LMFDB - Embedded newform 117.2.bc.a.50.12

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			50.12
Character	$\chi$	$=$	117.50
Dual form			117.2.bc.a.110.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.683347 + 2.55028i) q^{2} +(1.41657 + 0.996665i) q^{3} +(-4.30494 + 2.48546i) q^{4} +(-0.697740 - 2.60400i) q^{5} +(-1.57377 + 4.29371i) q^{6} +(1.60053 - 1.60053i) q^{7} +(-5.54651 - 5.54651i) q^{8} +(1.01332 + 2.82368i) q^{9} +O(q^{10})$	\(q+(0.683347 + 2.55028i) q^{2} +(1.41657 + 0.996665i) q^{3} +(-4.30494 + 2.48546i) q^{4} +(-0.697740 - 2.60400i) q^{5} +(-1.57377 + 4.29371i) q^{6} +(1.60053 - 1.60053i) q^{7} +(-5.54651 - 5.54651i) q^{8} +(1.01332 + 2.82368i) q^{9} +(6.16415 - 3.55887i) q^{10} +(-1.49528 + 0.400660i) q^{11} +(-8.57539 - 0.769767i) q^{12} +(2.76885 - 2.30943i) q^{13} +(5.17552 + 2.98809i) q^{14} +(1.60692 - 4.38416i) q^{15} +(5.38407 - 9.32548i) q^{16} +(-1.06695 + 1.84800i) q^{17} +(-6.50875 + 4.51380i) q^{18} +(-3.84372 + 1.02992i) q^{19} +(9.47586 + 9.47586i) q^{20} +(3.86245 - 0.672064i) q^{21} +(-2.04359 - 3.53961i) q^{22} -7.11178 q^{23} +(-2.32898 - 13.3850i) q^{24} +(-1.96386 + 1.13384i) q^{25} +(7.78180 + 5.48320i) q^{26} +(-1.37884 + 5.00987i) q^{27} +(-2.91213 + 10.8682i) q^{28} +(-0.203285 - 0.117367i) q^{29} +(12.2789 + 1.10221i) q^{30} +(6.02345 - 1.61398i) q^{31} +(12.3085 + 3.29805i) q^{32} +(-2.51749 - 0.922735i) q^{33} +(-5.44203 - 1.45819i) q^{34} +(-5.28454 - 3.05103i) q^{35} +(-11.3804 - 9.63722i) q^{36} +(2.21625 + 0.593843i) q^{37} +(-5.25318 - 9.09878i) q^{38} +(6.22399 - 0.511852i) q^{39} +(-10.5731 + 18.3131i) q^{40} +(5.99425 - 5.99425i) q^{41} +(4.35335 + 9.39109i) q^{42} -0.761002i q^{43} +(5.44127 - 5.44127i) q^{44} +(6.64585 - 4.60888i) q^{45} +(-4.85981 - 18.1371i) q^{46} +(-0.640422 + 2.39009i) q^{47} +(16.9213 - 7.84405i) q^{48} +1.87661i q^{49} +(-4.23360 - 4.23360i) q^{50} +(-3.35324 + 1.55443i) q^{51} +(-6.17971 + 16.8238i) q^{52} -3.34230i q^{53} +(-13.7188 - 0.0929427i) q^{54} +(2.08664 + 3.61416i) q^{55} -17.7547 q^{56} +(-6.47136 - 2.37195i) q^{57} +(0.160404 - 0.598636i) q^{58} +(-3.20908 + 11.9765i) q^{59} +(3.97892 + 22.8674i) q^{60} -9.67608 q^{61} +(8.23221 + 14.2586i) q^{62} +(6.14124 + 2.89754i) q^{63} +12.1076i q^{64} +(-7.94571 - 5.59870i) q^{65} +(0.632918 - 7.05086i) q^{66} +(-5.41390 - 5.41390i) q^{67} -10.6074i q^{68} +(-10.0743 - 7.08807i) q^{69} +(4.16982 - 15.5620i) q^{70} +(-0.833742 - 3.11157i) q^{71} +(10.0412 - 21.2820i) q^{72} +(-0.706395 + 0.706395i) q^{73} +6.05787i q^{74} +(-3.91200 - 0.351159i) q^{75} +(13.9871 - 13.9871i) q^{76} +(-1.75198 + 3.03451i) q^{77} +(5.55851 + 15.5232i) q^{78} +(4.39999 + 7.62101i) q^{79} +(-28.0403 - 7.51337i) q^{80} +(-6.94637 + 5.72258i) q^{81} +(19.3832 + 11.1909i) q^{82} +(3.82540 + 1.02501i) q^{83} +(-14.9572 + 12.4931i) q^{84} +(5.55666 + 1.48890i) q^{85} +(1.94077 - 0.520028i) q^{86} +(-0.170991 - 0.368865i) q^{87} +(10.5159 + 6.07133i) q^{88} +(0.560753 - 2.09276i) q^{89} +(16.2954 + 13.7993i) q^{90} +(0.735305 - 8.12794i) q^{91} +(30.6158 - 17.6760i) q^{92} +(10.1412 + 3.71705i) q^{93} -6.53304 q^{94} +(5.36383 + 9.29043i) q^{95} +(14.1487 + 16.9393i) q^{96} +(-0.451327 - 0.451327i) q^{97} +(-4.78588 + 1.28237i) q^{98} +(-2.64653 - 3.81621i) 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.683347	+	2.55028i	0.483199	+	1.80332i	0.588037	+	0.808834i	$0.299901\pi$
$2$	0.683347	+	2.55028i	0.483199	+	1.80332i	−0.104838	+	0.994489i	$0.533432\pi$
$3$	1.41657	+	0.996665i	0.817855	+	0.575425i
$3$	1.41657	+	0.996665i	0.817855	+	0.575425i
$4$	−4.30494	+	2.48546i	−2.15247	+	1.24273i
$5$	−0.697740	−	2.60400i	−0.312039	−	1.16455i	−0.926715	−	0.375766i	$-0.877380\pi$
$5$	−0.697740	−	2.60400i	−0.312039	−	1.16455i	0.614676	−	0.788780i	$-0.289287\pi$
$6$	−1.57377	+	4.29371i	−0.642490	+	1.75290i
$7$	1.60053	−	1.60053i	0.604944	−	0.604944i	−0.336677	−	0.941620i	$-0.609303\pi$
$7$	1.60053	−	1.60053i	0.604944	−	0.604944i	0.941620	+	0.336677i	$0.109303\pi$
$8$	−5.54651	−	5.54651i	−1.96099	−	1.96099i
$9$	1.01332	+	2.82368i	0.337773	+	0.941228i
$10$	6.16415	−	3.55887i	1.94928	−	1.12541i
$11$	−1.49528	+	0.400660i	−0.450845	+	0.120803i	−0.477095	−	0.878852i	$-0.658310\pi$
$11$	−1.49528	+	0.400660i	−0.450845	+	0.120803i	0.0262499	+	0.999655i	$0.491643\pi$
$12$	−8.57539	−	0.769767i	−2.47550	−	0.222213i
$13$	2.76885	−	2.30943i	0.767940	−	0.640522i
$13$	2.76885	−	2.30943i	0.767940	−	0.640522i
$14$	5.17552	+	2.98809i	1.38322	+	0.798601i
$15$	1.60692	−	4.38416i	0.414906	−	1.13198i
$16$	5.38407	−	9.32548i	1.34602	−	2.33137i
$17$	−1.06695	+	1.84800i	−0.258772	+	0.448207i	−0.965913	−	0.258866i	$-0.916651\pi$
$17$	−1.06695	+	1.84800i	−0.258772	+	0.448207i	0.707141	+	0.707073i	$0.249985\pi$
$18$	−6.50875	+	4.51380i	−1.53413	+	1.06391i
$19$	−3.84372	+	1.02992i	−0.881809	+	0.236280i	−0.671187	−	0.741288i	$-0.734215\pi$
$19$	−3.84372	+	1.02992i	−0.881809	+	0.236280i	−0.210622	+	0.977568i	$0.567549\pi$
$20$	9.47586	+	9.47586i	2.11887	+	2.11887i
$21$	3.86245	−	0.672064i	0.842855	−	0.146656i
$22$	−2.04359	−	3.53961i	−0.435695	−	0.754647i
$23$	−7.11178			−1.48291			−0.741455	−	0.671003i	$-0.765864\pi$
$23$	−7.11178			−1.48291			−0.741455	+	0.671003i	$0.765864\pi$
$24$	−2.32898	−	13.3850i	−0.475402	−	2.73220i
$25$	−1.96386	+	1.13384i	−0.392773	+	0.226767i
$26$	7.78180	+	5.48320i	1.52614	+	1.07534i
$27$	−1.37884	+	5.00987i	−0.265357	+	0.964150i
$28$	−2.91213	+	10.8682i	−0.550341	+	2.05390i
$29$	−0.203285	−	0.117367i	−0.0377491	−	0.0217944i	0.481007	−	0.876717i	$-0.340271\pi$
$29$	−0.203285	−	0.117367i	−0.0377491	−	0.0217944i	−0.518756	+	0.854922i	$0.673605\pi$
$30$	12.2789	+	1.10221i	2.24182	+	0.201236i
$31$	6.02345	−	1.61398i	1.08184	−	0.289879i	0.326493	−	0.945200i	$-0.394133\pi$
$31$	6.02345	−	1.61398i	1.08184	−	0.289879i	0.755351	+	0.655321i	$0.227466\pi$
$32$	12.3085	+	3.29805i	2.17585	+	0.583018i
$33$	−2.51749	−	0.922735i	−0.438239	−	0.160628i
$34$	−5.44203	−	1.45819i	−0.933300	−	0.250077i
$35$	−5.28454	−	3.05103i	−0.893250	−	0.515718i
$36$	−11.3804	−	9.63722i	−1.89673	−	1.60620i
$37$	2.21625	+	0.593843i	0.364349	+	0.0976271i	0.436349	−	0.899778i	$-0.356271\pi$
$37$	2.21625	+	0.593843i	0.364349	+	0.0976271i	−0.0719995	+	0.997405i	$0.522938\pi$
$38$	−5.25318	−	9.09878i	−0.852178	−	1.47602i
$39$	6.22399	−	0.511852i	0.996635	−	0.0819619i
$40$	−10.5731	+	18.3131i	−1.67175	+	2.89556i
$41$	5.99425	−	5.99425i	0.936145	−	0.936145i	−0.0619356	−	0.998080i	$-0.519727\pi$
$41$	5.99425	−	5.99425i	0.936145	−	0.936145i	0.998080	+	0.0619356i	$0.0197273\pi$
$42$	4.35335	+	9.39109i	0.671736	+	1.44908i
$43$		−	0.761002i		−	0.116052i	−0.998315	−	0.0580259i	$-0.981519\pi$
$43$		−	0.761002i		−	0.116052i	0.998315	−	0.0580259i	$-0.0184806\pi$
$44$	5.44127	−	5.44127i	0.820303	−	0.820303i
$45$	6.64585	−	4.60888i	0.990704	−	0.687051i
$46$	−4.85981	−	18.1371i	−0.716540	−	2.67416i
$47$	−0.640422	+	2.39009i	−0.0934152	+	0.348630i	−0.996774	−	0.0802545i	$-0.974427\pi$
$47$	−0.640422	+	2.39009i	−0.0934152	+	0.348630i	0.903359	+	0.428885i	$0.141093\pi$
$48$	16.9213	−	7.84405i	2.44238	−	1.13219i
$49$			1.87661i			0.268087i
$50$	−4.23360	−	4.23360i	−0.598722	−	0.598722i
$51$	−3.35324	+	1.55443i	−0.469547	+	0.217664i
$52$	−6.17971	+	16.8238i	−0.856972	+	2.33304i
$53$		−	3.34230i		−	0.459100i	−0.973297	−	0.229550i	$-0.926275\pi$
$53$		−	3.34230i		−	0.459100i	0.973297	−	0.229550i	$-0.0737254\pi$
$54$	−13.7188	−	0.0929427i	−1.86689	−	0.0126479i
$55$	2.08664	+	3.61416i	0.281362	+	0.487334i
$56$	−17.7547			−2.37257
$57$	−6.47136	−	2.37195i	−0.857153	−	0.314172i
$58$	0.160404	−	0.598636i	0.0210621	−	0.0786048i
$59$	−3.20908	+	11.9765i	−0.417787	+	1.55920i	0.361399	+	0.932411i	$0.382299\pi$
$59$	−3.20908	+	11.9765i	−0.417787	+	1.55920i	−0.779187	+	0.626792i	$0.784368\pi$
$60$	3.97892	+	22.8674i	0.513677	+	2.95217i
$61$	−9.67608			−1.23889			−0.619447	−	0.785038i	$-0.712643\pi$
$61$	−9.67608			−1.23889			−0.619447	+	0.785038i	$0.712643\pi$
$62$	8.23221	+	14.2586i	1.04549	+	1.81084i
$63$	6.14124	+	2.89754i	0.773723	+	0.365056i
$64$			12.1076i			1.51344i
$65$	−7.94571	−	5.59870i	−0.985544	−	0.694433i
$66$	0.632918	−	7.05086i	0.0779068	−	0.867901i
$67$	−5.41390	−	5.41390i	−0.661414	−	0.661414i	0.294300	−	0.955713i	$-0.404914\pi$
$67$	−5.41390	−	5.41390i	−0.661414	−	0.661414i	−0.955713	+	0.294300i	$0.904914\pi$
$68$		−	10.6074i		−	1.28633i
$69$	−10.0743	−	7.08807i	−1.21280	−	0.853303i
$70$	4.16982	−	15.5620i	0.498389	−	1.86001i
$71$	−0.833742	−	3.11157i	−0.0989469	−	0.369275i	0.898641	−	0.438684i	$-0.144555\pi$
$71$	−0.833742	−	3.11157i	−0.0989469	−	0.369275i	−0.997588	+	0.0694091i	$0.977889\pi$
$72$	10.0412	−	21.2820i	1.18337	−	2.50810i
$73$	−0.706395	+	0.706395i	−0.0826773	+	0.0826773i	−0.747236	−	0.664559i	$-0.768620\pi$
$73$	−0.706395	+	0.706395i	−0.0826773	+	0.0826773i	0.664559	+	0.747236i	$0.268620\pi$
$74$			6.05787i			0.704213i
$75$	−3.91200	−	0.351159i	−0.451718	−	0.0405483i
$76$	13.9871	−	13.9871i	1.60443	−	1.60443i
$77$	−1.75198	+	3.03451i	−0.199656	+	0.345815i
$78$	5.55851	+	15.5232i	0.629377	+	1.75765i
$79$	4.39999	+	7.62101i	0.495038	+	0.857430i	0.999984	−	0.00572053i	$-0.00182091\pi$
$79$	4.39999	+	7.62101i	0.495038	+	0.857430i	−0.504946	+	0.863151i	$0.668488\pi$
$80$	−28.0403	−	7.51337i	−3.13500	−	0.840020i
$81$	−6.94637	+	5.72258i	−0.771819	+	0.635842i
$82$	19.3832	+	11.1909i	2.14052	+	1.23583i
$83$	3.82540	+	1.02501i	0.419892	+	0.112510i	0.462578	−	0.886579i	$-0.346925\pi$
$83$	3.82540	+	1.02501i	0.419892	+	0.112510i	−0.0426854	+	0.999089i	$0.513591\pi$
$84$	−14.9572	+	12.4931i	−1.63197	+	1.36311i
$85$	5.55666	+	1.48890i	0.602704	+	0.161494i
$86$	1.94077	−	0.520028i	0.209279	−	0.0560761i
$87$	−0.170991	−	0.368865i	−0.0183322	−	0.0395464i
$88$	10.5159	+	6.07133i	1.12099	+	0.647206i
$89$	0.560753	−	2.09276i	0.0594397	−	0.221832i	−0.929817	−	0.368023i	$-0.880035\pi$
$89$	0.560753	−	2.09276i	0.0594397	−	0.221832i	0.989256	+	0.146191i	$0.0467014\pi$
$90$	16.2954	+	13.7993i	1.71768	+	1.45458i
$91$	0.735305	−	8.12794i	0.0770809	−	0.852040i
$92$	30.6158	−	17.6760i	3.19192	−	1.84285i
$93$	10.1412	+	3.71705i	1.05159	+	0.385441i
$94$	−6.53304			−0.673831
$95$	5.36383	+	9.29043i	0.550318	+	0.953178i
$96$	14.1487	+	16.9393i	1.44405	+	1.72886i
$97$	−0.451327	−	0.451327i	−0.0458253	−	0.0458253i	0.683823	−	0.729648i	$-0.260316\pi$
$97$	−0.451327	−	0.451327i	−0.0458253	−	0.0458253i	−0.729648	+	0.683823i	$0.760316\pi$
$98$	−4.78588	+	1.28237i	−0.483447	+	0.129539i
$99$	−2.64653	−	3.81621i	−0.265987	−	0.383543i
$100$	5.63620	−	9.76219i	0.563620	−	0.976219i
$101$	−2.92008	+	5.05773i	−0.290559	+	0.503262i	−0.973942	−	0.226797i	$-0.927174\pi$
$101$	−2.92008	+	5.05773i	−0.290559	+	0.503262i	0.683383	+	0.730060i	$0.260508\pi$
$102$	−6.25567	−	7.48950i	−0.619403	−	0.741571i
$103$	16.9587	+	9.79113i	1.67099	+	0.964749i	0.967083	+	0.254461i	$0.0818982\pi$
$103$	16.9587	+	9.79113i	1.67099	+	0.964749i	0.703911	+	0.710288i	$0.251435\pi$
$104$	−28.1667	−	2.54814i	−2.76197	−	0.249866i
$105$	−4.44504	−	9.58890i	−0.433792	−	0.935781i
$106$	8.52380	−	2.28395i	0.827905	−	0.221836i
$107$	3.36744	−	1.94419i	0.325543	−	0.187952i	−0.328318	−	0.944567i	$-0.606482\pi$
$107$	3.36744	−	1.94419i	0.325543	−	0.187952i	0.653861	+	0.756615i	$0.273148\pi$
$108$	−6.51602	−	24.9942i	−0.627004	−	2.40507i
$109$	−9.18667	−	9.18667i	−0.879924	−	0.879924i	0.113602	−	0.993526i	$-0.463761\pi$
$109$	−9.18667	−	9.18667i	−0.879924	−	0.879924i	−0.993526	+	0.113602i	$0.963761\pi$
$110$	−7.79125	+	7.79125i	−0.742866	+	0.742866i
$111$	2.54760	+	3.05008i	0.241808	+	0.289500i
$112$	−6.30835	−	23.5431i	−0.596083	−	2.22461i
$113$	12.0468	−	6.95524i	1.13327	−	0.654294i	0.188516	−	0.982070i	$-0.439632\pi$
$113$	12.0468	−	6.95524i	1.13327	−	0.654294i	0.944756	+	0.327776i	$0.106299\pi$
$114$	1.62696	−	18.1247i	0.152378	−	1.69753i
$115$	4.96218	+	18.5191i	0.462726	+	1.72692i
$116$	1.16684			0.108338
$117$	9.32683	+	5.47816i	0.862266	+	0.506456i
$118$	−32.7363			−3.01362
$119$	1.25011	+	4.66547i	0.114597	+	0.427682i
$120$	−33.2296	+	15.4039i	−3.03343	+	1.40618i
$121$	−7.45094	+	4.30180i	−0.677358	+	0.391073i
$122$	−6.61211	−	24.6767i	−0.598633	−	2.23413i
$123$	14.4655	−	2.51699i	1.30431	−	0.226949i
$124$	−21.9191	+	21.9191i	−1.96839	+	1.96839i
$125$	−5.20853	−	5.20853i	−0.465865	−	0.465865i
$126$	−3.19297	+	17.6419i	−0.284452	+	1.57167i
$127$	−16.7201	+	9.65336i	−1.48367	+	0.856597i	−0.999828	−	0.0185590i	$-0.994092\pi$
$127$	−16.7201	+	9.65336i	−1.48367	+	0.856597i	−0.483841	+	0.875156i	$0.660759\pi$
$128$	−6.26074	+	1.67756i	−0.553377	+	0.148277i
$129$	0.758464	−	1.07801i	0.0667790	−	0.0949134i
$130$	8.84860	−	24.0897i	0.776074	−	2.11280i
$131$	0.0772661	+	0.0446096i	0.00675077	+	0.00389756i	0.503372	−	0.864070i	$-0.332093\pi$
$131$	0.0772661	+	0.0446096i	0.00675077	+	0.00389756i	−0.496621	+	0.867968i	$0.665426\pi$
$132$	13.1311	−	2.28480i	1.14291	−	0.198866i
$133$	−4.50357	+	7.80040i	−0.390509	+	0.676381i
$134$	10.1074	−	17.5066i	0.873148	−	1.51234i
$135$	14.0078	+	0.0949004i	1.20560	+	0.00816772i
$136$	16.1678	−	4.33215i	1.38638	−	0.371478i
$137$	−1.00143	−	1.00143i	−0.0855580	−	0.0855580i	0.663033	−	0.748591i	$-0.269269\pi$
$137$	−1.00143	−	1.00143i	−0.0855580	−	0.0855580i	−0.748591	+	0.663033i	$0.769269\pi$
$138$	11.1923	−	30.5360i	0.952755	−	2.59939i
$139$	3.97548	+	6.88573i	0.337196	+	0.584040i	0.983904	−	0.178697i	$-0.0571883\pi$
$139$	3.97548	+	6.88573i	0.337196	+	0.584040i	−0.646709	+	0.762737i	$0.723855\pi$
$140$	30.3328			2.56359
$141$	−3.28932	+	2.74743i	−0.277011	+	0.231375i
$142$	7.36564	−	4.25256i	0.618111	−	0.356867i
$143$	−3.21491	+	4.56262i	−0.268844	+	0.381546i
$144$	31.7880	+	5.75323i	2.64900	+	0.479436i
$145$	−0.163783	+	0.611246i	−0.0136014	+	0.0507612i
$146$	−2.28422	−	1.31879i	−0.189043	−	0.109144i
$147$	−1.87035	+	2.65834i	−0.154264	+	0.219256i
$148$	−11.0168	+	2.95194i	−0.905574	+	0.242648i
$149$	15.9539	+	4.27483i	1.30699	+	0.350208i	0.844091	−	0.536201i	$-0.180141\pi$
$149$	15.9539	+	4.27483i	1.30699	+	0.350208i	0.462904	+	0.886409i	$0.346808\pi$
$150$	−1.77769	−	10.2167i	−0.145148	−	0.834187i
$151$	8.42619	+	2.25779i	0.685714	+	0.183736i	0.584823	−	0.811161i	$-0.301164\pi$
$151$	8.42619	+	2.25779i	0.685714	+	0.183736i	0.100891	+	0.994897i	$0.467831\pi$
$152$	27.0317	+	15.6067i	2.19256	+	1.26587i
$153$	−6.29933	−	1.14010i	−0.509271	−	0.0921717i
$154$	−8.93608	−	2.39442i	−0.720090	−	0.192947i
$155$	−8.40561	−	14.5589i	−0.675155	−	1.16940i
$156$	−25.5217	+	17.6729i	−2.04337	+	1.41497i
$157$	−0.854259	+	1.47962i	−0.0681773	+	0.118087i	−0.898099	−	0.439793i	$-0.855052\pi$
$157$	−0.854259	+	1.47962i	−0.0681773	+	0.118087i	0.829922	+	0.557880i	$0.188385\pi$
$158$	−16.4290	+	16.4290i	−1.30702	+	1.30702i
$159$	3.33115	−	4.73458i	0.264177	−	0.375477i
$160$		−	34.3525i		−	2.71580i
$161$	−11.3826	+	11.3826i	−0.897076	+	0.897076i
$162$	−19.3410	−	13.8047i	−1.51957	−	1.08460i
$163$	0.929365	+	3.46844i	0.0727935	+	0.271669i	0.992724	−	0.120413i	$-0.0384217\pi$
$163$	0.929365	+	3.46844i	0.0727935	+	0.271669i	−0.919930	+	0.392082i	$0.871755\pi$
$164$	−10.9064	+	40.7033i	−0.851648	+	3.17839i
$165$	−0.646250	+	7.19938i	−0.0503105	+	0.560471i
$166$			10.4563i			0.811566i
$167$	1.38816	+	1.38816i	0.107419	+	0.107419i	0.758774	−	0.651354i	$-0.225799\pi$
$167$	1.38816	+	1.38816i	0.107419	+	0.107419i	−0.651354	+	0.758774i	$0.725799\pi$
$168$	−25.1507	−	17.6955i	−1.94042	−	1.36524i
$169$	2.33303	−	12.7889i	0.179464	−	0.983765i
$170$			15.1885i			1.16490i
$171$	−6.80308	−	9.80980i	−0.520244	−	0.750174i
$172$	1.89144	+	3.27606i	0.144221	+	0.249798i
$173$	17.6248			1.33999			0.669994	−	0.742367i	$-0.266297\pi$
$173$	17.6248			1.33999			0.669994	+	0.742367i	$0.266297\pi$
$174$	0.823863	−	0.688139i	0.0624569	−	0.0521677i
$175$	−1.32848	+	4.95796i	−0.100424	+	0.374787i
$176$	−4.31436	+	16.1014i	−0.325207	+	1.21369i
$177$	−16.4824	+	13.7671i	−1.23889	+	1.03480i
$178$	5.72032			0.428756
$179$	−5.11814	−	8.86487i	−0.382548	−	0.662592i	0.608878	−	0.793264i	$-0.291620\pi$
$179$	−5.11814	−	8.86487i	−0.382548	−	0.662592i	−0.991426	+	0.130672i	$0.958287\pi$
$180$	−17.1548	+	36.3589i	−1.27864	+	2.71003i
$181$		−	16.0613i		−	1.19382i	−0.802306	−	0.596912i	$-0.796394\pi$
$181$		−	16.0613i		−	1.19382i	0.802306	−	0.596912i	$-0.203606\pi$
$182$	21.2310	−	3.67897i	1.57375	−	0.272703i
$183$	−13.7068	−	9.64381i	−1.01324	−	0.712891i
$184$	39.4456	+	39.4456i	2.90797	+	2.90797i
$185$		−	6.18547i		−	0.454765i
$186$	−2.54959	+	28.4030i	−0.186945	+	2.08261i
$187$	0.854964	−	3.19077i	0.0625212	−	0.233332i
$188$	−3.18348	−	11.8809i	−0.232179	−	0.866505i
$189$	5.81158	+	10.2253i	0.422731	+	0.743782i
$190$	−20.0279	+	20.0279i	−1.45298	+	1.45298i
$191$			5.97341i			0.432221i	0.976369	+	0.216111i	$0.0693372\pi$
$191$			5.97341i			0.432221i	−0.976369	+	0.216111i	$0.930663\pi$
$192$	−12.0672	+	17.1512i	−0.870874	+	1.23778i
$193$	1.32261	−	1.32261i	0.0952033	−	0.0952033i	−0.657901	−	0.753104i	$-0.728556\pi$
$193$	1.32261	−	1.32261i	0.0952033	−	0.0952033i	0.753104	+	0.657901i	$0.228556\pi$
$194$	0.842599	−	1.45942i	0.0604951	−	0.104781i
$195$	−5.67559	−	15.8501i	−0.406438	−	1.13505i
$196$	−4.66422	−	8.07867i	−0.333159	−	0.577048i
$197$	20.1278	+	5.39323i	1.43405	+	0.384252i	0.890445	−	0.455091i	$-0.150393\pi$
$197$	20.1278	+	5.39323i	1.43405	+	0.384252i	0.543603	+	0.839343i	$0.317060\pi$
$198$	7.92392	−	9.35720i	0.563128	−	0.664988i
$199$	6.00336	+	3.46604i	0.425567	+	0.245701i	0.697456	−	0.716627i	$-0.254315\pi$
$199$	6.00336	+	3.46604i	0.425567	+	0.245701i	−0.271889	+	0.962329i	$0.587648\pi$
$200$	17.1814	+	4.60375i	1.21491	+	0.325534i
$201$	−2.27330	−	13.0650i	−0.160346	−	0.921534i
$202$	−14.8941	−	3.99085i	−1.04794	−	0.280795i
$203$	−0.513212	+	0.137515i	−0.0360205	+	0.00965165i
$204$	10.5720	−	15.0261i	0.740189	−	1.05203i
$205$	−19.7915	−	11.4266i	−1.38230	−	0.798069i
$206$	−13.3815	+	49.9403i	−0.932332	+	3.47951i
$207$	−7.20650	−	20.0814i	−0.500886	−	1.39576i
$208$	−6.62892	−	38.2550i	−0.459633	−	2.65251i
$209$	5.33479	−	3.08005i	0.369015	−	0.213051i
$210$	21.4169	−	17.8887i	1.47791	−	1.23444i
$211$	−2.46133			−0.169445			−0.0847226	−	0.996405i	$-0.527000\pi$
$211$	−2.46133			−0.169445			−0.0847226	+	0.996405i	$0.527000\pi$
$212$	8.30713	+	14.3884i	0.570536	+	0.988197i
$213$	1.92014	−	5.23870i	0.131566	−	0.358950i
$214$	7.25938	+	7.25938i	0.496241	+	0.496241i
$215$	−1.98165	+	0.530982i	−0.135148	+	0.0362127i
$216$	35.4350	−	20.1396i	2.41105	−	1.37032i
$217$	7.05749	−	12.2239i	0.479094	−	0.829815i
$218$	17.1509	−	29.7063i	1.16161	−	2.01197i
$219$	−1.70469	+	0.296616i	−0.115193	+	0.0200434i
$220$	−17.9657	−	10.3725i	−1.21125	−	0.699314i
$221$	1.31363	+	7.58088i	0.0883646	+	0.509945i
$222$	−6.03767	+	8.58137i	−0.405222	+	0.575944i
$223$	−19.4990	+	5.22475i	−1.30575	+	0.349875i	−0.843622	−	0.536937i	$-0.819581\pi$
$223$	−19.4990	+	5.22475i	−1.30575	+	0.349875i	−0.462130	+	0.886812i	$0.652915\pi$
$224$	24.9787	−	14.4215i	1.66896	−	0.963575i
$225$	−5.19161	−	4.39639i	−0.346107	−	0.293093i
$226$	25.9700	+	25.9700i	1.72750	+	1.72750i
$227$	−14.0786	+	14.0786i	−0.934431	+	0.934431i	−0.997979	−	0.0635481i	$-0.979758\pi$
$227$	−14.0786	+	14.0786i	−0.934431	+	0.934431i	0.0635481	+	0.997979i	$0.479758\pi$
$228$	33.7542	−	5.87321i	2.23542	−	0.388963i
$229$	−6.28023	−	23.4382i	−0.415010	−	1.54884i	−0.784817	−	0.619728i	$-0.787243\pi$
$229$	−6.28023	−	23.4382i	−0.415010	−	1.54884i	0.369807	−	0.929109i	$-0.379424\pi$
$230$	−43.8381	+	25.3099i	−2.89060	+	1.66889i
$231$	−5.50618	+	2.55245i	−0.362280	+	0.167939i
$232$	0.476547	+	1.77850i	0.0312868	+	0.116764i
$233$	18.4755			1.21037			0.605184	−	0.796085i	$-0.293099\pi$
$233$	18.4755			1.21037			0.605184	+	0.796085i	$0.293099\pi$
$234$	−7.59740	+	27.5296i	−0.496658	+	1.79966i
$235$	6.67065			0.435145
$236$	−15.9521	−	59.5340i	−1.03839	−	3.87533i
$237$	−1.36272	+	15.1810i	−0.0885179	+	0.986110i
$238$	−11.0440	+	6.37626i	−0.715877	+	0.413311i
$239$	−3.34242	−	12.4741i	−0.216203	−	0.806882i	−0.985740	−	0.168278i	$-0.946179\pi$
$239$	−3.34242	−	12.4741i	−0.216203	−	0.806882i	0.769536	−	0.638603i	$-0.220487\pi$
$240$	−32.2326	−	38.5899i	−2.08060	−	2.49097i
$241$	2.68714	−	2.68714i	0.173094	−	0.173094i	−0.615243	−	0.788337i	$-0.710942\pi$
$241$	2.68714	−	2.68714i	0.173094	−	0.173094i	0.788337	+	0.615243i	$0.210942\pi$
$242$	−16.0624	−	16.0624i	−1.03253	−	1.03253i
$243$	−15.5435	+	1.18320i	−0.997115	+	0.0759022i
$244$	41.6549	−	24.0495i	2.66668	−	1.53961i
$245$	4.88669	−	1.30938i	0.312199	−	0.0836535i
$246$	16.3040	+	35.1712i	1.03950	+	2.24243i
$247$	−8.26413	+	11.7285i	−0.525834	+	0.746267i
$248$	−42.3611	−	24.4572i	−2.68993	−	1.55303i
$249$	4.39734	+	5.26464i	0.278670	+	0.333633i
$250$	9.72400	−	16.8425i	0.615000	−	1.06521i
$251$	9.87750	−	17.1083i	0.623462	−	1.07987i	−0.365374	−	0.930861i	$-0.619059\pi$
$251$	9.87750	−	17.1083i	0.623462	−	1.07987i	0.988836	−	0.149007i	$-0.0476077\pi$
$252$	−33.6393	+	2.79003i	−2.11908	+	0.175755i
$253$	10.6341	−	2.84941i	0.668562	−	0.179141i
$254$	−36.0444	−	36.0444i	−2.26163	−	2.26163i
$255$	6.38744	+	7.64726i	0.399997	+	0.478890i
$256$	3.55104	+	6.15059i	0.221940	+	0.384412i
$257$	−13.1426			−0.819814			−0.409907	−	0.912127i	$-0.634439\pi$
$257$	−13.1426			−0.819814			−0.409907	+	0.912127i	$0.634439\pi$
$258$	3.26752	+	1.19764i	0.203427	+	0.0745621i
$259$	4.49764	−	2.59671i	0.279470	−	0.161352i
$260$	48.1211	+	4.35334i	2.98434	+	0.269983i
$261$	0.125414	−	0.692942i	0.00776293	−	0.0428920i
$262$	−0.0609676	+	0.227534i	−0.00376659	+	0.0140571i
$263$	11.9389	+	6.89290i	0.736182	+	0.425035i	0.820679	−	0.571389i	$-0.193595\pi$
$263$	11.9389	+	6.89290i	0.736182	+	0.425035i	−0.0844978	+	0.996424i	$0.526929\pi$
$264$	8.84532	+	19.0812i	0.544392	+	1.17437i
$265$	−8.70335	+	2.33205i	−0.534642	+	0.143257i
$266$	−22.9707	−	6.15499i	−1.40843	−	0.377387i
$267$	2.88012	−	2.40565i	0.176261	−	0.147223i
$268$	36.7625	+	9.85049i	2.24563	+	0.601714i
$269$	−21.8626	−	12.6224i	−1.33299	−	0.769599i	−0.347229	−	0.937780i	$-0.612877\pi$
$269$	−21.8626	−	12.6224i	−1.33299	−	0.769599i	−0.985756	+	0.168181i	$0.946211\pi$
$270$	9.33015	+	35.7887i	0.567815	+	2.17803i
$271$	−18.4487	−	4.94331i	−1.12068	−	0.300285i	−0.349520	−	0.936929i	$-0.613655\pi$
$271$	−18.4487	−	4.94331i	−1.12068	−	0.300285i	−0.771158	+	0.636644i	$0.780322\pi$
$272$	11.4890	+	19.8996i	0.696624	+	1.20659i
$273$	9.14244	−	10.7809i	0.553326	−	0.652491i
$274$	1.86961	−	3.23826i	0.112947	−	0.195630i
$275$	2.48225	−	2.48225i	0.149685	−	0.149685i
$276$	60.9863	+	5.47442i	3.67095	+	0.329521i
$277$		−	0.185493i		−	0.0111452i	−0.999984	−	0.00557261i	$-0.998226\pi$
$277$		−	0.185493i		−	0.0111452i	0.999984	−	0.00557261i	$-0.00177383\pi$
$278$	−14.8439	+	14.8439i	−0.890280	+	0.890280i
$279$	10.6610	+	15.3728i	0.638259	+	0.920348i
$280$	12.3882	+	46.2333i	0.740335	+	2.76297i
$281$	2.41334	−	9.00672i	0.143968	−	0.537296i	−0.855831	−	0.517255i	$-0.826954\pi$
$281$	2.41334	−	9.00672i	0.143968	−	0.537296i	0.999799	−	0.0200406i	$-0.00637954\pi$
$282$	−9.25448	−	6.51125i	−0.551096	−	0.387739i
$283$		−	11.5127i		−	0.684360i	−0.939634	−	0.342180i	$-0.888835\pi$
$283$		−	11.5127i		−	0.684360i	0.939634	−	0.342180i	$-0.111165\pi$
$284$	11.3229	+	11.3229i	0.671888	+	0.671888i
$285$	−1.66123	+	18.5065i	−0.0984025	+	1.09623i
$286$	−13.8329	−	5.08109i	−0.817955	−	0.300451i
$287$		−	19.1880i		−	1.13263i
$288$	3.15976	+	38.0972i	0.186191	+	2.24490i
$289$	6.22325	+	10.7790i	0.366074	+	0.634058i
$290$	−1.67077			−0.0981111
$291$	−0.189512	−	1.08916i	−0.0111094	−	0.0638474i
$292$	1.28527	−	4.79670i	0.0752148	−	0.280705i
$293$	2.76556	−	10.3212i	0.161566	−	0.602972i	−0.836888	−	0.547375i	$-0.815627\pi$
$293$	2.76556	−	10.3212i	0.161566	−	0.602972i	0.998453	−	0.0555967i	$-0.0177061\pi$
$294$	−8.05761	−	2.95335i	−0.469929	−	0.172243i
$295$	33.4259			1.94613
$296$	−8.99870	−	15.5862i	−0.523039	−	0.905930i
$297$	0.0544941	−	8.04362i	0.00316207	−	0.466738i
$298$			43.6082i			2.52615i
$299$	−19.6914	+	16.4242i	−1.13879	+	0.949836i
$300$	17.7137	−	8.21138i	1.02270	−	0.474084i
$301$	−1.21801	−	1.21801i	−0.0702047	−	0.0702047i
$302$			23.0320i			1.32535i
$303$	−9.17734	+	4.25426i	−0.527225	+	0.244401i
$304$	−11.0903	+	41.3897i	−0.636074	+	2.37386i
$305$	6.75139	+	25.1965i	0.386584	+	1.44275i
$306$	−1.39705	−	16.8442i	−0.0798638	−	0.962917i
$307$	11.2905	−	11.2905i	0.644384	−	0.644384i	−0.307246	−	0.951630i	$-0.599407\pi$
$307$	11.2905	−	11.2905i	0.644384	−	0.644384i	0.951630	+	0.307246i	$0.0994075\pi$
$308$		−	17.4178i		−	0.992474i
$309$	14.2647	+	30.7720i	0.811490	+	1.75056i
$310$	31.3855	−	31.3855i	1.78258	−	1.78258i
$311$	3.28642	−	5.69225i	0.186356	−	0.322778i	−0.757677	−	0.652630i	$-0.773666\pi$
$311$	3.28642	−	5.69225i	0.186356	−	0.322778i	0.944033	+	0.329852i	$0.106999\pi$
$312$	−37.3604	−	31.6824i	−2.11511	−	1.79366i
$313$	10.7965	+	18.7000i	0.610253	+	1.05699i	0.991198	+	0.132391i	$0.0422654\pi$
$313$	10.7965	+	18.7000i	0.610253	+	1.05699i	−0.380945	+	0.924598i	$0.624401\pi$
$314$	−4.35721	−	1.16751i	−0.245891	−	0.0658864i
$315$	3.26023	−	18.0135i	0.183693	−	1.01495i
$316$	−37.8834	−	21.8720i	−2.13111	−	1.23039i
$317$	−5.93980	−	1.59156i	−0.333612	−	0.0893912i	0.0881244	−	0.996109i	$-0.471913\pi$
$317$	−5.93980	−	1.59156i	−0.333612	−	0.0893912i	−0.421737	+	0.906718i	$0.638579\pi$
$318$	14.3509	+	5.26002i	0.804756	+	0.294967i
$319$	0.350993	+	0.0940482i	0.0196518	+	0.00526569i
$320$	31.5281	−	8.44793i	1.76248	−	0.472254i
$321$	6.70792	+	0.602134i	0.374399	+	0.0336078i
$322$	−36.8072	−	21.2506i	−2.05119	−	1.18425i
$323$	2.19774	−	8.20207i	0.122285	−	0.456376i
$324$	15.6805	−	41.9002i	0.871138	−	2.32779i
$325$	−2.81911	+	7.67483i	−0.156376	+	0.425723i
$326$	−8.21043	+	4.74029i	−0.454733	+	0.262540i
$327$	−3.85749	−	22.1696i	−0.213320	−	1.22598i
$328$	−66.4943			−3.67153
$329$	2.80039	+	4.85043i	0.154391	+	0.267413i
$330$	−18.8021	+	3.27155i	−1.03502	+	0.180093i
$331$	−24.9879	−	24.9879i	−1.37346	−	1.37346i	−0.855258	−	0.518202i	$-0.826601\pi$
$331$	−24.9879	−	24.9879i	−1.37346	−	1.37346i	−0.518202	−	0.855258i	$-0.673399\pi$
$332$	−19.0157	+	5.09525i	−1.04362	+	0.279638i
$333$	0.568943	+	6.85974i	0.0311779	+	0.375911i
$334$	−2.59161	+	4.48880i	−0.141807	+	0.245616i
$335$	−10.3203	+	17.8753i	−0.563859	+	0.976633i
$336$	14.5284	−	39.6376i	0.792588	−	2.16241i
$337$	7.02186	+	4.05407i	0.382505	+	0.220839i	0.678908	−	0.734224i	$-0.262454\pi$
$337$	7.02186	+	4.05407i	0.382505	+	0.220839i	−0.296403	+	0.955063i	$0.595787\pi$
$338$	34.2097	−	2.78939i	1.86076	−	0.151723i
$339$	23.9972	+	2.15410i	1.30335	+	0.116995i
$340$	−27.6217	+	7.40120i	−1.49800	+	0.401387i
$341$	−8.36010	+	4.82671i	−0.452725	+	0.261381i
$342$	20.3689	−	24.0533i	1.10143	−	1.30065i
$343$	14.2073	+	14.2073i	0.767121	+	0.767121i
$344$	−4.22090	+	4.22090i	−0.227576	+	0.227576i
$345$	−11.4281	+	31.1792i	−0.615268	+	1.67863i
$346$	12.0438	+	44.9482i	0.647481	+	2.41643i
$347$	12.2388	−	7.06609i	0.657015	−	0.379328i	−0.134124	−	0.990965i	$-0.542822\pi$
$347$	12.2388	−	7.06609i	0.657015	−	0.379328i	0.791139	+	0.611637i	$0.209489\pi$
$348$	1.65290	+	1.16295i	0.0886049	+	0.0623405i
$349$	−3.79214	−	14.1525i	−0.202989	−	0.757565i	−0.990053	−	0.140694i	$-0.955067\pi$
$349$	−3.79214	−	14.1525i	−0.202989	−	0.757565i	0.787064	−	0.616871i	$-0.211600\pi$
$350$	−13.5520			−0.724386
$351$	7.75218	+	17.0559i	0.413781	+	0.910376i
$352$	−19.7261			−1.05140
$353$	8.21173	+	30.6466i	0.437066	+	1.63115i	0.736073	+	0.676902i	$0.236678\pi$
$353$	8.21173	+	30.6466i	0.437066	+	1.63115i	−0.299007	+	0.954251i	$0.596655\pi$
$354$	−46.3731	−	32.6271i	−2.46470	−	1.73411i
$355$	−7.52079	+	4.34213i	−0.399162	+	0.230456i
$356$	2.78746	+	10.4029i	0.147735	+	0.551354i
$357$	−2.87905	+	7.85488i	−0.152375	+	0.415724i
$358$	19.1105	−	19.1105i	1.01002	−	1.01002i
$359$	12.5293	+	12.5293i	0.661270	+	0.661270i	0.955679	−	0.294409i	$-0.0951229\pi$
$359$	12.5293	+	12.5293i	0.661270	+	0.661270i	−0.294409	+	0.955679i	$0.595123\pi$
$360$	−62.4244	−	11.2980i	−3.29006	−	0.595459i
$361$	−2.74106	+	1.58255i	−0.144267	+	0.0832923i
$362$	40.9608	−	10.9754i	2.15285	−	0.576855i
$363$	−14.8422	−	1.33230i	−0.779013	−	0.0699279i
$364$	17.0362	+	36.8178i	0.892940	+	1.92978i
$365$	2.33233	+	1.34657i	0.122080	+	0.0704829i
$366$	15.2280	−	41.5463i	0.795978	−	2.17166i
$367$	9.97333	−	17.2743i	0.520604	−	0.901712i	−0.479109	−	0.877755i	$-0.659040\pi$
$367$	9.97333	−	17.2743i	0.520604	−	0.901712i	0.999713	−	0.0239567i	$-0.00762638\pi$
$368$	−38.2903	+	66.3208i	−1.99602	+	3.45721i
$369$	22.9999	+	10.8518i	1.19733	+	0.564921i
$370$	15.7747	−	4.22682i	0.820088	−	0.219742i
$371$	−5.34944	−	5.34944i	−0.277729	−	0.277729i
$372$	−52.8958	+	9.20385i	−2.74252	+	0.477197i
$373$	−11.9342	−	20.6706i	−0.617928	−	1.07028i	−0.989863	−	0.142024i	$-0.954639\pi$
$373$	−11.9342	−	20.6706i	−0.617928	−	1.07028i	0.371935	−	0.928259i	$-0.378694\pi$
$374$	8.72161			0.450984
$375$	−2.18707	−	12.5694i	−0.112940	−	0.649081i
$376$	16.8088	−	9.70454i	0.866845	−	0.500473i
$377$	−0.833915	+	0.144503i	−0.0429488	+	0.00744228i
$378$	−22.1061	+	21.8086i	−1.13702	+	1.12171i
$379$	3.76589	−	14.0545i	0.193441	−	0.721931i	−0.799224	−	0.601033i	$-0.794756\pi$
$379$	3.76589	−	14.0545i	0.193441	−	0.721931i	0.992665	−	0.120898i	$-0.0385773\pi$
$380$	−46.1819	−	26.6631i	−2.36908	−	1.36779i
$381$	−33.3063	−	2.98973i	−1.70633	−	0.153168i
$382$	−15.2339	+	4.08191i	−0.779434	+	0.208849i
$383$	4.02159	+	1.07758i	0.205493	+	0.0550618i	0.360097	−	0.932915i	$-0.382743\pi$
$383$	4.02159	+	1.07758i	0.205493	+	0.0550618i	−0.154604	+	0.987977i	$0.549410\pi$
$384$	−10.5407	−	3.86349i	−0.537904	−	0.197158i
$385$	9.12431	+	2.44485i	0.465018	+	0.124601i
$386$	4.27682	+	2.46922i	0.217684	+	0.125680i
$387$	2.14883	−	0.771137i	0.109231	−	0.0391991i
$388$	3.06468	+	0.821180i	0.155586	+	0.0416891i
$389$	0.190514	+	0.329980i	0.00965945	+	0.0167307i	0.870815	−	0.491611i	$-0.163592\pi$
$389$	0.190514	+	0.329980i	0.00965945	+	0.0167307i	−0.861155	+	0.508342i	$0.830259\pi$
$390$	36.5440	−	25.3055i	1.85048	−	1.28139i
$391$	7.58789	−	13.1426i	0.383736	−	0.664650i
$392$	10.4086	−	10.4086i	0.525714	−	0.525714i
$393$	0.0649917	+	0.140201i	0.00327840	+	0.00707220i
$394$			55.0171i			2.77172i
$395$	16.7751	−	16.7751i	0.844046	−	0.844046i
$396$	20.8782	+	9.85070i	1.04917	+	0.495016i
$397$	4.01733	+	14.9929i	0.201624	+	0.752471i	0.990452	+	0.137857i	$0.0440214\pi$
$397$	4.01733	+	14.9929i	0.201624	+	0.752471i	−0.788828	+	0.614614i	$0.789312\pi$
$398$	−4.73702	+	17.6788i	−0.237445	+	0.886158i
$399$	−14.1540	+	6.56124i	−0.708586	+	0.328473i
$400$			24.4186i			1.22093i
$401$	−23.7432	−	23.7432i	−1.18568	−	1.18568i	−0.978251	−	0.207427i	$-0.933491\pi$
$401$	−23.7432	−	23.7432i	−1.18568	−	1.18568i	−0.207427	−	0.978251i	$-0.566509\pi$
$402$	31.7660	−	14.7255i	1.58434	−	0.734441i
$403$	12.9506	−	18.3796i	0.645117	−	0.915554i
$404$		−	29.0309i		−	1.44434i
$405$	19.7484	+	14.0955i	0.981305	+	0.700411i
$406$	−0.701404	−	1.21487i	−0.0348101	−	0.0602929i
$407$	−3.55185			−0.176059
$408$	27.2204	+	9.97710i	1.34761	+	0.493940i
$409$	5.61765	−	20.9654i	0.277775	−	1.03667i	−0.676184	−	0.736733i	$-0.736367\pi$
$409$	5.61765	−	20.9654i	0.277775	−	1.03667i	0.953959	−	0.299938i	$-0.0969659\pi$
$410$	15.6167	−	58.2822i	0.771253	−	2.87835i
$411$	−0.420502	−	2.41668i	−0.0207418	−	0.119206i
$412$	−97.3417			−4.79568
$413$	14.0325	+	24.3049i	0.690492	+	1.19597i
$414$	46.2888	−	32.1012i	2.27497	−	1.57769i
$415$		−	10.6765i		−	0.524091i
$416$	41.6969	−	19.2938i	2.04436	−	0.945958i
$417$	−1.23124	+	13.7163i	−0.0602941	+	0.671690i
$418$	11.5005	+	11.5005i	0.562508	+	0.562508i
$419$			31.6213i			1.54480i	0.635134	+	0.772402i	$0.280945\pi$
$419$			31.6213i			1.54480i	−0.635134	+	0.772402i	$0.719055\pi$
$420$	42.9684	+	30.2317i	2.09664	+	1.47515i
$421$	−1.73392	+	6.47108i	−0.0845062	+	0.315381i	−0.995220	−	0.0976561i	$-0.968865\pi$
$421$	−1.73392	+	6.47108i	−0.0845062	+	0.315381i	0.910714	+	0.413037i	$0.135532\pi$
$422$	−1.68194	−	6.27710i	−0.0818757	−	0.305564i
$423$	−7.39781	+	0.613569i	−0.359694	+	0.0298328i
$424$	−18.5381	+	18.5381i	−0.900288	+	0.900288i
$425$		−	4.83897i		−	0.234724i
$426$	14.6723	+	1.31705i	0.710875	+	0.0638114i
$427$	−15.4869	+	15.4869i	−0.749461	+	0.749461i
$428$	−9.66442	+	16.7393i	−0.467147	+	0.809123i
$429$	−9.10154	+	3.25906i	−0.439427	+	0.157349i
$430$	−2.70831	−	4.69093i	−0.130606	−	0.226217i
$431$	−6.56998	−	1.76042i	−0.316465	−	0.0847965i	0.0970903	−	0.995276i	$-0.469046\pi$
$431$	−6.56998	−	1.76042i	−0.316465	−	0.0847965i	−0.413555	+	0.910479i	$0.635713\pi$
$432$	39.2957	+	39.8318i	1.89062	+	1.91641i
$433$	21.3766	+	12.3418i	1.02729	+	0.593108i	0.916208	−	0.400703i	$-0.131234\pi$
$433$	21.3766	+	12.3418i	1.02729	+	0.593108i	0.111085	+	0.993811i	$0.464567\pi$
$434$	35.9972	+	9.64543i	1.72792	+	0.462995i
$435$	−0.841217	+	0.702634i	−0.0403333	+	0.0336887i
$436$	62.3811	+	16.7150i	2.98751	+	0.800502i
$437$	27.3357	−	7.32457i	1.30764	−	0.350382i
$438$	−1.92135	−	4.14476i	−0.0918057	−	0.198044i
$439$	20.0459	+	11.5735i	0.956740	+	0.552374i	0.895168	−	0.445728i	$-0.147055\pi$
$439$	20.0459	+	11.5735i	0.956740	+	0.552374i	0.0615720	+	0.998103i	$0.480389\pi$
$440$	8.47243	−	31.6195i	0.403907	−	1.50740i
$441$	−5.29894	+	1.90160i	−0.252331	+	0.0905523i
$442$	−18.4357	+	8.53051i	−0.876898	+	0.405755i
$443$	−20.9912	+	12.1193i	−0.997323	+	0.575805i	−0.907455	−	0.420149i	$-0.861978\pi$
$443$	−20.9912	+	12.1193i	−0.997323	+	0.575805i	−0.0898679	+	0.995954i	$0.528644\pi$
$444$	−18.5481	−	6.79843i	−0.880254	−	0.322639i
$445$	−5.84081			−0.276881
$446$	−26.6492	−	46.1578i	−1.26188	−	2.18563i
$447$	18.3392	+	21.9563i	0.867413	+	1.03850i
$448$	19.3785	+	19.3785i	0.915548	+	0.915548i
$449$	−5.97900	+	1.60207i	−0.282166	+	0.0756063i	−0.397127	−	0.917764i	$-0.629993\pi$
$449$	−5.97900	+	1.60207i	−0.282166	+	0.0756063i	0.114960	+	0.993370i	$0.463326\pi$
$450$	7.66437	−	16.2443i	0.361302	−	0.765766i
$451$	−6.56144	+	11.3648i	−0.308966	+	0.535145i
$452$	−34.5739	+	59.8838i	−1.62622	+	2.81670i
$453$	9.68600	+	11.5964i	0.455088	+	0.544847i
$454$	−45.5251	−	26.2839i	−2.13660	−	1.23356i
$455$	−21.6782	+	3.75646i	−1.01629	+	0.176105i
$456$	22.7374	+	49.0495i	1.06478	+	2.29695i
$457$	−33.0195	+	8.84754i	−1.54459	+	0.413870i	−0.927744	−	0.373217i	$-0.878255\pi$
$457$	−33.0195	+	8.84754i	−1.54459	+	0.413870i	−0.616842	+	0.787087i	$0.711588\pi$
$458$	55.4824	−	32.0328i	2.59252	−	1.49679i
$459$	−7.78712	−	7.89335i	−0.363472	−	0.368430i
$460$	−67.3903	−	67.3903i	−3.14209	−	3.14209i
$461$	6.89486	−	6.89486i	0.321126	−	0.321126i	−0.528073	−	0.849199i	$-0.677085\pi$
$461$	6.89486	−	6.89486i	0.321126	−	0.321126i	0.849199	+	0.528073i	$0.177085\pi$
$462$	−10.2721	−	12.2981i	−0.477902	−	0.572160i
$463$	−6.76311	−	25.2403i	−0.314308	−	1.17301i	−0.924632	−	0.380862i	$-0.875627\pi$
$463$	−6.76311	−	25.2403i	−0.314308	−	1.17301i	0.610324	−	0.792152i	$-0.291039\pi$
$464$	−2.18900	+	1.26382i	−0.101622	+	0.0586714i
$465$	2.60329	−	29.0013i	0.120725	−	1.34490i
$466$	12.6252	+	47.1177i	0.584849	+	2.18269i
$467$	−39.3270			−1.81984			−0.909918	−	0.414789i	$-0.863856\pi$
$467$	−39.3270			−1.81984			−0.909918	+	0.414789i	$0.863856\pi$
$468$	−53.7671	−	0.401687i	−2.48539	−	0.0185680i
$469$	−17.3302			−0.800236
$470$	4.55836	+	17.0120i	0.210262	+	0.784707i
$471$	−2.68480	+	1.24457i	−0.123709	+	0.0573467i
$472$	84.2268	−	48.6284i	3.87685	−	2.23830i
$473$	0.304903	+	1.13791i	0.0140194	+	0.0523213i
$474$	−39.6470	+	6.89856i	−1.82105	+	0.316861i
$475$	6.38077	−	6.38077i	0.292770	−	0.292770i
$476$	−16.9774	−	16.9774i	−0.778160	−	0.778160i
$477$	9.43758	−	3.38681i	0.432117	−	0.155071i
$478$	29.5284	−	17.0482i	1.35060	−	0.779769i
$479$	−6.11885	+	1.63954i	−0.279577	+	0.0749125i	−0.395883	−	0.918301i	$-0.629561\pi$
$479$	−6.11885	+	1.63954i	−0.279577	+	0.0749125i	0.116306	+	0.993213i	$0.462895\pi$
$480$	34.2379	−	48.6626i	1.56274	−	2.22113i
$481$	7.50790	−	3.47403i	0.342331	−	0.158402i
$482$	8.68923	+	5.01673i	0.395783	+	0.228506i
$483$	−27.4689	+	4.77957i	−1.24988	+	0.217478i
$484$	21.3839	−	37.0380i	0.971994	−	1.68354i
$485$	−0.860347	+	1.49016i	−0.0390663	+	0.0676649i
$486$	−13.6391	−	38.8318i	−0.618681	−	1.76145i
$487$	−0.371552	+	0.0995570i	−0.0168366	+	0.00451136i	−0.267228	−	0.963633i	$-0.586108\pi$
$487$	−0.371552	+	0.0995570i	−0.0168366	+	0.00451136i	0.250391	+	0.968145i	$0.419441\pi$
$488$	53.6684	+	53.6684i	2.42946	+	2.42946i
$489$	−2.14036	+	5.83954i	−0.0967906	+	0.264073i
$490$	6.67860	+	11.5677i	0.301709	+	0.522574i
$491$	10.8218			0.488380			0.244190	−	0.969727i	$-0.421478\pi$
$491$	10.8218			0.488380			0.244190	+	0.969727i	$0.421478\pi$
$492$	−56.0172	+	46.7889i	−2.52545	+	2.10941i
$493$	0.433788	−	0.250448i	0.0195368	−	0.0112796i
$494$	−35.5583	−	13.0612i	−1.59984	−	0.587653i
$495$	−8.09083	+	9.55430i	−0.363656	+	0.429434i
$496$	17.3796	−	64.8614i	0.780365	−	2.91236i
$497$	−6.31458	−	3.64573i	−0.283248	−	0.163533i
$498$	−10.4214	+	14.8120i	−0.466995	+	0.663743i
$499$	−29.7213	+	7.96381i	−1.33051	+	0.356509i	−0.852905	−	0.522066i	$-0.825162\pi$
$499$	−29.7213	+	7.96381i	−1.33051	+	0.356509i	−0.477605	+	0.878575i	$0.658495\pi$
$500$	35.3680	+	9.47682i	1.58170	+	0.423816i
$501$	0.582890	+	3.34995i	0.0260416	+	0.149665i
$502$	50.3808	+	13.4995i	2.24861	+	0.602512i
$503$	−12.5778	−	7.26179i	−0.560816	−	0.323787i	0.192657	−	0.981266i	$-0.438290\pi$
$503$	−12.5778	−	7.26179i	−0.560816	−	0.323787i	−0.753473	+	0.657479i	$0.771623\pi$
$504$	−17.9912	−	50.1337i	−0.801390	−	2.23313i
$505$	15.2078	+	4.07491i	0.676738	+	0.181331i
$506$	14.5336	+	25.1729i	0.646097	+	1.11907i
$507$	16.0512	−	15.7911i	0.712858	−	0.701309i
$508$	47.9860	−	83.1142i	2.12903	−	3.68759i
$509$	−16.4394	+	16.4394i	−0.728666	+	0.728666i	−0.970354	−	0.241688i	$-0.922299\pi$
$509$	−16.4394	+	16.4394i	−0.728666	+	0.728666i	0.241688	+	0.970354i	$0.422299\pi$
$510$	−15.1378	+	21.5155i	−0.670315	+	0.952723i
$511$			2.26121i			0.100030i
$512$	−22.4255	+	22.4255i	−0.991077	+	0.991077i
$513$	0.140081	−	20.6766i	0.00618471	−	0.912895i
$514$	−8.98097	−	33.5174i	−0.396133	−	1.47839i
$515$	13.6633	−	50.9923i	0.602079	−	2.24699i
$516$	−0.585794	+	6.52589i	−0.0257882	+	0.287286i
$517$		−	3.83045i		−	0.168463i
$518$	9.69580	+	9.69580i	0.426009	+	0.426009i
$519$	24.9667	+	17.5660i	1.09592	+	0.771062i
$520$	13.0177	+	75.1242i	0.570864	+	3.29441i
$521$			3.53656i			0.154940i	0.996995	+	0.0774698i	$0.0246841\pi$
$521$			3.53656i			0.154940i	−0.996995	+	0.0774698i	$0.975316\pi$
$522$	1.85290	−	0.153678i	0.0810992	−	0.00672632i
$523$	3.21981	+	5.57688i	0.140793	+	0.243860i	0.927795	−	0.373090i	$-0.121702\pi$
$523$	3.21981	+	5.57688i	0.140793	+	0.243860i	−0.787003	+	0.616950i	$0.788368\pi$
$524$	−0.443501			−0.0193744
$525$	−6.82331	+	5.69923i	−0.297794	+	0.248735i
$526$	−9.42048	+	35.1577i	−0.410753	+	1.53295i
$527$	−3.44405	+	12.8534i	−0.150025	+	0.559902i
$528$	−22.1593	+	18.5087i	−0.964360	+	0.805490i
$529$	27.5775			1.19902
$530$	−11.8948	−	20.6024i	−0.516677	−	0.894911i
$531$	−37.0696	+	3.07453i	−1.60868	+	0.133423i
$532$		−	44.7737i		−	1.94118i
$533$	2.75384	−	30.4405i	0.119282	−	1.31852i
$534$	8.10321	+	5.70124i	0.350660	+	0.246717i
$535$	−7.41229	−	7.41229i	−0.320461	−	0.320461i
$536$			60.0565i			2.59405i
$537$	1.58513	−	17.6587i	0.0684035	−	0.762031i
$538$	17.2509	−	64.3812i	0.743739	−	2.77567i
$539$	−0.751881	−	2.80606i	−0.0323858	−	0.120865i
$540$	−60.5385	+	34.4072i	−2.60516	+	1.48065i
$541$	−31.4961	+	31.4961i	−1.35412	+	1.35412i	−0.473127	+	0.880994i	$0.656875\pi$
$541$	−31.4961	+	31.4961i	−1.35412	+	1.35412i	−0.880994	+	0.473127i	$0.843125\pi$
$542$		−	50.4274i		−	2.16604i
$543$	16.0077	−	22.7518i	0.686956	−	0.976375i
$544$	−19.2273	+	19.2273i	−0.824363	+	0.824363i
$545$	−17.5122	+	30.3320i	−0.750141	+	1.29928i
$546$	33.7418	+	15.9487i	1.44402	+	0.682543i
$547$	10.2455	+	17.7458i	0.438067	+	0.758754i	0.997540	−	0.0700942i	$-0.0223300\pi$
$547$	10.2455	+	17.7458i	0.438067	+	0.758754i	−0.559474	+	0.828848i	$0.688997\pi$
$548$	6.80011	+	1.82208i	0.290486	+	0.0778355i
$549$	−9.80494	−	27.3222i	−0.418465	−	1.16608i
$550$	8.02667	+	4.63420i	0.342258	+	0.197603i
$551$	0.902248	+	0.241757i	0.0384371	+	0.0102992i
$552$	16.5632	+	95.1912i	0.704978	+	4.05161i
$553$	19.2400	+	5.15534i	0.818167	+	0.219227i
$554$	0.473061	−	0.126756i	0.0200984	−	0.00538536i
$555$	6.16484	−	8.76213i	0.261683	−	0.371932i
$556$	−34.2283	−	19.7617i	−1.45161	−	0.838085i
$557$	6.77282	−	25.2765i	0.286974	−	1.07100i	−0.660411	−	0.750904i	$-0.729618\pi$
$557$	6.77282	−	25.2765i	0.286974	−	1.07100i	0.947385	−	0.320096i	$-0.103715\pi$
$558$	−31.9199	+	37.6936i	−1.35128	+	1.59570i
$559$	−1.75748	−	2.10710i	−0.0743336	−	0.0891208i
$560$	−56.9047	+	32.8539i	−2.40466	+	1.38833i
$561$	4.39124	−	3.66782i	0.185398	−	0.154856i
$562$	24.6188			1.03848
$563$	−13.5515	−	23.4719i	−0.571128	−	0.989223i	−0.996450	−	0.0841810i	$-0.973173\pi$
$563$	−13.5515	−	23.4719i	−0.571128	−	0.989223i	0.425322	−	0.905042i	$-0.360161\pi$
$564$	7.33169	−	20.0030i	0.308720	−	0.842277i
$565$	−26.5170	−	26.5170i	−1.11558	−	1.11558i
$566$	29.3607	−	7.86717i	1.23412	−	0.330682i
$567$	−1.95873	+	20.2770i	−0.0822588	+	0.851556i
$568$	−12.6340	+	21.8827i	−0.530110	+	0.918177i
$569$	7.99380	−	13.8457i	0.335118	−	0.580441i	−0.648390	−	0.761309i	$-0.724557\pi$
$569$	7.99380	−	13.8457i	0.335118	−	0.580441i	0.983507	+	0.180868i	$0.0578906\pi$
$570$	−48.3319	+	8.40973i	−2.02440	+	0.352245i
$571$	11.0928	+	6.40445i	0.464221	+	0.268018i	0.713817	−	0.700332i	$-0.246965\pi$
$571$	11.0928	+	6.40445i	0.464221	+	0.268018i	−0.249597	+	0.968350i	$0.580298\pi$
$572$	2.49979	−	27.6323i	0.104522	−	1.15537i
$573$	−5.95349	+	8.46173i	−0.248711	+	0.353494i
$574$	48.9347	−	13.1120i	2.04250	−	0.547285i
$575$	13.9666	−	8.06360i	0.582446	−	0.336275i
$576$	−34.1879	+	12.2688i	−1.42450	+	0.511200i
$577$	3.19790	+	3.19790i	0.133130	+	0.133130i	0.770532	−	0.637402i	$-0.219991\pi$
$577$	3.19790	+	3.19790i	0.133130	+	0.133130i	−0.637402	+	0.770532i	$0.719991\pi$
$578$	−23.2369	+	23.2369i	−0.966526	+	0.966526i
$579$	3.19176	−	0.555364i	0.132645	−	0.0230801i
$580$	−0.814150	−	3.03845i	−0.0338057	−	0.126165i
$581$	7.76323	−	4.48211i	0.322073	−	0.185949i
$582$	2.64815	−	1.22758i	0.109769	−	0.0508849i
$583$	1.33912	+	4.99768i	0.0554608	+	0.206983i
$584$	7.83605			0.324258
$585$	7.75743	−	28.1094i	0.320730	−	1.16218i
$586$	28.2119			1.16542
$587$	3.01827	+	11.2643i	0.124577	+	0.464928i	0.999824	−	0.0187477i	$-0.00596794\pi$
$587$	3.01827	+	11.2643i	0.124577	+	0.464928i	−0.875247	+	0.483676i	$0.839301\pi$
$588$	1.44455	−	16.0926i	0.0595722	−	0.663649i
$589$	−21.4902	+	12.4074i	−0.885487	+	0.511236i
$590$	22.8415	+	85.2455i	0.940368	+	3.50950i
$591$	23.1371	+	27.7006i	0.951735	+	1.13945i
$592$	17.4703	−	17.4703i	0.718026	−	0.718026i
$593$	25.2582	+	25.2582i	1.03723	+	1.03723i	0.999280	+	0.0379511i	$0.0120831\pi$
$593$	25.2582	+	25.2582i	1.03723	+	1.03723i	0.0379511	+	0.999280i	$0.487917\pi$
$594$	20.5508	−	5.35760i	0.843207	−	0.219825i
$595$	11.2766	−	6.51057i	0.462297	−	0.266907i
$596$	−79.3054	+	21.2498i	−3.24848	+	0.870427i
$597$	5.04968	+	10.8932i	0.206669	+	0.445830i
$598$	−55.3424	−	38.9954i	−2.26312	−	1.59464i
$599$	−10.2097	−	5.89457i	−0.417157	−	0.240846i	0.276703	−	0.960955i	$-0.410758\pi$
$599$	−10.2097	−	5.89457i	−0.417157	−	0.240846i	−0.693860	+	0.720110i	$0.744091\pi$
$600$	19.7502	+	23.6456i	0.806299	+	0.965328i
$601$	−12.9491	+	22.4285i	−0.528204	+	0.914877i	0.471255	+	0.881997i	$0.343801\pi$
$601$	−12.9491	+	22.4285i	−0.528204	+	0.914877i	−0.999459	+	0.0328796i	$0.989532\pi$
$602$	2.27394	−	3.93858i	0.0926790	−	0.160525i
$603$	9.80114	−	20.7732i	0.399133	−	0.845948i
$604$	−41.8859	+	11.2233i	−1.70431	+	0.456669i
$605$	16.4007	+	16.4007i	0.666784	+	0.666784i
$606$	−17.1209	−	20.4977i	−0.695488	−	0.832662i
$607$	20.3558	+	35.2574i	0.826218	+	1.43105i	0.900985	+	0.433851i	$0.142846\pi$
$607$	20.3558	+	35.2574i	0.826218	+	1.43105i	−0.0747662	+	0.997201i	$0.523821\pi$
$608$	−50.7070			−2.05644
$609$	−0.864056	−	0.316702i	−0.0350133	−	0.0128334i
$610$	−59.6448	+	34.4359i	−2.41495	+	1.39427i
$611$	3.74652	+	8.09680i	0.151568	+	0.327562i
$612$	29.9519	−	10.7487i	1.21073	−	0.434488i
$613$	−8.59441	+	32.0748i	−0.347125	+	1.29549i	0.542985	+	0.839742i	$0.317294\pi$
$613$	−8.59441	+	32.0748i	−0.347125	+	1.29549i	−0.890110	+	0.455746i	$0.849373\pi$
$614$	36.5094	+	21.0787i	1.47340	+	0.850667i
$615$	−16.6474	−	35.9120i	−0.671289	−	1.44811i
$616$	26.5483	−	7.11360i	1.06966	−	0.286615i
$617$	−25.7499	−	6.89968i	−1.03665	−	0.277771i	−0.299928	−	0.953962i	$-0.596963\pi$
$617$	−25.7499	−	6.89968i	−1.03665	−	0.277771i	−0.736726	+	0.676191i	$0.763629\pi$
$618$	−68.7295	+	57.4069i	−2.76471	+	2.30925i
$619$	−27.4217	−	7.34762i	−1.10217	−	0.295326i	−0.338523	−	0.940958i	$-0.609927\pi$
$619$	−27.4217	−	7.34762i	−1.10217	−	0.295326i	−0.763648	+	0.645632i	$0.776594\pi$
$620$	72.3712	+	41.7835i	2.90650	+	1.67807i
$621$	9.80598	−	35.6291i	0.393500	−	1.42975i
$622$	16.7626	+	4.49153i	0.672120	+	0.180094i
$623$	−2.45202	−	4.24703i	−0.0982382	−	0.170154i
$624$	28.7371	−	60.7975i	1.15041	−	2.43385i
$625$	−15.5980	+	27.0165i	−0.623920	+	1.08066i
$626$	−40.3127	+	40.3127i	−1.61122	+	1.61122i
$627$	10.6269	+	0.953916i	0.424396	+	0.0380958i
$628$		−	8.49290i		−	0.338903i
$629$	−3.46204	+	3.46204i	−0.138041	+	0.138041i
$630$	48.1675	−	3.99498i	1.91904	−	0.159164i
$631$	−4.20481	−	15.6925i	−0.167391	−	0.624710i	−0.997723	−	0.0674422i	$-0.978516\pi$
$631$	−4.20481	−	15.6925i	−0.167391	−	0.624710i	0.830333	−	0.557268i	$-0.188150\pi$
$632$	17.8654	−	66.6746i	0.710647	−	2.65217i
$633$	−3.48664	−	2.45312i	−0.138581	−	0.0975029i
$634$		−	16.2358i		−	0.644805i
$635$	36.8037	+	36.8037i	1.46051	+	1.46051i
$636$	−2.57279	+	28.6615i	−0.102018	+	1.13650i
$637$	4.33390	+	5.19604i	0.171715	+	0.205874i
$638$			0.959398i			0.0379829i
$639$	7.94123	−	5.50723i	0.314150	−	0.217863i
$640$	8.73675	+	15.1325i	0.345350	+	0.598164i
$641$	39.3794			1.55539			0.777697	−	0.628640i	$-0.216388\pi$
$641$	39.3794			1.55539			0.777697	+	0.628640i	$0.216388\pi$
$642$	3.04822	+	17.5186i	0.120304	+	0.691403i
$643$	−8.38027	+	31.2756i	−0.330485	+	1.23339i	0.578196	+	0.815898i	$0.303757\pi$
$643$	−8.38027	+	31.2756i	−0.330485	+	1.23339i	−0.908681	+	0.417490i	$0.862910\pi$
$644$	20.7105	−	77.2925i	0.816106	−	3.04575i
$645$	−3.33635	−	1.22287i	−0.131369	−	0.0481505i
$646$	22.4194			0.882081
$647$	17.9872	+	31.1547i	0.707149	+	1.22482i	0.965910	+	0.258877i	$0.0833524\pi$
$647$	17.9872	+	31.1547i	0.707149	+	1.22482i	−0.258761	+	0.965941i	$0.583314\pi$
$648$	70.2684	+	6.78781i	2.76040	+	0.266650i
$649$		−	19.1940i		−	0.753429i
$650$	−21.4994	−	1.94497i	−0.843277	−	0.0762882i
$651$	22.1806	−	10.2821i	0.869325	−	0.402985i
$652$	−12.6215	−	12.6215i	−0.494297	−	0.494297i
$653$		−	49.6381i		−	1.94249i	−0.238085	−	0.971244i	$-0.576520\pi$
$653$		−	49.6381i		−	1.94249i	0.238085	−	0.971244i	$-0.423480\pi$
$654$	53.9027	−	24.9872i	2.10776	−	0.977077i
$655$	0.0622519	−	0.232327i	0.00243238	−	0.00907777i
$656$	−23.6258	−	88.1728i	−0.922433	−	3.44257i
$657$	−2.71044	−	1.27883i	−0.105744	−	0.0498920i
$658$	−10.4563	+	10.4563i	−0.407630	+	0.407630i
$659$		−	14.9919i		−	0.584002i	−0.956418	−	0.292001i	$-0.905679\pi$
$659$		−	14.9919i		−	0.584002i	0.956418	−	0.292001i	$-0.0943210\pi$
$660$	−15.1117	−	32.5991i	−0.588221	−	1.26892i
$661$	−4.74576	+	4.74576i	−0.184589	+	0.184589i	−0.793352	−	0.608763i	$-0.791666\pi$
$661$	−4.74576	+	4.74576i	−0.184589	+	0.184589i	0.608763	+	0.793352i	$0.291666\pi$
$662$	46.6509	−	80.8017i	1.81314	−	3.14045i
$663$	−5.69475	+	12.0481i	−0.221166	+	0.467908i
$664$	−15.5324	−	26.9029i	−0.602773	−	1.04403i
$665$	23.4546	+	6.28464i	0.909530	+	0.243708i
$666$	−17.1055	+	6.13855i	−0.662825	+	0.237864i
$667$	1.44572	+	0.834686i	0.0559784	+	0.0323192i
$668$	−9.42616	−	2.52573i	−0.364709	−	0.0977235i
$669$	−32.8290	−	12.0328i	−1.26924	−	0.465215i
$670$	−52.6395	−	14.1047i	−2.03364	−	0.544913i
$671$	14.4685	−	3.87682i	0.558549	−	0.149663i
$672$	49.7574	+	4.46645i	1.91943	+	0.172297i
$673$	33.2536	+	19.1990i	1.28183	+	0.740067i	0.977183	−	0.212398i	$-0.0681272\pi$
$673$	33.2536	+	19.1990i	1.28183	+	0.740067i	0.304650	+	0.952464i	$0.401461\pi$
$674$	−5.54067	+	20.6781i	−0.213419	+	0.796490i
$675$	−2.97253	−	11.4021i	−0.114413	−	0.438866i
$676$	21.7428	+	60.8542i	0.836262	+	2.34055i
$677$	27.2519	−	15.7339i	1.04737	−	0.604702i	0.125461	−	0.992099i	$-0.459959\pi$
$677$	27.2519	−	15.7339i	1.04737	−	0.604702i	0.921913	+	0.387397i	$0.126626\pi$
$678$	10.9048	+	62.6716i	0.418798	+	2.40689i
$679$	−1.44472			−0.0554434
$680$	−22.5618	−	39.0783i	−0.865207	−	1.49858i
$681$	−33.9750	+	5.91162i	−1.30192	+	0.226534i
$682$	−18.0223	−	18.0223i	−0.690111	−	0.690111i
$683$	−38.2622	+	10.2523i	−1.46406	+	0.392295i	−0.900891	−	0.434045i	$-0.857086\pi$
$683$	−38.2622	+	10.2523i	−1.46406	+	0.392295i	−0.563173	+	0.826339i	$0.690419\pi$
$684$	53.6686	+	25.3218i	2.05207	+	0.968204i
$685$	−1.90899	+	3.30647i	−0.0729387	+	0.126334i
$686$	−26.5241	+	45.9411i	−1.01269	+	1.75404i
$687$	14.4636	−	39.4610i	0.551822	−	1.50553i
$688$	−7.09671	−	4.09729i	−0.270560	−	0.156208i
$689$	−7.71881	−	9.25430i	−0.294063	−	0.352561i
$690$	−87.3251	−	7.83870i	−3.32441	−	0.298414i
$691$	−13.8461	+	3.71006i	−0.526731	+	0.141137i	−0.512378	−	0.858760i	$-0.671235\pi$
$691$	−13.8461	+	3.71006i	−0.526731	+	0.141137i	−0.0143528	+	0.999897i	$0.504569\pi$
$692$	−75.8736	+	43.8056i	−2.88428	+	1.66524i
$693$	−10.3438	−	1.87210i	−0.392929	−	0.0711153i
$694$	26.3839	+	26.3839i	1.00152	+	1.00152i
$695$	15.1566	−	15.1566i	0.574923	−	0.574923i
$696$	−1.09751	+	2.99431i	−0.0416008	+	0.113499i
$697$	4.68186	+	17.4729i	0.177338	+	0.661835i
$698$	33.5015	−	19.3421i	1.26805	−	0.732109i
$699$	26.1717	+	18.4139i	0.989906	+	0.696476i
$700$	−6.60377	−	24.6456i	−0.249599	−	0.931516i
$701$	−15.9193			−0.601265			−0.300633	−	0.953740i	$-0.597198\pi$
$701$	−15.9193			−0.601265			−0.300633	+	0.953740i	$0.597198\pi$
$702$	−38.2000	+	31.4254i	−1.44176	+	1.18607i
$703$	−9.13025			−0.344354
$704$	−4.85101	−	18.1042i	−0.182829	−	0.682328i
$705$	9.44941	+	6.64840i	0.355885	+	0.250393i
$706$	−72.5461	+	41.8845i	−2.73031	+	1.57634i
$707$	3.42137	+	12.7687i	0.128674	+	0.480217i
$708$	36.7383	−	100.233i	1.38071	−	3.76697i
$709$	36.4193	−	36.4193i	1.36776	−	1.36776i	0.504126	−	0.863630i	$-0.331815\pi$
$709$	36.4193	−	36.4193i	1.36776	−	1.36776i	0.863630	−	0.504126i	$-0.168185\pi$
$710$	−16.2130	−	16.2130i	−0.608462	−	0.608462i
$711$	−17.0607	+	20.1467i	−0.639827	+	0.755560i
$712$	−14.7177	+	8.49729i	−0.551570	+	0.318449i
$713$	−42.8375	+	11.4783i	−1.60428	+	0.429864i
$714$	−21.9996	−	1.97478i	−0.823313	−	0.0739044i
$715$	14.1243	+	5.18811i	0.528217	+	0.194024i
$716$	44.0665	+	25.4418i	1.64684	+	0.950805i
$717$	7.69773	−	21.0016i	0.287477	−	0.784321i
$718$	−23.3914	+	40.5151i	−0.872959	+	1.51201i
$719$	−7.69872	+	13.3346i	−0.287114	+	0.497296i	−0.973120	−	0.230300i	$-0.926029\pi$
$719$	−7.69872	+	13.3346i	−0.287114	+	0.497296i	0.686006	+	0.727596i	$0.259362\pi$
$720$	−7.19833	−	86.7903i	−0.268266	−	3.23448i
$721$	42.8140	−	11.4720i	1.59448	−	0.427239i
$722$	−5.90906	−	5.90906i	−0.219912	−	0.219912i
$723$	6.48469	−	1.12833i	0.241168	−	0.0419632i
$724$	39.9196	+	69.1427i	1.48360	+	2.56967i
$725$	0.532298			0.0197691
$726$	−6.74461	−	38.7622i	−0.250316	−	1.43860i
$727$	0.433980	−	0.250558i	0.0160954	−	0.00929270i	−0.491931	−	0.870634i	$-0.663709\pi$
$727$	0.433980	−	0.250558i	0.0160954	−	0.00929270i	0.508026	+	0.861342i	$0.330375\pi$
$728$	−49.1601	+	41.0033i	−1.82199	+	1.51968i
$729$	−23.1976	−	13.8156i	−0.859171	−	0.511688i
$730$	−1.84035	+	6.86829i	−0.0681145	+	0.254207i
$731$	1.40633	+	0.811948i	0.0520152	+	0.0300310i
$732$	82.9762	+	7.44833i	3.06689	+	0.275298i
$733$	5.49507	−	1.47240i	0.202965	−	0.0543844i	−0.155904	−	0.987772i	$-0.549829\pi$
$733$	5.49507	−	1.47240i	0.202965	−	0.0543844i	0.358869	+	0.933388i	$0.383162\pi$
$734$	50.8697	+	13.6305i	1.87763	+	0.503110i
$735$	8.22733	+	3.01556i	0.303470	+	0.111231i
$736$	−87.5353	−	23.4550i	−3.22659	−	0.864563i
$737$	10.2644	+	5.92618i	0.378096	+	0.218294i
$738$	−11.9582	+	66.0719i	−0.440187	+	2.43214i
$739$	−9.70292	−	2.59989i	−0.356928	−	0.0956385i	0.0758992	−	0.997115i	$-0.475817\pi$
$739$	−9.70292	−	2.59989i	−0.356928	−	0.0956385i	−0.432827	+	0.901477i	$0.642484\pi$
$740$	15.3737	+	26.6281i	0.565149	+	0.978867i
$741$	−23.3961	+	8.37763i	−0.859476	+	0.307760i
$742$	9.98708	−	17.2981i	0.366637	−	0.635034i
$743$	20.6248	−	20.6248i	0.756649	−	0.756649i	−0.219062	−	0.975711i	$-0.570300\pi$
$743$	20.6248	−	20.6248i	0.756649	−	0.756649i	0.975711	+	0.219062i	$0.0702997\pi$
$744$	−35.6316	−	76.8650i	−1.30632	−	2.81801i
$745$		−	44.5267i		−	1.63133i
$746$	44.5607	−	44.5607i	1.63148	−	1.63148i
$747$	0.982034	+	11.8404i	0.0359307	+	0.433217i
$748$	4.24995	+	15.8610i	0.155394	+	0.579937i
$749$	2.27795	−	8.50144i	0.0832346	−	0.310636i
$750$	30.5610	−	14.1669i	1.11593	−	0.517302i
$751$		−	14.3792i		−	0.524703i	−0.964972	−	0.262351i	$-0.915502\pi$
$751$		−	14.3792i		−	0.524703i	0.964972	−	0.262351i	$-0.0844980\pi$
$752$	18.8407	+	18.8407i	0.687048	+	0.687048i
$753$	31.0434	−	14.3905i	1.13128	−	0.524420i
$754$	−0.938377	−	2.02798i	−0.0341737	−	0.0738545i
$755$		−	23.5172i		−	0.855878i
$756$	−50.4331	−	29.5749i	−1.83423	−	1.07563i
$757$	−18.2836	−	31.6681i	−0.664529	−	1.15100i	−0.979413	−	0.201868i	$-0.935299\pi$
$757$	−18.2836	−	31.6681i	−0.664529	−	1.15100i	0.314883	−	0.949130i	$-0.398035\pi$
$758$	38.4164			1.39535
$759$	17.9038	+	6.56229i	0.649868	+	0.238196i
$760$	21.7789	−	81.2800i	0.790004	−	2.94834i
$761$	−2.70743	+	10.1043i	−0.0981443	+	0.366280i	−0.997477	−	0.0709847i	$-0.977386\pi$
$761$	−2.70743	+	10.1043i	−0.0981443	+	0.366280i	0.899333	+	0.437264i	$0.144053\pi$
$762$	−15.1351	−	86.9835i	−0.548286	−	3.15108i
$763$	−29.4071			−1.06461
$764$	−14.8467	−	25.7152i	−0.537133	−	0.930342i
$765$	1.42647	+	17.1990i	0.0515742	+	0.621830i
$766$			10.9925i			0.397177i
$767$	18.7734	+	40.5722i	0.677868	+	1.46498i
$768$	−1.09979	+	12.2519i	−0.0396852	+	0.442103i
$769$	−4.45261	−	4.45261i	−0.160565	−	0.160565i	0.622252	−	0.782817i	$-0.286218\pi$
$769$	−4.45261	−	4.45261i	−0.160565	−	0.160565i	−0.782817	+	0.622252i	$0.786218\pi$
$770$			24.9403i			0.898784i
$771$	−18.6174	−	13.0988i	−0.670489	−	0.471741i
$772$	−2.40646	+	8.98102i	−0.0866103	+	0.323234i
$773$	−1.54426	−	5.76325i	−0.0555431	−	0.207290i	0.932578	−	0.360970i	$-0.117554\pi$
$773$	−1.54426	−	5.76325i	−0.0555431	−	0.207290i	−0.988121	+	0.153680i	$0.950888\pi$
$774$	3.43501	+	4.95317i	0.123469	+	0.178038i
$775$	−9.99924	+	9.99924i	−0.359183	+	0.359183i
$776$			5.00657i			0.179726i
$777$	8.95925	+	0.804224i	0.321411	+	0.0288514i
$778$	−0.711356	+	0.711356i	−0.0255033	+	0.0255033i
$779$	−16.8666	+	29.2138i	−0.604308	+	1.04669i
$780$	63.8279	+	54.1274i	2.28540	+	1.93807i
$781$	2.49336	+	4.31862i	0.0892194	+	0.154533i
$782$	38.7025	+	10.3703i	1.38400	+	0.370842i
$783$	0.868288	−	0.856602i	0.0310301	−	0.0306125i
$784$	17.5003	+	10.1038i	0.625009	+	0.360849i
$785$	4.44899	+	1.19210i	0.158791	+	0.0425480i
$786$	−0.313140	+	0.261553i	−0.0111693	+	0.00932929i
$787$	15.7307	+	4.21503i	0.560739	+	0.150249i	0.528046	−	0.849216i	$-0.322925\pi$
$787$	15.7307	+	4.21503i	0.560739	+	0.150249i	0.0326929	+	0.999465i	$0.489592\pi$
$788$	−100.054	+	26.8093i	−3.56426	+	0.955041i
$789$	10.0423	+	21.6633i	0.357514	+	0.771234i
$790$	54.2444	+	31.3180i	1.92993	+	1.11425i
$791$	8.14925	−	30.4134i	0.289754	−	1.08138i
$792$	−6.48762	+	35.8456i	−0.230527	+	1.27372i
$793$	−26.7916	+	22.3463i	−0.951397	+	0.793539i
$794$	−35.4909	+	20.4907i	−1.25952	+	0.727186i
$795$	−14.6531	−	5.37081i	−0.519693	−	0.190483i
$796$	−34.4588			−1.22136
$797$	12.0486	+	20.8688i	0.426784	+	0.739212i	0.996585	−	0.0825705i	$-0.0263130\pi$
$797$	12.0486	+	20.8688i	0.426784	+	0.739212i	−0.569801	+	0.821783i	$0.692980\pi$
$798$	−26.4051	−	31.6131i	−0.934731	−	1.11909i
$799$	−3.73360	−	3.73360i	−0.132085	−	0.132085i
$800$	−27.9116	+	7.47890i	−0.986825	+	0.264419i
$801$	6.47751	−	0.537241i	0.228872	−	0.0189825i
$802$	44.3270	−	76.7766i	1.56524	−	2.71108i
$803$	0.773236	−	1.33928i	0.0272869	−	0.0472623i
$804$	42.2589	+	50.5938i	1.49036	+	1.78431i
$805$	37.5825	+	21.6983i	1.32461	+	0.764764i
$806$	55.7230	+	20.4682i	1.96276	+	0.720960i
$807$	−18.3895	−	39.6701i	−0.647342	−	1.39645i
$808$	44.2490	−	11.8565i	1.55667	−	0.417109i
$809$	−34.9272	+	20.1652i	−1.22797	+	0.708971i	−0.966606	−	0.256268i	$-0.917507\pi$
$809$	−34.9272	+	20.1652i	−1.22797	+	0.708971i	−0.261368	+	0.965239i	$0.584174\pi$
$810$	−22.4526	+	59.9961i	−0.788903	+	2.10805i
$811$	30.0454	+	30.0454i	1.05504	+	1.05504i	0.998395	+	0.0566424i	$0.0180395\pi$
$811$	30.0454	+	30.0454i	1.05504	+	1.05504i	0.0566424	+	0.998395i	$0.481961\pi$
$812$	1.86756	−	1.86756i	0.0655385	−	0.0655385i
$813$	−21.2069	−	25.3897i	−0.743760	−	0.890455i
$814$	−2.42714	−	9.05823i	−0.0850714	−	0.317491i
$815$	8.38337	−	4.84014i	0.293657	−	0.169543i
$816$	−3.55825	+	39.6398i	−0.124564	+	1.38767i
$817$	0.783772	+	2.92508i	0.0274207	+	0.102335i
$818$	57.3064			2.00367
$819$	23.6958	−	6.15992i	0.827999	−	0.215245i
$820$	113.601			3.96713
$821$	−7.19002	−	26.8335i	−0.250934	−	0.936497i	−0.970308	−	0.241874i	$-0.922238\pi$
$821$	−7.19002	−	26.8335i	−0.250934	−	0.936497i	0.719374	−	0.694623i	$-0.244429\pi$
$822$	5.87588	−	2.72383i	0.204945	−	0.0950045i
$823$	21.9400	−	12.6671i	0.764781	−	0.441547i	−0.0662284	−	0.997804i	$-0.521097\pi$
$823$	21.9400	−	12.6671i	0.764781	−	0.441547i	0.831010	+	0.556258i	$0.187763\pi$
$824$	−39.7552	−	148.368i	−1.38494	−	5.16866i
$825$	5.99024	−	1.04230i	0.208553	−	0.0362881i
$826$	−52.3955	+	52.3955i	−1.82307	+	1.82307i
$827$	−6.21133	−	6.21133i	−0.215989	−	0.215989i	0.590817	−	0.806806i	$-0.298806\pi$
$827$	−6.21133	−	6.21133i	−0.215989	−	0.215989i	−0.806806	+	0.590817i	$0.798806\pi$
$828$	80.9350	+	68.5378i	2.81269	+	2.38185i
$829$	−27.6454	+	15.9611i	−0.960166	+	0.554352i	−0.896224	−	0.443601i	$-0.853701\pi$
$829$	−27.6454	+	15.9611i	−0.960166	+	0.554352i	−0.0639420	+	0.997954i	$0.520367\pi$
$830$	27.2282	−	7.29578i	0.945106	−	0.253240i
$831$	0.184875	−	0.262764i	0.00641324	−	0.00911517i
$832$	27.9616	+	33.5240i	0.969394	+	1.16223i
$833$	−3.46798	−	2.00224i	−0.120158	−	0.0693734i
$834$	−35.8218	+	6.23298i	−1.24041	+	0.215830i
$835$	2.64620	−	4.58335i	0.0915755	−	0.158613i
$836$	−15.3106	+	26.5188i	−0.529529	+	0.917172i
$837$	−0.219519	+	32.4021i	−0.00758768	+	1.11998i
$838$	−80.6434	+	21.6083i	−2.78578	+	0.746447i
$839$	−15.8259	−	15.8259i	−0.546369	−	0.546369i	0.379019	−	0.925389i	$-0.376261\pi$
$839$	−15.8259	−	15.8259i	−0.546369	−	0.546369i	−0.925389	+	0.379019i	$0.876261\pi$
$840$	−28.5304	+	77.8394i	−0.984394	+	2.68571i
$841$	−14.4725	−	25.0670i	−0.499050	−	0.864380i
$842$	−17.6880			−0.609568
$843$	12.3953	−	10.3533i	0.426918	−	0.356587i
$844$	10.5959	−	6.11753i	0.364725	−	0.210574i
$845$	−34.9303	+	2.84814i	−1.20164	+	0.0979791i
$846$	−6.62004	−	18.4472i	−0.227602	−	0.634229i
$847$	−5.04029	+	18.8106i	−0.173186	+	0.646340i
$848$	−31.1685	−	17.9952i	−1.07033	−	0.617956i
$849$	11.4743	−	16.3085i	0.393797	−	0.559707i
$850$	12.3407	−	3.30669i	0.423284	−	0.113419i
$851$	−15.7615	−	4.22328i	−0.540297	−	0.144772i
$852$	4.75448	+	27.3247i	0.162886	+	0.936128i
$853$	29.4707	+	7.89664i	1.00906	+	0.270376i	0.725235	−	0.688501i	$-0.241731\pi$
$853$	29.4707	+	7.89664i	1.00906	+	0.270376i	0.283822	+	0.958877i	$0.408398\pi$
$854$	−50.0788	−	28.9130i	−1.71366	−	0.989382i
$855$	−20.7980	+	24.5599i	−0.711276	+	0.839932i
$856$	−29.4610	−	7.89406i	−1.00696	−	0.269814i
$857$	1.77173	+	3.06872i	0.0605211	+	0.104826i	0.894698	−	0.446671i	$-0.147390\pi$
$857$	1.77173	+	3.06872i	0.0605211	+	0.104826i	−0.834177	+	0.551496i	$0.814057\pi$
$858$	−14.5310	−	20.9844i	−0.496082	−	0.716397i
$859$	17.6074	−	30.4970i	0.600758	−	1.04054i	−0.391948	−	0.919987i	$-0.628199\pi$
$859$	17.6074	−	30.4970i	0.600758	−	1.04054i	0.992706	−	0.120557i	$-0.0384679\pi$
$860$	7.21115	−	7.21115i	0.245898	−	0.245898i
$861$	19.1240	−	27.1810i	0.651743	−	0.926326i
$862$		−	17.9583i		−	0.611662i
$863$	5.22630	−	5.22630i	0.177905	−	0.177905i	−0.612537	−	0.790442i	$-0.709851\pi$
$863$	5.22630	−	5.22630i	0.177905	−	0.177905i	0.790442	+	0.612537i	$0.209851\pi$
$864$	−33.4942	+	57.1165i	−1.13949	+	1.94314i
$865$	−12.2975	−	45.8950i	−0.418129	−	1.56048i
$866$	−16.8674	+	62.9501i	−0.573178	+	2.13913i
$867$	−1.92740	+	21.4717i	−0.0654578	+	0.729216i
$868$			70.1643i			2.38153i
$869$	−9.63266	−	9.63266i	−0.326766	−	0.326766i
$870$	−2.36676	−	1.66520i	−0.0802406	−	0.0564555i
$871$	−27.4933	−	2.48722i	−0.931576	−	0.0842762i
$872$			101.908i			3.45104i
$873$	0.817066	−	1.73174i	0.0276535	−	0.0586105i
$874$	37.3595	+	64.7085i	1.26370	+	2.18880i
$875$	−16.6728			−0.563644
$876$	6.60137	−	5.51385i	0.223040	−	0.186296i
$877$	−5.35167	+	19.9727i	−0.180713	+	0.674430i	0.814795	+	0.579750i	$0.196850\pi$
$877$	−5.35167	+	19.9727i	−0.180713	+	0.674430i	−0.995508	+	0.0946807i	$0.969817\pi$
$878$	−15.8175	+	59.0316i	−0.533813	+	1.99222i
$879$	14.2044	−	11.8643i	0.479102	−	0.400174i
$880$	44.9384			1.51487
$881$	−22.9876	−	39.8157i	−0.774472	−	1.34142i	−0.935091	−	0.354408i	$-0.884682\pi$
$881$	−22.9876	−	39.8157i	−0.774472	−	1.34142i	0.160619	−	0.987016i	$-0.448651\pi$
$882$	−8.47063	−	12.2144i	−0.285221	−	0.411279i
$883$			7.05482i			0.237414i	0.992929	+	0.118707i	$0.0378749\pi$
$883$			7.05482i			0.237414i	−0.992929	+	0.118707i	$0.962125\pi$
$884$	−24.4971	−	29.3702i	−0.823925	−	0.987828i
$885$	47.3499	+	33.3144i	1.59165	+	1.11985i
$886$	−45.2519	−	45.2519i	−1.52027	−	1.52027i
$887$		−	20.8953i		−	0.701597i	−0.936451	−	0.350798i	$-0.885910\pi$
$887$		−	20.8953i		−	0.701597i	0.936451	−	0.350798i	$-0.114090\pi$
$888$	2.78697	−	31.0476i	0.0935247	−	1.04189i
$889$	−11.3105	+	42.2115i	−0.379343	+	1.41573i
$890$	−3.99130	−	14.8957i	−0.133789	−	0.499306i
$891$	8.09399	−	11.3400i	0.271159	−	0.379904i
$892$	70.9562	−	70.9562i	2.37579	−	2.37579i
$893$		−	9.84641i		−	0.329497i
$894$	−43.4627	+	61.7738i	−1.45361	+	2.06603i
$895$	−19.5130	+	19.5130i	−0.652249	+	0.652249i
$896$	−7.33552	+	12.7055i	−0.245063	+	0.424461i
$897$	−44.2636	+	3.64018i	−1.47792	+	0.121542i
$898$	−8.17146	−	14.1534i	−0.272685	−	0.472304i
$899$	−1.41390	−	0.378854i	−0.0471563	−	0.0126355i
$900$	33.2766	+	6.02265i	1.10922	+	0.200755i
$901$	6.17657	+	3.56605i	0.205772	+	0.118802i
$902$	−33.4671	−	8.96748i	−1.11433	−	0.298584i
$903$	−0.511442	−	2.93933i	−0.0170197	−	0.0978148i
$904$	−105.395	−	28.2406i	−3.50539	−	0.939267i
$905$	−41.8236	+	11.2066i	−1.39026	+	0.372520i
$906$	−22.9552	+	32.6264i	−0.762636	+	1.08394i
$907$	2.71819	+	1.56935i	0.0902561	+	0.0521094i	0.544449	−	0.838794i	$-0.316739\pi$
$907$	2.71819	+	1.56935i	0.0902561	+	0.0521094i	−0.454193	+	0.890904i	$0.650072\pi$
$908$	25.6158	−	95.5993i	0.850089	−	3.17258i
$909$	−17.2404	−	3.12030i	−0.571827	−	0.103494i
$910$	−24.3938	−	52.7187i	−0.808646	−	1.74761i
$911$	18.1814	−	10.4970i	0.602375	−	0.347782i	−0.167600	−	0.985855i	$-0.553602\pi$
$911$	18.1814	−	10.4970i	0.602375	−	0.347782i	0.769975	+	0.638074i	$0.220268\pi$
$912$	−56.9618	+	47.5779i	−1.88619	+	1.57546i
$913$	−6.13074			−0.202898
$914$	−45.1275	−	78.1631i	−1.49268	−	2.58541i
$915$	−15.5487	+	42.4214i	−0.514025	+	1.40241i
$916$	85.2905	+	85.2905i	2.81808	+	2.81808i
$917$	0.195066	−	0.0522677i	0.00644164	−	0.00172603i
$918$	14.8090	−	25.2533i	0.488770	−	0.833482i
$919$	21.7742	−	37.7141i	0.718266	−	1.24407i	−0.243420	−	0.969921i	$-0.578269\pi$
$919$	21.7742	−	37.7141i	0.718266	−	1.24407i	0.961686	−	0.274153i	$-0.0883973\pi$
$920$	75.1936	−	130.239i	2.47906	−	4.29386i
$921$	27.2466	−	4.74090i	0.897807	−	0.156218i
$922$	22.2954	+	12.8723i	0.734261	+	0.423926i
$923$	−9.49446	−	6.68998i	−0.312514	−	0.220203i
$924$	17.3598	−	24.6735i	0.571094	−	0.811699i
$925$	−5.02573	+	1.34664i	−0.165245	+	0.0442773i
$926$	59.7483	−	34.4957i	1.96345	−	1.13360i
$927$	−10.4625	+	57.8076i	−0.343633	+	1.89865i
$928$	−2.11505	−	2.11505i	−0.0694299	−	0.0694299i
$929$	−21.2658	+	21.2658i	−0.697707	+	0.697707i	−0.963916	−	0.266208i	$-0.914229\pi$
$929$	−21.2658	+	21.2658i	−0.697707	+	0.697707i	0.266208	+	0.963916i	$0.414229\pi$
$930$	75.7405	−	13.1788i	2.48363	−	0.432150i
$931$	−1.93276	−	7.21314i	−0.0633435	−	0.236401i
$932$	−79.5357	+	45.9200i	−2.60528	+	1.50416i
$933$	10.3287	−	4.78799i	0.338147	−	0.156752i
$934$	−26.8740	−	100.295i	−0.879343	−	3.28175i
$935$	−8.90532			−0.291235
$936$	−21.3467	−	82.1160i	−0.697739	−	2.68404i
$937$	−12.6407			−0.412955			−0.206478	−	0.978451i	$-0.566200\pi$
$937$	−12.6407			−0.412955			−0.206478	+	0.978451i	$0.566200\pi$
$938$	−11.8426	−	44.1970i	−0.386673	−	1.44308i
$939$	−3.34376	+	37.2503i	−0.109119	+	1.21562i
$940$	−28.7167	+	16.5796i	−0.936636	+	0.540767i
$941$	1.12447	+	4.19656i	0.0366565	+	0.136804i	0.981829	−	0.189767i	$-0.0607733\pi$
$941$	1.12447	+	4.19656i	0.0366565	+	0.136804i	−0.945173	+	0.326571i	$0.894107\pi$
$942$	−5.00866	−	5.99653i	−0.163191	−	0.195378i
$943$	−42.6298	+	42.6298i	−1.38822	+	1.38822i
$944$	94.4084	+	94.4084i	3.07273	+	3.07273i
$945$	22.5718	−	22.2680i	0.734260	−	0.724378i
$946$	−2.69365	+	1.55518i	−0.0875780	+	0.0505632i
$947$	−16.2380	+	4.35096i	−0.527665	+	0.141387i	−0.512810	−	0.858502i	$-0.671395\pi$
$947$	−16.2380	+	4.35096i	−0.527665	+	0.141387i	−0.0148549	+	0.999890i	$0.504729\pi$
$948$	−31.8653	−	68.7401i	−1.03494	−	2.23257i
$949$	−0.324527	+	3.58727i	−0.0105346	+	0.116448i
$950$	20.6331	+	11.9125i	0.669425	+	0.386492i
$951$	−6.82786	−	8.17455i	−0.221409	−	0.265078i
$952$	18.9433	−	32.8108i	0.613956	−	1.06340i
$953$	−14.1311	+	24.4758i	−0.457751	+	0.792848i	−0.998842	−	0.0481162i	$-0.984678\pi$
$953$	−14.1311	+	24.4758i	−0.457751	+	0.792848i	0.541091	+	0.840964i	$0.318012\pi$
$954$	15.0865	+	21.7542i	0.488442	+	0.704317i
$955$	15.5548	−	4.16789i	0.503341	−	0.134870i
$956$	45.3927	+	45.3927i	1.46810	+	1.46810i
$957$	0.403470	+	0.483047i	0.0130423	+	0.0156147i
$958$	−8.36259	−	14.4844i	−0.270183	−	0.467971i
$959$	−3.20564			−0.103516
$960$	53.0814	+	19.4559i	1.71319	+	0.627937i
$961$	6.83023	−	3.94344i	0.220330	−	0.127208i
$962$	13.9902	+	16.7733i	0.451064	+	0.540793i
$963$	8.90208	+	7.53851i	0.286866	+	0.242925i
$964$	−4.88920	+	18.2467i	−0.157471	+	0.587688i
$965$	−4.36691	−	2.52124i	−0.140576	−	0.0811614i
$966$	−30.9601	−	66.7874i	−0.996123	−	2.14885i
$967$	27.2295	−	7.29613i	0.875643	−	0.234628i	0.207117	−	0.978316i	$-0.433592\pi$
$967$	27.2295	−	7.29613i	0.875643	−	0.234628i	0.668526	+	0.743688i	$0.266925\pi$
$968$	65.1866	+	17.4667i	2.09518	+	0.561401i
$969$	11.2880	−	9.42837i	0.362622	−	0.302883i
$970$	−4.38826	−	1.17583i	−0.140899	−	0.0377536i
$971$	48.3799	+	27.9321i	1.55258	+	0.896385i	0.997930	+	0.0643034i	$0.0204826\pi$
$971$	48.3799	+	27.9321i	1.55258	+	0.896385i	0.554654	+	0.832081i	$0.312851\pi$
$972$	63.9729	−	43.7262i	2.05193	−	1.40252i
$973$	17.3837	+	4.65794i	0.557295	+	0.149327i
$974$	−0.507797	−	0.879530i	−0.0162709	−	0.0281820i
$975$	−11.6427	+	8.06219i	−0.372865	+	0.258197i
$976$	−52.0967	+	90.2341i	−1.66757	+	2.88832i
$977$	3.30770	−	3.30770i	0.105823	−	0.105823i	−0.652213	−	0.758036i	$-0.726159\pi$
$977$	3.30770	−	3.30770i	0.105823	−	0.105823i	0.758036	+	0.652213i	$0.226159\pi$
$978$	−16.3551	−	1.46811i	−0.522978	−	0.0469450i
$979$			3.35394i			0.107192i
$980$	−17.7825	+	17.7825i	−0.568040	+	0.568040i
$981$	16.6312	−	35.2493i	0.530995	−	1.12542i
$982$	7.39502	+	27.5986i	0.235985	+	0.880707i
$983$	−2.34597	+	8.75529i	−0.0748249	+	0.279250i	−0.993194	−	0.116476i	$-0.962840\pi$
$983$	−2.34597	+	8.75529i	−0.0748249	+	0.279250i	0.918369	+	0.395726i	$0.129507\pi$
$984$	−94.1936	−	66.2725i	−3.00278	−	2.11269i
$985$		−	56.1760i		−	1.78992i
$986$	0.935140	+	0.935140i	0.0297809	+	0.0297809i
$987$	−0.867306	+	9.66200i	−0.0276067	+	0.307545i
$988$	6.42587	−	71.0306i	0.204434	−	2.25978i
$989$			5.41208i			0.172094i
$990$	−29.8950	−	14.1050i	−0.950126	−	0.448287i
$991$	−17.0282	−	29.4937i	−0.540919	−	0.936899i	−0.998852	−	0.0479121i	$-0.984743\pi$
$991$	−17.0282	−	29.4937i	−0.540919	−	0.936899i	0.457933	−	0.888987i	$-0.348590\pi$
$992$	79.4625			2.52294
$993$	−10.4924	−	60.3016i	−0.332968	−	1.91361i
$994$	4.98259	−	18.5953i	0.158038	−	0.589806i
$995$	4.83680	−	18.0512i	0.153337	−	0.572261i
$996$	−32.0153	−	11.7346i	−1.01444	−	0.371824i
$997$	−37.2970			−1.18121			−0.590604	−	0.806962i	$-0.701110\pi$
$997$	−37.2970			−1.18121			−0.590604	+	0.806962i	$0.701110\pi$
$998$	−40.6200	−	70.3558i	−1.28580	−	2.22708i
$999$	−6.03092	+	10.2843i	−0.190810	+	0.325381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.bc.a.50.12	yes	48
3.2	odd	2		351.2.bf.a.206.1		48
9.2	odd	6		117.2.x.a.11.1	✓	48
9.7	even	3		351.2.ba.a.89.12		48
13.6	odd	12		117.2.x.a.32.1	yes	48
39.32	even	12		351.2.ba.a.71.12		48
117.97	odd	12		351.2.bf.a.305.1		48
117.110	even	12	inner	117.2.bc.a.110.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.1	✓	48	9.2	odd	6
117.2.x.a.32.1	yes	48	13.6	odd	12
117.2.bc.a.50.12	yes	48	1.1	even	1	trivial
117.2.bc.a.110.12	yes	48	117.110	even	12	inner
351.2.ba.a.71.12		48	39.32	even	12
351.2.ba.a.89.12		48	9.7	even	3
351.2.bf.a.206.1		48	3.2	odd	2
351.2.bf.a.305.1		48	117.97	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.683347 + 2.55028i) q^{2} +(1.41657 + 0.996665i) q^{3} +(-4.30494 + 2.48546i) q^{4} +(-0.697740 - 2.60400i) q^{5} +(-1.57377 + 4.29371i) q^{6} +(1.60053 - 1.60053i) q^{7} +(-5.54651 - 5.54651i) q^{8} +(1.01332 + 2.82368i) q^{9} +O(q^{10})\)	\(q+(0.683347 + 2.55028i) q^{2} +(1.41657 + 0.996665i) q^{3} +(-4.30494 + 2.48546i) q^{4} +(-0.697740 - 2.60400i) q^{5} +(-1.57377 + 4.29371i) q^{6} +(1.60053 - 1.60053i) q^{7} +(-5.54651 - 5.54651i) q^{8} +(1.01332 + 2.82368i) q^{9} +(6.16415 - 3.55887i) q^{10} +(-1.49528 + 0.400660i) q^{11} +(-8.57539 - 0.769767i) q^{12} +(2.76885 - 2.30943i) q^{13} +(5.17552 + 2.98809i) q^{14} +(1.60692 - 4.38416i) q^{15} +(5.38407 - 9.32548i) q^{16} +(-1.06695 + 1.84800i) q^{17} +(-6.50875 + 4.51380i) q^{18} +(-3.84372 + 1.02992i) q^{19} +(9.47586 + 9.47586i) q^{20} +(3.86245 - 0.672064i) q^{21} +(-2.04359 - 3.53961i) q^{22} -7.11178 q^{23} +(-2.32898 - 13.3850i) q^{24} +(-1.96386 + 1.13384i) q^{25} +(7.78180 + 5.48320i) q^{26} +(-1.37884 + 5.00987i) q^{27} +(-2.91213 + 10.8682i) q^{28} +(-0.203285 - 0.117367i) q^{29} +(12.2789 + 1.10221i) q^{30} +(6.02345 - 1.61398i) q^{31} +(12.3085 + 3.29805i) q^{32} +(-2.51749 - 0.922735i) q^{33} +(-5.44203 - 1.45819i) q^{34} +(-5.28454 - 3.05103i) q^{35} +(-11.3804 - 9.63722i) q^{36} +(2.21625 + 0.593843i) q^{37} +(-5.25318 - 9.09878i) q^{38} +(6.22399 - 0.511852i) q^{39} +(-10.5731 + 18.3131i) q^{40} +(5.99425 - 5.99425i) q^{41} +(4.35335 + 9.39109i) q^{42} -0.761002i q^{43} +(5.44127 - 5.44127i) q^{44} +(6.64585 - 4.60888i) q^{45} +(-4.85981 - 18.1371i) q^{46} +(-0.640422 + 2.39009i) q^{47} +(16.9213 - 7.84405i) q^{48} +1.87661i q^{49} +(-4.23360 - 4.23360i) q^{50} +(-3.35324 + 1.55443i) q^{51} +(-6.17971 + 16.8238i) q^{52} -3.34230i q^{53} +(-13.7188 - 0.0929427i) q^{54} +(2.08664 + 3.61416i) q^{55} -17.7547 q^{56} +(-6.47136 - 2.37195i) q^{57} +(0.160404 - 0.598636i) q^{58} +(-3.20908 + 11.9765i) q^{59} +(3.97892 + 22.8674i) q^{60} -9.67608 q^{61} +(8.23221 + 14.2586i) q^{62} +(6.14124 + 2.89754i) q^{63} +12.1076i q^{64} +(-7.94571 - 5.59870i) q^{65} +(0.632918 - 7.05086i) q^{66} +(-5.41390 - 5.41390i) q^{67} -10.6074i q^{68} +(-10.0743 - 7.08807i) q^{69} +(4.16982 - 15.5620i) q^{70} +(-0.833742 - 3.11157i) q^{71} +(10.0412 - 21.2820i) q^{72} +(-0.706395 + 0.706395i) q^{73} +6.05787i q^{74} +(-3.91200 - 0.351159i) q^{75} +(13.9871 - 13.9871i) q^{76} +(-1.75198 + 3.03451i) q^{77} +(5.55851 + 15.5232i) q^{78} +(4.39999 + 7.62101i) q^{79} +(-28.0403 - 7.51337i) q^{80} +(-6.94637 + 5.72258i) q^{81} +(19.3832 + 11.1909i) q^{82} +(3.82540 + 1.02501i) q^{83} +(-14.9572 + 12.4931i) q^{84} +(5.55666 + 1.48890i) q^{85} +(1.94077 - 0.520028i) q^{86} +(-0.170991 - 0.368865i) q^{87} +(10.5159 + 6.07133i) q^{88} +(0.560753 - 2.09276i) q^{89} +(16.2954 + 13.7993i) q^{90} +(0.735305 - 8.12794i) q^{91} +(30.6158 - 17.6760i) q^{92} +(10.1412 + 3.71705i) q^{93} -6.53304 q^{94} +(5.36383 + 9.29043i) q^{95} +(14.1487 + 16.9393i) q^{96} +(-0.451327 - 0.451327i) q^{97} +(-4.78588 + 1.28237i) q^{98} +(-2.64653 - 3.81621i) 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

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