LMFDB - Embedded newform 84.2.o.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.o (of order $6$, degree $2$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$0.0777157 + 1.41208i$ of defining polynomial
Character	$\chi$	$=$	84.31
Dual form			84.2.o.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26175 - 0.638735i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.18404 - 1.61185i) q^{4} +(0.380152 - 0.219481i) q^{5} +(-0.0777157 + 1.41208i) q^{6} +(-2.02350 + 1.70453i) q^{7} +(0.464416 - 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.26175 - 0.638735i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.18404 - 1.61185i) q^{4} +(0.380152 - 0.219481i) q^{5} +(-0.0777157 + 1.41208i) q^{6} +(-2.02350 + 1.70453i) q^{7} +(0.464416 - 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.339468 - 0.519747i) q^{10} +(-1.83249 - 1.05799i) q^{11} +(0.803884 + 1.83133i) q^{12} +3.84803i q^{13} +(-1.46442 + 3.44318i) q^{14} +0.438962i q^{15} +(-1.19612 - 3.81698i) q^{16} +(-4.89158 - 2.82415i) q^{17} +(-1.18404 - 0.773342i) q^{18} +(1.48792 + 2.57715i) q^{19} +(0.0963438 - 0.872621i) q^{20} +(-0.464416 - 2.60467i) q^{21} +(-2.98792 - 0.164445i) q^{22} +(4.13127 - 2.38519i) q^{23} +(2.18404 + 1.79722i) q^{24} +(-2.40366 + 4.16325i) q^{25} +(2.45787 + 4.85526i) q^{26} +1.00000 q^{27} +(0.351547 + 5.27981i) q^{28} +7.02285 q^{29} +(0.280380 + 0.553861i) q^{30} +(3.71264 - 6.43048i) q^{31} +(-3.94724 - 4.05208i) q^{32} +(1.83249 - 1.05799i) q^{33} +(-7.97584 - 0.438962i) q^{34} +(-0.395127 + 1.09210i) q^{35} +(-1.98792 - 0.219481i) q^{36} +(2.64335 + 4.57842i) q^{37} +(3.52350 + 2.30134i) q^{38} +(-3.33249 - 1.92401i) q^{39} +(-0.435811 - 1.16257i) q^{40} -6.81813i q^{41} +(-2.24967 - 2.98981i) q^{42} -4.38646i q^{43} +(-3.87505 + 1.70100i) q^{44} +(-0.380152 - 0.219481i) q^{45} +(3.68914 - 5.64831i) q^{46} +(0.844569 + 1.46284i) q^{47} +(3.90366 + 0.872621i) q^{48} +(1.18914 - 6.89826i) q^{49} +(-0.373604 + 6.78829i) q^{50} +(4.89158 - 2.82415i) q^{51} +(6.20244 + 4.55620i) q^{52} +(-5.35599 + 9.27685i) q^{53} +(1.26175 - 0.638735i) q^{54} -0.928833 q^{55} +(3.81596 + 6.43727i) q^{56} -2.97584 q^{57} +(8.86109 - 4.48574i) q^{58} +(-4.05909 + 7.03055i) q^{59} +(0.707540 + 0.519747i) q^{60} +(5.35787 - 3.09337i) q^{61} +(0.577061 - 10.4851i) q^{62} +(2.48792 + 0.900140i) q^{63} +(-7.56863 - 2.59148i) q^{64} +(0.844569 + 1.46284i) q^{65} +(1.63637 - 2.50539i) q^{66} +(6.79878 + 3.92528i) q^{67} +(-10.3439 + 4.54058i) q^{68} +4.77038i q^{69} +(0.199011 + 1.63034i) q^{70} +1.16982i q^{71} +(-2.64845 + 0.992823i) q^{72} +(-8.69036 - 5.01738i) q^{73} +(6.25965 + 4.08843i) q^{74} +(-2.40366 - 4.16325i) q^{75} +(5.91574 + 0.653140i) q^{76} +(5.51142 - 0.982694i) q^{77} +(-5.43371 - 0.299052i) q^{78} +(-13.4958 + 7.79180i) q^{79} +(-1.29246 - 1.18851i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.35498 - 8.60279i) q^{82} -5.49645 q^{83} +(-4.74822 - 2.33546i) q^{84} -2.47939 q^{85} +(-2.80178 - 5.53462i) q^{86} +(-3.51142 + 6.08197i) q^{87} +(-3.80287 + 4.62137i) q^{88} +(-9.02285 + 5.20934i) q^{89} +(-0.619848 - 0.0341142i) q^{90} +(-6.55909 - 7.78650i) q^{91} +(1.04701 - 9.48314i) q^{92} +(3.71264 + 6.43048i) q^{93} +(2.00000 + 1.30628i) q^{94} +(1.13127 + 0.653140i) q^{95} +(5.48282 - 1.39237i) q^{96} -2.22605i q^{97} +(-2.90576 - 9.46343i) q^{98} +2.11598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.26175	−	0.638735i	0.892193	−	0.451654i
$2$	1.26175	−	0.638735i	0.892193	−	0.451654i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.18404	−	1.61185i	0.592018	−	0.805925i
$5$	0.380152	−	0.219481i	0.170009	−	0.0981549i	−0.412581	−	0.910921i	$-0.635373\pi$
$5$	0.380152	−	0.219481i	0.170009	−	0.0981549i	0.582590	+	0.812766i	$0.302039\pi$
$6$	−0.0777157	+	1.41208i	−0.0317273	+	0.576478i
$7$	−2.02350	+	1.70453i	−0.764813	+	0.644253i
$7$	−2.02350	+	1.70453i	−0.764813	+	0.644253i
$8$	0.464416	−	2.79004i	0.164196	−	0.986428i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.339468	−	0.519747i	0.107349	−	0.164358i
$11$	−1.83249	−	1.05799i	−0.552516	−	0.318995i	0.197620	−	0.980279i	$-0.436679\pi$
$11$	−1.83249	−	1.05799i	−0.552516	−	0.318995i	−0.750136	+	0.661283i	$0.770012\pi$
$12$	0.803884	+	1.83133i	0.232061	+	0.528659i
$13$			3.84803i			1.06725i	0.845721	+	0.533625i	$0.179171\pi$
$13$			3.84803i			1.06725i	−0.845721	+	0.533625i	$0.820829\pi$
$14$	−1.46442	+	3.44318i	−0.391382	+	0.920228i
$15$			0.438962i			0.113339i
$16$	−1.19612	−	3.81698i	−0.299029	−	0.954244i
$17$	−4.89158	−	2.82415i	−1.18638	−	0.684958i	−0.228899	−	0.973450i	$-0.573513\pi$
$17$	−4.89158	−	2.82415i	−1.18638	−	0.684958i	−0.957482	+	0.288492i	$0.906846\pi$
$18$	−1.18404	−	0.773342i	−0.279080	−	0.182278i
$19$	1.48792	+	2.57715i	0.341352	+	0.591240i	0.984684	−	0.174348i	$-0.0557817\pi$
$19$	1.48792	+	2.57715i	0.341352	+	0.591240i	−0.643332	+	0.765588i	$0.722448\pi$
$20$	0.0963438	−	0.872621i	0.0215431	−	0.195124i
$21$	−0.464416	−	2.60467i	−0.101344	−	0.568386i
$22$	−2.98792	−	0.164445i	−0.637027	−	0.0350597i
$23$	4.13127	−	2.38519i	0.861430	−	0.497347i	−0.00306100	−	0.999995i	$-0.500974\pi$
$23$	4.13127	−	2.38519i	0.861430	−	0.497347i	0.864491	+	0.502649i	$0.167641\pi$
$24$	2.18404	+	1.79722i	0.445815	+	0.366855i
$25$	−2.40366	+	4.16325i	−0.480731	+	0.832651i
$26$	2.45787	+	4.85526i	0.482028	+	0.952194i
$27$	1.00000			0.192450
$28$	0.351547	+	5.27981i	0.0664362	+	0.997791i
$29$	7.02285			1.30411			0.652055	−	0.758172i	$-0.273907\pi$
$29$	7.02285			1.30411			0.652055	+	0.758172i	$0.273907\pi$
$30$	0.280380	+	0.553861i	0.0511902	+	0.101121i
$31$	3.71264	−	6.43048i	0.666810	−	1.15495i	−0.311981	−	0.950088i	$-0.600993\pi$
$31$	3.71264	−	6.43048i	0.666810	−	1.15495i	0.978791	−	0.204861i	$-0.0656741\pi$
$32$	−3.94724	−	4.05208i	−0.697779	−	0.716313i
$33$	1.83249	−	1.05799i	0.318995	−	0.184172i
$34$	−7.97584	−	0.438962i	−1.36785	−	0.0752813i
$35$	−0.395127	+	1.09210i	−0.0667887	+	0.184599i
$36$	−1.98792	−	0.219481i	−0.331320	−	0.0365802i
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	0.997260	−	0.0739766i	$-0.0235690\pi$
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	−0.562696	+	0.826664i	$0.690236\pi$
$38$	3.52350	+	2.30134i	0.571588	+	0.373327i
$39$	−3.33249	−	1.92401i	−0.533625	−	0.308089i
$40$	−0.435811	−	1.16257i	−0.0689078	−	0.183818i
$41$		−	6.81813i		−	1.06481i	−0.846489	−	0.532407i	$-0.821288\pi$
$41$		−	6.81813i		−	1.06481i	0.846489	−	0.532407i	$-0.178712\pi$
$42$	−2.24967	−	2.98981i	−0.347132	−	0.461338i
$43$		−	4.38646i		−	0.668928i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$		−	4.38646i		−	0.668928i	0.942408	−	0.334464i	$-0.108555\pi$
$44$	−3.87505	+	1.70100i	−0.584186	+	0.256435i
$45$	−0.380152	−	0.219481i	−0.0566697	−	0.0327183i
$46$	3.68914	−	5.64831i	0.543934	−	0.832797i
$47$	0.844569	+	1.46284i	0.123193	+	0.213377i	0.921025	−	0.389503i	$-0.127353\pi$
$47$	0.844569	+	1.46284i	0.123193	+	0.213377i	−0.797832	+	0.602880i	$0.794020\pi$
$48$	3.90366	+	0.872621i	0.563444	+	0.125952i
$49$	1.18914	−	6.89826i	0.169877	−	0.985465i
$50$	−0.373604	+	6.78829i	−0.0528355	+	0.960010i
$51$	4.89158	−	2.82415i	0.684958	−	0.395461i
$52$	6.20244	+	4.55620i	0.860124	+	0.631832i
$53$	−5.35599	+	9.27685i	−0.735702	+	1.27427i	0.218712	+	0.975789i	$0.429814\pi$
$53$	−5.35599	+	9.27685i	−0.735702	+	1.27427i	−0.954415	+	0.298484i	$0.903519\pi$
$54$	1.26175	−	0.638735i	0.171703	−	0.0869208i
$55$	−0.928833			−0.125244
$56$	3.81596	+	6.43727i	0.509930	+	0.860216i
$57$	−2.97584			−0.394160
$58$	8.86109	−	4.48574i	1.16352	−	0.589006i
$59$	−4.05909	+	7.03055i	−0.528448	+	0.915299i	0.471002	+	0.882132i	$0.343893\pi$
$59$	−4.05909	+	7.03055i	−0.528448	+	0.915299i	−0.999450	+	0.0331668i	$0.989441\pi$
$60$	0.707540	+	0.519747i	0.0913431	+	0.0670990i
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	−0.116109	−	0.993237i	$-0.537042\pi$
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	0.802114	+	0.597171i	$0.203709\pi$
$62$	0.577061	−	10.4851i	0.0732868	−	1.33160i
$63$	2.48792	+	0.900140i	0.313449	+	0.113407i
$64$	−7.56863	−	2.59148i	−0.946079	−	0.323935i
$65$	0.844569	+	1.46284i	0.104756	+	0.181442i
$66$	1.63637	−	2.50539i	0.201424	−	0.308393i
$67$	6.79878	+	3.92528i	0.830604	+	0.479549i	0.854059	−	0.520176i	$-0.174134\pi$
$67$	6.79878	+	3.92528i	0.830604	+	0.479549i	−0.0234557	+	0.999725i	$0.507467\pi$
$68$	−10.3439	+	4.54058i	−1.25438	+	0.550627i
$69$			4.77038i			0.574287i
$70$	0.199011	+	1.63034i	0.0237864	+	0.194863i
$71$			1.16982i			0.138833i	0.997588	+	0.0694163i	$0.0221137\pi$
$71$			1.16982i			0.138833i	−0.997588	+	0.0694163i	$0.977886\pi$
$72$	−2.64845	+	0.992823i	−0.312123	+	0.117005i
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.103858	−	0.994592i	$-0.533119\pi$
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.913271	+	0.407352i	$0.866452\pi$
$74$	6.25965	+	4.08843i	0.727669	+	0.475270i
$75$	−2.40366	−	4.16325i	−0.277550	−	0.480731i
$76$	5.91574	+	0.653140i	0.678581	+	0.0749203i
$77$	5.51142	−	0.982694i	0.628085	−	0.111988i
$78$	−5.43371	−	0.299052i	−0.615246	−	0.0338610i
$79$	−13.4958	+	7.79180i	−1.51840	+	0.876646i	−0.518630	+	0.854999i	$0.673558\pi$
$79$	−13.4958	+	7.79180i	−1.51840	+	0.876646i	−0.999766	+	0.0216472i	$0.993109\pi$
$80$	−1.29246	−	1.18851i	−0.144501	−	0.132879i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.35498	−	8.60279i	−0.480927	−	0.950019i
$83$	−5.49645			−0.603314			−0.301657	−	0.953417i	$-0.597540\pi$
$83$	−5.49645			−0.603314			−0.301657	+	0.953417i	$0.597540\pi$
$84$	−4.74822	−	2.33546i	−0.518074	−	0.254819i
$85$	−2.47939			−0.268928
$86$	−2.80178	−	5.53462i	−0.302124	−	0.596814i
$87$	−3.51142	+	6.08197i	−0.376464	+	0.652055i
$88$	−3.80287	+	4.62137i	−0.405387	+	0.492640i
$89$	−9.02285	+	5.20934i	−0.956420	+	0.552189i	−0.895069	−	0.445927i	$-0.852874\pi$
$89$	−9.02285	+	5.20934i	−0.956420	+	0.552189i	−0.0613507	+	0.998116i	$0.519541\pi$
$90$	−0.619848	−	0.0341142i	−0.0653377	−	0.00359595i
$91$	−6.55909	−	7.78650i	−0.687579	−	0.816247i
$92$	1.04701	−	9.48314i	0.109158	−	0.988686i
$93$	3.71264	+	6.43048i	0.384983	+	0.666810i
$94$	2.00000	+	1.30628i	0.206284	+	0.134733i
$95$	1.13127	+	0.653140i	0.116066	+	0.0670108i
$96$	5.48282	−	1.39237i	0.559588	−	0.142108i
$97$		−	2.22605i		−	0.226021i	−0.993594	−	0.113011i	$-0.963951\pi$
$97$		−	2.22605i		−	0.226021i	0.993594	−	0.113011i	$-0.0360494\pi$
$98$	−2.90576	−	9.46343i	−0.293526	−	0.955951i
$99$			2.11598i			0.212664i
$100$	3.86452	+	8.80378i	0.386452	+	0.880378i
$101$	−0.664978	−	0.383925i	−0.0661678	−	0.0382020i	0.466551	−	0.884494i	$-0.345496\pi$
$101$	−0.664978	−	0.383925i	−0.0661678	−	0.0382020i	−0.532719	+	0.846292i	$0.678830\pi$
$102$	4.36807	−	6.68780i	0.432504	−	0.662191i
$103$	4.31939	+	7.48141i	0.425602	+	0.737165i	0.996476	−	0.0838727i	$-0.0267289\pi$
$103$	4.31939	+	7.48141i	0.425602	+	0.737165i	−0.570874	+	0.821038i	$0.693396\pi$
$104$	10.7361	+	1.78709i	1.05277	+	0.175238i
$105$	−0.748225	−	0.888241i	−0.0730193	−	0.0866835i
$106$	−0.832489	+	15.1261i	−0.0808585	+	1.46918i
$107$	−2.20346	+	1.27217i	−0.213016	+	0.122985i	−0.602712	−	0.797959i	$-0.705913\pi$
$107$	−2.20346	+	1.27217i	−0.213016	+	0.122985i	0.389696	+	0.920943i	$0.372580\pi$
$108$	1.18404	−	1.61185i	0.113934	−	0.155100i
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	−0.655705	−	0.755017i	$-0.727629\pi$
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	0.981716	+	0.190349i	$0.0609620\pi$
$110$	−1.17196	+	0.593278i	−0.111742	+	0.0565668i
$111$	−5.28670			−0.501792
$112$	8.92651	+	5.68485i	0.843475	+	0.537168i
$113$	13.6408			1.28322			0.641610	−	0.767031i	$-0.278267\pi$
$113$	13.6408			1.28322			0.641610	+	0.767031i	$0.278267\pi$
$114$	−3.75477	+	1.90077i	−0.351667	+	0.178024i
$115$	1.04701	−	1.81347i	0.0976340	−	0.169107i
$116$	8.31531	−	11.3198i	0.772057	−	1.05101i
$117$	3.33249	−	1.92401i	0.308089	−	0.177875i
$118$	−0.630909	+	11.4635i	−0.0580799	+	1.05530i
$119$	14.7120	−	2.62317i	1.34865	−	0.240465i
$120$	1.22472	+	0.203861i	0.111801	+	0.0186099i
$121$	−3.26132	−	5.64878i	−0.296484	−	0.513525i
$122$	4.78446	−	7.32532i	0.433165	−	0.663203i
$123$	5.90467	+	3.40907i	0.532407	+	0.307385i
$124$	−5.96907	−	13.5981i	−0.536038	−	1.22115i
$125$			4.30504i			0.385054i
$126$	3.71409	−	0.453368i	0.330877	−	0.0403892i
$127$			3.51914i			0.312273i	0.987735	+	0.156137i	$0.0499040\pi$
$127$			3.51914i			0.312273i	−0.987735	+	0.156137i	$0.950096\pi$
$128$	−11.2050	+	1.56454i	−0.990392	+	0.138287i
$129$	3.79878	+	2.19323i	0.334464	+	0.193103i
$130$	2.00000	+	1.30628i	0.175412	+	0.114568i
$131$	−9.80833	−	16.9885i	−0.856958	−	1.48429i	−0.874817	−	0.484454i	$-0.839018\pi$
$131$	−9.80833	−	16.9885i	−0.856958	−	1.48429i	0.0178590	−	0.999841i	$-0.494315\pi$
$132$	0.464416	−	4.20639i	0.0404223	−	0.366119i
$133$	−7.40366	−	2.67867i	−0.641978	−	0.232270i
$134$	11.0856	+	0.610111i	0.957649	+	0.0527056i
$135$	0.380152	−	0.219481i	0.0327183	−	0.0188899i
$136$	−10.1512	+	12.3361i	−0.870460	+	1.05781i
$137$	1.68914	−	2.92567i	0.144313	−	0.249957i	−0.784804	−	0.619745i	$-0.787236\pi$
$137$	1.68914	−	2.92567i	0.144313	−	0.249957i	0.929116	+	0.369788i	$0.120570\pi$
$138$	3.04701	+	6.01904i	0.259379	+	0.512375i
$139$	16.4481			1.39511			0.697556	−	0.716530i	$-0.254271\pi$
$139$	16.4481			1.39511			0.697556	+	0.716530i	$0.254271\pi$
$140$	1.29246	+	1.92997i	0.109233	+	0.163113i
$141$	−1.68914			−0.142251
$142$	0.747207	+	1.47603i	0.0627042	+	0.123866i
$143$	4.07117	−	7.05147i	0.340448	−	0.589673i
$144$	−2.70754	+	2.94435i	−0.225628	+	0.245363i
$145$	2.66975	−	1.54138i	0.221711	−	0.128005i
$146$	−14.1699	−	0.779858i	−1.17271	−	0.0645415i
$147$	5.37950	+	4.47895i	0.443693	+	0.369418i
$148$	10.5095	+	1.16033i	0.863879	+	0.0953786i
$149$	−3.23970	−	5.61132i	−0.265406	−	0.459697i	0.702264	−	0.711917i	$-0.252173\pi$
$149$	−3.23970	−	5.61132i	−0.265406	−	0.459697i	−0.967670	+	0.252220i	$0.918839\pi$
$150$	−5.69203	−	3.71770i	−0.464753	−	0.303549i
$151$	−6.72827	−	3.88457i	−0.547539	−	0.316122i	0.200590	−	0.979675i	$-0.435714\pi$
$151$	−6.72827	−	3.88457i	−0.547539	−	0.316122i	−0.748129	+	0.663554i	$0.769047\pi$
$152$	7.88137	−	2.95448i	0.639264	−	0.239640i
$153$			5.64831i			0.456639i
$154$	6.32637	−	4.76025i	0.509793	−	0.383592i
$155$		−	3.25942i		−	0.261803i
$156$	−7.04701	+	3.09337i	−0.564212	+	0.247668i
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	0.763116	−	0.646262i	$-0.223669\pi$
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	−0.178121	+	0.984009i	$0.557002\pi$
$158$	−12.0515	+	18.4516i	−0.958762	+	1.46793i
$159$	−5.35599	−	9.27685i	−0.424758	−	0.735702i
$160$	−2.38990	−	0.674063i	−0.188939	−	0.0532893i
$161$	−4.29401	+	11.8683i	−0.338415	+	0.935356i
$162$	−0.0777157	+	1.41208i	−0.00610592	+	0.110943i
$163$	−6.02285	+	3.47729i	−0.471746	+	0.272363i	−0.716970	−	0.697104i	$-0.754472\pi$
$163$	−6.02285	+	3.47729i	−0.471746	+	0.272363i	0.245224	+	0.969466i	$0.421138\pi$
$164$	−10.9898	−	8.07291i	−0.858159	−	0.630389i
$165$	0.464416	−	0.804393i	0.0361548	−	0.0626219i
$166$	−6.93516	+	3.51077i	−0.538273	+	0.272489i
$167$	8.12021			0.628361			0.314180	−	0.949363i	$-0.398270\pi$
$167$	8.12021			0.628361			0.314180	+	0.949363i	$0.398270\pi$
$168$	−7.48282	+	0.0860874i	−0.577312	+	0.00664178i
$169$	−1.80731			−0.139024
$170$	−3.12838	+	1.58367i	−0.239936	+	0.121462i
$171$	1.48792	−	2.57715i	0.113784	−	0.197080i
$172$	−7.07031	−	5.19372i	−0.539106	−	0.396018i
$173$	−1.22660	+	0.708177i	−0.0932565	+	0.0538417i	−0.545903	−	0.837848i	$-0.683813\pi$
$173$	−1.22660	+	0.708177i	−0.0932565	+	0.0538417i	0.452646	+	0.891690i	$0.350480\pi$
$174$	−0.545785	+	9.91680i	−0.0413759	+	0.751791i
$175$	−2.23260	−	12.5215i	−0.168768	−	0.946534i
$176$	−1.84645	+	8.26004i	−0.139181	+	0.622624i
$177$	−4.05909	−	7.03055i	−0.305100	−	0.528448i
$178$	−8.05721	+	12.3361i	−0.603913	+	0.924630i
$179$	9.29401	+	5.36590i	0.694667	+	0.401066i	0.805358	−	0.592789i	$-0.201973\pi$
$179$	9.29401	+	5.36590i	0.694667	+	0.401066i	−0.110691	+	0.993855i	$0.535306\pi$
$180$	−0.803884	+	0.352875i	−0.0599180	+	0.0263017i
$181$		−	1.21426i		−	0.0902549i	−0.998981	−	0.0451275i	$-0.985631\pi$
$181$		−	1.21426i		−	0.0902549i	0.998981	−	0.0451275i	$-0.0143694\pi$
$182$	−13.2494	−	5.63511i	−0.982114	−	0.417702i
$183$			6.18674i			0.457337i
$184$	−4.73615	−	12.6341i	−0.349153	−	0.931401i
$185$	2.00975	+	1.16033i	0.147760	+	0.0853092i
$186$	8.79180	+	5.74228i	0.644646	+	0.421045i
$187$	5.97584	+	10.3505i	0.436997	+	0.756901i
$188$	3.35787	+	0.370733i	0.244898	+	0.0270385i
$189$	−2.02350	+	1.70453i	−0.147188	+	0.123987i
$190$	1.84457	+	0.101518i	0.133819	+	0.00736493i
$191$	5.67473	−	3.27631i	0.410609	−	0.237065i	−0.280442	−	0.959871i	$-0.590481\pi$
$191$	5.67473	−	3.27631i	0.410609	−	0.237065i	0.691051	+	0.722806i	$0.257148\pi$
$192$	6.02861	−	5.25889i	0.435077	−	0.379528i
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	−0.801891	−	0.597470i	$-0.796173\pi$
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	0.918370	+	0.395723i	$0.129506\pi$
$194$	−1.42185	−	2.80872i	−0.102083	−	0.201654i
$195$	−1.68914			−0.120962
$196$	−9.71097	−	10.0845i	−0.693641	−	0.720321i
$197$	−19.2554			−1.37189			−0.685947	−	0.727652i	$-0.740612\pi$
$197$	−19.2554			−1.37189			−0.685947	+	0.727652i	$0.740612\pi$
$198$	1.35155	+	2.66984i	0.0960503	+	0.189737i
$199$	4.31086	−	7.46663i	0.305589	−	0.529296i	−0.671803	−	0.740730i	$-0.734480\pi$
$199$	4.31086	−	7.46663i	0.305589	−	0.529296i	0.977392	+	0.211434i	$0.0678133\pi$
$200$	10.4993	+	8.63978i	0.742416	+	0.610925i
$201$	−6.79878	+	3.92528i	−0.479549	+	0.276868i
$202$	−1.08426	−	0.0596741i	−0.0762886	−	0.00419865i
$203$	−14.2108	+	11.9707i	−0.997400	+	0.840177i
$204$	1.23970	−	11.2284i	0.0867961	−	0.786144i
$205$	−1.49645	−	2.59193i	−0.104517	−	0.181028i
$206$	10.2286	+	6.68073i	0.712663	+	0.465469i
$207$	−4.13127	−	2.38519i	−0.287143	−	0.165782i
$208$	14.6878	−	4.60269i	1.01842	−	0.319139i
$209$		−	6.29681i		−	0.435559i
$210$	−1.51142	−	0.642823i	−0.104298	−	0.0443590i
$211$		−	6.09787i		−	0.419795i	−0.977723	−	0.209897i	$-0.932687\pi$
$211$		−	6.09787i		−	0.419795i	0.977723	−	0.209897i	$-0.0673130\pi$
$212$	8.61120	+	19.6172i	0.591419	+	1.34731i
$213$	−1.01310	−	0.584912i	−0.0694163	−	0.0400775i
$214$	−1.96764	+	3.01258i	−0.134505	+	0.205936i
$215$	−0.962744	−	1.66752i	−0.0656586	−	0.113724i
$216$	0.464416	−	2.79004i	0.0315995	−	0.189838i
$217$	3.44842	+	19.3404i	0.234094	+	1.31291i
$218$	0.529035	−	9.61245i	0.0358308	−	0.651037i
$219$	8.69036	−	5.01738i	0.587240	−	0.339043i
$220$	−1.09977	+	1.49714i	−0.0741466	+	0.100937i
$221$	10.8674	−	18.8229i	0.731022	−	1.26617i
$222$	−6.67051	+	3.37680i	−0.447695	+	0.226636i
$223$	2.44944			0.164027			0.0820134	−	0.996631i	$-0.473865\pi$
$223$	2.44944			0.164027			0.0820134	+	0.996631i	$0.473865\pi$
$224$	14.8941	+	1.47120i	0.995157	+	0.0982988i
$225$	4.80731			0.320487
$226$	17.2113	−	8.71286i	1.14488	−	0.579571i
$227$	−11.6398	+	20.1607i	−0.772561	+	1.33811i	0.163595	+	0.986528i	$0.447691\pi$
$227$	−11.6398	+	20.1607i	−0.772561	+	1.33811i	−0.936155	+	0.351587i	$0.885642\pi$
$228$	−3.52350	+	4.79661i	−0.233350	+	0.317663i
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	−0.796065	−	0.605211i	$-0.793089\pi$
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	0.126095	+	0.992018i	$0.459756\pi$
$230$	0.162738	−	2.95691i	0.0107306	−	0.194973i
$231$	−1.90467	+	5.26438i	−0.125318	+	0.346371i
$232$	3.26153	−	19.5940i	0.214130	−	1.28641i
$233$	4.08426	+	7.07415i	0.267569	+	0.463443i	0.968234	−	0.250048i	$-0.0804463\pi$
$233$	4.08426	+	7.07415i	0.267569	+	0.463443i	−0.700664	+	0.713491i	$0.747113\pi$
$234$	2.97584	−	4.55620i	0.194537	−	0.297848i
$235$	0.642129	+	0.370733i	0.0418879	+	0.0241840i
$236$	6.52607	+	14.8671i	0.424811	+	0.967763i
$237$		−	15.5836i		−	1.01226i
$238$	16.8874	−	12.7068i	1.09465	−	0.823662i
$239$			18.1984i			1.17716i	0.808439	+	0.588579i	$0.200313\pi$
$239$			18.1984i			1.17716i	−0.808439	+	0.588579i	$0.799687\pi$
$240$	1.67551	−	0.525049i	0.108154	−	0.0338918i
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.988663	+	0.150149i	$0.0479753\pi$
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.624364	+	0.781133i	$0.285358\pi$
$242$	−7.72305	−	5.04424i	−0.496456	−	0.324256i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.35787	−	12.2987i	0.0869288	−	0.787346i
$245$	−1.06198	−	2.88338i	−0.0678476	−	0.184212i
$246$	9.62772	+	0.529876i	0.613841	+	0.0337836i
$247$	−9.91696	+	5.72556i	−0.631001	+	0.364309i
$248$	−16.2171	−	13.3448i	−1.02979	−	0.847398i
$249$	2.74822	−	4.76007i	0.174162	−	0.301657i
$250$	2.74978	+	5.43189i	0.173911	+	0.343543i
$251$	−20.3586			−1.28502			−0.642512	−	0.766276i	$-0.722108\pi$
$251$	−20.3586			−1.28502			−0.642512	+	0.766276i	$0.722108\pi$
$252$	4.39668	−	2.94435i	0.276965	−	0.185477i
$253$	−10.0940			−0.634605
$254$	2.24780	+	4.44028i	0.141039	+	0.278608i
$255$	1.23970	−	2.14722i	0.0776328	−	0.134464i
$256$	−13.1386	+	9.13109i	−0.821163	+	0.570693i
$257$	18.4350	−	10.6435i	1.14995	−	0.663922i	0.201072	−	0.979577i	$-0.435558\pi$
$257$	18.4350	−	10.6435i	1.14995	−	0.663922i	0.948874	+	0.315655i	$0.102224\pi$
$258$	6.19401	+	0.340896i	0.385622	+	0.0212233i
$259$	−13.1529	−	4.75877i	−0.817281	−	0.295696i
$260$	3.35787	+	0.370733i	0.208246	+	0.0229919i
$261$	−3.51142	−	6.08197i	−0.217352	−	0.376464i
$262$	−23.2268	−	15.1704i	−1.43496	−	0.937230i
$263$	−17.4760	−	10.0898i	−1.07762	−	0.622164i	−0.147366	−	0.989082i	$-0.547080\pi$
$263$	−17.4760	−	10.0898i	−1.07762	−	0.622164i	−0.930253	+	0.366918i	$0.880413\pi$
$264$	−2.10079	−	5.60406i	−0.129295	−	0.344906i
$265$			4.70215i			0.288851i
$266$	−11.0525	+	1.34915i	−0.677675	+	0.0827217i
$267$		−	10.4187i		−	0.637613i
$268$	14.3770	−	6.31094i	0.878213	−	0.385502i
$269$	14.1764	+	8.18475i	0.864351	+	0.499033i	0.865467	−	0.500966i	$-0.167022\pi$
$269$	14.1764	+	8.18475i	0.864351	+	0.499033i	−0.00111621	+	0.999999i	$0.500355\pi$
$270$	0.339468	−	0.519747i	0.0206593	−	0.0316308i
$271$	6.72696	+	11.6514i	0.408634	+	0.707775i	0.994737	−	0.102462i	$-0.0326720\pi$
$271$	6.72696	+	11.6514i	0.408634	+	0.707775i	−0.586103	+	0.810236i	$0.699339\pi$
$272$	−4.92883	+	22.0490i	−0.298854	+	1.33692i
$273$	10.0228	−	1.78709i	0.606610	−	0.108159i
$274$	0.262545	−	4.77038i	0.0158609	−	0.288189i
$275$	8.80935	−	5.08608i	0.531224	−	0.306702i
$276$	7.68914	+	5.64831i	0.462832	+	0.339988i
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	−0.905109	−	0.425180i	$-0.860211\pi$
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	0.820771	+	0.571257i	$0.193544\pi$
$278$	20.7535	−	10.5060i	1.24471	−	0.630107i
$279$	−7.42528			−0.444540
$280$	2.86350	+	1.60961i	0.171127	+	0.0961926i
$281$	−25.4502			−1.51823			−0.759115	−	0.650957i	$-0.774368\pi$
$281$	−25.4502			−1.51823			−0.759115	+	0.650957i	$0.774368\pi$
$282$	−2.13127	+	1.07891i	−0.126915	+	0.0642482i
$283$	−2.36975	+	4.10452i	−0.140867	+	0.243988i	−0.927823	−	0.373020i	$-0.878322\pi$
$283$	−2.36975	+	4.10452i	−0.140867	+	0.243988i	0.786957	+	0.617008i	$0.211656\pi$
$284$	1.88558	+	1.38511i	0.111889	+	0.0821914i
$285$	−1.13127	+	0.653140i	−0.0670108	+	0.0386887i
$286$	0.632787	−	11.4976i	0.0374175	−	0.679867i
$287$	11.6217	+	13.7965i	0.686009	+	0.814382i
$288$	−1.53558	+	5.44445i	−0.0904851	+	0.320817i
$289$	7.45168	+	12.9067i	0.438334	+	0.759217i
$290$	2.38403	−	3.65010i	0.139995	−	0.214341i
$291$	1.92782	+	1.11302i	0.113011	+	0.0652467i
$292$	−18.3770	+	8.06679i	−1.07543	+	0.472073i
$293$		−	3.22818i		−	0.188592i	−0.995544	−	0.0942960i	$-0.969940\pi$
$293$		−	3.22818i		−	0.188592i	0.995544	−	0.0942960i	$-0.0300600\pi$
$294$	9.64845	+	2.21526i	0.562709	+	0.129196i
$295$			3.56357i			0.207479i
$296$	14.0016	−	5.24876i	0.813826	−	0.305078i
$297$	−1.83249	−	1.05799i	−0.106332	−	0.0613907i
$298$	−7.67183	−	5.01079i	−0.444417	−	0.290267i
$299$	9.17828	+	15.8972i	0.530794	+	0.919362i
$300$	−9.55656	−	1.05511i	−0.551748	−	0.0609170i
$301$	7.47686	+	8.87601i	0.430959	+	0.511605i
$302$	−10.9706	−	0.603784i	−0.631288	−	0.0347439i
$303$	0.664978	−	0.383925i	0.0382020	−	0.0220559i
$304$	8.05721	−	8.76193i	0.462113	−	0.502531i
$305$	1.35787	−	2.35190i	0.0777515	−	0.134669i
$306$	3.60777	+	7.12676i	0.206242	+	0.407410i
$307$	5.45523			0.311347			0.155673	−	0.987809i	$-0.450245\pi$
$307$	5.45523			0.311347			0.155673	+	0.987809i	$0.450245\pi$
$308$	4.94177	−	10.0471i	0.281584	−	0.572488i
$309$	−8.63878			−0.491443
$310$	−2.08190	−	4.11258i	−0.118244	−	0.233579i
$311$	15.2625	−	26.4355i	0.865460	−	1.49902i	−0.00113066	−	0.999999i	$-0.500360\pi$
$311$	15.2625	−	26.4355i	0.865460	−	1.49902i	0.866590	−	0.499020i	$-0.166307\pi$
$312$	−6.91574	+	8.40423i	−0.391526	+	0.475796i
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.884228	−	0.467056i	$-0.845315\pi$
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.0376312	+	0.999292i	$0.511981\pi$
$314$	11.9517	+	0.657778i	0.674472	+	0.0371206i
$315$	1.14335	−	0.203861i	0.0644206	−	0.0114863i
$316$	−3.42030	+	30.9790i	−0.192407	+	1.74270i
$317$	−8.58259	−	14.8655i	−0.482046	−	0.834929i	0.517741	−	0.855537i	$-0.326773\pi$
$317$	−8.58259	−	14.8655i	−0.482046	−	0.834929i	−0.999788	+	0.0206085i	$0.993440\pi$
$318$	−12.6834	−	8.28403i	−0.711249	−	0.464545i
$319$	−12.8693	−	7.43009i	−0.720542	−	0.416005i
$320$	−3.44601	+	0.676014i	−0.192638	+	0.0377904i
$321$		−	2.54433i		−	0.142011i
$322$	2.16274	+	17.7176i	0.120525	+	0.987365i
$323$		−	16.8085i		−	0.935248i
$324$	0.803884	+	1.83133i	0.0446602	+	0.101741i
$325$	−16.0203	−	9.24933i	−0.888647	−	0.513061i
$326$	−5.37827	+	8.23448i	−0.297875	+	0.456066i
$327$	3.40366	+	5.89531i	0.188223	+	0.326011i
$328$	−19.0228	−	3.16645i	−1.05036	−	0.174838i
$329$	−4.20244	−	1.52046i	−0.231688	−	0.0838256i
$330$	0.0721849	−	1.31158i	0.00397365	−	0.0722003i
$331$	18.6081	−	10.7434i	1.02280	−	0.590511i	0.107883	−	0.994164i	$-0.465593\pi$
$331$	18.6081	−	10.7434i	1.02280	−	0.590511i	0.914912	+	0.403652i	$0.132259\pi$
$332$	−6.50800	+	8.85945i	−0.357173	+	0.486225i
$333$	2.64335	−	4.57842i	0.144855	−	0.250896i
$334$	10.2457	−	5.18666i	0.560619	−	0.283801i
$335$	3.44610			0.188280
$336$	−9.38648	+	4.88816i	−0.512074	+	0.266671i
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	−2.28038	+	1.15439i	−0.124036	+	0.0627907i
$339$	−6.82041	+	11.8133i	−0.370434	+	0.641610i
$340$	−2.93569	+	3.99640i	−0.159210	+	0.216735i
$341$	−13.6068	+	7.85586i	−0.736847	+	0.425419i
$342$	0.231269	−	4.20212i	0.0125056	−	0.227224i
$343$	9.35208	+	15.9856i	0.504965	+	0.863140i
$344$	−12.2384	−	2.03714i	−0.659850	−	0.109835i
$345$	1.04701	+	1.81347i	0.0563690	+	0.0976340i
$346$	−1.09533	+	1.67701i	−0.0588851	+	0.0901569i
$347$	−2.43838	−	1.40780i	−0.130899	−	0.0755746i	0.433121	−	0.901336i	$-0.357412\pi$
$347$	−2.43838	−	1.40780i	−0.130899	−	0.0755746i	−0.564020	+	0.825761i	$0.690746\pi$
$348$	5.64556	+	12.8612i	0.302634	+	0.689430i
$349$		−	9.54077i		−	0.510705i	−0.966848	−	0.255353i	$-0.917808\pi$
$349$		−	9.54077i		−	0.510705i	0.966848	−	0.255353i	$-0.0821916\pi$
$350$	−10.8149	−	14.3730i	−0.578080	−	0.768267i
$351$			3.84803i			0.205392i
$352$	2.94622	+	11.6015i	0.157034	+	0.618363i
$353$	8.63351	+	4.98456i	0.459516	+	0.265301i	0.711841	−	0.702341i	$-0.247862\pi$
$353$	8.63351	+	4.98456i	0.459516	+	0.265301i	−0.252325	+	0.967643i	$0.581195\pi$
$354$	−9.61221	−	6.27813i	−0.510883	−	0.333679i
$355$	0.256754	+	0.444711i	0.0136271	+	0.0236028i
$356$	−2.28670	+	20.7115i	−0.121195	+	1.09771i
$357$	−5.08426	+	14.0525i	−0.269088	+	0.743739i
$358$	15.1541	+	0.834029i	0.800920	+	0.0440798i
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$	−0.788909	+	0.958709i	−0.0415792	+	0.0505284i
$361$	5.07218	−	8.78528i	0.266957	−	0.462383i
$362$	−0.775587	−	1.53209i	−0.0407639	−	0.0805248i
$363$	6.52264			0.342350
$364$	−20.3169	+	1.35276i	−1.06489	+	0.0709040i
$365$	−4.40488			−0.230562
$366$	3.95168	+	7.80613i	0.206558	+	0.408033i
$367$	8.95234	−	15.5059i	0.467308	−	0.809402i	−0.531994	−	0.846748i	$-0.678557\pi$
$367$	8.95234	−	15.5059i	0.467308	−	0.809402i	0.999302	+	0.0373465i	$0.0118905\pi$
$368$	−14.0457	−	12.9160i	−0.732183	−	0.673293i
$369$	−5.90467	+	3.40907i	−0.307385	+	0.177469i
$370$	3.27695	+	0.180352i	0.170361	+	0.00937604i
$371$	−4.97482	−	27.9012i	−0.258280	−	1.44856i
$372$	14.7609	+	1.62971i	0.765316	+	0.0844964i
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	0.615560	−	0.788090i	$-0.288930\pi$
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	−0.990286	+	0.139045i	$0.955597\pi$
$374$	14.1512	+	9.24274i	0.731742	+	0.477931i
$375$	−3.72827	−	2.15252i	−0.192527	−	0.111156i
$376$	4.47360	−	1.67701i	0.230708	−	0.0864854i
$377$			27.0241i			1.39181i
$378$	−1.46442	+	3.44318i	−0.0753215	+	0.177098i
$379$		−	21.5969i		−	1.10936i	−0.832064	−	0.554679i	$-0.812841\pi$
$379$		−	21.5969i		−	1.10936i	0.832064	−	0.554679i	$-0.187159\pi$
$380$	2.39223	−	1.05010i	0.122719	−	0.0538689i
$381$	−3.04766	−	1.75957i	−0.156137	−	0.0901455i
$382$	5.06741	−	7.75853i	0.259271	−	0.396961i
$383$	−0.318169	−	0.551085i	−0.0162577	−	0.0281591i	0.857782	−	0.514013i	$-0.171842\pi$
$383$	−0.318169	−	0.551085i	−0.0162577	−	0.0281591i	−0.874040	+	0.485854i	$0.838509\pi$
$384$	4.24757	−	10.4861i	0.216758	−	0.535116i
$385$	1.87950	−	1.58323i	0.0957881	−	0.0806887i
$386$	0.251515	−	4.56997i	0.0128018	−	0.232606i
$387$	−3.79878	+	2.19323i	−0.193103	+	0.111488i
$388$	−3.58806	−	2.63572i	−0.182156	−	0.133809i
$389$	0.509547	−	0.882561i	0.0258351	−	0.0447476i	−0.852819	−	0.522207i	$-0.825109\pi$
$389$	0.509547	−	0.882561i	0.0258351	−	0.0447476i	0.878654	+	0.477459i	$0.158442\pi$
$390$	−2.13127	+	1.07891i	−0.107921	+	0.0546327i
$391$	−26.9446			−1.36265
$392$	−18.6942	−	6.52140i	−0.944197	−	0.329381i
$393$	19.6167			0.989530
$394$	−24.2956	+	12.2991i	−1.22399	+	0.619621i
$395$	−3.42030	+	5.92414i	−0.172094	+	0.298076i
$396$	3.41063	+	2.50539i	0.171391	+	0.125901i
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.315496	−	0.948927i	$-0.397829\pi$
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.979543	+	0.201236i	$0.0644957\pi$
$398$	0.670043	−	12.1745i	0.0335862	−	0.610254i
$399$	6.02163	−	5.07242i	0.301458	−	0.253939i
$400$	18.7661	+	4.19496i	0.938305	+	0.209748i
$401$	3.39513	+	5.88053i	0.169545	+	0.293660i	0.938260	−	0.345931i	$-0.112437\pi$
$401$	3.39513	+	5.88053i	0.169545	+	0.293660i	−0.768715	+	0.639591i	$0.779104\pi$
$402$	−6.07117	+	9.29535i	−0.302802	+	0.463610i
$403$	24.7447	+	14.2863i	1.23262	+	0.711654i
$404$	−1.40619	+	0.617263i	−0.0699605	+	0.0307100i
$405$			0.438962i			0.0218122i
$406$	−10.2844	+	24.1809i	−0.510405	+	1.20008i
$407$		−	11.1865i		−	0.554496i
$408$	−5.60777	−	14.9593i	−0.277626	−	0.740594i
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	0.577393	−	0.816467i	$-0.304070\pi$
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	−0.418384	+	0.908270i	$0.637404\pi$
$410$	−3.54370	−	2.31454i	−0.175011	−	0.114307i
$411$	1.68914	+	2.92567i	0.0833190	+	0.144313i
$412$	17.1732	+	1.89605i	0.846064	+	0.0934116i
$413$	−3.77021	−	21.1452i	−0.185520	−	1.04049i
$414$	−6.73615	−	0.370733i	−0.331063	−	0.0182206i
$415$	−2.08949	+	1.20637i	−0.102569	+	0.0592182i
$416$	15.5925	−	15.1891i	0.764485	−	0.744705i
$417$	−8.22407	+	14.2445i	−0.402734	+	0.697556i
$418$	−4.02199	−	7.94501i	−0.196722	−	0.388603i
$419$	20.7082			1.01166			0.505832	−	0.862632i	$-0.331186\pi$
$419$	20.7082			1.01166			0.505832	+	0.862632i	$0.331186\pi$
$420$	−2.31764	+	0.154316i	−0.113089	+	0.00752984i
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	−3.89492	−	7.69400i	−0.189602	−	0.374538i
$423$	0.844569	−	1.46284i	0.0410643	−	0.0711255i
$424$	23.3954	+	19.2518i	1.13618	+	0.934948i
$425$	23.5153	−	13.5766i	1.14066	−	0.658561i
$426$	−1.65188	−	0.0909137i	−0.0800339	−	0.00440478i
$427$	−5.56893	+	15.3921i	−0.269499	+	0.744876i
$428$	−0.558433	+	5.05793i	−0.0269929	+	0.244484i
$429$	4.07117	+	7.05147i	0.196558	+	0.340448i
$430$	−2.27985	−	1.48906i	−0.109944	−	0.0718089i
$431$	10.2723	+	5.93071i	0.494799	+	0.285672i	0.726563	−	0.687100i	$-0.241116\pi$
$431$	10.2723	+	5.93071i	0.494799	+	0.285672i	−0.231764	+	0.972772i	$0.574450\pi$
$432$	−1.19612	−	3.81698i	−0.0575481	−	0.183644i
$433$		−	16.9269i		−	0.813454i	−0.913550	−	0.406727i	$-0.866670\pi$
$433$		−	16.9269i		−	0.813454i	0.913550	−	0.406727i	$-0.133330\pi$
$434$	16.7045	+	22.2002i	0.801839	+	1.06564i
$435$			3.08276i			0.147807i
$436$	−5.47229	−	12.4664i	−0.262075	−	0.597034i
$437$	12.2940	+	7.09795i	0.588102	+	0.339541i
$438$	7.76030	−	11.8815i	0.370802	−	0.567721i
$439$	−1.17640	−	2.03759i	−0.0561467	−	0.0972489i	0.836586	−	0.547836i	$-0.184548\pi$
$439$	−1.17640	−	2.03759i	−0.0561467	−	0.0972489i	−0.892733	+	0.450587i	$0.851215\pi$
$440$	−0.431365	+	2.59148i	−0.0205645	+	0.123544i
$441$	−6.56863	+	2.41931i	−0.312792	+	0.115205i
$442$	1.68914	−	30.6913i	0.0803441	−	1.45983i
$443$	−1.38904	+	0.801965i	−0.0659955	+	0.0381025i	−0.532635	−	0.846345i	$-0.678798\pi$
$443$	−1.38904	+	0.801965i	−0.0659955	+	0.0381025i	0.466639	+	0.884448i	$0.345465\pi$
$444$	−6.25965	+	8.52137i	−0.297070	+	0.404406i
$445$	−2.28670	+	3.96069i	−0.108400	+	0.187755i
$446$	3.09059	−	1.56454i	0.146344	−	0.0740833i
$447$	6.47939			0.306465
$448$	19.7324	−	7.65711i	0.932269	−	0.361765i
$449$	1.35208			0.0638086			0.0319043	−	0.999491i	$-0.489843\pi$
$449$	1.35208			0.0638086			0.0319043	+	0.999491i	$0.489843\pi$
$450$	6.06564	−	3.07060i	0.285937	−	0.144749i
$451$	−7.21350	+	12.4942i	−0.339670	+	0.588327i
$452$	16.1512	−	21.9869i	0.759690	−	1.03418i
$453$	6.72827	−	3.88457i	0.316122	−	0.182513i
$454$	−1.80919	+	32.8726i	−0.0849095	+	1.54279i
$455$	−4.20244	−	1.52046i	−0.197013	−	0.0712802i
$456$	−1.38203	+	8.30271i	−0.0647195	+	0.388810i
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	−0.999782	−	0.0209017i	$-0.993346\pi$
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	0.481789	−	0.876287i	$-0.339987\pi$
$458$	−9.05345	+	13.8614i	−0.423040	+	0.647702i
$459$	−4.89158	−	2.82415i	−0.228319	−	0.131820i
$460$	−1.68335	−	3.83484i	−0.0784864	−	0.178800i
$461$			30.7842i			1.43376i	0.697195	+	0.716882i	$0.254431\pi$
$461$			30.7842i			1.43376i	−0.697195	+	0.716882i	$0.745569\pi$
$462$	0.959316	+	7.85892i	0.0446314	+	0.365630i
$463$			13.8120i			0.641897i	0.947097	+	0.320948i	$0.104002\pi$
$463$			13.8120i			0.641897i	−0.947097	+	0.320948i	$0.895998\pi$
$464$	−8.40014	−	26.8060i	−0.389967	−	1.24444i
$465$	2.82274	+	1.62971i	0.130901	+	0.0755759i
$466$	9.67183	+	6.31707i	0.448039	+	0.292632i
$467$	−8.51330	−	14.7455i	−0.393949	−	0.682339i	0.599018	−	0.800736i	$-0.295558\pi$
$467$	−8.51330	−	14.7455i	−0.393949	−	0.682339i	−0.992966	+	0.118397i	$0.962225\pi$
$468$	0.844569	−	7.64957i	0.0390402	−	0.353602i
$469$	−20.4481	+	3.64593i	−0.944207	+	0.168353i
$470$	1.04701	+	0.0576236i	0.0482949	+	0.00265798i
$471$	−7.32996	+	4.23195i	−0.337747	+	0.194998i
$472$	17.7304	+	14.5901i	0.816107	+	0.671564i
$473$	−4.64082	+	8.03814i	−0.213385	+	0.369594i
$474$	−9.95378	−	19.6626i	−0.457192	−	0.903135i
$475$	−14.3058			−0.656395
$476$	13.1914	−	26.8194i	0.604626	−	1.22927i
$477$	10.7120			0.490468
$478$	11.6240	+	22.9619i	0.531668	+	1.05025i
$479$	−15.8903	+	27.5227i	−0.726045	+	1.25755i	0.232498	+	0.972597i	$0.425310\pi$
$479$	−15.8903	+	27.5227i	−0.726045	+	1.25755i	−0.958543	+	0.284950i	$0.908023\pi$
$480$	1.77871	−	1.73269i	0.0811865	−	0.0790859i
$481$	−17.6179	+	10.1717i	−0.803306	+	0.463789i
$482$	40.8299	+	2.24713i	1.85975	+	0.102354i
$483$	−8.13127	−	9.65289i	−0.369986	−	0.439222i
$484$	−12.9665	−	1.43160i	−0.589386	−	0.0650726i
$485$	−0.488575	−	0.846237i	−0.0221851	−	0.0384257i
$486$	−1.18404	−	0.773342i	−0.0537090	−	0.0350795i
$487$	−4.99690	−	2.88496i	−0.226431	−	0.130730i	0.382493	−	0.923958i	$-0.375065\pi$
$487$	−4.99690	−	2.88496i	−0.226431	−	0.130730i	−0.608925	+	0.793228i	$0.708399\pi$
$488$	−6.14233	−	16.3853i	−0.278050	−	0.741727i
$489$		−	6.95459i		−	0.314497i
$490$	−3.18167	−	2.95979i	−0.143733	−	0.133709i
$491$			22.6443i			1.02192i	0.859603	+	0.510962i	$0.170711\pi$
$491$			22.6443i			1.02192i	−0.859603	+	0.510962i	$0.829289\pi$
$492$	12.4862	−	5.48099i	0.562924	−	0.247102i
$493$	−34.3528	−	19.8336i	−1.54717	−	0.893261i
$494$	−8.85563	+	13.5585i	−0.398434	+	0.610028i
$495$	0.464416	+	0.804393i	0.0208740	+	0.0361548i
$496$	−28.9858	−	6.47946i	−1.30150	−	0.290936i
$497$	−1.99400	−	2.36714i	−0.0894433	−	0.106181i
$498$	0.427160	−	7.76141i	0.0191415	−	0.347797i
$499$	−16.8383	+	9.72159i	−0.753785	+	0.435198i	−0.827060	−	0.562114i	$-0.809988\pi$
$499$	−16.8383	+	9.72159i	−0.753785	+	0.435198i	0.0732749	+	0.997312i	$0.476655\pi$
$500$	6.93907	+	5.09732i	0.310325	+	0.227959i
$501$	−4.06011	+	7.03231i	−0.181392	+	0.314180i
$502$	−25.6875	+	13.0037i	−1.14649	+	0.580385i
$503$	−11.7570			−0.524217			−0.262108	−	0.965038i	$-0.584418\pi$
$503$	−11.7570			−0.524217			−0.262108	+	0.965038i	$0.584418\pi$
$504$	3.66686	−	6.52336i	0.163335	−	0.290573i
$505$	−0.337057			−0.0149989
$506$	−12.7361	+	6.44740i	−0.566191	+	0.286622i
$507$	0.903656	−	1.56518i	0.0401328	−	0.0695120i
$508$	5.67232	+	4.16679i	0.251669	+	0.184871i
$509$	−17.4476	+	10.0734i	−0.773350	+	0.446494i	−0.834068	−	0.551661i	$-0.813994\pi$
$509$	−17.4476	+	10.0734i	−0.773350	+	0.446494i	0.0607186	+	0.998155i	$0.480661\pi$
$510$	0.192688	−	3.50109i	0.00853235	−	0.155031i
$511$	26.1373	−	4.66031i	1.15624	−	0.206160i
$512$	−10.7453	+	19.9133i	−0.474881	+	0.880050i
$513$	1.48792	+	2.57715i	0.0656933	+	0.113784i
$514$	16.4621	−	25.2045i	0.726112	−	1.11172i
$515$	3.28405	+	1.89605i	0.144713	+	0.0835499i
$516$	8.03305	−	3.52620i	0.353635	−	0.155232i
$517$		−	3.57417i		−	0.157192i
$518$	−19.6353	+	2.39682i	−0.862725	+	0.105310i
$519$		−	1.41635i		−	0.0621710i
$520$	4.47360	−	1.67701i	0.196180	−	0.0735419i
$521$	−31.0965	−	17.9536i	−1.36236	−	0.786559i	−0.372423	−	0.928063i	$-0.621473\pi$
$521$	−31.0965	−	17.9536i	−1.36236	−	0.786559i	−0.989938	+	0.141504i	$0.954806\pi$
$522$	−8.31531	−	5.43106i	−0.363951	−	0.237711i
$523$	−22.6480	−	39.2276i	−0.990330	−	1.71530i	−0.615312	−	0.788283i	$-0.710970\pi$
$523$	−22.6480	−	39.2276i	−0.990330	−	1.71530i	−0.375017	−	0.927018i	$-0.622363\pi$
$524$	−38.9964	−	4.30548i	−1.70356	−	0.188086i
$525$	11.9602	+	4.32725i	0.521986	+	0.188857i
$526$	−28.4951	−	1.56827i	−1.24245	−	0.0683799i
$527$	−36.3213	+	20.9701i	−1.58218	+	0.913473i
$528$	−6.23018	−	5.72909i	−0.271134	−	0.249327i
$529$	−0.121725	+	0.210835i	−0.00529241	+	0.00916672i
$530$	3.00343	+	5.93295i	0.130461	+	0.257711i
$531$	8.11818			0.352299
$532$	−13.0838	+	8.76193i	−0.567255	+	0.379878i
$533$	26.2364			1.13642
$534$	−6.65478	−	13.1458i	−0.287980	−	0.568874i
$535$	−0.558433	+	0.967234i	−0.0241432	+	0.0418172i
$536$	14.1091	−	17.1459i	0.609422	−	0.740590i
$537$	−9.29401	+	5.36590i	−0.401066	+	0.231556i
$538$	23.1150	+	1.27217i	0.996558	+	0.0548470i
$539$	−9.47736	+	11.3829i	−0.408219	+	0.490296i
$540$	0.0963438	−	0.872621i	0.00414598	−	0.0375516i
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	0.957432	+	0.288657i	$0.0932089\pi$
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	−0.228732	+	0.973490i	$0.573458\pi$
$542$	15.9299	+	10.4045i	0.684249	+	0.446911i
$543$	1.05158	+	0.607128i	0.0451275	+	0.0260543i
$544$	7.86452	+	30.9686i	0.337189	+	1.32777i
$545$		−	2.98815i		−	0.127998i
$546$	11.5049	−	8.65680i	0.492363	−	0.370477i
$547$			7.83251i			0.334894i	0.985881	+	0.167447i	$0.0535523\pi$
$547$			7.83251i			0.334894i	−0.985881	+	0.167447i	$0.946448\pi$
$548$	−2.71574	−	6.18674i	−0.116011	−	0.264284i
$549$	−5.35787	−	3.09337i	−0.228668	−	0.132022i
$550$	7.86656	−	12.0442i	0.335431	−	0.513567i
$551$	10.4494	+	18.0990i	0.445161	+	0.771042i
$552$	13.3096	+	2.21544i	0.566492	+	0.0942956i
$553$	14.0274	−	38.7708i	0.596506	−	1.64870i
$554$	−0.218172	+	3.96414i	−0.00926925	+	0.168420i
$555$	−2.00975	+	1.16033i	−0.0853092	+	0.0492533i
$556$	19.4752	−	26.5119i	0.825932	−	1.12436i
$557$	−7.69701	+	13.3316i	−0.326133	+	0.564879i	−0.981741	−	0.190223i	$-0.939079\pi$
$557$	−7.69701	+	13.3316i	−0.326133	+	0.564879i	0.655608	+	0.755101i	$0.272412\pi$
$558$	−9.36887	+	4.74278i	−0.396616	+	0.200778i
$559$	16.8792			0.713914
$560$	4.64115	+	0.201909i	0.196124	+	0.00853223i
$561$	−11.9517			−0.504600
$562$	−32.1118	+	16.2559i	−1.35455	+	0.685714i
$563$	8.22052	−	14.2384i	0.346453	−	0.600075i	−0.639163	−	0.769071i	$-0.720719\pi$
$563$	8.22052	−	14.2384i	0.346453	−	0.600075i	0.985617	+	0.168996i	$0.0540525\pi$
$564$	−2.00000	+	2.72263i	−0.0842152	+	0.114644i
$565$	5.18559	−	2.99390i	0.218159	−	0.125954i
$566$	−0.368333	+	6.69252i	−0.0154822	+	0.281308i
$567$	−0.464416	−	2.60467i	−0.0195037	−	0.109386i
$568$	3.26385	+	0.543286i	0.136948	+	0.0227958i
$569$	18.6146	+	32.2415i	0.780366	+	1.35163i	0.931729	+	0.363155i	$0.118300\pi$
$569$	18.6146	+	32.2415i	0.780366	+	1.35163i	−0.151363	+	0.988478i	$0.548366\pi$
$570$	−1.01020	+	1.54668i	−0.0423127	+	0.0647835i
$571$	17.9660	+	10.3727i	0.751854	+	0.434083i	0.826363	−	0.563137i	$-0.190406\pi$
$571$	17.9660	+	10.3727i	0.751854	+	0.434083i	−0.0745095	+	0.997220i	$0.523739\pi$
$572$	−6.54549	−	14.9113i	−0.273681	−	0.623473i
$573$			6.55261i			0.273739i
$574$	23.4760	+	9.98458i	0.979871	+	0.416748i
$575$			22.9327i			0.956361i
$576$	1.54003	+	7.85037i	0.0641679	+	0.327099i
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	0.195552	−	0.980693i	$-0.437350\pi$
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	−0.751530	+	0.659699i	$0.770684\pi$
$578$	17.6461	+	11.5254i	0.733982	+	0.479393i
$579$	1.61818	+	2.80276i	0.0672491	+	0.116479i
$580$	0.676608	−	6.12829i	0.0280946	−	0.254463i
$581$	11.1221	−	9.36888i	0.461422	−	0.388687i
$582$	3.14335	+	0.172999i	0.130296	+	0.00717104i
$583$	19.6296	−	11.3332i	0.812975	−	0.469371i
$584$	−18.0346	+	21.9163i	−0.746279	+	0.906902i
$585$	0.844569	−	1.46284i	0.0349186	−	0.0604808i
$586$	−2.06195	−	4.07316i	−0.0851783	−	0.168261i
$587$	34.0410			1.40502			0.702512	−	0.711672i	$-0.252062\pi$
$587$	34.0410			1.40502			0.702512	+	0.711672i	$0.252062\pi$
$588$	13.5889	−	3.36770i	0.560397	−	0.138881i
$589$	22.0965			0.910469
$590$	2.27618	+	4.49634i	0.0937086	+	0.185111i
$591$	9.62772	−	16.6757i	0.396032	−	0.685947i
$592$	14.3140	−	15.5659i	0.588300	−	0.639756i
$593$	27.5697	−	15.9173i	1.13215	−	0.653647i	0.187675	−	0.982231i	$-0.439905\pi$
$593$	27.5697	−	15.9173i	1.13215	−	0.653647i	0.944475	+	0.328584i	$0.106571\pi$
$594$	−2.98792	−	0.164445i	−0.122596	−	0.00674724i
$595$	5.01706	−	4.22620i	0.205679	−	0.173257i
$596$	−12.8805	−	1.42210i	−0.527606	−	0.0582516i
$597$	4.31086	+	7.46663i	0.176432	+	0.305589i
$598$	21.7348	+	14.1959i	0.888804	+	0.580514i
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	0.0849563	−	0.996385i	$-0.472925\pi$
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	−0.820416	+	0.571767i	$0.806258\pi$
$600$	−12.7319	+	4.77281i	−0.519779	+	0.194849i
$601$			15.8614i			0.646999i	0.946228	+	0.323499i	$0.104859\pi$
$601$			15.8614i			0.646999i	−0.946228	+	0.323499i	$0.895141\pi$
$602$	15.1034	+	6.42360i	0.615567	+	0.261806i
$603$		−	7.85056i		−	0.319699i
$604$	−14.2279	+	6.24549i	−0.578923	+	0.254125i
$605$	−2.47960	−	1.43160i	−0.100810	−	0.0582027i
$606$	0.593811	−	0.909163i	0.0241219	−	0.0369322i
$607$	−21.7151	−	37.6116i	−0.881388	−	1.52661i	−0.849798	−	0.527108i	$-0.823276\pi$
$607$	−21.7151	−	37.6116i	−0.881388	−	1.52661i	−0.0315900	−	0.999501i	$-0.510057\pi$
$608$	4.56965	−	16.2018i	0.185324	−	0.657070i
$609$	−3.26153	−	18.2922i	−0.132164	−	0.741238i
$610$	0.211056	−	3.83484i	0.00854539	−	0.155268i
$611$	−5.62903	+	3.24992i	−0.227726	+	0.131478i
$612$	9.10422	+	6.68780i	0.368016	+	0.270338i
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	−0.979104	−	0.203361i	$-0.934813\pi$
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	0.665668	+	0.746248i	$0.268147\pi$
$614$	6.88315	−	3.48445i	0.277781	−	0.140621i
$615$	2.99290			0.120685
$616$	−0.182159	−	15.8335i	−0.00733939	−	0.637949i
$617$	−19.8053			−0.797330			−0.398665	−	0.917097i	$-0.630526\pi$
$617$	−19.8053			−0.797330			−0.398665	+	0.917097i	$0.630526\pi$
$618$	−10.9000	+	5.51789i	−0.438462	+	0.221962i
$619$	−8.15665	+	14.1277i	−0.327844	+	0.567842i	−0.982084	−	0.188445i	$-0.939655\pi$
$619$	−8.15665	+	14.1277i	−0.327844	+	0.567842i	0.654240	+	0.756287i	$0.272989\pi$
$620$	−5.25369	−	3.85927i	−0.210993	−	0.154992i
$621$	4.13127	−	2.38519i	0.165782	−	0.0957144i
$622$	2.37228	−	43.1038i	0.0951197	−	1.72830i
$623$	9.37827	−	25.9209i	0.375733	−	1.03850i
$624$	−3.35787	+	15.0214i	−0.134422	+	0.601336i
$625$	−11.0734	−	19.1797i	−0.442936	−	0.767188i
$626$	−14.5639	+	22.2983i	−0.582090	+	0.891218i
$627$	5.45320	+	3.14840i	0.217780	+	0.125735i
$628$	15.5002	−	6.80400i	0.618526	−	0.271509i
$629$		−	29.8609i		−	1.19063i
$630$	1.31241	−	0.987521i	0.0522878	−	0.0393438i
$631$			27.3095i			1.08717i	0.839353	+	0.543587i	$0.182934\pi$
$631$			27.3095i			1.08717i	−0.839353	+	0.543587i	$0.817066\pi$
$632$	15.4718	+	41.2724i	0.615433	+	1.64173i
$633$	5.28091	+	3.04894i	0.209897	+	0.121184i
$634$	−20.3242	−	13.2746i	−0.807177	−	0.527200i
$635$	0.772384	+	1.33781i	0.0306511	+	0.0530893i
$636$	−21.2946	−	2.35108i	−0.844385	−	0.0932263i
$637$	26.5447	+	4.57583i	1.05174	+	0.181301i
$638$	−20.9837	−	1.15487i	−0.830753	−	0.0457217i
$639$	1.01310	−	0.584912i	0.0400775	−	0.0231388i
$640$	−3.91622	+	3.05405i	−0.154802	+	0.120722i
$641$	−4.89533	+	8.47896i	−0.193354	+	0.334899i	−0.946360	−	0.323115i	$-0.895270\pi$
$641$	−4.89533	+	8.47896i	−0.193354	+	0.334899i	0.753006	+	0.658014i	$0.228603\pi$
$642$	−1.62515	−	3.21032i	−0.0641397	−	0.126701i
$643$	−7.26458			−0.286487			−0.143244	−	0.989687i	$-0.545753\pi$
$643$	−7.26458			−0.286487			−0.143244	+	0.989687i	$0.545753\pi$
$644$	14.0457	+	20.9738i	0.553478	+	0.826485i
$645$	1.92549			0.0758160
$646$	−10.7361	−	21.2081i	−0.422408	−	0.834422i
$647$	23.0419	−	39.9098i	0.905872	−	1.56902i	0.0861302	−	0.996284i	$-0.472550\pi$
$647$	23.0419	−	39.9098i	0.905872	−	1.56902i	0.819742	−	0.572733i	$-0.194117\pi$
$648$	2.18404	+	1.79722i	0.0857971	+	0.0706013i
$649$	14.8765	−	8.58893i	0.583952	−	0.337145i
$650$	−26.1215	−	1.43764i	−1.02457	−	0.0563887i
$651$	−18.4735	−	6.68379i	−0.724034	−	0.261958i
$652$	−1.52640	+	13.8252i	−0.0597784	+	0.541435i
$653$	3.38990	+	5.87149i	0.132657	+	0.229769i	0.924700	−	0.380696i	$-0.124316\pi$
$653$	3.38990	+	5.87149i	0.132657	+	0.229769i	−0.792043	+	0.610465i	$0.790982\pi$
$654$	8.06011	+	5.26438i	0.315175	+	0.205854i
$655$	−7.45732	−	4.30548i	−0.291381	−	0.168229i
$656$	−26.0246	+	8.15527i	−1.01609	+	0.318410i
$657$			10.0348i			0.391493i
$658$	−6.27361	+	0.765800i	−0.244571	+	0.0298540i
$659$		−	29.3184i		−	1.14208i	−0.820921	−	0.571041i	$-0.806540\pi$
$659$		−	29.3184i		−	1.14208i	0.820921	−	0.571041i	$-0.193460\pi$
$660$	−0.746674	−	1.70100i	−0.0290643	−	0.0662113i
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.916986	−	0.398919i	$-0.130615\pi$
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.113019	+	0.993593i	$0.463948\pi$
$662$	16.6167	−	25.4412i	0.645825	−	0.988799i
$663$	10.8674	+	18.8229i	0.422056	+	0.731022i
$664$	−2.55264	+	15.3353i	−0.0990617	+	0.595125i
$665$	−3.40243	+	0.606658i	−0.131941	+	0.0235252i
$666$	0.410860	−	7.46523i	0.0159205	−	0.289272i
$667$	29.0133	−	16.7508i	1.12340	−	0.648595i
$668$	9.61462	−	13.0886i	0.372001	−	0.506411i
$669$	−1.22472	+	2.12128i	−0.0473504	+	0.0820134i
$670$	4.34812	−	2.20114i	0.167982	−	0.0850375i
$671$	−13.0910			−0.505372
$672$	−8.72117	+	12.1631i	−0.336426	+	0.469202i
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	7.45754	−	3.77522i	0.287254	−	0.145416i
$675$	−2.40366	+	4.16325i	−0.0925168	+	0.160244i
$676$	−2.13992	+	2.91312i	−0.0823048	+	0.112043i
$677$	−10.8219	+	6.24801i	−0.415919	+	0.240131i	−0.693330	−	0.720621i	$-0.743857\pi$
$677$	−10.8219	+	6.24801i	−0.415919	+	0.240131i	0.277411	+	0.960751i	$0.410524\pi$
$678$	−1.06011	+	19.2619i	−0.0407131	+	0.739748i
$679$	3.79437	+	4.50442i	0.145615	+	0.172864i
$680$	−1.15147	+	6.91760i	−0.0441569	+	0.265278i
$681$	−11.6398	−	20.1607i	−0.446038	−	0.772561i
$682$	−12.1505	+	18.6033i	−0.465268	+	0.712355i
$683$	39.1917	+	22.6273i	1.49963	+	0.865811i	1.00000		0.000428478i	$-0.000136389\pi$
$683$	39.1917	+	22.6273i	1.49963	+	0.865811i	0.499629	+	0.866240i	$0.333470\pi$
$684$	−2.39223	−	5.44975i	−0.0914693	−	0.208376i
$685$		−	1.48293i		−	0.0566600i
$686$	22.0105	+	14.1963i	0.840367	+	0.542019i
$687$		−	11.7069i		−	0.446647i
$688$	−16.7430	+	5.24671i	−0.638321	+	0.200029i
$689$	−35.6976	−	20.6100i	−1.35997	−	0.785179i
$690$	2.47939	+	1.61939i	0.0943888	+	0.0616492i
$691$	−5.29654	−	9.17388i	−0.201490	−	0.348991i	0.747519	−	0.664241i	$-0.231245\pi$
$691$	−5.29654	−	9.17388i	−0.201490	−	0.348991i	−0.949009	+	0.315250i	$0.897912\pi$
$692$	−0.310863	+	2.81560i	−0.0118172	+	0.107033i
$693$	−3.60675	−	4.28169i	−0.137009	−	0.162648i
$694$	−3.97584	−	0.218816i	−0.150921	−	0.00830615i
$695$	6.25279	−	3.61005i	0.237182	−	0.136937i
$696$	15.3382	+	12.6216i	0.581391	+	0.478420i
$697$	−19.2554	+	33.3514i	−0.729352	+	1.26327i
$698$	−6.09402	−	12.0381i	−0.230662	−	0.455648i
$699$	−8.16853			−0.308962
$700$	−22.8262	−	11.2273i	−0.862749	−	0.424351i
$701$	29.6566			1.12011			0.560057	−	0.828454i	$-0.310779\pi$
$701$	29.6566			1.12011			0.560057	+	0.828454i	$0.310779\pi$
$702$	2.45787	+	4.85526i	0.0927662	+	0.183250i
$703$	−7.86620	+	13.6246i	−0.296679	+	0.513863i
$704$	11.1277	+	12.7564i	0.419390	+	0.480774i
$705$	−0.642129	+	0.370733i	−0.0241840	+	0.0139626i
$706$	14.0772	+	0.774757i	0.529801	+	0.0291584i
$707$	2.00000	−	0.356603i	0.0752177	−	0.0134114i
$708$	−16.1383	−	1.78178i	−0.606514	−	0.0669636i
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	0.977793	+	0.209573i	$0.0672074\pi$
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	−0.307401	+	0.951580i	$0.599459\pi$
$710$	0.608012	+	0.397117i	0.0228183	+	0.0149036i
$711$	13.4958	+	7.79180i	0.506132	+	0.292215i
$712$	10.3439	+	27.5934i	0.387655	+	1.03411i
$713$		−	35.4214i		−	1.32654i
$714$	2.56076	+	20.9783i	0.0958340	+	0.785094i
$715$		−	3.57417i		−	0.133667i
$716$	19.6535	−	8.62712i	0.734485	−	0.322411i
$717$	−15.7603	−	9.09922i	−0.588579	−	0.339816i
$718$	5.35787	−	8.20324i	0.199954	−	0.306142i
$719$	−6.40447	−	11.0929i	−0.238846	−	0.413694i	0.721537	−	0.692376i	$-0.243436\pi$
$719$	−6.40447	−	11.0929i	−0.238846	−	0.413694i	−0.960384	+	0.278682i	$0.910103\pi$
$720$	−0.383048	+	1.71356i	−0.0142753	+	0.0638605i
$721$	−21.4926	−	7.77611i	−0.800427	−	0.289598i
$722$	0.788376	−	14.3246i	0.0293403	−	0.533107i
$723$	−25.0409	+	14.4574i	−0.931282	+	0.537676i
$724$	−1.95720	−	1.43772i	−0.0727387	−	0.0534325i
$725$	−16.8805	+	29.2379i	−0.626927	+	1.08587i
$726$	8.22996	−	4.16624i	0.305442	−	0.154624i
$727$	19.3286			0.716860			0.358430	−	0.933557i	$-0.383312\pi$
$727$	19.3286			0.716860			0.358430	+	0.933557i	$0.383312\pi$
$728$	−24.7708	+	14.6839i	−0.918066	+	0.544223i
$729$	1.00000			0.0370370
$730$	−5.55786	+	2.81355i	−0.205706	+	0.104134i
$731$	−12.3880	+	21.4567i	−0.458188	+	0.793604i
$732$	9.97209	+	7.32532i	0.368579	+	0.270752i
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.961798	−	0.273761i	$-0.911732\pi$
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.243815	+	0.969822i	$0.578399\pi$
$734$	1.39147	−	25.2828i	0.0513602	−	0.933204i
$735$	3.02807	+	0.521986i	0.111692	+	0.0192537i
$736$	−25.9721	−	7.32532i	−0.957344	−	0.270015i
$737$	−8.30580	−	14.3861i	−0.305948	−	0.529917i
$738$	−5.27275	+	8.07291i	−0.194092	+	0.297168i
$739$	−12.0072	−	6.93237i	−0.441693	−	0.255011i	0.262623	−	0.964899i	$-0.415413\pi$
$739$	−12.0072	−	6.93237i	−0.441693	−	0.255011i	−0.704315	+	0.709887i	$0.748746\pi$
$740$	4.24990	−	1.86554i	0.156229	−	0.0685787i
$741$		−	11.4511i		−	0.420667i
$742$	−24.0985	−	32.0268i	−0.884682	−	1.17574i
$743$		−	18.9927i		−	0.696773i	−0.937351	−	0.348387i	$-0.886730\pi$
$743$		−	18.9927i		−	0.696773i	0.937351	−	0.348387i	$-0.113270\pi$
$744$	19.6655	−	7.37199i	0.720973	−	0.270270i
$745$	−2.46315	−	1.42210i	−0.0902430	−	0.0521018i
$746$	−17.1381	−	11.1936i	−0.627471	−	0.409827i
$747$	2.74822	+	4.76007i	0.100552	+	0.174162i
$748$	23.7590	+	2.62317i	0.868715	+	0.0959125i
$749$	2.29026	−	6.33010i	0.0836841	−	0.231297i
$750$	−6.07904	−	0.334569i	−0.221975	−	0.0122167i
$751$	25.2868	−	14.5993i	0.922728	−	0.532737i	0.0382233	−	0.999269i	$-0.487830\pi$
$751$	25.2868	−	14.5993i	0.922728	−	0.532737i	0.884504	+	0.466532i	$0.154497\pi$
$752$	4.57341	−	4.97342i	0.166775	−	0.181362i
$753$	10.1793	−	17.6311i	0.370954	−	0.642512i
$754$	17.2612	+	34.0977i	0.628617	+	1.24177i
$755$	−3.41036			−0.124116
$756$	0.351547	+	5.27981i	0.0127856	+	0.192025i
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	−13.7947	−	27.2499i	−0.501045	−	0.989762i
$759$	5.04701	−	8.74167i	0.183195	−	0.317303i
$760$	2.34767	−	2.85296i	0.0851589	−	0.103488i
$761$	−0.203165	+	0.117298i	−0.00736474	+	0.00425204i	−0.503678	−	0.863892i	$-0.668020\pi$
$761$	−0.203165	+	0.117298i	−0.00736474	+	0.00425204i	0.496313	+	0.868144i	$0.334687\pi$
$762$	−4.96929	−	0.273492i	−0.180018	−	0.00990758i
$763$	3.16143	+	17.7308i	0.114451	+	0.641899i
$764$	1.43817	−	13.0261i	0.0520313	−	0.471267i
$765$	1.23970	+	2.14722i	0.0448213	+	0.0776328i
$766$	−0.753448	−	0.492107i	−0.0272232	−	0.0177806i
$767$	−27.0537	−	15.6195i	−0.976854	−	0.563987i
$768$	−1.33845	−	15.9439i	−0.0482971	−	0.575327i
$769$			34.8540i			1.25687i	0.777863	+	0.628434i	$0.216304\pi$
$769$			34.8540i			1.25687i	−0.777863	+	0.628434i	$0.783696\pi$
$770$	1.36020	−	3.19814i	0.0490181	−	0.115253i
$771$			21.2869i			0.766631i
$772$	−2.60165	−	5.92683i	−0.0936355	−	0.213311i
$773$	17.0362	+	9.83583i	0.612748	+	0.353770i	0.774040	−	0.633137i	$-0.218233\pi$
$773$	17.0362	+	9.83583i	0.612748	+	0.353770i	−0.161292	+	0.986907i	$0.551566\pi$
$774$	−3.39223	+	5.19372i	−0.121931	+	0.186685i
$775$	17.8478	+	30.9133i	0.641113	+	1.11044i
$776$	−6.21076	−	1.03381i	−0.222953	−	0.0371118i
$777$	10.6977	−	9.01136i	0.383777	−	0.323281i
$778$	0.0791996	−	1.43904i	0.00283944	−	0.0515920i
$779$	17.5714	−	10.1448i	0.629560	−	0.363476i
$780$	−2.00000	+	2.72263i	−0.0716115	+	0.0974860i
$781$	1.23766	−	2.14369i	0.0442870	−	0.0767073i
$782$	−33.9974	+	17.2104i	−1.21574	+	0.615444i
$783$	7.02285			0.250976
$784$	−27.7528	+	3.71221i	−0.991172	+	0.132579i
$785$	3.71533			0.132606
$786$	24.7514	−	12.5298i	0.882852	−	0.446925i
$787$	−19.4781	+	33.7370i	−0.694319	+	1.20260i	0.276091	+	0.961131i	$0.410961\pi$
$787$	−19.4781	+	33.7370i	−0.694319	+	1.20260i	−0.970410	+	0.241464i	$0.922373\pi$
$788$	−22.7991	+	31.0369i	−0.812186	+	1.10564i
$789$	17.4760	−	10.0898i	0.622164	−	0.359206i
$790$	−0.531622	+	9.65946i	−0.0189143	+	0.343668i
$791$	−27.6023	+	23.2512i	−0.981423	+	0.826718i
$792$	5.90366	+	0.982694i	0.209777	+	0.0349185i
$793$	11.9034	+	20.6172i	0.422701	+	0.732139i
$794$	23.0419	−	35.2787i	0.817728	−	1.25199i
$795$	−4.07218	−	2.35108i	−0.144426	−	0.0833841i
$796$	−6.93087	−	15.7892i	−0.245658	−	0.559634i
$797$			20.4557i			0.724579i	0.932066	+	0.362289i	$0.118005\pi$
$797$			20.4557i			0.724579i	−0.932066	+	0.362289i	$0.881995\pi$
$798$	4.35787	−	10.2464i	0.154267	−	0.362717i
$799$		−	9.54077i		−	0.337528i
$800$	26.3576	−	6.69355i	0.931883	−	0.236653i
$801$	9.02285	+	5.20934i	0.318807	+	0.184063i
$802$	8.03991	+	5.25119i	0.283899	+	0.185426i
$803$	10.6167	+	18.3886i	0.374654	+	0.648919i
$804$	−1.72305	+	15.6063i	−0.0607672	+	0.550391i
$805$	0.972496	+	5.45423i	0.0342760	+	0.192236i
$806$	40.3468	+	2.22055i	1.42116	+	0.0782154i
$807$	−14.1764	+	8.18475i	−0.499033	+	0.288117i
$808$	−1.37999	+	1.67701i	−0.0485480	+	0.0589972i
$809$	24.4650	−	42.3746i	0.860143	−	1.48981i	−0.0116472	−	0.999932i	$-0.503708\pi$
$809$	24.4650	−	42.3746i	0.860143	−	1.48981i	0.871790	−	0.489879i	$-0.162959\pi$
$810$	0.280380	+	0.553861i	0.00985155	+	0.0194607i
$811$	−51.9424			−1.82394			−0.911972	−	0.410253i	$-0.865440\pi$
$811$	−51.9424			−1.82394			−0.911972	+	0.410253i	$0.865440\pi$
$812$	2.46886	+	37.0793i	0.0866401	+	1.30123i
$813$	−13.4539			−0.471850
$814$	−7.14523	−	14.1146i	−0.250440	−	0.494718i
$815$	−1.52640	+	2.64380i	−0.0534674	+	0.0926083i
$816$	−16.6306	−	15.2930i	−0.582188	−	0.535363i
$817$	11.3046	−	6.52670i	0.395497	−	0.228340i
$818$	5.24335	+	0.288575i	0.183329	+	0.0100898i
$819$	−3.46376	+	9.57359i	−0.121034	+	0.334528i
$820$	−5.94965	−	0.656884i	−0.207771	−	0.0229394i
$821$	−15.7322	−	27.2490i	−0.549059	−	0.950998i	−0.998339	−	0.0576069i	$-0.981653\pi$
$821$	−15.7322	−	27.2490i	−0.549059	−	0.950998i	0.449281	−	0.893391i	$-0.351680\pi$
$822$	4.00000	+	2.61256i	0.139516	+	0.0911236i
$823$	−35.9504	−	20.7560i	−1.25315	−	0.723507i	−0.281417	−	0.959586i	$-0.590804\pi$
$823$	−35.9504	−	20.7560i	−1.25315	−	0.723507i	−0.971734	+	0.236078i	$0.924138\pi$
$824$	22.8794	−	8.57678i	0.797042	−	0.298786i
$825$			10.1722i			0.354149i
$826$	−18.2632	−	24.2718i	−0.635459	−	0.844524i
$827$		−	38.6850i		−	1.34521i	−0.740003	−	0.672604i	$-0.765176\pi$
$827$		−	38.6850i		−	1.34521i	0.740003	−	0.672604i	$-0.234824\pi$
$828$	−8.73615	+	3.83484i	−0.303602	+	0.133270i
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	0.647229	−	0.762296i	$-0.275928\pi$
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	−0.336553	+	0.941664i	$0.609261\pi$
$830$	−1.86587	+	2.85676i	−0.0647652	+	0.0991597i
$831$	−1.40366	−	2.43120i	−0.0486923	−	0.0843375i
$832$	9.97209	−	29.1243i	0.345720	−	1.00970i
$833$	−25.2985	+	30.3850i	−0.876541	+	1.05278i
$834$	−1.27828	+	23.2260i	−0.0442631	+	0.804251i
$835$	3.08692	−	1.78223i	0.106827	−	0.0616767i
$836$	−10.1495	−	7.45565i	−0.351028	−	0.257859i
$837$	3.71264	−	6.43048i	0.128328	−	0.222270i
$838$	26.1287	−	13.2271i	0.902599	−	0.456921i
$839$	−10.4794			−0.361789			−0.180894	−	0.983503i	$-0.557899\pi$
$839$	−10.4794			−0.361789			−0.180894	+	0.983503i	$0.557899\pi$
$840$	−2.82572	+	1.67506i	−0.0974964	+	0.0577952i
$841$	20.3204			0.700704
$842$	19.7564	−	10.0012i	0.680849	−	0.344665i
$843$	12.7251	−	22.0405i	0.438275	−	0.759115i
$844$	−9.82885	−	7.22010i	−0.338323	−	0.248526i
$845$	−0.687054	+	0.396671i	−0.0236354	+	0.0136459i
$846$	0.131272	−	2.38519i	0.00451324	−	0.0820046i
$847$	16.2278	+	5.87129i	0.557595	+	0.201740i
$848$	41.8159	+	9.34751i	1.43596	+	0.320995i
$849$	−2.36975	−	4.10452i	−0.0813295	−	0.140867i
$850$	20.9987	−	32.1503i	0.720249	−	1.10275i
$851$	21.8408	+	12.6098i	0.748693	+	0.432258i
$852$	−2.14233	+	0.940403i	−0.0733952	+	0.0322177i
$853$			25.5157i			0.873642i	0.899548	+	0.436821i	$0.143896\pi$
$853$			25.5157i			0.873642i	−0.899548	+	0.436821i	$0.856104\pi$
$854$	2.80487	+	22.9781i	0.0959806	+	0.786294i
$855$		−	1.30628i		−	0.0446739i
$856$	2.52607	+	6.73855i	0.0863394	+	0.230319i
$857$	−9.99828	−	5.77251i	−0.341535	−	0.197185i	0.319416	−	0.947615i	$-0.396513\pi$
$857$	−9.99828	−	5.77251i	−0.341535	−	0.197185i	−0.660951	+	0.750429i	$0.729847\pi$
$858$	9.64082	+	6.29681i	0.329132	+	0.214970i
$859$	16.4552	+	28.5013i	0.561445	+	0.972452i	0.997371	+	0.0724689i	$0.0230878\pi$
$859$	16.4552	+	28.5013i	0.561445	+	0.972452i	−0.435925	+	0.899983i	$0.643579\pi$
$860$	−3.82772	−	0.422608i	−0.130524	−	0.0144108i
$861$	−17.7590	+	3.16645i	−0.605225	+	0.107912i
$862$	16.7492	+	0.921819i	0.570481	+	0.0313973i
$863$	−49.6075	+	28.6409i	−1.68866	+	0.974948i	−0.733114	+	0.680106i	$0.761934\pi$
$863$	−49.6075	+	28.6409i	−1.68866	+	0.974948i	−0.955546	+	0.294842i	$0.904733\pi$
$864$	−3.94724	−	4.05208i	−0.134288	−	0.137854i
$865$	−0.310863	+	0.538430i	−0.0105696	+	0.0183072i
$866$	−10.8118	−	21.3575i	−0.367399	−	0.725758i
$867$	−14.9034			−0.506145
$868$	35.2569	+	17.3414i	1.19670	+	0.588606i
$869$	32.9745			1.11858
$870$	1.96907	+	3.88968i	0.0667576	+	0.131873i
$871$	−15.1046	+	26.1619i	−0.511799	+	0.886462i
$872$	−14.8674	−	12.2342i	−0.503474	−	0.414303i
$873$	−1.92782	+	1.11302i	−0.0652467	+	0.0376702i
$874$	20.0457	+	1.10324i	0.678056	+	0.0373178i
$875$	−7.33808	−	8.71126i	−0.248072	−	0.294494i
$876$	2.20244	−	19.9483i	0.0744135	−	0.673991i
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	−0.996066	−	0.0886159i	$-0.971756\pi$
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	0.421289	−	0.906926i	$-0.361578\pi$
$878$	−2.78581	−	1.81952i	−0.0940165	−	0.0614060i
$879$	2.79568	+	1.61409i	0.0942960	+	0.0544418i
$880$	1.11099	+	3.54533i	0.0374515	+	0.119513i
$881$		−	23.4638i		−	0.790514i	−0.918571	−	0.395257i	$-0.870656\pi$
$881$		−	23.4638i		−	0.790514i	0.918571	−	0.395257i	$-0.129344\pi$
$882$	−6.74269	+	7.24818i	−0.227038	+	0.244059i
$883$			8.14468i			0.274090i	0.990565	+	0.137045i	$0.0437606\pi$
$883$			8.14468i			0.274090i	−0.990565	+	0.137045i	$0.956239\pi$
$884$	−17.4723	−	39.8037i	−0.587657	−	1.33874i
$885$	−3.08614	−	1.78178i	−0.103740	−	0.0598940i
$886$	−1.24039	+	1.89911i	−0.0416716	+	0.0638019i
$887$	14.6109	+	25.3068i	0.490585	+	0.849718i	0.999941	−	0.0108376i	$-0.00344978\pi$
$887$	14.6109	+	25.3068i	0.490585	+	0.849718i	−0.509356	+	0.860556i	$0.670116\pi$
$888$	−2.45523	+	14.7501i	−0.0823922	+	0.494981i
$889$	−5.99849	−	7.12099i	−0.201183	−	0.238830i
$890$	−0.355425	+	6.45800i	−0.0119139	+	0.216473i
$891$	1.83249	−	1.05799i	0.0613907	−	0.0354439i
$892$	2.90023	−	3.94813i	0.0971068	−	0.132193i
$893$	−2.51330	+	4.35317i	−0.0841044	+	0.145673i
$894$	8.17539	−	4.13861i	0.273426	−	0.138416i
$895$	4.71085			0.157466
$896$	20.0066	−	22.2652i	0.668372	−	0.743827i
$897$	−18.3566			−0.612908
$898$	1.70599	−	0.863620i	0.0569296	−	0.0288194i
$899$	26.0733	−	45.1603i	0.869594	−	1.50618i
$900$	5.69203	−	7.74866i	0.189734	−	0.258289i
$901$	52.3985	−	30.2523i	1.74565	−	1.00785i
$902$	−1.12120	+	20.3720i	−0.0373320	+	0.678314i
$903$	−11.4253	+	2.03714i	−0.380210	+	0.0677919i
$904$	6.33502	−	38.0584i	0.210700	−	1.26580i
$905$	−0.266506	−	0.461602i	−0.00885896	−	0.0153442i
$906$	6.00820	−	9.19894i	0.199609	−	0.305614i
$907$	−48.5997	−	28.0591i	−1.61373	−	0.931686i	−0.988496	−	0.151246i	$-0.951671\pi$
$907$	−48.5997	−	28.0591i	−1.61373	−	0.931686i	−0.625231	−	0.780440i	$-0.714995\pi$
$908$	18.7141	+	42.6326i	0.621049	+	1.41481i
$909$			0.767851i			0.0254680i
$910$	−6.27361	+	0.765800i	−0.207968	+	0.0253860i
$911$			43.1536i			1.42974i	0.699256	+	0.714871i	$0.253515\pi$
$911$			43.1536i			1.42974i	−0.699256	+	0.714871i	$0.746485\pi$
$912$	3.55945	+	11.3587i	0.117865	+	0.376125i
$913$	10.0722	+	5.81518i	0.333341	+	0.192454i
$914$	−26.2226	−	17.1271i	−0.867368	−	0.566513i
$915$	1.35787	+	2.35190i	0.0448898	+	0.0777515i
$916$	−2.56945	+	23.2724i	−0.0848969	+	0.768943i
$917$	48.8047	+	17.6577i	1.61167	+	0.583110i
$918$	−7.97584	−	0.438962i	−0.263242	−	0.0144879i
$919$	33.3617	−	19.2614i	1.10050	−	0.635375i	0.164149	−	0.986435i	$-0.447512\pi$
$919$	33.3617	−	19.2614i	1.10050	−	0.635375i	0.936353	+	0.351060i	$0.114179\pi$
$920$	−4.57341	−	3.76340i	−0.150781	−	0.124076i
$921$	−2.72762	+	4.72437i	−0.0898780	+	0.155673i
$922$	19.6629	+	38.8420i	0.647565	+	1.27919i
$923$	−4.50151			−0.148169
$924$	6.23018	+	9.30327i	0.204958	+	0.306055i
$925$	−25.4148			−0.835635
$926$	8.82219	+	17.4273i	0.289915	+	0.572696i
$927$	4.31939	−	7.48141i	0.141867	−	0.245722i
$928$	−27.7208	−	28.4571i	−0.909981	−	0.934151i
$929$	−41.3034	+	23.8465i	−1.35512	+	0.782379i	−0.988961	−	0.148173i	$-0.952661\pi$
$929$	−41.3034	+	23.8465i	−1.35512	+	0.782379i	−0.366159	+	0.930552i	$0.619327\pi$
$930$	4.60255	+	0.253308i	0.150923	+	0.00830629i
$931$	19.5472	−	7.19947i	0.640634	−	0.235953i
$932$	16.2384	+	1.79284i	0.531906	+	0.0587263i
$933$	15.2625	+	26.4355i	0.499673	+	0.865460i
$934$	−20.1601	−	13.1674i	−0.659659	−	0.430850i
$935$	4.54346	+	2.62317i	0.148587	+	0.0857867i
$936$	−3.82041	−	10.1913i	−0.124874	−	0.333114i
$937$		−	6.18932i		−	0.202196i	−0.994876	−	0.101098i	$-0.967764\pi$
$937$		−	6.18932i		−	0.202196i	0.994876	−	0.101098i	$-0.0322356\pi$
$938$	−23.4717	+	17.6612i	−0.766378	+	0.576658i
$939$		−	18.8324i		−	0.614573i
$940$	1.35787	−	0.596054i	0.0442889	−	0.0194411i
$941$	−6.33052	−	3.65493i	−0.206369	−	0.119147i	0.393254	−	0.919430i	$-0.371349\pi$
$941$	−6.33052	−	3.65493i	−0.206369	−	0.119147i	−0.599623	+	0.800283i	$0.704683\pi$
$942$	−6.54549	+	10.0216i	−0.213264	+	0.326520i
$943$	−16.2625	−	28.1676i	−0.529581	−	0.917262i
$944$	31.6906	+	7.08409i	1.03144	+	0.230568i
$945$	−0.395127	+	1.09210i	−0.0128535	+	0.0355261i
$946$	−0.721329	+	13.1064i	−0.0234524	+	0.426125i
$947$	13.1805	−	7.60978i	0.428309	−	0.247285i	−0.270317	−	0.962771i	$-0.587128\pi$
$947$	13.1805	−	7.60978i	0.428309	−	0.247285i	0.698626	+	0.715487i	$0.253795\pi$
$948$	−25.1184	−	18.4516i	−0.815808	−	0.599279i
$949$	19.3070	−	33.4407i	0.626732	−	1.08553i
$950$	−18.0504	+	9.13761i	−0.585631	+	0.296463i
$951$	17.1652			0.556619
$952$	−0.486248	−	42.2653i	−0.0157594	−	1.36982i
$953$	17.5899			0.569792			0.284896	−	0.958558i	$-0.408041\pi$
$953$	17.5899			0.569792			0.284896	+	0.958558i	$0.408041\pi$
$954$	13.5159	−	6.84212i	0.437592	−	0.221522i
$955$	1.43817	−	2.49099i	0.0465382	−	0.0806066i
$956$	29.3331	+	21.5476i	0.948701	+	0.696899i
$957$	12.8693	−	7.43009i	0.416005	−	0.240181i
$958$	−2.46985	+	44.8765i	−0.0797971	+	1.44990i
$959$	1.56893	+	8.79930i	0.0506633	+	0.284144i
$960$	1.13756	−	3.32234i	0.0367146	−	0.107228i
$961$	−12.0674	−	20.9014i	−0.389271	−	0.674238i
$962$	−15.7324	+	24.0873i	−0.507233	+	0.776606i
$963$	2.20346	+	1.27217i	0.0710054	+	0.0409950i
$964$	52.9525	−	23.2441i	1.70548	−	0.748643i
$965$		−	1.42063i		−	0.0457318i
$966$	−16.4253	−	6.98583i	−0.528475	−	0.224765i
$967$		−	15.0905i		−	0.485279i	−0.970117	−	0.242640i	$-0.921987\pi$
$967$		−	15.0905i		−	0.485279i	0.970117	−	0.242640i	$-0.0780132\pi$
$968$	−17.2749	+	6.47583i	−0.555237	+	0.208141i
$969$	14.5566	+	8.40423i	0.467624	+	0.269983i
$970$	−1.15698	−	0.755672i	−0.0371485	−	0.0242632i
$971$	22.4660	+	38.9123i	0.720968	+	1.24875i	0.960612	+	0.277893i	$0.0896360\pi$
$971$	22.4660	+	38.9123i	0.720968	+	1.24875i	−0.239644	+	0.970861i	$0.577031\pi$
$972$	−1.98792	−	0.219481i	−0.0637626	−	0.00703985i
$973$	−33.2829	+	28.0364i	−1.06700	+	0.898805i
$974$	−8.14757	−	0.448413i	−0.261065	−	0.0143681i
$975$	16.0203	−	9.24933i	0.513061	−	0.296216i
$976$	−18.2159	−	16.7508i	−0.583078	−	0.536181i
$977$	−6.04122	+	10.4637i	−0.193276	+	0.334763i	−0.946334	−	0.323191i	$-0.895245\pi$
$977$	−6.04122	+	10.4637i	−0.193276	+	0.334763i	0.753058	+	0.657954i	$0.228578\pi$
$978$	−4.44214	−	8.77496i	−0.142044	−	0.280592i
$979$	22.0457			0.704584
$980$	−5.90500	−	1.70227i	−0.188628	−	0.0543770i
$981$	−6.80731			−0.217341
$982$	14.4637	+	28.5715i	0.461556	+	0.911755i
$983$	−8.67473	+	15.0251i	−0.276681	+	0.479225i	−0.970558	−	0.240868i	$-0.922568\pi$
$983$	−8.67473	+	15.0251i	−0.276681	+	0.479225i	0.693877	+	0.720094i	$0.255901\pi$
$984$	12.2537	−	14.8910i	0.390632	−	0.474709i
$985$	−7.32000	+	4.22620i	−0.233235	+	0.134658i
$986$	−56.0131	−	3.08276i	−1.78382	−	0.0981752i
$987$	3.41798	−	2.87919i	0.108795	−	0.0916456i
$988$	−2.51330	+	22.7639i	−0.0799588	+	0.724216i
$989$	−10.4625	−	18.1216i	−0.332689	−	0.576235i
$990$	1.09977	+	0.718306i	0.0349530	+	0.0228293i
$991$	42.5136	+	24.5452i	1.35049	+	0.779705i	0.988318	−	0.152407i	$-0.0487025\pi$
$991$	42.5136	+	24.5452i	1.35049	+	0.779705i	0.362171	+	0.932112i	$0.382036\pi$
$992$	−40.7115	+	10.3387i	−1.29259	+	0.328255i
$993$			21.4868i			0.681864i
$994$	−4.02791	−	1.71311i	−0.127758	−	0.0543365i
$995$		−	3.78461i		−	0.119980i
$996$	−4.41851	−	10.0658i	−0.140006	−	0.318948i
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	0.619570	−	0.784941i	$-0.287307\pi$
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	−0.369994	+	0.929034i	$0.620640\pi$
$998$	−15.0362	+	23.0214i	−0.475963	+	0.728730i
$999$	2.64335	+	4.57842i	0.0836320	+	0.144855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.o.a.31.4	yes	8
3.2	odd	2		252.2.bf.g.199.1		8
4.3	odd	2		84.2.o.b.31.1	yes	8
7.2	even	3		588.2.o.b.19.1		8
7.3	odd	6		588.2.b.a.391.6		8
7.4	even	3		588.2.b.b.391.6		8
7.5	odd	6		84.2.o.b.19.1	yes	8
7.6	odd	2		588.2.o.d.31.4		8
8.3	odd	2		1344.2.bl.i.703.3		8
8.5	even	2		1344.2.bl.j.703.3		8
12.11	even	2		252.2.bf.f.199.4		8
21.5	even	6		252.2.bf.f.19.4		8
21.11	odd	6		1764.2.b.i.1567.3		8
21.17	even	6		1764.2.b.j.1567.3		8
28.3	even	6		588.2.b.b.391.5		8
28.11	odd	6		588.2.b.a.391.5		8
28.19	even	6	inner	84.2.o.a.19.4	✓	8
28.23	odd	6		588.2.o.d.19.4		8
28.27	even	2		588.2.o.b.31.1		8
56.5	odd	6		1344.2.bl.i.1279.3		8
56.19	even	6		1344.2.bl.j.1279.3		8
84.11	even	6		1764.2.b.j.1567.4		8
84.47	odd	6		252.2.bf.g.19.1		8
84.59	odd	6		1764.2.b.i.1567.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	28.19	even	6	inner
84.2.o.a.31.4	yes	8	1.1	even	1	trivial
84.2.o.b.19.1	yes	8	7.5	odd	6
84.2.o.b.31.1	yes	8	4.3	odd	2
252.2.bf.f.19.4		8	21.5	even	6
252.2.bf.f.199.4		8	12.11	even	2
252.2.bf.g.19.1		8	84.47	odd	6
252.2.bf.g.199.1		8	3.2	odd	2
588.2.b.a.391.5		8	28.11	odd	6
588.2.b.a.391.6		8	7.3	odd	6
588.2.b.b.391.5		8	28.3	even	6
588.2.b.b.391.6		8	7.4	even	3
588.2.o.b.19.1		8	7.2	even	3
588.2.o.b.31.1		8	28.27	even	2
588.2.o.d.19.4		8	28.23	odd	6
588.2.o.d.31.4		8	7.6	odd	2
1344.2.bl.i.703.3		8	8.3	odd	2
1344.2.bl.i.1279.3		8	56.5	odd	6
1344.2.bl.j.703.3		8	8.5	even	2
1344.2.bl.j.1279.3		8	56.19	even	6
1764.2.b.i.1567.3		8	21.11	odd	6
1764.2.b.i.1567.4		8	84.59	odd	6
1764.2.b.j.1567.3		8	21.17	even	6
1764.2.b.j.1567.4		8	84.11	even	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26175 - 0.638735i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.18404 - 1.61185i) q^{4} +(0.380152 - 0.219481i) q^{5} +(-0.0777157 + 1.41208i) q^{6} +(-2.02350 + 1.70453i) q^{7} +(0.464416 - 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.26175 - 0.638735i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.18404 - 1.61185i) q^{4} +(0.380152 - 0.219481i) q^{5} +(-0.0777157 + 1.41208i) q^{6} +(-2.02350 + 1.70453i) q^{7} +(0.464416 - 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.339468 - 0.519747i) q^{10} +(-1.83249 - 1.05799i) q^{11} +(0.803884 + 1.83133i) q^{12} +3.84803i q^{13} +(-1.46442 + 3.44318i) q^{14} +0.438962i q^{15} +(-1.19612 - 3.81698i) q^{16} +(-4.89158 - 2.82415i) q^{17} +(-1.18404 - 0.773342i) q^{18} +(1.48792 + 2.57715i) q^{19} +(0.0963438 - 0.872621i) q^{20} +(-0.464416 - 2.60467i) q^{21} +(-2.98792 - 0.164445i) q^{22} +(4.13127 - 2.38519i) q^{23} +(2.18404 + 1.79722i) q^{24} +(-2.40366 + 4.16325i) q^{25} +(2.45787 + 4.85526i) q^{26} +1.00000 q^{27} +(0.351547 + 5.27981i) q^{28} +7.02285 q^{29} +(0.280380 + 0.553861i) q^{30} +(3.71264 - 6.43048i) q^{31} +(-3.94724 - 4.05208i) q^{32} +(1.83249 - 1.05799i) q^{33} +(-7.97584 - 0.438962i) q^{34} +(-0.395127 + 1.09210i) q^{35} +(-1.98792 - 0.219481i) q^{36} +(2.64335 + 4.57842i) q^{37} +(3.52350 + 2.30134i) q^{38} +(-3.33249 - 1.92401i) q^{39} +(-0.435811 - 1.16257i) q^{40} -6.81813i q^{41} +(-2.24967 - 2.98981i) q^{42} -4.38646i q^{43} +(-3.87505 + 1.70100i) q^{44} +(-0.380152 - 0.219481i) q^{45} +(3.68914 - 5.64831i) q^{46} +(0.844569 + 1.46284i) q^{47} +(3.90366 + 0.872621i) q^{48} +(1.18914 - 6.89826i) q^{49} +(-0.373604 + 6.78829i) q^{50} +(4.89158 - 2.82415i) q^{51} +(6.20244 + 4.55620i) q^{52} +(-5.35599 + 9.27685i) q^{53} +(1.26175 - 0.638735i) q^{54} -0.928833 q^{55} +(3.81596 + 6.43727i) q^{56} -2.97584 q^{57} +(8.86109 - 4.48574i) q^{58} +(-4.05909 + 7.03055i) q^{59} +(0.707540 + 0.519747i) q^{60} +(5.35787 - 3.09337i) q^{61} +(0.577061 - 10.4851i) q^{62} +(2.48792 + 0.900140i) q^{63} +(-7.56863 - 2.59148i) q^{64} +(0.844569 + 1.46284i) q^{65} +(1.63637 - 2.50539i) q^{66} +(6.79878 + 3.92528i) q^{67} +(-10.3439 + 4.54058i) q^{68} +4.77038i q^{69} +(0.199011 + 1.63034i) q^{70} +1.16982i q^{71} +(-2.64845 + 0.992823i) q^{72} +(-8.69036 - 5.01738i) q^{73} +(6.25965 + 4.08843i) q^{74} +(-2.40366 - 4.16325i) q^{75} +(5.91574 + 0.653140i) q^{76} +(5.51142 - 0.982694i) q^{77} +(-5.43371 - 0.299052i) q^{78} +(-13.4958 + 7.79180i) q^{79} +(-1.29246 - 1.18851i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.35498 - 8.60279i) q^{82} -5.49645 q^{83} +(-4.74822 - 2.33546i) q^{84} -2.47939 q^{85} +(-2.80178 - 5.53462i) q^{86} +(-3.51142 + 6.08197i) q^{87} +(-3.80287 + 4.62137i) q^{88} +(-9.02285 + 5.20934i) q^{89} +(-0.619848 - 0.0341142i) q^{90} +(-6.55909 - 7.78650i) q^{91} +(1.04701 - 9.48314i) q^{92} +(3.71264 + 6.43048i) q^{93} +(2.00000 + 1.30628i) q^{94} +(1.13127 + 0.653140i) q^{95} +(5.48282 - 1.39237i) q^{96} -2.22605i q^{97} +(-2.90576 - 9.46343i) q^{98} +2.11598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more