LMFDB - Embedded newform 195.2.v.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(4,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("195.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.v (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	195.49
Dual form			195.2.v.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.946062 - 1.63863i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.790065 + 1.36843i) q^{4} +(1.73576 + 1.40965i) q^{5} +(-1.63863 - 0.946062i) q^{6} +(1.37597 - 2.38324i) q^{7} -0.794445 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.946062 - 1.63863i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.790065 + 1.36843i) q^{4} +(1.73576 + 1.40965i) q^{5} +(-1.63863 - 0.946062i) q^{6} +(1.37597 - 2.38324i) q^{7} -0.794445 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.667754 - 4.17789i) q^{10} +(0.884982 - 0.510945i) q^{11} +1.58013i q^{12} +(3.58146 + 0.416136i) q^{13} -5.20700 q^{14} +(2.20804 + 0.352913i) q^{15} +(2.33172 + 4.03867i) q^{16} +(-6.16256 - 3.55795i) q^{17} -1.89212 q^{18} +(-1.78942 - 1.03312i) q^{19} +(-3.30038 + 1.26156i) q^{20} -2.75193i q^{21} +(-1.67449 - 0.966770i) q^{22} +(-5.94419 + 3.43188i) q^{23} +(-0.688010 + 0.397223i) q^{24} +(1.02576 + 4.89365i) q^{25} +(-2.70639 - 6.26236i) q^{26} -1.00000i q^{27} +(2.17421 + 3.76584i) q^{28} +(4.43512 + 7.68186i) q^{29} +(-1.51065 - 3.95204i) q^{30} -4.24890i q^{31} +(3.61746 - 6.26563i) q^{32} +(0.510945 - 0.884982i) q^{33} +13.4642i q^{34} +(5.74790 - 2.19712i) q^{35} +(0.790065 + 1.36843i) q^{36} +(1.77840 + 3.08028i) q^{37} +3.90959i q^{38} +(3.30970 - 1.43034i) q^{39} +(-1.37897 - 1.11989i) q^{40} +(2.74651 - 1.58570i) q^{41} +(-4.50939 + 2.60350i) q^{42} +(-3.52045 - 2.03253i) q^{43} +1.61472i q^{44} +(2.08868 - 0.798390i) q^{45} +(11.2471 + 6.49354i) q^{46} +8.29935 q^{47} +(4.03867 + 2.33172i) q^{48} +(-0.286571 - 0.496355i) q^{49} +(7.04844 - 6.31053i) q^{50} -7.11591 q^{51} +(-3.39904 + 4.57221i) q^{52} +7.33447i q^{53} +(-1.63863 + 0.946062i) q^{54} +(2.25637 + 0.360638i) q^{55} +(-1.09313 + 1.89336i) q^{56} -2.06624 q^{57} +(8.39180 - 14.5350i) q^{58} +(2.57839 + 1.48863i) q^{59} +(-2.22743 + 2.74273i) q^{60} +(-3.14470 + 5.44678i) q^{61} +(-6.96236 + 4.01972i) q^{62} +(-1.37597 - 2.38324i) q^{63} -4.36248 q^{64} +(5.62996 + 5.77092i) q^{65} -1.93354 q^{66} +(3.76054 + 6.51345i) q^{67} +(9.73764 - 5.62203i) q^{68} +(-3.43188 + 5.94419i) q^{69} +(-9.03812 - 7.34006i) q^{70} +(-10.2251 - 5.90349i) q^{71} +(-0.397223 + 0.688010i) q^{72} -11.5322 q^{73} +(3.36495 - 5.82827i) q^{74} +(3.33516 + 3.72515i) q^{75} +(2.82751 - 1.63247i) q^{76} -2.81217i q^{77} +(-5.47498 - 4.07017i) q^{78} -4.42686 q^{79} +(-1.64579 + 10.2971i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.19674 - 3.00034i) q^{82} +10.0599 q^{83} +(3.76584 + 2.17421i) q^{84} +(-5.68127 - 14.8628i) q^{85} +7.69161i q^{86} +(7.68186 + 4.43512i) q^{87} +(-0.703070 + 0.405917i) q^{88} +(0.576586 - 0.332892i) q^{89} +(-3.28428 - 2.66724i) q^{90} +(5.91972 - 7.96290i) q^{91} -10.8456i q^{92} +(-2.12445 - 3.67966i) q^{93} +(-7.85170 - 13.5995i) q^{94} +(-1.64967 - 4.31571i) q^{95} -7.23493i q^{96} +(-4.58471 + 7.94095i) q^{97} +(-0.542227 + 0.939164i) q^{98} -1.02189i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 20 * q^4 + 16 * q^9	$ 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) $ 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.946062	−	1.63863i	−0.668967	−	1.15868i	−0.978193	−	0.207696i	$-0.933404\pi$
$2$	−0.946062	−	1.63863i	−0.668967	−	1.15868i	0.309227	−	0.950988i	$-0.399930\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.790065	+	1.36843i	−0.395033	+	0.684216i
$5$	1.73576	+	1.40965i	0.776258	+	0.630416i
$5$	1.73576	+	1.40965i	0.776258	+	0.630416i
$6$	−1.63863	−	0.946062i	−0.668967	−	0.386228i
$7$	1.37597	−	2.38324i	0.520067	−	0.900782i	−0.479661	−	0.877454i	$-0.659240\pi$
$7$	1.37597	−	2.38324i	0.520067	−	0.900782i	0.999728	−	0.0233281i	$-0.00742624\pi$
$8$	−0.794445			−0.280879
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.667754	−	4.17789i	0.211162	−	1.32116i
$11$	0.884982	−	0.510945i	0.266832	−	0.154056i	−0.360615	−	0.932715i	$-0.617433\pi$
$11$	0.884982	−	0.510945i	0.266832	−	0.154056i	0.627447	+	0.778659i	$0.284100\pi$
$12$			1.58013i			0.456144i
$13$	3.58146	+	0.416136i	0.993317	+	0.115415i
$13$	3.58146	+	0.416136i	0.993317	+	0.115415i
$14$	−5.20700			−1.39163
$15$	2.20804	+	0.352913i	0.570114	+	0.0911217i
$16$	2.33172	+	4.03867i	0.582931	+	1.00967i
$17$	−6.16256	−	3.55795i	−1.49464	−	0.862930i	−0.494658	−	0.869088i	$-0.664707\pi$
$17$	−6.16256	−	3.55795i	−1.49464	−	0.862930i	−0.999981	+	0.00615723i	$0.998040\pi$
$18$	−1.89212			−0.445978
$19$	−1.78942	−	1.03312i	−0.410521	−	0.237014i	0.280493	−	0.959856i	$-0.409502\pi$
$19$	−1.78942	−	1.03312i	−0.410521	−	0.237014i	−0.691013	+	0.722842i	$0.742835\pi$
$20$	−3.30038	+	1.26156i	−0.737988	+	0.282093i
$21$		−	2.75193i		−	0.600521i
$22$	−1.67449	−	0.966770i	−0.357003	−	0.206116i
$23$	−5.94419	+	3.43188i	−1.23945	+	0.715597i	−0.968982	−	0.247132i	$-0.920512\pi$
$23$	−5.94419	+	3.43188i	−1.23945	+	0.715597i	−0.270468	+	0.962729i	$0.587179\pi$
$24$	−0.688010	+	0.397223i	−0.140439	+	0.0810827i
$25$	1.02576	+	4.89365i	0.205152	+	0.978730i
$26$	−2.70639	−	6.26236i	−0.530766	−	1.22815i
$27$		−	1.00000i		−	0.192450i
$28$	2.17421	+	3.76584i	0.410887	+	0.711676i
$29$	4.43512	+	7.68186i	0.823582	+	1.42649i	0.902998	+	0.429644i	$0.141361\pi$
$29$	4.43512	+	7.68186i	0.823582	+	1.42649i	−0.0794163	+	0.996842i	$0.525306\pi$
$30$	−1.51065	−	3.95204i	−0.275806	−	0.721540i
$31$		−	4.24890i		−	0.763125i	−0.924343	−	0.381563i	$-0.875386\pi$
$31$		−	4.24890i		−	0.763125i	0.924343	−	0.381563i	$-0.124614\pi$
$32$	3.61746	−	6.26563i	0.639483	−	1.10762i
$33$	0.510945	−	0.884982i	0.0889440	−	0.154056i
$34$			13.4642i			2.30909i
$35$	5.74790	−	2.19712i	0.971573	−	0.371380i
$36$	0.790065	+	1.36843i	0.131678	+	0.228072i
$37$	1.77840	+	3.08028i	0.292367	+	0.506395i	0.974369	−	0.224955i	$-0.0722237\pi$
$37$	1.77840	+	3.08028i	0.292367	+	0.506395i	−0.682002	+	0.731351i	$0.738890\pi$
$38$			3.90959i			0.634218i
$39$	3.30970	−	1.43034i	0.529976	−	0.229038i
$40$	−1.37897	−	1.11989i	−0.218034	−	0.177070i
$41$	2.74651	−	1.58570i	0.428933	−	0.247645i	−0.269959	−	0.962872i	$-0.587010\pi$
$41$	2.74651	−	1.58570i	0.428933	−	0.247645i	0.698892	+	0.715227i	$0.253677\pi$
$42$	−4.50939	+	2.60350i	−0.695814	+	0.401729i
$43$	−3.52045	−	2.03253i	−0.536864	−	0.309958i	0.206943	−	0.978353i	$-0.433648\pi$
$43$	−3.52045	−	2.03253i	−0.536864	−	0.309958i	−0.743807	+	0.668395i	$0.766982\pi$
$44$			1.61472i			0.243428i
$45$	2.08868	−	0.798390i	0.311362	−	0.119017i
$46$	11.2471	+	6.49354i	1.65830	+	0.957421i
$47$	8.29935			1.21058			0.605292	−	0.796003i	$-0.293056\pi$
$47$	8.29935			1.21058			0.605292	+	0.796003i	$0.293056\pi$
$48$	4.03867	+	2.33172i	0.582931	+	0.336555i
$49$	−0.286571	−	0.496355i	−0.0409387	−	0.0709078i
$50$	7.04844	−	6.31053i	0.996799	−	0.892444i
$51$	−7.11591			−0.996426
$52$	−3.39904	+	4.57221i	−0.471362	+	0.634051i
$53$			7.33447i			1.00747i	0.863859	+	0.503734i	$0.168041\pi$
$53$			7.33447i			1.00747i	−0.863859	+	0.503734i	$0.831959\pi$
$54$	−1.63863	+	0.946062i	−0.222989	+	0.128743i
$55$	2.25637	+	0.360638i	0.304250	+	0.0486284i
$56$	−1.09313	+	1.89336i	−0.146076	+	0.253011i
$57$	−2.06624			−0.273681
$58$	8.39180	−	14.5350i	1.10190	−	1.90854i
$59$	2.57839	+	1.48863i	0.335677	+	0.193803i	0.658359	−	0.752704i	$-0.271251\pi$
$59$	2.57839	+	1.48863i	0.335677	+	0.193803i	−0.322681	+	0.946508i	$0.604584\pi$
$60$	−2.22743	+	2.74273i	−0.287561	+	0.354085i
$61$	−3.14470	+	5.44678i	−0.402638	+	0.697389i	−0.994043	−	0.108985i	$-0.965240\pi$
$61$	−3.14470	+	5.44678i	−0.402638	+	0.697389i	0.591406	+	0.806374i	$0.298573\pi$
$62$	−6.96236	+	4.01972i	−0.884221	+	0.510505i
$63$	−1.37597	−	2.38324i	−0.173356	−	0.300261i
$64$	−4.36248			−0.545310
$65$	5.62996	+	5.77092i	0.698310	+	0.715795i
$66$	−1.93354			−0.238002
$67$	3.76054	+	6.51345i	0.459424	+	0.795745i	0.998931	−	0.0462362i	$-0.0147227\pi$
$67$	3.76054	+	6.51345i	0.459424	+	0.795745i	−0.539507	+	0.841981i	$0.681389\pi$
$68$	9.73764	−	5.62203i	1.18086	−	0.681771i
$69$	−3.43188	+	5.94419i	−0.413150	+	0.715597i
$70$	−9.03812	−	7.34006i	−1.08026	−	0.877305i
$71$	−10.2251	−	5.90349i	−1.21350	−	0.700615i	−0.249980	−	0.968251i	$-0.580424\pi$
$71$	−10.2251	−	5.90349i	−1.21350	−	0.700615i	−0.963520	+	0.267636i	$0.913757\pi$
$72$	−0.397223	+	0.688010i	−0.0468131	+	0.0810827i
$73$	−11.5322			−1.34974			−0.674869	−	0.737937i	$-0.735800\pi$
$73$	−11.5322			−1.34974			−0.674869	+	0.737937i	$0.735800\pi$
$74$	3.36495	−	5.82827i	0.391168	−	0.677523i
$75$	3.33516	+	3.72515i	0.385111	+	0.430143i
$76$	2.82751	−	1.63247i	0.324338	−	0.187257i
$77$		−	2.81217i		−	0.320477i
$78$	−5.47498	−	4.07017i	−0.619919	−	0.460856i
$79$	−4.42686			−0.498061			−0.249030	−	0.968496i	$-0.580112\pi$
$79$	−4.42686			−0.498061			−0.249030	+	0.968496i	$0.580112\pi$
$80$	−1.64579	+	10.2971i	−0.184005	+	1.15125i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.19674	−	3.00034i	−0.573884	−	0.331332i
$83$	10.0599			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$83$	10.0599			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$84$	3.76584	+	2.17421i	0.410887	+	0.237225i
$85$	−5.68127	−	14.8628i	−0.616220	−	1.61210i
$86$			7.69161i			0.829407i
$87$	7.68186	+	4.43512i	0.823582	+	0.475495i
$88$	−0.703070	+	0.405917i	−0.0749475	+	0.0432709i
$89$	0.576586	−	0.332892i	0.0611180	−	0.0352865i	−0.469130	−	0.883129i	$-0.655432\pi$
$89$	0.576586	−	0.332892i	0.0611180	−	0.0352865i	0.530248	+	0.847843i	$0.322099\pi$
$90$	−3.28428	−	2.66724i	−0.346194	−	0.281151i
$91$	5.91972	−	7.96290i	0.620555	−	0.834739i
$92$		−	10.8456i		−	1.13074i
$93$	−2.12445	−	3.67966i	−0.220295	−	0.381563i
$94$	−7.85170	−	13.5995i	−0.809841	−	1.40269i
$95$	−1.64967	−	4.31571i	−0.169252	−	0.442783i
$96$		−	7.23493i		−	0.738412i
$97$	−4.58471	+	7.94095i	−0.465507	+	0.806282i	−0.999224	−	0.0393812i	$-0.987461\pi$
$97$	−4.58471	+	7.94095i	−0.465507	+	0.806282i	0.533717	+	0.845663i	$0.320795\pi$
$98$	−0.542227	+	0.939164i	−0.0547732	+	0.0948699i
$99$		−	1.02189i		−	0.102704i
$100$	−7.50705	−	2.46262i	−0.750705	−	0.246262i
$101$	−3.63997	−	6.30462i	−0.362191	−	0.627333i	0.626130	−	0.779718i	$-0.284638\pi$
$101$	−3.63997	−	6.30462i	−0.362191	−	0.627333i	−0.988321	+	0.152386i	$0.951304\pi$
$102$	6.73209	+	11.6603i	0.666576	+	1.15454i
$103$			10.3328i			1.01812i	0.860731	+	0.509059i	$0.170007\pi$
$103$			10.3328i			1.01812i	−0.860731	+	0.509059i	$0.829993\pi$
$104$	−2.84527	−	0.330597i	−0.279002	−	0.0324177i
$105$	3.87927	−	4.77671i	0.378578	−	0.466159i
$106$	12.0185	−	6.93886i	1.16734	−	0.673962i
$107$	0.0652484	−	0.0376712i	0.00630780	−	0.00364181i	−0.496843	−	0.867841i	$-0.665507\pi$
$107$	0.0652484	−	0.0376712i	0.00630780	−	0.00364181i	0.503151	+	0.864199i	$0.332174\pi$
$108$	1.36843	+	0.790065i	0.131678	+	0.0760241i
$109$		−	9.88589i		−	0.946897i	−0.880822	−	0.473448i	$-0.843009\pi$
$109$		−	9.88589i		−	0.946897i	0.880822	−	0.473448i	$-0.156991\pi$
$110$	−1.54372	−	4.03854i	−0.147188	−	0.385060i
$111$	3.08028	+	1.77840i	0.292367	+	0.168798i
$112$	12.8335			1.21265
$113$	−14.1529	−	8.17117i	−1.33139	−	0.768679i	−0.345878	−	0.938280i	$-0.612419\pi$
$113$	−14.1529	−	8.17117i	−1.33139	−	0.768679i	−0.985513	+	0.169601i	$0.945752\pi$
$114$	1.95479	+	3.38580i	0.183083	+	0.317109i
$115$	−15.1555	−	2.42231i	−1.41326	−	0.225882i
$116$	−14.0161			−1.30137
$117$	2.15111	−	2.89356i	0.198870	−	0.267510i
$118$		−	5.63335i		−	0.518592i
$119$	−16.9589	+	9.79125i	−1.55462	+	0.897563i
$120$	−1.75417	−	0.280370i	−0.160133	−	0.0255941i
$121$	−4.97787	+	8.62193i	−0.452534	+	0.783811i
$122$	11.9003			1.07740
$123$	1.58570	−	2.74651i	0.142978	−	0.247645i
$124$	5.81434	+	3.35691i	0.522143	+	0.301459i
$125$	−5.11787	+	9.94019i	−0.457756	+	0.889078i
$126$	−2.60350	+	4.50939i	−0.231938	+	0.401729i
$127$	5.79465	−	3.34554i	0.514192	−	0.296869i	−0.220363	−	0.975418i	$-0.570724\pi$
$127$	5.79465	−	3.34554i	0.514192	−	0.296869i	0.734555	+	0.678549i	$0.237391\pi$
$128$	−3.10775	−	5.38279i	−0.274689	−	0.475776i
$129$	−4.06507			−0.357909
$130$	4.13010	−	14.6851i	0.362234	−	1.28796i
$131$	8.76259			0.765591			0.382796	−	0.923833i	$-0.374961\pi$
$131$	8.76259			0.765591			0.382796	+	0.923833i	$0.374961\pi$
$132$	0.807359	+	1.39839i	0.0702716	+	0.121714i
$133$	−4.92436	+	2.84308i	−0.426996	+	0.246526i
$134$	7.11541	−	12.3243i	0.614678	−	1.06465i
$135$	1.40965	−	1.73576i	0.121324	−	0.149391i
$136$	4.89581	+	2.82660i	0.419813	+	0.242379i
$137$	2.41918	−	4.19015i	0.206685	−	0.357989i	−0.743983	−	0.668198i	$-0.767066\pi$
$137$	2.41918	−	4.19015i	0.206685	−	0.357989i	0.950668	+	0.310209i	$0.100399\pi$
$138$	12.9871			1.10553
$139$	1.02518	−	1.77566i	0.0869546	−	0.150610i	−0.819268	−	0.573411i	$-0.805620\pi$
$139$	1.02518	−	1.77566i	0.0869546	−	0.150610i	0.906222	+	0.422801i	$0.138953\pi$
$140$	−1.53461	+	9.60148i	−0.129698	+	0.811474i
$141$	7.18745	−	4.14968i	0.605292	−	0.349466i
$142$			22.3402i			1.87475i
$143$	3.38215	−	1.46165i	0.282829	−	0.122230i
$144$	4.66345			0.388621
$145$	−3.13042	+	19.5859i	−0.259968	+	1.62652i
$146$	10.9101	+	18.8969i	0.902930	+	1.56392i
$147$	−0.496355	−	0.286571i	−0.0409387	−	0.0236359i
$148$	−5.62021			−0.461979
$149$	14.5291	+	8.38839i	1.19027	+	0.687203i	0.958368	−	0.285536i	$-0.0921715\pi$
$149$	14.5291	+	8.38839i	1.19027	+	0.687203i	0.231903	+	0.972739i	$0.425505\pi$
$150$	2.94886	−	8.98930i	0.240773	−	0.733973i
$151$		−	4.06055i		−	0.330443i	−0.986256	−	0.165221i	$-0.947166\pi$
$151$		−	4.06055i		−	0.330443i	0.986256	−	0.165221i	$-0.0528339\pi$
$152$	1.42160	+	0.820758i	0.115307	+	0.0665723i
$153$	−6.16256	+	3.55795i	−0.498213	+	0.287643i
$154$	−4.60810	+	2.66049i	−0.371331	+	0.214388i
$155$	5.98947	−	7.37509i	0.481086	−	0.592382i
$156$	−0.657549	+	5.65917i	−0.0526461	+	0.453096i
$157$		−	5.24178i		−	0.418339i	−0.977879	−	0.209170i	$-0.932924\pi$
$157$		−	5.24178i		−	0.418339i	0.977879	−	0.209170i	$-0.0670761\pi$
$158$	4.18808	+	7.25397i	0.333186	+	0.577095i
$159$	3.66724	+	6.35184i	0.290831	+	0.503734i
$160$	15.1114	−	5.77630i	1.19466	−	0.456656i
$161$			18.8886i			1.48863i
$162$	−0.946062	+	1.63863i	−0.0743296	+	0.128743i
$163$	−3.18565	+	5.51771i	−0.249519	+	0.432180i	−0.963393	−	0.268095i	$-0.913606\pi$
$163$	−3.18565	+	5.51771i	−0.249519	+	0.432180i	0.713873	+	0.700275i	$0.246939\pi$
$164$			5.01122i			0.391311i
$165$	2.13440	−	0.815866i	0.166163	−	0.0635151i
$166$	−9.51724	−	16.4843i	−0.738681	−	1.27943i
$167$	−4.55862	−	7.89577i	−0.352757	−	0.610993i	0.633975	−	0.773354i	$-0.281422\pi$
$167$	−4.55862	−	7.89577i	−0.352757	−	0.610993i	−0.986731	+	0.162361i	$0.948089\pi$
$168$			2.18626i			0.168674i
$169$	12.6537	+	2.98075i	0.973359	+	0.229288i
$170$	−18.9798	+	23.3706i	−1.45568	+	1.79245i
$171$	−1.78942	+	1.03312i	−0.136840	+	0.0790048i
$172$	5.56277	−	3.21167i	0.424157	−	0.244887i
$173$	−0.581446	−	0.335698i	−0.0442065	−	0.0255226i	0.477734	−	0.878505i	$-0.341458\pi$
$173$	−0.581446	−	0.335698i	−0.0442065	−	0.0255226i	−0.521940	+	0.852982i	$0.674792\pi$
$174$		−	16.7836i		−	1.27236i
$175$	13.0742	+	4.28887i	0.988315	+	0.324208i
$176$	4.12707	+	2.38276i	0.311089	+	0.179608i
$177$	2.97727			0.223785
$178$	−1.09097	−	0.629873i	−0.0817718	−	0.0472110i
$179$	−6.06066	−	10.4974i	−0.452995	−	0.784611i	0.545575	−	0.838062i	$-0.316311\pi$
$179$	−6.06066	−	10.4974i	−0.452995	−	0.784611i	−0.998570	+	0.0534510i	$0.982978\pi$
$180$	−0.557648	+	3.48900i	−0.0415646	+	0.260054i
$181$	−20.7519			−1.54248			−0.771240	−	0.636544i	$-0.780363\pi$
$181$	−20.7519			−1.54248			−0.771240	+	0.636544i	$0.780363\pi$
$182$	−18.6486	−	2.16682i	−1.38233	−	0.160615i
$183$			6.28940i			0.464926i
$184$	4.72234	−	2.72644i	0.348135	−	0.200996i
$185$	−1.25524	+	7.85357i	−0.0922871	+	0.577406i
$186$	−4.01972	+	6.96236i	−0.294740	+	0.510505i
$187$	−7.27167			−0.531757
$188$	−6.55703	+	11.3571i	−0.478220	+	0.828302i
$189$	−2.38324	−	1.37597i	−0.173356	−	0.100087i
$190$	−5.51116	+	6.78612i	−0.399821	+	0.492317i
$191$	8.36371	−	14.4864i	0.605177	−	1.04820i	−0.386846	−	0.922144i	$-0.626436\pi$
$191$	8.36371	−	14.4864i	0.605177	−	1.04820i	0.992023	−	0.126053i	$-0.0402311\pi$
$192$	−3.77802	+	2.18124i	−0.272655	+	0.157417i
$193$	−6.27603	−	10.8704i	−0.451759	−	0.782469i	0.546737	−	0.837304i	$-0.315870\pi$
$193$	−6.27603	−	10.8704i	−0.451759	−	0.782469i	−0.998495	+	0.0548358i	$0.982536\pi$
$194$	17.3497			1.24563
$195$	7.76115	+	2.18279i	0.555787	+	0.156313i
$196$	0.905638			0.0646884
$197$	−7.21490	−	12.4966i	−0.514040	−	0.890344i	−0.999867	−	0.0162890i	$-0.994815\pi$
$197$	−7.21490	−	12.4966i	−0.514040	−	0.890344i	0.485827	−	0.874055i	$-0.338519\pi$
$198$	−1.67449	+	0.966770i	−0.119001	+	0.0687054i
$199$	12.0423	−	20.8579i	0.853655	−	1.47857i	−0.0242314	−	0.999706i	$-0.507714\pi$
$199$	12.0423	−	20.8579i	0.853655	−	1.47857i	0.877887	−	0.478868i	$-0.158953\pi$
$200$	−0.814909	−	3.88774i	−0.0576228	−	0.274905i
$201$	6.51345	+	3.76054i	0.459424	+	0.265248i
$202$	−6.88727	+	11.9291i	−0.484587	+	0.839329i
$203$	24.4103			1.71327
$204$	5.62203	−	9.73764i	0.393621	−	0.681771i
$205$	7.00258	+	1.11923i	0.489082	+	0.0781702i
$206$	16.9316	−	9.77544i	1.17968	−	0.681087i
$207$			6.86376i			0.477065i
$208$	6.67034	+	15.4346i	0.462505	+	1.07020i
$209$	−2.11147			−0.146053
$210$	−11.4973	−	1.83762i	−0.793387	−	0.126808i
$211$	−5.75217	−	9.96306i	−0.395996	−	0.685885i	0.597232	−	0.802069i	$-0.296267\pi$
$211$	−5.75217	−	9.96306i	−0.395996	−	0.685885i	−0.993228	+	0.116184i	$0.962934\pi$
$212$	−10.0367	−	5.79471i	−0.689326	−	0.397982i
$213$	−11.8070			−0.809000
$214$	−0.123458	−	0.0712785i	−0.00843942	−	0.00487250i
$215$	−3.24551	−	8.49061i	−0.221342	−	0.579055i
$216$			0.794445i			0.0540552i
$217$	−10.1262	−	5.84635i	−0.687409	−	0.396876i
$218$	−16.1993	+	9.35266i	−1.09715	+	0.633442i
$219$	−9.98716	+	5.76609i	−0.674869	+	0.389636i
$220$	−2.27619	+	2.80277i	−0.153461	+	0.188963i
$221$	−20.5903	−	15.3071i	−1.38506	−	1.02967i
$222$		−	6.72991i		−	0.451682i
$223$	−13.0690	−	22.6361i	−0.875162	−	1.51582i	−0.856590	−	0.515997i	$-0.827422\pi$
$223$	−13.0690	−	22.6361i	−0.875162	−	1.51582i	−0.0185714	−	0.999828i	$-0.505912\pi$
$224$	−9.95502	−	17.2426i	−0.665148	−	1.15207i
$225$	4.75091	+	1.55849i	0.316727	+	0.103900i
$226$			30.9217i			2.05688i
$227$	−9.38852	+	16.2614i	−0.623138	+	1.07931i	0.365760	+	0.930709i	$0.380809\pi$
$227$	−9.38852	+	16.2614i	−0.623138	+	1.07931i	−0.988898	+	0.148597i	$0.952524\pi$
$228$	1.63247	−	2.82751i	0.108113	−	0.187257i
$229$		−	1.50355i		−	0.0993576i	−0.998765	−	0.0496788i	$-0.984180\pi$
$229$		−	1.50355i		−	0.0993576i	0.998765	−	0.0496788i	$-0.0158198\pi$
$230$	10.3688	+	27.1258i	0.683696	+	1.78862i
$231$	−1.40609	−	2.43541i	−0.0925136	−	0.160238i
$232$	−3.52346	−	6.10282i	−0.231327	−	0.400670i
$233$			9.60391i			0.629173i	0.949229	+	0.314587i	$0.101866\pi$
$233$			9.60391i			0.629173i	−0.949229	+	0.314587i	$0.898134\pi$
$234$	−6.77656	−	0.787381i	−0.442997	−	0.0514727i
$235$	14.4057	+	11.6992i	0.939726	+	0.763172i
$236$	−4.07419	+	2.35223i	−0.265207	+	0.153117i
$237$	−3.83377	+	2.21343i	−0.249030	+	0.143778i
$238$	32.0884	+	18.5263i	2.07998	+	1.20088i
$239$			0.817195i			0.0528599i	0.999651	+	0.0264300i	$0.00841390\pi$
$239$			0.817195i			0.0528599i	−0.999651	+	0.0264300i	$0.991586\pi$
$240$	3.72325	+	9.74044i	0.240335	+	0.628743i
$241$	4.26163	+	2.46046i	0.274516	+	0.158492i	0.630938	−	0.775833i	$-0.282670\pi$
$241$	4.26163	+	2.46046i	0.274516	+	0.158492i	−0.356422	+	0.934325i	$0.616003\pi$
$242$	18.8375			1.21092
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−4.96904	−	8.60662i	−0.318110	−	0.550983i
$245$	0.202269	−	1.26552i	0.0129225	−	0.0808511i
$246$	−6.00068			−0.382589
$247$	−5.97881	−	4.44472i	−0.380422	−	0.282811i
$248$			3.37552i			0.214346i
$249$	8.71209	−	5.02993i	0.552106	−	0.318759i
$250$	21.1301	−	1.01775i	1.33638	−	0.0643680i
$251$	−10.9223	+	18.9181i	−0.689412	+	1.19410i	0.282616	+	0.959233i	$0.408798\pi$
$251$	−10.9223	+	18.9181i	−0.689412	+	1.19410i	−0.972028	+	0.234864i	$0.924536\pi$
$252$	4.34841			0.273924
$253$	−3.50700	+	6.07431i	−0.220483	+	0.381888i
$254$	−10.9642	−	6.33018i	−0.687954	−	0.397191i
$255$	−12.3515	−	10.0310i	−0.773483	−	0.628163i
$256$	−10.2427	+	17.7409i	−0.640171	+	1.10881i
$257$	14.4681	−	8.35316i	0.902495	−	0.521056i	0.0244865	−	0.999700i	$-0.492205\pi$
$257$	14.4681	−	8.35316i	0.902495	−	0.521056i	0.878009	+	0.478644i	$0.158872\pi$
$258$	3.84580	+	6.66113i	0.239429	+	0.414704i
$259$	9.78809			0.608202
$260$	−12.3452	+	3.14481i	−0.765614	+	0.195033i
$261$	8.87025			0.549055
$262$	−8.28995	−	14.3586i	−0.512155	−	0.887078i
$263$	13.3507	−	7.70805i	0.823241	−	0.475298i	−0.0282918	−	0.999600i	$-0.509007\pi$
$263$	13.3507	−	7.70805i	0.823241	−	0.475298i	0.851533	+	0.524301i	$0.175673\pi$
$264$	−0.405917	+	0.703070i	−0.0249825	+	0.0432709i
$265$	−10.3391	+	12.7309i	−0.635123	+	0.782054i
$266$	9.31750	+	5.37946i	0.571293	+	0.329836i
$267$	0.332892	−	0.576586i	0.0203727	−	0.0352865i
$268$	−11.8843			−0.725949
$269$	9.44009	−	16.3507i	0.575572	−	0.996921i	−0.420407	−	0.907336i	$-0.638113\pi$
$269$	9.44009	−	16.3507i	0.575572	−	0.996921i	0.995979	−	0.0895849i	$-0.0285540\pi$
$270$	−4.17789	−	0.667754i	−0.254258	−	0.0406382i
$271$	−10.0140	+	5.78160i	−0.608308	+	0.351207i	−0.772303	−	0.635254i	$-0.780895\pi$
$271$	−10.0140	+	5.78160i	−0.608308	+	0.351207i	0.163995	+	0.986461i	$0.447562\pi$
$272$		−	33.1847i		−	2.01212i
$273$	1.14518	−	9.85593i	0.0693094	−	0.596508i
$274$	−9.15479			−0.553061
$275$	3.40816	+	3.80669i	0.205520	+	0.229552i
$276$	−5.42282	−	9.39260i	−0.326415	−	0.565368i
$277$	9.30128	+	5.37010i	0.558860	+	0.322658i	0.752688	−	0.658378i	$-0.228757\pi$
$277$	9.30128	+	5.37010i	0.558860	+	0.322658i	−0.193828	+	0.981036i	$0.562090\pi$
$278$	−3.87953			−0.232679
$279$	−3.67966	−	2.12445i	−0.220295	−	0.127188i
$280$	−4.56639	+	1.74549i	−0.272894	+	0.104313i
$281$		−	22.2403i		−	1.32674i	−0.748290	−	0.663372i	$-0.769125\pi$
$281$		−	22.2403i		−	1.32674i	0.748290	−	0.663372i	$-0.230875\pi$
$282$	−13.5995	−	7.85170i	−0.809841	−	0.467562i
$283$	26.0084	−	15.0160i	1.54604	−	0.892606i	0.547600	−	0.836740i	$-0.315541\pi$
$283$	26.0084	−	15.0160i	1.54604	−	0.892606i	0.998438	−	0.0558660i	$-0.0177920\pi$
$284$	16.1570	−	9.32828i	0.958744	−	0.553531i
$285$	−3.58651	−	2.91268i	−0.212447	−	0.172533i
$286$	−5.59482	−	4.15926i	−0.330829	−	0.245942i
$287$		−	8.72748i		−	0.515167i
$288$	−3.61746	−	6.26563i	−0.213161	−	0.369206i
$289$	16.8181	+	29.1297i	0.989298	+	1.71351i
$290$	35.0555	−	13.3999i	2.05853	−	0.786867i
$291$			9.16942i			0.537521i
$292$	9.11117	−	15.7810i	0.533191	−	0.923514i
$293$	10.5004	−	18.1872i	0.613439	−	1.06251i	−0.377217	−	0.926125i	$-0.623119\pi$
$293$	10.5004	−	18.1872i	0.613439	−	1.06251i	0.990656	−	0.136383i	$-0.0435477\pi$
$294$			1.08445i			0.0632466i
$295$	2.37702	+	6.21855i	0.138395	+	0.362058i
$296$	−1.41284	−	2.44712i	−0.0821198	−	0.142236i
$297$	−0.510945	−	0.884982i	−0.0296480	−	0.0513519i
$298$		−	31.7437i		−	1.83886i
$299$	−22.7170	+	9.81754i	−1.31376	+	0.567763i
$300$	−7.73261	+	1.62083i	−0.446442	+	0.0935788i
$301$	−9.68805	+	5.59340i	−0.558410	+	0.322398i
$302$	−6.65373	+	3.84153i	−0.382879	+	0.221055i
$303$	−6.30462	−	3.63997i	−0.362191	−	0.209111i
$304$		−	9.63582i		−	0.552652i
$305$	−13.1365	+	5.02139i	−0.752195	+	0.287524i
$306$	11.6603	+	6.73209i	0.666576	+	0.384848i
$307$	2.90135			0.165589			0.0827945	−	0.996567i	$-0.473615\pi$
$307$	2.90135			0.165589			0.0827945	+	0.996567i	$0.473615\pi$
$308$	3.84827	+	2.22180i	0.219275	+	0.126599i
$309$	5.16639	+	8.94845i	0.293906	+	0.509059i
$310$	−17.7514	−	2.83722i	−1.00821	−	0.161143i
$311$	22.7274			1.28875			0.644377	−	0.764708i	$-0.277117\pi$
$311$	22.7274			1.28875			0.644377	+	0.764708i	$0.277117\pi$
$312$	−2.62938	+	1.13633i	−0.148859	+	0.0643320i
$313$			24.0116i			1.35721i	0.734501	+	0.678607i	$0.237416\pi$
$313$			24.0116i			1.35721i	−0.734501	+	0.678607i	$0.762584\pi$
$314$	−8.58932	+	4.95905i	−0.484723	+	0.279855i
$315$	0.971193	−	6.07639i	0.0547205	−	0.342366i
$316$	3.49751	−	6.05786i	0.196750	−	0.340781i
$317$	−2.88089			−0.161807			−0.0809033	−	0.996722i	$-0.525781\pi$
$317$	−2.88089			−0.161807			−0.0809033	+	0.996722i	$0.525781\pi$
$318$	6.93886	−	12.0185i	0.389112	−	0.673962i
$319$	7.85001	+	4.53221i	0.439516	+	0.253755i
$320$	−7.57224	−	6.14958i	−0.423301	−	0.343772i
$321$	0.0376712	−	0.0652484i	0.00210260	−	0.00364181i
$322$	30.9514	−	17.8698i	1.72485	−	0.995845i
$323$	7.35159	+	12.7333i	0.409054	+	0.708502i
$324$	1.58013			0.0877850
$325$	1.63728	+	17.9533i	0.0908202	+	0.995867i
$326$	12.0553			0.667681
$327$	−4.94295	−	8.56144i	−0.273346	−	0.473448i
$328$	−2.18195	+	1.25975i	−0.120478	+	0.0695581i
$329$	11.4196	−	19.7794i	0.629585	−	1.09047i
$330$	−3.35617	−	2.72562i	−0.184751	−	0.150040i
$331$	−29.8008	−	17.2055i	−1.63800	−	0.945699i	−0.981521	−	0.191355i	$-0.938712\pi$
$331$	−29.8008	−	17.2055i	−1.63800	−	0.945699i	−0.656479	−	0.754345i	$-0.727955\pi$
$332$	−7.94794	+	13.7662i	−0.436200	+	0.755520i
$333$	3.55680			0.194912
$334$	−8.62548	+	14.9398i	−0.471965	+	0.817467i
$335$	−2.65429	+	16.6069i	−0.145019	+	0.907331i
$336$	11.1141	−	6.41675i	0.606326	−	0.350063i
$337$			32.4354i			1.76687i	0.468555	+	0.883434i	$0.344775\pi$
$337$			32.4354i			1.76687i	−0.468555	+	0.883434i	$0.655225\pi$
$338$	−7.08681	−	23.5546i	−0.385472	−	1.28120i
$339$	−16.3423			−0.887594
$340$	24.8274	+	3.96817i	1.34645	+	0.215204i
$341$	−2.17095	−	3.76020i	−0.117564	−	0.203626i
$342$	3.38580	+	1.95479i	0.183083	+	0.105703i
$343$	17.6863			0.954970
$344$	2.79681	+	1.61474i	0.150794	+	0.0870608i
$345$	−14.3362	+	5.47996i	−0.771835	+	0.295031i
$346$			1.27036i			0.0682952i
$347$	−20.8327	−	12.0278i	−1.11836	−	0.645684i	−0.177376	−	0.984143i	$-0.556761\pi$
$347$	−20.8327	−	12.0278i	−1.11836	−	0.645684i	−0.940981	+	0.338459i	$0.890094\pi$
$348$	−12.1383	+	7.00807i	−0.650683	+	0.375672i
$349$	−9.37984	+	5.41545i	−0.502091	+	0.289883i	−0.729577	−	0.683899i	$-0.760283\pi$
$349$	−9.37984	+	5.41545i	−0.502091	+	0.289883i	0.227485	+	0.973781i	$0.426950\pi$
$350$	−5.34112	−	25.4812i	−0.285495	−	1.36203i
$351$	0.416136	−	3.58146i	0.0222117	−	0.191164i
$352$		−	7.39330i		−	0.394064i
$353$	8.99965	+	15.5878i	0.479003	+	0.829657i	0.999710	−	0.0240781i	$-0.00766503\pi$
$353$	8.99965	+	15.5878i	0.479003	+	0.829657i	−0.520707	+	0.853735i	$0.674332\pi$
$354$	−2.81668	−	4.87863i	−0.149705	−	0.259296i
$355$	−9.42657	−	24.6610i	−0.500310	−	1.30887i
$356$			1.05203i			0.0557572i
$357$	−9.79125	+	16.9589i	−0.518208	+	0.897563i
$358$	−11.4675	+	19.8623i	−0.606077	+	1.04976i
$359$		−	4.17530i		−	0.220364i	−0.993911	−	0.110182i	$-0.964857\pi$
$359$		−	4.17530i		−	0.220364i	0.993911	−	0.110182i	$-0.0351434\pi$
$360$	−1.65934	+	0.634277i	−0.0874549	+	0.0334293i
$361$	−7.36532	−	12.7571i	−0.387648	−	0.671427i
$362$	19.6326	+	34.0047i	1.03187	+	1.78725i
$363$			9.95574i			0.522541i
$364$	6.21973	+	14.3919i	0.326002	+	0.754343i
$365$	−20.0171	−	16.2564i	−1.04775	−	0.850897i
$366$	10.3060	−	5.95016i	0.538702	−	0.311020i
$367$	5.80315	−	3.35045i	0.302922	−	0.174892i	−0.340833	−	0.940124i	$-0.610709\pi$
$367$	5.80315	−	3.35045i	0.302922	−	0.174892i	0.643755	+	0.765232i	$0.277376\pi$
$368$	−27.7204	−	16.0044i	−1.44503	−	0.834287i
$369$		−	3.17140i		−	0.165096i
$370$	14.0566	−	5.37309i	0.730768	−	0.279334i
$371$	17.4798	+	10.0920i	0.907508	+	0.523950i
$372$	6.71382			0.348095
$373$	9.37386	+	5.41200i	0.485360	+	0.280223i	0.722648	−	0.691217i	$-0.242925\pi$
$373$	9.37386	+	5.41200i	0.485360	+	0.280223i	−0.237287	+	0.971439i	$0.576258\pi$
$374$	6.87944	+	11.9155i	0.355728	+	0.616138i
$375$	0.537887	+	11.1674i	0.0277763	+	0.576682i
$376$	−6.59338			−0.340028
$377$	12.6875	+	29.3579i	0.653440	+	1.51201i
$378$			5.20700i			0.267819i
$379$	4.14426	−	2.39269i	0.212876	−	0.122904i	−0.389771	−	0.920912i	$-0.627446\pi$
$379$	4.14426	−	2.39269i	0.212876	−	0.122904i	0.602647	+	0.798008i	$0.294113\pi$
$380$	7.20911	+	1.15224i	0.369820	+	0.0591085i
$381$	3.34554	−	5.79465i	0.171397	−	0.296869i
$382$	−31.6504			−1.61937
$383$	−14.2319	+	24.6503i	−0.727214	+	1.25957i	0.230842	+	0.972991i	$0.425852\pi$
$383$	−14.2319	+	24.6503i	−0.727214	+	1.25957i	−0.958056	+	0.286581i	$0.907481\pi$
$384$	−5.38279	−	3.10775i	−0.274689	−	0.158592i
$385$	3.96419	−	4.88127i	0.202034	−	0.248772i
$386$	−11.8750	+	20.5681i	−0.604423	+	1.04689i
$387$	−3.52045	+	2.03253i	−0.178955	+	0.103319i
$388$	−7.24444	−	12.5477i	−0.367781	−	0.637015i
$389$	−32.2567			−1.63548			−0.817740	−	0.575588i	$-0.804773\pi$
$389$	−32.2567			−1.63548			−0.817740	+	0.575588i	$0.804773\pi$
$390$	−3.76575	−	14.7827i	−0.190686	−	0.748550i
$391$	48.8419			2.47004
$392$	0.227665	+	0.394327i	0.0114988	+	0.0199165i
$393$	7.58863	−	4.38130i	0.382796	−	0.221007i
$394$	−13.6515	+	23.6451i	−0.687752	+	1.19122i
$395$	−7.68399	−	6.24033i	−0.386623	−	0.313985i
$396$	1.39839	+	0.807359i	0.0702716	+	0.0405713i
$397$	−0.715962	+	1.24008i	−0.0359331	+	0.0622380i	−0.883433	−	0.468558i	$-0.844774\pi$
$397$	−0.715962	+	1.24008i	−0.0359331	+	0.0622380i	0.847500	+	0.530796i	$0.178107\pi$
$398$	−45.5710			−2.28427
$399$	−2.84308	+	4.92436i	−0.142332	+	0.246526i
$400$	−17.3720	+	15.5533i	−0.868602	+	0.777667i
$401$	−9.29750	+	5.36791i	−0.464295	+	0.268061i	−0.713848	−	0.700300i	$-0.753049\pi$
$401$	−9.29750	+	5.36791i	−0.464295	+	0.268061i	0.249554	+	0.968361i	$0.419716\pi$
$402$		−	14.2308i		−	0.709769i
$403$	1.76812	−	15.2173i	0.0880764	−	0.758025i
$404$	11.5033			0.572309
$405$	0.352913	−	2.20804i	0.0175364	−	0.109719i
$406$	−23.0937	−	39.9994i	−1.14612	−	1.98514i
$407$	3.14771	+	1.81733i	0.156026	+	0.0900816i
$408$	5.65320			0.279875
$409$	−7.49034	−	4.32455i	−0.370373	−	0.213835i	0.303248	−	0.952912i	$-0.401929\pi$
$409$	−7.49034	−	4.32455i	−0.370373	−	0.213835i	−0.673622	+	0.739076i	$0.735262\pi$
$410$	−4.79088	−	12.5335i	−0.236605	−	0.618984i
$411$		−	4.83837i		−	0.238659i
$412$	−14.1397	−	8.16357i	−0.696614	−	0.402190i
$413$	7.09555	−	4.09662i	0.349149	−	0.201581i
$414$	11.2471	−	6.49354i	0.552767	−	0.319140i
$415$	17.4615	+	14.1809i	0.857153	+	0.696113i
$416$	15.5631	−	20.9347i	0.763046	−	1.02641i
$417$		−	2.05036i		−	0.100407i
$418$	1.99758	+	3.45991i	0.0977049	+	0.169230i
$419$	−1.09766	−	1.90121i	−0.0536244	−	0.0928802i	0.837967	−	0.545721i	$-0.183744\pi$
$419$	−1.09766	−	1.90121i	−0.0536244	−	0.0928802i	−0.891592	+	0.452841i	$0.850411\pi$
$420$	3.47173	+	9.08243i	0.169403	+	0.443177i
$421$			1.72642i			0.0841406i	0.999115	+	0.0420703i	$0.0133954\pi$
$421$			1.72642i			0.0841406i	−0.999115	+	0.0420703i	$0.986605\pi$
$422$	−10.8838	+	18.8513i	−0.529816	+	0.917668i
$423$	4.14968	−	7.18745i	0.201764	−	0.349466i
$424$		−	5.82684i		−	0.282976i
$425$	11.0901	−	33.8070i	0.537948	−	1.63988i
$426$	11.1701	+	19.3472i	0.541194	+	0.937376i
$427$	8.65401	+	14.9892i	0.418797	+	0.725377i
$428$			0.119051i			0.00575454i
$429$	2.19820	−	2.95690i	0.106130	−	0.142761i
$430$	−10.8425	+	13.3508i	−0.522872	+	0.643834i
$431$	−12.9076	+	7.45221i	−0.621738	+	0.358960i	−0.777545	−	0.628827i	$-0.783535\pi$
$431$	−12.9076	+	7.45221i	−0.621738	+	0.358960i	0.155808	+	0.987787i	$0.450202\pi$
$432$	4.03867	−	2.33172i	0.194310	−	0.112185i
$433$	21.4234	+	12.3688i	1.02954	+	0.594405i	0.916853	−	0.399225i	$-0.130721\pi$
$433$	21.4234	+	12.3688i	1.02954	+	0.594405i	0.112688	+	0.993630i	$0.464054\pi$
$434$			22.1240i			1.06199i
$435$	7.08192	+	18.5271i	0.339552	+	0.888306i
$436$	13.5282	+	7.81050i	0.647882	+	0.374055i
$437$	14.1822			0.678427
$438$	18.8969	+	10.9101i	0.902930	+	0.521307i
$439$	−2.53103	−	4.38388i	−0.120800	−	0.209231i	0.799284	−	0.600954i	$-0.205213\pi$
$439$	−2.53103	−	4.38388i	−0.120800	−	0.209231i	−0.920083	+	0.391723i	$0.871879\pi$
$440$	−1.79257	−	0.286507i	−0.0854572	−	0.0136587i
$441$	−0.573141			−0.0272924
$442$	−5.60293	+	48.2213i	−0.266504	+	2.29366i
$443$		−	4.66874i		−	0.221818i	−0.993831	−	0.110909i	$-0.964624\pi$
$443$		−	4.66874i		−	0.221818i	0.993831	−	0.110909i	$-0.0353763\pi$
$444$	−4.86725	+	2.81011i	−0.230989	+	0.133362i
$445$	1.47008	+	0.234964i	0.0696885	+	0.0111383i
$446$	−24.7281	+	42.8303i	−1.17091	+	2.02807i
$447$	16.7768			0.793514
$448$	−6.00263	+	10.3969i	−0.283598	+	0.491205i
$449$	25.6870	+	14.8304i	1.21224	+	0.699889i	0.963247	−	0.268616i	$-0.0865661\pi$
$449$	25.6870	+	14.8304i	1.21224	+	0.699889i	0.248996	+	0.968505i	$0.419899\pi$
$450$	−1.94086	−	9.25939i	−0.0914931	−	0.436492i
$451$	1.62041	−	2.80663i	0.0763021	−	0.132159i
$452$	22.3634	−	12.9115i	1.05189	−	0.607306i
$453$	−2.03028	−	3.51654i	−0.0953907	−	0.165221i
$454$	35.5285			1.66743
$455$	21.5002	−	5.47697i	1.00794	−	0.256764i
$456$	1.64152			0.0768711
$457$	−2.43062	−	4.20995i	−0.113699	−	0.196933i	0.803560	−	0.595224i	$-0.202937\pi$
$457$	−2.43062	−	4.20995i	−0.113699	−	0.196933i	−0.917259	+	0.398291i	$0.869603\pi$
$458$	−2.46376	+	1.42245i	−0.115124	+	0.0664669i
$459$	−3.55795	+	6.16256i	−0.166071	+	0.287643i
$460$	15.2886	−	18.8255i	0.712834	−	0.877743i
$461$	8.07863	+	4.66420i	0.376259	+	0.217233i	0.676189	−	0.736728i	$-0.263630\pi$
$461$	8.07863	+	4.66420i	0.376259	+	0.217233i	−0.299930	+	0.953961i	$0.596963\pi$
$462$	−2.66049	+	4.60810i	−0.123777	+	0.214388i
$463$	−30.4425			−1.41478			−0.707392	−	0.706822i	$-0.750128\pi$
$463$	−30.4425			−1.41478			−0.707392	+	0.706822i	$0.750128\pi$
$464$	−20.6830	+	35.8240i	−0.960183	+	1.66309i
$465$	1.49949	−	9.38175i	0.0695372	−	0.435068i
$466$	15.7372	−	9.08589i	0.729013	−	0.420896i
$467$			17.1919i			0.795546i	0.917484	+	0.397773i	$0.130217\pi$
$467$			17.1919i			0.795546i	−0.917484	+	0.397773i	$0.869783\pi$
$468$	2.26013	+	5.22976i	0.104475	+	0.241746i
$469$	20.6975			0.955724
$470$	5.54193	−	34.6738i	0.255630	−	1.59938i
$471$	−2.62089	−	4.53951i	−0.120764	−	0.209170i
$472$	−2.04839	−	1.18264i	−0.0942847	−	0.0544353i
$473$	−4.15405			−0.191003
$474$	7.25397	+	4.18808i	0.333186	+	0.192365i
$475$	3.22022	−	9.81652i	0.147754	−	0.450413i
$476$		−	30.9429i		−	1.41827i
$477$	6.35184	+	3.66724i	0.290831	+	0.167911i
$478$	1.33908	−	0.773117i	0.0612480	−	0.0353615i
$479$	−33.3703	+	19.2663i	−1.52473	+	0.880301i	−0.525155	+	0.851006i	$0.675993\pi$
$479$	−33.3703	+	19.2663i	−1.52473	+	0.880301i	−0.999571	+	0.0292948i	$0.990674\pi$
$480$	10.1987	−	12.5581i	0.465507	−	0.573198i
$481$	5.08745	+	11.7720i	0.231968	+	0.536755i
$482$		−	9.31097i		−	0.424103i
$483$	9.44431	+	16.3580i	0.429731	+	0.744316i
$484$	−7.86569	−	13.6238i	−0.357531	−	0.619262i
$485$	−19.1520	+	7.32078i	−0.869646	+	0.332419i
$486$			1.89212i			0.0858285i
$487$	14.2507	−	24.6829i	0.645760	−	1.11849i	−0.338366	−	0.941015i	$-0.609874\pi$
$487$	14.2507	−	24.6829i	0.645760	−	1.11849i	0.984126	−	0.177474i	$-0.0567925\pi$
$488$	2.49829	−	4.32717i	0.113092	−	0.195882i
$489$			6.37130i			0.288120i
$490$	−2.26507	+	0.865817i	−0.102326	+	0.0391136i
$491$	2.49042	+	4.31353i	0.112391	+	0.194667i	0.916734	−	0.399499i	$-0.130816\pi$
$491$	2.49042	+	4.31353i	0.112391	+	0.194667i	−0.804343	+	0.594165i	$0.797482\pi$
$492$	2.50561	+	4.33985i	0.112962	+	0.195655i
$493$		−	63.1199i		−	2.84278i
$494$	−1.62692	+	14.0020i	−0.0731986	+	0.629980i
$495$	1.44051	−	1.77376i	0.0647461	−	0.0797245i
$496$	17.1599	−	9.90727i	0.770502	−	0.444849i
$497$	−28.1389	+	16.2460i	−1.26220	+	0.728733i
$498$	−16.4843	−	9.51724i	−0.738681	−	0.426478i
$499$			3.46759i			0.155231i	0.996983	+	0.0776153i	$0.0247306\pi$
$499$			3.46759i			0.155231i	−0.996983	+	0.0776153i	$0.975269\pi$
$500$	−9.55903	−	14.8569i	−0.427493	−	0.664419i
$501$	−7.89577	−	4.55862i	−0.352757	−	0.203664i
$502$	41.3328			1.84478
$503$	13.3859	+	7.72834i	0.596847	+	0.344590i	0.767800	−	0.640689i	$-0.221351\pi$
$503$	13.3859	+	7.72834i	0.596847	+	0.344590i	−0.170953	+	0.985279i	$0.554685\pi$
$504$	1.09313	+	1.89336i	0.0486919	+	0.0843369i
$505$	2.56918	−	16.0744i	0.114327	−	0.715303i
$506$	13.2714			0.589984
$507$	12.4488	−	3.74543i	0.552869	−	0.166340i
$508$			10.5728i			0.469091i
$509$	28.2636	−	16.3180i	1.25276	−	0.723281i	0.281103	−	0.959677i	$-0.409300\pi$
$509$	28.2636	−	16.3180i	1.25276	−	0.723281i	0.971657	+	0.236396i	$0.0759663\pi$
$510$	−4.75168	+	29.7295i	−0.210408	+	1.31644i
$511$	−15.8679	+	27.4840i	−0.701954	+	1.21582i
$512$	26.3300			1.16363
$513$	−1.03312	+	1.78942i	−0.0456134	+	0.0790048i
$514$	−27.3754	−	15.8052i	−1.20748	−	0.697138i
$515$	−14.5656	+	17.9353i	−0.641838	+	0.790322i
$516$	3.21167	−	5.56277i	0.141386	−	0.244887i
$517$	7.34478	−	4.24051i	0.323023	−	0.186497i
$518$	−9.26013	−	16.0390i	−0.406867	−	0.704714i
$519$	−0.671396			−0.0294710
$520$	−4.47269	−	4.58468i	−0.196141	−	0.201052i
$521$	4.28575			0.187762			0.0938810	−	0.995583i	$-0.470073\pi$
$521$	4.28575			0.187762			0.0938810	+	0.995583i	$0.470073\pi$
$522$	−8.39180	−	14.5350i	−0.367299	−	0.636181i
$523$	−27.6096	+	15.9404i	−1.20728	+	0.697025i	−0.962165	−	0.272468i	$-0.912160\pi$
$523$	−27.6096	+	15.9404i	−1.20728	+	0.697025i	−0.245118	+	0.969493i	$0.578827\pi$
$524$	−6.92302	+	11.9910i	−0.302433	+	0.523830i
$525$	13.4670	−	2.82282i	0.587748	−	0.123198i
$526$	−25.2612	−	14.5846i	−1.10144	−	0.635918i
$527$	−15.1174	+	26.1841i	−0.658524	+	1.14060i
$528$	4.76553			0.207393
$529$	12.0556	−	20.8810i	0.524158	−	0.907868i
$530$	30.6426	+	4.89763i	1.33103	+	0.212739i
$531$	2.57839	−	1.48863i	0.111892	−	0.0646012i
$532$		−	8.98488i		−	0.389544i
$533$	10.4964	−	4.53619i	0.454649	−	0.196484i
$534$	−1.25975			−0.0545145
$535$	0.166359	+	0.0265893i	0.00719234	+	0.00114956i
$536$	−2.98755	−	5.17458i	−0.129042	−	0.223508i
$537$	−10.4974	−	6.06066i	−0.452995	−	0.261537i
$538$	−35.7236			−1.54015
$539$	−0.507220	−	0.292843i	−0.0218475	−	0.0126137i
$540$	1.26156	+	3.30038i	0.0542889	+	0.142026i
$541$		−	8.89667i		−	0.382498i	−0.981542	−	0.191249i	$-0.938746\pi$
$541$		−	8.89667i		−	0.382498i	0.981542	−	0.191249i	$-0.0612538\pi$
$542$	18.9478	+	10.9395i	0.813876	+	0.469891i
$543$	−17.9717	+	10.3760i	−0.771240	+	0.445276i
$544$	−44.5857	+	25.7415i	−1.91159	+	1.10366i
$545$	13.9357	−	17.1596i	0.596939	−	0.735036i
$546$	−17.2336	+	7.44780i	−0.737530	+	0.318736i
$547$		−	24.4563i		−	1.04567i	−0.852433	−	0.522837i	$-0.824874\pi$
$547$		−	24.4563i		−	1.04567i	0.852433	−	0.522837i	$-0.175126\pi$
$548$	3.82263	+	6.62098i	0.163295	+	0.282834i
$549$	3.14470	+	5.44678i	0.134213	+	0.232463i
$550$	3.01341	−	9.18607i	0.128492	−	0.391695i
$551$		−	18.3281i		−	0.780803i
$552$	2.72644	−	4.72234i	0.116045	−	0.200996i
$553$	−6.09121	+	10.5503i	−0.259025	+	0.448644i
$554$		−	20.3218i		−	0.863389i
$555$	2.83972	+	7.42901i	0.120539	+	0.315344i
$556$	1.61992	+	2.80578i	0.0686998	+	0.118992i
$557$	−0.666552	−	1.15450i	−0.0282427	−	0.0489178i	0.851559	−	0.524259i	$-0.175658\pi$
$557$	−0.666552	−	1.15450i	−0.0282427	−	0.0489178i	−0.879801	+	0.475342i	$0.842324\pi$
$558$			8.03944i			0.340337i
$559$	−11.7625	−	8.74442i	−0.497502	−	0.369849i
$560$	22.2759	+	18.0908i	0.941330	+	0.764475i
$561$	−6.29745	+	3.63583i	−0.265878	+	0.153505i
$562$	−36.4435	+	21.0407i	−1.53728	+	0.887547i
$563$	12.1402	+	7.00913i	0.511647	+	0.295399i	0.733510	−	0.679678i	$-0.237881\pi$
$563$	12.1402	+	7.00913i	0.511647	+	0.295399i	−0.221864	+	0.975078i	$0.571214\pi$
$564$			13.1141i			0.552201i
$565$	−13.0476	−	34.1339i	−0.548915	−	1.43602i
$566$	−49.2111	−	28.4120i	−2.06850	−	1.19425i
$567$	−2.75193			−0.115570
$568$	8.12331	+	4.69000i	0.340847	+	0.196788i
$569$	11.4240	+	19.7870i	0.478920	+	0.829514i	0.999708	−	0.0241719i	$-0.00769492\pi$
$569$	11.4240	+	19.7870i	0.478920	+	0.829514i	−0.520787	+	0.853686i	$0.674362\pi$
$570$	−1.37974	+	8.63253i	−0.0577910	+	0.361577i
$571$	5.08850			0.212947			0.106473	−	0.994316i	$-0.466044\pi$
$571$	5.08850			0.212947			0.106473	+	0.994316i	$0.466044\pi$
$572$	−0.671942	+	5.78304i	−0.0280953	+	0.241801i
$573$		−	16.7274i		−	0.698798i
$574$	−14.3011	+	8.25673i	−0.596916	+	0.344629i
$575$	−22.8917	−	25.5685i	−0.954652	−	1.06628i
$576$	−2.18124	+	3.77802i	−0.0908850	+	0.157417i
$577$	36.2093			1.50741			0.753707	−	0.657211i	$-0.228264\pi$
$577$	36.2093			1.50741			0.753707	+	0.657211i	$0.228264\pi$
$578$	31.8218	−	55.1170i	1.32361	−	2.29257i
$579$	−10.8704	−	6.27603i	−0.451759	−	0.260823i
$580$	−24.3287	−	19.7579i	−1.01020	−	0.820402i
$581$	13.8420	−	23.9751i	0.574264	−	0.994654i
$582$	15.0253	−	8.67484i	0.622817	−	0.359584i
$583$	3.74751	+	6.49088i	0.155206	+	0.268825i
$584$	9.16168			0.379113
$585$	7.81275	−	1.99023i	0.323017	−	0.0822857i
$586$	−39.7360			−1.64148
$587$	0.845669	+	1.46474i	0.0349045	+	0.0604563i	0.882950	−	0.469467i	$-0.155554\pi$
$587$	0.845669	+	1.46474i	0.0349045	+	0.0604563i	−0.848045	+	0.529923i	$0.822221\pi$
$588$	0.784305	−	0.452819i	0.0323442	−	0.0186739i
$589$	−4.38963	+	7.60306i	−0.180872	+	0.313279i
$590$	7.94107	−	9.77818i	0.326929	−	0.402561i
$591$	−12.4966	−	7.21490i	−0.514040	−	0.296781i
$592$	−8.29348	+	14.3647i	−0.340860	+	0.590387i
$593$	−1.97200			−0.0809804			−0.0404902	−	0.999180i	$-0.512892\pi$
$593$	−1.97200			−0.0809804			−0.0404902	+	0.999180i	$0.512892\pi$
$594$	−0.966770	+	1.67449i	−0.0396671	+	0.0687054i
$595$	−43.2390	−	6.91091i	−1.77263	−	0.283320i
$596$	−22.9579	+	13.2547i	−0.940392	+	0.542935i
$597$		−	24.0846i		−	0.985716i
$598$	37.5790	+	27.9367i	1.53672	+	1.14242i
$599$	−13.7456			−0.561631			−0.280816	−	0.959762i	$-0.590605\pi$
$599$	−13.7456			−0.561631			−0.280816	+	0.959762i	$0.590605\pi$
$600$	−2.64960	−	2.95943i	−0.108169	−	0.120818i
$601$	−0.421642	−	0.730305i	−0.0171991	−	0.0297898i	0.857298	−	0.514821i	$-0.172142\pi$
$601$	−0.421642	−	0.730305i	−0.0171991	−	0.0297898i	−0.874497	+	0.485031i	$0.838808\pi$
$602$	18.3310	+	10.5834i	0.747115	+	0.431347i
$603$	7.52109			0.306282
$604$	5.55659	+	3.20810i	0.226095	+	0.130536i
$605$	−20.7943	+	7.94857i	−0.845410	+	0.323155i
$606$			13.7745i			0.559553i
$607$	−23.7921	−	13.7364i	−0.965691	−	0.557542i	−0.0677712	−	0.997701i	$-0.521589\pi$
$607$	−23.7921	−	13.7364i	−0.965691	−	0.557542i	−0.897920	+	0.440159i	$0.854922\pi$
$608$	−12.9463	+	7.47456i	−0.525042	+	0.303133i
$609$	21.1400	−	12.2052i	0.856635	−	0.494578i
$610$	20.6562	+	16.7753i	0.836343	+	0.679213i
$611$	29.7238	+	3.45366i	1.20249	+	0.139720i
$612$		−	11.2441i		−	0.454514i
$613$	4.53144	+	7.84868i	0.183023	+	0.317005i	0.942909	−	0.333052i	$-0.108078\pi$
$613$	4.53144	+	7.84868i	0.183023	+	0.317005i	−0.759885	+	0.650057i	$0.774745\pi$
$614$	−2.74486	−	4.75424i	−0.110773	−	0.191865i
$615$	6.62403	−	2.53201i	0.267107	−	0.102101i
$616$			2.23412i			0.0900151i
$617$	17.9320	−	31.0592i	0.721916	−	1.25040i	−0.238315	−	0.971188i	$-0.576595\pi$
$617$	17.9320	−	31.0592i	0.721916	−	1.25040i	0.960231	−	0.279207i	$-0.0900717\pi$
$618$	9.77544	−	16.9316i	0.393226	−	0.681087i
$619$			8.84216i			0.355396i	0.984085	+	0.177698i	$0.0568651\pi$
$619$			8.84216i			0.355396i	−0.984085	+	0.177698i	$0.943135\pi$
$620$	5.36024	+	14.0230i	0.215273	+	0.563177i
$621$	3.43188	+	5.94419i	0.137717	+	0.238532i
$622$	−21.5015	−	37.2418i	−0.862134	−	1.49326i
$623$		−	1.83219i		−	0.0734053i
$624$	13.4940	+	10.0316i	0.540192	+	0.401586i
$625$	−22.8956	+	10.0394i	−0.915826	+	0.401576i
$626$	39.3460	−	22.7164i	1.57258	−	0.907931i
$627$	−1.82859	+	1.05574i	−0.0730267	+	0.0421620i
$628$	7.17302	+	4.14135i	0.286235	+	0.165258i
$629$		−	25.3099i		−	1.00917i
$630$	−10.8757	+	4.15722i	−0.433300	+	0.165627i
$631$	22.0941	+	12.7560i	0.879550	+	0.507809i	0.870510	−	0.492151i	$-0.163789\pi$
$631$	22.0941	+	12.7560i	0.879550	+	0.507809i	0.00904022	+	0.999959i	$0.497122\pi$
$632$	3.51690			0.139895
$633$	−9.96306	−	5.75217i	−0.395996	−	0.228628i
$634$	2.72550	+	4.72070i	0.108243	+	0.187483i
$635$	14.7742	+	2.36137i	0.586296	+	0.0937081i
$636$	−11.5894			−0.459551
$637$	−0.819789	−	1.89693i	−0.0324812	−	0.0751589i
$638$		−	17.1510i		−	0.679014i
$639$	−10.2251	+	5.90349i	−0.404500	+	0.233538i
$640$	2.19353	−	13.7241i	0.0867070	−	0.542493i
$641$	−16.5425	+	28.6525i	−0.653391	+	1.13171i	0.328904	+	0.944363i	$0.393321\pi$
$641$	−16.5425	+	28.6525i	−0.653391	+	1.13171i	−0.982295	+	0.187342i	$0.940013\pi$
$642$	−0.142557			−0.00562628
$643$	−14.3769	+	24.9015i	−0.566970	+	0.982020i	0.429894	+	0.902879i	$0.358551\pi$
$643$	−14.3769	+	24.9015i	−0.566970	+	0.982020i	−0.996863	+	0.0791407i	$0.974782\pi$
$644$	−25.8478	−	14.9232i	−1.01855	−	0.588058i
$645$	−7.05600	−	5.73033i	−0.277830	−	0.225632i
$646$	13.9101	−	24.0930i	0.547286	−	0.947928i
$647$	−23.1838	+	13.3852i	−0.911451	+	0.526226i	−0.880898	−	0.473307i	$-0.843060\pi$
$647$	−23.1838	+	13.3852i	−0.911451	+	0.526226i	−0.0305530	+	0.999533i	$0.509727\pi$
$648$	0.397223	+	0.688010i	0.0156044	+	0.0270276i
$649$	3.04243			0.119426
$650$	27.8697	−	19.6678i	1.09314	−	0.771434i
$651$	−11.6927			−0.458273
$652$	−5.03374	−	8.71870i	−0.197137	−	0.341451i
$653$	−2.40659	+	1.38944i	−0.0941770	+	0.0543731i	−0.546349	−	0.837558i	$-0.683983\pi$
$653$	−2.40659	+	1.38944i	−0.0941770	+	0.0543731i	0.452172	+	0.891931i	$0.350649\pi$
$654$	−9.35266	+	16.1993i	−0.365718	+	0.633442i
$655$	15.2098	+	12.3522i	0.594296	+	0.482641i
$656$	12.8082	+	7.39483i	0.500077	+	0.288720i
$657$	−5.76609	+	9.98716i	−0.224956	+	0.389636i
$658$	−43.2147			−1.68468
$659$	−16.6376	+	28.8172i	−0.648110	+	1.12256i	0.335464	+	0.942053i	$0.391107\pi$
$659$	−16.6376	+	28.8172i	−0.648110	+	1.12256i	−0.983574	+	0.180506i	$0.942226\pi$
$660$	−0.569854	+	3.56537i	−0.0221816	+	0.138782i
$661$	24.1975	−	13.9704i	0.941174	−	0.543387i	0.0508461	−	0.998707i	$-0.483808\pi$
$661$	24.1975	−	13.9704i	0.941174	−	0.543387i	0.890328	+	0.455319i	$0.150475\pi$
$662$			65.1098i			2.53057i
$663$	−25.4853	−	2.96119i	−0.989767	−	0.115003i
$664$	−7.99200			−0.310150
$665$	−12.5553	−	2.00672i	−0.486873	−	0.0778172i
$666$	−3.36495	−	5.82827i	−0.130389	−	0.225841i
$667$	−52.7265	−	30.4417i	−2.04158	−	1.17871i
$668$	14.4064			0.557402
$669$	−22.6361	−	13.0690i	−0.875162	−	0.505275i
$670$	29.7236	−	11.3617i	1.14832	−	0.438943i
$671$			6.42707i			0.248114i
$672$	−17.2426	−	9.95502i	−0.665148	−	0.384023i
$673$	39.9467	−	23.0632i	1.53983	−	0.889021i	0.540982	−	0.841034i	$-0.318053\pi$
$673$	39.9467	−	23.0632i	1.53983	−	0.889021i	0.998848	−	0.0479875i	$-0.0152808\pi$
$674$	53.1495	−	30.6859i	2.04724	−	1.18198i
$675$	4.89365	−	1.02576i	0.188357	−	0.0394815i
$676$	−14.0762	+	14.9607i	−0.541391	+	0.575412i
$677$		−	25.6586i		−	0.986139i	−0.869990	−	0.493069i	$-0.835875\pi$
$677$		−	25.6586i		−	0.986139i	0.869990	−	0.493069i	$-0.164125\pi$
$678$	15.4609	+	26.7790i	0.593770	+	1.02844i
$679$	12.6168	+	21.8530i	0.484189	+	0.838641i
$680$	4.51346	+	11.8077i	0.173083	+	0.452805i
$681$			18.7770i			0.719538i
$682$	−4.10771	+	7.11476i	−0.157292	+	0.272438i
$683$	19.8728	−	34.4206i	0.760410	−	1.31707i	−0.182229	−	0.983256i	$-0.558331\pi$
$683$	19.8728	−	34.4206i	0.760410	−	1.31707i	0.942639	−	0.333813i	$-0.108335\pi$
$684$		−	3.26493i		−	0.124838i
$685$	10.1058	−	3.86291i	0.386122	−	0.147594i
$686$	−16.7323	−	28.9812i	−0.638843	−	1.10651i
$687$	−0.751777	−	1.30212i	−0.0286821	−	0.0496788i
$688$		−	18.9572i		−	0.722738i
$689$	−3.05214	+	26.2681i	−0.116277	+	1.00073i
$690$	22.5425	+	18.3073i	0.858179	+	0.696946i
$691$	24.5300	−	14.1624i	0.933166	−	0.538763i	0.0453542	−	0.998971i	$-0.485558\pi$
$691$	24.5300	−	14.1624i	0.933166	−	0.538763i	0.887811	+	0.460208i	$0.152225\pi$
$692$	0.918760	−	0.530446i	0.0349260	−	0.0201645i
$693$	−2.43541	−	1.40609i	−0.0925136	−	0.0534128i
$694$			45.5160i			1.72776i
$695$	4.28254	−	1.63699i	0.162446	−	0.0620944i
$696$	−6.10282	−	3.52346i	−0.231327	−	0.133557i
$697$	−22.5674			−0.854800
$698$	17.7478	+	10.2467i	0.671765	+	0.387843i
$699$	4.80196	+	8.31723i	0.181627	+	0.314587i
$700$	−16.1985	+	14.5027i	−0.612245	+	0.548149i
$701$	−4.25312			−0.160638			−0.0803191	−	0.996769i	$-0.525594\pi$
$701$	−4.25312			−0.160638			−0.0803191	+	0.996769i	$0.525594\pi$
$702$	−6.26236	+	2.70639i	−0.236358	+	0.102146i
$703$		−	7.34922i		−	0.277181i
$704$	−3.86072	+	2.22899i	−0.145506	+	0.0840080i
$705$	18.3253	+	2.92895i	0.690172	+	0.110311i
$706$	17.0284	−	29.4941i	0.640874	−	1.11003i
$707$	−20.0339			−0.753453
$708$	−2.35223	+	4.07419i	−0.0884024	+	0.153117i
$709$	−27.4094	−	15.8248i	−1.02938	−	0.594313i	−0.112573	−	0.993643i	$-0.535909\pi$
$709$	−27.4094	−	15.8248i	−1.02938	−	0.594313i	−0.916807	+	0.399330i	$0.869243\pi$
$710$	−31.4920	+	38.7774i	−1.18187	+	1.45529i
$711$	−2.21343	+	3.83377i	−0.0830101	+	0.143778i
$712$	−0.458066	+	0.264464i	−0.0171667	+	0.00991123i
$713$	14.5817	+	25.2563i	0.546090	+	0.945856i
$714$	37.0525			1.38666
$715$	7.93103	+	2.23057i	0.296604	+	0.0834185i
$716$	19.1533			0.715792
$717$	0.408597	+	0.707711i	0.0152593	+	0.0264300i
$718$	−6.84176	+	3.95009i	−0.255332	+	0.147416i
$719$	8.46811	−	14.6672i	0.315807	−	0.546994i	−0.663802	−	0.747909i	$-0.731058\pi$
$719$	8.46811	−	14.6672i	0.315807	−	0.546994i	0.979609	+	0.200915i	$0.0643914\pi$
$720$	8.09465	+	6.57384i	0.301670	+	0.244993i
$721$	24.6255	+	14.2176i	0.917103	+	0.529490i
$722$	−13.9361	+	24.1380i	−0.518648	+	0.898324i
$723$	4.92091			0.183011
$724$	16.3954	−	28.3977i	0.609330	−	1.05539i
$725$	−33.0430	+	29.5837i	−1.22719	+	1.09871i
$726$	16.3137	−	9.41875i	0.605460	−	0.349562i
$727$		−	0.165252i		−	0.00612885i	−0.999995	−	0.00306442i	$-0.999025\pi$
$727$		−	0.165252i		−	0.00612885i	0.999995	−	0.00306442i	$-0.000975438\pi$
$728$	−4.70289	+	6.32609i	−0.174301	+	0.234460i
$729$	−1.00000			−0.0370370
$730$	−7.70066	+	48.1801i	−0.285014	+	1.78323i
$731$	14.4633	+	25.0512i	0.534945	+	0.926552i
$732$	−8.60662	−	4.96904i	−0.318110	−	0.183661i
$733$	24.3707			0.900153			0.450076	−	0.892990i	$-0.351397\pi$
$733$	24.3707			0.900153			0.450076	+	0.892990i	$0.351397\pi$
$734$	−10.9803	−	6.33947i	−0.405289	−	0.233994i
$735$	−0.457590	−	1.19711i	−0.0168785	−	0.0441560i
$736$			49.6588i			1.83045i
$737$	6.65603	+	3.84286i	0.245178	+	0.141554i
$738$	−5.19674	+	3.00034i	−0.191295	+	0.110444i
$739$	2.35549	−	1.35994i	0.0866481	−	0.0500263i	−0.456050	−	0.889954i	$-0.650736\pi$
$739$	2.35549	−	1.35994i	0.0866481	−	0.0500263i	0.542698	+	0.839928i	$0.317403\pi$
$740$	−9.75536	−	7.92255i	−0.358614	−	0.291239i
$741$	−7.40016	−	0.859838i	−0.271852	−	0.0315869i
$742$		−	38.1906i		−	1.40202i
$743$	3.95135	+	6.84394i	0.144961	+	0.251080i	0.929358	−	0.369179i	$-0.120361\pi$
$743$	3.95135	+	6.84394i	0.144961	+	0.251080i	−0.784397	+	0.620259i	$0.787028\pi$
$744$	1.68776	+	2.92329i	0.0618763	+	0.107173i
$745$	13.3944	+	35.0413i	0.490733	+	1.28381i
$746$		−	20.4804i		−	0.749839i
$747$	5.02993	−	8.71209i	0.184035	−	0.318759i
$748$	5.74509	−	9.95079i	0.210061	−	0.363837i
$749$		−	0.207337i		−	0.00757594i
$750$	17.7903	−	11.4464i	0.649610	−	0.417965i
$751$	15.6733	+	27.1470i	0.571928	+	0.990608i	0.996368	+	0.0851520i	$0.0271376\pi$
$751$	15.6733	+	27.1470i	0.571928	+	0.990608i	−0.424440	+	0.905456i	$0.639529\pi$
$752$	19.3518	+	33.5183i	0.705688	+	1.22229i
$753$			21.8447i			0.796065i
$754$	36.1034	−	48.5644i	1.31481	−	1.76861i
$755$	5.72397	−	7.04816i	0.208316	−	0.256509i
$756$	3.76584	−	2.17421i	0.136962	−	0.0790751i
$757$	28.7796	−	16.6159i	1.04601	−	0.603917i	0.124483	−	0.992222i	$-0.460273\pi$
$757$	28.7796	−	16.6159i	1.04601	−	0.603917i	0.921531	+	0.388305i	$0.126939\pi$
$758$	−7.84144	−	4.52726i	−0.284814	−	0.164437i
$759$			7.01401i			0.254592i
$760$	1.31057	+	3.42860i	0.0475394	+	0.124368i
$761$	1.53292	+	0.885032i	0.0555683	+	0.0320824i	0.527527	−	0.849538i	$-0.323119\pi$
$761$	1.53292	+	0.885032i	0.0555683	+	0.0320824i	−0.471958	+	0.881621i	$0.656453\pi$
$762$	−12.6604			−0.458636
$763$	−23.5605	−	13.6027i	−0.852948	−	0.492450i
$764$	13.2158	+	22.8904i	0.478129	+	0.828144i
$765$	−15.7122	−	2.51129i	−0.568077	−	0.0907960i
$766$	53.8569			1.94593
$767$	8.61491	+	6.40443i	0.311066	+	0.231251i
$768$			20.4855i			0.739206i
$769$	22.2661	−	12.8554i	0.802937	−	0.463576i	−0.0415601	−	0.999136i	$-0.513233\pi$
$769$	22.2661	−	12.8554i	0.802937	−	0.463576i	0.844497	+	0.535560i	$0.179899\pi$
$770$	−11.7489	−	1.87784i	−0.423402	−	0.0676726i
$771$	8.35316	−	14.4681i	0.300832	−	0.521056i
$772$	19.8339			0.713837
$773$	8.50459	−	14.7304i	0.305889	−	0.529815i	−0.671570	−	0.740941i	$-0.734380\pi$
$773$	8.50459	−	14.7304i	0.305889	−	0.529815i	0.977459	+	0.211126i	$0.0677131\pi$
$774$	6.66113	+	3.84580i	0.239429	+	0.138235i
$775$	20.7926	−	4.35835i	0.746894	−	0.156556i
$776$	3.64230	−	6.30865i	0.130751	−	0.226467i
$777$	8.47673	−	4.89404i	0.304101	−	0.175573i
$778$	30.5168	+	52.8567i	1.09408	+	1.89500i
$779$	−6.55288			−0.234781
$780$	−9.11881	+	8.89607i	−0.326506	+	0.318530i
$781$	−12.0654			−0.431734
$782$	−46.2074	−	80.0336i	−1.65238	−	2.86200i
$783$	7.68186	−	4.43512i	0.274527	−	0.158498i
$784$	1.33641	−	2.31473i	0.0477288	−	0.0826688i
$785$	7.38909	−	9.09849i	0.263728	−	0.324739i
$786$	−14.3586	−	8.28995i	−0.512155	−	0.295693i
$787$	3.03490	−	5.25660i	0.108182	−	0.187378i	−0.806852	−	0.590754i	$-0.798830\pi$
$787$	3.03490	−	5.25660i	0.108182	−	0.187378i	0.915034	+	0.403377i	$0.132164\pi$
$788$	22.8010			0.812251
$789$	7.70805	−	13.3507i	0.274414	−	0.475298i
$790$	−2.95605	+	18.4949i	−0.105172	+	0.658020i
$791$	−38.9478	+	22.4865i	−1.38482	+	0.799528i
$792$			0.811835i			0.0288473i
$793$	−13.5292	+	18.1988i	−0.480436	+	0.646258i
$794$	2.70938			0.0961522
$795$	−2.58843	+	16.1948i	−0.0918021	+	0.574371i
$796$	19.0284	+	32.9581i	0.674443	+	1.16817i
$797$	−5.06243	−	2.92280i	−0.179321	−	0.103531i	0.407653	−	0.913137i	$-0.366347\pi$
$797$	−5.06243	−	2.92280i	−0.179321	−	0.103531i	−0.586973	+	0.809606i	$0.699681\pi$
$798$	10.7589			0.380862
$799$	−51.1452	−	29.5287i	−1.80939	−	1.04465i
$800$	34.3725	+	11.2756i	1.21525	+	0.398652i
$801$		−	0.665784i		−	0.0235243i
$802$	17.5920	+	10.1568i	0.621195	+	0.358647i
$803$	−10.2058	+	5.89230i	−0.360154	+	0.207935i
$804$	−10.2921	+	5.94215i	−0.362975	+	0.209563i
$805$	−26.6264	+	32.7862i	−0.938457	+	1.15556i
$806$	−26.6081	+	11.4992i	−0.937232	+	0.405041i
$807$		−	18.8802i		−	0.664614i
$808$	2.89176	+	5.00867i	0.101732	+	0.176204i
$809$	−15.0309	−	26.0343i	−0.528458	−	0.915316i	−0.999449	−	0.0331780i	$-0.989437\pi$
$809$	−15.0309	−	26.0343i	−0.528458	−	0.915316i	0.470992	−	0.882138i	$-0.343896\pi$
$810$	−3.95204	+	1.51065i	−0.138860	+	0.0530789i
$811$			23.9516i			0.841053i	0.907280	+	0.420527i	$0.138155\pi$
$811$			23.9516i			0.841053i	−0.907280	+	0.420527i	$0.861845\pi$
$812$	−19.2858	+	33.4039i	−0.676797	+	1.17225i
$813$	−5.78160	+	10.0140i	−0.202769	+	0.351207i
$814$		−	6.87722i		−	0.241046i
$815$	−13.3076	+	5.08678i	−0.466145	+	0.178182i
$816$	−16.5923	−	28.7388i	−0.580848	−	1.00606i
$817$	4.19971	+	7.27411i	0.146929	+	0.254489i
$818$			16.3652i			0.572194i
$819$	−3.93621	−	9.10808i	−0.137542	−	0.318262i
$820$	−7.06408	+	8.69830i	−0.246689	+	0.303758i
$821$	−24.4353	+	14.1077i	−0.852797	+	0.492362i	−0.861593	−	0.507599i	$-0.830533\pi$
$821$	−24.4353	+	14.1077i	−0.852797	+	0.492362i	0.00879689	+	0.999961i	$0.497200\pi$
$822$	−7.92828	+	4.57740i	−0.276531	+	0.159655i
$823$	8.17559	+	4.72018i	0.284983	+	0.164535i	0.635677	−	0.771955i	$-0.280721\pi$
$823$	8.17559	+	4.72018i	0.284983	+	0.164535i	−0.350694	+	0.936490i	$0.614054\pi$
$824$		−	8.20883i		−	0.285968i
$825$	4.85490	+	1.59261i	0.169026	+	0.0554474i
$826$	−13.4257	−	7.75131i	−0.467138	−	0.269702i
$827$	−23.2744			−0.809329			−0.404665	−	0.914465i	$-0.632612\pi$
$827$	−23.2744			−0.809329			−0.404665	+	0.914465i	$0.632612\pi$
$828$	−9.39260	−	5.42282i	−0.326415	−	0.188456i
$829$	6.05123	+	10.4810i	0.210168	+	0.364021i	0.951767	−	0.306822i	$-0.0992656\pi$
$829$	6.05123	+	10.4810i	0.210168	+	0.364021i	−0.741599	+	0.670843i	$0.765932\pi$
$830$	6.71751	−	42.0289i	0.233168	−	1.45885i
$831$	10.7402			0.372573
$832$	−15.6240	−	1.81539i	−0.541666	−	0.0629372i
$833$			4.07842i			0.141309i
$834$	−3.35977	+	1.93977i	−0.116339	+	0.0671686i
$835$	3.21759	−	20.1313i	0.111349	−	0.696671i
$836$	1.66820	−	2.88941i	0.0576959	−	0.0999322i
$837$	−4.24890			−0.146863
$838$	−2.07692	+	3.59732i	−0.0717459	+	0.124267i
$839$	19.1860	+	11.0770i	0.662374	+	0.382422i	0.793181	−	0.608986i	$-0.208423\pi$
$839$	19.1860	+	11.0770i	0.662374	+	0.382422i	−0.130807	+	0.991408i	$0.541757\pi$
$840$	−3.08187	+	3.79483i	−0.106335	+	0.130934i
$841$	−24.8407	+	43.0253i	−0.856574	+	1.48363i
$842$	2.82896	−	1.63330i	0.0974924	−	0.0562873i
$843$	−11.1201	−	19.2606i	−0.382998	−	0.663372i
$844$	18.1784			0.625725
$845$	17.7620	+	23.0111i	0.611030	+	0.791607i
$846$	−15.7034			−0.539894
$847$	13.6988	+	23.7270i	0.470695	+	0.815268i
$848$	−29.6215	+	17.1020i	−1.01721	+	0.587284i
$849$	15.0160	−	26.0084i	0.515346	−	0.892606i
$850$	−65.8890	+	13.8110i	−2.25997	+	0.473713i
$851$	−21.1423	−	12.2065i	−0.724750	−	0.418434i
$852$	9.32828	−	16.1570i	0.319581	−	0.553531i
$853$	−43.8476			−1.50131			−0.750657	−	0.660692i	$-0.770263\pi$
$853$	−43.8476			−1.50131			−0.750657	+	0.660692i	$0.770263\pi$
$854$	16.3744	−	28.3614i	0.560322	−	0.970506i
$855$	−4.56235	−	0.729203i	−0.156029	−	0.0249382i
$856$	−0.0518363	+	0.0299277i	−0.00177173	+	0.00102291i
$857$		−	9.97093i		−	0.340601i	−0.985392	−	0.170300i	$-0.945526\pi$
$857$		−	9.97093i		−	0.340601i	0.985392	−	0.170300i	$-0.0544738\pi$
$858$	−6.92489	−	0.804616i	−0.236412	−	0.0274691i
$859$	−17.7464			−0.605498			−0.302749	−	0.953070i	$-0.597904\pi$
$859$	−17.7464			−0.605498			−0.302749	+	0.953070i	$0.597904\pi$
$860$	14.1830	+	2.26688i	0.483636	+	0.0772999i
$861$	−4.36374	−	7.55822i	−0.148716	−	0.257583i
$862$	24.4228	+	14.1005i	0.831843	+	0.480265i
$863$	−57.4040			−1.95405			−0.977027	−	0.213117i	$-0.931638\pi$
$863$	−57.4040			−1.95405			−0.977027	+	0.213117i	$0.931638\pi$
$864$	−6.26563	−	3.61746i	−0.213161	−	0.123069i
$865$	−0.536036	−	1.40233i	−0.0182258	−	0.0476806i
$866$		−	46.8065i		−	1.59055i
$867$	29.1297	+	16.8181i	0.989298	+	0.571171i
$868$	16.0007	−	9.23799i	0.543098	−	0.313558i
$869$	−3.91769	+	2.26188i	−0.132899	+	0.0767290i
$870$	23.6591	−	29.1324i	0.802117	−	0.987680i
$871$	10.7577	+	24.8925i	0.364512	+	0.843452i
$872$			7.85380i			0.265963i
$873$	4.58471	+	7.94095i	0.155169	+	0.268761i
$874$	−13.4172	−	23.2393i	−0.453845	−	0.786082i
$875$	16.6479	+	25.8745i	0.562801	+	0.874718i
$876$		−	18.2223i		−	0.615676i
$877$	−2.33419	+	4.04293i	−0.0788199	+	0.136520i	−0.902741	−	0.430184i	$-0.858449\pi$
$877$	−2.33419	+	4.04293i	−0.0788199	+	0.136520i	0.823921	+	0.566704i	$0.191782\pi$
$878$	−4.78903	+	8.29484i	−0.161622	+	0.279937i
$879$		−	21.0008i		−	0.708338i
$880$	3.80475	+	9.95365i	0.128258	+	0.335537i
$881$	9.16855	+	15.8804i	0.308896	+	0.535024i	0.978121	−	0.208036i	$-0.0667071\pi$
$881$	9.16855	+	15.8804i	0.308896	+	0.535024i	−0.669225	+	0.743060i	$0.733374\pi$
$882$	0.542227	+	0.939164i	0.0182577	+	0.0316233i
$883$		−	14.4328i		−	0.485704i	−0.970063	−	0.242852i	$-0.921917\pi$
$883$		−	14.4328i		−	0.485704i	0.970063	−	0.242852i	$-0.0780829\pi$
$884$	37.2145	−	16.0829i	1.25166	−	0.540925i
$885$	5.16783	+	4.19691i	0.173715	+	0.141078i
$886$	−7.65032	+	4.41691i	−0.257017	+	0.148389i
$887$	−11.9503	+	6.89952i	−0.401253	+	0.231663i	−0.687024	−	0.726634i	$-0.741083\pi$
$887$	−11.9503	+	6.89952i	−0.401253	+	0.231663i	0.285772	+	0.958298i	$0.407750\pi$
$888$	−2.44712	−	1.41284i	−0.0821198	−	0.0474119i
$889$		−	18.4134i		−	0.617566i
$890$	−1.00577	−	2.63120i	−0.0337134	−	0.0881981i
$891$	−0.884982	−	0.510945i	−0.0296480	−	0.0171173i
$892$	41.3013			1.38287
$893$	−14.8510	−	8.57424i	−0.496970	−	0.286926i
$894$	−15.8719	−	27.4909i	−0.530834	−	0.919432i
$895$	4.27777	−	26.7644i	0.142990	−	0.894636i
$896$	−17.1047			−0.571427
$897$	−14.7647	+	19.8607i	−0.492980	+	0.663131i
$898$		−	56.1218i		−	1.87281i
$899$	32.6395	−	18.8444i	1.08859	−	0.628496i
$900$	−5.88622	+	5.26998i	−0.196207	+	0.175666i
$901$	26.0957	−	45.1991i	0.869374	−	1.50580i
$902$	−6.13203			−0.204174
$903$	−5.59340	+	9.68805i	−0.186137	+	0.322398i
$904$	11.2437	+	6.49154i	0.373959	+	0.215906i
$905$	−36.0205	−	29.2530i	−1.19736	−	0.972404i
$906$	−3.84153	+	6.65373i	−0.127626	+	0.221055i
$907$	−17.2730	+	9.97260i	−0.573542	+	0.331135i	−0.758563	−	0.651600i	$-0.774098\pi$
$907$	−17.2730	+	9.97260i	−0.573542	+	0.331135i	0.185021	+	0.982735i	$0.440765\pi$
$908$	−14.8351	−	25.6951i	−0.492319	−	0.852722i
$909$	−7.27994			−0.241460
$910$	−29.3152	−	30.0492i	−0.971789	−	0.996121i
$911$	−34.7472			−1.15123			−0.575613	−	0.817722i	$-0.695237\pi$
$911$	−34.7472			−1.15123			−0.575613	+	0.817722i	$0.695237\pi$
$912$	−4.81791	−	8.34486i	−0.159537	−	0.276326i
$913$	8.90279	−	5.14003i	0.294639	−	0.170110i
$914$	−4.59902	+	7.96574i	−0.152122	+	0.263483i
$915$	−8.86587	+	10.9169i	−0.293097	+	0.360902i
$916$	2.05751	+	1.18791i	0.0679821	+	0.0392495i
$917$	12.0570	−	20.8834i	0.398158	−	0.689631i
$918$	13.4642			0.444384
$919$	−28.0544	+	48.5917i	−0.925430	+	1.60289i	−0.134561	+	0.990905i	$0.542962\pi$
$919$	−28.0544	+	48.5917i	−0.925430	+	1.60289i	−0.790869	+	0.611986i	$0.790371\pi$
$920$	12.0402	+	1.92439i	0.396954	+	0.0634453i
$921$	2.51265	−	1.45068i	0.0827945	−	0.0478014i
$922$		−	17.6505i		−	0.581287i
$923$	−34.1642	−	25.3981i	−1.12453	−	0.835989i
$924$	4.44360			0.146184
$925$	−13.2496	+	11.8625i	−0.435645	+	0.390037i
$926$	28.8005	+	49.8839i	0.946443	+	1.63929i
$927$	8.94845	+	5.16639i	0.293906	+	0.169686i
$928$	64.1756			2.10667
$929$	5.48826	+	3.16865i	0.180064	+	0.103960i	0.587323	−	0.809353i	$-0.300182\pi$
$929$	5.48826	+	3.16865i	0.180064	+	0.103960i	−0.407259	+	0.913313i	$0.633515\pi$
$930$	−16.7918	+	6.41861i	−0.550625	+	0.210475i
$931$			1.18425i			0.0388122i
$932$	−13.1423	−	7.58772i	−0.430491	−	0.248544i
$933$	19.6825	−	11.3637i	0.644377	−	0.372031i
$934$	28.1711	−	16.2646i	0.921786	−	0.532193i
$935$	−12.6219	−	10.2505i	−0.412780	−	0.335228i
$936$	−1.70894	+	2.29878i	−0.0558585	+	0.0751379i
$937$			19.8962i			0.649982i	0.945717	+	0.324991i	$0.105361\pi$
$937$			19.8962i			0.649982i	−0.945717	+	0.324991i	$0.894639\pi$
$938$	−19.5811	−	33.9155i	−0.639347	−	1.10738i
$939$	12.0058	+	20.7946i	0.391794	+	0.678607i
$940$	−27.3910	+	10.4701i	−0.893397	+	0.341498i
$941$		−	34.3031i		−	1.11825i	−0.829084	−	0.559125i	$-0.811137\pi$
$941$		−	34.3031i		−	1.11825i	0.829084	−	0.559125i	$-0.188863\pi$
$942$	−4.95905	+	8.58932i	−0.161574	+	0.279855i
$943$	−10.8839	+	18.8514i	−0.354427	+	0.613886i
$944$			13.8843i			0.451896i
$945$	−2.19712	−	5.74790i	−0.0714722	−	0.186979i
$946$	3.92998	+	6.80693i	0.127775	+	0.221312i
$947$	17.7768	+	30.7903i	0.577668	+	1.00055i	0.995746	+	0.0921392i	$0.0293705\pi$
$947$	17.7768	+	30.7903i	0.577668	+	1.00055i	−0.418078	+	0.908411i	$0.637296\pi$
$948$		−	6.99501i		−	0.227187i
$949$	−41.3020	−	4.79895i	−1.34072	−	0.155781i
$950$	−19.1321	+	4.01029i	−0.620729	+	0.130111i
$951$	−2.49492	+	1.44044i	−0.0809033	+	0.0467096i
$952$	13.4730	−	7.77861i	0.436661	−	0.252106i
$953$	16.7026	+	9.64323i	0.541049	+	0.312375i	0.745504	−	0.666501i	$-0.232209\pi$
$953$	16.7026	+	9.64323i	0.541049	+	0.312375i	−0.204455	+	0.978876i	$0.565542\pi$
$954$		−	13.8777i		−	0.449308i
$955$	34.9382	−	13.3550i	1.13057	−	0.432158i
$956$	−1.11828	−	0.645637i	−0.0361676	−	0.0208814i
$957$	9.06441			0.293011
$958$	63.1407	+	36.4543i	2.03998	+	1.17778i
$959$	−6.65744	−	11.5310i	−0.214980	−	0.372356i
$960$	−9.63254	−	1.53957i	−0.310889	−	0.0496896i
$961$	12.9468			0.417640
$962$	14.4768	−	19.4734i	0.466751	−	0.627848i
$963$		−	0.0753424i		−	0.00242787i
$964$	−6.73394	+	3.88784i	−0.216886	+	0.125219i
$965$	4.42978	−	27.7155i	0.142600	−	0.892193i
$966$	17.8698	−	30.9514i	0.574952	−	0.995845i
$967$	42.9033			1.37968			0.689838	−	0.723964i	$-0.257682\pi$
$967$	42.9033			1.37968			0.689838	+	0.723964i	$0.257682\pi$
$968$	3.95465	−	6.84965i	0.127107	−	0.220156i
$969$	12.7333	+	7.35159i	0.409054	+	0.236167i
$970$	30.1150	+	24.4570i	0.966933	+	0.785268i
$971$	3.98693	−	6.90556i	0.127947	−	0.221610i	−0.794934	−	0.606696i	$-0.792495\pi$
$971$	3.98693	−	6.90556i	0.127947	−	0.221610i	0.922881	+	0.385085i	$0.125828\pi$
$972$	1.36843	−	0.790065i	0.0438925	−	0.0253414i
$973$	−2.82123	−	4.88651i	−0.0904444	−	0.156654i
$974$	−53.9281			−1.72797
$975$	10.3946	+	14.7293i	0.332892	+	0.471716i
$976$	−29.3303			−0.938840
$977$	16.4237	+	28.4467i	0.525441	+	0.910090i	0.999561	+	0.0296299i	$0.00943287\pi$
$977$	16.4237	+	28.4467i	0.525441	+	0.910090i	−0.474120	+	0.880460i	$0.657234\pi$
$978$	10.4402	−	6.02764i	0.333840	−	0.192743i
$979$	0.340179	−	0.589207i	0.0108722	−	0.0188311i
$980$	1.57197	+	1.27663i	0.0502149	+	0.0407806i
$981$	−8.56144	−	4.94295i	−0.273346	−	0.157816i
$982$	4.71217	−	8.16172i	0.150371	−	0.260451i
$983$	43.6529			1.39231			0.696155	−	0.717892i	$-0.254893\pi$
$983$	43.6529			1.39231			0.696155	+	0.717892i	$0.254893\pi$
$984$	−1.25975	+	2.18195i	−0.0401594	+	0.0695581i
$985$	5.09246	−	31.8616i	0.162259	−	1.01520i
$986$	−103.430	+	59.7153i	−3.29388	+	1.90172i
$987$		−	22.8393i		−	0.726982i
$988$	10.8059	−	4.66998i	0.343783	−	0.148572i
$989$	27.9017			0.887221
$990$	−4.26934	−	0.682371i	−0.135688	−	0.0216872i
$991$	−0.720062	−	1.24718i	−0.0228735	−	0.0396181i	0.854362	−	0.519678i	$-0.173948\pi$
$991$	−0.720062	−	1.24718i	−0.0228735	−	0.0396181i	−0.877236	+	0.480060i	$0.840615\pi$
$992$	−26.6221	−	15.3702i	−0.845251	−	0.488006i
$993$	−34.4110			−1.09200
$994$	53.2423	+	30.7394i	1.68874	+	0.974996i
$995$	50.3049	−	19.2289i	1.59477	−	0.609597i
$996$			15.8959i			0.503680i
$997$	−30.1307	−	17.3960i	−0.954249	−	0.550936i	−0.0598504	−	0.998207i	$-0.519062\pi$
$997$	−30.1307	−	17.3960i	−0.954249	−	0.550936i	−0.894398	+	0.447272i	$0.852396\pi$
$998$	5.68209	−	3.28055i	0.179863	−	0.103844i
$999$	3.08028	−	1.77840i	0.0974558	−	0.0562661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.v.a.49.4	yes	32
3.2	odd	2		585.2.bf.c.244.13		32
5.2	odd	4		975.2.bc.m.751.7		16
5.3	odd	4		975.2.bc.n.751.2		16
5.4	even	2	inner	195.2.v.a.49.13	yes	32
13.4	even	6	inner	195.2.v.a.4.13	yes	32
15.14	odd	2		585.2.bf.c.244.4		32
39.17	odd	6		585.2.bf.c.199.4		32
65.4	even	6	inner	195.2.v.a.4.4	✓	32
65.17	odd	12		975.2.bc.m.901.7		16
65.43	odd	12		975.2.bc.n.901.2		16
195.134	odd	6		585.2.bf.c.199.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.v.a.4.4	✓	32	65.4	even	6	inner
195.2.v.a.4.13	yes	32	13.4	even	6	inner
195.2.v.a.49.4	yes	32	1.1	even	1	trivial
195.2.v.a.49.13	yes	32	5.4	even	2	inner
585.2.bf.c.199.4		32	39.17	odd	6
585.2.bf.c.199.13		32	195.134	odd	6
585.2.bf.c.244.4		32	15.14	odd	2
585.2.bf.c.244.13		32	3.2	odd	2
975.2.bc.m.751.7		16	5.2	odd	4
975.2.bc.m.901.7		16	65.17	odd	12
975.2.bc.n.751.2		16	5.3	odd	4
975.2.bc.n.901.2		16	65.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.946062 - 1.63863i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.790065 + 1.36843i) q^{4} +(1.73576 + 1.40965i) q^{5} +(-1.63863 - 0.946062i) q^{6} +(1.37597 - 2.38324i) q^{7} -0.794445 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.946062 - 1.63863i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.790065 + 1.36843i) q^{4} +(1.73576 + 1.40965i) q^{5} +(-1.63863 - 0.946062i) q^{6} +(1.37597 - 2.38324i) q^{7} -0.794445 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.667754 - 4.17789i) q^{10} +(0.884982 - 0.510945i) q^{11} +1.58013i q^{12} +(3.58146 + 0.416136i) q^{13} -5.20700 q^{14} +(2.20804 + 0.352913i) q^{15} +(2.33172 + 4.03867i) q^{16} +(-6.16256 - 3.55795i) q^{17} -1.89212 q^{18} +(-1.78942 - 1.03312i) q^{19} +(-3.30038 + 1.26156i) q^{20} -2.75193i q^{21} +(-1.67449 - 0.966770i) q^{22} +(-5.94419 + 3.43188i) q^{23} +(-0.688010 + 0.397223i) q^{24} +(1.02576 + 4.89365i) q^{25} +(-2.70639 - 6.26236i) q^{26} -1.00000i q^{27} +(2.17421 + 3.76584i) q^{28} +(4.43512 + 7.68186i) q^{29} +(-1.51065 - 3.95204i) q^{30} -4.24890i q^{31} +(3.61746 - 6.26563i) q^{32} +(0.510945 - 0.884982i) q^{33} +13.4642i q^{34} +(5.74790 - 2.19712i) q^{35} +(0.790065 + 1.36843i) q^{36} +(1.77840 + 3.08028i) q^{37} +3.90959i q^{38} +(3.30970 - 1.43034i) q^{39} +(-1.37897 - 1.11989i) q^{40} +(2.74651 - 1.58570i) q^{41} +(-4.50939 + 2.60350i) q^{42} +(-3.52045 - 2.03253i) q^{43} +1.61472i q^{44} +(2.08868 - 0.798390i) q^{45} +(11.2471 + 6.49354i) q^{46} +8.29935 q^{47} +(4.03867 + 2.33172i) q^{48} +(-0.286571 - 0.496355i) q^{49} +(7.04844 - 6.31053i) q^{50} -7.11591 q^{51} +(-3.39904 + 4.57221i) q^{52} +7.33447i q^{53} +(-1.63863 + 0.946062i) q^{54} +(2.25637 + 0.360638i) q^{55} +(-1.09313 + 1.89336i) q^{56} -2.06624 q^{57} +(8.39180 - 14.5350i) q^{58} +(2.57839 + 1.48863i) q^{59} +(-2.22743 + 2.74273i) q^{60} +(-3.14470 + 5.44678i) q^{61} +(-6.96236 + 4.01972i) q^{62} +(-1.37597 - 2.38324i) q^{63} -4.36248 q^{64} +(5.62996 + 5.77092i) q^{65} -1.93354 q^{66} +(3.76054 + 6.51345i) q^{67} +(9.73764 - 5.62203i) q^{68} +(-3.43188 + 5.94419i) q^{69} +(-9.03812 - 7.34006i) q^{70} +(-10.2251 - 5.90349i) q^{71} +(-0.397223 + 0.688010i) q^{72} -11.5322 q^{73} +(3.36495 - 5.82827i) q^{74} +(3.33516 + 3.72515i) q^{75} +(2.82751 - 1.63247i) q^{76} -2.81217i q^{77} +(-5.47498 - 4.07017i) q^{78} -4.42686 q^{79} +(-1.64579 + 10.2971i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.19674 - 3.00034i) q^{82} +10.0599 q^{83} +(3.76584 + 2.17421i) q^{84} +(-5.68127 - 14.8628i) q^{85} +7.69161i q^{86} +(7.68186 + 4.43512i) q^{87} +(-0.703070 + 0.405917i) q^{88} +(0.576586 - 0.332892i) q^{89} +(-3.28428 - 2.66724i) q^{90} +(5.91972 - 7.96290i) q^{91} -10.8456i q^{92} +(-2.12445 - 3.67966i) q^{93} +(-7.85170 - 13.5995i) q^{94} +(-1.64967 - 4.31571i) q^{95} -7.23493i q^{96} +(-4.58471 + 7.94095i) q^{97} +(-0.542227 + 0.939164i) q^{98} -1.02189i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 20 * q^4 + 16 * q^9	\( 32 q - 20 q^{4} + 16 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} - 6 q^{15} - 28 q^{16} - 30 q^{20} - 4 q^{25} + 52 q^{26} - 24 q^{29} + 4 q^{30} - 2 q^{35} + 20 q^{36} + 4 q^{40} - 36 q^{41} + 12 q^{45} - 48 q^{46} - 28 q^{49} + 54 q^{50} - 40 q^{51} + 24 q^{55} - 56 q^{56} + 84 q^{59} - 32 q^{61} + 136 q^{64} + 20 q^{65} + 8 q^{66} - 24 q^{69} + 12 q^{71} + 40 q^{74} - 16 q^{75} + 48 q^{76} - 104 q^{79} + 66 q^{80} - 16 q^{81} - 48 q^{84} - 54 q^{85} - 48 q^{89} + 4 q^{90} + 12 q^{91} - 8 q^{94} + 12 q^{95}+O(q^{100}) \) 32 * q - 20 * q^4 + 16 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 - 6 * q^15 - 28 * q^16 - 30 * q^20 - 4 * q^25 + 52 * q^26 - 24 * q^29 + 4 * q^30 - 2 * q^35 + 20 * q^36 + 4 * q^40 - 36 * q^41 + 12 * q^45 - 48 * q^46 - 28 * q^49 + 54 * q^50 - 40 * q^51 + 24 * q^55 - 56 * q^56 + 84 * q^59 - 32 * q^61 + 136 * q^64 + 20 * q^65 + 8 * q^66 - 24 * q^69 + 12 * q^71 + 40 * q^74 - 16 * q^75 + 48 * q^76 - 104 * q^79 + 66 * q^80 - 16 * q^81 - 48 * q^84 - 54 * q^85 - 48 * q^89 + 4 * q^90 + 12 * q^91 - 8 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more