LMFDB - Embedded newform 833.2.bc.f.31.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(31,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.bc (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [160,16,0,16,0,0,0,-32,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	833.31
Dual form			833.2.bc.f.215.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.265771 - 0.203934i) q^{2} +(1.66409 - 1.89753i) q^{3} +(-0.488593 - 1.82345i) q^{4} +(0.891574 - 1.80793i) q^{5} +(-0.829238 + 0.164946i) q^{6} +(-0.498405 + 1.20326i) q^{8} +(-0.439851 - 3.34100i) q^{9} +(-0.605653 + 0.298675i) q^{10} +(1.42224 - 4.18979i) q^{11} +(-4.27312 - 2.10727i) q^{12} +(-0.719092 + 0.719092i) q^{13} +(-1.94695 - 4.70036i) q^{15} +(-2.89188 + 1.66963i) q^{16} +(-0.0308939 + 4.12299i) q^{17} +(-0.564443 + 0.977643i) q^{18} +(1.41223 - 1.84045i) q^{19} +(-3.73230 - 0.742400i) q^{20} +(-1.23243 + 0.823483i) q^{22} +(-0.715197 + 0.627211i) q^{23} +(1.45383 + 2.94807i) q^{24} +(0.570087 + 0.742952i) q^{25} +(0.337761 - 0.0444671i) q^{26} +(-0.776096 - 0.518571i) q^{27} +(2.17325 + 3.25249i) q^{29} +(-0.441117 + 1.64627i) q^{30} +(-2.81375 - 2.46759i) q^{31} +(3.69158 + 0.486005i) q^{32} +(-5.58352 - 9.67094i) q^{33} +(0.849027 - 1.08947i) q^{34} +(-5.87725 + 2.43444i) q^{36} +(9.38373 - 3.18535i) q^{37} +(-0.750659 + 0.201138i) q^{38} +(0.167866 + 2.56114i) q^{39} +(1.73104 + 1.97388i) q^{40} +(0.475427 - 0.711527i) q^{41} +(6.12887 + 2.53866i) q^{43} +(-8.33478 - 0.546290i) q^{44} +(-6.43247 - 2.18353i) q^{45} +(0.317988 - 0.0208420i) q^{46} +(-9.87359 - 2.64562i) q^{47} +(-1.64418 + 8.26585i) q^{48} -0.313715i q^{50} +(7.77210 + 6.91966i) q^{51} +(1.66257 + 0.959887i) q^{52} +(-1.68299 + 12.7836i) q^{53} +(0.100510 + 0.296093i) q^{54} +(-6.30683 - 6.30683i) q^{55} +(-1.14224 - 5.74242i) q^{57} +(0.0857057 - 1.30762i) q^{58} +(4.62592 - 3.54959i) q^{59} +(-7.61961 + 5.84674i) q^{60} +(-0.689702 + 10.5228i) q^{61} +(0.244589 + 1.22963i) q^{62} +(3.84042 + 3.84042i) q^{64} +(0.658947 + 1.94119i) q^{65} +(-0.488290 + 3.70893i) q^{66} +(-9.13774 - 5.27568i) q^{67} +(7.53317 - 1.95813i) q^{68} +2.40085i q^{69} +(1.33343 - 6.70358i) q^{71} +(4.23931 + 1.13592i) q^{72} +(-14.6203 + 0.958267i) q^{73} +(-3.14353 - 1.06708i) q^{74} +(2.35845 + 0.154581i) q^{75} +(-4.04598 - 1.67590i) q^{76} +(0.477687 - 0.714910i) q^{78} +(2.71719 + 3.09837i) q^{79} +(0.440250 + 6.71692i) q^{80} +(7.48952 - 2.00681i) q^{81} +(-0.271459 + 0.0921479i) q^{82} +(-2.28169 + 0.945109i) q^{83} +(7.42655 + 3.73181i) q^{85} +(-1.11116 - 1.92458i) q^{86} +(9.78819 + 1.28864i) q^{87} +(4.33254 + 3.79953i) q^{88} +(3.64634 - 13.6083i) q^{89} +(1.26427 + 1.89212i) q^{90} +(1.49313 + 0.997677i) q^{92} +(-9.36467 + 1.23288i) q^{93} +(2.08459 + 2.71669i) q^{94} +(-2.06831 - 4.19411i) q^{95} +(7.06534 - 6.19613i) q^{96} +(-4.35295 + 2.90855i) q^{97} +(-14.6237 - 2.90883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 128 q^{15} - 32 q^{18} - 96 q^{22} + 16 q^{23} - 32 q^{29} - 112 q^{30} - 16 q^{32} - 96 q^{36} - 48 q^{37} - 32 q^{43} + 16 q^{44} - 16 q^{46} + 48 q^{51}+ \cdots + 256 q^{99}+O(q^{100}) $ 160 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 128 * q^15 - 32 * q^18 - 96 * q^22 + 16 * q^23 - 32 * q^29 - 112 * q^30 - 16 * q^32 - 96 * q^36 - 48 * q^37 - 32 * q^43 + 16 * q^44 - 16 * q^46 + 48 * q^51 - 16 * q^53 - 32 * q^57 + 48 * q^58 - 48 * q^60 + 96 * q^64 + 32 * q^65 + 32 * q^71 + 80 * q^72 + 80 * q^74 + 224 * q^78 + 16 * q^79 + 64 * q^81 + 224 * q^85 - 48 * q^86 + 112 * q^88 + 512 * q^92 - 48 * q^93 + 48 * q^95 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.265771	−	0.203934i	−0.187929	−	0.144203i	0.510512	−	0.859871i	$-0.329456\pi$
$2$	−0.265771	−	0.203934i	−0.187929	−	0.144203i	−0.698441	+	0.715668i	$0.746122\pi$
$3$	1.66409	−	1.89753i	0.960764	−	1.09554i	−0.0346040	−	0.999401i	$-0.511017\pi$
$3$	1.66409	−	1.89753i	0.960764	−	1.09554i	0.995368	−	0.0961401i	$-0.0306497\pi$
$4$	−0.488593	−	1.82345i	−0.244296	−	0.911726i
$5$	0.891574	−	1.80793i	0.398724	−	0.808533i	−0.601231	−	0.799075i	$-0.705323\pi$
$5$	0.891574	−	1.80793i	0.398724	−	0.808533i	0.999955	−	0.00945738i	$-0.00301042\pi$
$6$	−0.829238	+	0.164946i	−0.338535	+	0.0673388i
$7$		0			0
$7$		0			0
$8$	−0.498405	+	1.20326i	−0.176213	+	0.425415i
$9$	−0.439851	−	3.34100i	−0.146617	−	1.11367i
$10$	−0.605653	+	0.298675i	−0.191524	+	0.0944494i
$11$	1.42224	−	4.18979i	0.428822	−	1.26327i	−0.491078	−	0.871116i	$-0.663397\pi$
$11$	1.42224	−	4.18979i	0.428822	−	1.26327i	0.919900	−	0.392153i	$-0.128270\pi$
$12$	−4.27312	−	2.10727i	−1.23354	−	0.608317i
$13$	−0.719092	+	0.719092i	−0.199440	+	0.199440i	−0.799760	−	0.600320i	$-0.795040\pi$
$13$	−0.719092	+	0.719092i	−0.199440	+	0.199440i	0.600320	+	0.799760i	$0.295040\pi$
$14$		0			0
$15$	−1.94695	−	4.70036i	−0.502701	−	1.21363i
$16$	−2.89188	+	1.66963i	−0.722970	+	0.417407i
$17$	−0.0308939	+	4.12299i	−0.00749287	+	0.999972i
$17$	−0.0308939	+	4.12299i	−0.00749287	+	0.999972i
$18$	−0.564443	+	0.977643i	−0.133040	+	0.230433i
$19$	1.41223	−	1.84045i	0.323987	−	0.422228i	−0.602755	−	0.797926i	$-0.705930\pi$
$19$	1.41223	−	1.84045i	0.323987	−	0.422228i	0.926742	+	0.375698i	$0.122597\pi$
$20$	−3.73230	−	0.742400i	−0.834567	−	0.166006i
$21$		0			0
$22$	−1.23243	+	0.823483i	−0.262755	+	0.175567i
$23$	−0.715197	+	0.627211i	−0.149129	+	0.130782i	−0.730660	−	0.682742i	$-0.760787\pi$
$23$	−0.715197	+	0.627211i	−0.149129	+	0.130782i	0.581531	+	0.813524i	$0.302454\pi$
$24$	1.45383	+	2.94807i	0.296761	+	0.601772i
$25$	0.570087	+	0.742952i	0.114017	+	0.148590i
$26$	0.337761	−	0.0444671i	0.0662404	−	0.00872071i
$27$	−0.776096	−	0.518571i	−0.149360	−	0.0997990i
$28$		0			0
$29$	2.17325	+	3.25249i	0.403562	+	0.603972i	0.976472	−	0.215646i	$-0.0691856\pi$
$29$	2.17325	+	3.25249i	0.403562	+	0.603972i	−0.572910	+	0.819618i	$0.694186\pi$
$30$	−0.441117	+	1.64627i	−0.0805365	+	0.300566i
$31$	−2.81375	−	2.46759i	−0.505364	−	0.443192i	0.368311	−	0.929703i	$-0.379936\pi$
$31$	−2.81375	−	2.46759i	−0.505364	−	0.443192i	−0.873675	+	0.486510i	$0.838270\pi$
$32$	3.69158	+	0.486005i	0.652585	+	0.0859144i
$33$	−5.58352	−	9.67094i	−0.971966	−	1.68350i
$34$	0.849027	−	1.08947i	0.145607	−	0.186843i
$35$		0			0
$36$	−5.87725	+	2.43444i	−0.979542	+	0.405740i
$37$	9.38373	−	3.18535i	1.54268	−	0.523668i	0.584881	−	0.811119i	$-0.301141\pi$
$37$	9.38373	−	3.18535i	1.54268	−	0.523668i	0.957795	+	0.287451i	$0.0928080\pi$
$38$	−0.750659	+	0.201138i	−0.121773	+	0.0326290i
$39$	0.167866	+	2.56114i	0.0268800	+	0.410110i
$40$	1.73104	+	1.97388i	0.273702	+	0.312097i
$41$	0.475427	−	0.711527i	0.0742492	−	0.111122i	−0.792487	−	0.609889i	$-0.791214\pi$
$41$	0.475427	−	0.711527i	0.0742492	−	0.111122i	0.866736	+	0.498768i	$0.166214\pi$
$42$		0			0
$43$	6.12887	+	2.53866i	0.934644	+	0.387142i	0.797438	−	0.603401i	$-0.206188\pi$
$43$	6.12887	+	2.53866i	0.934644	+	0.387142i	0.137205	+	0.990543i	$0.456188\pi$
$44$	−8.33478	−	0.546290i	−1.25651	−	0.0823563i
$45$	−6.43247	−	2.18353i	−0.958896	−	0.325501i
$46$	0.317988	−	0.0208420i	0.0468848	−	0.00307299i
$47$	−9.87359	−	2.64562i	−1.44021	−	0.385903i	−0.547604	−	0.836738i	$-0.684460\pi$
$47$	−9.87359	−	2.64562i	−1.44021	−	0.385903i	−0.892608	+	0.450834i	$0.851127\pi$
$48$	−1.64418	+	8.26585i	−0.237317	+	1.19307i
$49$		0			0
$50$		−	0.313715i		−	0.0443661i
$51$	7.77210	+	6.91966i	1.08831	+	0.968946i
$52$	1.66257	+	0.959887i	0.230557	+	0.133112i
$53$	−1.68299	+	12.7836i	−0.231177	+	1.75596i	0.344969	+	0.938614i	$0.387889\pi$
$53$	−1.68299	+	12.7836i	−0.231177	+	1.75596i	−0.576146	+	0.817347i	$0.695444\pi$
$54$	0.100510	+	0.296093i	0.0136777	+	0.0402932i
$55$	−6.30683	−	6.30683i	−0.850412	−	0.850412i
$56$		0			0
$57$	−1.14224	−	5.74242i	−0.151293	−	0.760603i
$58$	0.0857057	−	1.30762i	0.0112537	−	0.171698i
$59$	4.62592	−	3.54959i	0.602243	−	0.462118i	−0.262085	−	0.965045i	$-0.584410\pi$
$59$	4.62592	−	3.54959i	0.602243	−	0.462118i	0.864329	+	0.502927i	$0.167744\pi$
$60$	−7.61961	+	5.84674i	−0.983688	+	0.754810i
$61$	−0.689702	+	10.5228i	−0.0883073	+	1.34731i	0.691993	+	0.721904i	$0.256733\pi$
$61$	−0.689702	+	10.5228i	−0.0883073	+	1.34731i	−0.780301	+	0.625405i	$0.784934\pi$
$62$	0.244589	+	1.22963i	0.0310628	+	0.156163i
$63$		0			0
$64$	3.84042	+	3.84042i	0.480052	+	0.480052i
$65$	0.658947	+	1.94119i	0.0817323	+	0.240775i
$66$	−0.488290	+	3.70893i	−0.0601043	+	0.456537i
$67$	−9.13774	−	5.27568i	−1.11635	−	0.644526i	−0.175885	−	0.984411i	$-0.556279\pi$
$67$	−9.13774	−	5.27568i	−1.11635	−	0.644526i	−0.940467	+	0.339884i	$0.889612\pi$
$68$	7.53317	−	1.95813i	0.913531	−	0.237458i
$69$			2.40085i			0.289028i
$70$		0			0
$71$	1.33343	−	6.70358i	0.158249	−	0.795569i	−0.817373	−	0.576109i	$-0.804570\pi$
$71$	1.33343	−	6.70358i	0.158249	−	0.795569i	0.975621	−	0.219460i	$-0.0704296\pi$
$72$	4.23931	+	1.13592i	0.499607	+	0.133869i
$73$	−14.6203	+	0.958267i	−1.71118	+	0.112157i	−0.889247	−	0.457427i	$-0.848771\pi$
$73$	−14.6203	+	0.958267i	−1.71118	+	0.112157i	−0.821933	+	0.569584i	$0.807104\pi$
$74$	−3.14353	−	1.06708i	−0.365427	−	0.124046i
$75$	2.35845	+	0.154581i	0.272331	+	0.0178495i
$76$	−4.04598	−	1.67590i	−0.464105	−	0.192239i
$77$		0			0
$78$	0.477687	−	0.714910i	0.0540875	−	0.0809476i
$79$	2.71719	+	3.09837i	0.305708	+	0.348593i	0.884212	−	0.467087i	$-0.154696\pi$
$79$	2.71719	+	3.09837i	0.305708	+	0.348593i	−0.578503	+	0.815680i	$0.696363\pi$
$80$	0.440250	+	6.71692i	0.0492215	+	0.750975i
$81$	7.48952	−	2.00681i	0.832169	−	0.222979i
$82$	−0.271459	+	0.0921479i	−0.0299776	+	0.0101760i
$83$	−2.28169	+	0.945109i	−0.250448	+	0.103739i	−0.504376	−	0.863484i	$-0.668277\pi$
$83$	−2.28169	+	0.945109i	−0.250448	+	0.103739i	0.253928	+	0.967223i	$0.418277\pi$
$84$		0			0
$85$	7.42655	+	3.73181i	0.805522	+	0.404771i
$86$	−1.11116	−	1.92458i	−0.119819	−	0.207533i
$87$	9.78819	+	1.28864i	1.04940	+	0.138157i
$88$	4.33254	+	3.79953i	0.461850	+	0.405032i
$89$	3.64634	−	13.6083i	0.386511	−	1.44248i	−0.449261	−	0.893401i	$-0.648313\pi$
$89$	3.64634	−	13.6083i	0.386511	−	1.44248i	0.835772	−	0.549077i	$-0.185021\pi$
$90$	1.26427	+	1.89212i	0.133266	+	0.199447i
$91$		0			0
$92$	1.49313	+	0.997677i	0.155669	+	0.104015i
$93$	−9.36467	+	1.23288i	−0.971071	+	0.127844i
$94$	2.08459	+	2.71669i	0.215009	+	0.280205i
$95$	−2.06831	−	4.19411i	−0.212204	−	0.430307i
$96$	7.06534	−	6.19613i	0.721103	−	0.632390i
$97$	−4.35295	+	2.90855i	−0.441975	+	0.295318i	−0.756576	−	0.653906i	$-0.773129\pi$
$97$	−4.35295	+	2.90855i	−0.441975	+	0.295318i	0.314601	+	0.949224i	$0.398129\pi$
$98$		0			0
$99$	−14.6237	−	2.90883i	−1.46973	−	0.292348i
$100$	1.07620	−	1.40253i	0.107620	−	0.140253i
$101$	6.67712	−	11.5651i	0.664398	−	1.15077i	−0.315050	−	0.949075i	$-0.602021\pi$
$101$	6.67712	−	11.5651i	0.664398	−	1.15077i	0.979448	−	0.201696i	$-0.0646453\pi$
$102$	−0.654451	−	3.42404i	−0.0648003	−	0.339030i
$103$	−12.6852	+	7.32378i	−1.24991	+	0.721633i	−0.971091	−	0.238712i	$-0.923275\pi$
$103$	−12.6852	+	7.32378i	−1.24991	+	0.721633i	−0.278815	+	0.960345i	$0.589942\pi$
$104$	−0.506853	−	1.22365i	−0.0497010	−	0.119989i
$105$		0			0
$106$	3.05429	−	3.05429i	0.296659	−	0.296659i
$107$	−0.335449	−	0.165425i	−0.0324291	−	0.0159922i	0.426002	−	0.904722i	$-0.359922\pi$
$107$	−0.335449	−	0.165425i	−0.0324291	−	0.0159922i	−0.458431	+	0.888730i	$0.651588\pi$
$108$	−0.566394	+	1.66854i	−0.0545013	+	0.160556i
$109$	10.2477	−	5.05362i	0.981554	−	0.484049i	0.120583	−	0.992703i	$-0.461524\pi$
$109$	10.2477	−	5.05362i	0.981554	−	0.484049i	0.860971	+	0.508654i	$0.169857\pi$
$110$	0.390000	+	2.96235i	0.0371851	+	0.282449i
$111$	9.57109	−	23.1066i	0.908447	−	2.19319i
$112$		0			0
$113$	1.10240	−	0.219281i	0.103705	−	0.0206282i	−0.142965	−	0.989728i	$-0.545664\pi$
$113$	1.10240	−	0.219281i	0.103705	−	0.0206282i	0.246670	+	0.969100i	$0.420664\pi$
$114$	−0.867498	+	1.75911i	−0.0812487	+	0.164756i
$115$	0.496304	+	1.85223i	0.0462806	+	0.172722i
$116$	4.86893	−	5.55195i	0.452069	−	0.515486i
$117$	2.71878	+	2.08619i	0.251351	+	0.192869i
$118$	−1.95332			−0.179817
$119$		0			0
$120$	6.62611			0.604878
$121$	−6.80468	−	5.22141i	−0.618607	−	0.474674i
$122$	2.32926	−	2.65601i	0.210881	−	0.240464i
$123$	−0.558991	−	2.08618i	−0.0504025	−	0.188105i
$124$	−3.12476	+	6.33638i	−0.280612	+	0.569024i
$125$	11.7369	−	2.33462i	1.04978	−	0.208815i
$126$		0			0
$127$	2.61124	−	6.30409i	0.231710	−	0.559398i	−0.764669	−	0.644424i	$-0.777097\pi$
$127$	2.61124	−	6.30409i	0.231710	−	0.559398i	0.996379	+	0.0850259i	$0.0270973\pi$
$128$	−1.20949	−	9.18702i	−0.106905	−	0.812025i
$129$	15.0162	−	7.40517i	1.32210	−	0.651988i
$130$	0.220745	−	0.650295i	0.0193607	−	0.0570347i
$131$	−6.49860	−	3.20476i	−0.567785	−	0.280001i	0.135654	−	0.990756i	$-0.456687\pi$
$131$	−6.49860	−	3.20476i	−0.567785	−	0.280001i	−0.703439	+	0.710756i	$0.748353\pi$
$132$	−14.9064	+	14.9064i	−1.29744	+	1.29744i
$133$		0			0
$134$	1.35266	+	3.26561i	0.116852	+	0.282106i
$135$	−1.62949	+	0.940786i	−0.140244	+	0.0809700i
$136$	−4.94562	−	2.09209i	−0.424083	−	0.179395i
$137$	4.13366	−	7.15972i	0.353163	−	0.611696i	−0.633639	−	0.773629i	$-0.718439\pi$
$137$	4.13366	−	7.15972i	0.353163	−	0.611696i	0.986802	+	0.161933i	$0.0517728\pi$
$138$	0.489613	−	0.638076i	0.0416786	−	0.0543166i
$139$	20.1083	+	3.99980i	1.70557	+	0.339258i	0.949148	−	0.314829i	$-0.101947\pi$
$139$	20.1083	+	3.99980i	1.70557	+	0.339258i	0.756419	+	0.654088i	$0.226947\pi$
$140$		0			0
$141$	−21.4507	+	14.3329i	−1.80648	+	1.20705i
$142$	−1.72147	+	1.50969i	−0.144463	+	0.126690i
$143$	1.99012	+	4.03557i	0.166422	+	0.337471i
$144$	6.85023	+	8.92739i	0.570852	+	0.743949i
$145$	7.81790	−	1.02925i	0.649241	−	0.0854742i
$146$	4.08109	+	2.72690i	0.337753	+	0.225680i
$147$		0			0
$148$	−10.3932	−	15.5544i	−0.854312	−	1.27857i
$149$	0.105659	−	0.394325i	0.00865593	−	0.0323044i	−0.961463	−	0.274935i	$-0.911344\pi$
$149$	0.105659	−	0.394325i	0.00865593	−	0.0323044i	0.970119	+	0.242631i	$0.0780103\pi$
$150$	−0.595285	−	0.522051i	−0.0486048	−	0.0426253i
$151$	−9.49701	−	1.25031i	−0.772856	−	0.101748i	−0.266224	−	0.963911i	$-0.585776\pi$
$151$	−9.49701	−	1.25031i	−0.772856	−	0.101748i	−0.506632	+	0.862163i	$0.669110\pi$
$152$	1.51067	+	2.61656i	0.122532	+	0.212231i
$153$	13.7885	−	1.71029i	1.11474	−	0.138268i
$154$		0			0
$155$	−6.96991	+	2.88703i	−0.559836	+	0.231892i
$156$	4.58809	−	1.55745i	0.367341	−	0.124696i
$157$	−17.4977	+	4.68850i	−1.39647	+	0.374183i	−0.877076	−	0.480352i	$-0.840509\pi$
$157$	−17.4977	+	4.68850i	−1.39647	+	0.374183i	−0.519394	+	0.854535i	$0.673842\pi$
$158$	−0.0902916	−	1.37758i	−0.00718321	−	0.109595i
$159$	21.4566	+	24.4666i	1.70162	+	1.94033i
$160$	4.16998	−	6.24082i	0.329666	−	0.493380i
$161$		0			0
$162$	−2.39976	−	0.994012i	−0.188543	−	0.0780970i
$163$	−1.21200	−	0.0794387i	−0.0949312	−	0.00622212i	0.0178635	−	0.999840i	$-0.494314\pi$
$163$	−1.21200	−	0.0794387i	−0.0949312	−	0.00622212i	−0.112795	+	0.993618i	$0.535980\pi$
$164$	−1.52972	−	0.519272i	−0.119451	−	0.0405483i
$165$	−22.4626	+	1.47227i	−1.74871	+	0.114616i
$166$	0.799148	+	0.214131i	0.0620259	+	0.0166198i
$167$	−1.21609	+	6.11371i	−0.0941040	+	0.473093i	0.904781	+	0.425878i	$0.140035\pi$
$167$	−1.21609	+	6.11371i	−0.0941040	+	0.473093i	−0.998885	+	0.0472151i	$0.984965\pi$
$168$		0			0
$169$			11.9658i			0.920447i
$170$	−1.21272	−	2.50633i	−0.0930116	−	0.192227i
$171$	−6.77012	−	3.90873i	−0.517724	−	0.298908i
$172$	1.63461	−	12.4161i	0.124638	−	0.946716i
$173$	4.64099	+	13.6719i	0.352848	+	1.03946i	0.967979	+	0.251031i	$0.0807697\pi$
$173$	4.64099	+	13.6719i	0.352848	+	1.03946i	−0.615131	+	0.788425i	$0.710897\pi$
$174$	−2.33862	−	2.33862i	−0.177291	−	0.177291i
$175$		0			0
$176$	2.88243	+	14.4910i	0.217272	+	1.09230i
$177$	0.962485	−	14.6847i	0.0723448	−	1.10377i
$178$	−3.74428	+	2.87309i	−0.280646	+	0.215347i
$179$	5.53157	−	4.24452i	0.413449	−	0.317251i	−0.381007	−	0.924572i	$-0.624423\pi$
$179$	5.53157	−	4.24452i	0.413449	−	0.317251i	0.794456	+	0.607321i	$0.207756\pi$
$180$	−0.838705	+	12.7962i	−0.0625134	+	0.953770i
$181$	−1.46307	−	7.35534i	−0.108749	−	0.546718i	−0.996295	−	0.0859995i	$-0.972592\pi$
$181$	−1.46307	−	7.35534i	−0.108749	−	0.546718i	0.887546	−	0.460719i	$-0.152408\pi$
$182$		0			0
$183$	18.8197	+	18.8197i	1.39119	+	1.39119i
$184$	−0.398238	−	1.17317i	−0.0293585	−	0.0864872i
$185$	2.60740	−	19.8051i	0.191700	−	1.45610i
$186$	2.74029	+	1.58211i	0.200928	+	0.116006i
$187$	17.2305	+	5.99333i	1.26002	+	0.438276i
$188$			19.2967i			1.40735i
$189$		0			0
$190$	−0.305623	+	1.53647i	−0.0221722	+	0.111467i
$191$	−3.63962	−	0.975234i	−0.263354	−	0.0705655i	0.124726	−	0.992191i	$-0.460195\pi$
$191$	−3.63962	−	0.975234i	−0.263354	−	0.0705655i	−0.388080	+	0.921626i	$0.626862\pi$
$192$	13.6781	−	0.896511i	0.987133	−	0.0647001i
$193$	19.6593	+	6.67343i	1.41511	+	0.480364i	0.921179	−	0.389138i	$-0.127227\pi$
$193$	19.6593	+	6.67343i	1.41511	+	0.480364i	0.493928	+	0.869503i	$0.335561\pi$
$194$	1.75004	+	0.114704i	0.125646	+	0.00823524i
$195$	4.78003	+	1.97995i	0.342305	+	0.141787i
$196$		0			0
$197$	11.7306	−	17.5561i	0.835771	−	1.25082i	−0.130024	−	0.991511i	$-0.541505\pi$
$197$	11.7306	−	17.5561i	0.835771	−	1.25082i	0.965795	−	0.259308i	$-0.0834946\pi$
$198$	3.29335	+	3.75534i	0.234048	+	0.266880i
$199$	0.907813	+	13.8505i	0.0643531	+	0.981839i	0.900923	+	0.433979i	$0.142891\pi$
$199$	0.907813	+	13.8505i	0.0643531	+	0.981839i	−0.836570	+	0.547860i	$0.815443\pi$
$200$	−1.17810	+	0.315670i	−0.0833040	+	0.0223212i
$201$	−25.2168	+	8.55995i	−1.77866	+	0.603772i
$202$	−4.13310	+	1.71199i	−0.290804	+	0.120455i
$203$		0			0
$204$	8.82027	−	17.5529i	0.617543	−	1.22895i
$205$	−0.862515	−	1.49392i	−0.0602406	−	0.104340i
$206$	4.86491	+	0.640478i	0.338955	+	0.0446242i
$207$	2.41009	+	2.11360i	0.167513	+	0.146905i
$208$	0.878911	−	3.28014i	0.0609415	−	0.227437i
$209$	−5.70257	−	8.53450i	−0.394455	−	0.590343i
$210$		0			0
$211$	−2.83065	−	1.89138i	−0.194870	−	0.130208i	0.454308	−	0.890845i	$-0.349887\pi$
$211$	−2.83065	−	1.89138i	−0.194870	−	0.130208i	−0.649177	+	0.760637i	$0.724887\pi$
$212$	24.1326	−	3.17711i	1.65743	−	0.218205i
$213$	−10.5013	−	13.6856i	−0.719539	−	0.937722i
$214$	0.0554170	+	0.112374i	0.00378823	+	0.00768176i
$215$	10.0541	−	8.81718i	0.685682	−	0.601327i
$216$	1.01078	−	0.675384i	0.0687751	−	0.0459541i
$217$		0			0
$218$	−3.75415	−	0.746748i	−0.254263	−	0.0505761i
$219$	−22.5112	+	29.3372i	−1.52117	+	1.98242i
$220$	−8.41873	+	14.5817i	−0.567591	+	0.983096i
$221$	−2.94259	−	2.98702i	−0.197940	−	0.200929i
$222$	−7.25594	+	4.18922i	−0.486987	+	0.281162i
$223$	1.86869	+	4.51141i	0.125137	+	0.302107i	0.974016	−	0.226481i	$-0.0727220\pi$
$223$	1.86869	+	4.51141i	0.125137	+	0.302107i	−0.848879	+	0.528587i	$0.822722\pi$
$224$		0			0
$225$	2.23145	−	2.23145i	0.148764	−	0.148764i
$226$	−0.337705	−	0.166538i	−0.0224638	−	0.0110779i
$227$	0.870012	−	2.56297i	0.0577447	−	0.170111i	−0.914230	−	0.405195i	$-0.867203\pi$
$227$	0.870012	−	2.56297i	0.0577447	−	0.170111i	0.971975	+	0.235085i	$0.0755368\pi$
$228$	−9.91295	+	4.88852i	−0.656501	+	0.323750i
$229$	1.77999	+	13.5204i	0.117625	+	0.893453i	0.943911	+	0.330201i	$0.107117\pi$
$229$	1.77999	+	13.5204i	0.117625	+	0.893453i	−0.826285	+	0.563252i	$0.809550\pi$
$230$	0.245829	−	0.593484i	0.0162095	−	0.0391332i
$231$		0			0
$232$	−4.99674	+	0.993913i	−0.328052	+	0.0652536i
$233$	−0.196479	+	0.398420i	−0.0128718	+	0.0261014i	−0.903214	−	0.429191i	$-0.858799\pi$
$233$	−0.196479	+	0.398420i	−0.0128718	+	0.0261014i	0.890342	+	0.455293i	$0.150465\pi$
$234$	−0.297129	−	1.10890i	−0.0194239	−	0.0724912i
$235$	−13.5861	+	15.4920i	−0.886262	+	1.01059i
$236$	−8.73270	−	6.70084i	−0.568450	−	0.436187i
$237$	10.4009			0.675612
$238$		0			0
$239$	6.21322			0.401900			0.200950	−	0.979602i	$-0.435597\pi$
$239$	6.21322			0.401900			0.200950	+	0.979602i	$0.435597\pi$
$240$	13.4782	+	10.3422i	0.870014	+	0.667585i
$241$	−5.78145	+	6.59248i	−0.372416	+	0.424659i	−0.907442	−	0.420176i	$-0.861968\pi$
$241$	−5.78145	+	6.59248i	−0.372416	+	0.424659i	0.535027	+	0.844835i	$0.320302\pi$
$242$	0.743667	+	2.77540i	0.0478047	+	0.178410i
$243$	9.89376	−	20.0626i	0.634685	−	1.28701i
$244$	19.5248	−	3.88373i	1.24995	−	0.248630i
$245$		0			0
$246$	−0.276879	+	0.668445i	−0.0176532	+	0.0426185i
$247$	0.307932	+	2.33897i	0.0195932	+	0.148825i
$248$	4.37153	−	2.15580i	0.277592	−	0.136893i
$249$	−2.00357	+	5.90234i	−0.126971	+	0.374045i
$250$	−3.59544	−	1.77308i	−0.227396	−	0.112139i
$251$	9.03734	−	9.03734i	0.570432	−	0.570432i	−0.361817	−	0.932249i	$-0.617843\pi$
$251$	9.03734	−	9.03734i	0.570432	−	0.570432i	0.932249	+	0.361817i	$0.117843\pi$
$252$		0			0
$253$	1.61070	+	3.88857i	0.101264	+	0.244472i
$254$	−1.97961	+	1.14293i	−0.124212	+	0.0717137i
$255$	19.4397	−	7.88205i	1.21736	−	0.493593i
$256$	3.87908	−	6.71876i	0.242442	−	0.419922i
$257$	−0.816682	+	1.06432i	−0.0509432	+	0.0663905i	−0.818130	−	0.575033i	$-0.804989\pi$
$257$	−0.816682	+	1.06432i	−0.0509432	+	0.0663905i	0.767187	+	0.641424i	$0.221656\pi$
$258$	−5.50103	−	1.09422i	−0.342479	−	0.0681234i
$259$		0			0
$260$	3.21772	−	2.15001i	0.199554	−	0.133338i
$261$	9.91068	−	8.69143i	0.613456	−	0.537986i
$262$	1.07359	+	2.17702i	0.0663263	+	0.134496i
$263$	−1.91223	−	2.49206i	−0.117913	−	0.153667i	0.730668	−	0.682733i	$-0.239209\pi$
$263$	−1.91223	−	2.49206i	−0.117913	−	0.153667i	−0.848581	+	0.529066i	$0.822542\pi$
$264$	14.4195	−	1.89836i	0.887458	−	0.116836i
$265$	21.6114	+	14.4403i	1.32758	+	0.887058i
$266$		0			0
$267$	−19.7544	−	29.5645i	−1.20895	−	1.80932i
$268$	−5.15531	+	19.2399i	−0.314911	+	1.17526i
$269$	−5.30807	−	4.65506i	−0.323639	−	0.283824i	0.482073	−	0.876131i	$-0.339884\pi$
$269$	−5.30807	−	4.65506i	−0.323639	−	0.283824i	−0.805712	+	0.592307i	$0.798217\pi$
$270$	0.624929	+	0.0822735i	0.0380320	+	0.00500701i
$271$	−0.680454	−	1.17858i	−0.0413347	−	0.0715937i	0.844618	−	0.535370i	$-0.179828\pi$
$271$	−0.680454	−	1.17858i	−0.0413347	−	0.0715937i	−0.885953	+	0.463776i	$0.846494\pi$
$272$	−6.79451	−	11.9748i	−0.411978	−	0.726077i
$273$		0			0
$274$	−2.55872	+	1.05985i	−0.154578	+	0.0640282i
$275$	3.92362	−	1.33189i	0.236603	−	0.0803159i
$276$	4.37783	−	1.17304i	0.263514	−	0.0706084i
$277$	1.32132	+	20.1594i	0.0793902	+	1.21126i	0.832749	+	0.553650i	$0.186766\pi$
$277$	1.32132	+	20.1594i	0.0793902	+	1.21126i	−0.753359	+	0.657609i	$0.771568\pi$
$278$	−4.52853	−	5.16380i	−0.271603	−	0.309704i
$279$	−7.00660	+	10.4861i	−0.419474	+	0.627787i
$280$		0			0
$281$	9.10111	+	3.76980i	0.542927	+	0.224888i	0.637254	−	0.770654i	$-0.280070\pi$
$281$	9.10111	+	3.76980i	0.542927	+	0.224888i	−0.0943276	+	0.995541i	$0.530070\pi$
$282$	8.62395	+	0.565243i	0.513549	+	0.0336597i
$283$	13.4730	+	4.57347i	0.800887	+	0.271864i	0.691726	−	0.722160i	$-0.256850\pi$
$283$	13.4730	+	4.57347i	0.800887	+	0.271864i	0.109160	+	0.994024i	$0.465184\pi$
$284$	−12.8752	+	0.843883i	−0.764001	+	0.0500752i
$285$	−11.4003	−	3.05470i	−0.675296	−	0.180945i
$286$	0.294070	−	1.47839i	0.0173887	−	0.0874190i
$287$		0			0
$288$		−	12.5473i		−	0.739359i
$289$	−16.9981	−	0.254750i	−0.999888	−	0.0149853i
$290$	−2.28767	−	1.32079i	−0.134337	−	0.0775593i
$291$	−1.72464	+	13.1000i	−0.101100	+	0.767933i
$292$	8.89074	+	26.1913i	0.520291	+	1.53273i
$293$	−18.6006	−	18.6006i	−1.08666	−	1.08666i	−0.995870	−	0.0907866i	$-0.971062\pi$
$293$	−18.6006	−	18.6006i	−1.08666	−	1.08666i	−0.0907866	−	0.995870i	$-0.528938\pi$
$294$		0			0
$295$	−2.29308	−	11.5281i	−0.133508	−	0.671191i
$296$	−0.844110	+	12.8786i	−0.0490629	+	0.748555i
$297$	−3.27650	+	2.51415i	−0.190122	+	0.145886i
$298$	−0.108497	+	0.0832529i	−0.00628508	+	0.00482271i
$299$	0.0632700	−	0.965314i	0.00365900	−	0.0558256i
$300$	−0.870452	−	4.37606i	−0.0502556	−	0.252652i
$301$		0			0
$302$	2.26905	+	2.26905i	0.130569	+	0.130569i
$303$	−10.8338	−	31.9154i	−0.622387	−	1.83349i
$304$	−1.01112	+	7.68025i	−0.0579919	+	0.440493i
$305$	18.4096	+	10.6288i	1.05413	+	0.608604i
$306$	−4.01338	−	2.35739i	−0.229429	−	0.134763i
$307$		−	5.73107i		−	0.327090i	−0.986536	−	0.163545i	$-0.947707\pi$
$307$		−	5.73107i		−	0.327090i	0.986536	−	0.163545i	$-0.0522928\pi$
$308$		0			0
$309$	−7.21215	+	36.2579i	−0.410285	+	2.06264i
$310$	2.44116	+	0.654108i	0.138649	+	0.0371508i
$311$	−2.04247	+	0.133870i	−0.115818	+	0.00759110i	−0.123202	−	0.992382i	$-0.539316\pi$
$311$	−2.04247	+	0.133870i	−0.115818	+	0.00759110i	0.00738401	+	0.999973i	$0.497650\pi$
$312$	−3.16537	−	1.07450i	−0.179204	−	0.0608314i
$313$	−15.9030	−	1.04233i	−0.898888	−	0.0589163i	−0.391051	−	0.920369i	$-0.627888\pi$
$313$	−15.9030	−	1.04233i	−0.898888	−	0.0589163i	−0.507838	+	0.861453i	$0.669555\pi$
$314$	5.60653	+	2.32230i	0.316395	+	0.131055i
$315$		0			0
$316$	4.32212	−	6.46851i	0.243138	−	0.363882i
$317$	17.9159	+	20.4292i	1.00626	+	1.14742i	0.989052	+	0.147565i	$0.0471436\pi$
$317$	17.9159	+	20.4292i	1.00626	+	1.14742i	0.0172055	+	0.999852i	$0.494523\pi$
$318$	−0.712998	−	10.8782i	−0.0399829	−	0.610022i
$319$	16.7181	−	4.47961i	0.936036	−	0.250810i
$320$	10.3672	−	3.51920i	0.579546	−	0.196729i
$321$	−0.872117	+	0.361243i	−0.0486768	+	0.0201626i
$322$		0			0
$323$	7.54453	+	5.87945i	0.419789	+	0.327142i
$324$	−7.31865	−	12.6763i	−0.406592	−	0.704238i
$325$	−0.944196	−	0.124306i	−0.0523746	−	0.00689525i
$326$	0.305915	+	0.268280i	0.0169431	+	0.0148587i
$327$	7.46375	−	27.8551i	0.412746	−	1.54039i
$328$	0.619194	+	0.926689i	0.0341893	+	0.0511678i
$329$		0			0
$330$	6.27015	+	4.18958i	0.345160	+	0.230629i
$331$	8.11253	−	1.06804i	0.445905	−	0.0587045i	0.0957695	−	0.995404i	$-0.469469\pi$
$331$	8.11253	−	1.06804i	0.445905	−	0.0587045i	0.350136	+	0.936699i	$0.386135\pi$
$332$	2.83818	+	3.69879i	0.155765	+	0.202997i
$333$	−14.7697	−	29.9500i	−0.809375	−	1.64125i
$334$	1.56999	−	1.37685i	0.0859062	−	0.0753377i
$335$	−17.6850	+	11.8168i	−0.966237	+	0.645619i
$336$		0			0
$337$	10.1119	+	2.01138i	0.550829	+	0.109567i	0.462655	−	0.886538i	$-0.346897\pi$
$337$	10.1119	+	2.01138i	0.550829	+	0.109567i	0.0881739	+	0.996105i	$0.471897\pi$
$338$	2.44023	−	3.18017i	0.132731	−	0.172978i
$339$	1.41840	−	2.45674i	0.0770369	−	0.133432i
$340$	3.17621	−	15.3653i	0.172254	−	0.833300i
$341$	−14.3405	+	8.27950i	−0.776582	+	0.448360i
$342$	1.00218	+	2.41948i	0.0541918	+	0.130831i
$343$		0			0
$344$	−6.10932	+	6.10932i	−0.329392	+	0.329392i
$345$	4.34057	+	2.14053i	0.233688	+	0.115242i
$346$	1.55472	−	4.58006i	0.0835822	−	0.246225i
$347$	−18.2742	+	9.01186i	−0.981013	+	0.483782i	−0.860787	−	0.508965i	$-0.830028\pi$
$347$	−18.2742	+	9.01186i	−0.981013	+	0.483782i	−0.120225	+	0.992747i	$0.538362\pi$
$348$	−2.43266	−	18.4779i	−0.130404	−	0.990520i
$349$	−9.93559	+	23.9866i	−0.531840	+	1.28398i	0.398463	+	0.917184i	$0.369544\pi$
$349$	−9.93559	+	23.9866i	−0.531840	+	1.28398i	−0.930303	+	0.366791i	$0.880456\pi$
$350$		0			0
$351$	0.930984	−	0.185184i	0.0496923	−	0.00988441i
$352$	7.28658	−	14.7757i	0.388376	−	0.787548i
$353$	4.92826	+	18.3925i	0.262305	+	0.978934i	0.963880	+	0.266338i	$0.0858139\pi$
$353$	4.92826	+	18.3925i	0.262305	+	0.978934i	−0.701575	+	0.712596i	$0.747519\pi$
$354$	−3.25050	+	3.70648i	−0.172762	+	0.196997i
$355$	−10.9308	−	8.38749i	−0.580146	−	0.445162i
$356$	−26.5957			−1.40957
$357$		0			0
$358$	−2.33573			−0.123447
$359$	−7.23155	−	5.54896i	−0.381667	−	0.292863i	0.400054	−	0.916491i	$-0.368991\pi$
$359$	−7.23155	−	5.54896i	−0.381667	−	0.292863i	−0.781721	+	0.623628i	$0.785658\pi$
$360$	5.83332	−	6.65163i	0.307443	−	0.350572i
$361$	3.52469	+	13.1543i	0.185510	+	0.692333i
$362$	−1.11116	+	2.25321i	−0.0584012	+	0.118426i
$363$	−21.2314	+	4.22319i	−1.11436	+	0.221660i
$364$		0			0
$365$	−11.3026	+	27.2870i	−0.591607	+	1.42826i
$366$	−1.16377	−	8.83969i	−0.0608311	−	0.462058i
$367$	−15.5027	+	7.64508i	−0.809234	+	0.399070i	−0.799339	−	0.600881i	$-0.794817\pi$
$367$	−15.5027	+	7.64508i	−0.809234	+	0.399070i	−0.00989560	+	0.999951i	$0.503150\pi$
$368$	1.02105	−	3.00793i	0.0532261	−	0.156799i
$369$	−2.58633	−	1.27544i	−0.134639	−	0.0663966i
$370$	−4.73190	+	4.73190i	−0.246000	+	0.246000i
$371$		0			0
$372$	6.82361	+	16.4737i	0.353788	+	0.854119i
$373$	−12.2865	+	7.09359i	−0.636169	+	0.367292i	−0.783137	−	0.621849i	$-0.786382\pi$
$373$	−12.2865	+	7.09359i	−0.636169	+	0.367292i	0.146968	+	0.989141i	$0.453048\pi$
$374$	−3.35714	−	5.10674i	−0.173593	−	0.264063i
$375$	15.1013	−	26.1562i	0.779827	−	1.35070i
$376$	8.10441	−	10.5619i	0.417953	−	0.544687i
$377$	−3.90160	−	0.776077i	−0.200943	−	0.0399700i
$378$		0			0
$379$	−5.56998	+	3.72174i	−0.286111	+	0.191173i	−0.690341	−	0.723484i	$-0.742539\pi$
$379$	−5.56998	+	3.72174i	−0.286111	+	0.191173i	0.404230	+	0.914657i	$0.367539\pi$
$380$	−6.63720	+	5.82067i	−0.340481	+	0.298594i
$381$	−7.61688	−	15.4455i	−0.390225	−	0.791297i
$382$	0.768425	+	1.00143i	0.0393160	+	0.0512377i
$383$	23.5730	−	3.10344i	1.20452	−	0.158579i	0.498578	−	0.866845i	$-0.333856\pi$
$383$	23.5730	−	3.10344i	1.20452	−	0.158579i	0.705945	+	0.708266i	$0.250522\pi$
$384$	−19.4454	−	12.9930i	−0.992318	−	0.663046i
$385$		0			0
$386$	−3.86394	−	5.78280i	−0.196669	−	0.294337i
$387$	5.78588	−	21.5932i	0.294113	−	1.09764i
$388$	7.43042	+	6.51630i	0.377222	+	0.330815i
$389$	−8.41677	−	1.10809i	−0.426747	−	0.0561824i	−0.0859061	−	0.996303i	$-0.527379\pi$
$389$	−8.41677	−	1.10809i	−0.426747	−	0.0561824i	−0.340841	+	0.940121i	$0.610712\pi$
$390$	−0.866616	−	1.50102i	−0.0438828	−	0.0760072i
$391$	−2.56389	−	2.96813i	−0.129661	−	0.150105i
$392$		0			0
$393$	−16.8954	+	6.99830i	−0.852260	+	0.353018i
$394$	−6.69793	+	2.27364i	−0.337437	+	0.114544i
$395$	8.02422	−	2.15008i	0.403742	−	0.108182i
$396$	1.84091	+	28.0868i	0.0925090	+	1.41142i
$397$	−1.14713	−	1.30805i	−0.0575727	−	0.0656491i	0.722337	−	0.691542i	$-0.243068\pi$
$397$	−1.14713	−	1.30805i	−0.0575727	−	0.0656491i	−0.779909	+	0.625893i	$0.784735\pi$
$398$	2.58332	−	3.86621i	0.129490	−	0.193796i
$399$		0			0
$400$	−2.88908	−	1.19670i	−0.144454	−	0.0598348i
$401$	0.962269	+	0.0630704i	0.0480534	+	0.00314959i	0.0894109	−	0.995995i	$-0.471502\pi$
$401$	0.962269	+	0.0630704i	0.0480534	+	0.00314959i	−0.0413575	+	0.999144i	$0.513168\pi$
$402$	8.44756	+	2.86756i	0.421326	+	0.143021i
$403$	3.79777	−	0.248919i	0.189180	−	0.0123995i
$404$	−24.3508	−	6.52478i	−1.21150	−	0.324620i
$405$	3.04928	−	15.3298i	0.151520	−	0.761743i
$406$		0			0
$407$		−	43.8462i		−	2.17337i
$408$	−12.1998	+	5.90304i	−0.603979	+	0.292244i
$409$	−9.51518	−	5.49359i	−0.470495	−	0.271641i	0.245952	−	0.969282i	$-0.420900\pi$
$409$	−9.51518	−	5.49359i	−0.470495	−	0.271641i	−0.716447	+	0.697641i	$0.754233\pi$
$410$	−0.0754285	+	0.572937i	−0.00372515	+	0.0282953i
$411$	−6.70700	−	19.7582i	−0.330832	−	0.974600i
$412$	19.5524	+	19.5524i	0.963279	+	0.963279i
$413$		0			0
$414$	−0.209501	−	1.05323i	−0.0102964	−	0.0517635i
$415$	−0.325606	+	4.96779i	−0.0159834	+	0.243859i
$416$	−3.00407	+	2.30510i	−0.147286	+	0.113017i
$417$	41.0519	−	31.5002i	2.01032	−	1.54257i
$418$	−0.224891	+	3.43117i	−0.0109998	+	0.167824i
$419$	−4.51126	−	22.6796i	−0.220390	−	1.10797i	−0.919539	−	0.392998i	$-0.871438\pi$
$419$	−4.51126	−	22.6796i	−0.220390	−	1.10797i	0.699150	−	0.714975i	$-0.253562\pi$
$420$		0			0
$421$	2.85847	+	2.85847i	0.139313	+	0.139313i	0.773324	−	0.634011i	$-0.218593\pi$
$421$	2.85847	+	2.85847i	0.139313	+	0.139313i	−0.634011	+	0.773324i	$0.718593\pi$
$422$	0.366590	+	1.07994i	0.0178453	+	0.0525706i
$423$	−4.49611	+	34.1514i	−0.218609	+	1.66050i
$424$	−14.5431	−	8.39648i	−0.706276	−	0.407769i
$425$	−3.08080	+	2.32751i	−0.149441	+	0.112901i
$426$			5.77881i			0.279984i
$427$		0			0
$428$	−0.137747	+	0.692500i	−0.00665825	+	0.0334733i
$429$	10.9694	+	2.93923i	0.529606	+	0.141907i
$430$	−4.47020	+	0.292993i	−0.215572	+	0.0141294i
$431$	−3.91536	−	1.32908i	−0.188596	−	0.0640198i	0.225544	−	0.974233i	$-0.427584\pi$
$431$	−3.91536	−	1.32908i	−0.188596	−	0.0640198i	−0.414140	+	0.910213i	$0.635918\pi$
$432$	3.11020	+	0.203853i	0.149639	+	0.00980788i
$433$	−13.3279	−	5.52060i	−0.640499	−	0.265303i	0.0387077	−	0.999251i	$-0.487676\pi$
$433$	−13.3279	−	5.52060i	−0.640499	−	0.265303i	−0.679206	+	0.733947i	$0.737676\pi$
$434$		0			0
$435$	11.0567	−	16.5475i	0.530127	−	0.793391i
$436$	−14.2220	−	16.2171i	−0.681110	−	0.776657i
$437$	0.144330	+	2.20205i	0.00690423	+	0.105338i
$438$	11.9657	−	3.20619i	0.571742	−	0.153198i
$439$	−7.06074	+	2.39680i	−0.336991	+	0.114393i	−0.484805	−	0.874622i	$-0.661109\pi$
$439$	−7.06074	+	2.39680i	−0.336991	+	0.114393i	0.147814	+	0.989015i	$0.452776\pi$
$440$	10.7321	−	4.44537i	0.511632	−	0.211925i
$441$		0			0
$442$	0.172903	+	1.39396i	0.00822413	+	0.0663039i
$443$	1.12190	+	1.94318i	0.0533029	+	0.0923233i	0.891446	−	0.453128i	$-0.149692\pi$
$443$	1.12190	+	1.94318i	0.0533029	+	0.0923233i	−0.838143	+	0.545451i	$0.816358\pi$
$444$	−46.8102	−	6.16268i	−2.22152	−	0.292468i
$445$	−21.3519	−	18.7251i	−1.01218	−	0.887657i
$446$	0.423385	−	1.58009i	0.0200478	−	0.0748196i
$447$	−0.572418	−	0.856685i	−0.0270745	−	0.0405198i
$448$		0			0
$449$	−26.9497	−	18.0072i	−1.27184	−	0.849814i	−0.277990	−	0.960584i	$-0.589668\pi$
$449$	−26.9497	−	18.0072i	−1.27184	−	0.849814i	−0.993846	+	0.110770i	$0.964668\pi$
$450$	−1.04812	+	0.137988i	−0.0494091	+	0.00650482i
$451$	−2.30497	−	3.00390i	−0.108537	−	0.141448i
$452$	−0.938472	−	1.90303i	−0.0441420	−	0.0895112i
$453$	−18.1764	+	15.9403i	−0.854002	+	0.748939i
$454$	−0.753901	+	0.503740i	−0.0353823	+	0.0236417i
$455$		0			0
$456$	7.47891	+	1.48765i	0.350232	+	0.0696654i
$457$	10.0716	−	13.1256i	0.471130	−	0.613988i	−0.495984	−	0.868332i	$-0.665193\pi$
$457$	10.0716	−	13.1256i	0.471130	−	0.613988i	0.967114	+	0.254343i	$0.0818593\pi$
$458$	2.28419	−	3.95633i	0.106733	−	0.184867i
$459$	2.16204	−	3.18382i	0.100915	−	0.148608i
$460$	3.13497	−	1.80997i	0.146169	−	0.0843905i
$461$	−2.02862	−	4.89753i	−0.0944823	−	0.228101i	0.869572	−	0.493807i	$-0.164395\pi$
$461$	−2.02862	−	4.89753i	−0.0944823	−	0.228101i	−0.964054	+	0.265706i	$0.914395\pi$
$462$		0			0
$463$	−17.1634	+	17.1634i	−0.797649	+	0.797649i	−0.982724	−	0.185076i	$-0.940747\pi$
$463$	−17.1634	+	17.1634i	−0.797649	+	0.797649i	0.185076	+	0.982724i	$0.440747\pi$
$464$	−11.7152	−	5.77730i	−0.543865	−	0.268205i
$465$	−6.12033	+	18.0299i	−0.283823	+	0.836117i
$466$	0.133470	−	0.0658200i	0.00618287	−	0.00304905i
$467$	−4.51497	−	34.2946i	−0.208928	−	1.58696i	−0.698895	−	0.715224i	$-0.746325\pi$
$467$	−4.51497	−	34.2946i	−0.208928	−	1.58696i	0.489968	−	0.871741i	$-0.337009\pi$
$468$	2.47570	−	5.97687i	0.114439	−	0.276281i
$469$		0			0
$470$	6.77015	−	1.34667i	0.312284	−	0.0621171i
$471$	−20.2212	+	41.0046i	−0.931745	+	1.88939i
$472$	1.96549	+	7.33530i	0.0904689	+	0.337635i
$473$	19.3532	−	22.0681i	0.889860	−	1.01469i
$474$	−2.76426	−	2.12109i	−0.126967	−	0.0974251i
$475$	2.17246			0.0996793
$476$		0			0
$477$	43.4503			1.98945
$478$	−1.65130	−	1.26708i	−0.0755285	−	0.0579551i
$479$	−1.67453	+	1.90943i	−0.0765111	+	0.0872442i	−0.788829	−	0.614613i	$-0.789312\pi$
$479$	−1.67453	+	1.90943i	−0.0765111	+	0.0872442i	0.712318	+	0.701857i	$0.247646\pi$
$480$	−4.90293	−	18.2980i	−0.223787	−	0.835184i
$481$	−4.45721	+	9.03832i	−0.203231	+	0.412112i
$482$	2.88097	−	0.573060i	0.131225	−	0.0261022i
$483$		0			0
$484$	−6.19628	+	14.9591i	−0.281649	+	0.679961i
$485$	1.37748	+	10.4630i	0.0625483	+	0.475102i
$486$	−6.72091	+	3.31439i	−0.304867	+	0.150344i
$487$	−2.46365	+	7.25769i	−0.111639	+	0.328877i	−0.988362	−	0.152117i	$-0.951391\pi$
$487$	−2.46365	+	7.25769i	−0.111639	+	0.328877i	0.876724	+	0.480994i	$0.159724\pi$
$488$	−12.3179	−	6.07451i	−0.557605	−	0.274980i
$489$	−2.16762	+	2.16762i	−0.0980231	+	0.0980231i
$490$		0			0
$491$	−8.38519	−	20.2436i	−0.378418	−	0.913582i	−0.992263	−	0.124155i	$-0.960378\pi$
$491$	−8.38519	−	20.2436i	−0.378418	−	0.913582i	0.613845	−	0.789427i	$-0.289622\pi$
$492$	−3.53094	+	2.03859i	−0.159187	+	0.0919066i
$493$	−13.4771	+	8.85979i	−0.606979	+	0.399025i
$494$	0.395156	−	0.684430i	0.0177789	−	0.0307939i
$495$	−18.2971	+	23.8452i	−0.822392	+	1.07176i
$496$	12.2570	+	2.43806i	0.550354	+	0.109472i
$497$		0			0
$498$	1.73618	−	1.16008i	0.0778000	−	0.0519843i
$499$	20.1010	−	17.6281i	0.899843	−	0.789141i	−0.0783313	−	0.996927i	$-0.524959\pi$
$499$	20.1010	−	17.6281i	0.899843	−	0.789141i	0.978174	+	0.207786i	$0.0666259\pi$
$500$	−9.99163	−	20.2610i	−0.446839	−	0.906101i
$501$	9.57727	+	12.4813i	0.427881	+	0.557625i
$502$	−4.24488	+	0.558850i	−0.189458	+	0.0249427i
$503$	20.5674	+	13.7427i	0.917056	+	0.612757i	0.921983	−	0.387231i	$-0.126568\pi$
$503$	20.5674	+	13.7427i	0.917056	+	0.612757i	−0.00492696	+	0.999988i	$0.501568\pi$
$504$		0			0
$505$	−14.9558	−	22.3829i	−0.665524	−	0.996027i
$506$	0.364932	−	1.36195i	0.0162232	−	0.0605459i
$507$	22.7055	+	19.9122i	1.00839	+	0.884332i
$508$	−12.7710	−	1.68134i	−0.566624	−	0.0745974i
$509$	3.89884	+	6.75299i	0.172813	+	0.299321i	0.939402	−	0.342817i	$-0.111381\pi$
$509$	3.89884	+	6.75299i	0.172813	+	0.299321i	−0.766589	+	0.642138i	$0.778048\pi$
$510$	−6.77393	−	1.86958i	−0.299954	−	0.0827864i
$511$		0			0
$512$	−19.5230	+	8.08669i	−0.862803	+	0.357385i
$513$	−2.05043	+	0.696026i	−0.0905286	+	0.0307303i
$514$	0.434102	−	0.116317i	0.0191474	−	0.00513053i
$515$	1.93115	+	29.4636i	0.0850965	+	1.29832i
$516$	−20.8398	−	23.7632i	−0.917419	−	1.04612i
$517$	−25.1272	+	37.6056i	−1.10509	+	1.65389i
$518$		0			0
$519$	33.6659	+	13.9449i	1.47777	+	0.612113i
$520$	−2.66418	−	0.174619i	−0.116832	−	0.00765757i
$521$	−15.9020	−	5.39799i	−0.696678	−	0.236490i	−0.0494387	−	0.998777i	$-0.515743\pi$
$521$	−15.9020	−	5.39799i	−0.696678	−	0.236490i	−0.647239	+	0.762287i	$0.724077\pi$
$522$	−4.40645	+	0.288814i	−0.192865	+	0.0126410i
$523$	18.0437	+	4.83479i	0.788995	+	0.211411i	0.630747	−	0.775989i	$-0.282749\pi$
$523$	18.0437	+	4.83479i	0.788995	+	0.211411i	0.158248	+	0.987399i	$0.449415\pi$
$524$	−2.66855	+	13.4157i	−0.116576	+	0.586068i
$525$		0			0
$526$			1.05229i			0.0458818i
$527$	10.2608	−	11.5248i	0.446967	−	0.502029i
$528$	32.2937	+	18.6448i	1.40540	+	0.811411i
$529$	−2.88399	+	21.9061i	−0.125391	+	0.952438i
$530$	−2.79883	−	8.24509i	−0.121573	−	0.358144i
$531$	−13.8939	−	13.8939i	−0.602945	−	0.602945i
$532$		0			0
$533$	0.169777	+	0.853529i	0.00735387	+	0.0369704i
$534$	−0.779048	+	11.8860i	−0.0337127	+	0.514357i
$535$	−0.598155	+	0.458980i	−0.0258605	+	0.0198435i
$536$	10.9023	−	8.36562i	0.470907	−	0.361340i
$537$	1.15092	−	17.5596i	0.0496658	−	0.757753i
$538$	0.461412	+	2.31967i	0.0198929	+	0.100008i
$539$		0			0
$540$	2.51163	+	2.51163i	0.108084	+	0.108084i
$541$	7.53083	+	22.1851i	0.323776	+	0.953812i	0.979957	+	0.199209i	$0.0638372\pi$
$541$	7.53083	+	22.1851i	0.323776	+	0.953812i	−0.656181	+	0.754603i	$0.727829\pi$
$542$	−0.0595070	+	0.452001i	−0.00255605	+	0.0194151i
$543$	−16.3917	−	9.46374i	−0.703434	−	0.406128i
$544$	−2.11784	+	15.2053i	−0.0908018	+	0.651923i
$545$		−	23.0329i		−	0.986620i
$546$		0			0
$547$	−1.59327	+	8.00989i	−0.0681231	+	0.342478i	−0.999783	−	0.0208549i	$-0.993361\pi$
$547$	−1.59327	+	8.00989i	−0.0681231	+	0.342478i	0.931659	+	0.363333i	$0.118361\pi$
$548$	−15.0751	−	4.03936i	−0.643976	−	0.172553i
$549$	35.4601	−	2.32418i	1.51340	−	0.0991936i
$550$	−1.31440	−	0.446179i	−0.0560463	−	0.0190251i
$551$	9.05516	+	0.593507i	0.385763	+	0.0252842i
$552$	−2.88883	−	1.19659i	−0.122957	−	0.0509304i
$553$		0			0
$554$	3.76001	−	5.62725i	0.159747	−	0.239079i
$555$	−33.2420	−	37.9052i	−1.41104	−	1.60899i
$556$	−2.53135	−	38.6209i	−0.107353	−	1.63789i
$557$	−36.2237	+	9.70611i	−1.53485	+	0.411261i	−0.924596	−	0.380948i	$-0.875598\pi$
$557$	−36.2237	+	9.70611i	−1.53485	+	0.411261i	−0.610250	+	0.792209i	$0.708931\pi$
$558$	4.00062	−	1.35803i	0.169360	−	0.0574899i
$559$	−6.23275	+	2.58169i	−0.263617	+	0.109194i
$560$		0			0
$561$	40.0457	−	22.7220i	1.69073	−	0.959325i
$562$	−1.65002	−	2.85793i	−0.0696021	−	0.120554i
$563$	26.3628	+	3.47073i	1.11106	+	0.146274i	0.663641	−	0.748051i	$-0.269010\pi$
$563$	26.3628	+	3.47073i	1.11106	+	0.146274i	0.447419	+	0.894325i	$0.352343\pi$
$564$	36.6160	+	32.1114i	1.54181	+	1.35213i
$565$	0.586425	−	2.18857i	0.0246711	−	0.0920738i
$566$	−2.64805	−	3.96309i	−0.111306	−	0.166581i
$567$		0			0
$568$	7.40154	+	4.94555i	0.310562	+	0.207511i
$569$	7.99536	−	1.05261i	0.335183	−	0.0441277i	0.0389436	−	0.999241i	$-0.487601\pi$
$569$	7.99536	−	1.05261i	0.335183	−	0.0441277i	0.296239	+	0.955114i	$0.404267\pi$
$570$	2.40692	+	3.13676i	0.100815	+	0.131384i
$571$	−7.81219	−	15.8416i	−0.326930	−	0.662949i	0.669905	−	0.742447i	$-0.266335\pi$
$571$	−7.81219	−	15.8416i	−0.326930	−	0.662949i	−0.996835	+	0.0794982i	$0.974668\pi$
$572$	6.38630	−	5.60064i	0.267025	−	0.234174i
$573$	−7.90721	+	5.28343i	−0.330328	+	0.220718i
$574$		0			0
$575$	−0.873713	−	0.173792i	−0.0364363	−	0.00724764i
$576$	11.1416	−	14.5201i	0.464235	−	0.605002i
$577$	−0.115619	+	0.200258i	−0.00481327	+	0.00833683i	−0.868422	−	0.495826i	$-0.834865\pi$
$577$	−0.115619	+	0.200258i	−0.00481327	+	0.00833683i	0.863609	+	0.504163i	$0.168199\pi$
$578$	4.46565	+	3.53419i	0.185747	+	0.147003i
$579$	45.3779	−	26.1990i	1.88584	−	1.08879i
$580$	−5.69655	−	13.7527i	−0.236536	−	0.571049i
$581$		0			0
$582$	3.12988	−	3.12988i	0.129738	−	0.129738i
$583$	51.1669	+	25.2327i	2.11912	+	1.04503i
$584$	6.13381	−	18.0696i	0.253819	−	0.747726i
$585$	6.19570	−	3.05538i	0.256161	−	0.126324i
$586$	1.15022	+	8.73678i	0.0475151	+	0.360913i
$587$	−6.02142	+	14.5370i	−0.248531	+	0.600006i	−0.998080	−	0.0619427i	$-0.980270\pi$
$587$	−6.02142	+	14.5370i	−0.248531	+	0.600006i	0.749549	+	0.661949i	$0.230270\pi$
$588$		0			0
$589$	−8.51513	+	1.69376i	−0.350860	+	0.0697903i
$590$	−1.74153	+	3.53147i	−0.0716976	+	0.145388i
$591$	−13.7925	−	51.4741i	−0.567346	−	2.11736i
$592$	−21.8183	+	24.8790i	−0.896725	+	1.02252i
$593$	4.99068	+	3.82949i	0.204943	+	0.157258i	0.706134	−	0.708079i	$-0.250438\pi$
$593$	4.99068	+	3.82949i	0.204943	+	0.157258i	−0.501191	+	0.865337i	$0.667104\pi$
$594$	1.38352			0.0567664
$595$		0			0
$596$	−0.770657			−0.0315674
$597$	27.7925	+	21.3260i	1.13747	+	0.872814i
$598$	−0.213675	+	0.243650i	−0.00873783	+	0.00996359i
$599$	1.52484	+	5.69080i	0.0623034	+	0.232520i	0.990055	−	0.140678i	$-0.0449281\pi$
$599$	1.52484	+	5.69080i	0.0623034	+	0.232520i	−0.927752	+	0.373197i	$0.878261\pi$
$600$	−1.36147	+	2.76078i	−0.0555816	+	0.112708i
$601$	−15.6877	+	3.12047i	−0.639914	+	0.127287i	−0.504374	−	0.863485i	$-0.668277\pi$
$601$	−15.6877	+	3.12047i	−0.639914	+	0.127287i	−0.135539	+	0.990772i	$0.543277\pi$
$602$		0			0
$603$	−13.6068	+	32.8497i	−0.554112	+	1.33774i
$604$	2.36030	+	17.9282i	0.0960391	+	0.729490i
$605$	−15.5068	+	7.64713i	−0.630443	+	0.310900i
$606$	−3.62931	+	10.6916i	−0.147430	+	0.434316i
$607$	8.62051	+	4.25117i	0.349896	+	0.172549i	0.608740	−	0.793369i	$-0.291675\pi$
$607$	8.62051	+	4.25117i	0.349896	+	0.172549i	−0.258845	+	0.965919i	$0.583342\pi$
$608$	6.10781	−	6.10781i	0.247705	−	0.247705i
$609$		0			0
$610$	−2.72518	−	6.57917i	−0.110339	−	0.266383i
$611$	9.00246	−	5.19757i	0.364201	−	0.210271i
$612$	−9.85559	−	24.3071i	−0.398389	−	0.982555i
$613$	−13.4598	+	23.3130i	−0.543635	+	0.941603i	0.455057	+	0.890462i	$0.349619\pi$
$613$	−13.4598	+	23.3130i	−0.543635	+	0.941603i	−0.998691	+	0.0511403i	$0.983714\pi$
$614$	−1.16876	+	1.52315i	−0.0471672	+	0.0614695i
$615$	−4.27006	−	0.849369i	−0.172186	−	0.0342498i
$616$		0			0
$617$	−30.0466	+	20.0765i	−1.20963	+	0.808249i	−0.986052	−	0.166438i	$-0.946774\pi$
$617$	−30.0466	+	20.0765i	−1.20963	+	0.808249i	−0.223578	+	0.974686i	$0.571774\pi$
$618$	9.31099	−	8.16552i	0.374543	−	0.328465i
$619$	21.3984	+	43.3917i	0.860076	+	1.74406i	0.639664	+	0.768655i	$0.279074\pi$
$619$	21.3984	+	43.3917i	0.860076	+	1.74406i	0.220412	+	0.975407i	$0.429260\pi$
$620$	8.66980	+	11.2987i	0.348188	+	0.453767i
$621$	0.880315	−	0.115896i	0.0353258	−	0.00465073i
$622$	0.570130	+	0.380949i	0.0228601	+	0.0152747i
$623$		0			0
$624$	−4.76159	−	7.12622i	−0.190616	−	0.285277i
$625$	5.03161	−	18.7782i	0.201265	−	0.751130i
$626$	4.01398	+	3.52017i	0.160431	+	0.140694i
$627$	−25.6841	−	3.38137i	−1.02572	−	0.135039i
$628$	17.0985	+	29.6155i	0.682305	+	1.18179i
$629$	12.8433	+	38.7874i	0.512094	+	1.54656i
$630$		0			0
$631$	−25.3433	+	10.4976i	−1.00890	+	0.417901i	−0.825054	−	0.565053i	$-0.808856\pi$
$631$	−25.3433	+	10.4976i	−1.00890	+	0.417901i	−0.183848	+	0.982955i	$0.558856\pi$
$632$	−5.08239	+	1.72524i	−0.202167	+	0.0686263i
$633$	−8.29941	+	2.22382i	−0.329872	+	0.0883889i
$634$	−0.595341	−	9.08315i	−0.0236440	−	0.360738i
$635$	−9.06927	−	10.3415i	−0.359903	−	0.410391i
$636$	34.1301	−	51.0793i	1.35335	−	2.02543i
$637$		0			0
$638$	−5.35674	−	2.21884i	−0.212076	−	0.0878446i
$639$	−22.9832	−	1.50640i	−0.909202	−	0.0595922i
$640$	−17.6879	−	6.00422i	−0.699175	−	0.237338i
$641$	−24.0412	+	1.57575i	−0.949572	+	0.0622382i	−0.532311	−	0.846549i	$-0.678676\pi$
$641$	−24.0412	+	1.57575i	−0.949572	+	0.0622382i	−0.417261	+	0.908787i	$0.637010\pi$
$642$	0.305453	+	0.0818459i	0.0120553	+	0.00323020i
$643$	5.73102	−	28.8118i	0.226009	−	1.13623i	−0.686487	−	0.727142i	$-0.740848\pi$
$643$	5.73102	−	28.8118i	0.226009	−	1.13623i	0.912497	−	0.409084i	$-0.134152\pi$
$644$		0			0
$645$		−	33.7505i		−	1.32893i
$646$	−0.806101	−	3.10117i	−0.0317156	−	0.122014i
$647$	35.7298	+	20.6286i	1.40468	+	0.810994i	0.994869	−	0.101175i	$-0.0322601\pi$
$647$	35.7298	+	20.6286i	1.40468	+	0.810994i	0.409814	+	0.912169i	$0.365593\pi$
$648$	−1.31811	+	10.0120i	−0.0517802	+	0.393309i
$649$	−8.29287	−	24.4300i	−0.325524	−	0.958962i
$650$	0.225590	+	0.225590i	0.00884838	+	0.00884838i
$651$		0			0
$652$	0.447322	+	2.24884i	0.0175185	+	0.0880713i
$653$	−1.94162	+	29.6234i	−0.0759815	+	1.15925i	0.774263	+	0.632865i	$0.218121\pi$
$653$	−1.94162	+	29.6234i	−0.0759815	+	1.15925i	−0.850244	+	0.526389i	$0.823546\pi$
$654$	−7.66424	+	5.88098i	−0.299695	+	0.229964i
$655$	−11.5880	+	8.89176i	−0.452780	+	0.347430i
$656$	−0.186893	+	2.85143i	−0.00729694	+	0.111330i
$657$	9.63235	+	48.4251i	0.375794	+	1.88924i
$658$		0			0
$659$	33.7265	+	33.7265i	1.31380	+	1.31380i	0.918593	+	0.395205i	$0.129326\pi$
$659$	33.7265	+	33.7265i	1.31380	+	1.31380i	0.395205	+	0.918593i	$0.370674\pi$
$660$	13.6597	+	40.2400i	0.531701	+	1.56634i
$661$	1.68949	−	12.8330i	0.0657137	−	0.499145i	−0.926662	−	0.375896i	$-0.877335\pi$
$661$	1.68949	−	12.8330i	0.0657137	−	0.499145i	0.992376	−	0.123249i	$-0.0393315\pi$
$662$	−2.37389	−	1.37056i	−0.0922637	−	0.0532685i
$663$	−10.5647	+	0.612985i	−0.410300	+	0.0238064i
$664$		−	3.21651i		−	0.124825i
$665$		0			0
$666$	−2.18244	+	10.9719i	−0.0845680	+	0.425152i
$667$	−3.59430	−	0.963089i	−0.139172	−	0.0372909i
$668$	11.7422	−	0.769626i	0.454320	−	0.0297777i
$669$	11.6702	+	3.96151i	0.451197	+	0.153161i
$670$	7.11001	+	0.466015i	0.274684	+	0.0180037i
$671$	43.1075	+	17.8557i	1.66415	+	0.689311i
$672$		0			0
$673$	10.4270	−	15.6051i	0.401930	−	0.601531i	−0.574201	−	0.818715i	$-0.694687\pi$
$673$	10.4270	−	15.6051i	0.401930	−	0.601531i	0.976131	+	0.217184i	$0.0696871\pi$
$674$	−2.27726	−	2.59672i	−0.0877168	−	0.100022i
$675$	−0.0571692	−	0.872233i	−0.00220044	−	0.0335723i
$676$	21.8191	−	5.84641i	0.839196	−	0.224862i
$677$	1.26607	−	0.429773i	0.0486591	−	0.0165175i	−0.297004	−	0.954876i	$-0.595987\pi$
$677$	1.26607	−	0.429773i	0.0486591	−	0.0165175i	0.345663	+	0.938359i	$0.387654\pi$
$678$	−0.877982	+	0.363672i	−0.0337187	+	0.0139667i
$679$		0			0
$680$	−8.19175	+	7.07609i	−0.314139	+	0.271356i
$681$	−3.41555	−	5.91590i	−0.130884	−	0.226698i
$682$	5.49977	+	0.724058i	0.210597	+	0.0277256i
$683$	38.2095	+	33.5089i	1.46205	+	1.28218i	0.885101	+	0.465400i	$0.154089\pi$
$683$	38.2095	+	33.5089i	1.46205	+	1.28218i	0.576947	+	0.816782i	$0.304244\pi$
$684$	−3.81955	+	14.2548i	−0.146044	+	0.545044i
$685$	−9.25883	−	13.8568i	−0.353762	−	0.529442i
$686$		0			0
$687$	28.6175	+	19.1216i	1.09182	+	0.729534i
$688$	−21.9626	+	2.89143i	−0.837315	+	0.110235i
$689$	−7.98235	−	10.4028i	−0.304103	−	0.396315i
$690$	−0.717073	−	1.45408i	−0.0272985	−	0.0553559i
$691$	−13.2337	+	11.6056i	−0.503433	+	0.441499i	−0.873011	−	0.487701i	$-0.837836\pi$
$691$	−13.2337	+	11.6056i	−0.503433	+	0.441499i	0.369578	+	0.929200i	$0.379502\pi$
$692$	22.6625	−	15.1426i	0.861500	−	0.575636i
$693$		0			0
$694$	6.69459	+	1.33164i	0.254123	+	0.0505482i
$695$	25.1594	−	32.7884i	0.954352	−	1.24374i
$696$	−6.42905	+	11.1354i	−0.243692	+	0.422088i
$697$	2.91893	+	1.98216i	0.110562	+	0.0750797i
$698$	7.53228	−	4.34876i	0.285101	−	0.164603i
$699$	0.429056	+	1.03583i	0.0162284	+	0.0391788i
$700$		0			0
$701$	19.4751	−	19.4751i	0.735565	−	0.735565i	−0.236152	−	0.971716i	$-0.575886\pi$
$701$	19.4751	−	19.4751i	0.735565	−	0.735565i	0.971716	+	0.236152i	$0.0758862\pi$
$702$	−0.285194	−	0.140642i	−0.0107640	−	0.00530820i
$703$	7.38948	−	21.7687i	0.278700	−	0.821023i
$704$	21.5525	−	10.6285i	0.812292	−	0.400578i
$705$	6.78805	+	51.5603i	0.255653	+	1.94187i
$706$	2.44106	−	5.89324i	0.0918704	−	0.221795i
$707$		0			0
$708$	−27.2471	+	5.41978i	−1.02401	+	0.203688i
$709$	−6.88170	+	13.9547i	−0.258448	+	0.524080i	−0.986963	−	0.160950i	$-0.948544\pi$
$709$	−6.88170	+	13.9547i	−0.258448	+	0.524080i	0.728515	+	0.685030i	$0.240211\pi$
$710$	1.19460	+	4.45831i	0.0448325	+	0.167317i
$711$	9.15649	−	10.4410i	0.343395	−	0.391567i
$712$	14.5569	+	11.1699i	0.545544	+	0.418611i
$713$	3.56008			0.133326
$714$		0			0
$715$	9.07038			0.339213
$716$	−10.4424	−	8.01271i	−0.390250	−	0.299449i
$717$	10.3394	−	11.7898i	0.386131	−	0.440298i
$718$	0.790319	+	2.94951i	0.0294944	+	0.110075i
$719$	−9.09945	+	18.4519i	−0.339352	+	0.688138i	−0.997926	−	0.0643782i	$-0.979494\pi$
$719$	−9.09945	+	18.4519i	−0.339352	+	0.688138i	0.658573	+	0.752517i	$0.271160\pi$
$720$	22.2476	−	4.42533i	0.829120	−	0.164922i
$721$		0			0
$722$	1.74585	−	4.21485i	0.0649737	−	0.156860i
$723$	2.88858	+	21.9410i	0.107428	+	0.815993i
$724$	−12.6973	+	6.26160i	−0.471890	+	0.232711i
$725$	−1.17751	+	3.46882i	−0.0437315	+	0.128829i
$726$	6.50395	+	3.20739i	0.241384	+	0.119038i
$727$	5.81725	−	5.81725i	0.215750	−	0.215750i	−0.590955	−	0.806705i	$-0.701249\pi$
$727$	5.81725	−	5.81725i	0.215750	−	0.215750i	0.806705	+	0.590955i	$0.201249\pi$
$728$		0			0
$729$	−12.7036	−	30.6692i	−0.470503	−	1.13590i
$730$	8.56864	−	4.94711i	0.317140	−	0.183101i
$731$	−10.6562	+	25.1908i	−0.394134	+	0.931717i
$732$	25.1216	−	43.5119i	0.928521	−	1.60825i
$733$	8.97961	−	11.7025i	0.331669	−	0.432240i	−0.597514	−	0.801858i	$-0.703845\pi$
$733$	8.97961	−	11.7025i	0.331669	−	0.432240i	0.929184	+	0.369618i	$0.120512\pi$
$734$	5.67926	+	1.12968i	0.209625	+	0.0416971i
$735$		0			0
$736$	−2.94503	+	1.96781i	−0.108555	+	0.0725344i
$737$	−35.1000	+	30.7819i	−1.29293	+	1.13387i
$738$	0.427268	+	0.866414i	0.0157280	+	0.0318931i
$739$	−6.59394	−	8.59339i	−0.242562	−	0.316113i	0.656169	−	0.754614i	$-0.272176\pi$
$739$	−6.59394	−	8.59339i	−0.242562	−	0.316113i	−0.898730	+	0.438502i	$0.855509\pi$
$740$	−37.3877	+	4.92218i	−1.37440	+	0.180943i
$741$	4.95070	+	3.30796i	0.181869	+	0.121521i
$742$		0			0
$743$	−10.0900	−	15.1007i	−0.370165	−	0.553992i	0.598891	−	0.800830i	$-0.295608\pi$
$743$	−10.0900	−	15.1007i	−0.370165	−	0.553992i	−0.969057	+	0.246839i	$0.920608\pi$
$744$	3.18393	−	11.8826i	0.116728	−	0.435636i
$745$	−0.618711	−	0.542595i	−0.0226678	−	0.0198791i
$746$	4.71201	+	0.620348i	0.172519	+	0.0227125i
$747$	4.16122	+	7.20744i	0.152251	+	0.263706i
$748$	2.50984	−	34.3473i	0.0917689	−	1.25586i
$749$		0			0
$750$	−9.34762	+	3.87191i	−0.341327	+	0.141382i
$751$	−7.99750	+	2.71478i	−0.291833	+	0.0990639i	−0.463517	−	0.886088i	$-0.653413\pi$
$751$	−7.99750	+	2.71478i	−0.291833	+	0.0990639i	0.171684	+	0.985152i	$0.445079\pi$
$752$	32.9704	−	8.83440i	1.20231	−	0.322157i
$753$	−2.10969	−	32.1876i	−0.0768813	−	1.17298i
$754$	0.878666	+	1.00193i	0.0319991	+	0.0364880i
$755$	−10.7278	+	16.0552i	−0.390423	+	0.584310i
$756$		0			0
$757$	−0.111359	−	0.0461265i	−0.00404742	−	0.00167649i	0.380659	−	0.924716i	$-0.375697\pi$
$757$	−0.111359	−	0.0461265i	−0.00404742	−	0.00167649i	−0.384706	+	0.923039i	$0.625697\pi$
$758$	2.23933	+	0.146773i	0.0813362	+	0.00533105i
$759$	10.0590	+	3.41458i	0.365120	+	0.123942i
$760$	6.07744	−	0.398337i	0.220452	−	0.0144492i
$761$	45.0950	+	12.0832i	1.63469	+	0.438015i	0.955271	−	0.295732i	$-0.0955635\pi$
$761$	45.0950	+	12.0832i	1.63469	+	0.438015i	0.679423	+	0.733747i	$0.262230\pi$
$762$	−1.12551	+	5.65831i	−0.0407729	+	0.204979i
$763$		0			0
$764$			7.11317i			0.257346i
$765$	9.20140	−	26.4536i	0.332677	−	0.956431i
$766$	−6.89792	−	3.98252i	−0.249232	−	0.143894i
$767$	−0.773978	+	5.87894i	−0.0279467	+	0.212276i
$768$	−6.29392	−	18.5413i	−0.227112	−	0.669052i
$769$	20.2281	+	20.2281i	0.729443	+	0.729443i	0.970509	−	0.241066i	$-0.0774970\pi$
$769$	20.2281	+	20.2281i	0.729443	+	0.729443i	−0.241066	+	0.970509i	$0.577497\pi$
$770$		0			0
$771$	0.660550	+	3.32081i	0.0237891	+	0.119596i
$772$	2.56330	−	39.1084i	0.0922552	−	1.40754i
$773$	10.7386	−	8.23998i	0.386239	−	0.296372i	−0.397331	−	0.917675i	$-0.630063\pi$
$773$	10.7386	−	8.23998i	0.386239	−	0.296372i	0.783570	+	0.621304i	$0.213397\pi$
$774$	−5.94130	+	4.55892i	−0.213556	+	0.163867i
$775$	0.229220	−	3.49722i	0.00823383	−	0.125624i
$776$	−1.33020	−	6.68735i	−0.0477513	−	0.240062i
$777$		0			0
$778$	2.01096	+	2.01096i	0.0720964	+	0.0720964i
$779$	−0.638118	−	1.87984i	−0.0228630	−	0.0673521i
$780$	1.27486	−	9.68354i	0.0456474	−	0.346726i
$781$	−26.1902	−	15.1209i	−0.937157	−	0.541068i
$782$	0.0761076	+	1.31171i	0.00272160	+	0.0469065i
$783$		−	3.65123i		−	0.130484i
$784$		0			0
$785$	−7.12402	+	35.8149i	−0.254267	+	1.27829i
$786$	5.91750	+	1.58559i	0.211070	+	0.0565561i
$787$	−48.8583	+	3.20234i	−1.74161	+	0.114151i	−0.902741	−	0.430184i	$-0.858449\pi$
$787$	−48.8583	+	3.20234i	−1.74161	+	0.114151i	−0.838868	+	0.544335i	$0.816782\pi$
$788$	−37.7442	−	12.8124i	−1.34458	−	0.456423i
$789$	−7.91089	−	0.518507i	−0.281635	−	0.0184593i
$790$	−2.57108	−	1.06498i	−0.0914750	−	0.0378902i
$791$		0			0
$792$	10.7886	−	16.1463i	0.383356	−	0.573732i
$793$	−7.07091	−	8.06283i	−0.251095	−	0.286320i
$794$	0.0381188	+	0.581580i	0.00135278	+	0.0206395i
$795$	63.3642	−	16.9784i	2.24730	−	0.602161i
$796$	24.8123	−	8.42263i	0.879447	−	0.298532i
$797$	−5.31334	+	2.20086i	−0.188208	+	0.0779584i	−0.474797	−	0.880095i	$-0.657479\pi$
$797$	−5.31334	+	2.20086i	−0.188208	+	0.0779584i	0.286589	+	0.958054i	$0.407479\pi$
$798$		0			0
$799$	11.2129	−	40.6270i	0.396684	−	1.43728i
$800$	1.74344	+	3.01973i	0.0616400	+	0.106764i
$801$	−47.0692	−	6.19678i	−1.66311	−	0.218953i
$802$	−0.242881	−	0.213001i	−0.00857643	−	0.00752133i
$803$	−16.7787	+	62.6190i	−0.592108	+	2.20978i
$804$	27.9294	+	41.7993i	0.984994	+	1.47415i
$805$		0			0
$806$	−1.06010	−	0.708337i	−0.0373405	−	0.0249501i
$807$	−17.6662	+	2.32580i	−0.621881	+	0.0818722i
$808$	10.5879	+	13.7984i	0.372480	+	0.485426i
$809$	−24.3640	−	49.4053i	−0.856593	−	1.73700i	−0.652105	−	0.758129i	$-0.726114\pi$
$809$	−24.3640	−	49.4053i	−0.856593	−	1.73700i	−0.204488	−	0.978869i	$-0.565553\pi$
$810$	−3.93667	+	3.45237i	−0.138320	+	0.121304i
$811$	18.2766	−	12.2120i	0.641779	−	0.428823i	−0.191640	−	0.981465i	$-0.561381\pi$
$811$	18.2766	−	12.2120i	0.641779	−	0.428823i	0.833418	+	0.552643i	$0.186381\pi$
$812$		0			0
$813$	−3.36874	−	0.670083i	−0.118147	−	0.0235008i
$814$	−8.94171	+	11.6531i	−0.313407	+	0.408440i
$815$	−1.22421	+	2.12039i	−0.0428822	+	0.0742741i
$816$	−34.0292	−	7.03430i	−1.19126	−	0.246250i
$817$	13.3276	−	7.69471i	0.466275	−	0.269204i
$818$	1.40853	+	3.40050i	0.0492483	+	0.118896i
$819$		0			0
$820$	−2.30267	+	2.30267i	−0.0804128	+	0.0804128i
$821$	−48.7908	−	24.0610i	−1.70281	−	0.839734i	−0.990442	−	0.137929i	$-0.955955\pi$
$821$	−48.7908	−	24.0610i	−1.70281	−	0.839734i	−0.712369	−	0.701805i	$-0.752378\pi$
$822$	−2.24683	+	6.61894i	−0.0783672	+	0.230862i
$823$	33.4517	−	16.4965i	1.16605	−	0.575033i	0.246940	−	0.969031i	$-0.420575\pi$
$823$	33.4517	−	16.4965i	1.16605	−	0.575033i	0.919111	+	0.393998i	$0.128908\pi$
$824$	−2.49004	−	18.9137i	−0.0867445	−	0.658890i
$825$	4.00196	−	9.66158i	0.139330	−	0.336373i
$826$		0			0
$827$	−33.6889	+	6.70114i	−1.17148	+	0.233021i	−0.742217	−	0.670159i	$-0.766226\pi$
$827$	−33.6889	+	6.70114i	−1.17148	+	0.233021i	−0.429260	+	0.903181i	$0.641226\pi$
$828$	2.67649	−	5.42738i	0.0930143	−	0.188614i
$829$	6.63507	+	24.7624i	0.230446	+	0.860035i	0.980149	+	0.198261i	$0.0635294\pi$
$829$	6.63507	+	24.7624i	0.230446	+	0.860035i	−0.749704	+	0.661774i	$0.769804\pi$
$830$	1.09964	−	1.25389i	0.0381689	−	0.0435233i
$831$	40.4519	+	31.0398i	1.40326	+	1.07676i
$832$	−5.52322			−0.191483
$833$		0			0
$834$	−17.3344			−0.600240
$835$	9.96894	+	7.64944i	0.344989	+	0.264720i
$836$	−12.7760	+	14.5683i	−0.441868	+	0.503854i
$837$	0.904118	+	3.37422i	0.0312509	+	0.116630i
$838$	−3.42618	+	6.94760i	−0.118355	+	0.240001i
$839$	−42.6085	+	8.47535i	−1.47101	+	0.292602i	−0.864563	−	0.502524i	$-0.832405\pi$
$839$	−42.6085	+	8.47535i	−1.47101	+	0.292602i	−0.606445	+	0.795126i	$0.707405\pi$
$840$		0			0
$841$	5.24211	−	12.6556i	0.180763	−	0.436399i
$842$	−0.176762	−	1.34264i	−0.00609161	−	0.0462704i
$843$	22.2984	−	10.9964i	0.767998	−	0.378735i
$844$	−2.06580	+	6.08566i	−0.0711079	+	0.209477i
$845$	21.6334	+	10.6684i	0.744212	+	0.367005i
$846$	8.15955	−	8.15955i	0.280531	−	0.280531i
$847$		0			0
$848$	−16.4768	−	39.7786i	−0.565816	−	1.36600i
$849$	31.0986	−	17.9548i	1.06730	−	0.616207i
$850$	1.29345	+	0.00969189i	0.0443648	+	0.000332429i
$851$	−4.71333	+	8.16373i	−0.161571	+	0.279849i
$852$	−19.8242	+	25.8354i	−0.679165	+	0.885105i
$853$	−4.01867	−	0.799362i	−0.137596	−	0.0273696i	0.125812	−	0.992054i	$-0.459847\pi$
$853$	−4.01867	−	0.799362i	−0.137596	−	0.0273696i	−0.263408	+	0.964685i	$0.584847\pi$
$854$		0			0
$855$	−13.1028	+	8.75500i	−0.448106	+	0.299415i
$856$	0.366238	−	0.321182i	0.0125178	−	0.0109778i
$857$	−21.7881	−	44.1819i	−0.744268	−	1.50923i	−0.856840	−	0.515583i	$-0.827576\pi$
$857$	−21.7881	−	44.1819i	−0.744268	−	1.50923i	0.112572	−	0.993644i	$-0.464091\pi$
$858$	−2.31593	−	3.01818i	−0.0790647	−	0.103039i
$859$	−35.2594	+	4.64198i	−1.20303	+	0.158382i	−0.705276	−	0.708933i	$-0.749177\pi$
$859$	−35.2594	+	4.64198i	−1.20303	+	0.158382i	−0.497759	+	0.867316i	$0.665843\pi$
$860$	−20.9901	−	14.0251i	−0.715755	−	0.478252i
$861$		0			0
$862$	0.769545	+	1.15171i	0.0262108	+	0.0392272i
$863$	8.05648	−	30.0672i	0.274246	−	1.02350i	−0.682099	−	0.731260i	$-0.738933\pi$
$863$	8.05648	−	30.0672i	0.274246	−	1.02350i	0.956345	−	0.292240i	$-0.0944006\pi$
$864$	−2.61299	−	2.29153i	−0.0888958	−	0.0779595i
$865$	28.8557	+	3.79892i	0.981123	+	0.129167i
$866$	2.41634	+	4.18523i	0.0821106	+	0.142220i
$867$	−28.7698	+	31.8305i	−0.977073	+	1.08102i
$868$		0			0
$869$	16.8460	−	6.97784i	0.571462	−	0.236707i
$870$	−6.31313	+	2.14302i	−0.214035	+	0.0726552i
$871$	10.3646	−	2.77718i	0.351190	−	0.0941011i
$872$	0.973281	+	14.8494i	0.0329594	+	0.502864i
$873$	11.6321	+	13.2639i	0.393688	+	0.448915i
$874$	0.410713	−	0.614675i	0.0138926	−	0.0207917i
$875$		0			0
$876$	64.4938	+	26.7142i	2.17904	+	0.902590i
$877$	−36.4186	−	2.38700i	−1.22977	−	0.0806032i	−0.563373	−	0.826203i	$-0.690497\pi$
$877$	−36.4186	−	2.38700i	−1.22977	−	0.0806032i	−0.666394	+	0.745600i	$0.732163\pi$
$878$	2.36533	+	0.802921i	0.0798260	+	0.0270973i
$879$	−66.2483	+	4.34214i	−2.23450	+	0.146457i
$880$	28.7686	+	7.70853i	0.969790	+	0.259855i
$881$	4.79213	−	24.0916i	0.161451	−	0.811668i	−0.812157	−	0.583439i	$-0.801707\pi$
$881$	4.79213	−	24.0916i	0.161451	−	0.811668i	0.973608	−	0.228229i	$-0.0732934\pi$
$882$		0			0
$883$			0.405556i			0.0136480i	0.999977	+	0.00682402i	$0.00217217\pi$
$883$			0.405556i			0.0136480i	−0.999977	+	0.00682402i	$0.997828\pi$
$884$	−4.00897	+	6.82512i	−0.134836	+	0.229553i
$885$	−25.6908	−	14.8326i	−0.863587	−	0.498592i
$886$	0.0981119	−	0.745234i	0.00329613	−	0.0250366i
$887$	14.0485	+	41.3854i	0.471701	+	1.38959i	0.879231	+	0.476395i	$0.158057\pi$
$887$	14.0485	+	41.3854i	0.471701	+	1.38959i	−0.407530	+	0.913192i	$0.633610\pi$
$888$	23.0329	+	23.0329i	0.772935	+	0.772935i
$889$		0			0
$890$	1.85605	+	9.33098i	0.0622149	+	0.312775i
$891$	2.24380	−	34.2337i	0.0751700	−	1.14687i
$892$	7.31332	−	5.61171i	0.244868	−	0.187894i
$893$	−18.8129	+	14.4356i	−0.629549	+	0.483070i
$894$	−0.0225743	+	0.344418i	−0.000754998	+	0.0115190i
$895$	−2.74201	−	13.7850i	−0.0916553	−	0.460783i
$896$		0			0
$897$	−1.72643	−	1.72643i	−0.0576438	−	0.0576438i
$898$	3.49019	+	10.2818i	0.116469	+	0.343107i
$899$	1.91085	−	14.5144i	0.0637305	−	0.484081i
$900$	−5.15922	−	2.97868i	−0.171974	−	0.0992892i
$901$	−52.6546	−	7.33389i	−1.75418	−	0.244327i
$902$			1.26841i			0.0422335i
$903$		0			0
$904$	−0.285590	+	1.43576i	−0.00949859	+	0.0477526i
$905$	−14.6024	−	3.91270i	−0.485400	−	0.130063i
$906$	8.08152	−	0.529691i	0.268491	−	0.0175978i
$907$	20.0856	+	6.81814i	0.666931	+	0.226393i	0.634314	−	0.773075i	$-0.281282\pi$
$907$	20.0856	+	6.81814i	0.666931	+	0.226393i	0.0326171	+	0.999468i	$0.489616\pi$
$908$	−5.09854	−	0.334176i	−0.169201	−	0.0110900i
$909$	−41.5760	−	17.2213i	−1.37899	−	0.571196i
$910$		0			0
$911$	−19.3806	+	29.0052i	−0.642109	+	0.960984i	0.357524	+	0.933904i	$0.383621\pi$
$911$	−19.3806	+	29.0052i	−0.642109	+	0.960984i	−0.999633	+	0.0270803i	$0.991379\pi$
$912$	12.8909	+	14.6993i	0.426861	+	0.486742i
$913$	0.714685	+	10.9040i	0.0236526	+	0.360869i
$914$	−5.35349	+	1.43446i	−0.177078	+	0.0474478i
$915$	50.8038	−	17.2456i	1.67952	−	0.570121i
$916$	23.7841	−	9.85170i	0.785849	−	0.325509i
$917$		0			0
$918$	−1.22389	+	0.405255i	−0.0403945	+	0.0133754i
$919$	9.78562	+	16.9492i	0.322798	+	0.559102i	0.981064	−	0.193683i	$-0.0620432\pi$
$919$	9.78562	+	16.9492i	0.322798	+	0.559102i	−0.658266	+	0.752785i	$0.728710\pi$
$920$	−2.47607	−	0.325981i	−0.0816337	−	0.0107473i
$921$	−10.8749	−	9.53703i	−0.358340	−	0.314256i
$922$	−0.459620	+	1.71533i	−0.0151368	+	0.0564913i
$923$	3.86164	+	5.77935i	0.127107	+	0.190230i
$924$		0			0
$925$	7.71611	+	5.15574i	0.253704	+	0.169520i
$926$	8.06171	−	1.06134i	0.264924	−	0.0348779i
$927$	30.0483	+	39.1598i	0.986917	+	1.28618i
$928$	6.44198	+	13.0630i	0.211468	+	0.428815i
$929$	−3.67749	+	3.22507i	−0.120655	+	0.105811i	−0.717547	−	0.696510i	$-0.754735\pi$
$929$	−3.67749	+	3.22507i	−0.120655	+	0.105811i	0.596893	+	0.802321i	$0.296402\pi$
$930$	5.30351	−	3.54369i	0.173909	−	0.116202i
$931$		0			0
$932$	0.822498	+	0.163605i	0.0269418	+	0.00535906i
$933$	−3.14483	+	4.09842i	−0.102957	+	0.134176i
$934$	−5.79387	+	10.0353i	−0.189581	+	0.328364i
$935$	26.1978	−	25.8081i	0.856761	−	0.844016i
$936$	−3.86528	+	2.23162i	−0.126341	+	0.0729428i
$937$	19.6376	+	47.4093i	0.641531	+	1.54879i	0.824614	+	0.565696i	$0.191392\pi$
$937$	19.6376	+	47.4093i	0.641531	+	1.54879i	−0.183082	+	0.983098i	$0.558608\pi$
$938$		0			0
$939$	−28.4418	+	28.4418i	−0.928165	+	0.928165i
$940$	34.8871	+	17.2044i	1.13789	+	0.561146i
$941$	−11.9288	+	35.1412i	−0.388869	+	1.14557i	0.559616	+	0.828752i	$0.310949\pi$
$941$	−11.9288	+	35.1412i	−0.388869	+	1.14557i	−0.948486	+	0.316820i	$0.897385\pi$
$942$	13.7364	−	6.77406i	0.447557	−	0.220711i
$943$	0.106253	+	0.807074i	0.00346009	+	0.0262820i
$944$	−7.45110	+	17.9886i	−0.242513	+	0.585477i
$945$		0			0
$946$	−9.64394	+	1.91830i	−0.313552	+	0.0623693i
$947$	−3.78905	+	7.68344i	−0.123128	+	0.249678i	−0.949706	−	0.313144i	$-0.898618\pi$
$947$	−3.78905	+	7.68344i	−0.123128	+	0.249678i	0.826578	+	0.562822i	$0.190284\pi$
$948$	−5.08181	−	18.9656i	−0.165049	−	0.615973i
$949$	9.82428	−	11.2024i	0.318910	−	0.363647i
$950$	−0.577377	−	0.443037i	−0.0187326	−	0.0143740i
$951$	68.5788			2.22382
$952$		0			0
$953$	44.0920			1.42828			0.714140	−	0.700003i	$-0.246818\pi$
$953$	44.0920			1.42828			0.714140	+	0.700003i	$0.246818\pi$
$954$	−11.5478	−	8.86097i	−0.373875	−	0.286884i
$955$	−5.00815	+	5.71071i	−0.162060	+	0.184794i
$956$	−3.03573	−	11.3295i	−0.0981826	−	0.366423i
$957$	19.3203	−	39.1777i	0.624537	−	1.26643i
$958$	0.834438	−	0.165980i	0.0269595	−	0.00536257i
$959$		0			0
$960$	10.5742	−	25.5284i	0.341282	−	0.823927i
$961$	−2.21814	−	16.8484i	−0.0715528	−	0.543498i
$962$	3.02781	−	1.49315i	0.0976207	−	0.0481412i
$963$	−0.405138	+	1.19350i	−0.0130554	+	0.0384599i
$964$	14.8458	+	7.32116i	0.478152	+	0.235799i
$965$	29.5929	−	29.5929i	0.952628	−	0.952628i
$966$		0			0
$967$	5.82350	+	14.0592i	0.187271	+	0.452112i	0.989432	−	0.144995i	$-0.0463166\pi$
$967$	5.82350	+	14.0592i	0.187271	+	0.452112i	−0.802161	+	0.597107i	$0.796317\pi$
$968$	9.67418	−	5.58539i	0.310940	−	0.179521i
$969$	23.7112	−	4.53203i	0.761715	−	0.145590i
$970$	1.76767	−	3.06169i	0.0567564	−	0.0983049i
$971$	20.5408	−	26.7693i	0.659186	−	0.859067i	−0.337423	−	0.941353i	$-0.609555\pi$
$971$	20.5408	−	26.7693i	0.659186	−	0.859067i	0.996609	+	0.0822856i	$0.0262220\pi$
$972$	−41.4172	−	8.23838i	−1.32846	−	0.264246i
$973$		0			0
$974$	2.13486	−	1.42647i	0.0684052	−	0.0457069i
$975$	−1.80710	+	1.58479i	−0.0578736	+	0.0507538i
$976$	−15.5746	−	31.5823i	−0.498532	−	1.01092i
$977$	23.5402	+	30.6782i	0.753118	+	0.981482i	0.999923	+	0.0124170i	$0.00395256\pi$
$977$	23.5402	+	30.6782i	0.753118	+	0.981482i	−0.246805	+	0.969065i	$0.579381\pi$
$978$	1.01814	−	0.134041i	0.0325565	−	0.00428615i
$979$	−51.8300	−	34.6317i	−1.65649	−	1.10683i
$980$		0			0
$981$	−21.3916	−	32.0148i	−0.682982	−	1.02216i
$982$	−1.89981	+	7.09020i	−0.0606255	+	0.226257i
$983$	−23.1231	−	20.2784i	−0.737512	−	0.646780i	0.205836	−	0.978587i	$-0.434009\pi$
$983$	−23.1231	−	20.2784i	−0.737512	−	0.646780i	−0.943348	+	0.331806i	$0.892342\pi$
$984$	2.78882	+	0.367155i	0.0889043	+	0.0117045i
$985$	−21.2815	−	36.8607i	−0.678086	−	1.17448i
$986$	5.38864	+	0.393761i	0.171609	+	0.0125399i
$987$		0			0
$988$	4.11455	−	1.70430i	0.130901	−	0.0542211i
$989$	−5.97562	+	2.02845i	−0.190014	+	0.0645010i
$990$	9.72567	−	2.60599i	0.309102	−	0.0828237i
$991$	−0.916320	−	13.9803i	−0.0291079	−	0.444100i	−0.987393	−	0.158287i	$-0.949403\pi$
$991$	−0.916320	−	13.9803i	−0.0291079	−	0.444100i	0.958285	−	0.285813i	$-0.0922638\pi$
$992$	−9.18791	−	10.4768i	−0.291716	−	0.332639i
$993$	11.4734	−	17.1711i	0.364096	−	0.544909i
$994$		0			0
$995$	25.8502	+	10.7075i	0.819508	+	0.339451i
$996$	11.7416	+	0.769583i	0.372046	+	0.0243852i
$997$	16.4270	+	5.57622i	0.520249	+	0.176601i	0.569198	−	0.822201i	$-0.307254\pi$
$997$	16.4270	+	5.57622i	0.520249	+	0.176601i	−0.0489489	+	0.998801i	$0.515587\pi$
$998$	−8.93722	+	0.585776i	−0.282903	+	0.0185424i
$999$	−8.93451	−	2.39399i	−0.282675	−	0.0757426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.bc.f.31.4		160
7.2	even	3	inner	833.2.bc.f.558.4		160
7.3	odd	6		119.2.p.a.48.8	yes	80
7.4	even	3		119.2.p.a.48.7	✓	80
7.5	odd	6	inner	833.2.bc.f.558.3		160
7.6	odd	2	inner	833.2.bc.f.31.3		160
17.11	odd	16	inner	833.2.bc.f.521.3		160
119.11	odd	48		119.2.p.a.62.8	yes	80
119.45	even	48		119.2.p.a.62.7	yes	80
119.62	even	16	inner	833.2.bc.f.521.4		160
119.79	odd	48	inner	833.2.bc.f.215.3		160
119.96	even	48	inner	833.2.bc.f.215.4		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.p.a.48.7	✓	80	7.4	even	3
119.2.p.a.48.8	yes	80	7.3	odd	6
119.2.p.a.62.7	yes	80	119.45	even	48
119.2.p.a.62.8	yes	80	119.11	odd	48
833.2.bc.f.31.3		160	7.6	odd	2	inner
833.2.bc.f.31.4		160	1.1	even	1	trivial
833.2.bc.f.215.3		160	119.79	odd	48	inner
833.2.bc.f.215.4		160	119.96	even	48	inner
833.2.bc.f.521.3		160	17.11	odd	16	inner
833.2.bc.f.521.4		160	119.62	even	16	inner
833.2.bc.f.558.3		160	7.5	odd	6	inner
833.2.bc.f.558.4		160	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bc (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.265771 - 0.203934i) q^{2} +(1.66409 - 1.89753i) q^{3} +(-0.488593 - 1.82345i) q^{4} +(0.891574 - 1.80793i) q^{5} +(-0.829238 + 0.164946i) q^{6} +(-0.498405 + 1.20326i) q^{8} +(-0.439851 - 3.34100i) q^{9} +(-0.605653 + 0.298675i) q^{10} +(1.42224 - 4.18979i) q^{11} +(-4.27312 - 2.10727i) q^{12} +(-0.719092 + 0.719092i) q^{13} +(-1.94695 - 4.70036i) q^{15} +(-2.89188 + 1.66963i) q^{16} +(-0.0308939 + 4.12299i) q^{17} +(-0.564443 + 0.977643i) q^{18} +(1.41223 - 1.84045i) q^{19} +(-3.73230 - 0.742400i) q^{20} +(-1.23243 + 0.823483i) q^{22} +(-0.715197 + 0.627211i) q^{23} +(1.45383 + 2.94807i) q^{24} +(0.570087 + 0.742952i) q^{25} +(0.337761 - 0.0444671i) q^{26} +(-0.776096 - 0.518571i) q^{27} +(2.17325 + 3.25249i) q^{29} +(-0.441117 + 1.64627i) q^{30} +(-2.81375 - 2.46759i) q^{31} +(3.69158 + 0.486005i) q^{32} +(-5.58352 - 9.67094i) q^{33} +(0.849027 - 1.08947i) q^{34} +(-5.87725 + 2.43444i) q^{36} +(9.38373 - 3.18535i) q^{37} +(-0.750659 + 0.201138i) q^{38} +(0.167866 + 2.56114i) q^{39} +(1.73104 + 1.97388i) q^{40} +(0.475427 - 0.711527i) q^{41} +(6.12887 + 2.53866i) q^{43} +(-8.33478 - 0.546290i) q^{44} +(-6.43247 - 2.18353i) q^{45} +(0.317988 - 0.0208420i) q^{46} +(-9.87359 - 2.64562i) q^{47} +(-1.64418 + 8.26585i) q^{48} -0.313715i q^{50} +(7.77210 + 6.91966i) q^{51} +(1.66257 + 0.959887i) q^{52} +(-1.68299 + 12.7836i) q^{53} +(0.100510 + 0.296093i) q^{54} +(-6.30683 - 6.30683i) q^{55} +(-1.14224 - 5.74242i) q^{57} +(0.0857057 - 1.30762i) q^{58} +(4.62592 - 3.54959i) q^{59} +(-7.61961 + 5.84674i) q^{60} +(-0.689702 + 10.5228i) q^{61} +(0.244589 + 1.22963i) q^{62} +(3.84042 + 3.84042i) q^{64} +(0.658947 + 1.94119i) q^{65} +(-0.488290 + 3.70893i) q^{66} +(-9.13774 - 5.27568i) q^{67} +(7.53317 - 1.95813i) q^{68} +2.40085i q^{69} +(1.33343 - 6.70358i) q^{71} +(4.23931 + 1.13592i) q^{72} +(-14.6203 + 0.958267i) q^{73} +(-3.14353 - 1.06708i) q^{74} +(2.35845 + 0.154581i) q^{75} +(-4.04598 - 1.67590i) q^{76} +(0.477687 - 0.714910i) q^{78} +(2.71719 + 3.09837i) q^{79} +(0.440250 + 6.71692i) q^{80} +(7.48952 - 2.00681i) q^{81} +(-0.271459 + 0.0921479i) q^{82} +(-2.28169 + 0.945109i) q^{83} +(7.42655 + 3.73181i) q^{85} +(-1.11116 - 1.92458i) q^{86} +(9.78819 + 1.28864i) q^{87} +(4.33254 + 3.79953i) q^{88} +(3.64634 - 13.6083i) q^{89} +(1.26427 + 1.89212i) q^{90} +(1.49313 + 0.997677i) q^{92} +(-9.36467 + 1.23288i) q^{93} +(2.08459 + 2.71669i) q^{94} +(-2.06831 - 4.19411i) q^{95} +(7.06534 - 6.19613i) q^{96} +(-4.35295 + 2.90855i) q^{97} +(-14.6237 - 2.90883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 128 q^{15} - 32 q^{18} - 96 q^{22} + 16 q^{23} - 32 q^{29} - 112 q^{30} - 16 q^{32} - 96 q^{36} - 48 q^{37} - 32 q^{43} + 16 q^{44} - 16 q^{46} + 48 q^{51}+ \cdots + 256 q^{99}+O(q^{100}) \) 160 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9 - 128 * q^15 - 32 * q^18 - 96 * q^22 + 16 * q^23 - 32 * q^29 - 112 * q^30 - 16 * q^32 - 96 * q^36 - 48 * q^37 - 32 * q^43 + 16 * q^44 - 16 * q^46 + 48 * q^51 - 16 * q^53 - 32 * q^57 + 48 * q^58 - 48 * q^60 + 96 * q^64 + 32 * q^65 + 32 * q^71 + 80 * q^72 + 80 * q^74 + 224 * q^78 + 16 * q^79 + 64 * q^81 + 224 * q^85 - 48 * q^86 + 112 * q^88 + 512 * q^92 - 48 * q^93 + 48 * q^95 + 256 * q^99

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