LMFDB - Embedded newform 1001.2.i.b.144.4

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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.4
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.b.716.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270580 - 0.468659i) q^{2} +(-0.551742 + 0.955645i) q^{3} +(0.853573 - 1.47843i) q^{4} +(-1.64274 - 2.84530i) q^{5} +0.597162 q^{6} +(-2.51185 - 0.831024i) q^{7} -2.00616 q^{8} +(0.891162 + 1.54354i) q^{9} +O(q^{10})$	\(q+(-0.270580 - 0.468659i) q^{2} +(-0.551742 + 0.955645i) q^{3} +(0.853573 - 1.47843i) q^{4} +(-1.64274 - 2.84530i) q^{5} +0.597162 q^{6} +(-2.51185 - 0.831024i) q^{7} -2.00616 q^{8} +(0.891162 + 1.54354i) q^{9} +(-0.888984 + 1.53977i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.941904 + 1.63142i) q^{12} -1.00000 q^{13} +(0.290191 + 1.40206i) q^{14} +3.62547 q^{15} +(-1.16432 - 2.01666i) q^{16} +(0.625032 - 1.08259i) q^{17} +(0.482261 - 0.835301i) q^{18} +(-1.43548 - 2.48633i) q^{19} -5.60878 q^{20} +(2.18006 - 1.94193i) q^{21} -0.541160 q^{22} +(1.74487 + 3.02220i) q^{23} +(1.10688 - 1.91718i) q^{24} +(-2.89717 + 5.01805i) q^{25} +(0.270580 + 0.468659i) q^{26} -5.27722 q^{27} +(-3.37266 + 3.00426i) q^{28} -2.27304 q^{29} +(-0.980979 - 1.69911i) q^{30} +(-0.811924 + 1.40629i) q^{31} +(-2.63624 + 4.56611i) q^{32} +(0.551742 + 0.955645i) q^{33} -0.676485 q^{34} +(1.76179 + 8.51214i) q^{35} +3.04269 q^{36} +(2.42703 + 4.20374i) q^{37} +(-0.776827 + 1.34550i) q^{38} +(0.551742 - 0.955645i) q^{39} +(3.29559 + 5.70813i) q^{40} -9.47075 q^{41} +(-1.49998 - 0.496256i) q^{42} +2.48780 q^{43} +(-0.853573 - 1.47843i) q^{44} +(2.92789 - 5.07125i) q^{45} +(0.944253 - 1.63549i) q^{46} +(4.28619 + 7.42391i) q^{47} +2.56961 q^{48} +(5.61880 + 4.17482i) q^{49} +3.13567 q^{50} +(0.689712 + 1.19462i) q^{51} +(-0.853573 + 1.47843i) q^{52} +(-5.49420 + 9.51623i) q^{53} +(1.42791 + 2.47321i) q^{54} -3.28547 q^{55} +(5.03918 + 1.66717i) q^{56} +3.16807 q^{57} +(0.615039 + 1.06528i) q^{58} +(2.09531 - 3.62918i) q^{59} +(3.09460 - 5.36000i) q^{60} +(-1.64310 - 2.84594i) q^{61} +0.878762 q^{62} +(-0.955749 - 4.61771i) q^{63} -1.80401 q^{64} +(1.64274 + 2.84530i) q^{65} +(0.298581 - 0.517157i) q^{66} +(-3.21381 + 5.56648i) q^{67} +(-1.06702 - 1.84813i) q^{68} -3.85086 q^{69} +(3.51258 - 3.12890i) q^{70} -9.88827 q^{71} +(-1.78781 - 3.09658i) q^{72} +(5.16198 - 8.94081i) q^{73} +(1.31341 - 2.27490i) q^{74} +(-3.19698 - 5.53733i) q^{75} -4.90116 q^{76} +(-1.97561 + 1.75982i) q^{77} -0.597162 q^{78} +(2.37681 + 4.11675i) q^{79} +(-3.82534 + 6.62568i) q^{80} +(0.238175 - 0.412531i) q^{81} +(2.56260 + 4.43855i) q^{82} -4.48647 q^{83} +(-1.01017 - 4.88064i) q^{84} -4.10705 q^{85} +(-0.673148 - 1.16593i) q^{86} +(1.25413 - 2.17222i) q^{87} +(-1.00308 + 1.73739i) q^{88} +(-5.77251 - 9.99828i) q^{89} -3.16891 q^{90} +(2.51185 + 0.831024i) q^{91} +5.95748 q^{92} +(-0.895944 - 1.55182i) q^{93} +(2.31952 - 4.01752i) q^{94} +(-4.71625 + 8.16878i) q^{95} +(-2.90905 - 5.03862i) q^{96} -7.49044 q^{97} +(0.436230 - 3.76292i) q^{98} +1.78232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9} - 12 q^{10} + 11 q^{11} - 13 q^{12} - 22 q^{13} + 8 q^{14} + 30 q^{15} + 4 q^{16} + 2 q^{17} + 21 q^{18} - 9 q^{19} - 24 q^{20} - 9 q^{21} + 4 q^{22} + 27 q^{23} + 7 q^{24} + 7 q^{25} - 2 q^{26} - 4 q^{27} - 4 q^{28} + 42 q^{29} + 12 q^{30} + 2 q^{31} + 7 q^{32} + q^{33} - 20 q^{34} + 13 q^{35} + 48 q^{36} + 38 q^{37} - 9 q^{38} + q^{39} + 22 q^{40} + 6 q^{41} + 17 q^{42} - 46 q^{43} + 6 q^{44} + 6 q^{46} - 2 q^{47} + 24 q^{48} + 7 q^{49} + 14 q^{50} + 11 q^{51} + 6 q^{52} - 5 q^{53} + 37 q^{54} + 9 q^{56} - 44 q^{57} + 5 q^{58} + 16 q^{59} + 22 q^{60} - 11 q^{61} + 44 q^{62} - 16 q^{63} - 12 q^{64} - 6 q^{66} + 15 q^{67} - 12 q^{68} - 12 q^{69} + 7 q^{70} - 20 q^{71} + 32 q^{72} - 5 q^{73} + 20 q^{74} - 10 q^{75} + 14 q^{76} - 3 q^{77} + 12 q^{78} - 3 q^{79} + 21 q^{80} + 21 q^{81} - 4 q^{82} - 32 q^{83} + 32 q^{84} - 76 q^{85} + 15 q^{86} - 29 q^{87} - 8 q^{89} + 10 q^{90} - 15 q^{91} - 40 q^{92} + 40 q^{93} - 31 q^{94} + 23 q^{95} + 4 q^{96} - 14 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9 - 12 * q^10 + 11 * q^11 - 13 * q^12 - 22 * q^13 + 8 * q^14 + 30 * q^15 + 4 * q^16 + 2 * q^17 + 21 * q^18 - 9 * q^19 - 24 * q^20 - 9 * q^21 + 4 * q^22 + 27 * q^23 + 7 * q^24 + 7 * q^25 - 2 * q^26 - 4 * q^27 - 4 * q^28 + 42 * q^29 + 12 * q^30 + 2 * q^31 + 7 * q^32 + q^33 - 20 * q^34 + 13 * q^35 + 48 * q^36 + 38 * q^37 - 9 * q^38 + q^39 + 22 * q^40 + 6 * q^41 + 17 * q^42 - 46 * q^43 + 6 * q^44 + 6 * q^46 - 2 * q^47 + 24 * q^48 + 7 * q^49 + 14 * q^50 + 11 * q^51 + 6 * q^52 - 5 * q^53 + 37 * q^54 + 9 * q^56 - 44 * q^57 + 5 * q^58 + 16 * q^59 + 22 * q^60 - 11 * q^61 + 44 * q^62 - 16 * q^63 - 12 * q^64 - 6 * q^66 + 15 * q^67 - 12 * q^68 - 12 * q^69 + 7 * q^70 - 20 * q^71 + 32 * q^72 - 5 * q^73 + 20 * q^74 - 10 * q^75 + 14 * q^76 - 3 * q^77 + 12 * q^78 - 3 * q^79 + 21 * q^80 + 21 * q^81 - 4 * q^82 - 32 * q^83 + 32 * q^84 - 76 * q^85 + 15 * q^86 - 29 * q^87 - 8 * q^89 + 10 * q^90 - 15 * q^91 - 40 * q^92 + 40 * q^93 - 31 * q^94 + 23 * q^95 + 4 * q^96 - 14 * q^97 - 31 * q^98 - 8 * 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 $

$2$	−0.270580	−	0.468659i	−0.191329	−	0.331392i	0.754362	−	0.656459i	$-0.227946\pi$
$2$	−0.270580	−	0.468659i	−0.191329	−	0.331392i	−0.945691	+	0.325067i	$0.894613\pi$
$3$	−0.551742	+	0.955645i	−0.318548	+	0.551742i	−0.980185	−	0.198082i	$-0.936529\pi$
$3$	−0.551742	+	0.955645i	−0.318548	+	0.551742i	0.661637	+	0.749824i	$0.269862\pi$
$4$	0.853573	−	1.47843i	0.426786	−	0.739216i
$5$	−1.64274	−	2.84530i	−0.734654	−	1.27246i	−0.954875	−	0.297009i	$-0.904011\pi$
$5$	−1.64274	−	2.84530i	−0.734654	−	1.27246i	0.220221	−	0.975450i	$-0.429322\pi$
$6$	0.597162			0.243790
$7$	−2.51185	−	0.831024i	−0.949391	−	0.314098i
$7$	−2.51185	−	0.831024i	−0.949391	−	0.314098i
$8$	−2.00616			−0.709285
$9$	0.891162	+	1.54354i	0.297054	+	0.514513i
$10$	−0.888984	+	1.53977i	−0.281121	+	0.486917i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.941904	+	1.63142i	0.271904	+	0.470952i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.290191	+	1.40206i	0.0775567	+	0.374716i
$15$	3.62547			0.936092
$16$	−1.16432	−	2.01666i	−0.291080	−	0.504165i
$17$	0.625032	−	1.08259i	0.151592	−	0.262566i	−0.780221	−	0.625504i	$-0.784893\pi$
$17$	0.625032	−	1.08259i	0.151592	−	0.262566i	0.931813	+	0.362939i	$0.118227\pi$
$18$	0.482261	−	0.835301i	0.113670	−	0.196882i
$19$	−1.43548	−	2.48633i	−0.329323	−	0.570404i	0.653055	−	0.757311i	$-0.273487\pi$
$19$	−1.43548	−	2.48633i	−0.329323	−	0.570404i	−0.982378	+	0.186907i	$0.940154\pi$
$20$	−5.60878			−1.25416
$21$	2.18006	−	1.94193i	0.475728	−	0.423763i
$22$	−0.541160			−0.115376
$23$	1.74487	+	3.02220i	0.363830	+	0.630172i	0.988588	−	0.150647i	$-0.0481356\pi$
$23$	1.74487	+	3.02220i	0.363830	+	0.630172i	−0.624758	+	0.780819i	$0.714802\pi$
$24$	1.10688	−	1.91718i	0.225941	−	0.391342i
$25$	−2.89717	+	5.01805i	−0.579434	+	1.00361i
$26$	0.270580	+	0.468659i	0.0530651	+	0.0919115i
$27$	−5.27722			−1.01560
$28$	−3.37266	+	3.00426i	−0.637373	+	0.567752i
$29$	−2.27304			−0.422092			−0.211046	−	0.977476i	$-0.567687\pi$
$29$	−2.27304			−0.422092			−0.211046	+	0.977476i	$0.567687\pi$
$30$	−0.980979	−	1.69911i	−0.179101	−	0.310213i
$31$	−0.811924	+	1.40629i	−0.145826	+	0.252578i	−0.929681	−	0.368366i	$-0.879917\pi$
$31$	−0.811924	+	1.40629i	−0.145826	+	0.252578i	0.783855	+	0.620944i	$0.213251\pi$
$32$	−2.63624	+	4.56611i	−0.466026	+	0.807181i
$33$	0.551742	+	0.955645i	0.0960459	+	0.166356i
$34$	−0.676485			−0.116016
$35$	1.76179	+	8.51214i	0.297798	+	1.43881i
$36$	3.04269			0.507114
$37$	2.42703	+	4.20374i	0.399001	+	0.691091i	0.993603	−	0.112930i	$-0.0360235\pi$
$37$	2.42703	+	4.20374i	0.399001	+	0.691091i	−0.594602	+	0.804021i	$0.702690\pi$
$38$	−0.776827	+	1.34550i	−0.126018	+	0.218270i
$39$	0.551742	−	0.955645i	0.0883494	−	0.153026i
$40$	3.29559	+	5.70813i	0.521079	+	0.902535i
$41$	−9.47075			−1.47908			−0.739541	−	0.673111i	$-0.764958\pi$
$41$	−9.47075			−1.47908			−0.739541	+	0.673111i	$0.764958\pi$
$42$	−1.49998	−	0.496256i	−0.231452	−	0.0765739i
$43$	2.48780			0.379385			0.189693	−	0.981844i	$-0.439251\pi$
$43$	2.48780			0.379385			0.189693	+	0.981844i	$0.439251\pi$
$44$	−0.853573	−	1.47843i	−0.128681	−	0.222882i
$45$	2.92789	−	5.07125i	0.436464	−	0.755978i
$46$	0.944253	−	1.63549i	0.139222	−	0.241140i
$47$	4.28619	+	7.42391i	0.625206	+	1.08289i	0.988501	+	0.151214i	$0.0483183\pi$
$47$	4.28619	+	7.42391i	0.625206	+	1.08289i	−0.363295	+	0.931674i	$0.618348\pi$
$48$	2.56961			0.370892
$49$	5.61880	+	4.17482i	0.802685	+	0.596403i
$50$	3.13567			0.443450
$51$	0.689712	+	1.19462i	0.0965790	+	0.167280i
$52$	−0.853573	+	1.47843i	−0.118369	+	0.205022i
$53$	−5.49420	+	9.51623i	−0.754686	+	1.30716i	0.190844	+	0.981620i	$0.438878\pi$
$53$	−5.49420	+	9.51623i	−0.754686	+	1.30716i	−0.945530	+	0.325535i	$0.894456\pi$
$54$	1.42791	+	2.47321i	0.194314	+	0.336562i
$55$	−3.28547			−0.443013
$56$	5.03918	+	1.66717i	0.673388	+	0.222785i
$57$	3.16807			0.419621
$58$	0.615039	+	1.06528i	0.0807585	+	0.139878i
$59$	2.09531	−	3.62918i	0.272786	−	0.472479i	−0.696788	−	0.717277i	$-0.745388\pi$
$59$	2.09531	−	3.62918i	0.272786	−	0.472479i	0.969574	+	0.244798i	$0.0787215\pi$
$60$	3.09460	−	5.36000i	0.399511	−	0.691974i
$61$	−1.64310	−	2.84594i	−0.210378	−	0.364385i	0.741455	−	0.671003i	$-0.234136\pi$
$61$	−1.64310	−	2.84594i	−0.210378	−	0.364385i	−0.951833	+	0.306617i	$0.900803\pi$
$62$	0.878762			0.111603
$63$	−0.955749	−	4.61771i	−0.120413	−	0.581777i
$64$	−1.80401			−0.225502
$65$	1.64274	+	2.84530i	0.203756	+	0.352917i
$66$	0.298581	−	0.517157i	0.0367527	−	0.0636576i
$67$	−3.21381	+	5.56648i	−0.392629	+	0.680053i	−0.992795	−	0.119822i	$-0.961768\pi$
$67$	−3.21381	+	5.56648i	−0.392629	+	0.680053i	0.600166	+	0.799875i	$0.295101\pi$
$68$	−1.06702	−	1.84813i	−0.129395	−	0.224119i
$69$	−3.85086			−0.463590
$70$	3.51258	−	3.12890i	0.419833	−	0.373974i
$71$	−9.88827			−1.17352			−0.586761	−	0.809760i	$-0.699597\pi$
$71$	−9.88827			−1.17352			−0.586761	+	0.809760i	$0.699597\pi$
$72$	−1.78781	−	3.09658i	−0.210696	−	0.364936i
$73$	5.16198	−	8.94081i	0.604164	−	1.04644i	−0.388019	−	0.921651i	$-0.626841\pi$
$73$	5.16198	−	8.94081i	0.604164	−	1.04644i	0.992183	−	0.124791i	$-0.0398261\pi$
$74$	1.31341	−	2.27490i	0.152681	−	0.264451i
$75$	−3.19698	−	5.53733i	−0.369155	−	0.639396i
$76$	−4.90116			−0.562202
$77$	−1.97561	+	1.75982i	−0.225142	+	0.200550i
$78$	−0.597162			−0.0676152
$79$	2.37681	+	4.11675i	0.267412	+	0.463171i	0.968193	−	0.250206i	$-0.0804983\pi$
$79$	2.37681	+	4.11675i	0.267412	+	0.463171i	−0.700781	+	0.713377i	$0.747165\pi$
$80$	−3.82534	+	6.62568i	−0.427686	+	0.740774i
$81$	0.238175	−	0.412531i	0.0264639	−	0.0458368i
$82$	2.56260	+	4.43855i	0.282992	+	0.490156i
$83$	−4.48647			−0.492454			−0.246227	−	0.969212i	$-0.579191\pi$
$83$	−4.48647			−0.492454			−0.246227	+	0.969212i	$0.579191\pi$
$84$	−1.01017	−	4.88064i	−0.110218	−	0.532522i
$85$	−4.10705			−0.445472
$86$	−0.673148	−	1.16593i	−0.0725874	−	0.125725i
$87$	1.25413	−	2.17222i	0.134457	−	0.232886i
$88$	−1.00308	+	1.73739i	−0.106929	+	0.185206i
$89$	−5.77251	−	9.99828i	−0.611885	−	1.05982i	−0.990922	−	0.134434i	$-0.957078\pi$
$89$	−5.77251	−	9.99828i	−0.611885	−	1.05982i	0.379038	−	0.925381i	$-0.376255\pi$
$90$	−3.16891			−0.334033
$91$	2.51185	+	0.831024i	0.263314	+	0.0871150i
$92$	5.95748			0.621111
$93$	−0.895944	−	1.55182i	−0.0929051	−	0.160916i
$94$	2.31952	−	4.01752i	0.239240	−	0.414376i
$95$	−4.71625	+	8.16878i	−0.483877	+	0.838099i
$96$	−2.90905	−	5.03862i	−0.296904	−	0.514252i
$97$	−7.49044			−0.760539			−0.380269	−	0.924876i	$-0.624169\pi$
$97$	−7.49044			−0.760539			−0.380269	+	0.924876i	$0.624169\pi$
$98$	0.436230	−	3.76292i	0.0440659	−	0.380112i
$99$	1.78232			0.179130
$100$	4.94589	+	8.56653i	0.494589	+	0.856653i
$101$	−1.06467	+	1.84406i	−0.105939	+	0.183491i	−0.914121	−	0.405441i	$-0.867118\pi$
$101$	−1.06467	+	1.84406i	−0.105939	+	0.183491i	0.808183	+	0.588932i	$0.200451\pi$
$102$	0.373245	−	0.646479i	0.0369567	−	0.0640110i
$103$	4.30210	+	7.45146i	0.423898	+	0.734214i	0.996317	−	0.0857480i	$-0.0273280\pi$
$103$	4.30210	+	7.45146i	0.423898	+	0.734214i	−0.572418	+	0.819962i	$0.693995\pi$
$104$	2.00616			0.196720
$105$	−9.10663	−	3.01285i	−0.888717	−	0.294024i
$106$	5.94648			0.577574
$107$	−3.61987	−	6.26979i	−0.349946	−	0.606124i	0.636294	−	0.771447i	$-0.280467\pi$
$107$	−3.61987	−	6.26979i	−0.349946	−	0.606124i	−0.986239	+	0.165323i	$0.947133\pi$
$108$	−4.50449	+	7.80200i	−0.433445	+	0.750748i
$109$	8.37143	−	14.4997i	0.801837	−	1.38882i	−0.116568	−	0.993183i	$-0.537189\pi$
$109$	8.37143	−	14.4997i	0.801837	−	1.38882i	0.918406	−	0.395640i	$-0.129477\pi$
$110$	0.888984	+	1.53977i	0.0847613	+	0.146811i
$111$	−5.35638			−0.508405
$112$	1.24870	+	6.03313i	0.117991	+	0.570077i
$113$	−19.7179			−1.85490			−0.927451	−	0.373944i	$-0.878005\pi$
$113$	−19.7179			−1.85490			−0.927451	+	0.373944i	$0.878005\pi$
$114$	−0.857216	−	1.48474i	−0.0802856	−	0.139059i
$115$	5.73272	−	9.92935i	0.534578	−	0.925917i
$116$	−1.94020	+	3.36053i	−0.180143	+	0.312017i
$117$	−0.891162	−	1.54354i	−0.0823879	−	0.142700i
$118$	−2.26780			−0.208768
$119$	−2.46964	+	2.19988i	−0.226392	+	0.201663i
$120$	−7.27327			−0.663955
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.889183	+	1.54011i	−0.0805028	+	0.139435i
$123$	5.22541	−	9.05067i	0.471159	−	0.816072i
$124$	1.38607	+	2.40075i	0.124473	+	0.215593i
$125$	2.60978			0.233426
$126$	−1.90552	+	1.69738i	−0.169758	+	0.151215i
$127$	15.2633			1.35440			0.677199	−	0.735799i	$-0.263193\pi$
$127$	15.2633			1.35440			0.677199	+	0.735799i	$0.263193\pi$
$128$	5.76062	+	9.97768i	0.509171	+	0.881911i
$129$	−1.37262	+	2.37745i	−0.120853	+	0.209323i
$130$	0.888984	−	1.53977i	0.0779691	−	0.135046i
$131$	−2.31944	−	4.01739i	−0.202651	−	0.351001i	0.746731	−	0.665126i	$-0.231622\pi$
$131$	−2.31944	−	4.01739i	−0.202651	−	0.351001i	−0.949382	+	0.314125i	$0.898289\pi$
$132$	1.88381			0.163964
$133$	1.53952	+	7.43822i	0.133493	+	0.644975i
$134$	3.47837			0.300485
$135$	8.66908	+	15.0153i	0.746115	+	1.29231i
$136$	−1.25391	+	2.17184i	−0.107522	+	0.186234i
$137$	−1.27208	+	2.20330i	−0.108681	+	0.188241i	−0.915236	−	0.402918i	$-0.867996\pi$
$137$	−1.27208	+	2.20330i	−0.108681	+	0.188241i	0.806555	+	0.591159i	$0.201329\pi$
$138$	1.04197	+	1.80474i	0.0886982	+	0.153630i
$139$	−13.1453			−1.11497			−0.557485	−	0.830187i	$-0.688234\pi$
$139$	−13.1453			−1.11497			−0.557485	+	0.830187i	$0.688234\pi$
$140$	14.0884	+	4.66103i	1.19069	+	0.393929i
$141$	−9.45949			−0.796633
$142$	2.67557	+	4.63422i	0.224529	+	0.388895i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	2.07519	−	3.59434i	0.172933	−	0.299528i
$145$	3.73400	+	6.46748i	0.310092	+	0.537095i
$146$	−5.58691			−0.462376
$147$	−7.08977	+	3.06615i	−0.584754	+	0.252892i
$148$	8.28659			0.681154
$149$	−10.0121	−	17.3415i	−0.820224	−	1.42067i	−0.905516	−	0.424313i	$-0.860516\pi$
$149$	−10.0121	−	17.3415i	−0.820224	−	1.42067i	0.0852921	−	0.996356i	$-0.472818\pi$
$150$	−1.73008	+	2.99658i	−0.141260	+	0.244670i
$151$	7.26015	−	12.5750i	0.590823	−	1.02334i	−0.403299	−	0.915068i	$-0.632137\pi$
$151$	7.26015	−	12.5750i	0.590823	−	1.02334i	0.994122	−	0.108267i	$-0.0345301\pi$
$152$	2.87981	+	4.98798i	0.233584	+	0.404579i
$153$	2.22802			0.180125
$154$	1.35931	+	0.449717i	0.109537	+	0.0362393i
$155$	5.33511			0.428526
$156$	−0.941904	−	1.63142i	−0.0754126	−	0.130619i
$157$	9.17932	−	15.8990i	0.732589	−	1.26888i	−0.223183	−	0.974776i	$-0.571645\pi$
$157$	9.17932	−	15.8990i	0.732589	−	1.26888i	0.955773	−	0.294106i	$-0.0950218\pi$
$158$	1.28623	−	2.22782i	0.102327	−	0.177236i
$159$	−6.06276	−	10.5010i	−0.480808	−	0.832784i
$160$	17.3226			1.36947
$161$	−1.87133	−	9.04134i	−0.147481	−	0.712557i
$162$	−0.257782			−0.0202533
$163$	2.85040	+	4.93704i	0.223261	+	0.386699i	0.955796	−	0.294030i	$-0.0949966\pi$
$163$	2.85040	+	4.93704i	0.223261	+	0.386699i	−0.732536	+	0.680729i	$0.761663\pi$
$164$	−8.08398	+	14.0019i	−0.631252	+	1.09336i
$165$	1.81273	−	3.13975i	0.141121	−	0.244429i
$166$	1.21395	+	2.10262i	0.0942208	+	0.163195i
$167$	−1.50914			−0.116780			−0.0583902	−	0.998294i	$-0.518597\pi$
$167$	−1.50914			−0.116780			−0.0583902	+	0.998294i	$0.518597\pi$
$168$	−4.37354	+	3.89582i	−0.337426	+	0.300569i
$169$	1.00000			0.0769231
$170$	1.11129	+	1.92480i	0.0852318	+	0.147626i
$171$	2.55850	−	4.43145i	0.195653	−	0.338881i
$172$	2.12352	−	3.67804i	0.161917	−	0.280448i
$173$	−1.70351	−	2.95057i	−0.129515	−	0.224327i	0.793973	−	0.607952i	$-0.208009\pi$
$173$	−1.70351	−	2.95057i	−0.129515	−	0.224327i	−0.923489	+	0.383625i	$0.874676\pi$
$174$	−1.35737			−0.102902
$175$	11.4474	−	10.1970i	0.865340	−	0.770818i
$176$	−2.32864			−0.175528
$177$	2.31214	+	4.00474i	0.173791	+	0.301015i
$178$	−3.12385	+	5.41067i	−0.234143	+	0.405547i
$179$	4.49829	−	7.79127i	0.336218	−	0.582347i	−0.647500	−	0.762065i	$-0.724185\pi$
$179$	4.49829	−	7.79127i	0.336218	−	0.582347i	0.983718	+	0.179719i	$0.0575188\pi$
$180$	−4.99833	−	8.65737i	−0.372554	−	0.645282i
$181$	−3.07094			−0.228261			−0.114131	−	0.993466i	$-0.536408\pi$
$181$	−3.07094			−0.228261			−0.114131	+	0.993466i	$0.536408\pi$
$182$	−0.290191	−	1.40206i	−0.0215104	−	0.103928i
$183$	3.62628			0.268062
$184$	−3.50048	−	6.06301i	−0.258059	−	0.446971i
$185$	7.97395	−	13.8113i	0.586256	−	1.01543i
$186$	−0.484850	+	0.839784i	−0.0355509	+	0.0615759i
$187$	−0.625032	−	1.08259i	−0.0457068	−	0.0791666i
$188$	14.6343			1.06732
$189$	13.2556	+	4.38549i	0.964202	+	0.318998i
$190$	5.10449			0.370319
$191$	8.51861	+	14.7547i	0.616385	+	1.06761i	0.990140	+	0.140083i	$0.0447369\pi$
$191$	8.51861	+	14.7547i	0.616385	+	1.06761i	−0.373754	+	0.927528i	$0.621930\pi$
$192$	0.995350	−	1.72400i	0.0718332	−	0.124419i
$193$	4.38186	−	7.58961i	0.315413	−	0.546312i	−0.664112	−	0.747633i	$-0.731190\pi$
$193$	4.38186	−	7.58961i	0.315413	−	0.546312i	0.979525	+	0.201321i	$0.0645235\pi$
$194$	2.02676	+	3.51046i	0.145513	+	0.252036i
$195$	−3.62547			−0.259625
$196$	10.9682	−	4.74349i	0.783445	−	0.338821i
$197$	0.344441			0.0245404			0.0122702	−	0.999925i	$-0.496094\pi$
$197$	0.344441			0.0245404			0.0122702	+	0.999925i	$0.496094\pi$
$198$	−0.482261	−	0.835301i	−0.0342728	−	0.0593623i
$199$	−7.50022	+	12.9908i	−0.531676	+	0.920890i	0.467640	+	0.883919i	$0.345104\pi$
$199$	−7.50022	+	12.9908i	−0.531676	+	0.920890i	−0.999316	+	0.0369713i	$0.988229\pi$
$200$	5.81219	−	10.0670i	0.410984	−	0.711844i
$201$	−3.54638	−	6.14252i	−0.250143	−	0.433260i
$202$	1.15232			0.0810766
$203$	5.70953	+	1.88895i	0.400731	+	0.132578i
$204$	2.35488			0.164874
$205$	15.5580	+	26.9472i	1.08661	+	1.88207i
$206$	2.32813	−	4.03243i	0.162208	−	0.280953i
$207$	−3.10992	+	5.38654i	−0.216154	+	0.374390i
$208$	1.16432	+	2.01666i	0.0807310	+	0.139830i
$209$	−2.87097			−0.198589
$210$	1.05208	+	5.08312i	0.0726001	+	0.350769i
$211$	−19.4871			−1.34155			−0.670773	−	0.741663i	$-0.734038\pi$
$211$	−19.4871			−1.34155			−0.670773	+	0.741663i	$0.734038\pi$
$212$	9.37940	+	16.2456i	0.644180	+	1.11575i
$213$	5.45577	−	9.44968i	0.373823	−	0.647481i
$214$	−1.95893	+	3.39296i	−0.133910	+	0.231938i
$215$	−4.08680	−	7.07854i	−0.278717	−	0.482752i
$216$	10.5869			0.720350
$217$	3.20810	−	2.85767i	0.217780	−	0.193991i
$218$	−9.06057			−0.613659
$219$	5.69616	+	9.86603i	0.384911	+	0.666685i
$220$	−2.80439	+	4.85735i	−0.189072	+	0.327482i
$221$	−0.625032	+	1.08259i	−0.0420442	+	0.0728227i
$222$	1.44933	+	2.51031i	0.0972726	+	0.168481i
$223$	1.38692			0.0928752			0.0464376	−	0.998921i	$-0.485213\pi$
$223$	1.38692			0.0928752			0.0464376	+	0.998921i	$0.485213\pi$
$224$	10.4164	−	9.27860i	0.695975	−	0.619953i
$225$	−10.3274			−0.688493
$226$	5.33527	+	9.24095i	0.354897	+	0.614699i
$227$	−3.33021	+	5.76810i	−0.221034	+	0.382842i	−0.955122	−	0.296212i	$-0.904277\pi$
$227$	−3.33021	+	5.76810i	−0.221034	+	0.382842i	0.734088	+	0.679054i	$0.237610\pi$
$228$	2.70418	−	4.68377i	0.179088	−	0.310190i
$229$	−12.8946	−	22.3341i	−0.852097	−	1.47588i	−0.879312	−	0.476246i	$-0.841997\pi$
$229$	−12.8946	−	22.3341i	−0.852097	−	1.47588i	0.0272149	−	0.999630i	$-0.491336\pi$
$230$	−6.20464			−0.409122
$231$	−0.591729	−	2.85895i	−0.0389329	−	0.188105i
$232$	4.56008			0.299384
$233$	−0.668955	−	1.15866i	−0.0438247	−	0.0759067i	0.843281	−	0.537473i	$-0.180621\pi$
$233$	−0.668955	−	1.15866i	−0.0438247	−	0.0759067i	−0.887106	+	0.461566i	$0.847288\pi$
$234$	−0.482261	+	0.835301i	−0.0315264	+	0.0546054i
$235$	14.0822	−	24.3911i	0.918620	−	1.59110i
$236$	−3.57700	−	6.19554i	−0.232843	−	0.403296i
$237$	−5.24554			−0.340734
$238$	1.69923	+	0.562175i	0.110145	+	0.0364404i
$239$	18.1950			1.17694			0.588468	−	0.808521i	$-0.299731\pi$
$239$	18.1950			1.17694			0.588468	+	0.808521i	$0.299731\pi$
$240$	−4.22120	−	7.31133i	−0.272477	−	0.471944i
$241$	−1.36443	+	2.36326i	−0.0878907	+	0.152231i	−0.906619	−	0.421949i	$-0.861346\pi$
$241$	−1.36443	+	2.36326i	−0.0878907	+	0.152231i	0.818729	+	0.574181i	$0.194679\pi$
$242$	−0.270580	+	0.468659i	−0.0173935	+	0.0301265i
$243$	−7.65300	−	13.2554i	−0.490940	−	0.850334i
$244$	−5.61004			−0.359146
$245$	2.64842	−	22.8453i	0.169202	−	1.45953i
$246$	−5.65557			−0.360586
$247$	1.43548	+	2.48633i	0.0913377	+	0.158202i
$248$	1.62885	−	2.82125i	0.103432	−	0.179149i
$249$	2.47537	−	4.28747i	0.156870	−	0.271707i
$250$	−0.706155	−	1.22310i	−0.0446612	−	0.0773554i
$251$	−1.50136			−0.0947650			−0.0473825	−	0.998877i	$-0.515088\pi$
$251$	−1.50136			−0.0947650			−0.0473825	+	0.998877i	$0.515088\pi$
$252$	−7.64278	−	2.52855i	−0.481450	−	0.159283i
$253$	3.48973			0.219398
$254$	−4.12995	−	7.15328i	−0.259136	−	0.448836i
$255$	2.26603	−	3.92488i	0.141904	−	0.245786i
$256$	1.31340	−	2.27488i	0.0820876	−	0.142180i
$257$	−14.2590	−	24.6973i	−0.889451	−	1.54057i	−0.840526	−	0.541771i	$-0.817754\pi$
$257$	−14.2590	−	24.6973i	−0.889451	−	1.54057i	−0.0489245	−	0.998802i	$-0.515579\pi$
$258$	1.48562			0.0924904
$259$	−2.60293	−	12.5761i	−0.161738	−	0.781441i
$260$	5.60878			0.347842
$261$	−2.02564	−	3.50852i	−0.125384	−	0.217172i
$262$	−1.25519	+	2.17405i	−0.0775459	+	0.134313i
$263$	−10.0646	+	17.4323i	−0.620607	+	1.07492i	0.368766	+	0.929522i	$0.379781\pi$
$263$	−10.0646	+	17.4323i	−0.620607	+	1.07492i	−0.989373	+	0.145401i	$0.953553\pi$
$264$	−1.10688	−	1.91718i	−0.0681239	−	0.117994i
$265$	36.1021			2.21773
$266$	3.06942	−	2.73414i	0.188198	−	0.167641i
$267$	12.7397			0.779660
$268$	5.48644	+	9.50279i	0.335137	+	0.580475i
$269$	11.3613	−	19.6783i	0.692708	−	1.19981i	−0.278239	−	0.960512i	$-0.589751\pi$
$269$	11.3613	−	19.6783i	0.692708	−	1.19981i	0.970947	−	0.239294i	$-0.0769160\pi$
$270$	4.69136	−	8.12568i	0.285507	−	0.494513i
$271$	9.01108	+	15.6076i	0.547384	+	0.948097i	0.998453	+	0.0556078i	$0.0177096\pi$
$271$	9.01108	+	15.6076i	0.547384	+	0.948097i	−0.451069	+	0.892489i	$0.648957\pi$
$272$	−2.91094			−0.176502
$273$	−2.18006	+	1.94193i	−0.131943	+	0.117531i
$274$	1.37679			0.0831751
$275$	2.89717	+	5.01805i	0.174706	+	0.302600i
$276$	−3.28699	+	5.69324i	−0.197854	+	0.342693i
$277$	3.22509	−	5.58602i	0.193777	−	0.335632i	−0.752722	−	0.658339i	$-0.771260\pi$
$277$	3.22509	−	5.58602i	0.193777	−	0.335632i	0.946499	+	0.322707i	$0.104593\pi$
$278$	3.55686	+	6.16066i	0.213326	+	0.369492i
$279$	−2.89422			−0.173273
$280$	−3.53444	−	17.0767i	−0.211223	−	1.02053i
$281$	−30.1082			−1.79610			−0.898052	−	0.439889i	$-0.855018\pi$
$281$	−30.1082			−1.79610			−0.898052	+	0.439889i	$0.855018\pi$
$282$	2.55955	+	4.43327i	0.152419	+	0.263997i
$283$	−8.81189	+	15.2626i	−0.523813	+	0.907270i	0.475803	+	0.879552i	$0.342158\pi$
$283$	−8.81189	+	15.2626i	−0.523813	+	0.907270i	−0.999616	+	0.0277184i	$0.991176\pi$
$284$	−8.44036	+	14.6191i	−0.500843	+	0.867486i
$285$	−5.20430	−	9.01411i	−0.308276	−	0.533950i
$286$	0.541160			0.0319995
$287$	23.7891	+	7.87042i	1.40423	+	0.464576i
$288$	−9.39728			−0.553740
$289$	7.71867	+	13.3691i	0.454039	+	0.786419i
$290$	2.02069	−	3.49994i	0.118659	−	0.205524i
$291$	4.13279	−	7.15820i	0.242268	−	0.419621i
$292$	−8.81225	−	15.2633i	−0.515698	−	0.893215i
$293$	−25.9558			−1.51636			−0.758178	−	0.652047i	$-0.773910\pi$
$293$	−25.9558			−1.51636			−0.758178	+	0.652047i	$0.773910\pi$
$294$	3.35533	+	2.49304i	0.195687	+	0.145397i
$295$	−13.7682			−0.801614
$296$	−4.86901	−	8.43338i	−0.283006	−	0.490180i
$297$	−2.63861	+	4.57020i	−0.153108	+	0.265190i
$298$	−5.41815	+	9.38452i	−0.313865	+	0.543630i
$299$	−1.74487	−	3.02220i	−0.100908	−	0.174778i
$300$	−10.9154			−0.630202
$301$	−6.24898	−	2.06742i	−0.360185	−	0.119164i
$302$	−7.85781			−0.452166
$303$	−1.17485	−	2.03489i	−0.0674932	−	0.116902i
$304$	−3.34272	+	5.78977i	−0.191718	+	0.332066i
$305$	−5.39838	+	9.35027i	−0.309110	+	0.535395i
$306$	−0.602857	−	1.04418i	−0.0344631	−	0.0596918i
$307$	−3.62233			−0.206737			−0.103369	−	0.994643i	$-0.532962\pi$
$307$	−3.62233			−0.206737			−0.103369	+	0.994643i	$0.532962\pi$
$308$	0.915436	+	4.42294i	0.0521618	+	0.252020i
$309$	−9.49459			−0.540129
$310$	−1.44357	−	2.50034i	−0.0819895	−	0.142010i
$311$	6.32406	−	10.9536i	0.358605	−	0.621121i	−0.629123	−	0.777305i	$-0.716586\pi$
$311$	6.32406	−	10.9536i	0.358605	−	0.621121i	0.987728	+	0.156184i	$0.0499193\pi$
$312$	−1.10688	+	1.91718i	−0.0626649	+	0.108539i
$313$	−7.30280	−	12.6488i	−0.412778	−	0.714953i	0.582414	−	0.812892i	$-0.302108\pi$
$313$	−7.30280	−	12.6488i	−0.412778	−	0.714953i	−0.995192	+	0.0979391i	$0.968775\pi$
$314$	−9.93497			−0.560663
$315$	−11.5688	+	10.3051i	−0.651826	+	0.580626i
$316$	8.11511			0.456511
$317$	3.06811	+	5.31412i	0.172322	+	0.298471i	0.939231	−	0.343285i	$-0.111540\pi$
$317$	3.06811	+	5.31412i	0.172322	+	0.298471i	−0.766909	+	0.641756i	$0.778206\pi$
$318$	−3.28092	+	5.68273i	−0.183985	+	0.318672i
$319$	−1.13652	+	1.96851i	−0.0636328	+	0.110215i
$320$	2.96352	+	5.13297i	0.165666	+	0.286942i
$321$	7.98892			0.445898
$322$	−3.73096	+	3.32342i	−0.207918	+	0.185207i
$323$	−3.58889			−0.199691
$324$	−0.406600	−	0.704251i	−0.0225889	−	0.0391251i
$325$	2.89717	−	5.01805i	0.160706	−	0.278351i
$326$	1.54252	−	2.67173i	0.0854325	−	0.147973i
$327$	9.23773	+	16.0002i	0.510848	+	0.884814i
$328$	18.9998			1.04909
$329$	−4.59684	−	22.2097i	−0.253432	−	1.22446i
$330$	−1.96196			−0.108002
$331$	−3.86414	−	6.69289i	−0.212392	−	0.367874i	0.740070	−	0.672529i	$-0.234792\pi$
$331$	−3.86414	−	6.69289i	−0.212392	−	0.367874i	−0.952463	+	0.304655i	$0.901459\pi$
$332$	−3.82953	+	6.63294i	−0.210173	+	0.364030i
$333$	−4.32576	+	7.49243i	−0.237050	+	0.410583i
$334$	0.408342	+	0.707270i	0.0223435	+	0.0387001i
$335$	21.1178			1.15379
$336$	−6.45449	−	2.13541i	−0.352121	−	0.116496i
$337$	9.72220			0.529602			0.264801	−	0.964303i	$-0.414694\pi$
$337$	9.72220			0.529602			0.264801	+	0.964303i	$0.414694\pi$
$338$	−0.270580	−	0.468659i	−0.0147176	−	0.0254917i
$339$	10.8792	−	18.8433i	0.590876	−	1.02343i
$340$	−3.50567	+	6.07199i	−0.190121	+	0.329300i
$341$	0.811924	+	1.40629i	0.0439681	+	0.0761550i
$342$	−2.76912			−0.149737
$343$	−10.6442	−	15.1559i	−0.574733	−	0.818341i
$344$	−4.99092			−0.269092
$345$	6.32596	+	10.9569i	0.340578	+	0.589899i
$346$	−0.921872	+	1.59673i	−0.0495601	+	0.0858407i
$347$	8.37601	−	14.5077i	0.449648	−	0.778813i	−0.548715	−	0.836009i	$-0.684883\pi$
$347$	8.37601	−	14.5077i	0.449648	−	0.778813i	0.998363	+	0.0571966i	$0.0182162\pi$
$348$	−2.14098	−	3.70829i	−0.114769	−	0.198785i
$349$	10.2330			0.547761			0.273880	−	0.961764i	$-0.411693\pi$
$349$	10.2330			0.547761			0.273880	+	0.961764i	$0.411693\pi$
$350$	−7.87633	−	2.60581i	−0.421007	−	0.139287i
$351$	5.27722			0.281677
$352$	2.63624	+	4.56611i	0.140512	+	0.243374i
$353$	−9.91890	+	17.1800i	−0.527930	+	0.914401i	0.471540	+	0.881845i	$0.343698\pi$
$353$	−9.91890	+	17.1800i	−0.527930	+	0.914401i	−0.999470	+	0.0325567i	$0.989635\pi$
$354$	1.25124	−	2.16721i	0.0665026	−	0.115186i
$355$	16.2438	+	28.1351i	0.862133	+	1.49326i
$356$	−19.7090			−1.04458
$357$	−0.739699	−	3.57387i	−0.0391490	−	0.189149i
$358$	−4.86859			−0.257313
$359$	−0.584514	−	1.01241i	−0.0308495	−	0.0534329i	0.850188	−	0.526478i	$-0.176488\pi$
$359$	−0.584514	−	1.01241i	−0.0308495	−	0.0534329i	−0.881038	+	0.473046i	$0.843155\pi$
$360$	−5.87381	+	10.1737i	−0.309577	+	0.536203i
$361$	5.37877	−	9.31630i	0.283093	−	0.490332i
$362$	0.830935	+	1.43922i	0.0436730	+	0.0756438i
$363$	1.10348			0.0579179
$364$	3.37266	−	3.00426i	0.176775	−	0.157466i
$365$	−33.9191			−1.77541
$366$	−0.981199	−	1.69949i	−0.0512881	−	0.0888336i
$367$	−4.45439	+	7.71523i	−0.232517	+	0.402732i	−0.958548	−	0.284930i	$-0.908030\pi$
$367$	−4.45439	+	7.71523i	−0.232517	+	0.402732i	0.726031	+	0.687662i	$0.241363\pi$
$368$	4.06316	−	7.03760i	0.211807	−	0.366860i
$369$	−8.43997	−	14.6185i	−0.439367	−	0.761007i
$370$	−8.63037			−0.448671
$371$	21.7088	−	19.3376i	1.12707	−	1.00396i
$372$	−3.05902			−0.158603
$373$	−4.25392	−	7.36801i	−0.220260	−	0.381501i	0.734627	−	0.678471i	$-0.237357\pi$
$373$	−4.25392	−	7.36801i	−0.220260	−	0.381501i	−0.954887	+	0.296970i	$0.904024\pi$
$374$	−0.338242	+	0.585853i	−0.0174901	+	0.0302937i
$375$	−1.43993	+	2.49403i	−0.0743575	+	0.128791i
$376$	−8.59879	−	14.8935i	−0.443449	−	0.768076i
$377$	2.27304			0.117067
$378$	−1.53140	−	7.39897i	−0.0787666	−	0.380562i
$379$	−4.05612			−0.208349			−0.104175	−	0.994559i	$-0.533220\pi$
$379$	−4.05612			−0.208349			−0.104175	+	0.994559i	$0.533220\pi$
$380$	8.05132	+	13.9453i	0.413024	+	0.715379i
$381$	−8.42140	+	14.5863i	−0.431441	+	0.747279i
$382$	4.60994	−	7.98464i	0.235865	−	0.408530i
$383$	4.62609	+	8.01263i	0.236382	+	0.409426i	0.959673	−	0.281117i	$-0.0907049\pi$
$383$	4.62609	+	8.01263i	0.236382	+	0.409426i	−0.723291	+	0.690543i	$0.757372\pi$
$384$	−12.7135			−0.648783
$385$	8.25262	+	2.73031i	0.420593	+	0.139149i
$386$	−4.74258			−0.241391
$387$	2.21703	+	3.84001i	0.112698	+	0.195199i
$388$	−6.39364	+	11.0741i	−0.324588	+	0.562202i
$389$	−6.20705	+	10.7509i	−0.314710	+	0.545093i	−0.979376	−	0.202047i	$-0.935241\pi$
$389$	−6.20705	+	10.7509i	−0.314710	+	0.545093i	0.664666	+	0.747141i	$0.268574\pi$
$390$	0.980979	+	1.69911i	0.0496738	+	0.0860376i
$391$	4.36239			0.220615
$392$	−11.2722	−	8.37536i	−0.569332	−	0.423019i
$393$	5.11893			0.258216
$394$	−0.0931989	−	0.161425i	−0.00469530	−	0.00813249i
$395$	7.80894	−	13.5255i	0.392910	−	0.680541i
$396$	1.52134	−	2.63504i	0.0764504	−	0.132416i
$397$	16.4775	+	28.5398i	0.826982	+	1.43237i	0.900395	+	0.435072i	$0.143277\pi$
$397$	16.4775	+	28.5398i	0.826982	+	1.43237i	−0.0734140	+	0.997302i	$0.523389\pi$
$398$	8.11764			0.406900
$399$	−7.95772	−	2.63274i	−0.398384	−	0.131802i
$400$	13.4929			0.674646
$401$	−0.788859	−	1.36634i	−0.0393937	−	0.0682319i	0.845656	−	0.533728i	$-0.179209\pi$
$401$	−0.788859	−	1.36634i	−0.0393937	−	0.0682319i	−0.885050	+	0.465496i	$0.845876\pi$
$402$	−1.91916	+	3.32409i	−0.0957191	+	0.165790i
$403$	0.811924	−	1.40629i	0.0404448	−	0.0700524i
$404$	1.81755	+	3.14809i	0.0904264	+	0.156623i
$405$	−1.56504			−0.0777673
$406$	−0.659614	−	3.18693i	−0.0327361	−	0.158165i
$407$	4.85406			0.240607
$408$	−1.38367	−	2.39659i	−0.0685020	−	0.118649i
$409$	−5.69092	+	9.85697i	−0.281398	+	0.487396i	−0.971729	−	0.236098i	$-0.924131\pi$
$409$	−5.69092	+	9.85697i	−0.281398	+	0.487396i	0.690331	+	0.723493i	$0.257465\pi$
$410$	8.41935	−	14.5827i	0.415802	−	0.720190i
$411$	−1.40371	−	2.43130i	−0.0692401	−	0.119927i
$412$	14.6886			0.723656
$413$	−8.27905	+	7.37472i	−0.407385	+	0.362886i
$414$	3.36593			0.165426
$415$	7.37009	+	12.7654i	0.361783	+	0.626627i
$416$	2.63624	−	4.56611i	0.129252	−	0.223872i
$417$	7.25281	−	12.5622i	0.355172	−	0.615176i
$418$	0.776827	+	1.34550i	0.0379959	+	0.0658108i
$419$	20.6907			1.01081			0.505404	−	0.862883i	$-0.331343\pi$
$419$	20.6907			1.01081			0.505404	+	0.862883i	$0.331343\pi$
$420$	−12.2275	+	10.8918i	−0.596639	+	0.531468i
$421$	16.2443			0.791697			0.395848	−	0.918316i	$-0.370451\pi$
$421$	16.2443			0.791697			0.395848	+	0.918316i	$0.370451\pi$
$422$	5.27282	+	9.13279i	0.256677	+	0.444577i
$423$	−7.63939	+	13.2318i	−0.371440	+	0.643352i
$424$	11.0222	−	19.0911i	0.535287	−	0.927145i
$425$	3.62165	+	6.27287i	0.175676	+	0.304279i
$426$	−5.90490			−0.286093
$427$	1.76219	+	8.51404i	0.0852783	+	0.412023i
$428$	−12.3593			−0.597408
$429$	−0.551742	−	0.955645i	−0.0266383	−	0.0461390i
$430$	−2.21161	+	3.83062i	−0.106653	+	0.184729i
$431$	−15.8114	+	27.3861i	−0.761608	+	1.31914i	0.180413	+	0.983591i	$0.442256\pi$
$431$	−15.8114	+	27.3861i	−0.761608	+	1.31914i	−0.942021	+	0.335553i	$0.891077\pi$
$432$	6.14436	+	10.6423i	0.295621	+	0.512030i
$433$	−26.2543			−1.26170			−0.630850	−	0.775905i	$-0.717294\pi$
$433$	−26.2543			−1.26170			−0.630850	+	0.775905i	$0.717294\pi$
$434$	−2.20732	−	0.730272i	−0.105955	−	0.0350542i
$435$	−8.24082			−0.395117
$436$	−14.2912	−	24.7532i	−0.684427	−	1.18546i
$437$	5.00946	−	8.67664i	0.239635	−	0.415060i
$438$	3.08253	−	5.33911i	0.147289	−	0.255112i
$439$	−6.55734	−	11.3576i	−0.312965	−	0.542071i	0.666038	−	0.745918i	$-0.267989\pi$
$439$	−6.55734	−	11.3576i	−0.312965	−	0.542071i	−0.979003	+	0.203847i	$0.934655\pi$
$440$	6.59119			0.314222
$441$	−1.43673	+	12.3933i	−0.0684159	+	0.590155i
$442$	0.676485			0.0321771
$443$	−12.3163	−	21.3324i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$443$	−12.3163	−	21.3324i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$444$	−4.57206	+	7.91904i	−0.216980	+	0.375821i
$445$	−18.9654	+	32.8491i	−0.899048	+	1.55720i
$446$	−0.375274	−	0.649993i	−0.0177697	−	0.0307781i
$447$	22.0964			1.04512
$448$	4.53142	+	1.49918i	0.214089	+	0.0708296i
$449$	36.9669			1.74458			0.872289	−	0.488991i	$-0.162635\pi$
$449$	36.9669			1.74458			0.872289	+	0.488991i	$0.162635\pi$
$450$	2.79439	+	4.84002i	0.131729	+	0.228161i
$451$	−4.73538	+	8.20191i	−0.222980	+	0.386213i
$452$	−16.8306	+	29.1515i	−0.791647	+	1.37117i
$453$	8.01146	+	13.8763i	0.376411	+	0.651963i
$454$	3.60436			0.169161
$455$	−1.76179	−	8.51214i	−0.0825942	−	0.399055i
$456$	−6.35565			−0.297631
$457$	−7.58074	−	13.1302i	−0.354612	−	0.614206i	0.632439	−	0.774610i	$-0.282054\pi$
$457$	−7.58074	−	13.1302i	−0.354612	−	0.614206i	−0.987052	+	0.160404i	$0.948720\pi$
$458$	−6.97803	+	12.0863i	−0.326062	+	0.564756i
$459$	−3.29843	+	5.71304i	−0.153957	+	0.266662i
$460$	−9.78658	−	16.9509i	−0.456302	−	0.790338i
$461$	3.63694			0.169389			0.0846946	−	0.996407i	$-0.473009\pi$
$461$	3.63694			0.169389			0.0846946	+	0.996407i	$0.473009\pi$
$462$	−1.17976	+	1.05089i	−0.0548874	+	0.0488920i
$463$	−30.0922			−1.39851			−0.699253	−	0.714875i	$-0.746484\pi$
$463$	−30.0922			−1.39851			−0.699253	+	0.714875i	$0.746484\pi$
$464$	2.64654	+	4.58394i	0.122863	+	0.212804i
$465$	−2.94360	+	5.09847i	−0.136506	+	0.236436i
$466$	−0.362012	+	0.627023i	−0.0167699	+	0.0290463i
$467$	16.0384	+	27.7794i	0.742170	+	1.28548i	0.951505	+	0.307632i	$0.0995366\pi$
$467$	16.0384	+	27.7794i	0.742170	+	1.28548i	−0.209335	+	0.977844i	$0.567130\pi$
$468$	−3.04269			−0.140648
$469$	12.6985	−	11.3114i	0.586361	−	0.522312i
$470$	−15.2414			−0.703035
$471$	10.1292	+	17.5443i	0.466730	+	0.808401i
$472$	−4.20353	+	7.28072i	−0.193483	+	0.335122i
$473$	1.24390	−	2.15449i	0.0571945	−	0.0990638i
$474$	1.41934	+	2.45837i	0.0651923	+	0.112916i
$475$	16.6354			0.763283
$476$	1.14435	+	5.52896i	0.0524513	+	0.253419i
$477$	−19.5849			−0.896730
$478$	−4.92320	−	8.52723i	−0.225182	−	0.390026i
$479$	−16.2133	+	28.0822i	−0.740803	+	1.28311i	0.211327	+	0.977415i	$0.432221\pi$
$479$	−16.2133	+	28.0822i	−0.740803	+	1.28311i	−0.952130	+	0.305693i	$0.901112\pi$
$480$	−9.55761	+	16.5543i	−0.436243	+	0.755596i
$481$	−2.42703	−	4.20374i	−0.110663	−	0.191674i
$482$	1.47675			0.0672642
$483$	9.67280	+	3.20016i	0.440128	+	0.145612i
$484$	−1.70715			−0.0775975
$485$	12.3048	+	21.3126i	0.558733	+	0.967754i
$486$	−4.14150	+	7.17329i	−0.187862	+	0.325387i
$487$	−5.53768	+	9.59155i	−0.250936	+	0.434635i	−0.963784	−	0.266685i	$-0.914072\pi$
$487$	−5.53768	+	9.59155i	−0.250936	+	0.434635i	0.712848	+	0.701319i	$0.247405\pi$
$488$	3.29633	+	5.70941i	0.149218	+	0.258453i
$489$	−6.29074			−0.284477
$490$	−11.4233	+	4.94028i	−0.516050	+	0.223179i
$491$	32.1868			1.45257			0.726284	−	0.687394i	$-0.241246\pi$
$491$	32.1868			1.45257			0.726284	+	0.687394i	$0.241246\pi$
$492$	−8.92053	−	15.4508i	−0.402169	−	0.696577i
$493$	−1.42072	+	2.46076i	−0.0639860	+	0.110827i
$494$	0.776827	−	1.34550i	0.0349511	−	0.0605371i
$495$	−2.92789	−	5.07125i	−0.131599	−	0.227936i
$496$	3.78135			0.169788
$497$	24.8379	+	8.21739i	1.11413	+	0.368601i
$498$	−2.67915			−0.120055
$499$	6.84209	+	11.8508i	0.306294	+	0.530517i	0.977549	−	0.210710i	$-0.0675776\pi$
$499$	6.84209	+	11.8508i	0.306294	+	0.530517i	−0.671255	+	0.741227i	$0.734244\pi$
$500$	2.22764	−	3.85838i	0.0996231	−	0.172552i
$501$	0.832654	−	1.44220i	0.0372002	−	0.0644327i
$502$	0.406238	+	0.703625i	0.0181313	+	0.0314043i
$503$	−13.2905			−0.592593			−0.296296	−	0.955096i	$-0.595752\pi$
$503$	−13.2905			−0.592593			−0.296296	+	0.955096i	$0.595752\pi$
$504$	1.91739	+	9.26387i	0.0854071	+	0.412646i
$505$	6.99590			0.311313
$506$	−0.944253	−	1.63549i	−0.0419772	−	0.0727066i
$507$	−0.551742	+	0.955645i	−0.0245037	+	0.0424417i
$508$	13.0283	−	22.5657i	0.578039	−	1.00119i
$509$	10.2971	+	17.8352i	0.456413	+	0.790530i	0.998768	−	0.0496189i	$-0.0158007\pi$
$509$	10.2971	+	17.8352i	0.456413	+	0.790530i	−0.542355	+	0.840149i	$0.682467\pi$
$510$	−2.45257			−0.108602
$511$	−20.3961	+	18.1683i	−0.902273	+	0.803716i
$512$	21.6209			0.955520
$513$	7.57536	+	13.1209i	0.334460	+	0.579302i
$514$	−7.71639	+	13.3652i	−0.340355	+	0.589513i
$515$	14.1344	−	24.4816i	0.622838	−	1.07879i
$516$	2.34326	+	4.05865i	0.103156	+	0.178672i
$517$	8.57239			0.377013
$518$	−5.18959	+	4.62273i	−0.228018	+	0.203111i
$519$	3.75959			0.165028
$520$	−3.29559	−	5.70813i	−0.144521	−	0.250318i
$521$	5.68691	−	9.85002i	0.249148	−	0.431537i	−0.714142	−	0.700001i	$-0.753183\pi$
$521$	5.68691	−	9.85002i	0.249148	−	0.431537i	0.963290	+	0.268464i	$0.0865161\pi$
$522$	−1.09620	+	1.89867i	−0.0479793	+	0.0831026i
$523$	−18.7944	−	32.5528i	−0.821821	−	1.42344i	−0.904325	−	0.426844i	$-0.859625\pi$
$523$	−18.7944	−	32.5528i	−0.821821	−	1.42344i	0.0825045	−	0.996591i	$-0.473708\pi$
$524$	−7.91925			−0.345954
$525$	3.42868	+	16.5657i	0.149640	+	0.722987i
$526$	10.8931			0.474961
$527$	1.01496	+	1.75796i	0.0442122	+	0.0765777i
$528$	1.28481	−	2.22535i	0.0559140	−	0.0968459i
$529$	5.41088	−	9.37192i	0.235256	−	0.407475i
$530$	−9.76851	−	16.9196i	−0.424317	−	0.734939i
$531$	7.46904			0.324129
$532$	12.3110	+	4.07298i	0.533749	+	0.176586i
$533$	9.47075			0.410224
$534$	−3.44712	−	5.97059i	−0.149172	−	0.258373i
$535$	−11.8930	+	20.5992i	−0.514178	+	0.890583i
$536$	6.44741	−	11.1672i	0.278486	−	0.482351i
$537$	4.96379	+	8.59753i	0.214203	+	0.371011i
$538$	−12.2965			−0.530141
$539$	6.42490	−	2.77861i	0.276740	−	0.119683i
$540$	29.5988			1.27373
$541$	−10.4960	−	18.1796i	−0.451258	−	0.781602i	0.547206	−	0.836998i	$-0.315691\pi$
$541$	−10.4960	−	18.1796i	−0.451258	−	0.781602i	−0.998464	+	0.0553959i	$0.982358\pi$
$542$	4.87644	−	8.44624i	0.209461	−	0.362797i
$543$	1.69437	−	2.93473i	0.0727122	−	0.125941i
$544$	3.29547	+	5.70792i	0.141292	+	0.244725i
$545$	−55.0082			−2.35629
$546$	1.49998	+	0.496256i	0.0641933	+	0.0212378i
$547$	−1.10369			−0.0471904			−0.0235952	−	0.999722i	$-0.507511\pi$
$547$	−1.10369			−0.0471904			−0.0235952	+	0.999722i	$0.507511\pi$
$548$	2.17162	+	3.76135i	0.0927669	+	0.160677i
$549$	2.92854	−	5.07239i	0.124987	−	0.216484i
$550$	1.56783	−	2.71557i	0.0668526	−	0.115792i
$551$	3.26291	+	5.65153i	0.139005	+	0.240763i
$552$	7.72545			0.328817
$553$	−2.54907	−	12.3159i	−0.108397	−	0.523723i
$554$	−3.49058			−0.148301
$555$	8.79912	+	15.2405i	0.373502	+	0.646924i
$556$	−11.2205	+	19.4344i	−0.475854	+	0.824203i
$557$	−14.5550	+	25.2101i	−0.616717	+	1.06818i	0.373364	+	0.927685i	$0.378204\pi$
$557$	−14.5550	+	25.2101i	−0.616717	+	1.06818i	−0.990081	+	0.140500i	$0.955129\pi$
$558$	0.783119	+	1.35640i	0.0331521	+	0.0574211i
$559$	−2.48780			−0.105223
$560$	15.1148	−	13.4638i	0.638716	−	0.568948i
$561$	1.37942			0.0582393
$562$	8.14668	+	14.1105i	0.343647	+	0.595214i
$563$	−6.45333	+	11.1775i	−0.271975	+	0.471075i	−0.969368	−	0.245614i	$-0.921010\pi$
$563$	−6.45333	+	11.1775i	−0.271975	+	0.471075i	0.697392	+	0.716690i	$0.254344\pi$
$564$	−8.07436	+	13.9852i	−0.339992	+	0.588883i
$565$	32.3913	+	56.1034i	1.36271	+	2.36029i
$566$	9.53729			0.400882
$567$	−0.941084	+	0.838289i	−0.0395218	+	0.0352048i
$568$	19.8375			0.832361
$569$	−17.4091	−	30.1534i	−0.729825	−	1.26409i	−0.956957	−	0.290231i	$-0.906268\pi$
$569$	−17.4091	−	30.1534i	−0.729825	−	1.26409i	0.227131	−	0.973864i	$-0.427065\pi$
$570$	−2.81636	+	4.87808i	−0.117964	+	0.204320i
$571$	17.2245	−	29.8337i	0.720822	−	1.24850i	−0.239848	−	0.970810i	$-0.577098\pi$
$571$	17.2245	−	29.8337i	0.720822	−	1.24850i	0.960671	−	0.277691i	$-0.0895690\pi$
$572$	0.853573	+	1.47843i	0.0356897	+	0.0618163i
$573$	−18.8003			−0.785394
$574$	−2.74832	−	13.2786i	−0.114713	−	0.554236i
$575$	−20.2207			−0.843262
$576$	−1.60767	−	2.78456i	−0.0669862	−	0.116024i
$577$	7.33871	−	12.7110i	0.305515	−	0.529167i	−0.671861	−	0.740677i	$-0.734505\pi$
$577$	7.33871	−	12.7110i	0.305515	−	0.529167i	0.977376	+	0.211510i	$0.0678382\pi$
$578$	4.17704	−	7.23484i	0.173742	−	0.300930i
$579$	4.83531	+	8.37501i	0.200949	+	0.348053i
$580$	12.7490			0.529372
$581$	11.2693	+	3.72837i	0.467531	+	0.154679i
$582$	−4.47300			−0.185412
$583$	5.49420	+	9.51623i	0.227546	+	0.394122i
$584$	−10.3558	+	17.9367i	−0.428524	+	0.742225i
$585$	−2.92789	+	5.07125i	−0.121053	+	0.209671i
$586$	7.02314	+	12.1644i	0.290123	+	0.502508i
$587$	−30.2185			−1.24725			−0.623625	−	0.781723i	$-0.714341\pi$
$587$	−30.2185			−1.24725			−0.623625	+	0.781723i	$0.714341\pi$
$588$	−1.51854	+	13.0989i	−0.0626235	+	0.540190i
$589$	4.66201			0.192095
$590$	3.72539	+	6.45257i	0.153372	+	0.265648i
$591$	−0.190043	+	0.329163i	−0.00781731	+	0.0135400i
$592$	5.65167	−	9.78899i	0.232282	−	0.402325i
$593$	−12.7635	−	22.1071i	−0.524135	−	0.907828i	−0.999605	−	0.0280964i	$-0.991055\pi$
$593$	−12.7635	−	22.1071i	−0.524135	−	0.907828i	0.475470	−	0.879732i	$-0.342278\pi$
$594$	2.85582			0.117176
$595$	10.3163	+	3.41306i	0.422927	+	0.139922i
$596$	−34.1842			−1.40024
$597$	−8.27637	−	14.3351i	−0.338729	−	0.586696i
$598$	−0.944253	+	1.63549i	−0.0386134	+	0.0668803i
$599$	6.70098	−	11.6064i	0.273795	−	0.474226i	−0.696036	−	0.718007i	$-0.745054\pi$
$599$	6.70098	−	11.6064i	0.273795	−	0.474226i	0.969830	+	0.243781i	$0.0783878\pi$
$600$	6.41365	+	11.1088i	0.261836	+	0.453514i
$601$	−26.4953			−1.08076			−0.540382	−	0.841420i	$-0.681720\pi$
$601$	−26.4953			−1.08076			−0.540382	+	0.841420i	$0.681720\pi$
$602$	0.721935	+	3.48804i	0.0294239	+	0.142162i
$603$	−11.4561			−0.466528
$604$	−12.3941	−	21.4673i	−0.504310	−	0.873491i
$605$	−1.64274	+	2.84530i	−0.0667868	+	0.115678i
$606$	−0.635781	+	1.10120i	−0.0258268	+	0.0447334i
$607$	15.0713	+	26.1043i	0.611726	+	1.05954i	0.990949	+	0.134236i	$0.0428579\pi$
$607$	15.0713	+	26.1043i	0.611726	+	1.05954i	−0.379223	+	0.925305i	$0.623809\pi$
$608$	15.1371			0.613892
$609$	−4.95535	+	4.41407i	−0.200801	+	0.178867i
$610$	5.84278			0.236567
$611$	−4.28619	−	7.42391i	−0.173401	−	0.300339i
$612$	1.90178	−	3.29397i	0.0768747	−	0.133151i
$613$	8.61158	−	14.9157i	0.347819	−	0.602439i	−0.638043	−	0.770001i	$-0.720256\pi$
$613$	8.61158	−	14.9157i	0.347819	−	0.602439i	0.985862	+	0.167561i	$0.0535892\pi$
$614$	0.980130	+	1.69763i	0.0395548	+	0.0685109i
$615$	−34.3359			−1.38456
$616$	3.96340	−	3.53047i	0.159690	−	0.142247i
$617$	−42.0457			−1.69270			−0.846348	−	0.532631i	$-0.821203\pi$
$617$	−42.0457			−1.69270			−0.846348	+	0.532631i	$0.821203\pi$
$618$	2.56905	+	4.44972i	0.103342	+	0.178994i
$619$	17.4100	−	30.1549i	0.699766	−	1.21203i	−0.268782	−	0.963201i	$-0.586621\pi$
$619$	17.4100	−	30.1549i	0.699766	−	1.21203i	0.968548	−	0.248829i	$-0.0800456\pi$
$620$	4.55390	−	7.88759i	0.182889	−	0.316773i
$621$	−9.20804	−	15.9488i	−0.369506	−	0.640003i
$622$	−6.84466			−0.274446
$623$	6.19087	+	29.9113i	0.248032	+	1.19837i
$624$	−2.56961			−0.102867
$625$	10.1987	+	17.6646i	0.407947	+	0.706584i
$626$	−3.95198	+	6.84504i	−0.157953	+	0.273583i
$627$	1.58403	−	2.74363i	0.0632602	−	0.109570i
$628$	−15.6704	−	27.1420i	−0.625318	−	1.08308i
$629$	6.06789			0.241942
$630$	7.95984	+	2.63345i	0.317128	+	0.104919i
$631$	9.18992			0.365845			0.182923	−	0.983127i	$-0.441444\pi$
$631$	9.18992			0.365845			0.182923	+	0.983127i	$0.441444\pi$
$632$	−4.76826	−	8.25886i	−0.189671	−	0.328520i
$633$	10.7518	−	18.6227i	0.427347	−	0.740187i
$634$	1.66034	−	2.87579i	0.0659404	−	0.114212i
$635$	−25.0736	−	43.4287i	−0.995015	−	1.72342i
$636$	−20.7000			−0.820809
$637$	−5.61880	−	4.17482i	−0.222625	−	0.165412i
$638$	1.23008			0.0486992
$639$	−8.81205	−	15.2629i	−0.348599	−	0.603792i
$640$	18.9264	−	32.7814i	0.748130	−	1.29580i
$641$	−2.39261	+	4.14412i	−0.0945025	+	0.163683i	−0.909401	−	0.415921i	$-0.863459\pi$
$641$	−2.39261	+	4.14412i	−0.0945025	+	0.163683i	0.814898	+	0.579604i	$0.196793\pi$
$642$	−2.16164	−	3.74408i	−0.0853133	−	0.147767i
$643$	−10.7587			−0.424282			−0.212141	−	0.977239i	$-0.568044\pi$
$643$	−10.7587			−0.424282			−0.212141	+	0.977239i	$0.568044\pi$
$644$	−14.9643	−	4.95081i	−0.589677	−	0.195089i
$645$	9.01942			0.355139
$646$	0.971083	+	1.68197i	0.0382068	+	0.0661760i
$647$	5.85697	−	10.1446i	0.230261	−	0.398824i	−0.727624	−	0.685977i	$-0.759375\pi$
$647$	5.85697	−	10.1446i	0.230261	−	0.398824i	0.957885	+	0.287152i	$0.0927085\pi$
$648$	−0.477817	+	0.827604i	−0.0187704	+	0.0325114i
$649$	−2.09531	−	3.62918i	−0.0822481	−	0.142458i
$650$	−3.13567			−0.122991
$651$	0.960878	+	4.64250i	0.0376598	+	0.181954i
$652$	9.73210			0.381138
$653$	12.9394	+	22.4117i	0.506358	+	0.877038i	0.999973	+	0.00735714i	$0.00234187\pi$
$653$	12.9394	+	22.4117i	0.506358	+	0.877038i	−0.493615	+	0.869681i	$0.664325\pi$
$654$	4.99909	−	8.65869i	0.195480	−	0.338581i
$655$	−7.62047	+	13.1990i	−0.297756	+	0.515729i
$656$	11.0270	+	19.0993i	0.430531	+	0.745701i
$657$	18.4006			0.717877
$658$	−9.16494	+	8.16385i	−0.357287	+	0.318260i
$659$	−13.5042			−0.526048			−0.263024	−	0.964789i	$-0.584720\pi$
$659$	−13.5042			−0.526048			−0.263024	+	0.964789i	$0.584720\pi$
$660$	−3.09460	−	5.36000i	−0.120457	−	0.208638i
$661$	−24.3087	+	42.1039i	−0.945499	+	1.63765i	−0.190750	+	0.981639i	$0.561092\pi$
$661$	−24.3087	+	42.1039i	−0.945499	+	1.63765i	−0.754749	+	0.656014i	$0.772241\pi$
$662$	−2.09112	+	3.62192i	−0.0812737	+	0.140770i
$663$	−0.689712	−	1.19462i	−0.0267862	−	0.0463951i
$664$	9.00058			0.349290
$665$	18.6350	−	16.5994i	0.722633	−	0.643699i
$666$	4.68185			0.181418
$667$	−3.96615	−	6.86957i	−0.153570	−	0.265991i
$668$	−1.28816	+	2.23115i	−0.0498403	+	0.0863260i
$669$	−0.765223	+	1.32541i	−0.0295852	+	0.0512432i
$670$	−5.71405	−	9.89702i	−0.220753	−	0.382355i
$671$	−3.28621			−0.126863
$672$	3.11989	+	15.0738i	0.120352	+	0.581483i
$673$	−50.2403			−1.93662			−0.968311	−	0.249747i	$-0.919653\pi$
$673$	−50.2403			−1.93662			−0.968311	+	0.249747i	$0.919653\pi$
$674$	−2.63063	−	4.55639i	−0.101328	−	0.175506i
$675$	15.2890	−	26.4813i	0.588474	−	1.01927i
$676$	0.853573	−	1.47843i	0.0328297	−	0.0568627i
$677$	−1.15726	−	2.00443i	−0.0444769	−	0.0770363i	0.842930	−	0.538023i	$-0.180829\pi$
$677$	−1.15726	−	2.00443i	−0.0444769	−	0.0770363i	−0.887407	+	0.460987i	$0.847495\pi$
$678$	−11.7748			−0.452207
$679$	18.8149	+	6.22474i	0.722049	+	0.238884i
$680$	8.23940			0.315967
$681$	−3.67484	−	6.36500i	−0.140820	−	0.243907i
$682$	0.439381	−	0.761030i	0.0168248	−	0.0291413i
$683$	16.9324	−	29.3278i	0.647900	−	1.12220i	−0.335724	−	0.941960i	$-0.608981\pi$
$683$	16.9324	−	29.3278i	0.647900	−	1.12220i	0.983624	−	0.180235i	$-0.0576858\pi$
$684$	−4.36773	−	7.56513i	−0.167004	−	0.289260i
$685$	8.35874			0.319371
$686$	−4.22282	+	9.08938i	−0.161228	+	0.347034i
$687$	28.4579			1.08574
$688$	−2.89659	−	5.01704i	−0.110431	−	0.191273i
$689$	5.49420	−	9.51623i	0.209312	−	0.362540i
$690$	3.42336	−	5.92943i	0.130325	−	0.225729i
$691$	−11.8043	−	20.4457i	−0.449058	−	0.777792i	0.549267	−	0.835647i	$-0.314907\pi$
$691$	−11.8043	−	20.4457i	−0.449058	−	0.777792i	−0.998325	+	0.0578555i	$0.981574\pi$
$692$	−5.81628			−0.221102
$693$	−4.47693	−	1.48115i	−0.170065	−	0.0562644i
$694$	−9.06553			−0.344123
$695$	21.5943	+	37.4024i	0.819118	+	1.41875i
$696$	−2.51598	+	4.35781i	−0.0953682	+	0.165183i
$697$	−5.91952	+	10.2529i	−0.224218	+	0.388357i
$698$	−2.76885	−	4.79579i	−0.104803	−	0.181523i
$699$	1.47636			0.0558412
$700$	−5.30435	−	25.6280i	−0.200485	−	0.968648i
$701$	−49.5143			−1.87013			−0.935065	−	0.354477i	$-0.884659\pi$
$701$	−49.5143			−1.87013			−0.935065	+	0.354477i	$0.884659\pi$
$702$	−1.42791	−	2.47321i	−0.0538930	−	0.0933454i
$703$	6.96793	−	12.0688i	0.262801	−	0.455184i
$704$	−0.902007	+	1.56232i	−0.0339957	+	0.0588822i
$705$	15.5395	+	26.9151i	0.585250	+	1.01368i
$706$	10.7354			0.404033
$707$	4.20676	−	3.74725i	0.158211	−	0.140930i
$708$	7.89432			0.296687
$709$	−23.0086	−	39.8521i	−0.864108	−	1.49668i	−0.867930	−	0.496686i	$-0.834550\pi$
$709$	−23.0086	−	39.8521i	−0.864108	−	1.49668i	0.00382283	−	0.999993i	$-0.498783\pi$
$710$	8.79052	−	15.2256i	0.329902	−	0.571407i
$711$	−4.23624	+	7.33738i	−0.158871	+	0.275173i
$712$	11.5806	+	20.0581i	0.434001	+	0.751711i
$713$	−5.66679			−0.212223
$714$	−1.47478	+	1.31368i	−0.0551921	+	0.0491634i
$715$	3.28547			0.122870
$716$	−7.67923	−	13.3008i	−0.286986	−	0.497075i
$717$	−10.0389	+	17.3879i	−0.374911	+	0.649364i
$718$	−0.316316	+	0.547875i	−0.0118048	+	0.0204465i
$719$	−9.62188	−	16.6656i	−0.358836	−	0.621522i	0.628931	−	0.777461i	$-0.283493\pi$
$719$	−9.62188	−	16.6656i	−0.358836	−	0.621522i	−0.987767	+	0.155940i	$0.950159\pi$
$720$	−13.6360			−0.508183
$721$	−4.61390	−	22.2921i	−0.171830	−	0.830201i
$722$	−5.82155			−0.216656
$723$	−1.50563	−	2.60782i	−0.0559949	−	0.0969859i
$724$	−2.62127	+	4.54017i	−0.0974187	+	0.168734i
$725$	6.58538	−	11.4062i	0.244575	−	0.423616i
$726$	−0.298581	−	0.517157i	−0.0110814	−	0.0191935i
$727$	−2.72602			−0.101102			−0.0505512	−	0.998721i	$-0.516098\pi$
$727$	−2.72602			−0.101102			−0.0505512	+	0.998721i	$0.516098\pi$
$728$	−5.03918	−	1.66717i	−0.186764	−	0.0617893i
$729$	18.3190			0.678481
$730$	9.17783	+	15.8965i	0.339687	+	0.588355i
$731$	1.55495	−	2.69325i	0.0575120	−	0.0996136i
$732$	3.09529	−	5.36120i	0.114405	−	0.198156i
$733$	23.2442	+	40.2601i	0.858543	+	1.48704i	0.873319	+	0.487149i	$0.161963\pi$
$733$	23.2442	+	40.2601i	0.858543	+	1.48704i	−0.0147757	+	0.999891i	$0.504703\pi$
$734$	4.82108			0.177949
$735$	20.3708	+	15.1357i	0.751387	+	0.558288i
$736$	−18.3996			−0.678217
$737$	3.21381	+	5.56648i	0.118382	+	0.205044i
$738$	−4.56738	+	7.91093i	−0.168127	+	0.291205i
$739$	12.9044	−	22.3510i	0.474695	−	0.822195i	−0.524885	−	0.851173i	$-0.675892\pi$
$739$	12.9044	−	22.3510i	0.474695	−	0.822195i	0.999580	+	0.0289776i	$0.00922516\pi$
$740$	−13.6127	−	23.5779i	−0.500412	−	0.866740i
$741$	−3.16807			−0.116382
$742$	−14.9367	−	4.94167i	−0.548343	−	0.181415i
$743$	−40.0861			−1.47062			−0.735309	−	0.677732i	$-0.762963\pi$
$743$	−40.0861			−1.47062			−0.735309	+	0.677732i	$0.762963\pi$
$744$	1.79741	+	3.11320i	0.0658962	+	0.114136i
$745$	−32.8945	+	56.9750i	−1.20516	+	2.08740i
$746$	−2.30205	+	3.98727i	−0.0842841	+	0.145984i
$747$	−3.99817	−	6.92503i	−0.146285	−	0.253374i
$748$	−2.13404			−0.0780282
$749$	3.88222	+	18.7570i	0.141853	+	0.685365i
$750$	1.55846			0.0569070
$751$	−7.17508	−	12.4276i	−0.261822	−	0.453490i	0.704904	−	0.709303i	$-0.250990\pi$
$751$	−7.17508	−	12.4276i	−0.261822	−	0.453490i	−0.966726	+	0.255813i	$0.917657\pi$
$752$	9.98099	−	17.2876i	0.363969	−	0.630413i
$753$	0.828363	−	1.43477i	0.0301872	−	0.0522858i
$754$	−0.615039	−	1.06528i	−0.0223984	−	0.0387952i
$755$	−47.7061			−1.73620
$756$	17.7983	−	15.8541i	0.647316	−	0.576609i
$757$	31.4078			1.14154			0.570769	−	0.821111i	$-0.306645\pi$
$757$	31.4078			1.14154			0.570769	+	0.821111i	$0.306645\pi$
$758$	1.09751	+	1.90094i	0.0398632	+	0.0690451i
$759$	−1.92543	+	3.33495i	−0.0698888	+	0.121051i
$760$	9.46155	−	16.3879i	0.343206	−	0.594451i
$761$	14.8732	+	25.7612i	0.539154	+	0.933842i	0.998950	+	0.0458174i	$0.0145892\pi$
$761$	14.8732	+	25.7612i	0.539154	+	0.933842i	−0.459796	+	0.888025i	$0.652077\pi$
$762$	9.11466			0.330189
$763$	−33.0774	+	29.4643i	−1.19748	+	1.06668i
$764$	29.0850			1.05226
$765$	−3.66005	−	6.33939i	−0.132329	−	0.229201i
$766$	2.50346	−	4.33611i	0.0904536	−	0.156670i
$767$	−2.09531	+	3.62918i	−0.0756573	+	0.131042i
$768$	1.44932	+	2.51029i	0.0522977	+	0.0905823i
$769$	13.8098			0.497994			0.248997	−	0.968504i	$-0.419899\pi$
$769$	13.8098			0.497994			0.248997	+	0.968504i	$0.419899\pi$
$770$	−0.953413	−	4.60643i	−0.0343586	−	0.166004i
$771$	31.4691			1.13333
$772$	−7.48047	−	12.9566i	−0.269228	−	0.466317i
$773$	8.27978	−	14.3410i	0.297803	−	0.515810i	−0.677830	−	0.735219i	$-0.737079\pi$
$773$	8.27978	−	14.3410i	0.297803	−	0.515810i	0.975633	+	0.219409i	$0.0704128\pi$
$774$	1.19977	−	2.07806i	0.0431248	−	0.0746943i
$775$	−4.70456	−	8.14854i	−0.168993	−	0.292704i
$776$	15.0270			0.539439
$777$	13.4544	+	4.45128i	0.482675	+	0.159689i
$778$	6.71802			0.240853
$779$	13.5951	+	23.5474i	0.487096	+	0.843674i
$780$	−3.09460	+	5.36000i	−0.110804	+	0.191919i
$781$	−4.94414	+	8.56350i	−0.176915	+	0.306426i
$782$	−1.18038	−	2.04447i	−0.0422101	−	0.0731101i
$783$	11.9953			0.428677
$784$	1.87712	−	16.1920i	0.0670399	−	0.578286i
$785$	−60.3168			−2.15280
$786$	−1.38508	−	2.39903i	−0.0494042	−	0.0855706i
$787$	−19.9838	+	34.6130i	−0.712346	+	1.23382i	0.251628	+	0.967824i	$0.419034\pi$
$787$	−19.9838	+	34.6130i	−0.712346	+	1.23382i	−0.963974	+	0.265995i	$0.914299\pi$
$788$	0.294006	−	0.509233i	0.0104735	−	0.0181407i
$789$	−11.1061	−	19.2363i	−0.395387	−	0.684830i
$790$	−8.45177			−0.300701
$791$	49.5284	+	16.3860i	1.76103	+	0.582620i
$792$	−3.57563			−0.127054
$793$	1.64310	+	2.84594i	0.0583484	+	0.101062i
$794$	8.91696	−	15.4446i	0.316451	−	0.548109i
$795$	−19.9190	+	34.5008i	−0.706456	+	1.22362i
$796$	12.8040	+	22.1771i	0.453824	+	0.786047i
$797$	−39.3195			−1.39277			−0.696384	−	0.717669i	$-0.745209\pi$
$797$	−39.3195			−1.39277			−0.696384	+	0.717669i	$0.745209\pi$
$798$	0.919343	+	4.44182i	0.0325444	+	0.157239i
$799$	10.7160			0.379106
$800$	−15.2753	−	26.4576i	−0.540063	−	0.935416i
$801$	10.2885	−	17.8202i	0.363526	−	0.629645i
$802$	−0.426899	+	0.739411i	−0.0150743	+	0.0261095i
$803$	−5.16198	−	8.94081i	−0.182162	−	0.315514i
$804$	−12.1084			−0.427030
$805$	−22.6513	+	20.1770i	−0.798352	+	0.711147i
$806$	−0.878762			−0.0309531
$807$	12.5370	+	21.7147i	0.441322	+	0.764392i
$808$	2.13590	−	3.69949i	0.0751407	−	0.130148i
$809$	−9.60274	+	16.6324i	−0.337614	+	0.584765i	−0.983983	−	0.178260i	$-0.942953\pi$
$809$	−9.60274	+	16.6324i	−0.337614	+	0.584765i	0.646369	+	0.763025i	$0.276287\pi$
$810$	0.423468	+	0.733468i	0.0148791	+	0.0257714i
$811$	23.5977			0.828626			0.414313	−	0.910135i	$-0.364022\pi$
$811$	23.5977			0.828626			0.414313	+	0.910135i	$0.364022\pi$
$812$	7.66618	−	6.82880i	0.269030	−	0.239644i
$813$	−19.8872			−0.697473
$814$	−1.31341	−	2.27490i	−0.0460351	−	0.0797351i
$815$	9.36492	−	16.2205i	0.328039	−	0.568180i
$816$	1.60609	−	2.78183i	0.0562244	−	0.0973835i
$817$	−3.57119	−	6.18549i	−0.124940	−	0.216403i
$818$	6.15940			0.215358
$819$	0.955749	+	4.61771i	0.0333966	+	0.161356i
$820$	53.1194			1.85501
$821$	12.7632	+	22.1065i	0.445438	+	0.771522i	0.998083	−	0.0618955i	$-0.0197145\pi$
$821$	12.7632	+	22.1065i	0.445438	+	0.771522i	−0.552644	+	0.833417i	$0.686381\pi$
$822$	−0.759634	+	1.31573i	−0.0264953	+	0.0458912i
$823$	22.4937	−	38.9602i	0.784081	−	1.35807i	−0.145465	−	0.989363i	$-0.546468\pi$
$823$	22.4937	−	38.9602i	0.784081	−	1.35807i	0.929546	−	0.368705i	$-0.120199\pi$
$824$	−8.63070	−	14.9488i	−0.300665	−	0.520766i
$825$	−6.39396			−0.222609
$826$	5.69637	+	1.88459i	0.198202	+	0.0655734i
$827$	11.5962			0.403238			0.201619	−	0.979464i	$-0.435380\pi$
$827$	11.5962			0.403238			0.201619	+	0.979464i	$0.435380\pi$
$828$	5.30908	+	9.19560i	0.184503	+	0.319569i
$829$	−26.0202	+	45.0682i	−0.903717	+	1.56528i	−0.0810873	+	0.996707i	$0.525839\pi$
$829$	−26.0202	+	45.0682i	−0.903717	+	1.56528i	−0.822630	+	0.568577i	$0.807494\pi$
$830$	3.98840	−	6.90811i	0.138439	−	0.239784i
$831$	3.55884	+	6.16409i	0.123455	+	0.213830i
$832$	1.80401			0.0625430
$833$	8.03153	−	3.47344i	0.278276	−	0.120348i
$834$	−7.84987			−0.271819
$835$	2.47911	+	4.29395i	0.0857933	+	0.148598i
$836$	−2.45058	+	4.24453i	−0.0847551	+	0.146800i
$837$	4.28470	−	7.42131i	0.148101	−	0.256518i
$838$	−5.59850	−	9.69689i	−0.193397	−	0.334973i
$839$	37.7007			1.30157			0.650787	−	0.759261i	$-0.274439\pi$
$839$	37.7007			1.30157			0.650787	+	0.759261i	$0.274439\pi$
$840$	18.2694	+	6.04426i	0.630353	+	0.208547i
$841$	−23.8333			−0.821838
$842$	−4.39537	−	7.61301i	−0.151475	−	0.262362i
$843$	16.6119	−	28.7727i	0.572146	−	0.990986i
$844$	−16.6336	+	28.8103i	−0.572554	+	0.991692i
$845$	−1.64274	−	2.84530i	−0.0565119	−	0.0978814i
$846$	8.26826			0.284269
$847$	0.536238	+	2.59084i	0.0184253	+	0.0890223i
$848$	25.5880			0.878695
$849$	−9.72378	−	16.8421i	−0.333719	−	0.578019i
$850$	1.95989	−	3.39463i	0.0672237	−	0.116435i
$851$	−8.46969	+	14.6699i	−0.290337	+	0.502879i
$852$	−9.31380	−	16.1320i	−0.319086	−	0.552672i
$853$	28.2265			0.966455			0.483228	−	0.875495i	$-0.339464\pi$
$853$	28.2265			0.966455			0.483228	+	0.875495i	$0.339464\pi$
$854$	3.51336	−	3.12960i	0.120225	−	0.107093i
$855$	−16.8118			−0.574950
$856$	7.26203	+	12.5782i	0.248211	+	0.429914i
$857$	−1.56245	+	2.70625i	−0.0533724	+	0.0924438i	−0.891477	−	0.453065i	$-0.850330\pi$
$857$	−1.56245	+	2.70625i	−0.0533724	+	0.0924438i	0.838105	+	0.545509i	$0.183664\pi$
$858$	−0.298581	+	0.517157i	−0.0101934	+	0.0176555i
$859$	2.86289	+	4.95866i	0.0976804	+	0.169187i	0.910724	−	0.413015i	$-0.135524\pi$
$859$	2.86289	+	4.95866i	0.0976804	+	0.169187i	−0.813044	+	0.582203i	$0.802191\pi$
$860$	−13.9535			−0.475811
$861$	−20.6468	+	18.3915i	−0.703641	+	0.626781i
$862$	17.1130			0.582871
$863$	−21.6292	−	37.4629i	−0.736266	−	1.27525i	−0.954166	−	0.299279i	$-0.903254\pi$
$863$	−21.6292	−	37.4629i	−0.736266	−	1.27525i	0.217900	−	0.975971i	$-0.430079\pi$
$864$	13.9120	−	24.0963i	0.473297	−	0.819774i
$865$	−5.59684	+	9.69401i	−0.190298	+	0.329606i
$866$	7.10388	+	12.3043i	0.241400	+	0.418117i
$867$	−17.0349			−0.578534
$868$	−1.48653	−	7.18218i	−0.0504560	−	0.243779i
$869$	4.75361			0.161255
$870$	2.22980	+	3.86213i	0.0755974	+	0.130939i
$871$	3.21381	−	5.56648i	0.108896	−	0.188613i
$872$	−16.7944	+	29.0888i	−0.568731	+	0.985071i
$873$	−6.67520	−	11.5618i	−0.225921	−	0.391307i
$874$	−5.42184			−0.183396
$875$	−6.55539	−	2.16879i	−0.221613	−	0.0733186i
$876$	19.4483			0.657099
$877$	−11.3596	−	19.6754i	−0.383585	−	0.664390i	0.607986	−	0.793947i	$-0.291978\pi$
$877$	−11.3596	−	19.6754i	−0.383585	−	0.664390i	−0.991572	+	0.129558i	$0.958644\pi$
$878$	−3.54857	+	6.14630i	−0.119758	+	0.207428i
$879$	14.3209	−	24.8046i	0.483033	−	0.836637i
$880$	3.82534	+	6.62568i	0.128952	+	0.223352i
$881$	17.7518			0.598074			0.299037	−	0.954242i	$-0.403335\pi$
$881$	17.7518			0.598074			0.299037	+	0.954242i	$0.403335\pi$
$882$	6.19696	−	2.68003i	0.208663	−	0.0902414i
$883$	44.6153			1.50142			0.750712	−	0.660630i	$-0.229711\pi$
$883$	44.6153			1.50142			0.750712	+	0.660630i	$0.229711\pi$
$884$	1.06702	+	1.84813i	0.0358878	+	0.0621594i
$885$	7.59648	−	13.1575i	0.255353	−	0.442284i
$886$	−6.66508	+	11.5443i	−0.223918	+	0.387837i
$887$	−27.2325	−	47.1681i	−0.914379	−	1.58375i	−0.807808	−	0.589446i	$-0.799346\pi$
$887$	−27.2325	−	47.1681i	−0.914379	−	1.58375i	−0.106571	−	0.994305i	$-0.533987\pi$
$888$	10.7458			0.360604
$889$	−38.3391	−	12.6842i	−1.28585	−	0.425414i
$890$	20.5267			0.688056
$891$	−0.238175	−	0.412531i	−0.00797917	−	0.0138203i
$892$	1.18384	−	2.05047i	0.0396379	−	0.0686548i
$893$	12.3055	−	21.3138i	0.411789	−	0.713239i
$894$	−5.97884	−	10.3557i	−0.199962	−	0.346345i
$895$	−29.5580			−0.988016
$896$	−6.17812	−	29.8497i	−0.206396	−	0.997207i
$897$	3.85086			0.128577
$898$	−10.0025	−	17.3249i	−0.333788	−	0.578138i
$899$	1.84553	−	3.19656i	0.0615520	−	0.106611i
$900$	−8.81518	+	15.2683i	−0.293839	+	0.508945i
$901$	6.86810	+	11.8959i	0.228809	+	0.396310i
$902$	5.12519			0.170650
$903$	5.42354	−	4.83112i	0.180484	−	0.160770i
$904$	39.5572			1.31565
$905$	5.04475	+	8.73776i	0.167693	+	0.290453i
$906$	4.33548	−	7.50928i	0.144037	−	0.249479i
$907$	−15.3062	+	26.5111i	−0.508233	+	0.880286i	0.491721	+	0.870753i	$0.336368\pi$
$907$	−15.3062	+	26.5111i	−0.508233	+	0.880286i	−0.999955	+	0.00953321i	$0.996965\pi$
$908$	5.68516	+	9.84699i	0.188669	+	0.326784i
$909$	−3.79518			−0.125878
$910$	−3.51258	+	3.12890i	−0.116441	+	0.103722i
$911$	42.1308			1.39585			0.697927	−	0.716169i	$-0.254106\pi$
$911$	42.1308			1.39585			0.697927	+	0.716169i	$0.254106\pi$
$912$	−3.68864	−	6.38891i	−0.122143	−	0.211558i
$913$	−2.24323	+	3.88540i	−0.0742402	+	0.128588i
$914$	−4.10240	+	7.10556i	−0.135695	+	0.235031i
$915$	−5.95702	−	10.3179i	−0.196933	−	0.341098i
$916$	−44.0258			−1.45465
$917$	2.48754	+	12.0186i	0.0821460	+	0.396889i
$918$	3.56996			0.117826
$919$	20.2045	+	34.9952i	0.666484	+	1.15438i	0.978881	+	0.204432i	$0.0655349\pi$
$919$	20.2045	+	34.9952i	0.666484	+	1.15438i	−0.312397	+	0.949952i	$0.601132\pi$
$920$	−11.5007	+	19.9199i	−0.379168	+	0.656739i
$921$	1.99859	−	3.46166i	0.0658558	−	0.114066i
$922$	−0.984084	−	1.70448i	−0.0324091	−	0.0561341i
$923$	9.88827			0.325476
$924$	−4.73184	−	1.56549i	−0.155666	−	0.0515008i
$925$	−28.1261			−0.924780
$926$	8.14236	+	14.1030i	0.267575	+	0.463453i
$927$	−7.66773	+	13.2809i	−0.251841	+	0.436202i
$928$	5.99228	−	10.3789i	0.196706	−	0.340705i
$929$	30.1648	+	52.2470i	0.989676	+	1.71417i	0.618960	+	0.785423i	$0.287554\pi$
$929$	30.1648	+	52.2470i	0.989676	+	1.71417i	0.370716	+	0.928746i	$0.379112\pi$
$930$	3.18592			0.104470
$931$	2.31429	−	19.9631i	0.0758478	−	0.654264i
$932$	−2.28401			−0.0748152
$933$	6.97850	+	12.0871i	0.228466	+	0.395714i
$934$	8.67936	−	15.0331i	0.283997	−	0.491898i
$935$	−2.05353	+	3.55681i	−0.0671575	+	0.116320i
$936$	1.78781	+	3.09658i	0.0584365	+	0.101215i
$937$	50.0338			1.63453			0.817266	−	0.576261i	$-0.195489\pi$
$937$	50.0338			1.63453			0.817266	+	0.576261i	$0.195489\pi$
$938$	−8.73715	−	2.89061i	−0.285278	−	0.0943817i
$939$	16.1170			0.525959
$940$	−24.0403	−	41.6391i	−0.784109	−	1.35812i
$941$	−5.35219	+	9.27027i	−0.174477	+	0.302202i	−0.939980	−	0.341230i	$-0.889157\pi$
$941$	−5.35219	+	9.27027i	−0.174477	+	0.302202i	0.765503	+	0.643432i	$0.222490\pi$
$942$	5.48154	−	9.49430i	0.178598	−	0.309341i
$943$	−16.5252	−	28.6225i	−0.538135	−	0.932076i
$944$	−9.75843			−0.317610
$945$	−9.29737	−	44.9204i	−0.302444	−	1.46126i
$946$	−1.34630			−0.0437719
$947$	−16.9527	−	29.3629i	−0.550887	−	0.954165i	−0.998211	−	0.0597924i	$-0.980956\pi$
$947$	−16.9527	−	29.3629i	−0.550887	−	0.954165i	0.447324	−	0.894372i	$-0.352377\pi$
$948$	−4.47745	+	7.75516i	−0.145421	+	0.251876i
$949$	−5.16198	+	8.94081i	−0.167565	+	0.290231i
$950$	−4.50120	−	7.79631i	−0.146038	−	0.252946i
$951$	−6.77121			−0.219572
$952$	4.95450	−	4.41331i	0.160576	−	0.143036i
$953$	43.8184			1.41942			0.709709	−	0.704495i	$-0.248827\pi$
$953$	43.8184			1.41942			0.709709	+	0.704495i	$0.248827\pi$
$954$	5.29928	+	9.17862i	0.171571	+	0.297169i
$955$	27.9877	−	48.4761i	0.905660	−	1.56865i
$956$	15.5307	−	26.9000i	0.502300	−	0.870009i
$957$	−1.25413	−	2.17222i	−0.0405403	−	0.0702178i
$958$	17.5479			0.566948
$959$	5.02626	−	4.47723i	0.162306	−	0.144577i
$960$	−6.54040			−0.211090
$961$	14.1816	+	24.5632i	0.457470	+	0.792361i
$962$	−1.31341	+	2.27490i	−0.0423461	+	0.0733456i
$963$	6.45177	−	11.1748i	0.207905	−	0.360103i
$964$	2.32928	+	4.03443i	0.0750211	+	0.129940i
$965$	−28.7930			−0.926879
$966$	−1.11748	−	5.39914i	−0.0359545	−	0.173715i
$967$	54.4054			1.74956			0.874780	−	0.484521i	$-0.161006\pi$
$967$	54.4054			1.74956			0.874780	+	0.484521i	$0.161006\pi$
$968$	1.00308	+	1.73739i	0.0322402	+	0.0558417i
$969$	1.98014	−	3.42971i	0.0636113	−	0.110178i
$970$	6.65888	−	11.5335i	0.213804	−	0.370319i
$971$	12.1730	+	21.0843i	0.390652	+	0.676628i	0.992536	−	0.121955i	$-0.0389164\pi$
$971$	12.1730	+	21.0843i	0.390652	+	0.676628i	−0.601884	+	0.798584i	$0.705583\pi$
$972$	−26.1296			−0.838107
$973$	33.0191	+	10.9241i	1.05854	+	0.350210i
$974$	5.99355			0.192046
$975$	3.19698	+	5.53733i	0.102385	+	0.177337i
$976$	−3.82619	+	6.62716i	−0.122474	+	0.212130i
$977$	−7.05653	+	12.2223i	−0.225758	+	0.391025i	−0.956547	−	0.291579i	$-0.905819\pi$
$977$	−7.05653	+	12.2223i	−0.225758	+	0.391025i	0.730788	+	0.682604i	$0.239153\pi$
$978$	1.70215	+	2.94821i	0.0544288	+	0.0942734i
$979$	−11.5450			−0.368980
$980$	−31.5146	−	23.4157i	−1.00670	−	0.747986i
$981$	29.8412			0.952756
$982$	−8.70910	−	15.0846i	−0.277919	−	0.481369i
$983$	28.3641	−	49.1281i	0.904675	−	1.56694i	0.0833222	−	0.996523i	$-0.473447\pi$
$983$	28.3641	−	49.1281i	0.904675	−	1.56694i	0.821353	−	0.570420i	$-0.193220\pi$
$984$	−10.4830	+	18.1571i	−0.334186	+	0.578827i
$985$	−0.565826	−	0.980040i	−0.0180287	−	0.0312267i
$986$	1.53767			0.0489695
$987$	23.7608	+	7.86107i	0.756316	+	0.250221i
$988$	4.90116			0.155927
$989$	4.34087	+	7.51861i	0.138032	+	0.239078i
$990$	−1.58446	+	2.74436i	−0.0503574	+	0.0872215i
$991$	8.16958	−	14.1501i	0.259515	−	0.449493i	−0.706597	−	0.707616i	$-0.749771\pi$
$991$	8.16958	−	14.1501i	0.259515	−	0.449493i	0.966112	+	0.258123i	$0.0831039\pi$
$992$	−4.28086	−	7.41466i	−0.135917	−	0.235416i
$993$	8.52803			0.270629
$994$	−2.86948	−	13.8639i	−0.0910145	−	0.439738i
$995$	49.2835			1.56239
$996$	−4.22582	−	7.31934i	−0.133900	−	0.231922i
$997$	15.3037	−	26.5068i	0.484673	−	0.839478i	−0.515172	−	0.857087i	$-0.672272\pi$
$997$	15.3037	−	26.5068i	0.484673	−	0.839478i	0.999845	+	0.0176086i	$0.00560527\pi$
$998$	3.70267	−	6.41321i	0.117206	−	0.203007i
$999$	−12.8080	−	22.1841i	−0.405226	−	0.701872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.b.144.4	✓	22
7.2	even	3	inner	1001.2.i.b.716.4	yes	22
7.3	odd	6		7007.2.a.u.1.8		11
7.4	even	3		7007.2.a.v.1.8		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.b.144.4	✓	22	1.1	even	1	trivial
1001.2.i.b.716.4	yes	22	7.2	even	3	inner
7007.2.a.u.1.8		11	7.3	odd	6
7007.2.a.v.1.8		11	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)

\(f(q)\)	\(=\)	\(q+(-0.270580 - 0.468659i) q^{2} +(-0.551742 + 0.955645i) q^{3} +(0.853573 - 1.47843i) q^{4} +(-1.64274 - 2.84530i) q^{5} +0.597162 q^{6} +(-2.51185 - 0.831024i) q^{7} -2.00616 q^{8} +(0.891162 + 1.54354i) q^{9} +O(q^{10})\)	\(q+(-0.270580 - 0.468659i) q^{2} +(-0.551742 + 0.955645i) q^{3} +(0.853573 - 1.47843i) q^{4} +(-1.64274 - 2.84530i) q^{5} +0.597162 q^{6} +(-2.51185 - 0.831024i) q^{7} -2.00616 q^{8} +(0.891162 + 1.54354i) q^{9} +(-0.888984 + 1.53977i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.941904 + 1.63142i) q^{12} -1.00000 q^{13} +(0.290191 + 1.40206i) q^{14} +3.62547 q^{15} +(-1.16432 - 2.01666i) q^{16} +(0.625032 - 1.08259i) q^{17} +(0.482261 - 0.835301i) q^{18} +(-1.43548 - 2.48633i) q^{19} -5.60878 q^{20} +(2.18006 - 1.94193i) q^{21} -0.541160 q^{22} +(1.74487 + 3.02220i) q^{23} +(1.10688 - 1.91718i) q^{24} +(-2.89717 + 5.01805i) q^{25} +(0.270580 + 0.468659i) q^{26} -5.27722 q^{27} +(-3.37266 + 3.00426i) q^{28} -2.27304 q^{29} +(-0.980979 - 1.69911i) q^{30} +(-0.811924 + 1.40629i) q^{31} +(-2.63624 + 4.56611i) q^{32} +(0.551742 + 0.955645i) q^{33} -0.676485 q^{34} +(1.76179 + 8.51214i) q^{35} +3.04269 q^{36} +(2.42703 + 4.20374i) q^{37} +(-0.776827 + 1.34550i) q^{38} +(0.551742 - 0.955645i) q^{39} +(3.29559 + 5.70813i) q^{40} -9.47075 q^{41} +(-1.49998 - 0.496256i) q^{42} +2.48780 q^{43} +(-0.853573 - 1.47843i) q^{44} +(2.92789 - 5.07125i) q^{45} +(0.944253 - 1.63549i) q^{46} +(4.28619 + 7.42391i) q^{47} +2.56961 q^{48} +(5.61880 + 4.17482i) q^{49} +3.13567 q^{50} +(0.689712 + 1.19462i) q^{51} +(-0.853573 + 1.47843i) q^{52} +(-5.49420 + 9.51623i) q^{53} +(1.42791 + 2.47321i) q^{54} -3.28547 q^{55} +(5.03918 + 1.66717i) q^{56} +3.16807 q^{57} +(0.615039 + 1.06528i) q^{58} +(2.09531 - 3.62918i) q^{59} +(3.09460 - 5.36000i) q^{60} +(-1.64310 - 2.84594i) q^{61} +0.878762 q^{62} +(-0.955749 - 4.61771i) q^{63} -1.80401 q^{64} +(1.64274 + 2.84530i) q^{65} +(0.298581 - 0.517157i) q^{66} +(-3.21381 + 5.56648i) q^{67} +(-1.06702 - 1.84813i) q^{68} -3.85086 q^{69} +(3.51258 - 3.12890i) q^{70} -9.88827 q^{71} +(-1.78781 - 3.09658i) q^{72} +(5.16198 - 8.94081i) q^{73} +(1.31341 - 2.27490i) q^{74} +(-3.19698 - 5.53733i) q^{75} -4.90116 q^{76} +(-1.97561 + 1.75982i) q^{77} -0.597162 q^{78} +(2.37681 + 4.11675i) q^{79} +(-3.82534 + 6.62568i) q^{80} +(0.238175 - 0.412531i) q^{81} +(2.56260 + 4.43855i) q^{82} -4.48647 q^{83} +(-1.01017 - 4.88064i) q^{84} -4.10705 q^{85} +(-0.673148 - 1.16593i) q^{86} +(1.25413 - 2.17222i) q^{87} +(-1.00308 + 1.73739i) q^{88} +(-5.77251 - 9.99828i) q^{89} -3.16891 q^{90} +(2.51185 + 0.831024i) q^{91} +5.95748 q^{92} +(-0.895944 - 1.55182i) q^{93} +(2.31952 - 4.01752i) q^{94} +(-4.71625 + 8.16878i) q^{95} +(-2.90905 - 5.03862i) q^{96} -7.49044 q^{97} +(0.436230 - 3.76292i) q^{98} +1.78232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9} - 12 q^{10} + 11 q^{11} - 13 q^{12} - 22 q^{13} + 8 q^{14} + 30 q^{15} + 4 q^{16} + 2 q^{17} + 21 q^{18} - 9 q^{19} - 24 q^{20} - 9 q^{21} + 4 q^{22} + 27 q^{23} + 7 q^{24} + 7 q^{25} - 2 q^{26} - 4 q^{27} - 4 q^{28} + 42 q^{29} + 12 q^{30} + 2 q^{31} + 7 q^{32} + q^{33} - 20 q^{34} + 13 q^{35} + 48 q^{36} + 38 q^{37} - 9 q^{38} + q^{39} + 22 q^{40} + 6 q^{41} + 17 q^{42} - 46 q^{43} + 6 q^{44} + 6 q^{46} - 2 q^{47} + 24 q^{48} + 7 q^{49} + 14 q^{50} + 11 q^{51} + 6 q^{52} - 5 q^{53} + 37 q^{54} + 9 q^{56} - 44 q^{57} + 5 q^{58} + 16 q^{59} + 22 q^{60} - 11 q^{61} + 44 q^{62} - 16 q^{63} - 12 q^{64} - 6 q^{66} + 15 q^{67} - 12 q^{68} - 12 q^{69} + 7 q^{70} - 20 q^{71} + 32 q^{72} - 5 q^{73} + 20 q^{74} - 10 q^{75} + 14 q^{76} - 3 q^{77} + 12 q^{78} - 3 q^{79} + 21 q^{80} + 21 q^{81} - 4 q^{82} - 32 q^{83} + 32 q^{84} - 76 q^{85} + 15 q^{86} - 29 q^{87} - 8 q^{89} + 10 q^{90} - 15 q^{91} - 40 q^{92} + 40 q^{93} - 31 q^{94} + 23 q^{95} + 4 q^{96} - 14 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9 - 12 * q^10 + 11 * q^11 - 13 * q^12 - 22 * q^13 + 8 * q^14 + 30 * q^15 + 4 * q^16 + 2 * q^17 + 21 * q^18 - 9 * q^19 - 24 * q^20 - 9 * q^21 + 4 * q^22 + 27 * q^23 + 7 * q^24 + 7 * q^25 - 2 * q^26 - 4 * q^27 - 4 * q^28 + 42 * q^29 + 12 * q^30 + 2 * q^31 + 7 * q^32 + q^33 - 20 * q^34 + 13 * q^35 + 48 * q^36 + 38 * q^37 - 9 * q^38 + q^39 + 22 * q^40 + 6 * q^41 + 17 * q^42 - 46 * q^43 + 6 * q^44 + 6 * q^46 - 2 * q^47 + 24 * q^48 + 7 * q^49 + 14 * q^50 + 11 * q^51 + 6 * q^52 - 5 * q^53 + 37 * q^54 + 9 * q^56 - 44 * q^57 + 5 * q^58 + 16 * q^59 + 22 * q^60 - 11 * q^61 + 44 * q^62 - 16 * q^63 - 12 * q^64 - 6 * q^66 + 15 * q^67 - 12 * q^68 - 12 * q^69 + 7 * q^70 - 20 * q^71 + 32 * q^72 - 5 * q^73 + 20 * q^74 - 10 * q^75 + 14 * q^76 - 3 * q^77 + 12 * q^78 - 3 * q^79 + 21 * q^80 + 21 * q^81 - 4 * q^82 - 32 * q^83 + 32 * q^84 - 76 * q^85 + 15 * q^86 - 29 * q^87 - 8 * q^89 + 10 * q^90 - 15 * q^91 - 40 * q^92 + 40 * q^93 - 31 * q^94 + 23 * q^95 + 4 * q^96 - 14 * q^97 - 31 * q^98 - 8 * q^99

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