LMFDB - Embedded newform 315.2.bl.j.41.8

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			41.8
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.j.146.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02342 - 0.590871i) q^{2} +(-1.63294 - 0.577510i) q^{3} +(-0.301744 + 0.522636i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.01241 + 0.373820i) q^{6} +(2.45705 - 0.981280i) q^{7} +3.07665i q^{8} +(2.33296 + 1.88607i) q^{9} +O(q^{10})$	\(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} +(2.45705 - 0.981280i) 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} +(1.93478 - 2.45606i) 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} +(-4.57890 + 0.183398i) 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} +(-4.57777 + 2.89323i) 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} +(5.07418 - 4.82211i) 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} +(3.01905 + 7.55948i) 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} +(7.58297 + 2.34489i) 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} +(1.15962 + 2.90360i) 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} +(10.1762 - 12.9179i) 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} +(1.28581 - 2.44844i) 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} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 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} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 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 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * 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 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	−0.0924347	−	0.995719i	$-0.529465\pi$
$2$	1.02342	−	0.590871i	0.723666	−	0.417809i	0.816100	+	0.577910i	$0.196132\pi$
$3$	−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
$7$	2.45705	−	0.981280i	0.928677	−	0.370889i
$7$	2.45705	−	0.981280i	0.928677	−	0.370889i
$8$			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	0.636847	−	0.770990i	$-0.280238\pi$
$11$	5.38278	−	3.10775i	1.62297	−	0.937021i	0.986121	−	0.166031i	$-0.0530951\pi$
$12$	0.794556	−	0.679171i	0.229369	−	0.196060i
$13$	0.534292	+	0.308474i	0.148186	+	0.0855552i	0.572260	−	0.820072i	$-0.306067\pi$
$13$	0.534292	+	0.308474i	0.148186	+	0.0855552i	−0.424074	+	0.905628i	$0.639400\pi$
$14$	1.93478	−	2.45606i	0.517091	−	0.656409i
$15$	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	$-0.415660\pi$
$17$	2.15945			0.523744			0.261872	+	0.965103i	$0.415660\pi$
$18$	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
$21$	−4.57890	+	0.183398i	−0.999199	+	0.0400207i
$22$	3.67255	−	6.36105i	0.782991	−	1.35618i
$23$	−3.22334	−	1.86099i	−0.672112	−	0.388044i	0.124764	−	0.992186i	$-0.460183\pi$
$23$	−3.22334	−	1.86099i	−0.672112	−	0.388044i	−0.796877	+	0.604142i	$0.793516\pi$
$24$	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	−0.829293	−	0.558814i	$-0.811256\pi$
$29$	−4.09268	+	2.36291i	−0.759992	+	0.438781i	0.0693012	+	0.997596i	$0.477923\pi$
$30$	0.682467	−	1.92971i	0.124601	−	0.352315i
$31$	7.25875	+	4.19084i	1.30371	+	0.752698i	0.981038	−	0.193813i	$-0.0620856\pi$
$31$	7.25875	+	4.19084i	1.30371	+	0.752698i	0.322672	+	0.946511i	$0.395419\pi$
$32$	−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	$-0.820307\pi$
$41$	0.261960	−	0.453727i	0.0409112	−	0.0708603i	0.885756	+	0.464151i	$0.153641\pi$
$42$	−4.57777	+	2.89323i	−0.706365	+	0.446435i
$43$	2.75507	+	4.77192i	0.420144	+	0.727710i	0.995953	−	0.0898736i	$-0.0286463\pi$
$43$	2.75507	+	4.77192i	0.420144	+	0.727710i	−0.575809	+	0.817584i	$0.695313\pi$
$44$			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	$-0.324091\pi$
$47$	−3.25401	−	5.63611i	−0.474646	−	0.822112i	−0.999578	+	0.0290325i	$0.990757\pi$
$48$	−0.768310	−	4.13610i	−0.110896	−	0.596994i
$49$	5.07418	−	4.82211i	0.724883	−	0.688872i
$50$	−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	$-0.661397\pi$
$53$		−	12.7283i		−	1.74837i	0.485596	−	0.874183i	$-0.338603\pi$
$54$	−5.39993	−	2.92345i	−0.734838	−	0.397831i
$55$			6.21549i			0.838097i
$56$	3.01905	+	7.55948i	0.403438	+	1.01018i
$57$	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	$-0.717797\pi$
$59$	2.72719	−	4.72363i	0.355050	−	0.614965i	0.987127	+	0.159941i	$0.0511305\pi$
$60$	0.190901	+	1.02769i	0.0246453	+	0.132674i
$61$	−12.3587	+	7.13527i	−1.58236	+	0.913578i	−0.587850	+	0.808970i	$0.700026\pi$
$61$	−12.3587	+	7.13527i	−1.58236	+	0.913578i	−0.994513	+	0.104608i	$0.966641\pi$
$62$	9.90498			1.25793
$63$	7.58297	+	2.34489i	0.955365	+	0.295428i
$64$	−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	−0.874852	−	0.484391i	$-0.839041\pi$
$67$	−0.146773	+	0.254218i	−0.0179312	+	0.0310577i	0.856921	+	0.515448i	$0.172375\pi$
$68$	−0.651601	+	1.12861i	−0.0790183	+	0.136864i
$69$	4.18876	+	4.90040i	0.504268	+	0.589938i
$70$	1.15962	+	2.90360i	0.138601	+	0.347046i
$71$			5.45805i			0.647751i	0.946100	+	0.323876i	$0.104986\pi$
$71$			5.45805i			0.647751i	−0.946100	+	0.323876i	$0.895014\pi$
$72$	−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
$77$	10.1762	−	12.9179i	1.15968	−	1.47213i
$78$	−1.19053	−	0.421047i	−0.134801	−	0.0476741i
$79$	−2.85397	−	4.94322i	−0.321097	−	0.556156i	0.659618	−	0.751601i	$-0.270718\pi$
$79$	−2.85397	−	4.94322i	−0.321097	−	0.556156i	−0.980715	+	0.195445i	$0.937385\pi$
$80$	−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	−0.967241	−	0.253859i	$-0.918300\pi$
$83$	−6.40891	−	11.1006i	−0.703469	−	1.21844i	0.263772	−	0.964585i	$-0.415033\pi$
$84$	1.28581	−	2.44844i	0.140293	−	0.267147i
$85$	−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	$-0.483836\pi$
$89$	0.957722			0.101518			0.0507592	+	0.998711i	$0.483836\pi$
$90$	−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	$-0.625985\pi$
$97$	2.17426	−	1.25531i	0.220762	−	0.127457i	0.606303	+	0.795234i	$0.292652\pi$
$98$	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	−0.994078	−	0.108666i	$-0.965342\pi$
$101$	−5.94095	−	10.2900i	−0.591147	−	1.02390i	0.402932	−	0.915230i	$-0.367991\pi$
$102$	−4.34570	+	0.807246i	−0.430289	+	0.0799293i
$103$	3.77246	+	2.17803i	0.371711	+	0.214608i	0.674206	−	0.738543i	$-0.264486\pi$
$103$	3.77246	+	2.17803i	0.371711	+	0.214608i	−0.302494	+	0.953151i	$0.597819\pi$
$104$	−0.949065	+	1.64383i	−0.0930635	+	0.161191i
$105$	2.13063	−	4.05715i	0.207928	−	0.395937i
$106$	−7.52078	−	13.0264i	−0.730482	−	1.26523i
$107$			16.8978i			1.63357i	0.576943	+	0.816784i	$0.304245\pi$
$107$			16.8978i			1.63357i	−0.576943	+	0.816784i	$0.695755\pi$
$108$	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
$112$	5.04792	+	3.97654i	0.476984	+	0.375748i
$113$	−10.8082	−	6.24010i	−1.01675	−	0.587020i	−0.103588	−	0.994620i	$-0.533032\pi$
$113$	−10.8082	−	6.24010i	−1.01675	−	0.587020i	−0.913160	+	0.407601i	$0.866366\pi$
$114$	−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
$119$	5.30588	−	2.11903i	0.486389	−	0.194251i
$120$	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
$126$	9.14608	−	2.08076i	0.814797	−	0.185369i
$127$	−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	$-0.991973\pi$
$131$	−5.47102	+	9.47609i	−0.478005	+	0.827929i	0.521677	+	0.853143i	$0.325307\pi$
$132$	2.16623	−	6.12511i	0.188546	−	0.533122i
$133$	4.66686	+	11.6855i	0.404668	+	1.01326i
$134$			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	0.158563	−	0.987349i	$-0.449314\pi$
$137$	12.7922	−	7.38559i	1.09291	−	0.630994i	0.934351	+	0.356355i	$0.115981\pi$
$138$	7.18235	+	2.54014i	0.611403	+	0.216231i
$139$	2.22917	+	1.28701i	0.189076	+	0.109163i	0.591550	−	0.806268i	$-0.298516\pi$
$139$	2.22917	+	1.28701i	0.189076	+	0.109163i	−0.402474	+	0.915431i	$0.631850\pi$
$140$	−1.25425	−	0.988047i	−0.106004	−	0.0835052i
$141$	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
$147$	−11.0706	+	4.94381i	−0.913090	+	0.407758i
$148$	0.605998	−	1.04962i	0.0498127	−	0.0862782i
$149$	2.37768	+	1.37275i	0.194787	+	0.112460i	0.594222	−	0.804301i	$-0.297460\pi$
$149$	2.37768	+	1.37275i	0.194787	+	0.112460i	−0.399435	+	0.916762i	$0.630794\pi$
$150$	1.32994	+	1.55589i	0.108589	+	0.127038i
$151$	4.45760	+	7.72079i	0.362754	+	0.628309i	0.988413	−	0.151788i	$-0.0485031\pi$
$151$	4.45760	+	7.72079i	0.362754	+	0.628309i	−0.625659	+	0.780097i	$0.715170\pi$
$152$	−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	$-0.579733\pi$
$157$	−15.1714	−	8.75923i	−1.21081	−	0.699063i	−0.962936	+	0.269729i	$0.913066\pi$
$158$	−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	$-0.812451\pi$
$167$	0.847165	−	1.46733i	0.0655556	−	0.113546i	0.896940	+	0.442152i	$0.145785\pi$
$168$	−0.564251	−	14.0877i	−0.0435329	−	1.08689i
$169$	−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	$-0.275157\pi$
$173$	−4.39665	−	7.61522i	−0.334271	−	0.578974i	−0.983345	+	0.181751i	$0.941823\pi$
$174$	7.35285	−	6.28507i	0.557418	−	0.476470i
$175$	−2.07834	−	1.63723i	−0.157108	−	0.123763i
$176$	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	$0.123083\pi$
$179$			10.0909i			0.754226i	−0.926167	+	0.377113i	$0.876917\pi$
$180$	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	$0.990588\pi$
$182$	1.79137	−	0.715424i	0.132785	−	0.0530308i
$183$	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
$189$	−11.0283	−	8.20830i	−0.802192	−	0.597066i
$190$	−5.62023			−0.407735
$191$	14.7531	−	8.51768i	1.06749	−	0.616318i	0.139998	−	0.990152i	$-0.455290\pi$
$191$	14.7531	−	8.51768i	1.06749	−	0.616318i	0.927496	+	0.373834i	$0.121957\pi$
$192$	14.2676	+	5.04592i	1.02967	+	0.364158i
$193$	−9.88703	+	17.1248i	−0.711684	+	1.23267i	0.252541	+	0.967586i	$0.418734\pi$
$193$	−9.88703	+	17.1248i	−0.711684	+	1.23267i	−0.964225	+	0.265086i	$0.914600\pi$
$194$	1.48345	−	2.56941i	0.106505	−	0.184473i
$195$	1.05061	−	0.195159i	0.0752359	−	0.0139756i
$196$	0.989103	+	4.10699i	0.0706502	+	0.293356i
$197$			3.88854i			0.277047i	0.990359	+	0.138523i	$0.0442356\pi$
$197$			3.88854i			0.277047i	−0.990359	+	0.138523i	$0.955764\pi$
$198$	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
$203$	−7.73724	+	9.82185i	−0.543048	+	0.689359i
$204$	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
$210$	−0.216729	−	5.41108i	−0.0149557	−	0.373400i
$211$	−5.79495	+	10.0372i	−0.398941	+	0.690986i	−0.993596	−	0.112995i	$-0.963955\pi$
$211$	−5.79495	+	10.0372i	−0.398941	+	0.690986i	0.594655	+	0.803981i	$0.297289\pi$
$212$	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	$-0.361466\pi$
$223$	21.1708	−	12.2230i	1.41770	−	0.818511i	0.996097	+	0.0882674i	$0.0281330\pi$
$224$	−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	$-0.189255\pi$
$227$	−1.06827	−	1.85031i	−0.0709039	−	0.122809i	−0.899298	+	0.437337i	$0.855922\pi$
$228$	3.23007	+	3.77882i	0.213916	+	0.250259i
$229$	20.4349	+	11.7981i	1.35037	+	0.779639i	0.988302	−	0.152511i	$-0.0487360\pi$
$229$	20.4349	+	11.7981i	1.35037	+	0.779639i	0.362072	+	0.932150i	$0.382069\pi$
$230$	2.19921	−	3.80915i	0.145012	−	0.251168i
$231$	−24.0773	+	15.2173i	−1.58417	+	1.00122i
$232$	−7.26984	−	12.5917i	−0.477289	−	0.826688i
$233$			0.828258i			0.0542610i	0.999632	+	0.0271305i	$0.00863697\pi$
$233$			0.828258i			0.0542610i	−0.999632	+	0.0271305i	$0.991363\pi$
$234$	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
$238$	4.17806	−	5.30374i	0.270823	−	0.343790i
$239$	16.2406	+	9.37651i	1.05052	+	0.606516i	0.922794	−	0.385294i	$-0.125900\pi$
$239$	16.2406	+	9.37651i	1.05052	+	0.606516i	0.127723	+	0.991810i	$0.459233\pi$
$240$	3.96612	+	1.40267i	0.256012	+	0.0905421i
$241$	15.8128	−	9.12955i	1.01859	−	0.588086i	0.104898	−	0.994483i	$-0.466548\pi$
$241$	15.8128	−	9.12955i	1.01859	−	0.588086i	0.913697	+	0.406397i	$0.133215\pi$
$242$		−	32.6543i		−	2.09910i
$243$	2.00345	−	15.4592i	0.128521	−	0.991707i
$244$		−	8.61210i		−	0.551333i
$245$	1.63898	+	6.80542i	0.104710	+	0.434782i
$246$	−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	$-0.657592\pi$
$251$	−15.0543			−0.950219			−0.475109	+	0.879927i	$0.657592\pi$
$252$	−3.51364	+	3.25558i	−0.221338	+	0.205082i
$253$	−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	0.121302	+	0.992616i	$0.461293\pi$
$257$	−12.8086	+	22.1852i	−0.798979	+	1.38387i	−0.920282	+	0.391257i	$0.872040\pi$
$258$	−7.32816	−	8.57315i	−0.456232	−	0.533741i
$259$	−4.93454	+	1.97072i	−0.306617	+	0.122455i
$260$		−	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	−0.899992	−	0.435906i	$-0.856428\pi$
$263$	−15.7710	+	9.10540i	−0.972483	+	0.561463i	−0.0724906	+	0.997369i	$0.523095\pi$
$264$	−6.04914	−	32.5647i	−0.372299	−	2.00422i
$265$	11.0230	+	6.36415i	0.677139	+	0.390947i
$266$	11.6807	+	9.20160i	0.716192	+	0.564186i
$267$	−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	$-0.737483\pi$
$269$	−22.2650			−1.35752			−0.678761	+	0.734359i	$0.737483\pi$
$270$	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
$273$	−2.50305	−	1.31448i	−0.151491	−	0.0795562i
$274$	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	0.543514	−	0.839400i	$-0.317093\pi$
$277$	−7.57578	−	13.1216i	−0.455185	−	0.788403i	−0.998699	+	0.0509971i	$0.983760\pi$
$278$	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	−0.845334	−	0.534237i	$-0.820599\pi$
$281$	−13.4999	+	7.79419i	−0.805338	+	0.464962i	0.0399960	+	0.999200i	$0.487265\pi$
$282$	8.65530	+	10.1258i	0.515415	+	0.602980i
$283$	−12.1672	−	7.02475i	−0.723266	−	0.417578i	0.0926875	−	0.995695i	$-0.470454\pi$
$283$	−12.1672	−	7.02475i	−0.723266	−	0.417578i	−0.815954	+	0.578117i	$0.803788\pi$
$284$	−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	$-0.770776\pi$
$293$	3.34242	−	5.78924i	0.195266	−	0.338211i	0.946988	+	0.321270i	$0.104110\pi$
$294$	−8.40873	+	11.6009i	−0.490407	+	0.676577i
$295$	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
$301$	11.4519	+	9.02134i	0.660078	+	0.519981i
$302$	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	$0.863149\pi$
$308$	3.68076	+	9.21633i	0.209731	+	0.525149i
$309$	−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	−0.464069	−	0.885799i	$-0.653611\pi$
$311$	9.43641	−	16.3443i	0.535090	−	0.926803i	0.999159	−	0.0410038i	$-0.0130556\pi$
$312$	2.49909	−	2.13617i	0.141483	−	0.120937i
$313$	−15.4266	+	8.90656i	−0.871964	+	0.503429i	−0.868000	−	0.496563i	$-0.834595\pi$
$313$	−15.4266	+	8.90656i	−0.871964	+	0.503429i	−0.00396365	+	0.999992i	$0.501262\pi$
$314$	−20.7023			−1.16830
$315$	−5.82222	+	5.39461i	−0.328045	+	0.303952i
$316$	3.44467			0.193778
$317$	−22.7317	+	13.1242i	−1.27674	+	0.737127i	−0.976248	−	0.216656i	$-0.930485\pi$
$317$	−22.7317	+	13.1242i	−1.27674	+	0.737127i	−0.300494	+	0.953784i	$0.597152\pi$
$318$	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
$322$	−10.8072	+	4.31609i	−0.602259	+	0.240526i
$323$			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
$329$	−13.5259	−	10.6551i	−0.745705	−	0.587435i
$330$	−2.32348	−	12.5081i	−0.127903	−	0.688549i
$331$	−9.75588	−	16.8977i	−0.536232	−	0.928781i	−0.999103	−	0.0423550i	$-0.986514\pi$
$331$	−9.75588	−	16.8977i	−0.536232	−	0.928781i	0.462871	−	0.886426i	$-0.346819\pi$
$332$	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
$336$	−5.94644	−	9.40866i	−0.324405	−	0.513285i
$337$	10.2676	−	17.7840i	0.559311	−	0.968755i	−0.438243	−	0.898857i	$-0.644399\pi$
$337$	10.2676	−	17.7840i	0.559311	−	0.968755i	0.997554	−	0.0698988i	$-0.0222677\pi$
$338$	−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	0.351467	−	0.936200i	$-0.385683\pi$
$347$	−5.28238	−	3.04978i	−0.283573	−	0.163721i	−0.635040	+	0.772479i	$0.719016\pi$
$348$	−1.64704	+	4.65709i	−0.0882909	+	0.249646i
$349$	−27.8341	+	16.0700i	−1.48992	+	0.860207i	−0.999934	−	0.0115214i	$-0.996333\pi$
$349$	−27.8341	+	16.0700i	−1.48992	+	0.860207i	−0.489989	+	0.871729i	$0.662999\pi$
$350$	−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	$-0.150582\pi$
$353$	0.948987	+	1.64369i	0.0505095	+	0.0874850i	−0.839665	+	0.543104i	$0.817249\pi$
$354$	−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
$357$	−9.88792	+	0.396038i	−0.523324	+	0.0209606i
$358$	5.96239	+	10.3272i	0.315122	+	0.545807i
$359$		−	11.5006i		−	0.606976i	−0.952835	−	0.303488i	$-0.901849\pi$
$359$		−	11.5006i		−	0.606976i	0.952835	−	0.303488i	$-0.0981513\pi$
$360$	−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
$364$	−0.609573	+	0.773808i	−0.0319503	+	0.0405585i
$365$	−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	$-0.505789\pi$
$367$	16.0654	−	9.27534i	0.838605	−	0.484169i	0.856790	+	0.515666i	$0.172455\pi$
$368$		−	9.04007i		−	0.471246i
$369$	1.46691	−	0.564454i	0.0763641	−	0.0293843i
$370$		−	2.37331i		−	0.123383i
$371$	−12.4900	−	31.2741i	−0.648450	−	1.62367i
$372$	8.61379	−	1.60007i	0.446604	−	0.0829600i
$373$	−10.2802	+	17.8058i	−0.532288	+	0.921950i	0.467001	+	0.884257i	$0.345334\pi$
$373$	−10.2802	+	17.8058i	−0.532288	+	0.921950i	−0.999289	+	0.0376935i	$0.987999\pi$
$374$	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
$378$	−16.1366	−	1.88421i	−0.829978	−	0.0969131i
$379$	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	$-0.865456\pi$
$383$	−1.97163	+	3.41496i	−0.100746	+	0.174496i	0.811246	+	0.584704i	$0.198789\pi$
$384$	6.40162	−	1.18915i	0.326681	−	0.0606835i
$385$	6.09914	+	15.2718i	0.310841	+	0.778322i
$386$			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	0.435367	−	0.900253i	$-0.356619\pi$
$389$	28.2571	−	16.3142i	1.43269	−	0.827165i	0.997325	+	0.0730880i	$0.0232854\pi$
$390$	0.959901	−	0.820505i	0.0486065	−	0.0415479i
$391$	−6.96064	−	4.01873i	−0.352015	−	0.203236i
$392$	14.8359	+	15.6115i	0.749328	+	0.788498i
$393$	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
$399$	−0.872220	−	21.7768i	−0.0436656	−	1.09020i
$400$	1.21441	−	2.10343i	0.0607207	−	0.105171i
$401$	6.75815	+	3.90182i	0.337486	+	0.194848i	0.659160	−	0.752003i	$-0.270912\pi$
$401$	6.75815	+	3.90182i	0.337486	+	0.194848i	−0.321674	+	0.946851i	$0.604245\pi$
$402$	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	$-0.179479\pi$
$409$	16.2794	+	9.39890i	0.804963	+	0.464746i	−0.0402405	+	0.999190i	$0.512812\pi$
$410$	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	−0.350078	−	0.936721i	$-0.613845\pi$
$419$	13.0224	−	22.5554i	0.636185	−	1.10190i	0.986263	−	0.165184i	$-0.0528217\pi$
$420$	1.47751	+	2.33776i	0.0720950	+	0.114071i
$421$	−19.4365	−	33.6651i	−0.947279	−	1.64074i	−0.751122	−	0.660163i	$-0.770487\pi$
$421$	−19.4365	−	33.6651i	−0.947279	−	1.64074i	−0.196157	−	0.980572i	$-0.562846\pi$
$422$			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
$427$	−23.3641	+	29.6590i	−1.13067	+	1.43530i
$428$	−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	$-0.975990\pi$
$431$		−	3.12892i		−	0.150715i	0.997157	−	0.0753573i	$-0.0240097\pi$
$432$	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	$0.856522\pi$
$434$	24.3370	−	9.71956i	1.16821	−	0.466554i
$435$	−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	$-0.651878\pi$
$439$	1.68550	−	0.973121i	0.0804443	−	0.0464445i	0.539683	+	0.841869i	$0.318544\pi$
$440$	−19.1229			−0.911648
$441$	20.9327	−	1.67952i	0.996797	−	0.0799772i
$442$	1.57440			0.0748864
$443$	0.462264	−	0.266888i	0.0219628	−	0.0126802i	−0.488978	−	0.872296i	$-0.662630\pi$
$443$	0.462264	−	0.266888i	0.0219628	−	0.0126802i	0.510941	+	0.859616i	$0.329297\pi$
$444$	−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
$448$	−21.4682	+	8.57381i	−1.01427	+	0.405074i
$449$			19.0944i			0.901120i	0.892746	+	0.450560i	$0.148776\pi$
$449$			19.0944i			0.901120i	−0.892746	+	0.450560i	$0.851224\pi$
$450$	−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
$455$	−1.01008	+	1.28223i	−0.0473534	+	0.0601116i
$456$	23.8935	+	8.45025i	1.11891	+	0.395719i
$457$	11.5372	+	19.9830i	0.539688	+	0.934767i	0.998921	+	0.0464507i	$0.0147910\pi$
$457$	11.5372	+	19.9830i	0.539688	+	0.934767i	−0.459233	+	0.888316i	$0.651876\pi$
$458$	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	0.999395	+	0.0347688i	$0.0110695\pi$
$461$	11.3755	+	19.7029i	0.529808	+	0.917655i	−0.469587	+	0.882886i	$0.655597\pi$
$462$	−15.6497	+	29.8002i	−0.728088	+	1.38643i
$463$	6.06653	−	10.5075i	0.281935	−	0.488327i	−0.689926	−	0.723880i	$-0.742357\pi$
$463$	6.06653	−	10.5075i	0.281935	−	0.488327i	0.971861	+	0.235553i	$0.0756903\pi$
$464$	−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	$-0.465962\pi$
$467$	4.61293			0.213461			0.106731	+	0.994288i	$0.465962\pi$
$468$	−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	$-0.100129\pi$
$479$	4.54166	+	7.86639i	0.207514	+	0.359424i	−0.743417	+	0.668828i	$0.766796\pi$
$480$	−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
$483$	15.1007	+	7.93016i	0.687104	+	0.360835i
$484$	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
$490$	5.69848	+	5.99637i	0.257431	+	0.270888i
$491$	−9.25604	−	5.34398i	−0.417719	−	0.241170i	0.276382	−	0.961048i	$-0.410865\pi$
$491$	−9.25604	−	5.34398i	−0.417719	−	0.241170i	−0.694101	+	0.719878i	$0.744198\pi$
$492$	−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
$497$	5.35587	+	13.4107i	0.240244	+	0.601552i
$498$	17.0470	+	19.9431i	0.763892	+	0.893671i
$499$	10.4045	−	18.0211i	0.465768	−	0.806734i	−0.533468	−	0.845820i	$-0.679111\pi$
$499$	10.4045	−	18.0211i	0.465768	−	0.806734i	0.999236	+	0.0390866i	$0.0124448\pi$
$500$	−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	$-0.584645\pi$
$503$	−11.7879			−0.525595			−0.262797	+	0.964851i	$0.584645\pi$
$504$	−7.21439	+	23.3301i	−0.321355	+	1.03921i
$505$	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	$-0.863691\pi$
$509$	−2.14843	+	3.72118i	−0.0952273	+	0.164938i	0.814476	+	0.580197i	$0.197024\pi$
$510$	1.47375	−	4.16711i	0.0652590	−	0.184523i
$511$	0.399268	+	0.999736i	0.0176626	+	0.0442257i
$512$		−	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
$518$	−3.88565	+	4.93255i	−0.170726	+	0.216724i
$519$	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	$-0.317758\pi$
$521$	24.7319			1.08352			0.541761	+	0.840533i	$0.317758\pi$
$522$	−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
$525$	2.44828	+	3.87375i	0.106852	+	0.169064i
$526$	−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
$546$	−3.33835	+	0.133710i	−0.142868	+	0.00572227i
$547$	−5.24179	−	9.07905i	−0.224123	−	0.388192i	0.731933	−	0.681377i	$-0.238618\pi$
$547$	−5.24179	−	9.07905i	−0.224123	−	0.388192i	−0.956056	+	0.293184i	$0.905285\pi$
$548$			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
$553$	−11.8630	−	9.34519i	−0.504467	−	0.397398i
$554$	−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	$0.148776\pi$
$557$			21.2672i			0.901121i	−0.892746	+	0.450560i	$0.851224\pi$
$558$	23.1080	+	18.6815i	0.978238	+	0.790853i
$559$			3.39946i			0.143782i
$560$	−5.96774	+	2.38336i	−0.252183	+	0.100715i
$561$	−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	$-0.888210\pi$
$563$	−4.07042	+	7.05018i	−0.171548	+	0.297130i	0.767413	+	0.641153i	$0.221544\pi$
$564$	−6.41338	−	2.26818i	−0.270052	−	0.0955076i
$565$	10.8082	−	6.24010i	0.454703	−	0.262523i
$566$	−16.6029			−0.697871
$567$	13.2682	+	19.7726i	0.557211	+	0.830371i
$568$	−16.7925			−0.704597
$569$	30.1838	−	17.4266i	1.26537	−	0.730562i	0.291262	−	0.956643i	$-0.405925\pi$
$569$	30.1838	−	17.4266i	1.26537	−	0.730562i	0.974108	+	0.226081i	$0.0725915\pi$
$570$	9.17749	+	3.24574i	0.384403	+	0.135949i
$571$	5.67837	−	9.83523i	0.237633	−	0.411592i	−0.722402	−	0.691473i	$-0.756962\pi$
$571$	5.67837	−	9.83523i	0.237633	−	0.411592i	0.960034	+	0.279882i	$0.0902953\pi$
$572$	−1.15708	+	2.00412i	−0.0483798	+	0.0837963i
$573$	−29.0099	+	5.38879i	−1.21190	+	0.225120i
$574$	−0.607547	−	1.52125i	−0.0253585	−	0.0634957i
$575$			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
$581$	−26.6397	−	20.9857i	−1.10520	−	0.870632i
$582$	−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	0.998709	+	0.0508027i	$0.0161780\pi$
$587$	13.1643	+	22.8013i	0.543351	+	0.941111i	−0.455358	+	0.890308i	$0.650489\pi$
$588$	0.756685	−	7.27767i	0.0312052	−	0.300126i
$589$	−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	$-0.182761\pi$
$593$	40.8936			1.67930			0.839649	+	0.543129i	$0.182761\pi$
$594$	−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	0.539813	−	0.841785i	$-0.318495\pi$
$599$	1.97542	+	1.14051i	0.0807133	+	0.0465998i	−0.459100	+	0.888385i	$0.651828\pi$
$600$	−5.23929	+	0.973236i	−0.213893	+	0.0397322i
$601$	−20.8183	+	12.0194i	−0.849195	+	0.490283i	−0.860379	−	0.509654i	$-0.829773\pi$
$601$	−20.8183	+	12.0194i	−0.849195	+	0.490283i	0.0111841	+	0.999937i	$0.496440\pi$
$602$	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	$-0.0364244\pi$
$607$	34.2781	+	19.7905i	1.39131	+	0.803271i	0.397846	+	0.917452i	$0.369758\pi$
$608$	7.80693	−	13.5220i	0.316613	−	0.548389i
$609$	18.3066	−	11.5701i	0.741822	−	0.468845i
$610$	−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
$616$	39.7438	+	31.3085i	1.60132	+	1.26146i
$617$	2.49126	+	1.43833i	0.100294	+	0.0579050i	0.549308	−	0.835620i	$-0.314891\pi$
$617$	2.49126	+	1.43833i	0.100294	+	0.0579050i	−0.449014	+	0.893525i	$0.648225\pi$
$618$	−8.40593	−	2.97287i	−0.338136	−	0.119586i
$619$	31.1520	−	17.9856i	1.25211	−	0.722903i	0.280578	−	0.959831i	$-0.409474\pi$
$619$	31.1520	−	17.9856i	1.25211	−	0.722903i	0.971527	+	0.236928i	$0.0761405\pi$
$620$		−	5.05825i		−	0.203144i
$621$	0.529719	+	19.3328i	0.0212569	+	0.775797i
$622$		−	22.3028i		−	0.894260i
$623$	2.35317	−	0.939794i	0.0942778	−	0.0376520i
$624$	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
$630$	−2.77105	+	8.96111i	−0.110401	+	0.357019i
$631$	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
$637$	4.19859	−	1.01116i	0.166354	−	0.0400637i
$638$			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	−0.642659	−	0.766153i	$-0.722169\pi$
$641$	−7.60755	+	4.39222i	−0.300480	+	0.173482i	0.342178	+	0.939635i	$0.388835\pi$
$642$	−6.31672	−	34.0052i	−0.249301	−	1.34208i
$643$	38.1679	+	22.0362i	1.50520	+	0.869025i	0.999982	+	0.00603040i	$0.00191955\pi$
$643$	38.1679	+	22.0362i	1.50520	+	0.869025i	0.505213	+	0.862994i	$0.331414\pi$
$644$	3.67750	−	4.66831i	0.144914	−	0.183957i
$645$	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	$-0.669259\pi$
$647$	−25.7941			−1.01407			−0.507036	+	0.861925i	$0.669259\pi$
$648$	−27.0754	+	5.80085i	−1.06362	+	0.227879i
$649$		−	33.9017i		−	1.33076i
$650$	−0.364536	−	0.631395i	−0.0142983	−	0.0247653i
$651$	−34.0057	−	17.8582i	−1.33279	−	0.699919i
$652$	−3.57559	+	6.19310i	−0.140031	+	0.242540i
$653$	−11.9806	−	6.91698i	−0.468836	−	0.270682i	0.246916	−	0.969037i	$-0.420583\pi$
$653$	−11.9806	−	6.91698i	−0.468836	−	0.270682i	−0.715752	+	0.698354i	$0.753916\pi$
$654$	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	0.0379897	−	0.999278i	$-0.487905\pi$
$659$	23.6785	−	13.6708i	0.922385	−	0.532539i	0.884395	+	0.466739i	$0.154571\pi$
$660$	4.22138	+	4.93856i	0.164317	+	0.192233i
$661$	−22.8640	−	13.2006i	−0.889308	−	0.513442i	−0.0155920	−	0.999878i	$-0.504963\pi$
$661$	−22.8640	−	13.2006i	−0.889308	−	0.513442i	−0.873716	+	0.486436i	$0.838297\pi$
$662$	−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
$672$	13.3198	+	6.99496i	0.513824	+	0.269836i
$673$	−5.09999	−	8.83344i	−0.196590	−	0.340504i	0.750831	−	0.660495i	$-0.229653\pi$
$673$	−5.09999	−	8.83344i	−0.196590	−	0.340504i	−0.947421	+	0.319991i	$0.896320\pi$
$674$		−	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	$-0.201090\pi$
$677$	−2.80831	−	4.86413i	−0.107932	−	0.186944i	−0.914932	+	0.403607i	$0.867756\pi$
$678$	24.0832	+	8.51734i	0.924908	+	0.327106i
$679$	4.11045	−	5.21791i	0.157744	−	0.200245i
$680$	−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	$0.296310\pi$
$683$			41.9272i			1.60430i	−0.597124	+	0.802149i	$0.703690\pi$
$684$	−3.09218	−	8.03598i	−0.118233	−	0.307263i
$685$			14.7712i			0.564378i
$686$	−2.02596	−	21.7922i	−0.0773515	−	0.832029i
$687$	−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	$-0.960126\pi$
$691$	−36.2770	+	20.9446i	−1.38004	+	0.796769i	−0.387880	+	0.921710i	$0.626792\pi$
$692$	5.30665			0.201728
$693$	48.1048	−	10.9440i	1.82735	−	0.415727i
$694$	−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
$700$	1.48280	−	0.592191i	0.0560446	−	0.0223827i
$701$		−	26.4201i		−	0.997874i	−0.866638	−	0.498937i	$-0.833724\pi$
$701$		−	26.4201i		−	0.997874i	0.866638	−	0.498937i	$-0.166276\pi$
$702$	−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
$707$	−24.6946	−	19.4534i	−0.928736	−	0.731619i
$708$	−1.04125	−	5.60542i	−0.0391325	−	0.210665i
$709$	6.36004	+	11.0159i	0.238856	+	0.413711i	0.960386	−	0.278672i	$-0.0898942\pi$
$709$	6.36004	+	11.0159i	0.238856	+	0.413711i	−0.721530	+	0.692383i	$0.756561\pi$
$710$	−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
$714$	−9.88547	+	6.24779i	−0.369954	+	0.233818i
$715$	−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	$-0.820418\pi$
$719$	−45.3176			−1.69006			−0.845030	+	0.534718i	$0.820418\pi$
$720$	−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	$-0.724884\pi$
$727$	−8.49387	+	4.90394i	−0.315020	+	0.181877i	0.334150	+	0.942520i	$0.391551\pi$
$728$	−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	$-0.326696\pi$
$733$	0.977788	+	0.564526i	0.0361154	+	0.0208512i	−0.481834	+	0.876263i	$0.660029\pi$
$734$	10.9611	−	18.9851i	0.404580	−	0.700753i
$735$	1.25385	−	12.0593i	0.0462491	−	0.444816i
$736$	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
$742$	−31.2614	−	24.6264i	−1.14764	−	0.904065i
$743$	28.5598	+	16.4890i	1.04776	+	0.604924i	0.922021	−	0.387140i	$-0.126537\pi$
$743$	28.5598	+	16.4890i	1.04776	+	0.604924i	0.125738	+	0.992064i	$0.459870\pi$
$744$	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
$749$	16.5814	+	41.5186i	0.605873	+	1.51706i
$750$	−2.01241	+	0.373820i	−0.0734828	+	0.0136500i
$751$	−24.9073	+	43.1407i	−0.908880	+	1.57423i	−0.0932571	+	0.995642i	$0.529728\pi$
$751$	−24.9073	+	43.1407i	−0.908880	+	1.57423i	−0.815623	+	0.578584i	$0.803605\pi$
$752$	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
$756$	7.61768	−	3.28699i	0.277052	−	0.119547i
$757$	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	$-0.841579\pi$
$761$	−0.714506	+	1.23756i	−0.0259008	+	0.0448615i	0.852784	+	0.522263i	$0.174912\pi$
$762$	20.8242	−	3.86825i	0.754382	−	0.140132i
$763$	−18.4156	+	7.35471i	−0.666690	+	0.266258i
$764$			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	$-0.605939\pi$
$769$	−36.2876	−	20.9506i	−1.30856	−	0.755500i	−0.981856	+	0.189626i	$0.939273\pi$
$770$	15.2656	+	12.0256i	0.550134	+	0.433373i
$771$	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	$-0.550147\pi$
$773$	−8.72402			−0.313781			−0.156891	+	0.987616i	$0.550147\pi$
$774$	7.01534	+	18.2315i	0.252161	+	0.655318i
$775$		−	8.38169i		−	0.301079i
$776$	3.86214	+	6.68942i	0.138643	+	0.240136i
$777$	9.19590	−	0.368321i	0.329901	−	0.0132134i
$778$	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	$-0.171835\pi$
$787$	23.6087	+	13.6305i	0.841558	+	0.485874i	−0.0162352	+	0.999868i	$0.505168\pi$
$788$	−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	$-0.985861\pi$
$797$	−13.0160	+	22.5444i	−0.461051	+	0.798564i	0.537962	+	0.842969i	$0.319194\pi$
$798$	−13.7599	−	21.7714i	−0.487095	−	0.770698i
$799$	−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
$805$	6.09374	−	7.73555i	0.214776	−	0.272642i
$806$	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	$0.187920\pi$
$809$			31.6665i			1.11334i	−0.830735	+	0.556668i	$0.812080\pi$
$810$	−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	$-0.0251751\pi$
$812$	−2.79859	−	7.00744i	−0.0982111	−	0.245913i
$813$	−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
$819$	3.32819	+	3.59200i	0.116296	+	0.125515i
$820$	−0.316179			−0.0110414
$821$	1.92522	−	1.11153i	0.0671907	−	0.0387926i	−0.466028	−	0.884770i	$-0.654316\pi$
$821$	1.92522	−	1.11153i	0.0671907	−	0.0387926i	0.533219	+	0.845977i	$0.320982\pi$
$822$	−22.9823	+	19.6448i	−0.801600	+	0.685192i
$823$	7.46182	−	12.9243i	0.260103	−	0.450511i	−0.706166	−	0.708046i	$-0.749577\pi$
$823$	7.46182	−	12.9243i	0.260103	−	0.450511i	0.966269	+	0.257535i	$0.0829102\pi$
$824$	−6.70103	+	11.6065i	−0.233442	+	0.404333i
$825$	6.99498	+	8.18336i	0.243534	+	0.284908i
$826$	−6.32501	−	15.8373i	−0.220075	−	0.551051i
$827$			11.9293i			0.414824i	0.978254	+	0.207412i	$0.0665040\pi$
$827$			11.9293i			0.414824i	−0.978254	+	0.207412i	$0.933496\pi$
$828$	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
$833$	10.9574	−	10.4131i	0.379653	−	0.360793i
$834$	−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	$-0.220710\pi$
$839$	−4.89427	−	8.47713i	−0.168969	−	0.292663i	−0.938058	+	0.346479i	$0.887377\pi$
$840$	12.4824	+	6.55518i	0.430684	+	0.226175i
$841$	−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	$-0.396277\pi$
$853$	37.9865	−	21.9315i	1.30063	−	0.750921i	0.980513	+	0.196456i	$0.0629433\pi$
$854$	−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	$-0.146159\pi$
$857$	1.88477	+	3.26452i	0.0643825	+	0.111514i	−0.832037	+	0.554720i	$0.812826\pi$
$858$	−7.71685	+	1.43346i	−0.263449	+	0.0489376i
$859$	6.80837	+	3.93081i	0.232299	+	0.134118i	0.611632	−	0.791142i	$-0.290513\pi$
$859$	6.80837	+	3.93081i	0.232299	+	0.134118i	−0.379333	+	0.925260i	$0.623847\pi$
$860$	1.66265	−	2.87979i	0.0566959	−	0.0982002i
$861$	−1.11628	+	2.12562i	−0.0380426	+	0.0724408i
$862$	−1.84879	−	3.20219i	−0.0629699	−	0.109067i
$863$		−	50.5884i		−	1.72205i	−0.508565	−	0.861024i	$-0.669824\pi$
$863$		−	50.5884i		−	1.72205i	0.508565	−	0.861024i	$-0.330176\pi$
$864$	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
$868$	−8.28150	+	10.5127i	−0.281092	+	0.356826i
$869$	−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
$875$	2.45705	−	0.981280i	0.0830634	−	0.0331733i
$876$	0.276345	+	0.323293i	0.00933682	+	0.0109231i
$877$	−1.56847	+	2.71668i	−0.0529636	+	0.0917357i	−0.891292	−	0.453430i	$-0.850200\pi$
$877$	−1.56847	+	2.71668i	−0.0529636	+	0.0917357i	0.838328	+	0.545166i	$0.183533\pi$
$878$	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	$-0.419771\pi$
$881$	14.8044			0.498774			0.249387	+	0.968404i	$0.419771\pi$
$882$	20.4305	−	14.0874i	0.687932	−	0.474347i
$883$	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	$-0.887460\pi$
$887$	−5.04001	+	8.72956i	−0.169227	+	0.293110i	0.768921	+	0.639343i	$0.220794\pi$
$888$	−3.56837	+	10.0897i	−0.119747	+	0.338589i
$889$	−25.4253	+	10.1542i	−0.852737	+	0.340561i
$890$			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
$896$	−6.15467	+	7.81290i	−0.205613	+	0.261011i
$897$	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
$903$	−13.4903	−	21.3449i	−0.448931	−	0.710313i
$904$	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	−0.996077	−	0.0884889i	$-0.971796\pi$
$907$	−17.3071	−	29.9767i	−0.574672	−	0.995361i	0.421405	−	0.906873i	$-0.361537\pi$
$908$	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	−0.818166	−	0.574981i	$-0.805009\pi$
$911$	−22.0123	+	12.7088i	−0.729301	+	0.421062i	0.0888654	+	0.996044i	$0.471676\pi$
$912$	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
$924$	−0.687921	−	17.1754i	−0.0226309	−	0.565028i
$925$	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	$-0.159624\pi$
$929$	0.674311	+	1.16794i	0.0221234	+	0.0383189i	−0.854752	+	0.519037i	$0.826291\pi$
$930$	13.0410	−	11.1472i	0.427630	−	0.365530i
$931$	22.9334	+	24.1322i	0.751612	+	0.790902i
$932$	−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	$-0.305272\pi$
$938$	0.340402	+	0.852339i	0.0111145	+	0.0278299i
$939$	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	$-0.955177\pi$
$941$	−11.4575	+	19.8449i	−0.373503	+	0.646926i	0.616599	+	0.787278i	$0.288510\pi$
$942$	33.8055	+	11.9558i	1.10144	+	0.389540i
$943$	−1.68877	+	0.975011i	−0.0549939	+	0.0317507i
$944$	13.2477			0.431177
$945$	12.6228	−	5.44666i	0.410618	−	0.177180i
$946$	40.4725			1.31587
$947$	−1.16082	+	0.670199i	−0.0377216	+	0.0217786i	−0.518742	−	0.854931i	$-0.673600\pi$
$947$	−1.16082	+	0.670199i	−0.0377216	+	0.0217786i	0.481021	+	0.876709i	$0.340266\pi$
$948$	−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
$952$	6.51950	+	16.3243i	0.211298	+	0.529074i
$953$		−	13.3889i		−	0.433710i	−0.976204	−	0.216855i	$-0.930420\pi$
$953$		−	13.3889i		−	0.433710i	0.976204	−	0.216855i	$-0.0695800\pi$
$954$	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
$959$	24.1838	−	30.6995i	0.780935	−	0.991339i
$960$	−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
$966$	20.1400	−	0.806662i	0.647993	−	0.0259539i
$967$	−13.2117	+	22.8834i	−0.424860	+	0.735879i	−0.996407	−	0.0846898i	$-0.973010\pi$
$967$	−13.2117	+	22.8834i	−0.424860	+	0.735879i	0.571547	+	0.820569i	$0.306343\pi$
$968$	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	$-0.405581\pi$
$971$	18.2164			0.584593			0.292296	+	0.956328i	$0.405581\pi$
$972$	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	0.615896	−	0.787827i	$-0.288794\pi$
$977$	7.55063	+	4.35936i	0.241566	+	0.139468i	−0.374330	+	0.927295i	$0.622127\pi$
$978$	−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	$-0.148758\pi$
$983$	1.76302	+	3.05363i	0.0562315	+	0.0973957i	−0.836539	+	0.547907i	$0.815425\pi$
$984$	−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
$987$	15.9335	+	25.2104i	0.507168	+	0.802457i
$988$	−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
$994$	13.4053	+	10.5601i	0.425190	+	0.334946i
$995$	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	$-0.989676\pi$
$997$	−46.4513	+	26.8186i	−1.47113	+	0.849355i	−0.471652	+	0.881785i	$0.656342\pi$
$998$		−	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.j.41.8	yes	24
3.2	odd	2		945.2.bl.j.881.5		24
7.6	odd	2		315.2.bl.i.41.8	✓	24
9.2	odd	6		315.2.bl.i.146.8	yes	24
9.7	even	3		945.2.bl.i.251.5		24
21.20	even	2		945.2.bl.i.881.5		24
63.20	even	6	inner	315.2.bl.j.146.8	yes	24
63.34	odd	6		945.2.bl.j.251.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.8	✓	24	7.6	odd	2
315.2.bl.i.146.8	yes	24	9.2	odd	6
315.2.bl.j.41.8	yes	24	1.1	even	1	trivial
315.2.bl.j.146.8	yes	24	63.20	even	6	inner
945.2.bl.i.251.5		24	9.7	even	3
945.2.bl.i.881.5		24	21.20	even	2
945.2.bl.j.251.5		24	63.34	odd	6
945.2.bl.j.881.5		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.02342 - 0.590871i) q^{2} +(-1.63294 - 0.577510i) q^{3} +(-0.301744 + 0.522636i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.01241 + 0.373820i) q^{6} +(2.45705 - 0.981280i) q^{7} +3.07665i q^{8} +(2.33296 + 1.88607i) q^{9} +O(q^{10})\)	\(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} +(2.45705 - 0.981280i) 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} +(1.93478 - 2.45606i) 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} +(-4.57890 + 0.183398i) 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} +(-4.57777 + 2.89323i) 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} +(5.07418 - 4.82211i) 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} +(3.01905 + 7.55948i) 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} +(7.58297 + 2.34489i) 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} +(1.15962 + 2.90360i) 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} +(10.1762 - 12.9179i) 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} +(1.28581 - 2.44844i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * 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 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * 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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