LMFDB - Embedded newform 731.2.f.c.259.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.3
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68403i q^{2} +(0.675148 - 0.675148i) q^{3} -5.20400 q^{4} +(-0.573416 + 0.573416i) q^{5} +(-1.81211 - 1.81211i) q^{6} +(1.88065 + 1.88065i) q^{7} +8.59962i q^{8} +2.08835i q^{9} +O(q^{10})$	\(q-2.68403i q^{2} +(0.675148 - 0.675148i) q^{3} -5.20400 q^{4} +(-0.573416 + 0.573416i) q^{5} +(-1.81211 - 1.81211i) q^{6} +(1.88065 + 1.88065i) q^{7} +8.59962i q^{8} +2.08835i q^{9} +(1.53907 + 1.53907i) q^{10} +(4.38200 + 4.38200i) q^{11} +(-3.51347 + 3.51347i) q^{12} -2.59895 q^{13} +(5.04771 - 5.04771i) q^{14} +0.774282i q^{15} +12.6736 q^{16} +(-0.138307 + 4.12079i) q^{17} +5.60519 q^{18} -3.47907i q^{19} +(2.98406 - 2.98406i) q^{20} +2.53943 q^{21} +(11.7614 - 11.7614i) q^{22} +(-2.92787 - 2.92787i) q^{23} +(5.80602 + 5.80602i) q^{24} +4.34239i q^{25} +6.97564i q^{26} +(3.43539 + 3.43539i) q^{27} +(-9.78689 - 9.78689i) q^{28} +(-2.57225 + 2.57225i) q^{29} +2.07819 q^{30} +(-3.45517 + 3.45517i) q^{31} -16.8171i q^{32} +5.91699 q^{33} +(11.0603 + 0.371220i) q^{34} -2.15679 q^{35} -10.8678i q^{36} +(-2.46702 + 2.46702i) q^{37} -9.33792 q^{38} +(-1.75467 + 1.75467i) q^{39} +(-4.93116 - 4.93116i) q^{40} +(-5.75714 - 5.75714i) q^{41} -6.81590i q^{42} +1.00000i q^{43} +(-22.8039 - 22.8039i) q^{44} +(-1.19749 - 1.19749i) q^{45} +(-7.85848 + 7.85848i) q^{46} +5.63605 q^{47} +(8.55656 - 8.55656i) q^{48} +0.0736760i q^{49} +11.6551 q^{50} +(2.68876 + 2.87552i) q^{51} +13.5249 q^{52} +12.4286i q^{53} +(9.22068 - 9.22068i) q^{54} -5.02542 q^{55} +(-16.1729 + 16.1729i) q^{56} +(-2.34889 - 2.34889i) q^{57} +(6.90398 + 6.90398i) q^{58} -11.8980i q^{59} -4.02936i q^{60} +(-2.77142 - 2.77142i) q^{61} +(9.27376 + 9.27376i) q^{62} +(-3.92745 + 3.92745i) q^{63} -19.7903 q^{64} +(1.49028 - 1.49028i) q^{65} -15.8814i q^{66} +8.78722 q^{67} +(0.719750 - 21.4446i) q^{68} -3.95349 q^{69} +5.78888i q^{70} +(5.07790 - 5.07790i) q^{71} -17.9590 q^{72} +(7.51547 - 7.51547i) q^{73} +(6.62154 + 6.62154i) q^{74} +(2.93175 + 2.93175i) q^{75} +18.1051i q^{76} +16.4820i q^{77} +(4.70959 + 4.70959i) q^{78} +(4.07309 + 4.07309i) q^{79} +(-7.26726 + 7.26726i) q^{80} -1.62626 q^{81} +(-15.4523 + 15.4523i) q^{82} -15.1143i q^{83} -13.2152 q^{84} +(-2.28362 - 2.44223i) q^{85} +2.68403 q^{86} +3.47329i q^{87} +(-37.6835 + 37.6835i) q^{88} +7.35942 q^{89} +(-3.21411 + 3.21411i) q^{90} +(-4.88770 - 4.88770i) q^{91} +(15.2366 + 15.2366i) q^{92} +4.66549i q^{93} -15.1273i q^{94} +(1.99496 + 1.99496i) q^{95} +(-11.3540 - 11.3540i) q^{96} +(-7.30257 + 7.30257i) q^{97} +0.197748 q^{98} +(-9.15115 + 9.15115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	2.68403i		−	1.89789i	−0.315436	−	0.948947i	$-0.602151\pi$
$2$		−	2.68403i		−	1.89789i	0.315436	−	0.948947i	$-0.397849\pi$
$3$	0.675148	−	0.675148i	0.389797	−	0.389797i	−0.484818	−	0.874615i	$-0.661114\pi$
$3$	0.675148	−	0.675148i	0.389797	−	0.389797i	0.874615	+	0.484818i	$0.161114\pi$
$4$	−5.20400			−2.60200
$5$	−0.573416	+	0.573416i	−0.256440	+	0.256440i	−0.823604	−	0.567165i	$-0.808040\pi$
$5$	−0.573416	+	0.573416i	−0.256440	+	0.256440i	0.567165	+	0.823604i	$0.308040\pi$
$6$	−1.81211	−	1.81211i	−0.739793	−	0.739793i
$7$	1.88065	+	1.88065i	0.710818	+	0.710818i	0.966706	−	0.255888i	$-0.0823679\pi$
$7$	1.88065	+	1.88065i	0.710818	+	0.710818i	−0.255888	+	0.966706i	$0.582368\pi$
$8$			8.59962i			3.04043i
$9$			2.08835i			0.696117i
$10$	1.53907	+	1.53907i	0.486695	+	0.486695i
$11$	4.38200	+	4.38200i	1.32122	+	1.32122i	0.912788	+	0.408434i	$0.133925\pi$
$11$	4.38200	+	4.38200i	1.32122	+	1.32122i	0.408434	+	0.912788i	$0.366075\pi$
$12$	−3.51347	+	3.51347i	−1.01425	+	1.01425i
$13$	−2.59895			−0.720818			−0.360409	−	0.932794i	$-0.617363\pi$
$13$	−2.59895			−0.720818			−0.360409	+	0.932794i	$0.617363\pi$
$14$	5.04771	−	5.04771i	1.34906	−	1.34906i
$15$			0.774282i			0.199919i
$16$	12.6736			3.16840
$17$	−0.138307	+	4.12079i	−0.0335444	+	0.999437i
$17$	−0.138307	+	4.12079i	−0.0335444	+	0.999437i
$18$	5.60519			1.32116
$19$		−	3.47907i		−	0.798154i	−0.916918	−	0.399077i	$-0.869331\pi$
$19$		−	3.47907i		−	0.798154i	0.916918	−	0.399077i	$-0.130669\pi$
$20$	2.98406	−	2.98406i	0.667256	−	0.667256i
$21$	2.53943			0.554149
$22$	11.7614	−	11.7614i	2.50754	−	2.50754i
$23$	−2.92787	−	2.92787i	−0.610503	−	0.610503i	0.332574	−	0.943077i	$-0.392083\pi$
$23$	−2.92787	−	2.92787i	−0.610503	−	0.610503i	−0.943077	+	0.332574i	$0.892083\pi$
$24$	5.80602	+	5.80602i	1.18515	+	1.18515i
$25$			4.34239i			0.868477i
$26$			6.97564i			1.36804i
$27$	3.43539	+	3.43539i	0.661141	+	0.661141i
$28$	−9.78689	−	9.78689i	−1.84955	−	1.84955i
$29$	−2.57225	+	2.57225i	−0.477654	+	0.477654i	−0.904381	−	0.426727i	$-0.859667\pi$
$29$	−2.57225	+	2.57225i	−0.477654	+	0.477654i	0.426727	+	0.904381i	$0.359667\pi$
$30$	2.07819			0.379424
$31$	−3.45517	+	3.45517i	−0.620566	+	0.620566i	−0.945676	−	0.325110i	$-0.894599\pi$
$31$	−3.45517	+	3.45517i	−0.620566	+	0.620566i	0.325110	+	0.945676i	$0.394599\pi$
$32$		−	16.8171i		−	2.97287i
$33$	5.91699			1.03002
$34$	11.0603	+	0.371220i	1.89683	+	0.0636637i
$35$	−2.15679			−0.364564
$36$		−	10.8678i		−	1.81130i
$37$	−2.46702	+	2.46702i	−0.405575	+	0.405575i	−0.880192	−	0.474617i	$-0.842586\pi$
$37$	−2.46702	+	2.46702i	−0.405575	+	0.405575i	0.474617	+	0.880192i	$0.342586\pi$
$38$	−9.33792			−1.51481
$39$	−1.75467	+	1.75467i	−0.280972	+	0.280972i
$40$	−4.93116	−	4.93116i	−0.779686	−	0.779686i
$41$	−5.75714	−	5.75714i	−0.899114	−	0.899114i	0.0962439	−	0.995358i	$-0.469317\pi$
$41$	−5.75714	−	5.75714i	−0.899114	−	0.899114i	−0.995358	+	0.0962439i	$0.969317\pi$
$42$		−	6.81590i		−	1.05172i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−22.8039	−	22.8039i	−3.43782	−	3.43782i
$45$	−1.19749	−	1.19749i	−0.178512	−	0.178512i
$46$	−7.85848	+	7.85848i	−1.15867	+	1.15867i
$47$	5.63605			0.822102			0.411051	−	0.911612i	$-0.365162\pi$
$47$	5.63605			0.822102			0.411051	+	0.911612i	$0.365162\pi$
$48$	8.55656	−	8.55656i	1.23503	−	1.23503i
$49$			0.0736760i			0.0105251i
$50$	11.6551			1.64828
$51$	2.68876	+	2.87552i	0.376502	+	0.402653i
$52$	13.5249			1.87557
$53$			12.4286i			1.70720i	0.520931	+	0.853599i	$0.325585\pi$
$53$			12.4286i			1.70720i	−0.520931	+	0.853599i	$0.674415\pi$
$54$	9.22068	−	9.22068i	1.25478	−	1.25478i
$55$	−5.02542			−0.677627
$56$	−16.1729	+	16.1729i	−2.16119	+	2.16119i
$57$	−2.34889	−	2.34889i	−0.311118	−	0.311118i
$58$	6.90398	+	6.90398i	0.906537	+	0.906537i
$59$		−	11.8980i		−	1.54899i	−0.632582	−	0.774493i	$-0.718005\pi$
$59$		−	11.8980i		−	1.54899i	0.632582	−	0.774493i	$-0.281995\pi$
$60$		−	4.02936i		−	0.520188i
$61$	−2.77142	−	2.77142i	−0.354844	−	0.354844i	0.507065	−	0.861908i	$-0.330731\pi$
$61$	−2.77142	−	2.77142i	−0.354844	−	0.354844i	−0.861908	+	0.507065i	$0.830731\pi$
$62$	9.27376	+	9.27376i	1.17777	+	1.17777i
$63$	−3.92745	+	3.92745i	−0.494813	+	0.494813i
$64$	−19.7903			−2.47378
$65$	1.49028	−	1.49028i	0.184846	−	0.184846i
$66$		−	15.8814i		−	1.95486i
$67$	8.78722			1.07353			0.536765	−	0.843732i	$-0.319646\pi$
$67$	8.78722			1.07353			0.536765	+	0.843732i	$0.319646\pi$
$68$	0.719750	−	21.4446i	0.0872826	−	2.60054i
$69$	−3.95349			−0.475944
$70$			5.78888i			0.691904i
$71$	5.07790	−	5.07790i	0.602636	−	0.602636i	−0.338375	−	0.941011i	$-0.609877\pi$
$71$	5.07790	−	5.07790i	0.602636	−	0.602636i	0.941011	+	0.338375i	$0.109877\pi$
$72$	−17.9590			−2.11649
$73$	7.51547	−	7.51547i	0.879619	−	0.879619i	−0.113876	−	0.993495i	$-0.536327\pi$
$73$	7.51547	−	7.51547i	0.879619	−	0.879619i	0.993495	+	0.113876i	$0.0363267\pi$
$74$	6.62154	+	6.62154i	0.769738	+	0.769738i
$75$	2.93175	+	2.93175i	0.338530	+	0.338530i
$76$			18.1051i			2.07680i
$77$			16.4820i			1.87830i
$78$	4.70959	+	4.70959i	0.533256	+	0.533256i
$79$	4.07309	+	4.07309i	0.458259	+	0.458259i	0.898084	−	0.439825i	$-0.144959\pi$
$79$	4.07309	+	4.07309i	0.458259	+	0.458259i	−0.439825	+	0.898084i	$0.644959\pi$
$80$	−7.26726	+	7.26726i	−0.812504	+	0.812504i
$81$	−1.62626			−0.180696
$82$	−15.4523	+	15.4523i	−1.70642	+	1.70642i
$83$		−	15.1143i		−	1.65901i	−0.558496	−	0.829507i	$-0.688621\pi$
$83$		−	15.1143i		−	1.65901i	0.558496	−	0.829507i	$-0.311379\pi$
$84$	−13.2152			−1.44190
$85$	−2.28362	−	2.44223i	−0.247693	−	0.264897i
$86$	2.68403			0.289426
$87$			3.47329i			0.372376i
$88$	−37.6835	+	37.6835i	−4.01708	+	4.01708i
$89$	7.35942			0.780097			0.390049	−	0.920794i	$-0.372458\pi$
$89$	7.35942			0.780097			0.390049	+	0.920794i	$0.372458\pi$
$90$	−3.21411	+	3.21411i	−0.338797	+	0.338797i
$91$	−4.88770	−	4.88770i	−0.512370	−	0.512370i
$92$	15.2366	+	15.2366i	1.58853	+	1.58853i
$93$			4.66549i			0.483789i
$94$		−	15.1273i		−	1.56026i
$95$	1.99496	+	1.99496i	0.204678	+	0.204678i
$96$	−11.3540	−	11.3540i	−1.15881	−	1.15881i
$97$	−7.30257	+	7.30257i	−0.741464	+	0.741464i	−0.972860	−	0.231396i	$-0.925671\pi$
$97$	−7.30257	+	7.30257i	−0.741464	+	0.741464i	0.231396	+	0.972860i	$0.425671\pi$
$98$	0.197748			0.0199756
$99$	−9.15115	+	9.15115i	−0.919725	+	0.919725i
$100$		−	22.5978i		−	2.25978i
$101$	2.12546			0.211491			0.105745	−	0.994393i	$-0.466277\pi$
$101$	2.12546			0.211491			0.105745	+	0.994393i	$0.466277\pi$
$102$	7.71796	−	7.21671i	0.764192	−	0.714561i
$103$	6.24411			0.615250			0.307625	−	0.951508i	$-0.400466\pi$
$103$	6.24411			0.615250			0.307625	+	0.951508i	$0.400466\pi$
$104$		−	22.3499i		−	2.19159i
$105$	−1.45615	+	1.45615i	−0.142106	+	0.142106i
$106$	33.3586			3.24008
$107$	0.973231	−	0.973231i	0.0940858	−	0.0940858i	−0.658497	−	0.752583i	$-0.728808\pi$
$107$	0.973231	−	0.973231i	0.0940858	−	0.0940858i	0.752583	+	0.658497i	$0.228808\pi$
$108$	−17.8778	−	17.8778i	−1.72029	−	1.72029i
$109$	4.90444	+	4.90444i	0.469760	+	0.469760i	0.901837	−	0.432076i	$-0.142219\pi$
$109$	4.90444	+	4.90444i	0.469760	+	0.469760i	−0.432076	+	0.901837i	$0.642219\pi$
$110$			13.4884i			1.28606i
$111$			3.33120i			0.316184i
$112$	23.8346	+	23.8346i	2.25216	+	2.25216i
$113$	−13.7845	−	13.7845i	−1.29674	−	1.29674i	−0.930535	−	0.366203i	$-0.880657\pi$
$113$	−13.7845	−	13.7845i	−1.29674	−	1.29674i	−0.366203	−	0.930535i	$-0.619343\pi$
$114$	−6.30448	+	6.30448i	−0.590468	+	0.590468i
$115$	3.35778			0.313114
$116$	13.3860	−	13.3860i	1.24286	−	1.24286i
$117$		−	5.42751i		−	0.501773i
$118$	−31.9345			−2.93981
$119$	−8.00985	+	7.48964i	−0.734262	+	0.686574i
$120$	−6.65853			−0.607838
$121$			27.4038i			2.49125i
$122$	−7.43856	+	7.43856i	−0.673455	+	0.673455i
$123$	−7.77384			−0.700943
$124$	17.9807	−	17.9807i	1.61471	−	1.61471i
$125$	−5.35708	−	5.35708i	−0.479152	−	0.479152i
$126$	10.5414	+	10.5414i	0.939102	+	0.939102i
$127$		−	9.42367i		−	0.836215i	−0.908397	−	0.418108i	$-0.862693\pi$
$127$		−	9.42367i		−	0.836215i	0.908397	−	0.418108i	$-0.137307\pi$
$128$			19.4834i			1.72211i
$129$	0.675148	+	0.675148i	0.0594435	+	0.0594435i
$130$	−3.99995	−	3.99995i	−0.350819	−	0.350819i
$131$	8.68538	−	8.68538i	0.758845	−	0.758845i	−0.217267	−	0.976112i	$-0.569714\pi$
$131$	8.68538	−	8.68538i	0.758845	−	0.758845i	0.976112	+	0.217267i	$0.0697143\pi$
$132$	−30.7920			−2.68010
$133$	6.54291	−	6.54291i	0.567342	−	0.567342i
$134$		−	23.5851i		−	2.03744i
$135$	−3.93982			−0.339086
$136$	−35.4372	−	1.18939i	−3.03871	−	0.101989i
$137$	15.4024			1.31592			0.657959	−	0.753053i	$-0.271420\pi$
$137$	15.4024			1.31592			0.657959	+	0.753053i	$0.271420\pi$
$138$			10.6113i			0.903292i
$139$	−2.77605	+	2.77605i	−0.235461	+	0.235461i	−0.814968	−	0.579506i	$-0.803245\pi$
$139$	−2.77605	+	2.77605i	−0.235461	+	0.235461i	0.579506	+	0.814968i	$0.303245\pi$
$140$	11.2239			0.948595
$141$	3.80516	−	3.80516i	0.320453	−	0.320453i
$142$	−13.6292	−	13.6292i	−1.14374	−	1.14374i
$143$	−11.3886	−	11.3886i	−0.952360	−	0.952360i
$144$			26.4670i			2.20558i
$145$		−	2.94994i		−	0.244979i
$146$	−20.1717	−	20.1717i	−1.66942	−	1.66942i
$147$	0.0497422	+	0.0497422i	0.00410267	+	0.00410267i
$148$	12.8383	−	12.8383i	1.05531	−	1.05531i
$149$	12.0579			0.987825			0.493912	−	0.869512i	$-0.335566\pi$
$149$	12.0579			0.987825			0.493912	+	0.869512i	$0.335566\pi$
$150$	7.86890	−	7.86890i	0.642493	−	0.642493i
$151$			14.2038i			1.15589i	0.816076	+	0.577944i	$0.196145\pi$
$151$			14.2038i			1.15589i	−0.816076	+	0.577944i	$0.803855\pi$
$152$	29.9187			2.42673
$153$	−8.60565	−	0.288834i	−0.695725	−	0.0233508i
$154$	44.2381			3.56481
$155$		−	3.96250i		−	0.318275i
$156$	9.13132	−	9.13132i	0.731090	−	0.731090i
$157$	13.5577			1.08202			0.541011	−	0.841015i	$-0.318042\pi$
$157$	13.5577			1.08202			0.541011	+	0.841015i	$0.318042\pi$
$158$	10.9323	−	10.9323i	0.869727	−	0.869727i
$159$	8.39113	+	8.39113i	0.665460	+	0.665460i
$160$	9.64319	+	9.64319i	0.762361	+	0.762361i
$161$		−	11.0126i		−	0.867914i
$162$			4.36493i			0.342941i
$163$	1.14848	+	1.14848i	0.0899560	+	0.0899560i	0.750653	−	0.660697i	$-0.229739\pi$
$163$	1.14848	+	1.14848i	0.0899560	+	0.0899560i	−0.660697	+	0.750653i	$0.729739\pi$
$164$	29.9601	+	29.9601i	2.33949	+	2.33949i
$165$	−3.39290	+	3.39290i	−0.264137	+	0.264137i
$166$	−40.5673			−3.14863
$167$	−1.35822	+	1.35822i	−0.105103	+	0.105103i	−0.757703	−	0.652600i	$-0.773678\pi$
$167$	−1.35822	+	1.35822i	−0.105103	+	0.105103i	0.652600	+	0.757703i	$0.273678\pi$
$168$			21.8381i			1.68485i
$169$	−6.24548			−0.480422
$170$	−6.55502	+	6.12929i	−0.502747	+	0.470095i
$171$	7.26552			0.555608
$172$		−	5.20400i		−	0.396801i
$173$	−8.19931	+	8.19931i	−0.623382	+	0.623382i	−0.946395	−	0.323013i	$-0.895304\pi$
$173$	−8.19931	+	8.19931i	−0.623382	+	0.623382i	0.323013	+	0.946395i	$0.395304\pi$
$174$	9.32241			0.706730
$175$	−8.16650	+	8.16650i	−0.617330	+	0.617330i
$176$	55.5357	+	55.5357i	4.18616	+	4.18616i
$177$	−8.03290	−	8.03290i	−0.603790	−	0.603790i
$178$		−	19.7529i		−	1.48054i
$179$			5.02669i			0.375712i	0.982197	+	0.187856i	$0.0601539\pi$
$179$			5.02669i			0.375712i	−0.982197	+	0.187856i	$0.939846\pi$
$180$	6.23176	+	6.23176i	0.464488	+	0.464488i
$181$	10.4781	+	10.4781i	0.778834	+	0.778834i	0.979633	−	0.200798i	$-0.0643536\pi$
$181$	10.4781	+	10.4781i	0.778834	+	0.778834i	−0.200798	+	0.979633i	$0.564354\pi$
$182$	−13.1187	+	13.1187i	−0.972425	+	0.972425i
$183$	−3.74223			−0.276634
$184$	25.1786	−	25.1786i	1.85619	−	1.85619i
$185$		−	2.82925i		−	0.208011i
$186$	12.5223			0.918181
$187$	−18.6633	+	17.4512i	−1.36480	+	1.27616i
$188$	−29.3300			−2.13911
$189$			12.9215i			0.939902i
$190$	5.35452	−	5.35452i	0.388457	−	0.388457i
$191$	14.0064			1.01347			0.506733	−	0.862103i	$-0.330853\pi$
$191$	14.0064			1.01347			0.506733	+	0.862103i	$0.330853\pi$
$192$	−13.3613	+	13.3613i	−0.964272	+	0.964272i
$193$	−13.7048	−	13.7048i	−0.986494	−	0.986494i	0.0134157	−	0.999910i	$-0.495730\pi$
$193$	−13.7048	−	13.7048i	−0.986494	−	0.986494i	−0.999910	+	0.0134157i	$0.995730\pi$
$194$	19.6003	+	19.6003i	1.40722	+	1.40722i
$195$		−	2.01232i		−	0.144105i
$196$		−	0.383410i		−	0.0273864i
$197$	7.17102	+	7.17102i	0.510914	+	0.510914i	0.914806	−	0.403893i	$-0.132343\pi$
$197$	7.17102	+	7.17102i	0.510914	+	0.510914i	−0.403893	+	0.914806i	$0.632343\pi$
$198$	24.5619	+	24.5619i	1.74554	+	1.74554i
$199$	−11.0052	+	11.0052i	−0.780141	+	0.780141i	−0.979854	−	0.199713i	$-0.935999\pi$
$199$	−11.0052	+	11.0052i	−0.780141	+	0.780141i	0.199713	+	0.979854i	$0.435999\pi$
$200$	−37.3429			−2.64054
$201$	5.93267	−	5.93267i	0.418458	−	0.418458i
$202$		−	5.70478i		−	0.401387i
$203$	−9.67498			−0.679050
$204$	−13.9923	−	14.9642i	−0.979658	−	1.04770i
$205$	6.60248			0.461137
$206$		−	16.7594i		−	1.16768i
$207$	6.11442	−	6.11442i	0.424982	−	0.424982i
$208$	−32.9380			−2.28384
$209$	15.2453	−	15.2453i	1.05454	−	1.05454i
$210$	3.90835	+	3.90835i	0.269702	+	0.269702i
$211$	16.6319	+	16.6319i	1.14499	+	1.14499i	0.987525	+	0.157465i	$0.0503321\pi$
$211$	16.6319	+	16.6319i	1.14499	+	1.14499i	0.157465	+	0.987525i	$0.449668\pi$
$212$		−	64.6783i		−	4.44213i
$213$		−	6.85667i		−	0.469811i
$214$	−2.61218	−	2.61218i	−0.178565	−	0.178565i
$215$	−0.573416	−	0.573416i	−0.0391067	−	0.0391067i
$216$	−29.5430	+	29.5430i	−2.01015	+	2.01015i
$217$	−12.9959			−0.882219
$218$	13.1637	−	13.1637i	0.891555	−	0.891555i
$219$		−	10.1481i		−	0.685745i
$220$	26.1523			1.76319
$221$	0.359453	−	10.7097i	0.0241794	−	0.720412i
$222$	8.94103			0.600083
$223$		−	6.42299i		−	0.430116i	−0.976601	−	0.215058i	$-0.931006\pi$
$223$		−	6.42299i		−	0.430116i	0.976601	−	0.215058i	$-0.0689940\pi$
$224$	31.6270	−	31.6270i	2.11317	−	2.11317i
$225$	−9.06843			−0.604562
$226$	−36.9980	+	36.9980i	−2.46107	+	2.46107i
$227$	−2.30486	−	2.30486i	−0.152979	−	0.152979i	0.626468	−	0.779447i	$-0.284500\pi$
$227$	−2.30486	−	2.30486i	−0.152979	−	0.152979i	−0.779447	+	0.626468i	$0.784500\pi$
$228$	12.2236	+	12.2236i	0.809528	+	0.809528i
$229$			15.4629i			1.02182i	0.859634	+	0.510910i	$0.170692\pi$
$229$			15.4629i			1.02182i	−0.859634	+	0.510910i	$0.829308\pi$
$230$		−	9.01237i		−	0.594258i
$231$	11.1278	+	11.1278i	0.732154	+	0.732154i
$232$	−22.1203	−	22.1203i	−1.45227	−	1.45227i
$233$	12.6900	−	12.6900i	0.831352	−	0.831352i	−0.156349	−	0.987702i	$-0.549973\pi$
$233$	12.6900	−	12.6900i	0.831352	−	0.831352i	0.987702	+	0.156349i	$0.0499726\pi$
$234$	−14.5676			−0.952313
$235$	−3.23180	+	3.23180i	−0.210819	+	0.210819i
$236$			61.9171i			4.03046i
$237$	5.49988			0.357256
$238$	20.1024	+	21.4987i	1.30304	+	1.39355i
$239$	−15.3755			−0.994557			−0.497279	−	0.867591i	$-0.665667\pi$
$239$	−15.3755			−0.994557			−0.497279	+	0.867591i	$0.665667\pi$
$240$			9.81295i			0.633423i
$241$	2.67813	−	2.67813i	0.172513	−	0.172513i	−0.615569	−	0.788083i	$-0.711074\pi$
$241$	2.67813	−	2.67813i	0.172513	−	0.172513i	0.788083	+	0.615569i	$0.211074\pi$
$242$	73.5525			4.72814
$243$	−11.4041	+	11.4041i	−0.731576	+	0.731576i
$244$	14.4225	+	14.4225i	0.923303	+	0.923303i
$245$	−0.0422471	−	0.0422471i	−0.00269907	−	0.00269907i
$246$			20.8652i			1.33032i
$247$			9.04192i			0.575323i
$248$	−29.7131	−	29.7131i	−1.88678	−	1.88678i
$249$	−10.2044	−	10.2044i	−0.646679	−	0.646679i
$250$	−14.3785	+	14.3785i	−0.909379	+	0.909379i
$251$	17.5428			1.10729			0.553647	−	0.832752i	$-0.313236\pi$
$251$	17.5428			1.10729			0.553647	+	0.832752i	$0.313236\pi$
$252$	20.4385	−	20.4385i	1.28750	−	1.28750i
$253$		−	25.6598i		−	1.61322i
$254$	−25.2934			−1.58705
$255$	−3.19065	−	0.107089i	−0.199806	−	0.00670616i
$256$	12.7135			0.794595
$257$		−	15.1998i		−	0.948137i	−0.880488	−	0.474068i	$-0.842785\pi$
$257$		−	15.1998i		−	0.948137i	0.880488	−	0.474068i	$-0.157215\pi$
$258$	1.81211	−	1.81211i	0.112817	−	0.112817i
$259$	−9.27918			−0.576580
$260$	−7.75541	+	7.75541i	−0.480970	+	0.480970i
$261$	−5.37175	−	5.37175i	−0.332503	−	0.332503i
$262$	−23.3118	−	23.3118i	−1.44021	−	1.44021i
$263$			20.9377i			1.29107i	0.763730	+	0.645536i	$0.223366\pi$
$263$			20.9377i			1.29107i	−0.763730	+	0.645536i	$0.776634\pi$
$264$			50.8839i			3.13169i
$265$	−7.12675	−	7.12675i	−0.437793	−	0.437793i
$266$	−17.5613	−	17.5613i	−1.07675	−	1.07675i
$267$	4.96870	−	4.96870i	0.304079	−	0.304079i
$268$	−45.7287			−2.79332
$269$	13.1040	−	13.1040i	0.798965	−	0.798965i	−0.183967	−	0.982932i	$-0.558894\pi$
$269$	13.1040	−	13.1040i	0.798965	−	0.798965i	0.982932	+	0.183967i	$0.0588941\pi$
$270$			10.5746i			0.643548i
$271$	0.961309			0.0583954			0.0291977	−	0.999574i	$-0.490705\pi$
$271$	0.961309			0.0583954			0.0291977	+	0.999574i	$0.490705\pi$
$272$	−1.75285	+	52.2252i	−0.106282	+	3.16662i
$273$	−6.59984			−0.399441
$274$		−	41.3405i		−	2.49747i
$275$	−19.0283	+	19.0283i	−1.14745	+	1.14745i
$276$	20.5740			1.23841
$277$	−12.9026	+	12.9026i	−0.775245	+	0.775245i	−0.979018	−	0.203773i	$-0.934679\pi$
$277$	−12.9026	+	12.9026i	−0.775245	+	0.775245i	0.203773	+	0.979018i	$0.434679\pi$
$278$	7.45098	+	7.45098i	0.446880	+	0.446880i
$279$	−7.21560	−	7.21560i	−0.431986	−	0.431986i
$280$		−	18.5476i		−	1.10843i
$281$		−	22.1973i		−	1.32418i	−0.749424	−	0.662091i	$-0.769669\pi$
$281$		−	22.1973i		−	1.32418i	0.749424	−	0.662091i	$-0.230331\pi$
$282$	−10.2132	−	10.2132i	−0.608185	−	0.608185i
$283$	16.3383	+	16.3383i	0.971211	+	0.971211i	0.999597	−	0.0283856i	$-0.00903664\pi$
$283$	16.3383	+	16.3383i	0.971211	+	0.971211i	−0.0283856	+	0.999597i	$0.509037\pi$
$284$	−26.4254	+	26.4254i	−1.56806	+	1.56806i
$285$	2.69378			0.159566
$286$	−30.5672	+	30.5672i	−1.80748	+	1.80748i
$287$		−	21.6543i		−	1.27821i
$288$	35.1200			2.06946
$289$	−16.9617	−	1.13987i	−0.997750	−	0.0670511i
$290$	−7.91771			−0.464944
$291$			9.86063i			0.578040i
$292$	−39.1105	+	39.1105i	−2.28877	+	2.28877i
$293$	−26.9718			−1.57571			−0.787854	−	0.615863i	$-0.788808\pi$
$293$	−26.9718			−1.57571			−0.787854	+	0.615863i	$0.788808\pi$
$294$	0.133509	−	0.133509i	0.00778643	−	0.00778643i
$295$	6.82250	+	6.82250i	0.397222	+	0.397222i
$296$	−21.2154	−	21.2154i	−1.23312	−	1.23312i
$297$			30.1077i			1.74703i
$298$		−	32.3638i		−	1.87479i
$299$	7.60938	+	7.60938i	0.440062	+	0.440062i
$300$	−15.2568	−	15.2568i	−0.880854	−	0.880854i
$301$	−1.88065	+	1.88065i	−0.108399	+	0.108399i
$302$	38.1234			2.19375
$303$	1.43500	−	1.43500i	0.0824384	−	0.0824384i
$304$		−	44.0924i		−	2.52887i
$305$	3.17835			0.181992
$306$	−0.775238	+	23.0978i	−0.0443174	+	1.32041i
$307$	−5.36699			−0.306310			−0.153155	−	0.988202i	$-0.548943\pi$
$307$	−5.36699			−0.306310			−0.153155	+	0.988202i	$0.548943\pi$
$308$		−	85.7723i		−	4.88733i
$309$	4.21570	−	4.21570i	0.239823	−	0.239823i
$310$	−10.6354			−0.604053
$311$	−5.63505	+	5.63505i	−0.319535	+	0.319535i	−0.848588	−	0.529054i	$-0.822547\pi$
$311$	−5.63505	+	5.63505i	−0.319535	+	0.319535i	0.529054	+	0.848588i	$0.322547\pi$
$312$	−15.0895	−	15.0895i	−0.854276	−	0.854276i
$313$	18.1422	+	18.1422i	1.02546	+	1.02546i	0.999667	+	0.0257887i	$0.00820971\pi$
$313$	18.1422	+	18.1422i	1.02546	+	1.02546i	0.0257887	+	0.999667i	$0.491790\pi$
$314$		−	36.3892i		−	2.05356i
$315$		−	4.50413i		−	0.253779i
$316$	−21.1964	−	21.1964i	−1.19239	−	1.19239i
$317$	−16.5026	−	16.5026i	−0.926880	−	0.926880i	0.0706228	−	0.997503i	$-0.477501\pi$
$317$	−16.5026	−	16.5026i	−0.926880	−	0.926880i	−0.997503	+	0.0706228i	$0.977501\pi$
$318$	22.5220	−	22.5220i	1.26297	−	1.26297i
$319$	−22.5431			−1.26217
$320$	11.3481	−	11.3481i	0.634376	−	0.634376i
$321$		−	1.31415i		−	0.0733487i
$322$	−29.5581			−1.64721
$323$	14.3365	+	0.481180i	0.797704	+	0.0267736i
$324$	8.46306			0.470170
$325$		−	11.2856i		−	0.626014i
$326$	3.08255	−	3.08255i	0.170727	−	0.170727i
$327$	6.62245			0.366222
$328$	49.5092	−	49.5092i	2.73369	−	2.73369i
$329$	10.5994	+	10.5994i	0.584365	+	0.584365i
$330$	9.10664	+	9.10664i	0.501304	+	0.501304i
$331$		−	8.83548i		−	0.485642i	−0.970071	−	0.242821i	$-0.921927\pi$
$331$		−	8.83548i		−	0.485642i	0.970071	−	0.242821i	$-0.0780728\pi$
$332$			78.6550i			4.31676i
$333$	−5.15199	−	5.15199i	−0.282328	−	0.282328i
$334$	3.64551	+	3.64551i	0.199473	+	0.199473i
$335$	−5.03873	+	5.03873i	−0.275295	+	0.275295i
$336$	32.1838			1.75577
$337$	16.6613	−	16.6613i	0.907599	−	0.907599i	−0.0884787	−	0.996078i	$-0.528201\pi$
$337$	16.6613	−	16.6613i	0.907599	−	0.907599i	0.996078	+	0.0884787i	$0.0282005\pi$
$338$			16.7630i			0.911789i
$339$	−18.6132			−1.01093
$340$	11.8840	+	12.7094i	0.644498	+	0.689263i
$341$	−30.2811			−1.63981
$342$		−	19.5008i		−	1.05449i
$343$	13.0260	−	13.0260i	0.703337	−	0.703337i
$344$	−8.59962			−0.463660
$345$	2.26700	−	2.26700i	0.122051	−	0.122051i
$346$	22.0072	+	22.0072i	1.18311	+	1.18311i
$347$	−8.95744	−	8.95744i	−0.480861	−	0.480861i	0.424546	−	0.905406i	$-0.360434\pi$
$347$	−8.95744	−	8.95744i	−0.480861	−	0.480861i	−0.905406	+	0.424546i	$0.860434\pi$
$348$		−	18.0750i		−	0.968922i
$349$		−	12.7956i		−	0.684931i	−0.939530	−	0.342466i	$-0.888738\pi$
$349$		−	12.7956i		−	0.684931i	0.939530	−	0.342466i	$-0.111262\pi$
$350$	21.9191	+	21.9191i	1.17163	+	1.17163i
$351$	−8.92839	−	8.92839i	−0.476562	−	0.476562i
$352$	73.6924	−	73.6924i	3.92782	−	3.92782i
$353$	18.8058			1.00093			0.500466	−	0.865756i	$-0.333162\pi$
$353$	18.8058			1.00093			0.500466	+	0.865756i	$0.333162\pi$
$354$	−21.5605	+	21.5605i	−1.14593	+	1.14593i
$355$			5.82350i			0.309080i
$356$	−38.2984			−2.02981
$357$	−0.351222	+	10.4645i	−0.0185886	+	0.553837i
$358$	13.4918			0.713062
$359$			10.2863i			0.542890i	0.962454	+	0.271445i	$0.0875015\pi$
$359$			10.2863i			0.542890i	−0.962454	+	0.271445i	$0.912498\pi$
$360$	10.2980	−	10.2980i	0.542752	−	0.542752i
$361$	6.89607			0.362951
$362$	28.1236	−	28.1236i	1.47814	−	1.47814i
$363$	18.5016	+	18.5016i	0.971083	+	0.971083i
$364$	25.4356	+	25.4356i	1.33319	+	1.33319i
$365$			8.61898i			0.451138i
$366$			10.0443i			0.525021i
$367$	−0.729415	−	0.729415i	−0.0380751	−	0.0380751i	0.687813	−	0.725888i	$-0.258571\pi$
$367$	−0.729415	−	0.729415i	−0.0380751	−	0.0380751i	−0.725888	+	0.687813i	$0.758571\pi$
$368$	−37.1067	−	37.1067i	−1.93432	−	1.93432i
$369$	12.0229	−	12.0229i	0.625888	−	0.625888i
$370$	−7.59380			−0.394783
$371$	−23.3738	+	23.3738i	−1.21351	+	1.21351i
$372$		−	24.2792i		−	1.25882i
$373$	−22.9449			−1.18804			−0.594021	−	0.804449i	$-0.702460\pi$
$373$	−22.9449			−1.18804			−0.594021	+	0.804449i	$0.702460\pi$
$374$	46.8395	+	50.0929i	2.42201	+	2.59024i
$375$	−7.23364			−0.373544
$376$			48.4679i			2.49954i
$377$	6.68513	−	6.68513i	0.344302	−	0.344302i
$378$	34.6817			1.78383
$379$	12.3256	−	12.3256i	0.633125	−	0.633125i	−0.315725	−	0.948851i	$-0.602248\pi$
$379$	12.3256	−	12.3256i	0.633125	−	0.633125i	0.948851	+	0.315725i	$0.102248\pi$
$380$	−10.3818	−	10.3818i	−0.532573	−	0.532573i
$381$	−6.36237	−	6.36237i	−0.325954	−	0.325954i
$382$		−	37.5935i		−	1.92345i
$383$		−	21.5173i		−	1.09948i	−0.835335	−	0.549741i	$-0.814727\pi$
$383$		−	21.5173i		−	1.09948i	0.835335	−	0.549741i	$-0.185273\pi$
$384$	13.1542	+	13.1542i	0.671272	+	0.671272i
$385$	−9.45105	−	9.45105i	−0.481670	−	0.481670i
$386$	−36.7841	+	36.7841i	−1.87226	+	1.87226i
$387$	−2.08835			−0.106157
$388$	38.0026	−	38.0026i	1.92929	−	1.92929i
$389$		−	7.44290i		−	0.377370i	−0.982038	−	0.188685i	$-0.939578\pi$
$389$		−	7.44290i		−	0.377370i	0.982038	−	0.188685i	$-0.0604225\pi$
$390$	−5.40111			−0.273496
$391$	12.4701	−	11.6602i	0.630639	−	0.589681i
$392$	−0.633586			−0.0320009
$393$		−	11.7278i		−	0.591591i
$394$	19.2472	−	19.2472i	0.969660	−	0.969660i
$395$	−4.67116			−0.235031
$396$	47.6226	−	47.6226i	2.39312	−	2.39312i
$397$	−10.4554	−	10.4554i	−0.524743	−	0.524743i	0.394257	−	0.919000i	$-0.371002\pi$
$397$	−10.4554	−	10.4554i	−0.524743	−	0.524743i	−0.919000	+	0.394257i	$0.871002\pi$
$398$	29.5384	+	29.5384i	1.48063	+	1.48063i
$399$		−	8.83486i		−	0.442296i
$400$			55.0337i			2.75169i
$401$	11.3450	+	11.3450i	0.566542	+	0.566542i	0.931158	−	0.364616i	$-0.118800\pi$
$401$	11.3450	+	11.3450i	0.566542	+	0.566542i	−0.364616	+	0.931158i	$0.618800\pi$
$402$	−15.9234	−	15.9234i	−0.794189	−	0.794189i
$403$	8.97979	−	8.97979i	0.447315	−	0.447315i
$404$	−11.0609			−0.550299
$405$	0.932525	−	0.932525i	0.0463375	−	0.0463375i
$406$			25.9679i			1.28877i
$407$	−21.6209			−1.07171
$408$	−24.7284	+	23.1223i	−1.22424	+	1.14473i
$409$	12.2750			0.606959			0.303480	−	0.952838i	$-0.401852\pi$
$409$	12.2750			0.606959			0.303480	+	0.952838i	$0.401852\pi$
$410$		−	17.7212i		−	0.875189i
$411$	10.3989	−	10.3989i	0.512941	−	0.512941i
$412$	−32.4943			−1.60088
$413$	22.3759	−	22.3759i	1.10105	−	1.10105i
$414$	−16.4113	−	16.4113i	−0.806570	−	0.806570i
$415$	8.66681	+	8.66681i	0.425437	+	0.425437i
$416$			43.7067i			2.14290i
$417$			3.74848i			0.183564i
$418$	−40.9187	−	40.9187i	−2.00140	−	2.00140i
$419$	16.0103	+	16.0103i	0.782153	+	0.782153i	0.980194	−	0.198041i	$-0.0634578\pi$
$419$	16.0103	+	16.0103i	0.782153	+	0.782153i	−0.198041	+	0.980194i	$0.563458\pi$
$420$	7.57781	−	7.57781i	0.369759	−	0.369759i
$421$	25.9094			1.26275			0.631375	−	0.775478i	$-0.282491\pi$
$421$	25.9094			1.26275			0.631375	+	0.775478i	$0.282491\pi$
$422$	44.6406	−	44.6406i	2.17307	−	2.17307i
$423$			11.7700i			0.572279i
$424$	−106.881			−5.19061
$425$	−17.8940	−	0.600583i	−0.867989	−	0.0291326i
$426$	−18.4035			−0.891652
$427$		−	10.4241i		−	0.504459i
$428$	−5.06469	+	5.06469i	−0.244811	+	0.244811i
$429$	−15.3779			−0.742454
$430$	−1.53907	+	1.53907i	−0.0742203	+	0.0742203i
$431$	3.93524	+	3.93524i	0.189554	+	0.189554i	0.795503	−	0.605949i	$-0.207207\pi$
$431$	3.93524	+	3.93524i	0.189554	+	0.189554i	−0.605949	+	0.795503i	$0.707207\pi$
$432$	43.5388	+	43.5388i	2.09476	+	2.09476i
$433$		−	17.1823i		−	0.825729i	−0.910792	−	0.412865i	$-0.864528\pi$
$433$		−	17.1823i		−	0.825729i	0.910792	−	0.412865i	$-0.135472\pi$
$434$			34.8813i			1.67436i
$435$	−1.99164	−	1.99164i	−0.0954920	−	0.0954920i
$436$	−25.5227	−	25.5227i	−1.22232	−	1.22232i
$437$	−10.1863	+	10.1863i	−0.487275	+	0.487275i
$438$	−27.2378			−1.30147
$439$	−22.5486	+	22.5486i	−1.07619	+	1.07619i	−0.0793375	+	0.996848i	$0.525280\pi$
$439$	−22.5486	+	22.5486i	−1.07619	+	1.07619i	−0.996848	+	0.0793375i	$0.974720\pi$
$440$		−	43.2167i		−	2.06028i
$441$	−0.153861			−0.00732673
$442$	−28.7451	−	0.964781i	−1.36727	−	0.0458899i
$443$	−36.6808			−1.74276			−0.871380	−	0.490609i	$-0.836774\pi$
$443$	−36.6808			−1.74276			−0.871380	+	0.490609i	$0.836774\pi$
$444$		−	17.3356i		−	0.822710i
$445$	−4.22001	+	4.22001i	−0.200048	+	0.200048i
$446$	−17.2395			−0.816313
$447$	8.14089	−	8.14089i	0.385051	−	0.385051i
$448$	−37.2185	−	37.2185i	−1.75841	−	1.75841i
$449$	8.33601	+	8.33601i	0.393401	+	0.393401i	0.875898	−	0.482497i	$-0.160270\pi$
$449$	8.33601	+	8.33601i	0.393401	+	0.393401i	−0.482497	+	0.875898i	$0.660270\pi$
$450$			24.3399i			1.14739i
$451$		−	50.4555i		−	2.37586i
$452$	71.7346	+	71.7346i	3.37411	+	3.37411i
$453$	9.58967	+	9.58967i	0.450562	+	0.450562i
$454$	−6.18629	+	6.18629i	−0.290337	+	0.290337i
$455$	5.60538			0.262784
$456$	20.1995	−	20.1995i	0.945930	−	0.945930i
$457$			2.87142i			0.134319i	0.997742	+	0.0671597i	$0.0213937\pi$
$457$			2.87142i			0.134319i	−0.997742	+	0.0671597i	$0.978606\pi$
$458$	41.5030			1.93931
$459$	−14.6316	+	13.6814i	−0.682946	+	0.638591i
$460$	−17.4739			−0.814724
$461$		−	5.82503i		−	0.271299i	−0.990757	−	0.135649i	$-0.956688\pi$
$461$		−	5.82503i		−	0.271299i	0.990757	−	0.135649i	$-0.0433121\pi$
$462$	29.8673	−	29.8673i	1.38955	−	1.38955i
$463$	−35.6509			−1.65684			−0.828420	−	0.560108i	$-0.810760\pi$
$463$	−35.6509			−1.65684			−0.828420	+	0.560108i	$0.810760\pi$
$464$	−32.5996	+	32.5996i	−1.51340	+	1.51340i
$465$	−2.67527	−	2.67527i	−0.124063	−	0.124063i
$466$	−34.0604	−	34.0604i	−1.57782	−	1.57782i
$467$		−	8.12391i		−	0.375930i	−0.982176	−	0.187965i	$-0.939811\pi$
$467$		−	8.12391i		−	0.375930i	0.982176	−	0.187965i	$-0.0601891\pi$
$468$			28.2448i			1.30561i
$469$	16.5257	+	16.5257i	0.763084	+	0.763084i
$470$	8.67424	+	8.67424i	0.400113	+	0.400113i
$471$	9.15346	−	9.15346i	0.421769	−	0.421769i
$472$	102.318			4.70958
$473$	−4.38200	+	4.38200i	−0.201484	+	0.201484i
$474$		−	14.7618i		−	0.678033i
$475$	15.1075			0.693178
$476$	41.6833	−	38.9761i	1.91055	−	1.78647i
$477$	−25.9552			−1.18841
$478$			41.2682i			1.88756i
$479$	−14.3251	+	14.3251i	−0.654533	+	0.654533i	−0.954081	−	0.299549i	$-0.903164\pi$
$479$	−14.3251	+	14.3251i	−0.654533	+	0.654533i	0.299549	+	0.954081i	$0.403164\pi$
$480$	13.0212			0.594332
$481$	6.41164	−	6.41164i	0.292346	−	0.292346i
$482$	−7.18816	−	7.18816i	−0.327412	−	0.327412i
$483$	−7.43513	−	7.43513i	−0.338310	−	0.338310i
$484$		−	142.609i		−	6.48225i
$485$		−	8.37483i		−	0.380281i
$486$	30.6090	+	30.6090i	1.38845	+	1.38845i
$487$	−12.7651	−	12.7651i	−0.578444	−	0.578444i	0.356030	−	0.934474i	$-0.384130\pi$
$487$	−12.7651	−	12.7651i	−0.578444	−	0.578444i	−0.934474	+	0.356030i	$0.884130\pi$
$488$	23.8331	−	23.8331i	1.07888	−	1.07888i
$489$	1.55079			0.0701291
$490$	−0.113392	+	0.113392i	−0.00512254	+	0.00512254i
$491$			17.3842i			0.784537i	0.919851	+	0.392269i	$0.128310\pi$
$491$			17.3842i			0.784537i	−0.919851	+	0.392269i	$0.871690\pi$
$492$	40.4551			1.82385
$493$	−10.2439	−	10.9554i	−0.461363	−	0.493408i
$494$	24.2687			1.09190
$495$		−	10.4948i		−	0.471708i
$496$	−43.7894	+	43.7894i	−1.96620	+	1.96620i
$497$	19.0995			0.856729
$498$	−27.3889	+	27.3889i	−1.22733	+	1.22733i
$499$	−3.89840	−	3.89840i	−0.174516	−	0.174516i	0.614444	−	0.788960i	$-0.289380\pi$
$499$	−3.89840	−	3.89840i	−0.174516	−	0.174516i	−0.788960	+	0.614444i	$0.789380\pi$
$500$	27.8782	+	27.8782i	1.24675	+	1.24675i
$501$			1.83400i			0.0819373i
$502$		−	47.0854i		−	2.10153i
$503$	−30.3782	−	30.3782i	−1.35450	−	1.35450i	−0.880560	−	0.473936i	$-0.842833\pi$
$503$	−30.3782	−	30.3782i	−1.35450	−	1.35450i	−0.473936	−	0.880560i	$-0.657167\pi$
$504$	−33.7746	−	33.7746i	−1.50444	−	1.50444i
$505$	−1.21877	+	1.21877i	−0.0542346	+	0.0542346i
$506$	−68.8717			−3.06172
$507$	−4.21662	+	4.21662i	−0.187267	+	0.187267i
$508$			49.0408i			2.17583i
$509$	−24.2125			−1.07320			−0.536599	−	0.843837i	$-0.680291\pi$
$509$	−24.2125			−1.07320			−0.536599	+	0.843837i	$0.680291\pi$
$510$	−0.287429	+	8.56379i	−0.0127276	+	0.379211i
$511$	28.2679			1.25050
$512$			4.84342i			0.214051i
$513$	11.9520	−	11.9520i	0.527692	−	0.527692i
$514$	−40.7966			−1.79946
$515$	−3.58047	+	3.58047i	−0.157775	+	0.157775i
$516$	−3.51347	−	3.51347i	−0.154672	−	0.154672i
$517$	24.6971	+	24.6971i	1.08618	+	1.08618i
$518$			24.9056i			1.09429i
$519$			11.0715i			0.485985i
$520$	12.8158	+	12.8158i	0.562011	+	0.562011i
$521$	13.0537	+	13.0537i	0.571895	+	0.571895i	0.932658	−	0.360763i	$-0.117484\pi$
$521$	13.0537	+	13.0537i	0.571895	+	0.571895i	−0.360763	+	0.932658i	$0.617484\pi$
$522$	−14.4179	+	14.4179i	−0.631055	+	0.631055i
$523$	−3.12683			−0.136727			−0.0683634	−	0.997660i	$-0.521778\pi$
$523$	−3.12683			−0.136727			−0.0683634	+	0.997660i	$0.521778\pi$
$524$	−45.1987	+	45.1987i	−1.97451	+	1.97451i
$525$			11.0272i			0.481266i
$526$	56.1972			2.45032
$527$	−13.7601	−	14.7159i	−0.599400	−	0.641033i
$528$	74.9897			3.26351
$529$		−	5.85515i		−	0.254572i
$530$	−19.1284	+	19.1284i	−0.830885	+	0.830885i
$531$	24.8472			1.07828
$532$	−34.0493	+	34.0493i	−1.47622	+	1.47622i
$533$	14.9625	+	14.9625i	0.648097	+	0.648097i
$534$	−13.3361	−	13.3361i	−0.577110	−	0.577110i
$535$			1.11613i			0.0482547i
$536$			75.5667i			3.26399i
$537$	3.39376	+	3.39376i	0.146451	+	0.146451i
$538$	−35.1715	−	35.1715i	−1.51635	−	1.51635i
$539$	−0.322848	+	0.322848i	−0.0139061	+	0.0139061i
$540$	20.5028			0.882300
$541$	−11.9988	+	11.9988i	−0.515868	+	0.515868i	−0.916319	−	0.400450i	$-0.868854\pi$
$541$	−11.9988	+	11.9988i	−0.515868	+	0.515868i	0.400450	+	0.916319i	$0.368854\pi$
$542$		−	2.58018i		−	0.110828i
$543$	14.1486			0.607174
$544$	69.2996	+	2.32592i	2.97119	+	0.0997231i
$545$	−5.62458			−0.240930
$546$			17.7142i			0.758096i
$547$	10.4567	−	10.4567i	0.447097	−	0.447097i	−0.447291	−	0.894388i	$-0.647611\pi$
$547$	10.4567	−	10.4567i	0.447097	−	0.447097i	0.894388	+	0.447291i	$0.147611\pi$
$548$	−80.1543			−3.42402
$549$	5.78769	−	5.78769i	0.247013	−	0.247013i
$550$	51.0725	+	51.0725i	2.17774	+	2.17774i
$551$	8.94902	+	8.94902i	0.381241	+	0.381241i
$552$		−	33.9985i		−	1.44707i
$553$			15.3201i			0.651478i
$554$	34.6310	+	34.6310i	1.47133	+	1.47133i
$555$	−1.91017	−	1.91017i	−0.0810820	−	0.0810820i
$556$	14.4465	−	14.4465i	0.612670	−	0.612670i
$557$	24.4421			1.03564			0.517822	−	0.855488i	$-0.326743\pi$
$557$	24.4421			1.03564			0.517822	+	0.855488i	$0.326743\pi$
$558$	−19.3669	+	19.3669i	−0.819864	+	0.819864i
$559$		−	2.59895i		−	0.109924i
$560$	−27.3343			−1.15509
$561$	−0.818362	+	24.3827i	−0.0345513	+	1.02944i
$562$	−59.5782			−2.51316
$563$			10.1818i			0.429112i	0.976712	+	0.214556i	$0.0688304\pi$
$563$			10.1818i			0.429112i	−0.976712	+	0.214556i	$0.931170\pi$
$564$	−19.8021	+	19.8021i	−0.833818	+	0.833818i
$565$	15.8085			0.665070
$566$	43.8524	−	43.8524i	1.84326	−	1.84326i
$567$	−3.05843	−	3.05843i	−0.128442	−	0.128442i
$568$	43.6680	+	43.6680i	1.83227	+	1.83227i
$569$			2.94805i			0.123589i	0.998089	+	0.0617943i	$0.0196823\pi$
$569$			2.94805i			0.123589i	−0.998089	+	0.0617943i	$0.980318\pi$
$570$		−	7.23018i		−	0.302839i
$571$	9.14289	+	9.14289i	0.382618	+	0.382618i	0.872044	−	0.489427i	$-0.162794\pi$
$571$	9.14289	+	9.14289i	0.382618	+	0.382618i	−0.489427	+	0.872044i	$0.662794\pi$
$572$	59.2661	+	59.2661i	2.47804	+	2.47804i
$573$	9.45637	−	9.45637i	0.395046	−	0.395046i
$574$	−58.1207			−2.42591
$575$	12.7139	−	12.7139i	0.530208	−	0.530208i
$576$		−	41.3290i		−	1.72204i
$577$	−22.4710			−0.935478			−0.467739	−	0.883867i	$-0.654931\pi$
$577$	−22.4710			−0.935478			−0.467739	+	0.883867i	$0.654931\pi$
$578$	−3.05944	+	45.5258i	−0.127256	+	1.89362i
$579$	−18.5056			−0.769065
$580$			15.3515i			0.637435i
$581$	28.4248	−	28.4248i	1.17926	−	1.17926i
$582$	26.4662			1.09706
$583$	−54.4620	+	54.4620i	−2.25559	+	2.25559i
$584$	64.6302	+	64.6302i	2.67441	+	2.67441i
$585$	3.11222	+	3.11222i	0.128675	+	0.128675i
$586$			72.3929i			2.99052i
$587$			8.78585i			0.362631i	0.983425	+	0.181315i	$0.0580355\pi$
$587$			8.78585i			0.362631i	−0.983425	+	0.181315i	$0.941965\pi$
$588$	−0.258858	−	0.258858i	−0.0106751	−	0.0106751i
$589$	12.0208	+	12.0208i	0.495307	+	0.495307i
$590$	18.3118	−	18.3118i	0.753884	−	0.753884i
$591$	9.68299			0.398305
$592$	−31.2660	+	31.2660i	−1.28502	+	1.28502i
$593$		−	29.3362i		−	1.20469i	−0.798234	−	0.602347i	$-0.794232\pi$
$593$		−	29.3362i		−	1.20469i	0.798234	−	0.602347i	$-0.205768\pi$
$594$	80.8100			3.31567
$595$	0.298299	−	8.88767i	0.0122291	−	0.364359i
$596$	−62.7495			−2.57032
$597$			14.8603i			0.608193i
$598$	20.4238	−	20.4238i	0.835190	−	0.835190i
$599$	−9.99993			−0.408586			−0.204293	−	0.978910i	$-0.565490\pi$
$599$	−9.99993			−0.408586			−0.204293	+	0.978910i	$0.565490\pi$
$600$	−25.2120	+	25.2120i	−1.02927	+	1.02927i
$601$	22.3081	+	22.3081i	0.909966	+	0.909966i	0.996269	−	0.0863033i	$-0.0275054\pi$
$601$	22.3081	+	22.3081i	0.909966	+	0.909966i	−0.0863033	+	0.996269i	$0.527505\pi$
$602$	5.04771	+	5.04771i	0.205729	+	0.205729i
$603$			18.3508i			0.747302i
$604$		−	73.9166i		−	3.00762i
$605$	−15.7138	−	15.7138i	−0.638857	−	0.638857i
$606$	−3.85157	−	3.85157i	−0.156459	−	0.156459i
$607$	32.0475	−	32.0475i	1.30077	−	1.30077i	0.372893	−	0.927875i	$-0.378366\pi$
$607$	32.0475	−	32.0475i	1.30077	−	1.30077i	0.927875	−	0.372893i	$-0.121634\pi$
$608$	−58.5078			−2.37280
$609$	−6.53204	+	6.53204i	−0.264692	+	0.264692i
$610$		−	8.53078i		−	0.345401i
$611$	−14.6478			−0.592586
$612$	44.7838	+	1.50309i	1.81028	+	0.0607589i
$613$	45.7659			1.84847			0.924233	−	0.381829i	$-0.124706\pi$
$613$	45.7659			1.84847			0.924233	+	0.381829i	$0.124706\pi$
$614$			14.4051i			0.581344i
$615$	4.45765	−	4.45765i	0.179750	−	0.179750i
$616$	−141.739			−5.71082
$617$	17.8081	−	17.8081i	0.716925	−	0.716925i	−0.251049	−	0.967974i	$-0.580776\pi$
$617$	17.8081	−	17.8081i	0.716925	−	0.716925i	0.967974	+	0.251049i	$0.0807755\pi$
$618$	−11.3150	−	11.3150i	−0.455158	−	0.455158i
$619$	5.44767	+	5.44767i	0.218960	+	0.218960i	0.808060	−	0.589100i	$-0.200518\pi$
$619$	5.44767	+	5.44767i	0.218960	+	0.218960i	−0.589100	+	0.808060i	$0.700518\pi$
$620$			20.6208i			0.828153i
$621$		−	20.1167i		−	0.807257i
$622$	15.1246	+	15.1246i	0.606443	+	0.606443i
$623$	13.8405	+	13.8405i	0.554507	+	0.554507i
$624$	−22.2380	+	22.2380i	−0.890234	+	0.890234i
$625$	−15.5683			−0.622730
$626$	48.6941	−	48.6941i	1.94621	−	1.94621i
$627$		−	20.5856i		−	0.822111i
$628$	−70.5543			−2.81542
$629$	−9.82484	−	10.5072i	−0.391742	−	0.418951i
$630$	−12.0892			−0.481646
$631$		−	9.99311i		−	0.397819i	−0.980018	−	0.198910i	$-0.936260\pi$
$631$		−	9.99311i		−	0.397819i	0.980018	−	0.198910i	$-0.0637400\pi$
$632$	−35.0271	+	35.0271i	−1.39330	+	1.39330i
$633$	22.4580			0.892627
$634$	−44.2935	+	44.2935i	−1.75912	+	1.75912i
$635$	5.40369	+	5.40369i	0.214439	+	0.214439i
$636$	−43.6674	−	43.6674i	−1.73153	−	1.73153i
$637$		−	0.191480i		−	0.00758671i
$638$			60.5064i			2.39547i
$639$	10.6044	+	10.6044i	0.419505	+	0.419505i
$640$	−11.1721	−	11.1721i	−0.441617	−	0.441617i
$641$	−1.88760	+	1.88760i	−0.0745557	+	0.0745557i	−0.743401	−	0.668846i	$-0.766789\pi$
$641$	−1.88760	+	1.88760i	−0.0745557	+	0.0745557i	0.668846	+	0.743401i	$0.266789\pi$
$642$	−3.52721			−0.139208
$643$	−21.2687	+	21.2687i	−0.838756	+	0.838756i	−0.988695	−	0.149939i	$-0.952092\pi$
$643$	−21.2687	+	21.2687i	−0.838756	+	0.838756i	0.149939	+	0.988695i	$0.452092\pi$
$644$			57.3095i			2.25831i
$645$	−0.774282			−0.0304873
$646$	1.29150	−	38.4796i	0.0508134	−	1.51396i
$647$	28.6923			1.12801			0.564005	−	0.825771i	$-0.309260\pi$
$647$	28.6923			1.12801			0.564005	+	0.825771i	$0.309260\pi$
$648$		−	13.9852i		−	0.549392i
$649$	52.1370	−	52.1370i	2.04655	−	2.04655i
$650$	−30.2909			−1.18811
$651$	−8.77415	+	8.77415i	−0.343886	+	0.343886i
$652$	−5.97670	−	5.97670i	−0.234065	−	0.234065i
$653$	12.0214	+	12.0214i	0.470436	+	0.470436i	0.902056	−	0.431620i	$-0.142058\pi$
$653$	12.0214	+	12.0214i	0.470436	+	0.470436i	−0.431620	+	0.902056i	$0.642058\pi$
$654$		−	17.7748i		−	0.695051i
$655$			9.96068i			0.389196i
$656$	−72.9637	−	72.9637i	−2.84876	−	2.84876i
$657$	15.6949	+	15.6949i	0.612317	+	0.612317i
$658$	28.4491	−	28.4491i	1.10906	−	1.10906i
$659$	0.368127			0.0143402			0.00717009	−	0.999974i	$-0.497718\pi$
$659$	0.368127			0.0143402			0.00717009	+	0.999974i	$0.497718\pi$
$660$	17.6567	−	17.6567i	0.687284	−	0.687284i
$661$		−	10.4543i		−	0.406625i	−0.979114	−	0.203312i	$-0.934829\pi$
$661$		−	10.4543i		−	0.406625i	0.979114	−	0.203312i	$-0.0651707\pi$
$662$	−23.7147			−0.921697
$663$	−6.98794	−	7.47331i	−0.271389	−	0.290239i
$664$	129.978			5.04411
$665$			7.50362i			0.290978i
$666$	−13.8281	+	13.8281i	−0.535828	+	0.535828i
$667$	15.0624			0.583219
$668$	7.06820	−	7.06820i	0.273477	−	0.273477i
$669$	−4.33647	−	4.33647i	−0.167658	−	0.167658i
$670$	13.5241	+	13.5241i	0.522481	+	0.522481i
$671$		−	24.2887i		−	0.937654i
$672$		−	42.7058i		−	1.64741i
$673$	−29.2161	−	29.2161i	−1.12620	−	1.12620i	−0.990790	−	0.135407i	$-0.956766\pi$
$673$	−29.2161	−	29.2161i	−1.12620	−	1.12620i	−0.135407	−	0.990790i	$-0.543234\pi$
$674$	−44.7194	−	44.7194i	−1.72253	−	1.72253i
$675$	−14.9178	+	14.9178i	−0.574186	+	0.574186i
$676$	32.5015			1.25006
$677$	−24.4755	+	24.4755i	−0.940669	+	0.940669i	−0.998336	−	0.0576669i	$-0.981634\pi$
$677$	−24.4755	+	24.4755i	−0.940669	+	0.940669i	0.0576669	+	0.998336i	$0.481634\pi$
$678$			49.9583i			1.91864i
$679$	−27.4671			−1.05409
$680$	21.0023	−	19.6383i	0.805401	−	0.753093i
$681$	−3.11224			−0.119261
$682$			81.2752i			3.11219i
$683$	7.99004	−	7.99004i	0.305731	−	0.305731i	−0.537520	−	0.843251i	$-0.680639\pi$
$683$	7.99004	−	7.99004i	0.305731	−	0.305731i	0.843251	+	0.537520i	$0.180639\pi$
$684$	−37.8098			−1.44569
$685$	−8.83201	+	8.83201i	−0.337454	+	0.337454i
$686$	−34.9621	−	34.9621i	−1.33486	−	1.33486i
$687$	10.4398	+	10.4398i	0.398302	+	0.398302i
$688$			12.6736i			0.483177i
$689$		−	32.3012i		−	1.23058i
$690$	−6.08468	−	6.08468i	−0.231640	−	0.231640i
$691$	20.9226	+	20.9226i	0.795934	+	0.795934i	0.982452	−	0.186518i	$-0.0597202\pi$
$691$	20.9226	+	20.9226i	0.795934	+	0.795934i	−0.186518	+	0.982452i	$0.559720\pi$
$692$	42.6692	−	42.6692i	1.62204	−	1.62204i
$693$	−34.4202			−1.30751
$694$	−24.0420	+	24.0420i	−0.912622	+	0.912622i
$695$		−	3.18366i		−	0.120763i
$696$	−29.8690			−1.13218
$697$	24.5202	−	22.9277i	0.928768	−	0.868448i
$698$	−34.3437			−1.29993
$699$		−	17.1353i		−	0.648117i
$700$	42.4985	−	42.4985i	1.60629	−	1.60629i
$701$	−41.7015			−1.57504			−0.787522	−	0.616287i	$-0.788636\pi$
$701$	−41.7015			−1.57504			−0.787522	+	0.616287i	$0.788636\pi$
$702$	−23.9640	+	23.9640i	−0.904464	+	0.904464i
$703$	8.58292	+	8.58292i	0.323711	+	0.323711i
$704$	−86.7209	−	86.7209i	−3.26842	−	3.26842i
$705$			4.36389i			0.164354i
$706$		−	50.4753i		−	1.89966i
$707$	3.99723	+	3.99723i	0.150331	+	0.150331i
$708$	41.8032	+	41.8032i	1.57106	+	1.57106i
$709$	−0.327971	+	0.327971i	−0.0123172	+	0.0123172i	−0.713239	−	0.700921i	$-0.752772\pi$
$709$	−0.327971	+	0.327971i	−0.0123172	+	0.0123172i	0.700921	+	0.713239i	$0.252772\pi$
$710$	15.6304			0.586600
$711$	−8.50605	+	8.50605i	−0.319002	+	0.319002i
$712$			63.2882i			2.37183i
$713$	20.2326			0.757715
$714$	28.0869	+	0.942688i	1.05112	+	0.0352792i
$715$	13.0608			0.488446
$716$		−	26.1589i		−	0.977603i
$717$	−10.3807	+	10.3807i	−0.387675	+	0.387675i
$718$	27.6087			1.03035
$719$	32.7478	−	32.7478i	1.22129	−	1.22129i	0.254110	−	0.967175i	$-0.418217\pi$
$719$	32.7478	−	32.7478i	1.22129	−	1.22129i	0.967175	−	0.254110i	$-0.0817826\pi$
$720$	−15.1766	−	15.1766i	−0.565598	−	0.565598i
$721$	11.7430	+	11.7430i	0.437331	+	0.437331i
$722$		−	18.5092i		−	0.688842i
$723$		−	3.61626i		−	0.134490i
$724$	−54.5283	−	54.5283i	−2.02653	−	2.02653i
$725$	−11.1697	−	11.1697i	−0.414832	−	0.414832i
$726$	49.6588	−	49.6588i	1.84301	−	1.84301i
$727$	42.1066			1.56165			0.780824	−	0.624750i	$-0.214799\pi$
$727$	42.1066			1.56165			0.780824	+	0.624750i	$0.214799\pi$
$728$	42.0324	−	42.0324i	1.55782	−	1.55782i
$729$			10.5202i			0.389636i
$730$	23.1336			0.856212
$731$	−4.12079	−	0.138307i	−0.152413	−	0.00511547i
$732$	19.4746			0.719801
$733$		−	18.9608i		−	0.700333i	−0.936687	−	0.350167i	$-0.886125\pi$
$733$		−	18.9608i		−	0.700333i	0.936687	−	0.350167i	$-0.113875\pi$
$734$	−1.95777	+	1.95777i	−0.0722626	+	0.0722626i
$735$	−0.0570460			−0.00210417
$736$	−49.2382	+	49.2382i	−1.81494	+	1.81494i
$737$	38.5056	+	38.5056i	1.41837	+	1.41837i
$738$	−32.2698	−	32.2698i	−1.18787	−	1.18787i
$739$			3.49023i			0.128390i	0.997937	+	0.0641951i	$0.0204480\pi$
$739$			3.49023i			0.128390i	−0.997937	+	0.0641951i	$0.979552\pi$
$740$			14.7234i			0.541244i
$741$	6.10463	+	6.10463i	0.224259	+	0.224259i
$742$	62.7359	+	62.7359i	2.30311	+	2.30311i
$743$	11.2882	−	11.2882i	0.414124	−	0.414124i	−0.469048	−	0.883173i	$-0.655403\pi$
$743$	11.2882	−	11.2882i	0.414124	−	0.414124i	0.883173	+	0.469048i	$0.155403\pi$
$744$	−40.1215			−1.47093
$745$	−6.91422	+	6.91422i	−0.253317	+	0.253317i
$746$			61.5847i			2.25478i
$747$	31.5640			1.15487
$748$	97.1240	−	90.8161i	3.55120	−	3.32057i
$749$	3.66061			0.133756
$750$			19.4153i			0.708946i
$751$	−5.25341	+	5.25341i	−0.191700	+	0.191700i	−0.796430	−	0.604730i	$-0.793281\pi$
$751$	−5.25341	+	5.25341i	−0.191700	+	0.191700i	0.604730	+	0.796430i	$0.293281\pi$
$752$	71.4291			2.60475
$753$	11.8440	−	11.8440i	0.431620	−	0.431620i
$754$	−17.9431	−	17.9431i	−0.653448	−	0.653448i
$755$	−8.14469	−	8.14469i	−0.296416	−	0.296416i
$756$		−	67.2436i		−	2.44563i
$757$			24.0023i			0.872380i	0.899855	+	0.436190i	$0.143672\pi$
$757$			24.0023i			0.872380i	−0.899855	+	0.436190i	$0.856328\pi$
$758$	−33.0823	−	33.0823i	−1.20160	−	1.20160i
$759$	−17.3242	−	17.3242i	−0.628828	−	0.628828i
$760$	−17.1559	+	17.1559i	−0.622309	+	0.622309i
$761$	−4.61706			−0.167368			−0.0836842	−	0.996492i	$-0.526669\pi$
$761$	−4.61706			−0.167368			−0.0836842	+	0.996492i	$0.526669\pi$
$762$	−17.0768	+	17.0768i	−0.618626	+	0.618626i
$763$			18.4471i			0.667829i
$764$	−72.8892			−2.63704
$765$	5.10024	−	4.76900i	0.184400	−	0.172423i
$766$	−57.7529			−2.08670
$767$			30.9222i			1.11654i
$768$	8.58350	−	8.58350i	0.309731	−	0.309731i
$769$	2.70050			0.0973826			0.0486913	−	0.998814i	$-0.484495\pi$
$769$	2.70050			0.0973826			0.0486913	+	0.998814i	$0.484495\pi$
$770$	−25.3669	+	25.3669i	−0.914158	+	0.914158i
$771$	−10.2621	−	10.2621i	−0.369581	−	0.369581i
$772$	71.3199	+	71.3199i	2.56686	+	2.56686i
$773$			48.1334i			1.73124i	0.500702	+	0.865620i	$0.333075\pi$
$773$			48.1334i			1.73124i	−0.500702	+	0.865620i	$0.666925\pi$
$774$			5.60519i			0.201474i
$775$	−15.0037	−	15.0037i	−0.538948	−	0.538948i
$776$	−62.7993	−	62.7993i	−2.25436	−	2.25436i
$777$	−6.26482	+	6.26482i	−0.224749	+	0.224749i
$778$	−19.9769			−0.716208
$779$	−20.0295	+	20.0295i	−0.717631	+	0.717631i
$780$			10.4721i			0.374961i
$781$	44.5027			1.59243
$782$	−31.2962	−	33.4700i	−1.11915	−	1.19688i
$783$	−17.6733			−0.631593
$784$			0.933742i			0.0333479i
$785$	−7.77421	+	7.77421i	−0.277474	+	0.277474i
$786$	−31.4778			−1.12278
$787$	−14.7206	+	14.7206i	−0.524732	+	0.524732i	−0.918997	−	0.394265i	$-0.870999\pi$
$787$	−14.7206	+	14.7206i	−0.524732	+	0.524732i	0.394265	+	0.918997i	$0.370999\pi$
$788$	−37.3180	−	37.3180i	−1.32940	−	1.32940i
$789$	14.1360	+	14.1360i	0.503255	+	0.503255i
$790$			12.5375i			0.446065i
$791$		−	51.8477i		−	1.84349i
$792$	−78.6964	−	78.6964i	−2.79635	−	2.79635i
$793$	7.20276	+	7.20276i	0.255778	+	0.255778i
$794$	−28.0626	+	28.0626i	−0.995906	+	0.995906i
$795$	−9.62323			−0.341301
$796$	57.2713	−	57.2713i	2.02993	−	2.02993i
$797$		−	53.0008i		−	1.87739i	−0.344755	−	0.938693i	$-0.612038\pi$
$797$		−	53.0008i		−	1.87739i	0.344755	−	0.938693i	$-0.387962\pi$
$798$	−23.7130			−0.839431
$799$	−0.779505	+	23.2249i	−0.0275769	+	0.821639i
$800$	73.0263			2.58187
$801$			15.3691i			0.543039i
$802$	30.4503	−	30.4503i	1.07524	−	1.07524i
$803$	65.8655			2.32434
$804$	−30.8736	+	30.8736i	−1.08883	+	1.08883i
$805$	6.31480	+	6.31480i	0.222567	+	0.222567i
$806$	−24.1020	−	24.1020i	−0.848956	−	0.848956i
$807$		−	17.6943i		−	0.622868i
$808$			18.2781i			0.643022i
$809$	−12.7261	−	12.7261i	−0.447426	−	0.447426i	0.447072	−	0.894498i	$-0.352467\pi$
$809$	−12.7261	−	12.7261i	−0.447426	−	0.447426i	−0.894498	+	0.447072i	$0.852467\pi$
$810$	−2.50292	−	2.50292i	−0.0879437	−	0.0879437i
$811$	−28.2164	+	28.2164i	−0.990810	+	0.990810i	−0.999958	−	0.00914795i	$-0.997088\pi$
$811$	−28.2164	+	28.2164i	−0.990810	+	0.990810i	0.00914795	+	0.999958i	$0.497088\pi$
$812$	50.3486			1.76689
$813$	0.649026	−	0.649026i	0.0227623	−	0.0227623i
$814$			58.0311i			2.03399i
$815$	−1.31712			−0.0461366
$816$	34.0763	+	36.4432i	1.19291	+	1.27577i
$817$	3.47907			0.121717
$818$		−	32.9464i		−	1.15194i
$819$	10.2072	−	10.2072i	0.356670	−	0.356670i
$820$	−34.3593			−1.19988
$821$	31.2664	−	31.2664i	1.09120	−	1.09120i	0.0958032	−	0.995400i	$-0.469458\pi$
$821$	31.2664	−	31.2664i	1.09120	−	1.09120i	0.995400	−	0.0958032i	$-0.0305419\pi$
$822$	−27.9110	−	27.9110i	−0.973507	−	0.973507i
$823$	12.0309	+	12.0309i	0.419372	+	0.419372i	0.884987	−	0.465615i	$-0.154167\pi$
$823$	12.0309	+	12.0309i	0.419372	+	0.419372i	−0.465615	+	0.884987i	$0.654167\pi$
$824$			53.6970i			1.87062i
$825$			25.6939i			0.894546i
$826$	−60.0576	−	60.0576i	−2.08967	−	2.08967i
$827$	−7.51459	−	7.51459i	−0.261308	−	0.261308i	0.564277	−	0.825585i	$-0.309155\pi$
$827$	−7.51459	−	7.51459i	−0.261308	−	0.261308i	−0.825585	+	0.564277i	$0.809155\pi$
$828$	−31.8194	+	31.8194i	−1.10580	+	1.10580i
$829$	20.3558			0.706985			0.353493	−	0.935437i	$-0.384994\pi$
$829$	20.3558			0.706985			0.353493	+	0.935437i	$0.384994\pi$
$830$	23.2620	−	23.2620i	0.807434	−	0.807434i
$831$			17.4224i			0.604376i
$832$	51.4338			1.78315
$833$	−0.303603	−	0.0101899i	−0.0105192	−	0.000353060i
$834$	10.0610			0.348385
$835$		−	1.55766i		−	0.0539049i
$836$	−79.3364	+	79.3364i	−2.74391	+	2.74391i
$837$	−23.7397			−0.820563
$838$	42.9720	−	42.9720i	1.48444	−	1.48444i
$839$	−19.2983	−	19.2983i	−0.666252	−	0.666252i	0.290595	−	0.956846i	$-0.406147\pi$
$839$	−19.2983	−	19.2983i	−0.666252	−	0.666252i	−0.956846	+	0.290595i	$0.906147\pi$
$840$	−12.5224	−	12.5224i	−0.432062	−	0.432062i
$841$			15.7671i			0.543693i
$842$		−	69.5416i		−	2.39656i
$843$	−14.9865	−	14.9865i	−0.516162	−	0.516162i
$844$	−86.5526	−	86.5526i	−2.97926	−	2.97926i
$845$	3.58126	−	3.58126i	0.123199	−	0.123199i
$846$	31.5911			1.08612
$847$	−51.5369	+	51.5369i	−1.77083	+	1.77083i
$848$			157.515i			5.40909i
$849$	22.0615			0.757150
$850$	−1.61198	+	48.0281i	−0.0552905	+	1.64735i
$851$	14.4462			0.495210
$852$			35.6821i			1.22245i
$853$	−6.82978	+	6.82978i	−0.233847	+	0.233847i	−0.814296	−	0.580449i	$-0.802877\pi$
$853$	−6.82978	+	6.82978i	−0.233847	+	0.233847i	0.580449	+	0.814296i	$0.302877\pi$
$854$	−27.9786			−0.957409
$855$	−4.16617	+	4.16617i	−0.142480	+	0.142480i
$856$	8.36942	+	8.36942i	0.286061	+	0.286061i
$857$	−2.07042	−	2.07042i	−0.0707241	−	0.0707241i	0.670860	−	0.741584i	$-0.265925\pi$
$857$	−2.07042	−	2.07042i	−0.0707241	−	0.0707241i	−0.741584	+	0.670860i	$0.765925\pi$
$858$			41.2748i			1.40910i
$859$			45.0808i			1.53814i	0.639167	+	0.769068i	$0.279279\pi$
$859$			45.0808i			1.53814i	−0.639167	+	0.769068i	$0.720721\pi$
$860$	2.98406	+	2.98406i	0.101756	+	0.101756i
$861$	−14.6199	−	14.6199i	−0.498243	−	0.498243i
$862$	10.5623	−	10.5623i	0.359753	−	0.359753i
$863$	11.6927			0.398024			0.199012	−	0.979997i	$-0.436227\pi$
$863$	11.6927			0.398024			0.199012	+	0.979997i	$0.436227\pi$
$864$	57.7732	−	57.7732i	1.96548	−	1.96548i
$865$		−	9.40324i		−	0.319720i
$866$	−46.1178			−1.56715
$867$	−12.2213	+	10.6821i	−0.415056	+	0.362783i
$868$	67.6307			2.29553
$869$			35.6966i			1.21092i
$870$	−5.34562	+	5.34562i	−0.181234	+	0.181234i
$871$	−22.8375			−0.773819
$872$	−42.1764	+	42.1764i	−1.42827	+	1.42827i
$873$	−15.2503	−	15.2503i	−0.516145	−	0.516145i
$874$	27.3402	+	27.3402i	0.924797	+	0.924797i
$875$		−	20.1496i		−	0.681180i
$876$			52.8107i			1.78431i
$877$	−33.7190	−	33.7190i	−1.13861	−	1.13861i	−0.988700	−	0.149908i	$-0.952102\pi$
$877$	−33.7190	−	33.7190i	−1.13861	−	1.13861i	−0.149908	−	0.988700i	$-0.547898\pi$
$878$	60.5210	+	60.5210i	2.04249	+	2.04249i
$879$	−18.2099	+	18.2099i	−0.614206	+	0.614206i
$880$	−63.6902			−2.14700
$881$	−2.22035	+	2.22035i	−0.0748054	+	0.0748054i	−0.743520	−	0.668714i	$-0.766845\pi$
$881$	−2.22035	+	2.22035i	−0.0748054	+	0.0748054i	0.668714	+	0.743520i	$0.266845\pi$
$882$			0.412968i			0.0139054i
$883$	16.2920			0.548269			0.274135	−	0.961691i	$-0.411609\pi$
$883$	16.2920			0.548269			0.274135	+	0.961691i	$0.411609\pi$
$884$	−1.87059	+	55.7333i	−0.0629148	+	1.87451i
$885$	9.21240			0.309671
$886$			98.4524i			3.30757i
$887$	19.2784	−	19.2784i	0.647306	−	0.647306i	−0.305035	−	0.952341i	$-0.598668\pi$
$887$	19.2784	−	19.2784i	0.647306	−	0.647306i	0.952341	+	0.305035i	$0.0986683\pi$
$888$	−28.6471			−0.961332
$889$	17.7226	−	17.7226i	0.594397	−	0.594397i
$890$	11.3266	+	11.3266i	0.379669	+	0.379669i
$891$	−7.12627	−	7.12627i	−0.238739	−	0.238739i
$892$			33.4253i			1.11916i
$893$		−	19.6082i		−	0.656163i
$894$	−21.8504	−	21.8504i	−0.730786	−	0.730786i
$895$	−2.88238	−	2.88238i	−0.0963475	−	0.0963475i
$896$	−36.6415	+	36.6415i	−1.22411	+	1.22411i
$897$	10.2749			0.343069
$898$	22.3741	−	22.3741i	0.746633	−	0.746633i
$899$		−	17.7751i		−	0.592832i
$900$	47.1921			1.57307
$901$	−51.2155	−	1.71896i	−1.70624	−	0.0572669i
$902$	−135.424			−4.50913
$903$			2.53943i			0.0845070i
$904$	118.542	−	118.542i	3.94264	−	3.94264i
$905$	−12.0167			−0.399448
$906$	25.7389	−	25.7389i	0.855118	−	0.855118i
$907$	16.6990	+	16.6990i	0.554481	+	0.554481i	0.927731	−	0.373250i	$-0.121757\pi$
$907$	16.6990	+	16.6990i	0.554481	+	0.554481i	−0.373250	+	0.927731i	$0.621757\pi$
$908$	11.9945	+	11.9945i	0.398050	+	0.398050i
$909$			4.43870i			0.147222i
$910$		−	15.0450i		−	0.498736i
$911$	2.53692	+	2.53692i	0.0840521	+	0.0840521i	0.747883	−	0.663831i	$-0.231070\pi$
$911$	2.53692	+	2.53692i	0.0840521	+	0.0840521i	−0.663831	+	0.747883i	$0.731070\pi$
$912$	−29.7689	−	29.7689i	−0.985746	−	0.985746i
$913$	66.2310	−	66.2310i	2.19193	−	2.19193i
$914$	7.70697			0.254924
$915$	2.14586	−	2.14586i	0.0709399	−	0.0709399i
$916$		−	80.4692i		−	2.65878i
$917$	32.6683			1.07880
$918$	36.7211	+	39.2717i	1.21198	+	1.29616i
$919$	9.03764			0.298124			0.149062	−	0.988828i	$-0.452375\pi$
$919$	9.03764			0.298124			0.149062	+	0.988828i	$0.452375\pi$
$920$			28.8756i			0.952001i
$921$	−3.62351	+	3.62351i	−0.119399	+	0.119399i
$922$	−15.6345			−0.514896
$923$	−13.1972	+	13.1972i	−0.434391	+	0.434391i
$924$	−57.9090	−	57.9090i	−1.90507	−	1.90507i
$925$	−10.7127	−	10.7127i	−0.352233	−	0.352233i
$926$			95.6881i			3.14451i
$927$			13.0399i			0.428286i
$928$	43.2577	+	43.2577i	1.42000	+	1.42000i
$929$	17.6565	+	17.6565i	0.579291	+	0.579291i	0.934708	−	0.355417i	$-0.115661\pi$
$929$	17.6565	+	17.6565i	0.579291	+	0.579291i	−0.355417	+	0.934708i	$0.615661\pi$
$930$	−7.18050	+	7.18050i	−0.235458	+	0.235458i
$931$	0.256324			0.00840068
$932$	−66.0390	+	66.0390i	−2.16318	+	2.16318i
$933$			7.60899i			0.249107i
$934$	−21.8048			−0.713475
$935$	0.695051	−	20.7087i	0.0227306	−	0.677246i
$936$	46.6745			1.52560
$937$		−	20.2807i		−	0.662541i	−0.943536	−	0.331270i	$-0.892523\pi$
$937$		−	20.2807i		−	0.662541i	0.943536	−	0.331270i	$-0.107477\pi$
$938$	44.3553	−	44.3553i	1.44825	−	1.44825i
$939$	24.4973			0.799439
$940$	16.8183	−	16.8183i	0.548552	−	0.548552i
$941$	3.20896	+	3.20896i	0.104609	+	0.104609i	0.757474	−	0.652865i	$-0.226433\pi$
$941$	3.20896	+	3.20896i	0.104609	+	0.104609i	−0.652865	+	0.757474i	$0.726433\pi$
$942$	−24.5681	−	24.5681i	−0.800473	−	0.800473i
$943$			33.7123i			1.09782i
$944$		−	150.791i		−	4.90781i
$945$	−7.40941	−	7.40941i	−0.241028	−	0.241028i
$946$	11.7614	+	11.7614i	0.382396	+	0.382396i
$947$	−7.27470	+	7.27470i	−0.236396	+	0.236396i	−0.815356	−	0.578960i	$-0.803459\pi$
$947$	−7.27470	+	7.27470i	−0.236396	+	0.236396i	0.578960	+	0.815356i	$0.303459\pi$
$948$	−28.6214			−0.929579
$949$	−19.5323	+	19.5323i	−0.634045	+	0.634045i
$950$		−	40.5489i		−	1.31558i
$951$	−22.2834			−0.722590
$952$	−64.4081	−	68.8817i	−2.08748	−	2.23247i
$953$	11.0006			0.356343			0.178172	−	0.983999i	$-0.442982\pi$
$953$	11.0006			0.356343			0.178172	+	0.983999i	$0.442982\pi$
$954$			69.6646i			2.25547i
$955$	−8.03149	+	8.03149i	−0.259893	+	0.259893i
$956$	80.0140			2.58784
$957$	−15.2200	+	15.2200i	−0.491991	+	0.491991i
$958$	38.4491	+	38.4491i	1.24223	+	1.24223i
$959$	28.9666	+	28.9666i	0.935379	+	0.935379i
$960$		−	15.3232i		−	0.494555i
$961$			7.12367i			0.229796i
$962$	−17.2090	−	17.2090i	−0.554841	−	0.554841i
$963$	2.03245	+	2.03245i	0.0654947	+	0.0654947i
$964$	−13.9370	+	13.9370i	−0.448880	+	0.448880i
$965$	15.7171			0.505953
$966$	−19.9561	+	19.9561i	−0.642076	+	0.642076i
$967$			34.4729i			1.10857i	0.832326	+	0.554287i	$0.187009\pi$
$967$			34.4729i			1.10857i	−0.832326	+	0.554287i	$0.812991\pi$
$968$	−235.662			−7.57447
$969$	10.0041	−	9.35439i	0.321379	−	0.300506i
$970$	−22.4783			−0.721733
$971$		−	40.8226i		−	1.31006i	−0.755604	−	0.655029i	$-0.772656\pi$
$971$		−	40.8226i		−	1.31006i	0.755604	−	0.655029i	$-0.227344\pi$
$972$	59.3471	−	59.3471i	1.90356	−	1.90356i
$973$	−10.4415			−0.334740
$974$	−34.2620	+	34.2620i	−1.09782	+	1.09782i
$975$	−7.61947	−	7.61947i	−0.244018	−	0.244018i
$976$	−35.1239	−	35.1239i	−1.12429	−	1.12429i
$977$		−	55.1616i		−	1.76478i	−0.470521	−	0.882389i	$-0.655934\pi$
$977$		−	55.1616i		−	1.76478i	0.470521	−	0.882389i	$-0.344066\pi$
$978$		−	4.16236i		−	0.133098i
$979$	32.2490	+	32.2490i	1.03068	+	1.03068i
$980$	0.219854	+	0.219854i	0.00702297	+	0.00702297i
$981$	−10.2422	+	10.2422i	−0.327008	+	0.327008i
$982$	46.6596			1.48897
$983$	10.2063	−	10.2063i	0.325531	−	0.325531i	−0.525353	−	0.850884i	$-0.676067\pi$
$983$	10.2063	−	10.2063i	0.325531	−	0.325531i	0.850884	+	0.525353i	$0.176067\pi$
$984$		−	66.8521i		−	2.13117i
$985$	−8.22396			−0.262037
$986$	−29.4047	+	27.4949i	−0.936436	+	0.875617i
$987$	14.3123			0.455567
$988$		−	47.0541i		−	1.49699i
$989$	2.92787	−	2.92787i	0.0931009	−	0.0931009i
$990$	−28.1684			−0.895251
$991$	7.25195	−	7.25195i	0.230366	−	0.230366i	−0.582480	−	0.812845i	$-0.697917\pi$
$991$	7.25195	−	7.25195i	0.230366	−	0.230366i	0.812845	+	0.582480i	$0.197917\pi$
$992$	58.1058	+	58.1058i	1.84486	+	1.84486i
$993$	−5.96526	−	5.96526i	−0.189302	−	0.189302i
$994$		−	51.2636i		−	1.62598i
$995$		−	12.6212i		−	0.400118i
$996$	53.1038	+	53.1038i	1.68266	+	1.68266i
$997$	7.83381	+	7.83381i	0.248099	+	0.248099i	0.820190	−	0.572091i	$-0.193868\pi$
$997$	7.83381	+	7.83381i	0.248099	+	0.248099i	−0.572091	+	0.820190i	$0.693868\pi$
$998$	−10.4634	+	10.4634i	−0.331214	+	0.331214i
$999$	−16.9503			−0.536284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.3	✓	56
17.13	even	4	inner	731.2.f.c.302.26	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.3	✓	56	1.1	even	1	trivial
731.2.f.c.302.26	yes	56	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.68403i q^{2} +(0.675148 - 0.675148i) q^{3} -5.20400 q^{4} +(-0.573416 + 0.573416i) q^{5} +(-1.81211 - 1.81211i) q^{6} +(1.88065 + 1.88065i) q^{7} +8.59962i q^{8} +2.08835i q^{9} +O(q^{10})\)	\(q-2.68403i q^{2} +(0.675148 - 0.675148i) q^{3} -5.20400 q^{4} +(-0.573416 + 0.573416i) q^{5} +(-1.81211 - 1.81211i) q^{6} +(1.88065 + 1.88065i) q^{7} +8.59962i q^{8} +2.08835i q^{9} +(1.53907 + 1.53907i) q^{10} +(4.38200 + 4.38200i) q^{11} +(-3.51347 + 3.51347i) q^{12} -2.59895 q^{13} +(5.04771 - 5.04771i) q^{14} +0.774282i q^{15} +12.6736 q^{16} +(-0.138307 + 4.12079i) q^{17} +5.60519 q^{18} -3.47907i q^{19} +(2.98406 - 2.98406i) q^{20} +2.53943 q^{21} +(11.7614 - 11.7614i) q^{22} +(-2.92787 - 2.92787i) q^{23} +(5.80602 + 5.80602i) q^{24} +4.34239i q^{25} +6.97564i q^{26} +(3.43539 + 3.43539i) q^{27} +(-9.78689 - 9.78689i) q^{28} +(-2.57225 + 2.57225i) q^{29} +2.07819 q^{30} +(-3.45517 + 3.45517i) q^{31} -16.8171i q^{32} +5.91699 q^{33} +(11.0603 + 0.371220i) q^{34} -2.15679 q^{35} -10.8678i q^{36} +(-2.46702 + 2.46702i) q^{37} -9.33792 q^{38} +(-1.75467 + 1.75467i) q^{39} +(-4.93116 - 4.93116i) q^{40} +(-5.75714 - 5.75714i) q^{41} -6.81590i q^{42} +1.00000i q^{43} +(-22.8039 - 22.8039i) q^{44} +(-1.19749 - 1.19749i) q^{45} +(-7.85848 + 7.85848i) q^{46} +5.63605 q^{47} +(8.55656 - 8.55656i) q^{48} +0.0736760i q^{49} +11.6551 q^{50} +(2.68876 + 2.87552i) q^{51} +13.5249 q^{52} +12.4286i q^{53} +(9.22068 - 9.22068i) q^{54} -5.02542 q^{55} +(-16.1729 + 16.1729i) q^{56} +(-2.34889 - 2.34889i) q^{57} +(6.90398 + 6.90398i) q^{58} -11.8980i q^{59} -4.02936i q^{60} +(-2.77142 - 2.77142i) q^{61} +(9.27376 + 9.27376i) q^{62} +(-3.92745 + 3.92745i) q^{63} -19.7903 q^{64} +(1.49028 - 1.49028i) q^{65} -15.8814i q^{66} +8.78722 q^{67} +(0.719750 - 21.4446i) q^{68} -3.95349 q^{69} +5.78888i q^{70} +(5.07790 - 5.07790i) q^{71} -17.9590 q^{72} +(7.51547 - 7.51547i) q^{73} +(6.62154 + 6.62154i) q^{74} +(2.93175 + 2.93175i) q^{75} +18.1051i q^{76} +16.4820i q^{77} +(4.70959 + 4.70959i) q^{78} +(4.07309 + 4.07309i) q^{79} +(-7.26726 + 7.26726i) q^{80} -1.62626 q^{81} +(-15.4523 + 15.4523i) q^{82} -15.1143i q^{83} -13.2152 q^{84} +(-2.28362 - 2.44223i) q^{85} +2.68403 q^{86} +3.47329i q^{87} +(-37.6835 + 37.6835i) q^{88} +7.35942 q^{89} +(-3.21411 + 3.21411i) q^{90} +(-4.88770 - 4.88770i) q^{91} +(15.2366 + 15.2366i) q^{92} +4.66549i q^{93} -15.1273i q^{94} +(1.99496 + 1.99496i) q^{95} +(-11.3540 - 11.3540i) q^{96} +(-7.30257 + 7.30257i) q^{97} +0.197748 q^{98} +(-9.15115 + 9.15115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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