LMFDB - Embedded newform 1001.2.i.a.144.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.2
Root			$-0.571299 - 1.29368i$ of defining polynomial
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.a.716.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834713 - 1.44577i) q^{2} +(-1.40601 + 2.43529i) q^{3} +(-0.393492 + 0.681548i) q^{4} +(1.40601 + 2.43529i) q^{5} +4.69447 q^{6} +(-2.00000 + 1.73205i) q^{7} -2.02504 q^{8} +(-2.45374 - 4.25001i) q^{9} +O(q^{10})$	\(q+(-0.834713 - 1.44577i) q^{2} +(-1.40601 + 2.43529i) q^{3} +(-0.393492 + 0.681548i) q^{4} +(1.40601 + 2.43529i) q^{5} +4.69447 q^{6} +(-2.00000 + 1.73205i) q^{7} -2.02504 q^{8} +(-2.45374 - 4.25001i) q^{9} +(2.34723 - 4.06553i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.10651 - 1.91653i) q^{12} -1.00000 q^{13} +(4.17357 + 1.44577i) q^{14} -7.90748 q^{15} +(2.47731 + 4.29083i) q^{16} +(-2.51252 + 4.35181i) q^{17} +(-4.09634 + 7.09507i) q^{18} +(2.69033 + 4.65979i) q^{19} -2.21302 q^{20} +(-1.40601 - 7.30586i) q^{21} -1.66943 q^{22} +(-0.271795 - 0.470763i) q^{23} +(2.84723 - 4.93155i) q^{24} +(-1.45374 + 2.51796i) q^{25} +(0.834713 + 1.44577i) q^{26} +5.36389 q^{27} +(-0.393492 - 2.04464i) q^{28} -0.974958 q^{29} +(6.60048 + 11.4324i) q^{30} +(1.02683 - 1.77852i) q^{31} +(2.11065 - 3.65575i) q^{32} +(1.40601 + 2.43529i) q^{33} +8.38894 q^{34} +(-7.03006 - 2.43529i) q^{35} +3.86211 q^{36} +(-1.02357 - 1.77287i) q^{37} +(4.49130 - 7.77917i) q^{38} +(1.40601 - 2.43529i) q^{39} +(-2.84723 - 4.93155i) q^{40} +0.355616 q^{41} +(-9.38894 + 8.13106i) q^{42} -10.0834 q^{43} +(0.393492 + 0.681548i) q^{44} +(6.89998 - 11.9511i) q^{45} +(-0.453742 + 0.785905i) q^{46} +(-0.441221 - 0.764218i) q^{47} -13.9325 q^{48} +(1.00000 - 6.92820i) q^{49} +4.85383 q^{50} +(-7.06527 - 12.2374i) q^{51} +(0.393492 - 0.681548i) q^{52} +(4.53935 - 7.86238i) q^{53} +(-4.47731 - 7.75493i) q^{54} +2.81202 q^{55} +(4.05008 - 3.50748i) q^{56} -15.1305 q^{57} +(0.813810 + 1.40956i) q^{58} +(4.83707 - 8.37805i) q^{59} +(3.11153 - 5.38933i) q^{60} +(-4.13422 - 7.16067i) q^{61} -3.42842 q^{62} +(12.2687 + 4.25001i) q^{63} +2.86211 q^{64} +(-1.40601 - 2.43529i) q^{65} +(2.34723 - 4.06553i) q^{66} +(-4.14407 + 7.17774i) q^{67} +(-1.97731 - 3.42480i) q^{68} +1.52859 q^{69} +(2.34723 + 12.1966i) q^{70} -14.0601 q^{71} +(4.96893 + 8.60644i) q^{72} +(5.56527 - 9.63933i) q^{73} +(-1.70877 + 2.95968i) q^{74} +(-4.08796 - 7.08055i) q^{75} -4.23449 q^{76} +(0.500000 + 2.59808i) q^{77} -4.69447 q^{78} +(5.97731 + 10.3530i) q^{79} +(-6.96626 + 12.0659i) q^{80} +(-0.180475 + 0.312592i) q^{81} +(-0.296837 - 0.514137i) q^{82} -12.2493 q^{83} +(5.53254 + 1.91653i) q^{84} -14.1305 q^{85} +(8.41675 + 14.5782i) q^{86} +(1.37080 - 2.37430i) q^{87} +(-1.01252 + 1.75374i) q^{88} +(0.327907 + 0.567951i) q^{89} -23.0380 q^{90} +(2.00000 - 1.73205i) q^{91} +0.427797 q^{92} +(2.88746 + 5.00123i) q^{93} +(-0.736586 + 1.27581i) q^{94} +(-7.56527 + 13.1034i) q^{95} +(5.93519 + 10.2801i) q^{96} +0.952861 q^{97} +(-10.8513 + 4.33730i) q^{98} -4.90748 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.834713	−	1.44577i	−0.590231	−	1.02231i	−0.994201	−	0.107538i	$-0.965703\pi$
$2$	−0.834713	−	1.44577i	−0.590231	−	1.02231i	0.403970	−	0.914772i	$-0.367630\pi$
$3$	−1.40601	+	2.43529i	−0.811762	+	1.40601i	0.0998683	+	0.995001i	$0.468158\pi$
$3$	−1.40601	+	2.43529i	−0.811762	+	1.40601i	−0.911630	+	0.411012i	$0.865175\pi$
$4$	−0.393492	+	0.681548i	−0.196746	+	0.340774i
$5$	1.40601	+	2.43529i	0.628788	+	1.08909i	0.987795	+	0.155758i	$0.0497820\pi$
$5$	1.40601	+	2.43529i	0.628788	+	1.08909i	−0.359007	+	0.933335i	$0.616885\pi$
$6$	4.69447			1.91651
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−2.02504			−0.715960
$9$	−2.45374	−	4.25001i	−0.817914	−	1.41667i
$10$	2.34723	−	4.06553i	0.742261	−	1.28563i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.10651	−	1.91653i	−0.319421	−	0.553254i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	4.17357	+	1.44577i	1.11543	+	0.386397i
$15$	−7.90748			−2.04170
$16$	2.47731	+	4.29083i	0.619328	+	1.07271i
$17$	−2.51252	+	4.35181i	−0.609376	+	1.05547i	0.381968	+	0.924176i	$0.375247\pi$
$17$	−2.51252	+	4.35181i	−0.609376	+	1.05547i	−0.991343	+	0.131294i	$0.958087\pi$
$18$	−4.09634	+	7.09507i	−0.965517	+	1.67232i
$19$	2.69033	+	4.65979i	0.617204	+	1.06903i	0.989994	+	0.141112i	$0.0450679\pi$
$19$	2.69033	+	4.65979i	0.617204	+	1.06903i	−0.372790	+	0.927916i	$0.621599\pi$
$20$	−2.21302			−0.494846
$21$	−1.40601	−	7.30586i	−0.306817	−	1.59427i
$22$	−1.66943			−0.355923
$23$	−0.271795	−	0.470763i	−0.0566732	−	0.0981609i	0.836297	−	0.548277i	$-0.184716\pi$
$23$	−0.271795	−	0.470763i	−0.0566732	−	0.0981609i	−0.892970	+	0.450116i	$0.851383\pi$
$24$	2.84723	−	4.93155i	0.581189	−	1.00665i
$25$	−1.45374	+	2.51796i	−0.290748	+	0.503591i
$26$	0.834713	+	1.44577i	0.163701	+	0.283538i
$27$	5.36389			1.03228
$28$	−0.393492	−	2.04464i	−0.0743629	−	0.386401i
$29$	−0.974958			−0.181045			−0.0905226	−	0.995894i	$-0.528854\pi$
$29$	−0.974958			−0.181045			−0.0905226	+	0.995894i	$0.528854\pi$
$30$	6.60048	+	11.4324i	1.20508	+	2.08726i
$31$	1.02683	−	1.77852i	0.184424	−	0.319431i	−0.758959	−	0.651139i	$-0.774292\pi$
$31$	1.02683	−	1.77852i	0.184424	−	0.319431i	0.943382	+	0.331708i	$0.107625\pi$
$32$	2.11065	−	3.65575i	0.373113	−	0.646251i
$33$	1.40601	+	2.43529i	0.244755	+	0.423929i
$34$	8.38894			1.43869
$35$	−7.03006	−	2.43529i	−1.18830	−	0.411638i
$36$	3.86211			0.643685
$37$	−1.02357	−	1.77287i	−0.168274	−	0.291459i	0.769539	−	0.638600i	$-0.220486\pi$
$37$	−1.02357	−	1.77287i	−0.168274	−	0.291459i	−0.937813	+	0.347141i	$0.887153\pi$
$38$	4.49130	−	7.77917i	0.728586	−	1.26195i
$39$	1.40601	−	2.43529i	0.225142	−	0.389958i
$40$	−2.84723	−	4.93155i	−0.450187	−	0.779747i
$41$	0.355616			0.0555378			0.0277689	−	0.999614i	$-0.491160\pi$
$41$	0.355616			0.0555378			0.0277689	+	0.999614i	$0.491160\pi$
$42$	−9.38894	+	8.13106i	−1.44874	+	1.25465i
$43$	−10.0834			−1.53770			−0.768852	−	0.639426i	$-0.779172\pi$
$43$	−10.0834			−1.53770			−0.768852	+	0.639426i	$0.779172\pi$
$44$	0.393492	+	0.681548i	0.0593211	+	0.102747i
$45$	6.89998	−	11.9511i	1.02859	−	1.78157i
$46$	−0.453742	+	0.785905i	−0.0669006	+	0.115875i
$47$	−0.441221	−	0.764218i	−0.0643588	−	0.111473i	0.832051	−	0.554700i	$-0.187167\pi$
$47$	−0.441221	−	0.764218i	−0.0643588	−	0.111473i	−0.896409	+	0.443227i	$0.853834\pi$
$48$	−13.9325			−2.01099
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	4.85383			0.686435
$51$	−7.06527	−	12.2374i	−0.989336	−	1.71358i
$52$	0.393492	−	0.681548i	0.0545675	−	0.0945136i
$53$	4.53935	−	7.86238i	0.623527	−	1.07998i	−0.365296	−	0.930891i	$-0.619032\pi$
$53$	4.53935	−	7.86238i	0.623527	−	1.07998i	0.988824	−	0.149090i	$-0.0476344\pi$
$54$	−4.47731	−	7.75493i	−0.609285	−	1.05531i
$55$	2.81202			0.379173
$56$	4.05008	−	3.50748i	0.541215	−	0.468706i
$57$	−15.1305			−2.00409
$58$	0.813810	+	1.40956i	0.106859	+	0.185084i
$59$	4.83707	−	8.37805i	0.629732	−	1.09073i	−0.357873	−	0.933770i	$-0.616498\pi$
$59$	4.83707	−	8.37805i	0.629732	−	1.09073i	0.987605	−	0.156958i	$-0.0501688\pi$
$60$	3.11153	−	5.38933i	0.401697	−	0.695759i
$61$	−4.13422	−	7.16067i	−0.529332	−	0.916830i	−0.999415	−	0.0342079i	$-0.989109\pi$
$61$	−4.13422	−	7.16067i	−0.529332	−	0.916830i	0.470082	−	0.882622i	$-0.344224\pi$
$62$	−3.42842			−0.435410
$63$	12.2687	+	4.25001i	1.54571	+	0.535450i
$64$	2.86211			0.357764
$65$	−1.40601	−	2.43529i	−0.174394	−	0.302060i
$66$	2.34723	−	4.06553i	0.288925	−	0.500432i
$67$	−4.14407	+	7.17774i	−0.506279	+	0.876901i	0.493695	+	0.869635i	$0.335646\pi$
$67$	−4.14407	+	7.17774i	−0.506279	+	0.876901i	−0.999974	+	0.00726541i	$0.997687\pi$
$68$	−1.97731	−	3.42480i	−0.239784	−	0.415319i
$69$	1.52859			0.184021
$70$	2.34723	+	12.1966i	0.280548	+	1.45777i
$71$	−14.0601			−1.66863			−0.834315	−	0.551288i	$-0.814136\pi$
$71$	−14.0601			−1.66863			−0.834315	+	0.551288i	$0.814136\pi$
$72$	4.96893	+	8.60644i	0.585594	+	1.01428i
$73$	5.56527	−	9.63933i	0.651366	−	1.12820i	−0.331426	−	0.943481i	$-0.607530\pi$
$73$	5.56527	−	9.63933i	0.651366	−	1.12820i	0.982792	−	0.184717i	$-0.0591370\pi$
$74$	−1.70877	+	2.95968i	−0.198641	+	0.344056i
$75$	−4.08796	−	7.08055i	−0.472037	−	0.817592i
$76$	−4.23449			−0.485729
$77$	0.500000	+	2.59808i	0.0569803	+	0.296078i
$78$	−4.69447			−0.531544
$79$	5.97731	+	10.3530i	0.672500	+	1.16480i	0.977193	+	0.212354i	$0.0681129\pi$
$79$	5.97731	+	10.3530i	0.672500	+	1.16480i	−0.304693	+	0.952451i	$0.598554\pi$
$80$	−6.96626	+	12.0659i	−0.778852	+	1.34901i
$81$	−0.180475	+	0.312592i	−0.0200528	+	0.0347324i
$82$	−0.296837	−	0.514137i	−0.0327802	−	0.0567769i
$83$	−12.2493			−1.34453			−0.672267	−	0.740309i	$-0.734679\pi$
$83$	−12.2493			−1.34453			−0.672267	+	0.740309i	$0.734679\pi$
$84$	5.53254	+	1.91653i	0.603650	+	0.209110i
$85$	−14.1305			−1.53267
$86$	8.41675	+	14.5782i	0.907601	+	1.57201i
$87$	1.37080	−	2.37430i	0.146966	−	0.254552i
$88$	−1.01252	+	1.75374i	−0.107935	+	0.186949i
$89$	0.327907	+	0.567951i	0.0347581	+	0.0602027i	0.882881	−	0.469597i	$-0.155601\pi$
$89$	0.327907	+	0.567951i	0.0347581	+	0.0602027i	−0.848123	+	0.529799i	$0.822267\pi$
$90$	−23.0380			−2.42842
$91$	2.00000	−	1.73205i	0.209657	−	0.181568i
$92$	0.427797			0.0446009
$93$	2.88746	+	5.00123i	0.299416	+	0.518604i
$94$	−0.736586	+	1.27581i	−0.0759731	+	0.131589i
$95$	−7.56527	+	13.1034i	−0.776180	+	1.34438i
$96$	5.93519	+	10.2801i	0.605758	+	1.04920i
$97$	0.952861			0.0967483			0.0483742	−	0.998829i	$-0.484596\pi$
$97$	0.952861			0.0967483			0.0483742	+	0.998829i	$0.484596\pi$
$98$	−10.8513	+	4.33730i	−1.09614	+	0.438133i
$99$	−4.90748			−0.493221
$100$	−1.14407	−	1.98159i	−0.114407	−	0.198159i
$101$	−7.86625	+	13.6247i	−0.782721	+	1.35571i	0.147630	+	0.989043i	$0.452835\pi$
$101$	−7.86625	+	13.6247i	−0.782721	+	1.35571i	−0.930351	+	0.366670i	$0.880498\pi$
$102$	−11.7949	+	20.4294i	−1.16787	+	2.02282i
$103$	4.11153	+	7.12138i	0.405121	+	0.701690i	0.994336	−	0.106286i	$-0.0338961\pi$
$103$	4.11153	+	7.12138i	0.405121	+	0.701690i	−0.589215	+	0.807977i	$0.700563\pi$
$104$	2.02504			0.198572
$105$	15.8150	−	13.6962i	1.54338	−	1.33661i
$106$	−15.1562			−1.47210
$107$	1.34990	+	2.33810i	0.130500	+	0.226032i	0.923869	−	0.382708i	$-0.125008\pi$
$107$	1.34990	+	2.33810i	0.130500	+	0.226032i	−0.793370	+	0.608740i	$0.791675\pi$
$108$	−2.11065	+	3.65575i	−0.203097	+	0.351775i
$109$	4.79684	−	8.30837i	0.459454	−	0.795797i	−0.539478	−	0.841999i	$-0.681379\pi$
$109$	4.79684	−	8.30837i	0.459454	−	0.795797i	0.998932	+	0.0462023i	$0.0147119\pi$
$110$	−2.34723	−	4.06553i	−0.223800	−	0.387633i
$111$	5.75661			0.546393
$112$	−12.3866	−	4.29083i	−1.17042	−	0.405445i
$113$	−9.20924			−0.866332			−0.433166	−	0.901314i	$-0.642604\pi$
$113$	−9.20924			−0.866332			−0.433166	+	0.901314i	$0.642604\pi$
$114$	12.6297	+	21.8752i	1.18288	+	2.04880i
$115$	0.764295	−	1.32380i	0.0712709	−	0.123445i
$116$	0.383638	−	0.664480i	0.0356199	−	0.0616955i
$117$	2.45374	+	4.25001i	0.226849	+	0.392913i
$118$	−16.1502			−1.48675
$119$	−2.51252	−	13.0554i	−0.230322	−	1.19679i
$120$	16.0130			1.46178
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−6.90177	+	11.9542i	−0.624857	+	1.08228i
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	0.808096	+	1.39966i	0.0725691	+	0.125693i
$125$	5.88421			0.526299
$126$	−4.09634	−	21.2852i	−0.364931	−	1.89624i
$127$	4.80845			0.426681			0.213341	−	0.976978i	$-0.431566\pi$
$127$	4.80845			0.426681			0.213341	+	0.976978i	$0.431566\pi$
$128$	−6.61033	−	11.4494i	−0.584276	−	1.01200i
$129$	14.1774	−	24.5560i	1.24825	−	2.16203i
$130$	−2.34723	+	4.06553i	−0.205866	+	0.356570i
$131$	−3.76222	−	6.51635i	−0.328707	−	0.569336i	0.653549	−	0.756884i	$-0.273279\pi$
$131$	−3.76222	−	6.51635i	−0.328707	−	0.569336i	−0.982255	+	0.187548i	$0.939946\pi$
$132$	−2.21302			−0.192618
$133$	−13.4516	−	4.65979i	−1.16641	−	0.404055i
$134$	13.8364			1.19529
$135$	7.54170	+	13.0626i	0.649086	+	1.12425i
$136$	5.08796	−	8.81260i	0.436289	−	0.755675i
$137$	4.60384	−	7.97409i	0.393333	−	0.681272i	−0.599554	−	0.800334i	$-0.704655\pi$
$137$	4.60384	−	7.97409i	0.393333	−	0.681272i	0.992887	+	0.119062i	$0.0379887\pi$
$138$	−1.27593	−	2.20998i	−0.108615	−	0.188126i
$139$	−3.96290			−0.336129			−0.168064	−	0.985776i	$-0.553752\pi$
$139$	−3.96290			−0.336129			−0.168064	+	0.985776i	$0.553752\pi$
$140$	4.42603	−	3.83306i	0.374068	−	0.323952i
$141$	2.48145			0.208976
$142$	11.7362	+	20.3276i	0.984877	+	1.70586i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	12.1574	−	21.0572i	1.01311	−	1.75477i
$145$	−1.37080	−	2.37430i	−0.113839	−	0.197175i
$146$	−18.5816			−1.53783
$147$	15.4661	+	12.1764i	1.27563	+	1.00429i
$148$	1.61106			0.132429
$149$	−6.35049	−	10.9994i	−0.520253	−	0.901104i	−0.999723	−	0.0235456i	$-0.992504\pi$
$149$	−6.35049	−	10.9994i	−0.520253	−	0.901104i	0.479470	−	0.877558i	$-0.340829\pi$
$150$	−6.82455	+	11.8205i	−0.557222	+	0.965137i
$151$	−7.20363	+	12.4770i	−0.586223	+	1.01537i	0.408499	+	0.912759i	$0.366052\pi$
$151$	−7.20363	+	12.4770i	−0.586223	+	1.01537i	−0.994722	+	0.102609i	$0.967281\pi$
$152$	−5.44803	−	9.43626i	−0.441893	−	0.765382i
$153$	24.6603			1.99367
$154$	3.33885	−	2.89153i	0.269052	−	0.233006i
$155$	5.77493			0.463853
$156$	1.10651	+	1.91653i	0.0885916	+	0.153445i
$157$	−5.32938	+	9.23075i	−0.425331	+	0.736694i	−0.996451	−	0.0841718i	$-0.973176\pi$
$157$	−5.32938	+	9.23075i	−0.425331	+	0.736694i	0.571121	+	0.820866i	$0.306509\pi$
$158$	9.97868	−	17.2836i	0.793861	−	1.37501i
$159$	12.7648	+	22.1092i	1.01231	+	1.75337i
$160$	11.8704			0.938436
$161$	1.35898	+	0.470763i	0.107102	+	0.0371013i
$162$	0.602579			0.0473431
$163$	5.25927	+	9.10933i	0.411938	+	0.713498i	0.995102	−	0.0988570i	$-0.0315186\pi$
$163$	5.25927	+	9.10933i	0.411938	+	0.713498i	−0.583163	+	0.812355i	$0.698185\pi$
$164$	−0.139932	+	0.242369i	−0.0109268	+	0.0189258i
$165$	−3.95374	+	6.84808i	−0.307798	+	0.533122i
$166$	10.2246	+	17.7096i	0.793585	+	1.37453i
$167$	−19.2731			−1.49140			−0.745700	−	0.666282i	$-0.767885\pi$
$167$	−19.2731			−1.49140			−0.745700	+	0.666282i	$0.767885\pi$
$168$	2.84723	+	14.7947i	0.219669	+	1.14143i
$169$	1.00000			0.0769231
$170$	11.7949	+	20.4294i	0.904631	+	1.56687i
$171$	13.2027	−	22.8678i	1.00964	−	1.74875i
$172$	3.96773	−	6.87232i	0.302537	−	0.524009i
$173$	1.21804	+	2.10970i	0.0926057	+	0.160398i	0.908607	−	0.417653i	$-0.137147\pi$
$173$	1.21804	+	2.10970i	0.0926057	+	0.160398i	−0.816001	+	0.578050i	$0.803814\pi$
$174$	−4.57691			−0.346975
$175$	−1.45374	−	7.55387i	−0.109893	−	0.571019i
$176$	4.95462			0.373469
$177$	13.6020	+	23.5593i	1.02239	+	1.77082i
$178$	0.547416	−	0.948153i	0.0410306	−	0.0710670i
$179$	−7.51242	+	13.0119i	−0.561504	+	0.972554i	0.435861	+	0.900014i	$0.356444\pi$
$179$	−7.51242	+	13.0119i	−0.561504	+	0.972554i	−0.997365	+	0.0725402i	$0.976889\pi$
$180$	5.43017	+	9.40533i	0.404741	+	0.701032i
$181$	16.8232			1.25046			0.625231	−	0.780440i	$-0.285005\pi$
$181$	16.8232			1.25046			0.625231	+	0.780440i	$0.285005\pi$
$182$	−4.17357	−	1.44577i	−0.309365	−	0.107167i
$183$	23.2510			1.71877
$184$	0.550397	+	0.953315i	0.0405758	+	0.0702793i
$185$	2.87830	−	4.98537i	0.211617	−	0.366532i
$186$	4.82041	−	8.34919i	0.353449	−	0.612192i
$187$	2.51252	+	4.35181i	0.183734	+	0.318236i
$188$	0.694468			0.0506493
$189$	−10.7278	+	9.29054i	−0.780332	+	0.675787i
$190$	25.2593			1.83250
$191$	3.90068	+	6.75617i	0.282243	+	0.488860i	0.971937	−	0.235242i	$-0.0755882\pi$
$191$	3.90068	+	6.75617i	0.282243	+	0.488860i	−0.689694	+	0.724101i	$0.742255\pi$
$192$	−4.02416	+	6.97005i	−0.290419	+	0.503020i
$193$	13.3791	−	23.1732i	0.963047	−	1.66805i	0.248275	−	0.968690i	$-0.420136\pi$
$193$	13.3791	−	23.1732i	0.963047	−	1.66805i	0.714772	−	0.699357i	$-0.246530\pi$
$194$	−0.795365	−	1.37761i	−0.0571039	−	0.0989068i
$195$	7.90748			0.566267
$196$	4.32841	+	3.40774i	0.309172	+	0.243410i
$197$	−23.7021			−1.68871			−0.844353	−	0.535787i	$-0.820015\pi$
$197$	−23.7021			−1.68871			−0.844353	+	0.535787i	$0.820015\pi$
$198$	4.09634	+	7.09507i	0.291114	+	0.504225i
$199$	−7.87652	+	13.6425i	−0.558352	+	0.967093i	0.439283	+	0.898349i	$0.355233\pi$
$199$	−7.87652	+	13.6425i	−0.558352	+	0.967093i	−0.997634	+	0.0687444i	$0.978101\pi$
$200$	2.94389	−	5.09896i	0.208164	−	0.360551i
$201$	−11.6532	−	20.1840i	−0.821956	−	1.42367i
$202$	26.2642			1.84795
$203$	1.94992	−	1.68868i	0.136857	−	0.118522i
$204$	11.1205			0.778591
$205$	0.500000	+	0.866025i	0.0349215	+	0.0604858i
$206$	6.86389	−	11.8886i	0.478230	−	0.828319i
$207$	−1.33383	+	2.31026i	−0.0927077	+	0.160574i
$208$	−2.47731	−	4.29083i	−0.171771	−	0.297516i
$209$	5.38066			0.372188
$210$	−33.0024	−	11.4324i	−2.27738	−	0.788908i
$211$	8.27810			0.569888			0.284944	−	0.958544i	$-0.408025\pi$
$211$	8.27810			0.569888			0.284944	+	0.958544i	$0.408025\pi$
$212$	3.57239	+	6.18756i	0.245353	+	0.424964i
$213$	19.7687	−	34.2404i	1.35453	−	2.34611i
$214$	2.25356	−	3.90328i	0.154050	−	0.266823i
$215$	−14.1774	−	24.5560i	−0.966890	−	1.67470i
$216$	−10.8621			−0.739073
$217$	1.02683	+	5.33555i	0.0697056	+	0.362201i
$218$	−16.0159			−1.08474
$219$	15.6497	+	27.1060i	1.05751	+	1.83166i
$220$	−1.10651	+	1.91653i	−0.0746008	+	0.129212i
$221$	2.51252	−	4.35181i	0.169010	−	0.292735i
$222$	−4.80512	−	8.32270i	−0.322498	−	0.558583i
$223$	24.0546			1.61081			0.805407	−	0.592722i	$-0.201947\pi$
$223$	24.0546			1.61081			0.805407	+	0.592722i	$0.201947\pi$
$224$	2.11065	+	10.9672i	0.141024	+	0.732780i
$225$	14.2684			0.951229
$226$	7.68707	+	13.3144i	0.511336	+	0.885661i
$227$	−12.8326	+	22.2267i	−0.851731	+	1.47524i	0.0279148	+	0.999610i	$0.491113\pi$
$227$	−12.8326	+	22.2267i	−0.851731	+	1.47524i	−0.879645	+	0.475630i	$0.842220\pi$
$228$	5.95374	−	10.3122i	0.394296	−	0.682941i
$229$	−5.01242	−	8.68176i	−0.331230	−	0.573707i	0.651523	−	0.758629i	$-0.274130\pi$
$229$	−5.01242	−	8.68176i	−0.331230	−	0.573707i	−0.982753	+	0.184922i	$0.940797\pi$
$230$	−2.55187			−0.168265
$231$	−7.03006	−	2.43529i	−0.462544	−	0.160230i
$232$	1.97433			0.129621
$233$	−4.64941	−	8.05301i	−0.304593	−	0.527570i	0.672578	−	0.740026i	$-0.265187\pi$
$233$	−4.64941	−	8.05301i	−0.304593	−	0.527570i	−0.977171	+	0.212456i	$0.931854\pi$
$234$	4.09634	−	7.09507i	0.267786	−	0.463819i
$235$	1.24073	−	2.14900i	0.0809360	−	0.140185i
$236$	3.80669	+	6.59338i	0.247794	+	0.429193i
$237$	−33.6167			−2.18364
$238$	−16.7779	+	14.5301i	−1.08755	+	0.941844i
$239$	29.7540			1.92462			0.962312	−	0.271948i	$-0.0876678\pi$
$239$	29.7540			1.92462			0.962312	+	0.271948i	$0.0876678\pi$
$240$	−19.5893	−	33.9297i	−1.26448	−	2.19015i
$241$	−14.1437	+	24.4975i	−0.911073	+	1.57802i	−0.0985214	+	0.995135i	$0.531411\pi$
$241$	−14.1437	+	24.4975i	−0.911073	+	1.57802i	−0.812551	+	0.582889i	$0.801922\pi$
$242$	−0.834713	+	1.44577i	−0.0536574	+	0.0929373i
$243$	7.53834	+	13.0568i	0.483585	+	0.837593i
$244$	6.50712			0.416576
$245$	18.2782	−	7.30586i	1.16775	−	0.466754i
$246$	1.66943			0.106439
$247$	−2.69033	−	4.65979i	−0.171182	−	0.296495i
$248$	−2.07937	+	3.60157i	−0.132040	+	0.228700i
$249$	17.2226	−	29.8305i	1.09144	−	1.89043i
$250$	−4.91162	−	8.50718i	−0.310638	−	0.538041i
$251$	−6.74694			−0.425863			−0.212932	−	0.977067i	$-0.568301\pi$
$251$	−6.74694			−0.425863			−0.212932	+	0.977067i	$0.568301\pi$
$252$	−7.72422	+	6.68937i	−0.486580	+	0.421391i
$253$	−0.543591			−0.0341753
$254$	−4.01368	−	6.95190i	−0.251841	−	0.436201i
$255$	19.8677	−	34.4119i	1.24416	−	2.15496i
$256$	−8.17336	+	14.1567i	−0.510835	+	0.884792i
$257$	2.80690	+	4.86169i	0.175090	+	0.303264i	0.940192	−	0.340644i	$-0.110645\pi$
$257$	2.80690	+	4.86169i	0.175090	+	0.303264i	−0.765103	+	0.643908i	$0.777312\pi$
$258$	−47.3362			−2.94702
$259$	5.11785	+	1.77287i	0.318008	+	0.110161i
$260$	2.21302			0.137245
$261$	2.39230	+	4.14358i	0.148079	+	0.256481i
$262$	−6.28075	+	10.8786i	−0.388026	+	0.672080i
$263$	3.74398	−	6.48477i	0.230864	−	0.399868i	−0.727199	−	0.686427i	$-0.759178\pi$
$263$	3.74398	−	6.48477i	0.230864	−	0.399868i	0.958063	+	0.286559i	$0.0925115\pi$
$264$	−2.84723	−	4.93155i	−0.175235	−	0.303516i
$265$	25.5295			1.56827
$266$	4.49130	+	23.3375i	0.275380	+	1.43091i
$267$	−1.84416			−0.112861
$268$	−3.26131	−	5.64876i	−0.199216	−	0.345053i
$269$	−13.5398	+	23.4516i	−0.825537	+	1.42987i	0.0759713	+	0.997110i	$0.475794\pi$
$269$	−13.5398	+	23.4516i	−0.825537	+	1.42987i	−0.901508	+	0.432762i	$0.857539\pi$
$270$	12.5903	−	21.8071i	0.766222	−	1.32714i
$271$	−8.56783	−	14.8399i	−0.520459	−	0.901461i	−0.999717	−	0.0237873i	$-0.992428\pi$
$271$	−8.56783	−	14.8399i	−0.520459	−	0.901461i	0.479258	−	0.877674i	$-0.340906\pi$
$272$	−24.8972			−1.50961
$273$	1.40601	+	7.30586i	0.0850957	+	0.442170i
$274$	−15.3715			−0.928629
$275$	1.45374	+	2.51796i	0.0876640	+	0.151838i
$276$	−0.601488	+	1.04181i	−0.0362053	+	0.0627094i
$277$	−2.74073	+	4.74708i	−0.164674	+	0.285224i	−0.936540	−	0.350562i	$-0.885991\pi$
$277$	−2.74073	+	4.74708i	−0.164674	+	0.285224i	0.771865	+	0.635786i	$0.219324\pi$
$278$	3.30789	+	5.72943i	0.198394	+	0.343628i
$279$	−10.0783			−0.603371
$280$	14.2362	+	4.93155i	0.850774	+	0.294717i
$281$	2.97672			0.177576			0.0887882	−	0.996051i	$-0.471701\pi$
$281$	2.97672			0.177576			0.0887882	+	0.996051i	$0.471701\pi$
$282$	−2.07130	−	3.58760i	−0.123344	−	0.213638i
$283$	−5.00028	+	8.66073i	−0.297236	+	0.514827i	−0.975502	−	0.219989i	$-0.929398\pi$
$283$	−5.00028	+	8.66073i	−0.297236	+	0.514827i	0.678267	+	0.734816i	$0.262731\pi$
$284$	5.53254	−	9.58264i	0.328296	−	0.568625i
$285$	−21.2737	−	36.8472i	−1.26015	−	2.18264i
$286$	1.66943			0.0987152
$287$	−0.711231	+	0.615944i	−0.0419827	+	0.0363580i
$288$	−20.7159			−1.22070
$289$	−4.12552	−	7.14561i	−0.242678	−	0.420330i
$290$	−2.28846	+	3.96372i	−0.134383	+	0.232758i
$291$	−1.33973	+	2.32049i	−0.0785366	+	0.136029i
$292$	4.37978	+	7.58599i	0.256307	+	0.443937i
$293$	−26.2169			−1.53161			−0.765804	−	0.643075i	$-0.777658\pi$
$293$	−26.2169			−1.53161			−0.765804	+	0.643075i	$0.777658\pi$
$294$	4.69447	−	32.5242i	0.273787	−	1.89685i
$295$	27.2039			1.58387
$296$	2.07277	+	3.59015i	0.120477	+	0.208673i
$297$	2.68195	−	4.64527i	0.155622	−	0.269546i
$298$	−10.6017	+	18.3626i	−0.614139	+	1.06372i
$299$	0.271795	+	0.470763i	0.0157183	+	0.0272249i
$300$	6.43431			0.371485
$301$	20.1668	−	17.4650i	1.16240	−	1.00666i
$302$	24.0518			1.38403
$303$	−22.1201	−	38.3131i	−1.27077	−	2.20103i
$304$	−13.3296	+	23.0875i	−0.764503	+	1.32416i
$305$	11.6255	−	20.1360i	0.665675	−	1.15298i
$306$	−20.5843	−	35.6530i	−1.17673	−	2.03815i
$307$	29.6365			1.69144			0.845721	−	0.533626i	$-0.179171\pi$
$307$	29.6365			1.69144			0.845721	+	0.533626i	$0.179171\pi$
$308$	−1.96746	−	0.681548i	−0.112106	−	0.0388348i
$309$	−23.1234			−1.31545
$310$	−4.82041	−	8.34919i	−0.273781	−	0.474202i
$311$	−0.533043	+	0.923258i	−0.0302261	+	0.0523531i	−0.880743	−	0.473595i	$-0.842956\pi$
$311$	−0.533043	+	0.923258i	−0.0302261	+	0.0523531i	0.850517	+	0.525948i	$0.176289\pi$
$312$	−2.84723	+	4.93155i	−0.161193	+	0.279194i
$313$	10.9946	+	19.0431i	0.621449	+	1.07638i	0.989216	+	0.146464i	$0.0467892\pi$
$313$	10.9946	+	19.0431i	0.621449	+	1.07638i	−0.367767	+	0.929918i	$0.619877\pi$
$314$	17.7940			1.00417
$315$	6.89998	+	35.8534i	0.388770	+	2.02011i
$316$	−9.40809			−0.529246
$317$	5.26991	+	9.12775i	0.295987	+	0.512665i	0.975214	−	0.221263i	$-0.0710180\pi$
$317$	5.26991	+	9.12775i	0.295987	+	0.512665i	−0.679227	+	0.733929i	$0.737685\pi$
$318$	21.3098	−	36.9097i	1.19500	−	2.06979i
$319$	−0.487479	+	0.844339i	−0.0272936	+	0.0472739i
$320$	4.02416	+	6.97005i	0.224957	+	0.389638i
$321$	−7.59191			−0.423739
$322$	−0.453742	−	2.35771i	−0.0252861	−	0.131390i
$323$	−27.0380			−1.50444
$324$	−0.142031	−	0.246005i	−0.00789060	−	0.0136669i
$325$	1.45374	−	2.51796i	0.0806391	−	0.139671i
$326$	8.77997	−	15.2074i	0.486278	−	0.842257i
$327$	13.4888	+	23.3633i	0.745934	+	1.29200i
$328$	−0.720136			−0.0397629
$329$	2.20611	+	0.764218i	0.121627	+	0.0421327i
$330$	13.2010			0.726689
$331$	2.69902	+	4.67485i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$331$	2.69902	+	4.67485i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$332$	4.81999	−	8.34847i	0.264531	−	0.458182i
$333$	−5.02315	+	8.70036i	−0.275267	+	0.476777i
$334$	16.0875	+	27.8644i	0.880271	+	1.52467i
$335$	−23.3065			−1.27337
$336$	27.8651	−	24.1318i	1.52016	−	1.31650i
$337$	−26.9272			−1.46682			−0.733409	−	0.679788i	$-0.762072\pi$
$337$	−26.9272			−1.46682			−0.733409	+	0.679788i	$0.762072\pi$
$338$	−0.834713	−	1.44577i	−0.0454024	−	0.0786393i
$339$	12.9483	−	22.4271i	0.703255	−	1.21807i
$340$	5.56025	−	9.63064i	0.301547	−	0.522295i
$341$	−1.02683	−	1.77852i	−0.0556058	−	0.0963121i
$342$	−44.0820			−2.38368
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	20.4193			1.10094
$345$	2.14922	+	3.72255i	0.115710	+	0.200416i
$346$	2.03342	−	3.52199i	0.109318	−	0.189344i
$347$	0.240829	−	0.417128i	0.0129284	−	0.0223926i	−0.859489	−	0.511155i	$-0.829218\pi$
$347$	0.240829	−	0.417128i	0.0129284	−	0.0223926i	0.872417	+	0.488762i	$0.162551\pi$
$348$	1.07880	+	1.86854i	0.0578297	+	0.100164i
$349$	19.7897			1.05932			0.529659	−	0.848211i	$-0.322320\pi$
$349$	19.7897			1.05932			0.529659	+	0.848211i	$0.322320\pi$
$350$	−9.70766	+	8.40708i	−0.518896	+	0.449377i
$351$	−5.36389			−0.286303
$352$	−2.11065	−	3.65575i	−0.112498	−	0.194852i
$353$	9.52147	−	16.4917i	0.506777	−	0.877763i	−0.493192	−	0.869920i	$-0.664170\pi$
$353$	9.52147	−	16.4917i	0.506777	−	0.877763i	0.999969	−	0.00784288i	$-0.00249649\pi$
$354$	22.7075	−	39.3305i	1.20689	−	2.09039i
$355$	−19.7687	−	34.2404i	−1.04921	−	1.81729i
$356$	−0.516114			−0.0273540
$357$	35.3264	+	12.2374i	1.86967	+	0.647672i
$358$	25.0828			1.32567
$359$	−14.7353	−	25.5222i	−0.777698	−	1.34701i	−0.933266	−	0.359187i	$-0.883054\pi$
$359$	−14.7353	−	25.5222i	−0.777698	−	1.34701i	0.155568	−	0.987825i	$-0.450279\pi$
$360$	−13.9728	+	24.2015i	−0.736429	+	1.27553i
$361$	−4.97574	+	8.61823i	−0.261881	+	0.453591i
$362$	−14.0426	−	24.3225i	−0.738062	−	1.27836i
$363$	2.81202			0.147593
$364$	0.393492	+	2.04464i	0.0206246	+	0.107168i
$365$	31.2994			1.63828
$366$	−19.4079	−	33.6156i	−1.01447	−	1.75711i
$367$	−9.33520	+	16.1690i	−0.487293	+	0.844017i	−0.999893	−	0.0146106i	$-0.995349\pi$
$367$	−9.33520	+	16.1690i	−0.487293	+	0.844017i	0.512600	+	0.858628i	$0.328682\pi$
$368$	1.34664	−	2.33246i	0.0701987	−	0.121588i
$369$	−0.872589	−	1.51137i	−0.0454252	−	0.0786787i
$370$	−9.61023			−0.499612
$371$	4.53935	+	23.5871i	0.235671	+	1.22458i
$372$	−4.54477			−0.235635
$373$	14.5363	+	25.1775i	0.752659	+	1.30364i	0.946530	+	0.322617i	$0.104563\pi$
$373$	14.5363	+	25.1775i	0.752659	+	1.30364i	−0.193870	+	0.981027i	$0.562104\pi$
$374$	4.19447	−	7.26503i	0.216891	−	0.375666i
$375$	−8.27327	+	14.3297i	−0.427230	+	0.739984i
$376$	0.893492	+	1.54757i	0.0460783	+	0.0798100i
$377$	0.974958			0.0502129
$378$	22.3866	+	7.75493i	1.15144	+	0.398871i
$379$	−28.5244			−1.46520			−0.732600	−	0.680660i	$-0.761693\pi$
$379$	−28.5244			−1.46520			−0.732600	+	0.680660i	$0.761693\pi$
$380$	−5.95374	−	10.3122i	−0.305421	−	0.529004i
$381$	−6.76075	+	11.7100i	−0.346364	+	0.599919i
$382$	6.51189	−	11.2789i	0.333177	−	0.577080i
$383$	−12.5419	−	21.7232i	−0.640861	−	1.11000i	−0.985241	−	0.171173i	$-0.945244\pi$
$383$	−12.5419	−	21.7232i	−0.640861	−	1.11000i	0.344380	−	0.938830i	$-0.388089\pi$
$384$	37.1768			1.89717
$385$	−5.62405	+	4.87057i	−0.286628	+	0.248227i
$386$	−44.6708			−2.27368
$387$	24.7421	+	42.8545i	1.25771	+	2.17842i
$388$	−0.374943	+	0.649420i	−0.0190348	+	0.0329693i
$389$	−9.30323	+	16.1137i	−0.471692	+	0.816995i	−0.999475	−	0.0323841i	$-0.989690\pi$
$389$	−9.30323	+	16.1137i	−0.471692	+	0.816995i	0.527783	+	0.849379i	$0.323023\pi$
$390$	−6.60048	−	11.4324i	−0.334228	−	0.578900i
$391$	2.73157			0.138141
$392$	−2.02504	+	14.0299i	−0.102280	+	0.708617i
$393$	21.1589			1.06733
$394$	19.7845	+	34.2677i	0.996727	+	1.72638i
$395$	−16.8084	+	29.1129i	−0.845720	+	1.46483i
$396$	1.93105	−	3.34468i	0.0970391	−	0.168077i
$397$	7.42976	+	12.8687i	0.372889	+	0.645862i	0.990009	−	0.141007i	$-0.0450340\pi$
$397$	7.42976	+	12.8687i	0.372889	+	0.645862i	−0.617120	+	0.786869i	$0.711701\pi$
$398$	26.2985			1.31823
$399$	30.2611	−	26.2069i	1.51495	−	1.31198i
$400$	−14.4055			−0.720275
$401$	2.56204	+	4.43758i	0.127942	+	0.221602i	0.922879	−	0.385090i	$-0.125830\pi$
$401$	2.56204	+	4.43758i	0.127942	+	0.221602i	−0.794937	+	0.606692i	$0.792496\pi$
$402$	−19.4542	+	33.6957i	−0.970288	+	1.68059i
$403$	−1.02683	+	1.77852i	−0.0511499	+	0.0885942i
$404$	−6.19061	−	10.7224i	−0.307994	−	0.533461i
$405$	−1.01500			−0.0504358
$406$	−4.06905	−	1.40956i	−0.201944	−	0.0699553i
$407$	−2.04714			−0.101473
$408$	14.3075	+	24.7813i	0.708325	+	1.22686i
$409$	−0.389353	+	0.674378i	−0.0192522	+	0.0333459i	−0.875491	−	0.483234i	$-0.839462\pi$
$409$	−0.389353	+	0.674378i	−0.0192522	+	0.0333459i	0.856239	+	0.516580i	$0.172795\pi$
$410$	0.834713	−	1.44577i	0.0412235	−	0.0714013i
$411$	12.9461	+	22.4233i	0.638585	+	1.10606i
$412$	−6.47141			−0.318823
$413$	4.83707	+	25.1341i	0.238016	+	1.23677i
$414$	4.45347			0.218876
$415$	−17.2226	−	29.8305i	−0.845426	−	1.46432i
$416$	−2.11065	+	3.65575i	−0.103483	+	0.179238i
$417$	5.57189	−	9.65080i	0.272857	−	0.472602i
$418$	−4.49130	−	7.77917i	−0.219677	−	0.380492i
$419$	−25.0333			−1.22296			−0.611479	−	0.791261i	$-0.709425\pi$
$419$	−25.0333			−1.22296			−0.611479	+	0.791261i	$0.709425\pi$
$420$	3.11153	+	16.1680i	0.151827	+	0.788917i
$421$	−11.3347			−0.552421			−0.276210	−	0.961097i	$-0.589079\pi$
$421$	−11.3347			−0.552421			−0.276210	+	0.961097i	$0.589079\pi$
$422$	−6.90984	−	11.9682i	−0.336366	−	0.582602i
$423$	−2.16529	+	3.75039i	−0.105280	+	0.182350i
$424$	−9.19237	+	15.9216i	−0.446421	+	0.773224i
$425$	−7.30512	−	12.6528i	−0.354350	−	0.613752i
$426$	−66.0048			−3.19794
$427$	20.6711	+	7.16067i	1.00034	+	0.346529i
$428$	−2.12470			−0.102701
$429$	−1.40601	−	2.43529i	−0.0678829	−	0.117577i
$430$	−23.6681	+	40.9944i	−1.14138	+	1.97692i
$431$	−9.84488	+	17.0518i	−0.474211	+	0.821358i	−0.999564	−	0.0295266i	$-0.990600\pi$
$431$	−9.84488	+	17.0518i	−0.474211	+	0.821358i	0.525353	+	0.850885i	$0.323933\pi$
$432$	13.2880	+	23.0156i	0.639321	+	1.10734i
$433$	18.2999			0.879439			0.439720	−	0.898135i	$-0.355078\pi$
$433$	18.2999			0.879439			0.439720	+	0.898135i	$0.355078\pi$
$434$	6.85685	−	5.93820i	0.329139	−	0.285043i
$435$	7.70947			0.369641
$436$	3.77503	+	6.53854i	0.180791	+	0.313140i
$437$	1.46244	−	2.53302i	0.0699579	−	0.121171i
$438$	26.1260	−	45.2515i	1.24835	−	2.16220i
$439$	18.9568	+	32.8341i	0.904757	+	1.56709i	0.821243	+	0.570579i	$0.193281\pi$
$439$	18.9568	+	32.8341i	0.904757	+	1.56709i	0.0835146	+	0.996507i	$0.473385\pi$
$440$	−5.69447			−0.271473
$441$	−31.8986	+	12.7500i	−1.51898	+	0.607144i
$442$	−8.38894			−0.399021
$443$	10.5987	+	18.3575i	0.503560	+	0.872192i	0.999992	+	0.00411589i	$0.00131013\pi$
$443$	10.5987	+	18.3575i	0.503560	+	0.872192i	−0.496431	+	0.868076i	$0.665357\pi$
$444$	−2.26518	+	3.92340i	−0.107501	+	0.186196i
$445$	−0.922082	+	1.59709i	−0.0437109	+	0.0757095i
$446$	−20.0787	−	34.7773i	−0.950753	−	1.64675i
$447$	35.7155			1.68928
$448$	−5.72422	+	4.95732i	−0.270444	+	0.234211i
$449$	−41.4042			−1.95399			−0.976993	−	0.213270i	$-0.931589\pi$
$449$	−41.4042			−1.95399			−0.976993	+	0.213270i	$0.931589\pi$
$450$	−11.9100	−	20.6288i	−0.561445	−	0.972451i
$451$	0.177808	−	0.307972i	0.00837264	−	0.0145018i
$452$	3.62376	−	6.27653i	0.170447	−	0.295223i
$453$	−20.2568	−	35.0858i	−0.951747	−	1.64847i
$454$	42.8462			2.01087
$455$	7.03006	+	2.43529i	0.329574	+	0.114168i
$456$	30.6400			1.43485
$457$	11.4806	+	19.8849i	0.537038	+	0.930178i	0.999062	+	0.0433100i	$0.0137903\pi$
$457$	11.4806	+	19.8849i	0.537038	+	0.930178i	−0.462023	+	0.886868i	$0.652876\pi$
$458$	−8.36786	+	14.4936i	−0.391004	+	0.677240i
$459$	−13.4769	+	23.3427i	−0.629048	+	1.08954i
$460$	0.601488	+	1.04181i	0.0280445	+	0.0485745i
$461$	−17.5781			−0.818693			−0.409347	−	0.912379i	$-0.634243\pi$
$461$	−17.5781			−0.818693			−0.409347	+	0.912379i	$0.634243\pi$
$462$	2.34723	+	12.1966i	0.109203	+	0.567436i
$463$	−14.8836			−0.691699			−0.345849	−	0.938290i	$-0.612409\pi$
$463$	−14.8836			−0.691699			−0.345849	+	0.938290i	$0.612409\pi$
$464$	−2.41528	−	4.18338i	−0.112126	−	0.194209i
$465$	−8.11962	+	14.0636i	−0.376538	+	0.652184i
$466$	−7.76184	+	13.4439i	−0.359560	+	0.622777i
$467$	−17.3782	−	30.0999i	−0.804166	−	1.39286i	−0.916853	−	0.399226i	$-0.869279\pi$
$467$	−17.3782	−	30.0999i	−0.804166	−	1.39286i	0.112686	−	0.993631i	$-0.464054\pi$
$468$	−3.86211			−0.178526
$469$	−4.14407	−	21.5332i	−0.191355	−	0.994312i
$470$	−4.14260			−0.191084
$471$	−14.9863	−	25.9571i	−0.690534	−	1.19604i
$472$	−9.79526	+	16.9659i	−0.450863	+	0.780918i
$473$	−5.04170	+	8.73248i	−0.231818	+	0.401520i
$474$	28.0603	+	48.6019i	1.28885	+	2.23236i
$475$	−15.6442			−0.717804
$476$	9.88656	+	3.42480i	0.453150	+	0.156976i
$477$	−44.5536			−2.03997
$478$	−24.8360	−	43.0173i	−1.13597	−	1.96756i
$479$	7.85452	−	13.6044i	0.358882	−	0.621602i	−0.628892	−	0.777493i	$-0.716491\pi$
$479$	7.85452	−	13.6044i	0.358882	−	0.621602i	0.987774	+	0.155890i	$0.0498246\pi$
$480$	−16.6899	+	28.9078i	−0.761787	+	1.31945i
$481$	1.02357	+	1.77287i	0.0466708	+	0.0808361i
$482$	47.2236			2.15097
$483$	−3.05718	+	2.64760i	−0.139107	+	0.120470i
$484$	0.786983			0.0357720
$485$	1.33973	+	2.32049i	0.0608342	+	0.105368i
$486$	12.5847	−	21.7973i	0.570854	−	0.988748i
$487$	5.54328	−	9.60124i	0.251190	−	0.435074i	−0.712664	−	0.701506i	$-0.752511\pi$
$487$	5.54328	−	9.60124i	0.251190	−	0.435074i	0.963854	+	0.266432i	$0.0858448\pi$
$488$	8.37196	+	14.5007i	0.378981	+	0.656414i
$489$	−29.5784			−1.33758
$490$	−25.8196	−	20.3276i	−1.16641	−	0.918309i
$491$	−2.29760			−0.103689			−0.0518446	−	0.998655i	$-0.516510\pi$
$491$	−2.29760			−0.103689			−0.0518446	+	0.998655i	$0.516510\pi$
$492$	−0.393492	−	0.681548i	−0.0177400	−	0.0307265i
$493$	2.44960	−	4.24284i	0.110325	−	0.191088i
$494$	−4.49130	+	7.77917i	−0.202073	+	0.350001i
$495$	−6.89998	−	11.9511i	−0.310131	−	0.537163i
$496$	10.1751			0.456875
$497$	28.1202	−	24.3529i	1.26137	−	1.09237i
$498$	−57.5039			−2.57681
$499$	−9.99889	−	17.3186i	−0.447612	−	0.775286i	0.550618	−	0.834757i	$-0.314392\pi$
$499$	−9.99889	−	17.3186i	−0.447612	−	0.775286i	−0.998230	+	0.0594709i	$0.981059\pi$
$500$	−2.31539	+	4.01037i	−0.103547	+	0.179349i
$501$	27.0983	−	46.9356i	1.21066	−	2.09693i
$502$	5.63176	+	9.75449i	0.251358	+	0.435364i
$503$	16.3473			0.728892			0.364446	−	0.931225i	$-0.381258\pi$
$503$	16.3473			0.728892			0.364446	+	0.931225i	$0.381258\pi$
$504$	−24.8447	−	8.60644i	−1.10667	−	0.383361i
$505$	−44.2402			−1.96866
$506$	0.453742	+	0.785905i	0.0201713	+	0.0349377i
$507$	−1.40601	+	2.43529i	−0.0624432	+	0.108155i
$508$	−1.89209	+	3.27719i	−0.0839478	+	0.145402i
$509$	11.3141	+	19.5965i	0.501487	+	0.868601i	0.999999	+	0.00171802i	$0.000546865\pi$
$509$	11.3141	+	19.5965i	0.501487	+	0.868601i	−0.498511	+	0.866883i	$0.666120\pi$
$510$	−66.3354			−2.93738
$511$	5.56527	+	28.9180i	0.246193	+	1.27926i
$512$	0.848289			0.0374894
$513$	14.4306	+	24.9946i	0.637128	+	1.10354i
$514$	4.68591	−	8.11624i	0.206687	−	0.357992i
$515$	−11.5617	+	20.0255i	−0.509470	+	0.882429i
$516$	11.1574	+	19.3251i	0.491176	+	0.850741i
$517$	−0.882443			−0.0388098
$518$	−1.70877	−	8.87905i	−0.0750792	−	0.390123i
$519$	−6.85030			−0.300695
$520$	2.84723	+	4.93155i	0.124859	+	0.216263i
$521$	9.29585	−	16.1009i	0.407259	−	0.705393i	−0.587323	−	0.809353i	$-0.699818\pi$
$521$	9.29585	−	16.1009i	0.407259	−	0.705393i	0.994581	+	0.103960i	$0.0331514\pi$
$522$	3.99376	−	6.91740i	0.174802	−	0.302766i
$523$	−3.96508	−	6.86772i	−0.173381	−	0.300305i	0.766219	−	0.642580i	$-0.222136\pi$
$523$	−3.96508	−	6.86772i	−0.173381	−	0.300305i	−0.939600	+	0.342275i	$0.888803\pi$
$524$	5.92161			0.258687
$525$	20.4398	+	7.08055i	0.892066	+	0.309021i
$526$	−12.5006			−0.545052
$527$	5.15985	+	8.93712i	0.224767	+	0.389307i
$528$	−6.96626	+	12.0659i	−0.303168	+	0.525102i
$529$	11.3523	−	19.6627i	0.493576	−	0.854899i
$530$	−21.3098	−	36.9097i	−0.925640	−	1.60325i
$531$	−47.4757			−2.06027
$532$	8.46897	−	7.33435i	0.367177	−	0.317984i
$533$	−0.355616			−0.0154034
$534$	1.53935	+	2.66623i	0.0666141	+	0.115379i
$535$	−3.79596	+	6.57479i	−0.164113	+	0.284253i
$536$	8.39192	−	14.5352i	0.362476	−	0.627826i
$537$	−21.1251	−	36.5898i	−0.911616	−	1.57896i
$538$	45.2074			1.94903
$539$	−5.50000	−	4.33013i	−0.236902	−	0.186512i
$540$	−11.8704			−0.510820
$541$	−3.52051	−	6.09770i	−0.151358	−	0.262161i	0.780369	−	0.625320i	$-0.215031\pi$
$541$	−3.52051	−	6.09770i	−0.151358	−	0.262161i	−0.931727	+	0.363159i	$0.881698\pi$
$542$	−14.3034	+	24.7742i	−0.614382	+	1.06414i
$543$	−23.6537	+	40.9694i	−1.01508	+	1.75817i
$544$	10.6061	+	18.3703i	0.454732	+	0.787620i
$545$	26.9777			1.15560
$546$	9.38894	−	8.13106i	0.401809	−	0.347977i
$547$	−29.1019			−1.24431			−0.622153	−	0.782895i	$-0.713742\pi$
$547$	−29.1019			−1.24431			−0.622153	+	0.782895i	$0.713742\pi$
$548$	3.62315	+	6.27547i	0.154773	+	0.268075i
$549$	−20.2886	+	35.1409i	−0.865897	+	1.49978i
$550$	2.42692	−	4.20354i	0.103484	−	0.179240i
$551$	−2.62296	−	4.54310i	−0.111742	−	0.193542i
$552$	−3.09546			−0.131752
$553$	−29.8866	−	10.3530i	−1.27091	−	0.440255i
$554$	9.15088			0.388784
$555$	8.09386	+	14.0190i	0.343565	+	0.595073i
$556$	1.55937	−	2.70091i	0.0661320	−	0.114544i
$557$	14.6729	−	25.4143i	0.621712	−	1.07684i	−0.367454	−	0.930042i	$-0.619771\pi$
$557$	14.6729	−	25.4143i	0.621712	−	1.07684i	0.989167	−	0.146796i	$-0.0468960\pi$
$558$	8.41247	+	14.5708i	0.356128	+	0.616832i
$559$	10.0834			0.426483
$560$	−6.96626	−	36.1978i	−0.294378	−	1.52963i
$561$	−14.1305			−0.596592
$562$	−2.48471	−	4.30364i	−0.104811	−	0.181538i
$563$	−16.6889	+	28.9060i	−0.703353	+	1.21824i	0.263929	+	0.964542i	$0.414982\pi$
$563$	−16.6889	+	28.9060i	−0.703353	+	1.21824i	−0.967282	+	0.253702i	$0.918352\pi$
$564$	−0.976430	+	1.69123i	−0.0411151	+	0.0712135i
$565$	−12.9483	−	22.4271i	−0.544739	−	0.943516i
$566$	16.6952			0.701751
$567$	−0.180475	−	0.937775i	−0.00757924	−	0.0393829i
$568$	28.4723			1.19467
$569$	7.19980	+	12.4704i	0.301831	+	0.522787i	0.976551	−	0.215287i	$-0.0690687\pi$
$569$	7.19980	+	12.4704i	0.301831	+	0.522787i	−0.674719	+	0.738074i	$0.735735\pi$
$570$	−35.5149	+	61.5136i	−1.48756	+	2.57652i
$571$	−21.5542	+	37.3330i	−0.902015	+	1.56234i	−0.0771408	+	0.997020i	$0.524579\pi$
$571$	−21.5542	+	37.3330i	−0.902015	+	1.56234i	−0.824874	+	0.565316i	$0.808754\pi$
$572$	−0.393492	−	0.681548i	−0.0164527	−	0.0284969i
$573$	−21.9376			−0.916457
$574$	1.48418	+	0.514137i	0.0619487	+	0.0214597i
$575$	1.58048			0.0659106
$576$	−7.02288	−	12.1640i	−0.292620	−	0.506832i
$577$	10.1159	−	17.5213i	0.421132	−	0.729423i	−0.574918	−	0.818211i	$-0.694966\pi$
$577$	10.1159	−	17.5213i	0.421132	−	0.729423i	0.996051	+	0.0887883i	$0.0282995\pi$
$578$	−6.88725	+	11.9291i	−0.286472	+	0.496184i
$579$	37.6223	+	65.1638i	1.56353	+	2.70811i
$580$	2.15760			0.0895894
$581$	24.4986	−	21.2164i	1.01637	−	0.880204i
$582$	4.47317			0.185419
$583$	−4.53935	−	7.86238i	−0.188001	−	0.325627i
$584$	−11.2699	+	19.5201i	−0.466352	+	0.807745i
$585$	−6.89998	+	11.9511i	−0.285279	+	0.494118i
$586$	21.8836	+	37.9035i	0.904002	+	1.56578i
$587$	9.09050			0.375205			0.187603	−	0.982245i	$-0.439928\pi$
$587$	9.09050			0.375205			0.187603	+	0.982245i	$0.439928\pi$
$588$	−14.3846	+	5.74959i	−0.593211	+	0.237109i
$589$	11.0500			0.455308
$590$	−22.7075	−	39.3305i	−0.934851	−	1.61921i
$591$	33.3255	−	57.7214i	1.37083	−	2.37434i
$592$	5.07140	−	8.78393i	0.208433	−	0.361017i
$593$	8.52090	+	14.7586i	0.349912	+	0.606065i	0.986233	−	0.165359i	$-0.0528783\pi$
$593$	8.52090	+	14.7586i	0.349912	+	0.606065i	−0.636322	+	0.771424i	$0.719545\pi$
$594$	−8.95462			−0.367413
$595$	28.2611	−	24.4748i	1.15859	−	1.00337i
$596$	9.99546			0.409430
$597$	−22.1490	−	38.3631i	−0.906497	−	1.57010i
$598$	0.453742	−	0.785905i	0.0185549	−	0.0321380i
$599$	−0.0801678	+	0.138855i	−0.00327557	+	0.00567345i	−0.867659	−	0.497161i	$-0.834376\pi$
$599$	−0.0801678	+	0.138855i	−0.00327557	+	0.00567345i	0.864383	+	0.502834i	$0.167709\pi$
$600$	8.27829	+	14.3384i	0.337960	+	0.585363i
$601$	−40.7770			−1.66333			−0.831665	−	0.555278i	$-0.812612\pi$
$601$	−40.7770			−1.66333			−0.831665	+	0.555278i	$0.812612\pi$
$602$	−42.0837	−	14.5782i	−1.71521	−	0.594164i
$603$	40.6739			1.65637
$604$	−5.66913	−	9.81923i	−0.230674	−	0.399539i
$605$	1.40601	−	2.43529i	0.0571625	−	0.0990084i
$606$	−36.9278	+	63.9609i	−1.50009	+	2.59823i
$607$	1.68795	+	2.92362i	0.0685119	+	0.118666i	0.898246	−	0.439492i	$-0.144842\pi$
$607$	1.68795	+	2.92362i	0.0685119	+	0.118666i	−0.829735	+	0.558158i	$0.811508\pi$
$608$	22.7133			0.921148
$609$	1.37080	+	7.12290i	0.0555478	+	0.288635i
$610$	−38.8159			−1.57161
$611$	0.441221	+	0.764218i	0.0178499	+	0.0309169i
$612$	−9.70363	+	16.8072i	−0.392246	+	0.679390i
$613$	3.68293	−	6.37903i	0.148752	−	0.257646i	−0.782014	−	0.623260i	$-0.785808\pi$
$613$	3.68293	−	6.37903i	0.148752	−	0.257646i	0.930767	+	0.365614i	$0.119141\pi$
$614$	−24.7379	−	42.8474i	−0.998342	−	1.72918i
$615$	−2.81202			−0.113392
$616$	−1.01252	−	5.26121i	−0.0407956	−	0.211980i
$617$	18.5861			0.748249			0.374124	−	0.927379i	$-0.377943\pi$
$617$	18.5861			0.748249			0.374124	+	0.927379i	$0.377943\pi$
$618$	19.3014	+	33.4311i	0.776418	+	1.34480i
$619$	9.60493	−	16.6362i	0.386055	−	0.668667i	−0.605860	−	0.795571i	$-0.707171\pi$
$619$	9.60493	−	16.6362i	0.386055	−	0.668667i	0.991915	+	0.126905i	$0.0405042\pi$
$620$	−2.27239	+	3.93589i	−0.0912612	+	0.158069i
$621$	−1.45788	−	2.52512i	−0.0585028	−	0.101330i
$622$	1.77975			0.0713616
$623$	−1.63953	−	0.567951i	−0.0656865	−	0.0227545i
$624$	13.9325			0.557747
$625$	15.5420	+	26.9195i	0.621679	+	1.07678i
$626$	18.3546	−	31.7911i	0.733598	−	1.27063i
$627$	−7.56527	+	13.1034i	−0.302128	+	0.523301i
$628$	−4.19413	−	7.26445i	−0.167364	−	0.289883i
$629$	10.2870			0.410168
$630$	46.0761	−	39.9030i	1.83571	−	1.58977i
$631$	−13.9970			−0.557212			−0.278606	−	0.960405i	$-0.589872\pi$
$631$	−13.9970			−0.557212			−0.278606	+	0.960405i	$0.589872\pi$
$632$	−12.1043	−	20.9653i	−0.481483	−	0.833954i
$633$	−11.6391	+	20.1595i	−0.462613	+	0.801270i
$634$	8.79772	−	15.2381i	0.349402	−	0.605182i
$635$	6.76075	+	11.7100i	0.268292	+	0.464695i
$636$	−20.0913			−0.796672
$637$	−1.00000	+	6.92820i	−0.0396214	+	0.274505i
$638$	1.62762			0.0644381
$639$	34.4999	+	59.7556i	1.36480	+	2.36390i
$640$	18.5884	−	32.1961i	0.734772	−	1.27266i
$641$	−21.0865	+	36.5228i	−0.832865	+	1.44256i	0.0628924	+	0.998020i	$0.479967\pi$
$641$	−21.0865	+	36.5228i	−0.832865	+	1.44256i	−0.895757	+	0.444544i	$0.853366\pi$
$642$	6.33707	+	10.9761i	0.250104	+	0.433193i
$643$	22.2337			0.876810			0.438405	−	0.898778i	$-0.355544\pi$
$643$	22.2337			0.876810			0.438405	+	0.898778i	$0.355544\pi$
$644$	−0.855594	+	0.740966i	−0.0337151	+	0.0291981i
$645$	79.7344			3.13954
$646$	22.5690	+	39.0906i	0.887965	+	1.53800i
$647$	−2.40868	+	4.17196i	−0.0946950	+	0.164016i	−0.909481	−	0.415745i	$-0.863521\pi$
$647$	−2.40868	+	4.17196i	−0.0946950	+	0.164016i	0.814786	+	0.579761i	$0.196854\pi$
$648$	0.365469	−	0.633011i	0.0143570	−	0.0248670i
$649$	−4.83707	−	8.37805i	−0.189871	−	0.328867i
$650$	−4.85383			−0.190383
$651$	−14.4373	−	5.00123i	−0.565843	−	0.196014i
$652$	−8.27792			−0.324188
$653$	−22.6004	−	39.1450i	−0.884420	−	1.53186i	−0.846377	−	0.532585i	$-0.821221\pi$
$653$	−22.6004	−	39.1450i	−0.884420	−	1.53186i	−0.0380435	−	0.999276i	$-0.512113\pi$
$654$	22.5186	−	39.0034i	0.880547	−	1.52515i
$655$	10.5795	−	18.3241i	0.413373	−	0.715984i
$656$	0.880971	+	1.52589i	0.0343961	+	0.0595758i
$657$	−54.6230			−2.13104
$658$	−0.736586	−	3.82742i	−0.0287151	−	0.149208i
$659$	28.8043			1.12206			0.561028	−	0.827797i	$-0.310406\pi$
$659$	28.8043			1.12206			0.561028	+	0.827797i	$0.310406\pi$
$660$	−3.11153	−	5.38933i	−0.121116	−	0.209779i
$661$	24.9147	−	43.1534i	0.969068	−	1.67847i	0.270803	−	0.962635i	$-0.412711\pi$
$661$	24.9147	−	43.1534i	0.969068	−	1.67847i	0.698265	−	0.715840i	$-0.253956\pi$
$662$	4.50582	−	7.80431i	0.175124	−	0.303323i
$663$	7.06527	+	12.2374i	0.274392	+	0.475262i
$664$	24.8053			0.962632
$665$	−7.56527	−	39.3103i	−0.293369	−	1.52439i
$666$	16.7716			0.649885
$667$	0.264989	+	0.458975i	0.0102604	+	0.0177716i
$668$	7.58382	−	13.1356i	0.293427	−	0.508230i
$669$	−33.8210	+	58.5798i	−1.30760	+	2.26482i
$670$	19.4542	+	33.6957i	0.751582	+	1.30178i
$671$	−8.26843			−0.319199
$672$	−29.6760	−	10.2801i	−1.14478	−	0.396562i
$673$	31.3070			1.20680			0.603398	−	0.797440i	$-0.293813\pi$
$673$	31.3070			1.20680			0.603398	+	0.797440i	$0.293813\pi$
$674$	22.4765	+	38.9304i	0.865762	+	1.49954i
$675$	−7.79772	+	13.5060i	−0.300134	+	0.519848i
$676$	−0.393492	+	0.681548i	−0.0151343	+	0.0262134i
$677$	14.6991	+	25.4596i	0.564932	+	0.978491i	0.997056	+	0.0766768i	$0.0244310\pi$
$677$	14.6991	+	25.4596i	0.564932	+	0.978491i	−0.432124	+	0.901814i	$0.642236\pi$
$678$	−43.2325			−1.66033
$679$	−1.90572	+	1.65040i	−0.0731349	+	0.0633366i
$680$	28.6149			1.09733
$681$	−36.0856	−	62.5021i	−1.38280	−	2.39509i
$682$	−1.71421	+	2.96910i	−0.0656406	+	0.113693i
$683$	7.48370	−	12.9622i	0.286356	−	0.495983i	−0.686581	−	0.727053i	$-0.740889\pi$
$683$	7.48370	−	12.9622i	0.286356	−	0.495983i	0.972937	+	0.231070i	$0.0742227\pi$
$684$	10.3903	+	17.9966i	0.397285	+	0.688117i
$685$	25.8922			0.989291
$686$	14.1901	−	27.4695i	0.541781	−	1.04879i
$687$	28.1901			1.07552
$688$	−24.9797	−	43.2662i	−0.952343	−	1.64951i
$689$	−4.53935	+	7.86238i	−0.172935	+	0.299533i
$690$	3.58796	−	6.21453i	0.136591	−	0.236583i
$691$	4.11655	+	7.13007i	0.156601	+	0.271241i	0.933641	−	0.358211i	$-0.116613\pi$
$691$	4.11655	+	7.13007i	0.156601	+	0.271241i	−0.777040	+	0.629451i	$0.783280\pi$
$692$	−1.91715			−0.0728791
$693$	9.81497	−	8.50001i	0.372840	−	0.322889i
$694$	−0.804093			−0.0305229
$695$	−5.57189	−	9.65080i	−0.211354	−	0.366076i
$696$	−2.77593	+	4.80806i	−0.105222	+	0.182249i
$697$	−0.893492	+	1.54757i	−0.0338434	+	0.0586185i
$698$	−16.5187	−	28.6112i	−0.625242	−	1.08295i
$699$	26.1485			0.989027
$700$	5.72035	+	1.98159i	0.216209	+	0.0748970i
$701$	23.2808			0.879305			0.439653	−	0.898168i	$-0.355102\pi$
$701$	23.2808			0.879305			0.439653	+	0.898168i	$0.355102\pi$
$702$	4.47731	+	7.75493i	0.168985	+	0.292691i
$703$	5.50748	−	9.53923i	0.207718	−	0.359779i
$704$	1.43105	−	2.47866i	0.0539349	−	0.0934180i
$705$	3.48895	+	6.04304i	0.131401	+	0.227594i
$706$	−31.7908			−1.19646
$707$	−7.86625	−	40.8742i	−0.295841	−	1.53723i
$708$	−21.4090			−0.804600
$709$	−10.7711	−	18.6561i	−0.404517	−	0.700643i	0.589748	−	0.807587i	$-0.299227\pi$
$709$	−10.7711	−	18.6561i	−0.404517	−	0.700643i	−0.994265	+	0.106944i	$0.965894\pi$
$710$	−33.0024	+	57.1618i	−1.23856	+	2.14525i
$711$	29.3336	−	50.8072i	1.10009	−	1.90542i
$712$	−0.664025	−	1.15012i	−0.0248854	−	0.0431028i
$713$	−1.11635			−0.0418075
$714$	−11.7949	−	61.2883i	−0.441415	−	2.29366i
$715$	−2.81202			−0.105164
$716$	−5.91215	−	10.2401i	−0.220947	−	0.382692i
$717$	−41.8344	+	72.4594i	−1.56234	+	2.70605i
$718$	−24.5994	+	42.6075i	−0.918043	+	1.59010i
$719$	−13.2779	−	22.9979i	−0.495181	−	0.857679i	0.504804	−	0.863234i	$-0.331565\pi$
$719$	−13.2779	−	22.9979i	−0.495181	−	0.857679i	−0.999985	+	0.00555556i	$0.998232\pi$
$720$	68.3737			2.54814
$721$	−20.5576	−	7.12138i	−0.765607	−	0.265214i
$722$	16.6132			0.618281
$723$	−39.7723	−	68.8877i	−1.47915	−	2.56196i
$724$	−6.61981	+	11.4658i	−0.246023	+	0.426125i
$725$	1.41734	−	2.45490i	0.0526386	−	0.0911728i
$726$	−2.34723	−	4.06553i	−0.0871140	−	0.150886i
$727$	−20.6090			−0.764346			−0.382173	−	0.924091i	$-0.624824\pi$
$727$	−20.6090			−0.764346			−0.382173	+	0.924091i	$0.624824\pi$
$728$	−4.05008	+	3.50748i	−0.150106	+	0.129996i
$729$	−43.4789			−1.61033
$730$	−26.1260	−	45.2515i	−0.966966	−	1.67483i
$731$	25.3348	−	43.8811i	0.937040	−	1.62300i
$732$	−9.14909	+	15.8467i	−0.338160	+	0.585711i
$733$	2.40042	+	4.15766i	0.0886617	+	0.153567i	0.906946	−	0.421248i	$-0.138408\pi$
$733$	2.40042	+	4.15766i	0.0886617	+	0.153567i	−0.818284	+	0.574814i	$0.805074\pi$
$734$	31.1689			1.15046
$735$	−7.90748	+	54.7847i	−0.291672	+	2.02076i
$736$	−2.29466			−0.0845822
$737$	4.14407	+	7.17774i	0.152649	+	0.264395i
$738$	−1.45672	+	2.52312i	−0.0536227	+	0.0928773i
$739$	−9.34770	+	16.1907i	−0.343861	+	0.595584i	−0.985146	−	0.171718i	$-0.945068\pi$
$739$	−9.34770	+	16.1907i	−0.343861	+	0.595584i	0.641285	+	0.767302i	$0.278401\pi$
$740$	2.26518	+	3.92340i	0.0832696	+	0.144227i
$741$	15.1305			0.555834
$742$	30.3124	−	26.2513i	1.11280	−	0.963717i
$743$	−46.4145			−1.70278			−0.851392	−	0.524530i	$-0.824241\pi$
$743$	−46.4145			−1.70278			−0.851392	+	0.524530i	$0.824241\pi$
$744$	−5.84723	−	10.1277i	−0.214370	−	0.371300i
$745$	17.8577	−	30.9305i	0.654257	−	1.13321i
$746$	24.2672	−	42.0321i	0.888486	−	1.53890i
$747$	30.0566	+	52.0595i	1.09971	+	1.90476i
$748$	−3.95462			−0.144595
$749$	−6.74950	−	2.33810i	−0.246622	−	0.0854322i
$750$	27.6232			1.00866
$751$	−10.7811	−	18.6735i	−0.393409	−	0.681404i	0.599488	−	0.800384i	$-0.295371\pi$
$751$	−10.7811	−	18.6735i	−0.393409	−	0.681404i	−0.992897	+	0.118980i	$0.962038\pi$
$752$	2.18609	−	3.78641i	0.0797184	−	0.138076i
$753$	9.48628	−	16.4307i	0.345699	−	0.598769i
$754$	−0.813810	−	1.40956i	−0.0296372	−	0.0513332i
$755$	−40.5136			−1.47444
$756$	−2.11065	−	10.9672i	−0.0767635	−	0.398875i
$757$	2.65654			0.0965534			0.0482767	−	0.998834i	$-0.484627\pi$
$757$	2.65654			0.0965534			0.0482767	+	0.998834i	$0.484627\pi$
$758$	23.8097	+	41.2396i	0.864807	+	1.49789i
$759$	0.764295	−	1.32380i	0.0277422	−	0.0480508i
$760$	15.3200	−	26.5350i	0.555714	−	0.962526i
$761$	−4.94309	−	8.56168i	−0.179187	−	0.310361i	0.762415	−	0.647088i	$-0.224013\pi$
$761$	−4.94309	−	8.56168i	−0.179187	−	0.310361i	−0.941602	+	0.336727i	$0.890680\pi$
$762$	22.5731			0.817738
$763$	4.79684	+	24.9251i	0.173657	+	0.902349i
$764$	−6.13954			−0.222121
$765$	34.6727	+	60.0549i	1.25359	+	2.17129i
$766$	−20.9378	+	36.2653i	−0.756512	+	1.31032i
$767$	−4.83707	+	8.37805i	−0.174656	+	0.302514i
$768$	−22.9837	−	39.8089i	−0.829352	−	1.43648i
$769$	−2.10710			−0.0759838			−0.0379919	−	0.999278i	$-0.512096\pi$
$769$	−2.10710			−0.0759838			−0.0379919	+	0.999278i	$0.512096\pi$
$770$	11.7362	+	4.06553i	0.422942	+	0.146511i
$771$	−15.7861			−0.568524
$772$	10.5291	+	18.2370i	0.378951	+	0.656363i
$773$	−16.6415	+	28.8239i	−0.598553	+	1.03672i	0.394482	+	0.918904i	$0.370924\pi$
$773$	−16.6415	+	28.8239i	−0.598553	+	1.03672i	−0.993035	+	0.117820i	$0.962409\pi$
$774$	41.3051	−	71.5425i	1.48468	−	2.57154i
$775$	2.98548	+	5.17101i	0.107242	+	0.185748i
$776$	−1.92958			−0.0692680
$777$	−11.5132	+	9.97074i	−0.413034	+	0.357698i
$778$	31.0621			1.11363
$779$	0.956723	+	1.65709i	0.0342782	+	0.0593715i
$780$	−3.11153	+	5.38933i	−0.111411	+	0.192969i
$781$	−7.03006	+	12.1764i	−0.251555	+	0.435707i
$782$	−2.28007	−	3.94920i	−0.0815353	−	0.141223i
$783$	−5.22957			−0.186890
$784$	32.2051	−	12.8725i	1.15018	−	0.459732i
$785$	−29.9727			−1.06977
$786$	−17.6616	−	30.5908i	−0.629969	−	1.09114i
$787$	8.77257	−	15.1945i	0.312708	−	0.541627i	−0.666239	−	0.745738i	$-0.732097\pi$
$787$	8.77257	−	15.1945i	0.312708	−	0.541627i	0.978948	+	0.204111i	$0.0654304\pi$
$788$	9.32659	−	16.1541i	0.332246	−	0.575467i
$789$	10.5282	+	18.2353i	0.374813	+	0.649195i
$790$	56.1206			1.99668
$791$	18.4185	−	15.9509i	0.654886	−	0.567148i
$792$	9.93786			0.353126
$793$	4.13422	+	7.16067i	0.146810	+	0.254283i
$794$	12.4034	−	21.4834i	0.440181	−	0.762416i
$795$	−35.8948	+	62.1717i	−1.27306	+	2.20500i
$796$	−6.19869	−	10.7364i	−0.219707	−	0.380543i
$797$	10.5353			0.373180			0.186590	−	0.982438i	$-0.440256\pi$
$797$	10.5353			0.373180			0.186590	+	0.982438i	$0.440256\pi$
$798$	−63.1483	−	21.8752i	−2.23543	−	0.774374i
$799$	4.43431			0.156875
$800$	6.13667	+	10.6290i	0.216964	+	0.375793i
$801$	1.60920	−	2.78721i	0.0568582	−	0.0984813i
$802$	4.27713	−	7.40821i	0.151031	−	0.261593i
$803$	−5.56527	−	9.63933i	−0.196394	−	0.340165i
$804$	18.3418			0.646865
$805$	0.764295	+	3.97139i	0.0269379	+	0.139973i
$806$	3.42842			0.120761
$807$	−38.0743	−	65.9466i	−1.34028	−	2.32143i
$808$	15.9295	−	27.5907i	0.560397	−	0.970636i
$809$	−1.83528	+	3.17880i	−0.0645250	+	0.111761i	−0.896483	−	0.443078i	$-0.853887\pi$
$809$	−1.83528	+	3.17880i	−0.0645250	+	0.111761i	0.831958	+	0.554838i	$0.187220\pi$
$810$	0.847234	+	1.46745i	0.0297688	+	0.0515610i
$811$	−34.0583			−1.19595			−0.597974	−	0.801515i	$-0.704027\pi$
$811$	−34.0583			−1.19595			−0.597974	+	0.801515i	$0.704027\pi$
$812$	0.383638	+	1.99344i	0.0134631	+	0.0699561i
$813$	48.1859			1.68995
$814$	1.70877	+	2.95968i	0.0598925	+	0.103737i
$815$	−14.7892	+	25.6157i	−0.518043	+	0.897278i
$816$	35.0058	−	60.6318i	1.22545	−	2.12254i
$817$	−27.1277	−	46.9865i	−0.949077	−	1.64385i
$818$	1.29999			0.0454531
$819$	−12.2687	−	4.25001i	−0.428703	−	0.148507i
$820$	−0.786983			−0.0274826
$821$	13.6160	+	23.5835i	0.475200	+	0.823071i	0.999597	−	0.0284033i	$-0.00904228\pi$
$821$	13.6160	+	23.5835i	0.475200	+	0.823071i	−0.524396	+	0.851474i	$0.675709\pi$
$822$	21.6126	−	37.4341i	0.753825	−	1.30566i
$823$	−7.02181	+	12.1621i	−0.244765	+	0.423945i	−0.962065	−	0.272819i	$-0.912044\pi$
$823$	−7.02181	+	12.1621i	−0.244765	+	0.423945i	0.717301	+	0.696764i	$0.245377\pi$
$824$	−8.32602	−	14.4211i	−0.290051	−	0.502382i
$825$	−8.17592			−0.284649
$826$	32.3005	−	27.9731i	1.12388	−	0.973307i
$827$	46.0731			1.60212			0.801059	−	0.598586i	$-0.204270\pi$
$827$	46.0731			1.60212			0.801059	+	0.598586i	$0.204270\pi$
$828$	−1.04970	−	1.81814i	−0.0364797	−	0.0631847i
$829$	−9.03715	+	15.6528i	−0.313873	+	0.543644i	−0.979197	−	0.202910i	$-0.934960\pi$
$829$	−9.03715	+	15.6528i	−0.313873	+	0.543644i	0.665324	+	0.746555i	$0.268293\pi$
$830$	−28.7519	+	49.7998i	−0.997994	+	1.72858i
$831$	−7.70699	−	13.3489i	−0.267352	−	0.463068i
$832$	−2.86211			−0.0992258
$833$	27.6377	+	21.7591i	0.957591	+	0.753907i
$834$	−18.6037			−0.644194
$835$	−27.0983	−	46.9356i	−0.937775	−	1.62427i
$836$	−2.11724	+	3.66717i	−0.0732264	+	0.126832i
$837$	5.50779	−	9.53977i	0.190377	−	0.329743i
$838$	20.8956	+	36.1923i	0.721828	+	1.25024i
$839$	−32.7984			−1.13233			−0.566163	−	0.824293i	$-0.691573\pi$
$839$	−32.7984			−1.13233			−0.566163	+	0.824293i	$0.691573\pi$
$840$	−32.0260	+	27.7353i	−1.10500	+	0.956959i
$841$	−28.0495			−0.967223
$842$	9.46124	+	16.3874i	0.326056	+	0.564746i
$843$	−4.18531	+	7.24917i	−0.144150	+	0.249675i
$844$	−3.25736	+	5.64192i	−0.112123	+	0.194203i
$845$	1.40601	+	2.43529i	0.0483683	+	0.0837764i
$846$	7.22957			0.248558
$847$	2.50000	+	0.866025i	0.0859010	+	0.0297570i
$848$	44.9815			1.54467
$849$	−14.0609	−	24.3542i	−0.482569	−	0.835834i
$850$	−12.1953	+	21.1230i	−0.418297	+	0.724512i
$851$	−0.556403	+	0.963718i	−0.0190732	+	0.0330358i
$852$	15.5576	+	26.9466i	0.532996	+	0.923176i
$853$	−32.4303			−1.11039			−0.555197	−	0.831719i	$-0.687357\pi$
$853$	−32.4303			−1.11039			−0.555197	+	0.831719i	$0.687357\pi$
$854$	−6.90177	−	35.8626i	−0.236174	−	1.22719i
$855$	74.2529			2.53940
$856$	−2.73361	−	4.73474i	−0.0934327	−	0.161830i
$857$	16.0800	−	27.8514i	0.549284	−	0.951387i	−0.449040	−	0.893512i	$-0.648234\pi$
$857$	16.0800	−	27.8514i	0.549284	−	0.951387i	0.998324	−	0.0578758i	$-0.0184327\pi$
$858$	−2.34723	+	4.06553i	−0.0801332	+	0.138795i
$859$	−10.7095	−	18.5494i	−0.365404	−	0.632899i	0.623437	−	0.781874i	$-0.285736\pi$
$859$	−10.7095	−	18.5494i	−0.365404	−	0.632899i	−0.988841	+	0.148975i	$0.952403\pi$
$860$	22.3147			0.760926
$861$	−0.500000	−	2.59808i	−0.0170400	−	0.0885422i
$862$	32.8706			1.11958
$863$	−25.4893	−	44.1487i	−0.867666	−	1.50284i	−0.864376	−	0.502846i	$-0.832286\pi$
$863$	−25.4893	−	44.1487i	−0.867666	−	1.50284i	−0.00328960	−	0.999995i	$-0.501047\pi$
$864$	11.3213	−	19.6090i	0.385158	−	0.667113i
$865$	−3.42515	+	5.93254i	−0.116459	+	0.201712i
$866$	−15.2752	−	26.4574i	−0.519073	−	0.899060i
$867$	23.2021			0.787986
$868$	−4.04048	−	1.39966i	−0.137143	−	0.0475077i
$869$	11.9546			0.405533
$870$	−6.43519	−	11.1461i	−0.218173	−	0.377888i
$871$	4.14407	−	7.17774i	0.140416	−	0.243208i
$872$	−9.71379	+	16.8248i	−0.328951	+	0.569759i
$873$	−2.33807	−	4.04966i	−0.0791318	−	0.137060i
$874$	−4.88286			−0.165165
$875$	−11.7684	+	10.1917i	−0.397845	+	0.344544i
$876$	−24.6321			−0.832241
$877$	−11.5515	−	20.0077i	−0.390066	−	0.675613i	0.602392	−	0.798200i	$-0.294214\pi$
$877$	−11.5515	−	20.0077i	−0.390066	−	0.675613i	−0.992458	+	0.122587i	$0.960881\pi$
$878$	31.6469	−	54.8141i	1.06803	−	1.84989i
$879$	36.8613	−	63.8456i	1.24330	−	2.15346i
$880$	6.96626	+	12.0659i	0.234833	+	0.406742i
$881$	−10.0055			−0.337095			−0.168548	−	0.985694i	$-0.553908\pi$
$881$	−10.0055			−0.337095			−0.168548	+	0.985694i	$0.553908\pi$
$882$	45.0598	+	35.4754i	1.51724	+	1.19452i
$883$	−37.8542			−1.27390			−0.636948	−	0.770907i	$-0.719803\pi$
$883$	−37.8542			−1.27390			−0.636948	+	0.770907i	$0.719803\pi$
$884$	1.97731	+	3.42480i	0.0665042	+	0.115189i
$885$	−38.2490	+	66.2493i	−1.28573	+	2.22694i
$886$	17.6938	−	30.6465i	0.594434	−	1.02959i
$887$	−1.31568	−	2.27882i	−0.0441761	−	0.0765153i	0.843092	−	0.537770i	$-0.180733\pi$
$887$	−1.31568	−	2.27882i	−0.0441761	−	0.0765153i	−0.887268	+	0.461254i	$0.847400\pi$
$888$	−11.6574			−0.391196
$889$	−9.61691	+	8.32849i	−0.322541	+	0.279328i
$890$	3.07870			0.103198
$891$	0.180475	+	0.312592i	0.00604614	+	0.0104722i
$892$	−9.46528	+	16.3943i	−0.316921	+	0.548923i
$893$	2.37406	−	4.11199i	0.0794449	−	0.137603i
$894$	−29.8122	−	51.6362i	−0.997068	−	1.72697i
$895$	−42.2502			−1.41227
$896$	33.0517	+	11.4494i	1.10418	+	0.382499i
$897$	−1.52859			−0.0510382
$898$	34.5607	+	59.8608i	1.15330	+	1.99758i
$899$	−1.00111	+	1.73398i	−0.0333890	+	0.0578315i
$900$	−5.61451	+	9.72462i	−0.187150	+	0.324154i
$901$	22.8104	+	39.5088i	0.759925	+	1.31623i
$902$	−0.593674			−0.0197672
$903$	14.1774	+	73.6679i	0.471794	+	2.45151i
$904$	18.6491			0.620260
$905$	23.6537	+	40.9694i	0.786275	+	1.36187i
$906$	−33.8172	+	58.5731i	−1.12350	+	1.94596i
$907$	9.18619	−	15.9109i	0.305022	−	0.528314i	−0.672244	−	0.740330i	$-0.734669\pi$
$907$	9.18619	−	15.9109i	0.305022	−	0.528314i	0.977266	+	0.212015i	$0.0680027\pi$
$908$	−10.0991	−	17.4921i	−0.335149	−	0.580495i
$909$	77.2070			2.56079
$910$	−2.34723	−	12.1966i	−0.0778100	−	0.404313i
$911$	9.62540			0.318904			0.159452	−	0.987206i	$-0.449027\pi$
$911$	9.62540			0.318904			0.159452	+	0.987206i	$0.449027\pi$
$912$	−37.4831	−	64.9226i	−1.24119	−	2.14980i
$913$	−6.12464	+	10.6082i	−0.202696	+	0.351080i
$914$	19.1660	−	33.1964i	0.633954	−	1.09804i
$915$	32.6913	+	56.6229i	1.08074	+	1.87190i
$916$	7.88938			0.260672
$917$	18.8111	+	6.51635i	0.621197	+	0.215189i
$918$	44.9974			1.48513
$919$	−5.47061	−	9.47537i	−0.180459	−	0.312564i	0.761578	−	0.648073i	$-0.224425\pi$
$919$	−5.47061	−	9.47537i	−0.180459	−	0.312564i	−0.942037	+	0.335509i	$0.891092\pi$
$920$	−1.54773	+	2.68075i	−0.0510271	+	0.0883816i
$921$	−41.6692	+	72.1732i	−1.37305	+	2.37819i
$922$	14.6727	+	25.4138i	0.483218	+	0.836959i
$923$	14.0601			0.462795
$924$	4.42603	−	3.83306i	0.145606	−	0.126098i
$925$	5.95203			0.195701
$926$	12.4235	+	21.5182i	0.408262	+	0.707131i
$927$	20.1773	−	34.9480i	0.662708	−	1.14784i
$928$	−2.05779	+	3.56420i	−0.0675504	+	0.117001i
$929$	16.3839	+	28.3777i	0.537538	+	0.931043i	0.999036	+	0.0439019i	$0.0139789\pi$
$929$	16.3839	+	28.3777i	0.537538	+	0.931043i	−0.461498	+	0.887141i	$0.652688\pi$
$930$	27.1102			0.888979
$931$	34.9743	−	13.9794i	1.14624	−	0.458155i
$932$	7.31801			0.239709
$933$	−1.49893	−	2.59622i	−0.0490728	−	0.0849966i
$934$	−29.0116	+	50.2495i	−0.949288	+	1.64422i
$935$	−7.06527	+	12.2374i	−0.231059	+	0.400206i
$936$	−4.96893	−	8.60644i	−0.162415	−	0.281310i
$937$	−34.1654			−1.11614			−0.558068	−	0.829795i	$-0.688457\pi$
$937$	−34.1654			−1.11614			−0.558068	+	0.829795i	$0.688457\pi$
$938$	−27.6729	+	23.9654i	−0.903552	+	0.782499i
$939$	−61.8340			−2.01788
$940$	0.976430	+	1.69123i	0.0318476	+	0.0551617i
$941$	−5.01891	+	8.69301i	−0.163612	+	0.283384i	−0.936161	−	0.351570i	$-0.885648\pi$
$941$	−5.01891	+	8.69301i	−0.163612	+	0.283384i	0.772550	+	0.634954i	$0.218981\pi$
$942$	−25.0186	+	43.3335i	−0.815150	+	1.41188i
$943$	−0.0966547	−	0.167411i	−0.00314751	−	0.00545165i
$944$	47.9317			1.56004
$945$	−37.7085	−	13.0626i	−1.22666	−	0.424927i
$946$	16.8335			0.547304
$947$	28.4856	+	49.3385i	0.925657	+	1.60328i	0.790502	+	0.612460i	$0.209820\pi$
$947$	28.4856	+	49.3385i	0.925657	+	1.60328i	0.135155	+	0.990824i	$0.456847\pi$
$948$	13.2279	−	22.9114i	0.429622	−	0.744127i
$949$	−5.56527	+	9.63933i	−0.180656	+	0.312906i
$950$	13.0584	+	22.6178i	0.423670	+	0.733819i
$951$	−29.6382			−0.961085
$952$	5.08796	+	26.4378i	0.164902	+	0.856854i
$953$	43.2172			1.39994			0.699972	−	0.714170i	$-0.253196\pi$
$953$	43.2172			1.39994			0.699972	+	0.714170i	$0.253196\pi$
$954$	37.1894	+	64.4140i	1.20405	+	2.08548i
$955$	−10.9688	+	18.9985i	−0.354942	+	0.614778i
$956$	−11.7079	+	20.2787i	−0.378662	+	0.655861i
$957$	−1.37080	−	2.37430i	−0.0443118	−	0.0767503i
$958$	−26.2251			−0.847294
$959$	4.60384	+	23.9223i	0.148666	+	0.772490i
$960$	−22.6321			−0.730447
$961$	13.3913	+	23.1943i	0.431976	+	0.748204i
$962$	1.70877	−	2.95968i	0.0550931	−	0.0954240i
$963$	6.62462	−	11.4742i	0.213475	−	0.369750i
$964$	−11.1308	−	19.2791i	−0.358500	−	0.620939i
$965$	75.2446			2.42221
$966$	6.37967	+	2.20998i	0.205263	+	0.0711050i
$967$	−1.79686			−0.0577832			−0.0288916	−	0.999583i	$-0.509198\pi$
$967$	−1.79686			−0.0577832			−0.0288916	+	0.999583i	$0.509198\pi$
$968$	1.01252	+	1.75374i	0.0325437	+	0.0563673i
$969$	38.0158	−	65.8453i	1.22124	−	2.11526i
$970$	2.23659	−	3.87388i	0.0718125	−	0.124383i
$971$	−2.01874	−	3.49657i	−0.0647846	−	0.112210i	0.831814	−	0.555055i	$-0.187303\pi$
$971$	−2.01874	−	3.49657i	−0.0647846	−	0.112210i	−0.896598	+	0.442845i	$0.853969\pi$
$972$	−11.8651			−0.380573
$973$	7.92580	−	6.86395i	0.254090	−	0.220048i
$974$	−18.5082			−0.593040
$975$	4.08796	+	7.08055i	0.130919	+	0.226759i
$976$	20.4835	−	35.4784i	0.655661	−	1.13564i
$977$	−13.4610	+	23.3152i	−0.430657	+	0.745919i	−0.996930	−	0.0782983i	$-0.975051\pi$
$977$	−13.4610	+	23.3152i	−0.430657	+	0.745919i	0.566273	+	0.824218i	$0.308385\pi$
$978$	24.6895	+	42.7635i	0.789483	+	1.36742i
$979$	0.655814			0.0209599
$980$	−2.21302	+	15.3322i	−0.0706922	+	0.489770i
$981$	−47.0808			−1.50317
$982$	1.91784	+	3.32179i	0.0612006	+	0.106003i
$983$	−24.6185	+	42.6404i	−0.785207	+	1.36002i	0.143668	+	0.989626i	$0.454110\pi$
$983$	−24.6185	+	42.6404i	−0.785207	+	1.36002i	−0.928875	+	0.370393i	$0.879223\pi$
$984$	1.01252	−	1.75374i	0.0322780	−	0.0559071i
$985$	−33.3255	−	57.7214i	−1.06184	−	1.83916i
$986$	−8.17886			−0.260468
$987$	−4.96290	+	4.29800i	−0.157971	+	0.136807i
$988$	4.23449			0.134717
$989$	2.74062	+	4.74690i	0.0871467	+	0.150943i
$990$	−11.5190	+	19.9515i	−0.366098	+	0.634101i
$991$	9.04013	−	15.6580i	0.287169	−	0.497391i	−0.685964	−	0.727636i	$-0.740619\pi$
$991$	9.04013	−	15.6580i	0.287169	−	0.497391i	0.973133	+	0.230244i	$0.0739525\pi$
$992$	−4.33454	−	7.50764i	−0.137622	−	0.238368i
$993$	−15.1794			−0.481705
$994$	−58.6808	−	20.3276i	−1.86124	−	0.644754i
$995$	−44.2979			−1.40434
$996$	13.5539	+	23.4761i	0.429473	+	0.743869i
$997$	5.00670	−	8.67186i	0.158564	−	0.274641i	−0.775787	−	0.630995i	$-0.782647\pi$
$997$	5.00670	−	8.67186i	0.158564	−	0.274641i	0.934351	+	0.356354i	$0.115980\pi$
$998$	−16.6924	+	28.9121i	−0.528389	+	0.915196i
$999$	−5.49032	−	9.50951i	−0.173706	−	0.300868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.a.144.2	✓	8
7.2	even	3	inner	1001.2.i.a.716.2	yes	8
7.3	odd	6		7007.2.a.l.1.3		4
7.4	even	3		7007.2.a.m.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.a.144.2	✓	8	1.1	even	1	trivial
1001.2.i.a.716.2	yes	8	7.2	even	3	inner
7007.2.a.l.1.3		4	7.3	odd	6
7007.2.a.m.1.3		4	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.834713 - 1.44577i) q^{2} +(-1.40601 + 2.43529i) q^{3} +(-0.393492 + 0.681548i) q^{4} +(1.40601 + 2.43529i) q^{5} +4.69447 q^{6} +(-2.00000 + 1.73205i) q^{7} -2.02504 q^{8} +(-2.45374 - 4.25001i) q^{9} +O(q^{10})\)	\(q+(-0.834713 - 1.44577i) q^{2} +(-1.40601 + 2.43529i) q^{3} +(-0.393492 + 0.681548i) q^{4} +(1.40601 + 2.43529i) q^{5} +4.69447 q^{6} +(-2.00000 + 1.73205i) q^{7} -2.02504 q^{8} +(-2.45374 - 4.25001i) q^{9} +(2.34723 - 4.06553i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.10651 - 1.91653i) q^{12} -1.00000 q^{13} +(4.17357 + 1.44577i) q^{14} -7.90748 q^{15} +(2.47731 + 4.29083i) q^{16} +(-2.51252 + 4.35181i) q^{17} +(-4.09634 + 7.09507i) q^{18} +(2.69033 + 4.65979i) q^{19} -2.21302 q^{20} +(-1.40601 - 7.30586i) q^{21} -1.66943 q^{22} +(-0.271795 - 0.470763i) q^{23} +(2.84723 - 4.93155i) q^{24} +(-1.45374 + 2.51796i) q^{25} +(0.834713 + 1.44577i) q^{26} +5.36389 q^{27} +(-0.393492 - 2.04464i) q^{28} -0.974958 q^{29} +(6.60048 + 11.4324i) q^{30} +(1.02683 - 1.77852i) q^{31} +(2.11065 - 3.65575i) q^{32} +(1.40601 + 2.43529i) q^{33} +8.38894 q^{34} +(-7.03006 - 2.43529i) q^{35} +3.86211 q^{36} +(-1.02357 - 1.77287i) q^{37} +(4.49130 - 7.77917i) q^{38} +(1.40601 - 2.43529i) q^{39} +(-2.84723 - 4.93155i) q^{40} +0.355616 q^{41} +(-9.38894 + 8.13106i) q^{42} -10.0834 q^{43} +(0.393492 + 0.681548i) q^{44} +(6.89998 - 11.9511i) q^{45} +(-0.453742 + 0.785905i) q^{46} +(-0.441221 - 0.764218i) q^{47} -13.9325 q^{48} +(1.00000 - 6.92820i) q^{49} +4.85383 q^{50} +(-7.06527 - 12.2374i) q^{51} +(0.393492 - 0.681548i) q^{52} +(4.53935 - 7.86238i) q^{53} +(-4.47731 - 7.75493i) q^{54} +2.81202 q^{55} +(4.05008 - 3.50748i) q^{56} -15.1305 q^{57} +(0.813810 + 1.40956i) q^{58} +(4.83707 - 8.37805i) q^{59} +(3.11153 - 5.38933i) q^{60} +(-4.13422 - 7.16067i) q^{61} -3.42842 q^{62} +(12.2687 + 4.25001i) q^{63} +2.86211 q^{64} +(-1.40601 - 2.43529i) q^{65} +(2.34723 - 4.06553i) q^{66} +(-4.14407 + 7.17774i) q^{67} +(-1.97731 - 3.42480i) q^{68} +1.52859 q^{69} +(2.34723 + 12.1966i) q^{70} -14.0601 q^{71} +(4.96893 + 8.60644i) q^{72} +(5.56527 - 9.63933i) q^{73} +(-1.70877 + 2.95968i) q^{74} +(-4.08796 - 7.08055i) q^{75} -4.23449 q^{76} +(0.500000 + 2.59808i) q^{77} -4.69447 q^{78} +(5.97731 + 10.3530i) q^{79} +(-6.96626 + 12.0659i) q^{80} +(-0.180475 + 0.312592i) q^{81} +(-0.296837 - 0.514137i) q^{82} -12.2493 q^{83} +(5.53254 + 1.91653i) q^{84} -14.1305 q^{85} +(8.41675 + 14.5782i) q^{86} +(1.37080 - 2.37430i) q^{87} +(-1.01252 + 1.75374i) q^{88} +(0.327907 + 0.567951i) q^{89} -23.0380 q^{90} +(2.00000 - 1.73205i) q^{91} +0.427797 q^{92} +(2.88746 + 5.00123i) q^{93} +(-0.736586 + 1.27581i) q^{94} +(-7.56527 + 13.1034i) q^{95} +(5.93519 + 10.2801i) q^{96} +0.952861 q^{97} +(-10.8513 + 4.33730i) q^{98} -4.90748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q - 2 q^{2} - q^{3} - 4 q^{4} + q^{5} + 6 q^{6} - 16 q^{7} + 6 q^{8} - 3 q^{9} + 3 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{13} + 10 q^{14} - 30 q^{15} + 4 q^{16} - 9 q^{17} - 5 q^{18} + 4 q^{19} - 16 q^{20} - q^{21} - 4 q^{22} - 6 q^{23} + 7 q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{28} - 30 q^{29} + 11 q^{30} + 10 q^{31} + 2 q^{32} + q^{33} + 4 q^{34} - 5 q^{35} - 34 q^{36} - 9 q^{37} - 14 q^{38} + q^{39} - 7 q^{40} - 10 q^{41} - 12 q^{42} + 14 q^{43} + 4 q^{44} + 4 q^{45} + 13 q^{46} + 2 q^{47} - 56 q^{48} + 8 q^{49} + 2 q^{50} - 10 q^{51} + 4 q^{52} + 27 q^{53} - 20 q^{54} + 2 q^{55} - 12 q^{56} - 28 q^{57} + 10 q^{58} - 4 q^{59} - 5 q^{60} - 19 q^{61} - 88 q^{62} + 15 q^{63} - 42 q^{64} - q^{65} + 3 q^{66} + q^{67} - 16 q^{69} + 3 q^{70} - 10 q^{71} + 21 q^{72} - 2 q^{73} + 5 q^{74} - 2 q^{75} + 38 q^{76} + 4 q^{77} - 6 q^{78} + 32 q^{79} - 28 q^{80} - 4 q^{81} + 16 q^{82} + 40 q^{84} - 20 q^{85} + 22 q^{86} - 4 q^{87} + 3 q^{88} + 3 q^{89} - 58 q^{90} + 16 q^{91} - 30 q^{92} - 17 q^{93} - 5 q^{94} - 14 q^{95} + q^{96} + 6 q^{97} - 26 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 4 * q^4 + q^5 + 6 * q^6 - 16 * q^7 + 6 * q^8 - 3 * q^9 + 3 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^13 + 10 * q^14 - 30 * q^15 + 4 * q^16 - 9 * q^17 - 5 * q^18 + 4 * q^19 - 16 * q^20 - q^21 - 4 * q^22 - 6 * q^23 + 7 * q^24 + 5 * q^25 + 2 * q^26 + 2 * q^27 - 4 * q^28 - 30 * q^29 + 11 * q^30 + 10 * q^31 + 2 * q^32 + q^33 + 4 * q^34 - 5 * q^35 - 34 * q^36 - 9 * q^37 - 14 * q^38 + q^39 - 7 * q^40 - 10 * q^41 - 12 * q^42 + 14 * q^43 + 4 * q^44 + 4 * q^45 + 13 * q^46 + 2 * q^47 - 56 * q^48 + 8 * q^49 + 2 * q^50 - 10 * q^51 + 4 * q^52 + 27 * q^53 - 20 * q^54 + 2 * q^55 - 12 * q^56 - 28 * q^57 + 10 * q^58 - 4 * q^59 - 5 * q^60 - 19 * q^61 - 88 * q^62 + 15 * q^63 - 42 * q^64 - q^65 + 3 * q^66 + q^67 - 16 * q^69 + 3 * q^70 - 10 * q^71 + 21 * q^72 - 2 * q^73 + 5 * q^74 - 2 * q^75 + 38 * q^76 + 4 * q^77 - 6 * q^78 + 32 * q^79 - 28 * q^80 - 4 * q^81 + 16 * q^82 + 40 * q^84 - 20 * q^85 + 22 * q^86 - 4 * q^87 + 3 * q^88 + 3 * q^89 - 58 * q^90 + 16 * q^91 - 30 * q^92 - 17 * q^93 - 5 * q^94 - 14 * q^95 + q^96 + 6 * q^97 - 26 * q^98 - 6 * q^99

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