LMFDB - Embedded newform 124.2.j.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(15,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("124.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.j (of order $10$, degree $4$, 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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.1
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	124.15
Dual form			124.2.j.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39680 - 0.221232i) q^{2} +(-2.48990 - 1.80902i) q^{3} +(1.90211 + 0.618034i) q^{4} -1.61803 q^{5} +(3.07768 + 3.07768i) q^{6} +(0.224514 + 0.0729490i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(2.00000 + 6.15537i) q^{9} +O(q^{10})$	\(q+(-1.39680 - 0.221232i) q^{2} +(-2.48990 - 1.80902i) q^{3} +(1.90211 + 0.618034i) q^{4} -1.61803 q^{5} +(3.07768 + 3.07768i) q^{6} +(0.224514 + 0.0729490i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(2.00000 + 6.15537i) q^{9} +(2.26007 + 0.357960i) q^{10} +(-1.90211 + 5.85410i) q^{11} +(-3.61803 - 4.97980i) q^{12} +(-0.263932 + 0.363271i) q^{13} +(-0.297463 - 0.151565i) q^{14} +(4.02874 + 2.92705i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.54508 + 0.502029i) q^{17} +(-1.43184 - 9.04029i) q^{18} +(-2.93893 - 4.04508i) q^{19} +(-3.07768 - 1.00000i) q^{20} +(-0.427051 - 0.587785i) q^{21} +(3.95199 - 7.75621i) q^{22} +(0.224514 + 0.690983i) q^{23} +(3.95199 + 7.75621i) q^{24} -2.38197 q^{25} +(0.449028 - 0.449028i) q^{26} +(3.30220 - 10.1631i) q^{27} +(0.381966 + 0.277515i) q^{28} +(-4.30902 - 5.93085i) q^{29} +(-4.97980 - 4.97980i) q^{30} +(-1.76336 + 5.28115i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.3262 - 11.1352i) q^{33} +(2.26924 - 0.359413i) q^{34} +(-0.363271 - 0.118034i) q^{35} +12.9443i q^{36} +9.23305i q^{37} +(3.21020 + 6.30037i) q^{38} +(1.31433 - 0.427051i) q^{39} +(4.07768 + 2.07768i) q^{40} +(4.23607 - 3.07768i) q^{41} +(0.466469 + 0.915497i) q^{42} +(-2.12663 + 1.54508i) q^{43} +(-7.23607 + 9.95959i) q^{44} +(-3.23607 - 9.95959i) q^{45} +(-0.160734 - 1.01484i) q^{46} +(-3.30220 + 4.54508i) q^{47} +(-3.80423 - 11.7082i) q^{48} +(-5.61803 - 4.08174i) q^{49} +(3.32714 + 0.526966i) q^{50} +(4.75528 + 1.54508i) q^{51} +(-0.726543 + 0.527864i) q^{52} +(-8.78115 + 2.85317i) q^{53} +(-6.86092 + 13.4653i) q^{54} +(3.07768 - 9.47214i) q^{55} +(-0.472136 - 0.472136i) q^{56} +15.3884i q^{57} +(4.70675 + 9.23752i) q^{58} +(3.21644 - 4.42705i) q^{59} +(5.85410 + 8.05748i) q^{60} +0.898056i q^{61} +(3.63142 - 6.98662i) q^{62} +1.52786i q^{63} +(4.70228 + 6.47214i) q^{64} +(0.427051 - 0.587785i) q^{65} +(-23.8712 + 12.1630i) q^{66} -5.76393i q^{67} -3.24920 q^{68} +(0.690983 - 2.12663i) q^{69} +(0.481305 + 0.245237i) q^{70} +(6.29412 - 2.04508i) q^{71} +(2.86368 - 18.0806i) q^{72} +(-1.80902 - 0.587785i) q^{73} +(2.04264 - 12.8967i) q^{74} +(5.93085 + 4.30902i) q^{75} +(-3.09017 - 9.51057i) q^{76} +(-0.854102 + 1.17557i) q^{77} +(-1.93033 + 0.305735i) q^{78} +(2.07363 + 6.38197i) q^{79} +(-5.23607 - 3.80423i) q^{80} +(-10.8992 + 7.91872i) q^{81} +(-6.59783 + 3.36176i) q^{82} +(5.34307 - 3.88197i) q^{83} +(-0.449028 - 1.38197i) q^{84} +(2.50000 - 0.812299i) q^{85} +(3.31230 - 1.68770i) q^{86} +22.5623i q^{87} +(12.3107 - 12.3107i) q^{88} +(-2.33688 - 0.759299i) q^{89} +(2.31677 + 14.6275i) q^{90} +(-0.0857567 + 0.0623059i) q^{91} +1.45309i q^{92} +(13.9443 - 9.95959i) q^{93} +(5.61803 - 5.61803i) q^{94} +(4.75528 + 6.54508i) q^{95} +(2.72353 + 17.1957i) q^{96} +(0.454915 - 1.40008i) q^{97} +(6.94427 + 6.94427i) q^{98} -39.8384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9	$ 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9 + 6 * q^10 - 20 * q^12 - 20 * q^13 - 14 * q^14 + 8 * q^16 + 10 * q^17 - 24 * q^18 + 10 * q^21 + 20 * q^22 + 20 * q^24 - 28 * q^25 + 12 * q^28 - 30 * q^29 - 32 * q^32 + 60 * q^33 + 30 * q^34 + 10 * q^38 + 8 * q^40 + 16 * q^41 + 10 * q^42 - 40 * q^44 - 8 * q^45 - 10 * q^46 - 36 * q^49 + 2 * q^50 - 30 * q^53 - 50 * q^54 + 32 * q^56 + 20 * q^58 + 20 * q^60 + 38 * q^62 - 10 * q^65 - 20 * q^66 + 10 * q^69 - 8 * q^70 + 48 * q^72 - 10 * q^73 - 30 * q^74 + 20 * q^76 + 20 * q^77 - 24 * q^80 - 38 * q^81 - 4 * q^82 + 20 * q^85 + 20 * q^86 - 50 * q^89 + 32 * q^90 + 40 * q^93 + 36 * q^94 - 40 * q^96 + 26 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$2$	−1.39680	−	0.221232i	−0.987688	−	0.156434i
$3$	−2.48990	−	1.80902i	−1.43754	−	1.04444i	−0.988549	−	0.150902i	$-0.951782\pi$
$3$	−2.48990	−	1.80902i	−1.43754	−	1.04444i	−0.448995	−	0.893534i	$-0.648218\pi$
$4$	1.90211	+	0.618034i	0.951057	+	0.309017i
$5$	−1.61803			−0.723607			−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803			−0.723607			−0.361803	+	0.932254i	$0.617839\pi$
$6$	3.07768	+	3.07768i	1.25646	+	1.25646i
$7$	0.224514	+	0.0729490i	0.0848583	+	0.0275721i	0.351138	−	0.936324i	$-0.385795\pi$
$7$	0.224514	+	0.0729490i	0.0848583	+	0.0275721i	−0.266280	+	0.963896i	$0.585795\pi$
$8$	−2.52015	−	1.28408i	−0.891007	−	0.453990i
$9$	2.00000	+	6.15537i	0.666667	+	2.05179i
$10$	2.26007	+	0.357960i	0.714698	+	0.113197i
$11$	−1.90211	+	5.85410i	−0.573509	+	1.76508i	0.0676935	+	0.997706i	$0.478436\pi$
$11$	−1.90211	+	5.85410i	−0.573509	+	1.76508i	−0.641202	+	0.767372i	$0.721564\pi$
$12$	−3.61803	−	4.97980i	−1.04444	−	1.43754i
$13$	−0.263932	+	0.363271i	−0.0732016	+	0.100753i	−0.844048	−	0.536268i	$-0.819834\pi$
$13$	−0.263932	+	0.363271i	−0.0732016	+	0.100753i	0.770846	+	0.637021i	$0.219834\pi$
$14$	−0.297463	−	0.151565i	−0.0795003	−	0.0405074i
$15$	4.02874	+	2.92705i	1.04022	+	0.755761i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−1.54508	+	0.502029i	−0.374738	+	0.121760i	−0.490330	−	0.871537i	$-0.663124\pi$
$17$	−1.54508	+	0.502029i	−0.374738	+	0.121760i	0.115592	+	0.993297i	$0.463124\pi$
$18$	−1.43184	−	9.04029i	−0.337488	−	2.13082i
$19$	−2.93893	−	4.04508i	−0.674236	−	0.928006i	0.325611	−	0.945504i	$-0.394430\pi$
$19$	−2.93893	−	4.04508i	−0.674236	−	0.928006i	−0.999847	+	0.0174977i	$0.994430\pi$
$20$	−3.07768	−	1.00000i	−0.688191	−	0.223607i
$21$	−0.427051	−	0.587785i	−0.0931902	−	0.128265i
$22$	3.95199	−	7.75621i	0.842567	−	1.65363i
$23$	0.224514	+	0.690983i	0.0468144	+	0.144080i	0.971731	−	0.236089i	$-0.0758658\pi$
$23$	0.224514	+	0.690983i	0.0468144	+	0.144080i	−0.924917	+	0.380169i	$0.875866\pi$
$24$	3.95199	+	7.75621i	0.806696	+	1.58323i
$25$	−2.38197			−0.476393
$26$	0.449028	−	0.449028i	0.0880616	−	0.0880616i
$27$	3.30220	−	10.1631i	0.635508	−	1.95589i
$28$	0.381966	+	0.277515i	0.0721848	+	0.0524453i
$29$	−4.30902	−	5.93085i	−0.800164	−	1.10133i	−0.992767	−	0.120055i	$-0.961693\pi$
$29$	−4.30902	−	5.93085i	−0.800164	−	1.10133i	0.192603	−	0.981277i	$-0.438307\pi$
$30$	−4.97980	−	4.97980i	−0.909182	−	0.909182i
$31$	−1.76336	+	5.28115i	−0.316708	+	0.948523i
$31$	−1.76336	+	5.28115i	−0.316708	+	0.948523i
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	15.3262	−	11.1352i	2.66796	−	1.93838i
$34$	2.26924	−	0.359413i	0.389172	−	0.0616388i
$35$	−0.363271	−	0.118034i	−0.0614041	−	0.0199514i
$36$			12.9443i			2.15738i
$37$			9.23305i			1.51790i	0.651146	+	0.758952i	$0.274288\pi$
$37$			9.23305i			1.51790i	−0.651146	+	0.758952i	$0.725712\pi$
$38$	3.21020	+	6.30037i	0.520763	+	1.02205i
$39$	1.31433	−	0.427051i	0.210461	−	0.0683829i
$40$	4.07768	+	2.07768i	0.644738	+	0.328511i
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	−0.205628	−	0.978630i	$-0.565924\pi$
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	0.867190	+	0.497977i	$0.165924\pi$
$42$	0.466469	+	0.915497i	0.0719777	+	0.141264i
$43$	−2.12663	+	1.54508i	−0.324308	+	0.235623i	−0.738011	−	0.674788i	$-0.764235\pi$
$43$	−2.12663	+	1.54508i	−0.324308	+	0.235623i	0.413704	+	0.910412i	$0.364235\pi$
$44$	−7.23607	+	9.95959i	−1.09088	+	1.50147i
$45$	−3.23607	−	9.95959i	−0.482405	−	1.48469i
$46$	−0.160734	−	1.01484i	−0.0236990	−	0.149629i
$47$	−3.30220	+	4.54508i	−0.481675	+	0.662969i	−0.978826	−	0.204695i	$-0.934380\pi$
$47$	−3.30220	+	4.54508i	−0.481675	+	0.662969i	0.497151	+	0.867664i	$0.334380\pi$
$48$	−3.80423	−	11.7082i	−0.549093	−	1.68993i
$49$	−5.61803	−	4.08174i	−0.802576	−	0.583106i
$50$	3.32714	+	0.526966i	0.470528	+	0.0745243i
$51$	4.75528	+	1.54508i	0.665873	+	0.216355i
$52$	−0.726543	+	0.527864i	−0.100753	+	0.0732016i
$53$	−8.78115	+	2.85317i	−1.20618	+	0.391913i	−0.842033	−	0.539427i	$-0.818641\pi$
$53$	−8.78115	+	2.85317i	−1.20618	+	0.391913i	−0.364152	+	0.931340i	$0.618641\pi$
$54$	−6.86092	+	13.4653i	−0.933653	+	1.83240i
$55$	3.07768	−	9.47214i	0.414995	−	1.27722i
$56$	−0.472136	−	0.472136i	−0.0630918	−	0.0630918i
$57$			15.3884i			2.03825i
$58$	4.70675	+	9.23752i	0.618027	+	1.21295i
$59$	3.21644	−	4.42705i	0.418745	−	0.576353i	−0.546579	−	0.837407i	$-0.684070\pi$
$59$	3.21644	−	4.42705i	0.418745	−	0.576353i	0.965324	+	0.261055i	$0.0840702\pi$
$60$	5.85410	+	8.05748i	0.755761	+	1.04022i
$61$			0.898056i			0.114984i	0.998346	+	0.0574921i	$0.0183104\pi$
$61$			0.898056i			0.114984i	−0.998346	+	0.0574921i	$0.981690\pi$
$62$	3.63142	−	6.98662i	0.461191	−	0.887301i
$63$			1.52786i			0.192493i
$64$	4.70228	+	6.47214i	0.587785	+	0.809017i
$65$	0.427051	−	0.587785i	0.0529692	−	0.0729058i
$66$	−23.8712	+	12.1630i	−2.93834	+	1.49716i
$67$		−	5.76393i		−	0.704176i	−0.935967	−	0.352088i	$-0.885472\pi$
$67$		−	5.76393i		−	0.704176i	0.935967	−	0.352088i	$-0.114528\pi$
$68$	−3.24920			−0.394023
$69$	0.690983	−	2.12663i	0.0831846	−	0.256016i
$70$	0.481305	+	0.245237i	0.0575270	+	0.0293115i
$71$	6.29412	−	2.04508i	0.746975	−	0.242707i	0.0892960	−	0.996005i	$-0.471538\pi$
$71$	6.29412	−	2.04508i	0.746975	−	0.242707i	0.657679	+	0.753298i	$0.271538\pi$
$72$	2.86368	−	18.0806i	0.337488	−	2.13082i
$73$	−1.80902	−	0.587785i	−0.211729	−	0.0687951i	0.201232	−	0.979544i	$-0.435506\pi$
$73$	−1.80902	−	0.587785i	−0.211729	−	0.0687951i	−0.412961	+	0.910749i	$0.635506\pi$
$74$	2.04264	−	12.8967i	0.237453	−	1.49922i
$75$	5.93085	+	4.30902i	0.684836	+	0.497562i
$76$	−3.09017	−	9.51057i	−0.354467	−	1.09094i
$77$	−0.854102	+	1.17557i	−0.0973340	+	0.133969i
$78$	−1.93033	+	0.305735i	−0.218567	+	0.0346176i
$79$	2.07363	+	6.38197i	0.233301	+	0.718027i	0.997342	+	0.0728596i	$0.0232125\pi$
$79$	2.07363	+	6.38197i	0.233301	+	0.718027i	−0.764041	+	0.645168i	$0.776788\pi$
$80$	−5.23607	−	3.80423i	−0.585410	−	0.425325i
$81$	−10.8992	+	7.91872i	−1.21102	+	0.879858i
$82$	−6.59783	+	3.36176i	−0.728608	+	0.371245i
$83$	5.34307	−	3.88197i	0.586478	−	0.426101i	−0.254576	−	0.967053i	$-0.581936\pi$
$83$	5.34307	−	3.88197i	0.586478	−	0.426101i	0.841054	+	0.540952i	$0.181936\pi$
$84$	−0.449028	−	1.38197i	−0.0489930	−	0.150785i
$85$	2.50000	−	0.812299i	0.271163	−	0.0881062i
$86$	3.31230	−	1.68770i	0.357174	−	0.181989i
$87$			22.5623i			2.41893i
$88$	12.3107	−	12.3107i	1.31233	−	1.31233i
$89$	−2.33688	−	0.759299i	−0.247709	−	0.0804855i	0.182531	−	0.983200i	$-0.441571\pi$
$89$	−2.33688	−	0.759299i	−0.247709	−	0.0804855i	−0.430240	+	0.902715i	$0.641571\pi$
$90$	2.31677	+	14.6275i	0.244209	+	1.54187i
$91$	−0.0857567	+	0.0623059i	−0.00898975	+	0.00653143i
$92$			1.45309i			0.151495i
$93$	13.9443	−	9.95959i	1.44595	−	1.03276i
$94$	5.61803	−	5.61803i	0.579456	−	0.579456i
$95$	4.75528	+	6.54508i	0.487882	+	0.671512i
$96$	2.72353	+	17.1957i	0.277969	+	1.75502i
$97$	0.454915	−	1.40008i	0.0461896	−	0.142157i	−0.925302	−	0.379231i	$-0.876188\pi$
$97$	0.454915	−	1.40008i	0.0461896	−	0.142157i	0.971492	+	0.237074i	$0.0761885\pi$
$98$	6.94427	+	6.94427i	0.701477	+	0.701477i
$99$	−39.8384			−4.00391
$100$	−4.53077	−	1.47214i	−0.453077	−	0.147214i
$101$	2.76393	+	8.50651i	0.275022	+	0.846429i	0.989214	+	0.146480i	$0.0467943\pi$
$101$	2.76393	+	8.50651i	0.275022	+	0.846429i	−0.714192	+	0.699950i	$0.753206\pi$
$102$	−6.30037	−	3.21020i	−0.623829	−	0.317857i
$103$	−7.10642	−	9.78115i	−0.700217	−	0.963766i	−0.999953	−	0.00974339i	$-0.996899\pi$
$103$	−7.10642	−	9.78115i	−0.700217	−	0.963766i	0.299736	−	0.954022i	$-0.403101\pi$
$104$	1.13162	−	0.576587i	0.110964	−	0.0565390i
$105$	0.690983	+	0.951057i	0.0674330	+	0.0928136i
$106$	12.8967	−	2.04264i	1.25264	−	0.198399i
$107$	6.79615	−	2.20820i	0.657009	−	0.213475i	0.0385069	−	0.999258i	$-0.487740\pi$
$107$	6.79615	−	2.20820i	0.657009	−	0.213475i	0.618502	+	0.785783i	$0.287740\pi$
$108$	12.5623	−	17.2905i	1.20881	−	1.66378i
$109$	12.2812	+	8.92278i	1.17632	+	0.854647i	0.991752	−	0.128172i	$-0.0409110\pi$
$109$	12.2812	+	8.92278i	1.17632	+	0.854647i	0.184569	+	0.982820i	$0.440911\pi$
$110$	−6.39445	+	12.5498i	−0.609687	+	1.19658i
$111$	16.7027	−	22.9894i	1.58535	−	2.18205i
$112$	0.555029	+	0.763932i	0.0524453	+	0.0721848i
$113$	2.64590	−	8.14324i	0.248905	−	0.766051i	−0.746064	−	0.665874i	$-0.768059\pi$
$113$	2.64590	−	8.14324i	0.248905	−	0.766051i	0.994970	−	0.100178i	$-0.0319411\pi$
$114$	3.40441	−	21.4946i	0.318852	−	2.01315i
$115$	−0.363271	−	1.11803i	−0.0338752	−	0.104257i
$116$	−4.53077	−	13.9443i	−0.420671	−	1.29469i
$117$	−2.76393	−	0.898056i	−0.255526	−	0.0830253i
$118$	−5.47214	+	5.47214i	−0.503751	+	0.503751i
$119$	−0.383516			−0.0351568
$120$	−6.39445	−	12.5498i	−0.583731	−	1.14564i
$121$	−21.7533	−	15.8047i	−1.97757	−	1.43679i
$122$	0.198678	−	1.25441i	0.0179875	−	0.113569i
$123$	−16.1150			−1.45304
$124$	−6.61803	+	8.95554i	−0.594317	+	0.804231i
$125$	11.9443			1.06833
$126$	0.338012	−	2.13412i	0.0301125	−	0.190123i
$127$	−8.64527	−	6.28115i	−0.767143	−	0.557362i	0.133950	−	0.990988i	$-0.457234\pi$
$127$	−8.64527	−	6.28115i	−0.767143	−	0.557362i	−0.901093	+	0.433626i	$0.857234\pi$
$128$	−5.13632	−	10.0806i	−0.453990	−	0.891007i
$129$	8.09017			0.712300
$130$	−0.726543	+	0.726543i	−0.0637220	+	0.0637220i
$131$	−11.5514	−	3.75329i	−1.00925	−	0.327926i	−0.242696	−	0.970102i	$-0.578032\pi$
$131$	−11.5514	−	3.75329i	−1.00925	−	0.327926i	−0.766557	+	0.642176i	$0.778032\pi$
$132$	36.0341	−	11.7082i	3.13637	−	1.01907i
$133$	−0.364745	−	1.12257i	−0.0316274	−	0.0973392i
$134$	−1.27516	+	8.05107i	−0.110157	+	0.695507i
$135$	−5.34307	+	16.4443i	−0.459858	+	1.41530i
$136$	4.53849	+	0.718826i	0.389172	+	0.0616388i
$137$	−5.85410	+	8.05748i	−0.500150	+	0.688397i	−0.982220	−	0.187736i	$-0.939885\pi$
$137$	−5.85410	+	8.05748i	−0.500150	+	0.688397i	0.482070	+	0.876133i	$0.339885\pi$
$138$	−1.43564	+	2.81761i	−0.122210	+	0.239851i
$139$	4.02874	+	2.92705i	0.341713	+	0.248269i	0.745384	−	0.666635i	$-0.232266\pi$
$139$	4.02874	+	2.92705i	0.341713	+	0.248269i	−0.403671	+	0.914904i	$0.632266\pi$
$140$	−0.618034	−	0.449028i	−0.0522334	−	0.0379498i
$141$	16.4443	−	5.34307i	1.38486	−	0.449967i
$142$	−9.24408	+	1.46412i	−0.775746	+	0.122866i
$143$	−1.62460	−	2.23607i	−0.135856	−	0.186989i
$144$	−8.00000	+	24.6215i	−0.666667	+	2.05179i
$145$	6.97214	+	9.59632i	0.579004	+	0.796931i
$146$	2.39680	+	1.22123i	0.198361	+	0.101070i
$147$	6.60440	+	20.3262i	0.544721	+	1.67648i
$148$	−5.70634	+	17.5623i	−0.469058	+	1.44361i
$149$	4.14590			0.339645			0.169823	−	0.985475i	$-0.445681\pi$
$149$	4.14590			0.339645			0.169823	+	0.985475i	$0.445681\pi$
$150$	−7.33094	−	7.33094i	−0.598569	−	0.598569i
$151$	−2.66141	+	8.19098i	−0.216583	+	0.666573i	0.782455	+	0.622707i	$0.213967\pi$
$151$	−2.66141	+	8.19098i	−0.216583	+	0.666573i	−0.999037	+	0.0438654i	$0.986033\pi$
$152$	2.21232	+	13.9680i	0.179443	+	1.13296i
$153$	−6.18034	−	8.50651i	−0.499651	−	0.687710i
$154$	1.45309	−	1.45309i	0.117093	−	0.117093i
$155$	2.85317	−	8.54508i	0.229172	−	0.686358i
$156$	2.76393			0.221292
$157$	−13.7082	+	9.95959i	−1.09403	+	0.794862i	−0.980076	−	0.198624i	$-0.936353\pi$
$157$	−13.7082	+	9.95959i	−1.09403	+	0.794862i	−0.113958	+	0.993486i	$0.536353\pi$
$158$	−1.48455	−	9.37310i	−0.118105	−	0.745684i
$159$	27.0256	+	8.78115i	2.14327	+	0.696391i
$160$	6.47214	+	6.47214i	0.511667	+	0.511667i
$161$			0.171513i			0.0135172i
$162$	16.9759	−	8.64964i	1.33375	−	0.679580i
$163$	−1.95511	+	0.635255i	−0.153136	+	0.0497570i	−0.384582	−	0.923091i	$-0.625654\pi$
$163$	−1.95511	+	0.635255i	−0.153136	+	0.0497570i	0.231446	+	0.972848i	$0.425654\pi$
$164$	9.95959	−	3.23607i	0.777714	−	0.252694i
$165$	−24.7984	+	18.0171i	−1.93055	+	1.40263i
$166$	−8.32202	+	4.24028i	−0.645914	+	0.329110i
$167$	−16.8415	+	12.2361i	−1.30323	+	0.946855i	−0.999982	−	0.00605473i	$-0.998073\pi$
$167$	−16.8415	+	12.2361i	−1.30323	+	0.946855i	−0.303253	+	0.952910i	$0.598073\pi$
$168$	0.321469	+	2.02967i	0.0248018	+	0.156593i
$169$	3.95492	+	12.1720i	0.304224	+	0.936306i
$170$	−3.67171	+	0.581542i	−0.281607	+	0.0446022i
$171$	19.0211	−	26.1803i	1.45458	−	2.00206i
$172$	−5.00000	+	1.62460i	−0.381246	+	0.123874i
$173$	10.5451	+	7.66145i	0.801728	+	0.582489i	0.911421	−	0.411476i	$-0.134987\pi$
$173$	10.5451	+	7.66145i	0.801728	+	0.582489i	−0.109693	+	0.993966i	$0.534987\pi$
$174$	4.99150	−	31.5151i	0.378405	−	2.38915i
$175$	−0.534785	−	0.173762i	−0.0404259	−	0.0131352i
$176$	−19.9192	+	14.4721i	−1.50147	+	1.09088i
$177$	−16.0172	+	5.20431i	−1.20393	+	0.391180i
$178$	3.09618	+	1.57758i	0.232068	+	0.118245i
$179$	−1.31433	+	4.04508i	−0.0982375	+	0.302344i	−0.988084	−	0.153916i	$-0.950811\pi$
$179$	−1.31433	+	4.04508i	−0.0982375	+	0.302344i	0.889846	+	0.456260i	$0.150811\pi$
$180$		−	20.9443i		−	1.56109i
$181$		−	0.726543i		−	0.0540035i	−0.999635	−	0.0270017i	$-0.991404\pi$
$181$		−	0.726543i		−	0.0540035i	0.999635	−	0.0270017i	$-0.00859597\pi$
$182$	0.133569	−	0.0680569i	0.00990081	−	0.00504471i
$183$	1.62460	−	2.23607i	0.120094	−	0.165295i
$184$	0.321469	−	2.02967i	0.0236990	−	0.149629i
$185$		−	14.9394i		−	1.09837i
$186$	−21.6808	+	10.8267i	−1.58971	+	0.793850i
$187$		−	10.0000i		−	0.731272i
$188$	−9.09017	+	6.60440i	−0.662969	+	0.481675i
$189$	1.48278	−	2.04087i	0.107856	−	0.148451i
$190$	−5.19421	−	10.1942i	−0.376828	−	0.739566i
$191$			0.326238i			0.0236057i	0.999930	+	0.0118029i	$0.00375706\pi$
$191$			0.326238i			0.0236057i	−0.999930	+	0.0118029i	$0.996243\pi$
$192$		−	24.6215i		−	1.77690i
$193$	2.51722	−	7.74721i	0.181194	−	0.557656i	−0.818669	−	0.574266i	$-0.805287\pi$
$193$	2.51722	−	7.74721i	0.181194	−	0.557656i	0.999862	+	0.0166100i	$0.00528738\pi$
$194$	−0.945169	+	1.85500i	−0.0678592	+	0.133181i
$195$	−2.12663	+	0.690983i	−0.152291	+	0.0494823i
$196$	−8.16348	−	11.2361i	−0.583106	−	0.802576i
$197$	16.5451	+	5.37582i	1.17879	+	0.383012i	0.831916	−	0.554901i	$-0.187244\pi$
$197$	16.5451	+	5.37582i	1.17879	+	0.383012i	0.346872	+	0.937912i	$0.387244\pi$
$198$	55.6463	+	8.81351i	3.95461	+	0.626349i
$199$	−2.93893	−	2.13525i	−0.208335	−	0.151364i	0.478725	−	0.877965i	$-0.341099\pi$
$199$	−2.93893	−	2.13525i	−0.208335	−	0.151364i	−0.687060	+	0.726601i	$0.741099\pi$
$200$	6.00290	+	3.05863i	0.424469	+	0.216278i
$201$	−10.4271	+	14.3516i	−0.735467	+	1.01228i
$202$	−1.97876	−	12.4934i	−0.139225	−	0.879031i
$203$	−0.534785	−	1.64590i	−0.0375345	−	0.115519i
$204$	8.09017	+	5.87785i	0.566425	+	0.411532i
$205$	−6.85410	+	4.97980i	−0.478711	+	0.347804i
$206$	7.76237	+	15.2345i	0.540830	+	1.06144i
$207$	−3.80423	+	2.76393i	−0.264412	+	0.192107i
$208$	−1.70820	+	0.555029i	−0.118443	+	0.0384843i
$209$	29.2705	−	9.51057i	2.02468	−	0.657860i
$210$	−0.754763	−	1.48131i	−0.0520836	−	0.102220i
$211$		−	5.41641i		−	0.372881i	−0.982466	−	0.186440i	$-0.940305\pi$
$211$		−	5.41641i		−	0.372881i	0.982466	−	0.186440i	$-0.0596951\pi$
$212$	−18.4661			−1.26826
$213$	−19.3713	−	6.29412i	−1.32730	−	0.431266i
$214$	−9.98141	+	1.58090i	−0.682315	+	0.108068i
$215$	3.44095	−	2.50000i	0.234671	−	0.170499i
$216$	−21.3723	+	21.3723i	−1.45420	+	1.45420i
$217$	−0.781153	+	1.05706i	−0.0530281	+	0.0717577i
$218$	−15.1803	−	15.1803i	−1.02814	−	1.02814i
$219$	3.44095	+	4.73607i	0.232518	+	0.320034i
$220$	11.7082	−	16.1150i	0.789367	−	1.08647i
$221$	0.225425	−	0.693786i	0.0151637	−	0.0466691i
$222$	−28.4164	+	28.4164i	−1.90718	+	1.90718i
$223$	2.17963			0.145959			0.0729793	−	0.997333i	$-0.476749\pi$
$223$	2.17963			0.145959			0.0729793	+	0.997333i	$0.476749\pi$
$224$	−0.606260	−	1.18985i	−0.0405074	−	0.0795003i
$225$	−4.76393	−	14.6619i	−0.317595	−	0.977458i
$226$	−5.49734	+	10.7891i	−0.365678	+	0.717683i
$227$	13.4005	+	18.4443i	0.889426	+	1.22419i	0.973720	+	0.227748i	$0.0731364\pi$
$227$	13.4005	+	18.4443i	0.889426	+	1.22419i	−0.0842944	+	0.996441i	$0.526864\pi$
$228$	−9.51057	+	29.2705i	−0.629853	+	1.93849i
$229$	−6.90983	−	9.51057i	−0.456614	−	0.628476i	0.517188	−	0.855872i	$-0.326979\pi$
$229$	−6.90983	−	9.51057i	−0.456614	−	0.628476i	−0.973802	+	0.227396i	$0.926979\pi$
$230$	0.260074	+	1.64204i	0.0171487	+	0.108273i
$231$	4.25325	−	1.38197i	0.279844	−	0.0909267i
$232$	3.24367	+	20.4797i	0.212958	+	1.34456i
$233$	−1.07295	−	0.779543i	−0.0702912	−	0.0510696i	0.552085	−	0.833788i	$-0.313832\pi$
$233$	−1.07295	−	0.779543i	−0.0702912	−	0.0510696i	−0.622376	+	0.782718i	$0.713832\pi$
$234$	3.66199	+	1.86588i	0.239392	+	0.121976i
$235$	5.34307	−	7.35410i	0.348543	−	0.479729i
$236$	8.85410	−	6.43288i	0.576353	−	0.418745i
$237$	6.38197	−	19.6417i	0.414553	−	1.27586i
$238$	0.535696	+	0.0848458i	0.0347240	+	0.00549974i
$239$	−7.95148	−	24.4721i	−0.514338	−	1.58297i	−0.784482	−	0.620151i	$-0.787071\pi$
$239$	−7.95148	−	24.4721i	−0.514338	−	1.58297i	0.270144	−	0.962820i	$-0.412929\pi$
$240$	6.15537	+	18.9443i	0.397327	+	1.22285i
$241$	0.690983	+	0.224514i	0.0445101	+	0.0144622i	0.331187	−	0.943565i	$-0.392551\pi$
$241$	0.690983	+	0.224514i	0.0445101	+	0.0144622i	−0.286677	+	0.958027i	$0.592551\pi$
$242$	26.8885	+	26.8885i	1.72846	+	1.72846i
$243$	9.40456			0.603303
$244$	−0.555029	+	1.70820i	−0.0355321	+	0.109357i
$245$	9.09017	+	6.60440i	0.580750	+	0.421939i
$246$	22.5094	+	3.56514i	1.43515	+	0.227305i
$247$	2.24514			0.142855
$248$	11.2253	−	11.0450i	0.712809	−	0.701358i
$249$	−20.3262			−1.28812
$250$	−16.6838	−	2.64245i	−1.05518	−	0.167123i
$251$	−3.07768	−	2.23607i	−0.194262	−	0.141139i	0.486403	−	0.873735i	$-0.338309\pi$
$251$	−3.07768	−	2.23607i	−0.194262	−	0.141139i	−0.680664	+	0.732595i	$0.738309\pi$
$252$	−0.944272	+	2.90617i	−0.0594835	+	0.183072i
$253$	−4.47214			−0.281161
$254$	10.6861	+	10.6861i	0.670508	+	0.670508i
$255$	−7.69421	−	2.50000i	−0.481830	−	0.156556i
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−3.38197	−	10.4086i	−0.210961	−	0.649272i	−0.999416	−	0.0341788i	$-0.989118\pi$
$257$	−3.38197	−	10.4086i	−0.210961	−	0.649272i	0.788454	−	0.615093i	$-0.210882\pi$
$258$	−11.3004	−	1.78980i	−0.703530	−	0.111428i
$259$	−0.673542	+	2.07295i	−0.0418519	+	0.128807i
$260$	1.17557	−	0.854102i	0.0729058	−	0.0529692i
$261$	27.8885	−	38.3853i	1.72626	−	2.37599i
$262$	15.3047	+	7.79815i	0.945529	+	0.481771i
$263$	21.3193	+	15.4894i	1.31460	+	0.955115i	0.999983	+	0.00589693i	$0.00187706\pi$
$263$	21.3193	+	15.4894i	1.31460	+	0.955115i	0.314620	+	0.949218i	$0.398123\pi$
$264$	−52.9228	+	8.38215i	−3.25717	+	0.515886i
$265$	14.2082	−	4.61653i	0.872803	−	0.283591i
$266$	0.261129	+	1.64870i	0.0160108	+	0.101088i
$267$	4.44501	+	6.11803i	0.272030	+	0.374418i
$268$	3.56231	−	10.9637i	0.217602	−	0.669712i
$269$	−14.4336	−	19.8662i	−0.880034	−	1.21126i	−0.976412	−	0.215918i	$-0.930726\pi$
$269$	−14.4336	−	19.8662i	−0.880034	−	1.21126i	0.0963776	−	0.995345i	$-0.469274\pi$
$270$	11.1012	−	21.7873i	0.675598	−	1.32594i
$271$	1.81636	+	5.59017i	0.110336	+	0.339579i	0.990946	−	0.134263i	$-0.0428668\pi$
$271$	1.81636	+	5.59017i	0.110336	+	0.339579i	−0.880610	+	0.473842i	$0.842867\pi$
$272$	−6.18034	−	2.00811i	−0.374738	−	0.121760i
$273$	0.326238			0.0197448
$274$	9.95959	−	9.95959i	0.601681	−	0.601681i
$275$	4.53077	−	13.9443i	0.273216	−	0.840871i
$276$	2.62866	−	3.61803i	0.158226	−	0.217780i
$277$	−0.263932	−	0.363271i	−0.0158581	−	0.0218269i	0.801014	−	0.598645i	$-0.204294\pi$
$277$	−0.263932	−	0.363271i	−0.0158581	−	0.0218269i	−0.816872	+	0.576818i	$0.804294\pi$
$278$	−4.97980	−	4.97980i	−0.298668	−	0.298668i
$279$	−36.0341	−	0.291796i	−2.15731	−	0.0174694i
$280$	0.763932	+	0.763932i	0.0456537	+	0.0456537i
$281$	−12.8262	+	9.31881i	−0.765149	+	0.555913i	−0.900485	−	0.434886i	$-0.856789\pi$
$281$	−12.8262	+	9.31881i	−0.765149	+	0.555913i	0.135336	+	0.990800i	$0.456789\pi$
$282$	−24.1515	+	3.82521i	−1.43820	+	0.227788i
$283$	−2.76741	−	0.899187i	−0.164506	−	0.0534511i	0.225606	−	0.974219i	$-0.427564\pi$
$283$	−2.76741	−	0.899187i	−0.164506	−	0.0534511i	−0.390112	+	0.920767i	$0.627564\pi$
$284$	13.2361			0.785416
$285$		−	24.8990i		−	1.47489i
$286$	1.77455	+	3.48276i	0.104932	+	0.205940i
$287$	1.17557	−	0.381966i	0.0693917	−	0.0225467i
$288$	16.6215	−	32.6215i	0.979429	−	1.92224i
$289$	−11.6180	+	8.44100i	−0.683414	+	0.496529i
$290$	−7.61568	−	14.9466i	−0.447208	−	0.877696i
$291$	−3.66547	+	2.66312i	−0.214874	+	0.156115i
$292$	−3.07768	−	2.23607i	−0.180108	−	0.130856i
$293$	5.01722	+	15.4414i	0.293109	+	0.902097i	0.983850	+	0.178995i	$0.0572846\pi$
$293$	5.01722	+	15.4414i	0.293109	+	0.902097i	−0.690741	+	0.723102i	$0.742715\pi$
$294$	−4.72822	−	29.8528i	−0.275756	−	1.74105i
$295$	−5.20431	+	7.16312i	−0.303007	+	0.417053i
$296$	11.8560	−	23.2686i	0.689114	−	1.35246i
$297$	53.2148	+	38.6628i	3.08783	+	2.24344i
$298$	−5.79100	−	0.917204i	−0.335464	−	0.0531322i
$299$	−0.310271	−	0.100813i	−0.0179434	−	0.00583017i
$300$	8.61803	+	11.8617i	0.497562	+	0.684836i
$301$	−0.590170	+	0.191758i	−0.0340168	+	0.0110527i
$302$	5.52957	−	10.8524i	0.318191	−	0.624485i
$303$	8.50651	−	26.1803i	0.488686	−	1.50402i
$304$		−	20.0000i		−	1.14708i
$305$		−	1.45309i		−	0.0832034i
$306$	6.75080	+	13.2492i	0.385918	+	0.757406i
$307$	−11.8820	+	16.3541i	−0.678139	+	0.933378i	−0.999910	−	0.0134396i	$-0.995722\pi$
$307$	−11.8820	+	16.3541i	−0.678139	+	0.933378i	0.321771	+	0.946818i	$0.395722\pi$
$308$	−2.35114	+	1.70820i	−0.133969	+	0.0973340i
$309$			37.2097i			2.11679i
$310$	−5.87576	+	11.3046i	−0.333721	+	0.642057i
$311$			17.2361i			0.977368i	0.872461	+	0.488684i	$0.162523\pi$
$311$			17.2361i			0.977368i	−0.872461	+	0.488684i	$0.837477\pi$
$312$	−3.86067	−	0.611469i	−0.218567	−	0.0346176i
$313$	12.2361	−	16.8415i	0.691623	−	0.951938i	−0.308376	−	0.951264i	$-0.599786\pi$
$313$	12.2361	−	16.8415i	0.691623	−	0.951938i	1.00000		0.000673572i	$-0.000214405\pi$
$314$	21.3510	−	10.8789i	1.20491	−	0.613931i
$315$		−	2.47214i		−	0.139289i
$316$			13.4208i			0.754979i
$317$	−5.76393	+	17.7396i	−0.323735	+	0.996353i	0.648274	+	0.761407i	$0.275491\pi$
$317$	−5.76393	+	17.7396i	−0.323735	+	0.996353i	−0.972009	+	0.234946i	$0.924509\pi$
$318$	−35.8068	−	18.2445i	−2.00794	−	1.02310i
$319$	42.9161	−	13.9443i	2.40284	−	0.780729i
$320$	−7.60845	−	10.4721i	−0.425325	−	0.585410i
$321$	−20.9164	−	6.79615i	−1.16744	−	0.379324i
$322$	0.0379442	−	0.239570i	0.00211455	−	0.0133507i
$323$	6.57164	+	4.77458i	0.365656	+	0.265664i
$324$	−25.6255	+	8.32624i	−1.42364	+	0.462569i
$325$	0.628677	−	0.865300i	0.0348727	−	0.0479982i
$326$	2.87145	−	0.454792i	0.159035	−	0.0251886i
$327$	−14.4374	−	44.4336i	−0.798388	−	2.45719i
$328$	−14.6275	+	2.31677i	−0.807669	+	0.127922i
$329$	−1.07295	+	0.779543i	−0.0591536	+	0.0429776i
$330$	38.6244	−	19.6801i	2.12620	−	1.08335i
$331$	−6.82891	+	4.96149i	−0.375351	+	0.272708i	−0.759426	−	0.650593i	$-0.774520\pi$
$331$	−6.82891	+	4.96149i	−0.375351	+	0.272708i	0.384075	+	0.923302i	$0.374520\pi$
$332$	12.5623	−	4.08174i	0.689446	−	0.224015i
$333$	−56.8328	+	18.4661i	−3.11442	+	1.01194i
$334$	26.2313	−	13.3655i	1.43531	−	0.731327i
$335$			9.32624i			0.509547i
$336$		−	2.90617i		−	0.158545i
$337$	20.5902	+	6.69015i	1.12162	+	0.364436i	0.810385	−	0.585898i	$-0.199258\pi$
$337$	20.5902	+	6.69015i	1.12162	+	0.364436i	0.311233	+	0.950334i	$0.399258\pi$
$338$	−2.83141	−	17.8768i	−0.154008	−	0.972370i
$339$	−21.3193	+	15.4894i	−1.15790	+	0.841266i
$340$	5.25731			0.285118
$341$	−27.5623	−	20.3682i	−1.49258	−	1.10300i
$342$	−32.3607	+	32.3607i	−1.74987	+	1.74987i
$343$	−1.93487	−	2.66312i	−0.104473	−	0.143795i
$344$	7.34342	−	1.16308i	0.395931	−	0.0627093i
$345$	−1.11803	+	3.44095i	−0.0601929	+	0.185255i
$346$	−13.0344	−	13.0344i	−0.700736	−	0.700736i
$347$	−10.3431			−0.555247			−0.277624	−	0.960690i	$-0.589547\pi$
$347$	−10.3431			−0.555247			−0.277624	+	0.960690i	$0.589547\pi$
$348$	−13.9443	+	42.9161i	−0.747491	+	2.30054i
$349$	1.21885	+	3.75123i	0.0652434	+	0.200798i	0.978364	−	0.206891i	$-0.0663346\pi$
$349$	1.21885	+	3.75123i	0.0652434	+	0.200798i	−0.913121	+	0.407690i	$0.866335\pi$
$350$	0.708547	+	0.361023i	0.0378734	+	0.0192975i
$351$	2.82041	+	3.88197i	0.150543	+	0.207204i
$352$	31.0249	−	15.8080i	1.65363	−	0.842567i
$353$	6.64590	+	9.14729i	0.353725	+	0.486861i	0.948387	−	0.317115i	$-0.102714\pi$
$353$	6.64590	+	9.14729i	0.353725	+	0.486861i	−0.594662	+	0.803976i	$0.702714\pi$
$354$	23.5242	−	3.72587i	1.25030	−	0.198028i
$355$	−10.1841	+	3.30902i	−0.540516	+	0.175624i
$356$	−3.97574	−	2.88854i	−0.210714	−	0.153093i
$357$	0.954915	+	0.693786i	0.0505395	+	0.0367191i
$358$	2.73076	−	5.35941i	0.144325	−	0.283254i
$359$	−2.82041	+	3.88197i	−0.148856	+	0.204882i	−0.876933	−	0.480613i	$-0.840414\pi$
$359$	−2.82041	+	3.88197i	−0.148856	+	0.204882i	0.728077	+	0.685495i	$0.240414\pi$
$360$	−4.63354	+	29.2550i	−0.244209	+	1.54187i
$361$	−1.85410	+	5.70634i	−0.0975843	+	0.300334i
$362$	−0.160734	+	1.01484i	−0.00844801	+	0.0533386i
$363$	25.5725	+	78.7041i	1.34221	+	4.13090i
$364$	−0.201626	+	0.0655123i	−0.0105681	+	0.00343378i
$365$	2.92705	+	0.951057i	0.153209	+	0.0497806i
$366$	−2.76393	+	2.76393i	−0.144473	+	0.144473i
$367$	10.4086			0.543326			0.271663	−	0.962392i	$-0.412426\pi$
$367$	10.4086			0.543326			0.271663	+	0.962392i	$0.412426\pi$
$368$	−0.898056	+	2.76393i	−0.0468144	+	0.144080i
$369$	27.4164	+	19.9192i	1.42724	+	1.03695i
$370$	−3.30507	+	20.8674i	−0.171822	+	1.08484i
$371$	−2.17963			−0.113161
$372$	32.6789	−	10.3262i	1.69432	−	0.535390i
$373$	14.4164			0.746453			0.373227	−	0.927740i	$-0.378251\pi$
$373$	14.4164			0.746453			0.373227	+	0.927740i	$0.378251\pi$
$374$	−2.21232	+	13.9680i	−0.114396	+	0.722269i
$375$	−29.7400	−	21.6074i	−1.53577	−	1.11580i
$376$	14.1583	−	7.21400i	0.730157	−	0.372034i
$377$	3.29180			0.169536
$378$	−2.52265	+	2.52265i	−0.129751	+	0.129751i
$379$	24.5685	+	7.98278i	1.26200	+	0.410048i	0.862206	−	0.506558i	$-0.169082\pi$
$379$	24.5685	+	7.98278i	1.26200	+	0.410048i	0.399792	+	0.916606i	$0.369082\pi$
$380$	5.00000	+	15.3884i	0.256495	+	0.789409i
$381$	10.1631	+	31.2789i	0.520672	+	1.60246i
$382$	0.0721742	−	0.455690i	0.00369275	−	0.0233151i
$383$	−0.971301	+	2.98936i	−0.0496312	+	0.152749i	−0.972801	−	0.231644i	$-0.925589\pi$
$383$	−0.971301	+	2.98936i	−0.0496312	+	0.152749i	0.923169	+	0.384393i	$0.125589\pi$
$384$	−5.44705	+	34.3913i	−0.277969	+	1.75502i
$385$	1.38197	−	1.90211i	0.0704315	−	0.0969407i
$386$	−5.22999	+	10.2644i	−0.266199	+	0.522446i
$387$	−13.7638	−	10.0000i	−0.699654	−	0.508329i
$388$	1.73060	−	2.38197i	0.0878579	−	0.120926i
$389$	−26.8713	+	8.73102i	−1.36243	+	0.442680i	−0.896854	−	0.442327i	$-0.854153\pi$
$389$	−26.8713	+	8.73102i	−1.36243	+	0.442680i	−0.465576	+	0.885008i	$0.654153\pi$
$390$	3.12334	−	0.494689i	0.158157	−	0.0250496i
$391$	−0.693786	−	0.954915i	−0.0350863	−	0.0482921i
$392$	8.91699	+	17.5006i	0.450376	+	0.883913i
$393$	21.9721	+	30.2421i	1.10835	+	1.52551i
$394$	−21.9209	−	11.1693i	−1.10436	−	0.562699i
$395$	−3.35520	−	10.3262i	−0.168818	−	0.519569i
$396$	−75.7771	−	24.6215i	−3.80794	−	1.23728i
$397$	−12.0000			−0.602263			−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000			−0.602263			−0.301131	+	0.953583i	$0.597364\pi$
$398$	3.63271	+	3.63271i	0.182091	+	0.182091i
$399$	−1.12257	+	3.45492i	−0.0561988	+	0.172962i
$400$	−7.70820	−	5.60034i	−0.385410	−	0.280017i
$401$	−5.75329	−	7.91872i	−0.287306	−	0.395442i	0.640831	−	0.767682i	$-0.278590\pi$
$401$	−5.75329	−	7.91872i	−0.287306	−	0.395442i	−0.928137	+	0.372240i	$0.878590\pi$
$402$	17.7396	−	17.7396i	0.884769	−	0.884769i
$403$	−1.45309	−	2.03444i	−0.0723833	−	0.101343i
$404$			17.8885i			0.889988i
$405$	17.6353	−	12.8128i	0.876303	−	0.636671i
$406$	0.382864	+	2.41731i	0.0190012	+	0.119969i
$407$	−54.0512	−	17.5623i	−2.67922	−	0.870531i
$408$	−10.0000	−	10.0000i	−0.495074	−	0.495074i
$409$		−	36.0341i		−	1.78177i	−0.454225	−	0.890887i	$-0.650084\pi$
$409$		−	36.0341i		−	1.78177i	0.454225	−	0.890887i	$-0.349916\pi$
$410$	10.6755	−	5.43945i	0.527226	−	0.268635i
$411$	29.1522	−	9.47214i	1.43797	−	0.467226i
$412$	−7.47214	−	22.9969i	−0.368126	−	1.13297i
$413$	1.04508	−	0.759299i	0.0514253	−	0.0373626i
$414$	5.92522	−	3.01905i	0.291209	−	0.148378i
$415$	−8.64527	+	6.28115i	−0.424379	+	0.308330i
$416$	2.50881	−	0.397357i	0.123005	−	0.0194820i
$417$	−4.73607	−	14.5761i	−0.231926	−	0.713796i
$418$	−42.9892	+	6.80881i	−2.10267	+	0.333030i
$419$	11.8617	−	16.3262i	0.579482	−	0.797589i	−0.414156	−	0.910206i	$-0.635923\pi$
$419$	11.8617	−	16.3262i	0.579482	−	0.797589i	0.993638	+	0.112617i	$0.0359233\pi$
$420$	0.726543	+	2.23607i	0.0354516	+	0.109109i
$421$	−22.3262	−	16.2210i	−1.08811	−	0.790561i	−0.109034	−	0.994038i	$-0.534776\pi$
$421$	−22.3262	−	16.2210i	−1.08811	−	0.790561i	−0.979080	+	0.203477i	$0.934776\pi$
$422$	−1.19828	+	7.56565i	−0.0583314	+	0.368290i
$423$	−34.5811	−	11.2361i	−1.68139	−	0.546316i
$424$	25.7935	+	4.08529i	1.25264	+	0.198399i
$425$	3.68034	−	1.19581i	0.178523	−	0.0580055i
$426$	25.6654	+	13.0772i	1.24349	+	0.633592i
$427$	−0.0655123	+	0.201626i	−0.00317036	+	0.00975737i
$428$	14.2918			0.690820
$429$			8.50651i			0.410698i
$430$	−5.35941	+	2.73076i	−0.258454	+	0.131689i
$431$	7.71445	−	10.6180i	0.371592	−	0.511453i	−0.581741	−	0.813374i	$-0.697628\pi$
$431$	7.71445	−	10.6180i	0.371592	−	0.511453i	0.953333	+	0.301922i	$0.0976281\pi$
$432$	34.5811	−	25.1246i	1.66378	−	1.20881i
$433$			28.0827i			1.34957i	0.738016	+	0.674783i	$0.235763\pi$
$433$			28.0827i			1.34957i	−0.738016	+	0.674783i	$0.764237\pi$
$434$	1.32497	−	1.30368i	0.0636006	−	0.0625789i
$435$		−	36.5066i		−	1.75036i
$436$	17.8456	+	24.5623i	0.854647	+	1.17632i
$437$	2.13525	−	2.93893i	0.102143	−	0.140588i
$438$	−3.75856	−	7.37660i	−0.179591	−	0.352468i
$439$		−	4.52786i		−	0.216103i	−0.994145	−	0.108052i	$-0.965539\pi$
$439$		−	4.52786i		−	0.216103i	0.994145	−	0.108052i	$-0.0344612\pi$
$440$	−19.9192	+	19.9192i	−0.949610	+	0.949610i
$441$	13.8885	−	42.7445i	0.661359	−	2.03545i
$442$	−0.468362	+	0.919211i	−0.0222777	+	0.0437224i
$443$	−8.67802	+	2.81966i	−0.412305	+	0.133966i	−0.507823	−	0.861462i	$-0.669549\pi$
$443$	−8.67802	+	2.81966i	−0.412305	+	0.133966i	0.0955174	+	0.995428i	$0.469549\pi$
$444$	45.9787	−	33.4055i	2.18205	−	1.58535i
$445$	3.78115	+	1.22857i	0.179244	+	0.0582399i
$446$	−3.04451	−	0.482203i	−0.144162	−	0.0228330i
$447$	−10.3229	−	7.50000i	−0.488255	−	0.354738i
$448$	0.583592	+	1.79611i	0.0275721	+	0.0848583i
$449$	−14.5967	+	20.0907i	−0.688863	+	0.948139i	−0.999998	−	0.00222718i	$-0.999291\pi$
$449$	−14.5967	+	20.0907i	−0.688863	+	0.948139i	0.311134	+	0.950366i	$0.399291\pi$
$450$	3.41060	+	21.5337i	0.160777	+	1.01511i
$451$	9.95959	+	30.6525i	0.468979	+	1.44337i
$452$	10.0656	−	13.8541i	0.473446	−	0.651642i
$453$	21.4443	−	15.5802i	1.00754	−	0.732021i
$454$	−14.6375	−	28.7276i	−0.686970	−	1.34825i
$455$	0.138757	−	0.100813i	0.00650504	−	0.00472619i
$456$	19.7599	−	38.7811i	0.925344	−	1.81609i
$457$	22.8262	−	7.41669i	1.06777	−	0.346938i	0.278149	−	0.960538i	$-0.410279\pi$
$457$	22.8262	−	7.41669i	1.06777	−	0.346938i	0.789617	+	0.613600i	$0.210279\pi$
$458$	7.54763	+	14.8131i	0.352677	+	0.692168i
$459$			17.3607i			0.810327i
$460$		−	2.35114i		−	0.109623i
$461$	26.4058	+	8.57975i	1.22984	+	0.399599i	0.850656	−	0.525723i	$-0.176205\pi$
$461$	26.4058	+	8.57975i	1.22984	+	0.399599i	0.379183	+	0.925322i	$0.376205\pi$
$462$	−6.24669	+	0.989378i	−0.290622	+	0.0460301i
$463$	−19.9192	+	14.4721i	−0.925723	+	0.672577i	−0.944942	−	0.327238i	$-0.893882\pi$
$463$	−19.9192	+	14.4721i	−0.925723	+	0.672577i	0.0192188	+	0.999815i	$0.493882\pi$
$464$		−	29.3238i		−	1.36132i
$465$	−22.5623	+	16.1150i	−1.04630	+	0.747313i
$466$	1.32624	+	1.32624i	0.0614368	+	0.0614368i
$467$	−11.3799	−	15.6631i	−0.526600	−	0.724803i	0.460008	−	0.887915i	$-0.347847\pi$
$467$	−11.3799	−	15.6631i	−0.526600	−	0.724803i	−0.986608	+	0.163112i	$0.947847\pi$
$468$	−4.70228	−	3.41641i	−0.217363	−	0.157924i
$469$	0.420473	−	1.29408i	0.0194156	−	0.0597552i
$470$	−9.09017	+	9.09017i	−0.419298	+	0.419298i
$471$	52.1491			2.40290
$472$	−13.7906	+	7.02666i	−0.634763	+	0.323428i
$473$	−5.00000	−	15.3884i	−0.229900	−	0.707560i
$474$	−13.2597	+	26.0236i	−0.609038	+	1.19531i
$475$	7.00042	+	9.63525i	0.321201	+	0.442096i
$476$	−0.729490	−	0.237026i	−0.0334361	−	0.0108641i
$477$	−35.1246	−	48.3449i	−1.60825	−	2.21356i
$478$	5.69263	+	35.9419i	0.260375	+	1.64394i
$479$	−38.2138	+	12.4164i	−1.74603	+	0.567320i	−0.995607	−	0.0936351i	$-0.970151\pi$
$479$	−38.2138	+	12.4164i	−1.74603	+	0.567320i	−0.750425	+	0.660955i	$0.770151\pi$
$480$	−4.40676	−	27.8232i	−0.201140	−	1.26995i
$481$	−3.35410	−	2.43690i	−0.152934	−	0.111113i
$482$	−0.915497	−	0.466469i	−0.0416997	−	0.0212471i
$483$	0.310271	−	0.427051i	0.0141178	−	0.0194315i
$484$	−31.6094	−	43.5066i	−1.43679	−	1.97757i
$485$	−0.736068	+	2.26538i	−0.0334231	+	0.102866i
$486$	−13.1363	−	2.08059i	−0.595875	−	0.0943774i
$487$	6.01661	+	18.5172i	0.272639	+	0.839095i	0.989835	+	0.142224i	$0.0454253\pi$
$487$	6.01661	+	18.5172i	0.272639	+	0.839095i	−0.717196	+	0.696872i	$0.754575\pi$
$488$	1.15317	−	2.26323i	0.0522018	−	0.102452i
$489$	6.01722	+	1.95511i	0.272108	+	0.0884133i
$490$	−11.2361	−	11.2361i	−0.507594	−	0.507594i
$491$	11.0697			0.499566			0.249783	−	0.968302i	$-0.419641\pi$
$491$	11.0697			0.499566			0.249783	+	0.968302i	$0.419641\pi$
$492$	−30.6525	−	9.95959i	−1.38192	−	0.449013i
$493$	9.63525	+	7.00042i	0.433950	+	0.315283i
$494$	−3.13602	−	0.496696i	−0.141096	−	0.0223474i
$495$	64.4598			2.89725
$496$	−18.1231	+	12.9443i	−0.813750	+	0.581215i
$497$	1.56231			0.0700790
$498$	28.3917	+	4.49681i	1.27226	+	0.201507i
$499$	27.0256	+	19.6353i	1.20983	+	0.878995i	0.995216	−	0.0977036i	$-0.0311497\pi$
$499$	27.0256	+	19.6353i	1.20983	+	0.878995i	0.214617	+	0.976698i	$0.431150\pi$
$500$	22.7194	+	7.38197i	1.01604	+	0.330132i
$501$	64.0689			2.86239
$502$	3.80423	+	3.80423i	0.169791	+	0.169791i
$503$	14.9066	+	4.84346i	0.664654	+	0.215959i	0.621864	−	0.783125i	$-0.286376\pi$
$503$	14.9066	+	4.84346i	0.664654	+	0.215959i	0.0427896	+	0.999084i	$0.486376\pi$
$504$	1.96190	−	3.85044i	0.0873899	−	0.171512i
$505$	−4.47214	−	13.7638i	−0.199007	−	0.612482i
$506$	6.24669	+	0.989378i	0.277699	+	0.0439832i
$507$	12.1720	−	37.4615i	0.540576	−	1.66372i
$508$	−12.5623	−	17.2905i	−0.557362	−	0.767143i
$509$	−16.1180	+	22.1846i	−0.714419	+	0.983314i	0.285271	+	0.958447i	$0.407916\pi$
$509$	−16.1180	+	22.1846i	−0.714419	+	0.983314i	−0.999691	+	0.0248670i	$0.992084\pi$
$510$	10.1942	+	5.19421i	0.451407	+	0.230003i
$511$	−0.363271	−	0.263932i	−0.0160702	−	0.0116757i
$512$	−3.53971	−	22.3488i	−0.156434	−	0.987688i
$513$	−50.8156	+	16.5110i	−2.24356	+	0.728978i
$514$	2.42122	+	15.2870i	0.106795	+	0.674280i
$515$	11.4984	+	15.8262i	0.506682	+	0.697387i
$516$	15.3884	+	5.00000i	0.677437	+	0.220113i
$517$	−20.3262	−	27.9767i	−0.893947	−	1.23041i
$518$	1.39941	−	2.74649i	0.0614864	−	0.120674i
$519$	−12.3965	−	38.1525i	−0.544146	−	1.67471i
$520$	−1.83099	+	0.932938i	−0.0802944	+	0.0409120i
$521$	−35.6525			−1.56196			−0.780982	−	0.624554i	$-0.785281\pi$
$521$	−35.6525			−1.56196			−0.780982	+	0.624554i	$0.785281\pi$
$522$	−47.4468	+	47.4468i	−2.07669	+	2.07669i
$523$	−9.62908	+	29.6353i	−0.421050	+	1.29586i	0.485676	+	0.874139i	$0.338574\pi$
$523$	−9.62908	+	29.6353i	−0.421050	+	1.29586i	−0.906726	+	0.421720i	$0.861426\pi$
$524$	−19.6525	−	14.2784i	−0.858522	−	0.623753i
$525$	1.01722	+	1.40008i	0.0443952	+	0.0611047i
$526$	−26.3521	−	26.3521i	−1.14900	−	1.14900i
$527$	0.0732450	−	9.04508i	0.00319060	−	0.394010i
$528$	75.7771			3.29777
$529$	18.1803	−	13.2088i	0.790450	−	0.574295i
$530$	−20.8674	+	3.30507i	−0.906421	+	0.143563i
$531$	33.6830	+	10.9443i	1.46172	+	0.474941i
$532$		−	2.36068i		−	0.102348i
$533$			2.35114i			0.101839i
$534$	−4.85530	−	9.52906i	−0.210109	−	0.412363i
$535$	−10.9964	+	3.57295i	−0.475416	+	0.154472i
$536$	−7.40134	+	14.5260i	−0.319689	+	0.627426i
$537$	10.5902	−	7.69421i	0.457000	−	0.332030i
$538$	15.7659	+	30.9423i	0.679716	+	1.33402i
$539$	34.5811	−	25.1246i	1.48951	−	1.08219i
$540$	−20.3262	+	27.9767i	−0.874702	+	1.20392i
$541$	6.38197	+	19.6417i	0.274382	+	0.844461i	0.989382	+	0.145337i	$0.0464266\pi$
$541$	6.38197	+	19.6417i	0.274382	+	0.844461i	−0.715000	+	0.699124i	$0.753573\pi$
$542$	−1.30037	−	8.21020i	−0.0558556	−	0.352658i
$543$	−1.31433	+	1.80902i	−0.0564032	+	0.0776323i
$544$	8.18845	+	4.17223i	0.351077	+	0.178883i
$545$	−19.8713	−	14.4374i	−0.851194	−	0.618429i
$546$	−0.455690	−	0.0721742i	−0.0195017	−	0.00308877i
$547$	13.0373	+	4.23607i	0.557434	+	0.181121i	0.574166	−	0.818739i	$-0.305326\pi$
$547$	13.0373	+	4.23607i	0.557434	+	0.181121i	−0.0167324	+	0.999860i	$0.505326\pi$
$548$	−16.1150	+	11.7082i	−0.688397	+	0.500150i
$549$	−5.52786	+	1.79611i	−0.235923	+	0.0766562i
$550$	−9.41350	+	18.4750i	−0.401393	+	0.787778i
$551$	−11.3269	+	34.8607i	−0.482543	+	1.48511i
$552$	−4.47214	+	4.47214i	−0.190347	+	0.190347i
$553$			1.58411i			0.0673632i
$554$	0.288294	+	0.565808i	0.0122484	+	0.0240389i
$555$	−27.0256	+	37.1976i	−1.14717	+	1.57895i
$556$	5.85410	+	8.05748i	0.248269	+	0.341713i
$557$		−	31.8869i		−	1.35109i	−0.737318	−	0.675546i	$-0.763908\pi$
$557$		−	31.8869i		−	1.35109i	0.737318	−	0.675546i	$-0.236092\pi$
$558$	50.2680	+	8.37948i	2.12802	+	0.354732i
$559$		−	1.18034i		−	0.0499231i
$560$	−0.898056	−	1.23607i	−0.0379498	−	0.0522334i
$561$	−18.0902	+	24.8990i	−0.763768	+	1.05124i
$562$	19.9773	−	10.1790i	0.842693	−	0.429374i
$563$		−	26.6869i		−	1.12472i	−0.826893	−	0.562360i	$-0.809894\pi$
$563$		−	26.6869i		−	1.12472i	0.826893	−	0.562360i	$-0.190106\pi$
$564$	34.5811			1.45613
$565$	−4.28115	+	13.1760i	−0.180109	+	0.554320i
$566$	3.66660	+	1.86823i	0.154119	+	0.0785274i
$567$	−3.02468	+	0.982779i	−0.127025	+	0.0412728i
$568$	−18.4882	−	2.92824i	−0.775746	−	0.122866i
$569$	−23.6180	−	7.67396i	−0.990119	−	0.321709i	−0.231209	−	0.972904i	$-0.574268\pi$
$569$	−23.6180	−	7.67396i	−0.990119	−	0.321709i	−0.758911	+	0.651195i	$0.774268\pi$
$570$	−5.50845	+	34.7790i	−0.230723	+	1.45673i
$571$	−26.9399	−	19.5729i	−1.12740	−	0.819102i	−0.142084	−	0.989855i	$-0.545380\pi$
$571$	−26.9399	−	19.5729i	−1.12740	−	0.819102i	−0.985314	+	0.170752i	$0.945380\pi$
$572$	−1.70820	−	5.25731i	−0.0714236	−	0.219819i
$573$	0.590170	−	0.812299i	0.0246547	−	0.0339343i
$574$	−1.72654	+	0.273457i	−0.0720645	+	0.0114139i
$575$	−0.534785	−	1.64590i	−0.0223021	−	0.0686387i
$576$	−30.4338	+	41.8885i	−1.26808	+	1.74536i
$577$	15.3992	−	11.1882i	0.641077	−	0.465769i	−0.219143	−	0.975693i	$-0.570326\pi$
$577$	15.3992	−	11.1882i	0.641077	−	0.465769i	0.860220	+	0.509923i	$0.170326\pi$
$578$	18.0955	−	9.22012i	0.752674	−	0.383507i
$579$	−20.2825	+	14.7361i	−0.842910	+	0.612410i
$580$	7.33094	+	22.5623i	0.304401	+	0.936849i
$581$	1.48278	−	0.481784i	0.0615160	−	0.0199878i
$582$	5.70910	−	2.90893i	0.236650	−	0.120579i
$583$		−	56.8328i		−	2.35377i
$584$	3.80423	+	3.80423i	0.157420	+	0.157420i
$585$	4.47214	+	1.45309i	0.184900	+	0.0600777i
$586$	−3.59193	−	22.6786i	−0.148381	−	0.936843i
$587$	10.5474	−	7.66312i	0.435337	−	0.316291i	−0.348442	−	0.937330i	$-0.613289\pi$
$587$	10.5474	−	7.66312i	0.435337	−	0.316291i	0.783779	+	0.621039i	$0.213289\pi$
$588$			42.7445i			1.76276i
$589$	26.5451	−	8.38800i	1.09377	−	0.345621i
$590$	8.85410	−	8.85410i	0.364518	−	0.364518i
$591$	−31.4706	−	43.3156i	−1.29453	−	1.78177i
$592$	−21.7082	+	29.8788i	−0.892202	+	1.22801i
$593$	−1.85410	+	5.70634i	−0.0761388	+	0.234331i	−0.981881	−	0.189497i	$-0.939314\pi$
$593$	−1.85410	+	5.70634i	−0.0761388	+	0.234331i	0.905742	+	0.423829i	$0.139314\pi$
$594$	−65.7771	−	65.7771i	−2.69887	−	2.69887i
$595$	0.620541			0.0254397
$596$	7.88597	+	2.56231i	0.323022	+	0.104956i
$597$	3.45492	+	10.6331i	0.141400	+	0.435185i
$598$	0.411084	+	0.209458i	0.0168105	+	0.00856536i
$599$	21.8415	+	30.0623i	0.892421	+	1.22831i	0.972823	+	0.231550i	$0.0743797\pi$
$599$	21.8415	+	30.0623i	0.892421	+	1.22831i	−0.0804017	+	0.996763i	$0.525620\pi$
$600$	−9.41350	−	18.4750i	−0.384305	−	0.754240i
$601$	−24.1459	−	33.2340i	−0.984932	−	1.35564i	−0.934130	−	0.356933i	$-0.883822\pi$
$601$	−24.1459	−	33.2340i	−0.984932	−	1.35564i	−0.0508019	−	0.998709i	$-0.516178\pi$
$602$	0.866774	−	0.137283i	0.0353271	−	0.00559526i
$603$	35.4791	−	11.5279i	1.44482	−	0.469451i
$604$	−10.1246	+	13.9353i	−0.411965	+	0.567021i
$605$	35.1976	+	25.5725i	1.43098	+	1.03967i
$606$	−17.6738	+	34.6868i	−0.717950	+	1.40906i
$607$	1.45309	−	2.00000i	0.0589789	−	0.0811775i	−0.778509	−	0.627634i	$-0.784024\pi$
$607$	1.45309	−	2.00000i	0.0589789	−	0.0811775i	0.837488	+	0.546456i	$0.184024\pi$
$608$	−4.42463	+	27.9360i	−0.179443	+	1.13296i
$609$	−1.64590	+	5.06555i	−0.0666952	+	0.205267i
$610$	−0.321469	+	2.02967i	−0.0130159	+	0.0821790i
$611$	−0.779543	−	2.39919i	−0.0315369	−	0.0970607i
$612$	−6.49839	−	20.0000i	−0.262682	−	0.808452i
$613$	36.7082	+	11.9272i	1.48263	+	0.481736i	0.934898	−	0.354918i	$-0.115491\pi$
$613$	36.7082	+	11.9272i	1.48263	+	0.481736i	0.547733	+	0.836653i	$0.315491\pi$
$614$	20.2148	−	20.2148i	0.815802	−	0.815802i
$615$	26.0746			1.05143
$616$	3.66199	−	1.86588i	0.147546	−	0.0751783i
$617$	7.89919	+	5.73910i	0.318009	+	0.231047i	0.735326	−	0.677714i	$-0.237029\pi$
$617$	7.89919	+	5.73910i	0.318009	+	0.231047i	−0.417316	+	0.908761i	$0.637029\pi$
$618$	8.23197	−	51.9746i	0.331138	−	2.09073i
$619$	−43.0876			−1.73184			−0.865918	−	0.500186i	$-0.833265\pi$
$619$	−43.0876			−1.73184			−0.865918	+	0.500186i	$0.833265\pi$
$620$	10.7082	−	14.4904i	0.430052	−	0.581947i
$621$	7.76393			0.311556
$622$	3.81317	−	24.0754i	0.152894	−	0.965335i
$623$	−0.469272	−	0.340946i	−0.0188010	−	0.0136597i
$624$	5.25731	+	1.70820i	0.210461	+	0.0683829i
$625$	−7.41641			−0.296656
$626$	−20.8172	+	20.8172i	−0.832024	+	0.832024i
$627$	−90.0854	−	29.2705i	−3.59766	−	1.16895i
$628$	−32.2299	+	10.4721i	−1.28611	+	0.417884i
$629$	−4.63525	−	14.2658i	−0.184820	−	0.568817i
$630$	−0.546915	+	3.45309i	−0.0217896	+	0.137574i
$631$	−2.71441	+	8.35410i	−0.108059	+	0.332572i	−0.990436	−	0.137971i	$-0.955942\pi$
$631$	−2.71441	+	8.35410i	−0.108059	+	0.332572i	0.882377	+	0.470543i	$0.155942\pi$
$632$	2.96911	−	18.7462i	0.118105	−	0.745684i
$633$	−9.79837	+	13.4863i	−0.389450	+	0.536032i
$634$	11.9756	−	23.5035i	0.475613	−	0.933443i
$635$	13.9883	+	10.1631i	0.555110	+	0.403311i
$636$	45.9787	+	33.4055i	1.82317	+	1.32461i
$637$	2.96556	−	0.963568i	0.117500	−	0.0381780i
$638$	−63.0302	+	9.98300i	−2.49539	+	0.395231i
$639$	25.1765	+	34.6525i	0.995967	+	1.37083i
$640$	8.31073	+	16.3107i	0.328511	+	0.644738i
$641$	12.9271	+	17.7926i	0.510588	+	0.702764i	0.984018	−	0.178067i	$-0.0569845\pi$
$641$	12.9271	+	17.7926i	0.510588	+	0.702764i	−0.473430	+	0.880831i	$0.656984\pi$
$642$	27.7126	+	14.1203i	1.09373	+	0.557282i
$643$	2.82041	+	8.68034i	0.111226	+	0.342319i	0.991141	−	0.132812i	$-0.0424006\pi$
$643$	2.82041	+	8.68034i	0.111226	+	0.342319i	−0.879915	+	0.475131i	$0.842401\pi$
$644$	−0.106001	+	0.326238i	−0.00417703	+	0.0128556i
$645$	−13.0902			−0.515425
$646$	−8.12299	−	8.12299i	−0.319595	−	0.319595i
$647$	1.34708	−	4.14590i	0.0529593	−	0.162992i	−0.921079	−	0.389376i	$-0.872691\pi$
$647$	1.34708	−	4.14590i	0.0529593	−	0.162992i	0.974038	+	0.226384i	$0.0726905\pi$
$648$	37.6358	−	5.96093i	1.47847	−	0.234167i
$649$	19.7984	+	27.2501i	0.777154	+	1.06966i
$650$	−1.06957	+	1.06957i	−0.0419520	+	0.0419520i
$651$	3.85723	−	1.21885i	0.151177	−	0.0477704i
$652$	−4.11146			−0.161017
$653$	−29.2254	+	21.2335i	−1.14368	+	0.830932i	−0.987628	−	0.156817i	$-0.949877\pi$
$653$	−29.2254	+	21.2335i	−1.14368	+	0.830932i	−0.156052	+	0.987749i	$0.549877\pi$
$654$	10.3360	+	65.2590i	0.404170	+	2.55183i
$655$	18.6906	+	6.07295i	0.730303	+	0.237290i
$656$	20.9443			0.817736
$657$		−	12.3107i		−	0.480287i
$658$	1.67116	−	0.851497i	0.0651485	−	0.0331948i
$659$	−6.06961	+	1.97214i	−0.236438	+	0.0768235i	−0.424840	−	0.905269i	$-0.639669\pi$
$659$	−6.06961	+	1.97214i	−0.236438	+	0.0768235i	0.188401	+	0.982092i	$0.439669\pi$
$660$	−58.3045	+	18.9443i	−2.26950	+	0.737405i
$661$	21.8713	−	15.8904i	0.850696	−	0.618067i	−0.0746420	−	0.997210i	$-0.523781\pi$
$661$	21.8713	−	15.8904i	0.850696	−	0.618067i	0.925338	+	0.379144i	$0.123781\pi$
$662$	10.6363	−	5.41945i	0.413391	−	0.210633i
$663$	−1.81636	+	1.31966i	−0.0705414	+	0.0512514i
$664$	−18.4501	+	2.92220i	−0.716001	+	0.113403i
$665$	0.590170	+	1.81636i	0.0228858	+	0.0704353i
$666$	83.4695	−	13.2203i	3.23438	−	0.512275i
$667$	3.13068	−	4.30902i	0.121221	−	0.166846i
$668$	−39.5967	+	12.8658i	−1.53204	+	0.497791i
$669$	−5.42705	−	3.94298i	−0.209822	−	0.152445i
$670$	2.06326	−	13.0269i	0.0797107	−	0.503273i
$671$	−5.25731	−	1.70820i	−0.202956	−	0.0659445i
$672$	−0.642937	+	4.05934i	−0.0248018	+	0.156593i
$673$	−18.5795	+	6.03685i	−0.716188	+	0.232704i	−0.644370	−	0.764714i	$-0.722880\pi$
$673$	−18.5795	+	6.03685i	−0.716188	+	0.232704i	−0.0718184	+	0.997418i	$0.522880\pi$
$674$	−27.2803	−	13.9000i	−1.05080	−	0.535409i
$675$	−7.86572	+	24.2082i	−0.302752	+	0.931774i
$676$			25.5967i			0.984490i
$677$		−	7.95148i		−	0.305600i	−0.988257	−	0.152800i	$-0.951171\pi$
$677$		−	7.95148i		−	0.305600i	0.988257	−	0.152800i	$-0.0488291\pi$
$678$	33.2055	−	16.9191i	1.27525	−	0.649773i
$679$	0.204270	−	0.281153i	0.00783915	−	0.0107897i
$680$	−7.34342	−	1.16308i	−0.281607	−	0.0446022i
$681$		−	70.1662i		−	2.68877i
$682$	33.9930	+	34.5480i	1.30166	+	1.32291i
$683$		−	26.1246i		−	0.999630i	−0.866132	−	0.499815i	$-0.833401\pi$
$683$		−	26.1246i		−	0.999630i	0.866132	−	0.499815i	$-0.166599\pi$
$684$	52.3607	−	38.0423i	2.00206	−	1.45458i
$685$	9.47214	−	13.0373i	0.361912	−	0.498129i
$686$	2.11346	+	4.14791i	0.0806924	+	0.158368i
$687$			36.1803i			1.38037i
$688$	−10.5146			−0.400866
$689$	1.28115	−	3.94298i	0.0488080	−	0.150216i
$690$	2.32292	−	4.55899i	0.0884321	−	0.173558i
$691$	−34.9116	+	11.3435i	−1.32810	+	0.431526i	−0.885269	−	0.465080i	$-0.846026\pi$
$691$	−34.9116	+	11.3435i	−1.32810	+	0.431526i	−0.442830	+	0.896605i	$0.646026\pi$
$692$	15.3229	+	21.0902i	0.582489	+	0.801728i
$693$	−8.94427	−	2.90617i	−0.339765	−	0.110396i
$694$	14.4473	+	2.28822i	0.548411	+	0.0868598i
$695$	−6.51864	−	4.73607i	−0.247266	−	0.179649i
$696$	28.9718	−	56.8603i	1.09817	−	2.15529i
$697$	−5.00000	+	6.88191i	−0.189389	+	0.260671i
$698$	−0.872598	−	5.50937i	−0.0330283	−	0.208533i
$699$	1.26133	+	3.88197i	0.0477078	+	0.146829i
$700$	−0.909830	−	0.661030i	−0.0343883	−	0.0249846i
$701$	−21.2533	+	15.4414i	−0.802726	+	0.583214i	−0.911712	−	0.410829i	$-0.865239\pi$
$701$	−21.2533	+	15.4414i	−0.802726	+	0.583214i	0.108987	+	0.994043i	$0.465239\pi$
$702$	−3.08075	−	6.04630i	−0.116275	−	0.228203i
$703$	37.3485	−	27.1353i	1.40862	−	1.02343i
$704$	−46.8328	+	15.2169i	−1.76508	+	0.573509i
$705$	−26.6074	+	8.64527i	−1.00209	+	0.325600i
$706$	−7.25933	−	14.2472i	−0.273209	−	0.536202i
$707$			2.11146i			0.0794095i
$708$	−33.6830			−1.26588
$709$	38.8050	+	12.6085i	1.45735	+	0.473522i	0.927260	−	0.374419i	$-0.122158\pi$
$709$	38.8050	+	12.6085i	1.45735	+	0.473522i	0.530091	+	0.847941i	$0.322158\pi$
$710$	14.9572	−	2.36899i	0.561335	−	0.0889068i
$711$	−35.1361	+	25.5279i	−1.31771	+	0.957370i
$712$	4.91428	+	4.91428i	0.184171	+	0.184171i
$713$	−4.04508	−	0.0327561i	−0.151490	−	0.00122673i
$714$	−1.18034	−	1.18034i	−0.0441731	−	0.0441731i
$715$	2.62866	+	3.61803i	0.0983061	+	0.135307i
$716$	−5.00000	+	6.88191i	−0.186859	+	0.257189i
$717$	−24.4721	+	75.3175i	−0.913929	+	2.81278i
$718$	4.79837	−	4.79837i	0.179074	−	0.179074i
$719$	−12.5882			−0.469462			−0.234731	−	0.972060i	$-0.575421\pi$
$719$	−12.5882			−0.469462			−0.234731	+	0.972060i	$0.575421\pi$
$720$	12.9443	−	39.8384i	0.482405	−	1.48469i
$721$	−0.881966	−	2.71441i	−0.0328461	−	0.101090i
$722$	3.85224	−	7.56044i	0.143365	−	0.281370i
$723$	−1.31433	−	1.80902i	−0.0488804	−	0.0672781i
$724$	0.449028	−	1.38197i	0.0166880	−	0.0513604i
$725$	10.2639	+	14.1271i	0.381193	+	0.524667i
$726$	−18.3079	−	115.592i	−0.679470	−	4.29001i
$727$	22.4948	−	7.30902i	0.834287	−	0.271076i	0.139437	−	0.990231i	$-0.455471\pi$
$727$	22.4948	−	7.30902i	0.834287	−	0.271076i	0.694850	+	0.719154i	$0.255471\pi$
$728$	0.296125	−	0.0469016i	0.0109751	−	0.00173829i
$729$	9.28115	+	6.74315i	0.343746	+	0.249746i
$730$	−3.87811	−	1.97599i	−0.143535	−	0.0731348i
$731$	2.51014	−	3.45492i	0.0928410	−	0.127785i
$732$	4.47214	−	3.24920i	0.165295	−	0.120094i
$733$	−6.48936	+	19.9722i	−0.239690	+	0.737690i	0.756775	+	0.653676i	$0.226774\pi$
$733$	−6.48936	+	19.9722i	−0.239690	+	0.737690i	−0.996465	+	0.0840138i	$0.973226\pi$
$734$	−14.5388	−	2.30272i	−0.536636	−	0.0849948i
$735$	−10.6861	−	32.8885i	−0.394164	−	1.21311i
$736$	1.86588	−	3.66199i	0.0687771	−	0.134983i
$737$	33.7426	+	10.9637i	1.24293	+	0.403851i
$738$	−33.8885	−	33.8885i	−1.24745	−	1.24745i
$739$	26.0746			0.959168			0.479584	−	0.877496i	$-0.340788\pi$
$739$	26.0746			0.959168			0.479584	+	0.877496i	$0.340788\pi$
$740$	9.23305	−	28.4164i	0.339414	−	1.04461i
$741$	−5.59017	−	4.06150i	−0.205360	−	0.149203i
$742$	3.04451	+	0.482203i	0.111767	+	0.0177022i
$743$	−6.60440			−0.242292			−0.121146	−	0.992635i	$-0.538657\pi$
$743$	−6.60440			−0.242292			−0.121146	+	0.992635i	$0.538657\pi$
$744$	−47.9305	+	7.19409i	−1.75722	+	0.263748i
$745$	−6.70820			−0.245770
$746$	−20.1369	−	3.18937i	−0.737263	−	0.116771i
$747$	34.5811	+	25.1246i	1.26525	+	0.919261i
$748$	6.18034	−	19.0211i	0.225976	−	0.695481i
$749$	1.68692			0.0616386
$750$	36.7607	+	36.7607i	1.34231	+	1.34231i
$751$	31.0013	+	10.0729i	1.13126	+	0.367567i	0.814053	−	0.580791i	$-0.197257\pi$
$751$	31.0013	+	10.0729i	1.13126	+	0.367567i	0.317202	+	0.948358i	$0.397257\pi$
$752$	−21.3723	+	6.94427i	−0.779367	+	0.253232i
$753$	3.61803	+	11.1352i	0.131848	+	0.405788i
$754$	−4.59799	−	0.728250i	−0.167449	−	0.0265213i
$755$	4.30625	−	13.2533i	0.156721	−	0.482337i
$756$	4.08174	−	2.96556i	0.148451	−	0.107856i
$757$	−15.5279	+	21.3723i	−0.564370	+	0.776788i	−0.991874	−	0.127225i	$-0.959393\pi$
$757$	−15.5279	+	21.3723i	−0.564370	+	0.776788i	0.427504	+	0.904013i	$0.359393\pi$
$758$	−32.5512	−	16.5857i	−1.18231	−	0.602419i
$759$	11.1352	+	8.09017i	0.404181	+	0.293655i
$760$	−3.57960	−	22.6007i	−0.129846	−	0.819815i
$761$	25.2254	−	8.19624i	0.914421	−	0.297113i	0.186245	−	0.982503i	$-0.440368\pi$
$761$	25.2254	−	8.19624i	0.914421	−	0.297113i	0.728176	+	0.685390i	$0.240368\pi$
$762$	−7.27599	−	45.9388i	−0.263581	−	1.66419i
$763$	2.10638	+	2.89919i	0.0762562	+	0.104958i
$764$	−0.201626	+	0.620541i	−0.00729458	+	0.0224504i
$765$	10.0000	+	13.7638i	0.361551	+	0.497632i
$766$	2.01806	−	3.96066i	0.0729153	−	0.143104i
$767$	0.759299	+	2.33688i	0.0274167	+	0.0843799i
$768$	15.2169	−	46.8328i	0.549093	−	1.68993i
$769$	−11.9098			−0.429479			−0.214740	−	0.976671i	$-0.568890\pi$
$769$	−11.9098			−0.429479			−0.214740	+	0.976671i	$0.568890\pi$
$770$	−2.35114	+	2.35114i	−0.0847292	+	0.0847292i
$771$	−10.4086	+	32.0344i	−0.374857	+	1.15369i
$772$	9.57608	−	13.1803i	0.344651	−	0.474371i
$773$	−24.2320	−	33.3525i	−0.871565	−	1.19961i	−0.978687	−	0.205360i	$-0.934164\pi$
$773$	−24.2320	−	33.3525i	−0.871565	−	1.19961i	0.107122	−	0.994246i	$-0.465836\pi$
$774$	17.0130	+	17.0130i	0.611520	+	0.611520i
$775$	4.20025	−	12.5795i	0.150878	−	0.451870i
$776$	−2.94427	+	2.94427i	−0.105693	+	0.105693i
$777$	5.42705	−	3.94298i	0.194694	−	0.141454i
$778$	39.4655	−	6.25072i	1.41491	−	0.224099i
$779$	−24.8990	−	8.09017i	−0.892099	−	0.289860i
$780$	−4.47214			−0.160128
$781$			40.7364i			1.45766i
$782$	0.757825	+	1.48732i	0.0270998	+	0.0531863i
$783$	−74.5052	+	24.2082i	−2.66260	+	0.865131i
$784$	−8.58359	−	26.4176i	−0.306557	−	0.943485i
$785$	22.1803	−	16.1150i	0.791650	−	0.575168i
$786$	−24.0002	−	47.1031i	−0.856060	−	1.68011i
$787$	−25.2093	+	18.3156i	−0.898613	+	0.652880i	−0.938109	−	0.346339i	$-0.887425\pi$
$787$	−25.2093	+	18.3156i	−0.898613	+	0.652880i	0.0394965	+	0.999220i	$0.487425\pi$
$788$	28.1482	+	20.4508i	1.00274	+	0.728531i
$789$	−25.0623	−	77.1338i	−0.892242	−	2.74604i
$790$	2.40206	+	15.1660i	0.0854613	+	0.539582i
$791$	1.18808	−	1.63525i	0.0422433	−	0.0581430i
$792$	100.399	+	51.1556i	3.56751	+	1.81774i
$793$	−0.326238	−	0.237026i	−0.0115850	−	0.00841703i
$794$	16.7616	+	2.65478i	0.594848	+	0.0942146i
$795$	−43.7284	−	14.2082i	−1.55088	−	0.503913i
$796$	−4.27051	−	5.87785i	−0.151364	−	0.208335i
$797$	20.0000	−	6.49839i	0.708436	−	0.230185i	0.0674339	−	0.997724i	$-0.478519\pi$
$797$	20.0000	−	6.49839i	0.708436	−	0.230185i	0.641002	+	0.767539i	$0.278519\pi$
$798$	2.33235	−	4.57748i	0.0825641	−	0.162041i
$799$	2.82041	−	8.68034i	0.0997791	−	0.307088i
$800$	9.52786	+	9.52786i	0.336861	+	0.336861i
$801$		−	15.9030i		−	0.561903i
$802$	6.28433	+	12.3337i	0.221908	+	0.435518i
$803$	6.88191	−	9.47214i	0.242857	−	0.334264i
$804$	−28.7032	+	20.8541i	−1.01228	+	0.735467i
$805$		−	0.277515i		−	0.00978110i
$806$	1.57959	+	3.16318i	0.0556387	+	0.111418i
$807$			75.5755i			2.66038i
$808$	3.95751	−	24.9868i	0.139225	−	0.879031i
$809$	−13.3779	+	18.4131i	−0.470342	+	0.647370i	−0.976613	−	0.215004i	$-0.931023\pi$
$809$	−13.3779	+	18.4131i	−0.470342	+	0.647370i	0.506271	+	0.862374i	$0.331023\pi$
$810$	−27.4676	+	13.9954i	−0.965111	+	0.491749i
$811$		−	37.3607i		−	1.31191i	−0.754800	−	0.655955i	$-0.772266\pi$
$811$		−	37.3607i		−	1.31191i	0.754800	−	0.655955i	$-0.227734\pi$
$812$		−	3.46120i		−	0.121464i
$813$	5.59017	−	17.2048i	0.196056	−	0.603398i
$814$	71.6135	+	36.4889i	2.51005	+	1.27894i
$815$	3.16344	−	1.02786i	0.110810	−	0.0360045i
$816$	11.7557	+	16.1803i	0.411532	+	0.566425i
$817$	12.5000	+	4.06150i	0.437320	+	0.142094i
$818$	−7.97190	+	50.3326i	−0.278731	+	1.75984i
$819$	−0.555029	−	0.403252i	−0.0193943	−	0.0140908i
$820$	−16.1150	+	5.23607i	−0.562759	+	0.182851i
$821$	10.4508	−	14.3844i	0.364737	−	0.502018i	−0.586724	−	0.809787i	$-0.699583\pi$
$821$	10.4508	−	14.3844i	0.364737	−	0.502018i	0.951461	+	0.307769i	$0.0995826\pi$
$822$	−42.8154	+	6.78130i	−1.49336	+	0.236525i
$823$	−9.35156	−	28.7812i	−0.325975	−	1.00325i	−0.970999	−	0.239085i	$-0.923152\pi$
$823$	−9.35156	−	28.7812i	−0.325975	−	1.00325i	0.645024	−	0.764163i	$-0.276848\pi$
$824$	5.34946	+	33.7752i	0.186357	+	1.17661i
$825$	−36.5066	+	26.5236i	−1.27100	+	0.923433i
$826$	−1.62776	+	0.829384i	−0.0566369	+	0.0288580i
$827$	12.9515	−	9.40983i	0.450368	−	0.327212i	−0.339373	−	0.940652i	$-0.610215\pi$
$827$	12.9515	−	9.40983i	0.450368	−	0.327212i	0.789741	+	0.613440i	$0.210215\pi$
$828$	−8.94427	+	2.90617i	−0.310835	+	0.100996i
$829$	36.8328	−	11.9677i	1.27926	−	0.415656i	0.410938	−	0.911663i	$-0.365201\pi$
$829$	36.8328	−	11.9677i	1.27926	−	0.415656i	0.868318	+	0.496007i	$0.165201\pi$
$830$	13.4653	−	6.86092i	0.467388	−	0.238146i
$831$			1.38197i			0.0479399i
$832$	−3.59222			−0.124538
$833$	10.7295	+	3.48622i	0.371755	+	0.120790i
$834$	3.39065	+	21.4077i	0.117409	+	0.741289i
$835$	27.2501	−	19.7984i	0.943029	−	0.685151i
$836$	61.5537			2.12888
$837$	47.8500	+	35.3606i	1.65394	+	1.22224i
$838$	−20.1803	+	20.1803i	−0.697118	+	0.697118i
$839$	−2.93893	−	4.04508i	−0.101463	−	0.139652i	0.755267	−	0.655418i	$-0.227507\pi$
$839$	−2.93893	−	4.04508i	−0.101463	−	0.139652i	−0.856730	+	0.515766i	$0.827507\pi$
$840$	−0.520147	−	3.28408i	−0.0179468	−	0.113311i
$841$	−7.64590	+	23.5317i	−0.263652	+	0.811436i
$842$	27.5967	+	27.5967i	0.951047	+	0.951047i
$843$	48.7939			1.68055
$844$	3.34752	−	10.3026i	0.115227	−	0.354631i
$845$	−6.39919	−	19.6947i	−0.220139	−	0.677517i
$846$	45.8171	+	23.3450i	1.57523	+	0.802617i
$847$	−3.73098	−	5.13525i	−0.128198	−	0.176449i
$848$	−35.1246	−	11.4127i	−1.20618	−	0.391913i
$849$	5.26393	+	7.24518i	0.180658	+	0.248654i
$850$	−5.40526	+	0.856109i	−0.185399	+	0.0293643i
$851$	−6.37988	+	2.07295i	−0.218700	+	0.0710598i
$852$	−32.9565	−	23.9443i	−1.12907	−	0.820317i
$853$	−33.5623	−	24.3844i	−1.14915	−	0.834907i	−0.160784	−	0.986990i	$-0.551402\pi$
$853$	−33.5623	−	24.3844i	−1.14915	−	0.834907i	−0.988368	+	0.152082i	$0.951402\pi$
$854$	0.136114	−	0.267138i	0.00465772	−	0.00914129i
$855$	−30.7768	+	42.3607i	−1.05255	+	1.44870i
$856$	−19.9628	−	3.16180i	−0.682315	−	0.108068i
$857$	14.0344	−	43.1936i	0.479407	−	1.47546i	−0.360513	−	0.932754i	$-0.617398\pi$
$857$	14.0344	−	43.1936i	0.479407	−	1.47546i	0.839920	−	0.542710i	$-0.182602\pi$
$858$	1.88191	−	11.8819i	0.0642473	−	0.405642i
$859$	3.19620	+	9.83688i	0.109053	+	0.335630i	0.990660	−	0.136353i	$-0.0435382\pi$
$859$	3.19620	+	9.83688i	0.109053	+	0.335630i	−0.881607	+	0.471983i	$0.843538\pi$
$860$	8.09017	−	2.62866i	0.275873	−	0.0896364i
$861$	−3.61803	−	1.17557i	−0.123302	−	0.0400633i
$862$	−13.1246	+	13.1246i	−0.447026	+	0.447026i
$863$	−49.1369			−1.67264			−0.836320	−	0.548241i	$-0.815298\pi$
$863$	−49.1369			−1.67264			−0.836320	+	0.548241i	$0.815298\pi$
$864$	−53.8613	+	27.4437i	−1.83240	+	0.933653i
$865$	−17.0623	−	12.3965i	−0.580136	−	0.421493i
$866$	6.21278	−	39.2259i	0.211119	−	1.33295i
$867$	44.1976			1.50103
$868$	−2.13914	+	1.52786i	−0.0726071	+	0.0518591i
$869$	−41.3050			−1.40117
$870$	−8.07641	+	50.9925i	−0.273816	+	1.72881i
$871$	2.09387	+	1.52129i	0.0709481	+	0.0515468i
$872$	−19.4928	−	38.2567i	−0.660108	−	1.29553i
$873$	9.52786			0.322469
$874$	−3.63271	+	3.63271i	−0.122878	+	0.122878i
$875$	2.68166	+	0.871323i	0.0906565	+	0.0294561i
$876$	3.61803	+	11.1352i	0.122242	+	0.376222i
$877$	−8.52786	−	26.2461i	−0.287966	−	0.886267i	−0.985494	−	0.169710i	$-0.945717\pi$
$877$	−8.52786	−	26.2461i	−0.287966	−	0.886267i	0.697529	−	0.716557i	$-0.254283\pi$
$878$	−1.00171	+	6.32453i	−0.0338060	+	0.213443i
$879$	15.4414	−	47.5238i	0.520826	−	1.60294i
$880$	32.2299	−	23.4164i	1.08647	−	0.789367i
$881$	3.19098	−	4.39201i	0.107507	−	0.147971i	−0.751873	−	0.659308i	$-0.770850\pi$
$881$	3.19098	−	4.39201i	0.107507	−	0.147971i	0.859380	+	0.511337i	$0.170850\pi$
$882$	−28.8560	+	56.6331i	−0.971632	+	1.90694i
$883$	−45.6835	−	33.1910i	−1.53737	−	1.11697i	−0.951957	−	0.306231i	$-0.900932\pi$
$883$	−45.6835	−	33.1910i	−1.53737	−	1.11697i	−0.585414	−	0.810735i	$-0.699068\pi$
$884$	0.857567	−	1.18034i	0.0288431	−	0.0396991i
$885$	25.9164	−	8.42075i	0.871171	−	0.283060i
$886$	12.7453	−	2.01865i	0.428186	−	0.0678180i
$887$	26.3973	+	36.3328i	0.886336	+	1.21994i	0.974626	+	0.223842i	$0.0718599\pi$
$887$	26.3973	+	36.3328i	0.886336	+	1.21994i	−0.0882897	+	0.996095i	$0.528140\pi$
$888$	−71.6135	+	36.4889i	−2.40319	+	1.22449i
$889$	−1.48278	−	2.04087i	−0.0497308	−	0.0684486i
$890$	−5.00972	−	2.55258i	−0.167926	−	0.0855627i
$891$	−25.6255	−	78.8673i	−0.858487	−	2.64215i
$892$	4.14590	+	1.34708i	0.138815	+	0.0451037i
$893$	28.0902			0.940002
$894$	12.7598	+	12.7598i	0.426750	+	0.426750i
$895$	2.12663	−	6.54508i	0.0710853	−	0.218778i
$896$	−0.417806	−	2.63792i	−0.0139579	−	0.0881268i
$897$	0.590170	+	0.812299i	0.0197052	+	0.0271219i
$898$	24.8335	−	24.8335i	0.828704	−	0.828704i
$899$	38.9201	−	12.2984i	1.29806	−	0.410174i
$900$		−	30.8328i		−	1.02776i
$901$	12.1353	−	8.81678i	0.404284	−	0.293729i
$902$	−7.13028	−	45.0188i	−0.237412	−	1.49896i
$903$	1.81636	+	0.590170i	0.0604446	+	0.0196396i
$904$	−17.1246	+	17.1246i	−0.569556	+	0.569556i
$905$			1.17557i			0.0390773i
$906$	−33.4002	+	17.0183i	−1.10965	+	0.565394i
$907$	22.2376	−	7.22542i	0.738386	−	0.239916i	0.0844099	−	0.996431i	$-0.473099\pi$
$907$	22.2376	−	7.22542i	0.738386	−	0.239916i	0.653977	+	0.756515i	$0.273099\pi$
$908$	14.0902	+	43.3651i	0.467599	+	1.43912i
$909$	−46.8328	+	34.0260i	−1.55335	+	1.12857i
$910$	−0.216120	+	0.110118i	−0.00716429	+	0.00365039i
$911$	−23.7234	+	17.2361i	−0.785992	+	0.571056i	−0.906771	−	0.421623i	$-0.861461\pi$
$911$	−23.7234	+	17.2361i	−0.785992	+	0.571056i	0.120780	+	0.992679i	$0.461461\pi$
$912$	−36.1803	+	49.7980i	−1.19805	+	1.64898i
$913$	12.5623	+	38.6628i	0.415752	+	1.27955i
$914$	−33.5245	+	5.30977i	−1.10889	+	0.175631i
$915$	−2.62866	+	3.61803i	−0.0869007	+	0.119609i
$916$	−7.26543	−	22.3607i	−0.240056	−	0.738818i
$917$	−2.31966	−	1.68533i	−0.0766019	−	0.0556546i
$918$	3.84073	−	24.2494i	0.126763	−	0.800351i
$919$	−19.5232	−	6.34346i	−0.644010	−	0.209251i	−0.0312386	−	0.999512i	$-0.509945\pi$
$919$	−19.5232	−	6.34346i	−0.644010	−	0.209251i	−0.612771	+	0.790261i	$0.709945\pi$
$920$	−0.520147	+	3.28408i	−0.0171487	+	0.108273i
$921$	59.1697	−	19.2254i	1.94971	−	0.633498i
$922$	−34.9855	−	17.8260i	−1.15219	−	0.587068i
$923$	−0.918300	+	2.82624i	−0.0302262	+	0.0930268i
$924$	8.94427			0.294245
$925$		−	21.9928i		−	0.723119i
$926$	31.0249	−	15.8080i	1.01954	−	0.519482i
$927$	45.9937	−	63.3050i	1.51063	−	2.07921i
$928$	−6.48734	+	40.9595i	−0.212958	+	1.34456i
$929$			56.6799i			1.85961i	0.368057	+	0.929803i	$0.380023\pi$
$929$			56.6799i			1.85961i	−0.368057	+	0.929803i	$0.619977\pi$
$930$	35.0802	−	17.5179i	1.15033	−	0.574435i
$931$			34.7214i			1.13795i
$932$	−1.55909	−	2.14590i	−0.0510696	−	0.0702912i
$933$	31.1803	−	42.9161i	1.02080	−	1.40501i
$934$	12.4303	+	24.3959i	0.406733	+	0.798258i
$935$			16.1803i			0.529154i
$936$	5.81234	+	5.81234i	0.189982	+	0.189982i
$937$	−14.3435	+	44.1446i	−0.468580	+	1.44214i	0.385843	+	0.922565i	$0.373911\pi$
$937$	−14.3435	+	44.1446i	−0.468580	+	1.44214i	−0.854423	+	0.519578i	$0.826089\pi$
$938$	−0.873610	+	1.71456i	−0.0285244	+	0.0559823i
$939$	−60.9331	+	19.7984i	−1.98848	+	0.646096i
$940$	14.7082	−	10.6861i	0.479729	−	0.348543i
$941$	9.14590	+	2.97168i	0.298148	+	0.0968741i	0.454271	−	0.890863i	$-0.349900\pi$
$941$	9.14590	+	2.97168i	0.298148	+	0.0968741i	−0.156123	+	0.987738i	$0.549900\pi$
$942$	−72.8420	−	11.5370i	−2.37332	−	0.375897i
$943$	3.07768	+	2.23607i	0.100223	+	0.0728164i
$944$	20.8172	−	6.76393i	0.677544	−	0.220147i
$945$	−2.39919	+	3.30220i	−0.0780456	+	0.107420i
$946$	3.57960	+	22.6007i	0.116383	+	0.734813i
$947$	15.2169	+	46.8328i	0.494483	+	1.52186i	0.817761	+	0.575558i	$0.195215\pi$
$947$	15.2169	+	46.8328i	0.494483	+	1.52186i	−0.323278	+	0.946304i	$0.604785\pi$
$948$	24.2784	−	33.4164i	0.788527	−	1.08531i
$949$	0.690983	−	0.502029i	0.0224303	−	0.0162965i
$950$	−7.64658	−	15.0073i	−0.248088	−	0.486900i
$951$	46.4428	−	33.7426i	1.50601	−	1.09418i
$952$	0.966516	+	0.492464i	0.0313250	+	0.0159609i
$953$	−5.26393	+	1.71036i	−0.170515	+	0.0554038i	−0.393031	−	0.919525i	$-0.628573\pi$
$953$	−5.26393	+	1.71036i	−0.170515	+	0.0554038i	0.222515	+	0.974929i	$0.428573\pi$
$954$	38.3667	+	75.2989i	1.24217	+	2.43789i
$955$		−	0.527864i		−	0.0170813i
$956$		−	51.4631i		−	1.66443i
$957$	−132.082	−	42.9161i	−4.26961	−	1.38728i
$958$	56.1240	−	8.88917i	1.81328	−	0.287196i
$959$	−1.90211	+	1.38197i	−0.0614224	+	0.0446260i
$960$			39.8384i			1.28578i
$961$	−24.7812	−	18.6251i	−0.799392	−	0.600810i
$962$	4.14590	+	4.14590i	0.133669	+	0.133669i
$963$	27.1846	+	37.4164i	0.876012	+	1.20573i
$964$	1.17557	+	0.854102i	0.0378626	+	0.0275088i
$965$	−4.07295	+	12.5352i	−0.131113	+	0.403524i
$966$	−0.527864	+	0.527864i	−0.0169837	+	0.0169837i
$967$	33.5115			1.07766			0.538828	−	0.842416i	$-0.318867\pi$
$967$	33.5115			1.07766			0.538828	+	0.842416i	$0.318867\pi$
$968$	34.5270	+	67.7631i	1.10974	+	2.17799i
$969$	−7.72542	−	23.7764i	−0.248176	−	0.763808i
$970$	1.52932	−	3.00145i	0.0491034	−	0.0963708i
$971$	−13.1885	−	18.1525i	−0.423241	−	0.582541i	0.543145	−	0.839639i	$-0.317234\pi$
$971$	−13.1885	−	18.1525i	−0.423241	−	0.582541i	−0.966385	+	0.257098i	$0.917234\pi$
$972$	17.8885	+	5.81234i	0.573775	+	0.186431i
$973$	0.690983	+	0.951057i	0.0221519	+	0.0304895i
$974$	−4.30742	−	27.1960i	−0.138019	−	0.871415i
$975$	−3.13068	+	1.01722i	−0.100262	+	0.0325771i
$976$	−2.11146	+	2.90617i	−0.0675861	+	0.0930242i
$977$	−6.47214	−	4.70228i	−0.207062	−	0.150439i	0.479421	−	0.877585i	$-0.340847\pi$
$977$	−6.47214	−	4.70228i	−0.207062	−	0.150439i	−0.686483	+	0.727145i	$0.740847\pi$
$978$	−7.97233	−	4.06211i	−0.254927	−	0.129892i
$979$	8.89002	−	12.2361i	0.284126	−	0.391066i
$980$	13.2088	+	18.1803i	0.421939	+	0.580750i
$981$	−30.3607	+	93.4406i	−0.969342	+	2.98333i
$982$	−15.4621	−	2.44896i	−0.493416	−	0.0781494i
$983$	0.244758	+	0.753289i	0.00780658	+	0.0240262i	0.954884	−	0.296979i	$-0.0959792\pi$
$983$	0.244758	+	0.753289i	0.00780658	+	0.0240262i	−0.947077	+	0.321005i	$0.895979\pi$
$984$	40.6121	+	20.6929i	1.29467	+	0.659665i
$985$	−26.7705	−	8.69827i	−0.852979	−	0.277150i
$986$	−11.9098	−	11.9098i	−0.379286	−	0.379286i
$987$	4.08174			0.129923
$988$	4.27051	+	1.38757i	0.135863	+	0.0441446i
$989$	−1.54508	−	1.12257i	−0.0491308	−	0.0356956i
$990$	−90.0377	−	14.2606i	−2.86158	−	0.453230i
$991$	−12.9313			−0.410776			−0.205388	−	0.978681i	$-0.565846\pi$
$991$	−12.9313			−0.410776			−0.205388	+	0.978681i	$0.565846\pi$
$992$	28.1780	−	14.0712i	0.894654	−	0.446761i
$993$	25.9787			0.824410
$994$	−2.18223	−	0.345632i	−0.0692162	−	0.0109628i
$995$	4.75528	+	3.45492i	0.150753	+	0.109528i
$996$	−38.6628	−	12.5623i	−1.22508	−	0.398052i
$997$	−57.4721			−1.82016			−0.910080	−	0.414432i	$-0.863980\pi$
$997$	−57.4721			−1.82016			−0.910080	+	0.414432i	$0.863980\pi$
$998$	−33.4055	−	33.4055i	−1.05743	−	1.05743i
$999$	93.8366	+	30.4894i	2.96886	+	0.964641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.j.a.15.1	✓	8
4.3	odd	2	inner	124.2.j.a.15.2	yes	8
31.29	odd	10	inner	124.2.j.a.91.2	yes	8
124.91	even	10	inner	124.2.j.a.91.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.j.a.15.1	✓	8	1.1	even	1	trivial
124.2.j.a.15.2	yes	8	4.3	odd	2	inner
124.2.j.a.91.1	yes	8	124.91	even	10	inner
124.2.j.a.91.2	yes	8	31.29	odd	10	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39680 - 0.221232i) q^{2} +(-2.48990 - 1.80902i) q^{3} +(1.90211 + 0.618034i) q^{4} -1.61803 q^{5} +(3.07768 + 3.07768i) q^{6} +(0.224514 + 0.0729490i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(2.00000 + 6.15537i) q^{9} +O(q^{10})\)	\(q+(-1.39680 - 0.221232i) q^{2} +(-2.48990 - 1.80902i) q^{3} +(1.90211 + 0.618034i) q^{4} -1.61803 q^{5} +(3.07768 + 3.07768i) q^{6} +(0.224514 + 0.0729490i) q^{7} +(-2.52015 - 1.28408i) q^{8} +(2.00000 + 6.15537i) q^{9} +(2.26007 + 0.357960i) q^{10} +(-1.90211 + 5.85410i) q^{11} +(-3.61803 - 4.97980i) q^{12} +(-0.263932 + 0.363271i) q^{13} +(-0.297463 - 0.151565i) q^{14} +(4.02874 + 2.92705i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-1.54508 + 0.502029i) q^{17} +(-1.43184 - 9.04029i) q^{18} +(-2.93893 - 4.04508i) q^{19} +(-3.07768 - 1.00000i) q^{20} +(-0.427051 - 0.587785i) q^{21} +(3.95199 - 7.75621i) q^{22} +(0.224514 + 0.690983i) q^{23} +(3.95199 + 7.75621i) q^{24} -2.38197 q^{25} +(0.449028 - 0.449028i) q^{26} +(3.30220 - 10.1631i) q^{27} +(0.381966 + 0.277515i) q^{28} +(-4.30902 - 5.93085i) q^{29} +(-4.97980 - 4.97980i) q^{30} +(-1.76336 + 5.28115i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(15.3262 - 11.1352i) q^{33} +(2.26924 - 0.359413i) q^{34} +(-0.363271 - 0.118034i) q^{35} +12.9443i q^{36} +9.23305i q^{37} +(3.21020 + 6.30037i) q^{38} +(1.31433 - 0.427051i) q^{39} +(4.07768 + 2.07768i) q^{40} +(4.23607 - 3.07768i) q^{41} +(0.466469 + 0.915497i) q^{42} +(-2.12663 + 1.54508i) q^{43} +(-7.23607 + 9.95959i) q^{44} +(-3.23607 - 9.95959i) q^{45} +(-0.160734 - 1.01484i) q^{46} +(-3.30220 + 4.54508i) q^{47} +(-3.80423 - 11.7082i) q^{48} +(-5.61803 - 4.08174i) q^{49} +(3.32714 + 0.526966i) q^{50} +(4.75528 + 1.54508i) q^{51} +(-0.726543 + 0.527864i) q^{52} +(-8.78115 + 2.85317i) q^{53} +(-6.86092 + 13.4653i) q^{54} +(3.07768 - 9.47214i) q^{55} +(-0.472136 - 0.472136i) q^{56} +15.3884i q^{57} +(4.70675 + 9.23752i) q^{58} +(3.21644 - 4.42705i) q^{59} +(5.85410 + 8.05748i) q^{60} +0.898056i q^{61} +(3.63142 - 6.98662i) q^{62} +1.52786i q^{63} +(4.70228 + 6.47214i) q^{64} +(0.427051 - 0.587785i) q^{65} +(-23.8712 + 12.1630i) q^{66} -5.76393i q^{67} -3.24920 q^{68} +(0.690983 - 2.12663i) q^{69} +(0.481305 + 0.245237i) q^{70} +(6.29412 - 2.04508i) q^{71} +(2.86368 - 18.0806i) q^{72} +(-1.80902 - 0.587785i) q^{73} +(2.04264 - 12.8967i) q^{74} +(5.93085 + 4.30902i) q^{75} +(-3.09017 - 9.51057i) q^{76} +(-0.854102 + 1.17557i) q^{77} +(-1.93033 + 0.305735i) q^{78} +(2.07363 + 6.38197i) q^{79} +(-5.23607 - 3.80423i) q^{80} +(-10.8992 + 7.91872i) q^{81} +(-6.59783 + 3.36176i) q^{82} +(5.34307 - 3.88197i) q^{83} +(-0.449028 - 1.38197i) q^{84} +(2.50000 - 0.812299i) q^{85} +(3.31230 - 1.68770i) q^{86} +22.5623i q^{87} +(12.3107 - 12.3107i) q^{88} +(-2.33688 - 0.759299i) q^{89} +(2.31677 + 14.6275i) q^{90} +(-0.0857567 + 0.0623059i) q^{91} +1.45309i q^{92} +(13.9443 - 9.95959i) q^{93} +(5.61803 - 5.61803i) q^{94} +(4.75528 + 6.54508i) q^{95} +(2.72353 + 17.1957i) q^{96} +(0.454915 - 1.40008i) q^{97} +(6.94427 + 6.94427i) q^{98} -39.8384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9	\( 8 q - 2 q^{2} - 4 q^{5} + 4 q^{8} + 16 q^{9} + 6 q^{10} - 20 q^{12} - 20 q^{13} - 14 q^{14} + 8 q^{16} + 10 q^{17} - 24 q^{18} + 10 q^{21} + 20 q^{22} + 20 q^{24} - 28 q^{25} + 12 q^{28} - 30 q^{29} - 32 q^{32} + 60 q^{33} + 30 q^{34} + 10 q^{38} + 8 q^{40} + 16 q^{41} + 10 q^{42} - 40 q^{44} - 8 q^{45} - 10 q^{46} - 36 q^{49} + 2 q^{50} - 30 q^{53} - 50 q^{54} + 32 q^{56} + 20 q^{58} + 20 q^{60} + 38 q^{62} - 10 q^{65} - 20 q^{66} + 10 q^{69} - 8 q^{70} + 48 q^{72} - 10 q^{73} - 30 q^{74} + 20 q^{76} + 20 q^{77} - 24 q^{80} - 38 q^{81} - 4 q^{82} + 20 q^{85} + 20 q^{86} - 50 q^{89} + 32 q^{90} + 40 q^{93} + 36 q^{94} - 40 q^{96} + 26 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^5 + 4 * q^8 + 16 * q^9 + 6 * q^10 - 20 * q^12 - 20 * q^13 - 14 * q^14 + 8 * q^16 + 10 * q^17 - 24 * q^18 + 10 * q^21 + 20 * q^22 + 20 * q^24 - 28 * q^25 + 12 * q^28 - 30 * q^29 - 32 * q^32 + 60 * q^33 + 30 * q^34 + 10 * q^38 + 8 * q^40 + 16 * q^41 + 10 * q^42 - 40 * q^44 - 8 * q^45 - 10 * q^46 - 36 * q^49 + 2 * q^50 - 30 * q^53 - 50 * q^54 + 32 * q^56 + 20 * q^58 + 20 * q^60 + 38 * q^62 - 10 * q^65 - 20 * q^66 + 10 * q^69 - 8 * q^70 + 48 * q^72 - 10 * q^73 - 30 * q^74 + 20 * q^76 + 20 * q^77 - 24 * q^80 - 38 * q^81 - 4 * q^82 + 20 * q^85 + 20 * q^86 - 50 * q^89 + 32 * q^90 + 40 * q^93 + 36 * q^94 - 40 * q^96 + 26 * q^97 - 16 * q^98

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