LMFDB - Embedded newform 315.2.bl.j.41.11

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			41.11
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.j.146.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99878 - 1.15400i) q^{2} +(1.43832 - 0.965005i) q^{3} +(1.66342 - 2.88113i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.76127 - 3.58865i) q^{6} +(-2.42508 + 1.05782i) q^{7} -3.06234i q^{8} +(1.13753 - 2.77597i) q^{9} +O(q^{10})$	\(q+(1.99878 - 1.15400i) q^{2} +(1.43832 - 0.965005i) q^{3} +(1.66342 - 2.88113i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.76127 - 3.58865i) q^{6} +(-2.42508 + 1.05782i) q^{7} -3.06234i q^{8} +(1.13753 - 2.77597i) q^{9} +2.30799i q^{10} +(-0.565971 + 0.326763i) q^{11} +(-0.387773 - 5.74919i) q^{12} +(-0.0750048 - 0.0433040i) q^{13} +(-3.62648 + 4.91289i) q^{14} +(0.116559 + 1.72812i) q^{15} +(-0.207089 - 0.358689i) q^{16} +0.482385 q^{17} +(-0.929792 - 6.86127i) q^{18} +2.08485i q^{19} +(1.66342 + 2.88113i) q^{20} +(-2.46724 + 3.86170i) q^{21} +(-0.754168 + 1.30626i) q^{22} +(3.12120 + 1.80203i) q^{23} +(-2.95517 - 4.40462i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.199891 q^{26} +(-1.04270 - 5.09046i) q^{27} +(-0.986202 + 8.74656i) q^{28} +(-7.04603 + 4.06803i) q^{29} +(2.22723 + 3.31963i) q^{30} +(1.47914 + 0.853983i) q^{31} +(4.47627 + 2.58438i) q^{32} +(-0.498719 + 1.01615i) q^{33} +(0.964182 - 0.556671i) q^{34} +(0.296438 - 2.62909i) q^{35} +(-6.10574 - 7.89497i) q^{36} -10.9878 q^{37} +(2.40591 + 4.16716i) q^{38} +(-0.149670 + 0.0100950i) q^{39} +(2.65206 + 1.53117i) q^{40} +(4.19058 - 7.25830i) q^{41} +(-0.475072 + 10.5659i) q^{42} +(4.84249 + 8.38743i) q^{43} +2.17418i q^{44} +(1.83530 + 2.37312i) q^{45} +8.31814 q^{46} +(-6.00919 - 10.4082i) q^{47} +(-0.643998 - 0.316068i) q^{48} +(4.76202 - 5.13061i) q^{49} +(-1.99878 - 1.15400i) q^{50} +(0.693824 - 0.465504i) q^{51} +(-0.249529 + 0.144066i) q^{52} -3.22434i q^{53} +(-7.95850 - 8.97145i) q^{54} -0.653527i q^{55} +(3.23941 + 7.42641i) q^{56} +(2.01189 + 2.99868i) q^{57} +(-9.38898 + 16.2622i) q^{58} +(4.03221 - 6.98400i) q^{59} +(5.17283 + 2.53877i) q^{60} +(-5.21012 + 3.00807i) q^{61} +3.94198 q^{62} +(0.177889 + 7.93526i) q^{63} +12.7578 q^{64} +(0.0750048 - 0.0433040i) q^{65} +(0.175810 + 2.60659i) q^{66} +(0.729532 - 1.26359i) q^{67} +(0.802408 - 1.38981i) q^{68} +(6.22825 - 0.420085i) q^{69} +(-2.44145 - 5.59707i) q^{70} -9.97547i q^{71} +(-8.50096 - 3.48350i) q^{72} +8.43154i q^{73} +(-21.9622 + 12.6799i) q^{74} +(-1.55488 - 0.763119i) q^{75} +(6.00672 + 3.46798i) q^{76} +(1.02687 - 1.39112i) q^{77} +(-0.287507 + 0.192896i) q^{78} +(-5.08800 - 8.81267i) q^{79} +0.414179 q^{80} +(-6.41205 - 6.31550i) q^{81} -19.3437i q^{82} +(0.998645 + 1.72970i) q^{83} +(7.02201 + 13.5321i) q^{84} +(-0.241192 + 0.417758i) q^{85} +(19.3581 + 11.1764i) q^{86} +(-6.20878 + 12.6506i) q^{87} +(1.00066 + 1.73319i) q^{88} +14.2291 q^{89} +(6.40693 + 2.62541i) q^{90} +(0.227701 + 0.0256739i) q^{91} +(10.3837 - 5.99505i) q^{92} +(2.95158 - 0.199079i) q^{93} +(-24.0221 - 13.8692i) q^{94} +(-1.80553 - 1.04243i) q^{95} +(8.93225 - 0.602465i) q^{96} +(-14.6692 + 8.46925i) q^{97} +(3.59753 - 15.7503i) q^{98} +(0.263278 + 1.94282i) 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 $

$2$	1.99878	−	1.15400i	1.41335	−	0.815999i	0.417650	−	0.908608i	$-0.362854\pi$
$2$	1.99878	−	1.15400i	1.41335	−	0.815999i	0.995703	+	0.0926088i	$0.0295206\pi$
$3$	1.43832	−	0.965005i	0.830414	−	0.557146i
$3$	1.43832	−	0.965005i	0.830414	−	0.557146i
$4$	1.66342	−	2.88113i	0.831710	−	1.44056i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.76127	−	3.58865i	0.719037	−	1.46506i
$7$	−2.42508	+	1.05782i	−0.916594	+	0.399819i
$7$	−2.42508	+	1.05782i	−0.916594	+	0.399819i
$8$		−	3.06234i		−	1.08270i
$9$	1.13753	−	2.77597i	0.379176	−	0.925324i
$10$			2.30799i			0.729852i
$11$	−0.565971	+	0.326763i	−0.170647	+	0.0985228i	−0.582891	−	0.812551i	$-0.698078\pi$
$11$	−0.565971	+	0.326763i	−0.170647	+	0.0985228i	0.412244	+	0.911073i	$0.364745\pi$
$12$	−0.387773	−	5.74919i	−0.111941	−	1.65965i
$13$	−0.0750048	−	0.0433040i	−0.0208026	−	0.0120104i	0.489563	−	0.871968i	$-0.337156\pi$
$13$	−0.0750048	−	0.0433040i	−0.0208026	−	0.0120104i	−0.510365	+	0.859958i	$0.670490\pi$
$14$	−3.62648	+	4.91289i	−0.969218	+	1.31303i
$15$	0.116559	+	1.72812i	0.0300954	+	0.446200i
$16$	−0.207089	−	0.358689i	−0.0517723	−	0.0896723i
$17$	0.482385			0.116996			0.0584978	−	0.998288i	$-0.481369\pi$
$17$	0.482385			0.116996			0.0584978	+	0.998288i	$0.481369\pi$
$18$	−0.929792	−	6.86127i	−0.219154	−	1.61722i
$19$			2.08485i			0.478298i	0.970983	+	0.239149i	$0.0768684\pi$
$19$			2.08485i			0.478298i	−0.970983	+	0.239149i	$0.923132\pi$
$20$	1.66342	+	2.88113i	0.371952	+	0.644240i
$21$	−2.46724	+	3.86170i	−0.538395	+	0.842693i
$22$	−0.754168	+	1.30626i	−0.160789	+	0.278495i
$23$	3.12120	+	1.80203i	0.650816	+	0.375749i	0.788769	−	0.614690i	$-0.210719\pi$
$23$	3.12120	+	1.80203i	0.650816	+	0.375749i	−0.137953	+	0.990439i	$0.544052\pi$
$24$	−2.95517	−	4.40462i	−0.603222	−	0.899089i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.199891			−0.0392018
$27$	−1.04270	−	5.09046i	−0.200667	−	0.979659i
$28$	−0.986202	+	8.74656i	−0.186375	+	1.65295i
$29$	−7.04603	+	4.06803i	−1.30841	+	0.755414i	−0.981831	−	0.189755i	$-0.939231\pi$
$29$	−7.04603	+	4.06803i	−1.30841	+	0.755414i	−0.326583	+	0.945168i	$0.605897\pi$
$30$	2.22723	+	3.31963i	0.406634	+	0.606080i
$31$	1.47914	+	0.853983i	0.265662	+	0.153380i	0.626915	−	0.779088i	$-0.284318\pi$
$31$	1.47914	+	0.853983i	0.265662	+	0.153380i	−0.361253	+	0.932468i	$0.617651\pi$
$32$	4.47627	+	2.58438i	0.791300	+	0.456857i
$33$	−0.498719	+	1.01615i	−0.0868158	+	0.176890i
$34$	0.964182	−	0.556671i	0.165356	−	0.0954683i
$35$	0.296438	−	2.62909i	0.0501072	−	0.444398i
$36$	−6.10574	−	7.89497i	−1.01762	−	1.31583i
$37$	−10.9878			−1.80639			−0.903193	−	0.429235i	$-0.858783\pi$
$37$	−10.9878			−1.80639			−0.903193	+	0.429235i	$0.858783\pi$
$38$	2.40591	+	4.16716i	0.390291	+	0.676003i
$39$	−0.149670	+	0.0100950i	−0.0239663	+	0.00161649i
$40$	2.65206	+	1.53117i	0.419328	+	0.242099i
$41$	4.19058	−	7.25830i	0.654459	−	1.13356i	−0.327570	−	0.944827i	$-0.606230\pi$
$41$	4.19058	−	7.25830i	0.654459	−	1.13356i	0.982029	−	0.188729i	$-0.0604368\pi$
$42$	−0.475072	+	10.5659i	−0.0733052	+	1.63035i
$43$	4.84249	+	8.38743i	0.738472	+	1.27907i	0.953183	+	0.302394i	$0.0977858\pi$
$43$	4.84249	+	8.38743i	0.738472	+	1.27907i	−0.214711	+	0.976678i	$0.568881\pi$
$44$			2.17418i			0.327770i
$45$	1.83530	+	2.37312i	0.273590	+	0.353763i
$46$	8.31814			1.22644
$47$	−6.00919	−	10.4082i	−0.876531	−	1.51820i	−0.855123	−	0.518425i	$-0.826518\pi$
$47$	−6.00919	−	10.4082i	−0.876531	−	1.51820i	−0.0214082	−	0.999771i	$-0.506815\pi$
$48$	−0.643998	−	0.316068i	−0.0929531	−	0.0456204i
$49$	4.76202	−	5.13061i	0.680289	−	0.732944i
$50$	−1.99878	−	1.15400i	−0.282670	−	0.163200i
$51$	0.693824	−	0.465504i	0.0971548	−	0.0651836i
$52$	−0.249529	+	0.144066i	−0.0346034	+	0.0199783i
$53$		−	3.22434i		−	0.442897i	−0.975172	−	0.221449i	$-0.928922\pi$
$53$		−	3.22434i		−	0.442897i	0.975172	−	0.221449i	$-0.0710785\pi$
$54$	−7.95850	−	8.97145i	−1.08301	−	1.22086i
$55$		−	0.653527i		−	0.0881215i
$56$	3.23941	+	7.42641i	0.432884	+	0.992396i
$57$	2.01189	+	2.99868i	0.266482	+	0.397185i
$58$	−9.38898	+	16.2622i	−1.23283	+	2.13533i
$59$	4.03221	−	6.98400i	0.524949	−	0.909239i	−0.474629	−	0.880186i	$-0.657418\pi$
$59$	4.03221	−	6.98400i	0.524949	−	0.909239i	0.999578	−	0.0290526i	$-0.00924903\pi$
$60$	5.17283	+	2.53877i	0.667810	+	0.327754i
$61$	−5.21012	+	3.00807i	−0.667088	+	0.385143i	−0.794972	−	0.606646i	$-0.792515\pi$
$61$	−5.21012	+	3.00807i	−0.667088	+	0.385143i	0.127884	+	0.991789i	$0.459181\pi$
$62$	3.94198			0.500632
$63$	0.177889	+	7.93526i	0.0224119	+	0.999749i
$64$	12.7578			1.59473
$65$	0.0750048	−	0.0433040i	0.00930320	−	0.00537120i
$66$	0.175810	+	2.60659i	0.0216407	+	0.320849i
$67$	0.729532	−	1.26359i	0.0891266	−	0.154372i	−0.818016	−	0.575196i	$-0.804926\pi$
$67$	0.729532	−	1.26359i	0.0891266	−	0.154372i	0.907142	+	0.420824i	$0.138259\pi$
$68$	0.802408	−	1.38981i	0.0973063	−	0.168539i
$69$	6.22825	−	0.420085i	0.749794	−	0.0505723i
$70$	−2.44145	−	5.59707i	−0.291809	−	0.668978i
$71$		−	9.97547i		−	1.18387i	−0.805985	−	0.591935i	$-0.798364\pi$
$71$		−	9.97547i		−	1.18387i	0.805985	−	0.591935i	$-0.201636\pi$
$72$	−8.50096	−	3.48350i	−1.00185	−	0.410534i
$73$			8.43154i			0.986838i	0.869792	+	0.493419i	$0.164253\pi$
$73$			8.43154i			0.986838i	−0.869792	+	0.493419i	$0.835747\pi$
$74$	−21.9622	+	12.6799i	−2.55306	+	1.47401i
$75$	−1.55488	−	0.763119i	−0.179542	−	0.0881174i
$76$	6.00672	+	3.46798i	0.689018	+	0.397805i
$77$	1.02687	−	1.39112i	0.117022	−	0.158533i
$78$	−0.287507	+	0.192896i	−0.0325538	+	0.0218412i
$79$	−5.08800	−	8.81267i	−0.572444	−	0.991503i	−0.996314	−	0.0857796i	$-0.972662\pi$
$79$	−5.08800	−	8.81267i	−0.572444	−	0.991503i	0.423870	−	0.905723i	$-0.360671\pi$
$80$	0.414179			0.0463066
$81$	−6.41205	−	6.31550i	−0.712450	−	0.701722i
$82$		−	19.3437i		−	2.13615i
$83$	0.998645	+	1.72970i	0.109616	+	0.189860i	0.915615	−	0.402057i	$-0.131705\pi$
$83$	0.998645	+	1.72970i	0.109616	+	0.189860i	−0.805999	+	0.591917i	$0.798371\pi$
$84$	7.02201	+	13.5321i	0.766164	+	1.47647i
$85$	−0.241192	+	0.417758i	−0.0261610	+	0.0453122i
$86$	19.3581	+	11.1764i	2.08744	+	1.20519i
$87$	−6.20878	+	12.6506i	−0.665651	+	1.35628i
$88$	1.00066	+	1.73319i	0.106671	+	0.184759i
$89$	14.2291			1.50828			0.754141	−	0.656713i	$-0.228054\pi$
$89$	14.2291			1.50828			0.754141	+	0.656713i	$0.228054\pi$
$90$	6.40693	+	2.62541i	0.675350	+	0.276743i
$91$	0.227701	+	0.0256739i	0.0238695	+	0.00269136i
$92$	10.3837	−	5.99505i	1.08258	−	0.625027i
$93$	2.95158	−	0.199079i	0.306064	−	0.0206435i
$94$	−24.0221	−	13.8692i	−2.47769	−	1.43050i
$95$	−1.80553	−	1.04243i	−0.185244	−	0.106951i
$96$	8.93225	−	0.602465i	0.911643	−	0.0614888i
$97$	−14.6692	+	8.46925i	−1.48943	+	0.859922i	−0.999927	−	0.0120801i	$-0.996155\pi$
$97$	−14.6692	+	8.46925i	−1.48943	+	0.859922i	−0.489502	+	0.872002i	$0.662821\pi$
$98$	3.59753	−	15.7503i	0.363406	−	1.59102i
$99$	0.263278	+	1.94282i	0.0264604	+	0.195261i
$100$	−3.32684			−0.332684
$101$	6.17372	+	10.6932i	0.614309	+	1.06401i	0.990505	+	0.137474i	$0.0438983\pi$
$101$	6.17372	+	10.6932i	0.614309	+	1.06401i	−0.376197	+	0.926540i	$0.622768\pi$
$102$	0.849612	−	1.73111i	0.0841242	−	0.171406i
$103$	−8.36231	−	4.82798i	−0.823963	−	0.475715i	0.0278182	−	0.999613i	$-0.491144\pi$
$103$	−8.36231	−	4.82798i	−0.823963	−	0.475715i	−0.851781	+	0.523898i	$0.824477\pi$
$104$	−0.132612	+	0.229690i	−0.0130036	+	0.0225229i
$105$	−2.11071	−	4.06754i	−0.205985	−	0.396951i
$106$	−3.72088	−	6.44475i	−0.361404	−	0.625970i
$107$		−	10.5373i		−	1.01868i	−0.860565	−	0.509341i	$-0.829889\pi$
$107$		−	10.5373i		−	1.01868i	0.860565	−	0.509341i	$-0.170111\pi$
$108$	−16.4007	−	5.46343i	−1.57816	−	0.525718i
$109$	6.49233			0.621852			0.310926	−	0.950434i	$-0.399361\pi$
$109$	6.49233			0.621852			0.310926	+	0.950434i	$0.399361\pi$
$110$	−0.754168	−	1.30626i	−0.0719071	−	0.124547i
$111$	−15.8040	+	10.6033i	−1.50005	+	1.00642i
$112$	0.881638	+	0.650786i	0.0833069	+	0.0614935i
$113$	9.61660	+	5.55215i	0.904654	+	0.522302i	0.878707	−	0.477361i	$-0.158407\pi$
$113$	9.61660	+	5.55215i	0.904654	+	0.522302i	0.0259465	+	0.999663i	$0.491740\pi$
$114$	7.48181	+	3.67200i	0.700735	+	0.343914i
$115$	−3.12120	+	1.80203i	−0.291054	+	0.168040i
$116$			27.0673i			2.51314i
$117$	−0.205531	+	0.158952i	−0.0190013	+	0.0146951i
$118$		−	18.6126i		−	1.71343i
$119$	−1.16982	+	0.510278i	−0.107237	+	0.0467771i
$120$	5.29210	−	0.356943i	0.483100	−	0.0325843i
$121$	−5.28645	+	9.15640i	−0.480587	+	0.832400i
$122$	−6.94260	+	12.0249i	−0.628553	+	1.08869i
$123$	−0.976900	−	14.4837i	−0.0880841	−	1.30595i
$124$	4.92087	−	2.84106i	0.441907	−	0.255135i
$125$	1.00000			0.0894427
$126$	9.51283	+	15.6556i	0.847470	+	1.39471i
$127$	12.0793			1.07186			0.535932	−	0.844261i	$-0.319960\pi$
$127$	12.0793			1.07186			0.535932	+	0.844261i	$0.319960\pi$
$128$	16.5475	−	9.55372i	1.46261	−	0.844438i
$129$	15.0590	+	7.39079i	1.32587	+	0.650723i
$130$	0.0999455	−	0.173111i	0.00876580	−	0.0151828i
$131$	4.84734	−	8.39585i	0.423514	−	0.733549i	−0.572766	−	0.819719i	$-0.694130\pi$
$131$	4.84734	−	8.39585i	0.423514	−	0.733549i	0.996280	+	0.0861704i	$0.0274629\pi$
$132$	2.09809	+	3.12716i	0.182616	+	0.272185i
$133$	−2.20540	−	5.05593i	−0.191233	−	0.438405i
$134$		−	3.36751i		−	0.290909i
$135$	4.92982	+	1.64223i	0.424291	+	0.141340i
$136$		−	1.47723i		−	0.126671i
$137$	−12.6746	+	7.31770i	−1.08287	+	0.625193i	−0.931668	−	0.363310i	$-0.881647\pi$
$137$	−12.6746	+	7.31770i	−1.08287	+	0.625193i	−0.151198	+	0.988503i	$0.548313\pi$
$138$	11.9641	−	8.02705i	1.01846	−	0.683307i
$139$	5.20582	+	3.00558i	0.441552	+	0.254930i	0.704256	−	0.709946i	$-0.251281\pi$
$139$	5.20582	+	3.00558i	0.441552	+	0.254930i	−0.262704	+	0.964877i	$0.584614\pi$
$140$	−7.08165	−	5.22736i	−0.598508	−	0.441792i
$141$	−18.6871	−	9.17146i	−1.57374	−	0.772376i
$142$	−11.5117	−	19.9388i	−0.966038	−	1.67323i
$143$	0.0566007			0.00473319
$144$	−1.23128	+	0.166855i	−0.102607	+	0.0139046i
$145$		−	8.13605i		−	0.675662i
$146$	9.72998	+	16.8528i	0.805259	+	1.39475i
$147$	1.89825	−	11.9748i	0.156565	−	0.987668i
$148$	−18.2773	+	31.6573i	−1.50239	+	2.60221i
$149$	−7.89329	−	4.55719i	−0.646644	−	0.373340i	0.140526	−	0.990077i	$-0.455121\pi$
$149$	−7.89329	−	4.55719i	−0.646644	−	0.373340i	−0.787169	+	0.616737i	$0.788454\pi$
$150$	−3.98850	+	0.269018i	−0.325660	+	0.0219652i
$151$	6.65602	+	11.5286i	0.541659	+	0.938181i	0.998809	+	0.0487915i	$0.0155370\pi$
$151$	6.65602	+	11.5286i	0.541659	+	0.938181i	−0.457150	+	0.889390i	$0.651130\pi$
$152$	6.38452			0.517853
$153$	0.548727	−	1.33909i	0.0443620	−	0.108259i
$154$	0.447128	−	3.96555i	0.0360306	−	0.319553i
$155$	−1.47914	+	0.853983i	−0.118808	+	0.0685936i
$156$	−0.219878	+	0.448009i	−0.0176044	+	0.0358694i
$157$	2.64317	+	1.52604i	0.210948	+	0.121791i	0.601752	−	0.798683i	$-0.294470\pi$
$157$	2.64317	+	1.52604i	0.210948	+	0.121791i	−0.390804	+	0.920474i	$0.627803\pi$
$158$	−20.3396	−	11.7431i	−1.61813	−	0.934228i
$159$	−3.11150	−	4.63763i	−0.246758	−	0.367788i
$160$	−4.47627	+	2.58438i	−0.353880	+	0.204313i
$161$	−9.47539	−	1.06838i	−0.746765	−	0.0842001i
$162$	−20.1044	−	5.22382i	−1.57955	−	0.410422i
$163$	−10.0641			−0.788285			−0.394142	−	0.919049i	$-0.628958\pi$
$163$	−10.0641			−0.788285			−0.394142	+	0.919049i	$0.628958\pi$
$164$	−13.9414	−	24.1472i	−1.08864	−	1.88558i
$165$	−0.630657	−	0.939980i	−0.0490966	−	0.0731774i
$166$	3.99215	+	2.30487i	0.309851	+	0.178892i
$167$	1.66133	−	2.87751i	0.128557	−	0.222668i	−0.794560	−	0.607185i	$-0.792299\pi$
$167$	1.66133	−	2.87751i	0.128557	−	0.222668i	0.923118	+	0.384517i	$0.125632\pi$
$168$	11.8258	+	7.55551i	0.912383	+	0.582920i
$169$	−6.49625	−	11.2518i	−0.499712	−	0.865526i
$170$			1.11334i			0.0853894i
$171$	5.78749	+	2.37158i	0.442580	+	0.181359i
$172$	32.2203			2.45678
$173$	−7.74230	−	13.4101i	−0.588636	−	1.01955i	−0.994411	−	0.105575i	$-0.966332\pi$
$173$	−7.74230	−	13.4101i	−0.588636	−	1.01955i	0.405775	−	0.913973i	$-0.367002\pi$
$174$	2.18874	+	32.4507i	0.165928	+	2.46008i
$175$	2.12864	+	1.57127i	0.160910	+	0.118777i
$176$	0.234413	+	0.135338i	0.0176695	+	0.0102015i
$177$	−0.939982	−	13.9363i	−0.0706534	−	1.04752i
$178$	28.4409	−	16.4203i	2.13173	−	1.23076i
$179$			2.11808i			0.158313i	0.996862	+	0.0791565i	$0.0252227\pi$
$179$			2.11808i			0.158313i	−0.996862	+	0.0791565i	$0.974777\pi$
$180$	9.89012	−	1.34024i	0.737166	−	0.0998957i
$181$			5.27711i			0.392244i	0.980579	+	0.196122i	$0.0628349\pi$
$181$			5.27711i			0.392244i	−0.980579	+	0.196122i	$0.937165\pi$
$182$	0.484751	−	0.211449i	0.0359322	−	0.0156737i
$183$	−4.59102	+	9.35436i	−0.339378	+	0.691494i
$184$	5.51841	−	9.55817i	0.406823	−	0.704638i
$185$	5.49391	−	9.51573i	0.403920	−	0.699610i
$186$	5.66983	−	3.80403i	0.415732	−	0.278925i
$187$	−0.273016	+	0.157626i	−0.0199649	+	0.0115267i
$188$	−39.9832			−2.91608
$189$	7.91343	+	11.2418i	0.575617	+	0.817719i
$190$	−4.81182			−0.349086
$191$	14.1389	−	8.16308i	1.02305	−	0.590660i	0.108066	−	0.994144i	$-0.465534\pi$
$191$	14.1389	−	8.16308i	1.02305	−	0.590660i	0.914987	+	0.403484i	$0.132201\pi$
$192$	18.3498	−	12.3114i	1.32428	−	0.888495i
$193$	−1.06646	+	1.84716i	−0.0767653	+	0.132961i	−0.901853	−	0.432044i	$-0.857793\pi$
$193$	−1.06646	+	1.84716i	−0.0767653	+	0.132961i	0.825087	+	0.565005i	$0.191126\pi$
$194$	−19.5470	+	33.8564i	−1.40339	+	2.43075i
$195$	0.0660923	−	0.134665i	0.00473297	−	0.00964357i
$196$	−6.86070	−	22.2543i	−0.490050	−	1.58960i
$197$			18.7403i			1.33519i	0.744523	+	0.667597i	$0.232677\pi$
$197$			18.7403i			1.33519i	−0.744523	+	0.667597i	$0.767323\pi$
$198$	2.76825	+	3.57946i	0.196731	+	0.254381i
$199$			17.9194i			1.27027i	0.772400	+	0.635136i	$0.219056\pi$
$199$			17.9194i			1.27027i	−0.772400	+	0.635136i	$0.780944\pi$
$200$	−2.65206	+	1.53117i	−0.187529	+	0.108270i
$201$	−0.170067	−	2.52145i	−0.0119956	−	0.177849i
$202$	24.6799	+	14.2489i	1.73647	+	1.00255i
$203$	12.7839	−	17.3187i	0.897256	−	1.21554i
$204$	−0.187056	−	2.77332i	−0.0130965	−	0.194171i
$205$	4.19058	+	7.25830i	0.292683	+	0.506942i
$206$	−22.2859			−1.55273
$207$	8.55284	−	6.61451i	0.594463	−	0.459741i
$208$			0.0358712i			0.00248722i
$209$	−0.681253	−	1.17996i	−0.0471232	−	0.0816198i
$210$	−8.91279	−	5.69437i	−0.615041	−	0.392949i
$211$	9.57493	−	16.5843i	0.659166	−	1.14171i	−0.321666	−	0.946853i	$-0.604243\pi$
$211$	9.57493	−	16.5843i	0.659166	−	1.14171i	0.980832	−	0.194855i	$-0.0624237\pi$
$212$	−9.28973	−	5.36343i	−0.638021	−	0.368362i
$213$	−9.62638	−	14.3479i	−0.659589	−	0.983104i
$214$	−12.1600	−	21.0618i	−0.831243	−	1.43976i
$215$	−9.68497			−0.660510
$216$	−15.5887	+	3.19309i	−1.06068	+	0.217262i
$217$	−4.49040	−	0.506307i	−0.304828	−	0.0343703i
$218$	12.9768	−	7.49213i	0.878897	−	0.507431i
$219$	8.13649	+	12.1273i	0.549813	+	0.819484i
$220$	−1.88289	−	1.08709i	−0.126945	−	0.0732915i
$221$	−0.0361812	−	0.0208892i	−0.00243381	−	0.00140516i
$222$	−19.3526	+	39.4314i	−1.29886	+	2.64647i
$223$	3.84816	−	2.22173i	0.257692	−	0.148778i	−0.365589	−	0.930776i	$-0.619133\pi$
$223$	3.84816	−	2.22173i	0.257692	−	0.148778i	0.623281	+	0.781998i	$0.285799\pi$
$224$	−13.5891	−	1.53222i	−0.907961	−	0.102375i
$225$	−2.97283	+	0.402857i	−0.198189	+	0.0268571i
$226$	25.6286			1.70479
$227$	−2.75105	−	4.76495i	−0.182593	−	0.316261i	0.760170	−	0.649725i	$-0.225116\pi$
$227$	−2.75105	−	4.76495i	−0.182593	−	0.316261i	−0.942763	+	0.333464i	$0.891783\pi$
$228$	11.9862	−	0.808450i	0.793806	−	0.0535409i
$229$	5.36685	+	3.09855i	0.354652	+	0.204758i	0.666732	−	0.745297i	$-0.267693\pi$
$229$	5.36685	+	3.09855i	0.354652	+	0.204758i	−0.312080	+	0.950056i	$0.601026\pi$
$230$	−4.15907	+	7.20372i	−0.274241	+	0.474999i
$231$	0.134520	−	2.99181i	0.00885079	−	0.196847i
$232$	12.4577	+	21.5773i	0.817886	+	1.41662i
$233$		−	20.8359i		−	1.36501i	−0.730883	−	0.682503i	$-0.760891\pi$
$233$		−	20.8359i		−	1.36501i	0.730883	−	0.682503i	$-0.239109\pi$
$234$	−0.227382	+	0.554892i	−0.0148644	+	0.0362744i
$235$	12.0184			0.783993
$236$	−13.4145	−	23.2346i	−0.873211	−	1.51245i
$237$	−15.8224	−	7.76549i	−1.02778	−	0.504423i
$238$	−1.74936	+	2.36991i	−0.113394	+	0.153618i
$239$	13.7486	+	7.93776i	0.889323	+	0.513451i	0.873721	−	0.486427i	$-0.161700\pi$
$239$	13.7486	+	7.93776i	0.889323	+	0.513451i	0.0156023	+	0.999878i	$0.495033\pi$
$240$	0.595722	−	0.399685i	0.0384537	−	0.0257995i
$241$	22.1347	−	12.7795i	1.42582	−	0.823199i	0.429035	−	0.903288i	$-0.358854\pi$
$241$	22.1347	−	12.7795i	1.42582	−	0.823199i	0.996788	+	0.0800884i	$0.0255203\pi$
$242$			24.4022i			1.56863i
$243$	−15.3171	−	2.89605i	−0.982591	−	0.185782i
$244$			20.0147i			1.28131i
$245$	2.06223	+	6.68934i	0.131751	+	0.427366i
$246$	−18.6667	−	27.8224i	−1.19015	−	1.77389i
$247$	0.0902825	−	0.156374i	0.00574454	−	0.00994983i
$248$	2.61518	−	4.52963i	0.166064	−	0.287632i
$249$	3.10555	+	1.52417i	0.196806	+	0.0965904i
$250$	1.99878	−	1.15400i	0.126414	−	0.0729852i
$251$	−7.25724			−0.458073			−0.229036	−	0.973418i	$-0.573557\pi$
$251$	−7.25724			−0.458073			−0.229036	+	0.973418i	$0.573557\pi$
$252$	23.1584	+	12.6871i	1.45884	+	0.799215i
$253$	−2.35534			−0.148079
$254$	24.1439	−	13.9395i	1.51492	−	0.874640i
$255$	0.0562263	+	0.833621i	0.00352103	+	0.0522034i
$256$	9.29213	−	16.0944i	0.580758	−	1.00590i
$257$	−9.28527	+	16.0826i	−0.579199	+	1.00320i	0.416372	+	0.909194i	$0.363301\pi$
$257$	−9.28527	+	16.0826i	−0.579199	+	1.00320i	−0.995571	+	0.0940082i	$0.970032\pi$
$258$	38.6285	−	2.60543i	2.40491	−	0.162207i
$259$	26.6463	−	11.6232i	1.65572	−	0.722228i
$260$		−	0.288131i		−	0.0178691i
$261$	3.27767	+	24.1871i	0.202883	+	1.49714i
$262$		−	22.3753i		−	1.38235i
$263$	−6.70852	+	3.87316i	−0.413665	+	0.238830i	−0.692363	−	0.721549i	$-0.743430\pi$
$263$	−6.70852	+	3.87316i	−0.413665	+	0.238830i	0.278698	+	0.960379i	$0.410097\pi$
$264$	3.11181	+	1.52724i	0.191519	+	0.0939954i
$265$	2.79236	+	1.61217i	0.171533	+	0.0990348i
$266$	−10.2426	−	7.56067i	−0.628017	−	0.463574i
$267$	20.4660	−	13.7312i	1.25250	−	0.840333i
$268$	−2.42704	−	4.20375i	−0.148255	−	0.256785i
$269$	19.0552			1.16182			0.580908	−	0.813969i	$-0.302698\pi$
$269$	19.0552			1.16182			0.580908	+	0.813969i	$0.302698\pi$
$270$	11.7488	−	2.40654i	0.715006	−	0.146457i
$271$			8.77863i			0.533264i	0.963798	+	0.266632i	$0.0859108\pi$
$271$			8.77863i			0.533264i	−0.963798	+	0.266632i	$0.914089\pi$
$272$	−0.0998968	−	0.173026i	−0.00605713	−	0.0104913i
$273$	0.352282	−	0.182805i	0.0213211	−	0.0110639i
$274$	−16.8892	+	29.2530i	−1.02031	+	1.76724i
$275$	0.565971	+	0.326763i	0.0341293	+	0.0197046i
$276$	9.14988	−	18.6432i	0.550758	−	1.12219i
$277$	5.92517	+	10.2627i	0.356009	+	0.616626i	0.987290	−	0.158928i	$-0.0508039\pi$
$277$	5.92517	+	10.2627i	0.356009	+	0.616626i	−0.631281	+	0.775554i	$0.717471\pi$
$278$	13.8737			0.832091
$279$	4.05320	−	3.13463i	0.242659	−	0.187665i
$280$	−8.05116	−	0.907794i	−0.481149	−	0.0542510i
$281$	5.02131	−	2.89905i	0.299546	−	0.172943i	−0.342693	−	0.939447i	$-0.611339\pi$
$281$	5.02131	−	2.89905i	0.299546	−	0.172943i	0.642239	+	0.766505i	$0.278006\pi$
$282$	−47.9354	+	3.23316i	−2.85451	+	0.192532i
$283$	22.1081	+	12.7641i	1.31419	+	0.758748i	0.982787	−	0.184741i	$-0.0591445\pi$
$283$	22.1081	+	12.7641i	1.31419	+	0.758748i	0.331403	+	0.943489i	$0.392478\pi$
$284$	−28.7406	−	16.5934i	−1.70544	−	0.984637i
$285$	−3.60288	+	0.243008i	−0.213416	+	0.0143946i
$286$	0.113132	−	0.0653170i	0.00668966	−	0.00386228i
$287$	−2.48450	+	22.0348i	−0.146655	+	1.30068i
$288$	12.2660	−	9.48620i	0.722784	−	0.558980i
$289$	−16.7673			−0.986312
$290$	−9.38898	−	16.2622i	−0.551340	−	0.954949i
$291$	−12.9261	+	26.3373i	−0.757741	+	1.54392i
$292$	24.2924	+	14.0252i	1.42160	+	0.820762i
$293$	−13.1891	+	22.8443i	−0.770518	+	1.33458i	0.166761	+	0.985997i	$0.446669\pi$
$293$	−13.1891	+	22.8443i	−0.770518	+	1.33458i	−0.937279	+	0.348579i	$0.886664\pi$
$294$	−10.0247	−	26.1257i	−0.584655	−	1.52368i
$295$	4.03221	+	6.98400i	0.234764	+	0.406624i
$296$			33.6484i			1.95577i
$297$	2.25351	+	2.54034i	0.130762	+	0.147405i
$298$	−21.0360			−1.21858
$299$	−0.156070	−	0.270321i	−0.00902576	−	0.0156331i
$300$	−4.78506	+	3.21042i	−0.276266	+	0.185354i
$301$	−20.6158	−	15.2177i	−1.18828	−	0.877134i
$302$	26.6079	+	15.3621i	1.53111	+	0.883987i
$303$	19.1988	+	9.42257i	1.10294	+	0.541313i
$304$	0.747814	−	0.431750i	0.0428901	−	0.0247626i
$305$		−	6.01613i		−	0.344483i
$306$	−0.448518	−	3.30977i	−0.0256401	−	0.189207i
$307$			0.507358i			0.0289564i	0.999895	+	0.0144782i	$0.00460872\pi$
$307$			0.507358i			0.0289564i	−0.999895	+	0.0144782i	$0.995391\pi$
$308$	−2.29989	−	5.27255i	−0.131049	−	0.300432i
$309$	−16.6867	+	1.12549i	−0.949274	+	0.0640269i
$310$	−1.97099	+	3.41385i	−0.111945	+	0.193894i
$311$	−6.94049	+	12.0213i	−0.393559	+	0.681665i	−0.992916	−	0.118817i	$-0.962090\pi$
$311$	−6.94049	+	12.0213i	−0.393559	+	0.681665i	0.599357	+	0.800482i	$0.295423\pi$
$312$	0.0309142	+	0.458338i	0.00175017	+	0.0259483i
$313$	−27.1672	+	15.6850i	−1.53558	+	0.886568i	−0.536491	+	0.843906i	$0.680250\pi$
$313$	−27.1672	+	15.6850i	−1.53558	+	0.886568i	−0.999090	+	0.0426615i	$0.986416\pi$
$314$	7.04416			0.397525
$315$	−6.96108	−	3.81357i	−0.392213	−	0.214871i
$316$	−33.8539			−1.90443
$317$	−29.1324	+	16.8196i	−1.63624	+	0.944684i	−0.654129	+	0.756383i	$0.726965\pi$
$317$	−29.1324	+	16.8196i	−1.63624	+	0.944684i	−0.982111	+	0.188301i	$0.939702\pi$
$318$	−11.5710	−	5.67895i	−0.648871	−	0.318460i
$319$	2.65856	−	4.60477i	0.148851	−	0.257817i
$320$	−6.37890	+	11.0486i	−0.356592	+	0.617635i
$321$	−10.1686	−	15.1560i	−0.567554	−	0.845928i
$322$	−20.1721	+	8.79911i	−1.12415	+	0.490355i
$323$			1.00570i			0.0559587i
$324$	−28.8617	+	7.96861i	−1.60343	+	0.442701i
$325$			0.0866081i			0.00480415i
$326$	−20.1160	+	11.6140i	−1.11412	+	0.643240i
$327$	9.33805	−	6.26513i	0.516395	−	0.346463i
$328$	−22.2274	−	12.8330i	−1.22730	−	0.708582i
$329$	25.5828	+	18.8841i	1.41043	+	1.04112i
$330$	−2.34528	−	1.15104i	−0.129103	−	0.0633627i
$331$	9.82080	+	17.0101i	0.539800	+	0.934961i	0.998914	+	0.0465836i	$0.0148334\pi$
$331$	9.82080	+	17.0101i	0.539800	+	0.934961i	−0.459115	+	0.888377i	$0.651833\pi$
$332$	6.64466			0.364673
$333$	−12.4990	+	30.5019i	−0.684939	+	1.67149i
$334$		−	7.66868i		−	0.419611i
$335$	0.729532	+	1.26359i	0.0398586	+	0.0690371i
$336$	1.89609	+	0.0852535i	0.103440	+	0.00465096i
$337$	−5.08185	+	8.80202i	−0.276826	+	0.479477i	−0.970594	−	0.240722i	$-0.922616\pi$
$337$	−5.08185	+	8.80202i	−0.276826	+	0.479477i	0.693768	+	0.720198i	$0.255949\pi$
$338$	−25.9692	−	14.9933i	−1.41254	−	0.815528i
$339$	19.1896	−	1.29431i	1.04224	−	0.0702971i
$340$	0.802408	+	1.38981i	0.0435167	+	0.0753732i
$341$	−1.11620			−0.0604457
$342$	14.3047	−	1.93848i	0.773511	−	0.104821i
$343$	−6.12100	+	17.4795i	−0.330503	+	0.943805i
$344$	25.6851	−	14.8293i	1.38485	−	0.799544i
$345$	−2.75032	+	5.60387i	−0.148072	+	0.301702i
$346$	−30.9503	−	17.8692i	−1.66390	−	0.960653i
$347$	−2.04746	−	1.18210i	−0.109913	−	0.0634586i	0.444036	−	0.896009i	$-0.353546\pi$
$347$	−2.04746	−	1.18210i	−0.109913	−	0.0634586i	−0.553949	+	0.832551i	$0.686880\pi$
$348$	26.1201	+	38.9315i	1.40019	+	2.08695i
$349$	−5.25133	+	3.03186i	−0.281097	+	0.162292i	−0.633920	−	0.773399i	$-0.718555\pi$
$349$	−5.25133	+	3.03186i	−0.281097	+	0.162292i	0.352823	+	0.935690i	$0.385222\pi$
$350$	6.06793	+	0.684178i	0.324344	+	0.0365708i
$351$	−0.142230	+	0.426962i	−0.00759168	+	0.0227895i
$352$	−3.37792			−0.180044
$353$	13.5184	+	23.4146i	0.719512	+	1.24623i	0.961193	+	0.275875i	$0.0889677\pi$
$353$	13.5184	+	23.4146i	0.719512	+	1.24623i	−0.241682	+	0.970356i	$0.577699\pi$
$354$	−17.9613	−	26.7709i	−0.954632	−	1.42286i
$355$	8.63901	+	4.98774i	0.458511	+	0.264722i
$356$	23.6690	−	40.9958i	1.25445	−	2.17278i
$357$	−1.19016	+	1.86283i	−0.0629898	+	0.0985913i
$358$	2.44426	+	4.23359i	0.129183	+	0.223752i
$359$			5.17058i			0.272893i	0.990647	+	0.136446i	$0.0435682\pi$
$359$			5.17058i			0.272893i	−0.990647	+	0.136446i	$0.956432\pi$
$360$	7.26728	−	5.62030i	0.383019	−	0.296216i
$361$	14.6534			0.771231
$362$	6.08977	+	10.5478i	0.320071	+	0.554380i
$363$	1.23237	+	18.2713i	0.0646825	+	0.958994i
$364$	0.452731	−	0.613328i	0.0237296	−	0.0321471i
$365$	−7.30193	−	4.21577i	−0.382201	−	0.220664i
$366$	1.61845	+	23.9954i	0.0845975	+	1.25426i
$367$	17.0553	−	9.84686i	0.890277	−	0.514002i	0.0162442	−	0.999868i	$-0.494829\pi$
$367$	17.0553	−	9.84686i	0.890277	−	0.514002i	0.874033	+	0.485866i	$0.161496\pi$
$368$		−	1.49272i		−	0.0778135i
$369$	−15.3819	−	19.8895i	−0.800751	−	1.03540i
$370$		−	25.3598i		−	1.31839i
$371$	3.41078	+	7.81928i	0.177079	+	0.405957i
$372$	4.33614	−	8.83502i	0.224818	−	0.458075i
$373$	6.80350	−	11.7840i	0.352272	−	0.610153i	−0.634375	−	0.773025i	$-0.718743\pi$
$373$	6.80350	−	11.7840i	0.352272	−	0.610153i	0.986647	+	0.162872i	$0.0520759\pi$
$374$	−0.363799	+	0.630119i	−0.0188116	+	0.0325827i
$375$	1.43832	−	0.965005i	0.0742745	−	0.0498327i
$376$	−31.8735	+	18.4022i	−1.64375	+	0.949020i
$377$	0.704648			0.0362912
$378$	28.7902	+	13.3378i	1.48081	+	0.686022i
$379$	−12.9624			−0.665832			−0.332916	−	0.942957i	$-0.608033\pi$
$379$	−12.9624			−0.665832			−0.332916	+	0.942957i	$0.608033\pi$
$380$	−6.00672	+	3.46798i	−0.308138	+	0.177904i
$381$	17.3739	−	11.6566i	0.890091	−	0.597185i
$382$	18.8403	−	32.6324i	0.963956	−	1.66962i
$383$	2.40664	−	4.16842i	0.122973	−	0.212996i	−0.797966	−	0.602703i	$-0.794090\pi$
$383$	2.40664	−	4.16842i	0.122973	−	0.212996i	0.920939	+	0.389707i	$0.127424\pi$
$384$	14.5813	−	29.7098i	0.744097	−	1.51612i
$385$	0.691315	+	1.58485i	0.0352327	+	0.0807716i
$386$			4.92276i			0.250562i
$387$	28.7918	−	3.90166i	1.46357	−	0.198333i
$388$			56.3517i			2.86082i
$389$	23.1341	−	13.3565i	1.17295	−	0.677201i	0.218574	−	0.975820i	$-0.429859\pi$
$389$	23.1341	−	13.3565i	1.17295	−	0.677201i	0.954372	+	0.298619i	$0.0965261\pi$
$390$	−0.0232991	−	0.345436i	−0.00117980	−	0.0174919i
$391$	1.50562	+	0.869271i	0.0761425	+	0.0439609i
$392$	−15.7117	−	14.5829i	−0.793558	−	0.736548i
$393$	−1.13000	−	16.7536i	−0.0570012	−	0.845109i
$394$	21.6263	+	37.4578i	1.08952	+	1.88710i
$395$	10.1760			0.512010
$396$	6.03546	+	2.47319i	0.303293	+	0.124283i
$397$		−	10.3519i		−	0.519548i	−0.965670	−	0.259774i	$-0.916352\pi$
$397$		−	10.3519i		−	0.519548i	0.965670	−	0.259774i	$-0.0836480\pi$
$398$	20.6789	+	35.8170i	1.03654	+	1.79534i
$399$	−8.05107	−	5.14382i	−0.403058	−	0.257513i
$400$	−0.207089	+	0.358689i	−0.0103545	+	0.0179345i
$401$	−14.0043	−	8.08540i	−0.699343	−	0.403766i	0.107760	−	0.994177i	$-0.465632\pi$
$401$	−14.0043	−	8.08540i	−0.699343	−	0.403766i	−0.807103	+	0.590411i	$0.798966\pi$
$402$	−3.24967	−	4.84356i	−0.162079	−	0.241575i
$403$	−0.0739618	−	0.128106i	−0.00368430	−	0.00638140i
$404$	41.0780			2.04371
$405$	8.67541	−	2.39525i	0.431085	−	0.119021i
$406$	5.56651	−	49.3690i	0.276261	−	2.45014i
$407$	6.21878	−	3.59041i	0.308253	−	0.177970i
$408$	−1.42553	−	2.12472i	−0.0705743	−	0.105189i
$409$	−25.6083	−	14.7850i	−1.26625	−	0.731070i	−0.291974	−	0.956426i	$-0.594312\pi$
$409$	−25.6083	−	14.7850i	−1.26625	−	0.731070i	−0.974276	+	0.225356i	$0.927645\pi$
$410$	16.7521	+	9.67184i	0.827328	+	0.477658i
$411$	−11.1686	+	22.7563i	−0.550904	+	1.12248i
$412$	−27.8201	+	16.0619i	−1.37060	+	0.791314i
$413$	−2.39060	+	21.2021i	−0.117634	+	1.04329i
$414$	9.46212	−	23.0909i	0.465038	−	1.13486i
$415$	−1.99729			−0.0980431
$416$	−0.223828	−	0.387681i	−0.0109741	−	0.0190076i
$417$	10.3880	−	0.700656i	0.508705	−	0.0343113i
$418$	−2.72335	−	1.57233i	−0.133203	−	0.0769051i
$419$	1.88632	−	3.26720i	0.0921527	−	0.159613i	−0.816264	−	0.577679i	$-0.803959\pi$
$419$	1.88632	−	3.26720i	0.0921527	−	0.159613i	0.908417	+	0.418066i	$0.137292\pi$
$420$	−15.2301	−	0.684788i	−0.743153	−	0.0334143i
$421$	14.8123	+	25.6557i	0.721908	+	1.25038i	0.960234	+	0.279196i	$0.0900679\pi$
$421$	14.8123	+	25.6557i	0.721908	+	1.25038i	−0.238326	+	0.971185i	$0.576599\pi$
$422$		−	44.1978i		−	2.15151i
$423$	−35.7286	+	4.84169i	−1.73718	+	0.235411i
$424$	−9.87401			−0.479524
$425$	−0.241192	−	0.417758i	−0.0116996	−	0.0202642i
$426$	−35.7985	−	17.5695i	−1.73444	−	0.851247i
$427$	9.45296	−	12.8062i	0.457461	−	0.619735i
$428$	−30.3594	−	17.5280i	−1.46748	−	0.847247i
$429$	0.0814099	−	0.0546200i	0.00393051	−	0.00263708i
$430$	−19.3581	+	11.1764i	−0.933533	+	0.538975i
$431$		−	20.4190i		−	0.983548i	−0.870723	−	0.491774i	$-0.836349\pi$
$431$		−	20.4190i		−	0.983548i	0.870723	−	0.491774i	$-0.163651\pi$
$432$	−1.60996	+	1.42818i	−0.0774593	+	0.0687136i
$433$		−	30.5547i		−	1.46837i	−0.678952	−	0.734183i	$-0.737565\pi$
$433$		−	30.5547i		−	1.46837i	0.678952	−	0.734183i	$-0.262435\pi$
$434$	−9.55961	+	4.16991i	−0.458876	+	0.200162i
$435$	−7.85133	−	11.7022i	−0.376443	−	0.561080i
$436$	10.7995	−	18.7052i	0.517201	−	0.895818i
$437$	−3.75696	+	6.50724i	−0.179720	+	0.311284i
$438$	30.2579	+	14.8503i	1.44578	+	0.709573i
$439$	33.2281	−	19.1843i	1.58589	−	0.915615i	0.591918	−	0.805998i	$-0.298371\pi$
$439$	33.2281	−	19.1843i	1.58589	−	0.915615i	0.993974	−	0.109617i	$-0.0349623\pi$
$440$	−2.00132			−0.0954091
$441$	−8.82549	−	19.0555i	−0.420262	−	0.907403i
$442$	−0.0964244			−0.00458644
$443$	−2.22735	+	1.28596i	−0.105824	+	0.0610978i	−0.551978	−	0.833859i	$-0.686127\pi$
$443$	−2.22735	+	1.28596i	−0.105824	+	0.0610978i	0.446154	+	0.894956i	$0.352793\pi$
$444$	4.26078	+	63.1710i	0.202208	+	2.99796i
$445$	−7.11455	+	12.3228i	−0.337262	+	0.584155i
$446$	5.12775	−	8.88152i	0.242806	−	0.420552i
$447$	−15.7508	+	1.06236i	−0.744987	+	0.0502481i
$448$	−30.9387	+	13.4955i	−1.46172	+	0.637602i
$449$		−	2.69106i		−	0.126999i	−0.997982	−	0.0634995i	$-0.979774\pi$
$449$		−	2.69106i		−	0.126999i	0.997982	−	0.0634995i	$-0.0202261\pi$
$450$	−5.47714	+	4.23586i	−0.258195	+	0.199680i
$451$			5.47731i			0.257917i
$452$	31.9929	−	18.4711i	1.50482	−	0.868807i
$453$	20.6986	+	10.1587i	0.972506	+	0.477296i
$454$	−10.9975	−	6.34940i	−0.516138	−	0.297992i
$455$	−0.136085	+	0.184358i	−0.00637974	+	0.00864281i
$456$	9.18298	−	6.16109i	0.430032	−	0.288520i
$457$	−1.65035	−	2.85849i	−0.0772002	−	0.133715i	0.824841	−	0.565365i	$-0.191265\pi$
$457$	−1.65035	−	2.85849i	−0.0772002	−	0.133715i	−0.902041	+	0.431650i	$0.857931\pi$
$458$	14.3029			0.668330
$459$	−0.502982	−	2.45556i	−0.0234772	−	0.114616i
$460$			11.9901i			0.559042i
$461$	−6.89497	−	11.9424i	−0.321131	−	0.556215i	0.659591	−	0.751625i	$-0.270730\pi$
$461$	−6.89497	−	11.9424i	−0.321131	−	0.556215i	−0.980722	+	0.195410i	$0.937396\pi$
$462$	−3.18367	−	6.13522i	−0.148118	−	0.285436i
$463$	15.7138	−	27.2171i	0.730281	−	1.26488i	−0.226482	−	0.974015i	$-0.572722\pi$
$463$	15.7138	−	27.2171i	0.730281	−	1.26488i	0.956763	−	0.290868i	$-0.0939442\pi$
$464$	2.91831	+	1.68489i	0.135479	+	0.0782190i
$465$	−1.30338	+	2.65568i	−0.0604429	+	0.123154i
$466$	−24.0446	−	41.6465i	−1.11384	−	1.92924i
$467$	37.6638			1.74288			0.871438	−	0.490507i	$-0.163188\pi$
$467$	37.6638			1.74288			0.871438	+	0.490507i	$0.163188\pi$
$468$	0.116076	+	0.856564i	0.00536560	+	0.0395947i
$469$	−0.432523	+	3.83602i	−0.0199720	+	0.177131i
$470$	24.0221	−	13.8692i	1.10806	−	0.639738i
$471$	5.27436	−	0.355747i	0.243030	−	0.0163919i
$472$	−21.3873	−	12.3480i	−0.984432	−	0.568362i
$473$	−5.48141	−	3.16469i	−0.252036	−	0.145513i
$474$	−40.5870	+	2.73752i	−1.86422	+	0.125739i
$475$	1.80553	−	1.04243i	0.0828436	−	0.0478298i
$476$	−0.475729	+	4.21921i	−0.0218050	+	0.193387i
$477$	−8.95068	−	3.66778i	−0.409823	−	0.167936i
$478$	36.6406			1.67590
$479$	−2.61528	−	4.52980i	−0.119495	−	0.206972i	0.800072	−	0.599903i	$-0.204794\pi$
$479$	−2.61528	−	4.52980i	−0.119495	−	0.206972i	−0.919568	+	0.392931i	$0.871461\pi$
$480$	−3.94437	+	8.03678i	−0.180035	+	0.366827i
$481$	0.824139	+	0.475817i	0.0375775	+	0.0216954i
$482$	29.4950	−	51.0868i	1.34346	−	2.32694i
$483$	−14.6596	+	7.60713i	−0.667036	+	0.346136i
$484$	17.5872	+	30.4619i	0.799417	+	1.38463i
$485$		−	16.9385i		−	0.769138i
$486$	−33.9575	+	11.8873i	−1.54034	+	0.539219i
$487$	−30.2265			−1.36969			−0.684847	−	0.728687i	$-0.740131\pi$
$487$	−30.2265			−1.36969			−0.684847	+	0.728687i	$0.740131\pi$
$488$	9.21171	+	15.9552i	0.416995	+	0.722256i
$489$	−14.4755	+	9.71196i	−0.654603	+	0.439190i
$490$	11.8414	+	10.9907i	0.534941	+	0.496510i
$491$	17.8327	+	10.2957i	0.804776	+	0.464638i	0.845139	−	0.534547i	$-0.179518\pi$
$491$	17.8327	+	10.2957i	0.804776	+	0.464638i	−0.0403622	+	0.999185i	$0.512851\pi$
$492$	−43.3543	−	21.2779i	−1.95456	−	0.959281i
$493$	−3.39890	+	1.96235i	−0.153079	+	0.0883800i
$494$		−	0.416743i		−	0.0187501i
$495$	−1.81417	−	0.743406i	−0.0815410	−	0.0334136i
$496$		−	0.707403i		−	0.0317633i
$497$	10.5523	+	24.1913i	0.473335	+	1.08513i
$498$	7.96620	−	0.537307i	0.356974	−	0.0240773i
$499$	−2.97494	+	5.15275i	−0.133177	+	0.230669i	−0.924899	−	0.380212i	$-0.875851\pi$
$499$	−2.97494	+	5.15275i	−0.133177	+	0.230669i	0.791723	+	0.610881i	$0.209184\pi$
$500$	1.66342	−	2.88113i	0.0743904	−	0.128848i
$501$	−0.387286	−	5.74197i	−0.0173027	−	0.256532i
$502$	−14.5056	+	8.37483i	−0.647418	+	0.373787i
$503$	−14.1610			−0.631407			−0.315704	−	0.948858i	$-0.602241\pi$
$503$	−14.1610			−0.631407			−0.315704	+	0.948858i	$0.602241\pi$
$504$	24.3004	−	0.544755i	1.08243	−	0.0242653i
$505$	−12.3474			−0.549454
$506$	−4.70782	+	2.71806i	−0.209288	+	0.120833i
$507$	−20.2018	−	9.91482i	−0.897192	−	0.440333i
$508$	20.0929	−	34.8020i	0.891479	−	1.54409i
$509$	−8.11662	+	14.0584i	−0.359763	+	0.623127i	−0.987921	−	0.154958i	$-0.950476\pi$
$509$	−8.11662	+	14.0584i	−0.359763	+	0.623127i	0.628158	+	0.778086i	$0.283809\pi$
$510$	1.07438	+	1.60134i	0.0475744	+	0.0709086i
$511$	−8.91908	−	20.4472i	−0.394557	−	0.904529i
$512$		−	4.67750i		−	0.206718i
$513$	10.6129	−	2.17387i	0.468569	−	0.0959787i
$514$			42.8607i			1.89050i
$515$	8.36231	−	4.82798i	0.368487	−	0.212746i
$516$	46.3432	−	31.0928i	2.04014	−	1.36878i
$517$	6.80205	+	3.92717i	0.299154	+	0.172717i
$518$	39.8471	−	53.9819i	1.75078	−	2.37183i
$519$	−24.0767	−	11.8166i	−1.05685	−	0.518691i
$520$	−0.132612	−	0.229690i	−0.00581540	−	0.0100726i
$521$	−5.84600			−0.256118			−0.128059	−	0.991767i	$-0.540875\pi$
$521$	−5.84600			−0.256118			−0.128059	+	0.991767i	$0.540875\pi$
$522$	34.4632	+	44.5623i	1.50841	+	1.95044i
$523$		−	24.5735i		−	1.07453i	−0.843415	−	0.537263i	$-0.819458\pi$
$523$		−	24.5735i		−	1.07453i	0.843415	−	0.537263i	$-0.180542\pi$
$524$	−16.1263	−	27.9316i	−0.704482	−	1.22020i
$525$	4.57795	+	0.205838i	0.199798	+	0.00898349i
$526$	−8.93924	+	15.4832i	−0.389770	+	0.675101i
$527$	0.713516	+	0.411949i	0.0310812	+	0.0179448i
$528$	0.467763	−	0.0315498i	0.0203568	−	0.00137303i
$529$	−5.00540	−	8.66961i	−0.217626	−	0.376939i
$530$	7.44176			0.323249
$531$	−14.8006	−	19.1378i	−0.642292	−	0.830510i
$532$	−18.2353	−	2.05608i	−0.790600	−	0.0891426i
$533$	−0.628627	+	0.362938i	−0.0272289	+	0.0157206i
$534$	25.0614	−	51.0633i	1.08451	−	2.20972i
$535$	9.12559	+	5.26866i	0.394534	+	0.227784i
$536$	−3.86953	−	2.23407i	−0.167138	−	0.0964973i
$537$	2.04396	+	3.04648i	0.0882035	+	0.131465i
$538$	38.0872	−	21.9896i	1.64205	−	0.948041i
$539$	−1.01867	+	4.45983i	−0.0438772	+	0.192098i
$540$	12.9318	−	11.4717i	0.556497	−	0.493664i
$541$	4.93753			0.212281			0.106140	−	0.994351i	$-0.466151\pi$
$541$	4.93753			0.212281			0.106140	+	0.994351i	$0.466151\pi$
$542$	10.1305	+	17.5466i	0.435143	+	0.753690i
$543$	5.09244	+	7.59017i	0.218537	+	0.325725i
$544$	2.15929	+	1.24666i	0.0925786	+	0.0534503i
$545$	−3.24617	+	5.62252i	−0.139050	+	0.240842i
$546$	0.493178	−	0.771919i	0.0211061	−	0.0330351i
$547$	−5.07382	−	8.78811i	−0.216941	−	0.375752i	0.736930	−	0.675969i	$-0.236274\pi$
$547$	−5.07382	−	8.78811i	−0.216941	−	0.375752i	−0.953871	+	0.300216i	$0.902941\pi$
$548$			48.6896i			2.07992i
$549$	2.42364	+	17.8849i	0.103439	+	0.763310i
$550$	1.50834			0.0643157
$551$	−8.48123	−	14.6899i	−0.361313	−	0.625812i
$552$	−1.28644	−	19.0730i	−0.0547546	−	0.811801i
$553$	21.6610	+	15.9892i	0.921121	+	0.679931i
$554$	23.6863	+	13.6753i	1.00633	+	0.581006i
$555$	−1.28073	−	18.9883i	−0.0543639	−	0.806009i
$556$	17.3189	−	9.99909i	0.734486	−	0.424056i
$557$		−	34.6191i		−	1.46686i	−0.679767	−	0.733428i	$-0.737919\pi$
$557$		−	34.6191i		−	1.46686i	0.679767	−	0.733428i	$-0.262081\pi$
$558$	4.48412	−	10.9428i	0.189828	−	0.463247i
$559$		−	0.838797i		−	0.0354773i
$560$	−1.00442	+	0.438128i	−0.0424443	+	0.0185143i
$561$	−0.240574	+	0.490178i	−0.0101571	+	0.0206953i
$562$	6.69100	−	11.5891i	0.282243	−	0.488859i
$563$	−5.72120	+	9.90941i	−0.241120	+	0.417632i	−0.961034	−	0.276432i	$-0.910848\pi$
$563$	−5.72120	+	9.90941i	−0.241120	+	0.417632i	0.719914	+	0.694064i	$0.244181\pi$
$564$	−57.5087	+	38.5840i	−2.42155	+	1.62468i
$565$	−9.61660	+	5.55215i	−0.404573	+	0.233581i
$566$	58.9191			2.47655
$567$	22.2304	+	8.53278i	0.933590	+	0.358343i
$568$	−30.5483			−1.28178
$569$	11.2644	−	6.50350i	0.472228	−	0.272641i	−0.244944	−	0.969537i	$-0.578770\pi$
$569$	11.2644	−	6.50350i	0.472228	−	0.272641i	0.717172	+	0.696896i	$0.245436\pi$
$570$	−6.92094	+	4.64344i	−0.289886	+	0.194492i
$571$	−3.49984	+	6.06190i	−0.146464	+	0.253683i	−0.929918	−	0.367767i	$-0.880123\pi$
$571$	−3.49984	+	6.06190i	−0.146464	+	0.253683i	0.783454	+	0.621449i	$0.213456\pi$
$572$	0.0941507	−	0.163074i	0.00393664	−	0.00681845i
$573$	12.4588	−	25.3852i	0.520474	−	1.06048i
$574$	20.4622	+	46.9099i	0.854075	+	1.95798i
$575$		−	3.60405i		−	0.150299i
$576$	14.5124	−	35.4153i	0.604683	−	1.47564i
$577$			11.5006i			0.478777i	0.970924	+	0.239388i	$0.0769469\pi$
$577$			11.5006i			0.478777i	−0.970924	+	0.239388i	$0.923053\pi$
$578$	−33.5142	+	19.3494i	−1.39401	+	0.804830i
$579$	0.248611	+	3.68594i	0.0103319	+	0.153183i
$580$	−23.4410	−	13.5337i	−0.973335	−	0.561955i
$581$	−4.25152	−	3.13828i	−0.176383	−	0.130198i
$582$	4.55676	+	67.5592i	0.188884	+	2.80042i
$583$	1.05360	+	1.82488i	0.0436355	+	0.0755789i
$584$	25.8202			1.06845
$585$	−0.0348907	−	0.257471i	−0.00144255	−	0.0106451i
$586$			60.8810i			2.51497i
$587$	−9.62385	−	16.6690i	−0.397219	−	0.688003i	0.596163	−	0.802863i	$-0.296691\pi$
$587$	−9.62385	−	16.6690i	−0.397219	−	0.688003i	−0.993382	+	0.114861i	$0.963358\pi$
$588$	−31.3434	−	25.3883i	−1.29258	−	1.04699i
$589$	−1.78043	+	3.08379i	−0.0733612	+	0.127065i
$590$	16.1190	+	9.30632i	0.663610	+	0.383135i
$591$	18.0845	+	26.9546i	0.743898	+	1.10876i
$592$	2.27546	+	3.94121i	0.0935208	+	0.161983i
$593$	−22.7017			−0.932247			−0.466123	−	0.884720i	$-0.654350\pi$
$593$	−22.7017			−0.932247			−0.466123	+	0.884720i	$0.654350\pi$
$594$	7.43582	+	2.47703i	0.305095	+	0.101634i
$595$	0.142997	−	1.26823i	0.00586232	−	0.0519925i
$596$	−26.2597	+	15.1610i	−1.07564	+	0.621021i
$597$	17.2923	+	25.7738i	0.707727	+	1.05485i
$598$	−0.623900	−	0.360209i	−0.0255132	−	0.0147300i
$599$	−0.838230	−	0.483953i	−0.0342492	−	0.0197738i	0.482778	−	0.875743i	$-0.339628\pi$
$599$	−0.838230	−	0.483953i	−0.0342492	−	0.0197738i	−0.517027	+	0.855969i	$0.672961\pi$
$600$	−2.33693	+	4.76156i	−0.0954047	+	0.194390i
$601$	9.16454	−	5.29115i	0.373829	−	0.215830i	−0.301301	−	0.953529i	$-0.597421\pi$
$601$	9.16454	−	5.29115i	0.373829	−	0.215830i	0.675130	+	0.737699i	$0.264087\pi$
$602$	−58.7677	−	6.62624i	−2.39519	−	0.270066i
$603$	−2.67782	−	3.46253i	−0.109049	−	0.141005i
$604$	44.2870			1.80201
$605$	−5.28645	−	9.15640i	−0.214925	−	0.372261i
$606$	49.2478	−	3.32168i	2.00056	−	0.134934i
$607$	2.78138	+	1.60583i	0.112893	+	0.0651787i	0.555383	−	0.831595i	$-0.312572\pi$
$607$	2.78138	+	1.60583i	0.112893	+	0.0651787i	−0.442490	+	0.896773i	$0.645905\pi$
$608$	−5.38804	+	9.33236i	−0.218514	+	0.378477i
$609$	1.67471	−	37.2464i	0.0678625	−	1.50930i
$610$	−6.94260	−	12.0249i	−0.281098	−	0.486875i
$611$			1.04089i			0.0421099i
$612$	−2.94532	−	3.80842i	−0.119057	−	0.153946i
$613$	−20.1031			−0.811955			−0.405977	−	0.913883i	$-0.633069\pi$
$613$	−20.1031			−0.811955			−0.405977	+	0.913883i	$0.633069\pi$
$614$	0.585489	+	1.01410i	0.0236284	+	0.0409256i
$615$	13.0317	+	6.39582i	0.525489	+	0.257905i
$616$	−4.26009	−	3.14461i	−0.171644	−	0.126700i
$617$	−6.76096	−	3.90344i	−0.272186	−	0.157147i	0.357695	−	0.933839i	$-0.383563\pi$
$617$	−6.76096	−	3.90344i	−0.272186	−	0.157147i	−0.629881	+	0.776692i	$0.716896\pi$
$618$	−32.0543	+	21.5060i	−1.28941	+	0.865099i
$619$	−31.2796	+	18.0593i	−1.25723	+	0.725864i	−0.972536	−	0.232753i	$-0.925227\pi$
$619$	−31.2796	+	18.0593i	−1.25723	+	0.725864i	−0.284698	+	0.958617i	$0.591893\pi$
$620$			5.68213i			0.228200i
$621$	5.91868	−	17.7673i	0.237508	−	0.712978i
$622$			32.0372i			1.28458i
$623$	−34.5067	+	15.0519i	−1.38248	+	0.603040i
$624$	0.0346159	+	0.0515943i	0.00138575	+	0.00206542i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−36.2009	+	62.7017i	−1.44688	+	2.50606i
$627$	−2.11853	−	1.03975i	−0.0846060	−	0.0415238i
$628$	8.79341	−	5.07687i	0.350895	−	0.202589i
$629$	−5.30036			−0.211339
$630$	−18.3145	+	0.410566i	−0.729669	+	0.0163574i
$631$	7.21541			0.287241			0.143620	−	0.989633i	$-0.454126\pi$
$631$	7.21541			0.287241			0.143620	+	0.989633i	$0.454126\pi$
$632$	−26.9874	+	15.5812i	−1.07350	+	0.619785i
$633$	−2.23209	−	33.0934i	−0.0887177	−	1.31534i
$634$	−38.8196	+	67.2375i	−1.54172	+	2.67034i
$635$	−6.03964	+	10.4610i	−0.239676	+	0.415131i
$636$	−18.5373	+	1.25031i	−0.735053	+	0.0495781i
$637$	−0.579350	+	0.178606i	−0.0229547	+	0.00707661i
$638$		−	12.2719i		−	0.485849i
$639$	−27.6916	−	11.3474i	−1.09546	−	0.448896i
$640$			19.1074i			0.755288i
$641$	22.3794	−	12.9208i	0.883934	−	0.510340i	0.0119805	−	0.999928i	$-0.496186\pi$
$641$	22.3794	−	12.9208i	0.883934	−	0.510340i	0.871954	+	0.489589i	$0.162853\pi$
$642$	−37.8148	−	18.5591i	−1.49243	−	0.732470i
$643$	−34.8461	−	20.1184i	−1.37420	−	0.793393i	−0.382744	−	0.923854i	$-0.625021\pi$
$643$	−34.8461	−	20.1184i	−1.37420	−	0.793393i	−0.991453	+	0.130461i	$0.958354\pi$
$644$	−18.8397	+	25.5226i	−0.742387	+	1.00573i
$645$	−13.9301	+	9.34605i	−0.548497	+	0.368000i
$646$	1.16058	+	2.01018i	0.0456622	+	0.0790893i
$647$	−19.3906			−0.762325			−0.381162	−	0.924508i	$-0.624476\pi$
$647$	−19.3906			−0.762325			−0.381162	+	0.924508i	$0.624476\pi$
$648$	−19.3402	+	19.6359i	−0.759755	+	0.771370i
$649$			5.27031i			0.206878i
$650$	0.0999455	+	0.173111i	0.00392018	+	0.00678996i
$651$	−6.94722	+	3.60503i	−0.272283	+	0.141292i
$652$	−16.7409	+	28.9961i	−0.655624	+	1.13557i
$653$	4.99408	+	2.88333i	0.195434	+	0.112834i	0.594524	−	0.804078i	$-0.297341\pi$
$653$	4.99408	+	2.88333i	0.195434	+	0.112834i	−0.399090	+	0.916912i	$0.630674\pi$
$654$	11.4348	−	23.2987i	0.447135	−	0.911052i
$655$	4.84734	+	8.39585i	0.189401	+	0.328053i
$656$	−3.47130			−0.135531
$657$	23.4057	+	9.59113i	0.913145	+	0.374186i
$658$	72.9267	+	8.22271i	2.84298	+	0.320555i
$659$	−27.8770	+	16.0948i	−1.08593	+	0.626964i	−0.932491	−	0.361193i	$-0.882369\pi$
$659$	−27.8770	+	16.0948i	−1.08593	+	0.626964i	−0.153443	+	0.988157i	$0.549036\pi$
$660$	−3.75725	+	0.253420i	−0.146251	+	0.00986437i
$661$	−8.87863	−	5.12608i	−0.345339	−	0.199381i	0.317292	−	0.948328i	$-0.397227\pi$
$661$	−8.87863	−	5.12608i	−0.345339	−	0.199381i	−0.662630	+	0.748947i	$0.730560\pi$
$662$	39.2593	+	22.6663i	1.52585	+	0.880952i
$663$	−0.0721983	+	0.00486966i	−0.00280395	+	0.000189122i
$664$	5.29694	−	3.05819i	0.205561	−	0.118681i
$665$	5.48126	+	0.618029i	0.212554	+	0.0239662i
$666$	10.2164	+	75.3904i	0.395877	+	2.92132i
$667$	−29.3228			−1.13538
$668$	−5.52697	−	9.57300i	−0.213845	−	0.370390i
$669$	3.39090	−	6.90906i	0.131100	−	0.267120i
$670$	2.91635	+	1.68376i	0.112669	+	0.0650492i
$671$	1.96585	−	3.40495i	0.0758908	−	0.131447i
$672$	−21.0241	+	10.9098i	−0.811022	+	0.420853i
$673$	−16.5938	−	28.7413i	−0.639644	−	1.10790i	−0.985511	−	0.169612i	$-0.945748\pi$
$673$	−16.5938	−	28.7413i	−0.639644	−	1.10790i	0.345867	−	0.938284i	$-0.387585\pi$
$674$			23.4578i			0.903559i
$675$	−3.88712	+	3.44823i	−0.149615	+	0.132723i
$676$	−43.2239			−1.66246
$677$	22.7707	+	39.4399i	0.875147	+	1.51580i	0.856606	+	0.515972i	$0.172569\pi$
$677$	22.7707	+	39.4399i	0.875147	+	1.51580i	0.0185418	+	0.999828i	$0.494098\pi$
$678$	36.8622	−	24.7318i	1.41568	−	0.949818i
$679$	26.6149	−	36.0560i	1.02139	−	1.38370i
$680$	1.27931	+	0.738613i	0.0490595	+	0.0283245i
$681$	−8.55509	−	4.19875i	−0.327832	−	0.160897i
$682$	−2.23104	+	1.28809i	−0.0854311	+	0.0493236i
$683$		−	15.6062i		−	0.597154i	−0.954385	−	0.298577i	$-0.903488\pi$
$683$		−	15.6062i		−	0.597154i	0.954385	−	0.298577i	$-0.0965120\pi$
$684$	16.4598	−	12.7296i	0.629358	−	0.486727i
$685$		−	14.6354i		−	0.559190i
$686$	7.93676	+	42.0014i	0.303027	+	1.60362i
$687$	10.7094	−	0.722329i	0.408588	−	0.0275586i
$688$	2.00565	−	3.47390i	0.0764649	−	0.132441i
$689$	−0.139627	+	0.241841i	−0.00531936	+	0.00921340i
$690$	0.969554	+	14.3748i	0.0369103	+	0.547238i
$691$	−9.88640	+	5.70792i	−0.376096	+	0.217139i	−0.676119	−	0.736793i	$-0.736339\pi$
$691$	−9.88640	+	5.70792i	−0.376096	+	0.217139i	0.300022	+	0.953932i	$0.403006\pi$
$692$	−51.5148			−1.95830
$693$	−2.69363	−	4.43300i	−0.102323	−	0.168396i
$694$	−5.45657			−0.207129
$695$	−5.20582	+	3.00558i	−0.197468	+	0.114008i
$696$	38.7403	+	19.0134i	1.46845	+	0.720700i
$697$	2.02147	−	3.50129i	0.0765688	−	0.132621i
$698$	−6.99751	+	12.1200i	−0.264860	+	0.458750i
$699$	−20.1068	−	29.9687i	−0.760508	−	1.13352i
$700$	8.06785	−	3.51921i	0.304936	−	0.133013i
$701$		−	5.65240i		−	0.213488i	−0.994287	−	0.106744i	$-0.965957\pi$
$701$		−	5.65240i		−	0.213488i	0.994287	−	0.106744i	$-0.0340426\pi$
$702$	0.208426	+	1.01754i	0.00786652	+	0.0384045i
$703$		−	22.9080i		−	0.863990i
$704$	−7.22054	+	4.16878i	−0.272134	+	0.157117i
$705$	17.2863	−	11.5978i	0.651039	−	0.436799i
$706$	54.0407	+	31.2004i	2.03385	+	1.17424i
$707$	−26.2833	−	19.4012i	−0.988485	−	0.729656i
$708$	−41.7159	−	20.4737i	−1.56778	−	0.769451i
$709$	5.98411	+	10.3648i	0.224738	+	0.389257i	0.956241	−	0.292581i	$-0.0945141\pi$
$709$	5.98411	+	10.3648i	0.224738	+	0.389257i	−0.731503	+	0.681838i	$0.761181\pi$
$710$	23.0233			0.864050
$711$	−30.2515	+	4.09947i	−1.13452	+	0.153742i
$712$		−	43.5743i		−	1.63302i
$713$	3.07780	+	5.33091i	0.115265	+	0.199644i
$714$	−0.229168	+	5.09682i	−0.00857638	+	0.190744i
$715$	−0.0283003	+	0.0490176i	−0.00105837	+	0.00183316i
$716$	6.10247	+	3.52326i	0.228060	+	0.131670i
$717$	27.4349	−	1.85044i	1.02457	−	0.0691058i
$718$	5.96684	+	10.3349i	0.222680	+	0.385694i
$719$	−29.8830			−1.11445			−0.557224	−	0.830362i	$-0.688134\pi$
$719$	−29.8830			−1.11445			−0.557224	+	0.830362i	$0.688134\pi$
$720$	0.471140	−	1.14975i	0.0175584	−	0.0428486i
$721$	25.3864	+	2.86240i	0.945440	+	0.106601i
$722$	29.2889	−	16.9100i	1.09002	−	0.629324i
$723$	19.5045	−	39.7411i	0.725382	−	1.47799i
$724$	15.2040	+	8.77805i	0.565053	+	0.326234i
$725$	7.04603	+	4.06803i	0.261683	+	0.151083i
$726$	23.5483	+	35.0982i	0.873958	+	1.30262i
$727$	34.3143	−	19.8114i	1.27265	−	0.734764i	0.297163	−	0.954827i	$-0.403960\pi$
$727$	34.3143	−	19.8114i	1.27265	−	0.734764i	0.975486	+	0.220063i	$0.0706262\pi$
$728$	0.0786222	−	0.697296i	0.00291393	−	0.0258435i
$729$	−24.8256	+	10.6156i	−0.919465	+	0.393171i
$730$	−19.4600			−0.720245
$731$	2.33594	+	4.04597i	0.0863980	+	0.149646i
$732$	19.3143	+	28.7875i	0.713877	+	1.06402i
$733$	−3.13473	−	1.80984i	−0.115784	−	0.0668479i	0.440990	−	0.897512i	$-0.354628\pi$
$733$	−3.13473	−	1.80984i	−0.115784	−	0.0668479i	−0.556774	+	0.830664i	$0.687961\pi$
$734$	22.7265	−	39.3635i	0.838850	−	1.45293i
$735$	9.42139	+	7.63135i	0.347513	+	0.281486i
$736$	9.31423	+	16.1327i	0.343327	+	0.594660i
$737$			0.953537i			0.0351240i
$738$	−53.6975	−	22.0040i	−1.97663	−	0.809978i
$739$	−3.45751			−0.127187			−0.0635933	−	0.997976i	$-0.520256\pi$
$739$	−3.45751			−0.127187			−0.0635933	+	0.997976i	$0.520256\pi$
$740$	−18.2773	−	31.6573i	−0.671888	−	1.16374i
$741$	−0.0210465	−	0.312039i	−0.000773162	−	0.0114630i
$742$	15.8408	+	11.6930i	0.581535	+	0.429264i
$743$	14.0290	+	8.09963i	0.514673	+	0.297147i	0.734752	−	0.678335i	$-0.237298\pi$
$743$	14.0290	+	8.09963i	0.514673	+	0.297147i	−0.220079	+	0.975482i	$0.570632\pi$
$744$	−0.609647	−	9.03873i	−0.0223507	−	0.331376i
$745$	7.89329	−	4.55719i	0.289188	−	0.166963i
$746$		−	31.4049i		−	1.14981i
$747$	5.93760	−	0.804623i	0.217245	−	0.0294396i
$748$			1.04879i			0.0383476i
$749$	11.1466	+	25.5538i	0.407289	+	0.933717i
$750$	1.76127	−	3.58865i	0.0643127	−	0.131039i
$751$	−12.5636	+	21.7608i	−0.458452	+	0.794062i	−0.998879	−	0.0473285i	$-0.984929\pi$
$751$	−12.5636	+	21.7608i	−0.458452	+	0.794062i	0.540427	+	0.841391i	$0.318263\pi$
$752$	−2.48888	+	4.31087i	−0.0907601	+	0.157201i
$753$	−10.4382	+	7.00327i	−0.380390	+	0.255213i
$754$	1.40844	−	0.813162i	0.0512923	−	0.0296136i
$755$	−13.3120			−0.484475
$756$	45.5523	−	4.09980i	1.65672	−	0.149108i
$757$	19.8999			0.723276			0.361638	−	0.932319i	$-0.382218\pi$
$757$	19.8999			0.723276			0.361638	+	0.932319i	$0.382218\pi$
$758$	−25.9089	+	14.9585i	−0.941055	+	0.543318i
$759$	−3.38774	+	2.27292i	−0.122967	+	0.0825018i
$760$	−3.19226	+	5.52915i	−0.115795	+	0.200563i
$761$	−12.7182	+	22.0286i	−0.461034	+	0.798534i	−0.999013	−	0.0444240i	$-0.985855\pi$
$761$	−12.7182	+	22.0286i	−0.461034	+	0.798534i	0.537979	+	0.842958i	$0.319188\pi$
$762$	21.2749	−	43.3484i	0.770710	−	1.57035i
$763$	−15.7444	+	6.86774i	−0.569986	+	0.248629i
$764$		−	54.3145i		−	1.96503i
$765$	0.885320	+	1.14476i	0.0320088	+	0.0413887i
$766$		−	11.1090i		−	0.401385i
$767$	−0.604870	+	0.349222i	−0.0218406	+	0.0126097i
$768$	−2.16617	−	32.1159i	−0.0781648	−	1.15888i
$769$	−34.6454	−	20.0025i	−1.24934	−	0.721309i	−0.278366	−	0.960475i	$-0.589793\pi$
$769$	−34.6454	−	20.0025i	−1.24934	−	0.721309i	−0.970979	+	0.239166i	$0.923126\pi$
$770$	3.21071	+	2.37000i	0.115706	+	0.0854089i
$771$	2.16457	+	32.0922i	0.0779549	+	1.15577i
$772$	3.54793	+	6.14520i	0.127693	+	0.221171i
$773$	3.50263			0.125981			0.0629905	−	0.998014i	$-0.479936\pi$
$773$	3.50263			0.125981			0.0629905	+	0.998014i	$0.479936\pi$
$774$	53.0459	−	41.0242i	1.90670	−	1.47458i
$775$		−	1.70797i		−	0.0613520i
$776$	25.9357	+	44.9219i	0.931037	+	1.61260i
$777$	27.1095	−	42.4317i	0.972549	−	1.52223i
$778$	30.8267	−	53.3934i	1.10519	−	1.91425i
$779$	15.1325	+	8.73674i	0.542177	+	0.313026i
$780$	−0.278048	−	0.414425i	−0.00995572	−	0.0148388i
$781$	3.25962	+	5.64582i	0.116638	+	0.202023i
$782$	4.01254			0.143488
$783$	28.0550	+	31.6258i	1.00260	+	1.13021i
$784$	−2.82646	−	0.645591i	−0.100945	−	0.0230568i
$785$	−2.64317	+	1.52604i	−0.0943388	+	0.0544666i
$786$	−21.5923	−	32.1828i	−0.770171	−	1.14792i
$787$	6.79858	+	3.92516i	0.242343	+	0.139917i	0.616253	−	0.787548i	$-0.288650\pi$
$787$	6.79858	+	3.92516i	0.242343	+	0.139917i	−0.373910	+	0.927465i	$0.621983\pi$
$788$	53.9933	+	31.1730i	1.92343	+	1.11049i
$789$	−5.91137	+	12.0446i	−0.210450	+	0.428799i
$790$	20.3396	−	11.7431i	0.723650	−	0.417800i
$791$	−29.1942	−	3.29174i	−1.03803	−	0.117041i
$792$	5.94958	−	0.806245i	0.211409	−	0.0286487i
$793$	0.521046			0.0185029
$794$	−11.9461	−	20.6912i	−0.423950	−	0.734304i
$795$	5.57206	−	0.375826i	0.197621	−	0.0133292i
$796$	51.6280	+	29.8075i	1.82991	+	1.05650i
$797$	−4.81304	+	8.33644i	−0.170487	+	0.295292i	−0.938590	−	0.345034i	$-0.887867\pi$
$797$	−4.81304	+	8.33644i	−0.170487	+	0.295292i	0.768103	+	0.640326i	$0.221201\pi$
$798$	−22.0283	−	0.990454i	−0.779793	−	0.0350617i
$799$	−2.89874	−	5.02077i	−0.102550	−	0.177622i
$800$		−	5.16875i		−	0.182743i
$801$	16.1860	−	39.4996i	0.571905	−	1.39565i
$802$	−37.3221			−1.31789
$803$	−2.75512	−	4.77201i	−0.0972260	−	0.168400i
$804$	−7.54750	−	3.70424i	−0.266180	−	0.130638i
$805$	5.66294	−	7.67174i	0.199592	−	0.270393i
$806$	−0.295667	−	0.170704i	−0.0104144	−	0.00601277i
$807$	27.4075	−	18.3884i	0.964788	−	0.647301i
$808$	32.7462	−	18.9060i	1.15201	−	0.665112i
$809$		−	1.92031i		−	0.0675146i	−0.999430	−	0.0337573i	$-0.989253\pi$
$809$		−	1.92031i		−	0.0675146i	0.999430	−	0.0337573i	$-0.0107473\pi$
$810$	14.5761	−	14.7990i	0.512154	−	0.519983i
$811$			40.5060i			1.42236i	0.703011	+	0.711179i	$0.251838\pi$
$811$			40.5060i			1.42236i	−0.703011	+	0.711179i	$0.748162\pi$
$812$	−28.6324	−	65.6404i	−1.00480	−	2.30353i
$813$	8.47143	+	12.6265i	0.297106	+	0.442830i
$814$	8.28666	−	14.3529i	0.290447	−	0.503069i
$815$	5.03207	−	8.71581i	0.176266	−	0.305301i
$816$	−0.310655	−	0.152466i	−0.0108751	−	0.00533739i
$817$	−17.4865	+	10.0959i	−0.611777	+	0.353210i
$818$	−68.2473			−2.38621
$819$	0.330286	−	0.602886i	0.0115411	−	0.0210665i
$820$	27.8828			0.973709
$821$	−26.7884	+	15.4663i	−0.934922	+	0.539777i	−0.888365	−	0.459138i	$-0.848158\pi$
$821$	−26.7884	+	15.4663i	−0.934922	+	0.539777i	−0.0465569	+	0.998916i	$0.514825\pi$
$822$	3.93718	+	58.3733i	0.137325	+	2.03600i
$823$	1.01695	−	1.76141i	0.0354486	−	0.0613988i	−0.847757	−	0.530385i	$-0.822047\pi$
$823$	1.01695	−	1.76141i	0.0354486	−	0.0613988i	0.883205	+	0.468986i	$0.155381\pi$
$824$	−14.7849	+	25.6082i	−0.515057	+	0.892104i
$825$	1.12938	−	0.0761745i	0.0393198	−	0.00265205i
$826$	19.6889	+	45.1371i	0.685064	+	1.57052i
$827$			11.1374i			0.387284i	0.981072	+	0.193642i	$0.0620300\pi$
$827$			11.1374i			0.387284i	−0.981072	+	0.193642i	$0.937970\pi$
$828$	−4.83030	−	35.6445i	−0.167865	−	1.23873i
$829$		−	56.2270i		−	1.95285i	−0.215866	−	0.976423i	$-0.569258\pi$
$829$		−	56.2270i		−	1.95285i	0.215866	−	0.976423i	$-0.430742\pi$
$830$	−3.99215	+	2.30487i	−0.138569	+	0.0800031i
$831$	18.4259	+	9.04323i	0.639186	+	0.313706i
$832$	−0.956897	−	0.552464i	−0.0331744	−	0.0191533i
$833$	2.29713	−	2.47493i	0.0795907	−	0.0857512i
$834$	19.9549	−	13.3882i	0.690981	−	0.463596i
$835$	1.66133	+	2.87751i	0.0574927	+	0.0995802i
$836$	−4.53284			−0.156771
$837$	2.80487	−	8.41996i	0.0969505	−	0.291036i
$838$		−	8.70723i		−	0.300786i
$839$	−14.1521	−	24.5121i	−0.488584	−	0.846252i	0.511330	−	0.859384i	$-0.329153\pi$
$839$	−14.1521	−	24.5121i	−0.488584	−	0.846252i	−0.999914	+	0.0131325i	$0.995820\pi$
$840$	−12.4562	+	6.46372i	−0.429779	+	0.223019i
$841$	18.5977	−	32.2121i	0.641299	−	1.11076i
$842$	59.2132	+	34.1867i	2.04062	+	1.17815i
$843$	4.42464	−	9.01535i	0.152393	−	0.310505i
$844$	−31.8543	−	55.1732i	−1.09647	−	1.89914i
$845$	12.9925			0.446956
$846$	−65.8264	+	50.9082i	−2.26316	+	1.75026i
$847$	3.13421	−	27.7971i	0.107693	−	0.955121i
$848$	−1.15654	+	0.667726i	−0.0397156	+	0.0229298i
$849$	44.1160	−	2.97555i	1.51406	−	0.102121i
$850$	−0.964182	−	0.556671i	−0.0330712	−	0.0190937i
$851$	−34.2952	−	19.8003i	−1.17562	−	0.678747i
$852$	−57.3509	+	3.86822i	−1.96481	+	0.132523i
$853$	−14.9114	+	8.60907i	−0.510555	+	0.294769i	−0.733062	−	0.680162i	$-0.761909\pi$
$853$	−14.9114	+	8.60907i	−0.510555	+	0.294769i	0.222507	+	0.974931i	$0.428576\pi$
$854$	4.11610	−	36.5055i	0.140850	−	1.24919i
$855$	−4.94759	+	3.82632i	−0.169204	+	0.130858i
$856$	−32.2688			−1.10293
$857$	−3.29413	−	5.70559i	−0.112525	−	0.194899i	0.804263	−	0.594274i	$-0.202561\pi$
$857$	−3.29413	−	5.70559i	−0.112525	−	0.194899i	−0.916788	+	0.399375i	$0.869227\pi$
$858$	0.0996893	−	0.203120i	0.00340334	−	0.00693441i
$859$	29.3581	+	16.9499i	1.00169	+	0.578324i	0.908747	−	0.417348i	$-0.137040\pi$
$859$	29.3581	+	16.9499i	1.00169	+	0.578324i	0.0929399	+	0.995672i	$0.470374\pi$
$860$	−16.1102	+	27.9036i	−0.549352	+	0.951506i
$861$	17.6902	+	34.0907i	0.602882	+	1.16181i
$862$	−23.5635	−	40.8131i	−0.802575	−	1.39010i
$863$			37.5607i			1.27858i	0.768965	+	0.639291i	$0.220772\pi$
$863$			37.5607i			1.27858i	−0.768965	+	0.639291i	$0.779228\pi$
$864$	8.48827	−	25.4810i	0.288777	−	0.866881i
$865$	15.4846			0.526492
$866$	−35.2601	−	61.0722i	−1.19819	−	2.07532i
$867$	−24.1168	+	16.1805i	−0.819048	+	0.549520i
$868$	−8.92815	+	12.0952i	−0.303041	+	0.410538i
$869$	5.75931	+	3.32514i	0.195371	+	0.112798i
$870$	−29.1975	−	14.3298i	−0.989887	−	0.485827i
$871$	−0.109437	+	0.0631834i	−0.00370813	+	0.00214089i
$872$		−	19.8817i		−	0.673279i
$873$	6.82380	+	50.3553i	0.230951	+	1.70427i
$874$			17.3421i			0.586604i
$875$	−2.42508	+	1.05782i	−0.0819827	+	0.0357609i
$876$	48.4746	−	3.26953i	1.63780	−	0.110467i
$877$	−24.2649	+	42.0280i	−0.819368	+	1.41919i	0.0867814	+	0.996227i	$0.472342\pi$
$877$	−24.2649	+	42.0280i	−0.819368	+	1.41919i	−0.906149	+	0.422959i	$0.860991\pi$
$878$	44.2772	−	76.6903i	1.49428	−	2.58817i
$879$	3.07463	+	45.5850i	0.103705	+	1.53754i
$880$	−0.234413	+	0.135338i	−0.00790206	+	0.00456226i
$881$	38.7489			1.30548			0.652742	−	0.757580i	$-0.273619\pi$
$881$	38.7489			1.30548			0.652742	+	0.757580i	$0.273619\pi$
$882$	−39.6302	−	27.9031i	−1.33442	−	0.939547i
$883$	36.8138			1.23888			0.619441	−	0.785043i	$-0.287359\pi$
$883$	36.8138			1.23888			0.619441	+	0.785043i	$0.287359\pi$
$884$	−0.120369	+	0.0694950i	−0.00404845	+	0.00233737i
$885$	12.5392	+	6.15412i	0.421501	+	0.206868i
$886$	−2.96799	+	5.14071i	−0.0997115	+	0.172705i
$887$	11.8726	−	20.5640i	0.398644	−	0.690472i	−0.594915	−	0.803789i	$-0.702814\pi$
$887$	11.8726	−	20.5640i	0.398644	−	0.690472i	0.993559	+	0.113317i	$0.0361475\pi$
$888$	32.4709	+	48.3971i	1.08965	+	1.62410i
$889$	−29.2932	+	12.7777i	−0.982464	+	0.428552i
$890$			32.8407i			1.10082i
$891$	5.69271	+	1.47916i	0.190713	+	0.0495539i
$892$		−	14.7827i		−	0.494962i
$893$	21.6996	−	12.5283i	0.726150	−	0.419243i
$894$	−30.2564	+	20.2998i	−1.01193	+	0.678927i
$895$	−1.83431	−	1.05904i	−0.0613144	−	0.0353999i
$896$	−30.0229	+	40.6729i	−1.00300	+	1.35879i
$897$	−0.485340	−	0.238200i	−0.0162050	−	0.00795327i
$898$	−3.10548	−	5.37884i	−0.103631	−	0.179494i
$899$	−13.8961			−0.463461
$900$	−3.78438	+	9.23522i	−0.126146	+	0.307841i
$901$		−	1.55537i		−	0.0518170i
$902$	6.32080	+	10.9480i	0.210460	+	0.364527i
$903$	−44.3373	−	1.99353i	−1.47545	−	0.0663406i
$904$	17.0025	−	29.4493i	0.565496	−	0.979468i
$905$	−4.57011	−	2.63855i	−0.151916	−	0.0877085i
$906$	53.0951	−	3.58117i	1.76397	−	0.118977i
$907$	26.1712	+	45.3299i	0.869001	+	1.50515i	0.863019	+	0.505171i	$0.168571\pi$
$907$	26.1712	+	45.3299i	0.869001	+	1.50515i	0.00598157	+	0.999982i	$0.498096\pi$
$908$	−18.3046			−0.607459
$909$	36.7068	−	4.97426i	1.21749	−	0.164986i
$910$	−0.0592553	+	0.525532i	−0.00196429	+	0.0174212i
$911$	22.2259	−	12.8321i	0.736377	−	0.425147i	−0.0843738	−	0.996434i	$-0.526889\pi$
$911$	22.2259	−	12.8321i	0.736377	−	0.425147i	0.820750	+	0.571287i	$0.193556\pi$
$912$	0.658954	−	1.34264i	0.0218201	−	0.0444592i
$913$	−1.13041	−	0.652641i	−0.0374110	−	0.0215993i
$914$	−6.59739	−	3.80900i	−0.218222	−	0.125991i
$915$	−5.80560	−	8.65312i	−0.191927	−	0.286063i
$916$	17.8547	−	10.3084i	0.589935	−	0.340599i
$917$	−2.87388	+	25.4882i	−0.0949038	+	0.841695i
$918$	−3.83906	−	4.32769i	−0.126708	−	0.142835i
$919$	−47.1667			−1.55589			−0.777943	−	0.628335i	$-0.783737\pi$
$919$	−47.1667			−1.55589			−0.777943	+	0.628335i	$0.783737\pi$
$920$	5.51841	+	9.55817i	0.181937	+	0.315124i
$921$	0.489603	+	0.729743i	0.0161330	+	0.0240458i
$922$	−27.5631	−	15.9136i	−0.907742	−	0.524085i
$923$	−0.431978	+	0.748208i	−0.0142187	+	0.0246276i
$924$	−8.39603	−	5.36421i	−0.276209	−	0.176470i
$925$	5.49391	+	9.51573i	0.180639	+	0.312875i
$926$		−	72.5346i		−	2.38363i
$927$	−22.9147	+	17.7216i	−0.752618	+	0.582053i
$928$	−42.0532			−1.38047
$929$	−18.8930	−	32.7236i	−0.619858	−	1.07363i	−0.989511	−	0.144456i	$-0.953857\pi$
$929$	−18.8930	−	32.7236i	−0.619858	−	1.07363i	0.369653	−	0.929170i	$-0.379477\pi$
$930$	0.459473	+	6.81223i	0.0150667	+	0.223382i
$931$	10.6966	+	9.92810i	0.350565	+	0.325380i
$932$	−60.0309	−	34.6589i	−1.96638	−	1.13529i
$933$	1.61795	+	23.9881i	0.0529695	+	0.785334i
$934$	75.2818	−	43.4640i	2.46330	−	1.42218i
$935$		−	0.315251i		−	0.0103098i
$936$	0.486763	+	0.629405i	0.0159104	+	0.0205727i
$937$			33.8997i			1.10746i	0.832698	+	0.553728i	$0.186795\pi$
$937$			33.8997i			1.10746i	−0.832698	+	0.553728i	$0.813205\pi$
$938$	3.56223	+	8.16649i	0.116311	+	0.266645i
$939$	−23.9390	+	48.7765i	−0.781220	+	1.59176i
$940$	19.9916	−	34.6265i	0.652055	−	1.12939i
$941$	14.2020	−	24.5987i	0.462973	−	0.801894i	−0.536134	−	0.844133i	$-0.680116\pi$
$941$	14.2020	−	24.5987i	0.462973	−	0.801894i	0.999108	+	0.0422393i	$0.0134492\pi$
$942$	10.1318	−	6.79766i	0.330111	−	0.221480i
$943$	26.1593	−	15.1031i	0.851864	−	0.491824i
$944$	−3.34011			−0.108711
$945$	−13.6924	+	1.23234i	−0.445413	+	0.0400880i
$946$	−14.6082			−0.474953
$947$	−33.3271	+	19.2414i	−1.08298	+	0.625261i	−0.931700	−	0.363229i	$-0.881674\pi$
$947$	−33.3271	+	19.2414i	−1.08298	+	0.625261i	−0.151285	+	0.988490i	$0.548341\pi$
$948$	−48.6927	+	32.6692i	−1.58147	+	1.06105i
$949$	0.365120	−	0.632406i	0.0118523	−	0.0205288i
$950$	2.40591	−	4.16716i	0.0780581	−	0.135201i
$951$	−25.6707	+	52.3049i	−0.832431	+	1.69610i
$952$	1.56264	+	3.58239i	0.0506455	+	0.116106i
$953$		−	1.52230i		−	0.0493121i	−0.999696	−	0.0246560i	$-0.992151\pi$
$953$		−	1.52230i		−	0.0493121i	0.999696	−	0.0246560i	$-0.00784906\pi$
$954$	−22.1231	+	2.99797i	−0.716261	+	0.0970627i
$955$			16.3262i			0.528302i
$956$	45.7394	−	26.4077i	1.47932	−	0.854085i
$957$	−0.619759	−	9.18866i	−0.0200340	−	0.297027i
$958$	−10.4548	−	6.03606i	−0.337778	−	0.195016i
$959$	22.9962	−	31.1535i	0.742584	−	1.00600i
$960$	1.48704	+	22.0471i	0.0479940	+	0.711566i
$961$	−14.0414	−	24.3205i	−0.452949	−	0.784531i
$962$	2.19636			0.0708136
$963$	−29.2513	−	11.9865i	−0.942611	−	0.386260i
$964$		−	85.0306i		−	2.73865i
$965$	−1.06646	−	1.84716i	−0.0343305	−	0.0594621i
$966$	−20.5228	+	32.1222i	−0.660310	+	1.03351i
$967$	4.67218	−	8.09245i	0.150247	−	0.260235i	−0.781071	−	0.624442i	$-0.785326\pi$
$967$	4.67218	−	8.09245i	0.150247	−	0.260235i	0.931318	+	0.364206i	$0.118660\pi$
$968$	28.0400	+	16.1889i	0.901239	+	0.520331i
$969$	0.970507	+	1.44652i	0.0311772	+	0.0464689i
$970$	−19.5470	−	33.8564i	−0.627616	−	1.08706i
$971$	12.0291			0.386034			0.193017	−	0.981195i	$-0.438173\pi$
$971$	12.0291			0.386034			0.193017	+	0.981195i	$0.438173\pi$
$972$	−33.8226	+	39.3131i	−1.08486	+	1.26097i
$973$	−15.8039	−	1.78194i	−0.506650	−	0.0571263i
$974$	−60.4162	+	34.8813i	−1.93586	+	1.11767i
$975$	0.0835772	+	0.124570i	0.00267661	+	0.00398944i
$976$	2.15792	+	1.24588i	0.0690734	+	0.0398795i
$977$	2.05015	+	1.18366i	0.0655902	+	0.0378685i	0.532436	−	0.846470i	$-0.321277\pi$
$977$	2.05015	+	1.18366i	0.0655902	+	0.0378685i	−0.466846	+	0.884338i	$0.654610\pi$
$978$	−17.7257	+	36.1167i	−0.566806	+	1.15489i
$979$	−8.05325	+	4.64955i	−0.257383	+	0.148600i
$980$	22.7032	+	5.18563i	0.725226	+	0.165649i
$981$	7.38522	−	18.0225i	0.235792	−	0.575415i
$982$	47.5248			1.51658
$983$	−17.4636	−	30.2478i	−0.557001	−	0.964754i	−0.997745	−	0.0671214i	$-0.978619\pi$
$983$	−17.4636	−	30.2478i	−0.557001	−	0.964754i	0.440744	−	0.897633i	$-0.354715\pi$
$984$	−44.3539	+	2.99160i	−1.41395	+	0.0953687i
$985$	−16.2296	−	9.37017i	−0.517118	−	0.298558i
$986$	−4.52910	+	7.84464i	−0.144236	+	0.249824i
$987$	55.0196	+	2.47384i	1.75129	+	0.0787431i
$988$	−0.300355	−	0.520230i	−0.00955557	−	0.0165507i
$989$			34.9052i			1.10992i
$990$	−4.48402	+	0.607644i	−0.142512	+	0.0193122i
$991$	−40.9157			−1.29973			−0.649865	−	0.760050i	$-0.725175\pi$
$991$	−40.9157			−1.29973			−0.649865	+	0.760050i	$0.725175\pi$
$992$	4.41403	+	7.64532i	0.140145	+	0.242739i
$993$	30.5403	+	14.9889i	0.969167	+	0.475658i
$994$	49.0084	+	36.1759i	1.55445	+	1.14743i
$995$	−15.5187	−	8.95970i	−0.491974	−	0.284041i
$996$	9.55715	−	6.41214i	0.302830	−	0.203176i
$997$	2.80591	−	1.61999i	0.0888639	−	0.0513056i	−0.454910	−	0.890538i	$-0.650328\pi$
$997$	2.80591	−	1.61999i	0.0888639	−	0.0513056i	0.543773	+	0.839232i	$0.316995\pi$
$998$			13.7323i			0.434689i
$999$	11.4570	+	55.9330i	0.362482	+	1.76964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.41.11	yes	24
3.2	odd	2		945.2.bl.j.881.2		24
7.6	odd	2		315.2.bl.i.41.11	✓	24
9.2	odd	6		315.2.bl.i.146.11	yes	24
9.7	even	3		945.2.bl.i.251.2		24
21.20	even	2		945.2.bl.i.881.2		24
63.20	even	6	inner	315.2.bl.j.146.11	yes	24
63.34	odd	6		945.2.bl.j.251.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.11	✓	24	7.6	odd	2
315.2.bl.i.146.11	yes	24	9.2	odd	6
315.2.bl.j.41.11	yes	24	1.1	even	1	trivial
315.2.bl.j.146.11	yes	24	63.20	even	6	inner
945.2.bl.i.251.2		24	9.7	even	3
945.2.bl.i.881.2		24	21.20	even	2
945.2.bl.j.251.2		24	63.34	odd	6
945.2.bl.j.881.2		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)

\(f(q)\)	\(=\)	\(q+(1.99878 - 1.15400i) q^{2} +(1.43832 - 0.965005i) q^{3} +(1.66342 - 2.88113i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.76127 - 3.58865i) q^{6} +(-2.42508 + 1.05782i) q^{7} -3.06234i q^{8} +(1.13753 - 2.77597i) q^{9} +O(q^{10})\)	\(q+(1.99878 - 1.15400i) q^{2} +(1.43832 - 0.965005i) q^{3} +(1.66342 - 2.88113i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.76127 - 3.58865i) q^{6} +(-2.42508 + 1.05782i) q^{7} -3.06234i q^{8} +(1.13753 - 2.77597i) q^{9} +2.30799i q^{10} +(-0.565971 + 0.326763i) q^{11} +(-0.387773 - 5.74919i) q^{12} +(-0.0750048 - 0.0433040i) q^{13} +(-3.62648 + 4.91289i) q^{14} +(0.116559 + 1.72812i) q^{15} +(-0.207089 - 0.358689i) q^{16} +0.482385 q^{17} +(-0.929792 - 6.86127i) q^{18} +2.08485i q^{19} +(1.66342 + 2.88113i) q^{20} +(-2.46724 + 3.86170i) q^{21} +(-0.754168 + 1.30626i) q^{22} +(3.12120 + 1.80203i) q^{23} +(-2.95517 - 4.40462i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.199891 q^{26} +(-1.04270 - 5.09046i) q^{27} +(-0.986202 + 8.74656i) q^{28} +(-7.04603 + 4.06803i) q^{29} +(2.22723 + 3.31963i) q^{30} +(1.47914 + 0.853983i) q^{31} +(4.47627 + 2.58438i) q^{32} +(-0.498719 + 1.01615i) q^{33} +(0.964182 - 0.556671i) q^{34} +(0.296438 - 2.62909i) q^{35} +(-6.10574 - 7.89497i) q^{36} -10.9878 q^{37} +(2.40591 + 4.16716i) q^{38} +(-0.149670 + 0.0100950i) q^{39} +(2.65206 + 1.53117i) q^{40} +(4.19058 - 7.25830i) q^{41} +(-0.475072 + 10.5659i) q^{42} +(4.84249 + 8.38743i) q^{43} +2.17418i q^{44} +(1.83530 + 2.37312i) q^{45} +8.31814 q^{46} +(-6.00919 - 10.4082i) q^{47} +(-0.643998 - 0.316068i) q^{48} +(4.76202 - 5.13061i) q^{49} +(-1.99878 - 1.15400i) q^{50} +(0.693824 - 0.465504i) q^{51} +(-0.249529 + 0.144066i) q^{52} -3.22434i q^{53} +(-7.95850 - 8.97145i) q^{54} -0.653527i q^{55} +(3.23941 + 7.42641i) q^{56} +(2.01189 + 2.99868i) q^{57} +(-9.38898 + 16.2622i) q^{58} +(4.03221 - 6.98400i) q^{59} +(5.17283 + 2.53877i) q^{60} +(-5.21012 + 3.00807i) q^{61} +3.94198 q^{62} +(0.177889 + 7.93526i) q^{63} +12.7578 q^{64} +(0.0750048 - 0.0433040i) q^{65} +(0.175810 + 2.60659i) q^{66} +(0.729532 - 1.26359i) q^{67} +(0.802408 - 1.38981i) q^{68} +(6.22825 - 0.420085i) q^{69} +(-2.44145 - 5.59707i) q^{70} -9.97547i q^{71} +(-8.50096 - 3.48350i) q^{72} +8.43154i q^{73} +(-21.9622 + 12.6799i) q^{74} +(-1.55488 - 0.763119i) q^{75} +(6.00672 + 3.46798i) q^{76} +(1.02687 - 1.39112i) q^{77} +(-0.287507 + 0.192896i) q^{78} +(-5.08800 - 8.81267i) q^{79} +0.414179 q^{80} +(-6.41205 - 6.31550i) q^{81} -19.3437i q^{82} +(0.998645 + 1.72970i) q^{83} +(7.02201 + 13.5321i) q^{84} +(-0.241192 + 0.417758i) q^{85} +(19.3581 + 11.1764i) q^{86} +(-6.20878 + 12.6506i) q^{87} +(1.00066 + 1.73319i) q^{88} +14.2291 q^{89} +(6.40693 + 2.62541i) q^{90} +(0.227701 + 0.0256739i) q^{91} +(10.3837 - 5.99505i) q^{92} +(2.95158 - 0.199079i) q^{93} +(-24.0221 - 13.8692i) q^{94} +(-1.80553 - 1.04243i) q^{95} +(8.93225 - 0.602465i) q^{96} +(-14.6692 + 8.46925i) q^{97} +(3.59753 - 15.7503i) q^{98} +(0.263278 + 1.94282i) 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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