LMFDB - Embedded newform 105.3.k.c.62.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(62,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.62");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.k (of order $4$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 433x^{8} + 16 $ x^16 + 433*x^8 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			62.4
Root			$1.97320 - 0.817327i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.c.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +(-4.65877 + 1.81544i) q^{10} -2.58936i q^{11} +(2.56399 + 8.62705i) q^{12} +(8.94114 + 8.94114i) q^{13} +(1.29468 - 6.87923i) q^{14} +(14.8831 + 1.86906i) q^{15} -5.00000 q^{16} +(-0.581460 - 0.581460i) q^{17} +(-1.85519 + 8.80672i) q^{18} +16.5793 q^{19} +(-6.03161 + 13.7339i) q^{20} +(-13.2460 + 16.2955i) q^{21} +(1.83095 + 1.83095i) q^{22} +(-26.5115 - 26.5115i) q^{23} +(-18.4643 - 10.0035i) q^{24} +(16.9155 + 18.4083i) q^{25} -12.6447 q^{26} +(17.4790 - 20.5787i) q^{27} +(-11.8466 - 17.3395i) q^{28} +11.5528 q^{29} +(-11.8456 + 9.20232i) q^{30} -30.8307i q^{31} +(23.3345 - 23.3345i) q^{32} +(-2.21303 - 7.44617i) q^{33} +0.822309 q^{34} +(-34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 - 41.4929i) q^{37} +(-11.7233 + 11.7233i) q^{38} +(33.3536 + 18.0702i) q^{39} +(-12.7081 - 32.6114i) q^{40} +17.1489 q^{41} +(-2.15633 - 20.8890i) q^{42} +(-25.1548 + 25.1548i) q^{43} +7.76807 q^{44} +(44.3965 - 7.34521i) q^{45} +37.4929 q^{46} +(-45.2473 - 45.2473i) q^{47} +(-14.3784 + 4.27331i) q^{48} +(17.8128 - 45.6476i) q^{49} +(-24.9777 - 1.05561i) q^{50} +(-2.16905 - 1.17514i) q^{51} +(-26.8234 + 26.8234i) q^{52} +(-34.1600 - 34.1600i) q^{53} +(2.19185 + 26.9109i) q^{54} +(5.20600 - 11.8540i) q^{55} +(48.1546 + 9.06275i) q^{56} +(47.6769 - 14.1697i) q^{57} +(-8.16905 + 8.16905i) q^{58} +47.6223i q^{59} +(-5.60717 + 44.6493i) q^{60} +78.9936i q^{61} +(21.8006 + 21.8006i) q^{62} +(-24.1641 + 58.1816i) q^{63} +13.0000i q^{64} +(22.9557 + 58.9087i) q^{65} +(6.83008 + 3.70039i) q^{66} +(72.4786 + 72.4786i) q^{67} +(1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 - 28.8899i) q^{70} +49.0193i q^{71} +(-61.6470 - 12.9863i) q^{72} +(26.0359 + 26.0359i) q^{73} +58.6798 q^{74} +(64.3765 + 38.4795i) q^{75} +49.7380i q^{76} +(10.2250 + 14.9660i) q^{77} +(-36.3621 + 10.8069i) q^{78} -75.8024i q^{79} +(-22.8898 - 10.0527i) q^{80} +(32.6762 - 74.1166i) q^{81} +(-12.1261 + 12.1261i) q^{82} +(53.6785 - 53.6785i) q^{83} +(-48.8865 - 39.7380i) q^{84} +(-1.49286 - 3.83095i) q^{85} -35.5742i q^{86} +(33.2221 - 9.87373i) q^{87} +(-12.8167 + 12.8167i) q^{88} +14.0533i q^{89} +(-26.1992 + 36.5869i) q^{90} +(-86.9857 - 16.3708i) q^{91} +(79.5344 - 79.5344i) q^{92} +(-26.3499 - 88.6594i) q^{93} +63.9894 q^{94} +(75.8995 + 33.3333i) q^{95} +(47.1596 - 87.0458i) q^{96} +(-25.9664 + 25.9664i) q^{97} +(19.6822 + 44.8733i) q^{98} +(-12.7279 - 19.5214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{7}+O(q^{10}) $ 16 * q + 32 * q^7	$ 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) $ 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	0.707107i	−0.353553	+	0.353553i	−0.861430	−	0.507877i	$-0.830431\pi$
$2$	−0.707107	+	0.707107i	−0.353553	+	0.353553i	0.507877	+	0.861430i	$0.330431\pi$
$3$	2.87568	−	0.854662i	0.958561	−	0.284887i
$3$	2.87568	−	0.854662i	0.958561	−	0.284887i
$4$			3.00000i			0.750000i
$5$	4.57796	+	2.01054i	0.915592	+	0.402108i
$5$	4.57796	+	2.01054i	0.915592	+	0.402108i
$6$	−1.42908	+	2.63775i	−0.238180	+	0.439625i
$7$	−5.77983	+	3.94887i	−0.825689	+	0.564125i
$7$	−5.77983	+	3.94887i	−0.825689	+	0.564125i
$8$	−4.94975	−	4.94975i	−0.618718	−	0.618718i
$9$	7.53910	−	4.91548i	0.837678	−	0.546164i
$10$	−4.65877	+	1.81544i	−0.465877	+	0.181544i
$11$		−	2.58936i		−	0.235396i	−0.993049	−	0.117698i	$-0.962449\pi$
$11$		−	2.58936i		−	0.235396i	0.993049	−	0.117698i	$-0.0375515\pi$
$12$	2.56399	+	8.62705i	0.213666	+	0.718921i
$13$	8.94114	+	8.94114i	0.687780	+	0.687780i	0.961741	−	0.273961i	$-0.0883338\pi$
$13$	8.94114	+	8.94114i	0.687780	+	0.687780i	−0.273961	+	0.961741i	$0.588334\pi$
$14$	1.29468	−	6.87923i	0.0924770	−	0.491374i
$15$	14.8831	+	1.86906i	0.992207	+	0.124604i
$16$	−5.00000			−0.312500
$17$	−0.581460	−	0.581460i	−0.0342036	−	0.0342036i	0.689798	−	0.724002i	$-0.257699\pi$
$17$	−0.581460	−	0.581460i	−0.0342036	−	0.0342036i	−0.724002	+	0.689798i	$0.757699\pi$
$18$	−1.85519	+	8.80672i	−0.103066	+	0.489262i
$19$	16.5793			0.872596			0.436298	−	0.899802i	$-0.356289\pi$
$19$	16.5793			0.872596			0.436298	+	0.899802i	$0.356289\pi$
$20$	−6.03161	+	13.7339i	−0.301581	+	0.686694i
$21$	−13.2460	+	16.2955i	−0.630762	+	0.775977i
$22$	1.83095	+	1.83095i	0.0832251	+	0.0832251i
$23$	−26.5115	−	26.5115i	−1.15267	−	1.15267i	−0.986015	−	0.166657i	$-0.946703\pi$
$23$	−26.5115	−	26.5115i	−1.15267	−	1.15267i	−0.166657	−	0.986015i	$-0.553297\pi$
$24$	−18.4643	−	10.0035i	−0.769344	−	0.416814i
$25$	16.9155	+	18.4083i	0.676619	+	0.736333i
$26$	−12.6447			−0.486334
$27$	17.4790	−	20.5787i	0.647370	−	0.762176i
$28$	−11.8466	−	17.3395i	−0.423094	−	0.619267i
$29$	11.5528			0.398372			0.199186	−	0.979962i	$-0.436170\pi$
$29$	11.5528			0.398372			0.199186	+	0.979962i	$0.436170\pi$
$30$	−11.8456	+	9.20232i	−0.394852	+	0.306744i
$31$		−	30.8307i		−	0.994539i	−0.867596	−	0.497270i	$-0.834336\pi$
$31$		−	30.8307i		−	0.994539i	0.867596	−	0.497270i	$-0.165664\pi$
$32$	23.3345	−	23.3345i	0.729204	−	0.729204i
$33$	−2.21303	−	7.44617i	−0.0670614	−	0.225642i
$34$	0.822309			0.0241856
$35$	−34.3992	+	6.45724i	−0.982834	+	0.184493i
$36$	14.7464	+	22.6173i	0.409623	+	0.628259i
$37$	−41.4929	−	41.4929i	−1.12143	−	1.12143i	−0.991527	−	0.129902i	$-0.958534\pi$
$37$	−41.4929	−	41.4929i	−1.12143	−	1.12143i	−0.129902	−	0.991527i	$-0.541466\pi$
$38$	−11.7233	+	11.7233i	−0.308509	+	0.308509i
$39$	33.3536	+	18.0702i	0.855219	+	0.463339i
$40$	−12.7081	−	32.6114i	−0.317703	−	0.815285i
$41$	17.1489			0.418267			0.209133	−	0.977887i	$-0.432936\pi$
$41$	17.1489			0.418267			0.209133	+	0.977887i	$0.432936\pi$
$42$	−2.15633	−	20.8890i	−0.0513413	−	0.497357i
$43$	−25.1548	+	25.1548i	−0.584994	+	0.584994i	−0.936272	−	0.351277i	$-0.885748\pi$
$43$	−25.1548	+	25.1548i	−0.584994	+	0.584994i	0.351277	+	0.936272i	$0.385748\pi$
$44$	7.76807			0.176547
$45$	44.3965	−	7.34521i	0.986589	−	0.163227i
$46$	37.4929			0.815062
$47$	−45.2473	−	45.2473i	−0.962709	−	0.962709i	0.0366205	−	0.999329i	$-0.488341\pi$
$47$	−45.2473	−	45.2473i	−0.962709	−	0.962709i	−0.999329	+	0.0366205i	$0.988341\pi$
$48$	−14.3784	+	4.27331i	−0.299550	+	0.0890273i
$49$	17.8128	−	45.6476i	0.363526	−	0.931584i
$50$	−24.9777	−	1.05561i	−0.499554	−	0.0211122i
$51$	−2.16905	−	1.17514i	−0.0425304	−	0.0230420i
$52$	−26.8234	+	26.8234i	−0.515835	+	0.515835i
$53$	−34.1600	−	34.1600i	−0.644528	−	0.644528i	0.307137	−	0.951665i	$-0.400629\pi$
$53$	−34.1600	−	34.1600i	−0.644528	−	0.644528i	−0.951665	+	0.307137i	$0.900629\pi$
$54$	2.19185	+	26.9109i	0.0405897	+	0.498350i
$55$	5.20600	−	11.8540i	0.0946545	−	0.215527i
$56$	48.1546	+	9.06275i	0.859904	+	0.161835i
$57$	47.6769	−	14.1697i	0.836436	−	0.248592i
$58$	−8.16905	+	8.16905i	−0.140846	+	0.140846i
$59$			47.6223i			0.807158i	0.914945	+	0.403579i	$0.132234\pi$
$59$			47.6223i			0.807158i	−0.914945	+	0.403579i	$0.867766\pi$
$60$	−5.60717	+	44.6493i	−0.0934529	+	0.744155i
$61$			78.9936i			1.29498i	0.762075	+	0.647488i	$0.224181\pi$
$61$			78.9936i			1.29498i	−0.762075	+	0.647488i	$0.775819\pi$
$62$	21.8006	+	21.8006i	0.351623	+	0.351623i
$63$	−24.1641	+	58.1816i	−0.383557	+	0.923517i
$64$			13.0000i			0.203125i
$65$	22.9557	+	58.9087i	0.353165	+	0.906288i
$66$	6.83008	+	3.70039i	0.103486	+	0.0560665i
$67$	72.4786	+	72.4786i	1.08177	+	1.08177i	0.996345	+	0.0854251i	$0.0272248\pi$
$67$	72.4786	+	72.4786i	1.08177	+	1.08177i	0.0854251	+	0.996345i	$0.472775\pi$
$68$	1.74438	−	1.74438i	0.0256527	−	0.0256527i
$69$	−98.8969	−	53.5802i	−1.43329	−	0.776524i
$70$	19.7579	−	28.8899i	0.282256	−	0.412712i
$71$			49.0193i			0.690413i	0.938527	+	0.345207i	$0.112191\pi$
$71$			49.0193i			0.690413i	−0.938527	+	0.345207i	$0.887809\pi$
$72$	−61.6470	−	12.9863i	−0.856209	−	0.180365i
$73$	26.0359	+	26.0359i	0.356656	+	0.356656i	0.862579	−	0.505923i	$-0.168848\pi$
$73$	26.0359	+	26.0359i	0.356656	+	0.356656i	−0.505923	+	0.862579i	$0.668848\pi$
$74$	58.6798			0.792970
$75$	64.3765	+	38.4795i	0.858353	+	0.513060i
$76$			49.7380i			0.654447i
$77$	10.2250	+	14.9660i	0.132793	+	0.194364i
$78$	−36.3621	+	10.8069i	−0.466181	+	0.138550i
$79$		−	75.8024i		−	0.959524i	−0.877399	−	0.479762i	$-0.840723\pi$
$79$		−	75.8024i		−	0.959524i	0.877399	−	0.479762i	$-0.159277\pi$
$80$	−22.8898	−	10.0527i	−0.286123	−	0.125659i
$81$	32.6762	−	74.1166i	0.403410	−	0.915019i
$82$	−12.1261	+	12.1261i	−0.147880	+	0.147880i
$83$	53.6785	−	53.6785i	0.646729	−	0.646729i	−0.305472	−	0.952201i	$-0.598814\pi$
$83$	53.6785	−	53.6785i	0.646729	−	0.646729i	0.952201	+	0.305472i	$0.0988143\pi$
$84$	−48.8865	−	39.7380i	−0.581983	−	0.473071i
$85$	−1.49286	−	3.83095i	−0.0175630	−	0.0450700i
$86$		−	35.5742i		−	0.413654i
$87$	33.2221	−	9.87373i	0.381864	−	0.113491i
$88$	−12.8167	+	12.8167i	−0.145644	+	0.145644i
$89$			14.0533i			0.157903i	0.996878	+	0.0789514i	$0.0251572\pi$
$89$			14.0533i			0.157903i	−0.996878	+	0.0789514i	$0.974843\pi$
$90$	−26.1992	+	36.5869i	−0.291102	+	0.406521i
$91$	−86.9857	−	16.3708i	−0.955887	−	0.179899i
$92$	79.5344	−	79.5344i	0.864504	−	0.864504i
$93$	−26.3499	−	88.6594i	−0.283332	−	0.953327i
$94$	63.9894			0.680738
$95$	75.8995	+	33.3333i	0.798942	+	0.350877i
$96$	47.1596	−	87.0458i	0.491245	−	0.906727i
$97$	−25.9664	+	25.9664i	−0.267695	+	0.267695i	−0.828171	−	0.560476i	$-0.810618\pi$
$97$	−25.9664	+	25.9664i	−0.267695	+	0.267695i	0.560476	+	0.828171i	$0.310618\pi$
$98$	19.6822	+	44.8733i	0.200839	+	0.457891i
$99$	−12.7279	−	19.5214i	−0.128565	−	0.197186i
$100$	−55.2250	+	50.7464i	−0.552250	+	0.507464i
$101$	23.6924			0.234579			0.117289	−	0.993098i	$-0.462580\pi$
$101$	23.6924			0.234579			0.117289	+	0.993098i	$0.462580\pi$
$102$	2.36470	−	0.702797i	0.0231833	−	0.00689016i
$103$	−78.6519	−	78.6519i	−0.763611	−	0.763611i	0.213362	−	0.976973i	$-0.431559\pi$
$103$	−78.6519	−	78.6519i	−0.763611	−	0.763611i	−0.976973	+	0.213362i	$0.931559\pi$
$104$		−	88.5128i		−	0.851085i
$105$	−93.4024	+	47.9687i	−0.889547	+	0.456844i
$106$	48.3095			0.455750
$107$	−124.868	+	124.868i	−1.16699	+	1.16699i	−0.184083	+	0.982911i	$0.558931\pi$
$107$	−124.868	+	124.868i	−1.16699	+	1.16699i	−0.982911	+	0.184083i	$0.941069\pi$
$108$	61.7362	+	52.4370i	0.571632	+	0.485528i
$109$			72.9857i			0.669594i	0.942290	+	0.334797i	$0.108668\pi$
$109$			72.9857i			0.669594i	−0.942290	+	0.334797i	$0.891332\pi$
$110$	4.70083	+	12.0632i	0.0427348	+	0.109666i
$111$	−154.783	−	83.8579i	−1.39444	−	0.755477i
$112$	28.8991	−	19.7444i	0.258028	−	0.176289i
$113$	51.8276	+	51.8276i	0.458651	+	0.458651i	0.898212	−	0.439562i	$-0.144866\pi$
$113$	51.8276	+	51.8276i	0.458651	+	0.458651i	−0.439562	+	0.898212i	$0.644866\pi$
$114$	−23.6931	+	43.7321i	−0.207834	+	0.383615i
$115$	−68.0662	−	174.671i	−0.591880	−	1.51888i
$116$			34.6583i			0.298779i
$117$	111.358	+	23.4582i	0.951779	+	0.200498i
$118$	−33.6740	−	33.6740i	−0.285373	−	0.285373i
$119$	5.65685	+	1.06463i	0.0475366	+	0.00894644i
$120$	−64.4162	−	82.9189i	−0.536802	−	0.690991i
$121$	114.295			0.944589
$122$	−55.8569	−	55.8569i	−0.457843	−	0.457843i
$123$	49.3149	−	14.6565i	0.400934	−	0.119159i
$124$	92.4922			0.745905
$125$	40.4278	+	118.282i	0.323422	+	0.946255i
$126$	−24.0540	−	58.2272i	−0.190905	−	0.462121i
$127$	21.6476	+	21.6476i	0.170454	+	0.170454i	0.787179	−	0.616725i	$-0.211541\pi$
$127$	21.6476	+	21.6476i	0.170454	+	0.170454i	−0.616725	+	0.787179i	$0.711541\pi$
$128$	84.1457	+	84.1457i	0.657388	+	0.657388i
$129$	−50.8383	+	93.8359i	−0.394095	+	0.727410i
$130$	−57.8869	−	25.4226i	−0.445284	−	0.195559i
$131$	−217.662			−1.66154			−0.830771	−	0.556614i	$-0.812100\pi$
$131$	−217.662			−1.66154			−0.830771	+	0.556614i	$0.812100\pi$
$132$	22.3385	−	6.63908i	0.169231	−	0.0502960i
$133$	−95.8256	+	65.4696i	−0.720493	+	0.492253i
$134$	−102.500			−0.764927
$135$	121.393	−	59.0665i	0.899204	−	0.437530i
$136$			5.75616i			0.0423247i
$137$	−32.1683	+	32.1683i	−0.234805	+	0.234805i	−0.814695	−	0.579890i	$-0.803096\pi$
$137$	−32.1683	+	32.1683i	−0.234805	+	0.234805i	0.579890	+	0.814695i	$0.303096\pi$
$138$	107.818	−	32.0437i	0.781287	−	0.232201i
$139$	112.569			0.809851			0.404925	−	0.914350i	$-0.367298\pi$
$139$	112.569			0.809851			0.404925	+	0.914350i	$0.367298\pi$
$140$	−19.3717	−	103.198i	−0.138369	−	0.737125i
$141$	−168.788	−	91.4457i	−1.19708	−	0.648551i
$142$	−34.6619	−	34.6619i	−0.244098	−	0.244098i
$143$	23.1518	−	23.1518i	0.161901	−	0.161901i
$144$	−37.6955	+	24.5774i	−0.261774	+	0.170676i
$145$	52.8882	+	23.2273i	0.364746	+	0.160188i
$146$	−36.8203			−0.252194
$147$	12.2106	−	146.492i	0.0830654	−	0.996544i
$148$	124.479	−	124.479i	0.841071	−	0.841071i
$149$	24.7386			0.166031			0.0830155	−	0.996548i	$-0.473545\pi$
$149$	24.7386			0.166031			0.0830155	+	0.996548i	$0.473545\pi$
$150$	−72.7301	+	18.3119i	−0.484868	+	0.122079i
$151$	−116.676			−0.772690			−0.386345	−	0.922354i	$-0.626263\pi$
$151$	−116.676			−0.772690			−0.386345	+	0.922354i	$0.626263\pi$
$152$	−82.0634	−	82.0634i	−0.539891	−	0.539891i
$153$	−7.24185	−	1.52554i	−0.0473323	−	0.00997082i
$154$	−17.8128	−	3.35238i	−0.115667	−	0.0217687i
$155$	61.9863	−	141.142i	0.399912	−	0.910593i
$156$	−54.2107	+	100.061i	−0.347505	+	0.641414i
$157$	−142.879	+	142.879i	−0.910055	+	0.910055i	−0.996276	−	0.0862209i	$-0.972521\pi$
$157$	−142.879	+	142.879i	−0.910055	+	0.910055i	0.0862209	+	0.996276i	$0.472521\pi$
$158$	53.6004	+	53.6004i	0.339243	+	0.339243i
$159$	−127.429	−	69.0380i	−0.801437	−	0.434202i
$160$	153.740	−	59.9096i	0.960872	−	0.374435i
$161$	257.922	+	48.5412i	1.60200	+	0.301498i
$162$	29.3028	+	75.5139i	0.180881	+	0.466135i
$163$	97.1548	−	97.1548i	0.596041	−	0.596041i	−0.343215	−	0.939257i	$-0.611516\pi$
$163$	97.1548	−	97.1548i	0.596041	−	0.596041i	0.939257	+	0.343215i	$0.111516\pi$
$164$			51.4468i			0.313700i
$165$	4.83966	−	38.5377i	0.0293312	−	0.233562i
$166$			75.9128i			0.457306i
$167$	207.245	+	207.245i	1.24099	+	1.24099i	0.959592	+	0.281396i	$0.0907974\pi$
$167$	207.245	+	207.245i	1.24099	+	1.24099i	0.281396	+	0.959592i	$0.409203\pi$
$168$	146.223	−	15.0943i	0.870375	−	0.0898473i
$169$		−	9.11189i		−	0.0539165i
$170$	3.76450	+	1.65328i	0.0221441	+	0.00972520i
$171$	124.993	−	81.4952i	0.730954	−	0.476580i
$172$	−75.4643	−	75.4643i	−0.438746	−	0.438746i
$173$	−115.444	+	115.444i	−0.667307	+	0.667307i	−0.957092	−	0.289785i	$-0.906416\pi$
$173$	−115.444	+	115.444i	−0.667307	+	0.667307i	0.289785	+	0.957092i	$0.406416\pi$
$174$	−16.5098	+	30.4734i	−0.0948840	+	0.175134i
$175$	−170.461	−	39.5999i	−0.974061	−	0.226285i
$176$			12.9468i			0.0735613i
$177$	40.7010	+	136.947i	0.229949	+	0.773710i
$178$	−9.93722	−	9.93722i	−0.0558271	−	0.0558271i
$179$	−236.871			−1.32330			−0.661650	−	0.749813i	$-0.730143\pi$
$179$	−236.871			−1.32330			−0.661650	+	0.749813i	$0.730143\pi$
$180$	22.0356	+	133.189i	0.122420	+	0.739941i
$181$			227.866i			1.25893i	0.777030	+	0.629463i	$0.216725\pi$
$181$			227.866i			1.25893i	−0.777030	+	0.629463i	$0.783275\pi$
$182$	73.0841	−	49.9323i	0.401561	−	0.274353i
$183$	67.5128	+	227.160i	0.368923	+	1.24131i
$184$			262.450i			1.42636i
$185$	−106.530	−	273.376i	−0.575837	−	1.47771i
$186$	81.3238	+	44.0595i	0.437225	+	0.236879i
$187$	−1.50561	+	1.50561i	−0.00805138	+	0.00805138i
$188$	135.742	−	135.742i	0.722032	−	0.722032i
$189$	−19.7627	+	187.964i	−0.104565	+	0.994518i
$190$	−77.2393	+	30.0988i	−0.406523	+	0.158415i
$191$		−	370.941i		−	1.94210i	−0.238872	−	0.971051i	$-0.576778\pi$
$191$		−	370.941i		−	1.94210i	0.238872	−	0.971051i	$-0.423222\pi$
$192$	11.1106	+	37.3839i	0.0578678	+	0.194708i
$193$	81.6333	−	81.6333i	0.422971	−	0.422971i	−0.463255	−	0.886225i	$-0.653318\pi$
$193$	81.6333	−	81.6333i	0.422971	−	0.422971i	0.886225	+	0.463255i	$0.153318\pi$
$194$		−	36.7220i		−	0.189289i
$195$	116.360	+	149.783i	0.596720	+	0.768120i
$196$	136.943	+	53.4383i	0.698688	+	0.272645i
$197$	−182.194	+	182.194i	−0.924845	+	0.924845i	−0.997367	−	0.0725218i	$-0.976895\pi$
$197$	−182.194	+	182.194i	−0.924845	+	0.924845i	0.0725218	+	0.997367i	$0.476895\pi$
$198$	22.8037	+	4.80374i	0.115170	+	0.0242613i
$199$	31.2360			0.156965			0.0784824	−	0.996915i	$-0.474993\pi$
$199$	31.2360			0.156965			0.0784824	+	0.996915i	$0.474993\pi$
$200$	7.38926	−	174.844i	0.0369463	−	0.874220i
$201$	270.370	+	146.481i	1.34512	+	0.728760i
$202$	−16.7531	+	16.7531i	−0.0829360	+	0.0829360i
$203$	−66.7731	+	45.6205i	−0.328931	+	0.224731i
$204$	3.52543	−	6.50714i	0.0172815	−	0.0318978i
$205$	78.5071	+	34.4786i	0.382962	+	0.168188i
$206$	111.231			0.539954
$207$	−330.189	−	69.5562i	−1.59512	−	0.336020i
$208$	−44.7057	−	44.7057i	−0.214931	−	0.214931i
$209$		−	42.9298i		−	0.205406i
$210$	32.1265	−	99.9644i	0.152983	−	0.476021i
$211$	−96.5905			−0.457775			−0.228887	−	0.973453i	$-0.573509\pi$
$211$	−96.5905			−0.457775			−0.228887	+	0.973453i	$0.573509\pi$
$212$	102.480	−	102.480i	0.483396	−	0.483396i
$213$	41.8950	+	140.964i	0.196690	+	0.661803i
$214$		−	176.590i		−	0.825189i
$215$	−165.732	+	64.5829i	−0.770847	+	0.300386i
$216$	−188.376	+	15.3429i	−0.872112	+	0.0710320i
$217$	121.747	+	178.196i	0.561044	+	0.821181i
$218$	−51.6087	−	51.6087i	−0.236737	−	0.236737i
$219$	97.1228	+	52.6190i	0.443483	+	0.240270i
$220$	35.5619	+	15.6180i	0.161645	+	0.0709909i
$221$		−	10.3978i		−	0.0470491i
$222$	168.744	−	50.1514i	0.760110	−	0.225907i
$223$	−79.9490	−	79.9490i	−0.358516	−	0.358516i	0.504750	−	0.863266i	$-0.331585\pi$
$223$	−79.9490	−	79.9490i	−0.358516	−	0.358516i	−0.863266	+	0.504750i	$0.831585\pi$
$224$	−42.7244	+	227.015i	−0.190734	+	1.01346i
$225$	218.013	+	55.6347i	0.968948	+	0.247265i
$226$	−73.2952			−0.324315
$227$	−56.7824	−	56.7824i	−0.250143	−	0.250143i	0.570886	−	0.821029i	$-0.306600\pi$
$227$	−56.7824	−	56.7824i	−0.250143	−	0.250143i	−0.821029	+	0.570886i	$0.806600\pi$
$228$	42.5092	+	143.031i	0.186444	+	0.627327i
$229$	153.812			0.671668			0.335834	−	0.941921i	$-0.390982\pi$
$229$	153.812			0.671668			0.335834	+	0.941921i	$0.390982\pi$
$230$	171.641	+	75.3808i	0.746265	+	0.327743i
$231$	42.1949	+	34.2986i	0.182662	+	0.148479i
$232$	−57.1833	−	57.1833i	−0.246480	−	0.246480i
$233$	−50.2938	−	50.2938i	−0.215853	−	0.215853i	0.590895	−	0.806748i	$-0.298775\pi$
$233$	−50.2938	−	50.2938i	−0.215853	−	0.215853i	−0.806748	+	0.590895i	$0.798775\pi$
$234$	−95.3296	+	62.1547i	−0.407392	+	0.265618i
$235$	−116.169	−	298.112i	−0.494336	−	1.26856i
$236$	−142.867			−0.605368
$237$	−64.7854	−	217.984i	−0.273356	−	0.919762i
$238$	−4.75280	+	3.24720i	−0.0199698	+	0.0136437i
$239$	131.741			0.551216			0.275608	−	0.961270i	$-0.411121\pi$
$239$	131.741			0.551216			0.275608	+	0.961270i	$0.411121\pi$
$240$	−74.4155	−	9.34529i	−0.310065	−	0.0389387i
$241$		−	103.031i		−	0.427516i	−0.976887	−	0.213758i	$-0.931430\pi$
$241$		−	103.031i		−	0.427516i	0.976887	−	0.213758i	$-0.0685704\pi$
$242$	−80.8189	+	80.8189i	−0.333963	+	0.333963i
$243$	30.6217	−	241.063i	0.126015	−	0.992028i
$244$	−236.981			−0.971232
$245$	173.322	−	173.160i	0.707439	−	0.706775i
$246$	−24.5071	+	45.2346i	−0.0996225	+	0.183881i
$247$	148.238	+	148.238i	0.600154	+	0.600154i
$248$	−152.604	+	152.604i	−0.615340	+	0.615340i
$249$	108.485	−	200.239i	0.435684	−	0.804174i
$250$	−112.225	−	55.0512i	−0.448899	−	0.220205i
$251$	−363.395			−1.44779			−0.723895	−	0.689910i	$-0.757650\pi$
$251$	−363.395			−1.44779			−0.723895	+	0.689910i	$0.757650\pi$
$252$	−174.545	−	72.4924i	−0.692638	−	0.287668i
$253$	−68.6476	+	68.6476i	−0.271334	+	0.271334i
$254$	−30.6144			−0.120529
$255$	−7.56715	−	9.74072i	−0.0296751	−	0.0381989i
$256$	−171.000			−0.667969
$257$	86.9159	+	86.9159i	0.338194	+	0.338194i	0.855687	−	0.517493i	$-0.173135\pi$
$257$	86.9159	+	86.9159i	0.338194	+	0.338194i	−0.517493	+	0.855687i	$0.673135\pi$
$258$	−30.4039	−	102.300i	−0.117845	−	0.396512i
$259$	403.672	+	75.9714i	1.55858	+	0.293326i
$260$	−176.726	+	68.8671i	−0.679716	+	0.264874i
$261$	87.0976	−	56.7874i	0.333707	−	0.217576i
$262$	153.910	−	153.910i	0.587444	−	0.587444i
$263$	−97.6009	−	97.6009i	−0.371106	−	0.371106i	0.496774	−	0.867880i	$-0.334518\pi$
$263$	−97.6009	−	97.6009i	−0.371106	−	0.371106i	−0.867880	+	0.496774i	$0.834518\pi$
$264$	−25.9027	+	47.8106i	−0.0981164	+	0.181101i
$265$	−87.7032	−	225.063i	−0.330955	−	0.849295i
$266$	21.4649	−	114.053i	0.0806951	−	0.428770i
$267$	12.0109	+	40.4130i	0.0449845	+	0.151359i
$268$	−217.436	+	217.436i	−0.811327	+	0.811327i
$269$			119.813i			0.445403i	0.974887	+	0.222701i	$0.0714875\pi$
$269$			119.813i			0.445403i	−0.974887	+	0.222701i	$0.928512\pi$
$270$	−44.0712	+	127.604i	−0.163227	+	0.472607i
$271$		−	246.646i		−	0.910132i	−0.890458	−	0.455066i	$-0.849616\pi$
$271$		−	246.646i		−	0.910132i	0.890458	−	0.455066i	$-0.150384\pi$
$272$	2.90730	+	2.90730i	0.0106886	+	0.0106886i
$273$	−264.135	+	27.2662i	−0.967527	+	0.0998761i
$274$		−	45.4929i		−	0.166032i
$275$	47.6657	−	43.8002i	0.173330	−	0.159273i
$276$	160.741	−	296.691i	0.582393	−	1.07497i
$277$	51.1833	+	51.1833i	0.184777	+	0.184777i	0.793434	−	0.608656i	$-0.208291\pi$
$277$	51.1833	+	51.1833i	0.184777	+	0.184777i	−0.608656	+	0.793434i	$0.708291\pi$
$278$	−79.5985	+	79.5985i	−0.286325	+	0.286325i
$279$	−151.548	−	232.436i	−0.543182	−	0.833104i
$280$	202.229	+	138.306i	0.722246	+	0.493949i
$281$		−	6.33365i		−	0.0225397i	−0.999936	−	0.0112698i	$-0.996413\pi$
$281$		−	6.33365i		−	0.0225397i	0.999936	−	0.0112698i	$-0.00358738\pi$
$282$	184.013	−	54.6893i	0.652529	−	0.193934i
$283$	242.152	+	242.152i	0.855661	+	0.855661i	0.990823	−	0.135163i	$-0.0431558\pi$
$283$	242.152	+	242.152i	0.855661	+	0.855661i	−0.135163	+	0.990823i	$0.543156\pi$
$284$	−147.058			−0.517810
$285$	246.752	+	30.9877i	0.865795	+	0.108729i
$286$			32.7416i			0.114481i
$287$	−99.1178	+	67.7190i	−0.345358	+	0.235955i
$288$	61.2211	−	290.622i	0.212573	−	1.00910i
$289$		−	288.324i		−	0.997660i
$290$	−53.8218	+	20.9734i	−0.185592	+	0.0723221i
$291$	−52.4786	+	96.8635i	−0.180339	+	0.332864i
$292$	−78.1076	+	78.1076i	−0.267492	+	0.267492i
$293$	333.360	−	333.360i	1.13775	−	1.13775i	0.148895	−	0.988853i	$-0.452428\pi$
$293$	333.360	−	333.360i	1.13775	−	1.13775i	0.988853	−	0.148895i	$-0.0475717\pi$
$294$	94.9513	+	112.220i	0.322963	+	0.381700i
$295$	−95.7464	+	218.013i	−0.324564	+	0.739027i
$296$			410.758i			1.38770i
$297$	−53.2857	−	45.2594i	−0.179413	−	0.152388i
$298$	−17.4929	+	17.4929i	−0.0587009	+	0.0587009i
$299$		−	474.085i		−	1.58557i
$300$	−115.439	+	193.129i	−0.384795	+	0.643765i
$301$	46.0572	−	244.723i	0.153014	−	0.813034i
$302$	82.5025	−	82.5025i	0.273187	−	0.273187i
$303$	68.1319	−	20.2490i	0.224858	−	0.0668285i
$304$	−82.8966			−0.272686
$305$	−158.820	+	361.630i	−0.520720	+	1.18567i
$306$	6.19947	−	4.04204i	0.0202597	−	0.0132093i
$307$	115.748	−	115.748i	0.377030	−	0.377030i	−0.492999	−	0.870030i	$-0.664099\pi$
$307$	115.748	−	115.748i	0.377030	−	0.377030i	0.870030	+	0.492999i	$0.164099\pi$
$308$	−44.8981	+	30.6751i	−0.145773	+	0.0995946i
$309$	−293.399	−	158.957i	−0.949511	−	0.514424i
$310$	55.9714	+	143.633i	0.180553	+	0.463333i
$311$	87.4973			0.281342			0.140671	−	0.990056i	$-0.455074\pi$
$311$	87.4973			0.281342			0.140671	+	0.990056i	$0.455074\pi$
$312$	−75.6486	−	254.535i	−0.242463	−	0.815817i
$313$	74.9574	+	74.9574i	0.239481	+	0.239481i	0.816635	−	0.577154i	$-0.195837\pi$
$313$	74.9574	+	74.9574i	0.239481	+	0.239481i	−0.577154	+	0.816635i	$0.695837\pi$
$314$		−	202.061i		−	0.643506i
$315$	−227.599	+	217.770i	−0.722535	+	0.691334i
$316$	227.407			0.719643
$317$	393.091	−	393.091i	1.24003	−	1.24003i	0.280048	−	0.959986i	$-0.409650\pi$
$317$	393.091	−	393.091i	1.24003	−	1.24003i	0.959986	−	0.280048i	$-0.0903503\pi$
$318$	138.923	−	41.2883i	0.436864	−	0.129838i
$319$		−	29.9143i		−	0.0937751i
$320$	−26.1370	+	59.5135i	−0.0816781	+	0.185980i
$321$	−252.361	+	465.802i	−0.786173	+	1.45110i
$322$	−216.702	+	148.055i	−0.672988	+	0.459797i
$323$	−9.64022	−	9.64022i	−0.0298459	−	0.0298459i
$324$	222.350	+	98.0286i	0.686265	+	0.302557i
$325$	−13.3478	+	315.835i	−0.0410703	+	0.971801i
$326$			137.398i			0.421465i
$327$	62.3781	+	209.884i	0.190759	+	0.641846i
$328$	−84.8829	−	84.8829i	−0.258789	−	0.258789i
$329$	440.198	+	82.8456i	1.33799	+	0.251810i
$330$	23.8281	+	30.6724i	0.0722063	+	0.0929466i
$331$	244.986			0.740138			0.370069	−	0.929004i	$-0.379334\pi$
$331$	244.986			0.740138			0.370069	+	0.929004i	$0.379334\pi$
$332$	161.035	+	161.035i	0.485047	+	0.485047i
$333$	−516.776	−	108.862i	−1.55188	−	0.326912i
$334$	−293.089			−0.877511
$335$	186.083	+	477.525i	0.555472	+	1.42545i
$336$	66.2300	−	81.4776i	0.197113	−	0.242493i
$337$	−333.576	−	333.576i	−0.989840	−	0.989840i	0.0101086	−	0.999949i	$-0.496782\pi$
$337$	−333.576	−	333.576i	−0.989840	−	0.989840i	−0.999949	+	0.0101086i	$0.996782\pi$
$338$	6.44308	+	6.44308i	0.0190624	+	0.0190624i
$339$	193.335	+	104.745i	0.570309	+	0.308981i
$340$	11.4929	−	4.47857i	0.0338025	−	0.0131723i
$341$	−79.8317			−0.234111
$342$	−30.7577	+	146.009i	−0.0899348	+	0.426928i
$343$	77.3019	+	334.176i	0.225370	+	0.974273i
$344$	249.019			0.723894
$345$	−345.021	−	444.124i	−1.00006	−	1.28732i
$346$		−	163.263i		−	0.471857i
$347$	226.173	−	226.173i	0.651796	−	0.651796i	−0.301629	−	0.953425i	$-0.597531\pi$
$347$	226.173	−	226.173i	0.651796	−	0.651796i	0.953425	+	0.301629i	$0.0975305\pi$
$348$	29.6212	+	99.6664i	0.0851183	+	0.286398i
$349$	−247.335			−0.708696			−0.354348	−	0.935114i	$-0.615297\pi$
$349$	−247.335			−0.708696			−0.354348	+	0.935114i	$0.615297\pi$
$350$	148.535	−	92.5326i	0.424386	−	0.264379i
$351$	340.280	−	27.7152i	0.969458	−	0.0789607i
$352$	−60.4214	−	60.4214i	−0.171652	−	0.171652i
$353$	−276.422	+	276.422i	−0.783065	+	0.783065i	−0.980347	−	0.197281i	$-0.936789\pi$
$353$	−276.422	+	276.422i	−0.783065	+	0.783065i	0.197281	+	0.980347i	$0.436789\pi$
$354$	−125.616	−	68.0559i	−0.354847	−	0.192248i
$355$	−98.5552	+	224.409i	−0.277620	+	0.632137i
$356$	−42.1600			−0.118427
$357$	17.1772	−	1.77317i	0.0481154	−	0.00496687i
$358$	167.493	−	167.493i	0.467857	−	0.467857i
$359$	−392.633			−1.09368			−0.546842	−	0.837236i	$-0.684170\pi$
$359$	−392.633			−1.09368			−0.546842	+	0.837236i	$0.684170\pi$
$360$	−256.108	−	183.394i	−0.711412	−	0.509429i
$361$	−86.1262			−0.238577
$362$	−161.125	−	161.125i	−0.445098	−	0.445098i
$363$	328.677	−	97.6838i	0.905446	−	0.269101i
$364$	49.1124	−	260.957i	0.134924	−	0.716915i
$365$	66.8451	+	171.537i	0.183137	+	0.469965i
$366$	−208.365	−	112.888i	−0.569305	−	0.308437i
$367$	−232.458	+	232.458i	−0.633401	+	0.633401i	−0.948919	−	0.315519i	$-0.897821\pi$
$367$	−232.458	+	232.458i	−0.633401	+	0.633401i	0.315519	+	0.948919i	$0.397821\pi$
$368$	132.557	+	132.557i	0.360210	+	0.360210i
$369$	129.288	−	84.2951i	0.350373	−	0.228442i
$370$	268.634	+	117.978i	0.726037	+	0.318859i
$371$	332.332	+	62.5453i	0.895774	+	0.168586i
$372$	265.978	−	79.0496i	0.714995	−	0.212499i
$373$	−194.536	+	194.536i	−0.521543	+	0.521543i	−0.918037	−	0.396494i	$-0.870227\pi$
$373$	−194.536	+	194.536i	−0.521543	+	0.521543i	0.396494	+	0.918037i	$0.370227\pi$
$374$		−	2.12925i		−	0.00569319i
$375$	217.348	+	305.589i	0.579596	+	0.814904i
$376$			447.926i			1.19129i
$377$	103.295	+	103.295i	0.273992	+	0.273992i
$378$	−118.936	−	146.885i	−0.314646	−	0.388584i
$379$			345.209i			0.910843i	0.890276	+	0.455422i	$0.150511\pi$
$379$			345.209i			0.910843i	−0.890276	+	0.455422i	$0.849489\pi$
$380$	−100.000	+	227.698i	−0.263158	+	0.599207i
$381$	80.7531	+	43.7503i	0.211950	+	0.114830i
$382$	262.295	+	262.295i	0.686637	+	0.686637i
$383$	46.7051	−	46.7051i	0.121945	−	0.121945i	−0.643500	−	0.765446i	$-0.722518\pi$
$383$	46.7051	−	46.7051i	0.121945	−	0.121945i	0.765446	+	0.643500i	$0.222518\pi$
$384$	313.893	+	170.060i	0.817428	+	0.442865i
$385$	16.7201	+	89.0718i	0.0434288	+	0.231355i
$386$			115.447i			0.299085i
$387$	−65.9967	+	313.292i	−0.170534	+	0.809540i
$388$	−77.8991	−	77.8991i	−0.200771	−	0.200771i
$389$	747.341			1.92119			0.960593	−	0.277960i	$-0.0896582\pi$
$389$	747.341			1.92119			0.960593	+	0.277960i	$0.0896582\pi$
$390$	−188.192	−	23.6336i	−0.482544	−	0.0605991i
$391$			30.8307i			0.0788509i
$392$	−314.113	+	137.775i	−0.801309	+	0.351468i
$393$	−625.927	+	186.028i	−1.59269	+	0.473353i
$394$		−	257.662i		−	0.653964i
$395$	152.404	−	347.020i	0.385832	−	0.878533i
$396$	58.5643	−	38.1838i	0.147890	−	0.0964237i
$397$	320.867	−	320.867i	0.808230	−	0.808230i	−0.176135	−	0.984366i	$-0.556360\pi$
$397$	320.867	−	320.867i	0.808230	−	0.808230i	0.984366	+	0.176135i	$0.0563597\pi$
$398$	−22.0872	+	22.0872i	−0.0554954	+	0.0554954i
$399$	−219.610	+	270.168i	−0.550400	+	0.677114i
$400$	−84.5774	−	92.0417i	−0.211443	−	0.230104i
$401$			472.603i			1.17856i	0.807928	+	0.589281i	$0.200589\pi$
$401$			472.603i			1.17856i	−0.807928	+	0.589281i	$0.799411\pi$
$402$	−294.758	+	87.6030i	−0.733229	+	0.217918i
$403$	275.662	−	275.662i	0.684025	−	0.684025i
$404$			71.0773i			0.175934i
$405$	298.605	−	273.606i	0.737295	−	0.675571i
$406$	14.9571	−	79.4742i	0.0368402	−	0.195749i
$407$	−107.440	+	107.440i	−0.263980	+	0.263980i
$408$	4.91958	+	16.5529i	0.0120578	+	0.0405708i
$409$	121.806			0.297813			0.148907	−	0.988851i	$-0.452425\pi$
$409$	121.806			0.297813			0.148907	+	0.988851i	$0.452425\pi$
$410$	−79.8930	+	31.1329i	−0.194861	+	0.0759339i
$411$	−65.0128	+	119.999i	−0.158182	+	0.291968i
$412$	235.956	−	235.956i	0.572708	−	0.572708i
$413$	−188.054	−	275.249i	−0.455338	−	0.666462i
$414$	282.663	−	184.295i	0.682760	−	0.445158i
$415$	353.661	−	137.815i	0.852194	−	0.332085i
$416$	417.275			1.00306
$417$	323.713	−	96.2087i	0.776291	−	0.230716i
$418$	30.3559	+	30.3559i	0.0726219	+	0.0726219i
$419$			91.1169i			0.217463i	0.994071	+	0.108731i	$0.0346788\pi$
$419$			91.1169i			0.217463i	−0.994071	+	0.108731i	$0.965321\pi$
$420$	−143.906	−	280.207i	−0.342633	−	0.667160i
$421$	61.3238			0.145662			0.0728311	−	0.997344i	$-0.476797\pi$
$421$	61.3238			0.145662			0.0728311	+	0.997344i	$0.476797\pi$
$422$	68.2998	−	68.2998i	0.161848	−	0.161848i
$423$	−563.536	−	118.712i	−1.33224	−	0.280643i
$424$			338.167i			0.797563i
$425$	0.868036	−	20.5394i	0.00204244	−	0.0483280i
$426$	−129.301	−	70.0524i	−0.303523	−	0.164442i
$427$	−311.936	−	456.569i	−0.730528	−	1.06925i
$428$	−374.605	−	374.605i	−0.875245	−	0.875245i
$429$	46.7903	−	86.3643i	0.109068	−	0.201315i
$430$	71.5233	−	162.857i	0.166333	−	0.378738i
$431$		−	179.188i		−	0.415749i	−0.978156	−	0.207874i	$-0.933346\pi$
$431$		−	179.188i		−	0.415749i	0.978156	−	0.207874i	$-0.0666545\pi$
$432$	−87.3950	+	102.894i	−0.202303	+	0.238180i
$433$	−234.230	−	234.230i	−0.540947	−	0.540947i	0.382860	−	0.923806i	$-0.374939\pi$
$433$	−234.230	−	234.230i	−0.540947	−	0.540947i	−0.923806	+	0.382860i	$0.874939\pi$
$434$	−212.092	−	39.9159i	−0.488690	−	0.0919721i
$435$	171.941	+	21.5928i	0.395267	+	0.0496386i
$436$	−218.957			−0.502195
$437$	−439.542	−	439.542i	−1.00582	−	1.00582i
$438$	−105.883	+	31.4689i	−0.241743	+	0.0718468i
$439$	−526.311			−1.19889			−0.599443	−	0.800417i	$-0.704611\pi$
$439$	−526.311			−1.19889			−0.599443	+	0.800417i	$0.704611\pi$
$440$	−84.4426	+	32.9058i	−0.191915	+	0.0747859i
$441$	−90.0873	−	431.700i	−0.204280	−	0.978913i
$442$	7.35238	+	7.35238i	0.0166344	+	0.0166344i
$443$	207.809	+	207.809i	0.469094	+	0.469094i	0.901621	−	0.432527i	$-0.142378\pi$
$443$	207.809	+	207.809i	0.469094	+	0.469094i	−0.432527	+	0.901621i	$0.642378\pi$
$444$	251.574	−	464.348i	0.566608	−	1.04583i
$445$	−28.2548	+	64.3357i	−0.0634939	+	0.144575i
$446$	113.065			0.253509
$447$	71.1405	−	21.1432i	0.159151	−	0.0473002i
$448$	−51.3354	−	75.1377i	−0.114588	−	0.167718i
$449$	315.151			0.701895			0.350947	−	0.936395i	$-0.385860\pi$
$449$	315.151			0.701895			0.350947	+	0.936395i	$0.385860\pi$
$450$	−193.498	+	114.819i	−0.429996	+	0.255153i
$451$		−	44.4047i		−	0.0984583i
$452$	−155.483	+	155.483i	−0.343988	+	0.343988i
$453$	−335.524	+	99.7188i	−0.740670	+	0.220130i
$454$	80.3024			0.176878
$455$	−365.303	−	249.833i	−0.802864	−	0.549083i
$456$	−306.125	−	165.852i	−0.671327	−	0.363710i
$457$	−357.774	−	357.774i	−0.782875	−	0.782875i	0.197440	−	0.980315i	$-0.436737\pi$
$457$	−357.774	−	357.774i	−0.782875	−	0.782875i	−0.980315	+	0.197440i	$0.936737\pi$
$458$	−108.761	+	108.761i	−0.237470	+	0.237470i
$459$	−22.1291	+	1.80237i	−0.0482115	+	0.00392674i
$460$	524.012	−	204.198i	1.13916	−	0.443910i
$461$	−563.655			−1.22268			−0.611339	−	0.791369i	$-0.709369\pi$
$461$	−563.655			−1.22268			−0.611339	+	0.791369i	$0.709369\pi$
$462$	−54.0891	+	5.58352i	−0.117076	+	0.0120855i
$463$	−26.9857	+	26.9857i	−0.0582845	+	0.0582845i	−0.735648	−	0.677364i	$-0.763122\pi$
$463$	−26.9857	+	26.9857i	−0.0582845	+	0.0582845i	0.677364	+	0.735648i	$0.263122\pi$
$464$	−57.7639			−0.124491
$465$	57.6244	−	458.857i	0.123923	−	0.986788i
$466$	71.1262			0.152631
$467$	271.529	+	271.529i	0.581432	+	0.581432i	0.935297	−	0.353864i	$-0.115133\pi$
$467$	271.529	+	271.529i	0.581432	+	0.581432i	−0.353864	+	0.935297i	$0.615133\pi$
$468$	−70.3747	+	334.075i	−0.150373	+	0.713835i
$469$	−705.122	−	132.705i	−1.50346	−	0.282953i
$470$	292.941	+	128.653i	0.623278	+	0.273730i
$471$	−288.761	+	532.987i	−0.613080	+	1.13161i
$472$	235.718	−	235.718i	0.499403	−	0.499403i
$473$	65.1347	+	65.1347i	0.137705	+	0.137705i
$474$	199.948	+	108.327i	0.421831	+	0.228539i
$475$	280.447	+	305.198i	0.590415	+	0.642521i
$476$	−3.19388	+	16.9706i	−0.00670983	+	0.0356524i
$477$	−425.448	−	89.6231i	−0.891925	−	0.187889i
$478$	−93.1548	+	93.1548i	−0.194884	+	0.194884i
$479$			517.973i			1.08136i	0.841227	+	0.540682i	$0.181834\pi$
$479$			517.973i			1.08136i	−0.841227	+	0.540682i	$0.818166\pi$
$480$	390.904	−	303.676i	0.814382	−	0.632659i
$481$		−	741.987i		−	1.54259i
$482$	72.8542	+	72.8542i	0.151150	+	0.151150i
$483$	783.188	−	80.8471i	1.62151	−	0.167385i
$484$			342.886i			0.708442i
$485$	−171.079	+	66.6667i	−0.352741	+	0.137457i
$486$	148.804	+	192.110i	0.306182	+	0.395288i
$487$	369.310	+	369.310i	0.758336	+	0.758336i	0.976019	−	0.217684i	$-0.0698501\pi$
$487$	369.310	+	369.310i	0.758336	+	0.758336i	−0.217684	+	0.976019i	$0.569850\pi$
$488$	390.998	−	390.998i	0.801226	−	0.801226i
$489$	196.352	−	362.421i	0.401537	−	0.741147i
$490$	−0.115057	+	245.000i	−0.000234810	+	0.500000i
$491$		−	421.951i		−	0.859370i	−0.902979	−	0.429685i	$-0.858625\pi$
$491$		−	421.951i		−	0.859370i	0.902979	−	0.429685i	$-0.141375\pi$
$492$	43.9696	+	147.945i	0.0893692	+	0.300700i
$493$	−6.71748	−	6.71748i	−0.0136257	−	0.0136257i
$494$	−209.640			−0.424373
$495$	−19.0194	−	114.958i	−0.0384230	−	0.232239i
$496$			154.154i			0.310794i
$497$	−193.571	−	283.323i	−0.389479	−	0.570067i
$498$	64.8798	+	218.301i	0.130281	+	0.438356i
$499$		−	109.267i		−	0.218971i	−0.993988	−	0.109486i	$-0.965080\pi$
$499$		−	109.267i		−	0.218971i	0.993988	−	0.109486i	$-0.0349204\pi$
$500$	−354.846	+	121.283i	−0.709691	+	0.242567i
$501$	773.095	+	418.846i	1.54310	+	0.836021i
$502$	256.959	−	256.959i	0.511871	−	0.511871i
$503$	−134.096	+	134.096i	−0.266592	+	0.266592i	−0.827725	−	0.561133i	$-0.810365\pi$
$503$	−134.096	+	134.096i	−0.266592	+	0.266592i	0.561133	+	0.827725i	$0.310365\pi$
$504$	407.590	−	168.378i	0.808711	−	0.334083i
$505$	108.463	+	47.6345i	0.214778	+	0.0943258i
$506$		−	97.0824i		−	0.191862i
$507$	−7.78759	−	26.2029i	−0.0153601	−	0.0516823i
$508$	−64.9428	+	64.9428i	−0.127840	+	0.127840i
$509$			459.197i			0.902154i	0.892485	+	0.451077i	$0.148960\pi$
$509$			459.197i			0.902154i	−0.892485	+	0.451077i	$0.851040\pi$
$510$	12.2385	+	1.53694i	0.0239971	+	0.00301361i
$511$	−253.295	−	47.6704i	−0.495685	−	0.0932885i
$512$	−215.668	+	215.668i	−0.421226	+	0.421226i
$513$	289.790	−	341.181i	0.564893	−	0.665071i
$514$	−122.918			−0.239139
$515$	−201.933	−	518.198i	−0.392103	−	1.00621i
$516$	−281.508	−	152.515i	−0.545558	−	0.295571i
$517$	−117.161	+	117.161i	−0.226618	+	0.226618i
$518$	−339.159	+	231.719i	−0.654747	+	0.447334i
$519$	−233.315	+	430.646i	−0.449547	+	0.829762i
$520$	177.958	−	405.208i	0.342228	−	0.779247i
$521$	303.734			0.582983			0.291491	−	0.956573i	$-0.405848\pi$
$521$	303.734			0.582983			0.291491	+	0.956573i	$0.405848\pi$
$522$	−21.4325	+	101.742i	−0.0410585	+	0.194908i
$523$	249.060	+	249.060i	0.476215	+	0.476215i	0.903919	−	0.427704i	$-0.140677\pi$
$523$	249.060	+	249.060i	0.476215	+	0.476215i	−0.427704	+	0.903919i	$0.640677\pi$
$524$		−	652.986i		−	1.24616i
$525$	−524.035	+	31.8097i	−0.998163	+	0.0605899i
$526$	138.029			0.262412
$527$	−17.9268	+	17.9268i	−0.0340168	+	0.0340168i
$528$	11.0651	+	37.2308i	0.0209567	+	0.0705130i
$529$			876.714i			1.65730i
$530$	221.159	+	97.1281i	0.417281	+	0.183261i
$531$	234.086	+	359.029i	0.440840	+	0.676138i
$532$	−196.409	−	287.477i	−0.369190	−	0.540370i
$533$	153.331	+	153.331i	0.287675	+	0.287675i
$534$	−37.0692	−	20.0833i	−0.0694181	−	0.0376092i
$535$	−822.695	+	320.590i	−1.53775	+	0.599234i
$536$		−	717.501i		−	1.33862i
$537$	−681.165	+	202.444i	−1.26846	+	0.376992i
$538$	−84.7209	−	84.7209i	−0.157474	−	0.157474i
$539$	−118.198	−	46.1237i	−0.219291	−	0.0855726i
$540$	177.199	+	364.178i	0.328147	+	0.674403i
$541$	−198.562			−0.367028			−0.183514	−	0.983017i	$-0.558747\pi$
$541$	−198.562			−0.367028			−0.183514	+	0.983017i	$0.558747\pi$
$542$	174.405	+	174.405i	0.321780	+	0.321780i
$543$	194.748	+	655.270i	0.358653	+	1.20676i
$544$	−27.1362			−0.0498827
$545$	−146.741	+	334.126i	−0.269249	+	0.613075i
$546$	167.491	−	206.052i	0.306761	−	0.377384i
$547$	492.112	+	492.112i	0.899656	+	0.899656i	0.995405	−	0.0957494i	$-0.0305247\pi$
$547$	492.112	+	492.112i	0.899656	+	0.899656i	−0.0957494	+	0.995405i	$0.530525\pi$
$548$	−96.5049	−	96.5049i	−0.176104	−	0.176104i
$549$	388.291	+	595.541i	0.707270	+	1.08477i
$550$	−2.73335	+	64.6762i	−0.00496972	+	0.117593i
$551$	191.537			0.347617
$552$	224.306	+	754.723i	0.406352	+	1.36725i
$553$	299.334	+	438.125i	0.541291	+	0.792269i
$554$	−72.3842			−0.130657
$555$	−539.990	−	695.095i	−0.972955	−	1.25242i
$556$			337.708i			0.607388i
$557$	328.316	−	328.316i	0.589437	−	0.589437i	−0.348042	−	0.937479i	$-0.613153\pi$
$557$	328.316	−	328.316i	0.589437	−	0.589437i	0.937479	+	0.348042i	$0.113153\pi$
$558$	271.517	+	57.1967i	0.486590	+	0.102503i
$559$	−449.825			−0.804695
$560$	171.996	−	32.2862i	0.307136	−	0.0576539i
$561$	−3.04287	+	5.61644i	−0.00542400	+	0.0100115i
$562$	4.47857	+	4.47857i	0.00796898	+	0.00796898i
$563$	510.844	−	510.844i	0.907361	−	0.907361i	−0.0886978	−	0.996059i	$-0.528271\pi$
$563$	510.844	−	510.844i	0.907361	−	0.907361i	0.996059	+	0.0886978i	$0.0282706\pi$
$564$	274.337	−	506.364i	0.486414	−	0.897809i
$565$	133.063	+	341.466i	0.235510	+	0.604364i
$566$	−342.455			−0.605043
$567$	103.814	+	557.415i	0.183094	+	0.983095i
$568$	242.633	−	242.633i	0.427171	−	0.427171i
$569$	−789.111			−1.38684			−0.693419	−	0.720534i	$-0.743897\pi$
$569$	−789.111			−1.38684			−0.693419	+	0.720534i	$0.743897\pi$
$570$	−196.391	+	152.568i	−0.344546	+	0.267663i
$571$	−320.476			−0.561254			−0.280627	−	0.959817i	$-0.590542\pi$
$571$	−320.476			−0.561254			−0.280627	+	0.959817i	$0.590542\pi$
$572$	69.4554	+	69.4554i	0.121426	+	0.121426i
$573$	−317.030	−	1066.71i	−0.553280	−	1.86162i
$574$	22.2023	−	117.971i	0.0386800	−	0.205525i
$575$	39.5778	−	936.485i	0.0688309	−	1.62867i
$576$	63.9012	+	98.0084i	0.110940	+	0.170153i
$577$	313.311	−	313.311i	0.542999	−	0.542999i	−0.381408	−	0.924407i	$-0.624561\pi$
$577$	313.311	−	313.311i	0.542999	−	0.542999i	0.924407	+	0.381408i	$0.124561\pi$
$578$	203.876	+	203.876i	0.352726	+	0.352726i
$579$	164.983	−	304.520i	0.284944	−	0.525942i
$580$	−69.6819	+	158.665i	−0.120141	+	0.273560i
$581$	−98.2827	+	522.222i	−0.169161	+	0.898833i
$582$	−31.3849	−	105.601i	−0.0539260	−	0.181445i
$583$	−88.4524	+	88.4524i	−0.151719	+	0.151719i
$584$		−	257.742i		−	0.441339i
$585$	462.630	+	331.281i	0.790820	+	0.566292i
$586$			471.443i			0.804510i
$587$	−149.545	−	149.545i	−0.254762	−	0.254762i	0.568158	−	0.822920i	$-0.307656\pi$
$587$	−149.545	−	149.545i	−0.254762	−	0.254762i	−0.822920	+	0.568158i	$0.807656\pi$
$588$	439.476	+	36.6318i	0.747408	+	0.0622991i
$589$		−	511.152i		−	0.867831i
$590$	−86.4556	−	221.861i	−0.146535	−	0.376036i
$591$	−368.219	+	679.648i	−0.623044	+	1.15000i
$592$	207.464	+	207.464i	0.350446	+	0.350446i
$593$	198.048	−	198.048i	0.333977	−	0.333977i	−0.520118	−	0.854095i	$-0.674112\pi$
$593$	198.048	−	198.048i	0.333977	−	0.333977i	0.854095	+	0.520118i	$0.174112\pi$
$594$	69.6819	−	5.67547i	0.117310	−	0.00955466i
$595$	23.7564	+	16.2471i	0.0399267	+	0.0273061i
$596$			74.2159i			0.124523i
$597$	89.8248	−	26.6962i	0.150460	−	0.0447173i
$598$	335.229	+	335.229i	0.560584	+	0.560584i
$599$	−475.156			−0.793248			−0.396624	−	0.917981i	$-0.629818\pi$
$599$	−475.156			−0.793248			−0.396624	+	0.917981i	$0.629818\pi$
$600$	−128.183	−	509.111i	−0.213639	−	0.848518i
$601$		−	373.965i		−	0.622237i	−0.950371	−	0.311119i	$-0.899296\pi$
$601$		−	373.965i		−	0.622237i	0.950371	−	0.311119i	$-0.100704\pi$
$602$	140.478	+	205.613i	0.233352	+	0.341549i
$603$	902.690	+	190.157i	1.49700	+	0.315351i
$604$		−	350.029i		−	0.579518i
$605$	523.239	+	229.795i	0.864858	+	0.379826i
$606$	−33.8583	+	62.4948i	−0.0558718	+	0.103127i
$607$	−632.018	+	632.018i	−1.04122	+	1.04122i	−0.0421025	+	0.999113i	$0.513406\pi$
$607$	−632.018	+	632.018i	−1.04122	+	1.04122i	−0.999113	+	0.0421025i	$0.986594\pi$
$608$	386.871	−	386.871i	0.636300	−	0.636300i
$609$	−153.028	+	188.258i	−0.251278	+	0.309127i
$610$	−143.408	−	368.013i	−0.235096	−	0.603300i
$611$		−	809.125i		−	1.32426i
$612$	4.57661	−	21.7255i	0.00747812	−	0.0354992i
$613$	587.183	−	587.183i	0.957885	−	0.957885i	−0.0412636	−	0.999148i	$-0.513138\pi$
$613$	587.183	−	587.183i	0.957885	−	0.957885i	0.999148	+	0.0412636i	$0.0131383\pi$
$614$			163.693i			0.266601i
$615$	255.229	+	32.0523i	0.415007	+	0.0521176i
$616$	23.4667	−	124.689i	0.0380953	−	0.202418i
$617$	−111.144	+	111.144i	−0.180136	+	0.180136i	−0.791415	−	0.611279i	$-0.790655\pi$
$617$	−111.144	+	111.144i	−0.180136	+	0.180136i	0.611279	+	0.791415i	$0.290655\pi$
$618$	319.864	−	95.0646i	0.517579	−	0.153826i
$619$	716.455			1.15744			0.578720	−	0.815526i	$-0.303552\pi$
$619$	716.455			1.15744			0.578720	+	0.815526i	$0.303552\pi$
$620$	423.426	+	185.959i	0.682945	+	0.299934i
$621$	−1008.97	+	82.1785i	−1.62474	+	0.132333i
$622$	−61.8700	+	61.8700i	−0.0994694	+	0.0994694i
$623$	−55.4949	−	81.2259i	−0.0890769	−	0.130379i
$624$	−166.768	−	90.3512i	−0.267256	−	0.144794i
$625$	−52.7333	+	622.771i	−0.0843734	+	0.996434i
$626$	−106.006			−0.169338
$627$	−36.6905	−	123.452i	−0.0585175	−	0.196894i
$628$	−428.636	−	428.636i	−0.682541	−	0.682541i
$629$			48.2529i			0.0767137i
$630$	6.94979	−	314.923i	0.0110314	−	0.499878i
$631$	4.81666			0.00763338			0.00381669	−	0.999993i	$-0.498785\pi$
$631$	4.81666			0.00763338			0.00381669	+	0.999993i	$0.498785\pi$
$632$	−375.203	+	375.203i	−0.593675	+	0.593675i
$633$	−277.764	+	82.5522i	−0.438805	+	0.130414i
$634$			555.914i			0.876836i
$635$	55.5786	+	142.625i	0.0875254	+	0.224607i
$636$	207.114	−	382.286i	0.325651	−	0.601078i
$637$	567.409	−	248.875i	0.890751	−	0.390699i
$638$	21.1526	+	21.1526i	0.0331545	+	0.0331545i
$639$	240.953	+	369.562i	0.377079	+	0.578344i
$640$	216.038	+	554.394i	0.337559	+	0.866241i
$641$			121.164i			0.189024i	0.995524	+	0.0945120i	$0.0301291\pi$
$641$			121.164i			0.189024i	−0.995524	+	0.0945120i	$0.969871\pi$
$642$	−150.925	−	507.818i	−0.235086	−	0.790994i
$643$	524.336	+	524.336i	0.815453	+	0.815453i	0.985445	−	0.169993i	$-0.0543744\pi$
$643$	524.336	+	524.336i	0.815453	+	0.815453i	−0.169993	+	0.985445i	$0.554374\pi$
$644$	−145.624	+	773.766i	−0.226124	+	1.20150i
$645$	−421.396	+	327.365i	−0.653328	+	0.507543i
$646$	13.6333			0.0211042
$647$	−305.897	−	305.897i	−0.472792	−	0.472792i	0.430025	−	0.902817i	$-0.358505\pi$
$647$	−305.897	−	305.897i	−0.472792	−	0.472792i	−0.902817	+	0.430025i	$0.858505\pi$
$648$	−528.597	+	205.119i	−0.815736	+	0.316542i
$649$	123.311			0.190002
$650$	−213.891	−	232.768i	−0.329063	−	0.358104i
$651$	502.402	+	408.384i	0.771739	+	0.627317i
$652$	291.464	+	291.464i	0.447031	+	0.447031i
$653$	307.322	+	307.322i	0.470631	+	0.470631i	0.902119	−	0.431488i	$-0.142011\pi$
$653$	307.322	+	307.322i	0.470631	+	0.470631i	−0.431488	+	0.902119i	$0.642011\pi$
$654$	−192.518	−	104.302i	−0.294370	−	0.159484i
$655$	−996.449	−	437.618i	−1.52130	−	0.668119i
$656$	−85.7446			−0.130708
$657$	324.266	+	68.3085i	0.493555	+	0.103970i
$658$	−369.847	+	252.686i	−0.562078	+	0.384021i
$659$	−903.538			−1.37107			−0.685537	−	0.728038i	$-0.740432\pi$
$659$	−903.538			−1.37107			−0.685537	+	0.728038i	$0.740432\pi$
$660$	115.613	+	14.5190i	0.175171	+	0.0219984i
$661$		−	1162.10i		−	1.75809i	−0.476737	−	0.879046i	$-0.658180\pi$
$661$		−	1162.10i		−	1.75809i	0.476737	−	0.879046i	$-0.341820\pi$
$662$	−173.231	+	173.231i	−0.261678	+	0.261678i
$663$	−8.88664	−	29.9009i	−0.0134037	−	0.0450994i
$664$	−531.390			−0.800286
$665$	−570.315	+	107.057i	−0.857617	+	0.160987i
$666$	442.393	−	288.439i	0.664254	−	0.433092i
$667$	−306.281	−	306.281i	−0.459192	−	0.459192i
$668$	−621.735	+	621.735i	−0.930741	+	0.930741i
$669$	−298.237	−	161.579i	−0.445796	−	0.241523i
$670$	−469.242	−	206.080i	−0.700361	−	0.307583i
$671$	204.543			0.304832
$672$	71.1590	+	689.337i	0.105891	+	1.02580i
$673$	256.857	−	256.857i	0.381660	−	0.381660i	−0.490040	−	0.871700i	$-0.663018\pi$
$673$	256.857	−	256.857i	0.381660	−	0.381660i	0.871700	+	0.490040i	$0.163018\pi$
$674$	471.748			0.699923
$675$	674.486	−	26.3399i	0.999238	−	0.0390221i
$676$	27.3357			0.0404374
$677$	248.270	+	248.270i	0.366721	+	0.366721i	0.866280	−	0.499559i	$-0.166504\pi$
$677$	248.270	+	248.270i	0.366721	+	0.366721i	−0.499559	+	0.866280i	$0.666504\pi$
$678$	−210.774	+	62.6427i	−0.310876	+	0.0923933i
$679$	47.5432	−	252.619i	0.0700194	−	0.372046i
$680$	−11.5730	+	26.3515i	−0.0170191	+	0.0387522i
$681$	−211.818	−	114.758i	−0.311039	−	0.168514i
$682$	56.4496	−	56.4496i	0.0827706	−	0.0827706i
$683$	216.136	+	216.136i	0.316450	+	0.316450i	0.847402	−	0.530952i	$-0.178165\pi$
$683$	216.136	+	216.136i	0.316450	+	0.316450i	−0.530952	+	0.847402i	$0.678165\pi$
$684$	244.486	+	374.980i	0.357435	+	0.548216i
$685$	−211.941	+	82.5897i	−0.309403	+	0.120569i
$686$	−290.959	−	181.637i	−0.424138	−	0.264777i
$687$	442.314	−	131.457i	0.643835	−	0.191350i
$688$	125.774	−	125.774i	0.182811	−	0.182811i
$689$		−	610.859i		−	0.886587i
$690$	558.010	+	70.0763i	0.808710	+	0.101560i
$691$		−	167.027i		−	0.241717i	−0.992670	−	0.120859i	$-0.961435\pi$
$691$		−	167.027i		−	0.241717i	0.992670	−	0.120859i	$-0.0385648\pi$
$692$	−346.332	−	346.332i	−0.500480	−	0.500480i
$693$	150.653	+	62.5695i	0.217392	+	0.0902879i
$694$			319.857i			0.460889i
$695$	515.338	+	226.325i	0.741493	+	0.325647i
$696$	−213.314	−	115.569i	−0.306485	−	0.166047i
$697$	−9.97142	−	9.97142i	−0.0143062	−	0.0143062i
$698$	174.892	−	174.892i	0.250562	−	0.250562i
$699$	−187.613	−	101.645i	−0.268402	−	0.145415i
$700$	118.800	−	511.382i	0.169714	−	0.730546i
$701$			602.095i			0.858908i	0.903089	+	0.429454i	$0.141294\pi$
$701$			602.095i			0.858908i	−0.903089	+	0.429454i	$0.858706\pi$
$702$	−221.017	+	260.212i	−0.314838	+	0.370672i
$703$	−687.923	−	687.923i	−0.978554	−	0.978554i
$704$	33.6616			0.0478148
$705$	−588.850	−	757.990i	−0.835249	−	1.07516i
$706$		−	390.920i		−	0.553711i
$707$	−136.938	+	93.5584i	−0.193689	+	0.132332i
$708$	−410.840	+	122.103i	−0.580282	+	0.172462i
$709$		−	37.8334i		−	0.0533616i	−0.999644	−	0.0266808i	$-0.991506\pi$
$709$		−	37.8334i		−	0.0533616i	0.999644	−	0.0266808i	$-0.00849377\pi$
$710$	−88.9918	−	228.370i	−0.125341	−	0.321648i
$711$	−372.605	−	571.482i	−0.524057	−	0.803772i
$712$	69.5605	−	69.5605i	0.0976973	−	0.0976973i
$713$	−817.367	+	817.367i	−1.14638	+	1.14638i
$714$	−10.8923	+	13.3999i	−0.0152553	+	0.0187674i
$715$	152.536	−	59.4405i	0.213337	−	0.0831336i
$716$		−	710.612i		−	0.992475i
$717$	378.845	−	112.594i	0.528375	−	0.157035i
$718$	277.633	−	277.633i	0.386676	−	0.386676i
$719$			408.265i			0.567824i	0.958850	+	0.283912i	$0.0916324\pi$
$719$			408.265i			0.567824i	−0.958850	+	0.283912i	$0.908368\pi$
$720$	−221.982	+	36.7260i	−0.308309	+	0.0510084i
$721$	765.181	+	144.008i	1.06128	+	0.199734i
$722$	60.9004	−	60.9004i	0.0843496	−	0.0843496i
$723$	−88.0571	−	296.286i	−0.121794	−	0.409800i
$724$	−683.597			−0.944195
$725$	195.421	+	212.667i	0.269546	+	0.293334i
$726$	−163.337	+	301.483i	−0.224982	+	0.415265i
$727$	660.880	−	660.880i	0.909051	−	0.909051i	−0.0871447	−	0.996196i	$-0.527774\pi$
$727$	660.880	−	660.880i	0.909051	−	0.909051i	0.996196	+	0.0871447i	$0.0277742\pi$
$728$	349.526	+	511.589i	0.480118	+	0.702732i
$729$	−117.969	−	719.392i	−0.161823	−	0.986820i
$730$	−168.562	−	74.0286i	−0.230907	−	0.101409i
$731$	29.2530			0.0400178
$732$	−681.481	+	202.538i	−0.930985	+	0.276692i
$733$	526.757	+	526.757i	0.718632	+	0.718632i	0.968325	−	0.249693i	$-0.0803298\pi$
$733$	526.757	+	526.757i	0.718632	+	0.718632i	−0.249693	+	0.968325i	$0.580330\pi$
$734$		−	328.745i		−	0.447882i
$735$	350.427	−	646.085i	0.476772	−	0.879027i
$736$	−1237.26			−1.68107
$737$	187.673	−	187.673i	0.254644	−	0.254644i
$738$	−31.8144	+	151.026i	−0.0431090	+	0.204642i
$739$		−	276.981i		−	0.374805i	−0.982283	−	0.187402i	$-0.939993\pi$
$739$		−	276.981i		−	0.374805i	0.982283	−	0.187402i	$-0.0600069\pi$
$740$	820.127	−	319.589i	1.10828	−	0.431877i
$741$	552.979	+	299.592i	0.746261	+	0.404308i
$742$	−279.221	+	190.768i	−0.376308	+	0.257100i
$743$	698.839	+	698.839i	0.940563	+	0.940563i	0.998330	−	0.0577666i	$-0.0183979\pi$
$743$	698.839	+	698.839i	0.940563	+	0.940563i	−0.0577666	+	0.998330i	$0.518398\pi$
$744$	−308.416	+	569.267i	−0.414538	+	0.765143i
$745$	113.253	+	49.7380i	0.152017	+	0.0667624i
$746$		−	275.115i		−	0.368787i
$747$	140.832	−	668.543i	0.188531	−	0.894971i
$748$	−4.51683	−	4.51683i	−0.00603854	−	0.00603854i
$749$	228.628	−	1214.81i	0.305244	−	1.62190i
$750$	−369.773	−	62.3955i	−0.493030	−	0.0831940i
$751$	488.791			0.650853			0.325426	−	0.945567i	$-0.394492\pi$
$751$	488.791			0.650853			0.325426	+	0.945567i	$0.394492\pi$
$752$	226.237	+	226.237i	0.300846	+	0.300846i
$753$	−1045.01	+	310.580i	−1.38780	+	0.412457i
$754$	−146.081			−0.193742
$755$	−534.139	−	234.582i	−0.707469	−	0.310704i
$756$	−563.892	−	59.2882i	−0.745889	−	0.0784236i
$757$	−269.069	−	269.069i	−0.355441	−	0.355441i	0.506688	−	0.862129i	$-0.330870\pi$
$757$	−269.069	−	269.069i	−0.355441	−	0.355441i	−0.862129	+	0.506688i	$0.830870\pi$
$758$	−244.100	−	244.100i	−0.322032	−	0.322032i
$759$	−138.738	+	256.079i	−0.182791	+	0.337390i
$760$	−210.692	−	540.675i	−0.277226	−	0.711414i
$761$	973.280			1.27895			0.639475	−	0.768812i	$-0.279152\pi$
$761$	973.280			1.27895			0.639475	+	0.768812i	$0.279152\pi$
$762$	−88.0372	+	26.1649i	−0.115534	+	0.0343372i
$763$	−288.211	−	421.845i	−0.377734	−	0.552876i
$764$	1112.82			1.45658
$765$	−30.0857	−	21.5439i	−0.0393278	−	0.0281619i
$766$			66.0510i			0.0862285i
$767$	−425.798	+	425.798i	−0.555147	+	0.555147i
$768$	−491.742	+	146.147i	−0.640289	+	0.190296i
$769$	1055.77			1.37292			0.686458	−	0.727169i	$-0.259165\pi$
$769$	1055.77			1.37292			0.686458	+	0.727169i	$0.259165\pi$
$770$	−74.8062	−	51.1604i	−0.0971508	−	0.0664420i
$771$	324.226	+	175.659i	0.420527	+	0.227832i
$772$	244.900	+	244.900i	0.317228	+	0.317228i
$773$	545.306	−	545.306i	0.705441	−	0.705441i	−0.260132	−	0.965573i	$-0.583766\pi$
$773$	545.306	−	545.306i	0.705441	−	0.705441i	0.965573	+	0.260132i	$0.0837661\pi$
$774$	−174.864	−	268.198i	−0.225923	−	0.346509i
$775$	567.542	−	521.516i	0.732312	−	0.672924i
$776$	257.054			0.331255
$777$	1225.76	−	126.533i	1.57756	−	0.162848i
$778$	−528.450	+	528.450i	−0.679242	+	0.679242i
$779$	284.318			0.364978
$780$	−449.350	+	349.081i	−0.576090	+	0.447540i
$781$	126.929			0.162521
$782$	−21.8006	−	21.8006i	−0.0278780	−	0.0278780i
$783$	201.931	−	237.742i	0.257894	−	0.303629i
$784$	−89.0639	+	228.238i	−0.113602	+	0.291120i
$785$	−941.356	+	366.830i	−1.19918	+	0.467300i
$786$	311.056	−	574.139i	0.395745	−	0.730456i
$787$	−366.303	+	366.303i	−0.465442	+	0.465442i	−0.900434	−	0.434992i	$-0.856751\pi$
$787$	−366.303	+	366.303i	−0.465442	+	0.465442i	0.434992	+	0.900434i	$0.356751\pi$
$788$	−546.583	−	546.583i	−0.693634	−	0.693634i
$789$	−364.085	−	197.254i	−0.461451	−	0.250004i
$790$	137.615	+	353.146i	0.174196	+	0.447020i
$791$	−504.215	−	94.8938i	−0.637440	−	0.119967i
$792$	−33.6262	+	159.626i	−0.0424573	+	0.201548i
$793$	−706.293	+	706.293i	−0.890659	+	0.890659i
$794$			453.775i			0.571505i
$795$	−444.560	−	572.253i	−0.559194	−	0.719816i
$796$			93.7080i			0.117724i
$797$	−124.772	−	124.772i	−0.156552	−	0.156552i	0.624485	−	0.781037i	$-0.285309\pi$
$797$	−124.772	−	124.772i	−0.156552	−	0.156552i	−0.781037	+	0.624485i	$0.785309\pi$
$798$	−35.7506	−	346.325i	−0.0448002	−	0.433992i
$799$			52.6190i			0.0658561i
$800$	824.264	+	34.8351i	1.03033	+	0.0435438i
$801$	69.0789	+	105.950i	0.0862408	+	0.132272i
$802$	−334.181	−	334.181i	−0.416684	−	0.416684i
$803$	67.4162	−	67.4162i	0.0839554	−	0.0839554i
$804$	−439.442	+	811.110i	−0.546570	+	1.00884i
$805$	1083.16	+	740.782i	1.34554	+	0.920226i
$806$			389.845i			0.483678i
$807$	102.400	+	344.545i	0.126890	+	0.426946i
$808$	−117.272	−	117.272i	−0.145138	−	0.145138i
$809$	89.2503			0.110322			0.0551609	−	0.998477i	$-0.482433\pi$
$809$	89.2503			0.110322			0.0551609	+	0.998477i	$0.482433\pi$
$810$	−17.6765	+	404.614i	−0.0218229	+	0.499524i
$811$			959.059i			1.18256i	0.806465	+	0.591282i	$0.201378\pi$
$811$			959.059i			1.18256i	−0.806465	+	0.591282i	$0.798622\pi$
$812$	−136.861	−	200.319i	−0.168549	−	0.246698i
$813$	−210.799	−	709.275i	−0.259285	−	0.872417i
$814$		−	151.943i		−	0.186662i
$815$	640.104	−	249.438i	0.785404	−	0.306058i
$816$	10.8452	+	5.87572i	0.0132907	+	0.00720063i
$817$	−417.049	+	417.049i	−0.510464	+	0.510464i
$818$	−86.1295	+	86.1295i	−0.105293	+	0.105293i
$819$	−736.265	+	304.155i	−0.898980	+	0.371374i
$820$	−103.436	+	235.521i	−0.126141	+	0.287221i
$821$			699.817i			0.852396i	0.904630	+	0.426198i	$0.140147\pi$
$821$			699.817i			0.852396i	−0.904630	+	0.426198i	$0.859853\pi$
$822$	−38.8810	−	130.823i	−0.0473005	−	0.159152i
$823$	945.067	−	945.067i	1.14832	−	1.14832i	0.161436	−	0.986883i	$-0.448387\pi$
$823$	945.067	−	945.067i	1.14832	−	1.14832i	0.986883	−	0.161436i	$-0.0516125\pi$
$824$			778.614i			0.944920i
$825$	99.6372	−	166.694i	0.120772	−	0.202053i
$826$	327.605	+	61.6556i	0.396616	+	0.0746435i
$827$	459.616	−	459.616i	0.555763	−	0.555763i	−0.372335	−	0.928098i	$-0.621443\pi$
$827$	459.616	−	459.616i	0.555763	−	0.555763i	0.928098	+	0.372335i	$0.121443\pi$
$828$	208.669	−	990.567i	0.252015	−	1.19634i
$829$	−197.279			−0.237972			−0.118986	−	0.992896i	$-0.537964\pi$
$829$	−197.279			−0.237972			−0.118986	+	0.992896i	$0.537964\pi$
$830$	−152.626	+	347.526i	−0.183886	+	0.418706i
$831$	190.932	+	103.443i	0.229761	+	0.124480i
$832$	−116.235	+	116.235i	−0.139705	+	0.139705i
$833$	−36.8997	+	16.1849i	−0.0442974	+	0.0194296i
$834$	−160.870	+	296.930i	−0.192890	+	0.356031i
$835$	532.086	+	1365.43i	0.637228	+	1.63525i
$836$	128.789			0.154054
$837$	−634.457	−	538.890i	−0.758014	−	0.643835i
$838$	−64.4294	−	64.4294i	−0.0768847	−	0.0768847i
$839$			1160.48i			1.38317i	0.722296	+	0.691584i	$0.243087\pi$
$839$			1160.48i			1.38317i	−0.722296	+	0.691584i	$0.756913\pi$
$840$	699.751	+	224.886i	0.833037	+	0.267721i
$841$	−707.533			−0.841300
$842$	−43.3625	+	43.3625i	−0.0514994	+	0.0514994i
$843$	−5.41313	−	18.2136i	−0.00642127	−	0.0216057i
$844$		−	289.771i		−	0.343331i
$845$	18.3198	−	41.7139i	0.0216802	−	0.0493656i
$846$	482.422	−	314.538i	0.570239	−	0.371795i
$847$	−660.607	+	451.338i	−0.779937	+	0.532866i
$848$	170.800	+	170.800i	0.201415	+	0.201415i
$849$	903.310	+	489.394i	1.06397	+	0.576436i
$850$	13.9098	+	15.1373i	0.0163644	+	0.0178086i
$851$			2200.07i			2.58528i
$852$	−422.892	+	125.685i	−0.496352	+	0.147518i
$853$	727.157	+	727.157i	0.852470	+	0.852470i	0.990437	−	0.137967i	$-0.0440568\pi$
$853$	727.157	+	727.157i	0.852470	+	0.852470i	−0.137967	+	0.990437i	$0.544057\pi$
$854$	543.415	+	102.271i	0.636317	+	0.119756i
$855$	736.063	−	121.779i	0.860893	−	0.142431i
$856$	1236.13			1.44408
$857$	330.023	+	330.023i	0.385091	+	0.385091i	0.872932	−	0.487841i	$-0.162216\pi$
$857$	330.023	+	330.023i	0.385091	+	0.385091i	−0.487841	+	0.872932i	$0.662216\pi$
$858$	27.9830	+	94.1545i	0.0326142	+	0.109737i
$859$	900.965			1.04885			0.524427	−	0.851456i	$-0.324280\pi$
$859$	900.965			1.04885			0.524427	+	0.851456i	$0.324280\pi$
$860$	−193.749	−	497.196i	−0.225289	−	0.578135i
$861$	−227.155	+	279.451i	−0.263826	+	0.324565i
$862$	126.705	+	126.705i	0.146989	+	0.146989i
$863$	35.9749	+	35.9749i	0.0416859	+	0.0416859i	0.727642	−	0.685957i	$-0.240616\pi$
$863$	35.9749	+	35.9749i	0.0416859	+	0.0416859i	−0.685957	+	0.727642i	$0.740616\pi$
$864$	−72.3309	−	888.059i	−0.0837163	−	1.02785i
$865$	−760.604	+	296.394i	−0.879310	+	0.342652i
$866$	331.251			0.382507
$867$	−246.420	−	829.128i	−0.284221	−	0.956318i
$868$	−534.589	+	365.240i	−0.615886	+	0.420783i
$869$	−196.279			−0.225868
$870$	−136.849	+	106.312i	−0.157298	+	0.122198i
$871$			1296.08i			1.48804i
$872$	361.261	−	361.261i	0.414290	−	0.414290i
$873$	−68.1261	+	323.400i	−0.0780368	+	0.370447i
$874$	621.606			0.711220
$875$	−700.746	−	524.004i	−0.800852	−	0.598862i
$876$	−157.857	+	291.368i	−0.180202	+	0.332612i
$877$	−406.421	−	406.421i	−0.463422	−	0.463422i	0.436353	−	0.899775i	$-0.356270\pi$
$877$	−406.421	−	406.421i	−0.463422	−	0.463422i	−0.899775	+	0.436353i	$0.856270\pi$
$878$	372.158	−	372.158i	0.423870	−	0.423870i
$879$	673.728	−	1243.55i	0.766471	−	1.41473i
$880$	−26.0300	+	59.2699i	−0.0295795	+	0.0673522i
$881$	5.04486			0.00572629			0.00286315	−	0.999996i	$-0.499089\pi$
$881$	5.04486			0.00572629			0.00286315	+	0.999996i	$0.499089\pi$
$882$	368.960	+	241.557i	0.418322	+	0.273874i
$883$	−215.321	+	215.321i	−0.243852	+	0.243852i	−0.818442	−	0.574590i	$-0.805162\pi$
$883$	−215.321	+	215.321i	−0.243852	+	0.243852i	0.574590	+	0.818442i	$0.305162\pi$
$884$	31.1935			0.0352868
$885$	−89.0088	+	708.767i	−0.100575	+	0.800867i
$886$	−293.886			−0.331699
$887$	735.406	+	735.406i	0.829094	+	0.829094i	0.987391	−	0.158298i	$-0.0506006\pi$
$887$	735.406	+	735.406i	0.829094	+	0.829094i	−0.158298	+	0.987391i	$0.550601\pi$
$888$	351.060	+	1181.21i	0.395337	+	1.33019i
$889$	−210.603	−	39.6357i	−0.236899	−	0.0445846i
$890$	−25.5130	−	65.4713i	−0.0286663	−	0.0735633i
$891$	−191.914	−	84.6103i	−0.215392	−	0.0949611i
$892$	239.847	−	239.847i	0.268887	−	0.268887i
$893$	−750.170	−	750.170i	−0.840056	−	0.840056i
$894$	−35.3534	+	65.2544i	−0.0395452	+	0.0729915i
$895$	−1084.38	−	476.237i	−1.21160	−	0.532109i
$896$	−818.628	−	154.067i	−0.913648	−	0.171949i
$897$	−405.183	−	1363.32i	−0.451709	−	1.51987i
$898$	−222.845	+	222.845i	−0.248157	+	0.248157i
$899$		−	356.180i		−	0.396196i
$900$	−166.904	+	654.040i	−0.185449	+	0.726711i
$901$			39.7254i			0.0440903i
$902$	31.3989	+	31.3989i	0.0348103	+	0.0348103i
$903$	−76.7099	−	743.109i	−0.0849500	−	0.822934i
$904$		−	513.067i		−	0.567552i
$905$	−458.133	+	1043.16i	−0.506224	+	1.15266i
$906$	166.739	−	307.763i	0.184039	−	0.339694i
$907$	−553.040	−	553.040i	−0.609747	−	0.609747i	0.333133	−	0.942880i	$-0.391894\pi$
$907$	−553.040	−	553.040i	−0.609747	−	0.609747i	−0.942880	+	0.333133i	$0.891894\pi$
$908$	170.347	−	170.347i	0.187607	−	0.187607i
$909$	178.620	−	116.460i	0.196501	−	0.128118i
$910$	434.967	−	81.6498i	0.477986	−	0.0897250i
$911$		−	466.216i		−	0.511763i	−0.966708	−	0.255881i	$-0.917634\pi$
$911$		−	466.216i		−	0.511763i	0.966708	−	0.255881i	$-0.0823656\pi$
$912$	−238.384	+	70.8486i	−0.261386	+	0.0776849i
$913$	−138.993	−	138.993i	−0.152237	−	0.152237i
$914$	505.969			0.553576
$915$	−147.643	+	1175.67i	−0.161359	+	1.28488i
$916$			461.436i			0.503751i
$917$	1258.05	−	859.520i	1.37192	−	0.937318i
$918$	14.3731	−	16.9221i	0.0156570	−	0.0184336i
$919$			1125.94i			1.22518i	0.790401	+	0.612590i	$0.209872\pi$
$919$			1125.94i			1.22518i	−0.790401	+	0.612590i	$0.790128\pi$
$920$	−527.666	+	1201.49i	−0.573550	+	1.30596i
$921$	233.930	−	431.781i	0.253995	−	0.468818i
$922$	398.564	−	398.564i	0.432282	−	0.432282i
$923$	−438.289	+	438.289i	−0.474853	+	0.474853i
$924$	−102.896	+	126.585i	−0.111359	+	0.136996i
$925$	61.9428	−	1465.69i	0.0669652	−	1.58453i
$926$		−	38.1636i		−	0.0412133i
$927$	−979.577	−	206.353i	−1.05672	−	0.222603i
$928$	269.579	−	269.579i	0.290494	−	0.290494i
$929$		−	1846.32i		−	1.98743i	−0.111954	−	0.993713i	$-0.535711\pi$
$929$		−	1846.32i		−	1.98743i	0.111954	−	0.993713i	$-0.464289\pi$
$930$	283.714	+	365.207i	0.305069	+	0.392696i
$931$	295.324	−	756.806i	0.317211	−	0.812896i
$932$	150.881	−	150.881i	0.161890	−	0.161890i
$933$	251.615	−	74.7807i	0.269683	−	0.0801508i
$934$	−384.000			−0.411135
$935$	−9.91970	+	3.86554i	−0.0106093	+	0.00413426i
$936$	−435.083	−	667.307i	−0.464832	−	0.712935i
$937$	−814.593	+	814.593i	−0.869363	+	0.869363i	−0.992402	−	0.123039i	$-0.960736\pi$
$937$	−814.593	+	814.593i	−0.869363	+	0.869363i	0.123039	+	0.992402i	$0.460736\pi$
$938$	592.433	−	404.760i	0.631592	−	0.431514i
$939$	279.617	+	151.490i	0.297782	+	0.161332i
$940$	894.336	−	348.507i	0.951421	−	0.370752i
$941$	−1318.27			−1.40093			−0.700464	−	0.713687i	$-0.747024\pi$
$941$	−1318.27			−1.40093			−0.700464	+	0.713687i	$0.747024\pi$
$942$	−172.694	−	581.063i	−0.183327	−	0.616840i
$943$	−454.643	−	454.643i	−0.482124	−	0.482124i
$944$		−	238.111i		−	0.252237i
$945$	−468.382	+	820.758i	−0.495642	+	0.868527i
$946$	−92.1143			−0.0973724
$947$	−347.435	+	347.435i	−0.366880	+	0.366880i	−0.866338	−	0.499458i	$-0.833532\pi$
$947$	−347.435	+	347.435i	−0.366880	+	0.366880i	0.499458	+	0.866338i	$0.333532\pi$
$948$	653.951	−	194.356i	0.689821	−	0.205017i
$949$			465.581i			0.490602i
$950$	−414.113	−	17.5013i	−0.435909	−	0.0184224i
$951$	794.444	−	1466.36i	0.835378	−	1.54192i
$952$	−22.7304	−	33.2696i	−0.0238764	−	0.0349471i
$953$	−992.679	−	992.679i	−1.04164	−	1.04164i	−0.999095	−	0.0425407i	$-0.986455\pi$
$953$	−992.679	−	992.679i	−1.04164	−	1.04164i	−0.0425407	−	0.999095i	$-0.513545\pi$
$954$	364.211	−	237.464i	0.381772	−	0.248914i
$955$	745.792	−	1698.16i	0.780934	−	1.77817i
$956$			395.222i			0.413412i
$957$	−25.5666	−	86.0240i	−0.0267154	−	0.0898892i
$958$	−366.262	−	366.262i	−0.382320	−	0.382320i
$959$	58.8986	−	312.956i	0.0614167	−	0.326336i
$960$	−24.2977	+	193.480i	−0.0253101	+	0.201542i
$961$	10.4667			0.0108915
$962$	524.664	+	524.664i	0.545389	+	0.545389i
$963$	−327.608	+	1555.18i	−0.340195	+	1.61494i
$964$	309.094			0.320637
$965$	537.841	−	209.587i	0.557348	−	0.217189i
$966$	−496.630	+	610.965i	−0.514110	+	0.632469i
$967$	1047.59	+	1047.59i	1.08334	+	1.08334i	0.996196	+	0.0871396i	$0.0277726\pi$
$967$	1047.59	+	1047.59i	1.08334	+	1.08334i	0.0871396	+	0.996196i	$0.472227\pi$
$968$	−565.733	−	565.733i	−0.584434	−	0.584434i
$969$	−35.9613	−	19.4831i	−0.0371118	−	0.0201064i
$970$	73.8310	−	168.112i	0.0761144	−	0.173311i
$971$	379.480			0.390813			0.195407	−	0.980722i	$-0.437397\pi$
$971$	379.480			0.390813			0.195407	+	0.980722i	$0.437397\pi$
$972$	723.189	+	91.8652i	0.744021	+	0.0945115i
$973$	−650.631	+	444.522i	−0.668685	+	0.456857i
$974$	−522.283			−0.536224
$975$	231.548	+	919.650i	0.237485	+	0.943231i
$976$		−	394.968i		−	0.404680i
$977$	−305.408	+	305.408i	−0.312598	+	0.312598i	−0.845915	−	0.533318i	$-0.820945\pi$
$977$	−305.408	+	305.408i	−0.312598	+	0.312598i	0.533318	+	0.845915i	$0.320945\pi$
$978$	117.429	+	395.112i	0.120070	+	0.404000i
$979$	36.3891			0.0371697
$980$	519.479	+	519.967i	0.530081	+	0.530579i
$981$	358.760	+	550.247i	0.365708	+	0.560904i
$982$	298.364	+	298.364i	0.303833	+	0.303833i
$983$	−522.805	+	522.805i	−0.531846	+	0.531846i	−0.921121	−	0.389275i	$-0.872726\pi$
$983$	−522.805	+	522.805i	−0.531846	+	0.531846i	0.389275	+	0.921121i	$0.372726\pi$
$984$	−316.642	−	171.550i	−0.321791	−	0.174339i
$985$	−1200.39	+	467.771i	−1.21867	+	0.474894i
$986$	9.49996			0.00963484
$987$	1336.67	−	137.982i	1.35428	−	0.139800i
$988$	−444.714	+	444.714i	−0.450116	+	0.450116i
$989$	1333.78			1.34861
$990$	94.7366	+	67.8391i	0.0956935	+	0.0685243i
$991$	−1178.96			−1.18967			−0.594833	−	0.803849i	$-0.702782\pi$
$991$	−1178.96			−1.18967			−0.594833	+	0.803849i	$0.702782\pi$
$992$	−719.420	−	719.420i	−0.725222	−	0.725222i
$993$	704.501	−	209.380i	0.709467	−	0.210856i
$994$	337.215	+	63.4643i	0.339251	+	0.0638474i
$995$	142.997	+	62.8012i	0.143716	+	0.0631167i
$996$	600.718	+	325.456i	0.603130	+	0.326763i
$997$	−266.821	+	266.821i	−0.267624	+	0.267624i	−0.828142	−	0.560518i	$-0.810602\pi$
$997$	−266.821	+	266.821i	−0.267624	+	0.267624i	0.560518	+	0.828142i	$0.310602\pi$
$998$	77.2632	+	77.2632i	0.0774180	+	0.0774180i
$999$	−1579.12	+	128.617i	−1.58071	+	0.128746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.k.c.62.4	yes	16
3.2	odd	2	inner	105.3.k.c.62.6	yes	16
5.3	odd	4	inner	105.3.k.c.83.7	yes	16
7.6	odd	2	inner	105.3.k.c.62.1	✓	16
15.8	even	4	inner	105.3.k.c.83.1	yes	16
21.20	even	2	inner	105.3.k.c.62.7	yes	16
35.13	even	4	inner	105.3.k.c.83.6	yes	16
105.83	odd	4	inner	105.3.k.c.83.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.c.62.1	✓	16	7.6	odd	2	inner
105.3.k.c.62.4	yes	16	1.1	even	1	trivial
105.3.k.c.62.6	yes	16	3.2	odd	2	inner
105.3.k.c.62.7	yes	16	21.20	even	2	inner
105.3.k.c.83.1	yes	16	15.8	even	4	inner
105.3.k.c.83.4	yes	16	105.83	odd	4	inner
105.3.k.c.83.6	yes	16	35.13	even	4	inner
105.3.k.c.83.7	yes	16	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(2.87568 - 0.854662i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +(-4.65877 + 1.81544i) q^{10} -2.58936i q^{11} +(2.56399 + 8.62705i) q^{12} +(8.94114 + 8.94114i) q^{13} +(1.29468 - 6.87923i) q^{14} +(14.8831 + 1.86906i) q^{15} -5.00000 q^{16} +(-0.581460 - 0.581460i) q^{17} +(-1.85519 + 8.80672i) q^{18} +16.5793 q^{19} +(-6.03161 + 13.7339i) q^{20} +(-13.2460 + 16.2955i) q^{21} +(1.83095 + 1.83095i) q^{22} +(-26.5115 - 26.5115i) q^{23} +(-18.4643 - 10.0035i) q^{24} +(16.9155 + 18.4083i) q^{25} -12.6447 q^{26} +(17.4790 - 20.5787i) q^{27} +(-11.8466 - 17.3395i) q^{28} +11.5528 q^{29} +(-11.8456 + 9.20232i) q^{30} -30.8307i q^{31} +(23.3345 - 23.3345i) q^{32} +(-2.21303 - 7.44617i) q^{33} +0.822309 q^{34} +(-34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 - 41.4929i) q^{37} +(-11.7233 + 11.7233i) q^{38} +(33.3536 + 18.0702i) q^{39} +(-12.7081 - 32.6114i) q^{40} +17.1489 q^{41} +(-2.15633 - 20.8890i) q^{42} +(-25.1548 + 25.1548i) q^{43} +7.76807 q^{44} +(44.3965 - 7.34521i) q^{45} +37.4929 q^{46} +(-45.2473 - 45.2473i) q^{47} +(-14.3784 + 4.27331i) q^{48} +(17.8128 - 45.6476i) q^{49} +(-24.9777 - 1.05561i) q^{50} +(-2.16905 - 1.17514i) q^{51} +(-26.8234 + 26.8234i) q^{52} +(-34.1600 - 34.1600i) q^{53} +(2.19185 + 26.9109i) q^{54} +(5.20600 - 11.8540i) q^{55} +(48.1546 + 9.06275i) q^{56} +(47.6769 - 14.1697i) q^{57} +(-8.16905 + 8.16905i) q^{58} +47.6223i q^{59} +(-5.60717 + 44.6493i) q^{60} +78.9936i q^{61} +(21.8006 + 21.8006i) q^{62} +(-24.1641 + 58.1816i) q^{63} +13.0000i q^{64} +(22.9557 + 58.9087i) q^{65} +(6.83008 + 3.70039i) q^{66} +(72.4786 + 72.4786i) q^{67} +(1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 - 28.8899i) q^{70} +49.0193i q^{71} +(-61.6470 - 12.9863i) q^{72} +(26.0359 + 26.0359i) q^{73} +58.6798 q^{74} +(64.3765 + 38.4795i) q^{75} +49.7380i q^{76} +(10.2250 + 14.9660i) q^{77} +(-36.3621 + 10.8069i) q^{78} -75.8024i q^{79} +(-22.8898 - 10.0527i) q^{80} +(32.6762 - 74.1166i) q^{81} +(-12.1261 + 12.1261i) q^{82} +(53.6785 - 53.6785i) q^{83} +(-48.8865 - 39.7380i) q^{84} +(-1.49286 - 3.83095i) q^{85} -35.5742i q^{86} +(33.2221 - 9.87373i) q^{87} +(-12.8167 + 12.8167i) q^{88} +14.0533i q^{89} +(-26.1992 + 36.5869i) q^{90} +(-86.9857 - 16.3708i) q^{91} +(79.5344 - 79.5344i) q^{92} +(-26.3499 - 88.6594i) q^{93} +63.9894 q^{94} +(75.8995 + 33.3333i) q^{95} +(47.1596 - 87.0458i) q^{96} +(-25.9664 + 25.9664i) q^{97} +(19.6822 + 44.8733i) q^{98} +(-12.7279 - 19.5214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{7}+O(q^{10}) \) 16 * q + 32 * q^7	\( 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) \) 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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