LMFDB - Embedded newform 804.2.c.b.671.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.18
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27950 + 0.602386i) q^{2} +(-1.48757 - 0.887204i) q^{3} +(1.27426 - 1.54151i) q^{4} -3.40681i q^{5} +(2.43779 + 0.239089i) q^{6} +4.07118i q^{7} +(-0.701842 + 2.73997i) q^{8} +(1.42574 + 2.63956i) q^{9} +O(q^{10})$	\(q+(-1.27950 + 0.602386i) q^{2} +(-1.48757 - 0.887204i) q^{3} +(1.27426 - 1.54151i) q^{4} -3.40681i q^{5} +(2.43779 + 0.239089i) q^{6} +4.07118i q^{7} +(-0.701842 + 2.73997i) q^{8} +(1.42574 + 2.63956i) q^{9} +(2.05221 + 4.35902i) q^{10} +0.0181814 q^{11} +(-3.26319 + 1.16258i) q^{12} -1.41338 q^{13} +(-2.45242 - 5.20909i) q^{14} +(-3.02253 + 5.06787i) q^{15} +(-0.752507 - 3.92858i) q^{16} -2.82742i q^{17} +(-3.41427 - 2.51848i) q^{18} -4.54353i q^{19} +(-5.25163 - 4.34117i) q^{20} +(3.61196 - 6.05617i) q^{21} +(-0.0232632 + 0.0109522i) q^{22} -8.65504 q^{23} +(3.47495 - 3.45322i) q^{24} -6.60634 q^{25} +(1.80843 - 0.851403i) q^{26} +(0.220938 - 5.19145i) q^{27} +(6.27576 + 5.18775i) q^{28} +9.67218i q^{29} +(0.814532 - 8.30509i) q^{30} +6.54513i q^{31} +(3.32936 + 4.57333i) q^{32} +(-0.0270462 - 0.0161306i) q^{33} +(1.70320 + 3.61770i) q^{34} +13.8697 q^{35} +(5.88567 + 1.16570i) q^{36} -5.85711 q^{37} +(2.73696 + 5.81347i) q^{38} +(2.10251 + 1.25396i) q^{39} +(9.33454 + 2.39104i) q^{40} -1.44243i q^{41} +(-0.973375 + 9.92469i) q^{42} +7.62307i q^{43} +(0.0231679 - 0.0280268i) q^{44} +(8.99247 - 4.85722i) q^{45} +(11.0742 - 5.21367i) q^{46} +0.189335 q^{47} +(-2.36604 + 6.51167i) q^{48} -9.57448 q^{49} +(8.45284 - 3.97956i) q^{50} +(-2.50850 + 4.20599i) q^{51} +(-1.80102 + 2.17875i) q^{52} +13.6369i q^{53} +(2.84457 + 6.77558i) q^{54} -0.0619406i q^{55} +(-11.1549 - 2.85732i) q^{56} +(-4.03104 + 6.75883i) q^{57} +(-5.82638 - 12.3756i) q^{58} +11.1206 q^{59} +(3.96067 + 11.1171i) q^{60} +2.47299 q^{61} +(-3.94269 - 8.37452i) q^{62} +(-10.7461 + 5.80443i) q^{63} +(-7.01484 - 3.84605i) q^{64} +4.81513i q^{65} +(0.0443225 + 0.00434698i) q^{66} -1.00000i q^{67} +(-4.35850 - 3.60288i) q^{68} +(12.8750 + 7.67878i) q^{69} +(-17.7464 + 8.35492i) q^{70} +4.72490 q^{71} +(-8.23295 + 2.05392i) q^{72} -9.72698 q^{73} +(7.49420 - 3.52824i) q^{74} +(9.82740 + 5.86117i) q^{75} +(-7.00390 - 5.78965i) q^{76} +0.0740198i q^{77} +(-3.44554 - 0.337925i) q^{78} -4.33713i q^{79} +(-13.3839 + 2.56365i) q^{80} +(-4.93454 + 7.52664i) q^{81} +(0.868901 + 1.84560i) q^{82} +10.6111 q^{83} +(-4.73305 - 13.2850i) q^{84} -9.63249 q^{85} +(-4.59203 - 9.75375i) q^{86} +(8.58120 - 14.3881i) q^{87} +(-0.0127605 + 0.0498165i) q^{88} +13.7685i q^{89} +(-8.57998 + 11.6318i) q^{90} -5.75414i q^{91} +(-11.0288 + 13.3418i) q^{92} +(5.80686 - 9.73635i) q^{93} +(-0.242255 + 0.114053i) q^{94} -15.4789 q^{95} +(-0.895176 - 9.75698i) q^{96} +3.81023 q^{97} +(12.2506 - 5.76753i) q^{98} +(0.0259220 + 0.0479909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.27950	+	0.602386i	−0.904746	+	0.425951i
$2$	−1.27950	+	0.602386i	−0.904746	+	0.425951i
$3$	−1.48757	−	0.887204i	−0.858850	−	0.512227i
$3$	−1.48757	−	0.887204i	−0.858850	−	0.512227i
$4$	1.27426	−	1.54151i	0.637132	−	0.770755i
$5$		−	3.40681i		−	1.52357i	−0.647830	−	0.761785i	$-0.724323\pi$
$5$		−	3.40681i		−	1.52357i	0.647830	−	0.761785i	$-0.275677\pi$
$6$	2.43779	+	0.239089i	0.995225	+	0.0976078i
$7$			4.07118i			1.53876i	0.638791	+	0.769380i	$0.279435\pi$
$7$			4.07118i			1.53876i	−0.638791	+	0.769380i	$0.720565\pi$
$8$	−0.701842	+	2.73997i	−0.248138	+	0.968725i
$9$	1.42574	+	2.63956i	0.475246	+	0.879853i
$10$	2.05221	+	4.35902i	0.648966	+	1.37844i
$11$	0.0181814			0.00548190			0.00274095	−	0.999996i	$-0.499128\pi$
$11$	0.0181814			0.00548190			0.00274095	+	0.999996i	$0.499128\pi$
$12$	−3.26319	+	1.16258i	−0.942002	+	0.335607i
$13$	−1.41338			−0.392002			−0.196001	−	0.980604i	$-0.562796\pi$
$13$	−1.41338			−0.392002			−0.196001	+	0.980604i	$0.562796\pi$
$14$	−2.45242	−	5.20909i	−0.655436	−	1.39219i
$15$	−3.02253	+	5.06787i	−0.780415	+	1.30852i
$16$	−0.752507	−	3.92858i	−0.188127	−	0.982145i
$17$		−	2.82742i		−	0.685751i	−0.939381	−	0.342875i	$-0.888599\pi$
$17$		−	2.82742i		−	0.685751i	0.939381	−	0.342875i	$-0.111401\pi$
$18$	−3.41427	−	2.51848i	−0.804751	−	0.593612i
$19$		−	4.54353i		−	1.04236i	−0.853448	−	0.521179i	$-0.825493\pi$
$19$		−	4.54353i		−	1.04236i	0.853448	−	0.521179i	$-0.174507\pi$
$20$	−5.25163	−	4.34117i	−1.17430	−	0.970715i
$21$	3.61196	−	6.05617i	0.788195	−	1.32156i
$22$	−0.0232632	+	0.0109522i	−0.00495973	+	0.00233502i
$23$	−8.65504			−1.80470			−0.902350	−	0.431004i	$-0.858159\pi$
$23$	−8.65504			−1.80470			−0.902350	+	0.431004i	$0.858159\pi$
$24$	3.47495	−	3.45322i	0.709321	−	0.704886i
$25$	−6.60634			−1.32127
$26$	1.80843	−	0.851403i	0.354663	−	0.166974i
$27$	0.220938	−	5.19145i	0.0425195	−	0.999096i
$28$	6.27576	+	5.18775i	1.18601	+	0.980393i
$29$			9.67218i			1.79608i	0.439914	+	0.898040i	$0.355009\pi$
$29$			9.67218i			1.79608i	−0.439914	+	0.898040i	$0.644991\pi$
$30$	0.814532	−	8.30509i	0.148712	−	1.51630i
$31$			6.54513i			1.17554i	0.809028	+	0.587770i	$0.199994\pi$
$31$			6.54513i			1.17554i	−0.809028	+	0.587770i	$0.800006\pi$
$32$	3.32936	+	4.57333i	0.588553	+	0.808459i
$33$	−0.0270462	−	0.0161306i	−0.00470813	−	0.00280798i
$34$	1.70320	+	3.61770i	0.292096	+	0.620431i
$35$	13.8697			2.34441
$36$	5.88567	+	1.16570i	0.980945	+	0.194284i
$37$	−5.85711			−0.962903			−0.481451	−	0.876473i	$-0.659890\pi$
$37$	−5.85711			−0.962903			−0.481451	+	0.876473i	$0.659890\pi$
$38$	2.73696	+	5.81347i	0.443993	+	0.943069i
$39$	2.10251	+	1.25396i	0.336671	+	0.200794i
$40$	9.33454	+	2.39104i	1.47592	+	0.378056i
$41$		−	1.44243i		−	0.225270i	−0.993636	−	0.112635i	$-0.964071\pi$
$41$		−	1.44243i		−	0.225270i	0.993636	−	0.112635i	$-0.0359291\pi$
$42$	−0.973375	+	9.92469i	−0.150195	+	1.53141i
$43$			7.62307i			1.16251i	0.813723	+	0.581253i	$0.197438\pi$
$43$			7.62307i			1.16251i	−0.813723	+	0.581253i	$0.802562\pi$
$44$	0.0231679	−	0.0280268i	0.00349269	−	0.00422521i
$45$	8.99247	−	4.85722i	1.34052	−	0.724071i
$46$	11.0742	−	5.21367i	1.63280	−	0.768714i
$47$	0.189335			0.0276174			0.0138087	−	0.999905i	$-0.495604\pi$
$47$	0.189335			0.0276174			0.0138087	+	0.999905i	$0.495604\pi$
$48$	−2.36604	+	6.51167i	−0.341509	+	0.939879i
$49$	−9.57448			−1.36778
$50$	8.45284	−	3.97956i	1.19541	−	0.562795i
$51$	−2.50850	+	4.20599i	−0.351260	+	0.588957i
$52$	−1.80102	+	2.17875i	−0.249757	+	0.302138i
$53$			13.6369i			1.87318i	0.350432	+	0.936588i	$0.386035\pi$
$53$			13.6369i			1.87318i	−0.350432	+	0.936588i	$0.613965\pi$
$54$	2.84457	+	6.77558i	0.387096	+	0.922039i
$55$		−	0.0619406i		−	0.00835207i
$56$	−11.1549	−	2.85732i	−1.49063	−	0.381826i
$57$	−4.03104	+	6.75883i	−0.533924	+	0.895228i
$58$	−5.82638	−	12.3756i	−0.765042	−	1.62500i
$59$	11.1206			1.44778			0.723889	−	0.689916i	$-0.242353\pi$
$59$	11.1206			1.44778			0.723889	+	0.689916i	$0.242353\pi$
$60$	3.96067	+	11.1171i	0.511321	+	1.43521i
$61$	2.47299			0.316634			0.158317	−	0.987388i	$-0.449393\pi$
$61$	2.47299			0.316634			0.158317	+	0.987388i	$0.449393\pi$
$62$	−3.94269	−	8.37452i	−0.500722	−	1.06357i
$63$	−10.7461	+	5.80443i	−1.35388	+	0.731290i
$64$	−7.01484	−	3.84605i	−0.876855	−	0.480756i
$65$			4.81513i			0.597243i
$66$	0.0443225	+	0.00434698i	0.00545573	+	0.000535077i
$67$		−	1.00000i		−	0.122169i
$67$		−	1.00000i		−	0.122169i
$68$	−4.35850	−	3.60288i	−0.528546	−	0.436913i
$69$	12.8750	+	7.67878i	1.54997	+	0.924417i
$70$	−17.7464	+	8.35492i	−2.12110	+	0.998603i
$71$	4.72490			0.560743			0.280371	−	0.959892i	$-0.409542\pi$
$71$	4.72490			0.560743			0.280371	+	0.959892i	$0.409542\pi$
$72$	−8.23295	+	2.05392i	−0.970262	+	0.242057i
$73$	−9.72698			−1.13846			−0.569228	−	0.822179i	$-0.692758\pi$
$73$	−9.72698			−1.13846			−0.569228	+	0.822179i	$0.692758\pi$
$74$	7.49420	−	3.52824i	0.871182	−	0.410149i
$75$	9.82740	+	5.86117i	1.13477	+	0.676789i
$76$	−7.00390	−	5.78965i	−0.803402	−	0.664119i
$77$			0.0740198i			0.00843533i
$78$	−3.44554	−	0.337925i	−0.390131	−	0.0382625i
$79$		−	4.33713i		−	0.487965i	−0.969780	−	0.243982i	$-0.921546\pi$
$79$		−	4.33713i		−	0.487965i	0.969780	−	0.243982i	$-0.0784539\pi$
$80$	−13.3839	+	2.56365i	−1.49637	+	0.286624i
$81$	−4.93454	+	7.52664i	−0.548282	+	0.836294i
$82$	0.868901	+	1.84560i	0.0959541	+	0.203812i
$83$	10.6111			1.16472			0.582362	−	0.812929i	$-0.302129\pi$
$83$	10.6111			1.16472			0.582362	+	0.812929i	$0.302129\pi$
$84$	−4.73305	−	13.2850i	−0.516418	−	1.44952i
$85$	−9.63249			−1.04479
$86$	−4.59203	−	9.75375i	−0.495171	−	1.05177i
$87$	8.58120	−	14.3881i	0.920001	−	1.54256i
$88$	−0.0127605	+	0.0498165i	−0.00136027	+	0.00531046i
$89$			13.7685i			1.45946i	0.683734	+	0.729731i	$0.260355\pi$
$89$			13.7685i			1.45946i	−0.683734	+	0.729731i	$0.739645\pi$
$90$	−8.57998	+	11.6318i	−0.904410	+	1.22610i
$91$		−	5.75414i		−	0.603198i
$92$	−11.0288	+	13.3418i	−1.14983	+	1.39098i
$93$	5.80686	−	9.73635i	0.602144	−	1.00961i
$94$	−0.242255	+	0.114053i	−0.0249867	+	0.0117637i
$95$	−15.4789			−1.58810
$96$	−0.895176	−	9.75698i	−0.0913635	−	0.995818i
$97$	3.81023			0.386870			0.193435	−	0.981113i	$-0.438037\pi$
$97$	3.81023			0.386870			0.193435	+	0.981113i	$0.438037\pi$
$98$	12.2506	−	5.76753i	1.23750	−	0.582608i
$99$	0.0259220	+	0.0479909i	0.00260525	+	0.00482327i
$100$	−8.41821	+	10.1837i	−0.841821	+	1.01837i
$101$			1.93609i			0.192648i	0.995350	+	0.0963241i	$0.0307085\pi$
$101$			1.93609i			0.192648i	−0.995350	+	0.0963241i	$0.969291\pi$
$102$	0.676007	−	6.89267i	0.0669347	−	0.682476i
$103$			10.0576i			0.991009i	0.868605	+	0.495504i	$0.165017\pi$
$103$			10.0576i			0.991009i	−0.868605	+	0.495504i	$0.834983\pi$
$104$	0.991972	−	3.87263i	0.0972709	−	0.379742i
$105$	−20.6322	−	12.3053i	−2.01350	−	1.20087i
$106$	−8.21469	−	17.4485i	−0.797881	−	1.69475i
$107$	−11.3519			−1.09743			−0.548715	−	0.836010i	$-0.684883\pi$
$107$	−11.3519			−1.09743			−0.548715	+	0.836010i	$0.684883\pi$
$108$	−7.72115	−	6.95586i	−0.742968	−	0.669327i
$109$	10.0851			0.965980			0.482990	−	0.875626i	$-0.339551\pi$
$109$	10.0851			0.965980			0.482990	+	0.875626i	$0.339551\pi$
$110$	0.0373121	+	0.0792533i	0.00355757	+	0.00755650i
$111$	8.71287	+	5.19645i	0.826989	+	0.493225i
$112$	15.9939	−	3.06359i	1.51129	−	0.289482i
$113$		−	9.05540i		−	0.851860i	−0.904756	−	0.425930i	$-0.859947\pi$
$113$		−	9.05540i		−	0.851860i	0.904756	−	0.425930i	$-0.140053\pi$
$114$	1.08631	−	11.0762i	0.101742	−	1.03738i
$115$			29.4860i			2.74959i
$116$	14.9098	+	12.3249i	1.38434	+	1.14434i
$117$	−2.01512	−	3.73071i	−0.186298	−	0.344904i
$118$	−14.2288	+	6.69889i	−1.30987	+	0.616682i
$119$	11.5109			1.05521
$120$	−11.7645	−	11.8385i	−1.07394	−	1.08070i
$121$	−10.9997			−0.999970
$122$	−3.16420	+	1.48969i	−0.286473	+	0.134870i
$123$	−1.27973	+	2.14572i	−0.115390	+	0.193473i
$124$	10.0894	+	8.34022i	0.906053	+	0.748974i
$125$			5.47248i			0.489473i
$126$	10.2532	−	13.9001i	0.913426	−	1.23832i
$127$			2.98850i			0.265186i	0.991171	+	0.132593i	$0.0423304\pi$
$127$			2.98850i			0.265186i	−0.991171	+	0.132593i	$0.957670\pi$
$128$	11.2923	+	0.695395i	0.998109	+	0.0614648i
$129$	6.76321	−	11.3399i	0.595468	−	0.998419i
$130$	−2.90056	−	6.16098i	−0.254396	−	0.540354i
$131$	−19.7930			−1.72932			−0.864662	−	0.502354i	$-0.832467\pi$
$131$	−19.7930			−1.72932			−0.864662	+	0.502354i	$0.832467\pi$
$132$	−0.0593294	+	0.0211373i	−0.00516397	+	0.00183976i
$133$	18.4975			1.60394
$134$	0.602386	+	1.27950i	0.0520382	+	0.110532i
$135$	−17.6863	−	0.752693i	−1.52219	−	0.0647815i
$136$	7.74705	+	1.98440i	0.664304	+	0.170161i
$137$			10.7460i			0.918094i	0.888412	+	0.459047i	$0.151809\pi$
$137$			10.7460i			0.918094i	−0.888412	+	0.459047i	$0.848191\pi$
$138$	−21.0992	−	2.06933i	−1.79608	−	0.176153i
$139$		−	1.90591i		−	0.161657i	−0.996728	−	0.0808286i	$-0.974243\pi$
$139$		−	1.90591i		−	0.161657i	0.996728	−	0.0808286i	$-0.0257567\pi$
$140$	17.6737	−	21.3803i	1.49370	−	1.80697i
$141$	−0.281650	−	0.167979i	−0.0237192	−	0.0141464i
$142$	−6.04553	+	2.84621i	−0.507330	+	0.238849i
$143$	−0.0256973			−0.00214892
$144$	9.29684	−	7.58741i	0.774736	−	0.632285i
$145$	32.9513			2.73645
$146$	12.4457	−	5.85939i	1.03001	−	0.484927i
$147$	14.2427	+	8.49451i	1.17472	+	0.700616i
$148$	−7.46350	+	9.02879i	−0.613496	+	0.742162i
$149$			0.596193i			0.0488421i	0.999702	+	0.0244210i	$0.00777423\pi$
$149$			0.596193i			0.0488421i	−0.999702	+	0.0244210i	$0.992226\pi$
$150$	−16.1049	−	1.57950i	−1.31496	−	0.128966i
$151$			6.13669i			0.499397i	0.968324	+	0.249699i	$0.0803315\pi$
$151$			6.13669i			0.499397i	−0.968324	+	0.249699i	$0.919668\pi$
$152$	12.4491	+	3.18884i	1.00976	+	0.258649i
$153$	7.46315	−	4.03117i	0.603360	−	0.325901i
$154$	−0.0445884	−	0.0947086i	−0.00359304	−	0.00763184i
$155$	22.2980			1.79102
$156$	4.61214	−	1.64317i	0.369267	−	0.131559i
$157$	0.104333			0.00832670			0.00416335	−	0.999991i	$-0.498675\pi$
$157$	0.104333			0.00832670			0.00416335	+	0.999991i	$0.498675\pi$
$158$	2.61262	+	5.54937i	0.207849	+	0.441484i
$159$	12.0987	−	20.2859i	0.959492	−	1.60878i
$160$	15.5805	−	11.3425i	1.23174	−	0.896701i
$161$		−	35.2362i		−	2.77700i
$162$	1.77982	−	12.6029i	0.139836	−	0.990175i
$163$			16.4115i			1.28545i	0.766099	+	0.642723i	$0.222195\pi$
$163$			16.4115i			1.28545i	−0.766099	+	0.642723i	$0.777805\pi$
$164$	−2.22353	−	1.83804i	−0.173628	−	0.143527i
$165$	−0.0549539	+	0.0921411i	−0.00427816	+	0.00717317i
$166$	−13.5770	+	6.39200i	−1.05378	+	0.496115i
$167$	−18.8504			−1.45868			−0.729342	−	0.684149i	$-0.760174\pi$
$167$	−18.8504			−1.45868			−0.729342	+	0.684149i	$0.760174\pi$
$168$	14.0587	+	14.1471i	1.08465	+	1.09147i
$169$	−11.0023			−0.846334
$170$	12.3248	−	5.80247i	0.945270	−	0.445029i
$171$	11.9929	−	6.47789i	0.917121	−	0.495376i
$172$	11.7510	+	9.71379i	0.896008	+	0.740670i
$173$		−	14.6759i		−	1.11579i	−0.829912	−	0.557894i	$-0.811610\pi$
$173$		−	14.6759i		−	1.11579i	0.829912	−	0.557894i	$-0.188390\pi$
$174$	−2.31252	+	23.5788i	−0.175311	+	1.78750i
$175$		−	26.8956i		−	2.03311i
$176$	−0.0136816	−	0.0714271i	−0.00103129	−	0.00538402i
$177$	−16.5427	−	9.86623i	−1.24342	−	0.741592i
$178$	−8.29397	−	17.6169i	−0.621659	−	1.32044i
$179$	−0.933244			−0.0697539			−0.0348770	−	0.999392i	$-0.511104\pi$
$179$	−0.933244			−0.0697539			−0.0348770	+	0.999392i	$0.511104\pi$
$180$	3.97132	−	20.0514i	0.296005	−	1.49454i
$181$	−9.61458			−0.714646			−0.357323	−	0.933981i	$-0.616310\pi$
$181$	−9.61458			−0.714646			−0.357323	+	0.933981i	$0.616310\pi$
$182$	3.46621	+	7.36245i	0.256933	+	0.545741i
$183$	−3.67875	−	2.19404i	−0.271941	−	0.162188i
$184$	6.07446	−	23.7145i	0.447815	−	1.74826i
$185$			19.9540i			1.46705i
$186$	−1.56487	+	15.9557i	−0.114742	+	1.16993i
$187$		−	0.0514066i		−	0.00375922i
$188$	0.241263	−	0.291862i	0.0175959	−	0.0212863i
$189$	21.1353	+	0.899477i	1.53737	+	0.0654273i
$190$	19.8054	−	9.32429i	1.43683	−	0.676455i
$191$	−1.97688			−0.143042			−0.0715211	−	0.997439i	$-0.522785\pi$
$191$	−1.97688			−0.143042			−0.0715211	+	0.997439i	$0.522785\pi$
$192$	7.02285	+	11.9449i	0.506830	+	0.862046i
$193$	6.76831			0.487193			0.243597	−	0.969877i	$-0.421673\pi$
$193$	6.76831			0.487193			0.243597	+	0.969877i	$0.421673\pi$
$194$	−4.87520	+	2.29523i	−0.350019	+	0.164788i
$195$	4.27200	−	7.16285i	0.305924	−	0.512942i
$196$	−12.2004	+	14.7592i	−0.871457	+	1.05423i
$197$		−	5.67128i		−	0.404062i	−0.979379	−	0.202031i	$-0.935246\pi$
$197$		−	5.67128i		−	0.404062i	0.979379	−	0.202031i	$-0.0647542\pi$
$198$	−0.0620763	−	0.0457896i	−0.00441157	−	0.00325412i
$199$			6.40961i			0.454365i	0.973852	+	0.227183i	$0.0729514\pi$
$199$			6.40961i			0.454365i	−0.973852	+	0.227183i	$0.927049\pi$
$200$	4.63660	−	18.1011i	0.327857	−	1.27994i
$201$	−0.887204	+	1.48757i	−0.0625785	+	0.104925i
$202$	−1.16627	−	2.47724i	−0.0820587	−	0.174298i
$203$	−39.3772			−2.76374
$204$	3.28709	+	9.22642i	0.230143	+	0.645979i
$205$	−4.91409			−0.343215
$206$	−6.05858	−	12.8688i	−0.422121	−	0.896611i
$207$	−12.3398	−	22.8455i	−0.857677	−	1.58787i
$208$	1.06358	+	5.55259i	0.0737462	+	0.385003i
$209$		−	0.0826078i		−	0.00571410i
$210$	33.8115	+	3.31610i	2.33321	+	0.228833i
$211$		−	26.7538i		−	1.84181i	−0.389788	−	0.920904i	$-0.627452\pi$
$211$		−	26.7538i		−	1.84181i	0.389788	−	0.920904i	$-0.372548\pi$
$212$	21.0215	+	17.3770i	1.44376	+	1.19346i
$213$	−7.02863	−	4.19195i	−0.481594	−	0.287228i
$214$	14.5248	−	6.83822i	0.992895	−	0.467451i
$215$	25.9703			1.77116
$216$	14.0693	+	4.24894i	0.957298	+	0.289104i
$217$	−26.6464			−1.80887
$218$	−12.9040	+	6.07514i	−0.873967	+	0.411460i
$219$	14.4696	+	8.62981i	0.977764	+	0.583149i
$220$	−0.0954821	−	0.0789286i	−0.00643740	−	0.00532137i
$221$			3.99624i			0.268816i
$222$	−14.2784	−	1.40037i	−0.958305	−	0.0939868i
$223$			18.5206i			1.24023i	0.784510	+	0.620117i	$0.212915\pi$
$223$			18.5206i			1.24023i	−0.784510	+	0.620117i	$0.787085\pi$
$224$	−18.6189	+	13.5544i	−1.24402	+	0.905641i
$225$	−9.41891	−	17.4378i	−0.627927	−	1.16252i
$226$	5.45484	+	11.5864i	0.362851	+	0.770717i
$227$	−15.9032			−1.05554			−0.527768	−	0.849389i	$-0.676971\pi$
$227$	−15.9032			−1.05554			−0.527768	+	0.849389i	$0.676971\pi$
$228$	5.28220	+	14.8264i	0.349822	+	0.981903i
$229$	−5.52938			−0.365392			−0.182696	−	0.983169i	$-0.558482\pi$
$229$	−5.52938			−0.365392			−0.182696	+	0.983169i	$0.558482\pi$
$230$	−17.7620	−	37.7275i	−1.17119	−	2.48768i
$231$	0.0656706	−	0.110110i	0.00432081	−	0.00724469i
$232$	−26.5015	−	6.78834i	−1.73991	−	0.445676i
$233$			17.5986i			1.15292i	0.817125	+	0.576460i	$0.195566\pi$
$233$			17.5986i			1.15292i	−0.817125	+	0.576460i	$0.804434\pi$
$234$	4.82568	+	3.55958i	0.315464	+	0.232697i
$235$		−	0.645029i		−	0.0420771i
$236$	14.1706	−	17.1425i	0.922425	−	1.11588i
$237$	−3.84792	+	6.45179i	−0.249949	+	0.419089i
$238$	−14.7283	+	6.93402i	−0.954694	+	0.449466i
$239$	−9.65934			−0.624811			−0.312405	−	0.949949i	$-0.601135\pi$
$239$	−9.65934			−0.624811			−0.312405	+	0.949949i	$0.601135\pi$
$240$	22.1840	+	8.06065i	1.43197	+	0.520313i
$241$	−7.56300			−0.487175			−0.243588	−	0.969879i	$-0.578324\pi$
$241$	−7.56300			−0.487175			−0.243588	+	0.969879i	$0.578324\pi$
$242$	14.0741	−	6.62604i	0.904719	−	0.425938i
$243$	14.0181	−	6.81848i	0.899264	−	0.437406i
$244$	3.15124	−	3.81213i	0.201737	−	0.244047i
$245$			32.6184i			2.08391i
$246$	0.344871	−	3.51635i	0.0219881	−	0.224195i
$247$			6.42176i			0.408607i
$248$	−17.9334	−	4.59364i	−1.13877	−	0.291697i
$249$	−15.7848	−	9.41425i	−1.00032	−	0.596604i
$250$	−3.29654	−	7.00206i	−0.208492	−	0.442849i
$251$	−1.10166			−0.0695363			−0.0347681	−	0.999395i	$-0.511069\pi$
$251$	−1.10166			−0.0695363			−0.0347681	+	0.999395i	$0.511069\pi$
$252$	−4.74577	+	23.9616i	−0.298956	+	1.50944i
$253$	−0.157361			−0.00989319
$254$	−1.80023	−	3.82380i	−0.112956	−	0.239926i
$255$	14.3290	+	8.54598i	0.897318	+	0.535170i
$256$	−14.8675	+	5.91257i	−0.929217	+	0.369536i
$257$		−	13.2014i		−	0.823480i	−0.911301	−	0.411740i	$-0.864921\pi$
$257$		−	13.2014i		−	0.823480i	0.911301	−	0.411740i	$-0.135079\pi$
$258$	−1.82259	+	18.5835i	−0.113470	+	1.15696i
$259$		−	23.8453i		−	1.48168i
$260$	7.42257	+	6.13574i	0.460328	+	0.380523i
$261$	−25.5303	+	13.7900i	−1.58029	+	0.853580i
$262$	25.3253	−	11.9230i	1.56460	−	0.736607i
$263$	2.17844			0.134328			0.0671642	−	0.997742i	$-0.478605\pi$
$263$	2.17844			0.134328			0.0671642	+	0.997742i	$0.478605\pi$
$264$	0.0631795	−	0.0627844i	0.00388843	−	0.00386412i
$265$	46.4584			2.85392
$266$	−23.6676	+	11.1426i	−1.45116	+	0.683199i
$267$	12.2155	−	20.4817i	0.747576	−	1.25346i
$268$	−1.54151	−	1.27426i	−0.0941627	−	0.0778380i
$269$		−	4.89929i		−	0.298715i	−0.988783	−	0.149358i	$-0.952279\pi$
$269$		−	4.89929i		−	0.298715i	0.988783	−	0.149358i	$-0.0477206\pi$
$270$	23.0831	−	9.69089i	1.40479	−	0.589769i
$271$		−	8.79177i		−	0.534062i	−0.963688	−	0.267031i	$-0.913957\pi$
$271$		−	8.79177i		−	0.534062i	0.963688	−	0.267031i	$-0.0860426\pi$
$272$	−11.1078	+	2.12766i	−0.673507	+	0.129008i
$273$	−5.10509	+	8.55969i	−0.308974	+	0.518056i
$274$	−6.47325	−	13.7496i	−0.391063	−	0.830642i
$275$	−0.120113			−0.00724306
$276$	28.2430	−	10.0621i	1.70003	−	0.605669i
$277$	12.7809			0.767930			0.383965	−	0.923348i	$-0.374558\pi$
$277$	12.7809			0.767930			0.383965	+	0.923348i	$0.374558\pi$
$278$	1.14809	+	2.43862i	0.0688581	+	0.146259i
$279$	−17.2763	+	9.33165i	−1.03430	+	0.558671i
$280$	−9.73434	+	38.0026i	−0.581738	+	2.27109i
$281$			10.1526i			0.605651i	0.953046	+	0.302826i	$0.0979299\pi$
$281$			10.1526i			0.605651i	−0.953046	+	0.302826i	$0.902070\pi$
$282$	0.461561	+	0.0452681i	0.0274855	+	0.00269568i
$283$		−	0.978626i		−	0.0581733i	−0.999577	−	0.0290866i	$-0.990740\pi$
$283$		−	0.978626i		−	0.0581733i	0.999577	−	0.0290866i	$-0.00925987\pi$
$284$	6.02077	−	7.28349i	0.357267	−	0.432195i
$285$	23.0260	+	13.7330i	1.36394	+	0.813471i
$286$	0.0328799	−	0.0154797i	0.00194423	−	0.000915334i
$287$	5.87240			0.346637
$288$	−7.32479	+	15.3084i	−0.431618	+	0.902057i
$289$	9.00568			0.529746
$290$	−42.1613	+	19.8494i	−2.47580	+	1.16560i
$291$	−5.66799	−	3.38045i	−0.332263	−	0.198165i
$292$	−12.3947	+	14.9942i	−0.725347	+	0.877471i
$293$		−	20.6788i		−	1.20807i	−0.796959	−	0.604034i	$-0.793559\pi$
$293$		−	20.6788i		−	1.20807i	0.796959	−	0.604034i	$-0.206441\pi$
$294$	−23.3406	−	2.28916i	−1.36125	−	0.133506i
$295$		−	37.8857i		−	2.20579i
$296$	4.11076	−	16.0483i	0.238933	−	0.932787i
$297$	0.00401696	−	0.0943880i	0.000233088	−	0.00547695i
$298$	−0.359138	−	0.762832i	−0.0208043	−	0.0441897i
$299$	12.2329			0.707447
$300$	21.5577	−	7.68037i	1.24464	−	0.443426i
$301$	−31.0349			−1.78882
$302$	−3.69666	−	7.85193i	−0.212719	−	0.451828i
$303$	1.71771	−	2.88007i	0.0986797	−	0.165456i
$304$	−17.8496	+	3.41904i	−1.02375	+	0.196095i
$305$		−	8.42499i		−	0.482414i
$306$	−7.12081	+	9.65359i	−0.407070	+	0.551859i
$307$		−	3.57872i		−	0.204248i	−0.994772	−	0.102124i	$-0.967436\pi$
$307$		−	3.57872i		−	0.204248i	0.994772	−	0.102124i	$-0.0325639\pi$
$308$	0.114102	+	0.0943206i	0.00650158	+	0.00537442i
$309$	8.92318	−	14.9615i	0.507622	−	0.851128i
$310$	−28.5304	+	13.4320i	−1.62042	+	0.762886i
$311$	9.55945			0.542066			0.271033	−	0.962570i	$-0.412635\pi$
$311$	9.55945			0.542066			0.271033	+	0.962570i	$0.412635\pi$
$312$	−4.91144	+	4.88073i	−0.278055	+	0.276317i
$313$	−10.9429			−0.618529			−0.309264	−	0.950976i	$-0.600083\pi$
$313$	−10.9429			−0.618529			−0.309264	+	0.950976i	$0.600083\pi$
$314$	−0.133495	+	0.0628488i	−0.00753355	+	0.00354676i
$315$	19.7746	+	36.6099i	1.11417	+	2.06274i
$316$	−6.68573	−	5.52664i	−0.376102	−	0.310898i
$317$		−	23.1283i		−	1.29901i	−0.760356	−	0.649506i	$-0.774976\pi$
$317$		−	23.1283i		−	1.29901i	0.760356	−	0.649506i	$-0.225024\pi$
$318$	−3.26044	+	33.2440i	−0.182837	+	1.86423i
$319$			0.175854i			0.00984594i
$320$	−13.1027	+	23.8982i	−0.732465	+	1.33595i
$321$	16.8868	+	10.0714i	0.942527	+	0.562133i
$322$	21.2258	+	45.0848i	1.18287	+	2.51248i
$323$	−12.8465			−0.714797
$324$	5.31450	+	17.1976i	0.295250	+	0.955420i
$325$	9.33729			0.517940
$326$	−9.88603	−	20.9985i	−0.547537	−	1.16300i
$327$	−15.0024	−	8.94756i	−0.829632	−	0.494801i
$328$	3.95222	+	1.01236i	0.218225	+	0.0558982i
$329$			0.770818i			0.0424966i
$330$	0.0148093	−	0.150998i	0.000815227	−	0.00831219i
$331$		−	21.2638i		−	1.16876i	−0.811479	−	0.584381i	$-0.801337\pi$
$331$		−	21.2638i		−	1.16876i	0.811479	−	0.584381i	$-0.198663\pi$
$332$	13.5214	−	16.3572i	0.742083	−	0.897717i
$333$	−8.35071	−	15.4602i	−0.457616	−	0.847213i
$334$	24.1191	−	11.3552i	1.31974	−	0.621328i
$335$	−3.40681			−0.186134
$336$	−26.5102	−	9.63257i	−1.44625	−	0.525500i
$337$	19.4857			1.06145			0.530726	−	0.847543i	$-0.321919\pi$
$337$	19.4857			1.06145			0.530726	+	0.847543i	$0.321919\pi$
$338$	14.0775	−	6.62765i	0.765718	−	0.360497i
$339$	−8.03398	+	13.4705i	−0.436346	+	0.731620i
$340$	−12.2743	+	14.8486i	−0.665669	+	0.805277i
$341$			0.119000i			0.00644420i
$342$	−11.4428	+	15.5128i	−0.618756	+	0.838839i
$343$		−	10.4811i		−	0.565929i
$344$	−20.8870	−	5.35019i	−1.12615	−	0.288463i
$345$	26.1601	−	43.8626i	1.40841	−	2.36148i
$346$	8.84055	+	18.7779i	0.475271	+	1.00950i
$347$	21.1791			1.13695			0.568476	−	0.822700i	$-0.307533\pi$
$347$	21.1791			1.13695			0.568476	+	0.822700i	$0.307533\pi$
$348$	−11.2446	−	31.5622i	−0.602776	−	1.69191i
$349$	6.71345			0.359363			0.179681	−	0.983725i	$-0.442493\pi$
$349$	6.71345			0.359363			0.179681	+	0.983725i	$0.442493\pi$
$350$	16.2015	+	34.4130i	0.866007	+	1.83945i
$351$	−0.312270	+	7.33752i	−0.0166677	+	0.391648i
$352$	0.0605324	+	0.0831497i	0.00322639	+	0.00443189i
$353$			15.8425i			0.843212i	0.906779	+	0.421606i	$0.138533\pi$
$353$			15.8425i			0.843212i	−0.906779	+	0.421606i	$0.861467\pi$
$354$	27.1097	+	2.65882i	1.44086	+	0.141314i
$355$		−	16.0968i		−	0.854331i
$356$	21.2243	+	17.5447i	1.12489	+	0.929869i
$357$	−17.1233	−	10.2125i	−0.906264	−	0.540505i
$358$	1.19409	−	0.562173i	0.0631096	−	0.0297118i
$359$	−7.16273			−0.378034			−0.189017	−	0.981974i	$-0.560530\pi$
$359$	−7.16273			−0.378034			−0.189017	+	0.981974i	$0.560530\pi$
$360$	6.99733	+	28.0481i	0.368791	+	1.47826i
$361$	−1.64367			−0.0865088
$362$	12.3019	−	5.79168i	0.646573	−	0.304404i
$363$	16.3628	+	9.75895i	0.858824	+	0.512212i
$364$	−8.87006	−	7.33229i	−0.464918	−	0.384316i
$365$			33.1379i			1.73452i
$366$	6.02863	+	0.591265i	0.315122	+	0.0309059i
$367$			27.6682i			1.44427i	0.691753	+	0.722134i	$0.256839\pi$
$367$			27.6682i			1.44427i	−0.691753	+	0.722134i	$0.743161\pi$
$368$	6.51298	+	34.0020i	0.339512	+	1.77248i
$369$	3.80739	−	2.05653i	0.198205	−	0.107059i
$370$	−12.0200	−	25.5313i	−0.624891	−	1.32731i
$371$	−55.5183			−2.88237
$372$	−7.60921	−	21.3580i	−0.394519	−	1.10736i
$373$	26.6731			1.38108			0.690540	−	0.723295i	$-0.257373\pi$
$373$	26.6731			1.38108			0.690540	+	0.723295i	$0.257373\pi$
$374$	0.0309666	+	0.0657749i	0.00160124	+	0.00340114i
$375$	4.85520	−	8.14070i	0.250722	−	0.420384i
$376$	−0.132883	+	0.518773i	−0.00685294	+	0.0267537i
$377$		−	13.6705i		−	0.704067i
$378$	−27.5846	+	11.5807i	−1.41880	+	0.595648i
$379$			27.6728i			1.42146i	0.703466	+	0.710729i	$0.251635\pi$
$379$			27.6728i			1.42146i	−0.703466	+	0.710729i	$0.748365\pi$
$380$	−19.7242	+	23.8609i	−1.01183	+	1.22404i
$381$	2.65141	−	4.44561i	0.135836	−	0.227755i
$382$	2.52943	−	1.19085i	0.129417	−	0.0609289i
$383$	12.2190			0.624364			0.312182	−	0.950022i	$-0.398940\pi$
$383$	12.2190			0.624364			0.312182	+	0.950022i	$0.398940\pi$
$384$	−16.1812	−	11.0530i	−0.825742	−	0.564048i
$385$	0.252171			0.0128518
$386$	−8.66008	+	4.07713i	−0.440786	+	0.207520i
$387$	−20.1215	+	10.8685i	−1.02283	+	0.552477i
$388$	4.85523	−	5.87350i	0.246487	−	0.298182i
$389$			15.3668i			0.779129i	0.920999	+	0.389565i	$0.127374\pi$
$389$			15.3668i			0.779129i	−0.920999	+	0.389565i	$0.872626\pi$
$390$	−1.15125	+	11.7383i	−0.0582956	+	0.594391i
$391$			24.4714i			1.23757i
$392$	6.71977	−	26.2337i	0.339399	−	1.32500i
$393$	29.4435	+	17.5604i	1.48523	+	0.885807i
$394$	3.41630	+	7.25643i	0.172111	+	0.365574i
$395$	−14.7758			−0.743449
$396$	0.107010	+	0.0211941i	0.00537745	+	0.00106504i
$397$	−27.5307			−1.38173			−0.690863	−	0.722986i	$-0.742769\pi$
$397$	−27.5307			−1.38173			−0.690863	+	0.722986i	$0.742769\pi$
$398$	−3.86106	−	8.20113i	−0.193537	−	0.411085i
$399$	−27.5164	−	16.4111i	−1.37754	−	0.821581i
$400$	4.97132	+	25.9535i	0.248566	+	1.29768i
$401$			8.72712i			0.435811i	0.975970	+	0.217906i	$0.0699225\pi$
$401$			8.72712i			0.435811i	−0.975970	+	0.217906i	$0.930077\pi$
$402$	0.239089	−	2.43779i	0.0119247	−	0.121586i
$403$		−	9.25079i		−	0.460815i
$404$	2.98450	+	2.46709i	0.148485	+	0.122742i
$405$	25.6418	+	16.8110i	1.27415	+	0.835346i
$406$	50.3833	−	23.7202i	2.50048	−	1.17722i
$407$	−0.106491			−0.00527854
$408$	−9.76372	−	9.82515i	−0.483376	−	0.486417i
$409$	−30.1236			−1.48952			−0.744758	−	0.667335i	$-0.767435\pi$
$409$	−30.1236			−1.48952			−0.744758	+	0.667335i	$0.767435\pi$
$410$	6.28760	−	2.96018i	0.310523	−	0.146193i
$411$	9.53391	−	15.9855i	0.470273	−	0.788505i
$412$	15.5040	+	12.8161i	0.763825	+	0.631403i
$413$			45.2739i			2.22778i
$414$	29.5506	+	21.7976i	1.45233	+	1.07129i
$415$		−	36.1501i		−	1.77454i
$416$	−4.70566	−	6.46388i	−0.230714	−	0.316918i
$417$	−1.69093	+	2.83518i	−0.0828053	+	0.138839i
$418$	0.0497618	+	0.105697i	0.00243393	+	0.00516981i
$419$	−6.30793			−0.308163			−0.154081	−	0.988058i	$-0.549242\pi$
$419$	−6.30793			−0.308163			−0.154081	+	0.988058i	$0.549242\pi$
$420$	−45.2595	+	16.1246i	−2.20844	+	0.786800i
$421$	−19.6623			−0.958280			−0.479140	−	0.877739i	$-0.659051\pi$
$421$	−19.6623			−0.958280			−0.479140	+	0.877739i	$0.659051\pi$
$422$	16.1161	+	34.2316i	0.784520	+	1.66637i
$423$	0.269943	+	0.499762i	0.0131251	+	0.0242993i
$424$	−37.3647	−	9.57096i	−1.81459	−	0.464807i
$425$			18.6789i			0.906060i
$426$	11.5183	+	1.12967i	0.558065	+	0.0547329i
$427$			10.0680i			0.487223i
$428$	−14.4653	+	17.4991i	−0.699207	+	0.845849i
$429$	0.0382266	+	0.0227988i	0.00184560	+	0.00110074i
$430$	−33.2291	+	15.6441i	−1.60245	+	0.754428i
$431$	2.96785			0.142956			0.0714782	−	0.997442i	$-0.477228\pi$
$431$	2.96785			0.142956			0.0714782	+	0.997442i	$0.477228\pi$
$432$	−20.5613	+	3.03863i	−0.989256	+	0.146196i
$433$	−18.3023			−0.879551			−0.439776	−	0.898108i	$-0.644942\pi$
$433$	−18.3023			−0.879551			−0.439776	+	0.898108i	$0.644942\pi$
$434$	34.0942	−	16.0514i	1.63657	−	0.770492i
$435$	−49.0174	−	29.2345i	−2.35020	−	1.40169i
$436$	12.8511	−	15.5463i	0.615456	−	0.744534i
$437$			39.3244i			1.88114i
$438$	−23.7124	−	2.32562i	−1.13302	−	0.111122i
$439$			1.90946i			0.0911336i	0.998961	+	0.0455668i	$0.0145094\pi$
$439$			1.90946i			0.0911336i	−0.998961	+	0.0455668i	$0.985491\pi$
$440$	0.169715	+	0.0434725i	0.00809085	+	0.00207247i
$441$	−13.6507	−	25.2724i	−0.650033	−	1.20345i
$442$	−2.40728	−	5.11320i	−0.114502	−	0.243210i
$443$	0.762163			0.0362115			0.0181057	−	0.999836i	$-0.494236\pi$
$443$	0.762163			0.0362115			0.0181057	+	0.999836i	$0.494236\pi$
$444$	19.1129	−	6.80933i	0.907056	−	0.323157i
$445$	46.9067			2.22359
$446$	−11.1566	−	23.6972i	−0.528279	−	1.12210i
$447$	0.528945	−	0.886880i	0.0250182	−	0.0419480i
$448$	15.6579	−	28.5586i	0.739768	−	1.34927i
$449$		−	30.9058i		−	1.45854i	−0.684228	−	0.729268i	$-0.739861\pi$
$449$		−	30.9058i		−	1.45854i	0.684228	−	0.729268i	$-0.260139\pi$
$450$	22.5558	+	16.6379i	1.06329	+	0.784320i
$451$		−	0.0262255i		−	0.00123491i
$452$	−13.9590	−	11.5390i	−0.656575	−	0.542747i
$453$	5.44450	−	9.12877i	0.255805	−	0.428907i
$454$	20.3483	−	9.57988i	0.954991	−	0.449606i
$455$	−19.6032			−0.919014
$456$	−15.6898	−	15.7885i	−0.734743	−	0.739366i
$457$	−8.33955			−0.390108			−0.195054	−	0.980793i	$-0.562488\pi$
$457$	−8.33955			−0.390108			−0.195054	+	0.980793i	$0.562488\pi$
$458$	7.07487	−	3.33082i	0.330587	−	0.155639i
$459$	−14.6784	−	0.624685i	−0.685131	−	0.0291578i
$460$	45.4530	+	37.5730i	2.11926	+	1.75185i
$461$		−	27.8020i		−	1.29487i	−0.762121	−	0.647434i	$-0.775842\pi$
$461$		−	27.8020i		−	1.29487i	0.762121	−	0.647434i	$-0.224158\pi$
$462$	−0.0176973	+	0.180445i	−0.000823355	+	0.00839506i
$463$		−	27.2797i		−	1.26779i	−0.773417	−	0.633897i	$-0.781454\pi$
$463$		−	27.2797i		−	1.26779i	0.773417	−	0.633897i	$-0.218546\pi$
$464$	37.9979	−	7.27839i	1.76401	−	0.337891i
$465$	−33.1699	−	19.7829i	−1.53822	−	0.917409i
$466$	−10.6011	−	22.5174i	−0.491087	−	1.04310i
$467$	−3.41179			−0.157879			−0.0789394	−	0.996879i	$-0.525153\pi$
$467$	−3.41179			−0.157879			−0.0789394	+	0.996879i	$0.525153\pi$
$468$	−8.31872	−	1.64758i	−0.384533	−	0.0761596i
$469$	4.07118			0.187989
$470$	0.388556	+	0.825318i	0.0179228	+	0.0380691i
$471$	−0.155203	−	0.0925648i	−0.00715138	−	0.00426516i
$472$	−7.80490	+	30.4701i	−0.359249	+	1.40250i
$473$			0.138598i			0.00637275i
$474$	1.03696	−	10.5730i	0.0476292	−	0.485635i
$475$			30.0161i			1.37723i
$476$	14.6680	−	17.7442i	0.672305	−	0.813305i
$477$	−35.9955	+	19.4427i	−1.64812	+	0.890220i
$478$	12.3592	−	5.81865i	0.565295	−	0.266139i
$479$	−29.9047			−1.36638			−0.683190	−	0.730241i	$-0.739408\pi$
$479$	−29.9047			−1.36638			−0.683190	+	0.730241i	$0.739408\pi$
$480$	−33.2402	+	3.04969i	−1.51720	+	0.139199i
$481$	8.27835			0.377460
$482$	9.67689	−	4.55584i	0.440770	−	0.207513i
$483$	−31.2617	+	52.4163i	−1.42246	+	2.38503i
$484$	−14.0165	+	16.9561i	−0.637112	+	0.770732i
$485$		−	12.9807i		−	0.589424i
$486$	−13.8289	+	17.1686i	−0.627293	+	0.778784i
$487$			26.3630i			1.19462i	0.802010	+	0.597311i	$0.203764\pi$
$487$			26.3630i			1.19462i	−0.802010	+	0.597311i	$0.796236\pi$
$488$	−1.73565	+	6.77590i	−0.0785690	+	0.306731i
$489$	14.5603	−	24.4132i	0.658440	−	1.10400i
$490$	−19.6489	−	41.7354i	−0.887645	−	1.88541i
$491$	−11.9512			−0.539348			−0.269674	−	0.962952i	$-0.586916\pi$
$491$	−11.9512			−0.539348			−0.269674	+	0.962952i	$0.586916\pi$
$492$	1.67694	+	4.70694i	0.0756022	+	0.212205i
$493$	27.3474			1.23166
$494$	−3.86837	−	8.21667i	−0.174046	−	0.369685i
$495$	0.163496	−	0.0883111i	0.00734859	−	0.00396929i
$496$	25.7131	−	4.92526i	1.15455	−	0.221151i
$497$			19.2359i			0.862849i
$498$	25.8678	+	2.53701i	1.15916	+	0.113686i
$499$		−	24.3489i		−	1.09000i	−0.838435	−	0.545002i	$-0.816529\pi$
$499$		−	24.3489i		−	1.09000i	0.838435	−	0.545002i	$-0.183471\pi$
$500$	8.43588	+	6.97338i	0.377264	+	0.311859i
$501$	28.0413	+	16.7241i	1.25279	+	0.747178i
$502$	1.40958	−	0.663625i	0.0629127	−	0.0296190i
$503$	15.0087			0.669205			0.334603	−	0.942359i	$-0.391398\pi$
$503$	15.0087			0.669205			0.334603	+	0.942359i	$0.391398\pi$
$504$	−8.36189	−	33.5178i	−0.372468	−	1.49300i
$505$	6.59589			0.293513
$506$	0.201344	−	0.0947919i	0.00895083	−	0.00421401i
$507$	16.3668	+	9.76132i	0.726874	+	0.433516i
$508$	4.60680	+	3.80813i	0.204394	+	0.168959i
$509$			16.2190i			0.718893i	0.933166	+	0.359446i	$0.117034\pi$
$509$			16.2190i			0.718893i	−0.933166	+	0.359446i	$0.882966\pi$
$510$	−23.4820	−	2.30303i	−1.03980	−	0.101980i
$511$		−	39.6003i		−	1.75181i
$512$	15.4613	−	16.5211i	0.683301	−	0.730137i
$513$	−23.5875	−	1.00384i	−1.04141	−	0.0443205i
$514$	7.95233	+	16.8912i	0.350762	+	0.745041i
$515$	34.2644			1.50987
$516$	−8.86239	−	24.8755i	−0.390145	−	1.09508i
$517$	0.00344239			0.000151396
$518$	14.3641	+	30.5102i	0.631121	+	1.34054i
$519$	−13.0205	+	21.8315i	−0.571537	+	0.958294i
$520$	−13.1933	−	3.37946i	−0.578564	−	0.148199i
$521$		−	33.7767i		−	1.47978i	−0.672726	−	0.739892i	$-0.734877\pi$
$521$		−	33.7767i		−	1.47978i	0.672726	−	0.739892i	$-0.265123\pi$
$522$	24.3592	−	33.0235i	1.06617	−	1.44540i
$523$		−	39.1189i		−	1.71055i	−0.518173	−	0.855276i	$-0.673388\pi$
$523$		−	39.1189i		−	1.71055i	0.518173	−	0.855276i	$-0.326612\pi$
$524$	−25.2215	+	30.5111i	−1.10181	+	1.33289i
$525$	−23.8618	+	40.0091i	−1.04142	+	1.74614i
$526$	−2.78733	+	1.31226i	−0.121533	+	0.0572173i
$527$	18.5059			0.806128
$528$	−0.0430180	+	0.118391i	−0.00187212	+	0.00515232i
$529$	51.9096			2.25694
$530$	−59.4437	+	27.9859i	−2.58207	+	1.21563i
$531$	15.8551	+	29.3535i	0.688051	+	1.27383i
$532$	23.5707	−	28.5141i	1.02192	−	1.23624i
$533$			2.03871i			0.0883065i
$534$	−3.29191	+	33.5648i	−0.142455	+	1.45249i
$535$			38.6737i			1.67201i
$536$	2.73997	+	0.701842i	0.118349	+	0.0303149i
$537$	1.38827	+	0.827978i	0.0599082	+	0.0357299i
$538$	2.95126	+	6.26867i	0.127238	+	0.270261i
$539$	−0.174078			−0.00749805
$540$	−23.6973	+	26.3045i	−1.01977	+	1.13196i
$541$	−24.9934			−1.07455			−0.537276	−	0.843407i	$-0.680547\pi$
$541$	−24.9934			−1.07455			−0.537276	+	0.843407i	$0.680547\pi$
$542$	5.29604	+	11.2491i	0.227484	+	0.483191i
$543$	14.3024	+	8.53009i	0.613774	+	0.366061i
$544$	12.9308	−	9.41350i	0.554401	−	0.403600i
$545$		−	34.3581i		−	1.47174i
$546$	1.37575	−	14.0274i	0.0588768	−	0.600317i
$547$		−	2.92293i		−	0.124975i	−0.998046	−	0.0624877i	$-0.980097\pi$
$547$		−	2.92293i		−	0.124975i	0.998046	−	0.0624877i	$-0.0199034\pi$
$548$	16.5651	+	13.6933i	0.707626	+	0.584947i
$549$	3.52583	+	6.52759i	0.150479	+	0.278591i
$550$	0.153685	−	0.0723541i	0.00655313	−	0.00308519i
$551$	43.9459			1.87216
$552$	−30.0758	+	29.8877i	−1.28011	+	1.27211i
$553$	17.6572			0.750861
$554$	−16.3532	+	7.69903i	−0.694782	+	0.327100i
$555$	17.7033	−	29.6831i	0.751463	−	1.25998i
$556$	−2.93798	−	2.42863i	−0.124598	−	0.102997i
$557$		−	20.8125i		−	0.881852i	−0.897543	−	0.440926i	$-0.854650\pi$
$557$		−	20.8125i		−	0.881852i	0.897543	−	0.440926i	$-0.145350\pi$
$558$	16.4838	−	22.3468i	0.697815	−	0.946018i
$559$		−	10.7743i		−	0.455705i
$560$	−10.4371	−	54.4883i	−0.441046	−	2.30255i
$561$	−0.0456081	+	0.0764709i	−0.00192558	+	0.00322861i
$562$	−6.11576	−	12.9902i	−0.257978	−	0.547961i
$563$	−18.7695			−0.791040			−0.395520	−	0.918457i	$-0.629436\pi$
$563$	−18.7695			−0.791040			−0.395520	+	0.918457i	$0.629436\pi$
$564$	−0.617838	+	0.220117i	−0.0260157	+	0.00926859i
$565$	−30.8500			−1.29787
$566$	0.589510	+	1.25216i	0.0247790	+	0.0526320i
$567$	−30.6423	−	20.0894i	−1.28686	−	0.843674i
$568$	−3.31613	+	12.9461i	−0.139142	+	0.543205i
$569$		−	8.28124i		−	0.347167i	−0.984819	−	0.173584i	$-0.944465\pi$
$569$		−	8.28124i		−	0.347167i	0.984819	−	0.173584i	$-0.0555347\pi$
$570$	−37.7344	−	3.70085i	−1.58052	−	0.155011i
$571$			31.2373i			1.30724i	0.756822	+	0.653621i	$0.226751\pi$
$571$			31.2373i			1.30724i	−0.756822	+	0.653621i	$0.773249\pi$
$572$	−0.0327452	+	0.0396127i	−0.00136914	+	0.00165629i
$573$	2.94075	+	1.75390i	0.122852	+	0.0732701i
$574$	−7.51376	+	3.53745i	−0.313618	+	0.147650i
$575$	57.1781			2.38449
$576$	0.150537	−	23.9995i	0.00627239	−	0.999980i
$577$	6.88535			0.286641			0.143320	−	0.989676i	$-0.454222\pi$
$577$	6.88535			0.286641			0.143320	+	0.989676i	$0.454222\pi$
$578$	−11.5228	+	5.42489i	−0.479285	+	0.225646i
$579$	−10.0683	−	6.00487i	−0.418426	−	0.249554i
$580$	41.9886	−	50.7947i	1.74348	−	2.10914i
$581$			43.1998i			1.79223i
$582$	9.28855	+	0.910985i	0.385023	+	0.0377615i
$583$			0.247939i			0.0102686i
$584$	6.82680	−	26.6516i	0.282495	−	1.10285i
$585$	−12.7098	+	6.86512i	−0.525486	+	0.283838i
$586$	12.4566	+	26.4586i	0.514578	+	1.09299i
$587$	−14.9053			−0.615206			−0.307603	−	0.951515i	$-0.599527\pi$
$587$	−14.9053			−0.615206			−0.307603	+	0.951515i	$0.599527\pi$
$588$	31.2433	−	11.1311i	1.28845	−	0.459037i
$589$	29.7380			1.22533
$590$	22.8218	+	48.4749i	0.939559	+	1.99568i
$591$	−5.03158	+	8.43644i	−0.206972	+	0.347029i
$592$	4.40752	+	23.0101i	0.181148	+	0.945710i
$593$			4.72889i			0.194192i	0.995275	+	0.0970961i	$0.0309554\pi$
$593$			4.72889i			0.194192i	−0.995275	+	0.0970961i	$0.969045\pi$
$594$	0.0517182	+	0.123190i	0.00212203	+	0.00505453i
$595$		−	39.2155i		−	1.60768i
$596$	0.919038	+	0.759707i	0.0376453	+	0.0311188i
$597$	5.68663	−	9.53476i	0.232738	−	0.390232i
$598$	−15.6520	+	7.36892i	−0.640060	+	0.301338i
$599$	−2.24315			−0.0916528			−0.0458264	−	0.998949i	$-0.514592\pi$
$599$	−2.24315			−0.0916528			−0.0458264	+	0.998949i	$0.514592\pi$
$600$	−22.9567	+	22.8131i	−0.937203	+	0.931342i
$601$	14.2763			0.582343			0.291171	−	0.956671i	$-0.405955\pi$
$601$	14.2763			0.582343			0.291171	+	0.956671i	$0.405955\pi$
$602$	39.7092	−	18.6949i	1.61843	−	0.761949i
$603$	2.63956	−	1.42574i	0.107491	−	0.0580606i
$604$	9.45978	+	7.81976i	0.384913	+	0.318182i
$605$			37.4738i			1.52352i
$606$	−0.462899	+	4.71979i	−0.0188040	+	0.191728i
$607$		−	3.24114i		−	0.131554i	−0.997834	−	0.0657768i	$-0.979047\pi$
$607$		−	3.24114i		−	0.131554i	0.997834	−	0.0657768i	$-0.0209525\pi$
$608$	20.7791	−	15.1270i	0.842703	−	0.613482i
$609$	58.5764	+	34.9356i	2.37363	+	1.41566i
$610$	5.07509	+	10.7798i	0.205485	+	0.436462i
$611$	−0.267604			−0.0108261
$612$	3.29593	−	16.6413i	0.133230	−	0.672684i
$613$	−7.83484			−0.316446			−0.158223	−	0.987403i	$-0.550576\pi$
$613$	−7.83484			−0.316446			−0.158223	+	0.987403i	$0.550576\pi$
$614$	2.15577	+	4.57899i	0.0869997	+	0.184793i
$615$	7.31006	+	4.35980i	0.294770	+	0.175804i
$616$	−0.202812	−	0.0519501i	−0.00817152	−	0.00209313i
$617$		−	29.7670i		−	1.19837i	−0.800609	−	0.599187i	$-0.795490\pi$
$617$		−	29.7670i		−	1.19837i	0.800609	−	0.599187i	$-0.204510\pi$
$618$	−2.40468	+	24.5184i	−0.0967302	+	0.986277i
$619$			21.9159i			0.880875i	0.897783	+	0.440437i	$0.145177\pi$
$619$			21.9159i			0.880875i	−0.897783	+	0.440437i	$0.854823\pi$
$620$	28.4135	−	34.3726i	1.14111	−	1.38044i
$621$	−1.91222	+	44.9322i	−0.0767349	+	1.80307i
$622$	−12.2314	+	5.75847i	−0.490433	+	0.230894i
$623$	−56.0541			−2.24576
$624$	3.34413	−	9.20349i	0.133872	−	0.368435i
$625$	−14.3880			−0.575520
$626$	14.0015	−	6.59184i	0.559611	−	0.263463i
$627$	−0.0732900	+	0.122885i	−0.00292692	+	0.00490756i
$628$	0.132948	−	0.160831i	0.00530520	−	0.00641784i
$629$			16.5605i			0.660311i
$630$	−47.3550	−	34.9306i	−1.88667	−	1.39167i
$631$			23.4816i			0.934788i	0.884049	+	0.467394i	$0.154807\pi$
$631$			23.4816i			0.934788i	−0.884049	+	0.467394i	$0.845193\pi$
$632$	11.8836	+	3.04398i	0.472704	+	0.121083i
$633$	−23.7361	+	39.7982i	−0.943425	+	1.58184i
$634$	13.9321	+	29.5927i	0.553316	+	1.17528i
$635$	10.1812			0.404030
$636$	−15.8540	−	44.4999i	−0.628650	−	1.76454i
$637$	13.5324			0.536174
$638$	−0.105932	−	0.225006i	−0.00419389	−	0.00890807i
$639$	6.73648	+	12.4717i	0.266491	+	0.493371i
$640$	2.36908	−	38.4707i	0.0936460	−	1.52069i
$641$		−	41.9504i		−	1.65694i	−0.560033	−	0.828470i	$-0.689212\pi$
$641$		−	41.9504i		−	1.65694i	0.560033	−	0.828470i	$-0.310788\pi$
$642$	−27.6736	−	2.71412i	−1.09219	−	0.107118i
$643$			4.08169i			0.160966i	0.996756	+	0.0804831i	$0.0256463\pi$
$643$			4.08169i			0.160966i	−0.996756	+	0.0804831i	$0.974354\pi$
$644$	−54.3169	−	44.9002i	−2.14039	−	1.76931i
$645$	−38.6327	−	23.0410i	−1.52116	−	0.907237i
$646$	16.4371	−	7.73854i	0.646710	−	0.304469i
$647$	−1.95670			−0.0769257			−0.0384628	−	0.999260i	$-0.512246\pi$
$647$	−1.95670			−0.0769257			−0.0384628	+	0.999260i	$0.512246\pi$
$648$	−17.1595	−	18.8030i	−0.674088	−	0.738651i
$649$	0.202188			0.00793658
$650$	−11.9471	+	5.62465i	−0.468604	+	0.220617i
$651$	39.6384	+	23.6408i	1.55355	+	0.926555i
$652$	25.2984	+	20.9125i	0.990763	+	0.818998i
$653$			45.1364i			1.76632i	0.469069	+	0.883161i	$0.344589\pi$
$653$			45.1364i			1.76632i	−0.469069	+	0.883161i	$0.655411\pi$
$654$	24.5855	+	2.41125i	0.961368	+	0.0942872i
$655$			67.4310i			2.63475i
$656$	−5.66671	+	1.08544i	−0.221248	+	0.0423794i
$657$	−13.8681	−	25.6749i	−0.541047	−	1.00167i
$658$	−0.464330	−	0.986265i	−0.0181015	−	0.0384486i
$659$	38.5840			1.50302			0.751511	−	0.659721i	$-0.229326\pi$
$659$	38.5840			1.50302			0.751511	+	0.659721i	$0.229326\pi$
$660$	0.0720106	+	0.202124i	0.00280301	+	0.00786767i
$661$	27.8469			1.08312			0.541560	−	0.840662i	$-0.317834\pi$
$661$	27.8469			1.08312			0.541560	+	0.840662i	$0.317834\pi$
$662$	12.8090	+	27.2071i	0.497835	+	1.05743i
$663$	3.54548	−	5.94469i	0.137695	−	0.230873i
$664$	−7.44734	+	29.0742i	−0.289013	+	1.12830i
$665$		−	63.0175i		−	2.44371i
$666$	19.9978	+	14.7510i	0.774897	+	0.571590i
$667$		−	83.7131i		−	3.24138i
$668$	−24.0203	+	29.0580i	−0.929374	+	1.12429i
$669$	16.4316	−	27.5508i	0.635282	−	1.06517i
$670$	4.35902	−	2.05221i	0.168404	−	0.0792839i
$671$	0.0449624			0.00173575
$672$	39.7224	−	3.64442i	1.53232	−	0.140586i
$673$	−28.4643			−1.09722			−0.548609	−	0.836079i	$-0.684842\pi$
$673$	−28.4643			−1.09722			−0.548609	+	0.836079i	$0.684842\pi$
$674$	−24.9320	+	11.7379i	−0.960345	+	0.452127i
$675$	−1.45959	+	34.2965i	−0.0561796	+	1.32007i
$676$	−14.0199	+	16.9602i	−0.539226	+	0.652316i
$677$		−	10.7995i		−	0.415059i	−0.978229	−	0.207530i	$-0.933458\pi$
$677$		−	10.7995i		−	0.415059i	0.978229	−	0.207530i	$-0.0665424\pi$
$678$	2.16505	−	22.0752i	0.0831482	−	0.847792i
$679$			15.5121i			0.595300i
$680$	6.76048	−	26.3927i	0.259253	−	1.01211i
$681$	23.6572	+	14.1094i	0.906546	+	0.540674i
$682$	−0.0716837	−	0.152261i	−0.00274491	−	0.00583036i
$683$	−43.7404			−1.67368			−0.836839	−	0.547449i	$-0.815599\pi$
$683$	−43.7404			−1.67368			−0.836839	+	0.547449i	$0.815599\pi$
$684$	5.29640	−	26.7417i	0.202513	−	1.02250i
$685$	36.6096			1.39878
$686$	6.31369	+	13.4107i	0.241058	+	0.512022i
$687$	8.22535	+	4.90569i	0.313817	+	0.187164i
$688$	29.9478	−	5.73641i	1.14175	−	0.218699i
$689$		−	19.2742i		−	0.734289i
$690$	−7.04980	+	71.8809i	−0.268381	+	2.73646i
$691$		−	3.47398i		−	0.132156i	−0.997814	−	0.0660782i	$-0.978951\pi$
$691$		−	3.47398i		−	0.132156i	0.997814	−	0.0660782i	$-0.0210487\pi$
$692$	−22.6230	−	18.7010i	−0.859999	−	0.710904i
$693$	−0.195379	+	0.105533i	−0.00742185	+	0.00400886i
$694$	−27.0987	+	12.7580i	−1.02865	+	0.484285i
$695$	−6.49307			−0.246296
$696$	33.4002	+	33.6103i	1.26603	+	1.27400i
$697$	−4.07837			−0.154479
$698$	−8.58989	+	4.04408i	−0.325132	+	0.153071i
$699$	15.6135	−	26.1791i	0.590557	−	0.990185i
$700$	−41.4598	−	34.2720i	−1.56703	−	1.29536i
$701$		−	25.0833i		−	0.947383i	−0.880691	−	0.473691i	$-0.842921\pi$
$701$		−	25.0833i		−	0.947383i	0.880691	−	0.473691i	$-0.157079\pi$
$702$	−4.02047	−	9.57650i	−0.151743	−	0.361442i
$703$			26.6119i			1.00369i
$704$	−0.127540	−	0.0699266i	−0.00480683	−	0.00263546i
$705$	−0.572272	+	0.959527i	−0.0215530	+	0.0361379i
$706$	−9.54330	−	20.2706i	−0.359167	−	0.762893i
$707$	−7.88217			−0.296439
$708$	−36.2886	+	12.9285i	−1.36381	+	0.485884i
$709$	−49.9335			−1.87529			−0.937646	−	0.347590i	$-0.887000\pi$
$709$	−49.9335			−1.87529			−0.937646	+	0.347590i	$0.887000\pi$
$710$	9.69650	+	20.5960i	0.363903	+	0.772953i
$711$	11.4481	−	6.18361i	0.429337	−	0.231904i
$712$	−37.7253	−	9.66333i	−1.41382	−	0.362149i
$713$		−	56.6483i		−	2.12150i
$714$	28.0613	+	2.75214i	1.05017	+	0.102996i
$715$			0.0875459i			0.00327403i
$716$	−1.18920	+	1.43861i	−0.0444424	+	0.0537632i
$717$	14.3690	+	8.56980i	0.536619	+	0.320045i
$718$	9.16475	−	4.31473i	0.342025	−	0.161024i
$719$	45.0008			1.67825			0.839124	−	0.543940i	$-0.183068\pi$
$719$	45.0008			1.67825			0.839124	+	0.543940i	$0.183068\pi$
$720$	−25.8489	−	31.6725i	−0.963330	−	1.18037i
$721$	−40.9464			−1.52492
$722$	2.10308	−	0.990122i	0.0782685	−	0.0368485i
$723$	11.2505	+	6.70992i	0.418411	+	0.249545i
$724$	−12.2515	+	14.8210i	−0.455324	+	0.550817i
$725$		−	63.8977i		−	2.37310i
$726$	−26.8149	−	2.62990i	−0.995195	−	0.0976049i
$727$		−	40.2270i		−	1.49194i	−0.665982	−	0.745968i	$-0.731987\pi$
$727$		−	40.2270i		−	1.49194i	0.665982	−	0.745968i	$-0.268013\pi$
$728$	15.7661	+	4.03849i	0.584332	+	0.149677i
$729$	−26.9024	−	2.29398i	−0.996384	−	0.0849621i
$730$	−19.9618	−	42.4002i	−0.738820	−	1.56930i
$731$	21.5536			0.797190
$732$	−8.06983	+	2.87503i	−0.298269	+	0.106264i
$733$	50.9739			1.88276			0.941382	−	0.337341i	$-0.109528\pi$
$733$	50.9739			1.88276			0.941382	+	0.337341i	$0.109528\pi$
$734$	−16.6669	−	35.4016i	−0.615188	−	1.30670i
$735$	28.9392	−	48.5222i	1.06744	−	1.78977i
$736$	−28.8157	−	39.5824i	−1.06216	−	1.45903i
$737$		−	0.0181814i		−	0.000669721i
$738$	−3.63274	+	4.92486i	−0.133723	+	0.181287i
$739$			5.00613i			0.184154i	0.995752	+	0.0920768i	$0.0293505\pi$
$739$			5.00613i			0.184154i	−0.995752	+	0.0920768i	$0.970649\pi$
$740$	30.7594	+	25.4267i	1.13074	+	0.934704i
$741$	5.69741	−	9.55282i	0.209299	−	0.350932i
$742$	71.0360	−	33.4434i	2.60781	−	1.22775i
$743$	9.69596			0.355710			0.177855	−	0.984057i	$-0.443084\pi$
$743$	9.69596			0.355710			0.177855	+	0.984057i	$0.443084\pi$
$744$	22.6018	+	22.7440i	0.828621	+	0.833835i
$745$	2.03112			0.0744143
$746$	−34.1283	+	16.0675i	−1.24953	+	0.588272i
$747$	15.1287	+	28.0087i	0.553531	+	1.02479i
$748$	−0.0792437	−	0.0655055i	−0.00289744	−	0.00239512i
$749$		−	46.2156i		−	1.68868i
$750$	−1.30841	+	13.3408i	−0.0477764	+	0.487136i
$751$			16.7858i			0.612521i	0.951948	+	0.306260i	$0.0990778\pi$
$751$			16.7858i			0.612521i	−0.951948	+	0.306260i	$0.900922\pi$
$752$	−0.142476	−	0.743819i	−0.00519557	−	0.0271243i
$753$	1.63880	+	0.977399i	0.0597212	+	0.0356184i
$754$	8.23492	+	17.4915i	0.299898	+	0.637002i
$755$	20.9065			0.760867
$756$	28.3185	−	31.4341i	1.02993	−	1.14325i
$757$	−30.7776			−1.11863			−0.559316	−	0.828954i	$-0.688936\pi$
$757$	−30.7776			−1.11863			−0.559316	+	0.828954i	$0.688936\pi$
$758$	−16.6697	−	35.4075i	−0.605472	−	1.28606i
$759$	0.234085	+	0.139611i	0.00849677	+	0.00506756i
$760$	10.8638	−	42.4118i	0.394070	−	1.53844i
$761$			25.9132i			0.939351i	0.882839	+	0.469676i	$0.155629\pi$
$761$			25.9132i			0.939351i	−0.882839	+	0.469676i	$0.844371\pi$
$762$	−0.714518	+	7.28534i	−0.0258843	+	0.263920i
$763$			41.0583i			1.48641i
$764$	−2.51907	+	3.04738i	−0.0911367	+	0.110250i
$765$	−13.7334	−	25.4255i	−0.496532	−	0.919261i
$766$	−15.6343	+	7.36057i	−0.564891	+	0.265948i
$767$	−15.7177			−0.567532
$768$	27.3621	+	4.39510i	0.987344	+	0.158595i
$769$	41.2256			1.48663			0.743316	−	0.668940i	$-0.233252\pi$
$769$	41.2256			1.48663			0.743316	+	0.668940i	$0.233252\pi$
$770$	−0.322654	+	0.151904i	−0.0116276	+	0.00547425i
$771$	−11.7123	+	19.6380i	−0.421809	+	0.707246i
$772$	8.62460	−	10.4334i	0.310406	−	0.375507i
$773$			33.0029i			1.18703i	0.804823	+	0.593516i	$0.202260\pi$
$773$			33.0029i			1.18703i	−0.804823	+	0.593516i	$0.797740\pi$
$774$	19.1986	−	26.0272i	0.690078	−	0.935529i
$775$		−	43.2393i		−	1.55320i
$776$	−2.67418	+	10.4399i	−0.0959973	+	0.374770i
$777$	−21.1557	+	35.4716i	−0.758955	+	1.27254i
$778$	−9.25676	−	19.6619i	−0.331871	−	0.704914i
$779$	−6.55374			−0.234812
$780$	−5.59795	−	15.7127i	−0.200439	−	0.562604i
$781$	0.0859054			0.00307394
$782$	−14.7412	−	31.3113i	−0.527146	−	1.11969i
$783$	50.2127	+	2.13695i	1.79446	+	0.0763684i
$784$	7.20486	+	37.6141i	0.257317	+	1.34336i
$785$		−	0.355443i		−	0.0126863i
$786$	−48.2513	−	4.73230i	−1.72107	−	0.168796i
$787$		−	35.2562i		−	1.25675i	−0.777912	−	0.628373i	$-0.783721\pi$
$787$		−	35.2562i		−	1.25675i	0.777912	−	0.628373i	$-0.216279\pi$
$788$	−8.74234	−	7.22671i	−0.311433	−	0.257441i
$789$	−3.24059	−	1.93272i	−0.115368	−	0.0688067i
$790$	18.9056	−	8.90070i	0.672633	−	0.316673i
$791$	36.8661			1.31081
$792$	−0.149687	+	0.0373433i	−0.00531888	+	0.00132694i
$793$	−3.49528			−0.124121
$794$	35.2256	−	16.5841i	1.25011	−	0.588547i
$795$	−69.1102	−	41.2181i	−2.45109	−	1.46185i
$796$	9.88048	+	8.16753i	0.350204	+	0.289490i
$797$			35.4537i			1.25583i	0.778280	+	0.627917i	$0.216092\pi$
$797$			35.4537i			1.25583i	−0.778280	+	0.627917i	$0.783908\pi$
$798$	45.0931	+	4.42256i	1.59628	+	0.156557i
$799$		−	0.535331i		−	0.0189387i
$800$	−21.9948	−	30.2130i	−0.777635	−	1.06819i
$801$	−36.3429	+	19.6303i	−1.28411	+	0.693604i
$802$	−5.25709	−	11.1664i	−0.185634	−	0.394299i
$803$	−0.176850			−0.00624091
$804$	1.16258	+	3.26319i	0.0410009	+	0.115084i
$805$	−120.043			−4.23095
$806$	5.57254	+	11.8364i	0.196284	+	0.416920i
$807$	−4.34667	+	7.28805i	−0.153010	+	0.256552i
$808$	−5.30483	−	1.35883i	−0.186623	−	0.0478034i
$809$			36.3030i			1.27635i	0.769893	+	0.638173i	$0.220310\pi$
$809$			36.3030i			1.27635i	−0.769893	+	0.638173i	$0.779690\pi$
$810$	−42.9355	−	6.06351i	−1.50860	−	0.213050i
$811$			19.5886i			0.687850i	0.938997	+	0.343925i	$0.111757\pi$
$811$			19.5886i			0.687850i	−0.938997	+	0.343925i	$0.888243\pi$
$812$	−50.1769	+	60.7003i	−1.76086	+	2.13016i
$813$	−7.80009	+	13.0784i	−0.273561	+	0.458679i
$814$	0.136255	−	0.0641484i	0.00477574	−	0.00224840i
$815$	55.9107			1.95847
$816$	18.4112	+	6.68980i	0.644523	+	0.234190i
$817$	34.6356			1.21175
$818$	38.5432	−	18.1460i	1.34763	−	0.634460i
$819$	15.1884	−	8.20390i	0.530725	−	0.286667i
$820$	−6.26185	+	7.57512i	−0.218673	+	0.264535i
$821$		−	38.4408i		−	1.34159i	−0.741642	−	0.670796i	$-0.765953\pi$
$821$		−	38.4408i		−	1.34159i	0.741642	−	0.670796i	$-0.234047\pi$
$822$	−2.56926	+	26.1966i	−0.0896132	+	0.913710i
$823$		−	7.11764i		−	0.248105i	−0.992276	−	0.124053i	$-0.960411\pi$
$823$		−	7.11764i		−	0.248105i	0.992276	−	0.124053i	$-0.0395892\pi$
$824$	−27.5576	−	7.05887i	−0.960015	−	0.245907i
$825$	0.178676	+	0.106564i	0.00622070	+	0.00371009i
$826$	−27.2723	−	57.9282i	−0.948926	−	2.01558i
$827$	41.2771			1.43535			0.717673	−	0.696380i	$-0.245207\pi$
$827$	41.2771			1.43535			0.717673	+	0.696380i	$0.245207\pi$
$828$	−50.9407	−	10.0892i	−1.77031	−	0.350623i
$829$	14.9343			0.518688			0.259344	−	0.965785i	$-0.416494\pi$
$829$	14.9343			0.518688			0.259344	+	0.965785i	$0.416494\pi$
$830$	21.7763	+	46.2542i	0.755867	+	1.60551i
$831$	−19.0125	−	11.3393i	−0.659536	−	0.393355i
$832$	9.91466	+	5.43594i	0.343729	+	0.188457i
$833$			27.0711i			0.937958i
$834$	0.455683	−	4.64622i	0.0157790	−	0.160885i
$835$			64.2196i			2.22241i
$836$	−0.127341	−	0.105264i	−0.00440417	−	0.00364064i
$837$	33.9787	+	1.44607i	1.17448	+	0.0499834i
$838$	8.07103	−	3.79981i	0.278809	−	0.131262i
$839$	−7.49526			−0.258765			−0.129383	−	0.991595i	$-0.541300\pi$
$839$	−7.49526			−0.258765			−0.129383	+	0.991595i	$0.541300\pi$
$840$	48.1965	−	47.8952i	1.66294	−	1.65254i
$841$	−64.5511			−2.22590
$842$	25.1579	−	11.8443i	0.867000	−	0.408180i
$843$	9.00739	−	15.1027i	0.310231	−	0.520163i
$844$	−41.2413	−	34.0914i	−1.41958	−	1.17347i
$845$			37.4829i			1.28945i
$846$	−0.646442	−	0.476838i	−0.0222251	−	0.0163940i
$847$		−	44.7816i		−	1.53871i
$848$	53.5737	−	10.2619i	1.83973	−	0.352395i
$849$	−0.868241	+	1.45578i	−0.0297979	+	0.0499621i
$850$	−11.2519	−	23.8997i	−0.385937	−	0.819754i
$851$	50.6935			1.73775
$852$	−15.4183	+	5.49306i	−0.528221	+	0.188189i
$853$	−35.1989			−1.20519			−0.602594	−	0.798048i	$-0.705866\pi$
$853$	−35.1989			−1.20519			−0.602594	+	0.798048i	$0.705866\pi$
$854$	−6.06480	−	12.8820i	−0.207533	−	0.440813i
$855$	−22.0689	−	40.8575i	−0.754741	−	1.39730i
$856$	7.96723	−	31.1038i	0.272314	−	1.06311i
$857$		−	16.0664i		−	0.548817i	−0.961613	−	0.274408i	$-0.911518\pi$
$857$		−	16.0664i		−	0.548817i	0.961613	−	0.274408i	$-0.0884820\pi$
$858$	−0.0626448	−	0.00614396i	−0.00213866	−	0.000209751i
$859$		−	24.1648i		−	0.824491i	−0.911073	−	0.412246i	$-0.864745\pi$
$859$		−	24.1648i		−	0.824491i	0.911073	−	0.412246i	$-0.135255\pi$
$860$	33.0930	−	40.0335i	1.12846	−	1.36513i
$861$	−8.73562	−	5.21002i	−0.297709	−	0.177557i
$862$	−3.79738	+	1.78779i	−0.129339	+	0.0608924i
$863$	−10.2934			−0.350390			−0.175195	−	0.984534i	$-0.556056\pi$
$863$	−10.2934			−0.350390			−0.175195	+	0.984534i	$0.556056\pi$
$864$	24.4778	−	16.2738i	0.832753	−	0.553645i
$865$	−49.9980			−1.69998
$866$	23.4178	−	11.0250i	0.795771	−	0.374646i
$867$	−13.3966	−	7.98987i	−0.454972	−	0.271350i
$868$	−33.9545	+	41.0757i	−1.15249	+	1.39420i
$869$		−	0.0788551i		−	0.00267498i
$870$	80.3284	+	7.87830i	2.72339	+	0.267099i
$871$			1.41338i			0.0478907i
$872$	−7.07816	+	27.6329i	−0.239697	+	0.935769i
$873$	5.43239	+	10.0573i	0.183859	+	0.340389i
$874$	−23.6885	−	50.3158i	−0.801274	−	1.70196i
$875$	−22.2794			−0.753182
$876$	31.7410	−	11.3084i	1.07243	−	0.382074i
$877$	−6.30630			−0.212949			−0.106474	−	0.994315i	$-0.533956\pi$
$877$	−6.30630			−0.212949			−0.106474	+	0.994315i	$0.533956\pi$
$878$	−1.15023	−	2.44316i	−0.0388184	−	0.0824527i
$879$	−18.3463	+	30.7612i	−0.618805	+	1.03755i
$880$	−0.243339	+	0.0466107i	−0.00820294	+	0.00157125i
$881$			18.3362i			0.617762i	0.951101	+	0.308881i	$0.0999545\pi$
$881$			18.3362i			0.617762i	−0.951101	+	0.308881i	$0.900045\pi$
$882$	32.6899	+	24.1131i	1.10072	+	0.811932i
$883$			5.64834i			0.190082i	0.995473	+	0.0950409i	$0.0302982\pi$
$883$			5.64834i			0.190082i	−0.995473	+	0.0950409i	$0.969702\pi$
$884$	6.16024	+	5.09226i	0.207191	+	0.171271i
$885$	−33.6124	+	56.3577i	−1.12987	+	1.89444i
$886$	−0.975191	+	0.459116i	−0.0327622	+	0.0154243i
$887$	14.1161			0.473971			0.236986	−	0.971513i	$-0.423841\pi$
$887$	14.1161			0.473971			0.236986	+	0.971513i	$0.423841\pi$
$888$	−20.3531	+	20.2259i	−0.683007	+	0.678736i
$889$	−12.1667			−0.408058
$890$	−60.0174	+	28.2560i	−2.01179	+	0.947142i
$891$	−0.0897169	+	0.136845i	−0.00300563	+	0.00458448i
$892$	28.5497	+	23.6002i	0.955916	+	0.790192i
$893$		−	0.860251i		−	0.0287872i
$894$	−0.142544	+	1.45340i	−0.00476737	+	0.0486088i
$895$			3.17938i			0.106275i
$896$	−2.83108	+	45.9730i	−0.0945796	+	1.53585i
$897$	−18.1973	−	10.8531i	−0.607590	−	0.362373i
$898$	18.6172	+	39.5442i	0.621265	+	1.31961i
$899$	−63.3057			−2.11136
$900$	−38.8827	−	7.70101i	−1.29609	−	0.256700i
$901$	38.5574			1.28453
$902$	0.0157979	+	0.0335556i	0.000526011	+	0.00111728i
$903$	46.1666	+	27.5342i	1.53633	+	0.916282i
$904$	24.8115	+	6.35545i	0.825218	+	0.211379i
$905$			32.7550i			1.08881i
$906$	−1.46722	+	14.9600i	−0.0487451	+	0.497012i
$907$		−	39.6359i		−	1.31609i	−0.752980	−	0.658044i	$-0.771384\pi$
$907$		−	39.6359i		−	1.31609i	0.752980	−	0.658044i	$-0.228616\pi$
$908$	−20.2649	+	24.5150i	−0.672515	+	0.813559i
$909$	−5.11043	+	2.76036i	−0.169502	+	0.0915554i
$910$	25.0824	−	11.8087i	0.831475	−	0.391455i
$911$	−3.94166			−0.130593			−0.0652965	−	0.997866i	$-0.520799\pi$
$911$	−3.94166			−0.130593			−0.0652965	+	0.997866i	$0.520799\pi$
$912$	29.5860	+	10.7502i	0.979689	+	0.355974i
$913$	0.192926			0.00638491
$914$	10.6705	−	5.02362i	0.352948	−	0.166167i
$915$	−7.47468	+	12.5328i	−0.247105	+	0.414321i
$916$	−7.04589	+	8.52360i	−0.232803	+	0.281628i
$917$		−	80.5809i		−	2.66101i
$918$	19.1574	−	8.04279i	0.632289	−	0.265452i
$919$			43.1013i			1.42178i	0.703302	+	0.710891i	$0.251708\pi$
$919$			43.1013i			1.42178i	−0.703302	+	0.710891i	$0.748292\pi$
$920$	−80.7908	−	20.6945i	−2.66359	−	0.682278i
$921$	−3.17505	+	5.32360i	−0.104622	+	0.175419i
$922$	16.7475	+	35.5728i	0.551551	+	1.17153i
$923$	−6.67811			−0.219813
$924$	−0.0860536	−	0.241541i	−0.00283095	−	0.00794610i
$925$	38.6940			1.27225
$926$	16.4329	+	34.9045i	0.540018	+	1.14703i
$927$	−26.5477	+	14.3396i	−0.871942	+	0.470973i
$928$	−44.2341	+	32.2021i	−1.45206	+	1.05709i
$929$		−	6.75708i		−	0.221693i	−0.993838	−	0.110846i	$-0.964644\pi$
$929$		−	6.75708i		−	0.221693i	0.993838	−	0.110846i	$-0.0353561\pi$
$930$	54.3579	+	5.33121i	1.78247	+	0.174817i
$931$			43.5019i			1.42572i
$932$	27.1284	+	22.4252i	0.888619	+	0.734561i
$933$	−14.2204	−	8.48118i	−0.465554	−	0.277661i
$934$	4.36540	−	2.05521i	0.142840	−	0.0672486i
$935$	−0.175132			−0.00572744
$936$	11.6363	−	2.90299i	0.380345	−	0.0948871i
$937$	−29.6332			−0.968075			−0.484038	−	0.875047i	$-0.660830\pi$
$937$	−29.6332			−0.968075			−0.484038	+	0.875047i	$0.660830\pi$
$938$	−5.20909	+	2.45242i	−0.170083	+	0.0800743i
$939$	16.2783	+	9.70857i	0.531223	+	0.316827i
$940$	−0.994319	−	0.821937i	−0.0324311	−	0.0268086i
$941$			2.90008i			0.0945399i	0.998882	+	0.0472700i	$0.0150521\pi$
$941$			2.90008i			0.0945399i	−0.998882	+	0.0472700i	$0.984948\pi$
$942$	0.254343	+	0.0249450i	0.00828694	+	0.000812751i
$943$			12.4843i			0.406545i
$944$	−8.36833	−	43.6881i	−0.272366	−	1.42193i
$945$	3.06434	−	72.0040i	0.0996831	−	2.34229i
$946$	−0.0834896	−	0.177337i	−0.00271448	−	0.00576572i
$947$	57.1753			1.85795			0.928974	−	0.370146i	$-0.120692\pi$
$947$	57.1753			1.85795			0.928974	+	0.370146i	$0.120692\pi$
$948$	5.04224	+	14.1529i	0.163764	+	0.459664i
$949$	13.7480			0.446278
$950$	−18.0813	−	38.4057i	−0.586634	−	1.24605i
$951$	−20.5195	+	34.4050i	−0.665390	+	1.11566i
$952$	−8.07886	+	31.5396i	−0.261837	+	1.02220i
$953$			32.0568i			1.03842i	0.854647	+	0.519210i	$0.173774\pi$
$953$			32.0568i			1.03842i	−0.854647	+	0.519210i	$0.826226\pi$
$954$	34.3444	−	46.5602i	1.11194	−	1.50744i
$955$			6.73486i			0.217935i
$956$	−12.3085	+	14.8900i	−0.398087	+	0.481576i
$957$	0.156018	−	0.261595i	0.00504336	−	0.00845618i
$958$	38.2632	−	18.0141i	1.23623	−	0.582011i
$959$	−43.7489			−1.41273
$960$	40.6938	−	23.9255i	1.31339	−	0.772192i
$961$	−11.8387			−0.381894
$962$	−10.5922	+	4.98676i	−0.341506	+	0.160779i
$963$	−16.1848	−	29.9640i	−0.521549	−	0.965576i
$964$	−9.63725	+	11.6584i	−0.310395	+	0.375493i
$965$		−	23.0583i		−	0.742273i
$966$	8.42460	−	85.8985i	0.271057	−	2.76374i
$967$			40.0726i			1.28865i	0.764752	+	0.644325i	$0.222861\pi$
$967$			40.0726i			1.28865i	−0.764752	+	0.644325i	$0.777139\pi$
$968$	7.72003	−	30.1387i	0.248131	−	0.968695i
$969$	19.1101	+	11.3974i	0.613904	+	0.366139i
$970$	7.81939	+	16.6089i	0.251066	+	0.533279i
$971$	31.3391			1.00572			0.502860	−	0.864368i	$-0.332281\pi$
$971$	31.3391			1.00572			0.502860	+	0.864368i	$0.332281\pi$
$972$	7.35205	−	30.2976i	0.235817	−	0.971797i
$973$	7.75930			0.248752
$974$	−15.8807	−	33.7316i	−0.508850	−	1.08083i
$975$	−13.8899	−	8.28408i	−0.444833	−	0.265303i
$976$	−1.86094	−	9.71532i	−0.0595673	−	0.310980i
$977$		−	11.0385i		−	0.353154i	−0.984287	−	0.176577i	$-0.943497\pi$
$977$		−	11.0385i		−	0.353154i	0.984287	−	0.176577i	$-0.0565025\pi$
$978$	−3.92381	+	40.0078i	−0.125470	+	1.27931i
$979$			0.250332i			0.00800063i
$980$	50.2816	+	41.5644i	1.60619	+	1.32773i
$981$	14.3788	+	26.6203i	0.459078	+	0.849920i
$982$	15.2916	−	7.19921i	0.487973	−	0.229736i
$983$	−7.84603			−0.250250			−0.125125	−	0.992141i	$-0.539933\pi$
$983$	−7.84603			−0.250250			−0.125125	+	0.992141i	$0.539933\pi$
$984$	−4.98104	−	5.01238i	−0.158790	−	0.159789i
$985$	−19.3210			−0.615617
$986$	−34.9911	+	16.4737i	−1.11434	+	0.524628i
$987$	0.683872	−	1.14665i	0.0217679	−	0.0364982i
$988$	9.89920	+	8.18301i	0.314936	+	0.260336i
$989$		−	65.9779i		−	2.09798i
$990$	−0.155996	+	0.211482i	−0.00495789	+	0.00672134i
$991$		−	10.3007i		−	0.327214i	−0.986526	−	0.163607i	$-0.947687\pi$
$991$		−	10.3007i		−	0.327214i	0.986526	−	0.163607i	$-0.0523129\pi$
$992$	−29.9331	+	21.7911i	−0.950376	+	0.691867i
$993$	−18.8653	+	31.6314i	−0.598672	+	1.00379i
$994$	−11.5874	−	24.6124i	−0.367531	−	0.780659i
$995$	21.8363			0.692258
$996$	−34.6262	+	12.3363i	−1.09717	+	0.390889i
$997$	12.2763			0.388795			0.194398	−	0.980923i	$-0.437725\pi$
$997$	12.2763			0.388795			0.194398	+	0.980923i	$0.437725\pi$
$998$	14.6674	+	31.1545i	0.464289	+	0.986178i
$999$	−1.29406	+	30.4069i	−0.0409421	+	0.962032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.18	yes	128
3.2	odd	2	inner	804.2.c.b.671.111	yes	128
4.3	odd	2	inner	804.2.c.b.671.112	yes	128
12.11	even	2	inner	804.2.c.b.671.17	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.17	✓	128	12.11	even	2	inner
804.2.c.b.671.18	yes	128	1.1	even	1	trivial
804.2.c.b.671.111	yes	128	3.2	odd	2	inner
804.2.c.b.671.112	yes	128	4.3	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27950 + 0.602386i) q^{2} +(-1.48757 - 0.887204i) q^{3} +(1.27426 - 1.54151i) q^{4} -3.40681i q^{5} +(2.43779 + 0.239089i) q^{6} +4.07118i q^{7} +(-0.701842 + 2.73997i) q^{8} +(1.42574 + 2.63956i) q^{9} +O(q^{10})\)	\(q+(-1.27950 + 0.602386i) q^{2} +(-1.48757 - 0.887204i) q^{3} +(1.27426 - 1.54151i) q^{4} -3.40681i q^{5} +(2.43779 + 0.239089i) q^{6} +4.07118i q^{7} +(-0.701842 + 2.73997i) q^{8} +(1.42574 + 2.63956i) q^{9} +(2.05221 + 4.35902i) q^{10} +0.0181814 q^{11} +(-3.26319 + 1.16258i) q^{12} -1.41338 q^{13} +(-2.45242 - 5.20909i) q^{14} +(-3.02253 + 5.06787i) q^{15} +(-0.752507 - 3.92858i) q^{16} -2.82742i q^{17} +(-3.41427 - 2.51848i) q^{18} -4.54353i q^{19} +(-5.25163 - 4.34117i) q^{20} +(3.61196 - 6.05617i) q^{21} +(-0.0232632 + 0.0109522i) q^{22} -8.65504 q^{23} +(3.47495 - 3.45322i) q^{24} -6.60634 q^{25} +(1.80843 - 0.851403i) q^{26} +(0.220938 - 5.19145i) q^{27} +(6.27576 + 5.18775i) q^{28} +9.67218i q^{29} +(0.814532 - 8.30509i) q^{30} +6.54513i q^{31} +(3.32936 + 4.57333i) q^{32} +(-0.0270462 - 0.0161306i) q^{33} +(1.70320 + 3.61770i) q^{34} +13.8697 q^{35} +(5.88567 + 1.16570i) q^{36} -5.85711 q^{37} +(2.73696 + 5.81347i) q^{38} +(2.10251 + 1.25396i) q^{39} +(9.33454 + 2.39104i) q^{40} -1.44243i q^{41} +(-0.973375 + 9.92469i) q^{42} +7.62307i q^{43} +(0.0231679 - 0.0280268i) q^{44} +(8.99247 - 4.85722i) q^{45} +(11.0742 - 5.21367i) q^{46} +0.189335 q^{47} +(-2.36604 + 6.51167i) q^{48} -9.57448 q^{49} +(8.45284 - 3.97956i) q^{50} +(-2.50850 + 4.20599i) q^{51} +(-1.80102 + 2.17875i) q^{52} +13.6369i q^{53} +(2.84457 + 6.77558i) q^{54} -0.0619406i q^{55} +(-11.1549 - 2.85732i) q^{56} +(-4.03104 + 6.75883i) q^{57} +(-5.82638 - 12.3756i) q^{58} +11.1206 q^{59} +(3.96067 + 11.1171i) q^{60} +2.47299 q^{61} +(-3.94269 - 8.37452i) q^{62} +(-10.7461 + 5.80443i) q^{63} +(-7.01484 - 3.84605i) q^{64} +4.81513i q^{65} +(0.0443225 + 0.00434698i) q^{66} -1.00000i q^{67} +(-4.35850 - 3.60288i) q^{68} +(12.8750 + 7.67878i) q^{69} +(-17.7464 + 8.35492i) q^{70} +4.72490 q^{71} +(-8.23295 + 2.05392i) q^{72} -9.72698 q^{73} +(7.49420 - 3.52824i) q^{74} +(9.82740 + 5.86117i) q^{75} +(-7.00390 - 5.78965i) q^{76} +0.0740198i q^{77} +(-3.44554 - 0.337925i) q^{78} -4.33713i q^{79} +(-13.3839 + 2.56365i) q^{80} +(-4.93454 + 7.52664i) q^{81} +(0.868901 + 1.84560i) q^{82} +10.6111 q^{83} +(-4.73305 - 13.2850i) q^{84} -9.63249 q^{85} +(-4.59203 - 9.75375i) q^{86} +(8.58120 - 14.3881i) q^{87} +(-0.0127605 + 0.0498165i) q^{88} +13.7685i q^{89} +(-8.57998 + 11.6318i) q^{90} -5.75414i q^{91} +(-11.0288 + 13.3418i) q^{92} +(5.80686 - 9.73635i) q^{93} +(-0.242255 + 0.114053i) q^{94} -15.4789 q^{95} +(-0.895176 - 9.75698i) q^{96} +3.81023 q^{97} +(12.2506 - 5.76753i) q^{98} +(0.0259220 + 0.0479909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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