LMFDB - Embedded newform 105.3.k.c.62.7

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			62.7
Root			$-0.253395 - 0.611750i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.c.83.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.854662 - 2.87568i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 - 2.63775i) q^{6} +(3.94887 - 5.77983i) q^{7} +(4.94975 + 4.94975i) q^{8} +(-7.53910 - 4.91548i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.854662 - 2.87568i) 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} +(8.62705 + 2.56399i) q^{12} +(-8.94114 - 8.94114i) q^{13} +(-1.29468 - 6.87923i) q^{14} +(9.69428 - 11.4464i) q^{15} -5.00000 q^{16} +(-0.581460 - 0.581460i) q^{17} +(-8.80672 + 1.85519i) 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} +(-20.5787 + 17.4790i) q^{27} +(17.3395 + 11.8466i) q^{28} -11.5528 q^{29} +(-1.23896 - 14.9487i) q^{30} +30.8307i q^{31} +(-23.3345 + 23.3345i) q^{32} +(7.44617 + 2.21303i) 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} +(-20.8890 - 2.15633i) q^{42} +(-25.1548 + 25.1548i) q^{43} -7.76807 q^{44} +(-24.6310 - 37.6605i) q^{45} +37.4929 q^{46} +(-45.2473 - 45.2473i) q^{47} +(-4.27331 + 14.3784i) 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} +(-14.1697 + 47.6769i) q^{57} +(-8.16905 + 8.16905i) q^{58} +47.6223i q^{59} +(34.3393 + 29.0828i) q^{60} -78.9936i q^{61} +(21.8006 + 21.8006i) q^{62} +(-58.1816 + 24.1641i) 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} +(-12.9863 - 61.6470i) q^{72} +(-26.0359 - 26.0359i) q^{73} -58.6798 q^{74} +(67.3935 - 32.9106i) q^{75} -49.7380i q^{76} +(14.9660 + 10.2250i) q^{77} +(-10.8069 + 36.3621i) 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} +(-9.87373 + 33.2221i) q^{87} +(-12.8167 + 12.8167i) q^{88} +14.0533i q^{89} +(-44.0467 - 9.21327i) q^{90} +(-86.9857 + 16.3708i) q^{91} +(-79.5344 + 79.5344i) q^{92} +(88.6594 + 26.3499i) 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	−0.507877	−	0.861430i	$-0.669569\pi$
$2$	0.707107	−	0.707107i	0.353553	−	0.353553i	0.861430	+	0.507877i	$0.169569\pi$
$3$	0.854662	−	2.87568i	0.284887	−	0.958561i
$3$	0.854662	−	2.87568i	0.284887	−	0.958561i
$4$			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	$0.0375515\pi$
$11$			2.58936i			0.235396i	−0.993049	+	0.117698i	$0.962449\pi$
$12$	8.62705	+	2.56399i	0.718921	+	0.213666i
$13$	−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
$15$	9.69428	−	11.4464i	0.646285	−	0.763096i
$16$	−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	$0.757699\pi$
$18$	−8.80672	+	1.85519i	−0.489262	+	0.103066i
$19$	−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
$21$	−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	$0.0532972\pi$
$23$	26.5115	+	26.5115i	1.15267	+	1.15267i	0.166657	+	0.986015i	$0.446703\pi$
$24$	18.4643	−	10.0035i	0.769344	−	0.416814i
$25$	16.9155	+	18.4083i	0.676619	+	0.736333i
$26$	−12.6447			−0.486334
$27$	−20.5787	+	17.4790i	−0.762176	+	0.647370i
$28$	17.3395	+	11.8466i	0.619267	+	0.423094i
$29$	−11.5528			−0.398372			−0.199186	−	0.979962i	$-0.563830\pi$
$29$	−11.5528			−0.398372			−0.199186	+	0.979962i	$0.563830\pi$
$30$	−1.23896	−	14.9487i	−0.0412987	−	0.498291i
$31$			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
$33$	7.44617	+	2.21303i	0.225642	+	0.0670614i
$34$	−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	$-0.432936\pi$
$41$	17.1489			0.418267			0.209133	+	0.977887i	$0.432936\pi$
$42$	−20.8890	−	2.15633i	−0.497357	−	0.0513413i
$43$	−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
$45$	−24.6310	−	37.6605i	−0.547355	−	0.836900i
$46$	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	$0.988341\pi$
$48$	−4.27331	+	14.3784i	−0.0890273	+	0.299550i
$49$	−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	0.951665	−	0.307137i	$-0.0993710\pi$
$53$	34.1600	+	34.1600i	0.644528	+	0.644528i	−0.307137	+	0.951665i	$0.599371\pi$
$54$	−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
$57$	−14.1697	+	47.6769i	−0.248592	+	0.836436i
$58$	−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	$0.867766\pi$
$60$	34.3393	+	29.0828i	0.572322	+	0.484714i
$61$		−	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
$63$	−58.1816	+	24.1641i	−0.923517	+	0.383557i
$64$			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	$-0.887809\pi$
$71$		−	49.0193i		−	0.690413i	0.938527	−	0.345207i	$-0.112191\pi$
$72$	−12.9863	−	61.6470i	−0.180365	−	0.856209i
$73$	−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
$75$	67.3935	−	32.9106i	0.898581	−	0.438808i
$76$		−	49.7380i		−	0.654447i
$77$	14.9660	+	10.2250i	0.194364	+	0.132793i
$78$	−10.8069	+	36.3621i	−0.138550	+	0.466181i
$79$		−	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
$87$	−9.87373	+	33.2221i	−0.113491	+	0.381864i
$88$	−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	$0.974843\pi$
$90$	−44.0467	−	9.21327i	−0.489408	−	0.102370i
$91$	−86.9857	+	16.3708i	−0.955887	+	0.179899i
$92$	−79.5344	+	79.5344i	−0.864504	+	0.864504i
$93$	88.6594	+	26.3499i	0.953327	+	0.283332i
$94$	−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	$-0.462580\pi$
$101$	23.6924			0.234579			0.117289	+	0.993098i	$0.462580\pi$
$102$	−0.702797	+	2.36470i	−0.00689016	+	0.0231833i
$103$	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
$105$	−27.8769	−	101.232i	−0.265494	−	0.964112i
$106$	48.3095			0.455750
$107$	124.868	−	124.868i	1.16699	−	1.16699i	0.184083	−	0.982911i	$-0.441069\pi$
$107$	124.868	−	124.868i	1.16699	−	1.16699i	0.982911	−	0.184083i	$-0.0589315\pi$
$108$	−52.4370	−	61.7362i	−0.485528	−	0.571632i
$109$			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	0.439562	−	0.898212i	$-0.355134\pi$
$113$	−51.8276	−	51.8276i	−0.458651	−	0.458651i	−0.898212	+	0.439562i	$0.855134\pi$
$114$	23.6931	+	43.7321i	0.207834	+	0.383615i
$115$	68.0662	+	174.671i	0.591880	+	1.51888i
$116$		−	34.6583i		−	0.298779i
$117$	23.4582	+	111.358i	0.200498	+	0.951779i
$118$	33.6740	+	33.6740i	0.285373	+	0.285373i
$119$	−5.65685	+	1.06463i	−0.0475366	+	0.00894644i
$120$	104.641	−	8.67273i	0.872010	−	0.0722727i
$121$	114.295			0.944589
$122$	−55.8569	−	55.8569i	−0.457843	−	0.457843i
$123$	14.6565	−	49.3149i	0.119159	−	0.400934i
$124$	−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	$0.812100\pi$
$132$	−6.63908	+	22.3385i	−0.0502960	+	0.169231i
$133$	−65.4696	+	95.8256i	−0.492253	+	0.720493i
$134$	102.500			0.764927
$135$	−129.351	+	38.6439i	−0.958155	+	0.286251i
$136$		−	5.75616i		−	0.0423247i
$137$	32.1683	−	32.1683i	0.234805	−	0.234805i	−0.579890	−	0.814695i	$-0.696904\pi$
$137$	32.1683	−	32.1683i	0.234805	−	0.234805i	0.814695	+	0.579890i	$0.196904\pi$
$138$	32.0437	−	107.818i	0.232201	−	0.781287i
$139$	−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
$147$	−146.492	+	12.2106i	−0.996544	+	0.0830654i
$148$	124.479	−	124.479i	0.841071	−	0.841071i
$149$	−24.7386			−0.166031			−0.0830155	−	0.996548i	$-0.526455\pi$
$149$	−24.7386			−0.166031			−0.0830155	+	0.996548i	$0.526455\pi$
$150$	24.3831	−	70.9258i	0.162554	−	0.472838i
$151$	−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
$153$	1.52554	+	7.24185i	0.00997082	+	0.0473323i
$154$	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
$162$	75.5139	+	29.3028i	0.466135	+	0.180881i
$163$	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
$165$	29.6389	+	25.1020i	0.179630	+	0.152133i
$166$		−	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	$0.409203\pi$
$168$	15.0943	−	146.223i	0.0898473	−	0.870375i
$169$		−	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
$175$	173.194	−	25.0763i	0.989680	−	0.143293i
$176$		−	12.9468i		−	0.0735613i
$177$	136.947	+	40.7010i	0.773710	+	0.229949i
$178$	9.93722	+	9.93722i	0.0558271	+	0.0558271i
$179$	236.871			1.32330			0.661650	−	0.749813i	$-0.269857\pi$
$179$	236.871			1.32330			0.661650	+	0.749813i	$0.269857\pi$
$180$	112.982	−	73.8930i	0.627675	−	0.410516i
$181$		−	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
$183$	−227.160	−	67.5128i	−1.24131	−	0.368923i
$184$			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	$0.423222\pi$
$191$			370.941i			1.94210i	−0.238872	+	0.971051i	$0.576778\pi$
$192$	37.3839	+	11.1106i	0.194708	+	0.0578678i
$193$	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
$195$	−189.022	+	15.6663i	−0.969345	+	0.0803399i
$196$	136.943	−	53.4383i	0.698688	−	0.272645i
$197$	182.194	−	182.194i	0.924845	−	0.924845i	−0.0725218	−	0.997367i	$-0.523105\pi$
$197$	182.194	−	182.194i	0.924845	−	0.924845i	0.997367	+	0.0725218i	$0.0231047\pi$
$198$	−4.80374	−	22.8037i	−0.0242613	−	0.115170i
$199$	−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
$207$	−69.5562	−	330.189i	−0.336020	−	1.59512i
$208$	44.7057	+	44.7057i	0.214931	+	0.214931i
$209$		−	42.9298i		−	0.205406i
$210$	−91.2937	−	51.8697i	−0.434732	−	0.246999i
$211$	−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
$213$	−140.964	−	41.8950i	−0.661803	−	0.196690i
$214$		−	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
$222$	−50.1514	+	168.744i	−0.225907	+	0.760110i
$223$	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
$225$	−37.0418	−	221.930i	−0.164630	−	0.986355i
$226$	−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	$0.806600\pi$
$228$	−143.031	−	42.5092i	−0.627327	−	0.186444i
$229$	−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
$231$	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	0.806748	−	0.590895i	$-0.201225\pi$
$233$	50.2938	+	50.2938i	0.215853	+	0.215853i	−0.590895	+	0.806748i	$0.701225\pi$
$234$	95.3296	+	62.1547i	0.407392	+	0.265618i
$235$	−116.169	−	298.112i	−0.494336	−	1.26856i
$236$	−142.867			−0.605368
$237$	−217.984	−	64.7854i	−0.919762	−	0.273356i
$238$	−3.24720	+	4.75280i	−0.0136437	+	0.0199698i
$239$	−131.741			−0.551216			−0.275608	−	0.961270i	$-0.588879\pi$
$239$	−131.741			−0.551216			−0.275608	+	0.961270i	$0.588879\pi$
$240$	−48.4714	+	57.2322i	−0.201964	+	0.238467i
$241$			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
$243$	241.063	−	30.6217i	0.992028	−	0.126015i
$244$	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	$-0.757650\pi$
$251$	−363.395			−1.44779			−0.723895	+	0.689910i	$0.757650\pi$
$252$	−72.4924	−	174.545i	−0.287668	−	0.692638i
$253$	−68.6476	+	68.6476i	−0.271334	+	0.271334i
$254$	30.6144			0.120529
$255$	−12.2925	+	1.01881i	−0.0482058	+	0.00399533i
$256$	−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	$0.673135\pi$
$258$	102.300	+	30.4039i	0.396512	+	0.117845i
$259$	−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	0.867880	−	0.496774i	$-0.165482\pi$
$263$	97.6009	+	97.6009i	0.371106	+	0.371106i	−0.496774	+	0.867880i	$0.665482\pi$
$264$	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
$267$	40.4130	+	12.0109i	0.151359	+	0.0449845i
$268$	−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	$0.928512\pi$
$270$	−64.1395	+	118.790i	−0.237554	+	0.439964i
$271$			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
$273$	−27.2662	+	264.135i	−0.0998761	+	0.967527i
$274$		−	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	$0.00358738\pi$
$281$			6.33365i			0.0225397i	−0.999936	+	0.0112698i	$0.996413\pi$
$282$	−54.6893	+	184.013i	−0.193934	+	0.652529i
$283$	−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
$285$	−160.725	+	189.774i	−0.563946	+	0.665874i
$286$		−	32.7416i		−	0.114481i
$287$	67.7190	−	99.1178i	0.235955	−	0.345358i
$288$	290.622	−	61.2211i	1.00910	−	0.212573i
$289$		−	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
$297$	−45.2594	−	53.2857i	−0.152388	−	0.179413i
$298$	−17.4929	+	17.4929i	−0.0587009	+	0.0587009i
$299$		−	474.085i		−	1.58557i
$300$	98.7319	+	202.181i	0.329106	+	0.673935i
$301$	46.0572	+	244.723i	0.153014	+	0.813034i
$302$	−82.5025	+	82.5025i	−0.273187	+	0.273187i
$303$	20.2490	−	68.1319i	0.0668285	−	0.224858i
$304$	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	$-0.455074\pi$
$311$	87.4973			0.281342			0.140671	+	0.990056i	$0.455074\pi$
$312$	−254.535	−	75.6486i	−0.815817	−	0.242463i
$313$	−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
$315$	−314.936	−	6.35383i	−0.999797	−	0.0201709i
$316$	227.407			0.719643
$317$	−393.091	+	393.091i	−1.24003	+	1.24003i	−0.280048	+	0.959986i	$0.590350\pi$
$317$	−393.091	+	393.091i	−1.24003	+	1.24003i	−0.959986	+	0.280048i	$0.909650\pi$
$318$	41.2883	−	138.923i	0.129838	−	0.436864i
$319$		−	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
$327$	209.884	+	62.3781i	0.641846	+	0.190759i
$328$	84.8829	+	84.8829i	0.258789	+	0.258789i
$329$	−440.198	+	82.8456i	−1.33799	+	0.251810i
$330$	38.7076	−	3.20811i	0.117296	−	0.00972155i
$331$	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
$333$	108.862	+	516.776i	0.326912	+	1.55188i
$334$	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
$342$	146.009	−	30.7577i	0.426928	−	0.0899348i
$343$	−334.176	−	77.3019i	−0.974273	−	0.225370i
$344$	−249.019			−0.723894
$345$	560.471	−	46.4522i	1.62455	−	0.134644i
$346$			163.263i			0.471857i
$347$	−226.173	+	226.173i	−0.651796	+	0.651796i	−0.953425	−	0.301629i	$-0.902469\pi$
$347$	−226.173	+	226.173i	−0.651796	+	0.651796i	0.301629	+	0.953425i	$0.402469\pi$
$348$	−99.6664	−	29.6212i	−0.286398	−	0.0851183i
$349$	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	−0.980347	−	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
$357$	−1.77317	+	17.1772i	−0.00496687	+	0.0481154i
$358$	167.493	−	167.493i	0.467857	−	0.467857i
$359$	392.633			1.09368			0.546842	−	0.837236i	$-0.315830\pi$
$359$	392.633			1.09368			0.546842	+	0.837236i	$0.315830\pi$
$360$	64.4929	−	308.327i	0.179147	−	0.856464i
$361$	−86.1262			−0.238577
$362$	−161.125	−	161.125i	−0.445098	−	0.445098i
$363$	97.6838	−	328.677i	0.269101	−	0.905446i
$364$	−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
$372$	−79.0496	+	265.978i	−0.212499	+	0.714995i
$373$	−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
$375$	374.693	−	15.1664i	0.999182	−	0.0404437i
$376$		−	447.926i		−	1.19129i
$377$	103.295	+	103.295i	0.273992	+	0.273992i
$378$	146.885	+	118.936i	0.388584	+	0.314646i
$379$			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
$385$	47.9561	+	76.8996i	0.124561	+	0.199739i
$386$		−	115.447i		−	0.299085i
$387$	313.292	−	65.9967i	0.809540	−	0.170534i
$388$	77.8991	+	77.8991i	0.200771	+	0.200771i
$389$	−747.341			−1.92119			−0.960593	−	0.277960i	$-0.910342\pi$
$389$	−747.341			−1.92119			−0.960593	+	0.277960i	$0.910342\pi$
$390$	−122.581	+	144.737i	−0.314311	+	0.371120i
$391$		−	30.8307i		−	0.0788509i
$392$	137.775	−	314.113i	0.351468	−	0.801309i
$393$	−186.028	+	625.927i	−0.473353	+	1.59269i
$394$		−	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
$399$	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	$-0.799411\pi$
$401$		−	472.603i		−	1.17856i	0.807928	−	0.589281i	$-0.200589\pi$
$402$	87.6030	−	294.758i	0.217918	−	0.733229i
$403$	275.662	−	275.662i	0.684025	−	0.684025i
$404$			71.0773i			0.175934i
$405$	0.576206	+	405.000i	0.00142273	+	0.999999i
$406$	14.9571	+	79.4742i	0.0368402	+	0.195749i
$407$	107.440	−	107.440i	0.263980	−	0.263980i
$408$	−16.5529	−	4.91958i	−0.0405708	−	0.0120578i
$409$	−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
$417$	−96.2087	+	323.713i	−0.230716	+	0.776291i
$418$	−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	$0.965321\pi$
$420$	303.695	−	83.6308i	0.723084	−	0.199121i
$421$	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
$423$	118.712	+	563.536i	0.280643	+	1.33224i
$424$			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	$0.0666545\pi$
$431$			179.188i			0.415749i	−0.978156	+	0.207874i	$0.933346\pi$
$432$	102.894	−	87.3950i	0.238180	−	0.202303i
$433$	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
$435$	−111.996	+	132.238i	−0.257462	+	0.303996i
$436$	−218.957			−0.502195
$437$	−439.542	−	439.542i	−1.00582	−	1.00582i
$438$	−31.4689	+	105.883i	−0.0718468	+	0.241743i
$439$	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
$441$	−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	0.432527	−	0.901621i	$-0.357622\pi$
$443$	−207.809	−	207.809i	−0.469094	−	0.469094i	−0.901621	+	0.432527i	$0.857622\pi$
$444$	−251.574	−	464.348i	−0.566608	−	1.04583i
$445$	−28.2548	+	64.3357i	−0.0634939	+	0.144575i
$446$	113.065			0.253509
$447$	−21.1432	+	71.1405i	−0.0473002	+	0.159151i
$448$	75.1377	+	51.3354i	0.167718	+	0.114588i
$449$	−315.151			−0.701895			−0.350947	−	0.936395i	$-0.614140\pi$
$449$	−315.151			−0.701895			−0.350947	+	0.936395i	$0.614140\pi$
$450$	−183.121	−	130.736i	−0.406935	−	0.290524i
$451$			44.4047i			0.0984583i
$452$	155.483	−	155.483i	0.343988	−	0.343988i
$453$	−99.7188	+	335.524i	−0.220130	+	0.740670i
$454$	−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	$-0.709369\pi$
$461$	−563.655			−1.22268			−0.611339	+	0.791369i	$0.709369\pi$
$462$	5.58352	−	54.0891i	0.0120855	−	0.117076i
$463$	−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
$465$	352.902	+	298.882i	0.758929	+	0.642756i
$466$	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	$0.615133\pi$
$468$	−334.075	+	70.3747i	−0.713835	+	0.150373i
$469$	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
$477$	−89.6231	−	425.448i	−0.187889	−	0.891925i
$478$	−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	$0.818166\pi$
$480$	40.8857	+	493.309i	0.0851786	+	1.02773i
$481$			741.987i			1.54259i
$482$	72.8542	+	72.8542i	0.151150	+	0.151150i
$483$	80.8471	−	783.188i	0.167385	−	1.62151i
$484$			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	$0.141375\pi$
$491$			421.951i			0.859370i	−0.902979	+	0.429685i	$0.858625\pi$
$492$	147.945	+	43.9696i	0.300700	+	0.0893692i
$493$	6.71748	+	6.71748i	0.0136257	+	0.0136257i
$494$	209.640			0.424373
$495$	97.5165	−	63.7784i	0.197003	−	0.128845i
$496$		−	154.154i		−	0.310794i
$497$	−283.323	−	193.571i	−0.570067	−	0.389479i
$498$	−218.301	−	64.8798i	−0.438356	−	0.130281i
$499$		−	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
$507$	−26.2029	−	7.78759i	−0.0516823	−	0.0153601i
$508$	−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	$0.851040\pi$
$510$	−7.97170	+	9.41251i	−0.0156308	+	0.0184559i
$511$	−253.295	+	47.6704i	−0.495685	+	0.0932885i
$512$	215.668	−	215.668i	0.421226	−	0.421226i
$513$	341.181	−	289.790i	0.665071	−	0.564893i
$514$	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	$-0.405848\pi$
$521$	303.734			0.582983			0.291491	+	0.956573i	$0.405848\pi$
$522$	101.742	−	21.4325i	0.194908	−	0.0410585i
$523$	−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
$525$	75.9109	−	519.483i	0.144592	−	0.989491i
$526$	138.029			0.262412
$527$	17.9268	−	17.9268i	0.0340168	−	0.0340168i
$528$	−37.2308	−	11.0651i	−0.0705130	−	0.0209567i
$529$			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
$537$	202.444	−	681.165i	0.376992	−	1.26846i
$538$	84.7209	+	84.7209i	0.157474	+	0.157474i
$539$	118.198	−	46.1237i	0.219291	−	0.0855726i
$540$	−115.932	−	388.053i	−0.214688	−	0.718616i
$541$	−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
$543$	−655.270	−	194.748i	−1.20676	−	0.358653i
$544$	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
$552$	754.723	+	224.306i	1.36725	+	0.406352i
$553$	−438.125	−	299.334i	−0.792269	−	0.541291i
$554$	72.3842			0.130657
$555$	−877.189	+	72.7019i	−1.58052	+	0.130994i
$556$		−	337.708i		−	0.607388i
$557$	−328.316	+	328.316i	−0.589437	+	0.589437i	−0.937479	−	0.348042i	$-0.886847\pi$
$557$	−328.316	+	328.316i	−0.589437	+	0.589437i	0.348042	+	0.937479i	$0.386847\pi$
$558$	−57.1967	−	271.517i	−0.102503	−	0.486590i
$559$	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	−0.0886978	−	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
$567$	557.415	+	103.814i	0.983095	+	0.183094i
$568$	242.633	−	242.633i	0.427171	−	0.427171i
$569$	789.111			1.38684			0.693419	−	0.720534i	$-0.256103\pi$
$569$	789.111			1.38684			0.693419	+	0.720534i	$0.256103\pi$
$570$	20.5411	+	247.840i	0.0360371	+	0.434807i
$571$	−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
$573$	1066.71	+	317.030i	1.86162	+	0.553280i
$574$	−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
$582$	−105.601	−	31.3849i	−0.181445	−	0.0539260i
$583$	−88.4524	+	88.4524i	−0.151719	+	0.151719i
$584$		−	257.742i		−	0.441339i
$585$	−116.499	+	556.957i	−0.199143	+	0.952064i
$586$		−	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	$0.807656\pi$
$588$	−36.6318	−	439.476i	−0.0622991	−	0.747408i
$589$		−	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
$595$	−28.0373	−	6.49950i	−0.0471216	−	0.0109235i
$596$		−	74.2159i		−	0.124523i
$597$	−26.6962	+	89.8248i	−0.0447173	+	0.150460i
$598$	−335.229	−	335.229i	−0.560584	−	0.560584i
$599$	475.156			0.793248			0.396624	−	0.917981i	$-0.370182\pi$
$599$	475.156			0.793248			0.396624	+	0.917981i	$0.370182\pi$
$600$	496.480	+	170.682i	0.827467	+	0.284469i
$601$			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
$603$	−190.157	−	902.690i	−0.315351	−	1.49700i
$604$		−	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
$609$	153.028	+	188.258i	0.251278	+	0.309127i
$610$	−143.408	−	368.013i	−0.235096	−	0.603300i
$611$			809.125i			1.32426i
$612$	−21.7255	+	4.57661i	−0.0354992	+	0.00747812i
$613$	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
$615$	166.247	−	196.294i	0.270320	−	0.319177i
$616$	23.4667	+	124.689i	0.0380953	+	0.202418i
$617$	111.144	−	111.144i	0.180136	−	0.180136i	−0.611279	−	0.791415i	$-0.709345\pi$
$617$	111.144	−	111.144i	0.180136	−	0.180136i	0.791415	+	0.611279i	$0.209345\pi$
$618$	95.0646	−	319.864i	0.153826	−	0.517579i
$619$	−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
$627$	−123.452	−	36.6905i	−0.196894	−	0.0585175i
$628$	428.636	+	428.636i	0.682541	+	0.682541i
$629$			48.2529i			0.0767137i
$630$	−227.186	+	218.200i	−0.360613	+	0.346350i
$631$	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
$633$	−82.5522	+	277.764i	−0.130414	+	0.438805i
$634$			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	$-0.969871\pi$
$641$		−	121.164i		−	0.189024i	0.995524	−	0.0945120i	$-0.0301291\pi$
$642$	−507.818	−	150.925i	−0.790994	−	0.235086i
$643$	−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
$645$	44.0751	+	531.790i	0.0683334	+	0.824480i
$646$	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	$0.858505\pi$
$648$	−205.119	+	528.597i	−0.316542	+	0.815736i
$649$	−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	0.431488	−	0.902119i	$-0.357989\pi$
$653$	−307.322	−	307.322i	−0.470631	−	0.470631i	−0.902119	+	0.431488i	$0.857989\pi$
$654$	192.518	−	104.302i	0.294370	−	0.159484i
$655$	−996.449	−	437.618i	−1.52130	−	0.668119i
$656$	−85.7446			−0.130708
$657$	68.3085	+	324.266i	0.103970	+	0.493555i
$658$	−252.686	+	369.847i	−0.384021	+	0.562078i
$659$	903.538			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$659$	903.538			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$660$	−75.3059	+	88.9167i	−0.114100	+	0.134722i
$661$			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
$663$	29.9009	+	8.88664i	0.0450994	+	0.0134037i
$664$	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
$672$	689.337	+	71.1590i	1.02580	+	0.105891i
$673$	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
$675$	−669.858	−	83.1546i	−0.992383	−	0.123192i
$676$	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	$0.666504\pi$
$678$	−62.6427	+	210.774i	−0.0923933	+	0.310876i
$679$	−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	0.530952	−	0.847402i	$-0.321835\pi$
$683$	−216.136	−	216.136i	−0.316450	−	0.316450i	−0.847402	+	0.530952i	$0.821835\pi$
$684$	−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
$687$	−131.457	+	442.314i	−0.191350	+	0.643835i
$688$	125.774	−	125.774i	0.182811	−	0.182811i
$689$		−	610.859i		−	0.886587i
$690$	363.466	−	429.160i	0.526763	−	0.621970i
$691$			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
$693$	−62.5695	−	150.653i	−0.0902879	−	0.217392i
$694$			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	$-0.858706\pi$
$701$		−	602.095i		−	0.858908i	0.903089	−	0.429454i	$-0.141294\pi$
$702$	260.212	−	221.017i	0.370672	−	0.314838i
$703$	687.923	+	687.923i	0.978554	+	0.978554i
$704$	−33.6616			−0.0478148
$705$	−956.561	+	79.2803i	−1.35682	+	0.112454i
$706$			390.920i			0.553711i
$707$	93.5584	−	136.938i	0.132332	−	0.193689i
$708$	−122.103	+	410.840i	−0.172462	+	0.580282i
$709$		−	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
$717$	−112.594	+	378.845i	−0.157035	+	0.528375i
$718$	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	$0.908368\pi$
$720$	123.155	+	188.303i	0.171049	+	0.261531i
$721$	765.181	−	144.008i	1.06128	−	0.199734i
$722$	−60.9004	+	60.9004i	−0.0843496	+	0.0843496i
$723$	296.286	+	88.0571i	0.409800	+	0.121794i
$724$	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
$732$	202.538	−	681.481i	0.276692	−	0.930985i
$733$	−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
$735$	−695.185	−	238.628i	−0.945829	−	0.324664i
$736$	−1237.26			−1.68107
$737$	−187.673	+	187.673i	−0.254644	+	0.254644i
$738$	−151.026	+	31.8144i	−0.204642	+	0.0431090i
$739$		−	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	0.0577666	−	0.998330i	$-0.481602\pi$
$743$	−698.839	−	698.839i	−0.940563	−	0.940563i	−0.998330	+	0.0577666i	$0.981602\pi$
$744$	308.416	+	569.267i	0.414538	+	0.765143i
$745$	−113.253	−	49.7380i	−0.152017	−	0.0667624i
$746$			275.115i			0.368787i
$747$	−668.543	+	140.832i	−0.894971	+	0.188531i
$748$	4.51683	+	4.51683i	0.00603854	+	0.00603854i
$749$	−228.628	−	1214.81i	−0.305244	−	1.62190i
$750$	254.224	−	275.672i	0.338965	−	0.367563i
$751$	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
$753$	−310.580	+	1045.01i	−0.412457	+	1.38780i
$754$	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	$0.279152\pi$
$762$	26.1649	−	88.0372i	0.0343372	−	0.115534i
$763$	421.845	+	288.211i	0.552876	+	0.377734i
$764$	−1112.82			−1.45658
$765$	−7.57616	+	36.2200i	−0.00990347	+	0.0473465i
$766$		−	66.0510i		−	0.0862285i
$767$	425.798	−	425.798i	0.555147	−	0.555147i
$768$	−146.147	+	491.742i	−0.190296	+	0.640289i
$769$	−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	−0.260132	−	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
$777$	−126.533	+	1225.76i	−0.162848	+	1.57756i
$778$	−528.450	+	528.450i	−0.679242	+	0.679242i
$779$	−284.318			−0.364978
$780$	−46.9988	−	567.067i	−0.0602549	−	0.727008i
$781$	126.929			0.162521
$782$	−21.8006	−	21.8006i	−0.0278780	−	0.0278780i
$783$	237.742	−	201.931i	0.303629	−	0.257894i
$784$	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
$792$	159.626	−	33.6262i	0.201548	−	0.0424573i
$793$	−706.293	+	706.293i	−0.890659	+	0.890659i
$794$			453.775i			0.571505i
$795$	722.167	−	59.8536i	0.908386	−	0.0752876i
$796$		−	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	$0.785309\pi$
$798$	346.325	+	35.7506i	0.433992	+	0.0448002i
$799$			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
$807$	344.545	+	102.400i	0.426946	+	0.126890i
$808$	117.272	+	117.272i	0.145138	+	0.145138i
$809$	−89.2503			−0.110322			−0.0551609	−	0.998477i	$-0.517567\pi$
$809$	−89.2503			−0.110322			−0.0551609	+	0.998477i	$0.517567\pi$
$810$	286.785	+	285.971i	0.354056	+	0.353050i
$811$		−	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
$813$	709.275	+	210.799i	0.872417	+	0.259285i
$814$		−	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	$-0.859853\pi$
$821$		−	699.817i		−	0.852396i	0.904630	−	0.426198i	$-0.140147\pi$
$822$	−130.823	−	38.8810i	−0.159152	−	0.0473005i
$823$	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
$825$	85.2174	+	174.506i	0.103294	+	0.211522i
$826$	327.605	−	61.6556i	0.396616	−	0.0746435i
$827$	−459.616	+	459.616i	−0.555763	+	0.555763i	−0.928098	−	0.372335i	$-0.878557\pi$
$827$	−459.616	+	459.616i	−0.555763	+	0.555763i	0.372335	+	0.928098i	$0.378557\pi$
$828$	990.567	−	208.669i	1.19634	−	0.252015i
$829$	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
$837$	−538.890	−	634.457i	−0.643835	−	0.758014i
$838$	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	$0.756913\pi$
$840$	363.088	−	639.056i	0.432248	−	0.760780i
$841$	−707.533			−0.841300
$842$	43.3625	−	43.3625i	0.0514994	−	0.0514994i
$843$	18.2136	+	5.41313i	0.0216057	+	0.00642127i
$844$		−	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
$852$	125.685	−	422.892i	0.147518	−	0.496352i
$853$	−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
$855$	408.365	+	624.386i	0.477620	+	0.730276i
$856$	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	$0.662216\pi$
$858$	−94.1545	−	27.9830i	−0.109737	−	0.0326142i
$859$	−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
$861$	−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	0.685957	−	0.727642i	$-0.259384\pi$
$863$	−35.9749	−	35.9749i	−0.0416859	−	0.0416859i	−0.727642	+	0.685957i	$0.759384\pi$
$864$	72.3309	−	888.059i	0.0837163	−	1.02785i
$865$	−760.604	+	296.394i	−0.879310	+	0.342652i
$866$	331.251			0.382507
$867$	−829.128	−	246.420i	−0.956318	−	0.284221i
$868$	−365.240	+	534.589i	−0.420783	+	0.615886i
$869$	196.279			0.225868
$870$	14.3134	+	172.700i	0.0164522	+	0.198505i
$871$		−	1296.08i		−	1.48804i
$872$	−361.261	+	361.261i	−0.414290	+	0.414290i
$873$	−323.400	+	68.1261i	−0.370447	+	0.0780368i
$874$	−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	$-0.499089\pi$
$881$	5.04486			0.00572629			0.00286315	+	0.999996i	$0.499089\pi$
$882$	241.557	+	368.960i	0.273874	+	0.418322i
$883$	−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
$885$	545.106	+	461.664i	0.615939	+	0.521654i
$886$	−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	$0.550601\pi$
$888$	−1181.21	−	351.060i	−1.33019	−	0.395337i
$889$	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
$897$	−1363.32	−	405.183i	−1.51987	−	0.451709i
$898$	−222.845	+	222.845i	−0.248157	+	0.248157i
$899$		−	356.180i		−	0.396196i
$900$	665.790	−	111.125i	0.739767	−	0.123473i
$901$		−	39.7254i		−	0.0440903i
$902$	31.3989	+	31.3989i	0.0348103	+	0.0348103i
$903$	743.109	+	76.7099i	0.822934	+	0.0849500i
$904$		−	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	$0.0823656\pi$
$911$			466.216i			0.511763i	−0.966708	+	0.255881i	$0.917634\pi$
$912$	70.8486	−	238.384i	0.0776849	−	0.261386i
$913$	138.993	+	138.993i	0.152237	+	0.152237i
$914$	−505.969			−0.553576
$915$	−904.195	−	765.786i	−0.988191	−	0.836924i
$916$		−	461.436i		−	0.503751i
$917$	−859.520	+	1258.05i	−0.937318	+	1.37192i
$918$	16.9221	−	14.3731i	0.0184336	−	0.0156570i
$919$			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
$927$	−206.353	−	979.577i	−0.222603	−	1.05672i
$928$	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	$-0.464289\pi$
$930$	460.881	−	38.1981i	0.495571	−	0.0410732i
$931$	295.324	+	756.806i	0.317211	+	0.812896i
$932$	−150.881	+	150.881i	−0.161890	+	0.161890i
$933$	74.7807	−	251.615i	0.0801508	−	0.269683i
$934$	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	$-0.747024\pi$
$941$	−1318.27			−1.40093			−0.700464	+	0.713687i	$0.747024\pi$
$942$	−581.063	−	172.694i	−0.616840	−	0.183327i
$943$	454.643	+	454.643i	0.482124	+	0.482124i
$944$		−	238.111i		−	0.252237i
$945$	−287.435	+	900.225i	−0.304165	+	0.952620i
$946$	−92.1143			−0.0973724
$947$	347.435	−	347.435i	0.366880	−	0.366880i	−0.499458	−	0.866338i	$-0.666468\pi$
$947$	347.435	−	347.435i	0.366880	−	0.366880i	0.866338	+	0.499458i	$0.166468\pi$
$948$	194.356	−	653.951i	0.205017	−	0.689821i
$949$			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	$0.0135452\pi$
$953$	992.679	+	992.679i	1.04164	+	1.04164i	0.0425407	+	0.999095i	$0.486455\pi$
$954$	−364.211	−	237.464i	−0.381772	−	0.248914i
$955$	−745.792	+	1698.16i	−0.780934	+	1.77817i
$956$		−	395.222i		−	0.413412i
$957$	−86.0240	−	25.5666i	−0.0898892	−	0.0267154i
$958$	366.262	+	366.262i	0.382320	+	0.382320i
$959$	−58.8986	−	312.956i	−0.0614167	−	0.326336i
$960$	148.804	+	126.026i	0.155004	+	0.131277i
$961$	10.4667			0.0108915
$962$	524.664	+	524.664i	0.545389	+	0.545389i
$963$	−1555.18	+	327.608i	−1.61494	+	0.340195i
$964$	−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	$0.437397\pi$
$972$	91.8652	+	723.189i	0.0945115	+	0.744021i
$973$	−444.522	+	650.631i	−0.456857	+	0.668685i
$974$	522.283			0.536224
$975$	−896.834	−	308.317i	−0.919830	−	0.316222i
$976$			394.968i			0.404680i
$977$	305.408	−	305.408i	0.312598	−	0.312598i	−0.533318	−	0.845915i	$-0.679055\pi$
$977$	305.408	−	305.408i	0.312598	−	0.312598i	0.845915	+	0.533318i	$0.179055\pi$
$978$	−395.112	−	117.429i	−0.404000	−	0.120070i
$979$	−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	−0.921121	−	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
$987$	−137.982	+	1336.67i	−0.139800	+	1.35428i
$988$	−444.714	+	444.714i	−0.450116	+	0.450116i
$989$	−1333.78			−1.34861
$990$	23.8564	−	114.053i	0.0240974	−	0.115205i
$991$	−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
$993$	209.380	−	704.501i	0.210856	−	0.709467i
$994$	−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.62.7	yes	16
3.2	odd	2	inner	105.3.k.c.62.1	✓	16
5.3	odd	4	inner	105.3.k.c.83.4	yes	16
7.6	odd	2	inner	105.3.k.c.62.6	yes	16
15.8	even	4	inner	105.3.k.c.83.6	yes	16
21.20	even	2	inner	105.3.k.c.62.4	yes	16
35.13	even	4	inner	105.3.k.c.83.1	yes	16
105.83	odd	4	inner	105.3.k.c.83.7	yes	16

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.854662 - 2.87568i) q^{3} +3.00000i q^{4} +(4.57796 + 2.01054i) q^{5} +(-1.42908 - 2.63775i) q^{6} +(3.94887 - 5.77983i) q^{7} +(4.94975 + 4.94975i) q^{8} +(-7.53910 - 4.91548i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.854662 - 2.87568i) 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} +(8.62705 + 2.56399i) q^{12} +(-8.94114 - 8.94114i) q^{13} +(-1.29468 - 6.87923i) q^{14} +(9.69428 - 11.4464i) q^{15} -5.00000 q^{16} +(-0.581460 - 0.581460i) q^{17} +(-8.80672 + 1.85519i) 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} +(-20.5787 + 17.4790i) q^{27} +(17.3395 + 11.8466i) q^{28} -11.5528 q^{29} +(-1.23896 - 14.9487i) q^{30} +30.8307i q^{31} +(-23.3345 + 23.3345i) q^{32} +(7.44617 + 2.21303i) 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} +(-20.8890 - 2.15633i) q^{42} +(-25.1548 + 25.1548i) q^{43} -7.76807 q^{44} +(-24.6310 - 37.6605i) q^{45} +37.4929 q^{46} +(-45.2473 - 45.2473i) q^{47} +(-4.27331 + 14.3784i) 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} +(-14.1697 + 47.6769i) q^{57} +(-8.16905 + 8.16905i) q^{58} +47.6223i q^{59} +(34.3393 + 29.0828i) q^{60} -78.9936i q^{61} +(21.8006 + 21.8006i) q^{62} +(-58.1816 + 24.1641i) 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} +(-12.9863 - 61.6470i) q^{72} +(-26.0359 - 26.0359i) q^{73} -58.6798 q^{74} +(67.3935 - 32.9106i) q^{75} -49.7380i q^{76} +(14.9660 + 10.2250i) q^{77} +(-10.8069 + 36.3621i) 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} +(-9.87373 + 33.2221i) q^{87} +(-12.8167 + 12.8167i) q^{88} +14.0533i q^{89} +(-44.0467 - 9.21327i) q^{90} +(-86.9857 + 16.3708i) q^{91} +(-79.5344 + 79.5344i) q^{92} +(88.6594 + 26.3499i) 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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