LMFDB - Embedded newform 261.2.q.a.103.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(7,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([28, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.q (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			103.12
Character	$\chi$	$=$	261.103
Dual form			261.2.q.a.223.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0343571 - 0.458464i) q^{2} +(0.435012 + 1.67653i) q^{3} +(1.76865 - 0.266582i) q^{4} +(-0.522192 + 0.356024i) q^{5} +(0.753684 - 0.257038i) q^{6} +(4.23687 + 0.638606i) q^{7} +(-0.387591 - 1.69815i) q^{8} +(-2.62153 + 1.45862i) q^{9} +(0.181165 + 0.227174i) q^{10} +(-4.42276 + 1.36424i) q^{11} +(1.21632 + 2.84924i) q^{12} +(-2.37536 - 2.20401i) q^{13} +(0.147211 - 1.96439i) q^{14} +(-0.824046 - 0.720597i) q^{15} +(2.65311 - 0.818376i) q^{16} +5.92716 q^{17} +(0.758794 + 1.15176i) q^{18} +(-1.29397 - 1.62258i) q^{19} +(-0.828667 + 0.768890i) q^{20} +(0.772446 + 7.38106i) q^{21} +(0.777408 + 1.98080i) q^{22} +(-0.113983 + 1.52100i) q^{23} +(2.67840 - 1.38852i) q^{24} +(-1.68077 + 4.28254i) q^{25} +(-0.928849 + 1.16474i) q^{26} +(-3.58583 - 3.76056i) q^{27} +7.66380 q^{28} +(5.24806 - 1.20743i) q^{29} +(-0.302056 + 0.402553i) q^{30} +(-4.57847 + 3.12155i) q^{31} +(-1.73907 - 4.43107i) q^{32} +(-4.21115 - 6.82145i) q^{33} +(-0.203640 - 2.71739i) q^{34} +(-2.43982 + 1.17496i) q^{35} +(-4.24773 + 3.27865i) q^{36} +(-2.54928 - 11.1691i) q^{37} +(-0.699439 + 0.648984i) q^{38} +(2.66179 - 4.94114i) q^{39} +(0.806979 + 0.748767i) q^{40} +(3.23747 - 5.60746i) q^{41} +(3.35741 - 0.607730i) q^{42} +(2.87179 + 1.95795i) q^{43} +(-7.45865 + 3.59190i) q^{44} +(0.849636 - 1.69501i) q^{45} +0.701241 q^{46} +(-10.7059 + 3.30235i) q^{47} +(2.52617 + 4.09203i) q^{48} +(10.8543 + 3.34810i) q^{49} +(2.02114 + 0.623438i) q^{50} +(2.57839 + 9.93709i) q^{51} +(-4.78874 - 3.26490i) q^{52} +(-6.58201 - 3.16973i) q^{53} +(-1.60088 + 1.77317i) q^{54} +(1.82383 - 2.28701i) q^{55} +(-0.557728 - 7.44236i) q^{56} +(2.15743 - 2.87522i) q^{57} +(-0.733872 - 2.36456i) q^{58} +(1.00471 - 1.74020i) q^{59} +(-1.64955 - 1.05481i) q^{60} +(-13.1274 - 1.97864i) q^{61} +(1.58842 + 1.99182i) q^{62} +(-12.0386 + 4.50588i) q^{63} +(3.03128 - 1.45979i) q^{64} +(2.02508 + 0.305231i) q^{65} +(-2.98270 + 2.16502i) q^{66} +(4.67591 + 1.44233i) q^{67} +(10.4831 - 1.58007i) q^{68} +(-2.59960 + 0.470558i) q^{69} +(0.622500 + 1.07820i) q^{70} +(2.45901 - 10.7736i) q^{71} +(3.49304 + 3.88640i) q^{72} +(-3.11151 + 1.49842i) q^{73} +(-5.03306 + 1.55249i) q^{74} +(-7.91098 - 0.954918i) q^{75} +(-2.72113 - 2.52484i) q^{76} +(-19.6099 + 2.95572i) q^{77} +(-2.35678 - 1.05057i) q^{78} +(2.45964 - 2.28222i) q^{79} +(-1.09407 + 1.37192i) q^{80} +(4.74483 - 7.64765i) q^{81} +(-2.68205 - 1.29161i) q^{82} +(0.367887 - 0.937360i) q^{83} +(3.33384 + 12.8486i) q^{84} +(-3.09512 + 2.11021i) q^{85} +(0.798984 - 1.38388i) q^{86} +(4.30727 + 8.27330i) q^{87} +(4.03091 + 6.98174i) q^{88} +(2.60627 + 1.25512i) q^{89} +(-0.806291 - 0.331291i) q^{90} +(-8.65660 - 10.8550i) q^{91} +(0.203874 + 2.72051i) q^{92} +(-7.22507 - 6.31805i) q^{93} +(1.88183 + 4.79483i) q^{94} +(1.25338 + 0.386616i) q^{95} +(6.67232 - 4.84317i) q^{96} +(-5.78762 + 14.7466i) q^{97} +(1.16206 - 5.09132i) q^{98} +(9.60449 - 10.0275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) $ 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0343571	−	0.458464i	−0.0242941	−	0.324183i	−0.996089	−	0.0883551i	$-0.971839\pi$
$2$	−0.0343571	−	0.458464i	−0.0242941	−	0.324183i	0.971795	−	0.235828i	$-0.0757801\pi$
$3$	0.435012	+	1.67653i	0.251154	+	0.967947i
$3$	0.435012	+	1.67653i	0.251154	+	0.967947i
$4$	1.76865	−	0.266582i	0.884327	−	0.133291i
$5$	−0.522192	+	0.356024i	−0.233531	+	0.159219i	−0.674432	−	0.738337i	$-0.735611\pi$
$5$	−0.522192	+	0.356024i	−0.233531	+	0.159219i	0.440901	+	0.897556i	$0.354659\pi$
$6$	0.753684	−	0.257038i	0.307690	−	0.104935i
$7$	4.23687	+	0.638606i	1.60139	+	0.241370i	0.888151	−	0.459552i	$-0.151990\pi$
$7$	4.23687	+	0.638606i	1.60139	+	0.241370i	0.713237	+	0.700923i	$0.247228\pi$
$8$	−0.387591	−	1.69815i	−0.137034	−	0.600386i
$9$	−2.62153	+	1.45862i	−0.873843	+	0.486208i
$10$	0.181165	+	0.227174i	0.0572895	+	0.0718387i
$11$	−4.42276	+	1.36424i	−1.33351	+	0.411334i	−0.877900	−	0.478844i	$-0.841056\pi$
$11$	−4.42276	+	1.36424i	−1.33351	+	0.411334i	−0.455613	+	0.890178i	$0.650580\pi$
$12$	1.21632	+	2.84924i	0.351121	+	0.822505i
$13$	−2.37536	−	2.20401i	−0.658806	−	0.611283i	0.278230	−	0.960514i	$-0.410252\pi$
$13$	−2.37536	−	2.20401i	−0.658806	−	0.611283i	−0.937036	+	0.349232i	$0.886443\pi$
$14$	0.147211	−	1.96439i	0.0393438	−	0.525006i
$15$	−0.824046	−	0.720597i	−0.212768	−	0.186057i
$16$	2.65311	−	0.818376i	0.663278	−	0.204594i
$17$	5.92716			1.43755			0.718774	−	0.695244i	$-0.244704\pi$
$17$	5.92716			1.43755			0.718774	+	0.695244i	$0.244704\pi$
$18$	0.758794	+	1.15176i	0.178849	+	0.271473i
$19$	−1.29397	−	1.62258i	−0.296857	−	0.372246i	0.610926	−	0.791688i	$-0.290797\pi$
$19$	−1.29397	−	1.62258i	−0.296857	−	0.372246i	−0.907782	+	0.419442i	$0.862226\pi$
$20$	−0.828667	+	0.768890i	−0.185296	+	0.171929i
$21$	0.772446	+	7.38106i	0.168562	+	1.61068i
$22$	0.777408	+	1.98080i	0.165744	+	0.422309i
$23$	−0.113983	+	1.52100i	−0.0237672	+	0.317151i	0.972631	+	0.232355i	$0.0746430\pi$
$23$	−0.113983	+	1.52100i	−0.0237672	+	0.317151i	−0.996398	+	0.0847965i	$0.972976\pi$
$24$	2.67840	−	1.38852i	0.546725	−	0.283431i
$25$	−1.68077	+	4.28254i	−0.336155	+	0.856509i
$26$	−0.928849	+	1.16474i	−0.182162	+	0.228424i
$27$	−3.58583	−	3.76056i	−0.690093	−	0.723721i
$28$	7.66380			1.44832
$29$	5.24806	−	1.20743i	0.974540	−	0.224215i
$29$	5.24806	−	1.20743i	0.974540	−	0.224215i
$30$	−0.302056	+	0.402553i	−0.0551476	+	0.0734958i
$31$	−4.57847	+	3.12155i	−0.822318	+	0.560647i	−0.899778	−	0.436348i	$-0.856271\pi$
$31$	−4.57847	+	3.12155i	−0.822318	+	0.560647i	0.0774596	+	0.996995i	$0.475319\pi$
$32$	−1.73907	−	4.43107i	−0.307426	−	0.783309i
$33$	−4.21115	−	6.82145i	−0.733067	−	1.18746i
$34$	−0.203640	−	2.71739i	−0.0349240	−	0.466028i
$35$	−2.43982	+	1.17496i	−0.412405	+	0.198604i
$36$	−4.24773	+	3.27865i	−0.707956	+	0.546442i
$37$	−2.54928	−	11.1691i	−0.419100	−	1.83620i	−0.537545	−	0.843235i	$-0.680648\pi$
$37$	−2.54928	−	11.1691i	−0.419100	−	1.83620i	0.118445	−	0.992961i	$-0.462209\pi$
$38$	−0.699439	+	0.648984i	−0.113464	+	0.105279i
$39$	2.66179	−	4.94114i	0.426227	−	0.791216i
$40$	0.806979	+	0.748767i	0.127595	+	0.118391i
$41$	3.23747	−	5.60746i	0.505608	−	0.875738i	−0.494371	−	0.869251i	$-0.664602\pi$
$41$	3.23747	−	5.60746i	0.505608	−	0.875738i	0.999979	−	0.00648717i	$-0.00206494\pi$
$42$	3.35741	−	0.607730i	0.518060	−	0.0937748i
$43$	2.87179	+	1.95795i	0.437944	+	0.298585i	0.762149	−	0.647402i	$-0.224144\pi$
$43$	2.87179	+	1.95795i	0.437944	+	0.298585i	−0.324205	+	0.945987i	$0.605097\pi$
$44$	−7.45865	+	3.59190i	−1.12443	+	0.541499i
$45$	0.849636	−	1.69501i	0.126656	−	0.252677i
$46$	0.701241			0.103392
$47$	−10.7059	+	3.30235i	−1.56162	+	0.481697i	−0.950731	−	0.310018i	$-0.899665\pi$
$47$	−10.7059	+	3.30235i	−1.56162	+	0.481697i	−0.610891	+	0.791714i	$0.709189\pi$
$48$	2.52617	+	4.09203i	0.364621	+	0.590633i
$49$	10.8543	+	3.34810i	1.55061	+	0.478300i
$50$	2.02114	+	0.623438i	0.285832	+	0.0881675i
$51$	2.57839	+	9.93709i	0.361046	+	1.39147i
$52$	−4.78874	−	3.26490i	−0.664078	−	0.452761i
$53$	−6.58201	−	3.16973i	−0.904109	−	0.435396i	−0.0767375	−	0.997051i	$-0.524450\pi$
$53$	−6.58201	−	3.16973i	−0.904109	−	0.435396i	−0.827371	+	0.561656i	$0.810165\pi$
$54$	−1.60088	+	1.77317i	−0.217853	+	0.241298i
$55$	1.82383	−	2.28701i	0.245925	−	0.308380i
$56$	−0.557728	−	7.44236i	−0.0745295	−	0.994527i
$57$	2.15743	−	2.87522i	0.285758	−	0.380833i
$58$	−0.733872	−	2.36456i	−0.0963622	−	0.310482i
$59$	1.00471	−	1.74020i	0.130802	−	0.226555i	−0.793184	−	0.608982i	$-0.791578\pi$
$59$	1.00471	−	1.74020i	0.130802	−	0.226555i	0.923986	+	0.382427i	$0.124912\pi$
$60$	−1.64955	−	1.05481i	−0.212956	−	0.136176i
$61$	−13.1274	−	1.97864i	−1.68079	−	0.253338i	−0.761855	−	0.647747i	$-0.775711\pi$
$61$	−13.1274	−	1.97864i	−1.68079	−	0.253338i	−0.918935	+	0.394409i	$0.870949\pi$
$62$	1.58842	+	1.99182i	0.201730	+	0.252961i
$63$	−12.0386	+	4.50588i	−1.51672	+	0.567688i
$64$	3.03128	−	1.45979i	0.378910	−	0.182473i
$65$	2.02508	+	0.305231i	0.251180	+	0.0378592i
$66$	−2.98270	+	2.16502i	−0.367145	+	0.266496i
$67$	4.67591	+	1.44233i	0.571254	+	0.176208i	0.566906	−	0.823782i	$-0.308140\pi$
$67$	4.67591	+	1.44233i	0.571254	+	0.176208i	0.00434710	+	0.999991i	$0.498616\pi$
$68$	10.4831	−	1.58007i	1.27126	−	0.191612i
$69$	−2.59960	+	0.470558i	−0.312955	+	0.0566485i
$70$	0.622500	+	1.07820i	0.0744029	+	0.128870i
$71$	2.45901	−	10.7736i	0.291831	−	1.27860i	−0.590144	−	0.807298i	$-0.700929\pi$
$71$	2.45901	−	10.7736i	0.291831	−	1.27860i	0.881975	−	0.471297i	$-0.156214\pi$
$72$	3.49304	+	3.88640i	0.411659	+	0.458016i
$73$	−3.11151	+	1.49842i	−0.364175	+	0.175377i	−0.607018	−	0.794688i	$-0.707634\pi$
$73$	−3.11151	+	1.49842i	−0.364175	+	0.175377i	0.242843	+	0.970066i	$0.421920\pi$
$74$	−5.03306	+	1.55249i	−0.585081	+	0.180474i
$75$	−7.91098	−	0.954918i	−0.913482	−	0.110264i
$76$	−2.72113	−	2.52484i	−0.312135	−	0.289619i
$77$	−19.6099	+	2.95572i	−2.23476	+	0.336835i
$78$	−2.35678	−	1.05057i	−0.266853	−	0.118954i
$79$	2.45964	−	2.28222i	0.276732	−	0.256769i	−0.529581	−	0.848260i	$-0.677651\pi$
$79$	2.45964	−	2.28222i	0.276732	−	0.256769i	0.806312	+	0.591490i	$0.201460\pi$
$80$	−1.09407	+	1.37192i	−0.122321	+	0.153385i
$81$	4.74483	−	7.64765i	0.527204	−	0.849739i
$82$	−2.68205	−	1.29161i	−0.296182	−	0.142634i
$83$	0.367887	−	0.937360i	0.0403808	−	0.102889i	−0.909261	−	0.416227i	$-0.863352\pi$
$83$	0.367887	−	0.937360i	0.0403808	−	0.102889i	0.949642	+	0.313338i	$0.101447\pi$
$84$	3.33384	+	12.8486i	0.363752	+	1.40190i
$85$	−3.09512	+	2.11021i	−0.335712	+	0.228885i
$86$	0.798984	−	1.38388i	0.0861567	−	0.149228i
$87$	4.30727	+	8.27330i	0.461788	+	0.886990i
$88$	4.03091	+	6.98174i	0.429696	+	0.744256i
$89$	2.60627	+	1.25512i	0.276264	+	0.133042i	0.566886	−	0.823796i	$-0.308148\pi$
$89$	2.60627	+	1.25512i	0.276264	+	0.133042i	−0.290622	+	0.956838i	$0.593862\pi$
$90$	−0.806291	−	0.331291i	−0.0849906	−	0.0349212i
$91$	−8.65660	−	10.8550i	−0.907459	−	1.13792i
$92$	0.203874	+	2.72051i	0.0212554	+	0.283633i
$93$	−7.22507	−	6.31805i	−0.749205	−	0.655152i
$94$	1.88183	+	4.79483i	0.194096	+	0.494548i
$95$	1.25338	+	0.386616i	0.128594	+	0.0396660i
$96$	6.67232	−	4.84317i	0.680991	−	0.494304i
$97$	−5.78762	+	14.7466i	−0.587644	+	1.49729i	0.259400	+	0.965770i	$0.416475\pi$
$97$	−5.78762	+	14.7466i	−0.587644	+	1.49729i	−0.847044	+	0.531523i	$0.821620\pi$
$98$	1.16206	−	5.09132i	0.117386	−	0.514301i
$99$	9.60449	−	10.0275i	0.965287	−	1.00781i
$100$	−1.83106	+	8.02240i	−0.183106	+	0.802240i
$101$	6.41672	+	4.37485i	0.638487	+	0.435313i	0.838816	−	0.544415i	$-0.183248\pi$
$101$	6.41672	+	4.37485i	0.638487	+	0.435313i	−0.200328	+	0.979729i	$0.564201\pi$
$102$	4.46721	−	1.52351i	0.442319	−	0.150850i
$103$	9.54475	+	8.85623i	0.940472	+	0.872630i	0.992025	−	0.126040i	$-0.0402268\pi$
$103$	9.54475	+	8.85623i	0.940472	+	0.872630i	−0.0515534	+	0.998670i	$0.516417\pi$
$104$	−2.82207	+	4.88797i	−0.276727	+	0.479305i
$105$	−3.03120	−	3.57932i	−0.295815	−	0.349306i
$106$	−1.22707	+	3.12651i	−0.119183	+	0.303674i
$107$	1.82747	+	8.00666i	0.176668	+	0.774033i	0.983154	+	0.182780i	$0.0585096\pi$
$107$	1.82747	+	8.00666i	0.176668	+	0.774033i	−0.806486	+	0.591253i	$0.798633\pi$
$108$	−7.34458	−	5.69522i	−0.706733	−	0.548022i
$109$	−2.39868	+	3.00785i	−0.229752	+	0.288100i	−0.883323	−	0.468766i	$-0.844699\pi$
$109$	−2.39868	+	3.00785i	−0.229752	+	0.288100i	0.653571	+	0.756866i	$0.273270\pi$
$110$	−1.11117	−	0.757583i	−0.105946	−	0.0722327i
$111$	17.6165	−	9.13267i	1.67208	−	0.866835i
$112$	11.7635	−	1.77306i	1.11155	−	0.167539i
$113$	−0.597346	−	1.52201i	−0.0561936	−	0.143179i	0.900020	−	0.435849i	$-0.143552\pi$
$113$	−0.597346	−	1.52201i	−0.0561936	−	0.143179i	−0.956214	+	0.292670i	$0.905456\pi$
$114$	−1.39231	−	0.890317i	−0.130402	−	0.0833858i
$115$	−0.481993	−	0.834837i	−0.0449461	−	0.0778489i
$116$	8.96011	−	3.53457i	0.831926	−	0.328176i
$117$	9.44190	+	2.31313i	0.872904	+	0.213849i
$118$	−0.832339	−	0.400833i	−0.0766230	−	0.0368997i
$119$	25.1126	+	3.78512i	2.30207	+	0.346982i
$120$	−0.904288	+	1.67865i	−0.0825498	+	0.153239i
$121$	8.61104	−	5.87091i	0.782822	−	0.533719i
$122$	−0.456113	+	6.08641i	−0.0412946	+	0.551038i
$123$	10.8094	+	2.98841i	0.974653	+	0.269456i
$124$	−7.26558	+	6.74148i	−0.652469	+	0.605402i
$125$	−1.35018	−	5.91553i	−0.120764	−	0.529101i
$126$	2.47939	+	5.36444i	0.220882	+	0.477902i
$127$	1.96186	−	8.59546i	0.174087	−	0.762724i	−0.810201	−	0.586152i	$-0.800642\pi$
$127$	1.96186	−	8.59546i	0.174087	−	0.762724i	0.984288	−	0.176572i	$-0.0565007\pi$
$128$	−5.53352	−	9.58434i	−0.489099	−	0.847144i
$129$	−2.03331	+	5.66639i	−0.179023	+	0.498897i
$130$	0.0703616	−	0.938910i	0.00617112	−	0.0823479i
$131$	−0.153820	+	2.05258i	−0.0134393	+	0.179335i	0.986445	+	0.164095i	$0.0524703\pi$
$131$	−0.153820	+	2.05258i	−0.0134393	+	0.179335i	−0.999884	+	0.0152402i	$0.995149\pi$
$132$	−9.26654	−	10.9422i	−0.806548	−	0.952393i
$133$	−4.44619	−	7.70102i	−0.385533	−	0.667763i
$134$	0.500604	−	2.19329i	0.0432456	−	0.189471i
$135$	3.21134	+	0.687093i	0.276388	+	0.0591356i
$136$	−2.29732	−	10.0652i	−0.196993	−	0.863084i
$137$	−6.64029	+	6.16129i	−0.567318	+	0.526394i	−0.910845	−	0.412748i	$-0.864569\pi$
$137$	−6.64029	+	6.16129i	−0.567318	+	0.526394i	0.343527	+	0.939143i	$0.388378\pi$
$138$	0.305048	+	1.17565i	0.0259674	+	0.100078i
$139$	−0.157873	+	2.10666i	−0.0133906	+	0.178685i	0.986498	+	0.163772i	$0.0523661\pi$
$139$	−0.157873	+	2.10666i	−0.0133906	+	0.178685i	−0.999889	+	0.0149129i	$0.995253\pi$
$140$	−4.00197	+	2.72850i	−0.338229	+	0.230600i
$141$	−10.1937	−	16.5123i	−0.858465	−	1.39059i
$142$	−5.02380	−	0.757217i	−0.421588	−	0.0635442i
$143$	13.5125	+	6.50725i	1.12997	+	0.544164i
$144$	−5.76151	+	6.01529i	−0.480125	+	0.501274i
$145$	−2.31062	+	2.49895i	−0.191886	+	0.207526i
$146$	0.793875	+	1.37503i	0.0657016	+	0.113798i
$147$	−0.891465	+	19.6540i	−0.0735268	+	1.62104i
$148$	−7.48629	−	19.0747i	−0.615369	−	1.56793i
$149$	15.1713	−	2.28670i	1.24288	−	0.187334i	0.505508	−	0.862822i	$-0.331305\pi$
$149$	15.1713	−	2.28670i	1.24288	−	0.187334i	0.737371	+	0.675488i	$0.236067\pi$
$150$	−0.165997	+	3.65971i	−0.0135536	+	0.298814i
$151$	1.96074	+	1.33681i	0.159563	+	0.108788i	0.640469	−	0.767984i	$-0.278740\pi$
$151$	1.96074	+	1.33681i	0.159563	+	0.108788i	−0.480906	+	0.876772i	$0.659692\pi$
$152$	−2.25386	+	2.82625i	−0.182812	+	0.229239i
$153$	−15.5382	+	8.64550i	−1.25619	+	0.698947i
$154$	2.02883	+	8.88888i	0.163488	+	0.716286i
$155$	1.27949	−	3.26010i	0.102771	−	0.261857i
$156$	3.39057	−	9.44875i	0.271463	−	0.756505i
$157$	4.93371	−	8.54543i	0.393753	−	0.682000i	−0.599188	−	0.800608i	$-0.704510\pi$
$157$	4.93371	−	8.54543i	0.393753	−	0.682000i	0.992941	+	0.118608i	$0.0378433\pi$
$158$	−1.13082	−	1.04925i	−0.0899631	−	0.0834736i
$159$	2.45090	−	12.4138i	0.194369	−	0.984481i
$160$	2.48569	+	1.69472i	0.196511	+	0.133979i
$161$	−1.45426	+	6.37151i	−0.114611	+	0.502146i
$162$	−3.66919	−	1.91258i	−0.288279	−	0.150267i
$163$	−1.71011	+	7.49247i	−0.133946	+	0.586856i	0.862750	+	0.505631i	$0.168740\pi$
$163$	−1.71011	+	7.49247i	−0.133946	+	0.586856i	−0.996696	+	0.0812247i	$0.974117\pi$
$164$	4.23111	−	10.7807i	0.330394	−	0.841831i
$165$	4.62763	+	2.06283i	0.360260	+	0.160591i
$166$	−0.442385	−	0.136458i	−0.0343357	−	0.0105912i
$167$	7.61060	+	19.3915i	0.588926	+	1.50056i	0.845469	+	0.534025i	$0.179321\pi$
$167$	7.61060	+	19.3915i	0.588926	+	1.50056i	−0.256543	+	0.966533i	$0.582583\pi$
$168$	12.2347	−	4.17256i	0.943931	−	0.321920i
$169$	−0.186825	−	2.49301i	−0.0143712	−	0.191770i
$170$	1.07380	+	1.34650i	0.0823564	+	0.103272i
$171$	5.75891	+	2.36624i	0.440395	+	0.180951i
$172$	5.60116	+	2.69737i	0.427084	+	0.205673i
$173$	−0.247293	−	0.428325i	−0.0188014	−	0.0325649i	0.856472	−	0.516194i	$-0.172652\pi$
$173$	−0.247293	−	0.428325i	−0.0188014	−	0.0325649i	−0.875273	+	0.483629i	$0.839318\pi$
$174$	3.64502	−	2.25897i	0.276328	−	0.171252i
$175$	−9.85609	+	17.0712i	−0.745050	+	1.29046i
$176$	−10.6176	+	7.23897i	−0.800333	+	0.545658i
$177$	3.35457	+	0.927416i	0.252145	+	0.0697089i
$178$	0.485881	−	1.23800i	0.0364183	−	0.0927923i
$179$	6.88811	+	3.31714i	0.514841	+	0.247935i	0.673218	−	0.739444i	$-0.264912\pi$
$179$	6.88811	+	3.31714i	0.514841	+	0.247935i	−0.158376	+	0.987379i	$0.550626\pi$
$180$	1.05085	−	3.22438i	0.0783259	−	0.240331i
$181$	−1.48643	+	1.86393i	−0.110486	+	0.138545i	−0.833999	−	0.551765i	$-0.813954\pi$
$181$	−1.48643	+	1.86393i	−0.110486	+	0.138545i	0.723514	+	0.690310i	$0.242526\pi$
$182$	−4.67922	+	4.34169i	−0.346847	+	0.321827i
$183$	−2.39332	−	22.8692i	−0.176919	−	1.69054i
$184$	2.62707	−	0.395967i	0.193670	−	0.0291911i
$185$	5.30770	+	4.92483i	0.390230	+	0.362081i
$186$	−2.64836	+	3.52950i	−0.194188	+	0.258796i
$187$	−26.2144	+	8.08608i	−1.91699	+	0.591313i
$188$	−18.0548	+	8.69471i	−1.31678	+	0.634127i
$189$	−12.7912	−	18.2230i	−0.930422	−	1.32553i
$190$	0.134187	−	0.587912i	0.00973495	−	0.0426516i
$191$	5.60482	+	9.70784i	0.405551	+	0.702434i	0.994385	−	0.105819i	$-0.0337464\pi$
$191$	5.60482	+	9.70784i	0.405551	+	0.702434i	−0.588835	+	0.808253i	$0.700413\pi$
$192$	3.76602	+	4.44701i	0.271789	+	0.320936i
$193$	−8.01303	+	1.20777i	−0.576790	+	0.0869371i	−0.430958	−	0.902372i	$-0.641824\pi$
$193$	−8.01303	+	1.20777i	−0.576790	+	0.0869371i	−0.145833	+	0.989309i	$0.546586\pi$
$194$	6.95964	+	2.14676i	0.499673	+	0.154129i
$195$	0.369202	+	3.52789i	0.0264391	+	0.252637i
$196$	20.0900	+	3.02808i	1.43500	+	0.216291i
$197$	−10.0723	+	4.85056i	−0.717621	+	0.345588i	−0.756802	−	0.653644i	$-0.773239\pi$
$197$	−10.0723	+	4.85056i	−0.717621	+	0.345588i	0.0391809	+	0.999232i	$0.487525\pi$
$198$	−4.92725	−	4.05879i	−0.350164	−	0.288446i
$199$	1.88944	+	2.36928i	0.133939	+	0.167954i	0.844278	−	0.535906i	$-0.180030\pi$
$199$	1.88944	+	2.36928i	0.133939	+	0.167954i	−0.710339	+	0.703860i	$0.751458\pi$
$200$	7.92385	+	1.19433i	0.560301	+	0.0844517i
$201$	−0.384034	+	8.46675i	−0.0270877	+	0.597199i
$202$	1.78525	−	3.09214i	0.125610	−	0.217562i
$203$	23.0064	−	1.76430i	1.61474	−	0.123830i
$204$	7.20931	+	16.8879i	0.504753	+	1.18239i
$205$	0.305813	+	4.08079i	0.0213589	+	0.285014i
$206$	3.73233	−	4.68019i	0.260044	−	0.326085i
$207$	−1.91976	−	4.15362i	−0.133433	−	0.288696i
$208$	−8.10580	−	3.90355i	−0.562036	−	0.270662i
$209$	7.93651	+	5.41102i	0.548980	+	0.374288i
$210$	−1.53685	+	1.51267i	−0.106052	+	0.104384i
$211$	−7.72037	−	2.38142i	−0.531492	−	0.163944i	0.0173816	−	0.999849i	$-0.494467\pi$
$211$	−7.72037	−	2.38142i	−0.531492	−	0.163944i	−0.548874	+	0.835905i	$0.684943\pi$
$212$	−12.4863	−	3.85151i	−0.857562	−	0.264523i
$213$	19.1321	−	0.564043i	1.31091	−	0.0386476i
$214$	3.60798	−	1.11291i	0.246636	−	0.0760772i
$215$	−2.19670			−0.149814
$216$	−4.99616	+	7.54683i	−0.339946	+	0.513497i
$217$	−21.3919	+	10.3018i	−1.45217	+	0.699330i
$218$	1.46140	+	0.996367i	0.0989786	+	0.0674825i
$219$	−3.86570	−	4.56472i	−0.261220	−	0.308455i
$220$	2.61604	−	4.53112i	0.176374	−	0.305488i
$221$	−14.0791	−	13.0635i	−0.947065	−	0.878748i
$222$	−4.79225	−	7.76274i	−0.321635	−	0.521001i
$223$	−15.6661	+	14.5360i	−1.04908	+	0.973404i	−0.999678	−	0.0253749i	$-0.991922\pi$
$223$	−15.6661	+	14.5360i	−1.04908	+	0.973404i	−0.0494021	+	0.998779i	$0.515732\pi$
$224$	−4.53850	−	19.8844i	−0.303241	−	1.32859i
$225$	−1.84042	−	13.6784i	−0.122695	−	0.911895i
$226$	−0.677265	+	0.326154i	−0.0450510	+	0.0216954i
$227$	−0.204877	−	2.73390i	−0.0135982	−	0.181455i	−0.999867	−	0.0163075i	$-0.994809\pi$
$227$	−0.204877	−	2.73390i	−0.0135982	−	0.181455i	0.986269	−	0.165148i	$-0.0528101\pi$
$228$	3.04926	−	5.66040i	0.201942	−	0.374869i
$229$	4.36587	+	11.1241i	0.288505	+	0.735098i	0.999491	+	0.0318924i	$0.0101534\pi$
$229$	4.36587	+	11.1241i	0.288505	+	0.735098i	−0.710987	+	0.703206i	$0.751751\pi$
$230$	−0.366182	+	0.249659i	−0.0241454	+	0.0164620i
$231$	−13.4859	−	31.5909i	−0.887307	−	2.07853i
$232$	−4.08450	−	8.44399i	−0.268161	−	0.554375i
$233$	−16.7175			−1.09520			−0.547601	−	0.836739i	$-0.684459\pi$
$233$	−16.7175			−1.09520			−0.547601	+	0.836739i	$0.684459\pi$
$234$	0.736087	−	4.40824i	0.0481195	−	0.288176i
$235$	4.41484	−	5.53603i	0.287992	−	0.361131i
$236$	1.31307	−	3.34565i	0.0854737	−	0.217784i
$237$	4.89619	+	3.13088i	0.318041	+	0.203373i
$238$	0.872543	−	11.6433i	0.0565586	−	0.754722i
$239$	2.73070	+	6.95770i	0.176634	+	0.450056i	0.991582	−	0.129477i	$-0.0413299\pi$
$239$	2.73070	+	6.95770i	0.176634	+	0.450056i	−0.814948	+	0.579534i	$0.803235\pi$
$240$	−2.77601	−	1.23744i	−0.179190	−	0.0798767i
$241$	4.06317	−	3.77007i	0.261732	−	0.242852i	−0.538380	−	0.842702i	$-0.680964\pi$
$241$	4.06317	−	3.77007i	0.261732	−	0.242852i	0.800112	+	0.599850i	$0.204773\pi$
$242$	−2.98745	−	3.74614i	−0.192040	−	0.240811i
$243$	14.8856	+	4.62805i	0.954912	+	0.296890i
$244$	−23.7453			−1.52014
$245$	−6.86002	+	2.11604i	−0.438271	+	0.135189i
$246$	0.998698	−	5.05840i	0.0636746	−	0.322512i
$247$	−0.502556	+	6.70614i	−0.0319769	+	0.426701i
$248$	7.07543	+	6.56504i	0.449290	+	0.416881i
$249$	1.73155	+	0.209012i	0.109733	+	0.0132456i
$250$	−2.66567	+	0.822249i	−0.168592	+	0.0520036i
$251$	10.7135	+	13.4343i	0.676230	+	0.847965i	0.995001	−	0.0998666i	$-0.0318416\pi$
$251$	10.7135	+	13.4343i	0.676230	+	0.847965i	−0.318771	+	0.947832i	$0.603270\pi$
$252$	−20.0909	+	11.1786i	−1.26561	+	0.704186i
$253$	−1.57089	−	6.88254i	−0.0987613	−	0.432702i
$254$	−4.00811	−	0.604125i	−0.251491	−	0.0379062i
$255$	−4.88426	−	4.27110i	−0.305864	−	0.267466i
$256$	1.35575	−	0.924332i	0.0847341	−	0.0577708i
$257$	−13.2396	+	1.99554i	−0.825861	+	0.124479i	−0.548355	−	0.836245i	$-0.684746\pi$
$257$	−13.2396	+	1.99554i	−0.825861	+	0.124479i	−0.277506	+	0.960724i	$0.589508\pi$
$258$	2.66769	+	0.737519i	0.166083	+	0.0459159i
$259$	−3.66831	−	48.9502i	−0.227938	−	3.04162i
$260$	3.66302			0.227171
$261$	−11.9967	+	10.8203i	−0.742580	+	0.669758i
$262$	0.946320			0.0584638
$263$	−0.997767	−	13.3143i	−0.0615250	−	0.820994i	−0.939557	−	0.342392i	$-0.888763\pi$
$263$	−0.997767	−	13.3143i	−0.0615250	−	0.820994i	0.878032	−	0.478602i	$-0.158856\pi$
$264$	−9.95163	+	9.79509i	−0.612480	+	0.602846i
$265$	4.56557	−	0.688149i	0.280461	−	0.0422727i
$266$	−3.37788	+	2.30300i	−0.207111	+	0.141206i
$267$	−0.970483	+	4.91550i	−0.0593926	+	0.300823i
$268$	8.65456	+	1.30447i	0.528662	+	0.0796829i
$269$	5.22836	+	22.9069i	0.318779	+	1.39666i	0.839698	+	0.543054i	$0.182732\pi$
$269$	5.22836	+	22.9069i	0.318779	+	1.39666i	−0.520919	+	0.853606i	$0.674411\pi$
$270$	0.204675	−	1.49589i	0.0124561	−	0.0910370i
$271$	6.90238	+	8.65531i	0.419290	+	0.525773i	0.945954	−	0.324301i	$-0.105129\pi$
$271$	6.90238	+	8.65531i	0.419290	+	0.525773i	−0.526664	+	0.850073i	$0.676558\pi$
$272$	15.7254	−	4.85065i	0.953493	−	0.294114i
$273$	14.4331	−	19.2352i	0.873532	−	1.16416i
$274$	3.05287	+	2.83265i	0.184431	+	0.171126i
$275$	1.59124	−	21.2336i	0.0959555	−	1.28044i
$276$	−4.47235	+	1.52526i	−0.269204	+	0.0918098i
$277$	7.86978	−	2.42750i	0.472849	−	0.145855i	−0.0491664	−	0.998791i	$-0.515656\pi$
$277$	7.86978	−	2.42750i	0.472849	−	0.145855i	0.522016	+	0.852936i	$0.325180\pi$
$278$	0.971252			0.0582519
$279$	7.44944	−	14.8615i	0.445986	−	0.889735i
$280$	2.94090	+	3.68778i	0.175753	+	0.220387i
$281$	−4.73407	+	4.39258i	−0.282411	+	0.262039i	−0.808640	−	0.588304i	$-0.799796\pi$
$281$	−4.73407	+	4.39258i	−0.282411	+	0.262039i	0.526229	+	0.850343i	$0.323606\pi$
$282$	−7.22007	+	5.24076i	−0.429949	+	0.312083i
$283$	2.48146	+	6.32266i	0.147508	+	0.375843i	0.985462	−	0.169897i	$-0.0543436\pi$
$283$	2.48146	+	6.32266i	0.147508	+	0.375843i	−0.837954	+	0.545741i	$0.816248\pi$
$284$	1.47709	−	19.7103i	0.0876490	−	1.16959i
$285$	−0.102940	+	2.26951i	−0.00609766	+	0.134434i
$286$	2.51909	−	6.41854i	0.148957	−	0.379536i
$287$	17.2977	−	21.6906i	1.02105	−	1.28036i
$288$	11.0223	+	9.07953i	0.649493	+	0.535016i
$289$	18.1312			1.06654
$290$	1.22506	+	0.973477i	0.0719382	+	0.0571645i
$291$	−27.2409	−	3.28819i	−1.59689	−	0.192757i
$292$	−5.10373	+	3.47966i	−0.298673	+	0.203632i
$293$	0.114614	+	0.292032i	0.00669582	+	0.0170607i	0.934183	−	0.356795i	$-0.116131\pi$
$293$	0.114614	+	0.292032i	0.00669582	+	0.0170607i	−0.927487	+	0.373856i	$0.878035\pi$
$294$	9.04128	−	0.266551i	0.527298	−	0.0155456i
$295$	0.0949051	+	1.26642i	0.00552559	+	0.0737339i
$296$	−17.9788	+	8.65813i	−1.04500	+	0.503243i
$297$	20.9896	+	11.7401i	1.21794	+	0.681232i
$298$	−1.56961	−	6.87691i	−0.0909251	−	0.398369i
$299$	3.62306	−	3.36171i	0.209527	−	0.194413i
$300$	−14.2463	+	0.420004i	−0.822513	+	0.0242490i
$301$	10.9171	+	10.1295i	0.629249	+	0.583857i
$302$	0.545513	−	0.944856i	0.0313908	−	0.0543704i
$303$	−4.54323	+	12.6610i	−0.261002	+	0.727353i
$304$	−4.76092	−	3.24594i	−0.273058	−	0.186168i
$305$	7.55946	−	3.64044i	0.432853	−	0.208451i
$306$	4.49750	+	6.82668i	0.257105	+	0.390255i
$307$	17.8659			1.01966			0.509829	−	0.860276i	$-0.329709\pi$
$307$	17.8659			1.01966			0.509829	+	0.860276i	$0.329709\pi$
$308$	−33.8952	+	10.4553i	−1.93136	+	0.595745i
$309$	−10.6957	+	19.8547i	−0.608457	+	1.12949i
$310$	−1.53860	−	0.474594i	−0.0873863	−	0.0269551i
$311$	16.5871	+	5.11645i	0.940570	+	0.290127i	0.726872	−	0.686773i	$-0.240973\pi$
$311$	16.5871	+	5.11645i	0.940570	+	0.290127i	0.213697	+	0.976900i	$0.431449\pi$
$312$	−9.42248	−	2.60497i	−0.533443	−	0.147477i
$313$	14.7176	+	10.0343i	0.831891	+	0.567173i	0.902677	−	0.430318i	$-0.141599\pi$
$313$	14.7176	+	10.0343i	0.831891	+	0.567173i	−0.0707867	+	0.997491i	$0.522551\pi$
$314$	−4.08728	−	1.96833i	−0.230658	−	0.111079i
$315$	4.68224	−	6.63896i	0.263815	−	0.374063i
$316$	3.74186	−	4.69214i	0.210496	−	0.263954i
$317$	−1.25623	−	16.7633i	−0.0705571	−	0.941519i	−0.914369	−	0.404881i	$-0.867313\pi$
$317$	−1.25623	−	16.7633i	−0.0705571	−	0.941519i	0.843812	−	0.536638i	$-0.180306\pi$
$318$	−5.77550	−	0.697147i	−0.323874	−	0.0390941i
$319$	−21.5637	+	12.4998i	−1.20733	+	0.699855i
$320$	−1.06319	+	1.84150i	−0.0594341	+	0.102943i
$321$	−12.6285	+	6.54680i	−0.704852	+	0.365407i
$322$	2.97107	+	0.447817i	0.165571	+	0.0249559i
$323$	−7.66956	−	9.61732i	−0.426745	−	0.535122i
$324$	6.35324	−	14.7909i	0.352958	−	0.821718i
$325$	13.4312	−	6.46813i	0.745030	−	0.358787i
$326$	3.49378	+	0.526603i	0.193503	+	0.0291658i
$327$	−6.08622	−	2.71302i	−0.336569	−	0.150030i
$328$	−10.7771	−	3.32430i	−0.595067	−	0.183554i
$329$	−47.4686	+	7.15474i	−2.61703	+	0.394454i
$330$	0.786742	−	2.19247i	0.0433087	−	0.120692i
$331$	−1.64946	−	2.85695i	−0.0906627	−	0.157032i	0.817127	−	0.576457i	$-0.195565\pi$
$331$	−1.64946	−	2.85695i	−0.0906627	−	0.157032i	−0.907790	+	0.419425i	$0.862232\pi$
$332$	0.400781	−	1.75594i	0.0219957	−	0.0963695i
$333$	22.9746	+	25.5618i	1.25900	+	1.40078i
$334$	8.62881	−	4.15542i	0.472148	−	0.227374i
$335$	−2.95523	+	0.911567i	−0.161461	+	0.0498042i
$336$	8.08987	+	18.9506i	0.441339	+	1.03384i
$337$	−4.42223	−	4.10323i	−0.240894	−	0.223517i	0.550481	−	0.834848i	$-0.314444\pi$
$337$	−4.42223	−	4.10323i	−0.240894	−	0.223517i	−0.791376	+	0.611330i	$0.790635\pi$
$338$	−1.13654	+	0.171305i	−0.0618194	+	0.00931777i
$339$	2.29185	−	1.66357i	0.124476	−	0.0903525i
$340$	−4.91164	+	4.55734i	−0.266371	+	0.247156i
$341$	15.9910	−	20.0520i	0.865958	−	1.08588i
$342$	0.886975	−	2.72155i	0.0479621	−	0.147165i
$343$	16.8272	+	8.10356i	0.908585	+	0.437551i
$344$	2.21182	−	5.63561i	0.119253	−	0.303852i
$345$	1.18996	−	1.17124i	0.0640652	−	0.0630575i
$346$	−0.187875	+	0.128091i	−0.0101002	+	0.00688622i
$347$	−10.2358	+	17.7289i	−0.549485	+	0.951736i	0.448825	+	0.893620i	$0.351843\pi$
$347$	−10.2358	+	17.7289i	−0.549485	+	0.951736i	−0.998310	+	0.0581160i	$0.981491\pi$
$348$	9.82358	+	13.4844i	0.526599	+	0.722837i
$349$	−5.92429	−	10.2612i	−0.317120	−	0.549268i	0.662766	−	0.748827i	$-0.269383\pi$
$349$	−5.92429	−	10.2612i	−0.317120	−	0.549268i	−0.979886	+	0.199559i	$0.936049\pi$
$350$	8.16517	+	3.93214i	0.436447	+	0.210182i
$351$	0.229305	+	16.8359i	0.0122394	+	0.898634i
$352$	13.7365	+	17.2250i	0.732159	+	0.918098i
$353$	1.00294	+	13.3833i	0.0533810	+	0.712319i	0.958123	+	0.286358i	$0.0924448\pi$
$353$	1.00294	+	13.3833i	0.0533810	+	0.712319i	−0.904742	+	0.425961i	$0.859936\pi$
$354$	0.309933	−	1.56981i	0.0164728	−	0.0834346i
$355$	2.55160	+	6.50137i	0.135425	+	0.345057i
$356$	4.94419	+	1.52508i	0.262041	+	0.0808290i
$357$	4.57841	+	43.7488i	0.242315	+	2.31543i
$358$	1.28413	−	3.27191i	0.0678685	−	0.172926i
$359$	−1.37455	+	6.02228i	−0.0725457	+	0.317844i	−0.998161	−	0.0606228i	$-0.980691\pi$
$359$	−1.37455	+	6.02228i	−0.0725457	+	0.317844i	0.925615	+	0.378466i	$0.123548\pi$
$360$	−3.20769	−	0.785837i	−0.169060	−	0.0414172i
$361$	3.26947	−	14.3245i	0.172077	−	0.753920i
$362$	0.905614	+	0.617437i	0.0475980	+	0.0324518i
$363$	13.5887	+	11.8828i	0.713221	+	0.623685i
$364$	−18.2043	−	16.8911i	−0.954164	−	0.885335i
$365$	1.09133	−	1.89024i	0.0571228	−	0.0989396i
$366$	−10.4025	+	1.88297i	−0.543747	+	0.0984245i
$367$	−5.52750	+	14.0838i	−0.288533	+	0.735170i	0.710957	+	0.703236i	$0.248262\pi$
$367$	−5.52750	+	14.0838i	−0.288533	+	0.735170i	−0.999490	+	0.0319348i	$0.989833\pi$
$368$	0.942343	+	4.12867i	0.0491230	+	0.215222i
$369$	−0.307944	+	19.4224i	−0.0160309	+	1.01109i
$370$	2.07550	−	2.60259i	0.107900	−	0.135302i
$371$	−25.8629	−	17.6331i	−1.34274	−	0.915463i
$372$	−14.4629	−	9.24837i	−0.749868	−	0.479506i
$373$	25.2371	−	3.80388i	1.30673	−	0.196958i	0.541491	−	0.840706i	$-0.317860\pi$
$373$	25.2371	−	3.80388i	1.30673	−	0.196958i	0.765237	+	0.643749i	$0.222622\pi$
$374$	4.60782	+	11.7405i	0.238265	+	0.607089i
$375$	9.33024	−	4.83695i	0.481812	−	0.249779i
$376$	9.75740	+	16.9003i	0.503200	+	0.871567i
$377$	−15.1272	−	8.69869i	−0.779091	−	0.448005i
$378$	−7.91510	+	6.49038i	−0.407109	+	0.333829i
$379$	16.7038	+	8.04413i	0.858017	+	0.413199i	0.810547	−	0.585674i	$-0.199170\pi$
$379$	16.7038	+	8.04413i	0.858017	+	0.413199i	0.0474697	+	0.998873i	$0.484884\pi$
$380$	2.31986	+	0.349662i	0.119006	+	0.0179373i
$381$	15.2640	−	0.450007i	0.781999	−	0.0230545i
$382$	4.25812	−	2.90314i	0.217865	−	0.148538i
$383$	2.73284	−	36.4673i	0.139642	−	1.86339i	−0.285650	−	0.958334i	$-0.592210\pi$
$383$	2.73284	−	36.4673i	0.139642	−	1.86339i	0.425292	−	0.905056i	$-0.360171\pi$
$384$	13.6613	−	13.4464i	0.697151	−	0.686185i
$385$	9.18782	−	8.52505i	0.468255	−	0.434477i
$386$	0.829023	+	3.63219i	0.0421961	+	0.184873i
$387$	−10.3844	−	0.943971i	−0.527869	−	0.0479847i
$388$	−6.30512	+	27.6245i	−0.320094	+	1.40242i
$389$	−18.5256	−	32.0873i	−0.939286	−	1.62689i	−0.766807	−	0.641878i	$-0.778156\pi$
$389$	−18.5256	−	32.0873i	−0.939286	−	1.62689i	−0.172479	−	0.985013i	$-0.555178\pi$
$390$	1.60472	−	0.290473i	0.0812583	−	0.0147087i
$391$	−0.675599	+	9.01524i	−0.0341665	+	0.455920i
$392$	1.47855	−	19.7299i	0.0746780	−	0.996509i
$393$	−3.50814	+	0.635014i	−0.176962	+	0.0320322i
$394$	2.56986	+	4.45113i	0.129468	+	0.224245i
$395$	−0.471881	+	2.06745i	−0.0237429	+	0.104025i
$396$	14.3138	−	20.2956i	0.719298	−	1.01989i
$397$	−8.54068	−	37.4192i	−0.428645	−	1.87801i	−0.476524	−	0.879161i	$-0.658104\pi$
$397$	−8.54068	−	37.4192i	−0.428645	−	1.87801i	0.0478799	−	0.998853i	$-0.484754\pi$
$398$	1.02131	−	0.947641i	0.0511939	−	0.0475010i
$399$	10.9769	−	10.8042i	0.549531	−	0.540887i
$400$	−0.954549	+	12.7376i	−0.0477274	+	0.636878i
$401$	17.2764	−	11.7789i	0.862744	−	0.588209i	−0.0490782	−	0.998795i	$-0.515628\pi$
$401$	17.2764	−	11.7789i	0.862744	−	0.588209i	0.911822	+	0.410586i	$0.134676\pi$
$402$	3.89489	−	0.114827i	0.194260	−	0.00572707i
$403$	17.7555	+	2.67620i	0.884462	+	0.133311i
$404$	12.5152	+	6.02701i	0.622655	+	0.299855i
$405$	0.245037	+	5.68282i	0.0121760	+	0.282381i
$406$	−1.59930	−	10.4870i	−0.0793721	−	0.520461i
$407$	26.5123	+	45.9206i	1.31416	+	2.27620i
$408$	15.8753	−	8.23001i	0.785944	−	0.407446i
$409$	−2.81596	−	7.17495i	−0.139240	−	0.354778i	0.844195	−	0.536035i	$-0.180079\pi$
$409$	−2.81596	−	7.17495i	−0.139240	−	0.354778i	−0.983436	+	0.181257i	$0.941983\pi$
$410$	1.86039	−	0.280408i	0.0918779	−	0.0138484i
$411$	−13.2182	−	8.45244i	−0.652006	−	0.416928i
$412$	19.2423	+	13.1191i	0.947998	+	0.646334i
$413$	5.36812	−	6.73142i	0.264148	−	0.331231i
$414$	−1.83832	+	1.02285i	−0.0903487	+	0.0502702i
$415$	0.141616	+	0.620458i	0.00695163	+	0.0304571i
$416$	−5.63522	+	14.3583i	−0.276289	+	0.703973i
$417$	−3.60057	+	0.651745i	−0.176321	+	0.0319161i
$418$	2.20808	−	3.82451i	0.108001	−	0.187063i
$419$	−15.2428	−	14.1433i	−0.744660	−	0.690943i	0.213575	−	0.976927i	$-0.431489\pi$
$419$	−15.2428	−	14.1433i	−0.744660	−	0.690943i	−0.958235	+	0.285984i	$0.907680\pi$
$420$	−6.31533	−	5.52252i	−0.308156	−	0.269471i
$421$	−3.37360	−	2.30008i	−0.164419	−	0.112099i	0.478315	−	0.878188i	$-0.341248\pi$
$421$	−3.37360	−	2.30008i	−0.164419	−	0.112099i	−0.642734	+	0.766089i	$0.722200\pi$
$422$	−0.826544	+	3.62133i	−0.0402355	+	0.176283i
$423$	23.2491	−	24.2731i	1.13041	−	1.18020i
$424$	−2.83154	+	12.4058i	−0.137512	+	0.602479i
$425$	−9.96222	+	25.3833i	−0.483239	+	1.23127i
$426$	−0.915915	−	8.75197i	−0.0443762	−	0.424034i
$427$	−54.3555	−	16.7665i	−2.63045	−	0.811386i
$428$	5.36659	+	13.6738i	0.259404	+	0.660950i
$429$	−5.03155	+	25.4848i	−0.242926	+	1.23042i
$430$	0.0754724	+	1.00711i	0.00363960	+	0.0485671i
$431$	14.9959	+	18.8043i	0.722329	+	0.905772i	0.998467	−	0.0553458i	$-0.0176261\pi$
$431$	14.9959	+	18.8043i	0.722329	+	0.905772i	−0.276138	+	0.961118i	$0.589055\pi$
$432$	−12.5912	−	7.04264i	−0.605792	−	0.338839i
$433$	−24.5894	−	11.8416i	−1.18169	−	0.569071i	−0.263286	−	0.964718i	$-0.584806\pi$
$433$	−24.5894	−	11.8416i	−1.18169	−	0.569071i	−0.918403	+	0.395646i	$0.870521\pi$
$434$	5.45795	+	9.45345i	0.261990	+	0.453780i
$435$	−5.19472	−	2.78675i	−0.249068	−	0.133615i
$436$	−3.44060	+	5.95929i	−0.164775	+	0.285398i
$437$	2.61545	−	1.78318i	0.125114	−	0.0853012i
$438$	−1.95994	+	1.92911i	−0.0936497	+	0.0921766i
$439$	6.61202	−	16.8472i	0.315575	−	0.804071i	−0.681792	−	0.731546i	$-0.738799\pi$
$439$	6.61202	−	16.8472i	0.315575	−	0.804071i	0.997367	−	0.0725250i	$-0.0231057\pi$
$440$	−4.59058	−	2.21071i	−0.218847	−	0.105391i
$441$	−33.3384	+	7.05516i	−1.58754	+	0.335960i
$442$	−5.50544	+	6.90360i	−0.261867	+	0.328371i
$443$	23.8952	−	22.1715i	1.13530	−	1.05340i	0.137275	−	0.990533i	$-0.456165\pi$
$443$	23.8952	−	22.1715i	1.13530	−	1.05340i	0.998022	−	0.0628690i	$-0.0200250\pi$
$444$	28.7228	−	20.8487i	1.36313	−	0.989438i
$445$	−1.80783	+	0.272486i	−0.0856992	+	0.0129171i
$446$	7.20248	+	6.68292i	0.341047	+	0.316446i
$447$	10.4334	+	24.4404i	0.493484	+	1.15599i
$448$	13.7754	−	4.24914i	0.650825	−	0.200753i
$449$	12.4625	−	6.00162i	0.588141	−	0.283234i	−0.116051	−	0.993243i	$-0.537024\pi$
$449$	12.4625	−	6.00162i	0.588141	−	0.283234i	0.704192	+	0.710009i	$0.251309\pi$
$450$	−6.20783	+	1.31372i	−0.292640	+	0.0619292i
$451$	−6.66862	+	29.2171i	−0.314013	+	1.37578i
$452$	−1.46224	−	2.53267i	−0.0687780	−	0.119127i
$453$	−1.38826	+	3.86877i	−0.0652262	+	0.181771i
$454$	−1.24635	+	0.187858i	−0.0584943	+	0.00881660i
$455$	8.38507	+	2.58645i	0.393098	+	0.121255i
$456$	−5.71876	−	2.54922i	−0.267805	−	0.119378i
$457$	−10.0150	−	1.50952i	−0.468483	−	0.0706124i	−0.0894411	−	0.995992i	$-0.528508\pi$
$457$	−10.0150	−	1.50952i	−0.468483	−	0.0706124i	−0.379041	+	0.925380i	$0.623746\pi$
$458$	4.94997	−	2.38378i	0.231297	−	0.111387i
$459$	−21.2538	−	22.2895i	−0.992042	−	1.04038i
$460$	−1.07503	−	1.34805i	−0.0501236	−	0.0628530i
$461$	−26.2805	−	3.96115i	−1.22401	−	0.184489i	−0.494936	−	0.868929i	$-0.664809\pi$
$461$	−26.2805	−	3.96115i	−1.22401	−	0.184489i	−0.729069	+	0.684440i	$0.760047\pi$
$462$	−14.0199	+	7.26816i	−0.652266	+	0.338146i
$463$	8.61852	−	14.9277i	0.400537	−	0.693750i	−0.593254	−	0.805015i	$-0.702157\pi$
$463$	8.61852	−	14.9277i	0.400537	−	0.693750i	0.993791	+	0.111266i	$0.0354904\pi$
$464$	12.9355	−	7.49834i	0.600517	−	0.348102i
$465$	6.02226	+	0.726933i	0.279275	+	0.0337107i
$466$	0.574366	+	7.66438i	0.0266070	+	0.355046i
$467$	−23.7679	+	29.8040i	−1.09985	+	1.37917i	−0.181499	+	0.983391i	$0.558095\pi$
$467$	−23.7679	+	29.8040i	−1.09985	+	1.37917i	−0.918348	+	0.395774i	$0.870476\pi$
$468$	17.3161	+	1.57408i	0.800436	+	0.0727619i
$469$	18.8902	+	9.09703i	0.872267	+	0.420062i
$470$	−2.68975	−	1.83384i	−0.124069	−	0.0845888i
$471$	16.4729	+	4.55416i	0.759032	+	0.209845i
$472$	−3.34454	−	1.03165i	−0.153945	−	0.0474857i
$473$	−15.3724	−	4.74175i	−0.706822	−	0.218026i
$474$	1.26718	−	2.35229i	0.0582034	−	0.108044i
$475$	9.12365	−	2.81427i	0.418622	−	0.129128i
$476$	45.4246			2.08203
$477$	21.8784	−	1.29114i	1.00174	−	0.0591172i
$478$	3.09604	−	1.49097i	0.141609	−	0.0681955i
$479$	−3.56305	−	2.42925i	−0.162800	−	0.110995i	0.479180	−	0.877717i	$-0.340934\pi$
$479$	−3.56305	−	2.42925i	−0.162800	−	0.110995i	−0.641980	+	0.766722i	$0.721887\pi$
$480$	−1.75994	+	4.90457i	−0.0803301	+	0.223862i
$481$	−18.5615	+	32.1494i	−0.846329	+	1.46589i
$482$	−1.86804	−	1.73329i	−0.0850868	−	0.0789491i
$483$	−11.3147	+	0.333574i	−0.514835	+	0.0151781i
$484$	13.6649	−	12.6791i	0.621130	−	0.576325i
$485$	−2.22791	−	9.76110i	−0.101164	−	0.443229i
$486$	1.61037	−	6.98351i	0.0730478	−	0.316779i
$487$	5.97616	−	2.87797i	0.270806	−	0.130413i	−0.293553	−	0.955943i	$-0.594838\pi$
$487$	5.97616	−	2.87797i	0.270806	−	0.130413i	0.564359	+	0.825530i	$0.309123\pi$
$488$	1.72805	+	23.0592i	0.0782249	+	1.04384i
$489$	−13.3053	+	0.392261i	−0.601686	+	0.0177386i
$490$	1.20582	+	3.07237i	0.0544732	+	0.138795i
$491$	5.51204	−	3.75804i	0.248755	−	0.169598i	−0.432524	−	0.901623i	$-0.642377\pi$
$491$	5.51204	−	3.75804i	0.248755	−	0.169598i	0.681278	+	0.732025i	$0.261424\pi$
$492$	19.9148	+	2.40387i	0.897828	+	0.108375i
$493$	31.1061	−	7.15666i	1.40095	−	0.322320i
$494$	3.09179			0.139106
$495$	−1.44533	+	8.65573i	−0.0649629	+	0.389046i
$496$	−9.59259	+	12.0287i	−0.430720	+	0.540106i
$497$	17.2986	−	44.0762i	0.775950	−	1.97709i
$498$	0.0363332	−	0.801034i	0.00162813	−	0.0358952i
$499$	1.20171	−	16.0357i	0.0537960	−	0.717858i	−0.903470	−	0.428651i	$-0.858989\pi$
$499$	1.20171	−	16.0357i	0.0537960	−	0.717858i	0.957266	−	0.289208i	$-0.0933918\pi$
$500$	−3.96497	−	10.1026i	−0.177319	−	0.451801i
$501$	−29.1998	+	21.1949i	−1.30455	+	0.946920i
$502$	5.79105	−	5.37331i	0.258467	−	0.239823i
$503$	−3.00007	−	3.76197i	−0.133767	−	0.167738i	0.710437	−	0.703761i	$-0.248497\pi$
$503$	−3.00007	−	3.76197i	−0.133767	−	0.167738i	−0.844203	+	0.536023i	$0.819926\pi$
$504$	12.3177	+	18.6969i	0.548674	+	0.832824i
$505$	−4.90831			−0.218417
$506$	−3.10142	+	0.956662i	−0.137875	+	0.0425288i
$507$	4.09834	−	1.39771i	0.182014	−	0.0620744i
$508$	1.17845	−	15.7254i	0.0522855	−	0.697701i
$509$	−3.75614	−	3.48519i	−0.166488	−	0.154478i	0.592529	−	0.805549i	$-0.298130\pi$
$509$	−3.75614	−	3.48519i	−0.166488	−	0.154478i	−0.759017	+	0.651071i	$0.774320\pi$
$510$	−1.79033	+	2.38600i	−0.0792773	+	0.105654i
$511$	−14.1400	+	4.36161i	−0.625516	+	0.192946i
$512$	−14.2707	−	17.8949i	−0.630683	−	0.790851i
$513$	−1.46189	+	10.6844i	−0.0645438	+	0.471726i
$514$	1.36976	+	6.00130i	0.0604174	+	0.264706i
$515$	−8.13722	−	1.22649i	−0.358569	−	0.0540456i
$516$	−2.08567	+	10.5639i	−0.0918165	+	0.465050i
$517$	42.8446	−	29.2110i	1.88430	−	1.28470i
$518$	−22.3159	+	3.36358i	−0.980503	+	0.147787i
$519$	0.610525	−	0.600922i	0.0267991	−	0.0263776i
$520$	−0.266574	−	3.55718i	−0.0116900	−	0.155993i
$521$	−33.7915			−1.48043			−0.740216	−	0.672369i	$-0.765277\pi$
$521$	−33.7915			−1.48043			−0.740216	+	0.672369i	$0.765277\pi$
$522$	5.37287	+	5.12832i	0.235164	+	0.224460i
$523$	9.53593			0.416977			0.208488	−	0.978025i	$-0.433146\pi$
$523$	9.53593			0.416977			0.208488	+	0.978025i	$0.433146\pi$
$524$	0.275127	+	3.67132i	0.0120190	+	0.160382i
$525$	−32.9080	−	9.09787i	−1.43622	−	0.397063i
$526$	−6.06983	+	0.914880i	−0.264657	+	0.0398907i
$527$	−27.1374	+	18.5019i	−1.18212	+	0.805957i
$528$	−16.7552	−	14.6518i	−0.729175	−	0.637636i
$529$	20.4426	+	3.08123i	0.888811	+	0.133967i
$530$	−0.472351	−	2.06951i	−0.0205176	−	0.0898936i
$531$	−0.0955667	+	6.02749i	−0.00414724	+	0.261571i
$532$	−9.91671	−	12.4352i	−0.429944	−	0.539133i
$533$	−20.0491	+	6.18431i	−0.868421	+	0.267872i
$534$	2.28692	+	0.276049i	0.0989647	+	0.0119458i
$535$	−3.80486	−	3.53039i	−0.164498	−	0.152632i
$536$	0.636944	−	8.49943i	0.0275118	−	0.367119i
$537$	−2.56489	+	12.9911i	−0.110683	+	0.560609i
$538$	10.3224	−	3.18403i	0.445029	−	0.137273i
$539$	−52.5735			−2.26450
$540$	5.86292	+	0.359145i	0.252300	+	0.0154551i
$541$	18.8873	+	23.6840i	0.812030	+	1.01825i	0.999353	+	0.0359555i	$0.0114474\pi$
$541$	18.8873	+	23.6840i	0.812030	+	1.01825i	−0.187323	+	0.982298i	$0.559981\pi$
$542$	3.73100	−	3.46186i	0.160260	−	0.148700i
$543$	−3.77156	−	1.68123i	−0.161853	−	0.0721483i
$544$	−10.3077	−	26.2636i	−0.441940	−	1.12604i
$545$	0.181703	−	2.42466i	0.00778332	−	0.103861i
$546$	−9.31450	−	5.95619i	−0.398624	−	0.254901i
$547$	−12.0057	+	30.5899i	−0.513325	+	1.30793i	0.405798	+	0.913963i	$0.366994\pi$
$547$	−12.0057	+	30.5899i	−0.513325	+	1.30793i	−0.919124	+	0.393969i	$0.871102\pi$
$548$	−10.1019	+	12.6674i	−0.431531	+	0.541123i
$549$	37.2999	−	13.9609i	1.59192	−	0.595836i
$550$	−9.78953			−0.417427
$551$	−8.74998	−	6.95303i	−0.372762	−	0.296209i
$552$	1.80666	+	4.23212i	0.0768965	+	0.180131i
$553$	11.8786	−	8.09872i	0.505131	−	0.344393i
$554$	−1.38331	−	3.52460i	−0.0587710	−	0.149746i
$555$	−5.94773	+	11.0409i	−0.252467	+	0.468660i
$556$	0.282376	+	3.76804i	0.0119754	+	0.159801i
$557$	−2.62367	+	1.26349i	−0.111168	+	0.0535359i	−0.488641	−	0.872485i	$-0.662507\pi$
$557$	−2.62367	+	1.26349i	−0.111168	+	0.0535359i	0.377473	+	0.926021i	$0.376793\pi$
$558$	−7.06940	−	2.90470i	−0.299272	−	0.122966i
$559$	−2.50618	−	10.9803i	−0.106000	−	0.464417i
$560$	−5.51156	+	5.11398i	−0.232906	+	0.216105i
$561$	−24.9602	−	40.4318i	−1.05382	−	1.70703i
$562$	2.17649	+	2.01948i	0.0918095	+	0.0851868i
$563$	−7.13090	+	12.3511i	−0.300531	+	0.520536i	−0.976256	−	0.216618i	$-0.930497\pi$
$563$	−7.13090	+	12.3511i	−0.300531	+	0.520536i	0.675725	+	0.737154i	$0.263831\pi$
$564$	−22.4310	−	26.4871i	−0.944516	−	1.11531i
$565$	0.853803	+	0.582113i	0.0359198	+	0.0244897i
$566$	2.81345	−	1.35489i	0.118258	−	0.0569502i
$567$	24.9871	−	29.3721i	1.04936	−	1.23351i
$568$	−19.2483			−0.807642
$569$	33.3362	−	10.2828i	1.39753	−	0.431079i	0.497707	−	0.867345i	$-0.334175\pi$
$569$	33.3362	−	10.2828i	1.39753	−	0.431079i	0.899818	+	0.436266i	$0.143699\pi$
$570$	1.04403	−	0.0307795i	0.0437295	−	0.00128921i
$571$	−24.3913	−	7.52372i	−1.02074	−	0.314858i	−0.261180	−	0.965290i	$-0.584112\pi$
$571$	−24.3913	−	7.52372i	−1.02074	−	0.314858i	−0.759564	+	0.650432i	$0.774588\pi$
$572$	25.6336	+	7.90691i	1.07179	+	0.330604i
$573$	−13.8374	+	13.6197i	−0.578064	+	0.568971i
$574$	−10.5387	−	7.18514i	−0.439875	−	0.299902i
$575$	−6.32218	−	3.04460i	−0.263653	−	0.126969i
$576$	−5.81730	+	8.24836i	−0.242388	+	0.343682i
$577$	−21.7344	+	27.2540i	−0.904813	+	1.13460i	0.0855814	+	0.996331i	$0.472725\pi$
$577$	−21.7344	+	27.2540i	−0.904813	+	1.13460i	−0.990395	+	0.138269i	$0.955846\pi$
$578$	−0.622937	−	8.31252i	−0.0259108	−	0.345755i
$579$	−5.51063	−	12.9087i	−0.229014	−	0.536468i
$580$	−3.42051	+	5.03574i	−0.142029	+	0.209098i
$581$	2.15729	−	3.73654i	0.0894996	−	0.155018i
$582$	−0.571597	+	12.6019i	−0.0236935	+	0.522367i
$583$	33.4349	+	5.03951i	1.38473	+	0.208715i
$584$	3.75054	+	4.70303i	0.155199	+	0.194613i
$585$	−5.75401	+	2.15365i	−0.237899	+	0.0890425i
$586$	0.129948	−	0.0625797i	0.00536811	−	0.00258514i
$587$	−42.8185	−	6.45385i	−1.76731	−	0.266379i	−0.816766	−	0.576969i	$-0.804235\pi$
$587$	−42.8185	−	6.45385i	−1.76731	−	0.266379i	−0.950544	+	0.310590i	$0.899473\pi$
$588$	3.66271	+	34.9988i	0.151048	+	1.44333i
$589$	10.9894	+	3.38977i	0.452809	+	0.139673i
$590$	0.577347	−	0.0870211i	0.0237690	−	0.00358260i
$591$	−12.5137	−	14.7765i	−0.514745	−	0.607824i
$592$	−15.9041	−	27.5467i	−0.653654	−	1.13216i
$593$	−2.35323	+	10.3102i	−0.0966354	+	0.423387i	−0.999985	−	0.00551808i	$-0.998244\pi$
$593$	−2.35323	+	10.3102i	−0.0966354	+	0.423387i	0.903349	+	0.428906i	$0.141101\pi$
$594$	4.66129	−	10.0263i	0.191255	−	0.411385i
$595$	−14.4612	+	6.96415i	−0.592852	+	0.285502i
$596$	26.2231	−	8.08876i	1.07414	−	0.331329i
$597$	−3.15025	+	4.19838i	−0.128931	+	0.171828i
$598$	−1.66570	−	1.54554i	−0.0681155	−	0.0632020i
$599$	20.2100	−	3.04617i	0.825760	−	0.124463i	0.277452	−	0.960740i	$-0.410510\pi$
$599$	20.2100	−	3.04617i	0.825760	−	0.124463i	0.548308	+	0.836276i	$0.315272\pi$
$600$	1.44464	+	13.8041i	0.0589770	+	0.563552i
$601$	−15.0185	+	13.9351i	−0.612617	+	0.568425i	−0.924255	−	0.381775i	$-0.875313\pi$
$601$	−15.0185	+	13.9351i	−0.612617	+	0.568425i	0.311638	+	0.950201i	$0.399122\pi$
$602$	4.26895	−	5.35309i	0.173989	−	0.218176i
$603$	−14.3619	+	3.03929i	−0.584860	+	0.123770i
$604$	3.82424	+	1.84166i	0.155606	+	0.0749359i
$605$	−2.40643	+	6.13148i	−0.0978353	+	0.249280i
$606$	5.96068	+	1.64791i	0.242136	+	0.0669418i
$607$	15.0908	−	10.2887i	0.612515	−	0.417606i	−0.216935	−	0.976186i	$-0.569606\pi$
$607$	15.0908	−	10.2887i	0.612515	−	0.417606i	0.829451	+	0.558580i	$0.188654\pi$
$608$	−4.93948	+	8.55544i	−0.200323	+	0.346969i
$609$	12.9660	+	37.8036i	0.525408	+	1.53188i
$610$	−1.92873	−	3.34066i	−0.0780921	−	0.135259i
$611$	32.7089	+	15.7518i	1.32326	+	0.637248i
$612$	−25.1770	+	19.4331i	−1.01772	+	0.785536i
$613$	−26.7926	−	33.5968i	−1.08214	−	1.35696i	−0.929560	−	0.368672i	$-0.879813\pi$
$613$	−26.7926	−	33.5968i	−1.08214	−	1.35696i	−0.152582	−	0.988291i	$-0.548759\pi$
$614$	−0.613819	−	8.19084i	−0.0247717	−	0.330556i
$615$	−6.70854	+	2.28790i	−0.270515	+	0.0922569i
$616$	12.6199	+	32.1549i	0.508469	+	1.29556i
$617$	3.39116	+	1.04603i	0.136523	+	0.0421118i	0.362264	−	0.932076i	$-0.382004\pi$
$617$	3.39116	+	1.04603i	0.136523	+	0.0421118i	−0.225741	+	0.974187i	$0.572480\pi$
$618$	9.47011	+	4.22144i	0.380944	+	0.169811i
$619$	4.85694	−	12.3753i	0.195217	−	0.497405i	−0.799427	−	0.600763i	$-0.794864\pi$
$619$	4.85694	−	12.3753i	0.195217	−	0.497405i	0.994644	+	0.103358i	$0.0329588\pi$
$620$	1.39390	−	6.10707i	0.0559803	−	0.245266i
$621$	6.12856	−	5.02542i	0.245931	−	0.201663i
$622$	1.77582	−	7.78038i	0.0712039	−	0.311965i
$623$	10.2409	+	6.98215i	0.410294	+	0.279734i
$624$	3.01831	−	15.2877i	0.120829	−	0.611999i
$625$	−14.0511	−	13.0375i	−0.562045	−	0.521502i
$626$	4.09472	−	7.09226i	0.163658	−	0.283464i
$627$	−5.61928	+	15.6597i	−0.224412	+	0.625387i
$628$	6.44796	−	16.4291i	0.257302	−	0.655594i
$629$	−15.1100	−	66.2013i	−0.602476	−	2.63962i
$630$	−3.20459	−	1.91854i	−0.127674	−	0.0764366i
$631$	14.2958	−	17.9264i	0.569107	−	0.713637i	−0.411105	−	0.911588i	$-0.634857\pi$
$631$	14.2958	−	17.9264i	0.569107	−	0.713637i	0.980212	+	0.197950i	$0.0634285\pi$
$632$	−4.82888	−	3.29227i	−0.192082	−	0.130960i
$633$	0.634076	−	13.9794i	0.0252023	−	0.555631i
$634$	−7.64219	+	1.15187i	−0.303510	+	0.0457468i
$635$	2.03573	+	5.18695i	0.0807854	+	0.205838i
$636$	1.02550	−	22.6091i	0.0406638	−	0.896510i
$637$	−18.4036	−	31.8759i	−0.729175	−	1.26297i
$638$	6.47157	+	9.45670i	0.256212	+	0.374394i
$639$	9.26831	+	31.8302i	0.366649	+	1.25918i
$640$	6.30182	+	3.03479i	0.249101	+	0.119961i
$641$	39.2891	+	5.92188i	1.55183	+	0.233900i	0.868305	−	0.496030i	$-0.165210\pi$
$641$	39.2891	+	5.92188i	1.55183	+	0.233900i	0.683521	+	0.729931i	$0.260448\pi$
$642$	3.43535	+	5.56476i	0.135582	+	0.219624i
$643$	−2.63696	+	1.79785i	−0.103991	+	0.0709001i	−0.614199	−	0.789151i	$-0.710521\pi$
$643$	−2.63696	+	1.79785i	−0.103991	+	0.0709001i	0.510208	+	0.860051i	$0.329568\pi$
$644$	−0.873547	+	11.6567i	−0.0344226	+	0.459337i
$645$	−0.955593	−	3.68285i	−0.0376264	−	0.145012i
$646$	−4.14569	+	3.84664i	−0.163110	+	0.151344i
$647$	2.72386	+	11.9340i	0.107086	+	0.469175i	0.999827	+	0.0186044i	$0.00592230\pi$
$647$	2.72386	+	11.9340i	0.107086	+	0.469175i	−0.892741	+	0.450571i	$0.851221\pi$
$648$	−14.8259	−	5.09327i	−0.582417	−	0.200083i
$649$	−2.06952	+	9.06717i	−0.0812359	+	0.355918i
$650$	−3.42686	−	5.93550i	−0.134413	−	0.232809i
$651$	−26.5770	−	31.3828i	−1.04163	−	1.22999i
$652$	−1.02723	+	13.7075i	−0.0402295	+	0.536826i
$653$	−2.44778	+	32.6634i	−0.0957890	+	1.27822i	0.717583	+	0.696473i	$0.245248\pi$
$653$	−2.44778	+	32.6634i	−0.0957890	+	1.27822i	−0.813372	+	0.581743i	$0.802371\pi$
$654$	−1.03472	+	2.88352i	−0.0404606	+	0.112755i
$655$	−0.650446	−	1.12661i	−0.0254150	−	0.0440202i
$656$	4.00035	−	17.5267i	0.156187	−	0.684302i
$657$	5.97128	−	8.46669i	0.232962	−	0.330317i
$658$	4.91107	+	21.5168i	0.191454	+	0.838813i
$659$	−6.09596	+	5.65623i	−0.237465	+	0.220335i	−0.789924	−	0.613205i	$-0.789880\pi$
$659$	−6.09596	+	5.65623i	−0.237465	+	0.220335i	0.552459	+	0.833540i	$0.313690\pi$
$660$	8.73459	+	2.41479i	0.339993	+	0.0939957i
$661$	−1.43841	+	19.1942i	−0.0559475	+	0.746568i	0.896729	+	0.442581i	$0.145937\pi$
$661$	−1.43841	+	19.1942i	−0.0559475	+	0.746568i	−0.952676	+	0.303987i	$0.901682\pi$
$662$	−1.25314	+	0.854375i	−0.0487046	+	0.0332062i
$663$	15.7769	−	29.2869i	0.612722	−	1.13741i
$664$	−1.73437	−	0.261414i	−0.0673064	−	0.0101448i
$665$	5.06351	+	2.43846i	0.196355	+	0.0945594i
$666$	10.9298	−	11.4112i	0.423521	−	0.442177i
$667$	1.23832	+	8.11994i	0.0479479	+	0.314405i
$668$	18.6299	+	32.2680i	0.720813	+	1.24849i
$669$	−31.1851	−	19.9414i	−1.20568	−	0.770980i
$670$	0.519453	+	1.32355i	0.0200682	+	0.0511330i
$671$	60.7587	−	9.15789i	2.34556	−	0.353537i
$672$	31.3626	−	16.2589i	1.20984	−	0.627201i
$673$	−38.1105	−	25.9833i	−1.46905	−	1.00158i	−0.992475	−	0.122451i	$-0.960925\pi$
$673$	−38.1105	−	25.9833i	−1.46905	−	1.00158i	−0.476578	−	0.879132i	$-0.658123\pi$
$674$	−1.72925	+	2.16841i	−0.0666081	+	0.0835240i
$675$	22.1317	−	9.03580i	0.851851	−	0.347788i
$676$	−0.995020	−	4.35947i	−0.0382700	−	0.167672i
$677$	−12.2058	+	31.0999i	−0.469107	+	1.19527i	0.479141	+	0.877738i	$0.340948\pi$
$677$	−12.2058	+	31.0999i	−0.469107	+	1.19527i	−0.948249	+	0.317528i	$0.897147\pi$
$678$	−0.841426	−	0.993577i	−0.0323148	−	0.0381581i
$679$	−33.9387	+	58.7836i	−1.30245	+	2.25591i
$680$	4.78310	+	4.43807i	0.183423	+	0.170192i
$681$	4.49435	−	1.53276i	0.172224	−	0.0587356i
$682$	−9.74252	−	6.64234i	−0.373060	−	0.254348i
$683$	0.752437	−	3.29664i	0.0287912	−	0.126142i	−0.958490	−	0.285126i	$-0.907965\pi$
$683$	0.752437	−	3.29664i	0.0287912	−	0.126142i	0.987281	+	0.158984i	$0.0508217\pi$
$684$	10.8163	+	2.64984i	0.413572	+	0.101319i
$685$	1.27394	−	5.58148i	0.0486746	−	0.213257i
$686$	3.13705	−	7.99308i	0.119773	−	0.305177i
$687$	−16.7506	+	12.1586i	−0.639077	+	0.463880i
$688$	9.22152	+	2.84446i	0.351567	+	0.108444i
$689$	8.64852	+	22.0361i	0.329482	+	0.839507i
$690$	−0.577855	−	0.505312i	−0.0219986	−	0.0192369i
$691$	1.29245	+	17.2466i	0.0491673	+	0.656091i	0.966285	+	0.257475i	$0.0828905\pi$
$691$	1.29245	+	17.2466i	0.0491673	+	0.656091i	−0.917118	+	0.398617i	$0.869490\pi$
$692$	−0.551560	−	0.691634i	−0.0209672	−	0.0262920i
$693$	47.0966	−	36.3520i	1.78905	−	1.38090i
$694$	8.47971	+	4.08361i	0.321886	+	0.155012i
$695$	−0.667584	−	1.15629i	−0.0253229	−	0.0438605i
$696$	12.3798	−	10.5210i	0.469256	−	0.398799i
$697$	19.1890	−	33.2363i	0.726835	−	1.25892i
$698$	−4.50084	+	3.06862i	−0.170359	+	0.116149i
$699$	−7.27233	−	28.0275i	−0.275065	−	1.06010i
$700$	−12.8811	+	32.8206i	−0.486861	+	1.24050i
$701$	17.7129	+	8.53009i	0.669008	+	0.322177i	0.737375	−	0.675483i	$-0.236065\pi$
$701$	17.7129	+	8.53009i	0.669008	+	0.322177i	−0.0683679	+	0.997660i	$0.521779\pi$
$702$	7.71077	−	0.683561i	0.291024	−	0.0257993i
$703$	−14.8242	+	18.5889i	−0.559105	+	0.701095i
$704$	−11.4151	+	10.5917i	−0.430223	+	0.399189i
$705$	11.2019	+	4.99339i	0.421886	+	0.188062i
$706$	6.10128	−	0.919620i	0.229625	−	0.0346104i
$707$	24.3930	+	22.6334i	0.917394	+	0.851218i
$708$	6.18030	+	0.746011i	0.232270	+	0.0280368i
$709$	10.3444	−	3.19083i	0.388493	−	0.119834i	−0.0943545	−	0.995539i	$-0.530079\pi$
$709$	10.3444	−	3.19083i	0.388493	−	0.119834i	0.482848	+	0.875704i	$0.339603\pi$
$710$	2.89298	−	1.39318i	0.108571	−	0.0522853i
$711$	−3.11913	+	9.57059i	−0.116977	+	0.358925i
$712$	1.12120	−	4.91231i	0.0420189	−	0.184097i
$713$	−4.22602	−	7.31968i	−0.158266	−	0.274124i
$714$	19.8999	−	3.60212i	0.744735	−	0.134806i
$715$	−9.37283	+	1.41273i	−0.350524	+	0.0528330i
$716$	13.0670	+	4.03062i	0.488335	+	0.150632i
$717$	−10.4769	+	7.60479i	−0.391268	+	0.284006i
$718$	2.80822	+	0.423271i	0.104802	+	0.0157963i
$719$	14.4195	−	6.94407i	0.537757	−	0.258970i	−0.145234	−	0.989397i	$-0.546393\pi$
$719$	14.4195	−	6.94407i	0.537757	−	0.258970i	0.682990	+	0.730427i	$0.260679\pi$
$720$	0.867022	−	5.19237i	0.0323120	−	0.193508i
$721$	34.7842	+	43.6181i	1.29543	+	1.62442i
$722$	−6.67959	−	1.00679i	−0.248588	−	0.0374687i
$723$	8.08818	+	5.17202i	0.300803	+	0.192349i
$724$	−2.13210	+	3.69290i	−0.0792388	+	0.137246i
$725$	−3.64991	+	24.5045i	−0.135554	+	0.910073i
$726$	4.98096	−	6.63817i	0.184861	−	0.246366i
$727$	−1.38991	−	18.5471i	−0.0515491	−	0.687875i	−0.961789	−	0.273793i	$-0.911722\pi$
$727$	−1.38991	−	18.5471i	−0.0515491	−	0.687875i	0.910240	−	0.414082i	$-0.135897\pi$
$728$	−15.0782	+	18.9075i	−0.558837	+	0.700759i
$729$	−1.28368	+	26.9695i	−0.0475435	+	0.998869i
$730$	−0.904100	−	0.435392i	−0.0334623	−	0.0161146i
$731$	17.0216	+	11.6051i	0.629565	+	0.429230i
$732$	−10.3295	−	39.8097i	−0.381788	−	1.47141i
$733$	−7.59380	−	2.34238i	−0.280484	−	0.0865177i	0.151322	−	0.988485i	$-0.451647\pi$
$733$	−7.59380	−	2.34238i	−0.280484	−	0.0865177i	−0.431805	+	0.901967i	$0.642123\pi$
$734$	6.64684	+	2.05028i	0.245339	+	0.0756771i
$735$	−6.53180	−	10.5806i	−0.240929	−	0.390270i
$736$	6.93789	−	2.14006i	0.255734	−	0.0788835i
$737$	−22.6481			−0.834255
$738$	8.91503	−	0.526115i	0.328167	−	0.0193666i
$739$	−9.22132	+	4.44076i	−0.339212	+	0.163356i	−0.595732	−	0.803183i	$-0.703138\pi$
$739$	−9.22132	+	4.44076i	−0.339212	+	0.163356i	0.256521	+	0.966539i	$0.417424\pi$
$740$	10.7004	+	7.29538i	0.393353	+	0.268183i
$741$	−11.4617	+	2.07470i	−0.421056	+	0.0762160i
$742$	−7.19554	+	12.4630i	−0.264157	+	0.457533i
$743$	−34.1323	−	31.6701i	−1.25219	−	1.16186i	−0.979865	−	0.199659i	$-0.936017\pi$
$743$	−34.1323	−	31.6701i	−1.25219	−	1.16186i	−0.272326	−	0.962205i	$-0.587793\pi$
$744$	−7.92862	+	14.7181i	−0.290677	+	0.539591i
$745$	−7.10819	+	6.59544i	−0.260424	+	0.241638i
$746$	−2.61102	−	11.4396i	−0.0955961	−	0.418834i
$747$	0.402830	+	2.99392i	0.0147388	+	0.109542i
$748$	−44.2086	+	21.2898i	−1.61643	+	0.778430i
$749$	2.62965	+	35.0903i	0.0960854	+	1.28217i
$750$	−2.53813	−	4.11139i	−0.0926792	−	0.150127i
$751$	0.653659	+	1.66550i	0.0238524	+	0.0607748i	0.942304	−	0.334759i	$-0.108655\pi$
$751$	0.653659	+	1.66550i	0.0238524	+	0.0607748i	−0.918451	+	0.395534i	$0.870560\pi$
$752$	−25.7015	+	17.5230i	−0.937237	+	0.638997i
$753$	−17.8625	+	23.8056i	−0.650947	+	0.867524i
$754$	−3.46831	+	7.23414i	−0.126308	+	0.263452i
$755$	−1.49982			−0.0545840
$756$	−27.4811	−	28.8202i	−0.999477	−	1.04818i
$757$	32.0922	−	40.2424i	1.16641	−	1.46264i	0.306737	−	0.951794i	$-0.400763\pi$
$757$	32.0922	−	40.2424i	1.16641	−	1.46264i	0.859675	−	0.510841i	$-0.170666\pi$
$758$	3.11405	−	7.93446i	0.113107	−	0.288192i
$759$	10.8555	−	5.62764i	0.394028	−	0.204271i
$760$	0.170733	−	2.27827i	0.00619313	−	0.0826416i
$761$	−11.4804	−	29.2516i	−0.416165	−	1.06037i	−0.973216	−	0.229893i	$-0.926162\pi$
$761$	−11.4804	−	29.2516i	−0.416165	−	1.06037i	0.557051	−	0.830478i	$-0.311933\pi$
$762$	−0.730739	−	6.98253i	−0.0264719	−	0.252950i
$763$	−12.0837	+	11.2121i	−0.437461	+	0.405904i
$764$	12.5009	+	15.6757i	0.452267	+	0.567125i
$765$	5.03593	−	10.0466i	0.182074	−	0.363235i
$766$	−16.8128			−0.607471
$767$	−6.22197	+	1.91922i	−0.224662	+	0.0692992i
$768$	2.13944	+	1.87086i	0.0772004	+	0.0675088i
$769$	3.44829	−	46.0142i	0.124348	−	1.65931i	−0.491075	−	0.871118i	$-0.663396\pi$
$769$	3.44829	−	46.0142i	0.124348	−	1.65931i	0.615423	−	0.788197i	$-0.288985\pi$
$770$	−4.22409	−	3.91939i	−0.152226	−	0.141245i
$771$	−9.10496	−	21.3285i	−0.327907	−	0.768127i
$772$	−13.8503	+	4.27225i	−0.498483	+	0.153762i
$773$	8.31600	+	10.4279i	0.299106	+	0.375067i	0.908560	−	0.417755i	$-0.137183\pi$
$773$	8.31600	+	10.4279i	0.299106	+	0.375067i	−0.609454	+	0.792821i	$0.708611\pi$
$774$	−0.0759985	+	4.79330i	−0.00273171	+	0.172292i
$775$	−5.67279	−	24.8541i	−0.203773	−	0.892787i
$776$	27.2852	+	4.11258i	0.979481	+	0.147633i
$777$	80.4710	−	27.4440i	2.88688	−	0.984547i
$778$	−14.0744	+	9.59575i	−0.504591	+	0.344024i
$779$	−13.2878	+	2.00281i	−0.476083	+	0.0717580i
$780$	1.59346	+	6.14118i	0.0570550	+	0.219890i
$781$	3.82221	+	51.0039i	0.136770	+	1.82506i
$782$	4.15637			0.148631
$783$	−23.3593	−	15.4060i	−0.834792	−	0.550566i
$784$	31.5376			1.12634
$785$	0.466040	+	6.21888i	0.0166337	+	0.221961i
$786$	0.411660	+	1.58654i	0.0146834	+	0.0565899i
$787$	−4.44783	+	0.670403i	−0.158548	+	0.0238973i	−0.227837	−	0.973699i	$-0.573165\pi$
$787$	−4.44783	+	0.670403i	−0.158548	+	0.0238973i	0.0692885	+	0.997597i	$0.477927\pi$
$788$	−16.5213	+	11.2640i	−0.588548	+	0.401265i
$789$	21.8878	−	7.46466i	0.779226	−	0.265749i
$790$	0.964062	+	0.145309i	0.0342998	+	0.00516986i
$791$	−1.55891	−	6.83005i	−0.0554286	−	0.242849i
$792$	−20.7509	−	12.4233i	−0.737350	−	0.441441i
$793$	26.8213	+	33.6329i	0.952454	+	1.19434i
$794$	−16.8619	+	5.20121i	−0.598406	+	0.184584i
$795$	3.13978	+	7.35498i	0.111357	+	0.260854i
$796$	3.97337	+	3.68675i	0.140832	+	0.130673i
$797$	1.35297	−	18.0542i	0.0479247	−	0.639511i	−0.920586	−	0.390540i	$-0.872288\pi$
$797$	1.35297	−	18.0542i	0.0479247	−	0.639511i	0.968511	−	0.248971i	$-0.0800925\pi$
$798$	−5.33047	−	4.66130i	−0.188697	−	0.165008i
$799$	−63.4558	+	19.5735i	−2.24491	+	0.692462i
$800$	21.8992			0.774254
$801$	−8.66317	+	0.511251i	−0.306098	+	0.0180642i
$802$	−5.99375	−	7.51592i	−0.211647	−	0.265397i
$803$	11.7173	−	10.8720i	0.413493	−	0.383665i
$804$	1.57786	+	15.0771i	0.0556467	+	0.531729i
$805$	−1.50901	−	3.84490i	−0.0531857	−	0.135515i
$806$	0.616916	−	8.23218i	0.0217299	−	0.289966i
$807$	−36.1299	+	18.7303i	−1.27183	+	0.659338i
$808$	4.94207	−	12.5922i	0.173862	−	0.442992i
$809$	−11.6686	+	14.6319i	−0.410245	+	0.514430i	−0.943432	−	0.331567i	$-0.892423\pi$
$809$	−11.6686	+	14.6319i	−0.410245	+	0.514430i	0.533187	+	0.845997i	$0.320994\pi$
$810$	2.59695	−	0.307586i	0.0912474	−	0.0108075i
$811$	13.7741			0.483676			0.241838	−	0.970317i	$-0.422250\pi$
$811$	13.7741			0.483676			0.241838	+	0.970317i	$0.422250\pi$
$812$	40.2201	−	9.25353i	1.41145	−	0.324735i
$813$	−11.5083	+	15.3372i	−0.403614	+	0.537900i
$814$	20.1420	−	13.7326i	0.705978	−	0.481328i
$815$	−1.77450	−	4.52135i	−0.0621580	−	0.158376i
$816$	14.9730	+	24.2541i	0.524160	+	0.849063i
$817$	−0.539060	−	7.19325i	−0.0188593	−	0.251660i
$818$	−3.19271	+	1.53753i	−0.111630	+	0.0537583i
$819$	38.5270	+	15.8301i	1.34624	+	0.553148i
$820$	1.62874	+	7.13597i	0.0568780	+	0.249199i
$821$	14.9636	−	13.8842i	0.522232	−	0.484561i	−0.374443	−	0.927250i	$-0.622166\pi$
$821$	14.9636	−	13.8842i	0.522232	−	0.484561i	0.896675	+	0.442689i	$0.145976\pi$
$822$	−3.42099	+	6.35047i	−0.119321	+	0.221498i
$823$	−16.6546	−	15.4532i	−0.580544	−	0.538666i	0.334304	−	0.942465i	$-0.391499\pi$
$823$	−16.6546	−	15.4532i	−0.580544	−	0.538666i	−0.914847	+	0.403800i	$0.867689\pi$
$824$	11.3397	−	19.6410i	0.395038	−	0.684227i
$825$	36.2911	−	6.56912i	1.26350	−	0.228707i
$826$	−3.27054	−	2.22982i	−0.113797	−	0.0775853i
$827$	−27.0365	+	13.0201i	−0.940152	+	0.452753i	−0.840223	−	0.542241i	$-0.817576\pi$
$827$	−27.0365	+	13.0201i	−0.940152	+	0.452753i	−0.0999293	+	0.994995i	$0.531862\pi$
$828$	−4.50267	−	6.83453i	−0.156479	−	0.237516i
$829$	−7.44112			−0.258441			−0.129220	−	0.991616i	$-0.541247\pi$
$829$	−7.44112			−0.258441			−0.129220	+	0.991616i	$0.541247\pi$
$830$	0.279592	−	0.0862427i	0.00970478	−	0.00299353i
$831$	7.49324	+	12.1380i	0.259938	+	0.421061i
$832$	−10.4178	−	3.21345i	−0.361171	−	0.111406i
$833$	64.3351	+	19.8447i	2.22908	+	0.687579i
$834$	0.422506	+	1.62834i	0.0146302	+	0.0563847i
$835$	−10.8780	−	7.41652i	−0.376450	−	0.256659i
$836$	15.4794	+	7.45449i	0.535366	+	0.257819i
$837$	28.1564	+	6.02430i	0.973228	+	0.208230i
$838$	−5.96047	+	7.47419i	−0.205901	+	0.258192i
$839$	0.0989710	+	1.32068i	0.00341686	+	0.0455948i	0.998652	−	0.0519132i	$-0.0165319\pi$
$839$	0.0989710	+	1.32068i	0.00341686	+	0.0455948i	−0.995235	+	0.0975080i	$0.968913\pi$
$840$	−4.90335	+	6.53475i	−0.169182	+	0.225470i
$841$	26.0842	−	12.6734i	0.899455	−	0.437013i
$842$	−0.938597	+	1.62570i	−0.0323462	+	0.0560252i
$843$	−9.42368	−	6.02601i	−0.324569	−	0.207547i
$844$	−14.2895	−	2.15379i	−0.491865	−	0.0741367i
$845$	0.985131	+	1.23532i	0.0338895	+	0.0424961i
$846$	−11.9271	−	9.82489i	−0.410063	−	0.337787i
$847$	40.2331	−	19.3752i	1.38243	−	0.665741i
$848$	−20.0568	−	3.02308i	−0.688755	−	0.103813i
$849$	−9.52069	+	6.91069i	−0.326749	+	0.237174i
$850$	11.9796	+	3.69522i	0.410897	+	0.126745i
$851$	17.2789	−	2.60437i	0.592313	−	0.0892768i
$852$	33.6876	−	6.09785i	1.15412	−	0.208909i
$853$	−1.78403	−	3.09004i	−0.0610842	−	0.105801i	0.833866	−	0.551967i	$-0.186122\pi$
$853$	−1.78403	−	3.09004i	−0.0610842	−	0.105801i	−0.894950	+	0.446166i	$0.852789\pi$
$854$	−5.81931	+	25.4961i	−0.199133	+	0.872458i
$855$	−3.84970	+	0.814683i	−0.131657	+	0.0278616i
$856$	12.8882	−	6.20663i	0.440509	−	0.212138i
$857$	28.4871	−	8.78711i	0.973101	−	0.300162i	0.232865	−	0.972509i	$-0.425190\pi$
$857$	28.4871	−	8.78711i	0.973101	−	0.300162i	0.740236	+	0.672347i	$0.234714\pi$
$858$	11.8567	+	1.43120i	0.404782	+	0.0488604i
$859$	26.4930	+	24.5819i	0.903930	+	0.838725i	0.987474	−	0.157779i	$-0.0504334\pi$
$859$	26.4930	+	24.5819i	0.903930	+	0.838725i	−0.0835440	+	0.996504i	$0.526624\pi$
$860$	−3.88521	+	0.585601i	−0.132485	+	0.0199688i
$861$	43.8898	+	19.5645i	1.49576	+	0.666756i
$862$	8.10588	−	7.52116i	0.276087	−	0.256172i
$863$	13.6555	−	17.1234i	0.464837	−	0.582887i	−0.493061	−	0.869995i	$-0.664122\pi$
$863$	13.6555	−	17.1234i	0.464837	−	0.582887i	0.957898	+	0.287107i	$0.0926936\pi$
$864$	−10.4273	+	22.4289i	−0.354745	+	0.763047i
$865$	0.281629	+	0.135625i	0.00957566	+	0.00461140i
$866$	−4.58413	+	11.6802i	−0.155775	+	0.396908i
$867$	7.88731	+	30.3976i	0.267867	+	1.03236i
$868$	−35.0885	+	23.9229i	−1.19098	+	0.811998i
$869$	−7.76493	+	13.4492i	−0.263407	+	0.456234i
$870$	−1.09915	+	2.47733i	−0.0372647	+	0.0839895i
$871$	−7.92807	−	13.7318i	−0.268632	−	0.465285i
$872$	6.03749	+	2.90750i	0.204455	+	0.0984604i
$873$	−6.33735	−	47.1007i	−0.214487	−	1.59412i
$874$	−0.907383	−	1.13782i	−0.0306927	−	0.0384874i
$875$	−1.94285	−	25.9256i	−0.0656805	−	0.876445i
$876$	−8.05396	−	7.04288i	−0.272118	−	0.237957i
$877$	12.9487	+	32.9927i	0.437246	+	1.11409i	0.964431	+	0.264335i	$0.0851523\pi$
$877$	12.9487	+	32.9927i	0.437246	+	1.11409i	−0.527185	+	0.849751i	$0.676752\pi$
$878$	−7.95098	−	2.45255i	−0.268333	−	0.0827696i
$879$	−0.439742	+	0.319191i	−0.0148321	+	0.0107661i
$880$	2.96718	−	7.56026i	0.100024	−	0.254856i
$881$	11.8696	−	52.0041i	0.399897	−	1.75206i	−0.227900	−	0.973684i	$-0.573186\pi$
$881$	11.8696	−	52.0041i	0.399897	−	1.75206i	0.627797	−	0.778377i	$-0.283957\pi$
$882$	4.37995	+	15.0421i	0.147480	+	0.506493i
$883$	−3.98039	+	17.4392i	−0.133951	+	0.586877i	0.862744	+	0.505641i	$0.168744\pi$
$883$	−3.98039	+	17.4392i	−0.133951	+	0.586877i	−0.996695	+	0.0812361i	$0.974113\pi$
$884$	−28.3836	−	19.3516i	−0.954644	−	0.650865i
$885$	−2.08191	+	0.710020i	−0.0699827	+	0.0238670i
$886$	−10.9858	−	10.1933i	−0.369076	−	0.342452i
$887$	−6.23522	+	10.7997i	−0.209358	+	0.362619i	−0.951513	−	0.307610i	$-0.900471\pi$
$887$	−6.23522	+	10.7997i	−0.209358	+	0.362619i	0.742154	+	0.670229i	$0.233804\pi$
$888$	−22.3366	−	26.3756i	−0.749568	−	0.885109i
$889$	13.8013	−	35.1650i	0.462879	−	1.17940i
$890$	0.187037	+	0.819461i	0.00626948	+	0.0274684i
$891$	−10.5520	+	40.2968i	−0.353506	+	1.34999i
$892$	−23.8329	+	29.8855i	−0.797984	+	1.00064i
$893$	19.2115	+	13.0982i	0.642888	+	0.438313i
$894$	10.8466	−	5.62304i	0.362764	−	0.188063i
$895$	−4.77790	+	0.720152i	−0.159707	+	0.0240720i
$896$	−17.3242	−	44.1414i	−0.578761	−	1.47466i
$897$	7.21210	+	4.61180i	0.240805	+	0.153984i
$898$	−3.17970	−	5.50740i	−0.106108	−	0.183784i
$899$	−20.2590	+	21.9103i	−0.675676	+	0.730749i
$900$	−6.90148	−	23.7018i	−0.230049	−	0.790059i
$901$	−39.0126	−	18.7875i	−1.29970	−	0.625902i
$902$	13.6241	+	2.05350i	0.453633	+	0.0683742i
$903$	−12.2335	+	22.7093i	−0.407105	+	0.755718i
$904$	−2.35308	+	1.60430i	−0.0782623	+	0.0533583i
$905$	0.112599	−	1.50254i	0.00374293	−	0.0499460i
$906$	1.82139	+	0.503547i	0.0605116	+	0.0167292i
$907$	−0.665897	+	0.617862i	−0.0221108	+	0.0205158i	−0.691151	−	0.722711i	$-0.742896\pi$
$907$	−0.665897	+	0.617862i	−0.0221108	+	0.0205158i	0.669040	+	0.743226i	$0.266705\pi$
$908$	−1.09116	−	4.78070i	−0.0362116	−	0.158653i
$909$	−23.2029	−	2.10921i	−0.769591	−	0.0699579i
$910$	0.897707	−	3.93311i	0.0297587	−	0.130381i
$911$	−17.6018	−	30.4872i	−0.583173	−	1.01008i	−0.995101	−	0.0988684i	$-0.968478\pi$
$911$	−17.6018	−	30.4872i	−0.583173	−	1.01008i	0.411928	−	0.911217i	$-0.364856\pi$
$912$	3.37087	−	9.39387i	0.111621	−	0.311062i
$913$	−0.348290	+	4.64760i	−0.0115267	+	0.153813i
$914$	−0.347973	+	4.64338i	−0.0115099	+	0.153589i
$915$	9.39178	+	11.0901i	0.310483	+	0.366626i
$916$	10.6872	+	18.5107i	0.353114	+	0.611612i
$917$	−1.96251	+	8.59831i	−0.0648077	+	0.283941i
$918$	−9.48869	+	10.5099i	−0.313173	+	0.346878i
$919$	−1.91853	−	8.40564i	−0.0632865	−	0.277276i	0.933377	−	0.358898i	$-0.116847\pi$
$919$	−1.91853	−	8.40564i	−0.0632865	−	0.277276i	−0.996663	+	0.0816213i	$0.973990\pi$
$920$	−1.23086	+	1.14207i	−0.0405803	+	0.0376530i
$921$	7.77186	+	29.9527i	0.256091	+	0.986975i
$922$	−0.913121	+	12.1848i	−0.0300720	+	0.401283i
$923$	−29.5862	+	20.1716i	−0.973843	+	0.663955i
$924$	−32.2734	−	52.2782i	−1.06172	−	1.71983i
$925$	52.1171	+	7.85539i	1.71360	+	0.258284i
$926$	−7.13992	−	3.43840i	−0.234632	−	0.112993i
$927$	−37.9397	−	9.29467i	−1.24610	−	0.305277i
$928$	−14.4769	−	21.1547i	−0.475229	−	0.694436i
$929$	−20.6306	−	35.7333i	−0.676869	−	1.17237i	−0.975919	−	0.218134i	$-0.930003\pi$
$929$	−20.6306	−	35.7333i	−0.676869	−	1.17237i	0.299050	−	0.954237i	$-0.403330\pi$
$930$	0.126365	−	2.78596i	0.00414368	−	0.0913552i
$931$	−8.61251	−	21.9443i	−0.282264	−	0.719196i
$932$	−29.5675	+	4.45659i	−0.968517	+	0.145980i
$933$	−1.36231	+	30.0346i	−0.0445999	+	0.983288i
$934$	14.4806	+	9.87274i	0.473821	+	0.323046i
$935$	10.8101	−	13.5555i	0.353529	−	0.443311i
$936$	0.268432	−	16.9303i	0.00877398	−	0.553384i
$937$	6.19363	+	27.1361i	0.202337	+	0.886496i	0.969509	+	0.245055i	$0.0788060\pi$
$937$	6.19363	+	27.1361i	0.202337	+	0.886496i	−0.767172	+	0.641441i	$0.778337\pi$
$938$	3.52164	−	8.97300i	0.114986	−	0.292979i
$939$	−10.4205	+	29.0397i	−0.340061	+	0.947674i
$940$	6.33252	−	10.9682i	0.206544	−	0.357745i
$941$	10.3946	+	9.64478i	0.338854	+	0.314411i	0.831183	−	0.555998i	$-0.187664\pi$
$941$	10.3946	+	9.64478i	0.338854	+	0.314411i	−0.492329	+	0.870409i	$0.663854\pi$
$942$	1.52196	−	7.70870i	0.0495880	−	0.251163i
$943$	8.15995	+	5.56336i	0.265725	+	0.181168i
$944$	1.24146	−	5.43918i	0.0404060	−	0.177030i
$945$	13.1673	+	4.96191i	0.428331	+	0.161411i
$946$	−1.64577	+	7.21058i	−0.0535086	+	0.234436i
$947$	−5.30998	+	13.5296i	−0.172551	+	0.439653i	−0.990821	−	0.135181i	$-0.956838\pi$
$947$	−5.30998	+	13.5296i	−0.172551	+	0.439653i	0.818270	+	0.574835i	$0.194934\pi$
$948$	9.49429	+	4.23222i	0.308360	+	0.137456i
$949$	10.6935	+	3.29851i	0.347126	+	0.107074i
$950$	−1.60370	−	4.08617i	−0.0520310	−	0.132573i
$951$	27.5577	−	9.39834i	0.893620	−	0.304762i
$952$	−3.30574	−	44.1121i	−0.107140	−	1.42968i
$953$	−26.7646	−	33.5617i	−0.866990	−	1.08717i	−0.995434	−	0.0954541i	$-0.969570\pi$
$953$	−26.7646	−	33.5617i	−0.866990	−	1.08717i	0.128444	−	0.991717i	$-0.459002\pi$
$954$	−1.34362	−	9.98608i	−0.0435012	−	0.323311i
$955$	−6.38302	−	3.07390i	−0.206550	−	0.0994691i
$956$	6.68445	+	11.5778i	0.216191	+	0.374453i
$957$	−30.3368	−	30.7147i	−0.980650	−	0.992864i
$958$	−0.991305	+	1.71699i	−0.0320276	+	0.0554735i
$959$	−32.0687	+	21.8641i	−1.03555	+	0.706028i
$960$	−3.54983	−	0.981399i	−0.114570	−	0.0316745i
$961$	−0.107229	+	0.273214i	−0.00345899	+	0.00881337i
$962$	15.3770	+	7.40519i	0.495776	+	0.238753i
$963$	−16.4695	−	18.3241i	−0.530721	−	0.590486i
$964$	6.18131	−	7.75111i	0.199087	−	0.249647i
$965$	3.75434	−	3.48352i	0.120857	−	0.112138i
$966$	0.541671	+	5.17591i	0.0174280	+	0.166532i
$967$	50.1743	−	7.56257i	1.61350	−	0.243196i	0.720566	−	0.693387i	$-0.243882\pi$
$967$	50.1743	−	7.56257i	1.61350	−	0.243196i	0.892932	+	0.450191i	$0.148644\pi$
$968$	−13.3072	−	12.3473i	−0.427711	−	0.396858i
$969$	12.7874	−	17.0419i	0.410791	−	0.547465i
$970$	−4.39857	+	1.35678i	−0.141229	+	0.0435635i
$971$	1.57143	−	0.756763i	0.0504297	−	0.0242857i	−0.408499	−	0.912759i	$-0.633948\pi$
$971$	1.57143	−	0.756763i	0.0504297	−	0.0242857i	0.458929	+	0.888473i	$0.348233\pi$
$972$	27.5612	+	4.21720i	0.884027	+	0.135267i
$973$	−2.01421	+	8.82485i	−0.0645727	+	0.282912i
$974$	−1.52477	−	2.64097i	−0.0488566	−	0.0846222i
$975$	16.6868	+	19.7042i	0.534405	+	0.631038i
$976$	−36.4477	+	5.49361i	−1.16666	+	0.175846i
$977$	36.7811	+	11.3455i	1.17673	+	0.362974i	0.820622	−	0.571471i	$-0.193627\pi$
$977$	36.7811	+	11.3455i	1.17673	+	0.362974i	0.356109	+	0.934444i	$0.384103\pi$
$978$	0.636969	+	6.08652i	0.0203680	+	0.194625i
$979$	−13.2392	−	1.99549i	−0.423127	−	0.0637761i
$980$	−11.5689	+	5.57129i	−0.369555	+	0.177968i
$981$	1.90089	−	11.3839i	0.0606908	−	0.363461i
$982$	−1.91230	−	2.39795i	−0.0610240	−	0.0765217i
$983$	−26.7134	−	4.02640i	−0.852026	−	0.128422i	−0.291512	−	0.956567i	$-0.594158\pi$
$983$	−26.7134	−	4.02640i	−0.852026	−	0.128422i	−0.560514	+	0.828145i	$0.689396\pi$
$984$	0.885128	−	19.5143i	0.0282168	−	0.622093i
$985$	3.53275	−	6.11891i	0.112563	−	0.194965i
$986$	−4.34978	−	14.0151i	−0.138525	−	0.446333i
$987$	−32.6446	−	76.4703i	−1.03909	−	2.43408i
$988$	0.898887	+	11.9948i	0.0285974	+	0.381606i
$989$	−3.30539	+	4.14483i	−0.105105	+	0.131798i
$990$	4.01800	+	0.365247i	0.127700	+	0.0116083i
$991$	15.1076	+	7.27542i	0.479908	+	0.231111i	0.658167	−	0.752872i	$-0.271332\pi$
$991$	15.1076	+	7.27542i	0.479908	+	0.231111i	−0.178259	+	0.983984i	$0.557046\pi$
$992$	21.7941	+	14.8589i	0.691962	+	0.471772i
$993$	4.07224	−	4.00819i	0.129229	−	0.127196i
$994$	−20.8017	−	6.41646i	−0.659789	−	0.203518i
$995$	−1.83017	−	0.564533i	−0.0580204	−	0.0178969i
$996$	3.11823	−	0.0919302i	0.0988049	−	0.00291292i
$997$	13.1381	−	4.05257i	0.416088	−	0.128346i	−0.0796405	−	0.996824i	$-0.525377\pi$
$997$	13.1381	−	4.05257i	0.416088	−	0.128346i	0.495729	+	0.868477i	$0.334901\pi$
$998$	−7.39309			−0.234024
$999$	−32.8610	+	49.6374i	−1.03968	+	1.57046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.q.a.103.12	yes	336
3.2	odd	2		783.2.u.a.712.17		336
9.2	odd	6		783.2.u.a.451.17		336
9.7	even	3	inner	261.2.q.a.16.12	✓	336
29.20	even	7	inner	261.2.q.a.49.12	yes	336
87.20	odd	14		783.2.u.a.658.17		336
261.20	odd	42		783.2.u.a.397.17		336
261.223	even	21	inner	261.2.q.a.223.12	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.q.a.16.12	✓	336	9.7	even	3	inner
261.2.q.a.49.12	yes	336	29.20	even	7	inner
261.2.q.a.103.12	yes	336	1.1	even	1	trivial
261.2.q.a.223.12	yes	336	261.223	even	21	inner
783.2.u.a.397.17		336	261.20	odd	42
783.2.u.a.451.17		336	9.2	odd	6
783.2.u.a.658.17		336	87.20	odd	14
783.2.u.a.712.17		336	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0343571 - 0.458464i) q^{2} +(0.435012 + 1.67653i) q^{3} +(1.76865 - 0.266582i) q^{4} +(-0.522192 + 0.356024i) q^{5} +(0.753684 - 0.257038i) q^{6} +(4.23687 + 0.638606i) q^{7} +(-0.387591 - 1.69815i) q^{8} +(-2.62153 + 1.45862i) q^{9} +(0.181165 + 0.227174i) q^{10} +(-4.42276 + 1.36424i) q^{11} +(1.21632 + 2.84924i) q^{12} +(-2.37536 - 2.20401i) q^{13} +(0.147211 - 1.96439i) q^{14} +(-0.824046 - 0.720597i) q^{15} +(2.65311 - 0.818376i) q^{16} +5.92716 q^{17} +(0.758794 + 1.15176i) q^{18} +(-1.29397 - 1.62258i) q^{19} +(-0.828667 + 0.768890i) q^{20} +(0.772446 + 7.38106i) q^{21} +(0.777408 + 1.98080i) q^{22} +(-0.113983 + 1.52100i) q^{23} +(2.67840 - 1.38852i) q^{24} +(-1.68077 + 4.28254i) q^{25} +(-0.928849 + 1.16474i) q^{26} +(-3.58583 - 3.76056i) q^{27} +7.66380 q^{28} +(5.24806 - 1.20743i) q^{29} +(-0.302056 + 0.402553i) q^{30} +(-4.57847 + 3.12155i) q^{31} +(-1.73907 - 4.43107i) q^{32} +(-4.21115 - 6.82145i) q^{33} +(-0.203640 - 2.71739i) q^{34} +(-2.43982 + 1.17496i) q^{35} +(-4.24773 + 3.27865i) q^{36} +(-2.54928 - 11.1691i) q^{37} +(-0.699439 + 0.648984i) q^{38} +(2.66179 - 4.94114i) q^{39} +(0.806979 + 0.748767i) q^{40} +(3.23747 - 5.60746i) q^{41} +(3.35741 - 0.607730i) q^{42} +(2.87179 + 1.95795i) q^{43} +(-7.45865 + 3.59190i) q^{44} +(0.849636 - 1.69501i) q^{45} +0.701241 q^{46} +(-10.7059 + 3.30235i) q^{47} +(2.52617 + 4.09203i) q^{48} +(10.8543 + 3.34810i) q^{49} +(2.02114 + 0.623438i) q^{50} +(2.57839 + 9.93709i) q^{51} +(-4.78874 - 3.26490i) q^{52} +(-6.58201 - 3.16973i) q^{53} +(-1.60088 + 1.77317i) q^{54} +(1.82383 - 2.28701i) q^{55} +(-0.557728 - 7.44236i) q^{56} +(2.15743 - 2.87522i) q^{57} +(-0.733872 - 2.36456i) q^{58} +(1.00471 - 1.74020i) q^{59} +(-1.64955 - 1.05481i) q^{60} +(-13.1274 - 1.97864i) q^{61} +(1.58842 + 1.99182i) q^{62} +(-12.0386 + 4.50588i) q^{63} +(3.03128 - 1.45979i) q^{64} +(2.02508 + 0.305231i) q^{65} +(-2.98270 + 2.16502i) q^{66} +(4.67591 + 1.44233i) q^{67} +(10.4831 - 1.58007i) q^{68} +(-2.59960 + 0.470558i) q^{69} +(0.622500 + 1.07820i) q^{70} +(2.45901 - 10.7736i) q^{71} +(3.49304 + 3.88640i) q^{72} +(-3.11151 + 1.49842i) q^{73} +(-5.03306 + 1.55249i) q^{74} +(-7.91098 - 0.954918i) q^{75} +(-2.72113 - 2.52484i) q^{76} +(-19.6099 + 2.95572i) q^{77} +(-2.35678 - 1.05057i) q^{78} +(2.45964 - 2.28222i) q^{79} +(-1.09407 + 1.37192i) q^{80} +(4.74483 - 7.64765i) q^{81} +(-2.68205 - 1.29161i) q^{82} +(0.367887 - 0.937360i) q^{83} +(3.33384 + 12.8486i) q^{84} +(-3.09512 + 2.11021i) q^{85} +(0.798984 - 1.38388i) q^{86} +(4.30727 + 8.27330i) q^{87} +(4.03091 + 6.98174i) q^{88} +(2.60627 + 1.25512i) q^{89} +(-0.806291 - 0.331291i) q^{90} +(-8.65660 - 10.8550i) q^{91} +(0.203874 + 2.72051i) q^{92} +(-7.22507 - 6.31805i) q^{93} +(1.88183 + 4.79483i) q^{94} +(1.25338 + 0.386616i) q^{95} +(6.67232 - 4.84317i) q^{96} +(-5.78762 + 14.7466i) q^{97} +(1.16206 - 5.09132i) q^{98} +(9.60449 - 10.0275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 5 q^{2} - 10 q^{3} + 21 q^{4} - 9 q^{5} - 40 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 28 q^{10} - q^{11} - 22 q^{12} - 5 q^{13} - 9 q^{14} - 26 q^{15} + 21 q^{16} - 60 q^{17} - 90 q^{18} - 20 q^{19}+ \cdots + 196 q^{99}+O(q^{100}) \) 336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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