LMFDB - Embedded newform 804.2.c.b.671.17

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

$q$-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	$0.275677\pi$
$5$			3.40681i			1.52357i	−0.647830	+	0.761785i	$0.724323\pi$
$6$	2.43779	−	0.239089i	0.995225	−	0.0976078i
$7$		−	4.07118i		−	1.53876i	−0.638791	−	0.769380i	$-0.720565\pi$
$7$		−	4.07118i		−	1.53876i	0.638791	−	0.769380i	$-0.279435\pi$
$8$	−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	$0.111401\pi$
$17$			2.82742i			0.685751i	−0.939381	+	0.342875i	$0.888599\pi$
$18$	−3.41427	+	2.51848i	−0.804751	+	0.593612i
$19$			4.54353i			1.04236i	0.853448	+	0.521179i	$0.174507\pi$
$19$			4.54353i			1.04236i	−0.853448	+	0.521179i	$0.825493\pi$
$20$	−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	$-0.644991\pi$
$29$		−	9.67218i		−	1.79608i	0.439914	−	0.898040i	$-0.355009\pi$
$30$	0.814532	+	8.30509i	0.148712	+	1.51630i
$31$		−	6.54513i		−	1.17554i	−0.809028	−	0.587770i	$-0.800006\pi$
$31$		−	6.54513i		−	1.17554i	0.809028	−	0.587770i	$-0.199994\pi$
$32$	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	$0.0359291\pi$
$41$			1.44243i			0.225270i	−0.993636	+	0.112635i	$0.964071\pi$
$42$	−0.973375	−	9.92469i	−0.150195	−	1.53141i
$43$		−	7.62307i		−	1.16251i	−0.813723	−	0.581253i	$-0.802562\pi$
$43$		−	7.62307i		−	1.16251i	0.813723	−	0.581253i	$-0.197438\pi$
$44$	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	$-0.613965\pi$
$53$		−	13.6369i		−	1.87318i	0.350432	−	0.936588i	$-0.386035\pi$
$54$	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	$0.0784539\pi$
$79$			4.33713i			0.487965i	−0.969780	+	0.243982i	$0.921546\pi$
$80$	−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	$-0.739645\pi$
$89$		−	13.7685i		−	1.45946i	0.683734	−	0.729731i	$-0.260355\pi$
$90$	−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	$-0.969291\pi$
$101$		−	1.93609i		−	0.192648i	0.995350	−	0.0963241i	$-0.0307085\pi$
$102$	0.676007	+	6.89267i	0.0669347	+	0.682476i
$103$		−	10.0576i		−	0.991009i	−0.868605	−	0.495504i	$-0.834983\pi$
$103$		−	10.0576i		−	0.991009i	0.868605	−	0.495504i	$-0.165017\pi$
$104$	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	$0.140053\pi$
$113$			9.05540i			0.851860i	−0.904756	+	0.425930i	$0.859947\pi$
$114$	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	$-0.957670\pi$
$127$		−	2.98850i		−	0.265186i	0.991171	−	0.132593i	$-0.0423304\pi$
$128$	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	$-0.848191\pi$
$137$		−	10.7460i		−	0.918094i	0.888412	−	0.459047i	$-0.151809\pi$
$138$	−21.0992	+	2.06933i	−1.79608	+	0.176153i
$139$			1.90591i			0.161657i	0.996728	+	0.0808286i	$0.0257567\pi$
$139$			1.90591i			0.161657i	−0.996728	+	0.0808286i	$0.974243\pi$
$140$	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	$-0.992226\pi$
$149$		−	0.596193i		−	0.0488421i	0.999702	−	0.0244210i	$-0.00777423\pi$
$150$	−16.1049	+	1.57950i	−1.31496	+	0.128966i
$151$		−	6.13669i		−	0.499397i	−0.968324	−	0.249699i	$-0.919668\pi$
$151$		−	6.13669i		−	0.499397i	0.968324	−	0.249699i	$-0.0803315\pi$
$152$	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	$-0.777805\pi$
$163$		−	16.4115i		−	1.28545i	0.766099	−	0.642723i	$-0.222195\pi$
$164$	−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	$0.188390\pi$
$173$			14.6759i			1.11579i	−0.829912	+	0.557894i	$0.811610\pi$
$174$	−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	$0.0647542\pi$
$197$			5.67128i			0.404062i	−0.979379	+	0.202031i	$0.935246\pi$
$198$	−0.0620763	+	0.0457896i	−0.00441157	+	0.00325412i
$199$		−	6.40961i		−	0.454365i	−0.973852	−	0.227183i	$-0.927049\pi$
$199$		−	6.40961i		−	0.454365i	0.973852	−	0.227183i	$-0.0729514\pi$
$200$	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	$0.372548\pi$
$211$			26.7538i			1.84181i	−0.389788	+	0.920904i	$0.627452\pi$
$212$	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	$-0.787085\pi$
$223$		−	18.5206i		−	1.24023i	0.784510	−	0.620117i	$-0.212915\pi$
$224$	−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	$-0.804434\pi$
$233$		−	17.5986i		−	1.15292i	0.817125	−	0.576460i	$-0.195566\pi$
$234$	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	$0.135079\pi$
$257$			13.2014i			0.823480i	−0.911301	+	0.411740i	$0.864921\pi$
$258$	−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	$0.0477206\pi$
$269$			4.89929i			0.298715i	−0.988783	+	0.149358i	$0.952279\pi$
$270$	23.0831	+	9.69089i	1.40479	+	0.589769i
$271$			8.79177i			0.534062i	0.963688	+	0.267031i	$0.0860426\pi$
$271$			8.79177i			0.534062i	−0.963688	+	0.267031i	$0.913957\pi$
$272$	−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	$-0.902070\pi$
$281$		−	10.1526i		−	0.605651i	0.953046	−	0.302826i	$-0.0979299\pi$
$282$	0.461561	−	0.0452681i	0.0274855	−	0.00269568i
$283$			0.978626i			0.0581733i	0.999577	+	0.0290866i	$0.00925987\pi$
$283$			0.978626i			0.0581733i	−0.999577	+	0.0290866i	$0.990740\pi$
$284$	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	$0.206441\pi$
$293$			20.6788i			1.20807i	−0.796959	+	0.604034i	$0.793559\pi$
$294$	−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	$0.0325639\pi$
$307$			3.57872i			0.204248i	−0.994772	+	0.102124i	$0.967436\pi$
$308$	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	$0.225024\pi$
$317$			23.1283i			1.29901i	−0.760356	+	0.649506i	$0.774976\pi$
$318$	−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	$0.198663\pi$
$331$			21.2638i			1.16876i	−0.811479	+	0.584381i	$0.801337\pi$
$332$	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	$-0.861467\pi$
$353$		−	15.8425i		−	0.843212i	0.906779	−	0.421606i	$-0.138533\pi$
$354$	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	$-0.743161\pi$
$367$		−	27.6682i		−	1.44427i	0.691753	−	0.722134i	$-0.256839\pi$
$368$	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	$-0.748365\pi$
$379$		−	27.6728i		−	1.42146i	0.703466	−	0.710729i	$-0.251635\pi$
$380$	−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	$-0.872626\pi$
$389$		−	15.3668i		−	0.779129i	0.920999	−	0.389565i	$-0.127374\pi$
$390$	−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	$-0.930077\pi$
$401$		−	8.72712i		−	0.435811i	0.975970	−	0.217906i	$-0.0699225\pi$
$402$	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	$-0.985491\pi$
$439$		−	1.90946i		−	0.0911336i	0.998961	−	0.0455668i	$-0.0145094\pi$
$440$	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	$0.260139\pi$
$449$			30.9058i			1.45854i	−0.684228	+	0.729268i	$0.739861\pi$
$450$	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	$0.224158\pi$
$461$			27.8020i			1.29487i	−0.762121	+	0.647434i	$0.775842\pi$
$462$	−0.0176973	−	0.180445i	−0.000823355	−	0.00839506i
$463$			27.2797i			1.26779i	0.773417	+	0.633897i	$0.218546\pi$
$463$			27.2797i			1.26779i	−0.773417	+	0.633897i	$0.781454\pi$
$464$	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	$-0.796236\pi$
$487$		−	26.3630i		−	1.19462i	0.802010	−	0.597311i	$-0.203764\pi$
$488$	−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	$0.183471\pi$
$499$			24.3489i			1.09000i	−0.838435	+	0.545002i	$0.816529\pi$
$500$	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	$-0.882966\pi$
$509$		−	16.2190i		−	0.718893i	0.933166	−	0.359446i	$-0.117034\pi$
$510$	−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	$0.265123\pi$
$521$			33.7767i			1.47978i	−0.672726	+	0.739892i	$0.734877\pi$
$522$	24.3592	+	33.0235i	1.06617	+	1.44540i
$523$			39.1189i			1.71055i	0.518173	+	0.855276i	$0.326612\pi$
$523$			39.1189i			1.71055i	−0.518173	+	0.855276i	$0.673388\pi$
$524$	−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	$0.0199034\pi$
$547$			2.92293i			0.124975i	−0.998046	+	0.0624877i	$0.980097\pi$
$548$	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	$0.145350\pi$
$557$			20.8125i			0.881852i	−0.897543	+	0.440926i	$0.854650\pi$
$558$	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	$0.0555347\pi$
$569$			8.28124i			0.347167i	−0.984819	+	0.173584i	$0.944465\pi$
$570$	−37.7344	+	3.70085i	−1.58052	+	0.155011i
$571$		−	31.2373i		−	1.30724i	−0.756822	−	0.653621i	$-0.773249\pi$
$571$		−	31.2373i		−	1.30724i	0.756822	−	0.653621i	$-0.226751\pi$
$572$	−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	$-0.969045\pi$
$593$		−	4.72889i		−	0.194192i	0.995275	−	0.0970961i	$-0.0309554\pi$
$594$	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	$0.0209525\pi$
$607$			3.24114i			0.131554i	−0.997834	+	0.0657768i	$0.979047\pi$
$608$	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	$0.204510\pi$
$617$			29.7670i			1.19837i	−0.800609	+	0.599187i	$0.795490\pi$
$618$	−2.40468	−	24.5184i	−0.0967302	−	0.986277i
$619$		−	21.9159i		−	0.880875i	−0.897783	−	0.440437i	$-0.854823\pi$
$619$		−	21.9159i		−	0.880875i	0.897783	−	0.440437i	$-0.145177\pi$
$620$	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	$-0.845193\pi$
$631$		−	23.4816i		−	0.934788i	0.884049	−	0.467394i	$-0.154807\pi$
$632$	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	$0.310788\pi$
$641$			41.9504i			1.65694i	−0.560033	+	0.828470i	$0.689212\pi$
$642$	−27.6736	+	2.71412i	−1.09219	+	0.107118i
$643$		−	4.08169i		−	0.160966i	−0.996756	−	0.0804831i	$-0.974354\pi$
$643$		−	4.08169i		−	0.160966i	0.996756	−	0.0804831i	$-0.0256463\pi$
$644$	−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	$-0.655411\pi$
$653$		−	45.1364i		−	1.76632i	0.469069	−	0.883161i	$-0.344589\pi$
$654$	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	$0.0665424\pi$
$677$			10.7995i			0.415059i	−0.978229	+	0.207530i	$0.933458\pi$
$678$	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	$0.0210487\pi$
$691$			3.47398i			0.132156i	−0.997814	+	0.0660782i	$0.978951\pi$
$692$	−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	$0.157079\pi$
$701$			25.0833i			0.947383i	−0.880691	+	0.473691i	$0.842921\pi$
$702$	−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	$0.268013\pi$
$727$			40.2270i			1.49194i	−0.665982	+	0.745968i	$0.731987\pi$
$728$	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	$-0.970649\pi$
$739$		−	5.00613i		−	0.184154i	0.995752	−	0.0920768i	$-0.0293505\pi$
$740$	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	$-0.900922\pi$
$751$		−	16.7858i		−	0.612521i	0.951948	−	0.306260i	$-0.0990778\pi$
$752$	−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	$-0.844371\pi$
$761$		−	25.9132i		−	0.939351i	0.882839	−	0.469676i	$-0.155629\pi$
$762$	−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	$-0.797740\pi$
$773$		−	33.0029i		−	1.18703i	0.804823	−	0.593516i	$-0.202260\pi$
$774$	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	$0.216279\pi$
$787$			35.2562i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$788$	−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	$-0.783908\pi$
$797$		−	35.4537i		−	1.25583i	0.778280	−	0.627917i	$-0.216092\pi$
$798$	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	$-0.779690\pi$
$809$		−	36.3030i		−	1.27635i	0.769893	−	0.638173i	$-0.220310\pi$
$810$	−42.9355	+	6.06351i	−1.50860	+	0.213050i
$811$		−	19.5886i		−	0.687850i	−0.938997	−	0.343925i	$-0.888243\pi$
$811$		−	19.5886i		−	0.687850i	0.938997	−	0.343925i	$-0.111757\pi$
$812$	−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	$0.234047\pi$
$821$			38.4408i			1.34159i	−0.741642	+	0.670796i	$0.765953\pi$
$822$	−2.56926	−	26.1966i	−0.0896132	−	0.913710i
$823$			7.11764i			0.248105i	0.992276	+	0.124053i	$0.0395892\pi$
$823$			7.11764i			0.248105i	−0.992276	+	0.124053i	$0.960411\pi$
$824$	−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	$0.0884820\pi$
$857$			16.0664i			0.548817i	−0.961613	+	0.274408i	$0.911518\pi$
$858$	−0.0626448	+	0.00614396i	−0.00213866	+	0.000209751i
$859$			24.1648i			0.824491i	0.911073	+	0.412246i	$0.135255\pi$
$859$			24.1648i			0.824491i	−0.911073	+	0.412246i	$0.864745\pi$
$860$	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	$-0.900045\pi$
$881$		−	18.3362i		−	0.617762i	0.951101	−	0.308881i	$-0.0999545\pi$
$882$	32.6899	−	24.1131i	1.10072	−	0.811932i
$883$		−	5.64834i		−	0.190082i	−0.995473	−	0.0950409i	$-0.969702\pi$
$883$		−	5.64834i		−	0.190082i	0.995473	−	0.0950409i	$-0.0302982\pi$
$884$	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	$0.228616\pi$
$907$			39.6359i			1.31609i	−0.752980	+	0.658044i	$0.771384\pi$
$908$	−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	$-0.748292\pi$
$919$		−	43.1013i		−	1.42178i	0.703302	−	0.710891i	$-0.251708\pi$
$920$	−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	$0.0353561\pi$
$929$			6.75708i			0.221693i	−0.993838	+	0.110846i	$0.964644\pi$
$930$	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	$-0.984948\pi$
$941$		−	2.90008i		−	0.0945399i	0.998882	−	0.0472700i	$-0.0150521\pi$
$942$	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	$-0.826226\pi$
$953$		−	32.0568i		−	1.03842i	0.854647	−	0.519210i	$-0.173774\pi$
$954$	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	$-0.777139\pi$
$967$		−	40.0726i		−	1.28865i	0.764752	−	0.644325i	$-0.222861\pi$
$968$	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	$0.0565025\pi$
$977$			11.0385i			0.353154i	−0.984287	+	0.176577i	$0.943497\pi$
$978$	−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	$0.0523129\pi$
$991$			10.3007i			0.327214i	−0.986526	+	0.163607i	$0.947687\pi$
$992$	−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.671.17	✓	128
3.2	odd	2	inner	804.2.c.b.671.112	yes	128
4.3	odd	2	inner	804.2.c.b.671.111	yes	128
12.11	even	2	inner	804.2.c.b.671.18	yes	128

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