LMFDB - Embedded newform 105.3.k.c.62.6

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			62.6
Root			$0.253395 + 0.611750i$ of defining polynomial
Character	$\chi$	$=$	105.62
Dual form			105.3.k.c.83.6

$q$-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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

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

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
$7$	−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	$0.0375515\pi$
$11$			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	0.961741	−	0.273961i	$-0.0883338\pi$
$13$	8.94114	+	8.94114i	0.687780	+	0.687780i	−0.273961	+	0.961741i	$0.588334\pi$
$14$	−1.29468	+	6.87923i	−0.0924770	+	0.491374i
$15$	9.69428	−	11.4464i	0.646285	−	0.763096i
$16$	−5.00000			−0.312500
$17$	0.581460	+	0.581460i	0.0342036	+	0.0342036i	0.724002	−	0.689798i	$-0.242301\pi$
$17$	0.581460	+	0.581460i	0.0342036	+	0.0342036i	−0.689798	+	0.724002i	$0.742301\pi$
$18$	−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	0.986015	+	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
$28$	−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	$-0.834336\pi$
$31$		−	30.8307i		−	0.994539i	0.867596	−	0.497270i	$-0.165664\pi$
$32$	−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	−0.991527	−	0.129902i	$-0.958534\pi$
$37$	−41.4929	−	41.4929i	−1.12143	−	1.12143i	−0.129902	−	0.991527i	$-0.541466\pi$
$38$	11.7233	−	11.7233i	0.308509	−	0.308509i
$39$	−33.3536	+	18.0702i	−0.855219	+	0.463339i
$40$	−12.7081	−	32.6114i	−0.317703	−	0.815285i
$41$	−17.1489			−0.418267			−0.209133	−	0.977887i	$-0.567064\pi$
$41$	−17.1489			−0.418267			−0.209133	+	0.977887i	$0.567064\pi$
$42$	−18.6760	−	9.60250i	−0.444666	−	0.228631i
$43$	−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	0.999329	−	0.0366205i	$-0.0116593\pi$
$47$	45.2473	+	45.2473i	0.962709	+	0.962709i	−0.0366205	+	0.999329i	$0.511659\pi$
$48$	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	$-0.867766\pi$
$59$		−	47.6223i		−	0.807158i	0.914945	−	0.403579i	$-0.132234\pi$
$60$	34.3393	+	29.0828i	0.572322	+	0.484714i
$61$			78.9936i			1.29498i	0.762075	+	0.647488i	$0.224181\pi$
$61$			78.9936i			1.29498i	−0.762075	+	0.647488i	$0.775819\pi$
$62$	−21.8006	−	21.8006i	−0.351623	−	0.351623i
$63$	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	0.996345	+	0.0854251i	$0.0272248\pi$
$67$	72.4786	+	72.4786i	1.08177	+	1.08177i	0.0854251	+	0.996345i	$0.472775\pi$
$68$	−1.74438	+	1.74438i	−0.0256527	+	0.0256527i
$69$	−98.8969	+	53.5802i	−1.43329	+	0.776524i
$70$	19.7579	−	28.8899i	0.282256	−	0.412712i
$71$		−	49.0193i		−	0.690413i	−0.938527	−	0.345207i	$-0.887809\pi$
$71$		−	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	0.862579	−	0.505923i	$-0.168848\pi$
$73$	26.0359	+	26.0359i	0.356656	+	0.356656i	−0.505923	+	0.862579i	$0.668848\pi$
$74$	−58.6798			−0.792970
$75$	−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	$-0.840723\pi$
$79$		−	75.8024i		−	0.959524i	0.877399	−	0.479762i	$-0.159277\pi$
$80$	22.8898	+	10.0527i	0.286123	+	0.125659i
$81$	32.6762	+	74.1166i	0.403410	+	0.915019i
$82$	−12.1261	+	12.1261i	−0.147880	+	0.147880i
$83$	−53.6785	+	53.6785i	−0.646729	+	0.646729i	−0.952201	−	0.305472i	$-0.901186\pi$
$83$	−53.6785	+	53.6785i	−0.646729	+	0.646729i	0.305472	+	0.952201i	$0.401186\pi$
$84$	59.9877	−	19.2477i	0.714139	−	0.229140i
$85$	−1.49286	−	3.83095i	−0.0175630	−	0.0450700i
$86$			35.5742i			0.413654i
$87$	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	$-0.974843\pi$
$89$		−	14.0533i		−	0.157903i	0.996878	−	0.0789514i	$-0.0251572\pi$
$90$	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	−0.828171	−	0.560476i	$-0.810618\pi$
$97$	−25.9664	+	25.9664i	−0.267695	+	0.267695i	0.560476	+	0.828171i	$0.310618\pi$
$98$	−19.6822	−	44.8733i	−0.200839	−	0.457891i
$99$	12.7279	−	19.5214i	0.128565	−	0.197186i
$100$	−55.2250	+	50.7464i	−0.552250	+	0.507464i
$101$	−23.6924			−0.234579			−0.117289	−	0.993098i	$-0.537420\pi$
$101$	−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	0.213362	−	0.976973i	$-0.431559\pi$
$103$	−78.6519	−	78.6519i	−0.763611	−	0.763611i	−0.976973	+	0.213362i	$0.931559\pi$
$104$			88.5128i			0.851085i
$105$	−10.8307	+	104.440i	−0.103150	+	0.994666i
$106$	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
$112$	28.8991	−	19.7444i	0.258028	−	0.176289i
$113$	−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
$126$	43.5754	−	45.4993i	0.345837	−	0.361105i
$127$	21.6476	+	21.6476i	0.170454	+	0.170454i	0.787179	−	0.616725i	$-0.211541\pi$
$127$	21.6476	+	21.6476i	0.170454	+	0.170454i	−0.616725	+	0.787179i	$0.711541\pi$
$128$	−84.1457	−	84.1457i	−0.657388	−	0.657388i
$129$	−50.8383	−	93.8359i	−0.394095	−	0.727410i
$130$	−57.8869	−	25.4226i	−0.445284	−	0.195559i
$131$	217.662			1.66154			0.830771	−	0.556614i	$-0.187900\pi$
$131$	217.662			1.66154			0.830771	+	0.556614i	$0.187900\pi$
$132$	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	−0.579890	−	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	$-0.367298\pi$
$139$	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	−0.996276	−	0.0862209i	$-0.972521\pi$
$157$	−142.879	+	142.879i	−0.910055	+	0.910055i	0.0862209	+	0.996276i	$0.472521\pi$
$158$	−53.6004	−	53.6004i	−0.339243	−	0.339243i
$159$	−127.429	+	69.0380i	−0.801437	+	0.434202i
$160$	153.740	−	59.9096i	0.960872	−	0.374435i
$161$	−257.922	−	48.5412i	−1.60200	−	0.301498i
$162$	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	$-0.909203\pi$
$167$	−207.245	−	207.245i	−1.24099	−	1.24099i	−0.281396	−	0.959592i	$-0.590797\pi$
$168$	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	−0.289785	−	0.957092i	$-0.593584\pi$
$173$	115.444	−	115.444i	0.667307	−	0.667307i	0.957092	+	0.289785i	$0.0935837\pi$
$174$	−16.5098	−	30.4734i	−0.0948840	−	0.175134i
$175$	−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	$0.216725\pi$
$181$			227.866i			1.25893i	−0.777030	+	0.629463i	$0.783275\pi$
$182$	−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	$0.423222\pi$
$191$			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	$-0.474993\pi$
$199$	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	0.504750	−	0.863266i	$-0.331585\pi$
$223$	−79.9490	−	79.9490i	−0.358516	−	0.358516i	−0.863266	+	0.504750i	$0.831585\pi$
$224$	42.7244	−	227.015i	0.190734	−	1.01346i
$225$	−37.0418	−	221.930i	−0.164630	−	0.986355i
$226$	−73.2952			−0.324315
$227$	56.7824	+	56.7824i	0.250143	+	0.250143i	0.821029	−	0.570886i	$-0.193400\pi$
$227$	56.7824	+	56.7824i	0.250143	+	0.250143i	−0.570886	+	0.821029i	$0.693400\pi$
$228$	−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	0.806748	−	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
$238$	−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	$-0.931430\pi$
$241$		−	103.031i		−	0.427516i	0.976887	−	0.213758i	$-0.0685704\pi$
$242$	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	0.517493	−	0.855687i	$-0.326865\pi$
$257$	−86.9159	−	86.9159i	−0.338194	−	0.338194i	−0.855687	+	0.517493i	$0.826865\pi$
$258$	−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	$-0.928512\pi$
$269$		−	119.813i		−	0.445403i	0.974887	−	0.222701i	$-0.0714875\pi$
$270$	−64.1395	+	118.790i	−0.237554	+	0.439964i
$271$		−	246.646i		−	0.910132i	−0.890458	−	0.455066i	$-0.849616\pi$
$271$		−	246.646i		−	0.910132i	0.890458	−	0.455066i	$-0.150384\pi$
$272$	−2.90730	−	2.90730i	−0.0106886	−	0.0106886i
$273$	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	0.793434	−	0.608656i	$-0.208291\pi$
$277$	51.1833	+	51.1833i	0.184777	+	0.184777i	−0.608656	+	0.793434i	$0.708291\pi$
$278$	79.5985	−	79.5985i	0.286325	−	0.286325i
$279$	−151.548	+	232.436i	−0.543182	+	0.833104i
$280$	202.229	+	138.306i	0.722246	+	0.493949i
$281$			6.33365i			0.0225397i	0.999936	+	0.0112698i	$0.00358738\pi$
$281$			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	0.990823	−	0.135163i	$-0.0431558\pi$
$283$	242.152	+	242.152i	0.855661	+	0.855661i	−0.135163	+	0.990823i	$0.543156\pi$
$284$	147.058			0.517810
$285$	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	−0.148895	+	0.988853i	$0.547572\pi$
$293$	−333.360	+	333.360i	−1.13775	+	1.13775i	−0.988853	+	0.148895i	$0.952428\pi$
$294$	145.863	−	18.2483i	0.496132	−	0.0620689i
$295$	−95.7464	+	218.013i	−0.324564	+	0.739027i
$296$		−	410.758i		−	1.38770i
$297$	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	−0.492999	−	0.870030i	$-0.664099\pi$
$307$	115.748	−	115.748i	0.377030	−	0.377030i	0.870030	+	0.492999i	$0.164099\pi$
$308$	44.8981	−	30.6751i	0.145773	−	0.0995946i
$309$	293.399	−	158.957i	0.949511	−	0.514424i
$310$	55.9714	+	143.633i	0.180553	+	0.463333i
$311$	−87.4973			−0.281342			−0.140671	−	0.990056i	$-0.544926\pi$
$311$	−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	0.816635	−	0.577154i	$-0.195837\pi$
$313$	74.9574	+	74.9574i	0.239481	+	0.239481i	−0.577154	+	0.816635i	$0.695837\pi$
$314$			202.061i			0.643506i
$315$	−291.079	−	120.407i	−0.924062	−	0.382243i
$316$	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
$322$	−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	0.0101086	−	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
$343$	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	−0.953425	−	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	$-0.615297\pi$
$349$	−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	−0.197281	−	0.980347i	$-0.563211\pi$
$353$	276.422	−	276.422i	0.783065	−	0.783065i	0.980347	+	0.197281i	$0.0632113\pi$
$354$	125.616	−	68.0559i	0.354847	−	0.192248i
$355$	−98.5552	+	224.409i	−0.277620	+	0.632137i
$356$	42.1600			0.118427
$357$	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	−0.948919	−	0.315519i	$-0.897821\pi$
$367$	−232.458	+	232.458i	−0.633401	+	0.633401i	0.315519	+	0.948919i	$0.397821\pi$
$368$	−132.557	−	132.557i	−0.360210	−	0.360210i
$369$	129.288	+	84.2951i	0.350373	+	0.228442i
$370$	268.634	+	117.978i	0.726037	+	0.318859i
$371$	−332.332	−	62.5453i	−0.895774	−	0.168586i
$372$	−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
$378$	93.5992	+	164.196i	0.247617	+	0.434380i
$379$			345.209i			0.910843i	0.890276	+	0.455422i	$0.150511\pi$
$379$			345.209i			0.910843i	−0.890276	+	0.455422i	$0.849489\pi$
$380$	100.000	−	227.698i	0.263158	−	0.599207i
$381$	−80.7531	+	43.7503i	−0.211950	+	0.114830i
$382$	262.295	+	262.295i	0.686637	+	0.686637i
$383$	−46.7051	+	46.7051i	−0.121945	+	0.121945i	−0.765446	−	0.643500i	$-0.777482\pi$
$383$	−46.7051	+	46.7051i	−0.121945	+	0.121945i	0.643500	+	0.765446i	$0.277482\pi$
$384$	313.893	−	170.060i	0.817428	−	0.442865i
$385$	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	−0.176135	−	0.984366i	$-0.556360\pi$
$397$	320.867	−	320.867i	0.808230	−	0.808230i	0.984366	+	0.176135i	$0.0563597\pi$
$398$	22.0872	−	22.0872i	0.0554954	−	0.0554954i
$399$	−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	$-0.799411\pi$
$401$		−	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	$-0.452425\pi$
$409$	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	$-0.965321\pi$
$419$		−	91.1169i		−	0.217463i	0.994071	−	0.108731i	$-0.0346788\pi$
$420$	−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	$0.0666545\pi$
$431$			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	0.382860	−	0.923806i	$-0.374939\pi$
$433$	−234.230	−	234.230i	−0.540947	−	0.540947i	−0.923806	+	0.382860i	$0.874939\pi$
$434$	212.092	+	39.9159i	0.488690	+	0.0919721i
$435$	−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	0.432527	−	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
$448$	−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	0.197440	−	0.980315i	$-0.436737\pi$
$457$	−357.774	−	357.774i	−0.782875	−	0.782875i	−0.980315	+	0.197440i	$0.936737\pi$
$458$	108.761	−	108.761i	0.237470	−	0.237470i
$459$	22.1291	+	1.80237i	0.0482115	+	0.00392674i
$460$	524.012	−	204.198i	1.13916	−	0.443910i
$461$	563.655			1.22268			0.611339	−	0.791369i	$-0.290631\pi$
$461$	563.655			1.22268			0.611339	+	0.791369i	$0.290631\pi$
$462$	24.8643	−	48.3588i	0.0538189	−	0.104673i
$463$	−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	0.353864	−	0.935297i	$-0.384867\pi$
$467$	−271.529	−	271.529i	−0.581432	−	0.581432i	−0.935297	+	0.353864i	$0.884867\pi$
$468$	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	$-0.818166\pi$
$479$		−	517.973i		−	1.08136i	0.841227	−	0.540682i	$-0.181834\pi$
$480$	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	0.976019	−	0.217684i	$-0.0698501\pi$
$487$	369.310	+	369.310i	0.758336	+	0.758336i	−0.217684	+	0.976019i	$0.569850\pi$
$488$	−390.998	+	390.998i	−0.801226	+	0.801226i
$489$	196.352	+	362.421i	0.401537	+	0.741147i
$490$	−0.115057	+	245.000i	−0.000234810	+	0.500000i
$491$			421.951i			0.859370i	0.902979	+	0.429685i	$0.141375\pi$
$491$			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
$497$	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	$-0.965080\pi$
$499$		−	109.267i		−	0.218971i	0.993988	−	0.109486i	$-0.0349204\pi$
$500$	354.846	−	121.283i	0.709691	−	0.242567i
$501$	773.095	−	418.846i	1.54310	−	0.836021i
$502$	256.959	−	256.959i	0.511871	−	0.511871i
$503$	134.096	−	134.096i	0.266592	−	0.266592i	−0.561133	−	0.827725i	$-0.689635\pi$
$503$	134.096	−	134.096i	0.266592	−	0.266592i	0.827725	+	0.561133i	$0.189635\pi$
$504$	318.495	+	305.028i	0.631934	+	0.605214i
$505$	108.463	+	47.6345i	0.214778	+	0.0943258i
$506$			97.0824i			0.191862i
$507$	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	$-0.851040\pi$
$509$		−	459.197i		−	0.902154i	0.892485	−	0.451077i	$-0.148960\pi$
$510$	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	0.903919	−	0.427704i	$-0.140677\pi$
$523$	249.060	+	249.060i	0.476215	+	0.476215i	−0.427704	+	0.903919i	$0.640677\pi$
$524$			652.986i			1.24616i
$525$	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	0.995405	−	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
$553$	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	−0.937479	−	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
$560$	−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	−0.996059	−	0.0886978i	$-0.971729\pi$
$563$	−510.844	+	510.844i	−0.907361	+	0.907361i	0.0886978	+	0.996059i	$0.471729\pi$
$564$	−274.337	−	506.364i	−0.486414	−	0.897809i
$565$	133.063	+	341.466i	0.235510	+	0.604364i
$566$	342.455			0.605043
$567$	−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	−0.381408	−	0.924407i	$-0.624561\pi$
$577$	313.311	−	313.311i	0.542999	−	0.542999i	0.924407	+	0.381408i	$0.124561\pi$
$578$	−203.876	−	203.876i	−0.352726	−	0.352726i
$579$	164.983	+	304.520i	0.284944	+	0.525942i
$580$	−69.6819	+	158.665i	−0.120141	+	0.273560i
$581$	98.2827	−	522.222i	0.169161	−	0.898833i
$582$	−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	0.822920	−	0.568158i	$-0.192344\pi$
$587$	149.545	+	149.545i	0.254762	+	0.254762i	−0.568158	+	0.822920i	$0.692344\pi$
$588$	−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	−0.854095	−	0.520118i	$-0.825888\pi$
$593$	−198.048	+	198.048i	−0.333977	+	0.333977i	0.520118	+	0.854095i	$0.325888\pi$
$594$	69.6819	+	5.67547i	0.117310	+	0.00955466i
$595$	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	$-0.899296\pi$
$601$		−	373.965i		−	0.622237i	0.950371	−	0.311119i	$-0.100704\pi$
$602$	−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	−0.0421025	+	0.999113i	$0.513406\pi$
$607$	−632.018	+	632.018i	−1.04122	+	1.04122i	−0.999113	+	0.0421025i	$0.986594\pi$
$608$	−386.871	+	386.871i	−0.636300	+	0.636300i
$609$	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	−0.0412636	−	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	$-0.303552\pi$
$619$	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	$-0.969871\pi$
$641$		−	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	0.985445	−	0.169993i	$-0.0543744\pi$
$643$	524.336	+	524.336i	0.815453	+	0.815453i	−0.169993	+	0.985445i	$0.554374\pi$
$644$	145.624	−	773.766i	0.226124	−	1.20150i
$645$	44.0751	+	531.790i	0.0683334	+	0.824480i
$646$	13.6333			0.0211042
$647$	305.897	+	305.897i	0.472792	+	0.472792i	0.902817	−	0.430025i	$-0.141495\pi$
$647$	305.897	+	305.897i	0.472792	+	0.472792i	−0.430025	+	0.902817i	$0.641495\pi$
$648$	−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	0.431488	−	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
$658$	−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	$-0.658180\pi$
$661$		−	1162.10i		−	1.75809i	0.476737	−	0.879046i	$-0.341820\pi$
$662$	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	−0.490040	−	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	0.499559	−	0.866280i	$-0.333496\pi$
$677$	−248.270	−	248.270i	−0.366721	−	0.366721i	−0.866280	+	0.499559i	$0.833496\pi$
$678$	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	$-0.961435\pi$
$691$		−	167.027i		−	0.241717i	0.992670	−	0.120859i	$-0.0385648\pi$
$692$	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	$-0.858706\pi$
$701$		−	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
$707$	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	$-0.991506\pi$
$709$		−	37.8334i		−	0.0533616i	0.999644	−	0.0266808i	$-0.00849377\pi$
$710$	88.9918	+	228.370i	0.125341	+	0.321648i
$711$	−372.605	+	571.482i	−0.524057	+	0.803772i
$712$	69.5605	−	69.5605i	0.0976973	−	0.0976973i
$713$	817.367	−	817.367i	1.14638	−	1.14638i
$714$	−5.27586	−	16.4428i	−0.00738916	−	0.0230292i
$715$	152.536	−	59.4405i	0.213337	−	0.0831336i
$716$			710.612i			0.992475i
$717$	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	$-0.908368\pi$
$719$		−	408.265i		−	0.567824i	0.958850	−	0.283912i	$-0.0916324\pi$
$720$	−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	−0.0871447	−	0.996196i	$-0.527774\pi$
$727$	660.880	−	660.880i	0.909051	−	0.909051i	0.996196	+	0.0871447i	$0.0277742\pi$
$728$	−349.526	−	511.589i	−0.480118	−	0.702732i
$729$	117.969	−	719.392i	0.161823	−	0.986820i
$730$	−168.562	−	74.0286i	−0.230907	−	0.101409i
$731$	−29.2530			−0.0400178
$732$	202.538	−	681.481i	0.276692	−	0.930985i
$733$	526.757	+	526.757i	0.718632	+	0.718632i	0.968325	−	0.249693i	$-0.0803298\pi$
$733$	526.757	+	526.757i	0.718632	+	0.718632i	−0.249693	+	0.968325i	$0.580330\pi$
$734$			328.745i			0.447882i
$735$	−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	$-0.939993\pi$
$739$		−	276.981i		−	0.374805i	0.982283	−	0.187402i	$-0.0600069\pi$
$740$	−820.127	+	319.589i	−1.10828	+	0.431877i
$741$	−552.979	+	299.592i	−0.746261	+	0.404308i
$742$	−279.221	+	190.768i	−0.376308	+	0.257100i
$743$	−698.839	−	698.839i	−0.940563	−	0.940563i	0.0577666	−	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
$756$	−546.865	−	149.757i	−0.723367	−	0.198092i
$757$	−269.069	−	269.069i	−0.355441	−	0.355441i	0.506688	−	0.862129i	$-0.330870\pi$
$757$	−269.069	−	269.069i	−0.355441	−	0.355441i	−0.862129	+	0.506688i	$0.830870\pi$
$758$	244.100	+	244.100i	0.322032	+	0.322032i
$759$	−138.738	−	256.079i	−0.182791	−	0.337390i
$760$	−210.692	−	540.675i	−0.277226	−	0.711414i
$761$	−973.280			−1.27895			−0.639475	−	0.768812i	$-0.720848\pi$
$761$	−973.280			−1.27895			−0.639475	+	0.768812i	$0.720848\pi$
$762$	−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	−0.965573	−	0.260132i	$-0.916234\pi$
$773$	−545.306	+	545.306i	−0.705441	+	0.705441i	0.260132	+	0.965573i	$0.416234\pi$
$774$	174.864	−	268.198i	0.225923	−	0.346509i
$775$	567.542	−	521.516i	0.732312	−	0.672924i
$776$	−257.054			−0.331255
$777$	−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	−0.900434	−	0.434992i	$-0.856751\pi$
$787$	−366.303	+	366.303i	−0.465442	+	0.465442i	0.434992	+	0.900434i	$0.356751\pi$
$788$	546.583	+	546.583i	0.693634	+	0.693634i
$789$	−364.085	+	197.254i	−0.461451	+	0.250004i
$790$	137.615	+	353.146i	0.174196	+	0.447020i
$791$	504.215	+	94.8938i	0.637440	+	0.119967i
$792$	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	0.781037	−	0.624485i	$-0.214691\pi$
$797$	124.772	+	124.772i	0.156552	+	0.156552i	−0.624485	+	0.781037i	$0.714691\pi$
$798$	−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	$0.201378\pi$
$811$			959.059i			1.18256i	−0.806465	+	0.591282i	$0.798622\pi$
$812$	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	$-0.859853\pi$
$821$		−	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	$-0.537964\pi$
$829$	−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	$-0.756913\pi$
$839$		−	1160.48i		−	1.38317i	0.722296	−	0.691584i	$-0.243087\pi$
$840$	−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	0.990437	−	0.137967i	$-0.0440568\pi$
$853$	727.157	+	727.157i	0.852470	+	0.852470i	−0.137967	+	0.990437i	$0.544057\pi$
$854$	−543.415	−	102.271i	−0.636317	−	0.119756i
$855$	408.365	+	624.386i	0.477620	+	0.730276i
$856$	1236.13			1.44408
$857$	−330.023	−	330.023i	−0.385091	−	0.385091i	0.487841	−	0.872932i	$-0.337784\pi$
$857$	−330.023	−	330.023i	−0.385091	−	0.385091i	−0.872932	+	0.487841i	$0.837784\pi$
$858$	−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	0.685957	−	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
$868$	−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	0.436353	−	0.899775i	$-0.356270\pi$
$877$	−406.421	−	406.421i	−0.463422	−	0.463422i	−0.899775	+	0.436353i	$0.856270\pi$
$878$	−372.158	+	372.158i	−0.423870	+	0.423870i
$879$	−673.728	−	1243.55i	−0.766471	−	1.41473i
$880$	−26.0300	+	59.2699i	−0.0295795	+	0.0673522i
$881$	−5.04486			−0.00572629			−0.00286315	−	0.999996i	$-0.500911\pi$
$881$	−5.04486			−0.00572629			−0.00286315	+	0.999996i	$0.500911\pi$
$882$	−72.1874	+	435.052i	−0.0818451	+	0.493256i
$883$	−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	0.158298	−	0.987391i	$-0.449399\pi$
$887$	−735.406	−	735.406i	−0.829094	−	0.829094i	−0.987391	+	0.158298i	$0.949399\pi$
$888$	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	0.333133	−	0.942880i	$-0.391894\pi$
$907$	−553.040	−	553.040i	−0.609747	−	0.609747i	−0.942880	+	0.333133i	$0.891894\pi$
$908$	−170.347	+	170.347i	−0.187607	+	0.187607i
$909$	178.620	+	116.460i	0.196501	+	0.128118i
$910$	434.967	−	81.6498i	0.477986	−	0.0897250i
$911$			466.216i			0.511763i	0.966708	+	0.255881i	$0.0823656\pi$
$911$			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
$917$	−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	$0.209872\pi$
$919$			1125.94i			1.22518i	−0.790401	+	0.612590i	$0.790128\pi$
$920$	527.666	−	1201.49i	0.573550	−	1.30596i
$921$	233.930	+	431.781i	0.253995	+	0.468818i
$922$	398.564	−	398.564i	0.432282	−	0.432282i
$923$	438.289	−	438.289i	0.474853	−	0.474853i
$924$	49.8392	+	155.330i	0.0539386	+	0.168106i
$925$	61.9428	−	1465.69i	0.0669652	−	1.58453i
$926$			38.1636i			0.0412133i
$927$	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	$0.464289\pi$
$929$			1846.32i			1.98743i	−0.111954	+	0.993713i	$0.535711\pi$
$930$	−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	−0.992402	−	0.123039i	$-0.960736\pi$
$937$	−814.593	+	814.593i	−0.869363	+	0.869363i	0.123039	+	0.992402i	$0.460736\pi$
$938$	−592.433	+	404.760i	−0.631592	+	0.431514i
$939$	−279.617	+	151.490i	−0.297782	+	0.161332i
$940$	894.336	−	348.507i	0.951421	−	0.370752i
$941$	1318.27			1.40093			0.700464	−	0.713687i	$-0.252976\pi$
$941$	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	−0.499458	−	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
$952$	−22.7304	−	33.2696i	−0.0238764	−	0.0349471i
$953$	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
$966$	−240.551	−	749.703i	−0.249017	−	0.776091i
$967$	1047.59	+	1047.59i	1.08334	+	1.08334i	0.996196	+	0.0871396i	$0.0277726\pi$
$967$	1047.59	+	1047.59i	1.08334	+	1.08334i	0.0871396	+	0.996196i	$0.472227\pi$
$968$	565.733	+	565.733i	0.584434	+	0.584434i
$969$	−35.9613	+	19.4831i	−0.0371118	+	0.0201064i
$970$	73.8310	−	168.112i	0.0761144	−	0.173311i
$971$	−379.480			−0.390813			−0.195407	−	0.980722i	$-0.562603\pi$
$971$	−379.480			−0.390813			−0.195407	+	0.980722i	$0.562603\pi$
$972$	−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	−0.533318	−	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
$980$	−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	−0.389275	−	0.921121i	$-0.627274\pi$
$983$	522.805	−	522.805i	0.531846	−	0.531846i	0.921121	+	0.389275i	$0.127274\pi$
$984$	316.642	−	171.550i	0.321791	−	0.174339i
$985$	−1200.39	+	467.771i	−1.21867	+	0.474894i
$986$	−9.49996			−0.00963484
$987$	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	−0.828142	−	0.560518i	$-0.810602\pi$
$997$	−266.821	+	266.821i	−0.267624	+	0.267624i	0.560518	+	0.828142i	$0.310602\pi$
$998$	−77.2632	−	77.2632i	−0.0774180	−	0.0774180i
$999$	−1579.12	−	128.617i	−1.58071	−	0.128746i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.854662 + 2.87568i) q^{3} +3.00000i q^{4} +(-4.57796 - 2.01054i) q^{5} +(1.42908 + 2.63775i) q^{6} +(-5.77983 + 3.94887i) q^{7} +(4.94975 + 4.94975i) q^{8} +(-7.53910 - 4.91548i) q^{9} +O(q^{10})\)	\(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

Properties

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