LMFDB - Embedded newform 105.3.k.c.83.6

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			83.6
Root			$0.253395 - 0.611750i$ of defining polynomial
Character	$\chi$	$=$	105.83
Dual form			105.3.k.c.62.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +(-4.65877 - 1.81544i) q^{10} -2.58936i q^{11} +(-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} +(-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} +(20.5787 + 17.4790i) q^{27} +(-11.8466 + 17.3395i) 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} +(34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 + 41.4929i) q^{37} +(11.7233 + 11.7233i) q^{38} +(-33.3536 - 18.0702i) q^{39} +(-12.7081 + 32.6114i) q^{40} -17.1489 q^{41} +(-18.6760 + 9.60250i) 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} +(62.9853 + 1.36038i) q^{63} -13.0000i q^{64} +(-22.9557 + 58.9087i) q^{65} +(-6.83008 - 3.70039i) q^{66} +(72.4786 - 72.4786i) q^{67} +(-1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 + 28.8899i) q^{70} +49.0193i q^{71} +(-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} +(-10.2250 + 14.9660i) 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} +(59.9877 + 19.2477i) 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} +(-19.6822 + 44.8733i) q^{98} +(12.7279 + 19.5214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{7}+O(q^{10}) $ 16 * q + 32 * q^7	$ 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) $ 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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	$-0.169569\pi$
$2$	0.707107	+	0.707107i	0.353553	+	0.353553i	−0.507877	+	0.861430i	$0.669569\pi$
$3$	−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
$7$	−5.77983	−	3.94887i	−0.825689	−	0.564125i
$7$	−5.77983	−	3.94887i	−0.825689	−	0.564125i
$8$	4.94975	−	4.94975i	0.618718	−	0.618718i
$9$	−7.53910	+	4.91548i	−0.837678	+	0.546164i
$10$	−4.65877	−	1.81544i	−0.465877	−	0.181544i
$11$		−	2.58936i		−	0.235396i	−0.993049	−	0.117698i	$-0.962449\pi$
$11$		−	2.58936i		−	0.235396i	0.993049	−	0.117698i	$-0.0375515\pi$
$12$	−8.62705	+	2.56399i	−0.718921	+	0.213666i
$13$	8.94114	−	8.94114i	0.687780	−	0.687780i	−0.273961	−	0.961741i	$-0.588334\pi$
$13$	8.94114	−	8.94114i	0.687780	−	0.687780i	0.961741	+	0.273961i	$0.0883338\pi$
$14$	−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	$-0.742301\pi$
$17$	0.581460	−	0.581460i	0.0342036	−	0.0342036i	0.724002	+	0.689798i	$0.242301\pi$
$18$	−8.80672	−	1.85519i	−0.489262	−	0.103066i
$19$	16.5793			0.872596			0.436298	−	0.899802i	$-0.356289\pi$
$19$	16.5793			0.872596			0.436298	+	0.899802i	$0.356289\pi$
$20$	6.03161	+	13.7339i	0.301581	+	0.686694i
$21$	−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	0.166657	−	0.986015i	$-0.446703\pi$
$23$	26.5115	−	26.5115i	1.15267	−	1.15267i	0.986015	−	0.166657i	$-0.0532972\pi$
$24$	−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
$28$	−11.8466	+	17.3395i	−0.423094	+	0.619267i
$29$	−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
$35$	34.3992	+	6.45724i	0.982834	+	0.184493i
$36$	14.7464	+	22.6173i	0.409623	+	0.628259i
$37$	−41.4929	+	41.4929i	−1.12143	+	1.12143i	−0.129902	+	0.991527i	$0.541466\pi$
$37$	−41.4929	+	41.4929i	−1.12143	+	1.12143i	−0.991527	+	0.129902i	$0.958534\pi$
$38$	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	$0.567064\pi$
$42$	−18.6760	+	9.60250i	−0.444666	+	0.228631i
$43$	−25.1548	−	25.1548i	−0.584994	−	0.584994i	0.351277	−	0.936272i	$-0.385748\pi$
$43$	−25.1548	−	25.1548i	−0.584994	−	0.584994i	−0.936272	+	0.351277i	$0.885748\pi$
$44$	−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	$-0.511659\pi$
$47$	45.2473	−	45.2473i	0.962709	−	0.962709i	0.999329	+	0.0366205i	$0.0116593\pi$
$48$	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	−0.307137	−	0.951665i	$-0.599371\pi$
$53$	34.1600	−	34.1600i	0.644528	−	0.644528i	0.951665	+	0.307137i	$0.0993710\pi$
$54$	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
$63$	62.9853	+	1.36038i	0.999767	+	0.0215933i
$64$		−	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	0.0854251	−	0.996345i	$-0.472775\pi$
$67$	72.4786	−	72.4786i	1.08177	−	1.08177i	0.996345	−	0.0854251i	$-0.0272248\pi$
$68$	−1.74438	−	1.74438i	−0.0256527	−	0.0256527i
$69$	−98.8969	−	53.5802i	−1.43329	−	0.776524i
$70$	19.7579	+	28.8899i	0.282256	+	0.412712i
$71$			49.0193i			0.690413i	0.938527	+	0.345207i	$0.112191\pi$
$71$			49.0193i			0.690413i	−0.938527	+	0.345207i	$0.887809\pi$
$72$	−12.9863	+	61.6470i	−0.180365	+	0.856209i
$73$	26.0359	−	26.0359i	0.356656	−	0.356656i	−0.505923	−	0.862579i	$-0.668848\pi$
$73$	26.0359	−	26.0359i	0.356656	−	0.356656i	0.862579	+	0.505923i	$0.168848\pi$
$74$	−58.6798			−0.792970
$75$	−67.3935	−	32.9106i	−0.898581	−	0.438808i
$76$		−	49.7380i		−	0.654447i
$77$	−10.2250	+	14.9660i	−0.132793	+	0.194364i
$78$	−10.8069	−	36.3621i	−0.138550	−	0.466181i
$79$			75.8024i			0.959524i	0.877399	+	0.479762i	$0.159277\pi$
$79$			75.8024i			0.959524i	−0.877399	+	0.479762i	$0.840723\pi$
$80$	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	$-0.401186\pi$
$83$	−53.6785	−	53.6785i	−0.646729	−	0.646729i	−0.952201	+	0.305472i	$0.901186\pi$
$84$	59.9877	+	19.2477i	0.714139	+	0.229140i
$85$	−1.49286	+	3.83095i	−0.0175630	+	0.0450700i
$86$		−	35.5742i		−	0.413654i
$87$	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	$-0.310618\pi$
$97$	−25.9664	−	25.9664i	−0.267695	−	0.267695i	−0.828171	+	0.560476i	$0.810618\pi$
$98$	−19.6822	+	44.8733i	−0.200839	+	0.457891i
$99$	12.7279	+	19.5214i	0.128565	+	0.197186i
$100$	−55.2250	−	50.7464i	−0.552250	−	0.507464i
$101$	−23.6924			−0.234579			−0.117289	−	0.993098i	$-0.537420\pi$
$101$	−23.6924			−0.234579			−0.117289	+	0.993098i	$0.537420\pi$
$102$	−0.702797	−	2.36470i	−0.00689016	−	0.0231833i
$103$	−78.6519	+	78.6519i	−0.763611	+	0.763611i	−0.976973	−	0.213362i	$-0.931559\pi$
$103$	−78.6519	+	78.6519i	−0.763611	+	0.763611i	0.213362	+	0.976973i	$0.431559\pi$
$104$		−	88.5128i		−	0.851085i
$105$	−10.8307	−	104.440i	−0.103150	−	0.994666i
$106$	48.3095			0.455750
$107$	124.868	+	124.868i	1.16699	+	1.16699i	0.982911	+	0.184083i	$0.0589315\pi$
$107$	124.868	+	124.868i	1.16699	+	1.16699i	0.184083	+	0.982911i	$0.441069\pi$
$108$	52.4370	−	61.7362i	0.485528	−	0.571632i
$109$		−	72.9857i		−	0.669594i	−0.942290	−	0.334797i	$-0.891332\pi$
$109$		−	72.9857i		−	0.669594i	0.942290	−	0.334797i	$-0.108668\pi$
$110$	−4.70083	+	12.0632i	−0.0427348	+	0.109666i
$111$	154.783	+	83.8579i	1.39444	+	0.755477i
$112$	28.8991	+	19.7444i	0.258028	+	0.176289i
$113$	−51.8276	+	51.8276i	−0.458651	+	0.458651i	−0.898212	−	0.439562i	$-0.855134\pi$
$113$	−51.8276	+	51.8276i	−0.458651	+	0.458651i	0.439562	+	0.898212i	$0.355134\pi$
$114$	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
$126$	43.5754	+	45.4993i	0.345837	+	0.361105i
$127$	21.6476	−	21.6476i	0.170454	−	0.170454i	−0.616725	−	0.787179i	$-0.711541\pi$
$127$	21.6476	−	21.6476i	0.170454	−	0.170454i	0.787179	+	0.616725i	$0.211541\pi$
$128$	−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	$0.187900\pi$
$132$	6.63908	+	22.3385i	0.0502960	+	0.169231i
$133$	−95.8256	−	65.4696i	−0.720493	−	0.492253i
$134$	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	0.814695	−	0.579890i	$-0.196904\pi$
$137$	32.1683	+	32.1683i	0.234805	+	0.234805i	−0.579890	+	0.814695i	$0.696904\pi$
$138$	−32.0437	−	107.818i	−0.232201	−	0.781287i
$139$	112.569			0.809851			0.404925	−	0.914350i	$-0.367298\pi$
$139$	112.569			0.809851			0.404925	+	0.914350i	$0.367298\pi$
$140$	19.3717	−	103.198i	0.138369	−	0.737125i
$141$	−168.788	−	91.4457i	−1.19708	−	0.648551i
$142$	−34.6619	+	34.6619i	−0.244098	+	0.244098i
$143$	−23.1518	−	23.1518i	−0.161901	−	0.161901i
$144$	37.6955	−	24.5774i	0.261774	−	0.170676i
$145$	52.8882	−	23.2273i	0.364746	−	0.160188i
$146$	36.8203			0.252194
$147$	116.044	−	90.2372i	0.789416	−	0.613859i
$148$	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	$-0.472521\pi$
$157$	−142.879	−	142.879i	−0.910055	−	0.910055i	−0.996276	+	0.0862209i	$0.972521\pi$
$158$	−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	0.939257	−	0.343215i	$-0.111516\pi$
$163$	97.1548	+	97.1548i	0.596041	+	0.596041i	−0.343215	+	0.939257i	$0.611516\pi$
$164$			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	−0.281396	+	0.959592i	$0.590797\pi$
$167$	−207.245	+	207.245i	−1.24099	+	1.24099i	−0.959592	+	0.281396i	$0.909203\pi$
$168$	67.2175	+	130.732i	0.400104	+	0.778165i
$169$			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	$-0.0935837\pi$
$173$	115.444	+	115.444i	0.667307	+	0.667307i	−0.289785	+	0.957092i	$0.593584\pi$
$174$	−16.5098	+	30.4734i	−0.0948840	+	0.175134i
$175$	−170.461	+	39.5999i	−0.974061	+	0.226285i
$176$			12.9468i			0.0735613i
$177$	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	$-0.216725\pi$
$182$	−73.0841	−	49.9323i	−0.401561	−	0.274353i
$183$	−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
$189$	−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	$-0.423222\pi$
$192$	−37.3839	+	11.1106i	−0.194708	+	0.0578678i
$193$	81.6333	+	81.6333i	0.422971	+	0.422971i	0.886225	−	0.463255i	$-0.153318\pi$
$193$	81.6333	+	81.6333i	0.422971	+	0.422971i	−0.463255	+	0.886225i	$0.653318\pi$
$194$		−	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	0.997367	−	0.0725218i	$-0.0231047\pi$
$197$	182.194	+	182.194i	0.924845	+	0.924845i	−0.0725218	+	0.997367i	$0.523105\pi$
$198$	−4.80374	+	22.8037i	−0.0242613	+	0.115170i
$199$	31.2360			0.156965			0.0784824	−	0.996915i	$-0.474993\pi$
$199$	31.2360			0.156965			0.0784824	+	0.996915i	$0.474993\pi$
$200$	−7.38926	−	174.844i	−0.0369463	−	0.874220i
$201$	−270.370	−	146.481i	−1.34512	−	0.728760i
$202$	−16.7531	−	16.7531i	−0.0829360	−	0.0829360i
$203$	66.7731	+	45.6205i	0.328931	+	0.224731i
$204$	−3.52543	+	6.50714i	−0.0172815	+	0.0318978i
$205$	78.5071	−	34.4786i	0.382962	−	0.168188i
$206$	−111.231			−0.539954
$207$	−69.5562	+	330.189i	−0.336020	+	1.59512i
$208$	−44.7057	+	44.7057i	−0.214931	+	0.214931i
$209$		−	42.9298i		−	0.205406i
$210$	66.1917	−	81.5086i	0.315199	−	0.388136i
$211$	−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
$217$	121.747	−	178.196i	0.561044	−	0.821181i
$218$	51.6087	−	51.6087i	0.236737	−	0.236737i
$219$	−97.1228	−	52.6190i	−0.443483	−	0.240270i
$220$	35.5619	−	15.6180i	0.161645	−	0.0709909i
$221$		−	10.3978i		−	0.0470491i
$222$	50.1514	+	168.744i	0.225907	+	0.760110i
$223$	−79.9490	+	79.9490i	−0.358516	+	0.358516i	−0.863266	−	0.504750i	$-0.831585\pi$
$223$	−79.9490	+	79.9490i	−0.358516	+	0.358516i	0.504750	+	0.863266i	$0.331585\pi$
$224$	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	$-0.693400\pi$
$227$	56.7824	−	56.7824i	0.250143	−	0.250143i	0.821029	+	0.570886i	$0.193400\pi$
$228$	−143.031	+	42.5092i	−0.627327	+	0.186444i
$229$	153.812			0.671668			0.335834	−	0.941921i	$-0.390982\pi$
$229$	153.812			0.671668			0.335834	+	0.941921i	$0.390982\pi$
$230$	−171.641	+	75.3808i	−0.746265	+	0.327743i
$231$	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	$-0.701225\pi$
$233$	50.2938	−	50.2938i	0.215853	−	0.215853i	0.806748	+	0.590895i	$0.201225\pi$
$234$	−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
$238$	−4.75280	−	3.24720i	−0.0199698	−	0.0136437i
$239$	−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
$245$	−173.322	−	173.160i	−0.707439	−	0.706775i
$246$	−24.5071	+	45.2346i	−0.0996225	+	0.183881i
$247$	148.238	−	148.238i	0.600154	−	0.600154i
$248$	152.604	+	152.604i	0.615340	+	0.615340i
$249$	−108.485	+	200.239i	−0.435684	+	0.804174i
$250$	−112.225	+	55.0512i	−0.448899	+	0.220205i
$251$	363.395			1.44779			0.723895	−	0.689910i	$-0.242350\pi$
$251$	363.395			1.44779			0.723895	+	0.689910i	$0.242350\pi$
$252$	4.08114	−	188.956i	0.0161950	−	0.749825i
$253$	−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	$-0.826865\pi$
$257$	−86.9159	+	86.9159i	−0.338194	+	0.338194i	0.517493	+	0.855687i	$0.326865\pi$
$258$	−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	−0.496774	−	0.867880i	$-0.665482\pi$
$263$	97.6009	−	97.6009i	0.371106	−	0.371106i	0.867880	+	0.496774i	$0.165482\pi$
$264$	−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
$273$	121.421	+	236.152i	0.444764	+	0.865025i
$274$			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	−0.608656	−	0.793434i	$-0.708291\pi$
$277$	51.1833	−	51.1833i	0.184777	−	0.184777i	0.793434	+	0.608656i	$0.208291\pi$
$278$	79.5985	+	79.5985i	0.286325	+	0.286325i
$279$	−151.548	−	232.436i	−0.543182	−	0.833104i
$280$	202.229	−	138.306i	0.722246	−	0.493949i
$281$		−	6.33365i		−	0.0225397i	−0.999936	−	0.0112698i	$-0.996413\pi$
$281$		−	6.33365i		−	0.0225397i	0.999936	−	0.0112698i	$-0.00358738\pi$
$282$	−54.6893	−	184.013i	−0.193934	−	0.652529i
$283$	242.152	−	242.152i	0.855661	−	0.855661i	−0.135163	−	0.990823i	$-0.543156\pi$
$283$	242.152	−	242.152i	0.855661	−	0.855661i	0.990823	+	0.135163i	$0.0431558\pi$
$284$	147.058			0.517810
$285$	160.725	+	189.774i	0.563946	+	0.665874i
$286$		−	32.7416i		−	0.114481i
$287$	99.1178	+	67.7190i	0.345358	+	0.235955i
$288$	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	−0.988853	−	0.148895i	$-0.952428\pi$
$293$	−333.360	−	333.360i	−1.13775	−	1.13775i	−0.148895	−	0.988853i	$-0.547572\pi$
$294$	145.863	+	18.2483i	0.496132	+	0.0620689i
$295$	−95.7464	−	218.013i	−0.324564	−	0.739027i
$296$			410.758i			1.38770i
$297$	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	$-0.164099\pi$
$307$	115.748	+	115.748i	0.377030	+	0.377030i	−0.492999	+	0.870030i	$0.664099\pi$
$308$	44.8981	+	30.6751i	0.145773	+	0.0995946i
$309$	293.399	+	158.957i	0.949511	+	0.514424i
$310$	55.9714	−	143.633i	0.180553	−	0.463333i
$311$	−87.4973			−0.281342			−0.140671	−	0.990056i	$-0.544926\pi$
$311$	−87.4973			−0.281342			−0.140671	+	0.990056i	$0.544926\pi$
$312$	−254.535	+	75.6486i	−0.815817	+	0.242463i
$313$	74.9574	−	74.9574i	0.239481	−	0.239481i	−0.577154	−	0.816635i	$-0.695837\pi$
$313$	74.9574	−	74.9574i	0.239481	−	0.239481i	0.816635	+	0.577154i	$0.195837\pi$
$314$		−	202.061i		−	0.643506i
$315$	−291.079	+	120.407i	−0.924062	+	0.382243i
$316$	227.407			0.719643
$317$	−393.091	−	393.091i	−1.24003	−	1.24003i	−0.959986	−	0.280048i	$-0.909650\pi$
$317$	−393.091	−	393.091i	−1.24003	−	1.24003i	−0.280048	−	0.959986i	$-0.590350\pi$
$318$	−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
$322$	−216.702	−	148.055i	−0.672988	−	0.459797i
$323$	9.64022	−	9.64022i	0.0298459	−	0.0298459i
$324$	−222.350	−	98.0286i	−0.686265	−	0.302557i
$325$	−13.3478	−	315.835i	−0.0410703	−	0.971801i
$326$			137.398i			0.421465i
$327$	−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
$336$	32.0796	−	99.9795i	0.0954749	−	0.297558i
$337$	−333.576	+	333.576i	−0.989840	+	0.989840i	−0.999949	−	0.0101086i	$-0.996782\pi$
$337$	−333.576	+	333.576i	−0.989840	+	0.989840i	0.0101086	+	0.999949i	$0.496782\pi$
$338$	−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
$343$	77.3019	−	334.176i	0.225370	−	0.974273i
$344$	−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	0.301629	−	0.953425i	$-0.402469\pi$
$347$	−226.173	−	226.173i	−0.651796	−	0.651796i	−0.953425	+	0.301629i	$0.902469\pi$
$348$	99.6664	−	29.6212i	0.286398	−	0.0851183i
$349$	−247.335			−0.708696			−0.354348	−	0.935114i	$-0.615297\pi$
$349$	−247.335			−0.708696			−0.354348	+	0.935114i	$0.615297\pi$
$350$	−148.535	−	92.5326i	−0.424386	−	0.264379i
$351$	340.280	−	27.7152i	0.969458	−	0.0789607i
$352$	−60.4214	+	60.4214i	−0.171652	+	0.171652i
$353$	276.422	+	276.422i	0.783065	+	0.783065i	0.980347	−	0.197281i	$-0.0632113\pi$
$353$	276.422	+	276.422i	0.783065	+	0.783065i	−0.197281	+	0.980347i	$0.563211\pi$
$354$	125.616	+	68.0559i	0.354847	+	0.192248i
$355$	−98.5552	−	224.409i	−0.277620	−	0.632137i
$356$	42.1600			0.118427
$357$	7.89623	+	15.3574i	0.0221183	+	0.0430180i
$358$	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	$-0.397821\pi$
$367$	−232.458	−	232.458i	−0.633401	−	0.633401i	−0.948919	+	0.315519i	$0.897821\pi$
$368$	−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	0.396494	−	0.918037i	$-0.370227\pi$
$373$	−194.536	−	194.536i	−0.521543	−	0.521543i	−0.918037	+	0.396494i	$0.870227\pi$
$374$		−	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
$378$	93.5992	−	164.196i	0.247617	−	0.434380i
$379$		−	345.209i		−	0.910843i	−0.890276	−	0.455422i	$-0.849489\pi$
$379$		−	345.209i		−	0.910843i	0.890276	−	0.455422i	$-0.150511\pi$
$380$	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	$-0.277482\pi$
$383$	−46.7051	−	46.7051i	−0.121945	−	0.121945i	−0.765446	+	0.643500i	$0.777482\pi$
$384$	313.893	+	170.060i	0.817428	+	0.442865i
$385$	16.7201	−	89.0718i	0.0434288	−	0.231355i
$386$			115.447i			0.299085i
$387$	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
$392$	314.113	+	137.775i	0.801309	+	0.351468i
$393$	−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	$-0.0563597\pi$
$397$	320.867	+	320.867i	0.808230	+	0.808230i	−0.176135	+	0.984366i	$0.556360\pi$
$398$	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	$0.799411\pi$
$402$	−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	$-0.452425\pi$
$409$	121.806			0.297813			0.148907	+	0.988851i	$0.452425\pi$
$410$	79.8930	+	31.1329i	0.194861	+	0.0759339i
$411$	65.0128	−	119.999i	0.158182	−	0.291968i
$412$	235.956	+	235.956i	0.572708	+	0.572708i
$413$	188.054	−	275.249i	0.455338	−	0.666462i
$414$	−282.663	+	184.295i	−0.682760	+	0.445158i
$415$	353.661	+	137.815i	0.852194	+	0.332085i
$416$	−417.275			−1.00306
$417$	−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	$0.965321\pi$
$420$	−313.320	+	32.4922i	−0.745999	+	0.0773623i
$421$	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
$427$	−311.936	+	456.569i	−0.730528	+	1.06925i
$428$	374.605	−	374.605i	0.875245	−	0.875245i
$429$	−46.7903	+	86.3643i	−0.109068	+	0.201315i
$430$	71.5233	+	162.857i	0.166333	+	0.378738i
$431$		−	179.188i		−	0.415749i	−0.978156	−	0.207874i	$-0.933346\pi$
$431$		−	179.188i		−	0.415749i	0.978156	−	0.207874i	$-0.0666545\pi$
$432$	−102.894	−	87.3950i	−0.238180	−	0.202303i
$433$	−234.230	+	234.230i	−0.540947	+	0.540947i	−0.923806	−	0.382860i	$-0.874939\pi$
$433$	−234.230	+	234.230i	−0.540947	+	0.540947i	0.382860	+	0.923806i	$0.374939\pi$
$434$	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	$-0.704611\pi$
$439$	−526.311			−1.19889			−0.599443	+	0.800417i	$0.704611\pi$
$440$	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	$-0.857622\pi$
$443$	−207.809	+	207.809i	−0.469094	+	0.469094i	0.432527	+	0.901621i	$0.357622\pi$
$444$	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
$448$	−51.3354	+	75.1377i	−0.114588	+	0.167718i
$449$	−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
$455$	365.303	−	249.833i	0.802864	−	0.549083i
$456$	−306.125	−	165.852i	−0.671327	−	0.363710i
$457$	−357.774	+	357.774i	−0.782875	+	0.782875i	−0.980315	−	0.197440i	$-0.936737\pi$
$457$	−357.774	+	357.774i	−0.782875	+	0.782875i	0.197440	+	0.980315i	$0.436737\pi$
$458$	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	$0.290631\pi$
$462$	24.8643	+	48.3588i	0.0538189	+	0.104673i
$463$	−26.9857	−	26.9857i	−0.0582845	−	0.0582845i	0.677364	−	0.735648i	$-0.263122\pi$
$463$	−26.9857	−	26.9857i	−0.0582845	−	0.0582845i	−0.735648	+	0.677364i	$0.763122\pi$
$464$	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	$-0.884867\pi$
$467$	−271.529	+	271.529i	−0.581432	+	0.581432i	0.353864	+	0.935297i	$0.384867\pi$
$468$	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
$483$	360.025	+	700.216i	0.745394	+	1.44972i
$484$		−	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	−0.217684	−	0.976019i	$-0.569850\pi$
$487$	369.310	−	369.310i	0.758336	−	0.758336i	0.976019	+	0.217684i	$0.0698501\pi$
$488$	−390.998	−	390.998i	−0.801226	−	0.801226i
$489$	196.352	−	362.421i	0.401537	−	0.741147i
$490$	−0.115057	−	245.000i	−0.000234810	−	0.500000i
$491$		−	421.951i		−	0.859370i	−0.902979	−	0.429685i	$-0.858625\pi$
$491$		−	421.951i		−	0.859370i	0.902979	−	0.429685i	$-0.141375\pi$
$492$	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
$497$	193.571	−	283.323i	0.389479	−	0.570067i
$498$	−218.301	+	64.8798i	−0.438356	+	0.130281i
$499$			109.267i			0.218971i	0.993988	+	0.109486i	$0.0349204\pi$
$499$			109.267i			0.218971i	−0.993988	+	0.109486i	$0.965080\pi$
$500$	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	$-0.189635\pi$
$503$	134.096	+	134.096i	0.266592	+	0.266592i	−0.561133	+	0.827725i	$0.689635\pi$
$504$	318.495	−	305.028i	0.631934	−	0.605214i
$505$	108.463	−	47.6345i	0.214778	−	0.0943258i
$506$		−	97.0824i		−	0.191862i
$507$	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
$518$	339.159	+	231.719i	0.654747	+	0.447334i
$519$	233.315	−	430.646i	0.449547	−	0.829762i
$520$	177.958	+	405.208i	0.342228	+	0.779247i
$521$	−303.734			−0.582983			−0.291491	−	0.956573i	$-0.594152\pi$
$521$	−303.734			−0.582983			−0.291491	+	0.956573i	$0.594152\pi$
$522$	101.742	+	21.4325i	0.194908	+	0.0410585i
$523$	249.060	−	249.060i	0.476215	−	0.476215i	−0.427704	−	0.903919i	$-0.640677\pi$
$523$	249.060	−	249.060i	0.476215	−	0.476215i	0.903919	+	0.427704i	$0.140677\pi$
$524$		−	652.986i		−	1.24616i
$525$	259.563	+	456.346i	0.494406	+	0.869231i
$526$	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
$532$	−196.409	+	287.477i	−0.369190	+	0.540370i
$533$	−153.331	+	153.331i	−0.287675	+	0.287675i
$534$	37.0692	+	20.0833i	0.0694181	+	0.0376092i
$535$	−822.695	−	320.590i	−1.53775	−	0.599234i
$536$		−	717.501i		−	1.33862i
$537$	−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
$546$	−81.1272	+	252.842i	−0.148585	+	0.463080i
$547$	492.112	−	492.112i	0.899656	−	0.899656i	−0.0957494	−	0.995405i	$-0.530525\pi$
$547$	492.112	−	492.112i	0.899656	−	0.899656i	0.995405	+	0.0957494i	$0.0305247\pi$
$548$	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
$553$	299.334	−	438.125i	0.541291	−	0.792269i
$554$	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	0.348042	−	0.937479i	$-0.386847\pi$
$557$	−328.316	−	328.316i	−0.589437	−	0.589437i	−0.937479	+	0.348042i	$0.886847\pi$
$558$	57.1967	−	271.517i	0.102503	−	0.486590i
$559$	−449.825			−0.804695
$560$	−171.996	−	32.2862i	−0.307136	−	0.0576539i
$561$	−3.04287	+	5.61644i	−0.00542400	+	0.0100115i
$562$	4.47857	−	4.47857i	0.00796898	−	0.00796898i
$563$	−510.844	−	510.844i	−0.907361	−	0.907361i	0.0886978	−	0.996059i	$-0.471729\pi$
$563$	−510.844	−	510.844i	−0.907361	−	0.907361i	−0.996059	+	0.0886978i	$0.971729\pi$
$564$	−274.337	+	506.364i	−0.486414	+	0.897809i
$565$	133.063	−	341.466i	0.235510	−	0.604364i
$566$	342.455			0.605043
$567$	−481.540	+	299.347i	−0.849276	+	0.527948i
$568$	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	$-0.124561\pi$
$577$	313.311	+	313.311i	0.542999	+	0.542999i	−0.381408	+	0.924407i	$0.624561\pi$
$578$	−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	$-0.692344\pi$
$587$	149.545	−	149.545i	0.254762	−	0.254762i	0.822920	+	0.568158i	$0.192344\pi$
$588$	−270.712	−	348.132i	−0.460394	−	0.592062i
$589$			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	$-0.325888\pi$
$593$	−198.048	−	198.048i	−0.333977	−	0.333977i	−0.854095	+	0.520118i	$0.825888\pi$
$594$	69.6819	−	5.67547i	0.117310	−	0.00955466i
$595$	23.7564	−	16.2471i	0.0399267	−	0.0273061i
$596$			74.2159i			0.124523i
$597$	−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	$0.899296\pi$
$602$	−140.478	+	205.613i	−0.233352	+	0.341549i
$603$	−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	−0.999113	−	0.0421025i	$-0.986594\pi$
$607$	−632.018	−	632.018i	−1.04122	−	1.04122i	−0.0421025	−	0.999113i	$-0.513406\pi$
$608$	−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
$612$	21.7255	+	4.57661i	0.0354992	+	0.00747812i
$613$	587.183	+	587.183i	0.957885	+	0.957885i	0.999148	−	0.0412636i	$-0.0131383\pi$
$613$	587.183	+	587.183i	0.957885	+	0.957885i	−0.0412636	+	0.999148i	$0.513138\pi$
$614$			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	0.791415	−	0.611279i	$-0.209345\pi$
$617$	111.144	+	111.144i	0.180136	+	0.180136i	−0.611279	+	0.791415i	$0.709345\pi$
$618$	95.0646	+	319.864i	0.153826	+	0.517579i
$619$	716.455			1.15744			0.578720	−	0.815526i	$-0.303552\pi$
$619$	716.455			1.15744			0.578720	+	0.815526i	$0.303552\pi$
$620$	−423.426	+	185.959i	−0.682945	+	0.299934i
$621$	1008.97	−	82.1785i	1.62474	−	0.132333i
$622$	−61.8700	−	61.8700i	−0.0994694	−	0.0994694i
$623$	55.4949	−	81.2259i	0.0890769	−	0.130379i
$624$	166.768	+	90.3512i	0.267256	+	0.144794i
$625$	−52.7333	−	622.771i	−0.0843734	−	0.996434i
$626$	106.006			0.169338
$627$	−123.452	+	36.6905i	−0.196894	+	0.0585175i
$628$	−428.636	+	428.636i	−0.682541	+	0.682541i
$629$			48.2529i			0.0767137i
$630$	−290.965	−	120.684i	−0.461849	−	0.191562i
$631$	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
$637$	567.409	+	248.875i	0.890751	+	0.390699i
$638$	−21.1526	+	21.1526i	−0.0331545	+	0.0331545i
$639$	−240.953	−	369.562i	−0.377079	−	0.578344i
$640$	216.038	−	554.394i	0.337559	−	0.866241i
$641$			121.164i			0.189024i	0.995524	+	0.0945120i	$0.0301291\pi$
$641$			121.164i			0.189024i	−0.995524	+	0.0945120i	$0.969871\pi$
$642$	507.818	−	150.925i	0.790994	−	0.235086i
$643$	524.336	−	524.336i	0.815453	−	0.815453i	−0.169993	−	0.985445i	$-0.554374\pi$
$643$	524.336	−	524.336i	0.815453	−	0.815453i	0.985445	+	0.169993i	$0.0543744\pi$
$644$	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	$-0.641495\pi$
$647$	305.897	−	305.897i	0.472792	−	0.472792i	0.902817	+	0.430025i	$0.141495\pi$
$648$	−205.119	−	528.597i	−0.316542	−	0.815736i
$649$	123.311			0.190002
$650$	213.891	−	232.768i	0.329063	−	0.358104i
$651$	−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	$-0.857989\pi$
$653$	−307.322	+	307.322i	−0.470631	+	0.470631i	0.431488	+	0.902119i	$0.357989\pi$
$654$	−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
$658$	−369.847	−	252.686i	−0.562078	−	0.384021i
$659$	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
$665$	570.315	+	107.057i	0.857617	+	0.160987i
$666$	442.393	−	288.439i	0.664254	−	0.433092i
$667$	−306.281	+	306.281i	−0.459192	+	0.459192i
$668$	621.735	+	621.735i	0.930741	+	0.930741i
$669$	298.237	+	161.579i	0.445796	+	0.241523i
$670$	−469.242	+	206.080i	−0.700361	+	0.307583i
$671$	−204.543			−0.304832
$672$	616.307	−	316.883i	0.917124	−	0.471552i
$673$	256.857	+	256.857i	0.381660	+	0.381660i	0.871700	−	0.490040i	$-0.163018\pi$
$673$	256.857	+	256.857i	0.381660	+	0.381660i	−0.490040	+	0.871700i	$0.663018\pi$
$674$	−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	$-0.833496\pi$
$677$	−248.270	+	248.270i	−0.366721	+	0.366721i	0.499559	+	0.866280i	$0.333496\pi$
$678$	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	−0.847402	−	0.530952i	$-0.821835\pi$
$683$	−216.136	+	216.136i	−0.316450	+	0.316450i	0.530952	+	0.847402i	$0.321835\pi$
$684$	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
$693$	3.52251	−	163.091i	0.00508298	−	0.235341i
$694$		−	319.857i		−	0.460889i
$695$	−515.338	+	226.325i	−0.741493	+	0.325647i
$696$	213.314	+	115.569i	0.306485	+	0.166047i
$697$	−9.97142	+	9.97142i	−0.0143062	+	0.0143062i
$698$	−174.892	−	174.892i	−0.250562	−	0.250562i
$699$	−187.613	−	101.645i	−0.268402	−	0.145415i
$700$	118.800	+	511.382i	0.169714	+	0.730546i
$701$			602.095i			0.858908i	0.903089	+	0.429454i	$0.141294\pi$
$701$			602.095i			0.858908i	−0.903089	+	0.429454i	$0.858706\pi$
$702$	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
$707$	136.938	+	93.5584i	0.193689	+	0.132332i
$708$	−122.103	−	410.840i	−0.172462	−	0.580282i
$709$			37.8334i			0.0533616i	0.999644	+	0.0266808i	$0.00849377\pi$
$709$			37.8334i			0.0533616i	−0.999644	+	0.0266808i	$0.991506\pi$
$710$	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
$717$	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	$-0.0277742\pi$
$727$	660.880	+	660.880i	0.909051	+	0.909051i	−0.0871447	+	0.996196i	$0.527774\pi$
$728$	−349.526	+	511.589i	−0.480118	+	0.702732i
$729$	117.969	+	719.392i	0.161823	+	0.986820i
$730$	−168.562	+	74.0286i	−0.230907	+	0.101409i
$731$	−29.2530			−0.0400178
$732$	202.538	+	681.481i	0.276692	+	0.930985i
$733$	526.757	−	526.757i	0.718632	−	0.718632i	−0.249693	−	0.968325i	$-0.580330\pi$
$733$	526.757	−	526.757i	0.718632	−	0.718632i	0.968325	+	0.249693i	$0.0803298\pi$
$734$		−	328.745i		−	0.447882i
$735$	−349.820	+	646.414i	−0.475946	+	0.879474i
$736$	−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	$0.0600069\pi$
$739$			276.981i			0.374805i	−0.982283	+	0.187402i	$0.939993\pi$
$740$	−820.127	−	319.589i	−1.10828	−	0.431877i
$741$	−552.979	−	299.592i	−0.746261	−	0.404308i
$742$	−279.221	−	190.768i	−0.376308	−	0.257100i
$743$	−698.839	+	698.839i	−0.940563	+	0.940563i	−0.998330	−	0.0577666i	$-0.981602\pi$
$743$	−698.839	+	698.839i	−0.940563	+	0.940563i	0.0577666	+	0.998330i	$0.481602\pi$
$744$	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
$756$	−546.865	+	149.757i	−0.723367	+	0.198092i
$757$	−269.069	+	269.069i	−0.355441	+	0.355441i	−0.862129	−	0.506688i	$-0.830870\pi$
$757$	−269.069	+	269.069i	−0.355441	+	0.355441i	0.506688	+	0.862129i	$0.330870\pi$
$758$	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	$0.720848\pi$
$762$	−26.1649	−	88.0372i	−0.0343372	−	0.115534i
$763$	−288.211	+	421.845i	−0.377734	+	0.552876i
$764$	−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	$-0.259165\pi$
$769$	1055.77			1.37292			0.686458	+	0.727169i	$0.259165\pi$
$770$	74.8062	−	51.1604i	0.0971508	−	0.0664420i
$771$	324.226	+	175.659i	0.420527	+	0.227832i
$772$	244.900	−	244.900i	0.317228	−	0.317228i
$773$	−545.306	−	545.306i	−0.705441	−	0.705441i	0.260132	−	0.965573i	$-0.416234\pi$
$773$	−545.306	−	545.306i	−0.705441	−	0.705441i	−0.965573	+	0.260132i	$0.916234\pi$
$774$	174.864	+	268.198i	0.225923	+	0.346509i
$775$	567.542	+	521.516i	0.732312	+	0.672924i
$776$	−257.054			−0.331255
$777$	−563.473	−	1095.90i	−0.725190	−	1.41043i
$778$	−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	$-0.356751\pi$
$787$	−366.303	−	366.303i	−0.465442	−	0.465442i	−0.900434	+	0.434992i	$0.856751\pi$
$788$	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	$-0.714691\pi$
$797$	124.772	−	124.772i	0.156552	−	0.156552i	0.781037	+	0.624485i	$0.214691\pi$
$798$	−309.635	+	159.203i	−0.388014	+	0.199502i
$799$		−	52.6190i		−	0.0658561i
$800$	−824.264	+	34.8351i	−1.03033	+	0.0435438i
$801$	−69.0789	−	105.950i	−0.0862408	−	0.132272i
$802$	−334.181	+	334.181i	−0.416684	+	0.416684i
$803$	−67.4162	−	67.4162i	−0.0839554	−	0.0839554i
$804$	−439.442	+	811.110i	−0.546570	+	1.00884i
$805$	1083.16	−	740.782i	1.34554	−	0.920226i
$806$			389.845i			0.483678i
$807$	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	$-0.201378\pi$
$812$	136.861	−	200.319i	0.168549	−	0.246698i
$813$	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
$819$	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	$0.859853\pi$
$822$	130.823	−	38.8810i	0.159152	−	0.0473005i
$823$	945.067	+	945.067i	1.14832	+	1.14832i	0.986883	+	0.161436i	$0.0516125\pi$
$823$	945.067	+	945.067i	1.14832	+	1.14832i	0.161436	+	0.986883i	$0.448387\pi$
$824$			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	0.372335	−	0.928098i	$-0.378557\pi$
$827$	−459.616	−	459.616i	−0.555763	−	0.555763i	−0.928098	+	0.372335i	$0.878557\pi$
$828$	990.567	+	208.669i	1.19634	+	0.252015i
$829$	−197.279			−0.237972			−0.118986	−	0.992896i	$-0.537964\pi$
$829$	−197.279			−0.237972			−0.118986	+	0.992896i	$0.537964\pi$
$830$	152.626	+	347.526i	0.183886	+	0.418706i
$831$	−190.932	−	103.443i	−0.229761	−	0.124480i
$832$	−116.235	−	116.235i	−0.139705	−	0.139705i
$833$	36.8997	+	16.1849i	0.0442974	+	0.0194296i
$834$	160.870	−	296.930i	0.192890	−	0.356031i
$835$	532.086	−	1365.43i	0.637228	−	1.63525i
$836$	−128.789			−0.154054
$837$	−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	$0.756913\pi$
$840$	−570.561	−	463.342i	−0.679239	−	0.551597i
$841$	−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
$847$	−660.607	−	451.338i	−0.779937	−	0.532866i
$848$	−170.800	+	170.800i	−0.201415	+	0.201415i
$849$	−903.310	−	489.394i	−1.06397	−	0.576436i
$850$	13.9098	−	15.1373i	0.0163644	−	0.0178086i
$851$			2200.07i			2.58528i
$852$	−125.685	−	422.892i	−0.147518	−	0.496352i
$853$	727.157	−	727.157i	0.852470	−	0.852470i	−0.137967	−	0.990437i	$-0.544057\pi$
$853$	727.157	−	727.157i	0.852470	−	0.852470i	0.990437	+	0.137967i	$0.0440568\pi$
$854$	−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	$-0.837784\pi$
$857$	−330.023	+	330.023i	−0.385091	+	0.385091i	0.487841	+	0.872932i	$0.337784\pi$
$858$	−94.1545	+	27.9830i	−0.109737	+	0.0326142i
$859$	900.965			1.04885			0.524427	−	0.851456i	$-0.324280\pi$
$859$	900.965			1.04885			0.524427	+	0.851456i	$0.324280\pi$
$860$	193.749	−	497.196i	0.225289	−	0.578135i
$861$	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	$-0.759384\pi$
$863$	−35.9749	+	35.9749i	−0.0416859	+	0.0416859i	0.685957	+	0.727642i	$0.259384\pi$
$864$	−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
$868$	−534.589	−	365.240i	−0.615886	−	0.420783i
$869$	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
$875$	700.746	−	524.004i	0.800852	−	0.598862i
$876$	−157.857	+	291.368i	−0.180202	+	0.332612i
$877$	−406.421	+	406.421i	−0.463422	+	0.463422i	−0.899775	−	0.436353i	$-0.856270\pi$
$877$	−406.421	+	406.421i	−0.463422	+	0.463422i	0.436353	+	0.899775i	$0.356270\pi$
$878$	−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	$0.500911\pi$
$882$	−72.1874	−	435.052i	−0.0818451	−	0.493256i
$883$	−215.321	−	215.321i	−0.243852	−	0.243852i	0.574590	−	0.818442i	$-0.305162\pi$
$883$	−215.321	−	215.321i	−0.243852	−	0.243852i	−0.818442	+	0.574590i	$0.805162\pi$
$884$	−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	$-0.949399\pi$
$887$	−735.406	+	735.406i	−0.829094	+	0.829094i	0.158298	+	0.987391i	$0.449399\pi$
$888$	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
$903$	664.383	−	341.601i	0.735751	−	0.378296i
$904$			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	−0.942880	−	0.333133i	$-0.891894\pi$
$907$	−553.040	+	553.040i	−0.609747	+	0.609747i	0.333133	+	0.942880i	$0.391894\pi$
$908$	−170.347	−	170.347i	−0.187607	−	0.187607i
$909$	178.620	−	116.460i	0.196501	−	0.128118i
$910$	434.967	+	81.6498i	0.477986	+	0.0897250i
$911$		−	466.216i		−	0.511763i	−0.966708	−	0.255881i	$-0.917634\pi$
$911$		−	466.216i		−	0.511763i	0.966708	−	0.255881i	$-0.0823656\pi$
$912$	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
$917$	−1258.05	−	859.520i	−1.37192	−	0.937318i
$918$	16.9221	+	14.3731i	0.0184336	+	0.0156570i
$919$		−	1125.94i		−	1.22518i	−0.790401	−	0.612590i	$-0.790128\pi$
$919$		−	1125.94i		−	1.22518i	0.790401	−	0.612590i	$-0.209872\pi$
$920$	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
$927$	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	$-0.460736\pi$
$937$	−814.593	−	814.593i	−0.869363	−	0.869363i	−0.992402	+	0.123039i	$0.960736\pi$
$938$	−592.433	−	404.760i	−0.631592	−	0.431514i
$939$	−279.617	−	151.490i	−0.297782	−	0.161332i
$940$	894.336	+	348.507i	0.951421	+	0.370752i
$941$	1318.27			1.40093			0.700464	−	0.713687i	$-0.252976\pi$
$941$	1318.27			1.40093			0.700464	+	0.713687i	$0.252976\pi$
$942$	−581.063	+	172.694i	−0.616840	+	0.183327i
$943$	−454.643	+	454.643i	−0.482124	+	0.482124i
$944$		−	238.111i		−	0.252237i
$945$	595.026	+	734.145i	0.629657	+	0.776873i
$946$	−92.1143			−0.0973724
$947$	347.435	+	347.435i	0.366880	+	0.366880i	0.866338	−	0.499458i	$-0.166468\pi$
$947$	347.435	+	347.435i	0.366880	+	0.366880i	−0.499458	+	0.866338i	$0.666468\pi$
$948$	−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
$952$	−22.7304	+	33.2696i	−0.0238764	+	0.0349471i
$953$	992.679	−	992.679i	1.04164	−	1.04164i	0.0425407	−	0.999095i	$-0.486455\pi$
$953$	992.679	−	992.679i	1.04164	−	1.04164i	0.999095	−	0.0425407i	$-0.0135452\pi$
$954$	−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
$966$	−240.551	+	749.703i	−0.249017	+	0.776091i
$967$	1047.59	−	1047.59i	1.08334	−	1.08334i	0.0871396	−	0.996196i	$-0.472227\pi$
$967$	1047.59	−	1047.59i	1.08334	−	1.08334i	0.996196	−	0.0871396i	$-0.0277726\pi$
$968$	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	$0.562603\pi$
$972$	−91.8652	+	723.189i	−0.0945115	+	0.744021i
$973$	−650.631	−	444.522i	−0.668685	−	0.456857i
$974$	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	0.845915	−	0.533318i	$-0.179055\pi$
$977$	305.408	+	305.408i	0.312598	+	0.312598i	−0.533318	+	0.845915i	$0.679055\pi$
$978$	395.112	−	117.429i	0.404000	−	0.120070i
$979$	36.3891			0.0371697
$980$	−519.479	+	519.967i	−0.530081	+	0.530579i
$981$	358.760	+	550.247i	0.365708	+	0.560904i
$982$	298.364	−	298.364i	0.303833	−	0.303833i
$983$	522.805	+	522.805i	0.531846	+	0.531846i	0.921121	−	0.389275i	$-0.127274\pi$
$983$	522.805	+	522.805i	0.531846	+	0.531846i	−0.389275	+	0.921121i	$0.627274\pi$
$984$	316.642	+	171.550i	0.321791	+	0.174339i
$985$	−1200.39	−	467.771i	−1.21867	−	0.474894i
$986$	−9.49996			−0.00963484
$987$	614.458	+	1195.06i	0.622551	+	1.21080i
$988$	−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	$-0.310602\pi$
$997$	−266.821	−	266.821i	−0.267624	−	0.267624i	−0.828142	+	0.560518i	$0.810602\pi$
$998$	−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.83.6	yes	16
3.2	odd	2	inner	105.3.k.c.83.4	yes	16
5.2	odd	4	inner	105.3.k.c.62.1	✓	16
7.6	odd	2	inner	105.3.k.c.83.7	yes	16
15.2	even	4	inner	105.3.k.c.62.7	yes	16
21.20	even	2	inner	105.3.k.c.83.1	yes	16
35.27	even	4	inner	105.3.k.c.62.4	yes	16
105.62	odd	4	inner	105.3.k.c.62.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.k.c.62.1	✓	16	5.2	odd	4	inner
105.3.k.c.62.4	yes	16	35.27	even	4	inner
105.3.k.c.62.6	yes	16	105.62	odd	4	inner
105.3.k.c.62.7	yes	16	15.2	even	4	inner
105.3.k.c.83.1	yes	16	21.20	even	2	inner
105.3.k.c.83.4	yes	16	3.2	odd	2	inner
105.3.k.c.83.6	yes	16	1.1	even	1	trivial
105.3.k.c.83.7	yes	16	7.6	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.854662 - 2.87568i) q^{3} -3.00000i q^{4} +(-4.57796 + 2.01054i) q^{5} +(1.42908 - 2.63775i) q^{6} +(-5.77983 - 3.94887i) q^{7} +(4.94975 - 4.94975i) q^{8} +(-7.53910 + 4.91548i) q^{9} +(-4.65877 - 1.81544i) q^{10} -2.58936i q^{11} +(-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} +(-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} +(20.5787 + 17.4790i) q^{27} +(-11.8466 + 17.3395i) 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} +(34.3992 + 6.45724i) q^{35} +(14.7464 + 22.6173i) q^{36} +(-41.4929 + 41.4929i) q^{37} +(11.7233 + 11.7233i) q^{38} +(-33.3536 - 18.0702i) q^{39} +(-12.7081 + 32.6114i) q^{40} -17.1489 q^{41} +(-18.6760 + 9.60250i) 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} +(62.9853 + 1.36038i) q^{63} -13.0000i q^{64} +(-22.9557 + 58.9087i) q^{65} +(-6.83008 - 3.70039i) q^{66} +(72.4786 - 72.4786i) q^{67} +(-1.74438 - 1.74438i) q^{68} +(-98.8969 - 53.5802i) q^{69} +(19.7579 + 28.8899i) q^{70} +49.0193i q^{71} +(-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} +(-10.2250 + 14.9660i) 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} +(59.9877 + 19.2477i) 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} +(-19.6822 + 44.8733i) q^{98} +(12.7279 + 19.5214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{7}+O(q^{10}) \) 16 * q + 32 * q^7	\( 16 q + 32 q^{7} + 80 q^{15} - 80 q^{16} + 8 q^{18} - 64 q^{21} - 64 q^{22} + 224 q^{25} - 96 q^{28} - 128 q^{30} + 96 q^{36} - 384 q^{37} - 112 q^{42} + 64 q^{43} + 320 q^{46} - 128 q^{51} + 408 q^{57} - 224 q^{58} - 120 q^{60} - 72 q^{63} + 320 q^{67} + 128 q^{70} + 56 q^{72} - 424 q^{78} + 896 q^{81} + 256 q^{85} + 448 q^{88} - 832 q^{91} + 32 q^{93}+O(q^{100}) \) 16 * q + 32 * q^7 + 80 * q^15 - 80 * q^16 + 8 * q^18 - 64 * q^21 - 64 * q^22 + 224 * q^25 - 96 * q^28 - 128 * q^30 + 96 * q^36 - 384 * q^37 - 112 * q^42 + 64 * q^43 + 320 * q^46 - 128 * q^51 + 408 * q^57 - 224 * q^58 - 120 * q^60 - 72 * q^63 + 320 * q^67 + 128 * q^70 + 56 * q^72 - 424 * q^78 + 896 * q^81 + 256 * q^85 + 448 * q^88 - 832 * q^91 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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