0.791595i	$-0.709251\pi$
$757$	136.675	−	136.675i	0.180548	−	0.180548i	0.791595	+	0.611047i	$0.209251\pi$
$758$	137.523	−	513.243i	0.181429	−	0.677101i
$759$		0			0
$760$	16.7387	−	71.6159i	0.0220246	−	0.0942315i
$761$	−191.516	−	331.716i	−0.251664	−	0.435895i	0.712320	−	0.701855i	$-0.247644\pi$
$761$	−191.516	−	331.716i	−0.251664	−	0.435895i	−0.963984	+	0.265960i	$0.914311\pi$
$762$		0			0
$763$	46.4882	+	143.463i	0.0609282	+	0.188025i
$764$		−	375.758i		−	0.491829i
$765$		0			0
$766$	−688.674	+	1192.82i	−0.899052	+	1.55720i
$767$	−100.772	−	376.085i	−0.131384	−	0.490332i
$768$		0			0
$769$		−	210.497i		−	0.273729i	−0.990590	−	0.136864i	$-0.956298\pi$
$769$		−	210.497i		−	0.273729i	0.990590	−	0.136864i	$-0.0437024\pi$
$770$	−117.489	−	1399.40i	−0.152583	−	1.81740i
$771$		0			0
$772$	−1166.53	−	312.571i	−1.51105	−	0.404885i
$773$	415.715	−	111.390i	0.537794	−	0.144101i	0.0203089	−	0.999794i	$-0.493535\pi$
$773$	415.715	−	111.390i	0.537794	−	0.144101i	0.517485	+	0.855692i	$0.326868\pi$
$774$		0			0
$775$	215.355	−	435.527i	0.277877	−	0.561971i
$776$	160.913			0.207362
$777$		0			0
$778$	630.931	+	630.931i	0.810965	+	0.810965i
$779$	265.315	−	153.180i	0.340584	−	0.196637i
$780$		0			0
$781$	−815.505	+	1412.50i	−1.04418	+	1.80857i
$782$	−216.512	−	58.0142i	−0.276869	−	0.0741869i
$783$		0			0
$784$	452.869	−	327.933i	0.577639	−	0.418282i
$785$	318.330	−	96.3794i	0.405516	−	0.122776i
$786$		0			0
$787$	−190.107	−	709.488i	−0.241559	−	0.901510i	−0.975082	−	0.221845i	$-0.928792\pi$
$787$	−190.107	−	709.488i	−0.241559	−	0.901510i	0.733523	−	0.679665i	$-0.237875\pi$
$788$	−916.549	+	245.589i	−1.16313	+	0.311661i
$789$		0			0
$790$	−579.989	−	1915.63i	−0.734163	−	2.42485i
$791$	−6.32449	−	122.537i	−0.00799556	−	0.154914i
$792$		0			0
$793$	−113.910	+	425.119i	−0.143645	+	0.536089i
$794$	−232.607	−	134.296i	−0.292956	−	0.169138i
$795$		0			0
$796$	307.131	+	531.966i	0.385843	+	0.668299i
$797$	−657.078	+	657.078i	−0.824439	+	0.824439i	−0.986741	−	0.162302i	$-0.948108\pi$
$797$	−657.078	+	657.078i	−0.824439	+	0.824439i	0.162302	+	0.986741i	$0.448108\pi$
$798$		0			0
$799$			622.665i			0.779305i
$800$	−362.298	−	1071.04i	−0.452872	−	1.33880i
$801$		0			0
$802$	−75.2765	−	280.936i	−0.0938610	−	0.350294i
$803$	−16.9128	+	63.1194i	−0.0210620	+	0.0786045i
$804$		0			0
$805$	−152.878	−	219.970i	−0.189910	−	0.273254i
$806$	−323.951			−0.401925
$807$		0			0
$808$	183.554	−	49.1832i	0.227171	−	0.0608703i
$809$	−366.207	−	211.430i	−0.452666	−	0.261347i	0.256289	−	0.966600i	$-0.417500\pi$
$809$	−366.207	−	211.430i	−0.452666	−	0.261347i	−0.708956	+	0.705253i	$0.750833\pi$
$810$		0			0
$811$	549.264			0.677268			0.338634	−	0.940918i	$-0.390035\pi$
$811$	549.264			0.677268			0.338634	+	0.940918i	$0.390035\pi$
$812$	−1205.63	+	390.677i	−1.48477	+	0.481129i
$813$		0			0
$814$	1575.04	−	909.352i	1.93494	−	1.11714i
$815$	284.597	+	66.5184i	0.349199	+	0.0816177i
$816$		0			0
$817$	−334.737	−	89.6925i	−0.409715	−	0.109783i
$818$	−567.335	−	567.335i	−0.693564	−	0.693564i
$819$		0			0
$820$	−673.911	+	1259.19i	−0.821843	+	1.53560i
$821$	97.9130	+	169.590i	0.119261	+	0.206566i	0.919475	−	0.393149i	$-0.128614\pi$
$821$	97.9130	+	169.590i	0.119261	+	0.206566i	−0.800214	+	0.599714i	$0.795281\pi$
$822$		0			0
$823$	−1419.82	+	380.440i	−1.72518	+	0.462260i	−0.979063	−	0.203559i	$-0.934749\pi$
$823$	−1419.82	+	380.440i	−1.72518	+	0.462260i	−0.746114	+	0.665818i	$0.768083\pi$
$824$	−305.636	+	176.459i	−0.370917	+	0.214149i
$825$		0			0
$826$	−75.2663	−	1458.28i	−0.0911214	−	1.76547i
$827$	645.663	−	645.663i	0.780729	−	0.780729i	−0.199225	−	0.979954i	$-0.563842\pi$
$827$	645.663	−	645.663i	0.780729	−	0.780729i	0.979954	+	0.199225i	$0.0638423\pi$
$828$		0			0
$829$	946.305	+	546.349i	1.14150	+	0.659046i	0.946802	−	0.321816i	$-0.104293\pi$
$829$	946.305	+	546.349i	1.14150	+	0.659046i	0.194700	+	0.980863i	$0.437627\pi$
$830$	1789.51	−	1111.47i	2.15603	−	1.33912i
$831$		0			0
$832$	−353.044	+	353.044i	−0.424332	+	0.424332i
$833$	−448.578	+	171.378i	−0.538510	+	0.205736i
$834$		0			0
$835$	−479.835	−	449.894i	−0.574653	−	0.538796i
$836$	175.050	−	303.196i	0.209390	−	0.362675i
$837$		0			0
$838$	399.001	−	1489.09i	0.476134	−	1.77696i
$839$		−	682.503i		−	0.813472i	−0.913546	−	0.406736i	$-0.866667\pi$
$839$		−	682.503i		−	0.813472i	0.913546	−	0.406736i	$-0.133333\pi$
$840$		0			0
$841$	−507.268			−0.603173
$842$	1357.38	+	363.710i	1.61210	+	0.431960i
$843$		0			0
$844$	−109.131	−	63.0065i	−0.129302	−	0.0746523i
$845$	−689.083	+	22.1913i	−0.815483	+	0.0262619i
$846$		0			0
$847$	86.5744	−	405.719i	0.102213	−	0.479007i
$848$	−324.803	−	324.803i	−0.383022	−	0.383022i
$849$		0			0
$850$	47.1087	+	730.650i	0.0554220	+	0.859588i
$851$	173.461	−	300.443i	0.203832	−	0.353047i
$852$		0			0
$853$	201.182	+	201.182i	0.235852	+	0.235852i	0.815130	−	0.579278i	$-0.196665\pi$
$853$	201.182	+	201.182i	0.235852	+	0.235852i	−0.579278	+	0.815130i	$0.696665\pi$
$854$	−750.526	+	1470.11i	−0.878836	+	1.72144i
$855$		0			0
$856$	84.4059	+	146.195i	0.0986050	+	0.170789i
$857$	337.813	+	1260.74i	0.394181	+	1.47110i	0.823171	+	0.567794i	$0.192203\pi$
$857$	337.813	+	1260.74i	0.394181	+	1.47110i	−0.428990	+	0.903309i	$0.641130\pi$
$858$		0			0
$859$	1064.26	−	614.453i	1.23896	−	0.715313i	0.270076	−	0.962839i	$-0.412951\pi$
$859$	1064.26	−	614.453i	1.23896	−	0.715313i	0.968881	+	0.247526i	$0.0796177\pi$
$860$	1546.21	−	468.139i	1.79791	−	0.544347i
$861$		0			0
$862$	−572.987	+	572.987i	−0.664718	+	0.664718i
$863$	259.341	−	967.875i	0.300511	−	1.12152i	−0.636229	−	0.771500i	$-0.719507\pi$
$863$	259.341	−	967.875i	0.300511	−	1.12152i	0.936741	−	0.350024i	$-0.113827\pi$
$864$		0			0
$865$	1179.01	+	275.568i	1.36302	+	0.318575i
$866$	286.740	+	496.649i	0.331109	+	0.573498i
$867$		0			0
$868$	−656.012	−	139.983i	−0.755775	−	0.161271i
$869$		−	1798.46i		−	2.06957i
$870$		0			0
$871$	309.637	−	536.307i	0.355496	−	0.615737i
$872$	−15.5089	−	57.8801i	−0.0177855	−	0.0663762i
$873$		0			0
$874$		−	120.959i		−	0.138397i
$875$	−520.615	+	703.267i	−0.594989	+	0.803734i
$876$		0			0
$877$	−330.906	−	88.6659i	−0.377315	−	0.101101i	0.0651767	−	0.997874i	$-0.479239\pi$
$877$	−330.906	−	88.6659i	−0.377315	−	0.101101i	−0.442492	+	0.896772i	$0.645906\pi$
$878$	−1354.37	+	362.902i	−1.54256	+	0.413328i
$879$		0			0
$880$	−24.6565	−	765.631i	−0.0280187	−	0.870035i
$881$	−291.629			−0.331021			−0.165510	−	0.986208i	$-0.552927\pi$
$881$	−291.629			−0.331021			−0.165510	+	0.986208i	$0.552927\pi$
$882$		0			0
$883$	993.613	+	993.613i	1.12527	+	1.12527i	0.990936	+	0.134333i	$0.0428892\pi$
$883$	993.613	+	993.613i	1.12527	+	1.12527i	0.134333	+	0.990936i	$0.457111\pi$
$884$	233.417	−	134.763i	0.264046	−	0.152447i
$885$		0			0
$886$	459.543	−	795.952i	0.518672	−	0.898366i
$887$	88.2058	+	23.6347i	0.0994428	+	0.0266456i	0.308197	−	0.951322i	$-0.400274\pi$
$887$	88.2058	+	23.6347i	0.0994428	+	0.0266456i	−0.208755	+	0.977968i	$0.566941\pi$
$888$		0			0
$889$	−208.389	+	10.7556i	−0.234409	+	0.0120985i
$890$	102.815	+	339.584i	0.115522	+	0.381555i
$891$		0			0
$892$	−106.443	−	397.251i	−0.119331	−	0.445349i
$893$	−324.563	+	86.9663i	−0.363452	+	0.0973867i
$894$		0			0
$895$	−623.838	+	1165.63i	−0.697026	+	1.30238i
$896$	−508.635	+	329.739i	−0.567673	+	0.368012i
$897$		0			0
$898$	−430.180	+	1605.45i	−0.479043	+	1.78781i
$899$	−618.004	−	356.805i	−0.687435	−	0.396891i
$900$		0			0
$901$	197.248	+	341.643i	0.218921	+	0.379183i
$902$	−1643.57	+	1643.57i	−1.82214	+	1.82214i
$903$		0			0
$904$			48.7538i			0.0539312i
$905$	−46.0312	−	1429.36i	−0.0508632	−	1.57940i
$906$		0			0
$907$	13.3362	+	49.7713i	0.0147036	+	0.0548746i	0.972888	−	0.231277i	$-0.0742905\pi$
$907$	13.3362	+	49.7713i	0.0147036	+	0.0548746i	−0.958184	+	0.286152i	$0.907624\pi$
$908$	525.758	−	1962.16i	0.579029	−	2.16097i
$909$		0			0
$910$	574.190	+	103.322i	0.630978	+	0.113541i
$911$	−30.4579			−0.0334334			−0.0167167	−	0.999860i	$-0.505321\pi$
$911$	−30.4579			−0.0334334			−0.0167167	+	0.999860i	$0.505321\pi$
$912$		0			0
$913$	1828.37	−	489.910i	2.00260	−	0.536594i
$914$	−1329.08	−	767.347i	−1.45414	−	0.839548i
$915$		0			0
$916$	−1853.63			−2.02361
$917$	−182.920	+	857.228i	−0.199476	+	0.934818i
$918$		0			0
$919$	408.961	−	236.114i	0.445007	−	0.256925i	−0.260712	−	0.965417i	$-0.583957\pi$
$919$	408.961	−	236.114i	0.445007	−	0.256925i	0.705719	+	0.708492i	$0.250624\pi$
$920$	56.1588	+	90.4179i	0.0610422	+	0.0982803i
$921$		0			0
$922$	−404.879	−	108.487i	−0.439131	−	0.117665i
$923$	−479.127	−	479.127i	−0.519097	−	0.519097i
$924$		0			0
$925$	−1111.18	−	222.257i	−1.20128	−	0.240278i
$926$	930.991	+	1612.52i	1.00539	+	1.74139i
$927$		0			0
$928$	−1604.07	+	429.808i	−1.72852	+	0.463155i
$929$	−747.921	+	431.812i	−0.805081	+	0.464814i	−0.845245	−	0.534379i	$-0.820545\pi$
$929$	−747.921	+	431.812i	−0.805081	+	0.464814i	0.0401635	+	0.999193i	$0.487212\pi$
$930$		0			0
$931$	−151.982	−	209.885i	−0.163246	−	0.225440i
$932$	−84.6681	+	84.6681i	−0.0908456	+	0.0908456i
$933$		0			0
$934$	−1148.52	−	663.098i	−1.22968	−	0.709955i
$935$	−149.732	+	640.623i	−0.160141	+	0.685158i
$936$		0			0
$937$	−543.193	+	543.193i	−0.579715	+	0.579715i	−0.934825	−	0.355110i	$-0.884443\pi$
$937$	−543.193	+	543.193i	−0.579715	+	0.579715i	0.355110	+	0.934825i	$0.384443\pi$
$938$	1555.44	−	1724.74i	1.65825	−	1.83874i
$939$		0			0
$940$	1071.40	−	1142.70i	1.13979	−	1.21564i
$941$	−215.568	+	373.375i	−0.229084	+	0.396785i	−0.957537	−	0.288311i	$-0.906906\pi$
$941$	−215.568	+	373.375i	−0.229084	+	0.396785i	0.728453	+	0.685096i	$0.240240\pi$
$942$		0			0
$943$	−114.754	+	428.268i	−0.121690	+	0.454155i
$944$		−	796.521i		−	0.843772i
$945$		0			0
$946$	2629.24			2.77933
$947$	671.694	+	179.980i	0.709287	+	0.190053i	0.595387	−	0.803439i	$-0.296999\pi$
$947$	671.694	+	179.980i	0.709287	+	0.190053i	0.113900	+	0.993492i	$0.463666\pi$
$948$		0			0
$949$	−23.5103	−	13.5737i	−0.0247738	−	0.0143031i
$950$	−374.270	+	126.604i	−0.393969	+	0.133267i
$951$		0			0
$952$	181.512	−	58.8177i	0.190664	−	0.0617833i
$953$	936.706	+	936.706i	0.982902	+	0.982902i	0.999856	−	0.0169540i	$-0.00539688\pi$
$953$	936.706	+	936.706i	0.982902	+	0.982902i	−0.0169540	+	0.999856i	$0.505397\pi$
$954$		0			0
$955$	−323.685	+	201.041i	−0.338937	+	0.210515i
$956$	−124.914	+	216.357i	−0.130663	+	0.226315i
$957$		0			0
$958$	−464.828	−	464.828i	−0.485207	−	0.485207i
$959$	−116.624	+	228.441i	−0.121611	+	0.238207i
$960$		0			0
$961$	291.651	+	505.154i	0.303487	+	0.525654i
$962$	195.554	+	729.817i	0.203279	+	0.758646i
$963$		0			0
$964$	497.965	−	287.500i	0.516561	−	0.298237i
$965$	354.874	+	1172.11i	0.367745	+	1.21462i
$966$		0			0
$967$	−580.505	+	580.505i	−0.600315	+	0.600315i	−0.940396	−	0.340081i	$-0.889545\pi$
$967$	−580.505	+	580.505i	−0.600315	+	0.600315i	0.340081	+	0.940396i	$0.389545\pi$
$968$	−42.6633	+	159.221i	−0.0440736	+	0.164485i
$969$		0			0
$970$	−456.101	−	734.341i	−0.470207	−	0.757053i
$971$	−460.985	−	798.449i	−0.474753	−	0.822296i	0.524829	−	0.851208i	$-0.324129\pi$
$971$	−460.985	−	798.449i	−0.474753	−	0.822296i	−0.999582	+	0.0289117i	$0.990796\pi$
$972$		0			0
$973$	−396.838	+	440.031i	−0.407850	+	0.452242i
$974$			1156.80i			1.18768i
$975$		0			0
$976$	−450.186	+	779.745i	−0.461256	+	0.798919i
$977$	−23.7849	−	88.7663i	−0.0243448	−	0.0908560i	0.952685	−	0.303961i	$-0.0983091\pi$
$977$	−23.7849	−	88.7663i	−0.0243448	−	0.0908560i	−0.977029	+	0.213105i	$0.931642\pi$
$978$		0			0
$979$			318.812i			0.325651i
$980$	1118.11	+	457.345i	1.14093	+	0.466679i
$981$		0			0
$982$	822.810	+	220.471i	0.837892	+	0.224513i
$983$	558.417	−	149.627i	0.568074	−	0.152215i	0.0366611	−	0.999328i	$-0.488328\pi$
$983$	558.417	−	149.627i	0.568074	−	0.152215i	0.531413	+	0.847113i	$0.321661\pi$
$984$		0			0
$985$	701.936	+	658.136i	0.712625	+	0.668158i
$986$	1075.37			1.09064
$987$		0			0
$988$	102.846	+	102.846i	0.104095	+	0.104095i
$989$	434.341	−	250.767i	0.439172	−	0.253556i
$990$		0			0
$991$	−823.906	+	1427.05i	−0.831389	+	1.44001i	0.0655482	+	0.997849i	$0.479120\pi$
$991$	−823.906	+	1427.05i	−0.831389	+	1.44001i	−0.896937	+	0.442158i	$0.854213\pi$
$992$	−848.998	−	227.488i	−0.855844	−	0.229323i
$993$		0			0
$994$	−1382.36	−	2132.34i	−1.39070	−	2.14522i
$995$	293.922	−	549.186i	0.295399	−	0.551945i
$996$		0			0
$997$	−466.765	−	1741.99i	−0.468170	−	1.74723i	−0.646161	−	0.763201i	$-0.723627\pi$
$997$	−466.765	−	1741.99i	−0.468170	−	1.74723i	0.177991	−	0.984032i	$-0.443040\pi$
$998$	−1463.52	+	392.150i	−1.46646	+	0.392936i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.ca.b.298.3		64
3.2	odd	2		105.3.v.a.88.14	yes	64
5.2	odd	4	inner	315.3.ca.b.172.14		64
7.2	even	3	inner	315.3.ca.b.163.14		64
15.2	even	4		105.3.v.a.67.3	yes	64
21.2	odd	6		105.3.v.a.58.3	yes	64
35.2	odd	12	inner	315.3.ca.b.37.3		64
105.2	even	12		105.3.v.a.37.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.v.a.37.14	✓	64	105.2	even	12
105.3.v.a.58.3	yes	64	21.2	odd	6
105.3.v.a.67.3	yes	64	15.2	even	4
105.3.v.a.88.14	yes	64	3.2	odd	2
315.3.ca.b.37.3		64	35.2	odd	12	inner
315.3.ca.b.163.14		64	7.2	even	3	inner
315.3.ca.b.172.14		64	5.2	odd	4	inner
315.3.ca.b.298.3		64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.88660 - 0.773463i) q^{2} +(4.27013 + 2.46536i) q^{4} +(-0.160937 - 4.99741i) q^{5} +(5.19830 + 4.68804i) q^{7} +(-1.96674 - 1.96674i) q^{8} +O(q^{10})\)	\(q+(-2.88660 - 0.773463i) q^{2} +(4.27013 + 2.46536i) q^{4} +(-0.160937 - 4.99741i) q^{5} +(5.19830 + 4.68804i) q^{7} +(-1.96674 - 1.96674i) q^{8} +(-3.40075 + 14.5500i) q^{10} +(-6.71313 + 11.6275i) q^{11} +(-3.94411 - 3.94411i) q^{13} +(-11.3794 - 17.5532i) q^{14} +(-5.70544 - 9.88212i) q^{16} +(2.53643 + 9.46609i) q^{17} +(-4.57992 + 2.64422i) q^{19} +(11.6332 - 21.7363i) q^{20} +(28.3716 - 28.3716i) q^{22} +(1.98091 - 7.39285i) q^{23} +(-24.9482 + 1.60854i) q^{25} +(8.33445 + 14.4357i) q^{26} +(10.6397 + 32.8342i) q^{28} +36.7188i q^{29} +(-9.71723 + 16.8307i) q^{31} +(11.7054 + 43.6852i) q^{32} -29.2867i q^{34} +(22.5914 - 26.7325i) q^{35} +(43.7832 + 11.7317i) q^{37} +(15.2656 - 4.09041i) q^{38} +(-9.51208 + 10.1451i) q^{40} -57.9301 q^{41} +(46.3359 + 46.3359i) q^{43} +(-57.3319 + 33.1006i) q^{44} +(-11.4362 + 19.8080i) q^{46} +(61.3721 + 16.4446i) q^{47} +(5.04463 + 48.7396i) q^{49} +(73.2597 + 14.6533i) q^{50} +(-7.11820 - 26.5655i) q^{52} +(38.8830 - 10.4187i) q^{53} +(59.1877 + 31.6770i) q^{55} +(-1.00355 - 19.4438i) q^{56} +(28.4006 - 105.992i) q^{58} +(60.4517 + 34.9018i) q^{59} +(-39.4523 - 68.3334i) q^{61} +(41.0677 - 41.0677i) q^{62} -89.5118i q^{64} +(-19.0756 + 20.3451i) q^{65} +(28.7353 + 107.241i) q^{67} +(-12.5064 + 46.6746i) q^{68} +(-85.8891 + 59.6925i) q^{70} +121.479 q^{71} +(4.70119 - 1.25968i) q^{73} +(-117.311 - 67.7293i) q^{74} -26.0758 q^{76} +(-89.4070 + 28.9718i) q^{77} +(-116.005 + 66.9753i) q^{79} +(-48.4668 + 30.1028i) q^{80} +(167.221 + 44.8068i) q^{82} +(-99.6896 - 99.6896i) q^{83} +(46.8977 - 14.1990i) q^{85} +(-97.9142 - 169.592i) q^{86} +(36.0712 - 9.66526i) q^{88} +(20.5641 - 11.8727i) q^{89} +(-2.01253 - 38.9928i) q^{91} +(26.6847 - 26.6847i) q^{92} +(-164.438 - 94.9381i) q^{94} +(13.9513 + 22.4622i) q^{95} +(-40.9086 + 40.9086i) q^{97} +(23.1364 - 144.594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{5} - 4 q^{7} - 24 q^{8}+O(q^{10}) \) 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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