LMFDB - Embedded newform 156.2.w.c.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.2
Character	$\chi$	$=$	156.67
Dual form			156.2.w.c.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31582 + 0.518286i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.46276 - 1.36394i) q^{4} +(0.713774 - 0.713774i) q^{5} +(-0.880389 + 1.10676i) q^{6} +(-0.872392 - 3.25581i) q^{7} +(-1.21781 + 2.55283i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.31582 + 0.518286i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.46276 - 1.36394i) q^{4} +(0.713774 - 0.713774i) q^{5} +(-0.880389 + 1.10676i) q^{6} +(-0.872392 - 3.25581i) q^{7} +(-1.21781 + 2.55283i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.569258 + 1.30914i) q^{10} +(-2.40848 - 0.645351i) q^{11} +(0.584815 - 1.91259i) q^{12} +(3.54378 - 0.664535i) q^{13} +(2.83535 + 3.83191i) q^{14} +(0.261259 - 0.975034i) q^{15} +(0.279324 - 3.99024i) q^{16} +(3.10126 + 1.79051i) q^{17} +(-0.209060 + 1.39868i) q^{18} +(1.65671 - 0.443914i) q^{19} +(0.0705324 - 2.01763i) q^{20} +(-2.38342 - 2.38342i) q^{21} +(3.50360 - 0.399119i) q^{22} +(1.49159 + 2.58350i) q^{23} +(0.221758 + 2.81972i) q^{24} +3.98105i q^{25} +(-4.31856 + 2.71110i) q^{26} -1.00000i q^{27} +(-5.71684 - 3.57257i) q^{28} +(-1.52342 - 2.63864i) q^{29} +(0.161577 + 1.41837i) q^{30} +(-0.507621 - 0.507621i) q^{31} +(1.70055 + 5.39520i) q^{32} +(-2.40848 + 0.645351i) q^{33} +(-5.00869 - 0.748650i) q^{34} +(-2.94661 - 1.70122i) q^{35} +(-0.449829 - 1.94876i) q^{36} +(-2.37631 + 8.86852i) q^{37} +(-1.94985 + 1.44276i) q^{38} +(2.73674 - 2.34740i) q^{39} +(0.952900 + 2.69139i) q^{40} +(-10.3471 - 2.77250i) q^{41} +(4.37144 + 1.90085i) q^{42} +(-5.30296 + 9.18500i) q^{43} +(-4.40325 + 2.34104i) q^{44} +(-0.261259 - 0.975034i) q^{45} +(-3.30165 - 2.62635i) q^{46} +(4.11506 - 4.11506i) q^{47} +(-1.75322 - 3.59531i) q^{48} +(-3.77707 + 2.18069i) q^{49} +(-2.06333 - 5.23834i) q^{50} +3.58103 q^{51} +(4.27731 - 5.80557i) q^{52} +2.75497 q^{53} +(0.518286 + 1.31582i) q^{54} +(-2.17975 + 1.25848i) q^{55} +(9.37394 + 1.73790i) q^{56} +(1.21279 - 1.21279i) q^{57} +(3.37212 + 2.68241i) q^{58} +(3.00480 + 11.2141i) q^{59} +(-0.947730 - 1.78258i) q^{60} +(6.36711 - 11.0282i) q^{61} +(0.931030 + 0.404844i) q^{62} +(-3.25581 - 0.872392i) q^{63} +(-5.03387 - 6.21773i) q^{64} +(2.05513 - 3.00379i) q^{65} +(2.83465 - 2.09745i) q^{66} +(-3.36363 + 12.5532i) q^{67} +(6.97855 - 1.61085i) q^{68} +(2.58350 + 1.49159i) q^{69} +(4.75892 + 0.711316i) q^{70} +(10.4181 - 2.79152i) q^{71} +(1.60191 + 2.33107i) q^{72} +(-1.37327 - 1.37327i) q^{73} +(-1.46964 - 12.9010i) q^{74} +(1.99053 + 3.44769i) q^{75} +(1.81789 - 2.90899i) q^{76} +8.40456i q^{77} +(-2.38443 + 4.50716i) q^{78} +1.96309i q^{79} +(-2.64875 - 3.04750i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(15.0519 - 1.71466i) q^{82} +(-7.07500 - 7.07500i) q^{83} +(-6.73721 - 0.235520i) q^{84} +(3.49162 - 0.935577i) q^{85} +(2.21728 - 14.8342i) q^{86} +(-2.63864 - 1.52342i) q^{87} +(4.58055 - 5.36252i) q^{88} +(2.87118 - 10.7154i) q^{89} +(0.849117 + 1.14756i) q^{90} +(-5.25517 - 10.9582i) q^{91} +(5.70557 + 1.74460i) q^{92} +(-0.693423 - 0.185802i) q^{93} +(-3.28189 + 7.54745i) q^{94} +(0.865661 - 1.49937i) q^{95} +(4.17031 + 3.82210i) q^{96} +(3.45104 + 12.8795i) q^{97} +(3.83971 - 4.82700i) q^{98} +(-1.76313 + 1.76313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.31582	+	0.518286i	−0.930424	+	0.366484i
$2$	−1.31582	+	0.518286i	−0.930424	+	0.366484i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	1.46276	−	1.36394i	0.731379	−	0.681971i
$5$	0.713774	−	0.713774i	0.319209	−	0.319209i	−0.529254	−	0.848463i	$-0.677528\pi$
$5$	0.713774	−	0.713774i	0.319209	−	0.319209i	0.848463	+	0.529254i	$0.177528\pi$
$6$	−0.880389	+	1.10676i	−0.359417	+	0.451832i
$7$	−0.872392	−	3.25581i	−0.329733	−	1.23058i	−0.909467	−	0.415776i	$-0.863510\pi$
$7$	−0.872392	−	3.25581i	−0.329733	−	1.23058i	0.579734	−	0.814806i	$-0.303156\pi$
$8$	−1.21781	+	2.55283i	−0.430562	+	0.902561i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.569258	+	1.30914i	−0.180015	+	0.413985i
$11$	−2.40848	−	0.645351i	−0.726184	−	0.194581i	−0.123255	−	0.992375i	$-0.539333\pi$
$11$	−2.40848	−	0.645351i	−0.726184	−	0.194581i	−0.602929	+	0.797795i	$0.706000\pi$
$12$	0.584815	−	1.91259i	0.168821	−	0.552117i
$13$	3.54378	−	0.664535i	0.982868	−	0.184309i
$13$	3.54378	−	0.664535i	0.982868	−	0.184309i
$14$	2.83535	+	3.83191i	0.757780	+	1.02412i
$15$	0.261259	−	0.975034i	0.0674569	−	0.251753i
$16$	0.279324	−	3.99024i	0.0698309	−	0.997559i
$17$	3.10126	+	1.79051i	0.752166	+	0.434263i	0.826476	−	0.562972i	$-0.190342\pi$
$17$	3.10126	+	1.79051i	0.752166	+	0.434263i	−0.0743102	+	0.997235i	$0.523675\pi$
$18$	−0.209060	+	1.39868i	−0.0492760	+	0.329671i
$19$	1.65671	−	0.443914i	0.380075	−	0.101841i	−0.0637231	−	0.997968i	$-0.520297\pi$
$19$	1.65671	−	0.443914i	0.380075	−	0.101841i	0.443798	+	0.896127i	$0.353631\pi$
$20$	0.0705324	−	2.01763i	0.0157715	−	0.451155i
$21$	−2.38342	−	2.38342i	−0.520105	−	0.520105i
$22$	3.50360	−	0.399119i	0.746970	−	0.0850924i
$23$	1.49159	+	2.58350i	0.311017	+	0.538697i	0.978583	−	0.205854i	$-0.0659971\pi$
$23$	1.49159	+	2.58350i	0.311017	+	0.538697i	−0.667566	+	0.744551i	$0.732664\pi$
$24$	0.221758	+	2.81972i	0.0452662	+	0.575573i
$25$			3.98105i			0.796211i
$26$	−4.31856	+	2.71110i	−0.846939	+	0.531691i
$27$		−	1.00000i		−	0.192450i
$28$	−5.71684	−	3.57257i	−1.08038	−	0.675153i
$29$	−1.52342	−	2.63864i	−0.282892	−	0.489984i	0.689204	−	0.724568i	$-0.257961\pi$
$29$	−1.52342	−	2.63864i	−0.282892	−	0.489984i	−0.972096	+	0.234584i	$0.924627\pi$
$30$	0.161577	+	1.41837i	0.0294997	+	0.258959i
$31$	−0.507621	−	0.507621i	−0.0911713	−	0.0911713i	0.660050	−	0.751222i	$-0.270535\pi$
$31$	−0.507621	−	0.507621i	−0.0911713	−	0.0911713i	−0.751222	+	0.660050i	$0.770535\pi$
$32$	1.70055	+	5.39520i	0.300617	+	0.953745i
$33$	−2.40848	+	0.645351i	−0.419263	+	0.112341i
$34$	−5.00869	−	0.748650i	−0.858984	−	0.128392i
$35$	−2.94661	−	1.70122i	−0.498067	−	0.287559i
$36$	−0.449829	−	1.94876i	−0.0749716	−	0.324793i
$37$	−2.37631	+	8.86852i	−0.390664	+	1.45798i	0.438379	+	0.898790i	$0.355553\pi$
$37$	−2.37631	+	8.86852i	−0.390664	+	1.45798i	−0.829042	+	0.559186i	$0.811114\pi$
$38$	−1.94985	+	1.44276i	−0.316308	+	0.234046i
$39$	2.73674	−	2.34740i	0.438229	−	0.375884i
$40$	0.952900	+	2.69139i	0.150667	+	0.425545i
$41$	−10.3471	−	2.77250i	−1.61595	−	0.432992i	−0.666141	−	0.745826i	$-0.732055\pi$
$41$	−10.3471	−	2.77250i	−1.61595	−	0.432992i	−0.949808	+	0.312833i	$0.898722\pi$
$42$	4.37144	+	1.90085i	0.674528	+	0.293308i
$43$	−5.30296	+	9.18500i	−0.808694	+	1.40070i	0.105075	+	0.994464i	$0.466492\pi$
$43$	−5.30296	+	9.18500i	−0.808694	+	1.40070i	−0.913769	+	0.406235i	$0.866841\pi$
$44$	−4.40325	+	2.34104i	−0.663814	+	0.352925i
$45$	−0.261259	−	0.975034i	−0.0389463	−	0.145349i
$46$	−3.30165	−	2.62635i	−0.486802	−	0.387234i
$47$	4.11506	−	4.11506i	0.600243	−	0.600243i	−0.340134	−	0.940377i	$-0.610472\pi$
$47$	4.11506	−	4.11506i	0.600243	−	0.600243i	0.940377	+	0.340134i	$0.110472\pi$
$48$	−1.75322	−	3.59531i	−0.253055	−	0.518938i
$49$	−3.77707	+	2.18069i	−0.539581	+	0.311527i
$50$	−2.06333	−	5.23834i	−0.291798	−	0.740814i
$51$	3.58103			0.501444
$52$	4.27731	−	5.80557i	0.593156	−	0.805087i
$53$	2.75497			0.378425			0.189212	−	0.981936i	$-0.439407\pi$
$53$	2.75497			0.378425			0.189212	+	0.981936i	$0.439407\pi$
$54$	0.518286	+	1.31582i	0.0705299	+	0.179060i
$55$	−2.17975	+	1.25848i	−0.293917	+	0.169693i
$56$	9.37394	+	1.73790i	1.25265	+	0.232237i
$57$	1.21279	−	1.21279i	0.160639	−	0.160639i
$58$	3.37212	+	2.68241i	0.442781	+	0.352217i
$59$	3.00480	+	11.2141i	0.391191	+	1.45995i	0.828172	+	0.560475i	$0.189381\pi$
$59$	3.00480	+	11.2141i	0.391191	+	1.45995i	−0.436980	+	0.899471i	$0.643952\pi$
$60$	−0.947730	−	1.78258i	−0.122351	−	0.230130i
$61$	6.36711	−	11.0282i	0.815225	−	1.41201i	−0.0939415	−	0.995578i	$-0.529947\pi$
$61$	6.36711	−	11.0282i	0.815225	−	1.41201i	0.909166	−	0.416433i	$-0.136720\pi$
$62$	0.931030	+	0.404844i	0.118241	+	0.0514152i
$63$	−3.25581	−	0.872392i	−0.410194	−	0.109911i
$64$	−5.03387	−	6.21773i	−0.629233	−	0.777216i
$65$	2.05513	−	3.00379i	0.254908	−	0.372574i
$66$	2.83465	−	2.09745i	0.348921	−	0.258178i
$67$	−3.36363	+	12.5532i	−0.410933	+	1.53362i	0.381911	+	0.924199i	$0.375266\pi$
$67$	−3.36363	+	12.5532i	−0.410933	+	1.53362i	−0.792844	+	0.609424i	$0.791401\pi$
$68$	6.97855	−	1.61085i	0.846273	−	0.195344i
$69$	2.58350	+	1.49159i	0.311017	+	0.179566i
$70$	4.75892	+	0.711316i	0.568800	+	0.0850185i
$71$	10.4181	−	2.79152i	1.23640	−	0.331292i	0.419332	−	0.907833i	$-0.362264\pi$
$71$	10.4181	−	2.79152i	1.23640	−	0.331292i	0.817069	+	0.576541i	$0.195598\pi$
$72$	1.60191	+	2.33107i	0.188787	+	0.274719i
$73$	−1.37327	−	1.37327i	−0.160729	−	0.160729i	0.622161	−	0.782890i	$-0.286255\pi$
$73$	−1.37327	−	1.37327i	−0.160729	−	0.160729i	−0.782890	+	0.622161i	$0.786255\pi$
$74$	−1.46964	−	12.9010i	−0.170842	−	1.49971i
$75$	1.99053	+	3.44769i	0.229846	+	0.398105i
$76$	1.81789	−	2.90899i	0.208526	−	0.333684i
$77$			8.40456i			0.957789i
$78$	−2.38443	+	4.50716i	−0.269983	+	0.510336i
$79$			1.96309i			0.220865i	0.993884	+	0.110433i	$0.0352236\pi$
$79$			1.96309i			0.220865i	−0.993884	+	0.110433i	$0.964776\pi$
$80$	−2.64875	−	3.04750i	−0.296140	−	0.340721i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	15.0519	−	1.71466i	1.66220	−	0.189353i
$83$	−7.07500	−	7.07500i	−0.776582	−	0.776582i	0.202666	−	0.979248i	$-0.435040\pi$
$83$	−7.07500	−	7.07500i	−0.776582	−	0.776582i	−0.979248	+	0.202666i	$0.935040\pi$
$84$	−6.73721	−	0.235520i	−0.735090	−	0.0256974i
$85$	3.49162	−	0.935577i	0.378719	−	0.101478i
$86$	2.21728	−	14.8342i	0.239095	−	1.59962i
$87$	−2.63864	−	1.52342i	−0.282892	−	0.163328i
$88$	4.58055	−	5.36252i	0.488288	−	0.571647i
$89$	2.87118	−	10.7154i	0.304345	−	1.13583i	−0.629163	−	0.777273i	$-0.716602\pi$
$89$	2.87118	−	10.7154i	0.304345	−	1.13583i	0.933508	−	0.358557i	$-0.116731\pi$
$90$	0.849117	+	1.14756i	0.0895048	+	0.120963i
$91$	−5.25517	−	10.9582i	−0.550891	−	1.14873i
$92$	5.70557	+	1.74460i	0.594847	+	0.181887i
$93$	−0.693423	−	0.185802i	−0.0719046	−	0.0192668i
$94$	−3.28189	+	7.54745i	−0.338501	+	0.778460i
$95$	0.865661	−	1.49937i	0.0888150	−	0.153832i
$96$	4.17031	+	3.82210i	0.425631	+	0.390092i
$97$	3.45104	+	12.8795i	0.350400	+	1.30771i	0.886175	+	0.463351i	$0.153353\pi$
$97$	3.45104	+	12.8795i	0.350400	+	1.30771i	−0.535775	+	0.844361i	$0.679980\pi$
$98$	3.83971	−	4.82700i	0.387870	−	0.487600i
$99$	−1.76313	+	1.76313i	−0.177201	+	0.177201i
$100$	5.42993	+	5.82332i	0.542993	+	0.582332i
$101$	−15.5726	+	8.99084i	−1.54953	+	0.894622i	−0.551353	+	0.834272i	$0.685888\pi$
$101$	−15.5726	+	8.99084i	−1.54953	+	0.894622i	−0.998177	+	0.0603501i	$0.980778\pi$
$102$	−4.71198	+	1.85600i	−0.466556	+	0.183771i
$103$	9.43927			0.930079			0.465039	−	0.885290i	$-0.346040\pi$
$103$	9.43927			0.930079			0.465039	+	0.885290i	$0.346040\pi$
$104$	−2.61922	+	9.85595i	−0.256835	+	0.966455i
$105$	−3.40245			−0.332045
$106$	−3.62505	+	1.42787i	−0.352096	+	0.138687i
$107$	−3.08032	+	1.77842i	−0.297785	+	0.171926i	−0.641448	−	0.767167i	$-0.721666\pi$
$107$	−3.08032	+	1.77842i	−0.297785	+	0.171926i	0.343662	+	0.939093i	$0.388332\pi$
$108$	−1.36394	−	1.46276i	−0.131245	−	0.140754i
$109$	−1.65580	+	1.65580i	−0.158597	+	0.158597i	−0.781945	−	0.623348i	$-0.785772\pi$
$109$	−1.65580	+	1.65580i	−0.158597	+	0.158597i	0.623348	+	0.781945i	$0.285772\pi$
$110$	2.21590	−	2.78566i	0.211278	−	0.265602i
$111$	2.37631	+	8.86852i	0.225550	+	0.841763i
$112$	−13.2351	+	2.57162i	−1.25060	+	0.242996i
$113$	5.26613	−	9.12120i	0.495396	−	0.858051i	−0.504590	−	0.863359i	$-0.668356\pi$
$113$	5.26613	−	9.12120i	0.495396	−	0.858051i	0.999986	+	0.00530832i	$0.00168970\pi$
$114$	−0.967243	+	2.22439i	−0.0905906	+	0.208333i
$115$	2.90869	+	0.779381i	0.271237	+	0.0726777i
$116$	−5.82735	−	1.78184i	−0.541056	−	0.165440i
$117$	1.19639	−	3.40127i	0.110606	−	0.314448i
$118$	−9.76586	−	13.1983i	−0.899020	−	1.21500i
$119$	3.12406	−	11.6591i	0.286382	−	1.06879i
$120$	2.17093	+	1.85436i	0.198178	+	0.169279i
$121$	−4.14198	−	2.39137i	−0.376543	−	0.217397i
$122$	−2.66222	+	17.8110i	−0.241026	+	1.61254i
$123$	−10.3471	+	2.77250i	−0.932969	+	0.249988i
$124$	−1.43489	−	0.0501611i	−0.128857	−	0.00450460i
$125$	6.41044	+	6.41044i	0.573367	+	0.573367i
$126$	4.73621	−	0.539533i	0.421935	−	0.0480654i
$127$	−4.76872	−	8.25966i	−0.423155	−	0.732926i	0.573091	−	0.819492i	$-0.305744\pi$
$127$	−4.76872	−	8.25966i	−0.423155	−	0.732926i	−0.996246	+	0.0865656i	$0.972411\pi$
$128$	9.84622	+	5.57242i	0.870291	+	0.492537i
$129$			10.6059i			0.933799i
$130$	−1.14736	+	5.01759i	−0.100630	+	0.440072i
$131$			3.54939i			0.310112i	0.987906	+	0.155056i	$0.0495557\pi$
$131$			3.54939i			0.310112i	−0.987906	+	0.155056i	$0.950444\pi$
$132$	−2.64280	+	4.22902i	−0.230027	+	0.368089i
$133$	−2.89060	−	5.00666i	−0.250647	−	0.434133i
$134$	−2.08025	−	18.2611i	−0.179706	−	1.57752i
$135$	−0.713774	−	0.713774i	−0.0614319	−	0.0614319i
$136$	−8.34762	+	5.73647i	−0.715803	+	0.491899i
$137$	−0.606797	+	0.162591i	−0.0518422	+	0.0138911i	−0.284647	−	0.958632i	$-0.591876\pi$
$137$	−0.606797	+	0.162591i	−0.0518422	+	0.0138911i	0.232805	+	0.972523i	$0.425210\pi$
$138$	−4.17249	−	0.623662i	−0.355186	−	0.0530896i
$139$	4.85349	+	2.80216i	0.411667	+	0.237676i	0.691506	−	0.722371i	$-0.256948\pi$
$139$	4.85349	+	2.80216i	0.411667	+	0.237676i	−0.279839	+	0.960047i	$0.590281\pi$
$140$	−6.63054	+	1.53052i	−0.560383	+	0.129353i
$141$	1.50622	−	5.62127i	0.126846	−	0.473397i
$142$	−12.2615	+	9.07269i	−1.02896	+	0.761363i
$143$	−8.96399	−	0.686462i	−0.749607	−	0.0574048i
$144$	−3.31598	−	2.23702i	−0.276332	−	0.186418i
$145$	−2.97077	−	0.796016i	−0.246709	−	0.0661055i
$146$	2.51872	+	1.09523i	0.208451	+	0.0906417i
$147$	−2.18069	+	3.77707i	−0.179860	+	0.311527i
$148$	8.62018	+	16.2137i	0.708574	+	1.33275i
$149$	1.94039	+	7.24164i	0.158963	+	0.593258i	0.998733	+	0.0503164i	$0.0160230\pi$
$149$	1.94039	+	7.24164i	0.158963	+	0.593258i	−0.839770	+	0.542942i	$0.817310\pi$
$150$	−4.40606	−	3.50488i	−0.359754	−	0.286172i
$151$	9.17890	−	9.17890i	0.746969	−	0.746969i	−0.226940	−	0.973909i	$-0.572872\pi$
$151$	9.17890	−	9.17890i	0.746969	−	0.746969i	0.973909	+	0.226940i	$0.0728722\pi$
$152$	−0.884324	+	4.76989i	−0.0717281	+	0.386890i
$153$	3.10126	−	1.79051i	0.250722	−	0.144754i
$154$	−4.35597	−	11.0589i	−0.351014	−	0.891150i
$155$	−0.724653			−0.0582055
$156$	0.801475	−	7.16642i	0.0641693	−	0.573773i
$157$	−4.49673			−0.358878			−0.179439	−	0.983769i	$-0.557428\pi$
$157$	−4.49673			−0.358878			−0.179439	+	0.983769i	$0.557428\pi$
$158$	−1.01744	−	2.58308i	−0.0809436	−	0.205498i
$159$	2.38588	−	1.37749i	0.189212	−	0.109242i
$160$	5.06476	+	2.63715i	0.400404	+	0.208485i
$161$	7.11015	−	7.11015i	0.560358	−	0.560358i
$162$	1.10676	+	0.880389i	0.0869552	+	0.0691699i
$163$	−2.18356	−	8.14917i	−0.171030	−	0.638293i	−0.997194	−	0.0748627i	$-0.976148\pi$
$163$	−2.18356	−	8.14917i	−0.171030	−	0.638293i	0.826164	−	0.563430i	$-0.190519\pi$
$164$	−18.9169	+	10.0574i	−1.47716	+	0.785349i
$165$	−1.25848	+	2.17975i	−0.0979723	+	0.169693i
$166$	12.9763	+	5.64254i	1.00716	+	0.437946i
$167$	16.1711	+	4.33302i	1.25135	+	0.335299i	0.822859	−	0.568245i	$-0.192378\pi$
$167$	16.1711	+	4.33302i	1.25135	+	0.335299i	0.428494	+	0.903544i	$0.359044\pi$
$168$	8.98702	−	3.18190i	0.693364	−	0.245489i
$169$	12.1168	−	4.70993i	0.932061	−	0.362303i
$170$	−4.10944	+	3.04071i	−0.315180	+	0.233212i
$171$	0.443914	−	1.65671i	0.0339469	−	0.126692i
$172$	4.77086	+	20.6684i	0.363774	+	1.57595i
$173$	−8.38866	−	4.84320i	−0.637778	−	0.368221i	0.145980	−	0.989288i	$-0.453366\pi$
$173$	−8.38866	−	4.84320i	−0.637778	−	0.368221i	−0.783758	+	0.621066i	$0.786700\pi$
$174$	4.26154	+	0.636973i	0.323067	+	0.0482888i
$175$	12.9616	−	3.47304i	0.979802	−	0.262537i
$176$	−3.24785	+	9.43014i	−0.244816	+	0.710824i
$177$	8.20926	+	8.20926i	0.617046	+	0.617046i
$178$	1.77569	+	15.5876i	0.133094	+	1.16834i
$179$	3.66514	+	6.34820i	0.273945	+	0.474487i	0.969868	−	0.243629i	$-0.0783380\pi$
$179$	3.66514	+	6.34820i	0.273945	+	0.474487i	−0.695923	+	0.718116i	$0.745005\pi$
$180$	−1.71205	−	1.06990i	−0.127609	−	0.0797453i
$181$		−	20.8307i		−	1.54834i	−0.632980	−	0.774168i	$-0.718169\pi$
$181$		−	20.8307i		−	1.54834i	0.632980	−	0.774168i	$-0.281831\pi$
$182$	12.5943	+	11.6953i	0.933553	+	0.866911i
$183$		−	12.7342i		−	0.941341i
$184$	−8.41171	+	0.661542i	−0.620119	+	0.0487695i
$185$	4.63397	+	8.02627i	0.340696	+	0.590103i
$186$	1.00872	−	0.114910i	0.0739627	−	0.00842559i
$187$	−6.31381	−	6.31381i	−0.461712	−	0.461712i
$188$	0.406634	−	11.6320i	0.0296569	−	0.848353i
$189$	−3.25581	+	0.872392i	−0.236825	+	0.0634572i
$190$	−0.361951	+	2.42156i	−0.0262587	+	0.175678i
$191$	−20.9905	−	12.1189i	−1.51882	−	0.876890i	−0.999755	−	0.0221546i	$-0.992947\pi$
$191$	−20.9905	−	12.1189i	−1.51882	−	0.876890i	−0.519064	−	0.854736i	$-0.673719\pi$
$192$	−7.46832	−	2.86778i	−0.538980	−	0.206964i
$193$	1.87524	−	6.99850i	0.134983	−	0.503763i	−0.865015	−	0.501746i	$-0.832691\pi$
$193$	1.87524	−	6.99850i	0.134983	−	0.503763i	0.999998	−	0.00201722i	$-0.000642101\pi$
$194$	−11.2162	−	15.1584i	−0.805276	−	1.08831i
$195$	0.277903	−	3.62892i	0.0199010	−	0.259873i
$196$	−2.55060	+	8.34152i	−0.182186	+	0.595823i
$197$	9.93162	+	2.66117i	0.707599	+	0.189601i	0.594632	−	0.803998i	$-0.297298\pi$
$197$	9.93162	+	2.66117i	0.707599	+	0.189601i	0.112967	+	0.993599i	$0.463965\pi$
$198$	1.40615	−	3.23377i	0.0999310	−	0.229814i
$199$	1.17933	−	2.04266i	0.0836007	−	0.144801i	−0.821193	−	0.570650i	$-0.806691\pi$
$199$	1.17933	−	2.04266i	0.0836007	−	0.144801i	0.904794	+	0.425849i	$0.140025\pi$
$200$	−10.1629	−	4.84817i	−0.718629	−	0.342818i
$201$	3.36363	+	12.5532i	0.237252	+	0.885438i
$202$	15.8309	−	19.9014i	1.11386	−	1.40026i
$203$	−7.26190	+	7.26190i	−0.509686	+	0.509686i
$204$	5.23817	−	4.88431i	0.366746	−	0.341970i
$205$	−9.36445	+	5.40657i	−0.654042	+	0.377611i
$206$	−12.4204	+	4.89224i	−0.865368	+	0.340859i
$207$	2.98317			0.207345
$208$	−1.66179	−	14.3261i	−0.115224	−	0.993339i
$209$	−4.27663			−0.295821
$210$	4.47700	−	1.76344i	0.308943	−	0.121689i
$211$	−15.0604	+	8.69510i	−1.03680	+	0.598595i	−0.918925	−	0.394433i	$-0.870941\pi$
$211$	−15.0604	+	8.69510i	−1.03680	+	0.598595i	−0.117873	+	0.993029i	$0.537608\pi$
$212$	4.02986	−	3.75762i	0.276772	−	0.258075i
$213$	7.62657	−	7.62657i	0.522564	−	0.522564i
$214$	3.13141	−	3.93657i	0.214059	−	0.269098i
$215$	2.77090	+	10.3411i	0.188974	+	0.705259i
$216$	2.55283	+	1.21781i	0.173698	+	0.0828616i
$217$	−1.20987	+	2.09556i	−0.0821315	+	0.142256i
$218$	1.32056	−	3.03692i	0.0894395	−	0.205686i
$219$	−1.87592	−	0.502652i	−0.126763	−	0.0339661i
$220$	−1.47195	+	4.81389i	−0.0992390	+	0.324553i
$221$	12.1800	+	4.28429i	0.819318	+	0.288193i
$222$	−7.72323	−	10.4378i	−0.518349	−	0.700536i
$223$	−2.58140	+	9.63390i	−0.172863	+	0.645133i	0.824043	+	0.566528i	$0.191714\pi$
$223$	−2.58140	+	9.63390i	−0.172863	+	0.645133i	−0.996906	+	0.0786059i	$0.974953\pi$
$224$	16.0822	−	10.2434i	1.07454	−	0.684415i
$225$	3.44769	+	1.99053i	0.229846	+	0.132702i
$226$	−2.20188	+	14.7312i	−0.146467	+	0.979906i
$227$	14.8006	−	3.96580i	0.982349	−	0.263220i	0.268316	−	0.963331i	$-0.413533\pi$
$227$	14.8006	−	3.96580i	0.982349	−	0.263220i	0.714034	+	0.700111i	$0.246866\pi$
$228$	0.119844	−	3.42821i	0.00793684	−	0.227039i
$229$	−3.48635	−	3.48635i	−0.230385	−	0.230385i	0.582469	−	0.812853i	$-0.302087\pi$
$229$	−3.48635	−	3.48635i	−0.230385	−	0.230385i	−0.812853	+	0.582469i	$0.802087\pi$
$230$	−4.23125	+	0.482010i	−0.279001	+	0.0317828i
$231$	4.20228	+	7.27856i	0.276490	+	0.478894i
$232$	8.59124	−	0.675662i	0.564043	−	0.0443594i
$233$			11.0704i			0.725249i	0.931935	+	0.362624i	$0.118119\pi$
$233$			11.0704i			0.725249i	−0.931935	+	0.362624i	$0.881881\pi$
$234$	0.188605	+	5.09553i	0.0123295	+	0.333105i
$235$		−	5.87444i		−	0.383206i
$236$	19.6906	+	12.3051i	1.28175	+	0.800993i
$237$	0.981547	+	1.70009i	0.0637583	+	0.110433i
$238$	1.93208	+	16.9605i	0.125238	+	1.09938i
$239$	−18.3174	−	18.3174i	−1.18485	−	1.18485i	−0.978471	−	0.206383i	$-0.933831\pi$
$239$	−18.3174	−	18.3174i	−1.18485	−	1.18485i	−0.206383	−	0.978471i	$-0.566169\pi$
$240$	−3.81764	−	1.31484i	−0.246427	−	0.0848723i
$241$	−15.2233	+	4.07907i	−0.980620	+	0.262756i	−0.713306	−	0.700853i	$-0.752803\pi$
$241$	−15.2233	+	4.07907i	−0.980620	+	0.262756i	−0.267314	+	0.963609i	$0.586136\pi$
$242$	6.68950	+	0.999881i	0.430018	+	0.0642748i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.72823	−	24.8159i	−0.366712	−	1.58868i
$245$	−1.13945	+	4.25249i	−0.0727969	+	0.271682i
$246$	12.1780	−	9.01089i	0.776440	−	0.574513i
$247$	5.57602	−	2.67407i	0.354793	−	0.170147i
$248$	1.91405	−	0.677682i	0.121543	−	0.0430328i
$249$	−9.66463	−	2.58963i	−0.612471	−	0.164111i
$250$	−11.7574	−	5.11254i	−0.743605	−	0.323345i
$251$	−10.2628	+	17.7757i	−0.647781	+	1.12199i	0.335870	+	0.941908i	$0.390970\pi$
$251$	−10.2628	+	17.7757i	−0.647781	+	1.12199i	−0.983652	+	0.180082i	$0.942364\pi$
$252$	−5.95236	+	3.16464i	−0.374963	+	0.199354i
$253$	−1.92519	−	7.18491i	−0.121036	−	0.451711i
$254$	10.5556	+	8.39665i	0.662319	+	0.526853i
$255$	2.55604	−	2.55604i	0.160066	−	0.160066i
$256$	−15.8440	−	2.22913i	−0.990247	−	0.139321i
$257$	22.7988	−	13.1629i	1.42215	−	0.821080i	0.425670	−	0.904879i	$-0.360039\pi$
$257$	22.7988	−	13.1629i	1.42215	−	0.821080i	0.996483	+	0.0837987i	$0.0267053\pi$
$258$	−5.49691	−	13.9555i	−0.342222	−	0.868830i
$259$	30.9473			1.92297
$260$	−1.09083	−	7.19690i	−0.0676505	−	0.446333i
$261$	−3.04684			−0.188595
$262$	−1.83960	−	4.67035i	−0.113651	−	0.288535i
$263$	−12.2857	+	7.09315i	−0.757568	+	0.437382i	−0.828422	−	0.560105i	$-0.810761\pi$
$263$	−12.2857	+	7.09315i	−0.757568	+	0.437382i	0.0708539	+	0.997487i	$0.477428\pi$
$264$	1.28561	−	6.93435i	0.0791237	−	0.426780i
$265$	1.96643	−	1.96643i	0.120797	−	0.120797i
$266$	6.39839	+	5.08970i	0.392310	+	0.312070i
$267$	−2.87118	−	10.7154i	−0.175714	−	0.655772i
$268$	12.2017	+	22.9502i	0.745339	+	1.40190i
$269$	−8.23524	+	14.2639i	−0.502111	+	0.869682i	0.497886	+	0.867243i	$0.334110\pi$
$269$	−8.23524	+	14.2639i	−0.502111	+	0.869682i	−0.999997	+	0.00243974i	$0.999223\pi$
$270$	1.30914	+	0.569258i	0.0796715	+	0.0346439i
$271$	−10.7015	−	2.86746i	−0.650071	−	0.174186i	−0.0813101	−	0.996689i	$-0.525910\pi$
$271$	−10.7015	−	2.86746i	−0.650071	−	0.174186i	−0.568761	+	0.822503i	$0.692577\pi$
$272$	8.01082	−	11.8746i	0.485727	−	0.720005i
$273$	−10.0302	−	6.86246i	−0.607055	−	0.415335i
$274$	0.714167	−	0.528435i	0.0431444	−	0.0319239i
$275$	2.56917	−	9.58829i	0.154927	−	0.578196i
$276$	5.81347	−	1.34192i	0.349930	−	0.0807739i
$277$	−25.7495	−	14.8665i	−1.54714	−	0.893240i	−0.998359	−	0.0572715i	$-0.981760\pi$
$277$	−25.7495	−	14.8665i	−1.54714	−	0.893240i	−0.548778	−	0.835968i	$-0.684907\pi$
$278$	−7.83863	−	1.17164i	−0.470130	−	0.0702703i
$279$	−0.693423	+	0.185802i	−0.0415141	+	0.0111237i
$280$	7.93134	−	5.45041i	0.473988	−	0.325724i
$281$	0.120824	+	0.120824i	0.00720778	+	0.00720778i	0.710701	−	0.703494i	$-0.248378\pi$
$281$	0.120824	+	0.120824i	0.00720778	+	0.00720778i	−0.703494	+	0.710701i	$0.748378\pi$
$282$	0.931523	+	8.17723i	0.0554714	+	0.486947i
$283$	7.09875	+	12.2954i	0.421977	+	0.730885i	0.996133	−	0.0878606i	$-0.0280030\pi$
$283$	7.09875	+	12.2954i	0.421977	+	0.730885i	−0.574156	+	0.818746i	$0.694670\pi$
$284$	11.4317	−	18.2930i	0.678346	−	1.08549i
$285$		−	1.73132i		−	0.102555i
$286$	12.1508	−	3.74266i	0.718490	−	0.221308i
$287$			36.1070i			2.13133i
$288$	5.52265	+	1.22488i	0.325425	+	0.0721769i
$289$	−2.08813	−	3.61675i	−0.122831	−	0.212750i
$290$	4.32156	−	0.492298i	0.253771	−	0.0289087i
$291$	9.42842	+	9.42842i	0.552704	+	0.552704i
$292$	−3.88182	−	0.135701i	−0.227167	−	0.00794132i
$293$	−12.6675	+	3.39425i	−0.740044	+	0.198294i	−0.609097	−	0.793095i	$-0.708468\pi$
$293$	−12.6675	+	3.39425i	−0.740044	+	0.198294i	−0.130946	+	0.991389i	$0.541802\pi$
$294$	0.911791	−	6.10016i	0.0531767	−	0.355768i
$295$	10.1490	+	5.85956i	0.590900	+	0.341157i
$296$	−19.7459	−	16.8665i	−1.14771	−	0.980346i
$297$	−0.645351	+	2.40848i	−0.0374470	+	0.139754i
$298$	−6.30645	−	8.52301i	−0.365323	−	0.493725i
$299$	7.00268	+	8.16415i	0.404975	+	0.472145i
$300$	7.61411	+	2.32818i	0.439601	+	0.134417i
$301$	34.5309	+	9.25252i	1.99033	+	0.533307i
$302$	−7.32047	+	16.8351i	−0.421246	+	0.968750i
$303$	−8.99084	+	15.5726i	−0.516510	+	0.894622i
$304$	−1.30856	−	6.73465i	−0.0750512	−	0.386259i
$305$	−3.32694	−	12.4163i	−0.190500	−	0.710955i
$306$	−3.15270	+	3.96333i	−0.180228	+	0.226569i
$307$	15.6742	−	15.6742i	0.894575	−	0.894575i	−0.100374	−	0.994950i	$-0.532004\pi$
$307$	15.6742	−	15.6742i	0.894575	−	0.894575i	0.994950	+	0.100374i	$0.0320040\pi$
$308$	11.4633	+	12.2938i	0.653184	+	0.700507i
$309$	8.17464	−	4.71963i	0.465039	−	0.268491i
$310$	0.953512	−	0.375578i	0.0541558	−	0.0213314i
$311$	−3.08092			−0.174703			−0.0873516	−	0.996178i	$-0.527840\pi$
$311$	−3.08092			−0.174703			−0.0873516	+	0.996178i	$0.527840\pi$
$312$	2.65966	+	9.84511i	0.150574	+	0.557370i
$313$	−0.908180			−0.0513334			−0.0256667	−	0.999671i	$-0.508171\pi$
$313$	−0.908180			−0.0513334			−0.0256667	+	0.999671i	$0.508171\pi$
$314$	5.91688	−	2.33059i	0.333909	−	0.131523i
$315$	−2.94661	+	1.70122i	−0.166022	+	0.0958531i
$316$	2.67755	+	2.87153i	0.150624	+	0.161536i
$317$	−5.86027	+	5.86027i	−0.329145	+	0.329145i	−0.852261	−	0.523116i	$-0.824769\pi$
$317$	−5.86027	+	5.86027i	−0.329145	+	0.329145i	0.523116	+	0.852261i	$0.324769\pi$
$318$	−2.42545	+	3.04909i	−0.136012	+	0.170985i
$319$	1.96628	+	7.33826i	0.110091	+	0.410864i
$320$	−8.03110	−	0.845012i	−0.448952	−	0.0472376i
$321$	−1.77842	+	3.08032i	−0.0992618	+	0.171926i
$322$	−5.67057	+	13.0408i	−0.316009	+	0.726733i
$323$	5.93271	+	1.58967i	0.330105	+	0.0884514i
$324$	−1.91259	−	0.584815i	−0.106255	−	0.0324897i
$325$	2.64555	+	14.1080i	0.146749	+	0.782570i
$326$	7.09678	+	9.59112i	0.393054	+	0.531203i
$327$	−0.606067	+	2.26187i	−0.0335156	+	0.125082i
$328$	19.6786	−	23.0380i	1.08657	−	1.27206i
$329$	−16.9878	−	9.80791i	−0.936568	−	0.540728i
$330$	0.526195	−	3.52040i	0.0289661	−	0.193792i
$331$	−26.4946	+	7.09920i	−1.45627	+	0.390207i	−0.898201	−	0.439585i	$-0.855126\pi$
$331$	−26.4946	+	7.09920i	−1.45627	+	0.390207i	−0.558073	+	0.829792i	$0.688459\pi$
$332$	−19.9989	−	0.699125i	−1.09758	−	0.0383695i
$333$	6.49221	+	6.49221i	0.355771	+	0.355771i
$334$	−23.5239	+	2.67977i	−1.28717	+	0.146630i
$335$	6.55931	+	11.3611i	0.358373	+	0.620721i
$336$	−10.1762	+	8.84466i	−0.555155	+	0.482516i
$337$		−	5.47102i		−	0.298025i	−0.988835	−	0.149013i	$-0.952390\pi$
$337$		−	5.47102i		−	0.298025i	0.988835	−	0.149013i	$-0.0476095\pi$
$338$	−13.5024	+	12.4774i	−0.734434	+	0.678680i
$339$		−	10.5323i		−	0.572034i
$340$	3.83132	−	6.13089i	0.207783	−	0.332494i
$341$	0.895001	+	1.55019i	0.0484670	+	0.0839474i
$342$	0.274539	+	2.41000i	0.0148454	+	0.130318i
$343$	−6.28894	−	6.28894i	−0.339571	−	0.339571i
$344$	−16.9897	−	24.7232i	−0.916024	−	1.33298i
$345$	2.90869	−	0.779381i	0.156599	−	0.0419605i
$346$	13.5481	+	2.02504i	0.728351	+	0.108867i
$347$	−1.82152	−	1.05166i	−0.0977844	−	0.0564558i	0.450310	−	0.892872i	$-0.351313\pi$
$347$	−1.82152	−	1.05166i	−0.0977844	−	0.0564558i	−0.548095	+	0.836416i	$0.684647\pi$
$348$	−5.93755	+	1.37056i	−0.318286	+	0.0734697i
$349$	−5.35524	+	19.9860i	−0.286659	+	1.06983i	0.660959	+	0.750422i	$0.270150\pi$
$349$	−5.35524	+	19.9860i	−0.286659	+	1.06983i	−0.947618	+	0.319405i	$0.896517\pi$
$350$	−15.2550	+	11.2877i	−0.815416	+	0.603353i
$351$	−0.664535	−	3.54378i	−0.0354703	−	0.189153i
$352$	−0.613939	−	14.0917i	−0.0327230	−	0.751089i
$353$	−24.8443	−	6.65700i	−1.32233	−	0.354316i	−0.472478	−	0.881343i	$-0.656640\pi$
$353$	−24.8443	−	6.65700i	−1.32233	−	0.354316i	−0.849849	+	0.527026i	$0.823307\pi$
$354$	−15.0566	−	6.54715i	−0.800252	−	0.347977i
$355$	5.44365	−	9.42868i	0.288919	−	0.500422i
$356$	−10.4153	−	19.5902i	−0.552012	−	1.03828i
$357$	−3.12406	−	11.6591i	−0.165343	−	0.617067i
$358$	−8.11284	−	6.45349i	−0.428777	−	0.341078i
$359$	8.57373	−	8.57373i	0.452504	−	0.452504i	−0.443681	−	0.896185i	$-0.646328\pi$
$359$	8.57373	−	8.57373i	0.452504	−	0.452504i	0.896185	+	0.443681i	$0.146328\pi$
$360$	2.80726	+	0.520457i	0.147956	+	0.0274305i
$361$	−13.9069	+	8.02913i	−0.731940	+	0.422586i
$362$	10.7963	+	27.4095i	0.567440	+	1.44061i
$363$	−4.78274			−0.251029
$364$	−22.6333	−	8.86138i	−1.18631	−	0.464463i
$365$	−1.96041			−0.102613
$366$	6.59997	+	16.7559i	0.344986	+	0.875846i
$367$	−5.73176	+	3.30923i	−0.299195	+	0.172741i	−0.642081	−	0.766636i	$-0.721929\pi$
$367$	−5.73176	+	3.30923i	−0.299195	+	0.172741i	0.342886	+	0.939377i	$0.388596\pi$
$368$	10.7254	−	5.23014i	0.559101	−	0.272640i
$369$	−7.57462	+	7.57462i	−0.394319	+	0.394319i
$370$	−10.2574	−	8.15940i	−0.533256	−	0.424187i
$371$	−2.40342	−	8.96968i	−0.124779	−	0.465682i
$372$	−1.26773	+	0.674005i	−0.0657289	+	0.0349455i
$373$	−0.0585684	+	0.101443i	−0.00303255	+	0.00525254i	−0.867538	−	0.497371i	$-0.834299\pi$
$373$	−0.0585684	+	0.101443i	−0.00303255	+	0.00525254i	0.864505	+	0.502624i	$0.167632\pi$
$374$	11.5802	+	5.03547i	0.598798	+	0.260378i
$375$	8.75683	+	2.34639i	0.452201	+	0.121167i
$376$	5.49367	+	15.5164i	0.283314	+	0.800198i
$377$	−7.15214	−	8.33841i	−0.368354	−	0.429450i
$378$	3.83191	−	2.83535i	0.197092	−	0.145835i
$379$	−2.13426	+	7.96516i	−0.109629	+	0.409143i	−0.998829	−	0.0483765i	$-0.984595\pi$
$379$	−2.13426	+	7.96516i	−0.109629	+	0.409143i	0.889200	+	0.457519i	$0.151262\pi$
$380$	−0.778800	−	3.37393i	−0.0399516	−	0.173079i
$381$	−8.25966	−	4.76872i	−0.423155	−	0.244309i
$382$	33.9007	+	5.06714i	1.73451	+	0.259258i
$383$	−8.21931	+	2.20236i	−0.419987	+	0.112535i	−0.462622	−	0.886555i	$-0.653091\pi$
$383$	−8.21931	+	2.20236i	−0.419987	+	0.112535i	0.0426351	+	0.999091i	$0.486425\pi$
$384$	11.3133	−	0.0972519i	0.577329	−	0.00496287i
$385$	5.99896	+	5.99896i	0.305735	+	0.305735i
$386$	1.15975	+	10.1807i	0.0590297	+	0.518183i
$387$	5.30296	+	9.18500i	0.269565	+	0.466900i
$388$	22.6149	+	14.1325i	1.14810	+	0.717470i
$389$			21.5980i			1.09506i	0.836785	+	0.547532i	$0.184433\pi$
$389$			21.5980i			1.09506i	−0.836785	+	0.547532i	$0.815567\pi$
$390$	1.51515	+	4.91904i	0.0767227	+	0.249085i
$391$			10.6828i			0.540253i
$392$	−0.967171	−	12.2979i	−0.0488495	−	0.621136i
$393$	1.77469	+	3.07386i	0.0895215	+	0.155056i
$394$	−14.4475	+	1.64581i	−0.727853	+	0.0829146i
$395$	1.40121	+	1.40121i	0.0705023	+	0.0705023i
$396$	−0.174226	+	4.98384i	−0.00875518	+	0.250447i
$397$	−8.99240	+	2.40951i	−0.451316	+	0.120930i	−0.477315	−	0.878732i	$-0.658390\pi$
$397$	−8.99240	+	2.40951i	−0.451316	+	0.120930i	0.0259992	+	0.999662i	$0.491723\pi$
$398$	−0.493103	+	3.29901i	−0.0247170	+	0.165364i
$399$	−5.00666	−	2.89060i	−0.250647	−	0.144711i
$400$	15.8853	+	1.11200i	0.794267	+	0.0556001i
$401$	0.807475	−	3.01354i	0.0403234	−	0.150489i	−0.942829	−	0.333277i	$-0.891846\pi$
$401$	0.807475	−	3.01354i	0.0403234	−	0.150489i	0.983152	+	0.182788i	$0.0585122\pi$
$402$	−10.9321	−	14.7745i	−0.545244	−	0.736884i
$403$	−2.13623	−	1.46157i	−0.106413	−	0.0728057i
$404$	−10.5160	+	34.3915i	−0.523188	+	1.71104i
$405$	−0.975034	−	0.261259i	−0.0484498	−	0.0129821i
$406$	5.79160	−	13.3191i	0.287432	−	0.661016i
$407$	11.4466	−	19.8261i	0.567388	−	0.982744i
$408$	−4.36102	+	9.14174i	−0.215902	+	0.452584i
$409$	1.18671	+	4.42887i	0.0586791	+	0.218994i	0.989039	−	0.147654i	$-0.0471722\pi$
$409$	1.18671	+	4.42887i	0.0586791	+	0.218994i	−0.930360	+	0.366647i	$0.880506\pi$
$410$	9.51977	−	11.9675i	0.470148	−	0.591034i
$411$	−0.444206	+	0.444206i	−0.0219111	+	0.0219111i
$412$	13.8074	−	12.8746i	0.680240	−	0.634287i
$413$	33.8895	−	19.5661i	1.66759	−	0.962785i
$414$	−3.92531	+	1.54614i	−0.192919	+	0.0759885i
$415$	−10.0999			−0.495785
$416$	9.61166	+	17.9893i	0.471250	+	0.881999i
$417$	5.60432			0.274445
$418$	5.62727	−	2.21652i	0.275239	−	0.108414i
$419$	32.8608	−	18.9722i	1.60536	−	0.926854i	0.614967	−	0.788553i	$-0.289169\pi$
$419$	32.8608	−	18.9722i	1.60536	−	0.926854i	0.990390	−	0.138301i	$-0.0441641\pi$
$420$	−4.97696	+	4.64074i	−0.242851	+	0.226445i
$421$	19.3254	−	19.3254i	0.941860	−	0.941860i	−0.0565402	−	0.998400i	$-0.518007\pi$
$421$	19.3254	−	19.3254i	0.941860	−	0.941860i	0.998400	+	0.0565402i	$0.0180069\pi$
$422$	15.3101	−	19.2468i	0.745286	−	0.936917i
$423$	−1.50622	−	5.62127i	−0.0732347	−	0.273316i
$424$	−3.35504	+	7.03298i	−0.162935	+	0.341551i
$425$	−7.12813	+	12.3463i	−0.345765	+	0.598882i
$426$	−6.08244	+	13.9879i	−0.294695	+	0.677718i
$427$	−41.4602	−	11.1092i	−2.00640	−	0.537613i
$428$	−2.08009	+	6.80277i	−0.100545	+	0.328824i
$429$	−8.10627	+	3.88750i	−0.391375	+	0.187690i
$430$	−9.00567	−	12.1709i	−0.434292	−	0.586935i
$431$	3.72019	−	13.8839i	0.179195	−	0.668765i	−0.816604	−	0.577198i	$-0.804146\pi$
$431$	3.72019	−	13.8839i	0.179195	−	0.668765i	0.995799	−	0.0915666i	$-0.0291874\pi$
$432$	−3.99024	−	0.279324i	−0.191980	−	0.0134390i
$433$	11.3486	+	6.55212i	0.545379	+	0.314875i	0.747256	−	0.664536i	$-0.231371\pi$
$433$	11.3486	+	6.55212i	0.545379	+	0.314875i	−0.201877	+	0.979411i	$0.564704\pi$
$434$	0.505872	−	3.38444i	0.0242827	−	0.162458i
$435$	−2.97077	+	0.796016i	−0.142438	+	0.0381661i
$436$	−0.163620	+	4.68046i	−0.00783599	+	0.224154i
$437$	3.61797	+	3.61797i	0.173071	+	0.173071i
$438$	2.72889	−	0.310866i	0.130391	−	0.0148538i
$439$	−9.50522	−	16.4635i	−0.453660	−	0.785761i	0.544950	−	0.838468i	$-0.316548\pi$
$439$	−9.50522	−	16.4635i	−0.453660	−	0.785761i	−0.998610	+	0.0527068i	$0.983215\pi$
$440$	−0.558155	−	7.09711i	−0.0266090	−	0.338341i
$441$			4.36138i			0.207685i
$442$	−18.2472	+	0.675400i	−0.867932	+	0.0321255i
$443$		−	38.2925i		−	1.81933i	−0.415341	−	0.909666i	$-0.636338\pi$
$443$		−	38.2925i		−	1.81933i	0.415341	−	0.909666i	$-0.363662\pi$
$444$	15.5721	+	9.73135i	0.739020	+	0.461830i
$445$	−5.59900	−	9.69776i	−0.265418	−	0.459718i
$446$	−1.59647	−	14.0144i	−0.0755951	−	0.663599i
$447$	5.30125	+	5.30125i	0.250741	+	0.250741i
$448$	−15.8523	+	21.8136i	−0.748949	+	1.03060i
$449$	25.6526	−	6.87361i	1.21062	−	0.324386i	0.403617	−	0.914928i	$-0.367753\pi$
$449$	25.6526	−	6.87361i	1.21062	−	0.324386i	0.807006	+	0.590543i	$0.201086\pi$
$450$	−5.56820	−	0.832280i	−0.262488	−	0.0392340i
$451$	23.1316	+	13.3550i	1.08923	+	0.628864i
$452$	−4.73772	−	20.5248i	−0.222844	−	0.965406i
$453$	3.35971	−	12.5386i	0.157853	−	0.589116i
$454$	−17.4195	+	12.8892i	−0.817536	+	0.604921i
$455$	−11.5727	−	4.07064i	−0.542534	−	0.190835i
$456$	1.61910	+	4.57301i	0.0758213	+	0.214151i
$457$	36.1734	+	9.69262i	1.69212	+	0.453402i	0.970935	−	0.239342i	$-0.0769318\pi$
$457$	36.1734	+	9.69262i	1.69212	+	0.453402i	0.721183	+	0.692744i	$0.243599\pi$
$458$	6.39434	+	2.78048i	0.298788	+	0.129923i
$459$	1.79051	−	3.10126i	0.0835740	−	0.144754i
$460$	5.31774	−	2.82724i	0.247941	−	0.131821i
$461$	−3.71169	−	13.8522i	−0.172870	−	0.645161i	−0.996905	−	0.0786211i	$-0.974948\pi$
$461$	−3.71169	−	13.8522i	−0.172870	−	0.645161i	0.824034	−	0.566540i	$-0.191718\pi$
$462$	−9.30182	−	7.39929i	−0.432760	−	0.344246i
$463$	−16.6155	+	16.6155i	−0.772185	+	0.772185i	−0.978488	−	0.206303i	$-0.933857\pi$
$463$	−16.6155	+	16.6155i	−0.772185	+	0.772185i	0.206303	+	0.978488i	$0.433857\pi$
$464$	−10.9543	+	5.34177i	−0.508542	+	0.247986i
$465$	−0.627568	+	0.362326i	−0.0291028	+	0.0168025i
$466$	−5.73766	−	14.5667i	−0.265792	−	0.674789i
$467$	−18.2453			−0.844290			−0.422145	−	0.906528i	$-0.638723\pi$
$467$	−18.2453			−0.844290			−0.422145	+	0.906528i	$0.638723\pi$
$468$	−2.88911	−	6.60704i	−0.133549	−	0.305411i
$469$	43.8054			2.02275
$470$	3.04464	+	7.72970i	0.140439	+	0.356545i
$471$	−3.89428	+	2.24837i	−0.179439	+	0.103599i
$472$	−32.2868	−	5.98588i	−1.48612	−	0.275523i
$473$	18.6996	−	18.6996i	0.859810	−	0.859810i
$474$	−2.17267	−	1.72829i	−0.0997941	−	0.0793828i
$475$	1.76724	+	6.59544i	0.0810867	+	0.302620i
$476$	−11.3327	−	21.3155i	−0.519431	−	0.976996i
$477$	1.37749	−	2.38588i	0.0630708	−	0.109242i
$478$	33.5961	+	14.6087i	1.53665	+	0.668187i
$479$	34.5595	+	9.26018i	1.57906	+	0.423108i	0.938635	−	0.344911i	$-0.112091\pi$
$479$	34.5595	+	9.26018i	1.57906	+	0.423108i	0.640427	+	0.768019i	$0.278758\pi$
$480$	5.70478	−	0.248543i	0.260386	−	0.0113444i
$481$	−2.52769	+	33.0073i	−0.115253	+	1.50500i
$482$	17.9170	−	13.2574i	0.816097	−	0.603856i
$483$	2.60249	−	9.71264i	0.118418	−	0.441940i
$484$	−9.32040	+	2.15142i	−0.423655	+	0.0977917i
$485$	11.6563	+	6.72976i	0.529285	+	0.305583i
$486$	1.39868	+	0.209060i	0.0634452	+	0.00948316i
$487$	−11.0683	+	2.96575i	−0.501554	+	0.134391i	−0.500721	−	0.865609i	$-0.666932\pi$
$487$	−11.0683	+	2.96575i	−0.501554	+	0.134391i	−0.000832957		1.00000i	$0.500265\pi$
$488$	20.3991	+	29.6844i	0.923422	+	1.34375i
$489$	−5.96561	−	5.96561i	−0.269774	−	0.269774i
$490$	−0.704697	−	6.18607i	−0.0318350	−	0.279458i
$491$	−16.3825	−	28.3753i	−0.739331	−	1.28056i	−0.952797	−	0.303609i	$-0.901808\pi$
$491$	−16.3825	−	28.3753i	−0.739331	−	1.28056i	0.213465	−	0.976951i	$-0.431525\pi$
$492$	−11.3538	+	18.1684i	−0.511869	+	0.819094i
$493$		−	10.9108i		−	0.491398i
$494$	−5.95109	+	6.40857i	−0.267752	+	0.288335i
$495$			2.51695i			0.113129i
$496$	−2.16732	+	1.88374i	−0.0973154	+	0.0845822i
$497$	−18.1773	−	31.4841i	−0.815365	−	1.41225i
$498$	14.0591	−	1.60156i	0.630002	−	0.0717678i
$499$	3.38914	+	3.38914i	0.151719	+	0.151719i	0.778885	−	0.627167i	$-0.215785\pi$
$499$	3.38914	+	3.38914i	0.151719	+	0.151719i	−0.627167	+	0.778885i	$0.715785\pi$
$500$	18.1204	+	0.633455i	0.810369	+	0.0283290i
$501$	16.1711	−	4.33302i	0.722469	−	0.193585i
$502$	4.29108	−	28.7086i	0.191520	−	1.28133i
$503$	15.1603	+	8.75279i	0.675963	+	0.390267i	0.798332	−	0.602217i	$-0.205716\pi$
$503$	15.1603	+	8.75279i	0.675963	+	0.390267i	−0.122369	+	0.992485i	$0.539049\pi$
$504$	6.19204	−	7.24912i	0.275815	−	0.322901i
$505$	−4.69788	+	17.5327i	−0.209053	+	0.780197i
$506$	6.25704	+	8.45624i	0.278159	+	0.375926i
$507$	8.13848	−	10.1373i	0.361442	−	0.450214i
$508$	−18.2412	−	5.57763i	−0.809321	−	0.247467i
$509$	5.00435	+	1.34091i	0.221814	+	0.0594348i	0.368014	−	0.929820i	$-0.380038\pi$
$509$	5.00435	+	1.34091i	0.221814	+	0.0594348i	−0.146200	+	0.989255i	$0.546704\pi$
$510$	−2.03853	+	4.68805i	−0.0902675	+	0.207590i
$511$	−3.27308	+	5.66914i	−0.144793	+	0.250788i
$512$	22.0031	−	5.27857i	0.972409	−	0.233282i
$513$	−0.443914	−	1.65671i	−0.0195993	−	0.0731454i
$514$	−23.1770	+	29.1363i	−1.02229	+	1.28515i
$515$	6.73750	−	6.73750i	0.296890	−	0.296890i
$516$	14.4659	+	15.5139i	0.636824	+	0.682961i
$517$	−12.5667	+	7.25538i	−0.552683	+	0.319091i
$518$	−40.7211	+	16.0396i	−1.78918	+	0.704739i
$519$	−9.68639			−0.425185
$520$	5.16539	+	8.90445i	0.226517	+	0.390486i
$521$	11.1730			0.489498			0.244749	−	0.969586i	$-0.421294\pi$
$521$	11.1730			0.489498			0.244749	+	0.969586i	$0.421294\pi$
$522$	4.00909	−	1.57914i	0.175473	−	0.0691169i
$523$	11.8722	−	6.85440i	0.519134	−	0.299722i	−0.217446	−	0.976072i	$-0.569773\pi$
$523$	11.8722	−	6.85440i	0.519134	−	0.299722i	0.736580	+	0.676350i	$0.236439\pi$
$524$	4.84116	+	5.19190i	0.211487	+	0.226809i
$525$	9.48852	−	9.48852i	0.414113	−	0.414113i
$526$	12.4895	−	15.7008i	0.544566	−	0.684587i
$527$	−0.665362	−	2.48316i	−0.0289836	−	0.108168i
$528$	1.90235	+	9.79067i	0.0827894	+	0.426084i
$529$	7.05035	−	12.2116i	0.306537	−	0.530937i
$530$	−1.56829	+	3.60664i	−0.0681222	+	0.156662i
$531$	11.2141	+	3.00480i	0.486649	+	0.130397i
$532$	−11.0570	−	3.38093i	−0.479384	−	0.146582i
$533$	−38.5104	−	2.94912i	−1.66807	−	0.127741i
$534$	9.33161	+	12.6114i	0.403818	+	0.545750i
$535$	−0.929259	+	3.46804i	−0.0401754	+	0.149936i
$536$	−27.9500	−	23.8743i	−1.20726	−	1.03121i
$537$	6.34820	+	3.66514i	0.273945	+	0.158162i
$538$	3.44332	−	23.0369i	0.148452	−	0.993189i
$539$	10.5043	−	2.81462i	0.452452	−	0.121234i
$540$	−2.01763	−	0.0705324i	−0.0868248	−	0.00303523i
$541$	−2.42461	−	2.42461i	−0.104242	−	0.104242i	0.653062	−	0.757304i	$-0.273484\pi$
$541$	−2.42461	−	2.42461i	−0.104242	−	0.104242i	−0.757304	+	0.653062i	$0.773484\pi$
$542$	15.5674	−	1.77339i	0.668678	−	0.0761736i
$543$	−10.4154	−	18.0399i	−0.446966	−	0.774168i
$544$	−4.38634	+	19.7767i	−0.188063	+	0.847921i
$545$			2.36374i			0.101252i
$546$	16.7546	+	3.83124i	0.717032	+	0.163962i
$547$		−	19.9422i		−	0.852666i	−0.904566	−	0.426333i	$-0.859805\pi$
$547$		−	19.9422i		−	0.852666i	0.904566	−	0.426333i	$-0.140195\pi$
$548$	−0.665833	+	1.06547i	−0.0284430	+	0.0455145i
$549$	−6.36711	−	11.0282i	−0.271742	−	0.470670i
$550$	1.58891	+	13.9480i	0.0677515	+	0.594746i
$551$	−3.69519	−	3.69519i	−0.157420	−	0.157420i
$552$	−6.95398	+	4.77876i	−0.295981	+	0.203398i
$553$	6.39146	−	1.71259i	0.271793	−	0.0728266i
$554$	41.5867	+	6.21597i	1.76685	+	0.264091i
$555$	8.02627	+	4.63397i	0.340696	+	0.196701i
$556$	10.9215	−	2.52099i	0.463173	−	0.106914i
$557$	0.256682	−	0.957951i	0.0108760	−	0.0405897i	−0.960275	−	0.279057i	$-0.909978\pi$
$557$	0.256682	−	0.957951i	0.0108760	−	0.0405897i	0.971151	+	0.238467i	$0.0766449\pi$
$558$	0.816120	−	0.603873i	0.0345491	−	0.0255640i
$559$	−12.6888	+	36.0736i	−0.536679	+	1.52575i
$560$	−7.61134	+	11.2825i	−0.321638	+	0.476771i
$561$	−8.62483	−	2.31102i	−0.364141	−	0.0975712i
$562$	−0.221605	−	0.0963614i	−0.00934783	−	0.00406476i
$563$	−6.77214	+	11.7297i	−0.285412	+	0.494347i	−0.972709	−	0.232029i	$-0.925464\pi$
$563$	−6.77214	+	11.7297i	−0.285412	+	0.494347i	0.687297	+	0.726376i	$0.258797\pi$
$564$	−5.46386	−	10.2770i	−0.230070	−	0.432738i
$565$	−2.75165	−	10.2693i	−0.115763	−	0.432033i
$566$	−15.7132	−	12.4993i	−0.660475	−	0.525386i
$567$	−2.38342	+	2.38342i	−0.100094	+	0.100094i
$568$	−5.56101	+	29.9952i	−0.233335	+	1.25857i
$569$	−21.2148	+	12.2484i	−0.889372	+	0.513479i	−0.873737	−	0.486399i	$-0.838310\pi$
$569$	−21.2148	+	12.2484i	−0.889372	+	0.513479i	−0.0156347	+	0.999878i	$0.504977\pi$
$570$	0.897321	+	2.27811i	0.0375846	+	0.0954194i
$571$	36.4003			1.52330			0.761652	−	0.647986i	$-0.224388\pi$
$571$	36.4003			1.52330			0.761652	+	0.647986i	$0.224388\pi$
$572$	−14.0484	+	11.2222i	−0.587395	+	0.469225i
$573$	−24.2377			−1.01255
$574$	−18.7138	−	47.5103i	−0.781098	−	1.98304i
$575$	−10.2851	+	5.93808i	−0.428916	+	0.247635i
$576$	−7.90165	+	1.25059i	−0.329235	+	0.0521080i
$577$	−28.0308	+	28.0308i	−1.16694	+	1.16694i	−0.184013	+	0.982924i	$0.558909\pi$
$577$	−28.0308	+	28.0308i	−1.16694	+	1.16694i	−0.982924	+	0.184013i	$0.941091\pi$
$578$	4.62211	+	3.67673i	0.192254	+	0.152932i
$579$	−1.87524	−	6.99850i	−0.0779324	−	0.290848i
$580$	−5.43124	+	2.88758i	−0.225520	+	0.119900i
$581$	−16.8627	+	29.2071i	−0.699583	+	1.21171i
$582$	−17.2927	−	7.51947i	−0.716806	−	0.311692i
$583$	−6.63530	−	1.77792i	−0.274806	−	0.0736341i
$584$	5.17811	−	1.83334i	0.214272	−	0.0758641i
$585$	−1.57379	−	3.28169i	−0.0650682	−	0.135681i
$586$	14.9089	−	11.0316i	0.615883	−	0.455712i
$587$	−5.36587	+	20.0257i	−0.221473	+	0.826549i	0.762314	+	0.647208i	$0.224063\pi$
$587$	−5.36587	+	20.0257i	−0.221473	+	0.826549i	−0.983787	+	0.179342i	$0.942603\pi$
$588$	1.96188	+	8.49927i	0.0809064	+	0.350504i
$589$	−1.06632	−	0.615639i	−0.0439369	−	0.0253670i
$590$	−16.3912	−	2.45000i	−0.674817	−	0.100865i
$591$	9.93162	−	2.66117i	0.408532	−	0.109466i
$592$	34.7237	+	11.9592i	1.42714	+	0.491522i
$593$	4.90626	+	4.90626i	0.201476	+	0.201476i	0.800632	−	0.599156i	$-0.204497\pi$
$593$	4.90626	+	4.90626i	0.201476	+	0.201476i	−0.599156	+	0.800632i	$0.704497\pi$
$594$	−0.399119	−	3.50360i	−0.0163760	−	0.143754i
$595$	−6.09212	−	10.5519i	−0.249753	−	0.432584i
$596$	12.7155	+	7.94619i	0.520847	+	0.325489i
$597$		−	2.35867i		−	0.0965338i
$598$	−13.4456	−	7.11315i	−0.549833	−	0.290879i
$599$			41.4625i			1.69411i	0.531504	+	0.847056i	$0.321627\pi$
$599$			41.4625i			1.69411i	−0.531504	+	0.847056i	$0.678373\pi$
$600$	−11.2255	+	0.882830i	−0.458277	+	0.0360414i
$601$	5.21651	+	9.03526i	0.212786	+	0.368556i	0.952585	−	0.304271i	$-0.0984130\pi$
$601$	5.21651	+	9.03526i	0.212786	+	0.368556i	−0.739799	+	0.672827i	$0.765080\pi$
$602$	−50.2319	+	5.72225i	−2.04730	+	0.233221i
$603$	9.18962	+	9.18962i	0.374230	+	0.374230i
$604$	0.907024	−	25.9460i	0.0369063	−	1.05573i
$605$	−4.66333	+	1.24954i	−0.189591	+	0.0508009i
$606$	3.75925	−	25.1505i	0.152709	−	1.02167i
$607$	−24.7951	−	14.3155i	−1.00640	−	0.581047i	−0.0962660	−	0.995356i	$-0.530690\pi$
$607$	−24.7951	−	14.3155i	−1.00640	−	0.581047i	−0.910136	+	0.414309i	$0.864023\pi$
$608$	5.21231	+	8.18337i	0.211387	+	0.331879i
$609$	−2.65804	+	9.91994i	−0.107709	+	0.401976i
$610$	10.8128	+	14.6133i	0.437799	+	0.591675i
$611$	11.8483	−	17.3175i	0.479330	−	0.700590i
$612$	2.09424	−	6.84902i	0.0846545	−	0.276855i
$613$	−3.02686	−	0.811044i	−0.122254	−	0.0327578i	0.197173	−	0.980369i	$-0.436824\pi$
$613$	−3.02686	−	0.811044i	−0.122254	−	0.0327578i	−0.319427	+	0.947611i	$0.603490\pi$
$614$	−12.5007	+	28.7482i	−0.504487	+	1.16018i
$615$	−5.40657	+	9.36445i	−0.218014	+	0.377611i
$616$	−21.4554	−	10.2352i	−0.864463	−	0.412387i
$617$	−2.96599	−	11.0692i	−0.119406	−	0.445630i	0.880172	−	0.474654i	$-0.157427\pi$
$617$	−2.96599	−	11.0692i	−0.119406	−	0.445630i	−0.999579	+	0.0290238i	$0.990760\pi$
$618$	−8.31023	+	10.4470i	−0.334286	+	0.420240i
$619$	−4.28016	+	4.28016i	−0.172034	+	0.172034i	−0.787873	−	0.615838i	$-0.788817\pi$
$619$	−4.28016	+	4.28016i	−0.172034	+	0.172034i	0.615838	+	0.787873i	$0.288817\pi$
$620$	−1.05999	+	0.988385i	−0.0425703	+	0.0396945i
$621$	2.58350	−	1.49159i	0.103672	−	0.0598552i
$622$	4.05394	−	1.59680i	0.162548	−	0.0640259i
$623$	−37.3921			−1.49808
$624$	−8.60222	−	11.5759i	−0.344365	−	0.463407i
$625$	−10.7540			−0.430162
$626$	1.19500	−	0.470697i	0.0477618	−	0.0188128i
$627$	−3.70367	+	2.13831i	−0.147910	+	0.0853961i
$628$	−6.57763	+	6.13328i	−0.262476	+	0.244745i
$629$	−23.2488	+	23.2488i	−0.926989	+	0.926989i
$630$	2.99548	−	3.76569i	0.119343	−	0.150029i
$631$	8.33716	+	31.1147i	0.331897	+	1.23866i	0.907194	+	0.420713i	$0.138220\pi$
$631$	8.33716	+	31.1147i	0.331897	+	1.23866i	−0.575297	+	0.817945i	$0.695113\pi$
$632$	−5.01144	−	2.39068i	−0.199344	−	0.0950961i
$633$	−8.69510	+	15.0604i	−0.345599	+	0.598595i
$634$	4.67375	−	10.7483i	0.185618	−	0.426871i
$635$	−9.29932	−	2.49174i	−0.369032	−	0.0988819i
$636$	1.61115	−	5.26913i	0.0638862	−	0.208935i
$637$	−11.9360	+	10.2379i	−0.472920	+	0.405640i
$638$	−6.39059	−	8.63672i	−0.253006	−	0.341931i
$639$	2.79152	−	10.4181i	0.110431	−	0.412133i
$640$	11.0054	−	3.05053i	0.435028	−	0.120583i
$641$	22.1062	+	12.7630i	0.873142	+	0.504109i	0.868391	−	0.495880i	$-0.165154\pi$
$641$	22.1062	+	12.7630i	0.873142	+	0.504109i	0.00475109	+	0.999989i	$0.498488\pi$
$642$	0.743594	−	4.97487i	0.0293473	−	0.196342i
$643$	−3.94968	+	1.05831i	−0.155760	+	0.0417358i	−0.335856	−	0.941913i	$-0.609026\pi$
$643$	−3.94968	+	1.05831i	−0.155760	+	0.0417358i	0.180096	+	0.983649i	$0.442359\pi$
$644$	0.702597	−	20.0983i	0.0276862	−	0.791982i
$645$	7.57023	+	7.57023i	0.298078	+	0.298078i
$646$	−8.63028	+	0.983133i	−0.339554	+	0.0386808i
$647$	9.45014	+	16.3681i	0.371523	+	0.643497i	0.989800	−	0.142463i	$-0.0455022\pi$
$647$	9.45014	+	16.3681i	0.371523	+	0.643497i	−0.618277	+	0.785960i	$0.712169\pi$
$648$	2.81972	−	0.221758i	0.110769	−	0.00871148i
$649$		−	28.9480i		−	1.13631i
$650$	−10.7930	−	17.1924i	−0.423338	−	0.674341i
$651$			2.41975i			0.0948373i
$652$	−14.3090	−	8.94202i	−0.560385	−	0.350196i
$653$	−3.84248	−	6.65536i	−0.150368	−	0.260444i	0.780995	−	0.624537i	$-0.214712\pi$
$653$	−3.84248	−	6.65536i	−0.150368	−	0.260444i	−0.931363	+	0.364093i	$0.881379\pi$
$654$	−0.374823	−	3.29033i	−0.0146568	−	0.128662i
$655$	2.53346	+	2.53346i	0.0989906	+	0.0989906i
$656$	−13.9531	+	40.5130i	−0.544779	+	1.58177i
$657$	−1.87592	+	0.502652i	−0.0731867	+	0.0196103i
$658$	27.4362	+	4.10089i	1.06957	+	0.159869i
$659$	5.48027	+	3.16403i	0.213481	+	0.123253i	0.602928	−	0.797796i	$-0.294001\pi$
$659$	5.48027	+	3.16403i	0.213481	+	0.123253i	−0.389447	+	0.921049i	$0.627334\pi$
$660$	1.13220	+	4.90493i	0.0440708	+	0.190924i
$661$	−2.03830	+	7.60706i	−0.0792809	+	0.295880i	−0.994170	−	0.107825i	$-0.965611\pi$
$661$	−2.03830	+	7.60706i	−0.0792809	+	0.295880i	0.914889	+	0.403706i	$0.132278\pi$
$662$	31.1827	−	23.0730i	1.21195	−	0.896759i
$663$	12.6904	−	2.37972i	0.492853	−	0.0924205i
$664$	26.6773	−	9.44525i	1.03528	−	0.366547i
$665$	−5.63686	−	1.51039i	−0.218588	−	0.0585705i
$666$	−11.9074	−	5.17775i	−0.461402	−	0.200634i
$667$	4.54462	−	7.87152i	0.175969	−	0.304786i
$668$	29.5643	−	15.7182i	1.14388	−	0.608156i
$669$	2.58140	+	9.63390i	0.0998025	+	0.372468i
$670$	−14.5191	−	11.5495i	−0.560924	−	0.446196i
$671$	−22.4521	+	22.4521i	−0.866753	+	0.866753i
$672$	8.80590	−	16.9121i	0.339695	−	0.652400i
$673$	−11.3794	+	6.56992i	−0.438645	+	0.253252i	−0.703023	−	0.711167i	$-0.748167\pi$
$673$	−11.3794	+	6.56992i	−0.438645	+	0.253252i	0.264378	+	0.964419i	$0.414833\pi$
$674$	2.83555	+	7.19887i	0.109221	+	0.277290i
$675$	3.98105			0.153231
$676$	11.2999	−	23.4161i	0.434610	−	0.900619i
$677$	5.78458			0.222320			0.111160	−	0.993803i	$-0.464543\pi$
$677$	5.78458			0.222320			0.111160	+	0.993803i	$0.464543\pi$
$678$	5.45873	+	13.8585i	0.209641	+	0.532234i
$679$	38.9225	−	22.4719i	1.49371	−	0.862392i
$680$	−1.86377	+	10.0529i	−0.0714723	+	0.385510i
$681$	10.8348	−	10.8348i	0.415190	−	0.415190i
$682$	−1.98110	−	1.57590i	−0.0758603	−	0.0603443i
$683$	−0.696994	−	2.60122i	−0.0266697	−	0.0995328i	0.951308	−	0.308242i	$-0.0997406\pi$
$683$	−0.696994	−	2.60122i	−0.0266697	−	0.0995328i	−0.977978	+	0.208709i	$0.933074\pi$
$684$	−1.61032	−	3.02884i	−0.0615720	−	0.115810i
$685$	−0.317063	+	0.549169i	−0.0121144	+	0.0209827i
$686$	11.5346	+	5.01563i	0.440392	+	0.191498i
$687$	−4.76244	−	1.27609i	−0.181699	−	0.0486860i
$688$	35.1691	+	23.7257i	1.34081	+	0.904532i
$689$	9.76303	−	1.83078i	0.371942	−	0.0697470i
$690$	−3.42337	+	2.53306i	−0.130325	+	0.0964319i
$691$	3.85080	−	14.3714i	0.146491	−	0.546713i	−0.853193	−	0.521595i	$-0.825337\pi$
$691$	3.85080	−	14.3714i	0.146491	−	0.546713i	0.999684	−	0.0251178i	$-0.00799609\pi$
$692$	−18.8764	+	4.35722i	−0.717574	+	0.165637i
$693$	7.27856	+	4.20228i	0.276490	+	0.159631i
$694$	2.94185	+	0.439719i	0.111671	+	0.0166915i
$695$	5.46440	−	1.46418i	0.207277	−	0.0555396i
$696$	7.10240	−	4.88076i	0.269216	−	0.185005i
$697$	−27.1249	−	27.1249i	−1.02743	−	1.02743i
$698$	−3.31196	−	29.0735i	−0.125360	−	1.10045i
$699$	5.53522	+	9.58728i	0.209361	+	0.362624i
$700$	14.2226	−	22.7590i	0.537564	−	0.860211i
$701$		−	22.9570i		−	0.867073i	−0.901136	−	0.433537i	$-0.857265\pi$
$701$		−	22.9570i		−	0.867073i	0.901136	−	0.433537i	$-0.142735\pi$
$702$	2.71110	+	4.31856i	0.102324	+	0.162993i
$703$			15.7474i			0.593926i
$704$	8.11136	+	18.2239i	0.305708	+	0.686839i
$705$	−2.93722	−	5.08742i	−0.110622	−	0.191603i
$706$	36.1408	−	4.11704i	1.36018	−	0.154947i
$707$	42.8579	+	42.8579i	1.61184	+	1.61184i
$708$	23.2051	+	0.811207i	0.872102	+	0.0304870i
$709$	24.8361	−	6.65482i	0.932740	−	0.249927i	0.239718	−	0.970843i	$-0.422945\pi$
$709$	24.8361	−	6.65482i	0.932740	−	0.249927i	0.693023	+	0.720916i	$0.256278\pi$
$710$	−2.27610	+	15.2278i	−0.0854206	+	0.571489i
$711$	1.70009	+	0.981547i	0.0637583	+	0.0368109i
$712$	23.8580	+	20.3790i	0.894117	+	0.763735i
$713$	0.554279	−	2.06860i	0.0207579	−	0.0774696i
$714$	10.1535	+	13.7222i	0.379984	+	0.513539i
$715$	−6.88824	+	5.90829i	−0.257606	+	0.220957i
$716$	14.0198	+	4.28685i	0.523944	+	0.160207i
$717$	−25.0220	−	6.70464i	−0.934465	−	0.250389i
$718$	−6.83782	+	15.7251i	−0.255185	+	0.586856i
$719$	0.137607	−	0.238343i	0.00513189	−	0.00888869i	−0.863448	−	0.504438i	$-0.831700\pi$
$719$	0.137607	−	0.238343i	0.00513189	−	0.00888869i	0.868580	+	0.495549i	$0.165033\pi$
$720$	−3.96359	+	0.770137i	−0.147714	+	0.0287013i
$721$	−8.23474	−	30.7325i	−0.306678	−	1.14454i
$722$	14.1375	−	17.7726i	0.526144	−	0.661428i
$723$	−11.1442	+	11.1442i	−0.414459	+	0.414459i
$724$	−28.4119	−	30.4703i	−1.05592	−	1.13242i
$725$	10.5046	−	6.06482i	0.390130	−	0.225242i
$726$	6.29322	−	2.47883i	0.233563	−	0.0919980i
$727$	−10.6846			−0.396272			−0.198136	−	0.980175i	$-0.563489\pi$
$727$	−10.6846			−0.396272			−0.198136	+	0.980175i	$0.563489\pi$
$728$	34.3741	−	0.0705724i	1.27399	−	0.00261559i
$729$	−1.00000			−0.0370370
$730$	2.57954	−	1.01605i	0.0954732	−	0.0376058i
$731$	−32.8917	+	18.9900i	−1.21654	+	0.702372i
$732$	−17.3687	−	18.6271i	−0.641967	−	0.688477i
$733$	−11.6468	+	11.6468i	−0.430186	+	0.430186i	−0.888691	−	0.458506i	$-0.848385\pi$
$733$	−11.6468	+	11.6468i	−0.430186	+	0.430186i	0.458506	+	0.888691i	$0.348385\pi$
$734$	5.82683	−	7.32505i	0.215072	−	0.270372i
$735$	1.13945	+	4.25249i	0.0420293	+	0.156856i
$736$	−11.4020	+	12.4408i	−0.420283	+	0.458572i
$737$	16.2025	−	28.0635i	0.596826	−	1.03373i
$738$	6.04101	−	13.8927i	0.222372	−	0.511396i
$739$	15.5149	+	4.15720i	0.570724	+	0.152925i	0.532629	−	0.846349i	$-0.321204\pi$
$739$	15.5149	+	4.15720i	0.570724	+	0.152925i	0.0380956	+	0.999274i	$0.487871\pi$
$740$	17.7258	+	5.42003i	0.651612	+	0.199244i
$741$	3.49194	−	5.10382i	0.128279	−	0.187494i
$742$	7.81132	+	10.5568i	0.286763	+	0.387553i
$743$	4.48750	−	16.7476i	0.164630	−	0.614409i	−0.833457	−	0.552585i	$-0.813641\pi$
$743$	4.48750	−	16.7476i	0.164630	−	0.614409i	0.998087	−	0.0618243i	$-0.0196918\pi$
$744$	1.31878	−	1.54392i	0.0483488	−	0.0566027i
$745$	6.55390	+	3.78389i	0.240116	+	0.138631i
$746$	0.0244886	−	0.163836i	0.000896592	−	0.00599847i
$747$	−9.66463	+	2.58963i	−0.353610	+	0.0947496i
$748$	−17.8473	−	0.623907i	−0.652561	−	0.0228123i
$749$	8.47745	+	8.47745i	0.309759	+	0.309759i
$750$	−12.7385	+	1.45113i	−0.465144	+	0.0529877i
$751$	−10.8876	−	18.8579i	−0.397295	−	0.688135i	0.596096	−	0.802913i	$-0.296718\pi$
$751$	−10.8876	−	18.8579i	−0.397295	−	0.688135i	−0.993391	+	0.114778i	$0.963384\pi$
$752$	−15.2706	−	17.5695i	−0.556862	−	0.640693i
$753$			20.5256i			0.747994i
$754$	13.7326	+	7.26498i	0.500112	+	0.264575i
$755$		−	13.1033i		−	0.476879i
$756$	−3.57257	+	5.71684i	−0.129933	+	0.207919i
$757$	14.0285	+	24.2980i	0.509873	+	0.883126i	0.999935	+	0.0114381i	$0.00364095\pi$
$757$	14.0285	+	24.2980i	0.509873	+	0.883126i	−0.490062	+	0.871688i	$0.663026\pi$
$758$	−1.31994	−	11.5869i	−0.0479423	−	0.420854i
$759$	−5.25972	−	5.25972i	−0.190916	−	0.190916i
$760$	2.77342	+	4.03583i	0.100603	+	0.146395i
$761$	−6.67398	+	1.78829i	−0.241932	+	0.0648254i	−0.377747	−	0.925909i	$-0.623301\pi$
$761$	−6.67398	+	1.78829i	−0.241932	+	0.0648254i	0.135816	+	0.990734i	$0.456635\pi$
$762$	13.3398	+	1.99390i	0.483249	+	0.0722313i
$763$	6.83550	+	3.94648i	0.247462	+	0.142872i
$764$	−47.2334	+	10.9028i	−1.70885	+	0.394451i
$765$	0.935577	−	3.49162i	0.0338258	−	0.126240i
$766$	9.67367	−	7.15786i	0.349524	−	0.258624i
$767$	18.1005	+	37.7434i	0.653570	+	1.36283i
$768$	−14.8358	+	5.99149i	−0.535342	+	0.216199i
$769$	17.6759	+	4.73624i	0.637409	+	0.170793i	0.563029	−	0.826437i	$-0.309636\pi$
$769$	17.6759	+	4.73624i	0.637409	+	0.170793i	0.0743794	+	0.997230i	$0.476302\pi$
$770$	−11.0027	−	4.78436i	−0.396511	−	0.172416i
$771$	13.1629	−	22.7988i	0.474051	−	0.821080i
$772$	−6.80252	−	12.7948i	−0.244828	−	0.460496i
$773$	5.65201	+	21.0936i	0.203289	+	0.758684i	0.989964	+	0.141317i	$0.0451337\pi$
$773$	5.65201	+	21.0936i	0.203289	+	0.758684i	−0.786676	+	0.617366i	$0.788200\pi$
$774$	−11.7382	−	9.33734i	−0.421921	−	0.335624i
$775$	2.02086	−	2.02086i	0.0725916	−	0.0725916i
$776$	−37.0818	−	6.87485i	−1.33116	−	0.246793i
$777$	26.8012	−	15.4737i	0.961487	−	0.555114i
$778$	−11.1940	−	28.4191i	−0.401323	−	1.01887i
$779$	−18.3729			−0.658278
$780$	−4.54314	−	5.68728i	−0.162670	−	0.203637i
$781$	−26.8933			−0.962318
$782$	−5.53675	−	14.0566i	−0.197994	−	0.502664i
$783$	−2.63864	+	1.52342i	−0.0942974	+	0.0544426i
$784$	7.64644	+	15.6805i	0.273087	+	0.560018i
$785$	−3.20965	+	3.20965i	−0.114557	+	0.114557i
$786$	−3.92832	−	3.12484i	−0.140118	−	0.111459i
$787$	−9.21387	−	34.3866i	−0.328439	−	1.22575i	−0.910809	−	0.412828i	$-0.864541\pi$
$787$	−9.21387	−	34.3866i	−0.328439	−	1.22575i	0.582370	−	0.812924i	$-0.302125\pi$
$788$	18.1572	−	9.65351i	0.646825	−	0.343892i
$789$	−7.09315	+	12.2857i	−0.252523	+	0.437382i
$790$	−2.56996	−	1.11751i	−0.0914350	−	0.0397591i
$791$	−34.2911	−	9.18826i	−1.21925	−	0.326697i
$792$	−2.35381	−	6.64813i	−0.0836389	−	0.236231i
$793$	15.2351	−	43.3126i	0.541013	−	1.53807i
$794$	10.5836	−	7.83112i	0.375596	−	0.277916i
$795$	0.719763	−	2.68619i	0.0255274	−	0.0952694i
$796$	−1.06100	−	4.59647i	−0.0376060	−	0.162917i
$797$	10.3939	+	6.00090i	0.368170	+	0.212563i	0.672658	−	0.739953i	$-0.265152\pi$
$797$	10.3939	+	6.00090i	0.368170	+	0.212563i	−0.304489	+	0.952516i	$0.598486\pi$
$798$	8.08602	+	1.20862i	0.286242	+	0.0427846i
$799$	20.1299	−	5.39380i	0.712145	−	0.190819i
$800$	−21.4786	+	6.76996i	−0.759382	+	0.239354i
$801$	−7.84422	−	7.84422i	−0.277162	−	0.277162i
$802$	0.499385	+	4.38377i	0.0176339	+	0.154796i
$803$	2.42126	+	4.19374i	0.0854442	+	0.147994i
$804$	22.0421	+	13.7746i	0.777364	+	0.485792i
$805$		−	10.1501i		−	0.357743i
$806$	3.56840	+	0.815977i	0.125691	+	0.0287416i
$807$			16.4705i			0.579788i
$808$	−3.98758	−	50.7033i	−0.140283	−	1.78374i
$809$	25.9963	+	45.0269i	0.913981	+	1.58306i	0.808386	+	0.588653i	$0.200341\pi$
$809$	25.9963	+	45.0269i	0.913981	+	1.58306i	0.105595	+	0.994409i	$0.466325\pi$
$810$	1.41837	−	0.161577i	0.0498366	−	0.00567722i
$811$	14.8484	+	14.8484i	0.521398	+	0.521398i	0.917993	−	0.396595i	$-0.129808\pi$
$811$	14.8484	+	14.8484i	0.521398	+	0.521398i	−0.396595	+	0.917993i	$0.629808\pi$
$812$	−0.717593	+	20.5272i	−0.0251826	+	0.720364i
$813$	−10.7015	+	2.86746i	−0.375319	+	0.100566i
$814$	−4.78606	+	32.0202i	−0.167751	+	1.12231i
$815$	−7.37524	−	4.25810i	−0.258343	−	0.149155i
$816$	1.00027	−	14.2891i	0.0350163	−	0.500220i
$817$	−4.70811	+	17.5709i	−0.164716	+	0.614729i
$818$	−3.85692	−	5.21253i	−0.134854	−	0.182252i
$819$	−12.1176	−	0.927967i	−0.423424	−	0.0324258i
$820$	−6.32368	+	20.6811i	−0.220833	+	0.722214i
$821$	9.69953	+	2.59898i	0.338516	+	0.0907051i	0.424073	−	0.905628i	$-0.360600\pi$
$821$	9.69953	+	2.59898i	0.338516	+	0.0907051i	−0.0855565	+	0.996333i	$0.527267\pi$
$822$	0.354269	−	0.814721i	0.0123566	−	0.0284167i
$823$	28.5811	−	49.5039i	0.996275	−	1.72560i	0.423453	−	0.905918i	$-0.360818\pi$
$823$	28.5811	−	49.5039i	0.996275	−	1.72560i	0.572822	−	0.819680i	$-0.305849\pi$
$824$	−11.4953	+	24.0968i	−0.400456	+	0.839453i
$825$	−2.56917	−	9.58829i	−0.0894472	−	0.333821i
$826$	−34.4516	+	43.3099i	−1.19872	+	1.50694i
$827$	−3.07415	+	3.07415i	−0.106899	+	0.106899i	−0.758533	−	0.651634i	$-0.774084\pi$
$827$	−3.07415	+	3.07415i	−0.106899	+	0.106899i	0.651634	+	0.758533i	$0.274084\pi$
$828$	4.36366	−	4.06887i	0.151648	−	0.141403i
$829$	15.3145	−	8.84180i	0.531893	−	0.307089i	−0.209894	−	0.977724i	$-0.567312\pi$
$829$	15.3145	−	8.84180i	0.531893	−	0.307089i	0.741787	+	0.670636i	$0.233979\pi$
$830$	13.2896	−	5.23465i	0.461290	−	0.181697i
$831$	−29.7329			−1.03142
$832$	−21.9708	−	18.6891i	−0.761701	−	0.647928i
$833$	−15.6182			−0.541139
$834$	−7.37427	+	2.90464i	−0.255350	+	0.100580i
$835$	14.6353	−	8.44968i	0.506475	−	0.292413i
$836$	−6.25568	+	5.83308i	−0.216357	+	0.201741i
$837$	−0.507621	+	0.507621i	−0.0175459	+	0.0175459i
$838$	−33.4059	+	41.9953i	−1.15399	+	1.45070i
$839$	−7.87505	−	29.3901i	−0.271877	−	1.01466i	−0.957906	−	0.287084i	$-0.907314\pi$
$839$	−7.87505	−	29.3901i	−0.271877	−	1.01466i	0.686029	−	0.727574i	$-0.259352\pi$
$840$	4.14354	−	8.68586i	0.142966	−	0.299691i
$841$	9.85838	−	17.0752i	0.339944	−	0.588800i
$842$	−15.4126	+	35.4447i	−0.531153	+	1.22151i
$843$	0.165049	+	0.0442248i	0.00568460	+	0.00152318i
$844$	−10.1700	+	33.2603i	−0.350067	+	1.14487i
$845$	5.28682	−	12.0105i	0.181872	−	0.413173i
$846$	4.89534	+	6.61593i	0.168305	+	0.227460i
$847$	−4.17243	+	15.5717i	−0.143366	+	0.535050i
$848$	0.769529	−	10.9930i	0.0264257	−	0.377501i
$849$	12.2954	+	7.09875i	0.421977	+	0.243628i
$850$	2.98041	−	19.9399i	0.102227	−	0.683932i
$851$	−26.4563	+	7.08895i	−0.906911	+	0.243006i
$852$	0.753629	−	21.5580i	0.0258189	−	0.738566i
$853$	−14.4358	−	14.4358i	−0.494272	−	0.494272i	0.415377	−	0.909649i	$-0.363650\pi$
$853$	−14.4358	−	14.4358i	−0.494272	−	0.494272i	−0.909649	+	0.415377i	$0.863650\pi$
$854$	60.3119	−	6.87053i	2.06383	−	0.235105i
$855$	−0.865661	−	1.49937i	−0.0296050	−	0.0512773i
$856$	−0.788758	−	10.0293i	−0.0269592	−	0.342795i
$857$		−	23.0450i		−	0.787203i	−0.919281	−	0.393602i	$-0.871229\pi$
$857$		−	23.0450i		−	0.787203i	0.919281	−	0.393602i	$-0.128771\pi$
$858$	8.65155	−	9.31662i	0.295359	−	0.318064i
$859$		−	13.0285i		−	0.444527i	−0.974987	−	0.222264i	$-0.928655\pi$
$859$		−	13.0285i		−	0.444527i	0.974987	−	0.222264i	$-0.0713445\pi$
$860$	18.1579	+	11.3472i	0.619178	+	0.386937i
$861$	18.0535	+	31.2696i	0.615262	+	1.06566i
$862$	2.30076	+	20.1968i	0.0783641	+	0.687907i
$863$	3.63659	+	3.63659i	0.123791	+	0.123791i	0.766288	−	0.642497i	$-0.222102\pi$
$863$	3.63659	+	3.63659i	0.123791	+	0.123791i	−0.642497	+	0.766288i	$0.722102\pi$
$864$	5.39520	−	1.70055i	0.183548	−	0.0578537i
$865$	−9.44456	+	2.53066i	−0.321125	+	0.0860451i
$866$	−18.3286	−	2.73957i	−0.622830	−	0.0930945i
$867$	−3.61675	−	2.08813i	−0.122831	−	0.0709166i
$868$	1.08847	+	4.71550i	0.0369452	+	0.160054i
$869$	1.26688	−	4.72807i	0.0429761	−	0.160389i
$870$	3.49643	−	2.58712i	0.118540	−	0.0877117i
$871$	−3.57791	+	46.7212i	−0.121233	+	1.58309i
$872$	−2.21053	−	6.24344i	−0.0748579	−	0.211430i
$873$	12.8795	+	3.45104i	0.435904	+	0.116800i
$874$	−6.63574	−	2.88545i	−0.224457	−	0.0976018i
$875$	15.2788	−	26.4636i	0.516517	−	0.894634i
$876$	−3.42961	+	1.82339i	−0.115876	+	0.0616067i
$877$	−6.11070	−	22.8054i	−0.206344	−	0.770085i	−0.989036	−	0.147676i	$-0.952821\pi$
$877$	−6.11070	−	22.8054i	−0.206344	−	0.770085i	0.782692	−	0.622409i	$-0.213846\pi$
$878$	21.0400	+	16.7366i	0.710065	+	0.564833i
$879$	−9.27326	+	9.27326i	−0.312779	+	0.312779i
$880$	4.41276	+	9.04922i	0.148754	+	0.305049i
$881$	−34.5553	+	19.9505i	−1.16420	+	0.672149i	−0.952306	−	0.305144i	$-0.901295\pi$
$881$	−34.5553	+	19.9505i	−1.16420	+	0.672149i	−0.211890	+	0.977293i	$0.567962\pi$
$882$	−2.26044	−	5.73879i	−0.0761131	−	0.193235i
$883$	10.3078			0.346884			0.173442	−	0.984844i	$-0.444511\pi$
$883$	10.3078			0.346884			0.173442	+	0.984844i	$0.444511\pi$
$884$	23.6600	−	10.3460i	0.795771	−	0.347973i
$885$	11.7191			0.393934
$886$	19.8465	+	50.3860i	0.666756	+	1.69275i
$887$	17.7126	−	10.2264i	0.594730	−	0.343367i	−0.172236	−	0.985056i	$-0.555099\pi$
$887$	17.7126	−	10.2264i	0.594730	−	0.343367i	0.766965	+	0.641688i	$0.221766\pi$
$888$	−25.5337	−	4.73387i	−0.856856	−	0.158858i
$889$	−22.7317	+	22.7317i	−0.762397	+	0.762397i
$890$	12.3935	+	9.85860i	0.415431	+	0.330461i
$891$	0.645351	+	2.40848i	0.0216201	+	0.0806872i
$892$	9.36412	+	17.6129i	0.313534	+	0.589725i
$893$	4.99072	−	8.64418i	0.167008	−	0.289266i
$894$	−9.72305	−	4.22792i	−0.325187	−	0.141403i
$895$	7.14726	+	1.91510i	0.238907	+	0.0640148i
$896$	9.55299	−	36.9188i	0.319143	−	1.23337i
$897$	10.1466	+	3.56903i	0.338784	+	0.119166i
$898$	−30.1917	+	22.3398i	−1.00751	+	0.745490i
$899$	−0.566109	+	2.11275i	−0.0188808	+	0.0704641i
$900$	7.75810	−	1.79079i	0.258603	−	0.0596932i
$901$	8.54389	+	4.93281i	0.284638	+	0.164336i
$902$	−37.3588	−	5.58402i	−1.24391	−	0.185927i
$903$	34.5309	−	9.25252i	1.14912	−	0.307905i
$904$	16.8717	+	24.5514i	0.561145	+	0.816569i
$905$	−14.8684	−	14.8684i	−0.494243	−	0.494243i
$906$	2.07782	+	18.2398i	0.0690310	+	0.605978i
$907$	−11.7107	−	20.2836i	−0.388849	−	0.673505i	0.603446	−	0.797404i	$-0.293794\pi$
$907$	−11.7107	−	20.2836i	−0.388849	−	0.673505i	−0.992295	+	0.123898i	$0.960460\pi$
$908$	16.2405	−	25.9881i	0.538961	−	0.862447i
$909$			17.9817i			0.596415i
$910$	17.3373	−	0.641719i	0.574725	−	0.0212728i
$911$		−	46.4109i		−	1.53766i	−0.639452	−	0.768831i	$-0.720839\pi$
$911$		−	46.4109i		−	1.53766i	0.639452	−	0.768831i	$-0.279161\pi$
$912$	−4.50057	−	5.17810i	−0.149029	−	0.171464i
$913$	12.4742	+	21.6059i	0.412834	+	0.715050i
$914$	−52.6211	+	5.99443i	−1.74055	+	0.198278i
$915$	−9.08936	−	9.08936i	−0.300485	−	0.300485i
$916$	−9.85487	−	0.344508i	−0.325614	−	0.0113829i
$917$	11.5561	−	3.09646i	0.381617	−	0.102254i
$918$	−0.748650	+	5.00869i	−0.0247091	+	0.165312i
$919$	−1.03971	−	0.600275i	−0.0342967	−	0.0198012i	0.482754	−	0.875756i	$-0.339637\pi$
$919$	−1.03971	−	0.600275i	−0.0342967	−	0.0198012i	−0.517050	+	0.855955i	$0.672970\pi$
$920$	−5.53187	+	6.47625i	−0.182380	+	0.213516i
$921$	5.73717	−	21.4114i	0.189046	−	0.705529i
$922$	12.0633	+	16.3033i	0.397284	+	0.536920i
$923$	35.0644	−	16.8157i	1.15416	−	0.553496i
$924$	16.0745	+	4.91511i	0.528811	+	0.161695i
$925$	−35.3061	−	9.46023i	−1.16086	−	0.311050i
$926$	13.2514	−	30.4745i	0.435467	−	1.00145i
$927$	4.71963	−	8.17464i	0.155013	−	0.268491i
$928$	11.6453	−	12.7063i	0.382277	−	0.417104i
$929$	8.57523	+	32.0032i	0.281344	+	1.04999i	0.951470	+	0.307743i	$0.0995737\pi$
$929$	8.57523	+	32.0032i	0.281344	+	1.04999i	−0.670125	+	0.742248i	$0.733760\pi$
$930$	0.637977	−	0.802016i	0.0209201	−	0.0262991i
$931$	−5.28946	+	5.28946i	−0.173355	+	0.173355i
$932$	15.0994	+	16.1934i	0.494599	+	0.530432i
$933$	−2.66816	+	1.54046i	−0.0873516	+	0.0504325i
$934$	24.0075	−	9.45627i	0.785548	−	0.309419i
$935$	−9.01327			−0.294766
$936$	7.22589	+	7.19628i	0.236186	+	0.235218i
$937$	−0.761911			−0.0248905			−0.0124453	−	0.999923i	$-0.503962\pi$
$937$	−0.761911			−0.0248905			−0.0124453	+	0.999923i	$0.503962\pi$
$938$	−57.6400	+	22.7038i	−1.88201	+	0.741304i
$939$	−0.786507	+	0.454090i	−0.0256667	+	0.0148187i
$940$	−8.01240	−	8.59289i	−0.261336	−	0.280269i
$941$	2.93449	−	2.93449i	0.0956615	−	0.0956615i	−0.657656	−	0.753318i	$-0.728452\pi$
$941$	2.93449	−	2.93449i	0.0956615	−	0.0956615i	0.753318	+	0.657656i	$0.228452\pi$
$942$	3.95887	−	4.97680i	0.128987	−	0.162153i
$943$	−8.27085	−	30.8672i	−0.269336	−	1.00518i
$944$	45.5860	−	8.85750i	1.48370	−	0.288287i
$945$	−1.70122	+	2.94661i	−0.0553408	+	0.0958531i
$946$	−14.9136	+	34.2971i	−0.484882	+	1.11509i
$947$	−30.1973	−	8.09135i	−0.981282	−	0.262934i	−0.267698	−	0.963503i	$-0.586263\pi$
$947$	−30.1973	−	8.09135i	−0.981282	−	0.262934i	−0.713584	+	0.700569i	$0.752929\pi$
$948$	3.75459	+	1.14805i	0.121943	+	0.0372868i
$949$	−5.77916	−	3.95399i	−0.187599	−	0.128352i
$950$	−5.74370	−	7.76247i	−0.186350	−	0.251848i
$951$	−2.14501	+	8.00527i	−0.0695566	+	0.259589i
$952$	25.9593	+	22.1738i	0.841345	+	0.718658i
$953$	33.8619	+	19.5502i	1.09689	+	0.633292i	0.935404	−	0.353582i	$-0.115036\pi$
$953$	33.8619	+	19.5502i	1.09689	+	0.633292i	0.161491	+	0.986874i	$0.448370\pi$
$954$	−0.575955	+	3.85331i	−0.0186472	+	0.124756i
$955$	−23.6326	+	6.33234i	−0.764733	+	0.204910i
$956$	−51.7778	−	1.81006i	−1.67461	−	0.0585414i
$957$	5.37198	+	5.37198i	0.173651	+	0.173651i
$958$	−50.2734	+	5.72698i	−1.62426	+	0.185030i
$959$	1.05873	+	1.83377i	0.0341882	+	0.0592157i
$960$	−7.37764	+	3.28375i	−0.238112	+	0.105983i
$961$		−	30.4846i		−	0.983376i
$962$	−13.7812	−	44.7416i	−0.444325	−	1.44253i
$963$			3.55684i			0.114618i
$964$	−16.7044	+	26.7304i	−0.538013	+	0.860929i
$965$	−3.65685	−	6.33385i	−0.117718	−	0.203894i
$966$	1.60952	+	14.1289i	0.0517854	+	0.454590i
$967$	−7.25186	−	7.25186i	−0.233204	−	0.233204i	0.580825	−	0.814029i	$-0.302730\pi$
$967$	−7.25186	−	7.25186i	−0.233204	−	0.233204i	−0.814029	+	0.580825i	$0.802730\pi$
$968$	11.1489	−	7.66151i	0.358339	−	0.246250i
$969$	5.93271	−	1.58967i	0.190586	−	0.0510674i
$970$	−18.8255	−	2.81385i	−0.604451	−	0.0903473i
$971$	23.6793	+	13.6712i	0.759905	+	0.438731i	0.829262	−	0.558861i	$-0.188761\pi$
$971$	23.6793	+	13.6712i	0.759905	+	0.438731i	−0.0693567	+	0.997592i	$0.522095\pi$
$972$	−1.94876	+	0.449829i	−0.0625064	+	0.0144283i
$973$	4.88917	−	18.2466i	0.156740	−	0.584960i
$974$	13.0268	−	9.63896i	0.417406	−	0.308852i
$975$	9.34511	+	10.8951i	0.299283	+	0.348922i
$976$	−42.2265	−	28.4867i	−1.35164	−	0.911837i
$977$	3.17560	+	0.850899i	0.101596	+	0.0272227i	0.309259	−	0.950978i	$-0.399919\pi$
$977$	3.17560	+	0.850899i	0.101596	+	0.0272227i	−0.207663	+	0.978200i	$0.566586\pi$
$978$	10.9416	+	4.75777i	0.349872	+	0.152137i
$979$	−13.8304	+	23.9549i	−0.442021	+	0.765603i
$980$	4.13341	+	7.77451i	0.132037	+	0.248348i
$981$	0.606067	+	2.26187i	0.0193502	+	0.0722160i
$982$	36.2629	+	28.8459i	1.15720	+	0.920511i
$983$	−10.7403	+	10.7403i	−0.342561	+	0.342561i	−0.857329	−	0.514768i	$-0.827878\pi$
$983$	−10.7403	+	10.7403i	−0.342561	+	0.342561i	0.514768	+	0.857329i	$0.327878\pi$
$984$	5.52313	−	29.7908i	0.176071	−	0.949697i
$985$	8.98841	−	5.18946i	0.286395	−	0.165350i
$986$	5.65493	+	14.3567i	0.180090	+	0.457209i
$987$	−19.6158			−0.624379
$988$	4.50908	−	11.5169i	0.143453	−	0.366401i
$989$	−31.6393			−1.00607
$990$	−1.30450	−	3.31186i	−0.0414598	−	0.105258i
$991$	16.8863	−	9.74929i	0.536410	−	0.309696i	−0.207213	−	0.978296i	$-0.566439\pi$
$991$	16.8863	−	9.74929i	0.536410	−	0.309696i	0.743623	+	0.668599i	$0.233106\pi$
$992$	1.87548	−	3.60194i	0.0595466	−	0.114362i
$993$	−19.3954	+	19.3954i	−0.615494	+	0.615494i
$994$	40.2358	+	32.0063i	1.27620	+	1.01518i
$995$	−0.616224	−	2.29978i	−0.0195356	−	0.0729079i
$996$	−17.6691	+	9.39400i	−0.559868	+	0.297660i
$997$	11.5467	−	19.9994i	0.365686	−	0.633387i	−0.623200	−	0.782063i	$-0.714168\pi$
$997$	11.5467	−	19.9994i	0.365686	−	0.633387i	0.988886	+	0.148675i	$0.0475009\pi$
$998$	−6.21604	−	2.70295i	−0.196765	−	0.0855603i
$999$	8.86852	+	2.37631i	0.280588	+	0.0751832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.67.2	yes	24
3.2	odd	2		468.2.cb.h.379.5		24
4.3	odd	2		156.2.w.d.67.2	yes	24
12.11	even	2		468.2.cb.g.379.5		24
13.7	odd	12		156.2.w.d.7.2	yes	24
39.20	even	12		468.2.cb.g.163.5		24
52.7	even	12	inner	156.2.w.c.7.2	✓	24
156.59	odd	12		468.2.cb.h.163.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.7.2	✓	24	52.7	even	12	inner
156.2.w.c.67.2	yes	24	1.1	even	1	trivial
156.2.w.d.7.2	yes	24	13.7	odd	12
156.2.w.d.67.2	yes	24	4.3	odd	2
468.2.cb.g.163.5		24	39.20	even	12
468.2.cb.g.379.5		24	12.11	even	2
468.2.cb.h.163.5		24	156.59	odd	12
468.2.cb.h.379.5		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31582 + 0.518286i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.46276 - 1.36394i) q^{4} +(0.713774 - 0.713774i) q^{5} +(-0.880389 + 1.10676i) q^{6} +(-0.872392 - 3.25581i) q^{7} +(-1.21781 + 2.55283i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.31582 + 0.518286i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.46276 - 1.36394i) q^{4} +(0.713774 - 0.713774i) q^{5} +(-0.880389 + 1.10676i) q^{6} +(-0.872392 - 3.25581i) q^{7} +(-1.21781 + 2.55283i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.569258 + 1.30914i) q^{10} +(-2.40848 - 0.645351i) q^{11} +(0.584815 - 1.91259i) q^{12} +(3.54378 - 0.664535i) q^{13} +(2.83535 + 3.83191i) q^{14} +(0.261259 - 0.975034i) q^{15} +(0.279324 - 3.99024i) q^{16} +(3.10126 + 1.79051i) q^{17} +(-0.209060 + 1.39868i) q^{18} +(1.65671 - 0.443914i) q^{19} +(0.0705324 - 2.01763i) q^{20} +(-2.38342 - 2.38342i) q^{21} +(3.50360 - 0.399119i) q^{22} +(1.49159 + 2.58350i) q^{23} +(0.221758 + 2.81972i) q^{24} +3.98105i q^{25} +(-4.31856 + 2.71110i) q^{26} -1.00000i q^{27} +(-5.71684 - 3.57257i) q^{28} +(-1.52342 - 2.63864i) q^{29} +(0.161577 + 1.41837i) q^{30} +(-0.507621 - 0.507621i) q^{31} +(1.70055 + 5.39520i) q^{32} +(-2.40848 + 0.645351i) q^{33} +(-5.00869 - 0.748650i) q^{34} +(-2.94661 - 1.70122i) q^{35} +(-0.449829 - 1.94876i) q^{36} +(-2.37631 + 8.86852i) q^{37} +(-1.94985 + 1.44276i) q^{38} +(2.73674 - 2.34740i) q^{39} +(0.952900 + 2.69139i) q^{40} +(-10.3471 - 2.77250i) q^{41} +(4.37144 + 1.90085i) q^{42} +(-5.30296 + 9.18500i) q^{43} +(-4.40325 + 2.34104i) q^{44} +(-0.261259 - 0.975034i) q^{45} +(-3.30165 - 2.62635i) q^{46} +(4.11506 - 4.11506i) q^{47} +(-1.75322 - 3.59531i) q^{48} +(-3.77707 + 2.18069i) q^{49} +(-2.06333 - 5.23834i) q^{50} +3.58103 q^{51} +(4.27731 - 5.80557i) q^{52} +2.75497 q^{53} +(0.518286 + 1.31582i) q^{54} +(-2.17975 + 1.25848i) q^{55} +(9.37394 + 1.73790i) q^{56} +(1.21279 - 1.21279i) q^{57} +(3.37212 + 2.68241i) q^{58} +(3.00480 + 11.2141i) q^{59} +(-0.947730 - 1.78258i) q^{60} +(6.36711 - 11.0282i) q^{61} +(0.931030 + 0.404844i) q^{62} +(-3.25581 - 0.872392i) q^{63} +(-5.03387 - 6.21773i) q^{64} +(2.05513 - 3.00379i) q^{65} +(2.83465 - 2.09745i) q^{66} +(-3.36363 + 12.5532i) q^{67} +(6.97855 - 1.61085i) q^{68} +(2.58350 + 1.49159i) q^{69} +(4.75892 + 0.711316i) q^{70} +(10.4181 - 2.79152i) q^{71} +(1.60191 + 2.33107i) q^{72} +(-1.37327 - 1.37327i) q^{73} +(-1.46964 - 12.9010i) q^{74} +(1.99053 + 3.44769i) q^{75} +(1.81789 - 2.90899i) q^{76} +8.40456i q^{77} +(-2.38443 + 4.50716i) q^{78} +1.96309i q^{79} +(-2.64875 - 3.04750i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(15.0519 - 1.71466i) q^{82} +(-7.07500 - 7.07500i) q^{83} +(-6.73721 - 0.235520i) q^{84} +(3.49162 - 0.935577i) q^{85} +(2.21728 - 14.8342i) q^{86} +(-2.63864 - 1.52342i) q^{87} +(4.58055 - 5.36252i) q^{88} +(2.87118 - 10.7154i) q^{89} +(0.849117 + 1.14756i) q^{90} +(-5.25517 - 10.9582i) q^{91} +(5.70557 + 1.74460i) q^{92} +(-0.693423 - 0.185802i) q^{93} +(-3.28189 + 7.54745i) q^{94} +(0.865661 - 1.49937i) q^{95} +(4.17031 + 3.82210i) q^{96} +(3.45104 + 12.8795i) q^{97} +(3.83971 - 4.82700i) q^{98} +(-1.76313 + 1.76313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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