LMFDB - Embedded newform 847.2.f.w.323.4

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			323.4
Root			$0.751051 + 2.31150i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.w.729.4

$q$-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	$0.0290972\pi$
$2$	1.96628	+	1.42858i	1.39037	+	1.01016i	0.394543	+	0.918877i	$0.370903\pi$
$3$	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	0.884189	−	0.467129i	$-0.154712\pi$
$13$	2.57131	+	1.86816i	0.713152	+	0.518135i	−0.171037	+	0.985265i	$0.554712\pi$
$14$	−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	−0.990082	−	0.140494i	$-0.955131\pi$
$17$	−4.79276	+	3.48215i	−1.16242	+	0.844544i	−0.172334	+	0.985039i	$0.555131\pi$
$18$	0.708281	+	2.17986i	0.166943	+	0.513799i
$19$	0.884474	−	2.72213i	0.202912	−	0.624500i	−0.796880	−	0.604137i	$-0.793518\pi$
$19$	0.884474	−	2.72213i	0.202912	−	0.624500i	0.999793	−	0.0203626i	$-0.00648206\pi$
$20$	−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	$0.0370572\pi$
$29$	1.38918	+	4.27547i	0.257965	+	0.793934i	−0.735266	+	0.677779i	$0.762943\pi$
$30$	−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	−0.958358	−	0.285569i	$-0.907818\pi$
$41$	−0.0971810	+	0.299092i	−0.0151771	+	0.0467104i	0.943181	+	0.332279i	$0.107818\pi$
$42$	2.82005	+	2.04888i	0.435143	+	0.316150i
$43$	−0.132562			−0.0202155			−0.0101078	−	0.999949i	$-0.503217\pi$
$43$	−0.132562			−0.0202155			−0.0101078	+	0.999949i	$0.503217\pi$
$44$		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	−0.453495	−	0.891259i	$-0.649823\pi$
$61$	1.98383	−	1.44134i	0.254004	−	0.184545i	0.707499	+	0.706714i	$0.249823\pi$
$62$	−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	0.961562	−	0.274586i	$-0.0885409\pi$
$73$	0.190055	+	0.584930i	0.0222443	+	0.0684608i	−0.939318	+	0.343047i	$0.888541\pi$
$74$	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	0.127533	−	0.991834i	$-0.459294\pi$
$79$	−6.90033	−	5.01339i	−0.776348	−	0.564050i	−0.903881	+	0.427784i	$0.859294\pi$
$80$	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	−0.629189	−	0.777252i	$-0.716613\pi$
$83$	−0.768997	+	0.558709i	−0.0844083	+	0.0613262i	0.544781	+	0.838579i	$0.316613\pi$
$84$	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	0.963013	−	0.269456i	$-0.0868438\pi$
$101$	10.0934	+	7.33330i	1.00433	+	0.729690i	0.0413196	+	0.999146i	$0.486844\pi$
$102$	−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	$-0.699461\pi$
$107$	3.76646	−	11.5920i	0.364117	−	1.12064i	0.950532	−	0.310627i	$-0.100539\pi$
$108$	17.8754	+	12.9873i	1.72006	+	1.24970i
$109$	0.886088			0.0848718			0.0424359	−	0.999099i	$-0.486488\pi$
$109$	0.886088			0.0848718			0.0424359	+	0.999099i	$0.486488\pi$
$110$		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	−0.261086	−	0.965316i	$-0.584081\pi$
$127$	6.49462	−	4.71861i	0.576304	−	0.418709i	0.837390	+	0.546606i	$0.184081\pi$
$128$	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	$-0.498589\pi$
$131$	0.101461			0.00886466			0.00443233	+	0.999990i	$0.498589\pi$
$132$		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	0.888326	−	0.459213i	$-0.151869\pi$
$139$	−1.18209	−	3.63810i	−0.100264	−	0.308580i	−0.988590	+	0.150634i	$0.951869\pi$
$140$	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	−0.414501	−	0.910049i	$-0.636044\pi$
$149$	3.94172	−	2.86383i	0.322918	−	0.234614i	0.737420	+	0.675435i	$0.236044\pi$
$150$	3.67942	+	11.3241i	0.300424	+	0.924609i
$151$	−5.24521	+	16.1431i	−0.426849	+	1.31371i	0.474363	+	0.880329i	$0.342678\pi$
$151$	−5.24521	+	16.1431i	−0.426849	+	1.31371i	−0.901212	+	0.433378i	$0.857322\pi$
$152$	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	−0.298557	−	0.954392i	$-0.596505\pi$
$167$	−16.7803	−	12.1916i	−1.29850	−	0.943413i	−0.999940	+	0.0109787i	$0.996505\pi$
$168$	−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	$0.405701\pi$
$173$	−6.66099	+	20.5004i	−0.506426	+	1.55862i	−0.798361	+	0.602180i	$0.794299\pi$
$174$	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	$0.672991\pi$
$193$	−20.7127	+	15.0486i	−1.49093	+	1.08322i	−0.973824	+	0.227303i	$0.927009\pi$
$194$	−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	$-0.630608\pi$
$197$	−11.1977			−0.797802			−0.398901	+	0.916994i	$0.630608\pi$
$198$		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	0.909269	−	0.416208i	$-0.136641\pi$
$211$	11.5395	+	8.38393i	0.794411	+	0.577174i	−0.114858	+	0.993382i	$0.536641\pi$
$212$	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	0.999329	−	0.0366150i	$-0.0116575\pi$
$227$	2.55126	+	7.85197i	0.169333	+	0.521154i	−0.829996	+	0.557769i	$0.811658\pi$
$228$	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	0.873316	−	0.487155i	$-0.161965\pi$
$233$	10.3778	+	7.53992i	0.679873	+	0.493957i	−0.193443	+	0.981112i	$0.561965\pi$
$234$	−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	−0.988417	−	0.151765i	$-0.951504\pi$
$239$	−1.53924	+	4.73730i	−0.0995653	+	0.306430i	0.888851	+	0.458196i	$0.151504\pi$
$240$	−5.04013	−	3.66187i	−0.325339	−	0.236372i
$241$	−2.62686			−0.169211			−0.0846053	−	0.996415i	$-0.526963\pi$
$241$	−2.62686			−0.169211			−0.0846053	+	0.996415i	$0.526963\pi$
$242$		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	$-0.467192\pi$
$263$	3.33709			0.205774			0.102887	+	0.994693i	$0.467192\pi$
$264$		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	0.925125	−	0.379663i	$-0.123960\pi$
$271$	−0.765113	−	2.35478i	−0.0464773	−	0.143042i	−0.971602	+	0.236621i	$0.923960\pi$
$272$	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	0.455385	−	0.890295i	$-0.349502\pi$
$277$	−4.17105	−	3.03045i	−0.250614	−	0.182082i	−0.705999	+	0.708213i	$0.749502\pi$
$278$	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	0.110015	−	0.993930i	$-0.464910\pi$
$281$	18.2599	−	13.2666i	1.08930	−	0.791419i	0.979280	+	0.202510i	$0.0649100\pi$
$282$	−10.0984	−	31.0798i	−0.601354	−	1.85078i
$283$	−2.62280	+	8.07216i	−0.155909	+	0.479840i	−0.998252	−	0.0591027i	$-0.981176\pi$
$283$	−2.62280	+	8.07216i	−0.155909	+	0.479840i	0.842342	+	0.538943i	$0.181176\pi$
$284$	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	$0.155554\pi$
$293$	7.60988	+	23.4208i	0.444574	+	1.36826i	−0.438376	+	0.898792i	$0.644446\pi$
$294$	−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	$-0.458151\pi$
$307$	4.59391			0.262188			0.131094	+	0.991370i	$0.458151\pi$
$308$		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	0.882563	−	0.470194i	$-0.155816\pi$
$337$	−1.97928	−	6.09161i	−0.107818	−	0.331831i	−0.990382	+	0.138363i	$0.955816\pi$
$338$	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	−0.140093	−	0.990138i	$-0.544740\pi$
$347$	14.1254	−	10.2627i	0.758293	−	0.550932i	0.898386	+	0.439206i	$0.144740\pi$
$348$	7.78441	+	23.9580i	0.417288	+	1.28428i
$349$	−6.68246	+	20.5665i	−0.357704	+	1.10090i	0.596721	+	0.802449i	$0.296470\pi$
$349$	−6.68246	+	20.5665i	−0.357704	+	1.10090i	−0.954425	+	0.298451i	$0.903530\pi$
$350$	−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	0.825385	−	0.564570i	$-0.190958\pi$
$359$	−3.30084	−	10.1589i	−0.174212	−	0.536168i	−0.999597	+	0.0284023i	$0.990958\pi$
$360$	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	$-0.756739\pi$
$373$	−27.8851			−1.44383			−0.721917	+	0.691980i	$0.756739\pi$
$374$		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	0.113536	−	0.993534i	$-0.463782\pi$
$409$	−16.1039	−	11.7002i	−0.796286	−	0.578536i	−0.909822	+	0.414998i	$0.863782\pi$
$410$	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	0.141681	−	0.989912i	$-0.454749\pi$
$431$	−15.6950	−	11.4031i	−0.756000	−	0.549266i	−0.897681	+	0.440646i	$0.854749\pi$
$432$	−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	$-0.773449\pi$
$439$	−31.7315			−1.51446			−0.757232	+	0.653146i	$0.773449\pi$
$440$		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	−0.764140	−	0.645051i	$-0.776836\pi$
$457$	−8.26867	+	6.00754i	−0.386792	+	0.281021i	0.377348	+	0.926072i	$0.376836\pi$
$458$	−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	$-0.672216\pi$
$461$	−22.1160			−1.03004			−0.515022	+	0.857177i	$0.672216\pi$
$462$		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	−0.122314	−	0.992491i	$-0.539032\pi$
$479$	17.1544	−	12.4634i	0.783804	−	0.569467i	0.906118	+	0.423025i	$0.139032\pi$
$480$	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	0.979107	−	0.203344i	$-0.0651811\pi$
$491$	1.49504	+	4.60125i	0.0674701	+	0.207652i	−0.911637	+	0.410996i	$0.865181\pi$
$492$	−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	$0.316779\pi$
$503$	−8.72684	+	26.8585i	−0.389111	+	1.19756i	−0.933454	+	0.358697i	$0.883221\pi$
$504$	−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	−0.110420	−	0.993885i	$-0.535220\pi$
$523$	18.3113	−	13.3040i	0.800699	−	0.581742i	0.911119	+	0.412143i	$0.135220\pi$
$524$	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	$-0.929596\pi$
$541$	−34.5582	−	25.1080i	−1.48577	−	1.07948i	−0.510134	−	0.860095i	$-0.670404\pi$
$542$	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	$-0.500087\pi$
$547$	13.7459	−	42.3056i	0.587733	−	1.80886i	0.588007	−	0.808856i	$-0.299913\pi$
$548$	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	$-0.922397\pi$
$557$	−7.72268	−	23.7680i	−0.327220	−	1.00708i	0.643208	−	0.765691i	$-0.277603\pi$
$558$	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	0.423490	−	0.905901i	$-0.360805\pi$
$563$	−7.28929	−	5.29598i	−0.307207	−	0.223199i	−0.730697	+	0.682702i	$0.760805\pi$
$564$	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	$-0.690560\pi$
$569$	9.01521	−	27.7460i	0.377937	−	1.16317i	0.941475	−	0.337082i	$-0.109440\pi$
$570$	10.1592	+	7.38106i	0.425520	+	0.309158i
$571$	1.78994			0.0749067			0.0374533	−	0.999298i	$-0.488075\pi$
$571$	1.78994			0.0749067			0.0374533	+	0.999298i	$0.488075\pi$
$572$		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	$-0.815957\pi$
$593$	−40.7867			−1.67491			−0.837454	+	0.546508i	$0.815957\pi$
$594$		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	$-0.820090\pi$
$601$	−11.6715	−	35.9213i	−0.476092	−	1.46526i	0.368387	−	0.929673i	$-0.379910\pi$
$602$	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	0.941112	−	0.338095i	$-0.109782\pi$
$607$	22.4295	+	16.2960i	0.910385	+	0.661433i	−0.0307275	+	0.999528i	$0.509782\pi$
$608$	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	$-0.638780\pi$
$613$	11.1946	−	34.4534i	0.452145	−	1.39156i	0.874454	−	0.485108i	$-0.161220\pi$
$614$	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	$-0.532871\pi$
$659$	−5.29247			−0.206165			−0.103083	+	0.994673i	$0.532871\pi$
$660$		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	0.843130	−	0.537710i	$-0.180711\pi$
$673$	15.3650	+	11.1633i	0.592278	+	0.430315i	−0.250851	+	0.968026i	$0.580711\pi$
$674$	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	−0.963809	−	0.266595i	$-0.914101\pi$
$677$	−26.2299	+	19.0571i	−1.00810	+	0.732424i	−0.0442864	+	0.999019i	$0.514101\pi$
$678$	−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	−0.999982	−	0.00592402i	$-0.998114\pi$
$701$	−4.96426	+	15.2784i	−0.187498	+	0.577058i	0.812485	+	0.582982i	$0.198114\pi$
$702$	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	$0.176072\pi$
$733$	12.7601	+	39.2716i	0.471305	+	1.45053i	−0.379571	+	0.925163i	$0.623928\pi$
$734$	−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	−0.0808639	−	0.996725i	$-0.525768\pi$
$739$	−28.6469	−	20.8132i	−1.05379	−	0.765626i	−0.972930	+	0.231099i	$0.925768\pi$
$740$	−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	−0.526464	−	0.850197i	$-0.676483\pi$
$743$	3.25555	−	2.36530i	0.119435	−	0.0867743i	0.645899	+	0.763423i	$0.276483\pi$
$744$	−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	0.688919	−	0.724838i	$-0.258085\pi$
$761$	5.86055	+	4.25794i	0.212445	+	0.154350i	−0.476474	+	0.879188i	$0.658085\pi$
$762$	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	$-0.205363\pi$
$769$	44.3139			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$770$		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	−0.940319	−	0.340294i	$-0.889473\pi$
$787$	−25.4517	+	18.4917i	−0.907255	+	0.659159i	0.0330644	+	0.999453i	$0.489473\pi$
$788$	−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	−0.508634	−	0.860983i	$-0.669849\pi$
$809$	4.35271	−	3.16243i	0.153033	−	0.111185i	0.661667	+	0.749798i	$0.269849\pi$
$810$	4.99258	+	15.3656i	0.175421	+	0.539891i
$811$	4.23351	−	13.0294i	0.148659	−	0.457524i	−0.848805	−	0.528707i	$-0.822677\pi$
$811$	4.23351	−	13.0294i	0.148659	−	0.457524i	0.997463	+	0.0711822i	$0.0226772\pi$
$812$	−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	0.888858	−	0.458182i	$-0.151499\pi$
$821$	−2.85258	−	8.77935i	−0.0995559	−	0.306401i	−0.988414	+	0.151781i	$0.951499\pi$
$822$	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	0.649067	−	0.760731i	$-0.275159\pi$
$827$	3.62752	+	2.63555i	0.126141	+	0.0916471i	−0.522926	+	0.852378i	$0.675159\pi$
$828$	−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	−0.674421	−	0.738347i	$-0.735607\pi$
$853$	−5.27519	+	3.83265i	−0.180619	+	0.131227i	0.493802	+	0.869574i	$0.335607\pi$
$854$	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	$-0.193371\pi$
$857$	48.0736			1.64216			0.821082	+	0.570810i	$0.193371\pi$
$858$		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	$-0.751094\pi$
$877$	8.25311	−	25.4004i	0.278688	−	0.857712i	0.988220	−	0.153039i	$-0.0489062\pi$
$878$	−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	$-0.967850\pi$
$887$	−7.42409	−	22.8490i	−0.249277	−	0.767194i	0.745627	−	0.666363i	$-0.232150\pi$
$888$	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	−0.928571	−	0.371154i	$-0.878962\pi$
$919$	−26.1475	+	18.9973i	−0.862527	+	0.626663i	0.0660439	+	0.997817i	$0.478962\pi$
$920$	−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	0.0368058	−	0.999322i	$-0.488282\pi$
$937$	−27.6178	−	20.0655i	−0.902233	−	0.655510i	−0.939038	+	0.343812i	$0.888282\pi$
$938$	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	−0.600625	−	0.799531i	$-0.705081\pi$
$941$	−0.792327	+	0.575660i	−0.0258291	+	0.0187660i	0.574796	+	0.818297i	$0.305081\pi$
$942$	−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	0.999211	−	0.0397147i	$-0.0126449\pi$
$953$	5.17049	+	15.9131i	0.167489	+	0.515477i	−0.831722	+	0.555192i	$0.812645\pi$
$954$	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	$-0.300710\pi$
$967$	36.4439			1.17196			0.585978	+	0.810327i	$0.300710\pi$
$968$		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	$0.188410\pi$
$997$	15.3596	+	47.2721i	0.486444	+	1.49712i	−0.343434	+	0.939177i	$0.611590\pi$
$998$	−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.w.323.4		16
11.2	odd	10		847.2.f.x.148.4		16
11.3	even	5	inner	847.2.f.w.729.4		16
11.4	even	5		77.2.f.b.64.1	✓	16
11.5	even	5		847.2.a.p.1.1		8
11.6	odd	10		847.2.a.o.1.8		8
11.7	odd	10		847.2.f.x.372.4		16
11.8	odd	10		847.2.f.v.729.1		16
11.9	even	5		77.2.f.b.71.1	yes	16
11.10	odd	2		847.2.f.v.323.1		16
33.5	odd	10		7623.2.a.ct.1.8		8
33.17	even	10		7623.2.a.cw.1.1		8
33.20	odd	10		693.2.m.i.379.4		16
33.26	odd	10		693.2.m.i.64.4		16
77.4	even	15		539.2.q.g.471.1		32
77.6	even	10		5929.2.a.bs.1.8		8
77.9	even	15		539.2.q.g.214.1		32
77.20	odd	10		539.2.f.e.148.1		16
77.26	odd	30		539.2.q.f.361.4		32
77.27	odd	10		5929.2.a.bt.1.1		8
77.31	odd	30		539.2.q.f.324.4		32
77.37	even	15		539.2.q.g.361.4		32
77.48	odd	10		539.2.f.e.295.1		16
77.53	even	15		539.2.q.g.324.4		32
77.59	odd	30		539.2.q.f.471.1		32
77.75	odd	30		539.2.q.f.214.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.1	✓	16	11.4	even	5
77.2.f.b.71.1	yes	16	11.9	even	5
539.2.f.e.148.1		16	77.20	odd	10
539.2.f.e.295.1		16	77.48	odd	10
539.2.q.f.214.1		32	77.75	odd	30
539.2.q.f.324.4		32	77.31	odd	30
539.2.q.f.361.4		32	77.26	odd	30
539.2.q.f.471.1		32	77.59	odd	30
539.2.q.g.214.1		32	77.9	even	15
539.2.q.g.324.4		32	77.53	even	15
539.2.q.g.361.4		32	77.37	even	15
539.2.q.g.471.1		32	77.4	even	15
693.2.m.i.64.4		16	33.26	odd	10
693.2.m.i.379.4		16	33.20	odd	10
847.2.a.o.1.8		8	11.6	odd	10
847.2.a.p.1.1		8	11.5	even	5
847.2.f.v.323.1		16	11.10	odd	2
847.2.f.v.729.1		16	11.8	odd	10
847.2.f.w.323.4		16	1.1	even	1	trivial
847.2.f.w.729.4		16	11.3	even	5	inner
847.2.f.x.148.4		16	11.2	odd	10
847.2.f.x.372.4		16	11.7	odd	10
5929.2.a.bs.1.8		8	77.6	even	10
5929.2.a.bt.1.1		8	77.27	odd	10
7623.2.a.ct.1.8		8	33.5	odd	10
7623.2.a.cw.1.1		8	33.17	even	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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