LMFDB - Embedded newform 1001.2.i.d.716.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, 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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			716.3
Character	$\chi$	$=$	1001.716
Dual form			1001.2.i.d.144.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27968 + 2.21648i) q^{2} +(1.33068 + 2.30480i) q^{3} +(-2.27518 - 3.94073i) q^{4} +(1.23753 - 2.14346i) q^{5} -6.81138 q^{6} +(-2.63170 - 0.272277i) q^{7} +6.52730 q^{8} +(-2.04140 + 3.53582i) q^{9} +O(q^{10})$	\(q+(-1.27968 + 2.21648i) q^{2} +(1.33068 + 2.30480i) q^{3} +(-2.27518 - 3.94073i) q^{4} +(1.23753 - 2.14346i) q^{5} -6.81138 q^{6} +(-2.63170 - 0.272277i) q^{7} +6.52730 q^{8} +(-2.04140 + 3.53582i) q^{9} +(3.16729 + 5.48591i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(6.05506 - 10.4877i) q^{12} -1.00000 q^{13} +(3.97124 - 5.48468i) q^{14} +6.58701 q^{15} +(-3.80252 + 6.58616i) q^{16} +(-3.45334 - 5.98137i) q^{17} +(-5.22470 - 9.04945i) q^{18} +(1.65010 - 2.85806i) q^{19} -11.2624 q^{20} +(-2.87440 - 6.42787i) q^{21} +2.55937 q^{22} +(2.24165 - 3.88264i) q^{23} +(8.68573 + 15.0441i) q^{24} +(-0.562958 - 0.975073i) q^{25} +(1.27968 - 2.21648i) q^{26} -2.88174 q^{27} +(4.91463 + 10.9903i) q^{28} -4.82099 q^{29} +(-8.42929 + 14.6000i) q^{30} +(-4.76298 - 8.24972i) q^{31} +(-3.20474 - 5.55077i) q^{32} +(1.33068 - 2.30480i) q^{33} +17.6767 q^{34} +(-3.84043 + 5.30401i) q^{35} +18.5782 q^{36} +(-0.300685 + 0.520801i) q^{37} +(4.22321 + 7.31482i) q^{38} +(-1.33068 - 2.30480i) q^{39} +(8.07773 - 13.9910i) q^{40} -2.83361 q^{41} +(17.9255 + 1.85458i) q^{42} +6.51660 q^{43} +(-2.27518 + 3.94073i) q^{44} +(5.05260 + 8.75136i) q^{45} +(5.73719 + 9.93711i) q^{46} +(2.52044 - 4.36554i) q^{47} -20.2397 q^{48} +(6.85173 + 1.43310i) q^{49} +2.88163 q^{50} +(9.19057 - 15.9185i) q^{51} +(2.27518 + 3.94073i) q^{52} +(4.50223 + 7.79809i) q^{53} +(3.68772 - 6.38731i) q^{54} -2.47506 q^{55} +(-17.1779 - 1.77723i) q^{56} +8.78301 q^{57} +(6.16933 - 10.6856i) q^{58} +(1.30453 + 2.25951i) q^{59} +(-14.9866 - 25.9576i) q^{60} +(1.38917 - 2.40612i) q^{61} +24.3804 q^{62} +(6.33509 - 8.74940i) q^{63} +1.19414 q^{64} +(-1.23753 + 2.14346i) q^{65} +(3.40569 + 5.89883i) q^{66} +(-8.13877 - 14.0968i) q^{67} +(-15.7139 + 27.2174i) q^{68} +11.9316 q^{69} +(-6.84169 - 15.2997i) q^{70} +5.66827 q^{71} +(-13.3249 + 23.0793i) q^{72} +(-3.34495 - 5.79362i) q^{73} +(-0.769562 - 1.33292i) q^{74} +(1.49823 - 2.59501i) q^{75} -15.0171 q^{76} +(1.08005 + 2.41526i) q^{77} +6.81138 q^{78} +(-8.22391 + 14.2442i) q^{79} +(9.41146 + 16.3011i) q^{80} +(2.28955 + 3.96561i) q^{81} +(3.62613 - 6.28064i) q^{82} -5.26198 q^{83} +(-18.7907 + 25.9518i) q^{84} -17.0945 q^{85} +(-8.33918 + 14.4439i) q^{86} +(-6.41518 - 11.1114i) q^{87} +(-3.26365 - 5.65281i) q^{88} +(-6.32507 + 10.9553i) q^{89} -25.8629 q^{90} +(2.63170 + 0.272277i) q^{91} -20.4006 q^{92} +(12.6760 - 21.9554i) q^{93} +(6.45074 + 11.1730i) q^{94} +(-4.08410 - 7.07386i) q^{95} +(8.52895 - 14.7726i) q^{96} +4.67310 q^{97} +(-11.9445 + 13.3528i) q^{98} +4.08281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.27968	+	2.21648i	−0.904873	+	1.56729i	−0.0837848	+	0.996484i	$0.526701\pi$
$2$	−1.27968	+	2.21648i	−0.904873	+	1.56729i	−0.821088	+	0.570802i	$0.806633\pi$
$3$	1.33068	+	2.30480i	0.768267	+	1.33068i	0.938502	+	0.345274i	$0.112214\pi$
$3$	1.33068	+	2.30480i	0.768267	+	1.33068i	−0.170235	+	0.985403i	$0.554453\pi$
$4$	−2.27518	−	3.94073i	−1.13759	−	1.97036i
$5$	1.23753	−	2.14346i	0.553440	−	0.958586i	−0.444583	−	0.895738i	$-0.646648\pi$
$5$	1.23753	−	2.14346i	0.553440	−	0.958586i	0.998023	−	0.0628486i	$-0.0200185\pi$
$6$	−6.81138			−2.78074
$7$	−2.63170	−	0.272277i	−0.994691	−	0.102911i
$7$	−2.63170	−	0.272277i	−0.994691	−	0.102911i
$8$	6.52730			2.30775
$9$	−2.04140	+	3.53582i	−0.680468	+	1.17861i
$10$	3.16729	+	5.48591i	1.00159	+	1.73480i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	6.05506	−	10.4877i	1.74794	−	3.02753i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	3.97124	−	5.48468i	1.06136	−	1.46584i
$15$	6.58701			1.70076
$16$	−3.80252	+	6.58616i	−0.950630	+	1.64654i
$17$	−3.45334	−	5.98137i	−0.837559	−	1.45069i	−0.891930	−	0.452174i	$-0.850649\pi$
$17$	−3.45334	−	5.98137i	−0.837559	−	1.45069i	0.0543711	−	0.998521i	$-0.482685\pi$
$18$	−5.22470	−	9.04945i	−1.23147	−	2.13298i
$19$	1.65010	−	2.85806i	0.378559	−	0.655684i	−0.612294	−	0.790630i	$-0.709753\pi$
$19$	1.65010	−	2.85806i	0.378559	−	0.655684i	0.990853	+	0.134947i	$0.0430864\pi$
$20$	−11.2624			−2.51835
$21$	−2.87440	−	6.42787i	−0.627247	−	1.40268i
$22$	2.55937			0.545659
$23$	2.24165	−	3.88264i	0.467415	−	0.809587i	−0.531892	−	0.846813i	$-0.678519\pi$
$23$	2.24165	−	3.88264i	0.467415	−	0.809587i	0.999307	+	0.0372253i	$0.0118519\pi$
$24$	8.68573	+	15.0441i	1.77297	+	3.07087i
$25$	−0.562958	−	0.975073i	−0.112592	−	0.195015i
$26$	1.27968	−	2.21648i	0.250967	−	0.434687i
$27$	−2.88174			−0.554591
$28$	4.91463	+	10.9903i	0.928777	+	2.07697i
$29$	−4.82099			−0.895235			−0.447617	−	0.894225i	$-0.647727\pi$
$29$	−4.82099			−0.895235			−0.447617	+	0.894225i	$0.647727\pi$
$30$	−8.42929	+	14.6000i	−1.53897	+	2.66557i
$31$	−4.76298	−	8.24972i	−0.855456	−	1.48169i	−0.876221	−	0.481909i	$-0.839943\pi$
$31$	−4.76298	−	8.24972i	−0.855456	−	1.48169i	0.0207646	−	0.999784i	$-0.493390\pi$
$32$	−3.20474	−	5.55077i	−0.566523	−	0.981247i
$33$	1.33068	−	2.30480i	0.231641	−	0.401214i
$34$	17.6767			3.03154
$35$	−3.84043	+	5.30401i	−0.649151	+	0.896542i
$36$	18.5782			3.09637
$37$	−0.300685	+	0.520801i	−0.0494322	+	0.0856192i	−0.889683	−	0.456579i	$-0.849075\pi$
$37$	−0.300685	+	0.520801i	−0.0494322	+	0.0856192i	0.840251	+	0.542198i	$0.182408\pi$
$38$	4.22321	+	7.31482i	0.685096	+	1.18662i
$39$	−1.33068	−	2.30480i	−0.213079	−	0.369064i
$40$	8.07773	−	13.9910i	1.27720	−	2.21218i
$41$	−2.83361			−0.442536			−0.221268	−	0.975213i	$-0.571020\pi$
$41$	−2.83361			−0.442536			−0.221268	+	0.975213i	$0.571020\pi$
$42$	17.9255	+	1.85458i	2.76597	+	0.286168i
$43$	6.51660			0.993772			0.496886	−	0.867816i	$-0.334477\pi$
$43$	6.51660			0.993772			0.496886	+	0.867816i	$0.334477\pi$
$44$	−2.27518	+	3.94073i	−0.342996	+	0.594087i
$45$	5.05260	+	8.75136i	0.753197	+	1.30458i
$46$	5.73719	+	9.93711i	0.845903	+	1.46515i
$47$	2.52044	−	4.36554i	0.367645	−	0.636779i	−0.621552	−	0.783373i	$-0.713498\pi$
$47$	2.52044	−	4.36554i	0.367645	−	0.636779i	0.989197	+	0.146594i	$0.0468310\pi$
$48$	−20.2397			−2.92135
$49$	6.85173	+	1.43310i	0.978819	+	0.204729i
$50$	2.88163			0.407525
$51$	9.19057	−	15.9185i	1.28694	−	2.22904i
$52$	2.27518	+	3.94073i	0.315511	+	0.546480i
$53$	4.50223	+	7.79809i	0.618428	+	1.07115i	0.989773	+	0.142654i	$0.0455637\pi$
$53$	4.50223	+	7.79809i	0.618428	+	1.07115i	−0.371344	+	0.928495i	$0.621103\pi$
$54$	3.68772	−	6.38731i	0.501835	−	0.869203i
$55$	−2.47506			−0.333737
$56$	−17.1779	−	1.77723i	−2.29550	−	0.237493i
$57$	8.78301			1.16334
$58$	6.16933	−	10.6856i	0.810073	−	1.40309i
$59$	1.30453	+	2.25951i	0.169836	+	0.294164i	0.938362	−	0.345654i	$-0.112343\pi$
$59$	1.30453	+	2.25951i	0.169836	+	0.294164i	−0.768526	+	0.639818i	$0.779010\pi$
$60$	−14.9866	−	25.9576i	−1.93477	−	3.35111i
$61$	1.38917	−	2.40612i	0.177865	−	0.308072i	−0.763284	−	0.646063i	$-0.776414\pi$
$61$	1.38917	−	2.40612i	0.177865	−	0.308072i	0.941149	+	0.337991i	$0.109747\pi$
$62$	24.3804			3.09632
$63$	6.33509	−	8.74940i	0.798147	−	1.10232i
$64$	1.19414			0.149267
$65$	−1.23753	+	2.14346i	−0.153497	+	0.265864i
$66$	3.40569	+	5.89883i	0.419212	+	0.726096i
$67$	−8.13877	−	14.0968i	−0.994309	−	1.72219i	−0.589417	−	0.807829i	$-0.700643\pi$
$67$	−8.13877	−	14.0968i	−0.994309	−	1.72219i	−0.404891	−	0.914365i	$-0.632691\pi$
$68$	−15.7139	+	27.2174i	−1.90560	+	3.30059i
$69$	11.9316			1.43640
$70$	−6.84169	−	15.2997i	−0.817738	−	1.82866i
$71$	5.66827			0.672700			0.336350	−	0.941737i	$-0.390808\pi$
$71$	5.66827			0.672700			0.336350	+	0.941737i	$0.390808\pi$
$72$	−13.3249	+	23.0793i	−1.57035	+	2.71993i
$73$	−3.34495	−	5.79362i	−0.391496	−	0.678092i	0.601151	−	0.799136i	$-0.294709\pi$
$73$	−3.34495	−	5.79362i	−0.391496	−	0.678092i	−0.992647	+	0.121044i	$0.961376\pi$
$74$	−0.769562	−	1.33292i	−0.0894598	−	0.154949i
$75$	1.49823	−	2.59501i	0.173001	−	0.299646i
$76$	−15.0171			−1.72258
$77$	1.08005	+	2.41526i	0.123083	+	0.275245i
$78$	6.81138			0.771237
$79$	−8.22391	+	14.2442i	−0.925262	+	1.60260i	−0.134123	+	0.990965i	$0.542822\pi$
$79$	−8.22391	+	14.2442i	−0.925262	+	1.60260i	−0.791139	+	0.611636i	$0.790512\pi$
$80$	9.41146	+	16.3011i	1.05223	+	1.82252i
$81$	2.28955	+	3.96561i	0.254394	+	0.440623i
$82$	3.62613	−	6.28064i	0.400439	−	0.693581i
$83$	−5.26198			−0.577578			−0.288789	−	0.957393i	$-0.593253\pi$
$83$	−5.26198			−0.577578			−0.288789	+	0.957393i	$0.593253\pi$
$84$	−18.7907	+	25.9518i	−2.05023	+	2.83157i
$85$	−17.0945			−1.85415
$86$	−8.33918	+	14.4439i	−0.899237	+	1.55752i
$87$	−6.41518	−	11.1114i	−0.687779	−	1.19127i
$88$	−3.26365	−	5.65281i	−0.347906	−	0.602591i
$89$	−6.32507	+	10.9553i	−0.670456	+	1.16126i	0.307318	+	0.951607i	$0.400568\pi$
$89$	−6.32507	+	10.9553i	−0.670456	+	1.16126i	−0.977775	+	0.209658i	$0.932765\pi$
$90$	−25.8629			−2.72619
$91$	2.63170	+	0.272277i	0.275878	+	0.0285424i
$92$	−20.4006			−2.12691
$93$	12.6760	−	21.9554i	1.31444	−	2.27667i
$94$	6.45074	+	11.1730i	0.665343	+	1.15241i
$95$	−4.08410	−	7.07386i	−0.419019	−	0.725763i
$96$	8.52895	−	14.7726i	0.870482	−	1.50772i
$97$	4.67310			0.474481			0.237241	−	0.971451i	$-0.423757\pi$
$97$	4.67310			0.474481			0.237241	+	0.971451i	$0.423757\pi$
$98$	−11.9445	+	13.3528i	−1.20658	+	1.34883i
$99$	4.08281			0.410338
$100$	−2.56166	+	4.43693i	−0.256166	+	0.443693i
$101$	−5.13538	−	8.89473i	−0.510989	−	0.885059i	−0.999919	−	0.0127360i	$-0.995946\pi$
$101$	−5.13538	−	8.89473i	−0.510989	−	0.885059i	0.488930	−	0.872323i	$-0.337387\pi$
$102$	23.5220	+	40.7414i	2.32903	+	4.03400i
$103$	0.319605	−	0.553572i	0.0314916	−	0.0545451i	−0.849850	−	0.527025i	$-0.823308\pi$
$103$	0.319605	−	0.553572i	0.0314916	−	0.0545451i	0.881342	+	0.472479i	$0.156641\pi$
$104$	−6.52730			−0.640054
$105$	−17.3351	−	1.79349i	−1.69173	−	0.175027i
$106$	−23.0457			−2.23840
$107$	4.25956	−	7.37777i	0.411787	−	0.713236i	−0.583298	−	0.812258i	$-0.698238\pi$
$107$	4.25956	−	7.37777i	0.411787	−	0.713236i	0.995085	+	0.0990221i	$0.0315715\pi$
$108$	6.55648	+	11.3562i	0.630897	+	1.09275i
$109$	−0.615140	−	1.06545i	−0.0589198	−	0.102052i	0.835061	−	0.550157i	$-0.185432\pi$
$109$	−0.615140	−	1.06545i	−0.0589198	−	0.102052i	−0.893981	+	0.448105i	$0.852099\pi$
$110$	3.16729	−	5.48591i	0.301989	−	0.523061i
$111$	−1.60046			−0.151909
$112$	11.8004	−	16.2975i	1.11503	−	1.53997i
$113$	3.17268			0.298461			0.149230	−	0.988802i	$-0.452320\pi$
$113$	3.17268			0.298461			0.149230	+	0.988802i	$0.452320\pi$
$114$	−11.2395	+	19.4673i	−1.05267	+	1.82328i
$115$	−5.54820	−	9.60977i	−0.517373	−	0.896116i
$116$	10.9686	+	18.9982i	1.01841	+	1.76394i
$117$	2.04140	−	3.53582i	0.188728	−	0.326886i
$118$	−6.67755			−0.614718
$119$	7.45959	+	16.6815i	0.683819	+	1.52919i
$120$	42.9954			3.92492
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.55540	+	6.15814i	0.321891	+	0.557532i
$123$	−3.77063	−	6.53092i	−0.339986	−	0.588873i
$124$	−21.6733	+	37.5392i	−1.94632	+	3.37112i
$125$	9.58858			0.857629
$126$	11.2859	+	25.2380i	1.00543	+	2.24838i
$127$	2.53846			0.225252			0.112626	−	0.993637i	$-0.464074\pi$
$127$	2.53846			0.225252			0.112626	+	0.993637i	$0.464074\pi$
$128$	4.88137	−	8.45477i	0.431456	−	0.747303i
$129$	8.67149	+	15.0195i	0.763482	+	1.32239i
$130$	−3.16729	−	5.48591i	−0.277790	−	0.481146i
$131$	−9.45487	+	16.3763i	−0.826076	+	1.43080i	0.0750189	+	0.997182i	$0.476098\pi$
$131$	−9.45487	+	16.3763i	−0.826076	+	1.43080i	−0.901094	+	0.433623i	$0.857235\pi$
$132$	−12.1101			−1.05405
$133$	−5.12076	+	7.07228i	−0.444026	+	0.613244i
$134$	41.6602			3.59889
$135$	−3.56624	+	6.17691i	−0.306933	+	0.531624i
$136$	−22.5410	−	39.0422i	−1.93288	−	3.34784i
$137$	−9.15266	−	15.8529i	−0.781964	−	1.35440i	−0.930796	−	0.365539i	$-0.880885\pi$
$137$	−9.15266	−	15.8529i	−0.781964	−	1.35440i	0.148831	−	0.988863i	$-0.452449\pi$
$138$	−15.2687	+	26.4462i	−1.29976	+	2.25125i
$139$	−13.9288			−1.18142			−0.590712	−	0.806882i	$-0.701153\pi$
$139$	−13.9288			−1.18142			−0.590712	+	0.806882i	$0.701153\pi$
$140$	29.6393	+	3.06649i	2.50498	+	0.259166i
$141$	13.4156			1.12980
$142$	−7.25359	+	12.5636i	−0.608708	+	1.05431i
$143$	0.500000	+	0.866025i	0.0418121	+	0.0724207i
$144$	−15.5250	−	26.8900i	−1.29375	−	2.24084i
$145$	−5.96611	+	10.3336i	−0.495459	+	0.858159i
$146$	17.1219			1.41702
$147$	5.81442	+	17.6989i	0.479565	+	1.45978i
$148$	2.73645			0.224934
$149$	6.28253	−	10.8817i	0.514685	−	0.891461i	−0.485170	−	0.874420i	$-0.661242\pi$
$149$	6.28253	−	10.8817i	0.514685	−	0.891461i	0.999855	−	0.0170409i	$-0.00542456\pi$
$150$	3.83453	+	6.64159i	0.313088	+	0.542284i
$151$	−7.28465	−	12.6174i	−0.592816	−	1.02679i	−0.993851	−	0.110725i	$-0.964683\pi$
$151$	−7.28465	−	12.6174i	−0.592816	−	1.02679i	0.401035	−	0.916063i	$-0.368651\pi$
$152$	10.7707	−	18.6554i	0.873619	−	1.51315i
$153$	28.1987			2.27973
$154$	−6.73550	−	0.696856i	−0.542762	−	0.0561543i
$155$	−23.5773			−1.89378
$156$	−6.05506	+	10.4877i	−0.484793	+	0.839685i
$157$	−8.06957	−	13.9769i	−0.644022	−	1.11548i	−0.984526	−	0.175236i	$-0.943931\pi$
$157$	−8.06957	−	13.9769i	−0.644022	−	1.11548i	0.340504	−	0.940243i	$-0.389402\pi$
$158$	−21.0480	−	36.4562i	−1.67449	−	2.90030i
$159$	−11.9820	+	20.7535i	−0.950236	+	1.64586i
$160$	−15.8638			−1.25415
$161$	−6.95650	+	9.60762i	−0.548249	+	0.757187i
$162$	−11.7196			−0.920777
$163$	1.93379	−	3.34942i	0.151466	−	0.262347i	−0.780301	−	0.625405i	$-0.784934\pi$
$163$	1.93379	−	3.34942i	0.151466	−	0.262347i	0.931767	+	0.363058i	$0.118267\pi$
$164$	6.44698	+	11.1665i	0.503425	+	0.871957i
$165$	−3.29351	−	5.70452i	−0.256399	−	0.444096i
$166$	6.73367	−	11.6631i	0.522634	−	0.905229i
$167$	4.93658			0.382004			0.191002	−	0.981590i	$-0.438826\pi$
$167$	4.93658			0.382004			0.191002	+	0.981590i	$0.438826\pi$
$168$	−18.7621	−	41.9566i	−1.44753	−	3.23702i
$169$	1.00000			0.0769231
$170$	21.8755	−	37.8895i	1.67777	−	2.90599i
$171$	6.73705	+	11.6689i	0.515195	+	0.892344i
$172$	−14.8264	−	25.6801i	−1.13050	−	1.95809i
$173$	−4.20367	+	7.28097i	−0.319599	+	0.553562i	−0.980404	−	0.196996i	$-0.936882\pi$
$173$	−4.20367	+	7.28097i	−0.319599	+	0.553562i	0.660805	+	0.750557i	$0.270215\pi$
$174$	32.8376			2.48941
$175$	1.21605	+	2.71938i	0.0919247	+	0.205566i
$176$	7.60504			0.573251
$177$	−3.47182	+	6.01337i	−0.260958	+	0.451993i
$178$	−16.1882	−	28.0388i	−1.21336	−	2.10159i
$179$	6.69800	+	11.6013i	0.500632	+	0.867119i	1.00000		0.000729527i	$0.000232216\pi$
$179$	6.69800	+	11.6013i	0.500632	+	0.867119i	−0.499368	+	0.866390i	$0.666434\pi$
$180$	22.9911	−	39.8218i	1.71366	−	2.96814i
$181$	20.6995			1.53858			0.769291	−	0.638899i	$-0.220610\pi$
$181$	20.6995			1.53858			0.769291	+	0.638899i	$0.220610\pi$
$182$	−3.97124	+	5.48468i	−0.294368	+	0.406552i
$183$	7.39417			0.546593
$184$	14.6319	−	25.3432i	1.07868	−	1.86832i
$185$	0.744212	+	1.28901i	0.0547156	+	0.0947701i
$186$	32.4425	+	56.1920i	2.37880	+	4.12020i
$187$	−3.45334	+	5.98137i	−0.252533	+	0.437401i
$188$	−22.9378			−1.67291
$189$	7.58389	+	0.784632i	0.551647	+	0.0570736i
$190$	20.9054			1.51664
$191$	−0.00281757	+	0.00488017i	−0.000203872	+	0.000353117i	−0.866127	−	0.499823i	$-0.833398\pi$
$191$	−0.00281757	+	0.00488017i	−0.000203872	+	0.000353117i	0.865923	+	0.500177i	$0.166732\pi$
$192$	1.58901	+	2.75224i	0.114677	+	0.198626i
$193$	−2.04706	−	3.54560i	−0.147350	−	0.255218i	0.782897	−	0.622151i	$-0.213741\pi$
$193$	−2.04706	−	3.54560i	−0.147350	−	0.255218i	−0.930247	+	0.366933i	$0.880408\pi$
$194$	−5.98009	+	10.3578i	−0.429345	+	0.743648i
$195$	−6.58701			−0.471706
$196$	−9.94144	−	30.2614i	−0.710103	−	2.16153i
$197$	19.4971			1.38911			0.694554	−	0.719441i	$-0.255602\pi$
$197$	19.4971			1.38911			0.694554	+	0.719441i	$0.255602\pi$
$198$	−5.22470	+	9.04945i	−0.371304	+	0.643117i
$199$	−10.5509	−	18.2746i	−0.747930	−	1.29545i	−0.948813	−	0.315838i	$-0.897714\pi$
$199$	−10.5509	−	18.2746i	−0.747930	−	1.29545i	0.200883	−	0.979615i	$-0.435619\pi$
$200$	−3.67460	−	6.36459i	−0.259833	−	0.450045i
$201$	21.6602	−	37.5165i	1.52779	−	2.64621i
$202$	26.2866			1.84952
$203$	12.6874	+	1.31264i	0.890481	+	0.0921295i
$204$	−83.6408			−5.85603
$205$	−3.50668	+	6.07375i	−0.244917	+	0.424209i
$206$	0.817986	+	1.41679i	0.0569918	+	0.0987127i
$207$	9.15221	+	15.8521i	0.636123	+	1.10180i
$208$	3.80252	−	6.58616i	0.263657	−	0.456668i
$209$	−3.30020			−0.228280
$210$	26.1586	−	36.1277i	1.80512	−	2.49304i
$211$	15.6068			1.07442			0.537209	−	0.843449i	$-0.319479\pi$
$211$	15.6068			1.07442			0.537209	+	0.843449i	$0.319479\pi$
$212$	20.4867	−	35.4841i	1.40704	−	2.43706i
$213$	7.54264	+	13.0642i	0.516813	+	0.895146i
$214$	10.9018	+	18.8824i	0.745230	+	1.29078i
$215$	8.06448	−	13.9681i	0.549993	−	0.952616i
$216$	−18.8100			−1.27986
$217$	10.2885	+	23.0077i	0.698432	+	1.56186i
$218$	3.14874			0.213260
$219$	8.90209	−	15.4189i	0.601548	−	1.04191i
$220$	5.63120	+	9.75353i	0.379656	+	0.657583i
$221$	3.45334	+	5.98137i	0.232297	+	0.402350i
$222$	2.04808	−	3.54738i	0.137458	−	0.238084i
$223$	−23.1059			−1.54728			−0.773642	−	0.633623i	$-0.781567\pi$
$223$	−23.1059			−1.54728			−0.773642	+	0.633623i	$0.781567\pi$
$224$	6.92258	+	15.4806i	0.462534	+	1.03434i
$225$	4.59690			0.306460
$226$	−4.06003	+	7.03217i	−0.270069	+	0.467773i
$227$	9.09691	+	15.7563i	0.603783	+	1.04578i	0.992242	+	0.124318i	$0.0396741\pi$
$227$	9.09691	+	15.7563i	0.603783	+	1.04578i	−0.388459	+	0.921466i	$0.626993\pi$
$228$	−19.9829	−	34.6114i	−1.32340	−	2.29220i
$229$	6.16160	−	10.6722i	0.407170	−	0.705240i	−0.587401	−	0.809296i	$-0.699849\pi$
$229$	6.16160	−	10.6722i	0.407170	−	0.705240i	0.994571	+	0.104056i	$0.0331822\pi$
$230$	28.3998			1.87263
$231$	−4.12949	+	5.70324i	−0.271701	+	0.375246i
$232$	−31.4680			−2.06598
$233$	−11.7782	+	20.4004i	−0.771615	+	1.33648i	0.165062	+	0.986283i	$0.447218\pi$
$233$	−11.7782	+	20.4004i	−0.771615	+	1.33648i	−0.936677	+	0.350194i	$0.886116\pi$
$234$	5.22470	+	9.04945i	0.341550	+	0.591581i
$235$	−6.23825	−	10.8050i	−0.406938	−	0.704838i
$236$	5.93608	−	10.2816i	0.386406	−	0.669275i
$237$	−43.7735			−2.84339
$238$	−46.5200	−	4.81297i	−3.01544	−	0.311978i
$239$	−2.13263			−0.137948			−0.0689741	−	0.997618i	$-0.521973\pi$
$239$	−2.13263			−0.137948			−0.0689741	+	0.997618i	$0.521973\pi$
$240$	−25.0472	+	43.3831i	−1.61679	+	2.80037i
$241$	0.758745	+	1.31418i	0.0488750	+	0.0846540i	0.889428	−	0.457075i	$-0.151103\pi$
$241$	0.758745	+	1.31418i	0.0488750	+	0.0846540i	−0.840553	+	0.541729i	$0.817770\pi$
$242$	−1.27968	−	2.21648i	−0.0822612	−	0.142481i
$243$	−10.4159	+	18.0409i	−0.668181	+	1.15732i
$244$	−12.6425			−0.809351
$245$	11.5510	−	12.9129i	0.737968	−	0.824977i
$246$	19.3008			1.23058
$247$	−1.65010	+	2.85806i	−0.104993	+	0.181854i
$248$	−31.0894	−	53.8484i	−1.97418	−	3.41938i
$249$	−7.00200	−	12.1278i	−0.443734	−	0.768570i
$250$	−12.2704	+	21.2529i	−0.776045	+	1.34415i
$251$	−16.0503			−1.01309			−0.506544	−	0.862214i	$-0.669077\pi$
$251$	−16.0503			−1.01309			−0.506544	+	0.862214i	$0.669077\pi$
$252$	−48.8924	−	5.05843i	−3.07993	−	0.318651i
$253$	−4.48329			−0.281862
$254$	−3.24843	+	5.62644i	−0.203825	+	0.353034i
$255$	−22.7472	−	39.3993i	−1.42449	−	2.46728i
$256$	13.6873	+	23.7072i	0.855459	+	1.48170i
$257$	−0.890708	+	1.54275i	−0.0555609	+	0.0962342i	−0.892468	−	0.451111i	$-0.851028\pi$
$257$	−0.890708	+	1.54275i	−0.0555609	+	0.0962342i	0.836907	+	0.547345i	$0.184361\pi$
$258$	−44.3870			−2.76342
$259$	0.933115	−	1.28872i	0.0579809	−	0.0800775i
$260$	11.2624			0.698465
$261$	9.84158	−	17.0461i	0.609179	−	1.05513i
$262$	−24.1985	−	41.9130i	−1.49499	−	2.58939i
$263$	−8.48071	−	14.6890i	−0.522943	−	0.905764i	−0.999644	−	0.0266982i	$-0.991501\pi$
$263$	−8.48071	−	14.6890i	−0.522943	−	0.905764i	0.476700	−	0.879066i	$-0.341833\pi$
$264$	8.68573	−	15.0441i	0.534570	−	0.925902i
$265$	22.2866			1.36905
$266$	−9.12259	−	20.4003i	−0.559342	−	1.25082i
$267$	−33.6665			−2.06036
$268$	−37.0343	+	64.1453i	−2.26223	+	3.91830i
$269$	14.3101	+	24.7857i	0.872499	+	1.51121i	0.859403	+	0.511299i	$0.170835\pi$
$269$	14.3101	+	24.7857i	0.872499	+	1.51121i	0.0130962	+	0.999914i	$0.495831\pi$
$270$	−9.12731	−	15.8090i	−0.555471	−	0.962103i
$271$	10.1123	−	17.5150i	0.614278	−	1.06396i	−0.376232	−	0.926525i	$-0.622780\pi$
$271$	10.1123	−	17.5150i	0.614278	−	1.06396i	0.990511	−	0.137436i	$-0.0438862\pi$
$272$	52.5256			3.18483
$273$	2.87440	+	6.42787i	0.173967	+	0.389032i
$274$	46.8500			2.83031
$275$	−0.562958	+	0.975073i	−0.0339477	+	0.0587991i
$276$	−27.1466	−	47.0193i	−1.63403	−	2.83023i
$277$	1.34160	+	2.32372i	0.0806088	+	0.139619i	0.903512	−	0.428564i	$-0.140980\pi$
$277$	1.34160	+	2.32372i	0.0806088	+	0.139619i	−0.822903	+	0.568182i	$0.807647\pi$
$278$	17.8244	−	30.8728i	1.06904	−	1.85163i
$279$	38.8927			2.32844
$280$	−25.0676	+	34.6209i	−1.49808	+	2.06899i
$281$	8.64838			0.515919			0.257959	−	0.966156i	$-0.416950\pi$
$281$	8.64838			0.515919			0.257959	+	0.966156i	$0.416950\pi$
$282$	−17.1677	+	29.7353i	−1.02232	+	1.77071i
$283$	−4.07246	−	7.05371i	−0.242083	−	0.419299i	0.719225	−	0.694778i	$-0.244497\pi$
$283$	−4.07246	−	7.05371i	−0.242083	−	0.419299i	−0.961307	+	0.275478i	$0.911164\pi$
$284$	−12.8963	−	22.3371i	−0.765256	−	1.32546i
$285$	10.8692	−	18.8261i	0.643838	−	1.11516i
$286$	−2.55937			−0.151339
$287$	7.45724	+	0.771528i	0.440187	+	0.0455419i
$288$	26.1687			1.54200
$289$	−15.3512	+	26.5890i	−0.903010	+	1.56406i
$290$	−15.2695	−	26.4475i	−0.896654	−	1.55305i
$291$	6.21839	+	10.7706i	0.364528	+	0.631382i
$292$	−15.2207	+	26.3630i	−0.890724	+	1.54278i
$293$	31.6783			1.85067			0.925333	−	0.379154i	$-0.123785\pi$
$293$	31.6783			1.85067			0.925333	+	0.379154i	$0.123785\pi$
$294$	−46.6698	−	9.76142i	−2.72184	−	0.569298i
$295$	6.45758			0.375975
$296$	−1.96266	+	3.39942i	−0.114077	+	0.197588i
$297$	1.44087	+	2.49566i	0.0836078	+	0.144813i
$298$	16.0793	+	27.8502i	0.931449	+	1.61332i
$299$	−2.24165	+	3.88264i	−0.129638	+	0.224539i
$300$	−13.6350			−0.787216
$301$	−17.1498	−	1.77432i	−0.988495	−	0.102270i
$302$	37.2882			2.14569
$303$	13.6671	−	23.6720i	0.785152	−	1.35992i
$304$	12.5491	+	21.7356i	0.719739	+	1.24662i
$305$	−3.43829	−	5.95529i	−0.196876	−	0.340999i
$306$	−36.0854	+	62.5017i	−2.06286	+	3.57299i
$307$	−15.5414			−0.886995			−0.443498	−	0.896276i	$-0.646263\pi$
$307$	−15.5414			−0.886995			−0.443498	+	0.896276i	$0.646263\pi$
$308$	7.06057	−	9.75134i	0.402313	−	0.555634i
$309$	1.70116			0.0967759
$310$	30.1715	−	52.2586i	1.71363	−	2.96809i
$311$	−5.92980	−	10.2707i	−0.336248	−	0.582399i	0.647476	−	0.762086i	$-0.275825\pi$
$311$	−5.92980	−	10.2707i	−0.336248	−	0.582399i	−0.983724	+	0.179687i	$0.942491\pi$
$312$	−8.68573	−	15.0441i	−0.491733	−	0.851706i
$313$	11.5077	−	19.9319i	0.650453	−	1.12662i	−0.332561	−	0.943082i	$-0.607913\pi$
$313$	11.5077	−	19.9319i	0.650453	−	1.12662i	0.983013	−	0.183535i	$-0.0587541\pi$
$314$	41.3060			2.33103
$315$	−10.9141	−	24.4067i	−0.614943	−	1.37516i
$316$	74.8435			4.21027
$317$	−5.30271	+	9.18457i	−0.297830	+	0.515857i	−0.975639	−	0.219381i	$-0.929596\pi$
$317$	−5.30271	+	9.18457i	−0.297830	+	0.515857i	0.677809	+	0.735238i	$0.262930\pi$
$318$	−30.6664	−	53.1157i	−1.71969	−	2.97858i
$319$	2.41049	+	4.17510i	0.134962	+	0.233760i
$320$	1.47778	−	2.55959i	0.0826103	−	0.143085i
$321$	22.6724			1.26545
$322$	−12.3929	−	27.7136i	−0.690632	−	1.54442i
$323$	−22.7935			−1.26826
$324$	10.4183	−	18.0449i	0.578792	−	1.00250i
$325$	0.562958	+	0.975073i	0.0312273	+	0.0540873i
$326$	4.94928	+	8.57240i	0.274115	+	0.474781i
$327$	1.63711	−	2.83555i	0.0905322	−	0.156806i
$328$	−18.4959			−1.02126
$329$	−7.82170	+	10.8025i	−0.431224	+	0.595563i
$330$	16.8586			0.928034
$331$	−13.8406	+	23.9726i	−0.760748	+	1.31766i	0.181717	+	0.983351i	$0.441835\pi$
$331$	−13.8406	+	23.9726i	−0.760748	+	1.31766i	−0.942465	+	0.334304i	$0.891499\pi$
$332$	11.9720	+	20.7360i	0.657046	+	1.13804i
$333$	−1.22764	−	2.12633i	−0.0672742	−	0.116522i
$334$	−6.31726	+	10.9418i	−0.345665	+	0.598710i
$335$	−40.2879			−2.20116
$336$	53.2649	+	5.51080i	2.90584	+	0.300639i
$337$	17.2822			0.941423			0.470712	−	0.882287i	$-0.343997\pi$
$337$	17.2822			0.941423			0.470712	+	0.882287i	$0.343997\pi$
$338$	−1.27968	+	2.21648i	−0.0696056	+	0.120560i
$339$	4.22181	+	7.31240i	0.229298	+	0.397155i
$340$	38.8929	+	67.3646i	2.10927	+	3.65336i
$341$	−4.76298	+	8.24972i	−0.257930	+	0.446748i
$342$	−34.4851			−1.86474
$343$	−17.6415	−	5.63707i	−0.952553	−	0.304373i
$344$	42.5358			2.29338
$345$	14.7657	−	25.5750i	0.794961	−	1.37691i
$346$	−10.7587	−	18.6347i	−0.578393	−	1.00181i
$347$	13.0606	+	22.6216i	0.701130	+	1.21439i	0.968070	+	0.250679i	$0.0806539\pi$
$347$	13.0606	+	22.6216i	0.701130	+	1.21439i	−0.266941	+	0.963713i	$0.586013\pi$
$348$	−29.1913	+	50.5609i	−1.56482	+	2.71035i
$349$	5.72089			0.306232			0.153116	−	0.988208i	$-0.451069\pi$
$349$	5.72089			0.306232			0.153116	+	0.988208i	$0.451069\pi$
$350$	−7.58361	−	0.784602i	−0.405361	−	0.0419388i
$351$	2.88174			0.153816
$352$	−3.20474	+	5.55077i	−0.170813	+	0.295857i
$353$	−3.92327	−	6.79531i	−0.208815	−	0.361678i	0.742527	−	0.669817i	$-0.233627\pi$
$353$	−3.92327	−	6.79531i	−0.208815	−	0.361678i	−0.951341	+	0.308139i	$0.900294\pi$
$354$	−8.88566	−	15.3904i	−0.472268	−	0.817992i
$355$	7.01465	−	12.1497i	0.372299	−	0.644841i
$356$	57.5627			3.05082
$357$	−28.5211	+	39.3905i	−1.50950	+	2.08477i
$358$	−34.2852			−1.81203
$359$	12.2286	−	21.1806i	0.645403	−	1.11787i	−0.338806	−	0.940856i	$-0.610023\pi$
$359$	12.2286	−	21.1806i	0.645403	−	1.11787i	0.984208	−	0.177014i	$-0.0566437\pi$
$360$	32.9798	+	57.1227i	1.73819	+	3.01063i
$361$	4.05434	+	7.02232i	0.213386	+	0.369596i
$362$	−26.4888	+	45.8799i	−1.39222	+	2.41140i
$363$	−2.66135			−0.139685
$364$	−4.91463	−	10.9903i	−0.257597	−	0.576048i
$365$	−16.5579			−0.866679
$366$	−9.46219	+	16.3890i	−0.494597	+	0.856667i
$367$	−9.07499	−	15.7184i	−0.473711	−	0.820491i	0.525836	−	0.850586i	$-0.323752\pi$
$367$	−9.07499	−	15.7184i	−0.473711	−	0.820491i	−0.999547	+	0.0300946i	$0.990419\pi$
$368$	17.0478	+	29.5277i	0.888678	+	1.53924i
$369$	5.78456	−	10.0191i	0.301132	−	0.521576i
$370$	−3.80942			−0.198043
$371$	−9.72529	−	21.7481i	−0.504912	−	1.12911i
$372$	−115.360			−5.98116
$373$	2.12186	−	3.67517i	0.109866	−	0.190293i	−0.805850	−	0.592120i	$-0.798291\pi$
$373$	2.12186	−	3.67517i	0.109866	−	0.190293i	0.915716	+	0.401827i	$0.131625\pi$
$374$	−8.83837	−	15.3085i	−0.457021	−	0.791584i
$375$	12.7593	+	22.0998i	0.658888	+	1.14123i
$376$	16.4517	−	28.4952i	0.848431	−	1.46953i
$377$	4.82099			0.248293
$378$	−11.4441	+	15.8054i	−0.588621	+	0.812944i
$379$	13.5471			0.695869			0.347935	−	0.937519i	$-0.386883\pi$
$379$	13.5471			0.695869			0.347935	+	0.937519i	$0.386883\pi$
$380$	−18.5841	+	32.1886i	−0.953344	+	1.65124i
$381$	3.37788	+	5.85065i	0.173054	+	0.299738i
$382$	−0.00721118	−	0.0124901i	−0.000368956	−	0.000639051i
$383$	14.9668	−	25.9233i	0.764770	−	1.32462i	−0.175598	−	0.984462i	$-0.556186\pi$
$383$	14.9668	−	25.9233i	0.764770	−	1.32462i	0.940368	−	0.340158i	$-0.110481\pi$
$384$	25.9821			1.32589
$385$	6.51362	+	0.673901i	0.331965	+	0.0343452i
$386$	10.4783			0.533333
$387$	−13.3030	+	23.0415i	−0.676230	+	1.17126i
$388$	−10.6321	−	18.4154i	−0.539765	−	0.934900i
$389$	−0.719196	−	1.24568i	−0.0364647	−	0.0631586i	0.847217	−	0.531247i	$-0.178276\pi$
$389$	−0.719196	−	1.24568i	−0.0364647	−	0.0631586i	−0.883682	+	0.468088i	$0.844943\pi$
$390$	8.42929	−	14.6000i	0.426834	−	0.739297i
$391$	−30.9647			−1.56595
$392$	44.7233	+	9.35430i	2.25887	+	0.472464i
$393$	−50.3255			−2.53859
$394$	−24.9501	+	43.2148i	−1.25697	+	2.17713i
$395$	20.3547	+	35.2553i	1.02415	+	1.77389i
$396$	−9.28912	−	16.0892i	−0.466796	−	0.808514i
$397$	2.28652	−	3.96037i	0.114757	−	0.198765i	−0.802925	−	0.596079i	$-0.796724\pi$
$397$	2.28652	−	3.96037i	0.114757	−	0.198765i	0.917683	+	0.397314i	$0.130058\pi$
$398$	54.0070			2.70713
$399$	−23.1143	−	2.39141i	−1.15716	−	0.119720i
$400$	8.56264			0.428132
$401$	−13.9628	+	24.1842i	−0.697268	+	1.20770i	0.272143	+	0.962257i	$0.412268\pi$
$401$	−13.9628	+	24.1842i	−0.697268	+	1.20770i	−0.969410	+	0.245446i	$0.921066\pi$
$402$	55.4363	+	96.0184i	2.76491	+	4.78896i
$403$	4.76298	+	8.24972i	0.237261	+	0.410948i
$404$	−23.3678	+	40.4742i	−1.16259	+	2.01367i
$405$	11.3335			0.563167
$406$	−19.1453	+	26.4416i	−0.950165	+	1.31227i
$407$	0.601369			0.0298088
$408$	59.9896	−	103.905i	2.96993	−	5.14407i
$409$	14.1481	+	24.5053i	0.699580	+	1.21171i	0.968612	+	0.248577i	$0.0799628\pi$
$409$	14.1481	+	24.5053i	0.699580	+	1.21171i	−0.269032	+	0.963131i	$0.586704\pi$
$410$	−8.97488	−	15.5450i	−0.443238	−	0.767711i
$411$	24.3585	−	42.1901i	1.20151	−	2.08108i
$412$	−2.90863			−0.143298
$413$	−2.81793	−	6.30157i	−0.138661	−	0.310080i
$414$	−46.8477			−2.30244
$415$	−6.51186	+	11.2789i	−0.319655	+	0.553658i
$416$	3.20474	+	5.55077i	0.157125	+	0.272149i
$417$	−18.5347	−	32.1031i	−0.907649	−	1.57209i
$418$	4.22321	−	7.31482i	0.206564	−	0.357779i
$419$	27.8573			1.36092			0.680460	−	0.732785i	$-0.261780\pi$
$419$	27.8573			1.36092			0.680460	+	0.732785i	$0.261780\pi$
$420$	32.3727	+	72.3932i	1.57963	+	3.53243i
$421$	21.3945			1.04270			0.521351	−	0.853342i	$-0.325428\pi$
$421$	21.3945			1.04270			0.521351	+	0.853342i	$0.325428\pi$
$422$	−19.9718	+	34.5922i	−0.972212	+	1.68392i
$423$	10.2905	+	17.8237i	0.500341	+	0.866616i
$424$	29.3874	+	50.9004i	1.42718	+	2.47194i
$425$	−3.88818	+	6.73452i	−0.188604	+	0.326672i
$426$	−38.6087			−1.87060
$427$	−4.31102	+	5.95395i	−0.208625	+	0.288132i
$428$	−38.7650			−1.87378
$429$	−1.33068	+	2.30480i	−0.0642457	+	0.111277i
$430$	20.6400	+	35.7495i	0.995347	+	1.72399i
$431$	−10.5413	−	18.2580i	−0.507756	−	0.879459i	−0.999960	−	0.00897872i	$-0.997142\pi$
$431$	−10.5413	−	18.2580i	−0.507756	−	0.879459i	0.492204	−	0.870480i	$-0.336191\pi$
$432$	10.9579	−	18.9796i	0.527211	−	0.913156i
$433$	10.0562			0.483268			0.241634	−	0.970367i	$-0.422317\pi$
$433$	10.0562			0.483268			0.241634	+	0.970367i	$0.422317\pi$
$434$	−64.1620	−	6.63823i	−3.07988	−	0.318645i
$435$	−31.7559			−1.52258
$436$	−2.79911	+	4.84820i	−0.134053	+	0.232187i
$437$	−7.39788	−	12.8135i	−0.353889	−	0.612953i
$438$	22.7837	+	39.4626i	1.08865	+	1.88559i
$439$	16.0230	−	27.7526i	0.764735	−	1.32456i	−0.175651	−	0.984452i	$-0.556203\pi$
$439$	16.0230	−	27.7526i	0.764735	−	1.32456i	0.940386	−	0.340108i	$-0.110464\pi$
$440$	−16.1555			−0.770181
$441$	−19.0544	+	21.3009i	−0.907350	+	1.01433i
$442$	−17.6767			−0.840797
$443$	7.86844	−	13.6285i	0.373841	−	0.647511i	−0.616312	−	0.787502i	$-0.711374\pi$
$443$	7.86844	−	13.6285i	0.373841	−	0.647511i	0.990153	+	0.139991i	$0.0447073\pi$
$444$	3.64133	+	6.30696i	0.172810	+	0.299315i
$445$	15.6549	+	27.1151i	0.742115	+	1.28538i
$446$	29.5682	−	51.2136i	1.40009	−	2.42504i
$447$	33.4401			1.58166
$448$	−3.14261	−	0.325136i	−0.148474	−	0.0153612i
$449$	−31.1907			−1.47198			−0.735989	−	0.676994i	$-0.763282\pi$
$449$	−31.1907			−1.47198			−0.735989	+	0.676994i	$0.763282\pi$
$450$	−5.88258	+	10.1889i	−0.277308	+	0.480311i
$451$	1.41681	+	2.45398i	0.0667149	+	0.115554i
$452$	−7.21842	−	12.5027i	−0.339526	−	0.588076i
$453$	19.3870	−	33.5793i	0.910882	−	1.57769i
$454$	−46.5647			−2.18539
$455$	3.84043	−	5.30401i	0.180042	−	0.248656i
$456$	57.3293			2.68469
$457$	−5.61924	+	9.73282i	−0.262857	+	0.455282i	−0.967000	−	0.254776i	$-0.917998\pi$
$457$	−5.61924	+	9.73282i	−0.262857	+	0.455282i	0.704143	+	0.710058i	$0.251331\pi$
$458$	15.7698	+	27.3141i	0.736874	+	1.27630i
$459$	9.95164	+	17.2368i	0.464503	+	0.804543i
$460$	−25.2463	+	43.7279i	−1.17712	+	2.03882i
$461$	−8.75503			−0.407763			−0.203881	−	0.978996i	$-0.565356\pi$
$461$	−8.75503			−0.407763			−0.203881	+	0.978996i	$0.565356\pi$
$462$	−7.35666	−	16.4513i	−0.342263	−	0.765382i
$463$	−33.0084			−1.53403			−0.767016	−	0.641628i	$-0.778259\pi$
$463$	−33.0084			−1.53403			−0.767016	+	0.641628i	$0.778259\pi$
$464$	18.3319	−	31.7518i	0.851037	−	1.47404i
$465$	−31.3738	−	54.3410i	−1.45492	−	2.52000i
$466$	−30.1447	−	52.2122i	−1.39643	−	2.41868i
$467$	−8.57532	+	14.8529i	−0.396818	+	0.687309i	−0.993331	−	0.115294i	$-0.963219\pi$
$467$	−8.57532	+	14.8529i	−0.396818	+	0.687309i	0.596513	+	0.802603i	$0.296552\pi$
$468$	−18.5782			−0.858780
$469$	17.5806	+	39.3145i	0.811797	+	1.81537i
$470$	31.9319			1.47291
$471$	21.4760	−	37.1975i	0.989562	−	1.71397i
$472$	8.51507	+	14.7485i	0.391938	+	0.678856i
$473$	−3.25830	−	5.64354i	−0.149817	−	0.259490i
$474$	56.0162	−	97.0229i	2.57291	−	4.45641i
$475$	−3.71575			−0.170490
$476$	48.7651	−	67.3495i	2.23515	−	3.08696i
$477$	−36.7635			−1.68328
$478$	2.72909	−	4.72692i	0.124826	−	0.216204i
$479$	14.8196	+	25.6683i	0.677125	+	1.17281i	0.975843	+	0.218473i	$0.0701076\pi$
$479$	14.8196	+	25.6683i	0.677125	+	1.17281i	−0.298718	+	0.954341i	$0.596559\pi$
$480$	−21.1097	−	36.5630i	−0.963520	−	1.66886i
$481$	0.300685	−	0.520801i	0.0137100	−	0.0237465i
$482$	−3.88381			−0.176903
$483$	−31.4005	−	3.24871i	−1.42877	−	0.147821i
$484$	4.55036			0.206834
$485$	5.78310	−	10.0166i	0.262597	−	0.454831i
$486$	−26.6581	−	46.1732i	−1.20924	−	2.09446i
$487$	−15.7401	−	27.2627i	−0.713253	−	1.23539i	−0.963630	−	0.267242i	$-0.913888\pi$
$487$	−15.7401	−	27.2627i	−0.713253	−	1.23539i	0.250377	−	0.968149i	$-0.419446\pi$
$488$	9.06755	−	15.7055i	0.410469	−	0.710953i
$489$	10.2930			0.465466
$490$	13.8395	+	42.1270i	0.625207	+	1.90311i
$491$	0.603228			0.0272233			0.0136117	−	0.999907i	$-0.495667\pi$
$491$	0.603228			0.0272233			0.0136117	+	0.999907i	$0.495667\pi$
$492$	−17.1577	+	29.7180i	−0.773529	+	1.33979i
$493$	16.6485	+	28.8361i	0.749812	+	1.29871i
$494$	−4.22321	−	7.31482i	−0.190011	−	0.329109i
$495$	5.05260	−	8.75136i	0.227097	−	0.393344i
$496$	72.4453			3.25289
$497$	−14.9172	−	1.54334i	−0.669128	−	0.0692282i
$498$	35.8414			1.60609
$499$	6.41845	−	11.1171i	0.287329	−	0.497669i	−0.685842	−	0.727750i	$-0.740566\pi$
$499$	6.41845	−	11.1171i	0.287329	−	0.497669i	0.973171	+	0.230081i	$0.0738992\pi$
$500$	−21.8157	−	37.7860i	−0.975630	−	1.68984i
$501$	6.56900	+	11.3778i	0.293481	+	0.508324i
$502$	20.5393	−	35.5752i	0.916716	−	1.58780i
$503$	32.7945			1.46224			0.731118	−	0.682251i	$-0.238999\pi$
$503$	32.7945			1.46224			0.731118	+	0.682251i	$0.238999\pi$
$504$	41.3511	−	57.1099i	1.84192	−	2.54388i
$505$	−25.4207			−1.13121
$506$	5.73719	−	9.93711i	0.255049	−	0.441758i
$507$	1.33068	+	2.30480i	0.0590975	+	0.102360i
$508$	−5.77546	−	10.0034i	−0.256244	−	0.443828i
$509$	−16.4973	+	28.5741i	−0.731230	+	1.26653i	0.225128	+	0.974329i	$0.427720\pi$
$509$	−16.4973	+	28.5741i	−0.731230	+	1.26653i	−0.956358	+	0.292198i	$0.905613\pi$
$510$	116.437			5.15591
$511$	7.22544	+	16.1578i	0.319635	+	0.714781i
$512$	−50.5364			−2.23341
$513$	−4.75516	+	8.23618i	−0.209946	+	0.363636i
$514$	−2.27965	−	3.94847i	−0.100551	−	0.174159i
$515$	−0.791041	−	1.37012i	−0.0348574	−	0.0603749i
$516$	39.4584	−	68.3439i	1.73706	−	3.00867i
$517$	−5.04089			−0.221698
$518$	1.66234	+	3.71739i	0.0730389	+	0.163333i
$519$	−22.3749			−0.982149
$520$	−8.07773	+	13.9910i	−0.354232	+	0.613547i
$521$	2.85505	+	4.94508i	0.125082	+	0.216648i	0.921765	−	0.387749i	$-0.126747\pi$
$521$	2.85505	+	4.94508i	0.125082	+	0.216648i	−0.796683	+	0.604397i	$0.793414\pi$
$522$	25.1882	+	43.6273i	1.10246	+	1.90951i
$523$	−3.39418	+	5.87889i	−0.148417	+	0.257066i	−0.930643	−	0.365930i	$-0.880751\pi$
$523$	−3.39418	+	5.87889i	−0.148417	+	0.257066i	0.782226	+	0.622995i	$0.214084\pi$
$524$	86.0461			3.75894
$525$	−4.64947	+	6.42137i	−0.202919	+	0.280252i
$526$	43.4105			1.89279
$527$	−32.8964	+	56.9782i	−1.43299	+	2.48201i
$528$	10.1199	+	17.5281i	0.440410	+	0.762813i
$529$	1.45005	+	2.51156i	0.0630457	+	0.109198i
$530$	−28.5197	+	49.3976i	−1.23882	+	2.14570i
$531$	−10.6523			−0.462271
$532$	39.5205	+	4.08881i	1.71343	+	0.177272i
$533$	2.83361			0.122737
$534$	43.0825	−	74.6211i	1.86436	−	3.22917i
$535$	−10.5427	−	18.2604i	−0.455799	−	0.789467i
$536$	−53.1242	−	92.0138i	−2.29462	−	3.97439i
$537$	−17.8257	+	30.8751i	−0.769238	+	1.33236i
$538$	−73.2493			−3.15800
$539$	−2.18476	−	6.65032i	−0.0941043	−	0.286450i
$540$	32.4553			1.39666
$541$	2.87288	−	4.97598i	0.123515	−	0.213934i	−0.797637	−	0.603138i	$-0.793917\pi$
$541$	2.87288	−	4.97598i	0.123515	−	0.213934i	0.921151	+	0.389204i	$0.127250\pi$
$542$	25.8811	+	44.8273i	1.11169	+	1.92550i
$543$	27.5444	+	47.7082i	1.18204	+	2.04736i
$544$	−22.1341	+	38.3375i	−0.948993	+	1.64370i
$545$	−3.04502			−0.130434
$546$	−17.9255	−	1.85458i	−0.767142	−	0.0793688i
$547$	3.00514			0.128490			0.0642452	−	0.997934i	$-0.479536\pi$
$547$	3.00514			0.128490			0.0642452	+	0.997934i	$0.479536\pi$
$548$	−41.6479	+	72.1362i	−1.77911	+	3.08151i
$549$	5.67173	+	9.82373i	0.242064	+	0.419266i
$550$	−1.44082	−	2.49557i	−0.0614366	−	0.106411i
$551$	−7.95511	+	13.7787i	−0.338899	+	0.586991i
$552$	77.8813			3.31485
$553$	25.5213	−	35.2474i	1.08527	−	1.49887i
$554$	−6.86728			−0.291763
$555$	−1.98061	+	3.43052i	−0.0840723	+	0.145618i
$556$	31.6905	+	54.8895i	1.34398	+	2.32783i
$557$	21.7554	+	37.6814i	0.921805	+	1.59661i	0.796621	+	0.604479i	$0.206619\pi$
$557$	21.7554	+	37.6814i	0.921805	+	1.59661i	0.125183	+	0.992134i	$0.460048\pi$
$558$	−49.7703	+	86.2047i	−2.10695	+	3.64934i
$559$	−6.51660			−0.275623
$560$	−20.3298	−	45.4623i	−0.859089	−	1.92113i
$561$	−18.3811			−0.776053
$562$	−11.0672	+	19.1689i	−0.466841	+	0.808592i
$563$	−6.77851	−	11.7407i	−0.285680	−	0.494813i	0.687094	−	0.726569i	$-0.258886\pi$
$563$	−6.77851	−	11.7407i	−0.285680	−	0.494813i	−0.972774	+	0.231756i	$0.925553\pi$
$564$	−30.5229	−	52.8672i	−1.28524	−	2.22611i
$565$	3.92629	−	6.80053i	0.165180	−	0.286100i
$566$	20.8458			0.876216
$567$	−4.94566	−	11.0597i	−0.207698	−	0.464464i
$568$	36.9985			1.55242
$569$	−15.1171	+	26.1836i	−0.633743	+	1.09767i	0.353038	+	0.935609i	$0.385149\pi$
$569$	−15.1171	+	26.1836i	−0.633743	+	1.09767i	−0.986780	+	0.162065i	$0.948185\pi$
$570$	27.8183	+	48.1828i	1.16518	+	2.01815i
$571$	−12.2461	−	21.2109i	−0.512483	−	0.887647i	−0.999895	−	0.0144748i	$-0.995392\pi$
$571$	−12.2461	−	21.2109i	−0.512483	−	0.887647i	0.487412	−	0.873172i	$-0.337941\pi$
$572$	2.27518	−	3.94073i	0.0951300	−	0.164770i
$573$	−0.0149971			−0.000626512
$574$	−11.2530	+	15.5415i	−0.469690	+	0.648689i
$575$	−5.04781			−0.210508
$576$	−2.43771	+	4.22224i	−0.101571	+	0.175927i
$577$	−9.26485	−	16.0472i	−0.385701	−	0.668053i	0.606165	−	0.795339i	$-0.292707\pi$
$577$	−9.26485	−	16.0472i	−0.385701	−	0.668053i	−0.991866	+	0.127285i	$0.959374\pi$
$578$	−39.2893	−	68.0510i	−1.63422	−	2.83055i
$579$	5.44794	−	9.43611i	0.226409	−	0.392151i
$580$	54.2959			2.25451
$581$	13.8480	+	1.43272i	0.574511	+	0.0594391i
$582$	−31.8303			−1.31941
$583$	4.50223	−	7.79809i	0.186463	−	0.322964i
$584$	−21.8335	−	37.8167i	−0.903475	−	1.56487i
$585$	−5.05260	−	8.75136i	−0.208899	−	0.361824i
$586$	−40.5382	+	70.2142i	−1.67462	+	2.90052i
$587$	5.23101			0.215907			0.107953	−	0.994156i	$-0.465570\pi$
$587$	5.23101			0.215907			0.107953	+	0.994156i	$0.465570\pi$
$588$	56.5176	−	63.1811i	2.33074	−	2.60555i
$589$	−31.4376			−1.29536
$590$	−8.26366	+	14.3131i	−0.340210	+	0.589260i
$591$	25.9443	+	44.9368i	1.06721	+	1.84845i
$592$	−2.28672	−	3.96071i	−0.0939835	−	0.162784i
$593$	12.6644	−	21.9354i	0.520066	−	0.900781i	−0.479662	−	0.877453i	$-0.659241\pi$
$593$	12.6644	−	21.9354i	0.520066	−	0.900781i	0.999728	−	0.0233274i	$-0.00742603\pi$
$594$	−7.37543			−0.302618
$595$	44.9875	+	4.65443i	1.84431	+	0.190813i
$596$	−57.1756			−2.34200
$597$	28.0796	−	48.6352i	1.14922	−	1.99051i
$598$	−5.73719	−	9.93711i	−0.234611	−	0.406359i
$599$	15.8061	+	27.3770i	0.645820	+	1.11859i	0.984112	+	0.177552i	$0.0568176\pi$
$599$	15.8061	+	27.3770i	0.645820	+	1.11859i	−0.338292	+	0.941041i	$0.609849\pi$
$600$	9.77941	−	16.9384i	0.399243	−	0.691509i
$601$	4.36846			0.178193			0.0890966	−	0.996023i	$-0.471602\pi$
$601$	4.36846			0.178193			0.0890966	+	0.996023i	$0.471602\pi$
$602$	25.8790	−	35.7415i	1.05475	−	1.45671i
$603$	66.4581			2.70638
$604$	−33.1478	+	57.4136i	−1.34876	+	2.33613i
$605$	1.23753	+	2.14346i	0.0503127	+	0.0871442i
$606$	34.9790	+	60.5854i	1.42093	+	2.46112i
$607$	12.6519	−	21.9137i	0.513524	−	0.889450i	−0.486353	−	0.873763i	$-0.661673\pi$
$607$	12.6519	−	21.9137i	0.513524	−	0.889450i	0.999877	−	0.0156874i	$-0.00499366\pi$
$608$	−21.1526			−0.857850
$609$	13.8575	+	30.9886i	0.561533	+	1.25572i
$610$	17.5997			0.712590
$611$	−2.52044	+	4.36554i	−0.101966	+	0.176611i
$612$	−64.1571	−	111.123i	−2.59340	−	4.49189i
$613$	−3.46775	−	6.00632i	−0.140061	−	0.242593i	0.787458	−	0.616368i	$-0.211397\pi$
$613$	−3.46775	−	6.00632i	−0.140061	−	0.242593i	−0.927519	+	0.373775i	$0.878063\pi$
$614$	19.8881	−	34.4472i	0.802618	−	1.39017i
$615$	−18.6651			−0.752647
$616$	7.04983	+	15.7651i	0.284046	+	0.635195i
$617$	−4.98006			−0.200490			−0.100245	−	0.994963i	$-0.531963\pi$
$617$	−4.98006			−0.200490			−0.100245	+	0.994963i	$0.531963\pi$
$618$	−2.17695	+	3.77059i	−0.0875699	+	0.151675i
$619$	0.315333	+	0.546173i	0.0126743	+	0.0219526i	0.872293	−	0.488984i	$-0.162632\pi$
$619$	0.315333	+	0.546173i	0.0126743	+	0.0219526i	−0.859619	+	0.510936i	$0.829299\pi$
$620$	53.6426	+	92.9117i	2.15434	+	3.73142i
$621$	−6.45984	+	11.1888i	−0.259225	+	0.448990i
$622$	30.3531			1.21705
$623$	19.6286	−	27.1091i	0.786404	−	1.08610i
$624$	20.2397			0.810237
$625$	14.6809	−	25.4281i	0.587238	−	1.01713i
$626$	29.4524	+	51.0130i	1.17715	+	2.03889i
$627$	−4.39150	−	7.60631i	−0.175380	−	0.303767i
$628$	−36.7194	+	63.5999i	−1.46527	+	2.53791i
$629$	4.15347			0.165610
$630$	68.0635	+	7.04187i	2.71171	+	0.280555i
$631$	−33.0103			−1.31412			−0.657059	−	0.753839i	$-0.728200\pi$
$631$	−33.0103			−1.31412			−0.657059	+	0.753839i	$0.728200\pi$
$632$	−53.6799	+	92.9764i	−2.13527	+	3.69840i
$633$	20.7677	+	35.9706i	0.825440	+	1.42970i
$634$	−13.5716	−	23.5067i	−0.538997	−	0.933570i
$635$	3.14142	−	5.44110i	0.124664	−	0.215924i
$636$	109.045			4.32391
$637$	−6.85173	−	1.43310i	−0.271475	−	0.0567817i
$638$	−12.3387			−0.488493
$639$	−11.5712	+	20.0420i	−0.457751	+	0.792848i
$640$	−12.0817	−	20.9261i	−0.477570	−	0.827175i
$641$	11.6175	+	20.1221i	0.458864	+	0.794776i	0.998901	−	0.0468652i	$-0.0149231\pi$
$641$	11.6175	+	20.1221i	0.458864	+	0.794776i	−0.540037	+	0.841641i	$0.681590\pi$
$642$	−29.0135	+	50.2528i	−1.14507	+	1.98332i
$643$	−26.4692			−1.04384			−0.521921	−	0.852994i	$-0.674784\pi$
$643$	−26.4692			−1.04384			−0.521921	+	0.852994i	$0.674784\pi$
$644$	53.6883	+	5.55461i	2.11561	+	0.218882i
$645$	42.9249			1.69017
$646$	29.1684	−	50.5212i	1.14762	−	1.98773i
$647$	−21.2586	−	36.8210i	−0.835762	−	1.44758i	−0.893409	−	0.449245i	$-0.851693\pi$
$647$	−21.2586	−	36.8210i	−0.835762	−	1.44758i	0.0576472	−	0.998337i	$-0.481640\pi$
$648$	14.9446	+	25.8847i	0.587078	+	1.01685i
$649$	1.30453	−	2.25951i	0.0512073	−	0.0886937i
$650$	−2.88163			−0.113027
$651$	−39.3374	+	54.3288i	−1.54175	+	2.12932i
$652$	−17.5989			−0.689225
$653$	−3.11850	+	5.40140i	−0.122036	+	0.211373i	−0.920571	−	0.390576i	$-0.872276\pi$
$653$	−3.11850	+	5.40140i	−0.122036	+	0.211373i	0.798534	+	0.601949i	$0.205609\pi$
$654$	4.18996	+	7.25722i	0.163840	+	0.283780i
$655$	23.4014	+	40.5323i	0.914367	+	1.58373i
$656$	10.7749	−	18.6626i	0.420688	−	0.728653i
$657$	27.3136			1.06560
$658$	−13.9343	−	31.1604i	−0.543215	−	1.21476i
$659$	0.895886			0.0348988			0.0174494	−	0.999848i	$-0.494445\pi$
$659$	0.895886			0.0348988			0.0174494	+	0.999848i	$0.494445\pi$
$660$	−14.9866	+	25.9576i	−0.583354	+	1.01040i
$661$	7.69374	+	13.3260i	0.299252	+	0.518320i	0.975965	−	0.217927i	$-0.0699296\pi$
$661$	7.69374	+	13.3260i	0.299252	+	0.518320i	−0.676713	+	0.736247i	$0.736596\pi$
$662$	−35.4232	−	61.3548i	−1.37676	−	2.38462i
$663$	−9.19057	+	15.9185i	−0.356932	+	0.618225i
$664$	−34.3466			−1.33290
$665$	8.82208	+	19.7283i	0.342106	+	0.765031i
$666$	6.28395			0.243498
$667$	−10.8069	+	18.7182i	−0.418446	+	0.724770i
$668$	−11.2316	−	19.4537i	−0.434564	−	0.752687i
$669$	−30.7465	−	53.2544i	−1.18873	−	2.05894i
$670$	51.5557	−	89.2971i	1.99177	−	3.44985i
$671$	−2.77835			−0.107257
$672$	−26.4679	+	36.5548i	−1.02102	+	1.41013i
$673$	−12.5318			−0.483067			−0.241534	−	0.970392i	$-0.577650\pi$
$673$	−12.5318			−0.483067			−0.241534	+	0.970392i	$0.577650\pi$
$674$	−22.1158	+	38.3057i	−0.851868	+	1.47548i
$675$	1.62230	+	2.80991i	0.0624424	+	0.108153i
$676$	−2.27518	−	3.94073i	−0.0875069	−	0.151566i
$677$	4.05593	−	7.02507i	0.155882	−	0.269995i	−0.777498	−	0.628886i	$-0.783511\pi$
$677$	4.05593	−	7.02507i	0.155882	−	0.269995i	0.933380	+	0.358890i	$0.116845\pi$
$678$	−21.6103			−0.829940
$679$	−12.2982	−	1.27238i	−0.471962	−	0.0488293i
$680$	−111.581			−4.27892
$681$	−24.2101	+	41.9332i	−0.927734	+	1.60688i
$682$	−12.1902	−	21.1141i	−0.466787	−	0.808499i
$683$	18.2109	+	31.5422i	0.696820	+	1.20693i	0.969563	+	0.244841i	$0.0787358\pi$
$683$	18.2109	+	31.5422i	0.696820	+	1.20693i	−0.272743	+	0.962087i	$0.587931\pi$
$684$	30.6560	−	53.0977i	1.17216	−	2.03024i
$685$	−45.3067			−1.73108
$686$	35.0700	−	31.8884i	1.33898	−	1.21750i
$687$	32.7964			1.25126
$688$	−24.7795	+	42.9193i	−0.944709	+	1.63628i
$689$	−4.50223	−	7.79809i	−0.171521	−	0.297083i
$690$	37.7909	+	65.4558i	1.43868	+	2.49186i
$691$	−0.0211388	+	0.0366135i	−0.000804159	+	0.00139284i	−0.866427	−	0.499303i	$-0.833589\pi$
$691$	−0.0211388	+	0.0366135i	−0.000804159	+	0.00139284i	0.865623	+	0.500696i	$0.166923\pi$
$692$	38.2564			1.45429
$693$	−10.7447	−	1.11165i	−0.408159	−	0.0422283i
$694$	−66.8537			−2.53773
$695$	−17.2373	+	29.8559i	−0.653847	+	1.13250i
$696$	−41.8738	−	72.5275i	−1.58722	−	2.74915i
$697$	9.78545	+	16.9489i	0.370650	+	0.641985i
$698$	−7.32092	+	12.6802i	−0.277101	+	0.479953i
$699$	−62.6919			−2.37123
$700$	7.94961	−	10.9792i	0.300467	−	0.414975i
$701$	2.17156			0.0820188			0.0410094	−	0.999159i	$-0.486943\pi$
$701$	2.17156			0.0820188			0.0410094	+	0.999159i	$0.486943\pi$
$702$	−3.68772	+	6.38731i	−0.139184	+	0.241074i
$703$	0.992320	+	1.71875i	0.0374261	+	0.0648238i
$704$	−0.597068	−	1.03415i	−0.0225028	−	0.0389761i
$705$	16.6022	−	28.7558i	0.625275	−	1.08301i
$706$	20.0822			0.755803
$707$	11.0930	+	24.8066i	0.417194	+	0.932946i
$708$	31.5961			1.18745
$709$	13.2731	−	22.9896i	0.498480	−	0.863393i	−0.501518	−	0.865147i	$-0.667225\pi$
$709$	13.2731	−	22.9896i	0.498480	−	0.863393i	0.999998	+	0.00175380i	$0.000558251\pi$
$710$	17.9531	+	31.0956i	0.673766	+	1.16700i
$711$	−33.5767	−	58.1565i	−1.25922	−	2.18104i
$712$	−41.2857	+	71.5088i	−1.54725	+	2.67991i
$713$	−42.7076			−1.59941
$714$	−50.8101	−	113.624i	−1.90152	−	4.25226i
$715$	2.47506			0.0925620
$716$	30.4783	−	52.7899i	1.13903	−	1.97285i
$717$	−2.83784	−	4.91528i	−0.105981	−	0.183565i
$718$	31.2976	+	54.2090i	1.16801	+	2.02306i
$719$	9.20590	−	15.9451i	0.343322	−	0.594652i	−0.641725	−	0.766935i	$-0.721781\pi$
$719$	9.20590	−	15.9451i	0.343322	−	0.594652i	0.985047	+	0.172283i	$0.0551144\pi$
$720$	−76.8504			−2.86404
$721$	−0.991831	+	1.36982i	−0.0369377	+	0.0510146i
$722$	−20.7531			−0.772349
$723$	−2.01929	+	3.49751i	−0.0750981	+	0.130074i
$724$	−47.0951	−	81.5710i	−1.75027	−	3.03156i
$725$	2.71401	+	4.70081i	0.100796	+	0.174584i
$726$	3.40569	−	5.89883i	0.126397	−	0.218926i
$727$	34.3421			1.27368			0.636839	−	0.770997i	$-0.280242\pi$
$727$	34.3421			1.27368			0.636839	+	0.770997i	$0.280242\pi$
$728$	17.1779	+	1.77723i	0.636656	+	0.0658686i
$729$	−41.7036			−1.54458
$730$	21.1888	−	36.7002i	0.784234	−	1.35833i
$731$	−22.5040	−	38.9781i	−0.832342	−	1.44166i
$732$	−16.8231	−	29.1384i	−0.621798	−	1.07699i
$733$	8.81373	−	15.2658i	0.325542	−	0.563856i	−0.656080	−	0.754692i	$-0.727786\pi$
$733$	8.81373	−	15.2658i	0.325542	−	0.563856i	0.981622	+	0.190836i	$0.0611198\pi$
$734$	46.4525			1.71459
$735$	45.1324	+	9.43987i	1.66473	+	0.348195i
$736$	−28.7356			−1.05921
$737$	−8.13877	+	14.0968i	−0.299795	+	0.519261i
$738$	14.8048	+	25.6427i	0.544972	+	0.943919i
$739$	17.4395	+	30.2061i	0.641522	+	1.11115i	0.985093	+	0.172022i	$0.0550301\pi$
$739$	17.4395	+	30.2061i	0.641522	+	1.11115i	−0.343571	+	0.939127i	$0.611637\pi$
$740$	3.38643	−	5.86547i	0.124488	−	0.215619i
$741$	−8.78301			−0.322652
$742$	60.6494	+	6.27481i	2.22651	+	0.230356i
$743$	−31.8697			−1.16919			−0.584593	−	0.811326i	$-0.698746\pi$
$743$	−31.8697			−1.16919			−0.584593	+	0.811326i	$0.698746\pi$
$744$	82.7399	−	143.310i	3.03339	−	5.25399i
$745$	−15.5496	−	26.9328i	−0.569695	−	0.986740i
$746$	5.43062	+	9.40610i	0.198829	+	0.344382i
$747$	10.7418	−	18.6054i	0.393023	−	0.680737i
$748$	31.4279			1.14912
$749$	−13.2187	+	18.2563i	−0.483000	+	0.667072i
$750$	−65.3115			−2.38484
$751$	−4.48453	+	7.76744i	−0.163643	+	0.283438i	−0.936173	−	0.351541i	$-0.885658\pi$
$751$	−4.48453	+	7.76744i	−0.163643	+	0.283438i	0.772530	+	0.634979i	$0.218991\pi$
$752$	19.1681	+	33.2001i	0.698988	+	1.21068i
$753$	−21.3578	−	36.9928i	−0.778322	−	1.34809i
$754$	−6.16933	+	10.6856i	−0.224674	+	0.389147i
$755$	−36.0599			−1.31235
$756$	−14.1627	−	31.6712i	−0.515092	−	1.15187i
$757$	−15.4668			−0.562150			−0.281075	−	0.959686i	$-0.590691\pi$
$757$	−15.4668			−0.562150			−0.281075	+	0.959686i	$0.590691\pi$
$758$	−17.3360	+	30.0269i	−0.629673	+	1.09063i
$759$	−5.96581	−	10.3331i	−0.216545	−	0.375068i
$760$	−26.6581	−	46.1732i	−0.966992	−	1.67488i
$761$	−21.3224	+	36.9315i	−0.772936	+	1.33876i	0.163011	+	0.986624i	$0.447879\pi$
$761$	−21.3224	+	36.9315i	−0.772936	+	1.33876i	−0.935947	+	0.352141i	$0.885454\pi$
$762$	−17.2904			−0.626367
$763$	1.32877	+	2.97145i	0.0481047	+	0.107574i
$764$	0.0256419			0.000927690
$765$	34.8967	−	60.4429i	1.26169	−	2.18532i
$766$	38.3056	+	66.3473i	1.38404	+	2.39723i
$767$	−1.30453	−	2.25951i	−0.0471039	−	0.0815864i
$768$	−36.4269	+	63.0932i	−1.31444	+	2.27668i
$769$	12.4040			0.447301			0.223651	−	0.974669i	$-0.428203\pi$
$769$	12.4040			0.447301			0.223651	+	0.974669i	$0.428203\pi$
$770$	−9.82906	+	13.5749i	−0.354215	+	0.489206i
$771$	−4.74098			−0.170742
$772$	−9.31483	+	16.1338i	−0.335248	+	0.580667i
$773$	10.8444	+	18.7831i	0.390046	+	0.675580i	0.992455	−	0.122607i	$-0.0391256\pi$
$773$	10.8444	+	18.7831i	0.390046	+	0.675580i	−0.602409	+	0.798188i	$0.705792\pi$
$774$	−34.0473	−	58.9716i	−1.22380	−	2.11969i
$775$	−5.36272	+	9.28850i	−0.192635	+	0.333653i
$776$	30.5027			1.09498
$777$	4.21193	+	0.435768i	0.151102	+	0.0156331i
$778$	3.68137			0.131984
$779$	−4.67575	+	8.09864i	−0.167526	+	0.290164i
$780$	14.9866	+	25.9576i	0.536607	+	0.929431i
$781$	−2.83413	−	4.90886i	−0.101413	−	0.175653i
$782$	39.6250	−	68.6325i	1.41699	−	2.45429i
$783$	13.8928			0.496489
$784$	−35.4925	+	39.6772i	−1.26759	+	1.41704i
$785$	−39.9453			−1.42571
$786$	64.4007	−	111.545i	2.29710	−	3.97869i
$787$	−6.84738	−	11.8600i	−0.244083	−	0.422764i	0.717791	−	0.696259i	$-0.245154\pi$
$787$	−6.84738	−	11.8600i	−0.244083	−	0.422764i	−0.961873	+	0.273495i	$0.911820\pi$
$788$	−44.3593	−	76.8325i	−1.58023	−	2.73705i
$789$	22.5702	−	39.0927i	0.803520	−	1.39174i
$790$	−104.190			−3.70692
$791$	−8.34956	−	0.863848i	−0.296876	−	0.0307149i
$792$	26.6497			0.946957
$793$	−1.38917	+	2.40612i	−0.0493310	+	0.0854438i
$794$	5.85205	+	10.1360i	0.207681	+	0.359715i
$795$	29.6562	+	51.3661i	1.05180	+	1.82177i
$796$	−48.0102	+	83.1560i	−1.70167	+	2.94739i
$797$	11.9000			0.421520			0.210760	−	0.977538i	$-0.432406\pi$
$797$	11.9000			0.421520			0.210760	+	0.977538i	$0.432406\pi$
$798$	34.8795	−	48.1720i	1.23472	−	1.70527i
$799$	−34.8158			−1.23170
$800$	−3.60827	+	6.24971i	−0.127572	+	0.220961i
$801$	−25.8241	−	44.7286i	−0.912449	−	1.58041i
$802$	−35.7359	−	61.8963i	−1.26188	−	2.18564i
$803$	−3.34495	+	5.79362i	−0.118041	+	0.204452i
$804$	−197.123			−6.95199
$805$	11.9847	+	26.8007i	0.422406	+	0.944601i
$806$	−24.3804			−0.858764
$807$	−38.0841	+	65.9636i	−1.34062	+	2.32203i
$808$	−33.5201	−	58.0586i	−1.17923	−	2.04249i
$809$	−23.6918	−	41.0354i	−0.832960	−	1.44273i	−0.895680	−	0.444698i	$-0.853311\pi$
$809$	−23.6918	−	41.0354i	−0.832960	−	1.44273i	0.0627204	−	0.998031i	$-0.480022\pi$
$810$	−14.5033	+	25.1205i	−0.509595	+	0.882644i
$811$	−21.2885			−0.747542			−0.373771	−	0.927521i	$-0.621935\pi$
$811$	−21.2885			−0.747542			−0.373771	+	0.927521i	$0.621935\pi$
$812$	−23.6934	−	52.9841i	−0.831474	−	1.85938i
$813$	53.8248			1.88772
$814$	−0.769562	+	1.33292i	−0.0269731	+	0.0467189i
$815$	−4.78624	−	8.29002i	−0.167655	−	0.290387i
$816$	69.8947	+	121.061i	2.44680	+	4.23799i
$817$	10.7530	−	18.6248i	0.376201	−	0.651600i
$818$	−72.4205			−2.53212
$819$	−6.33509	+	8.74940i	−0.221366	+	0.305729i
$820$	31.9133			1.11446
$821$	0.928858	−	1.60883i	0.0324174	−	0.0561485i	−0.849362	−	0.527811i	$-0.823013\pi$
$821$	0.928858	−	1.60883i	0.0324174	−	0.0561485i	0.881779	+	0.471663i	$0.156346\pi$
$822$	62.3423	+	107.980i	2.17444	+	3.76623i
$823$	23.4685	+	40.6486i	0.818059	+	1.41692i	0.907110	+	0.420893i	$0.138283\pi$
$823$	23.4685	+	40.6486i	0.818059	+	1.41692i	−0.0890506	+	0.996027i	$0.528383\pi$
$824$	2.08616	−	3.61333i	0.0726747	−	0.125876i
$825$	−2.99646			−0.104323
$826$	17.5733	+	1.81814i	0.611454	+	0.0632613i
$827$	1.05019			0.0365186			0.0182593	−	0.999833i	$-0.494188\pi$
$827$	1.05019			0.0365186			0.0182593	+	0.999833i	$0.494188\pi$
$828$	41.6458	−	72.1327i	1.44729	−	2.50678i
$829$	−17.0972	−	29.6132i	−0.593811	−	1.02851i	−0.993714	−	0.111953i	$-0.964289\pi$
$829$	−17.0972	−	29.6132i	−0.593811	−	1.02851i	0.399903	−	0.916558i	$-0.369044\pi$
$830$	−16.6662	−	28.8668i	−0.578494	−	1.00198i
$831$	−3.57047	+	6.18423i	−0.123858	+	0.214529i
$832$	−1.19414			−0.0413992
$833$	−15.0895	−	45.9317i	−0.522819	−	1.59144i
$834$	94.8743			3.28523
$835$	6.10917	−	10.5814i	0.211416	−	0.366184i
$836$	7.50855	+	13.0052i	0.259689	+	0.449794i
$837$	13.7257	+	23.7736i	0.474429	+	0.821735i
$838$	−35.6486	+	61.7451i	−1.23146	+	2.13295i
$839$	−52.8541			−1.82473			−0.912364	−	0.409381i	$-0.865745\pi$
$839$	−52.8541			−1.82473			−0.912364	+	0.409381i	$0.865745\pi$
$840$	−113.151	−	11.7067i	−3.90409	−	0.403918i
$841$	−5.75810			−0.198555
$842$	−27.3781	+	47.4203i	−0.943512	+	1.63421i
$843$	11.5082	+	19.9328i	0.396363	+	0.686522i
$844$	−35.5083	−	61.5022i	−1.22225	−	2.11699i
$845$	1.23753	−	2.14346i	0.0425723	−	0.0737374i
$846$	−52.6743			−1.81098
$847$	1.55165	−	2.14298i	0.0533153	−	0.0736338i
$848$	−68.4792			−2.35159
$849$	10.8383	−	18.7724i	0.371968	−	0.644268i
$850$	−9.95127	−	17.2361i	−0.341326	−	0.591194i
$851$	1.34806	+	2.33490i	0.0462108	+	0.0800394i
$852$	34.3217	−	59.4469i	1.17584	−	2.03662i
$853$	33.7922			1.15702			0.578511	−	0.815674i	$-0.303634\pi$
$853$	33.7922			1.15702			0.578511	+	0.815674i	$0.303634\pi$
$854$	−7.68005	−	17.1745i	−0.262806	−	0.587698i
$855$	33.3492			1.14052
$856$	27.8034	−	48.1569i	0.950301	−	1.64597i
$857$	−10.4823	−	18.1559i	−0.358068	−	0.620193i	0.629570	−	0.776944i	$-0.283231\pi$
$857$	−10.4823	−	18.1559i	−0.358068	−	0.620193i	−0.987638	+	0.156751i	$0.949898\pi$
$858$	−3.40569	−	5.89883i	−0.116268	−	0.201383i
$859$	−5.37610	+	9.31168i	−0.183430	+	0.317711i	−0.943046	−	0.332661i	$-0.892053\pi$
$859$	−5.37610	+	9.31168i	−0.183430	+	0.317711i	0.759616	+	0.650372i	$0.225387\pi$
$860$	−73.3925			−2.50266
$861$	8.14496	+	18.2141i	0.277579	+	0.620735i
$862$	53.9580			1.83782
$863$	−6.47482	+	11.2147i	−0.220405	+	0.381753i	−0.954931	−	0.296827i	$-0.904071\pi$
$863$	−6.47482	+	11.2147i	−0.220405	+	0.381753i	0.734526	+	0.678581i	$0.237405\pi$
$864$	9.23523	+	15.9959i	0.314189	+	0.544191i
$865$	10.4043	+	18.0208i	0.353758	+	0.612726i
$866$	−12.8687	+	22.2892i	−0.437296	+	0.757419i
$867$	−81.7098			−2.77501
$868$	67.2587	−	92.8909i	2.28291	−	3.15292i
$869$	16.4478			0.557954
$870$	40.6375	−	70.3862i	1.37774	−	2.38631i
$871$	8.13877	+	14.0968i	0.275772	+	0.477651i
$872$	−4.01521	−	6.95454i	−0.135972	−	0.235510i
$873$	−9.53969	+	16.5232i	−0.322869	+	0.559226i
$874$	37.8678			1.28090
$875$	−25.2343	−	2.61075i	−0.853076	−	0.0882595i
$876$	−81.0154			−2.73726
$877$	−6.86246	+	11.8861i	−0.231729	+	0.401366i	−0.958317	−	0.285707i	$-0.907771\pi$
$877$	−6.86246	+	11.8861i	−0.231729	+	0.401366i	0.726588	+	0.687073i	$0.241105\pi$
$878$	41.0087	+	71.0291i	1.38398	+	2.39712i
$879$	42.1536	+	73.0122i	1.42181	+	2.46264i
$880$	9.41146	−	16.3011i	0.317260	−	0.549511i
$881$	−9.62643			−0.324323			−0.162161	−	0.986764i	$-0.551847\pi$
$881$	−9.62643			−0.324323			−0.162161	+	0.986764i	$0.551847\pi$
$882$	−22.8295	−	69.4920i	−0.768708	−	2.33992i
$883$	−6.00751			−0.202169			−0.101084	−	0.994878i	$-0.532231\pi$
$883$	−6.00751			−0.202169			−0.101084	+	0.994878i	$0.532231\pi$
$884$	15.7139	−	27.2174i	0.528517	−	0.915419i
$885$	8.59296	+	14.8834i	0.288849	+	0.500302i
$886$	20.1382	+	34.8804i	0.676557	+	1.17183i
$887$	−17.7225	+	30.6963i	−0.595065	+	1.03068i	0.398473	+	0.917180i	$0.369540\pi$
$887$	−17.7225	+	30.6963i	−0.595065	+	1.03068i	−0.993538	+	0.113502i	$0.963793\pi$
$888$	−10.4467			−0.350567
$889$	−6.68048	−	0.691165i	−0.224056	−	0.0231809i
$890$	−80.1334			−2.68608
$891$	2.28955	−	3.96561i	0.0767027	−	0.132853i
$892$	52.5700	+	91.0539i	1.76017	+	3.04871i
$893$	−8.31797	−	14.4072i	−0.278350	−	0.482117i
$894$	−42.7927	+	74.1192i	−1.43120	+	2.47892i
$895$	33.1559			1.10828
$896$	−15.1483	+	20.9214i	−0.506071	+	0.698934i
$897$	−11.9316			−0.398385
$898$	39.9142	−	69.1333i	1.33195	−	2.30701i
$899$	22.9623	+	39.7718i	0.765834	+	1.32646i
$900$	−10.4588	−	18.1151i	−0.348626	−	0.603838i
$901$	31.0955	−	53.8589i	1.03594	−	1.79430i
$902$	−7.25226			−0.241474
$903$	−18.7313	−	41.8878i	−0.623340	−	1.39394i
$904$	20.7090			0.688772
$905$	25.6162	−	44.3686i	0.851513	−	1.47486i
$906$	49.6185	+	85.9418i	1.64847	+	2.85523i
$907$	−6.38125	−	11.0526i	−0.211886	−	0.366997i	0.740419	−	0.672146i	$-0.234627\pi$
$907$	−6.38125	−	11.0526i	−0.211886	−	0.366997i	−0.952305	+	0.305149i	$0.901294\pi$
$908$	41.3942	−	71.6969i	1.37372	−	2.37934i
$909$	41.9335			1.39085
$910$	6.84169	+	15.2997i	0.226800	+	0.507179i
$911$	37.8413			1.25374			0.626868	−	0.779125i	$-0.284336\pi$
$911$	37.8413			1.25374			0.626868	+	0.779125i	$0.284336\pi$
$912$	−33.3976	+	57.8463i	−1.10590	+	1.91548i
$913$	2.63099	+	4.55701i	0.0870731	+	0.150815i
$914$	−14.3817	−	24.9098i	−0.475705	−	0.823944i
$915$	9.15050	−	15.8491i	0.302506	−	0.523956i
$916$	−56.0750			−1.85277
$917$	29.3413	−	40.5233i	0.968935	−	1.33820i
$918$	−50.9398			−1.68126
$919$	21.3652	−	37.0056i	0.704773	−	1.22070i	−0.262001	−	0.965068i	$-0.584382\pi$
$919$	21.3652	−	37.0056i	0.704773	−	1.22070i	0.966774	−	0.255634i	$-0.0822843\pi$
$920$	−36.2148	−	62.7259i	−1.19397	−	2.06801i
$921$	−20.6806	−	35.8199i	−0.681449	−	1.18030i
$922$	11.2037	−	19.4053i	0.368973	−	0.639080i
$923$	−5.66827			−0.186573
$924$	31.8702	+	3.29731i	1.04845	+	0.108473i
$925$	0.677092			0.0222626
$926$	42.2404	−	73.1624i	1.38810	−	2.40427i
$927$	1.30489	+	2.26013i	0.0428581	+	0.0742324i
$928$	15.4500	+	26.7602i	0.507171	+	0.878446i
$929$	−26.3193	+	45.5863i	−0.863507	+	1.49564i	0.00501422	+	0.999987i	$0.498404\pi$
$929$	−26.3193	+	45.5863i	−0.863507	+	1.49564i	−0.868522	+	0.495651i	$0.834929\pi$
$930$	160.594			5.26609
$931$	15.4019	−	17.2179i	0.504778	−	0.564293i
$932$	107.190			3.51113
$933$	15.7813	−	27.3340i	0.516656	−	0.894875i
$934$	−21.9474	−	38.0140i	−0.718140	−	1.24386i
$935$	8.54723	+	14.8042i	0.279524	+	0.484150i
$936$	13.3249	−	23.0793i	0.435537	−	0.754372i
$937$	19.1160			0.624494			0.312247	−	0.950001i	$-0.398918\pi$
$937$	19.1160			0.624494			0.312247	+	0.950001i	$0.398918\pi$
$938$	−109.637	−	11.3431i	−3.57978	−	0.370366i
$939$	61.2521			1.99889
$940$	−28.3863	+	49.1664i	−0.925858	+	1.60363i
$941$	1.18908	+	2.05955i	0.0387630	+	0.0671395i	0.884756	−	0.466054i	$-0.154325\pi$
$941$	1.18908	+	2.05955i	0.0387630	+	0.0671395i	−0.845993	+	0.533194i	$0.820992\pi$
$942$	54.9650	+	95.2021i	1.79086	+	3.10185i
$943$	−6.35196	+	11.0019i	−0.206848	+	0.358272i
$944$	−19.8420			−0.645803
$945$	11.0671	−	15.2848i	0.360013	−	0.497214i
$946$	16.6784			0.542260
$947$	−1.16234	+	2.01323i	−0.0377710	+	0.0654212i	−0.884293	−	0.466933i	$-0.845359\pi$
$947$	−1.16234	+	2.01323i	−0.0377710	+	0.0654212i	0.846522	+	0.532354i	$0.178692\pi$
$948$	99.5925	+	172.499i	3.23461	+	5.60252i
$949$	3.34495	+	5.79362i	0.108582	+	0.188069i
$950$	4.75499	−	8.23588i	0.154272	−	0.267207i
$951$	−28.2248			−0.915252
$952$	48.6910	+	108.885i	1.57808	+	3.52898i
$953$	33.1381			1.07345			0.536724	−	0.843758i	$-0.319662\pi$
$953$	33.1381			1.07345			0.536724	+	0.843758i	$0.319662\pi$
$954$	47.0456	−	81.4854i	1.52316	−	2.63819i
$955$	0.00697364	+	0.0120787i	0.000225662	+	0.000390858i
$956$	4.85211	+	8.40410i	0.156928	+	0.271808i
$957$	−6.41518	+	11.1114i	−0.207373	+	0.359181i
$958$	−75.8576			−2.45085
$959$	19.7707	+	44.2121i	0.638430	+	1.42768i
$960$	7.86578			0.253867
$961$	−29.8719	+	51.7397i	−0.963611	+	1.66902i
$962$	0.769562	+	1.33292i	0.0248117	+	0.0429751i
$963$	17.3910	+	30.1220i	0.560416	+	0.970669i
$964$	3.45256	−	5.98001i	0.111199	−	0.192603i
$965$	−10.1332			−0.326198
$966$	47.3834	−	65.4412i	1.52454	−	2.10554i
$967$	56.0127			1.80125			0.900624	−	0.434599i	$-0.143110\pi$
$967$	56.0127			1.80125			0.900624	+	0.434599i	$0.143110\pi$
$968$	−3.26365	+	5.65281i	−0.104898	+	0.181688i
$969$	−30.3307	−	52.5344i	−0.974364	−	1.68765i
$970$	14.8011	+	25.6362i	0.475234	+	0.823129i
$971$	24.7069	−	42.7936i	0.792882	−	1.37331i	−0.131294	−	0.991344i	$-0.541913\pi$
$971$	24.7069	−	42.7936i	0.792882	−	1.37331i	0.924176	−	0.381968i	$-0.124754\pi$
$972$	94.7922			3.04046
$973$	36.6564	+	3.79249i	1.17515	+	0.121582i
$974$	80.5695			2.58161
$975$	−1.49823	+	2.59501i	−0.0479818	+	0.0831070i
$976$	10.5647	+	18.2986i	0.338168	+	0.585725i
$977$	14.9707	+	25.9299i	0.478954	+	0.829572i	0.999709	−	0.0241341i	$-0.00768287\pi$
$977$	14.9707	+	25.9299i	0.478954	+	0.829572i	−0.520755	+	0.853706i	$0.674350\pi$
$978$	−13.1718	+	22.8142i	−0.421187	+	0.729517i
$979$	12.6501			0.404300
$980$	−77.1670	−	16.1402i	−2.46501	−	0.515580i
$981$	5.02300			0.160372
$982$	−0.771941	+	1.33704i	−0.0246336	+	0.0426667i
$983$	15.8578	+	27.4665i	0.505785	+	0.876045i	0.999978	+	0.00669299i	$0.00213046\pi$
$983$	15.8578	+	27.4665i	0.505785	+	0.876045i	−0.494192	+	0.869353i	$0.664536\pi$
$984$	−24.6120	−	42.6293i	−0.784602	−	1.35897i
$985$	24.1282	−	41.7912i	0.768788	−	1.33158i
$986$	−85.2193			−2.71394
$987$	−35.3059	−	3.65276i	−1.12380	−	0.116269i
$988$	15.0171			0.477757
$989$	14.6079	−	25.3016i	0.464504	−	0.804545i
$990$	12.9314	+	22.3979i	0.410988	+	0.711853i
$991$	22.0622	+	38.2128i	0.700829	+	1.21387i	0.968176	+	0.250271i	$0.0805196\pi$
$991$	22.0622	+	38.2128i	0.700829	+	1.21387i	−0.267347	+	0.963600i	$0.586147\pi$
$992$	−30.5282	+	52.8764i	−0.969272	+	1.67883i
$993$	−73.6695			−2.33783
$994$	22.5101	−	31.0886i	0.713976	−	0.986072i
$995$	−52.2280			−1.65574
$996$	−31.8616	+	55.1860i	−1.00957	+	1.74863i
$997$	5.97313	+	10.3458i	0.189171	+	0.327654i	0.944974	−	0.327145i	$-0.106087\pi$
$997$	5.97313	+	10.3458i	0.189171	+	0.327654i	−0.755803	+	0.654799i	$0.772753\pi$
$998$	16.4272	+	28.4527i	0.519993	+	0.900654i
$999$	0.866495	−	1.50081i	0.0274147	−	0.0474837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.716.3	yes	50
7.2	even	3		7007.2.a.bh.1.23		25
7.4	even	3	inner	1001.2.i.d.144.3	✓	50
7.5	odd	6		7007.2.a.bi.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.3	✓	50	7.4	even	3	inner
1001.2.i.d.716.3	yes	50	1.1	even	1	trivial
7007.2.a.bh.1.23		25	7.2	even	3
7007.2.a.bi.1.23		25	7.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27968 + 2.21648i) q^{2} +(1.33068 + 2.30480i) q^{3} +(-2.27518 - 3.94073i) q^{4} +(1.23753 - 2.14346i) q^{5} -6.81138 q^{6} +(-2.63170 - 0.272277i) q^{7} +6.52730 q^{8} +(-2.04140 + 3.53582i) q^{9} +O(q^{10})\)	\(q+(-1.27968 + 2.21648i) q^{2} +(1.33068 + 2.30480i) q^{3} +(-2.27518 - 3.94073i) q^{4} +(1.23753 - 2.14346i) q^{5} -6.81138 q^{6} +(-2.63170 - 0.272277i) q^{7} +6.52730 q^{8} +(-2.04140 + 3.53582i) q^{9} +(3.16729 + 5.48591i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(6.05506 - 10.4877i) q^{12} -1.00000 q^{13} +(3.97124 - 5.48468i) q^{14} +6.58701 q^{15} +(-3.80252 + 6.58616i) q^{16} +(-3.45334 - 5.98137i) q^{17} +(-5.22470 - 9.04945i) q^{18} +(1.65010 - 2.85806i) q^{19} -11.2624 q^{20} +(-2.87440 - 6.42787i) q^{21} +2.55937 q^{22} +(2.24165 - 3.88264i) q^{23} +(8.68573 + 15.0441i) q^{24} +(-0.562958 - 0.975073i) q^{25} +(1.27968 - 2.21648i) q^{26} -2.88174 q^{27} +(4.91463 + 10.9903i) q^{28} -4.82099 q^{29} +(-8.42929 + 14.6000i) q^{30} +(-4.76298 - 8.24972i) q^{31} +(-3.20474 - 5.55077i) q^{32} +(1.33068 - 2.30480i) q^{33} +17.6767 q^{34} +(-3.84043 + 5.30401i) q^{35} +18.5782 q^{36} +(-0.300685 + 0.520801i) q^{37} +(4.22321 + 7.31482i) q^{38} +(-1.33068 - 2.30480i) q^{39} +(8.07773 - 13.9910i) q^{40} -2.83361 q^{41} +(17.9255 + 1.85458i) q^{42} +6.51660 q^{43} +(-2.27518 + 3.94073i) q^{44} +(5.05260 + 8.75136i) q^{45} +(5.73719 + 9.93711i) q^{46} +(2.52044 - 4.36554i) q^{47} -20.2397 q^{48} +(6.85173 + 1.43310i) q^{49} +2.88163 q^{50} +(9.19057 - 15.9185i) q^{51} +(2.27518 + 3.94073i) q^{52} +(4.50223 + 7.79809i) q^{53} +(3.68772 - 6.38731i) q^{54} -2.47506 q^{55} +(-17.1779 - 1.77723i) q^{56} +8.78301 q^{57} +(6.16933 - 10.6856i) q^{58} +(1.30453 + 2.25951i) q^{59} +(-14.9866 - 25.9576i) q^{60} +(1.38917 - 2.40612i) q^{61} +24.3804 q^{62} +(6.33509 - 8.74940i) q^{63} +1.19414 q^{64} +(-1.23753 + 2.14346i) q^{65} +(3.40569 + 5.89883i) q^{66} +(-8.13877 - 14.0968i) q^{67} +(-15.7139 + 27.2174i) q^{68} +11.9316 q^{69} +(-6.84169 - 15.2997i) q^{70} +5.66827 q^{71} +(-13.3249 + 23.0793i) q^{72} +(-3.34495 - 5.79362i) q^{73} +(-0.769562 - 1.33292i) q^{74} +(1.49823 - 2.59501i) q^{75} -15.0171 q^{76} +(1.08005 + 2.41526i) q^{77} +6.81138 q^{78} +(-8.22391 + 14.2442i) q^{79} +(9.41146 + 16.3011i) q^{80} +(2.28955 + 3.96561i) q^{81} +(3.62613 - 6.28064i) q^{82} -5.26198 q^{83} +(-18.7907 + 25.9518i) q^{84} -17.0945 q^{85} +(-8.33918 + 14.4439i) q^{86} +(-6.41518 - 11.1114i) q^{87} +(-3.26365 - 5.65281i) q^{88} +(-6.32507 + 10.9553i) q^{89} -25.8629 q^{90} +(2.63170 + 0.272277i) q^{91} -20.4006 q^{92} +(12.6760 - 21.9554i) q^{93} +(6.45074 + 11.1730i) q^{94} +(-4.08410 - 7.07386i) q^{95} +(8.52895 - 14.7726i) q^{96} +4.67310 q^{97} +(-11.9445 + 13.3528i) q^{98} +4.08281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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