LMFDB - Embedded newform 183.2.g.c.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [183,2,Mod(11,183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(183, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("183.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 183 = 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	183.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.46126235699$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	183.11
Dual form			183.2.g.c.50.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79987 - 1.79987i) q^{2} +(-1.70524 - 0.303587i) q^{3} -4.47903i q^{4} -0.391521 q^{5} +(-3.61561 + 2.52278i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(-4.46193 - 4.46193i) q^{8} +(2.81567 + 1.03538i) q^{9} +O(q^{10})$	\(q+(1.79987 - 1.79987i) q^{2} +(-1.70524 - 0.303587i) q^{3} -4.47903i q^{4} -0.391521 q^{5} +(-3.61561 + 2.52278i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(-4.46193 - 4.46193i) q^{8} +(2.81567 + 1.03538i) q^{9} +(-0.704685 + 0.704685i) q^{10} +(-2.18888 - 2.18888i) q^{11} +(-1.35978 + 7.63781i) q^{12} +5.70332 q^{13} -2.38793 q^{14} +(0.667636 + 0.118861i) q^{15} -7.10367 q^{16} +(2.44623 + 2.44623i) q^{17} +(6.93136 - 3.20429i) q^{18} +4.76840i q^{19} +1.75363i q^{20} +(0.929803 + 1.33258i) q^{21} -7.87938 q^{22} +(2.39114 - 2.39114i) q^{23} +(6.25406 + 8.96323i) q^{24} -4.84671 q^{25} +(10.2652 - 10.2652i) q^{26} +(-4.48706 - 2.62036i) q^{27} +(-2.97122 + 2.97122i) q^{28} +(2.95735 + 2.95735i) q^{29} +(1.41559 - 0.987722i) q^{30} +(6.42776 - 6.42776i) q^{31} +(-3.86180 + 3.86180i) q^{32} +(3.06805 + 4.39708i) q^{33} +8.80576 q^{34} +(0.259720 + 0.259720i) q^{35} +(4.63748 - 12.6115i) q^{36} +(-2.88263 + 2.88263i) q^{37} +(8.58247 + 8.58247i) q^{38} +(-9.72551 - 1.73145i) q^{39} +(1.74694 + 1.74694i) q^{40} -3.26017 q^{41} +(4.07198 + 0.724943i) q^{42} +(-7.40298 + 7.40298i) q^{43} +(-9.80407 + 9.80407i) q^{44} +(-1.10239 - 0.405371i) q^{45} -8.60748i q^{46} +10.0743i q^{47} +(12.1134 + 2.15658i) q^{48} -6.11990i q^{49} +(-8.72343 + 8.72343i) q^{50} +(-3.42875 - 4.91404i) q^{51} -25.5454i q^{52} +(1.16414 - 1.16414i) q^{53} +(-12.7924 + 3.35981i) q^{54} +(0.856992 + 0.856992i) q^{55} +5.91975i q^{56} +(1.44762 - 8.13125i) q^{57} +10.6457 q^{58} +(5.04835 + 5.04835i) q^{59} +(0.532380 - 2.99036i) q^{60} +(-1.72475 + 7.61743i) q^{61} -23.1382i q^{62} +(-1.18098 - 2.55464i) q^{63} -0.305907i q^{64} -2.23297 q^{65} +(13.4362 + 2.39208i) q^{66} +(-2.77574 + 2.77574i) q^{67} +(10.9567 - 10.9567i) q^{68} +(-4.80339 + 3.35155i) q^{69} +0.934923 q^{70} +(-8.79121 - 8.79121i) q^{71} +(-7.94354 - 17.1831i) q^{72} -11.4364 q^{73} +10.3767i q^{74} +(8.26479 + 1.47140i) q^{75} +21.3578 q^{76} +2.90404i q^{77} +(-20.6210 + 14.3882i) q^{78} +(1.86878 + 1.86878i) q^{79} +2.78123 q^{80} +(6.85599 + 5.83055i) q^{81} +(-5.86786 + 5.86786i) q^{82} -5.41338i q^{83} +(5.96866 - 4.16462i) q^{84} +(-0.957748 - 0.957748i) q^{85} +26.6487i q^{86} +(-4.14517 - 5.94079i) q^{87} +19.5332i q^{88} +(10.3517 + 10.3517i) q^{89} +(-2.71377 + 1.25455i) q^{90} +(-3.78337 - 3.78337i) q^{91} +(-10.7100 - 10.7100i) q^{92} +(-12.9122 + 9.00947i) q^{93} +(18.1324 + 18.1324i) q^{94} -1.86693i q^{95} +(7.75767 - 5.41289i) q^{96} -3.49985i q^{97} +(-11.0150 - 11.0150i) q^{98} +(-3.89685 - 8.42948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/183\mathbb{Z}\right)^\times$.

$n$	$62$	$124$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.79987	−	1.79987i	1.27270	−	1.27270i	0.328030	−	0.944667i	$-0.393615\pi$
$2$	1.79987	−	1.79987i	1.27270	−	1.27270i	0.944667	−	0.328030i	$-0.106385\pi$
$3$	−1.70524	−	0.303587i	−0.984519	−	0.175276i
$3$	−1.70524	−	0.303587i	−0.984519	−	0.175276i
$4$		−	4.47903i		−	2.23952i
$5$	−0.391521			−0.175093			−0.0875467	−	0.996160i	$-0.527903\pi$
$5$	−0.391521			−0.175093			−0.0875467	+	0.996160i	$0.527903\pi$
$6$	−3.61561	+	2.52278i	−1.47607	+	1.02992i
$7$	−0.663363	−	0.663363i	−0.250728	−	0.250728i	0.570541	−	0.821269i	$-0.306733\pi$
$7$	−0.663363	−	0.663363i	−0.250728	−	0.250728i	−0.821269	+	0.570541i	$0.806733\pi$
$8$	−4.46193	−	4.46193i	−1.57753	−	1.57753i
$9$	2.81567	+	1.03538i	0.938557	+	0.345125i
$10$	−0.704685	+	0.704685i	−0.222841	+	0.222841i
$11$	−2.18888	−	2.18888i	−0.659972	−	0.659972i	0.295401	−	0.955373i	$-0.404547\pi$
$11$	−2.18888	−	2.18888i	−0.659972	−	0.659972i	−0.955373	+	0.295401i	$0.904547\pi$
$12$	−1.35978	+	7.63781i	−0.392533	+	2.20485i
$13$	5.70332			1.58182			0.790908	−	0.611935i	$-0.209609\pi$
$13$	5.70332			1.58182			0.790908	+	0.611935i	$0.209609\pi$
$14$	−2.38793			−0.638200
$15$	0.667636	+	0.118861i	0.172383	+	0.0306897i
$16$	−7.10367			−1.77592
$17$	2.44623	+	2.44623i	0.593297	+	0.593297i	0.938521	−	0.345223i	$-0.112197\pi$
$17$	2.44623	+	2.44623i	0.593297	+	0.593297i	−0.345223	+	0.938521i	$0.612197\pi$
$18$	6.93136	−	3.20429i	1.63374	−	0.755259i
$19$			4.76840i			1.09395i	0.837151	+	0.546973i	$0.184220\pi$
$19$			4.76840i			1.09395i	−0.837151	+	0.546973i	$0.815780\pi$
$20$			1.75363i			0.392125i
$21$	0.929803	+	1.33258i	0.202900	+	0.290793i
$22$	−7.87938			−1.67989
$23$	2.39114	−	2.39114i	0.498588	−	0.498588i	−0.412410	−	0.910998i	$-0.635313\pi$
$23$	2.39114	−	2.39114i	0.498588	−	0.498588i	0.910998	+	0.412410i	$0.135313\pi$
$24$	6.25406	+	8.96323i	1.27660	+	1.82961i
$25$	−4.84671			−0.969342
$26$	10.2652	−	10.2652i	2.01317	−	2.01317i
$27$	−4.48706	−	2.62036i	−0.863535	−	0.504289i
$28$	−2.97122	+	2.97122i	−0.561508	+	0.561508i
$29$	2.95735	+	2.95735i	0.549166	+	0.549166i	0.926200	−	0.377034i	$-0.123056\pi$
$29$	2.95735	+	2.95735i	0.549166	+	0.549166i	−0.377034	+	0.926200i	$0.623056\pi$
$30$	1.41559	−	0.987722i	0.258450	−	0.180332i
$31$	6.42776	−	6.42776i	1.15446	−	1.15446i	0.168811	−	0.985648i	$-0.446007\pi$
$31$	6.42776	−	6.42776i	1.15446	−	1.15446i	0.985648	−	0.168811i	$-0.0539929\pi$
$32$	−3.86180	+	3.86180i	−0.682676	+	0.682676i
$33$	3.06805	+	4.39708i	0.534078	+	0.765433i
$34$	8.80576			1.51018
$35$	0.259720	+	0.259720i	0.0439007	+	0.0439007i
$36$	4.63748	−	12.6115i	0.772914	−	2.10191i
$37$	−2.88263	+	2.88263i	−0.473901	+	0.473901i	−0.903175	−	0.429274i	$-0.858770\pi$
$37$	−2.88263	+	2.88263i	−0.473901	+	0.473901i	0.429274	+	0.903175i	$0.358770\pi$
$38$	8.58247	+	8.58247i	1.39226	+	1.39226i
$39$	−9.72551	−	1.73145i	−1.55733	−	0.277254i
$40$	1.74694	+	1.74694i	0.276215	+	0.276215i
$41$	−3.26017			−0.509152			−0.254576	−	0.967053i	$-0.581936\pi$
$41$	−3.26017			−0.509152			−0.254576	+	0.967053i	$0.581936\pi$
$42$	4.07198	+	0.724943i	0.628321	+	0.111861i
$43$	−7.40298	+	7.40298i	−1.12894	+	1.12894i	−0.138595	+	0.990349i	$0.544259\pi$
$43$	−7.40298	+	7.40298i	−1.12894	+	1.12894i	−0.990349	+	0.138595i	$0.955741\pi$
$44$	−9.80407	+	9.80407i	−1.47802	+	1.47802i
$45$	−1.10239	−	0.405371i	−0.164335	−	0.0604291i
$46$		−	8.60748i		−	1.26910i
$47$			10.0743i			1.46949i	0.678343	+	0.734745i	$0.262698\pi$
$47$			10.0743i			1.46949i	−0.678343	+	0.734745i	$0.737302\pi$
$48$	12.1134	+	2.15658i	1.74842	+	0.311276i
$49$		−	6.11990i		−	0.874271i
$50$	−8.72343	+	8.72343i	−1.23368	+	1.23368i
$51$	−3.42875	−	4.91404i	−0.480122	−	0.688103i
$52$		−	25.5454i		−	3.54250i
$53$	1.16414	−	1.16414i	0.159907	−	0.159907i	−0.622619	−	0.782525i	$-0.713931\pi$
$53$	1.16414	−	1.16414i	0.159907	−	0.159907i	0.782525	+	0.622619i	$0.213931\pi$
$54$	−12.7924	+	3.35981i	−1.74083	+	0.457212i
$55$	0.856992	+	0.856992i	0.115557	+	0.115557i
$56$			5.91975i			0.791060i
$57$	1.44762	−	8.13125i	0.191742	−	1.07701i
$58$	10.6457			1.39784
$59$	5.04835	+	5.04835i	0.657240	+	0.657240i	0.954726	−	0.297486i	$-0.0961483\pi$
$59$	5.04835	+	5.04835i	0.657240	+	0.657240i	−0.297486	+	0.954726i	$0.596148\pi$
$60$	0.532380	−	2.99036i	0.0687300	−	0.386054i
$61$	−1.72475	+	7.61743i	−0.220832	+	0.975312i
$61$	−1.72475	+	7.61743i	−0.220832	+	0.975312i
$62$		−	23.1382i		−	2.93856i
$63$	−1.18098	−	2.55464i	−0.148790	−	0.321854i
$64$		−	0.305907i		−	0.0382383i
$65$	−2.23297			−0.276966
$66$	13.4362	+	2.39208i	1.65388	+	0.294444i
$67$	−2.77574	+	2.77574i	−0.339111	+	0.339111i	−0.856033	−	0.516922i	$-0.827078\pi$
$67$	−2.77574	+	2.77574i	−0.339111	+	0.339111i	0.516922	+	0.856033i	$0.327078\pi$
$68$	10.9567	−	10.9567i	1.32870	−	1.32870i
$69$	−4.80339	+	3.35155i	−0.578260	+	0.403479i
$70$	0.934923			0.111745
$71$	−8.79121	−	8.79121i	−1.04332	−	1.04332i	−0.999018	−	0.0443063i	$-0.985892\pi$
$71$	−8.79121	−	8.79121i	−1.04332	−	1.04332i	−0.0443063	−	0.999018i	$-0.514108\pi$
$72$	−7.94354	−	17.1831i	−0.936155	−	2.02505i
$73$	−11.4364			−1.33853			−0.669266	−	0.743023i	$-0.733391\pi$
$73$	−11.4364			−1.33853			−0.669266	+	0.743023i	$0.733391\pi$
$74$			10.3767i			1.20626i
$75$	8.26479	+	1.47140i	0.954336	+	0.169902i
$76$	21.3578			2.44991
$77$			2.90404i			0.330946i
$78$	−20.6210	+	14.3882i	−2.33487	+	1.62915i
$79$	1.86878	+	1.86878i	0.210255	+	0.210255i	0.804376	−	0.594121i	$-0.202500\pi$
$79$	1.86878	+	1.86878i	0.210255	+	0.210255i	−0.594121	+	0.804376i	$0.702500\pi$
$80$	2.78123			0.310951
$81$	6.85599	+	5.83055i	0.761777	+	0.647839i
$82$	−5.86786	+	5.86786i	−0.647997	+	0.647997i
$83$		−	5.41338i		−	0.594195i	−0.954847	−	0.297098i	$-0.903981\pi$
$83$		−	5.41338i		−	0.594195i	0.954847	−	0.297098i	$-0.0960187\pi$
$84$	5.96866	−	4.16462i	0.651235	−	0.454397i
$85$	−0.957748	−	0.957748i	−0.103882	−	0.103882i
$86$			26.6487i			2.87361i
$87$	−4.14517	−	5.94079i	−0.444409	−	0.636920i
$88$			19.5332i			2.08225i
$89$	10.3517	+	10.3517i	1.09728	+	1.09728i	0.994727	+	0.102556i	$0.0327020\pi$
$89$	10.3517	+	10.3517i	1.09728	+	1.09728i	0.102556	+	0.994727i	$0.467298\pi$
$90$	−2.71377	+	1.25455i	−0.286057	+	0.132241i
$91$	−3.78337	−	3.78337i	−0.396605	−	0.396605i
$92$	−10.7100	−	10.7100i	−1.11660	−	1.11660i
$93$	−12.9122	+	9.00947i	−1.33894	+	0.934239i
$94$	18.1324	+	18.1324i	1.87022	+	1.87022i
$95$		−	1.86693i		−	0.191543i
$96$	7.75767	−	5.41289i	0.791764	−	0.552451i
$97$		−	3.49985i		−	0.355356i	−0.984089	−	0.177678i	$-0.943141\pi$
$97$		−	3.49985i		−	0.355356i	0.984089	−	0.177678i	$-0.0568586\pi$
$98$	−11.0150	−	11.0150i	−1.11268	−	1.11268i
$99$	−3.89685	−	8.42948i	−0.391648	−	0.847194i
$100$			21.7086i			2.17086i
$101$	−1.50782	+	1.50782i	−0.150034	+	0.150034i	−0.778133	−	0.628099i	$-0.783833\pi$
$101$	−1.50782	+	1.50782i	−0.150034	+	0.150034i	0.628099	+	0.778133i	$0.283833\pi$
$102$	−15.0159	−	2.67331i	−1.48680	−	0.264697i
$103$	−7.67833			−0.756568			−0.378284	−	0.925690i	$-0.623486\pi$
$103$	−7.67833			−0.756568			−0.378284	+	0.925690i	$0.623486\pi$
$104$	−25.4478	−	25.4478i	−2.49536	−	2.49536i
$105$	−0.364037	−	0.521732i	−0.0355264	−	0.0509159i
$106$		−	4.19059i		−	0.407026i
$107$	−2.63497			−0.254732			−0.127366	−	0.991856i	$-0.540652\pi$
$107$	−2.63497			−0.254732			−0.127366	+	0.991856i	$0.540652\pi$
$108$	−11.7367	+	20.0977i	−1.12936	+	1.93390i
$109$		−	0.711454i		−	0.0681450i	−0.999419	−	0.0340725i	$-0.989152\pi$
$109$		−	0.711454i		−	0.0681450i	0.999419	−	0.0340725i	$-0.0108477\pi$
$110$	3.08494			0.294138
$111$	5.79069	−	4.04044i	0.549628	−	0.383501i
$112$	4.71231	+	4.71231i	0.445271	+	0.445271i
$113$	19.6197			1.84566			0.922832	−	0.385202i	$-0.125868\pi$
$113$	19.6197			1.84566			0.922832	+	0.385202i	$0.125868\pi$
$114$	−12.0296	−	17.2407i	−1.12668	−	1.61474i
$115$	−0.936183	+	0.936183i	−0.0872995	+	0.0872995i
$116$	13.2461	−	13.2461i	1.22987	−	1.22987i
$117$	16.0587	+	5.90508i	1.48462	+	0.545925i
$118$	18.1727			1.67293
$119$		−	3.24547i		−	0.297512i
$120$	−2.44859	−	3.50929i	−0.223525	−	0.320353i
$121$		−	1.41761i		−	0.128873i
$122$	10.6060	+	16.8147i	0.960225	+	1.52233i
$123$	5.55936	+	0.989744i	0.501270	+	0.0892422i
$124$	−28.7901	−	28.7901i	−2.58543	−	2.58543i
$125$	3.85519			0.344819
$126$	−6.72361	−	2.47240i	−0.598987	−	0.220259i
$127$			0.376694i			0.0334262i	0.999860	+	0.0167131i	$0.00532019\pi$
$127$			0.376694i			0.0334262i	−0.999860	+	0.0167131i	$0.994680\pi$
$128$	−8.27418	−	8.27418i	−0.731341	−	0.731341i
$129$	14.8713	−	10.3764i	1.30934	−	0.913590i
$130$	−4.01904	+	4.01904i	−0.352493	+	0.352493i
$131$		−	10.2228i		−	0.893169i	−0.894742	−	0.446584i	$-0.852640\pi$
$131$		−	10.2228i		−	0.893169i	0.894742	−	0.446584i	$-0.147360\pi$
$132$	19.6946	−	13.7419i	1.71420	−	1.19608i
$133$	3.16318	−	3.16318i	0.274282	−	0.274282i
$134$			9.99192i			0.863170i
$135$	1.75678	+	1.02593i	0.151199	+	0.0882977i
$136$		−	21.8298i		−	1.87189i
$137$		−	10.7179i		−	0.915695i	−0.889031	−	0.457847i	$-0.848621\pi$
$137$		−	10.7179i		−	0.915695i	0.889031	−	0.457847i	$-0.151379\pi$
$138$	−2.61312	+	14.6778i	−0.222443	+	1.24946i
$139$	0.0726317	−	0.0726317i	0.00616054	−	0.00616054i	−0.704020	−	0.710180i	$-0.748613\pi$
$139$	0.0726317	−	0.0726317i	0.00616054	−	0.00616054i	0.710180	+	0.704020i	$0.248613\pi$
$140$	1.16330	−	1.16330i	0.0983164	−	0.0983164i
$141$	3.05843	−	17.1791i	0.257566	−	1.44674i
$142$	−31.6460			−2.65567
$143$	−12.4839	−	12.4839i	−1.04395	−	1.04395i
$144$	−20.0016	−	7.35496i	−1.66680	−	0.612914i
$145$	−1.15786	−	1.15786i	−0.0961553	−	0.0961553i
$146$	−20.5840	+	20.5840i	−1.70355	+	1.70355i
$147$	−1.85792	+	10.4359i	−0.153239	+	0.860737i
$148$	12.9114	+	12.9114i	1.06131	+	1.06131i
$149$	9.53197			0.780889			0.390445	−	0.920626i	$-0.372321\pi$
$149$	9.53197			0.780889			0.390445	+	0.920626i	$0.372321\pi$
$150$	17.5238	−	12.2272i	1.43082	−	0.998347i
$151$	8.00673	−	8.00673i	0.651579	−	0.651579i	−0.301794	−	0.953373i	$-0.597586\pi$
$151$	8.00673	−	8.00673i	0.651579	−	0.651579i	0.953373	+	0.301794i	$0.0975856\pi$
$152$	21.2762	−	21.2762i	1.72573	−	1.72573i
$153$	4.35500	+	9.42053i	0.352081	+	0.761605i
$154$	5.22689	+	5.22689i	0.421195	+	0.421195i
$155$	−2.51660	+	2.51660i	−0.202138	+	0.202138i
$156$	−7.75523	+	43.5609i	−0.620916	+	3.48766i
$157$	−9.87449	+	9.87449i	−0.788070	+	0.788070i	−0.981178	−	0.193107i	$-0.938143\pi$
$157$	−9.87449	+	9.87449i	−0.788070	+	0.788070i	0.193107	+	0.981178i	$0.438143\pi$
$158$	6.72712			0.535181
$159$	−2.33855	+	1.63172i	−0.185459	+	0.129403i
$160$	1.51197	−	1.51197i	0.119532	−	0.119532i
$161$	−3.17239			−0.250020
$162$	22.8341	−	1.84566i	1.79401	−	0.145009i
$163$			13.8507i			1.08487i	0.840097	+	0.542437i	$0.182498\pi$
$163$			13.8507i			1.08487i	−0.840097	+	0.542437i	$0.817502\pi$
$164$			14.6024i			1.14025i
$165$	−1.20120	−	1.72155i	−0.0935136	−	0.134022i
$166$	−9.74335	−	9.74335i	−0.756231	−	0.756231i
$167$	−2.80077			−0.216730			−0.108365	−	0.994111i	$-0.534562\pi$
$167$	−2.80077			−0.216730			−0.108365	+	0.994111i	$0.534562\pi$
$168$	1.79716	−	10.0946i	0.138654	−	0.778814i
$169$	19.5278			1.50214
$170$	−3.44764			−0.264422
$171$	−4.93708	+	13.4262i	−0.377548	+	1.02673i
$172$	33.1582	+	33.1582i	2.52829	+	2.52829i
$173$	−17.3471	+	17.3471i	−1.31888	+	1.31888i	−0.404209	+	0.914667i	$0.632453\pi$
$173$	−17.3471	+	17.3471i	−1.31888	+	1.31888i	−0.914667	+	0.404209i	$0.867547\pi$
$174$	−18.1534	−	3.23188i	−1.37620	−	0.245008i
$175$	3.21513	+	3.21513i	0.243041	+	0.243041i
$176$	15.5491	+	15.5491i	1.17206	+	1.17206i
$177$	−7.07603	−	10.1413i	−0.531867	−	0.762264i
$178$	37.2635			2.79302
$179$		−	18.4014i		−	1.37539i	−0.726001	−	0.687694i	$-0.758623\pi$
$179$		−	18.4014i		−	1.37539i	0.726001	−	0.687694i	$-0.241377\pi$
$180$	−1.81567	+	4.93765i	−0.135332	+	0.368031i
$181$	2.87325	−	2.87325i	0.213567	−	0.213567i	−0.592214	−	0.805781i	$-0.701746\pi$
$181$	2.87325	−	2.87325i	0.213567	−	0.213567i	0.805781	+	0.592214i	$0.201746\pi$
$182$	−13.6191			−1.00952
$183$	5.25366	−	12.4659i	0.388362	−	0.921507i
$184$	−21.3382			−1.57307
$185$	1.12861	−	1.12861i	0.0829769	−	0.0829769i
$186$	−7.02446	+	39.4561i	−0.515058	+	2.89306i
$187$		−	10.7090i		−	0.783119i
$188$	45.1232			3.29095
$189$	1.23830	+	4.71480i	0.0900729	+	0.342951i
$190$	−3.36022	−	3.36022i	−0.243776	−	0.243776i
$191$	6.47982	+	6.47982i	0.468863	+	0.468863i	0.901546	−	0.432683i	$-0.142433\pi$
$191$	6.47982	+	6.47982i	0.468863	+	0.468863i	−0.432683	+	0.901546i	$0.642433\pi$
$192$	−0.0928693	+	0.521644i	−0.00670226	+	0.0376464i
$193$	3.43734	−	3.43734i	0.247425	−	0.247425i	−0.572488	−	0.819913i	$-0.694022\pi$
$193$	3.43734	−	3.43734i	0.247425	−	0.247425i	0.819913	+	0.572488i	$0.194022\pi$
$194$	−6.29926	−	6.29926i	−0.452261	−	0.452261i
$195$	3.80774	+	0.677900i	0.272678	+	0.0485454i
$196$	−27.4112			−1.95795
$197$	−18.9624			−1.35101			−0.675506	−	0.737355i	$-0.736075\pi$
$197$	−18.9624			−1.35101			−0.675506	+	0.737355i	$0.736075\pi$
$198$	−22.1857	−	8.15812i	−1.57667	−	0.579772i
$199$	13.8999			0.985340			0.492670	−	0.870216i	$-0.336021\pi$
$199$	13.8999			0.985340			0.492670	+	0.870216i	$0.336021\pi$
$200$	21.6257	+	21.6257i	1.52917	+	1.52917i
$201$	5.57597	−	3.89062i	0.393299	−	0.274423i
$202$			5.42776i			0.381896i
$203$		−	3.92359i		−	0.275382i
$204$	−22.0101	+	15.3575i	−1.54102	+	1.07524i
$205$	1.27642			0.0891492
$206$	−13.8200	+	13.8200i	−0.962882	+	0.962882i
$207$	9.20841	−	4.25694i	0.640029	−	0.295878i
$208$	−40.5145			−2.80917
$209$	10.4374	−	10.4374i	0.721973	−	0.721973i
$210$	−1.59427	−	0.283830i	−0.110015	−	0.0195862i
$211$	−10.3273	+	10.3273i	−0.710960	+	0.710960i	−0.966736	−	0.255776i	$-0.917669\pi$
$211$	−10.3273	+	10.3273i	−0.710960	+	0.710960i	0.255776	+	0.966736i	$0.417669\pi$
$212$	−5.21422	−	5.21422i	−0.358114	−	0.358114i
$213$	12.3222	+	17.6600i	0.844303	+	1.21004i
$214$	−4.74259	+	4.74259i	−0.324197	+	0.324197i
$215$	2.89842	−	2.89842i	0.197671	−	0.197671i
$216$	8.32907	+	31.7128i	0.566721	+	2.15778i
$217$	−8.52787			−0.578910
$218$	−1.28052	−	1.28052i	−0.0867279	−	0.0867279i
$219$	19.5018	+	3.47195i	1.31781	+	0.234612i
$220$	3.83850	−	3.83850i	0.258791	−	0.258791i
$221$	13.9516	+	13.9516i	0.938487	+	0.938487i
$222$	3.15022	−	17.6947i	0.211429	−	1.18759i
$223$	11.9527	+	11.9527i	0.800410	+	0.800410i	0.983160	−	0.182749i	$-0.0584997\pi$
$223$	11.9527	+	11.9527i	0.800410	+	0.800410i	−0.182749	+	0.983160i	$0.558500\pi$
$224$	5.12354			0.342331
$225$	−13.6467	−	5.01817i	−0.909783	−	0.334544i
$226$	35.3128	−	35.3128i	2.34897	−	2.34897i
$227$	2.73246	−	2.73246i	0.181360	−	0.181360i	−0.610589	−	0.791948i	$-0.709067\pi$
$227$	2.73246	−	2.73246i	0.181360	−	0.181360i	0.791948	+	0.610589i	$0.209067\pi$
$228$	−36.4201	−	6.48395i	−2.41198	−	0.429410i
$229$		−	24.6475i		−	1.62875i	−0.580336	−	0.814377i	$-0.697079\pi$
$229$		−	24.6475i		−	1.62875i	0.580336	−	0.814377i	$-0.302921\pi$
$230$			3.37001i			0.222212i
$231$	0.881629	−	4.95208i	0.0580070	−	0.325823i
$232$		−	26.3909i		−	1.73265i
$233$	−4.30207	+	4.30207i	−0.281838	+	0.281838i	−0.833842	−	0.552004i	$-0.813863\pi$
$233$	−4.30207	+	4.30207i	−0.281838	+	0.281838i	0.552004	+	0.833842i	$0.313863\pi$
$234$	39.5318	−	18.2751i	2.58427	−	1.19468i
$235$		−	3.94430i		−	0.257298i
$236$	22.6117	−	22.6117i	1.47190	−	1.47190i
$237$	−2.61938	−	3.75406i	−0.170147	−	0.243852i
$238$	−5.84141	−	5.84141i	−0.378642	−	0.378642i
$239$			1.85284i			0.119850i	0.998203	+	0.0599250i	$0.0190862\pi$
$239$			1.85284i			0.119850i	−0.998203	+	0.0599250i	$0.980914\pi$
$240$	−4.74266	−	0.844346i	−0.306138	−	0.0545023i
$241$	−2.20404			−0.141975			−0.0709874	−	0.997477i	$-0.522615\pi$
$241$	−2.20404			−0.141975			−0.0709874	+	0.997477i	$0.522615\pi$
$242$	−2.55150	−	2.55150i	−0.164017	−	0.164017i
$243$	−9.92102	−	12.0239i	−0.636434	−	0.771331i
$244$	34.1187	+	7.72522i	2.18423	+	0.494557i
$245$			2.39607i			0.153079i
$246$	11.7875	−	8.22469i	0.751544	−	0.524387i
$247$			27.1957i			1.73042i
$248$	−57.3604			−3.64239
$249$	−1.64343	+	9.23109i	−0.104148	+	0.584997i
$250$	6.93883	−	6.93883i	0.438850	−	0.438850i
$251$	−18.0661	+	18.0661i	−1.14032	+	1.14032i	−0.151929	+	0.988391i	$0.548548\pi$
$251$	−18.0661	+	18.0661i	−1.14032	+	1.14032i	−0.988391	+	0.151929i	$0.951452\pi$
$252$	−11.4423	+	5.28965i	−0.720798	+	0.333217i
$253$	−10.4679			−0.658109
$254$	0.677999	+	0.677999i	0.0425414	+	0.0425414i
$255$	1.34243	+	1.92395i	0.0840661	+	0.120482i
$256$	−29.1730			−1.82331
$257$			9.82678i			0.612978i	0.951874	+	0.306489i	$0.0991542\pi$
$257$			9.82678i			0.612978i	−0.951874	+	0.306489i	$0.900846\pi$
$258$	8.09021	−	45.4424i	0.503674	−	2.82912i
$259$	3.82445			0.237640
$260$			10.0015i			0.620269i
$261$	5.26495	+	11.3889i	0.325892	+	0.704954i
$262$	−18.3996	−	18.3996i	−1.13673	−	1.13673i
$263$	−14.8597			−0.916291			−0.458145	−	0.888877i	$-0.651486\pi$
$263$	−14.8597			−0.916291			−0.458145	+	0.888877i	$0.651486\pi$
$264$	5.93004	−	33.3088i	0.364969	−	2.05002i
$265$	−0.455785	+	0.455785i	−0.0279986	+	0.0279986i
$266$		−	11.3866i		−	0.698156i
$267$	−14.5095	−	20.7948i	−0.887969	−	1.27262i
$268$	12.4326	+	12.4326i	0.759444	+	0.759444i
$269$		−	17.7465i		−	1.08202i	−0.841015	−	0.541012i	$-0.818041\pi$
$269$		−	17.7465i		−	1.08202i	0.841015	−	0.541012i	$-0.181959\pi$
$270$	5.00849	−	1.31543i	0.304807	−	0.0800547i
$271$			2.48831i			0.151154i	0.997140	+	0.0755769i	$0.0240798\pi$
$271$			2.48831i			0.151154i	−0.997140	+	0.0755769i	$0.975920\pi$
$272$	−17.3772	−	17.3772i	−1.05365	−	1.05365i
$273$	5.30296	+	7.60012i	0.320950	+	0.459980i
$274$	−19.2908	−	19.2908i	−1.16540	−	1.16540i
$275$	10.6089	+	10.6089i	0.639739	+	0.639739i
$276$	15.0117	+	21.5145i	0.903598	+	1.29502i
$277$	−19.0307	−	19.0307i	−1.14344	−	1.14344i	−0.987816	−	0.155626i	$-0.950260\pi$
$277$	−19.0307	−	19.0307i	−1.14344	−	1.14344i	−0.155626	−	0.987816i	$-0.549740\pi$
$278$		−	0.261455i		−	0.0156810i
$279$	24.7536	−	11.4433i	1.48196	−	0.685093i
$280$		−	2.31770i		−	0.138509i
$281$	−2.10759	−	2.10759i	−0.125728	−	0.125728i	0.641443	−	0.767171i	$-0.278336\pi$
$281$	−2.10759	−	2.10759i	−0.125728	−	0.125728i	−0.767171	+	0.641443i	$0.778336\pi$
$282$	−25.4153	−	36.4248i	−1.51346	−	2.16907i
$283$			16.3591i			0.972447i	0.873835	+	0.486223i	$0.161626\pi$
$283$			16.3591i			0.972447i	−0.873835	+	0.486223i	$0.838374\pi$
$284$	−39.3761	+	39.3761i	−2.33654	+	2.33654i
$285$	−0.566774	+	3.18355i	−0.0335728	+	0.188577i
$286$	−44.9386			−2.65728
$287$	2.16267	+	2.16267i	0.127658	+	0.127658i
$288$	−14.8720	+	6.87513i	−0.876338	+	0.405121i
$289$		−	5.03195i		−	0.295997i
$290$	−4.16800			−0.244753
$291$	−1.06251	+	5.96808i	−0.0622854	+	0.349855i
$292$			51.2241i			2.99766i
$293$	−17.4544			−1.01969			−0.509847	−	0.860265i	$-0.670298\pi$
$293$	−17.4544			−1.01969			−0.509847	+	0.860265i	$0.670298\pi$
$294$	15.4392	+	22.1272i	0.900431	+	1.29048i
$295$	−1.97654	−	1.97654i	−0.115078	−	0.115078i
$296$	25.7241			1.49518
$297$	4.08598	+	15.5573i	0.237092	+	0.902726i
$298$	17.1563	−	17.1563i	0.993836	−	0.993836i
$299$	13.6375	−	13.6375i	0.788675	−	0.788675i
$300$	6.59044	−	37.0183i	0.380499	−	2.13725i
$301$	9.82172			0.566115
$302$		−	28.8221i		−	1.65852i
$303$	3.02895	−	2.11344i	0.174009	−	0.121414i
$304$		−	33.8731i		−	1.94276i
$305$	0.675276	−	2.98238i	0.0386662	−	0.170771i
$306$	24.7941	+	9.11727i	1.41738	+	0.521199i
$307$	0.460601	+	0.460601i	0.0262879	+	0.0262879i	0.720129	−	0.693841i	$-0.244083\pi$
$307$	0.460601	+	0.460601i	0.0262879	+	0.0262879i	−0.693841	+	0.720129i	$0.744083\pi$
$308$	13.0073			0.741160
$309$	13.0934	+	2.33104i	0.744856	+	0.132608i
$310$			9.05909i			0.514522i
$311$	−8.81079	−	8.81079i	−0.499614	−	0.499614i	0.411704	−	0.911318i	$-0.364934\pi$
$311$	−8.81079	−	8.81079i	−0.499614	−	0.499614i	−0.911318	+	0.411704i	$0.864934\pi$
$312$	35.6689	+	51.1201i	2.01935	+	2.89411i
$313$	6.06190	−	6.06190i	0.342639	−	0.342639i	−0.514720	−	0.857358i	$-0.672104\pi$
$313$	6.06190	−	6.06190i	0.342639	−	0.342639i	0.857358	+	0.514720i	$0.172104\pi$
$314$			35.5455i			2.00595i
$315$	0.462378	+	1.00019i	0.0260521	+	0.0563546i
$316$	8.37034	−	8.37034i	0.470869	−	0.470869i
$317$			0.297271i			0.0166964i	0.999965	+	0.00834819i	$0.00265734\pi$
$317$			0.297271i			0.0166964i	−0.999965	+	0.00834819i	$0.997343\pi$
$318$	−1.27221	+	7.14595i	−0.0713419	+	0.400725i
$319$		−	12.9466i		−	0.724868i
$320$			0.119769i			0.00669528i
$321$	4.49325	+	0.799943i	0.250789	+	0.0446484i
$322$	−5.70988	+	5.70988i	−0.318199	+	0.318199i
$323$	−11.6646	+	11.6646i	−0.649034	+	0.649034i
$324$	26.1152	−	30.7082i	1.45085	−	1.70601i
$325$	−27.6423			−1.53332
$326$	24.9295	+	24.9295i	1.38072	+	1.38072i
$327$	−0.215988	+	1.21320i	−0.0119442	+	0.0670900i
$328$	14.5466	+	14.5466i	0.803203	+	0.803203i
$329$	6.68293	−	6.68293i	0.368442	−	0.368442i
$330$	−5.26056	−	0.936548i	−0.289584	−	0.0515553i
$331$	7.79724	+	7.79724i	0.428575	+	0.428575i	0.888143	−	0.459568i	$-0.151996\pi$
$331$	7.79724	+	7.79724i	0.428575	+	0.428575i	−0.459568	+	0.888143i	$0.651996\pi$
$332$	−24.2467			−1.33071
$333$	−11.1011	+	5.13192i	−0.608338	+	0.281228i
$334$	−5.04102	+	5.04102i	−0.275832	+	0.275832i
$335$	1.08676	−	1.08676i	0.0593760	−	0.0593760i
$336$	−6.60501	−	9.46620i	−0.360333	−	0.516423i
$337$	−17.8635	−	17.8635i	−0.973084	−	0.973084i	0.0265628	−	0.999647i	$-0.491544\pi$
$337$	−17.8635	−	17.8635i	−0.973084	−	0.973084i	−0.999647	+	0.0265628i	$0.991544\pi$
$338$	35.1475	−	35.1475i	1.91177	−	1.91177i
$339$	−33.4562	−	5.95628i	−1.81709	−	0.323501i
$340$	−4.28979	+	4.28979i	−0.232646	+	0.232646i
$341$	−28.1392			−1.52382
$342$	15.2793	+	33.0515i	0.826211	+	1.78722i
$343$	−8.70325	+	8.70325i	−0.469931	+	0.469931i
$344$	66.0631			3.56188
$345$	1.88063	−	1.31220i	0.101250	−	0.0706465i
$346$			62.4449i			3.35706i
$347$			6.13041i			0.329098i	0.986369	+	0.164549i	$0.0526168\pi$
$347$			6.13041i			0.329098i	−0.986369	+	0.164549i	$0.947383\pi$
$348$	−26.6090	+	18.5663i	−1.42639	+	0.995261i
$349$	17.2170	+	17.2170i	0.921606	+	0.921606i	0.997143	−	0.0755369i	$-0.0240671\pi$
$349$	17.2170	+	17.2170i	0.921606	+	0.921606i	−0.0755369	+	0.997143i	$0.524067\pi$
$350$	11.5736			0.618635
$351$	−25.5911	−	14.9448i	−1.36595	−	0.797692i
$352$	16.9060			0.901094
$353$	−2.78490			−0.148225			−0.0741126	−	0.997250i	$-0.523612\pi$
$353$	−2.78490			−0.148225			−0.0741126	+	0.997250i	$0.523612\pi$
$354$	−30.9888	−	5.51700i	−1.64704	−	0.293225i
$355$	3.44194	+	3.44194i	0.182679	+	0.182679i
$356$	46.3658	−	46.3658i	2.45738	−	2.45738i
$357$	−0.985282	+	5.53430i	−0.0521467	+	0.292906i
$358$	−33.1201	−	33.1201i	−1.75045	−	1.75045i
$359$	0.310453	+	0.310453i	0.0163851	+	0.0163851i	0.715252	−	0.698867i	$-0.246312\pi$
$359$	0.310453	+	0.310453i	0.0163851	+	0.0163851i	−0.698867	+	0.715252i	$0.746312\pi$
$360$	3.11006	+	6.72753i	0.163915	+	0.354572i
$361$	−3.73760			−0.196716
$362$		−	10.3429i		−	0.543612i
$363$	−0.430366	+	2.41735i	−0.0225884	+	0.126878i
$364$	−16.9458	+	16.9458i	−0.888203	+	0.888203i
$365$	4.47759			0.234368
$366$	−12.9811	−	31.8929i	−0.678532	−	1.66707i
$367$	−18.6336			−0.972666			−0.486333	−	0.873773i	$-0.661666\pi$
$367$	−18.6336			−0.972666			−0.486333	+	0.873773i	$0.661666\pi$
$368$	−16.9859	+	16.9859i	−0.885451	+	0.885451i
$369$	−9.17955	−	3.37550i	−0.477868	−	0.175721i
$370$		−	4.06269i		−	0.211209i
$371$	−1.54449			−0.0801861
$372$	40.3537	+	57.8344i	2.09224	+	2.99857i
$373$	2.12557	+	2.12557i	0.110058	+	0.110058i	0.759991	−	0.649933i	$-0.225203\pi$
$373$	2.12557	+	2.12557i	0.110058	+	0.110058i	−0.649933	+	0.759991i	$0.725203\pi$
$374$	−19.2748	−	19.2748i	−0.996674	−	0.996674i
$375$	−6.57402	−	1.17039i	−0.339481	−	0.0604385i
$376$	44.9509	−	44.9509i	2.31816	−	2.31816i
$377$	16.8667	+	16.8667i	0.868679	+	0.868679i
$378$	10.7148	+	6.25723i	0.551108	+	0.321837i
$379$	23.0398			1.18348			0.591739	−	0.806130i	$-0.298442\pi$
$379$	23.0398			1.18348			0.591739	+	0.806130i	$0.298442\pi$
$380$	−8.36202			−0.428963
$381$	0.114359	−	0.642353i	0.00585881	−	0.0329087i
$382$	23.3256			1.19344
$383$	10.3803	+	10.3803i	0.530410	+	0.530410i	0.920694	−	0.390285i	$-0.127623\pi$
$383$	10.3803	+	10.3803i	0.530410	+	0.530410i	−0.390285	+	0.920694i	$0.627623\pi$
$384$	11.5975	+	16.6214i	0.591833	+	0.848206i
$385$		−	1.13699i		−	0.0579465i
$386$		−	12.3735i		−	0.629795i
$387$	−28.5092	+	13.1795i	−1.44921	+	0.669951i
$388$	−15.6759			−0.795826
$389$	−19.7841	+	19.7841i	−1.00309	+	1.00309i	−0.00309955	+	0.999995i	$0.500987\pi$
$389$	−19.7841	+	19.7841i	−1.00309	+	1.00309i	−0.999995	+	0.00309955i	$0.999013\pi$
$390$	8.07355	−	5.63329i	0.408820	−	0.285253i
$391$	11.6986			0.591622
$392$	−27.3065	+	27.3065i	−1.37919	+	1.37919i
$393$	−3.10350	+	17.4323i	−0.156551	+	0.879342i
$394$	−34.1297	+	34.1297i	−1.71943	+	1.71943i
$395$	−0.731668	−	0.731668i	−0.0368142	−	0.0368142i
$396$	−37.7559	+	17.4541i	−1.89731	+	0.877103i
$397$	6.70708	−	6.70708i	0.336619	−	0.336619i	−0.518474	−	0.855093i	$-0.673500\pi$
$397$	6.70708	−	6.70708i	0.336619	−	0.336619i	0.855093	+	0.518474i	$0.173500\pi$
$398$	25.0180	−	25.0180i	1.25404	−	1.25404i
$399$	−6.35426	+	4.43367i	−0.318111	+	0.221961i
$400$	34.4294			1.72147
$401$	−27.1768	−	27.1768i	−1.35714	−	1.35714i	−0.877418	−	0.479727i	$-0.840736\pi$
$401$	−27.1768	−	27.1768i	−1.35714	−	1.35714i	−0.479727	−	0.877418i	$-0.659264\pi$
$402$	3.03342	−	17.0386i	0.151293	−	0.849808i
$403$	36.6596	−	36.6596i	1.82614	−	1.82614i
$404$	6.75360	+	6.75360i	0.336004	+	0.336004i
$405$	−2.68426	−	2.28278i	−0.133382	−	0.113432i
$406$	−7.06193	−	7.06193i	−0.350478	−	0.350478i
$407$	12.6195			0.625523
$408$	−6.62723	+	37.2249i	−0.328097	+	1.84291i
$409$	0.729859	−	0.729859i	0.0360892	−	0.0360892i	−0.688832	−	0.724921i	$-0.741876\pi$
$409$	0.729859	−	0.729859i	0.0360892	−	0.0360892i	0.724921	+	0.688832i	$0.241876\pi$
$410$	2.29739	−	2.29739i	0.113460	−	0.113460i
$411$	−3.25382	+	18.2766i	−0.160499	+	0.901519i
$412$			34.3915i			1.69435i
$413$		−	6.69778i		−	0.329576i
$414$	8.91197	−	24.2358i	0.438000	−	1.19113i
$415$			2.11945i			0.104040i
$416$	−22.0251	+	22.0251i	−1.07987	+	1.07987i
$417$	−0.145904	+	0.101804i	−0.00714497	+	0.00498538i
$418$		−	37.5720i		−	1.83771i
$419$	−25.5523	+	25.5523i	−1.24831	+	1.24831i	−0.291847	+	0.956465i	$0.594270\pi$
$419$	−25.5523	+	25.5523i	−1.24831	+	1.24831i	−0.956465	+	0.291847i	$0.905730\pi$
$420$	−2.33686	+	1.63053i	−0.114027	+	0.0795619i
$421$	4.47729	+	4.47729i	0.218210	+	0.218210i	0.807744	−	0.589534i	$-0.200689\pi$
$421$	4.47729	+	4.47729i	0.218210	+	0.218210i	−0.589534	+	0.807744i	$0.700689\pi$
$422$			37.1755i			1.80967i
$423$	−10.4307	+	28.3660i	−0.507158	+	1.37920i
$424$	−10.3886			−0.504515
$425$	−11.8562	−	11.8562i	−0.575108	−	0.575108i
$426$	53.9639	+	9.60731i	2.61456	+	0.465476i
$427$	6.19725	−	3.90898i	0.299906	−	0.189169i
$428$			11.8021i			0.570477i
$429$	17.4980	+	25.0779i	0.844813	+	1.21077i
$430$		−	10.4335i		−	0.503150i
$431$	13.6495			0.657473			0.328736	−	0.944422i	$-0.393377\pi$
$431$	13.6495			0.657473			0.328736	+	0.944422i	$0.393377\pi$
$432$	31.8746	+	18.6142i	1.53357	+	0.895575i
$433$	10.4859	−	10.4859i	0.503922	−	0.503922i	−0.408732	−	0.912654i	$-0.634029\pi$
$433$	10.4859	−	10.4859i	0.503922	−	0.503922i	0.912654	+	0.408732i	$0.134029\pi$
$434$	−15.3490	+	15.3490i	−0.736777	+	0.736777i
$435$	1.62292	+	2.32594i	0.0778130	+	0.111520i
$436$	−3.18663			−0.152612
$437$	11.4019	+	11.4019i	0.545428	+	0.545428i
$438$	41.3497	−	28.8516i	1.97576	−	1.37858i
$439$	−32.6124			−1.55651			−0.778253	−	0.627951i	$-0.783894\pi$
$439$	−32.6124			−1.55651			−0.778253	+	0.627951i	$0.783894\pi$
$440$		−	7.64767i		−	0.364588i
$441$	6.33640	−	17.2316i	0.301733	−	0.820553i
$442$	50.2220			2.38882
$443$			5.66108i			0.268966i	0.990916	+	0.134483i	$0.0429374\pi$
$443$			5.66108i			0.268966i	−0.990916	+	0.134483i	$0.957063\pi$
$444$	−18.0972	−	25.9367i	−0.858857	−	1.23090i
$445$	−4.05292	−	4.05292i	−0.192127	−	0.192127i
$446$	43.0264			2.03736
$447$	−16.2543	−	2.89378i	−0.768801	−	0.136871i
$448$	−0.202927	+	0.202927i	−0.00958740	+	0.00958740i
$449$			5.75228i			0.271467i	0.990745	+	0.135733i	$0.0433390\pi$
$449$			5.75228i			0.271467i	−0.990745	+	0.135733i	$0.956661\pi$
$450$	−33.5943	+	15.5303i	−1.58365	+	0.732104i
$451$	7.13611	+	7.13611i	0.336026	+	0.336026i
$452$		−	87.8772i		−	4.13339i
$453$	−16.0841	+	11.2226i	−0.755698	+	0.527286i
$454$		−	9.83611i		−	0.461631i
$455$	1.48127	+	1.48127i	0.0694429	+	0.0694429i
$456$	−42.7402	+	29.8218i	−2.00149	+	1.39654i
$457$	3.74026	+	3.74026i	0.174962	+	0.174962i	0.789155	−	0.614194i	$-0.210519\pi$
$457$	3.74026	+	3.74026i	0.174962	+	0.174962i	−0.614194	+	0.789155i	$0.710519\pi$
$458$	−44.3622	−	44.3622i	−2.07291	−	2.07291i
$459$	−4.56637	−	17.3864i	−0.213140	−	0.811526i
$460$	4.19319	+	4.19319i	0.195509	+	0.195509i
$461$		−	29.1895i		−	1.35949i	−0.733449	−	0.679745i	$-0.762090\pi$
$461$		−	29.1895i		−	1.35949i	0.733449	−	0.679745i	$-0.237910\pi$
$462$	−7.32627	−	10.4999i	−0.340849	−	0.488499i
$463$		−	16.8600i		−	0.783550i	−0.920061	−	0.391775i	$-0.871861\pi$
$463$		−	16.8600i		−	0.783550i	0.920061	−	0.391775i	$-0.128139\pi$
$464$	−21.0080	−	21.0080i	−0.975273	−	0.975273i
$465$	5.05541	−	3.52740i	0.234439	−	0.163579i
$466$			15.4863i			0.717388i
$467$	14.7420	−	14.7420i	0.682179	−	0.682179i	−0.278312	−	0.960491i	$-0.589775\pi$
$467$	14.7420	−	14.7420i	0.682179	−	0.682179i	0.960491	+	0.278312i	$0.0897748\pi$
$468$	26.4490	−	71.9273i	1.22261	−	3.32484i
$469$	3.68264			0.170049
$470$	−7.09922	−	7.09922i	−0.327463	−	0.327463i
$471$	19.8361	−	13.8406i	0.914000	−	0.637741i
$472$		−	45.0508i		−	2.07363i
$473$	32.4085			1.49014
$474$	−11.4713	−	2.04227i	−0.526896	−	0.0938044i
$475$		−	23.1110i		−	1.06041i
$476$	−14.5366			−0.666282
$477$	4.48315	−	2.07251i	0.205269	−	0.0948937i
$478$	3.33486	+	3.33486i	0.152533	+	0.152533i
$479$	−9.78103			−0.446907			−0.223453	−	0.974715i	$-0.571733\pi$
$479$	−9.78103			−0.446907			−0.223453	+	0.974715i	$0.571733\pi$
$480$	−3.03729	+	2.11926i	−0.138633	+	0.0967305i
$481$	−16.4405	+	16.4405i	−0.749624	+	0.749624i
$482$	−3.96698	+	3.96698i	−0.180691	+	0.180691i
$483$	5.40968	+	0.963097i	0.246149	+	0.0438224i
$484$	−6.34950			−0.288614
$485$			1.37026i			0.0622205i
$486$	−39.4978	−	3.78484i	−1.79166	−	0.171684i
$487$			6.47579i			0.293446i	0.989178	+	0.146723i	$0.0468726\pi$
$487$			6.47579i			0.293446i	−0.989178	+	0.146723i	$0.953127\pi$
$488$	41.6841	−	26.2927i	1.88695	−	1.19021i
$489$	4.20490	−	23.6188i	0.190152	−	1.06808i
$490$	4.31260	+	4.31260i	0.194823	+	0.194823i
$491$	37.2230			1.67985			0.839926	−	0.542701i	$-0.182598\pi$
$491$	37.2230			1.67985			0.839926	+	0.542701i	$0.182598\pi$
$492$	4.43309	−	24.9005i	0.199859	−	1.12260i
$493$			14.4687i			0.651637i
$494$	48.9486	+	48.9486i	2.20230	+	2.20230i
$495$	1.52570	+	3.30032i	0.0685750	+	0.148338i
$496$	−45.6607	+	45.6607i	−2.05022	+	2.05022i
$497$			11.6635i			0.523180i
$498$	13.6568	+	19.5727i	0.611975	+	0.877073i
$499$	11.3511	−	11.3511i	0.508146	−	0.508146i	−0.405811	−	0.913957i	$-0.633011\pi$
$499$	11.3511	−	11.3511i	0.508146	−	0.508146i	0.913957	+	0.405811i	$0.133011\pi$
$500$		−	17.2675i		−	0.772227i
$501$	4.77599	+	0.850279i	0.213375	+	0.0379876i
$502$			65.0330i			2.90256i
$503$			11.8424i			0.528025i	0.964519	+	0.264012i	$0.0850460\pi$
$503$			11.8424i			0.528025i	−0.964519	+	0.264012i	$0.914954\pi$
$504$	−6.12916	+	16.6681i	−0.273015	+	0.742454i
$505$	0.590345	−	0.590345i	0.0262700	−	0.0262700i
$506$	−18.8407	+	18.8407i	−0.837573	+	0.837573i
$507$	−33.2996	−	5.92840i	−1.47889	−	0.263289i
$508$	1.68723			0.0748585
$509$	3.15650	+	3.15650i	0.139910	+	0.139910i	0.773593	−	0.633683i	$-0.218458\pi$
$509$	3.15650	+	3.15650i	0.139910	+	0.139910i	−0.633683	+	0.773593i	$0.718458\pi$
$510$	5.87904	+	1.04666i	0.260328	+	0.0463468i
$511$	7.58649	+	7.58649i	0.335607	+	0.335607i
$512$	−35.9592	+	35.9592i	−1.58919	+	1.58919i
$513$	12.4949	−	21.3961i	0.551664	−	0.944660i
$514$	17.6869	+	17.6869i	0.780135	+	0.780135i
$515$	3.00623			0.132470
$516$	−46.4762	−	66.6090i	−2.04600	−	2.93230i
$517$	22.0515	−	22.0515i	0.969823	−	0.969823i
$518$	6.88350	−	6.88350i	0.302444	−	0.302444i
$519$	34.8473	−	24.3146i	1.52963	−	1.06729i
$520$	9.96334	+	9.96334i	0.436921	+	0.436921i
$521$	14.3976	−	14.3976i	0.630768	−	0.630768i	−0.317492	−	0.948261i	$-0.602841\pi$
$521$	14.3976	−	14.3976i	0.630768	−	0.630768i	0.948261	+	0.317492i	$0.102841\pi$
$522$	29.9747	+	11.0223i	1.31196	+	0.482431i
$523$	−14.5527	+	14.5527i	−0.636345	+	0.636345i	−0.949652	−	0.313307i	$-0.898563\pi$
$523$	−14.5527	+	14.5527i	−0.636345	+	0.636345i	0.313307	+	0.949652i	$0.398563\pi$
$524$	−45.7882			−2.00027
$525$	−4.50648	−	6.45863i	−0.196679	−	0.281878i
$526$	−26.7455	+	26.7455i	−1.16616	+	1.16616i
$527$	31.4475			1.36988
$528$	−21.7944	−	31.2354i	−0.948478	−	1.35934i
$529$			11.5649i			0.502820i
$530$			1.64070i			0.0712675i
$531$	8.98756	+	19.4414i	0.390027	+	0.843687i
$532$	−14.1680	−	14.1680i	−0.614259	−	0.614259i
$533$	−18.5938			−0.805385
$534$	−63.5431	−	11.3127i	−2.74978	−	0.489549i
$535$	1.03165			0.0446019
$536$	24.7703			1.06991
$537$	−5.58644	+	31.3788i	−0.241073	+	1.35410i
$538$	−31.9413	−	31.9413i	−1.37709	−	1.37709i
$539$	−13.3957	+	13.3957i	−0.576995	+	0.576995i
$540$	4.59516	−	7.86866i	0.197744	−	0.338613i
$541$	11.6316	+	11.6316i	0.500082	+	0.500082i	0.911463	−	0.411382i	$-0.134954\pi$
$541$	11.6316	+	11.6316i	0.500082	+	0.500082i	−0.411382	+	0.911463i	$0.634954\pi$
$542$	4.47862	+	4.47862i	0.192373	+	0.192373i
$543$	−5.77186	+	4.02729i	−0.247694	+	0.172828i
$544$	−18.8937			−0.810059
$545$			0.278549i			0.0119317i
$546$	23.2238	+	4.13458i	0.993888	+	0.176944i
$547$	15.0972	−	15.0972i	0.645508	−	0.645508i	−0.306396	−	0.951904i	$-0.599123\pi$
$547$	15.0972	−	15.0972i	0.645508	−	0.645508i	0.951904	+	0.306396i	$0.0991233\pi$
$548$	−48.0060			−2.05071
$549$	−12.7432	+	19.6624i	−0.543868	+	0.839171i
$550$	38.1891			1.62839
$551$	−14.1018	+	14.1018i	−0.600757	+	0.600757i
$552$	36.3867	+	6.47800i	1.54872	+	0.275722i
$553$		−	2.47936i		−	0.105433i
$554$	−68.5053			−2.91051
$555$	−2.26718	+	1.58191i	−0.0962362	+	0.0671485i
$556$	−0.325320	−	0.325320i	−0.0137966	−	0.0137966i
$557$	−2.45901	−	2.45901i	−0.104191	−	0.104191i	0.653089	−	0.757281i	$-0.273473\pi$
$557$	−2.45901	−	2.45901i	−0.104191	−	0.104191i	−0.757281	+	0.653089i	$0.773473\pi$
$558$	23.9567	−	65.1496i	1.01417	−	2.75800i
$559$	−42.2216	+	42.2216i	−1.78578	+	1.78578i
$560$	−1.84497	−	1.84497i	−0.0779640	−	0.0779640i
$561$	−3.25111	+	18.2614i	−0.137262	+	0.770996i
$562$	−7.58677			−0.320029
$563$	25.9000			1.09155			0.545777	−	0.837931i	$-0.316235\pi$
$563$	25.9000			1.09155			0.545777	+	0.837931i	$0.316235\pi$
$564$	−76.9458	−	13.6988i	−3.24000	−	0.576824i
$565$	−7.68151			−0.323164
$566$	29.4442	+	29.4442i	1.23763	+	1.23763i
$567$	−0.680240	−	8.41578i	−0.0285674	−	0.353430i
$568$			78.4514i			3.29175i
$569$		−	27.5132i		−	1.15341i	−0.816951	−	0.576707i	$-0.804337\pi$
$569$		−	27.5132i		−	1.15341i	0.816951	−	0.576707i	$-0.195663\pi$
$570$	4.70985	+	6.75008i	0.197274	+	0.282730i
$571$	−10.9419			−0.457904			−0.228952	−	0.973438i	$-0.573530\pi$
$571$	−10.9419			−0.457904			−0.228952	+	0.973438i	$0.573530\pi$
$572$	−55.9157	+	55.9157i	−2.33795	+	2.33795i
$573$	−9.08244	−	13.0168i	−0.379424	−	0.543785i
$574$	7.78504			0.324941
$575$	−11.5892	+	11.5892i	−0.483303	+	0.483303i
$576$	0.316728	−	0.861332i	0.0131970	−	0.0358888i
$577$	−9.84224	+	9.84224i	−0.409738	+	0.409738i	−0.881647	−	0.471909i	$-0.843565\pi$
$577$	−9.84224	+	9.84224i	−0.409738	+	0.409738i	0.471909	+	0.881647i	$0.343565\pi$
$578$	−9.05684	−	9.05684i	−0.376715	−	0.376715i
$579$	−6.90502	+	4.81795i	−0.286963	+	0.200227i
$580$	−5.18611	+	5.18611i	−0.215341	+	0.215341i
$581$	−3.59103	+	3.59103i	−0.148981	+	0.148981i
$582$	8.82936	+	12.6541i	0.365989	+	0.524530i
$583$	−5.09632			−0.211068
$584$	51.0284	+	51.0284i	2.11157	+	2.11157i
$585$	−6.28730	−	2.31196i	−0.259948	−	0.0955878i
$586$	−31.4155	+	31.4155i	−1.29776	+	1.29776i
$587$	−21.8048	−	21.8048i	−0.899982	−	0.899982i	0.0954525	−	0.995434i	$-0.469570\pi$
$587$	−21.8048	−	21.8048i	−0.899982	−	0.899982i	−0.995434	+	0.0954525i	$0.969570\pi$
$588$	46.7427	+	8.32169i	1.92763	+	0.343181i
$589$	30.6501	+	30.6501i	1.26292	+	1.26292i
$590$	−7.11500			−0.292920
$591$	32.3353	+	5.75672i	1.33010	+	0.236800i
$592$	20.4772	−	20.4772i	0.841609	−	0.841609i
$593$	10.2435	−	10.2435i	0.420652	−	0.420652i	−0.464776	−	0.885428i	$-0.653865\pi$
$593$	10.2435	−	10.2435i	0.420652	−	0.420652i	0.885428	+	0.464776i	$0.153865\pi$
$594$	35.3553	+	20.6468i	1.45064	+	0.847150i
$595$			1.27067i			0.0520923i
$596$		−	42.6940i		−	1.74881i
$597$	−23.7027	−	4.21984i	−0.970087	−	0.172707i
$598$		−	49.0912i		−	2.00749i
$599$	6.59437	−	6.59437i	0.269439	−	0.269439i	−0.559435	−	0.828874i	$-0.688982\pi$
$599$	6.59437	−	6.59437i	0.269439	−	0.269439i	0.828874	+	0.559435i	$0.188982\pi$
$600$	−30.3116	−	43.4422i	−1.23747	−	1.77352i
$601$			3.74917i			0.152932i	0.997072	+	0.0764659i	$0.0243636\pi$
$601$			3.74917i			0.152932i	−0.997072	+	0.0764659i	$0.975636\pi$
$602$	17.6778	−	17.6778i	0.720493	−	0.720493i
$603$	−10.6895	+	4.94163i	−0.435310	+	0.201239i
$604$	−35.8624	−	35.8624i	−1.45922	−	1.45922i
$605$			0.555022i			0.0225648i
$606$	1.64780	−	9.25563i	0.0669372	−	0.375984i
$607$	29.6866			1.20494			0.602472	−	0.798140i	$-0.294183\pi$
$607$	29.6866			1.20494			0.602472	+	0.798140i	$0.294183\pi$
$608$	−18.4146	−	18.4146i	−0.746810	−	0.746810i
$609$	−1.19115	+	6.69065i	−0.0482678	+	0.271119i
$610$	−4.15248	−	6.58329i	−0.168129	−	0.266550i
$611$			57.4571i			2.32446i
$612$	42.1949	−	19.5062i	1.70563	−	0.788491i
$613$		−	8.28921i		−	0.334798i	−0.985889	−	0.167399i	$-0.946463\pi$
$613$		−	8.28921i		−	0.334798i	0.985889	−	0.167399i	$-0.0535368\pi$
$614$	1.65804			0.0669130
$615$	−2.17660	−	0.387505i	−0.0877691	−	0.0156257i
$616$	12.9576	−	12.9576i	0.522078	−	0.522078i
$617$	27.3790	−	27.3790i	1.10224	−	1.10224i	0.108097	−	0.994140i	$-0.465524\pi$
$617$	27.3790	−	27.3790i	1.10224	−	1.10224i	0.994140	−	0.108097i	$-0.0344757\pi$
$618$	27.7619	−	19.3708i	1.11675	−	0.779206i
$619$	40.3793			1.62298			0.811491	−	0.584365i	$-0.198656\pi$
$619$	40.3793			1.62298			0.811491	+	0.584365i	$0.198656\pi$
$620$	11.2719	+	11.2719i	0.452692	+	0.452692i
$621$	−16.9949	+	4.46354i	−0.681981	+	0.179116i
$622$	−31.7165			−1.27172
$623$		−	13.7339i		−	0.550238i
$624$	69.0868	+	12.2997i	2.76569	+	0.492381i
$625$	22.7242			0.908967
$626$		−	21.8212i		−	0.872150i
$627$	−20.9670	+	14.6297i	−0.837341	+	0.584252i
$628$	44.2282	+	44.2282i	1.76490	+	1.76490i
$629$	−14.1031			−0.562328
$630$	2.63243	+	0.967996i	0.104879	+	0.0385659i
$631$	20.0011	−	20.0011i	0.796232	−	0.796232i	−0.186267	−	0.982499i	$-0.559639\pi$
$631$	20.0011	−	20.0011i	0.796232	−	0.796232i	0.982499	+	0.186267i	$0.0596390\pi$
$632$		−	16.6767i		−	0.663365i
$633$	20.7457	−	14.4752i	0.824568	−	0.575339i
$634$	0.535047	+	0.535047i	0.0212494	+	0.0212494i
$635$		−	0.147484i		−	0.00585271i
$636$	7.30851	+	10.4744i	0.289801	+	0.415339i
$637$		−	34.9037i		−	1.38294i
$638$	−23.3021	−	23.3021i	−0.922538	−	0.922538i
$639$	−15.6509	−	33.8553i	−0.619141	−	1.33930i
$640$	3.23951	+	3.23951i	0.128053	+	0.128053i
$641$	2.82884	+	2.82884i	0.111733	+	0.111733i	0.760763	−	0.649030i	$-0.224825\pi$
$641$	2.82884	+	2.82884i	0.111733	+	0.111733i	−0.649030	+	0.760763i	$0.724825\pi$
$642$	9.52704	−	6.64746i	0.376002	−	0.262354i
$643$	−1.77447	−	1.77447i	−0.0699784	−	0.0699784i	0.671251	−	0.741230i	$-0.265757\pi$
$643$	−1.77447	−	1.77447i	−0.0699784	−	0.0699784i	−0.741230	+	0.671251i	$0.765757\pi$
$644$			14.2092i			0.559923i
$645$	−5.82242	+	4.06257i	−0.229257	+	0.159964i
$646$			41.9893i			1.65205i
$647$	−20.6640	−	20.6640i	−0.812384	−	0.812384i	0.172607	−	0.984991i	$-0.444781\pi$
$647$	−20.6640	−	20.6640i	−0.812384	−	0.812384i	−0.984991	+	0.172607i	$0.944781\pi$
$648$	−4.57545	−	56.6064i	−0.179741	−	2.22371i
$649$		−	22.1005i		−	0.867520i
$650$	−49.7525	+	49.7525i	−1.95145	+	1.95145i
$651$	14.5420	+	2.58895i	0.569948	+	0.101469i
$652$	62.0379			2.42959
$653$	27.3691	+	27.3691i	1.07104	+	1.07104i	0.997276	+	0.0737597i	$0.0234998\pi$
$653$	27.3691	+	27.3691i	1.07104	+	1.07104i	0.0737597	+	0.997276i	$0.476500\pi$
$654$	1.79484	+	2.57234i	0.0701840	+	0.100587i
$655$			4.00243i			0.156388i
$656$	23.1591			0.904212
$657$	−32.2012	−	11.8410i	−1.25629	−	0.461961i
$658$		−	24.0567i		−	0.937829i
$659$	50.7738			1.97787			0.988933	−	0.148361i	$-0.0473999\pi$
$659$	50.7738			1.97787			0.988933	+	0.148361i	$0.0473999\pi$
$660$	−7.71086	+	5.38023i	−0.300145	+	0.209425i
$661$	−32.6307	−	32.6307i	−1.26919	−	1.26919i	−0.946508	−	0.322681i	$-0.895416\pi$
$661$	−32.6307	−	32.6307i	−1.26919	−	1.26919i	−0.322681	−	0.946508i	$-0.604584\pi$
$662$	28.0680			1.09089
$663$	−19.5553	−	28.0263i	−0.759464	−	1.08845i
$664$	−24.1541	+	24.1541i	−0.937360	+	0.937360i
$665$	−1.23845	+	1.23845i	−0.0480250	+	0.0480250i
$666$	−10.7438	+	29.2173i	−0.416312	+	1.13215i
$667$	14.1429			0.547615
$668$			12.5448i			0.485371i
$669$	−16.7535	−	24.0108i	−0.647727	−	0.928312i
$670$		−	3.91204i		−	0.151135i
$671$	20.4489	−	12.8984i	0.789422	−	0.497936i
$672$	−8.73686	−	1.55544i	−0.337032	−	0.0600024i
$673$	−18.6326	−	18.6326i	−0.718235	−	0.718235i	0.250009	−	0.968244i	$-0.419566\pi$
$673$	−18.6326	−	18.6326i	−0.718235	−	0.718235i	−0.968244	+	0.250009i	$0.919566\pi$
$674$	−64.3036			−2.47688
$675$	21.7475	+	12.7001i	0.837061	+	0.488829i
$676$		−	87.4659i		−	3.36407i
$677$	17.7167	+	17.7167i	0.680907	+	0.680907i	0.960205	−	0.279298i	$-0.0901016\pi$
$677$	17.7167	+	17.7167i	0.680907	+	0.680907i	−0.279298	+	0.960205i	$0.590102\pi$
$678$	−70.9372	+	49.4962i	−2.72433	+	1.90089i
$679$	−2.32167	+	2.32167i	−0.0890975	+	0.0890975i
$680$			8.54680i			0.327755i
$681$	−5.48903	+	3.82995i	−0.210340	+	0.146764i
$682$	−50.6468	+	50.6468i	−1.93937	+	1.93937i
$683$		−	20.8306i		−	0.797060i	−0.917155	−	0.398530i	$-0.869521\pi$
$683$		−	20.8306i		−	0.797060i	0.917155	−	0.398530i	$-0.130479\pi$
$684$	60.1365	+	22.1133i	2.29938	+	0.845525i
$685$			4.19629i			0.160332i
$686$			31.3294i			1.19616i
$687$	−7.48267	+	42.0299i	−0.285481	+	1.60354i
$688$	52.5883	−	52.5883i	2.00491	−	2.00491i
$689$	6.63946	−	6.63946i	0.252943	−	0.252943i
$690$	1.02309	−	5.74666i	0.0389484	−	0.218772i
$691$	10.8802			0.413903			0.206951	−	0.978351i	$-0.433646\pi$
$691$	10.8802			0.413903			0.206951	+	0.978351i	$0.433646\pi$
$692$	77.6982	+	77.6982i	2.95364	+	2.95364i
$693$	−3.00678	+	8.17683i	−0.114218	+	0.310612i
$694$	11.0339	+	11.0339i	0.418842	+	0.418842i
$695$	−0.0284368	+	0.0284368i	−0.00107867	+	0.00107867i
$696$	−8.01194	+	45.0028i	−0.303692	+	1.70583i
$697$	−7.97510	−	7.97510i	−0.302079	−	0.302079i
$698$	61.9767			2.34585
$699$	8.64210	−	6.02999i	0.326874	−	0.228075i
$700$	14.4007	−	14.4007i	0.544294	−	0.544294i
$701$	−15.6679	+	15.6679i	−0.591767	+	0.591767i	−0.938109	−	0.346341i	$-0.887424\pi$
$701$	−15.6679	+	15.6679i	−0.591767	+	0.591767i	0.346341	+	0.938109i	$0.387424\pi$
$702$	−72.9592	+	19.1620i	−2.75367	+	0.723225i
$703$	−13.7455	−	13.7455i	−0.518422	−	0.518422i
$704$	−0.669593	+	0.669593i	−0.0252362	+	0.0252362i
$705$	−1.19744	+	6.72598i	−0.0450982	+	0.253315i
$706$	−5.01244	+	5.01244i	−0.188646	+	0.188646i
$707$	2.00047			0.0752354
$708$	−45.4230	+	31.6938i	−1.70710	+	1.19112i
$709$	−6.32954	+	6.32954i	−0.237711	+	0.237711i	−0.815902	−	0.578191i	$-0.803759\pi$
$709$	−6.32954	+	6.32954i	−0.237711	+	0.237711i	0.578191	+	0.815902i	$0.303759\pi$
$710$	12.3901			0.464991
$711$	3.32699	+	7.19677i	0.124772	+	0.269900i
$712$		−	92.3775i		−	3.46199i
$713$		−	30.7394i		−	1.15120i
$714$	8.18762	+	11.7344i	0.306414	+	0.439148i
$715$	4.88770	+	4.88770i	0.182790	+	0.182790i
$716$	−82.4206			−3.08020
$717$	0.562497	−	3.15953i	0.0210068	−	0.117995i
$718$	1.11755			0.0417065
$719$	10.6871			0.398562			0.199281	−	0.979942i	$-0.436139\pi$
$719$	10.6871			0.398562			0.199281	+	0.979942i	$0.436139\pi$
$720$	7.83103	+	2.87962i	0.291845	+	0.107317i
$721$	5.09352	+	5.09352i	0.189692	+	0.189692i
$722$	−6.72718	+	6.72718i	−0.250360	+	0.250360i
$723$	3.75841	+	0.669118i	0.139777	+	0.0248848i
$724$	−12.8694	−	12.8694i	−0.478287	−	0.478287i
$725$	−14.3334	−	14.3334i	−0.532330	−	0.532330i
$726$	3.57631	+	5.12551i	0.132729	+	0.190226i
$727$	−2.70797			−0.100433			−0.0502166	−	0.998738i	$-0.515991\pi$
$727$	−2.70797			−0.100433			−0.0502166	+	0.998738i	$0.515991\pi$
$728$			33.7622i			1.25131i
$729$	13.2674	+	23.5154i	0.491385	+	0.870942i
$730$	8.05907	−	8.05907i	0.298280	−	0.298280i
$731$	−36.2187			−1.33960
$732$	−55.8352	−	23.5313i	−2.06373	−	0.869743i
$733$	32.0011			1.18199			0.590993	−	0.806677i	$-0.298736\pi$
$733$	32.0011			1.18199			0.590993	+	0.806677i	$0.298736\pi$
$734$	−33.5380	+	33.5380i	−1.23791	+	1.23791i
$735$	0.727415	−	4.08586i	0.0268311	−	0.150709i
$736$			18.4682i			0.680748i
$737$	12.1515			0.447607
$738$	−22.5974	+	10.4465i	−0.831822	+	0.384542i
$739$	−27.6875	−	27.6875i	−1.01850	−	1.01850i	−0.999826	−	0.0186742i	$-0.994055\pi$
$739$	−27.6875	−	27.6875i	−1.01850	−	1.01850i	−0.0186742	−	0.999826i	$-0.505945\pi$
$740$	−5.05507	−	5.05507i	−0.185828	−	0.185828i
$741$	8.25625	−	46.3751i	0.303301	−	1.70363i
$742$	−2.77988	+	2.77988i	−0.102053	+	0.102053i
$743$	13.6537	+	13.6537i	0.500906	+	0.500906i	0.911719	−	0.410814i	$-0.134755\pi$
$743$	13.6537	+	13.6537i	0.500906	+	0.500906i	−0.410814	+	0.911719i	$0.634755\pi$
$744$	97.8131	+	17.4139i	3.58600	+	0.638423i
$745$	−3.73196			−0.136729
$746$	7.65148			0.280141
$747$	5.60488	−	15.2423i	0.205072	−	0.557686i
$748$	−47.9659			−1.75381
$749$	1.74794	+	1.74794i	0.0638684	+	0.0638684i
$750$	−13.9389	+	9.72581i	−0.508976	+	0.355136i
$751$		−	24.2558i		−	0.885107i	−0.896742	−	0.442554i	$-0.854073\pi$
$751$		−	24.2558i		−	0.885107i	0.896742	−	0.442554i	$-0.145927\pi$
$752$		−	71.5646i		−	2.60969i
$753$	36.2916	−	25.3223i	1.32254	−	0.922797i
$754$	60.7156			2.21113
$755$	−3.13480	+	3.13480i	−0.114087	+	0.114087i
$756$	21.1177	−	5.54637i	0.768045	−	0.201720i
$757$	−19.7288			−0.717055			−0.358527	−	0.933519i	$-0.616721\pi$
$757$	−19.7288			−0.717055			−0.358527	+	0.933519i	$0.616721\pi$
$758$	41.4686	−	41.4686i	1.50621	−	1.50621i
$759$	17.8502	+	3.17791i	0.647921	+	0.115351i
$760$	−8.33008	+	8.33008i	−0.302164	+	0.302164i
$761$	−18.7714	−	18.7714i	−0.680464	−	0.680464i	0.279641	−	0.960105i	$-0.409785\pi$
$761$	−18.7714	−	18.7714i	−0.680464	−	0.680464i	−0.960105	+	0.279641i	$0.909785\pi$
$762$	−0.950317	−	1.36198i	−0.0344264	−	0.0493393i
$763$	−0.471952	+	0.471952i	−0.0170858	+	0.0170858i
$764$	29.0233	−	29.0233i	1.05003	−	1.05003i
$765$	−1.70507	−	3.68833i	−0.0616471	−	0.133352i
$766$	37.3664			1.35010
$767$	28.7924	+	28.7924i	1.03963	+	1.03963i
$768$	49.7469	+	8.85655i	1.79509	+	0.319583i
$769$	−12.2389	+	12.2389i	−0.441347	+	0.441347i	−0.892464	−	0.451118i	$-0.851025\pi$
$769$	−12.2389	+	12.2389i	−0.441347	+	0.441347i	0.451118	+	0.892464i	$0.351025\pi$
$770$	−2.04643	−	2.04643i	−0.0737484	−	0.0737484i
$771$	2.98328	−	16.7570i	0.107440	−	0.603488i
$772$	−15.3960	−	15.3960i	−0.554113	−	0.554113i
$773$	−14.0621			−0.505780			−0.252890	−	0.967495i	$-0.581381\pi$
$773$	−14.0621			−0.505780			−0.252890	+	0.967495i	$0.581381\pi$
$774$	−27.5915	+	75.0341i	−0.991755	+	2.69704i
$775$	−31.1535	+	31.1535i	−1.11907	+	1.11907i
$776$	−15.6161	+	15.6161i	−0.560584	+	0.560584i
$777$	−6.52160	−	1.16105i	−0.233961	−	0.0416526i
$778$			71.2175i			2.55327i
$779$		−	15.5458i		−	0.556985i
$780$	3.03634	−	17.0550i	0.108718	−	0.610667i
$781$			38.4858i			1.37713i
$782$	21.0558	−	21.0558i	0.752955	−	0.752955i
$783$	−5.52047	−	21.0191i	−0.197286	−	0.751162i
$784$			43.4737i			1.55263i
$785$	3.86607	−	3.86607i	0.137986	−	0.137986i
$786$	25.7899	+	36.9616i	0.919894	+	1.31838i
$787$	7.07183	+	7.07183i	0.252084	+	0.252084i	0.821824	−	0.569741i	$-0.192956\pi$
$787$	7.07183	+	7.07183i	0.252084	+	0.252084i	−0.569741	+	0.821824i	$0.692956\pi$
$788$			84.9330i			3.02561i
$789$	25.3394	+	4.51122i	0.902106	+	0.160604i
$790$	−2.63381			−0.0937066
$791$	−13.0150	−	13.0150i	−0.462759	−	0.462759i
$792$	−20.2242	+	54.9992i	−0.718637	+	1.95431i
$793$	−9.83681	+	43.4446i	−0.349315	+	1.54276i
$794$		−	24.1437i		−	0.856827i
$795$	0.915591	−	0.638851i	0.0324727	−	0.0226577i
$796$		−	62.2583i		−	2.20669i
$797$	−27.0167			−0.956982			−0.478491	−	0.878092i	$-0.658816\pi$
$797$	−27.0167			−0.956982			−0.478491	+	0.878092i	$0.658816\pi$
$798$	−3.45682	+	19.4168i	−0.122370	+	0.687348i
$799$	−24.6441	+	24.6441i	−0.871844	+	0.871844i
$800$	18.7170	−	18.7170i	0.661746	−	0.661746i
$801$	18.4292	+	39.8651i	0.651162	+	1.40856i
$802$	−97.8292			−3.45447
$803$	25.0330	+	25.0330i	0.883394	+	0.883394i
$804$	−17.4262	−	24.9750i	−0.614575	−	0.880799i
$805$	1.24206			0.0437768
$806$		−	131.965i		−	4.64825i
$807$	−5.38761	+	30.2620i	−0.189653	+	1.06527i
$808$	13.4556			0.473366
$809$		−	23.0766i		−	0.811331i	−0.914022	−	0.405666i	$-0.867040\pi$
$809$		−	23.0766i		−	0.811331i	0.914022	−	0.405666i	$-0.132960\pi$
$810$	−8.94002	+	0.722614i	−0.314120	+	0.0253901i
$811$	−22.0359	−	22.0359i	−0.773784	−	0.773784i	0.204982	−	0.978766i	$-0.434286\pi$
$811$	−22.0359	−	22.0359i	−0.773784	−	0.773784i	−0.978766	+	0.204982i	$0.934286\pi$
$812$	−17.5739			−0.616722
$813$	0.755417	−	4.24315i	0.0264936	−	0.148814i
$814$	22.7133	−	22.7133i	0.796101	−	0.796101i
$815$		−	5.42285i		−	0.189954i
$816$	24.3567	+	34.9077i	0.852656	+	1.22201i
$817$	−35.3003	−	35.3003i	−1.23500	−	1.23500i
$818$		−	2.62729i		−	0.0918612i
$819$	−6.73551	−	14.5699i	−0.235358	−	0.509114i
$820$		−	5.71714i		−	0.199651i
$821$	10.6019	+	10.6019i	0.370008	+	0.370008i	0.867480	−	0.497472i	$-0.165738\pi$
$821$	10.6019	+	10.6019i	0.370008	+	0.370008i	−0.497472	+	0.867480i	$0.665738\pi$
$822$	27.0390	+	38.7519i	0.943094	+	1.35163i
$823$	14.8138	+	14.8138i	0.516378	+	0.516378i	0.916474	−	0.400095i	$-0.131023\pi$
$823$	14.8138	+	14.8138i	0.516378	+	0.516378i	−0.400095	+	0.916474i	$0.631023\pi$
$824$	34.2601	+	34.2601i	1.19351	+	1.19351i
$825$	−14.8699	−	21.3114i	−0.517705	−	0.741966i
$826$	−12.0551	−	12.0551i	−0.419451	−	0.419451i
$827$		−	22.6006i		−	0.785900i	−0.919560	−	0.392950i	$-0.871455\pi$
$827$		−	22.6006i		−	0.785900i	0.919560	−	0.392950i	$-0.128545\pi$
$828$	−19.0670	−	41.2448i	−0.662623	−	1.43335i
$829$			24.1669i			0.839351i	0.907674	+	0.419676i	$0.137856\pi$
$829$			24.1669i			0.839351i	−0.907674	+	0.419676i	$0.862144\pi$
$830$	3.81472	+	3.81472i	0.132411	+	0.132411i
$831$	26.6744	+	38.2293i	0.925323	+	1.32616i
$832$		−	1.74468i		−	0.0604860i
$833$	14.9707	−	14.9707i	0.518703	−	0.518703i
$834$	−0.0793742	+	0.445842i	−0.00274850	+	0.0154383i
$835$	1.09656			0.0379481
$836$	−46.7497	−	46.7497i	−1.61687	−	1.61687i
$837$	−45.6848	+	11.9987i	−1.57910	+	0.414735i
$838$			91.9814i			3.17745i
$839$	−0.560283			−0.0193431			−0.00967157	−	0.999953i	$-0.503079\pi$
$839$	−0.560283			−0.0193431			−0.00967157	+	0.999953i	$0.503079\pi$
$840$	−0.703625	+	3.95224i	−0.0242774	+	0.136365i
$841$		−	11.5082i		−	0.396834i
$842$	16.1170			0.555429
$843$	2.95411	+	4.23379i	0.101745	+	0.145819i
$844$	46.2563	+	46.2563i	1.59221	+	1.59221i
$845$	−7.64556			−0.263015
$846$	32.2810	+	69.8288i	1.10985	+	2.40076i
$847$	−0.940386	+	0.940386i	−0.0323121	+	0.0323121i
$848$	−8.26966	+	8.26966i	−0.283981	+	0.283981i
$849$	4.96641	−	27.8961i	0.170447	−	0.957393i
$850$	−42.6790			−1.46388
$851$			13.7856i			0.472563i
$852$	79.0997	−	55.1915i	2.70991	−	1.89083i
$853$			6.52640i			0.223460i	0.993739	+	0.111730i	$0.0356391\pi$
$853$			6.52640i			0.223460i	−0.993739	+	0.111730i	$0.964361\pi$
$854$	4.11858	−	18.1899i	0.140935	−	0.622444i
$855$	1.93297	−	5.25665i	0.0661062	−	0.179774i
$856$	11.7570	+	11.7570i	0.401847	+	0.401847i
$857$	4.00200			0.136706			0.0683528	−	0.997661i	$-0.478226\pi$
$857$	4.00200			0.136706			0.0683528	+	0.997661i	$0.478226\pi$
$858$	76.6310	+	13.6428i	2.61614	+	0.465757i
$859$		−	16.5497i		−	0.564668i	−0.959316	−	0.282334i	$-0.908891\pi$
$859$		−	16.5497i		−	0.564668i	0.959316	−	0.282334i	$-0.0911087\pi$
$860$	−12.9821	−	12.9821i	−0.442687	−	0.442687i
$861$	−3.03131	−	4.34443i	−0.103307	−	0.148058i
$862$	24.5673	−	24.5673i	0.836764	−	0.836764i
$863$			53.0063i			1.80436i	0.431364	+	0.902178i	$0.358033\pi$
$863$			53.0063i			1.80436i	−0.431364	+	0.902178i	$0.641967\pi$
$864$	27.4474	−	7.20881i	0.933780	−	0.245249i
$865$	6.79175	−	6.79175i	0.230926	−	0.230926i
$866$		−	37.7466i		−	1.28268i
$867$	−1.52763	+	8.58067i	−0.0518812	+	0.291415i
$868$			38.1966i			1.29648i
$869$		−	8.18109i		−	0.277524i
$870$	7.10742	+	1.26535i	0.240964	+	0.0428994i
$871$	−15.8309	+	15.8309i	−0.536411	+	0.536411i
$872$	−3.17446	+	3.17446i	−0.107501	+	0.107501i
$873$	3.62366	−	9.85443i	0.122642	−	0.333522i
$874$	41.0439			1.38833
$875$	−2.55739	−	2.55739i	−0.0864556	−	0.0864556i
$876$	15.5510	−	87.3492i	0.525418	−	2.95126i
$877$	−29.8526	−	29.8526i	−1.00805	−	1.00805i	−0.999967	−	0.00808257i	$-0.997427\pi$
$877$	−29.8526	−	29.8526i	−1.00805	−	1.00805i	−0.00808257	−	0.999967i	$-0.502573\pi$
$878$	−58.6980	+	58.6980i	−1.98096	+	1.98096i
$879$	29.7638	+	5.29891i	1.00391	+	0.178728i
$880$	−6.08779	−	6.08779i	−0.205219	−	0.205219i
$881$	−54.4998			−1.83615			−0.918073	−	0.396411i	$-0.870256\pi$
$881$	−54.4998			−1.83615			−0.918073	+	0.396411i	$0.870256\pi$
$882$	−19.6099	−	42.4193i	−0.660301	−	1.42833i
$883$	19.7637	−	19.7637i	0.665101	−	0.665101i	−0.291477	−	0.956578i	$-0.594147\pi$
$883$	19.7637	−	19.7637i	0.665101	−	0.665101i	0.956578	+	0.291477i	$0.0941466\pi$
$884$	62.4897	−	62.4897i	2.10176	−	2.10176i
$885$	2.77041	+	3.97051i	0.0931264	+	0.133467i
$886$	10.1892	+	10.1892i	0.342313	+	0.342313i
$887$	−1.50534	+	1.50534i	−0.0505442	+	0.0505442i	−0.731927	−	0.681383i	$-0.761379\pi$
$887$	−1.50534	+	1.50534i	−0.0505442	+	0.0505442i	0.681383	+	0.731927i	$0.261379\pi$
$888$	−43.8658	−	7.80951i	−1.47204	−	0.262070i
$889$	0.249885	−	0.249885i	0.00838087	−	0.00838087i
$890$	−14.5894			−0.489039
$891$	−2.24457	−	27.7693i	−0.0751960	−	0.930308i
$892$	53.5364	−	53.5364i	1.79253	−	1.79253i
$893$	−48.0383			−1.60754
$894$	−34.4639	+	24.0471i	−1.15265	+	0.804255i
$895$			7.20454i			0.240821i
$896$			10.9776i			0.366735i
$897$	−27.3953	+	19.1150i	−0.914701	+	0.638230i
$898$	10.3533	+	10.3533i	0.345495	+	0.345495i
$899$	38.0182			1.26798
$900$	−22.4765	+	61.1242i	−0.749218	+	2.03747i
$901$	5.69549			0.189744
$902$	25.6881			0.855320
$903$	−16.7484	−	2.98175i	−0.557351	−	0.0992263i
$904$	−87.5415	−	87.5415i	−2.91159	−	2.91159i
$905$	−1.12494	+	1.12494i	−0.0373942	+	0.0373942i
$906$	−8.75001	+	49.1485i	−0.290700	+	1.63285i
$907$	40.1001	+	40.1001i	1.33150	+	1.33150i	0.904027	+	0.427475i	$0.140597\pi$
$907$	40.1001	+	40.1001i	1.33150	+	1.33150i	0.427475	+	0.904027i	$0.359403\pi$
$908$	−12.2388	−	12.2388i	−0.406158	−	0.406158i
$909$	−5.80670	+	2.68437i	−0.192596	+	0.0890350i
$910$	5.33216			0.176760
$911$			22.3526i			0.740575i	0.928917	+	0.370287i	$0.120741\pi$
$911$			22.3526i			0.740575i	−0.928917	+	0.370287i	$0.879259\pi$
$912$	−10.2834	+	57.7617i	−0.340518	+	1.91268i
$913$	−11.8492	+	11.8492i	−0.392152	+	0.392152i
$914$	13.4639			0.445347
$915$	−2.05692	+	4.88066i	−0.0679996	+	0.161350i
$916$	−110.397			−3.64762
$917$	−6.78141	+	6.78141i	−0.223942	+	0.223942i
$918$	−39.5120	−	23.0743i	−1.30409	−	0.761564i
$919$			51.1471i			1.68719i	0.536982	+	0.843594i	$0.319564\pi$
$919$			51.1471i			1.68719i	−0.536982	+	0.843594i	$0.680436\pi$
$920$	8.35436			0.275435
$921$	−0.645601	−	0.925266i	−0.0212733	−	0.0304885i
$922$	−52.5372	−	52.5372i	−1.73022	−	1.73022i
$923$	−50.1391	−	50.1391i	−1.65035	−	1.65035i
$924$	−22.1805	−	3.94885i	−0.729686	−	0.129908i
$925$	13.9713	−	13.9713i	0.459372	−	0.459372i
$926$	−30.3457	−	30.3457i	−0.997223	−	0.997223i
$927$	−21.6196	−	7.94996i	−0.710082	−	0.261111i
$928$	−22.8414			−0.749804
$929$	55.3731			1.81673			0.908367	−	0.418175i	$-0.137330\pi$
$929$	55.3731			1.81673			0.908367	+	0.418175i	$0.137330\pi$
$930$	2.75022	−	15.4479i	0.0901833	−	0.506557i
$931$	29.1821			0.956405
$932$	19.2691	+	19.2691i	0.631180	+	0.631180i
$933$	12.3497	+	17.6993i	0.404309	+	0.579450i
$934$		−	53.0673i		−	1.73641i
$935$			4.19279i			0.137119i
$936$	−45.3045	−	98.0006i	−1.48083	−	3.20325i
$937$	31.7186			1.03620			0.518100	−	0.855320i	$-0.326639\pi$
$937$	31.7186			1.03620			0.518100	+	0.855320i	$0.326639\pi$
$938$	6.62827	−	6.62827i	0.216421	−	0.216421i
$939$	−12.1773	+	8.49666i	−0.397391	+	0.277278i
$940$	−17.6667			−0.576223
$941$	−18.2926	+	18.2926i	−0.596321	+	0.596321i	−0.939332	−	0.343010i	$-0.888553\pi$
$941$	−18.2926	+	18.2926i	−0.596321	+	0.596321i	0.343010	+	0.939332i	$0.388553\pi$
$942$	10.7912	−	60.6135i	0.351595	−	1.97490i
$943$	−7.79553	+	7.79553i	−0.253857	+	0.253857i
$944$	−35.8618	−	35.8618i	−1.16720	−	1.16720i
$945$	−0.484819	−	1.84594i	−0.0157712	−	0.0600485i
$946$	58.3309	−	58.3309i	1.89650	−	1.89650i
$947$	−7.82017	+	7.82017i	−0.254121	+	0.254121i	−0.822658	−	0.568537i	$-0.807510\pi$
$947$	−7.82017	+	7.82017i	−0.254121	+	0.254121i	0.568537	+	0.822658i	$0.307510\pi$
$948$	−16.8146	+	11.7323i	−0.546111	+	0.381047i
$949$	−65.2255			−2.11731
$950$	−41.5968	−	41.5968i	−1.34958	−	1.34958i
$951$	0.0902475	−	0.506917i	0.00292648	−	0.0164379i
$952$	−14.4810	+	14.4810i	−0.469333	+	0.469333i
$953$	−1.61430	−	1.61430i	−0.0522923	−	0.0522923i	0.680477	−	0.732769i	$-0.261773\pi$
$953$	−1.61430	−	1.61430i	−0.0522923	−	0.0522923i	−0.732769	+	0.680477i	$0.761773\pi$
$954$	4.33883	−	11.7993i	0.140475	−	0.382017i
$955$	−2.53698	−	2.53698i	−0.0820948	−	0.0820948i
$956$	8.29892			0.268406
$957$	−3.93041	+	22.0770i	−0.127052	+	0.713647i
$958$	−17.6045	+	17.6045i	−0.568777	+	0.568777i
$959$	−7.10988	+	7.10988i	−0.229590	+	0.229590i
$960$	0.0363602	−	0.204234i	0.00117352	−	0.00659163i
$961$		−	51.6322i		−	1.66555i
$962$			59.1815i			1.90809i
$963$	−7.41921	−	2.72818i	−0.239081	−	0.0879145i
$964$			9.87197i			0.317955i
$965$	−1.34579	+	1.34579i	−0.0433225	+	0.0433225i
$966$	11.4701	−	8.00326i	0.369046	−	0.257501i
$967$			23.9366i			0.769749i	0.922969	+	0.384874i	$0.125755\pi$
$967$			23.9366i			0.769749i	−0.922969	+	0.384874i	$0.874245\pi$
$968$	−6.32525	+	6.32525i	−0.203301	+	0.203301i
$969$	23.4321	−	16.3497i	0.752747	−	0.525227i
$970$	2.46629	+	2.46629i	0.0791878	+	0.0791878i
$971$		−	29.5545i		−	0.948448i	−0.880404	−	0.474224i	$-0.842729\pi$
$971$		−	29.5545i		−	0.948448i	0.880404	−	0.474224i	$-0.157271\pi$
$972$	−53.8553	+	44.4366i	−1.72741	+	1.42530i
$973$	−0.0963623			−0.00308923
$974$	11.6556	+	11.6556i	0.373468	+	0.373468i
$975$	47.1368	+	8.39185i	1.50958	+	0.268754i
$976$	12.2521	−	54.1117i	0.392179	−	1.73207i
$977$		−	21.4844i		−	0.687347i	−0.939089	−	0.343674i	$-0.888329\pi$
$977$		−	21.4844i		−	0.687347i	0.939089	−	0.343674i	$-0.111671\pi$
$978$	−34.9424	−	50.0789i	−1.11734	−	1.60135i
$979$		−	45.3175i		−	1.44835i
$980$	10.7321			0.342823
$981$	0.736622	−	2.00322i	0.0235185	−	0.0639579i
$982$	66.9965	−	66.9965i	2.13794	−	2.13794i
$983$	−5.47918	+	5.47918i	−0.174759	+	0.174759i	−0.789067	−	0.614308i	$-0.789435\pi$
$983$	−5.47918	+	5.47918i	−0.174759	+	0.174759i	0.614308	+	0.789067i	$0.289435\pi$
$984$	−20.3893	−	29.2216i	−0.649986	−	0.931551i
$985$	7.42415			0.236553
$986$	26.0417	+	26.0417i	0.829336	+	0.829336i
$987$	−13.4248	+	9.36713i	−0.427317	+	0.298159i
$988$	121.810			3.87530
$989$			35.4032i			1.12576i
$990$	8.68618	+	3.19407i	0.276065	+	0.101514i
$991$	−36.5310			−1.16044			−0.580222	−	0.814458i	$-0.697034\pi$
$991$	−36.5310			−1.16044			−0.580222	+	0.814458i	$0.697034\pi$
$992$			49.6454i			1.57624i
$993$	−10.9290	−	15.6633i	−0.346821	−	0.497059i
$994$	20.9928	+	20.9928i	0.665850	+	0.665850i
$995$	−5.44211			−0.172527
$996$	41.3464	+	7.36098i	1.31011	+	0.233241i
$997$	8.47046	−	8.47046i	0.268262	−	0.268262i	−0.560138	−	0.828400i	$-0.689252\pi$
$997$	8.47046	−	8.47046i	0.268262	−	0.268262i	0.828400	+	0.560138i	$0.189252\pi$
$998$		−	40.8610i		−	1.29343i
$999$	20.4880	−	5.38099i	0.648213	−	0.170247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.g.c.11.14	yes	28
3.2	odd	2	inner	183.2.g.c.11.1	✓	28
61.50	odd	4	inner	183.2.g.c.50.1	yes	28
183.50	even	4	inner	183.2.g.c.50.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.1	✓	28	3.2	odd	2	inner
183.2.g.c.11.14	yes	28	1.1	even	1	trivial
183.2.g.c.50.1	yes	28	61.50	odd	4	inner
183.2.g.c.50.14	yes	28	183.50	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79987 - 1.79987i) q^{2} +(-1.70524 - 0.303587i) q^{3} -4.47903i q^{4} -0.391521 q^{5} +(-3.61561 + 2.52278i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(-4.46193 - 4.46193i) q^{8} +(2.81567 + 1.03538i) q^{9} +O(q^{10})\)	\(q+(1.79987 - 1.79987i) q^{2} +(-1.70524 - 0.303587i) q^{3} -4.47903i q^{4} -0.391521 q^{5} +(-3.61561 + 2.52278i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(-4.46193 - 4.46193i) q^{8} +(2.81567 + 1.03538i) q^{9} +(-0.704685 + 0.704685i) q^{10} +(-2.18888 - 2.18888i) q^{11} +(-1.35978 + 7.63781i) q^{12} +5.70332 q^{13} -2.38793 q^{14} +(0.667636 + 0.118861i) q^{15} -7.10367 q^{16} +(2.44623 + 2.44623i) q^{17} +(6.93136 - 3.20429i) q^{18} +4.76840i q^{19} +1.75363i q^{20} +(0.929803 + 1.33258i) q^{21} -7.87938 q^{22} +(2.39114 - 2.39114i) q^{23} +(6.25406 + 8.96323i) q^{24} -4.84671 q^{25} +(10.2652 - 10.2652i) q^{26} +(-4.48706 - 2.62036i) q^{27} +(-2.97122 + 2.97122i) q^{28} +(2.95735 + 2.95735i) q^{29} +(1.41559 - 0.987722i) q^{30} +(6.42776 - 6.42776i) q^{31} +(-3.86180 + 3.86180i) q^{32} +(3.06805 + 4.39708i) q^{33} +8.80576 q^{34} +(0.259720 + 0.259720i) q^{35} +(4.63748 - 12.6115i) q^{36} +(-2.88263 + 2.88263i) q^{37} +(8.58247 + 8.58247i) q^{38} +(-9.72551 - 1.73145i) q^{39} +(1.74694 + 1.74694i) q^{40} -3.26017 q^{41} +(4.07198 + 0.724943i) q^{42} +(-7.40298 + 7.40298i) q^{43} +(-9.80407 + 9.80407i) q^{44} +(-1.10239 - 0.405371i) q^{45} -8.60748i q^{46} +10.0743i q^{47} +(12.1134 + 2.15658i) q^{48} -6.11990i q^{49} +(-8.72343 + 8.72343i) q^{50} +(-3.42875 - 4.91404i) q^{51} -25.5454i q^{52} +(1.16414 - 1.16414i) q^{53} +(-12.7924 + 3.35981i) q^{54} +(0.856992 + 0.856992i) q^{55} +5.91975i q^{56} +(1.44762 - 8.13125i) q^{57} +10.6457 q^{58} +(5.04835 + 5.04835i) q^{59} +(0.532380 - 2.99036i) q^{60} +(-1.72475 + 7.61743i) q^{61} -23.1382i q^{62} +(-1.18098 - 2.55464i) q^{63} -0.305907i q^{64} -2.23297 q^{65} +(13.4362 + 2.39208i) q^{66} +(-2.77574 + 2.77574i) q^{67} +(10.9567 - 10.9567i) q^{68} +(-4.80339 + 3.35155i) q^{69} +0.934923 q^{70} +(-8.79121 - 8.79121i) q^{71} +(-7.94354 - 17.1831i) q^{72} -11.4364 q^{73} +10.3767i q^{74} +(8.26479 + 1.47140i) q^{75} +21.3578 q^{76} +2.90404i q^{77} +(-20.6210 + 14.3882i) q^{78} +(1.86878 + 1.86878i) q^{79} +2.78123 q^{80} +(6.85599 + 5.83055i) q^{81} +(-5.86786 + 5.86786i) q^{82} -5.41338i q^{83} +(5.96866 - 4.16462i) q^{84} +(-0.957748 - 0.957748i) q^{85} +26.6487i q^{86} +(-4.14517 - 5.94079i) q^{87} +19.5332i q^{88} +(10.3517 + 10.3517i) q^{89} +(-2.71377 + 1.25455i) q^{90} +(-3.78337 - 3.78337i) q^{91} +(-10.7100 - 10.7100i) q^{92} +(-12.9122 + 9.00947i) q^{93} +(18.1324 + 18.1324i) q^{94} -1.86693i q^{95} +(7.75767 - 5.41289i) q^{96} -3.49985i q^{97} +(-11.0150 - 11.0150i) q^{98} +(-3.89685 - 8.42948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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