LMFDB - Embedded newform 117.2.bc.a.110.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(20,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 11]))

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

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

chi := DirichletCharacter("117.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.bc (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			110.2
Character	$\chi$	$=$	117.110
Dual form			117.2.bc.a.50.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.477221 + 1.78101i) q^{2} +(1.66170 - 0.488620i) q^{3} +(-1.21221 - 0.699872i) q^{4} +(0.672617 - 2.51024i) q^{5} +(0.0772390 + 3.19269i) q^{6} +(1.99353 + 1.99353i) q^{7} +(-0.782609 + 0.782609i) q^{8} +(2.52250 - 1.62388i) q^{9} +O(q^{10})$	\(q+(-0.477221 + 1.78101i) q^{2} +(1.66170 - 0.488620i) q^{3} +(-1.21221 - 0.699872i) q^{4} +(0.672617 - 2.51024i) q^{5} +(0.0772390 + 3.19269i) q^{6} +(1.99353 + 1.99353i) q^{7} +(-0.782609 + 0.782609i) q^{8} +(2.52250 - 1.62388i) q^{9} +(4.14978 + 2.39588i) q^{10} +(-6.08140 - 1.62951i) q^{11} +(-2.35631 - 0.570667i) q^{12} +(-3.52535 + 0.756266i) q^{13} +(-4.50185 + 2.59914i) q^{14} +(-0.108864 - 4.49993i) q^{15} +(-2.42010 - 4.19174i) q^{16} +(2.31896 + 4.01655i) q^{17} +(1.68836 + 5.26756i) q^{18} +(0.390218 + 0.104559i) q^{19} +(-2.57220 + 2.57220i) q^{20} +(4.28672 + 2.33857i) q^{21} +(5.80434 - 10.0534i) q^{22} -4.26737 q^{23} +(-0.918064 + 1.68286i) q^{24} +(-1.51877 - 0.876864i) q^{25} +(0.335449 - 6.63959i) q^{26} +(3.39819 - 3.93095i) q^{27} +(-1.02137 - 3.81179i) q^{28} +(5.22693 - 3.01777i) q^{29} +(8.06638 + 1.95357i) q^{30} +(-2.27098 - 0.608508i) q^{31} +(6.48234 - 1.73694i) q^{32} +(-10.9017 + 0.263738i) q^{33} +(-8.26018 + 2.21331i) q^{34} +(6.34511 - 3.66335i) q^{35} +(-4.19432 + 0.203061i) q^{36} +(1.60869 - 0.431046i) q^{37} +(-0.372440 + 0.645085i) q^{38} +(-5.48854 + 2.97924i) q^{39} +(1.43814 + 2.49093i) q^{40} +(-1.18032 - 1.18032i) q^{41} +(-6.21073 + 6.51869i) q^{42} -2.99100i q^{43} +(6.23151 + 6.23151i) q^{44} +(-2.37965 - 7.42434i) q^{45} +(2.03648 - 7.60024i) q^{46} +(1.25642 + 4.68901i) q^{47} +(-6.06965 - 5.78291i) q^{48} +0.948297i q^{49} +(2.28650 - 2.28650i) q^{50} +(5.81598 + 5.54122i) q^{51} +(4.80276 + 1.55053i) q^{52} +0.186317i q^{53} +(5.37938 + 7.92814i) q^{54} +(-8.18091 + 14.1698i) q^{55} -3.12030 q^{56} +(0.699515 - 0.0169230i) q^{57} +(2.88028 + 10.7494i) q^{58} +(1.07545 + 4.01364i) q^{59} +(-3.01741 + 5.53106i) q^{60} +0.0950990 q^{61} +(2.16752 - 3.75426i) q^{62} +(8.26592 + 1.79143i) q^{63} +2.69361i q^{64} +(-0.472797 + 9.35815i) q^{65} +(4.73279 - 19.5419i) q^{66} +(-2.70944 + 2.70944i) q^{67} -6.49189i q^{68} +(-7.09110 + 2.08512i) q^{69} +(3.49646 + 13.0490i) q^{70} +(-1.56243 + 5.83108i) q^{71} +(-0.703270 + 3.24499i) q^{72} +(-1.49562 - 1.49562i) q^{73} +3.07079i q^{74} +(-2.95220 - 0.714984i) q^{75} +(-0.399850 - 0.399850i) q^{76} +(-8.87497 - 15.3719i) q^{77} +(-2.68682 - 11.1969i) q^{78} +(-2.84121 + 4.92112i) q^{79} +(-12.1501 + 3.25561i) q^{80} +(3.72603 - 8.19248i) q^{81} +(2.66543 - 1.53889i) q^{82} +(15.0939 - 4.04440i) q^{83} +(-3.55972 - 5.83500i) q^{84} +(11.6423 - 3.11954i) q^{85} +(5.32701 + 1.42737i) q^{86} +(7.21106 - 7.56861i) q^{87} +(6.03462 - 3.48409i) q^{88} +(0.0313812 + 0.117116i) q^{89} +(14.3585 - 0.695139i) q^{90} +(-8.53551 - 5.52023i) q^{91} +(5.17297 + 2.98661i) q^{92} +(-4.07103 + 0.0984881i) q^{93} -8.95077 q^{94} +(0.524935 - 0.909214i) q^{95} +(9.92301 - 6.05367i) q^{96} +(11.2137 - 11.2137i) q^{97} +(-1.68893 - 0.452547i) q^{98} +(-17.9865 + 5.76503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.477221	+	1.78101i	−0.337446	+	1.25937i	0.563747	+	0.825948i	$0.309359\pi$
$2$	−0.477221	+	1.78101i	−0.337446	+	1.25937i	−0.901193	+	0.433418i	$0.857307\pi$
$3$	1.66170	−	0.488620i	0.959384	−	0.282105i
$3$	1.66170	−	0.488620i	0.959384	−	0.282105i
$4$	−1.21221	−	0.699872i	−0.606107	−	0.349936i
$5$	0.672617	−	2.51024i	0.300804	−	1.12261i	−0.635694	−	0.771941i	$-0.719286\pi$
$5$	0.672617	−	2.51024i	0.300804	−	1.12261i	0.936498	−	0.350673i	$-0.114047\pi$
$6$	0.0772390	+	3.19269i	0.0315327	+	1.30341i
$7$	1.99353	+	1.99353i	0.753482	+	0.753482i	0.975127	−	0.221645i	$-0.0711427\pi$
$7$	1.99353	+	1.99353i	0.753482	+	0.753482i	−0.221645	+	0.975127i	$0.571143\pi$
$8$	−0.782609	+	0.782609i	−0.276694	+	0.276694i
$9$	2.52250	−	1.62388i	0.840834	−	0.541293i
$10$	4.14978	+	2.39588i	1.31228	+	0.757644i
$11$	−6.08140	−	1.62951i	−1.83361	−	0.491315i	−0.835321	−	0.549763i	$-0.814718\pi$
$11$	−6.08140	−	1.62951i	−1.83361	−	0.491315i	−0.998290	+	0.0584482i	$0.981385\pi$
$12$	−2.35631	−	0.570667i	−0.680208	−	0.164737i
$13$	−3.52535	+	0.756266i	−0.977755	+	0.209750i
$13$	−3.52535	+	0.756266i	−0.977755	+	0.209750i
$14$	−4.50185	+	2.59914i	−1.20317	+	0.694650i
$15$	−0.108864	−	4.49993i	−0.0281086	−	1.16188i
$16$	−2.42010	−	4.19174i	−0.605026	−	1.04794i
$17$	2.31896	+	4.01655i	0.562430	+	0.974157i	0.997284	+	0.0736558i	$0.0234666\pi$
$17$	2.31896	+	4.01655i	0.562430	+	0.974157i	−0.434854	+	0.900501i	$0.643200\pi$
$18$	1.68836	+	5.26756i	0.397950	+	1.24157i
$19$	0.390218	+	0.104559i	0.0895221	+	0.0239874i	0.303302	−	0.952894i	$-0.401911\pi$
$19$	0.390218	+	0.104559i	0.0895221	+	0.0239874i	−0.213780	+	0.976882i	$0.568578\pi$
$20$	−2.57220	+	2.57220i	−0.575162	+	0.575162i
$21$	4.28672	+	2.33857i	0.935439	+	0.510318i
$22$	5.80434	−	10.0534i	1.23749	−	2.14340i
$23$	−4.26737			−0.889808			−0.444904	−	0.895578i	$-0.646762\pi$
$23$	−4.26737			−0.889808			−0.444904	+	0.895578i	$0.646762\pi$
$24$	−0.918064	+	1.68286i	−0.187399	+	0.343512i
$25$	−1.51877	−	0.876864i	−0.303755	−	0.175373i
$26$	0.335449	−	6.63959i	0.0657869	−	1.30213i
$27$	3.39819	−	3.93095i	0.653981	−	0.756511i
$28$	−1.02137	−	3.81179i	−0.193020	−	0.720361i
$29$	5.22693	−	3.01777i	0.970617	−	0.560386i	0.0711925	−	0.997463i	$-0.477320\pi$
$29$	5.22693	−	3.01777i	0.970617	−	0.560386i	0.899424	+	0.437077i	$0.143986\pi$
$30$	8.06638	+	1.95357i	1.47271	+	0.356671i
$31$	−2.27098	−	0.608508i	−0.407881	−	0.109291i	0.0490441	−	0.998797i	$-0.484383\pi$
$31$	−2.27098	−	0.608508i	−0.407881	−	0.109291i	−0.456925	+	0.889505i	$0.651049\pi$
$32$	6.48234	−	1.73694i	1.14593	−	0.307050i
$33$	−10.9017	+	0.263738i	−1.89774	+	0.0459109i
$34$	−8.26018	+	2.21331i	−1.41661	+	0.379579i
$35$	6.34511	−	3.66335i	1.07252	−	0.619220i
$36$	−4.19432	+	0.203061i	−0.699053	+	0.0338434i
$37$	1.60869	−	0.431046i	0.264466	−	0.0708635i	−0.124149	−	0.992264i	$-0.539620\pi$
$37$	1.60869	−	0.431046i	0.264466	−	0.0708635i	0.388615	+	0.921400i	$0.372953\pi$
$38$	−0.372440	+	0.645085i	−0.0604178	+	0.104647i
$39$	−5.48854	+	2.97924i	−0.878871	+	0.477060i
$40$	1.43814	+	2.49093i	0.227390	+	0.393851i
$41$	−1.18032	−	1.18032i	−0.184335	−	0.184335i	0.608907	−	0.793242i	$-0.291608\pi$
$41$	−1.18032	−	1.18032i	−0.184335	−	0.184335i	−0.793242	+	0.608907i	$0.791608\pi$
$42$	−6.21073	+	6.51869i	−0.958337	+	1.00586i
$43$		−	2.99100i		−	0.456123i	−0.973647	−	0.228062i	$-0.926761\pi$
$43$		−	2.99100i		−	0.456123i	0.973647	−	0.228062i	$-0.0732388\pi$
$44$	6.23151	+	6.23151i	0.939436	+	0.939436i
$45$	−2.37965	−	7.42434i	−0.354737	−	1.10676i
$46$	2.03648	−	7.60024i	0.300262	−	1.12059i
$47$	1.25642	+	4.68901i	0.183267	+	0.683962i	0.994995	+	0.0999262i	$0.0318607\pi$
$47$	1.25642	+	4.68901i	0.183267	+	0.683962i	−0.811728	+	0.584036i	$0.801473\pi$
$48$	−6.06965	−	5.78291i	−0.876079	−	0.834691i
$49$			0.948297i			0.135471i
$50$	2.28650	−	2.28650i	0.323359	−	0.323359i
$51$	5.81598	+	5.54122i	0.814400	+	0.775926i
$52$	4.80276	+	1.55053i	0.666023	+	0.215020i
$53$			0.186317i			0.0255926i	0.999918	+	0.0127963i	$0.00407330\pi$
$53$			0.186317i			0.0255926i	−0.999918	+	0.0127963i	$0.995927\pi$
$54$	5.37938	+	7.92814i	0.732041	+	1.07888i
$55$	−8.18091	+	14.1698i	−1.10311	+	1.91065i
$56$	−3.12030			−0.416968
$57$	0.699515	−	0.0169230i	0.0926530	−	0.00224150i
$58$	2.88028	+	10.7494i	0.378200	+	1.41146i
$59$	1.07545	+	4.01364i	0.140012	+	0.522532i	0.999927	+	0.0120945i	$0.00384988\pi$
$59$	1.07545	+	4.01364i	0.140012	+	0.522532i	−0.859915	+	0.510438i	$0.829483\pi$
$60$	−3.01741	+	5.53106i	−0.389545	+	0.714057i
$61$	0.0950990			0.0121762			0.00608809	−	0.999981i	$-0.498062\pi$
$61$	0.0950990			0.0121762			0.00608809	+	0.999981i	$0.498062\pi$
$62$	2.16752	−	3.75426i	0.275276	−	0.476791i
$63$	8.26592	+	1.79143i	1.04141	+	0.225699i
$64$			2.69361i			0.336702i
$65$	−0.472797	+	9.35815i	−0.0586433	+	1.16074i
$66$	4.73279	−	19.5419i	0.582566	−	2.40544i
$67$	−2.70944	+	2.70944i	−0.331010	+	0.331010i	−0.852970	−	0.521960i	$-0.825201\pi$
$67$	−2.70944	+	2.70944i	−0.331010	+	0.331010i	0.521960	+	0.852970i	$0.325201\pi$
$68$		−	6.49189i		−	0.787258i
$69$	−7.09110	+	2.08512i	−0.853668	+	0.251019i
$70$	3.49646	+	13.0490i	0.417907	+	1.55965i
$71$	−1.56243	+	5.83108i	−0.185427	+	0.692022i	0.809112	+	0.587655i	$0.199949\pi$
$71$	−1.56243	+	5.83108i	−0.185427	+	0.692022i	−0.994539	+	0.104368i	$0.966718\pi$
$72$	−0.703270	+	3.24499i	−0.0828811	+	0.382426i
$73$	−1.49562	−	1.49562i	−0.175049	−	0.175049i	0.614144	−	0.789194i	$-0.289501\pi$
$73$	−1.49562	−	1.49562i	−0.175049	−	0.175049i	−0.789194	+	0.614144i	$0.789501\pi$
$74$			3.07079i			0.356972i
$75$	−2.95220	−	0.714984i	−0.340891	−	0.0825592i
$76$	−0.399850	−	0.399850i	−0.0458659	−	0.0458659i
$77$	−8.87497	−	15.3719i	−1.01140	−	1.75179i
$78$	−2.68682	−	11.1969i	−0.304222	−	1.26780i
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	−0.980417	−	0.196931i	$-0.936902\pi$
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	0.660756	+	0.750601i	$0.270236\pi$
$80$	−12.1501	+	3.25561i	−1.35842	+	0.363988i
$81$	3.72603	−	8.19248i	0.414004	−	0.910275i
$82$	2.66543	−	1.53889i	0.294348	−	0.169942i
$83$	15.0939	−	4.04440i	1.65677	−	0.443931i	0.695275	−	0.718743i	$-0.255282\pi$
$83$	15.0939	−	4.04440i	1.65677	−	0.443931i	0.961498	+	0.274812i	$0.0886157\pi$
$84$	−3.55972	−	5.83500i	−0.388398	−	0.636651i
$85$	11.6423	−	3.11954i	1.26278	−	0.338362i
$86$	5.32701	+	1.42737i	0.574426	+	0.153917i
$87$	7.21106	−	7.56861i	0.773106	−	0.811440i
$88$	6.03462	−	3.48409i	0.643293	−	0.371405i
$89$	0.0313812	+	0.117116i	0.00332640	+	0.0124143i	0.967569	−	0.252607i	$-0.0812878\pi$
$89$	0.0313812	+	0.117116i	0.00332640	+	0.0124143i	−0.964243	+	0.265021i	$0.914621\pi$
$90$	14.3585	−	0.695139i	1.51351	−	0.0732741i
$91$	−8.53551	−	5.52023i	−0.894764	−	0.578678i
$92$	5.17297	+	2.98661i	0.539319	+	0.311376i
$93$	−4.07103	+	0.0984881i	−0.422146	+	0.0102127i
$94$	−8.95077			−0.923201
$95$	0.524935	−	0.909214i	0.0538572	−	0.0932833i
$96$	9.92301	−	6.05367i	1.01276	−	0.617850i
$97$	11.2137	−	11.2137i	1.13858	−	1.13858i	0.149879	−	0.988704i	$-0.452112\pi$
$97$	11.2137	−	11.2137i	1.13858	−	1.13858i	0.988704	−	0.149879i	$-0.0478885\pi$
$98$	−1.68893	−	0.452547i	−0.170608	−	0.0457141i
$99$	−17.9865	+	5.76503i	−1.80771	+	0.579407i
$100$	1.22739	+	2.12589i	0.122739	+	0.212589i
$101$	−1.75051	−	3.03197i	−0.174182	−	0.301693i	0.765696	−	0.643203i	$-0.222395\pi$
$101$	−1.75051	−	3.03197i	−0.174182	−	0.301693i	−0.939878	+	0.341510i	$0.889062\pi$
$102$	−12.6445	+	7.71394i	−1.25199	+	0.763794i
$103$	−10.5831	+	6.11018i	−1.04279	+	0.602054i	−0.920622	−	0.390456i	$-0.872317\pi$
$103$	−10.5831	+	6.11018i	−1.04279	+	0.602054i	−0.122166	+	0.992510i	$0.538984\pi$
$104$	2.16711	−	3.35083i	0.212502	−	0.328576i
$105$	8.75370	−	9.18775i	0.854274	−	0.896632i
$106$	−0.331833	−	0.0889144i	−0.0322305	−	0.00863613i
$107$	3.96991	+	2.29203i	0.383786	+	0.221579i	0.679464	−	0.733709i	$-0.262212\pi$
$107$	3.96991	+	2.29203i	0.383786	+	0.221579i	−0.295678	+	0.955288i	$0.595546\pi$
$108$	−6.87049	+	2.38685i	−0.661113	+	0.229675i
$109$	−7.19868	+	7.19868i	−0.689508	+	0.689508i	−0.962123	−	0.272615i	$-0.912111\pi$
$109$	−7.19868	+	7.19868i	−0.689508	+	0.689508i	0.272615	+	0.962123i	$0.412111\pi$
$110$	−21.3324	−	21.3324i	−2.03396	−	2.03396i
$111$	2.46254	−	1.50230i	0.233734	−	0.142592i
$112$	3.53181	−	13.1809i	0.333724	−	1.24548i
$113$	13.4282	+	7.75279i	1.26322	+	0.729322i	0.973697	−	0.227849i	$-0.0731692\pi$
$113$	13.4282	+	7.75279i	1.26322	+	0.729322i	0.289525	+	0.957170i	$0.406503\pi$
$114$	−0.303683	+	1.25392i	−0.0284425	+	0.117440i
$115$	−2.87031	+	10.7121i	−0.267658	+	0.998912i
$116$	−8.44821			−0.784397
$117$	−7.66461	+	7.63242i	−0.708593	+	0.705617i
$118$	−7.66158			−0.705305
$119$	−3.38420	+	12.6300i	−0.310229	+	1.15779i
$120$	3.60688	+	3.43648i	0.329261	+	0.313706i
$121$	24.8019	+	14.3194i	2.25471	+	1.30176i
$122$	−0.0453832	+	0.169372i	−0.00410880	+	0.0153343i
$123$	−2.53806	−	1.38461i	−0.228849	−	0.124846i
$124$	2.32704	+	2.32704i	0.208974	+	0.208974i
$125$	5.96543	−	5.96543i	0.533564	−	0.533564i
$126$	−7.13522	+	13.8668i	−0.635656	+	1.23535i
$127$	2.41225	+	1.39271i	0.214052	+	0.123583i	0.603193	−	0.797595i	$-0.293895\pi$
$127$	2.41225	+	1.39271i	0.214052	+	0.123583i	−0.389141	+	0.921178i	$0.627228\pi$
$128$	8.16731	+	2.18843i	0.721895	+	0.193431i
$129$	−1.46146	−	4.97015i	−0.128674	−	0.437597i
$130$	−16.4413	−	5.30796i	−1.44200	−	0.465539i
$131$	−11.1980	+	6.46515i	−0.978370	+	0.564862i	−0.901778	−	0.432200i	$-0.857737\pi$
$131$	−11.1980	+	6.46515i	−0.978370	+	0.564862i	−0.0765926	+	0.997062i	$0.524404\pi$
$132$	13.3998	+	7.31007i	1.16630	+	0.636260i
$133$	0.569470	+	0.986350i	0.0493793	+	0.0855274i
$134$	−3.53254	−	6.11854i	−0.305165	−	0.528561i
$135$	−7.58195	−	11.1743i	−0.652550	−	0.961730i
$136$	−4.95822	−	1.32855i	−0.425164	−	0.113922i
$137$	−0.300887	+	0.300887i	−0.0257065	+	0.0257065i	−0.719843	−	0.694137i	$-0.755786\pi$
$137$	−0.300887	+	0.300887i	−0.0257065	+	0.0257065i	0.694137	+	0.719843i	$0.255786\pi$
$138$	−0.329607	−	13.6244i	−0.0280580	−	1.15979i
$139$	−4.36753	+	7.56478i	−0.370449	+	0.641636i	−0.989635	−	0.143608i	$-0.954129\pi$
$139$	−4.36753	+	7.56478i	−0.370449	+	0.641636i	0.619186	+	0.785245i	$0.287463\pi$
$140$	−10.2555			−0.866749
$141$	4.37893	+	7.17782i	0.368772	+	0.604482i
$142$	−9.63961	−	5.56543i	−0.808938	−	0.467040i
$143$	22.6714	+	1.14542i	1.89588	+	0.0957845i
$144$	−12.9116	−	6.64372i	−1.07597	−	0.553643i
$145$	−4.05961	−	15.1507i	−0.337132	−	1.25819i
$146$	3.37746	−	1.94998i	0.279521	−	0.161381i
$147$	0.463356	+	1.57579i	0.0382170	+	0.129969i
$148$	−2.25175	−	0.603354i	−0.185093	−	0.0495954i
$149$	2.49557	−	0.668687i	0.204445	−	0.0547810i	−0.155143	−	0.987892i	$-0.549584\pi$
$149$	2.49557	−	0.668687i	0.204445	−	0.0547810i	0.359588	+	0.933111i	$0.382917\pi$
$150$	2.68225	−	4.91670i	0.219005	−	0.401447i
$151$	1.31486	−	0.352316i	0.107002	−	0.0286711i	−0.204921	−	0.978779i	$-0.565694\pi$
$151$	1.31486	−	0.352316i	0.107002	−	0.0286711i	0.311923	+	0.950107i	$0.399027\pi$
$152$	−0.387216	+	0.223559i	−0.0314074	+	0.0181331i
$153$	12.3720	+	6.36605i	1.00021	+	0.514665i
$154$	31.6129	−	8.47064i	2.54744	−	0.682584i
$155$	−3.05501	+	5.29143i	−0.245384	+	0.425018i
$156$	8.73838	+	0.229801i	0.699630	+	0.0183988i
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	0.513613	−	0.858022i	$-0.328307\pi$
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	−0.999875	+	0.0157906i	$0.994973\pi$
$158$	−7.40869	−	7.40869i	−0.589404	−	0.589404i
$159$	0.0910382	+	0.309603i	0.00721980	+	0.0245531i
$160$		−	17.4405i		−	1.37879i
$161$	−8.50712	−	8.50712i	−0.670455	−	0.670455i
$162$	12.8128	+	10.5457i	1.00667	+	0.828551i
$163$	6.32949	−	23.6220i	0.495764	−	1.85022i	−0.0299426	−	0.999552i	$-0.509532\pi$
$163$	6.32949	−	23.6220i	0.495764	−	1.85022i	0.525707	−	0.850666i	$-0.323801\pi$
$164$	0.604726	+	2.25687i	0.0472212	+	0.176232i
$165$	−6.67061	+	27.5432i	−0.519306	+	2.14424i
$166$			28.8125i			2.23629i
$167$	−5.44679	+	5.44679i	−0.421485	+	0.421485i	−0.885715	−	0.464230i	$-0.846331\pi$
$167$	−5.44679	+	5.44679i	−0.421485	+	0.421485i	0.464230	+	0.885715i	$0.346331\pi$
$168$	−5.18501	+	1.52464i	−0.400032	+	0.117629i
$169$	11.8561	−	5.33220i	0.912009	−	0.410169i
$170$			22.2238i			1.70448i
$171$	1.15412	−	0.369918i	0.0882575	−	0.0282883i
$172$	−2.09332	+	3.62573i	−0.159614	+	0.276460i
$173$	−11.6046			−0.882279			−0.441139	−	0.897439i	$-0.645426\pi$
$173$	−11.6046			−0.882279			−0.441139	+	0.897439i	$0.645426\pi$
$174$	10.0385	+	16.4549i	0.761019	+	1.24744i
$175$	−1.27966	−	4.77577i	−0.0967334	−	0.361014i
$176$	7.88714	+	29.4352i	0.594516	+	2.21876i
$177$	3.74823	+	6.14399i	0.281734	+	0.461811i
$178$	−0.223561			−0.0167566
$179$	2.75530	−	4.77232i	0.205941	−	0.356700i	−0.744491	−	0.667632i	$-0.767308\pi$
$179$	2.75530	−	4.77232i	0.205941	−	0.356700i	0.950432	+	0.310932i	$0.100641\pi$
$180$	−2.31144	+	10.6653i	−0.172285	+	0.794947i
$181$			9.65258i			0.717471i	0.933439	+	0.358735i	$0.116792\pi$
$181$			9.65258i			0.717471i	−0.933439	+	0.358735i	$0.883208\pi$
$182$	13.9049	−	12.5675i	1.03070	−	0.931563i
$183$	0.158026	−	0.0464672i	0.0116816	−	0.00343496i
$184$	3.33968	−	3.33968i	0.246205	−	0.246205i
$185$		−	4.32812i		−	0.318210i
$186$	1.76737	−	7.29755i	0.129590	−	0.535082i
$187$	−7.55751	−	28.2050i	−0.552660	−	2.06255i
$188$	1.75866	−	6.56341i	0.128264	−	0.478686i
$189$	14.6108	−	1.06207i	1.06278	−	0.0772544i
$190$	1.36881	+	1.36881i	0.0993040	+	0.0993040i
$191$		−	7.27544i		−	0.526433i	−0.964737	−	0.263216i	$-0.915217\pi$
$191$		−	7.27544i		−	0.526433i	0.964737	−	0.263216i	$-0.0847833\pi$
$192$	1.31615	+	4.47598i	0.0949851	+	0.323026i
$193$	−9.06750	−	9.06750i	−0.652693	−	0.652693i	0.300948	−	0.953641i	$-0.402697\pi$
$193$	−9.06750	−	9.06750i	−0.652693	−	0.652693i	−0.953641	+	0.300948i	$0.902697\pi$
$194$	14.6204	+	25.3233i	1.04968	+	1.81810i
$195$	3.78693	+	15.7815i	0.271187	+	1.13013i
$196$	0.663686	−	1.14954i	0.0474062	−	0.0821099i
$197$	−15.2346	+	4.08211i	−1.08542	+	0.290838i	−0.756816	−	0.653628i	$-0.773246\pi$
$197$	−15.2346	+	4.08211i	−1.08542	+	0.290838i	−0.328608	+	0.944467i	$0.606579\pi$
$198$	−1.68407	−	34.7853i	−0.119682	−	2.47208i
$199$	−21.4175	+	12.3654i	−1.51825	+	0.876560i	−0.518477	+	0.855091i	$0.673501\pi$
$199$	−21.4175	+	12.3654i	−1.51825	+	0.876560i	−0.999770	+	0.0214686i	$0.993166\pi$
$200$	1.87485	−	0.502364i	0.132572	−	0.0355225i
$201$	−3.17839	+	5.82615i	−0.224186	+	0.410945i
$202$	6.23536	−	1.67076i	0.438718	−	0.117554i
$203$	16.4360	+	4.40402i	1.15358	+	0.309102i
$204$	−3.17207	−	10.7876i	−0.222089	−	0.755282i
$205$	−3.75678	+	2.16898i	−0.262385	+	0.151488i
$206$	−5.83181	−	21.7646i	−0.406321	−	1.51641i
$207$	−10.7645	+	6.92970i	−0.748181	+	0.481647i
$208$	11.7018	+	12.9471i	0.811372	+	0.897719i
$209$	−2.20269	−	1.27173i	−0.152363	−	0.0879671i
$210$	12.1860	+	19.9750i	0.840917	+	1.37841i
$211$	14.4023			0.991498			0.495749	−	0.868466i	$-0.334894\pi$
$211$	14.4023			0.991498			0.495749	+	0.868466i	$0.334894\pi$
$212$	0.130398	−	0.225856i	0.00895578	−	0.0155119i
$213$	0.252883	+	10.4530i	0.0173272	+	0.716225i
$214$	−5.97665	+	5.97665i	−0.408556	+	0.408556i
$215$	−7.50814	−	2.01180i	−0.512051	−	0.137204i
$216$	0.416943	+	5.73584i	0.0283694	+	0.390275i
$217$	−3.31419	−	5.74035i	−0.224982	−	0.389680i
$218$	−9.38557	−	16.2563i	−0.635671	−	1.10101i
$219$	−3.21607	−	1.75449i	−0.217322	−	0.118557i
$220$	19.8340	−	11.4512i	1.33721	−	0.772038i
$221$	−11.2127	−	12.4060i	−0.754248	−	0.834517i
$222$	1.50045	+	5.10274i	0.100704	+	0.342473i
$223$	−0.984477	−	0.263790i	−0.0659254	−	0.0176647i	0.225706	−	0.974196i	$-0.427531\pi$
$223$	−0.984477	−	0.263790i	−0.0659254	−	0.0176647i	−0.291631	+	0.956531i	$0.594198\pi$
$224$	16.3853	+	9.46008i	1.09479	+	0.632078i
$225$	−5.25503	+	0.254413i	−0.350335	+	0.0169609i
$226$	−20.2161	+	20.2161i	−1.34475	+	1.34475i
$227$	5.49340	+	5.49340i	0.364609	+	0.364609i	0.865507	−	0.500897i	$-0.166997\pi$
$227$	5.49340	+	5.49340i	0.364609	+	0.364609i	−0.500897	+	0.865507i	$0.666997\pi$
$228$	−0.859806	−	0.469057i	−0.0569420	−	0.0310640i
$229$	4.06263	−	15.1620i	0.268466	−	1.00193i	−0.691628	−	0.722254i	$-0.743106\pi$
$229$	4.06263	−	15.1620i	0.268466	−	1.00193i	0.960094	−	0.279676i	$-0.0902272\pi$
$230$	−17.7087	−	10.2241i	−1.16768	−	0.674158i
$231$	−22.2586	−	21.2070i	−1.46451	−	1.39532i
$232$	−1.72891	+	6.45237i	−0.113508	+	0.423619i
$233$	−9.38345			−0.614730			−0.307365	−	0.951592i	$-0.599447\pi$
$233$	−9.38345			−0.614730			−0.307365	+	0.951592i	$0.599447\pi$
$234$	−9.93572	−	17.2931i	−0.649518	−	1.13049i
$235$	12.6156			0.822953
$236$	1.50536	−	5.61808i	0.0979905	−	0.365706i
$237$	−2.31669	+	9.56570i	−0.150485	+	0.621359i
$238$	−20.8792	−	12.0546i	−1.35340	−	0.781384i
$239$	−4.63155	+	17.2852i	−0.299590	+	1.11809i	0.637913	+	0.770108i	$0.279798\pi$
$239$	−4.63155	+	17.2852i	−0.299590	+	1.11809i	−0.937503	+	0.347977i	$0.886869\pi$
$240$	−18.5991	+	11.3466i	−1.20056	+	0.732421i
$241$	−10.7084	−	10.7084i	−0.689788	−	0.689788i	0.272397	−	0.962185i	$-0.412184\pi$
$241$	−10.7084	−	10.7084i	−0.689788	−	0.689788i	−0.962185	+	0.272397i	$0.912184\pi$
$242$	−37.3389	+	37.3389i	−2.40024	+	2.40024i
$243$	2.18855	−	15.4341i	0.140395	−	0.990096i
$244$	−0.115280	−	0.0665571i	−0.00738006	−	0.00426088i
$245$	2.38045	+	0.637841i	0.152082	+	0.0407502i
$246$	3.67722	−	3.85955i	0.234451	−	0.246076i
$247$	−1.45473	−	0.0734965i	−0.0925621	−	0.00467647i
$248$	2.25352	−	1.30107i	0.143098	−	0.0826179i
$249$	23.1054	−	14.0958i	1.46425	−	0.893284i
$250$	7.77767	+	13.4713i	0.491903	+	0.852002i
$251$	−8.02608	−	13.9016i	−0.506602	−	0.877460i	−0.999971	−	0.00763991i	$-0.997568\pi$
$251$	−8.02608	−	13.9016i	−0.506602	−	0.877460i	0.493369	−	0.869820i	$-0.335765\pi$
$252$	−8.76629	−	7.95668i	−0.552225	−	0.501224i
$253$	25.9516	+	6.95371i	1.63156	+	0.437176i
$254$	−3.63161	+	3.63161i	−0.227868	+	0.227868i
$255$	17.8217	−	10.8724i	1.11604	−	0.680856i
$256$	−10.4888	+	18.1672i	−0.655552	+	1.13545i
$257$	14.3574			0.895588			0.447794	−	0.894137i	$-0.352210\pi$
$257$	14.3574			0.895588			0.447794	+	0.894137i	$0.352210\pi$
$258$	9.54934	−	0.231022i	0.594516	−	0.0143828i
$259$	4.06626	+	2.34766i	0.252665	+	0.145876i
$260$	7.12264	−	11.0132i	0.441727	−	0.683008i
$261$	8.28445	−	16.1002i	0.512795	−	0.996580i
$262$	−6.17060	−	23.0290i	−0.381221	−	1.42274i
$263$	−15.6938	+	9.06082i	−0.967721	+	0.558714i	−0.898541	−	0.438890i	$-0.855372\pi$
$263$	−15.6938	+	9.06082i	−0.967721	+	0.558714i	−0.0691806	+	0.997604i	$0.522038\pi$
$264$	8.32534	−	8.73815i	0.512389	−	0.537796i
$265$	0.467701	+	0.125320i	0.0287306	+	0.00769835i
$266$	−2.02846	+	0.543525i	−0.124373	+	0.0333257i
$267$	0.109371	+	0.179279i	0.00669343	+	0.0109717i
$268$	5.18067	−	1.38816i	0.316460	−	0.0847952i
$269$	−2.52163	+	1.45587i	−0.153747	+	0.0887657i	−0.574900	−	0.818224i	$-0.694959\pi$
$269$	−2.52163	+	1.45587i	−0.153747	+	0.0887657i	0.421153	+	0.906990i	$0.361626\pi$
$270$	23.5198	−	8.17094i	1.43137	−	0.497267i
$271$	13.0634	−	3.50032i	0.793544	−	0.212629i	0.160796	−	0.986988i	$-0.448594\pi$
$271$	13.0634	−	3.50032i	0.793544	−	0.212629i	0.632748	+	0.774358i	$0.281927\pi$
$272$	11.2242	−	19.4409i	0.680569	−	1.17878i
$273$	−16.8808	−	5.00236i	−1.02167	−	0.302757i
$274$	−0.392294	−	0.679474i	−0.0236994	−	0.0410485i
$275$	7.80741	+	7.80741i	0.470805	+	0.470805i
$276$	10.0552	+	2.43525i	0.605254	+	0.146585i
$277$			25.2517i			1.51723i	0.651540	+	0.758615i	$0.274123\pi$
$277$			25.2517i			1.51723i	−0.651540	+	0.758615i	$0.725877\pi$
$278$	−11.3887	−	11.3887i	−0.683048	−	0.683048i
$279$	−6.71671	+	2.15284i	−0.402119	+	0.128887i
$280$	−2.09877	+	7.83271i	−0.125425	+	0.468094i
$281$	−5.40894	−	20.1864i	−0.322670	−	1.20422i	−0.916633	−	0.399729i	$-0.869104\pi$
$281$	−5.40894	−	20.1864i	−0.322670	−	1.20422i	0.593963	−	0.804492i	$-0.297563\pi$
$282$	−14.8735	+	4.37352i	−0.885704	+	0.260439i
$283$		−	2.16398i		−	0.128635i	−0.997929	−	0.0643177i	$-0.979513\pi$
$283$		−	2.16398i		−	0.128635i	0.997929	−	0.0643177i	$-0.0204871\pi$
$284$	5.97502	−	5.97502i	0.354552	−	0.354552i
$285$	0.428025	−	1.76733i	0.0253540	−	0.104688i
$286$	−12.8593	+	39.8314i	−0.760384	+	2.35528i
$287$		−	4.70599i		−	0.277786i
$288$	13.5311	−	14.9080i	0.797330	−	0.878460i
$289$	−2.25512	+	3.90599i	−0.132654	+	0.229764i
$290$	28.9208			1.69829
$291$	13.1546	−	24.1132i	0.771139	−	1.41354i
$292$	0.766270	+	2.85976i	0.0448425	+	0.167355i
$293$	−8.29952	−	30.9742i	−0.484863	−	1.80953i	−0.580676	−	0.814135i	$-0.697212\pi$
$293$	−8.29952	−	30.9742i	−0.484863	−	1.80953i	0.0958129	−	0.995399i	$-0.469455\pi$
$294$	−3.02762	+	0.0732455i	−0.176574	+	0.00427176i
$295$	10.7986			0.628718
$296$	−0.921631	+	1.59631i	−0.0535687	+	0.0927837i
$297$	−27.0712	+	18.3683i	−1.57083	+	1.06584i
$298$			4.76376i			0.275957i
$299$	15.0440	−	3.22727i	0.870015	−	0.186638i
$300$	3.07830	+	2.93288i	0.177726	+	0.169330i
$301$	5.96264	−	5.96264i	0.343681	−	0.343681i
$302$			2.50992i			0.144429i
$303$	−4.39031	−	4.18290i	−0.252216	−	0.240301i
$304$	−0.506085	−	1.88873i	−0.0290260	−	0.108326i
$305$	0.0639652	−	0.238721i	0.00366264	−	0.0136691i
$306$	−17.2422	+	18.9966i	−0.985670	+	1.08596i
$307$	18.5795	+	18.5795i	1.06039	+	1.06039i	0.998055	+	0.0623341i	$0.0198544\pi$
$307$	18.5795	+	18.5795i	1.06039	+	1.06039i	0.0623341	+	0.998055i	$0.480146\pi$
$308$			24.8454i			1.41570i
$309$	−14.6005	+	15.3244i	−0.830591	+	0.871776i
$310$	−7.96618	−	7.96618i	−0.452449	−	0.452449i
$311$	−3.45338	−	5.98144i	−0.195823	−	0.339176i	0.751347	−	0.659908i	$-0.229405\pi$
$311$	−3.45338	−	5.98144i	−0.195823	−	0.339176i	−0.947170	+	0.320732i	$0.896071\pi$
$312$	1.96380	−	6.62696i	0.111178	−	0.375178i
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	0.124613	+	0.992205i	$0.460231\pi$
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	−0.921582	+	0.388185i	$0.873102\pi$
$314$	21.7029	−	5.81527i	1.22476	−	0.328175i
$315$	10.0567	−	19.5445i	0.566632	−	1.10121i
$316$	6.88831	−	3.97697i	0.387498	−	0.223722i
$317$	−0.698082	+	0.187051i	−0.0392082	+	0.0105058i	−0.278370	−	0.960474i	$-0.589794\pi$
$317$	−0.698082	+	0.187051i	−0.0392082	+	0.0105058i	0.239162	+	0.970980i	$0.423127\pi$
$318$	−0.594853	+	0.0143909i	−0.0333577	+	0.000807004i
$319$	−36.7045	+	9.83495i	−2.05506	+	0.550651i
$320$	6.76162	+	1.81177i	0.377986	+	0.101281i
$321$	7.71673	+	1.86889i	0.430706	+	0.104311i
$322$	19.2111	−	11.0915i	1.07059	−	0.618106i
$323$	0.484934	+	1.80980i	0.0269824	+	0.100700i
$324$	−10.2504	+	7.32329i	−0.569469	+	0.406849i
$325$	6.01734	+	1.94265i	0.333782	+	0.107759i
$326$	39.0505	+	22.5458i	2.16281	+	1.24870i
$327$	−8.44464	+	15.4795i	−0.466989	+	0.856016i
$328$	1.84745			0.102009
$329$	−6.84296	+	11.8524i	−0.377265	+	0.653442i
$330$	−45.8715	−	25.0246i	−2.52514	−	1.37756i
$331$	−3.42545	+	3.42545i	−0.188280	+	0.188280i	−0.794952	−	0.606672i	$-0.792504\pi$
$331$	−3.42545	+	3.42545i	−0.188280	+	0.188280i	0.606672	+	0.794952i	$0.292504\pi$
$332$	−21.1276	−	5.66113i	−1.15953	−	0.310695i
$333$	3.35795	−	3.69962i	0.184014	−	0.202738i
$334$	−7.10148	−	12.3001i	−0.388575	−	0.673032i
$335$	4.97892	+	8.62375i	0.272028	+	0.471166i
$336$	−0.571629	−	23.6284i	−0.0311849	−	1.28903i
$337$	21.7282	−	12.5448i	1.18361	−	0.683359i	0.226765	−	0.973949i	$-0.427185\pi$
$337$	21.7282	−	12.5448i	1.18361	−	0.683359i	0.956848	+	0.290590i	$0.0938516\pi$
$338$	3.83872	+	23.6605i	0.208799	+	1.28696i
$339$	26.1019	+	6.32153i	1.41766	+	0.343338i
$340$	−16.2962	−	4.36656i	−0.883787	−	0.236810i
$341$	12.8192	+	7.40117i	0.694198	+	0.400796i
$342$	0.108060	+	2.23203i	0.00584320	+	0.120694i
$343$	12.0642	−	12.0642i	0.651407	−	0.651407i
$344$	2.34078	+	2.34078i	0.126207	+	0.126207i
$345$	0.464564	+	19.2029i	0.0250113	+	1.03385i
$346$	5.53794	−	20.6679i	0.297721	−	1.11111i
$347$	−23.7482	−	13.7111i	−1.27487	−	0.736048i	−0.298972	−	0.954262i	$-0.596644\pi$
$347$	−23.7482	−	13.7111i	−1.27487	−	0.736048i	−0.975901	+	0.218214i	$0.929977\pi$
$348$	−14.0384	+	4.12796i	−0.752537	+	0.221282i
$349$	0.265695	−	0.991586i	0.0142223	−	0.0530784i	−0.958450	−	0.285261i	$-0.907920\pi$
$349$	0.265695	−	0.991586i	0.0142223	−	0.0530784i	0.972672	+	0.232182i	$0.0745865\pi$
$350$	9.11638			0.487291
$351$	−9.00694	+	16.4279i	−0.480755	+	0.876855i
$352$	−42.2520			−2.25204
$353$	−4.96485	+	18.5291i	−0.264252	+	0.986203i	0.698454	+	0.715655i	$0.253872\pi$
$353$	−4.96485	+	18.5291i	−0.264252	+	0.986203i	−0.962706	+	0.270548i	$0.912795\pi$
$354$	−12.7313	+	3.74360i	−0.676659	+	0.198970i
$355$	13.5865	+	7.84418i	0.721097	+	0.416326i
$356$	0.0439257	−	0.163933i	0.00232806	−	0.00868842i
$357$	0.547738	+	22.6409i	0.0289894	+	1.19828i
$358$	7.18467	+	7.18467i	0.379721	+	0.379721i
$359$	18.1179	−	18.1179i	0.956226	−	0.956226i	−0.0428555	−	0.999081i	$-0.513646\pi$
$359$	18.1179	−	18.1179i	0.956226	−	0.956226i	0.999081	+	0.0428555i	$0.0136455\pi$
$360$	7.67269	+	3.94802i	0.404386	+	0.208079i
$361$	−16.3131	−	9.41840i	−0.858587	−	0.495705i
$362$	−17.1914	−	4.60641i	−0.903558	−	0.242108i
$363$	48.2100	+	11.6758i	2.53037	+	0.612822i
$364$	6.48340	+	12.6655i	0.339823	+	0.663851i
$365$	−4.76035	+	2.74839i	−0.249168	+	0.143857i
$366$	0.00734535	+	0.303621i	0.000383947	+	0.0158705i
$367$	−11.6527	−	20.1831i	−0.608268	−	1.05355i	−0.991526	−	0.129910i	$-0.958531\pi$
$367$	−11.6527	−	20.1831i	−0.608268	−	1.05355i	0.383258	−	0.923641i	$-0.374802\pi$
$368$	10.3275	+	17.8877i	0.538357	+	0.932461i
$369$	−4.89404	−	1.06066i	−0.254774	−	0.0552157i
$370$	7.70843	+	2.06547i	0.400742	+	0.107379i
$371$	−0.371428	+	0.371428i	−0.0192836	+	0.0192836i
$372$	5.00388	+	2.72981i	0.259439	+	0.141534i
$373$	−3.51100	+	6.08123i	−0.181793	+	0.314874i	−0.942491	−	0.334231i	$-0.891523\pi$
$373$	−3.51100	+	6.08123i	−0.181793	+	0.314874i	0.760698	+	0.649106i	$0.224857\pi$
$374$	53.8401			2.78400
$375$	6.99794	−	12.8276i	0.361372	−	0.662414i
$376$	−4.65294	−	2.68638i	−0.239957	−	0.138539i
$377$	−16.1445	+	14.5916i	−0.831484	+	0.751507i
$378$	−5.08102	+	26.5289i	−0.261340	+	1.36450i
$379$	2.49511	+	9.31188i	0.128165	+	0.478319i	0.999933	−	0.0116007i	$-0.00369271\pi$
$379$	2.49511	+	9.31188i	0.128165	+	0.478319i	−0.871767	+	0.489920i	$0.837026\pi$
$380$	−1.27267	+	0.734774i	−0.0652864	+	0.0376931i
$381$	4.68894	+	1.13560i	0.240222	+	0.0581786i
$382$	12.9577	+	3.47199i	0.662971	+	0.177643i
$383$	22.3537	−	5.98966i	1.14222	−	0.306057i	0.362377	−	0.932032i	$-0.381965\pi$
$383$	22.3537	−	5.98966i	1.14222	−	0.306057i	0.779844	+	0.625974i	$0.215299\pi$
$384$	14.6409	−	0.354200i	0.747142	−	0.0180752i
$385$	−44.5566	+	11.9389i	−2.27082	+	0.608463i
$386$	20.4765	−	11.8221i	1.04223	−	0.601731i
$387$	−4.85702	−	7.54481i	−0.246896	−	0.383524i
$388$	−21.4416	+	5.74527i	−1.08853	+	0.291672i
$389$	2.26345	−	3.92041i	0.114761	−	0.198772i	−0.802923	−	0.596083i	$-0.796723\pi$
$389$	2.26345	−	3.92041i	0.114761	−	0.198772i	0.917684	+	0.397310i	$0.130056\pi$
$390$	−29.9142	−	0.786682i	−1.51476	−	0.0398352i
$391$	−9.89585	−	17.1401i	−0.500455	−	0.866813i
$392$	−0.742145	−	0.742145i	−0.0374840	−	0.0374840i
$393$	−15.4487	+	16.2147i	−0.779282	+	0.817923i
$394$		−	29.0812i		−	1.46509i
$395$	10.4422	+	10.4422i	0.525402	+	0.525402i
$396$	25.8382	+	5.59978i	1.29842	+	0.281399i
$397$	−2.03359	+	7.58947i	−0.102063	+	0.380905i	−0.997995	−	0.0632859i	$-0.979842\pi$
$397$	−2.03359	+	7.58947i	−0.102063	+	0.380905i	0.895932	+	0.444191i	$0.146509\pi$
$398$	−11.8021	−	44.0459i	−0.591583	−	2.20782i
$399$	1.42824	+	1.36077i	0.0715013	+	0.0681235i
$400$			8.48840i			0.424420i
$401$	−0.183248	+	0.183248i	−0.00915098	+	0.00915098i	−0.711667	−	0.702516i	$-0.752060\pi$
$401$	−0.183248	+	0.183248i	−0.00915098	+	0.00915098i	0.702516	+	0.711667i	$0.252060\pi$
$402$	−8.85966	−	8.44111i	−0.441880	−	0.421004i
$403$	8.46620	+	0.427734i	0.421731	+	0.0213069i
$404$			4.90053i			0.243811i
$405$	−18.0589	−	14.8636i	−0.897354	−	0.738580i
$406$	−15.6872	+	27.1711i	−0.778544	+	1.34848i
$407$	−10.4855			−0.519745
$408$	−8.88824	+	0.215028i	−0.440034	+	0.0106455i
$409$	9.55921	+	35.6754i	0.472672	+	1.76404i	0.630108	+	0.776508i	$0.283011\pi$
$409$	9.55921	+	35.6754i	0.472672	+	1.76404i	−0.157435	+	0.987529i	$0.550323\pi$
$410$	−2.07016	−	7.72596i	−0.102238	−	0.381558i
$411$	−0.352965	+	0.647004i	−0.0174105	+	0.0319144i
$412$	17.1054			0.842721
$413$	−5.85736	+	10.1453i	−0.288222	+	0.499215i
$414$	−7.20485	−	22.4786i	−0.354099	−	1.10476i
$415$		−	40.6097i		−	1.99345i
$416$	−21.5389	+	11.0257i	−1.05603	+	0.540578i
$417$	−3.56123	+	14.7045i	−0.174394	+	0.720081i
$418$	3.31613	−	3.31613i	0.162197	−	0.162197i
$419$		−	29.1073i		−	1.42199i	−0.703199	−	0.710993i	$-0.748246\pi$
$419$		−	29.1073i		−	1.42199i	0.703199	−	0.710993i	$-0.251754\pi$
$420$	−17.0416	+	5.01104i	−0.831545	+	0.244514i
$421$	1.88779	+	7.04531i	0.0920051	+	0.343368i	0.996548	−	0.0830142i	$-0.0264547\pi$
$421$	1.88779	+	7.04531i	0.0920051	+	0.343368i	−0.904543	+	0.426382i	$0.859788\pi$
$422$	−6.87309	+	25.6507i	−0.334577	+	1.24866i
$423$	10.7837	+	9.78776i	0.524321	+	0.475897i
$424$	−0.145813	−	0.145813i	−0.00708132	−	0.00708132i
$425$		−	8.13364i		−	0.394540i
$426$	−18.7375	−	4.53798i	−0.907836	−	0.219866i
$427$	0.189582	+	0.189582i	0.00917453	+	0.00917453i
$428$	−3.20825	−	5.55686i	−0.155077	−	0.268601i
$429$	38.2327	−	9.17434i	1.84589	−	0.442941i
$430$	7.16608	−	12.4120i	0.345579	−	0.598560i
$431$	14.6266	−	3.91918i	0.704537	−	0.188780i	0.111275	−	0.993790i	$-0.464506\pi$
$431$	14.6266	−	3.91918i	0.704537	−	0.188780i	0.593262	+	0.805009i	$0.297840\pi$
$432$	−24.7015	−	4.73102i	−1.18845	−	0.227621i
$433$	26.0240	−	15.0250i	1.25063	−	0.722054i	0.279399	−	0.960175i	$-0.409865\pi$
$433$	26.0240	−	15.0250i	1.25063	−	0.722054i	0.971235	+	0.238121i	$0.0765316\pi$
$434$	11.8052	−	3.16320i	0.566669	−	0.151838i
$435$	−14.1488	−	23.1923i	−0.678381	−	1.11198i
$436$	13.7645	−	3.68818i	0.659199	−	0.176632i
$437$	−1.66520	−	0.446190i	−0.0796575	−	0.0213442i
$438$	4.65954	−	4.89058i	0.222641	−	0.233681i
$439$	13.5780	−	7.83924i	0.648041	−	0.374146i	−0.139664	−	0.990199i	$-0.544602\pi$
$439$	13.5780	−	7.83924i	0.648041	−	0.374146i	0.787705	+	0.616052i	$0.211269\pi$
$440$	−4.68692	−	17.4918i	−0.223440	−	0.833890i
$441$	1.53992	+	2.39208i	0.0733295	+	0.113909i
$442$	27.4461	−	14.0496i	1.30548	−	0.668270i
$443$	11.9145	+	6.87886i	0.566076	+	0.326824i	0.755581	−	0.655056i	$-0.227355\pi$
$443$	11.9145	+	6.87886i	0.566076	+	0.326824i	−0.189504	+	0.981880i	$0.560688\pi$
$444$	−4.03654	+	0.0976538i	−0.191566	+	0.00463445i
$445$	0.315098			0.0149371
$446$	0.939626	−	1.62748i	0.0444926	−	0.0770634i
$447$	3.82016	−	2.33054i	0.180688	−	0.110231i
$448$	−5.36979	+	5.36979i	−0.253699	+	0.253699i
$449$	−11.5500	−	3.09482i	−0.545079	−	0.146054i	−0.0242366	−	0.999706i	$-0.507715\pi$
$449$	−11.5500	−	3.09482i	−0.545079	−	0.146054i	−0.520843	+	0.853653i	$0.674382\pi$
$450$	2.05470	−	9.48068i	0.0968594	−	0.446924i
$451$	5.25465	+	9.10132i	0.247432	+	0.428564i
$452$	−10.8519	−	18.7961i	−0.510432	−	0.884094i
$453$	2.01276	−	1.22791i	0.0945676	−	0.0576923i
$454$	−12.4054	+	7.16224i	−0.582213	+	0.336141i
$455$	−19.5983	+	17.7132i	−0.918780	+	0.830407i
$456$	−0.534202	+	0.560690i	−0.0250163	+	0.0262567i
$457$	37.9781	+	10.1762i	1.77654	+	0.476023i	0.989946	−	0.141446i	$-0.0451750\pi$
$457$	37.9781	+	10.1762i	1.77654	+	0.476023i	0.786596	+	0.617468i	$0.211842\pi$
$458$	25.0649	+	14.4712i	1.17120	+	0.676195i
$459$	23.6691	+	4.53329i	1.10478	+	0.211596i
$460$	10.9765	−	10.9765i	0.511784	−	0.511784i
$461$	−12.7210	−	12.7210i	−0.592474	−	0.592474i	0.345825	−	0.938299i	$-0.387599\pi$
$461$	−12.7210	−	12.7210i	−0.592474	−	0.592474i	−0.938299	+	0.345825i	$0.887599\pi$
$462$	48.3922	−	29.5223i	2.25141	−	1.37350i
$463$	−8.75526	+	32.6751i	−0.406891	+	1.51854i	0.393649	+	0.919261i	$0.371213\pi$
$463$	−8.75526	+	32.6751i	−0.406891	+	1.51854i	−0.800540	+	0.599279i	$0.795454\pi$
$464$	−25.2994	−	14.6066i	−1.17450	−	0.678095i
$465$	−2.49101	+	10.2855i	−0.115518	+	0.476979i
$466$	4.47798	−	16.7120i	0.207438	−	0.774171i
$467$	15.4828			0.716459			0.358229	−	0.933634i	$-0.383381\pi$
$467$	15.4828			0.716459			0.358229	+	0.933634i	$0.383381\pi$
$468$	14.6329	−	3.88788i	0.676404	−	0.179717i
$469$	−10.8027			−0.498821
$470$	−6.02044	+	22.4686i	−0.277702	+	1.03640i
$471$	−15.2810	−	14.5591i	−0.704110	−	0.670846i
$472$	−3.98277	−	2.29945i	−0.183322	−	0.105841i
$473$	−4.87385	+	18.1895i	−0.224100	+	0.836353i
$474$	−15.9311	−	8.69100i	−0.731738	−	0.399191i
$475$	−0.500969	−	0.500969i	−0.0229860	−	0.0229860i
$476$	12.9418	−	12.9418i	0.593185	−	0.593185i
$477$	0.302556	+	0.469985i	0.0138531	+	0.0215191i
$478$	−28.5748	−	16.4977i	−1.30698	−	0.754587i
$479$	−29.7901	−	7.98222i	−1.36114	−	0.364717i	−0.496907	−	0.867804i	$-0.665531\pi$
$479$	−29.7901	−	7.98222i	−1.36114	−	0.364717i	−0.864236	+	0.503087i	$0.832198\pi$
$480$	−8.52178	−	28.9809i	−0.388964	−	1.32279i
$481$	−5.34519	+	2.73618i	−0.243720	+	0.124759i
$482$	24.1820	−	13.9615i	1.10146	−	0.635929i
$483$	−18.2930	−	9.97954i	−0.832362	−	0.454085i
$484$	−20.0434	−	34.7163i	−0.911065	−	1.57801i
$485$	−20.6067	−	35.6918i	−0.935700	−	1.62068i
$486$	26.4438	+	11.2633i	1.19952	+	0.510913i
$487$	−36.9964	−	9.91314i	−1.67647	−	0.449207i	−0.709623	−	0.704582i	$-0.751135\pi$
$487$	−36.9964	−	9.91314i	−1.67647	−	0.449207i	−0.966842	+	0.255374i	$0.917801\pi$
$488$	−0.0744253	+	0.0744253i	−0.00336907	+	0.00336907i
$489$	−1.02444	−	42.3454i	−0.0463267	−	1.91493i
$490$	−2.27200	+	3.93523i	−0.102639	+	0.177775i
$491$	−32.8792			−1.48382			−0.741909	−	0.670501i	$-0.766079\pi$
$491$	−32.8792			−1.48382			−0.741909	+	0.670501i	$0.766079\pi$
$492$	2.10762	+	3.45476i	0.0950190	+	0.155753i
$493$	24.2421	+	13.9962i	1.09181	+	0.630355i
$494$	0.825124	−	2.55581i	0.0371241	−	0.114991i
$495$	2.37361	+	49.0280i	0.106686	+	2.20365i
$496$	2.94531	+	10.9920i	0.132248	+	0.493557i
$497$	−14.7392	+	8.50967i	−0.661142	+	0.381711i
$498$	14.0784	+	47.8778i	0.630867	+	2.14546i
$499$	−18.6315	−	4.99230i	−0.834061	−	0.223486i	−0.183576	−	0.983005i	$-0.558767\pi$
$499$	−18.6315	−	4.99230i	−0.834061	−	0.223486i	−0.650485	+	0.759520i	$0.725434\pi$
$500$	−11.4064	+	3.05634i	−0.510110	+	0.136684i
$501$	−6.38953	+	11.7123i	−0.285463	+	0.523269i
$502$	28.5891	−	7.66043i	1.27599	−	0.341902i
$503$	−14.1918	+	8.19366i	−0.632783	+	0.365337i	−0.781829	−	0.623493i	$-0.785713\pi$
$503$	−14.1918	+	8.19366i	−0.632783	+	0.365337i	0.149046	+	0.988830i	$0.452380\pi$
$504$	−7.87097	+	5.06699i	−0.350601	+	0.225702i
$505$	−8.78841	+	2.35485i	−0.391079	+	0.104789i
$506$	−24.7693	+	42.9016i	−1.10113	+	1.90721i
$507$	17.0959	−	14.6537i	0.759256	−	0.650792i
$508$	−1.94944	−	3.37653i	−0.0864925	−	0.149809i
$509$	−7.64282	−	7.64282i	−0.338762	−	0.338762i	0.517139	−	0.855901i	$-0.326997\pi$
$509$	−7.64282	−	7.64282i	−0.338762	−	0.338762i	−0.855901	+	0.517139i	$0.826997\pi$
$510$	10.8590	+	36.9293i	0.480843	+	1.63525i
$511$		−	5.96312i		−	0.263793i
$512$	−15.3927	−	15.3927i	−0.680269	−	0.680269i
$513$	1.73705	−	1.17862i	0.0766925	−	0.0520372i
$514$	−6.85164	+	25.5707i	−0.302213	+	1.12787i
$515$	8.21962	+	30.6761i	0.362200	+	1.35175i
$516$	−1.70686	+	7.04772i	−0.0751405	+	0.310259i
$517$		−	30.5631i		−	1.34416i
$518$	−6.12171	+	6.12171i	−0.268972	+	0.268972i
$519$	−19.2833	+	5.67022i	−0.846444	+	0.248895i
$520$	−6.95375	−	7.69378i	−0.304942	−	0.337395i
$521$			18.8001i			0.823648i	0.911263	+	0.411824i	$0.135108\pi$
$521$			18.8001i			0.823648i	−0.911263	+	0.411824i	$0.864892\pi$
$522$	24.7212	+	22.4381i	1.08202	+	0.982088i
$523$	−1.02893	+	1.78216i	−0.0449919	+	0.0779283i	−0.887644	−	0.460530i	$-0.847660\pi$
$523$	−1.02893	+	1.78216i	−0.0449919	+	0.0779283i	0.842652	+	0.538458i	$0.180993\pi$
$524$	18.0991			0.790663
$525$	−4.45995	−	7.31063i	−0.194648	−	0.319062i
$526$	−8.64803	−	32.2749i	−0.377072	−	1.40725i
$527$	−2.82221	−	10.5326i	−0.122937	−	0.458809i
$528$	27.4887	+	45.0587i	1.19629	+	1.96093i
$529$	−4.78954			−0.208241
$530$	−0.446393	+	0.773176i	−0.0193901	+	0.0335846i
$531$	9.23051	+	8.37802i	0.400570	+	0.363575i
$532$		−	1.59422i		−	0.0691183i
$533$	5.05366	+	3.26839i	0.218898	+	0.141570i
$534$	−0.371492	+	0.109236i	−0.0160760	+	0.00472712i
$535$	8.42378	−	8.42378i	0.364192	−	0.364192i
$536$		−	4.24085i		−	0.183177i
$537$	2.24664	−	9.27646i	0.0969495	−	0.400309i
$538$	−1.38954	−	5.18583i	−0.0599073	−	0.223577i
$539$	1.54526	−	5.76697i	0.0665589	−	0.248401i
$540$	1.37037	+	18.8520i	0.0589713	+	0.811262i
$541$	23.9398	+	23.9398i	1.02925	+	1.02925i	0.999559	+	0.0296937i	$0.00945319\pi$
$541$	23.9398	+	23.9398i	1.02925	+	1.02925i	0.0296937	+	0.999559i	$0.490547\pi$
$542$			24.9365i			1.07111i
$543$	4.71644	+	16.0397i	0.202402	+	0.688330i
$544$	22.0088	+	22.0088i	0.943618	+	0.943618i
$545$	13.2285	+	22.9124i	0.566645	+	0.981458i
$546$	16.9651	−	27.6776i	0.726040	−	1.18449i
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	−0.988092	−	0.153867i	$-0.950827\pi$
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	0.627298	+	0.778779i	$0.284161\pi$
$548$	0.575322	−	0.154157i	0.0245766	−	0.00658527i
$549$	0.239887	−	0.154429i	0.0102381	−	0.00659088i
$550$	−17.6310	+	10.1792i	−0.751787	+	0.434044i
$551$	2.35518	−	0.631067i	0.100334	−	0.0268844i
$552$	3.91772	−	7.18139i	0.166749	−	0.305660i
$553$	−15.4744	+	4.14636i	−0.658039	+	0.176321i
$554$	−44.9736	−	12.0506i	−1.91075	−	0.511983i
$555$	−2.11480	−	7.19204i	−0.0897684	−	0.305285i
$556$	10.5888	−	6.11342i	0.449063	−	0.259267i
$557$	6.49382	+	24.2353i	0.275152	+	1.02688i	0.955739	+	0.294215i	$0.0950580\pi$
$557$	6.49382	+	24.2353i	0.275152	+	1.02688i	−0.680587	+	0.732667i	$0.738275\pi$
$558$	−0.628884	−	12.9899i	−0.0266228	−	0.549907i
$559$	2.26199	+	10.5443i	0.0956721	+	0.445977i
$560$	−30.7117	−	17.7314i	−1.29780	−	0.749288i
$561$	−26.3398	−	43.1756i	−1.11207	−	1.82287i
$562$	38.5335			1.62544
$563$	−4.00167	+	6.93109i	−0.168650	+	0.292111i	−0.937945	−	0.346783i	$-0.887274\pi$
$563$	−4.00167	+	6.93109i	−0.168650	+	0.292111i	0.769295	+	0.638893i	$0.220607\pi$
$564$	−0.284642	−	11.7657i	−0.0119856	−	0.495427i
$565$	28.4935	−	28.4935i	1.19873	−	1.19873i
$566$	3.85408	+	1.03270i	0.161999	+	0.0434075i
$567$	23.7599	−	8.90398i	0.997821	−	0.373932i
$568$	−3.34068	−	5.78623i	−0.140172	−	0.242785i
$569$	3.43410	+	5.94804i	0.143965	+	0.249355i	0.928986	−	0.370114i	$-0.120681\pi$
$569$	3.43410	+	5.94804i	0.143965	+	0.249355i	−0.785021	+	0.619469i	$0.787348\pi$
$570$	2.94338	+	1.60573i	0.123285	+	0.0672565i
$571$	−8.78114	+	5.06979i	−0.367479	+	0.212164i	−0.672357	−	0.740227i	$-0.734718\pi$
$571$	−8.78114	+	5.06979i	−0.367479	+	0.212164i	0.304877	+	0.952392i	$0.401384\pi$
$572$	−26.6809	−	17.2556i	−1.11559	−	0.721491i
$573$	−3.55492	−	12.0896i	−0.148509	−	0.505051i
$574$	8.38142	+	2.24579i	0.349834	+	0.0937377i
$575$	6.48117	+	3.74191i	0.270283	+	0.156048i
$576$	4.37410	+	6.79465i	0.182254	+	0.283110i
$577$	−6.26722	+	6.26722i	−0.260908	+	0.260908i	−0.825423	−	0.564515i	$-0.809063\pi$
$577$	−6.26722	+	6.26722i	−0.260908	+	0.260908i	0.564515	+	0.825423i	$0.309063\pi$
$578$	−5.88042	−	5.88042i	−0.244593	−	0.244593i
$579$	−19.4980	−	10.6369i	−0.810311	−	0.442055i
$580$	−5.68241	+	21.2071i	−0.235949	+	0.880575i
$581$	38.1528	+	22.0275i	1.58284	+	0.913855i
$582$	36.6681	+	34.9359i	1.51994	+	1.44814i
$583$	0.303605	−	1.13307i	0.0125740	−	0.0469269i
$584$	2.34097			0.0968701
$585$	14.0039	+	24.3737i	0.578989	+	1.00773i
$586$	59.1262			2.44248
$587$	−2.97754	+	11.1123i	−0.122896	+	0.458656i	−0.999756	−	0.0220910i	$-0.992968\pi$
$587$	−2.97754	+	11.1123i	−0.122896	+	0.458656i	0.876860	+	0.480747i	$0.159634\pi$
$588$	0.541162	−	2.23448i	0.0223171	−	0.0921484i
$589$	−0.822554	−	0.474902i	−0.0338927	−	0.0195680i
$590$	−5.15331	+	19.2324i	−0.212158	+	0.791786i
$591$	−23.3208	+	14.2272i	−0.959291	+	0.585228i
$592$	−5.70002	−	5.70002i	−0.234269	−	0.234269i
$593$	−12.5514	+	12.5514i	−0.515426	+	0.515426i	−0.916184	−	0.400758i	$-0.868747\pi$
$593$	−12.5514	+	12.5514i	−0.515426	+	0.515426i	0.400758	+	0.916184i	$0.368747\pi$
$594$	−19.7952	−	56.9799i	−0.812207	−	2.33791i
$595$	29.4281	+	16.9903i	1.20643	+	0.696535i
$596$	−3.49316	−	0.935990i	−0.143086	−	0.0383397i
$597$	−29.5475	+	31.0126i	−1.20930	+	1.26926i
$598$	−1.43149	+	28.3336i	−0.0585378	+	1.15865i
$599$	37.6976	−	21.7647i	1.54028	−	0.889283i	0.541462	−	0.840725i	$-0.317871\pi$
$599$	37.6976	−	21.7647i	1.54028	−	0.889283i	0.998820	−	0.0485576i	$-0.0154625\pi$
$600$	2.86997	−	1.75086i	0.117166	−	0.0714788i
$601$	−14.2443	−	24.6718i	−0.581036	−	1.00638i	−0.995357	−	0.0962533i	$-0.969314\pi$
$601$	−14.2443	−	24.6718i	−0.581036	−	1.00638i	0.414321	−	0.910131i	$-0.364019\pi$
$602$	7.77404	+	13.4650i	0.316846	+	0.548794i
$603$	−2.43476	+	11.2344i	−0.0991511	+	0.457498i
$604$	−1.84047	−	0.493152i	−0.0748876	−	0.0200661i
$605$	52.6272	−	52.6272i	2.13960	−	2.13960i
$606$	9.54494	−	5.82302i	0.387737	−	0.236544i
$607$	−14.8033	+	25.6401i	−0.600848	+	1.04070i	0.391845	+	0.920031i	$0.371837\pi$
$607$	−14.8033	+	25.6401i	−0.600848	+	1.04070i	−0.992693	+	0.120668i	$0.961496\pi$
$608$	2.71114			0.109951
$609$	29.4637	−	0.712798i	1.19393	−	0.0288840i
$610$	0.394640	+	0.227846i	0.0159785	+	0.00922520i
$611$	−7.97544	−	15.5802i	−0.322652	−	0.630307i
$612$	−10.5420	−	16.3758i	−0.426137	−	0.661953i
$613$	−8.67578	−	32.3784i	−0.350411	−	1.30775i	−0.886161	−	0.463377i	$-0.846638\pi$
$613$	−8.67578	−	32.3784i	−0.350411	−	1.30775i	0.535750	−	0.844377i	$-0.320029\pi$
$614$	−41.9569	+	24.2238i	−1.69324	+	0.977594i
$615$	−5.18285	+	5.43983i	−0.208992	+	0.219355i
$616$	18.9758	+	5.08455i	0.764557	+	0.204862i
$617$	32.7357	−	8.77151i	1.31789	−	0.353128i	0.469703	−	0.882824i	$-0.344361\pi$
$617$	32.7357	−	8.77151i	1.31789	−	0.353128i	0.848187	+	0.529697i	$0.177694\pi$
$618$	−20.3253	−	33.3167i	−0.817605	−	1.34020i
$619$	−25.9724	+	6.95927i	−1.04392	+	0.279717i	−0.739736	−	0.672897i	$-0.765050\pi$
$619$	−25.9724	+	6.95927i	−1.04392	+	0.279717i	−0.304181	+	0.952614i	$0.598383\pi$
$620$	7.40664	−	4.27623i	0.297458	−	0.171737i
$621$	−14.5013	+	16.7748i	−0.581918	+	0.673150i
$622$	12.3010	−	3.29605i	0.493227	−	0.132160i
$623$	−0.170915	+	0.296034i	−0.00684757	+	0.0118603i
$624$	25.7710	+	15.7965i	1.03167	+	0.632366i
$625$	−15.3465	−	26.5810i	−0.613862	−	1.06324i
$626$	−36.7664	−	36.7664i	−1.46948	−	1.46948i
$627$	−4.28161	−	1.03695i	−0.170991	−	0.0414117i
$628$			17.0569i			0.680643i
$629$	5.46179	+	5.46179i	0.217776	+	0.217776i
$630$	30.0097	+	27.2382i	1.19562	+	1.08520i
$631$	−0.0679900	+	0.253742i	−0.00270664	+	0.0101013i	−0.967266	−	0.253765i	$-0.918331\pi$
$631$	−0.0679900	+	0.253742i	−0.00270664	+	0.0101013i	0.964559	+	0.263866i	$0.0849977\pi$
$632$	−1.62776	−	6.07486i	−0.0647486	−	0.241645i
$633$	23.9324	−	7.03726i	0.951227	−	0.279706i
$634$		−	1.33256i		−	0.0529226i
$635$	5.11857	−	5.11857i	0.203124	−	0.203124i
$636$	0.106325	−	0.439021i	0.00421606	−	0.0174083i
$637$	−0.717165	−	3.34307i	−0.0284151	−	0.132457i
$638$		−	70.0647i		−	2.77389i
$639$	5.52773	+	17.2461i	0.218674	+	0.682246i
$640$	10.9870	−	19.0300i	0.434297	−	0.752225i
$641$	31.2053			1.23254			0.616268	−	0.787537i	$-0.288644\pi$
$641$	31.2053			1.23254			0.616268	+	0.787537i	$0.288644\pi$
$642$	−7.01110	+	12.8517i	−0.276706	+	0.507217i
$643$	−11.4741	−	42.8219i	−0.452494	−	1.68873i	−0.695352	−	0.718669i	$-0.744752\pi$
$643$	−11.4741	−	42.8219i	−0.452494	−	1.68873i	0.242858	−	0.970062i	$-0.421915\pi$
$644$	4.35855	+	16.2663i	0.171751	+	0.640984i
$645$	−13.4593	+	0.325613i	−0.529959	+	0.0128210i
$646$	−3.45469			−0.135923
$647$	5.33648	−	9.24306i	0.209799	−	0.363382i	−0.741852	−	0.670563i	$-0.766052\pi$
$647$	5.33648	−	9.24306i	0.209799	−	0.363382i	0.951651	+	0.307181i	$0.0993858\pi$
$648$	3.49548	+	9.32753i	0.137315	+	0.366420i
$649$		−	26.1610i		−	1.02691i
$650$	−6.33149	+	9.78989i	−0.248341	+	0.383991i
$651$	−8.31204	−	7.91936i	−0.325774	−	0.310384i
$652$	−24.2051	+	24.2051i	−0.947944	+	0.947944i
$653$			35.1382i			1.37506i	0.726154	+	0.687532i	$0.241306\pi$
$653$			35.1382i			1.37506i	−0.726154	+	0.687532i	$0.758694\pi$
$654$	−23.5392	−	22.4271i	−0.920454	−	0.876970i
$655$	8.69714	+	32.4582i	0.339825	+	1.26825i
$656$	−2.09109	+	7.80407i	−0.0816435	+	0.304698i
$657$	−6.20142	−	1.34400i	−0.241940	−	0.0524344i
$658$	−17.8436	−	17.8436i	−0.695616	−	0.695616i
$659$		−	9.60362i		−	0.374104i	−0.982350	−	0.187052i	$-0.940107\pi$
$659$		−	9.60362i		−	0.374104i	0.982350	−	0.187052i	$-0.0598933\pi$
$660$	27.3630	−	28.7197i	1.06510	−	1.11791i
$661$	8.21987	+	8.21987i	0.319716	+	0.319716i	0.848658	−	0.528942i	$-0.177411\pi$
$661$	8.21987	+	8.21987i	0.319716	+	0.319716i	−0.528942	+	0.848658i	$0.677411\pi$
$662$	−4.46607	−	7.73546i	−0.173579	−	0.300647i
$663$	−24.6940	−	15.1363i	−0.959034	−	0.587845i
$664$	−8.64745	+	14.9778i	−0.335586	+	0.581252i
$665$	2.85901	−	0.766070i	0.110868	−	0.0297069i
$666$	4.98660	+	7.74608i	0.193227	+	0.300154i
$667$	−22.3053	+	12.8779i	−0.863663	+	0.498636i
$668$	10.4147	−	2.79062i	0.402958	−	0.107972i
$669$	−1.76480	+	0.0426948i	−0.0682311	+	0.00165068i
$670$	−17.7351	+	4.75209i	−0.685165	+	0.183589i
$671$	−0.578335	−	0.154964i	−0.0223264	−	0.00598233i
$672$	31.8499	+	7.71363i	1.22864	+	0.297560i
$673$	−21.0558	+	12.1566i	−0.811640	+	0.468601i	−0.847525	−	0.530755i	$-0.821908\pi$
$673$	−21.0558	+	12.1566i	−0.811640	+	0.468601i	0.0358851	+	0.999356i	$0.488575\pi$
$674$	11.9733	+	44.6849i	0.461194	+	1.72120i
$675$	−8.60798	+	2.99047i	−0.331321	+	0.115103i
$676$	−18.1040	−	1.83400i	−0.696308	−	0.0705386i
$677$	−36.2277	−	20.9161i	−1.39234	−	0.803871i	−0.398770	−	0.917051i	$-0.630563\pi$
$677$	−36.2277	−	20.9161i	−1.39234	−	0.803871i	−0.993574	+	0.113180i	$0.963896\pi$
$678$	−23.7151	+	43.4710i	−0.910772	+	1.66949i
$679$	44.7098			1.71580
$680$	−6.66997	+	11.5527i	−0.255782	+	0.443027i
$681$	11.8126	+	6.44420i	0.452658	+	0.246942i
$682$	−19.2992	+	19.2992i	−0.739003	+	0.739003i
$683$	9.97708	+	2.67335i	0.381763	+	0.102293i	0.444596	−	0.895731i	$-0.353347\pi$
$683$	9.97708	+	2.67335i	0.381763	+	0.102293i	−0.0628338	+	0.998024i	$0.520014\pi$
$684$	−1.65793	−	0.359314i	−0.0633926	−	0.0137387i
$685$	0.552918	+	0.957682i	0.0211259	+	0.0365911i
$686$	15.7292	+	27.2438i	0.600545	+	1.04017i
$687$	−0.657544	−	27.1797i	−0.0250869	−	1.03697i
$688$	−12.5375	+	7.23853i	−0.477988	+	0.275966i
$689$	−0.140905	−	0.656832i	−0.00536806	−	0.0250233i
$690$	−34.4222	−	8.33661i	−1.31043	−	0.317369i
$691$	−0.659509	−	0.176715i	−0.0250889	−	0.00672256i	0.246253	−	0.969206i	$-0.420801\pi$
$691$	−0.659509	−	0.176715i	−0.0250889	−	0.00672256i	−0.271342	+	0.962483i	$0.587467\pi$
$692$	14.0672	+	8.12171i	0.534755	+	0.308741i
$693$	−47.3492	−	24.3638i	−1.79865	−	0.925503i
$694$	35.7527	−	35.7527i	1.35715	−	1.35715i
$695$	16.0517	+	16.0517i	0.608878	+	0.608878i
$696$	0.279827	+	11.5667i	0.0106068	+	0.438434i
$697$	2.00370	−	7.47791i	0.0758955	−	0.283246i
$698$	1.63923	+	0.946411i	0.0620458	+	0.0358222i
$699$	−15.5925	+	4.58494i	−0.589762	+	0.173418i
$700$	−1.79120	+	6.68485i	−0.0677010	+	0.252664i
$701$	48.1896			1.82010			0.910049	−	0.414502i	$-0.136044\pi$
$701$	48.1896			1.82010			0.910049	+	0.414502i	$0.136044\pi$
$702$	−24.9599	−	23.8812i	−0.942053	−	0.901337i
$703$	0.672807			0.0253754
$704$	4.38926	−	16.3809i	0.165427	−	0.617380i
$705$	20.9634	−	6.16424i	0.789528	−	0.232159i
$706$	−30.6312	−	17.6849i	−1.15282	−	0.665581i
$707$	2.55463	−	9.53401i	0.0960767	−	0.358563i
$708$	−0.243645	−	10.0711i	−0.00915673	−	0.378495i
$709$	13.1437	+	13.1437i	0.493620	+	0.493620i	0.909445	−	0.415824i	$-0.136507\pi$
$709$	13.1437	+	13.1437i	0.493620	+	0.493620i	−0.415824	+	0.909445i	$0.636507\pi$
$710$	−20.4543	+	20.4543i	−0.767638	+	0.767638i
$711$	0.824347	+	17.0273i	0.0309154	+	0.638574i
$712$	−0.116215	−	0.0670970i	−0.00435536	−	0.00251457i
$713$	9.69113	+	2.59673i	0.362936	+	0.0972483i
$714$	−40.5851	−	9.82917i	−1.51886	−	0.367847i
$715$	18.1244	−	56.1402i	0.677815	−	2.09953i
$716$	−6.68002	+	3.85671i	−0.249644	+	0.144132i
$717$	0.749624	+	30.9859i	0.0279952	+	1.15719i
$718$	23.6220	+	40.9144i	0.881563	+	1.52691i
$719$	−17.7360	−	30.7196i	−0.661439	−	1.14565i	−0.980238	−	0.197824i	$-0.936613\pi$
$719$	−17.7360	−	30.7196i	−0.661439	−	1.14565i	0.318798	−	0.947823i	$-0.396721\pi$
$720$	−25.3619	+	27.9425i	−0.945182	+	1.04136i
$721$	−33.2786	−	8.91697i	−1.23936	−	0.332085i
$722$	24.5593	−	24.5593i	0.914001	−	0.914001i
$723$	−23.0265	−	12.5618i	−0.856364	−	0.467179i
$724$	6.75557	−	11.7010i	0.251069	−	0.434864i
$725$	−10.5847			−0.393106
$726$	−43.8016	+	80.2907i	−1.62563	+	2.97987i
$727$	−0.212677	−	0.122789i	−0.00788777	−	0.00455400i	0.496051	−	0.868293i	$-0.334783\pi$
$727$	−0.212677	−	0.122789i	−0.00788777	−	0.00455400i	−0.503939	+	0.863739i	$0.668116\pi$
$728$	11.0001	−	2.35978i	0.407692	−	0.0874592i
$729$	−3.90467	−	26.7162i	−0.144617	−	0.989488i
$730$	−2.62318	−	9.78984i	−0.0970882	−	0.362338i
$731$	12.0135	−	6.93600i	0.444336	−	0.256537i
$732$	−0.224083	−	0.0542698i	−0.00828233	−	0.00200587i
$733$	0.851305	+	0.228106i	0.0314437	+	0.00842530i	0.274507	−	0.961585i	$-0.411485\pi$
$733$	0.851305	+	0.228106i	0.0314437	+	0.00842530i	−0.243063	+	0.970011i	$0.578152\pi$
$734$	41.5073	−	11.1219i	1.53206	−	0.410515i
$735$	4.26727	−	0.103236i	0.157400	−	0.00380790i
$736$	−27.6625	+	7.41215i	−1.01965	+	0.273216i
$737$	20.8922	−	12.0621i	0.769574	−	0.444314i
$738$	4.22459	−	8.21018i	0.155509	−	0.302221i
$739$	−19.4340	+	5.20731i	−0.714890	+	0.191554i	−0.597890	−	0.801578i	$-0.703994\pi$
$739$	−19.4340	+	5.20731i	−0.714890	+	0.191554i	−0.116999	+	0.993132i	$0.537328\pi$
$740$	−3.02913	+	5.24661i	−0.111353	+	0.192869i
$741$	−2.45323	+	0.588679i	−0.0901218	+	0.0216257i
$742$	−0.484265	−	0.838771i	−0.0177779	−	0.0307923i
$743$	21.9020	+	21.9020i	0.803507	+	0.803507i	0.983642	−	0.180135i	$-0.0576536\pi$
$743$	21.9020	+	21.9020i	0.803507	+	0.803507i	−0.180135	+	0.983642i	$0.557654\pi$
$744$	3.10894	−	3.26310i	0.113979	−	0.119631i
$745$		−	6.71426i		−	0.245992i
$746$	−9.15522	−	9.15522i	−0.335197	−	0.335197i
$747$	31.5068	−	34.7127i	1.15277	−	1.27007i
$748$	−10.5786	+	39.4798i	−0.386791	+	1.44352i
$749$	3.34490	+	12.4833i	0.122220	+	0.456131i
$750$	19.5065	+	18.5850i	0.712278	+	0.678628i
$751$		−	31.5860i		−	1.15259i	−0.817242	−	0.576295i	$-0.804498\pi$
$751$		−	31.5860i		−	1.15259i	0.817242	−	0.576295i	$-0.195502\pi$
$752$	16.6144	−	16.6144i	0.605867	−	0.605867i
$753$	−20.1295	−	19.1786i	−0.733561	−	0.698906i
$754$	−18.2834	−	35.7170i	−0.665842	−	1.30074i
$755$		−	3.53759i		−	0.128746i
$756$	−18.4548	−	8.93824i	−0.671193	−	0.325081i
$757$	6.66044	−	11.5362i	0.242078	−	0.419291i	−0.719228	−	0.694774i	$-0.755504\pi$
$757$	6.66044	−	11.5362i	0.242078	−	0.419291i	0.961306	+	0.275483i	$0.0888377\pi$
$758$	−17.7753			−0.645628
$759$	46.5215	−	1.12547i	1.68862	−	0.0408519i
$760$	0.300740	+	1.12238i	0.0109090	+	0.0407129i
$761$	1.86457	+	6.95866i	0.0675905	+	0.252251i	0.991451	−	0.130478i	$-0.0416510\pi$
$761$	1.86457	+	6.95866i	0.0675905	+	0.252251i	−0.923861	+	0.382729i	$0.874984\pi$
$762$	−4.26018	+	7.80913i	−0.154330	+	0.282895i
$763$	−28.7015			−1.03906
$764$	−5.09188	+	8.81939i	−0.184218	+	0.319074i
$765$	24.3019	−	26.7747i	0.878638	−	0.968042i
$766$			42.6706i			1.54175i
$767$	−6.82673	−	13.3362i	−0.246499	−	0.481541i
$768$	−8.55247	+	35.3135i	−0.308611	+	1.27427i
$769$	−27.9015	+	27.9015i	−1.00615	+	1.00615i	−0.00617137	+	0.999981i	$0.501964\pi$
$769$	−27.9015	+	27.9015i	−1.00615	+	1.00615i	−0.999981	+	0.00617137i	$0.998036\pi$
$770$		−	85.0534i		−	3.06511i
$771$	23.8577	−	7.01529i	0.859213	−	0.252650i
$772$	4.64566	+	17.3378i	0.167201	+	0.624003i
$773$	−12.7625	+	47.6302i	−0.459034	+	1.71314i	0.216916	+	0.976190i	$0.430400\pi$
$773$	−12.7625	+	47.6302i	−0.459034	+	1.71314i	−0.675950	+	0.736947i	$0.736267\pi$
$774$	15.7553	−	5.04988i	0.566311	−	0.181514i
$775$	2.91553	+	2.91553i	0.104729	+	0.104729i
$776$			17.5519i			0.630078i
$777$	7.90402	+	1.91425i	0.283555	+	0.0686733i
$778$	5.90213	+	5.90213i	0.211601	+	0.211601i
$779$	−0.337169	−	0.583993i	−0.0120803	−	0.0209237i
$780$	6.45444	−	21.7809i	0.231106	−	0.779880i
$781$	19.0036	−	32.9152i	0.680001	−	1.17780i
$782$	35.2493	−	9.44501i	1.26051	−	0.337753i
$783$	5.89939	−	30.8017i	0.210827	−	1.10076i
$784$	3.97501	−	2.29498i	0.141965	−	0.0819634i
$785$	−30.5891	+	8.19632i	−1.09177	+	0.292539i
$786$	−21.5061	−	35.2522i	−0.767098	−	1.25741i
$787$	48.2254	−	12.9220i	1.71905	−	0.460618i	0.741436	−	0.671024i	$-0.234145\pi$
$787$	48.2254	−	12.9220i	1.71905	−	0.460618i	0.977614	+	0.210406i	$0.0674786\pi$
$788$	21.3246	+	5.71391i	0.759657	+	0.203550i
$789$	−21.6511	+	22.7247i	−0.770800	+	0.809020i
$790$	−23.5808	+	13.6144i	−0.838968	+	0.484378i
$791$	11.3141	+	42.2249i	0.402285	+	1.50135i
$792$	9.56460	−	18.5881i	0.339863	−	0.660500i
$793$	−0.335257	+	0.0719201i	−0.0119053	+	0.00255396i
$794$	−12.5465	−	7.24371i	−0.445257	−	0.257070i
$795$	0.838413	−	0.0202833i	0.0297354	−	0.000719373i
$796$	34.6168			1.22696
$797$	0.375653	−	0.650650i	0.0133063	−	0.0230472i	−0.859296	−	0.511479i	$-0.829098\pi$
$797$	0.375653	−	0.650650i	0.0133063	−	0.0230472i	0.872602	+	0.488432i	$0.162431\pi$
$798$	−3.10512	+	1.89432i	−0.109920	+	0.0670583i
$799$	−15.9201	+	15.9201i	−0.563212	+	0.563212i
$800$	−11.3683	−	3.04612i	−0.401929	−	0.107696i
$801$	0.269342	+	0.244467i	0.00951673	+	0.00863781i
$802$	−0.238917	−	0.413817i	−0.00843647	−	0.0146124i
$803$	6.65835	+	11.5326i	0.234968	+	0.406977i
$804$	7.93045	−	4.83808i	0.279685	−	0.170626i
$805$	−27.0770	+	15.6329i	−0.954337	+	0.550987i
$806$	−4.80205	+	14.8743i	−0.169145	+	0.523924i
$807$	−3.47884	+	3.65133i	−0.122461	+	0.128533i
$808$	3.74281	+	1.00288i	0.131672	+	0.0352813i
$809$	−24.5450	−	14.1711i	−0.862958	−	0.498229i	0.00204394	−	0.999998i	$-0.499349\pi$
$809$	−24.5450	−	14.1711i	−0.862958	−	0.498229i	−0.865002	+	0.501769i	$0.832683\pi$
$810$	35.0904	−	25.0699i	1.23295	−	0.880866i
$811$	−14.9696	+	14.9696i	−0.525652	+	0.525652i	−0.919273	−	0.393621i	$-0.871222\pi$
$811$	−14.9696	+	14.9696i	−0.525652	+	0.525652i	0.393621	+	0.919273i	$0.371222\pi$
$812$	−16.8417	−	16.8417i	−0.591029	−	0.591029i
$813$	19.9971	−	12.1995i	0.701329	−	0.427856i
$814$	5.00388	−	18.6747i	0.175386	−	0.654548i
$815$	−55.0396	−	31.7771i	−1.92795	−	1.11310i
$816$	9.15209	−	37.7894i	0.320387	−	1.32289i
$817$	0.312735	−	1.16714i	0.0109412	−	0.0408331i
$818$	−68.1002			−2.38107
$819$	−30.4950	−	0.0641668i	−1.06558	−	0.00224217i
$820$	6.07203			0.212045
$821$	10.1140	−	37.7460i	0.352981	−	1.31734i	−0.530025	−	0.847982i	$-0.677817\pi$
$821$	10.1140	−	37.7460i	0.352981	−	1.31734i	0.883006	−	0.469362i	$-0.155516\pi$
$822$	−0.983880	−	0.937400i	−0.0343168	−	0.0326956i
$823$	38.5876	+	22.2786i	1.34508	+	0.776582i	0.987548	−	0.157319i	$-0.0502851\pi$
$823$	38.5876	+	22.2786i	1.34508	+	0.776582i	0.357532	+	0.933901i	$0.383618\pi$
$824$	3.50058	−	13.0643i	0.121948	−	0.455118i
$825$	16.7884	+	9.15873i	0.584499	+	0.318866i
$826$	−15.2736	−	15.2736i	−0.531435	−	0.531435i
$827$	6.18902	−	6.18902i	0.215213	−	0.215213i	−0.591265	−	0.806478i	$-0.701371\pi$
$827$	6.18902	−	6.18902i	0.215213	−	0.215213i	0.806478	+	0.591265i	$0.201371\pi$
$828$	17.8987	−	0.866535i	0.622023	−	0.0301142i
$829$	15.4468	+	8.91823i	0.536490	+	0.309743i	0.743655	−	0.668563i	$-0.233090\pi$
$829$	15.4468	+	8.91823i	0.536490	+	0.309743i	−0.207165	+	0.978306i	$0.566424\pi$
$830$	72.3264	+	19.3798i	2.51049	+	0.672683i
$831$	12.3385	+	41.9608i	0.428017	+	1.45560i
$832$	−2.03709	−	9.49592i	−0.0706234	−	0.329212i
$833$	−3.80888	+	2.19906i	−0.131970	+	0.0761929i
$834$	−24.4893	−	13.3599i	−0.847996	−	0.462614i
$835$	10.0092	+	17.3364i	0.346381	+	0.599949i
$836$	1.78009	+	3.08321i	0.0615657	+	0.106635i
$837$	−10.1092	+	6.85929i	−0.349426	+	0.237092i
$838$	51.8405	+	13.8906i	1.79080	+	0.479844i
$839$	−23.4795	+	23.4795i	−0.810604	+	0.810604i	−0.984724	−	0.174121i	$-0.944292\pi$
$839$	−23.4795	+	23.4795i	−0.810604	+	0.810604i	0.174121	+	0.984724i	$0.444292\pi$
$840$	0.339689	+	14.0411i	0.0117204	+	0.484465i
$841$	3.71387	−	6.43261i	0.128064	−	0.221814i
$842$	−13.4487			−0.463472
$843$	−18.8515	−	30.9009i	−0.649281	−	1.06428i
$844$	−17.4587	−	10.0798i	−0.600954	−	0.346961i
$845$	−5.41048	−	33.3483i	−0.186126	−	1.14722i
$846$	−22.5783	+	14.5350i	−0.776259	+	0.499723i
$847$	20.8971	+	77.9892i	0.718034	+	2.67974i
$848$	0.780993	−	0.450906i	0.0268194	−	0.0154842i
$849$	−1.05736	−	3.59589i	−0.0362886	−	0.123411i
$850$	14.4861	+	3.88154i	0.496870	+	0.133136i
$851$	−6.86486	+	1.83943i	−0.235324	+	0.0630549i
$852$	7.00918	−	12.8482i	0.240131	−	0.440172i
$853$	18.1694	−	4.86849i	0.622110	−	0.166694i	0.0660230	−	0.997818i	$-0.478969\pi$
$853$	18.1694	−	4.86849i	0.622110	−	0.166694i	0.556087	+	0.831124i	$0.312302\pi$
$854$	−0.428121	+	0.247176i	−0.0146500	+	0.00845818i
$855$	−0.152304	−	3.14592i	−0.00520870	−	0.107588i
$856$	−4.90065	+	1.31312i	−0.167501	+	0.0448817i
$857$	16.1683	−	28.0043i	0.552298	−	0.956607i	−0.445811	−	0.895127i	$-0.647085\pi$
$857$	16.1683	−	28.0043i	0.552298	−	0.956607i	0.998108	−	0.0614802i	$-0.0195821\pi$
$858$	−1.90584	+	72.4711i	−0.0650644	+	2.47412i
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	0.969865	−	0.243644i	$-0.0783427\pi$
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	−0.695934	+	0.718106i	$0.745009\pi$
$860$	7.69346	+	7.69346i	0.262345	+	0.262345i
$861$	−2.29944	−	7.81994i	−0.0783646	−	0.266503i
$862$			27.9204i			0.950974i
$863$	23.7439	+	23.7439i	0.808250	+	0.808250i	0.984369	−	0.176119i	$-0.0563543\pi$
$863$	23.7439	+	23.7439i	0.808250	+	0.808250i	−0.176119	+	0.984369i	$0.556354\pi$
$864$	15.2004	−	31.3842i	0.517127	−	1.06771i
$865$	−7.80543	+	29.1303i	−0.265393	+	0.990458i
$866$	14.3405	+	53.5193i	0.487308	+	1.81866i
$867$	−1.83880	+	7.59248i	−0.0624489	+	0.257854i
$868$			9.27804i			0.314917i
$869$	25.2975	−	25.2975i	0.858160	−	0.858160i
$870$	48.0578	−	14.1313i	1.62931	−	0.479096i
$871$	7.50264	−	11.6007i	0.254217	−	0.393076i
$872$		−	11.2675i		−	0.381565i
$873$	10.0769	−	46.4965i	0.341052	−	1.57367i
$874$	1.58934	−	2.75282i	0.0537602	−	0.0931155i
$875$	23.7845			0.804062
$876$	2.67064	+	4.37765i	0.0902327	+	0.147907i
$877$	8.33096	+	31.0916i	0.281317	+	1.04989i	0.951489	+	0.307683i	$0.0995535\pi$
$877$	8.33096	+	31.0916i	0.281317	+	1.04989i	−0.670172	+	0.742206i	$0.733780\pi$
$878$	7.48210	+	27.9236i	0.252508	+	0.942375i
$879$	−28.9259	−	47.4146i	−0.975648	−	1.59926i
$880$	79.1946			2.66965
$881$	−21.3604	+	36.9973i	−0.719650	+	1.24647i	0.241489	+	0.970404i	$0.422364\pi$
$881$	−21.3604	+	36.9973i	−0.719650	+	1.24647i	−0.961139	+	0.276066i	$0.910969\pi$
$882$	−4.99521	+	1.60106i	−0.168197	+	0.0539107i
$883$			30.7720i			1.03556i	0.855514	+	0.517780i	$0.173241\pi$
$883$			30.7720i			1.03556i	−0.855514	+	0.517780i	$0.826759\pi$
$884$	4.90960	+	22.8862i	0.165128	+	0.769745i
$885$	17.9440	−	5.27640i	0.603182	−	0.177364i
$886$	−17.9372	+	17.9372i	−0.602612	+	0.602612i
$887$			25.5690i			0.858525i	0.903180	+	0.429262i	$0.141226\pi$
$887$			25.5690i			0.858525i	−0.903180	+	0.429262i	$0.858774\pi$
$888$	−0.751486	+	3.10292i	−0.0252182	+	0.104127i
$889$	2.03247	+	7.58529i	0.0681670	+	0.254403i
$890$	−0.150371	+	0.561193i	−0.00504045	+	0.0188112i
$891$	−36.0092	+	43.7501i	−1.20635	+	1.46568i
$892$	1.00878	+	1.00878i	0.0337764	+	0.0337764i
$893$			1.96110i			0.0656259i
$894$	2.32766	+	7.91594i	0.0778487	+	0.264749i
$895$	−10.1264	−	10.1264i	−0.338488	−	0.338488i
$896$	11.9191	+	20.6444i	0.398188	+	0.689682i
$897$	23.4217	−	12.7135i	0.782026	−	0.424492i
$898$	11.0238	−	19.0938i	0.367870	−	0.637169i
$899$	−13.7066	+	3.67268i	−0.457141	+	0.122491i
$900$	6.54828	+	3.36945i	0.218276	+	0.112315i
$901$	−0.748352	+	0.432061i	−0.0249312	+	0.0143940i
$902$	−18.7172	+	5.01525i	−0.623214	+	0.166990i
$903$	6.99466	−	12.8216i	0.232768	−	0.426676i
$904$	−16.5765	+	4.44165i	−0.551325	+	0.147727i
$905$	24.2303	+	6.49249i	0.805443	+	0.215818i
$906$	1.22639	+	4.17073i	0.0407442	+	0.138563i
$907$	−38.7229	+	22.3567i	−1.28577	+	0.742342i	−0.977898	−	0.209085i	$-0.932952\pi$
$907$	−38.7229	+	22.3567i	−1.28577	+	0.742342i	−0.307876	+	0.951426i	$0.599618\pi$
$908$	−2.81450	−	10.5038i	−0.0934023	−	0.348582i
$909$	−9.33922	−	4.80554i	−0.309762	−	0.159390i
$910$	−22.1947	−	43.3578i	−0.735747	−	1.43730i
$911$	28.6386	+	16.5345i	0.948840	+	0.547813i	0.892720	−	0.450611i	$-0.148794\pi$
$911$	28.6386	+	16.5345i	0.948840	+	0.547813i	0.0561197	+	0.998424i	$0.482127\pi$
$912$	−1.76383	−	2.89123i	−0.0584064	−	0.0957382i
$913$	−98.3826			−3.25599
$914$	−36.2479	+	62.7832i	−1.19897	+	2.07668i
$915$	−0.0103529	−	0.427938i	−0.000342255	−	0.0141472i
$916$	−15.5362	+	15.5362i	−0.513331	+	0.513331i
$917$	−35.2119	−	9.43499i	−1.16280	−	0.311571i
$918$	−19.3692	+	39.9916i	−0.639280	+	1.31992i
$919$	−7.33901	−	12.7115i	−0.242092	−	0.419315i	0.719218	−	0.694784i	$-0.244500\pi$
$919$	−7.33901	−	12.7115i	−0.242092	−	0.419315i	−0.961310	+	0.275469i	$0.911167\pi$
$920$	−6.13708	−	10.6297i	−0.202334	−	0.350452i
$921$	39.9519	+	21.7953i	1.31646	+	0.718180i
$922$	28.7269	−	16.5855i	0.946069	−	0.546213i
$923$	1.09827	−	21.7382i	0.0361500	−	0.715522i
$924$	12.1399	+	41.2856i	0.399374	+	1.35820i
$925$	−2.82120	−	0.755938i	−0.0927604	−	0.0248551i
$926$	−54.0165	−	31.1865i	−1.77509	−	1.02485i
$927$	−16.7738	+	32.5987i	−0.550924	+	1.07068i
$928$	28.6411	−	28.6411i	0.940189	−	0.940189i
$929$	−35.3524	−	35.3524i	−1.15987	−	1.15987i	−0.984502	−	0.175372i	$-0.943887\pi$
$929$	−35.3524	−	35.3524i	−1.15987	−	1.15987i	−0.175372	−	0.984502i	$-0.556113\pi$
$930$	−17.1298	−	9.34498i	−0.561710	−	0.306434i
$931$	−0.0991526	+	0.370042i	−0.00324959	+	0.0121277i
$932$	11.3748	+	6.56722i	0.372592	+	0.215116i
$933$	−8.66114	−	8.25197i	−0.283553	−	0.270157i
$934$	−7.38872	+	27.5751i	−0.241766	+	0.902284i
$935$	−75.8847			−2.48170
$936$	0.0251903	−	11.9716i	0.000823370	−	0.391303i
$937$	12.7044			0.415036			0.207518	−	0.978231i	$-0.433462\pi$
$937$	12.7044			0.415036			0.207518	+	0.978231i	$0.433462\pi$
$938$	5.15526	−	19.2397i	0.168325	−	0.628198i
$939$	−11.4968	+	47.4708i	−0.375184	+	1.54915i
$940$	−15.2928	−	8.82933i	−0.498798	−	0.287981i
$941$	0.320048	−	1.19444i	0.0104333	−	0.0389375i	−0.960513	−	0.278235i	$-0.910251\pi$
$941$	0.320048	−	1.19444i	0.0104333	−	0.0389375i	0.970946	+	0.239298i	$0.0769172\pi$
$942$	33.2223	−	20.2677i	1.08244	−	0.660357i
$943$	5.03685	+	5.03685i	0.164022	+	0.164022i
$944$	14.2214	−	14.2214i	0.462869	−	0.462869i
$945$	7.16143	−	37.3911i	0.232961	−	1.21633i
$946$	−30.0698	−	17.3608i	−0.977653	−	0.564448i
$947$	−16.2266	−	4.34789i	−0.527292	−	0.141287i	−0.0146546	−	0.999893i	$-0.504665\pi$
$947$	−16.2266	−	4.34789i	−0.527292	−	0.141287i	−0.512638	+	0.858605i	$0.671332\pi$
$948$	9.50309	−	9.97429i	0.308646	−	0.323950i
$949$	6.40367	+	4.14150i	0.207872	+	0.134439i
$950$	1.13130	−	0.653159i	0.0367044	−	0.0211913i
$951$	−1.06861	+	0.651919i	−0.0346520	+	0.0211399i
$952$	−7.23585	−	12.5329i	−0.234515	−	0.406192i
$953$	−3.87222	−	6.70688i	−0.125433	−	0.217257i	0.796469	−	0.604680i	$-0.206699\pi$
$953$	−3.87222	−	6.70688i	−0.125433	−	0.217257i	−0.921902	+	0.387422i	$0.873365\pi$
$954$	−0.981436	+	0.314570i	−0.0317752	+	0.0101846i
$955$	−18.2631	−	4.89359i	−0.590981	−	0.158353i
$956$	17.7118	−	17.7118i	0.572842	−	0.572842i
$957$	−56.1864	+	34.2773i	−1.81625	+	1.10803i
$958$	28.4329	−	49.2472i	0.918624	−	1.59110i
$959$	−1.19965			−0.0387388
$960$	12.1211	−	0.293238i	0.391206	−	0.00946422i
$961$	−22.0597	−	12.7362i	−0.711603	−	0.410844i
$962$	−2.32234	−	10.8256i	−0.0748751	−	0.349031i
$963$	13.7361	−	0.665008i	0.442639	−	0.0214296i
$964$	5.48636	+	20.4754i	0.176704	+	0.659467i
$965$	−28.8606	+	16.6627i	−0.929055	+	0.536390i
$966$	26.5035	−	27.8177i	0.852736	−	0.895019i
$967$	18.8877	+	5.06094i	0.607387	+	0.162749i	0.549387	−	0.835568i	$-0.314861\pi$
$967$	18.8877	+	5.06094i	0.607387	+	0.162749i	0.0579995	+	0.998317i	$0.481528\pi$
$968$	−30.6166	+	8.20369i	−0.984055	+	0.263677i
$969$	1.69012	+	2.77039i	0.0542944	+	0.0889979i
$970$	73.4014	−	19.6678i	2.35678	−	0.631497i
$971$	46.5819	−	26.8941i	1.49489	−	0.863073i	0.494903	−	0.868948i	$-0.335204\pi$
$971$	46.5819	−	26.8941i	1.49489	−	0.863073i	0.999983	+	0.00587546i	$0.00187023\pi$
$972$	−13.4549	+	17.1777i	−0.431565	+	0.550974i
$973$	−23.7874	+	6.37381i	−0.762588	+	0.204335i
$974$	35.3109	−	61.1602i	1.13143	−	1.95970i
$975$	10.9482	+	0.287916i	0.350624	+	0.00922071i
$976$	−0.230149	−	0.398630i	−0.00736690	−	0.0127598i
$977$	31.2770	+	31.2770i	1.00064	+	1.00064i	1.00000		0.000639826i	$0.000203663\pi$
$977$	31.2770	+	31.2770i	1.00064	+	1.00064i	0.000639826		1.00000i	$0.499796\pi$
$978$	75.9066	+	18.3836i	2.42722	+	0.587842i
$979$		−	0.763367i		−	0.0243973i
$980$	−2.43921	−	2.43921i	−0.0779178	−	0.0779178i
$981$	−6.46889	+	29.8485i	−0.206536	+	0.952988i
$982$	15.6906	−	58.5583i	0.500708	−	1.86867i
$983$	−12.5790	−	46.9456i	−0.401209	−	1.49733i	−0.810942	−	0.585127i	$-0.801045\pi$
$983$	−12.5790	−	46.9456i	−0.401209	−	1.49733i	0.409733	−	0.912206i	$-0.365622\pi$
$984$	3.06991	−	0.902701i	0.0978653	−	0.0287771i
$985$			40.9883i			1.30600i
$986$	−36.4961	+	36.4961i	−1.16227	+	1.16227i
$987$	−5.57967	+	23.0387i	−0.177603	+	0.733330i
$988$	1.71200	+	1.10722i	0.0544661	+	0.0352252i
$989$			12.7637i			0.405862i
$990$	−88.4523	−	19.1698i	−2.81120	−	0.609256i
$991$	20.5994	−	35.6792i	0.654362	−	1.13339i	−0.327691	−	0.944785i	$-0.606271\pi$
$991$	20.5994	−	35.6792i	0.654362	−	1.13339i	0.982053	−	0.188604i	$-0.0603961\pi$
$992$	−15.7782			−0.500959
$993$	−4.01833	+	7.36581i	−0.127518	+	0.233747i
$994$	−8.12198	−	30.3116i	−0.257614	−	0.961427i
$995$	16.6344	+	62.0803i	0.527345	+	1.96808i
$996$	−37.8739	+	0.916263i	−1.20008	+	0.0290329i
$997$	−30.0081			−0.950367			−0.475183	−	0.879887i	$-0.657618\pi$
$997$	−30.0081			−0.950367			−0.475183	+	0.879887i	$0.657618\pi$
$998$	17.7827	−	30.8005i	0.562901	−	0.974973i
$999$	3.77219	−	7.78843i	0.119347	−	0.246415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.110.2	yes	48
3.2	odd	2		351.2.bf.a.305.11		48
9.4	even	3		351.2.ba.a.71.2		48
9.5	odd	6		117.2.x.a.32.11	yes	48
13.11	odd	12		117.2.x.a.11.11	✓	48
39.11	even	12		351.2.ba.a.89.2		48
117.50	even	12	inner	117.2.bc.a.50.2	yes	48
117.76	odd	12		351.2.bf.a.206.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.11	✓	48	13.11	odd	12
117.2.x.a.32.11	yes	48	9.5	odd	6
117.2.bc.a.50.2	yes	48	117.50	even	12	inner
117.2.bc.a.110.2	yes	48	1.1	even	1	trivial
351.2.ba.a.71.2		48	9.4	even	3
351.2.ba.a.89.2		48	39.11	even	12
351.2.bf.a.206.11		48	117.76	odd	12
351.2.bf.a.305.11		48	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.477221 + 1.78101i) q^{2} +(1.66170 - 0.488620i) q^{3} +(-1.21221 - 0.699872i) q^{4} +(0.672617 - 2.51024i) q^{5} +(0.0772390 + 3.19269i) q^{6} +(1.99353 + 1.99353i) q^{7} +(-0.782609 + 0.782609i) q^{8} +(2.52250 - 1.62388i) q^{9} +O(q^{10})\)	\(q+(-0.477221 + 1.78101i) q^{2} +(1.66170 - 0.488620i) q^{3} +(-1.21221 - 0.699872i) q^{4} +(0.672617 - 2.51024i) q^{5} +(0.0772390 + 3.19269i) q^{6} +(1.99353 + 1.99353i) q^{7} +(-0.782609 + 0.782609i) q^{8} +(2.52250 - 1.62388i) q^{9} +(4.14978 + 2.39588i) q^{10} +(-6.08140 - 1.62951i) q^{11} +(-2.35631 - 0.570667i) q^{12} +(-3.52535 + 0.756266i) q^{13} +(-4.50185 + 2.59914i) q^{14} +(-0.108864 - 4.49993i) q^{15} +(-2.42010 - 4.19174i) q^{16} +(2.31896 + 4.01655i) q^{17} +(1.68836 + 5.26756i) q^{18} +(0.390218 + 0.104559i) q^{19} +(-2.57220 + 2.57220i) q^{20} +(4.28672 + 2.33857i) q^{21} +(5.80434 - 10.0534i) q^{22} -4.26737 q^{23} +(-0.918064 + 1.68286i) q^{24} +(-1.51877 - 0.876864i) q^{25} +(0.335449 - 6.63959i) q^{26} +(3.39819 - 3.93095i) q^{27} +(-1.02137 - 3.81179i) q^{28} +(5.22693 - 3.01777i) q^{29} +(8.06638 + 1.95357i) q^{30} +(-2.27098 - 0.608508i) q^{31} +(6.48234 - 1.73694i) q^{32} +(-10.9017 + 0.263738i) q^{33} +(-8.26018 + 2.21331i) q^{34} +(6.34511 - 3.66335i) q^{35} +(-4.19432 + 0.203061i) q^{36} +(1.60869 - 0.431046i) q^{37} +(-0.372440 + 0.645085i) q^{38} +(-5.48854 + 2.97924i) q^{39} +(1.43814 + 2.49093i) q^{40} +(-1.18032 - 1.18032i) q^{41} +(-6.21073 + 6.51869i) q^{42} -2.99100i q^{43} +(6.23151 + 6.23151i) q^{44} +(-2.37965 - 7.42434i) q^{45} +(2.03648 - 7.60024i) q^{46} +(1.25642 + 4.68901i) q^{47} +(-6.06965 - 5.78291i) q^{48} +0.948297i q^{49} +(2.28650 - 2.28650i) q^{50} +(5.81598 + 5.54122i) q^{51} +(4.80276 + 1.55053i) q^{52} +0.186317i q^{53} +(5.37938 + 7.92814i) q^{54} +(-8.18091 + 14.1698i) q^{55} -3.12030 q^{56} +(0.699515 - 0.0169230i) q^{57} +(2.88028 + 10.7494i) q^{58} +(1.07545 + 4.01364i) q^{59} +(-3.01741 + 5.53106i) q^{60} +0.0950990 q^{61} +(2.16752 - 3.75426i) q^{62} +(8.26592 + 1.79143i) q^{63} +2.69361i q^{64} +(-0.472797 + 9.35815i) q^{65} +(4.73279 - 19.5419i) q^{66} +(-2.70944 + 2.70944i) q^{67} -6.49189i q^{68} +(-7.09110 + 2.08512i) q^{69} +(3.49646 + 13.0490i) q^{70} +(-1.56243 + 5.83108i) q^{71} +(-0.703270 + 3.24499i) q^{72} +(-1.49562 - 1.49562i) q^{73} +3.07079i q^{74} +(-2.95220 - 0.714984i) q^{75} +(-0.399850 - 0.399850i) q^{76} +(-8.87497 - 15.3719i) q^{77} +(-2.68682 - 11.1969i) q^{78} +(-2.84121 + 4.92112i) q^{79} +(-12.1501 + 3.25561i) q^{80} +(3.72603 - 8.19248i) q^{81} +(2.66543 - 1.53889i) q^{82} +(15.0939 - 4.04440i) q^{83} +(-3.55972 - 5.83500i) q^{84} +(11.6423 - 3.11954i) q^{85} +(5.32701 + 1.42737i) q^{86} +(7.21106 - 7.56861i) q^{87} +(6.03462 - 3.48409i) q^{88} +(0.0313812 + 0.117116i) q^{89} +(14.3585 - 0.695139i) q^{90} +(-8.53551 - 5.52023i) q^{91} +(5.17297 + 2.98661i) q^{92} +(-4.07103 + 0.0984881i) q^{93} -8.95077 q^{94} +(0.524935 - 0.909214i) q^{95} +(9.92301 - 6.05367i) q^{96} +(11.2137 - 11.2137i) q^{97} +(-1.68893 - 0.452547i) q^{98} +(-17.9865 + 5.76503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} - 30 q^{8} - 2 q^{9} - 12 q^{10} + 6 q^{11} - 18 q^{12} - 2 q^{13} - 12 q^{14} + 4 q^{15} + 14 q^{16} - 2 q^{18} - 4 q^{19} - 6 q^{20} + 22 q^{21} + 2 q^{22} - 12 q^{23} - 18 q^{24} + 48 q^{26} - 32 q^{27} - 6 q^{29} + 66 q^{30} + 6 q^{31} + 30 q^{32} - 56 q^{33} - 6 q^{34} - 6 q^{35} - 6 q^{36} - 6 q^{37} - 36 q^{38} - 32 q^{39} - 12 q^{40} + 18 q^{41} + 80 q^{42} - 12 q^{44} + 34 q^{45} - 12 q^{46} + 30 q^{47} + 22 q^{48} - 12 q^{50} - 16 q^{52} - 56 q^{54} - 4 q^{55} - 12 q^{56} - 2 q^{57} - 28 q^{58} + 30 q^{59} - 58 q^{60} - 4 q^{61} - 18 q^{62} - 2 q^{63} + 30 q^{65} + 32 q^{66} - 16 q^{67} - 48 q^{69} - 46 q^{70} + 48 q^{71} + 126 q^{72} - 22 q^{73} + 24 q^{75} - 18 q^{76} - 72 q^{77} + 94 q^{78} + 8 q^{79} + 54 q^{80} - 14 q^{81} - 12 q^{82} + 72 q^{83} - 110 q^{84} + 78 q^{85} + 102 q^{86} + 14 q^{87} - 6 q^{88} + 114 q^{90} - 16 q^{91} + 120 q^{92} - 44 q^{93} - 52 q^{94} - 6 q^{95} + 16 q^{96} + 48 q^{97} - 36 q^{98} - 32 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 - 30 * q^8 - 2 * q^9 - 12 * q^10 + 6 * q^11 - 18 * q^12 - 2 * q^13 - 12 * q^14 + 4 * q^15 + 14 * q^16 - 2 * q^18 - 4 * q^19 - 6 * q^20 + 22 * q^21 + 2 * q^22 - 12 * q^23 - 18 * q^24 + 48 * q^26 - 32 * q^27 - 6 * q^29 + 66 * q^30 + 6 * q^31 + 30 * q^32 - 56 * q^33 - 6 * q^34 - 6 * q^35 - 6 * q^36 - 6 * q^37 - 36 * q^38 - 32 * q^39 - 12 * q^40 + 18 * q^41 + 80 * q^42 - 12 * q^44 + 34 * q^45 - 12 * q^46 + 30 * q^47 + 22 * q^48 - 12 * q^50 - 16 * q^52 - 56 * q^54 - 4 * q^55 - 12 * q^56 - 2 * q^57 - 28 * q^58 + 30 * q^59 - 58 * q^60 - 4 * q^61 - 18 * q^62 - 2 * q^63 + 30 * q^65 + 32 * q^66 - 16 * q^67 - 48 * q^69 - 46 * q^70 + 48 * q^71 + 126 * q^72 - 22 * q^73 + 24 * q^75 - 18 * q^76 - 72 * q^77 + 94 * q^78 + 8 * q^79 + 54 * q^80 - 14 * q^81 - 12 * q^82 + 72 * q^83 - 110 * q^84 + 78 * q^85 + 102 * q^86 + 14 * q^87 - 6 * q^88 + 114 * q^90 - 16 * q^91 + 120 * q^92 - 44 * q^93 - 52 * q^94 - 6 * q^95 + 16 * q^96 + 48 * q^97 - 36 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more