LMFDB - Embedded newform 315.2.bl.i.146.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.8
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.i.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02342 + 0.590871i) q^{2} +(1.63294 - 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.01241 + 0.373820i) q^{6} +(-2.07834 - 1.63723i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} +O(q^{10})$	\(q+(1.02342 + 0.590871i) q^{2} +(1.63294 - 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.01241 + 0.373820i) q^{6} +(-2.07834 - 1.63723i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} +1.18174i q^{10} +(5.38278 + 3.10775i) q^{11} +(-0.794556 - 0.679171i) q^{12} +(-0.534292 + 0.308474i) q^{13} +(-1.15962 - 2.90360i) q^{14} +(1.31661 + 1.12541i) q^{15} +(1.21441 - 2.10343i) q^{16} -2.15945 q^{17} +(3.50202 - 0.551763i) q^{18} +4.75589i q^{19} +(0.301744 - 0.522636i) q^{20} +(-4.33931 - 1.47323i) q^{21} +(3.67255 + 6.36105i) q^{22} +(-3.22334 + 1.86099i) q^{23} +(-1.77680 - 5.02397i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.729072 q^{26} +(2.72036 - 4.42715i) q^{27} +(-0.228548 + 1.58024i) q^{28} +(-4.09268 - 2.36291i) q^{29} +(0.682467 + 1.92971i) q^{30} +(-7.25875 + 4.19084i) q^{31} +(-2.84321 + 1.64153i) q^{32} +(10.5845 + 1.96615i) q^{33} +(-2.21002 - 1.27596i) q^{34} +(0.378711 - 2.61851i) q^{35} +(-1.68969 - 0.650179i) q^{36} -2.00832 q^{37} +(-2.81012 + 4.86727i) q^{38} +(-0.694319 + 0.812277i) q^{39} +(2.66446 - 1.53832i) q^{40} +(-0.261960 - 0.453727i) q^{41} +(-3.57044 - 4.07170i) q^{42} +(2.75507 - 4.77192i) q^{43} -3.75098i q^{44} +(2.79987 + 1.07737i) q^{45} -4.39843 q^{46} +(3.25401 - 5.63611i) q^{47} +(0.768310 - 4.13610i) q^{48} +(1.63898 + 6.80542i) q^{49} +(-1.02342 + 0.590871i) q^{50} +(-3.52625 + 1.24710i) q^{51} +(0.322439 + 0.186160i) q^{52} +12.7283i q^{53} +(5.39993 - 2.92345i) q^{54} +6.21549i q^{55} +(-5.03717 + 6.39432i) q^{56} +(2.74658 + 7.76607i) q^{57} +(-2.79235 - 4.83649i) q^{58} +(-2.72719 - 4.72363i) q^{59} +(0.190901 - 1.02769i) q^{60} +(12.3587 + 7.13527i) q^{61} -9.90498 q^{62} +(-7.93662 + 0.100310i) q^{63} -8.73737 q^{64} +(-0.534292 - 0.308474i) q^{65} +(9.67061 + 8.26625i) q^{66} +(-0.146773 - 0.254218i) q^{67} +(0.651601 + 1.12861i) q^{68} +(-4.18876 + 4.90040i) q^{69} +(1.93478 - 2.45606i) q^{70} -5.45805i q^{71} +(-5.80279 - 7.17771i) q^{72} +0.406885i q^{73} +(-2.05535 - 1.18666i) q^{74} +(-0.316330 + 1.70292i) q^{75} +(2.48560 - 1.43506i) q^{76} +(-6.09914 - 15.2718i) q^{77} +(-1.19053 + 0.421047i) q^{78} +(-2.85397 + 4.94322i) q^{79} +2.42883 q^{80} +(1.88544 - 8.80029i) q^{81} -0.619137i q^{82} +(6.40891 - 11.1006i) q^{83} +(0.539399 + 2.71242i) q^{84} +(-1.07973 - 1.87014i) q^{85} +(5.63917 - 3.25578i) q^{86} +(-8.04769 - 1.49492i) q^{87} +(9.56144 - 16.5609i) q^{88} -0.957722 q^{89} +(2.22885 + 2.75696i) q^{90} +(1.61548 + 0.233645i) q^{91} +(1.94525 + 1.12309i) q^{92} +(-9.43283 + 11.0354i) q^{93} +(6.66043 - 3.84540i) q^{94} +(-4.11872 + 2.37795i) q^{95} +(-3.69478 + 4.32249i) q^{96} +(-2.17426 - 1.25531i) q^{97} +(-2.34376 + 7.93321i) q^{98} +(18.4193 - 2.90205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	$ 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.02342	+	0.590871i	0.723666	+	0.417809i	0.816100	−	0.577910i	$-0.196132\pi$
$2$	1.02342	+	0.590871i	0.723666	+	0.417809i	−0.0924347	+	0.995719i	$0.529465\pi$
$3$	1.63294	−	0.577510i	0.942776	−	0.333426i
$3$	1.63294	−	0.577510i	0.942776	−	0.333426i
$4$	−0.301744	−	0.522636i	−0.150872	−	0.261318i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.01241	+	0.373820i	0.821563	+	0.152611i
$7$	−2.07834	−	1.63723i	−0.785538	−	0.618814i
$7$	−2.07834	−	1.63723i	−0.785538	−	0.618814i
$8$		−	3.07665i		−	1.08776i
$9$	2.33296	−	1.88607i	0.777655	−	0.628692i
$10$			1.18174i			0.373699i
$11$	5.38278	+	3.10775i	1.62297	+	0.937021i	0.986121	+	0.166031i	$0.0530951\pi$
$11$	5.38278	+	3.10775i	1.62297	+	0.937021i	0.636847	+	0.770990i	$0.280238\pi$
$12$	−0.794556	−	0.679171i	−0.229369	−	0.196060i
$13$	−0.534292	+	0.308474i	−0.148186	+	0.0855552i	−0.572260	−	0.820072i	$-0.693933\pi$
$13$	−0.534292	+	0.308474i	−0.148186	+	0.0855552i	0.424074	+	0.905628i	$0.360600\pi$
$14$	−1.15962	−	2.90360i	−0.309921	−	0.776019i
$15$	1.31661	+	1.12541i	0.339946	+	0.290580i
$16$	1.21441	−	2.10343i	0.303603	−	0.525856i
$17$	−2.15945			−0.523744			−0.261872	−	0.965103i	$-0.584340\pi$
$17$	−2.15945			−0.523744			−0.261872	+	0.965103i	$0.584340\pi$
$18$	3.50202	−	0.551763i	0.825435	−	0.130052i
$19$			4.75589i			1.09108i	0.838086	+	0.545538i	$0.183675\pi$
$19$			4.75589i			1.09108i	−0.838086	+	0.545538i	$0.816325\pi$
$20$	0.301744	−	0.522636i	0.0674720	−	0.116865i
$21$	−4.33931	−	1.47323i	−0.946915	−	0.321484i
$22$	3.67255	+	6.36105i	0.782991	+	1.35618i
$23$	−3.22334	+	1.86099i	−0.672112	+	0.388044i	−0.796877	−	0.604142i	$-0.793516\pi$
$23$	−3.22334	+	1.86099i	−0.672112	+	0.388044i	0.124764	+	0.992186i	$0.460183\pi$
$24$	−1.77680	−	5.02397i	−0.362687	−	1.02551i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.729072			−0.142983
$27$	2.72036	−	4.42715i	0.523533	−	0.852006i
$28$	−0.228548	+	1.58024i	−0.0431914	+	0.298637i
$29$	−4.09268	−	2.36291i	−0.759992	−	0.438781i	0.0693012	−	0.997596i	$-0.477923\pi$
$29$	−4.09268	−	2.36291i	−0.759992	−	0.438781i	−0.829293	+	0.558814i	$0.811256\pi$
$30$	0.682467	+	1.92971i	0.124601	+	0.352315i
$31$	−7.25875	+	4.19084i	−1.30371	+	0.752698i	−0.981038	−	0.193813i	$-0.937914\pi$
$31$	−7.25875	+	4.19084i	−1.30371	+	0.752698i	−0.322672	+	0.946511i	$0.604581\pi$
$32$	−2.84321	+	1.64153i	−0.502613	+	0.290184i
$33$	10.5845	+	1.96615i	1.84252	+	0.342262i
$34$	−2.21002	−	1.27596i	−0.379015	−	0.218825i
$35$	0.378711	−	2.61851i	0.0640138	−	0.442608i
$36$	−1.68969	−	0.650179i	−0.281615	−	0.108363i
$37$	−2.00832			−0.330166			−0.165083	−	0.986280i	$-0.552789\pi$
$37$	−2.00832			−0.330166			−0.165083	+	0.986280i	$0.552789\pi$
$38$	−2.81012	+	4.86727i	−0.455861	+	0.789575i
$39$	−0.694319	+	0.812277i	−0.111180	+	0.130068i
$40$	2.66446	−	1.53832i	0.421287	−	0.243230i
$41$	−0.261960	−	0.453727i	−0.0409112	−	0.0708603i	0.844845	−	0.535012i	$-0.179693\pi$
$41$	−0.261960	−	0.453727i	−0.0409112	−	0.0708603i	−0.885756	+	0.464151i	$0.846359\pi$
$42$	−3.57044	−	4.07170i	−0.550931	−	0.628276i
$43$	2.75507	−	4.77192i	0.420144	−	0.727710i	−0.575809	−	0.817584i	$-0.695313\pi$
$43$	2.75507	−	4.77192i	0.420144	−	0.727710i	0.995953	+	0.0898736i	$0.0286463\pi$
$44$		−	3.75098i		−	0.565481i
$45$	2.79987	+	1.07737i	0.417380	+	0.160605i
$46$	−4.39843			−0.648513
$47$	3.25401	−	5.63611i	0.474646	−	0.822112i	−0.524932	−	0.851144i	$-0.675909\pi$
$47$	3.25401	−	5.63611i	0.474646	−	0.822112i	0.999578	+	0.0290325i	$0.00924263\pi$
$48$	0.768310	−	4.13610i	0.110896	−	0.596994i
$49$	1.63898	+	6.80542i	0.234140	+	0.972203i
$50$	−1.02342	+	0.590871i	−0.144733	+	0.0835617i
$51$	−3.52625	+	1.24710i	−0.493773	+	0.174630i
$52$	0.322439	+	0.186160i	0.0447142	+	0.0258158i
$53$			12.7283i			1.74837i	0.485596	+	0.874183i	$0.338603\pi$
$53$			12.7283i			1.74837i	−0.485596	+	0.874183i	$0.661397\pi$
$54$	5.39993	−	2.92345i	0.734838	−	0.397831i
$55$			6.21549i			0.838097i
$56$	−5.03717	+	6.39432i	−0.673120	+	0.854476i
$57$	2.74658	+	7.76607i	0.363793	+	1.02864i
$58$	−2.79235	−	4.83649i	−0.366653	−	0.635062i
$59$	−2.72719	−	4.72363i	−0.355050	−	0.614965i	0.632076	−	0.774906i	$-0.282203\pi$
$59$	−2.72719	−	4.72363i	−0.355050	−	0.614965i	−0.987127	+	0.159941i	$0.948870\pi$
$60$	0.190901	−	1.02769i	0.0246453	−	0.132674i
$61$	12.3587	+	7.13527i	1.58236	+	0.913578i	0.994513	+	0.104608i	$0.0333589\pi$
$61$	12.3587	+	7.13527i	1.58236	+	0.913578i	0.587850	+	0.808970i	$0.299974\pi$
$62$	−9.90498			−1.25793
$63$	−7.93662	+	0.100310i	−0.999920	+	0.0126378i
$64$	−8.73737			−1.09217
$65$	−0.534292	−	0.308474i	−0.0662708	−	0.0382615i
$66$	9.67061	+	8.26625i	1.19037	+	1.01751i
$67$	−0.146773	−	0.254218i	−0.0179312	−	0.0310577i	0.856921	−	0.515448i	$-0.172375\pi$
$67$	−0.146773	−	0.254218i	−0.0179312	−	0.0310577i	−0.874852	+	0.484391i	$0.839041\pi$
$68$	0.651601	+	1.12861i	0.0790183	+	0.136864i
$69$	−4.18876	+	4.90040i	−0.504268	+	0.589938i
$70$	1.93478	−	2.45606i	0.231250	−	0.293555i
$71$		−	5.45805i		−	0.647751i	−0.946100	−	0.323876i	$-0.895014\pi$
$71$		−	5.45805i		−	0.647751i	0.946100	−	0.323876i	$-0.104986\pi$
$72$	−5.80279	−	7.17771i	−0.683865	−	0.845901i
$73$			0.406885i			0.0476223i	0.999716	+	0.0238111i	$0.00758004\pi$
$73$			0.406885i			0.0476223i	−0.999716	+	0.0238111i	$0.992420\pi$
$74$	−2.05535	−	1.18666i	−0.238929	−	0.137946i
$75$	−0.316330	+	1.70292i	−0.0365266	+	0.196636i
$76$	2.48560	−	1.43506i	0.285118	−	0.164613i
$77$	−6.09914	−	15.2718i	−0.695062	−	1.74038i
$78$	−1.19053	+	0.421047i	−0.134801	+	0.0476741i
$79$	−2.85397	+	4.94322i	−0.321097	+	0.556156i	−0.980715	−	0.195445i	$-0.937385\pi$
$79$	−2.85397	+	4.94322i	−0.321097	+	0.556156i	0.659618	+	0.751601i	$0.270718\pi$
$80$	2.42883			0.271551
$81$	1.88544	−	8.80029i	0.209494	−	0.977810i
$82$		−	0.619137i		−	0.0683722i
$83$	6.40891	−	11.1006i	0.703469	−	1.21844i	−0.263772	−	0.964585i	$-0.584967\pi$
$83$	6.40891	−	11.1006i	0.703469	−	1.21844i	0.967241	−	0.253859i	$-0.0816999\pi$
$84$	0.539399	+	2.71242i	0.0588533	+	0.295949i
$85$	−1.07973	−	1.87014i	−0.117113	−	0.202845i
$86$	5.63917	−	3.25578i	0.608087	−	0.351079i
$87$	−8.04769	−	1.49492i	−0.862803	−	0.160272i
$88$	9.56144	−	16.5609i	1.01925	−	1.76540i
$89$	−0.957722			−0.101518			−0.0507592	−	0.998711i	$-0.516164\pi$
$89$	−0.957722			−0.101518			−0.0507592	+	0.998711i	$0.516164\pi$
$90$	2.22885	+	2.75696i	0.234942	+	0.290609i
$91$	1.61548	+	0.233645i	0.169348	+	0.0244926i
$92$	1.94525	+	1.12309i	0.202806	+	0.117090i
$93$	−9.43283	+	11.0354i	−0.978139	+	1.14432i
$94$	6.66043	−	3.84540i	0.686971	−	0.396623i
$95$	−4.11872	+	2.37795i	−0.422572	+	0.243972i
$96$	−3.69478	+	4.32249i	−0.377097	+	0.441162i
$97$	−2.17426	−	1.25531i	−0.220762	−	0.127457i	0.385541	−	0.922691i	$-0.374015\pi$
$97$	−2.17426	−	1.25531i	−0.220762	−	0.127457i	−0.606303	+	0.795234i	$0.707348\pi$
$98$	−2.34376	+	7.93321i	−0.236756	+	0.801375i
$99$	18.4193	−	2.90205i	1.85121	−	0.291667i
$100$	0.603488			0.0603488
$101$	5.94095	−	10.2900i	0.591147	−	1.02390i	−0.402932	−	0.915230i	$-0.632009\pi$
$101$	5.94095	−	10.2900i	0.591147	−	1.02390i	0.994078	−	0.108666i	$-0.0346579\pi$
$102$	−4.34570	−	0.807246i	−0.430289	−	0.0799293i
$103$	−3.77246	+	2.17803i	−0.371711	+	0.214608i	−0.674206	−	0.738543i	$-0.735514\pi$
$103$	−3.77246	+	2.17803i	−0.371711	+	0.214608i	0.302494	+	0.953151i	$0.402181\pi$
$104$	0.949065	+	1.64383i	0.0930635	+	0.161191i
$105$	−0.893803	−	4.49457i	−0.0872263	−	0.438625i
$106$	−7.52078	+	13.0264i	−0.730482	+	1.26523i
$107$		−	16.8978i		−	1.63357i	−0.576943	−	0.816784i	$-0.695755\pi$
$107$		−	16.8978i		−	1.63357i	0.576943	−	0.816784i	$-0.304245\pi$
$108$	−3.13464	−	0.0858893i	−0.301631	−	0.00826470i
$109$	−7.49502			−0.717892			−0.358946	−	0.933358i	$-0.616864\pi$
$109$	−7.49502			−0.717892			−0.358946	+	0.933358i	$0.616864\pi$
$110$	−3.67255	+	6.36105i	−0.350164	+	0.606502i
$111$	−3.27946	+	1.15982i	−0.311272	+	0.110086i
$112$	−5.96774	+	2.38336i	−0.563899	+	0.225206i
$113$	−10.8082	+	6.24010i	−1.01675	+	0.587020i	−0.913160	−	0.407601i	$-0.866366\pi$
$113$	−10.8082	+	6.24010i	−1.01675	+	0.587020i	−0.103588	+	0.994620i	$0.533032\pi$
$114$	−1.77785	+	9.57081i	−0.166511	+	0.896388i
$115$	−3.22334	−	1.86099i	−0.300578	−	0.173539i
$116$			2.85198i			0.264799i
$117$	−0.664680	+	1.72737i	−0.0614497	+	0.159696i
$118$		−	6.44567i		−	0.593372i
$119$	4.48807	+	3.53551i	0.411421	+	0.324100i
$120$	3.46249	−	4.05074i	0.316081	−	0.369780i
$121$	13.8162	+	23.9303i	1.25602	+	2.17548i
$122$	8.43205	+	14.6047i	0.763402	+	1.32225i
$123$	−0.689796	−	0.589624i	−0.0621968	−	0.0531646i
$124$	4.38057	+	2.52912i	0.393387	+	0.227122i
$125$	−1.00000			−0.0894427
$126$	−8.18175	−	4.58686i	−0.728888	−	0.408630i
$127$	−10.3479			−0.918228			−0.459114	−	0.888377i	$-0.651833\pi$
$127$	−10.3479			−0.918228			−0.459114	+	0.888377i	$0.651833\pi$
$128$	−3.25557	−	1.87960i	−0.287754	−	0.166135i
$129$	1.74302	−	9.38332i	0.153464	−	0.826155i
$130$	−0.364536	−	0.631395i	−0.0319719	−	0.0553770i
$131$	5.47102	+	9.47609i	0.478005	+	0.827929i	0.999682	−	0.0252138i	$-0.00802664\pi$
$131$	5.47102	+	9.47609i	0.478005	+	0.827929i	−0.521677	+	0.853143i	$0.674693\pi$
$132$	−2.16623	−	6.12511i	−0.188546	−	0.533122i
$133$	7.78647	−	9.88435i	0.675173	−	0.857082i
$134$		−	0.346896i		−	0.0299672i
$135$	5.19420	+	0.142322i	0.447046	+	0.0122491i
$136$			6.64387i			0.569707i
$137$	12.7922	+	7.38559i	1.09291	+	0.630994i	0.934351	−	0.356355i	$-0.115981\pi$
$137$	12.7922	+	7.38559i	1.09291	+	0.630994i	0.158563	+	0.987349i	$0.449314\pi$
$138$	−7.18235	+	2.54014i	−0.611403	+	0.216231i
$139$	−2.22917	+	1.28701i	−0.189076	+	0.109163i	−0.591550	−	0.806268i	$-0.701484\pi$
$139$	−2.22917	+	1.28701i	−0.189076	+	0.109163i	0.402474	+	0.915431i	$0.368150\pi$
$140$	−1.48280	+	0.592191i	−0.125319	+	0.0500493i
$141$	2.05868	−	11.0826i	0.173372	−	0.933327i
$142$	3.22500	−	5.58586i	0.270636	−	0.468755i
$143$	−3.83463			−0.320668
$144$	−1.13403	−	7.19769i	−0.0945029	−	0.599807i
$145$		−	4.72582i		−	0.392458i
$146$	−0.240416	+	0.416413i	−0.0198970	+	0.0344626i
$147$	6.60655	+	10.1663i	0.544899	+	0.838502i
$148$	0.605998	+	1.04962i	0.0498127	+	0.0862782i
$149$	2.37768	−	1.37275i	0.194787	−	0.112460i	−0.399435	−	0.916762i	$-0.630794\pi$
$149$	2.37768	−	1.37275i	0.194787	−	0.112460i	0.594222	+	0.804301i	$0.297460\pi$
$150$	−1.32994	+	1.55589i	−0.108589	+	0.127038i
$151$	4.45760	−	7.72079i	0.362754	−	0.628309i	−0.625659	−	0.780097i	$-0.715170\pi$
$151$	4.45760	−	7.72079i	0.362754	−	0.628309i	0.988413	+	0.151788i	$0.0485031\pi$
$152$	14.6322			1.18683
$153$	−5.03792	+	4.07289i	−0.407292	+	0.329273i
$154$	2.78167	−	19.2332i	0.224153	−	1.54986i
$155$	−7.25875	−	4.19084i	−0.583037	−	0.336617i
$156$	0.634032	+	0.117776i	0.0507632	+	0.00942963i
$157$	15.1714	−	8.75923i	1.21081	−	0.699063i	0.247876	−	0.968792i	$-0.420267\pi$
$157$	15.1714	−	8.75923i	1.21081	−	0.699063i	0.962936	+	0.269729i	$0.0869340\pi$
$158$	−5.84161	+	3.37265i	−0.464733	+	0.268314i
$159$	7.35072	+	20.7845i	0.582950	+	1.64832i
$160$	−2.84321	−	1.64153i	−0.224775	−	0.129774i
$161$	9.74605	+	1.40956i	0.768097	+	0.111089i
$162$	7.12943	−	7.89232i	0.560141	−	0.620079i
$163$	11.8497			0.928143			0.464071	−	0.885798i	$-0.346388\pi$
$163$	11.8497			0.928143			0.464071	+	0.885798i	$0.346388\pi$
$164$	−0.158090	+	0.273819i	−0.0123447	+	0.0213817i
$165$	3.58951	+	10.1495i	0.279443	+	0.790138i
$166$	13.1180	−	7.57367i	1.01815	−	0.587831i
$167$	−0.847165	−	1.46733i	−0.0655556	−	0.113546i	0.831385	−	0.555697i	$-0.187549\pi$
$167$	−0.847165	−	1.46733i	−0.0655556	−	0.113546i	−0.896940	+	0.442152i	$0.854215\pi$
$168$	−4.53260	+	13.3505i	−0.349698	+	1.03002i
$169$	−6.30969	+	10.9287i	−0.485361	+	0.840669i
$170$		−	2.55191i		−	0.195723i
$171$	8.96997	+	11.0953i	0.685951	+	0.848481i
$172$	−3.32530			−0.253552
$173$	4.39665	−	7.61522i	0.334271	−	0.578974i	−0.649074	−	0.760726i	$-0.724843\pi$
$173$	4.39665	−	7.61522i	0.334271	−	0.578974i	0.983345	+	0.181751i	$0.0581766\pi$
$174$	−7.35285	−	6.28507i	−0.557418	−	0.476470i
$175$	2.45705	−	0.981280i	0.185735	−	0.0741778i
$176$	13.0738	−	7.54818i	0.985477	−	0.568965i
$177$	−7.18128	−	6.13841i	−0.539778	−	0.461392i
$178$	−0.980150	−	0.565890i	−0.0734653	−	0.0424152i
$179$		−	10.0909i		−	0.754226i	−0.926167	−	0.377113i	$-0.876917\pi$
$179$		−	10.0909i		−	0.754226i	0.926167	−	0.377113i	$-0.123083\pi$
$180$	−0.281773	−	1.78840i	−0.0210021	−	0.133300i
$181$			0.795517i			0.0591303i	0.999563	+	0.0295652i	$0.00941226\pi$
$181$			0.795517i			0.0591303i	−0.999563	+	0.0295652i	$0.990588\pi$
$182$	1.51526	+	1.19366i	0.112318	+	0.0884797i
$183$	24.3016	+	4.51420i	1.79643	+	0.333699i
$184$	5.72563	+	9.91708i	0.422099	+	0.731097i
$185$	−1.00416	−	1.73925i	−0.0738273	−	0.127873i
$186$	−16.1742	+	5.72023i	−1.18595	+	0.419427i
$187$	−11.6238	−	6.71103i	−0.850019	−	0.490759i
$188$	−3.92751			−0.286443
$189$	−12.9021	+	4.74728i	−0.938487	+	0.345314i
$190$	−5.62023			−0.407735
$191$	14.7531	+	8.51768i	1.06749	+	0.616318i	0.927496	−	0.373834i	$-0.121957\pi$
$191$	14.7531	+	8.51768i	1.06749	+	0.616318i	0.139998	+	0.990152i	$0.455290\pi$
$192$	−14.2676	+	5.04592i	−1.02967	+	0.364158i
$193$	−9.88703	−	17.1248i	−0.711684	−	1.23267i	−0.964225	−	0.265086i	$-0.914600\pi$
$193$	−9.88703	−	17.1248i	−0.711684	−	1.23267i	0.252541	−	0.967586i	$-0.418734\pi$
$194$	−1.48345	−	2.56941i	−0.106505	−	0.184473i
$195$	−1.05061	−	0.195159i	−0.0752359	−	0.0139756i
$196$	3.06221	−	2.91008i	0.218729	−	0.207863i
$197$		−	3.88854i		−	0.277047i	−0.990359	−	0.138523i	$-0.955764\pi$
$197$		−	3.88854i		−	0.277047i	0.990359	−	0.138523i	$-0.0442356\pi$
$198$	20.5653	+	7.91339i	1.46152	+	0.562380i
$199$		−	1.72285i		−	0.122130i	−0.998134	−	0.0610649i	$-0.980550\pi$
$199$		−	1.72285i		−	0.122130i	0.998134	−	0.0610649i	$-0.0194497\pi$
$200$	2.66446	+	1.53832i	0.188405	+	0.108776i
$201$	−0.386485	−	0.330360i	−0.0272605	−	0.0233018i
$202$	12.1601	−	7.02066i	0.855585	−	0.493972i
$203$	4.63735	+	11.6116i	0.325478	+	0.814972i
$204$	1.71581	+	1.46664i	0.120130	+	0.102685i
$205$	0.261960	−	0.453727i	0.0182961	−	0.0316897i
$206$	−5.14774			−0.358660
$207$	−4.00996	+	10.4211i	−0.278711	+	0.724316i
$208$			1.49846i			0.103899i
$209$	−14.7801	+	25.5999i	−1.02236	+	1.77078i
$210$	1.74097	−	5.12794i	0.120138	−	0.353861i
$211$	−5.79495	−	10.0372i	−0.398941	−	0.690986i	0.594655	−	0.803981i	$-0.297289\pi$
$211$	−5.79495	−	10.0372i	−0.398941	−	0.690986i	−0.993596	+	0.112995i	$0.963955\pi$
$212$	6.65227	−	3.84069i	0.456880	−	0.263780i
$213$	−3.15208	−	8.91265i	−0.215977	−	0.610684i
$214$	9.98439	−	17.2935i	0.682519	−	1.18216i
$215$	5.51013			0.375788
$216$	−13.6208	−	8.36958i	−0.926777	−	0.569478i
$217$	21.9475	+	3.17424i	1.48989	+	0.215481i
$218$	−7.67053	−	4.42858i	−0.519514	−	0.299942i
$219$	0.234980	+	0.664417i	0.0158785	+	0.0448972i
$220$	3.24844	−	1.87549i	0.219010	−	0.126445i
$221$	1.15378	−	0.666134i	0.0776115	−	0.0448090i
$222$	−4.04156	−	0.750750i	−0.271252	−	0.0503870i
$223$	−21.1708	−	12.2230i	−1.41770	−	0.818511i	−0.421607	−	0.906779i	$-0.638534\pi$
$223$	−21.1708	−	12.2230i	−1.41770	−	0.818511i	−0.996097	+	0.0882674i	$0.971867\pi$
$224$	8.59670	+	1.24333i	0.574391	+	0.0830734i
$225$	0.466907	+	2.96344i	0.0311271	+	0.197563i
$226$	−14.7484			−0.981047
$227$	1.06827	−	1.85031i	0.0709039	−	0.122809i	−0.828394	−	0.560146i	$-0.810745\pi$
$227$	1.06827	−	1.85031i	0.0709039	−	0.122809i	0.899298	+	0.437337i	$0.144078\pi$
$228$	3.23007	−	3.77882i	0.213916	−	0.250259i
$229$	−20.4349	+	11.7981i	−1.35037	+	0.779639i	−0.988302	−	0.152511i	$-0.951264\pi$
$229$	−20.4349	+	11.7981i	−1.35037	+	0.779639i	−0.362072	+	0.932150i	$0.617931\pi$
$230$	−2.19921	−	3.80915i	−0.145012	−	0.251168i
$231$	−18.7791	−	21.4155i	−1.23557	−	1.40904i
$232$	−7.26984	+	12.5917i	−0.477289	+	0.826688i
$233$		−	0.828258i		−	0.0542610i	−0.999632	−	0.0271305i	$-0.991363\pi$
$233$		−	0.828258i		−	0.0542610i	0.999632	−	0.0271305i	$-0.00863697\pi$
$234$	−1.70090	+	1.37508i	−0.111191	+	0.0898921i
$235$	6.50802			0.424537
$236$	−1.64583	+	2.85066i	−0.107134	+	0.185562i
$237$	−1.80559	+	9.72017i	−0.117286	+	0.631393i
$238$	2.50414	+	6.27017i	0.162319	+	0.406435i
$239$	16.2406	−	9.37651i	1.05052	−	0.606516i	0.127723	−	0.991810i	$-0.459233\pi$
$239$	16.2406	−	9.37651i	1.05052	−	0.606516i	0.922794	+	0.385294i	$0.125900\pi$
$240$	3.96612	−	1.40267i	0.256012	−	0.0905421i
$241$	−15.8128	−	9.12955i	−1.01859	−	0.588086i	−0.104898	−	0.994483i	$-0.533452\pi$
$241$	−15.8128	−	9.12955i	−1.01859	−	0.588086i	−0.913697	+	0.406397i	$0.866785\pi$
$242$			32.6543i			2.09910i
$243$	−2.00345	−	15.4592i	−0.128521	−	0.991707i
$244$		−	8.61210i		−	0.551333i
$245$	−5.07418	+	4.82211i	−0.324177	+	0.308073i
$246$	−0.357558	−	1.01101i	−0.0227971	−	0.0644597i
$247$	−1.46707	−	2.54104i	−0.0933473	−	0.161682i
$248$	12.8938	+	22.3326i	0.818754	+	1.41812i
$249$	4.05466	−	21.8277i	0.256953	−	1.38327i
$250$	−1.02342	−	0.590871i	−0.0647266	−	0.0373699i
$251$	15.0543			0.950219			0.475109	−	0.879927i	$-0.342408\pi$
$251$	15.0543			0.950219			0.475109	+	0.879927i	$0.342408\pi$
$252$	2.44725	+	4.11770i	0.154162	+	0.259390i
$253$	−23.1340			−1.45442
$254$	−10.5902	−	6.11427i	−0.664490	−	0.383643i
$255$	−2.84315	−	2.43027i	−0.178045	−	0.152189i
$256$	6.51617	+	11.2863i	0.407261	+	0.705396i
$257$	12.8086	+	22.1852i	0.798979	+	1.38387i	0.920282	+	0.391257i	$0.127960\pi$
$257$	12.8086	+	22.1852i	0.798979	+	1.38387i	−0.121302	+	0.992616i	$0.538707\pi$
$258$	7.32816	−	8.57315i	0.456232	−	0.533741i
$259$	4.17396	+	3.28807i	0.259358	+	0.204311i
$260$			0.372320i			0.0230903i
$261$	−14.0047	+	2.20652i	−0.866869	+	0.136580i
$262$			12.9307i			0.798859i
$263$	−15.7710	−	9.10540i	−0.972483	−	0.561463i	−0.0724906	−	0.997369i	$-0.523095\pi$
$263$	−15.7710	−	9.10540i	−0.972483	−	0.561463i	−0.899992	+	0.435906i	$0.856428\pi$
$264$	6.04914	−	32.5647i	0.372299	−	2.00422i
$265$	−11.0230	+	6.36415i	−0.677139	+	0.390947i
$266$	13.8092	−	5.51502i	0.846696	−	0.338148i
$267$	−1.56390	+	0.553094i	−0.0957091	+	0.0338488i
$268$	−0.0885758	+	0.153418i	−0.00541063	+	0.00937148i
$269$	22.2650			1.35752			0.678761	−	0.734359i	$-0.262517\pi$
$269$	22.2650			1.35752			0.678761	+	0.734359i	$0.262517\pi$
$270$	5.23175	+	3.21476i	0.318394	+	0.195644i
$271$		−	27.3015i		−	1.65845i	−0.558918	−	0.829223i	$-0.688783\pi$
$271$		−	27.3015i		−	1.65845i	0.558918	−	0.829223i	$-0.311217\pi$
$272$	−2.62247	+	4.54224i	−0.159010	+	0.275414i
$273$	2.77291	−	0.551430i	0.167824	−	0.0333740i
$274$	8.72786	+	15.1171i	0.527269	+	0.913257i
$275$	−5.38278	+	3.10775i	−0.324594	+	0.187404i
$276$	3.82506	+	0.710533i	0.230241	+	0.0427690i
$277$	−7.57578	+	13.1216i	−0.455185	+	0.788403i	−0.998699	−	0.0509971i	$-0.983760\pi$
$277$	−7.57578	+	13.1216i	−0.455185	+	0.788403i	0.543514	+	0.839400i	$0.317093\pi$
$278$	−3.04183			−0.182437
$279$	−9.03017	+	23.4676i	−0.540622	+	1.40497i
$280$	−8.05623	−	1.16516i	−0.481452	−	0.0696317i
$281$	−13.4999	−	7.79419i	−0.805338	−	0.464962i	0.0399960	−	0.999200i	$-0.487265\pi$
$281$	−13.4999	−	7.79419i	−0.805338	−	0.464962i	−0.845334	+	0.534237i	$0.820599\pi$
$282$	8.65530	−	10.1258i	0.515415	−	0.602980i
$283$	12.1672	−	7.02475i	0.723266	−	0.417578i	−0.0926875	−	0.995695i	$-0.529546\pi$
$283$	12.1672	−	7.02475i	0.723266	−	0.417578i	0.815954	+	0.578117i	$0.196212\pi$
$284$	−2.85257	+	1.64693i	−0.169269	+	0.0977275i
$285$	−5.35233	+	6.26164i	−0.317044	+	0.370908i
$286$	−3.92443	−	2.26577i	−0.232056	−	0.133978i
$287$	−0.198414	+	1.37189i	−0.0117120	+	0.0809799i
$288$	−3.53706	+	9.19213i	−0.208423	+	0.541651i
$289$	−12.3368			−0.725692
$290$	2.79235	−	4.83649i	0.163972	−	0.284008i
$291$	−4.27538	−	0.794183i	−0.250627	−	0.0465558i
$292$	0.212653	−	0.122775i	0.0124446	−	0.00718487i
$293$	−3.34242	−	5.78924i	−0.195266	−	0.338211i	0.751721	−	0.659481i	$-0.229224\pi$
$293$	−3.34242	−	5.78924i	−0.195266	−	0.338211i	−0.946988	+	0.321270i	$0.895890\pi$
$294$	0.754292	+	14.3080i	0.0439912	+	0.834458i
$295$	2.72719	−	4.72363i	0.158783	−	0.275021i
$296$			6.17889i			0.359141i
$297$	28.4015	−	15.3762i	1.64802	−	0.892217i
$298$	3.24448			0.187948
$299$	1.14814	−	1.98863i	0.0663984	−	0.115005i
$300$	0.985458	−	0.348520i	0.0568954	−	0.0201218i
$301$	−13.5387	+	5.40699i	−0.780356	+	0.311653i
$302$	9.12397	−	5.26773i	0.525026	−	0.303124i
$303$	3.75860	−	20.2339i	0.215926	−	1.16241i
$304$	10.0037	+	5.77562i	0.573749	+	0.331254i
$305$			14.2705i			0.817129i
$306$	−7.56245	+	1.19150i	−0.432316	+	0.0681138i
$307$			14.6061i			0.833615i	0.908995	+	0.416808i	$0.136851\pi$
$307$			14.6061i			0.833615i	−0.908995	+	0.416808i	$0.863149\pi$
$308$	−6.14120	+	7.79580i	−0.349927	+	0.444207i
$309$	−4.90235	+	5.73522i	−0.278885	+	0.326265i
$310$	−4.95249	−	8.57797i	−0.281283	−	0.487196i
$311$	−9.43641	−	16.3443i	−0.535090	−	0.926803i	−0.999159	−	0.0410038i	$-0.986944\pi$
$311$	−9.43641	−	16.3443i	−0.535090	−	0.926803i	0.464069	−	0.885799i	$-0.346389\pi$
$312$	2.49909	+	2.13617i	0.141483	+	0.120937i
$313$	15.4266	+	8.90656i	0.871964	+	0.503429i	0.868000	−	0.496563i	$-0.165405\pi$
$313$	15.4266	+	8.90656i	0.871964	+	0.503429i	0.00396365	+	0.999992i	$0.498738\pi$
$314$	20.7023			1.16830
$315$	−4.05518	−	6.82316i	−0.228484	−	0.384442i
$316$	3.44467			0.193778
$317$	−22.7317	−	13.1242i	−1.27674	−	0.737127i	−0.300494	−	0.953784i	$-0.597152\pi$
$317$	−22.7317	−	13.1242i	−1.27674	−	0.737127i	−0.976248	+	0.216656i	$0.930485\pi$
$318$	−4.75809	+	25.6146i	−0.266821	+	1.43639i
$319$	−14.6866	−	25.4380i	−0.822295	−	1.42426i
$320$	−4.36869	−	7.56679i	−0.244217	−	0.422996i
$321$	−9.75863	−	27.5930i	−0.544674	−	1.54009i
$322$	9.14142	+	7.20122i	0.509431	+	0.401308i
$323$		−	10.2701i		−	0.571445i
$324$	−5.16827	+	1.67003i	−0.287126	+	0.0927797i
$325$		−	0.616947i		−	0.0342221i
$326$	12.1272	+	7.00166i	0.671665	+	0.387786i
$327$	−12.2389	+	4.32845i	−0.676812	+	0.239364i
$328$	−1.39596	+	0.805958i	−0.0770790	+	0.0445016i
$329$	−15.9905	+	6.38619i	−0.881586	+	0.352082i
$330$	−2.32348	+	12.5081i	−0.127903	+	0.688549i
$331$	−9.75588	+	16.8977i	−0.536232	+	0.928781i	0.462871	+	0.886426i	$0.346819\pi$
$331$	−9.75588	+	16.8977i	−0.536232	+	0.928781i	−0.999103	+	0.0423550i	$0.986514\pi$
$332$	−7.73540			−0.424535
$333$	−4.68534	+	3.78784i	−0.256755	+	0.207572i
$334$		−	2.00226i		−	0.109559i
$335$	0.146773	−	0.254218i	0.00801907	−	0.0138894i
$336$	−8.36854	+	7.33831i	−0.456541	+	0.400337i
$337$	10.2676	+	17.7840i	0.559311	+	0.968755i	0.997554	+	0.0698988i	$0.0222677\pi$
$337$	10.2676	+	17.7840i	0.559311	+	0.968755i	−0.438243	+	0.898857i	$0.644399\pi$
$338$	−12.9149	+	7.45642i	−0.702478	+	0.405576i
$339$	−14.0453	+	16.4315i	−0.762838	+	0.892438i
$340$	−0.651601	+	1.12861i	−0.0353380	+	0.0612073i
$341$	−52.0963			−2.82117
$342$	2.62412	+	16.6552i	0.141896	+	0.900613i
$343$	7.73567	−	16.8273i	0.417687	−	0.908591i
$344$	−14.6815	−	8.47637i	−0.791574	−	0.457015i
$345$	−6.33825	−	1.17738i	−0.341240	−	0.0633878i
$346$	8.99921	−	5.19570i	0.483801	−	0.279322i
$347$	−5.28238	+	3.04978i	−0.283573	+	0.163721i	−0.635040	−	0.772479i	$-0.719016\pi$
$347$	−5.28238	+	3.04978i	−0.283573	+	0.163721i	0.351467	+	0.936200i	$0.385683\pi$
$348$	1.64704	+	4.65709i	0.0882909	+	0.249646i
$349$	27.8341	+	16.0700i	1.48992	+	0.860207i	0.999934	−	0.0115214i	$-0.00366744\pi$
$349$	27.8341	+	16.0700i	1.48992	+	0.860207i	0.489989	+	0.871729i	$0.337001\pi$
$350$	3.09440	+	0.447538i	0.165402	+	0.0239219i
$351$	−0.0878049	+	3.20455i	−0.00468668	+	0.171046i
$352$	−20.4058			−1.08763
$353$	−0.948987	+	1.64369i	−0.0505095	+	0.0874850i	−0.890175	−	0.455619i	$-0.849418\pi$
$353$	−0.948987	+	1.64369i	−0.0505095	+	0.0874850i	0.839665	+	0.543104i	$0.182751\pi$
$354$	−3.72244	−	10.5254i	−0.197845	−	0.559417i
$355$	4.72681	−	2.72902i	0.250873	−	0.144842i
$356$	0.288987	+	0.500540i	0.0153163	+	0.0265286i
$357$	9.37053	+	3.18136i	0.495941	+	0.168375i
$358$	5.96239	−	10.3272i	0.315122	−	0.545807i
$359$			11.5006i			0.606976i	0.952835	+	0.303488i	$0.0981513\pi$
$359$			11.5006i			0.606976i	−0.952835	+	0.303488i	$0.901849\pi$
$360$	3.31469	−	8.61422i	0.174699	−	0.454009i
$361$	−3.61851			−0.190448
$362$	−0.470048	+	0.814147i	−0.0247052	+	0.0427906i
$363$	36.3809	+	31.0977i	1.90950	+	1.63221i
$364$	−0.365351	−	0.914809i	−0.0191496	−	0.0479490i
$365$	−0.352373	+	0.203442i	−0.0184440	+	0.0106487i
$366$	22.2034	+	18.9790i	1.16059	+	0.992049i
$367$	−16.0654	−	9.27534i	−0.838605	−	0.484169i	0.0181848	−	0.999835i	$-0.494211\pi$
$367$	−16.0654	−	9.27534i	−0.838605	−	0.484169i	−0.856790	+	0.515666i	$0.827545\pi$
$368$			9.04007i			0.471246i
$369$	−1.46691	−	0.564454i	−0.0763641	−	0.0293843i
$370$		−	2.37331i		−	0.123383i
$371$	20.8391	−	26.4537i	1.08191	−	1.37341i
$372$	8.61379	+	1.60007i	0.446604	+	0.0829600i
$373$	−10.2802	−	17.8058i	−0.532288	−	0.921950i	−0.999289	−	0.0376935i	$-0.987999\pi$
$373$	−10.2802	−	17.8058i	−0.532288	−	0.921950i	0.467001	−	0.884257i	$-0.345334\pi$
$374$	−7.93070	−	13.7364i	−0.410087	−	0.710291i
$375$	−1.63294	+	0.577510i	−0.0843245	+	0.0298225i
$376$	−17.3403	−	10.0115i	−0.894260	−	0.516301i
$377$	2.91558			0.150160
$378$	−16.0092	−	2.76500i	−0.823426	−	0.142216i
$379$	9.97838			0.512555			0.256278	−	0.966603i	$-0.417504\pi$
$379$	9.97838			0.512555			0.256278	+	0.966603i	$0.417504\pi$
$380$	2.48560	+	1.43506i	0.127509	+	0.0736171i
$381$	−16.8975	+	5.97602i	−0.865684	+	0.306161i
$382$	10.0657	+	17.4343i	0.515006	+	0.892016i
$383$	1.97163	+	3.41496i	0.100746	+	0.174496i	0.911992	−	0.410208i	$-0.134544\pi$
$383$	1.97163	+	3.41496i	0.100746	+	0.174496i	−0.811246	+	0.584704i	$0.801211\pi$
$384$	−6.40162	−	1.18915i	−0.326681	−	0.0606835i
$385$	10.1762	−	12.9179i	0.518626	−	0.658357i
$386$		−	23.3678i		−	1.18939i
$387$	−2.57272	−	16.3290i	−0.130779	−	0.830048i
$388$			1.51513i			0.0769189i
$389$	28.2571	+	16.3142i	1.43269	+	0.827165i	0.997325	−	0.0730880i	$-0.0232854\pi$
$389$	28.2571	+	16.3142i	1.43269	+	0.827165i	0.435367	+	0.900253i	$0.356619\pi$
$390$	−0.959901	−	0.820505i	−0.0486065	−	0.0415479i
$391$	6.96064	−	4.01873i	0.352015	−	0.203236i
$392$	20.9379	−	5.04256i	1.05752	−	0.254688i
$393$	14.4064	+	12.3143i	0.726705	+	0.621173i
$394$	2.29762	−	3.97960i	0.115753	−	0.200489i
$395$	−5.70794			−0.287198
$396$	−7.07462	−	8.75089i	−0.355513	−	0.439749i
$397$			16.7556i			0.840940i	0.907306	+	0.420470i	$0.138135\pi$
$397$			16.7556i			0.840940i	−0.907306	+	0.420470i	$0.861865\pi$
$398$	1.01798	−	1.76320i	0.0510269	−	0.0883812i
$399$	7.00651	−	20.6373i	0.350764	−	1.03316i
$400$	1.21441	+	2.10343i	0.0607207	+	0.105171i
$401$	6.75815	−	3.90182i	0.337486	−	0.194848i	−0.321674	−	0.946851i	$-0.604245\pi$
$401$	6.75815	−	3.90182i	0.337486	−	0.194848i	0.659160	+	0.752003i	$0.270912\pi$
$402$	−0.200336	−	0.566458i	−0.00999184	−	0.0282524i
$403$	2.58553	−	4.47827i	0.128794	−	0.223078i
$404$	−7.17058			−0.356750
$405$	8.56400	−	2.76730i	0.425548	−	0.137508i
$406$	−2.11499	+	14.6236i	−0.104965	+	0.725755i
$407$	−10.8103	−	6.24135i	−0.535848	−	0.309372i
$408$	3.83690	+	10.8490i	0.189955	+	0.537107i
$409$	−16.2794	+	9.39890i	−0.804963	+	0.464746i	−0.845204	−	0.534444i	$-0.820521\pi$
$409$	−16.2794	+	9.39890i	−0.804963	+	0.464746i	0.0402405	+	0.999190i	$0.487188\pi$
$410$	0.536188	−	0.309568i	0.0264805	−	0.0152885i
$411$	25.1541	+	4.67257i	1.24076	+	0.230481i
$412$	2.27663	+	1.31442i	0.112162	+	0.0647566i
$413$	−2.06563	+	14.2823i	−0.101643	+	0.702788i
$414$	−10.2614	+	8.29576i	−0.504319	+	0.407715i
$415$	12.8178			0.629202
$416$	1.01274	−	1.75411i	0.0496535	−	0.0860023i
$417$	−2.89683	+	3.38898i	−0.141859	+	0.165959i
$418$	−30.2525	+	17.4663i	−1.47970	+	0.854303i
$419$	−13.0224	−	22.5554i	−0.636185	−	1.10190i	−0.986263	−	0.165184i	$-0.947178\pi$
$419$	−13.0224	−	22.5554i	−0.636185	−	1.10190i	0.350078	−	0.936721i	$-0.386155\pi$
$420$	−2.07932	+	1.82334i	−0.101461	+	0.0889700i
$421$	−19.4365	+	33.6651i	−0.947279	+	1.64074i	−0.196157	+	0.980572i	$0.562846\pi$
$421$	−19.4365	+	33.6651i	−0.947279	+	1.64074i	−0.751122	+	0.660163i	$0.770487\pi$
$422$		−	13.6963i		−	0.666724i
$423$	−3.03864	−	19.2862i	−0.147744	−	0.937725i
$424$	39.1605			1.90180
$425$	1.07973	−	1.87014i	0.0523744	−	0.0907151i
$426$	2.04033	−	10.9838i	0.0988542	−	0.532168i
$427$	−14.0034	−	35.0634i	−0.677672	−	1.69684i
$428$	−8.83138	+	5.09880i	−0.426881	+	0.246460i
$429$	−6.26171	+	2.21454i	−0.302318	+	0.106919i
$430$	5.63917	+	3.25578i	0.271945	+	0.157007i
$431$			3.12892i			0.150715i	0.997157	+	0.0753573i	$0.0240097\pi$
$431$			3.12892i			0.150715i	−0.997157	+	0.0753573i	$0.975990\pi$
$432$	−6.00855	−	11.0985i	−0.289086	−	0.533975i
$433$			18.1302i			0.871282i	0.900120	+	0.435641i	$0.143478\pi$
$433$			18.1302i			0.871282i	−0.900120	+	0.435641i	$0.856522\pi$
$434$	20.5859	+	16.2167i	0.988155	+	0.778427i
$435$	−2.72921	−	7.71696i	−0.130856	−	0.370000i
$436$	2.26158	+	3.91716i	0.108310	+	0.187598i
$437$	−8.85069	−	15.3298i	−0.423386	−	0.733326i
$438$	−0.152102	+	0.818819i	−0.00726770	+	0.0391247i
$439$	−1.68550	−	0.973121i	−0.0804443	−	0.0464445i	0.459238	−	0.888313i	$-0.348122\pi$
$439$	−1.68550	−	0.973121i	−0.0804443	−	0.0464445i	−0.539683	+	0.841869i	$0.681456\pi$
$440$	19.1229			0.911648
$441$	16.6592	+	12.7856i	0.793296	+	0.608837i
$442$	1.57440			0.0748864
$443$	0.462264	+	0.266888i	0.0219628	+	0.0126802i	0.510941	−	0.859616i	$-0.329297\pi$
$443$	0.462264	+	0.266888i	0.0219628	+	0.0126802i	−0.488978	+	0.872296i	$0.662630\pi$
$444$	1.59572	+	1.36399i	0.0757296	+	0.0647322i
$445$	−0.478861	−	0.829412i	−0.0227002	−	0.0393179i
$446$	−14.4444	−	25.0184i	−0.683962	−	1.18466i
$447$	3.08982	−	3.61475i	0.146144	−	0.170972i
$448$	18.1592	+	14.3051i	0.857942	+	0.675850i
$449$		−	19.0944i		−	0.901120i	−0.892746	−	0.450560i	$-0.851224\pi$
$449$		−	19.0944i		−	0.901120i	0.892746	−	0.450560i	$-0.148776\pi$
$450$	−1.27317	+	3.30872i	−0.0600179	+	0.155975i
$451$		−	3.25642i		−	0.153339i
$452$	6.52261	+	3.76583i	0.306798	+	0.177130i
$453$	2.82014	−	15.1819i	0.132502	−	0.713306i
$454$	2.18658	−	1.26242i	0.102621	−	0.0592485i
$455$	0.605398	+	1.51587i	0.0283815	+	0.0710651i
$456$	23.8935	−	8.45025i	1.11891	−	0.395719i
$457$	11.5372	−	19.9830i	0.539688	−	0.934767i	−0.459233	−	0.888316i	$-0.651876\pi$
$457$	11.5372	−	19.9830i	0.539688	−	0.934767i	0.998921	−	0.0464507i	$-0.0147910\pi$
$458$	−27.8845			−1.30296
$459$	−5.87447	+	9.56022i	−0.274197	+	0.446233i
$460$			2.24618i			0.104728i
$461$	−11.3755	+	19.7029i	−0.529808	+	0.917655i	0.469587	+	0.882886i	$0.344403\pi$
$461$	−11.3755	+	19.7029i	−0.529808	+	0.917655i	−0.999395	+	0.0347688i	$0.988931\pi$
$462$	−6.56508	−	33.0130i	−0.305435	−	1.53591i
$463$	6.06653	+	10.5075i	0.281935	+	0.488327i	0.971861	−	0.235553i	$-0.0756903\pi$
$463$	6.06653	+	10.5075i	0.281935	+	0.488327i	−0.689926	+	0.723880i	$0.742357\pi$
$464$	−9.94041	+	5.73910i	−0.461472	+	0.266431i
$465$	−14.2733	−	2.65138i	−0.661910	−	0.122955i
$466$	0.489393	−	0.847654i	0.0226707	−	0.0392668i
$467$	−4.61293			−0.213461			−0.106731	−	0.994288i	$-0.534038\pi$
$467$	−4.61293			−0.213461			−0.106731	+	0.994288i	$0.534038\pi$
$468$	1.10335	−	0.173839i	0.0510024	−	0.00803570i
$469$	−0.111169	+	0.768653i	−0.00513331	+	0.0354931i
$470$	6.66043	+	3.84540i	0.307223	+	0.177375i
$471$	19.7155	−	23.0649i	0.908440	−	1.06278i
$472$	−14.5330	+	8.39061i	−0.668934	+	0.386209i
$473$	29.6598	−	17.1241i	1.36376	−	0.787367i
$474$	−7.59124	+	8.88092i	−0.348677	+	0.407914i
$475$	−4.11872	−	2.37795i	−0.188980	−	0.109108i
$476$	0.493537	−	3.41245i	0.0226212	−	0.156409i
$477$	24.0065	+	29.6947i	1.09918	+	1.35963i
$478$	22.1612			1.01363
$479$	−4.54166	+	7.86639i	−0.207514	+	0.359424i	−0.950931	−	0.309404i	$-0.899871\pi$
$479$	−4.54166	+	7.86639i	−0.207514	+	0.359424i	0.743417	+	0.668828i	$0.233204\pi$
$480$	−5.59078	−	1.03853i	−0.255183	−	0.0474021i
$481$	1.07303	−	0.619513i	0.0489259	−	0.0282474i
$482$	−10.7888	−	18.6867i	−0.491415	−	0.851155i
$483$	16.7287	−	3.32673i	0.761183	−	0.151371i
$484$	8.33790	−	14.4417i	0.378995	−	0.656439i
$485$		−	2.51062i		−	0.114001i
$486$	7.08401	−	17.0050i	0.321337	−	0.771361i
$487$	23.6659			1.07240			0.536201	−	0.844090i	$-0.319859\pi$
$487$	23.6659			1.07240			0.536201	+	0.844090i	$0.319859\pi$
$488$	21.9527	−	38.0232i	0.993753	−	1.72123i
$489$	19.3499	−	6.84334i	0.875031	−	0.309466i
$490$	−8.04225	+	1.93685i	−0.363312	+	0.0874978i
$491$	−9.25604	+	5.34398i	−0.417719	+	0.241170i	−0.694101	−	0.719878i	$-0.744198\pi$
$491$	−9.25604	+	5.34398i	−0.417719	+	0.241170i	0.276382	+	0.961048i	$0.410865\pi$
$492$	−0.100017	+	0.538427i	−0.00450911	+	0.0242742i
$493$	8.83794	+	5.10259i	0.398041	+	0.229809i
$494$		−	3.46739i		−	0.156005i
$495$	11.7229	+	14.5005i	0.526905	+	0.651750i
$496$			20.3577i			0.914086i
$497$	−8.93606	+	11.3437i	−0.400837	+	0.508833i
$498$	17.0470	−	19.9431i	0.763892	−	0.893671i
$499$	10.4045	+	18.0211i	0.465768	+	0.806734i	0.999236	−	0.0390866i	$-0.0124448\pi$
$499$	10.4045	+	18.0211i	0.465768	+	0.806734i	−0.533468	+	0.845820i	$0.679111\pi$
$500$	0.301744	+	0.522636i	0.0134944	+	0.0233730i
$501$	−2.23077	−	1.90682i	−0.0996633	−	0.0851903i
$502$	15.4068	+	8.89514i	0.687641	+	0.397010i
$503$	11.7879			0.525595			0.262797	−	0.964851i	$-0.415355\pi$
$503$	11.7879			0.525595			0.262797	+	0.964851i	$0.415355\pi$
$504$	0.308617	+	24.4182i	0.0137469	+	1.08767i
$505$	11.8819			0.528738
$506$	−23.6757	−	13.6692i	−1.05252	−	0.607670i
$507$	−3.99189	+	21.4898i	−0.177286	+	0.954395i
$508$	3.12242	+	5.40819i	0.138535	+	0.239949i
$509$	2.14843	+	3.72118i	0.0952273	+	0.164938i	0.909703	−	0.415259i	$-0.136309\pi$
$509$	2.14843	+	3.72118i	0.0952273	+	0.164938i	−0.814476	+	0.580197i	$0.802976\pi$
$510$	−1.47375	−	4.16711i	−0.0652590	−	0.184523i
$511$	0.666163	−	0.845644i	0.0294693	−	0.0374091i
$512$			22.9193i			1.01290i
$513$	21.0551	+	12.9377i	0.929603	+	0.571214i
$514$			30.2729i			1.33528i
$515$	−3.77246	−	2.17803i	−0.166234	−	0.0959755i
$516$	−5.43000	+	1.92039i	−0.239043	+	0.0845406i
$517$	35.0312	−	20.2253i	1.54067	−	0.889507i
$518$	2.32888	+	5.83135i	0.102325	+	0.256215i
$519$	2.78158	−	14.9743i	0.122098	−	0.657298i
$520$	−0.949065	+	1.64383i	−0.0416193	+	0.0720867i
$521$	−24.7319			−1.08352			−0.541761	−	0.840533i	$-0.682242\pi$
$521$	−24.7319			−1.08352			−0.541761	+	0.840533i	$0.682242\pi$
$522$	−15.6364	−	6.01678i	−0.684388	−	0.263347i
$523$		−	11.1055i		−	0.485608i	−0.970075	−	0.242804i	$-0.921933\pi$
$523$		−	11.1055i		−	0.485608i	0.970075	−	0.242804i	$-0.0780671\pi$
$524$	3.30170	−	5.71870i	0.144235	−	0.249823i
$525$	3.44551	−	3.02134i	0.150374	−	0.131862i
$526$	−10.7602	−	18.6373i	−0.469168	−	0.812623i
$527$	15.6749	−	9.04992i	0.682810	−	0.394221i
$528$	16.9896	−	19.8760i	0.739377	−	0.864990i
$529$	−4.57340	+	7.92136i	−0.198843	+	0.344407i
$530$	−15.0416			−0.653363
$531$	−15.2716	−	5.87638i	−0.662730	−	0.255013i
$532$	−7.51544	−	1.08695i	−0.325836	−	0.0471251i
$533$	0.279926	+	0.161615i	0.0121249	+	0.00700034i
$534$	−1.92733	−	0.358016i	−0.0834037	−	0.0154929i
$535$	14.6339	−	8.44888i	0.632678	−	0.365277i
$536$	−0.782141	+	0.451569i	−0.0337833	+	0.0195048i
$537$	−5.82757	−	16.4777i	−0.251478	−	0.711066i
$538$	22.7864	+	13.1558i	0.982393	+	0.567185i
$539$	−12.3273	+	41.7256i	−0.530973	+	1.79725i
$540$	−1.49294	−	2.75762i	−0.0642458	−	0.118669i
$541$	26.6470			1.14564			0.572821	−	0.819680i	$-0.305849\pi$
$541$	26.6470			1.14564			0.572821	+	0.819680i	$0.305849\pi$
$542$	16.1316	−	27.9408i	0.692913	−	1.20016i
$543$	0.459419	+	1.29903i	0.0197156	+	0.0557467i
$544$	6.13977	−	3.54480i	0.263240	−	0.151982i
$545$	−3.74751	−	6.49087i	−0.160526	−	0.278039i
$546$	3.16367	+	1.07409i	0.135393	+	0.0459667i
$547$	−5.24179	+	9.07905i	−0.224123	+	0.388192i	−0.956056	−	0.293184i	$-0.905285\pi$
$547$	−5.24179	+	9.07905i	−0.224123	+	0.388192i	0.731933	+	0.681377i	$0.238618\pi$
$548$		−	8.91424i		−	0.380797i
$549$	42.2900	−	6.66301i	1.80489	−	0.284370i
$550$	−7.34510			−0.313196
$551$	11.2377	−	19.4643i	0.478744	−	0.829209i
$552$	15.0768	+	12.8874i	0.641711	+	0.548522i
$553$	14.0247	−	5.60109i	0.596391	−	0.238183i
$554$	−15.5064	+	8.95261i	−0.658803	+	0.380360i
$555$	−2.64417	−	2.26018i	−0.112239	−	0.0959393i
$556$	1.34528	+	0.776697i	0.0570525	+	0.0329393i
$557$		−	21.2672i		−	0.901121i	−0.892746	−	0.450560i	$-0.851224\pi$
$557$		−	21.2672i		−	0.901121i	0.892746	−	0.450560i	$-0.148776\pi$
$558$	−23.1080	+	18.6815i	−0.978238	+	0.790853i
$559$			3.39946i			0.143782i
$560$	−5.04792	−	3.97654i	−0.213314	−	0.168039i
$561$	−22.8567	−	4.24580i	−0.965010	−	0.179258i
$562$	−9.21071	−	15.9534i	−0.388531	−	0.672955i
$563$	4.07042	+	7.05018i	0.171548	+	0.297130i	0.938961	−	0.344023i	$-0.111790\pi$
$563$	4.07042	+	7.05018i	0.171548	+	0.297130i	−0.767413	+	0.641153i	$0.778456\pi$
$564$	−6.41338	+	2.26818i	−0.270052	+	0.0955076i
$565$	−10.8082	−	6.24010i	−0.454703	−	0.262523i
$566$	16.6029			0.697871
$567$	−18.3267	+	15.2031i	−0.769647	+	0.638469i
$568$	−16.7925			−0.704597
$569$	30.1838	+	17.4266i	1.26537	+	0.730562i	0.974108	−	0.226081i	$-0.0725915\pi$
$569$	30.1838	+	17.4266i	1.26537	+	0.730562i	0.291262	+	0.956643i	$0.405925\pi$
$570$	−9.17749	+	3.24574i	−0.384403	+	0.135949i
$571$	5.67837	+	9.83523i	0.237633	+	0.411592i	0.960034	−	0.279882i	$-0.0902953\pi$
$571$	5.67837	+	9.83523i	0.237633	+	0.411592i	−0.722402	+	0.691473i	$0.756962\pi$
$572$	1.15708	+	2.00412i	0.0483798	+	0.0837963i
$573$	29.0099	+	5.38879i	1.21190	+	0.225120i
$574$	−1.01367	+	1.28678i	−0.0423097	+	0.0537090i
$575$		−	3.72199i		−	0.155218i
$576$	−20.3840	+	16.4793i	−0.849332	+	0.686639i
$577$			24.7185i			1.02905i	0.857477	+	0.514523i	$0.172031\pi$
$577$			24.7185i			1.02905i	−0.857477	+	0.514523i	$0.827969\pi$
$578$	−12.6257	−	7.28943i	−0.525159	−	0.303201i
$579$	−26.0347	−	22.2539i	−1.08196	−	0.924841i
$580$	−2.46988	+	1.42599i	−0.102556	+	0.0592109i
$581$	−31.4940	+	12.5779i	−1.30659	+	0.521818i
$582$	−3.90624	−	3.33898i	−0.161919	−	0.138405i
$583$	−39.5563	+	68.5136i	−1.63826	+	2.83754i
$584$	1.25184			0.0518016
$585$	−1.82829	+	0.288057i	−0.0755904	+	0.0119097i
$586$		−	7.89975i		−	0.326336i
$587$	−13.1643	+	22.8013i	−0.543351	+	0.941111i	0.455358	+	0.890308i	$0.349511\pi$
$587$	−13.1643	+	22.8013i	−0.543351	+	0.941111i	−0.998709	+	0.0508027i	$0.983822\pi$
$588$	3.31979	−	6.52044i	0.136906	−	0.268898i
$589$	−19.9312	−	34.5218i	−0.821251	−	1.42245i
$590$	5.58211	−	3.22283i	0.229812	−	0.132682i
$591$	−2.24567	−	6.34974i	−0.0923745	−	0.261193i
$592$	−2.43893	+	4.22435i	−0.100239	+	0.173620i
$593$	−40.8936			−1.67930			−0.839649	−	0.543129i	$-0.817239\pi$
$593$	−40.8936			−1.67930			−0.839649	+	0.543129i	$0.817239\pi$
$594$	38.1520	+	1.04537i	1.56539	+	0.0428919i
$595$	−0.817808	+	5.65454i	−0.0335268	+	0.231813i
$596$	−1.43490	−	0.828441i	−0.0587758	−	0.0339342i
$597$	−0.994965	−	2.81331i	−0.0407212	−	0.115141i
$598$	2.35005	−	1.35680i	0.0961005	−	0.0554836i
$599$	1.97542	−	1.14051i	0.0807133	−	0.0465998i	−0.459100	−	0.888385i	$-0.651828\pi$
$599$	1.97542	−	1.14051i	0.0807133	−	0.0465998i	0.539813	+	0.841785i	$0.318495\pi$
$600$	5.23929	+	0.973236i	0.213893	+	0.0397322i
$601$	20.8183	+	12.0194i	0.849195	+	0.490283i	0.860379	−	0.509654i	$-0.170227\pi$
$601$	20.8183	+	12.0194i	0.849195	+	0.490283i	−0.0111841	+	0.999937i	$0.503560\pi$
$602$	−17.0505	−	2.46600i	−0.694928	−	0.100506i
$603$	−0.821891	−	0.316257i	−0.0334700	−	0.0128790i
$604$	−5.38022			−0.218918
$605$	−13.8162	+	23.9303i	−0.561708	+	0.972906i
$606$	15.8022	−	18.4869i	0.641922	−	0.750979i
$607$	−34.2781	+	19.7905i	−1.39131	+	0.803271i	−0.993460	−	0.114181i	$-0.963576\pi$
$607$	−34.2781	+	19.7905i	−1.39131	+	0.803271i	−0.397846	+	0.917452i	$0.630242\pi$
$608$	−7.80693	−	13.5220i	−0.316613	−	0.548389i
$609$	14.2783	+	16.2828i	0.578586	+	0.659814i
$610$	−8.43205	+	14.6047i	−0.341404	+	0.591328i
$611$			4.01511i			0.162434i
$612$	3.64880	+	1.40403i	0.147494	+	0.0567546i
$613$	−2.41792			−0.0976588			−0.0488294	−	0.998807i	$-0.515549\pi$
$613$	−2.41792			−0.0976588			−0.0488294	+	0.998807i	$0.515549\pi$
$614$	−8.63033	+	14.9482i	−0.348292	+	0.603259i
$615$	0.165731	−	0.892192i	0.00668293	−	0.0359767i
$616$	−46.9859	+	18.7649i	−1.89311	+	0.756060i
$617$	2.49126	−	1.43833i	0.100294	−	0.0579050i	−0.449014	−	0.893525i	$-0.648225\pi$
$617$	2.49126	−	1.43833i	0.100294	−	0.0579050i	0.549308	+	0.835620i	$0.314891\pi$
$618$	−8.40593	+	2.97287i	−0.338136	+	0.119586i
$619$	−31.1520	−	17.9856i	−1.25211	−	0.722903i	−0.280578	−	0.959831i	$-0.590526\pi$
$619$	−31.1520	−	17.9856i	−1.25211	−	0.722903i	−0.971527	+	0.236928i	$0.923860\pi$
$620$			5.05825i			0.203144i
$621$	−0.529719	+	19.3328i	−0.0212569	+	0.775797i
$622$		−	22.3028i		−	0.894260i
$623$	1.99047	+	1.56801i	0.0797465	+	0.0628209i
$624$	0.865375	+	2.44689i	0.0346427	+	0.0979539i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.5253	+	18.2303i	0.420674	+	0.728628i
$627$	−9.35078	+	50.3387i	−0.373434	+	2.01033i
$628$	−9.15578	−	5.28609i	−0.365355	−	0.210938i
$629$	4.33687			0.172922
$630$	−0.118540	−	9.37903i	−0.00472274	−	0.373670i
$631$	12.1096			0.482075			0.241038	−	0.970516i	$-0.422512\pi$
$631$	12.1096			0.482075			0.241038	+	0.970516i	$0.422512\pi$
$632$	15.2086	+	8.78067i	0.604964	+	0.349276i
$633$	−15.2593	−	13.0434i	−0.606504	−	0.518428i
$634$	−15.5094	−	26.8630i	−0.615956	−	1.06687i
$635$	−5.17395	−	8.96155i	−0.205322	−	0.355628i
$636$	8.64469	−	10.1134i	0.342784	−	0.401020i
$637$	−2.97499	−	3.13050i	−0.117873	−	0.124035i
$638$		−	34.7116i		−	1.37425i
$639$	−10.2943	−	12.7334i	−0.407236	−	0.503727i
$640$		−	3.75920i		−	0.148596i
$641$	−7.60755	−	4.39222i	−0.300480	−	0.173482i	0.342178	−	0.939635i	$-0.388835\pi$
$641$	−7.60755	−	4.39222i	−0.300480	−	0.173482i	−0.642659	+	0.766153i	$0.722169\pi$
$642$	6.31672	−	34.0052i	0.249301	−	1.34208i
$643$	−38.1679	+	22.0362i	−1.50520	+	0.869025i	−0.505213	+	0.862994i	$0.668586\pi$
$643$	−38.1679	+	22.0362i	−1.50520	+	0.869025i	−0.999982	+	0.00603040i	$0.998080\pi$
$644$	−2.20413	−	5.51896i	−0.0868548	−	0.217478i
$645$	8.99770	−	3.18216i	0.354284	−	0.125297i
$646$	6.06831	−	10.5106i	0.238754	−	0.413535i
$647$	25.7941			1.01407			0.507036	−	0.861925i	$-0.330741\pi$
$647$	25.7941			1.01407			0.507036	+	0.861925i	$0.330741\pi$
$648$	−27.0754	−	5.80085i	−1.06362	−	0.227879i
$649$		−	33.9017i		−	1.33076i
$650$	0.364536	−	0.631395i	0.0142983	−	0.0247653i
$651$	37.6720	−	7.49158i	1.47648	−	0.293618i
$652$	−3.57559	−	6.19310i	−0.140031	−	0.242540i
$653$	−11.9806	+	6.91698i	−0.468836	+	0.270682i	−0.715752	−	0.698354i	$-0.753916\pi$
$653$	−11.9806	+	6.91698i	−0.468836	+	0.270682i	0.246916	+	0.969037i	$0.420583\pi$
$654$	−15.0830	−	2.80179i	−0.589794	−	0.109559i
$655$	−5.47102	+	9.47609i	−0.213770	+	0.370261i
$656$	−1.27251			−0.0496831
$657$	0.767415	+	0.949248i	0.0299397	+	0.0370337i
$658$	−20.1384	−	2.91259i	−0.785077	−	0.113545i
$659$	23.6785	+	13.6708i	0.922385	+	0.532539i	0.884395	−	0.466739i	$-0.154571\pi$
$659$	23.6785	+	13.6708i	0.922385	+	0.532539i	0.0379897	+	0.999278i	$0.487905\pi$
$660$	4.22138	−	4.93856i	0.164317	−	0.192233i
$661$	22.8640	−	13.2006i	0.889308	−	0.513442i	0.0155920	−	0.999878i	$-0.495037\pi$
$661$	22.8640	−	13.2006i	0.889308	−	0.513442i	0.873716	+	0.486436i	$0.161703\pi$
$662$	−19.9687	+	11.5289i	−0.776105	+	0.448084i
$663$	1.49935	−	1.75407i	0.0582298	−	0.0681225i
$664$	−34.1525	−	19.7180i	−1.32537	−	0.765205i
$665$	12.4533	+	1.80111i	0.482920	+	0.0698440i
$666$	−7.03318	+	1.10812i	−0.272530	+	0.0429386i
$667$	17.5894			0.681066
$668$	−0.511254	+	0.885518i	−0.0197810	+	0.0342617i
$669$	−41.6295	−	7.73299i	−1.60949	−	0.298975i
$670$	0.300420	−	0.173448i	0.0116063	−	0.00670087i
$671$	44.3492	+	76.8151i	1.71208	+	2.96542i
$672$	14.7559	−	2.93440i	0.569221	−	0.113197i
$673$	−5.09999	+	8.83344i	−0.196590	+	0.340504i	−0.947421	−	0.319991i	$-0.896320\pi$
$673$	−5.09999	+	8.83344i	−0.196590	+	0.340504i	0.750831	+	0.660495i	$0.229653\pi$
$674$			24.2673i			0.934740i
$675$	2.47385	+	4.56947i	0.0952184	+	0.175879i
$676$	7.61564			0.292909
$677$	2.80831	−	4.86413i	0.107932	−	0.186944i	−0.807000	−	0.590551i	$-0.798910\pi$
$677$	2.80831	−	4.86413i	0.107932	−	0.186944i	0.914932	+	0.403607i	$0.132244\pi$
$678$	−24.0832	+	8.51734i	−0.924908	+	0.327106i
$679$	2.46362	+	6.16871i	0.0945450	+	0.236733i
$680$	−5.75376	+	3.32194i	−0.220647	+	0.127390i
$681$	0.675854	−	3.63837i	0.0258988	−	0.139423i
$682$	−53.3163	−	30.7822i	−2.04159	−	1.17871i
$683$		−	41.9272i		−	1.60430i	−0.597124	−	0.802149i	$-0.703690\pi$
$683$		−	41.9272i		−	1.60430i	0.597124	−	0.802149i	$-0.296310\pi$
$684$	3.09218	−	8.03598i	0.118233	−	0.307263i
$685$			14.7712i			0.564378i
$686$	17.8596	−	12.6506i	0.681883	−	0.483003i
$687$	−26.5553	+	31.0669i	−1.01315	+	1.18527i
$688$	−6.69158	−	11.5902i	−0.255114	−	0.441871i
$689$	−3.92635	−	6.80063i	−0.149582	−	0.259083i
$690$	−5.79100	−	4.95003i	−0.220460	−	0.188445i
$691$	36.2770	+	20.9446i	1.38004	+	0.796769i	0.992164	−	0.124941i	$-0.0398742\pi$
$691$	36.2770	+	20.9446i	1.38004	+	0.796769i	0.387880	+	0.921710i	$0.373208\pi$
$692$	−5.30665			−0.201728
$693$	−43.0328	−	24.1251i	−1.63468	−	0.916435i
$694$	−7.20811			−0.273616
$695$	−2.22917	−	1.28701i	−0.0845573	−	0.0488192i
$696$	−4.59934	+	24.7599i	−0.174337	+	0.938522i
$697$	0.565689	+	0.979802i	0.0214270	+	0.0371127i
$698$	18.9906	+	32.8926i	0.718804	+	1.24500i
$699$	−0.478327	−	1.35249i	−0.0180920	−	0.0511560i
$700$	−1.25425	−	0.988047i	−0.0474063	−	0.0373447i
$701$			26.4201i			0.997874i	0.866638	+	0.498937i	$0.166276\pi$
$701$			26.4201i			0.997874i	−0.866638	+	0.498937i	$0.833724\pi$
$702$	−1.98334	+	3.22771i	−0.0748562	+	0.121822i
$703$		−	9.55135i		−	0.360236i
$704$	−47.0313	−	27.1535i	−1.77256	−	1.02339i
$705$	10.6272	−	3.75845i	0.400243	−	0.141551i
$706$	−1.94242	+	1.12146i	−0.0731040	+	0.0422066i
$707$	−29.1944	+	11.6595i	−1.09797	+	0.438500i
$708$	−1.04125	+	5.60542i	−0.0391325	+	0.210665i
$709$	6.36004	−	11.0159i	0.238856	−	0.413711i	−0.721530	−	0.692383i	$-0.756561\pi$
$709$	6.36004	−	11.0159i	0.238856	−	0.413711i	0.960386	+	0.278672i	$0.0898942\pi$
$710$	6.45000			0.242064
$711$	2.66508	+	16.9152i	0.0999481	+	0.634368i
$712$			2.94657i			0.110428i
$713$	15.5983	−	27.0170i	0.584160	−	1.01179i
$714$	7.71019	+	8.79263i	0.288547	+	0.329056i
$715$	−1.91732	−	3.32089i	−0.0717036	−	0.124194i
$716$	−5.27384	+	3.04486i	−0.197093	+	0.113792i
$717$	21.1048	−	24.6904i	0.788174	−	0.922078i
$718$	−6.79534	+	11.7699i	−0.253600	+	0.439248i
$719$	45.3176			1.69006			0.845030	−	0.534718i	$-0.179582\pi$
$719$	45.3176			1.69006			0.845030	+	0.534718i	$0.179582\pi$
$720$	5.66636	−	4.58095i	0.211173	−	0.170722i
$721$	11.4064	+	1.64969i	0.424796	+	0.0614376i
$722$	−3.70325	−	2.13807i	−0.137821	−	0.0795708i
$723$	−31.0938	−	5.77590i	−1.15639	−	0.214808i
$724$	0.415766	−	0.240043i	0.0154518	−	0.00892111i
$725$	4.09268	−	2.36291i	0.151998	−	0.0877563i
$726$	18.8582	+	53.3224i	0.699893	+	1.97898i
$727$	8.49387	+	4.90394i	0.315020	+	0.181877i	0.649171	−	0.760643i	$-0.275116\pi$
$727$	8.49387	+	4.90394i	0.315020	+	0.181877i	−0.334150	+	0.942520i	$0.608449\pi$
$728$	0.718843	−	4.97027i	0.0266421	−	0.184210i
$729$	−12.1993	−	24.0868i	−0.451827	−	0.892106i
$730$	−0.480833			−0.0177964
$731$	−5.94943	+	10.3047i	−0.220048	+	0.381134i
$732$	−4.97358	−	14.0630i	−0.183829	−	0.519784i
$733$	−0.977788	+	0.564526i	−0.0361154	+	0.0208512i	−0.517949	−	0.855411i	$-0.673304\pi$
$733$	−0.977788	+	0.564526i	−0.0361154	+	0.0208512i	0.481834	+	0.876263i	$0.339971\pi$
$734$	−10.9611	−	18.9851i	−0.404580	−	0.700753i
$735$	−5.50100	+	10.8046i	−0.202907	+	0.398533i
$736$	6.10975	−	10.5824i	0.225208	−	0.390072i
$737$		−	1.82453i		−	0.0672076i
$738$	−1.16774	−	1.44442i	−0.0429851	−	0.0531700i
$739$	9.04830			0.332847			0.166423	−	0.986054i	$-0.446778\pi$
$739$	9.04830			0.332847			0.166423	+	0.986054i	$0.446778\pi$
$740$	−0.605998	+	1.04962i	−0.0222769	+	0.0385848i
$741$	−3.86310	−	3.30210i	−0.141915	−	0.121306i
$742$	36.9578	−	14.7600i	1.35676	−	0.541856i
$743$	28.5598	−	16.4890i	1.04776	−	0.604924i	0.125738	−	0.992064i	$-0.459870\pi$
$743$	28.5598	−	16.4890i	1.04776	−	0.604924i	0.922021	+	0.387140i	$0.126537\pi$
$744$	33.9520	+	29.0215i	1.24474	+	1.06398i
$745$	2.37768	+	1.37275i	0.0871114	+	0.0502938i
$746$		−	24.2971i		−	0.889578i
$747$	−5.98472	−	37.9849i	−0.218969	−	1.38979i
$748$			8.10005i			0.296167i
$749$	−27.6655	+	35.1193i	−1.01087	+	1.28323i
$750$	−2.01241	−	0.373820i	−0.0734828	−	0.0136500i
$751$	−24.9073	−	43.1407i	−0.908880	−	1.57423i	−0.815623	−	0.578584i	$-0.803605\pi$
$751$	−24.9073	−	43.1407i	−0.908880	−	1.57423i	−0.0932571	−	0.995642i	$-0.529728\pi$
$752$	−7.90343	−	13.6891i	−0.288208	−	0.499192i
$753$	24.5827	−	8.69401i	0.895844	−	0.316827i
$754$	2.98386	+	1.72273i	0.108666	+	0.0627382i
$755$	8.91520			0.324457
$756$	6.37422	+	5.31062i	0.231828	+	0.193145i
$757$	0.640276			0.0232712			0.0116356	−	0.999932i	$-0.496296\pi$
$757$	0.640276			0.0232712			0.0116356	+	0.999932i	$0.496296\pi$
$758$	10.2121	+	5.89593i	0.370918	+	0.214150i
$759$	−37.7764	+	13.3601i	−1.37119	+	0.484942i
$760$	7.31611	+	12.6719i	0.265383	+	0.459657i
$761$	0.714506	+	1.23756i	0.0259008	+	0.0448615i	0.878685	−	0.477401i	$-0.158421\pi$
$761$	0.714506	+	1.23756i	0.0259008	+	0.0448615i	−0.852784	+	0.522263i	$0.825088\pi$
$762$	−20.8242	−	3.86825i	−0.754382	−	0.140132i
$763$	15.5772	+	12.2710i	0.563932	+	0.444241i
$764$		−	10.2806i		−	0.371940i
$765$	−6.04618	−	2.32653i	−0.218600	−	0.0841157i
$766$			4.65991i			0.168369i
$767$	2.91423	+	1.68253i	0.105227	+	0.0607528i
$768$	17.1585	+	14.6667i	0.619153	+	0.529240i
$769$	36.2876	−	20.9506i	1.30856	−	0.755500i	0.326707	−	0.945126i	$-0.394061\pi$
$769$	36.2876	−	20.9506i	1.30856	−	0.755500i	0.981856	+	0.189626i	$0.0607275\pi$
$770$	18.0473	−	7.20760i	0.650379	−	0.259744i
$771$	33.7278	+	28.8299i	1.21468	+	1.03828i
$772$	−5.96670	+	10.3346i	−0.214746	+	0.371952i
$773$	8.72402			0.313781			0.156891	−	0.987616i	$-0.449853\pi$
$773$	8.72402			0.313781			0.156891	+	0.987616i	$0.449853\pi$
$774$	7.01534	−	18.2315i	0.252161	−	0.655318i
$775$		−	8.38169i		−	0.301079i
$776$	−3.86214	+	6.68942i	−0.138643	+	0.240136i
$777$	8.71472	+	2.95871i	0.312639	+	0.106143i
$778$	19.2792	+	33.3926i	0.691193	+	1.19718i
$779$	2.15788	−	1.24585i	0.0773140	−	0.0446373i
$780$	0.215019	+	0.607976i	0.00769891	+	0.0217690i
$781$	16.9622	−	29.3794i	0.606956	−	1.05128i
$782$	9.49819			0.339655
$783$	−21.5945	+	11.6910i	−0.771725	+	0.417801i
$784$	16.3051	+	4.81713i	0.582325	+	0.172040i
$785$	15.1714	+	8.75923i	0.541492	+	0.312630i
$786$	7.46759	+	21.1149i	0.266360	+	0.753145i
$787$	−23.6087	+	13.6305i	−0.841558	+	0.485874i	−0.857794	−	0.513994i	$-0.828165\pi$
$787$	−23.6087	+	13.6305i	−0.841558	+	0.485874i	0.0162352	+	0.999868i	$0.494832\pi$
$788$	−2.03229	+	1.17334i	−0.0723973	+	0.0417986i
$789$	−31.0115	−	5.76062i	−1.10404	−	0.205084i
$790$	−5.84161	−	3.37265i	−0.207835	−	0.119994i
$791$	32.6795	+	4.72639i	1.16195	+	0.168051i
$792$	−8.92860	−	56.6696i	−0.317264	−	2.01367i
$793$	−8.80418			−0.312646
$794$	−9.90040	+	17.1480i	−0.351352	+	0.608560i
$795$	−14.3245	+	16.7582i	−0.508039	+	0.594351i
$796$	−0.900425	+	0.519861i	−0.0319147	+	0.0184260i
$797$	13.0160	+	22.5444i	0.461051	+	0.798564i	0.999014	−	0.0444045i	$-0.0141391\pi$
$797$	13.0160	+	22.5444i	0.461051	+	0.798564i	−0.537962	+	0.842969i	$0.680806\pi$
$798$	19.3645	−	16.9806i	0.685498	−	0.601108i
$799$	−7.02688	+	12.1709i	−0.248593	+	0.430576i
$800$		−	3.28305i		−	0.116073i
$801$	−2.23433	+	1.80634i	−0.0789462	+	0.0638237i
$802$	9.22189			0.325636
$803$	−1.26450	+	2.19017i	−0.0446231	+	0.0772894i
$804$	−0.0560383	+	0.301675i	−0.00197632	+	0.0106393i
$805$	3.65231	+	9.14511i	0.128727	+	0.322323i
$806$	5.29215	−	3.05543i	0.186408	−	0.107623i
$807$	36.3574	−	12.8583i	1.27984	−	0.452633i
$808$	−31.6588	−	18.2782i	−1.11375	−	0.643025i
$809$		−	31.6665i		−	1.11334i	−0.830735	−	0.556668i	$-0.812080\pi$
$809$		−	31.6665i		−	1.11334i	0.830735	−	0.556668i	$-0.187920\pi$
$810$	10.3997	+	2.22811i	0.365407	+	0.0782877i
$811$		−	4.49997i		−	0.158015i	−0.996874	−	0.0790076i	$-0.974825\pi$
$811$		−	4.49997i		−	0.158015i	0.996874	−	0.0790076i	$-0.0251751\pi$
$812$	4.66933	−	5.92737i	0.163861	−	0.208010i
$813$	−15.7669	−	44.5816i	−0.552968	−	1.56354i
$814$	−7.37565	−	12.7750i	−0.258517	−	0.447764i
$815$	5.92487	+	10.2622i	0.207539	+	0.359468i
$816$	−1.65913	+	8.93170i	−0.0580811	+	0.312672i
$817$	22.6947	+	13.1028i	0.793988	+	0.458409i
$818$	−22.2141			−0.776699
$819$	4.20953	−	2.50183i	0.147093	−	0.0874211i
$820$	−0.316179			−0.0110414
$821$	1.92522	+	1.11153i	0.0671907	+	0.0387926i	0.533219	−	0.845977i	$-0.320982\pi$
$821$	1.92522	+	1.11153i	0.0671907	+	0.0387926i	−0.466028	+	0.884770i	$0.654316\pi$
$822$	22.9823	+	19.6448i	0.801600	+	0.685192i
$823$	7.46182	+	12.9243i	0.260103	+	0.450511i	0.966269	−	0.257535i	$-0.0829102\pi$
$823$	7.46182	+	12.9243i	0.260103	+	0.450511i	−0.706166	+	0.708046i	$0.749577\pi$
$824$	6.70103	+	11.6065i	0.233442	+	0.404333i
$825$	−6.99498	+	8.18336i	−0.243534	+	0.284908i
$826$	−10.5530	+	13.3963i	−0.367187	+	0.466116i
$827$		−	11.9293i		−	0.414824i	−0.978254	−	0.207412i	$-0.933496\pi$
$827$		−	11.9293i		−	0.414824i	0.978254	−	0.207412i	$-0.0665040\pi$
$828$	6.65642	−	1.04875i	0.231326	−	0.0364467i
$829$			7.29726i			0.253444i	0.991938	+	0.126722i	$0.0404457\pi$
$829$			7.29726i			0.253444i	−0.991938	+	0.126722i	$0.959554\pi$
$830$	13.1180	+	7.57367i	0.455332	+	0.262886i
$831$	−4.79289	+	25.8019i	−0.166264	+	0.895058i
$832$	4.66831	−	2.69525i	0.161845	−	0.0934410i
$833$	−3.53929	−	14.6960i	−0.122629	−	0.509185i
$834$	−4.96712	+	1.75669i	−0.171997	+	0.0608292i
$835$	0.847165	−	1.46733i	0.0293174	−	0.0507792i
$836$	17.8392			0.616983
$837$	−1.19289	+	43.5362i	−0.0412325	+	1.50483i
$838$		−	30.7782i		−	1.06321i
$839$	4.89427	−	8.47713i	0.168969	−	0.292663i	−0.769089	−	0.639142i	$-0.779290\pi$
$839$	4.89427	−	8.47713i	0.168969	−	0.292663i	0.938058	+	0.346479i	$0.112623\pi$
$840$	−13.8282	+	2.74992i	−0.477118	+	0.0948812i
$841$	−3.33332	−	5.77347i	−0.114942	−	0.199085i
$842$	−39.7834	+	22.9690i	−1.37103	+	0.791563i
$843$	−26.5458	−	4.93107i	−0.914284	−	0.169835i
$844$	−3.49718	+	6.05730i	−0.120378	+	0.208501i
$845$	−12.6194			−0.434120
$846$	8.28583	−	21.5332i	0.284873	−	0.740328i
$847$	10.4647	−	72.3555i	0.359571	−	2.48617i
$848$	26.7730	+	15.4574i	0.919389	+	0.530810i
$849$	15.8114	−	18.4977i	0.542647	−	0.634838i
$850$	2.21002	−	1.27596i	0.0758031	−	0.0437649i
$851$	6.47349	−	3.73747i	0.221908	−	0.128119i
$852$	−3.70695	+	4.33673i	−0.126998	+	0.148574i
$853$	−37.9865	−	21.9315i	−1.30063	−	0.750921i	−0.320120	−	0.947377i	$-0.603723\pi$
$853$	−37.9865	−	21.9315i	−1.30063	−	0.750921i	−0.980513	+	0.196456i	$0.937057\pi$
$854$	6.38662	−	44.1587i	0.218545	−	1.51108i
$855$	−5.12385	+	13.3159i	−0.175232	+	0.455394i
$856$	−51.9885			−1.77693
$857$	−1.88477	+	3.26452i	−0.0643825	+	0.111514i	−0.896420	−	0.443206i	$-0.853841\pi$
$857$	−1.88477	+	3.26452i	−0.0643825	+	0.111514i	0.832037	+	0.554720i	$0.187174\pi$
$858$	−7.71685	−	1.43346i	−0.263449	−	0.0489376i
$859$	−6.80837	+	3.93081i	−0.232299	+	0.134118i	−0.611632	−	0.791142i	$-0.709487\pi$
$859$	−6.80837	+	3.93081i	−0.232299	+	0.134118i	0.379333	+	0.925260i	$0.376153\pi$
$860$	−1.66265	−	2.87979i	−0.0566959	−	0.0982002i
$861$	0.468281	+	2.35479i	0.0159590	+	0.0802510i
$862$	−1.84879	+	3.20219i	−0.0629699	+	0.109067i
$863$			50.5884i			1.72205i	0.508565	+	0.861024i	$0.330176\pi$
$863$			50.5884i			1.72205i	−0.508565	+	0.861024i	$0.669824\pi$
$864$	−0.467249	+	17.0528i	−0.0158961	+	0.580150i
$865$	8.79329			0.298981
$866$	−10.7126	+	18.5548i	−0.364029	+	0.630517i
$867$	−20.1452	+	7.12461i	−0.684166	+	0.241964i
$868$	−4.96356	−	12.4284i	−0.168474	−	0.421846i
$869$	−30.7246	+	17.7388i	−1.04226	+	0.601749i
$870$	1.76661	−	9.51029i	0.0598936	−	0.322429i
$871$	0.156839	+	0.0905513i	0.00531430	+	0.00306821i
$872$			23.0595i			0.780894i
$873$	−7.44007	+	1.17222i	−0.251808	+	0.0396737i
$874$		−	20.9184i		−	0.707577i
$875$	2.07834	+	1.63723i	0.0702606	+	0.0553484i
$876$	0.276345	−	0.323293i	0.00933682	−	0.0109231i
$877$	−1.56847	−	2.71668i	−0.0529636	−	0.0917357i	0.838328	−	0.545166i	$-0.183533\pi$
$877$	−1.56847	−	2.71668i	−0.0529636	−	0.0917357i	−0.891292	+	0.453430i	$0.850200\pi$
$878$	−1.14998	−	1.99182i	−0.0388099	−	0.0672206i
$879$	−8.80131	−	7.52319i	−0.296861	−	0.253751i
$880$	13.0738	+	7.54818i	0.440719	+	0.254449i
$881$	−14.8044			−0.498774			−0.249387	−	0.968404i	$-0.580229\pi$
$881$	−14.8044			−0.498774			−0.249387	+	0.968404i	$0.580229\pi$
$882$	9.49471	+	22.9284i	0.319704	+	0.772040i
$883$	30.1484			1.01458			0.507288	−	0.861777i	$-0.330648\pi$
$883$	30.1484			1.01458			0.507288	+	0.861777i	$0.330648\pi$
$884$	−0.696291	−	0.402004i	−0.0234188	−	0.0135209i
$885$	1.72538	−	9.28838i	0.0579982	−	0.312225i
$886$	0.315393	+	0.546276i	0.0105958	+	0.0183525i
$887$	5.04001	+	8.72956i	0.169227	+	0.293110i	0.938148	−	0.346234i	$-0.112540\pi$
$887$	5.04001	+	8.72956i	0.169227	+	0.293110i	−0.768921	+	0.639343i	$0.779206\pi$
$888$	3.56837	+	10.0897i	0.119747	+	0.338589i
$889$	21.5064	+	16.9419i	0.721303	+	0.568212i
$890$		−	1.13178i		−	0.0379373i
$891$	37.4980	−	41.5105i	1.25623	−	1.39065i
$892$			14.7528i			0.493962i
$893$	26.8047	+	15.4757i	0.896987	+	0.517876i
$894$	5.29803	−	1.87372i	0.177193	−	0.0626666i
$895$	8.73894	−	5.04543i	0.292110	−	0.168650i
$896$	3.68883	+	9.23655i	0.123235	+	0.308571i
$897$	0.726379	−	3.91037i	0.0242531	−	0.130563i
$898$	11.2823	−	19.5415i	0.376496	−	0.652109i
$899$	39.6103			1.32108
$900$	1.40792	−	1.13822i	0.0469305	−	0.0379408i
$901$		−	27.4861i		−	0.915696i
$902$	1.92412	−	3.33268i	0.0640662	−	0.110966i
$903$	−18.9852	+	16.6480i	−0.631788	+	0.554010i
$904$	19.1986	+	33.2530i	0.638536	+	1.10598i
$905$	−0.688938	+	0.397759i	−0.0229011	+	0.0132219i
$906$	11.8567	−	13.8711i	0.393913	−	0.460835i
$907$	−17.3071	+	29.9767i	−0.574672	+	0.995361i	0.421405	+	0.906873i	$0.361537\pi$
$907$	−17.3071	+	29.9767i	−0.574672	+	0.995361i	−0.996077	+	0.0884889i	$0.971796\pi$
$908$	−1.28938			−0.0427896
$909$	−5.54774	−	35.2113i	−0.184007	−	1.16789i
$910$	−0.276108	+	1.90908i	−0.00915288	+	0.0632854i
$911$	−22.0123	−	12.7088i	−0.729301	−	0.421062i	0.0888654	−	0.996044i	$-0.471676\pi$
$911$	−22.0123	−	12.7088i	−0.729301	−	0.421062i	−0.818166	+	0.574981i	$0.805009\pi$
$912$	19.6708	+	3.65400i	0.651366	+	0.120996i
$913$	68.9954	−	39.8345i	2.28341	−	1.31833i
$914$	23.6148	−	13.6340i	0.781107	−	0.450972i
$915$	8.24138	+	23.3029i	0.272452	+	0.770370i
$916$	12.3322	+	7.12000i	0.407467	+	0.235251i
$917$	4.14387	−	28.6518i	0.136843	−	0.946166i
$918$	−11.6609	+	6.31304i	−0.384867	+	0.208361i
$919$	−15.4066			−0.508217			−0.254108	−	0.967176i	$-0.581782\pi$
$919$	−15.4066			−0.508217			−0.254108	+	0.967176i	$0.581782\pi$
$920$	−5.72563	+	9.91708i	−0.188768	+	0.326956i
$921$	8.43518	+	23.8509i	0.277949	+	0.785913i
$922$	−23.2837	+	13.4429i	−0.766808	+	0.442717i
$923$	1.68366	+	2.91619i	0.0554185	+	0.0959876i
$924$	−5.52604	+	16.2766i	−0.181793	+	0.535462i
$925$	1.00416	−	1.73925i	0.0330166	−	0.0571863i
$926$			14.3381i			0.471180i
$927$	−4.69308	+	12.1964i	−0.154141	+	0.400583i
$928$	15.5151			0.509309
$929$	−0.674311	+	1.16794i	−0.0221234	+	0.0383189i	−0.876875	−	0.480718i	$-0.840376\pi$
$929$	−0.674311	+	1.16794i	−0.0221234	+	0.0383189i	0.854752	+	0.519037i	$0.173709\pi$
$930$	−13.0410	−	11.1472i	−0.427630	−	0.365530i
$931$	−32.3658	+	7.79480i	−1.06075	+	0.255464i
$932$	−0.432878	+	0.249922i	−0.0141794	+	0.00818647i
$933$	−24.8481	−	21.2397i	−0.813490	−	0.695355i
$934$	−4.72096	−	2.72565i	−0.154475	−	0.0891859i
$935$		−	13.4221i		−	0.438948i
$936$	5.31452	+	2.04499i	0.173711	+	0.0668425i
$937$		−	50.1179i		−	1.63728i	−0.574307	−	0.818640i	$-0.694728\pi$
$937$		−	50.1179i		−	1.63728i	0.574307	−	0.818640i	$-0.305272\pi$
$938$	−0.567947	+	0.720966i	−0.0185441	+	0.0235404i
$939$	30.3343	+	5.63482i	0.989923	+	0.183886i
$940$	−1.96376	−	3.40133i	−0.0640507	−	0.110939i
$941$	11.4575	+	19.8449i	0.373503	+	0.646926i	0.990102	−	0.140351i	$-0.0448232\pi$
$941$	11.4575	+	19.8449i	0.373503	+	0.646926i	−0.616599	+	0.787278i	$0.711490\pi$
$942$	33.8055	−	11.9558i	1.10144	−	0.389540i
$943$	1.68877	+	0.975011i	0.0549939	+	0.0317507i
$944$	−13.2477			−0.431177
$945$	−10.5623	−	8.79988i	−0.343592	−	0.286260i
$946$	40.4725			1.31587
$947$	−1.16082	−	0.670199i	−0.0377216	−	0.0217786i	0.481021	−	0.876709i	$-0.340266\pi$
$947$	−1.16082	−	0.670199i	−0.0377216	−	0.0217786i	−0.518742	+	0.854931i	$0.673600\pi$
$948$	5.62493	−	1.98933i	0.182689	−	0.0646106i
$949$	−0.125513	−	0.217395i	−0.00407433	−	0.00705695i
$950$	−2.81012	−	4.86727i	−0.0911722	−	0.157915i
$951$	−44.6989	−	8.30314i	−1.44946	−	0.269248i
$952$	10.8775	−	13.8082i	0.352543	−	0.447527i
$953$			13.3889i			0.433710i	0.976204	+	0.216855i	$0.0695800\pi$
$953$			13.3889i			0.433710i	−0.976204	+	0.216855i	$0.930420\pi$
$954$	7.02300	+	44.5748i	0.227378	+	1.44316i
$955$			17.0354i			0.551251i
$956$	−9.80100	−	5.65861i	−0.316987	−	0.183013i
$957$	−38.6731	−	33.0570i	−1.25012	−	1.06858i
$958$	−9.29603	+	5.36707i	−0.300341	+	0.173402i
$959$	−14.4947	−	36.2935i	−0.468057	−	1.17198i
$960$	−11.5037	−	9.83312i	−0.371280	−	0.317363i
$961$	19.6263	−	33.9938i	0.633107	−	1.09657i
$962$	1.46421			0.0472080
$963$	−31.8705	−	39.4219i	−1.02701	−	1.27035i
$964$			11.0191i			0.354903i
$965$	9.88703	−	17.1248i	0.318275	−	0.551268i
$966$	19.0861	+	6.47988i	0.614086	+	0.208487i
$967$	−13.2117	−	22.8834i	−0.424860	−	0.735879i	0.571547	−	0.820569i	$-0.306343\pi$
$967$	−13.2117	−	22.8834i	−0.424860	−	0.735879i	−0.996407	+	0.0846898i	$0.973010\pi$
$968$	73.6252	−	42.5075i	2.36640	−	1.36624i
$969$	−5.93110	−	16.7704i	−0.190534	−	0.538744i
$970$	1.48345	−	2.56941i	0.0476307	−	0.0824987i
$971$	−18.2164			−0.584593			−0.292296	−	0.956328i	$-0.594419\pi$
$971$	−18.2164			−0.584593			−0.292296	+	0.956328i	$0.594419\pi$
$972$	−7.47499	+	5.71179i	−0.239761	+	0.183206i
$973$	6.74011	+	0.974812i	0.216078	+	0.0312510i
$974$	24.2201	+	13.9835i	0.776061	+	0.448059i
$975$	−0.356293	−	1.00744i	−0.0114105	−	0.0322638i
$976$	30.0170	−	17.3303i	0.960822	−	0.554731i
$977$	7.55063	−	4.35936i	0.241566	−	0.139468i	−0.374330	−	0.927295i	$-0.622127\pi$
$977$	7.55063	−	4.35936i	0.241566	−	0.139468i	0.615896	+	0.787827i	$0.288794\pi$
$978$	23.8465	+	4.42967i	0.762528	+	0.141645i
$979$	−5.15520	−	2.97636i	−0.164761	−	0.0951248i
$980$	4.05131	+	1.19691i	0.129414	+	0.0382338i
$981$	−17.4856	+	14.1362i	−0.558272	+	0.451333i
$982$	−12.6304			−0.403052
$983$	−1.76302	+	3.05363i	−0.0562315	+	0.0973957i	−0.892771	−	0.450511i	$-0.851242\pi$
$983$	−1.76302	+	3.05363i	−0.0562315	+	0.0973957i	0.836539	+	0.547907i	$0.184575\pi$
$984$	−1.81407	+	2.12226i	−0.0578303	+	0.0676551i
$985$	3.36757	−	1.94427i	0.107300	−	0.0619496i
$986$	6.02994	+	10.4442i	0.192032	+	0.332610i
$987$	−22.4234	+	19.6629i	−0.713746	+	0.625878i
$988$	−0.885358	+	1.53348i	−0.0281670	+	0.0487866i
$989$			20.5087i			0.652137i
$990$	3.42948	+	21.7668i	0.108996	+	0.691794i
$991$	−42.4009			−1.34691			−0.673454	−	0.739229i	$-0.735190\pi$
$991$	−42.4009			−1.34691			−0.673454	+	0.739229i	$0.735190\pi$
$992$	13.7588	−	23.8309i	0.436841	−	0.756631i
$993$	−6.17215	+	33.2270i	−0.195867	+	1.05443i
$994$	−15.8480	+	6.32926i	−0.502667	+	0.200752i
$995$	1.49203	−	0.861427i	0.0473007	−	0.0273091i
$996$	−12.6314	+	4.46727i	−0.400242	+	0.141551i
$997$	46.4513	+	26.8186i	1.47113	+	0.849355i	0.999474	−	0.0324296i	$-0.0103245\pi$
$997$	46.4513	+	26.8186i	1.47113	+	0.849355i	0.471652	+	0.881785i	$0.343658\pi$
$998$			24.5908i			0.778407i
$999$	−5.46334	+	8.89113i	−0.172852	+	0.281303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.i.146.8	yes	24
3.2	odd	2		945.2.bl.i.251.5		24
7.6	odd	2		315.2.bl.j.146.8	yes	24
9.4	even	3		945.2.bl.j.881.5		24
9.5	odd	6		315.2.bl.j.41.8	yes	24
21.20	even	2		945.2.bl.j.251.5		24
63.13	odd	6		945.2.bl.i.881.5		24
63.41	even	6	inner	315.2.bl.i.41.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.8	✓	24	63.41	even	6	inner
315.2.bl.i.146.8	yes	24	1.1	even	1	trivial
315.2.bl.j.41.8	yes	24	9.5	odd	6
315.2.bl.j.146.8	yes	24	7.6	odd	2
945.2.bl.i.251.5		24	3.2	odd	2
945.2.bl.i.881.5		24	63.13	odd	6
945.2.bl.j.251.5		24	21.20	even	2
945.2.bl.j.881.5		24	9.4	even	3

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02342 + 0.590871i) q^{2} +(1.63294 - 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.01241 + 0.373820i) q^{6} +(-2.07834 - 1.63723i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} +O(q^{10})\)	\(q+(1.02342 + 0.590871i) q^{2} +(1.63294 - 0.577510i) q^{3} +(-0.301744 - 0.522636i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.01241 + 0.373820i) q^{6} +(-2.07834 - 1.63723i) q^{7} -3.07665i q^{8} +(2.33296 - 1.88607i) q^{9} +1.18174i q^{10} +(5.38278 + 3.10775i) q^{11} +(-0.794556 - 0.679171i) q^{12} +(-0.534292 + 0.308474i) q^{13} +(-1.15962 - 2.90360i) q^{14} +(1.31661 + 1.12541i) q^{15} +(1.21441 - 2.10343i) q^{16} -2.15945 q^{17} +(3.50202 - 0.551763i) q^{18} +4.75589i q^{19} +(0.301744 - 0.522636i) q^{20} +(-4.33931 - 1.47323i) q^{21} +(3.67255 + 6.36105i) q^{22} +(-3.22334 + 1.86099i) q^{23} +(-1.77680 - 5.02397i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.729072 q^{26} +(2.72036 - 4.42715i) q^{27} +(-0.228548 + 1.58024i) q^{28} +(-4.09268 - 2.36291i) q^{29} +(0.682467 + 1.92971i) q^{30} +(-7.25875 + 4.19084i) q^{31} +(-2.84321 + 1.64153i) q^{32} +(10.5845 + 1.96615i) q^{33} +(-2.21002 - 1.27596i) q^{34} +(0.378711 - 2.61851i) q^{35} +(-1.68969 - 0.650179i) q^{36} -2.00832 q^{37} +(-2.81012 + 4.86727i) q^{38} +(-0.694319 + 0.812277i) q^{39} +(2.66446 - 1.53832i) q^{40} +(-0.261960 - 0.453727i) q^{41} +(-3.57044 - 4.07170i) q^{42} +(2.75507 - 4.77192i) q^{43} -3.75098i q^{44} +(2.79987 + 1.07737i) q^{45} -4.39843 q^{46} +(3.25401 - 5.63611i) q^{47} +(0.768310 - 4.13610i) q^{48} +(1.63898 + 6.80542i) q^{49} +(-1.02342 + 0.590871i) q^{50} +(-3.52625 + 1.24710i) q^{51} +(0.322439 + 0.186160i) q^{52} +12.7283i q^{53} +(5.39993 - 2.92345i) q^{54} +6.21549i q^{55} +(-5.03717 + 6.39432i) q^{56} +(2.74658 + 7.76607i) q^{57} +(-2.79235 - 4.83649i) q^{58} +(-2.72719 - 4.72363i) q^{59} +(0.190901 - 1.02769i) q^{60} +(12.3587 + 7.13527i) q^{61} -9.90498 q^{62} +(-7.93662 + 0.100310i) q^{63} -8.73737 q^{64} +(-0.534292 - 0.308474i) q^{65} +(9.67061 + 8.26625i) q^{66} +(-0.146773 - 0.254218i) q^{67} +(0.651601 + 1.12861i) q^{68} +(-4.18876 + 4.90040i) q^{69} +(1.93478 - 2.45606i) q^{70} -5.45805i q^{71} +(-5.80279 - 7.17771i) q^{72} +0.406885i q^{73} +(-2.05535 - 1.18666i) q^{74} +(-0.316330 + 1.70292i) q^{75} +(2.48560 - 1.43506i) q^{76} +(-6.09914 - 15.2718i) q^{77} +(-1.19053 + 0.421047i) q^{78} +(-2.85397 + 4.94322i) q^{79} +2.42883 q^{80} +(1.88544 - 8.80029i) q^{81} -0.619137i q^{82} +(6.40891 - 11.1006i) q^{83} +(0.539399 + 2.71242i) q^{84} +(-1.07973 - 1.87014i) q^{85} +(5.63917 - 3.25578i) q^{86} +(-8.04769 - 1.49492i) q^{87} +(9.56144 - 16.5609i) q^{88} -0.957722 q^{89} +(2.22885 + 2.75696i) q^{90} +(1.61548 + 0.233645i) q^{91} +(1.94525 + 1.12309i) q^{92} +(-9.43283 + 11.0354i) q^{93} +(6.66043 - 3.84540i) q^{94} +(-4.11872 + 2.37795i) q^{95} +(-3.69478 + 4.32249i) q^{96} +(-2.17426 - 1.25531i) q^{97} +(-2.34376 + 7.93321i) q^{98} +(18.4193 - 2.90205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9	\( 24 q + 6 q^{2} - 5 q^{3} + 18 q^{4} + 12 q^{5} - q^{6} + q^{9} + 9 q^{11} + 18 q^{12} - 3 q^{13} + 9 q^{14} + 2 q^{15} - 18 q^{16} - 18 q^{17} + 2 q^{18} - 18 q^{20} + 4 q^{21} - 9 q^{22} + 9 q^{23} + 7 q^{24} - 12 q^{25} + 18 q^{26} + 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} + 42 q^{31} + 18 q^{32} - 13 q^{33} + 39 q^{34} + 9 q^{35} - 21 q^{36} + 12 q^{38} - 21 q^{39} + 6 q^{40} + 33 q^{41} + 26 q^{42} + 18 q^{43} - q^{45} - 30 q^{46} + 17 q^{48} - 6 q^{50} - 12 q^{51} - 129 q^{52} - 52 q^{54} + 6 q^{56} + 6 q^{57} - 15 q^{58} - 12 q^{59} + 15 q^{60} + 15 q^{61} - 12 q^{62} - 83 q^{63} - 60 q^{64} - 3 q^{65} - 29 q^{66} - 15 q^{67} - 9 q^{68} - 61 q^{69} + 18 q^{70} + 61 q^{72} - 18 q^{74} + 7 q^{75} - 54 q^{76} - 57 q^{77} - 66 q^{78} + 21 q^{79} - 36 q^{80} + q^{81} + 30 q^{83} - 42 q^{84} - 9 q^{85} - 102 q^{86} - 10 q^{87} - 9 q^{88} - 102 q^{89} + 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} + 156 q^{94} - 18 q^{95} + 42 q^{96} + 45 q^{97} - 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 - 5 * q^3 + 18 * q^4 + 12 * q^5 - q^6 + q^9 + 9 * q^11 + 18 * q^12 - 3 * q^13 + 9 * q^14 + 2 * q^15 - 18 * q^16 - 18 * q^17 + 2 * q^18 - 18 * q^20 + 4 * q^21 - 9 * q^22 + 9 * q^23 + 7 * q^24 - 12 * q^25 + 18 * q^26 + 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 + 42 * q^31 + 18 * q^32 - 13 * q^33 + 39 * q^34 + 9 * q^35 - 21 * q^36 + 12 * q^38 - 21 * q^39 + 6 * q^40 + 33 * q^41 + 26 * q^42 + 18 * q^43 - q^45 - 30 * q^46 + 17 * q^48 - 6 * q^50 - 12 * q^51 - 129 * q^52 - 52 * q^54 + 6 * q^56 + 6 * q^57 - 15 * q^58 - 12 * q^59 + 15 * q^60 + 15 * q^61 - 12 * q^62 - 83 * q^63 - 60 * q^64 - 3 * q^65 - 29 * q^66 - 15 * q^67 - 9 * q^68 - 61 * q^69 + 18 * q^70 + 61 * q^72 - 18 * q^74 + 7 * q^75 - 54 * q^76 - 57 * q^77 - 66 * q^78 + 21 * q^79 - 36 * q^80 + q^81 + 30 * q^83 - 42 * q^84 - 9 * q^85 - 102 * q^86 - 10 * q^87 - 9 * q^88 - 102 * q^89 + 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 + 156 * q^94 - 18 * q^95 + 42 * q^96 + 45 * q^97 - 3 * q^98 + 23 * q^99

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