LMFDB - Embedded newform 234.2.z.a.41.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.09566 - 1.34146i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.60132 + 0.964970i) q^{5} +(-1.40553 - 1.01217i) q^{6} +(-2.35233 - 2.35233i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.599043 + 2.93958i) q^{9} +(-3.22885 + 1.86418i) q^{10} +(-1.64094 - 6.12407i) q^{11} +(-1.61960 - 0.613909i) q^{12} +(3.47507 - 0.961205i) q^{13} +(-2.88100 - 1.66335i) q^{14} +(5.24030 + 3.77375i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.38308 + 2.39556i) q^{17} +(0.182189 + 2.99446i) q^{18} +(0.703205 + 2.62440i) q^{19} +(-2.63635 + 2.63635i) q^{20} +(-0.578199 + 5.73292i) q^{21} +(-3.17005 - 5.49069i) q^{22} +0.183009 q^{23} +(-1.72331 - 0.173806i) q^{24} +(7.70819 - 4.45033i) q^{25} +(3.10788 - 1.82787i) q^{26} +(4.59969 - 2.41720i) q^{27} +(-3.21334 - 0.861011i) q^{28} +(-0.821481 - 0.474282i) q^{29} +(6.03846 + 2.28887i) q^{30} +(-0.573581 - 2.14063i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.41729 + 8.91117i) q^{33} +(-0.715935 + 2.67190i) q^{34} +(10.7414 + 6.20155i) q^{35} +(0.951005 + 2.84527i) q^{36} +(1.96458 - 7.33191i) q^{37} +(1.35849 + 2.35297i) q^{38} +(-5.09692 - 3.60851i) q^{39} +(-1.86418 + 3.22885i) q^{40} +(1.66875 + 1.66875i) q^{41} +(0.925290 + 5.68722i) q^{42} -3.66698i q^{43} +(-4.48313 - 4.48313i) q^{44} +(-0.679266 - 11.1644i) q^{45} +(0.176773 - 0.0473661i) q^{46} +(-5.15065 - 1.38011i) q^{47} +(-1.70957 + 0.278141i) q^{48} +4.06688i q^{49} +(6.29371 - 6.29371i) q^{50} +(4.72895 - 0.769383i) q^{51} +(2.52889 - 2.56996i) q^{52} -3.43327i q^{53} +(3.81734 - 3.52532i) q^{54} +(11.8191 + 20.4712i) q^{55} -3.32669 q^{56} +(2.75005 - 3.81878i) q^{57} +(-0.916243 - 0.245507i) q^{58} +(4.52756 + 1.21315i) q^{59} +(6.42511 + 0.648011i) q^{60} -8.27980 q^{61} +(-1.10807 - 1.91924i) q^{62} +(8.32400 - 5.50571i) q^{63} -1.00000i q^{64} +(-11.5873 + 6.81494i) q^{65} +(-3.89224 + 10.2684i) q^{66} +(5.28097 - 5.28097i) q^{67} +2.76616i q^{68} +(-0.200516 - 0.245499i) q^{69} +(11.9805 + 3.21016i) q^{70} +(-11.7943 + 3.16027i) q^{71} +(1.65501 + 2.50219i) q^{72} +(2.16027 + 2.16027i) q^{73} -7.59055i q^{74} +(-14.4155 - 5.46419i) q^{75} +(1.92119 + 1.92119i) q^{76} +(-10.5458 + 18.2658i) q^{77} +(-5.85720 - 2.16638i) q^{78} +(6.31331 + 10.9350i) q^{79} +(-0.964970 + 3.60132i) q^{80} +(-8.28230 - 3.52187i) q^{81} +(2.04380 + 1.17999i) q^{82} +(1.74879 - 6.52658i) q^{83} +(2.36572 + 5.25395i) q^{84} +(2.66926 - 9.96181i) q^{85} +(-0.949085 - 3.54203i) q^{86} +(0.263835 + 1.62164i) q^{87} +(-5.49069 - 3.17005i) q^{88} +(-0.643808 - 0.172508i) q^{89} +(-3.54569 - 10.6082i) q^{90} +(-10.4356 - 5.91342i) q^{91} +(0.158490 - 0.0915043i) q^{92} +(-2.24313 + 3.11485i) q^{93} -5.33235 q^{94} +(-5.06492 - 8.77271i) q^{95} +(-1.57933 + 0.711134i) q^{96} +(4.14023 - 4.14023i) q^{97} +(1.05259 + 3.92830i) q^{98} +(18.9852 - 1.15510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.09566	−	1.34146i	−0.632582	−	0.774494i
$3$	−1.09566	−	1.34146i	−0.632582	−	0.774494i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−3.60132	+	0.964970i	−1.61056	+	0.431548i	−0.948209	−	0.317648i	$-0.897107\pi$
$5$	−3.60132	+	0.964970i	−1.61056	+	0.431548i	−0.662349	+	0.749195i	$0.730440\pi$
$6$	−1.40553	−	1.01217i	−0.573803	−	0.413219i
$7$	−2.35233	−	2.35233i	−0.889096	−	0.889096i	0.105340	−	0.994436i	$-0.466407\pi$
$7$	−2.35233	−	2.35233i	−0.889096	−	0.889096i	−0.994436	+	0.105340i	$0.966407\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.599043	+	2.93958i	−0.199681	+	0.979861i
$10$	−3.22885	+	1.86418i	−1.02105	+	0.589505i
$11$	−1.64094	−	6.12407i	−0.494762	−	1.84648i	−0.531362	−	0.847145i	$-0.678319\pi$
$11$	−1.64094	−	6.12407i	−0.494762	−	1.84648i	0.0366000	−	0.999330i	$-0.488347\pi$
$12$	−1.61960	−	0.613909i	−0.467539	−	0.177220i
$13$	3.47507	−	0.961205i	0.963810	−	0.266590i
$13$	3.47507	−	0.961205i	0.963810	−	0.266590i
$14$	−2.88100	−	1.66335i	−0.769980	−	0.444548i
$15$	5.24030	+	3.77375i	1.35304	+	0.974378i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.38308	+	2.39556i	−0.335446	+	0.581010i	−0.983570	−	0.180525i	$-0.942220\pi$
$17$	−1.38308	+	2.39556i	−0.335446	+	0.581010i	0.648124	+	0.761534i	$0.275554\pi$
$18$	0.182189	+	2.99446i	0.0429424	+	0.705802i
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	0.998480	+	0.0551104i	$0.0175511\pi$
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	−0.837154	+	0.546967i	$0.815782\pi$
$20$	−2.63635	+	2.63635i	−0.589505	+	0.589505i
$21$	−0.578199	+	5.73292i	−0.126173	+	1.25102i
$22$	−3.17005	−	5.49069i	−0.675857	−	1.17062i
$23$	0.183009			0.0381599			0.0190800	−	0.999818i	$-0.493926\pi$
$23$	0.183009			0.0381599			0.0190800	+	0.999818i	$0.493926\pi$
$24$	−1.72331	−	0.173806i	−0.351769	−	0.0354780i
$25$	7.70819	−	4.45033i	1.54164	−	0.890065i
$26$	3.10788	−	1.82787i	0.609505	−	0.358474i
$27$	4.59969	−	2.41720i	0.885211	−	0.465190i
$28$	−3.21334	−	0.861011i	−0.607264	−	0.162716i
$29$	−0.821481	−	0.474282i	−0.152545	−	0.0880720i	0.421784	−	0.906696i	$-0.361404\pi$
$29$	−0.821481	−	0.474282i	−0.152545	−	0.0880720i	−0.574330	+	0.818624i	$0.694737\pi$
$30$	6.03846	+	2.28887i	1.10247	+	0.417889i
$31$	−0.573581	−	2.14063i	−0.103018	−	0.384469i	0.895095	−	0.445876i	$-0.147108\pi$
$31$	−0.573581	−	2.14063i	−0.103018	−	0.384469i	−0.998113	+	0.0614072i	$0.980441\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−6.41729	+	8.91117i	−1.11711	+	1.55124i
$34$	−0.715935	+	2.67190i	−0.122782	+	0.458228i
$35$	10.7414	+	6.20155i	1.81563	+	1.04825i
$36$	0.951005	+	2.84527i	0.158501	+	0.474212i
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	−0.593357	−	0.804939i	$-0.702198\pi$
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	0.916332	−	0.400419i	$-0.131136\pi$
$38$	1.35849	+	2.35297i	0.220376	+	0.381702i
$39$	−5.09692	−	3.60851i	−0.816161	−	0.577825i
$40$	−1.86418	+	3.22885i	−0.294753	+	0.510526i
$41$	1.66875	+	1.66875i	0.260615	+	0.260615i	0.825304	−	0.564689i	$-0.191004\pi$
$41$	1.66875	+	1.66875i	0.260615	+	0.260615i	−0.564689	+	0.825304i	$0.691004\pi$
$42$	0.925290	+	5.68722i	0.142775	+	0.877557i
$43$		−	3.66698i		−	0.559209i	−0.960115	−	0.279605i	$-0.909797\pi$
$43$		−	3.66698i		−	0.559209i	0.960115	−	0.279605i	$-0.0902034\pi$
$44$	−4.48313	−	4.48313i	−0.675857	−	0.675857i
$45$	−0.679266	−	11.1644i	−0.101259	−	1.66429i
$46$	0.176773	−	0.0473661i	0.0260637	−	0.00698375i
$47$	−5.15065	−	1.38011i	−0.751300	−	0.201310i	−0.137205	−	0.990543i	$-0.543812\pi$
$47$	−5.15065	−	1.38011i	−0.751300	−	0.201310i	−0.614095	+	0.789232i	$0.710479\pi$
$48$	−1.70957	+	0.278141i	−0.246756	+	0.0401462i
$49$			4.06688i			0.580983i
$50$	6.29371	−	6.29371i	0.890065	−	0.890065i
$51$	4.72895	−	0.769383i	0.662185	−	0.107735i
$52$	2.52889	−	2.56996i	0.350694	−	0.356389i
$53$		−	3.43327i		−	0.471596i	−0.971802	−	0.235798i	$-0.924230\pi$
$53$		−	3.43327i		−	0.471596i	0.971802	−	0.235798i	$-0.0757704\pi$
$54$	3.81734	−	3.52532i	0.519474	−	0.479736i
$55$	11.8191	+	20.4712i	1.59368	+	2.76034i
$56$	−3.32669			−0.444548
$57$	2.75005	−	3.81878i	0.364253	−	0.505809i
$58$	−0.916243	−	0.245507i	−0.120309	−	0.0322366i
$59$	4.52756	+	1.21315i	0.589438	+	0.157939i	0.541196	−	0.840896i	$-0.317972\pi$
$59$	4.52756	+	1.21315i	0.589438	+	0.157939i	0.0482414	+	0.998836i	$0.484638\pi$
$60$	6.42511	+	0.648011i	0.829478	+	0.0836579i
$61$	−8.27980			−1.06012			−0.530060	−	0.847960i	$-0.677831\pi$
$61$	−8.27980			−1.06012			−0.530060	+	0.847960i	$0.677831\pi$
$62$	−1.10807	−	1.91924i	−0.140725	−	0.243744i
$63$	8.32400	−	5.50571i	1.04873	−	0.693655i
$64$		−	1.00000i		−	0.125000i
$65$	−11.5873	+	6.81494i	−1.43723	+	0.845289i
$66$	−3.89224	+	10.2684i	−0.479102	+	1.26396i
$67$	5.28097	−	5.28097i	0.645174	−	0.645174i	−0.306649	−	0.951823i	$-0.599208\pi$
$67$	5.28097	−	5.28097i	0.645174	−	0.645174i	0.951823	+	0.306649i	$0.0992078\pi$
$68$			2.76616i			0.335446i
$69$	−0.200516	−	0.245499i	−0.0241393	−	0.0295546i
$70$	11.9805	+	3.21016i	1.43194	+	0.383687i
$71$	−11.7943	+	3.16027i	−1.39972	+	0.375055i	−0.878245	−	0.478210i	$-0.841286\pi$
$71$	−11.7943	+	3.16027i	−1.39972	+	0.375055i	−0.521478	+	0.853265i	$0.674619\pi$
$72$	1.65501	+	2.50219i	0.195045	+	0.294885i
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	0.822134	−	0.569294i	$-0.192783\pi$
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	−0.569294	+	0.822134i	$0.692783\pi$
$74$		−	7.59055i		−	0.882384i
$75$	−14.4155	−	5.46419i	−1.66456	−	0.630950i
$76$	1.92119	+	1.92119i	0.220376	+	0.220376i
$77$	−10.5458	+	18.2658i	−1.20180	+	2.08158i
$78$	−5.85720	−	2.16638i	−0.663198	−	0.245294i
$79$	6.31331	+	10.9350i	0.710302	+	1.23028i	0.964744	+	0.263191i	$0.0847751\pi$
$79$	6.31331	+	10.9350i	0.710302	+	1.23028i	−0.254441	+	0.967088i	$0.581892\pi$
$80$	−0.964970	+	3.60132i	−0.107887	+	0.402639i
$81$	−8.28230	−	3.52187i	−0.920255	−	0.391319i
$82$	2.04380	+	1.17999i	0.225700	+	0.130308i
$83$	1.74879	−	6.52658i	0.191955	−	0.716385i	−0.801079	−	0.598558i	$-0.795741\pi$
$83$	1.74879	−	6.52658i	0.191955	−	0.716385i	0.993034	−	0.117827i	$-0.0375928\pi$
$84$	2.36572	+	5.25395i	0.258121	+	0.573253i
$85$	2.66926	−	9.96181i	0.289522	−	1.08051i
$86$	−0.949085	−	3.54203i	−0.102342	−	0.381947i
$87$	0.263835	+	1.62164i	0.0282861	+	0.173858i
$88$	−5.49069	−	3.17005i	−0.585309	−	0.337928i
$89$	−0.643808	−	0.172508i	−0.0682435	−	0.0182858i	0.224536	−	0.974466i	$-0.427913\pi$
$89$	−0.643808	−	0.172508i	−0.0682435	−	0.0182858i	−0.292779	+	0.956180i	$0.594580\pi$
$90$	−3.54569	−	10.6082i	−0.373748	−	1.11820i
$91$	−10.4356	−	5.91342i	−1.09394	−	0.619895i
$92$	0.158490	−	0.0915043i	0.0165237	−	0.00953998i
$93$	−2.24313	+	3.11485i	−0.232601	+	0.322995i
$94$	−5.33235			−0.549990
$95$	−5.06492	−	8.77271i	−0.519650	−	0.900061i
$96$	−1.57933	+	0.711134i	−0.161190	+	0.0725798i
$97$	4.14023	−	4.14023i	0.420377	−	0.420377i	−0.464957	−	0.885334i	$-0.653930\pi$
$97$	4.14023	−	4.14023i	0.420377	−	0.420377i	0.885334	+	0.464957i	$0.153930\pi$
$98$	1.05259	+	3.92830i	0.106327	+	0.396819i
$99$	18.9852	−	1.15510i	1.90808	−	0.116092i
$100$	4.45033	−	7.70819i	0.445033	−	0.770819i
$101$	−4.67593	+	8.09895i	−0.465272	+	0.805875i	−0.999214	−	0.0396462i	$-0.987377\pi$
$101$	−4.67593	+	8.09895i	−0.465272	+	0.805875i	0.533942	+	0.845521i	$0.320710\pi$
$102$	4.36868	−	1.96711i	0.432564	−	0.194773i
$103$	−0.256212	−	0.147924i	−0.0252453	−	0.0145754i	0.487324	−	0.873221i	$-0.337973\pi$
$103$	−0.256212	−	0.147924i	−0.0252453	−	0.0145754i	−0.512570	+	0.858646i	$0.671306\pi$
$104$	1.77757	−	3.13692i	0.174305	−	0.307600i
$105$	−3.44981	−	21.2040i	−0.336667	−	2.06930i
$106$	−0.888596	−	3.31629i	−0.0863081	−	0.322106i
$107$	16.2026	−	9.35458i	1.56636	−	0.904341i	0.569777	−	0.821799i	$-0.307030\pi$
$107$	16.2026	−	9.35458i	1.56636	−	0.904341i	0.996588	−	0.0825417i	$-0.0263038\pi$
$108$	2.77485	−	4.39320i	0.267010	−	0.422736i
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	−0.976743	−	0.214414i	$-0.931216\pi$
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	0.214414	+	0.976743i	$0.431216\pi$
$110$	16.7147	+	16.7147i	1.59368	+	1.59368i
$111$	−11.9880	+	5.39790i	−1.13785	+	0.512346i
$112$	−3.21334	+	0.861011i	−0.303632	+	0.0813579i
$113$	6.05263	−	3.49449i	0.569384	−	0.328734i	−0.187519	−	0.982261i	$-0.560045\pi$
$113$	6.05263	−	3.49449i	0.569384	−	0.328734i	0.756903	+	0.653527i	$0.226711\pi$
$114$	1.66797	−	4.40042i	0.156220	−	0.412137i
$115$	−0.659072	+	0.176598i	−0.0614588	+	0.0164678i
$116$	−0.948565			−0.0880720
$117$	0.743827	+	10.7910i	0.0687668	+	0.997633i
$118$	4.68727			0.431498
$119$	8.88860	−	2.38169i	0.814817	−	0.218330i
$120$	6.37390	−	1.03701i	0.581855	−	0.0946656i
$121$	−25.2852	+	14.5984i	−2.29866	+	1.32713i
$122$	−7.99767	+	2.14297i	−0.724075	+	0.194015i
$123$	0.410178	−	4.06696i	0.0369845	−	0.366706i
$124$	−1.56705	−	1.56705i	−0.140725	−	0.140725i
$125$	−10.2835	+	10.2835i	−0.919782	+	0.919782i
$126$	6.61539	−	7.47252i	0.589345	−	0.665705i
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	−0.560554	−	0.828118i	$-0.689412\pi$
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	0.436894	+	0.899513i	$0.356078\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−4.91912	+	4.01778i	−0.433104	+	0.353746i
$130$	−9.42862	+	9.58173i	−0.826945	+	0.840374i
$131$	8.16562	+	4.71442i	0.713434	+	0.411901i	0.812331	−	0.583197i	$-0.198198\pi$
$131$	8.16562	+	4.71442i	0.713434	+	0.411901i	−0.0988974	+	0.995098i	$0.531532\pi$
$132$	−1.10195	+	10.9259i	−0.0959122	+	0.950981i
$133$	4.51927	−	7.82760i	0.391870	−	0.678739i
$134$	3.73421	−	6.46785i	0.322587	−	0.558737i
$135$	−14.2324	+	13.1437i	−1.22493	+	1.13123i
$136$	0.715935	+	2.67190i	0.0613909	+	0.229114i
$137$	11.4753	−	11.4753i	0.980398	−	0.980398i	−0.0194137	−	0.999812i	$-0.506180\pi$
$137$	11.4753	−	11.4753i	0.980398	−	0.980398i	0.999812	+	0.0194137i	$0.00617995\pi$
$138$	−0.257223	−	0.185237i	−0.0218963	−	0.0157684i
$139$	−4.44710	−	7.70260i	−0.377198	−	0.653326i	0.613456	−	0.789729i	$-0.289779\pi$
$139$	−4.44710	−	7.70260i	−0.377198	−	0.653326i	−0.990653	+	0.136403i	$0.956446\pi$
$140$	12.4031			1.04825
$141$	3.79201	+	8.42155i	0.319345	+	0.709222i
$142$	−10.5745	+	6.10517i	−0.887389	+	0.512334i
$143$	−11.5888	−	19.7043i	−0.969108	−	1.64775i
$144$	2.24623	+	1.98858i	0.187186	+	0.165715i
$145$	3.41608	+	0.915337i	0.283690	+	0.0760146i
$146$	2.64578	+	1.52754i	0.218966	+	0.126420i
$147$	5.45557	−	4.45593i	0.449967	−	0.367519i
$148$	−1.96458	−	7.33191i	−0.161487	−	0.602679i
$149$	6.12277	−	22.8505i	0.501597	−	1.87199i	0.0121988	−	0.999926i	$-0.496117\pi$
$149$	6.12277	−	22.8505i	0.501597	−	1.87199i	0.489398	−	0.872060i	$-0.337216\pi$
$150$	−15.3386	−	1.54699i	−1.25239	−	0.126311i
$151$	−0.0389086	+	0.145209i	−0.00316634	+	0.0118169i	−0.967491	−	0.252906i	$-0.918614\pi$
$151$	−0.0389086	+	0.145209i	−0.00316634	+	0.0118169i	0.964325	+	0.264723i	$0.0852804\pi$
$152$	2.35297	+	1.35849i	0.190851	+	0.110188i
$153$	−6.21343	−	5.50072i	−0.502326	−	0.444707i
$154$	−5.45890	+	20.3729i	−0.439890	+	1.64169i
$155$	4.13129	+	7.15561i	0.331833	+	0.574752i
$156$	−6.21832	−	0.576603i	−0.497864	−	0.0461652i
$157$	0.888484	−	1.53890i	0.0709087	−	0.122818i	−0.828391	−	0.560150i	$-0.810743\pi$
$157$	0.888484	−	1.53890i	0.0709087	−	0.122818i	0.899300	+	0.437333i	$0.144077\pi$
$158$	8.92836	+	8.92836i	0.710302	+	0.710302i
$159$	−4.60561	+	3.76171i	−0.365248	+	0.298323i
$160$			3.72836i			0.294753i
$161$	−0.430496	−	0.430496i	−0.0339278	−	0.0339278i
$162$	−8.91161	−	1.25825i	−0.700162	−	0.0988576i
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	−0.477953	−	0.878385i	$-0.658621\pi$
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	0.0252727	+	0.999681i	$0.491955\pi$
$164$	2.27956	+	0.610806i	0.178004	+	0.0476959i
$165$	14.5117	−	38.2844i	1.12973	−	2.98044i
$166$		−	6.75681i		−	0.524430i
$167$	−12.5881	+	12.5881i	−0.974099	+	0.974099i	−0.999673	−	0.0255737i	$-0.991859\pi$
$167$	−12.5881	+	12.5881i	−0.974099	+	0.974099i	0.0255737	+	0.999673i	$0.491859\pi$
$168$	3.64493	+	4.46263i	0.281213	+	0.344300i
$169$	11.1522	−	6.68050i	0.857859	−	0.513885i
$170$		−	10.3132i		−	0.790989i
$171$	−8.13588	+	0.495003i	−0.622166	+	0.0378538i
$172$	−1.83349	−	3.17570i	−0.139802	−	0.242145i
$173$	14.4245			1.09667			0.548335	−	0.836258i	$-0.315262\pi$
$173$	14.4245			1.09667			0.548335	+	0.836258i	$0.315262\pi$
$174$	0.674556	+	1.49810i	0.0511380	+	0.113571i
$175$	−28.6008	−	7.66356i	−2.16202	−	0.579311i
$176$	−6.12407	−	1.64094i	−0.461619	−	0.123690i
$177$	−3.33328	−	7.40276i	−0.250544	−	0.556425i
$178$	−0.666519			−0.0499577
$179$	7.51417	+	13.0149i	0.561636	+	0.972782i	0.997354	+	0.0726986i	$0.0231611\pi$
$179$	7.51417	+	13.0149i	0.561636	+	0.972782i	−0.435718	+	0.900083i	$0.643506\pi$
$180$	−6.17048	−	9.32905i	−0.459920	−	0.695346i
$181$			7.25012i			0.538897i	0.963015	+	0.269449i	$0.0868414\pi$
$181$			7.25012i			0.538897i	−0.963015	+	0.269449i	$0.913159\pi$
$182$	−11.6105	−	3.01101i	−0.860626	−	0.223191i
$183$	9.07187	+	11.1070i	0.670612	+	0.821056i
$184$	0.129407	−	0.129407i	0.00953998	−	0.00953998i
$185$			28.3003i			2.08068i
$186$	−1.36051	+	3.58928i	−0.0997575	+	0.263179i
$187$	16.9401	+	4.53910i	1.23879	+	0.331932i
$188$	−5.15065	+	1.38011i	−0.375650	+	0.100655i
$189$	−16.5060	−	5.13393i	−1.20064	−	0.373438i
$190$	−7.16289	−	7.16289i	−0.519650	−	0.519650i
$191$			3.18481i			0.230445i	0.993340	+	0.115222i	$0.0367581\pi$
$191$			3.18481i			0.230445i	−0.993340	+	0.115222i	$0.963242\pi$
$192$	−1.34146	+	1.09566i	−0.0968117	+	0.0790727i
$193$	10.0288	+	10.0288i	0.721890	+	0.721890i	0.968990	−	0.247100i	$-0.0794777\pi$
$193$	10.0288	+	10.0288i	0.721890	+	0.721890i	−0.247100	+	0.968990i	$0.579478\pi$
$194$	2.92759	−	5.07073i	0.210189	−	0.364057i
$195$	21.8377	+	8.07703i	1.56383	+	0.578408i
$196$	2.03344	+	3.52202i	0.145246	+	0.251573i
$197$	0.0907674	−	0.338748i	0.00646691	−	0.0241348i	−0.962617	−	0.270866i	$-0.912690\pi$
$197$	0.0907674	−	0.338748i	0.00646691	−	0.0241348i	0.969084	+	0.246731i	$0.0793566\pi$
$198$	18.0393	−	6.02947i	1.28200	−	0.428495i
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.250350	−	0.968155i	$-0.580546\pi$
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.963622	+	0.267268i	$0.913879\pi$
$200$	2.30366	−	8.59737i	0.162893	−	0.607926i
$201$	−12.8704	−	1.29806i	−0.907808	−	0.0915579i
$202$	−2.42044	+	9.03320i	−0.170301	+	0.635574i
$203$	0.816725	+	3.04806i	0.0573229	+	0.213932i
$204$	3.71070	−	3.03078i	0.259801	−	0.212197i
$205$	−7.62000	−	4.39941i	−0.532204	−	0.307268i
$206$	−0.285767	−	0.0765711i	−0.0199103	−	0.00533496i
$207$	−0.109630	+	0.537969i	−0.00761981	+	0.0373914i
$208$	0.905106	−	3.49010i	0.0627578	−	0.241995i
$209$	14.9181	−	8.61294i	1.03190	−	0.595770i
$210$	−8.82026	−	19.5886i	−0.608656	−	1.35174i
$211$	−9.27751			−0.638690			−0.319345	−	0.947639i	$-0.603463\pi$
$211$	−9.27751			−0.638690			−0.319345	+	0.947639i	$0.603463\pi$
$212$	−1.71664	−	2.97330i	−0.117899	−	0.204207i
$213$	17.1619	+	12.3590i	1.17592	+	0.846824i
$214$	13.2294	−	13.2294i	0.904341	−	0.904341i
$215$	3.53853	+	13.2060i	0.241326	+	0.900639i
$216$	1.54325	−	4.96169i	0.105005	−	0.337600i
$217$	−3.68622	+	6.38472i	−0.250237	+	0.433423i
$218$	−5.62783	+	9.74768i	−0.381165	+	0.660196i
$219$	0.530992	−	5.26485i	0.0358811	−	0.355766i
$220$	20.4712	+	11.8191i	1.38017	+	0.796842i
$221$	−2.50367	+	9.65417i	−0.168415	+	0.649409i
$222$	−10.1824	+	8.31669i	−0.683401	+	0.558180i
$223$	4.00521	+	14.9476i	0.268209	+	1.00097i	0.960257	+	0.279117i	$0.0900418\pi$
$223$	4.00521	+	14.9476i	0.268209	+	1.00097i	−0.692048	+	0.721851i	$0.743291\pi$
$224$	−2.88100	+	1.66335i	−0.192495	+	0.111137i
$225$	8.46456	+	25.3248i	0.564304	+	1.68832i
$226$	4.94195	−	4.94195i	0.328734	−	0.328734i
$227$	−5.20029	−	5.20029i	−0.345156	−	0.345156i	0.513146	−	0.858301i	$-0.328480\pi$
$227$	−5.20029	−	5.20029i	−0.345156	−	0.345156i	−0.858301	+	0.513146i	$0.828480\pi$
$228$	0.472227	−	4.68218i	0.0312740	−	0.310085i
$229$	23.9064	−	6.40571i	1.57978	−	0.423301i	0.640923	−	0.767605i	$-0.278552\pi$
$229$	23.9064	−	6.40571i	1.57978	−	0.423301i	0.938858	+	0.344304i	$0.111885\pi$
$230$	−0.590908	+	0.341161i	−0.0389633	+	0.0224955i
$231$	36.0575	−	5.86643i	2.37241	−	0.385983i
$232$	−0.916243	+	0.245507i	−0.0601543	+	0.0161183i
$233$	18.0279			1.18105			0.590525	−	0.807019i	$-0.298921\pi$
$233$	18.0279			1.18105			0.590525	+	0.807019i	$0.298921\pi$
$234$	3.51141	+	10.2308i	0.229548	+	0.668811i
$235$	19.8809			1.29689
$236$	4.52756	−	1.21315i	0.294719	−	0.0789697i
$237$	7.75159	−	20.4501i	0.503520	−	1.32838i
$238$	7.96930	−	4.60108i	0.516573	−	0.298244i
$239$	27.5256	−	7.37545i	1.78048	−	0.477078i	0.789809	−	0.613353i	$-0.210180\pi$
$239$	27.5256	−	7.37545i	1.78048	−	0.477078i	0.990671	+	0.136275i	$0.0435130\pi$
$240$	5.88831	−	2.65136i	0.380089	−	0.171145i
$241$	5.67035	+	5.67035i	0.365259	+	0.365259i	0.865745	−	0.500486i	$-0.166845\pi$
$241$	5.67035	+	5.67035i	0.365259	+	0.365259i	−0.500486	+	0.865745i	$0.666845\pi$
$242$	−20.6453	+	20.6453i	−1.32713	+	1.32713i
$243$	4.35015	+	14.9692i	0.279062	+	0.960273i
$244$	−7.17052	+	4.13990i	−0.459045	+	0.265030i
$245$	−3.92442	−	14.6461i	−0.250722	−	0.935706i
$246$	−0.656406	−	4.03454i	−0.0418509	−	0.257233i
$247$	4.96626	+	8.44402i	0.315996	+	0.537280i
$248$	−1.91924	−	1.10807i	−0.121872	−	0.0703627i
$249$	−10.6712	+	4.80499i	−0.676263	+	0.304504i
$250$	−7.27151	+	12.5946i	−0.459891	+	0.796554i
$251$	3.03917	−	5.26399i	0.191830	−	0.332260i	−0.754026	−	0.656844i	$-0.771891\pi$
$251$	3.03917	−	5.26399i	0.191830	−	0.332260i	0.945857	+	0.324584i	$0.105224\pi$
$252$	4.45594	−	8.93009i	0.280698	−	0.562543i
$253$	−0.300306	−	1.12076i	−0.0188801	−	0.0704614i
$254$	−1.13784	+	1.13784i	−0.0713947	+	0.0713947i
$255$	−16.2880	+	7.33408i	−1.01999	+	0.459278i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.638781			−0.0398461			−0.0199230	−	0.999802i	$-0.506342\pi$
$257$	−0.638781			−0.0398461			−0.0199230	+	0.999802i	$0.506342\pi$
$258$	−3.71163	+	5.15404i	−0.231076	+	0.320876i
$259$	−21.8684	+	12.6257i	−1.35883	+	0.784524i
$260$	−6.62741	+	11.6955i	−0.411015	+	0.725327i
$261$	1.88630	−	2.13070i	0.116759	−	0.131887i
$262$	9.10757	+	2.44037i	0.562667	+	0.150766i
$263$	−4.87985	−	2.81738i	−0.300905	−	0.173727i	0.341945	−	0.939720i	$-0.388914\pi$
$263$	−4.87985	−	2.81738i	−0.300905	−	0.173727i	−0.642849	+	0.765993i	$0.722248\pi$
$264$	1.76344	+	10.8389i	0.108532	+	0.667086i
$265$	3.31300	+	12.3643i	0.203516	+	0.759533i
$266$	2.33934	−	8.73055i	0.143434	−	0.535305i
$267$	0.473984	+	1.05265i	0.0290073	+	0.0644214i
$268$	1.93297	−	7.21395i	0.118075	−	0.440662i
$269$	17.6754	+	10.2049i	1.07769	+	0.622202i	0.930271	−	0.366873i	$-0.119572\pi$
$269$	17.6754	+	10.2049i	1.07769	+	0.622202i	0.147415	+	0.989075i	$0.452905\pi$
$270$	−10.3456	+	16.3794i	−0.629615	+	0.996820i
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	−0.565204	−	0.824951i	$-0.691202\pi$
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	0.901956	−	0.431827i	$-0.142131\pi$
$272$	1.38308	+	2.39556i	0.0838615	+	0.145252i
$273$	3.50122	+	20.4780i	0.211904	+	1.23939i
$274$	8.11424	−	14.0543i	0.490199	−	0.849049i
$275$	−39.9027	−	39.9027i	−2.40623	−	2.40623i
$276$	−0.296401	−	0.112351i	−0.0178413	−	0.00676271i
$277$		−	4.82222i		−	0.289739i	−0.989451	−	0.144869i	$-0.953724\pi$
$277$		−	4.82222i		−	0.289739i	0.989451	−	0.144869i	$-0.0462762\pi$
$278$	−6.28914	−	6.28914i	−0.377198	−	0.377198i
$279$	6.63617	−	0.403757i	0.397297	−	0.0241723i
$280$	11.9805	−	3.21016i	0.715970	−	0.191844i
$281$	−3.64034	−	0.975427i	−0.217165	−	0.0581891i	0.148596	−	0.988898i	$-0.452525\pi$
$281$	−3.64034	−	0.975427i	−0.217165	−	0.0581891i	−0.365761	+	0.930709i	$0.619191\pi$
$282$	5.84246	+	7.15315i	0.347913	+	0.425964i
$283$		−	12.5997i		−	0.748977i	−0.927232	−	0.374489i	$-0.877818\pi$
$283$		−	12.5997i		−	0.748977i	0.927232	−	0.374489i	$-0.122182\pi$
$284$	−8.63401	+	8.63401i	−0.512334	+	0.512334i
$285$	−6.21880	+	16.4063i	−0.368370	+	0.971828i
$286$	−16.2938	−	16.0334i	−0.963473	−	0.948077i
$287$		−	7.85090i		−	0.463424i
$288$	2.68438	+	1.33945i	0.158178	+	0.0789279i
$289$	4.67418	+	8.09592i	0.274952	+	0.476231i
$290$	3.53659			0.207676
$291$	−10.0903	−	1.01766i	−0.591502	−	0.0596566i
$292$	2.95098	+	0.790714i	0.172693	+	0.0462730i
$293$	−28.7098	−	7.69277i	−1.67724	−	0.449416i	−0.710195	−	0.704005i	$-0.751393\pi$
$293$	−28.7098	−	7.69277i	−1.67724	−	0.449416i	−0.967050	+	0.254588i	$0.918060\pi$
$294$	4.11639	−	5.71610i	0.240073	−	0.333370i
$295$	−17.4758			−1.01748
$296$	−3.79528	−	6.57361i	−0.220596	−	0.382083i
$297$	−22.3509	−	24.2023i	−1.29693	−	1.40436i
$298$		−	23.6566i		−	1.37039i
$299$	0.635967	−	0.175909i	0.0367789	−	0.0101731i
$300$	−15.2163	+	2.47564i	−0.878514	+	0.142931i
$301$	−8.62594	+	8.62594i	−0.497191	+	0.497191i
$302$			0.150331i			0.00865059i
$303$	15.9877	−	2.60114i	0.918468	−	0.149431i
$304$	2.62440	+	0.703205i	0.150519	+	0.0403315i
$305$	29.8182	−	7.98976i	1.70738	−	0.457492i
$306$	−7.42541	−	3.70513i	−0.424482	−	0.211808i
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.921376	−	0.388674i	$-0.872933\pi$
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.388674	−	0.921376i	$-0.627067\pi$
$308$			21.0916i			1.20180i
$309$	0.0822875	+	0.505773i	0.00468117	+	0.0287724i
$310$	5.84253	+	5.84253i	0.331833	+	0.331833i
$311$	11.8059	−	20.4483i	0.669449	−	1.15952i	−0.308610	−	0.951189i	$-0.599864\pi$
$311$	11.8059	−	20.4483i	0.669449	−	1.15952i	0.978058	−	0.208331i	$-0.0668030\pi$
$312$	−6.15567	+	1.05246i	−0.348496	+	0.0595840i
$313$	8.71521	+	15.0952i	0.492613	+	0.853230i	0.999964	−	0.00850920i	$-0.00270860\pi$
$313$	8.71521	+	15.0952i	0.492613	+	0.853230i	−0.507351	+	0.861739i	$0.669375\pi$
$314$	0.459913	−	1.71642i	0.0259544	−	0.0968631i
$315$	−24.6645	+	27.8602i	−1.38969	+	1.56975i
$316$	10.9350	+	6.31331i	0.615140	+	0.355151i
$317$	0.162090	−	0.604929i	0.00910389	−	0.0339762i	−0.961224	−	0.275767i	$-0.911068\pi$
$317$	0.162090	−	0.604929i	0.00910389	−	0.0339762i	0.970328	+	0.241791i	$0.0777348\pi$
$318$	−3.47507	+	4.82555i	−0.194872	+	0.270604i
$319$	−1.55654	+	5.80907i	−0.0871493	+	0.325246i
$320$	0.964970	+	3.60132i	0.0539435	+	0.201320i
$321$	−30.3014	−	11.4857i	−1.69126	−	0.641070i
$322$	−0.527248	−	0.304407i	−0.0293824	−	0.0169639i
$323$	−7.25949	−	1.94518i	−0.403929	−	0.108232i
$324$	−8.93361	+	1.09112i	−0.496312	+	0.0606176i
$325$	22.5088	−	22.8743i	1.24856	−	1.26884i
$326$	−5.18170	+	2.99166i	−0.286988	+	0.165693i
$327$	19.3970	+	1.95630i	1.07265	+	0.108184i
$328$	2.35997			0.130308
$329$	8.86954	+	15.3625i	0.488994	+	0.846962i
$330$	4.10846	−	40.7358i	0.226163	−	2.24243i
$331$	−21.8617	+	21.8617i	−1.20163	+	1.20163i	−0.227958	+	0.973671i	$0.573205\pi$
$331$	−21.8617	+	21.8617i	−1.20163	+	1.20163i	−0.973671	+	0.227958i	$0.926795\pi$
$332$	−1.74879	−	6.52658i	−0.0959774	−	0.358192i
$333$	20.3759	+	10.1672i	1.11659	+	0.557158i
$334$	−8.90116	+	15.4173i	−0.487050	+	0.843595i
$335$	−13.9225	+	24.1144i	−0.760666	+	1.31751i
$336$	4.67575	+	3.36719i	0.255083	+	0.183695i
$337$	−7.79004	−	4.49758i	−0.424350	−	0.244999i	0.272586	−	0.962131i	$-0.412121\pi$
$337$	−7.79004	−	4.49758i	−0.424350	−	0.244999i	−0.696937	+	0.717132i	$0.745454\pi$
$338$	9.04313	−	9.33926i	0.491881	−	0.507989i
$339$	−11.3194	−	4.29059i	−0.614784	−	0.233033i
$340$	−2.66926	−	9.96181i	−0.144761	−	0.540255i
$341$	−12.1682	+	7.02529i	−0.658943	+	0.380441i
$342$	−7.73054	+	2.58386i	−0.418020	+	0.139719i
$343$	−6.89966	+	6.89966i	−0.372547	+	0.372547i
$344$	−2.59295	−	2.59295i	−0.139802	−	0.139802i
$345$	0.959021	+	0.690629i	0.0516319	+	0.0371822i
$346$	13.9330	−	3.73332i	0.749040	−	0.200705i
$347$	6.43324	−	3.71423i	0.345354	−	0.199390i	−0.317283	−	0.948331i	$-0.602770\pi$
$347$	6.43324	−	3.71423i	0.345354	−	0.199390i	0.662637	+	0.748940i	$0.269437\pi$
$348$	1.03931	+	1.27246i	0.0557128	+	0.0682112i
$349$	−34.8605	+	9.34084i	−1.86604	+	0.500004i	−0.866040	+	0.499976i	$0.833342\pi$
$349$	−34.8605	+	9.34084i	−1.86604	+	0.500004i	−1.00000		2.82454e-5i	$0.999991\pi$
$350$	−29.6097			−1.58271
$351$	13.6608	−	12.8212i	0.729160	−	0.684344i
$352$	−6.34010			−0.337928
$353$	−2.96901	+	0.795543i	−0.158024	+	0.0423425i	−0.336964	−	0.941518i	$-0.609400\pi$
$353$	−2.96901	+	0.795543i	−0.158024	+	0.0423425i	0.178940	+	0.983860i	$0.442733\pi$
$354$	−5.13567	−	6.28780i	−0.272958	−	0.334193i
$355$	39.4254	−	22.7622i	2.09248	−	1.20809i
$356$	−0.643808	+	0.172508i	−0.0341217	+	0.00914289i
$357$	−12.9339	−	9.31419i	−0.684533	−	0.492959i
$358$	10.6266	+	10.6266i	0.561636	+	0.561636i
$359$	−9.73682	+	9.73682i	−0.513890	+	0.513890i	−0.915716	−	0.401826i	$-0.868376\pi$
$359$	−9.73682	+	9.73682i	−0.513890	+	0.513890i	0.401826	+	0.915716i	$0.368376\pi$
$360$	−8.37476	−	7.41413i	−0.441388	−	0.390759i
$361$	10.0615	−	5.80903i	0.529554	−	0.305738i
$362$	1.87647	+	7.00308i	0.0986250	+	0.368074i
$363$	47.2873	+	17.9242i	2.48194	+	0.940777i
$364$	−11.9942	+	0.0966037i	−0.628665	+	0.00506341i
$365$	−9.86442	−	5.69522i	−0.516327	−	0.298102i
$366$	11.6375	+	8.38060i	0.608300	+	0.438061i
$367$	7.93848	−	13.7499i	0.414385	−	0.717736i	−0.580978	−	0.813919i	$-0.697330\pi$
$367$	7.93848	−	13.7499i	0.414385	−	0.717736i	0.995364	+	0.0961826i	$0.0306633\pi$
$368$	0.0915043	−	0.158490i	0.00476999	−	0.00826187i
$369$	−5.90509	+	3.90578i	−0.307407	+	0.203327i
$370$	7.32466	+	27.3360i	0.380791	+	1.42113i
$371$	−8.07618	+	8.07618i	−0.419294	+	0.419294i
$372$	−0.385180	+	3.81910i	−0.0199706	+	0.198011i
$373$	0.362643	+	0.628115i	0.0187769	+	0.0325226i	0.875261	−	0.483651i	$-0.160689\pi$
$373$	0.362643	+	0.628115i	0.0187769	+	0.0325226i	−0.856484	+	0.516173i	$0.827356\pi$
$374$	17.5377			0.906854
$375$	25.0621	+	2.52767i	1.29420	+	0.130528i
$376$	−4.61795	+	2.66617i	−0.238153	+	0.137497i
$377$	−3.31058	−	0.858551i	−0.170504	−	0.0442176i
$378$	−17.2723	−	0.686922i	−0.888394	−	0.0353314i
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	0.182850	−	0.983141i	$-0.441468\pi$
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	−0.333217	+	0.942850i	$0.608134\pi$
$380$	−8.77271	−	5.06492i	−0.450030	−	0.259825i
$381$	2.60619	+	0.987875i	0.133519	+	0.0506104i
$382$	0.824290	+	3.07629i	0.0421744	+	0.157397i
$383$	−0.508512	+	1.89779i	−0.0259837	+	0.0969727i	−0.977700	−	0.210006i	$-0.932652\pi$
$383$	−0.508512	+	1.89779i	−0.0259837	+	0.0969727i	0.951716	+	0.306979i	$0.0993182\pi$
$384$	−1.01217	+	1.40553i	−0.0516523	+	0.0717254i
$385$	20.3527	−	75.9574i	1.03727	−	3.87115i
$386$	12.2827	+	7.09144i	0.625175	+	0.360945i
$387$	10.7794	+	2.19668i	0.547947	+	0.111663i
$388$	1.51543	−	5.65566i	0.0769343	−	0.287123i
$389$	−11.5891	−	20.0729i	−0.587591	−	1.01774i	−0.994547	−	0.104289i	$-0.966743\pi$
$389$	−11.5891	−	20.0729i	−0.587591	−	1.01774i	0.406956	−	0.913448i	$-0.366590\pi$
$390$	23.1841	+	2.14978i	1.17397	+	0.108859i
$391$	−0.253115	+	0.438409i	−0.0128006	+	0.0221713i
$392$	2.87572	+	2.87572i	0.145246	+	0.145246i
$393$	−2.62255	−	16.1193i	−0.132290	−	0.813111i
$394$		−	0.350698i		−	0.0176679i
$395$	−33.2881	−	33.2881i	−1.67491	−	1.67491i
$396$	15.8641	−	10.4929i	0.797201	−	0.527290i
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	−0.353160	−	0.935563i	$-0.614893\pi$
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	0.161936	+	0.986801i	$0.448226\pi$
$398$	−19.1007	−	5.11801i	−0.957430	−	0.256543i
$399$	−15.4520	+	2.51399i	−0.773569	+	0.125857i
$400$		−	8.90065i		−	0.445033i
$401$	−15.7326	+	15.7326i	−0.785651	+	0.785651i	−0.980778	−	0.195127i	$-0.937488\pi$
$401$	−15.7326	+	15.7326i	−0.785651	+	0.785651i	0.195127	+	0.980778i	$0.437488\pi$
$402$	−12.7678	+	2.07728i	−0.636801	+	0.103605i
$403$	−4.05082	−	6.88751i	−0.201786	−	0.343091i
$404$			9.35186i			0.465272i
$405$	33.2257	+	4.69121i	1.65100	+	0.233108i
$406$	1.57779	+	2.73282i	0.0783045	+	0.135627i
$407$	−48.1249			−2.38546
$408$	2.79984	−	3.88791i	0.138613	−	0.192480i
$409$	27.3204	+	7.32049i	1.35091	+	0.361975i	0.860470	−	0.509501i	$-0.170170\pi$
$409$	27.3204	+	7.32049i	1.35091	+	0.361975i	0.490439	+	0.871476i	$0.336837\pi$
$410$	−8.49901	−	2.27730i	−0.419736	−	0.112468i
$411$	−27.9667	−	2.82061i	−1.37949	−	0.139130i
$412$	−0.295848			−0.0145754
$413$	−7.79655	−	13.5040i	−0.383643	−	0.664490i
$414$	0.0333422	+	0.548013i	0.00163868	+	0.0269333i
$415$			25.1918i			1.23662i
$416$	−0.0290390	−	3.60543i	−0.00142375	−	0.176771i
$417$	−5.46022	+	14.4051i	−0.267388	+	0.705419i
$418$	12.1805	−	12.1805i	0.595770	−	0.595770i
$419$		−	11.2240i		−	0.548326i	−0.961683	−	0.274163i	$-0.911599\pi$
$419$		−	11.2240i		−	0.548326i	0.961683	−	0.274163i	$-0.0884008\pi$
$420$	−13.5896	−	16.6383i	−0.663106	−	0.811865i
$421$	0.958636	+	0.256866i	0.0467211	+	0.0125189i	0.282104	−	0.959384i	$-0.408968\pi$
$421$	0.958636	+	0.256866i	0.0467211	+	0.0125189i	−0.235383	+	0.971903i	$0.575634\pi$
$422$	−8.96138	+	2.40120i	−0.436233	+	0.116888i
$423$	7.14242	−	14.3140i	0.347276	−	0.695972i
$424$	−2.42769	−	2.42769i	−0.117899	−	0.117899i
$425$			24.6206i			1.19428i
$426$	19.7759	+	7.49603i	0.958145	+	0.363184i
$427$	19.4768	+	19.4768i	0.942548	+	0.942548i
$428$	9.35458	−	16.2026i	0.452171	−	0.783182i
$429$	−13.7350	+	37.1352i	−0.663134	+	1.79291i
$430$	6.83591	+	11.8401i	0.329657	+	0.570982i
$431$	1.41740	−	5.28983i	0.0682740	−	0.254802i	−0.923350	−	0.383959i	$-0.874560\pi$
$431$	1.41740	−	5.28983i	0.0682740	−	0.254802i	0.991624	+	0.129157i	$0.0412271\pi$
$432$	0.206488	−	5.19205i	0.00993466	−	0.249803i
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	0.0968497	−	0.995299i	$-0.469123\pi$
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	−0.813529	+	0.581524i	$0.802457\pi$
$434$	−1.90813	+	7.12122i	−0.0915930	+	0.341830i
$435$	−2.51499	−	5.58545i	−0.120584	−	0.267802i
$436$	−2.91318	+	10.8721i	−0.139516	+	0.520681i
$437$	0.128693	+	0.480287i	0.00615620	+	0.0229752i
$438$	−0.849745	−	5.22289i	−0.0406024	−	0.249559i
$439$	−4.45830	−	2.57400i	−0.212783	−	0.122850i	0.389821	−	0.920891i	$-0.372537\pi$
$439$	−4.45830	−	2.57400i	−0.212783	−	0.122850i	−0.602604	+	0.798040i	$0.705870\pi$
$440$	22.8327	+	6.11801i	1.08851	+	0.291664i
$441$	−11.9549	−	2.43624i	−0.569282	−	0.116011i
$442$	0.0803264	+	9.97320i	0.00382074	+	0.474377i
$443$	19.9015	−	11.4901i	0.945547	−	0.545912i	0.0538522	−	0.998549i	$-0.482850\pi$
$443$	19.9015	−	11.4901i	0.945547	−	0.545912i	0.891695	+	0.452637i	$0.149517\pi$
$444$	−7.68296	+	10.6687i	−0.364617	+	0.506315i
$445$	2.48502			0.117801
$446$	7.73747	+	13.4017i	0.366380	+	0.634589i
$447$	−37.3616	+	16.8230i	−1.76714	+	0.795700i
$448$	−2.35233	+	2.35233i	−0.111137	+	0.111137i
$449$	4.11231	+	15.3473i	0.194072	+	0.724286i	0.992505	+	0.122203i	$0.0389958\pi$
$449$	4.11231	+	15.3473i	0.194072	+	0.724286i	−0.798433	+	0.602083i	$0.794338\pi$
$450$	14.7307	+	22.2711i	0.694411	+	1.04987i
$451$	7.48123	−	12.9579i	0.352277	−	0.610162i
$452$	3.49449	−	6.05263i	0.164367	−	0.284692i
$453$	0.237423	−	0.106906i	0.0111551	−	0.00502286i
$454$	−6.36903	−	3.67716i	−0.298913	−	0.172578i
$455$	43.2880	+	11.2261i	2.02937	+	0.526288i
$456$	−0.755702	−	4.64486i	−0.0353890	−	0.217516i
$457$	6.71190	+	25.0491i	0.313969	+	1.17175i	0.924945	+	0.380100i	$0.124111\pi$
$457$	6.71190	+	25.0491i	0.313969	+	1.17175i	−0.610976	+	0.791649i	$0.709223\pi$
$458$	21.4339	−	12.3749i	1.00154	−	0.578240i
$459$	−0.571179	+	14.3620i	−0.0266603	+	0.670362i
$460$	−0.482474	+	0.482474i	−0.0224955	+	0.0224955i
$461$	−1.18882	−	1.18882i	−0.0553688	−	0.0553688i	0.678880	−	0.734249i	$-0.262466\pi$
$461$	−1.18882	−	1.18882i	−0.0553688	−	0.0553688i	−0.734249	+	0.678880i	$0.762466\pi$
$462$	33.3106	−	14.9989i	1.54975	−	0.697813i
$463$	−16.7848	+	4.49747i	−0.780055	+	0.209015i	−0.626809	−	0.779173i	$-0.715639\pi$
$463$	−16.7848	+	4.49747i	−0.780055	+	0.209015i	−0.153246	+	0.988188i	$0.548973\pi$
$464$	−0.821481	+	0.474282i	−0.0381363	+	0.0220180i
$465$	5.07247	−	13.3821i	0.235230	−	0.620581i
$466$	17.4137	−	4.66597i	0.806672	−	0.216147i
$467$	0.582570			0.0269581			0.0134791	−	0.999909i	$-0.495709\pi$
$467$	0.582570			0.0269581			0.0134791	+	0.999909i	$0.495709\pi$
$468$	6.03970	+	8.97341i	0.279185	+	0.414796i
$469$	−24.8452			−1.14724
$470$	19.2035	−	5.14556i	0.885791	−	0.237347i
$471$	−3.03785	+	0.494248i	−0.139977	+	0.0227737i
$472$	4.05930	−	2.34364i	0.186844	−	0.107875i
$473$	−22.4568	+	6.01729i	−1.03257	+	0.276675i
$474$	2.19458	−	21.7595i	0.100800	−	0.999449i
$475$	17.0998	+	17.0998i	0.784595	+	0.784595i
$476$	6.50691	−	6.50691i	0.298244	−	0.298244i
$477$	10.0924	+	2.05668i	0.462099	+	0.0941688i
$478$	24.6787	−	14.2483i	1.12878	−	0.651701i
$479$	−2.02458	−	7.55584i	−0.0925055	−	0.345235i	0.904124	−	0.427270i	$-0.140525\pi$
$479$	−2.02458	−	7.55584i	−0.0925055	−	0.345235i	−0.996629	+	0.0820351i	$0.973858\pi$
$480$	5.00145	−	4.08503i	0.228284	−	0.186455i
$481$	−0.220422	−	27.3672i	−0.0100504	−	1.24784i
$482$	6.94473	+	4.00954i	0.316324	+	0.182630i
$483$	−0.105815	+	1.04917i	−0.00481477	+	0.0477390i
$484$	−14.5984	+	25.2852i	−0.663565	+	1.14933i
$485$	−10.9151	+	18.9055i	−0.495629	+	0.858454i
$486$	8.07623	+	13.3332i	0.366345	+	0.604807i
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	0.990425	−	0.138049i	$-0.0440831\pi$
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	−0.926758	+	0.375659i	$0.877416\pi$
$488$	−5.85470	+	5.85470i	−0.265030	+	0.265030i
$489$	8.40971	+	6.05616i	0.380300	+	0.273869i
$490$	−7.58139	−	13.1314i	−0.342492	−	0.593214i
$491$	2.40308			0.108449			0.0542247	−	0.998529i	$-0.482731\pi$
$491$	2.40308			0.108449			0.0542247	+	0.998529i	$0.482731\pi$
$492$	−1.67826	−	3.72718i	−0.0756616	−	0.168034i
$493$	2.27235	−	1.31194i	0.102341	−	0.0590868i
$494$	6.98252	+	6.87094i	0.314158	+	0.309138i
$495$	−67.2571	+	22.4800i	−3.02298	+	1.01040i
$496$	−2.14063	−	0.573581i	−0.0961172	−	0.0257545i
$497$	35.1780	+	20.3100i	1.57795	+	0.911028i
$498$	−9.06401	+	7.40319i	−0.406168	+	0.331745i
$499$	1.61344	+	6.02143i	0.0722273	+	0.269556i	0.992590	−	0.121509i	$-0.0387734\pi$
$499$	1.61344	+	6.02143i	0.0722273	+	0.269556i	−0.920363	+	0.391065i	$0.872107\pi$
$500$	−3.76401	+	14.0475i	−0.168332	+	0.628222i
$501$	30.6789	+	3.09415i	1.37063	+	0.138236i
$502$	1.57319	−	5.87122i	0.0702148	−	0.262045i
$503$	11.8442	+	6.83823i	0.528105	+	0.304901i	0.740244	−	0.672338i	$-0.234710\pi$
$503$	11.8442	+	6.83823i	0.528105	+	0.304901i	−0.212140	+	0.977239i	$0.568043\pi$
$504$	1.99283	−	9.77909i	0.0887678	−	0.435595i
$505$	9.02426	−	33.6790i	0.401574	−	1.49870i
$506$	−0.580146	−	1.00484i	−0.0257907	−	0.0446707i
$507$	−21.1807	−	7.64064i	−0.940666	−	0.339333i
$508$	−0.804578	+	1.39357i	−0.0356974	+	0.0618297i
$509$	5.61611	+	5.61611i	0.248930	+	0.248930i	0.820531	−	0.571602i	$-0.193678\pi$
$509$	5.61611	+	5.61611i	0.248930	+	0.248930i	−0.571602	+	0.820531i	$0.693678\pi$
$510$	−13.8348	+	11.2998i	−0.612616	+	0.500365i
$511$		−	10.1633i		−	0.449599i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	9.57821	+	10.3716i	0.422888	+	0.457918i
$514$	−0.617015	+	0.165329i	−0.0272154	+	0.00729234i
$515$	1.06544	+	0.285484i	0.0469490	+	0.0125799i
$516$	−2.25119	+	5.93906i	−0.0991032	+	0.261452i
$517$			33.8076i			1.48686i
$518$	−17.8555	+	17.8555i	−0.784524	+	0.784524i
$519$	−15.8043	−	19.3499i	−0.693734	−	0.849365i
$520$	−3.37456	+	13.0123i	−0.147984	+	0.570629i
$521$		−	40.0151i		−	1.75309i	−0.481316	−	0.876547i	$-0.659841\pi$
$521$		−	40.0151i		−	1.75309i	0.481316	−	0.876547i	$-0.340159\pi$
$522$	1.27056	−	2.54630i	0.0556107	−	0.111449i
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	0.955388	−	0.295353i	$-0.0954371\pi$
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	−0.733477	+	0.679714i	$0.762104\pi$
$524$	9.42885			0.411901
$525$	21.0565	+	46.7636i	0.918980	+	2.04093i
$526$	−5.44277	−	1.45838i	−0.237316	−	0.0635886i
$527$	5.92133	+	1.58662i	0.257937	+	0.0691141i
$528$	4.50866	+	10.0131i	0.196214	+	0.435765i
$529$	−22.9665			−0.998544
$530$	6.40023	+	11.0855i	0.278008	+	0.481525i
$531$	−6.27837	+	12.5824i	−0.272458	+	0.546029i
$532$		−	9.03853i		−	0.391870i
$533$	7.40304	+	4.19501i	0.320661	+	0.181706i
$534$	0.730280	+	0.894110i	0.0316023	+	0.0386919i
$535$	−49.3238	+	49.3238i	−2.13245	+	2.13245i
$536$		−	7.46843i		−	0.322587i
$537$	9.22604	−	24.3400i	0.398133	−	1.05035i
$538$	19.7143	+	5.28243i	0.849944	+	0.227742i
$539$	24.9058	−	6.67350i	1.07277	−	0.287448i
$540$	−5.75380	+	18.4990i	−0.247604	+	0.796068i
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.998836	+	0.0482280i	$0.0153574\pi$
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.0482280	+	0.998836i	$0.484643\pi$
$542$		−	21.4190i		−	0.920026i
$543$	9.72577	−	7.94369i	0.417373	−	0.340897i
$544$	1.95597	+	1.95597i	0.0838615	+	0.0838615i
$545$	20.9826	−	36.3429i	0.898794	−	1.55676i
$546$	8.68203	+	18.8741i	0.371556	+	0.807736i
$547$	−3.38921	−	5.87029i	−0.144912	−	0.250996i	0.784428	−	0.620220i	$-0.212957\pi$
$547$	−3.38921	−	5.87029i	−0.144912	−	0.250996i	−0.929340	+	0.369224i	$0.879623\pi$
$548$	4.20024	−	15.6755i	0.179425	−	0.669624i
$549$	4.95995	−	24.3392i	0.211686	−	1.03877i
$550$	−48.8707	−	28.2155i	−2.08385	−	1.20311i
$551$	0.667035	−	2.48941i	0.0284167	−	0.106052i
$552$	−0.315380	−	0.0318080i	−0.0134235	−	0.00135384i
$553$	10.8717	−	40.5736i	0.462310	−	1.72536i
$554$	−1.24808	−	4.65790i	−0.0530259	−	0.197895i
$555$	37.9638	−	31.0076i	1.61147	−	1.31620i
$556$	−7.70260	−	4.44710i	−0.326663	−	0.188599i
$557$	41.9906	+	11.2513i	1.77920	+	0.476734i	0.990437	−	0.137967i	$-0.0440568\pi$
$557$	41.9906	+	11.2513i	1.77920	+	0.476734i	0.788760	+	0.614701i	$0.210723\pi$
$558$	6.30554	−	2.10757i	0.266935	−	0.0892204i
$559$	−3.52472	−	12.7430i	−0.149080	−	0.538972i
$560$	10.7414	−	6.20155i	0.453907	−	0.262063i
$561$	−12.4717	−	27.6979i	−0.526554	−	1.16941i
$562$	−3.76876			−0.158976
$563$	0.819395	+	1.41923i	0.0345334	+	0.0598136i	0.882776	−	0.469795i	$-0.155672\pi$
$563$	0.819395	+	1.41923i	0.0345334	+	0.0598136i	−0.848242	+	0.529609i	$0.822339\pi$
$564$	7.49475	+	5.39727i	0.315586	+	0.227266i
$565$	−18.4254	+	18.4254i	−0.775161	+	0.775161i
$566$	−3.26105	−	12.1704i	−0.137072	−	0.511561i
$567$	11.1981	+	27.7673i	0.470275	+	1.16612i
$568$	−6.10517	+	10.5745i	−0.256167	+	0.443694i
$569$	1.54435	−	2.67489i	0.0647424	−	0.112137i	−0.831837	−	0.555020i	$-0.812711\pi$
$569$	1.54435	−	2.67489i	0.0647424	−	0.112137i	0.896580	+	0.442882i	$0.146044\pi$
$570$	−1.76063	+	17.4569i	−0.0737447	+	0.731187i
$571$	−5.59791	−	3.23195i	−0.234265	−	0.135253i	0.378273	−	0.925694i	$-0.376518\pi$
$571$	−5.59791	−	3.23195i	−0.234265	−	0.135253i	−0.612538	+	0.790441i	$0.709851\pi$
$572$	−19.8884	−	11.2700i	−0.831574	−	0.471221i
$573$	4.27231	−	3.48948i	0.178478	−	0.145775i
$574$	−2.03196	−	7.58339i	−0.0848125	−	0.316525i
$575$	1.41067	−	0.814448i	0.0588288	−	0.0339648i
$576$	2.93958	+	0.599043i	0.122483	+	0.0249601i
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.432795	−	0.901492i	$-0.357527\pi$
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.901492	−	0.432795i	$-0.142473\pi$
$578$	6.61029	+	6.61029i	0.274952	+	0.274952i
$579$	2.46507	−	24.4415i	0.102445	−	1.01575i
$580$	3.41608	−	0.915337i	0.141845	−	0.0380073i
$581$	−19.4664	+	11.2389i	−0.807601	+	0.466269i
$582$	−10.0098	+	1.62857i	−0.414921	+	0.0675062i
$583$	−21.0256	+	5.63379i	−0.870791	+	0.233328i
$584$	3.05508			0.126420
$585$	−13.0918	−	38.1442i	−0.541279	−	1.57707i
$586$	−29.7226			−1.22783
$587$	−21.8823	+	5.86335i	−0.903181	+	0.242007i	−0.680382	−	0.732858i	$-0.738186\pi$
$587$	−21.8823	+	5.86335i	−0.903181	+	0.242007i	−0.222799	+	0.974864i	$0.571519\pi$
$588$	2.49669	−	6.58673i	0.102962	−	0.271632i
$589$	5.21452	−	3.01060i	0.214861	−	0.124050i
$590$	−16.8803	+	4.52308i	−0.694953	+	0.186212i
$591$	−0.553869	+	0.249393i	−0.0227831	+	0.0102587i
$592$	−5.36733	−	5.36733i	−0.220596	−	0.220596i
$593$	−14.2009	+	14.2009i	−0.583160	+	0.583160i	−0.935770	−	0.352610i	$-0.885294\pi$
$593$	−14.2009	+	14.2009i	−0.583160	+	0.583160i	0.352610	+	0.935770i	$0.385294\pi$
$594$	−27.8533	−	17.5928i	−1.14284	−	0.721842i
$595$	−29.7124	+	17.1545i	−1.21809	+	0.703265i
$596$	−6.12277	−	22.8505i	−0.250799	−	0.935993i
$597$	5.50009	+	33.8059i	0.225104	+	1.38358i
$598$	0.568769	−	0.334515i	0.0232587	−	0.0136793i
$599$	−8.75479	−	5.05458i	−0.357711	−	0.206525i	0.310365	−	0.950617i	$-0.399549\pi$
$599$	−8.75479	−	5.05458i	−0.357711	−	0.206525i	−0.668076	+	0.744093i	$0.732882\pi$
$600$	−14.0571	+	6.32955i	−0.573878	+	0.258403i
$601$	7.72707	−	13.3837i	0.315194	−	0.545931i	−0.664285	−	0.747479i	$-0.731264\pi$
$601$	7.72707	−	13.3837i	0.315194	−	0.545931i	0.979479	+	0.201548i	$0.0645972\pi$
$602$	−6.09946	+	10.5646i	−0.248595	+	0.430580i
$603$	12.3603	+	18.6874i	0.503352	+	0.761009i
$604$	0.0389086	+	0.145209i	0.00158317	+	0.00590846i
$605$	76.9730	−	76.9730i	3.12940	−	3.12940i
$606$	14.7697	−	6.65042i	0.599977	−	0.270155i
$607$	14.1563	+	24.5194i	0.574586	+	0.995213i	0.996086	+	0.0883842i	$0.0281703\pi$
$607$	14.1563	+	24.5194i	0.574586	+	0.995213i	−0.421500	+	0.906828i	$0.638496\pi$
$608$	2.71697			0.110188
$609$	3.19400	−	4.43525i	0.129427	−	0.179726i
$610$	26.7342	−	15.4350i	1.08244	−	0.624946i
$611$	−19.2254	+	0.154846i	−0.777778	+	0.00626440i
$612$	−8.13135	−	1.65705i	−0.328690	−	0.0669822i
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	0.0317379	−	0.999496i	$-0.489896\pi$
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	−0.472262	+	0.881458i	$0.656562\pi$
$614$	−28.1127	−	16.2309i	−1.13454	−	0.655025i
$615$	2.44732	+	15.0422i	0.0986853	+	0.606561i
$616$	5.45890	+	20.3729i	0.219945	+	0.820847i
$617$	−9.90643	+	36.9713i	−0.398818	+	1.48841i	0.416361	+	0.909199i	$0.363305\pi$
$617$	−9.90643	+	36.9713i	−0.398818	+	1.48841i	−0.815179	+	0.579209i	$0.803362\pi$
$618$	0.210387	+	0.467242i	0.00846302	+	0.0187952i
$619$	−6.82214	+	25.4606i	−0.274205	+	1.02335i	0.682168	+	0.731196i	$0.261037\pi$
$619$	−6.82214	+	25.4606i	−0.274205	+	1.02335i	−0.956372	+	0.292150i	$0.905629\pi$
$620$	7.15561	+	4.13129i	0.287376	+	0.165917i
$621$	0.841783	−	0.442369i	0.0337796	−	0.0177516i
$622$	6.11116	−	22.8072i	0.245035	−	0.914484i
$623$	1.10865	+	1.92024i	0.0444172	+	0.0769328i
$624$	−5.67353	+	2.60981i	−0.227123	+	0.104476i
$625$	4.85917	−	8.41632i	0.194367	−	0.336653i
$626$	12.3252	+	12.3252i	0.492613	+	0.492613i
$627$	−27.8991	−	10.5751i	−1.11418	−	0.422330i
$628$		−	1.77697i		−	0.0709087i
$629$	14.8469	+	14.8469i	0.591984	+	0.591984i
$630$	−16.6133	+	33.2946i	−0.661891	+	1.32649i
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.599963	−	0.800028i	$-0.295182\pi$
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.919597	+	0.392863i	$0.128515\pi$
$632$	12.1964	+	3.26801i	0.485146	+	0.129994i
$633$	10.1650	+	12.4454i	0.404023	+	0.494661i
$634$		−	0.626268i		−	0.0248723i
$635$	4.24229	−	4.24229i	0.168350	−	0.168350i
$636$	−2.10772	+	5.56054i	−0.0835764	+	0.220490i
$637$	3.90910	+	14.1327i	0.154884	+	0.559957i
$638$			6.01399i			0.238096i
$639$	−2.22459	−	36.5634i	−0.0880034	−	1.44643i
$640$	1.86418	+	3.22885i	0.0736881	+	0.127632i
$641$	−33.6899			−1.33067			−0.665335	−	0.746545i	$-0.731711\pi$
$641$	−33.6899			−1.33067			−0.665335	+	0.746545i	$0.731711\pi$
$642$	−32.2416	−	3.25176i	−1.27248	−	0.128337i
$643$	−22.2328	−	5.95725i	−0.876775	−	0.234931i	−0.207760	−	0.978180i	$-0.566617\pi$
$643$	−22.2328	−	5.95725i	−0.876775	−	0.234931i	−0.669015	+	0.743249i	$0.733284\pi$
$644$	−0.588069	−	0.157572i	−0.0231731	−	0.00620923i
$645$	13.8383	−	19.2161i	0.544881	−	0.756633i
$646$	−7.51558			−0.295697
$647$	3.32926	+	5.76644i	0.130887	+	0.226702i	0.924019	−	0.382348i	$-0.124884\pi$
$647$	3.32926	+	5.76644i	0.130887	+	0.226702i	−0.793132	+	0.609050i	$0.791551\pi$
$648$	−8.34681	+	3.36613i	−0.327894	+	0.132234i
$649$		−	29.7178i		−	1.16652i
$650$	15.8215	−	27.9206i	0.620571	−	1.09514i
$651$	12.6037	−	2.05058i	0.493978	−	0.0803685i
$652$	−4.23084	+	4.23084i	−0.165693	+	0.165693i
$653$			21.1724i			0.828539i	0.910154	+	0.414270i	$0.135963\pi$
$653$			21.1724i			0.828539i	−0.910154	+	0.414270i	$0.864037\pi$
$654$	19.2424	−	3.13066i	0.752436	−	0.122419i
$655$	−33.9563	−	9.09855i	−1.32678	−	0.355510i
$656$	2.27956	−	0.610806i	0.0890018	−	0.0238480i
$657$	−7.64439	+	5.05620i	−0.298236	+	0.197261i
$658$	12.5434	+	12.5434i	0.488994	+	0.488994i
$659$			39.5999i			1.54259i	0.636477	+	0.771296i	$0.280391\pi$
$659$			39.5999i			1.54259i	−0.636477	+	0.771296i	$0.719609\pi$
$660$	−6.57475	−	40.4111i	−0.255922	−	1.57300i
$661$	17.5774	+	17.5774i	0.683682	+	0.683682i	0.960828	−	0.277146i	$-0.0893884\pi$
$661$	17.5774	+	17.5774i	0.683682	+	0.683682i	−0.277146	+	0.960828i	$0.589388\pi$
$662$	−15.4586	+	26.7750i	−0.600815	+	1.04064i
$663$	15.6939	−	7.21914i	0.609500	−	0.280368i
$664$	−3.37840	−	5.85157i	−0.131108	−	0.227085i
$665$	−8.72191	+	32.5506i	−0.338221	+	1.26226i
$666$	22.3131	+	4.54707i	0.864613	+	0.176195i
$667$	−0.150338	−	0.0867978i	−0.00582112	−	0.00336082i
$668$	−4.60758	+	17.1957i	−0.178273	+	0.665322i
$669$	15.6633	−	21.7504i	0.605580	−	0.840920i
$670$	−7.20681	+	26.8962i	−0.278423	+	1.03909i
$671$	13.5866	+	50.7060i	0.524506	+	1.95748i
$672$	5.38792	+	2.04229i	0.207844	+	0.0787829i
$673$	−7.01709	−	4.05132i	−0.270489	−	0.156167i	0.358621	−	0.933483i	$-0.383247\pi$
$673$	−7.01709	−	4.05132i	−0.270489	−	0.156167i	−0.629110	+	0.777316i	$0.716580\pi$
$674$	−8.68866	−	2.32812i	−0.334675	−	0.0896758i
$675$	24.6980	−	39.1024i	0.950625	−	1.50505i
$676$	6.31781	−	11.3616i	0.242993	−	0.436983i
$677$	−1.64864	+	0.951842i	−0.0633623	+	0.0365822i	−0.531346	−	0.847155i	$-0.678314\pi$
$677$	−1.64864	+	0.951842i	−0.0633623	+	0.0365822i	0.467984	+	0.883737i	$0.344980\pi$
$678$	−12.0442	−	1.21473i	−0.462553	−	0.0466513i
$679$	−19.4784			−0.747511
$680$	−5.15661	−	8.93152i	−0.197747	−	0.342508i
$681$	−1.27823	+	12.6738i	−0.0489817	+	0.485660i
$682$	−9.93526	+	9.93526i	−0.380441	+	0.380441i
$683$	1.49884	+	5.59375i	0.0573515	+	0.214039i	0.988655	−	0.150206i	$-0.0479938\pi$
$683$	1.49884	+	5.59375i	0.0573515	+	0.214039i	−0.931303	+	0.364245i	$0.881327\pi$
$684$	−6.79837	+	4.49662i	−0.259942	+	0.171933i
$685$	−30.2528	+	52.3993i	−1.15590	+	2.00208i
$686$	−4.87879	+	8.45032i	−0.186273	+	0.322635i
$687$	−34.7864	−	25.0511i	−1.32718	−	0.955758i
$688$	−3.17570	−	1.83349i	−0.121072	−	0.0699012i
$689$	−3.30008	−	11.9308i	−0.125723	−	0.454529i
$690$	1.10509	+	0.418883i	0.0420701	+	0.0159466i
$691$	−12.2505	−	45.7194i	−0.466030	−	1.73925i	−0.653451	−	0.756968i	$-0.726680\pi$
$691$	−12.2505	−	45.7194i	−0.466030	−	1.73925i	0.187421	−	0.982280i	$-0.439987\pi$
$692$	12.4919	−	7.21223i	0.474872	−	0.274168i
$693$	−47.3765	−	41.9422i	−1.79969	−	1.59325i
$694$	5.25272	−	5.25272i	0.199390	−	0.199390i
$695$	23.4482	+	23.4482i	0.889440	+	0.889440i
$696$	1.33323	+	0.960113i	0.0505360	+	0.0363930i
$697$	−6.30562	+	1.68959i	−0.238842	+	0.0639976i
$698$	−31.2551	+	18.0451i	−1.18302	+	0.683018i
$699$	−19.7526	−	24.1838i	−0.747110	−	0.914715i
$700$	−28.6008	+	7.66356i	−1.08101	+	0.289655i
$701$	−28.7797			−1.08700			−0.543498	−	0.839411i	$-0.682900\pi$
$701$	−28.7797			−1.08700			−0.543498	+	0.839411i	$0.682900\pi$
$702$	9.87696	−	15.9200i	0.372782	−	0.600861i
$703$	20.6233			0.777824
$704$	−6.12407	+	1.64094i	−0.230809	+	0.0618452i
$705$	−21.7828	−	26.6695i	−0.820387	−	1.00443i
$706$	−2.66194	+	1.53687i	−0.100183	+	0.0578409i
$707$	30.0507	−	8.05205i	1.13017	−	0.302829i
$708$	−6.58808	−	4.74434i	−0.247595	−	0.178303i
$709$	22.9651	+	22.9651i	0.862473	+	0.862473i	0.991625	−	0.129152i	$-0.0412254\pi$
$709$	22.9651	+	22.9651i	0.862473	+	0.862473i	−0.129152	+	0.991625i	$0.541225\pi$
$710$	32.1907	−	32.1907i	1.20809	−	1.20809i
$711$	−35.9262	+	12.0080i	−1.34734	+	0.450334i
$712$	−0.577222	+	0.333259i	−0.0216323	+	0.0124894i
$713$	−0.104970	−	0.391754i	−0.00393117	−	0.0146713i
$714$	−14.9038	−	5.64929i	−0.557763	−	0.211419i
$715$	60.7491	+	59.7784i	2.27189	+	2.23558i
$716$	13.0149	+	7.51417i	0.486391	+	0.280818i
$717$	−40.0526	−	28.8435i	−1.49579	−	1.07718i
$718$	−6.88497	+	11.9251i	−0.256945	+	0.445042i
$719$	13.4021	−	23.2131i	0.499813	−	0.865701i	−0.500187	−	0.865917i	$-0.666735\pi$
$719$	13.4021	−	23.2131i	0.499813	−	0.865701i	1.00000		0.000215949i	$6.87386e-5\pi$
$720$	−10.0083	−	4.99395i	−0.372988	−	0.186114i
$721$	0.254728	+	0.950659i	0.00948658	+	0.0354044i
$722$	8.21520	−	8.21520i	0.305738	−	0.305738i
$723$	1.39377	−	13.8194i	0.0518347	−	0.513947i
$724$	3.62506	+	6.27879i	0.134724	+	0.233349i
$725$	−8.44284			−0.313559
$726$	50.3152	+	5.07459i	1.86737	+	0.188336i
$727$	2.56179	−	1.47905i	0.0950116	−	0.0548550i	−0.451741	−	0.892149i	$-0.649197\pi$
$727$	2.56179	−	1.47905i	0.0950116	−	0.0548550i	0.546753	+	0.837294i	$0.315864\pi$
$728$	−11.5605	+	3.19763i	−0.428460	+	0.118512i
$729$	15.3143	−	22.2367i	0.567196	−	0.823583i
$730$	−11.0023	−	2.94806i	−0.407214	−	0.109113i
$731$	8.78449	+	5.07173i	0.324906	+	0.187585i
$732$	13.4100	+	5.08304i	0.495648	+	0.187875i
$733$	−12.5601	−	46.8751i	−0.463920	−	1.73137i	−0.660447	−	0.750873i	$-0.729633\pi$
$733$	−12.5601	−	46.8751i	−0.463920	−	1.73137i	0.196527	−	0.980498i	$-0.437034\pi$
$734$	4.10926	−	15.3360i	0.151676	−	0.566061i
$735$	−15.3474	+	21.3117i	−0.566097	+	0.786093i
$736$	0.0473661	−	0.176773i	0.00174594	−	0.00651593i
$737$	−41.0068	−	23.6753i	−1.51050	−	0.872090i
$738$	−4.69299	+	5.30105i	−0.172751	+	0.195134i
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	0.415084	+	0.909783i	$0.363752\pi$
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	−0.814365	+	0.580354i	$0.802914\pi$
$740$	14.1501	+	24.5088i	0.520170	+	0.900960i
$741$	5.88599	−	15.9139i	0.216227	−	0.584610i
$742$	−5.71072	+	9.89126i	−0.209647	+	0.363119i
$743$	28.9049	+	28.9049i	1.06042	+	1.06042i	0.998054	+	0.0623634i	$0.0198638\pi$
$743$	28.9049	+	28.9049i	1.06042	+	1.06042i	0.0623634	+	0.998054i	$0.480136\pi$
$744$	0.616402	+	3.78866i	0.0225984	+	0.138899i
$745$			88.2002i			3.23140i
$746$	0.512854	+	0.512854i	0.0187769	+	0.0187769i
$747$	18.1378	+	9.05042i	0.663628	+	0.331137i
$748$	16.9401	−	4.53910i	0.619393	−	0.165966i
$749$	−60.1188	−	16.1088i	−2.19669	−	0.588602i
$750$	24.8623	−	4.04501i	0.907845	−	0.147703i
$751$		−	26.3667i		−	0.962135i	−0.876683	−	0.481068i	$-0.840249\pi$
$751$		−	26.3667i		−	0.962135i	0.876683	−	0.481068i	$-0.159751\pi$
$752$	−3.77054	+	3.77054i	−0.137497	+	0.137497i
$753$	−10.3913	+	1.69063i	−0.378682	+	0.0616102i
$754$	−3.41999	+	0.0275454i	−0.124549	+	0.00100314i
$755$		−	0.560489i		−	0.0203983i
$756$	−16.8616	+	3.80690i	−0.613250	+	0.138455i
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	0.736388	−	0.676560i	$-0.236530\pi$
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	−0.954112	+	0.299451i	$0.903197\pi$
$758$	−3.03059			−0.110076
$759$	−1.17442	+	1.63082i	−0.0426287	+	0.0591951i
$760$	−9.78468	−	2.62180i	−0.354928	−	0.0951026i
$761$	−11.9700	−	3.20735i	−0.433911	−	0.116266i	0.0352503	−	0.999379i	$-0.488777\pi$
$761$	−11.9700	−	3.20735i	−0.433911	−	0.116266i	−0.469162	+	0.883112i	$0.655444\pi$
$762$	2.77307	+	0.279681i	0.100458	+	0.0101318i
$763$	37.4441			1.35557
$764$	1.59241	+	2.75813i	0.0576112	+	0.0997856i
$765$	27.6846	+	13.8141i	1.00094	+	0.499449i
$766$			1.96474i			0.0709889i
$767$	16.8996	−	0.136114i	0.610211	−	0.00491478i
$768$	−0.613909	+	1.61960i	−0.0221525	+	0.0584424i
$769$	3.34750	−	3.34750i	0.120714	−	0.120714i	−0.644169	−	0.764883i	$-0.722797\pi$
$769$	3.34750	−	3.34750i	0.120714	−	0.120714i	0.764883	+	0.644169i	$0.222797\pi$
$770$		−	78.6369i		−	2.83388i
$771$	0.699889	+	0.856901i	0.0252059	+	0.0308605i
$772$	13.6996	+	3.67080i	0.493060	+	0.132115i
$773$	−26.0869	+	6.98997i	−0.938281	+	0.251412i	−0.695382	−	0.718640i	$-0.744765\pi$
$773$	−26.0869	+	6.98997i	−0.938281	+	0.251412i	−0.242899	+	0.970052i	$0.578098\pi$
$774$	10.9806	−	0.668084i	0.394691	−	0.0240138i
$775$	−13.9478	−	13.9478i	−0.501019	−	0.501019i
$776$		−	5.85517i		−	0.210189i
$777$	40.8973	+	15.5021i	1.46718	+	0.556134i
$778$	−16.3895	−	16.3895i	−0.587591	−	0.587591i
$779$	−3.20599	+	5.55294i	−0.114867	+	0.198955i
$780$	22.9506	−	3.92396i	0.821762	−	0.140500i
$781$	38.7074	+	67.0431i	1.38506	+	2.39899i
$782$	−0.131022	+	0.488982i	−0.00468534	+	0.0174859i
$783$	−4.92499	−	0.195867i	−0.176005	−	0.00699972i
$784$	3.52202	+	2.03344i	0.125786	+	0.0726228i
$785$	−1.71472	+	6.39942i	−0.0612010	+	0.228405i
$786$	−6.70517	−	14.8913i	−0.239166	−	0.531154i
$787$	9.26059	−	34.5610i	0.330104	−	1.23197i	−0.578976	−	0.815345i	$-0.696547\pi$
$787$	9.26059	−	34.5610i	0.330104	−	1.23197i	0.909080	−	0.416622i	$-0.136786\pi$
$788$	−0.0907674	−	0.338748i	−0.00323345	−	0.0120674i
$789$	1.56726	+	9.63304i	0.0557960	+	0.342945i
$790$	−40.7695	−	23.5383i	−1.45051	−	0.837454i
$791$	−22.4579	−	6.01759i	−0.798513	−	0.213961i
$792$	12.6078	−	14.2413i	0.447998	−	0.506044i
$793$	−28.7728	+	7.95858i	−1.02175	+	0.282617i
$794$	−3.41606	+	1.97226i	−0.121231	+	0.0699930i
$795$	12.9563	−	17.9914i	0.459513	−	0.638089i
$796$	−19.7745			−0.700887
$797$	2.86188	+	4.95693i	0.101373	+	0.175583i	0.912251	−	0.409633i	$-0.134343\pi$
$797$	2.86188	+	4.95693i	0.101373	+	0.175583i	−0.810878	+	0.585216i	$0.801010\pi$
$798$	−14.2748	+	6.42761i	−0.505324	+	0.227535i
$799$	10.4299	−	10.4299i	0.368984	−	0.368984i
$800$	−2.30366	−	8.59737i	−0.0814466	−	0.303963i
$801$	0.892769	−	1.78919i	0.0315445	−	0.0632178i
$802$	−11.1247	+	19.2685i	−0.392825	+	0.680393i
$803$	9.68477	−	16.7745i	0.341768	−	0.591960i
$804$	−11.7951	+	5.31105i	−0.415982	+	0.187306i
$805$	1.96577	+	1.13494i	0.0692842	+	0.0400013i
$806$	−5.69541	−	5.60440i	−0.200612	−	0.197406i
$807$	−5.67679	−	34.8919i	−0.199833	−	1.22825i
$808$	2.42044	+	9.03320i	0.0851507	+	0.317787i
$809$	31.6723	−	18.2860i	1.11354	−	0.642903i	0.173796	−	0.984782i	$-0.444397\pi$
$809$	31.6723	−	18.2860i	1.11354	−	0.642903i	0.939744	+	0.341879i	$0.111063\pi$
$810$	33.3077	−	4.06807i	1.17031	−	0.142937i
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	−0.431160	−	0.902275i	$-0.641896\pi$
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	0.902275	+	0.431160i	$0.141896\pi$
$812$	2.23133	+	2.23133i	0.0783045	+	0.0783045i
$813$	−33.8277	+	15.2318i	−1.18639	+	0.534202i
$814$	−46.4850	+	12.4556i	−1.62930	+	0.436570i
$815$	19.3192	−	11.1540i	0.676724	−	0.390707i
$816$	1.69817	−	4.48008i	0.0594478	−	0.156834i
$817$	9.62361	−	2.57864i	0.336687	−	0.0902151i
$818$	28.2842			0.988934
$819$	23.6343	−	27.1338i	0.825851	−	0.948131i
$820$	−8.79882			−0.307268
$821$	2.96745	−	0.795127i	0.103565	−	0.0277501i	−0.206664	−	0.978412i	$-0.566261\pi$
$821$	2.96745	−	0.795127i	0.103565	−	0.0277501i	0.310229	+	0.950662i	$0.399594\pi$
$822$	−27.7437	+	4.51381i	−0.967674	+	0.157437i
$823$	39.1048	−	22.5772i	1.36311	−	0.786990i	0.373071	−	0.927803i	$-0.378305\pi$
$823$	39.1048	−	22.5772i	1.36311	−	0.786990i	0.990036	+	0.140812i	$0.0449714\pi$
$824$	−0.285767	+	0.0765711i	−0.00995517	+	0.00266748i
$825$	−9.80805	+	97.2480i	−0.341473	+	3.38574i
$826$	−11.0260	−	11.0260i	−0.383643	−	0.383643i
$827$	−9.71124	+	9.71124i	−0.337693	+	0.337693i	−0.855498	−	0.517806i	$-0.826749\pi$
$827$	−9.71124	+	9.71124i	−0.337693	+	0.337693i	0.517806	+	0.855498i	$0.326749\pi$
$828$	0.174042	+	0.520710i	0.00604838	+	0.0180959i
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	−0.690205	−	0.723614i	$-0.742480\pi$
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	0.281566	+	0.959542i	$0.409146\pi$
$830$	6.52012	+	24.3334i	0.226317	+	0.844625i
$831$	−6.46882	+	5.28353i	−0.224401	+	0.183283i
$832$	−0.961205	−	3.47507i	−0.0333238	−	0.120476i
$833$	−9.74247	−	5.62482i	−0.337557	−	0.194888i
$834$	−1.54586	+	15.3274i	−0.0535289	+	0.530746i
$835$	33.1867	−	57.4810i	1.14847	−	1.98921i
$836$	8.61294	−	14.9181i	0.297885	−	0.515952i
$837$	−7.81263	−	8.45979i	−0.270044	−	0.292413i
$838$	−2.90497	−	10.8415i	−0.100351	−	0.374514i
$839$	−31.4296	+	31.4296i	−1.08507	+	1.08507i	−0.0890420	+	0.996028i	$0.528381\pi$
$839$	−31.4296	+	31.4296i	−1.08507	+	1.08507i	−0.996028	+	0.0890420i	$0.971619\pi$
$840$	−17.4329	−	12.5541i	−0.601491	−	0.433158i
$841$	−14.0501	−	24.3355i	−0.484487	−	0.839155i
$842$	0.992453			0.0342022
$843$	2.68009	+	5.95212i	0.0923073	+	0.205002i
$844$	−8.03456	+	4.63875i	−0.276561	+	0.159672i
$845$	−33.7160	+	34.8201i	−1.15987	+	1.19785i
$846$	3.19431	−	15.6749i	0.109823	−	0.538914i
$847$	93.8193	+	25.1388i	3.22367	+	0.863780i
$848$	−2.97330	−	1.71664i	−0.102104	−	0.0589495i
$849$	−16.9021	+	13.8051i	−0.580078	+	0.473789i
$850$	6.37228	+	23.7817i	0.218568	+	0.815705i
$851$	0.359535	−	1.34180i	0.0123247	−	0.0459964i
$852$	21.0422	+	2.12223i	0.720893	+	0.0727064i
$853$	4.11168	−	15.3450i	0.140781	−	0.525403i	−0.859126	−	0.511765i	$-0.828992\pi$
$853$	4.11168	−	15.3450i	0.140781	−	0.525403i	0.999907	−	0.0136383i	$-0.00434133\pi$
$854$	23.8541	+	13.7722i	0.816270	+	0.471274i
$855$	28.8222	−	9.63354i	0.985699	−	0.329460i
$856$	4.84229	−	18.0717i	0.165506	−	0.617676i
$857$	11.7570	+	20.3638i	0.401613	+	0.695614i	0.993921	−	0.110098i	$-0.0351164\pi$
$857$	11.7570	+	20.3638i	0.401613	+	0.695614i	−0.592308	+	0.805712i	$0.701783\pi$
$858$	−3.65572	+	39.4248i	−0.124804	+	1.34594i
$859$	−4.23525	+	7.33567i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$859$	−4.23525	+	7.33567i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$860$	9.66743	+	9.66743i	0.329657	+	0.329657i
$861$	−10.5317	+	8.60195i	−0.358919	+	0.293154i
$862$		−	5.47643i		−	0.186528i
$863$	−4.48332	−	4.48332i	−0.152614	−	0.152614i	0.626670	−	0.779284i	$-0.284417\pi$
$863$	−4.48332	−	4.48332i	−0.152614	−	0.152614i	−0.779284	+	0.626670i	$0.784417\pi$
$864$	−1.14435	−	5.06858i	−0.0389315	−	0.172436i
$865$	−51.9470	+	13.9192i	−1.76625	+	0.473266i
$866$	−16.6334	−	4.45692i	−0.565227	−	0.151452i
$867$	5.73904	−	15.1406i	0.194908	−	0.514203i
$868$			7.37243i			0.250237i
$869$	56.6067	−	56.6067i	1.92025	−	1.92025i
$870$	−3.87491	−	4.74420i	−0.131372	−	0.160843i
$871$	13.2756	−	23.4278i	0.449828	−	0.793822i
$872$			11.2557i			0.381165i
$873$	9.69038	+	14.6507i	0.327970	+	0.495852i
$874$	0.248615	+	0.430614i	0.00840952	+	0.0145657i
$875$	48.3802			1.63555
$876$	−2.17257	−	4.82499i	−0.0734044	−	0.163021i
$877$	12.3035	+	3.29672i	0.415461	+	0.111322i	0.460493	−	0.887663i	$-0.347673\pi$
$877$	12.3035	+	3.29672i	0.415461	+	0.111322i	−0.0450327	+	0.998986i	$0.514339\pi$
$878$	−4.97259	−	1.33240i	−0.167817	−	0.0449664i
$879$	21.1367	+	46.9418i	0.712924	+	1.58331i
$880$	23.6382			0.796842
$881$	28.5401	+	49.4329i	0.961541	+	1.66544i	0.718634	+	0.695389i	$0.244768\pi$
$881$	28.5401	+	49.4329i	0.961541	+	1.66544i	0.242907	+	0.970050i	$0.421899\pi$
$882$	−12.1781	+	0.740941i	−0.410059	+	0.0249488i
$883$		−	35.3145i		−	1.18843i	−0.804307	−	0.594214i	$-0.797463\pi$
$883$		−	35.3145i		−	1.18843i	0.804307	−	0.594214i	$-0.202537\pi$
$884$	2.65884	+	9.61259i	0.0894266	+	0.323306i
$885$	19.1476	+	23.4432i	0.643640	+	0.788033i
$886$	16.2495	−	16.2495i	0.545912	−	0.545912i
$887$		−	38.4986i		−	1.29266i	−0.763059	−	0.646328i	$-0.776304\pi$
$887$		−	38.4986i		−	1.29266i	0.763059	−	0.646328i	$-0.223696\pi$
$888$	−4.65991	+	12.2937i	−0.156376	+	0.412549i
$889$	5.17076	+	1.38550i	0.173422	+	0.0464682i
$890$	2.40035	−	0.643171i	0.0804598	−	0.0215591i
$891$	−7.97744	+	56.5005i	−0.267254	+	1.89284i
$892$	10.9424	+	10.9424i	0.366380	+	0.366380i
$893$		−	14.4879i		−	0.484818i
$894$	−31.7344	+	25.9197i	−1.06136	+	0.866883i
$895$	−39.6199	−	39.6199i	−1.32435	−	1.32435i
$896$	−1.66335	+	2.88100i	−0.0555685	+	0.0962474i
$897$	−0.932781	−	0.660389i	−0.0311446	−	0.0220498i
$898$	7.94437	+	13.7601i	0.265107	+	0.459179i
$899$	−0.544079	+	2.03053i	−0.0181460	+	0.0677219i
$900$	19.9929	+	17.6996i	0.666431	+	0.589988i
$901$	8.22462	+	4.74849i	0.274002	+	0.158195i
$902$	3.87257	−	14.4526i	0.128942	−	0.481220i
$903$	21.0225	+	2.12025i	0.699585	+	0.0705574i
$904$	1.80888	−	6.75083i	0.0601625	−	0.224529i
$905$	−6.99615	−	26.1100i	−0.232560	−	0.867925i
$906$	0.201664	−	0.164712i	0.00669983	−	0.00547220i
$907$	32.8532	+	18.9678i	1.09087	+	0.629815i	0.933809	−	0.357773i	$-0.116464\pi$
$907$	32.8532	+	18.9678i	1.09087	+	0.629815i	0.157064	+	0.987588i	$0.449797\pi$
$908$	−7.10373	−	1.90344i	−0.235746	−	0.0631678i
$909$	−21.0064	−	18.5969i	−0.696740	−	0.616820i
$910$	44.7186	−	0.360173i	1.48241	−	0.0119396i
$911$	−36.1297	+	20.8595i	−1.19703	+	0.691107i	−0.959892	−	0.280369i	$-0.909543\pi$
$911$	−36.1297	+	20.8595i	−1.19703	+	0.691107i	−0.237140	+	0.971476i	$0.576210\pi$
$912$	−1.93213	−	4.29100i	−0.0639793	−	0.142089i
$913$	−42.8388			−1.41776
$914$	12.9664	+	22.4584i	0.428890	+	0.742859i
$915$	−43.3887	−	31.2459i	−1.43438	−	1.03296i
$916$	17.5007	−	17.5007i	0.578240	−	0.578240i
$917$	−8.11834	−	30.2981i	−0.268091	−	1.00053i
$918$	3.16545	+	14.0205i	0.104475	+	0.462745i
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	0.446570	+	0.894748i	$0.352645\pi$
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	−0.998160	+	0.0606329i	$0.980688\pi$
$920$	−0.341161	+	0.590908i	−0.0112477	+	0.0194817i
$921$	−5.64205	+	55.9416i	−0.185912	+	1.84334i
$922$	−1.45600	−	0.840621i	−0.0479508	−	0.0276844i
$923$	−37.9482	+	22.3188i	−1.24908	+	0.734634i
$924$	28.2935	−	23.1092i	0.930789	−	0.760238i
$925$	−17.4860	−	65.2588i	−0.574937	−	2.14570i
$926$	−15.0488	+	8.68844i	−0.494535	+	0.285520i
$927$	0.588317	−	0.664543i	0.0193229	−	0.0218265i
$928$	−0.670737	+	0.670737i	−0.0220180	+	0.0220180i
$929$	−7.83681	−	7.83681i	−0.257117	−	0.257117i	0.566763	−	0.823881i	$-0.308195\pi$
$929$	−7.83681	−	7.83681i	−0.257117	−	0.257117i	−0.823881	+	0.566763i	$0.808195\pi$
$930$	1.43609	−	14.2390i	0.0470912	−	0.466915i
$931$	−10.6731	+	2.85985i	−0.349797	+	0.0937277i
$932$	15.6127	−	9.01397i	0.511409	−	0.295262i
$933$	−40.3659	+	6.56739i	−1.32152	+	0.215007i
$934$	0.562720	−	0.150780i	0.0184128	−	0.00493368i
$935$	−65.3869			−2.13838
$936$	8.15639	+	7.10446i	0.266600	+	0.232216i
$937$	−10.8175			−0.353392			−0.176696	−	0.984265i	$-0.556541\pi$
$937$	−10.8175			−0.353392			−0.176696	+	0.984265i	$0.556541\pi$
$938$	−23.9986	+	6.43040i	−0.783581	+	0.209960i
$939$	10.7007	−	28.2304i	0.349204	−	0.921263i
$940$	17.2174	−	9.94045i	0.561569	−	0.324222i
$941$	12.7176	−	3.40767i	0.414582	−	0.111087i	−0.0454978	−	0.998964i	$-0.514487\pi$
$941$	12.7176	−	3.40767i	0.414582	−	0.111087i	0.460080	+	0.887877i	$0.347821\pi$
$942$	−2.80642	+	1.26366i	−0.0914382	+	0.0411723i
$943$	0.305396	+	0.305396i	0.00994507	+	0.00994507i
$944$	3.31440	−	3.31440i	0.107875	−	0.107875i
$945$	64.3975	+	2.56109i	2.09485	+	0.0833123i
$946$	−20.1342	+	11.6245i	−0.654621	+	0.377945i
$947$	13.1139	+	48.9419i	0.426146	+	1.59040i	0.761409	+	0.648272i	$0.224508\pi$
$947$	13.1139	+	48.9419i	0.426146	+	1.59040i	−0.335263	+	0.942125i	$0.608825\pi$
$948$	−3.51198	−	21.5861i	−0.114064	−	0.701084i
$949$	9.58355	+	5.43062i	0.311095	+	0.176285i
$950$	20.9429	+	12.0914i	0.679479	+	0.392297i
$951$	−0.989085	+	0.445360i	−0.0320733	+	0.0144418i
$952$	4.60108	−	7.96930i	0.149122	−	0.258287i
$953$	12.0254	−	20.8285i	0.389540	−	0.674702i	−0.602848	−	0.797856i	$-0.705967\pi$
$953$	12.0254	−	20.8285i	0.389540	−	0.674702i	0.992388	+	0.123154i	$0.0393008\pi$
$954$	10.2808	−	0.625504i	0.332853	−	0.0202515i
$955$	−3.07325	−	11.4695i	−0.0994480	−	0.371145i
$956$	20.1501	−	20.1501i	0.651701	−	0.651701i
$957$	9.49809	−	4.27675i	0.307030	−	0.138248i
$958$	−3.91119	−	6.77438i	−0.126365	−	0.218870i
$959$	−53.9871			−1.74334
$960$	3.77375	−	5.24030i	0.121797	−	0.169130i
$961$	22.5935	−	13.0443i	0.728822	−	0.420785i
$962$	−7.29607	−	26.3777i	−0.235235	−	0.850450i
$963$	17.7925	+	53.2327i	0.573355	+	1.71540i
$964$	7.74584	+	2.07549i	0.249477	+	0.0668471i
$965$	−45.7944	−	26.4394i	−1.47417	−	0.851115i
$966$	0.169336	+	1.04081i	0.00544830	+	0.0334875i
$967$	−8.54089	−	31.8750i	−0.274656	−	1.02503i	−0.956071	−	0.293134i	$-0.905302\pi$
$967$	−8.54089	−	31.8750i	−0.274656	−	1.02503i	0.681415	−	0.731897i	$-0.261365\pi$
$968$	−7.55670	+	28.2020i	−0.242882	+	0.906446i
$969$	5.34458	+	11.8696i	0.171693	+	0.381306i
$970$	−5.65007	+	21.0863i	−0.181413	+	0.677042i
$971$	1.82907	+	1.05601i	0.0586976	+	0.0338891i	0.529062	−	0.848583i	$-0.322544\pi$
$971$	1.82907	+	1.05601i	0.0586976	+	0.0338891i	−0.470364	+	0.882472i	$0.655877\pi$
$972$	11.2519	+	10.7886i	0.360906	+	0.346045i
$973$	−7.65800	+	28.5800i	−0.245504	+	0.916234i
$974$	2.71428	+	4.70128i	0.0869712	+	0.150639i
$975$	−55.3471	−	5.13214i	−1.77253	−	0.164360i
$976$	−4.13990	+	7.17052i	−0.132515	+	0.229523i
$977$	−28.9129	−	28.9129i	−0.925007	−	0.925007i	0.0723711	−	0.997378i	$-0.476943\pi$
$977$	−28.9129	−	28.9129i	−0.925007	−	0.925007i	−0.997378	+	0.0723711i	$0.976943\pi$
$978$	9.69060	+	3.67321i	0.309871	+	0.117456i
$979$			4.22579i			0.135057i
$980$	−10.7217	−	10.7217i	−0.342492	−	0.342492i
$981$	−18.6282	−	28.1637i	−0.594754	−	0.899199i
$982$	2.32119	−	0.621962i	0.0740723	−	0.0198476i
$983$	19.9648	+	5.34955i	0.636777	+	0.170624i	0.562743	−	0.826632i	$-0.309746\pi$
$983$	19.9648	+	5.34955i	0.636777	+	0.170624i	0.0740342	+	0.997256i	$0.476413\pi$
$984$	−2.58574	−	3.16582i	−0.0824303	−	0.100922i
$985$			1.30753i			0.0416613i
$986$	1.85536	−	1.85536i	0.0590868	−	0.0590868i
$987$	10.8902	−	28.7303i	0.346638	−	0.914495i
$988$	8.52292	+	4.82961i	0.271150	+	0.153650i
$989$		−	0.671089i		−	0.0213394i
$990$	−59.1471	+	39.1214i	−1.87982	+	1.24336i
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	0.578242	−	0.815866i	$-0.303739\pi$
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	−0.995681	+	0.0928392i	$0.970406\pi$
$992$	−2.21615			−0.0703627
$993$	53.2798	+	5.37359i	1.69078	+	0.170526i
$994$	39.2359	+	10.5132i	1.24449	+	0.333460i
$995$	71.2141	+	19.0818i	2.25764	+	0.604933i
$996$	−6.83907	+	9.49687i	−0.216704	+	0.300920i
$997$	−57.4068			−1.81809			−0.909045	−	0.416697i	$-0.863188\pi$
$997$	−57.4068			−1.81809			−0.909045	+	0.416697i	$0.863188\pi$
$998$	3.11692	+	5.39866i	0.0986644	+	0.170892i
$999$	−8.68624	−	38.4733i	−0.274820	−	1.21724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.41.9	yes	56
3.2	odd	2		702.2.bc.a.665.7		56
9.2	odd	6		234.2.y.a.119.10	yes	56
9.7	even	3		702.2.bb.a.197.7		56
13.7	odd	12		234.2.y.a.59.10	✓	56
39.20	even	12		702.2.bb.a.449.7		56
117.7	odd	12		702.2.bc.a.683.7		56
117.20	even	12	inner	234.2.z.a.137.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.10	✓	56	13.7	odd	12
234.2.y.a.119.10	yes	56	9.2	odd	6
234.2.z.a.41.9	yes	56	1.1	even	1	trivial
234.2.z.a.137.9	yes	56	117.20	even	12	inner
702.2.bb.a.197.7		56	9.7	even	3
702.2.bb.a.449.7		56	39.20	even	12
702.2.bc.a.665.7		56	3.2	odd	2
702.2.bc.a.683.7		56	117.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.09566 - 1.34146i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-3.60132 + 0.964970i) q^{5} +(-1.40553 - 1.01217i) q^{6} +(-2.35233 - 2.35233i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.599043 + 2.93958i) q^{9} +(-3.22885 + 1.86418i) q^{10} +(-1.64094 - 6.12407i) q^{11} +(-1.61960 - 0.613909i) q^{12} +(3.47507 - 0.961205i) q^{13} +(-2.88100 - 1.66335i) q^{14} +(5.24030 + 3.77375i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.38308 + 2.39556i) q^{17} +(0.182189 + 2.99446i) q^{18} +(0.703205 + 2.62440i) q^{19} +(-2.63635 + 2.63635i) q^{20} +(-0.578199 + 5.73292i) q^{21} +(-3.17005 - 5.49069i) q^{22} +0.183009 q^{23} +(-1.72331 - 0.173806i) q^{24} +(7.70819 - 4.45033i) q^{25} +(3.10788 - 1.82787i) q^{26} +(4.59969 - 2.41720i) q^{27} +(-3.21334 - 0.861011i) q^{28} +(-0.821481 - 0.474282i) q^{29} +(6.03846 + 2.28887i) q^{30} +(-0.573581 - 2.14063i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.41729 + 8.91117i) q^{33} +(-0.715935 + 2.67190i) q^{34} +(10.7414 + 6.20155i) q^{35} +(0.951005 + 2.84527i) q^{36} +(1.96458 - 7.33191i) q^{37} +(1.35849 + 2.35297i) q^{38} +(-5.09692 - 3.60851i) q^{39} +(-1.86418 + 3.22885i) q^{40} +(1.66875 + 1.66875i) q^{41} +(0.925290 + 5.68722i) q^{42} -3.66698i q^{43} +(-4.48313 - 4.48313i) q^{44} +(-0.679266 - 11.1644i) q^{45} +(0.176773 - 0.0473661i) q^{46} +(-5.15065 - 1.38011i) q^{47} +(-1.70957 + 0.278141i) q^{48} +4.06688i q^{49} +(6.29371 - 6.29371i) q^{50} +(4.72895 - 0.769383i) q^{51} +(2.52889 - 2.56996i) q^{52} -3.43327i q^{53} +(3.81734 - 3.52532i) q^{54} +(11.8191 + 20.4712i) q^{55} -3.32669 q^{56} +(2.75005 - 3.81878i) q^{57} +(-0.916243 - 0.245507i) q^{58} +(4.52756 + 1.21315i) q^{59} +(6.42511 + 0.648011i) q^{60} -8.27980 q^{61} +(-1.10807 - 1.91924i) q^{62} +(8.32400 - 5.50571i) q^{63} -1.00000i q^{64} +(-11.5873 + 6.81494i) q^{65} +(-3.89224 + 10.2684i) q^{66} +(5.28097 - 5.28097i) q^{67} +2.76616i q^{68} +(-0.200516 - 0.245499i) q^{69} +(11.9805 + 3.21016i) q^{70} +(-11.7943 + 3.16027i) q^{71} +(1.65501 + 2.50219i) q^{72} +(2.16027 + 2.16027i) q^{73} -7.59055i q^{74} +(-14.4155 - 5.46419i) q^{75} +(1.92119 + 1.92119i) q^{76} +(-10.5458 + 18.2658i) q^{77} +(-5.85720 - 2.16638i) q^{78} +(6.31331 + 10.9350i) q^{79} +(-0.964970 + 3.60132i) q^{80} +(-8.28230 - 3.52187i) q^{81} +(2.04380 + 1.17999i) q^{82} +(1.74879 - 6.52658i) q^{83} +(2.36572 + 5.25395i) q^{84} +(2.66926 - 9.96181i) q^{85} +(-0.949085 - 3.54203i) q^{86} +(0.263835 + 1.62164i) q^{87} +(-5.49069 - 3.17005i) q^{88} +(-0.643808 - 0.172508i) q^{89} +(-3.54569 - 10.6082i) q^{90} +(-10.4356 - 5.91342i) q^{91} +(0.158490 - 0.0915043i) q^{92} +(-2.24313 + 3.11485i) q^{93} -5.33235 q^{94} +(-5.06492 - 8.77271i) q^{95} +(-1.57933 + 0.711134i) q^{96} +(4.14023 - 4.14023i) q^{97} +(1.05259 + 3.92830i) q^{98} +(18.9852 - 1.15510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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