LMFDB - Embedded newform 1295.2.j.a.186.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] 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("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			186.11
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.306680 + 0.531185i) q^{2} +(-0.923254 + 1.59912i) q^{3} +(0.811895 - 1.40624i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.13257 q^{6} +(2.55098 - 0.701777i) q^{7} +2.22269 q^{8} +(-0.204795 - 0.354715i) q^{9} +(0.306680 - 0.531185i) q^{10} +(0.610494 - 1.05741i) q^{11} +(1.49917 + 2.59664i) q^{12} -0.894144 q^{13} +(1.15511 + 1.13982i) q^{14} +1.84651 q^{15} +(-0.942136 - 1.63183i) q^{16} +(3.26775 - 5.65992i) q^{17} +(0.125613 - 0.217568i) q^{18} +(-3.62207 - 6.27362i) q^{19} -1.62379 q^{20} +(-1.23298 + 4.72725i) q^{21} +0.748905 q^{22} +(1.33143 + 2.30610i) q^{23} +(-2.05210 + 3.55435i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.274216 - 0.474956i) q^{26} -4.78321 q^{27} +(1.08426 - 4.15707i) q^{28} -7.01553 q^{29} +(0.566287 + 0.980838i) q^{30} +(-0.422759 + 0.732240i) q^{31} +(2.80056 - 4.85070i) q^{32} +(1.12728 + 1.95251i) q^{33} +4.00862 q^{34} +(-1.88325 - 1.85833i) q^{35} -0.665087 q^{36} +(-0.500000 - 0.866025i) q^{37} +(2.22163 - 3.84798i) q^{38} +(0.825521 - 1.42985i) q^{39} +(-1.11134 - 1.92490i) q^{40} +5.41518 q^{41} +(-2.88917 + 0.794814i) q^{42} +11.9780 q^{43} +(-0.991314 - 1.71701i) q^{44} +(-0.204795 + 0.354715i) q^{45} +(-0.816645 + 1.41447i) q^{46} +(-4.22567 - 7.31907i) q^{47} +3.47932 q^{48} +(6.01502 - 3.58044i) q^{49} -0.613360 q^{50} +(6.03393 + 10.4511i) q^{51} +(-0.725951 + 1.25738i) q^{52} +(-4.62310 + 8.00744i) q^{53} +(-1.46692 - 2.54077i) q^{54} -1.22099 q^{55} +(5.67004 - 1.55983i) q^{56} +13.3764 q^{57} +(-2.15152 - 3.72655i) q^{58} +(-1.52723 + 2.64525i) q^{59} +(1.49917 - 2.59664i) q^{60} +(-0.697727 - 1.20850i) q^{61} -0.518607 q^{62} +(-0.771358 - 0.761151i) q^{63} -0.333046 q^{64} +(0.447072 + 0.774351i) q^{65} +(-0.691430 + 1.19759i) q^{66} +(5.75859 - 9.97416i) q^{67} +(-5.30614 - 9.19051i) q^{68} -4.91699 q^{69} +(0.409562 - 1.57026i) q^{70} +5.48766 q^{71} +(-0.455195 - 0.788420i) q^{72} +(4.56109 - 7.90003i) q^{73} +(0.306680 - 0.531185i) q^{74} +(-0.923254 - 1.59912i) q^{75} -11.7630 q^{76} +(0.815296 - 3.12586i) q^{77} +1.01268 q^{78} +(6.67586 + 11.5629i) q^{79} +(-0.942136 + 1.63183i) q^{80} +(5.03050 - 8.71309i) q^{81} +(1.66073 + 2.87647i) q^{82} -9.04827 q^{83} +(5.64662 + 5.57189i) q^{84} -6.53551 q^{85} +(3.67341 + 6.36253i) q^{86} +(6.47712 - 11.2187i) q^{87} +(1.35694 - 2.35028i) q^{88} +(7.48032 + 12.9563i) q^{89} -0.251226 q^{90} +(-2.28094 + 0.627489i) q^{91} +4.32392 q^{92} +(-0.780628 - 1.35209i) q^{93} +(2.59186 - 4.48923i) q^{94} +(-3.62207 + 6.27362i) q^{95} +(5.17125 + 8.95686i) q^{96} +0.0414843 q^{97} +(3.74656 + 2.09704i) q^{98} -0.500104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.306680	+	0.531185i	0.216855	+	0.375605i	0.953845	−	0.300300i	$-0.0970866\pi$
$2$	0.306680	+	0.531185i	0.216855	+	0.375605i	−0.736989	+	0.675904i	$0.763753\pi$
$3$	−0.923254	+	1.59912i	−0.533041	+	0.923254i	0.466215	+	0.884672i	$0.345617\pi$
$3$	−0.923254	+	1.59912i	−0.533041	+	0.923254i	−0.999255	+	0.0385821i	$0.987716\pi$
$4$	0.811895	−	1.40624i	0.405947	−	0.703122i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.13257			−0.462371
$7$	2.55098	−	0.701777i	0.964181	−	0.265247i
$7$	2.55098	−	0.701777i	0.964181	−	0.265247i
$8$	2.22269			0.785839
$9$	−0.204795	−	0.354715i	−0.0682649	−	0.118238i
$10$	0.306680	−	0.531185i	0.0969807	−	0.167976i
$11$	0.610494	−	1.05741i	0.184071	−	0.318820i	−0.759192	−	0.650867i	$-0.774406\pi$
$11$	0.610494	−	1.05741i	0.184071	−	0.318820i	0.943263	+	0.332046i	$0.107739\pi$
$12$	1.49917	+	2.59664i	0.432773	+	0.749585i
$13$	−0.894144			−0.247991			−0.123995	−	0.992283i	$-0.539571\pi$
$13$	−0.894144			−0.247991			−0.123995	+	0.992283i	$0.539571\pi$
$14$	1.15511	+	1.13982i	0.308716	+	0.304631i
$15$	1.84651			0.476766
$16$	−0.942136	−	1.63183i	−0.235534	−	0.407957i
$17$	3.26775	−	5.65992i	0.792547	−	1.37273i	−0.131839	−	0.991271i	$-0.542088\pi$
$17$	3.26775	−	5.65992i	0.792547	−	1.37273i	0.924385	−	0.381460i	$-0.124579\pi$
$18$	0.125613	−	0.217568i	0.0296072	−	0.0512812i
$19$	−3.62207	−	6.27362i	−0.830961	−	1.43927i	−0.897277	−	0.441468i	$-0.854458\pi$
$19$	−3.62207	−	6.27362i	−0.830961	−	1.43927i	0.0663165	−	0.997799i	$-0.478875\pi$
$20$	−1.62379			−0.363090
$21$	−1.23298	+	4.72725i	−0.269058	+	1.03157i
$22$	0.748905			0.159667
$23$	1.33143	+	2.30610i	0.277622	+	0.480856i	0.970793	−	0.239917i	$-0.0771203\pi$
$23$	1.33143	+	2.30610i	0.277622	+	0.480856i	−0.693171	+	0.720773i	$0.743787\pi$
$24$	−2.05210	+	3.55435i	−0.418884	+	0.725528i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.274216	−	0.474956i	−0.0537782	−	0.0931465i
$27$	−4.78321			−0.920530
$28$	1.08426	−	4.15707i	0.204906	−	0.785612i
$29$	−7.01553			−1.30275			−0.651376	−	0.758755i	$-0.725808\pi$
$29$	−7.01553			−1.30275			−0.651376	+	0.758755i	$0.725808\pi$
$30$	0.566287	+	0.980838i	0.103389	+	0.179076i
$31$	−0.422759	+	0.732240i	−0.0759298	+	0.131514i	−0.901490	−	0.432799i	$-0.857526\pi$
$31$	−0.422759	+	0.732240i	−0.0759298	+	0.131514i	0.825560	+	0.564314i	$0.190859\pi$
$32$	2.80056	−	4.85070i	0.495073	−	0.857492i
$33$	1.12728	+	1.95251i	0.196235	+	0.339888i
$34$	4.00862			0.687472
$35$	−1.88325	−	1.85833i	−0.318327	−	0.314115i
$36$	−0.665087			−0.110848
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	2.22163	−	3.84798i	0.360397	−	0.624226i
$39$	0.825521	−	1.42985i	0.132189	−	0.228958i
$40$	−1.11134	−	1.92490i	−0.175719	−	0.304354i
$41$	5.41518			0.845709			0.422855	−	0.906198i	$-0.361028\pi$
$41$	5.41518			0.845709			0.422855	+	0.906198i	$0.361028\pi$
$42$	−2.88917	+	0.794814i	−0.445809	+	0.122642i
$43$	11.9780			1.82663			0.913313	−	0.407259i	$-0.133515\pi$
$43$	11.9780			1.82663			0.913313	+	0.407259i	$0.133515\pi$
$44$	−0.991314	−	1.71701i	−0.149446	−	0.258848i
$45$	−0.204795	+	0.354715i	−0.0305290	+	0.0528778i
$46$	−0.816645	+	1.41447i	−0.120408	+	0.208552i
$47$	−4.22567	−	7.31907i	−0.616377	−	1.06760i	−0.990141	−	0.140073i	$-0.955266\pi$
$47$	−4.22567	−	7.31907i	−0.616377	−	1.06760i	0.373764	−	0.927524i	$-0.378067\pi$
$48$	3.47932			0.502197
$49$	6.01502	−	3.58044i	0.859288	−	0.511491i
$50$	−0.613360			−0.0867422
$51$	6.03393	+	10.4511i	0.844919	+	1.46344i
$52$	−0.725951	+	1.25738i	−0.100671	+	0.174368i
$53$	−4.62310	+	8.00744i	−0.635032	+	1.09991i	0.351477	+	0.936197i	$0.385680\pi$
$53$	−4.62310	+	8.00744i	−0.635032	+	1.09991i	−0.986508	+	0.163711i	$0.947654\pi$
$54$	−1.46692	−	2.54077i	−0.199622	−	0.345755i
$55$	−1.22099			−0.164638
$56$	5.67004	−	1.55983i	0.757690	−	0.208441i
$57$	13.3764			1.77174
$58$	−2.15152	−	3.72655i	−0.282509	−	0.489320i
$59$	−1.52723	+	2.64525i	−0.198829	+	0.344382i	−0.948149	−	0.317826i	$-0.897047\pi$
$59$	−1.52723	+	2.64525i	−0.198829	+	0.344382i	0.749320	+	0.662208i	$0.230380\pi$
$60$	1.49917	−	2.59664i	0.193542	−	0.335225i
$61$	−0.697727	−	1.20850i	−0.0893348	−	0.154732i	0.817895	−	0.575367i	$-0.195141\pi$
$61$	−0.697727	−	1.20850i	−0.0893348	−	0.154732i	−0.907230	+	0.420635i	$0.861807\pi$
$62$	−0.518607			−0.0658632
$63$	−0.771358	−	0.761151i	−0.0971820	−	0.0958960i
$64$	−0.333046			−0.0416308
$65$	0.447072	+	0.774351i	0.0554524	+	0.0960464i
$66$	−0.691430	+	1.19759i	−0.0851091	+	0.147413i
$67$	5.75859	−	9.97416i	0.703523	−	1.21854i	−0.263699	−	0.964605i	$-0.584942\pi$
$67$	5.75859	−	9.97416i	0.703523	−	1.21854i	0.967222	−	0.253933i	$-0.0817242\pi$
$68$	−5.30614	−	9.19051i	−0.643465	−	1.11451i
$69$	−4.91699			−0.591936
$70$	0.409562	−	1.57026i	0.0489520	−	0.187683i
$71$	5.48766			0.651265			0.325632	−	0.945496i	$-0.394423\pi$
$71$	5.48766			0.651265			0.325632	+	0.945496i	$0.394423\pi$
$72$	−0.455195	−	0.788420i	−0.0536452	−	0.0929162i
$73$	4.56109	−	7.90003i	0.533835	−	0.924629i	−0.465384	−	0.885109i	$-0.654084\pi$
$73$	4.56109	−	7.90003i	0.533835	−	0.924629i	0.999219	−	0.0395199i	$-0.0125829\pi$
$74$	0.306680	−	0.531185i	0.0356508	−	0.0617490i
$75$	−0.923254	−	1.59912i	−0.106608	−	0.184651i
$76$	−11.7630			−1.34931
$77$	0.815296	−	3.12586i	0.0929116	−	0.356224i
$78$	1.01268			0.114664
$79$	6.67586	+	11.5629i	0.751093	+	1.30093i	0.947293	+	0.320367i	$0.103806\pi$
$79$	6.67586	+	11.5629i	0.751093	+	1.30093i	−0.196200	+	0.980564i	$0.562860\pi$
$80$	−0.942136	+	1.63183i	−0.105334	+	0.182444i
$81$	5.03050	−	8.71309i	0.558945	−	0.968121i
$82$	1.66073	+	2.87647i	0.183397	+	0.317652i
$83$	−9.04827			−0.993177			−0.496588	−	0.867986i	$-0.665414\pi$
$83$	−9.04827			−0.993177			−0.496588	+	0.867986i	$0.665414\pi$
$84$	5.64662	+	5.57189i	0.616096	+	0.607944i
$85$	−6.53551			−0.708875
$86$	3.67341	+	6.36253i	0.396114	+	0.686089i
$87$	6.47712	−	11.2187i	0.694420	−	1.20277i
$88$	1.35694	−	2.35028i	0.144650	−	0.250541i
$89$	7.48032	+	12.9563i	0.792912	+	1.37336i	0.924157	+	0.382014i	$0.124769\pi$
$89$	7.48032	+	12.9563i	0.792912	+	1.37336i	−0.131245	+	0.991350i	$0.541897\pi$
$90$	−0.251226			−0.0264815
$91$	−2.28094	+	0.627489i	−0.239108	+	0.0657788i
$92$	4.32392			0.450800
$93$	−0.780628	−	1.35209i	−0.0809473	−	0.140205i
$94$	2.59186	−	4.48923i	0.267329	−	0.463028i
$95$	−3.62207	+	6.27362i	−0.371617	+	0.643659i
$96$	5.17125	+	8.95686i	0.527788	+	0.914156i
$97$	0.0414843			0.00421209			0.00210604	−	0.999998i	$-0.499330\pi$
$97$	0.0414843			0.00421209			0.00210604	+	0.999998i	$0.499330\pi$
$98$	3.74656	+	2.09704i	0.378460	+	0.211833i
$99$	−0.500104			−0.0502623
$100$	0.811895	+	1.40624i	0.0811895	+	0.140624i
$101$	1.36191	−	2.35890i	0.135515	−	0.234719i	−0.790279	−	0.612747i	$-0.790064\pi$
$101$	1.36191	−	2.35890i	0.135515	−	0.234719i	0.925794	+	0.378028i	$0.123398\pi$
$102$	−3.70097	+	6.41027i	−0.366451	+	0.634711i
$103$	4.24225	+	7.34779i	0.418001	+	0.724000i	0.995738	−	0.0922234i	$-0.0293974\pi$
$103$	4.24225	+	7.34779i	0.418001	+	0.724000i	−0.577737	+	0.816223i	$0.696064\pi$
$104$	−1.98740			−0.194881
$105$	4.71041	−	1.29584i	0.459689	−	0.126461i
$106$	−5.67125			−0.550840
$107$	8.68507	+	15.0430i	0.839617	+	1.45426i	0.890215	+	0.455541i	$0.150554\pi$
$107$	8.68507	+	15.0430i	0.839617	+	1.45426i	−0.0505978	+	0.998719i	$0.516113\pi$
$108$	−3.88347	+	6.72636i	−0.373687	+	0.647244i
$109$	4.99861	−	8.65785i	0.478780	−	0.829272i	−0.520924	−	0.853603i	$-0.674412\pi$
$109$	4.99861	−	8.65785i	0.478780	−	0.829272i	0.999704	+	0.0243315i	$0.00774571\pi$
$110$	−0.374453	−	0.648571i	−0.0357027	−	0.0618388i
$111$	1.84651			0.175263
$112$	−3.54855	−	3.50159i	−0.335307	−	0.330869i
$113$	13.8605			1.30388			0.651942	−	0.758269i	$-0.273955\pi$
$113$	13.8605			1.30388			0.651942	+	0.758269i	$0.273955\pi$
$114$	4.10227	+	7.10533i	0.384212	+	0.665475i
$115$	1.33143	−	2.30610i	0.124156	−	0.215045i
$116$	−5.69588	+	9.86555i	−0.528849	+	0.915993i
$117$	0.183116	+	0.317166i	0.0169291	+	0.0293220i
$118$	−1.87349			−0.172469
$119$	4.36398	−	16.7316i	0.400046	−	1.53378i
$120$	4.10421			0.374661
$121$	4.75459	+	8.23520i	0.432236	+	0.748654i
$122$	0.427958	−	0.741245i	0.0387455	−	0.0671092i
$123$	−4.99959	+	8.65954i	−0.450798	+	0.780804i
$124$	0.686472	+	1.18900i	0.0616470	+	0.106776i
$125$	1.00000			0.0894427
$126$	0.167752	−	0.643164i	0.0149445	−	0.0572976i
$127$	−10.4305			−0.925560			−0.462780	−	0.886473i	$-0.653148\pi$
$127$	−10.4305			−0.925560			−0.462780	+	0.886473i	$0.653148\pi$
$128$	−5.70325	−	9.87832i	−0.504101	−	0.873128i
$129$	−11.0587	+	19.1543i	−0.973666	+	1.68644i
$130$	−0.274216	+	0.474956i	−0.0240503	+	0.0416564i
$131$	6.50246	+	11.2626i	0.568123	+	0.984018i	0.996752	+	0.0805369i	$0.0256635\pi$
$131$	6.50246	+	11.2626i	0.568123	+	0.984018i	−0.428629	+	0.903481i	$0.641003\pi$
$132$	3.66094			0.318644
$133$	−13.6425	−	13.4620i	−1.18296	−	1.16730i
$134$	7.06417			0.610251
$135$	2.39161	+	4.14238i	0.205837	+	0.356520i
$136$	7.26320	−	12.5802i	0.622814	−	1.07875i
$137$	−5.22238	+	9.04543i	−0.446178	+	0.772803i	−0.998133	−	0.0610705i	$-0.980549\pi$
$137$	−5.22238	+	9.04543i	−0.446178	+	0.772803i	0.551955	+	0.833874i	$0.313882\pi$
$138$	−1.50794	−	2.61183i	−0.128365	−	0.222334i
$139$	−18.4314			−1.56333			−0.781666	−	0.623697i	$-0.785630\pi$
$139$	−18.4314			−1.56333			−0.781666	+	0.623697i	$0.785630\pi$
$140$	−4.14226	+	1.13954i	−0.350085	+	0.0963085i
$141$	15.6055			1.31422
$142$	1.68295	+	2.91496i	0.141230	+	0.244618i
$143$	−0.545869	+	0.945474i	−0.0456479	+	0.0790645i
$144$	−0.385889	+	0.668379i	−0.0321574	+	0.0556983i
$145$	3.50777	+	6.07563i	0.291304	+	0.504554i
$146$	5.59517			0.463060
$147$	0.172174	+	12.9244i	0.0142007	+	1.06599i
$148$	−1.62379			−0.133475
$149$	−4.61790	−	7.99844i	−0.378313	−	0.655257i	0.612504	−	0.790468i	$-0.290162\pi$
$149$	−4.61790	−	7.99844i	−0.378313	−	0.655257i	−0.990817	+	0.135210i	$0.956829\pi$
$150$	0.566287	−	0.980838i	0.0462371	−	0.0800850i
$151$	−9.72939	+	16.8518i	−0.791767	+	1.37138i	0.133105	+	0.991102i	$0.457505\pi$
$151$	−9.72939	+	16.8518i	−0.791767	+	1.37138i	−0.924872	+	0.380278i	$0.875828\pi$
$152$	−8.05074	−	13.9443i	−0.653001	−	1.13103i
$153$	−2.67687			−0.216413
$154$	1.91044	−	0.525564i	0.153948	−	0.0423512i
$155$	0.845518			0.0679137
$156$	−1.34047	−	2.32177i	−0.107324	−	0.185890i
$157$	5.09901	−	8.83175i	0.406945	−	0.704850i	−0.587600	−	0.809151i	$-0.699927\pi$
$157$	5.09901	−	8.83175i	0.406945	−	0.704850i	0.994546	+	0.104301i	$0.0332606\pi$
$158$	−4.09471	+	7.09224i	−0.325757	+	0.564228i
$159$	−8.53659	−	14.7858i	−0.676996	−	1.17259i
$160$	−5.60111			−0.442807
$161$	5.01482	+	4.94846i	0.395223	+	0.389993i
$162$	6.17102			0.484841
$163$	−11.8692	−	20.5580i	−0.929667	−	1.61023i	−0.783878	−	0.620915i	$-0.786761\pi$
$163$	−11.8692	−	20.5580i	−0.929667	−	1.61023i	−0.145789	−	0.989316i	$-0.546572\pi$
$164$	4.39656	−	7.61506i	0.343314	−	0.594636i
$165$	1.12728	−	1.95251i	0.0877588	−	0.152003i
$166$	−2.77492	−	4.80631i	−0.215376	−	0.373042i
$167$	6.50639			0.503480			0.251740	−	0.967795i	$-0.418997\pi$
$167$	6.50639			0.503480			0.251740	+	0.967795i	$0.418997\pi$
$168$	−2.74052	+	10.5072i	−0.211436	+	0.810648i
$169$	−12.2005			−0.938501
$170$	−2.00431	−	3.47157i	−0.153724	−	0.266257i
$171$	−1.48356	+	2.56961i	−0.113451	+	0.196503i
$172$	9.72486	−	16.8440i	0.741514	−	1.28434i
$173$	−0.0346485	−	0.0600129i	−0.00263428	−	0.00456270i	0.864705	−	0.502280i	$-0.167505\pi$
$173$	−0.0346485	−	0.0600129i	−0.00263428	−	0.00456270i	−0.867340	+	0.497717i	$0.834172\pi$
$174$	7.94561			0.602355
$175$	−0.667734	+	2.56010i	−0.0504760	+	0.193526i
$176$	−2.30067			−0.173420
$177$	−2.82005	−	4.88447i	−0.211968	−	0.367139i
$178$	−4.58813	+	7.94687i	−0.343895	+	0.595643i
$179$	−6.53518	+	11.3193i	−0.488462	+	0.846041i	−0.999912	−	0.0132719i	$-0.995775\pi$
$179$	−6.53518	+	11.3193i	−0.488462	+	0.846041i	0.511450	+	0.859313i	$0.329109\pi$
$180$	0.332544	+	0.575982i	0.0247863	+	0.0429312i
$181$	−20.2904			−1.50817			−0.754085	−	0.656777i	$-0.771919\pi$
$181$	−20.2904			−1.50817			−0.754085	+	0.656777i	$0.771919\pi$
$182$	−1.03283	−	1.01917i	−0.0765587	−	0.0755456i
$183$	2.57672			0.190476
$184$	2.95935	+	5.12575i	0.218166	+	0.377875i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	0.478806	−	0.829316i	0.0351078	−	0.0608084i
$187$	−3.98989	−	6.91069i	−0.291770	−	0.505360i
$188$	−13.7232			−1.00087
$189$	−12.2019	+	3.35675i	−0.887557	+	0.244167i
$190$	−4.44327			−0.322349
$191$	11.1521	+	19.3160i	0.806936	+	1.39765i	0.914976	+	0.403508i	$0.132209\pi$
$191$	11.1521	+	19.3160i	0.806936	+	1.39765i	−0.108040	+	0.994147i	$0.534458\pi$
$192$	0.307486	−	0.532582i	0.0221909	−	0.0384358i
$193$	9.94192	−	17.2199i	0.715635	−	1.23952i	−0.247079	−	0.968995i	$-0.579471\pi$
$193$	9.94192	−	17.2199i	0.715635	−	1.23952i	0.962714	−	0.270521i	$-0.0871960\pi$
$194$	0.0127224	+	0.0220358i	0.000913415	+	0.00158208i
$195$	−1.65104			−0.118234
$196$	−0.151407	−	11.3655i	−0.0108148	−	0.811823i
$197$	5.56939			0.396802			0.198401	−	0.980121i	$-0.436425\pi$
$197$	5.56939			0.396802			0.198401	+	0.980121i	$0.436425\pi$
$198$	−0.153372	−	0.265648i	−0.0108997	−	0.0188788i
$199$	−2.99412	+	5.18597i	−0.212247	+	0.367623i	−0.952418	−	0.304796i	$-0.901412\pi$
$199$	−2.99412	+	5.18597i	−0.212247	+	0.367623i	0.740170	+	0.672420i	$0.234745\pi$
$200$	−1.11134	+	1.92490i	−0.0785839	+	0.136111i
$201$	10.6333	+	18.4174i	0.750013	+	1.29906i
$202$	1.67068			0.117549
$203$	−17.8965	+	4.92334i	−1.25609	+	0.345551i
$204$	19.5957			1.37197
$205$	−2.70759	−	4.68969i	−0.189106	−	0.327542i
$206$	−2.60203	+	4.50684i	−0.181292	+	0.314007i
$207$	0.545339	−	0.944555i	0.0379037	−	0.0656511i
$208$	0.842405	+	1.45909i	0.0584103	+	0.101170i
$209$	−8.84502			−0.611823
$210$	2.13292	+	2.10469i	0.147185	+	0.145238i
$211$	8.23779			0.567113			0.283557	−	0.958956i	$-0.408486\pi$
$211$	8.23779			0.567113			0.283557	+	0.958956i	$0.408486\pi$
$212$	7.50694	+	13.0024i	0.515579	+	0.893009i
$213$	−5.06650	+	8.77543i	−0.347151	+	0.601283i
$214$	−5.32707	+	9.22676i	−0.364151	+	0.630728i
$215$	−5.98899	−	10.3732i	−0.408446	−	0.707449i
$216$	−10.6316			−0.723388
$217$	−0.564582	+	2.16461i	−0.0383263	+	0.146944i
$218$	6.13190			0.415305
$219$	8.42208	+	14.5875i	0.569111	+	0.985730i
$220$	−0.991314	+	1.71701i	−0.0668344	+	0.115761i
$221$	−2.92184	+	5.06078i	−0.196544	+	0.340425i
$222$	0.566287	+	0.980838i	0.0380067	+	0.0658295i
$223$	−19.8585			−1.32982			−0.664911	−	0.746923i	$-0.731530\pi$
$223$	−19.8585			−1.32982			−0.664911	+	0.746923i	$0.731530\pi$
$224$	3.74005	−	14.3394i	0.249893	−	0.958093i
$225$	0.409589			0.0273060
$226$	4.25073	+	7.36248i	0.282754	+	0.489745i
$227$	−2.65801	+	4.60380i	−0.176418	+	0.305565i	−0.940651	−	0.339375i	$-0.889784\pi$
$227$	−2.65801	+	4.60380i	−0.176418	+	0.305565i	0.764233	+	0.644940i	$0.223118\pi$
$228$	10.8602	−	18.8104i	0.719235	−	1.24575i
$229$	5.74141	+	9.94442i	0.379403	+	0.657146i	0.990976	−	0.134043i	$-0.0427959\pi$
$229$	5.74141	+	9.94442i	0.379403	+	0.657146i	−0.611572	+	0.791189i	$0.709463\pi$
$230$	1.63329			0.107696
$231$	4.24590	+	4.18972i	0.279360	+	0.275663i
$232$	−15.5933			−1.02375
$233$	−10.3777	−	17.9746i	−0.679863	−	1.17756i	−0.975022	−	0.222109i	$-0.928706\pi$
$233$	−10.3777	−	17.9746i	−0.679863	−	1.17756i	0.295159	−	0.955448i	$-0.404628\pi$
$234$	−0.112316	+	0.194537i	−0.00734232	+	0.0127173i
$235$	−4.22567	+	7.31907i	−0.275652	+	0.477444i
$236$	2.47991	+	4.29532i	0.161428	+	0.279602i
$237$	−24.6541			−1.60145
$238$	10.2259	−	2.81316i	0.662848	−	0.182350i
$239$	4.52752			0.292861			0.146430	−	0.989221i	$-0.453222\pi$
$239$	4.52752			0.292861			0.146430	+	0.989221i	$0.453222\pi$
$240$	−1.73966	−	3.01318i	−0.112295	−	0.194500i
$241$	10.7241	−	18.5746i	0.690798	−	1.19650i	−0.280778	−	0.959773i	$-0.590593\pi$
$241$	10.7241	−	18.5746i	0.690798	−	1.19650i	0.971577	−	0.236725i	$-0.0760741\pi$
$242$	−2.91628	+	5.05114i	−0.187465	+	0.324700i
$243$	2.11404	+	3.66163i	0.135616	+	0.234893i
$244$	−2.26593			−0.145061
$245$	−6.10826	−	3.41894i	−0.390243	−	0.218428i
$246$	−6.13309			−0.391032
$247$	3.23865	+	5.60951i	0.206071	+	0.356925i
$248$	−0.939661	+	1.62754i	−0.0596686	+	0.103349i
$249$	8.35385	−	14.4693i	0.529404	−	0.916954i
$250$	0.306680	+	0.531185i	0.0193961	+	0.0335951i
$251$	13.7926			0.870582			0.435291	−	0.900290i	$-0.356646\pi$
$251$	13.7926			0.870582			0.435291	+	0.900290i	$0.356646\pi$
$252$	−1.69663	+	0.466743i	−0.106877	+	0.0294020i
$253$	3.25132			0.204409
$254$	−3.19883	−	5.54054i	−0.200713	−	0.347645i
$255$	6.03393	−	10.4511i	0.377859	−	0.654472i
$256$	3.16510	−	5.48211i	0.197819	−	0.342632i
$257$	10.4218	+	18.0511i	0.650096	+	1.12600i	0.983099	+	0.183074i	$0.0586047\pi$
$257$	10.4218	+	18.0511i	0.650096	+	1.12600i	−0.333003	+	0.942926i	$0.608062\pi$
$258$	−13.5660			−0.844579
$259$	−1.88325	−	1.85833i	−0.117019	−	0.115471i
$260$	1.45190			0.0900431
$261$	1.43674	+	2.48851i	0.0889322	+	0.154035i
$262$	−3.98835	+	6.90802i	−0.246401	+	0.426779i
$263$	11.4010	−	19.7471i	0.703015	−	1.21766i	−0.264388	−	0.964416i	$-0.585170\pi$
$263$	11.4010	−	19.7471i	0.703015	−	1.21766i	0.967403	−	0.253241i	$-0.0814966\pi$
$264$	2.50560	+	4.33982i	0.154209	+	0.267097i
$265$	9.24620			0.567990
$266$	2.96692	−	11.3752i	0.181914	−	0.697460i
$267$	−27.6249			−1.69062
$268$	−9.35073	−	16.1959i	−0.571187	−	0.989325i
$269$	−4.60329	+	7.97314i	−0.280668	+	0.486131i	−0.971549	−	0.236837i	$-0.923889\pi$
$269$	−4.60329	+	7.97314i	−0.280668	+	0.486131i	0.690882	+	0.722968i	$0.257223\pi$
$270$	−1.46692	+	2.54077i	−0.0892736	+	0.154626i
$271$	−9.70939	−	16.8172i	−0.589803	−	1.02157i	−0.994258	−	0.107011i	$-0.965872\pi$
$271$	−9.70939	−	16.8172i	−0.589803	−	1.02157i	0.404454	−	0.914558i	$-0.367461\pi$
$272$	−12.3147			−0.746687
$273$	1.10246	−	4.22684i	0.0667238	−	0.255820i
$274$	−6.40640			−0.387025
$275$	0.610494	+	1.05741i	0.0368142	+	0.0637640i
$276$	−3.99208	+	6.91448i	−0.240295	+	0.416203i
$277$	12.0909	−	20.9420i	0.726469	−	1.25828i	−0.231897	−	0.972740i	$-0.574493\pi$
$277$	12.0909	−	20.9420i	0.726469	−	1.25828i	0.958366	−	0.285541i	$-0.0921733\pi$
$278$	−5.65255	−	9.79050i	−0.339017	−	0.587195i
$279$	0.346315			0.0207334
$280$	−4.18587	−	4.13048i	−0.250154	−	0.246843i
$281$	−27.6954			−1.65217			−0.826086	−	0.563544i	$-0.809437\pi$
$281$	−27.6954			−1.65217			−0.826086	+	0.563544i	$0.809437\pi$
$282$	4.78588	+	8.28939i	0.284995	+	0.493626i
$283$	2.51376	−	4.35395i	0.149427	−	0.258816i	−0.781589	−	0.623794i	$-0.785590\pi$
$283$	2.51376	−	4.35395i	0.149427	−	0.258816i	0.931016	+	0.364979i	$0.118924\pi$
$284$	4.45540	−	7.71698i	0.264379	−	0.457918i
$285$	−6.68819	−	11.5843i	−0.396174	−	0.686193i
$286$	−0.669629			−0.0395960
$287$	13.8140	−	3.80025i	0.815417	−	0.224322i
$288$	−2.29416			−0.135184
$289$	−12.8564	−	22.2680i	−0.756261	−	1.30988i
$290$	−2.15152	+	3.72655i	−0.126342	+	0.218830i
$291$	−0.0383005	+	0.0663384i	−0.00224522	+	0.00388883i
$292$	−7.40624	−	12.8280i	−0.433418	−	0.750701i
$293$	15.0493			0.879190			0.439595	−	0.898196i	$-0.355122\pi$
$293$	15.0493			0.879190			0.439595	+	0.898196i	$0.355122\pi$
$294$	−6.81245	+	4.05511i	−0.397310	+	0.236499i
$295$	3.05447			0.177838
$296$	−1.11134	−	1.92490i	−0.0645955	−	0.111883i
$297$	−2.92012	+	5.05780i	−0.169443	+	0.293483i
$298$	2.83243	−	4.90592i	0.164079	−	0.284192i
$299$	−1.19049	−	2.06199i	−0.0688478	−	0.119248i
$300$	−2.99834			−0.173109
$301$	30.5556	−	8.40587i	1.76120	−	0.484506i
$302$	−11.9352			−0.686796
$303$	2.51478	+	4.35573i	0.144470	+	0.250230i
$304$	−6.82497	+	11.8212i	−0.391439	+	0.677992i
$305$	−0.697727	+	1.20850i	−0.0399518	+	0.0691985i
$306$	−0.820944	−	1.42192i	−0.0469302	−	0.0812856i
$307$	6.13202			0.349973			0.174987	−	0.984571i	$-0.444012\pi$
$307$	6.13202			0.349973			0.174987	+	0.984571i	$0.444012\pi$
$308$	−3.73378	−	3.68437i	−0.212752	−	0.209937i
$309$	−15.6667			−0.891247
$310$	0.259304	+	0.449127i	0.0147275	+	0.0255087i
$311$	−8.52719	+	14.7695i	−0.483533	+	0.837503i	−0.999821	−	0.0189117i	$-0.993980\pi$
$311$	−8.52719	+	14.7695i	−0.483533	+	0.837503i	0.516289	+	0.856415i	$0.327313\pi$
$312$	1.83488	−	3.17810i	0.103879	−	0.179924i
$313$	0.960649	+	1.66389i	0.0542991	+	0.0940488i	0.891897	−	0.452238i	$-0.149374\pi$
$313$	0.960649	+	1.66389i	0.0542991	+	0.0940488i	−0.837598	+	0.546287i	$0.816041\pi$
$314$	6.25506			0.352993
$315$	−0.273497	+	1.04859i	−0.0154098	+	0.0590814i
$316$	21.6804			1.21962
$317$	9.81040	+	16.9921i	0.551007	+	0.954372i	0.998202	+	0.0599357i	$0.0190896\pi$
$317$	9.81040	+	16.9921i	0.551007	+	0.954372i	−0.447195	+	0.894436i	$0.647577\pi$
$318$	5.23600	−	9.06902i	0.293620	−	0.508565i
$319$	−4.28294	+	7.41827i	−0.239799	+	0.415344i
$320$	0.166523	+	0.288427i	0.00930893	+	0.0161235i
$321$	−32.0741			−1.79020
$322$	−1.09060	+	4.18139i	−0.0607770	+	0.233020i
$323$	−47.3442			−2.63430
$324$	−8.16848	−	14.1482i	−0.453804	−	0.786012i
$325$	0.447072	−	0.774351i	0.0247991	−	0.0429533i
$326$	7.28009	−	12.6095i	0.403207	−	0.698375i
$327$	9.22998	+	15.9868i	0.510419	+	0.884071i
$328$	12.0363			0.664591
$329$	−15.9160	−	15.7053i	−0.877475	−	0.865864i
$330$	1.38286			0.0761239
$331$	10.2630	+	17.7760i	0.564104	+	0.977056i	0.997132	+	0.0756760i	$0.0241115\pi$
$331$	10.2630	+	17.7760i	0.564104	+	0.977056i	−0.433029	+	0.901380i	$0.642555\pi$
$332$	−7.34624	+	12.7241i	−0.403177	+	0.698324i
$333$	−0.204795	+	0.354715i	−0.0112227	+	0.0194383i
$334$	1.99538	+	3.45610i	0.109182	+	0.189109i
$335$	−11.5172			−0.629250
$336$	8.87569	−	2.44171i	0.484208	−	0.133206i
$337$	−15.7590			−0.858449			−0.429224	−	0.903198i	$-0.641213\pi$
$337$	−15.7590			−0.858449			−0.429224	+	0.903198i	$0.641213\pi$
$338$	−3.74165	−	6.48073i	−0.203519	−	0.352505i
$339$	−12.7967	+	22.1646i	−0.695023	+	1.20381i
$340$	−5.30614	+	9.19051i	−0.287766	+	0.498426i
$341$	0.516184	+	0.894057i	0.0279529	+	0.0484159i
$342$	−1.81992			−0.0984098
$343$	12.8315	−	13.3548i	0.692838	−	0.721094i
$344$	26.6233			1.43543
$345$	2.45849	+	4.25824i	0.132361	+	0.229256i
$346$	0.0212520	−	0.0368095i	0.00114251	−	0.00197889i
$347$	−16.6891	+	28.9063i	−0.895916	+	1.55177i	−0.0632496	+	0.997998i	$0.520146\pi$
$347$	−16.6891	+	28.9063i	−0.895916	+	1.55177i	−0.832667	+	0.553775i	$0.813187\pi$
$348$	−10.5175	−	18.2168i	−0.563796	−	0.976523i
$349$	−17.1211			−0.916473			−0.458236	−	0.888830i	$-0.651519\pi$
$349$	−17.1211			−0.916473			−0.458236	+	0.888830i	$0.651519\pi$
$350$	−1.56467	+	0.430442i	−0.0836351	+	0.0230081i
$351$	4.27688			0.228283
$352$	−3.41945	−	5.92265i	−0.182257	−	0.315679i
$353$	−3.60262	+	6.23993i	−0.191748	+	0.332118i	−0.945830	−	0.324663i	$-0.894749\pi$
$353$	−3.60262	+	6.23993i	−0.191748	+	0.332118i	0.754081	+	0.656781i	$0.228082\pi$
$354$	1.72970	−	2.99594i	0.0919328	−	0.159232i
$355$	−2.74383	−	4.75245i	−0.145627	−	0.252234i
$356$	24.2929			1.28752
$357$	22.7268	+	22.4260i	1.20283	+	1.18691i
$358$	−8.01683			−0.423703
$359$	6.41812	+	11.1165i	0.338735	+	0.586707i	0.984195	−	0.177088i	$-0.0566676\pi$
$359$	6.41812	+	11.1165i	0.338735	+	0.586707i	−0.645460	+	0.763794i	$0.723334\pi$
$360$	−0.455195	+	0.788420i	−0.0239909	+	0.0415534i
$361$	−16.7388	+	28.9925i	−0.880992	+	1.52592i
$362$	−6.22265	−	10.7779i	−0.327055	−	0.566476i
$363$	−17.5588			−0.921597
$364$	−0.969484	+	3.71702i	−0.0508148	+	0.194825i
$365$	−9.12217			−0.477476
$366$	0.790228	+	1.36871i	0.0413059	+	0.0715439i
$367$	−13.1887	+	22.8436i	−0.688447	+	1.19242i	0.283893	+	0.958856i	$0.408374\pi$
$367$	−13.1887	+	22.8436i	−0.688447	+	1.19242i	−0.972340	+	0.233569i	$0.924960\pi$
$368$	2.50877	−	4.34532i	0.130779	−	0.226516i
$369$	−1.10900	−	1.92085i	−0.0577323	−	0.0999952i
$370$	−0.613360			−0.0318871
$371$	−6.17401	+	23.6712i	−0.320538	+	1.22895i
$372$	−2.53515			−0.131441
$373$	9.05719	+	15.6875i	0.468963	+	0.812268i	0.999371	−	0.0354746i	$-0.0112943\pi$
$373$	9.05719	+	15.6875i	0.468963	+	0.812268i	−0.530407	+	0.847743i	$0.677961\pi$
$374$	2.44724	−	4.23874i	0.126544	−	0.219180i
$375$	−0.923254	+	1.59912i	−0.0476766	+	0.0825783i
$376$	−9.39234	−	16.2680i	−0.484373	−	0.838958i
$377$	6.27290			0.323071
$378$	−5.52513	−	5.45202i	−0.284182	−	0.280421i
$379$	7.36478			0.378303			0.189152	−	0.981948i	$-0.439426\pi$
$379$	7.36478			0.378303			0.189152	+	0.981948i	$0.439426\pi$
$380$	5.88149	+	10.1870i	0.301714	+	0.522584i
$381$	9.63002	−	16.6797i	0.493361	−	0.854526i
$382$	−6.84024	+	11.8476i	−0.349977	+	0.606178i
$383$	6.57836	+	11.3941i	0.336138	+	0.582209i	0.983703	−	0.179802i	$-0.0575456\pi$
$383$	6.57836	+	11.3941i	0.336138	+	0.582209i	−0.647564	+	0.762011i	$0.724212\pi$
$384$	21.0622			1.07483
$385$	−3.11472	+	0.856861i	−0.158741	+	0.0436697i
$386$	12.1960			0.620758
$387$	−2.45303	−	4.24877i	−0.124694	−	0.215977i
$388$	0.0336809	−	0.0583370i	0.00170989	−	0.00296161i
$389$	−7.20366	+	12.4771i	−0.365240	+	0.632614i	−0.988815	−	0.149150i	$-0.952346\pi$
$389$	−7.20366	+	12.4771i	−0.365240	+	0.632614i	0.623575	+	0.781764i	$0.285680\pi$
$390$	−0.506342	−	0.877010i	−0.0256396	−	0.0444091i
$391$	17.4031			0.880114
$392$	13.3695	−	7.95820i	0.675262	−	0.401950i
$393$	−24.0137			−1.21133
$394$	1.70802	+	2.95838i	0.0860488	+	0.149041i
$395$	6.67586	−	11.5629i	0.335899	−	0.581794i
$396$	−0.406032	+	0.703268i	−0.0204039	+	0.0353405i
$397$	17.5248	+	30.3539i	0.879546	+	1.52342i	0.851840	+	0.523802i	$0.175487\pi$
$397$	17.5248	+	30.3539i	0.879546	+	1.52342i	0.0277058	+	0.999616i	$0.491180\pi$
$398$	−3.67295			−0.184108
$399$	34.1229	−	9.38723i	1.70828	−	0.469949i
$400$	1.88427			0.0942136
$401$	−10.4891	−	18.1676i	−0.523799	−	0.907246i	−0.999616	−	0.0277019i	$-0.991181\pi$
$401$	−10.4891	−	18.1676i	−0.523799	−	0.907246i	0.475818	−	0.879544i	$-0.342152\pi$
$402$	−6.52202	+	11.2965i	−0.325289	+	0.563417i
$403$	0.378007	−	0.654728i	0.0188299	−	0.0326143i
$404$	−2.21146	−	3.83036i	−0.110024	−	0.190567i
$405$	−10.0610			−0.499935
$406$	−8.10370	−	7.99647i	−0.402180	−	0.396858i
$407$	−1.22099			−0.0605221
$408$	13.4115	+	23.2295i	0.663970	+	1.15003i
$409$	3.90204	−	6.75854i	0.192944	−	0.334188i	−0.753281	−	0.657699i	$-0.771530\pi$
$409$	3.90204	−	6.75854i	0.192944	−	0.334188i	0.946224	+	0.323511i	$0.104863\pi$
$410$	1.66073	−	2.87647i	0.0820175	−	0.142058i
$411$	−9.64316	−	16.7025i	−0.475662	−	0.823871i
$412$	13.7770			0.678746
$413$	−2.03957	+	7.81975i	−0.100361	+	0.384785i
$414$	0.668979			0.0328785
$415$	4.52413	+	7.83603i	0.222081	+	0.384656i
$416$	−2.50410	+	4.33723i	−0.122774	+	0.212650i
$417$	17.0169	−	29.4741i	0.833320	−	1.44335i
$418$	−2.71259	−	4.69834i	−0.132677	−	0.229804i
$419$	22.9107			1.11926			0.559631	−	0.828742i	$-0.310943\pi$
$419$	22.9107			1.11926			0.559631	+	0.828742i	$0.310943\pi$
$420$	2.00209	−	7.67606i	0.0976922	−	0.374553i
$421$	−5.90725			−0.287902			−0.143951	−	0.989585i	$-0.545981\pi$
$421$	−5.90725			−0.287902			−0.143951	+	0.989585i	$0.545981\pi$
$422$	2.52637	+	4.37579i	0.122982	+	0.213010i
$423$	−1.73079	+	2.99781i	−0.0841538	+	0.145759i
$424$	−10.2757	+	17.7980i	−0.499032	+	0.864350i
$425$	3.26775	+	5.65992i	0.158509	+	0.274546i
$426$	−6.21517			−0.301126
$427$	−2.62799	−	2.59321i	−0.127177	−	0.125494i
$428$	28.2054			1.36336
$429$	−1.00795	−	1.74582i	−0.0486644	−	0.0842892i
$430$	3.67341	−	6.36253i	0.177147	−	0.306828i
$431$	9.14309	−	15.8363i	0.440407	−	0.762808i	−0.557312	−	0.830303i	$-0.688167\pi$
$431$	9.14309	−	15.8363i	0.440407	−	0.762808i	0.997720	+	0.0674951i	$0.0215007\pi$
$432$	4.50644	+	7.80538i	0.216816	+	0.375536i
$433$	2.02060			0.0971040			0.0485520	−	0.998821i	$-0.484539\pi$
$433$	2.02060			0.0971040			0.0485520	+	0.998821i	$0.484539\pi$
$434$	−1.32296	+	0.363946i	−0.0635040	+	0.0174700i
$435$	−12.9542			−0.621108
$436$	−8.11670	−	14.0585i	−0.388719	−	0.673281i
$437$	9.64507	−	16.7057i	0.461386	−	0.799144i
$438$	−5.16576	+	8.94737i	−0.246830	+	0.427522i
$439$	6.35313	+	11.0039i	0.303218	+	0.525190i	0.976863	−	0.213866i	$-0.0686055\pi$
$439$	6.35313	+	11.0039i	0.303218	+	0.525190i	−0.673645	+	0.739055i	$0.735272\pi$
$440$	−2.71388			−0.129379
$441$	−2.50188	−	1.40036i	−0.119137	−	0.0666839i
$442$	−3.58428			−0.170487
$443$	1.58322	+	2.74222i	0.0752211	+	0.130287i	0.901182	−	0.433440i	$-0.142700\pi$
$443$	1.58322	+	2.74222i	0.0752211	+	0.130287i	−0.825961	+	0.563727i	$0.809367\pi$
$444$	1.49917	−	2.59664i	0.0711474	−	0.123231i
$445$	7.48032	−	12.9563i	0.354601	−	0.614187i
$446$	−6.09020	−	10.5485i	−0.288379	−	0.499487i
$447$	17.0540			0.806625
$448$	−0.849595	+	0.233724i	−0.0401396	+	0.0110424i
$449$	−34.1666			−1.61242			−0.806211	−	0.591629i	$-0.798485\pi$
$449$	−34.1666			−1.61242			−0.806211	+	0.591629i	$0.798485\pi$
$450$	0.125613	+	0.217568i	0.00592145	+	0.0102562i
$451$	3.30594	−	5.72605i	0.155670	−	0.269629i
$452$	11.2532	−	19.4912i	0.529308	−	0.916788i
$453$	−17.9654	−	31.1170i	−0.844088	−	1.46200i
$454$	−3.26063			−0.153029
$455$	1.68389	+	1.66161i	0.0789422	+	0.0778975i
$456$	29.7315			1.39230
$457$	12.9349	+	22.4040i	0.605071	+	1.04801i	0.992040	+	0.125921i	$0.0401885\pi$
$457$	12.9349	+	22.4040i	0.605071	+	1.04801i	−0.386970	+	0.922092i	$0.626478\pi$
$458$	−3.52155	+	6.09951i	−0.164551	+	0.285011i
$459$	−15.6304	+	27.0726i	−0.729563	+	1.26364i
$460$	−2.16196	−	3.74463i	−0.100802	−	0.174594i
$461$	−29.0280			−1.35197			−0.675984	−	0.736917i	$-0.736281\pi$
$461$	−29.0280			−1.35197			−0.675984	+	0.736917i	$0.736281\pi$
$462$	−0.923383	+	3.54026i	−0.0429596	+	0.164708i
$463$	−15.3934			−0.715393			−0.357696	−	0.933838i	$-0.616438\pi$
$463$	−15.3934			−0.715393			−0.357696	+	0.933838i	$0.616438\pi$
$464$	6.60959	+	11.4481i	0.306842	+	0.531467i
$465$	−0.780628	+	1.35209i	−0.0362008	+	0.0627015i
$466$	6.36524	−	11.0249i	0.294864	−	0.510720i
$467$	17.9105	+	31.0219i	0.828800	+	1.43552i	0.898980	+	0.437990i	$0.144309\pi$
$467$	17.9105	+	31.0219i	0.828800	+	1.43552i	−0.0701798	+	0.997534i	$0.522357\pi$
$468$	0.594683			0.0274892
$469$	7.69041	−	29.4852i	0.355110	−	1.36150i
$470$	−5.18371			−0.239107
$471$	9.41536	+	16.3079i	0.433837	+	0.751428i
$472$	−3.39456	+	5.87956i	−0.156247	+	0.270628i
$473$	7.31249	−	12.6656i	0.336229	−	0.582365i
$474$	−7.56090	−	13.0959i	−0.347284	−	0.601513i
$475$	7.24415			0.332384
$476$	−19.9856	−	19.7211i	−0.916037	−	0.903915i
$477$	3.78715			0.173402
$478$	1.38850	+	2.40495i	0.0635084	+	0.110000i
$479$	−10.2728	+	17.7930i	−0.469375	+	0.812981i	−0.999387	−	0.0350090i	$-0.988854\pi$
$479$	−10.2728	+	17.7930i	−0.469375	+	0.812981i	0.530012	+	0.847990i	$0.322187\pi$
$480$	5.17125	−	8.95686i	0.236034	−	0.408823i
$481$	0.447072	+	0.774351i	0.0203847	+	0.0353074i
$482$	13.1554			0.599214
$483$	−12.5431	+	3.45063i	−0.570733	+	0.157009i
$484$	15.4409			0.701860
$485$	−0.0207421	−	0.0359264i	−0.000941852	−	0.00163134i
$486$	−1.29667	+	2.24590i	−0.0588181	+	0.101876i
$487$	−21.5982	+	37.4091i	−0.978706	+	1.69517i	−0.311588	+	0.950217i	$0.600861\pi$
$487$	−21.5982	+	37.4091i	−0.978706	+	1.69517i	−0.667118	+	0.744952i	$0.732472\pi$
$488$	−1.55083	−	2.68612i	−0.0702028	−	0.121595i
$489$	43.8331			1.98220
$490$	−0.0571916	−	4.29314i	−0.00258365	−	0.193944i
$491$	8.73043			0.393999			0.196999	−	0.980404i	$-0.436880\pi$
$491$	8.73043			0.393999			0.196999	+	0.980404i	$0.436880\pi$
$492$	8.11828	+	14.0613i	0.366000	+	0.633931i
$493$	−22.9250	+	39.7073i	−1.03249	+	1.78833i
$494$	−1.98646	+	3.44065i	−0.0893751	+	0.154802i
$495$	0.250052	+	0.433103i	0.0112390	+	0.0194665i
$496$	1.59319			0.0715362
$497$	13.9989	−	3.85111i	0.627937	−	0.172746i
$498$	10.2478			0.459216
$499$	−7.24609	−	12.5506i	−0.324380	−	0.561842i	0.657007	−	0.753885i	$-0.271822\pi$
$499$	−7.24609	−	12.5506i	−0.324380	−	0.561842i	−0.981387	+	0.192042i	$0.938489\pi$
$500$	0.811895	−	1.40624i	0.0363090	−	0.0628891i
$501$	−6.00705	+	10.4045i	−0.268375	+	0.464839i
$502$	4.22992	+	7.32643i	0.188790	+	0.326995i
$503$	31.0306			1.38359			0.691793	−	0.722096i	$-0.256821\pi$
$503$	31.0306			1.38359			0.691793	+	0.722096i	$0.256821\pi$
$504$	−1.71449	−	1.69180i	−0.0763694	−	0.0753588i
$505$	−2.72382			−0.121209
$506$	0.997114	+	1.72705i	0.0443271	+	0.0767769i
$507$	11.2642	−	19.5101i	0.500259	−	0.866474i
$508$	−8.46849	+	14.6679i	−0.375729	+	0.650781i
$509$	−10.7434	−	18.6081i	−0.476193	−	0.824791i	0.523435	−	0.852066i	$-0.324650\pi$
$509$	−10.7434	−	18.6081i	−0.476193	−	0.824791i	−0.999628	+	0.0272748i	$0.991317\pi$
$510$	7.40194			0.327764
$511$	6.09119	−	23.3537i	0.269458	−	1.03311i
$512$	−18.9303			−0.836609
$513$	17.3251	+	30.0080i	0.764924	+	1.32489i
$514$	−6.39233	+	11.0718i	−0.281954	+	0.488358i
$515$	4.24225	−	7.34779i	0.186936	−	0.323782i
$516$	17.9570	+	31.1025i	0.790514	+	1.36921i
$517$	−10.3190			−0.453828
$518$	0.409562	−	1.57026i	0.0179951	−	0.0689935i
$519$	0.127957			0.00561671
$520$	0.993701	+	1.72114i	0.0435767	+	0.0754770i
$521$	2.86889	−	4.96906i	0.125688	−	0.217698i	−0.796314	−	0.604884i	$-0.793219\pi$
$521$	2.86889	−	4.96906i	0.125688	−	0.217698i	0.922002	+	0.387186i	$0.126553\pi$
$522$	−0.881241	+	1.52635i	−0.0385709	+	0.0668067i
$523$	3.00532	+	5.20536i	0.131413	+	0.227615i	0.924222	−	0.381857i	$-0.124715\pi$
$523$	3.00532	+	5.20536i	0.131413	+	0.227615i	−0.792808	+	0.609471i	$0.791382\pi$
$524$	21.1173			0.922512
$525$	−3.47743	−	3.43141i	−0.151768	−	0.149759i
$526$	13.9858			0.609810
$527$	2.76295	+	4.78556i	0.120356	+	0.208462i
$528$	2.12411	−	3.67906i	0.0924398	−	0.160110i
$529$	7.95459	−	13.7778i	0.345852	−	0.599033i
$530$	2.83562	+	4.91145i	0.123172	+	0.213340i
$531$	1.25108			0.0542921
$532$	−30.0071	+	8.25498i	−1.30097	+	0.357899i
$533$	−4.84195			−0.209728
$534$	−8.47201	−	14.6739i	−0.366620	−	0.635004i
$535$	8.68507	−	15.0430i	0.375488	−	0.650365i
$536$	12.7995	−	22.1694i	0.552856	−	0.957574i
$537$	−12.0673	−	20.9011i	−0.520740	−	0.901949i
$538$	−5.64695			−0.243457
$539$	−0.113849	−	8.54616i	−0.00490381	−	0.368109i
$540$	7.76693			0.334235
$541$	0.860663	+	1.49071i	0.0370028	+	0.0640907i	0.883934	−	0.467612i	$-0.154886\pi$
$541$	0.860663	+	1.49071i	0.0370028	+	0.0640907i	−0.846931	+	0.531703i	$0.821552\pi$
$542$	5.95535	−	10.3150i	0.255804	−	0.443066i
$543$	18.7331	−	32.4468i	0.803916	−	1.39242i
$544$	−18.3031	−	31.7018i	−0.784737	−	1.35920i
$545$	−9.99723			−0.428234
$546$	2.58334	−	0.710678i	0.110557	−	0.0304142i
$547$	30.3531			1.29780			0.648901	−	0.760872i	$-0.275229\pi$
$547$	30.3531			1.29780			0.648901	+	0.760872i	$0.275229\pi$
$548$	8.48005	+	14.6879i	0.362250	+	0.627435i
$549$	−0.285782	+	0.494989i	−0.0121969	+	0.0211256i
$550$	−0.374453	+	0.648571i	−0.0159667	+	0.0276552i
$551$	25.4108	+	44.0128i	1.08254	+	1.87501i
$552$	−10.9289			−0.465166
$553$	25.1446	+	24.8119i	1.06926	+	1.05511i
$554$	14.8321			0.630155
$555$	−0.923254	−	1.59912i	−0.0391899	−	0.0678790i
$556$	−14.9644	+	25.9191i	−0.634631	+	1.09921i
$557$	3.59513	−	6.22695i	0.152331	−	0.263844i	−0.779753	−	0.626087i	$-0.784655\pi$
$557$	3.59513	−	6.22695i	0.152331	−	0.263844i	0.932084	+	0.362243i	$0.117989\pi$
$558$	0.106208	+	0.183958i	0.00449614	+	0.00778755i
$559$	−10.7100			−0.452986
$560$	−1.25819	+	4.82393i	−0.0531684	+	0.203848i
$561$	14.7347			0.622100
$562$	−8.49364	−	14.7114i	−0.358282	−	0.620563i
$563$	−15.1285	+	26.2034i	−0.637592	+	1.10434i	0.348368	+	0.937358i	$0.386736\pi$
$563$	−15.1285	+	26.2034i	−0.637592	+	1.10434i	−0.985960	+	0.166984i	$0.946597\pi$
$564$	12.6700	−	21.9451i	0.533503	−	0.924054i
$565$	−6.93023	−	12.0035i	−0.291557	−	0.504992i
$566$	3.08368			0.129617
$567$	6.71808	−	25.7572i	0.282133	−	1.08170i
$568$	12.1973			0.511789
$569$	−14.9224	−	25.8464i	−0.625581	−	1.08354i	−0.988428	−	0.151689i	$-0.951529\pi$
$569$	−14.9224	−	25.8464i	−0.625581	−	1.08354i	0.362847	−	0.931849i	$-0.381805\pi$
$570$	4.10227	−	7.10533i	0.171825	−	0.297610i
$571$	20.9683	−	36.3181i	0.877495	−	1.51987i	0.0234134	−	0.999726i	$-0.492547\pi$
$571$	20.9683	−	36.3181i	0.877495	−	1.51987i	0.854081	−	0.520140i	$-0.174120\pi$
$572$	0.886377	+	1.53525i	0.0370613	+	0.0641920i
$573$	−41.1848			−1.72052
$574$	6.25512	+	6.17235i	0.261084	+	0.257629i
$575$	−2.66286			−0.111049
$576$	0.0682061	+	0.118137i	0.00284192	+	0.00492235i
$577$	13.3864	−	23.1858i	0.557281	−	0.965240i	−0.440441	−	0.897782i	$-0.645178\pi$
$577$	13.3864	−	23.1858i	0.557281	−	0.965240i	0.997722	−	0.0674579i	$-0.0214888\pi$
$578$	7.88562	−	13.6583i	0.327999	−	0.568110i
$579$	18.3578	+	31.7967i	0.762926	+	1.32143i
$580$	11.3918			0.473017
$581$	−23.0820	+	6.34987i	−0.957602	+	0.263437i
$582$	−0.0469840			−0.00194755
$583$	5.64475	+	9.77700i	0.233782	+	0.404922i
$584$	10.1379	−	17.5593i	0.419508	−	0.726609i
$585$	0.183116	−	0.317166i	0.00757091	−	0.0131132i
$586$	4.61532	+	7.99397i	0.190657	+	0.330228i
$587$	8.99965			0.371455			0.185728	−	0.982601i	$-0.440536\pi$
$587$	8.99965			0.371455			0.185728	+	0.982601i	$0.440536\pi$
$588$	18.3146	+	10.2511i	0.755283	+	0.422750i
$589$	6.12506			0.252379
$590$	0.936744	+	1.62249i	0.0385651	+	0.0667968i
$591$	−5.14196	+	8.90613i	−0.211512	+	0.366349i
$592$	−0.942136	+	1.63183i	−0.0387215	+	0.0670677i
$593$	12.6349	+	21.8842i	0.518852	+	0.898678i	0.999760	+	0.0219070i	$0.00697378\pi$
$593$	12.6349	+	21.8842i	0.518852	+	0.898678i	−0.480908	+	0.876771i	$0.659693\pi$
$594$	−3.58217			−0.146978
$595$	−16.6720	+	4.58647i	−0.683484	+	0.188027i
$596$	−14.9970			−0.614301
$597$	−5.52866	−	9.57592i	−0.226273	−	0.391916i
$598$	0.730198	−	1.26474i	0.0298600	−	0.0517191i
$599$	1.43234	−	2.48088i	0.0585236	−	0.101366i	−0.835279	−	0.549826i	$-0.814694\pi$
$599$	1.43234	−	2.48088i	0.0585236	−	0.101366i	0.893803	+	0.448460i	$0.148027\pi$
$600$	−2.05210	−	3.55435i	−0.0837768	−	0.145106i
$601$	−8.34798			−0.340521			−0.170261	−	0.985399i	$-0.554461\pi$
$601$	−8.34798			−0.340521			−0.170261	+	0.985399i	$0.554461\pi$
$602$	13.8359	+	13.6528i	0.563908	+	0.556446i
$603$	−4.71731			−0.192104
$604$	15.7985	+	27.3638i	0.642831	+	1.11342i
$605$	4.75459	−	8.23520i	0.193302	−	0.334808i
$606$	−1.54246	+	2.67163i	−0.0626584	+	0.108527i
$607$	−7.78775	−	13.4888i	−0.316095	−	0.547493i	0.663575	−	0.748110i	$-0.269039\pi$
$607$	−7.78775	−	13.4888i	−0.316095	−	0.547493i	−0.979670	+	0.200617i	$0.935705\pi$
$608$	−40.5753			−1.64554
$609$	8.64999	−	33.1642i	0.350515	−	1.34388i
$610$	−0.855916			−0.0346550
$611$	3.77835	+	6.54430i	0.152856	+	0.264754i
$612$	−2.17334	+	3.76434i	−0.0878521	+	0.152164i
$613$	17.7265	−	30.7032i	0.715967	−	1.24009i	−0.246618	−	0.969113i	$-0.579319\pi$
$613$	17.7265	−	30.7032i	0.715967	−	1.24009i	0.962585	−	0.270979i	$-0.0873474\pi$
$614$	1.88057	+	3.25724i	0.0758936	+	0.131452i
$615$	9.99917			0.403206
$616$	1.81215	−	6.94780i	0.0730135	−	0.279935i
$617$	−23.2116			−0.934462			−0.467231	−	0.884135i	$-0.654748\pi$
$617$	−23.2116			−0.934462			−0.467231	+	0.884135i	$0.654748\pi$
$618$	−4.80466	−	8.32192i	−0.193272	−	0.334757i
$619$	−18.9396	+	32.8044i	−0.761248	+	1.31852i	0.180960	+	0.983491i	$0.442080\pi$
$619$	−18.9396	+	32.8044i	−0.761248	+	1.31852i	−0.942208	+	0.335030i	$0.891254\pi$
$620$	0.686472	−	1.18900i	0.0275694	−	0.0477516i
$621$	−6.36851	−	11.0306i	−0.255559	−	0.442642i
$622$	−10.4605			−0.419427
$623$	28.1746	+	27.8017i	1.12879	+	1.11385i
$624$	−3.11101			−0.124540
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.589224	+	1.02057i	−0.0235501	+	0.0407900i
$627$	8.16620	−	14.1443i	0.326126	−	0.564868i
$628$	−8.27972	−	14.3409i	−0.330397	−	0.572264i
$629$	−6.53551			−0.260588
$630$	−0.640872	+	0.176304i	−0.0255330	+	0.00702414i
$631$	14.3898			0.572850			0.286425	−	0.958103i	$-0.407533\pi$
$631$	14.3898			0.572850			0.286425	+	0.958103i	$0.407533\pi$
$632$	14.8384	+	25.7008i	0.590238	+	1.02232i
$633$	−7.60557	+	13.1732i	−0.302294	+	0.523589i
$634$	−6.01731	+	10.4223i	−0.238978	+	0.413922i
$635$	5.21526	+	9.03310i	0.206961	+	0.358468i
$636$	−27.7232			−1.09930
$637$	−5.37829	+	3.20143i	−0.213096	+	0.126845i
$638$	−5.25397			−0.208007
$639$	−1.12384	−	1.94655i	−0.0444585	−	0.0770044i
$640$	−5.70325	+	9.87832i	−0.225441	+	0.390475i
$641$	−1.29369	+	2.24074i	−0.0510977	+	0.0885039i	−0.890443	−	0.455095i	$-0.849605\pi$
$641$	−1.29369	+	2.24074i	−0.0510977	+	0.0885039i	0.839345	+	0.543599i	$0.182939\pi$
$642$	−9.83648	−	17.0373i	−0.388215	−	0.672408i
$643$	−13.0819			−0.515900			−0.257950	−	0.966158i	$-0.583047\pi$
$643$	−13.0819			−0.515900			−0.257950	+	0.966158i	$0.583047\pi$
$644$	11.0302	−	3.03443i	0.434653	−	0.119573i
$645$	22.1174			0.870873
$646$	−14.5195	−	25.1485i	−0.571263	−	0.989456i
$647$	−11.0716	+	19.1765i	−0.435268	+	0.753906i	−0.997317	−	0.0731974i	$-0.976680\pi$
$647$	−11.0716	+	19.1765i	−0.435268	+	0.753906i	0.562050	+	0.827104i	$0.310013\pi$
$648$	11.1812	−	19.3665i	0.439240	−	0.760787i
$649$	1.86473	+	3.22981i	0.0731972	+	0.126781i
$650$	0.548432			0.0215113
$651$	−2.94023	−	2.90132i	−0.115237	−	0.113712i
$652$	−38.5461			−1.50958
$653$	−1.17318	−	2.03201i	−0.0459101	−	0.0795186i	0.842157	−	0.539232i	$-0.181285\pi$
$653$	−1.17318	−	2.03201i	−0.0459101	−	0.0795186i	−0.888067	+	0.459713i	$0.847952\pi$
$654$	−5.66130	+	9.80565i	−0.221374	+	0.383431i
$655$	6.50246	−	11.2626i	0.254072	−	0.440066i
$656$	−5.10184	−	8.83664i	−0.199193	−	0.345013i
$657$	−3.73634			−0.145769
$658$	3.46134	−	13.2708i	0.134937	−	0.517351i
$659$	−12.8538			−0.500713			−0.250356	−	0.968154i	$-0.580548\pi$
$659$	−12.8538			−0.500713			−0.250356	+	0.968154i	$0.580548\pi$
$660$	−1.83047	−	3.17046i	−0.0712509	−	0.123410i
$661$	−5.11932	+	8.86692i	−0.199118	+	0.344883i	−0.948243	−	0.317546i	$-0.897141\pi$
$661$	−5.11932	+	8.86692i	−0.199118	+	0.344883i	0.749124	+	0.662429i	$0.230475\pi$
$662$	−6.29489	+	10.9031i	−0.244658	+	0.423760i
$663$	−5.39520	−	9.34476i	−0.209532	−	0.362921i
$664$	−20.1115			−0.780477
$665$	−4.83717	+	18.5458i	−0.187577	+	0.719174i
$666$	−0.251226			−0.00973480
$667$	−9.34069	−	16.1785i	−0.361673	−	0.626436i
$668$	5.28251	−	9.14957i	0.204386	−	0.354007i
$669$	18.3344	−	31.7561i	0.708849	−	1.22776i
$670$	−3.53209	−	6.11775i	−0.136456	−	0.236349i
$671$	−1.70383			−0.0657758
$672$	19.4775	+	19.2197i	0.751360	+	0.741417i
$673$	−9.56675			−0.368771			−0.184386	−	0.982854i	$-0.559030\pi$
$673$	−9.56675			−0.368771			−0.184386	+	0.982854i	$0.559030\pi$
$674$	−4.83298	−	8.37096i	−0.186159	−	0.322437i
$675$	2.39161	−	4.14238i	0.0920530	−	0.159440i
$676$	−9.90553	+	17.1569i	−0.380982	+	0.659880i
$677$	−7.74837	−	13.4206i	−0.297794	−	0.515795i	0.677837	−	0.735212i	$-0.262918\pi$
$677$	−7.74837	−	13.4206i	−0.297794	−	0.515795i	−0.975631	+	0.219418i	$0.929584\pi$
$678$	−15.6980			−0.602878
$679$	0.105826	−	0.0291127i	0.00406121	−	0.00111724i
$680$	−14.5264			−0.557062
$681$	−4.90803	−	8.50095i	−0.188076	−	0.325757i
$682$	−0.316607	+	0.548379i	−0.0121235	+	0.0209985i
$683$	1.72698	−	2.99122i	0.0660812	−	0.114456i	−0.831092	−	0.556135i	$-0.812284\pi$
$683$	1.72698	−	2.99122i	0.0660812	−	0.114456i	0.897173	+	0.441679i	$0.145617\pi$
$684$	2.40899	+	4.17250i	0.0921102	+	0.159540i
$685$	10.4448			0.399074
$686$	11.0291	+	2.72026i	0.421092	+	0.103860i
$687$	−21.2031			−0.808950
$688$	−11.2849	−	19.5460i	−0.430232	−	0.745184i
$689$	4.13372	−	7.15981i	0.157482	−	0.272767i
$690$	−1.50794	+	2.61183i	−0.0574064	+	0.0994307i
$691$	0.866437	+	1.50071i	0.0329608	+	0.0570898i	0.882035	−	0.471183i	$-0.156173\pi$
$691$	0.866437	+	1.50071i	0.0329608	+	0.0570898i	−0.849074	+	0.528273i	$0.822840\pi$
$692$	−0.112524			−0.00427751
$693$	−1.27576	+	0.350961i	−0.0484620	+	0.0133319i
$694$	−20.4728			−0.777137
$695$	9.21571	+	15.9621i	0.349572	+	0.605476i
$696$	14.3966	−	24.9357i	0.545702	−	0.945184i
$697$	17.6955	−	30.6495i	0.670264	−	1.16093i
$698$	−5.25071	−	9.09449i	−0.198742	−	0.344231i
$699$	38.3249			1.44958
$700$	3.05800	+	3.01753i	0.115581	+	0.114052i
$701$	−30.4442			−1.14986			−0.574930	−	0.818202i	$-0.694971\pi$
$701$	−30.4442			−1.14986			−0.574930	+	0.818202i	$0.694971\pi$
$702$	1.31163	+	2.27182i	0.0495044	+	0.0857441i
$703$	−3.62207	+	6.27362i	−0.136609	+	0.236614i
$704$	−0.203323	+	0.352166i	−0.00766302	+	0.0132727i
$705$	−7.80273	−	13.5147i	−0.293868	−	0.508994i
$706$	−4.41941			−0.166327
$707$	1.81879	−	6.97327i	0.0684026	−	0.262257i
$708$	−9.15833			−0.344191
$709$	−2.74858	−	4.76068i	−0.103225	−	0.178791i	0.809787	−	0.586725i	$-0.199583\pi$
$709$	−2.74858	−	4.76068i	−0.103225	−	0.178791i	−0.913012	+	0.407934i	$0.866250\pi$
$710$	1.68295	−	2.91496i	0.0631601	−	0.109397i
$711$	2.73436	−	4.73605i	0.102547	−	0.177616i
$712$	16.6264	+	28.7978i	0.623101	+	1.07924i
$713$	−2.25150			−0.0843192
$714$	−4.94253	+	18.9497i	−0.184970	+	0.709176i
$715$	1.09174			0.0408287
$716$	10.6118	+	18.3801i	0.396580	+	0.686896i
$717$	−4.18005	+	7.24005i	−0.156107	+	0.270385i
$718$	−3.93661	+	6.81842i	−0.146913	+	0.254461i
$719$	11.1786	+	19.3619i	0.416892	+	0.722077i	0.995625	−	0.0934395i	$-0.0297862\pi$
$719$	11.1786	+	19.3619i	0.416892	+	0.722077i	−0.578733	+	0.815517i	$0.696453\pi$
$720$	0.771778			0.0287625
$721$	15.9784	+	15.7670i	0.595067	+	0.587193i
$722$	−20.5339			−0.764191
$723$	19.8021	+	34.2982i	0.736447	+	1.27556i
$724$	−16.4736	+	28.5332i	−0.612238	+	1.06043i
$725$	3.50777	−	6.07563i	0.130275	−	0.225643i
$726$	−5.38493	−	9.32697i	−0.199853	−	0.346156i
$727$	11.1657			0.414113			0.207056	−	0.978329i	$-0.433612\pi$
$727$	11.1657			0.414113			0.207056	+	0.978329i	$0.433612\pi$
$728$	−5.06983	+	1.39471i	−0.187900	+	0.0516915i
$729$	22.3758			0.828734
$730$	−2.79759	−	4.84556i	−0.103543	−	0.179342i
$731$	39.1411	−	67.7944i	1.44769	−	2.50747i
$732$	2.09202	−	3.62349i	0.0773234	−	0.133928i
$733$	−22.5737	−	39.0988i	−0.833778	−	1.44415i	−0.895021	−	0.446023i	$-0.852840\pi$
$733$	−22.5737	−	39.0988i	−0.833778	−	1.44415i	0.0612434	−	0.998123i	$-0.480493\pi$
$734$	−16.1789			−0.597174
$735$	11.1068	−	6.61131i	0.409680	−	0.243862i
$736$	14.9150			0.549773
$737$	−7.03117	−	12.1783i	−0.258996	−	0.448595i
$738$	0.680217	−	1.17817i	0.0250391	−	0.0433690i
$739$	10.7162	−	18.5610i	0.394202	−	0.682777i	−0.598797	−	0.800901i	$-0.704354\pi$
$739$	10.7162	−	18.5610i	0.394202	−	0.682777i	0.992999	+	0.118123i	$0.0376878\pi$
$740$	0.811895	+	1.40624i	0.0298458	+	0.0516945i
$741$	−11.9604			−0.439376
$742$	−14.4673	+	3.97995i	−0.531110	+	0.146109i
$743$	2.90342			0.106516			0.0532581	−	0.998581i	$-0.483039\pi$
$743$	2.90342			0.106516			0.0532581	+	0.998581i	$0.483039\pi$
$744$	−1.73509	−	3.00527i	−0.0636116	−	0.110178i
$745$	−4.61790	+	7.99844i	−0.169187	+	0.293040i
$746$	−5.55532	+	9.62209i	−0.203395	+	0.352290i
$747$	1.85304	+	3.20956i	0.0677991	+	0.117431i
$748$	−12.9575			−0.473772
$749$	32.7123	+	32.2794i	1.19528	+	1.17946i
$750$	−1.13257			−0.0413557
$751$	10.8341	+	18.7652i	0.395342	+	0.684752i	0.993145	−	0.116891i	$-0.0372929\pi$
$751$	10.8341	+	18.7652i	0.395342	+	0.684752i	−0.597803	+	0.801643i	$0.703960\pi$
$752$	−7.96231	+	13.7911i	−0.290355	+	0.502910i
$753$	−12.7341	+	22.0561i	−0.464055	+	0.803768i
$754$	1.92377	+	3.33207i	0.0700596	+	0.121347i
$755$	19.4588			0.708178
$756$	−5.18625	+	19.8841i	−0.188622	+	0.723179i
$757$	−7.17306			−0.260709			−0.130355	−	0.991467i	$-0.541612\pi$
$757$	−7.17306			−0.260709			−0.130355	+	0.991467i	$0.541612\pi$
$758$	2.25863	+	3.91206i	0.0820371	+	0.142093i
$759$	−3.00179	+	5.19926i	−0.108958	+	0.188721i
$760$	−8.05074	+	13.9443i	−0.292031	+	0.505812i
$761$	−14.1292	−	24.4725i	−0.512184	−	0.887129i	−0.999900	−	0.0141268i	$-0.995503\pi$
$761$	−14.1292	−	24.4725i	−0.512184	−	0.887129i	0.487716	−	0.873002i	$-0.337830\pi$
$762$	11.8133			0.427952
$763$	6.67549	−	25.5939i	0.241669	−	0.926563i
$764$	36.2173			1.31029
$765$	1.33844	+	2.31824i	0.0483913	+	0.0838162i
$766$	−4.03490	+	6.98866i	−0.145787	+	0.252510i
$767$	1.36557	−	2.36523i	0.0493077	−	0.0854035i
$768$	5.84438	+	10.1228i	0.210891	+	0.365274i
$769$	20.4331			0.736837			0.368418	−	0.929660i	$-0.379899\pi$
$769$	20.4331			0.736837			0.368418	+	0.929660i	$0.379899\pi$
$770$	−1.41037	−	1.39171i	−0.0508264	−	0.0501538i
$771$	−38.4880			−1.38611
$772$	−16.1436	−	27.9615i	−0.581021	−	1.00636i
$773$	12.3091	−	21.3200i	0.442728	−	0.766827i	−0.555163	−	0.831742i	$-0.687344\pi$
$773$	12.3091	−	21.3200i	0.442728	−	0.766827i	0.997891	+	0.0649145i	$0.0206775\pi$
$774$	1.50459	−	2.60602i	0.0540813	−	0.0936716i
$775$	−0.422759	−	0.732240i	−0.0151860	−	0.0263029i
$776$	0.0922066			0.00331002
$777$	4.71041	−	1.29584i	0.168985	−	0.0464879i
$778$	−8.83687			−0.316817
$779$	−19.6142	−	33.9728i	−0.702751	−	1.21720i
$780$	−1.34047	+	2.32177i	−0.0479966	+	0.0831326i
$781$	3.35018	−	5.80269i	0.119879	−	0.207636i
$782$	5.33719	+	9.24429i	0.190858	+	0.330575i
$783$	33.5568			1.19922
$784$	−11.5096	−	6.44221i	−0.411058	−	0.230079i
$785$	−10.1980			−0.363983
$786$	−7.36452	−	12.7557i	−0.262684	−	0.454981i
$787$	−10.4718	+	18.1376i	−0.373278	+	0.646537i	−0.990068	−	0.140591i	$-0.955100\pi$
$787$	−10.4718	+	18.1376i	−0.373278	+	0.646537i	0.616790	+	0.787128i	$0.288433\pi$
$788$	4.52176	−	7.83191i	0.161081	−	0.279000i
$789$	21.0520	+	36.4631i	0.749471	+	1.29812i
$790$	8.18941			0.291366
$791$	35.3578	−	9.72696i	1.25718	−	0.345851i
$792$	−1.11157			−0.0394981
$793$	0.623869	+	1.08057i	0.0221542	+	0.0383722i
$794$	−10.7490	+	18.6179i	−0.381469	+	0.660723i
$795$	−8.53659	+	14.7858i	−0.302762	+	0.524398i
$796$	4.86182	+	8.42092i	0.172323	+	0.298472i
$797$	−3.87594			−0.137293			−0.0686463	−	0.997641i	$-0.521868\pi$
$797$	−3.87594			−0.137293			−0.0686463	+	0.997641i	$0.521868\pi$
$798$	15.4512	+	15.2467i	0.546965	+	0.539727i
$799$	−55.2338			−1.95403
$800$	2.80056	+	4.85070i	0.0990146	+	0.171498i
$801$	3.06386	−	5.30676i	0.108256	−	0.187505i
$802$	6.43357	−	11.1433i	0.227177	−	0.393482i
$803$	−5.56903	−	9.64585i	−0.196527	−	0.340395i
$804$	34.5324			1.21786
$805$	1.77808	−	6.81719i	0.0626692	−	0.240274i
$806$	0.463709			0.0163335
$807$	−8.50001	−	14.7225i	−0.299215	−	0.518255i
$808$	3.02710	−	5.24310i	0.106493	−	0.184452i
$809$	3.65295	−	6.32710i	0.128431	−	0.222449i	−0.794638	−	0.607084i	$-0.792339\pi$
$809$	3.65295	−	6.32710i	0.128431	−	0.222449i	0.923069	+	0.384635i	$0.125673\pi$
$810$	−3.08551	−	5.34426i	−0.108414	−	0.187778i
$811$	−25.5843			−0.898387			−0.449194	−	0.893434i	$-0.648289\pi$
$811$	−25.5843			−0.898387			−0.449194	+	0.893434i	$0.648289\pi$
$812$	−7.60667	+	29.1641i	−0.266942	+	1.02346i
$813$	35.8569			1.25756
$814$	−0.374453	−	0.648571i	−0.0131246	−	0.0227324i
$815$	−11.8692	+	20.5580i	−0.415760	+	0.720117i
$816$	11.3696	−	19.6927i	0.398014	−	0.689381i
$817$	−43.3852	−	75.1453i	−1.51785	−	2.62900i
$818$	4.78671			0.167363
$819$	0.689705	+	0.680578i	0.0241002	+	0.0237813i
$820$	−8.79312			−0.307069
$821$	5.35642	+	9.27760i	0.186941	+	0.323790i	0.944229	−	0.329290i	$-0.106810\pi$
$821$	5.35642	+	9.27760i	0.186941	+	0.323790i	−0.757288	+	0.653081i	$0.773476\pi$
$822$	5.91473	−	10.2446i	0.206300	−	0.357322i
$823$	26.4244	−	45.7685i	0.921098	−	1.59539i	0.123379	−	0.992360i	$-0.460627\pi$
$823$	26.4244	−	45.7685i	0.921098	−	1.59539i	0.797719	−	0.603029i	$-0.206040\pi$
$824$	9.42920	+	16.3318i	0.328482	+	0.568947i
$825$	−2.25456			−0.0784938
$826$	−4.77923	+	1.31477i	−0.166291	+	0.0457467i
$827$	37.3813			1.29988			0.649938	−	0.759988i	$-0.274795\pi$
$827$	37.3813			1.29988			0.649938	+	0.759988i	$0.274795\pi$
$828$	−0.885516	−	1.53376i	−0.0307738	−	0.0533018i
$829$	−4.61059	+	7.98578i	−0.160132	+	0.277358i	−0.934916	−	0.354869i	$-0.884525\pi$
$829$	−4.61059	+	7.98578i	−0.160132	+	0.277358i	0.774784	+	0.632227i	$0.217859\pi$
$830$	−2.77492	+	4.80631i	−0.0963190	+	0.166829i
$831$	22.3259	+	38.6695i	0.774475	+	1.34143i
$832$	0.297791			0.0103241
$833$	−0.609391	−	45.7445i	−0.0211141	−	1.58495i
$834$	20.8749			0.722840
$835$	−3.25320	−	5.63470i	−0.112581	−	0.194997i
$836$	−7.18123	+	12.4382i	−0.248368	+	0.430186i
$837$	2.02215	−	3.50246i	0.0698956	−	0.121063i
$838$	7.02626	+	12.1698i	0.242718	+	0.420400i
$839$	−30.7541			−1.06175			−0.530874	−	0.847451i	$-0.678136\pi$
$839$	−30.7541			−1.06175			−0.530874	+	0.847451i	$0.678136\pi$
$840$	10.4698	−	2.88024i	0.361241	−	0.0993777i
$841$	20.2177			0.697163
$842$	−1.81164	−	3.13785i	−0.0624331	−	0.108137i
$843$	25.5699	−	44.2884i	0.880675	−	1.52537i
$844$	6.68822	−	11.5843i	0.230218	−	0.398749i
$845$	6.10025	+	10.5659i	0.209855	+	0.363480i
$846$	−2.12319			−0.0729969
$847$	17.9082	+	17.6712i	0.615331	+	0.607189i
$848$	17.4224			0.598286
$849$	4.64167	+	8.03961i	0.159302	+	0.275919i
$850$	−2.00431	+	3.47157i	−0.0687472	+	0.119074i
$851$	1.33143	−	2.30610i	0.0456408	−	0.0790522i
$852$	8.22693	+	14.2495i	0.281850	+	0.488178i
$853$	29.1851			0.999280			0.499640	−	0.866233i	$-0.333466\pi$
$853$	29.1851			0.999280			0.499640	+	0.866233i	$0.333466\pi$
$854$	0.571525	−	2.19123i	0.0195572	−	0.0749825i
$855$	2.96713			0.101474
$856$	19.3042	+	33.4358i	0.659804	+	1.14281i
$857$	7.68678	−	13.3139i	0.262575	−	0.454794i	−0.704350	−	0.709853i	$-0.748761\pi$
$857$	7.68678	−	13.3139i	0.262575	−	0.454794i	0.966926	+	0.255059i	$0.0820948\pi$
$858$	0.618237	−	1.07082i	0.0211063	−	0.0365571i
$859$	−12.4476	−	21.5598i	−0.424705	−	0.735611i	0.571687	−	0.820471i	$-0.306289\pi$
$859$	−12.4476	−	21.5598i	−0.424705	−	0.735611i	−0.996393	+	0.0848601i	$0.972956\pi$
$860$	−19.4497			−0.663230
$861$	−6.67679	+	25.5989i	−0.227544	+	0.872409i
$862$	11.2160			0.382019
$863$	−6.76622	−	11.7194i	−0.230325	−	0.398934i	0.727579	−	0.686024i	$-0.240646\pi$
$863$	−6.76622	−	11.7194i	−0.230325	−	0.398934i	−0.957904	+	0.287090i	$0.907312\pi$
$864$	−13.3957	+	23.2020i	−0.455729	+	0.789346i
$865$	−0.0346485	+	0.0600129i	−0.00117808	+	0.00204050i
$866$	0.619678	+	1.07331i	0.0210575	+	0.0364727i
$867$	47.4790			1.61247
$868$	2.58559	+	2.55138i	0.0877608	+	0.0865994i
$869$	16.3023			0.553017
$870$	−3.97280	−	6.88110i	−0.134691	−	0.233291i
$871$	−5.14900	+	8.91833i	−0.174467	+	0.302186i
$872$	11.1104	−	19.2437i	0.376244	−	0.651674i
$873$	−0.00849576	−	0.0147151i	−0.000287538	−	0.000498030i
$874$	11.8318			0.400217
$875$	2.55098	−	0.701777i	0.0862389	−	0.0237244i
$876$	27.3514			0.924117
$877$	−11.6679	−	20.2094i	−0.393997	−	0.682423i	0.598975	−	0.800767i	$-0.295575\pi$
$877$	−11.6679	−	20.2094i	−0.393997	−	0.682423i	−0.992973	+	0.118344i	$0.962241\pi$
$878$	−3.89676	+	6.74938i	−0.131509	+	0.227781i
$879$	−13.8943	+	24.0657i	−0.468644	+	0.811715i
$880$	1.15034	+	1.99244i	0.0387779	+	0.0671652i
$881$	16.5070			0.556134			0.278067	−	0.960562i	$-0.410306\pi$
$881$	16.5070			0.556134			0.278067	+	0.960562i	$0.410306\pi$
$882$	−0.0234251	−	1.75842i	−0.000788763	−	0.0592092i
$883$	40.7966			1.37292			0.686458	−	0.727170i	$-0.259165\pi$
$883$	40.7966			1.37292			0.686458	+	0.727170i	$0.259165\pi$
$884$	4.74446	+	8.21764i	0.159573	+	0.276389i
$885$	−2.82005	+	4.88447i	−0.0947949	+	0.164190i
$886$	−0.971085	+	1.68197i	−0.0326242	+	0.0565068i
$887$	−18.8418	−	32.6350i	−0.632646	−	1.09578i	−0.987009	−	0.160667i	$-0.948635\pi$
$887$	−18.8418	−	32.6350i	−0.632646	−	1.09578i	0.354363	−	0.935108i	$-0.384698\pi$
$888$	4.10421			0.137728
$889$	−26.6081	+	7.31990i	−0.892407	+	0.245502i
$890$	9.17625			0.307589
$891$	−6.14218	−	10.6386i	−0.205771	−	0.356406i
$892$	−16.1230	+	27.9258i	−0.539838	+	0.935026i
$893$	−30.6114	+	53.0204i	−1.02437	+	1.77426i
$894$	5.23011	+	9.05882i	0.174921	+	0.302972i
$895$	13.0704			0.436894
$896$	−21.4813	−	21.1970i	−0.717639	−	0.708142i
$897$	4.39649			0.146795
$898$	−10.4782	−	18.1488i	−0.349662	−	0.605633i
$899$	2.96588	−	5.13706i	0.0989177	−	0.171330i
$900$	0.332544	−	0.575982i	0.0110848	−	0.0191994i
$901$	30.2143	+	52.3327i	1.00658	+	1.74346i
$902$	4.05546			0.135032
$903$	−14.7686	+	56.6229i	−0.491467	+	1.88429i
$904$	30.8075			1.02464
$905$	10.1452	+	17.5720i	0.337237	+	0.584112i
$906$	11.0193	−	19.0859i	0.366090	−	0.634087i
$907$	25.9823	−	45.0026i	0.862727	−	1.49429i	−0.00655986	−	0.999978i	$-0.502088\pi$
$907$	25.9823	−	45.0026i	0.862727	−	1.49429i	0.869287	−	0.494308i	$-0.164579\pi$
$908$	4.31604	+	7.47560i	0.143233	+	0.248087i
$909$	−1.11565			−0.0370037
$910$	−0.366207	+	1.40404i	−0.0121396	+	0.0465436i
$911$	12.2789			0.406818			0.203409	−	0.979094i	$-0.434798\pi$
$911$	12.2789			0.406818			0.203409	+	0.979094i	$0.434798\pi$
$912$	−12.6024	−	21.8279i	−0.417306	−	0.722795i
$913$	−5.52392	+	9.56770i	−0.182815	+	0.316645i
$914$	−7.93377	+	13.7417i	−0.262426	+	0.454535i
$915$	−1.28836	−	2.23150i	−0.0425918	−	0.0737712i
$916$	18.6457			0.616071
$917$	24.4915	+	24.1674i	0.808780	+	0.798078i
$918$	−19.1741			−0.632839
$919$	21.0446	+	36.4503i	0.694196	+	1.20238i	0.970451	+	0.241299i	$0.0775733\pi$
$919$	21.0446	+	36.4503i	0.694196	+	1.20238i	−0.276255	+	0.961084i	$0.589093\pi$
$920$	2.95935	−	5.12575i	0.0975669	−	0.168991i
$921$	−5.66141	+	9.80585i	−0.186550	+	0.323114i
$922$	−8.90230	−	15.4192i	−0.293182	−	0.507805i
$923$	−4.90675			−0.161508
$924$	9.33899	−	2.56916i	0.307230	−	0.0845192i
$925$	1.00000			0.0328798
$926$	−4.72085	−	8.17676i	−0.155137	−	0.268705i
$927$	1.73758	−	3.00958i	0.0570697	−	0.0988475i
$928$	−19.6474	+	34.0303i	−0.644957	+	1.11710i
$929$	−18.1807	−	31.4900i	−0.596491	−	1.03315i	−0.993335	−	0.115266i	$-0.963228\pi$
$929$	−18.1807	−	31.4900i	−0.596491	−	1.03315i	0.396844	−	0.917886i	$-0.370106\pi$
$930$	−0.957612			−0.0314013
$931$	−44.2491	−	24.7673i	−1.45021	−	0.811715i
$932$	−33.7023			−1.10395
$933$	−15.7455	−	27.2720i	−0.515485	−	0.892846i
$934$	−10.9856	+	19.0276i	−0.359460	+	0.622603i
$935$	−3.98989	+	6.91069i	−0.130483	+	0.226004i
$936$	0.407009	+	0.704961i	0.0133035	+	0.0230424i
$937$	43.7966			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$937$	43.7966			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$938$	18.0206	−	4.95747i	0.588393	−	0.161867i
$939$	−3.54769			−0.115775
$940$	6.86160	+	11.8846i	0.223801	+	0.387634i
$941$	16.8960	−	29.2647i	0.550793	−	0.954002i	−0.447424	−	0.894322i	$-0.647659\pi$
$941$	16.8960	−	29.2647i	0.550793	−	0.954002i	0.998218	−	0.0596803i	$-0.0190081\pi$
$942$	−5.77501	+	10.0026i	−0.188160	+	0.325902i
$943$	7.20993	+	12.4880i	0.234788	+	0.406664i
$944$	5.75545			0.187324
$945$	9.00797	+	8.88877i	0.293029	+	0.289152i
$946$	8.97038			0.291652
$947$	−3.74367	−	6.48423i	−0.121653	−	0.210709i	0.798767	−	0.601641i	$-0.205486\pi$
$947$	−3.74367	−	6.48423i	−0.121653	−	0.210709i	−0.920420	+	0.390932i	$0.872153\pi$
$948$	−20.0165	+	34.6696i	−0.650106	+	1.12602i
$949$	−4.07827	+	7.06376i	−0.132386	+	0.229299i
$950$	2.22163	+	3.84798i	0.0720794	+	0.124845i
$951$	−36.2300			−1.17484
$952$	9.69977	−	37.1891i	0.314371	−	1.20530i
$953$	−12.2657			−0.397325			−0.198662	−	0.980068i	$-0.563660\pi$
$953$	−12.2657			−0.397325			−0.198662	+	0.980068i	$0.563660\pi$
$954$	1.16144	+	2.01168i	0.0376031	+	0.0651304i
$955$	11.1521	−	19.3160i	0.360873	−	0.625050i
$956$	3.67587	−	6.36679i	0.118886	−	0.205917i
$957$	−7.90849	−	13.6979i	−0.255645	−	0.442790i
$958$	−12.6018			−0.407146
$959$	−6.97433	+	26.7397i	−0.225213	+	0.863469i
$960$	−0.614973			−0.0198482
$961$	15.1425	+	26.2277i	0.488469	+	0.846054i
$962$	−0.274216	+	0.474956i	−0.00884108	+	0.0153132i
$963$	3.55731	−	6.16145i	0.114633	−	0.198550i
$964$	−17.4136	−	30.1613i	−0.560856	−	0.971430i
$965$	−19.8838			−0.640084
$966$	−5.67965	−	5.60450i	−0.182740	−	0.180322i
$967$	−25.6492			−0.824822			−0.412411	−	0.910998i	$-0.635313\pi$
$967$	−25.6492			−0.824822			−0.412411	+	0.910998i	$0.635313\pi$
$968$	10.5680	+	18.3043i	0.339668	+	0.588322i
$969$	43.7107	−	75.7091i	1.40419	−	2.43213i
$970$	0.0127224	−	0.0220358i	0.000408491	−	0.000707528i
$971$	5.93240	+	10.2752i	0.190380	+	0.329748i	0.945376	−	0.325981i	$-0.105695\pi$
$971$	5.93240	+	10.2752i	0.190380	+	0.329748i	−0.754996	+	0.655729i	$0.772361\pi$
$972$	6.86552			0.220212
$973$	−47.0182	+	12.9347i	−1.50733	+	0.414669i
$974$	−26.4949			−0.848951
$975$	0.825521	+	1.42985i	0.0264378	+	0.0457917i
$976$	−1.31471	+	2.27714i	−0.0420828	+	0.0728895i
$977$	10.6480	−	18.4428i	0.340659	−	0.590038i	−0.643896	−	0.765113i	$-0.722683\pi$
$977$	10.6480	−	18.4428i	0.340659	−	0.590038i	0.984555	+	0.175074i	$0.0560166\pi$
$978$	13.4427	+	23.2835i	0.429851	+	0.744524i
$979$	18.2668			0.583808
$980$	−9.76712	+	5.81388i	−0.311999	+	0.185718i
$981$	−4.09476			−0.130736
$982$	2.67745	+	4.63748i	0.0854408	+	0.147988i
$983$	−15.4808	+	26.8136i	−0.493762	+	0.855221i	−0.999974	−	0.00718808i	$-0.997712\pi$
$983$	−15.4808	+	26.8136i	−0.493762	+	0.855221i	0.506212	+	0.862409i	$0.331045\pi$
$984$	−11.1125	+	19.2474i	−0.354254	+	0.613586i
$985$	−2.78469	−	4.82323i	−0.0887277	−	0.153681i
$986$	−28.1226			−0.895606
$987$	39.8092	−	10.9515i	1.26714	−	0.348592i
$988$	10.5178			0.334615
$989$	15.9478	+	27.6225i	0.507112	+	0.878343i
$990$	−0.153372	+	0.265648i	−0.00487448	+	0.00844284i
$991$	−29.7406	+	51.5123i	−0.944743	+	1.63634i	−0.188478	+	0.982077i	$0.560355\pi$
$991$	−29.7406	+	51.5123i	−0.944743	+	1.63634i	−0.756265	+	0.654265i	$0.772978\pi$
$992$	2.36792	+	4.10136i	0.0751816	+	0.130218i
$993$	−37.9013			−1.20276
$994$	6.33884	+	6.25496i	0.201056	+	0.198395i
$995$	5.98824			0.189840
$996$	−13.5649	−	23.4951i	−0.429820	−	0.744470i
$997$	17.5287	−	30.3606i	0.555140	−	0.961530i	−0.442753	−	0.896644i	$-0.645998\pi$
$997$	17.5287	−	30.3606i	0.555140	−	0.961530i	0.997893	−	0.0648864i	$-0.0206685\pi$
$998$	4.44446	−	7.69804i	0.140687	−	0.243677i
$999$	2.39161	+	4.14238i	0.0756671	+	0.131059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.11	✓	38
7.2	even	3	inner	1295.2.j.a.926.11	yes	38
7.3	odd	6		9065.2.a.s.1.9		19
7.4	even	3		9065.2.a.r.1.9		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.11	✓	38	1.1	even	1	trivial
1295.2.j.a.926.11	yes	38	7.2	even	3	inner
9065.2.a.r.1.9		19	7.4	even	3
9065.2.a.s.1.9		19	7.3	odd	6

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:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.306680 + 0.531185i) q^{2} +(-0.923254 + 1.59912i) q^{3} +(0.811895 - 1.40624i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.13257 q^{6} +(2.55098 - 0.701777i) q^{7} +2.22269 q^{8} +(-0.204795 - 0.354715i) q^{9} +(0.306680 - 0.531185i) q^{10} +(0.610494 - 1.05741i) q^{11} +(1.49917 + 2.59664i) q^{12} -0.894144 q^{13} +(1.15511 + 1.13982i) q^{14} +1.84651 q^{15} +(-0.942136 - 1.63183i) q^{16} +(3.26775 - 5.65992i) q^{17} +(0.125613 - 0.217568i) q^{18} +(-3.62207 - 6.27362i) q^{19} -1.62379 q^{20} +(-1.23298 + 4.72725i) q^{21} +0.748905 q^{22} +(1.33143 + 2.30610i) q^{23} +(-2.05210 + 3.55435i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.274216 - 0.474956i) q^{26} -4.78321 q^{27} +(1.08426 - 4.15707i) q^{28} -7.01553 q^{29} +(0.566287 + 0.980838i) q^{30} +(-0.422759 + 0.732240i) q^{31} +(2.80056 - 4.85070i) q^{32} +(1.12728 + 1.95251i) q^{33} +4.00862 q^{34} +(-1.88325 - 1.85833i) q^{35} -0.665087 q^{36} +(-0.500000 - 0.866025i) q^{37} +(2.22163 - 3.84798i) q^{38} +(0.825521 - 1.42985i) q^{39} +(-1.11134 - 1.92490i) q^{40} +5.41518 q^{41} +(-2.88917 + 0.794814i) q^{42} +11.9780 q^{43} +(-0.991314 - 1.71701i) q^{44} +(-0.204795 + 0.354715i) q^{45} +(-0.816645 + 1.41447i) q^{46} +(-4.22567 - 7.31907i) q^{47} +3.47932 q^{48} +(6.01502 - 3.58044i) q^{49} -0.613360 q^{50} +(6.03393 + 10.4511i) q^{51} +(-0.725951 + 1.25738i) q^{52} +(-4.62310 + 8.00744i) q^{53} +(-1.46692 - 2.54077i) q^{54} -1.22099 q^{55} +(5.67004 - 1.55983i) q^{56} +13.3764 q^{57} +(-2.15152 - 3.72655i) q^{58} +(-1.52723 + 2.64525i) q^{59} +(1.49917 - 2.59664i) q^{60} +(-0.697727 - 1.20850i) q^{61} -0.518607 q^{62} +(-0.771358 - 0.761151i) q^{63} -0.333046 q^{64} +(0.447072 + 0.774351i) q^{65} +(-0.691430 + 1.19759i) q^{66} +(5.75859 - 9.97416i) q^{67} +(-5.30614 - 9.19051i) q^{68} -4.91699 q^{69} +(0.409562 - 1.57026i) q^{70} +5.48766 q^{71} +(-0.455195 - 0.788420i) q^{72} +(4.56109 - 7.90003i) q^{73} +(0.306680 - 0.531185i) q^{74} +(-0.923254 - 1.59912i) q^{75} -11.7630 q^{76} +(0.815296 - 3.12586i) q^{77} +1.01268 q^{78} +(6.67586 + 11.5629i) q^{79} +(-0.942136 + 1.63183i) q^{80} +(5.03050 - 8.71309i) q^{81} +(1.66073 + 2.87647i) q^{82} -9.04827 q^{83} +(5.64662 + 5.57189i) q^{84} -6.53551 q^{85} +(3.67341 + 6.36253i) q^{86} +(6.47712 - 11.2187i) q^{87} +(1.35694 - 2.35028i) q^{88} +(7.48032 + 12.9563i) q^{89} -0.251226 q^{90} +(-2.28094 + 0.627489i) q^{91} +4.32392 q^{92} +(-0.780628 - 1.35209i) q^{93} +(2.59186 - 4.48923i) q^{94} +(-3.62207 + 6.27362i) q^{95} +(5.17125 + 8.95686i) q^{96} +0.0414843 q^{97} +(3.74656 + 2.09704i) q^{98} -0.500104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more