LMFDB - Embedded newform 286.2.j.b.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [286,2,Mod(23,286)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(286, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("286.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 286 = 2 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	286.j (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:	$2.28372149781$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 44x^{14} + 784x^{12} + 7200x^{10} + 35724x^{8} + 90936x^{6} + 101124x^{4} + 42336x^{2} + 5184 $ x^16 + 44x^14 + 784x^12 + 7200x^10 + 35724x^8 + 90936x^6 + 101124x^4 + 42336*x^2 + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-3.23409i$ of defining polynomial
Character	$\chi$	$=$	286.23
Dual form			286.2.j.b.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.61705 - 2.80080i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.38822i q^{5} +(2.80080 + 1.61705i) q^{6} +(3.39370 + 1.95936i) q^{7} +1.00000i q^{8} +(-3.72967 + 6.45998i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.61705 - 2.80080i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.38822i q^{5} +(2.80080 + 1.61705i) q^{6} +(3.39370 + 1.95936i) q^{7} +1.00000i q^{8} +(-3.72967 + 6.45998i) q^{9} +(-1.19411 - 2.06826i) q^{10} +(0.866025 - 0.500000i) q^{11} -3.23409 q^{12} +(0.581485 - 3.55835i) q^{13} -3.91871 q^{14} +(6.68894 - 3.86186i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.577065 - 0.999507i) q^{17} -7.45934i q^{18} +(7.24916 + 4.18531i) q^{19} +(2.06826 + 1.19411i) q^{20} -12.6735i q^{21} +(-0.500000 + 0.866025i) q^{22} +(-0.535560 - 0.927618i) q^{23} +(2.80080 - 1.61705i) q^{24} -0.703602 q^{25} +(1.27560 + 3.37237i) q^{26} +14.4219 q^{27} +(3.39370 - 1.95936i) q^{28} +(-1.06063 - 1.83706i) q^{29} +(-3.86186 + 6.68894i) q^{30} -2.61922i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.80080 - 1.61705i) q^{33} +1.15413i q^{34} +(-4.67937 + 8.10491i) q^{35} +(3.72967 + 6.45998i) q^{36} +(1.01461 - 0.585786i) q^{37} -8.37061 q^{38} +(-10.9065 + 4.12539i) q^{39} -2.38822 q^{40} +(-4.75743 + 2.74670i) q^{41} +(6.33673 + 10.9755i) q^{42} +(2.85415 - 4.94354i) q^{43} -1.00000i q^{44} +(-15.4279 - 8.90728i) q^{45} +(0.927618 + 0.535560i) q^{46} +7.13295i q^{47} +(-1.61705 + 2.80080i) q^{48} +(4.17814 + 7.23676i) q^{49} +(0.609337 - 0.351801i) q^{50} -3.73256 q^{51} +(-2.79088 - 2.28276i) q^{52} +10.5155 q^{53} +(-12.4897 + 7.21096i) q^{54} +(1.19411 + 2.06826i) q^{55} +(-1.95936 + 3.39370i) q^{56} -27.0713i q^{57} +(1.83706 + 1.06063i) q^{58} +(5.58283 + 3.22325i) q^{59} -7.72372i q^{60} +(-4.49730 + 7.78954i) q^{61} +(1.30961 + 2.26831i) q^{62} +(-25.3148 + 14.6155i) q^{63} -1.00000 q^{64} +(8.49813 + 1.38871i) q^{65} +3.23409 q^{66} +(7.43183 - 4.29077i) q^{67} +(-0.577065 - 0.999507i) q^{68} +(-1.73205 + 3.00000i) q^{69} -9.35875i q^{70} +(1.31292 + 0.758013i) q^{71} +(-6.45998 - 3.72967i) q^{72} +7.00309i q^{73} +(-0.585786 + 1.01461i) q^{74} +(1.13776 + 1.97065i) q^{75} +(7.24916 - 4.18531i) q^{76} +3.91871 q^{77} +(7.38264 - 9.02596i) q^{78} -9.72593 q^{79} +(2.06826 - 1.19411i) q^{80} +(-12.1319 - 21.0130i) q^{81} +(2.74670 - 4.75743i) q^{82} -7.20240i q^{83} +(-10.9755 - 6.33673i) q^{84} +(2.38704 + 1.37816i) q^{85} +5.70831i q^{86} +(-3.43017 + 5.94123i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-11.0570 + 6.38373i) q^{89} +17.8146 q^{90} +(8.94546 - 10.9367i) q^{91} -1.07112 q^{92} +(-7.33592 + 4.23540i) q^{93} +(-3.56648 - 6.17732i) q^{94} +(-9.99544 + 17.3126i) q^{95} -3.23409i q^{96} +(-14.5485 - 8.39957i) q^{97} +(-7.23676 - 4.17814i) q^{98} +7.45934i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 8 q^{4} - 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 + 8 * q^4 - 20 * q^9	$ 16 q - 4 q^{3} + 8 q^{4} - 20 q^{9} - 2 q^{10} - 8 q^{12} + 10 q^{13} + 16 q^{14} - 30 q^{15} - 8 q^{16} + 14 q^{17} + 6 q^{19} - 8 q^{22} + 14 q^{23} - 12 q^{25} + 4 q^{26} + 20 q^{27} - 2 q^{29} - 6 q^{30} - 10 q^{35} + 20 q^{36} - 24 q^{38} - 14 q^{39} - 4 q^{40} - 48 q^{41} + 6 q^{42} + 2 q^{43} - 12 q^{45} + 12 q^{46} - 4 q^{48} + 40 q^{49} + 60 q^{51} + 2 q^{52} + 24 q^{53} - 18 q^{54} + 2 q^{55} + 8 q^{56} - 18 q^{58} + 54 q^{59} - 22 q^{61} + 14 q^{62} - 54 q^{63} - 16 q^{64} + 54 q^{65} + 8 q^{66} - 12 q^{67} - 14 q^{68} - 36 q^{71} - 12 q^{72} + 6 q^{74} + 40 q^{75} + 6 q^{76} - 16 q^{77} + 6 q^{78} - 24 q^{79} - 44 q^{81} + 6 q^{82} - 54 q^{84} + 30 q^{85} - 48 q^{87} + 8 q^{88} - 30 q^{89} + 108 q^{90} + 46 q^{91} + 28 q^{92} - 72 q^{93} + 6 q^{94} - 8 q^{95} - 90 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q - 4 * q^3 + 8 * q^4 - 20 * q^9 - 2 * q^10 - 8 * q^12 + 10 * q^13 + 16 * q^14 - 30 * q^15 - 8 * q^16 + 14 * q^17 + 6 * q^19 - 8 * q^22 + 14 * q^23 - 12 * q^25 + 4 * q^26 + 20 * q^27 - 2 * q^29 - 6 * q^30 - 10 * q^35 + 20 * q^36 - 24 * q^38 - 14 * q^39 - 4 * q^40 - 48 * q^41 + 6 * q^42 + 2 * q^43 - 12 * q^45 + 12 * q^46 - 4 * q^48 + 40 * q^49 + 60 * q^51 + 2 * q^52 + 24 * q^53 - 18 * q^54 + 2 * q^55 + 8 * q^56 - 18 * q^58 + 54 * q^59 - 22 * q^61 + 14 * q^62 - 54 * q^63 - 16 * q^64 + 54 * q^65 + 8 * q^66 - 12 * q^67 - 14 * q^68 - 36 * q^71 - 12 * q^72 + 6 * q^74 + 40 * q^75 + 6 * q^76 - 16 * q^77 + 6 * q^78 - 24 * q^79 - 44 * q^81 + 6 * q^82 - 54 * q^84 + 30 * q^85 - 48 * q^87 + 8 * q^88 - 30 * q^89 + 108 * q^90 + 46 * q^91 + 28 * q^92 - 72 * q^93 + 6 * q^94 - 8 * q^95 - 90 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/286\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.61705	−	2.80080i	−0.933602	−	1.61705i	−0.777109	−	0.629366i	$-0.783315\pi$
$3$	−1.61705	−	2.80080i	−0.933602	−	1.61705i	−0.156493	−	0.987679i	$-0.550019\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			2.38822i			1.06805i	0.845470	+	0.534023i	$0.179320\pi$
$5$			2.38822i			1.06805i	−0.845470	+	0.534023i	$0.820680\pi$
$6$	2.80080	+	1.61705i	1.14342	+	0.660156i
$7$	3.39370	+	1.95936i	1.28270	+	0.740567i	0.977341	−	0.211671i	$-0.0678905\pi$
$7$	3.39370	+	1.95936i	1.28270	+	0.740567i	0.305358	+	0.952238i	$0.401224\pi$
$8$			1.00000i			0.353553i
$9$	−3.72967	+	6.45998i	−1.24322	+	2.15333i
$10$	−1.19411	−	2.06826i	−0.377611	−	0.654041i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	−3.23409			−0.933602
$13$	0.581485	−	3.55835i	0.161275	−	0.986910i
$13$	0.581485	−	3.55835i	0.161275	−	0.986910i
$14$	−3.91871			−1.04732
$15$	6.68894	−	3.86186i	1.72708	−	0.997129i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.577065	−	0.999507i	0.139959	−	0.242416i	−0.787522	−	0.616287i	$-0.788636\pi$
$17$	0.577065	−	0.999507i	0.139959	−	0.242416i	0.927481	+	0.373871i	$0.121970\pi$
$18$		−	7.45934i		−	1.75818i
$19$	7.24916	+	4.18531i	1.66307	+	0.960175i	0.971236	+	0.238121i	$0.0765314\pi$
$19$	7.24916	+	4.18531i	1.66307	+	0.960175i	0.691836	+	0.722054i	$0.256802\pi$
$20$	2.06826	+	1.19411i	0.462477	+	0.267011i
$21$		−	12.6735i		−	2.76558i
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−0.535560	−	0.927618i	−0.111672	−	0.193422i	0.804772	−	0.593583i	$-0.202287\pi$
$23$	−0.535560	−	0.927618i	−0.111672	−	0.193422i	−0.916445	+	0.400162i	$0.868954\pi$
$24$	2.80080	−	1.61705i	0.571712	−	0.330078i
$25$	−0.703602			−0.140720
$26$	1.27560	+	3.37237i	0.250165	+	0.661375i
$27$	14.4219			2.77550
$28$	3.39370	−	1.95936i	0.641349	−	0.370283i
$29$	−1.06063	−	1.83706i	−0.196954	−	0.341134i	0.750585	−	0.660773i	$-0.229772\pi$
$29$	−1.06063	−	1.83706i	−0.196954	−	0.341134i	−0.947539	+	0.319639i	$0.896438\pi$
$30$	−3.86186	+	6.68894i	−0.705076	+	1.22123i
$31$		−	2.61922i		−	0.470426i	−0.971944	−	0.235213i	$-0.924421\pi$
$31$		−	2.61922i		−	0.470426i	0.971944	−	0.235213i	$-0.0755787\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.80080	−	1.61705i	−0.487558	−	0.281491i
$34$			1.15413i			0.197932i
$35$	−4.67937	+	8.10491i	−0.790959	+	1.36998i
$36$	3.72967	+	6.45998i	0.621612	+	1.07666i
$37$	1.01461	−	0.585786i	0.166801	−	0.0963027i	−0.414276	−	0.910152i	$-0.635965\pi$
$37$	1.01461	−	0.585786i	0.166801	−	0.0963027i	0.581077	+	0.813849i	$0.302632\pi$
$38$	−8.37061			−1.35789
$39$	−10.9065	+	4.12539i	−1.74644	+	0.660591i
$40$	−2.38822			−0.377611
$41$	−4.75743	+	2.74670i	−0.742986	+	0.428963i	−0.823154	−	0.567818i	$-0.807788\pi$
$41$	−4.75743	+	2.74670i	−0.742986	+	0.428963i	0.0801682	+	0.996781i	$0.474454\pi$
$42$	6.33673	+	10.9755i	0.977779	+	1.69356i
$43$	2.85415	−	4.94354i	0.435254	−	0.753883i	−0.562062	−	0.827095i	$-0.689992\pi$
$43$	2.85415	−	4.94354i	0.435254	−	0.753883i	0.997316	+	0.0732123i	$0.0233251\pi$
$44$		−	1.00000i		−	0.150756i
$45$	−15.4279	−	8.90728i	−2.29985	−	1.32782i
$46$	0.927618	+	0.535560i	0.136770	+	0.0789641i
$47$			7.13295i			1.04045i	0.854030	+	0.520224i	$0.174152\pi$
$47$			7.13295i			1.04045i	−0.854030	+	0.520224i	$0.825848\pi$
$48$	−1.61705	+	2.80080i	−0.233400	+	0.404261i
$49$	4.17814	+	7.23676i	0.596878	+	1.03382i
$50$	0.609337	−	0.351801i	0.0861733	−	0.0497522i
$51$	−3.73256			−0.522663
$52$	−2.79088	−	2.28276i	−0.387026	−	0.316561i
$53$	10.5155			1.44441			0.722207	−	0.691677i	$-0.243128\pi$
$53$	10.5155			1.44441			0.722207	+	0.691677i	$0.243128\pi$
$54$	−12.4897	+	7.21096i	−1.69964	+	0.981287i
$55$	1.19411	+	2.06826i	0.161014	+	0.278884i
$56$	−1.95936	+	3.39370i	−0.261830	+	0.453503i
$57$		−	27.0713i		−	3.58568i
$58$	1.83706	+	1.06063i	0.241218	+	0.139267i
$59$	5.58283	+	3.22325i	0.726822	+	0.419631i	0.817258	−	0.576271i	$-0.195493\pi$
$59$	5.58283	+	3.22325i	0.726822	+	0.419631i	−0.0904364	+	0.995902i	$0.528826\pi$
$60$		−	7.72372i		−	0.997129i
$61$	−4.49730	+	7.78954i	−0.575820	+	0.997349i	0.420132	+	0.907463i	$0.361984\pi$
$61$	−4.49730	+	7.78954i	−0.575820	+	0.997349i	−0.995952	+	0.0898860i	$0.971350\pi$
$62$	1.30961	+	2.26831i	0.166321	+	0.288076i
$63$	−25.3148	+	14.6155i	−3.18936	+	1.84138i
$64$	−1.00000			−0.125000
$65$	8.49813	+	1.38871i	1.05406	+	0.172249i
$66$	3.23409			0.398089
$67$	7.43183	−	4.29077i	0.907943	−	0.524201i	0.0281741	−	0.999603i	$-0.491031\pi$
$67$	7.43183	−	4.29077i	0.907943	−	0.524201i	0.879769	+	0.475402i	$0.157697\pi$
$68$	−0.577065	−	0.999507i	−0.0699795	−	0.121208i
$69$	−1.73205	+	3.00000i	−0.208514	+	0.361158i
$70$		−	9.35875i		−	1.11858i
$71$	1.31292	+	0.758013i	0.155815	+	0.0899596i	0.575880	−	0.817534i	$-0.304660\pi$
$71$	1.31292	+	0.758013i	0.155815	+	0.0899596i	−0.420065	+	0.907494i	$0.637993\pi$
$72$	−6.45998	−	3.72967i	−0.761316	−	0.439546i
$73$			7.00309i			0.819650i	0.912164	+	0.409825i	$0.134410\pi$
$73$			7.00309i			0.819650i	−0.912164	+	0.409825i	$0.865590\pi$
$74$	−0.585786	+	1.01461i	−0.0680963	+	0.117946i
$75$	1.13776	+	1.97065i	0.131377	+	0.227551i
$76$	7.24916	−	4.18531i	0.831536	−	0.480088i
$77$	3.91871			0.446578
$78$	7.38264	−	9.02596i	0.835920	−	1.02199i
$79$	−9.72593			−1.09425			−0.547126	−	0.837050i	$-0.684278\pi$
$79$	−9.72593			−1.09425			−0.547126	+	0.837050i	$0.684278\pi$
$80$	2.06826	−	1.19411i	0.231239	−	0.133506i
$81$	−12.1319	−	21.0130i	−1.34799	−	2.33478i
$82$	2.74670	−	4.75743i	0.303323	−	0.525370i
$83$		−	7.20240i		−	0.790566i	−0.918559	−	0.395283i	$-0.870647\pi$
$83$		−	7.20240i		−	0.790566i	0.918559	−	0.395283i	$-0.129353\pi$
$84$	−10.9755	−	6.33673i	−1.19753	−	0.691394i
$85$	2.38704	+	1.37816i	0.258911	+	0.149482i
$86$			5.70831i			0.615543i
$87$	−3.43017	+	5.94123i	−0.367753	+	0.636967i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−11.0570	+	6.38373i	−1.17203	+	0.676674i	−0.954158	−	0.299302i	$-0.903246\pi$
$89$	−11.0570	+	6.38373i	−1.17203	+	0.676674i	−0.217876	+	0.975976i	$0.569913\pi$
$90$	17.8146			1.87782
$91$	8.94546	−	10.9367i	0.937739	−	1.14647i
$92$	−1.07112			−0.111672
$93$	−7.33592	+	4.23540i	−0.760700	+	0.439190i
$94$	−3.56648	−	6.17732i	−0.367854	−	0.637142i
$95$	−9.99544	+	17.3126i	−1.02551	+	1.77624i
$96$		−	3.23409i		−	0.330078i
$97$	−14.5485	−	8.39957i	−1.47717	−	0.852847i	−0.477506	−	0.878628i	$-0.658459\pi$
$97$	−14.5485	−	8.39957i	−1.47717	−	0.852847i	−0.999668	+	0.0257814i	$0.991793\pi$
$98$	−7.23676	−	4.17814i	−0.731023	−	0.422056i
$99$			7.45934i			0.749692i
$100$	−0.351801	+	0.609337i	−0.0351801	+	0.0609337i
$101$	−7.56376	−	13.1008i	−0.752622	−	1.30358i	−0.946548	−	0.322564i	$-0.895455\pi$
$101$	−7.56376	−	13.1008i	−0.752622	−	1.30358i	0.193926	−	0.981016i	$-0.437878\pi$
$102$	3.23250	−	1.86628i	0.320065	−	0.184789i
$103$	9.09330			0.895989			0.447995	−	0.894036i	$-0.352138\pi$
$103$	9.09330			0.895989			0.447995	+	0.894036i	$0.352138\pi$
$104$	3.55835	+	0.581485i	0.348925	+	0.0570193i
$105$	30.2670			2.95376
$106$	−9.10668	+	5.25774i	−0.884519	+	0.510677i
$107$	0.874109	+	1.51400i	0.0845033	+	0.146364i	0.905179	−	0.425030i	$-0.139736\pi$
$107$	0.874109	+	1.51400i	0.0845033	+	0.146364i	−0.820676	+	0.571394i	$0.806403\pi$
$108$	7.21096	−	12.4897i	0.693875	−	1.20183i
$109$			5.31756i			0.509330i	0.967029	+	0.254665i	$0.0819651\pi$
$109$			5.31756i			0.509330i	−0.967029	+	0.254665i	$0.918035\pi$
$110$	−2.06826	−	1.19411i	−0.197201	−	0.113854i
$111$	−3.28135	−	1.89449i	−0.311452	−	0.179817i
$112$		−	3.91871i		−	0.370283i
$113$	0.475848	−	0.824192i	0.0447640	−	0.0775335i	−0.842775	−	0.538266i	$-0.819080\pi$
$113$	0.475848	−	0.824192i	0.0447640	−	0.0775335i	0.887539	+	0.460732i	$0.152413\pi$
$114$	13.5357	+	23.4444i	1.26773	+	2.19577i
$115$	2.21536	−	1.27904i	0.206583	−	0.119271i
$116$	−2.12126			−0.196954
$117$	20.8181	+	17.0279i	1.92464	+	1.57423i
$118$	−6.44649			−0.593448
$119$	3.91678	−	2.26135i	0.359050	−	0.207298i
$120$	3.86186	+	6.68894i	0.352538	+	0.610614i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		−	8.99459i		−	0.814332i
$123$	15.3860	+	8.88309i	1.38731	+	0.800961i
$124$	−2.26831	−	1.30961i	−0.203700	−	0.117606i
$125$			10.2608i			0.917749i
$126$	14.6155	−	25.3148i	1.30205	−	2.25522i
$127$	−2.67520	−	4.63358i	−0.237385	−	0.411164i	0.722578	−	0.691290i	$-0.242957\pi$
$127$	−2.67520	−	4.63358i	−0.237385	−	0.411164i	−0.959963	+	0.280126i	$0.909624\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−18.4612			−1.62542
$130$	−8.05396	+	3.04641i	−0.706379	+	0.267187i
$131$	−6.92979			−0.605458			−0.302729	−	0.953077i	$-0.597898\pi$
$131$	−6.92979			−0.605458			−0.302729	+	0.953077i	$0.597898\pi$
$132$	−2.80080	+	1.61705i	−0.243779	+	0.140746i
$133$	16.4010	+	28.4074i	1.42215	+	2.46323i
$134$	−4.29077	+	7.43183i	−0.370666	+	0.642012i
$135$			34.4427i			2.96436i
$136$	0.999507	+	0.577065i	0.0857070	+	0.0494830i
$137$	16.3343	+	9.43062i	1.39553	+	0.805712i	0.993921	−	0.110097i	$-0.0351162\pi$
$137$	16.3343	+	9.43062i	1.39553	+	0.805712i	0.401613	+	0.915809i	$0.368450\pi$
$138$		−	3.46410i		−	0.294884i
$139$	4.95718	−	8.58608i	0.420462	−	0.728262i	−0.575522	−	0.817786i	$-0.695201\pi$
$139$	4.95718	−	8.58608i	0.420462	−	0.728262i	0.995985	+	0.0895240i	$0.0285346\pi$
$140$	4.67937	+	8.10491i	0.395479	+	0.684990i
$141$	19.9780	−	11.5343i	1.68245	−	0.971364i
$142$	−1.51603			−0.127222
$143$	−1.27560	−	3.37237i	−0.106671	−	0.282011i
$144$	7.45934			0.621612
$145$	4.38732	−	2.53302i	0.364347	−	0.210356i
$146$	−3.50155	−	6.06486i	−0.289790	−	0.501931i
$147$	13.5125	−	23.4043i	1.11449	−	1.93036i
$148$		−	1.17157i		−	0.0963027i
$149$	−13.2403	−	7.64429i	−1.08469	−	0.626245i	−0.152531	−	0.988299i	$-0.548742\pi$
$149$	−13.2403	−	7.64429i	−1.08469	−	0.626245i	−0.932157	+	0.362054i	$0.882076\pi$
$150$	−1.97065	−	1.13776i	−0.160903	−	0.0928974i
$151$		−	0.741721i		−	0.0603604i	−0.999544	−	0.0301802i	$-0.990392\pi$
$151$		−	0.741721i		−	0.0603604i	0.999544	−	0.0301802i	$-0.00960811\pi$
$152$	−4.18531	+	7.24916i	−0.339473	+	0.587985i
$153$	4.30453	+	7.45566i	0.348001	+	0.602755i
$154$	−3.39370	+	1.95936i	−0.273472	+	0.157889i
$155$	6.25528			0.502436
$156$	−1.88058	+	11.5080i	−0.150567	+	0.921380i
$157$	−23.2033			−1.85182			−0.925911	−	0.377742i	$-0.876700\pi$
$157$	−23.2033			−1.85182			−0.925911	+	0.377742i	$0.876700\pi$
$158$	8.42290	−	4.86297i	0.670090	−	0.386877i
$159$	−17.0040	−	29.4518i	−1.34851	−	2.33568i
$160$	−1.19411	+	2.06826i	−0.0944027	+	0.163510i
$161$		−	4.19741i		−	0.330802i
$162$	21.0130	+	12.1319i	1.65094	+	0.953171i
$163$	−16.2334	−	9.37237i	−1.27150	−	0.734101i	−0.296229	−	0.955117i	$-0.595729\pi$
$163$	−16.2334	−	9.37237i	−1.27150	−	0.734101i	−0.975270	+	0.221016i	$0.929063\pi$
$164$			5.49341i			0.428963i
$165$	3.86186	−	6.68894i	0.300646	−	0.520733i
$166$	3.60120	+	6.23746i	0.279507	+	0.484121i
$167$	−1.23326	+	0.712024i	−0.0954327	+	0.0550981i	−0.546957	−	0.837161i	$-0.684214\pi$
$167$	−1.23326	+	0.712024i	−0.0954327	+	0.0550981i	0.451524	+	0.892259i	$0.350880\pi$
$168$	12.6735			0.977779
$169$	−12.3238	−	4.13826i	−0.947981	−	0.318327i
$170$	−2.75632			−0.211400
$171$	−54.0740	+	31.2196i	−4.13514	+	2.38742i
$172$	−2.85415	−	4.94354i	−0.217627	−	0.376941i
$173$	6.26263	−	10.8472i	0.476139	−	0.824697i	−0.523487	−	0.852033i	$-0.675369\pi$
$173$	6.26263	−	10.8472i	0.476139	−	0.824697i	0.999626	+	0.0273367i	$0.00870262\pi$
$174$		−	6.86034i		−	0.520081i
$175$	−2.38782	−	1.37861i	−0.180502	−	0.104213i
$176$	−0.866025	−	0.500000i	−0.0652791	−	0.0376889i
$177$		−	20.8485i		−	1.56707i
$178$	6.38373	−	11.0570i	0.478481	−	0.828753i
$179$	−1.35506	−	2.34704i	−0.101282	−	0.175426i	0.810931	−	0.585142i	$-0.198961\pi$
$179$	−1.35506	−	2.34704i	−0.101282	−	0.175426i	−0.912213	+	0.409716i	$0.865628\pi$
$180$	−15.4279	+	8.90728i	−1.14993	+	0.663910i
$181$	2.96325			0.220257			0.110128	−	0.993917i	$-0.464874\pi$
$181$	2.96325			0.220257			0.110128	+	0.993917i	$0.464874\pi$
$182$	−2.27867	+	13.9442i	−0.168906	+	1.03361i
$183$	29.0893			2.15034
$184$	0.927618	−	0.535560i	0.0683849	−	0.0394820i
$185$	1.39899	+	2.42312i	0.102856	+	0.178151i
$186$	4.23540	−	7.33592i	0.310554	−	0.537896i
$187$		−	1.15413i		−	0.0843984i
$188$	6.17732	+	3.56648i	0.450527	+	0.260112i
$189$	48.9437	+	28.2577i	3.56013	+	2.05544i
$190$		−	19.9909i		−	1.45029i
$191$	−5.38945	+	9.33480i	−0.389967	+	0.675443i	−0.992445	−	0.122693i	$-0.960847\pi$
$191$	−5.38945	+	9.33480i	−0.389967	+	0.675443i	0.602478	+	0.798136i	$0.294180\pi$
$192$	1.61705	+	2.80080i	0.116700	+	0.202131i
$193$	18.1368	−	10.4713i	1.30551	−	0.753739i	0.324170	−	0.945999i	$-0.394915\pi$
$193$	18.1368	−	10.4713i	1.30551	−	0.753739i	0.981344	+	0.192260i	$0.0615815\pi$
$194$	16.7991			1.20611
$195$	−9.85235	−	26.0472i	−0.705541	−	1.86528i
$196$	8.35629			0.596878
$197$	−12.2126	+	7.05092i	−0.870109	+	0.502358i	−0.867384	−	0.497639i	$-0.834201\pi$
$197$	−12.2126	+	7.05092i	−0.870109	+	0.502358i	−0.00272441	+	0.999996i	$0.500867\pi$
$198$	−3.72967	−	6.45998i	−0.265056	−	0.459091i
$199$	−5.49270	+	9.51364i	−0.389367	+	0.674404i	−0.992365	−	0.123339i	$-0.960640\pi$
$199$	−5.49270	+	9.51364i	−0.389367	+	0.674404i	0.602997	+	0.797743i	$0.293973\pi$
$200$		−	0.703602i		−	0.0497522i
$201$	−24.0352	−	13.8767i	−1.69531	−	0.978790i
$202$	13.1008	+	7.56376i	0.921770	+	0.532184i
$203$		−	8.31260i		−	0.583430i
$204$	−1.86628	+	3.23250i	−0.130666	+	0.226320i
$205$	−6.55974	−	11.3618i	−0.458152	−	0.793542i
$206$	−7.87503	+	4.54665i	−0.548679	+	0.316780i
$207$	7.98986			0.555333
$208$	−3.37237	+	1.27560i	−0.233832	+	0.0884466i
$209$	8.37061			0.579007
$210$	−26.2120	+	15.1335i	−1.80880	+	1.04431i
$211$	−0.692499	−	1.19944i	−0.0476736	−	0.0825731i	0.841204	−	0.540718i	$-0.181847\pi$
$211$	−0.692499	−	1.19944i	−0.0476736	−	0.0825731i	−0.888878	+	0.458145i	$0.848514\pi$
$212$	5.25774	−	9.10668i	0.361103	−	0.625449i
$213$		−	4.90297i		−	0.335946i
$214$	−1.51400	−	0.874109i	−0.103495	−	0.0597528i
$215$	11.8063	+	6.81635i	0.805181	+	0.464871i
$216$			14.4219i			0.981287i
$217$	5.13198	−	8.88885i	0.348382	−	0.603414i
$218$	−2.65878	−	4.60514i	−0.180075	−	0.311899i
$219$	19.6143	−	11.3243i	1.32541	−	0.765227i
$220$	2.38822			0.161014
$221$	−3.22104	−	2.63460i	−0.216671	−	0.177222i
$222$	3.78897			0.254299
$223$	−7.24466	+	4.18271i	−0.485139	+	0.280095i	−0.722555	−	0.691313i	$-0.757033\pi$
$223$	−7.24466	+	4.18271i	−0.485139	+	0.280095i	0.237417	+	0.971408i	$0.423699\pi$
$224$	1.95936	+	3.39370i	0.130915	+	0.226751i
$225$	2.62420	−	4.54526i	0.174947	−	0.303017i
$226$			0.951695i			0.0633058i
$227$	0.569919	+	0.329043i	0.0378268	+	0.0218393i	0.518794	−	0.854899i	$-0.326381\pi$
$227$	0.569919	+	0.329043i	0.0378268	+	0.0218393i	−0.480967	+	0.876739i	$0.659714\pi$
$228$	−23.4444	−	13.5357i	−1.55265	−	0.896421i
$229$			5.21273i			0.344467i	0.985056	+	0.172233i	$0.0550983\pi$
$229$			5.21273i			0.344467i	−0.985056	+	0.172233i	$0.944902\pi$
$230$	−1.27904	+	2.21536i	−0.0843372	+	0.146076i
$231$	−6.33673	−	10.9755i	−0.416926	−	0.722138i
$232$	1.83706	−	1.06063i	0.120609	−	0.0696337i
$233$	−8.82754			−0.578311			−0.289156	−	0.957282i	$-0.593375\pi$
$233$	−8.82754			−0.578311			−0.289156	+	0.957282i	$0.593375\pi$
$234$	−26.5430	−	4.33750i	−1.73517	−	0.283551i
$235$	−17.0351			−1.11125
$236$	5.58283	−	3.22325i	0.363411	−	0.209815i
$237$	15.7273	+	27.2404i	1.02160	+	1.76946i
$238$	−2.26135	+	3.91678i	−0.146582	+	0.253887i
$239$		−	7.30848i		−	0.472746i	−0.971662	−	0.236373i	$-0.924041\pi$
$239$		−	7.30848i		−	0.472746i	0.971662	−	0.236373i	$-0.0759588\pi$
$240$	−6.68894	−	3.86186i	−0.431769	−	0.249282i
$241$	−13.4873	−	7.78691i	−0.868795	−	0.501599i	−0.00184744	−	0.999998i	$-0.500588\pi$
$241$	−13.4873	−	7.78691i	−0.868795	−	0.501599i	−0.866948	+	0.498399i	$0.833921\pi$
$242$			1.00000i			0.0642824i
$243$	−17.6027	+	30.4888i	−1.12922	+	1.95586i
$244$	4.49730	+	7.78954i	0.287910	+	0.498674i
$245$	−17.2830	+	9.97833i	−1.10417	+	0.637492i
$246$	−17.7662			−1.13273
$247$	19.1081	−	23.3614i	1.21582	−	1.48645i
$248$	2.61922			0.166321
$249$	−20.1725	+	11.6466i	−1.27838	+	0.738074i
$250$	−5.13038	−	8.88607i	−0.324473	−	0.562004i
$251$	9.13700	−	15.8258i	0.576723	−	0.998913i	−0.419130	−	0.907926i	$-0.637665\pi$
$251$	9.13700	−	15.8258i	0.576723	−	0.998913i	0.995852	−	0.0909863i	$-0.0290020\pi$
$252$			29.2310i			1.84138i
$253$	−0.927618	−	0.535560i	−0.0583188	−	0.0336704i
$254$	4.63358	+	2.67520i	0.290737	+	0.167857i
$255$		−	8.91419i		−	0.558228i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.87233	−	6.70707i	−0.241549	−	0.418376i	0.719606	−	0.694382i	$-0.244322\pi$
$257$	−3.87233	−	6.70707i	−0.241549	−	0.418376i	−0.961156	+	0.276006i	$0.910989\pi$
$258$	15.9879	−	9.23059i	0.995361	−	0.574672i
$259$	4.59105			0.285274
$260$	5.45173	−	6.66524i	0.338102	−	0.413361i
$261$	15.8232			0.979431
$262$	6.00137	−	3.46489i	0.370766	−	0.214062i
$263$	−1.56963	−	2.71869i	−0.0967878	−	0.167641i	0.813566	−	0.581473i	$-0.197523\pi$
$263$	−1.56963	−	2.71869i	−0.0967878	−	0.167641i	−0.910353	+	0.413832i	$0.864190\pi$
$264$	1.61705	−	2.80080i	0.0995223	−	0.172378i
$265$			25.1133i			1.54270i
$266$	−28.4074	−	16.4010i	−1.74177	−	1.00561i
$267$	35.7592	+	20.6456i	2.18843	+	1.26349i
$268$		−	8.58154i		−	0.524201i
$269$	−1.98821	+	3.44369i	−0.121224	+	0.209965i	−0.920250	−	0.391330i	$-0.872015\pi$
$269$	−1.98821	+	3.44369i	−0.121224	+	0.209965i	0.799027	+	0.601295i	$0.205348\pi$
$270$	−17.2214	−	29.8283i	−1.04806	−	1.81529i
$271$	−9.92563	+	5.73056i	−0.602939	+	0.348107i	−0.770197	−	0.637806i	$-0.779842\pi$
$271$	−9.92563	+	5.73056i	−0.602939	+	0.348107i	0.167258	+	0.985913i	$0.446509\pi$
$272$	−1.15413			−0.0699795
$273$	−45.0967	−	7.36943i	−2.72937	−	0.446018i
$274$	−18.8612			−1.13945
$275$	−0.609337	+	0.351801i	−0.0367444	+	0.0212144i
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	−1.35793	+	2.35200i	−0.0815900	+	0.141318i	−0.903933	−	0.427674i	$-0.859333\pi$
$277$	−1.35793	+	2.35200i	−0.0815900	+	0.141318i	0.822343	+	0.568992i	$0.192666\pi$
$278$			9.91435i			0.594623i
$279$	16.9201	+	9.76883i	1.01298	+	0.584844i
$280$	−8.10491	−	4.67937i	−0.484361	−	0.279646i
$281$			9.61705i			0.573705i	0.957975	+	0.286853i	$0.0926090\pi$
$281$			9.61705i			0.573705i	−0.957975	+	0.286853i	$0.907391\pi$
$282$	−11.5343	+	19.9780i	−0.686858	+	1.18967i
$283$	4.64628	+	8.04759i	0.276193	+	0.478380i	0.970435	−	0.241361i	$-0.0775939\pi$
$283$	4.64628	+	8.04759i	0.276193	+	0.478380i	−0.694243	+	0.719741i	$0.744261\pi$
$284$	1.31292	−	0.758013i	0.0779073	−	0.0449798i
$285$	64.6523			3.82967
$286$	2.79088	+	2.28276i	0.165028	+	0.134982i
$287$	−21.5271			−1.27070
$288$	−6.45998	+	3.72967i	−0.380658	+	0.219773i
$289$	7.83399	+	13.5689i	0.460823	+	0.798169i
$290$	−2.53302	+	4.38732i	−0.148744	+	0.257632i
$291$			54.3299i			3.18488i
$292$	6.06486	+	3.50155i	0.354919	+	0.204913i
$293$	−29.2907	−	16.9110i	−1.71118	−	0.987950i	−0.932976	−	0.359938i	$-0.882798\pi$
$293$	−29.2907	−	16.9110i	−1.71118	−	0.987950i	−0.778204	−	0.628012i	$-0.783869\pi$
$294$			27.0250i			1.57613i
$295$	−7.69783	+	13.3330i	−0.448185	+	0.776279i
$296$	0.585786	+	1.01461i	0.0340481	+	0.0589731i
$297$	12.4897	−	7.21096i	0.724729	−	0.418422i
$298$	15.2886			0.885644
$299$	−3.61221	+	1.36632i	−0.208900	+	0.0790162i
$300$	2.27551			0.131377
$301$	19.3723	−	11.1846i	1.11660	−	0.644670i
$302$	0.370860	+	0.642349i	0.0213406	+	0.0369630i
$303$	−24.4619	+	42.3692i	−1.40530	+	2.43405i
$304$		−	8.37061i		−	0.480088i
$305$	−18.6032	−	10.7405i	−1.06521	−	0.615001i
$306$	−7.45566	−	4.30453i	−0.426212	−	0.246074i
$307$			6.77842i			0.386865i	0.981114	+	0.193432i	$0.0619620\pi$
$307$			6.77842i			0.386865i	−0.981114	+	0.193432i	$0.938038\pi$
$308$	1.95936	−	3.39370i	0.111645	−	0.193374i
$309$	−14.7043	−	25.4685i	−0.836497	−	1.44885i
$310$	−5.41723	+	3.12764i	−0.307678	+	0.177638i
$311$	12.4786			0.707598			0.353799	−	0.935322i	$-0.384890\pi$
$311$	12.4786			0.707598			0.353799	+	0.935322i	$0.384890\pi$
$312$	−4.12539	−	10.9065i	−0.233554	−	0.617461i
$313$	−12.5453			−0.709101			−0.354550	−	0.935037i	$-0.615366\pi$
$313$	−12.5453			−0.709101			−0.354550	+	0.935037i	$0.615366\pi$
$314$	20.0946	−	11.6016i	1.13400	−	0.654718i
$315$	−34.9051	−	60.4573i	−1.96668	−	3.40638i
$316$	−4.86297	+	8.42290i	−0.273563	+	0.473825i
$317$		−	21.7954i		−	1.22415i	−0.790800	−	0.612075i	$-0.790335\pi$
$317$		−	21.7954i		−	1.22415i	0.790800	−	0.612075i	$-0.209665\pi$
$318$	29.4518	+	17.0040i	1.65158	+	0.953538i
$319$	−1.83706	−	1.06063i	−0.102856	−	0.0593839i
$320$		−	2.38822i		−	0.133506i
$321$	2.82695	−	4.89641i	0.157785	−	0.273291i
$322$	2.09871	+	3.63507i	0.116956	+	0.202574i
$323$	8.36648	−	4.83039i	0.465524	−	0.268770i
$324$	−24.2638			−1.34799
$325$	−0.409134	+	2.50366i	−0.0226947	+	0.138878i
$326$	18.7447			1.03817
$327$	14.8934	−	8.59873i	0.823609	−	0.475511i
$328$	−2.74670	−	4.75743i	−0.151661	−	0.262685i
$329$	−13.9760	+	24.2071i	−0.770521	+	1.33458i
$330$			7.72372i			0.425177i
$331$	29.0919	+	16.7962i	1.59903	+	0.923202i	0.991674	+	0.128775i	$0.0411043\pi$
$331$	29.0919	+	16.7962i	1.59903	+	0.923202i	0.607359	+	0.794428i	$0.292229\pi$
$332$	−6.23746	−	3.60120i	−0.342325	−	0.197642i
$333$			8.73916i			0.478903i
$334$	0.712024	−	1.23326i	0.0389602	−	0.0674811i
$335$	10.2473	+	17.7489i	0.559870	+	0.969724i
$336$	−10.9755	+	6.33673i	−0.598765	+	0.345697i
$337$	−9.44785			−0.514657			−0.257329	−	0.966324i	$-0.582842\pi$
$337$	−9.44785			−0.514657			−0.257329	+	0.966324i	$0.582842\pi$
$338$	12.7418	−	2.57804i	0.693063	−	0.140227i
$339$	−3.07787			−0.167167
$340$	2.38704	−	1.37816i	0.129456	−	0.0747412i
$341$	−1.30961	−	2.26831i	−0.0709193	−	0.122836i
$342$	31.2196	−	54.0740i	1.68816	−	2.92399i
$343$			5.31490i			0.286978i
$344$	4.94354	+	2.85415i	0.266538	+	0.153886i
$345$	−7.16466	−	4.13652i	−0.385733	−	0.222703i
$346$			12.5253i			0.673362i
$347$	13.7611	−	23.8350i	0.738737	−	1.27953i	−0.214328	−	0.976762i	$-0.568756\pi$
$347$	13.7611	−	23.8350i	0.738737	−	1.27953i	0.953064	−	0.302768i	$-0.0979106\pi$
$348$	3.43017	+	5.94123i	0.183877	+	0.318483i
$349$	−1.28701	+	0.743058i	−0.0688923	+	0.0397750i	−0.534050	−	0.845453i	$-0.679331\pi$
$349$	−1.28701	+	0.743058i	−0.0688923	+	0.0397750i	0.465158	+	0.885228i	$0.345997\pi$
$350$	2.75721			0.147379
$351$	8.38613	−	51.3183i	0.447618	−	2.73917i
$352$	1.00000			0.0533002
$353$	27.6110	−	15.9412i	1.46959	−	0.848466i	0.470168	−	0.882577i	$-0.344193\pi$
$353$	27.6110	−	15.9412i	1.46959	−	0.848466i	0.999418	+	0.0341110i	$0.0108600\pi$
$354$	10.4243	+	18.0554i	0.554044	+	0.959632i
$355$	−1.81030	+	3.13554i	−0.0960809	+	0.166417i
$356$			12.7675i			0.676674i
$357$	−12.6672	−	7.31342i	−0.670420	−	0.387067i
$358$	2.34704	+	1.35506i	0.124045	+	0.0716173i
$359$		−	18.3795i		−	0.970034i	−0.874505	−	0.485017i	$-0.838813\pi$
$359$		−	18.3795i		−	0.970034i	0.874505	−	0.485017i	$-0.161187\pi$
$360$	8.90728	−	15.4279i	0.469455	−	0.813120i
$361$	25.5336	+	44.2254i	1.34387	+	2.32765i
$362$	−2.56625	+	1.48163i	−0.134879	+	0.0778725i
$363$	−3.23409			−0.169746
$364$	−4.99869	−	13.2153i	−0.262003	−	0.692671i
$365$	−16.7249			−0.875423
$366$	−25.1921	+	14.5447i	−1.31681	+	0.760262i
$367$	11.0161	+	19.0805i	0.575037	+	0.995994i	0.996038	+	0.0889331i	$0.0283457\pi$
$367$	11.0161	+	19.0805i	0.575037	+	0.995994i	−0.421000	+	0.907060i	$0.638321\pi$
$368$	−0.535560	+	0.927618i	−0.0279180	+	0.0483554i
$369$		−	40.9772i		−	2.13319i
$370$	−2.42312	−	1.39899i	−0.125972	−	0.0727299i
$371$	35.6864	+	20.6036i	1.85275	+	1.06968i
$372$			8.47079i			0.439190i
$373$	−6.25297	+	10.8305i	−0.323767	+	0.560780i	−0.981262	−	0.192678i	$-0.938283\pi$
$373$	−6.25297	+	10.8305i	−0.323767	+	0.560780i	0.657495	+	0.753459i	$0.271616\pi$
$374$	0.577065	+	0.999507i	0.0298393	+	0.0516833i
$375$	28.7384	−	16.5921i	1.48404	−	0.856812i
$376$	−7.13295			−0.367854
$377$	−7.15366	+	2.70587i	−0.368432	+	0.139359i
$378$	−56.5153			−2.90683
$379$	−1.85398	+	1.07040i	−0.0952326	+	0.0549826i	−0.546860	−	0.837224i	$-0.684177\pi$
$379$	−1.85398	+	1.07040i	−0.0952326	+	0.0549826i	0.451627	+	0.892207i	$0.350844\pi$
$380$	9.99544	+	17.3126i	0.512755	+	0.888118i
$381$	−8.65183	+	14.9854i	−0.443247	+	0.767726i
$382$		−	10.7789i		−	0.551497i
$383$	−31.9266	−	18.4328i	−1.63137	−	0.941873i	−0.983670	−	0.179980i	$-0.942397\pi$
$383$	−31.9266	−	18.4328i	−1.63137	−	0.941873i	−0.647702	−	0.761894i	$-0.724270\pi$
$384$	−2.80080	−	1.61705i	−0.142928	−	0.0825195i
$385$			9.35875i			0.476966i
$386$	−10.4713	+	18.1368i	−0.532974	+	0.923138i
$387$	21.2901	+	36.8756i	1.08224	+	1.87449i
$388$	−14.5485	+	8.39957i	−0.738587	+	0.426423i
$389$	−3.62824			−0.183959			−0.0919794	−	0.995761i	$-0.529319\pi$
$389$	−3.62824			−0.183959			−0.0919794	+	0.995761i	$0.529319\pi$
$390$	21.5560	+	17.6314i	1.09153	+	0.892800i
$391$	−1.23621			−0.0625180
$392$	−7.23676	+	4.17814i	−0.365511	+	0.211028i
$393$	11.2058	+	19.4090i	0.565257	+	0.979053i
$394$	7.05092	−	12.2126i	0.355220	−	0.615260i
$395$		−	23.2277i		−	1.16871i
$396$	6.45998	+	3.72967i	0.324626	+	0.187423i
$397$	11.5249	+	6.65393i	0.578420	+	0.333951i	0.760505	−	0.649332i	$-0.224951\pi$
$397$	11.5249	+	6.65393i	0.578420	+	0.333951i	−0.182085	+	0.983283i	$0.558285\pi$
$398$		−	10.9854i		−	0.550648i
$399$	53.0423	−	91.8720i	2.65544	−	4.59935i
$400$	0.351801	+	0.609337i	0.0175901	+	0.0304669i
$401$	9.01085	−	5.20242i	0.449981	−	0.259796i	−0.257841	−	0.966187i	$-0.583011\pi$
$401$	9.01085	−	5.20242i	0.449981	−	0.259796i	0.707822	+	0.706391i	$0.249678\pi$
$402$	27.7535			1.38422
$403$	−9.32011	−	1.52304i	−0.464268	−	0.0758679i
$404$	−15.1275			−0.752622
$405$	50.1838	−	28.9736i	2.49365	−	1.43971i
$406$	4.15630	+	7.19892i	0.206274	+	0.357276i
$407$	0.585786	−	1.01461i	0.0290363	−	0.0502924i
$408$		−	3.73256i		−	0.184789i
$409$	−16.8420	−	9.72376i	−0.832786	−	0.480809i	0.0220198	−	0.999758i	$-0.492990\pi$
$409$	−16.8420	−	9.72376i	−0.832786	−	0.480809i	−0.854806	+	0.518949i	$0.826324\pi$
$410$	11.3618	+	6.55974i	0.561119	+	0.323962i
$411$		−	60.9989i		−	3.00886i
$412$	4.54665	−	7.87503i	0.223997	−	0.387975i
$413$	12.6310	+	21.8775i	0.621529	+	1.07652i
$414$	−6.91942	+	3.99493i	−0.340071	+	0.196340i
$415$	17.2009			0.844360
$416$	2.28276	−	2.79088i	0.111921	−	0.136834i
$417$	−32.0639			−1.57018
$418$	−7.24916	+	4.18531i	−0.354568	+	0.204710i
$419$	6.36864	+	11.0308i	0.311129	+	0.538890i	0.978607	−	0.205739i	$-0.0659597\pi$
$419$	6.36864	+	11.0308i	0.311129	+	0.538890i	−0.667478	+	0.744629i	$0.732626\pi$
$420$	15.1335	−	26.2120i	0.738440	−	1.27902i
$421$			21.2899i			1.03761i	0.854894	+	0.518803i	$0.173622\pi$
$421$			21.2899i			1.03761i	−0.854894	+	0.518803i	$0.826378\pi$
$422$	1.19944	+	0.692499i	0.0583880	+	0.0337103i
$423$	−46.0787	−	26.6036i	−2.24043	−	1.29351i
$424$			10.5155i			0.510677i
$425$	−0.406024	+	0.703255i	−0.0196951	+	0.0341129i
$426$	2.45148	+	4.24609i	0.118775	+	0.205724i
$427$	−30.5250	+	17.6236i	−1.47721	+	0.852866i
$428$	1.74822			0.0845033
$429$	−7.38264	+	9.02596i	−0.356437	+	0.435778i
$430$	−13.6327			−0.657427
$431$	30.7867	−	17.7747i	1.48294	−	0.856178i	0.483132	−	0.875547i	$-0.339499\pi$
$431$	30.7867	−	17.7747i	1.48294	−	0.856178i	0.999812	+	0.0193689i	$0.00616571\pi$
$432$	−7.21096	−	12.4897i	−0.346937	−	0.600913i
$433$	−9.75895	+	16.9030i	−0.468985	+	0.812306i	−0.999371	−	0.0354498i	$-0.988714\pi$
$433$	−9.75895	+	16.9030i	−0.468985	+	0.812306i	0.530386	+	0.847756i	$0.322047\pi$
$434$			10.2640i			0.492686i
$435$	−14.1890	−	8.19201i	−0.680309	−	0.392777i
$436$	4.60514	+	2.65878i	0.220546	+	0.127332i
$437$		−	8.96594i		−	0.428899i
$438$	−11.3243	+	19.6143i	−0.541097	+	0.937207i
$439$	−4.59965	−	7.96683i	−0.219529	−	0.380236i	0.735135	−	0.677921i	$-0.237119\pi$
$439$	−4.59965	−	7.96683i	−0.219529	−	0.380236i	−0.954664	+	0.297685i	$0.903786\pi$
$440$	−2.06826	+	1.19411i	−0.0986005	+	0.0569270i
$441$	−62.3324			−2.96821
$442$	4.10680	+	0.671110i	0.195341	+	0.0319214i
$443$	−9.27465			−0.440652			−0.220326	−	0.975426i	$-0.570712\pi$
$443$	−9.27465			−0.440652			−0.220326	+	0.975426i	$0.570712\pi$
$444$	−3.28135	+	1.89449i	−0.155726	+	0.0899083i
$445$	−15.2458	−	26.4064i	−0.722719	−	1.25179i
$446$	4.18271	−	7.24466i	0.198057	−	0.343045i
$447$			49.4447i			2.33865i
$448$	−3.39370	−	1.95936i	−0.160337	−	0.0925708i
$449$	5.66250	+	3.26925i	0.267230	+	0.154285i	0.627628	−	0.778513i	$-0.284026\pi$
$449$	5.66250	+	3.26925i	0.267230	+	0.154285i	−0.360398	+	0.932799i	$0.617359\pi$
$450$			5.24841i			0.247412i
$451$	−2.74670	+	4.75743i	−0.129337	+	0.224019i
$452$	−0.475848	−	0.824192i	−0.0223820	−	0.0387668i
$453$	−2.07742	+	1.19940i	−0.0976055	+	0.0563526i
$454$	−0.658085			−0.0308855
$455$	26.1192	+	21.3637i	1.22448	+	1.00155i
$456$	27.0713			1.26773
$457$	0.217086	−	0.125334i	0.0101548	−	0.00586290i	−0.494914	−	0.868942i	$-0.664800\pi$
$457$	0.217086	−	0.125334i	0.0101548	−	0.00586290i	0.505069	+	0.863079i	$0.331467\pi$
$458$	−2.60636	−	4.51436i	−0.121787	−	0.210942i
$459$	8.32239	−	14.4148i	0.388456	−	0.672825i
$460$		−	2.55807i		−	0.119271i
$461$	−16.8434	−	9.72457i	−0.784477	−	0.452918i	0.0535374	−	0.998566i	$-0.482950\pi$
$461$	−16.8434	−	9.72457i	−0.784477	−	0.452918i	−0.838015	+	0.545648i	$0.816284\pi$
$462$	10.9755	+	6.33673i	0.510628	+	0.294811i
$463$		−	12.1144i		−	0.563005i	−0.959561	−	0.281502i	$-0.909167\pi$
$463$		−	12.1144i		−	0.563005i	0.959561	−	0.281502i	$-0.0908327\pi$
$464$	−1.06063	+	1.83706i	−0.0492385	+	0.0852836i
$465$	−10.1151	−	17.5198i	−0.469075	−	0.812462i
$466$	7.64487	−	4.41377i	0.354142	−	0.204464i
$467$	−7.68809			−0.355762			−0.177881	−	0.984052i	$-0.556924\pi$
$467$	−7.68809			−0.355762			−0.177881	+	0.984052i	$0.556924\pi$
$468$	25.1556	−	9.51511i	1.16282	−	0.439836i
$469$	33.6286			1.55282
$470$	14.7528	−	8.51754i	0.680496	−	0.392885i
$471$	37.5207	+	64.9878i	1.72886	+	2.99448i
$472$	−3.22325	+	5.58283i	−0.148362	+	0.256970i
$473$		−	5.70831i		−	0.262468i
$474$	−27.2404	−	15.7273i	−1.25119	−	0.722377i
$475$	−5.10053	−	2.94479i	−0.234028	−	0.135116i
$476$		−	4.52270i		−	0.207298i
$477$	−39.2193	+	67.9299i	−1.79573	+	3.11029i
$478$	3.65424	+	6.32933i	0.167141	+	0.289497i
$479$	−11.8997	+	6.87030i	−0.543711	+	0.313912i	−0.746582	−	0.665294i	$-0.768306\pi$
$479$	−11.8997	+	6.87030i	−0.543711	+	0.313912i	0.202870	+	0.979206i	$0.434973\pi$
$480$	7.72372			0.352538
$481$	−1.49445	−	3.95097i	−0.0681412	−	0.180149i
$482$	15.5738			0.709368
$483$	−11.7561	+	6.78740i	−0.534922	+	0.308838i
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	20.0600	−	34.7450i	0.910879	−	1.57769i
$486$		−	35.2054i		−	1.59695i
$487$	−3.81826	−	2.20447i	−0.173022	−	0.0998943i	0.410988	−	0.911641i	$-0.365184\pi$
$487$	−3.81826	−	2.20447i	−0.173022	−	0.0998943i	−0.584010	+	0.811746i	$0.698517\pi$
$488$	−7.78954	−	4.49730i	−0.352616	−	0.203583i
$489$			60.6222i			2.74143i
$490$	9.97833	−	17.2830i	0.450775	−	0.780766i
$491$	−9.46134	−	16.3875i	−0.426984	−	0.739558i	0.569619	−	0.821909i	$-0.307091\pi$
$491$	−9.46134	−	16.3875i	−0.426984	−	0.739558i	−0.996603	+	0.0823504i	$0.973757\pi$
$492$	15.3860	−	8.88309i	0.693653	−	0.400481i
$493$	−2.44821			−0.110262
$494$	−4.86738	+	29.7856i	−0.218994	+	1.34012i
$495$	−17.8146			−0.800705
$496$	−2.26831	+	1.30961i	−0.101850	+	0.0588032i
$497$	2.97043	+	5.14494i	0.133242	+	0.230782i
$498$	11.6466	−	20.1725i	0.521897	−	0.903952i
$499$		−	16.5285i		−	0.739915i	−0.929049	−	0.369958i	$-0.879372\pi$
$499$		−	16.5285i		−	0.739915i	0.929049	−	0.369958i	$-0.120628\pi$
$500$	8.88607	+	5.13038i	0.397397	+	0.229437i
$501$	3.98848	+	2.30275i	0.178192	+	0.102879i
$502$			18.2740i			0.815609i
$503$	−14.0835	+	24.3933i	−0.627952	+	1.08764i	0.360010	+	0.932948i	$0.382773\pi$
$503$	−14.0835	+	24.3933i	−0.627952	+	1.08764i	−0.987962	+	0.154696i	$0.950560\pi$
$504$	−14.6155	−	25.3148i	−0.651026	−	1.12761i
$505$	31.2877	−	18.0639i	1.39228	−	0.803834i
$506$	1.07112			0.0476171
$507$	8.33761	+	41.2082i	0.370286	+	1.83012i
$508$	−5.35040			−0.237385
$509$	4.45335	−	2.57114i	0.197391	−	0.113964i	−0.398047	−	0.917365i	$-0.630312\pi$
$509$	4.45335	−	2.57114i	0.197391	−	0.113964i	0.595438	+	0.803401i	$0.296978\pi$
$510$	4.45709	+	7.71991i	0.197363	+	0.341844i
$511$	−13.7215	+	23.7664i	−0.607005	+	1.05136i
$512$		−	1.00000i		−	0.0441942i
$513$	104.547	+	60.3601i	4.61585	+	2.66497i
$514$	6.70707	+	3.87233i	0.295836	+	0.170801i
$515$			21.7168i			0.956957i
$516$	−9.23059	+	15.9879i	−0.406354	+	0.703826i
$517$	3.56648	+	6.17732i	0.156853	+	0.271678i
$518$	−3.97597	+	2.29553i	−0.174694	+	0.100860i
$519$	−40.5078			−1.77810
$520$	−1.38871	+	8.49813i	−0.0608992	+	0.372668i
$521$	27.1371			1.18890			0.594449	−	0.804133i	$-0.297370\pi$
$521$	27.1371			1.18890			0.594449	+	0.804133i	$0.297370\pi$
$522$	−13.7033	+	7.91160i	−0.599777	+	0.346281i
$523$	−6.51845	−	11.2903i	−0.285032	−	0.493690i	0.687585	−	0.726104i	$-0.258671\pi$
$523$	−6.51845	−	11.2903i	−0.285032	−	0.493690i	−0.972617	+	0.232414i	$0.925337\pi$
$524$	−3.46489	+	6.00137i	−0.151365	+	0.262171i
$525$			8.91708i			0.389173i
$526$	2.71869	+	1.56963i	0.118540	+	0.0684393i
$527$	−2.61793	−	1.51146i	−0.114039	−	0.0658403i
$528$			3.23409i			0.140746i
$529$	10.9264	−	18.9250i	0.475059	−	0.822826i
$530$	−12.5567	−	21.7488i	−0.545426	−	0.944706i
$531$	−41.6442	+	24.0433i	−1.80720	+	1.04339i
$532$	32.8020			1.42215
$533$	7.00737	+	18.5258i	0.303523	+	0.802441i
$534$	−41.2911			−1.78684
$535$	−3.61577	+	2.08756i	−0.156323	+	0.0902533i
$536$	4.29077	+	7.43183i	0.185333	+	0.321006i
$537$	−4.38240	+	7.59054i	−0.189114	+	0.327556i
$538$		−	3.97643i		−	0.171436i
$539$	7.23676	+	4.17814i	0.311709	+	0.179965i
$540$	29.8283	+	17.2214i	1.28360	+	0.741090i
$541$			17.1543i			0.737519i	0.929525	+	0.368759i	$0.120217\pi$
$541$			17.1543i			0.737519i	−0.929525	+	0.368759i	$0.879783\pi$
$542$	5.73056	−	9.92563i	0.246149	−	0.426342i
$543$	−4.79171	−	8.29949i	−0.205632	−	0.356165i
$544$	0.999507	−	0.577065i	0.0428535	−	0.0247415i
$545$	−12.6995			−0.543987
$546$	42.7396	−	16.1662i	1.82908	−	0.691850i
$547$	5.19197			0.221992			0.110996	−	0.993821i	$-0.464596\pi$
$547$	5.19197			0.221992			0.110996	+	0.993821i	$0.464596\pi$
$548$	16.3343	−	9.43062i	0.697767	−	0.402856i
$549$	−33.5469	−	58.1049i	−1.43175	−	2.47986i
$550$	0.351801	−	0.609337i	0.0150008	−	0.0259822i
$551$		−	17.7562i		−	0.756441i
$552$	−3.00000	−	1.73205i	−0.127688	−	0.0737210i
$553$	−33.0069	−	19.0566i	−1.40360	−	0.810367i
$554$		−	2.71586i		−	0.115386i
$555$	4.52445	−	7.83658i	0.192052	−	0.332644i
$556$	−4.95718	−	8.58608i	−0.210231	−	0.364131i
$557$	21.7440	−	12.5539i	0.921323	−	0.531926i	0.0372661	−	0.999305i	$-0.488135\pi$
$557$	21.7440	−	12.5539i	0.921323	−	0.531926i	0.884057	+	0.467379i	$0.154802\pi$
$558$	−19.5377			−0.827095
$559$	−15.9312	−	13.0307i	−0.673819	−	0.551139i
$560$	9.35875			0.395479
$561$	−3.23250	+	1.86628i	−0.136476	+	0.0787945i
$562$	−4.80852	−	8.32861i	−0.202835	−	0.351321i
$563$	17.1294	−	29.6689i	0.721917	−	1.25040i	−0.238314	−	0.971188i	$-0.576595\pi$
$563$	17.1294	−	29.6689i	0.721917	−	1.25040i	0.960231	−	0.279208i	$-0.0900720\pi$
$564$		−	23.0686i		−	0.971364i
$565$	1.96835	+	1.13643i	0.0828093	+	0.0478100i
$566$	−8.04759	−	4.64628i	−0.338266	−	0.195298i
$567$		−	95.0826i		−	3.99310i
$568$	−0.758013	+	1.31292i	−0.0318055	+	0.0550888i
$569$	15.9081	+	27.5536i	0.666901	+	1.15511i	0.978766	+	0.204980i	$0.0657129\pi$
$569$	15.9081	+	27.5536i	0.666901	+	1.15511i	−0.311865	+	0.950126i	$0.600954\pi$
$570$	−55.9905	+	32.3262i	−2.34519	+	1.35399i
$571$	−40.2689			−1.68520			−0.842600	−	0.538540i	$-0.818976\pi$
$571$	−40.2689			−1.68520			−0.842600	+	0.538540i	$0.818976\pi$
$572$	−3.55835	−	0.581485i	−0.148782	−	0.0243131i
$573$	34.8599			1.45630
$574$	18.6430	−	10.7635i	0.778143	−	0.449261i
$575$	0.376821	+	0.652674i	0.0157145	+	0.0272184i
$576$	3.72967	−	6.45998i	0.155403	−	0.269166i
$577$		−	10.4030i		−	0.433081i	−0.976274	−	0.216540i	$-0.930523\pi$
$577$		−	10.4030i		−	0.433081i	0.976274	−	0.216540i	$-0.0694773\pi$
$578$	−13.5689	−	7.83399i	−0.564391	−	0.325851i
$579$	−58.6560	−	33.8651i	−2.43766	−	1.40738i
$580$		−	5.06604i		−	0.210356i
$581$	14.1121	−	24.4428i	0.585467	−	1.01406i
$582$	−27.1650	−	47.0511i	−1.12602	−	1.95033i
$583$	9.10668	−	5.25774i	0.377160	−	0.217754i
$584$	−7.00309			−0.289790
$585$	−40.6663	+	49.7183i	−1.68135	+	2.05560i
$586$	33.8220			1.39717
$587$	−7.55694	+	4.36300i	−0.311908	+	0.180080i	−0.647780	−	0.761827i	$-0.724302\pi$
$587$	−7.55694	+	4.36300i	−0.311908	+	0.180080i	0.335872	+	0.941908i	$0.390969\pi$
$588$	−13.5125	−	23.4043i	−0.557246	−	0.965178i
$589$	10.9622	−	18.9871i	0.451691	−	0.782352i
$590$		−	15.3957i		−	0.633829i
$591$	39.4965	+	22.8033i	1.62467	+	0.938004i
$592$	−1.01461	−	0.585786i	−0.0417003	−	0.0240757i
$593$			6.48140i			0.266159i	0.991105	+	0.133080i	$0.0424866\pi$
$593$			6.48140i			0.266159i	−0.991105	+	0.133080i	$0.957513\pi$
$594$	−7.21096	+	12.4897i	−0.295869	+	0.512461i
$595$	5.40061	+	9.35413i	0.221403	+	0.383482i
$596$	−13.2403	+	7.64429i	−0.542344	+	0.313122i
$597$	35.5278			1.45406
$598$	2.44511	−	2.98937i	0.0999879	−	0.122244i
$599$	29.7830			1.21690			0.608450	−	0.793593i	$-0.291792\pi$
$599$	29.7830			1.21690			0.608450	+	0.793593i	$0.291792\pi$
$600$	−1.97065	+	1.13776i	−0.0804515	+	0.0464487i
$601$	6.54759	+	11.3408i	0.267082	+	0.462600i	0.968107	−	0.250537i	$-0.0806072\pi$
$601$	6.54759	+	11.3408i	0.267082	+	0.462600i	−0.701025	+	0.713137i	$0.747274\pi$
$602$	−11.1846	+	19.3723i	−0.455850	+	0.789556i
$603$			64.0126i			2.60680i
$604$	−0.642349	−	0.370860i	−0.0261368	−	0.0150901i
$605$	2.06826	+	1.19411i	0.0840867	+	0.0485475i
$606$		−	48.9238i		−	1.98739i
$607$	−0.852879	+	1.47723i	−0.0346173	+	0.0599589i	−0.882815	−	0.469721i	$-0.844355\pi$
$607$	−0.852879	+	1.47723i	−0.0346173	+	0.0599589i	0.848198	+	0.529680i	$0.177688\pi$
$608$	4.18531	+	7.24916i	0.169737	+	0.293992i
$609$	−23.2820	+	13.4418i	−0.943433	+	0.544691i
$610$	21.4811			0.869743
$611$	25.3816	+	4.14771i	1.02683	+	0.167798i
$612$	8.60906			0.348001
$613$	−4.79886	+	2.77062i	−0.193824	+	0.111904i	−0.593771	−	0.804634i	$-0.702362\pi$
$613$	−4.79886	+	2.77062i	−0.193824	+	0.111904i	0.399948	+	0.916538i	$0.369028\pi$
$614$	−3.38921	−	5.87029i	−0.136777	−	0.236905i
$615$	−21.2148	+	36.7451i	−0.855463	+	1.48170i
$616$			3.91871i			0.157889i
$617$	−11.5081	−	6.64420i	−0.463298	−	0.267485i	0.250132	−	0.968212i	$-0.419526\pi$
$617$	−11.5081	−	6.64420i	−0.463298	−	0.267485i	−0.713430	+	0.700726i	$0.752859\pi$
$618$	25.4685	+	14.7043i	1.02450	+	0.591493i
$619$			7.12717i			0.286465i	0.989689	+	0.143233i	$0.0457497\pi$
$619$			7.12717i			0.286465i	−0.989689	+	0.143233i	$0.954250\pi$
$620$	3.12764	−	5.41723i	0.125609	−	0.217561i
$621$	−7.72381	−	13.3780i	−0.309946	−	0.536842i
$622$	−10.8068	+	6.23931i	−0.433313	+	0.250174i
$623$	−50.0320			−2.00449
$624$	9.02596	+	7.38264i	0.361328	+	0.295542i
$625$	−28.0230			−1.12092
$626$	10.8645	−	6.27264i	0.434234	−	0.250705i
$627$	−13.5357	−	23.4444i	−0.540562	−	0.936281i
$628$	−11.6016	+	20.0946i	−0.462955	+	0.801862i
$629$		−	1.35215i		−	0.0539137i
$630$	60.4573	+	34.9051i	2.40868	+	1.39065i
$631$	35.2594	+	20.3570i	1.40366	+	0.810401i	0.994766	−	0.102183i	$-0.0325827\pi$
$631$	35.2594	+	20.3570i	1.40366	+	0.810401i	0.408890	+	0.912584i	$0.365916\pi$
$632$		−	9.72593i		−	0.386877i
$633$	−2.23961	+	3.87911i	−0.0890163	+	0.154181i
$634$	10.8977	+	18.8753i	0.432802	+	0.749636i
$635$	11.0660	−	6.38897i	0.439141	−	0.253538i
$636$	−34.0080			−1.34851
$637$	28.1805	−	10.6592i	1.11655	−	0.422335i
$638$	2.12126			0.0839814
$639$	−9.79350	+	5.65428i	−0.387425	+	0.223680i
$640$	1.19411	+	2.06826i	0.0472014	+	0.0817552i
$641$	−21.4093	+	37.0819i	−0.845615	+	1.46465i	0.0394712	+	0.999221i	$0.487433\pi$
$641$	−21.4093	+	37.0819i	−0.845615	+	1.46465i	−0.885086	+	0.465427i	$0.845901\pi$
$642$			5.65389i			0.223141i
$643$	−35.9494	−	20.7554i	−1.41771	−	0.818513i	−0.421609	−	0.906778i	$-0.638534\pi$
$643$	−35.9494	−	20.7554i	−1.41771	−	0.818513i	−0.996097	+	0.0882649i	$0.971868\pi$
$644$	−3.63507	−	2.09871i	−0.143242	−	0.0827006i
$645$		−	44.0894i		−	1.73602i
$646$	−4.83039	+	8.36648i	−0.190049	+	0.329175i
$647$	13.4542	+	23.3034i	0.528941	+	0.916153i	0.999430	+	0.0337470i	$0.0107440\pi$
$647$	13.4542	+	23.3034i	0.528941	+	0.916153i	−0.470489	+	0.882406i	$0.655923\pi$
$648$	21.0130	−	12.1319i	0.825470	−	0.476585i
$649$	6.44649			0.253047
$650$	−0.897512	−	2.37280i	−0.0352033	−	0.0930690i
$651$	−33.1946			−1.30100
$652$	−16.2334	+	9.37237i	−0.635750	+	0.367050i
$653$	1.68437	+	2.91741i	0.0659143	+	0.114167i	0.897099	−	0.441829i	$-0.145670\pi$
$653$	1.68437	+	2.91741i	0.0659143	+	0.114167i	−0.831185	+	0.555996i	$0.812337\pi$
$654$	−8.59873	+	14.8934i	−0.336237	+	0.582380i
$655$		−	16.5499i		−	0.646657i
$656$	4.75743	+	2.74670i	0.185746	+	0.107241i
$657$	−45.2398	−	26.1192i	−1.76497	−	1.01901i
$658$		−	27.9520i		−	1.08968i
$659$	19.5994	−	33.9472i	0.763484	−	1.32239i	−0.177560	−	0.984110i	$-0.556820\pi$
$659$	19.5994	−	33.9472i	0.763484	−	1.32239i	0.941044	−	0.338284i	$-0.109846\pi$
$660$	−3.86186	−	6.68894i	−0.150323	−	0.260367i
$661$	−15.0024	+	8.66166i	−0.583527	+	0.336899i	−0.762534	−	0.646948i	$-0.776045\pi$
$661$	−15.0024	+	8.66166i	−0.583527	+	0.336899i	0.179007	+	0.983848i	$0.442712\pi$
$662$	−33.5924			−1.30560
$663$	−2.17043	+	13.2818i	−0.0842925	+	0.515822i
$664$	7.20240			0.279507
$665$	−67.8431	+	39.1692i	−2.63084	+	1.51892i
$666$	−4.36958	−	7.56833i	−0.169318	−	0.293267i
$667$	−1.13606	+	1.96772i	−0.0439885	+	0.0761903i
$668$			1.42405i			0.0550981i
$669$	23.4299	+	13.5273i	0.905852	+	0.522994i
$670$	−17.7489	−	10.2473i	−0.685698	−	0.395888i
$671$			8.99459i			0.347232i
$672$	6.33673	−	10.9755i	0.244445	−	0.423391i
$673$	−19.8511	−	34.3831i	−0.765204	−	1.32537i	−0.940139	−	0.340792i	$-0.889305\pi$
$673$	−19.8511	−	34.3831i	−0.765204	−	1.32537i	0.174935	−	0.984580i	$-0.444028\pi$
$674$	8.18208	−	4.72393i	0.315162	−	0.181959i
$675$	−10.1473			−0.390569
$676$	−9.74571	+	8.60355i	−0.374835	+	0.330906i
$677$	13.0488			0.501506			0.250753	−	0.968051i	$-0.419322\pi$
$677$	13.0488			0.501506			0.250753	+	0.968051i	$0.419322\pi$
$678$	2.66551	−	1.53893i	0.102368	−	0.0591024i
$679$	−32.9155	−	57.0113i	−1.26318	−	2.18789i
$680$	−1.37816	+	2.38704i	−0.0528500	+	0.0915389i
$681$		−	2.12831i		−	0.0815569i
$682$	2.26831	+	1.30961i	0.0868581	+	0.0501475i
$683$	−2.79663	−	1.61464i	−0.107010	−	0.0617823i	0.445540	−	0.895262i	$-0.353012\pi$
$683$	−2.79663	−	1.61464i	−0.107010	−	0.0617823i	−0.552550	+	0.833480i	$0.686345\pi$
$684$			62.4393i			2.38742i
$685$	−22.5224	+	39.0100i	−0.860537	+	1.49049i
$686$	−2.65745	−	4.60284i	−0.101462	−	0.175737i
$687$	14.5998	−	8.42922i	0.557018	−	0.321595i
$688$	−5.70831			−0.217627
$689$	6.11460	−	37.4178i	0.232948	−	1.42551i
$690$	8.27304			0.314949
$691$	10.0044	−	5.77607i	0.380587	−	0.219732i	−0.297487	−	0.954726i	$-0.596148\pi$
$691$	10.0044	−	5.77607i	0.380587	−	0.219732i	0.678074	+	0.734994i	$0.262815\pi$
$692$	−6.26263	−	10.8472i	−0.238069	−	0.412348i
$693$	−14.6155	+	25.3148i	−0.555197	+	0.961629i
$694$			27.5223i			1.04473i
$695$	20.5055	+	11.8388i	0.777817	+	0.449073i
$696$	−5.94123	−	3.43017i	−0.225202	−	0.130020i
$697$			6.34011i			0.240149i
$698$	0.743058	−	1.28701i	0.0281252	−	0.0487142i
$699$	14.2745	+	24.7242i	0.539912	+	0.935156i
$700$	−2.38782	+	1.37861i	−0.0902510	+	0.0521064i
$701$	−21.2257			−0.801683			−0.400841	−	0.916147i	$-0.631282\pi$
$701$	−21.2257			−0.801683			−0.400841	+	0.916147i	$0.631282\pi$
$702$	18.3965	+	48.6360i	0.694332	+	1.83565i
$703$	9.80678			0.369870
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	27.5465	+	47.7119i	1.03746	+	1.79693i
$706$	−15.9412	+	27.6110i	−0.599956	+	1.03915i
$707$		−	59.2804i		−	2.22947i
$708$	−18.0554	−	10.4243i	−0.678562	−	0.391768i
$709$	28.7567	+	16.6027i	1.07998	+	0.623526i	0.930891	−	0.365297i	$-0.119033\pi$
$709$	28.7567	+	16.6027i	1.07998	+	0.623526i	0.149089	+	0.988824i	$0.452366\pi$
$710$		−	3.62061i		−	0.135879i
$711$	36.2745	−	62.8293i	1.36040	−	2.35628i
$712$	−6.38373	−	11.0570i	−0.239241	−	0.414377i
$713$	−2.42963	+	1.40275i	−0.0909905	+	0.0525334i
$714$	14.6268			0.547396
$715$	8.05396	−	3.04641i	0.301201	−	0.113929i
$716$	−2.71013			−0.101282
$717$	−20.4696	+	11.8181i	−0.764452	+	0.441357i
$718$	9.18976	+	15.9171i	0.342959	+	0.594022i
$719$	−12.6104	+	21.8419i	−0.470289	+	0.814564i	−0.999423	−	0.0339741i	$-0.989184\pi$
$719$	−12.6104	+	21.8419i	−0.470289	+	0.814564i	0.529134	+	0.848538i	$0.322517\pi$
$720$			17.8146i			0.663910i
$721$	30.8599	+	17.8170i	1.14928	+	0.663540i
$722$	−44.2254	−	25.5336i	−1.64590	−	0.950261i
$723$			50.3672i			1.87317i
$724$	1.48163	−	2.56625i	0.0550642	−	0.0953740i
$725$	0.746261	+	1.29256i	0.0277154	+	0.0480046i
$726$	2.80080	−	1.61705i	0.103948	−	0.0600142i
$727$	−42.4070			−1.57279			−0.786394	−	0.617725i	$-0.788054\pi$
$727$	−42.4070			−1.57279			−0.786394	+	0.617725i	$0.788054\pi$
$728$	10.9367	+	8.94546i	0.405339	+	0.331541i
$729$	41.0663			1.52098
$730$	14.4842	−	8.36247i	0.536085	−	0.309509i
$731$	−3.29407	−	5.70549i	−0.121835	−	0.211025i
$732$	14.5447	−	25.1921i	0.537586	−	0.931126i
$733$			31.0453i			1.14669i	0.819316	+	0.573343i	$0.194354\pi$
$733$			31.0453i			1.14669i	−0.819316	+	0.573343i	$0.805646\pi$
$734$	−19.0805	−	11.0161i	−0.704274	−	0.406613i
$735$	55.8947	+	32.2708i	2.06171	+	1.19033i
$736$		−	1.07112i		−	0.0394820i
$737$	4.29077	−	7.43183i	0.158053	−	0.273755i
$738$	20.4886	+	35.4873i	0.754196	+	1.30631i
$739$	−7.27048	+	4.19761i	−0.267449	+	0.154412i	−0.627728	−	0.778433i	$-0.716015\pi$
$739$	−7.27048	+	4.19761i	−0.267449	+	0.154412i	0.360279	+	0.932845i	$0.382682\pi$
$740$	2.79797			0.102856
$741$	−96.3293	−	15.7416i	−3.53875	−	0.578281i
$742$	−41.2072			−1.51276
$743$	22.2340	−	12.8368i	0.815688	−	0.470937i	−0.0332395	−	0.999447i	$-0.510582\pi$
$743$	22.2340	−	12.8368i	0.815688	−	0.470937i	0.848927	+	0.528510i	$0.177249\pi$
$744$	−4.23540	−	7.33592i	−0.155277	−	0.268948i
$745$	18.2563	−	31.6208i	0.668858	−	1.15850i
$746$		−	12.5059i		−	0.457875i
$747$	46.5274	+	26.8626i	1.70235	+	0.982851i
$748$	−0.999507	−	0.577065i	−0.0365456	−	0.0210996i
$749$			6.85076i			0.250321i
$750$	−16.5921	+	28.7384i	−0.605858	+	1.04938i
$751$	−12.1212	−	20.9946i	−0.442310	−	0.766103i	0.555551	−	0.831483i	$-0.312508\pi$
$751$	−12.1212	−	20.9946i	−0.442310	−	0.766103i	−0.997860	+	0.0653796i	$0.979174\pi$
$752$	6.17732	−	3.56648i	0.225264	−	0.130056i
$753$	−59.0998			−2.15372
$754$	4.84232	−	5.92018i	0.176347	−	0.215600i
$755$	1.77139			0.0644676
$756$	48.9437	−	28.2577i	1.78007	−	1.02772i
$757$	21.2536	+	36.8123i	0.772474	+	1.33796i	0.936203	+	0.351459i	$0.114314\pi$
$757$	21.2536	+	36.8123i	0.772474	+	1.33796i	−0.163729	+	0.986505i	$0.552352\pi$
$758$	1.07040	−	1.85398i	0.0388785	−	0.0673396i
$759$			3.46410i			0.125739i
$760$	−17.3126	−	9.99544i	−0.627994	−	0.362573i
$761$	26.6585	+	15.3913i	0.966371	+	0.557935i	0.898128	−	0.439734i	$-0.144927\pi$
$761$	26.6585	+	15.3913i	0.966371	+	0.557935i	0.0682432	+	0.997669i	$0.478261\pi$
$762$		−	17.3037i		−	0.626846i
$763$	−10.4190	+	18.0462i	−0.377193	+	0.653317i
$764$	5.38945	+	9.33480i	0.194983	+	0.337721i
$765$	−17.8058	+	10.2802i	−0.643769	+	0.371680i
$766$	36.8656			1.33201
$767$	14.7158	−	17.9914i	0.531356	−	0.649632i
$768$	3.23409			0.116700
$769$	44.9612	−	25.9584i	1.62134	−	0.936083i	0.634783	−	0.772691i	$-0.281090\pi$
$769$	44.9612	−	25.9584i	1.62134	−	0.936083i	0.986561	−	0.163393i	$-0.0522438\pi$
$770$	−4.67937	−	8.10491i	−0.168633	−	0.292081i
$771$	−12.5235	+	21.6913i	−0.451022	+	0.781193i
$772$		−	20.9426i		−	0.753739i
$773$	−5.44613	−	3.14433i	−0.195884	−	0.113094i	0.398850	−	0.917016i	$-0.369409\pi$
$773$	−5.44613	−	3.14433i	−0.195884	−	0.113094i	−0.594734	+	0.803922i	$0.702743\pi$
$774$	−36.8756	−	21.2901i	−1.32546	−	0.765257i
$775$			1.84289i			0.0661985i
$776$	8.39957	−	14.5485i	0.301527	−	0.522260i
$777$	−7.42394	−	12.8586i	−0.266332	−	0.461301i
$778$	3.14215	−	1.81412i	0.112651	−	0.0650393i
$779$	−45.9832			−1.64752
$780$	−27.4837	−	4.49123i	−0.984076	−	0.160812i
$781$	1.51603			0.0542477
$782$	1.07059	−	0.618107i	0.0382843	−	0.0221035i
$783$	−15.2963	−	26.4940i	−0.546646	−	0.946818i
$784$	4.17814	−	7.23676i	0.149219	−	0.258456i
$785$		−	55.4145i		−	1.97783i
$786$	−19.4090	−	11.2058i	−0.692295	−	0.399697i
$787$	−11.3186	−	6.53482i	−0.403466	−	0.232941i	0.284512	−	0.958672i	$-0.408168\pi$
$787$	−11.3186	−	6.53482i	−0.403466	−	0.232941i	−0.687979	+	0.725731i	$0.741502\pi$
$788$			14.1018i			0.502358i
$789$	−5.07634	+	8.79248i	−0.180723	+	0.313021i
$790$	11.6138	+	20.1158i	0.413202	+	0.715687i
$791$	3.22977	−	1.86471i	0.114837	−	0.0663014i
$792$	−7.45934			−0.265056
$793$	25.1028	+	20.5325i	0.891428	+	0.729129i
$794$	−13.3079			−0.472278
$795$	70.3375	−	40.6094i	2.49461	−	1.44027i
$796$	5.49270	+	9.51364i	0.194684	+	0.337202i
$797$	−7.78060	+	13.4764i	−0.275603	+	0.477358i	−0.970287	−	0.241957i	$-0.922211\pi$
$797$	−7.78060	+	13.4764i	−0.275603	+	0.477358i	0.694684	+	0.719315i	$0.255544\pi$
$798$			106.085i			3.75536i
$799$	7.12944	+	4.11618i	0.252221	+	0.145620i
$800$	−0.609337	−	0.351801i	−0.0215433	−	0.0124380i
$801$		−	95.2369i		−	3.36503i
$802$	−5.20242	+	9.01085i	−0.183704	+	0.318184i
$803$	3.50155	+	6.06486i	0.123567	+	0.214024i
$804$	−24.0352	+	13.8767i	−0.847657	+	0.489395i
$805$	10.0243			0.353312
$806$	8.83297	−	3.34106i	0.311128	−	0.117684i
$807$	12.8601			0.452698
$808$	13.1008	−	7.56376i	0.460885	−	0.266092i
$809$	−22.7081	−	39.3316i	−0.798374	−	1.38282i	−0.920674	−	0.390331i	$-0.872360\pi$
$809$	−22.7081	−	39.3316i	−0.798374	−	1.38282i	0.122300	−	0.992493i	$-0.460973\pi$
$810$	−28.9736	+	50.1838i	−1.01803	+	1.76328i
$811$			3.39071i			0.119064i	0.998226	+	0.0595320i	$0.0189608\pi$
$811$			3.39071i			0.119064i	−0.998226	+	0.0595320i	$0.981039\pi$
$812$	−7.19892	−	4.15630i	−0.252633	−	0.145858i
$813$	32.1004	+	18.5332i	1.12581	+	0.649987i
$814$			1.17157i			0.0410636i
$815$	22.3833	−	38.7690i	0.784053	−	1.35802i
$816$	1.86628	+	3.23250i	0.0653329	+	0.113160i
$817$	41.3805	−	23.8910i	1.44772	−	0.835841i
$818$	19.4475			0.679967
$819$	37.2869	+	98.5776i	1.30291	+	3.44458i
$820$	−13.1195			−0.458152
$821$	8.03450	−	4.63872i	0.280406	−	0.161893i	−0.353201	−	0.935547i	$-0.614907\pi$
$821$	8.03450	−	4.63872i	0.280406	−	0.161893i	0.633607	+	0.773655i	$0.281574\pi$
$822$	30.4995	+	52.8266i	1.06379	+	1.84254i
$823$	15.3830	−	26.6441i	0.536217	−	0.928754i	−0.462887	−	0.886417i	$-0.653186\pi$
$823$	15.3830	−	26.6441i	0.536217	−	0.928754i	0.999103	−	0.0423370i	$-0.0134803\pi$
$824$			9.09330i			0.316780i
$825$	1.97065	+	1.13776i	0.0686093	+	0.0396116i
$826$	−21.8775	−	12.6310i	−0.761215	−	0.439488i
$827$		−	13.0368i		−	0.453333i	−0.973972	−	0.226666i	$-0.927217\pi$
$827$		−	13.0368i		−	0.453333i	0.973972	−	0.226666i	$-0.0727827\pi$
$828$	3.99493	−	6.91942i	0.138833	−	0.240466i
$829$	−14.5790	−	25.2515i	−0.506348	−	0.877021i	−0.999973	−	0.00734588i	$-0.997662\pi$
$829$	−14.5790	−	25.2515i	−0.506348	−	0.877021i	0.493625	−	0.869675i	$-0.335672\pi$
$830$	−14.8964	+	8.60046i	−0.517063	+	0.298526i
$831$	8.78332			0.304690
$832$	−0.581485	+	3.55835i	−0.0201594	+	0.123364i
$833$	9.64425			0.334153
$834$	27.7682	−	16.0320i	0.961533	−	0.555141i
$835$	−1.70047	−	2.94530i	−0.0588472	−	0.101926i
$836$	4.18531	−	7.24916i	0.144752	−	0.250718i
$837$		−	37.7742i		−	1.30567i
$838$	−11.0308	−	6.36864i	−0.381053	−	0.220001i
$839$	−10.0023	−	5.77483i	−0.345318	−	0.199369i	0.317303	−	0.948324i	$-0.397223\pi$
$839$	−10.0023	−	5.77483i	−0.345318	−	0.199369i	−0.662621	+	0.748955i	$0.730556\pi$
$840$			30.2670i			1.04431i
$841$	12.2501	−	21.2178i	0.422418	−	0.731650i
$842$	−10.6449	−	18.4376i	−0.366849	−	0.635401i
$843$	26.9355	−	15.5512i	0.927707	−	0.535612i
$844$	−1.38500			−0.0476736
$845$	9.88308	−	29.4318i	0.339988	−	1.01249i
$846$	53.2071			1.82930
$847$	3.39370	−	1.95936i	0.116609	−	0.0673242i
$848$	−5.25774	−	9.10668i	−0.180552	−	0.312725i
$849$	15.0265	−	26.0266i	0.515708	−	0.893232i
$850$		−	0.812049i		−	0.0278530i
$851$	−1.08677	−	0.627448i	−0.0372540	−	0.0215086i
$852$	−4.24609	−	2.45148i	−0.145469	−	0.0839864i
$853$			47.4969i			1.62626i	0.582079	+	0.813132i	$0.302239\pi$
$853$			47.4969i			1.62626i	−0.582079	+	0.813132i	$0.697761\pi$
$854$	17.6236	−	30.5250i	0.603067	−	1.04454i
$855$	−74.5594	−	129.141i	−2.54988	−	4.41652i
$856$	−1.51400	+	0.874109i	−0.0517475	+	0.0298764i
$857$	−24.1917			−0.826372			−0.413186	−	0.910647i	$-0.635584\pi$
$857$	−24.1917			−0.826372			−0.413186	+	0.910647i	$0.635584\pi$
$858$	1.88058	−	11.5080i	0.0642018	−	0.392878i
$859$	−41.4686			−1.41489			−0.707446	−	0.706768i	$-0.750153\pi$
$859$	−41.4686			−1.41489			−0.707446	+	0.706768i	$0.750153\pi$
$860$	11.8063	−	6.81635i	0.402590	−	0.232436i
$861$	34.8102	+	60.2931i	1.18633	+	2.05478i
$862$	−17.7747	+	30.7867i	−0.605410	+	1.04860i
$863$		−	20.3423i		−	0.692460i	−0.938150	−	0.346230i	$-0.887462\pi$
$863$		−	20.3423i		−	0.692460i	0.938150	−	0.346230i	$-0.112538\pi$
$864$	12.4897	+	7.21096i	0.424910	+	0.245322i
$865$	25.9055	+	14.9565i	0.880813	+	0.508538i
$866$		−	19.5179i		−	0.663245i
$867$	25.3358	−	43.8830i	0.860450	−	1.49034i
$868$	−5.13198	−	8.88885i	−0.174191	−	0.301707i
$869$	−8.42290	+	4.86297i	−0.285727	+	0.164965i
$870$	16.3840			0.555470
$871$	−10.9466	−	28.9401i	−0.370911	−	0.980598i
$872$	−5.31756			−0.180075
$873$	108.522	−	62.6552i	3.67292	−	2.12056i
$874$	4.48297	+	7.76473i	0.151639	+	0.262646i
$875$	−20.1045	+	34.8219i	−0.679655	+	1.17720i
$876$		−	22.6486i		−	0.765227i
$877$	13.0950	+	7.56043i	0.442188	+	0.255297i	0.704525	−	0.709679i	$-0.251160\pi$
$877$	13.0950	+	7.56043i	0.442188	+	0.255297i	−0.262337	+	0.964976i	$0.584493\pi$
$878$	7.96683	+	4.59965i	0.268867	+	0.155231i
$879$			109.383i			3.68941i
$880$	1.19411	−	2.06826i	0.0402535	−	0.0697210i
$881$	10.9581	+	18.9800i	0.369188	+	0.639452i	0.989439	−	0.144952i	$-0.0463027\pi$
$881$	10.9581	+	18.9800i	0.369188	+	0.639452i	−0.620251	+	0.784403i	$0.712969\pi$
$882$	53.9815	−	31.1662i	1.81765	−	1.04942i
$883$	42.5451			1.43176			0.715878	−	0.698225i	$-0.246027\pi$
$883$	42.5451			1.43176			0.715878	+	0.698225i	$0.246027\pi$
$884$	−3.89215	+	1.47220i	−0.130907	+	0.0495156i
$885$	49.7909			1.67370
$886$	8.03208	−	4.63732i	0.269843	−	0.155794i
$887$	−14.3781	−	24.9036i	−0.482769	−	0.836181i	0.517035	−	0.855964i	$-0.327036\pi$
$887$	−14.3781	−	24.9036i	−0.482769	−	0.836181i	−0.999804	+	0.0197834i	$0.993702\pi$
$888$	1.89449	−	3.28135i	0.0635748	−	0.110115i
$889$		−	20.9667i		−	0.703199i
$890$	26.4064	+	15.2458i	0.885146	+	0.511039i
$891$	−21.0130	−	12.1319i	−0.703963	−	0.406433i
$892$			8.36542i			0.280095i
$893$	−29.8536	+	51.7079i	−0.999012	+	1.73034i
$894$	−24.7223	−	42.8203i	−0.826839	−	1.43213i
$895$	5.60525	−	3.23619i	0.187363	−	0.108174i
$896$	3.91871			0.130915
$897$	9.66790	+	7.90770i	0.322802	+	0.264031i
$898$	−6.53849			−0.218192
$899$	−4.81167	+	2.77802i	−0.160478	+	0.0926522i
$900$	−2.62420	−	4.54526i	−0.0874735	−	0.151509i
$901$	6.06813	−	10.5103i	0.202159	−	0.350149i
$902$		−	5.49341i		−	0.182910i
$903$	−62.6518	−	36.1720i	−2.08492	−	1.20373i
$904$	0.824192	+	0.475848i	0.0274122	+	0.0158265i
$905$			7.07690i			0.235244i
$906$	1.19940	−	2.07742i	0.0398473	−	0.0690175i
$907$	−21.7361	−	37.6480i	−0.721736	−	1.25008i	−0.960304	−	0.278957i	$-0.910011\pi$
$907$	−21.7361	−	37.6480i	−0.721736	−	1.25008i	0.238568	−	0.971126i	$-0.423322\pi$
$908$	0.569919	−	0.329043i	0.0189134	−	0.0109197i
$909$	112.841			3.74271
$910$	−33.3017	−	5.44197i	−1.10394	−	0.180400i
$911$	−20.1691			−0.668232			−0.334116	−	0.942532i	$-0.608438\pi$
$911$	−20.1691			−0.668232			−0.334116	+	0.942532i	$0.608438\pi$
$912$	−23.4444	+	13.5357i	−0.776323	+	0.448210i
$913$	−3.60120	−	6.23746i	−0.119182	−	0.206430i
$914$	−0.125334	+	0.217086i	−0.00414570	+	0.00718056i
$915$			69.4717i			2.29666i
$916$	4.51436	+	2.60636i	0.149158	+	0.0861167i
$917$	−23.5176	−	13.5779i	−0.776621	−	0.448382i
$918$			16.6448i			0.549360i
$919$	20.3495	−	35.2464i	0.671269	−	1.16267i	−0.306276	−	0.951943i	$-0.599083\pi$
$919$	20.3495	−	35.2464i	0.671269	−	1.16267i	0.977545	−	0.210729i	$-0.0675837\pi$
$920$	1.27904	+	2.21536i	0.0421686	+	0.0730381i
$921$	18.9850	−	10.9610i	0.625578	−	0.361178i
$922$	19.4491			0.640523
$923$	3.46072	−	4.23105i	0.113911	−	0.139267i
$924$	−12.6735			−0.416926
$925$	−0.713883	+	0.412160i	−0.0234723	+	0.0135517i
$926$	6.05721	+	10.4914i	0.199052	+	0.344769i
$927$	−33.9150	+	58.7425i	−1.11391	+	1.92936i
$928$		−	2.12126i		−	0.0696337i
$929$	12.1067	+	6.98982i	0.397209	+	0.229328i	0.685279	−	0.728281i	$-0.259680\pi$
$929$	12.1067	+	6.98982i	0.397209	+	0.229328i	−0.288070	+	0.957609i	$0.593014\pi$
$930$	17.5198	+	10.1151i	0.574497	+	0.331686i
$931$			69.9472i			2.29243i
$932$	−4.41377	+	7.64487i	−0.144578	+	0.250416i
$933$	−20.1785	−	34.9502i	−0.660614	−	1.14422i
$934$	6.65808	−	3.84404i	0.217859	−	0.125781i
$935$	2.75632			0.0901413
$936$	−17.0279	+	20.8181i	−0.556573	+	0.680462i
$937$	−36.9852			−1.20825			−0.604126	−	0.796889i	$-0.706478\pi$
$937$	−36.9852			−1.20825			−0.604126	+	0.796889i	$0.706478\pi$
$938$	−29.1232	+	16.8143i	−0.950906	+	0.549006i
$939$	20.2863	+	35.1369i	0.662018	+	1.14665i
$940$	−8.51754	+	14.7528i	−0.277811	+	0.481184i
$941$			39.7092i			1.29448i	0.762286	+	0.647241i	$0.224077\pi$
$941$			39.7092i			1.29448i	−0.762286	+	0.647241i	$0.775923\pi$
$942$	−64.9878	−	37.5207i	−2.11742	−	1.22249i
$943$	5.09578	+	2.94205i	0.165941	+	0.0958064i
$944$		−	6.44649i		−	0.209815i
$945$	−67.4855	+	116.888i	−2.19530	+	3.80238i
$946$	2.85415	+	4.94354i	0.0927966	+	0.160728i
$947$	42.8699	−	24.7510i	1.39309	−	0.804298i	0.399430	−	0.916764i	$-0.369208\pi$
$947$	42.8699	−	24.7510i	1.39309	−	0.804298i	0.993656	+	0.112465i	$0.0358747\pi$
$948$	31.4545			1.02160
$949$	24.9195	+	4.07219i	0.808920	+	0.132189i
$950$	5.88958			0.191083
$951$	−61.0446	+	35.2441i	−1.97951	+	1.14287i
$952$	2.26135	+	3.91678i	0.0732908	+	0.126943i
$953$	−16.8221	+	29.1367i	−0.544920	+	0.943829i	0.453692	+	0.891159i	$0.350107\pi$
$953$	−16.8221	+	29.1367i	−0.544920	+	0.943829i	−0.998612	+	0.0526704i	$0.983227\pi$
$954$		−	78.4386i		−	2.53954i
$955$	−22.2936	−	12.8712i	−0.721403	−	0.416502i
$956$	−6.32933	−	3.65424i	−0.204705	−	0.118187i
$957$			6.86034i			0.221763i
$958$	6.87030	−	11.8997i	0.221969	−	0.384462i
$959$	36.9559	+	64.0094i	1.19337	+	2.06697i
$960$	−6.68894	+	3.86186i	−0.215885	+	0.124641i
$961$	24.1397			0.778700
$962$	3.26972	+	2.67442i	0.105420	+	0.0862266i
$963$	−13.0405			−0.420226
$964$	−13.4873	+	7.78691i	−0.434398	+	0.250800i
$965$	25.0077	+	43.3147i	0.805027	+	1.39435i
$966$	6.78740	−	11.7561i	0.218381	−	0.378247i
$967$			4.49705i			0.144615i	0.997382	+	0.0723077i	$0.0230364\pi$
$967$			4.49705i			0.144615i	−0.997382	+	0.0723077i	$0.976964\pi$
$968$	0.866025	+	0.500000i	0.0278351	+	0.0160706i
$969$	−27.0580	−	15.6219i	−0.869227	−	0.501848i
$970$			40.1201i			1.28818i
$971$	−17.8306	+	30.8834i	−0.572210	+	0.991097i	0.424129	+	0.905602i	$0.360580\pi$
$971$	−17.8306	+	30.8834i	−0.572210	+	0.991097i	−0.996339	+	0.0854947i	$0.972753\pi$
$972$	17.6027	+	30.4888i	0.564608	+	0.977929i
$973$	33.6464	−	19.4257i	1.07865	−	0.622761i
$974$	4.40895			0.141272
$975$	7.67386	−	2.90263i	0.245760	−	0.0929587i
$976$	8.99459			0.287910
$977$	−42.3506	+	24.4511i	−1.35492	+	0.782261i	−0.988933	−	0.148361i	$-0.952600\pi$
$977$	−42.3506	+	24.4511i	−1.35492	+	0.782261i	−0.365982	+	0.930622i	$0.619267\pi$
$978$	−30.3111	−	52.5003i	−0.969242	−	1.67878i
$979$	−6.38373	+	11.0570i	−0.204025	+	0.353382i
$980$			19.9567i			0.637492i
$981$	−34.3513	−	19.8327i	−1.09675	−	0.633211i
$982$	16.3875	+	9.46134i	0.522947	+	0.301923i
$983$			48.2431i			1.53872i	0.638817	+	0.769359i	$0.279424\pi$
$983$			48.2431i			1.53872i	−0.638817	+	0.769359i	$0.720576\pi$
$984$	−8.88309	+	15.3860i	−0.283183	+	0.490486i
$985$	−16.8392	−	29.1663i	−0.536541	−	0.929315i
$986$	2.12021	−	1.22411i	0.0675213	−	0.0389835i
$987$	90.3992			2.87744
$988$	−10.6775	−	28.2288i	−0.339697	−	0.898077i
$989$	−6.11429			−0.194423
$990$	15.4279	−	8.90728i	0.490330	−	0.283092i
$991$	18.0962	+	31.3435i	0.574844	+	0.995658i	0.996059	+	0.0886976i	$0.0282705\pi$
$991$	18.0962	+	31.3435i	0.574844	+	0.995658i	−0.421215	+	0.906961i	$0.638396\pi$
$992$	1.30961	−	2.26831i	0.0415801	−	0.0720189i
$993$		−	108.641i		−	3.44761i
$994$	−5.14494	−	2.97043i	−0.163188	−	0.0942165i
$995$	−22.7207	−	13.1178i	−0.720294	−	0.415862i
$996$			23.2932i			0.738074i
$997$	−10.5413	+	18.2580i	−0.333845	+	0.578236i	−0.983262	−	0.182196i	$-0.941679\pi$
$997$	−10.5413	+	18.2580i	−0.333845	+	0.578236i	0.649417	+	0.760432i	$0.275013\pi$
$998$	8.26423	+	14.3141i	0.261600	+	0.453104i
$999$	14.6326	−	8.44816i	0.462956	−	0.267288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	286.2.j.b.23.1	✓	16
13.2	odd	12		3718.2.a.bn.1.8		8
13.4	even	6	inner	286.2.j.b.199.1	yes	16
13.11	odd	12		3718.2.a.bo.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
286.2.j.b.23.1	✓	16	1.1	even	1	trivial
286.2.j.b.199.1	yes	16	13.4	even	6	inner
3718.2.a.bn.1.8		8	13.2	odd	12
3718.2.a.bo.1.8		8	13.11	odd	12

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:	\( N \)	\(=\)	\( 286 = 2 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	286.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.61705 - 2.80080i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.38822i q^{5} +(2.80080 + 1.61705i) q^{6} +(3.39370 + 1.95936i) q^{7} +1.00000i q^{8} +(-3.72967 + 6.45998i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.61705 - 2.80080i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.38822i q^{5} +(2.80080 + 1.61705i) q^{6} +(3.39370 + 1.95936i) q^{7} +1.00000i q^{8} +(-3.72967 + 6.45998i) q^{9} +(-1.19411 - 2.06826i) q^{10} +(0.866025 - 0.500000i) q^{11} -3.23409 q^{12} +(0.581485 - 3.55835i) q^{13} -3.91871 q^{14} +(6.68894 - 3.86186i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.577065 - 0.999507i) q^{17} -7.45934i q^{18} +(7.24916 + 4.18531i) q^{19} +(2.06826 + 1.19411i) q^{20} -12.6735i q^{21} +(-0.500000 + 0.866025i) q^{22} +(-0.535560 - 0.927618i) q^{23} +(2.80080 - 1.61705i) q^{24} -0.703602 q^{25} +(1.27560 + 3.37237i) q^{26} +14.4219 q^{27} +(3.39370 - 1.95936i) q^{28} +(-1.06063 - 1.83706i) q^{29} +(-3.86186 + 6.68894i) q^{30} -2.61922i q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.80080 - 1.61705i) q^{33} +1.15413i q^{34} +(-4.67937 + 8.10491i) q^{35} +(3.72967 + 6.45998i) q^{36} +(1.01461 - 0.585786i) q^{37} -8.37061 q^{38} +(-10.9065 + 4.12539i) q^{39} -2.38822 q^{40} +(-4.75743 + 2.74670i) q^{41} +(6.33673 + 10.9755i) q^{42} +(2.85415 - 4.94354i) q^{43} -1.00000i q^{44} +(-15.4279 - 8.90728i) q^{45} +(0.927618 + 0.535560i) q^{46} +7.13295i q^{47} +(-1.61705 + 2.80080i) q^{48} +(4.17814 + 7.23676i) q^{49} +(0.609337 - 0.351801i) q^{50} -3.73256 q^{51} +(-2.79088 - 2.28276i) q^{52} +10.5155 q^{53} +(-12.4897 + 7.21096i) q^{54} +(1.19411 + 2.06826i) q^{55} +(-1.95936 + 3.39370i) q^{56} -27.0713i q^{57} +(1.83706 + 1.06063i) q^{58} +(5.58283 + 3.22325i) q^{59} -7.72372i q^{60} +(-4.49730 + 7.78954i) q^{61} +(1.30961 + 2.26831i) q^{62} +(-25.3148 + 14.6155i) q^{63} -1.00000 q^{64} +(8.49813 + 1.38871i) q^{65} +3.23409 q^{66} +(7.43183 - 4.29077i) q^{67} +(-0.577065 - 0.999507i) q^{68} +(-1.73205 + 3.00000i) q^{69} -9.35875i q^{70} +(1.31292 + 0.758013i) q^{71} +(-6.45998 - 3.72967i) q^{72} +7.00309i q^{73} +(-0.585786 + 1.01461i) q^{74} +(1.13776 + 1.97065i) q^{75} +(7.24916 - 4.18531i) q^{76} +3.91871 q^{77} +(7.38264 - 9.02596i) q^{78} -9.72593 q^{79} +(2.06826 - 1.19411i) q^{80} +(-12.1319 - 21.0130i) q^{81} +(2.74670 - 4.75743i) q^{82} -7.20240i q^{83} +(-10.9755 - 6.33673i) q^{84} +(2.38704 + 1.37816i) q^{85} +5.70831i q^{86} +(-3.43017 + 5.94123i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-11.0570 + 6.38373i) q^{89} +17.8146 q^{90} +(8.94546 - 10.9367i) q^{91} -1.07112 q^{92} +(-7.33592 + 4.23540i) q^{93} +(-3.56648 - 6.17732i) q^{94} +(-9.99544 + 17.3126i) q^{95} -3.23409i q^{96} +(-14.5485 - 8.39957i) q^{97} +(-7.23676 - 4.17814i) q^{98} +7.45934i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 8 q^{4} - 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 + 8 * q^4 - 20 * q^9	\( 16 q - 4 q^{3} + 8 q^{4} - 20 q^{9} - 2 q^{10} - 8 q^{12} + 10 q^{13} + 16 q^{14} - 30 q^{15} - 8 q^{16} + 14 q^{17} + 6 q^{19} - 8 q^{22} + 14 q^{23} - 12 q^{25} + 4 q^{26} + 20 q^{27} - 2 q^{29} - 6 q^{30} - 10 q^{35} + 20 q^{36} - 24 q^{38} - 14 q^{39} - 4 q^{40} - 48 q^{41} + 6 q^{42} + 2 q^{43} - 12 q^{45} + 12 q^{46} - 4 q^{48} + 40 q^{49} + 60 q^{51} + 2 q^{52} + 24 q^{53} - 18 q^{54} + 2 q^{55} + 8 q^{56} - 18 q^{58} + 54 q^{59} - 22 q^{61} + 14 q^{62} - 54 q^{63} - 16 q^{64} + 54 q^{65} + 8 q^{66} - 12 q^{67} - 14 q^{68} - 36 q^{71} - 12 q^{72} + 6 q^{74} + 40 q^{75} + 6 q^{76} - 16 q^{77} + 6 q^{78} - 24 q^{79} - 44 q^{81} + 6 q^{82} - 54 q^{84} + 30 q^{85} - 48 q^{87} + 8 q^{88} - 30 q^{89} + 108 q^{90} + 46 q^{91} + 28 q^{92} - 72 q^{93} + 6 q^{94} - 8 q^{95} - 90 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^3 + 8 * q^4 - 20 * q^9 - 2 * q^10 - 8 * q^12 + 10 * q^13 + 16 * q^14 - 30 * q^15 - 8 * q^16 + 14 * q^17 + 6 * q^19 - 8 * q^22 + 14 * q^23 - 12 * q^25 + 4 * q^26 + 20 * q^27 - 2 * q^29 - 6 * q^30 - 10 * q^35 + 20 * q^36 - 24 * q^38 - 14 * q^39 - 4 * q^40 - 48 * q^41 + 6 * q^42 + 2 * q^43 - 12 * q^45 + 12 * q^46 - 4 * q^48 + 40 * q^49 + 60 * q^51 + 2 * q^52 + 24 * q^53 - 18 * q^54 + 2 * q^55 + 8 * q^56 - 18 * q^58 + 54 * q^59 - 22 * q^61 + 14 * q^62 - 54 * q^63 - 16 * q^64 + 54 * q^65 + 8 * q^66 - 12 * q^67 - 14 * q^68 - 36 * q^71 - 12 * q^72 + 6 * q^74 + 40 * q^75 + 6 * q^76 - 16 * q^77 + 6 * q^78 - 24 * q^79 - 44 * q^81 + 6 * q^82 - 54 * q^84 + 30 * q^85 - 48 * q^87 + 8 * q^88 - 30 * q^89 + 108 * q^90 + 46 * q^91 + 28 * q^92 - 72 * q^93 + 6 * q^94 - 8 * q^95 - 90 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

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