LMFDB - Embedded newform 850.2.v.d.207.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			207.5
Character	$\chi$	$=$	850.207
Dual form			850.2.v.d.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 - 0.382683i) q^{2} +(2.47936 - 1.65666i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.92460 + 0.581740i) q^{6} +(2.11600 - 0.420899i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(2.25467 - 5.44325i) q^{9} +(0.581141 + 2.92159i) q^{11} +(2.92460 + 0.581740i) q^{12} +5.10274 q^{13} +(-2.11600 - 0.420899i) q^{14} +1.00000i q^{16} +(-2.91101 - 2.91993i) q^{17} +(-4.16608 + 4.16608i) q^{18} +(2.47306 + 5.97048i) q^{19} +(4.54905 - 4.54905i) q^{21} +(0.581141 - 2.92159i) q^{22} +(-0.847753 + 1.26875i) q^{23} +(-2.47936 - 1.65666i) q^{24} +(-4.71431 - 1.95273i) q^{26} +(-1.68223 - 8.45716i) q^{27} +(1.79386 + 1.19862i) q^{28} +(-3.82051 - 5.71779i) q^{29} +(-0.942552 + 4.73853i) q^{31} +(0.382683 - 0.923880i) q^{32} +(6.28093 + 6.28093i) q^{33} +(1.57202 + 3.81166i) q^{34} +(5.44325 - 2.25467i) q^{36} +(-4.04382 - 6.05201i) q^{37} -6.46241i q^{38} +(12.6515 - 8.45347i) q^{39} +(2.01733 - 3.01915i) q^{41} +(-5.94362 + 2.46193i) q^{42} +(1.73529 - 0.718779i) q^{43} +(-1.65495 + 2.47681i) q^{44} +(1.26875 - 0.847753i) q^{46} +4.65062i q^{47} +(1.65666 + 2.47936i) q^{48} +(-2.16684 + 0.897536i) q^{49} +(-12.0548 - 2.41701i) q^{51} +(3.60818 + 3.60818i) q^{52} +(-1.11881 + 2.70105i) q^{53} +(-1.68223 + 8.45716i) q^{54} +(-1.19862 - 1.79386i) q^{56} +(16.0226 + 10.7060i) q^{57} +(1.34158 + 6.74460i) q^{58} +(-3.66553 - 1.51831i) q^{59} +(-3.45296 - 2.30720i) q^{61} +(2.68416 - 4.01713i) q^{62} +(2.47982 - 12.4669i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-3.39921 - 8.20642i) q^{66} +(2.25590 - 2.25590i) q^{67} +(0.00630415 - 4.12310i) q^{68} +4.55013i q^{69} +(5.63509 + 1.12089i) q^{71} -5.89173 q^{72} +(-9.62889 - 1.91531i) q^{73} +(1.42000 + 7.13883i) q^{74} +(-2.47306 + 5.97048i) q^{76} +(2.45939 + 5.93749i) q^{77} +(-14.9235 + 2.96847i) q^{78} +(-15.1407 + 3.01167i) q^{79} +(-5.68322 - 5.68322i) q^{81} +(-3.01915 + 2.01733i) q^{82} +(-9.03070 - 3.74064i) q^{83} +6.43332 q^{84} -1.87826 q^{86} +(-18.9448 - 7.84720i) q^{87} +(2.47681 - 1.65495i) q^{88} +(-5.41083 - 5.41083i) q^{89} +(10.7974 - 2.14774i) q^{91} +(-1.49660 + 0.297691i) q^{92} +(5.51318 + 13.3100i) q^{93} +(1.77972 - 4.29662i) q^{94} +(-0.581740 - 2.92460i) q^{96} +(2.63292 + 0.523720i) q^{97} +2.34537 q^{98} +(17.2132 + 3.42392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	2.47936	−	1.65666i	1.43146	−	0.956470i	0.432976	−	0.901405i	$-0.357463\pi$
$3$	2.47936	−	1.65666i	1.43146	−	0.956470i	0.998483	−	0.0550648i	$-0.0175366\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−2.92460	+	0.581740i	−1.19396	+	0.237494i
$7$	2.11600	−	0.420899i	0.799774	−	0.159085i	0.221749	−	0.975104i	$-0.428824\pi$
$7$	2.11600	−	0.420899i	0.799774	−	0.159085i	0.578025	+	0.816019i	$0.303824\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	2.25467	−	5.44325i	0.751556	−	1.81442i
$10$		0			0
$11$	0.581141	+	2.92159i	0.175220	+	0.880893i	0.963936	+	0.266134i	$0.0857465\pi$
$11$	0.581141	+	2.92159i	0.175220	+	0.880893i	−0.788715	+	0.614758i	$0.789253\pi$
$12$	2.92460	+	0.581740i	0.844260	+	0.167934i
$13$	5.10274			1.41524			0.707622	−	0.706591i	$-0.249768\pi$
$13$	5.10274			1.41524			0.707622	+	0.706591i	$0.249768\pi$
$14$	−2.11600	−	0.420899i	−0.565526	−	0.112490i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	−2.91101	−	2.91993i	−0.706025	−	0.708187i
$17$	−2.91101	−	2.91993i	−0.706025	−	0.708187i
$18$	−4.16608	+	4.16608i	−0.981955	+	0.981955i
$19$	2.47306	+	5.97048i	0.567358	+	1.36972i	0.903774	+	0.428010i	$0.140785\pi$
$19$	2.47306	+	5.97048i	0.567358	+	1.36972i	−0.336416	+	0.941713i	$0.609215\pi$
$20$		0			0
$21$	4.54905	−	4.54905i	0.992684	−	0.992684i
$22$	0.581141	−	2.92159i	0.123900	−	0.622885i
$23$	−0.847753	+	1.26875i	−0.176769	+	0.264553i	−0.909265	−	0.416218i	$-0.863355\pi$
$23$	−0.847753	+	1.26875i	−0.176769	+	0.264553i	0.732496	+	0.680771i	$0.238355\pi$
$24$	−2.47936	−	1.65666i	−0.506097	−	0.338163i
$25$		0			0
$26$	−4.71431	−	1.95273i	−0.924553	−	0.382962i
$27$	−1.68223	−	8.45716i	−0.323746	−	1.62758i
$28$	1.79386	+	1.19862i	0.339008	+	0.226518i
$29$	−3.82051	−	5.71779i	−0.709450	−	1.06177i	−0.994650	−	0.103300i	$-0.967060\pi$
$29$	−3.82051	−	5.71779i	−0.709450	−	1.06177i	0.285200	−	0.958468i	$-0.407940\pi$
$30$		0			0
$31$	−0.942552	+	4.73853i	−0.169287	+	0.851065i	0.799020	+	0.601304i	$0.205352\pi$
$31$	−0.942552	+	4.73853i	−0.169287	+	0.851065i	−0.968308	+	0.249761i	$0.919648\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	6.28093	+	6.28093i	1.09337	+	1.09337i
$34$	1.57202	+	3.81166i	0.269599	+	0.653694i
$35$		0			0
$36$	5.44325	−	2.25467i	0.907208	−	0.375778i
$37$	−4.04382	−	6.05201i	−0.664801	−	0.994945i	−0.998631	−	0.0523113i	$-0.983341\pi$
$37$	−4.04382	−	6.05201i	−0.664801	−	0.994945i	0.333830	−	0.942633i	$-0.391659\pi$
$38$		−	6.46241i		−	1.04834i
$39$	12.6515	−	8.45347i	2.02586	−	1.35364i
$40$		0			0
$41$	2.01733	−	3.01915i	0.315054	−	0.471511i	−0.639819	−	0.768525i	$-0.720991\pi$
$41$	2.01733	−	3.01915i	0.315054	−	0.471511i	0.954873	+	0.297014i	$0.0959908\pi$
$42$	−5.94362	+	2.46193i	−0.917120	+	0.379884i
$43$	1.73529	−	0.718779i	0.264629	−	0.109613i	−0.246424	−	0.969162i	$-0.579256\pi$
$43$	1.73529	−	0.718779i	0.264629	−	0.109613i	0.511053	+	0.859549i	$0.329256\pi$
$44$	−1.65495	+	2.47681i	−0.249493	+	0.373392i
$45$		0			0
$46$	1.26875	−	0.847753i	0.187067	−	0.124994i
$47$			4.65062i			0.678363i	0.940721	+	0.339182i	$0.110150\pi$
$47$			4.65062i			0.678363i	−0.940721	+	0.339182i	$0.889850\pi$
$48$	1.65666	+	2.47936i	0.239118	+	0.357865i
$49$	−2.16684	+	0.897536i	−0.309549	+	0.128219i
$50$		0			0
$51$	−12.0548	−	2.41701i	−1.68801	−	0.338449i
$52$	3.60818	+	3.60818i	0.500364	+	0.500364i
$53$	−1.11881	+	2.70105i	−0.153680	+	0.371017i	−0.981904	−	0.189381i	$-0.939352\pi$
$53$	−1.11881	+	2.70105i	−0.153680	+	0.371017i	0.828223	+	0.560398i	$0.189352\pi$
$54$	−1.68223	+	8.45716i	−0.228923	+	1.15087i
$55$		0			0
$56$	−1.19862	−	1.79386i	−0.160172	−	0.239715i
$57$	16.0226	+	10.7060i	2.12225	+	1.41804i
$58$	1.34158	+	6.74460i	0.176159	+	0.885609i
$59$	−3.66553	−	1.51831i	−0.477211	−	0.197667i	0.131095	−	0.991370i	$-0.458151\pi$
$59$	−3.66553	−	1.51831i	−0.477211	−	0.197667i	−0.608306	+	0.793703i	$0.708151\pi$
$60$		0			0
$61$	−3.45296	−	2.30720i	−0.442107	−	0.295406i	0.314523	−	0.949250i	$-0.398155\pi$
$61$	−3.45296	−	2.30720i	−0.442107	−	0.295406i	−0.756630	+	0.653844i	$0.773155\pi$
$62$	2.68416	−	4.01713i	0.340889	−	0.510176i
$63$	2.47982	−	12.4669i	0.312428	−	1.57068i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$		0			0
$66$	−3.39921	−	8.20642i	−0.418414	−	1.01014i
$67$	2.25590	−	2.25590i	0.275602	−	0.275602i	−0.555749	−	0.831350i	$-0.687568\pi$
$67$	2.25590	−	2.25590i	0.275602	−	0.275602i	0.831350	+	0.555749i	$0.187568\pi$
$68$	0.00630415	−	4.12310i	0.000764491	−	0.499999i
$69$			4.55013i			0.547771i
$70$		0			0
$71$	5.63509	+	1.12089i	0.668762	+	0.133025i	0.517783	−	0.855512i	$-0.326757\pi$
$71$	5.63509	+	1.12089i	0.668762	+	0.133025i	0.150979	+	0.988537i	$0.451757\pi$
$72$	−5.89173			−0.694347
$73$	−9.62889	−	1.91531i	−1.12698	−	0.224170i	−0.403810	−	0.914843i	$-0.632314\pi$
$73$	−9.62889	−	1.91531i	−1.12698	−	0.224170i	−0.723167	+	0.690674i	$0.757314\pi$
$74$	1.42000	+	7.13883i	0.165072	+	0.829873i
$75$		0			0
$76$	−2.47306	+	5.97048i	−0.283679	+	0.684861i
$77$	2.45939	+	5.93749i	0.280274	+	0.676640i
$78$	−14.9235	+	2.96847i	−1.68975	+	0.336113i
$79$	−15.1407	+	3.01167i	−1.70346	+	0.338839i	−0.948462	−	0.316890i	$-0.897361\pi$
$79$	−15.1407	+	3.01167i	−1.70346	+	0.338839i	−0.754996	+	0.655729i	$0.772361\pi$
$80$		0			0
$81$	−5.68322	−	5.68322i	−0.631469	−	0.631469i
$82$	−3.01915	+	2.01733i	−0.333409	+	0.222777i
$83$	−9.03070	−	3.74064i	−0.991249	−	0.410589i	−0.172668	−	0.984980i	$-0.555239\pi$
$83$	−9.03070	−	3.74064i	−0.991249	−	0.410589i	−0.818581	+	0.574391i	$0.805239\pi$
$84$	6.43332			0.701933
$85$		0			0
$86$	−1.87826			−0.202538
$87$	−18.9448	−	7.84720i	−2.03110	−	0.841309i
$88$	2.47681	−	1.65495i	0.264028	−	0.176418i
$89$	−5.41083	−	5.41083i	−0.573547	−	0.573547i	0.359571	−	0.933118i	$-0.382923\pi$
$89$	−5.41083	−	5.41083i	−0.573547	−	0.573547i	−0.933118	+	0.359571i	$0.882923\pi$
$90$		0			0
$91$	10.7974	−	2.14774i	1.13188	−	0.225144i
$92$	−1.49660	+	0.297691i	−0.156031	+	0.0310365i
$93$	5.51318	+	13.3100i	0.571690	+	1.38018i
$94$	1.77972	−	4.29662i	0.183564	−	0.443162i
$95$		0			0
$96$	−0.581740	−	2.92460i	−0.0593736	−	0.298491i
$97$	2.63292	+	0.523720i	0.267332	+	0.0531757i	0.326936	−	0.945046i	$-0.393984\pi$
$97$	2.63292	+	0.523720i	0.267332	+	0.0531757i	−0.0596039	+	0.998222i	$0.518984\pi$
$98$	2.34537			0.236919
$99$	17.2132	+	3.42392i	1.72999	+	0.344117i
$100$		0			0
$101$			12.8077i			1.27441i	0.770693	+	0.637207i	$0.219910\pi$
$101$			12.8077i			1.27441i	−0.770693	+	0.637207i	$0.780090\pi$
$102$	10.2122	+	6.84619i	1.01116	+	0.677873i
$103$	8.68917	−	8.68917i	0.856170	−	0.856170i	−0.134715	−	0.990884i	$-0.543012\pi$
$103$	8.68917	−	8.68917i	0.856170	−	0.856170i	0.990884	+	0.134715i	$0.0430118\pi$
$104$	−1.95273	−	4.71431i	−0.191481	−	0.462276i
$105$		0			0
$106$	2.06729	−	2.06729i	0.200793	−	0.200793i
$107$	0.486150	−	2.44404i	0.0469978	−	0.236274i	−0.950145	−	0.311807i	$-0.899066\pi$
$107$	0.486150	−	2.44404i	0.0469978	−	0.236274i	0.997143	+	0.0755328i	$0.0240658\pi$
$108$	4.79060	−	7.16964i	0.460976	−	0.689899i
$109$	15.1896	+	10.1494i	1.45490	+	0.972132i	0.996518	+	0.0833759i	$0.0265702\pi$
$109$	15.1896	+	10.1494i	1.45490	+	0.972132i	0.458380	+	0.888756i	$0.348430\pi$
$110$		0			0
$111$	−20.0522	−	8.30589i	−1.90327	−	0.788360i
$112$	0.420899	+	2.11600i	0.0397712	+	0.199944i
$113$	−10.4494	−	6.98206i	−0.982997	−	0.656817i	−0.0433845	−	0.999058i	$-0.513814\pi$
$113$	−10.4494	−	6.98206i	−0.982997	−	0.656817i	−0.939612	+	0.342241i	$0.888814\pi$
$114$	−10.7060	−	16.0226i	−1.00271	−	1.50066i
$115$		0			0
$116$	1.34158	−	6.74460i	0.124563	−	0.626220i
$117$	11.5050	−	27.7755i	1.06364	−	2.56784i
$118$	2.80547	+	2.80547i	0.258265	+	0.258265i
$119$	−7.38871	−	4.95334i	−0.677322	−	0.454072i
$120$		0			0
$121$	1.96470	−	0.813807i	0.178610	−	0.0739825i
$122$	2.30720	+	3.45296i	0.208884	+	0.312617i
$123$		−	10.8276i		−	0.976289i
$124$	−4.01713	+	2.68416i	−0.360749	+	0.241045i
$125$		0			0
$126$	−7.06194	+	10.5689i	−0.629128	+	0.941556i
$127$	−2.06022	+	0.853371i	−0.182815	+	0.0757245i	−0.472213	−	0.881484i	$-0.656545\pi$
$127$	−2.06022	+	0.853371i	−0.182815	+	0.0757245i	0.289398	+	0.957209i	$0.406545\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	3.11163	−	4.65688i	0.273964	−	0.410016i
$130$		0			0
$131$	10.4931	−	7.01129i	0.916790	−	0.612579i	−0.00511864	−	0.999987i	$-0.501629\pi$
$131$	10.4931	−	7.01129i	0.916790	−	0.612579i	0.921909	+	0.387407i	$0.126629\pi$
$132$			8.88257i			0.773128i
$133$	7.74596	+	11.5927i	0.671660	+	1.00521i
$134$	−2.94747	+	1.22088i	−0.254623	+	0.105468i
$135$		0			0
$136$	−1.58367	+	3.80684i	−0.135798	+	0.326433i
$137$	2.33320	+	2.33320i	0.199339	+	0.199339i	0.799717	−	0.600378i	$-0.204983\pi$
$137$	2.33320	+	2.33320i	0.199339	+	0.199339i	−0.600378	+	0.799717i	$0.704983\pi$
$138$	1.74126	−	4.20377i	0.148226	−	0.357849i
$139$	2.59433	−	13.0426i	0.220049	−	1.10626i	−0.699906	−	0.714235i	$-0.746775\pi$
$139$	2.59433	−	13.0426i	0.220049	−	1.10626i	0.919955	−	0.392024i	$-0.128225\pi$
$140$		0			0
$141$	7.70448	+	11.5306i	0.648834	+	0.971049i
$142$	−4.77720	−	3.19202i	−0.400894	−	0.267869i
$143$	2.96541	+	14.9081i	0.247980	+	1.24668i
$144$	5.44325	+	2.25467i	0.453604	+	0.187889i
$145$		0			0
$146$	8.16298	+	5.45433i	0.675573	+	0.451403i
$147$	−3.88548	+	5.81503i	−0.320469	+	0.479615i
$148$	1.42000	−	7.13883i	0.116723	−	0.586809i
$149$	−5.78244	+	5.78244i	−0.473716	+	0.473716i	−0.903115	−	0.429399i	$-0.858725\pi$
$149$	−5.78244	+	5.78244i	−0.473716	+	0.473716i	0.429399	+	0.903115i	$0.358725\pi$
$150$		0			0
$151$	3.31607	+	8.00571i	0.269858	+	0.651495i	0.999476	−	0.0323595i	$-0.0103021\pi$
$151$	3.31607	+	8.00571i	0.269858	+	0.651495i	−0.729618	+	0.683855i	$0.760302\pi$
$152$	4.56961	−	4.56961i	0.370644	−	0.370644i
$153$	−22.4573	+	9.26191i	−1.81556	+	0.748781i
$154$		−	6.42670i		−	0.517878i
$155$		0			0
$156$	14.9235	+	2.96847i	1.19483	+	0.237667i
$157$	−6.12399			−0.488747			−0.244374	−	0.969681i	$-0.578582\pi$
$157$	−6.12399			−0.488747			−0.244374	+	0.969681i	$0.578582\pi$
$158$	15.1407	+	3.01167i	1.20453	+	0.239595i
$159$	1.70077	+	8.55035i	0.134880	+	0.678087i
$160$		0			0
$161$	−1.25983	+	3.04150i	−0.0992887	+	0.239704i
$162$	3.07574	+	7.42549i	0.241653	+	0.583401i
$163$	12.9467	−	2.57526i	1.01407	−	0.201710i	0.340034	−	0.940413i	$-0.389561\pi$
$163$	12.9467	−	2.57526i	1.01407	−	0.201710i	0.674031	+	0.738703i	$0.264561\pi$
$164$	3.56132	−	0.708391i	0.278093	−	0.0553161i
$165$		0			0
$166$	6.91180	+	6.91180i	0.536460	+	0.536460i
$167$	−14.6882	+	9.81435i	−1.13661	+	0.759457i	−0.973846	−	0.227209i	$-0.927040\pi$
$167$	−14.6882	+	9.81435i	−1.13661	+	0.759457i	−0.162761	+	0.986665i	$0.552040\pi$
$168$	−5.94362	−	2.46193i	−0.458560	−	0.189942i
$169$	13.0379			1.00292
$170$		0			0
$171$	38.0747			2.91165
$172$	1.73529	+	0.718779i	0.132314	+	0.0548064i
$173$	−8.19533	+	5.47594i	−0.623079	+	0.416328i	−0.826638	−	0.562734i	$-0.809749\pi$
$173$	−8.19533	+	5.47594i	−0.623079	+	0.416328i	0.203558	+	0.979063i	$0.434749\pi$
$174$	14.4997	+	14.4997i	1.09922	+	1.09922i
$175$		0			0
$176$	−2.92159	+	0.581141i	−0.220223	+	0.0438051i
$177$	−11.6035	+	2.30807i	−0.872170	+	0.173485i
$178$	2.92832	+	7.06959i	0.219487	+	0.529888i
$179$	0.836227	−	2.01883i	0.0625026	−	0.150895i	−0.889542	−	0.456853i	$-0.848977\pi$
$179$	0.836227	−	2.01883i	0.0625026	−	0.150895i	0.952045	+	0.305958i	$0.0989767\pi$
$180$		0			0
$181$	2.38233	+	11.9768i	0.177077	+	0.890225i	0.962503	+	0.271270i	$0.0874437\pi$
$181$	2.38233	+	11.9768i	0.177077	+	0.890225i	−0.785426	+	0.618955i	$0.787556\pi$
$182$	−10.7974	−	2.14774i	−0.800357	−	0.159201i
$183$	−12.3834			−0.915405
$184$	1.49660	+	0.297691i	0.110330	+	0.0219461i
$185$		0			0
$186$		−	14.4066i		−	1.05635i
$187$	6.83913	−	10.2017i	0.500127	−	0.746021i
$188$	−3.28849	+	3.28849i	−0.239838	+	0.239838i
$189$	−7.11923	−	17.1873i	−0.517848	−	1.25019i
$190$		0			0
$191$	−3.12333	+	3.12333i	−0.225996	+	0.225996i	−0.811018	−	0.585021i	$-0.801086\pi$
$191$	−3.12333	+	3.12333i	−0.225996	+	0.225996i	0.585021	+	0.811018i	$0.301086\pi$
$192$	−0.581740	+	2.92460i	−0.0419835	+	0.211065i
$193$	−13.1386	+	19.6632i	−0.945734	+	1.41539i	−0.0363943	+	0.999338i	$0.511587\pi$
$193$	−13.1386	+	19.6632i	−0.945734	+	1.41539i	−0.909340	+	0.416054i	$0.863413\pi$
$194$	−2.23208	−	1.49143i	−0.160254	−	0.107078i
$195$		0			0
$196$	−2.16684	−	0.897536i	−0.154775	−	0.0641097i
$197$	0.300658	+	1.51151i	0.0214210	+	0.107691i	0.990017	−	0.140951i	$-0.0450160\pi$
$197$	0.300658	+	1.51151i	0.0214210	+	0.107691i	−0.968596	+	0.248641i	$0.920016\pi$
$198$	−14.5927	−	9.75051i	−1.03706	−	0.692938i
$199$	−2.72577	−	4.07940i	−0.193224	−	0.289181i	0.722189	−	0.691696i	$-0.243136\pi$
$199$	−2.72577	−	4.07940i	−0.193224	−	0.289181i	−0.915413	+	0.402515i	$0.868136\pi$
$200$		0			0
$201$	1.85594	−	9.33042i	0.130908	−	0.658117i
$202$	4.90129	−	11.8328i	0.344854	−	0.832551i
$203$	−10.4908	−	10.4908i	−0.736311	−	0.736311i
$204$	−6.81493	−	10.2331i	−0.477140	−	0.716460i
$205$		0			0
$206$	−11.3530	+	4.70255i	−0.790998	+	0.327642i
$207$	4.99473	+	7.47515i	0.347158	+	0.519559i
$208$			5.10274i			0.353811i
$209$	−16.0061	+	10.6949i	−1.10717	+	0.739785i
$210$		0			0
$211$	−14.8005	+	22.1505i	−1.01891	+	1.52490i	−0.177777	+	0.984071i	$0.556890\pi$
$211$	−14.8005	+	22.1505i	−1.01891	+	1.52490i	−0.841131	+	0.540832i	$0.818110\pi$
$212$	−2.70105	+	1.11881i	−0.185509	+	0.0768402i
$213$	15.8283	−	6.55631i	1.08454	−	0.449231i
$214$	−1.38444	+	2.07196i	−0.0946381	+	0.141636i
$215$		0			0
$216$	−7.16964	+	4.79060i	−0.487832	+	0.325959i
$217$			10.4235i			0.707591i
$218$	−10.1494	−	15.1896i	−0.687401	−	1.02877i
$219$	−27.0465	+	11.2030i	−1.82763	+	0.757030i
$220$		0			0
$221$	−14.8541	−	14.8996i	−0.999198	−	1.00226i
$222$	15.3473	+	15.3473i	1.03004	+	1.03004i
$223$	3.78056	−	9.12708i	0.253165	−	0.611195i	−0.745291	−	0.666739i	$-0.767690\pi$
$223$	3.78056	−	9.12708i	0.253165	−	0.611195i	0.998456	+	0.0555446i	$0.0176895\pi$
$224$	0.420899	−	2.11600i	0.0281225	−	0.141381i
$225$		0			0
$226$	6.98206	+	10.4494i	0.464440	+	0.695084i
$227$	6.88241	+	4.59868i	0.456801	+	0.305225i	0.762599	−	0.646872i	$-0.223923\pi$
$227$	6.88241	+	4.59868i	0.456801	+	0.305225i	−0.305797	+	0.952097i	$0.598923\pi$
$228$	3.75944	+	18.9000i	0.248975	+	1.25168i
$229$	21.1923	+	8.77812i	1.40042	+	0.580074i	0.949862	−	0.312671i	$-0.101224\pi$
$229$	21.1923	+	8.77812i	1.40042	+	0.580074i	0.450562	+	0.892745i	$0.351224\pi$
$230$		0			0
$231$	15.9341	+	10.6468i	1.04839	+	0.700509i
$232$	−3.82051	+	5.71779i	−0.250829	+	0.375392i
$233$	5.40843	−	27.1900i	0.354318	−	1.78128i	−0.233576	−	0.972339i	$-0.575043\pi$
$233$	5.40843	−	27.1900i	0.354318	−	1.78128i	0.587894	−	0.808938i	$-0.299957\pi$
$234$	−21.2584	+	21.2584i	−1.38971	+	1.38971i
$235$		0			0
$236$	−1.51831	−	3.66553i	−0.0988336	−	0.238605i
$237$	−32.5499	+	32.5499i	−2.11434	+	2.11434i
$238$	4.93072	+	7.40383i	0.319611	+	0.479919i
$239$			21.8340i			1.41232i	0.708051	+	0.706161i	$0.249575\pi$
$239$			21.8340i			1.41232i	−0.708051	+	0.706161i	$0.750425\pi$
$240$		0			0
$241$	−10.9377	−	2.17563i	−0.704556	−	0.140145i	−0.170206	−	0.985408i	$-0.554443\pi$
$241$	−10.9377	−	2.17563i	−0.704556	−	0.140145i	−0.534350	+	0.845264i	$0.679443\pi$
$242$	−2.12658			−0.136702
$243$	1.86561	+	0.371092i	0.119679	+	0.0238056i
$244$	−0.810180	−	4.07305i	−0.0518664	−	0.260750i
$245$		0			0
$246$	−4.14353	+	10.0034i	−0.264182	+	0.637791i
$247$	12.6193	+	30.4658i	0.802950	+	1.93849i
$248$	4.73853	−	0.942552i	0.300897	−	0.0598521i
$249$	−28.5873	+	5.68637i	−1.81165	+	0.360359i
$250$		0			0
$251$	−5.63823	−	5.63823i	−0.355882	−	0.355882i	0.506411	−	0.862292i	$-0.330972\pi$
$251$	−5.63823	−	5.63823i	−0.355882	−	0.355882i	−0.862292	+	0.506411i	$0.830972\pi$
$252$	10.5689	−	7.06194i	0.665781	−	0.444861i
$253$	−4.19944	−	1.73947i	−0.264017	−	0.109359i
$254$	2.22997			0.139921
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	11.0133	+	4.56187i	0.686992	+	0.284561i	0.698746	−	0.715370i	$-0.253742\pi$
$257$	11.0133	+	4.56187i	0.686992	+	0.284561i	−0.0117544	+	0.999931i	$0.503742\pi$
$258$	−4.65688	+	3.11163i	−0.289925	+	0.193722i
$259$	−11.1040	−	11.1040i	−0.689971	−	0.689971i
$260$		0			0
$261$	−39.7373	+	7.90425i	−2.45968	+	0.489261i
$262$	−12.3775	+	2.46204i	−0.764685	+	0.152105i
$263$	5.39184	+	13.0171i	0.332475	+	0.802666i	0.998395	+	0.0566422i	$0.0180394\pi$
$263$	5.39184	+	13.0171i	0.332475	+	0.802666i	−0.665919	+	0.746024i	$0.731961\pi$
$264$	3.39921	−	8.20642i	0.209207	−	0.505070i
$265$		0			0
$266$	−2.72002	−	13.6745i	−0.166775	−	0.838436i
$267$	−22.3793	−	4.45151i	−1.36959	−	0.272428i
$268$	3.19032			0.194880
$269$	−4.26081	−	0.847528i	−0.259786	−	0.0516747i	0.0634787	−	0.997983i	$-0.479781\pi$
$269$	−4.26081	−	0.847528i	−0.259786	−	0.0516747i	−0.323265	+	0.946308i	$0.604781\pi$
$270$		0			0
$271$		−	3.27703i		−	0.199065i	−0.995034	−	0.0995326i	$-0.968265\pi$
$271$		−	3.27703i		−	0.199065i	0.995034	−	0.0995326i	$-0.0317347\pi$
$272$	2.91993	−	2.91101i	0.177047	−	0.176506i
$273$	23.2126	−	23.2126i	1.40489	−	1.40489i
$274$	−1.26272	−	3.04848i	−0.0762837	−	0.184165i
$275$		0			0
$276$	−3.21743	+	3.21743i	−0.193666	+	0.193666i
$277$	−3.34480	+	16.8154i	−0.200970	+	1.01034i	0.740195	+	0.672393i	$0.234733\pi$
$277$	−3.34480	+	16.8154i	−0.200970	+	1.01034i	−0.941164	+	0.337950i	$0.890267\pi$
$278$	−7.38804	+	11.0570i	−0.443105	+	0.663154i
$279$	23.6678	+	15.8143i	1.41696	+	0.946780i
$280$		0			0
$281$	26.4043	+	10.9370i	1.57515	+	0.652447i	0.987635	−	0.156769i	$-0.0501079\pi$
$281$	26.4043	+	10.9370i	1.57515	+	0.652447i	0.587511	+	0.809216i	$0.300108\pi$
$282$	−2.70545	−	13.6012i	−0.161107	−	0.809942i
$283$	2.50708	+	1.67518i	0.149030	+	0.0995789i	0.627850	−	0.778334i	$-0.283935\pi$
$283$	2.50708	+	1.67518i	0.149030	+	0.0995789i	−0.478820	+	0.877913i	$0.658935\pi$
$284$	3.19202	+	4.77720i	0.189412	+	0.283475i
$285$		0			0
$286$	2.96541	−	14.9081i	0.175348	−	0.881535i
$287$	2.99792	−	7.23761i	0.176961	−	0.427223i
$288$	−4.16608	−	4.16608i	−0.245489	−	0.245489i
$289$	−0.0519853	+	16.9999i	−0.00305796	+	0.999995i
$290$		0			0
$291$	7.39558	−	3.06335i	0.433536	−	0.179577i
$292$	−5.45433	−	8.16298i	−0.319190	−	0.477702i
$293$			7.90877i			0.462035i	0.972950	+	0.231018i	$0.0742055\pi$
$293$			7.90877i			0.462035i	−0.972950	+	0.231018i	$0.925794\pi$
$294$	5.81503	−	3.88548i	0.339139	−	0.226606i
$295$		0			0
$296$	−4.04382	+	6.05201i	−0.235043	+	0.351766i
$297$	23.7308	−	9.82960i	1.37700	−	0.570371i
$298$	7.55512	−	3.12943i	0.437656	−	0.181283i
$299$	−4.32586	+	6.47411i	−0.250171	+	0.374407i
$300$		0			0
$301$	3.36934	−	2.25132i	0.194205	−	0.129764i
$302$		−	8.66532i		−	0.498633i
$303$	21.2179	+	31.7549i	1.21894	+	1.82427i
$304$	−5.97048	+	2.47306i	−0.342431	+	0.141839i
$305$		0			0
$306$	24.2922	+	0.0371424i	1.38869	+	0.00212329i
$307$	10.8126	+	10.8126i	0.617106	+	0.617106i	0.944788	−	0.327682i	$-0.106267\pi$
$307$	10.8126	+	10.8126i	0.617106	+	0.617106i	−0.327682	+	0.944788i	$0.606267\pi$
$308$	−2.45939	+	5.93749i	−0.140137	+	0.338320i
$309$	7.14862	−	35.9386i	0.406671	−	2.04447i
$310$		0			0
$311$	0.359069	+	0.537385i	0.0203609	+	0.0304723i	0.841510	−	0.540241i	$-0.181667\pi$
$311$	0.359069	+	0.537385i	0.0203609	+	0.0304723i	−0.821150	+	0.570713i	$0.806667\pi$
$312$	−12.6515	−	8.45347i	−0.716251	−	0.478584i
$313$	−0.645545	−	3.24537i	−0.0364883	−	0.183439i	0.958243	−	0.285955i	$-0.0923108\pi$
$313$	−0.645545	−	3.24537i	−0.0364883	−	0.183439i	−0.994731	+	0.102516i	$0.967311\pi$
$314$	5.65783	+	2.34355i	0.319290	+	0.132254i
$315$		0			0
$316$	−12.8356	−	8.57650i	−0.722061	−	0.482466i
$317$	7.87772	−	11.7898i	0.442457	−	0.662183i	−0.541477	−	0.840715i	$-0.682135\pi$
$317$	7.87772	−	11.7898i	0.442457	−	0.662183i	0.983934	+	0.178532i	$0.0571348\pi$
$318$	1.70077	−	8.55035i	0.0953745	−	0.479480i
$319$	14.4848	−	14.4848i	0.810993	−	0.810993i
$320$		0			0
$321$	−2.84359	−	6.86503i	−0.158714	−	0.383169i
$322$	2.32787	−	2.32787i	0.129727	−	0.129727i
$323$	10.2343	−	24.6013i	0.569451	−	1.36885i
$324$		−	8.03729i		−	0.446516i
$325$		0			0
$326$	−12.9467	−	2.57526i	−0.717053	−	0.142631i
$327$	54.4744			3.01244
$328$	−3.56132	−	0.708391i	−0.196641	−	0.0391144i
$329$	1.95744	+	9.84074i	0.107917	+	0.542537i
$330$		0			0
$331$	10.8628	−	26.2251i	0.597073	−	1.44146i	−0.279477	−	0.960152i	$-0.590161\pi$
$331$	10.8628	−	26.2251i	0.597073	−	1.44146i	0.876550	−	0.481310i	$-0.159839\pi$
$332$	−3.74064	−	9.03070i	−0.205294	−	0.495624i
$333$	−42.0601	+	8.36627i	−2.30488	+	0.458469i
$334$	17.3259	−	3.44634i	0.948032	−	0.188575i
$335$		0			0
$336$	4.54905	+	4.54905i	0.248171	+	0.248171i
$337$	2.20255	−	1.47169i	0.119980	−	0.0801683i	−0.494132	−	0.869387i	$-0.664514\pi$
$337$	2.20255	−	1.47169i	0.119980	−	0.0801683i	0.614112	+	0.789219i	$0.289514\pi$
$338$	−12.0455	−	4.98940i	−0.655187	−	0.271387i
$339$	−37.4747			−2.03535
$340$		0			0
$341$	−14.3918			−0.779360
$342$	−35.1765	−	14.5706i	−1.90213	−	0.787886i
$343$	−16.7643	+	11.2015i	−0.905187	+	0.604827i
$344$	−1.32813	−	1.32813i	−0.0716080	−	0.0716080i
$345$		0			0
$346$	9.66705	−	1.92290i	0.519704	−	0.103376i
$347$	21.2587	−	4.22862i	1.14123	−	0.227004i	0.411940	−	0.911211i	$-0.364851\pi$
$347$	21.2587	−	4.22862i	1.14123	−	0.227004i	0.729288	+	0.684207i	$0.239851\pi$
$348$	−7.84720	−	18.9448i	−0.420654	−	1.01555i
$349$	2.37113	−	5.72441i	0.126923	−	0.306420i	−0.847626	−	0.530595i	$-0.821969\pi$
$349$	2.37113	−	5.72441i	0.126923	−	0.306420i	0.974549	+	0.224174i	$0.0719686\pi$
$350$		0			0
$351$	−8.58400	−	43.1547i	−0.458180	−	2.30343i
$352$	2.92159	+	0.581141i	0.155721	+	0.0309749i
$353$	−18.7851			−0.999831			−0.499915	−	0.866074i	$-0.666636\pi$
$353$	−18.7851			−0.999831			−0.499915	+	0.866074i	$0.666636\pi$
$354$	11.6035	+	2.30807i	0.616718	+	0.122673i
$355$		0			0
$356$		−	7.65207i		−	0.405559i
$357$	−26.5252	−	0.0405567i	−1.40386	−	0.00214649i
$358$	−1.54515	+	1.54515i	−0.0816635	+	0.0816635i
$359$	−0.798627	−	1.92806i	−0.0421499	−	0.101759i	0.901402	−	0.432982i	$-0.142539\pi$
$359$	−0.798627	−	1.92806i	−0.0421499	−	0.101759i	−0.943552	+	0.331223i	$0.892539\pi$
$360$		0			0
$361$	−16.0956	+	16.0956i	−0.847139	+	0.847139i
$362$	2.38233	−	11.9768i	0.125212	−	0.629484i
$363$	3.52301	−	5.27256i	0.184910	−	0.276738i
$364$	9.15360	+	6.11624i	0.479779	+	0.320578i
$365$		0			0
$366$	11.4407	+	4.73891i	0.598017	+	0.247707i
$367$	0.264915	+	1.33182i	0.0138285	+	0.0695204i	0.987083	−	0.160208i	$-0.0512163\pi$
$367$	0.264915	+	1.33182i	0.0138285	+	0.0695204i	−0.973255	+	0.229728i	$0.926216\pi$
$368$	−1.26875	−	0.847753i	−0.0661383	−	0.0441922i
$369$	−11.8856	−	17.7880i	−0.618737	−	0.926006i
$370$		0			0
$371$	−1.23054	+	6.18633i	−0.0638863	+	0.321178i
$372$	−5.51318	+	13.3100i	−0.285845	+	0.690091i
$373$	6.12982	+	6.12982i	0.317390	+	0.317390i	0.847764	−	0.530374i	$-0.177948\pi$
$373$	6.12982	+	6.12982i	0.317390	+	0.317390i	−0.530374	+	0.847764i	$0.677948\pi$
$374$	−10.2226	+	6.80790i	−0.528596	+	0.352028i
$375$		0			0
$376$	4.29662	−	1.77972i	0.221581	−	0.0917819i
$377$	−19.4950	−	29.1764i	−1.00405	−	1.50266i
$378$			18.6034i			0.956857i
$379$	9.90108	−	6.61569i	0.508584	−	0.339825i	−0.274658	−	0.961542i	$-0.588565\pi$
$379$	9.90108	−	6.61569i	0.508584	−	0.339825i	0.783242	+	0.621717i	$0.213565\pi$
$380$		0			0
$381$	−3.69429	+	5.52889i	−0.189264	+	0.283254i
$382$	4.08083	−	1.69034i	0.208793	−	0.0864851i
$383$	13.9138	−	5.76328i	0.710962	−	0.294490i	0.00225919	−	0.999997i	$-0.499281\pi$
$383$	13.9138	−	5.76328i	0.710962	−	0.294490i	0.708702	+	0.705507i	$0.249281\pi$
$384$	1.65666	−	2.47936i	0.0845408	−	0.126524i
$385$		0			0
$386$	19.6632	−	13.1386i	1.00083	−	0.668735i
$387$		−	11.0662i		−	0.562527i
$388$	1.49143	+	2.23208i	0.0757158	+	0.113317i
$389$	24.1120	−	9.98753i	1.22253	−	0.506388i	0.324315	−	0.945949i	$-0.394866\pi$
$389$	24.1120	−	9.98753i	1.22253	−	0.506388i	0.898213	+	0.439561i	$0.144866\pi$
$390$		0			0
$391$	6.17249	−	1.21798i	0.312156	−	0.0615957i
$392$	1.65843	+	1.65843i	0.0837634	+	0.0837634i
$393$	14.4010	−	34.7670i	0.726433	−	1.75376i
$394$	0.300658	−	1.51151i	0.0151469	−	0.0761487i
$395$		0			0
$396$	9.75051	+	14.5927i	0.489981	+	0.733309i
$397$	−21.0338	−	14.0544i	−1.05566	−	0.705368i	−0.0985598	−	0.995131i	$-0.531424\pi$
$397$	−21.0338	−	14.0544i	−1.05566	−	0.705368i	−0.957098	+	0.289763i	$0.906424\pi$
$398$	0.957161	+	4.81198i	0.0479782	+	0.241203i
$399$	38.4101	+	15.9100i	1.92291	+	0.796495i
$400$		0			0
$401$	−8.53692	−	5.70419i	−0.426314	−	0.284854i	0.323847	−	0.946110i	$-0.395024\pi$
$401$	−8.53692	−	5.70419i	−0.426314	−	0.284854i	−0.750160	+	0.661256i	$0.770024\pi$
$402$	−5.28526	+	7.90995i	−0.263605	+	0.394512i
$403$	−4.80959	+	24.1795i	−0.239583	+	1.20446i
$404$	−9.05641	+	9.05641i	−0.450573	+	0.450573i
$405$		0			0
$406$	5.67759	+	13.7069i	0.281774	+	0.680263i
$407$	15.3315	−	15.3315i	0.759953	−	0.759953i
$408$	2.38014	+	12.0621i	0.117834	+	0.597163i
$409$		−	18.8720i		−	0.933158i	−0.884480	−	0.466579i	$-0.845486\pi$
$409$		−	18.8720i		−	0.933158i	0.884480	−	0.466579i	$-0.154514\pi$
$410$		0			0
$411$	9.65016	+	1.91954i	0.476007	+	0.0946838i
$412$	12.2883			0.605403
$413$	−8.39532	−	1.66993i	−0.413107	−	0.0821720i
$414$	−1.75392	−	8.81754i	−0.0862003	−	0.433358i
$415$		0			0
$416$	1.95273	−	4.71431i	0.0957406	−	0.231138i
$417$	−15.1748	−	36.6352i	−0.743113	−	1.79403i
$418$	18.8805	−	3.75557i	0.923476	−	0.183691i
$419$	2.17804	−	0.433238i	0.106404	−	0.0211651i	−0.141601	−	0.989924i	$-0.545225\pi$
$419$	2.17804	−	0.433238i	0.106404	−	0.0211651i	0.248005	+	0.968759i	$0.420225\pi$
$420$		0			0
$421$	−19.5353	−	19.5353i	−0.952094	−	0.952094i	0.0468096	−	0.998904i	$-0.485095\pi$
$421$	−19.5353	−	19.5353i	−0.952094	−	0.952094i	−0.998904	+	0.0468096i	$0.985095\pi$
$422$	22.1505	−	14.8005i	1.07827	−	0.720476i
$423$	25.3145	+	10.4856i	1.23083	+	0.509828i
$424$	2.92359			0.141982
$425$		0			0
$426$	−17.1325			−0.830071
$427$	−8.27758	−	3.42869i	−0.400580	−	0.165926i
$428$	2.07196	−	1.38444i	0.100152	−	0.0669193i
$429$	32.0499	+	32.0499i	1.54738	+	1.54738i
$430$		0			0
$431$	26.3843	−	5.24817i	1.27089	−	0.252796i	0.486838	−	0.873492i	$-0.338150\pi$
$431$	26.3843	−	5.24817i	1.27089	−	0.252796i	0.784051	+	0.620697i	$0.213150\pi$
$432$	8.45716	−	1.68223i	0.406895	−	0.0809365i
$433$	−2.65966	−	6.42099i	−0.127815	−	0.308573i	0.846998	−	0.531596i	$-0.178408\pi$
$433$	−2.65966	−	6.42099i	−0.127815	−	0.308573i	−0.974813	+	0.223023i	$0.928408\pi$
$434$	3.98889	−	9.63002i	0.191473	−	0.462256i
$435$		0			0
$436$	3.56398	+	17.9173i	0.170684	+	0.858085i
$437$	−9.67161	−	1.92380i	−0.462656	−	0.0920279i
$438$	29.2749			1.39881
$439$	11.9718	+	2.38134i	0.571382	+	0.113655i	0.472321	−	0.881426i	$-0.343416\pi$
$439$	11.9718	+	2.38134i	0.571382	+	0.113655i	0.0990609	+	0.995081i	$0.468416\pi$
$440$		0			0
$441$			13.8183i			0.658015i
$442$	8.02159	+	19.4499i	0.381548	+	0.925137i
$443$	−18.3210	+	18.3210i	−0.870456	+	0.870456i	−0.992522	−	0.122066i	$-0.961048\pi$
$443$	−18.3210	+	18.3210i	−0.870456	+	0.870456i	0.122066	+	0.992522i	$0.461048\pi$
$444$	−8.30589	−	20.0522i	−0.394180	−	0.951635i
$445$		0			0
$446$	−6.98556	+	6.98556i	−0.330776	+	0.330776i
$447$	−4.75724	+	23.9163i	−0.225010	+	1.13120i
$448$	−1.19862	+	1.79386i	−0.0566294	+	0.0847520i
$449$	−31.2145	−	20.8568i	−1.47310	−	0.984295i	−0.994328	−	0.106356i	$-0.966082\pi$
$449$	−31.2145	−	20.8568i	−1.47310	−	0.984295i	−0.478773	−	0.877939i	$-0.658918\pi$
$450$		0			0
$451$	9.99306	+	4.13926i	0.470555	+	0.194910i
$452$	−2.45178	−	12.3259i	−0.115322	−	0.579762i
$453$	21.4844	+	14.3554i	1.00943	+	0.674478i
$454$	−4.59868	−	6.88241i	−0.215827	−	0.323007i
$455$		0			0
$456$	3.75944	−	18.9000i	0.176052	−	0.885072i
$457$	6.88648	−	16.6254i	0.322136	−	0.777705i	−0.676994	−	0.735989i	$-0.736718\pi$
$457$	6.88648	−	16.6254i	0.322136	−	0.777705i	0.999130	−	0.0417158i	$-0.0132824\pi$
$458$	−16.2199	−	16.2199i	−0.757904	−	0.757904i
$459$	−19.7973	+	29.5309i	−0.924060	+	1.37839i
$460$		0			0
$461$	22.1601	−	9.17900i	1.03210	−	0.427508i	0.198628	−	0.980075i	$-0.436351\pi$
$461$	22.1601	−	9.17900i	1.03210	−	0.427508i	0.833469	+	0.552566i	$0.186351\pi$
$462$	−10.6468	−	15.9341i	−0.495335	−	0.741321i
$463$		−	35.3808i		−	1.64428i	−0.569283	−	0.822142i	$-0.692779\pi$
$463$		−	35.3808i		−	1.64428i	0.569283	−	0.822142i	$-0.307221\pi$
$464$	5.71779	−	3.82051i	0.265442	−	0.177363i
$465$		0			0
$466$	−15.4019	+	23.0506i	−0.713479	+	1.06780i
$467$	−20.7488	+	8.59445i	−0.960142	+	0.397704i	−0.807033	−	0.590506i	$-0.798928\pi$
$467$	−20.7488	+	8.59445i	−0.960142	+	0.397704i	−0.153108	+	0.988209i	$0.548928\pi$
$468$	27.7755	−	11.5050i	1.28392	−	0.531818i
$469$	3.82398	−	5.72299i	0.176575	−	0.264263i
$470$		0			0
$471$	−15.1836	+	10.1453i	−0.699622	+	0.467472i
$472$			3.96754i			0.182621i
$473$	3.10842	+	4.65208i	0.142925	+	0.213903i
$474$	42.5285	−	17.6159i	1.95340	−	0.809123i
$475$		0			0
$476$	−1.72207	−	8.72715i	−0.0789310	−	0.400008i
$477$	12.1799	+	12.1799i	0.557681	+	0.557681i
$478$	8.35550	−	20.1720i	0.382172	−	0.922644i
$479$	−3.75915	+	18.8985i	−0.171760	+	0.863496i	0.794764	+	0.606919i	$0.207595\pi$
$479$	−3.75915	+	18.8985i	−0.171760	+	0.863496i	−0.966524	+	0.256577i	$0.917405\pi$
$480$		0			0
$481$	−20.6346	−	30.8818i	−0.940856	−	1.40809i
$482$	9.27249	+	6.19568i	0.422350	+	0.282206i
$483$	1.91515	+	9.62809i	0.0871421	+	0.438093i
$484$	1.96470	+	0.813807i	0.0893048	+	0.0369912i
$485$		0			0
$486$	−1.58158	−	1.05678i	−0.0717422	−	0.0479366i
$487$	−17.2975	+	25.8876i	−0.783826	+	1.17308i	0.197420	+	0.980319i	$0.436744\pi$
$487$	−17.2975	+	25.8876i	−0.783826	+	1.17308i	−0.981246	+	0.192760i	$0.938256\pi$
$488$	−0.810180	+	4.07305i	−0.0366751	+	0.184378i
$489$	27.8333	−	27.8333i	1.25866	−	1.25866i
$490$		0			0
$491$	−12.1296	−	29.2835i	−0.547403	−	1.32155i	−0.919404	−	0.393315i	$-0.871328\pi$
$491$	−12.1296	−	29.2835i	−0.547403	−	1.32155i	0.372001	−	0.928232i	$-0.378672\pi$
$492$	7.65624	−	7.65624i	0.345170	−	0.345170i
$493$	−5.57400	+	27.8002i	−0.251041	+	1.25206i
$494$		−	32.9759i		−	1.48366i
$495$		0			0
$496$	−4.73853	−	0.942552i	−0.212766	−	0.0423218i
$497$	12.3957			0.556021
$498$	28.5873	+	5.68637i	1.28103	+	0.254812i
$499$	−5.07928	−	25.5353i	−0.227380	−	1.14312i	−0.910723	−	0.413018i	$-0.864475\pi$
$499$	−5.07928	−	25.5353i	−0.227380	−	1.14312i	0.683343	−	0.730098i	$-0.260525\pi$
$500$		0			0
$501$	−20.1584	+	48.6666i	−0.900609	+	2.17426i
$502$	3.05139	+	7.36670i	0.136190	+	0.328792i
$503$	−19.6945	+	3.91748i	−0.878134	+	0.174672i	−0.613517	−	0.789682i	$-0.710246\pi$
$503$	−19.6945	+	3.91748i	−0.878134	+	0.174672i	−0.264617	+	0.964353i	$0.585246\pi$
$504$	−12.4669	+	2.47982i	−0.555321	+	0.110460i
$505$		0			0
$506$	3.21411	+	3.21411i	0.142885	+	0.142885i
$507$	32.3257	−	21.5993i	1.43563	−	0.959260i
$508$	−2.06022	−	0.853371i	−0.0914075	−	0.0378622i
$509$	−2.28523			−0.101291			−0.0506455	−	0.998717i	$-0.516128\pi$
$509$	−2.28523			−0.101291			−0.0506455	+	0.998717i	$0.516128\pi$
$510$		0			0
$511$	−21.1809			−0.936988
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	46.3331	−	30.9588i	2.04566	−	1.36686i
$514$	−8.42923	−	8.42923i	−0.371797	−	0.371797i
$515$		0			0
$516$	5.49317	−	1.09266i	0.241823	−	0.0481016i
$517$	−13.5872	+	2.70267i	−0.597565	+	0.118863i
$518$	6.00946	+	14.5081i	0.264040	+	0.637450i
$519$	−11.2474	+	27.1537i	−0.493707	+	1.19191i
$520$		0			0
$521$	4.26245	+	21.4288i	0.186741	+	0.938812i	0.954531	+	0.298110i	$0.0963563\pi$
$521$	4.26245	+	21.4288i	0.186741	+	0.938812i	−0.767790	+	0.640701i	$0.778644\pi$
$522$	39.7373	+	7.90425i	1.73926	+	0.345960i
$523$	−38.7971			−1.69648			−0.848239	−	0.529614i	$-0.822337\pi$
$523$	−38.7971			−1.69648			−0.848239	+	0.529614i	$0.822337\pi$
$524$	12.3775	+	2.46204i	0.540714	+	0.107555i
$525$		0			0
$526$		−	14.0896i		−	0.614334i
$527$	16.5800	−	11.0417i	0.722234	−	0.480986i
$528$	−6.28093	+	6.28093i	−0.273342	+	0.273342i
$529$	7.91067	+	19.0981i	0.343942	+	0.830350i
$530$		0			0
$531$	−16.5291	+	16.5291i	−0.717301	+	0.717301i
$532$	−2.72002	+	13.6745i	−0.117928	+	0.592863i
$533$	10.2939	−	15.4059i	0.445878	−	0.667304i
$534$	18.9722	+	12.6768i	0.821008	+	0.548580i
$535$		0			0
$536$	−2.94747	−	1.22088i	−0.127311	−	0.0527341i
$537$	−1.27120	−	6.39075i	−0.0548563	−	0.275781i
$538$	3.61214	+	2.41356i	0.155731	+	0.104056i
$539$	−3.88147	−	5.80904i	−0.167187	−	0.250213i
$540$		0			0
$541$	2.10863	−	10.6008i	0.0906572	−	0.455765i	−0.908616	−	0.417634i	$-0.862860\pi$
$541$	2.10863	−	10.6008i	0.0906572	−	0.455765i	0.999273	−	0.0381310i	$-0.0121404\pi$
$542$	−1.25406	+	3.02758i	−0.0538666	+	0.130046i
$543$	25.7480	+	25.7480i	1.10495	+	1.10495i
$544$	−3.81166	+	1.57202i	−0.163424	+	0.0673997i
$545$		0			0
$546$	−30.3287	+	12.5626i	−1.29795	+	0.537628i
$547$	−13.3892	−	20.0384i	−0.572482	−	0.856780i	0.426376	−	0.904546i	$-0.359790\pi$
$547$	−13.3892	−	20.0384i	−0.572482	−	0.856780i	−0.998859	+	0.0477657i	$0.984790\pi$
$548$			3.29965i			0.140954i
$549$	−20.3439	+	13.5934i	−0.868258	+	0.580151i
$550$		0			0
$551$	24.6897	−	36.9507i	1.05182	−	1.57415i
$552$	4.20377	−	1.74126i	0.178924	−	0.0741129i
$553$	−30.7701	+	12.7454i	−1.30848	+	0.541989i
$554$	9.52519	−	14.2554i	0.404686	−	0.605656i
$555$		0			0
$556$	11.0570	−	7.38804i	0.468921	−	0.313323i
$557$			33.9956i			1.44044i	0.693746	+	0.720220i	$0.255959\pi$
$557$			33.9956i			1.44044i	−0.693746	+	0.720220i	$0.744041\pi$
$558$	−15.8143	−	23.6678i	−0.669475	−	1.00194i
$559$	8.85471	−	3.66774i	0.374514	−	0.155129i
$560$		0			0
$561$	0.0559971	−	36.6237i	0.00236420	−	1.54626i
$562$	−20.2089	−	20.2089i	−0.852463	−	0.852463i
$563$	2.94572	−	7.11160i	0.124147	−	0.299718i	−0.849571	−	0.527475i	$-0.823139\pi$
$563$	2.94572	−	7.11160i	0.124147	−	0.299718i	0.973718	+	0.227756i	$0.0731390\pi$
$564$	−2.70545	+	13.6012i	−0.113920	+	0.572715i
$565$		0			0
$566$	−1.67518	−	2.50708i	−0.0704129	−	0.105380i
$567$	−14.4178	−	9.63365i	−0.605490	−	0.404575i
$568$	−1.12089	−	5.63509i	−0.0470315	−	0.236443i
$569$	−18.4941	−	7.66052i	−0.775314	−	0.321146i	−0.0402912	−	0.999188i	$-0.512829\pi$
$569$	−18.4941	−	7.66052i	−0.775314	−	0.321146i	−0.735023	+	0.678042i	$0.762829\pi$
$570$		0			0
$571$	8.82341	+	5.89561i	0.369248	+	0.246724i	0.726325	−	0.687351i	$-0.241227\pi$
$571$	8.82341	+	5.89561i	0.369248	+	0.246724i	−0.357077	+	0.934075i	$0.616227\pi$
$572$	−8.44477	+	12.6385i	−0.353093	+	0.528442i
$573$	−2.56958	+	12.9181i	−0.107346	+	0.539663i
$574$	−5.53943	+	5.53943i	−0.231211	+	0.231211i
$575$		0			0
$576$	2.25467	+	5.44325i	0.0939445	+	0.226802i
$577$	26.0481	−	26.0481i	1.08440	−	1.08440i	0.0883015	−	0.996094i	$-0.471856\pi$
$577$	26.0481	−	26.0481i	1.08440	−	1.08440i	0.996094	−	0.0883015i	$-0.0281439\pi$
$578$	6.55362	−	15.6860i	0.272594	−	0.652451i
$579$			70.5183i			2.93064i
$580$		0			0
$581$	−20.6834	−	4.11419i	−0.858093	−	0.170685i
$582$	−8.00491			−0.331814
$583$	−8.54154	−	1.69902i	−0.353755	−	0.0703662i
$584$	1.91531	+	9.62889i	0.0792559	+	0.398446i
$585$		0			0
$586$	3.02656	−	7.30675i	0.125026	−	0.301839i
$587$	−6.90430	−	16.6684i	−0.284971	−	0.687980i	0.714967	−	0.699159i	$-0.246442\pi$
$587$	−6.90430	−	16.6684i	−0.284971	−	0.687980i	−0.999938	+	0.0111781i	$0.996442\pi$
$588$	−6.85929	+	1.36440i	−0.282872	+	0.0562668i
$589$	−30.6223	+	6.09115i	−1.26177	+	0.250982i
$590$		0			0
$591$	3.24949	+	3.24949i	0.133666	+	0.133666i
$592$	6.05201	−	4.04382i	0.248736	−	0.166200i
$593$	−19.0530	−	7.89203i	−0.782414	−	0.324087i	−0.0445250	−	0.999008i	$-0.514177\pi$
$593$	−19.0530	−	7.89203i	−0.782414	−	0.324087i	−0.737889	+	0.674922i	$0.764177\pi$
$594$	−25.6860			−1.05391
$595$		0			0
$596$	−8.17761			−0.334968
$597$	−13.5163	−	5.59864i	−0.553185	−	0.229137i
$598$	6.47411	−	4.32586i	0.264746	−	0.176898i
$599$	8.03343	+	8.03343i	0.328237	+	0.328237i	0.851916	−	0.523679i	$-0.175441\pi$
$599$	8.03343	+	8.03343i	0.328237	+	0.328237i	−0.523679	+	0.851916i	$0.675441\pi$
$600$		0			0
$601$	16.8364	−	3.34896i	0.686770	−	0.136607i	0.160642	−	0.987013i	$-0.448644\pi$
$601$	16.8364	−	3.34896i	0.686770	−	0.136607i	0.526127	+	0.850406i	$0.323644\pi$
$602$	−3.97440	+	0.790558i	−0.161985	+	0.0322207i
$603$	−7.19311	−	17.3657i	−0.292926	−	0.707186i
$604$	−3.31607	+	8.00571i	−0.134929	+	0.325748i
$605$		0			0
$606$	−7.45075	−	37.4574i	−0.302666	−	1.52160i
$607$	15.0490	+	2.99343i	0.610821	+	0.121500i	0.490801	−	0.871272i	$-0.336704\pi$
$607$	15.0490	+	2.99343i	0.610821	+	0.121500i	0.120020	+	0.992772i	$0.461704\pi$
$608$	6.46241			0.262085
$609$	−43.3902	−	8.63085i	−1.75826	−	0.349740i
$610$		0			0
$611$			23.7309i			0.960050i
$612$	−22.4288	−	9.33054i	−0.906632	−	0.377165i
$613$	5.02517	−	5.02517i	0.202965	−	0.202965i	−0.598304	−	0.801269i	$-0.704159\pi$
$613$	5.02517	−	5.02517i	0.202965	−	0.202965i	0.801269	+	0.598304i	$0.204159\pi$
$614$	−5.85173	−	14.1273i	−0.236156	−	0.570132i
$615$		0			0
$616$	4.54436	−	4.54436i	0.183098	−	0.183098i
$617$	1.51726	−	7.62776i	0.0610824	−	0.307082i	−0.938151	−	0.346226i	$-0.887463\pi$
$617$	1.51726	−	7.62776i	0.0610824	−	0.307082i	0.999234	+	0.0391439i	$0.0124631\pi$
$618$	−20.3576	+	30.4672i	−0.818901	+	1.22557i
$619$	23.2443	+	15.5314i	0.934268	+	0.624258i	0.926736	−	0.375714i	$-0.122602\pi$
$619$	23.2443	+	15.5314i	0.934268	+	0.624258i	0.00753243	+	0.999972i	$0.497602\pi$
$620$		0			0
$621$	12.1562	+	5.03525i	0.487810	+	0.202058i
$622$	−0.126088	−	0.633889i	−0.00505568	−	0.0254166i
$623$	−13.7267	−	9.17192i	−0.549950	−	0.367465i
$624$	8.45347	+	12.6515i	0.338410	+	0.506466i
$625$		0			0
$626$	−0.645545	+	3.24537i	−0.0258011	+	0.129711i
$627$	−21.9671	+	53.0332i	−0.877281	+	2.11794i
$628$	−4.33031	−	4.33031i	−0.172798	−	0.172798i
$629$	−5.89982	+	29.4252i	−0.235241	+	1.17326i
$630$		0			0
$631$	16.9058	−	7.00260i	0.673008	−	0.278769i	−0.0198927	−	0.999802i	$-0.506332\pi$
$631$	16.9058	−	7.00260i	0.673008	−	0.278769i	0.692901	+	0.721033i	$0.256332\pi$
$632$	8.57650	+	12.8356i	0.341155	+	0.510574i
$633$			79.4383i			3.15739i
$634$	−11.7898	+	7.87772i	−0.468234	+	0.312864i
$635$		0			0
$636$	−4.84339	+	7.24864i	−0.192053	+	0.287427i
$637$	−11.0568	+	4.57989i	−0.438088	+	0.181462i
$638$	−18.9253	+	7.83912i	−0.749260	+	0.310354i
$639$	18.8065	−	28.1460i	0.743975	−	1.11344i
$640$		0			0
$641$	−29.4328	+	19.6664i	−1.16253	+	0.776776i	−0.978521	−	0.206149i	$-0.933907\pi$
$641$	−29.4328	+	19.6664i	−1.16253	+	0.776776i	−0.184007	+	0.982925i	$0.558907\pi$
$642$			7.43066i			0.293265i
$643$	−5.81925	−	8.70912i	−0.229489	−	0.343454i	0.698798	−	0.715319i	$-0.253719\pi$
$643$	−5.81925	−	8.70912i	−0.229489	−	0.343454i	−0.928287	+	0.371865i	$0.878719\pi$
$644$	−3.04150	+	1.25983i	−0.119852	+	0.0496443i
$645$		0			0
$646$	−18.8698	+	18.8122i	−0.742421	+	0.740154i
$647$	−1.76443	−	1.76443i	−0.0693668	−	0.0693668i	0.671572	−	0.740939i	$-0.265619\pi$
$647$	−1.76443	−	1.76443i	−0.0693668	−	0.0693668i	−0.740939	+	0.671572i	$0.765619\pi$
$648$	−3.07574	+	7.42549i	−0.120826	+	0.291701i
$649$	2.30570	−	11.5915i	0.0905065	−	0.455007i
$650$		0			0
$651$	17.2681	+	25.8435i	0.676789	+	1.01289i
$652$	10.9757	+	7.33373i	0.429842	+	0.287211i
$653$	−2.34838	−	11.8061i	−0.0918991	−	0.462008i	−0.999143	−	0.0414020i	$-0.986818\pi$
$653$	−2.34838	−	11.8061i	−0.0918991	−	0.462008i	0.907243	−	0.420606i	$-0.138182\pi$
$654$	−50.3278	−	20.8465i	−1.96797	−	0.815161i
$655$		0			0
$656$	3.01915	+	2.01733i	0.117878	+	0.0787634i
$657$	−32.1354	+	48.0941i	−1.25372	+	1.87633i
$658$	1.95744	−	9.84074i	0.0763091	−	0.383632i
$659$	−21.1376	+	21.1376i	−0.823403	+	0.823403i	−0.986594	−	0.163192i	$-0.947821\pi$
$659$	−21.1376	+	21.1376i	−0.823403	+	0.823403i	0.163192	+	0.986594i	$0.447821\pi$
$660$		0			0
$661$	−7.99380	−	19.2988i	−0.310923	−	0.750634i	−0.999671	−	0.0256340i	$-0.991840\pi$
$661$	−7.99380	−	19.2988i	−0.310923	−	0.750634i	0.688748	−	0.725000i	$-0.258160\pi$
$662$	−20.0718	+	20.0718i	−0.780114	+	0.780114i
$663$	−61.5123	−	12.3334i	−2.38894	−	0.478988i
$664$			9.77476i			0.379334i
$665$		0			0
$666$	42.0601	+	8.36627i	1.62980	+	0.324186i
$667$	10.4933			0.406303
$668$	−17.3259	−	3.44634i	−0.670360	−	0.133343i
$669$	−5.74706	−	28.8924i	−0.222194	−	1.11704i
$670$		0			0
$671$	4.73403	−	11.4290i	0.182755	−	0.441210i
$672$	−2.46193	−	5.94362i	−0.0949709	−	0.229280i
$673$	35.6232	−	7.08590i	1.37317	−	0.273141i	0.547272	−	0.836955i	$-0.315666\pi$
$673$	35.6232	−	7.08590i	1.37317	−	0.273141i	0.825902	+	0.563813i	$0.190666\pi$
$674$	−2.59808	+	0.516790i	−0.100074	+	0.0199060i
$675$		0			0
$676$	9.21920	+	9.21920i	0.354585	+	0.354585i
$677$	−5.06304	+	3.38302i	−0.194588	+	0.130020i	−0.649048	−	0.760748i	$-0.724832\pi$
$677$	−5.06304	+	3.38302i	−0.194588	+	0.130020i	0.454459	+	0.890767i	$0.349832\pi$
$678$	34.6221	+	14.3409i	1.32965	+	0.550761i
$679$	5.79170			0.222265
$680$		0			0
$681$	24.6824			0.945831
$682$	13.2963	+	5.50750i	0.509141	+	0.210893i
$683$	20.5178	−	13.7095i	0.785091	−	0.524581i	−0.0972115	−	0.995264i	$-0.530992\pi$
$683$	20.5178	−	13.7095i	0.785091	−	0.524581i	0.882303	+	0.470683i	$0.155992\pi$
$684$	26.9229	+	26.9229i	1.02942	+	1.02942i
$685$		0			0
$686$	19.7748	−	3.93346i	0.755007	−	0.150180i
$687$	67.0855	−	13.3441i	2.55947	−	0.509111i
$688$	0.718779	+	1.73529i	0.0274032	+	0.0661572i
$689$	−5.70900	+	13.7827i	−0.217495	+	0.525080i
$690$		0			0
$691$	−5.00947	−	25.1843i	−0.190569	−	0.958057i	−0.951130	−	0.308790i	$-0.900076\pi$
$691$	−5.00947	−	25.1843i	−0.190569	−	0.958057i	0.760561	−	0.649267i	$-0.224924\pi$
$692$	−9.66705	−	1.92290i	−0.367486	−	0.0730975i
$693$	37.8644			1.43835
$694$	−21.2587	−	4.22862i	−0.806970	−	0.160516i
$695$		0			0
$696$			20.5057i			0.777268i
$697$	−14.6882	+	2.89832i	−0.556354	+	0.109782i
$698$	−4.38127	+	4.38127i	−0.165834	+	0.165834i
$699$	−31.6350	−	76.3737i	−1.19655	−	2.88872i
$700$		0			0
$701$	−11.3764	+	11.3764i	−0.429679	+	0.429679i	−0.888519	−	0.458840i	$-0.848265\pi$
$701$	−11.3764	+	11.3764i	−0.429679	+	0.429679i	0.458840	+	0.888519i	$0.348265\pi$
$702$	−8.58400	+	43.1547i	−0.323982	+	1.62877i
$703$	26.1328	−	39.1106i	0.985619	−	1.47508i
$704$	−2.47681	−	1.65495i	−0.0933481	−	0.0623732i
$705$		0			0
$706$	17.3552	+	7.18875i	0.653171	+	0.270552i
$707$	5.39075	+	27.1011i	0.202740	+	1.01924i
$708$	−9.83695	−	6.57284i	−0.369695	−	0.247022i
$709$	−3.94521	−	5.90443i	−0.148165	−	0.221745i	0.749962	−	0.661481i	$-0.230072\pi$
$709$	−3.94521	−	5.90443i	−0.148165	−	0.221745i	−0.898127	+	0.439736i	$0.855072\pi$
$710$		0			0
$711$	−17.7439	+	89.2047i	−0.665449	+	3.34544i
$712$	−2.92832	+	7.06959i	−0.109743	+	0.264944i
$713$	−5.21297	−	5.21297i	−0.195227	−	0.195227i
$714$	24.4906	+	10.1882i	0.916538	+	0.381285i
$715$		0			0
$716$	2.01883	−	0.836227i	0.0754473	−	0.0312513i
$717$	36.1714	+	54.1343i	1.35084	+	2.02168i
$718$			2.08691i			0.0778829i
$719$	29.9430	−	20.0073i	1.11669	−	0.746146i	0.146670	−	0.989186i	$-0.453145\pi$
$719$	29.9430	−	20.0073i	1.11669	−	0.746146i	0.970016	+	0.243040i	$0.0781446\pi$
$720$		0			0
$721$	14.7291	−	22.0436i	0.548539	−	0.820946i
$722$	21.0300	−	8.71090i	0.782655	−	0.324186i
$723$	−30.7226	+	12.7257i	−1.14259	+	0.473275i
$724$	−6.78429	+	10.1534i	−0.252136	+	0.377348i
$725$		0			0
$726$	−5.27256	+	3.52301i	−0.195683	+	0.130751i
$727$		−	32.6875i		−	1.21231i	−0.795345	−	0.606156i	$-0.792711\pi$
$727$		−	32.6875i		−	1.21231i	0.795345	−	0.606156i	$-0.207289\pi$
$728$	−6.11624	−	9.15360i	−0.226683	−	0.339255i
$729$	27.5167	−	11.3978i	1.01914	−	0.422141i
$730$		0			0
$731$	−7.15023	−	2.97454i	−0.264461	−	0.110017i
$732$	−8.75636	−	8.75636i	−0.323645	−	0.323645i
$733$	−8.14076	+	19.6535i	−0.300686	+	0.725920i	0.699253	+	0.714874i	$0.253516\pi$
$733$	−8.14076	+	19.6535i	−0.300686	+	0.725920i	−0.999939	+	0.0110459i	$0.996484\pi$
$734$	0.264915	−	1.33182i	0.00977821	−	0.0491584i
$735$		0			0
$736$	0.847753	+	1.26875i	0.0312486	+	0.0467668i
$737$	7.90180	+	5.27981i	0.291066	+	0.194484i
$738$	4.17365	+	20.9824i	0.153634	+	0.772371i
$739$	−29.6823	−	12.2948i	−1.09188	−	0.452271i	−0.237218	−	0.971456i	$-0.576236\pi$
$739$	−29.6823	−	12.2948i	−1.09188	−	0.452271i	−0.854662	+	0.519185i	$0.826236\pi$
$740$		0			0
$741$	81.7592	+	54.6298i	3.00350	+	2.00687i
$742$	3.50428	−	5.24452i	0.128646	−	0.192532i
$743$	2.43650	−	12.2491i	0.0893863	−	0.449375i	−0.910008	−	0.414590i	$-0.863925\pi$
$743$	2.43650	−	12.2491i	0.0893863	−	0.449375i	0.999395	−	0.0347858i	$-0.0110749\pi$
$744$	10.1870	−	10.1870i	0.373475	−	0.373475i
$745$		0			0
$746$	−3.31743	−	8.00899i	−0.121460	−	0.293230i
$747$	−40.7225	+	40.7225i	−1.48996	+	1.48996i
$748$	12.0497	−	2.37768i	0.440580	−	0.0869367i
$749$		−	5.37621i		−	0.196443i
$750$		0			0
$751$	1.41399	+	0.281260i	0.0515972	+	0.0102633i	0.220821	−	0.975314i	$-0.429126\pi$
$751$	1.41399	+	0.281260i	0.0515972	+	0.0102633i	−0.169224	+	0.985578i	$0.554126\pi$
$752$	−4.65062			−0.169591
$753$	−23.3198	−	4.63859i	−0.849820	−	0.169040i
$754$	6.84575	+	34.4159i	0.249307	+	1.25335i
$755$		0			0
$756$	7.11923	−	17.1873i	0.258924	−	0.625097i
$757$	−10.3778	−	25.0542i	−0.377187	−	0.910610i	−0.992491	−	0.122320i	$-0.960967\pi$
$757$	−10.3778	−	25.0542i	−0.377187	−	0.910610i	0.615304	−	0.788290i	$-0.289033\pi$
$758$	−11.6791	+	2.32312i	−0.424205	+	0.0843796i
$759$	−13.2936	+	2.64426i	−0.482528	+	0.0959807i
$760$		0			0
$761$	−23.9731	−	23.9731i	−0.869023	−	0.869023i	0.123342	−	0.992364i	$-0.460639\pi$
$761$	−23.9731	−	23.9731i	−0.869023	−	0.869023i	−0.992364	+	0.123342i	$0.960639\pi$
$762$	5.52889	−	3.69429i	0.200291	−	0.133830i
$763$	36.4131	+	15.0828i	1.31824	+	0.546034i
$764$	−4.41706			−0.159804
$765$		0			0
$766$	−15.0602			−0.544146
$767$	−18.7042	−	7.74754i	−0.675370	−	0.279747i
$768$	−2.47936	+	1.65666i	−0.0894662	+	0.0597794i
$769$	15.9323	+	15.9323i	0.574535	+	0.574535i	0.933392	−	0.358858i	$-0.116834\pi$
$769$	15.9323	+	15.9323i	0.574535	+	0.574535i	−0.358858	+	0.933392i	$0.616834\pi$
$770$		0			0
$771$	34.8634	−	6.93476i	1.25558	−	0.249749i
$772$	−23.1944	+	4.61365i	−0.834784	+	0.166049i
$773$	13.5036	+	32.6005i	0.485690	+	1.17256i	0.956868	+	0.290522i	$0.0938288\pi$
$773$	13.5036	+	32.6005i	0.485690	+	1.17256i	−0.471178	+	0.882038i	$0.656171\pi$
$774$	−4.23485	+	10.2238i	−0.152219	+	0.367488i
$775$		0			0
$776$	−0.523720	−	2.63292i	−0.0188005	−	0.0945163i
$777$	−45.9264	−	9.13534i	−1.64760	−	0.327728i
$778$	−26.0987			−0.935683
$779$	23.0147	+	4.57791i	0.824588	+	0.164021i
$780$		0			0
$781$			17.1148i			0.612417i
$782$	−6.16874	−	1.23685i	−0.220594	−	0.0442295i
$783$	−41.9293	+	41.9293i	−1.49843	+	1.49843i
$784$	−0.897536	−	2.16684i	−0.0320549	−	0.0773873i
$785$		0			0
$786$	−26.6095	+	26.6095i	−0.949131	+	0.949131i
$787$	7.92509	−	39.8421i	0.282499	−	1.42022i	−0.535275	−	0.844678i	$-0.679792\pi$
$787$	7.92509	−	39.8421i	0.282499	−	1.42022i	0.817774	−	0.575540i	$-0.195208\pi$
$788$	−0.856201	+	1.28139i	−0.0305009	+	0.0456478i
$789$	34.9331	+	23.3415i	1.24365	+	0.830981i
$790$		0			0
$791$	−25.0497	−	10.3759i	−0.890665	−	0.368926i
$792$	−3.42392	−	17.2132i	−0.121664	−	0.611645i
$793$	−17.6196	−	11.7730i	−0.625689	−	0.418072i
$794$	14.0544	+	21.0338i	0.498771	+	0.746463i
$795$		0			0
$796$	0.957161	−	4.81198i	0.0339257	−	0.170556i
$797$	12.3988	−	29.9332i	0.439186	−	1.06029i	−0.537044	−	0.843554i	$-0.680459\pi$
$797$	12.3988	−	29.9332i	0.439186	−	1.06029i	0.976230	−	0.216736i	$-0.0695409\pi$
$798$	−29.3978	−	29.3978i	−1.04067	−	1.04067i
$799$	13.5795	−	13.5380i	0.480408	−	0.478941i
$800$		0			0
$801$	−41.6521	+	17.2529i	−1.47170	+	0.609600i
$802$	5.70419	+	8.53692i	0.201422	+	0.301449i
$803$		−	29.2447i		−	1.03202i
$804$	7.90995	−	5.28526i	0.278962	−	0.186397i
$805$		0			0
$806$	13.6966	−	20.4984i	0.482441	−	0.722024i
$807$	−11.9681	+	4.95737i	−0.421299	+	0.174508i
$808$	11.8328	−	4.90129i	0.416275	−	0.172427i
$809$	2.83469	−	4.24242i	0.0996626	−	0.149156i	−0.778287	−	0.627909i	$-0.783911\pi$
$809$	2.83469	−	4.24242i	0.0996626	−	0.149156i	0.877950	+	0.478753i	$0.158911\pi$
$810$		0			0
$811$	−17.3551	+	11.5963i	−0.609421	+	0.407202i	−0.821629	−	0.570022i	$-0.806934\pi$
$811$	−17.3551	+	11.5963i	−0.609421	+	0.407202i	0.212208	+	0.977224i	$0.431934\pi$
$812$		−	14.8363i		−	0.520651i
$813$	−5.42890	−	8.12493i	−0.190400	−	0.284954i
$814$	−20.0315	+	8.29733i	−0.702105	+	0.290821i
$815$		0			0
$816$	2.41701	−	12.0548i	0.0846123	−	0.422001i
$817$	8.58292	+	8.58292i	0.300278	+	0.300278i
$818$	−7.22198	+	17.4354i	−0.252511	+	0.609615i
$819$	12.6539	−	63.6154i	0.442163	−	2.22290i
$820$		0			0
$821$	−12.5463	−	18.7769i	−0.437870	−	0.655318i	0.545252	−	0.838272i	$-0.316434\pi$
$821$	−12.5463	−	18.7769i	−0.437870	−	0.655318i	−0.983121	+	0.182954i	$0.941434\pi$
$822$	−8.18101	−	5.46638i	−0.285346	−	0.190662i
$823$	−5.50950	−	27.6981i	−0.192049	−	0.965496i	−0.949777	−	0.312926i	$-0.898691\pi$
$823$	−5.50950	−	27.6981i	−0.192049	−	0.965496i	0.757728	−	0.652570i	$-0.226309\pi$
$824$	−11.3530	−	4.70255i	−0.395499	−	0.163821i
$825$		0			0
$826$	7.11721	+	4.75557i	0.247639	+	0.165467i
$827$	−13.1935	+	19.7455i	−0.458783	+	0.686617i	−0.986677	−	0.162693i	$-0.947982\pi$
$827$	−13.1935	+	19.7455i	−0.458783	+	0.686617i	0.527894	+	0.849310i	$0.322982\pi$
$828$	−1.75392	+	8.81754i	−0.0609528	+	0.306431i
$829$	−29.1861	+	29.1861i	−1.01367	+	1.01367i	−0.0137698	+	0.999905i	$0.504383\pi$
$829$	−29.1861	+	29.1861i	−1.01367	+	1.01367i	−0.999905	+	0.0137698i	$0.995617\pi$
$830$		0			0
$831$	19.5644	+	47.2327i	0.678683	+	1.63848i
$832$	−3.60818	+	3.60818i	−0.125091	+	0.125091i
$833$	8.92846	+	3.71429i	0.309353	+	0.128693i
$834$			39.6537i			1.37309i
$835$		0			0
$836$	−18.8805	−	3.75557i	−0.652996	−	0.129889i
$837$	41.6601			1.43998
$838$	−2.17804	−	0.433238i	−0.0752390	−	0.0149660i
$839$	−2.28546	−	11.4898i	−0.0789027	−	0.396671i	−0.999974	−	0.00727558i	$-0.997684\pi$
$839$	−2.28546	−	11.4898i	−0.0789027	−	0.396671i	0.921071	−	0.389395i	$-0.127316\pi$
$840$		0			0
$841$	−6.99907	+	16.8972i	−0.241347	+	0.582664i
$842$	10.5724	+	25.5242i	0.364351	+	0.879620i
$843$	83.5845	−	16.6260i	2.87880	−	0.572630i
$844$	−26.1283	+	5.19724i	−0.899373	+	0.178896i
$845$		0			0
$846$	−19.3749	−	19.3749i	−0.666122	−	0.666122i
$847$	3.81479	−	2.54896i	0.131078	−	0.0875834i
$848$	−2.70105	−	1.11881i	−0.0927544	−	0.0384201i
$849$	8.99114			0.308575
$850$		0			0
$851$	11.1067			0.380732
$852$	15.8283	+	6.55631i	0.542270	+	0.224616i
$853$	7.11121	−	4.75156i	0.243483	−	0.162690i	−0.427841	−	0.903854i	$-0.640726\pi$
$853$	7.11121	−	4.75156i	0.243483	−	0.162690i	0.671324	+	0.741164i	$0.265726\pi$
$854$	6.33539	+	6.33539i	0.216792	+	0.216792i
$855$		0			0
$856$	−2.44404	+	0.486150i	−0.0835355	+	0.0166162i
$857$	38.0331	−	7.56525i	1.29919	−	0.258424i	0.503427	−	0.864038i	$-0.332072\pi$
$857$	38.0331	−	7.56525i	1.29919	−	0.258424i	0.795759	+	0.605614i	$0.207072\pi$
$858$	−17.3453	−	41.8752i	−0.592158	−	1.42960i
$859$	3.49731	−	8.44324i	0.119327	−	0.288080i	−0.852919	−	0.522044i	$-0.825170\pi$
$859$	3.49731	−	8.44324i	0.119327	−	0.288080i	0.972245	+	0.233964i	$0.0751698\pi$
$860$		0			0
$861$	−4.55731	−	22.9112i	−0.155313	−	0.780810i
$862$	−26.3843	−	5.24817i	−0.898654	−	0.178753i
$863$	40.0088			1.36191			0.680957	−	0.732323i	$-0.261564\pi$
$863$	40.0088			1.36191			0.680957	+	0.732323i	$0.261564\pi$
$864$	−8.45716	−	1.68223i	−0.287719	−	0.0572308i
$865$		0			0
$866$			6.95003i			0.236172i
$867$	28.0341	+	42.2350i	0.952088	+	1.43438i
$868$	−7.37050	+	7.37050i	−0.250171	+	0.250171i
$869$	−17.5977	−	42.4846i	−0.596962	−	1.44119i
$870$		0			0
$871$	11.5112	−	11.5112i	0.390044	−	0.390044i
$872$	3.56398	−	17.9173i	0.120692	−	0.606758i
$873$	8.78710	−	13.1508i	0.297398	−	0.445088i
$874$	8.19919	+	5.47853i	0.277342	+	0.185314i
$875$		0			0
$876$	−27.0465	−	11.2030i	−0.913816	−	0.378515i
$877$	−0.434606	−	2.18491i	−0.0146756	−	0.0737792i	0.972753	−	0.231842i	$-0.0744752\pi$
$877$	−0.434606	−	2.18491i	−0.0146756	−	0.0737792i	−0.987429	+	0.158063i	$0.949475\pi$
$878$	−10.1492	−	6.78147i	−0.342519	−	0.228864i
$879$	13.1021	+	19.6087i	0.441923	+	0.661385i
$880$		0			0
$881$	−6.84061	+	34.3901i	−0.230466	+	1.15863i	0.676179	+	0.736737i	$0.263635\pi$
$881$	−6.84061	+	34.3901i	−0.230466	+	1.15863i	−0.906645	+	0.421894i	$0.861365\pi$
$882$	5.28804	−	12.7665i	0.178058	−	0.429869i
$883$	8.59552	+	8.59552i	0.289262	+	0.289262i	0.836788	−	0.547526i	$-0.184430\pi$
$883$	8.59552	+	8.59552i	0.289262	+	0.289262i	−0.547526	+	0.836788i	$0.684430\pi$
$884$	0.0321684	−	21.0391i	0.00108194	−	0.707621i
$885$		0			0
$886$	23.9375	−	9.91525i	0.804197	−	0.333109i
$887$	3.09981	+	4.63920i	0.104082	+	0.155769i	0.879855	−	0.475243i	$-0.157640\pi$
$887$	3.09981	+	4.63920i	0.104082	+	0.155769i	−0.775773	+	0.631012i	$0.782640\pi$
$888$			21.7043i			0.728350i
$889$	−4.00025	+	2.67288i	−0.134164	+	0.0896456i
$890$		0			0
$891$	13.3013	−	19.9068i	0.445610	−	0.666903i
$892$	9.12708	−	3.78056i	0.305597	−	0.126583i
$893$	−27.7665	+	11.5013i	−0.929170	+	0.384875i
$894$	13.5475	−	20.2752i	0.453095	−	0.678105i
$895$		0			0
$896$	1.79386	−	1.19862i	0.0599287	−	0.0400431i
$897$			23.2181i			0.775230i
$898$	20.8568	+	31.2145i	0.696002	+	1.04164i
$899$	30.6950	−	12.7143i	1.02373	−	0.424045i
$900$		0			0
$901$	11.1437	−	4.59594i	0.371252	−	0.153113i
$902$	−7.64836	−	7.64836i	−0.254662	−	0.254662i
$903$	4.62414	−	11.1637i	0.153882	−	0.371503i
$904$	−2.45178	+	12.3259i	−0.0815448	+	0.409954i
$905$		0			0
$906$	−14.3554	−	21.4844i	−0.476928	−	0.713773i
$907$	−0.544935	−	0.364114i	−0.0180943	−	0.0120902i	0.546490	−	0.837465i	$-0.315964\pi$
$907$	−0.544935	−	0.364114i	−0.0180943	−	0.0120902i	−0.564584	+	0.825375i	$0.690964\pi$
$908$	1.61484	+	8.11835i	0.0535904	+	0.269417i
$909$	69.7155	+	28.8771i	2.31232	+	0.957793i
$910$		0			0
$911$	−0.784565	−	0.524230i	−0.0259938	−	0.0173685i	0.542505	−	0.840052i	$-0.317476\pi$
$911$	−0.784565	−	0.524230i	−0.0259938	−	0.0173685i	−0.568499	+	0.822684i	$0.692476\pi$
$912$	−10.7060	+	16.0226i	−0.354510	+	0.530562i
$913$	5.68051	−	28.5579i	0.187998	−	0.945127i
$914$	−12.7246	+	12.7246i	−0.420891	+	0.420891i
$915$		0			0
$916$	8.77812	+	21.1923i	0.290037	+	0.700212i
$917$	19.2525	−	19.2525i	0.635773	−	0.635773i
$918$	29.5913	−	19.7069i	0.976660	−	0.650425i
$919$		−	7.40165i		−	0.244158i	−0.992520	−	0.122079i	$-0.961044\pi$
$919$		−	7.40165i		−	0.244158i	0.992520	−	0.122079i	$-0.0389561\pi$
$920$		0			0
$921$	44.7210	+	8.89556i	1.47361	+	0.293119i
$922$	−23.9859			−0.789933
$923$	28.7544	+	5.71960i	0.946462	+	0.188263i
$924$	3.73867	+	18.7955i	0.122993	+	0.618328i
$925$		0			0
$926$	−13.5396	+	32.6876i	−0.444940	+	1.07418i
$927$	−27.7061	−	66.8885i	−0.909989	−	2.19691i
$928$	−6.74460	+	1.34158i	−0.221402	+	0.0440397i
$929$	45.9163	−	9.13333i	1.50647	−	0.299655i	0.628285	−	0.777983i	$-0.283757\pi$
$929$	45.9163	−	9.13333i	1.50647	−	0.299655i	0.878181	+	0.478328i	$0.158757\pi$
$930$		0			0
$931$	−10.7174	−	10.7174i	−0.351250	−	0.351250i
$932$	23.0506	−	15.4019i	0.755047	−	0.504506i
$933$	1.78052	+	0.737517i	0.0582917	+	0.0241452i
$934$	22.4584			0.734861
$935$		0			0
$936$	−30.0639			−0.982671
$937$	20.4567	+	8.47343i	0.668291	+	0.276815i	0.690923	−	0.722929i	$-0.257205\pi$
$937$	20.4567	+	8.47343i	0.668291	+	0.276815i	−0.0226319	+	0.999744i	$0.507205\pi$
$938$	−5.72299	+	3.82398i	−0.186862	+	0.124857i
$939$	−6.97700	−	6.97700i	−0.227686	−	0.227686i
$940$		0			0
$941$	16.4307	−	3.26827i	0.535626	−	0.106543i	0.0801364	−	0.996784i	$-0.474464\pi$
$941$	16.4307	−	3.26827i	0.535626	−	0.106543i	0.455489	+	0.890241i	$0.349464\pi$
$942$	17.9102	−	3.56257i	0.583547	−	0.116075i
$943$	2.12035	+	5.11898i	0.0690481	+	0.166697i
$944$	1.51831	−	3.66553i	0.0494168	−	0.119303i
$945$		0			0
$946$	−1.09153	−	5.48751i	−0.0354888	−	0.178414i
$947$	−41.4186	−	8.23868i	−1.34592	−	0.267721i	−0.531041	−	0.847346i	$-0.678199\pi$
$947$	−41.4186	−	8.23868i	−1.34592	−	0.267721i	−0.814883	+	0.579625i	$0.803199\pi$
$948$	−46.0325			−1.49507
$949$	−49.1337	−	9.77330i	−1.59495	−	0.317255i
$950$		0			0
$951$		−	42.2819i		−	1.37109i
$952$	−1.74875	+	8.72184i	−0.0566773	+	0.282676i
$953$	−24.8733	+	24.8733i	−0.805725	+	0.805725i	−0.983984	−	0.178259i	$-0.942954\pi$
$953$	−24.8733	+	24.8733i	−0.805725	+	0.805725i	0.178259	+	0.983984i	$0.442954\pi$
$954$	−6.59173	−	15.9138i	−0.213415	−	0.515230i
$955$		0			0
$956$	−15.4390	+	15.4390i	−0.499332	+	0.499332i
$957$	11.9167	−	59.9094i	0.385213	−	1.93659i
$958$	10.7052	−	16.0214i	0.345868	−	0.517628i
$959$	5.91911	+	3.95502i	0.191138	+	0.127714i
$960$		0			0
$961$	7.07502	+	2.93057i	0.228226	+	0.0945345i
$962$	7.24590	+	36.4276i	0.233617	+	1.17447i
$963$	−12.2074	−	8.15673i	−0.393378	−	0.262847i
$964$	−6.19568	−	9.27249i	−0.199549	−	0.298647i
$965$		0			0
$966$	1.91515	−	9.62809i	0.0616188	−	0.309779i
$967$	−17.9448	+	43.3226i	−0.577066	+	1.39316i	0.318369	+	0.947967i	$0.396865\pi$
$967$	−17.9448	+	43.3226i	−0.577066	+	1.39316i	−0.895435	+	0.445193i	$0.853135\pi$
$968$	−1.50372	−	1.50372i	−0.0483314	−	0.0483314i
$969$	−15.3814	−	77.9502i	−0.494122	−	2.50412i
$970$		0			0
$971$	4.40078	−	1.82286i	0.141228	−	0.0584985i	−0.310950	−	0.950426i	$-0.600647\pi$
$971$	4.40078	−	1.82286i	0.141228	−	0.0584985i	0.452178	+	0.891928i	$0.350647\pi$
$972$	1.05678	+	1.58158i	0.0338963	+	0.0507294i
$973$		−	28.6901i		−	0.919764i
$974$	25.8876	−	17.2975i	0.829492	−	0.554249i
$975$		0			0
$976$	2.30720	−	3.45296i	0.0738516	−	0.110527i
$977$	2.57938	−	1.06842i	0.0825218	−	0.0341816i	−0.341041	−	0.940049i	$-0.610779\pi$
$977$	2.57938	−	1.06842i	0.0825218	−	0.0341816i	0.423562	+	0.905867i	$0.360779\pi$
$978$	−36.3659	+	15.0633i	−1.16285	+	0.481670i
$979$	12.6638	−	18.9527i	0.404736	−	0.605730i
$980$		0			0
$981$	89.4929	−	59.7973i	2.85729	−	1.90918i
$982$			31.6963i			1.01147i
$983$	−7.38005	−	11.0450i	−0.235387	−	0.352281i	0.694905	−	0.719102i	$-0.255446\pi$
$983$	−7.38005	−	11.0450i	−0.235387	−	0.352281i	−0.930292	+	0.366820i	$0.880446\pi$
$984$	−10.0034	+	4.14353i	−0.318896	+	0.132091i
$985$		0			0
$986$	15.7884	−	23.5510i	0.502805	−	0.750015i
$987$	21.1559	+	21.1559i	0.673400	+	0.673400i
$988$	−12.6193	+	30.4658i	−0.401475	+	0.969246i
$989$	−0.559142	+	2.81100i	−0.0177797	+	0.0893845i
$990$		0			0
$991$	7.46029	+	11.1651i	0.236984	+	0.354671i	0.930830	−	0.365451i	$-0.119085\pi$
$991$	7.46029	+	11.1651i	0.236984	+	0.354671i	−0.693847	+	0.720123i	$0.744085\pi$
$992$	4.01713	+	2.68416i	0.127544	+	0.0852222i
$993$	−16.5132	−	83.0174i	−0.524030	−	2.63448i
$994$	−11.4521	−	4.74361i	−0.363238	−	0.150458i
$995$		0			0
$996$	−24.2352	−	16.1934i	−0.767920	−	0.513108i
$997$	3.11894	−	4.66783i	0.0987780	−	0.147832i	−0.778789	−	0.627286i	$-0.784166\pi$
$997$	3.11894	−	4.66783i	0.0987780	−	0.147832i	0.877567	+	0.479455i	$0.159166\pi$
$998$	−5.07928	+	25.5353i	−0.160782	+	0.808305i
$999$	−44.3802	+	44.3802i	−1.40413	+	1.40413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.207.5		40
5.2	odd	4		170.2.o.b.3.1	✓	40
5.3	odd	4		850.2.s.d.343.5		40
5.4	even	2		170.2.r.b.37.1	yes	40
17.6	odd	16		850.2.s.d.57.5		40
85.23	even	16	inner	850.2.v.d.193.5		40
85.57	even	16		170.2.r.b.23.1	yes	40
85.74	odd	16		170.2.o.b.57.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.3.1	✓	40	5.2	odd	4
170.2.o.b.57.1	yes	40	85.74	odd	16
170.2.r.b.23.1	yes	40	85.57	even	16
170.2.r.b.37.1	yes	40	5.4	even	2
850.2.s.d.57.5		40	17.6	odd	16
850.2.s.d.343.5		40	5.3	odd	4
850.2.v.d.193.5		40	85.23	even	16	inner
850.2.v.d.207.5		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{2} +(2.47936 - 1.65666i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-2.92460 + 0.581740i) q^{6} +(2.11600 - 0.420899i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(2.25467 - 5.44325i) q^{9} +(0.581141 + 2.92159i) q^{11} +(2.92460 + 0.581740i) q^{12} +5.10274 q^{13} +(-2.11600 - 0.420899i) q^{14} +1.00000i q^{16} +(-2.91101 - 2.91993i) q^{17} +(-4.16608 + 4.16608i) q^{18} +(2.47306 + 5.97048i) q^{19} +(4.54905 - 4.54905i) q^{21} +(0.581141 - 2.92159i) q^{22} +(-0.847753 + 1.26875i) q^{23} +(-2.47936 - 1.65666i) q^{24} +(-4.71431 - 1.95273i) q^{26} +(-1.68223 - 8.45716i) q^{27} +(1.79386 + 1.19862i) q^{28} +(-3.82051 - 5.71779i) q^{29} +(-0.942552 + 4.73853i) q^{31} +(0.382683 - 0.923880i) q^{32} +(6.28093 + 6.28093i) q^{33} +(1.57202 + 3.81166i) q^{34} +(5.44325 - 2.25467i) q^{36} +(-4.04382 - 6.05201i) q^{37} -6.46241i q^{38} +(12.6515 - 8.45347i) q^{39} +(2.01733 - 3.01915i) q^{41} +(-5.94362 + 2.46193i) q^{42} +(1.73529 - 0.718779i) q^{43} +(-1.65495 + 2.47681i) q^{44} +(1.26875 - 0.847753i) q^{46} +4.65062i q^{47} +(1.65666 + 2.47936i) q^{48} +(-2.16684 + 0.897536i) q^{49} +(-12.0548 - 2.41701i) q^{51} +(3.60818 + 3.60818i) q^{52} +(-1.11881 + 2.70105i) q^{53} +(-1.68223 + 8.45716i) q^{54} +(-1.19862 - 1.79386i) q^{56} +(16.0226 + 10.7060i) q^{57} +(1.34158 + 6.74460i) q^{58} +(-3.66553 - 1.51831i) q^{59} +(-3.45296 - 2.30720i) q^{61} +(2.68416 - 4.01713i) q^{62} +(2.47982 - 12.4669i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(-3.39921 - 8.20642i) q^{66} +(2.25590 - 2.25590i) q^{67} +(0.00630415 - 4.12310i) q^{68} +4.55013i q^{69} +(5.63509 + 1.12089i) q^{71} -5.89173 q^{72} +(-9.62889 - 1.91531i) q^{73} +(1.42000 + 7.13883i) q^{74} +(-2.47306 + 5.97048i) q^{76} +(2.45939 + 5.93749i) q^{77} +(-14.9235 + 2.96847i) q^{78} +(-15.1407 + 3.01167i) q^{79} +(-5.68322 - 5.68322i) q^{81} +(-3.01915 + 2.01733i) q^{82} +(-9.03070 - 3.74064i) q^{83} +6.43332 q^{84} -1.87826 q^{86} +(-18.9448 - 7.84720i) q^{87} +(2.47681 - 1.65495i) q^{88} +(-5.41083 - 5.41083i) q^{89} +(10.7974 - 2.14774i) q^{91} +(-1.49660 + 0.297691i) q^{92} +(5.51318 + 13.3100i) q^{93} +(1.77972 - 4.29662i) q^{94} +(-0.581740 - 2.92460i) q^{96} +(2.63292 + 0.523720i) q^{97} +2.34537 q^{98} +(17.2132 + 3.42392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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