LMFDB - Embedded newform 1295.2.j.a.186.16

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			186.16
Character	$\chi$	$=$	1295.186
Dual form			1295.2.j.a.926.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.983510 + 1.70349i) q^{2} +(-1.61976 + 2.80550i) q^{3} +(-0.934584 + 1.61875i) q^{4} +(-0.500000 - 0.866025i) q^{5} -6.37219 q^{6} +(0.615110 - 2.57325i) q^{7} +0.257349 q^{8} +(-3.74723 - 6.49039i) q^{9} +(0.983510 - 1.70349i) q^{10} +(1.78366 - 3.08938i) q^{11} +(-3.02760 - 5.24395i) q^{12} -6.33329 q^{13} +(4.98848 - 1.48299i) q^{14} +3.23951 q^{15} +(2.12227 + 3.67589i) q^{16} +(1.15092 - 1.99345i) q^{17} +(7.37087 - 12.7667i) q^{18} +(-1.62200 - 2.80939i) q^{19} +1.86917 q^{20} +(6.22294 + 5.89374i) q^{21} +7.01698 q^{22} +(1.00375 + 1.73854i) q^{23} +(-0.416844 + 0.721994i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.22885 - 10.7887i) q^{26} +14.5598 q^{27} +(3.59058 + 3.40063i) q^{28} +9.47054 q^{29} +(3.18609 + 5.51848i) q^{30} +(3.52325 - 6.10245i) q^{31} +(-3.91721 + 6.78480i) q^{32} +(5.77818 + 10.0081i) q^{33} +4.52776 q^{34} +(-2.53606 + 0.753926i) q^{35} +14.0084 q^{36} +(-0.500000 - 0.866025i) q^{37} +(3.19051 - 5.52613i) q^{38} +(10.2584 - 17.7681i) q^{39} +(-0.128675 - 0.222871i) q^{40} -9.54095 q^{41} +(-3.91960 + 16.3973i) q^{42} -5.09374 q^{43} +(3.33395 + 5.77458i) q^{44} +(-3.74723 + 6.49039i) q^{45} +(-1.97439 + 3.41975i) q^{46} +(-0.117078 - 0.202785i) q^{47} -13.7503 q^{48} +(-6.24328 - 3.16567i) q^{49} -1.96702 q^{50} +(3.72841 + 6.45780i) q^{51} +(5.91899 - 10.2520i) q^{52} +(4.00742 - 6.94105i) q^{53} +(14.3198 + 24.8025i) q^{54} -3.56731 q^{55} +(0.158298 - 0.662226i) q^{56} +10.5090 q^{57} +(9.31437 + 16.1330i) q^{58} +(5.39920 - 9.35169i) q^{59} +(-3.02760 + 5.24395i) q^{60} +(-2.66498 - 4.61588i) q^{61} +13.8606 q^{62} +(-19.0064 + 5.65026i) q^{63} -6.92135 q^{64} +(3.16665 + 5.48479i) q^{65} +(-11.3658 + 19.6861i) q^{66} +(1.71601 - 2.97221i) q^{67} +(2.15126 + 3.72609i) q^{68} -6.50331 q^{69} +(-3.77854 - 3.57866i) q^{70} -10.9250 q^{71} +(-0.964347 - 1.67030i) q^{72} +(-5.48065 + 9.49276i) q^{73} +(0.983510 - 1.70349i) q^{74} +(-1.61976 - 2.80550i) q^{75} +6.06359 q^{76} +(-6.85263 - 6.49012i) q^{77} +40.3569 q^{78} +(0.976843 + 1.69194i) q^{79} +(2.12227 - 3.67589i) q^{80} +(-12.3417 + 21.3765i) q^{81} +(-9.38362 - 16.2529i) q^{82} +9.65897 q^{83} +(-15.3563 + 4.56517i) q^{84} -2.30184 q^{85} +(-5.00975 - 8.67714i) q^{86} +(-15.3400 + 26.5696i) q^{87} +(0.459023 - 0.795051i) q^{88} +(-4.89536 - 8.47901i) q^{89} -14.7417 q^{90} +(-3.89567 + 16.2972i) q^{91} -3.75235 q^{92} +(11.4136 + 19.7690i) q^{93} +(0.230295 - 0.398882i) q^{94} +(-1.62200 + 2.80939i) q^{95} +(-12.6898 - 21.9795i) q^{96} +18.9483 q^{97} +(-0.747639 - 13.7488i) q^{98} -26.7351 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 $

$2$	0.983510	+	1.70349i	0.695447	+	1.20455i	0.970030	+	0.242986i	$0.0781268\pi$
$2$	0.983510	+	1.70349i	0.695447	+	1.20455i	−0.274583	+	0.961563i	$0.588540\pi$
$3$	−1.61976	+	2.80550i	−0.935167	+	1.61976i	−0.160832	+	0.986982i	$0.551418\pi$
$3$	−1.61976	+	2.80550i	−0.935167	+	1.61976i	−0.774335	+	0.632775i	$0.781916\pi$
$4$	−0.934584	+	1.61875i	−0.467292	+	0.809373i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−6.37219			−2.60144
$7$	0.615110	−	2.57325i	0.232490	−	0.972599i
$7$	0.615110	−	2.57325i	0.232490	−	0.972599i
$8$	0.257349			0.0909868
$9$	−3.74723	−	6.49039i	−1.24908	−	2.16346i
$10$	0.983510	−	1.70349i	0.311013	−	0.538691i
$11$	1.78366	−	3.08938i	0.537793	−	0.931484i	−0.461230	−	0.887281i	$-0.652592\pi$
$11$	1.78366	−	3.08938i	0.537793	−	0.931484i	0.999023	−	0.0442037i	$-0.0140750\pi$
$12$	−3.02760	−	5.24395i	−0.873992	−	1.51380i
$13$	−6.33329			−1.75654			−0.878269	−	0.478166i	$-0.841302\pi$
$13$	−6.33329			−1.75654			−0.878269	+	0.478166i	$0.841302\pi$
$14$	4.98848	−	1.48299i	1.33323	−	0.396345i
$15$	3.23951			0.836439
$16$	2.12227	+	3.67589i	0.530568	+	0.918971i
$17$	1.15092	−	1.99345i	0.279139	−	0.483482i	−0.692032	−	0.721866i	$-0.743284\pi$
$17$	1.15092	−	1.99345i	0.279139	−	0.483482i	0.971171	+	0.238384i	$0.0766178\pi$
$18$	7.37087	−	12.7667i	1.73733	−	3.00915i
$19$	−1.62200	−	2.80939i	−0.372113	−	0.644519i	0.617777	−	0.786353i	$-0.288033\pi$
$19$	−1.62200	−	2.80939i	−0.372113	−	0.644519i	−0.989890	+	0.141834i	$0.954700\pi$
$20$	1.86917			0.417959
$21$	6.22294	+	5.89374i	1.35796	+	1.28612i
$22$	7.01698			1.49602
$23$	1.00375	+	1.73854i	0.209296	+	0.362511i	0.951493	−	0.307671i	$-0.0995495\pi$
$23$	1.00375	+	1.73854i	0.209296	+	0.362511i	−0.742197	+	0.670182i	$0.766216\pi$
$24$	−0.416844	+	0.721994i	−0.0850878	+	0.147376i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.22885	−	10.7887i	−1.22158	−	2.11584i
$27$	14.5598			2.80204
$28$	3.59058	+	3.40063i	0.678555	+	0.642659i
$29$	9.47054			1.75864			0.879318	−	0.476235i	$-0.157999\pi$
$29$	9.47054			1.75864			0.879318	+	0.476235i	$0.157999\pi$
$30$	3.18609	+	5.51848i	0.581699	+	1.00753i
$31$	3.52325	−	6.10245i	0.632794	−	1.09603i	−0.354184	−	0.935176i	$-0.615241\pi$
$31$	3.52325	−	6.10245i	0.632794	−	1.09603i	0.986978	−	0.160856i	$-0.0514254\pi$
$32$	−3.91721	+	6.78480i	−0.692471	+	1.19939i
$33$	5.77818	+	10.0081i	1.00585	+	1.74219i
$34$	4.52776			0.776504
$35$	−2.53606	+	0.753926i	−0.428672	+	0.127437i
$36$	14.0084			2.33473
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i
$38$	3.19051	−	5.52613i	0.517570	−	0.896457i
$39$	10.2584	−	17.7681i	1.64266	−	2.84517i
$40$	−0.128675	−	0.222871i	−0.0203453	−	0.0352390i
$41$	−9.54095			−1.49005			−0.745023	−	0.667038i	$-0.767562\pi$
$41$	−9.54095			−1.49005			−0.745023	+	0.667038i	$0.767562\pi$
$42$	−3.91960	+	16.3973i	−0.604808	+	2.53015i
$43$	−5.09374			−0.776788			−0.388394	−	0.921493i	$-0.626970\pi$
$43$	−5.09374			−0.776788			−0.388394	+	0.921493i	$0.626970\pi$
$44$	3.33395	+	5.77458i	0.502612	+	0.870550i
$45$	−3.74723	+	6.49039i	−0.558604	+	0.967530i
$46$	−1.97439	+	3.41975i	−0.291108	+	0.504214i
$47$	−0.117078	−	0.202785i	−0.0170776	−	0.0295792i	0.857360	−	0.514717i	$-0.172103\pi$
$47$	−0.117078	−	0.202785i	−0.0170776	−	0.0295792i	−0.874438	+	0.485137i	$0.838770\pi$
$48$	−13.7503			−1.98468
$49$	−6.24328	−	3.16567i	−0.891897	−	0.452239i
$50$	−1.96702			−0.278179
$51$	3.72841	+	6.45780i	0.522082	+	0.904273i
$52$	5.91899	−	10.2520i	0.820816	−	1.42170i
$53$	4.00742	−	6.94105i	0.550461	−	0.953426i	−0.447780	−	0.894144i	$-0.647785\pi$
$53$	4.00742	−	6.94105i	0.550461	−	0.953426i	0.998241	−	0.0592827i	$-0.0188814\pi$
$54$	14.3198	+	24.8025i	1.94867	+	3.37520i
$55$	−3.56731			−0.481016
$56$	0.158298	−	0.662226i	0.0211535	−	0.0884936i
$57$	10.5090			1.39195
$58$	9.31437	+	16.1330i	1.22304	+	2.11836i
$59$	5.39920	−	9.35169i	0.702916	−	1.21749i	−0.264522	−	0.964380i	$-0.585214\pi$
$59$	5.39920	−	9.35169i	0.702916	−	1.21749i	0.967438	−	0.253107i	$-0.0814524\pi$
$60$	−3.02760	+	5.24395i	−0.390861	+	0.676992i
$61$	−2.66498	−	4.61588i	−0.341216	−	0.591003i	0.643443	−	0.765494i	$-0.277505\pi$
$61$	−2.66498	−	4.61588i	−0.341216	−	0.591003i	−0.984659	+	0.174491i	$0.944172\pi$
$62$	13.8606			1.76030
$63$	−19.0064	+	5.65026i	−2.39458	+	0.711866i
$64$	−6.92135			−0.865169
$65$	3.16665	+	5.48479i	0.392774	+	0.680304i
$66$	−11.3658	+	19.6861i	−1.39903	+	2.42320i
$67$	1.71601	−	2.97221i	0.209644	−	0.363114i	−0.741959	−	0.670446i	$-0.766103\pi$
$67$	1.71601	−	2.97221i	0.209644	−	0.363114i	0.951602	+	0.307332i	$0.0994363\pi$
$68$	2.15126	+	3.72609i	0.260878	+	0.451855i
$69$	−6.50331			−0.782907
$70$	−3.77854	−	3.57866i	−0.451622	−	0.427731i
$71$	−10.9250			−1.29656			−0.648279	−	0.761403i	$-0.724511\pi$
$71$	−10.9250			−1.29656			−0.648279	+	0.761403i	$0.724511\pi$
$72$	−0.964347	−	1.67030i	−0.113649	−	0.196846i
$73$	−5.48065	+	9.49276i	−0.641462	+	1.11104i	0.343645	+	0.939100i	$0.388338\pi$
$73$	−5.48065	+	9.49276i	−0.641462	+	1.11104i	−0.985107	+	0.171944i	$0.944995\pi$
$74$	0.983510	−	1.70349i	0.114331	−	0.198027i
$75$	−1.61976	−	2.80550i	−0.187033	−	0.323951i
$76$	6.06359			0.695542
$77$	−6.85263	−	6.49012i	−0.780929	−	0.739617i
$78$	40.3569			4.56952
$79$	0.976843	+	1.69194i	0.109903	+	0.190358i	0.915731	−	0.401792i	$-0.131613\pi$
$79$	0.976843	+	1.69194i	0.109903	+	0.190358i	−0.805828	+	0.592150i	$0.798279\pi$
$80$	2.12227	−	3.67589i	0.237277	−	0.410977i
$81$	−12.3417	+	21.3765i	−1.37130	+	2.37517i
$82$	−9.38362	−	16.2529i	−1.03625	−	1.79483i
$83$	9.65897			1.06021			0.530105	−	0.847932i	$-0.322153\pi$
$83$	9.65897			1.06021			0.530105	+	0.847932i	$0.322153\pi$
$84$	−15.3563	+	4.56517i	−1.67551	+	0.498101i
$85$	−2.30184			−0.249669
$86$	−5.00975	−	8.67714i	−0.540215	−	0.935680i
$87$	−15.3400	+	26.5696i	−1.64462	+	2.84856i
$88$	0.459023	−	0.795051i	0.0489320	−	0.0847527i
$89$	−4.89536	−	8.47901i	−0.518907	−	0.898773i	−0.999759	−	0.0219711i	$-0.993006\pi$
$89$	−4.89536	−	8.47901i	−0.518907	−	0.898773i	0.480852	−	0.876802i	$-0.340328\pi$
$90$	−14.7417			−1.55392
$91$	−3.89567	+	16.2972i	−0.408378	+	1.70841i
$92$	−3.75235			−0.391209
$93$	11.4136	+	19.7690i	1.18354	+	2.04995i
$94$	0.230295	−	0.398882i	0.0237531	−	0.0411415i
$95$	−1.62200	+	2.80939i	−0.166414	+	0.288238i
$96$	−12.6898	−	21.9795i	−1.29515	−	2.24327i
$97$	18.9483			1.92391			0.961957	−	0.273202i	$-0.0880827\pi$
$97$	18.9483			1.92391			0.961957	+	0.273202i	$0.0880827\pi$
$98$	−0.747639	−	13.7488i	−0.0755229	−	1.38884i
$99$	−26.7351			−2.68698
$100$	−0.934584	−	1.61875i	−0.0934584	−	0.161875i
$101$	3.23197	−	5.59794i	0.321593	−	0.557016i	−0.659224	−	0.751947i	$-0.729115\pi$
$101$	3.23197	−	5.59794i	0.321593	−	0.557016i	0.980817	+	0.194931i	$0.0624483\pi$
$102$	−7.33387	+	12.7026i	−0.726161	+	1.25775i
$103$	0.172992	+	0.299630i	0.0170454	+	0.0295234i	0.874422	−	0.485166i	$-0.161241\pi$
$103$	0.172992	+	0.299630i	0.0170454	+	0.0295234i	−0.857377	+	0.514689i	$0.827907\pi$
$104$	−1.62987			−0.159822
$105$	1.99266	−	8.33610i	0.194464	−	0.813520i
$106$	15.7653			1.53126
$107$	1.12998	+	1.95718i	0.109239	+	0.189208i	0.915462	−	0.402404i	$-0.131825\pi$
$107$	1.12998	+	1.95718i	0.109239	+	0.189208i	−0.806223	+	0.591612i	$0.798492\pi$
$108$	−13.6074	+	23.5687i	−1.30937	+	2.26790i
$109$	2.02054	−	3.49968i	0.193533	−	0.335209i	−0.752886	−	0.658151i	$-0.771339\pi$
$109$	2.02054	−	3.49968i	0.193533	−	0.335209i	0.946419	+	0.322942i	$0.104672\pi$
$110$	−3.50849	−	6.07688i	−0.334521	−	0.579408i
$111$	3.23951			0.307481
$112$	10.7644	−	3.20007i	1.01714	−	0.302379i
$113$	2.69997			0.253992			0.126996	−	0.991903i	$-0.459466\pi$
$113$	2.69997			0.253992			0.126996	+	0.991903i	$0.459466\pi$
$114$	10.3357	+	17.9020i	0.968028	+	1.67667i
$115$	1.00375	−	1.73854i	0.0936000	−	0.162120i
$116$	−8.85102	+	15.3304i	−0.821796	+	1.42339i
$117$	23.7323	+	41.1055i	2.19405	+	3.80021i
$118$	21.2407			1.95536
$119$	−4.42171	−	4.18779i	−0.405337	−	0.383895i
$120$	0.833687			0.0761049
$121$	−0.862863	−	1.49452i	−0.0784421	−	0.135866i
$122$	5.24207	−	9.07953i	0.474595	−	0.822022i
$123$	15.4540	−	26.7672i	1.39344	−	2.41351i
$124$	6.58554	+	11.4065i	0.591399	+	1.02433i
$125$	1.00000			0.0894427
$126$	−28.3181	−	26.8201i	−2.52278	−	2.38932i
$127$	−21.3955			−1.89854			−0.949271	−	0.314460i	$-0.898177\pi$
$127$	−21.3955			−1.89854			−0.949271	+	0.314460i	$0.898177\pi$
$128$	1.02720	+	1.77915i	0.0907921	+	0.157256i
$129$	8.25063	−	14.2905i	0.726427	−	1.25821i
$130$	−6.22885	+	10.7887i	−0.546307	+	0.946231i
$131$	5.51077	+	9.54494i	0.481478	+	0.833945i	0.999774	−	0.0212564i	$-0.00676662\pi$
$131$	5.51077	+	9.54494i	0.481478	+	0.833945i	−0.518296	+	0.855202i	$0.673433\pi$
$132$	−21.6008			−1.88011
$133$	−8.22699	+	2.44574i	−0.713371	+	0.212073i
$134$	6.75084			0.583184
$135$	−7.27992	−	12.6092i	−0.626556	−	1.08523i
$136$	0.296188	−	0.513013i	0.0253979	−	0.0439905i
$137$	0.298649	−	0.517275i	0.0255153	−	0.0441938i	−0.852986	−	0.521934i	$-0.825211\pi$
$137$	0.298649	−	0.517275i	0.0255153	−	0.0441938i	0.878501	+	0.477740i	$0.158544\pi$
$138$	−6.39607	−	11.0783i	−0.544470	−	0.943050i
$139$	−20.1669			−1.71053			−0.855265	−	0.518190i	$-0.826606\pi$
$139$	−20.1669			−1.71053			−0.855265	+	0.518190i	$0.826606\pi$
$140$	1.14974	−	4.80984i	0.0971712	−	0.406506i
$141$	0.758551			0.0638815
$142$	−10.7448	−	18.6106i	−0.901687	−	1.56177i
$143$	−11.2964	+	19.5660i	−0.944654	+	1.63619i
$144$	15.9053	−	27.5488i	1.32544	−	2.29573i
$145$	−4.73527	−	8.20173i	−0.393243	−	0.681117i
$146$	−21.5611			−1.78441
$147$	18.9939	−	12.3879i	1.56659	−	1.02174i
$148$	1.86917			0.153645
$149$	−10.2260	−	17.7120i	−0.837748	−	1.45102i	−0.891773	−	0.452483i	$-0.850538\pi$
$149$	−10.2260	−	17.7120i	−0.837748	−	1.45102i	0.0540247	−	0.998540i	$-0.482795\pi$
$150$	3.18609	−	5.51848i	0.260144	−	0.450582i
$151$	9.48049	−	16.4207i	0.771511	−	1.33630i	−0.165223	−	0.986256i	$-0.552834\pi$
$151$	9.48049	−	16.4207i	0.771511	−	1.33630i	0.936734	−	0.350041i	$-0.113832\pi$
$152$	−0.417422	−	0.722996i	−0.0338574	−	0.0586427i
$153$	−17.2510			−1.39466
$154$	4.31622	−	18.0565i	0.347811	−	1.45503i
$155$	−7.04650			−0.565988
$156$	19.1747	+	33.2115i	1.53520	+	2.65905i
$157$	3.60975	−	6.25227i	0.288090	−	0.498986i	−0.685264	−	0.728295i	$-0.740313\pi$
$157$	3.60975	−	6.25227i	0.288090	−	0.498986i	0.973354	+	0.229309i	$0.0736466\pi$
$158$	−1.92147	+	3.32808i	−0.152864	+	0.264768i
$159$	12.9821	+	22.4856i	1.02955	+	1.78323i
$160$	7.83441			0.619365
$161$	5.09113	−	1.51350i	0.401237	−	0.119281i
$162$	−48.5529			−3.81468
$163$	−1.99204	−	3.45031i	−0.156028	−	0.270249i	0.777405	−	0.629001i	$-0.216536\pi$
$163$	−1.99204	−	3.45031i	−0.156028	−	0.270249i	−0.933433	+	0.358752i	$0.883202\pi$
$164$	8.91682	−	15.4444i	0.696287	−	1.20600i
$165$	5.77818	−	10.0081i	0.449831	−	0.779130i
$166$	9.49969	+	16.4539i	0.737319	+	1.27707i
$167$	−12.5627			−0.972129			−0.486065	−	0.873923i	$-0.661568\pi$
$167$	−12.5627			−0.972129			−0.486065	+	0.873923i	$0.661568\pi$
$168$	1.60147	+	1.51675i	0.123556	+	0.117020i
$169$	27.1106			2.08543
$170$	−2.26388	−	3.92115i	−0.173632	−	0.300739i
$171$	−12.1560	+	21.0549i	−0.929595	+	1.61011i
$172$	4.76053	−	8.24548i	0.362987	−	0.628712i
$173$	12.2084	+	21.1455i	0.928185	+	1.60766i	0.786357	+	0.617772i	$0.211964\pi$
$173$	12.2084	+	21.1455i	0.928185	+	1.60766i	0.141827	+	0.989891i	$0.454702\pi$
$174$	−60.3481			−4.57498
$175$	1.92095	+	1.81933i	0.145210	+	0.137528i
$176$	15.1416			1.14134
$177$	17.4908	+	30.2949i	1.31469	+	2.27711i
$178$	9.62927	−	16.6784i	0.721744	−	1.25010i
$179$	1.78379	−	3.08961i	0.133327	−	0.230928i	−0.791630	−	0.611000i	$-0.790767\pi$
$179$	1.78379	−	3.08961i	0.133327	−	0.230928i	0.924957	+	0.380072i	$0.124101\pi$
$180$	−7.00420	−	12.1316i	−0.522062	−	0.904238i
$181$	20.3869			1.51535			0.757674	−	0.652633i	$-0.226336\pi$
$181$	20.3869			1.51535			0.757674	+	0.652633i	$0.226336\pi$
$182$	−31.5935	+	9.39219i	−2.34186	+	0.696195i
$183$	17.2665			1.27638
$184$	0.258314	+	0.447413i	0.0190432	+	0.0329837i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$	−22.4508	+	38.8859i	−1.64617	+	2.85126i
$187$	−4.10568	−	7.11125i	−0.300237	−	0.520026i
$188$	0.437677			0.0319208
$189$	8.95592	−	37.4662i	0.651447	−	2.72526i
$190$	−6.38103			−0.462928
$191$	6.91646	+	11.9797i	0.500457	+	0.866818i	1.00000		0.000528214i	$0.000168136\pi$
$191$	6.91646	+	11.9797i	0.500457	+	0.866818i	−0.499542	+	0.866289i	$0.666499\pi$
$192$	11.2109	−	19.4179i	0.809077	−	1.40136i
$193$	3.72339	−	6.44911i	0.268016	−	0.464217i	−0.700334	−	0.713816i	$-0.746965\pi$
$193$	3.72339	−	6.44911i	0.268016	−	0.464217i	0.968349	+	0.249599i	$0.0802987\pi$
$194$	18.6359	+	32.2783i	1.33798	+	2.31745i
$195$	−20.5168			−1.46924
$196$	10.9593	−	7.14770i	0.782806	−	0.510550i
$197$	1.33109			0.0948360			0.0474180	−	0.998875i	$-0.484901\pi$
$197$	1.33109			0.0948360			0.0474180	+	0.998875i	$0.484901\pi$
$198$	−26.2942	−	45.5429i	−1.86865	−	3.23659i
$199$	−3.03350	+	5.25417i	−0.215039	+	0.372458i	−0.953285	−	0.302074i	$-0.902321\pi$
$199$	−3.03350	+	5.25417i	−0.215039	+	0.372458i	0.738246	+	0.674532i	$0.235655\pi$
$200$	−0.128675	+	0.222871i	−0.00909868	+	0.0157594i
$201$	5.55903	+	9.62853i	0.392104	+	0.679144i
$202$	12.7147			0.894603
$203$	5.82543	−	24.3701i	0.408865	−	1.71045i
$204$	−13.9381			−0.975860
$205$	4.77048	+	8.26271i	0.333185	+	0.577093i
$206$	−0.340278	+	0.589378i	−0.0237083	+	0.0410639i
$207$	7.52255	−	13.0294i	0.522853	−	0.905608i
$208$	−13.4410	−	23.2805i	−0.931964	−	1.61421i
$209$	−11.5724			−0.800479
$210$	16.1603	−	4.80416i	1.11516	−	0.331519i
$211$	−10.6274			−0.731622			−0.365811	−	0.930689i	$-0.619208\pi$
$211$	−10.6274			−0.731622			−0.365811	+	0.930689i	$0.619208\pi$
$212$	7.49053	+	12.9740i	0.514452	+	0.891057i
$213$	17.6958	−	30.6501i	1.21250	−	2.10011i
$214$	−2.22269	+	3.84981i	−0.151940	+	0.263168i
$215$	2.54687	+	4.41131i	0.173695	+	0.300849i
$216$	3.74697			0.254949
$217$	−13.5360	−	12.8199i	−0.918881	−	0.870271i
$218$	7.94890			0.538367
$219$	−17.7546	−	30.7519i	−1.19975	−	2.07802i
$220$	3.33395	−	5.77458i	0.224775	−	0.389322i
$221$	−7.28910	+	12.6251i	−0.490318	+	0.849255i
$222$	3.18609	+	5.51848i	0.213837	+	0.370376i
$223$	−5.53349			−0.370550			−0.185275	−	0.982687i	$-0.559318\pi$
$223$	−5.53349			−0.370550			−0.185275	+	0.982687i	$0.559318\pi$
$224$	15.0495	+	14.2534i	1.00554	+	0.952343i
$225$	7.49445			0.499630
$226$	2.65545	+	4.59937i	0.176638	+	0.305946i
$227$	−3.70627	+	6.41945i	−0.245994	+	0.426074i	−0.962411	−	0.271599i	$-0.912448\pi$
$227$	−3.70627	+	6.41945i	−0.245994	+	0.426074i	0.716417	+	0.697673i	$0.245781\pi$
$228$	−9.82155	+	17.0114i	−0.650448	+	1.12661i
$229$	8.43096	+	14.6028i	0.557133	+	0.964983i	0.997734	+	0.0672801i	$0.0214321\pi$
$229$	8.43096	+	14.6028i	0.557133	+	0.964983i	−0.440601	+	0.897703i	$0.645235\pi$
$230$	3.94879			0.260375
$231$	29.3076	−	8.71264i	1.92830	−	0.573250i
$232$	2.43724			0.160013
$233$	1.42894	+	2.47499i	0.0936128	+	0.162142i	0.909029	−	0.416733i	$-0.136825\pi$
$233$	1.42894	+	2.47499i	0.0936128	+	0.162142i	−0.815416	+	0.578875i	$0.803492\pi$
$234$	−46.6819	+	80.8554i	−3.05169	+	5.28568i
$235$	−0.117078	+	0.202785i	−0.00763732	+	0.0132282i
$236$	10.0920	+	17.4799i	0.656934	+	1.13784i
$237$	−6.32899			−0.411112
$238$	2.78507	−	11.6511i	0.180529	−	0.755227i
$239$	−5.79807			−0.375046			−0.187523	−	0.982260i	$-0.560046\pi$
$239$	−5.79807			−0.375046			−0.187523	+	0.982260i	$0.560046\pi$
$240$	6.87514	+	11.9081i	0.443788	+	0.768664i
$241$	1.18936	−	2.06003i	0.0766134	−	0.132698i	−0.825173	−	0.564880i	$-0.808923\pi$
$241$	1.18936	−	2.06003i	0.0766134	−	0.132698i	0.901787	+	0.432181i	$0.142256\pi$
$242$	1.69727	−	2.93976i	0.109105	−	0.188975i
$243$	−18.1415	−	31.4220i	−1.16378	−	2.01572i
$244$	9.96259			0.637789
$245$	0.380087	+	6.98967i	0.0242829	+	0.446554i
$246$	60.7968			3.87626
$247$	10.2726	+	17.7927i	0.653631	+	1.13212i
$248$	0.906706	−	1.57046i	0.0575759	−	0.0997244i
$249$	−15.6452	+	27.0982i	−0.991473	+	1.71728i
$250$	0.983510	+	1.70349i	0.0622026	+	0.107738i
$251$	−6.57244			−0.414849			−0.207424	−	0.978251i	$-0.566508\pi$
$251$	−6.57244			−0.414849			−0.207424	+	0.978251i	$0.566508\pi$
$252$	8.61671	−	36.0472i	0.542802	−	2.27076i
$253$	7.16137			0.450231
$254$	−21.0427	−	36.4470i	−1.32033	−	2.28689i
$255$	3.72841	−	6.45780i	0.233482	−	0.404403i
$256$	−8.94186	+	15.4878i	−0.558866	+	0.967985i
$257$	−1.26163	−	2.18520i	−0.0786981	−	0.136309i	0.823990	−	0.566604i	$-0.191743\pi$
$257$	−1.26163	−	2.18520i	−0.0786981	−	0.136309i	−0.902688	+	0.430295i	$0.858410\pi$
$258$	32.4583			2.02076
$259$	−2.53606	+	0.753926i	−0.157583	+	0.0468467i
$260$	−11.8380			−0.734160
$261$	−35.4883	−	61.4675i	−2.19667	−	3.80474i
$262$	−10.8398	+	18.7751i	−0.669685	+	1.15993i
$263$	2.16063	−	3.74232i	0.133230	−	0.230762i	−0.791690	−	0.610923i	$-0.790798\pi$
$263$	2.16063	−	3.74232i	0.133230	−	0.230762i	0.924920	+	0.380162i	$0.124132\pi$
$264$	1.48701	+	2.57558i	0.0915193	+	0.158516i
$265$	−8.01483			−0.492347
$266$	−12.2576	−	11.6092i	−0.751563	−	0.711805i
$267$	31.7172			1.94106
$268$	3.20751	+	5.55556i	0.195930	+	0.339360i
$269$	5.21878	−	9.03919i	0.318195	−	0.551129i	−0.661917	−	0.749577i	$-0.730257\pi$
$269$	5.21878	−	9.03919i	0.318195	−	0.551129i	0.980111	+	0.198448i	$0.0635901\pi$
$270$	14.3198	−	24.8025i	0.871473	−	1.50944i
$271$	14.7139	+	25.4853i	0.893809	+	1.54812i	0.835272	+	0.549837i	$0.185310\pi$
$271$	14.7139	+	25.4853i	0.893809	+	1.54812i	0.0585364	+	0.998285i	$0.481357\pi$
$272$	9.77025			0.592408
$273$	−39.4117	−	37.3268i	−2.38530	−	2.25912i
$274$	1.17490			0.0709781
$275$	1.78366	+	3.08938i	0.107559	+	0.186297i
$276$	6.07789	−	10.5272i	0.365846	−	0.633664i
$277$	5.44310	−	9.42772i	0.327044	−	0.566457i	−0.654880	−	0.755733i	$-0.727281\pi$
$277$	5.44310	−	9.42772i	0.327044	−	0.566457i	0.981924	+	0.189276i	$0.0606141\pi$
$278$	−19.8343	−	34.3540i	−1.18958	−	2.06042i
$279$	−52.8097			−3.16163
$280$	−0.652653	+	0.194022i	−0.0390035	+	0.0115951i
$281$	−8.87180			−0.529248			−0.264624	−	0.964352i	$-0.585248\pi$
$281$	−8.87180			−0.529248			−0.264624	+	0.964352i	$0.585248\pi$
$282$	0.746043	+	1.29218i	0.0444262	+	0.0769484i
$283$	12.4666	−	21.5929i	0.741065	−	1.28356i	−0.210945	−	0.977498i	$-0.567654\pi$
$283$	12.4666	−	21.5929i	0.741065	−	1.28356i	0.952011	−	0.306065i	$-0.0990124\pi$
$284$	10.2103	−	17.6848i	0.605871	−	1.04940i
$285$	−5.25450	−	9.10107i	−0.311250	−	0.539101i
$286$	−44.4406			−2.62782
$287$	−5.86874	+	24.5513i	−0.346421	+	1.44922i
$288$	58.7146			3.45979
$289$	5.85078	+	10.1338i	0.344163	+	0.596108i
$290$	9.31437	−	16.1330i	0.546959	−	0.947361i
$291$	−30.6917	+	53.1596i	−1.79918	+	3.11627i
$292$	−10.2443	−	17.7436i	−0.599500	−	1.03836i
$293$	−2.27327			−0.132806			−0.0664030	−	0.997793i	$-0.521152\pi$
$293$	−2.27327			−0.132806			−0.0664030	+	0.997793i	$0.521152\pi$
$294$	39.7834	+	20.1723i	2.32021	+	1.17647i
$295$	−10.7984			−0.628707
$296$	−0.128675	−	0.222871i	−0.00747907	−	0.0129541i
$297$	25.9698	−	44.9810i	1.50692	−	2.61006i
$298$	20.1148	−	34.8398i	1.16522	−	2.01822i
$299$	−6.35703	−	11.0107i	−0.367636	−	0.636765i
$300$	6.05520			0.349597
$301$	−3.13321	+	13.1075i	−0.180595	+	0.755503i
$302$	37.2966			2.14618
$303$	10.4700	+	18.1346i	0.601487	+	1.04181i
$304$	6.88467	−	11.9246i	0.394863	−	0.683923i
$305$	−2.66498	+	4.61588i	−0.152596	+	0.264305i
$306$	−16.9665	−	29.3869i	−0.969912	−	1.67994i
$307$	−1.62044			−0.0924833			−0.0462417	−	0.998930i	$-0.514724\pi$
$307$	−1.62044			−0.0924833			−0.0462417	+	0.998930i	$0.514724\pi$
$308$	16.9102	−	5.02711i	0.963549	−	0.286446i
$309$	−1.12082			−0.0637611
$310$	−6.93030	−	12.0036i	−0.393615	−	0.681761i
$311$	−4.16829	+	7.21969i	−0.236362	+	0.409391i	−0.959668	−	0.281137i	$-0.909289\pi$
$311$	−4.16829	+	7.21969i	−0.236362	+	0.409391i	0.723306	+	0.690528i	$0.242622\pi$
$312$	2.63999	−	4.57260i	0.149460	−	0.258872i
$313$	−5.23811	−	9.07267i	−0.296075	−	0.512818i	0.679159	−	0.733991i	$-0.262345\pi$
$313$	−5.23811	−	9.07267i	−0.296075	−	0.512818i	−0.975234	+	0.221174i	$0.929011\pi$
$314$	14.2009			0.801403
$315$	14.3965	+	13.6349i	0.811149	+	0.768238i
$316$	−3.65177			−0.205428
$317$	−8.86368	−	15.3523i	−0.497834	−	0.862273i	0.502163	−	0.864773i	$-0.332538\pi$
$317$	−8.86368	−	15.3523i	−0.497834	−	0.862273i	−0.999997	+	0.00249948i	$0.999204\pi$
$318$	−25.5360	+	44.2297i	−1.43199	+	2.48028i
$319$	16.8922	−	29.2581i	0.945782	−	1.63814i
$320$	3.46067	+	5.99406i	0.193458	+	0.335078i
$321$	−7.32117			−0.408628
$322$	7.58541	+	7.18414i	0.422719	+	0.400356i
$323$	−7.46717			−0.415484
$324$	−23.0688	−	39.9563i	−1.28160	−	2.21979i
$325$	3.16665	−	5.48479i	0.175654	−	0.304241i
$326$	3.91838	−	6.78683i	0.217019	−	0.375888i
$327$	6.54558	+	11.3373i	0.361971	+	0.626953i
$328$	−2.45536			−0.135575
$329$	−0.593833	+	0.176536i	−0.0327391	+	0.00973276i
$330$	22.7316			1.25133
$331$	−3.35646	−	5.81356i	−0.184488	−	0.319542i	0.758916	−	0.651188i	$-0.225729\pi$
$331$	−3.35646	−	5.81356i	−0.184488	−	0.319542i	−0.943404	+	0.331646i	$0.892396\pi$
$332$	−9.02712	+	15.6354i	−0.495427	+	0.858105i
$333$	−3.74723	+	6.49039i	−0.205347	+	0.355671i
$334$	−12.3555	−	21.4004i	−0.676064	−	1.17098i
$335$	−3.43202			−0.187511
$336$	−8.45794	+	35.3830i	−0.461418	+	1.93030i
$337$	−8.67915			−0.472783			−0.236392	−	0.971658i	$-0.575965\pi$
$337$	−8.67915			−0.472783			−0.236392	+	0.971658i	$0.575965\pi$
$338$	26.6635	+	46.1826i	1.45030	+	2.51200i
$339$	−4.37330	+	7.57477i	−0.237525	+	0.411405i
$340$	2.15126	−	3.72609i	0.116668	−	0.202076i
$341$	−12.5685	−	21.7693i	−0.680624	−	1.17888i
$342$	−47.8223			−2.58593
$343$	−11.9864	+	14.1183i	−0.647204	+	0.762317i
$344$	−1.31087			−0.0706775
$345$	3.25166	+	5.63204i	0.175063	+	0.303219i
$346$	−24.0141	+	41.5936i	−1.29101	+	2.23609i
$347$	−4.58073	+	7.93406i	−0.245907	+	0.425923i	−0.962386	−	0.271685i	$-0.912419\pi$
$347$	−4.58073	+	7.93406i	−0.245907	+	0.425923i	0.716480	+	0.697608i	$0.245752\pi$
$348$	−28.6730	−	49.6631i	−1.53703	−	2.66222i
$349$	25.5586			1.36812			0.684061	−	0.729425i	$-0.260212\pi$
$349$	25.5586			1.36812			0.684061	+	0.729425i	$0.260212\pi$
$350$	−1.20993	+	5.06164i	−0.0646737	+	0.270556i
$351$	−92.2117			−4.92190
$352$	13.9739	+	24.2035i	0.744811	+	1.29005i
$353$	−13.2661	+	22.9776i	−0.706084	+	1.22297i	0.260215	+	0.965551i	$0.416206\pi$
$353$	−13.2661	+	22.9776i	−0.706084	+	1.22297i	−0.966299	+	0.257422i	$0.917127\pi$
$354$	−34.4047	+	59.5907i	−1.82859	+	3.16721i
$355$	5.46250	+	9.46132i	0.289919	+	0.502155i
$356$	18.3005			0.969924
$357$	18.9110	−	5.62190i	1.00087	−	0.297542i
$358$	7.01749			0.370886
$359$	−0.829559	−	1.43684i	−0.0437825	−	0.0758334i	0.843304	−	0.537437i	$-0.180608\pi$
$359$	−0.829559	−	1.43684i	−0.0437825	−	0.0758334i	−0.887086	+	0.461604i	$0.847274\pi$
$360$	−0.964347	+	1.67030i	−0.0508255	+	0.0880324i
$361$	4.23821	−	7.34079i	0.223064	−	0.386357i
$362$	20.0508	+	34.7289i	1.05384	+	1.82531i
$363$	5.59052			0.293426
$364$	−22.7402	−	21.5372i	−1.19191	−	1.12885i
$365$	10.9613			0.573741
$366$	16.9818	+	29.4133i	0.887651	+	1.53746i
$367$	3.40233	−	5.89301i	0.177600	−	0.307613i	−0.763458	−	0.645858i	$-0.776500\pi$
$367$	3.40233	−	5.89301i	0.177600	−	0.307613i	0.941058	+	0.338245i	$0.109833\pi$
$368$	−4.26046	+	7.37933i	−0.222092	+	0.384674i
$369$	35.7521	+	61.9245i	1.86118	+	3.22366i
$370$	−1.96702			−0.102261
$371$	−15.3961	−	14.5816i	−0.799325	−	0.757040i
$372$	−42.6679			−2.21223
$373$	7.00472	+	12.1325i	0.362691	+	0.628199i	0.988403	−	0.151855i	$-0.0485248\pi$
$373$	7.00472	+	12.1325i	0.362691	+	0.628199i	−0.625712	+	0.780054i	$0.715191\pi$
$374$	8.07596	−	13.9880i	0.417598	−	0.723301i
$375$	−1.61976	+	2.80550i	−0.0836439	+	0.144875i
$376$	−0.0301299	−	0.0521866i	−0.00155383	−	0.00269132i
$377$	−59.9797			−3.08911
$378$	72.6315	−	21.5921i	3.73576	−	1.11058i
$379$	1.04346			0.0535987			0.0267993	−	0.999641i	$-0.491468\pi$
$379$	1.04346			0.0535987			0.0267993	+	0.999641i	$0.491468\pi$
$380$	−3.03180	−	5.25123i	−0.155528	−	0.269382i
$381$	34.6555	−	60.0251i	1.77545	−	3.07518i
$382$	−13.6048	+	23.5642i	−0.696083	+	1.20565i
$383$	−5.86671	−	10.1614i	−0.299775	−	0.519225i	0.676309	−	0.736618i	$-0.263578\pi$
$383$	−5.86671	−	10.1614i	−0.299775	−	0.519225i	−0.976084	+	0.217392i	$0.930245\pi$
$384$	−6.65523			−0.339623
$385$	−2.19429	+	9.17961i	−0.111831	+	0.467836i
$386$	14.6480			0.745563
$387$	19.0874	+	33.0604i	0.970267	+	1.68055i
$388$	−17.7088	+	30.6726i	−0.899029	+	1.55716i
$389$	1.59800	−	2.76782i	0.0810219	−	0.140334i	−0.822667	−	0.568523i	$-0.807515\pi$
$389$	1.59800	−	2.76782i	0.0810219	−	0.140334i	0.903689	+	0.428189i	$0.140848\pi$
$390$	−20.1785	−	34.9501i	−1.02178	−	1.76977i
$391$	4.62093			0.233690
$392$	−1.60670	−	0.814684i	−0.0811508	−	0.0411477i
$393$	−35.7045			−1.80105
$394$	1.30914	+	2.26749i	0.0659534	+	0.114235i
$395$	0.976843	−	1.69194i	0.0491503	−	0.0851308i
$396$	24.9862	−	43.2773i	1.25560	−	2.17477i
$397$	−0.109526	−	0.189704i	−0.00549693	−	0.00952097i	0.863264	−	0.504753i	$-0.168416\pi$
$397$	−0.109526	−	0.189704i	−0.00549693	−	0.00952097i	−0.868761	+	0.495232i	$0.835083\pi$
$398$	−11.9339			−0.598192
$399$	6.46420	−	27.0424i	0.323615	−	1.35381i
$400$	−4.24455			−0.212227
$401$	−4.02680	−	6.97462i	−0.201089	−	0.348296i	0.747791	−	0.663935i	$-0.231115\pi$
$401$	−4.02680	−	6.97462i	−0.201089	−	0.348296i	−0.948880	+	0.315638i	$0.897781\pi$
$402$	−10.9347	+	18.9395i	−0.545375	+	0.944617i
$403$	−22.3138	+	38.6486i	−1.11153	+	1.92522i
$404$	6.04110	+	10.4635i	0.300556	+	0.520578i
$405$	24.6835			1.22653
$406$	47.2436	−	14.0447i	2.34466	−	0.697027i
$407$	−3.56731			−0.176825
$408$	0.959505	+	1.66191i	0.0475026	+	0.0822769i
$409$	−12.1814	+	21.0988i	−0.602330	+	1.04327i	0.390137	+	0.920757i	$0.372428\pi$
$409$	−12.1814	+	21.0988i	−0.602330	+	1.04327i	−0.992467	+	0.122510i	$0.960906\pi$
$410$	−9.38362	+	16.2529i	−0.463424	+	0.802674i
$411$	0.967477	+	1.67572i	0.0477221	+	0.0826572i
$412$	−0.646700			−0.0318606
$413$	−20.7432	−	19.6458i	−1.02070	−	0.966709i
$414$	29.5940			1.45447
$415$	−4.82948	−	8.36491i	−0.237070	−	0.410617i
$416$	24.8088	−	42.9701i	1.21635	−	2.10678i
$417$	32.6654	−	56.5782i	1.59963	−	2.77064i
$418$	−11.3816	−	19.7134i	−0.556690	−	0.964216i
$419$	14.7610			0.721121			0.360560	−	0.932736i	$-0.382585\pi$
$419$	14.7610			0.721121			0.360560	+	0.932736i	$0.382585\pi$
$420$	11.6317	+	11.0164i	0.567570	+	0.537545i
$421$	19.4321			0.947063			0.473532	−	0.880777i	$-0.342979\pi$
$421$	19.4321			0.947063			0.473532	+	0.880777i	$0.342979\pi$
$422$	−10.4522	−	18.1037i	−0.508804	−	0.881274i
$423$	−0.877435	+	1.51976i	−0.0426624	+	0.0738934i
$424$	1.03131	−	1.78627i	0.0500847	−	0.0867492i
$425$	1.15092	+	1.99345i	0.0558277	+	0.0966964i
$426$	69.6161			3.37291
$427$	−13.5171	+	4.01840i	−0.654138	+	0.194464i
$428$	−4.22424			−0.204186
$429$	−36.5949	−	63.3842i	−1.76682	−	3.06022i
$430$	−5.00975	+	8.67714i	−0.241591	+	0.418449i
$431$	−17.8441	+	30.9068i	−0.859519	+	1.48873i	0.0128699	+	0.999917i	$0.495903\pi$
$431$	−17.8441	+	30.9068i	−0.859519	+	1.48873i	−0.872389	+	0.488813i	$0.837430\pi$
$432$	30.9000	+	53.5203i	1.48668	+	2.57500i
$433$	30.2919			1.45574			0.727869	−	0.685717i	$-0.240511\pi$
$433$	30.2919			1.45574			0.727869	+	0.685717i	$0.240511\pi$
$434$	8.52580	−	35.6669i	0.409252	−	1.71206i
$435$	30.6800			1.47099
$436$	3.77673	+	6.54150i	0.180873	+	0.313281i
$437$	3.25617	−	5.63985i	0.155764	−	0.269790i
$438$	34.9237	−	60.4897i	1.66872	−	2.89031i
$439$	3.35872	+	5.81747i	0.160303	+	0.277653i	0.934977	−	0.354707i	$-0.115420\pi$
$439$	3.35872	+	5.81747i	0.160303	+	0.277653i	−0.774674	+	0.632360i	$0.782086\pi$
$440$	−0.918046			−0.0437661
$441$	2.84854	+	52.3838i	0.135645	+	2.49447i
$442$	−28.6756			−1.36396
$443$	−5.11683	−	8.86260i	−0.243108	−	0.421075i	0.718490	−	0.695537i	$-0.244834\pi$
$443$	−5.11683	−	8.86260i	−0.243108	−	0.421075i	−0.961598	+	0.274462i	$0.911500\pi$
$444$	−3.02760	+	5.24395i	−0.143683	+	0.248867i
$445$	−4.89536	+	8.47901i	−0.232062	+	0.401944i
$446$	−5.44224	−	9.42624i	−0.257698	−	0.446346i
$447$	66.2547			3.13374
$448$	−4.25739	+	17.8104i	−0.201143	+	0.841462i
$449$	−20.5772			−0.971099			−0.485549	−	0.874209i	$-0.661380\pi$
$449$	−20.5772			−0.971099			−0.485549	+	0.874209i	$0.661380\pi$
$450$	7.37087	+	12.7667i	0.347466	+	0.601829i
$451$	−17.0178	+	29.4757i	−0.801336	+	1.38796i
$452$	−2.52335	+	4.37057i	−0.118688	+	0.205574i
$453$	30.7122	+	53.1951i	1.44298	+	2.49932i
$454$	−14.5806			−0.684302
$455$	16.0616	−	4.77483i	0.752979	−	0.223848i
$456$	2.70449			0.126649
$457$	0.529586	+	0.917270i	0.0247730	+	0.0429081i	0.878146	−	0.478393i	$-0.158780\pi$
$457$	0.529586	+	0.917270i	0.0247730	+	0.0429081i	−0.853373	+	0.521301i	$0.825447\pi$
$458$	−16.5839	+	28.7241i	−0.774913	+	1.34219i
$459$	16.7572	−	29.0243i	0.782159	−	1.35474i
$460$	1.87617	+	3.24963i	0.0874771	+	0.151515i
$461$	−26.4670			−1.23269			−0.616346	−	0.787475i	$-0.711388\pi$
$461$	−26.4670			−1.23269			−0.616346	+	0.787475i	$0.711388\pi$
$462$	43.6662	+	41.3562i	2.03154	+	1.92407i
$463$	−12.3467			−0.573799			−0.286899	−	0.957961i	$-0.592625\pi$
$463$	−12.3467			−0.573799			−0.286899	+	0.957961i	$0.592625\pi$
$464$	20.0991	+	34.8126i	0.933076	+	1.61614i
$465$	11.4136	−	19.7690i	0.529294	−	0.916764i
$466$	−2.81075	+	4.86836i	−0.130205	+	0.225522i
$467$	−5.15112	−	8.92200i	−0.238365	−	0.412861i	0.721880	−	0.692018i	$-0.243278\pi$
$467$	−5.15112	−	8.92200i	−0.238365	−	0.412861i	−0.960245	+	0.279157i	$0.909945\pi$
$468$	−88.7192			−4.10105
$469$	−6.59273	−	6.24396i	−0.304424	−	0.288319i
$470$	−0.460589			−0.0212454
$471$	11.6938	+	20.2543i	0.538824	+	0.933270i
$472$	1.38948	−	2.40665i	0.0639561	−	0.110775i
$473$	−9.08549	+	15.7365i	−0.417751	+	0.723566i
$474$	−6.22463	−	10.7814i	−0.285907	−	0.495205i
$475$	3.24401			0.148845
$476$	10.9114	−	3.24378i	0.500125	−	0.148678i
$477$	−60.0668			−2.75027
$478$	−5.70246	−	9.87694i	−0.260824	−	0.451761i
$479$	−9.35783	+	16.2082i	−0.427570	+	0.740573i	−0.996657	−	0.0817046i	$-0.973964\pi$
$479$	−9.35783	+	16.2082i	−0.427570	+	0.740573i	0.569087	+	0.822278i	$0.307297\pi$
$480$	−12.6898	+	21.9795i	−0.579209	+	1.00322i
$481$	3.16665	+	5.48479i	0.144387	+	0.250085i
$482$	4.67899			0.213122
$483$	−4.00026	+	16.7347i	−0.182018	+	0.761454i
$484$	3.22567			0.146621
$485$	−9.47417	−	16.4098i	−0.430200	−	0.745128i
$486$	35.6846	−	61.8076i	1.61869	−	2.80365i
$487$	−1.77309	+	3.07108i	−0.0803464	+	0.139164i	−0.903399	−	0.428801i	$-0.858936\pi$
$487$	−1.77309	+	3.07108i	−0.0803464	+	0.139164i	0.823052	+	0.567966i	$0.192269\pi$
$488$	−0.685831	−	1.18789i	−0.0310461	−	0.0537734i
$489$	12.9065			0.583650
$490$	−11.5330	+	7.52189i	−0.521008	+	0.339804i
$491$	8.00137			0.361097			0.180548	−	0.983566i	$-0.442213\pi$
$491$	8.00137			0.361097			0.180548	+	0.983566i	$0.442213\pi$
$492$	28.8862	+	50.0323i	1.30229	+	2.25563i
$493$	10.8998	−	18.8790i	0.490903	−	0.850269i
$494$	−20.2064	+	34.9986i	−0.909131	+	1.57466i
$495$	13.3675	+	23.1532i	0.600826	+	1.04066i
$496$	29.9092			1.34296
$497$	−6.72008	+	28.1128i	−0.301437	+	1.26103i
$498$	−61.5488			−2.75807
$499$	−7.81355	−	13.5335i	−0.349782	−	0.605841i	0.636428	−	0.771336i	$-0.280411\pi$
$499$	−7.81355	−	13.5335i	−0.349782	−	0.605841i	−0.986211	+	0.165495i	$0.947078\pi$
$500$	−0.934584	+	1.61875i	−0.0417959	+	0.0723926i
$501$	20.3485	−	35.2446i	0.909103	−	1.57461i
$502$	−6.46406	−	11.1961i	−0.288505	−	0.499705i
$503$	25.7276			1.14714			0.573568	−	0.819158i	$-0.305559\pi$
$503$	25.7276			1.14714			0.573568	+	0.819158i	$0.305559\pi$
$504$	−4.89128	+	1.45409i	−0.217875	+	0.0647704i
$505$	−6.46394			−0.287642
$506$	7.04328	+	12.1993i	0.313112	+	0.542326i
$507$	−43.9125	+	76.0587i	−1.95022	+	3.37789i
$508$	19.9959	−	34.6339i	0.887173	−	1.53663i
$509$	−9.45772	−	16.3813i	−0.419206	−	0.726087i	0.576654	−	0.816989i	$-0.304358\pi$
$509$	−9.45772	−	16.3813i	−0.419206	−	0.726087i	−0.995860	+	0.0909022i	$0.971025\pi$
$510$	14.6677			0.649498
$511$	21.0561	+	19.9422i	0.931467	+	0.882191i
$512$	−31.0689			−1.37306
$513$	−23.6161	−	40.9043i	−1.04268	−	1.80597i
$514$	2.48164	−	4.29833i	0.109461	−	0.189591i
$515$	0.172992	−	0.299630i	0.00762292	−	0.0132033i
$516$	15.4218	+	26.7113i	0.678907	+	1.17590i
$517$	−0.835307			−0.0367368
$518$	−3.77854	−	3.57866i	−0.166020	−	0.157237i
$519$	−79.0984			−3.47203
$520$	0.814934	+	1.41151i	0.0357372	+	0.0618987i
$521$	16.7068	−	28.9370i	0.731938	−	1.26775i	−0.224116	−	0.974562i	$-0.571950\pi$
$521$	16.7068	−	28.9370i	0.731938	−	1.26775i	0.956054	−	0.293191i	$-0.0947171\pi$
$522$	69.8061	−	120.908i	3.05533	−	5.29199i
$523$	11.4936	+	19.9076i	0.502582	+	0.870497i	0.999996	+	0.00298387i	$0.000949795\pi$
$523$	11.4936	+	19.9076i	0.502582	+	0.870497i	−0.497414	+	0.867513i	$0.665717\pi$
$524$	−20.6011			−0.899964
$525$	−8.21560	+	2.44235i	−0.358558	+	0.106593i
$526$	8.50001			0.370618
$527$	−8.10994	−	14.0468i	−0.353275	−	0.611889i
$528$	−24.5258	+	42.4799i	−1.06735	+	1.84870i
$529$	9.48498	−	16.4285i	0.412390	−	0.714281i
$530$	−7.88267	−	13.6532i	−0.342401	−	0.593056i
$531$	−80.9281			−3.51198
$532$	3.72978	−	15.6032i	0.161706	−	0.676483i
$533$	60.4256			2.61732
$534$	31.1941	+	54.0299i	1.34990	+	2.33810i
$535$	1.12998	−	1.95718i	0.0488532	−	0.0846163i
$536$	0.441614	−	0.764897i	0.0190748	−	0.0330385i
$537$	5.77860	+	10.0088i	0.249365	+	0.431913i
$538$	20.5309			0.885149
$539$	−20.9158	+	13.6414i	−0.900909	+	0.587577i
$540$	27.2148			1.17114
$541$	0.0740345	+	0.128232i	0.00318299	+	0.00551311i	0.867613	−	0.497241i	$-0.165653\pi$
$541$	0.0740345	+	0.128232i	0.00318299	+	0.00551311i	−0.864430	+	0.502754i	$0.832320\pi$
$542$	−28.9426	+	50.1301i	−1.24319	+	2.15327i
$543$	−33.0219	+	57.1956i	−1.41710	+	2.45450i
$544$	9.01676	+	15.6175i	0.386590	+	0.669594i
$545$	−4.04109			−0.173101
$546$	24.8240	−	103.849i	1.06237	−	4.44431i
$547$	−31.7066			−1.35568			−0.677839	−	0.735210i	$-0.737083\pi$
$547$	−31.7066			−1.35568			−0.677839	+	0.735210i	$0.737083\pi$
$548$	0.558225	+	0.966874i	0.0238462	+	0.0413028i
$549$	−19.9726	+	34.5935i	−0.852409	+	1.47641i
$550$	−3.50849	+	6.07688i	−0.149602	+	0.259119i
$551$	−15.3613	−	26.6065i	−0.654411	−	1.13347i
$552$	−1.67362			−0.0712342
$553$	4.95466	−	1.47293i	0.210694	−	0.0626355i
$554$	21.4134			0.909767
$555$	−1.61976	−	2.80550i	−0.0687549	−	0.119087i
$556$	18.8476	−	32.6450i	0.799317	−	1.38446i
$557$	−6.00727	+	10.4049i	−0.254536	+	0.440869i	−0.964769	−	0.263097i	$-0.915256\pi$
$557$	−6.00727	+	10.4049i	−0.254536	+	0.440869i	0.710233	+	0.703966i	$0.248589\pi$
$558$	−51.9388	−	89.9607i	−2.19875	−	3.80834i
$559$	32.2601			1.36446
$560$	−8.15356	−	7.72223i	−0.344551	−	0.326324i
$561$	26.6008			1.12309
$562$	−8.72551	−	15.1130i	−0.368063	−	0.637504i
$563$	−2.70123	+	4.67866i	−0.113843	+	0.197182i	−0.917317	−	0.398158i	$-0.869649\pi$
$563$	−2.70123	+	4.67866i	−0.113843	+	0.197182i	0.803474	+	0.595340i	$0.202983\pi$
$564$	−0.708930	+	1.22790i	−0.0298513	+	0.0517040i
$565$	−1.34999	−	2.33824i	−0.0567943	−	0.0983706i
$566$	49.0443			2.06149
$567$	47.4157	+	44.9074i	1.99127	+	1.88593i
$568$	−2.81154			−0.117970
$569$	−0.828233	−	1.43454i	−0.0347213	−	0.0601391i	0.848143	−	0.529768i	$-0.177721\pi$
$569$	−0.828233	−	1.43454i	−0.0347213	−	0.0601391i	−0.882864	+	0.469629i	$0.844388\pi$
$570$	10.3357	−	17.9020i	0.432915	−	0.749832i
$571$	−4.68870	+	8.12107i	−0.196216	+	0.339856i	−0.947298	−	0.320352i	$-0.896199\pi$
$571$	−4.68870	+	8.12107i	−0.196216	+	0.339856i	0.751082	+	0.660208i	$0.229532\pi$
$572$	−21.1149	−	36.5721i	−0.882858	−	1.52916i
$573$	−44.8119			−1.87205
$574$	−47.5948	+	14.1491i	−1.98657	+	0.590573i
$575$	−2.00750			−0.0837184
$576$	25.9359	+	44.9222i	1.08066	+	1.87176i
$577$	8.04526	−	13.9348i	0.334928	−	0.580113i	−0.648543	−	0.761178i	$-0.724621\pi$
$577$	8.04526	−	13.9348i	0.334928	−	0.580113i	0.983471	+	0.181065i	$0.0579545\pi$
$578$	−11.5086	+	19.9335i	−0.478694	+	0.829123i
$579$	12.0620	+	20.8920i	0.501279	+	0.868241i
$580$	17.7020			0.735037
$581$	5.94133	−	24.8550i	0.246488	−	1.03116i
$582$	−120.742			−5.00494
$583$	−14.2957	−	24.7609i	−0.592068	−	1.02549i
$584$	−1.41044	+	2.44296i	−0.0583645	+	0.101090i
$585$	23.7323	−	41.1055i	0.981209	−	1.69950i
$586$	−2.23579	−	3.87250i	−0.0923596	−	0.159971i
$587$	−21.2890			−0.878690			−0.439345	−	0.898318i	$-0.644789\pi$
$587$	−21.2890			−0.878690			−0.439345	+	0.898318i	$0.644789\pi$
$588$	2.30150	+	42.3238i	0.0949123	+	1.74541i
$589$	−22.8589			−0.941884
$590$	−10.6203	−	18.3950i	−0.437232	−	0.757309i
$591$	−2.15604	+	3.73437i	−0.0886875	+	0.153611i
$592$	2.12227	−	3.67589i	0.0872249	−	0.151078i
$593$	0.396699	+	0.687102i	0.0162905	+	0.0282159i	0.874056	−	0.485826i	$-0.161481\pi$
$593$	0.396699	+	0.687102i	0.0162905	+	0.0282159i	−0.857765	+	0.514042i	$0.828148\pi$
$594$	102.166			4.19193
$595$	−1.41588	+	5.92321i	−0.0580455	+	0.242828i
$596$	38.2283			1.56589
$597$	−9.82706	−	17.0210i	−0.402195	−	0.696622i
$598$	12.5044	−	21.6583i	0.511343	−	0.885672i
$599$	−21.5597	+	37.3425i	−0.880905	+	1.52577i	−0.0305676	+	0.999533i	$0.509731\pi$
$599$	−21.5597	+	37.3425i	−0.880905	+	1.52577i	−0.850337	+	0.526239i	$0.823602\pi$
$600$	−0.416844	−	0.721994i	−0.0170176	−	0.0294753i
$601$	−44.8265			−1.82851			−0.914255	−	0.405140i	$-0.867223\pi$
$601$	−44.8265			−1.82851			−0.914255	+	0.405140i	$0.867223\pi$
$602$	−25.4100	+	7.55396i	−1.03564	+	0.307876i
$603$	−25.7211			−1.04744
$604$	17.7206	+	30.6930i	0.721042	+	1.24888i
$605$	−0.862863	+	1.49452i	−0.0350804	+	0.0607610i
$606$	−20.5947	+	35.6711i	−0.836604	+	1.44904i
$607$	−3.72353	−	6.44934i	−0.151133	−	0.261771i	0.780511	−	0.625142i	$-0.214959\pi$
$607$	−3.72353	−	6.44934i	−0.151133	−	0.261771i	−0.931644	+	0.363371i	$0.881626\pi$
$608$	25.4149			1.03071
$609$	58.9346	+	55.8169i	2.38815	+	2.26182i
$610$	−10.4841			−0.424490
$611$	0.741489	+	1.28430i	0.0299974	+	0.0519570i
$612$	16.1225	−	27.9250i	0.651714	−	1.12880i
$613$	−10.6158	+	18.3870i	−0.428766	+	0.742645i	−0.996764	−	0.0803853i	$-0.974385\pi$
$613$	−10.6158	+	18.3870i	−0.428766	+	0.742645i	0.567998	+	0.823030i	$0.307718\pi$
$614$	−1.59372	−	2.76040i	−0.0643172	−	0.111401i
$615$	−30.9081			−1.24633
$616$	−1.76352	−	1.67023i	−0.0710542	−	0.0672954i
$617$	6.95318			0.279924			0.139962	−	0.990157i	$-0.455302\pi$
$617$	6.95318			0.279924			0.139962	+	0.990157i	$0.455302\pi$
$618$	−1.10233	−	1.90930i	−0.0443424	−	0.0768033i
$619$	23.9455	−	41.4748i	0.962450	−	1.66701i	0.246135	−	0.969236i	$-0.420839\pi$
$619$	23.9455	−	41.4748i	0.962450	−	1.66701i	0.716315	−	0.697777i	$-0.245827\pi$
$620$	6.58554	−	11.4065i	0.264482	−	0.458096i
$621$	14.6144	+	25.3129i	0.586457	+	1.01577i
$622$	−16.3982			−0.657509
$623$	−24.8298	+	7.38147i	−0.994786	+	0.295733i
$624$	87.0845			3.48617
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.3035	−	17.8461i	0.411809	−	0.713274i
$627$	18.7445	−	32.4664i	0.748582	−	1.29658i
$628$	6.74723	+	11.6865i	0.269244	+	0.466344i
$629$	−2.30184			−0.0917802
$630$	−9.06780	+	37.9343i	−0.361270	+	1.51134i
$631$	10.8564			0.432185			0.216092	−	0.976373i	$-0.430669\pi$
$631$	10.8564			0.432185			0.216092	+	0.976373i	$0.430669\pi$
$632$	0.251390	+	0.435420i	0.00999975	+	0.0173201i
$633$	17.2138	−	29.8152i	0.684189	−	1.18505i
$634$	17.4350	−	30.1984i	0.692434	−	1.19933i
$635$	10.6977	+	18.5290i	0.424527	+	0.735302i
$636$	−48.5314			−1.92439
$637$	39.5405	+	20.0491i	1.56665	+	0.794375i
$638$	66.4546			2.63096
$639$	40.9384	+	70.9075i	1.61950	+	2.80506i
$640$	1.02720	−	1.77915i	0.0406035	−	0.0703272i
$641$	11.5721	−	20.0434i	0.457069	−	0.791667i	−0.541736	−	0.840549i	$-0.682233\pi$
$641$	11.5721	−	20.0434i	0.457069	−	0.791667i	0.998805	+	0.0488823i	$0.0155659\pi$
$642$	−7.20044	−	12.4715i	−0.284179	−	0.492212i
$643$	18.9522			0.747403			0.373701	−	0.927549i	$-0.378088\pi$
$643$	18.9522			0.747403			0.373701	+	0.927549i	$0.378088\pi$
$644$	−2.30811	+	9.65575i	−0.0909522	+	0.380490i
$645$	−16.5013			−0.649736
$646$	−7.34404	−	12.7202i	−0.288947	−	0.500471i
$647$	8.48391	−	14.6946i	0.333537	−	0.577703i	−0.649666	−	0.760220i	$-0.725091\pi$
$647$	8.48391	−	14.6946i	0.333537	−	0.577703i	0.983203	+	0.182517i	$0.0584244\pi$
$648$	−3.17614	+	5.50124i	−0.124771	+	0.216109i
$649$	−19.2606	−	33.3604i	−0.756046	−	1.30951i
$650$	12.4577			0.488632
$651$	57.8912	−	17.2100i	2.26894	−	0.674515i
$652$	7.44690			0.291643
$653$	11.0360	+	19.1150i	0.431873	+	0.748026i	0.997035	−	0.0769540i	$-0.0245195\pi$
$653$	11.0360	+	19.1150i	0.431873	+	0.748026i	−0.565161	+	0.824980i	$0.691186\pi$
$654$	−12.8753	+	22.3007i	−0.503464	+	0.872024i
$655$	5.51077	−	9.54494i	0.215324	−	0.372952i
$656$	−20.2485	−	35.0715i	−0.790572	−	1.36931i
$657$	82.1490			3.20494
$658$	−0.884768	−	0.837963i	−0.0344919	−	0.0326672i
$659$	23.0232			0.896858			0.448429	−	0.893818i	$-0.351984\pi$
$659$	23.0232			0.896858			0.448429	+	0.893818i	$0.351984\pi$
$660$	10.8004	+	18.7068i	0.420405	+	0.728162i
$661$	3.87977	−	6.71996i	0.150906	−	0.261376i	−0.780655	−	0.624962i	$-0.785114\pi$
$661$	3.87977	−	6.71996i	0.150906	−	0.261376i	0.931561	+	0.363586i	$0.118448\pi$
$662$	6.60223	−	11.4354i	0.256603	−	0.444449i
$663$	−23.6131	−	40.8991i	−0.917058	−	1.58839i
$664$	2.48573			0.0964650
$665$	6.23157	+	5.90192i	0.241650	+	0.228866i
$666$	−14.7417			−0.571231
$667$	9.50604	+	16.4649i	0.368075	+	0.637525i
$668$	11.7409	−	20.3358i	0.454268	−	0.786816i
$669$	8.96291	−	15.5242i	0.346526	−	0.600201i
$670$	−3.37542	−	5.84640i	−0.130404	−	0.225866i
$671$	−19.0136			−0.734013
$672$	−64.3644	+	19.1344i	−2.48291	+	0.738126i
$673$	29.3726			1.13223			0.566116	−	0.824326i	$-0.308446\pi$
$673$	29.3726			1.13223			0.566116	+	0.824326i	$0.308446\pi$
$674$	−8.53603	−	14.7848i	−0.328796	−	0.569491i
$675$	−7.27992	+	12.6092i	−0.280204	+	0.485328i
$676$	−25.3371	+	43.8851i	−0.974504	+	1.68789i
$677$	−17.9378	−	31.0693i	−0.689407	−	1.19409i	−0.972030	−	0.234857i	$-0.924538\pi$
$677$	−17.9378	−	31.0693i	−0.689407	−	1.19409i	0.282622	−	0.959231i	$-0.408796\pi$
$678$	−17.2047			−0.660743
$679$	11.6553	−	48.7589i	0.447290	−	1.87120i
$680$	−0.592376			−0.0227166
$681$	−12.0065	−	20.7959i	−0.460091	−	0.796900i
$682$	24.7226	−	42.8207i	0.946676	−	1.63969i
$683$	1.14850	−	1.98926i	0.0439461	−	0.0761170i	−0.843216	−	0.537575i	$-0.819340\pi$
$683$	1.14850	−	1.98926i	0.0439461	−	0.0761170i	0.887162	+	0.461458i	$0.152674\pi$
$684$	−22.7217	−	39.3551i	−0.868785	−	1.50478i
$685$	−0.597298			−0.0228216
$686$	−35.8391	−	6.53318i	−1.36834	−	0.249438i
$687$	−54.6244			−2.08405
$688$	−10.8103	−	18.7240i	−0.412139	−	0.713846i
$689$	−25.3801	+	43.9597i	−0.966906	+	1.67473i
$690$	−6.39607	+	11.0783i	−0.243494	+	0.421745i
$691$	−2.40001	−	4.15695i	−0.0913008	−	0.158138i	0.816758	−	0.576981i	$-0.195769\pi$
$691$	−2.40001	−	4.15695i	−0.0913008	−	0.158138i	−0.908059	+	0.418843i	$0.862436\pi$
$692$	−45.6390			−1.73493
$693$	−16.4450	+	68.7961i	−0.624695	+	2.61335i
$694$	−18.0208			−0.684059
$695$	10.0834	+	17.4650i	0.382486	+	0.662486i
$696$	−3.94774	+	6.83768i	−0.149639	+	0.259182i
$697$	−10.9809	+	19.0194i	−0.415929	+	0.720411i
$698$	25.1372	+	43.5388i	0.951455	+	1.64797i
$699$	−9.25813			−0.350175
$700$	−4.74032	+	1.40921i	−0.179167	+	0.0532633i
$701$	−5.38502			−0.203389			−0.101695	−	0.994816i	$-0.532426\pi$
$701$	−5.38502			−0.203389			−0.101695	+	0.994816i	$0.532426\pi$
$702$	−90.6912	−	157.082i	−3.42292	−	5.92867i
$703$	−1.62200	+	2.80939i	−0.0611750	+	0.105958i
$704$	−12.3453	+	21.3827i	−0.465281	+	0.805891i
$705$	−0.379276	−	0.656925i	−0.0142843	−	0.0247412i
$706$	−52.1894			−1.96417
$707$	−12.4169	−	11.7600i	−0.466986	−	0.442282i
$708$	−65.3864			−2.45737
$709$	8.79156	+	15.2274i	0.330174	+	0.571878i	0.982546	−	0.186021i	$-0.0595592\pi$
$709$	8.79156	+	15.2274i	0.330174	+	0.571878i	−0.652372	+	0.757899i	$0.726226\pi$
$710$	−10.7448	+	18.6106i	−0.403247	+	0.698444i
$711$	7.32090	−	12.6802i	0.274555	−	0.475544i
$712$	−1.25982	−	2.18207i	−0.0472137	−	0.0817765i
$713$	14.1458			0.529765
$714$	28.1760	+	26.6854i	1.05446	+	0.998677i
$715$	22.5928			0.844924
$716$	3.33420	+	5.77500i	0.124605	+	0.215822i
$717$	9.39146	−	16.2665i	0.350730	−	0.607483i
$718$	1.63176	−	2.82629i	0.0608967	−	0.105476i
$719$	−13.1402	−	22.7596i	−0.490048	−	0.848788i	0.509886	−	0.860242i	$-0.329688\pi$
$719$	−13.1402	−	22.7596i	−0.490048	−	0.848788i	−0.999934	+	0.0114535i	$0.996354\pi$
$720$	−31.8106			−1.18551
$721$	0.877433	−	0.260846i	0.0326773	−	0.00971440i
$722$	16.6733			0.620515
$723$	3.85295	+	6.67350i	0.143293	+	0.248190i
$724$	−19.0533	+	33.0013i	−0.708110	+	1.22648i
$725$	−4.73527	+	8.20173i	−0.175864	+	0.304605i
$726$	5.49833	+	9.52338i	0.204062	+	0.353446i
$727$	8.27982			0.307082			0.153541	−	0.988142i	$-0.450932\pi$
$727$	8.27982			0.307082			0.153541	+	0.988142i	$0.450932\pi$
$728$	−1.00255	+	4.19407i	−0.0371569	+	0.155442i
$729$	43.4887			1.61069
$730$	10.7805	+	18.6725i	0.399006	+	0.691099i
$731$	−5.86248	+	10.1541i	−0.216832	+	0.375563i
$732$	−16.1370	+	27.9501i	−0.596440	+	1.03306i
$733$	7.73742	+	13.4016i	0.285788	+	0.495000i	0.972800	−	0.231646i	$-0.0744112\pi$
$733$	7.73742	+	13.4016i	0.285788	+	0.495000i	−0.687012	+	0.726646i	$0.741078\pi$
$734$	13.3849			0.494046
$735$	−20.2252	−	10.2552i	−0.746017	−	0.378270i
$736$	−15.7276			−0.579725
$737$	−6.12154	−	10.6028i	−0.225490	−	0.390560i
$738$	−70.3251	+	121.807i	−2.58870	+	4.48377i
$739$	23.5418	−	40.7757i	0.866001	−	1.49996i	−4.89876e−5	−	1.00000i	$-0.500016\pi$
$739$	23.5418	−	40.7757i	0.866001	−	1.49996i	0.866050	−	0.499958i	$-0.166651\pi$
$740$	−0.934584	−	1.61875i	−0.0343560	−	0.0595063i
$741$	−66.5566			−2.44502
$742$	9.69742	−	40.5682i	0.356004	−	1.48931i
$743$	5.40873			0.198427			0.0992136	−	0.995066i	$-0.468367\pi$
$743$	5.40873			0.198427			0.0992136	+	0.995066i	$0.468367\pi$
$744$	2.93729	+	5.08753i	0.107686	+	0.186518i
$745$	−10.2260	+	17.7120i	−0.374652	+	0.648917i
$746$	−13.7784	+	23.8649i	−0.504464	+	0.873757i
$747$	−36.1943	−	62.6904i	−1.32428	−	2.29372i
$748$	15.3484			0.561194
$749$	5.73139	−	1.70384i	0.209420	−	0.0622570i
$750$	−6.37219			−0.232679
$751$	8.63112	+	14.9495i	0.314954	+	0.545516i	0.979428	−	0.201795i	$-0.0646776\pi$
$751$	8.63112	+	14.9495i	0.314954	+	0.545516i	−0.664474	+	0.747312i	$0.731344\pi$
$752$	0.496943	−	0.860730i	0.0181216	−	0.0313876i
$753$	10.6458	−	18.4390i	0.387953	−	0.671954i
$754$	−58.9906	−	102.175i	−2.14831	−	3.72099i
$755$	−18.9610			−0.690061
$756$	52.2782	+	49.5127i	1.90134	+	1.80076i
$757$	21.2594			0.772685			0.386343	−	0.922355i	$-0.373738\pi$
$757$	21.2594			0.772685			0.386343	+	0.922355i	$0.373738\pi$
$758$	1.02625	+	1.77751i	0.0372750	+	0.0645622i
$759$	−11.5997	+	20.0912i	−0.421042	+	0.729266i
$760$	−0.417422	+	0.722996i	−0.0151415	+	0.0262258i
$761$	5.98220	+	10.3615i	0.216855	+	0.375603i	0.953845	−	0.300300i	$-0.0970869\pi$
$761$	5.98220	+	10.3615i	0.216855	+	0.375603i	−0.736990	+	0.675904i	$0.763754\pi$
$762$	136.336			4.93893
$763$	−7.76272	−	7.35206i	−0.281029	−	0.266163i
$764$	−25.8560			−0.935439
$765$	8.62550	+	14.9398i	0.311856	+	0.540150i
$766$	11.5399	−	19.9878i	0.416955	−	0.722187i
$767$	−34.1947	+	59.2270i	−1.23470	+	2.13856i
$768$	−28.9673	−	50.1728i	−1.04527	−	1.81046i
$769$	24.0583			0.867566			0.433783	−	0.901017i	$-0.357178\pi$
$769$	24.0583			0.867566			0.433783	+	0.901017i	$0.357178\pi$
$770$	−17.7955	+	5.29028i	−0.641304	+	0.190649i
$771$	8.17411			0.294384
$772$	6.95965	+	12.0545i	0.250483	+	0.433850i
$773$	−14.1727	+	24.5478i	−0.509757	+	0.882925i	0.490179	+	0.871622i	$0.336931\pi$
$773$	−14.1727	+	24.5478i	−0.509757	+	0.882925i	−0.999936	+	0.0113030i	$0.996402\pi$
$774$	−37.5453	+	65.0304i	−1.34954	+	2.33747i
$775$	3.52325	+	6.10245i	0.126559	+	0.219206i
$776$	4.87635			0.175051
$777$	1.99266	−	8.33610i	0.0714863	−	0.299056i
$778$	6.28661			0.225386
$779$	15.4755	+	26.8043i	0.554466	+	0.960363i
$780$	19.1747	−	33.2115i	0.686563	−	1.18916i
$781$	−19.4864	+	33.7515i	−0.697280	+	1.20772i
$782$	4.54473	+	7.87170i	0.162519	+	0.281491i
$783$	137.890			4.92778
$784$	−1.61330	−	29.6680i	−0.0576178	−	1.05957i
$785$	−7.21950			−0.257675
$786$	−35.1157	−	60.8222i	−1.25254	−	2.16945i
$787$	−2.06663	+	3.57951i	−0.0736675	+	0.127596i	−0.900506	−	0.434843i	$-0.856804\pi$
$787$	−2.06663	+	3.57951i	−0.0736675	+	0.127596i	0.826839	+	0.562439i	$0.190137\pi$
$788$	−1.24401	+	2.15469i	−0.0443161	+	0.0767578i
$789$	6.99940	+	12.1233i	0.249185	+	0.431601i
$790$	3.84294			0.136726
$791$	1.66078	−	6.94771i	0.0590505	−	0.247032i
$792$	−6.88025			−0.244479
$793$	16.8781	+	29.2337i	0.599359	+	1.03812i
$794$	0.215439	−	0.373152i	0.00764565	−	0.0132427i
$795$	12.9821	−	22.4856i	0.460427	−	0.797483i
$796$	−5.67012	−	9.82093i	−0.200972	−	0.348094i
$797$	26.3553			0.933554			0.466777	−	0.884375i	$-0.345415\pi$
$797$	26.3553			0.933554			0.466777	+	0.884375i	$0.345415\pi$
$798$	52.4240	−	15.5847i	1.85579	−	0.551693i
$799$	−0.538988			−0.0190680
$800$	−3.91721	−	6.78480i	−0.138494	−	0.239879i
$801$	−36.6880	+	63.5455i	−1.29631	+	2.24527i
$802$	7.92080	−	13.7192i	0.279693	−	0.484443i
$803$	19.5512	+	33.8637i	0.689947	+	1.19502i
$804$	−20.7815			−0.732908
$805$	−3.85630	−	3.65230i	−0.135917	−	0.128727i
$806$	−87.7832			−3.09203
$807$	16.9063	+	29.2826i	0.595130	+	1.03080i
$808$	0.831746	−	1.44063i	0.0292607	−	0.0506810i
$809$	−8.81945	+	15.2757i	−0.310075	+	0.537066i	−0.978378	−	0.206823i	$-0.933688\pi$
$809$	−8.81945	+	15.2757i	−0.310075	+	0.537066i	0.668303	+	0.743889i	$0.267021\pi$
$810$	24.2765	+	42.0480i	0.852988	+	1.47742i
$811$	21.5918			0.758191			0.379096	−	0.925357i	$-0.376235\pi$
$811$	21.5918			0.758191			0.379096	+	0.925357i	$0.376235\pi$
$812$	34.0047	+	32.2058i	1.19333	+	1.13020i
$813$	−95.3321			−3.34344
$814$	−3.50849	−	6.07688i	−0.122972	−	0.212995i
$815$	−1.99204	+	3.45031i	−0.0697780	+	0.120859i
$816$	−15.8254	+	27.4105i	−0.554001	+	0.959558i
$817$	8.26207	+	14.3103i	0.289053	+	0.500655i
$818$	−47.9220			−1.67555
$819$	120.373	−	35.7848i	4.20617	−	1.25042i
$820$	−17.8336			−0.622778
$821$	0.854442	+	1.47994i	0.0298202	+	0.0516502i	0.880550	−	0.473953i	$-0.157173\pi$
$821$	0.854442	+	1.47994i	0.0298202	+	0.0516502i	−0.850730	+	0.525603i	$0.823840\pi$
$822$	−1.90305	+	3.29617i	−0.0663764	+	0.114967i
$823$	4.69906	−	8.13900i	0.163799	−	0.283708i	−0.772429	−	0.635101i	$-0.780959\pi$
$823$	4.69906	−	8.13900i	0.163799	−	0.283708i	0.936228	+	0.351393i	$0.114292\pi$
$824$	0.0445193	+	0.0771096i	0.00155090	+	0.00268624i
$825$	−11.5564			−0.402341
$826$	13.0654	−	54.6577i	0.454602	−	1.90178i
$827$	42.3517			1.47271			0.736357	−	0.676593i	$-0.236544\pi$
$827$	42.3517			1.47271			0.736357	+	0.676593i	$0.236544\pi$
$828$	14.0609	+	24.3542i	0.488650	+	0.846367i
$829$	−15.0470	+	26.0621i	−0.522603	+	0.905175i	0.477051	+	0.878876i	$0.341706\pi$
$829$	−15.0470	+	26.0621i	−0.522603	+	0.905175i	−0.999654	+	0.0262994i	$0.991628\pi$
$830$	9.49969	−	16.4539i	0.329739	−	0.571125i
$831$	17.6330	+	30.5412i	0.611682	+	1.05946i
$832$	43.8349			1.51970
$833$	−13.4961	+	8.80222i	−0.467612	+	0.304979i
$834$	128.507			4.44984
$835$	6.28134	+	10.8796i	0.217375	+	0.376504i
$836$	10.8154	−	18.7328i	0.374057	−	0.647886i
$837$	51.2980	−	88.8507i	1.77312	−	3.07113i
$838$	14.5176	+	25.1452i	0.501501	+	0.868625i
$839$	47.1325			1.62720			0.813598	−	0.581428i	$-0.197506\pi$
$839$	47.1325			1.62720			0.813598	+	0.581428i	$0.197506\pi$
$840$	0.512810	−	2.14529i	0.0176936	−	0.0740195i
$841$	60.6912			2.09280
$842$	19.1117	+	33.1024i	0.658632	+	1.14078i
$843$	14.3702	−	24.8899i	0.494935	−	0.857252i
$844$	9.93222	−	17.2031i	0.341881	−	0.592155i
$845$	−13.5553	−	23.4784i	−0.466316	−	0.807683i
$846$	−3.45187			−0.118678
$847$	−4.37654	+	1.30107i	−0.150380	+	0.0447053i
$848$	34.0193			1.16823
$849$	40.3859	+	69.9504i	1.38604	+	2.40069i
$850$	−2.26388	+	3.92115i	−0.0776504	+	0.134494i
$851$	1.00375	−	1.73854i	0.0344080	−	0.0595965i
$852$	33.0765	+	57.2902i	1.13318	+	1.96273i
$853$	52.5939			1.80078			0.900390	−	0.435084i	$-0.143281\pi$
$853$	52.5939			1.80078			0.900390	+	0.435084i	$0.143281\pi$
$854$	−20.1395	−	19.0741i	−0.689159	−	0.652702i
$855$	24.3121			0.831455
$856$	0.290799	+	0.503679i	0.00993932	+	0.0172154i
$857$	−23.2040	+	40.1905i	−0.792633	+	1.37288i	0.131698	+	0.991290i	$0.457957\pi$
$857$	−23.2040	+	40.1905i	−0.792633	+	1.37288i	−0.924331	+	0.381591i	$0.875376\pi$
$858$	71.9829	−	124.678i	2.45746	−	4.25644i
$859$	−16.0660	−	27.8272i	−0.548166	−	0.949452i	−0.998400	−	0.0565412i	$-0.981993\pi$
$859$	−16.0660	−	27.8272i	−0.548166	−	0.949452i	0.450234	−	0.892911i	$-0.351341\pi$
$860$	−9.52106			−0.324665
$861$	−59.3728	−	56.2319i	−2.02342	−	1.91638i
$862$	−70.1993			−2.39100
$863$	−13.2713	−	22.9865i	−0.451759	−	0.782469i	0.546737	−	0.837305i	$-0.315870\pi$
$863$	−13.2713	−	22.9865i	−0.451759	−	0.782469i	−0.998495	+	0.0548356i	$0.982537\pi$
$864$	−57.0339	+	98.7856i	−1.94033	+	3.36076i
$865$	12.2084	−	21.1455i	0.415097	−	0.718969i
$866$	29.7924	+	51.6020i	1.01239	+	1.75351i
$867$	−37.9074			−1.28740
$868$	33.4027	−	9.93003i	1.13376	−	0.337047i
$869$	6.96941			0.236421
$870$	30.1740	+	52.2630i	1.02300	+	1.77188i
$871$	−10.8680	+	18.8239i	−0.368247	+	0.637823i
$872$	0.519986	−	0.900642i	0.0176089	−	0.0304996i
$873$	−71.0038	−	122.982i	−2.40311	−	4.16231i
$874$	12.8099			0.433301
$875$	0.615110	−	2.57325i	0.0207945	−	0.0869919i
$876$	66.3728			2.24253
$877$	13.4280	+	23.2580i	0.453431	+	0.785365i	0.998596	−	0.0529630i	$-0.0168665\pi$
$877$	13.4280	+	23.2580i	0.453431	+	0.785365i	−0.545166	+	0.838328i	$0.683533\pi$
$878$	−6.60667	+	11.4431i	−0.222964	+	0.386185i
$879$	3.68215	−	6.37768i	0.124196	−	0.215114i
$880$	−7.57082	−	13.1130i	−0.255212	−	0.442040i
$881$	9.03418			0.304369			0.152185	−	0.988352i	$-0.451369\pi$
$881$	9.03418			0.304369			0.152185	+	0.988352i	$0.451369\pi$
$882$	−86.4336	+	56.3724i	−2.91037	+	1.89816i
$883$	14.7310			0.495739			0.247869	−	0.968793i	$-0.420270\pi$
$883$	14.7310			0.495739			0.247869	+	0.968793i	$0.420270\pi$
$884$	−13.6245	−	23.5984i	−0.458243	−	0.793700i
$885$	17.4908	−	30.2949i	0.587946	−	1.01835i
$886$	10.0649	−	17.4329i	0.338137	−	0.585670i
$887$	1.89655	+	3.28492i	0.0636799	+	0.110297i	0.896108	−	0.443837i	$-0.146383\pi$
$887$	1.89655	+	3.28492i	0.0636799	+	0.110297i	−0.832428	+	0.554134i	$0.813050\pi$
$888$	0.833687			0.0279767
$889$	−13.1606	+	55.0560i	−0.441392	+	1.84652i
$890$	−19.2585			−0.645548
$891$	44.0269	+	76.2568i	1.47496	+	2.55470i
$892$	5.17151	−	8.95732i	0.173155	−	0.299913i
$893$	−0.379802	+	0.657836i	−0.0127096	+	0.0220136i
$894$	65.1621	+	112.864i	2.17935	+	3.77474i
$895$	−3.56757			−0.119251
$896$	5.21006	−	1.54886i	0.174056	−	0.0517437i
$897$	41.1874			1.37521
$898$	−20.2379	−	35.0531i	−0.675347	−	1.16974i
$899$	33.3671	−	57.7935i	1.11285	−	1.92752i
$900$	−7.00420	+	12.1316i	−0.233473	+	0.404387i
$901$	−9.22441	−	15.9772i	−0.307310	−	0.532276i
$902$	−66.9487			−2.22915
$903$	−31.6981	−	30.0212i	−1.05485	−	0.999043i
$904$	0.694836			0.0231099
$905$	−10.1935	−	17.6556i	−0.338842	−	0.586892i
$906$	−60.4115	+	104.636i	−2.00704	+	3.47629i
$907$	19.5388	−	33.8422i	0.648775	−	1.12371i	−0.334641	−	0.942346i	$-0.608615\pi$
$907$	19.5388	−	33.8422i	0.648775	−	1.12371i	0.983416	−	0.181366i	$-0.0580518\pi$
$908$	−6.92764	−	11.9990i	−0.229902	−	0.398202i
$909$	−48.4437			−1.60678
$910$	23.9306	+	22.6647i	0.793292	+	0.751326i
$911$	−49.6251			−1.64415			−0.822076	−	0.569378i	$-0.807184\pi$
$911$	−49.6251			−1.64415			−0.822076	+	0.569378i	$0.807184\pi$
$912$	22.3030	+	38.6299i	0.738526	+	1.27916i
$913$	17.2283	−	29.8403i	0.570173	−	0.987568i
$914$	−1.04171	+	1.80429i	−0.0344566	+	0.0596806i
$915$	−8.63324	−	14.9532i	−0.285406	−	0.494338i
$916$	−31.5177			−1.04138
$917$	27.9513	−	8.30943i	0.923033	−	0.274402i
$918$	65.9234			2.17580
$919$	27.4122	+	47.4793i	0.904245	+	1.56620i	0.821928	+	0.569592i	$0.192899\pi$
$919$	27.4122	+	47.4793i	0.904245	+	1.56620i	0.0823169	+	0.996606i	$0.473768\pi$
$920$	0.258314	−	0.447413i	0.00851636	−	0.0147508i
$921$	2.62472	−	4.54614i	0.0864874	−	0.149801i
$922$	−26.0306	−	45.0863i	−0.857272	−	1.48484i
$923$	69.1912			2.27745
$924$	−13.2869	+	55.5843i	−0.437106	+	1.82859i
$925$	1.00000			0.0328798
$926$	−12.1431	−	21.0324i	−0.399046	−	0.691169i
$927$	1.29648	−	2.24556i	0.0425819	−	0.0737540i
$928$	−37.0981	+	64.2557i	−1.21780	+	2.10930i
$929$	3.31197	+	5.73650i	0.108662	+	0.188208i	0.915229	−	0.402935i	$-0.132010\pi$
$929$	3.31197	+	5.73650i	0.108662	+	0.188208i	−0.806566	+	0.591144i	$0.798677\pi$
$930$	44.9016			1.47238
$931$	1.23300	+	22.6746i	0.0404101	+	0.743128i
$932$	−5.34185			−0.174978
$933$	−13.5032	−	23.3883i	−0.442076	−	0.765699i
$934$	10.1323	−	17.5497i	0.331541	−	0.574245i
$935$	−4.10568	+	7.11125i	−0.134270	+	0.232563i
$936$	6.10749	+	10.5785i	0.199629	+	0.345768i
$937$	−21.5436			−0.703799			−0.351899	−	0.936038i	$-0.614464\pi$
$937$	−21.5436			−0.703799			−0.351899	+	0.936038i	$0.614464\pi$
$938$	4.15251	−	17.3716i	0.135584	−	0.567204i
$939$	33.9378			1.10752
$940$	−0.218838	−	0.379039i	−0.00713772	−	0.0123629i
$941$	18.9000	−	32.7358i	0.616123	−	1.06716i	−0.374064	−	0.927403i	$-0.622036\pi$
$941$	18.9000	−	32.7358i	0.616123	−	1.06716i	0.990186	−	0.139753i	$-0.0446308\pi$
$942$	−23.0020	+	39.8407i	−0.749446	+	1.29808i
$943$	−9.57672	−	16.5874i	−0.311861	−	0.540159i
$944$	45.8343			1.49178
$945$	−36.9246	+	10.9770i	−1.20116	+	0.357083i
$946$	−35.7427			−1.16209
$947$	6.26643	+	10.8538i	0.203632	+	0.352700i	0.949696	−	0.313174i	$-0.101392\pi$
$947$	6.26643	+	10.8538i	0.203632	+	0.352700i	−0.746064	+	0.665874i	$0.768059\pi$
$948$	5.91497	−	10.2450i	0.192109	−	0.332743i
$949$	34.7105	−	60.1204i	1.12675	−	1.95159i
$950$	3.19051	+	5.52613i	0.103514	+	0.179291i
$951$	57.4280			1.86223
$952$	−1.13792	−	1.07773i	−0.0368803	−	0.0349293i
$953$	−11.3621			−0.368055			−0.184027	−	0.982921i	$-0.558914\pi$
$953$	−11.3621			−0.368055			−0.184027	+	0.982921i	$0.558914\pi$
$954$	−59.0763	−	102.323i	−1.91267	−	3.31283i
$955$	6.91646	−	11.9797i	0.223811	−	0.387653i
$956$	5.41878	−	9.38560i	0.175256	−	0.303552i
$957$	54.7225	+	94.7822i	1.76893	+	3.06387i
$958$	−36.8141			−1.18941
$959$	−1.14738	−	1.08668i	−0.0370508	−	0.0350907i
$960$	−22.4218			−0.723661
$961$	−9.32657	−	16.1541i	−0.300857	−	0.521100i
$962$	−6.22885	+	10.7887i	−0.200826	+	0.347841i
$963$	8.46857	−	14.6680i	0.272896	−	0.472670i
$964$	2.22311	+	3.85055i	0.0716017	+	0.124018i
$965$	−7.44679			−0.239721
$966$	−32.4416	+	9.64433i	−1.04379	+	0.310301i
$967$	−17.9505			−0.577250			−0.288625	−	0.957442i	$-0.593198\pi$
$967$	−17.9505			−0.577250			−0.288625	+	0.957442i	$0.593198\pi$
$968$	−0.222057	−	0.384615i	−0.00713719	−	0.0123620i
$969$	12.0950	−	20.9492i	0.388547	−	0.672984i
$970$	18.6359	−	32.2783i	0.598362	−	1.03639i
$971$	−2.34462	−	4.06101i	−0.0752426	−	0.130324i	0.825949	−	0.563745i	$-0.190640\pi$
$971$	−2.34462	−	4.06101i	−0.0752426	−	0.130324i	−0.901192	+	0.433421i	$0.857306\pi$
$972$	67.8189			2.17529
$973$	−12.4048	+	51.8945i	−0.397681	+	1.66366i
$974$	−6.97541			−0.223507
$975$	10.2584	+	17.7681i	0.328531	+	0.569033i
$976$	11.3116	−	19.5923i	0.362077	−	0.627135i
$977$	−14.4154	+	24.9682i	−0.461190	+	0.798804i	−0.999021	−	0.0442488i	$-0.985911\pi$
$977$	−14.4154	+	24.9682i	−0.461190	+	0.798804i	0.537831	+	0.843053i	$0.319244\pi$
$978$	12.6936	+	21.9860i	0.405898	+	0.703035i
$979$	−34.9266			−1.11626
$980$	−11.6697	−	5.91717i	−0.372776	−	0.189017i
$981$	−30.2857			−0.966949
$982$	7.86943	+	13.6302i	0.251123	+	0.434959i
$983$	−25.5429	+	44.2416i	−0.814693	+	1.41109i	0.0948559	+	0.995491i	$0.469761\pi$
$983$	−25.5429	+	44.2416i	−0.814693	+	1.41109i	−0.909548	+	0.415598i	$0.863572\pi$
$984$	3.97709	−	6.88851i	0.126785	−	0.219598i
$985$	−0.665543	−	1.15276i	−0.0212060	−	0.0367298i
$986$	42.8803			1.36559
$987$	0.466593	−	1.95195i	0.0148518	−	0.0621311i
$988$	−38.4025			−1.22175
$989$	−5.11283	−	8.85569i	−0.162579	−	0.281595i
$990$	−26.2942	+	45.5429i	−0.835685	+	1.44745i
$991$	−21.5862	+	37.3883i	−0.685707	+	1.18768i	0.287507	+	0.957779i	$0.407174\pi$
$991$	−21.5862	+	37.3883i	−0.685707	+	1.18768i	−0.973214	+	0.229901i	$0.926160\pi$
$992$	27.6026	+	47.8091i	0.876383	+	1.51794i
$993$	21.7466			0.690108
$994$	−54.4991	+	16.2016i	−1.72861	+	0.513885i
$995$	6.06700			0.192337
$996$	−29.2435	−	50.6512i	−0.926615	−	1.60494i
$997$	−13.4262	+	23.2548i	−0.425211	+	0.736487i	−0.996440	−	0.0843034i	$-0.973133\pi$
$997$	−13.4262	+	23.2548i	−0.425211	+	0.736487i	0.571229	+	0.820791i	$0.306467\pi$
$998$	15.3694	−	26.6206i	0.486510	−	0.842660i
$999$	−7.27992	−	12.6092i	−0.230327	−	0.398937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.186.16	✓	38
7.2	even	3	inner	1295.2.j.a.926.16	yes	38
7.3	odd	6		9065.2.a.s.1.4		19
7.4	even	3		9065.2.a.r.1.4		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.16	✓	38	1.1	even	1	trivial
1295.2.j.a.926.16	yes	38	7.2	even	3	inner
9065.2.a.r.1.4		19	7.4	even	3
9065.2.a.s.1.4		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+(0.983510 + 1.70349i) q^{2} +(-1.61976 + 2.80550i) q^{3} +(-0.934584 + 1.61875i) q^{4} +(-0.500000 - 0.866025i) q^{5} -6.37219 q^{6} +(0.615110 - 2.57325i) q^{7} +0.257349 q^{8} +(-3.74723 - 6.49039i) q^{9} +(0.983510 - 1.70349i) q^{10} +(1.78366 - 3.08938i) q^{11} +(-3.02760 - 5.24395i) q^{12} -6.33329 q^{13} +(4.98848 - 1.48299i) q^{14} +3.23951 q^{15} +(2.12227 + 3.67589i) q^{16} +(1.15092 - 1.99345i) q^{17} +(7.37087 - 12.7667i) q^{18} +(-1.62200 - 2.80939i) q^{19} +1.86917 q^{20} +(6.22294 + 5.89374i) q^{21} +7.01698 q^{22} +(1.00375 + 1.73854i) q^{23} +(-0.416844 + 0.721994i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-6.22885 - 10.7887i) q^{26} +14.5598 q^{27} +(3.59058 + 3.40063i) q^{28} +9.47054 q^{29} +(3.18609 + 5.51848i) q^{30} +(3.52325 - 6.10245i) q^{31} +(-3.91721 + 6.78480i) q^{32} +(5.77818 + 10.0081i) q^{33} +4.52776 q^{34} +(-2.53606 + 0.753926i) q^{35} +14.0084 q^{36} +(-0.500000 - 0.866025i) q^{37} +(3.19051 - 5.52613i) q^{38} +(10.2584 - 17.7681i) q^{39} +(-0.128675 - 0.222871i) q^{40} -9.54095 q^{41} +(-3.91960 + 16.3973i) q^{42} -5.09374 q^{43} +(3.33395 + 5.77458i) q^{44} +(-3.74723 + 6.49039i) q^{45} +(-1.97439 + 3.41975i) q^{46} +(-0.117078 - 0.202785i) q^{47} -13.7503 q^{48} +(-6.24328 - 3.16567i) q^{49} -1.96702 q^{50} +(3.72841 + 6.45780i) q^{51} +(5.91899 - 10.2520i) q^{52} +(4.00742 - 6.94105i) q^{53} +(14.3198 + 24.8025i) q^{54} -3.56731 q^{55} +(0.158298 - 0.662226i) q^{56} +10.5090 q^{57} +(9.31437 + 16.1330i) q^{58} +(5.39920 - 9.35169i) q^{59} +(-3.02760 + 5.24395i) q^{60} +(-2.66498 - 4.61588i) q^{61} +13.8606 q^{62} +(-19.0064 + 5.65026i) q^{63} -6.92135 q^{64} +(3.16665 + 5.48479i) q^{65} +(-11.3658 + 19.6861i) q^{66} +(1.71601 - 2.97221i) q^{67} +(2.15126 + 3.72609i) q^{68} -6.50331 q^{69} +(-3.77854 - 3.57866i) q^{70} -10.9250 q^{71} +(-0.964347 - 1.67030i) q^{72} +(-5.48065 + 9.49276i) q^{73} +(0.983510 - 1.70349i) q^{74} +(-1.61976 - 2.80550i) q^{75} +6.06359 q^{76} +(-6.85263 - 6.49012i) q^{77} +40.3569 q^{78} +(0.976843 + 1.69194i) q^{79} +(2.12227 - 3.67589i) q^{80} +(-12.3417 + 21.3765i) q^{81} +(-9.38362 - 16.2529i) q^{82} +9.65897 q^{83} +(-15.3563 + 4.56517i) q^{84} -2.30184 q^{85} +(-5.00975 - 8.67714i) q^{86} +(-15.3400 + 26.5696i) q^{87} +(0.459023 - 0.795051i) q^{88} +(-4.89536 - 8.47901i) q^{89} -14.7417 q^{90} +(-3.89567 + 16.2972i) q^{91} -3.75235 q^{92} +(11.4136 + 19.7690i) q^{93} +(0.230295 - 0.398882i) q^{94} +(-1.62200 + 2.80939i) q^{95} +(-12.6898 - 21.9795i) q^{96} +18.9483 q^{97} +(-0.747639 - 13.7488i) q^{98} -26.7351 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

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