LMFDB - Embedded newform 273.2.by.c.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.2
Character	$\chi$	$=$	273.223
Dual form			273.2.by.c.202.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11902 - 0.567791i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(2.11902 - 0.567791i) q^{6} +(-2.49394 + 0.883331i) q^{7} +(-1.26060 - 1.26060i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.11902 - 0.567791i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(2.11902 - 0.567791i) q^{6} +(-2.49394 + 0.883331i) q^{7} +(-1.26060 - 1.26060i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.65710 - 8.06633i) q^{10} +(-0.698323 + 2.60618i) q^{11} -2.81265 q^{12} +(-0.373866 - 3.58612i) q^{13} +(5.78626 - 0.455764i) q^{14} +(-4.10107 - 1.09888i) q^{15} +(-0.857159 - 1.48464i) q^{16} +(-0.599399 + 1.03819i) q^{17} +(-1.55123 + 1.55123i) q^{18} +(-1.89568 + 0.507945i) q^{19} +(3.09075 + 11.5349i) q^{20} +(1.71815 - 2.01196i) q^{21} +(2.95953 - 5.12605i) q^{22} +(-4.65282 + 2.68631i) q^{23} +(1.72201 + 0.461412i) q^{24} +13.0263i q^{25} +(-1.24393 + 7.81134i) q^{26} +1.00000i q^{27} +(-7.31704 - 1.35564i) q^{28} +(1.47928 + 2.56220i) q^{29} +(8.06633 + 4.65710i) q^{30} +(3.36721 + 3.36721i) q^{31} +(1.89620 + 7.07671i) q^{32} +(-0.698323 - 2.60618i) q^{33} +(1.85961 - 1.85961i) q^{34} +(-10.1392 - 4.83535i) q^{35} +(2.43582 - 1.40632i) q^{36} +(-1.03769 + 3.87273i) q^{37} +4.30539 q^{38} +(2.11684 + 2.91873i) q^{39} -7.56914i q^{40} +(1.42770 - 5.32825i) q^{41} +(-4.78317 + 3.28783i) q^{42} +(-9.78317 - 5.64832i) q^{43} +(-5.36612 + 5.36612i) q^{44} +(4.10107 - 1.09888i) q^{45} +(11.3847 - 3.05052i) q^{46} +(2.97828 - 2.97828i) q^{47} +(1.48464 + 0.857159i) q^{48} +(5.43945 - 4.40594i) q^{49} +(7.39621 - 27.6030i) q^{50} -1.19880i q^{51} +(4.13256 - 9.26092i) q^{52} -11.0603 q^{53} +(0.567791 - 2.11902i) q^{54} +(-9.92075 + 5.72775i) q^{55} +(4.25739 + 2.03033i) q^{56} +(1.38773 - 1.38773i) q^{57} +(-1.67985 - 6.26927i) q^{58} +(3.14721 + 11.7455i) q^{59} +(-8.44410 - 8.44410i) q^{60} +(4.55683 + 2.63089i) q^{61} +(-5.22332 - 9.04706i) q^{62} +(-0.481982 + 2.60148i) q^{63} -12.6437i q^{64} +(9.64379 - 11.8886i) q^{65} +5.91905i q^{66} +(4.15530 + 1.11341i) q^{67} +(-2.92006 + 1.68590i) q^{68} +(2.68631 - 4.65282i) q^{69} +(18.7397 + 16.0032i) q^{70} +(0.800761 + 2.98848i) q^{71} +(-1.72201 + 0.461412i) q^{72} +(-4.78407 + 4.78407i) q^{73} +(4.39780 - 7.61721i) q^{74} +(-6.51315 - 11.2811i) q^{75} +(-5.33186 - 1.42867i) q^{76} +(-0.560542 - 7.11650i) q^{77} +(-2.82839 - 7.38678i) q^{78} -1.16895 q^{79} +(1.88383 - 7.03054i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.05066 + 10.4801i) q^{82} +(3.24002 + 3.24002i) q^{83} +(7.01456 - 2.48450i) q^{84} +(-4.91635 + 1.31733i) q^{85} +(17.5237 + 17.5237i) q^{86} +(-2.56220 - 1.47928i) q^{87} +(4.16566 - 2.40505i) q^{88} +(-4.80209 - 1.28672i) q^{89} -9.31419 q^{90} +(4.10012 + 8.61330i) q^{91} -15.1113 q^{92} +(-4.59969 - 1.23248i) q^{93} +(-8.00209 + 4.62001i) q^{94} +(-7.21613 - 4.16623i) q^{95} +(-5.18051 - 5.18051i) q^{96} +(14.7483 - 3.95180i) q^{97} +(-14.0280 + 6.24783i) q^{98} +(1.90786 + 1.90786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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 $

$2$	−2.11902	−	0.567791i	−1.49838	−	0.401489i	−0.585820	−	0.810441i	$-0.699227\pi$
$2$	−2.11902	−	0.567791i	−1.49838	−	0.401489i	−0.912556	+	0.408953i	$0.865894\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.43582	+	1.40632i	1.21791	+	0.703161i
$5$	3.00219	+	3.00219i	1.34262	+	1.34262i	0.893442	+	0.449179i	$0.148283\pi$
$5$	3.00219	+	3.00219i	1.34262	+	1.34262i	0.449179	+	0.893442i	$0.351717\pi$
$6$	2.11902	−	0.567791i	0.865088	−	0.231800i
$7$	−2.49394	+	0.883331i	−0.942620	+	0.333868i
$7$	−2.49394	+	0.883331i	−0.942620	+	0.333868i
$8$	−1.26060	−	1.26060i	−0.445690	−	0.445690i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−4.65710	−	8.06633i	−1.47270	−	2.55080i
$11$	−0.698323	+	2.60618i	−0.210552	+	0.785792i	0.777133	+	0.629337i	$0.216673\pi$
$11$	−0.698323	+	2.60618i	−0.210552	+	0.785792i	−0.987685	+	0.156455i	$0.949993\pi$
$12$	−2.81265			−0.811941
$13$	−0.373866	−	3.58612i	−0.103692	−	0.994609i
$13$	−0.373866	−	3.58612i	−0.103692	−	0.994609i
$14$	5.78626	−	0.455764i	1.54644	−	0.121808i
$15$	−4.10107	−	1.09888i	−1.05889	−	0.283729i
$16$	−0.857159	−	1.48464i	−0.214290	−	0.371161i
$17$	−0.599399	+	1.03819i	−0.145376	+	0.251798i	−0.929513	−	0.368789i	$-0.879772\pi$
$17$	−0.599399	+	1.03819i	−0.145376	+	0.251798i	0.784137	+	0.620587i	$0.213106\pi$
$18$	−1.55123	+	1.55123i	−0.365629	+	0.365629i
$19$	−1.89568	+	0.507945i	−0.434898	+	0.116531i	−0.469624	−	0.882866i	$-0.655611\pi$
$19$	−1.89568	+	0.507945i	−0.434898	+	0.116531i	0.0347266	+	0.999397i	$0.488944\pi$
$20$	3.09075	+	11.5349i	0.691114	+	2.57927i
$21$	1.71815	−	2.01196i	0.374931	−	0.439045i
$22$	2.95953	−	5.12605i	0.630973	−	1.09288i
$23$	−4.65282	+	2.68631i	−0.970181	+	0.560134i	−0.899291	−	0.437350i	$-0.855917\pi$
$23$	−4.65282	+	2.68631i	−0.970181	+	0.560134i	−0.0708893	+	0.997484i	$0.522584\pi$
$24$	1.72201	+	0.461412i	0.351505	+	0.0941854i
$25$			13.0263i			2.60526i
$26$	−1.24393	+	7.81134i	−0.243955	+	1.53193i
$27$			1.00000i			0.192450i
$28$	−7.31704	−	1.35564i	−1.38279	−	0.256193i
$29$	1.47928	+	2.56220i	0.274696	+	0.475788i	0.970058	−	0.242872i	$-0.0780894\pi$
$29$	1.47928	+	2.56220i	0.274696	+	0.475788i	−0.695362	+	0.718659i	$0.744756\pi$
$30$	8.06633	+	4.65710i	1.47270	+	0.850266i
$31$	3.36721	+	3.36721i	0.604768	+	0.604768i	0.941574	−	0.336806i	$-0.109347\pi$
$31$	3.36721	+	3.36721i	0.604768	+	0.604768i	−0.336806	+	0.941574i	$0.609347\pi$
$32$	1.89620	+	7.07671i	0.335204	+	1.25100i
$33$	−0.698323	−	2.60618i	−0.121563	−	0.453677i
$34$	1.85961	−	1.85961i	0.318921	−	0.318921i
$35$	−10.1392	−	4.83535i	−1.71384	−	0.817324i
$36$	2.43582	−	1.40632i	0.405970	−	0.234387i
$37$	−1.03769	+	3.87273i	−0.170596	+	0.636673i	0.826664	+	0.562696i	$0.190236\pi$
$37$	−1.03769	+	3.87273i	−0.170596	+	0.636673i	−0.997260	+	0.0739770i	$0.976431\pi$
$38$	4.30539			0.698426
$39$	2.11684	+	2.91873i	0.338965	+	0.467371i
$40$		−	7.56914i		−	1.19679i
$41$	1.42770	−	5.32825i	0.222969	−	0.832133i	−0.760239	−	0.649644i	$-0.774918\pi$
$41$	1.42770	−	5.32825i	0.222969	−	0.832133i	0.983208	−	0.182489i	$-0.0584154\pi$
$42$	−4.78317	+	3.28783i	−0.738058	+	0.507324i
$43$	−9.78317	−	5.64832i	−1.49192	−	0.861360i	−0.491963	−	0.870616i	$-0.663720\pi$
$43$	−9.78317	−	5.64832i	−1.49192	−	0.861360i	−0.999957	+	0.00925580i	$0.997054\pi$
$44$	−5.36612	+	5.36612i	−0.808973	+	0.808973i
$45$	4.10107	−	1.09888i	0.611351	−	0.163811i
$46$	11.3847	−	3.05052i	1.67858	−	0.449775i
$47$	2.97828	−	2.97828i	0.434427	−	0.434427i	−0.455704	−	0.890131i	$-0.650613\pi$
$47$	2.97828	−	2.97828i	0.434427	−	0.434427i	0.890131	+	0.455704i	$0.150613\pi$
$48$	1.48464	+	0.857159i	0.214290	+	0.123720i
$49$	5.43945	−	4.40594i	0.777065	−	0.629421i
$50$	7.39621	−	27.6030i	1.04598	−	3.90366i
$51$		−	1.19880i		−	0.167865i
$52$	4.13256	−	9.26092i	0.573084	−	1.28426i
$53$	−11.0603			−1.51925			−0.759627	−	0.650359i	$-0.774618\pi$
$53$	−11.0603			−1.51925			−0.759627	+	0.650359i	$0.774618\pi$
$54$	0.567791	−	2.11902i	0.0772665	−	0.288363i
$55$	−9.92075	+	5.72775i	−1.33771	+	0.772329i
$56$	4.25739	+	2.03033i	0.568918	+	0.271315i
$57$	1.38773	−	1.38773i	0.183809	−	0.183809i
$58$	−1.67985	−	6.26927i	−0.220575	−	0.823196i
$59$	3.14721	+	11.7455i	0.409731	+	1.52914i	0.795160	+	0.606400i	$0.207387\pi$
$59$	3.14721	+	11.7455i	0.409731	+	1.52914i	−0.385428	+	0.922738i	$0.625946\pi$
$60$	−8.44410	−	8.44410i	−1.09013	−	1.09013i
$61$	4.55683	+	2.63089i	0.583442	+	0.336851i	0.762500	−	0.646988i	$-0.223972\pi$
$61$	4.55683	+	2.63089i	0.583442	+	0.336851i	−0.179058	+	0.983839i	$0.557305\pi$
$62$	−5.22332	−	9.04706i	−0.663362	−	1.14898i
$63$	−0.481982	+	2.60148i	−0.0607240	+	0.327756i
$64$		−	12.6437i		−	1.58046i
$65$	9.64379	−	11.8886i	1.19616	−	1.47460i
$66$			5.91905i			0.728585i
$67$	4.15530	+	1.11341i	0.507651	+	0.136025i	0.503549	−	0.863967i	$-0.332028\pi$
$67$	4.15530	+	1.11341i	0.507651	+	0.136025i	0.00410235	+	0.999992i	$0.498694\pi$
$68$	−2.92006	+	1.68590i	−0.354109	+	0.204445i
$69$	2.68631	−	4.65282i	0.323394	−	0.560134i
$70$	18.7397	+	16.0032i	2.23983	+	1.91274i
$71$	0.800761	+	2.98848i	0.0950329	+	0.354668i	0.997024	−	0.0770861i	$-0.0245616\pi$
$71$	0.800761	+	2.98848i	0.0950329	+	0.354668i	−0.901992	+	0.431754i	$0.857895\pi$
$72$	−1.72201	+	0.461412i	−0.202941	+	0.0543780i
$73$	−4.78407	+	4.78407i	−0.559933	+	0.559933i	−0.929288	−	0.369355i	$-0.879579\pi$
$73$	−4.78407	+	4.78407i	−0.559933	+	0.559933i	0.369355	+	0.929288i	$0.379579\pi$
$74$	4.39780	−	7.61721i	0.511234	−	0.885483i
$75$	−6.51315	−	11.2811i	−0.752074	−	1.30263i
$76$	−5.33186	−	1.42867i	−0.611607	−	0.163879i
$77$	−0.560542	−	7.11650i	−0.0638797	−	0.811000i
$78$	−2.82839	−	7.38678i	−0.320252	−	0.836389i
$79$	−1.16895			−0.131517			−0.0657584	−	0.997836i	$-0.520947\pi$
$79$	−1.16895			−0.131517			−0.0657584	+	0.997836i	$0.520947\pi$
$80$	1.88383	−	7.03054i	0.210618	−	0.786038i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.05066	+	10.4801i	−0.668184	+	1.15733i
$83$	3.24002	+	3.24002i	0.355639	+	0.355639i	0.862202	−	0.506564i	$-0.169085\pi$
$83$	3.24002	+	3.24002i	0.355639	+	0.355639i	−0.506564	+	0.862202i	$0.669085\pi$
$84$	7.01456	−	2.48450i	0.765352	−	0.271081i
$85$	−4.91635	+	1.31733i	−0.533253	+	0.142885i
$86$	17.5237	+	17.5237i	1.88963	+	1.88963i
$87$	−2.56220	−	1.47928i	−0.274696	−	0.158596i
$88$	4.16566	−	2.40505i	0.444061	−	0.256379i
$89$	−4.80209	−	1.28672i	−0.509020	−	0.136392i	−0.00483713	−	0.999988i	$-0.501540\pi$
$89$	−4.80209	−	1.28672i	−0.509020	−	0.136392i	−0.504183	+	0.863597i	$0.668206\pi$
$90$	−9.31419			−0.981802
$91$	4.10012	+	8.61330i	0.429810	+	0.902919i
$92$	−15.1113			−1.57546
$93$	−4.59969	−	1.23248i	−0.476966	−	0.127803i
$94$	−8.00209	+	4.62001i	−0.825352	+	0.476517i
$95$	−7.21613	−	4.16623i	−0.740359	−	0.427447i
$96$	−5.18051	−	5.18051i	−0.528733	−	0.528733i
$97$	14.7483	−	3.95180i	1.49746	−	0.401244i	0.585214	−	0.810879i	$-0.301010\pi$
$97$	14.7483	−	3.95180i	1.49746	−	0.401244i	0.912250	+	0.409634i	$0.134344\pi$
$98$	−14.0280	+	6.24783i	−1.41704	+	0.631126i
$99$	1.90786	+	1.90786i	0.191747	+	0.191747i
$100$	−18.3192	+	31.7298i	−1.83192	+	3.17298i
$101$	0.803086	+	1.39099i	0.0799101	+	0.138408i	0.903211	−	0.429197i	$-0.141203\pi$
$101$	0.803086	+	1.39099i	0.0799101	+	0.138408i	−0.823301	+	0.567605i	$0.807870\pi$
$102$	−0.680666	+	2.54028i	−0.0673960	+	0.251525i
$103$	14.4997			1.42870			0.714351	−	0.699787i	$-0.246722\pi$
$103$	14.4997			1.42870			0.714351	+	0.699787i	$0.246722\pi$
$104$	−4.04937	+	4.99196i	−0.397073	+	0.489502i
$105$	11.1985	−	0.882067i	1.09286	−	0.0860809i
$106$	23.4371	+	6.27995i	2.27641	+	0.609963i
$107$	1.91021	+	3.30858i	0.184667	+	0.319852i	0.943464	−	0.331475i	$-0.107546\pi$
$107$	1.91021	+	3.30858i	0.184667	+	0.319852i	−0.758797	+	0.651327i	$0.774213\pi$
$108$	−1.40632	+	2.43582i	−0.135323	+	0.234387i
$109$	9.59246	−	9.59246i	0.918791	−	0.918791i	−0.0781507	−	0.996942i	$-0.524902\pi$
$109$	9.59246	−	9.59246i	0.918791	−	0.918791i	0.996942	+	0.0781507i	$0.0249015\pi$
$110$	24.2745	−	6.50432i	2.31448	−	0.620163i
$111$	−1.03769	−	3.87273i	−0.0984936	−	0.367583i
$112$	3.44913	+	2.94545i	0.325912	+	0.278319i
$113$	−1.57880	+	2.73457i	−0.148521	+	0.257247i	−0.930681	−	0.365831i	$-0.880785\pi$
$113$	−1.57880	+	2.73457i	−0.148521	+	0.257247i	0.782160	+	0.623078i	$0.214118\pi$
$114$	−3.72857	+	2.15269i	−0.349213	+	0.201618i
$115$	−22.0335	−	5.90385i	−2.05463	−	0.550537i
$116$			8.32140i			0.772623i
$117$	−3.29260	−	1.46928i	−0.304401	−	0.135835i
$118$		−	26.6760i		−	2.45573i
$119$	0.577799	−	3.11865i	0.0529668	−	0.285886i
$120$	3.78457	+	6.55506i	0.345482	+	0.598393i
$121$	3.22177	+	1.86009i	0.292888	+	0.169099i
$122$	−8.16224	−	8.16224i	−0.738974	−	0.738974i
$123$	1.42770	+	5.32825i	0.128731	+	0.480432i
$124$	3.46654	+	12.9373i	0.311304	+	1.16180i
$125$	−24.0965	+	24.0965i	−2.15526	+	2.15526i
$126$	2.49843	−	5.23893i	0.222578	−	0.466721i
$127$	5.77265	−	3.33284i	0.512240	−	0.295742i	−0.221514	−	0.975157i	$-0.571100\pi$
$127$	5.77265	−	3.33284i	0.512240	−	0.295742i	0.733754	+	0.679415i	$0.237767\pi$
$128$	−3.38658	+	12.6389i	−0.299335	+	1.11713i
$129$	11.2966			0.994613
$130$	−27.1857	+	19.7166i	−2.38434	+	1.72926i
$131$		−	9.80212i		−	0.856415i	−0.903680	−	0.428207i	$-0.859145\pi$
$131$		−	9.80212i		−	0.856415i	0.903680	−	0.428207i	$-0.140855\pi$
$132$	1.96414	−	7.33026i	0.170956	−	0.638017i
$133$	4.27901	−	2.94129i	0.371038	−	0.255042i
$134$	−8.17300	−	4.71868i	−0.706039	−	0.407632i
$135$	−3.00219	+	3.00219i	−0.258388	+	0.258388i
$136$	2.06435	−	0.553140i	0.177016	−	0.0474314i
$137$	6.48757	−	1.73834i	0.554271	−	0.148516i	0.0291978	−	0.999574i	$-0.490705\pi$
$137$	6.48757	−	1.73834i	0.554271	−	0.148516i	0.525073	+	0.851057i	$0.324038\pi$
$138$	−8.33418	+	8.33418i	−0.709452	+	0.709452i
$139$	0.304839	+	0.175999i	0.0258561	+	0.0149280i	0.512872	−	0.858465i	$-0.328581\pi$
$139$	0.304839	+	0.175999i	0.0258561	+	0.0149280i	−0.487016	+	0.873393i	$0.661915\pi$
$140$	−17.8972	−	26.0371i	−1.51259	−	2.20053i
$141$	−1.09013	+	4.06841i	−0.0918052	+	0.342622i
$142$		−	6.78733i		−	0.569580i
$143$	9.60714	+	1.52991i	0.803389	+	0.127937i
$144$	−1.71432			−0.142860
$145$	−3.25111	+	12.1333i	−0.269990	+	1.00762i
$146$	12.8539	−	7.42121i	1.06380	−	0.614184i
$147$	−2.50773	+	6.53539i	−0.206834	+	0.539030i
$148$	−7.97395	+	7.97395i	−0.655455	+	0.655455i
$149$	3.05452	+	11.3996i	0.250236	+	0.933892i	0.970679	+	0.240379i	$0.0772716\pi$
$149$	3.05452	+	11.3996i	0.250236	+	0.933892i	−0.720443	+	0.693514i	$0.756062\pi$
$150$	7.39621	+	27.6030i	0.603898	+	2.25378i
$151$	−12.2745	−	12.2745i	−0.998884	−	0.998884i	0.00111530	−	0.999999i	$-0.499645\pi$
$151$	−12.2745	−	12.2745i	−0.998884	−	0.998884i	−0.999999	+	0.00111530i	$0.999645\pi$
$152$	3.03001	+	1.74938i	0.245766	+	0.141893i
$153$	0.599399	+	1.03819i	0.0484585	+	0.0839326i
$154$	−2.85288	+	15.3983i	−0.229891	+	1.24083i
$155$			20.2180i			1.62395i
$156$	1.05155	+	10.0865i	0.0841916	+	0.807564i
$157$		−	4.41109i		−	0.352043i	−0.984386	−	0.176022i	$-0.943677\pi$
$157$		−	4.41109i		−	0.352043i	0.984386	−	0.176022i	$-0.0563228\pi$
$158$	2.47702	+	0.663716i	0.197061	+	0.0528024i
$159$	9.57853	−	5.53017i	0.759627	−	0.438571i
$160$	−15.5529	+	26.9384i	−1.22956	+	2.12967i
$161$	9.23095	−	10.8095i	0.727501	−	0.851905i
$162$	0.567791	+	2.11902i	0.0446098	+	0.166486i
$163$	−0.610931	+	0.163698i	−0.0478518	+	0.0128219i	−0.282666	−	0.959219i	$-0.591219\pi$
$163$	−0.610931	+	0.163698i	−0.0478518	+	0.0128219i	0.234814	+	0.972040i	$0.424552\pi$
$164$	10.9709	−	10.9709i	0.856680	−	0.856680i
$165$	5.72775	−	9.92075i	0.445904	−	0.772329i
$166$	−5.02603	−	8.70534i	−0.390096	−	0.675665i
$167$	16.3769	+	4.38817i	1.26728	+	0.339567i	0.828988	−	0.559266i	$-0.188917\pi$
$167$	16.3769	+	4.38817i	1.26728	+	0.339567i	0.438292	+	0.898833i	$0.355584\pi$
$168$	−4.70218	+	0.370374i	−0.362781	+	0.0285750i
$169$	−12.7204	+	2.68145i	−0.978496	+	0.206266i
$170$	11.1658			0.856380
$171$	−0.507945	+	1.89568i	−0.0388435	+	0.144966i
$172$	−15.8867	−	27.5166i	−1.21135	−	2.09812i
$173$	−4.60670	+	7.97903i	−0.350241	+	0.606634i	−0.986291	−	0.165013i	$-0.947234\pi$
$173$	−4.60670	+	7.97903i	−0.350241	+	0.606634i	0.636051	+	0.771647i	$0.280567\pi$
$174$	4.58943	+	4.58943i	0.347924	+	0.347924i
$175$	−11.5065	−	32.4868i	−0.869812	−	2.45577i
$176$	4.46782	−	1.19715i	0.336774	−	0.0902384i
$177$	−8.59833	−	8.59833i	−0.646290	−	0.646290i
$178$	9.44515	+	5.45316i	0.707944	+	0.408732i
$179$	2.35631	−	1.36042i	0.176119	−	0.101682i	−0.409349	−	0.912378i	$-0.634244\pi$
$179$	2.35631	−	1.36042i	0.176119	−	0.101682i	0.585468	+	0.810696i	$0.300911\pi$
$180$	11.5349	+	3.09075i	0.859757	+	0.230371i
$181$	15.4525			1.14858			0.574288	−	0.818653i	$-0.305279\pi$
$181$	15.4525			1.14858			0.574288	+	0.818653i	$0.305279\pi$
$182$	−3.79771	−	20.5798i	−0.281505	−	1.52548i
$183$	−5.26177			−0.388962
$184$	9.25172	+	2.47899i	0.682046	+	0.182754i
$185$	−14.7420	+	8.51132i	−1.08386	+	0.625765i
$186$	9.04706	+	5.22332i	0.663362	+	0.382992i
$187$	−2.28713	−	2.28713i	−0.167252	−	0.167252i
$188$	11.4430	−	3.06614i	0.834566	−	0.223621i
$189$	−0.883331	−	2.49394i	−0.0642529	−	0.181407i
$190$	12.9256	+	12.9256i	0.937721	+	0.937721i
$191$	1.63770	−	2.83658i	0.118500	−	0.205248i	−0.800673	−	0.599101i	$-0.795525\pi$
$191$	1.63770	−	2.83658i	0.118500	−	0.205248i	0.919173	+	0.393853i	$0.128858\pi$
$192$	6.32186	+	10.9498i	0.456241	+	0.790232i
$193$	−5.44447	+	20.3190i	−0.391901	+	1.46260i	0.435093	+	0.900385i	$0.356715\pi$
$193$	−5.44447	+	20.3190i	−0.391901	+	1.46260i	−0.826995	+	0.562210i	$0.809951\pi$
$194$	−33.4958			−2.40486
$195$	−2.40745	+	15.1177i	−0.172401	+	1.08260i
$196$	19.4457	−	3.08247i	1.38898	−	0.220176i
$197$	20.1959	+	5.41149i	1.43890	+	0.385553i	0.892149	−	0.451741i	$-0.149197\pi$
$197$	20.1959	+	5.41149i	1.43890	+	0.385553i	0.546753	+	0.837294i	$0.315864\pi$
$198$	−2.95953	−	5.12605i	−0.210324	−	0.364293i
$199$	12.4685	−	21.5960i	0.883867	−	1.53090i	0.0368601	−	0.999320i	$-0.488264\pi$
$199$	12.4685	−	21.5960i	0.883867	−	1.53090i	0.847007	−	0.531582i	$-0.178402\pi$
$200$	16.4210	−	16.4210i	1.16114	−	1.16114i
$201$	−4.15530	+	1.11341i	−0.293092	+	0.0785339i
$202$	−0.911969	−	3.40352i	−0.0641659	−	0.239471i
$203$	−5.95251	−	5.08326i	−0.417784	−	0.356775i
$204$	1.68590	−	2.92006i	0.118036	−	0.204445i
$205$	20.2827	−	11.7102i	1.41660	−	0.817876i
$206$	−30.7253	−	8.23282i	−2.14073	−	0.573608i
$207$			5.37262i			0.373423i
$208$	−5.00364	+	3.62893i	−0.346940	+	0.251621i
$209$		−	5.29518i		−	0.366275i
$210$	−24.2307	−	4.48928i	−1.67208	−	0.309789i
$211$	5.46157	+	9.45972i	0.375990	+	0.651234i	0.990475	−	0.137695i	$-0.0439694\pi$
$211$	5.46157	+	9.45972i	0.375990	+	0.651234i	−0.614485	+	0.788929i	$0.710636\pi$
$212$	−26.9410	−	15.5544i	−1.85032	−	1.06828i
$213$	−2.18772	−	2.18772i	−0.149900	−	0.149900i
$214$	−2.16919	−	8.09554i	−0.148283	−	0.553400i
$215$	−12.4136	−	46.3283i	−0.846602	−	3.15956i
$216$	1.26060	−	1.26060i	0.0857731	−	0.0857731i
$217$	−11.3720	−	5.42325i	−0.771979	−	0.368154i
$218$	−25.7731	+	14.8801i	−1.74558	+	1.00781i
$219$	1.75109	−	6.53517i	0.118328	−	0.441606i
$220$	−32.2202			−2.17229
$221$	3.94716	+	1.76137i	0.265515	+	0.118483i
$222$			8.79560i			0.590322i
$223$	3.99267	−	14.9009i	0.267369	−	0.997835i	−0.693415	−	0.720538i	$-0.743895\pi$
$223$	3.99267	−	14.9009i	0.267369	−	0.997835i	0.960784	−	0.277297i	$-0.0894385\pi$
$224$	−10.9801	−	15.9739i	−0.733637	−	1.06730i
$225$	11.2811	+	6.51315i	0.752074	+	0.434210i
$226$	4.89819	−	4.89819i	0.325823	−	0.325823i
$227$	18.6556	−	4.99875i	1.23822	−	0.331779i	0.420442	−	0.907319i	$-0.361875\pi$
$227$	18.6556	−	4.99875i	1.23822	−	0.331779i	0.817773	+	0.575541i	$0.195208\pi$
$228$	5.33186	−	1.42867i	0.353111	−	0.0946159i
$229$	−12.6136	+	12.6136i	−0.833528	+	0.833528i	−0.987998	−	0.154470i	$-0.950633\pi$
$229$	−12.6136	+	12.6136i	−0.833528	+	0.833528i	0.154470	+	0.987998i	$0.450633\pi$
$230$	43.3373	+	25.0208i	2.85758	+	1.64982i
$231$	4.04369	+	5.88280i	0.266055	+	0.387060i
$232$	1.36512	−	5.09470i	0.0896245	−	0.334483i
$233$		−	24.9418i		−	1.63399i	−0.576643	−	0.816996i	$-0.695638\pi$
$233$		−	24.9418i		−	1.63399i	0.576643	−	0.816996i	$-0.304362\pi$
$234$	6.14285	+	4.98295i	0.401571	+	0.325745i
$235$	17.8827			1.16654
$236$	−8.85197	+	33.0360i	−0.576214	+	2.15046i
$237$	1.01234	−	0.584473i	0.0657584	−	0.0379656i
$238$	−2.99511	+	6.28042i	−0.194144	+	0.407099i
$239$	−4.67931	+	4.67931i	−0.302680	+	0.302680i	−0.842061	−	0.539382i	$-0.818658\pi$
$239$	−4.67931	+	4.67931i	−0.302680	+	0.302680i	0.539382	+	0.842061i	$0.318658\pi$
$240$	1.88383	+	7.03054i	0.121600	+	0.453819i
$241$	0.169033	+	0.630839i	0.0108884	+	0.0406359i	0.971156	−	0.238444i	$-0.0766373\pi$
$241$	0.169033	+	0.630839i	0.0108884	+	0.0406359i	−0.960268	+	0.279080i	$0.909971\pi$
$242$	−5.77086	−	5.77086i	−0.370965	−	0.370965i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	7.39975	+	12.8167i	0.473721	+	0.820508i
$245$	29.5578	+	3.10279i	1.88838	+	0.198230i
$246$		−	12.1013i		−	0.771552i
$247$	2.53028	+	6.60821i	0.160998	+	0.420470i
$248$		−	8.48941i		−	0.539078i
$249$	−4.42595	−	1.18593i	−0.280483	−	0.0751553i
$250$	64.7428	−	37.3793i	4.09470	−	2.36407i
$251$	−9.89477	+	17.1382i	−0.624552	+	1.08176i	0.364075	+	0.931370i	$0.381385\pi$
$251$	−9.89477	+	17.1382i	−0.624552	+	1.08176i	−0.988627	+	0.150386i	$0.951948\pi$
$252$	−4.83254	+	5.65892i	−0.304422	+	0.356478i
$253$	−3.75182	−	14.0020i	−0.235875	−	0.880298i
$254$	−14.1247	+	3.78471i	−0.886265	+	0.237474i
$255$	3.59902	−	3.59902i	0.225379	−	0.225379i
$256$	1.70879	−	2.95971i	0.106799	−	0.184982i
$257$	7.97194	+	13.8078i	0.497276	+	0.861307i	0.999995	−	0.00314245i	$-0.00100027\pi$
$257$	7.97194	+	13.8078i	0.497276	+	0.861307i	−0.502719	+	0.864450i	$0.667667\pi$
$258$	−23.9378	−	6.41412i	−1.49030	−	0.399326i
$259$	−0.832955	−	10.5750i	−0.0517573	−	0.657097i
$260$	40.2098	−	15.3963i	2.49371	−	0.954838i
$261$	2.95857			0.183131
$262$	−5.56555	+	20.7709i	−0.343841	+	1.28323i
$263$	−0.217727	−	0.377114i	−0.0134256	−	0.0232538i	0.859235	−	0.511582i	$-0.170940\pi$
$263$	−0.217727	−	0.377114i	−0.0134256	−	0.0232538i	−0.872660	+	0.488328i	$0.837607\pi$
$264$	−2.40505	+	4.16566i	−0.148020	+	0.256379i
$265$	−33.2052	−	33.2052i	−2.03978	−	2.03978i
$266$	−10.7374	+	3.80308i	−0.658350	+	0.233182i
$267$	4.80209	−	1.28672i	0.293883	−	0.0787457i
$268$	8.55576	+	8.55576i	0.522626	+	0.522626i
$269$	−14.2630	−	8.23477i	−0.869633	−	0.502083i	−0.00240680	−	0.999997i	$-0.500766\pi$
$269$	−14.2630	−	8.23477i	−0.869633	−	0.502083i	−0.867226	+	0.497914i	$0.834099\pi$
$270$	8.06633	−	4.65710i	0.490901	−	0.283422i
$271$	22.4966	+	6.02794i	1.36657	+	0.366171i	0.866224	−	0.499655i	$-0.166540\pi$
$271$	22.4966	+	6.02794i	1.36657	+	0.366171i	0.500345	+	0.865826i	$0.333207\pi$
$272$	2.05512			0.124610
$273$	−7.85746	−	5.40928i	−0.475555	−	0.327384i
$274$	−14.7343			−0.890133
$275$	−33.9489	−	9.09658i	−2.04719	−	0.548544i
$276$	13.0867	−	7.55563i	0.787729	−	0.454796i
$277$	7.08167	+	4.08860i	0.425496	+	0.245660i	0.697426	−	0.716657i	$-0.254329\pi$
$277$	7.08167	+	4.08860i	0.425496	+	0.245660i	−0.271930	+	0.962317i	$0.587662\pi$
$278$	−0.546031	−	0.546031i	−0.0327488	−	0.0327488i
$279$	4.59969	−	1.23248i	0.275376	−	0.0737868i
$280$	6.68605	+	18.8770i	0.399568	+	1.12811i
$281$	3.14177	+	3.14177i	0.187422	+	0.187422i	0.794581	−	0.607159i	$-0.207691\pi$
$281$	3.14177	+	3.14177i	0.187422	+	0.187422i	−0.607159	+	0.794581i	$0.707691\pi$
$282$	4.62001	−	8.00209i	0.275117	−	0.476517i
$283$	−6.35147	−	11.0011i	−0.377555	−	0.653945i	0.613151	−	0.789966i	$-0.289902\pi$
$283$	−6.35147	−	11.0011i	−0.377555	−	0.653945i	−0.990706	+	0.136021i	$0.956569\pi$
$284$	−2.25226	+	8.40554i	−0.133647	+	0.498777i
$285$	8.33247			0.493573
$286$	−19.4891	−	8.69675i	−1.15241	−	0.514250i
$287$	1.14601	+	14.5495i	0.0676469	+	0.858827i
$288$	7.07671	+	1.89620i	0.416999	+	0.111735i
$289$	7.78144	+	13.4779i	0.457732	+	0.792815i
$290$	13.7783	−	23.8648i	0.809092	−	1.40139i
$291$	−10.7965	+	10.7965i	−0.632903	+	0.632903i
$292$	−18.3811	+	4.92520i	−1.07567	+	0.288226i
$293$	1.47718	+	5.51290i	0.0862977	+	0.322067i	0.995557	−	0.0941633i	$-0.0300176\pi$
$293$	1.47718	+	5.51290i	0.0862977	+	0.322067i	−0.909259	+	0.416231i	$0.863351\pi$
$294$	9.02467	−	12.4248i	0.526330	−	0.724627i
$295$	−25.8138	+	44.7109i	−1.50294	+	2.60317i
$296$	6.19009	−	3.57385i	0.359792	−	0.207726i
$297$	−2.60618	−	0.698323i	−0.151226	−	0.0405208i
$298$		−	25.8904i		−	1.49979i
$299$	11.3729	+	15.6812i	0.657714	+	0.906870i
$300$		−	36.6384i		−	2.11532i
$301$	29.3880	+	5.44478i	1.69389	+	0.313832i
$302$	19.0406	+	32.9793i	1.09566	+	1.89774i
$303$	−1.39099	−	0.803086i	−0.0799101	−	0.0461361i
$304$	2.37901	+	2.37901i	0.136446	+	0.136446i
$305$	5.78205	+	21.5789i	0.331079	+	1.23560i
$306$	−0.680666	−	2.54028i	−0.0389111	−	0.145218i
$307$	−10.2283	+	10.2283i	−0.583760	+	0.583760i	−0.935934	−	0.352174i	$-0.885442\pi$
$307$	−10.2283	+	10.2283i	−0.583760	+	0.583760i	0.352174	+	0.935934i	$0.385442\pi$
$308$	8.64271	−	18.1228i	0.492464	−	1.03264i
$309$	−12.5571	+	7.24987i	−0.714351	+	0.412431i
$310$	11.4796	−	42.8424i	0.651997	−	2.43328i
$311$	−14.6147			−0.828724			−0.414362	−	0.910112i	$-0.635995\pi$
$311$	−14.6147			−0.828724			−0.414362	+	0.910112i	$0.635995\pi$
$312$	1.01087	−	6.34785i	0.0572295	−	0.359376i
$313$			17.9984i			1.01733i	0.860965	+	0.508665i	$0.169861\pi$
$313$			17.9984i			1.01733i	−0.860965	+	0.508665i	$0.830139\pi$
$314$	−2.50457	+	9.34720i	−0.141341	+	0.527493i
$315$	−9.25714	+	6.36314i	−0.521581	+	0.358522i
$316$	−2.84734	−	1.64392i	−0.160176	−	0.0924775i
$317$	−12.0835	+	12.0835i	−0.678674	+	0.678674i	−0.959700	−	0.281026i	$-0.909325\pi$
$317$	−12.0835	+	12.0835i	−0.678674	+	0.678674i	0.281026	+	0.959700i	$0.409325\pi$
$318$	−23.4371	+	6.27995i	−1.31429	+	0.352162i
$319$	−7.71056	+	2.06604i	−0.431708	+	0.115676i
$320$	37.9588	−	37.9588i	2.12196	−	2.12196i
$321$	−3.30858	−	1.91021i	−0.184667	−	0.106617i
$322$	−25.6981	+	17.6643i	−1.43210	+	0.984391i
$323$	0.608923	−	2.27253i	0.0338814	−	0.126447i
$324$		−	2.81265i		−	0.156258i
$325$	46.7138	−	4.87009i	2.59122	−	0.270144i
$326$	1.38752			0.0768478
$327$	−3.51108	+	13.1035i	−0.194163	+	0.724627i
$328$	−8.51656	+	4.91704i	−0.470248	+	0.271498i
$329$	−4.79684	+	10.0585i	−0.264458	+	0.554541i
$330$	−17.7701	+	17.7701i	−0.978214	+	0.978214i
$331$	2.57122	+	9.59594i	0.141327	+	0.527441i	0.999891	+	0.0147345i	$0.00469030\pi$
$331$	2.57122	+	9.59594i	0.141327	+	0.527441i	−0.858564	+	0.512706i	$0.828643\pi$
$332$	3.33560	+	12.4486i	0.183065	+	0.683208i
$333$	2.83504	+	2.83504i	0.155359	+	0.155359i
$334$	−32.2114	−	18.5973i	−1.76253	−	1.01760i
$335$	9.13234	+	15.8177i	0.498953	+	0.864212i
$336$	−4.45976	−	0.826270i	−0.243300	−	0.0450767i
$337$		−	6.44780i		−	0.351234i	−0.984459	−	0.175617i	$-0.943808\pi$
$337$		−	6.44780i		−	0.351234i	0.984459	−	0.175617i	$-0.0561920\pi$
$338$	28.4774	+	1.54049i	1.54897	+	0.0837915i
$339$		−	3.15761i		−	0.171498i
$340$	−13.8280	−	3.70519i	−0.749926	−	0.200942i
$341$	−11.1269	+	6.42414i	−0.602558	+	0.347887i
$342$	2.15269	−	3.72857i	0.116404	−	0.201618i
$343$	−9.67375	+	15.7930i	−0.522334	+	0.852741i
$344$	5.21241	+	19.4530i	0.281034	+	1.04883i
$345$	22.0335	−	5.90385i	1.18624	−	0.317853i
$346$	14.2921	−	14.2921i	0.768349	−	0.768349i
$347$	6.00501	−	10.4010i	0.322366	−	0.558354i	−0.658610	−	0.752484i	$-0.728855\pi$
$347$	6.00501	−	10.4010i	0.322366	−	0.558354i	0.980976	+	0.194131i	$0.0621886\pi$
$348$	−4.16070	−	7.20655i	−0.223037	−	0.386311i
$349$	−24.5954	−	6.59031i	−1.31656	−	0.352771i	−0.468872	−	0.883266i	$-0.655339\pi$
$349$	−24.5954	−	6.59031i	−1.31656	−	0.352771i	−0.847688	+	0.530495i	$0.822006\pi$
$350$	5.93692	+	75.3736i	0.317342	+	4.02889i
$351$	3.58612	−	0.373866i	0.191413	−	0.0199555i
$352$	−19.7673			−1.05360
$353$	−2.43053	+	9.07084i	−0.129364	+	0.482792i	−0.999958	−	0.00921021i	$-0.997068\pi$
$353$	−2.43053	+	9.07084i	−0.129364	+	0.482792i	0.870594	+	0.492003i	$0.163735\pi$
$354$	13.3380	+	23.1021i	0.708907	+	1.22786i
$355$	−6.56796	+	11.3760i	−0.348591	+	0.603777i
$356$	−9.88750	−	9.88750i	−0.524036	−	0.524036i
$357$	1.05893	+	2.98973i	0.0560448	+	0.158233i
$358$	−5.76551	+	1.54486i	−0.304716	+	0.0816485i
$359$	−16.2790	−	16.2790i	−0.859171	−	0.859171i	0.132070	−	0.991240i	$-0.457838\pi$
$359$	−16.2790	−	16.2790i	−0.859171	−	0.859171i	−0.991240	+	0.132070i	$0.957838\pi$
$360$	−6.55506	−	3.78457i	−0.345482	−	0.199464i
$361$	−13.1189	+	7.57420i	−0.690469	+	0.398642i
$362$	−32.7442	−	8.77379i	−1.72100	−	0.461140i
$363$	−3.72018			−0.195259
$364$	−2.12591	+	26.7466i	−0.111428	+	1.40190i
$365$	−28.7254			−1.50356
$366$	11.1498	+	2.98759i	0.582810	+	0.156164i
$367$	−19.6200	+	11.3276i	−1.02416	+	0.591297i	−0.915305	−	0.402761i	$-0.868051\pi$
$367$	−19.6200	+	11.3276i	−1.02416	+	0.591297i	−0.108851	+	0.994058i	$0.534717\pi$
$368$	7.97642	+	4.60519i	0.415799	+	0.240062i
$369$	−3.90055	−	3.90055i	−0.203055	−	0.203055i
$370$	36.0714	−	9.66529i	1.87526	−	0.502475i
$371$	27.5838	−	9.76993i	1.43208	−	0.507230i
$372$	−9.47076	−	9.47076i	−0.491036	−	0.491036i
$373$	11.0535	−	19.1453i	0.572330	−	0.991305i	−0.423996	−	0.905664i	$-0.639373\pi$
$373$	11.0535	−	19.1453i	0.572330	−	0.991305i	0.996326	−	0.0856409i	$-0.0272938\pi$
$374$	3.54787	+	6.14510i	0.183456	+	0.317755i
$375$	8.81994	−	32.9164i	0.455460	−	1.69980i
$376$	−7.50885			−0.387240
$377$	8.63527	−	6.26280i	0.444739	−	0.322551i
$378$	0.455764	+	5.78626i	0.0234420	+	0.297613i
$379$	−1.03041	−	0.276097i	−0.0529284	−	0.0141821i	0.232258	−	0.972654i	$-0.425389\pi$
$379$	−1.03041	−	0.276097i	−0.0529284	−	0.0141821i	−0.285186	+	0.958472i	$0.592055\pi$
$380$	−11.7181	−	20.2964i	−0.601128	−	1.04118i
$381$	−3.33284	+	5.77265i	−0.170747	+	0.295742i
$382$	−5.08092	+	5.08092i	−0.259962	+	0.259962i
$383$	−12.0580	+	3.23092i	−0.616133	+	0.165092i	−0.553369	−	0.832936i	$-0.686658\pi$
$383$	−12.0580	+	3.23092i	−0.616133	+	0.165092i	−0.0627635	+	0.998028i	$0.519991\pi$
$384$	−3.38658	−	12.6389i	−0.172821	−	0.644977i
$385$	19.6822	−	23.0479i	1.00310	−	1.17463i
$386$	23.0739	−	39.9652i	1.17443	−	2.03417i
$387$	−9.78317	+	5.64832i	−0.497307	+	0.287120i
$388$	41.4818	+	11.1150i	2.10592	+	0.564279i
$389$		−	19.0137i		−	0.964031i	−0.876163	−	0.482015i	$-0.839905\pi$
$389$		−	19.0137i		−	0.964031i	0.876163	−	0.482015i	$-0.160095\pi$
$390$	13.6852	−	30.6679i	0.692975	−	1.55293i
$391$		−	6.44068i		−	0.325719i
$392$	−12.4111	−	1.30284i	−0.626856	−	0.0658035i
$393$	4.90106	+	8.48888i	0.247226	+	0.428207i
$394$	−39.7231	−	22.9341i	−2.00122	−	1.15541i
$395$	−3.50940	−	3.50940i	−0.176577	−	0.176577i
$396$	1.96414	+	7.33026i	0.0987015	+	0.368359i
$397$	0.702815	+	2.62294i	0.0352733	+	0.131642i	0.981317	−	0.192397i	$-0.0616260\pi$
$397$	0.702815	+	2.62294i	0.0352733	+	0.131642i	−0.946044	+	0.324038i	$0.894959\pi$
$398$	−38.6830	+	38.6830i	−1.93900	+	1.93900i
$399$	−2.23509	+	4.68674i	−0.111894	+	0.234630i
$400$	19.3394	−	11.1656i	0.966970	−	0.558281i
$401$	0.821135	−	3.06452i	0.0410055	−	0.153035i	−0.942388	−	0.334523i	$-0.891425\pi$
$401$	0.821135	−	3.06452i	0.0410055	−	0.153035i	0.983393	+	0.181488i	$0.0580915\pi$
$402$	9.43736			0.470693
$403$	10.8163	−	13.3341i	0.538799	−	0.664218i
$404$			4.51759i			0.224759i
$405$	1.09888	−	4.10107i	0.0546037	−	0.203784i
$406$	9.72728	+	14.1513i	0.482757	+	0.702318i
$407$	−9.36838	−	5.40884i	−0.464373	−	0.268106i
$408$	−1.51121	+	1.51121i	−0.0748159	+	0.0748159i
$409$	2.97815	−	0.797992i	0.147260	−	0.0394582i	−0.184436	−	0.982845i	$-0.559046\pi$
$409$	2.97815	−	0.797992i	0.147260	−	0.0394582i	0.331696	+	0.943386i	$0.392379\pi$
$410$	−49.6284	+	13.2979i	−2.45097	+	0.656735i
$411$	−4.74923	+	4.74923i	−0.234262	+	0.234262i
$412$	35.3188	+	20.3913i	1.74003	+	1.00461i
$413$	−18.2241	−	26.5126i	−0.896751	−	1.30460i
$414$	3.05052	−	11.3847i	0.149925	−	0.559527i
$415$			19.4543i			0.954976i
$416$	24.6690	−	9.44572i	1.20950	−	0.463115i
$417$	−0.351998			−0.0172374
$418$	−3.00655	+	11.2206i	−0.147055	+	0.548818i
$419$	29.0623	−	16.7791i	1.41979	−	0.819715i	0.423508	−	0.905893i	$-0.360799\pi$
$419$	29.0623	−	16.7791i	1.41979	−	0.819715i	0.996280	+	0.0861779i	$0.0274653\pi$
$420$	28.5180	+	13.6001i	1.39154	+	0.663618i
$421$	18.2634	−	18.2634i	0.890104	−	0.890104i	−0.104429	−	0.994532i	$-0.533301\pi$
$421$	18.2634	−	18.2634i	0.890104	−	0.890104i	0.994532	+	0.104429i	$0.0333014\pi$
$422$	−6.20205	−	23.1464i	−0.301911	−	1.12675i
$423$	−1.09013	−	4.06841i	−0.0530038	−	0.197813i
$424$	13.9427	+	13.9427i	0.677116	+	0.677116i
$425$	−13.5238	−	7.80795i	−0.655999	−	0.378741i
$426$	3.39366	+	5.87800i	0.164424	+	0.284790i
$427$	−13.6884	−	2.53608i	−0.662428	−	0.122730i
$428$			10.7455i			0.519402i
$429$	−9.08498	+	3.47863i	−0.438627	+	0.167950i
$430$			105.219i			5.07411i
$431$	−16.9380	−	4.53851i	−0.815873	−	0.218612i	−0.173331	−	0.984864i	$-0.555453\pi$
$431$	−16.9380	−	4.53851i	−0.815873	−	0.218612i	−0.642541	+	0.766251i	$0.722120\pi$
$432$	1.48464	−	0.857159i	0.0714299	−	0.0412401i
$433$	17.6656	−	30.5978i	0.848957	−	1.47044i	−0.0331835	−	0.999449i	$-0.510565\pi$
$433$	17.6656	−	30.5978i	0.848957	−	1.47044i	0.882140	−	0.470987i	$-0.156102\pi$
$434$	21.0182	+	17.9489i	1.00890	+	0.861574i
$435$	−3.25111	−	12.1333i	−0.155879	−	0.581747i
$436$	36.8556	−	9.87543i	1.76506	−	0.472947i
$437$	7.45575	−	7.45575i	0.356657	−	0.356657i
$438$	−7.42121	+	12.8539i	−0.354599	+	0.614184i
$439$	9.35887	+	16.2100i	0.446674	+	0.773663i	0.998167	−	0.0605168i	$-0.0192749\pi$
$439$	9.35887	+	16.2100i	0.446674	+	0.773663i	−0.551493	+	0.834180i	$0.685942\pi$
$440$	19.7265	+	5.28570i	0.940425	+	0.251986i
$441$	−1.09593	−	6.91368i	−0.0521873	−	0.329223i
$442$	−7.36404	−	5.97354i	−0.350272	−	0.284133i
$443$	30.4948			1.44885			0.724426	−	0.689353i	$-0.242105\pi$
$443$	30.4948			1.44885			0.724426	+	0.689353i	$0.242105\pi$
$444$	2.91867	−	10.8926i	0.138514	−	0.516941i
$445$	−10.5538	−	18.2798i	−0.500299	−	0.866544i
$446$	−16.9211	+	29.3083i	−0.801239	+	1.38779i
$447$	−8.34509	−	8.34509i	−0.394709	−	0.394709i
$448$	11.1686	+	31.5326i	0.527666	+	1.48978i
$449$	−19.0888	+	5.11484i	−0.900859	+	0.241384i	−0.679385	−	0.733782i	$-0.737753\pi$
$449$	−19.0888	+	5.11484i	−0.900859	+	0.241384i	−0.221474	+	0.975166i	$0.571087\pi$
$450$	−20.2068	−	20.2068i	−0.952559	−	0.952559i
$451$	12.8894	+	7.44168i	0.606937	+	0.350415i
$452$	−7.69138	+	4.44062i	−0.361772	+	0.208869i
$453$	16.7673	+	4.49278i	0.787795	+	0.211089i
$454$	−42.3699			−1.98852
$455$	−13.5494	+	38.1681i	−0.635207	+	1.78935i
$456$	−3.49875			−0.163844
$457$	7.87442	+	2.10994i	0.368350	+	0.0986990i	0.438246	−	0.898855i	$-0.355600\pi$
$457$	7.87442	+	2.10994i	0.368350	+	0.0986990i	−0.0698958	+	0.997554i	$0.522267\pi$
$458$	33.8903	−	19.5666i	1.58359	−	0.914286i
$459$	−1.03819	−	0.599399i	−0.0484585	−	0.0279775i
$460$	−45.3669	−	45.3669i	−2.11524	−	2.11524i
$461$	−32.2015	+	8.62836i	−1.49977	+	0.401863i	−0.913024	−	0.407907i	$-0.866259\pi$
$461$	−32.2015	+	8.62836i	−1.49977	+	0.401863i	−0.586748	+	0.809769i	$0.699592\pi$
$462$	−5.22848	−	14.7618i	−0.243251	−	0.686779i
$463$	1.66118	+	1.66118i	0.0772018	+	0.0772018i	0.744653	−	0.667452i	$-0.232615\pi$
$463$	1.66118	+	1.66118i	0.0772018	+	0.0772018i	−0.667452	+	0.744653i	$0.732615\pi$
$464$	2.53596	−	4.39242i	0.117729	−	0.203913i
$465$	−10.1090	−	17.5093i	−0.468794	−	0.811974i
$466$	−14.1617	+	52.8523i	−0.656029	+	2.44833i
$467$	12.2930			0.568854			0.284427	−	0.958698i	$-0.408197\pi$
$467$	12.2930			0.568854			0.284427	+	0.958698i	$0.408197\pi$
$468$	−5.95391	−	8.20936i	−0.275219	−	0.379478i
$469$	−11.3466	+	0.893731i	−0.523936	+	0.0412687i
$470$	−37.8939	−	10.1537i	−1.74792	−	0.468353i
$471$	2.20554	+	3.82011i	0.101626	+	0.176022i
$472$	10.8391	−	18.7738i	0.498908	−	0.864135i
$473$	21.5523	−	21.5523i	0.990978	−	0.990978i
$474$	−2.47702	+	0.663716i	−0.113773	+	0.0304855i
$475$	−6.61664	−	24.6937i	−0.303592	−	1.13302i
$476$	5.79324	−	6.78390i	0.265533	−	0.310939i
$477$	−5.53017	+	9.57853i	−0.253209	+	0.438571i
$478$	12.5724	−	7.25871i	0.575050	−	0.332005i
$479$	−22.8035	−	6.11018i	−1.04192	−	0.279181i	−0.303010	−	0.952987i	$-0.597992\pi$
$479$	−22.8035	−	6.11018i	−1.04192	−	0.279181i	−0.738908	+	0.673806i	$0.764658\pi$
$480$		−	31.1058i		−	1.41978i
$481$	14.2760	+	2.27341i	0.650930	+	0.103659i
$482$		−	1.43274i		−	0.0652594i
$483$	−2.58951	+	13.9768i	−0.117827	+	0.635964i
$484$	5.23177	+	9.06169i	0.237808	+	0.411895i
$485$	56.1413	+	32.4132i	2.54925	+	1.47181i
$486$	−1.55123	−	1.55123i	−0.0703653	−	0.0703653i
$487$	−2.73616	−	10.2115i	−0.123987	−	0.462726i	0.875814	−	0.482648i	$-0.160325\pi$
$487$	−2.73616	−	10.2115i	−0.123987	−	0.462726i	−0.999802	+	0.0199217i	$0.993658\pi$
$488$	−2.42785	−	9.06085i	−0.109903	−	0.410165i
$489$	0.447232	−	0.447232i	0.0202245	−	0.0202245i
$490$	−60.8719	−	23.3575i	−2.74991	−	1.05518i
$491$	9.46863	−	5.46672i	0.427313	−	0.246710i	−0.270888	−	0.962611i	$-0.587317\pi$
$491$	9.46863	−	5.46672i	0.427313	−	0.246710i	0.698201	+	0.715901i	$0.253984\pi$
$492$	−4.01561	+	14.9865i	−0.181038	+	0.675643i
$493$	−3.54672			−0.159736
$494$	−1.60964	−	15.4396i	−0.0724210	−	0.694661i
$495$			11.4555i			0.514886i
$496$	2.11287	−	7.88533i	0.0948705	−	0.354062i
$497$	−4.63687	−	6.74575i	−0.207992	−	0.302588i
$498$	8.70534	+	5.02603i	0.390096	+	0.225222i
$499$	−21.1483	+	21.1483i	−0.946727	+	0.946727i	−0.998651	−	0.0519238i	$-0.983465\pi$
$499$	−21.1483	+	21.1483i	−0.946727	+	0.946727i	0.0519238	+	0.998651i	$0.483465\pi$
$500$	−92.5823	+	24.8073i	−4.14041	+	1.10942i
$501$	−16.3769	+	4.38817i	−0.731664	+	0.196049i
$502$	30.6982	−	30.6982i	1.37013	−	1.37013i
$503$	6.00891	+	3.46924i	0.267924	+	0.154686i	0.627944	−	0.778259i	$-0.283897\pi$
$503$	6.00891	+	3.46924i	0.267924	+	0.154686i	−0.360020	+	0.932945i	$0.617230\pi$
$504$	3.88702	−	2.67184i	0.173141	−	0.119013i
$505$	−1.76499	+	6.58703i	−0.0785409	+	0.293119i
$506$			31.8008i			1.41372i
$507$	9.67550	−	8.68243i	0.429704	−	0.385600i
$508$	18.7482			0.831817
$509$	2.48325	−	9.26762i	0.110068	−	0.410780i	−0.888803	−	0.458290i	$-0.848462\pi$
$509$	2.48325	−	9.26762i	0.110068	−	0.410780i	0.998871	+	0.0475103i	$0.0151287\pi$
$510$	−9.66990	+	5.58292i	−0.428190	+	0.247216i
$511$	7.70526	−	16.1571i	0.340861	−	0.714748i
$512$	13.2032	−	13.2032i	0.583504	−	0.583504i
$513$	−0.507945	−	1.89568i	−0.0224263	−	0.0836961i
$514$	−9.05279	−	33.7855i	−0.399301	−	1.49021i
$515$	43.5310	+	43.5310i	1.91821	+	1.91821i
$516$	27.5166	+	15.8867i	1.21135	+	0.699374i
$517$	5.68213	+	9.84174i	0.249900	+	0.432839i
$518$	−4.23932	+	22.8816i	−0.186265	+	1.00536i
$519$		−	9.21339i		−	0.404423i
$520$	−27.1438	+	2.82984i	−1.19033	+	0.124097i
$521$			17.8193i			0.780676i	0.920672	+	0.390338i	$0.127642\pi$
$521$			17.8193i			0.780676i	−0.920672	+	0.390338i	$0.872358\pi$
$522$	−6.26927	−	1.67985i	−0.274399	−	0.0735249i
$523$	−6.40070	+	3.69545i	−0.279883	+	0.161591i	−0.633370	−	0.773849i	$-0.718329\pi$
$523$	−6.40070	+	3.69545i	−0.279883	+	0.161591i	0.353487	+	0.935439i	$0.384996\pi$
$524$	13.7849	−	23.8762i	0.602198	−	1.04304i
$525$	26.2084	+	22.3811i	1.14383	+	0.976793i
$526$	0.247246	+	0.922736i	0.0107805	+	0.0402332i
$527$	−5.51410	+	1.47750i	−0.240198	+	0.0643608i
$528$	−3.27067	+	3.27067i	−0.142338	+	0.142338i
$529$	2.93251	−	5.07925i	0.127500	−	0.220837i
$530$	51.5090	+	89.2163i	2.23741	+	3.87531i
$531$	11.7455	+	3.14721i	0.509713	+	0.136577i
$532$	14.5593	−	1.14679i	0.631227	−	0.0497196i
$533$	−19.6415	−	3.12785i	−0.850767	−	0.135482i
$534$	−10.9063			−0.471963
$535$	−4.19817	+	15.6678i	−0.181503	+	0.677377i
$536$	−3.83461	−	6.64175i	−0.165630	−	0.286880i
$537$	−1.36042	+	2.35631i	−0.0587063	+	0.101682i
$538$	25.5481	+	25.5481i	1.10146	+	1.10146i
$539$	7.68418	+	17.2530i	0.330981	+	0.743138i
$540$	−11.5349	+	3.09075i	−0.496381	+	0.133005i
$541$	−17.3442	−	17.3442i	−0.745687	−	0.745687i	0.227979	−	0.973666i	$-0.426788\pi$
$541$	−17.3442	−	17.3442i	−0.745687	−	0.745687i	−0.973666	+	0.227979i	$0.926788\pi$
$542$	−44.2481	−	25.5467i	−1.90062	−	1.09732i
$543$	−13.3823	+	7.72625i	−0.574288	+	0.331565i
$544$	−8.48354	−	2.27316i	−0.363729	−	0.0974608i
$545$	57.5968			2.46718
$546$	13.5788	+	15.9238i	0.581119	+	0.681475i
$547$	26.8037			1.14604			0.573022	−	0.819540i	$-0.305771\pi$
$547$	26.8037			1.14604			0.573022	+	0.819540i	$0.305771\pi$
$548$	18.2472	+	4.88933i	0.779483	+	0.208862i
$549$	4.55683	−	2.63089i	0.194481	−	0.112284i
$550$	66.7735	+	38.5517i	2.84723	+	1.64385i
$551$	−4.10570	−	4.10570i	−0.174909	−	0.174909i
$552$	−9.25172	+	2.47899i	−0.393779	+	0.105513i
$553$	2.91528	−	1.03257i	0.123970	−	0.0439092i
$554$	−12.6847	−	12.6847i	−0.538923	−	0.538923i
$555$	8.51132	−	14.7420i	0.361285	−	0.625765i
$556$	0.495023	+	0.857405i	0.0209936	+	0.0363621i
$557$	−3.42508	+	12.7826i	−0.145125	+	0.541615i	0.854624	+	0.519247i	$0.173787\pi$
$557$	−3.42508	+	12.7826i	−0.145125	+	0.541615i	−0.999750	+	0.0223686i	$0.992879\pi$
$558$	−10.4466			−0.442242
$559$	−16.5979	+	37.1953i	−0.702017	+	1.57319i
$560$	1.51214	+	19.1978i	0.0638997	+	0.811254i
$561$	3.12428	+	0.837148i	0.131907	+	0.0353444i
$562$	−4.87361	−	8.44134i	−0.205581	−	0.356077i
$563$	8.52959	−	14.7737i	0.359479	−	0.622636i	−0.628395	−	0.777895i	$-0.716288\pi$
$563$	8.52959	−	14.7737i	0.359479	−	0.622636i	0.987874	+	0.155258i	$0.0496210\pi$
$564$	−8.37685	+	8.37685i	−0.352729	+	0.352729i
$565$	−12.9496	+	3.46983i	−0.544793	+	0.145977i
$566$	7.21260	+	26.9178i	0.303168	+	1.13144i
$567$	2.01196	+	1.71815i	0.0844942	+	0.0721554i
$568$	2.75784	−	4.77673i	0.115717	−	0.200427i
$569$	−26.6276	+	15.3735i	−1.11629	+	0.644489i	−0.940450	−	0.339931i	$-0.889596\pi$
$569$	−26.6276	+	15.3735i	−1.11629	+	0.644489i	−0.175837	+	0.984419i	$0.556263\pi$
$570$	−17.6567	−	4.73110i	−0.739557	−	0.198164i
$571$			4.14822i			0.173598i	0.996226	+	0.0867988i	$0.0276637\pi$
$571$			4.14822i			0.173598i	−0.996226	+	0.0867988i	$0.972336\pi$
$572$	21.2497	+	17.2373i	0.888496	+	0.720728i
$573$			3.27541i			0.136832i
$574$	5.83262	−	31.4813i	0.243449	−	1.31401i
$575$	−34.9927	−	60.6091i	−1.45930	−	2.52757i
$576$	−10.9498	−	6.32186i	−0.456241	−	0.263411i
$577$	−8.22860	−	8.22860i	−0.342561	−	0.342561i	0.514768	−	0.857329i	$-0.327878\pi$
$577$	−8.22860	−	8.22860i	−0.342561	−	0.342561i	−0.857329	+	0.514768i	$0.827878\pi$
$578$	−8.83646	−	32.9781i	−0.367548	−	1.37171i
$579$	−5.44447	−	20.3190i	−0.226264	−	0.844430i
$580$	−24.9824	+	24.9824i	−1.03734	+	1.03734i
$581$	−10.9424	−	5.21840i	−0.453968	−	0.216496i
$582$	29.0082	−	16.7479i	1.20243	−	0.694223i
$583$	7.72369	−	28.8252i	0.319883	−	1.19382i
$584$	12.0616			0.499113
$585$	−5.47396	−	14.2961i	−0.226320	−	0.591070i
$586$		−	12.5207i		−	0.517225i
$587$	−2.86420	+	10.6893i	−0.118218	+	0.441196i	−0.999508	−	0.0313808i	$-0.990010\pi$
$587$	−2.86420	+	10.6893i	−0.118218	+	0.441196i	0.881289	+	0.472577i	$0.156676\pi$
$588$	−15.2993	+	12.3924i	−0.630931	+	0.511052i
$589$	−8.09348	−	4.67278i	−0.333486	−	0.192538i
$590$	80.0865	−	80.0865i	3.29711	−	3.29711i
$591$	−20.1959	+	5.41149i	−0.830750	+	0.222599i
$592$	6.63909	−	1.77894i	0.272865	−	0.0731139i
$593$	9.97769	−	9.97769i	0.409734	−	0.409734i	−0.471911	−	0.881646i	$-0.656436\pi$
$593$	9.97769	−	9.97769i	0.409734	−	0.409734i	0.881646	+	0.471911i	$0.156436\pi$
$594$	5.12605	+	2.95953i	0.210324	+	0.121431i
$595$	11.0974	−	7.62811i	0.454951	−	0.312722i
$596$	−8.59127	+	32.0631i	−0.351912	+	1.31335i
$597$			24.9370i			1.02060i
$598$	−15.1959	−	39.6864i	−0.621406	−	1.62290i
$599$	34.7079			1.41813			0.709063	−	0.705145i	$-0.249118\pi$
$599$	34.7079			1.41813			0.709063	+	0.705145i	$0.249118\pi$
$600$	−6.01050	+	22.4315i	−0.245378	+	0.915761i
$601$	11.2636	−	6.50302i	0.459450	−	0.265264i	−0.252363	−	0.967633i	$-0.581208\pi$
$601$	11.2636	−	6.50302i	0.459450	−	0.265264i	0.711813	+	0.702369i	$0.247874\pi$
$602$	−59.1823	−	28.2238i	−2.41209	−	1.15032i
$603$	3.04189	−	3.04189i	0.123875	−	0.123875i
$604$	−12.6366	−	47.1604i	−0.514175	−	1.91893i
$605$	4.08802	+	15.2567i	0.166202	+	0.620273i
$606$	2.49155	+	2.49155i	0.101212	+	0.101212i
$607$	−18.9672	−	10.9507i	−0.769856	−	0.444477i	0.0629670	−	0.998016i	$-0.479944\pi$
$607$	−18.9672	−	10.9507i	−0.769856	−	0.444477i	−0.832823	+	0.553539i	$0.813277\pi$
$608$	−7.18915	−	12.4520i	−0.291559	−	0.504994i
$609$	7.69665	+	1.42598i	0.311884	+	0.0577835i
$610$		−	49.0092i		−	1.98432i
$611$	−11.7939	−	9.56698i	−0.477132	−	0.387039i
$612$			3.37179i			0.136297i
$613$	−10.3087	−	2.76221i	−0.416365	−	0.111565i	0.0445537	−	0.999007i	$-0.485813\pi$
$613$	−10.3087	−	2.76221i	−0.416365	−	0.111565i	−0.460919	+	0.887442i	$0.652480\pi$
$614$	27.4815	−	15.8665i	1.10906	−	0.640319i
$615$	−11.7102	+	20.2827i	−0.472201	+	0.817876i
$616$	−8.26445	+	9.67769i	−0.332984	+	0.389925i
$617$	5.78797	+	21.6010i	0.233015	+	0.869624i	0.979034	+	0.203699i	$0.0652963\pi$
$617$	5.78797	+	21.6010i	0.233015	+	0.869624i	−0.746019	+	0.665925i	$0.768037\pi$
$618$	30.7253	−	8.23282i	1.23595	−	0.331172i
$619$	−5.50453	+	5.50453i	−0.221246	+	0.221246i	−0.809023	−	0.587777i	$-0.800003\pi$
$619$	−5.50453	+	5.50453i	−0.221246	+	0.221246i	0.587777	+	0.809023i	$0.300003\pi$
$620$	−28.4330	+	49.2474i	−1.14190	+	1.97782i
$621$	−2.68631	−	4.65282i	−0.107798	−	0.186711i
$622$	30.9689	+	8.29810i	1.24174	+	0.332723i
$623$	13.1127	−	1.03284i	0.525349	−	0.0413800i
$624$	2.51881	−	5.64456i	0.100833	−	0.225963i
$625$	−79.5531			−3.18213
$626$	10.2193	−	38.1390i	0.408446	−	1.52434i
$627$	2.64759	+	4.58576i	0.105735	+	0.183138i
$628$	6.20341	−	10.7446i	0.247543	−	0.428757i
$629$	−3.39863	−	3.39863i	−0.135512	−	0.135512i
$630$	23.2290	−	8.22751i	0.925466	−	0.327792i
$631$	−20.7278	+	5.55399i	−0.825160	+	0.221101i	−0.646601	−	0.762828i	$-0.723810\pi$
$631$	−20.7278	+	5.55399i	−0.825160	+	0.221101i	−0.178559	+	0.983929i	$0.557143\pi$
$632$	1.47358	+	1.47358i	0.0586157	+	0.0586157i
$633$	−9.45972	−	5.46157i	−0.375990	−	0.217078i
$634$	32.4660	−	18.7442i	1.28939	−	0.744429i
$635$	27.3364	+	7.32477i	1.08481	+	0.290675i
$636$	31.1088			1.23354
$637$	−17.8339	−	17.8593i	−0.706603	−	0.707610i
$638$	17.5119			0.693304
$639$	2.98848	+	0.800761i	0.118223	+	0.0316776i
$640$	−48.1116	+	27.7772i	−1.90178	+	1.09799i
$641$	−40.6530	−	23.4710i	−1.60570	−	0.927050i	−0.990318	−	0.138818i	$-0.955670\pi$
$641$	−40.6530	−	23.4710i	−1.60570	−	0.927050i	−0.615379	−	0.788231i	$-0.710997\pi$
$642$	5.92635	+	5.92635i	0.233894	+	0.233894i
$643$	22.4152	−	6.00613i	0.883968	−	0.236859i	0.211850	−	0.977302i	$-0.432051\pi$
$643$	22.4152	−	6.00613i	0.883968	−	0.236859i	0.672118	+	0.740444i	$0.265385\pi$
$644$	37.6866	−	13.3482i	1.48506	−	0.525995i
$645$	33.9147	+	33.9147i	1.33539	+	1.33539i
$646$	−2.58064	+	4.46981i	−0.101534	+	0.175862i
$647$	−6.98028	−	12.0902i	−0.274423	−	0.475315i	0.695566	−	0.718462i	$-0.255154\pi$
$647$	−6.98028	−	12.0902i	−0.274423	−	0.475315i	−0.969989	+	0.243147i	$0.921820\pi$
$648$	−0.461412	+	1.72201i	−0.0181260	+	0.0676471i
$649$	−32.8087			−1.28786
$650$	−101.753	−	16.2038i	−3.99108	−	0.635567i
$651$	12.5600	−	0.989311i	0.492266	−	0.0387741i
$652$	−1.71833	−	0.460426i	−0.0672951	−	0.0180317i
$653$	−13.4921	−	23.3689i	−0.527985	−	0.914497i	−0.999468	−	0.0326216i	$-0.989614\pi$
$653$	−13.4921	−	23.3689i	−0.527985	−	0.914497i	0.471483	−	0.881875i	$-0.343719\pi$
$654$	14.8801	−	25.7731i	0.581859	−	1.00781i
$655$	29.4278	−	29.4278i	1.14984	−	1.14984i
$656$	−9.13431	+	2.44753i	−0.356635	+	0.0955601i
$657$	1.75109	+	6.53517i	0.0683166	+	0.254961i
$658$	15.8757	−	18.5905i	0.618900	−	0.724733i
$659$	2.76889	−	4.79586i	0.107861	−	0.186820i	−0.807043	−	0.590493i	$-0.798933\pi$
$659$	2.76889	−	4.79586i	0.107861	−	0.186820i	0.914903	+	0.403673i	$0.132267\pi$
$660$	27.9035	−	16.1101i	1.08614	−	0.627085i
$661$	36.8331	+	9.86941i	1.43264	+	0.383875i	0.889951	−	0.456057i	$-0.150739\pi$
$661$	36.8331	+	9.86941i	1.43264	+	0.383875i	0.542692	+	0.839932i	$0.317405\pi$
$662$		−	21.7939i		−	0.847046i
$663$	−4.29903	+	0.448190i	−0.166960	+	0.0174062i
$664$		−	8.16876i		−	0.317009i
$665$	21.6767	+	4.01610i	0.840588	+	0.155738i
$666$	−4.39780	−	7.61721i	−0.170411	−	0.295161i
$667$	−13.7657	−	7.94763i	−0.533010	−	0.307733i
$668$	33.7200	+	33.7200i	1.30466	+	1.30466i
$669$	3.99267	+	14.9009i	0.154366	+	0.576100i
$670$	−10.3705	−	38.7033i	−0.400648	−	1.49524i
$671$	−10.0387	+	10.0387i	−0.387540	+	0.387540i
$672$	17.4960	+	8.34376i	0.674922	+	0.321868i
$673$	5.72219	−	3.30371i	0.220574	−	0.127349i	−0.385642	−	0.922649i	$-0.626020\pi$
$673$	5.72219	−	3.30371i	0.220574	−	0.127349i	0.606216	+	0.795300i	$0.292687\pi$
$674$	−3.66100	+	13.6630i	−0.141016	+	0.526281i
$675$	−13.0263			−0.501383
$676$	−34.7557	−	11.3575i	−1.33676	−	0.436827i
$677$		−	21.3320i		−	0.819855i	−0.912118	−	0.409928i	$-0.865554\pi$
$677$		−	21.3320i		−	0.819855i	0.912118	−	0.409928i	$-0.134446\pi$
$678$	−1.79286	+	6.69105i	−0.0688544	+	0.256968i
$679$	−33.2906	+	22.8832i	−1.27758	+	0.878176i
$680$	7.85819	+	4.53693i	0.301348	+	0.173983i
$681$	−13.6568	+	13.6568i	−0.523331	+	0.523331i
$682$	27.2258	−	7.29513i	1.04253	−	0.279345i
$683$	−1.32430	+	0.354846i	−0.0506730	+	0.0135778i	−0.284067	−	0.958805i	$-0.591684\pi$
$683$	−1.32430	+	0.354846i	−0.0506730	+	0.0135778i	0.233393	+	0.972382i	$0.425017\pi$
$684$	−3.90319	+	3.90319i	−0.149242	+	0.149242i
$685$	24.6958	+	14.2581i	0.943576	+	0.544774i
$686$	29.4660	−	27.9730i	1.12502	−	1.06802i
$687$	4.61689	−	17.2305i	0.176145	−	0.657383i
$688$			19.3660i			0.738323i
$689$	4.13508	+	39.6636i	0.157534	+	1.51106i
$690$	−50.0416			−1.90505
$691$	8.87327	−	33.1155i	0.337555	−	1.25977i	−0.563517	−	0.826104i	$-0.690552\pi$
$691$	8.87327	−	33.1155i	0.337555	−	1.25977i	0.901072	−	0.433669i	$-0.142781\pi$
$692$	−22.4422	+	12.9570i	−0.853124	+	0.492551i
$693$	−6.44334	−	3.07281i	−0.244762	−	0.116726i
$694$	−18.6303	+	18.6303i	−0.707197	+	0.707197i
$695$	0.386803	+	1.44357i	0.0146723	+	0.0547577i
$696$	1.36512	+	5.09470i	0.0517447	+	0.193114i
$697$	4.67597	+	4.67597i	0.177115	+	0.177115i
$698$	48.3762	+	27.9300i	1.83107	+	1.05717i
$699$	12.4709	+	21.6002i	0.471693	+	0.816996i
$700$	17.6590	−	95.3140i	0.667449	−	3.60253i
$701$			42.5906i			1.60862i	0.594208	+	0.804312i	$0.297466\pi$
$701$			42.5906i			1.60862i	−0.594208	+	0.804312i	$0.702534\pi$
$702$	−7.81134	−	1.24393i	−0.294820	−	0.0469492i
$703$		−	7.86853i		−	0.296767i
$704$	32.9518	+	8.82940i	1.24192	+	0.332771i
$705$	−15.4869	+	8.94137i	−0.583271	+	0.336751i
$706$	10.3007	−	17.8413i	0.387671	−	0.671466i
$707$	−3.23155	−	2.75964i	−0.121535	−	0.103787i
$708$	−8.85197	−	33.0360i	−0.332678	−	1.24157i
$709$	37.3239	−	10.0009i	1.40173	−	0.375592i	0.522764	−	0.852478i	$-0.324901\pi$
$709$	37.3239	−	10.0009i	1.40173	−	0.375592i	0.878965	+	0.476886i	$0.158234\pi$
$710$	20.3769	−	20.3769i	0.764730	−	0.764730i
$711$	−0.584473	+	1.01234i	−0.0219195	+	0.0379656i
$712$	4.43148	+	7.67556i	0.166077	+	0.287654i
$713$	−24.7124	−	6.62166i	−0.925486	−	0.247983i
$714$	−0.546369	−	6.93655i	−0.0204473	−	0.259594i
$715$	24.2494	+	33.4355i	0.906876	+	1.25042i
$716$	7.65273			0.285996
$717$	1.71275	−	6.39206i	0.0639637	−	0.238716i
$718$	25.2525	+	43.7385i	0.942413	+	1.63231i
$719$	25.0297	−	43.3527i	0.933450	−	1.61678i	0.156076	−	0.987745i	$-0.450116\pi$
$719$	25.0297	−	43.3527i	0.933450	−	1.61678i	0.777375	−	0.629038i	$-0.216551\pi$
$720$	−5.14671	−	5.14671i	−0.191807	−	0.191807i
$721$	−36.1615	+	12.8081i	−1.34672	+	0.476997i
$722$	32.0998	−	8.60112i	1.19463	−	0.320101i
$723$	−0.461806	−	0.461806i	−0.0171748	−	0.0171748i
$724$	37.6396	+	21.7312i	1.39886	+	0.807634i
$725$	−33.3759	+	19.2696i	−1.23955	+	0.715655i
$726$	7.88314	+	2.11228i	0.292571	+	0.0783941i
$727$	5.22923			0.193941			0.0969707	−	0.995287i	$-0.469085\pi$
$727$	5.22923			0.193941			0.0969707	+	0.995287i	$0.469085\pi$
$728$	5.68932	−	16.0266i	0.210860	−	0.593984i
$729$	−1.00000			−0.0370370
$730$	60.8698	+	16.3100i	2.25289	+	0.603661i
$731$	11.7280	−	6.77119i	0.433777	−	0.250442i
$732$	−12.8167	−	7.39975i	−0.473721	−	0.273503i
$733$	−10.0406	−	10.0406i	−0.370858	−	0.370858i	0.496932	−	0.867790i	$-0.334460\pi$
$733$	−10.0406	−	10.0406i	−0.370858	−	0.370858i	−0.867790	+	0.496932i	$0.834460\pi$
$734$	48.0070	−	12.8634i	1.77197	−	0.474798i
$735$	−27.1492	+	12.0918i	−1.00141	+	0.446012i
$736$	−27.8329	−	27.8329i	−1.02593	−	1.02593i
$737$	−5.80349	+	10.0519i	−0.213774	+	0.370268i
$738$	6.05066	+	10.4801i	0.222728	+	0.385776i
$739$	−1.48318	+	5.53532i	−0.0545598	+	0.203620i	−0.987825	−	0.155567i	$-0.950279\pi$
$739$	−1.48318	+	5.53532i	−0.0545598	+	0.203620i	0.933265	+	0.359187i	$0.116946\pi$
$740$	−47.8786			−1.76005
$741$	−5.49539	−	4.45774i	−0.201878	−	0.163759i
$742$	−63.9979	+	5.04090i	−2.34944	+	0.185057i
$743$	0.617584	+	0.165481i	0.0226569	+	0.00607091i	0.270130	−	0.962824i	$-0.412933\pi$
$743$	0.617584	+	0.165481i	0.0226569	+	0.00607091i	−0.247473	+	0.968895i	$0.579600\pi$
$744$	4.24471	+	7.35205i	0.155618	+	0.269539i
$745$	−25.0536	+	43.3941i	−0.917892	+	1.58984i
$746$	−34.2932	+	34.2932i	−1.25556	+	1.25556i
$747$	4.42595	−	1.18593i	0.161937	−	0.0433909i
$748$	−2.35460	−	8.78749i	−0.0860928	−	0.321303i
$749$	−7.68650	−	6.56404i	−0.280859	−	0.239845i
$750$	−37.3793	+	64.7428i	−1.36490	+	2.36407i
$751$	−22.0888	+	12.7530i	−0.806031	+	0.465362i	−0.845576	−	0.533856i	$-0.820743\pi$
$751$	−22.0888	+	12.7530i	−0.806031	+	0.465362i	0.0395448	+	0.999218i	$0.487409\pi$
$752$	−6.97454	−	1.86882i	−0.254335	−	0.0681490i
$753$		−	19.7895i		−	0.721171i
$754$	−21.8543	+	8.36799i	−0.795887	+	0.304744i
$755$		−	73.7008i		−	2.68225i
$756$	1.35564	−	7.31704i	0.0493043	−	0.266118i
$757$	8.06785	+	13.9739i	0.293231	+	0.507891i	0.974572	−	0.224075i	$-0.0719362\pi$
$757$	8.06785	+	13.9739i	0.293231	+	0.507891i	−0.681341	+	0.731966i	$0.738603\pi$
$758$	2.02669	+	1.17011i	0.0736127	+	0.0425003i
$759$	10.2502	+	10.2502i	0.372058	+	0.372058i
$760$	3.84470	+	14.3486i	0.139462	+	0.520479i
$761$	−6.42639	−	23.9836i	−0.232957	−	0.869406i	−0.979059	−	0.203575i	$-0.934744\pi$
$761$	−6.42639	−	23.9836i	−0.232957	−	0.869406i	0.746103	−	0.665831i	$-0.231923\pi$
$762$	10.3400	−	10.3400i	0.374580	−	0.374580i
$763$	−15.4497	+	32.3963i	−0.559316	+	1.17283i
$764$	7.97831	−	4.60628i	0.288645	−	0.166649i
$765$	−1.31733	+	4.91635i	−0.0476283	+	0.177751i
$766$	27.3856			0.989481
$767$	40.9442	−	15.6775i	1.47841	−	0.566082i
$768$			3.41758i			0.123321i
$769$	−3.09729	+	11.5592i	−0.111691	+	0.416837i	−0.999018	−	0.0443040i	$-0.985893\pi$
$769$	−3.09729	+	11.5592i	−0.111691	+	0.416837i	0.887327	+	0.461141i	$0.152560\pi$
$770$	−54.7935	+	37.6637i	−1.97462	+	1.35731i
$771$	−13.8078	−	7.97194i	−0.497276	−	0.287102i
$772$	−41.8368	+	41.8368i	−1.50574	+	1.50574i
$773$	1.00730	−	0.269904i	0.0362299	−	0.00970777i	−0.240659	−	0.970610i	$-0.577363\pi$
$773$	1.00730	−	0.269904i	0.0362299	−	0.00970777i	0.276888	+	0.960902i	$0.410697\pi$
$774$	23.9378	−	6.41412i	0.860428	−	0.230551i
$775$	−43.8623	+	43.8623i	−1.57558	+	1.57558i
$776$	−23.5734	−	13.6101i	−0.846235	−	0.488574i
$777$	6.00885	+	8.74172i	0.215566	+	0.313608i
$778$	−10.7958	+	40.2904i	−0.387047	+	1.44448i
$779$			10.8258i			0.387875i
$780$	−27.1246	+	33.4385i	−0.971215	+	1.19729i
$781$	−8.34771			−0.298704
$782$	−3.65696	+	13.6480i	−0.130773	+	0.488050i
$783$	−2.56220	+	1.47928i	−0.0915654	+	0.0528653i
$784$	−11.2037	−	4.29905i	−0.400133	−	0.153538i
$785$	13.2429	−	13.2429i	0.472660	−	0.472660i
$786$	−5.56555	−	20.7709i	−0.198517	−	0.740874i
$787$	12.4106	+	46.3169i	0.442389	+	1.65102i	0.722738	+	0.691122i	$0.242883\pi$
$787$	12.4106	+	46.3169i	0.442389	+	1.65102i	−0.280349	+	0.959898i	$0.590450\pi$
$788$	41.5834	+	41.5834i	1.48135	+	1.48135i
$789$	0.377114	+	0.217727i	0.0134256	+	0.00775128i
$790$	5.44390	+	9.42910i	0.193685	+	0.335472i
$791$	1.52191	−	8.21446i	0.0541129	−	0.292072i
$792$		−	4.81009i		−	0.170919i
$793$	7.73102	−	17.3249i	0.274537	−	0.615226i
$794$		−	5.95712i		−	0.211410i
$795$	45.3592	+	12.1540i	1.60872	+	0.431057i
$796$	60.7420	−	35.0694i	2.15294	−	1.24300i
$797$	−22.8940	+	39.6535i	−0.810946	+	1.40460i	0.101257	+	0.994860i	$0.467713\pi$
$797$	−22.8940	+	39.6535i	−0.810946	+	1.40460i	−0.912203	+	0.409739i	$0.865620\pi$
$798$	7.39729	−	8.66225i	0.261861	−	0.306640i
$799$	1.30684	+	4.87720i	0.0462327	+	0.172543i
$800$	−92.1834	+	24.7005i	−3.25917	+	0.873293i
$801$	−3.51537	+	3.51537i	−0.124210	+	0.124210i
$802$	−3.48001	+	6.02755i	−0.122883	+	0.212840i
$803$	−9.12732	−	15.8090i	−0.322096	−	0.557887i
$804$	−11.6874	−	3.13163i	−0.412182	−	0.110444i
$805$	60.1652	−	4.73901i	2.12054	−	0.167028i
$806$	−30.4910	+	22.1138i	−1.07400	+	0.778926i
$807$	16.4695			0.579755
$808$	0.741108	−	2.76585i	0.0260721	−	0.0973023i
$809$	−14.8591	−	25.7367i	−0.522418	−	0.904855i	−0.999660	−	0.0260831i	$-0.991697\pi$
$809$	−14.8591	−	25.7367i	−0.522418	−	0.904855i	0.477241	−	0.878772i	$-0.341637\pi$
$810$	−4.65710	+	8.06633i	−0.163634	+	0.283422i
$811$	34.3752	+	34.3752i	1.20708	+	1.20708i	0.971970	+	0.235107i	$0.0755440\pi$
$811$	34.3752	+	34.3752i	1.20708	+	1.20708i	0.235107	+	0.971970i	$0.424456\pi$
$812$	−7.35055	−	20.7531i	−0.257954	−	0.728290i
$813$	−22.4966	+	6.02794i	−0.788989	+	0.211409i
$814$	16.7807	+	16.7807i	0.588164	+	0.588164i
$815$	−2.32559	−	1.34268i	−0.0814617	−	0.0470319i
$816$	−1.77979	+	1.02756i	−0.0623050	+	0.0359718i
$817$	21.4148	+	5.73807i	0.749207	+	0.200750i
$818$	−6.76385			−0.236493
$819$	9.50940	+	0.755839i	0.332285	+	0.0264111i
$820$	65.8733			2.30039
$821$	−30.4555	−	8.16053i	−1.06291	−	0.284805i	−0.315330	−	0.948982i	$-0.602115\pi$
$821$	−30.4555	−	8.16053i	−1.06291	−	0.284805i	−0.747575	+	0.664177i	$0.768782\pi$
$822$	12.7603	−	7.36716i	0.445067	−	0.256959i
$823$	−1.78884	−	1.03279i	−0.0623550	−	0.0360007i	0.468498	−	0.883464i	$-0.344795\pi$
$823$	−1.78884	−	1.03279i	−0.0623550	−	0.0360007i	−0.530853	+	0.847464i	$0.678129\pi$
$824$	−18.2784	−	18.2784i	−0.636758	−	0.636758i
$825$	33.9489	−	9.09658i	1.18195	−	0.316702i
$826$	23.5637	+	66.5283i	0.819887	+	2.31482i
$827$	15.5395	+	15.5395i	0.540360	+	0.540360i	0.923634	−	0.383275i	$-0.125204\pi$
$827$	15.5395	+	15.5395i	0.540360	+	0.540360i	−0.383275	+	0.923634i	$0.625204\pi$
$828$	−7.55563	+	13.0867i	−0.262576	+	0.454796i
$829$	7.58600	+	13.1393i	0.263473	+	0.456348i	0.967162	−	0.254159i	$-0.0817987\pi$
$829$	7.58600	+	13.1393i	0.263473	+	0.456348i	−0.703690	+	0.710508i	$0.748465\pi$
$830$	11.0460	−	41.2242i	0.383412	−	1.43091i
$831$	−8.17720			−0.283664
$832$	−45.3418	+	4.72706i	−1.57194	+	0.163881i
$833$	1.31380	+	8.28810i	0.0455205	+	0.287166i
$834$	0.745892	+	0.199861i	0.0258281	+	0.00692063i
$835$	35.9924	+	62.3406i	1.24557	+	2.15739i
$836$	7.44673	−	12.8981i	0.257550	−	0.446091i
$837$	−3.36721	+	3.36721i	−0.116388	+	0.116388i
$838$	−71.1108	+	19.0541i	−2.45648	+	0.658212i
$839$	−14.3405	−	53.5194i	−0.495088	−	1.84769i	−0.529535	−	0.848288i	$-0.677634\pi$
$839$	−14.3405	−	53.5194i	−0.495088	−	1.84769i	0.0344471	−	0.999407i	$-0.489033\pi$
$840$	−15.2288	−	13.0049i	−0.525442	−	0.448712i
$841$	10.1234	−	17.5343i	0.349084	−	0.604631i
$842$	−49.0703	+	28.3308i	−1.69108	+	0.976343i
$843$	−4.29173	−	1.14997i	−0.147815	−	0.0396070i
$844$			30.7229i			1.05753i
$845$	−46.2395	−	30.1390i	−1.59069	−	1.03681i
$846$			9.24001i			0.317678i
$847$	−9.67797	−	1.79306i	−0.332539	−	0.0616103i
$848$	9.48046	+	16.4206i	0.325560	+	0.563887i
$849$	11.0011	+	6.35147i	0.377555	+	0.217982i
$850$	24.2239	+	24.2239i	0.830873	+	0.830873i
$851$	−5.57514	−	20.8067i	−0.191113	−	0.713244i
$852$	−2.25226	−	8.40554i	−0.0771611	−	0.287969i
$853$	−31.2556	+	31.2556i	−1.07017	+	1.07017i	−0.0728280	+	0.997345i	$0.523202\pi$
$853$	−31.2556	+	31.2556i	−1.07017	+	1.07017i	−0.997345	+	0.0728280i	$0.976798\pi$
$854$	27.5661	+	13.1462i	0.943291	+	0.449852i
$855$	−7.21613	+	4.16623i	−0.246786	+	0.142482i
$856$	1.76279	−	6.57881i	0.0602508	−	0.224859i
$857$	−4.67560			−0.159715			−0.0798577	−	0.996806i	$-0.525447\pi$
$857$	−4.67560			−0.159715			−0.0798577	+	0.996806i	$0.525447\pi$
$858$	21.2264	−	2.21293i	0.724658	−	0.0755483i
$859$		−	4.70689i		−	0.160597i	−0.996771	−	0.0802986i	$-0.974413\pi$
$859$		−	4.70689i		−	0.160597i	0.996771	−	0.0802986i	$-0.0255874\pi$
$860$	34.9151	−	130.305i	1.19060	−	4.44337i
$861$	−8.26720	−	12.0272i	−0.281746	−	0.409886i
$862$	33.3150	+	19.2344i	1.13471	+	0.655127i
$863$	−31.1015	+	31.1015i	−1.05871	+	1.05871i	−0.0605431	+	0.998166i	$0.519283\pi$
$863$	−31.1015	+	31.1015i	−1.05871	+	1.05871i	−0.998166	+	0.0605431i	$0.980717\pi$
$864$	−7.07671	+	1.89620i	−0.240754	+	0.0645100i
$865$	−37.7848	+	10.1244i	−1.28472	+	0.344240i
$866$	−54.8070	+	54.8070i	−1.86242	+	1.86242i
$867$	−13.4779	−	7.78144i	−0.457732	−	0.264272i
$868$	−20.0732	−	29.2027i	−0.681330	−	0.991205i
$869$	0.816302	−	3.04648i	0.0276912	−	0.103345i
$870$			27.5567i			0.934259i
$871$	2.43929	−	15.3177i	0.0826522	−	0.519019i
$872$	−24.1845			−0.818992
$873$	3.95180	−	14.7483i	0.133748	−	0.499155i
$874$	−20.0322	+	11.5656i	−0.677599	+	0.391212i
$875$	38.8100	−	81.3804i	1.31202	−	2.75116i
$876$	13.4559	−	13.4559i	0.454633	−	0.454633i
$877$	6.66722	+	24.8824i	0.225136	+	0.840220i	0.982350	+	0.187052i	$0.0598934\pi$
$877$	6.66722	+	24.8824i	0.225136	+	0.840220i	−0.757214	+	0.653167i	$0.773440\pi$
$878$	−10.6278	−	39.6633i	−0.358669	−	1.33857i
$879$	−4.03573	−	4.03573i	−0.136122	−	0.136122i
$880$	17.0073	+	9.81918i	0.573316	+	0.331004i
$881$	−9.58023	−	16.5935i	−0.322766	−	0.559048i	0.658291	−	0.752763i	$-0.271279\pi$
$881$	−9.58023	−	16.5935i	−0.322766	−	0.559048i	−0.981058	+	0.193716i	$0.937946\pi$
$882$	−1.60321	+	15.2725i	−0.0539830	+	0.514252i
$883$			8.19989i			0.275948i	0.990436	+	0.137974i	$0.0440591\pi$
$883$			8.19989i			0.275948i	−0.990436	+	0.137974i	$0.955941\pi$
$884$	7.13753	+	9.84137i	0.240061	+	0.331001i
$885$		−	51.6276i		−	1.73544i
$886$	−64.6192	−	17.3147i	−2.17092	−	0.581697i
$887$	−3.31720	+	1.91519i	−0.111381	+	0.0643057i	−0.554655	−	0.832080i	$-0.687150\pi$
$887$	−3.31720	+	1.91519i	−0.111381	+	0.0643057i	0.443275	+	0.896386i	$0.353817\pi$
$888$	−3.57385	+	6.19009i	−0.119931	+	0.207726i
$889$	−11.4526	+	13.4111i	−0.384109	+	0.449792i
$890$	11.9847	+	44.7276i	0.401729	+	1.49927i
$891$	2.60618	−	0.698323i	0.0873103	−	0.0233947i
$892$	30.6808	−	30.6808i	1.02727	−	1.02727i
$893$	−4.13305	+	7.15866i	−0.138307	+	0.239555i
$894$	12.9452	+	22.4217i	0.432952	+	0.749894i
$895$	11.1583	+	2.98986i	0.372982	+	0.0999401i
$896$	−2.71840	−	34.5121i	−0.0908154	−	1.15297i
$897$	−17.6899	−	7.89388i	−0.590648	−	0.263569i
$898$	43.3539			1.44674
$899$	−3.64639	+	13.6085i	−0.121614	+	0.453869i
$900$	18.3192	+	31.7298i	0.610640	+	1.05766i
$901$	6.62955	−	11.4827i	0.220862	−	0.382545i
$902$	−23.0876	−	23.0876i	−0.768732	−	0.768732i
$903$	−28.1731	+	9.97867i	−0.937542	+	0.332069i
$904$	5.43745	−	1.45696i	0.180847	−	0.0484578i
$905$	46.3914	+	46.3914i	1.54210	+	1.54210i
$906$	−32.9793	−	19.0406i	−1.09566	−	0.632581i
$907$	26.5418	−	15.3239i	0.881305	−	0.508821i	0.0102163	−	0.999948i	$-0.496748\pi$
$907$	26.5418	−	15.3239i	0.881305	−	0.508821i	0.871088	+	0.491126i	$0.163415\pi$
$908$	52.4716	+	14.0597i	1.74133	+	0.466588i
$909$	1.60617			0.0532734
$910$	50.3831	−	73.1859i	1.67018	−	2.42609i
$911$	−17.6785			−0.585714			−0.292857	−	0.956156i	$-0.594606\pi$
$911$	−17.6785			−0.585714			−0.292857	+	0.956156i	$0.594606\pi$
$912$	−3.24979	−	0.870778i	−0.107611	−	0.0288344i
$913$	−10.7067	+	6.18149i	−0.354339	+	0.204578i
$914$	−15.4881	−	8.94204i	−0.512300	−	0.295776i
$915$	−15.7969	−	15.7969i	−0.522228	−	0.522228i
$916$	−48.4631	+	12.9857i	−1.60127	+	0.429058i
$917$	8.65851	+	24.4459i	0.285929	+	0.807274i
$918$	1.85961	+	1.85961i	0.0613764	+	0.0613764i
$919$	6.76666	−	11.7202i	0.223212	−	0.386614i	−0.732570	−	0.680692i	$-0.761679\pi$
$919$	6.76666	−	11.7202i	0.223212	−	0.386614i	0.955781	+	0.294078i	$0.0950126\pi$
$920$	20.3330	+	35.2178i	0.670360	+	1.16110i
$921$	3.74382	−	13.9721i	0.123363	−	0.460397i
$922$	73.1348			2.40856
$923$	10.4177	−	3.98892i	0.342902	−	0.131297i
$924$	1.57661	+	20.0162i	0.0518665	+	0.658484i
$925$	−50.4474	−	13.5173i	−1.65870	−	0.444447i
$926$	−2.57688	−	4.46329i	−0.0846816	−	0.146673i
$927$	7.24987	−	12.5571i	0.238117	−	0.412431i
$928$	−15.3269	+	15.3269i	−0.503130	+	0.503130i
$929$	48.9198	−	13.1080i	1.60501	−	0.430060i	0.658456	−	0.752619i	$-0.271210\pi$
$929$	48.9198	−	13.1080i	1.60501	−	0.430060i	0.946549	+	0.322559i	$0.104543\pi$
$930$	11.4796	+	42.8424i	0.376430	+	1.40486i
$931$	−8.07346	+	11.1152i	−0.264597	+	0.364285i
$932$	35.0762	−	60.7538i	1.14896	−	1.99006i
$933$	12.6567	−	7.30736i	0.414362	−	0.239232i
$934$	−26.0492	−	6.97987i	−0.852357	−	0.228388i
$935$		−	13.7328i		−	0.449111i
$936$	2.29848	+	6.00283i	0.0751282	+	0.196209i
$937$		−	24.1481i		−	0.788885i	−0.918921	−	0.394443i	$-0.870938\pi$
$937$		−	24.1481i		−	0.788885i	0.918921	−	0.394443i	$-0.129062\pi$
$938$	24.5511	+	4.54864i	0.801622	+	0.148518i
$939$	−8.99920	−	15.5871i	−0.293678	−	0.508665i
$940$	43.5592	+	25.1489i	1.42074	+	0.820267i
$941$	−11.0345	−	11.0345i	−0.359716	−	0.359716i	0.503992	−	0.863708i	$-0.331864\pi$
$941$	−11.0345	−	11.0345i	−0.359716	−	0.359716i	−0.863708	+	0.503992i	$0.831864\pi$
$942$	−2.50457	−	9.34720i	−0.0816034	−	0.304548i
$943$	7.67049	+	28.6266i	0.249785	+	0.932212i
$944$	14.7403	−	14.7403i	0.479755	−	0.479755i
$945$	4.83535	−	10.1392i	0.157294	−	0.329828i
$946$	−57.9071	+	33.4327i	−1.88272	+	1.08699i
$947$	−6.74864	+	25.1863i	−0.219301	+	0.818444i	0.765307	+	0.643666i	$0.222587\pi$
$947$	−6.74864	+	25.1863i	−0.219301	+	0.818444i	−0.984608	+	0.174778i	$0.944079\pi$
$948$	3.28783			0.106784
$949$	18.9448	+	15.3676i	0.614976	+	0.498855i
$950$			56.0833i			1.81958i
$951$	4.42285	−	16.5063i	0.143421	−	0.535254i
$952$	−4.65975	+	3.20300i	−0.151023	+	0.103810i
$953$	2.70119	+	1.55953i	0.0875001	+	0.0505182i	0.543112	−	0.839661i	$-0.317246\pi$
$953$	2.70119	+	1.55953i	0.0875001	+	0.0505182i	−0.455612	+	0.890179i	$0.650579\pi$
$954$	17.1571	−	17.1571i	0.555483	−	0.555483i
$955$	13.4327	−	3.59927i	0.434671	−	0.116470i
$956$	−17.9786	+	4.81735i	−0.581470	+	0.155804i
$957$	5.64452	−	5.64452i	0.182461	−	0.182461i
$958$	44.8518	+	25.8952i	1.44910	+	0.836636i
$959$	−14.6441	+	10.0660i	−0.472882	+	0.325048i
$960$	−13.8939	+	51.8527i	−0.448424	+	1.67354i
$961$		−	8.32384i		−	0.268511i
$962$	−28.9604	−	12.9232i	−0.933720	−	0.416661i
$963$	3.82041			0.123111
$964$	−0.475429	+	1.77433i	−0.0153126	+	0.0571472i
$965$	−77.3469	+	44.6563i	−2.48989	+	1.43754i
$966$	13.4231	−	28.1468i	0.431881	−	0.905607i
$967$	10.4152	−	10.4152i	0.334930	−	0.334930i	−0.519525	−	0.854455i	$-0.673891\pi$
$967$	10.4152	−	10.4152i	0.334930	−	0.334930i	0.854455	+	0.519525i	$0.173891\pi$
$968$	−1.71654	−	6.40620i	−0.0551715	−	0.205903i
$969$	0.608923	+	2.27253i	0.0195614	+	0.0730042i
$970$	−100.561	−	100.561i	−3.22881	−	3.22881i
$971$	17.7603	+	10.2539i	0.569955	+	0.329064i	0.757131	−	0.653263i	$-0.226600\pi$
$971$	17.7603	+	10.2539i	0.569955	+	0.329064i	−0.187176	+	0.982326i	$0.559934\pi$
$972$	1.40632	+	2.43582i	0.0451078	+	0.0781290i
$973$	−0.915716	−	0.169657i	−0.0293565	−	0.00543895i
$974$			23.1919i			0.743117i
$975$	−38.0203	+	27.5745i	−1.21762	+	0.883092i
$976$		−	9.02035i		−	0.288734i
$977$	21.0235	+	5.63323i	0.672601	+	0.180223i	0.578926	−	0.815380i	$-0.303472\pi$
$977$	21.0235	+	5.63323i	0.672601	+	0.180223i	0.0936748	+	0.995603i	$0.470139\pi$
$978$	−1.20163	+	0.693762i	−0.0384239	+	0.0221840i
$979$	6.70682	−	11.6166i	0.214351	−	0.371267i
$980$	67.6339	+	49.1256i	2.16049	+	1.56926i
$981$	−3.51108	−	13.1035i	−0.112100	−	0.418364i
$982$	−23.1682	+	6.20790i	−0.739327	+	0.198102i
$983$	4.97085	−	4.97085i	0.158546	−	0.158546i	−0.623376	−	0.781922i	$-0.714240\pi$
$983$	4.97085	−	4.97085i	0.158546	−	0.158546i	0.781922	+	0.623376i	$0.214240\pi$
$984$	4.91704	−	8.51656i	0.156749	−	0.271498i
$985$	44.3858	+	76.8784i	1.41425	+	2.44955i
$986$	7.51559	+	2.01380i	0.239345	+	0.0641323i
$987$	−0.875042	−	11.1093i	−0.0278529	−	0.353613i
$988$	−3.12997	+	19.6548i	−0.0995775	+	0.625303i
$989$	60.6925			1.92991
$990$	6.50432	−	24.2745i	0.206721	−	0.771493i
$991$	−16.0062	−	27.7236i	−0.508454	−	0.880668i	−0.999952	−	0.00978927i	$-0.996884\pi$
$991$	−16.0062	−	27.7236i	−0.508454	−	0.880668i	0.491498	−	0.870879i	$-0.336449\pi$
$992$	−17.4438	+	30.2136i	−0.553843	+	0.959283i
$993$	−7.02472	−	7.02472i	−0.222923	−	0.222923i
$994$	5.99546	+	16.9272i	0.190164	+	0.536897i
$995$	102.268	−	27.4027i	3.24212	−	0.868723i
$996$	−9.11304	−	9.11304i	−0.288758	−	0.288758i
$997$	−38.9153	−	22.4677i	−1.23246	−	0.711561i	−0.264917	−	0.964271i	$-0.585345\pi$
$997$	−38.9153	−	22.4677i	−1.23246	−	0.711561i	−0.967542	+	0.252711i	$0.918678\pi$
$998$	56.8215	−	32.8059i	1.79865	−	1.03845i
$999$	−3.87273	−	1.03769i	−0.122528	−	0.0328312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.223.2	yes	32
3.2	odd	2		819.2.fm.f.496.7		32
7.6	odd	2		273.2.by.d.223.2	yes	32
13.7	odd	12		273.2.by.d.202.2	yes	32
21.20	even	2		819.2.fm.e.496.7		32
39.20	even	12		819.2.fm.e.748.7		32
91.20	even	12	inner	273.2.by.c.202.2	✓	32
273.20	odd	12		819.2.fm.f.748.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.2	✓	32	91.20	even	12	inner
273.2.by.c.223.2	yes	32	1.1	even	1	trivial
273.2.by.d.202.2	yes	32	13.7	odd	12
273.2.by.d.223.2	yes	32	7.6	odd	2
819.2.fm.e.496.7		32	21.20	even	2
819.2.fm.e.748.7		32	39.20	even	12
819.2.fm.f.496.7		32	3.2	odd	2
819.2.fm.f.748.7		32	273.20	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11902 - 0.567791i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(2.11902 - 0.567791i) q^{6} +(-2.49394 + 0.883331i) q^{7} +(-1.26060 - 1.26060i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.11902 - 0.567791i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.43582 + 1.40632i) q^{4} +(3.00219 + 3.00219i) q^{5} +(2.11902 - 0.567791i) q^{6} +(-2.49394 + 0.883331i) q^{7} +(-1.26060 - 1.26060i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-4.65710 - 8.06633i) q^{10} +(-0.698323 + 2.60618i) q^{11} -2.81265 q^{12} +(-0.373866 - 3.58612i) q^{13} +(5.78626 - 0.455764i) q^{14} +(-4.10107 - 1.09888i) q^{15} +(-0.857159 - 1.48464i) q^{16} +(-0.599399 + 1.03819i) q^{17} +(-1.55123 + 1.55123i) q^{18} +(-1.89568 + 0.507945i) q^{19} +(3.09075 + 11.5349i) q^{20} +(1.71815 - 2.01196i) q^{21} +(2.95953 - 5.12605i) q^{22} +(-4.65282 + 2.68631i) q^{23} +(1.72201 + 0.461412i) q^{24} +13.0263i q^{25} +(-1.24393 + 7.81134i) q^{26} +1.00000i q^{27} +(-7.31704 - 1.35564i) q^{28} +(1.47928 + 2.56220i) q^{29} +(8.06633 + 4.65710i) q^{30} +(3.36721 + 3.36721i) q^{31} +(1.89620 + 7.07671i) q^{32} +(-0.698323 - 2.60618i) q^{33} +(1.85961 - 1.85961i) q^{34} +(-10.1392 - 4.83535i) q^{35} +(2.43582 - 1.40632i) q^{36} +(-1.03769 + 3.87273i) q^{37} +4.30539 q^{38} +(2.11684 + 2.91873i) q^{39} -7.56914i q^{40} +(1.42770 - 5.32825i) q^{41} +(-4.78317 + 3.28783i) q^{42} +(-9.78317 - 5.64832i) q^{43} +(-5.36612 + 5.36612i) q^{44} +(4.10107 - 1.09888i) q^{45} +(11.3847 - 3.05052i) q^{46} +(2.97828 - 2.97828i) q^{47} +(1.48464 + 0.857159i) q^{48} +(5.43945 - 4.40594i) q^{49} +(7.39621 - 27.6030i) q^{50} -1.19880i q^{51} +(4.13256 - 9.26092i) q^{52} -11.0603 q^{53} +(0.567791 - 2.11902i) q^{54} +(-9.92075 + 5.72775i) q^{55} +(4.25739 + 2.03033i) q^{56} +(1.38773 - 1.38773i) q^{57} +(-1.67985 - 6.26927i) q^{58} +(3.14721 + 11.7455i) q^{59} +(-8.44410 - 8.44410i) q^{60} +(4.55683 + 2.63089i) q^{61} +(-5.22332 - 9.04706i) q^{62} +(-0.481982 + 2.60148i) q^{63} -12.6437i q^{64} +(9.64379 - 11.8886i) q^{65} +5.91905i q^{66} +(4.15530 + 1.11341i) q^{67} +(-2.92006 + 1.68590i) q^{68} +(2.68631 - 4.65282i) q^{69} +(18.7397 + 16.0032i) q^{70} +(0.800761 + 2.98848i) q^{71} +(-1.72201 + 0.461412i) q^{72} +(-4.78407 + 4.78407i) q^{73} +(4.39780 - 7.61721i) q^{74} +(-6.51315 - 11.2811i) q^{75} +(-5.33186 - 1.42867i) q^{76} +(-0.560542 - 7.11650i) q^{77} +(-2.82839 - 7.38678i) q^{78} -1.16895 q^{79} +(1.88383 - 7.03054i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.05066 + 10.4801i) q^{82} +(3.24002 + 3.24002i) q^{83} +(7.01456 - 2.48450i) q^{84} +(-4.91635 + 1.31733i) q^{85} +(17.5237 + 17.5237i) q^{86} +(-2.56220 - 1.47928i) q^{87} +(4.16566 - 2.40505i) q^{88} +(-4.80209 - 1.28672i) q^{89} -9.31419 q^{90} +(4.10012 + 8.61330i) q^{91} -15.1113 q^{92} +(-4.59969 - 1.23248i) q^{93} +(-8.00209 + 4.62001i) q^{94} +(-7.21613 - 4.16623i) q^{95} +(-5.18051 - 5.18051i) q^{96} +(14.7483 - 3.95180i) q^{97} +(-14.0280 + 6.24783i) q^{98} +(1.90786 + 1.90786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more