LMFDB - Embedded newform 183.2.g.c.11.1

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			11.1
Character	$\chi$	$=$	183.11
Dual form			183.2.g.c.50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79987 + 1.79987i) q^{2} +(1.70524 - 0.303587i) q^{3} -4.47903i q^{4} +0.391521 q^{5} +(-2.52278 + 3.61561i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(4.46193 + 4.46193i) q^{8} +(2.81567 - 1.03538i) q^{9} +O(q^{10})$	\(q+(-1.79987 + 1.79987i) q^{2} +(1.70524 - 0.303587i) q^{3} -4.47903i q^{4} +0.391521 q^{5} +(-2.52278 + 3.61561i) 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} +(-3.20429 + 6.93136i) q^{18} +4.76840i q^{19} -1.75363i q^{20} +(-1.33258 - 0.929803i) q^{21} -7.87938 q^{22} +(-2.39114 + 2.39114i) q^{23} +(8.96323 + 6.25406i) 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} +(-0.987722 + 1.41559i) q^{30} +(6.42776 - 6.42776i) q^{31} +(3.86180 - 3.86180i) q^{32} +(4.39708 + 3.06805i) 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} +(-4.91404 - 3.42875i) q^{51} -25.5454i q^{52} +(-1.16414 + 1.16414i) q^{53} +(-3.35981 + 12.7924i) 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} +(-2.55464 - 1.18098i) 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} +(-3.35155 + 4.80339i) q^{69} +0.934923 q^{70} +(8.79121 + 8.79121i) q^{71} +(17.1831 + 7.94354i) q^{72} -11.4364 q^{73} -10.3767i q^{74} +(-8.26479 + 1.47140i) q^{75} +21.3578 q^{76} -2.90404i q^{77} +(-14.3882 + 20.6210i) 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} +(-4.16462 + 5.96866i) q^{84} +(-0.957748 - 0.957748i) q^{85} -26.6487i q^{86} +(-5.94079 - 4.14517i) q^{87} +19.5332i q^{88} +(-10.3517 - 10.3517i) q^{89} +(-1.25455 + 2.71377i) q^{90} +(-3.78337 - 3.78337i) q^{91} +(10.7100 + 10.7100i) q^{92} +(9.00947 - 12.9122i) q^{93} +(18.1324 + 18.1324i) q^{94} +1.86693i q^{95} +(5.41289 - 7.75767i) q^{96} -3.49985i q^{97} +(11.0150 + 11.0150i) q^{98} +(8.42948 + 3.89685i) 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	$0.606385\pi$
$2$	−1.79987	+	1.79987i	−1.27270	+	1.27270i	−0.944667	+	0.328030i	$0.893615\pi$
$3$	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	$-0.472097\pi$
$5$	0.391521			0.175093			0.0875467	+	0.996160i	$0.472097\pi$
$6$	−2.52278	+	3.61561i	−1.02992	+	1.47607i
$7$	−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	0.955373	−	0.295401i	$-0.0954533\pi$
$11$	2.18888	+	2.18888i	0.659972	+	0.659972i	−0.295401	+	0.955373i	$0.595453\pi$
$12$	−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	0.345223	−	0.938521i	$-0.387803\pi$
$17$	−2.44623	−	2.44623i	−0.593297	−	0.593297i	−0.938521	+	0.345223i	$0.887803\pi$
$18$	−3.20429	+	6.93136i	−0.755259	+	1.63374i
$19$			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
$21$	−1.33258	−	0.929803i	−0.290793	−	0.202900i
$22$	−7.87938			−1.67989
$23$	−2.39114	+	2.39114i	−0.498588	+	0.498588i	−0.910998	−	0.412410i	$-0.864687\pi$
$23$	−2.39114	+	2.39114i	−0.498588	+	0.498588i	0.412410	+	0.910998i	$0.364687\pi$
$24$	8.96323	+	6.25406i	1.82961	+	1.27660i
$25$	−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	0.377034	−	0.926200i	$-0.376944\pi$
$29$	−2.95735	−	2.95735i	−0.549166	−	0.549166i	−0.926200	+	0.377034i	$0.876944\pi$
$30$	−0.987722	+	1.41559i	−0.180332	+	0.258450i
$31$	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
$33$	4.39708	+	3.06805i	0.765433	+	0.534078i
$34$	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	$-0.418064\pi$
$41$	3.26017			0.509152			0.254576	+	0.967053i	$0.418064\pi$
$42$	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	$-0.737302\pi$
$47$		−	10.0743i		−	1.46949i	0.678343	−	0.734745i	$-0.262698\pi$
$48$	−12.1134	+	2.15658i	−1.74842	+	0.311276i
$49$		−	6.11990i		−	0.874271i
$50$	8.72343	−	8.72343i	1.23368	−	1.23368i
$51$	−4.91404	−	3.42875i	−0.688103	−	0.480122i
$52$		−	25.5454i		−	3.54250i
$53$	−1.16414	+	1.16414i	−0.159907	+	0.159907i	−0.782525	−	0.622619i	$-0.786069\pi$
$53$	−1.16414	+	1.16414i	−0.159907	+	0.159907i	0.622619	+	0.782525i	$0.286069\pi$
$54$	−3.35981	+	12.7924i	−0.457212	+	1.74083i
$55$	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	0.297486	−	0.954726i	$-0.403852\pi$
$59$	−5.04835	−	5.04835i	−0.657240	−	0.657240i	−0.954726	+	0.297486i	$0.903852\pi$
$60$	−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
$63$	−2.55464	−	1.18098i	−0.321854	−	0.148790i
$64$		−	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
$69$	−3.35155	+	4.80339i	−0.403479	+	0.578260i
$70$	0.934923			0.111745
$71$	8.79121	+	8.79121i	1.04332	+	1.04332i	0.999018	+	0.0443063i	$0.0141078\pi$
$71$	8.79121	+	8.79121i	1.04332	+	1.04332i	0.0443063	+	0.999018i	$0.485892\pi$
$72$	17.1831	+	7.94354i	2.02505	+	0.936155i
$73$	−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
$78$	−14.3882	+	20.6210i	−1.62915	+	2.33487i
$79$	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	$0.0960187\pi$
$83$			5.41338i			0.594195i	−0.954847	+	0.297098i	$0.903981\pi$
$84$	−4.16462	+	5.96866i	−0.454397	+	0.651235i
$85$	−0.957748	−	0.957748i	−0.103882	−	0.103882i
$86$		−	26.6487i		−	2.87361i
$87$	−5.94079	−	4.14517i	−0.636920	−	0.444409i
$88$			19.5332i			2.08225i
$89$	−10.3517	−	10.3517i	−1.09728	−	1.09728i	−0.994727	−	0.102556i	$-0.967298\pi$
$89$	−10.3517	−	10.3517i	−1.09728	−	1.09728i	−0.102556	−	0.994727i	$-0.532702\pi$
$90$	−1.25455	+	2.71377i	−0.132241	+	0.286057i
$91$	−3.78337	−	3.78337i	−0.396605	−	0.396605i
$92$	10.7100	+	10.7100i	1.11660	+	1.11660i
$93$	9.00947	−	12.9122i	0.934239	−	1.33894i
$94$	18.1324	+	18.1324i	1.87022	+	1.87022i
$95$			1.86693i			0.191543i
$96$	5.41289	−	7.75767i	0.552451	−	0.791764i
$97$		−	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
$99$	8.42948	+	3.89685i	0.847194	+	0.391648i
$100$			21.7086i			2.17086i
$101$	1.50782	−	1.50782i	0.150034	−	0.150034i	−0.628099	−	0.778133i	$-0.716167\pi$
$101$	1.50782	−	1.50782i	0.150034	−	0.150034i	0.778133	+	0.628099i	$0.216167\pi$
$102$	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
$105$	−0.521732	−	0.364037i	−0.0509159	−	0.0355264i
$106$		−	4.19059i		−	0.407026i
$107$	2.63497			0.254732			0.127366	−	0.991856i	$-0.459348\pi$
$107$	2.63497			0.254732			0.127366	+	0.991856i	$0.459348\pi$
$108$	−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
$111$	−4.04044	+	5.79069i	−0.383501	+	0.549628i
$112$	4.71231	+	4.71231i	0.445271	+	0.445271i
$113$	−19.6197			−1.84566			−0.922832	−	0.385202i	$-0.874132\pi$
$113$	−19.6197			−1.84566			−0.922832	+	0.385202i	$0.874132\pi$
$114$	−17.2407	−	12.0296i	−1.61474	−	1.12668i
$115$	−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
$120$	3.50929	+	2.44859i	0.320353	+	0.223525i
$121$		−	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
$129$	−10.3764	+	14.8713i	−0.913590	+	1.30934i
$130$	−4.01904	+	4.01904i	−0.352493	+	0.352493i
$131$			10.2228i			0.893169i	0.894742	+	0.446584i	$0.147360\pi$
$131$			10.2228i			0.893169i	−0.894742	+	0.446584i	$0.852640\pi$
$132$	13.7419	−	19.6946i	1.19608	−	1.71420i
$133$	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	$0.151379\pi$
$137$			10.7179i			0.915695i	−0.889031	+	0.457847i	$0.848621\pi$
$138$	−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	$-0.627679\pi$
$149$	−9.53197			−0.780889			−0.390445	+	0.920626i	$0.627679\pi$
$150$	12.2272	−	17.5238i	0.998347	−	1.43082i
$151$	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
$153$	−9.42053	−	4.35500i	−0.761605	−	0.352081i
$154$	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
$159$	−1.63172	+	2.33855i	−0.129403	+	0.185459i
$160$	1.51197	−	1.51197i	0.119532	−	0.119532i
$161$	3.17239			0.250020
$162$	−1.84566	+	22.8341i	−0.145009	+	1.79401i
$163$			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
$165$	1.72155	+	1.20120i	0.134022	+	0.0935136i
$166$	−9.74335	−	9.74335i	−0.756231	−	0.756231i
$167$	2.80077			0.216730			0.108365	−	0.994111i	$-0.465438\pi$
$167$	2.80077			0.216730			0.108365	+	0.994111i	$0.465438\pi$
$168$	−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	$-0.367547\pi$
$173$	17.3471	−	17.3471i	1.31888	−	1.31888i	0.914667	−	0.404209i	$-0.132453\pi$
$174$	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
$177$	−10.1413	−	7.07603i	−0.762264	−	0.531867i
$178$	37.2635			2.79302
$179$			18.4014i			1.37539i	0.726001	+	0.687694i	$0.241377\pi$
$179$			18.4014i			1.37539i	−0.726001	+	0.687694i	$0.758623\pi$
$180$	−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
$183$	−0.628560	+	13.5131i	−0.0464645	+	0.998920i
$184$	−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
$189$	−4.71480	−	1.23830i	−0.342951	−	0.0900729i
$190$	−3.36022	−	3.36022i	−0.243776	−	0.243776i
$191$	−6.47982	−	6.47982i	−0.468863	−	0.468863i	0.432683	−	0.901546i	$-0.357567\pi$
$191$	−6.47982	−	6.47982i	−0.468863	−	0.468863i	−0.901546	+	0.432683i	$0.857567\pi$
$192$	−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	$-0.263925\pi$
$197$	18.9624			1.35101			0.675506	+	0.737355i	$0.263925\pi$
$198$	−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
$201$	−3.89062	+	5.57597i	−0.274423	+	0.393299i
$202$			5.42776i			0.381896i
$203$			3.92359i			0.275382i
$204$	−15.3575	+	22.0101i	−1.07524	+	1.54102i
$205$	1.27642			0.0891492
$206$	13.8200	−	13.8200i	0.962882	−	0.962882i
$207$	−4.25694	+	9.20841i	−0.295878	+	0.640029i
$208$	−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
$213$	17.6600	+	12.3222i	1.21004	+	0.844303i
$214$	−4.74259	+	4.74259i	−0.324197	+	0.324197i
$215$	−2.89842	+	2.89842i	−0.197671	+	0.197671i
$216$	31.7128	+	8.32907i	2.15778	+	0.566721i
$217$	−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	−0.791948	−	0.610589i	$-0.790933\pi$
$227$	−2.73246	+	2.73246i	−0.181360	+	0.181360i	0.610589	+	0.791948i	$0.290933\pi$
$228$	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	−0.552004	−	0.833842i	$-0.686137\pi$
$233$	4.30207	−	4.30207i	0.281838	−	0.281838i	0.833842	+	0.552004i	$0.186137\pi$
$234$	−18.2751	+	39.5318i	−1.19468	+	2.58427i
$235$		−	3.94430i		−	0.257298i
$236$	−22.6117	+	22.6117i	−1.47190	+	1.47190i
$237$	3.75406	+	2.61938i	0.243852	+	0.170147i
$238$	−5.84141	−	5.84141i	−0.378642	−	0.378642i
$239$		−	1.85284i		−	0.119850i	−0.998203	−	0.0599250i	$-0.980914\pi$
$239$		−	1.85284i		−	0.119850i	0.998203	−	0.0599250i	$-0.0190862\pi$
$240$	−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
$246$	−8.22469	+	11.7875i	−0.524387	+	0.751544i
$247$			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	$-0.451452\pi$
$251$	18.0661	−	18.0661i	1.14032	−	1.14032i	0.988391	−	0.151929i	$-0.0485485\pi$
$252$	−5.28965	+	11.4423i	−0.333217	+	0.720798i
$253$	−10.4679			−0.658109
$254$	−0.677999	−	0.677999i	−0.0425414	−	0.0425414i
$255$	−1.92395	−	1.34243i	−0.120482	−	0.0840661i
$256$	−29.1730			−1.82331
$257$		−	9.82678i		−	0.612978i	−0.951874	−	0.306489i	$-0.900846\pi$
$257$		−	9.82678i		−	0.612978i	0.951874	−	0.306489i	$-0.0991542\pi$
$258$	−8.09021	−	45.4424i	−0.503674	−	2.82912i
$259$	3.82445			0.237640
$260$		−	10.0015i		−	0.620269i
$261$	−11.3889	−	5.26495i	−0.704954	−	0.325892i
$262$	−18.3996	−	18.3996i	−1.13673	−	1.13673i
$263$	14.8597			0.916291			0.458145	−	0.888877i	$-0.348514\pi$
$263$	14.8597			0.916291			0.458145	+	0.888877i	$0.348514\pi$
$264$	5.93004	+	33.3088i	0.364969	+	2.05002i
$265$	−0.455785	+	0.455785i	−0.0279986	+	0.0279986i
$266$			11.3866i			0.698156i
$267$	−20.7948	−	14.5095i	−1.27262	−	0.887969i
$268$	12.4326	+	12.4326i	0.759444	+	0.759444i
$269$			17.7465i			1.08202i	0.841015	+	0.541012i	$0.181959\pi$
$269$			17.7465i			1.08202i	−0.841015	+	0.541012i	$0.818041\pi$
$270$	−1.31543	+	5.00849i	−0.0800547	+	0.304807i
$271$			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
$273$	−7.60012	−	5.30296i	−0.459980	−	0.320950i
$274$	−19.2908	−	19.2908i	−1.16540	−	1.16540i
$275$	−10.6089	−	10.6089i	−0.639739	−	0.639739i
$276$	21.5145	+	15.0117i	1.29502	+	0.903598i
$277$	−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
$279$	11.4433	−	24.7536i	0.685093	−	1.48196i
$280$		−	2.31770i		−	0.138509i
$281$	2.10759	+	2.10759i	0.125728	+	0.125728i	0.767171	−	0.641443i	$-0.221664\pi$
$281$	2.10759	+	2.10759i	0.125728	+	0.125728i	−0.641443	+	0.767171i	$0.721664\pi$
$282$	36.4248	+	25.4153i	2.16907	+	1.51346i
$283$			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
$288$	6.87513	−	14.8720i	0.405121	−	0.876338i
$289$		−	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	$-0.329702\pi$
$293$	17.4544			1.01969			0.509847	+	0.860265i	$0.329702\pi$
$294$	22.1272	+	15.4392i	1.29048	+	0.900431i
$295$	−1.97654	−	1.97654i	−0.115078	−	0.115078i
$296$	−25.7241			−1.49518
$297$	15.5573	+	4.08598i	0.902726	+	0.237092i
$298$	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
$303$	2.11344	−	3.02895i	0.121414	−	0.174009i
$304$		−	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	0.911318	−	0.411704i	$-0.135066\pi$
$311$	8.81079	+	8.81079i	0.499614	+	0.499614i	−0.411704	+	0.911318i	$0.635066\pi$
$312$	51.1201	+	35.6689i	2.89411	+	2.01935i
$313$	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
$315$	−1.00019	−	0.462378i	−0.0563546	−	0.0260521i
$316$	8.37034	−	8.37034i	0.470869	−	0.470869i
$317$		−	0.297271i		−	0.0166964i	−0.999965	−	0.00834819i	$-0.997343\pi$
$317$		−	0.297271i		−	0.0166964i	0.999965	−	0.00834819i	$-0.00265734\pi$
$318$	−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
$333$	−5.13192	+	11.1011i	−0.281228	+	0.608338i
$334$	−5.04102	+	5.04102i	−0.275832	+	0.275832i
$335$	−1.08676	+	1.08676i	−0.0593760	+	0.0593760i
$336$	9.46620	+	6.60501i	0.516423	+	0.360333i
$337$	−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
$342$	−33.0515	−	15.2793i	−1.78722	−	0.826211i
$343$	−8.70325	+	8.70325i	−0.469931	+	0.469931i
$344$	−66.0631			−3.56188
$345$	−1.31220	+	1.88063i	−0.0706465	+	0.101250i
$346$			62.4449i			3.35706i
$347$		−	6.13041i		−	0.329098i	−0.986369	−	0.164549i	$-0.947383\pi$
$347$		−	6.13041i		−	0.329098i	0.986369	−	0.164549i	$-0.0526168\pi$
$348$	−18.5663	+	26.6090i	−0.995261	+	1.42639i
$349$	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	$-0.476388\pi$
$353$	2.78490			0.148225			0.0741126	+	0.997250i	$0.476388\pi$
$354$	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	0.698867	−	0.715252i	$-0.253688\pi$
$359$	−0.310453	−	0.310453i	−0.0163851	−	0.0163851i	−0.715252	+	0.698867i	$0.753688\pi$
$360$	6.72753	+	3.11006i	0.354572	+	0.163915i
$361$	−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
$366$	−23.1905	−	25.4532i	−1.21219	−	1.33046i
$367$	−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
$372$	−57.8344	−	40.3537i	−2.99857	−	2.09224i
$373$	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	0.390285	−	0.920694i	$-0.372377\pi$
$383$	−10.3803	−	10.3803i	−0.530410	−	0.530410i	−0.920694	+	0.390285i	$0.872377\pi$
$384$	16.6214	+	11.5975i	0.848206	+	0.591833i
$385$		−	1.13699i		−	0.0579465i
$386$			12.3735i			0.629795i
$387$	−13.1795	+	28.5092i	−0.669951	+	1.44921i
$388$	−15.6759			−0.795826
$389$	19.7841	−	19.7841i	1.00309	−	1.00309i	0.00309955	−	0.999995i	$-0.499013\pi$
$389$	19.7841	−	19.7841i	1.00309	−	1.00309i	0.999995	−	0.00309955i	$-0.000986620\pi$
$390$	−5.63329	+	8.07355i	−0.285253	+	0.408820i
$391$	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
$396$	17.4541	−	37.7559i	0.877103	−	1.89731i
$397$	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
$399$	4.43367	−	6.35426i	0.221961	−	0.318111i
$400$	34.4294			1.72147
$401$	27.1768	+	27.1768i	1.35714	+	1.35714i	0.877418	+	0.479727i	$0.159264\pi$
$401$	27.1768	+	27.1768i	1.35714	+	1.35714i	0.479727	+	0.877418i	$0.340736\pi$
$402$	−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
$417$	0.101804	−	0.145904i	0.00498538	−	0.00714497i
$418$		−	37.5720i		−	1.83771i
$419$	25.5523	−	25.5523i	1.24831	−	1.24831i	0.291847	−	0.956465i	$-0.405730\pi$
$419$	25.5523	−	25.5523i	1.24831	−	1.24831i	0.956465	−	0.291847i	$-0.0942697\pi$
$420$	−1.63053	+	2.33686i	−0.0795619	+	0.114027i
$421$	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
$429$	25.0779	+	17.4980i	1.21077	+	0.844813i
$430$		−	10.4335i		−	0.503150i
$431$	−13.6495			−0.657473			−0.328736	−	0.944422i	$-0.606623\pi$
$431$	−13.6495			−0.657473			−0.328736	+	0.944422i	$0.606623\pi$
$432$	−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
$435$	−2.32594	−	1.62292i	−0.111520	−	0.0778130i
$436$	−3.18663			−0.152612
$437$	−11.4019	−	11.4019i	−0.545428	−	0.545428i
$438$	28.8516	−	41.3497i	1.37858	−	1.97576i
$439$	−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	$-0.957063\pi$
$443$		−	5.66108i		−	0.268966i	0.990916	−	0.134483i	$-0.0429374\pi$
$444$	25.9367	+	18.0972i	1.23090	+	0.858857i
$445$	−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	$-0.956661\pi$
$449$		−	5.75228i		−	0.271467i	0.990745	−	0.135733i	$-0.0433390\pi$
$450$	15.5303	−	33.5943i	0.732104	−	1.58365i
$451$	7.13611	+	7.13611i	0.336026	+	0.336026i
$452$			87.8772i			4.13339i
$453$	11.2226	−	16.0841i	0.527286	−	0.755698i
$454$		−	9.83611i		−	0.461631i
$455$	−1.48127	−	1.48127i	−0.0694429	−	0.0694429i
$456$	−29.8218	+	42.7402i	−1.39654	+	2.00149i
$457$	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
$459$	−17.3864	−	4.56637i	−0.811526	−	0.213140i
$460$	4.19319	+	4.19319i	0.195509	+	0.195509i
$461$			29.1895i			1.35949i	0.733449	+	0.679745i	$0.237910\pi$
$461$			29.1895i			1.35949i	−0.733449	+	0.679745i	$0.762090\pi$
$462$	10.4999	+	7.32627i	0.488499	+	0.340849i
$463$		−	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
$465$	3.52740	−	5.05541i	0.163579	−	0.234439i
$466$			15.4863i			0.717388i
$467$	−14.7420	+	14.7420i	−0.682179	+	0.682179i	−0.960491	−	0.278312i	$-0.910225\pi$
$467$	−14.7420	+	14.7420i	−0.682179	+	0.682179i	0.278312	+	0.960491i	$0.410225\pi$
$468$	−26.4490	−	71.9273i	−1.22261	−	3.32484i
$469$	3.68264			0.170049
$470$	7.09922	+	7.09922i	0.327463	+	0.327463i
$471$	−13.8406	+	19.8361i	−0.637741	+	0.914000i
$472$		−	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
$477$	−2.07251	+	4.48315i	−0.0948937	+	0.205269i
$478$	3.33486	+	3.33486i	0.152533	+	0.152533i
$479$	9.78103			0.446907			0.223453	−	0.974715i	$-0.428267\pi$
$479$	9.78103			0.446907			0.223453	+	0.974715i	$0.428267\pi$
$480$	2.11926	−	3.03729i	0.0967305	−	0.138633i
$481$	−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
$486$	3.78484	+	39.4978i	0.171684	+	1.79166i
$487$			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	$-0.817402\pi$
$491$	−37.2230			−1.67985			−0.839926	+	0.542701i	$0.817402\pi$
$492$	−4.43309	−	24.9005i	−0.199859	−	1.12260i
$493$			14.4687i			0.651637i
$494$	−48.9486	−	48.9486i	−2.20230	−	2.20230i
$495$	3.30032	+	1.52570i	0.148338	+	0.0685750i
$496$	−45.6607	+	45.6607i	−2.05022	+	2.05022i
$497$		−	11.6635i		−	0.523180i
$498$	−19.5727	−	13.6568i	−0.877073	−	0.611975i
$499$	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	$-0.914954\pi$
$503$		−	11.8424i		−	0.528025i	0.964519	−	0.264012i	$-0.0850460\pi$
$504$	−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	0.633683	−	0.773593i	$-0.281542\pi$
$509$	−3.15650	−	3.15650i	−0.139910	−	0.139910i	−0.773593	+	0.633683i	$0.781542\pi$
$510$	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
$516$	66.6090	+	46.4762i	2.93230	+	2.04600i
$517$	22.0515	−	22.0515i	0.969823	−	0.969823i
$518$	−6.88350	+	6.88350i	−0.302444	+	0.302444i
$519$	24.3146	−	34.8473i	1.06729	−	1.52963i
$520$	9.96334	+	9.96334i	0.436921	+	0.436921i
$521$	−14.3976	+	14.3976i	−0.630768	+	0.630768i	−0.948261	−	0.317492i	$-0.897159\pi$
$521$	−14.3976	+	14.3976i	−0.630768	+	0.630768i	0.317492	+	0.948261i	$0.397159\pi$
$522$	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
$525$	6.45863	+	4.50648i	0.281878	+	0.196679i
$526$	−26.7455	+	26.7455i	−1.16616	+	1.16616i
$527$	−31.4475			−1.36988
$528$	−31.2354	−	21.7944i	−1.35934	−	0.948478i
$529$			11.5649i			0.502820i
$530$		−	1.64070i		−	0.0712675i
$531$	−19.4414	−	8.98756i	−0.843687	−	0.390027i
$532$	−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
$543$	4.02729	−	5.77186i	0.172828	−	0.247694i
$544$	−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
$549$	3.03057	+	23.2339i	0.129341	+	0.991600i
$550$	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
$555$	−1.58191	+	2.26718i	−0.0671485	+	0.0962362i
$556$	−0.325320	−	0.325320i	−0.0137966	−	0.0137966i
$557$	2.45901	+	2.45901i	0.104191	+	0.104191i	0.757281	−	0.653089i	$-0.226527\pi$
$557$	2.45901	+	2.45901i	0.104191	+	0.104191i	−0.653089	+	0.757281i	$0.726527\pi$
$558$	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	$-0.683765\pi$
$563$	−25.9000			−1.09155			−0.545777	+	0.837931i	$0.683765\pi$
$564$	−76.9458	+	13.6988i	−3.24000	+	0.576824i
$565$	−7.68151			−0.323164
$566$	−29.4442	−	29.4442i	−1.23763	−	1.23763i
$567$	−8.41578	−	0.680240i	−0.353430	−	0.0285674i
$568$			78.4514i			3.29175i
$569$			27.5132i			1.15341i	0.816951	+	0.576707i	$0.195663\pi$
$569$			27.5132i			1.15341i	−0.816951	+	0.576707i	$0.804337\pi$
$570$	−6.75008	−	4.70985i	−0.282730	−	0.197274i
$571$	−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
$573$	−13.0168	−	9.08244i	−0.543785	−	0.379424i
$574$	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
$579$	4.81795	−	6.90502i	0.200227	−	0.286963i
$580$	−5.18611	+	5.18611i	−0.215341	+	0.215341i
$581$	3.59103	−	3.59103i	0.148981	−	0.148981i
$582$	12.6541	+	8.82936i	0.524530	+	0.365989i
$583$	−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	0.995434	−	0.0954525i	$-0.0304298\pi$
$587$	21.8048	+	21.8048i	0.899982	+	0.899982i	−0.0954525	+	0.995434i	$0.530430\pi$
$588$	−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	−0.885428	−	0.464776i	$-0.846135\pi$
$593$	−10.2435	+	10.2435i	−0.420652	+	0.420652i	0.464776	+	0.885428i	$0.346135\pi$
$594$	−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	−0.828874	−	0.559435i	$-0.811018\pi$
$599$	−6.59437	+	6.59437i	−0.269439	+	0.269439i	0.559435	+	0.828874i	$0.311018\pi$
$600$	−43.4422	−	30.3116i	−1.77352	−	1.23747i
$601$			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
$603$	−4.94163	+	10.6895i	−0.201239	+	0.435310i
$604$	−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
$612$	−19.5062	+	42.1949i	−0.788491	+	1.70563i
$613$		−	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	$0.534476\pi$
$617$	−27.3790	+	27.3790i	−1.10224	+	1.10224i	−0.994140	+	0.108097i	$0.965524\pi$
$618$	19.3708	−	27.7619i	0.779206	−	1.11675i
$619$	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
$621$	−4.46354	+	16.9949i	−0.179116	+	0.681981i
$622$	−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
$627$	−14.6297	+	20.9670i	−0.584252	+	0.837341i
$628$	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
$633$	−14.4752	+	20.7457i	−0.575339	+	0.824568i
$634$	0.535047	+	0.535047i	0.0212494	+	0.0212494i
$635$			0.147484i			0.00585271i
$636$	10.4744	+	7.30851i	0.415339	+	0.289801i
$637$		−	34.9037i		−	1.38294i
$638$	23.3021	+	23.3021i	0.922538	+	0.922538i
$639$	33.8553	+	15.6509i	1.33930	+	0.619141i
$640$	3.23951	+	3.23951i	0.128053	+	0.128053i
$641$	−2.82884	−	2.82884i	−0.111733	−	0.111733i	0.649030	−	0.760763i	$-0.275175\pi$
$641$	−2.82884	−	2.82884i	−0.111733	−	0.111733i	−0.760763	+	0.649030i	$0.775175\pi$
$642$	−6.64746	+	9.52704i	−0.262354	+	0.376002i
$643$	−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
$645$	−4.06257	+	5.82242i	−0.159964	+	0.229257i
$646$			41.9893i			1.65205i
$647$	20.6640	+	20.6640i	0.812384	+	0.812384i	0.984991	−	0.172607i	$-0.0552191\pi$
$647$	20.6640	+	20.6640i	0.812384	+	0.812384i	−0.172607	+	0.984991i	$0.555219\pi$
$648$	56.6064	+	4.57545i	2.22371	+	0.179741i
$649$		−	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	$-0.976500\pi$
$653$	−27.3691	−	27.3691i	−1.07104	−	1.07104i	−0.0737597	−	0.997276i	$-0.523500\pi$
$654$	2.57234	+	1.79484i	0.100587	+	0.0701840i
$655$			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	$-0.952600\pi$
$659$	−50.7738			−1.97787			−0.988933	+	0.148361i	$0.952600\pi$
$660$	5.38023	−	7.71086i	0.209425	−	0.300145i
$661$	−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
$663$	−28.0263	−	19.5553i	−1.08845	−	0.759464i
$664$	−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
$669$	24.0108	+	16.7535i	0.928312	+	0.647727i
$670$		−	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	0.279298	−	0.960205i	$-0.409898\pi$
$677$	−17.7167	−	17.7167i	−0.680907	−	0.680907i	−0.960205	+	0.279298i	$0.909898\pi$
$678$	49.4962	−	70.9372i	1.90089	−	2.72433i
$679$	−2.32167	+	2.32167i	−0.0890975	+	0.0890975i
$680$		−	8.54680i		−	0.327755i
$681$	−3.82995	+	5.48903i	−0.146764	+	0.210340i
$682$	−50.6468	+	50.6468i	−1.93937	+	1.93937i
$683$			20.8306i			0.797060i	0.917155	+	0.398530i	$0.130479\pi$
$683$			20.8306i			0.797060i	−0.917155	+	0.398530i	$0.869521\pi$
$684$	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
$699$	6.02999	−	8.64210i	0.228075	−	0.326874i
$700$	14.4007	−	14.4007i	0.544294	−	0.544294i
$701$	15.6679	−	15.6679i	0.591767	−	0.591767i	−0.346341	−	0.938109i	$-0.612576\pi$
$701$	15.6679	−	15.6679i	0.591767	−	0.591767i	0.938109	+	0.346341i	$0.112576\pi$
$702$	−19.1620	+	72.9592i	−0.723225	+	2.75367i
$703$	−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
$708$	−31.6938	+	45.4230i	−1.19112	+	1.70710i
$709$	−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
$711$	7.19677	+	3.32699i	0.269900	+	0.124772i
$712$		−	92.3775i		−	3.46199i
$713$			30.7394i			1.15120i
$714$	−11.7344	−	8.18762i	−0.439148	−	0.306414i
$715$	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	$-0.563861\pi$
$719$	−10.6871			−0.398562			−0.199281	+	0.979942i	$0.563861\pi$
$720$	−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
$726$	5.12551	+	3.57631i	0.190226	+	0.132729i
$727$	−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
$732$	60.5258	+	2.81534i	2.23710	+	0.104058i
$733$	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
$738$	−10.4465	+	22.5974i	−0.384542	+	0.831822i
$739$	−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	0.410814	−	0.911719i	$-0.365245\pi$
$743$	−13.6537	−	13.6537i	−0.500906	−	0.500906i	−0.911719	+	0.410814i	$0.865245\pi$
$744$	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
$750$	9.72581	−	13.9389i	0.355136	−	0.508976i
$751$		−	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
$753$	25.3223	−	36.2916i	0.922797	−	1.32254i
$754$	60.7156			2.21113
$755$	3.13480	−	3.13480i	0.114087	−	0.114087i
$756$	−5.54637	+	21.1177i	−0.201720	+	0.768045i
$757$	−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	0.960105	−	0.279641i	$-0.0902153\pi$
$761$	18.7714	+	18.7714i	0.680464	+	0.680464i	−0.279641	+	0.960105i	$0.590215\pi$
$762$	−1.36198	−	0.950317i	−0.0493393	−	0.0344264i
$763$	−0.471952	+	0.471952i	−0.0170858	+	0.0170858i
$764$	−29.0233	+	29.0233i	−1.05003	+	1.05003i
$765$	−3.68833	−	1.70507i	−0.133352	−	0.0616471i
$766$	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	$-0.418619\pi$
$773$	14.0621			0.505780			0.252890	+	0.967495i	$0.418619\pi$
$774$	−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
$783$	−21.0191	−	5.52047i	−0.751162	−	0.197286i
$784$			43.4737i			1.55263i
$785$	−3.86607	+	3.86607i	−0.137986	+	0.137986i
$786$	−36.9616	−	25.7899i	−1.31838	−	0.919894i
$787$	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
$795$	−0.638851	+	0.915591i	−0.0226577	+	0.0324727i
$796$		−	62.2583i		−	2.20669i
$797$	27.0167			0.956982			0.478491	−	0.878092i	$-0.341184\pi$
$797$	27.0167			0.956982			0.478491	+	0.878092i	$0.341184\pi$
$798$	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
$801$	−39.8651	−	18.4292i	−1.40856	−	0.651162i
$802$	−97.8292			−3.45447
$803$	−25.0330	−	25.0330i	−0.883394	−	0.883394i
$804$	24.9750	+	17.4262i	0.880799	+	0.614575i
$805$	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	$0.132960\pi$
$809$			23.0766i			0.811331i	−0.914022	+	0.405666i	$0.867040\pi$
$810$	−0.722614	+	8.94002i	−0.0253901	+	0.314120i
$811$	−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
$816$	34.9077	+	24.3567i	1.22201	+	0.852656i
$817$	−35.3003	−	35.3003i	−1.23500	−	1.23500i
$818$			2.62729i			0.0918612i
$819$	−14.5699	−	6.73551i	−0.509114	−	0.235358i
$820$		−	5.71714i		−	0.199651i
$821$	−10.6019	−	10.6019i	−0.370008	−	0.370008i	0.497472	−	0.867480i	$-0.334262\pi$
$821$	−10.6019	−	10.6019i	−0.370008	−	0.370008i	−0.867480	+	0.497472i	$0.834262\pi$
$822$	−38.7519	−	27.0390i	−1.35163	−	0.943094i
$823$	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
$825$	−21.3114	−	14.8699i	−0.741966	−	0.517705i
$826$	−12.0551	−	12.0551i	−0.419451	−	0.419451i
$827$			22.6006i			0.785900i	0.919560	+	0.392950i	$0.128545\pi$
$827$			22.6006i			0.785900i	−0.919560	+	0.392950i	$0.871455\pi$
$828$	41.2448	+	19.0670i	1.43335	+	0.662623i
$829$			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
$831$	−38.2293	−	26.6744i	−1.32616	−	0.925323i
$832$		−	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
$837$	11.9987	−	45.6848i	0.414735	−	1.57910i
$838$			91.9814i			3.17745i
$839$	0.560283			0.0193431			0.00967157	−	0.999953i	$-0.496921\pi$
$839$	0.560283			0.0193431			0.00967157	+	0.999953i	$0.496921\pi$
$840$	−0.703625	−	3.95224i	−0.0242774	−	0.136365i
$841$		−	11.5082i		−	0.396834i
$842$	−16.1170			−0.555429
$843$	4.23379	+	2.95411i	0.145819	+	0.101745i
$844$	46.2563	+	46.2563i	1.59221	+	1.59221i
$845$	7.64556			0.263015
$846$	69.8288	+	32.2810i	2.40076	+	1.10985i
$847$	−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
$852$	55.1915	−	79.0997i	1.89083	−	2.70991i
$853$			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	$-0.521774\pi$
$857$	−4.00200			−0.136706			−0.0683528	+	0.997661i	$0.521774\pi$
$858$	−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
$861$	−4.34443	−	3.03131i	−0.148058	−	0.103307i
$862$	24.5673	−	24.5673i	0.836764	−	0.836764i
$863$		−	53.0063i		−	1.80436i	−0.431364	−	0.902178i	$-0.641967\pi$
$863$		−	53.0063i		−	1.80436i	0.431364	−	0.902178i	$-0.358033\pi$
$864$	7.20881	−	27.4474i	0.245249	−	0.933780i
$865$	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	$-0.129744\pi$
$881$	54.4998			1.83615			0.918073	+	0.396411i	$0.129744\pi$
$882$	42.4193	+	19.6099i	1.42833	+	0.660301i
$883$	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
$885$	−3.97051	−	2.77041i	−0.133467	−	0.0931264i
$886$	10.1892	+	10.1892i	0.342313	+	0.342313i
$887$	1.50534	−	1.50534i	0.0505442	−	0.0505442i	−0.681383	−	0.731927i	$-0.738621\pi$
$887$	1.50534	−	1.50534i	0.0505442	−	0.0505442i	0.731927	+	0.681383i	$0.238621\pi$
$888$	−43.8658	+	7.80951i	−1.47204	+	0.262070i
$889$	0.249885	−	0.249885i	0.00838087	−	0.00838087i
$890$	14.5894			0.489039
$891$	27.7693	+	2.24457i	0.930308	+	0.0751960i
$892$	53.5364	−	53.5364i	1.79253	−	1.79253i
$893$	48.0383			1.60754
$894$	24.0471	−	34.4639i	0.804255	−	1.15265i
$895$			7.20454i			0.240821i
$896$		−	10.9776i		−	0.366735i
$897$	−19.1150	+	27.3953i	−0.638230	+	0.914701i
$898$	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
$909$	2.68437	−	5.80670i	0.0890350	−	0.192596i
$910$	5.33216			0.176760
$911$		−	22.3526i		−	0.740575i	−0.928917	−	0.370287i	$-0.879259\pi$
$911$		−	22.3526i		−	0.740575i	0.928917	−	0.370287i	$-0.120741\pi$
$912$	−10.2834	−	57.7617i	−0.340518	−	1.91268i
$913$	−11.8492	+	11.8492i	−0.392152	+	0.392152i
$914$	−13.4639			−0.445347
$915$	−0.246094	+	5.29067i	−0.00813563	+	0.174904i
$916$	−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
$921$	0.925266	+	0.645601i	0.0304885	+	0.0212733i
$922$	−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	$-0.862670\pi$
$929$	−55.3731			−1.81673			−0.908367	+	0.418175i	$0.862670\pi$
$930$	2.75022	+	15.4479i	0.0901833	+	0.506557i
$931$	29.1821			0.956405
$932$	−19.2691	−	19.2691i	−0.631180	−	0.631180i
$933$	17.6993	+	12.3497i	0.579450	+	0.404309i
$934$		−	53.0673i		−	1.73641i
$935$		−	4.19279i		−	0.137119i
$936$	98.0006	+	45.3045i	3.20325	+	1.48083i
$937$	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
$939$	8.49666	−	12.1773i	0.277278	−	0.397391i
$940$	−17.6667			−0.576223
$941$	18.2926	−	18.2926i	0.596321	−	0.596321i	−0.343010	−	0.939332i	$-0.611447\pi$
$941$	18.2926	−	18.2926i	0.596321	−	0.596321i	0.939332	+	0.343010i	$0.111447\pi$
$942$	−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
$945$	−1.84594	−	0.484819i	−0.0600485	−	0.0157712i
$946$	58.3309	−	58.3309i	1.89650	−	1.89650i
$947$	7.82017	−	7.82017i	0.254121	−	0.254121i	−0.568537	−	0.822658i	$-0.692490\pi$
$947$	7.82017	−	7.82017i	0.254121	−	0.254121i	0.822658	+	0.568537i	$0.192490\pi$
$948$	11.7323	−	16.8146i	0.381047	−	0.546111i
$949$	−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	0.732769	−	0.680477i	$-0.238227\pi$
$953$	1.61430	+	1.61430i	0.0522923	+	0.0522923i	−0.680477	+	0.732769i	$0.738227\pi$
$954$	−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
$966$	−8.00326	+	11.4701i	−0.257501	+	0.369046i
$967$			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
$969$	16.3497	−	23.4321i	0.525227	−	0.752747i
$970$	2.46629	+	2.46629i	0.0791878	+	0.0791878i
$971$			29.5545i			0.948448i	0.880404	+	0.474224i	$0.157271\pi$
$971$			29.5545i			0.948448i	−0.880404	+	0.474224i	$0.842729\pi$
$972$	−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	$0.111671\pi$
$977$			21.4844i			0.687347i	−0.939089	+	0.343674i	$0.888329\pi$
$978$	−50.0789	−	34.9424i	−1.60135	−	1.11734i
$979$		−	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	−0.614308	−	0.789067i	$-0.710565\pi$
$983$	5.47918	−	5.47918i	0.174759	−	0.174759i	0.789067	+	0.614308i	$0.210565\pi$
$984$	29.2216	+	20.3893i	0.931551	+	0.649986i
$985$	7.42415			0.236553
$986$	−26.0417	−	26.0417i	−0.829336	−	0.829336i
$987$	−9.36713	+	13.4248i	−0.298159	+	0.427317i
$988$	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
$993$	15.6633	+	10.9290i	0.497059	+	0.346821i
$994$	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
$999$	−5.38099	+	20.4880i	−0.170247	+	0.648213i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.79987 + 1.79987i) q^{2} +(1.70524 - 0.303587i) q^{3} -4.47903i q^{4} +0.391521 q^{5} +(-2.52278 + 3.61561i) q^{6} +(-0.663363 - 0.663363i) q^{7} +(4.46193 + 4.46193i) q^{8} +(2.81567 - 1.03538i) q^{9} +O(q^{10})\)	\(q+(-1.79987 + 1.79987i) q^{2} +(1.70524 - 0.303587i) q^{3} -4.47903i q^{4} +0.391521 q^{5} +(-2.52278 + 3.61561i) 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} +(-3.20429 + 6.93136i) q^{18} +4.76840i q^{19} -1.75363i q^{20} +(-1.33258 - 0.929803i) q^{21} -7.87938 q^{22} +(-2.39114 + 2.39114i) q^{23} +(8.96323 + 6.25406i) 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} +(-0.987722 + 1.41559i) q^{30} +(6.42776 - 6.42776i) q^{31} +(3.86180 - 3.86180i) q^{32} +(4.39708 + 3.06805i) 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} +(-4.91404 - 3.42875i) q^{51} -25.5454i q^{52} +(-1.16414 + 1.16414i) q^{53} +(-3.35981 + 12.7924i) 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} +(-2.55464 - 1.18098i) 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} +(-3.35155 + 4.80339i) q^{69} +0.934923 q^{70} +(8.79121 + 8.79121i) q^{71} +(17.1831 + 7.94354i) q^{72} -11.4364 q^{73} -10.3767i q^{74} +(-8.26479 + 1.47140i) q^{75} +21.3578 q^{76} -2.90404i q^{77} +(-14.3882 + 20.6210i) 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} +(-4.16462 + 5.96866i) q^{84} +(-0.957748 - 0.957748i) q^{85} -26.6487i q^{86} +(-5.94079 - 4.14517i) q^{87} +19.5332i q^{88} +(-10.3517 - 10.3517i) q^{89} +(-1.25455 + 2.71377i) q^{90} +(-3.78337 - 3.78337i) q^{91} +(10.7100 + 10.7100i) q^{92} +(9.00947 - 12.9122i) q^{93} +(18.1324 + 18.1324i) q^{94} +1.86693i q^{95} +(5.41289 - 7.75767i) q^{96} -3.49985i q^{97} +(11.0150 + 11.0150i) q^{98} +(8.42948 + 3.89685i) 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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