LMFDB - Embedded newform 847.2.f.v.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.751051 + 2.31150i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.v.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96628 - 1.42858i) q^{2} +(0.443194 - 1.36401i) q^{3} +(1.20736 + 3.71587i) q^{4} +(-1.01825 + 0.739805i) q^{5} +(-2.82005 + 2.04888i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.43233 - 4.40826i) q^{8} +(0.762946 + 0.554312i) q^{9} +O(q^{10})$	\(q+(-1.96628 - 1.42858i) q^{2} +(0.443194 - 1.36401i) q^{3} +(1.20736 + 3.71587i) q^{4} +(-1.01825 + 0.739805i) q^{5} +(-2.82005 + 2.04888i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.43233 - 4.40826i) q^{8} +(0.762946 + 0.554312i) q^{9} +3.05904 q^{10} +5.60359 q^{12} +(-2.57131 - 1.86816i) q^{13} +(-0.751051 + 2.31150i) q^{14} +(0.557818 + 1.71679i) q^{15} +(-2.79210 + 2.02858i) q^{16} +(4.79276 - 3.48215i) q^{17} +(-0.708281 - 2.17986i) q^{18} +(-0.884474 + 2.72213i) q^{19} +(-3.97842 - 2.89049i) q^{20} -1.43421 q^{21} +6.76343 q^{23} +(-5.37811 - 3.90743i) q^{24} +(-1.05555 + 3.24866i) q^{25} +(2.38707 + 7.34665i) q^{26} +(4.57511 - 3.32401i) q^{27} +(3.16091 - 2.29654i) q^{28} +(-1.38918 - 4.27547i) q^{29} +(1.35575 - 4.17257i) q^{30} +(-7.86972 - 5.71769i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(1.01825 + 0.739805i) q^{35} +(-1.13860 + 3.50426i) q^{36} +(-1.68567 - 5.18797i) q^{37} +(5.62791 - 4.08892i) q^{38} +(-3.68778 + 2.67933i) q^{39} +(1.80277 + 5.54837i) q^{40} +(0.0971810 - 0.299092i) q^{41} +(2.82005 + 2.04888i) q^{42} +0.132562 q^{43} -1.18696 q^{45} +(-13.2988 - 9.66213i) q^{46} +(2.89705 - 8.91620i) q^{47} +(1.52956 + 4.70751i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.71650 - 4.87983i) q^{50} +(-2.62556 - 8.08065i) q^{51} +(3.83736 - 11.8102i) q^{52} +(-3.52078 - 2.55800i) q^{53} -13.7446 q^{54} -4.63512 q^{56} +(3.32102 + 2.41286i) q^{57} +(-3.37635 + 10.3913i) q^{58} +(-2.14670 - 6.60685i) q^{59} +(-5.70587 + 4.14556i) q^{60} +(-1.98383 + 1.44134i) q^{61} +(7.30586 + 22.4851i) q^{62} +(0.291419 - 0.896896i) q^{63} +(7.31882 + 5.31744i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(18.7258 + 13.6051i) q^{68} +(2.99751 - 9.22539i) q^{69} +(-0.945296 - 2.90932i) q^{70} +(0.0943396 - 0.0685417i) q^{71} +(3.53634 - 2.56930i) q^{72} +(-0.190055 - 0.584930i) q^{73} +(-4.09695 + 12.6091i) q^{74} +(3.96340 + 2.87958i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(6.90033 + 5.01339i) q^{79} +(1.34232 - 4.13122i) q^{80} +(-1.63207 - 5.02300i) q^{81} +(-0.618364 + 0.449267i) q^{82} +(0.768997 - 0.558709i) q^{83} +(-1.73160 - 5.32933i) q^{84} +(-2.30414 + 7.09142i) q^{85} +(-0.260654 - 0.189376i) q^{86} -6.44746 q^{87} +10.0552 q^{89} +(2.33388 + 1.69567i) q^{90} +(-0.982152 + 3.02275i) q^{91} +(8.16590 + 25.1320i) q^{92} +(-11.2868 + 8.20034i) q^{93} +(-18.4339 + 13.3930i) q^{94} +(-1.11323 - 3.42616i) q^{95} +(-0.390979 + 1.20331i) q^{96} +(-14.2201 - 10.3315i) q^{97} +2.43045 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.96628	−	1.42858i	−1.39037	−	1.01016i	−0.995825	−	0.0912842i	$-0.970903\pi$
$2$	−1.96628	−	1.42858i	−1.39037	−	1.01016i	−0.394543	−	0.918877i	$-0.629097\pi$
$3$	0.443194	−	1.36401i	0.255878	−	0.787512i	−0.737777	−	0.675044i	$-0.764124\pi$
$3$	0.443194	−	1.36401i	0.255878	−	0.787512i	0.993655	−	0.112468i	$-0.0358755\pi$
$4$	1.20736	+	3.71587i	0.603680	+	1.85794i
$5$	−1.01825	+	0.739805i	−0.455377	+	0.330851i	−0.791715	−	0.610891i	$-0.790812\pi$
$5$	−1.01825	+	0.739805i	−0.455377	+	0.330851i	0.336338	+	0.941741i	$0.390812\pi$
$6$	−2.82005	+	2.04888i	−1.15128	+	0.836454i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	1.43233	−	4.40826i	0.506405	−	1.55855i
$9$	0.762946	+	0.554312i	0.254315	+	0.184771i
$10$	3.05904			0.967354
$11$		0			0
$11$		0			0
$12$	5.60359			1.61762
$13$	−2.57131	−	1.86816i	−0.713152	−	0.518135i	0.171037	−	0.985265i	$-0.445288\pi$
$13$	−2.57131	−	1.86816i	−0.713152	−	0.518135i	−0.884189	+	0.467129i	$0.845288\pi$
$14$	−0.751051	+	2.31150i	−0.200727	+	0.617774i
$15$	0.557818	+	1.71679i	0.144028	+	0.443272i
$16$	−2.79210	+	2.02858i	−0.698026	+	0.507145i
$17$	4.79276	−	3.48215i	1.16242	−	0.844544i	0.172334	−	0.985039i	$-0.444869\pi$
$17$	4.79276	−	3.48215i	1.16242	−	0.844544i	0.990082	+	0.140494i	$0.0448691\pi$
$18$	−0.708281	−	2.17986i	−0.166943	−	0.513799i
$19$	−0.884474	+	2.72213i	−0.202912	+	0.624500i	0.796880	+	0.604137i	$0.206482\pi$
$19$	−0.884474	+	2.72213i	−0.202912	+	0.624500i	−0.999793	+	0.0203626i	$0.993518\pi$
$20$	−3.97842	−	2.89049i	−0.889602	−	0.646333i
$21$	−1.43421			−0.312969
$22$		0			0
$23$	6.76343			1.41027			0.705136	−	0.709072i	$-0.250886\pi$
$23$	6.76343			1.41027			0.705136	+	0.709072i	$0.250886\pi$
$24$	−5.37811	−	3.90743i	−1.09780	−	0.797600i
$25$	−1.05555	+	3.24866i	−0.211111	+	0.649733i
$26$	2.38707	+	7.34665i	0.468144	+	1.44080i
$27$	4.57511	−	3.32401i	0.880481	−	0.639707i
$28$	3.16091	−	2.29654i	0.597356	−	0.434004i
$29$	−1.38918	−	4.27547i	−0.257965	−	0.793934i	−0.993231	−	0.116156i	$-0.962943\pi$
$29$	−1.38918	−	4.27547i	−0.257965	−	0.793934i	0.735266	−	0.677779i	$-0.237057\pi$
$30$	1.35575	−	4.17257i	0.247525	−	0.761803i
$31$	−7.86972	−	5.71769i	−1.41344	−	1.02693i	−0.992811	−	0.119697i	$-0.961808\pi$
$31$	−7.86972	−	5.71769i	−1.41344	−	1.02693i	−0.420634	−	0.907231i	$-0.638192\pi$
$32$	−0.882184			−0.155950
$33$		0			0
$34$	−14.3984			−2.46931
$35$	1.01825	+	0.739805i	0.172116	+	0.125050i
$36$	−1.13860	+	3.50426i	−0.189767	+	0.584044i
$37$	−1.68567	−	5.18797i	−0.277123	−	0.852897i	−0.988650	−	0.150238i	$-0.951996\pi$
$37$	−1.68567	−	5.18797i	−0.277123	−	0.852897i	0.711527	−	0.702659i	$-0.248004\pi$
$38$	5.62791	−	4.08892i	0.912968	−	0.663310i
$39$	−3.68778	+	2.67933i	−0.590518	+	0.429036i
$40$	1.80277	+	5.54837i	0.285044	+	0.877274i
$41$	0.0971810	−	0.299092i	0.0151771	−	0.0467104i	−0.943181	−	0.332279i	$-0.892182\pi$
$41$	0.0971810	−	0.299092i	0.0151771	−	0.0467104i	0.958358	+	0.285569i	$0.0921824\pi$
$42$	2.82005	+	2.04888i	0.435143	+	0.316150i
$43$	0.132562			0.0202155			0.0101078	−	0.999949i	$-0.496783\pi$
$43$	0.132562			0.0202155			0.0101078	+	0.999949i	$0.496783\pi$
$44$		0			0
$45$	−1.18696			−0.176941
$46$	−13.2988	−	9.66213i	−1.96080	−	1.42460i
$47$	2.89705	−	8.91620i	0.422578	−	1.30056i	−0.482716	−	0.875777i	$-0.660350\pi$
$47$	2.89705	−	8.91620i	0.422578	−	1.30056i	0.905294	−	0.424785i	$-0.139650\pi$
$48$	1.52956	+	4.70751i	0.220774	+	0.679471i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	6.71650	−	4.87983i	0.949857	−	0.690112i
$51$	−2.62556	−	8.08065i	−0.367652	−	1.13152i
$52$	3.83736	−	11.8102i	0.532147	−	1.63778i
$53$	−3.52078	−	2.55800i	−0.483616	−	0.351368i	0.319108	−	0.947718i	$-0.396617\pi$
$53$	−3.52078	−	2.55800i	−0.483616	−	0.351368i	−0.802724	+	0.596351i	$0.796617\pi$
$54$	−13.7446			−1.87040
$55$		0			0
$56$	−4.63512			−0.619393
$57$	3.32102	+	2.41286i	0.439880	+	0.319592i
$58$	−3.37635	+	10.3913i	−0.443336	+	1.36445i
$59$	−2.14670	−	6.60685i	−0.279476	−	0.860139i	−0.988000	−	0.154452i	$-0.950639\pi$
$59$	−2.14670	−	6.60685i	−0.279476	−	0.860139i	0.708524	−	0.705686i	$-0.249361\pi$
$60$	−5.70587	+	4.14556i	−0.736625	+	0.535190i
$61$	−1.98383	+	1.44134i	−0.254004	+	0.184545i	−0.707499	−	0.706714i	$-0.750177\pi$
$61$	−1.98383	+	1.44134i	−0.254004	+	0.184545i	0.453495	+	0.891259i	$0.350177\pi$
$62$	7.30586	+	22.4851i	0.927845	+	2.85561i
$63$	0.291419	−	0.896896i	0.0367154	−	0.112998i
$64$	7.31882	+	5.31744i	0.914853	+	0.664679i
$65$	4.00032			0.496179
$66$		0			0
$67$	−9.41987			−1.15082			−0.575410	−	0.817865i	$-0.695158\pi$
$67$	−9.41987			−1.15082			−0.575410	+	0.817865i	$0.695158\pi$
$68$	18.7258	+	13.6051i	2.27084	+	1.64986i
$69$	2.99751	−	9.22539i	0.360858	−	1.11061i
$70$	−0.945296	−	2.90932i	−0.112985	−	0.347731i
$71$	0.0943396	−	0.0685417i	0.0111961	−	0.00813441i	−0.582173	−	0.813065i	$-0.697797\pi$
$71$	0.0943396	−	0.0685417i	0.0111961	−	0.00813441i	0.593369	+	0.804930i	$0.297797\pi$
$72$	3.53634	−	2.56930i	0.416762	−	0.302795i
$73$	−0.190055	−	0.584930i	−0.0222443	−	0.0684608i	0.939318	−	0.343047i	$-0.111459\pi$
$73$	−0.190055	−	0.584930i	−0.0222443	−	0.0684608i	−0.961562	+	0.274586i	$0.911459\pi$
$74$	−4.09695	+	12.6091i	−0.476261	+	1.46578i
$75$	3.96340	+	2.87958i	0.457654	+	0.332505i
$76$	−11.1830			−1.28277
$77$		0			0
$78$	11.0789			1.25443
$79$	6.90033	+	5.01339i	0.776348	+	0.564050i	0.903881	−	0.427784i	$-0.140706\pi$
$79$	6.90033	+	5.01339i	0.776348	+	0.564050i	−0.127533	+	0.991834i	$0.540706\pi$
$80$	1.34232	−	4.13122i	0.150075	−	0.461885i
$81$	−1.63207	−	5.02300i	−0.181341	−	0.558111i
$82$	−0.618364	+	0.449267i	−0.0682868	+	0.0496133i
$83$	0.768997	−	0.558709i	0.0844083	−	0.0613262i	−0.544781	−	0.838579i	$-0.683387\pi$
$83$	0.768997	−	0.558709i	0.0844083	−	0.0613262i	0.629189	+	0.777252i	$0.283387\pi$
$84$	−1.73160	−	5.32933i	−0.188933	−	0.581477i
$85$	−2.30414	+	7.09142i	−0.249919	+	0.769172i
$86$	−0.260654	−	0.189376i	−0.0281070	−	0.0204209i
$87$	−6.44746			−0.691241
$88$		0			0
$89$	10.0552			1.06585			0.532923	−	0.846164i	$-0.321094\pi$
$89$	10.0552			1.06585			0.532923	+	0.846164i	$0.321094\pi$
$90$	2.33388	+	1.69567i	0.246013	+	0.178739i
$91$	−0.982152	+	3.02275i	−0.102957	+	0.316870i
$92$	8.16590	+	25.1320i	0.851353	+	2.62020i
$93$	−11.2868	+	8.20034i	−1.17039	+	0.850336i
$94$	−18.4339	+	13.3930i	−1.90132	+	1.38139i
$95$	−1.11323	−	3.42616i	−0.114215	−	0.351516i
$96$	−0.390979	+	1.20331i	−0.0399041	+	0.122812i
$97$	−14.2201	−	10.3315i	−1.44383	−	1.04901i	−0.987224	−	0.159337i	$-0.949064\pi$
$97$	−14.2201	−	10.3315i	−1.44383	−	1.04901i	−0.456608	−	0.889668i	$-0.650936\pi$
$98$	2.43045			0.245513
$99$		0			0
$100$	−13.3461			−1.33461
$101$	−10.0934	−	7.33330i	−1.00433	−	0.729690i	−0.0413196	−	0.999146i	$-0.513156\pi$
$101$	−10.0934	−	7.33330i	−1.00433	−	0.729690i	−0.963013	+	0.269456i	$0.913156\pi$
$102$	−6.38130	+	19.6396i	−0.631843	+	1.94461i
$103$	2.53951	+	7.81581i	0.250225	+	0.770114i	0.994733	+	0.102500i	$0.0326843\pi$
$103$	2.53951	+	7.81581i	0.250225	+	0.770114i	−0.744508	+	0.667614i	$0.767316\pi$
$104$	−11.9183	+	8.65915i	−1.16869	+	0.849100i
$105$	1.46039	−	1.06103i	0.142519	−	0.103546i
$106$	3.26852	+	10.0595i	0.317466	+	0.977061i
$107$	−3.76646	+	11.5920i	−0.364117	+	1.12064i	0.586414	+	0.810011i	$0.300539\pi$
$107$	−3.76646	+	11.5920i	−0.364117	+	1.12064i	−0.950532	+	0.310627i	$0.899461\pi$
$108$	17.8754	+	12.9873i	1.72006	+	1.24970i
$109$	−0.886088			−0.0848718			−0.0424359	−	0.999099i	$-0.513512\pi$
$109$	−0.886088			−0.0848718			−0.0424359	+	0.999099i	$0.513512\pi$
$110$		0			0
$111$	−7.82353			−0.742577
$112$	2.79210	+	2.02858i	0.263829	+	0.191683i
$113$	1.40449	−	4.32257i	0.132123	−	0.406633i	−0.863008	−	0.505190i	$-0.831423\pi$
$113$	1.40449	−	4.32257i	0.132123	−	0.406633i	0.995131	+	0.0985566i	$0.0314225\pi$
$114$	−3.08307	−	9.48872i	−0.288756	−	0.888700i
$115$	−6.88689	+	5.00362i	−0.642206	+	0.466590i
$116$	14.2098	−	10.3241i	1.31935	−	0.958565i
$117$	−0.926221	−	2.85061i	−0.0856291	−	0.263539i
$118$	−5.21744	+	16.0576i	−0.480304	+	1.47823i
$119$	−4.79276	−	3.48215i	−0.439352	−	0.319208i
$120$	8.36702			0.763801
$121$		0			0
$122$	5.95984			0.539579
$123$	−0.364895	−	0.265112i	−0.0329015	−	0.0239043i
$124$	11.7446	−	36.1462i	1.05470	−	3.24602i
$125$	−3.27325	−	10.0740i	−0.292768	−	0.901047i
$126$	−1.85430	+	1.34723i	−0.165194	+	0.120021i
$127$	−6.49462	+	4.71861i	−0.576304	+	0.418709i	−0.837390	−	0.546606i	$-0.815919\pi$
$127$	−6.49462	+	4.71861i	−0.576304	+	0.418709i	0.261086	+	0.965316i	$0.415919\pi$
$128$	−6.24921	−	19.2331i	−0.552357	−	1.69998i
$129$	0.0587507	−	0.180816i	0.00517271	−	0.0159200i
$130$	−7.86574	−	5.71479i	−0.689871	−	0.501220i
$131$	−0.101461			−0.00886466			−0.00443233	−	0.999990i	$-0.501411\pi$
$131$	−0.101461			−0.00886466			−0.00443233	+	0.999990i	$0.501411\pi$
$132$		0			0
$133$	2.86222			0.248186
$134$	18.5221	+	13.4571i	1.60006	+	1.16251i
$135$	−2.19951	+	6.76938i	−0.189303	+	0.582616i
$136$	−8.48538	−	26.1153i	−0.727615	−	2.23937i
$137$	3.69243	−	2.68271i	0.315465	−	0.229199i	−0.418773	−	0.908091i	$-0.637540\pi$
$137$	3.69243	−	2.68271i	0.315465	−	0.229199i	0.734238	+	0.678892i	$0.237540\pi$
$138$	−19.0732	+	13.8575i	−1.62362	+	1.17963i
$139$	1.18209	+	3.63810i	0.100264	+	0.308580i	0.988590	−	0.150634i	$-0.0481314\pi$
$139$	1.18209	+	3.63810i	0.100264	+	0.308580i	−0.888326	+	0.459213i	$0.848131\pi$
$140$	−1.51962	+	4.67691i	−0.128431	+	0.395271i
$141$	−10.8778	−	7.90322i	−0.916080	−	0.665571i
$142$	−0.283415			−0.0237837
$143$		0			0
$144$	−3.25469			−0.271224
$145$	4.57755	+	3.32579i	0.380145	+	0.276192i
$146$	−0.461920	+	1.42164i	−0.0382288	+	0.117656i
$147$	0.443194	+	1.36401i	0.0365540	+	0.112502i
$148$	17.2426	−	12.5275i	1.41733	−	1.02975i
$149$	−3.94172	+	2.86383i	−0.322918	+	0.234614i	−0.737420	−	0.675435i	$-0.763956\pi$
$149$	−3.94172	+	2.86383i	−0.322918	+	0.234614i	0.414501	+	0.910049i	$0.363956\pi$
$150$	−3.67942	−	11.3241i	−0.300424	−	0.924609i
$151$	5.24521	−	16.1431i	0.426849	−	1.31371i	−0.474363	−	0.880329i	$-0.657322\pi$
$151$	5.24521	−	16.1431i	0.426849	−	1.31371i	0.901212	−	0.433378i	$-0.142678\pi$
$152$	10.7330	+	7.79798i	0.870561	+	0.632499i
$153$	5.58681			0.451667
$154$		0			0
$155$	12.2434			0.983410
$156$	−14.4085	−	10.4684i	−1.15361	−	0.838144i
$157$	0.693691	−	2.13496i	0.0553625	−	0.170388i	−0.919552	−	0.392969i	$-0.871448\pi$
$157$	0.693691	−	2.13496i	0.0553625	−	0.170388i	0.974914	+	0.222580i	$0.0714480\pi$
$158$	−6.40593	−	19.7154i	−0.509628	−	1.56847i
$159$	−5.04952	+	3.66869i	−0.400453	+	0.290946i
$160$	0.898287	−	0.652644i	0.0710158	−	0.0515960i
$161$	−2.09001	−	6.43240i	−0.164716	−	0.506944i
$162$	−3.96667	+	12.2082i	−0.311651	+	0.959164i
$163$	12.8126	+	9.30890i	1.00356	+	0.729129i	0.962849	−	0.270042i	$-0.0870374\pi$
$163$	12.8126	+	9.30890i	1.00356	+	0.729129i	0.0407118	+	0.999171i	$0.487037\pi$
$164$	1.22872			0.0959470
$165$		0			0
$166$	−2.31022			−0.179308
$167$	16.7803	+	12.1916i	1.29850	+	0.943413i	0.999940	−	0.0109787i	$-0.00349470\pi$
$167$	16.7803	+	12.1916i	1.29850	+	0.943413i	0.298557	+	0.954392i	$0.403495\pi$
$168$	−2.05426	+	6.32235i	−0.158489	+	0.487780i
$169$	−0.895639	−	2.75649i	−0.0688953	−	0.212038i
$170$	14.6613	−	10.6520i	1.12447	−	0.816974i
$171$	−2.18372	+	1.58656i	−0.166993	+	0.121327i
$172$	0.160050	+	0.492583i	0.0122037	+	0.0375591i
$173$	6.66099	−	20.5004i	0.506426	−	1.55862i	−0.291935	−	0.956438i	$-0.594299\pi$
$173$	6.66099	−	20.5004i	0.506426	−	1.55862i	0.798361	−	0.602180i	$-0.205701\pi$
$174$	12.6775	+	9.21075i	0.961079	+	0.698265i
$175$	3.41585			0.258214
$176$		0			0
$177$	−9.96322			−0.748881
$178$	−19.7712	−	14.3647i	−1.48192	−	1.07668i
$179$	1.47760	−	4.54758i	0.110441	−	0.339902i	−0.880528	−	0.473994i	$-0.842812\pi$
$179$	1.47760	−	4.54758i	0.110441	−	0.339902i	0.990969	+	0.134092i	$0.0428118\pi$
$180$	−1.43308	−	4.41057i	−0.106816	−	0.328745i
$181$	6.35309	−	4.61579i	0.472221	−	0.343089i	−0.326085	−	0.945340i	$-0.605730\pi$
$181$	6.35309	−	4.61579i	0.472221	−	0.343089i	0.798306	+	0.602252i	$0.205730\pi$
$182$	6.24944	−	4.54048i	0.463239	−	0.336563i
$183$	1.08678	+	3.34477i	0.0803371	+	0.247252i
$184$	9.68746	−	29.8149i	0.714169	−	2.19799i
$185$	5.55453	+	4.03560i	0.408377	+	0.296703i
$186$	33.9079			2.48625
$187$		0			0
$188$	36.6293			2.67146
$189$	−4.57511	−	3.32401i	−0.332790	−	0.241786i
$190$	−2.70564	+	8.32712i	−0.196288	+	0.604112i
$191$	−2.72871	−	8.39810i	−0.197442	−	0.607665i	−0.999939	−	0.0110091i	$-0.996496\pi$
$191$	−2.72871	−	8.39810i	−0.197442	−	0.607665i	0.802497	−	0.596656i	$-0.203504\pi$
$192$	10.4967	−	7.62630i	0.757534	−	0.550381i
$193$	20.7127	−	15.0486i	1.49093	−	1.08322i	0.517106	−	0.855921i	$-0.327009\pi$
$193$	20.7127	−	15.0486i	1.49093	−	1.08322i	0.973824	−	0.227303i	$-0.0729908\pi$
$194$	13.2012	+	40.6292i	0.947793	+	2.91701i
$195$	1.77292	−	5.45648i	0.126961	−	0.390747i
$196$	−3.16091	−	2.29654i	−0.225779	−	0.164038i
$197$	11.1977			0.797802			0.398901	−	0.916994i	$-0.369392\pi$
$197$	11.1977			0.797802			0.398901	+	0.916994i	$0.369392\pi$
$198$		0			0
$199$	−12.2503			−0.868400			−0.434200	−	0.900817i	$-0.642969\pi$
$199$	−12.2503			−0.868400			−0.434200	+	0.900817i	$0.642969\pi$
$200$	12.8090	+	9.30631i	0.905736	+	0.658056i
$201$	−4.17483	+	12.8488i	−0.294470	+	0.906285i
$202$	9.37022	+	28.8386i	0.659287	+	2.02908i
$203$	−3.63693	+	2.64238i	−0.255262	+	0.185459i
$204$	26.8567	−	19.5125i	1.88034	−	1.36615i
$205$	0.122315	+	0.376447i	0.00854285	+	0.0262922i
$206$	6.17216	−	18.9959i	0.430035	−	1.32351i
$207$	5.16013	+	3.74905i	0.358654	+	0.260577i
$208$	10.9691			0.760568
$209$		0			0
$210$	−4.38730			−0.302752
$211$	−11.5395	−	8.38393i	−0.794411	−	0.577174i	0.114858	−	0.993382i	$-0.463359\pi$
$211$	−11.5395	−	8.38393i	−0.794411	−	0.577174i	−0.909269	+	0.416208i	$0.863359\pi$
$212$	5.25434	−	16.1712i	0.360869	−	1.11064i
$213$	−0.0516809	−	0.159058i	−0.00354112	−	0.0108984i
$214$	23.9660	−	17.4123i	1.63828	−	1.19028i
$215$	−0.134982	+	0.0980700i	−0.00920568	+	0.00668832i
$216$	−8.10004	−	24.9294i	−0.551138	−	1.69623i
$217$	−3.00597	+	9.25141i	−0.204058	+	0.628027i
$218$	1.74229	+	1.26585i	0.118003	+	0.0857343i
$219$	−0.882082			−0.0596056
$220$		0			0
$221$	−18.8289			−1.26657
$222$	15.3832	+	11.1766i	1.03245	+	0.750122i
$223$	−0.915926	+	2.81893i	−0.0613350	+	0.188770i	−0.977029	−	0.213107i	$-0.931642\pi$
$223$	−0.915926	+	2.81893i	−0.0613350	+	0.188770i	0.915694	+	0.401876i	$0.131642\pi$
$224$	0.272610	+	0.839006i	0.0182145	+	0.0560585i
$225$	−2.60611	+	1.89345i	−0.173740	+	0.126230i
$226$	−8.93677	+	6.49294i	−0.594465	+	0.431904i
$227$	−2.55126	−	7.85197i	−0.169333	−	0.521154i	0.829996	−	0.557769i	$-0.188342\pi$
$227$	−2.55126	−	7.85197i	−0.169333	−	0.521154i	−0.999329	+	0.0366150i	$0.988342\pi$
$228$	−4.95623	+	15.2537i	−0.328234	+	1.01020i
$229$	−10.6047	−	7.70475i	−0.700777	−	0.509145i	0.179408	−	0.983775i	$-0.442582\pi$
$229$	−10.6047	−	7.70475i	−0.700777	−	0.509145i	−0.880185	+	0.474630i	$0.842582\pi$
$230$	20.6896			1.36423
$231$		0			0
$232$	−20.8371			−1.36802
$233$	−10.3778	−	7.53992i	−0.679873	−	0.493957i	0.193443	−	0.981112i	$-0.438035\pi$
$233$	−10.3778	−	7.53992i	−0.679873	−	0.493957i	−0.873316	+	0.487155i	$0.838035\pi$
$234$	−2.25114	+	6.92828i	−0.147161	+	0.452916i
$235$	3.64632	+	11.2222i	0.237860	+	0.732056i
$236$	21.9584	−	15.9537i	1.42937	−	1.03850i
$237$	9.89650	−	7.19023i	0.642847	−	0.467056i
$238$	4.44936	+	13.6937i	0.288409	+	0.887633i
$239$	1.53924	−	4.73730i	0.0995653	−	0.306430i	−0.888851	−	0.458196i	$-0.848496\pi$
$239$	1.53924	−	4.73730i	0.0995653	−	0.306430i	0.988417	+	0.151765i	$0.0484958\pi$
$240$	−5.04013	−	3.66187i	−0.325339	−	0.236372i
$241$	2.62686			0.169211			0.0846053	−	0.996415i	$-0.473037\pi$
$241$	2.62686			0.169211			0.0846053	+	0.996415i	$0.473037\pi$
$242$		0			0
$243$	9.39070			0.602414
$244$	−7.75104	−	5.63146i	−0.496209	−	0.360517i
$245$	0.388938	−	1.19703i	0.0248484	−	0.0764754i
$246$	0.338751	+	1.04257i	0.0215980	+	0.0664717i
$247$	7.35964	−	5.34709i	0.468283	−	0.340227i
$248$	−36.4771	+	26.5021i	−2.31630	+	1.68289i
$249$	−0.421270	−	1.29654i	−0.0266969	−	0.0821646i
$250$	−7.95547	+	24.4844i	−0.503148	+	1.54853i
$251$	21.2148	+	15.4134i	1.33906	+	0.972888i	0.999478	+	0.0323129i	$0.0102873\pi$
$251$	21.2148	+	15.4134i	1.33906	+	0.972888i	0.339587	+	0.940575i	$0.389713\pi$
$252$	3.68460			0.232108
$253$		0			0
$254$	19.5112			1.22424
$255$	8.65159	+	6.28575i	0.541784	+	0.393629i
$256$	−9.59733	+	29.5375i	−0.599833	+	1.84610i
$257$	9.25561	+	28.4858i	0.577349	+	1.77690i	0.628037	+	0.778183i	$0.283859\pi$
$257$	9.25561	+	28.4858i	0.577349	+	1.77690i	−0.0506881	+	0.998715i	$0.516141\pi$
$258$	−0.373831	+	0.271604i	−0.0232737	+	0.0169093i
$259$	−4.41315	+	3.20634i	−0.274220	+	0.199232i
$260$	4.82983	+	14.8647i	0.299533	+	0.921868i
$261$	1.31007	−	4.03199i	0.0810915	−	0.249574i
$262$	0.199500	+	0.144945i	0.0123251	+	0.00895474i
$263$	−3.33709			−0.205774			−0.102887	−	0.994693i	$-0.532808\pi$
$263$	−3.33709			−0.205774			−0.102887	+	0.994693i	$0.532808\pi$
$264$		0			0
$265$	5.47747			0.336478
$266$	−5.62791	−	4.08892i	−0.345070	−	0.250708i
$267$	4.45639	−	13.7154i	0.272727	−	0.839366i
$268$	−11.3732	−	35.0030i	−0.694727	−	2.13815i
$269$	1.40430	−	1.02028i	0.0856218	−	0.0622079i	−0.544151	−	0.838987i	$-0.683148\pi$
$269$	1.40430	−	1.02028i	0.0856218	−	0.0622079i	0.629773	+	0.776780i	$0.283148\pi$
$270$	13.9955	−	10.1683i	0.851737	−	0.618823i
$271$	0.765113	+	2.35478i	0.0464773	+	0.143042i	0.971602	−	0.236621i	$-0.0760399\pi$
$271$	0.765113	+	2.35478i	0.0464773	+	0.143042i	−0.925125	+	0.379663i	$0.876040\pi$
$272$	−6.31807	+	19.4450i	−0.383089	+	1.17903i
$273$	3.68778	+	2.67933i	0.223195	+	0.162161i
$274$	−11.0928			−0.670141
$275$		0			0
$276$	37.8995			2.28128
$277$	4.17105	+	3.03045i	0.250614	+	0.182082i	0.705999	−	0.708213i	$-0.250498\pi$
$277$	4.17105	+	3.03045i	0.250614	+	0.182082i	−0.455385	+	0.890295i	$0.650498\pi$
$278$	2.87302	−	8.84223i	0.172312	−	0.530322i
$279$	−2.83478	−	8.72457i	−0.169714	−	0.522326i
$280$	4.71972	−	3.42908i	0.282057	−	0.204927i
$281$	−18.2599	+	13.2666i	−1.08930	+	0.791419i	−0.979280	−	0.202510i	$-0.935090\pi$
$281$	−18.2599	+	13.2666i	−1.08930	+	0.791419i	−0.110015	+	0.993930i	$0.535090\pi$
$282$	10.0984	+	31.0798i	0.601354	+	1.85078i
$283$	2.62280	−	8.07216i	0.155909	−	0.479840i	−0.842342	−	0.538943i	$-0.818824\pi$
$283$	2.62280	−	8.07216i	0.155909	−	0.479840i	0.998252	+	0.0591027i	$0.0188239\pi$
$284$	0.368594	+	0.267799i	0.0218720	+	0.0158910i
$285$	−5.16669			−0.306049
$286$		0			0
$287$	−0.314484			−0.0185634
$288$	−0.673058	−	0.489005i	−0.0396603	−	0.0288149i
$289$	5.59195	−	17.2102i	0.328938	−	1.01237i
$290$	−4.24957	−	13.0788i	−0.249544	−	0.768016i
$291$	−20.3945	+	14.8175i	−1.19555	+	0.868618i
$292$	1.94406	−	1.41244i	0.113767	−	0.0826569i
$293$	−7.60988	−	23.4208i	−0.444574	−	1.36826i	−0.882950	−	0.469467i	$-0.844446\pi$
$293$	−7.60988	−	23.4208i	−0.444574	−	1.36826i	0.438376	−	0.898792i	$-0.355554\pi$
$294$	1.07716	−	3.31516i	0.0628214	−	0.193344i
$295$	7.07366	+	5.13932i	0.411844	+	0.299223i
$296$	−25.2843			−1.46962
$297$		0			0
$298$	11.8417			0.685973
$299$	−17.3908	−	12.6352i	−1.00574	−	0.730712i
$300$	−5.91489	+	18.2042i	−0.341497	+	1.05102i
$301$	−0.0409639	−	0.126074i	−0.00236112	−	0.00726678i
$302$	−33.3753	+	24.2486i	−1.92053	+	1.39535i
$303$	−14.4760	+	10.5175i	−0.831627	+	0.604212i
$304$	−3.05252	−	9.39470i	−0.175074	−	0.538823i
$305$	0.953737	−	2.93530i	0.0546108	−	0.168075i
$306$	−10.9852	−	7.98123i	−0.627984	−	0.456257i
$307$	−4.59391			−0.262188			−0.131094	−	0.991370i	$-0.541849\pi$
$307$	−4.59391			−0.262188			−0.131094	+	0.991370i	$0.541849\pi$
$308$		0			0
$309$	11.7863			0.670502
$310$	−24.0738	−	17.4907i	−1.36730	−	0.993403i
$311$	−0.683154	+	2.10253i	−0.0387381	+	0.119224i	−0.968556	−	0.248798i	$-0.919965\pi$
$311$	−0.683154	+	2.10253i	−0.0387381	+	0.119224i	0.929817	+	0.368021i	$0.119965\pi$
$312$	6.52906	+	20.0944i	0.369635	+	1.13762i
$313$	7.84688	−	5.70110i	0.443532	−	0.322245i	−0.343505	−	0.939151i	$-0.611614\pi$
$313$	7.84688	−	5.70110i	0.443532	−	0.322245i	0.787037	+	0.616906i	$0.211614\pi$
$314$	−4.41396	+	3.20693i	−0.249094	+	0.180977i
$315$	0.366789	+	1.12886i	0.0206662	+	0.0636041i
$316$	−10.2979	+	31.6937i	−0.579303	+	1.78291i
$317$	−5.22252	−	3.79439i	−0.293326	−	0.213114i	0.431383	−	0.902169i	$-0.358026\pi$
$317$	−5.22252	−	3.79439i	−0.293326	−	0.213114i	−0.724709	+	0.689055i	$0.758026\pi$
$318$	15.1698			0.850680
$319$		0			0
$320$	−11.3863			−0.636513
$321$	14.1423	+	10.2750i	0.789347	+	0.573494i
$322$	−5.07968	+	15.6337i	−0.283080	+	0.871229i
$323$	5.23978	+	16.1264i	0.291549	+	0.897297i
$324$	16.6943	−	12.1291i	0.927463	−	0.673841i
$325$	8.78319	−	6.38136i	0.487204	−	0.353974i
$326$	−11.8946	−	36.6078i	−0.658780	−	2.02752i
$327$	−0.392709	+	1.20863i	−0.0217169	+	0.0668376i
$328$	−1.17928	−	0.856798i	−0.0651149	−	0.0473087i
$329$	−9.37505			−0.516863
$330$		0			0
$331$	3.62076			0.199015			0.0995075	−	0.995037i	$-0.468273\pi$
$331$	3.62076			0.199015			0.0995075	+	0.995037i	$0.468273\pi$
$332$	3.00455	+	2.18293i	0.164896	+	0.119804i
$333$	1.58968	−	4.89253i	0.0871139	−	0.268109i
$334$	−15.5780	−	47.9441i	−0.852389	−	2.62338i
$335$	9.59182	−	6.96886i	0.524057	−	0.380750i
$336$	4.00445	−	2.90940i	0.218461	−	0.158721i
$337$	1.97928	+	6.09161i	0.107818	+	0.331831i	0.990382	−	0.138363i	$-0.0441840\pi$
$337$	1.97928	+	6.09161i	0.107818	+	0.331831i	−0.882563	+	0.470194i	$0.844184\pi$
$338$	−2.17681	+	6.69953i	−0.118403	+	0.364406i
$339$	−5.27357	−	3.83147i	−0.286421	−	0.208097i
$340$	−29.1327			−1.57994
$341$		0			0
$342$	6.56033			0.354742
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	0.189872	−	0.584367i	0.0102372	−	0.0315070i
$345$	3.77276	+	11.6114i	0.203119	+	0.625135i
$346$	−42.3839	+	30.7937i	−2.27857	+	1.65548i
$347$	−14.1254	+	10.2627i	−0.758293	+	0.550932i	−0.898386	−	0.439206i	$-0.855260\pi$
$347$	−14.1254	+	10.2627i	−0.758293	+	0.550932i	0.140093	+	0.990138i	$0.455260\pi$
$348$	−7.78441	−	23.9580i	−0.417288	−	1.28428i
$349$	6.68246	−	20.5665i	0.357704	−	1.10090i	−0.596721	−	0.802449i	$-0.703530\pi$
$349$	6.68246	−	20.5665i	0.357704	−	1.10090i	0.954425	−	0.298451i	$-0.0964699\pi$
$350$	−6.71650	−	4.87983i	−0.359012	−	0.260838i
$351$	−17.9738			−0.959371
$352$		0			0
$353$	4.40150			0.234268			0.117134	−	0.993116i	$-0.462629\pi$
$353$	4.40150			0.234268			0.117134	+	0.993116i	$0.462629\pi$
$354$	19.5905	+	14.2333i	1.04122	+	0.756491i
$355$	−0.0453542	+	0.139586i	−0.00240715	+	0.00740844i
$356$	12.1402	+	37.3637i	0.643430	+	1.98027i
$357$	−6.87381	+	4.99412i	−0.363801	+	0.264317i
$358$	−9.40197	+	6.83093i	−0.496909	+	0.361026i
$359$	3.30084	+	10.1589i	0.174212	+	0.536168i	0.999597	−	0.0284023i	$-0.00904194\pi$
$359$	3.30084	+	10.1589i	0.174212	+	0.536168i	−0.825385	+	0.564570i	$0.809042\pi$
$360$	−1.70011	+	5.23240i	−0.0896037	+	0.275772i
$361$	8.74362	+	6.35261i	0.460191	+	0.334348i
$362$	−19.0860			−1.00314
$363$		0			0
$364$	−12.4180			−0.650879
$365$	0.626258	+	0.455003i	0.0327799	+	0.0238160i
$366$	2.64137	−	8.12929i	0.138067	−	0.424925i
$367$	3.15715	+	9.71670i	0.164802	+	0.507207i	0.999022	−	0.0442244i	$-0.0140817\pi$
$367$	3.15715	+	9.71670i	0.164802	+	0.507207i	−0.834220	+	0.551432i	$0.814082\pi$
$368$	−18.8842	+	13.7202i	−0.984406	+	0.715213i
$369$	0.239934	−	0.174323i	0.0124905	−	0.00907487i
$370$	−5.15655	−	15.8702i	−0.268076	−	0.825054i
$371$	−1.34482	+	4.13893i	−0.0698195	+	0.214882i
$372$	−44.0987	−	32.0396i	−2.28641	−	1.66117i
$373$	27.8851			1.44383			0.721917	−	0.691980i	$-0.243261\pi$
$373$	27.8851			1.44383			0.721917	+	0.691980i	$0.243261\pi$
$374$		0			0
$375$	−15.1918			−0.784499
$376$	−35.1554	−	25.5419i	−1.81300	−	1.31722i
$377$	−4.41526	+	13.5888i	−0.227397	+	0.699857i
$378$	4.24731	+	13.0719i	0.218458	+	0.672344i
$379$	−0.928776	+	0.674795i	−0.0477080	+	0.0346619i	−0.611384	−	0.791334i	$-0.709387\pi$
$379$	−0.928776	+	0.674795i	−0.0477080	+	0.0346619i	0.563676	+	0.825996i	$0.309387\pi$
$380$	11.3871	−	8.27322i	0.584146	−	0.424407i
$381$	3.55787	+	10.9500i	0.182275	+	0.560985i
$382$	−6.63200	+	20.4112i	−0.339322	+	1.04433i
$383$	16.1412	+	11.7273i	0.824777	+	0.599235i	0.918077	−	0.396403i	$-0.129742\pi$
$383$	16.1412	+	11.7273i	0.824777	+	0.599235i	−0.0933000	+	0.995638i	$0.529742\pi$
$384$	−29.0038			−1.48009
$385$		0			0
$386$	−62.2251			−3.16717
$387$	0.101138	+	0.0734808i	0.00514111	+	0.00373524i
$388$	21.2218	−	65.3139i	1.07737	−	3.31581i
$389$	0.803445	+	2.47275i	0.0407363	+	0.125373i	0.969356	−	0.245658i	$-0.0790041\pi$
$389$	0.803445	+	2.47275i	0.0407363	+	0.125373i	−0.928620	+	0.371032i	$0.879004\pi$
$390$	−11.2811	+	8.19619i	−0.571240	+	0.415030i
$391$	32.4155	−	23.5512i	1.63932	−	1.19104i
$392$	1.43233	+	4.40826i	0.0723436	+	0.222651i
$393$	−0.0449668	+	0.138393i	−0.00226827	+	0.00698103i
$394$	−22.0178	−	15.9968i	−1.10924	−	0.805909i
$395$	−10.7352			−0.540148
$396$		0			0
$397$	8.77237			0.440272			0.220136	−	0.975469i	$-0.429350\pi$
$397$	8.77237			0.440272			0.220136	+	0.975469i	$0.429350\pi$
$398$	24.0875	+	17.5006i	1.20740	+	0.877224i
$399$	1.26852	−	3.90410i	0.0635053	−	0.195449i
$400$	−3.64296	−	11.2119i	−0.182148	−	0.560594i
$401$	−22.9385	+	16.6658i	−1.14549	+	0.832249i	−0.987875	−	0.155252i	$-0.950381\pi$
$401$	−22.9385	+	16.6658i	−1.14549	+	0.832249i	−0.157617	+	0.987500i	$0.550381\pi$
$402$	26.5645	−	19.3002i	1.32492	−	0.962607i
$403$	9.55389	+	29.4039i	0.475913	+	1.46471i
$404$	15.0632	−	46.3598i	0.749422	−	2.30648i
$405$	5.37790	+	3.90727i	0.267230	+	0.194154i
$406$	10.9261			0.542252
$407$		0			0
$408$	−39.3822			−1.94971
$409$	16.1039	+	11.7002i	0.796286	+	0.578536i	0.909822	−	0.414998i	$-0.136218\pi$
$409$	16.1039	+	11.7002i	0.796286	+	0.578536i	−0.113536	+	0.993534i	$0.536218\pi$
$410$	0.297281	−	0.914937i	0.0146817	−	0.0451855i
$411$	−2.02278	−	6.22547i	−0.0997763	−	0.307080i
$412$	−25.9764	+	18.8730i	−1.27977	+	0.929805i
$413$	−5.62012	+	4.08326i	−0.276548	+	0.200924i
$414$	−4.79041	−	14.7434i	−0.235436	−	0.724596i
$415$	−0.369698	+	1.13781i	−0.0181478	+	0.0558531i
$416$	2.26836	+	1.64806i	0.111216	+	0.0808029i
$417$	5.48631			0.268666
$418$		0			0
$419$	−30.8957			−1.50935			−0.754676	−	0.656097i	$-0.772206\pi$
$419$	−30.8957			−1.50935			−0.754676	+	0.656097i	$0.772206\pi$
$420$	5.70587	+	4.14556i	0.278418	+	0.202283i
$421$	−7.47609	+	23.0090i	−0.364362	+	1.12139i	0.586017	+	0.810299i	$0.300695\pi$
$421$	−7.47609	+	23.0090i	−0.364362	+	1.12139i	−0.950379	+	0.311093i	$0.899305\pi$
$422$	10.7127	+	32.9703i	0.521486	+	1.60497i
$423$	7.15265	−	5.19671i	0.347774	−	0.252673i
$424$	−16.3192	+	11.8566i	−0.792531	+	0.575808i
$425$	6.25330	+	19.2457i	0.303330	+	0.933552i
$426$	−0.125608	+	0.386582i	−0.00608573	+	0.0187300i
$427$	1.98383	+	1.44134i	0.0960045	+	0.0697513i
$428$	−47.6218			−2.30188
$429$		0			0
$430$	0.405513			0.0195556
$431$	15.6950	+	11.4031i	0.756000	+	0.549266i	0.897681	−	0.440646i	$-0.145251\pi$
$431$	15.6950	+	11.4031i	0.756000	+	0.549266i	−0.141681	+	0.989912i	$0.545251\pi$
$432$	−6.03115	+	18.5620i	−0.290174	+	0.893063i
$433$	−6.60917	−	20.3409i	−0.317616	−	0.977522i	−0.974664	−	0.223674i	$-0.928195\pi$
$433$	−6.60917	−	20.3409i	−0.317616	−	0.977522i	0.657048	−	0.753849i	$-0.271805\pi$
$434$	19.1270	−	13.8966i	0.918125	−	0.667057i
$435$	6.56516	−	4.76987i	0.314775	−	0.228698i
$436$	−1.06983	−	3.29259i	−0.0512354	−	0.157686i
$437$	−5.98208	+	18.4109i	−0.286162	+	0.880715i
$438$	1.73442	+	1.26013i	0.0828737	+	0.0602113i
$439$	31.7315			1.51446			0.757232	−	0.653146i	$-0.226551\pi$
$439$	31.7315			1.51446			0.757232	+	0.653146i	$0.226551\pi$
$440$		0			0
$441$	−0.943053			−0.0449073
$442$	37.0228	+	26.8986i	1.76100	+	1.27944i
$443$	−0.514855	+	1.58456i	−0.0244615	+	0.0752847i	−0.962542	−	0.271133i	$-0.912602\pi$
$443$	−0.514855	+	1.58456i	−0.0244615	+	0.0752847i	0.938081	+	0.346417i	$0.112602\pi$
$444$	−9.44582	−	29.0712i	−0.448279	−	1.37966i
$445$	−10.2387	+	7.43886i	−0.485362	+	0.352636i
$446$	5.82805	−	4.23432i	0.275966	−	0.200501i
$447$	2.15935	+	6.64578i	0.102134	+	0.314335i
$448$	2.79554	−	8.60379i	0.132077	−	0.406491i
$449$	13.9036	+	10.1016i	0.656151	+	0.476722i	0.865361	−	0.501149i	$-0.167089\pi$
$449$	13.9036	+	10.1016i	0.656151	+	0.476722i	−0.209210	+	0.977871i	$0.567089\pi$
$450$	7.82927			0.369076
$451$		0			0
$452$	17.7578			0.835258
$453$	−19.6947	−	14.3091i	−0.925339	−	0.672298i
$454$	−6.20072	+	19.0839i	−0.291014	+	0.895650i
$455$	−1.23617	−	3.80453i	−0.0579524	−	0.178359i
$456$	15.3933	−	11.1839i	0.720858	−	0.523734i
$457$	8.26867	−	6.00754i	0.386792	−	0.281021i	−0.377348	−	0.926072i	$-0.623164\pi$
$457$	8.26867	−	6.00754i	0.386792	−	0.281021i	0.764140	+	0.645051i	$0.223164\pi$
$458$	9.84486	+	30.2994i	0.460020	+	1.41580i
$459$	10.3527	−	31.8624i	0.483224	−	1.48721i
$460$	−26.9078	−	19.5496i	−1.25458	−	0.911506i
$461$	22.1160			1.03004			0.515022	−	0.857177i	$-0.327784\pi$
$461$	22.1160			1.03004			0.515022	+	0.857177i	$0.327784\pi$
$462$		0			0
$463$	−30.3717			−1.41149			−0.705747	−	0.708464i	$-0.749389\pi$
$463$	−30.3717			−1.41149			−0.705747	+	0.708464i	$0.749389\pi$
$464$	12.5519	+	9.11947i	0.582706	+	0.423361i
$465$	5.42618	−	16.7001i	0.251633	−	0.774447i
$466$	9.63424	+	29.6512i	0.446298	+	1.37356i
$467$	−20.3799	+	14.8068i	−0.943067	+	0.685178i	−0.949157	−	0.314803i	$-0.898062\pi$
$467$	−20.3799	+	14.8068i	−0.943067	+	0.685178i	0.00608981	+	0.999981i	$0.498062\pi$
$468$	9.47424	−	6.88344i	0.437947	−	0.318187i
$469$	2.91090	+	8.95883i	0.134413	+	0.413680i
$470$	8.86220	−	27.2751i	0.408783	−	1.25810i
$471$	−2.60467	−	1.89240i	−0.120017	−	0.0871973i
$472$	−32.1995			−1.48210
$473$		0			0
$474$	−29.7311			−1.36560
$475$	−7.90968	−	5.74672i	−0.362921	−	0.263677i
$476$	7.15262	−	22.0135i	0.327840	−	1.00899i
$477$	−1.26823	−	3.90322i	−0.0580685	−	0.178716i
$478$	−9.79421	+	7.11591i	−0.447977	+	0.325474i
$479$	−17.1544	+	12.4634i	−0.783804	+	0.569467i	−0.906118	−	0.423025i	$-0.860968\pi$
$479$	−17.1544	+	12.4634i	−0.783804	+	0.569467i	0.122314	+	0.992491i	$0.460968\pi$
$480$	−0.492098	−	1.51452i	−0.0224611	−	0.0691281i
$481$	−5.35759	+	16.4890i	−0.244285	+	0.751832i
$482$	−5.16513	−	3.75268i	−0.235265	−	0.170930i
$483$	−9.70015			−0.441372
$484$		0			0
$485$	22.1230			1.00455
$486$	−18.4647	−	13.4154i	−0.837577	−	0.608535i
$487$	−5.19759	+	15.9965i	−0.235525	+	0.724873i	0.761526	+	0.648134i	$0.224451\pi$
$487$	−5.19759	+	15.9965i	−0.235525	+	0.724873i	−0.997051	+	0.0767381i	$0.975549\pi$
$488$	3.51229	+	10.8097i	0.158994	+	0.489333i
$489$	18.3759	−	13.3509i	0.830988	−	0.603748i
$490$	−2.47482	+	1.79806i	−0.111801	+	0.0812281i
$491$	−1.49504	−	4.60125i	−0.0674701	−	0.207652i	0.911637	−	0.410996i	$-0.134819\pi$
$491$	−1.49504	−	4.60125i	−0.0674701	−	0.207652i	−0.979107	+	0.203344i	$0.934819\pi$
$492$	0.544562	−	1.67599i	0.0245508	−	0.0755595i
$493$	−21.5458	−	15.6540i	−0.970376	−	0.705019i
$494$	−22.1099			−0.994770
$495$		0			0
$496$	33.5719			1.50742
$497$	−0.0943396	−	0.0685417i	−0.00423171	−	0.00307452i
$498$	−1.02388	+	3.15117i	−0.0458810	+	0.141207i
$499$	9.45084	+	29.0867i	0.423078	+	1.30210i	0.904823	+	0.425788i	$0.140003\pi$
$499$	9.45084	+	29.0867i	0.423078	+	1.30210i	−0.481745	+	0.876311i	$0.659997\pi$
$500$	33.4818	−	24.3259i	1.49735	−	1.08789i
$501$	24.0664	−	17.4852i	1.07521	−	0.781183i
$502$	−19.6947	−	60.6142i	−0.879019	−	2.70534i
$503$	8.72684	−	26.8585i	0.389111	−	1.19756i	−0.544343	−	0.838863i	$-0.683221\pi$
$503$	8.72684	−	26.8585i	0.389111	−	1.19756i	0.933454	−	0.358697i	$-0.116779\pi$
$504$	−3.53634	−	2.56930i	−0.157521	−	0.114446i
$505$	15.7029			0.698768
$506$		0			0
$507$	−4.15683			−0.184611
$508$	−25.3751	−	18.4361i	−1.12584	−	0.817970i
$509$	−1.29807	+	3.99505i	−0.0575360	+	0.177078i	−0.975694	−	0.219136i	$-0.929676\pi$
$509$	−1.29807	+	3.99505i	−0.0575360	+	0.177078i	0.918158	+	0.396214i	$0.129676\pi$
$510$	−8.03171	−	24.7191i	−0.355650	−	1.09458i
$511$	−0.497571	+	0.361506i	−0.0220112	+	0.0159921i
$512$	28.3466	−	20.5950i	1.25275	−	0.910179i
$513$	5.00183	+	15.3941i	0.220836	+	0.679664i
$514$	22.4953	−	69.2335i	0.992226	−	3.05376i
$515$	−8.36804	−	6.07973i	−0.368740	−	0.267905i
$516$	0.742823			0.0327009
$517$		0			0
$518$	13.2580			0.582523
$519$	−25.0107	−	18.1713i	−1.09785	−	0.797633i
$520$	5.72977	−	17.6344i	0.251267	−	0.773321i
$521$	−6.38026	−	19.6364i	−0.279524	−	0.860287i	−0.987987	−	0.154539i	$-0.950611\pi$
$521$	−6.38026	−	19.6364i	−0.279524	−	0.860287i	0.708462	−	0.705749i	$-0.249389\pi$
$522$	−8.33601	+	6.05646i	−0.364857	+	0.265084i
$523$	−18.3113	+	13.3040i	−0.800699	+	0.581742i	−0.911119	−	0.412143i	$-0.864780\pi$
$523$	−18.3113	+	13.3040i	−0.800699	+	0.581742i	0.110420	+	0.993885i	$0.464780\pi$
$524$	−0.122500	−	0.377015i	−0.00535142	−	0.0164700i
$525$	1.51388	−	4.65925i	0.0660713	−	0.203347i
$526$	6.56164	+	4.76731i	0.286101	+	0.207865i
$527$	−57.6275			−2.51030
$528$		0			0
$529$	22.7440			0.988869
$530$	−10.7702	−	7.82502i	−0.467828	−	0.339897i
$531$	2.02445	−	6.23061i	0.0878535	−	0.270385i
$532$	3.45573	+	10.6356i	0.149825	+	0.461113i
$533$	−0.808636	+	0.587508i	−0.0350259	+	0.0254478i
$534$	−28.3560	+	20.6019i	−1.22709	+	0.891530i
$535$	−4.74058	−	14.5900i	−0.204953	−	0.630781i
$536$	−13.4924	+	41.5252i	−0.582781	+	1.79362i
$537$	−5.54808	−	4.03092i	−0.239418	−	0.173947i
$538$	−4.21881			−0.181886
$539$		0			0
$540$	−27.8098			−1.19674
$541$	34.5582	+	25.1080i	1.48577	+	1.07948i	0.975639	+	0.219383i	$0.0704043\pi$
$541$	34.5582	+	25.1080i	1.48577	+	1.07948i	0.510134	+	0.860095i	$0.329596\pi$
$542$	1.85957	−	5.72317i	0.0798754	−	0.245831i
$543$	−3.48033	−	10.7114i	−0.149355	−	0.459669i
$544$	−4.22810	+	3.07189i	−0.181278	+	0.131706i
$545$	0.902263	−	0.655532i	0.0386487	−	0.0280799i
$546$	−3.42355	−	10.5366i	−0.146515	−	0.450926i
$547$	−13.7459	+	42.3056i	−0.587733	+	1.80886i	0.000274240		1.00000i	$0.499913\pi$
$547$	−13.7459	+	42.3056i	−0.587733	+	1.80886i	−0.588007	+	0.808856i	$0.700087\pi$
$548$	14.4267	+	10.4816i	0.616277	+	0.447752i
$549$	−2.31251			−0.0986955
$550$		0			0
$551$	12.8671			0.548156
$552$	−36.3745	−	26.4276i	−1.54820	−	1.12483i
$553$	2.63569	−	8.11183i	0.112081	−	0.344950i
$554$	−3.87220	−	11.9174i	−0.164514	−	0.506322i
$555$	7.96634	−	5.78788i	0.338152	−	0.245682i
$556$	−12.0915	+	8.78500i	−0.512794	+	0.372567i
$557$	7.72268	+	23.7680i	0.327220	+	1.00708i	0.970428	+	0.241389i	$0.0776030\pi$
$557$	7.72268	+	23.7680i	0.327220	+	1.00708i	−0.643208	+	0.765691i	$0.722397\pi$
$558$	−6.88981	+	21.2047i	−0.291669	+	0.897665i
$559$	−0.340857	−	0.247647i	−0.0144167	−	0.0104744i
$560$	−4.34382			−0.183560
$561$		0			0
$562$	54.8565			2.31398
$563$	7.28929	+	5.29598i	0.307207	+	0.223199i	0.730697	−	0.682702i	$-0.239195\pi$
$563$	7.28929	+	5.29598i	0.307207	+	0.223199i	−0.423490	+	0.905901i	$0.639195\pi$
$564$	16.2339	−	49.9627i	0.683569	−	2.10381i
$565$	1.76773	+	5.44052i	0.0743690	+	0.228884i
$566$	−16.6889	+	12.1252i	−0.701487	+	0.509660i
$567$	−4.27282	+	3.10438i	−0.179442	+	0.130372i
$568$	−0.167024	−	0.514048i	−0.00700818	−	0.0215690i
$569$	−9.01521	+	27.7460i	−0.377937	+	1.16317i	0.563538	+	0.826090i	$0.309440\pi$
$569$	−9.01521	+	27.7460i	−0.377937	+	1.16317i	−0.941475	+	0.337082i	$0.890560\pi$
$570$	10.1592	+	7.38106i	0.425520	+	0.309158i
$571$	−1.78994			−0.0749067			−0.0374533	−	0.999298i	$-0.511925\pi$
$571$	−1.78994			−0.0749067			−0.0374533	+	0.999298i	$0.511925\pi$
$572$		0			0
$573$	−12.6645			−0.529065
$574$	0.618364	+	0.449267i	0.0258100	+	0.0187521i
$575$	−7.13917	+	21.9721i	−0.297724	+	0.916300i
$576$	2.63634	+	8.11383i	0.109848	+	0.338076i
$577$	17.4626	−	12.6873i	0.726978	−	0.528180i	−0.161628	−	0.986852i	$-0.551675\pi$
$577$	17.4626	−	12.6873i	0.726978	−	0.528180i	0.888606	+	0.458671i	$0.151675\pi$
$578$	−35.5816	+	25.8515i	−1.48000	+	1.07528i
$579$	−11.3468	−	34.9218i	−0.471556	−	1.45130i
$580$	−6.83145	+	21.0250i	−0.283660	+	0.873017i
$581$	−0.768997	−	0.558709i	−0.0319034	−	0.0231791i
$582$	61.2694			2.53970
$583$		0			0
$584$	−2.85074			−0.117965
$585$	3.05203	+	2.21743i	0.126186	+	0.0916793i
$586$	−18.4955	+	56.9232i	−0.764040	+	2.35147i
$587$	1.70687	+	5.25321i	0.0704501	+	0.216823i	0.980082	−	0.198591i	$-0.0636366\pi$
$587$	1.70687	+	5.25321i	0.0704501	+	0.216823i	−0.909632	+	0.415414i	$0.863637\pi$
$588$	−4.53340	+	3.29371i	−0.186954	+	0.135830i
$589$	22.5249	−	16.3653i	0.928121	−	0.674319i
$590$	−6.56684	−	20.2106i	−0.270352	−	0.832059i
$591$	4.96275	−	15.2738i	0.204140	−	0.628279i
$592$	15.2308	+	11.0658i	0.625982	+	0.454802i
$593$	40.7867			1.67491			0.837454	−	0.546508i	$-0.184043\pi$
$593$	40.7867			1.67491			0.837454	+	0.546508i	$0.184043\pi$
$594$		0			0
$595$	7.45636			0.305681
$596$	−15.4007	−	11.1893i	−0.630837	−	0.458330i
$597$	−5.42925	+	16.7095i	−0.222205	+	0.683875i
$598$	16.1448	+	49.6886i	0.660210	+	2.03192i
$599$	21.4510	−	15.5851i	0.876465	−	0.636789i	−0.0558491	−	0.998439i	$-0.517787\pi$
$599$	21.4510	−	15.5851i	0.876465	−	0.636789i	0.932314	+	0.361650i	$0.117787\pi$
$600$	18.3708	−	13.3472i	0.749985	−	0.544896i
$601$	11.6715	+	35.9213i	0.476092	+	1.46526i	0.844479	+	0.535589i	$0.179910\pi$
$601$	11.6715	+	35.9213i	0.476092	+	1.46526i	−0.368387	+	0.929673i	$0.620090\pi$
$602$	−0.0995608	+	0.306417i	−0.00405780	+	0.0124886i
$603$	−7.18685	−	5.22155i	−0.292671	−	0.212638i
$604$	66.3186			2.69847
$605$		0			0
$606$	43.4890			1.76662
$607$	−22.4295	−	16.2960i	−0.910385	−	0.661433i	0.0307275	−	0.999528i	$-0.490218\pi$
$607$	−22.4295	−	16.2960i	−0.910385	−	0.661433i	−0.941112	+	0.338095i	$0.890218\pi$
$608$	0.780268	−	2.40142i	0.0316441	−	0.0973904i
$609$	1.99238	+	6.13190i	0.0807351	+	0.248477i
$610$	−6.06864	+	4.40912i	−0.245712	+	0.178520i
$611$	−24.1061	+	17.5141i	−0.975229	+	0.708546i
$612$	6.74530	+	20.7599i	0.272662	+	0.839169i
$613$	−11.1946	+	34.4534i	−0.452145	+	1.39156i	0.422309	+	0.906452i	$0.361220\pi$
$613$	−11.1946	+	34.4534i	−0.452145	+	1.39156i	−0.874454	+	0.485108i	$0.838780\pi$
$614$	9.03289	+	6.56278i	0.364538	+	0.264852i
$615$	0.567687			0.0228914
$616$		0			0
$617$	41.1920			1.65833			0.829163	−	0.559007i	$-0.188817\pi$
$617$	41.1920			1.65833			0.829163	+	0.559007i	$0.188817\pi$
$618$	−23.1752	−	16.8378i	−0.932244	−	0.677315i
$619$	−11.0441	+	33.9903i	−0.443901	+	1.36619i	0.439784	+	0.898104i	$0.355055\pi$
$619$	−11.0441	+	33.9903i	−0.443901	+	1.36619i	−0.883685	+	0.468082i	$0.844945\pi$
$620$	14.7821	+	45.4947i	0.593665	+	1.82711i
$621$	30.9435	−	22.4817i	1.24172	−	0.902161i
$622$	4.34691	−	3.15822i	0.174295	−	0.126633i
$623$	−3.10722	−	9.56303i	−0.124488	−	0.383135i
$624$	4.86143	−	14.9619i	0.194613	−	0.598957i
$625$	−3.03159	−	2.20258i	−0.121264	−	0.0881032i
$626$	−23.5736			−0.942192
$627$		0			0
$628$	8.77077			0.349992
$629$	−26.1443	−	18.9949i	−1.04244	−	0.757378i
$630$	0.891464	−	2.74364i	0.0355168	−	0.109309i
$631$	0.854456	+	2.62975i	0.0340154	+	0.104689i	0.966623	−	0.256204i	$-0.0824720\pi$
$631$	0.854456	+	2.62975i	0.0340154	+	0.104689i	−0.932607	+	0.360893i	$0.882472\pi$
$632$	31.9838	−	23.2376i	1.27225	−	0.924343i
$633$	−16.5500	+	12.0243i	−0.657804	+	0.477922i
$634$	4.84833	+	14.9216i	0.192552	+	0.592614i
$635$	3.12231	−	9.60950i	0.123905	−	0.381341i
$636$	−19.7290	−	14.3340i	−0.782306	−	0.568378i
$637$	3.17831			0.125929
$638$		0			0
$639$	0.109970			0.00435033
$640$	20.5920	+	14.9610i	0.813971	+	0.591385i
$641$	11.8930	−	36.6028i	0.469744	−	1.44572i	−0.383173	−	0.923676i	$-0.625169\pi$
$641$	11.8930	−	36.6028i	0.469744	−	1.44572i	0.852917	−	0.522046i	$-0.174831\pi$
$642$	−13.1290	−	40.4070i	−0.518161	−	1.59474i
$643$	21.3404	−	15.5047i	0.841582	−	0.611445i	−0.0812301	−	0.996695i	$-0.525885\pi$
$643$	21.3404	−	15.5047i	0.841582	−	0.611445i	0.922812	+	0.385250i	$0.125885\pi$
$644$	21.3786	−	15.5325i	0.842435	−	0.612065i
$645$	0.0739455	+	0.227581i	0.00291160	+	0.00896098i
$646$	12.7350	−	39.1944i	0.501054	−	1.54208i
$647$	22.1032	+	16.0589i	0.868968	+	0.631342i	0.930310	−	0.366775i	$-0.119538\pi$
$647$	22.1032	+	16.0589i	0.868968	+	0.631342i	−0.0613422	+	0.998117i	$0.519538\pi$
$648$	−24.4803			−0.961678
$649$		0			0
$650$	−26.3865			−1.03496
$651$	11.2868	+	8.20034i	0.442365	+	0.321397i
$652$	−19.1213	+	58.8492i	−0.748846	+	2.30471i
$653$	−2.61479	−	8.04751i	−0.102325	−	0.314923i	0.886768	−	0.462214i	$-0.152945\pi$
$653$	−2.61479	−	8.04751i	−0.102325	−	0.314923i	−0.989093	+	0.147290i	$0.952945\pi$
$654$	2.49881	−	1.81549i	0.0977112	−	0.0709913i
$655$	0.103313	−	0.0750611i	0.00403676	−	0.00293288i
$656$	0.335394	+	1.03224i	0.0130949	+	0.0403021i
$657$	0.179232	−	0.551619i	0.00699251	−	0.0215207i
$658$	18.4339	+	13.3930i	0.718630	+	0.522115i
$659$	5.29247			0.206165			0.103083	−	0.994673i	$-0.467129\pi$
$659$	5.29247			0.206165			0.103083	+	0.994673i	$0.467129\pi$
$660$		0			0
$661$	−19.2700			−0.749517			−0.374759	−	0.927122i	$-0.622274\pi$
$661$	−19.2700			−0.749517			−0.374759	+	0.927122i	$0.622274\pi$
$662$	−7.11942	−	5.17256i	−0.276704	−	0.201037i
$663$	−8.34485	+	25.6828i	−0.324087	+	0.997437i
$664$	−1.36147	−	4.19019i	−0.0528355	−	0.162611i
$665$	−2.91446	+	2.11748i	−0.113018	+	0.0821124i
$666$	−10.1151	+	7.34908i	−0.391954	+	0.284771i
$667$	−9.39565	−	28.9168i	−0.363801	−	1.11966i
$668$	−25.0425	+	77.0730i	−0.968925	+	2.98204i
$669$	3.43912	+	2.49867i	0.132964	+	0.0966041i
$670$	−28.8158			−1.11325
$671$		0			0
$672$	1.26523			0.0488074
$673$	−15.3650	−	11.1633i	−0.592278	−	0.430315i	0.250851	−	0.968026i	$-0.419289\pi$
$673$	−15.3650	−	11.1633i	−0.592278	−	0.430315i	−0.843130	+	0.537710i	$0.819289\pi$
$674$	4.81055	−	14.8054i	0.185296	−	0.570281i
$675$	5.96932	+	18.3717i	0.229759	+	0.707126i
$676$	9.16142	−	6.65616i	0.352362	−	0.256006i
$677$	26.2299	−	19.0571i	1.00810	−	0.732424i	0.0442864	−	0.999019i	$-0.485899\pi$
$677$	26.2299	−	19.0571i	1.00810	−	0.732424i	0.963809	+	0.266595i	$0.0858986\pi$
$678$	4.89572	+	15.0675i	0.188019	+	0.578663i
$679$	−5.43159	+	16.7167i	−0.208445	+	0.641529i
$680$	27.9605	+	20.3145i	1.07224	+	0.779025i
$681$	−11.8409			−0.453744
$682$		0			0
$683$	15.1260			0.578779			0.289389	−	0.957211i	$-0.406548\pi$
$683$	15.1260			0.578779			0.289389	+	0.957211i	$0.406548\pi$
$684$	−8.53200	−	6.19886i	−0.326229	−	0.237019i
$685$	−1.77515	+	5.46335i	−0.0678250	+	0.208744i
$686$	−0.751051	−	2.31150i	−0.0286753	−	0.0882534i
$687$	−15.2093	+	11.0502i	−0.580271	+	0.421592i
$688$	−0.370127	+	0.268913i	−0.0141109	+	0.0102522i
$689$	4.27425	+	13.1548i	0.162836	+	0.501157i
$690$	9.16952	−	28.2209i	0.349078	−	1.07435i
$691$	25.4119	+	18.4628i	0.966712	+	0.702358i	0.954700	−	0.297570i	$-0.0961762\pi$
$691$	25.4119	+	18.4628i	0.966712	+	0.702358i	0.0120125	+	0.999928i	$0.496176\pi$
$692$	84.2192			3.20153
$693$		0			0
$694$	42.4357			1.61084
$695$	−3.89515	−	2.83000i	−0.147752	−	0.107348i
$696$	−9.23489	+	28.4221i	−0.350048	+	1.07734i
$697$	−0.575718	−	1.77188i	−0.0218069	−	0.0671146i
$698$	−42.5205	+	30.8930i	−1.60943	+	1.16932i
$699$	−14.8839	+	10.8138i	−0.562962	+	0.409016i
$700$	4.12416	+	12.6929i	0.155879	+	0.479745i
$701$	4.96426	−	15.2784i	0.187498	−	0.577058i	−0.812485	−	0.582982i	$-0.801886\pi$
$701$	4.96426	−	15.2784i	0.187498	−	0.577058i	0.999982	+	0.00592402i	$0.00188568\pi$
$702$	35.3415	+	25.6771i	1.33388	+	0.969120i
$703$	15.6133			0.588865
$704$		0			0
$705$	16.9232			0.637366
$706$	−8.65457	−	6.28791i	−0.325719	−	0.236649i
$707$	−3.85534	+	11.8655i	−0.144995	+	0.446249i
$708$	−12.0292	−	37.0221i	−0.452085	−	1.39137i
$709$	−32.1162	+	23.3338i	−1.20615	+	0.876318i	−0.994875	−	0.101109i	$-0.967761\pi$
$709$	−32.1162	+	23.3338i	−1.20615	+	0.876318i	−0.211273	+	0.977427i	$0.567761\pi$
$710$	0.288589	−	0.209672i	0.0108306	−	0.00786886i
$711$	2.48560	+	7.64988i	0.0932172	+	0.286893i
$712$	14.4023	−	44.3258i	0.539749	−	1.66118i
$713$	−53.2263	−	38.6712i	−1.99334	−	1.44825i
$714$	20.6503			0.772819
$715$		0			0
$716$	18.6822			0.698187
$717$	−5.77954	−	4.19909i	−0.215841	−	0.156818i
$718$	8.02253	−	24.6908i	0.299398	−	0.921453i
$719$	−3.04765	−	9.37971i	−0.113658	−	0.349804i	0.878007	−	0.478649i	$-0.158873\pi$
$719$	−3.04765	−	9.37971i	−0.113658	−	0.349804i	−0.991665	+	0.128845i	$0.958873\pi$
$720$	3.31410	−	2.40784i	0.123509	−	0.0897347i
$721$	6.64852	−	4.83043i	0.247604	−	0.179895i
$722$	−8.11714	−	24.9820i	−0.302089	−	0.929734i
$723$	1.16421	−	3.58306i	0.0432973	−	0.133255i
$724$	24.8221	+	18.0343i	0.922507	+	0.670241i
$725$	15.3559			0.570305
$726$		0			0
$727$	−31.5764			−1.17111			−0.585553	−	0.810634i	$-0.699122\pi$
$727$	−31.5764			−1.17111			−0.585553	+	0.810634i	$0.699122\pi$
$728$	11.9183	+	8.65915i	0.441722	+	0.320930i
$729$	9.05812	−	27.8780i	0.335486	−	1.03252i
$730$	−0.581387	−	1.78933i	−0.0215181	−	0.0662259i
$731$	0.635338	−	0.461600i	0.0234988	−	0.0170729i
$732$	−11.1166	+	8.07667i	−0.410881	+	0.298522i
$733$	−12.7601	−	39.2716i	−0.471305	−	1.45053i	−0.850876	−	0.525366i	$-0.823928\pi$
$733$	−12.7601	−	39.2716i	−0.471305	−	1.45053i	0.379571	−	0.925163i	$-0.376072\pi$
$734$	7.67329	−	23.6160i	0.283226	−	0.871681i
$735$	−1.46039	−	1.06103i	−0.0538672	−	0.0391368i
$736$	−5.96659			−0.219931
$737$		0			0
$738$	−0.720812			−0.0265335
$739$	28.6469	+	20.8132i	1.05379	+	0.765626i	0.972930	−	0.231099i	$-0.0742321\pi$
$739$	28.6469	+	20.8132i	1.05379	+	0.765626i	0.0808639	+	0.996725i	$0.474232\pi$
$740$	−8.28946	+	25.5123i	−0.304727	+	0.937853i
$741$	−4.03174	−	12.4084i	−0.148110	−	0.455835i
$742$	8.55709	−	6.21709i	0.314141	−	0.228237i
$743$	−3.25555	+	2.36530i	−0.119435	+	0.0867743i	−0.645899	−	0.763423i	$-0.723517\pi$
$743$	−3.25555	+	2.36530i	−0.119435	+	0.0867743i	0.526464	+	0.850197i	$0.323517\pi$
$744$	19.9828	+	61.5007i	0.732605	+	2.25473i
$745$	1.89500	−	5.83221i	0.0694274	−	0.213676i
$746$	−54.8298	−	39.8361i	−2.00746	−	1.45850i
$747$	0.896402			0.0327976
$748$		0			0
$749$	12.1885			0.445359
$750$	29.8712	+	21.7027i	1.09074	+	0.792471i
$751$	7.54588	−	23.2238i	0.275353	−	0.847450i	−0.713773	−	0.700378i	$-0.753015\pi$
$751$	7.54588	−	23.2238i	0.275353	−	0.847450i	0.989126	−	0.147072i	$-0.0469850\pi$
$752$	9.99838	+	30.7719i	0.364603	+	1.12213i
$753$	30.4264	−	22.1060i	1.10880	−	0.805589i
$754$	28.0943	−	20.4117i	1.02313	−	0.743351i
$755$	6.60179	+	20.3182i	0.240264	+	0.739456i
$756$	6.82780	−	21.0138i	0.248325	−	0.764265i
$757$	1.06566	+	0.774247i	0.0387321	+	0.0281405i	0.606983	−	0.794715i	$-0.292380\pi$
$757$	1.06566	+	0.774247i	0.0387321	+	0.0281405i	−0.568251	+	0.822855i	$0.692380\pi$
$758$	2.79023			0.101346
$759$		0			0
$760$	−16.6979			−0.605696
$761$	−5.86055	−	4.25794i	−0.212445	−	0.154350i	0.476474	−	0.879188i	$-0.341915\pi$
$761$	−5.86055	−	4.25794i	−0.212445	−	0.154350i	−0.688919	+	0.724838i	$0.741915\pi$
$762$	8.64723	−	26.6134i	0.313256	−	0.964103i
$763$	0.273816	+	0.842720i	0.00991281	+	0.0305085i
$764$	27.9117	−	20.2791i	1.00981	−	0.733671i
$765$	−5.68880	+	4.13315i	−0.205679	+	0.149434i
$766$	−14.9847	−	46.1181i	−0.541419	−	1.66632i
$767$	−6.82286	+	20.9986i	−0.246359	+	0.758216i
$768$	36.0361	+	26.1817i	1.30034	+	0.944752i
$769$	−44.3139			−1.59800			−0.798999	−	0.601332i	$-0.794637\pi$
$769$	−44.3139			−1.59800			−0.798999	+	0.601332i	$0.794637\pi$
$770$		0			0
$771$	42.9570			1.54706
$772$	80.9265	+	58.7965i	2.91261	+	2.11613i
$773$	5.88861	−	18.1233i	0.211799	−	0.651849i	−0.787567	−	0.616229i	$-0.788659\pi$
$773$	5.88861	−	18.1233i	0.211799	−	0.651849i	0.999365	−	0.0356198i	$-0.0113405\pi$
$774$	−0.0938911	−	0.288967i	−0.00337485	−	0.0103867i
$775$	26.8818	−	19.5308i	0.965622	−	0.701565i
$776$	−65.9118	+	47.8877i	−2.36610	+	1.71907i
$777$	2.41760	+	7.44062i	0.0867310	+	0.266931i
$778$	1.95273	−	6.00990i	0.0700089	−	0.215465i
$779$	0.728215	+	0.529079i	0.0260910	+	0.0189562i
$780$	22.4161			0.802626
$781$		0			0
$782$	−97.3828			−3.48240
$783$	−20.5674	−	14.9431i	−0.735018	−	0.534022i
$784$	1.06649	−	3.28231i	0.0380889	−	0.117225i
$785$	0.873101	+	2.68713i	0.0311623	+	0.0959077i
$786$	0.286124	−	0.207881i	0.0102057	−	0.00741488i
$787$	25.4517	−	18.4917i	0.907255	−	0.659159i	−0.0330644	−	0.999453i	$-0.510527\pi$
$787$	25.4517	−	18.4917i	0.907255	−	0.659159i	0.940319	+	0.340294i	$0.110527\pi$
$788$	13.5196	+	41.6092i	0.481617	+	1.48227i
$789$	−1.47898	+	4.55182i	−0.0526530	+	0.162049i
$790$	21.1084	+	15.3362i	0.751004	+	0.545636i
$791$	−4.54502			−0.161602
$792$		0			0
$793$	7.79370			0.276763
$794$	−17.2489	−	12.5321i	−0.612141	−	0.444746i
$795$	2.42758	−	7.47133i	0.0860974	−	0.264981i
$796$	−14.7905	−	45.5205i	−0.524236	−	1.61343i
$797$	10.1493	−	7.37392i	0.359508	−	0.261198i	−0.393339	−	0.919394i	$-0.628680\pi$
$797$	10.1493	−	7.37392i	0.359508	−	0.261198i	0.752847	+	0.658196i	$0.228680\pi$
$798$	−8.07159	+	5.86435i	−0.285731	+	0.207596i
$799$	−17.1626	−	52.8212i	−0.607171	−	1.86868i
$800$	0.931193	−	2.86592i	0.0329227	−	0.101326i
$801$	7.67154	+	5.57370i	0.271061	+	0.196937i
$802$	68.9118			2.43336
$803$		0			0
$804$	−52.7850			−1.86159
$805$	6.88689	+	5.00362i	0.242731	+	0.176354i
$806$	23.2203	−	71.4647i	0.817900	−	2.51724i
$807$	−0.769302	−	2.36767i	−0.0270807	−	0.0833458i
$808$	−46.7841	+	33.9907i	−1.64586	+	1.19579i
$809$	−4.35271	+	3.16243i	−0.153033	+	0.111185i	−0.661667	−	0.749798i	$-0.730151\pi$
$809$	−4.35271	+	3.16243i	−0.153033	+	0.111185i	0.508634	+	0.860983i	$0.330151\pi$
$810$	−4.99258	−	15.3656i	−0.175421	−	0.539891i
$811$	−4.23351	+	13.0294i	−0.148659	+	0.457524i	−0.997463	−	0.0711822i	$-0.977323\pi$
$811$	−4.23351	+	13.0294i	−0.148659	+	0.457524i	0.848805	+	0.528707i	$0.177323\pi$
$812$	−14.2098	−	10.3241i	−0.498668	−	0.362303i
$813$	3.55103			0.124540
$814$		0			0
$815$	−19.9333			−0.698231
$816$	23.7231	+	17.2358i	0.830474	+	0.603375i
$817$	−0.117248	+	0.360851i	−0.00410198	+	0.0126246i
$818$	−14.9501	−	46.0115i	−0.522716	−	1.60876i
$819$	−2.42488	+	1.76178i	−0.0847321	+	0.0615614i
$820$	−1.25115	+	0.909014i	−0.0436921	+	0.0317442i
$821$	2.85258	+	8.77935i	0.0995559	+	0.306401i	0.988414	−	0.151781i	$-0.0485007\pi$
$821$	2.85258	+	8.77935i	0.0995559	+	0.306401i	−0.888858	+	0.458182i	$0.848501\pi$
$822$	−4.91627	+	15.1307i	−0.171474	+	0.527744i
$823$	10.0663	+	7.31362i	0.350890	+	0.254937i	0.749242	−	0.662296i	$-0.230418\pi$
$823$	10.0663	+	7.31362i	0.350890	+	0.254937i	−0.398352	+	0.917233i	$0.630418\pi$
$824$	38.0915			1.32698
$825$		0			0
$826$	16.8840			0.587469
$827$	−3.62752	−	2.63555i	−0.126141	−	0.0916471i	0.522926	−	0.852378i	$-0.324841\pi$
$827$	−3.62752	−	2.63555i	−0.126141	−	0.0916471i	−0.649067	+	0.760731i	$0.724841\pi$
$828$	−7.70087	+	23.7008i	−0.267624	+	0.823661i
$829$	−11.3958	−	35.0726i	−0.395792	−	1.21812i	−0.928343	−	0.371725i	$-0.878766\pi$
$829$	−11.3958	−	35.0726i	−0.395792	−	1.21812i	0.532551	−	0.846398i	$-0.321234\pi$
$830$	2.35239	−	1.70911i	0.0816528	−	0.0593242i
$831$	5.98215	−	4.34629i	0.207519	−	0.150771i
$832$	−8.88510	−	27.3455i	−0.308035	−	0.948035i
$833$	−1.83067	+	5.63423i	−0.0634290	+	0.195215i
$834$	−10.7876	−	7.83765i	−0.373544	−	0.271396i
$835$	−26.1060			−0.903435
$836$		0			0
$837$	−55.0105			−1.90144
$838$	60.7495	+	44.1371i	2.09856	+	1.52469i
$839$	2.83185	−	8.71555i	0.0977665	−	0.300894i	−0.890198	−	0.455573i	$-0.849434\pi$
$839$	2.83185	−	8.71555i	0.0977665	−	0.300894i	0.987965	+	0.154679i	$0.0494343\pi$
$840$	−2.58555	−	7.95751i	−0.0892100	−	0.274560i
$841$	7.11170	−	5.16695i	0.245231	−	0.178171i
$842$	47.5704	−	34.5619i	1.63938	−	1.19108i
$843$	10.0031	+	30.7864i	0.344526	+	1.06034i
$844$	17.2213	−	53.0017i	0.592782	−	1.82439i
$845$	2.95126	+	2.14421i	0.101526	+	0.0737632i
$846$	−21.4880			−0.738774
$847$		0			0
$848$	15.0195			0.515771
$849$	−9.84810	−	7.15507i	−0.337986	−	0.245561i
$850$	15.1983	−	46.7757i	0.521299	−	1.60439i
$851$	−11.4009	−	35.0885i	−0.390819	−	1.20282i
$852$	0.528640	−	0.384080i	0.0181109	−	0.0131583i
$853$	5.27519	−	3.83265i	0.180619	−	0.131227i	−0.493802	−	0.869574i	$-0.664393\pi$
$853$	5.27519	−	3.83265i	0.180619	−	0.131227i	0.674421	+	0.738347i	$0.264393\pi$
$854$	−1.84169	−	5.66815i	−0.0630214	−	0.193960i
$855$	1.04983	−	3.23105i	0.0359035	−	0.110500i
$856$	45.7056	+	33.2070i	1.56218	+	1.13499i
$857$	−48.0736			−1.64216			−0.821082	−	0.570810i	$-0.806629\pi$
$857$	−48.0736			−1.64216			−0.821082	+	0.570810i	$0.806629\pi$
$858$		0			0
$859$	−0.316298			−0.0107920			−0.00539598	−	0.999985i	$-0.501718\pi$
$859$	−0.316298			−0.0107920			−0.00539598	+	0.999985i	$0.501718\pi$
$860$	−0.527387	−	0.383169i	−0.0179838	−	0.0130660i
$861$	−0.139378	+	0.428960i	−0.00474998	+	0.0146189i
$862$	−14.5704	−	44.8432i	−0.496271	−	1.52736i
$863$	−2.93425	+	2.13186i	−0.0998830	+	0.0725692i	−0.636606	−	0.771189i	$-0.719662\pi$
$863$	−2.93425	+	2.13186i	−0.0998830	+	0.0725692i	0.536723	+	0.843759i	$0.319662\pi$
$864$	−4.03609	+	2.93239i	−0.137311	+	0.0997620i
$865$	8.38373	+	25.8025i	0.285055	+	0.877310i
$866$	−16.0633	+	49.4377i	−0.545852	+	1.67996i
$867$	−20.9966	−	15.2550i	−0.713083	−	0.518085i
$868$	−38.0064			−1.29002
$869$		0			0
$870$	−19.7231			−0.668675
$871$	24.2214	+	17.5979i	0.820710	+	0.596280i
$872$	−1.26917	+	3.90610i	−0.0429795	+	0.132277i
$873$	−5.12228	−	15.7648i	−0.173363	−	0.533556i
$874$	38.0640	−	27.6551i	1.28753	−	0.935448i
$875$	−8.56947	+	6.22608i	−0.289701	+	0.210480i
$876$	−1.06499	−	3.27770i	−0.0359827	−	0.110743i
$877$	−8.25311	+	25.4004i	−0.278688	+	0.857712i	0.709533	+	0.704673i	$0.248906\pi$
$877$	−8.25311	+	25.4004i	−0.278688	+	0.857712i	−0.988220	+	0.153039i	$0.951094\pi$
$878$	−62.3930	−	45.3312i	−2.10566	−	1.52985i
$879$	−35.3189			−1.19128
$880$		0			0
$881$	2.91937			0.0983560			0.0491780	−	0.998790i	$-0.484340\pi$
$881$	2.91937			0.0983560			0.0491780	+	0.998790i	$0.484340\pi$
$882$	1.85430	+	1.34723i	0.0624376	+	0.0453636i
$883$	−13.9544	+	42.9472i	−0.469603	+	1.44529i	0.383497	+	0.923542i	$0.374720\pi$
$883$	−13.9544	+	42.9472i	−0.469603	+	1.44529i	−0.853100	+	0.521748i	$0.825280\pi$
$884$	−22.7332	−	69.9657i	−0.764602	−	2.35320i
$885$	10.1451	−	7.37084i	0.341023	−	0.247768i
$886$	3.27602	−	2.38017i	0.110060	−	0.0799634i
$887$	7.42409	+	22.8490i	0.249277	+	0.767194i	0.994904	+	0.100831i	$0.0321501\pi$
$887$	7.42409	+	22.8490i	0.249277	+	0.767194i	−0.745627	+	0.666363i	$0.767850\pi$
$888$	−11.2059	+	34.4881i	−0.376044	+	1.15735i
$889$	6.49462	+	4.71861i	0.217822	+	0.158257i
$890$	30.7592			1.03105
$891$		0			0
$892$	−11.5806			−0.387749
$893$	21.7087	+	15.7723i	0.726454	+	0.527800i
$894$	5.24819	−	16.1523i	0.175526	−	0.540212i
$895$	1.85975	+	5.72372i	0.0621646	+	0.191323i
$896$	−16.3606	+	11.8867i	−0.546571	+	0.397107i
$897$	−24.9421	+	18.1215i	−0.832791	+	0.605058i
$898$	−12.9074	−	39.7249i	−0.430726	−	1.32564i
$899$	−13.5133	+	41.5897i	−0.450694	+	1.38709i
$900$	−10.1823	−	7.39788i	−0.339411	−	0.246596i
$901$	−25.7816			−0.858909
$902$		0			0
$903$	−0.190121			−0.00632684
$904$	−17.0433	−	12.3827i	−0.566852	−	0.411842i
$905$	−3.05427	+	9.40009i	−0.101527	+	0.312469i
$906$	18.2836	+	56.2712i	0.607432	+	1.86948i
$907$	12.9661	−	9.42041i	0.430532	−	0.312800i	−0.351330	−	0.936252i	$-0.614270\pi$
$907$	12.9661	−	9.42041i	0.430532	−	0.312800i	0.781861	+	0.623452i	$0.214270\pi$
$908$	26.0966	−	18.9603i	0.866048	−	0.629220i
$909$	−3.63579	−	11.1898i	−0.120592	−	0.371143i
$910$	−3.00444	+	9.24673i	−0.0995964	+	0.306526i
$911$	13.2714	+	9.64223i	0.439701	+	0.319461i	0.785516	−	0.618841i	$-0.212398\pi$
$911$	13.2714	+	9.64223i	0.439701	+	0.319461i	−0.345815	+	0.938303i	$0.612398\pi$
$912$	−14.1673			−0.469127
$913$		0			0
$914$	−24.8408			−0.821660
$915$	−3.58109	−	2.60182i	−0.118387	−	0.0860134i
$916$	15.8262	−	48.7081i	0.522913	−	1.60936i
$917$	0.0313531	+	0.0964948i	0.00103537	+	0.00318654i
$918$	−65.8745	+	47.8606i	−2.17418	+	1.57964i
$919$	26.1475	−	18.9973i	0.862527	−	0.626663i	−0.0660439	−	0.997817i	$-0.521038\pi$
$919$	26.1475	−	18.9973i	0.862527	−	0.626663i	0.928571	+	0.371154i	$0.121038\pi$
$920$	12.1929	+	37.5260i	0.401989	+	1.23720i
$921$	−2.03599	+	6.26614i	−0.0670882	+	0.206476i
$922$	−43.4861	−	31.5945i	−1.43214	−	1.04051i
$923$	−0.370623			−0.0121992
$924$		0			0
$925$	18.6333			0.612659
$926$	59.7193	+	43.3886i	1.96250	+	1.42584i
$927$	−2.39489	+	7.37072i	−0.0786585	+	0.242086i
$928$	1.22552	+	3.77175i	0.0402295	+	0.123814i
$929$	6.63015	−	4.81708i	0.217528	−	0.158043i	−0.473685	−	0.880694i	$-0.657077\pi$
$929$	6.63015	−	4.81708i	0.217528	−	0.158043i	0.691213	+	0.722651i	$0.257077\pi$
$930$	−34.5268	+	25.0852i	−1.13218	+	0.822576i
$931$	−0.884474	−	2.72213i	−0.0289875	−	0.0892142i
$932$	15.4876	−	47.6660i	0.507314	−	1.56135i
$933$	2.56511	+	1.86366i	0.0839778	+	0.0610135i
$934$	61.2253			2.00335
$935$		0			0
$936$	−13.8929			−0.454103
$937$	27.6178	+	20.0655i	0.902233	+	0.655510i	0.939038	−	0.343812i	$-0.111718\pi$
$937$	27.6178	+	20.0655i	0.902233	+	0.655510i	−0.0368058	+	0.999322i	$0.511718\pi$
$938$	7.07480	−	21.7740i	0.231000	−	0.710946i
$939$	−4.29866	−	13.2299i	−0.140282	−	0.431742i
$940$	−37.2979	+	27.0985i	−1.21652	+	0.883856i
$941$	0.792327	−	0.575660i	0.0258291	−	0.0187660i	−0.574796	−	0.818297i	$-0.694919\pi$
$941$	0.792327	−	0.575660i	0.0258291	−	0.0187660i	0.600625	+	0.799531i	$0.294919\pi$
$942$	2.41805	+	7.44198i	0.0787842	+	0.242473i
$943$	0.657277	−	2.02289i	0.0214039	−	0.0658744i
$944$	19.3963	+	14.0923i	0.631297	+	0.458664i
$945$	7.11775			0.231540
$946$		0			0
$947$	0.935599			0.0304029			0.0152014	−	0.999884i	$-0.495161\pi$
$947$	0.935599			0.0304029			0.0152014	+	0.999884i	$0.495161\pi$
$948$	38.6666	+	28.0929i	1.25583	+	0.912416i
$949$	−0.604054	+	1.85909i	−0.0196084	+	0.0603485i
$950$	7.34295	+	22.5993i	0.238237	+	0.733217i
$951$	−7.49017	+	5.44193i	−0.242886	+	0.176467i
$952$	−22.2150	+	16.1401i	−0.719993	+	0.523105i
$953$	−5.17049	−	15.9131i	−0.167489	−	0.515477i	0.831722	−	0.555192i	$-0.187355\pi$
$953$	−5.17049	−	15.9131i	−0.167489	−	0.515477i	−0.999211	+	0.0397147i	$0.987355\pi$
$954$	−3.08238	+	9.48660i	−0.0997958	+	0.307140i
$955$	8.99147	+	6.53269i	0.290957	+	0.211393i
$956$	19.4616			0.629434
$957$		0			0
$958$	51.5353			1.66503
$959$	−3.69243	−	2.68271i	−0.119235	−	0.0866291i
$960$	−5.04633	+	15.5310i	−0.162870	+	0.501262i
$961$	19.6611	+	60.5105i	0.634228	+	1.95195i
$962$	34.0904	−	24.7681i	1.09912	−	0.798556i
$963$	−9.29918	+	6.75625i	−0.299662	+	0.217717i
$964$	3.17156	+	9.76106i	0.102149	+	0.314383i
$965$	−9.95770	+	30.6467i	−0.320550	+	0.986551i
$966$	19.0732	+	13.8575i	0.613670	+	0.445857i
$967$	−36.4439			−1.17196			−0.585978	−	0.810327i	$-0.699290\pi$
$967$	−36.4439			−1.17196			−0.585978	+	0.810327i	$0.699290\pi$
$968$		0			0
$969$	24.3188			0.781233
$970$	−43.4999	−	31.6045i	−1.39670	−	1.01476i
$971$	−10.2723	+	31.6148i	−0.329653	+	1.01457i	0.639644	+	0.768671i	$0.279082\pi$
$971$	−10.2723	+	31.6148i	−0.329653	+	1.01457i	−0.969296	+	0.245895i	$0.920918\pi$
$972$	11.3380	+	34.8946i	0.363665	+	1.11925i
$973$	3.09475	−	2.24847i	0.0992133	−	0.0720827i
$974$	33.0723	−	24.0284i	1.05971	−	0.769921i
$975$	−4.81159	−	14.8086i	−0.154094	−	0.474253i
$976$	2.61519	−	8.04874i	0.0837103	−	0.257634i
$977$	−18.2568	−	13.2643i	−0.584086	−	0.424363i	0.256109	−	0.966648i	$-0.417559\pi$
$977$	−18.2568	−	13.2643i	−0.584086	−	0.424363i	−0.840195	+	0.542285i	$0.817559\pi$
$978$	−55.2050			−1.76526
$979$		0			0
$980$	4.91760			0.157087
$981$	−0.676037	−	0.491170i	−0.0215842	−	0.0156818i
$982$	−3.63362	+	11.1831i	−0.115953	+	0.356868i
$983$	−4.66763	−	14.3655i	−0.148874	−	0.458188i	0.848615	−	0.529012i	$-0.177437\pi$
$983$	−4.66763	−	14.3655i	−0.148874	−	0.458188i	−0.997489	+	0.0708236i	$0.977437\pi$
$984$	−1.69133	+	1.22882i	−0.0539177	+	0.0391735i
$985$	−11.4021	+	8.28410i	−0.363301	+	0.263953i
$986$	20.0021	+	61.5601i	0.636996	+	1.96047i
$987$	−4.15497	+	12.7877i	−0.132254	+	0.407036i
$988$	28.7548	+	20.8916i	0.914813	+	0.664651i
$989$	0.896574			0.0285094
$990$		0			0
$991$	−55.1534			−1.75201			−0.876003	−	0.482305i	$-0.839800\pi$
$991$	−55.1534			−1.75201			−0.876003	+	0.482305i	$0.839800\pi$
$992$	6.94254	+	5.04405i	0.220426	+	0.160149i
$993$	1.60470	−	4.93876i	0.0509236	−	0.156727i
$994$	0.0875802	+	0.269544i	0.00277788	+	0.00854942i
$995$	12.4739	−	9.06282i	0.395449	−	0.287311i
$996$	4.30914	−	3.13077i	0.136540	−	0.0992023i
$997$	−15.3596	−	47.2721i	−0.486444	−	1.49712i	−0.829878	−	0.557944i	$-0.811590\pi$
$997$	−15.3596	−	47.2721i	−0.486444	−	1.49712i	0.343434	−	0.939177i	$-0.388410\pi$
$998$	22.9698	−	70.6938i	0.727097	−	2.23777i
$999$	−24.9570	−	18.1323i	−0.789606	−	0.573682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.v.323.1		16
11.2	odd	10		77.2.f.b.71.1	yes	16
11.3	even	5	inner	847.2.f.v.729.1		16
11.4	even	5		847.2.f.x.372.4		16
11.5	even	5		847.2.a.o.1.8		8
11.6	odd	10		847.2.a.p.1.1		8
11.7	odd	10		77.2.f.b.64.1	✓	16
11.8	odd	10		847.2.f.w.729.4		16
11.9	even	5		847.2.f.x.148.4		16
11.10	odd	2		847.2.f.w.323.4		16
33.2	even	10		693.2.m.i.379.4		16
33.5	odd	10		7623.2.a.cw.1.1		8
33.17	even	10		7623.2.a.ct.1.8		8
33.29	even	10		693.2.m.i.64.4		16
77.2	odd	30		539.2.q.g.214.1		32
77.6	even	10		5929.2.a.bt.1.1		8
77.13	even	10		539.2.f.e.148.1		16
77.18	odd	30		539.2.q.g.471.1		32
77.24	even	30		539.2.q.f.324.4		32
77.27	odd	10		5929.2.a.bs.1.8		8
77.40	even	30		539.2.q.f.361.4		32
77.46	odd	30		539.2.q.g.324.4		32
77.51	odd	30		539.2.q.g.361.4		32
77.62	even	10		539.2.f.e.295.1		16
77.68	even	30		539.2.q.f.214.1		32
77.73	even	30		539.2.q.f.471.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	11.7	odd	10
77.2.f.b.71.1	yes	16	11.2	odd	10
539.2.f.e.148.1		16	77.13	even	10
539.2.f.e.295.1		16	77.62	even	10
539.2.q.f.214.1		32	77.68	even	30
539.2.q.f.324.4		32	77.24	even	30
539.2.q.f.361.4		32	77.40	even	30
539.2.q.f.471.1		32	77.73	even	30
539.2.q.g.214.1		32	77.2	odd	30
539.2.q.g.324.4		32	77.46	odd	30
539.2.q.g.361.4		32	77.51	odd	30
539.2.q.g.471.1		32	77.18	odd	30
693.2.m.i.64.4		16	33.29	even	10
693.2.m.i.379.4		16	33.2	even	10
847.2.a.o.1.8		8	11.5	even	5
847.2.a.p.1.1		8	11.6	odd	10
847.2.f.v.323.1		16	1.1	even	1	trivial
847.2.f.v.729.1		16	11.3	even	5	inner
847.2.f.w.323.4		16	11.10	odd	2
847.2.f.w.729.4		16	11.8	odd	10
847.2.f.x.148.4		16	11.9	even	5
847.2.f.x.372.4		16	11.4	even	5
5929.2.a.bs.1.8		8	77.27	odd	10
5929.2.a.bt.1.1		8	77.6	even	10
7623.2.a.ct.1.8		8	33.17	even	10
7623.2.a.cw.1.1		8	33.5	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.96628 - 1.42858i) q^{2} +(0.443194 - 1.36401i) q^{3} +(1.20736 + 3.71587i) q^{4} +(-1.01825 + 0.739805i) q^{5} +(-2.82005 + 2.04888i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.43233 - 4.40826i) q^{8} +(0.762946 + 0.554312i) q^{9} +O(q^{10})\)	\(q+(-1.96628 - 1.42858i) q^{2} +(0.443194 - 1.36401i) q^{3} +(1.20736 + 3.71587i) q^{4} +(-1.01825 + 0.739805i) q^{5} +(-2.82005 + 2.04888i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(1.43233 - 4.40826i) q^{8} +(0.762946 + 0.554312i) q^{9} +3.05904 q^{10} +5.60359 q^{12} +(-2.57131 - 1.86816i) q^{13} +(-0.751051 + 2.31150i) q^{14} +(0.557818 + 1.71679i) q^{15} +(-2.79210 + 2.02858i) q^{16} +(4.79276 - 3.48215i) q^{17} +(-0.708281 - 2.17986i) q^{18} +(-0.884474 + 2.72213i) q^{19} +(-3.97842 - 2.89049i) q^{20} -1.43421 q^{21} +6.76343 q^{23} +(-5.37811 - 3.90743i) q^{24} +(-1.05555 + 3.24866i) q^{25} +(2.38707 + 7.34665i) q^{26} +(4.57511 - 3.32401i) q^{27} +(3.16091 - 2.29654i) q^{28} +(-1.38918 - 4.27547i) q^{29} +(1.35575 - 4.17257i) q^{30} +(-7.86972 - 5.71769i) q^{31} -0.882184 q^{32} -14.3984 q^{34} +(1.01825 + 0.739805i) q^{35} +(-1.13860 + 3.50426i) q^{36} +(-1.68567 - 5.18797i) q^{37} +(5.62791 - 4.08892i) q^{38} +(-3.68778 + 2.67933i) q^{39} +(1.80277 + 5.54837i) q^{40} +(0.0971810 - 0.299092i) q^{41} +(2.82005 + 2.04888i) q^{42} +0.132562 q^{43} -1.18696 q^{45} +(-13.2988 - 9.66213i) q^{46} +(2.89705 - 8.91620i) q^{47} +(1.52956 + 4.70751i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.71650 - 4.87983i) q^{50} +(-2.62556 - 8.08065i) q^{51} +(3.83736 - 11.8102i) q^{52} +(-3.52078 - 2.55800i) q^{53} -13.7446 q^{54} -4.63512 q^{56} +(3.32102 + 2.41286i) q^{57} +(-3.37635 + 10.3913i) q^{58} +(-2.14670 - 6.60685i) q^{59} +(-5.70587 + 4.14556i) q^{60} +(-1.98383 + 1.44134i) q^{61} +(7.30586 + 22.4851i) q^{62} +(0.291419 - 0.896896i) q^{63} +(7.31882 + 5.31744i) q^{64} +4.00032 q^{65} -9.41987 q^{67} +(18.7258 + 13.6051i) q^{68} +(2.99751 - 9.22539i) q^{69} +(-0.945296 - 2.90932i) q^{70} +(0.0943396 - 0.0685417i) q^{71} +(3.53634 - 2.56930i) q^{72} +(-0.190055 - 0.584930i) q^{73} +(-4.09695 + 12.6091i) q^{74} +(3.96340 + 2.87958i) q^{75} -11.1830 q^{76} +11.0789 q^{78} +(6.90033 + 5.01339i) q^{79} +(1.34232 - 4.13122i) q^{80} +(-1.63207 - 5.02300i) q^{81} +(-0.618364 + 0.449267i) q^{82} +(0.768997 - 0.558709i) q^{83} +(-1.73160 - 5.32933i) q^{84} +(-2.30414 + 7.09142i) q^{85} +(-0.260654 - 0.189376i) q^{86} -6.44746 q^{87} +10.0552 q^{89} +(2.33388 + 1.69567i) q^{90} +(-0.982152 + 3.02275i) q^{91} +(8.16590 + 25.1320i) q^{92} +(-11.2868 + 8.20034i) q^{93} +(-18.4339 + 13.3930i) q^{94} +(-1.11323 - 3.42616i) q^{95} +(-0.390979 + 1.20331i) q^{96} +(-14.2201 - 10.3315i) q^{97} +2.43045 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

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