LMFDB - Embedded newform 105.3.k.c.62.1

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			62.1
Root			$-1.97320 + 0.817327i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.c.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.87568 + 0.854662i) q^{3} +3.00000i q^{4} +(-4.57796 - 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(3.94887 - 5.77983i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +O(q^{10})$	\(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} +(3.94887 - 5.77983i) 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} +(-6.41591 + 19.9959i) 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} +(17.3395 + 11.8466i) 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} +(-29.6984 + 18.5205i) 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} +(-9.60250 - 18.6760i) 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} +(1.36038 - 62.9853i) 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} +(7.90396 - 34.0959i) 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} +(-14.9660 - 10.2250i) 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} +(-59.9877 - 19.2477i) 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} +(44.8733 + 19.6822i) 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
$7$	3.94887	−	5.77983i	0.564125	−	0.825689i
$7$	3.94887	−	5.77983i	0.564125	−	0.825689i
$8$	−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	0.273961	−	0.961741i	$-0.411666\pi$
$13$	−8.94114	−	8.94114i	−0.687780	−	0.687780i	−0.961741	+	0.273961i	$0.911666\pi$
$14$	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	0.724002	−	0.689798i	$-0.242301\pi$
$17$	0.581460	+	0.581460i	0.0342036	+	0.0342036i	−0.689798	+	0.724002i	$0.742301\pi$
$18$	−1.85519	+	8.80672i	−0.103066	+	0.489262i
$19$	−16.5793			−0.872596			−0.436298	−	0.899802i	$-0.643711\pi$
$19$	−16.5793			−0.872596			−0.436298	+	0.899802i	$0.643711\pi$
$20$	6.03161	−	13.7339i	0.301581	−	0.686694i
$21$	−6.41591	+	19.9959i	−0.305520	+	0.952186i
$22$	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
$28$	17.3395	+	11.8466i	0.619267	+	0.423094i
$29$	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	$0.165664\pi$
$31$			30.8307i			0.994539i	−0.867596	+	0.497270i	$0.834336\pi$
$32$	23.3345	−	23.3345i	0.729204	−	0.729204i
$33$	2.21303	+	7.44617i	0.0670614	+	0.225642i
$34$	−0.822309			−0.0241856
$35$	−29.6984	+	18.5205i	−0.848524	+	0.529156i
$36$	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	$-0.567064\pi$
$41$	−17.1489			−0.418267			−0.209133	+	0.977887i	$0.567064\pi$
$42$	−9.60250	−	18.6760i	−0.228631	−	0.444666i
$43$	−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	0.999329	−	0.0366205i	$-0.0116593\pi$
$47$	45.2473	+	45.2473i	0.962709	+	0.962709i	−0.0366205	+	0.999329i	$0.511659\pi$
$48$	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	$-0.867766\pi$
$59$		−	47.6223i		−	0.807158i	0.914945	−	0.403579i	$-0.132234\pi$
$60$	−5.60717	+	44.6493i	−0.0934529	+	0.744155i
$61$		−	78.9936i		−	1.29498i	−0.762075	−	0.647488i	$-0.775819\pi$
$61$		−	78.9936i		−	1.29498i	0.762075	−	0.647488i	$-0.224181\pi$
$62$	−21.8006	−	21.8006i	−0.351623	−	0.351623i
$63$	1.36038	−	62.9853i	0.0215933	−	0.999767i
$64$			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
$70$	7.90396	−	34.0959i	0.112914	−	0.487084i
$71$			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	0.505923	−	0.862579i	$-0.331152\pi$
$73$	−26.0359	−	26.0359i	−0.356656	−	0.356656i	−0.862579	+	0.505923i	$0.831152\pi$
$74$	58.6798			0.792970
$75$	−64.3765	−	38.4795i	−0.858353	−	0.513060i
$76$		−	49.7380i		−	0.654447i
$77$	−14.9660	−	10.2250i	−0.194364	−	0.132793i
$78$	−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	−0.952201	−	0.305472i	$-0.901186\pi$
$83$	−53.6785	+	53.6785i	−0.646729	+	0.646729i	0.305472	+	0.952201i	$0.401186\pi$
$84$	−59.9877	−	19.2477i	−0.714139	−	0.229140i
$85$	−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	$-0.974843\pi$
$89$		−	14.0533i		−	0.157903i	0.996878	−	0.0789514i	$-0.0251572\pi$
$90$	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	−0.560476	−	0.828171i	$-0.689382\pi$
$97$	25.9664	−	25.9664i	0.267695	−	0.267695i	0.828171	+	0.560476i	$0.189382\pi$
$98$	44.8733	+	19.6822i	0.457891	+	0.200839i
$99$	−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	$-0.537420\pi$
$101$	−23.6924			−0.234579			−0.117289	+	0.993098i	$0.537420\pi$
$102$	2.36470	−	0.702797i	0.0231833	−	0.00689016i
$103$	78.6519	+	78.6519i	0.763611	+	0.763611i	0.976973	−	0.213362i	$-0.0684415\pi$
$103$	78.6519	+	78.6519i	0.763611	+	0.763611i	−0.213362	+	0.976973i	$0.568441\pi$
$104$			88.5128i			0.851085i
$105$	69.5743	−	78.6411i	0.662612	−	0.748962i
$106$	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
$112$	−19.7444	+	28.8991i	−0.176289	+	0.258028i
$113$	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
$126$	43.5754	+	45.4993i	0.345837	+	0.361105i
$127$	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	$-0.187900\pi$
$131$	217.662			1.66154			0.830771	+	0.556614i	$0.187900\pi$
$132$	−22.3385	+	6.63908i	−0.169231	+	0.0502960i
$133$	−65.4696	+	95.8256i	−0.492253	+	0.720493i
$134$	−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	$-0.632702\pi$
$139$	−112.569			−0.809851			−0.404925	+	0.914350i	$0.632702\pi$
$140$	−55.5614	−	89.0951i	−0.396867	−	0.636393i
$141$	−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
$147$	90.2372	+	116.044i	0.613859	+	0.789416i
$148$	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	−0.0862209	−	0.996276i	$-0.527479\pi$
$157$	142.879	−	142.879i	0.910055	−	0.910055i	0.996276	+	0.0862209i	$0.0274791\pi$
$158$	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	$-0.909203\pi$
$167$	−207.245	−	207.245i	−1.24099	−	1.24099i	−0.281396	−	0.959592i	$-0.590797\pi$
$168$	130.732	−	67.2175i	0.778165	−	0.400104i
$169$		−	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	−0.289785	−	0.957092i	$-0.593584\pi$
$173$	115.444	−	115.444i	0.667307	−	0.667307i	0.957092	+	0.289785i	$0.0935837\pi$
$174$	16.5098	−	30.4734i	0.0948840	−	0.175134i
$175$	173.194	−	25.0763i	0.989680	−	0.143293i
$176$			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	$-0.783275\pi$
$181$		−	227.866i		−	1.25893i	0.777030	−	0.629463i	$-0.216725\pi$
$182$	49.9323	−	73.0841i	0.274353	−	0.401561i
$183$	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
$189$	49.9192	+	182.288i	0.264123	+	0.964489i
$190$	−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	$-0.525007\pi$
$199$	−31.2360			−0.156965			−0.0784824	+	0.996915i	$0.525007\pi$
$200$	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
$203$	45.6205	−	66.7731i	0.224731	−	0.328931i
$204$	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
$210$	6.41115	+	104.804i	0.0305293	+	0.499067i
$211$	−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
$217$	178.196	+	121.747i	0.821181	+	0.561044i
$218$	−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	0.863266	−	0.504750i	$-0.168415\pi$
$223$	79.9490	+	79.9490i	0.358516	+	0.358516i	−0.504750	+	0.863266i	$0.668415\pi$
$224$	−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	0.821029	−	0.570886i	$-0.193400\pi$
$227$	56.7824	+	56.7824i	0.250143	+	0.250143i	−0.570886	+	0.821029i	$0.693400\pi$
$228$	42.5092	+	143.031i	0.186444	+	0.627327i
$229$	−153.812			−0.671668			−0.335834	−	0.941921i	$-0.609018\pi$
$229$	−153.812			−0.671668			−0.335834	+	0.941921i	$0.609018\pi$
$230$	−171.641	−	75.3808i	−0.746265	−	0.327743i
$231$	51.7765	+	16.6131i	0.224141	+	0.0719181i
$232$	−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
$238$	−3.24720	+	4.75280i	−0.0136437	+	0.0199698i
$239$	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	$0.0685704\pi$
$241$			103.031i			0.427516i	−0.976887	+	0.213758i	$0.931430\pi$
$242$	−80.8189	+	80.8189i	−0.333963	+	0.333963i
$243$	−30.6217	+	241.063i	−0.126015	+	0.992028i
$244$	236.981			0.971232
$245$	−10.2300	+	244.786i	−0.0417551	+	0.999128i
$246$	−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	$-0.242350\pi$
$251$	363.395			1.44779			0.723895	+	0.689910i	$0.242350\pi$
$252$	188.956	+	4.08114i	0.749825	+	0.0161950i
$253$	−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	0.517493	−	0.855687i	$-0.326865\pi$
$257$	−86.9159	−	86.9159i	−0.338194	−	0.338194i	−0.855687	+	0.517493i	$0.826865\pi$
$258$	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	$-0.928512\pi$
$269$		−	119.813i		−	0.445403i	0.974887	−	0.222701i	$-0.0714875\pi$
$270$	−44.0712	+	127.604i	−0.163227	+	0.472607i
$271$			246.646i			0.910132i	0.890458	+	0.455066i	$0.150384\pi$
$271$			246.646i			0.910132i	−0.890458	+	0.455066i	$0.849616\pi$
$272$	−2.90730	−	2.90730i	−0.0106886	−	0.0106886i
$273$	236.152	−	121.421i	0.865025	−	0.444764i
$274$		−	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
$280$	238.671	+	55.3277i	0.852396	+	0.197599i
$281$		−	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	0.135163	−	0.990823i	$-0.456844\pi$
$283$	−242.152	−	242.152i	−0.855661	−	0.855661i	−0.990823	+	0.135163i	$0.956844\pi$
$284$	−147.058			−0.517810
$285$	−246.752	−	30.9877i	−0.865795	−	0.108729i
$286$		−	32.7416i		−	0.114481i
$287$	−67.7190	+	99.1178i	−0.235955	+	0.345358i
$288$	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	$0.547572\pi$
$293$	−333.360	+	333.360i	−1.13775	+	1.13775i	−0.988853	+	0.148895i	$0.952428\pi$
$294$	−145.863	−	18.2483i	−0.496132	−	0.0620689i
$295$	−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	−0.870030	−	0.492999i	$-0.835901\pi$
$307$	−115.748	+	115.748i	−0.377030	+	0.377030i	0.492999	+	0.870030i	$0.335901\pi$
$308$	30.6751	−	44.8981i	0.0995946	−	0.145773i
$309$	−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	$-0.544926\pi$
$311$	−87.4973			−0.281342			−0.140671	+	0.990056i	$0.544926\pi$
$312$	−75.6486	−	254.535i	−0.242463	−	0.815817i
$313$	−74.9574	−	74.9574i	−0.239481	−	0.239481i	0.577154	−	0.816635i	$-0.304163\pi$
$313$	−74.9574	−	74.9574i	−0.239481	−	0.239481i	−0.816635	+	0.577154i	$0.804163\pi$
$314$			202.061i			0.643506i
$315$	−132.862	+	285.609i	−0.421784	+	0.906696i
$316$	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
$322$	148.055	−	216.702i	0.459797	−	0.672988i
$323$	−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
$336$	32.0796	−	99.9795i	0.0954749	−	0.297558i
$337$	−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
$343$	−334.176	−	77.3019i	−0.974273	−	0.225370i
$344$	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	$-0.384703\pi$
$349$	247.335			0.708696			0.354348	+	0.935114i	$0.384703\pi$
$350$	−104.735	+	140.198i	−0.299243	+	0.400567i
$351$	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	−0.197281	−	0.980347i	$-0.563211\pi$
$353$	276.422	−	276.422i	0.783065	−	0.783065i	0.980347	+	0.197281i	$0.0632113\pi$
$354$	−125.616	−	68.0559i	−0.354847	−	0.192248i
$355$	98.5552	−	224.409i	0.277620	−	0.632137i
$356$	42.1600			0.118427
$357$	−15.3574	+	7.89623i	−0.0430180	+	0.0221183i
$358$	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	−0.315519	−	0.948919i	$-0.602179\pi$
$367$	232.458	−	232.458i	0.633401	−	0.633401i	0.948919	+	0.315519i	$0.102179\pi$
$368$	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
$378$	−164.196	−	93.5992i	−0.434380	−	0.247617i
$379$			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	−0.765446	−	0.643500i	$-0.777482\pi$
$383$	−46.7051	+	46.7051i	−0.121945	+	0.121945i	0.643500	+	0.765446i	$0.277482\pi$
$384$	−313.893	−	170.060i	−0.817428	−	0.442865i
$385$	47.9561	+	76.8996i	0.124561	+	0.199739i
$386$			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
$392$	−137.775	+	314.113i	−0.351468	+	0.801309i
$393$	−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	−0.984366	−	0.176135i	$-0.943640\pi$
$397$	−320.867	+	320.867i	−0.808230	+	0.808230i	0.176135	+	0.984366i	$0.443640\pi$
$398$	22.0872	−	22.0872i	0.0554954	−	0.0554954i
$399$	106.371	−	331.518i	0.266595	−	0.830873i
$400$	−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	$-0.547575\pi$
$409$	−121.806			−0.297813			−0.148907	+	0.988851i	$0.547575\pi$
$410$	−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
$413$	−275.249	−	188.054i	−0.666462	−	0.455338i
$414$	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	$-0.965321\pi$
$419$		−	91.1169i		−	0.217463i	0.994071	−	0.108731i	$-0.0346788\pi$
$420$	235.923	+	208.723i	0.561722	+	0.496959i
$421$	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
$427$	−456.569	−	311.936i	−1.06925	−	0.730528i
$428$	−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	0.923806	−	0.382860i	$-0.125061\pi$
$433$	234.230	+	234.230i	0.540947	+	0.540947i	−0.382860	+	0.923806i	$0.625061\pi$
$434$	−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	$-0.295389\pi$
$439$	526.311			1.19889			0.599443	+	0.800417i	$0.295389\pi$
$440$	84.4426	−	32.9058i	0.191915	−	0.0747859i
$441$	−358.672	−	256.584i	−0.813316	−	0.581823i
$442$	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
$448$	75.1377	+	51.3354i	0.167718	+	0.114588i
$449$	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
$455$	431.131	+	99.9431i	0.947542	+	0.219655i
$456$	−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	$-0.290631\pi$
$461$	563.655			1.22268			0.611339	+	0.791369i	$0.290631\pi$
$462$	−48.3588	+	24.8643i	−0.104673	+	0.0538189i
$463$	−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	0.353864	−	0.935297i	$-0.384867\pi$
$467$	−271.529	−	271.529i	−0.581432	−	0.581432i	−0.935297	+	0.353864i	$0.884867\pi$
$468$	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	$-0.818166\pi$
$479$		−	517.973i		−	1.08136i	0.841227	−	0.540682i	$-0.181834\pi$
$480$	390.904	−	303.676i	0.814382	−	0.632659i
$481$			741.987i			1.54259i
$482$	−72.8542	−	72.8542i	−0.151150	−	0.151150i
$483$	700.216	−	360.025i	1.44972	−	0.745394i
$484$			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
$490$	−165.856	−	180.324i	−0.338482	−	0.368008i
$491$		−	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
$497$	283.323	+	193.571i	0.570067	+	0.389479i
$498$	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	−0.561133	−	0.827725i	$-0.689635\pi$
$503$	134.096	−	134.096i	0.266592	−	0.266592i	0.827725	+	0.561133i	$0.189635\pi$
$504$	−318.495	+	305.028i	−0.631934	+	0.605214i
$505$	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	$-0.851040\pi$
$509$		−	459.197i		−	0.902154i	0.892485	−	0.451077i	$-0.148960\pi$
$510$	−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
$518$	231.719	−	339.159i	0.447334	−	0.654747i
$519$	−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	$-0.594152\pi$
$521$	−303.734			−0.582983			−0.291491	+	0.956573i	$0.594152\pi$
$522$	−21.4325	+	101.742i	−0.0410585	+	0.194908i
$523$	−249.060	−	249.060i	−0.476215	−	0.476215i	0.427704	−	0.903919i	$-0.359323\pi$
$523$	−249.060	−	249.060i	−0.476215	−	0.476215i	−0.903919	+	0.427704i	$0.859323\pi$
$524$			652.986i			1.24616i
$525$	−476.619	+	220.134i	−0.907846	+	0.419303i
$526$	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
$532$	−287.477	−	196.409i	−0.540370	−	0.369190i
$533$	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
$546$	−81.1272	+	252.842i	−0.148585	+	0.463080i
$547$	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
$553$	−438.125	−	299.334i	−0.792269	−	0.541291i
$554$	−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
$560$	148.492	−	92.6023i	0.265164	−	0.165361i
$561$	−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	−0.996059	−	0.0886978i	$-0.971729\pi$
$563$	−510.844	+	510.844i	−0.907361	+	0.907361i	0.0886978	+	0.996059i	$0.471729\pi$
$564$	274.337	−	506.364i	0.486414	−	0.897809i
$565$	−133.063	−	341.466i	−0.235510	−	0.604364i
$566$	342.455			0.605043
$567$	−299.347	−	481.540i	−0.527948	−	0.849276i
$568$	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	−0.924407	−	0.381408i	$-0.875439\pi$
$577$	−313.311	+	313.311i	−0.542999	+	0.542999i	0.381408	+	0.924407i	$0.375439\pi$
$578$	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	0.822920	−	0.568158i	$-0.192344\pi$
$587$	149.545	+	149.545i	0.254762	+	0.254762i	−0.568158	+	0.822920i	$0.692344\pi$
$588$	−348.132	+	270.712i	−0.592062	+	0.460394i
$589$		−	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	−0.854095	−	0.520118i	$-0.825888\pi$
$593$	−198.048	+	198.048i	−0.333977	+	0.333977i	0.520118	+	0.854095i	$0.325888\pi$
$594$	−69.6819	+	5.67547i	−0.117310	+	0.00955466i
$595$	−28.0373	−	6.49950i	−0.0471216	−	0.0109235i
$596$			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	$0.100704\pi$
$601$			373.965i			0.622237i	−0.950371	+	0.311119i	$0.899296\pi$
$602$	−205.613	−	140.478i	−0.341549	−	0.233352i
$603$	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	$-0.486594\pi$
$607$	632.018	−	632.018i	1.04122	−	1.04122i	0.999113	−	0.0421025i	$-0.0134056\pi$
$608$	−386.871	+	386.871i	−0.636300	+	0.636300i
$609$	−74.1216	+	231.008i	−0.121710	+	0.379324i
$610$	−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	$-0.696448\pi$
$619$	−716.455			−1.15744			−0.578720	+	0.815526i	$0.696448\pi$
$620$	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
$623$	−81.2259	−	55.4949i	−0.130379	−	0.0890769i
$624$	−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
$630$	−108.009	−	295.904i	−0.171442	−	0.469689i
$631$	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
$637$	−248.875	+	567.409i	−0.390699	+	0.890751i
$638$	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	0.169993	−	0.985445i	$-0.445626\pi$
$643$	−524.336	−	524.336i	−0.815453	−	0.815453i	−0.985445	+	0.169993i	$0.945626\pi$
$644$	−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	0.902817	−	0.430025i	$-0.141495\pi$
$647$	305.897	+	305.897i	0.472792	+	0.472792i	−0.430025	+	0.902817i	$0.641495\pi$
$648$	−528.597	+	205.119i	−0.815736	+	0.316542i
$649$	−123.311			−0.190002
$650$	213.891	+	232.768i	0.329063	+	0.358104i
$651$	−616.488	−	197.807i	−0.946986	−	0.303851i
$652$	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
$658$	−252.686	+	369.847i	−0.384021	+	0.562078i
$659$	−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	$0.341820\pi$
$661$			1162.10i			1.75809i	−0.476737	+	0.879046i	$0.658180\pi$
$662$	−173.231	+	173.231i	−0.261678	+	0.261678i
$663$	8.88664	+	29.9009i	0.0134037	+	0.0450994i
$664$	531.390			0.800286
$665$	492.379	−	307.057i	0.740419	−	0.461739i
$666$	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
$672$	316.883	+	616.307i	0.471552	+	0.917124i
$673$	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	0.499559	−	0.866280i	$-0.333496\pi$
$677$	−248.270	−	248.270i	−0.366721	−	0.366721i	−0.866280	+	0.499559i	$0.833496\pi$
$678$	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	$0.0385648\pi$
$691$			167.027i			0.241717i	−0.992670	+	0.120859i	$0.961435\pi$
$692$	346.332	+	346.332i	0.500480	+	0.500480i
$693$	−163.091	−	3.52251i	−0.235341	−	0.00508298i
$694$			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
$700$	75.2290	+	519.582i	0.107470	+	0.742260i
$701$			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
$707$	−93.5584	+	136.938i	−0.132332	+	0.193689i
$708$	−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
$714$	5.27586	−	16.4428i	0.00738916	−	0.0230292i
$715$	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	$-0.908368\pi$
$719$		−	408.265i		−	0.567824i	0.958850	−	0.283912i	$-0.0916324\pi$
$720$	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	−0.996196	−	0.0871447i	$-0.972226\pi$
$727$	−660.880	+	660.880i	−0.909051	+	0.909051i	0.0871447	+	0.996196i	$0.472226\pi$
$728$	511.589	+	349.526i	0.702732	+	0.480118i
$729$	−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	0.249693	−	0.968325i	$-0.419670\pi$
$733$	−526.757	−	526.757i	−0.718632	−	0.718632i	−0.968325	+	0.249693i	$0.919670\pi$
$734$			328.745i			0.447882i
$735$	−179.791	−	712.671i	−0.244614	−	0.969620i
$736$	−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
$742$	190.768	−	279.221i	0.257100	−	0.376308i
$743$	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
$756$	−546.865	+	149.757i	−0.723367	+	0.198092i
$757$	−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	$-0.720848\pi$
$761$	−973.280			−1.27895			−0.639475	+	0.768812i	$0.720848\pi$
$762$	88.0372	−	26.1649i	0.115534	−	0.0343372i
$763$	421.845	+	288.211i	0.552876	+	0.377734i
$764$	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	$-0.740835\pi$
$769$	−1055.77			−1.37292			−0.686458	+	0.727169i	$0.740835\pi$
$770$	−88.2863	−	20.4662i	−0.114658	−	0.0265795i
$771$	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	−0.965573	−	0.260132i	$-0.916234\pi$
$773$	−545.306	+	545.306i	−0.705441	+	0.705441i	0.260132	+	0.965573i	$0.416234\pi$
$774$	−174.864	−	268.198i	−0.225923	−	0.346509i
$775$	−567.542	+	521.516i	−0.732312	+	0.672924i
$776$	−257.054			−0.331255
$777$	1095.90	−	563.473i	1.41043	−	0.725190i
$778$	−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	−0.434992	−	0.900434i	$-0.643249\pi$
$787$	366.303	−	366.303i	0.465442	−	0.465442i	0.900434	+	0.434992i	$0.143249\pi$
$788$	−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	0.781037	−	0.624485i	$-0.214691\pi$
$797$	124.772	+	124.772i	0.156552	+	0.156552i	−0.624485	+	0.781037i	$0.714691\pi$
$798$	159.203	+	309.635i	0.199502	+	0.388014i
$799$			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
$805$	1278.35	+	296.342i	1.58801	+	0.368127i
$806$			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	$-0.798622\pi$
$811$		−	959.059i		−	1.18256i	0.806465	−	0.591282i	$-0.201378\pi$
$812$	200.319	+	136.861i	0.246698	+	0.168549i
$813$	−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
$819$	−575.324	+	550.997i	−0.702471	+	0.672768i
$820$	−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	$-0.462036\pi$
$829$	197.279			0.237972			0.118986	+	0.992896i	$0.462036\pi$
$830$	−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
$833$	16.1849	−	36.8997i	0.0194296	−	0.0442974i
$834$	−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	$-0.756913\pi$
$839$		−	1160.48i		−	1.38317i	0.722296	−	0.691584i	$-0.243087\pi$
$840$	−733.629	+	44.8781i	−0.873367	+	0.0534263i
$841$	−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
$847$	451.338	−	660.607i	0.532866	−	0.779937i
$848$	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	0.137967	−	0.990437i	$-0.455943\pi$
$853$	−727.157	−	727.157i	−0.852470	−	0.852470i	−0.990437	+	0.137967i	$0.955943\pi$
$854$	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	0.487841	−	0.872932i	$-0.337784\pi$
$857$	−330.023	−	330.023i	−0.385091	−	0.385091i	−0.872932	+	0.487841i	$0.837784\pi$
$858$	27.9830	+	94.1545i	0.0326142	+	0.109737i
$859$	−900.965			−1.04885			−0.524427	−	0.851456i	$-0.675720\pi$
$859$	−900.965			−1.04885			−0.524427	+	0.851456i	$0.675720\pi$
$860$	193.749	+	497.196i	0.225289	+	0.578135i
$861$	110.026	−	342.908i	0.127789	−	0.398267i
$862$	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
$868$	−365.240	+	534.589i	−0.420783	+	0.615886i
$869$	−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
$875$	−843.293	−	233.415i	−0.963763	−	0.266760i
$876$	−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	$-0.500911\pi$
$881$	−5.04486			−0.00572629			−0.00286315	+	0.999996i	$0.500911\pi$
$882$	435.052	−	72.1874i	0.493256	−	0.0818451i
$883$	−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	0.158298	−	0.987391i	$-0.449399\pi$
$887$	−735.406	−	735.406i	−0.829094	−	0.829094i	−0.987391	+	0.158298i	$0.949399\pi$
$888$	−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
$903$	−341.601	−	664.383i	−0.378296	−	0.735751i
$904$		−	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
$910$	−375.526	+	234.185i	−0.412666	+	0.257347i
$911$		−	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
$917$	859.520	−	1258.05i	0.937318	−	1.37192i
$918$	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
$924$	−49.8392	+	155.330i	−0.0539386	+	0.168106i
$925$	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	$0.464289\pi$
$929$			1846.32i			1.98743i	−0.111954	+	0.993713i	$0.535711\pi$
$930$	−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	−0.123039	−	0.992402i	$-0.539264\pi$
$937$	814.593	−	814.593i	0.869363	−	0.869363i	0.992402	+	0.123039i	$0.0392640\pi$
$938$	−404.760	+	592.433i	−0.431514	+	0.631592i
$939$	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	$-0.252976\pi$
$941$	1318.27			1.40093			0.700464	+	0.713687i	$0.252976\pi$
$942$	−172.694	−	581.063i	−0.183327	−	0.616840i
$943$	454.643	+	454.643i	0.482124	+	0.482124i
$944$			238.111i			0.252237i
$945$	137.970	−	934.874i	0.146000	−	0.989285i
$946$	−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
$952$	−33.2696	−	22.7304i	−0.0349471	−	0.0238764i
$953$	−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
$966$	−240.551	+	749.703i	−0.249017	+	0.776091i
$967$	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	$-0.562603\pi$
$971$	−379.480			−0.390813			−0.195407	+	0.980722i	$0.562603\pi$
$972$	−723.189	−	91.8652i	−0.744021	−	0.0945115i
$973$	−444.522	+	650.631i	−0.456857	+	0.668685i
$974$	−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
$980$	−734.359	−	30.6900i	−0.749346	−	0.0313163i
$981$	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	−0.389275	−	0.921121i	$-0.627274\pi$
$983$	522.805	−	522.805i	0.531846	−	0.531846i	0.921121	+	0.389275i	$0.127274\pi$
$984$	−316.642	−	171.550i	−0.321791	−	0.174339i
$985$	1200.39	−	467.771i	1.21867	−	0.474894i
$986$	−9.49996			−0.00963484
$987$	−1195.06	+	614.458i	−1.21080	+	0.622551i
$988$	−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	−0.560518	−	0.828142i	$-0.689398\pi$
$997$	266.821	−	266.821i	0.267624	−	0.267624i	0.828142	+	0.560518i	$0.189398\pi$
$998$	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.62.1	✓	16
3.2	odd	2	inner	105.3.k.c.62.7	yes	16
5.3	odd	4	inner	105.3.k.c.83.6	yes	16
7.6	odd	2	inner	105.3.k.c.62.4	yes	16
15.8	even	4	inner	105.3.k.c.83.4	yes	16
21.20	even	2	inner	105.3.k.c.62.6	yes	16
35.13	even	4	inner	105.3.k.c.83.7	yes	16
105.83	odd	4	inner	105.3.k.c.83.1	yes	16

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.87568 + 0.854662i) q^{3} +3.00000i q^{4} +(-4.57796 - 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(3.94887 - 5.77983i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(7.53910 - 4.91548i) q^{9} +O(q^{10})\)	\(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} +(3.94887 - 5.77983i) 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} +(-6.41591 + 19.9959i) 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} +(17.3395 + 11.8466i) 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} +(-29.6984 + 18.5205i) 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} +(-9.60250 - 18.6760i) 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} +(1.36038 - 62.9853i) 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} +(7.90396 - 34.0959i) 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} +(-14.9660 - 10.2250i) 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} +(-59.9877 - 19.2477i) 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} +(44.8733 + 19.6822i) 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

Properties

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