LMFDB - Embedded newform 775.2.bl.a.276.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(51,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("775.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bl (of order $15$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
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} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			276.1
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	775.276
Dual form			775.2.bl.a.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.284315 - 0.206567i) q^{2} +(-0.302431 + 2.87744i) q^{3} +(-0.579869 + 1.78465i) q^{4} +(0.508398 + 0.880572i) q^{6} +(-1.05848 + 0.224987i) q^{7} +(0.420982 + 1.29565i) q^{8} +(-5.25377 - 1.11672i) q^{9} +(-1.62690 - 1.80686i) q^{11} +(-4.95987 - 2.20827i) q^{12} +(-2.62521 + 1.16882i) q^{13} +(-0.254466 + 0.282614i) q^{14} +(-2.64890 - 1.92454i) q^{16} +(1.22101 - 1.35606i) q^{17} +(-1.72440 + 0.767753i) q^{18} +(1.93514 + 0.861580i) q^{19} +(-0.327269 - 3.11375i) q^{21} +(-0.835790 - 0.177653i) q^{22} +(0.136652 + 0.420572i) q^{23} +(-3.85547 + 0.819506i) q^{24} +(-0.504947 + 0.874594i) q^{26} +(2.11998 - 6.52462i) q^{27} +(0.212256 - 2.01948i) q^{28} +(2.55579 - 1.85689i) q^{29} +(1.15354 + 5.44696i) q^{31} -3.87532 q^{32} +(5.69116 - 4.13487i) q^{33} +(0.0670322 - 0.637769i) q^{34} +(5.03946 - 8.72860i) q^{36} +(1.57338 + 2.72517i) q^{37} +(0.728163 - 0.154776i) q^{38} +(-2.56926 - 7.90738i) q^{39} +(0.726079 + 6.90818i) q^{41} +(-0.736246 - 0.817684i) q^{42} +(7.68509 + 3.42162i) q^{43} +(4.16801 - 1.85572i) q^{44} +(0.125728 + 0.0913471i) q^{46} +(-6.44144 - 4.67998i) q^{47} +(6.33887 - 7.04003i) q^{48} +(-5.32506 + 2.37087i) q^{49} +(3.53273 + 3.92349i) q^{51} +(-0.563659 - 5.36285i) q^{52} +(-4.86824 - 1.03478i) q^{53} +(-0.745029 - 2.29296i) q^{54} +(-0.737104 - 1.27670i) q^{56} +(-3.06439 + 5.30768i) q^{57} +(0.343078 - 1.05588i) q^{58} +(1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +(1.45313 + 1.31037i) q^{62} +5.81225 q^{63} +(4.19600 - 3.04857i) q^{64} +(0.763955 - 2.35121i) q^{66} +(-3.21879 + 5.57511i) q^{67} +(1.71208 + 2.96541i) q^{68} +(-1.25150 + 0.266015i) q^{69} +(-1.64121 - 0.348850i) q^{71} +(-0.764860 - 7.27716i) q^{72} +(-9.60883 - 10.6717i) q^{73} +(1.01026 + 0.449798i) q^{74} +(-2.65975 + 2.95395i) q^{76} +(2.12856 + 1.54649i) q^{77} +(-2.36388 - 1.71746i) q^{78} +(-2.30692 + 2.56210i) q^{79} +(3.41274 + 1.51945i) q^{81} +(1.63344 + 1.81412i) q^{82} +(1.34357 + 12.7832i) q^{83} +(5.74674 + 1.22151i) q^{84} +(2.89178 - 0.614667i) q^{86} +(4.57015 + 7.91573i) q^{87} +(1.65616 - 2.86855i) q^{88} +(0.698188 - 2.14880i) q^{89} +(2.51576 - 1.82781i) q^{91} -0.829816 q^{92} +(-16.0222 + 1.67190i) q^{93} -2.79812 q^{94} +(1.17202 - 11.1510i) q^{96} +(-1.05463 + 3.24582i) q^{97} +(-1.02425 + 1.77405i) q^{98} +(6.52961 + 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 12 q^{3} - 14 q^{4} + 11 q^{6} - 2 q^{7} - 17 q^{8} - 10 q^{9} - 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 2 q^{16} + 6 q^{17} + 3 q^{18} + 16 q^{19} + 9 q^{21} - 9 q^{22} - q^{23} - 20 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q + 6 * q^2 + 12 * q^3 - 14 * q^4 + 11 * q^6 - 2 * q^7 - 17 * q^8 - 10 * q^9 - 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 2 * q^16 + 6 * q^17 + 3 * q^18 + 16 * q^19 + 9 * q^21 - 9 * q^22 - q^23 - 20 * q^24 + 9 * q^26 - 9 * q^27 + 30 * q^28 - 14 * q^29 + 15 * q^31 + 42 * q^32 + 13 * q^33 - 32 * q^34 + q^36 + 8 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 - 69 * q^42 - 23 * q^43 + 39 * q^44 + 34 * q^46 - 14 * q^47 - 34 * q^48 + 2 * q^49 - 42 * q^51 - 29 * q^52 - 6 * q^53 - 46 * q^54 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 - 60 * q^61 + 25 * q^62 + 46 * q^63 + 23 * q^64 - 30 * q^66 - 13 * q^67 - 30 * q^68 + 38 * q^69 - 14 * q^71 - 37 * q^72 - 2 * q^73 + 13 * q^74 - 12 * q^76 - 18 * q^77 + 15 * q^78 + 18 * q^79 + 23 * q^81 - 14 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 17 * q^88 + q^89 + 8 * q^91 + 64 * q^92 - 17 * q^93 + 44 * q^94 + 8 * q^96 - 3 * q^97 + 10 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{8}{15}\right)$	$1$

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 $

$2$	0.284315	−	0.206567i	0.201041	−	0.146065i	−0.482710	−	0.875780i	$-0.660347\pi$
$2$	0.284315	−	0.206567i	0.201041	−	0.146065i	0.683751	+	0.729715i	$0.260347\pi$
$3$	−0.302431	+	2.87744i	−0.174609	+	1.66129i	0.459597	+	0.888128i	$0.347994\pi$
$3$	−0.302431	+	2.87744i	−0.174609	+	1.66129i	−0.634206	+	0.773164i	$0.718673\pi$
$4$	−0.579869	+	1.78465i	−0.289934	+	0.892327i
$5$		0			0
$5$		0			0
$6$	0.508398	+	0.880572i	0.207553	+	0.359492i
$7$	−1.05848	+	0.224987i	−0.400067	+	0.0850369i	−0.403551	−	0.914957i	$-0.632224\pi$
$7$	−1.05848	+	0.224987i	−0.400067	+	0.0850369i	0.00348400	+	0.999994i	$0.498891\pi$
$8$	0.420982	+	1.29565i	0.148840	+	0.458081i
$9$	−5.25377	−	1.11672i	−1.75126	−	0.372241i
$10$		0			0
$11$	−1.62690	−	1.80686i	−0.490530	−	0.544789i	0.446158	−	0.894954i	$-0.352792\pi$
$11$	−1.62690	−	1.80686i	−0.490530	−	0.544789i	−0.936688	+	0.350165i	$0.886125\pi$
$12$	−4.95987	−	2.20827i	−1.43179	−	0.637474i
$13$	−2.62521	+	1.16882i	−0.728103	+	0.324172i	−0.737097	−	0.675787i	$-0.763804\pi$
$13$	−2.62521	+	1.16882i	−0.728103	+	0.324172i	0.00899389	+	0.999960i	$0.497137\pi$
$14$	−0.254466	+	0.282614i	−0.0680090	+	0.0755317i
$15$		0			0
$16$	−2.64890	−	1.92454i	−0.662226	−	0.481135i
$17$	1.22101	−	1.35606i	0.296137	−	0.328894i	−0.576653	−	0.816989i	$-0.695641\pi$
$17$	1.22101	−	1.35606i	0.296137	−	0.328894i	0.872790	+	0.488095i	$0.162308\pi$
$18$	−1.72440	+	0.767753i	−0.406445	+	0.180961i
$19$	1.93514	+	0.861580i	0.443951	+	0.197660i	0.616523	−	0.787337i	$-0.288541\pi$
$19$	1.93514	+	0.861580i	0.443951	+	0.197660i	−0.172571	+	0.984997i	$0.555208\pi$
$20$		0			0
$21$	−0.327269	−	3.11375i	−0.0714159	−	0.679477i
$22$	−0.835790	−	0.177653i	−0.178191	−	0.0378757i
$23$	0.136652	+	0.420572i	0.0284939	+	0.0876953i	0.964292	−	0.264841i	$-0.0853194\pi$
$23$	0.136652	+	0.420572i	0.0284939	+	0.0876953i	−0.935798	+	0.352536i	$0.885319\pi$
$24$	−3.85547	+	0.819506i	−0.786995	+	0.167281i
$25$		0			0
$26$	−0.504947	+	0.874594i	−0.0990283	+	0.171522i
$27$	2.11998	−	6.52462i	0.407990	−	1.25566i
$28$	0.212256	−	2.01948i	0.0401126	−	0.381646i
$29$	2.55579	−	1.85689i	0.474599	−	0.344816i	−0.324632	−	0.945840i	$-0.605240\pi$
$29$	2.55579	−	1.85689i	0.474599	−	0.344816i	0.799231	+	0.601024i	$0.205240\pi$
$30$		0			0
$31$	1.15354	+	5.44696i	0.207181	+	0.978303i
$31$	1.15354	+	5.44696i	0.207181	+	0.978303i
$32$	−3.87532			−0.685067
$33$	5.69116	−	4.13487i	0.990704	−	0.719789i
$34$	0.0670322	−	0.637769i	0.0114959	−	0.109376i
$35$		0			0
$36$	5.03946	−	8.72860i	0.839910	−	1.45477i
$37$	1.57338	+	2.72517i	0.258661	+	0.448015i	0.965884	−	0.258977i	$-0.0833853\pi$
$37$	1.57338	+	2.72517i	0.258661	+	0.448015i	−0.707222	+	0.706991i	$0.750052\pi$
$38$	0.728163	−	0.154776i	0.118124	−	0.0251079i
$39$	−2.56926	−	7.90738i	−0.411412	−	1.26619i
$40$		0			0
$41$	0.726079	+	6.90818i	0.113395	+	1.07888i	0.892209	+	0.451623i	$0.149155\pi$
$41$	0.726079	+	6.90818i	0.113395	+	1.07888i	−0.778814	+	0.627254i	$0.784179\pi$
$42$	−0.736246	−	0.817684i	−0.113605	−	0.126171i
$43$	7.68509	+	3.42162i	1.17197	+	0.521793i	0.898021	−	0.439953i	$-0.145005\pi$
$43$	7.68509	+	3.42162i	1.17197	+	0.521793i	0.273944	+	0.961746i	$0.411672\pi$
$44$	4.16801	−	1.85572i	0.628351	−	0.279760i
$45$		0			0
$46$	0.125728	+	0.0913471i	0.0185377	+	0.0134684i
$47$	−6.44144	−	4.67998i	−0.939580	−	0.682645i	0.00873953	−	0.999962i	$-0.497218\pi$
$47$	−6.44144	−	4.67998i	−0.939580	−	0.682645i	−0.948320	+	0.317317i	$0.897218\pi$
$48$	6.33887	−	7.04003i	0.914937	−	1.01614i
$49$	−5.32506	+	2.37087i	−0.760723	+	0.338696i
$50$		0			0
$51$	3.53273	+	3.92349i	0.494681	+	0.549399i
$52$	−0.563659	−	5.36285i	−0.0781654	−	0.743694i
$53$	−4.86824	−	1.03478i	−0.668704	−	0.142137i	−0.138964	−	0.990297i	$-0.544377\pi$
$53$	−4.86824	−	1.03478i	−0.668704	−	0.142137i	−0.529740	+	0.848160i	$0.677711\pi$
$54$	−0.745029	−	2.29296i	−0.101386	−	0.312033i
$55$		0			0
$56$	−0.737104	−	1.27670i	−0.0984997	−	0.170606i
$57$	−3.06439	+	5.30768i	−0.405889	+	0.703020i
$58$	0.343078	−	1.05588i	0.0450483	−	0.138644i
$59$	1.25580	−	11.9481i	0.163491	−	1.55551i	−0.538068	−	0.842902i	$-0.680846\pi$
$59$	1.25580	−	11.9481i	0.163491	−	1.55551i	0.701559	−	0.712612i	$-0.252488\pi$
$60$		0			0
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$	1.45313	+	1.31037i	0.184548	+	0.166417i
$63$	5.81225			0.732274
$64$	4.19600	−	3.04857i	0.524499	−	0.381071i
$65$		0			0
$66$	0.763955	−	2.35121i	0.0940363	−	0.289414i
$67$	−3.21879	+	5.57511i	−0.393238	+	0.681108i	−0.992875	−	0.119164i	$-0.961979\pi$
$67$	−3.21879	+	5.57511i	−0.393238	+	0.681108i	0.599636	+	0.800273i	$0.295312\pi$
$68$	1.71208	+	2.96541i	0.207620	+	0.359609i
$69$	−1.25150	+	0.266015i	−0.150663	+	0.0320244i
$70$		0			0
$71$	−1.64121	−	0.348850i	−0.194776	−	0.0414009i	0.109491	−	0.993988i	$-0.465078\pi$
$71$	−1.64121	−	0.348850i	−0.194776	−	0.0414009i	−0.304266	+	0.952587i	$0.598411\pi$
$72$	−0.764860	−	7.27716i	−0.0901396	−	0.857621i
$73$	−9.60883	−	10.6717i	−1.12463	−	1.24903i	−0.965114	−	0.261830i	$-0.915674\pi$
$73$	−9.60883	−	10.6717i	−1.12463	−	1.24903i	−0.159514	−	0.987196i	$-0.550993\pi$
$74$	1.01026	+	0.449798i	0.117441	+	0.0522880i
$75$		0			0
$76$	−2.65975	+	2.95395i	−0.305094	+	0.338841i
$77$	2.12856	+	1.54649i	0.242572	+	0.176239i
$78$	−2.36388	−	1.71746i	−0.267657	−	0.194464i
$79$	−2.30692	+	2.56210i	−0.259549	+	0.288259i	−0.858809	−	0.512296i	$-0.828795\pi$
$79$	−2.30692	+	2.56210i	−0.259549	+	0.288259i	0.599260	+	0.800555i	$0.295462\pi$
$80$		0			0
$81$	3.41274	+	1.51945i	0.379194	+	0.168828i
$82$	1.63344	+	1.81412i	0.180383	+	0.200336i
$83$	1.34357	+	12.7832i	0.147476	+	1.40314i	0.778631	+	0.627482i	$0.215914\pi$
$83$	1.34357	+	12.7832i	0.147476	+	1.40314i	−0.631155	+	0.775657i	$0.717419\pi$
$84$	5.74674	+	1.22151i	0.627021	+	0.133277i
$85$		0			0
$86$	2.89178	−	0.614667i	0.311829	−	0.0662812i
$87$	4.57015	+	7.91573i	0.489972	+	0.848656i
$88$	1.65616	−	2.86855i	0.176547	−	0.305789i
$89$	0.698188	−	2.14880i	0.0740078	−	0.227773i	−0.907209	−	0.420680i	$-0.861792\pi$
$89$	0.698188	−	2.14880i	0.0740078	−	0.227773i	0.981217	+	0.192907i	$0.0617916\pi$
$90$		0			0
$91$	2.51576	−	1.82781i	0.263724	−	0.191606i
$92$	−0.829816			−0.0865143
$93$	−16.0222	+	1.67190i	−1.66142	+	0.173368i
$94$	−2.79812			−0.288604
$95$		0			0
$96$	1.17202	−	11.1510i	0.119619	−	1.13810i
$97$	−1.05463	+	3.24582i	−0.107082	+	0.329563i	−0.990213	−	0.139562i	$-0.955431\pi$
$97$	−1.05463	+	3.24582i	−0.107082	+	0.329563i	0.883132	+	0.469125i	$0.155431\pi$
$98$	−1.02425	+	1.77405i	−0.103465	+	0.179207i
$99$	6.52961	+	11.3096i	0.656251	+	1.13666i
$100$		0			0
$101$	5.47495	+	16.8502i	0.544778	+	1.67665i	0.721518	+	0.692395i	$0.243445\pi$
$101$	5.47495	+	16.8502i	0.544778	+	1.67665i	−0.176741	+	0.984257i	$0.556555\pi$
$102$	1.81487	+	0.385763i	0.179699	+	0.0381962i
$103$	0.843947	+	8.02962i	0.0831566	+	0.791182i	0.954037	+	0.299688i	$0.0968824\pi$
$103$	0.843947	+	8.02962i	0.0831566	+	0.791182i	−0.870881	+	0.491494i	$0.836451\pi$
$104$	−2.61955	−	2.90930i	−0.256868	−	0.285281i
$105$		0			0
$106$	−1.59786	+	0.711414i	−0.155198	+	0.0690987i
$107$	8.13074	−	9.03010i	0.786028	−	0.872972i	−0.208438	−	0.978036i	$-0.566838\pi$
$107$	8.13074	−	9.03010i	0.786028	−	0.872972i	0.994466	+	0.105063i	$0.0335045\pi$
$108$	10.4149	+	7.56685i	1.00217	+	0.728121i
$109$	0.511381	+	0.371540i	0.0489815	+	0.0355871i	0.612007	−	0.790853i	$-0.290363\pi$
$109$	0.511381	+	0.371540i	0.0489815	+	0.0355871i	−0.563025	+	0.826440i	$0.690363\pi$
$110$		0			0
$111$	−8.31735	+	3.70312i	−0.789448	+	0.351485i
$112$	3.23680	+	1.44112i	0.305849	+	0.136173i
$113$	7.56140	+	8.39779i	0.711317	+	0.789998i	0.985135	−	0.171784i	$-0.0549531\pi$
$113$	7.56140	+	8.39779i	0.711317	+	0.789998i	−0.273818	+	0.961782i	$0.588286\pi$
$114$	0.225139	+	2.14205i	0.0210862	+	0.200622i
$115$		0			0
$116$	1.83188	+	5.63796i	0.170086	+	0.523472i
$117$	15.0975	−	3.20907i	1.39576	−	0.296679i
$118$	−2.11104	−	3.65643i	−0.194337	−	0.336602i
$119$	−0.987313	+	1.71008i	−0.0905068	+	0.156762i
$120$		0			0
$121$	0.531887	−	5.06056i	0.0483533	−	0.460051i
$122$	−4.10412	+	2.98182i	−0.371570	+	0.269961i
$123$	−20.0975			−1.81213
$124$	−10.3898	−	1.09986i	−0.933034	−	0.0987702i
$125$		0			0
$126$	1.65251	−	1.20062i	0.147217	−	0.106960i
$127$	0.0123141	−	0.117161i	0.00109270	−	0.0103963i	−0.993962	−	0.109725i	$-0.965003\pi$
$127$	0.0123141	−	0.117161i	0.00109270	−	0.0103963i	0.995055	+	0.0993289i	$0.0316696\pi$
$128$	2.95833	−	9.10481i	0.261482	−	0.804759i
$129$	−12.1697	+	21.0786i	−1.07149	+	1.85587i
$130$		0			0
$131$	−5.65756	+	1.20255i	−0.494303	+	0.105067i	−0.448317	−	0.893875i	$-0.647976\pi$
$131$	−5.65756	+	1.20255i	−0.494303	+	0.105067i	−0.0459863	+	0.998942i	$0.514643\pi$
$132$	4.07918	+	12.5544i	0.355047	+	1.09272i
$133$	−2.24215	−	0.476583i	−0.194419	−	0.0413250i
$134$	0.236483	+	2.24998i	0.0204290	+	0.194369i
$135$		0			0
$136$	2.27101	+	1.01112i	0.194737	+	0.0867026i
$137$	−10.7848	+	4.80170i	−0.921407	+	0.410237i	−0.811931	−	0.583753i	$-0.801584\pi$
$137$	−10.7848	+	4.80170i	−0.921407	+	0.410237i	−0.109475	+	0.993990i	$0.534917\pi$
$138$	−0.300870	+	0.334150i	−0.0256118	+	0.0284448i
$139$	12.4767	+	9.06482i	1.05826	+	0.768868i	0.973765	−	0.227556i	$-0.0730734\pi$
$139$	12.4767	+	9.06482i	1.05826	+	0.768868i	0.0844915	+	0.996424i	$0.473073\pi$
$140$		0			0
$141$	15.4145	−	17.1195i	1.29813	−	1.44172i
$142$	−0.538681	+	0.239836i	−0.0452051	+	0.0201266i
$143$	6.38286	+	2.84183i	0.533762	+	0.237646i
$144$	11.7675	+	13.0692i	0.980628	+	1.08910i
$145$		0			0
$146$	−4.93635	−	1.04925i	−0.408535	−	0.0868368i
$147$	−5.21157	−	16.0396i	−0.429843	−	1.32292i
$148$	−5.77583	+	1.22769i	−0.474770	+	0.100916i
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	0.999927	−	0.0120817i	$-0.00384583\pi$
$149$	5.97511	+	10.3492i	0.489500	+	0.847840i	−0.510427	+	0.859921i	$0.670512\pi$
$150$		0			0
$151$	−1.33561	+	4.11059i	−0.108691	+	0.334515i	−0.990579	−	0.136943i	$-0.956272\pi$
$151$	−1.33561	+	4.11059i	−0.108691	+	0.334515i	0.881888	+	0.471458i	$0.156272\pi$
$152$	−0.301646	+	2.86997i	−0.0244667	+	0.232785i
$153$	−7.92923	+	5.76092i	−0.641040	+	0.465743i
$154$	0.924636			0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	−7.04204	+	5.11634i	−0.562016	+	0.408328i	−0.832196	−	0.554481i	$-0.812917\pi$
$157$	−7.04204	+	5.11634i	−0.562016	+	0.408328i	0.270180	+	0.962810i	$0.412917\pi$
$158$	−0.126648	+	1.20498i	−0.0100756	+	0.0958628i
$159$	4.44982	−	13.6951i	0.352893	−	1.08609i
$160$		0			0
$161$	−0.239267	−	0.414422i	−0.0188568	−	0.0326610i
$162$	1.28416	−	0.272957i	0.100893	−	0.0214455i
$163$	−0.966575	−	2.97481i	−0.0757080	−	0.233005i	0.906040	−	0.423192i	$-0.139091\pi$
$163$	−0.966575	−	2.97481i	−0.0757080	−	0.233005i	−0.981748	+	0.190187i	$0.939091\pi$
$164$	−12.7497	−	2.71004i	−0.995588	−	0.211619i
$165$		0			0
$166$	3.02258	+	3.35692i	0.234598	+	0.260547i
$167$	12.2003	+	5.43194i	0.944090	+	0.420336i	0.820275	−	0.571969i	$-0.193820\pi$
$167$	12.2003	+	5.43194i	0.944090	+	0.420336i	0.123815	+	0.992305i	$0.460487\pi$
$168$	3.89656	−	1.73486i	0.300626	−	0.133847i
$169$	−3.17310	+	3.52408i	−0.244085	+	0.271083i
$170$		0			0
$171$	−9.20462	−	6.68755i	−0.703895	−	0.511410i
$172$	−10.5628	+	11.7311i	−0.805402	+	0.894490i
$173$	−17.3982	+	7.74619i	−1.32276	+	0.588932i	−0.941960	−	0.335724i	$-0.891019\pi$
$173$	−17.3982	+	7.74619i	−1.32276	+	0.588932i	−0.380803	+	0.924656i	$0.624352\pi$
$174$	2.93449	+	1.30652i	0.222463	+	0.0990469i
$175$		0			0
$176$	0.832136	+	7.91724i	0.0627246	+	0.596785i
$177$	34.0002	+	7.22697i	2.55561	+	0.543213i
$178$	−0.245366	−	0.755159i	−0.0183910	−	0.0566016i
$179$	0.0775964	−	0.0164936i	0.00579983	−	0.00123279i	−0.205011	−	0.978760i	$-0.565723\pi$
$179$	0.0775964	−	0.0164936i	0.00579983	−	0.00123279i	0.210811	+	0.977527i	$0.432390\pi$
$180$		0			0
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	−0.903414	−	0.428769i	$-0.858947\pi$
$181$	−1.08143	+	1.87308i	−0.0803817	+	0.139225i	0.823032	+	0.567995i	$0.192281\pi$
$182$	0.337704	−	1.03935i	0.0250323	−	0.0770415i
$183$	4.36564	−	41.5363i	0.322717	−	3.07045i
$184$	−0.487386	+	0.354107i	−0.0359306	+	0.0261051i
$185$		0			0
$186$	−4.20998	+	3.78500i	−0.308691	+	0.277529i
$187$	−4.43668			−0.324442
$188$	12.0873	−	8.78195i	0.881559	−	0.640490i
$189$	−0.776000	+	7.38314i	−0.0564457	+	0.537045i
$190$		0			0
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	−0.753072	−	0.657939i	$-0.771429\pi$
$191$	2.67085	−	4.62604i	0.193256	−	0.334729i	0.946327	+	0.323210i	$0.104762\pi$
$192$	7.50308	+	12.9957i	0.541488	+	0.937885i
$193$	−2.08705	+	0.443616i	−0.150229	+	0.0319322i	−0.282412	−	0.959293i	$-0.591135\pi$
$193$	−2.08705	+	0.443616i	−0.150229	+	0.0319322i	0.132183	+	0.991225i	$0.457801\pi$
$194$	0.370632	+	1.14069i	0.0266098	+	0.0818966i
$195$		0			0
$196$	−1.14334	−	10.8782i	−0.0816673	−	0.777013i
$197$	3.93163	+	4.36652i	0.280117	+	0.311102i	0.866742	−	0.498758i	$-0.166210\pi$
$197$	3.93163	+	4.36652i	0.280117	+	0.311102i	−0.586624	+	0.809859i	$0.699544\pi$
$198$	4.19266	+	1.86669i	0.297959	+	0.132660i
$199$	6.32901	−	2.81786i	0.448652	−	0.199753i	−0.169958	−	0.985451i	$-0.554363\pi$
$199$	6.32901	−	2.81786i	0.448652	−	0.199753i	0.618609	+	0.785699i	$0.287696\pi$
$200$		0			0
$201$	−15.0686	−	10.9480i	−1.06286	−	0.772211i
$202$	5.03729	+	3.65981i	0.354423	+	0.257503i
$203$	−2.28748	+	2.54050i	−0.160549	+	0.178308i
$204$	−9.05059	+	4.02958i	−0.633668	+	0.282127i
$205$		0			0
$206$	1.89860	+	2.10861i	0.132282	+	0.146914i
$207$	−0.248276	−	2.36219i	−0.0172564	−	0.164184i
$208$	9.20337	+	1.95624i	0.638139	+	0.135641i
$209$	−1.59153	−	4.89823i	−0.110089	−	0.338818i
$210$		0			0
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	−0.996027	−	0.0890568i	$-0.971615\pi$
$211$	−8.35437	−	14.4702i	−0.575139	−	0.996170i	0.420888	−	0.907113i	$-0.361719\pi$
$212$	4.66966	−	8.08808i	0.320713	−	0.555492i
$213$	1.50015	−	4.61698i	0.102788	−	0.316350i
$214$	0.446370	−	4.24693i	0.0305133	−	0.290314i
$215$		0			0
$216$	9.34610			0.635921
$217$	−2.44649	−	5.50596i	−0.166078	−	0.373769i
$218$	0.222141			0.0150453
$219$	33.6132	−	24.4214i	2.27137	−	1.65024i
$220$		0			0
$221$	−1.62040	+	4.98709i	−0.109000	+	0.335468i
$222$	−1.59980	+	2.77094i	−0.107372	+	0.185973i
$223$	−3.13078	−	5.42267i	−0.209653	−	0.363129i	0.741952	−	0.670453i	$-0.233900\pi$
$223$	−3.13078	−	5.42267i	−0.209653	−	0.363129i	−0.951605	+	0.307323i	$0.900567\pi$
$224$	4.10195	−	0.871895i	0.274073	−	0.0582560i
$225$		0			0
$226$	3.88452	+	0.825681i	0.258395	+	0.0549235i
$227$	−0.820289	−	7.80452i	−0.0544445	−	0.518004i	−0.987426	−	0.158081i	$-0.949469\pi$
$227$	−0.820289	−	7.80452i	−0.0544445	−	0.518004i	0.932982	−	0.359924i	$-0.117197\pi$
$228$	−7.69543	−	8.54664i	−0.509642	−	0.566015i
$229$	11.6687	+	5.19524i	0.771089	+	0.343311i	0.754285	−	0.656548i	$-0.227984\pi$
$229$	11.6687	+	5.19524i	0.771089	+	0.343311i	0.0168049	+	0.999859i	$0.494651\pi$
$230$		0			0
$231$	−5.09368	+	5.65711i	−0.335140	+	0.372210i
$232$	3.48183	+	2.52969i	0.228593	+	0.166083i
$233$	10.2887	+	7.47514i	0.674032	+	0.489713i	0.871373	−	0.490622i	$-0.163230\pi$
$233$	10.2887	+	7.47514i	0.674032	+	0.489713i	−0.197340	+	0.980335i	$0.563230\pi$
$234$	3.62955	−	4.03103i	0.237271	−	0.263517i
$235$		0			0
$236$	20.5951	+	9.16951i	1.34062	+	0.596884i
$237$	−6.67460	−	7.41290i	−0.433562	−	0.481520i
$238$	0.0725373	+	0.690146i	0.00470189	+	0.0447355i
$239$	24.8690	+	5.28607i	1.60864	+	0.341928i	0.922638	−	0.385668i	$-0.126029\pi$
$239$	24.8690	+	5.28607i	1.60864	+	0.341928i	0.686006	+	0.727596i	$0.259362\pi$
$240$		0			0
$241$	−2.30939	+	0.490876i	−0.148761	+	0.0316201i	−0.281690	−	0.959505i	$-0.590895\pi$
$241$	−2.30939	+	0.490876i	−0.148761	+	0.0316201i	0.132929	+	0.991126i	$0.457562\pi$
$242$	−0.894121	−	1.54866i	−0.0574763	−	0.0995519i
$243$	4.88634	−	8.46339i	0.313459	−	0.542927i
$244$	8.37048	−	25.7617i	0.535865	−	1.64922i
$245$		0			0
$246$	−5.71401	+	4.15147i	−0.364312	+	0.264688i
$247$	−6.08718			−0.387318
$248$	−6.57173	+	3.78765i	−0.417305	+	0.240516i
$249$	−37.1893			−2.35677
$250$		0			0
$251$	−0.246336	+	2.34373i	−0.0155486	+	0.147935i	−0.999542	−	0.0302716i	$-0.990363\pi$
$251$	−0.246336	+	2.34373i	−0.0155486	+	0.147935i	0.983993	+	0.178206i	$0.0570294\pi$
$252$	−3.37034	+	10.3728i	−0.212312	+	0.653428i
$253$	0.537595	−	0.931142i	0.0337983	−	0.0585404i
$254$	−0.0207005	−	0.0358542i	−0.00129886	−	0.00224970i
$255$		0			0
$256$	2.16580	+	6.66565i	0.135363	+	0.416603i
$257$	−25.4455	−	5.40862i	−1.58725	−	0.337380i	−0.672089	−	0.740470i	$-0.734603\pi$
$257$	−25.4455	−	5.40862i	−1.58725	−	0.337380i	−0.915160	+	0.403090i	$0.867936\pi$
$258$	0.894103	+	8.50682i	0.0556644	+	0.529612i
$259$	−2.27851	−	2.53054i	−0.141580	−	0.157240i
$260$		0			0
$261$	−15.5012	+	6.90157i	−0.959499	+	0.427196i
$262$	−1.36012	+	1.51057i	−0.0840285	+	0.0933232i
$263$	18.5552	+	13.4812i	1.14417	+	0.831285i	0.987694	−	0.156398i	$-0.0499881\pi$
$263$	18.5552	+	13.4812i	1.14417	+	0.831285i	0.156471	+	0.987683i	$0.449988\pi$
$264$	7.75322	+	5.63304i	0.477178	+	0.346690i
$265$		0			0
$266$	−0.735922	+	0.327654i	−0.0451223	+	0.0200897i
$267$	5.97190	+	2.65886i	0.365474	+	0.162720i
$268$	−8.08316	−	8.97726i	−0.493758	−	0.548374i
$269$	1.78193	+	16.9539i	0.108646	+	1.03370i	0.903994	+	0.427546i	$0.140622\pi$
$269$	1.78193	+	16.9539i	0.108646	+	1.03370i	−0.795347	+	0.606154i	$0.792712\pi$
$270$		0			0
$271$	2.23929	+	6.89184i	0.136027	+	0.418649i	0.995748	−	0.0921146i	$-0.0293626\pi$
$271$	2.23929	+	6.89184i	0.136027	+	0.418649i	−0.859721	+	0.510764i	$0.829363\pi$
$272$	−5.84413	+	1.24221i	−0.354352	+	0.0753199i
$273$	4.49857	+	7.79175i	0.272266	+	0.471578i
$274$	−2.07440	+	3.59297i	−0.125319	+	0.217059i
$275$		0			0
$276$	0.250962	−	2.38775i	0.0151062	−	0.143725i
$277$	12.2188	−	8.87748i	0.734157	−	0.533396i	−0.156719	−	0.987643i	$-0.550092\pi$
$277$	12.2188	−	8.87748i	0.734157	−	0.533396i	0.890876	+	0.454247i	$0.150092\pi$
$278$	5.41979			0.325058
$279$	0.0223278	−	29.9052i	0.00133673	−	1.79038i
$280$		0			0
$281$	2.01209	−	1.46187i	0.120031	−	0.0872078i	−0.526150	−	0.850392i	$-0.676365\pi$
$281$	2.01209	−	1.46187i	0.120031	−	0.0872078i	0.646181	+	0.763184i	$0.276365\pi$
$282$	0.846240	−	8.05144i	0.0503929	−	0.479456i
$283$	1.46052	−	4.49503i	0.0868192	−	0.267202i	−0.898216	−	0.439554i	$-0.855137\pi$
$283$	1.46052	−	4.49503i	0.0868192	−	0.267202i	0.985035	+	0.172352i	$0.0551366\pi$
$284$	1.57426	−	2.72670i	0.0934153	−	0.161800i
$285$		0			0
$286$	2.40177	−	0.510512i	0.142020	−	0.0301872i
$287$	−2.32279	−	7.14881i	−0.137110	−	0.421981i
$288$	20.3600	+	4.32766i	1.19973	+	0.255010i
$289$	1.42893	+	13.5953i	0.0840546	+	0.799726i
$290$		0			0
$291$	−9.02071	−	4.01628i	−0.528804	−	0.235439i
$292$	24.6171	−	10.9602i	1.44061	−	0.641400i
$293$	7.05858	−	7.83935i	0.412367	−	0.457980i	−0.500802	−	0.865562i	$-0.666961\pi$
$293$	7.05858	−	7.83935i	0.412367	−	0.457980i	0.913169	+	0.407582i	$0.133628\pi$
$294$	−4.79497	−	3.48375i	−0.279648	−	0.203177i
$295$		0			0
$296$	−2.86850	+	3.18579i	−0.166728	+	0.185170i
$297$	−15.2381	+	6.78443i	−0.884203	+	0.393673i
$298$	3.83662	+	1.70817i	0.222249	+	0.0989517i
$299$	−0.850314	−	0.944369i	−0.0491749	−	0.0546143i
$300$		0			0
$301$	−8.90432	−	1.89267i	−0.513237	−	0.109092i
$302$	0.469377	+	1.44459i	0.0270096	+	0.0831271i
$303$	−50.1411	+	10.6578i	−2.88053	+	0.612276i
$304$	−3.46785	−	6.00650i	−0.198895	−	0.344496i
$305$		0			0
$306$	−1.06438	+	3.27583i	−0.0608467	+	0.187267i
$307$	0.276844	−	2.63399i	0.0158003	−	0.150330i	−0.983777	−	0.179394i	$-0.942586\pi$
$307$	0.276844	−	2.63399i	0.0158003	−	0.150330i	0.999578	+	0.0290645i	$0.00925283\pi$
$308$	−3.99424	+	2.90198i	−0.227593	+	0.165356i
$309$	−23.3600			−1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	9.16358	−	6.65773i	0.518786	−	0.376920i
$313$	−2.78834	+	26.5293i	−0.157607	+	1.49953i	0.574595	+	0.818438i	$0.305160\pi$
$313$	−2.78834	+	26.5293i	−0.157607	+	1.49953i	−0.732201	+	0.681088i	$0.761507\pi$
$314$	−0.945290	+	2.90930i	−0.0533458	+	0.164181i
$315$		0			0
$316$	−3.23474	−	5.60274i	−0.181969	−	0.315179i
$317$	10.5055	−	2.23302i	0.590050	−	0.125419i	0.0967957	−	0.995304i	$-0.469141\pi$
$317$	10.5055	−	2.23302i	0.590050	−	0.125419i	0.493254	+	0.869885i	$0.335807\pi$
$318$	−1.56381	−	4.81291i	−0.0876941	−	0.269895i
$319$	−7.51318	−	1.59698i	−0.420657	−	0.0894135i
$320$		0			0
$321$	23.5246	+	26.1267i	1.31301	+	1.45825i
$322$	−0.153633	−	0.0684017i	−0.00856162	−	0.00381188i
$323$	3.53117	−	1.57218i	0.196480	−	0.0874784i
$324$	−4.69064	+	5.20948i	−0.260591	+	0.289416i
$325$		0			0
$326$	−0.889309	−	0.646121i	−0.0492543	−	0.0357853i
$327$	−1.22374	+	1.35911i	−0.0676732	+	0.0751587i
$328$	−8.64492	+	3.84897i	−0.477336	+	0.212524i
$329$	7.87106	+	3.50442i	0.433945	+	0.193205i
$330$		0			0
$331$	−2.05373	−	19.5400i	−0.112883	−	1.07401i	−0.893518	−	0.449027i	$-0.851771\pi$
$331$	−2.05373	−	19.5400i	−0.112883	−	1.07401i	0.780635	−	0.624987i	$-0.214896\pi$
$332$	−23.5927	−	5.01478i	−1.29482	−	0.275222i
$333$	−5.22289	−	16.0744i	−0.286213	−	0.880872i
$334$	4.59080	−	0.975804i	0.251197	−	0.0533936i
$335$		0			0
$336$	−5.12565	+	8.87788i	−0.279627	+	0.484328i
$337$	−5.92655	+	18.2401i	−0.322840	+	0.993599i	0.649566	+	0.760305i	$0.274950\pi$
$337$	−5.92655	+	18.2401i	−0.322840	+	0.993599i	−0.972406	+	0.233294i	$0.925050\pi$
$338$	−0.174200	+	1.65741i	−0.00947525	+	0.0901510i
$339$	−26.4510	+	19.2178i	−1.43662	+	1.04376i
$340$		0			0
$341$	7.96520	−	10.9460i	0.431340	−	0.592757i
$342$	−3.99844			−0.216211
$343$	11.2313	−	8.15999i	0.606431	−	0.440598i
$344$	−1.19794	+	11.3976i	−0.0645885	+	0.614519i
$345$		0			0
$346$	−3.34647	+	5.79626i	−0.179907	+	0.311609i
$347$	5.32998	+	9.23180i	0.286128	+	0.495589i	0.972882	−	0.231301i	$-0.0742983\pi$
$347$	5.32998	+	9.23180i	0.286128	+	0.495589i	−0.686754	+	0.726890i	$0.740965\pi$
$348$	−16.7769	+	3.56605i	−0.899338	+	0.191160i
$349$	−5.77910	−	17.7862i	−0.309348	−	0.952075i	−0.978019	−	0.208517i	$-0.933136\pi$
$349$	−5.77910	−	17.7862i	−0.309348	−	0.952075i	0.668671	−	0.743559i	$-0.266864\pi$
$350$		0			0
$351$	2.06072	+	19.6064i	0.109993	+	1.04651i
$352$	6.30478	+	7.00216i	0.336046	+	0.373217i
$353$	11.5675	+	5.15020i	0.615678	+	0.274117i	0.690787	−	0.723058i	$-0.257264\pi$
$353$	11.5675	+	5.15020i	0.615678	+	0.274117i	−0.0751097	+	0.997175i	$0.523931\pi$
$354$	11.1596	−	4.96859i	0.593127	−	0.264077i
$355$		0			0
$356$	3.43001	+	2.49205i	0.181790	+	0.132078i
$357$	−4.62205	−	3.35812i	−0.244625	−	0.177730i
$358$	0.0186548	−	0.0207182i	0.000985936	−	0.00109499i
$359$	−20.7175	+	9.22402i	−1.09343	+	0.486825i	−0.872574	−	0.488482i	$-0.837551\pi$
$359$	−20.7175	+	9.22402i	−1.09343	+	0.486825i	−0.220853	+	0.975307i	$0.570884\pi$
$360$		0			0
$361$	−9.71104	−	10.7852i	−0.511107	−	0.567642i
$362$	0.0794517	+	0.755932i	0.00417589	+	0.0397309i
$363$	14.4006	+	3.06095i	0.755837	+	0.160658i
$364$	1.80319	+	5.54965i	0.0945129	+	0.290881i
$365$		0			0
$366$	−7.33880	−	12.7112i	−0.383605	−	0.664424i
$367$	4.35984	−	7.55147i	0.227582	−	0.394183i	−0.729509	−	0.683971i	$-0.760251\pi$
$367$	4.35984	−	7.55147i	0.227582	−	0.394183i	0.957091	+	0.289788i	$0.0935847\pi$
$368$	0.447430	−	1.37705i	0.0233239	−	0.0717836i
$369$	3.89987	−	37.1048i	0.203019	−	1.93160i
$370$		0			0
$371$	5.38574			0.279614
$372$	6.30699	−	29.5635i	0.327002	−	1.53280i
$373$	−25.4134			−1.31586			−0.657928	−	0.753081i	$-0.728567\pi$
$373$	−25.4134			−1.31586			−0.657928	+	0.753081i	$0.728567\pi$
$374$	−1.26141	+	0.916471i	−0.0652262	+	0.0473896i
$375$		0			0
$376$	3.35188	−	10.3160i	0.172860	−	0.532009i
$377$	−4.53913	+	7.86200i	−0.233777	+	0.404914i
$378$	1.30448	+	2.25943i	0.0670954	+	0.116213i
$379$	−21.6150	+	4.59441i	−1.11029	+	0.235999i	−0.726326	−	0.687350i	$-0.758774\pi$
$379$	−21.6150	+	4.59441i	−1.11029	+	0.235999i	−0.383961	+	0.923349i	$0.625440\pi$
$380$		0			0
$381$	0.333399	+	0.0708662i	0.0170806	+	0.00363059i
$382$	−0.196226	−	1.86696i	−0.0100398	−	0.0955220i
$383$	17.8274	+	19.7993i	0.910938	+	1.01170i	0.999877	+	0.0156617i	$0.00498547\pi$
$383$	17.8274	+	19.7993i	0.910938	+	1.01170i	−0.0889398	+	0.996037i	$0.528348\pi$
$384$	25.3039	+	11.2660i	1.29128	+	0.574916i
$385$		0			0
$386$	−0.501743	+	0.557242i	−0.0255380	+	0.0283629i
$387$	−36.5547	−	26.5585i	−1.85818	−	1.35005i
$388$	−5.18112	−	3.76430i	−0.263032	−	0.191104i
$389$	−8.66862	+	9.62748i	−0.439517	+	0.488133i	−0.921681	−	0.387948i	$-0.873184\pi$
$389$	−8.66862	+	9.62748i	−0.439517	+	0.488133i	0.482165	+	0.876081i	$0.339851\pi$
$390$		0			0
$391$	0.737176	+	0.328212i	0.0372806	+	0.0165984i
$392$	−5.31357	−	5.90132i	−0.268376	−	0.298062i
$393$	−1.74925	−	16.6430i	−0.0882379	−	0.839528i
$394$	2.01980	+	0.429321i	0.101756	+	0.0216289i
$395$		0			0
$396$	−23.9701	+	5.09500i	−1.20454	+	0.256033i
$397$	−1.46363	−	2.53508i	−0.0734574	−	0.127232i	0.826957	−	0.562265i	$-0.190070\pi$
$397$	−1.46363	−	2.53508i	−0.0734574	−	0.127232i	−0.900414	+	0.435033i	$0.856737\pi$
$398$	1.21736	−	2.10852i	0.0610205	−	0.105691i
$399$	2.04944	−	6.30752i	0.102600	−	0.315771i
$400$		0			0
$401$	9.93025	−	7.21475i	0.495893	−	0.360287i	−0.311553	−	0.950229i	$-0.600849\pi$
$401$	9.93025	−	7.21475i	0.495893	−	0.360287i	0.807446	+	0.589942i	$0.200849\pi$
$402$	−6.54572			−0.326471
$403$	−9.39479	−	12.9511i	−0.467988	−	0.645142i
$404$	−33.2464			−1.65407
$405$		0			0
$406$	−0.125581	+	1.19482i	−0.00623246	+	0.0592979i
$407$	2.36426	−	7.27645i	0.117192	−	0.360680i
$408$	−3.59625	+	6.22889i	−0.178041	+	0.308376i
$409$	8.59861	+	14.8932i	0.425174	+	0.736423i	0.996437	−	0.0843442i	$-0.0268795\pi$
$409$	8.59861	+	14.8932i	0.425174	+	0.736423i	−0.571263	+	0.820767i	$0.693546\pi$
$410$		0			0
$411$	−10.5549	−	32.4848i	−0.520637	−	1.60236i
$412$	−14.8195	−	3.14997i	−0.730102	−	0.155188i
$413$	1.35893	+	12.9294i	0.0668687	+	0.636213i
$414$	−0.558539	−	0.620320i	−0.0274507	−	0.0304871i
$415$		0			0
$416$	10.1735	−	4.52955i	0.498799	−	0.222080i
$417$	−29.8568	+	33.1594i	−1.46210	+	1.62382i
$418$	−1.46431	−	1.06388i	−0.0716217	−	0.0520362i
$419$	−18.7251	−	13.6046i	−0.914782	−	0.664628i	0.0274378	−	0.999624i	$-0.491265\pi$
$419$	−18.7251	−	13.6046i	−0.914782	−	0.664628i	−0.942220	+	0.334996i	$0.891265\pi$
$420$		0			0
$421$	26.6593	−	11.8695i	1.29929	−	0.578483i	0.363686	−	0.931522i	$-0.381518\pi$
$421$	26.6593	−	11.8695i	1.29929	−	0.578483i	0.935609	+	0.353038i	$0.114851\pi$
$422$	−5.36434	−	2.38836i	−0.261132	−	0.116263i
$423$	28.6156	+	31.7808i	1.39134	+	1.54524i
$424$	−0.708734	−	6.74315i	−0.0344192	−	0.327476i
$425$		0			0
$426$	−0.527201	−	1.62256i	−0.0255430	−	0.0786132i
$427$	15.2793	−	3.24771i	0.739416	−	0.157168i
$428$	11.4008	+	19.7468i	0.551080	+	0.954498i
$429$	−10.1076	+	17.5069i	−0.487999	+	0.845239i
$430$		0			0
$431$	−3.17267	+	30.1859i	−0.152822	+	1.45401i	0.602220	+	0.798330i	$0.294283\pi$
$431$	−3.17267	+	30.1859i	−0.152822	+	1.45401i	−0.755042	+	0.655676i	$0.772384\pi$
$432$	−18.1725	+	13.2031i	−0.874326	+	0.635235i
$433$	13.8400			0.665107			0.332553	−	0.943084i	$-0.392090\pi$
$433$	13.8400			0.665107			0.332553	+	0.943084i	$0.392090\pi$
$434$	−1.83292	−	1.06006i	−0.0879830	−	0.0508846i
$435$		0			0
$436$	−0.959605	+	0.697194i	−0.0459567	+	0.0333895i
$437$	−0.0979154	+	0.931602i	−0.00468393	+	0.0445646i
$438$	4.51207	−	13.8867i	0.215595	−	0.663534i
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	−0.977995	−	0.208626i	$-0.933101\pi$
$439$	−6.46006	+	11.1892i	−0.308322	+	0.534029i	0.669674	+	0.742656i	$0.266434\pi$
$440$		0			0
$441$	30.6242	−	6.50938i	1.45830	−	0.309970i
$442$	0.569463	+	1.75263i	0.0270866	+	0.0833639i
$443$	23.2391	+	4.93962i	1.10412	+	0.234688i	0.723693	−	0.690122i	$-0.242443\pi$
$443$	23.2391	+	4.93962i	1.10412	+	0.234688i	0.380429	+	0.924810i	$0.375776\pi$
$444$	−1.78582	−	16.9909i	−0.0847511	−	0.806353i
$445$		0			0
$446$	−2.01027	−	0.895031i	−0.0951892	−	0.0423809i
$447$	−31.5863	+	14.0631i	−1.49398	+	0.665163i
$448$	−3.75549	+	4.17089i	−0.177430	+	0.197056i
$449$	15.7054	+	11.4106i	0.741181	+	0.538500i	0.893081	−	0.449896i	$-0.148539\pi$
$449$	15.7054	+	11.4106i	0.741181	+	0.538500i	−0.151900	+	0.988396i	$0.548539\pi$
$450$		0			0
$451$	11.3009	−	12.5509i	0.532137	−	0.590998i
$452$	−19.3718	+	8.62487i	−0.911171	+	0.405680i
$453$	−11.4241	−	5.08632i	−0.536749	−	0.238976i
$454$	−1.84538	−	2.04950i	−0.0866078	−	0.0961877i
$455$		0			0
$456$	−8.16695	−	1.73594i	−0.382452	−	0.0812928i
$457$	−7.52208	−	23.1506i	−0.351868	−	1.08294i	−0.957803	−	0.287424i	$-0.907201\pi$
$457$	−7.52208	−	23.1506i	−0.351868	−	1.08294i	0.605935	−	0.795514i	$-0.292799\pi$
$458$	4.39075	−	0.933283i	0.205166	−	0.0436094i
$459$	−6.25931	−	10.8414i	−0.292159	−	0.506035i
$460$		0			0
$461$	−11.8487	+	36.4665i	−0.551848	+	1.69841i	0.152279	+	0.988338i	$0.451339\pi$
$461$	−11.8487	+	36.4665i	−0.551848	+	1.69841i	−0.704126	+	0.710075i	$0.748661\pi$
$462$	−0.279639	+	2.66059i	−0.0130100	+	0.123782i
$463$	−5.33489	+	3.87603i	−0.247934	+	0.180134i	−0.704810	−	0.709396i	$-0.748968\pi$
$463$	−5.33489	+	3.87603i	−0.247934	+	0.180134i	0.456877	+	0.889530i	$0.348968\pi$
$464$	−10.3437			−0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	31.0674	−	22.5718i	1.43763	−	1.04450i	0.449096	−	0.893484i	$-0.351746\pi$
$467$	31.0674	−	22.5718i	1.43763	−	1.04450i	0.988532	−	0.151014i	$-0.0482539\pi$
$468$	−3.02749	+	28.8046i	−0.139946	+	1.33149i
$469$	2.15270	−	6.62532i	0.0994024	−	0.305929i
$470$		0			0
$471$	−12.5922	−	21.8104i	−0.580220	−	1.00497i
$472$	16.0092	−	3.40287i	0.736885	−	0.156630i
$473$	−6.32051	−	19.4525i	−0.290617	−	0.894429i
$474$	−3.42895	−	0.728845i	−0.157497	−	0.0334770i
$475$		0			0
$476$	−2.47938	−	2.75363i	−0.113642	−	0.126212i
$477$	24.4210	+	10.8729i	1.11816	+	0.497838i
$478$	8.16256	−	3.63421i	0.373347	−	0.166225i
$479$	5.03531	−	5.59228i	0.230069	−	0.255518i	−0.617046	−	0.786927i	$-0.711671\pi$
$479$	5.03531	−	5.59228i	0.230069	−	0.255518i	0.847115	+	0.531409i	$0.178337\pi$
$480$		0			0
$481$	−7.31567	−	5.31515i	−0.333566	−	0.242350i
$482$	−0.555195	+	0.616606i	−0.0252884	+	0.0280856i
$483$	1.26484	−	0.563141i	0.0575520	−	0.0256238i
$484$	8.72293	+	3.88370i	0.396497	+	0.176532i
$485$		0			0
$486$	−0.358996	−	3.41562i	−0.0162844	−	0.154936i
$487$	24.4852	+	5.20450i	1.10953	+	0.235838i	0.726004	−	0.687691i	$-0.241375\pi$
$487$	24.4852	+	5.20450i	1.10953	+	0.235838i	0.383528	+	0.923529i	$0.374709\pi$
$488$	−6.07693	−	18.7029i	−0.275090	−	0.846639i
$489$	8.85217	−	1.88159i	0.400309	−	0.0850883i
$490$		0			0
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.0635377	−	0.997979i	$-0.479762\pi$
$491$	19.8550	−	34.3899i	0.896044	−	1.55199i	0.832507	−	0.554015i	$-0.186905\pi$
$492$	11.6539	−	35.8670i	0.525399	−	1.61701i
$493$	0.602573	−	5.73310i	0.0271385	−	0.258206i
$494$	−1.73068	+	1.25741i	−0.0778668	+	0.0565735i
$495$		0			0
$496$	7.42729	−	16.6485i	0.333495	−	0.747539i
$497$	1.81567			0.0814440
$498$	−10.5735	+	7.68207i	−0.473808	+	0.344242i
$499$	2.47252	−	23.5245i	0.110685	−	1.05310i	−0.788351	−	0.615226i	$-0.789065\pi$
$499$	2.47252	−	23.5245i	0.110685	−	1.05310i	0.899036	−	0.437875i	$-0.144269\pi$
$500$		0			0
$501$	−19.3199	+	33.4630i	−0.863148	+	1.49502i
$502$	0.414099	+	0.717241i	0.0184822	+	0.0320120i
$503$	−19.7453	+	4.19699i	−0.880400	+	0.187135i	−0.625867	−	0.779930i	$-0.715255\pi$
$503$	−19.7453	+	4.19699i	−0.880400	+	0.187135i	−0.254532	+	0.967064i	$0.581922\pi$
$504$	2.44685	+	7.53063i	0.108991	+	0.335441i
$505$		0			0
$506$	−0.0394968	−	0.375787i	−0.00175585	−	0.0167058i
$507$	−9.18070	−	10.1962i	−0.407729	−	0.452829i
$508$	0.201951	+	0.0899143i	0.00896012	+	0.00398930i
$509$	10.8155	−	4.81536i	0.479387	−	0.213437i	−0.152793	−	0.988258i	$-0.548827\pi$
$509$	10.8155	−	4.81536i	0.479387	−	0.213437i	0.632180	+	0.774821i	$0.282160\pi$
$510$		0			0
$511$	12.5717	+	9.13389i	0.556140	+	0.404060i
$512$	17.4827	+	12.7019i	0.772633	+	0.561351i
$513$	9.72394	−	10.7995i	0.429322	−	0.476811i
$514$	−8.35179	+	3.71845i	−0.368381	+	0.164014i
$515$		0			0
$516$	−30.5611	−	33.9416i	−1.34538	−	1.49419i
$517$	2.02354	+	19.2526i	0.0889950	+	0.846731i
$518$	−1.17054	−	0.248806i	−0.0514306	−	0.0109319i
$519$	−17.0275	−	52.4051i	−0.747422	−	2.30033i
$520$		0			0
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	0.962039	+	0.272911i	$0.0879865\pi$
$521$	16.3742	+	28.3610i	0.717368	+	1.24252i	−0.244672	+	0.969606i	$0.578680\pi$
$522$	−2.98158	+	5.16425i	−0.130500	+	0.226033i
$523$	9.11682	−	28.0587i	0.398651	−	1.22692i	−0.527431	−	0.849598i	$-0.676845\pi$
$523$	9.11682	−	28.0587i	0.398651	−	1.22692i	0.926082	−	0.377323i	$-0.123155\pi$
$524$	1.13451	−	10.7941i	0.0495611	−	0.471543i
$525$		0			0
$526$	8.06030			0.351446
$527$	8.79490	+	5.08650i	0.383112	+	0.221571i
$528$	−23.0331			−1.00239
$529$	18.4492	−	13.4041i	0.802138	−	0.582788i
$530$		0			0
$531$	−19.9404	+	61.3703i	−0.865340	+	2.66324i
$532$	2.15069	−	3.72510i	0.0932441	−	0.161504i
$533$	−9.98053	−	17.2868i	−0.432305	−	0.748774i
$534$	2.24713	−	0.477643i	0.0972430	−	0.0206696i
$535$		0			0
$536$	−8.57845	−	1.82340i	−0.370532	−	0.0787591i
$537$	0.0239919	+	0.228267i	0.00103533	+	0.00985047i
$538$	4.00875	+	4.45217i	0.172830	+	0.191947i
$539$	12.9472	+	5.76446i	0.557675	+	0.248293i
$540$		0			0
$541$	8.87657	−	9.85843i	0.381634	−	0.423847i	−0.521470	−	0.853270i	$-0.674616\pi$
$541$	8.87657	−	9.85843i	0.381634	−	0.423847i	0.903104	+	0.429423i	$0.141283\pi$
$542$	2.06029	+	1.49689i	0.0884970	+	0.0642968i
$543$	−5.06264	−	3.67822i	−0.217258	−	0.157848i
$544$	−4.73179	+	5.25519i	−0.202874	+	0.225314i
$545$		0			0
$546$	2.88853	+	1.28605i	0.123618	+	0.0550381i
$547$	−25.2689	−	28.0640i	−1.08042	−	1.19993i	−0.978738	−	0.205114i	$-0.934244\pi$
$547$	−25.2689	−	28.0640i	−1.08042	−	1.19993i	−0.101684	−	0.994817i	$-0.532423\pi$
$548$	−2.31560	−	22.0315i	−0.0989175	−	0.941137i
$549$	75.8388	+	16.1200i	3.23672	+	0.687986i
$550$		0			0
$551$	6.54568	−	1.39133i	0.278855	−	0.0592725i
$552$	−0.871520	−	1.50952i	−0.0370944	−	0.0642493i
$553$	1.86539	−	3.23095i	0.0793245	−	0.137394i
$554$	1.64019	−	5.04800i	0.0696852	−	0.214469i
$555$		0			0
$556$	−23.4124	+	17.0101i	−0.992907	+	0.721389i
$557$	11.3637			0.481496			0.240748	−	0.970588i	$-0.422607\pi$
$557$	11.3637			0.481496			0.240748	+	0.970588i	$0.422607\pi$
$558$	−6.17108	−	8.50711i	−0.261243	−	0.360135i
$559$	−24.1743			−1.02246
$560$		0			0
$561$	1.34179	−	12.7663i	0.0566505	−	0.538993i
$562$	0.270094	−	0.831262i	0.0113932	−	0.0350647i
$563$	−10.0933	+	17.4821i	−0.425381	+	0.736781i	−0.996456	−	0.0841167i	$-0.973193\pi$
$563$	−10.0933	+	17.4821i	−0.425381	+	0.736781i	0.571075	+	0.820898i	$0.306526\pi$
$564$	21.6140	+	37.4365i	0.910113	+	1.57636i
$565$		0			0
$566$	−0.513276	−	1.57970i	−0.0215746	−	0.0663998i
$567$	−3.95417	−	0.840485i	−0.166060	−	0.0352971i
$568$	−0.238933	−	2.27329i	−0.0100254	−	0.0953852i
$569$	−20.7361	−	23.0298i	−0.869304	−	0.965460i	0.130358	−	0.991467i	$-0.458387\pi$
$569$	−20.7361	−	23.0298i	−0.869304	−	0.965460i	−0.999662	+	0.0260074i	$0.991721\pi$
$570$		0			0
$571$	−9.50060	+	4.22994i	−0.397588	+	0.177017i	−0.595784	−	0.803145i	$-0.703158\pi$
$571$	−9.50060	+	4.22994i	−0.397588	+	0.177017i	0.198196	+	0.980162i	$0.436492\pi$
$572$	−8.77291	+	9.74330i	−0.366814	+	0.407388i
$573$	12.5034	+	9.08427i	0.522338	+	0.379501i
$574$	−2.13711	−	1.55270i	−0.0892012	−	0.0648085i
$575$		0			0
$576$	−25.4492	+	11.3307i	−1.06038	+	0.472113i
$577$	−4.94581	−	2.20201i	−0.205897	−	0.0916711i	0.301197	−	0.953562i	$-0.402614\pi$
$577$	−4.94581	−	2.20201i	−0.205897	−	0.0916711i	−0.507094	+	0.861891i	$0.669280\pi$
$578$	3.21461	+	3.57019i	0.133710	+	0.148500i
$579$	−0.645291	−	6.13953i	−0.0268174	−	0.255150i
$580$		0			0
$581$	−4.29819	−	13.2285i	−0.178319	−	0.548809i
$582$	−3.39435	+	0.721492i	−0.140700	+	0.0299068i
$583$	6.05046	+	10.4797i	0.250585	+	0.434025i
$584$	9.78162	−	16.9423i	0.404766	−	0.701076i
$585$		0			0
$586$	0.387510	−	3.68691i	0.0160079	−	0.152305i
$587$	−10.1635	+	7.38424i	−0.419494	+	0.304780i	−0.777434	−	0.628964i	$-0.783479\pi$
$587$	−10.1635	+	7.38424i	−0.419494	+	0.304780i	0.357940	+	0.933744i	$0.383479\pi$
$588$	31.6471			1.30510
$589$	−2.46073	+	11.5345i	−0.101393	+	0.475270i
$590$		0			0
$591$	−13.7535	+	9.99247i	−0.565741	+	0.411035i
$592$	1.07697	−	10.2467i	0.0442634	−	0.421138i
$593$	−8.36510	+	25.7451i	−0.343513	+	1.05723i	0.618861	+	0.785500i	$0.287594\pi$
$593$	−8.36510	+	25.7451i	−0.343513	+	1.05723i	−0.962375	+	0.271726i	$0.912406\pi$
$594$	−2.93098	+	5.07660i	−0.120259	+	0.208295i
$595$		0			0
$596$	−21.9345	+	4.66233i	−0.898473	+	0.190976i
$597$	6.19413	+	19.0636i	0.253509	+	0.780220i
$598$	−0.436832	−	0.0928516i	−0.0178634	−	0.00379698i
$599$	1.50051	+	14.2764i	0.0613094	+	0.583320i	0.981448	+	0.191727i	$0.0614089\pi$
$599$	1.50051	+	14.2764i	0.0613094	+	0.583320i	−0.920139	+	0.391592i	$0.871924\pi$
$600$		0			0
$601$	0.584684	+	0.260318i	0.0238498	+	0.0106186i	0.418627	−	0.908158i	$-0.362512\pi$
$601$	0.584684	+	0.260318i	0.0238498	+	0.0106186i	−0.394777	+	0.918777i	$0.629178\pi$
$602$	−2.92260	+	1.30122i	−0.119116	+	0.0530339i
$603$	23.1366	−	25.6958i	0.942197	−	1.04642i
$604$	−6.56150	−	4.76721i	−0.266984	−	0.193975i
$605$		0			0
$606$	−12.0543	+	13.3877i	−0.489673	+	0.543837i
$607$	5.95432	−	2.65104i	0.241679	−	0.107602i	−0.282323	−	0.959319i	$-0.591105\pi$
$607$	5.95432	−	2.65104i	0.241679	−	0.107602i	0.524002	+	0.851717i	$0.324438\pi$
$608$	−7.49929	−	3.33890i	−0.304136	−	0.135410i
$609$	−6.61834	−	7.35041i	−0.268189	−	0.297854i
$610$		0			0
$611$	22.3802	+	4.75706i	0.905405	+	0.192450i
$612$	−5.68333	−	17.4915i	−0.229735	−	0.707052i
$613$	10.2171	−	2.17170i	0.412663	−	0.0877143i	0.00309833	−	0.999995i	$-0.499014\pi$
$613$	10.2171	−	2.17170i	0.412663	−	0.0877143i	0.409565	+	0.912281i	$0.365680\pi$
$614$	−0.465385	−	0.806070i	−0.0187814	−	0.0325303i
$615$		0			0
$616$	−1.10762	+	3.40892i	−0.0446274	+	0.137349i
$617$	2.26862	−	21.5845i	0.0913311	−	0.868958i	−0.848930	−	0.528505i	$-0.822753\pi$
$617$	2.26862	−	21.5845i	0.0913311	−	0.868958i	0.940262	−	0.340453i	$-0.110580\pi$
$618$	−6.64159	+	4.82540i	−0.267164	+	0.194106i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	1.56738	−	1.13877i	0.0628462	−	0.0456604i
$623$	−0.255566	+	2.43155i	−0.0102390	+	0.0974178i
$624$	−8.41235	+	25.8906i	−0.336764	+	1.03645i
$625$		0			0
$626$	4.68731	+	8.11866i	0.187343	+	0.324487i
$627$	14.5757	−	3.09816i	0.582098	−	0.123729i
$628$	−5.04743	−	15.5344i	−0.201414	−	0.619890i
$629$	5.61660	+	1.19385i	0.223949	+	0.0476018i
$630$		0			0
$631$	18.2275	+	20.2436i	0.725624	+	0.805887i	0.987232	−	0.159287i	$-0.0509196\pi$
$631$	18.2275	+	20.2436i	0.725624	+	0.805887i	−0.261609	+	0.965174i	$0.584253\pi$
$632$	−4.29075	−	1.91037i	−0.170677	−	0.0759903i
$633$	44.1638	−	19.6630i	1.75535	−	0.781533i
$634$	2.52561	−	2.80498i	0.100305	−	0.111400i
$635$		0			0
$636$	21.8607	+	15.8828i	0.866835	+	0.629792i
$637$	11.2083	−	12.4481i	0.444089	−	0.493210i
$638$	−2.46599	+	1.09793i	−0.0976295	+	0.0434675i
$639$	8.23296	+	3.66555i	0.325691	+	0.145007i
$640$		0			0
$641$	−4.30742	−	40.9824i	−0.170133	−	1.61871i	−0.663013	−	0.748608i	$-0.730722\pi$
$641$	−4.30742	−	40.9824i	−0.170133	−	1.61871i	0.492880	−	0.870097i	$-0.335944\pi$
$642$	12.0853	+	2.56881i	0.476969	+	0.101383i
$643$	9.52156	+	29.3044i	0.375494	+	1.15565i	0.943145	+	0.332382i	$0.107852\pi$
$643$	9.52156	+	29.3044i	0.375494	+	1.15565i	−0.567651	+	0.823269i	$0.692148\pi$
$644$	0.878342	−	0.186697i	0.0346115	−	0.00735691i
$645$		0			0
$646$	0.679205	−	1.17642i	0.0267230	−	0.0462855i
$647$	−2.75525	+	8.47978i	−0.108320	+	0.333375i	−0.990495	−	0.137547i	$-0.956078\pi$
$647$	−2.75525	+	8.47978i	−0.108320	+	0.333375i	0.882175	+	0.470921i	$0.156078\pi$
$648$	−0.531973	+	5.06138i	−0.0208979	+	0.198830i
$649$	−23.6317	+	17.1694i	−0.927623	+	0.673958i
$650$		0			0
$651$	16.5830	−	5.37445i	0.649938	−	0.210641i
$652$	5.86949			0.229867
$653$	31.7469	−	23.0655i	1.24235	−	0.902623i	0.244601	−	0.969624i	$-0.421343\pi$
$653$	31.7469	−	23.0655i	1.24235	−	0.902623i	0.997753	+	0.0670010i	$0.0213431\pi$
$654$	−0.0671825	+	0.639199i	−0.00262704	+	0.0249946i
$655$		0			0
$656$	11.3718	−	19.6965i	0.443993	−	0.769018i
$657$	38.5652	+	66.7969i	1.50457	+	2.60600i
$658$	2.96175	−	0.629540i	0.115461	−	0.0245420i
$659$	10.1832	+	31.3407i	0.396681	+	1.22086i	0.927644	+	0.373465i	$0.121830\pi$
$659$	10.1832	+	31.3407i	0.396681	+	1.22086i	−0.530963	+	0.847395i	$0.678170\pi$
$660$		0			0
$661$	0.0177359	+	0.168746i	0.000689846	+	0.00656345i	0.994861	−	0.101246i	$-0.0322830\pi$
$661$	0.0177359	+	0.168746i	0.000689846	+	0.00656345i	−0.994172	+	0.107810i	$0.965616\pi$
$662$	−4.62022	−	5.13127i	−0.179570	−	0.199433i
$663$	−13.8600	−	6.17087i	−0.538278	−	0.239657i
$664$	−15.9969	+	7.12229i	−0.620801	+	0.276398i
$665$		0			0
$666$	−4.80539	−	3.49132i	−0.186205	−	0.135286i
$667$	1.13021	+	0.821147i	0.0437620	+	0.0317950i
$668$	−16.7687	+	18.6236i	−0.648801	+	0.720567i
$669$	16.5503	−	7.36866i	0.639871	−	0.284889i
$670$		0			0
$671$	23.4846	+	26.0823i	0.906612	+	1.00689i
$672$	1.26827	+	12.0668i	0.0489246	+	0.465487i
$673$	−14.2676	−	3.03267i	−0.549976	−	0.116901i	−0.0754613	−	0.997149i	$-0.524043\pi$
$673$	−14.2676	−	3.03267i	−0.549976	−	0.116901i	−0.474514	+	0.880248i	$0.657376\pi$
$674$	2.08278	+	6.41015i	0.0802258	+	0.246910i
$675$		0			0
$676$	−4.44929	−	7.70639i	−0.171126	−	0.296400i
$677$	7.88341	−	13.6545i	0.302984	−	0.524784i	−0.673826	−	0.738890i	$-0.735350\pi$
$677$	7.88341	−	13.6545i	0.302984	−	0.524784i	0.976810	+	0.214106i	$0.0686837\pi$
$678$	−3.55065	+	10.9278i	−0.136362	+	0.419679i
$679$	0.386039	−	3.67291i	0.0148148	−	0.140953i
$680$		0			0
$681$	22.7051			0.870063
$682$	0.00355200	−	4.75744i	0.000136013	−	0.182172i
$683$	−20.5935			−0.787988			−0.393994	−	0.919113i	$-0.628907\pi$
$683$	−20.5935			−0.787988			−0.393994	+	0.919113i	$0.628907\pi$
$684$	17.2724	−	12.5492i	0.660428	−	0.479829i
$685$		0			0
$686$	1.50763	−	4.64001i	0.0575616	−	0.177156i
$687$	−18.4780	+	32.0048i	−0.704979	+	1.22106i
$688$	−13.7720	−	23.8538i	−0.525053	−	0.909418i
$689$	13.9896	−	2.97359i	0.532962	−	0.113285i
$690$		0			0
$691$	5.82165	+	1.23743i	0.221466	+	0.0470741i	0.317308	−	0.948322i	$-0.397221\pi$
$691$	5.82165	+	1.23743i	0.221466	+	0.0470741i	−0.0958421	+	0.995397i	$0.530554\pi$
$692$	−3.73557	−	35.5416i	−0.142005	−	1.35109i
$693$	−9.45597	−	10.5019i	−0.359203	−	0.398935i
$694$	3.42238	+	1.52374i	0.129912	+	0.0578404i
$695$		0			0
$696$	−8.33206	+	9.25369i	−0.315826	+	0.350760i
$697$	10.2545	+	7.45032i	0.388417	+	0.282201i
$698$	−5.31713	−	3.86312i	−0.201256	−	0.146221i
$699$	−24.6209	+	27.3443i	−0.931248	+	1.03426i
$700$		0			0
$701$	−24.3281	−	10.8316i	−0.918859	−	0.409103i	−0.107871	−	0.994165i	$-0.534403\pi$
$701$	−24.3281	−	10.8316i	−0.918859	−	0.409103i	−0.810988	+	0.585062i	$0.801070\pi$
$702$	4.63592	+	5.14871i	0.174972	+	0.194326i
$703$	0.696753	+	6.62916i	0.0262785	+	0.250024i
$704$	−12.3348	−	2.62185i	−0.464886	−	0.0988146i
$705$		0			0
$706$	4.35268	−	0.925191i	0.163815	−	0.0348200i
$707$	−9.58617	−	16.6037i	−0.360525	−	0.624448i
$708$	−32.6133	+	56.4879i	−1.22568	+	2.12295i
$709$	−0.816662	+	2.51343i	−0.0306704	+	0.0943938i	−0.965220	−	0.261439i	$-0.915803\pi$
$709$	−0.816662	+	2.51343i	−0.0306704	+	0.0943938i	0.934550	+	0.355833i	$0.115803\pi$
$710$		0			0
$711$	14.9812	−	10.8845i	0.561839	−	0.408200i
$712$	3.07802			0.115354
$713$	−2.13321	+	1.22948i	−0.0798892	+	0.0460445i
$714$	−2.00779			−0.0751398
$715$		0			0
$716$	−0.0155603	+	0.148047i	−0.000581518	+	0.00553277i
$717$	−22.7315	+	69.9605i	−0.848925	+	2.61272i
$718$	−3.98491	+	6.90207i	−0.148716	+	0.257583i
$719$	−2.59912	−	4.50181i	−0.0969308	−	0.167889i	0.813482	−	0.581590i	$-0.197569\pi$
$719$	−2.59912	−	4.50181i	−0.0969308	−	0.167889i	−0.910413	+	0.413701i	$0.864236\pi$
$720$		0			0
$721$	−2.69986	−	8.30930i	−0.100548	−	0.309455i
$722$	−4.98886	−	1.06041i	−0.185666	−	0.0394645i
$723$	−0.714035	−	6.79359i	−0.0265552	−	0.252656i
$724$	−2.71572	−	3.01611i	−0.100929	−	0.112093i
$725$		0			0
$726$	4.72660	−	2.10442i	0.175421	−	0.0781023i
$727$	−16.1973	+	17.9889i	−0.600723	+	0.667171i	−0.964429	−	0.264343i	$-0.914845\pi$
$727$	−16.1973	+	17.9889i	−0.600723	+	0.667171i	0.363705	+	0.931514i	$0.381512\pi$
$728$	3.42729	+	2.49007i	0.127024	+	0.0922882i
$729$	31.9419	+	23.2071i	1.18303	+	0.859524i
$730$		0			0
$731$	14.0235	−	6.24366i	0.518677	−	0.230930i
$732$	71.5963	+	31.8767i	2.64628	+	1.17820i
$733$	−27.0080	−	29.9954i	−0.997562	−	1.10790i	−0.994161	−	0.107910i	$-0.965584\pi$
$733$	−27.0080	−	29.9954i	−0.997562	−	1.10790i	−0.00340093	−	0.999994i	$-0.501083\pi$
$734$	−0.320315	−	3.04759i	−0.0118230	−	0.112489i
$735$		0			0
$736$	−0.529571	−	1.62985i	−0.0195202	−	0.0600771i
$737$	15.3101	−	3.25427i	0.563955	−	0.119872i
$738$	−6.55583	−	11.3550i	−0.241324	−	0.417985i
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	−0.916640	−	0.399715i	$-0.869109\pi$
$739$	−3.04893	+	5.28089i	−0.112157	+	0.194261i	0.804483	+	0.593976i	$0.202442\pi$
$740$		0			0
$741$	1.84095	−	17.5155i	0.0676292	−	0.643449i
$742$	1.53125	−	1.11251i	0.0562138	−	0.0408417i
$743$	−16.2263			−0.595284			−0.297642	−	0.954678i	$-0.596200\pi$
$743$	−16.2263			−0.595284			−0.297642	+	0.954678i	$0.596200\pi$
$744$	−8.91125	−	20.0553i	−0.326702	−	0.735262i
$745$		0			0
$746$	−7.22540	+	5.24956i	−0.264541	+	0.192200i
$747$	7.21649	−	68.6603i	0.264038	−	2.51215i
$748$	2.57269	−	7.91793i	0.0940670	−	0.289508i
$749$	−6.57456	+	11.3875i	−0.240229	+	0.416089i
$750$		0			0
$751$	−35.6481	+	7.57723i	−1.30082	+	0.276497i	−0.805697	−	0.592328i	$-0.798209\pi$
$751$	−35.6481	+	7.57723i	−1.30082	+	0.276497i	−0.495119	+	0.868825i	$0.664876\pi$
$752$	8.05593	+	24.7936i	0.293770	+	0.904130i
$753$	−6.66944	−	1.41763i	−0.243048	−	0.0516614i
$754$	0.333487	+	3.17292i	0.0121449	+	0.115551i
$755$		0			0
$756$	−12.7264	−	5.66615i	−0.462854	−	0.206076i
$757$	−39.7960	+	17.7183i	−1.44641	+	0.643984i	−0.971713	−	0.236164i	$-0.924110\pi$
$757$	−39.7960	+	17.7183i	−1.44641	+	0.643984i	−0.474699	+	0.880148i	$0.657443\pi$
$758$	−5.19641	+	5.77120i	−0.188742	+	0.209619i
$759$	2.51672	+	1.82851i	0.0913512	+	0.0663705i
$760$		0			0
$761$	2.20765	−	2.45184i	0.0800272	−	0.0888792i	−0.701801	−	0.712373i	$-0.747621\pi$
$761$	2.20765	−	2.45184i	0.0800272	−	0.0888792i	0.781828	+	0.623494i	$0.214287\pi$
$762$	0.109429	−	0.0487209i	0.00396419	−	0.00176497i
$763$	−0.624878	−	0.278214i	−0.0226221	−	0.0100720i
$764$	6.70714	+	7.44903i	0.242656	+	0.269497i
$765$		0			0
$766$	9.15848	+	1.94669i	0.330909	+	0.0703369i
$767$	10.6685	+	32.8342i	0.385216	+	1.18557i
$768$	−19.8350	+	4.21607i	−0.715735	+	0.152134i
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	0.902501	+	0.430688i	$0.141729\pi$
$769$	22.8568	+	39.5891i	0.824237	+	1.42762i	−0.0782634	+	0.996933i	$0.524938\pi$
$770$		0			0
$771$	23.2585	−	71.5823i	0.837635	−	2.57798i
$772$	0.418515	−	3.98190i	0.0150627	−	0.143312i
$773$	24.2710	−	17.6339i	0.872969	−	0.634249i	−0.0584131	−	0.998292i	$-0.518604\pi$
$773$	24.2710	−	17.6339i	0.872969	−	0.634249i	0.931382	+	0.364044i	$0.118604\pi$
$774$	−15.8791			−0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	7.97058	−	5.79097i	0.285943	−	0.207750i
$778$	−0.475900	+	4.52789i	−0.0170618	+	0.162333i
$779$	−4.54689	+	13.9939i	−0.162909	+	0.501383i
$780$		0			0
$781$	2.03977	+	3.53298i	0.0729886	+	0.126420i
$782$	0.277388	−	0.0589606i	0.00991937	−	0.00210843i
$783$	−6.69730	−	20.6122i	−0.239342	−	0.736619i
$784$	18.6684	+	3.96809i	0.666729	+	0.141718i
$785$		0			0
$786$	−3.93523	−	4.37051i	−0.140365	−	0.155891i
$787$	39.4944	+	17.5840i	1.40782	+	0.626803i	0.963168	−	0.268899i	$-0.0866599\pi$
$787$	39.4944	+	17.5840i	1.40782	+	0.626803i	0.444654	+	0.895702i	$0.353327\pi$
$788$	−10.0725	+	4.48459i	−0.358820	+	0.159757i
$789$	−44.4030	+	49.3145i	−1.58079	+	1.75564i
$790$		0			0
$791$	−9.89298	−	7.18767i	−0.351754	−	0.255564i
$792$	−11.9045	+	13.2212i	−0.423006	+	0.469796i
$793$	37.8953	−	16.8721i	1.34570	−	0.599145i
$794$	−0.939794	−	0.418423i	−0.0333520	−	0.0148493i
$795$		0			0
$796$	1.35890	+	12.9291i	0.0481649	+	0.458259i
$797$	22.3250	+	4.74532i	0.790792	+	0.168088i	0.585564	−	0.810626i	$-0.300873\pi$
$797$	22.3250	+	4.74532i	0.790792	+	0.168088i	0.205228	+	0.978714i	$0.434206\pi$
$798$	−0.720239	−	2.21667i	−0.0254962	−	0.0784691i
$799$	−14.2114	+	3.02072i	−0.502763	+	0.106865i
$800$		0			0
$801$	−6.06773	+	10.5096i	−0.214393	+	0.371339i
$802$	1.33299	−	4.10252i	0.0470695	−	0.144865i
$803$	−3.64960	+	34.7236i	−0.128792	+	1.22537i
$804$	28.2762	−	20.5438i	0.997223	−	0.724525i
$805$		0			0
$806$	−5.34635	−	1.74155i	−0.188317	−	0.0613435i
$807$	−49.3229			−1.73625
$808$	−19.5270	+	14.1872i	−0.686959	+	0.499105i
$809$	2.22002	−	21.1221i	0.0780517	−	0.742613i	−0.883582	−	0.468276i	$-0.844875\pi$
$809$	2.22002	−	21.1221i	0.0780517	−	0.742613i	0.961634	−	0.274336i	$-0.0884581\pi$
$810$		0			0
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	−0.884062	−	0.467370i	$-0.845202\pi$
$811$	−1.06157	+	1.83869i	−0.0372767	+	0.0645652i	0.846785	+	0.531935i	$0.178535\pi$
$812$	−3.20748	−	5.55551i	−0.112560	−	0.194960i
$813$	−20.5081	+	4.35913i	−0.719250	+	0.152881i
$814$	−0.830879	−	2.55718i	−0.0291223	−	0.0896292i
$815$		0			0
$816$	−1.80693	−	17.1918i	−0.0632553	−	0.601834i
$817$	11.9237	+	13.2426i	0.417158	+	0.463301i
$818$	5.52116	+	2.45818i	0.193043	+	0.0859482i
$819$	−15.2584	+	6.79347i	−0.533171	+	0.237383i
$820$		0			0
$821$	−33.8104	−	24.5647i	−1.17999	−	0.857313i	−0.187819	−	0.982204i	$-0.560142\pi$
$821$	−33.8104	−	24.5647i	−1.17999	−	0.857313i	−0.992171	+	0.124891i	$0.960142\pi$
$822$	−9.71121	−	7.05561i	−0.338717	−	0.246093i
$823$	−10.9058	+	12.1121i	−0.380153	+	0.422203i	−0.902608	−	0.430464i	$-0.858350\pi$
$823$	−10.9058	+	12.1121i	−0.380153	+	0.422203i	0.522454	+	0.852667i	$0.325016\pi$
$824$	−10.0483	+	4.47378i	−0.350049	+	0.155852i
$825$		0			0
$826$	3.05714	+	3.39530i	0.106372	+	0.118138i
$827$	−3.24974	−	30.9192i	−0.113005	−	1.07517i	−0.893209	−	0.449642i	$-0.851552\pi$
$827$	−3.24974	−	30.9192i	−0.113005	−	1.07517i	0.780205	−	0.625524i	$-0.215115\pi$
$828$	4.35966	+	0.926674i	0.151509	+	0.0322041i
$829$	−8.66756	−	26.6760i	−0.301037	−	0.926496i	−0.981126	−	0.193367i	$-0.938059\pi$
$829$	−8.66756	−	26.6760i	−0.301037	−	0.926496i	0.680090	−	0.733129i	$-0.261941\pi$
$830$		0			0
$831$	21.8491	+	37.8437i	0.757936	+	1.31278i
$832$	−7.45215	+	12.9075i	−0.258357	+	0.447487i
$833$	−3.28688	+	10.1160i	−0.113884	+	0.350498i
$834$	−1.63912	+	15.5951i	−0.0567579	+	0.540015i
$835$		0			0
$836$	9.66453			0.334255
$837$	37.9848	+	4.02104i	1.31295	+	0.138988i
$838$	−8.13409			−0.280987
$839$	18.6621	−	13.5588i	0.644287	−	0.468102i	−0.217034	−	0.976164i	$-0.569638\pi$
$839$	18.6621	−	13.5588i	0.644287	−	0.468102i	0.861320	+	0.508062i	$0.169638\pi$
$840$		0			0
$841$	−5.87746	+	18.0890i	−0.202671	+	0.623757i
$842$	5.12779	−	8.88160i	0.176715	−	0.306080i
$843$	3.59793	+	6.23179i	0.123919	+	0.214634i
$844$	30.6687	−	6.51884i	1.05566	−	0.224388i
$845$		0			0
$846$	14.7007	+	3.12473i	0.505420	+	0.107430i
$847$	0.575568	+	5.47617i	0.0197768	+	0.188163i
$848$	10.9040	+	12.1101i	0.374446	+	0.415864i
$849$	12.4925	+	5.56202i	0.428741	+	0.190888i
$850$		0			0
$851$	−0.931124	+	1.03412i	−0.0319185	+	0.0354491i
$852$	7.36982	+	5.35449i	0.252486	+	0.183442i
$853$	24.2874	+	17.6458i	0.831585	+	0.604182i	0.920007	−	0.391901i	$-0.128182\pi$
$853$	24.2874	+	17.6458i	0.831585	+	0.604182i	−0.0884221	+	0.996083i	$0.528182\pi$
$854$	3.67326	−	4.07957i	0.125696	−	0.139600i
$855$		0			0
$856$	15.1227	+	6.73307i	0.516884	+	0.230132i
$857$	36.5261	+	40.5663i	1.24771	+	1.38572i	0.892572	+	0.450904i	$0.148898\pi$
$857$	36.5261	+	40.5663i	1.24771	+	1.38572i	0.355135	+	0.934815i	$0.384435\pi$
$858$	0.742598	+	7.06535i	0.0253519	+	0.241207i
$859$	−9.13238	−	1.94115i	−0.311593	−	0.0662311i	0.0494610	−	0.998776i	$-0.484250\pi$
$859$	−9.13238	−	1.94115i	−0.311593	−	0.0662311i	−0.361054	+	0.932545i	$0.617583\pi$
$860$		0			0
$861$	21.2728	−	4.52167i	0.724974	−	0.154098i
$862$	5.33338	+	9.23768i	0.181656	+	0.314637i
$863$	6.65836	−	11.5326i	0.226653	−	0.392575i	−0.730161	−	0.683275i	$-0.760555\pi$
$863$	6.65836	−	11.5326i	0.226653	−	0.392575i	0.956814	+	0.290700i	$0.0938882\pi$
$864$	−8.21560	+	25.2850i	−0.279500	+	0.860214i
$865$		0			0
$866$	3.93491	−	2.85888i	0.133714	−	0.0971487i
$867$	−39.5520			−1.34326
$868$	11.2449	−	1.17340i	0.381676	−	0.0398276i
$869$	8.38250			0.284357
$870$		0			0
$871$	1.93371	−	18.3980i	0.0655213	−	0.623394i
$872$	−0.266104	+	0.818983i	−0.00901141	+	0.0277343i
$873$	9.16547	−	15.8751i	0.310204	−	0.537290i
$874$	0.164599	+	0.285094i	0.00556766	+	0.00964346i
$875$		0			0
$876$	24.0925	+	74.1490i	0.814010	+	2.50526i
$877$	−41.6359	−	8.84998i	−1.40594	−	0.298843i	−0.558402	−	0.829571i	$-0.688585\pi$
$877$	−41.6359	−	8.84998i	−1.40594	−	0.298843i	−0.847542	+	0.530728i	$0.821919\pi$
$878$	0.474617	+	4.51568i	0.0160175	+	0.152397i
$879$	20.4225	+	22.6815i	0.688835	+	0.765029i
$880$		0			0
$881$	−5.27402	+	2.34814i	−0.177686	+	0.0791110i	−0.493652	−	0.869660i	$-0.664338\pi$
$881$	−5.27402	+	2.34814i	−0.177686	+	0.0791110i	0.315966	+	0.948771i	$0.397672\pi$
$882$	7.36230	−	8.17666i	0.247902	−	0.275323i
$883$	22.0029	+	15.9860i	0.740457	+	0.537973i	0.892854	−	0.450346i	$-0.148699\pi$
$883$	22.0029	+	15.9860i	0.740457	+	0.537973i	−0.152397	+	0.988319i	$0.548699\pi$
$884$	−7.96061	−	5.78372i	−0.267744	−	0.194528i
$885$		0			0
$886$	7.62758	−	3.39602i	0.256254	−	0.114091i
$887$	6.73437	+	2.99834i	0.226118	+	0.100674i	0.516669	−	0.856185i	$-0.327172\pi$
$887$	6.73437	+	2.99834i	0.226118	+	0.100674i	−0.290551	+	0.956860i	$0.593839\pi$
$888$	−8.29940	−	9.21742i	−0.278510	−	0.309316i
$889$	0.0133254	+	0.126783i	0.000446920	+	0.00425216i
$890$		0			0
$891$	−2.80677	−	8.63835i	−0.0940304	−	0.289396i
$892$	11.4930	−	2.44292i	0.384815	−	0.0817950i
$893$	−8.43290	−	14.6062i	−0.282196	−	0.488778i
$894$	−6.07548	+	10.5230i	−0.203194	+	0.351943i
$895$		0			0
$896$	−1.08287	+	10.3028i	−0.0361762	+	0.344193i
$897$	2.97453	−	2.16112i	0.0993166	−	0.0721578i
$898$	6.82232			0.227664
$899$	13.0626	+	11.7793i	0.435663	+	0.392862i
$900$		0			0
$901$	−7.34737	+	5.33818i	−0.244776	+	0.177841i
$902$	0.620408	−	5.90278i	0.0206573	−	0.196541i
$903$	8.13900	−	25.0493i	0.270849	−	0.833588i
$904$	−7.69738	+	13.3322i	−0.256011	+	0.443424i
$905$		0			0
$906$	−4.29869	+	0.913715i	−0.142814	+	0.0303562i
$907$	−5.09354	−	15.6763i	−0.169128	−	0.520523i	0.830189	−	0.557482i	$-0.188233\pi$
$907$	−5.09354	−	15.6763i	−0.169128	−	0.520523i	−0.999317	+	0.0369599i	$0.988233\pi$
$908$	14.4040	+	3.06167i	0.478014	+	0.101605i
$909$	−9.94714	−	94.6408i	−0.329926	−	3.13904i
$910$		0			0
$911$	40.9333	+	18.2247i	1.35618	+	0.603810i	0.950648	−	0.310271i	$-0.100420\pi$
$911$	40.9333	+	18.2247i	1.35618	+	0.603810i	0.405531	+	0.914081i	$0.367087\pi$
$912$	18.3321	−	8.16199i	0.607038	−	0.270271i
$913$	20.9116	−	23.2247i	0.692073	−	0.768625i
$914$	−6.92078	−	5.02824i	−0.228919	−	0.166319i
$915$		0			0
$916$	−16.0380	+	17.8120i	−0.529911	+	0.588526i
$917$	5.71785	−	2.54575i	0.188820	−	0.0840681i
$918$	−4.01909	−	1.78942i	−0.132650	−	0.0590595i
$919$	−6.93006	−	7.69662i	−0.228602	−	0.253888i	0.617921	−	0.786240i	$-0.287975\pi$
$919$	−6.93006	−	7.69662i	−0.228602	−	0.253888i	−0.846523	+	0.532352i	$0.821308\pi$
$920$		0			0
$921$	7.49544	+	1.59320i	0.246983	+	0.0524979i
$922$	4.16401	+	12.8155i	0.137134	+	0.422056i
$923$	4.71626	−	1.00247i	0.155238	−	0.0329968i
$924$	−7.14231	−	12.3708i	−0.234965	−	0.406971i
$925$		0			0
$926$	−0.716131	+	2.20402i	−0.0235335	+	0.0724287i
$927$	4.53296	−	43.1282i	0.148882	−	1.41652i
$928$	−9.90452	+	7.19606i	−0.325132	+	0.236222i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	−19.3066	+	14.0271i	−0.632409	+	0.459472i
$933$	−1.66725	+	15.8629i	−0.0545834	+	0.519327i
$934$	4.17034	−	12.8350i	0.136458	−	0.419974i
$935$		0			0
$936$	10.5136	+	18.2101i	0.343648	+	0.595216i
$937$	−33.8116	+	7.18687i	−1.10458	+	0.234785i	−0.723887	−	0.689918i	$-0.757646\pi$
$937$	−33.8116	+	7.18687i	−1.10458	+	0.234785i	−0.380689	+	0.924703i	$0.624313\pi$
$938$	−0.756528	−	2.32835i	−0.0247015	−	0.0760235i
$939$	−75.4933	−	16.0466i	−2.46363	−	0.523661i
$940$		0			0
$941$	−14.8206	−	16.4600i	−0.483138	−	0.536580i	0.451457	−	0.892293i	$-0.350905\pi$
$941$	−14.8206	−	16.4600i	−0.483138	−	0.536580i	−0.934595	+	0.355713i	$0.884238\pi$
$942$	−8.08546	−	3.59988i	−0.263439	−	0.117290i
$943$	−2.80617	+	1.24939i	−0.0913814	+	0.0406856i
$944$	−26.3211	+	29.2326i	−0.856680	+	0.951440i
$945$		0			0
$946$	−5.81526	−	4.22504i	−0.189071	−	0.137368i
$947$	18.7909	−	20.8694i	0.610622	−	0.678165i	−0.355966	−	0.934499i	$-0.615848\pi$
$947$	18.7909	−	20.8694i	0.610622	−	0.678165i	0.966588	+	0.256334i	$0.0825148\pi$
$948$	17.0998	−	7.61334i	0.555377	−	0.247270i
$949$	37.6985	+	16.7844i	1.22374	+	0.544846i
$950$		0			0
$951$	3.24818	+	30.9044i	0.105330	+	1.00214i
$952$	−2.63130	−	0.559300i	−0.0852809	−	0.0181270i
$953$	−2.36916	−	7.29152i	−0.0767446	−	0.236196i	0.905323	−	0.424723i	$-0.139629\pi$
$953$	−2.36916	−	7.29152i	−0.0767446	−	0.236196i	−0.982068	+	0.188527i	$0.939629\pi$
$954$	9.18925	−	1.95324i	0.297513	−	0.0632383i
$955$		0			0
$956$	−23.8546	+	41.3173i	−0.771512	+	1.33630i
$957$	6.86743	−	21.1358i	0.221992	−	0.683222i
$958$	0.276434	−	2.63009i	0.00893118	−	0.0849745i
$959$	10.3352	−	7.50893i	0.333740	−	0.242476i
$960$		0			0
$961$	−28.3387	+	12.5665i	−0.914152	+	0.405372i
$962$	−3.17789			−0.102459
$963$	−52.8011	+	38.3622i	−1.70149	+	1.23621i
$964$	0.463100	−	4.40610i	0.0149154	−	0.141911i
$965$		0			0
$966$	0.243285	−	0.421383i	0.00782758	−	0.0135578i
$967$	−0.925182	−	1.60246i	−0.0297518	−	0.0515317i	0.850766	−	0.525545i	$-0.176138\pi$
$967$	−0.925182	−	1.60246i	−0.0297518	−	0.0515317i	−0.880518	+	0.474013i	$0.842805\pi$
$968$	6.78063	−	1.44127i	0.217938	−	0.0463241i
$969$	3.45592	+	10.6362i	0.111020	+	0.341685i
$970$		0			0
$971$	−5.16072	−	49.1010i	−0.165615	−	1.57573i	−0.689723	−	0.724074i	$-0.742268\pi$
$971$	−5.16072	−	49.1010i	−0.165615	−	1.57573i	0.524107	−	0.851652i	$-0.324399\pi$
$972$	12.2708	+	13.6281i	0.393585	+	0.437121i
$973$	−15.2457	−	6.78784i	−0.488756	−	0.217608i
$974$	8.03659	−	3.57812i	0.257509	−	0.114650i
$975$		0			0
$976$	38.2373	+	27.7810i	1.22395	+	0.889248i
$977$	−28.8192	−	20.9383i	−0.922007	−	0.669877i	0.0220160	−	0.999758i	$-0.492992\pi$
$977$	−28.8192	−	20.9383i	−0.922007	−	0.669877i	−0.944023	+	0.329881i	$0.892992\pi$
$978$	2.12813	−	2.36353i	0.0680501	−	0.0755773i
$979$	−5.01847	+	2.23437i	−0.160391	+	0.0714107i
$980$		0			0
$981$	−2.27177	−	2.52306i	−0.0725321	−	0.0805550i
$982$	−1.45874	−	13.8789i	−0.0465501	−	0.442895i
$983$	−6.24409	−	1.32722i	−0.199156	−	0.0423318i	0.107254	−	0.994232i	$-0.465794\pi$
$983$	−6.24409	−	1.32722i	−0.199156	−	0.0423318i	−0.306409	+	0.951900i	$0.599128\pi$
$984$	−8.46068	−	26.0393i	−0.269717	−	0.830103i
$985$		0			0
$986$	−1.01295	−	1.75448i	−0.0322588	−	0.0558739i
$987$	−12.4642	+	21.5887i	−0.396740	+	0.687175i
$988$	3.52977	−	10.8635i	0.112297	−	0.345614i
$989$	−0.388855	+	3.69971i	−0.0123649	+	0.117644i
$990$		0			0
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$	−4.47033	−	21.1087i	−0.141933	−	0.670202i
$993$	56.8463			1.80396
$994$	0.516222	−	0.375058i	0.0163736	−	0.0118961i
$995$		0			0
$996$	21.5649	−	66.3699i	0.683310	−	2.10301i
$997$	2.66158	−	4.60999i	0.0842931	−	0.146000i	−0.820797	−	0.571220i	$-0.806470\pi$
$997$	2.66158	−	4.60999i	0.0842931	−	0.146000i	0.905090	+	0.425221i	$0.139803\pi$
$998$	−4.15641	−	7.19911i	−0.131569	−	0.227884i
$999$	21.1162	−	4.48839i	0.668087	−	0.142006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bl.a.276.1		16
5.2	odd	4		775.2.ck.a.524.3		32
5.3	odd	4		775.2.ck.a.524.2		32
5.4	even	2		31.2.g.a.28.2	yes	16
15.14	odd	2		279.2.y.c.28.1		16
20.19	odd	2		496.2.bg.c.369.1		16
31.10	even	15	inner	775.2.bl.a.351.1		16
155.4	even	10		961.2.g.s.448.1		16
155.9	even	30		961.2.c.j.439.4		16
155.14	even	30		961.2.a.i.1.4		8
155.19	even	30		961.2.d.o.374.3		16
155.24	odd	30		961.2.d.q.628.2		16
155.29	odd	10		961.2.g.j.732.2		16
155.34	odd	30		961.2.d.q.531.2		16
155.39	even	10		961.2.c.j.521.4		16
155.44	odd	30		961.2.g.m.547.1		16
155.49	even	30		961.2.g.s.547.1		16
155.54	odd	10		961.2.c.i.521.4		16
155.59	even	30		961.2.d.p.531.2		16
155.64	even	10		961.2.g.k.732.2		16
155.69	even	30		961.2.d.p.628.2		16
155.72	odd	60		775.2.ck.a.599.2		32
155.74	odd	30		961.2.d.n.374.3		16
155.79	odd	30		961.2.a.j.1.4		8
155.84	odd	30		961.2.c.i.439.4		16
155.89	odd	10		961.2.g.m.448.1		16
155.99	odd	6		961.2.d.n.388.3		16
155.103	odd	60		775.2.ck.a.599.3		32
155.104	odd	30		961.2.g.n.846.1		16
155.109	even	10		961.2.g.t.844.1		16
155.114	odd	30		961.2.g.l.816.2		16
155.119	odd	6		961.2.g.j.235.2		16
155.129	even	6		961.2.g.k.235.2		16
155.134	even	30		31.2.g.a.10.2	✓	16
155.139	odd	10		961.2.g.n.844.1		16
155.144	even	30		961.2.g.t.846.1		16
155.149	even	6		961.2.d.o.388.3		16
155.154	odd	2		961.2.g.l.338.2		16
465.14	odd	30		8649.2.a.bf.1.5		8
465.134	odd	30		279.2.y.c.10.1		16
465.389	even	30		8649.2.a.be.1.5		8
620.599	odd	30		496.2.bg.c.289.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	155.134	even	30
31.2.g.a.28.2	yes	16	5.4	even	2
279.2.y.c.10.1		16	465.134	odd	30
279.2.y.c.28.1		16	15.14	odd	2
496.2.bg.c.289.1		16	620.599	odd	30
496.2.bg.c.369.1		16	20.19	odd	2
775.2.bl.a.276.1		16	1.1	even	1	trivial
775.2.bl.a.351.1		16	31.10	even	15	inner
775.2.ck.a.524.2		32	5.3	odd	4
775.2.ck.a.524.3		32	5.2	odd	4
775.2.ck.a.599.2		32	155.72	odd	60
775.2.ck.a.599.3		32	155.103	odd	60
961.2.a.i.1.4		8	155.14	even	30
961.2.a.j.1.4		8	155.79	odd	30
961.2.c.i.439.4		16	155.84	odd	30
961.2.c.i.521.4		16	155.54	odd	10
961.2.c.j.439.4		16	155.9	even	30
961.2.c.j.521.4		16	155.39	even	10
961.2.d.n.374.3		16	155.74	odd	30
961.2.d.n.388.3		16	155.99	odd	6
961.2.d.o.374.3		16	155.19	even	30
961.2.d.o.388.3		16	155.149	even	6
961.2.d.p.531.2		16	155.59	even	30
961.2.d.p.628.2		16	155.69	even	30
961.2.d.q.531.2		16	155.34	odd	30
961.2.d.q.628.2		16	155.24	odd	30
961.2.g.j.235.2		16	155.119	odd	6
961.2.g.j.732.2		16	155.29	odd	10
961.2.g.k.235.2		16	155.129	even	6
961.2.g.k.732.2		16	155.64	even	10
961.2.g.l.338.2		16	155.154	odd	2
961.2.g.l.816.2		16	155.114	odd	30
961.2.g.m.448.1		16	155.89	odd	10
961.2.g.m.547.1		16	155.44	odd	30
961.2.g.n.844.1		16	155.139	odd	10
961.2.g.n.846.1		16	155.104	odd	30
961.2.g.s.448.1		16	155.4	even	10
961.2.g.s.547.1		16	155.49	even	30
961.2.g.t.844.1		16	155.109	even	10
961.2.g.t.846.1		16	155.144	even	30
8649.2.a.be.1.5		8	465.389	even	30
8649.2.a.bf.1.5		8	465.14	odd	30

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bl (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.284315 - 0.206567i) q^{2} +(-0.302431 + 2.87744i) q^{3} +(-0.579869 + 1.78465i) q^{4} +(0.508398 + 0.880572i) q^{6} +(-1.05848 + 0.224987i) q^{7} +(0.420982 + 1.29565i) q^{8} +(-5.25377 - 1.11672i) q^{9} +(-1.62690 - 1.80686i) q^{11} +(-4.95987 - 2.20827i) q^{12} +(-2.62521 + 1.16882i) q^{13} +(-0.254466 + 0.282614i) q^{14} +(-2.64890 - 1.92454i) q^{16} +(1.22101 - 1.35606i) q^{17} +(-1.72440 + 0.767753i) q^{18} +(1.93514 + 0.861580i) q^{19} +(-0.327269 - 3.11375i) q^{21} +(-0.835790 - 0.177653i) q^{22} +(0.136652 + 0.420572i) q^{23} +(-3.85547 + 0.819506i) q^{24} +(-0.504947 + 0.874594i) q^{26} +(2.11998 - 6.52462i) q^{27} +(0.212256 - 2.01948i) q^{28} +(2.55579 - 1.85689i) q^{29} +(1.15354 + 5.44696i) q^{31} -3.87532 q^{32} +(5.69116 - 4.13487i) q^{33} +(0.0670322 - 0.637769i) q^{34} +(5.03946 - 8.72860i) q^{36} +(1.57338 + 2.72517i) q^{37} +(0.728163 - 0.154776i) q^{38} +(-2.56926 - 7.90738i) q^{39} +(0.726079 + 6.90818i) q^{41} +(-0.736246 - 0.817684i) q^{42} +(7.68509 + 3.42162i) q^{43} +(4.16801 - 1.85572i) q^{44} +(0.125728 + 0.0913471i) q^{46} +(-6.44144 - 4.67998i) q^{47} +(6.33887 - 7.04003i) q^{48} +(-5.32506 + 2.37087i) q^{49} +(3.53273 + 3.92349i) q^{51} +(-0.563659 - 5.36285i) q^{52} +(-4.86824 - 1.03478i) q^{53} +(-0.745029 - 2.29296i) q^{54} +(-0.737104 - 1.27670i) q^{56} +(-3.06439 + 5.30768i) q^{57} +(0.343078 - 1.05588i) q^{58} +(1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +(1.45313 + 1.31037i) q^{62} +5.81225 q^{63} +(4.19600 - 3.04857i) q^{64} +(0.763955 - 2.35121i) q^{66} +(-3.21879 + 5.57511i) q^{67} +(1.71208 + 2.96541i) q^{68} +(-1.25150 + 0.266015i) q^{69} +(-1.64121 - 0.348850i) q^{71} +(-0.764860 - 7.27716i) q^{72} +(-9.60883 - 10.6717i) q^{73} +(1.01026 + 0.449798i) q^{74} +(-2.65975 + 2.95395i) q^{76} +(2.12856 + 1.54649i) q^{77} +(-2.36388 - 1.71746i) q^{78} +(-2.30692 + 2.56210i) q^{79} +(3.41274 + 1.51945i) q^{81} +(1.63344 + 1.81412i) q^{82} +(1.34357 + 12.7832i) q^{83} +(5.74674 + 1.22151i) q^{84} +(2.89178 - 0.614667i) q^{86} +(4.57015 + 7.91573i) q^{87} +(1.65616 - 2.86855i) q^{88} +(0.698188 - 2.14880i) q^{89} +(2.51576 - 1.82781i) q^{91} -0.829816 q^{92} +(-16.0222 + 1.67190i) q^{93} -2.79812 q^{94} +(1.17202 - 11.1510i) q^{96} +(-1.05463 + 3.24582i) q^{97} +(-1.02425 + 1.77405i) q^{98} +(6.52961 + 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 12 q^{3} - 14 q^{4} + 11 q^{6} - 2 q^{7} - 17 q^{8} - 10 q^{9} - 7 q^{11} - 5 q^{12} + 7 q^{13} - 6 q^{14} - 2 q^{16} + 6 q^{17} + 3 q^{18} + 16 q^{19} + 9 q^{21} - 9 q^{22} - q^{23} - 20 q^{24}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q + 6 * q^2 + 12 * q^3 - 14 * q^4 + 11 * q^6 - 2 * q^7 - 17 * q^8 - 10 * q^9 - 7 * q^11 - 5 * q^12 + 7 * q^13 - 6 * q^14 - 2 * q^16 + 6 * q^17 + 3 * q^18 + 16 * q^19 + 9 * q^21 - 9 * q^22 - q^23 - 20 * q^24 + 9 * q^26 - 9 * q^27 + 30 * q^28 - 14 * q^29 + 15 * q^31 + 42 * q^32 + 13 * q^33 - 32 * q^34 + q^36 + 8 * q^37 - 8 * q^38 - 3 * q^39 - 8 * q^41 - 69 * q^42 - 23 * q^43 + 39 * q^44 + 34 * q^46 - 14 * q^47 - 34 * q^48 + 2 * q^49 - 42 * q^51 - 29 * q^52 - 6 * q^53 - 46 * q^54 - 30 * q^56 + 17 * q^57 + 15 * q^58 + 4 * q^59 - 60 * q^61 + 25 * q^62 + 46 * q^63 + 23 * q^64 - 30 * q^66 - 13 * q^67 - 30 * q^68 + 38 * q^69 - 14 * q^71 - 37 * q^72 - 2 * q^73 + 13 * q^74 - 12 * q^76 - 18 * q^77 + 15 * q^78 + 18 * q^79 + 23 * q^81 - 14 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 17 * q^88 + q^89 + 8 * q^91 + 64 * q^92 - 17 * q^93 + 44 * q^94 + 8 * q^96 - 3 * q^97 + 10 * q^98 + 6 * q^99

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