LMFDB - Embedded newform 403.2.r.a.218.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.26
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34884 - 0.778756i) q^{2} +(1.55629 + 2.69558i) q^{3} +(0.212922 - 0.368791i) q^{4} -3.93166i q^{5} +(4.19840 + 2.42395i) q^{6} +(0.334531 + 0.193142i) q^{7} +2.45177i q^{8} +(-3.34410 + 5.79215i) q^{9} +O(q^{10})$	\(q+(1.34884 - 0.778756i) q^{2} +(1.55629 + 2.69558i) q^{3} +(0.212922 - 0.368791i) q^{4} -3.93166i q^{5} +(4.19840 + 2.42395i) q^{6} +(0.334531 + 0.193142i) q^{7} +2.45177i q^{8} +(-3.34410 + 5.79215i) q^{9} +(-3.06180 - 5.30320i) q^{10} +(3.49001 - 2.01496i) q^{11} +1.32548 q^{12} +(2.63743 + 2.45845i) q^{13} +0.601640 q^{14} +(10.5981 - 6.11882i) q^{15} +(2.33517 + 4.04464i) q^{16} +(-0.762516 + 1.32072i) q^{17} +10.4170i q^{18} +(-7.12111 - 4.11138i) q^{19} +(-1.44996 - 0.837136i) q^{20} +1.20234i q^{21} +(3.13832 - 5.43573i) q^{22} +(-1.71876 - 2.97698i) q^{23} +(-6.60894 + 3.81567i) q^{24} -10.4579 q^{25} +(5.47201 + 1.26216i) q^{26} -11.4798 q^{27} +(0.142458 - 0.0822481i) q^{28} +(-1.05886 - 1.83400i) q^{29} +(9.53013 - 16.5067i) q^{30} +1.00000i q^{31} +(2.05298 + 1.18529i) q^{32} +(10.8630 + 6.27173i) q^{33} +2.37526i q^{34} +(0.759366 - 1.31526i) q^{35} +(1.42406 + 2.46655i) q^{36} +(-2.57744 + 1.48809i) q^{37} -12.8070 q^{38} +(-2.52235 + 10.9355i) q^{39} +9.63951 q^{40} +(0.913972 - 0.527682i) q^{41} +(0.936329 + 1.62177i) q^{42} +(5.54621 - 9.60631i) q^{43} -1.71611i q^{44} +(22.7728 + 13.1479i) q^{45} +(-4.63669 - 2.67699i) q^{46} +2.35312i q^{47} +(-7.26843 + 12.5893i) q^{48} +(-3.42539 - 5.93295i) q^{49} +(-14.1061 + 8.14418i) q^{50} -4.74680 q^{51} +(1.46822 - 0.449201i) q^{52} -1.26233 q^{53} +(-15.4845 + 8.94000i) q^{54} +(-7.92213 - 13.7215i) q^{55} +(-0.473538 + 0.820192i) q^{56} -25.5940i q^{57} +(-2.85647 - 1.64918i) q^{58} +(1.30053 + 0.750861i) q^{59} -5.21132i q^{60} +(-4.96903 + 8.60662i) q^{61} +(0.778756 + 1.34884i) q^{62} +(-2.23741 + 1.29177i) q^{63} -5.64848 q^{64} +(9.66580 - 10.3695i) q^{65} +19.5366 q^{66} +(-4.58026 + 2.64442i) q^{67} +(0.324712 + 0.562418i) q^{68} +(5.34980 - 9.26612i) q^{69} -2.36544i q^{70} +(2.35566 + 1.36004i) q^{71} +(-14.2010 - 8.19896i) q^{72} -8.58823i q^{73} +(-2.31771 + 4.01440i) q^{74} +(-16.2756 - 28.1902i) q^{75} +(-3.03248 + 1.75080i) q^{76} +1.55669 q^{77} +(5.11380 + 16.7145i) q^{78} -4.04223 q^{79} +(15.9021 - 9.18110i) q^{80} +(-7.83372 - 13.5684i) q^{81} +(0.821871 - 1.42352i) q^{82} +12.5086i q^{83} +(0.443412 + 0.256004i) q^{84} +(5.19261 + 2.99795i) q^{85} -17.2766i q^{86} +(3.29579 - 5.70847i) q^{87} +(4.94021 + 8.55669i) q^{88} +(12.4324 - 7.17786i) q^{89} +40.9559 q^{90} +(0.407471 + 1.33182i) q^{91} -1.46385 q^{92} +(-2.69558 + 1.55629i) q^{93} +(1.83251 + 3.17399i) q^{94} +(-16.1645 + 27.9978i) q^{95} +7.37864i q^{96} +(4.75884 + 2.74752i) q^{97} +(-9.24065 - 5.33509i) q^{98} +26.9529i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.34884	−	0.778756i	0.953777	−	0.550664i	0.0595251	−	0.998227i	$-0.481041\pi$
$2$	1.34884	−	0.778756i	0.953777	−	0.550664i	0.894252	+	0.447563i	$0.147708\pi$
$3$	1.55629	+	2.69558i	0.898527	+	1.55629i	0.829378	+	0.558687i	$0.188695\pi$
$3$	1.55629	+	2.69558i	0.898527	+	1.55629i	0.0691483	+	0.997606i	$0.477972\pi$
$4$	0.212922	−	0.368791i	0.106461	−	0.184396i
$5$		−	3.93166i		−	1.75829i	−0.476553	−	0.879146i	$-0.658114\pi$
$5$		−	3.93166i		−	1.75829i	0.476553	−	0.879146i	$-0.341886\pi$
$6$	4.19840	+	2.42395i	1.71399	+	0.989572i
$7$	0.334531	+	0.193142i	0.126441	+	0.0730006i	0.561886	−	0.827214i	$-0.310076\pi$
$7$	0.334531	+	0.193142i	0.126441	+	0.0730006i	−0.435446	+	0.900215i	$0.643409\pi$
$8$			2.45177i			0.866831i
$9$	−3.34410	+	5.79215i	−1.11470	+	1.93072i
$10$	−3.06180	−	5.30320i	−0.968227	−	1.67702i
$11$	3.49001	−	2.01496i	1.05228	−	0.607533i	0.128992	−	0.991646i	$-0.458826\pi$
$11$	3.49001	−	2.01496i	1.05228	−	0.607533i	0.923286	+	0.384113i	$0.125493\pi$
$12$	1.32548			0.382632
$13$	2.63743	+	2.45845i	0.731490	+	0.681852i
$13$	2.63743	+	2.45845i	0.731490	+	0.681852i
$14$	0.601640			0.160795
$15$	10.5981	−	6.11882i	2.73642	−	1.57987i
$16$	2.33517	+	4.04464i	0.583793	+	1.01116i
$17$	−0.762516	+	1.32072i	−0.184937	+	0.320321i	−0.943555	−	0.331215i	$-0.892542\pi$
$17$	−0.762516	+	1.32072i	−0.184937	+	0.320321i	0.758618	+	0.651536i	$0.225875\pi$
$18$			10.4170i			2.45530i
$19$	−7.12111	−	4.11138i	−1.63370	−	0.943214i	−0.982940	−	0.183927i	$-0.941119\pi$
$19$	−7.12111	−	4.11138i	−1.63370	−	0.943214i	−0.650755	−	0.759287i	$-0.725548\pi$
$20$	−1.44996	−	0.837136i	−0.324221	−	0.187189i
$21$			1.20234i			0.262372i
$22$	3.13832	−	5.43573i	0.669092	−	1.15890i
$23$	−1.71876	−	2.97698i	−0.358387	−	0.620744i	0.629305	−	0.777159i	$-0.283340\pi$
$23$	−1.71876	−	2.97698i	−0.358387	−	0.620744i	−0.987691	+	0.156415i	$0.950006\pi$
$24$	−6.60894	+	3.81567i	−1.34904	+	0.778870i
$25$	−10.4579			−2.09159
$26$	5.47201	+	1.26216i	1.07315	+	0.247530i
$27$	−11.4798			−2.20930
$28$	0.142458	−	0.0822481i	0.0269220	−	0.0155434i
$29$	−1.05886	−	1.83400i	−0.196625	−	0.340565i	0.750807	−	0.660522i	$-0.229665\pi$
$29$	−1.05886	−	1.83400i	−0.196625	−	0.340565i	−0.947432	+	0.319957i	$0.896331\pi$
$30$	9.53013	−	16.5067i	1.73996	−	3.01369i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	2.05298	+	1.18529i	0.362920	+	0.209532i
$33$	10.8630	+	6.27173i	1.89100	+	1.09177i
$34$			2.37526i			0.407353i
$35$	0.759366	−	1.31526i	0.128356	−	0.222320i
$36$	1.42406	+	2.46655i	0.237344	+	0.411092i
$37$	−2.57744	+	1.48809i	−0.423729	+	0.244640i	−0.696672	−	0.717390i	$-0.745336\pi$
$37$	−2.57744	+	1.48809i	−0.423729	+	0.244640i	0.272942	+	0.962030i	$0.412003\pi$
$38$	−12.8070			−2.07758
$39$	−2.52235	+	10.9355i	−0.403899	+	1.75108i
$40$	9.63951			1.52414
$41$	0.913972	−	0.527682i	0.142738	−	0.0824101i	−0.426930	−	0.904285i	$-0.640405\pi$
$41$	0.913972	−	0.527682i	0.142738	−	0.0824101i	0.569668	+	0.821875i	$0.307072\pi$
$42$	0.936329	+	1.62177i	0.144479	+	0.250245i
$43$	5.54621	−	9.60631i	0.845789	−	1.46495i	−0.0391461	−	0.999233i	$-0.512464\pi$
$43$	5.54621	−	9.60631i	0.845789	−	1.46495i	0.884935	−	0.465715i	$-0.154203\pi$
$44$		−	1.71611i		−	0.258714i
$45$	22.7728	+	13.1479i	3.39476	+	1.95997i
$46$	−4.63669	−	2.67699i	−0.683642	−	0.394701i
$47$			2.35312i			0.343238i	0.985163	+	0.171619i	$0.0548998\pi$
$47$			2.35312i			0.343238i	−0.985163	+	0.171619i	$0.945100\pi$
$48$	−7.26843	+	12.5893i	−1.04911	+	1.81711i
$49$	−3.42539	−	5.93295i	−0.489342	−	0.847565i
$50$	−14.1061	+	8.14418i	−1.99491	+	1.15176i
$51$	−4.74680			−0.664684
$52$	1.46822	−	0.449201i	0.203606	−	0.0622930i
$53$	−1.26233			−0.173394			−0.0866971	−	0.996235i	$-0.527631\pi$
$53$	−1.26233			−0.173394			−0.0866971	+	0.996235i	$0.527631\pi$
$54$	−15.4845	+	8.94000i	−2.10718	+	1.21658i
$55$	−7.92213	−	13.7215i	−1.06822	−	1.85021i
$56$	−0.473538	+	0.820192i	−0.0632792	+	0.109603i
$57$		−	25.5940i		−	3.39001i
$58$	−2.85647	−	1.64918i	−0.375073	−	0.216549i
$59$	1.30053	+	0.750861i	0.169315	+	0.0977538i	0.582263	−	0.813001i	$-0.302168\pi$
$59$	1.30053	+	0.750861i	0.169315	+	0.0977538i	−0.412948	+	0.910755i	$0.635501\pi$
$60$		−	5.21132i		−	0.672778i
$61$	−4.96903	+	8.60662i	−0.636220	+	1.10196i	0.350036	+	0.936736i	$0.386169\pi$
$61$	−4.96903	+	8.60662i	−0.636220	+	1.10196i	−0.986255	+	0.165228i	$0.947164\pi$
$62$	0.778756	+	1.34884i	0.0989021	+	0.171303i
$63$	−2.23741	+	1.29177i	−0.281887	+	0.162748i
$64$	−5.64848			−0.706060
$65$	9.66580	−	10.3695i	1.19889	−	1.28617i
$66$	19.5366			2.40479
$67$	−4.58026	+	2.64442i	−0.559568	+	0.323067i	−0.752972	−	0.658052i	$-0.771381\pi$
$67$	−4.58026	+	2.64442i	−0.559568	+	0.323067i	0.193404	+	0.981119i	$0.438047\pi$
$68$	0.324712	+	0.562418i	0.0393772	+	0.0682033i
$69$	5.34980	−	9.26612i	0.644040	−	1.11551i
$70$		−	2.36544i		−	0.282725i
$71$	2.35566	+	1.36004i	0.279565	+	0.161407i	0.633227	−	0.773966i	$-0.281730\pi$
$71$	2.35566	+	1.36004i	0.279565	+	0.161407i	−0.353661	+	0.935374i	$0.615063\pi$
$72$	−14.2010	−	8.19896i	−1.67361	−	0.966256i
$73$		−	8.58823i		−	1.00518i	−0.864526	−	0.502588i	$-0.832381\pi$
$73$		−	8.58823i		−	1.00518i	0.864526	−	0.502588i	$-0.167619\pi$
$74$	−2.31771	+	4.01440i	−0.269429	+	0.466664i
$75$	−16.2756	−	28.1902i	−1.87935	−	3.25512i
$76$	−3.03248	+	1.75080i	−0.347849	+	0.200831i
$77$	1.55669			0.177401
$78$	5.11380	+	16.7145i	0.579024	+	1.89255i
$79$	−4.04223			−0.454786			−0.227393	−	0.973803i	$-0.573020\pi$
$79$	−4.04223			−0.454786			−0.227393	+	0.973803i	$0.573020\pi$
$80$	15.9021	−	9.18110i	1.77791	−	1.02648i
$81$	−7.83372	−	13.5684i	−0.870413	−	1.50760i
$82$	0.821871	−	1.42352i	0.0907604	−	0.157202i
$83$			12.5086i			1.37300i	0.727131	+	0.686499i	$0.240853\pi$
$83$			12.5086i			1.37300i	−0.727131	+	0.686499i	$0.759147\pi$
$84$	0.443412	+	0.256004i	0.0483803	+	0.0279324i
$85$	5.19261	+	2.99795i	0.563217	+	0.325174i
$86$		−	17.2766i		−	1.86298i
$87$	3.29579	−	5.70847i	0.353346	−	0.612013i
$88$	4.94021	+	8.55669i	0.526628	+	0.912147i
$89$	12.4324	−	7.17786i	1.31783	−	0.760851i	0.334453	−	0.942412i	$-0.391448\pi$
$89$	12.4324	−	7.17786i	1.31783	−	0.760851i	0.983380	+	0.181561i	$0.0581151\pi$
$90$	40.9559			4.31713
$91$	0.407471	+	1.33182i	0.0427146	+	0.139613i
$92$	−1.46385			−0.152617
$93$	−2.69558	+	1.55629i	−0.279519	+	0.161380i
$94$	1.83251	+	3.17399i	0.189009	+	0.327373i
$95$	−16.1645	+	27.9978i	−1.65845	+	2.87251i
$96$			7.37864i			0.753080i
$97$	4.75884	+	2.74752i	0.483187	+	0.278968i	0.721744	−	0.692161i	$-0.243341\pi$
$97$	4.75884	+	2.74752i	0.483187	+	0.278968i	−0.238557	+	0.971129i	$0.576674\pi$
$98$	−9.24065	−	5.33509i	−0.933446	−	0.538925i
$99$			26.9529i			2.70887i
$100$	−2.22672	+	3.85680i	−0.222672	+	0.385680i
$101$	8.40005	+	14.5493i	0.835836	+	1.44771i	0.893348	+	0.449366i	$0.148350\pi$
$101$	8.40005	+	14.5493i	0.835836	+	1.44771i	−0.0575114	+	0.998345i	$0.518317\pi$
$102$	−6.40269	+	3.69660i	−0.633961	+	0.366017i
$103$	5.85472			0.576882			0.288441	−	0.957498i	$-0.406863\pi$
$103$	5.85472			0.576882			0.288441	+	0.957498i	$0.406863\pi$
$104$	−6.02755	+	6.46635i	−0.591050	+	0.634078i
$105$	4.72719			0.461326
$106$	−1.70269	+	0.983046i	−0.165379	+	0.0954819i
$107$	−2.18710	−	3.78817i	−0.211435	−	0.366216i	0.740729	−	0.671804i	$-0.234480\pi$
$107$	−2.18710	−	3.78817i	−0.211435	−	0.366216i	−0.952164	+	0.305588i	$0.901147\pi$
$108$	−2.44431	+	4.23367i	−0.235204	+	0.407385i
$109$		−	9.80332i		−	0.938988i	−0.882936	−	0.469494i	$-0.844436\pi$
$109$		−	9.80332i		−	0.938988i	0.882936	−	0.469494i	$-0.155564\pi$
$110$	−21.3714	−	12.3388i	−2.03769	−	1.17646i
$111$	−8.02252	−	4.63180i	−0.761464	−	0.439631i
$112$			1.80407i			0.170469i
$113$	5.35565	−	9.27626i	0.503817	−	0.872637i	−0.496173	−	0.868224i	$-0.665262\pi$
$113$	5.35565	−	9.27626i	0.503817	−	0.872637i	0.999990	−	0.00441339i	$-0.00140483\pi$
$114$	−19.9315	−	34.5224i	−1.86676	−	3.23332i
$115$	−11.7045	+	6.75759i	−1.09145	+	0.630148i
$116$	−0.901816			−0.0837315
$117$	−23.0595	+	7.05506i	−2.13186	+	0.652240i
$118$	2.33895			0.215318
$119$	−0.510170	+	0.294547i	−0.0467672	+	0.0270011i
$120$	15.0019	+	25.9841i	1.36948	+	2.37201i
$121$	2.62011	−	4.53817i	0.238192	−	0.412561i
$122$			15.4787i			1.40137i
$123$	2.84482	+	1.64246i	0.256509	+	0.148095i
$124$	0.368791	+	0.212922i	0.0331184	+	0.0191209i
$125$			21.4587i			1.91933i
$126$	−2.01195	+	3.48479i	−0.179238	+	0.310450i
$127$	7.49734	+	12.9858i	0.665282	+	1.15230i	0.979209	+	0.202855i	$0.0650219\pi$
$127$	7.49734	+	12.9858i	0.665282	+	1.15230i	−0.313927	+	0.949447i	$0.601645\pi$
$128$	−11.7249	+	6.76937i	−1.03634	+	0.598333i
$129$	34.5261			3.03985
$130$	4.96238	−	21.5141i	0.435230	−	1.88691i
$131$	−20.2449			−1.76880			−0.884402	−	0.466727i	$-0.845433\pi$
$131$	−20.2449			−1.76880			−0.884402	+	0.466727i	$0.845433\pi$
$132$	4.62592	−	2.67078i	0.402635	−	0.232461i
$133$	−1.58815	−	2.75076i	−0.137710	−	0.238522i
$134$	−4.11871	+	7.13382i	−0.355802	+	0.616268i
$135$			45.1348i			3.88459i
$136$	−3.23809	−	1.86951i	−0.277664	−	0.160309i
$137$	0.175152	+	0.101124i	0.0149642	+	0.00863959i	0.507463	−	0.861673i	$-0.330583\pi$
$137$	0.175152	+	0.101124i	0.0149642	+	0.00863959i	−0.492499	+	0.870313i	$0.663917\pi$
$138$		−	16.6647i		−	1.41860i
$139$	−3.03947	+	5.26452i	−0.257805	+	0.446531i	−0.965654	−	0.259833i	$-0.916333\pi$
$139$	−3.03947	+	5.26452i	−0.257805	+	0.446531i	0.707849	+	0.706364i	$0.249666\pi$
$140$	−0.323371	−	0.560096i	−0.0273299	−	0.0473367i
$141$	−6.34302	+	3.66215i	−0.534179	+	0.308408i
$142$	4.23656			0.355524
$143$	14.1583	+	3.26572i	1.18398	+	0.273093i
$144$	−31.2362			−2.60302
$145$	−7.21065	+	4.16307i	−0.598812	+	0.345724i
$146$	−6.68814	−	11.5842i	−0.553514	−	0.958715i
$147$	10.6618	−	18.4668i	0.879373	−	1.52312i
$148$			1.26738i			0.104178i
$149$	17.4832	+	10.0939i	1.43228	+	0.826927i	0.997294	−	0.0735101i	$-0.0234201\pi$
$149$	17.4832	+	10.0939i	1.43228	+	0.826927i	0.434986	+	0.900437i	$0.356753\pi$
$150$	−43.9066	−	25.3495i	−3.58496	−	2.06978i
$151$			10.2751i			0.836177i	0.908406	+	0.418088i	$0.137300\pi$
$151$			10.2751i			0.836177i	−0.908406	+	0.418088i	$0.862700\pi$
$152$	10.0801	−	17.4593i	0.817607	−	1.41614i
$153$	−5.09986	−	8.83322i	−0.412299	−	0.714123i
$154$	2.09973	−	1.21228i	0.169201	−	0.0976883i
$155$	3.93166			0.315798
$156$	3.49584	+	3.25862i	0.279891	+	0.260898i
$157$	7.72860			0.616809			0.308405	−	0.951255i	$-0.400205\pi$
$157$	7.72860			0.616809			0.308405	+	0.951255i	$0.400205\pi$
$158$	−5.45234	+	3.14791i	−0.433765	+	0.250434i
$159$	−1.96455	−	3.40271i	−0.155799	−	0.269852i
$160$	4.66016	−	8.07163i	0.368418	−	0.638119i
$161$		−	1.32786i		−	0.104650i
$162$	−21.1329	−	12.2011i	−1.66036	−	0.958609i
$163$	−3.50186	−	2.02180i	−0.274287	−	0.158360i	0.356547	−	0.934277i	$-0.383954\pi$
$163$	−3.50186	−	2.02180i	−0.274287	−	0.158360i	−0.630834	+	0.775918i	$0.717287\pi$
$164$		−	0.449420i		−	0.0350938i
$165$	24.6583	−	42.7095i	1.91965	−	3.32493i
$166$	9.74115	+	16.8722i	0.756060	+	1.30953i
$167$	−7.12438	+	4.11326i	−0.551301	+	0.318294i	−0.749647	−	0.661838i	$-0.769777\pi$
$167$	−7.12438	+	4.11326i	−0.551301	+	0.318294i	0.198346	+	0.980132i	$0.436443\pi$
$168$	−2.94786			−0.227432
$169$	0.912023	+	12.9680i	0.0701556	+	0.997536i
$170$	9.33869			0.716245
$171$	47.6274	−	27.4977i	3.64216	−	2.10280i
$172$	−2.36182	−	4.09079i	−0.180087	−	0.311919i
$173$	−3.16826	+	5.48758i	−0.240878	+	0.417213i	−0.960965	−	0.276671i	$-0.910769\pi$
$173$	−3.16826	+	5.48758i	−0.240878	+	0.417213i	0.720087	+	0.693884i	$0.244102\pi$
$174$		−	10.2665i		−	0.778298i
$175$	−3.49850	−	2.01986i	−0.264462	−	0.152687i
$176$	16.2995	+	9.41055i	1.22862	+	0.709347i
$177$			4.67424i			0.351338i
$178$	11.1796	−	19.3636i	0.837946	−	1.45137i
$179$	4.75915	+	8.24309i	0.355716	+	0.616117i	0.987240	−	0.159238i	$-0.0509039\pi$
$179$	4.75915	+	8.24309i	0.355716	+	0.616117i	−0.631525	+	0.775356i	$0.717571\pi$
$180$	9.69763	−	5.59893i	0.722819	−	0.417320i
$181$	−11.0298			−0.819841			−0.409920	−	0.912121i	$-0.634443\pi$
$181$	−11.0298			−0.819841			−0.409920	+	0.912121i	$0.634443\pi$
$182$	1.58678	+	1.47910i	0.117620	+	0.109639i
$183$	−30.9331			−2.28664
$184$	7.29887	−	4.21400i	0.538080	−	0.310661i
$185$	5.85065	+	10.1336i	0.430148	+	0.745039i
$186$	−2.42395	+	4.19840i	−0.177732	+	0.307841i
$187$			6.14575i			0.449422i
$188$	0.867810	+	0.501031i	0.0632916	+	0.0365414i
$189$	−3.84036	−	2.21724i	−0.279345	−	0.161280i
$190$			50.3529i			3.65298i
$191$	3.62865	−	6.28501i	0.262560	−	0.454767i	−0.704361	−	0.709841i	$-0.748767\pi$
$191$	3.62865	−	6.28501i	0.262560	−	0.454767i	0.966921	+	0.255074i	$0.0820999\pi$
$192$	−8.79069	−	15.2259i	−0.634414	−	1.09884i
$193$	8.75000	−	5.05181i	0.629839	−	0.363637i	−0.150851	−	0.988557i	$-0.548201\pi$
$193$	8.75000	−	5.05181i	0.629839	−	0.363637i	0.780690	+	0.624919i	$0.214868\pi$
$194$	8.55858			0.614470
$195$	42.9945	+	9.91701i	3.07890	+	0.710172i
$196$	−2.91736			−0.208383
$197$	7.72939	−	4.46257i	0.550696	−	0.317945i	−0.198706	−	0.980059i	$-0.563674\pi$
$197$	7.72939	−	4.46257i	0.550696	−	0.317945i	0.749403	+	0.662114i	$0.230341\pi$
$198$	20.9897	+	36.3553i	1.49167	+	2.58366i
$199$	−0.215237	+	0.372802i	−0.0152578	+	0.0264272i	−0.873553	−	0.486728i	$-0.838190\pi$
$199$	−0.215237	+	0.372802i	−0.0152578	+	0.0264272i	0.858296	+	0.513155i	$0.171524\pi$
$200$		−	25.6404i		−	1.81305i
$201$	−14.2565	−	8.23098i	−1.00557	−	0.580568i
$202$	22.6607	+	13.0832i	1.59440	+	0.920529i
$203$		−	0.818038i		−	0.0574150i
$204$	−1.01070	+	1.75058i	−0.0707629	+	0.122565i
$205$	−2.07466	−	3.59342i	−0.144901	−	0.250976i
$206$	7.89710	−	4.55939i	0.550217	−	0.317668i
$207$	22.9909			1.59797
$208$	−3.78471	+	16.4083i	−0.262422	+	1.13771i
$209$	−33.1370			−2.29213
$210$	6.37625	−	3.68133i	0.440003	−	0.254036i
$211$	2.13951	+	3.70573i	0.147290	+	0.255113i	0.930225	−	0.366990i	$-0.119612\pi$
$211$	2.13951	+	3.70573i	0.147290	+	0.255113i	−0.782935	+	0.622103i	$0.786278\pi$
$212$	−0.268777	+	0.465536i	−0.0184597	+	0.0319731i
$213$			8.46649i			0.580115i
$214$	−5.90011	−	3.40643i	−0.403324	−	0.232859i
$215$	−37.7687	−	21.8058i	−2.57581	−	1.48714i
$216$		−	28.1459i		−	1.91509i
$217$	−0.193142	+	0.334531i	−0.0131113	+	0.0227094i
$218$	−7.63440	−	13.2232i	−0.517067	−	0.895586i
$219$	23.1503	−	13.3658i	1.56435	−	0.903178i
$220$	−6.74717			−0.454894
$221$	−5.25800	+	1.60868i	−0.353691	+	0.108212i
$222$	−14.4282			−0.968356
$223$	5.96804	−	3.44565i	0.399650	−	0.230738i	−0.286683	−	0.958025i	$-0.592553\pi$
$223$	5.96804	−	3.44565i	0.399650	−	0.230738i	0.686333	+	0.727288i	$0.259219\pi$
$224$	0.457858	+	0.793033i	0.0305919	+	0.0529867i
$225$	34.9724	−	60.5740i	2.33149	−	4.03826i
$226$		−	16.6830i		−	1.10974i
$227$	−6.22577	−	3.59445i	−0.413219	−	0.238572i	0.278953	−	0.960305i	$-0.410013\pi$
$227$	−6.22577	−	3.59445i	−0.413219	−	0.238572i	−0.692172	+	0.721733i	$0.743346\pi$
$228$	−9.43886	−	5.44953i	−0.625104	−	0.360904i
$229$			19.9206i			1.31639i	0.752847	+	0.658196i	$0.228680\pi$
$229$			19.9206i			1.31639i	−0.752847	+	0.658196i	$0.771320\pi$
$230$	−10.5250	+	18.2299i	−0.693999	+	1.20204i
$231$	2.42266	+	4.19618i	0.159400	+	0.276088i
$232$	4.49653	−	2.59607i	0.295212	−	0.170441i
$233$	0.794951			0.0520790			0.0260395	−	0.999661i	$-0.491710\pi$
$233$	0.794951			0.0520790			0.0260395	+	0.999661i	$0.491710\pi$
$234$	−25.6096	+	27.4739i	−1.67415	+	1.79603i
$235$	9.25167			0.603512
$236$	0.553822	−	0.319749i	0.0360508	−	0.0208139i
$237$	−6.29090	−	10.8962i	−0.408638	−	0.707781i
$238$	−0.458760	+	0.794596i	−0.0297370	+	0.0515060i
$239$		−	10.5487i		−	0.682337i	−0.940002	−	0.341168i	$-0.889177\pi$
$239$		−	10.5487i		−	0.682337i	0.940002	−	0.341168i	$-0.110823\pi$
$240$	49.4968	+	28.5770i	3.19500	+	1.84464i
$241$	−17.2232	−	9.94381i	−1.10944	−	0.640537i	−0.170758	−	0.985313i	$-0.554622\pi$
$241$	−17.2232	−	9.94381i	−1.10944	−	0.640537i	−0.938685	+	0.344776i	$0.887955\pi$
$242$		−	8.16172i		−	0.524655i
$243$	7.16335	−	12.4073i	0.459529	−	0.795928i
$244$	2.11603	+	3.66507i	0.135465	+	0.234632i
$245$	−23.3263	+	13.4675i	−1.49027	+	0.860405i
$246$	5.11629			0.326203
$247$	−8.67378	−	28.3504i	−0.551899	−	1.80389i
$248$	−2.45177			−0.155687
$249$	−33.7179	+	19.4671i	−2.13679	+	1.23367i
$250$	16.7111	+	28.9445i	1.05690	+	1.83061i
$251$	−1.61943	+	2.80494i	−0.102218	+	0.177046i	−0.912598	−	0.408858i	$-0.865927\pi$
$251$	−1.61943	+	2.80494i	−0.102218	+	0.177046i	0.810380	+	0.585904i	$0.199260\pi$
$252$			1.10018i			0.0693050i
$253$	−11.9970	−	6.92647i	−0.754245	−	0.435463i
$254$	20.2255	+	11.6772i	1.26906	+	0.732693i
$255$			18.6628i			1.16871i
$256$	−4.89489	+	8.47821i	−0.305931	+	0.529888i
$257$	2.32971	+	4.03518i	0.145324	+	0.251708i	0.929494	−	0.368838i	$-0.120244\pi$
$257$	2.32971	+	4.03518i	0.145324	+	0.251708i	−0.784170	+	0.620546i	$0.786911\pi$
$258$	46.5704	−	26.8874i	2.89934	−	1.67394i
$259$	−1.14965			−0.0714355
$260$	−1.76611	−	5.77254i	−0.109529	−	0.357998i
$261$	14.1637			0.876712
$262$	−27.3072	+	15.7658i	−1.68704	+	0.974016i
$263$	−2.61128	−	4.52287i	−0.161018	−	0.278892i	0.774216	−	0.632922i	$-0.218144\pi$
$263$	−2.61128	−	4.52287i	−0.161018	−	0.278892i	−0.935234	+	0.354030i	$0.884811\pi$
$264$	−15.3768	+	26.6335i	−0.946379	+	1.63918i
$265$			4.96305i			0.304877i
$266$	−4.28435	−	2.47357i	−0.262690	−	0.151664i
$267$	38.6970	+	22.3417i	2.36822	+	1.36729i
$268$			2.25222i			0.137576i
$269$	−8.19404	+	14.1925i	−0.499599	+	0.865332i	−1.00000		0.000462433i	$-0.999853\pi$
$269$	−8.19404	+	14.1925i	−0.499599	+	0.865332i	0.500400	+	0.865794i	$0.333186\pi$
$270$	35.1490	+	60.8799i	2.13910	+	3.70503i
$271$	22.7179	−	13.1162i	1.38002	−	0.796753i	0.387855	−	0.921720i	$-0.373216\pi$
$271$	22.7179	−	13.1162i	1.38002	−	0.796753i	0.992161	+	0.124968i	$0.0398827\pi$
$272$	−7.12242			−0.431860
$273$	−2.95590	+	3.17108i	−0.178899	+	0.191923i
$274$	0.315003			0.0190300
$275$	−36.4983	+	21.0723i	−2.20093	+	1.27071i
$276$	−2.27818	−	3.94592i	−0.137130	−	0.237516i
$277$	12.6172	−	21.8536i	0.758093	−	1.31305i	−0.185730	−	0.982601i	$-0.559465\pi$
$277$	12.6172	−	21.8536i	0.758093	−	1.31305i	0.943822	−	0.330454i	$-0.107202\pi$
$278$			9.46804i			0.567855i
$279$	−5.79215	−	3.34410i	−0.346767	−	0.200206i
$280$	3.22471	+	1.86179i	0.192714	+	0.111263i
$281$		−	7.22657i		−	0.431101i	−0.976493	−	0.215551i	$-0.930845\pi$
$281$		−	7.22657i		−	0.431101i	0.976493	−	0.215551i	$-0.0691546\pi$
$282$	−5.70384	+	9.87934i	−0.339659	+	0.588306i
$283$	3.44518	+	5.96723i	0.204795	+	0.354715i	0.950067	−	0.312045i	$-0.101014\pi$
$283$	3.44518	+	5.96723i	0.204795	+	0.354715i	−0.745272	+	0.666760i	$0.767681\pi$
$284$	1.00314	−	0.579165i	0.0595256	−	0.0343671i
$285$	−100.627			−5.96063
$286$	21.6406	−	6.62092i	1.27963	−	0.391503i
$287$	0.407669			0.0240639
$288$	−13.7308	+	7.92747i	−0.809094	+	0.467130i
$289$	7.33714	+	12.7083i	0.431596	+	0.747547i
$290$	−6.48403	+	11.2307i	−0.380755	+	0.659488i
$291$			17.1038i			1.00264i
$292$	−3.16727	−	1.82862i	−0.185350	−	0.107012i
$293$	24.1356	+	13.9347i	1.41002	+	0.814075i	0.995389	−	0.0959156i	$-0.0305779\pi$
$293$	24.1356	+	13.9347i	1.41002	+	0.814075i	0.414629	+	0.909990i	$0.363911\pi$
$294$		−	33.2119i		−	1.93696i
$295$	2.95213	−	5.11324i	0.171880	−	0.297704i
$296$	−3.64844	−	6.31929i	−0.212062	−	0.367301i
$297$	−40.0648	+	23.1314i	−2.32479	+	1.34222i
$298$	31.4428			1.82144
$299$	2.78567	−	12.0771i	0.161099	−	0.698435i
$300$	−13.8617			−0.800308
$301$	3.71075	−	2.14241i	0.213884	−	0.123486i
$302$	8.00181	+	13.8595i	0.460452	+	0.797527i
$303$	−26.1459	+	45.2860i	−1.50204	+	2.60161i
$304$		−	38.4031i		−	2.20257i
$305$	33.8383	+	19.5365i	1.93757	+	1.11866i
$306$	−13.7578	−	7.94309i	−0.786483	−	0.454076i
$307$		−	20.5031i		−	1.17018i	−0.810970	−	0.585088i	$-0.801060\pi$
$307$		−	20.5031i		−	1.17018i	0.810970	−	0.585088i	$-0.198940\pi$
$308$	0.331453	−	0.574093i	0.0188863	−	0.0327120i
$309$	9.11166	+	15.7819i	0.518344	+	0.897798i
$310$	5.30320	−	3.06180i	0.301201	−	0.173899i
$311$	−12.3549			−0.700583			−0.350291	−	0.936641i	$-0.613917\pi$
$311$	−12.3549			−0.700583			−0.350291	+	0.936641i	$0.613917\pi$
$312$	−26.8112	−	6.18421i	−1.51789	−	0.350112i
$313$	7.93108			0.448291			0.224146	−	0.974556i	$-0.428041\pi$
$313$	7.93108			0.448291			0.224146	+	0.974556i	$0.428041\pi$
$314$	10.4247	−	6.01869i	0.588299	−	0.339654i
$315$	5.07880	+	8.79673i	0.286158	+	0.495640i
$316$	−0.860679	+	1.49074i	−0.0484170	+	0.0838606i
$317$		−	19.1555i		−	1.07588i	−0.842983	−	0.537940i	$-0.819203\pi$
$317$		−	19.1555i		−	1.07588i	0.842983	−	0.537940i	$-0.180797\pi$
$318$	−5.29976	−	3.05982i	−0.297196	−	0.171586i
$319$	−7.39085	−	4.26711i	−0.413808	−	0.238912i
$320$			22.2079i			1.24146i
$321$	6.80754	−	11.7910i	0.379960	−	0.658109i
$322$	−1.03408	−	1.79107i	−0.0576268	−	0.0998126i
$323$	10.8599	−	6.26998i	0.604262	−	0.348871i
$324$	−6.67187			−0.370660
$325$	−27.5820	−	25.7103i	−1.52998	−	1.42615i
$326$	−6.29796			−0.348812
$327$	26.4256	−	15.2568i	1.46134	−	0.843706i
$328$	1.29375	+	2.24085i	0.0714356	+	0.123730i
$329$	−0.454485	+	0.787192i	−0.0250566	+	0.0433993i
$330$		−	76.8112i		−	4.22832i
$331$	−23.1894	−	13.3884i	−1.27460	−	0.735892i	−0.298752	−	0.954331i	$-0.596570\pi$
$331$	−23.1894	−	13.3884i	−1.27460	−	0.735892i	−0.975851	+	0.218439i	$0.929904\pi$
$332$	4.61306	+	2.66335i	0.253175	+	0.146171i
$333$		−	19.9053i		−	1.09080i
$334$	−6.40645	+	11.0963i	−0.350546	+	0.607163i
$335$	10.3969	+	18.0080i	0.568046	+	0.983884i
$336$	−4.86303	+	2.80767i	−0.265300	+	0.153171i
$337$	18.3890			1.00171			0.500856	−	0.865531i	$-0.333019\pi$
$337$	18.3890			1.00171			0.500856	+	0.865531i	$0.333019\pi$
$338$	11.3291	+	16.7815i	0.616220	+	0.912795i
$339$	33.3399			1.81077
$340$	2.21124	−	1.27666i	0.119921	−	0.0692365i
$341$	2.01496	+	3.49001i	0.109116	+	0.188995i
$342$	42.8280	−	74.1803i	2.31587	−	4.01121i
$343$		−	5.35032i		−	0.288890i
$344$	23.5524	+	13.5980i	1.26986	+	0.733155i
$345$	−36.4312	−	21.0336i	−1.96139	−	1.13241i
$346$			9.86920i			0.530571i
$347$	6.81729	−	11.8079i	0.365971	−	0.633881i	−0.622960	−	0.782254i	$-0.714070\pi$
$347$	6.81729	−	11.8079i	0.365971	−	0.633881i	0.988932	+	0.148373i	$0.0474035\pi$
$348$	−1.40349	−	2.43092i	−0.0752350	−	0.130311i
$349$	10.3581	−	5.98024i	0.554455	−	0.320115i	−0.196462	−	0.980511i	$-0.562945\pi$
$349$	10.3581	−	5.98024i	0.554455	−	0.320115i	0.750917	+	0.660397i	$0.229612\pi$
$350$	−6.29192			−0.336317
$351$	−30.2772	−	28.2227i	−1.61608	−	1.50641i
$352$	9.55325			0.509190
$353$	21.3229	−	12.3108i	1.13490	−	0.655236i	0.189739	−	0.981835i	$-0.439236\pi$
$353$	21.3229	−	12.3108i	1.13490	−	0.655236i	0.945163	+	0.326599i	$0.105903\pi$
$354$	3.64009	+	6.30483i	0.193469	+	0.335098i
$355$	5.34722	−	9.26165i	0.283801	−	0.491557i
$356$		−	6.11329i		−	0.324004i
$357$	−1.58795	−	0.916803i	−0.0840432	−	0.0485224i
$358$	12.8387	+	7.41243i	0.678547	+	0.391759i
$359$			17.7747i			0.938110i	0.883169	+	0.469055i	$0.155405\pi$
$359$			17.7747i			0.938110i	−0.883169	+	0.469055i	$0.844595\pi$
$360$	−32.2355	+	55.8335i	−1.69896	+	2.94269i
$361$	24.3068	+	42.1007i	1.27931	+	2.21582i
$362$	−14.8775	+	8.58954i	−0.781945	+	0.451456i
$363$	16.3107			0.856088
$364$	0.577925	+	0.133303i	0.0302915	+	0.00698696i
$365$	−33.7660			−1.76739
$366$	−41.7240	+	24.0893i	−2.18095	+	1.25917i
$367$	−6.67953	−	11.5693i	−0.348668	−	0.603911i	0.637345	−	0.770579i	$-0.280033\pi$
$367$	−6.67953	−	11.5693i	−0.348668	−	0.603911i	−0.986013	+	0.166667i	$0.946699\pi$
$368$	8.02721	−	13.9035i	0.418447	−	0.724772i
$369$			7.05848i			0.367450i
$370$	15.7832	+	9.11246i	0.820532	+	0.473734i
$371$	−0.422288	−	0.243808i	−0.0219241	−	0.0126579i
$372$			1.32548i			0.0687227i
$373$	7.17793	−	12.4325i	0.371659	−	0.643732i	−0.618162	−	0.786051i	$-0.712122\pi$
$373$	7.17793	−	12.4325i	0.371659	−	0.643732i	0.989821	+	0.142318i	$0.0454557\pi$
$374$	4.78604	+	8.28967i	0.247480	+	0.428648i
$375$	−57.8438	+	33.3961i	−2.98704	+	1.72457i
$376$	−5.76930			−0.297529
$377$	1.71613	−	7.44018i	0.0883854	−	0.383189i
$378$	−6.90674			−0.355244
$379$	24.0127	−	13.8637i	1.23345	−	0.712132i	0.265701	−	0.964055i	$-0.414396\pi$
$379$	24.0127	−	13.8637i	1.23345	−	0.712132i	0.967747	+	0.251924i	$0.0810632\pi$
$380$	6.88356	+	11.9227i	0.353119	+	0.611620i
$381$	−23.3361	+	40.4194i	−1.19555	+	2.07075i
$382$		−	11.3033i		−	0.578329i
$383$	2.79605	+	1.61430i	0.142872	+	0.0824869i	0.569732	−	0.821831i	$-0.307047\pi$
$383$	2.79605	+	1.61430i	0.142872	+	0.0824869i	−0.426860	+	0.904318i	$0.640380\pi$
$384$	−36.4947	−	21.0703i	−1.86236	−	1.07524i
$385$		−	6.12037i		−	0.311923i
$386$	7.86826	−	13.6282i	0.400484	−	0.693658i
$387$	37.0941	+	64.2489i	1.88560	+	3.26596i
$388$	2.02652	−	1.17001i	0.102881	−	0.0593984i
$389$	−25.3812			−1.28688			−0.643438	−	0.765498i	$-0.722493\pi$
$389$	−25.3812			−1.28688			−0.643438	+	0.765498i	$0.722493\pi$
$390$	65.7159	−	20.1057i	3.32765	−	1.01809i
$391$	5.24233			0.265116
$392$	14.5462	−	8.39827i	0.734695	−	0.424177i
$393$	−31.5070	−	54.5717i	−1.58932	−	2.75278i
$394$	6.95050	−	12.0386i	0.350161	−	0.606497i
$395$			15.8927i			0.799647i
$396$	9.93999	+	5.73886i	0.499503	+	0.288388i
$397$	−17.0403	−	9.83822i	−0.855228	−	0.493766i	0.00718321	−	0.999974i	$-0.497713\pi$
$397$	−17.0403	−	9.83822i	−0.855228	−	0.493766i	−0.862411	+	0.506208i	$0.831047\pi$
$398$			0.670469i			0.0336076i
$399$	4.94327	−	8.56200i	0.247473	−	0.428636i
$400$	−24.4211	−	42.2986i	−1.22105	−	2.11493i
$401$	4.98848	−	2.88010i	0.249113	−	0.143825i	−0.370245	−	0.928934i	$-0.620726\pi$
$401$	4.98848	−	2.88010i	0.249113	−	0.143825i	0.619358	+	0.785109i	$0.287393\pi$
$402$	−25.6397			−1.27879
$403$	−2.45845	+	2.63743i	−0.122464	+	0.131380i
$404$	7.15421			0.355935
$405$	−53.3463	+	30.7995i	−2.65080	+	1.53044i
$406$	−0.637052	−	1.10341i	−0.0316164	−	0.0547611i
$407$	−5.99687	+	10.3869i	−0.297254	+	0.514859i
$408$		−	11.6380i		−	0.576169i
$409$	−12.5781	−	7.26196i	−0.621946	−	0.359081i	0.155680	−	0.987808i	$-0.450243\pi$
$409$	−12.5781	−	7.26196i	−0.621946	−	0.359081i	−0.777626	+	0.628727i	$0.783576\pi$
$410$	−5.59680	−	3.23131i	−0.276406	−	0.159583i
$411$			0.629513i			0.0310516i
$412$	1.24660	−	2.15917i	0.0614154	−	0.106375i
$413$	0.290045	+	0.502373i	0.0142722	+	0.0247201i
$414$	31.0111	−	17.9043i	1.52411	−	0.879947i
$415$	49.1795			2.41413
$416$	2.50061	+	8.17328i	0.122603	+	0.400728i
$417$	−18.9213			−0.926578
$418$	−44.6967	+	25.8056i	−2.18619	+	1.26220i
$419$	3.77019	+	6.53017i	0.184186	+	0.319020i	0.943302	−	0.331936i	$-0.107702\pi$
$419$	3.77019	+	6.53017i	0.184186	+	0.319020i	−0.759116	+	0.650955i	$0.774368\pi$
$420$	1.00652	−	1.74335i	0.0491132	−	0.0850666i
$421$			10.0401i			0.489324i	0.969608	+	0.244662i	$0.0786770\pi$
$421$			10.0401i			0.489324i	−0.969608	+	0.244662i	$0.921323\pi$
$422$	5.77172	+	3.33231i	0.280963	+	0.162214i
$423$	−13.6296	−	7.86907i	−0.662695	−	0.382607i
$424$		−	3.09494i		−	0.150303i
$425$	7.97434	−	13.8120i	0.386813	−	0.669979i
$426$	6.59333	+	11.4200i	0.319448	+	0.553300i
$427$	−3.32459	+	1.91945i	−0.160888	+	0.0928889i
$428$	−1.86272			−0.0900382
$429$	13.2315	+	43.2473i	0.638822	+	2.08800i
$430$	−67.9256			−3.27566
$431$	−23.8888	+	13.7922i	−1.15068	+	0.664348i	−0.949054	−	0.315114i	$-0.897957\pi$
$431$	−23.8888	+	13.7922i	−1.15068	+	0.664348i	−0.201630	+	0.979462i	$0.564624\pi$
$432$	−26.8074	−	46.4318i	−1.28977	−	2.23395i
$433$	−15.7733	+	27.3201i	−0.758015	+	1.31292i	0.185847	+	0.982579i	$0.440497\pi$
$433$	−15.7733	+	27.3201i	−0.758015	+	1.31292i	−0.943862	+	0.330341i	$0.892836\pi$
$434$			0.601640i			0.0288797i
$435$	−22.4438	−	12.9579i	−1.07610	−	0.621285i
$436$	−3.61538	−	2.08734i	−0.173145	−	0.0999655i
$437$			28.2659i			1.35214i
$438$	20.8174	−	36.0568i	0.994694	−	1.72286i
$439$	−10.4942	−	18.1764i	−0.500859	−	0.867514i	−1.00000		0.000992689i	$-0.999684\pi$
$439$	−10.4942	−	18.1764i	−0.500859	−	0.867514i	0.499140	−	0.866521i	$-0.333649\pi$
$440$	33.6420	−	19.4232i	1.60382	−	0.925966i
$441$	45.8194			2.18188
$442$	−5.83945	+	6.26456i	−0.277754	+	0.297975i
$443$	−20.0487			−0.952541			−0.476270	−	0.879299i	$-0.658012\pi$
$443$	−20.0487			−0.952541			−0.476270	+	0.879299i	$0.658012\pi$
$444$	−3.41634	+	1.97242i	−0.162132	+	0.0936071i
$445$	−28.2209	−	48.8800i	−1.33780	−	2.31713i
$446$	5.36664	−	9.29530i	0.254118	−	0.440145i
$447$			62.8365i			2.97206i
$448$	−1.88959	−	1.09096i	−0.0892748	−	0.0515428i
$449$	−26.9074	−	15.5350i	−1.26984	−	0.733142i	−0.294882	−	0.955534i	$-0.595280\pi$
$449$	−26.9074	−	15.5350i	−1.26984	−	0.733142i	−0.974957	+	0.222392i	$0.928614\pi$
$450$		−	108.940i		−	5.13547i
$451$	2.12651	−	3.68323i	0.100134	−	0.173437i
$452$	−2.28067	−	3.95023i	−0.107274	−	0.185803i
$453$	−27.6974	+	15.9911i	−1.30134	+	0.751327i
$454$	−11.1968			−0.525492
$455$	5.23628	−	1.60204i	0.245481	−	0.0751046i
$456$	62.7506			2.93857
$457$	−12.6727	+	7.31661i	−0.592806	+	0.342257i	−0.766206	−	0.642595i	$-0.777858\pi$
$457$	−12.6727	+	7.31661i	−0.592806	+	0.342257i	0.173400	+	0.984851i	$0.444525\pi$
$458$	15.5133	+	26.8698i	0.724889	+	1.25554i
$459$	8.75357	−	15.1616i	0.408582	−	0.707684i
$460$			5.75535i			0.268344i
$461$	27.5347	+	15.8972i	1.28242	+	0.740405i	0.977290	−	0.211906i	$-0.0679671\pi$
$461$	27.5347	+	15.8972i	1.28242	+	0.740405i	0.305129	+	0.952311i	$0.401300\pi$
$462$	6.53560	+	3.77333i	0.304064	+	0.175551i
$463$		−	18.3858i		−	0.854459i	−0.904143	−	0.427230i	$-0.859490\pi$
$463$		−	18.3858i		−	0.854459i	0.904143	−	0.427230i	$-0.140510\pi$
$464$	4.94523	−	8.56539i	0.229577	−	0.397638i
$465$	6.11882	+	10.5981i	0.283753	+	0.491475i
$466$	1.07227	−	0.619073i	0.0496717	−	0.0286780i
$467$	−29.4316			−1.36193			−0.680965	−	0.732316i	$-0.738440\pi$
$467$	−29.4316			−1.36193			−0.680965	+	0.732316i	$0.738440\pi$
$468$	−2.30804	+	10.0063i	−0.106689	+	0.462543i
$469$	−2.04299			−0.0943363
$470$	12.4791	−	7.20479i	0.575616	−	0.332332i
$471$	12.0280	+	20.8331i	0.554219	+	0.959936i
$472$	−1.84094	+	3.18860i	−0.0847360	+	0.146767i
$473$		−	44.7015i		−	2.05538i
$474$	−16.9709	−	9.79815i	−0.779499	−	0.450044i
$475$	74.4722	+	42.9965i	3.41702	+	1.97282i
$476$			0.250862i			0.0114982i
$477$	4.22135	−	7.31160i	0.193283	−	0.334775i
$478$	−8.21484	−	14.2285i	−0.375738	−	0.650797i
$479$	−18.0631	+	10.4287i	−0.825325	+	0.476502i	−0.852249	−	0.523136i	$-0.824762\pi$
$479$	−18.0631	+	10.4287i	−0.825325	+	0.476502i	0.0269243	+	0.999637i	$0.491429\pi$
$480$	29.0103			1.32413
$481$	−10.4562	−	2.41180i	−0.476762	−	0.109969i
$482$	−30.9752			−1.41088
$483$	3.57935	−	2.06654i	0.162866	−	0.0940306i
$484$	−1.11576	−	1.93255i	−0.0507163	−	0.0878432i
$485$	10.8023	−	18.7101i	0.490507	−	0.849583i
$486$		−	22.3140i		−	1.01218i
$487$	−3.82795	−	2.21007i	−0.173461	−	0.100148i	0.410756	−	0.911745i	$-0.365265\pi$
$487$	−3.82795	−	2.21007i	−0.173461	−	0.100148i	−0.584217	+	0.811598i	$0.698598\pi$
$488$	−21.1014	−	12.1829i	−0.955217	−	0.551495i
$489$		−	12.5861i		−	0.569162i
$490$	−20.9758	+	36.3311i	−0.947588	+	1.64127i
$491$	−1.65327	−	2.86354i	−0.0746109	−	0.129230i	0.826306	−	0.563221i	$-0.190438\pi$
$491$	−1.65327	−	2.86354i	−0.0746109	−	0.129230i	−0.900917	+	0.433991i	$0.857105\pi$
$492$	1.21145	−	0.699429i	0.0546162	−	0.0315327i
$493$	3.22958			0.145453
$494$	−33.7776	−	31.4855i	−1.51973	−	1.41660i
$495$	105.970			4.76298
$496$	−4.04464	+	2.33517i	−0.181610	+	0.104852i
$497$	0.525361	+	0.909951i	0.0235656	+	0.0408169i
$498$	−30.3202	+	52.5161i	−1.35868	+	2.35330i
$499$		−	22.4108i		−	1.00325i	−0.865086	−	0.501624i	$-0.832736\pi$
$499$		−	22.4108i		−	1.00325i	0.865086	−	0.501624i	$-0.167264\pi$
$500$	7.91380	+	4.56903i	0.353916	+	0.204333i
$501$	−22.1753	−	12.8029i	−0.990717	−	0.571991i
$502$			5.04457i			0.225150i
$503$	−20.0569	+	34.7395i	−0.894291	+	1.54896i	−0.0596122	+	0.998222i	$0.518986\pi$
$503$	−20.0569	+	34.7395i	−0.894291	+	1.54896i	−0.834679	+	0.550737i	$0.814347\pi$
$504$	−3.16712	−	5.48561i	−0.141075	−	0.244348i
$505$	57.2029	−	33.0261i	2.54550	−	1.46964i
$506$	−21.5761			−0.959175
$507$	−33.5368	+	22.6404i	−1.48942	+	1.00550i
$508$	6.38539			0.283306
$509$	29.2473	−	16.8859i	1.29636	−	0.748455i	0.316588	−	0.948563i	$-0.397463\pi$
$509$	29.2473	−	16.8859i	1.29636	−	0.748455i	0.979774	+	0.200108i	$0.0641294\pi$
$510$	14.5337	+	25.1732i	0.643565	+	1.11469i
$511$	1.65874	−	2.87303i	0.0733785	−	0.127095i
$512$		−	11.8298i		−	0.522807i
$513$	81.7493	+	47.1980i	3.60932	+	2.08384i
$514$	6.28485	+	3.62856i	0.277213	+	0.160049i
$515$		−	23.0187i		−	1.01433i
$516$	7.35136	−	12.7329i	0.323626	−	0.560536i
$517$	4.74144	+	8.21241i	0.208528	+	0.361182i
$518$	−1.55069	+	0.895294i	−0.0681336	+	0.0393369i
$519$	−19.7230			−0.865742
$520$	25.4235	+	23.6983i	1.11489	+	1.03924i
$521$	−10.5292			−0.461293			−0.230647	−	0.973038i	$-0.574084\pi$
$521$	−10.5292			−0.461293			−0.230647	+	0.973038i	$0.574084\pi$
$522$	19.1047	−	11.0301i	0.836188	−	0.482773i
$523$	6.94737	+	12.0332i	0.303787	+	0.526175i	0.976991	−	0.213282i	$-0.0684154\pi$
$523$	6.94737	+	12.0332i	0.303787	+	0.526175i	−0.673203	+	0.739457i	$0.735082\pi$
$524$	−4.31058	+	7.46614i	−0.188308	+	0.326160i
$525$		−	12.5740i		−	0.548774i
$526$	−7.04442	−	4.06710i	−0.307151	−	0.177334i
$527$	−1.32072	−	0.762516i	−0.0575313	−	0.0332157i
$528$			58.5823i			2.54947i
$529$	5.59171	−	9.68513i	0.243118	−	0.421093i
$530$	3.86500	+	6.69438i	0.167885	+	0.290785i
$531$	−8.69820	+	5.02191i	−0.377470	+	0.217932i
$532$	−1.35261			−0.0586431
$533$	3.70781	+	0.855235i	0.160603	+	0.0370443i
$534$	69.5949			3.01167
$535$	−14.8938	+	8.59893i	−0.643914	+	0.371764i
$536$	−6.48349	−	11.2297i	−0.280044	−	0.485051i
$537$	−14.8133	+	25.6573i	−0.639240	+	1.10720i
$538$			25.5246i			1.10045i
$539$	−23.9093	−	13.8040i	−1.02985	−	0.594582i
$540$	16.6453	+	9.61019i	0.716301	+	0.413557i
$541$			27.7598i			1.19349i	0.802431	+	0.596744i	$0.203539\pi$
$541$			27.7598i			1.19349i	−0.802431	+	0.596744i	$0.796461\pi$
$542$	20.4286	−	35.3834i	0.877485	−	1.51985i
$543$	−17.1657	−	29.7318i	−0.736649	−	1.27591i
$544$	−3.13087	+	1.80761i	−0.134235	+	0.0775005i
$545$	−38.5433			−1.65101
$546$	−1.51755	+	6.57922i	−0.0649450	+	0.281565i
$547$	−36.7202			−1.57004			−0.785021	−	0.619469i	$-0.787348\pi$
$547$	−36.7202			−1.57004			−0.785021	+	0.619469i	$0.787348\pi$
$548$	0.0745872	−	0.0430629i	0.00318621	−	0.00183956i
$549$	−33.2339	−	57.5628i	−1.41839	−	2.45672i
$550$	−32.8204	+	56.8466i	−1.39947	+	2.42395i
$551$			17.4135i			0.741838i
$552$	22.7184	+	13.1165i	0.966958	+	0.558274i
$553$	−1.35225	−	0.780722i	−0.0575035	−	0.0331997i
$554$		−	39.3028i		−	1.66982i
$555$	−18.2107	+	31.5418i	−0.773000	+	1.33887i
$556$	1.29434	+	2.24186i	0.0548923	+	0.0950762i
$557$	19.7951	−	11.4287i	0.838746	−	0.484250i	−0.0180919	−	0.999836i	$-0.505759\pi$
$557$	19.7951	−	11.4287i	0.838746	−	0.484250i	0.856838	+	0.515586i	$0.172426\pi$
$558$	−10.4170			−0.440985
$559$	38.2444	−	11.7008i	1.61756	−	0.494893i
$560$	7.09301			0.299734
$561$	−16.5664	+	9.56459i	−0.699432	+	0.403817i
$562$	−5.62774	−	9.74753i	−0.237392	−	0.411175i
$563$	6.59564	−	11.4240i	0.277973	−	0.481463i	−0.692908	−	0.721026i	$-0.743671\pi$
$563$	6.59564	−	11.4240i	0.277973	−	0.481463i	0.970881	+	0.239563i	$0.0770041\pi$
$564$			3.11900i			0.131334i
$565$	−36.4711	−	21.0566i	−1.53435	−	0.885857i
$566$	9.29403	+	5.36591i	0.390657	+	0.225546i
$567$		−	6.05206i		−	0.254163i
$568$	−3.33450	+	5.77553i	−0.139913	+	0.242336i
$569$	−0.808452	−	1.40028i	−0.0338921	−	0.0587028i	0.848582	−	0.529064i	$-0.177457\pi$
$569$	−0.808452	−	1.40028i	−0.0338921	−	0.0587028i	−0.882474	+	0.470361i	$0.844124\pi$
$570$	−135.730	+	78.3639i	−5.68511	+	3.28230i
$571$	−25.0746			−1.04934			−0.524670	−	0.851306i	$-0.675811\pi$
$571$	−25.0746			−1.04934			−0.524670	+	0.851306i	$0.675811\pi$
$572$	4.21898	−	4.52612i	0.176405	−	0.189247i
$573$	22.5890			0.943669
$574$	0.549882	−	0.317475i	0.0229516	−	0.0132511i
$575$	17.9747	+	31.1331i	0.749597	+	1.29834i
$576$	18.8891	−	32.7168i	0.787045	−	1.36320i
$577$			26.8857i			1.11927i	0.828740	+	0.559633i	$0.189058\pi$
$577$			26.8857i			1.11927i	−0.828740	+	0.559633i	$0.810942\pi$
$578$	19.7933	+	11.4277i	0.823294	+	0.475329i
$579$	27.2351	+	15.7242i	1.13185	+	0.653476i
$580$			3.54563i			0.147224i
$581$	−2.41593	+	4.18451i	−0.100230	+	0.173603i
$582$	13.3197	+	23.0703i	0.552118	+	0.956296i
$583$	−4.40554	+	2.54354i	−0.182459	+	0.105343i
$584$	21.0563			0.871318
$585$	27.7381	+	90.6623i	1.14683	+	3.74842i
$586$	43.4070			1.79313
$587$	−26.8577	+	15.5063i	−1.10854	+	0.640015i	−0.938450	−	0.345414i	$-0.887738\pi$
$587$	−26.8577	+	15.5063i	−1.10854	+	0.640015i	−0.170088	+	0.985429i	$0.554405\pi$
$588$	−4.54027	−	7.86398i	−0.187238	−	0.324305i
$589$	4.11138	−	7.12111i	0.169406	−	0.293420i
$590$		−	9.19595i		−	0.378591i
$591$	24.0584	+	13.8901i	0.989631	+	0.571364i
$592$	−12.0375	−	6.94988i	−0.494740	−	0.285638i
$593$		−	16.1249i		−	0.662169i	−0.943601	−	0.331085i	$-0.892585\pi$
$593$		−	16.1249i		−	0.662169i	0.943601	−	0.331085i	$-0.107415\pi$
$594$	−36.0275	+	62.4014i	−1.47822	+	2.56036i
$595$	1.15806	+	2.00582i	0.0474757	+	0.0822304i
$596$	7.44511	−	4.29844i	0.304964	−	0.176071i
$597$	−1.33989			−0.0548381
$598$	−5.64766	−	18.4594i	−0.230950	−	0.754863i
$599$	47.4928			1.94050			0.970252	−	0.242097i	$-0.0778354\pi$
$599$	47.4928			1.94050			0.970252	+	0.242097i	$0.0778354\pi$
$600$	69.1158	−	39.9040i	2.82164	−	1.62908i
$601$	−0.568035	−	0.983865i	−0.0231706	−	0.0401327i	0.854208	−	0.519932i	$-0.174043\pi$
$601$	−0.568035	−	0.983865i	−0.0231706	−	0.0401327i	−0.877378	+	0.479799i	$0.840709\pi$
$602$	3.33682	−	5.77955i	0.135999	−	0.235557i
$603$		−	35.3728i		−	1.44049i
$604$	3.78937	+	2.18780i	0.154187	+	0.0890201i
$605$	−17.8425	−	10.3014i	−0.725402	−	0.418811i
$606$			81.4451i			3.30848i
$607$	−5.54869	+	9.61061i	−0.225214	+	0.390083i	−0.956384	−	0.292113i	$-0.905642\pi$
$607$	−5.54869	+	9.61061i	−0.225214	+	0.390083i	0.731169	+	0.682196i	$0.238975\pi$
$608$	−9.74636	−	16.8812i	−0.395267	−	0.684622i
$609$	2.20509	−	1.27311i	0.0893546	−	0.0515889i
$610$	60.8568			2.46402
$611$	−5.78504	+	6.20618i	−0.234037	+	0.251075i
$612$	−4.34348			−0.175575
$613$	−15.7879	+	9.11514i	−0.637667	+	0.368157i	−0.783715	−	0.621120i	$-0.786678\pi$
$613$	−15.7879	+	9.11514i	−0.637667	+	0.368157i	0.146048	+	0.989277i	$0.453345\pi$
$614$	−15.9669	−	27.6556i	−0.644374	−	1.11609i
$615$	6.45758	−	11.1848i	0.260395	−	0.451017i
$616$			3.81664i			0.153777i
$617$	27.3674	+	15.8006i	1.10177	+	0.636106i	0.936685	−	0.350173i	$-0.113877\pi$
$617$	27.3674	+	15.8006i	1.10177	+	0.636106i	0.165084	+	0.986280i	$0.447211\pi$
$618$	24.5804	+	14.1915i	0.988770	+	0.570866i
$619$			20.5534i			0.826111i	0.910706	+	0.413055i	$0.135538\pi$
$619$			20.5534i			0.826111i	−0.910706	+	0.413055i	$0.864462\pi$
$620$	0.837136	−	1.44996i	0.0336202	−	0.0582319i
$621$	19.7311	+	34.1753i	0.791783	+	1.37141i
$622$	−16.6649	+	9.62146i	−0.668200	+	0.385785i
$623$	5.54537			0.222170
$624$	−50.1201	+	15.3342i	−2.00641	+	0.613860i
$625$	32.0788			1.28315
$626$	10.6978	−	6.17638i	0.427570	−	0.246858i
$627$	−51.5709	−	89.3235i	−2.05954	−	3.56724i
$628$	1.64559	−	2.85024i	0.0656661	−	0.113737i
$629$		−	4.53876i		−	0.180972i
$630$	13.7010	+	7.91028i	0.545862	+	0.315153i
$631$	18.1113	+	10.4566i	0.721000	+	0.416269i	0.815121	−	0.579291i	$-0.196671\pi$
$631$	18.1113	+	10.4566i	0.721000	+	0.416269i	−0.0941208	+	0.995561i	$0.530004\pi$
$632$		−	9.91061i		−	0.394223i
$633$	−6.65940	+	11.5344i	−0.264687	+	0.458452i
$634$	−14.9175	−	25.8378i	−0.592448	−	1.02615i
$635$	51.0557	−	29.4770i	2.02608	−	1.16976i
$636$	−1.67319			−0.0663461
$637$	5.55167	−	24.0689i	0.219965	−	0.953644i
$638$	−13.2922			−0.526241
$639$	−15.7551	+	9.09623i	−0.623263	+	0.359841i
$640$	26.6148	+	46.0983i	1.05204	+	1.82219i
$641$	15.1333	−	26.2116i	0.597729	−	1.03530i	−0.395426	−	0.918498i	$-0.629403\pi$
$641$	15.1333	−	26.2116i	0.597729	−	1.03530i	0.993155	−	0.116800i	$-0.0372635\pi$
$642$		−	21.2056i		−	0.836920i
$643$	−20.3995	−	11.7777i	−0.804478	−	0.464465i	0.0405568	−	0.999177i	$-0.487087\pi$
$643$	−20.3995	−	11.7777i	−0.804478	−	0.464465i	−0.845034	+	0.534712i	$0.820420\pi$
$644$	−0.489702	−	0.282730i	−0.0192970	−	0.0111411i
$645$		−	135.745i		−	5.34495i
$646$	9.76557	−	16.9145i	0.384221	−	0.665491i
$647$	6.68235	+	11.5742i	0.262710	+	0.455028i	0.966961	−	0.254924i	$-0.0820503\pi$
$647$	6.68235	+	11.5742i	0.262710	+	0.455028i	−0.704251	+	0.709951i	$0.748717\pi$
$648$	33.2665	−	19.2064i	1.30683	−	0.754501i
$649$	6.05182			0.237555
$650$	−57.2260	−	13.1996i	−2.24459	−	0.517731i
$651$	−1.20234			−0.0471234
$652$	−1.49125	+	0.860971i	−0.0584017	+	0.0337182i
$653$	−3.99327	−	6.91654i	−0.156269	−	0.270665i	0.777252	−	0.629190i	$-0.216613\pi$
$653$	−3.99327	−	6.91654i	−0.156269	−	0.270665i	−0.933520	+	0.358525i	$0.883280\pi$
$654$	23.7627	−	41.1582i	0.929196	−	1.60941i
$655$			79.5960i			3.11007i
$656$	4.26856	+	2.46446i	0.166659	+	0.0962208i
$657$	49.7443	+	28.7199i	1.94071	+	1.12047i
$658$			1.41573i			0.0551910i
$659$	9.53212	−	16.5101i	0.371319	−	0.643143i	−0.618450	−	0.785824i	$-0.712239\pi$
$659$	9.53212	−	16.5101i	0.371319	−	0.643143i	0.989769	+	0.142681i	$0.0455724\pi$
$660$	−10.5006	−	18.1875i	−0.408735	−	0.707949i
$661$	15.7355	−	9.08488i	0.612039	−	0.353361i	−0.161724	−	0.986836i	$-0.551705\pi$
$661$	15.7355	−	9.08488i	0.612039	−	0.353361i	0.773763	+	0.633475i	$0.218372\pi$
$662$	−41.7051			−1.62092
$663$	−12.5193	−	11.6698i	−0.486210	−	0.453216i
$664$	−30.6682			−1.19016
$665$	−10.8151	+	6.24408i	−0.419390	+	0.242135i
$666$	−15.5013	−	26.8491i	−0.600665	−	1.04038i
$667$	−3.63985	+	6.30441i	−0.140936	+	0.244108i
$668$			3.50321i			0.135543i
$669$	18.5761	+	10.7249i	0.718192	+	0.414648i
$670$	28.0477	+	16.1934i	1.08358	+	0.625604i
$671$			40.0496i			1.54610i
$672$	−1.42512	+	2.46838i	−0.0549753	+	0.0952200i
$673$	6.23632	+	10.8016i	0.240392	+	0.416372i	0.960826	−	0.277152i	$-0.0893905\pi$
$673$	6.23632	+	10.8016i	0.240392	+	0.416372i	−0.720434	+	0.693524i	$0.756057\pi$
$674$	24.8039	−	14.3205i	0.955410	−	0.551606i
$675$	120.056			4.62094
$676$	4.97666	+	2.42482i	0.191410	+	0.0932622i
$677$	−6.96465			−0.267673			−0.133837	−	0.991003i	$-0.542730\pi$
$677$	−6.96465			−0.267673			−0.133837	+	0.991003i	$0.542730\pi$
$678$	44.9703	−	25.9636i	1.72707	−	0.997127i
$679$	1.06132	+	1.83826i	0.0407297	+	0.0705459i
$680$	−7.35028	+	12.7311i	−0.281870	+	0.488214i
$681$		−	22.3761i		−	0.857453i
$682$	5.43573	+	3.13832i	0.208145	+	0.120173i
$683$	4.28697	+	2.47508i	0.164036	+	0.0947064i	0.579771	−	0.814780i	$-0.303142\pi$
$683$	4.28697	+	2.47508i	0.164036	+	0.0947064i	−0.415734	+	0.909486i	$0.636475\pi$
$684$		−	23.4194i		−	0.895465i
$685$	0.397584	−	0.688636i	0.0151909	−	0.0263114i
$686$	−4.16660	−	7.21676i	−0.159081	−	0.275537i
$687$	−53.6976	+	31.0023i	−2.04869	+	1.18281i
$688$	51.8054			1.97506
$689$	−3.32930	−	3.10338i	−0.126836	−	0.118229i
$690$	−65.5201			−2.49431
$691$	−28.3429	+	16.3638i	−1.07821	+	0.622507i	−0.930414	−	0.366511i	$-0.880552\pi$
$691$	−28.3429	+	16.3638i	−1.07821	+	0.622507i	−0.147799	+	0.989017i	$0.547219\pi$
$692$	1.34918	+	2.33685i	0.0512882	+	0.0888338i
$693$	−5.20572	+	9.01658i	−0.197749	+	0.342511i
$694$		−	21.2360i		−	0.806108i
$695$	20.6983	+	11.9502i	0.785132	+	0.453296i
$696$	13.9959	+	8.08051i	0.530511	+	0.306291i
$697$			1.60946i			0.0609628i
$698$	9.31429	−	16.1328i	0.352551	−	0.610636i
$699$	1.23718	+	2.14285i	0.0467943	+	0.0810502i
$700$	−1.48982	+	0.860145i	−0.0563097	+	0.0325104i
$701$	39.5337			1.49317			0.746583	−	0.665292i	$-0.231693\pi$
$701$	39.5337			1.49317			0.746583	+	0.665292i	$0.231693\pi$
$702$	−62.8179	−	14.4894i	−2.37091	−	0.546868i
$703$	24.4724			0.922992
$704$	−19.7132	+	11.3814i	−0.742971	+	0.428955i
$705$	14.3983	+	24.9386i	0.542272	+	0.939242i
$706$	19.1742	−	33.2106i	0.721629	−	1.24990i
$707$			6.48959i			0.244066i
$708$	1.72382	+	0.995248i	0.0647851	+	0.0374037i
$709$	−33.8354	−	19.5349i	−1.27071	−	0.733648i	−0.295592	−	0.955314i	$-0.595517\pi$
$709$	−33.8354	−	19.5349i	−1.27071	−	0.733648i	−0.975123	+	0.221667i	$0.928850\pi$
$710$		−	16.6567i		−	0.625115i
$711$	13.5176	−	23.4132i	0.506950	−	0.878064i
$712$	17.5984	+	30.4814i	0.659529	+	1.14234i
$713$	2.97698	−	1.71876i	0.111489	−	0.0643681i
$714$	−2.85586			−0.106878
$715$	12.8397	−	55.6657i	0.480178	−	2.08178i
$716$	4.05331			0.151479
$717$	28.4348	−	16.4168i	1.06192	−	0.613098i
$718$	13.8421	+	23.9753i	0.516583	+	0.894748i
$719$	12.5080	−	21.6645i	0.466469	−	0.807949i	−0.532797	−	0.846243i	$-0.678859\pi$
$719$	12.5080	−	21.6645i	0.466469	−	0.807949i	0.999267	+	0.0382942i	$0.0121924\pi$
$720$			122.810i			4.57686i
$721$	1.95858	+	1.13079i	0.0729414	+	0.0421128i
$722$	65.5723	+	37.8582i	2.44035	+	1.40894i
$723$		−	61.9019i		−	2.30216i
$724$	−2.34849	+	4.06770i	−0.0872810	+	0.151175i
$725$	11.0735	+	19.1798i	0.411258	+	0.712321i
$726$	22.0006	−	12.7020i	0.816518	−	0.471417i
$727$	−42.7085			−1.58397			−0.791986	−	0.610540i	$-0.790953\pi$
$727$	−42.7085			−1.58397			−0.791986	+	0.610540i	$0.790953\pi$
$728$	−3.26532	+	0.999024i	−0.121021	+	0.0370263i
$729$	−2.40917			−0.0892286
$730$	−45.5451	+	26.2955i	−1.68570	+	0.973239i
$731$	8.45814	+	14.6499i	0.312836	+	0.541847i
$732$	−6.58633	+	11.4079i	−0.243438	+	0.421647i
$733$			16.7037i			0.616965i	0.951230	+	0.308482i	$0.0998211\pi$
$733$			16.7037i			0.616965i	−0.951230	+	0.308482i	$0.900179\pi$
$734$	−18.0193	−	10.4034i	−0.665104	−	0.383998i
$735$	−72.6053	−	41.9187i	−2.67809	−	1.54619i
$736$		−	8.14893i		−	0.300374i
$737$	−10.6568	+	18.4581i	−0.392547	+	0.679912i
$738$	5.49684	+	9.52080i	0.202341	+	0.350466i
$739$	27.0391	−	15.6110i	0.994649	−	0.574261i	0.0879886	−	0.996121i	$-0.471956\pi$
$739$	27.0391	−	15.6110i	0.994649	−	0.574261i	0.906661	+	0.421860i	$0.138623\pi$
$740$	4.98292			0.183176
$741$	62.9217	−	67.5024i	2.31149	−	2.47976i
$742$	−0.759468			−0.0278809
$743$	−40.5132	+	23.3903i	−1.48628	+	0.858107i	−0.999878	−	0.0156259i	$-0.995026\pi$
$743$	−40.5132	+	23.3903i	−1.48628	+	0.858107i	−0.486407	+	0.873733i	$0.661693\pi$
$744$	−3.81567	−	6.60894i	−0.139889	−	0.242295i
$745$	39.6859	−	68.7380i	1.45398	−	2.51837i
$746$		−	22.3594i		−	0.818637i
$747$	−72.4517	−	41.8300i	−2.65087	−	1.53048i
$748$	2.26650	+	1.30856i	0.0828714	+	0.0478458i
$749$		−	1.68968i		−	0.0617395i
$750$	−52.0149	+	90.0924i	−1.89931	+	3.28971i
$751$	−4.60438	−	7.97502i	−0.168016	−	0.291013i	0.769706	−	0.638398i	$-0.220403\pi$
$751$	−4.60438	−	7.97502i	−0.168016	−	0.291013i	−0.937722	+	0.347386i	$0.887069\pi$
$752$	−9.51752	+	5.49494i	−0.347068	+	0.200380i
$753$	−10.0812			−0.367381
$754$	−3.47929	−	11.3721i	−0.126708	−	0.414147i
$755$	40.3982			1.47024
$756$	−1.63539	+	0.944195i	−0.0594787	+	0.0343401i
$757$	0.861232	+	1.49170i	0.0313020	+	0.0542167i	0.881252	−	0.472647i	$-0.156701\pi$
$757$	0.861232	+	1.49170i	0.0313020	+	0.0542167i	−0.849950	+	0.526863i	$0.823368\pi$
$758$	21.5929	−	37.4000i	0.784290	−	1.35843i
$759$		−	43.1185i		−	1.56510i
$760$	−68.6441	−	39.6317i	−2.48998	−	1.43759i
$761$	−6.13109	−	3.53979i	−0.222252	−	0.128317i	0.384741	−	0.923025i	$-0.374291\pi$
$761$	−6.13109	−	3.53979i	−0.222252	−	0.128317i	−0.606993	+	0.794708i	$0.707624\pi$
$762$			72.6926i			2.63338i
$763$	1.89343	−	3.27951i	0.0685467	−	0.118726i
$764$	−1.54524	−	2.67643i	−0.0559047	−	0.0968299i
$765$	−34.7292	+	20.0509i	−1.25564	+	0.724942i
$766$	5.02859			0.181690
$767$	1.58409	+	5.17763i	0.0571983	+	0.186953i
$768$	−30.4716			−1.09955
$769$	10.8757	−	6.27909i	0.392188	−	0.226430i	−0.290920	−	0.956747i	$-0.593961\pi$
$769$	10.8757	−	6.27909i	0.392188	−	0.226430i	0.683108	+	0.730318i	$0.260628\pi$
$770$	−4.76627	−	8.25543i	−0.171765	−	0.297505i
$771$	−7.25144	+	12.5599i	−0.261154	+	0.452332i
$772$		−	4.30256i		−	0.154853i
$773$	−41.5793	−	24.0058i	−1.49550	−	0.863430i	−0.495517	−	0.868598i	$-0.665021\pi$
$773$	−41.5793	−	24.0058i	−1.49550	−	0.863430i	−0.999987	+	0.00516857i	$0.998355\pi$
$774$	100.068	+	57.7746i	3.59689	+	2.07666i
$775$		−	10.4579i		−	0.375660i
$776$	−6.73627	+	11.6676i	−0.241818	+	0.418841i
$777$	−1.78919	−	3.09896i	−0.0641867	−	0.111175i
$778$	−34.2352	+	19.7657i	−1.22739	+	0.708636i
$779$	−8.67799			−0.310921
$780$	12.8118	−	13.7445i	0.458735	−	0.492130i
$781$	10.9617			0.392241
$782$	7.07109	−	4.08250i	0.252862	−	0.145990i
$783$	12.1555	+	21.0540i	0.434403	+	0.752409i
$784$	15.9978	−	27.7089i	0.571349	−	0.989605i
$785$		−	30.3862i		−	1.08453i
$786$	−84.9961	−	49.0725i	−3.03171	−	1.75036i
$787$	−45.3009	−	26.1545i	−1.61480	−	0.932307i	−0.988235	−	0.152941i	$-0.951126\pi$
$787$	−45.3009	−	26.1545i	−1.61480	−	0.932307i	−0.626568	−	0.779367i	$-0.715541\pi$
$788$		−	3.80071i		−	0.135395i
$789$	8.12783	−	14.0778i	0.289358	−	0.501184i
$790$	12.3765	+	21.4367i	0.440336	+	0.762685i
$791$	3.58326	−	2.06880i	0.127406	−	0.0735580i
$792$	−66.0822			−2.34813
$793$	−34.2644	+	10.4832i	−1.21677	+	0.372269i
$794$	−30.6463			−1.08760
$795$	−13.3783	+	7.72396i	−0.474479	+	0.273941i
$796$	0.0916574	+	0.158755i	0.00324871	+	0.00562693i
$797$	−1.57178	+	2.72241i	−0.0556754	+	0.0964326i	−0.892520	−	0.451008i	$-0.851065\pi$
$797$	−1.57178	+	2.72241i	−0.0556754	+	0.0964326i	0.836844	+	0.547441i	$0.184398\pi$
$798$		−	15.3984i		−	0.545098i
$799$	−3.10780	−	1.79429i	−0.109946	−	0.0634775i
$800$	−21.4700	−	12.3957i	−0.759079	−	0.438254i
$801$			96.0139i			3.39248i
$802$	4.48579	−	7.76962i	0.158399	−	0.274355i
$803$	−17.3049	−	29.9730i	−0.610678	−	1.05772i
$804$	−6.07103	+	3.50511i	−0.214109	+	0.123616i
$805$	−5.22068			−0.184005
$806$	−1.26216	+	5.47201i	−0.0444577	+	0.192743i
$807$	−51.0093			−1.79561
$808$	−35.6715	+	20.5950i	−1.25492	+	0.724529i
$809$	27.3312	+	47.3391i	0.960915	+	1.66435i	0.720211	+	0.693755i	$0.244045\pi$
$809$	27.3312	+	47.3391i	0.960915	+	1.66435i	0.240704	+	0.970599i	$0.422622\pi$
$810$	−47.9706	+	83.0875i	−1.68551	+	2.91940i
$811$			33.0229i			1.15959i	0.814762	+	0.579796i	$0.196868\pi$
$811$			33.0229i			1.15959i	−0.814762	+	0.579796i	$0.803132\pi$
$812$	−0.301685	−	0.174178i	−0.0105871	−	0.00611245i
$813$	70.7115	+	40.8253i	2.47996	+	1.43181i
$814$			18.6804i			0.654747i
$815$	−7.94903	+	13.7681i	−0.278442	+	0.482277i
$816$	−11.0846	−	19.1991i	−0.388038	−	0.672102i
$817$	−78.9903	+	45.6051i	−2.76352	+	1.59552i
$818$	−22.6212			−0.790931
$819$	−9.07675	−	2.09362i	−0.317167	−	0.0731571i
$820$	−1.76697			−0.0617051
$821$	33.6432	−	19.4239i	1.17415	−	0.677899i	0.219500	−	0.975613i	$-0.429558\pi$
$821$	33.6432	−	19.4239i	1.17415	−	0.677899i	0.954655	+	0.297714i	$0.0962242\pi$
$822$	0.490237	+	0.849116i	0.0170990	+	0.0296163i
$823$	11.9488	−	20.6959i	0.416508	−	0.721413i	−0.579078	−	0.815272i	$-0.696587\pi$
$823$	11.9488	−	20.6959i	0.416508	−	0.721413i	0.995585	+	0.0938597i	$0.0299205\pi$
$824$			14.3544i			0.500059i
$825$	−113.604	−	65.5894i	−3.95519	−	2.28353i
$826$	0.782451	+	0.451748i	0.0272250	+	0.0157183i
$827$		−	22.3088i		−	0.775752i	−0.921712	−	0.387876i	$-0.873209\pi$
$827$		−	22.3088i		−	0.775752i	0.921712	−	0.387876i	$-0.126791\pi$
$828$	4.89525	−	8.47883i	0.170122	−	0.294660i
$829$	−3.19511	−	5.53410i	−0.110971	−	0.192207i	0.805191	−	0.593015i	$-0.202063\pi$
$829$	−3.19511	−	5.53410i	−0.110971	−	0.192207i	−0.916162	+	0.400808i	$0.868729\pi$
$830$	66.3356	−	38.2989i	2.30254	−	1.32937i
$831$	78.5441			2.72467
$832$	−14.8974	−	13.8865i	−0.516476	−	0.481428i
$833$	10.4477			0.361990
$834$	−25.5218	+	14.7350i	−0.883749	+	0.510233i
$835$	16.1719	+	28.0106i	0.559653	+	0.969348i
$836$	−7.05559	+	12.2206i	−0.244023	+	0.422660i
$837$		−	11.4798i		−	0.396802i
$838$	10.1708	+	5.87212i	0.351345	+	0.202849i
$839$	6.48916	+	3.74652i	0.224031	+	0.129344i	0.607815	−	0.794078i	$-0.292046\pi$
$839$	6.48916	+	3.74652i	0.224031	+	0.129344i	−0.383785	+	0.923423i	$0.625379\pi$
$840$			11.5900i			0.399892i
$841$	12.2576	−	21.2309i	0.422677	−	0.732098i
$842$	7.81878	+	13.5425i	0.269453	+	0.466706i
$843$	19.4798	−	11.2467i	0.670920	−	0.387356i
$844$	1.82219			0.0627223
$845$	50.9856	−	3.58576i	1.75396	−	0.123354i
$846$	−24.5123			−0.842752
$847$	1.75302	−	1.01211i	0.0602344	−	0.0347764i
$848$	−2.94775	−	5.10566i	−0.101226	−	0.175329i
$849$	−10.7234	+	18.5735i	−0.368027	+	0.637442i
$850$		−	24.8403i		−	0.852014i
$851$	8.86002	+	5.11534i	0.303718	+	0.175351i
$852$	3.12237	+	1.80270i	0.106971	+	0.0617595i
$853$		−	7.20149i		−	0.246574i	−0.992371	−	0.123287i	$-0.960656\pi$
$853$		−	7.20149i		−	0.246574i	0.992371	−	0.123287i	$-0.0393436\pi$
$854$	−2.98957	+	5.17809i	−0.102301	+	0.177191i
$855$	−108.112	−	187.255i	−3.69734	−	6.40398i
$856$	9.28770	−	5.36226i	0.317447	−	0.183278i
$857$	19.6227			0.670300			0.335150	−	0.942165i	$-0.391213\pi$
$857$	19.6227			0.670300			0.335150	+	0.942165i	$0.391213\pi$
$858$	51.5263	+	48.0298i	1.75908	+	1.63971i
$859$	−29.6441			−1.01145			−0.505723	−	0.862696i	$-0.668774\pi$
$859$	−29.6441			−1.01145			−0.505723	+	0.862696i	$0.668774\pi$
$860$	−16.0836	+	9.28585i	−0.548445	+	0.316645i
$861$	0.634453	+	1.09890i	0.0216221	+	0.0374506i
$862$	−21.4815	+	37.2071i	−0.731664	+	1.26728i
$863$		−	4.20129i		−	0.143014i	−0.997440	−	0.0715068i	$-0.977219\pi$
$863$		−	4.20129i		−	0.143014i	0.997440	−	0.0715068i	$-0.0227808\pi$
$864$	−23.5680	−	13.6070i	−0.801798	−	0.462918i
$865$	21.5753	+	12.4565i	0.733582	+	0.423534i
$866$			49.1341i			1.66964i
$867$	−22.8375	+	39.5557i	−0.775602	+	1.34338i
$868$	0.0822481	+	0.142458i	0.00279168	+	0.00483533i
$869$	−14.1074	+	8.14492i	−0.478561	+	0.276298i
$870$	−40.3642			−1.36848
$871$	−18.5813	−	4.28591i	−0.629602	−	0.145223i
$872$	24.0355			0.813944
$873$	−31.8281	+	18.3759i	−1.07722	+	0.621931i
$874$	22.0122	+	38.1263i	0.744575	+	1.28964i
$875$	−4.14458	+	7.17861i	−0.140112	+	0.242681i
$876$		−	11.3835i		−	0.384612i
$877$	11.1460	+	6.43515i	0.376374	+	0.217300i	0.676239	−	0.736682i	$-0.263608\pi$
$877$	11.1460	+	6.43515i	0.376374	+	0.217300i	−0.299866	+	0.953981i	$0.596942\pi$
$878$	−28.3100	−	16.3448i	−0.955417	−	0.551610i
$879$			86.7460i			2.92587i
$880$	36.9991	−	64.0843i	1.24724	−	2.16028i
$881$	9.72849	+	16.8502i	0.327761	+	0.567699i	0.982067	−	0.188531i	$-0.0603725\pi$
$881$	9.72849	+	16.8502i	0.327761	+	0.567699i	−0.654306	+	0.756230i	$0.727039\pi$
$882$	61.8033	−	35.6822i	2.08103	−	1.20148i
$883$	−31.3682			−1.05562			−0.527812	−	0.849361i	$-0.676988\pi$
$883$	−31.3682			−1.05562			−0.527812	+	0.849361i	$0.676988\pi$
$884$	−0.526274	+	2.28163i	−0.0177005	+	0.0767394i
$885$	18.3775			0.617754
$886$	−27.0425	+	15.6130i	−0.908512	+	0.524530i
$887$	17.5355	+	30.3723i	0.588783	+	1.01980i	0.994392	+	0.105756i	$0.0337261\pi$
$887$	17.5355	+	30.3723i	0.588783	+	1.01980i	−0.405609	+	0.914047i	$0.632941\pi$
$888$	11.3561	−	19.6693i	0.381086	−	0.660060i
$889$			5.79219i			0.194264i
$890$	−76.1312	−	43.9544i	−2.55192	−	1.47335i
$891$	−54.6795	−	31.5692i	−1.83183	−	1.05761i
$892$		−	2.93462i		−	0.0982582i
$893$	9.67456	−	16.7568i	0.323747	−	0.560746i
$894$	48.9343	+	84.7567i	1.63661	+	2.83469i
$895$	32.4090	−	18.7113i	1.08331	−	0.625451i
$896$	−5.22978			−0.174715
$897$	36.8900	−	11.2865i	1.23172	−	0.376844i
$898$	−48.3919			−1.61486
$899$	1.83400	−	1.05886i	0.0611672	−	0.0353149i
$900$	−14.8928	−	25.7950i	−0.496426	−	0.859834i
$901$	0.962546	−	1.66718i	0.0320670	−	0.0555418i
$902$		−	6.62414i		−	0.220560i
$903$	11.5500	+	6.66842i	0.384362	+	0.221911i
$904$	22.7432	+	13.1308i	0.756429	+	0.436724i
$905$			43.3655i			1.44152i
$906$	−24.9063	+	43.1390i	−0.827457	+	1.43320i
$907$	−22.1205	−	38.3139i	−0.734500	−	1.27219i	−0.954943	−	0.296791i	$-0.904084\pi$
$907$	−22.1205	−	38.3139i	−0.734500	−	1.27219i	0.220443	−	0.975400i	$-0.429250\pi$
$908$	−2.65120	+	1.53067i	−0.0879833	+	0.0507972i
$909$	−112.362			−3.72683
$910$	5.81533	−	6.23868i	0.192776	−	0.206810i
$911$	55.3587			1.83411			0.917057	−	0.398756i	$-0.130558\pi$
$911$	55.3587			1.83411			0.917057	+	0.398756i	$0.130558\pi$
$912$	103.519	−	59.7665i	3.42784	−	1.97907i
$913$	25.2043	+	43.6551i	0.834141	+	1.44477i
$914$	−11.3957	+	19.7379i	−0.376937	+	0.652873i
$915$			121.618i			4.02058i
$916$	7.34655	+	4.24153i	0.242737	+	0.140144i
$917$	−6.77254	−	3.91013i	−0.223649	−	0.129124i
$918$		−	27.2676i		−	0.899964i
$919$	−5.39811	+	9.34979i	−0.178067	+	0.308421i	−0.941218	−	0.337799i	$-0.890318\pi$
$919$	−5.39811	+	9.34979i	−0.178067	+	0.308421i	0.763151	+	0.646220i	$0.223651\pi$
$920$	−16.5680	−	28.6967i	−0.546232	−	0.946101i
$921$	55.2679	−	31.9089i	1.82114	−	1.05143i
$922$	49.5201			1.63086
$923$	2.86928	+	9.37828i	0.0944435	+	0.308690i
$924$	2.06335			0.0678793
$925$	26.9547	−	15.5623i	0.886266	−	0.511686i
$926$	−14.3180	−	24.7996i	−0.470520	−	0.814964i
$927$	−19.5788	+	33.9114i	−0.643051	+	1.11380i
$928$		−	5.02022i		−	0.164797i
$929$	−12.0761	−	6.97215i	−0.396205	−	0.228749i	0.288640	−	0.957438i	$-0.406797\pi$
$929$	−12.0761	−	6.97215i	−0.396205	−	0.228749i	−0.684845	+	0.728689i	$0.740130\pi$
$930$	16.5067	+	9.53013i	0.541275	+	0.312505i
$931$			56.3323i			1.84622i
$932$	0.169262	−	0.293171i	0.00554437	−	0.00960314i
$933$	−19.2279	−	33.3037i	−0.629492	−	1.09031i
$934$	−39.6986	+	22.9200i	−1.29898	+	0.749966i
$935$	24.1630			0.790214
$936$	−17.2974	−	56.5366i	−0.565382	−	1.84796i
$937$	−33.0062			−1.07827			−0.539133	−	0.842221i	$-0.681248\pi$
$937$	−33.0062			−1.07827			−0.539133	+	0.842221i	$0.681248\pi$
$938$	−2.75567	+	1.59099i	−0.0899759	+	0.0519476i
$939$	12.3431	+	21.3789i	0.402802	+	0.697673i
$940$	1.96988	−	3.41193i	0.0642504	−	0.111285i
$941$		−	22.1716i		−	0.722772i	−0.932416	−	0.361386i	$-0.882304\pi$
$941$		−	22.1716i		−	0.722772i	0.932416	−	0.361386i	$-0.117696\pi$
$942$	32.4477	+	18.7337i	1.05720	+	0.610377i
$943$	−3.14180	−	1.81392i	−0.102311	−	0.0590693i
$944$			7.01356i			0.228272i
$945$	−8.71741	+	15.0990i	−0.283577	+	0.491171i
$946$	−34.8116	−	60.2954i	−1.13182	−	1.96037i
$947$	29.2080	−	16.8632i	0.949132	−	0.547982i	0.0563208	−	0.998413i	$-0.482063\pi$
$947$	29.2080	−	16.8632i	0.949132	−	0.547982i	0.892811	+	0.450431i	$0.148730\pi$
$948$	−5.35787			−0.174016
$949$	21.1138	−	22.6508i	0.685382	−	0.735277i
$950$	133.935			4.34543
$951$	51.6352	−	29.8116i	1.67439	−	0.966707i
$952$	−0.722161	−	1.25082i	−0.0234054	−	0.0405393i
$953$	−4.28453	+	7.42102i	−0.138790	+	0.240390i	−0.927039	−	0.374966i	$-0.877654\pi$
$953$	−4.28453	+	7.42102i	−0.138790	+	0.240390i	0.788249	+	0.615356i	$0.210988\pi$
$954$		−	13.1496i		−	0.425735i
$955$	−24.7105	−	14.2666i	−0.799613	−	0.461657i
$956$	−3.89026	−	2.24604i	−0.125820	−	0.0726422i
$957$		−	26.5635i		−	0.858676i
$958$	−16.2429	+	28.1335i	−0.524784	+	0.908953i
$959$	0.0390624	+	0.0676581i	0.00126139	+	0.00218479i
$960$	−59.8631	+	34.5620i	−1.93207	+	1.11548i
$961$	−1.00000			−0.0322581
$962$	−15.9820	+	4.88969i	−0.515281	+	0.157650i
$963$	29.2555			0.942746
$964$	−7.33438	+	4.23451i	−0.236224	+	0.136384i
$965$	−19.8620	−	34.4020i	−0.639381	−	1.10744i
$966$	3.21865	−	5.57487i	0.103559	−	0.179369i
$967$			38.8918i			1.25068i	0.780353	+	0.625339i	$0.215039\pi$
$967$			38.8918i			1.25068i	−0.780353	+	0.625339i	$0.784961\pi$
$968$	11.1265	+	6.42391i	0.357621	+	0.206472i
$969$	33.8025	+	19.5159i	1.08589	+	0.626940i
$970$		−	33.6494i		−	1.08042i
$971$	13.4253	−	23.2534i	0.430840	−	0.746236i	−0.566106	−	0.824332i	$-0.691551\pi$
$971$	13.4253	−	23.2534i	0.430840	−	0.746236i	0.996946	+	0.0780960i	$0.0248841\pi$
$972$	−3.05047	−	5.28356i	−0.0978438	−	0.169470i
$973$	−2.03360	+	1.17410i	−0.0651941	+	0.0376398i
$974$	−6.88442			−0.220591
$975$	26.3785	−	114.362i	0.844790	−	3.66253i
$976$	−46.4142			−1.48568
$977$	28.7656	−	16.6078i	0.920292	−	0.531331i	0.0365639	−	0.999331i	$-0.488359\pi$
$977$	28.7656	−	16.6078i	0.920292	−	0.531331i	0.883728	+	0.468000i	$0.155025\pi$
$978$	−9.80148	−	16.9767i	−0.313417	−	0.542854i
$979$	28.9262	−	50.1016i	0.924484	−	1.60125i
$980$			11.4701i			0.366398i
$981$	56.7823	+	32.7833i	1.81292	+	1.04669i
$982$	−4.46000	−	2.57498i	−0.142324	−	0.0821710i
$983$		−	10.7635i		−	0.343301i	−0.985158	−	0.171651i	$-0.945090\pi$
$983$		−	10.7635i		−	0.343301i	0.985158	−	0.171651i	$-0.0549100\pi$
$984$	−4.02692	+	6.97483i	−0.128374	+	0.222349i
$985$	−17.5453	−	30.3893i	−0.559039	−	0.968285i
$986$	4.35621	−	2.51506i	0.138730	−	0.0800958i
$987$	−2.82925			−0.0900560
$988$	−12.3022	−	2.83760i	−0.391385	−	0.0902759i
$989$	−38.1304			−1.21248
$990$	142.937	−	82.5244i	4.54282	−	2.62280i
$991$	−27.4734	−	47.5852i	−0.872720	−	1.51160i	−0.859172	−	0.511687i	$-0.829021\pi$
$991$	−27.4734	−	47.5852i	−0.872720	−	1.51160i	−0.0135477	−	0.999908i	$-0.504313\pi$
$992$	−1.18529	+	2.05298i	−0.0376330	+	0.0651823i
$993$		−	83.3450i		−	2.64487i
$994$	1.41726	+	0.818256i	0.0449528	+	0.0259535i
$995$	1.46573	+	0.846240i	0.0464668	+	0.0268276i
$996$			16.5798i			0.525352i
$997$	−7.56205	+	13.0979i	−0.239493	+	0.414813i	−0.960569	−	0.278042i	$-0.910314\pi$
$997$	−7.56205	+	13.0979i	−0.239493	+	0.414813i	0.721076	+	0.692856i	$0.243648\pi$
$998$	−17.4526	−	30.2288i	−0.552452	−	0.956875i
$999$	29.5887	−	17.0830i	0.936144	−	0.540483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.26	✓	68
13.2	odd	12		5239.2.a.q.1.28		34
13.4	even	6	inner	403.2.r.a.342.26	yes	68
13.11	odd	12		5239.2.a.r.1.7		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.26	✓	68	1.1	even	1	trivial
403.2.r.a.342.26	yes	68	13.4	even	6	inner
5239.2.a.q.1.28		34	13.2	odd	12
5239.2.a.r.1.7		34	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34884 - 0.778756i) q^{2} +(1.55629 + 2.69558i) q^{3} +(0.212922 - 0.368791i) q^{4} -3.93166i q^{5} +(4.19840 + 2.42395i) q^{6} +(0.334531 + 0.193142i) q^{7} +2.45177i q^{8} +(-3.34410 + 5.79215i) q^{9} +O(q^{10})\)	\(q+(1.34884 - 0.778756i) q^{2} +(1.55629 + 2.69558i) q^{3} +(0.212922 - 0.368791i) q^{4} -3.93166i q^{5} +(4.19840 + 2.42395i) q^{6} +(0.334531 + 0.193142i) q^{7} +2.45177i q^{8} +(-3.34410 + 5.79215i) q^{9} +(-3.06180 - 5.30320i) q^{10} +(3.49001 - 2.01496i) q^{11} +1.32548 q^{12} +(2.63743 + 2.45845i) q^{13} +0.601640 q^{14} +(10.5981 - 6.11882i) q^{15} +(2.33517 + 4.04464i) q^{16} +(-0.762516 + 1.32072i) q^{17} +10.4170i q^{18} +(-7.12111 - 4.11138i) q^{19} +(-1.44996 - 0.837136i) q^{20} +1.20234i q^{21} +(3.13832 - 5.43573i) q^{22} +(-1.71876 - 2.97698i) q^{23} +(-6.60894 + 3.81567i) q^{24} -10.4579 q^{25} +(5.47201 + 1.26216i) q^{26} -11.4798 q^{27} +(0.142458 - 0.0822481i) q^{28} +(-1.05886 - 1.83400i) q^{29} +(9.53013 - 16.5067i) q^{30} +1.00000i q^{31} +(2.05298 + 1.18529i) q^{32} +(10.8630 + 6.27173i) q^{33} +2.37526i q^{34} +(0.759366 - 1.31526i) q^{35} +(1.42406 + 2.46655i) q^{36} +(-2.57744 + 1.48809i) q^{37} -12.8070 q^{38} +(-2.52235 + 10.9355i) q^{39} +9.63951 q^{40} +(0.913972 - 0.527682i) q^{41} +(0.936329 + 1.62177i) q^{42} +(5.54621 - 9.60631i) q^{43} -1.71611i q^{44} +(22.7728 + 13.1479i) q^{45} +(-4.63669 - 2.67699i) q^{46} +2.35312i q^{47} +(-7.26843 + 12.5893i) q^{48} +(-3.42539 - 5.93295i) q^{49} +(-14.1061 + 8.14418i) q^{50} -4.74680 q^{51} +(1.46822 - 0.449201i) q^{52} -1.26233 q^{53} +(-15.4845 + 8.94000i) q^{54} +(-7.92213 - 13.7215i) q^{55} +(-0.473538 + 0.820192i) q^{56} -25.5940i q^{57} +(-2.85647 - 1.64918i) q^{58} +(1.30053 + 0.750861i) q^{59} -5.21132i q^{60} +(-4.96903 + 8.60662i) q^{61} +(0.778756 + 1.34884i) q^{62} +(-2.23741 + 1.29177i) q^{63} -5.64848 q^{64} +(9.66580 - 10.3695i) q^{65} +19.5366 q^{66} +(-4.58026 + 2.64442i) q^{67} +(0.324712 + 0.562418i) q^{68} +(5.34980 - 9.26612i) q^{69} -2.36544i q^{70} +(2.35566 + 1.36004i) q^{71} +(-14.2010 - 8.19896i) q^{72} -8.58823i q^{73} +(-2.31771 + 4.01440i) q^{74} +(-16.2756 - 28.1902i) q^{75} +(-3.03248 + 1.75080i) q^{76} +1.55669 q^{77} +(5.11380 + 16.7145i) q^{78} -4.04223 q^{79} +(15.9021 - 9.18110i) q^{80} +(-7.83372 - 13.5684i) q^{81} +(0.821871 - 1.42352i) q^{82} +12.5086i q^{83} +(0.443412 + 0.256004i) q^{84} +(5.19261 + 2.99795i) q^{85} -17.2766i q^{86} +(3.29579 - 5.70847i) q^{87} +(4.94021 + 8.55669i) q^{88} +(12.4324 - 7.17786i) q^{89} +40.9559 q^{90} +(0.407471 + 1.33182i) q^{91} -1.46385 q^{92} +(-2.69558 + 1.55629i) q^{93} +(1.83251 + 3.17399i) q^{94} +(-16.1645 + 27.9978i) q^{95} +7.37864i q^{96} +(4.75884 + 2.74752i) q^{97} +(-9.24065 - 5.33509i) q^{98} +26.9529i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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