LMFDB - Embedded newform 968.2.o.c.245.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.4
Character	$\chi$	$=$	968.245
Dual form			968.2.o.c.565.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.323190 + 1.37679i) q^{2} +(2.66099 - 0.864609i) q^{3} +(-1.79110 - 0.889929i) q^{4} +(0.681209 - 0.937603i) q^{5} +(0.330378 + 3.94306i) q^{6} +(-0.935846 + 2.88024i) q^{7} +(1.80411 - 2.17835i) q^{8} +(3.90628 - 2.83808i) q^{9} +O(q^{10})$	\(q+(-0.323190 + 1.37679i) q^{2} +(2.66099 - 0.864609i) q^{3} +(-1.79110 - 0.889929i) q^{4} +(0.681209 - 0.937603i) q^{5} +(0.330378 + 3.94306i) q^{6} +(-0.935846 + 2.88024i) q^{7} +(1.80411 - 2.17835i) q^{8} +(3.90628 - 2.83808i) q^{9} +(1.07072 + 1.24090i) q^{10} +(-5.53553 - 0.819496i) q^{12} +(-2.43570 - 3.35245i) q^{13} +(-3.66302 - 2.21933i) q^{14} +(1.00203 - 3.08393i) q^{15} +(2.41605 + 3.18790i) q^{16} +(5.91501 + 4.29750i) q^{17} +(2.64497 + 6.29536i) q^{18} +(4.54406 - 1.47646i) q^{19} +(-2.05451 + 1.07311i) q^{20} +8.47343i q^{21} +5.24264 q^{23} +(2.91730 - 7.35641i) q^{24} +(1.13003 + 3.47788i) q^{25} +(5.40281 - 2.26997i) q^{26} +(3.00700 - 4.13878i) q^{27} +(4.23940 - 4.32595i) q^{28} +(-2.91163 - 0.946045i) q^{29} +(3.92208 + 2.37628i) q^{30} +(5.18921 - 3.77018i) q^{31} +(-5.16991 + 2.29610i) q^{32} +(-7.82843 + 6.75481i) q^{34} +(2.06301 + 2.83950i) q^{35} +(-9.52221 + 1.60696i) q^{36} +(-6.42420 - 2.08735i) q^{37} +(0.564173 + 6.73339i) q^{38} +(-9.37994 - 6.81492i) q^{39} +(-0.813450 - 3.17545i) q^{40} +(-0.387640 - 1.19303i) q^{41} +(-11.6661 - 2.73853i) q^{42} -7.39104i q^{43} -5.59587i q^{45} +(-1.69437 + 7.21801i) q^{46} +(0.255998 + 0.787881i) q^{47} +(9.18538 + 6.39403i) q^{48} +(-1.75684 - 1.27642i) q^{49} +(-5.15351 + 0.431799i) q^{50} +(19.4554 + 6.32146i) q^{51} +(1.37913 + 8.17217i) q^{52} +(4.65158 + 6.40236i) q^{53} +(4.72640 + 5.47762i) q^{54} +(4.58579 + 7.23486i) q^{56} +(10.8152 - 7.85767i) q^{57} +(2.24351 - 3.70295i) q^{58} +(-4.86543 - 1.58087i) q^{59} +(-4.53922 + 4.63189i) q^{60} +(3.07191 - 4.22813i) q^{61} +(3.51364 + 8.36293i) q^{62} +(4.51866 + 13.9070i) q^{63} +(-1.49039 - 7.85995i) q^{64} -4.80249 q^{65} -2.79793i q^{67} +(-6.76988 - 12.9612i) q^{68} +(13.9506 - 4.53283i) q^{69} +(-4.57613 + 1.92264i) q^{70} +(-6.13703 - 4.45881i) q^{71} +(0.865035 - 13.6294i) q^{72} +(-0.387640 + 1.19303i) q^{73} +(4.95008 - 8.17016i) q^{74} +(6.01400 + 8.27756i) q^{75} +(-9.45280 - 1.39942i) q^{76} +(12.4142 - 10.7117i) q^{78} +(-11.8300 + 8.59501i) q^{79} +(4.63482 - 0.0936773i) q^{80} +(-0.0530189 + 0.163176i) q^{81} +(1.76784 - 0.148122i) q^{82} +(-0.527057 + 0.725432i) q^{83} +(7.54075 - 15.1767i) q^{84} +(8.05871 - 2.61843i) q^{85} +(10.1759 + 2.38871i) q^{86} -8.56578 q^{87} +0.656854 q^{89} +(7.70433 + 1.80853i) q^{90} +(11.9353 - 3.87801i) q^{91} +(-9.39008 - 4.66558i) q^{92} +(10.5487 - 14.5191i) q^{93} +(-1.16748 + 0.0978201i) q^{94} +(1.71113 - 5.26630i) q^{95} +(-11.7718 + 10.5799i) q^{96} +(-9.01418 + 6.54918i) q^{97} +(2.32515 - 2.00627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{4} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^4 + 16 * q^9	$ 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49} + 192 q^{56} + 32 q^{60} + 16 q^{64} - 8 q^{70} - 72 q^{71} + 352 q^{78} - 56 q^{80} + 24 q^{81} + 56 q^{82} + 32 q^{86} - 160 q^{89} + 16 q^{92} + 24 q^{97}+O(q^{100}) $ 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.323190	+	1.37679i	−0.228530	+	0.973537i
$2$	−0.323190	+	1.37679i	−0.228530	+	0.973537i
$3$	2.66099	−	0.864609i	1.53632	−	0.499182i	0.585965	−	0.810336i	$-0.300716\pi$
$3$	2.66099	−	0.864609i	1.53632	−	0.499182i	0.950359	+	0.311154i	$0.100716\pi$
$4$	−1.79110	−	0.889929i	−0.895548	−	0.444964i
$5$	0.681209	−	0.937603i	0.304646	−	0.419309i	−0.629056	−	0.777360i	$-0.716559\pi$
$5$	0.681209	−	0.937603i	0.304646	−	0.419309i	0.933702	+	0.358051i	$0.116559\pi$
$6$	0.330378	+	3.94306i	0.134876	+	1.60975i
$7$	−0.935846	+	2.88024i	−0.353716	+	1.08863i	0.603034	+	0.797716i	$0.293959\pi$
$7$	−0.935846	+	2.88024i	−0.353716	+	1.08863i	−0.956750	+	0.290911i	$0.906041\pi$
$8$	1.80411	−	2.17835i	0.637849	−	0.770162i
$9$	3.90628	−	2.83808i	1.30209	−	0.946026i
$10$	1.07072	+	1.24090i	0.338592	+	0.392409i
$11$		0			0
$11$		0			0
$12$	−5.53553	−	0.819496i	−1.59797	−	0.236568i
$13$	−2.43570	−	3.35245i	−0.675542	−	0.929803i	0.324328	−	0.945945i	$-0.394862\pi$
$13$	−2.43570	−	3.35245i	−0.675542	−	0.929803i	−0.999870	+	0.0161415i	$0.994862\pi$
$14$	−3.66302	−	2.21933i	−0.978984	−	0.593140i
$15$	1.00203	−	3.08393i	0.258723	−	0.796268i
$16$	2.41605	+	3.18790i	0.604013	+	0.796974i
$17$	5.91501	+	4.29750i	1.43460	+	1.04230i	0.989137	+	0.146997i	$0.0469609\pi$
$17$	5.91501	+	4.29750i	1.43460	+	1.04230i	0.445463	+	0.895300i	$0.353039\pi$
$18$	2.64497	+	6.29536i	0.623424	+	1.48383i
$19$	4.54406	−	1.47646i	1.04248	−	0.338722i	0.262767	−	0.964859i	$-0.415365\pi$
$19$	4.54406	−	1.47646i	1.04248	−	0.338722i	0.779713	+	0.626137i	$0.215365\pi$
$20$	−2.05451	+	1.07311i	−0.459403	+	0.239955i
$21$			8.47343i			1.84905i
$22$		0			0
$23$	5.24264			1.09317			0.546583	−	0.837405i	$-0.315928\pi$
$23$	5.24264			1.09317			0.546583	+	0.837405i	$0.315928\pi$
$24$	2.91730	−	7.35641i	0.595492	−	1.50162i
$25$	1.13003	+	3.47788i	0.226006	+	0.695575i
$26$	5.40281	−	2.26997i	1.05958	−	0.445177i
$27$	3.00700	−	4.13878i	0.578698	−	0.796509i
$28$	4.23940	−	4.32595i	0.801170	−	0.817527i
$29$	−2.91163	−	0.946045i	−0.540676	−	0.175676i	0.0259322	−	0.999664i	$-0.491745\pi$
$29$	−2.91163	−	0.946045i	−0.540676	−	0.175676i	−0.566608	+	0.823987i	$0.691745\pi$
$30$	3.92208	+	2.37628i	0.716071	+	0.433848i
$31$	5.18921	−	3.77018i	0.932009	−	0.677144i	−0.0144747	−	0.999895i	$-0.504608\pi$
$31$	5.18921	−	3.77018i	0.932009	−	0.677144i	0.946484	+	0.322751i	$0.104608\pi$
$32$	−5.16991	+	2.29610i	−0.913919	+	0.405897i
$33$		0			0
$34$	−7.82843	+	6.75481i	−1.34256	+	1.15844i
$35$	2.06301	+	2.83950i	0.348713	+	0.479962i
$36$	−9.52221	+	1.60696i	−1.58704	+	0.267827i
$37$	−6.42420	−	2.08735i	−1.05613	−	0.343158i	−0.271060	−	0.962562i	$-0.587374\pi$
$37$	−6.42420	−	2.08735i	−1.05613	−	0.343158i	−0.785072	+	0.619404i	$0.787374\pi$
$38$	0.564173	+	6.73339i	0.0915209	+	1.09230i
$39$	−9.37994	−	6.81492i	−1.50199	−	1.09126i
$40$	−0.813450	−	3.17545i	−0.128618	−	0.502082i
$41$	−0.387640	−	1.19303i	−0.0605392	−	0.186320i	0.916213	−	0.400691i	$-0.131230\pi$
$41$	−0.387640	−	1.19303i	−0.0605392	−	0.186320i	−0.976752	+	0.214371i	$0.931230\pi$
$42$	−11.6661	−	2.73853i	−1.80012	−	0.422564i
$43$		−	7.39104i		−	1.12712i	−0.826074	−	0.563561i	$-0.809431\pi$
$43$		−	7.39104i		−	1.12712i	0.826074	−	0.563561i	$-0.190569\pi$
$44$		0			0
$45$		−	5.59587i		−	0.834182i
$46$	−1.69437	+	7.21801i	−0.249821	+	1.06424i
$47$	0.255998	+	0.787881i	0.0373412	+	0.114924i	0.967990	−	0.250990i	$-0.0807562\pi$
$47$	0.255998	+	0.787881i	0.0373412	+	0.114924i	−0.930648	+	0.365915i	$0.880756\pi$
$48$	9.18538	+	6.39403i	1.32580	+	0.922898i
$49$	−1.75684	−	1.27642i	−0.250977	−	0.182346i
$50$	−5.15351	+	0.431799i	−0.728817	+	0.0610656i
$51$	19.4554	+	6.32146i	2.72431	+	0.885181i
$52$	1.37913	+	8.17217i	0.191251	+	1.13328i
$53$	4.65158	+	6.40236i	0.638944	+	0.879431i	0.998559	−	0.0536696i	$-0.0170918\pi$
$53$	4.65158	+	6.40236i	0.638944	+	0.879431i	−0.359614	+	0.933101i	$0.617092\pi$
$54$	4.72640	+	5.47762i	0.643181	+	0.745410i
$55$		0			0
$56$	4.58579	+	7.23486i	0.612801	+	0.966798i
$57$	10.8152	−	7.85767i	1.43250	−	1.04077i
$58$	2.24351	−	3.70295i	0.294588	−	0.486221i
$59$	−4.86543	−	1.58087i	−0.633425	−	0.205812i	−0.0253333	−	0.999679i	$-0.508065\pi$
$59$	−4.86543	−	1.58087i	−0.633425	−	0.205812i	−0.608092	+	0.793867i	$0.708065\pi$
$60$	−4.53922	+	4.63189i	−0.586010	+	0.597974i
$61$	3.07191	−	4.22813i	0.393318	−	0.541356i	−0.565733	−	0.824588i	$-0.691407\pi$
$61$	3.07191	−	4.22813i	0.393318	−	0.541356i	0.959051	+	0.283232i	$0.0914067\pi$
$62$	3.51364	+	8.36293i	0.446233	+	1.06209i
$63$	4.51866	+	13.9070i	0.569298	+	1.75212i
$64$	−1.49039	−	7.85995i	−0.186298	−	0.982493i
$65$	−4.80249			−0.595676
$66$		0			0
$67$		−	2.79793i		−	0.341822i	−0.985286	−	0.170911i	$-0.945329\pi$
$67$		−	2.79793i		−	0.341822i	0.985286	−	0.170911i	$-0.0546710\pi$
$68$	−6.76988	−	12.9612i	−0.820968	−	1.57177i
$69$	13.9506	−	4.53283i	1.67946	−	0.545689i
$70$	−4.57613	+	1.92264i	−0.546952	+	0.229799i
$71$	−6.13703	−	4.45881i	−0.728331	−	0.529164i	0.160704	−	0.987003i	$-0.448624\pi$
$71$	−6.13703	−	4.45881i	−0.728331	−	0.529164i	−0.889035	+	0.457839i	$0.848624\pi$
$72$	0.865035	−	13.6294i	0.101945	−	1.60624i
$73$	−0.387640	+	1.19303i	−0.0453698	+	0.139634i	−0.971175	−	0.238366i	$-0.923388\pi$
$73$	−0.387640	+	1.19303i	−0.0453698	+	0.139634i	0.925806	+	0.378000i	$0.123388\pi$
$74$	4.95008	−	8.17016i	0.575435	−	0.949762i
$75$	6.01400	+	8.27756i	0.694437	+	0.955811i
$76$	−9.45280	−	1.39942i	−1.08431	−	0.160524i
$77$		0			0
$78$	12.4142	−	10.7117i	1.40563	−	1.21286i
$79$	−11.8300	+	8.59501i	−1.33098	+	0.967014i	−0.331256	+	0.943541i	$0.607472\pi$
$79$	−11.8300	+	8.59501i	−1.33098	+	0.967014i	−0.999724	+	0.0234730i	$0.992528\pi$
$80$	4.63482	−	0.0936773i	0.518189	−	0.0104734i
$81$	−0.0530189	+	0.163176i	−0.00589099	+	0.0181306i
$82$	1.76784	−	0.148122i	0.195225	−	0.0163574i
$83$	−0.527057	+	0.725432i	−0.0578520	+	0.0796265i	−0.836963	−	0.547260i	$-0.815671\pi$
$83$	−0.527057	+	0.725432i	−0.0578520	+	0.0796265i	0.779111	+	0.626886i	$0.215671\pi$
$84$	7.54075	−	15.1767i	0.822763	−	1.65592i
$85$	8.05871	−	2.61843i	0.874090	−	0.284009i
$86$	10.1759	+	2.38871i	1.09730	+	0.257581i
$87$	−8.56578			−0.918348
$88$		0			0
$89$	0.656854			0.0696264			0.0348132	−	0.999394i	$-0.488916\pi$
$89$	0.656854			0.0696264			0.0348132	+	0.999394i	$0.488916\pi$
$90$	7.70433	+	1.80853i	0.812107	+	0.190636i
$91$	11.9353	−	3.87801i	1.25116	−	0.406526i
$92$	−9.39008	−	4.66558i	−0.978983	−	0.486420i
$93$	10.5487	−	14.5191i	1.09385	−	1.50556i
$94$	−1.16748	+	0.0978201i	−0.120417	+	0.0100894i
$95$	1.71113	−	5.26630i	0.175558	−	0.540311i
$96$	−11.7718	+	10.5799i	−1.20146	+	1.07980i
$97$	−9.01418	+	6.54918i	−0.915251	+	0.664969i	−0.942337	−	0.334664i	$-0.891377\pi$
$97$	−9.01418	+	6.54918i	−0.915251	+	0.664969i	0.0270864	+	0.999633i	$0.491377\pi$
$98$	2.32515	−	2.00627i	0.234876	−	0.202664i
$99$		0			0
$100$	1.07107	−	7.23486i	0.107107	−	0.723486i
$101$	−2.43570	−	3.35245i	−0.242361	−	0.333582i	0.670457	−	0.741949i	$-0.266098\pi$
$101$	−2.43570	−	3.35245i	−0.242361	−	0.333582i	−0.912818	+	0.408367i	$0.866098\pi$
$102$	−14.9911	+	24.7430i	−1.48434	+	2.44992i
$103$	−4.11416	+	12.6621i	−0.405380	+	1.24763i	0.515197	+	0.857072i	$0.327719\pi$
$103$	−4.11416	+	12.6621i	−0.405380	+	1.24763i	−0.920577	+	0.390561i	$0.872281\pi$
$104$	−11.6971	−	0.742392i	−1.14699	−	0.0727975i
$105$	7.94472	+	5.77217i	0.775325	+	0.563307i
$106$	−10.3180	+	4.33507i	−1.00218	+	0.421060i
$107$	−11.5734	+	3.76041i	−1.11884	+	0.363533i	−0.809324	−	0.587362i	$-0.800166\pi$
$107$	−11.5734	+	3.76041i	−1.11884	+	0.363533i	−0.309514	+	0.950895i	$0.600166\pi$
$108$	−9.06905	+	4.73694i	−0.872670	+	0.455812i
$109$			10.4525i			1.00117i	0.865688	+	0.500584i	$0.166881\pi$
$109$			10.4525i			1.00117i	−0.865688	+	0.500584i	$0.833119\pi$
$110$		0			0
$111$	−18.8995			−1.79386
$112$	−11.4430	+	3.97543i	−1.08126	+	0.375643i
$113$	−4.16718	−	12.8253i	−0.392015	−	1.20650i	−0.931262	−	0.364351i	$-0.881291\pi$
$113$	−4.16718	−	12.8253i	−0.392015	−	1.20650i	0.539246	−	0.842148i	$-0.318709\pi$
$114$	7.32301	+	17.4297i	0.685863	+	1.63244i
$115$	3.57133	−	4.91552i	0.333029	−	0.458374i
$116$	4.37309	+	4.28560i	0.406032	+	0.397908i
$117$	−19.0290	−	6.18291i	−1.75924	−	0.571610i
$118$	3.74899	−	6.18775i	0.345122	−	0.569628i
$119$	−17.9134	+	13.0148i	−1.64212	+	1.19307i
$120$	−4.91010	−	7.74652i	−0.448229	−	0.707158i
$121$		0			0
$122$	4.82843	+	5.59587i	0.437145	+	0.506626i
$123$	−2.06301	−	2.83950i	−0.186016	−	0.256029i
$124$	−12.6496	+	2.13473i	−1.13596	+	0.191705i
$125$	9.54175	+	3.10030i	0.853440	+	0.277299i
$126$	−20.6074	+	1.72664i	−1.83585	+	0.153821i
$127$	−4.47979	−	3.25475i	−0.397517	−	0.288813i	0.371012	−	0.928628i	$-0.379011\pi$
$127$	−4.47979	−	3.25475i	−0.397517	−	0.288813i	−0.768529	+	0.639815i	$0.779011\pi$
$128$	11.3032	+	0.488309i	0.999068	+	0.0431609i
$129$	−6.39035	−	19.6675i	−0.562639	−	1.73163i
$130$	1.55212	−	6.61202i	0.136130	−	0.579912i
$131$		−	10.9008i		−	0.952411i	−0.879334	−	0.476206i	$-0.842012\pi$
$131$		−	10.9008i		−	0.952411i	0.879334	−	0.476206i	$-0.157988\pi$
$132$		0			0
$133$			14.4697i			1.25468i
$134$	3.85216	+	0.904264i	0.332776	+	0.0781165i
$135$	−1.83214	−	5.63875i	−0.157686	−	0.485306i
$136$	20.0328	−	5.13177i	1.71780	−	0.440046i
$137$	−2.42705	−	1.76336i	−0.207357	−	0.150654i	0.479260	−	0.877673i	$-0.340905\pi$
$137$	−2.42705	−	1.76336i	−0.207357	−	0.150654i	−0.686617	+	0.727019i	$0.740905\pi$
$138$	1.73205	+	20.6720i	0.147442	+	1.75972i
$139$	−5.39686	−	1.75355i	−0.457756	−	0.148734i	0.0710573	−	0.997472i	$-0.477363\pi$
$139$	−5.39686	−	1.75355i	−0.457756	−	0.148734i	−0.528813	+	0.848738i	$0.677363\pi$
$140$	−1.16811	−	6.92175i	−0.0987232	−	0.584994i
$141$	1.36242	+	1.87521i	0.114736	+	0.157921i
$142$	8.12227	−	7.00835i	0.681606	−	0.588128i
$143$		0			0
$144$	18.4853	+	5.59587i	1.54044	+	0.466322i
$145$	−2.87044	+	2.08550i	−0.238377	+	0.173191i
$146$	−1.51727	−	0.919275i	−0.125570	−	0.0760797i
$147$	−5.77854	−	1.87756i	−0.476606	−	0.154859i
$148$	9.64878	+	9.45573i	0.793124	+	0.777256i
$149$	−11.8698	+	16.3373i	−0.972408	+	1.33841i	−0.0315873	+	0.999501i	$0.510056\pi$
$149$	−11.8698	+	16.3373i	−0.972408	+	1.33841i	−0.940821	+	0.338904i	$0.889944\pi$
$150$	−13.3401	+	5.60479i	−1.08922	+	0.457629i
$151$	−1.87169	−	5.76047i	−0.152316	−	0.468781i	0.845563	−	0.533876i	$-0.179265\pi$
$151$	−1.87169	−	5.76047i	−0.152316	−	0.468781i	−0.997879	+	0.0650949i	$0.979265\pi$
$152$	4.98175	−	12.5622i	0.404073	−	1.01893i
$153$	35.3023			2.85402
$154$		0			0
$155$		−	7.43370i		−	0.597089i
$156$	10.7356	+	20.5537i	0.859534	+	1.64561i
$157$	−2.01533	+	0.654819i	−0.160841	+	0.0522603i	−0.388331	−	0.921520i	$-0.626948\pi$
$157$	−2.01533	+	0.654819i	−0.160841	+	0.0522603i	0.227490	+	0.973780i	$0.426948\pi$
$158$	−8.01017	−	19.0653i	−0.637255	−	1.51675i
$159$	17.9134	+	13.0148i	1.42062	+	1.03214i
$160$	−1.36895	+	6.41145i	−0.108225	+	0.506869i
$161$	−4.90630	+	15.1000i	−0.386671	+	1.19005i
$162$	−0.207523	−	0.125733i	−0.0163046	−	0.00987848i
$163$	3.85350	+	5.30389i	0.301829	+	0.415432i	0.932811	−	0.360365i	$-0.117348\pi$
$163$	3.85350	+	5.30389i	0.301829	+	0.415432i	−0.630982	+	0.775797i	$0.717348\pi$
$164$	−0.367414	+	2.48181i	−0.0286902	+	0.193797i
$165$		0			0
$166$	−0.828427	−	0.960099i	−0.0642984	−	0.0745181i
$167$	2.45008	−	1.78008i	0.189593	−	0.137747i	−0.488940	−	0.872317i	$-0.662616\pi$
$167$	2.45008	−	1.78008i	0.189593	−	0.137747i	0.678532	+	0.734570i	$0.262616\pi$
$168$	18.4581	+	15.2870i	1.42407	+	1.17942i
$169$	−1.28909	+	3.96740i	−0.0991605	+	0.305185i
$170$	1.00054	+	11.9414i	0.0767377	+	0.915863i
$171$	13.5601	−	18.6639i	1.03697	−	1.42726i
$172$	−6.57750	+	13.2381i	−0.501529	+	1.00939i
$173$	2.05883	−	0.668955i	0.156530	−	0.0508597i	−0.229704	−	0.973261i	$-0.573776\pi$
$173$	2.05883	−	0.668955i	0.156530	−	0.0508597i	0.386234	+	0.922401i	$0.373776\pi$
$174$	2.76837	−	11.7933i	0.209870	−	0.894046i
$175$	−11.0746			−0.837164
$176$		0			0
$177$	−14.3137			−1.07588
$178$	−0.212289	+	0.904350i	−0.0159117	+	0.0677839i
$179$	−9.27431	+	3.01340i	−0.693194	+	0.225232i	−0.634363	−	0.773035i	$-0.718737\pi$
$179$	−9.27431	+	3.01340i	−0.693194	+	0.225232i	−0.0588314	+	0.998268i	$0.518737\pi$
$180$	−4.97992	+	10.0227i	−0.371181	+	0.747051i
$181$	−12.4755	+	17.1710i	−0.927294	+	1.27631i	0.0336123	+	0.999435i	$0.489299\pi$
$181$	−12.4755	+	17.1710i	−0.927294	+	1.27631i	−0.960906	+	0.276875i	$0.910701\pi$
$182$	1.48184	+	17.6857i	0.109841	+	1.31095i
$183$	4.51866	−	13.9070i	0.334029	−	1.02804i
$184$	9.45829	−	11.4203i	0.697275	−	0.841915i
$185$	−6.33333	+	4.60143i	−0.465636	+	0.338304i
$186$	16.5804	+	19.2158i	1.21574	+	1.40897i
$187$		0			0
$188$	0.242641	−	1.63899i	0.0176964	−	0.119536i
$189$	9.10658	+	12.5341i	0.662407	+	0.911724i
$190$	6.69757	+	4.05788i	0.485893	+	0.294389i
$191$	0.639995	−	1.96970i	0.0463084	−	0.142523i	−0.925229	−	0.379410i	$-0.876127\pi$
$191$	0.639995	−	1.96970i	0.0463084	−	0.142523i	0.971537	+	0.236887i	$0.0761271\pi$
$192$	−10.7617	−	19.6267i	−0.776657	−	1.41643i
$193$	11.8300	+	8.59501i	0.851543	+	0.618682i	0.925571	−	0.378574i	$-0.123585\pi$
$193$	11.8300	+	8.59501i	0.851543	+	0.618682i	−0.0740280	+	0.997256i	$0.523585\pi$
$194$	−6.10355	−	14.5273i	−0.438210	−	1.04300i
$195$	−12.7794	+	4.15228i	−0.915151	+	0.297351i
$196$	2.01075	+	3.84965i	0.143625	+	0.274975i
$197$		−	6.49435i		−	0.462704i	−0.972870	−	0.231352i	$-0.925685\pi$
$197$		−	6.49435i		−	0.462704i	0.972870	−	0.231352i	$-0.0743148\pi$
$198$		0			0
$199$	11.1716			0.791932			0.395966	−	0.918265i	$-0.370410\pi$
$199$	11.1716			0.791932			0.395966	+	0.918265i	$0.370410\pi$
$200$	9.61471	+	3.81287i	0.679863	+	0.269610i
$201$	−2.41912	−	7.44528i	−0.170631	−	0.525149i
$202$	5.40281	−	2.26997i	0.380141	−	0.159714i
$203$	5.44967	−	7.50083i	0.382492	−	0.526455i
$204$	−29.2209	−	28.6363i	−2.04587	−	2.00494i
$205$	−1.38266	−	0.449252i	−0.0965689	−	0.0313771i
$206$	−16.1034	−	9.75659i	−1.12198	−	0.679774i
$207$	20.4792	−	14.8790i	1.42340	−	1.03416i
$208$	4.80249	−	15.8645i	0.332993	−	1.10000i
$209$		0			0
$210$	−10.5147	+	9.07269i	−0.725585	+	0.626075i
$211$	2.01780	+	2.77726i	0.138911	+	0.191195i	0.872805	−	0.488070i	$-0.162299\pi$
$211$	2.01780	+	2.77726i	0.138911	+	0.191195i	−0.733893	+	0.679265i	$0.762299\pi$
$212$	−2.63380	−	15.6068i	−0.180890	−	1.07188i
$213$	−20.1857	−	6.55874i	−1.38310	−	0.449397i
$214$	−1.43690	−	17.1494i	−0.0982246	−	1.17231i
$215$	−6.92986	−	5.03484i	−0.472613	−	0.343373i
$216$	−3.59074	−	14.0171i	−0.244319	−	0.953743i
$217$	6.00271	+	18.4745i	0.407491	+	1.25413i
$218$	−14.3909	−	3.37814i	−0.974674	−	0.228797i
$219$			3.50981i			0.237171i
$220$		0			0
$221$		−	30.2972i		−	2.03801i
$222$	6.10813	−	26.0206i	0.409951	−	1.74639i
$223$	0.0840767	+	0.258761i	0.00563019	+	0.0173280i	0.953832	−	0.300340i	$-0.0971002\pi$
$223$	0.0840767	+	0.258761i	0.00563019	+	0.0173280i	−0.948202	+	0.317668i	$0.897100\pi$
$224$	−1.77508	−	17.0393i	−0.118603	−	1.13849i
$225$	14.2847	+	10.3784i	0.952313	+	0.691896i
$226$	19.0045	−	1.59233i	1.26416	−	0.105920i
$227$	−21.5143	−	6.99041i	−1.42795	−	0.463970i	−0.509833	−	0.860273i	$-0.670293\pi$
$227$	−21.5143	−	6.99041i	−1.42795	−	0.463970i	−0.918120	+	0.396303i	$0.870293\pi$
$228$	−26.3638	+	4.44913i	−1.74598	+	0.294651i
$229$	−0.116877	−	0.160867i	−0.00772345	−	0.0106304i	0.805138	−	0.593088i	$-0.202091\pi$
$229$	−0.116877	−	0.160867i	−0.00772345	−	0.0106304i	−0.812861	+	0.582457i	$0.802091\pi$
$230$	5.61341	+	6.50562i	0.370138	+	0.428968i
$231$		0			0
$232$	−7.31371	+	4.63577i	−0.480168	+	0.304353i
$233$	−6.92986	+	5.03484i	−0.453990	+	0.329843i	−0.791169	−	0.611597i	$-0.790527\pi$
$233$	−6.92986	+	5.03484i	−0.453990	+	0.329843i	0.337179	+	0.941441i	$0.390527\pi$
$234$	14.6626	−	24.2007i	0.958522	−	1.58205i
$235$	0.913108	+	0.296687i	0.0595646	+	0.0193537i
$236$	7.30759	+	7.16138i	0.475684	+	0.466166i
$237$	−24.0483	+	33.0996i	−1.56210	+	2.15005i
$238$	−12.1292	−	28.8692i	−0.786222	−	1.87131i
$239$	−5.61507	−	17.2814i	−0.363209	−	1.11784i	−0.951095	−	0.308899i	$-0.900040\pi$
$239$	−5.61507	−	17.2814i	−0.363209	−	1.11784i	0.587886	−	0.808944i	$-0.299960\pi$
$240$	12.2522	−	4.25658i	0.790878	−	0.274761i
$241$	11.0746			0.713380			0.356690	−	0.934223i	$-0.383905\pi$
$241$	11.0746			0.713380			0.356690	+	0.934223i	$0.383905\pi$
$242$		0			0
$243$			15.8275i			1.01533i
$244$	−9.26483	+	4.83920i	−0.593120	+	0.309798i
$245$	−2.39355	+	0.777711i	−0.152918	+	0.0496861i
$246$	4.57613	−	1.92264i	0.291763	−	0.122583i
$247$	−16.0177	−	11.6376i	−1.01918	−	0.740480i
$248$	1.14914	−	18.1057i	0.0729702	−	1.14971i
$249$	−0.775280	+	2.38607i	−0.0491314	+	0.151211i
$250$	−7.35226	+	12.1350i	−0.464998	+	0.767484i
$251$	−6.86050	−	9.44267i	−0.433031	−	0.596016i	0.535615	−	0.844463i	$-0.320080\pi$
$251$	−6.86050	−	9.44267i	−0.433031	−	0.596016i	−0.968646	+	0.248447i	$0.920080\pi$
$252$	4.28289	−	28.9301i	0.269797	−	1.82242i
$253$		0			0
$254$	5.92893	−	5.11582i	0.372014	−	0.320995i
$255$	19.1802	−	13.9353i	1.20111	−	0.872660i
$256$	−4.32537	+	15.4043i	−0.270336	+	0.962766i
$257$	0.468074	−	1.44058i	0.0291976	−	0.0898611i	−0.935396	−	0.353603i	$-0.884957\pi$
$257$	0.468074	−	1.44058i	0.0291976	−	0.0898611i	0.964593	+	0.263741i	$0.0849566\pi$
$258$	29.1433	−	2.44184i	1.81438	−	0.152022i
$259$	12.0241	−	16.5498i	0.747143	−	1.02835i
$260$	8.60173	+	4.27388i	0.533456	+	0.265054i
$261$	−14.0586	+	4.56791i	−0.870205	+	0.282747i
$262$	15.0082	+	3.52304i	0.927208	+	0.217654i
$263$	−11.5942			−0.714931			−0.357466	−	0.933926i	$-0.616359\pi$
$263$	−11.5942			−0.714931			−0.357466	+	0.933926i	$0.616359\pi$
$264$		0			0
$265$	9.17157			0.563405
$266$	−19.9217	−	4.67647i	−1.22148	−	0.286732i
$267$	1.74788	−	0.567922i	0.106969	−	0.0347563i
$268$	−2.48996	+	5.01137i	−0.152099	+	0.306118i
$269$	17.8083	−	24.5110i	1.08579	−	1.49446i	0.232804	−	0.972524i	$-0.425210\pi$
$269$	17.8083	−	24.5110i	1.08579	−	1.49446i	0.852985	−	0.521936i	$-0.174790\pi$
$270$	8.35550	−	0.700085i	0.508499	−	0.0426058i
$271$	9.19789	−	28.3082i	0.558732	−	1.71960i	−0.127146	−	0.991884i	$-0.540582\pi$
$271$	9.19789	−	28.3082i	0.558732	−	1.71960i	0.685878	−	0.727717i	$-0.259418\pi$
$272$	0.590977	+	29.2394i	0.0358332	+	1.77290i
$273$	28.4068	−	20.6387i	1.71926	−	1.24911i
$274$	3.21217	−	2.77164i	0.194054	−	0.167441i
$275$		0			0
$276$	−29.0208	−	4.29632i	−1.74685	−	0.258608i
$277$	16.6320	+	22.8920i	0.999320	+	1.37545i	0.925742	+	0.378156i	$0.123442\pi$
$277$	16.6320	+	22.8920i	0.999320	+	1.37545i	0.0735781	+	0.997289i	$0.476558\pi$
$278$	4.15847	−	6.86361i	0.249409	−	0.411652i
$279$	9.57043	−	29.4548i	0.572967	−	1.76341i
$280$	9.90730	+	0.628798i	0.592075	+	0.0375779i
$281$	−14.7005	−	10.6805i	−0.876956	−	0.637146i	0.0554886	−	0.998459i	$-0.482328\pi$
$281$	−14.7005	−	10.6805i	−0.876956	−	0.637146i	−0.932444	+	0.361314i	$0.882328\pi$
$282$	−3.02208	+	1.26971i	−0.179962	+	0.0756104i
$283$	1.20604	−	0.391865i	0.0716914	−	0.0232939i	−0.272952	−	0.962028i	$-0.588000\pi$
$283$	1.20604	−	0.391865i	0.0716914	−	0.0232939i	0.344643	+	0.938734i	$0.388000\pi$
$284$	7.02399	+	13.4477i	0.416797	+	0.797973i
$285$		−	15.4930i		−	0.917729i
$286$		0			0
$287$	3.79899			0.224247
$288$	−13.6786	+	23.6418i	−0.806018	+	1.39311i
$289$	11.2655	+	34.6716i	0.662675	+	2.03950i
$290$	−1.94359	−	4.62601i	−0.114132	−	0.271648i
$291$	−18.3242	+	25.2211i	−1.07418	+	1.47848i
$292$	1.75602	−	1.79187i	0.102763	−	0.104861i
$293$	27.9406	+	9.07844i	1.63230	+	0.530368i	0.974800	−	0.223082i	$-0.0716119\pi$
$293$	27.9406	+	9.07844i	1.63230	+	0.530368i	0.657505	+	0.753450i	$0.271612\pi$
$294$	4.45257	−	7.34902i	0.259679	−	0.428604i
$295$	−4.79661	+	3.48494i	−0.279269	+	0.202901i
$296$	−16.1369	+	10.2283i	−0.937940	+	0.594510i
$297$		0			0
$298$	−18.6569	−	21.6222i	−1.08076	−	1.25254i
$299$	−12.7695	−	17.5757i	−0.738479	−	1.01643i
$300$	−3.40522	−	20.1779i	−0.196600	−	1.16497i
$301$	21.2879	+	6.91687i	1.22702	+	0.398682i
$302$	8.53587	−	0.715197i	0.491184	−	0.0411550i
$303$	−9.37994	−	6.81492i	−0.538863	−	0.391507i
$304$	15.6855	+	10.9188i	0.899624	+	0.626236i
$305$	−1.87169	−	5.76047i	−0.107173	−	0.329844i
$306$	−11.4094	+	48.6039i	−0.652229	+	2.77850i
$307$		−	20.8281i		−	1.18872i	−0.804199	−	0.594361i	$-0.797405\pi$
$307$		−	20.8281i		−	1.18872i	0.804199	−	0.594361i	$-0.202595\pi$
$308$		0			0
$309$			37.2509i			2.11913i
$310$	10.2346	+	2.40250i	0.581288	+	0.136453i
$311$	−2.00406	−	6.16787i	−0.113640	−	0.349748i	0.878021	−	0.478622i	$-0.158864\pi$
$311$	−2.00406	−	6.16787i	−0.113640	−	0.349748i	−0.991661	+	0.128874i	$0.958864\pi$
$312$	−31.7677	+	8.13789i	−1.79849	+	0.460717i
$313$	−3.09726	−	2.25029i	−0.175068	−	0.127194i	0.496801	−	0.867865i	$-0.334508\pi$
$313$	−3.09726	−	2.25029i	−0.175068	−	0.127194i	−0.671868	+	0.740671i	$0.734508\pi$
$314$	−0.250215	−	2.98631i	−0.0141204	−	0.168527i
$315$	16.1174	+	5.23687i	0.908114	+	0.295064i
$316$	28.8376	−	4.86662i	1.62224	−	0.273769i
$317$	−11.9111	−	16.3943i	−0.668996	−	0.920793i	0.330742	−	0.943721i	$-0.392701\pi$
$317$	−11.9111	−	16.3943i	−0.668996	−	0.920793i	−0.999737	+	0.0229280i	$0.992701\pi$
$318$	−23.7081	+	20.4567i	−1.32948	+	1.14715i
$319$		0			0
$320$	−8.38478	−	3.95687i	−0.468723	−	0.221196i
$321$	−27.5453	+	20.0128i	−1.53743	+	1.11701i
$322$	−19.2039	−	11.6351i	−1.07019	−	0.648400i
$323$	33.2232	+	10.7949i	1.84859	+	0.600643i
$324$	0.240177	−	0.245080i	0.0133431	−	0.0136156i
$325$	8.90700	−	12.2594i	0.494071	−	0.680031i
$326$	−8.54774	+	3.59129i	−0.473416	+	0.198903i
$327$	9.03733	+	27.8140i	0.499765	+	1.53812i
$328$	−3.29818	−	1.30795i	−0.182112	−	0.0722193i
$329$	−2.50886			−0.138318
$330$		0			0
$331$			7.43370i			0.408593i	0.978909	+	0.204297i	$0.0654907\pi$
$331$			7.43370i			0.408593i	−0.978909	+	0.204297i	$0.934509\pi$
$332$	1.58959	−	0.830275i	0.0872402	−	0.0455673i
$333$	−31.0188	+	10.0786i	−1.69982	+	0.552305i
$334$	1.65896	+	3.94854i	0.0907743	+	0.216055i
$335$	−2.62335	−	1.90598i	−0.143329	−	0.104135i
$336$	−27.0124	+	20.4723i	−1.47365	+	1.11685i
$337$	−4.13102	+	12.7140i	−0.225031	+	0.692575i	0.773257	+	0.634092i	$0.218626\pi$
$337$	−4.13102	+	12.7140i	−0.225031	+	0.692575i	−0.998288	+	0.0584823i	$0.981374\pi$
$338$	−5.04566	−	3.05702i	−0.274447	−	0.166280i
$339$	−22.1777	−	30.5249i	−1.20453	−	1.65789i
$340$	−16.7641	−	2.48181i	−0.909163	−	0.134595i
$341$		0			0
$342$	21.3137	+	24.7013i	1.15251	+	1.33570i
$343$	−11.8300	+	8.59501i	−0.638761	+	0.464087i
$344$	−16.1002	−	13.3342i	−0.868067	−	0.718934i
$345$	5.25329	−	16.1680i	0.282828	−	0.870454i
$346$	0.255616	+	3.05078i	0.0137420	+	0.164011i
$347$	1.53596	−	2.11406i	0.0824545	−	0.113489i	−0.765797	−	0.643082i	$-0.777655\pi$
$347$	1.53596	−	2.11406i	0.0824545	−	0.113489i	0.848252	+	0.529593i	$0.177655\pi$
$348$	15.3421	+	7.62293i	0.822425	+	0.408632i
$349$	21.7641	−	7.07157i	1.16500	−	0.378532i	0.338228	−	0.941064i	$-0.390173\pi$
$349$	21.7641	−	7.07157i	1.16500	−	0.378532i	0.826776	+	0.562532i	$0.190173\pi$
$350$	3.57921	−	15.2474i	0.191317	−	0.815010i
$351$	−21.1992			−1.13153
$352$		0			0
$353$	22.7990			1.21347			0.606734	−	0.794905i	$-0.292479\pi$
$353$	22.7990			1.21347			0.606734	+	0.794905i	$0.292479\pi$
$354$	4.62605	−	19.7070i	0.245872	−	1.04741i
$355$	−8.36120	+	2.71672i	−0.443766	+	0.144188i
$356$	−1.17649	−	0.584553i	−0.0623538	−	0.0309813i
$357$	−36.4146	+	50.1204i	−1.92726	+	2.65265i
$358$	−1.15146	−	13.7427i	−0.0608566	−	0.726322i
$359$	6.22979	−	19.1733i	0.328796	−	1.01193i	−0.640902	−	0.767622i	$-0.721440\pi$
$359$	6.22979	−	19.1733i	0.328796	−	1.01193i	0.969698	−	0.244307i	$-0.0785603\pi$
$360$	−12.1897	−	10.0955i	−0.642455	−	0.532082i
$361$	3.09726	−	2.25029i	0.163014	−	0.118436i
$362$	−19.6089	−	22.7256i	−1.03062	−	1.19443i
$363$		0			0
$364$	−24.8284	−	3.67567i	−1.30136	−	0.192657i
$365$	0.854528	+	1.17616i	0.0447281	+	0.0615629i
$366$	17.6866	+	10.7159i	0.924496	+	0.560127i
$367$	−6.20230	+	19.0887i	−0.323757	+	0.996423i	0.648241	+	0.761435i	$0.275505\pi$
$367$	−6.20230	+	19.0887i	−0.323757	+	0.996423i	−0.971998	+	0.234988i	$0.924495\pi$
$368$	12.6665	+	16.7130i	0.660287	+	0.871225i
$369$	−4.90015	−	3.56017i	−0.255092	−	0.185335i
$370$	−4.28834	−	10.2068i	−0.222940	−	0.530626i
$371$	−22.7935	+	7.40605i	−1.18338	+	0.384503i
$372$	−31.8147	+	16.6174i	−1.64951	+	0.861573i
$373$			11.9063i			0.616486i	0.951308	+	0.308243i	$0.0997409\pi$
$373$			11.9063i			0.616486i	−0.951308	+	0.308243i	$0.900259\pi$
$374$		0			0
$375$	28.0711			1.44958
$376$	2.17813	+	0.863770i	0.112328	+	0.0445456i
$377$	3.92028	+	12.0654i	0.201905	+	0.621399i
$378$	−20.2000	+	8.48694i	−1.03898	+	0.436521i
$379$	−6.29617	+	8.66593i	−0.323412	+	0.445139i	−0.939505	−	0.342535i	$-0.888715\pi$
$379$	−6.29617	+	8.66593i	−0.323412	+	0.445139i	0.616093	+	0.787674i	$0.288715\pi$
$380$	−7.75143	+	7.90968i	−0.397640	+	0.405758i
$381$	−14.7348	−	4.78761i	−0.754885	−	0.245277i
$382$	2.50503	+	1.51773i	0.128168	+	0.0776536i
$383$	5.85942	−	4.25712i	0.299402	−	0.217529i	−0.427934	−	0.903810i	$-0.640758\pi$
$383$	5.85942	−	4.25712i	0.299402	−	0.217529i	0.727336	+	0.686282i	$0.240758\pi$
$384$	30.4998	−	8.47343i	1.55644	−	0.432408i
$385$		0			0
$386$	−15.6569	+	13.5096i	−0.796913	+	0.687621i
$387$	−20.9763	−	28.8715i	−1.06629	−	1.46762i
$388$	21.9736	−	3.70824i	1.11554	−	0.188258i
$389$	−7.33731	−	2.38404i	−0.372016	−	0.120875i	0.117041	−	0.993127i	$-0.462659\pi$
$389$	−7.33731	−	2.38404i	−0.372016	−	0.120875i	−0.489057	+	0.872252i	$0.662659\pi$
$390$	−1.58664	−	18.9365i	−0.0803425	−	0.958887i
$391$	31.0103	+	22.5303i	1.56826	+	1.13940i
$392$	−5.95001	+	1.52421i	−0.300521	+	0.0769841i
$393$	−9.42497	−	29.0071i	−0.475427	−	1.46321i
$394$	8.94135	+	2.09891i	0.450459	+	0.105742i
$395$			16.9469i			0.852689i
$396$		0			0
$397$		−	21.0257i		−	1.05525i	−0.849478	−	0.527624i	$-0.823083\pi$
$397$		−	21.0257i		−	1.05525i	0.849478	−	0.527624i	$-0.176917\pi$
$398$	−3.61054	+	15.3809i	−0.180980	+	0.770975i
$399$	12.5106	+	38.5038i	0.626315	+	1.92760i
$400$	−8.35689	+	12.0052i	−0.417845	+	0.600258i
$401$	−31.9204	−	23.1916i	−1.59403	−	1.15813i	−0.897884	−	0.440232i	$-0.854896\pi$
$401$	−31.9204	−	23.1916i	−1.59403	−	1.15813i	−0.696147	−	0.717899i	$-0.745104\pi$
$402$	11.0324	−	0.924376i	0.550247	−	0.0461037i
$403$	−25.2787	−	8.21355i	−1.25922	−	0.409146i
$404$	1.37913	+	8.17217i	0.0686142	+	0.406580i
$405$	0.116877	+	0.160867i	0.00580766	+	0.00799356i
$406$	8.56578	+	9.92724i	0.425113	+	0.492681i
$407$		0			0
$408$	48.8701	−	30.9761i	2.41943	−	1.53355i
$409$	23.6600	−	17.1900i	1.16991	−	0.849992i	0.178915	−	0.983865i	$-0.442741\pi$
$409$	23.6600	−	17.1900i	1.16991	−	0.849992i	0.990998	+	0.133873i	$0.0427414\pi$
$410$	1.06539	−	1.75843i	0.0526157	−	0.0868428i
$411$	−7.98298	−	2.59383i	−0.393771	−	0.127944i
$412$	18.6372	−	19.0177i	0.918190	−	0.936935i
$413$	9.10658	−	12.5341i	0.448106	−	0.616765i
$414$	13.8666	+	33.0043i	0.681506	+	1.62207i
$415$	0.321131	+	0.988341i	0.0157637	+	0.0485158i
$416$	20.2899	+	11.7393i	0.994794	+	0.575564i
$417$	−15.8771			−0.777506
$418$		0			0
$419$		−	22.3835i		−	1.09350i	−0.837295	−	0.546752i	$-0.815864\pi$
$419$		−	22.3835i		−	1.09350i	0.837295	−	0.546752i	$-0.184136\pi$
$420$	−9.09293	−	17.4088i	−0.443690	−	0.849460i
$421$	7.52642	−	2.44548i	0.366815	−	0.119186i	−0.119809	−	0.992797i	$-0.538228\pi$
$421$	7.52642	−	2.44548i	0.366815	−	0.119186i	0.486624	+	0.873611i	$0.338228\pi$
$422$	−4.47584	+	1.88050i	−0.217880	+	0.0915414i
$423$	3.23607	+	2.35114i	0.157343	+	0.114316i
$424$	22.3385	+	1.41778i	1.08485	+	0.0688537i
$425$	−8.26205	+	25.4280i	−0.400768	+	1.23344i
$426$	15.5538	−	25.6718i	0.753585	−	1.24380i
$427$	9.30317	+	12.8047i	0.450212	+	0.619664i
$428$	24.0755	+	3.56420i	1.16373	+	0.172282i
$429$		0			0
$430$	9.17157	−	7.91375i	0.442293	−	0.381635i
$431$	11.4096	−	8.28959i	0.549583	−	0.399296i	−0.278048	−	0.960567i	$-0.589688\pi$
$431$	11.4096	−	8.28959i	0.549583	−	0.399296i	0.827632	+	0.561271i	$0.189688\pi$
$432$	20.4591	−	0.413512i	0.984338	−	0.0198951i
$433$	−4.52922	+	13.9395i	−0.217660	+	0.669889i	0.781294	+	0.624164i	$0.214560\pi$
$433$	−4.52922	+	13.9395i	−0.217660	+	0.669889i	−0.998954	+	0.0457260i	$0.985440\pi$
$434$	−27.3754	+	2.29371i	−1.31406	+	0.110102i
$435$	−5.83508	+	8.03131i	−0.279771	+	0.385072i
$436$	9.30198	−	18.7214i	0.445484	−	0.896595i
$437$	23.8229	−	7.74053i	1.13960	−	0.370280i
$438$	−4.83227	−	1.13433i	−0.230895	−	0.0542006i
$439$	20.6796			0.986984			0.493492	−	0.869750i	$-0.335720\pi$
$439$	20.6796			0.986984			0.493492	+	0.869750i	$0.335720\pi$
$440$		0			0
$441$	−10.4853			−0.499299
$442$	41.7129	+	9.79175i	1.98408	+	0.465746i
$443$	−26.1534	+	8.49774i	−1.24258	+	0.403740i	−0.855258	−	0.518203i	$-0.826601\pi$
$443$	−26.1534	+	8.49774i	−1.24258	+	0.403740i	−0.387326	+	0.921943i	$0.626601\pi$
$444$	33.8508	+	16.8192i	1.60649	+	0.798204i
$445$	0.447455	−	0.615869i	0.0212114	−	0.0291950i
$446$	−0.383433	+	0.0321268i	−0.0181561	+	0.00152125i
$447$	−17.4599	+	53.7362i	−0.825827	+	2.54163i
$448$	24.0333	+	3.06303i	1.13547	+	0.144715i
$449$	−23.1839	+	16.8441i	−1.09412	+	0.794921i	−0.980089	−	0.198557i	$-0.936375\pi$
$449$	−23.1839	+	16.8441i	−1.09412	+	0.794921i	−0.114026	+	0.993478i	$0.536375\pi$
$450$	−18.9056	+	16.3128i	−0.891218	+	0.768993i
$451$		0			0
$452$	−3.94975	+	26.6798i	−0.185780	+	1.25491i
$453$	−9.96111	−	13.7103i	−0.468014	−	0.644166i
$454$	16.5775	−	27.3614i	0.778022	−	1.28413i
$455$	4.49439	−	13.8323i	0.210700	−	0.648469i
$456$	2.39499	−	37.7353i	0.112156	−	1.76712i
$457$	2.87044	+	2.08550i	0.134274	+	0.0975555i	0.652895	−	0.757449i	$-0.273554\pi$
$457$	2.87044	+	2.08550i	0.134274	+	0.0975555i	−0.518621	+	0.855004i	$0.673554\pi$
$458$	0.259254	−	0.108924i	0.0121141	−	0.00508969i
$459$	35.5729	−	11.5583i	1.66040	−	0.539496i
$460$	−10.7711	+	5.62594i	−0.502203	+	0.262311i
$461$			32.6256i			1.51953i	0.650200	+	0.759763i	$0.274685\pi$
$461$			32.6256i			1.51953i	−0.650200	+	0.759763i	$0.725315\pi$
$462$		0			0
$463$	−17.7279			−0.823886			−0.411943	−	0.911210i	$-0.635150\pi$
$463$	−17.7279			−0.823886			−0.411943	+	0.911210i	$0.635150\pi$
$464$	−4.01876	−	11.5677i	−0.186566	−	0.537015i
$465$	−6.42724	−	19.7810i	−0.298056	−	0.917323i
$466$	−4.69225	−	11.1682i	−0.217364	−	0.517355i
$467$	4.13566	−	5.69225i	0.191376	−	0.263406i	−0.702537	−	0.711647i	$-0.747949\pi$
$467$	4.13566	−	5.69225i	0.191376	−	0.263406i	0.893913	+	0.448241i	$0.147949\pi$
$468$	28.5805	+	28.0087i	1.32113	+	1.29470i
$469$	8.05871	+	2.61843i	0.372117	+	0.120908i
$470$	−0.703583	+	1.16127i	−0.0324538	+	0.0535654i
$471$	−4.79661	+	3.48494i	−0.221016	+	0.160578i
$472$	−12.2215	+	7.74652i	−0.562538	+	0.356563i
$473$		0			0
$474$	−37.7990	−	43.8068i	−1.73617	−	2.01211i
$475$	10.2699	+	14.1352i	0.471213	+	0.648569i
$476$	43.6668	−	7.36918i	2.00147	−	0.337766i
$477$	36.3408	+	11.8078i	1.66393	+	0.540644i
$478$	25.6076	−	2.14559i	1.17126	−	0.0981371i
$479$	−2.45008	−	1.78008i	−0.111947	−	0.0813341i	0.530403	−	0.847745i	$-0.322040\pi$
$479$	−2.45008	−	1.78008i	−0.111947	−	0.0813341i	−0.642350	+	0.766411i	$0.722040\pi$
$480$	1.90062	+	18.2444i	0.0867509	+	0.832740i
$481$	8.64969	+	26.6210i	0.394392	+	1.21381i
$482$	−3.57921	+	15.2474i	−0.163029	+	0.694502i
$483$			44.4231i			2.02132i
$484$		0			0
$485$			12.9131i			0.586353i
$486$	−21.7911	−	5.11529i	−0.988466	−	0.232034i
$487$	−4.66631	−	14.3614i	−0.211451	−	0.650779i	−0.999387	−	0.0350212i	$-0.988850\pi$
$487$	−4.66631	−	14.3614i	−0.211451	−	0.650779i	0.787936	−	0.615757i	$-0.211150\pi$
$488$	−3.66826	−	14.3197i	−0.166054	−	0.648222i
$489$	14.8399	+	10.7818i	0.671084	+	0.487571i
$490$	−0.297173	−	3.54676i	−0.0134249	−	0.160226i
$491$	25.7051	+	8.35209i	1.16005	+	0.376925i	0.824922	−	0.565246i	$-0.191219\pi$
$491$	25.7051	+	8.35209i	1.16005	+	0.376925i	0.335133	+	0.942171i	$0.391219\pi$
$492$	1.16811	+	6.92175i	0.0526624	+	0.312056i
$493$	−13.1567	−	18.1086i	−0.592547	−	0.815570i
$494$	21.1992	−	18.2919i	0.953798	−	0.822991i
$495$		0			0
$496$	24.5563	+	7.43370i	1.10261	+	0.333783i
$497$	18.5858	−	13.5033i	0.833685	−	0.605708i
$498$	−3.03455	−	1.83855i	−0.135981	−	0.0823874i
$499$	−27.5230	−	8.94277i	−1.23210	−	0.400334i	−0.380625	−	0.924729i	$-0.624291\pi$
$499$	−27.5230	−	8.94277i	−1.23210	−	0.400334i	−0.851475	+	0.524396i	$0.824291\pi$
$500$	−14.3311	−	14.0444i	−0.640908	−	0.628085i
$501$	4.98056	−	6.85515i	0.222515	−	0.306265i
$502$	15.2178	−	6.39369i	0.679204	−	0.285364i
$503$	2.64697	+	8.14654i	0.118023	+	0.363236i	0.992565	−	0.121712i	$-0.0388384\pi$
$503$	2.64697	+	8.14654i	0.118023	+	0.363236i	−0.874543	+	0.484948i	$0.838838\pi$
$504$	38.4465	+	15.2466i	1.71254	+	0.679135i
$505$	−4.80249			−0.213708
$506$		0			0
$507$			11.6718i			0.518362i
$508$	5.12723	+	9.81627i	0.227484	+	0.435527i
$509$	−32.1210	+	10.4368i	−1.42374	+	0.462601i	−0.916788	−	0.399374i	$-0.869227\pi$
$509$	−32.1210	+	10.4368i	−1.42374	+	0.462601i	−0.506951	+	0.861975i	$0.669227\pi$
$510$	12.9871	+	30.9109i	0.575076	+	1.36876i
$511$	−3.07345	−	2.23299i	−0.135961	−	0.0987817i
$512$	−19.8105	−	10.9336i	−0.875509	−	0.483202i
$513$	7.55327	−	23.2466i	0.333485	−	1.02636i
$514$	1.83210	+	1.11002i	0.0808106	+	0.0489609i
$515$	9.06942	+	12.4830i	0.399646	+	0.550066i
$516$	−6.05692	+	40.9133i	−0.266641	+	1.80111i
$517$		0			0
$518$	18.8995	+	21.9034i	0.830396	+	0.962381i
$519$	4.90015	−	3.56017i	0.215093	−	0.156274i
$520$	−8.66422	+	10.4615i	−0.379951	+	0.458767i
$521$	−4.78522	+	14.7274i	−0.209644	+	0.645218i	0.789847	+	0.613305i	$0.210160\pi$
$521$	−4.78522	+	14.7274i	−0.209644	+	0.645218i	−0.999491	+	0.0319136i	$0.989840\pi$
$522$	−1.74546	−	20.8320i	−0.0763966	−	0.911792i
$523$	−23.5664	+	32.4364i	−1.03049	+	1.41834i	−0.125906	+	0.992042i	$0.540184\pi$
$523$	−23.5664	+	32.4364i	−1.03049	+	1.41834i	−0.904581	+	0.426302i	$0.859816\pi$
$524$	−9.70098	+	19.5245i	−0.423789	+	0.852930i
$525$	−29.4695	+	9.57523i	−1.28616	+	0.417897i
$526$	3.74714	−	15.9628i	0.163383	−	0.696012i
$527$	46.8966			2.04285
$528$		0			0
$529$	4.48528			0.195012
$530$	−2.96416	+	12.6273i	−0.128755	+	0.548496i
$531$	−23.4924	+	7.63314i	−1.01948	+	0.331250i
$532$	12.8770	−	25.9167i	0.558289	−	1.12363i
$533$	−3.05541	+	4.20542i	−0.132345	+	0.182157i
$534$	0.217010	+	2.59001i	0.00939095	+	0.112081i
$535$	−4.35810	+	13.4128i	−0.188417	+	0.579888i
$536$	−6.09487	−	5.04777i	−0.263258	−	0.218031i
$537$	−22.0734	+	16.0373i	−0.952539	+	0.692060i
$538$	27.9910	+	32.4399i	1.20678	+	1.39858i
$539$		0			0
$540$	−1.73654	+	11.7300i	−0.0747290	+	0.504780i
$541$	−2.43570	−	3.35245i	−0.104719	−	0.144133i	0.753441	−	0.657515i	$-0.228392\pi$
$541$	−2.43570	−	3.35245i	−0.104719	−	0.144133i	−0.858160	+	0.513382i	$0.828392\pi$
$542$	36.0018	+	21.8125i	1.54641	+	0.936926i
$543$	−18.3509	+	56.4783i	−0.787513	+	2.42371i
$544$	−40.4475	−	8.63624i	−1.73417	−	0.370276i
$545$	9.80030	+	7.12034i	0.419799	+	0.305002i
$546$	19.2344	+	45.7804i	0.823156	+	1.95922i
$547$	33.4409	−	10.8656i	1.42983	−	0.464579i	0.511118	−	0.859511i	$-0.329232\pi$
$547$	33.4409	−	10.8656i	1.42983	−	0.464579i	0.918711	+	0.394931i	$0.129232\pi$
$548$	2.77782	+	5.31824i	0.118663	+	0.227184i
$549$		−	25.2346i		−	1.07699i
$550$		0			0
$551$	−14.6274			−0.623149
$552$	15.2944	−	38.5670i	0.650971	−	1.64152i
$553$	−13.6846	−	42.1168i	−0.581928	−	1.79099i
$554$	−36.8927	+	15.5003i	−1.56742	+	0.658544i
$555$	−12.8745	+	17.7202i	−0.546492	+	0.752182i
$556$	8.10576	+	7.94359i	0.343761	+	0.336883i
$557$	21.2645	+	6.90925i	0.901006	+	0.292755i	0.722652	−	0.691212i	$-0.242923\pi$
$557$	21.2645	+	6.90925i	0.901006	+	0.292755i	0.178354	+	0.983966i	$0.442923\pi$
$558$	37.4599	+	22.6959i	1.58580	+	0.960796i
$559$	−24.7781	+	18.0023i	−1.04800	+	0.761418i
$560$	−4.06766	+	13.4370i	−0.171890	+	0.567819i
$561$		0			0
$562$	19.4558	−	16.7876i	0.820695	−	0.708142i
$563$	17.1591	+	23.6174i	0.723168	+	0.995355i	0.999413	+	0.0342679i	$0.0109100\pi$
$563$	17.1591	+	23.6174i	0.723168	+	0.995355i	−0.276245	+	0.961087i	$0.589090\pi$
$564$	−0.771421	−	4.57113i	−0.0324827	−	0.192479i
$565$	−14.8637	−	4.82952i	−0.625322	−	0.203179i
$566$	0.149737	+	1.78710i	0.00629390	+	0.0751176i
$567$	−0.420367	−	0.305414i	−0.0176537	−	0.0128262i
$568$	−20.7847	+	5.32439i	−0.872107	+	0.223407i
$569$	7.16563	+	22.0536i	0.300399	+	0.924533i	0.981354	+	0.192208i	$0.0615648\pi$
$569$	7.16563	+	22.0536i	0.300399	+	0.924533i	−0.680955	+	0.732325i	$0.738435\pi$
$570$	21.3307	+	5.00720i	0.893443	+	0.209728i
$571$		−	38.3771i		−	1.60603i	−0.595957	−	0.803016i	$-0.703227\pi$
$571$		−	38.3771i		−	1.60603i	0.595957	−	0.803016i	$-0.296773\pi$
$572$		0			0
$573$		−	5.79471i		−	0.242077i
$574$	−1.22780	+	5.23041i	−0.0512472	+	0.218313i
$575$	5.92434	+	18.2332i	0.247062	+	0.760379i
$576$	−28.1290	−	26.4733i	−1.17204	−	1.10305i
$577$	29.6560	+	21.5464i	1.23460	+	0.896987i	0.997226	−	0.0744326i	$-0.0237146\pi$
$577$	29.6560	+	21.5464i	1.23460	+	0.896987i	0.237370	+	0.971419i	$0.423715\pi$
$578$	−51.3763	+	4.30468i	−2.13697	+	0.179051i
$579$	38.9109	+	12.6429i	1.61708	+	0.525422i
$580$	6.99718	−	1.18084i	0.290542	−	0.0490317i
$581$	−1.59617	−	2.19694i	−0.0662204	−	0.0911445i
$582$	−28.8019	−	33.3797i	−1.19388	−	1.38363i
$583$		0			0
$584$	1.89949	+	2.99678i	0.0786017	+	0.124007i
$585$	−18.7599	+	13.6298i	−0.775625	+	0.563525i
$586$	−21.5292	+	35.5342i	−0.889363	+	1.46790i
$587$	33.2232	+	10.7949i	1.37127	+	0.445553i	0.899790	−	0.436324i	$-0.143720\pi$
$587$	33.2232	+	10.7949i	1.37127	+	0.445553i	0.471480	+	0.881877i	$0.343720\pi$
$588$	8.67902	+	8.50538i	0.357917	+	0.350756i
$589$	18.0136	−	24.7936i	0.742237	−	1.02160i
$590$	−3.24781	−	7.73021i	−0.133710	−	0.318248i
$591$	−5.61507	−	17.2814i	−0.230973	−	0.710863i
$592$	−8.86696	−	25.5228i	−0.364430	−	1.04898i
$593$	−17.1316			−0.703509			−0.351754	−	0.936092i	$-0.614415\pi$
$593$	−17.1316			−0.703509			−0.351754	+	0.936092i	$0.614415\pi$
$594$		0			0
$595$			25.6614i			1.05202i
$596$	35.7989	−	18.6985i	1.46638	−	0.765919i
$597$	29.7275	−	9.65904i	1.21666	−	0.395318i
$598$	28.3250	−	11.9006i	1.15830	−	0.486652i
$599$	24.8931	+	18.0859i	1.01710	+	0.738969i	0.965687	−	0.259708i	$-0.0836263\pi$
$599$	24.8931	+	18.0859i	1.01710	+	0.738969i	0.0514169	+	0.998677i	$0.483626\pi$
$600$	28.8813	+	1.83304i	1.17907	+	0.0748337i
$601$	12.0719	−	37.1536i	0.492425	−	1.51553i	−0.328508	−	0.944501i	$-0.606546\pi$
$601$	12.0719	−	37.1536i	0.492425	−	1.51553i	0.820932	−	0.571026i	$-0.193454\pi$
$602$	−16.4031	+	27.0735i	−0.668541	+	1.10343i
$603$	−7.94075	−	10.9295i	−0.323372	−	0.445084i
$604$	−1.77403	+	11.9832i	−0.0721843	+	0.487591i
$605$		0			0
$606$	12.4142	−	10.7117i	0.504293	−	0.435132i
$607$	−20.7896	+	15.1045i	−0.843823	+	0.613073i	−0.923436	−	0.383752i	$-0.874632\pi$
$607$	−20.7896	+	15.1045i	−0.843823	+	0.613073i	0.0796128	+	0.996826i	$0.474632\pi$
$608$	−20.1023	+	18.0668i	−0.815255	+	0.732704i
$609$	8.01625	−	24.6715i	0.324835	−	0.999739i
$610$	8.53587	−	0.715197i	0.345607	−	0.0289575i
$611$	2.01780	−	2.77726i	0.0816314	−	0.112356i
$612$	−63.2299	−	31.4166i	−2.55592	−	1.26994i
$613$	−15.7642	+	5.12209i	−0.636709	+	0.206879i	−0.609545	−	0.792752i	$-0.708648\pi$
$613$	−15.7642	+	5.12209i	−0.636709	+	0.206879i	−0.0271644	+	0.999631i	$0.508648\pi$
$614$	28.6759	+	6.73143i	1.15726	+	0.271658i
$615$	−4.06766			−0.164024
$616$		0			0
$617$	−25.7990			−1.03863			−0.519314	−	0.854583i	$-0.673813\pi$
$617$	−25.7990			−1.03863			−0.519314	+	0.854583i	$0.673813\pi$
$618$	−51.2866	−	12.0391i	−2.06305	−	0.484284i
$619$	10.1874	−	3.31009i	0.409467	−	0.133044i	−0.0970386	−	0.995281i	$-0.530937\pi$
$619$	10.1874	−	3.31009i	0.409467	−	0.133044i	0.506505	+	0.862237i	$0.330937\pi$
$620$	−6.61546	+	13.3145i	−0.265683	+	0.534722i
$621$	15.7646	−	21.6981i	0.632613	−	0.870717i
$622$	9.13955	−	0.765778i	0.366462	−	0.0307049i
$623$	−0.614714	+	1.89190i	−0.0246280	+	0.0757972i
$624$	−0.937163	−	46.3675i	−0.0375165	−	1.85619i
$625$	−5.38551	+	3.91280i	−0.215420	+	0.156512i
$626$	4.09918	−	3.53701i	0.163836	−	0.141367i
$627$		0			0
$628$	4.19239	+	0.620653i	0.167295	+	0.0247667i
$629$	−29.0288	−	39.9547i	−1.15745	−	1.59310i
$630$	−12.4190	+	20.4978i	−0.494787	+	0.816651i
$631$	13.4066	−	41.2614i	0.533710	−	1.64259i	−0.212711	−	0.977115i	$-0.568229\pi$
$631$	13.4066	−	41.2614i	0.533710	−	1.64259i	0.746421	−	0.665474i	$-0.231771\pi$
$632$	−2.61972	+	41.2762i	−0.104207	+	1.64188i
$633$	7.77059	+	5.64567i	0.308853	+	0.224395i
$634$	26.4210	−	11.1007i	1.04931	−	0.440863i
$635$	−6.10334	+	1.98309i	−0.242204	+	0.0786967i
$636$	−20.5023	−	39.2524i	−0.812969	−	1.55646i
$637$			8.99869i			0.356541i
$638$		0			0
$639$	−36.6274			−1.44896
$640$	8.15766	−	10.2652i	0.322460	−	0.405770i
$641$	2.41912	+	7.44528i	0.0955494	+	0.294071i	0.987396	−	0.158266i	$-0.0505904\pi$
$641$	2.41912	+	7.44528i	0.0955494	+	0.294071i	−0.891847	+	0.452337i	$0.850590\pi$
$642$	−18.6511	−	44.3921i	−0.736100	−	1.75201i
$643$	−17.2923	+	23.8009i	−0.681943	+	0.938614i	−0.999955	−	0.00947257i	$-0.996985\pi$
$643$	−17.2923	+	23.8009i	−0.681943	+	0.938614i	0.318012	+	0.948087i	$0.396985\pi$
$644$	22.2256	−	22.6794i	0.875812	−	0.893693i
$645$	−22.7935	−	7.40605i	−0.897492	−	0.291613i
$646$	−25.5997	+	42.2526i	−1.00721	+	1.66241i
$647$	7.59244	−	5.51623i	0.298490	−	0.216866i	−0.428452	−	0.903564i	$-0.640941\pi$
$647$	7.59244	−	5.51623i	0.298490	−	0.216866i	0.726942	+	0.686699i	$0.240941\pi$
$648$	0.259801	+	0.409880i	0.0102059	+	0.0161016i
$649$		0			0
$650$	14.0000	+	16.2252i	0.549125	+	0.636404i
$651$	31.9464	+	43.9704i	1.25208	+	1.72334i
$652$	−2.18191	−	12.9291i	−0.0854501	−	0.506343i
$653$	32.1210	+	10.4368i	1.25699	+	0.408422i	0.860422	−	0.509583i	$-0.170200\pi$
$653$	32.1210	+	10.4368i	1.25699	+	0.408422i	0.396571	+	0.918004i	$0.370200\pi$
$654$	−41.2148	+	3.45328i	−1.61163	+	0.135034i
$655$	−10.2207	−	7.42575i	−0.399355	−	0.290148i
$656$	2.86671	−	4.11819i	0.111926	−	0.160788i
$657$	1.87169	+	5.76047i	0.0730216	+	0.224738i
$658$	0.810838	−	3.45417i	0.0316098	−	0.134658i
$659$			14.2568i			0.555366i	0.960673	+	0.277683i	$0.0895665\pi$
$659$			14.2568i			0.555366i	−0.960673	+	0.277683i	$0.910433\pi$
$660$		0			0
$661$			48.6414i			1.89193i	0.324265	+	0.945966i	$0.394883\pi$
$661$			48.6414i			1.89193i	−0.324265	+	0.945966i	$0.605117\pi$
$662$	−10.2346	−	2.40250i	−0.397780	−	0.0933757i
$663$	−26.1952	−	80.6206i	−1.01734	−	3.13105i
$664$	0.629374	+	2.45687i	0.0244244	+	0.0953451i
$665$	13.5669	+	9.85690i	0.526100	+	0.382234i
$666$	−3.85117	−	45.9636i	−0.149230	−	1.78106i
$667$	−15.2646	−	4.95978i	−0.591049	−	0.192043i
$668$	−5.97247	+	1.00791i	−0.231082	+	0.0389972i
$669$	0.447455	+	0.615869i	0.0172996	+	0.0238109i
$670$	3.47197	−	2.99581i	0.134134	−	0.115738i
$671$		0			0
$672$	−19.4558	−	43.8068i	−0.750525	−	1.68988i
$673$	35.4900	−	25.7850i	1.36804	−	0.993940i	0.370153	−	0.928971i	$-0.379305\pi$
$673$	35.4900	−	25.7850i	1.36804	−	0.993940i	0.997887	−	0.0649689i	$-0.0206948\pi$
$674$	−16.1694	−	9.79658i	−0.622821	−	0.377350i
$675$	17.7922	+	5.78103i	0.684821	+	0.222512i
$676$	5.83958	−	5.95880i	0.224599	−	0.229185i
$677$	−0.854528	+	1.17616i	−0.0328422	+	0.0452034i	−0.825122	−	0.564954i	$-0.808894\pi$
$677$	−0.854528	+	1.17616i	−0.0328422	+	0.0452034i	0.792280	+	0.610158i	$0.208894\pi$
$678$	49.1940	−	20.6686i	1.88928	−	0.793774i
$679$	−10.4273	−	32.0920i	−0.400164	−	1.23158i
$680$	8.83493	−	22.2786i	0.338804	−	0.854345i
$681$	−63.2933			−2.42540
$682$		0			0
$683$		−	31.6550i		−	1.21124i	−0.795752	−	0.605622i	$-0.792924\pi$
$683$		−	31.6550i		−	1.21124i	0.795752	−	0.605622i	$-0.207076\pi$
$684$	−40.8969	+	21.3613i	−1.56373	+	0.816768i
$685$	−3.30666	+	1.07440i	−0.126341	+	0.0410506i
$686$	−8.01017	−	19.0653i	−0.305830	−	0.727915i
$687$	−0.450096	−	0.327014i	−0.0171722	−	0.0124764i
$688$	23.5619	−	17.8571i	0.898287	−	0.680797i
$689$	10.1337	−	31.1884i	0.386065	−	1.18818i
$690$	20.5621	+	12.4580i	0.782784	+	0.474268i
$691$	−16.7280	−	23.0241i	−0.636363	−	0.875879i	0.362052	−	0.932158i	$-0.382076\pi$
$691$	−16.7280	−	23.0241i	−0.636363	−	0.875879i	−0.998415	+	0.0562792i	$0.982076\pi$
$692$	−4.28289	−	0.634051i	−0.162811	−	0.0241030i
$693$		0			0
$694$	2.41421	+	2.79793i	0.0916423	+	0.106208i
$695$	−5.32052	+	3.86558i	−0.201819	+	0.146630i
$696$	−15.4536	+	18.6592i	−0.585767	+	0.707276i
$697$	2.83417	−	8.72268i	0.107352	−	0.330395i
$698$	2.70214	+	32.2500i	0.102277	+	1.22068i
$699$	−14.0871	+	19.3893i	−0.532825	+	0.733370i
$700$	19.8357	+	9.85564i	0.749721	+	0.372508i
$701$	0.676176	−	0.219703i	0.0255388	−	0.00829807i	−0.296220	−	0.955120i	$-0.595726\pi$
$701$	0.676176	−	0.219703i	0.0255388	−	0.00829807i	0.321759	+	0.946822i	$0.395726\pi$
$702$	6.85138	−	29.1869i	0.258588	−	1.10159i
$703$	−32.2739			−1.21723
$704$		0			0
$705$	2.68629			0.101172
$706$	−7.36840	+	31.3894i	−0.277314	+	1.18136i
$707$	11.9353	−	3.87801i	0.448873	−	0.145848i
$708$	25.6372	+	12.7382i	0.963506	+	0.478730i
$709$	−5.33279	+	7.33996i	−0.200277	+	0.275658i	−0.897328	−	0.441363i	$-0.854495\pi$
$709$	−5.33279	+	7.33996i	−0.200277	+	0.275658i	0.697051	+	0.717021i	$0.254495\pi$
$710$	−1.03809	−	12.3896i	−0.0389589	−	0.464974i
$711$	−21.8180	+	67.1490i	−0.818240	+	2.51828i
$712$	1.18504	−	1.43086i	0.0444111	−	0.0536236i
$713$	27.2052	−	19.7657i	1.01884	−	0.740231i
$714$	−57.2364	−	66.3336i	−2.14202	−	2.48247i
$715$		0			0
$716$	19.2929	+	2.85617i	0.721009	+	0.106740i
$717$	−29.8833	−	41.1309i	−1.11601	−	1.53606i
$718$	24.3842	+	14.7737i	0.910011	+	0.551351i
$719$	−11.8706	+	36.5341i	−0.442700	+	1.36249i	0.442286	+	0.896874i	$0.354168\pi$
$719$	−11.8706	+	36.5341i	−0.442700	+	1.36249i	−0.884986	+	0.465617i	$0.845832\pi$
$720$	17.8390	−	13.5199i	0.664822	−	0.503857i
$721$	−32.6196	−	23.6995i	−1.21482	−	0.882616i
$722$	2.09717	+	4.99155i	0.0780488	+	0.185766i
$723$	29.4695	−	9.57523i	1.09598	−	0.356107i
$724$	37.6257	−	19.6526i	1.39835	−	0.730385i
$725$		−	11.1953i		−	0.415785i
$726$		0			0
$727$	6.07107			0.225163			0.112582	−	0.993642i	$-0.464088\pi$
$727$	6.07107			0.225163			0.112582	+	0.993642i	$0.464088\pi$
$728$	13.0849	−	32.9956i	0.484959	−	1.22290i
$729$	13.5255	+	41.6273i	0.500946	+	1.54175i
$730$	−1.89550	+	0.796383i	−0.0701554	+	0.0294755i
$731$	31.7630	−	43.7180i	1.17480	−	1.61697i
$732$	−20.4696	+	20.8875i	−0.756579	+	0.772025i
$733$	14.9114	+	4.84500i	0.550764	+	0.178954i	0.571161	−	0.820838i	$-0.306493\pi$
$733$	14.9114	+	4.84500i	0.550764	+	0.178954i	−0.0203970	+	0.999792i	$0.506493\pi$
$734$	−24.2766	−	14.7085i	−0.896066	−	0.542902i
$735$	−5.69680	+	4.13897i	−0.210130	+	0.152668i
$736$	−27.1040	+	12.0376i	−0.999065	+	0.443713i
$737$		0			0
$738$	6.48528	−	5.59587i	0.238727	−	0.205987i
$739$	2.01780	+	2.77726i	0.0742260	+	0.102163i	0.844516	−	0.535531i	$-0.179888\pi$
$739$	2.01780	+	2.77726i	0.0742260	+	0.102163i	−0.770290	+	0.637694i	$0.779888\pi$
$740$	15.4386	−	2.60540i	0.567533	−	0.0957764i
$741$	−52.6850	−	17.1184i	−1.93543	−	0.628859i
$742$	−2.82995	−	33.7754i	−0.103891	−	1.23993i
$743$	−24.5008	−	17.8008i	−0.898846	−	0.653050i	0.0393236	−	0.999227i	$-0.487480\pi$
$743$	−24.5008	−	17.8008i	−0.898846	−	0.653050i	−0.938169	+	0.346177i	$0.887480\pi$
$744$	−12.5965	−	49.1727i	−0.461810	−	1.80276i
$745$	7.23214	+	22.2582i	0.264965	+	0.815479i
$746$	−16.3925	−	3.84800i	−0.600171	−	0.140885i
$747$			4.32957i			0.158411i
$748$		0			0
$749$		−	36.8532i		−	1.34659i
$750$	−9.07229	+	38.6479i	−0.331273	+	1.41122i
$751$	7.18237	+	22.1051i	0.262088	+	0.806625i	0.992350	+	0.123457i	$0.0393983\pi$
$751$	7.18237	+	22.1051i	0.262088	+	0.806625i	−0.730261	+	0.683168i	$0.760602\pi$
$752$	−1.89318	+	2.71966i	−0.0690371	+	0.0991757i
$753$	−26.4200	−	19.1952i	−0.962797	−	0.699513i
$754$	−17.8785	+	1.49799i	−0.651096	+	0.0545536i
$755$	−6.67605	−	2.16918i	−0.242966	−	0.0789446i
$756$	−5.15628	−	30.5541i	−0.187532	−	1.11124i
$757$	28.7076	+	39.5126i	1.04340	+	1.43611i	0.894398	+	0.447273i	$0.147605\pi$
$757$	28.7076	+	39.5126i	1.04340	+	1.43611i	0.148998	+	0.988838i	$0.452395\pi$
$758$	−9.89630	−	11.4692i	−0.359450	−	0.416581i
$759$		0			0
$760$	−8.38478	−	13.2284i	−0.304148	−	0.479845i
$761$	−25.5156	+	18.5382i	−0.924940	+	0.672008i	−0.944749	−	0.327795i	$-0.893694\pi$
$761$	−25.5156	+	18.5382i	−0.924940	+	0.672008i	0.0198085	+	0.999804i	$0.493694\pi$
$762$	11.3537	−	18.7394i	0.411300	−	0.678855i
$763$	−30.1057	−	9.78193i	−1.08990	−	0.354130i
$764$	−2.89919	+	2.95838i	−0.104889	+	0.107030i
$765$	24.0483	−	33.0996i	0.869466	−	1.19672i
$766$	3.96745	+	9.44304i	0.143350	+	0.341191i
$767$	6.55092	+	20.1617i	0.236540	+	0.727995i
$768$	1.80889	+	44.7304i	0.0652726	+	1.61407i
$769$	22.9733			0.828437			0.414218	−	0.910178i	$-0.364055\pi$
$769$	22.9733			0.828437			0.414218	+	0.910178i	$0.364055\pi$
$770$		0			0
$771$		−	4.23808i		−	0.152631i
$772$	−13.5398	−	25.9224i	−0.487306	−	0.932966i
$773$	2.58266	−	0.839157i	0.0928918	−	0.0301824i	−0.262202	−	0.965013i	$-0.584449\pi$
$773$	2.58266	−	0.839157i	0.0928918	−	0.0301824i	0.355094	+	0.934831i	$0.384449\pi$
$774$	46.5292	−	19.5490i	1.67246	−	0.702675i
$775$	18.9762	+	13.7870i	0.681644	+	0.495244i
$776$	−1.99617	+	31.4514i	−0.0716581	+	1.12904i
$777$	17.6870	−	54.4350i	0.634518	−	1.95285i
$778$	5.65366	−	9.33143i	0.202694	−	0.334548i
$779$	−3.52292	−	4.84888i	−0.126222	−	0.173729i
$780$	26.5844	+	3.93562i	0.951873	+	0.140918i
$781$		0			0
$782$	−41.0416	+	35.4130i	−1.46765	+	1.26637i
$783$	−12.6707	+	9.20584i	−0.452816	+	0.328990i
$784$	−0.175528	−	8.68452i	−0.00626887	−	0.310161i
$785$	−0.758898	+	2.33565i	−0.0270862	+	0.0833628i
$786$	42.9827	−	3.60140i	1.53314	−	0.128458i
$787$	−7.41626	+	10.2076i	−0.264361	+	0.363862i	−0.920476	−	0.390799i	$-0.872199\pi$
$787$	−7.41626	+	10.2076i	−0.264361	+	0.363862i	0.656115	+	0.754661i	$0.272199\pi$
$788$	−5.77951	+	11.6320i	−0.205887	+	0.414373i
$789$	−30.8522	+	10.0245i	−1.09837	+	0.356881i
$790$	−23.3322	−	5.47705i	−0.830124	−	0.194865i
$791$	40.8396			1.45209
$792$		0			0
$793$	−21.6569			−0.769057
$794$	28.9479	+	6.79529i	1.02732	+	0.241156i
$795$	24.4055	−	7.92982i	0.865573	−	0.281242i
$796$	−20.0094	−	9.94190i	−0.709213	−	0.352381i
$797$	16.5627	−	22.7966i	0.586681	−	0.807498i	−0.407727	−	0.913104i	$-0.633678\pi$
$797$	16.5627	−	22.7966i	0.586681	−	0.807498i	0.994408	+	0.105606i	$0.0336784\pi$
$798$	−57.0549	+	4.78048i	−2.01972	+	0.169227i
$799$	−1.87169	+	5.76047i	−0.0662157	+	0.203791i
$800$	−13.8277	−	15.3856i	−0.488883	−	0.543964i
$801$	2.56586	−	1.86420i	0.0906601	−	0.0658684i
$802$	42.2463	−	36.4524i	1.49177	−	1.28718i
$803$		0			0
$804$	−2.29289	+	15.4881i	−0.0808641	+	0.546221i
$805$	10.8156	+	14.8865i	0.381201	+	0.524679i
$806$	19.4781	−	32.1489i	0.686088	−	1.13240i
$807$	26.1952	−	80.6206i	0.922116	−	2.83798i
$808$	−11.6971	−	0.742392i	−0.411501	−	0.0261172i
$809$	−1.01485	−	0.737335i	−0.0356804	−	0.0259233i	0.569802	−	0.821782i	$-0.307020\pi$
$809$	−1.01485	−	0.737335i	−0.0356804	−	0.0259233i	−0.605483	+	0.795859i	$0.707020\pi$
$810$	−0.259254	+	0.108924i	−0.00910925	+	0.00382721i
$811$	−35.9993	+	11.6969i	−1.26411	+	0.410733i	−0.862955	−	0.505280i	$-0.831389\pi$
$811$	−35.9993	+	11.6969i	−1.26411	+	0.410733i	−0.401150	+	0.916013i	$0.631389\pi$
$812$	−16.4361	+	8.58489i	−0.576794	+	0.301271i
$813$		−	83.2805i		−	2.92077i
$814$		0			0
$815$	7.59798			0.266146
$816$	26.8533	+	77.2949i	0.940052	+	2.70586i
$817$	−10.9125	−	33.5853i	−0.381781	−	1.17500i
$818$	16.0203	+	38.1305i	0.560138	+	1.33320i
$819$	35.6165	−	49.0219i	1.24454	−	1.71296i
$820$	2.07667	+	2.03512i	0.0725204	+	0.0710694i
$821$	−23.9995	−	7.79791i	−0.837589	−	0.272149i	−0.141350	−	0.989960i	$-0.545144\pi$
$821$	−23.9995	−	7.79791i	−0.837589	−	0.272149i	−0.696238	+	0.717811i	$0.745144\pi$
$822$	6.15117	−	10.1526i	0.214547	−	0.354112i
$823$	22.4324	−	16.2981i	0.781943	−	0.568115i	−0.123619	−	0.992330i	$-0.539450\pi$
$823$	22.4324	−	16.2981i	0.781943	−	0.568115i	0.905561	+	0.424215i	$0.139450\pi$
$824$	20.1600	+	31.8059i	0.702308	+	1.10801i
$825$		0			0
$826$	14.3137	+	16.5888i	0.498038	+	0.577197i
$827$	10.9700	+	15.0989i	0.381465	+	0.525041i	0.955972	−	0.293458i	$-0.0948062\pi$
$827$	10.9700	+	15.0989i	0.381465	+	0.525041i	−0.574507	+	0.818500i	$0.694806\pi$
$828$	−49.9215	+	8.42472i	−1.73489	+	0.292779i
$829$	−40.9388	−	13.3018i	−1.42186	−	0.461991i	−0.505669	−	0.862728i	$-0.668754\pi$
$829$	−40.9388	−	13.3018i	−1.42186	−	0.461991i	−0.916193	+	0.400737i	$0.868754\pi$
$830$	−1.46452	+	0.122708i	−0.0508344	+	0.00425927i
$831$	64.0502	+	46.5352i	2.22188	+	1.61429i
$832$	−22.7200	+	24.1409i	−0.787673	+	0.836936i
$833$	−4.90630	−	15.1000i	−0.169993	−	0.523186i
$834$	5.13133	−	21.8595i	0.177683	−	0.756931i
$835$		−	3.50981i		−	0.121462i
$836$		0			0
$837$		−	32.8139i		−	1.13422i
$838$	30.8173	+	7.23411i	1.06457	+	0.249898i
$839$	1.00203	+	3.08393i	0.0345940	+	0.106469i	0.966862	−	0.255298i	$-0.0821735\pi$
$839$	1.00203	+	3.08393i	0.0345940	+	0.106469i	−0.932268	+	0.361767i	$0.882174\pi$
$840$	26.9069	−	6.89271i	0.928377	−	0.237821i
$841$	−15.8789	−	11.5367i	−0.547549	−	0.397817i
$842$	0.934450	+	11.1527i	0.0322033	+	0.384346i
$843$	−48.3523	−	15.7106i	−1.66534	−	0.541102i
$844$	−1.14251	−	6.77004i	−0.0393267	−	0.233035i
$845$	2.84171	+	3.91128i	0.0977579	+	0.134552i
$846$	−4.28289	+	3.69552i	−0.147249	+	0.127055i
$847$		0			0
$848$	−9.17157	+	30.2972i	−0.314953	+	1.04041i
$849$	2.87044	−	2.08550i	0.0985133	−	0.0715741i
$850$	−32.3387	−	19.5932i	−1.10921	−	0.672040i
$851$	−33.6798	−	10.9432i	−1.15453	−	0.375129i
$852$	30.3178	+	29.7112i	1.03867	+	1.01789i
$853$	28.1743	−	38.7786i	0.964669	−	1.32775i	0.0199748	−	0.999800i	$-0.493641\pi$
$853$	28.1743	−	38.7786i	0.964669	−	1.32775i	0.944694	−	0.327952i	$-0.106359\pi$
$854$	−20.6361	+	8.67015i	−0.706152	+	0.296686i
$855$	−8.26205	−	25.4280i	−0.282556	−	0.869618i
$856$	−12.6881	+	31.9950i	−0.433671	+	1.09357i
$857$	−31.7543			−1.08470			−0.542352	−	0.840151i	$-0.682466\pi$
$857$	−31.7543			−1.08470			−0.542352	+	0.840151i	$0.682466\pi$
$858$		0			0
$859$			32.5327i			1.11000i	0.831850	+	0.555001i	$0.187282\pi$
$859$			32.5327i			1.11000i	−0.831850	+	0.555001i	$0.812718\pi$
$860$	7.93140	+	15.1850i	0.270459	+	0.517803i
$861$	10.1091	−	3.28464i	0.344517	−	0.111940i
$862$	7.72554	+	18.3878i	0.263133	+	0.626291i
$863$	−40.8435	−	29.6745i	−1.39033	−	1.01013i	−0.995829	−	0.0912350i	$-0.970919\pi$
$863$	−40.8435	−	29.6745i	−1.39033	−	1.01013i	−0.394498	−	0.918897i	$-0.629081\pi$
$864$	−6.04285	+	28.3015i	−0.205582	+	0.962836i
$865$	0.775280	−	2.38607i	0.0263603	−	0.0811287i
$866$	−17.7280	−	10.7409i	−0.602420	−	0.364990i
$867$	59.9547	+	82.5205i	2.03617	+	2.80254i
$868$	5.68951	−	38.4315i	0.193114	−	1.30445i
$869$		0			0
$870$	−9.17157	−	10.6293i	−0.310945	−	0.360368i
$871$	−9.37994	+	6.81492i	−0.317827	+	0.230915i
$872$	22.7692	+	18.8575i	0.771061	+	0.638594i
$873$	−16.6248	+	51.1659i	−0.562664	+	1.73170i
$874$	2.95775	+	35.3008i	0.100048	+	1.19407i
$875$	−17.8592	+	24.5811i	−0.603752	+	0.830993i
$876$	3.12348	−	6.28641i	0.105533	−	0.212398i
$877$	−17.1468	+	5.57134i	−0.579007	+	0.188131i	−0.583856	−	0.811857i	$-0.698457\pi$
$877$	−17.1468	+	5.57134i	−0.579007	+	0.188131i	0.00484842	+	0.999988i	$0.498457\pi$
$878$	−6.68345	+	28.4715i	−0.225555	+	0.960866i
$879$	82.1989			2.77250
$880$		0			0
$881$	−29.8284			−1.00495			−0.502473	−	0.864593i	$-0.667576\pi$
$881$	−29.8284			−1.00495			−0.502473	+	0.864593i	$0.667576\pi$
$882$	3.38874	−	14.4360i	0.114105	−	0.486086i
$883$	26.9881	−	8.76898i	0.908223	−	0.295100i	0.182596	−	0.983188i	$-0.441550\pi$
$883$	26.9881	−	8.76898i	0.908223	−	0.295100i	0.725627	+	0.688088i	$0.241550\pi$
$884$	−26.9624	+	54.2652i	−0.906842	+	1.82514i
$885$	−9.75062	+	13.4206i	−0.327764	+	0.451128i
$886$	−3.24710	−	38.7541i	−0.109088	−	1.30197i
$887$	4.83979	−	14.8954i	0.162504	−	0.500137i	−0.836339	−	0.548212i	$-0.815309\pi$
$887$	4.83979	−	14.8954i	0.162504	−	0.500137i	0.998844	+	0.0480750i	$0.0153087\pi$
$888$	−34.0967	+	41.1696i	−1.14421	+	1.38156i
$889$	13.5669	−	9.85690i	0.455018	−	0.330590i
$890$	0.703309	+	0.815094i	0.0235750	+	0.0273220i
$891$		0			0
$892$	0.0796898	−	0.538289i	0.00266821	−	0.0180233i
$893$	2.32654	+	3.20221i	0.0778548	+	0.107158i
$894$	−68.3405	−	41.4056i	−2.28565	−	1.38481i
$895$	−3.49236	+	10.7484i	−0.116737	+	0.359279i
$896$	−11.9845	+	32.0988i	−0.400373	+	1.07235i
$897$	−49.1756	−	35.7282i	−1.64193	−	1.19293i
$898$	−15.6979	−	37.3632i	−0.523847	−	1.24682i
$899$	−18.6758	+	6.06814i	−0.622873	+	0.202384i
$900$	−16.3492	−	31.3011i	−0.544973	−	1.04337i
$901$			57.8602i			1.92760i
$902$		0			0
$903$	62.6274			2.08411
$904$	−35.4559	−	14.0606i	−1.17925	−	0.467649i
$905$	7.60119	+	23.3941i	0.252672	+	0.777645i
$906$	22.0955	−	9.28332i	0.734074	−	0.308418i
$907$	−24.0560	+	33.1103i	−0.798767	+	1.09941i	0.194194	+	0.980963i	$0.437791\pi$
$907$	−24.0560	+	33.1103i	−0.798767	+	1.09941i	−0.992961	+	0.118445i	$0.962209\pi$
$908$	32.3132	+	31.6667i	1.07235	+	1.05090i
$909$	−19.0290	−	6.18291i	−0.631154	−	0.205074i
$910$	17.5916	+	10.6583i	0.583157	+	0.353319i
$911$	23.3227	−	16.9449i	0.772715	−	0.561410i	−0.130069	−	0.991505i	$-0.541520\pi$
$911$	23.3227	−	16.9449i	0.772715	−	0.561410i	0.902784	+	0.430095i	$0.141520\pi$
$912$	51.1795	+	15.4930i	1.69472	+	0.513026i
$913$		0			0
$914$	−3.79899	+	3.27798i	−0.125659	+	0.108426i
$915$	−9.96111	−	13.7103i	−0.329304	−	0.453248i
$916$	0.0661775	+	0.392141i	0.00218656	+	0.0129567i
$917$	31.3970	+	10.2015i	1.03682	+	0.336884i
$918$	4.41658	+	52.7119i	0.145769	+	1.73975i
$919$	20.7896	+	15.1045i	0.685785	+	0.498252i	0.875272	−	0.483631i	$-0.160682\pi$
$919$	20.7896	+	15.1045i	0.685785	+	0.498252i	−0.189487	+	0.981883i	$0.560682\pi$
$920$	−4.26463	−	16.6477i	−0.140601	−	0.548859i
$921$	−18.0081	−	55.4234i	−0.593389	−	1.82626i
$922$	−44.9186	−	10.5443i	−1.47931	−	0.347257i
$923$			31.4344i			1.03468i
$924$		0			0
$925$		−	24.7013i		−	0.812175i
$926$	5.72949	−	24.4076i	0.188283	−	0.802084i
$927$	19.8649	+	61.1380i	0.652450	+	2.00803i
$928$	17.2251	−	1.79443i	0.565440	−	0.0589049i
$929$	30.8100	+	22.3848i	1.01084	+	0.734421i	0.964386	−	0.264499i	$-0.0852067\pi$
$929$	30.8100	+	22.3848i	1.01084	+	0.734421i	0.0464577	+	0.998920i	$0.485207\pi$
$930$	29.3115	−	2.45593i	0.961162	−	0.0805332i
$931$	−9.86776	−	3.20623i	−0.323403	−	0.105080i
$932$	16.8927	−	2.85080i	0.553339	−	0.0933811i
$933$	−10.6656	−	14.6799i	−0.349176	−	0.480599i
$934$	6.50043	+	7.53362i	0.212701	+	0.246507i
$935$		0			0
$936$	−47.7990	+	30.2972i	−1.56236	+	0.990295i
$937$	9.97443	−	7.24684i	0.325850	−	0.236744i	−0.412817	−	0.910814i	$-0.635455\pi$
$937$	9.97443	−	7.24684i	0.325850	−	0.236744i	0.738668	+	0.674070i	$0.235455\pi$
$938$	−6.20952	+	10.2489i	−0.202748	+	0.334638i
$939$	−10.1874	−	3.31009i	−0.332454	−	0.108021i
$940$	−1.37143	−	1.34400i	−0.0447313	−	0.0438363i
$941$	−5.18014	+	7.12985i	−0.168868	+	0.232427i	−0.885061	−	0.465476i	$-0.845883\pi$
$941$	−5.18014	+	7.12985i	−0.168868	+	0.232427i	0.716193	+	0.697903i	$0.245883\pi$
$942$	−3.24781	−	7.73021i	−0.105819	−	0.251864i
$943$	−2.03226	−	6.25464i	−0.0661794	−	0.203679i
$944$	−6.71548	−	19.3300i	−0.218570	−	0.629137i
$945$	17.9555			0.584094
$946$		0			0
$947$		−	6.47360i		−	0.210364i	−0.994453	−	0.105182i	$-0.966458\pi$
$947$		−	6.47360i		−	0.210364i	0.994453	−	0.105182i	$-0.0335425\pi$
$948$	72.5290	−	37.8833i	2.35563	−	1.23039i
$949$	4.94376	−	1.60633i	0.160481	−	0.0521435i
$950$	−22.7804	+	9.57106i	−0.739093	+	0.310526i
$951$	−45.8700	−	33.3265i	−1.48744	−	1.08069i
$952$	−3.96687	+	62.5017i	−0.128567	+	2.02569i
$953$	−13.4895	+	41.5164i	−0.436967	+	1.34485i	0.454090	+	0.890956i	$0.349964\pi$
$953$	−13.4895	+	41.5164i	−0.436967	+	1.34485i	−0.891057	+	0.453891i	$0.850036\pi$
$954$	−28.0019	+	46.2174i	−0.906594	+	1.49634i
$955$	−1.41083	−	1.94184i	−0.0456534	−	0.0628365i
$956$	−5.32209	+	35.9497i	−0.172129	+	1.16270i
$957$		0			0
$958$	3.24264	−	2.79793i	0.104765	−	0.0903971i
$959$	7.35023	−	5.34025i	0.237351	−	0.172446i
$960$	−25.7330	−	3.27966i	−0.830528	−	0.105851i
$961$	3.13409	−	9.64574i	0.101100	−	0.311153i
$962$	−39.4470	+	3.30516i	−1.27182	+	0.106563i
$963$	−34.5364	+	47.5353i	−1.11292	+	1.53180i
$964$	−19.8357	−	9.85564i	−0.638866	−	0.317429i
$965$	16.1174	−	5.23687i	0.518838	−	0.168581i
$966$	−61.1613	−	14.3571i	−1.96783	−	0.461932i
$967$	9.60498			0.308875			0.154438	−	0.988003i	$-0.450643\pi$
$967$	9.60498			0.308875			0.154438	+	0.988003i	$0.450643\pi$
$968$		0			0
$969$	97.7401			3.13986
$970$	−17.7786	−	4.17338i	−0.570836	−	0.133999i
$971$	14.2181	−	4.61973i	0.456280	−	0.148254i	−0.0718547	−	0.997415i	$-0.522892\pi$
$971$	14.2181	−	4.61973i	0.456280	−	0.148254i	0.528134	+	0.849161i	$0.322892\pi$
$972$	14.0853	−	28.3486i	0.451788	−	0.909281i
$973$	10.1013	−	13.9032i	0.323831	−	0.445716i
$974$	21.2808	−	1.78306i	0.681880	−	0.0571329i
$975$	13.1018	−	40.3233i	0.419595	−	1.29138i
$976$	20.9007	−	0.422438i	0.669016	−	0.0135219i
$977$	30.4889	−	22.1514i	0.975425	−	0.708688i	0.0187433	−	0.999824i	$-0.494033\pi$
$977$	30.4889	−	22.1514i	0.975425	−	0.708688i	0.956681	+	0.291137i	$0.0940335\pi$
$978$	−19.6404	+	16.9469i	−0.628031	+	0.541901i
$979$		0			0
$980$	4.97918	+	0.737132i	0.159054	+	0.0235468i
$981$	29.6650	+	40.8304i	0.947131	+	1.30361i
$982$	−19.8067	+	32.6912i	−0.632057	+	1.04322i
$983$	5.64638	−	17.3778i	0.180092	−	0.554265i	−0.819738	−	0.572739i	$-0.805881\pi$
$983$	5.64638	−	17.3778i	0.180092	−	0.554265i	0.999829	+	0.0184741i	$0.00588081\pi$
$984$	−9.90730	−	0.628798i	−0.315833	−	0.0200454i
$985$	−6.08913	−	4.42401i	−0.194016	−	0.140961i
$986$	29.1838	−	12.2614i	0.929402	−	0.390484i
$987$	−6.67605	+	2.16918i	−0.212501	+	0.0690458i
$988$	18.3327	+	35.0986i	0.583241	+	1.11664i
$989$		−	38.7485i		−	1.23213i
$990$		0			0
$991$	11.4558			0.363907			0.181953	−	0.983307i	$-0.441758\pi$
$991$	11.4558			0.363907			0.181953	+	0.983307i	$0.441758\pi$
$992$	−18.1710	+	31.4064i	−0.576930	+	0.997155i
$993$	6.42724	+	19.7810i	0.203962	+	0.627732i
$994$	12.5845	+	29.9528i	0.399157	+	0.950045i
$995$	7.61017	−	10.4745i	0.241259	−	0.332064i
$996$	3.51203	−	3.58373i	0.111283	−	0.113555i
$997$	6.85267	+	2.22657i	0.217026	+	0.0705161i	0.415512	−	0.909588i	$-0.363602\pi$
$997$	6.85267	+	2.22657i	0.217026	+	0.0705161i	−0.198486	+	0.980104i	$0.563602\pi$
$998$	21.2075	−	35.0032i	0.671311	−	1.10801i
$999$	−27.9567	+	20.3117i	−0.884510	+	0.642634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.c.245.4		32
8.5	even	2	inner	968.2.o.c.245.1		32
11.2	odd	10		968.2.c.c.485.4	yes	8
11.3	even	5	inner	968.2.o.c.269.8		32
11.4	even	5	inner	968.2.o.c.565.1		32
11.5	even	5	inner	968.2.o.c.493.3		32
11.6	odd	10	inner	968.2.o.c.493.6		32
11.7	odd	10	inner	968.2.o.c.565.8		32
11.8	odd	10	inner	968.2.o.c.269.1		32
11.9	even	5		968.2.c.c.485.5	yes	8
11.10	odd	2	inner	968.2.o.c.245.5		32
44.31	odd	10		3872.2.c.c.1937.8		8
44.35	even	10		3872.2.c.c.1937.7		8
88.5	even	10	inner	968.2.o.c.493.8		32
88.13	odd	10		968.2.c.c.485.3	✓	8
88.21	odd	2	inner	968.2.o.c.245.8		32
88.29	odd	10	inner	968.2.o.c.565.5		32
88.35	even	10		3872.2.c.c.1937.1		8
88.37	even	10	inner	968.2.o.c.565.4		32
88.53	even	10		968.2.c.c.485.6	yes	8
88.61	odd	10	inner	968.2.o.c.493.1		32
88.69	even	10	inner	968.2.o.c.269.3		32
88.75	odd	10		3872.2.c.c.1937.2		8
88.85	odd	10	inner	968.2.o.c.269.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
968.2.c.c.485.3	✓	8	88.13	odd	10
968.2.c.c.485.4	yes	8	11.2	odd	10
968.2.c.c.485.5	yes	8	11.9	even	5
968.2.c.c.485.6	yes	8	88.53	even	10
968.2.o.c.245.1		32	8.5	even	2	inner
968.2.o.c.245.4		32	1.1	even	1	trivial
968.2.o.c.245.5		32	11.10	odd	2	inner
968.2.o.c.245.8		32	88.21	odd	2	inner
968.2.o.c.269.1		32	11.8	odd	10	inner
968.2.o.c.269.3		32	88.69	even	10	inner
968.2.o.c.269.6		32	88.85	odd	10	inner
968.2.o.c.269.8		32	11.3	even	5	inner
968.2.o.c.493.1		32	88.61	odd	10	inner
968.2.o.c.493.3		32	11.5	even	5	inner
968.2.o.c.493.6		32	11.6	odd	10	inner
968.2.o.c.493.8		32	88.5	even	10	inner
968.2.o.c.565.1		32	11.4	even	5	inner
968.2.o.c.565.4		32	88.37	even	10	inner
968.2.o.c.565.5		32	88.29	odd	10	inner
968.2.o.c.565.8		32	11.7	odd	10	inner
3872.2.c.c.1937.1		8	88.35	even	10
3872.2.c.c.1937.2		8	88.75	odd	10
3872.2.c.c.1937.7		8	44.35	even	10
3872.2.c.c.1937.8		8	44.31	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.323190 + 1.37679i) q^{2} +(2.66099 - 0.864609i) q^{3} +(-1.79110 - 0.889929i) q^{4} +(0.681209 - 0.937603i) q^{5} +(0.330378 + 3.94306i) q^{6} +(-0.935846 + 2.88024i) q^{7} +(1.80411 - 2.17835i) q^{8} +(3.90628 - 2.83808i) q^{9} +O(q^{10})\)	\(q+(-0.323190 + 1.37679i) q^{2} +(2.66099 - 0.864609i) q^{3} +(-1.79110 - 0.889929i) q^{4} +(0.681209 - 0.937603i) q^{5} +(0.330378 + 3.94306i) q^{6} +(-0.935846 + 2.88024i) q^{7} +(1.80411 - 2.17835i) q^{8} +(3.90628 - 2.83808i) q^{9} +(1.07072 + 1.24090i) q^{10} +(-5.53553 - 0.819496i) q^{12} +(-2.43570 - 3.35245i) q^{13} +(-3.66302 - 2.21933i) q^{14} +(1.00203 - 3.08393i) q^{15} +(2.41605 + 3.18790i) q^{16} +(5.91501 + 4.29750i) q^{17} +(2.64497 + 6.29536i) q^{18} +(4.54406 - 1.47646i) q^{19} +(-2.05451 + 1.07311i) q^{20} +8.47343i q^{21} +5.24264 q^{23} +(2.91730 - 7.35641i) q^{24} +(1.13003 + 3.47788i) q^{25} +(5.40281 - 2.26997i) q^{26} +(3.00700 - 4.13878i) q^{27} +(4.23940 - 4.32595i) q^{28} +(-2.91163 - 0.946045i) q^{29} +(3.92208 + 2.37628i) q^{30} +(5.18921 - 3.77018i) q^{31} +(-5.16991 + 2.29610i) q^{32} +(-7.82843 + 6.75481i) q^{34} +(2.06301 + 2.83950i) q^{35} +(-9.52221 + 1.60696i) q^{36} +(-6.42420 - 2.08735i) q^{37} +(0.564173 + 6.73339i) q^{38} +(-9.37994 - 6.81492i) q^{39} +(-0.813450 - 3.17545i) q^{40} +(-0.387640 - 1.19303i) q^{41} +(-11.6661 - 2.73853i) q^{42} -7.39104i q^{43} -5.59587i q^{45} +(-1.69437 + 7.21801i) q^{46} +(0.255998 + 0.787881i) q^{47} +(9.18538 + 6.39403i) q^{48} +(-1.75684 - 1.27642i) q^{49} +(-5.15351 + 0.431799i) q^{50} +(19.4554 + 6.32146i) q^{51} +(1.37913 + 8.17217i) q^{52} +(4.65158 + 6.40236i) q^{53} +(4.72640 + 5.47762i) q^{54} +(4.58579 + 7.23486i) q^{56} +(10.8152 - 7.85767i) q^{57} +(2.24351 - 3.70295i) q^{58} +(-4.86543 - 1.58087i) q^{59} +(-4.53922 + 4.63189i) q^{60} +(3.07191 - 4.22813i) q^{61} +(3.51364 + 8.36293i) q^{62} +(4.51866 + 13.9070i) q^{63} +(-1.49039 - 7.85995i) q^{64} -4.80249 q^{65} -2.79793i q^{67} +(-6.76988 - 12.9612i) q^{68} +(13.9506 - 4.53283i) q^{69} +(-4.57613 + 1.92264i) q^{70} +(-6.13703 - 4.45881i) q^{71} +(0.865035 - 13.6294i) q^{72} +(-0.387640 + 1.19303i) q^{73} +(4.95008 - 8.17016i) q^{74} +(6.01400 + 8.27756i) q^{75} +(-9.45280 - 1.39942i) q^{76} +(12.4142 - 10.7117i) q^{78} +(-11.8300 + 8.59501i) q^{79} +(4.63482 - 0.0936773i) q^{80} +(-0.0530189 + 0.163176i) q^{81} +(1.76784 - 0.148122i) q^{82} +(-0.527057 + 0.725432i) q^{83} +(7.54075 - 15.1767i) q^{84} +(8.05871 - 2.61843i) q^{85} +(10.1759 + 2.38871i) q^{86} -8.56578 q^{87} +0.656854 q^{89} +(7.70433 + 1.80853i) q^{90} +(11.9353 - 3.87801i) q^{91} +(-9.39008 - 4.66558i) q^{92} +(10.5487 - 14.5191i) q^{93} +(-1.16748 + 0.0978201i) q^{94} +(1.71113 - 5.26630i) q^{95} +(-11.7718 + 10.5799i) q^{96} +(-9.01418 + 6.54918i) q^{97} +(2.32515 - 2.00627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{4} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^4 + 16 * q^9	\( 32 q - 8 q^{4} + 16 q^{9} - 64 q^{12} - 8 q^{14} + 8 q^{15} + 8 q^{16} - 24 q^{20} + 32 q^{23} + 16 q^{25} - 8 q^{26} + 40 q^{31} - 160 q^{34} + 24 q^{38} - 40 q^{42} + 16 q^{47} - 8 q^{48} - 40 q^{49} + 192 q^{56} + 32 q^{60} + 16 q^{64} - 8 q^{70} - 72 q^{71} + 352 q^{78} - 56 q^{80} + 24 q^{81} + 56 q^{82} + 32 q^{86} - 160 q^{89} + 16 q^{92} + 24 q^{97}+O(q^{100}) \) 32 * q - 8 * q^4 + 16 * q^9 - 64 * q^12 - 8 * q^14 + 8 * q^15 + 8 * q^16 - 24 * q^20 + 32 * q^23 + 16 * q^25 - 8 * q^26 + 40 * q^31 - 160 * q^34 + 24 * q^38 - 40 * q^42 + 16 * q^47 - 8 * q^48 - 40 * q^49 + 192 * q^56 + 32 * q^60 + 16 * q^64 - 8 * q^70 - 72 * q^71 + 352 * q^78 - 56 * q^80 + 24 * q^81 + 56 * q^82 + 32 * q^86 - 160 * q^89 + 16 * q^92 + 24 * q^97

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