LMFDB - Embedded newform 77.2.f.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(15,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("77.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			15.2
Root			$0.453245 + 1.39494i$ of defining polynomial
Character	$\chi$	$=$	77.15
Dual form			77.2.f.a.36.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18661 + 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.837913 - 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(1.18661 + 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.837913 - 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} -0.684570 q^{10} +(-2.22899 - 2.45593i) q^{11} -0.244812 q^{12} +(1.28012 + 0.930062i) q^{13} +(0.453245 - 1.39494i) q^{14} +(-0.233366 - 0.718226i) q^{15} +(3.46236 - 2.51555i) q^{16} +(-4.22899 + 3.07254i) q^{17} +(0.173124 + 0.532822i) q^{18} +(1.30464 - 4.01528i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} +1.61803 q^{21} +(-0.527635 - 4.83590i) q^{22} -1.80505 q^{23} +(3.54946 + 2.57883i) q^{24} +(-1.47777 + 4.54811i) q^{25} +(0.717177 + 2.20724i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.122406 - 0.0889332i) q^{28} +(0.840363 + 2.58637i) q^{29} +(0.342285 - 1.05345i) q^{30} +(-1.04675 - 0.760512i) q^{31} +0.854102 q^{32} +(4.89378 - 2.20210i) q^{33} -7.66708 q^{34} +(0.377594 + 0.274338i) q^{35} +(-0.0178588 + 0.0549637i) q^{36} +(-0.600175 - 1.84715i) q^{37} +(5.00978 - 3.63982i) q^{38} +(-2.07128 + 1.50487i) q^{39} +(0.391081 + 1.20362i) q^{40} +(-0.321724 + 0.990166i) q^{41} +(1.91998 + 1.39494i) q^{42} +8.70820 q^{43} +(0.249184 - 0.435572i) q^{44} -0.178276 q^{45} +(-2.14190 - 1.55618i) q^{46} +(-1.97626 + 6.08229i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-5.67457 + 4.12281i) q^{50} +(-2.61366 - 8.04402i) q^{51} +(-0.0739811 + 0.227690i) q^{52} +(10.6826 + 7.76137i) q^{53} -8.02616 q^{54} +(1.51541 + 0.315846i) q^{55} -2.71154 q^{56} +(5.52656 + 4.01528i) q^{57} +(-1.23259 + 3.79351i) q^{58} +(-2.65875 - 8.18278i) q^{59} +(0.0924396 - 0.0671613i) q^{60} +(12.3295 - 8.95793i) q^{61} +(-0.586436 - 1.80486i) q^{62} +(0.118034 - 0.363271i) q^{63} +(-5.91123 - 4.29476i) q^{64} -0.738517 q^{65} +(7.70550 + 1.60600i) q^{66} -4.67583 q^{67} +(-0.639856 - 0.464883i) q^{68} +(0.902527 - 2.77769i) q^{69} +(0.211544 + 0.651065i) q^{70} +(-7.88234 + 5.72685i) q^{71} +(0.837913 - 0.608780i) q^{72} +(-4.11611 - 12.6681i) q^{73} +(0.880296 - 2.70927i) q^{74} +(-6.25993 - 4.54811i) q^{75} +0.638786 q^{76} +(-1.64693 + 2.87882i) q^{77} -3.75519 q^{78} +(-2.89815 - 2.10563i) q^{79} +(-0.617255 + 1.89971i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-1.23541 + 0.897575i) q^{82} +(13.9627 - 10.1445i) q^{83} +(0.0756511 + 0.232830i) q^{84} +(0.753927 - 2.32035i) q^{85} +(10.3333 + 7.50755i) q^{86} -4.40020 q^{87} +(-8.20113 + 3.69034i) q^{88} -8.91982 q^{89} +(-0.211544 - 0.153696i) q^{90} +(0.488963 - 1.50487i) q^{91} +(-0.0843952 - 0.259742i) q^{92} +(1.69369 - 1.23053i) q^{93} +(-7.58873 + 5.51353i) q^{94} +(0.608919 + 1.87406i) q^{95} +(-0.427051 + 1.31433i) q^{96} +(2.18727 + 1.58915i) q^{97} -1.46673 q^{98} +(-0.137407 - 1.25936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9	\( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20} + 4 q^{21} - q^{22} - 16 q^{23} + 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} + 7 q^{28} - 9 q^{29} + 14 q^{30} - 11 q^{31} - 20 q^{32} + 10 q^{33} - 24 q^{34} - 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} - 5 q^{39} - 16 q^{40} - 22 q^{41} - 3 q^{42} + 16 q^{43} + 29 q^{44} + 18 q^{45} + 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} - 34 q^{50} + 3 q^{51} + 21 q^{52} + 2 q^{53} + 4 q^{54} + 26 q^{55} - 18 q^{56} - 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} + 7 q^{61} - 5 q^{62} - 8 q^{63} + q^{64} + 24 q^{65} + 18 q^{66} - 30 q^{67} + 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} + 3 q^{72} + 3 q^{73} - 9 q^{74} + 5 q^{75} - 52 q^{76} - 5 q^{77} - 18 q^{78} - 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} + 23 q^{83} + 4 q^{84} - 10 q^{85} - 17 q^{86} + 12 q^{87} - 7 q^{88} - 34 q^{89} + 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} - 30 q^{94} + 24 q^{95} + 10 q^{96} + 30 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.18661	+	0.862123i	0.839061	+	0.609613i	0.922108	−	0.386932i	$-0.126465\pi$
$2$	1.18661	+	0.862123i	0.839061	+	0.609613i	−0.0830475	+	0.996546i	$0.526465\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.0467549	+	0.143897i	0.0233775	+	0.0719485i
$5$	−0.377594	+	0.274338i	−0.168865	+	0.122688i	−0.669008	−	0.743255i	$-0.733281\pi$
$5$	−0.377594	+	0.274338i	−0.168865	+	0.122688i	0.500143	+	0.865943i	$0.333281\pi$
$6$	−1.91998	+	1.39494i	−0.783827	+	0.569484i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.837913	−	2.57883i	0.296247	−	0.911755i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$	−0.684570			−0.216480
$11$	−2.22899	−	2.45593i	−0.672067	−	0.740490i
$11$	−2.22899	−	2.45593i	−0.672067	−	0.740490i
$12$	−0.244812			−0.0706712
$13$	1.28012	+	0.930062i	0.355042	+	0.257953i	0.750981	−	0.660324i	$-0.229581\pi$
$13$	1.28012	+	0.930062i	0.355042	+	0.257953i	−0.395939	+	0.918277i	$0.629581\pi$
$14$	0.453245	−	1.39494i	0.121135	−	0.372815i
$15$	−0.233366	−	0.718226i	−0.0602548	−	0.185445i
$16$	3.46236	−	2.51555i	0.865590	−	0.628888i
$17$	−4.22899	+	3.07254i	−1.02568	+	0.745201i	−0.967440	−	0.253101i	$-0.918549\pi$
$17$	−4.22899	+	3.07254i	−1.02568	+	0.745201i	−0.0582418	+	0.998303i	$0.518549\pi$
$18$	0.173124	+	0.532822i	0.0408058	+	0.125587i
$19$	1.30464	−	4.01528i	0.299306	−	0.921169i	−0.682435	−	0.730946i	$-0.739079\pi$
$19$	1.30464	−	4.01528i	0.299306	−	0.921169i	0.981741	−	0.190223i	$-0.0609211\pi$
$20$	−0.0571308	−	0.0415079i	−0.0127748	−	0.00928146i
$21$	1.61803			0.353084
$22$	−0.527635	−	4.83590i	−0.112492	−	1.03102i
$23$	−1.80505			−0.376380			−0.188190	−	0.982133i	$-0.560262\pi$
$23$	−1.80505			−0.376380			−0.188190	+	0.982133i	$0.560262\pi$
$24$	3.54946	+	2.57883i	0.724530	+	0.526402i
$25$	−1.47777	+	4.54811i	−0.295554	+	0.909621i
$26$	0.717177	+	2.20724i	0.140650	+	0.432876i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	0.122406	−	0.0889332i	0.0231326	−	0.0168068i
$29$	0.840363	+	2.58637i	0.156051	+	0.480277i	0.998266	−	0.0588657i	$-0.0187484\pi$
$29$	0.840363	+	2.58637i	0.156051	+	0.480277i	−0.842215	+	0.539143i	$0.818748\pi$
$30$	0.342285	−	1.05345i	0.0624924	−	0.192332i
$31$	−1.04675	−	0.760512i	−0.188003	−	0.136592i	0.489803	−	0.871833i	$-0.337069\pi$
$31$	−1.04675	−	0.760512i	−0.188003	−	0.136592i	−0.677805	+	0.735241i	$0.737069\pi$
$32$	0.854102			0.150985
$33$	4.89378	−	2.20210i	0.851898	−	0.383337i
$34$	−7.66708			−1.31489
$35$	0.377594	+	0.274338i	0.0638250	+	0.0463716i
$36$	−0.0178588	+	0.0549637i	−0.00297647	+	0.00916062i
$37$	−0.600175	−	1.84715i	−0.0986682	−	0.303669i	0.889524	−	0.456888i	$-0.151036\pi$
$37$	−0.600175	−	1.84715i	−0.0986682	−	0.303669i	−0.988192	+	0.153219i	$0.951036\pi$
$38$	5.00978	−	3.63982i	0.812693	−	0.590456i
$39$	−2.07128	+	1.50487i	−0.331670	+	0.240972i
$40$	0.391081	+	1.20362i	0.0618353	+	0.190309i
$41$	−0.321724	+	0.990166i	−0.0502449	+	0.154638i	−0.973031	−	0.230675i	$-0.925907\pi$
$41$	−0.321724	+	0.990166i	−0.0502449	+	0.154638i	0.922786	+	0.385313i	$0.125907\pi$
$42$	1.91998	+	1.39494i	0.296259	+	0.215245i
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	0.249184	−	0.435572i	0.0375659	−	0.0656650i
$45$	−0.178276			−0.0265758
$46$	−2.14190	−	1.55618i	−0.315805	−	0.229446i
$47$	−1.97626	+	6.08229i	−0.288266	+	0.887193i	0.697134	+	0.716941i	$0.254458\pi$
$47$	−1.97626	+	6.08229i	−0.288266	+	0.887193i	−0.985401	+	0.170252i	$0.945542\pi$
$48$	2.13986	+	6.58580i	0.308862	+	0.950578i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−5.67457	+	4.12281i	−0.802505	+	0.583054i
$51$	−2.61366	−	8.04402i	−0.365986	−	1.12639i
$52$	−0.0739811	+	0.227690i	−0.0102593	+	0.0315750i
$53$	10.6826	+	7.76137i	1.46737	+	1.06611i	0.981366	+	0.192149i	$0.0615458\pi$
$53$	10.6826	+	7.76137i	1.46737	+	1.06611i	0.486004	+	0.873957i	$0.338454\pi$
$54$	−8.02616			−1.09222
$55$	1.51541	+	0.315846i	0.204338	+	0.0425887i
$56$	−2.71154			−0.362345
$57$	5.52656	+	4.01528i	0.732011	+	0.531837i
$58$	−1.23259	+	3.79351i	−0.161847	+	0.498112i
$59$	−2.65875	−	8.18278i	−0.346139	−	1.06531i	−0.960971	−	0.276649i	$-0.910776\pi$
$59$	−2.65875	−	8.18278i	−0.346139	−	1.06531i	0.614832	−	0.788658i	$-0.289224\pi$
$60$	0.0924396	−	0.0671613i	0.0119339	−	0.00867048i
$61$	12.3295	−	8.95793i	1.57864	−	1.14695i	0.660399	−	0.750915i	$-0.270387\pi$
$61$	12.3295	−	8.95793i	1.57864	−	1.14695i	0.918237	−	0.396031i	$-0.129613\pi$
$62$	−0.586436	−	1.80486i	−0.0744774	−	0.229218i
$63$	0.118034	−	0.363271i	0.0148709	−	0.0457679i
$64$	−5.91123	−	4.29476i	−0.738904	−	0.536845i
$65$	−0.738517			−0.0916018
$66$	7.70550	+	1.60600i	0.948482	+	0.197685i
$67$	−4.67583			−0.571243			−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583			−0.571243			−0.285622	+	0.958342i	$0.592200\pi$
$68$	−0.639856	−	0.464883i	−0.0775939	−	0.0563753i
$69$	0.902527	−	2.77769i	0.108651	−	0.334395i
$70$	0.211544	+	0.651065i	0.0252843	+	0.0778172i
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	−0.947324	−	0.320277i	$-0.896224\pi$
$71$	−7.88234	+	5.72685i	−0.935461	+	0.679652i	0.0118626	+	0.999930i	$0.496224\pi$
$72$	0.837913	−	0.608780i	0.0987490	−	0.0717454i
$73$	−4.11611	−	12.6681i	−0.481754	−	1.48269i	−0.836627	−	0.547773i	$-0.815476\pi$
$73$	−4.11611	−	12.6681i	−0.481754	−	1.48269i	0.354873	−	0.934915i	$-0.384524\pi$
$74$	0.880296	−	2.70927i	0.102332	−	0.314947i
$75$	−6.25993	−	4.54811i	−0.722835	−	0.525170i
$76$	0.638786			0.0732737
$77$	−1.64693	+	2.87882i	−0.187685	+	0.328072i
$78$	−3.75519			−0.425191
$79$	−2.89815	−	2.10563i	−0.326068	−	0.236902i	0.412692	−	0.910870i	$-0.364588\pi$
$79$	−2.89815	−	2.10563i	−0.326068	−	0.236902i	−0.738760	+	0.673968i	$0.764588\pi$
$80$	−0.617255	+	1.89971i	−0.0690112	+	0.212395i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	−1.23541	+	0.897575i	−0.136428	+	0.0991206i
$83$	13.9627	−	10.1445i	1.53261	−	1.11351i	0.577842	−	0.816148i	$-0.303895\pi$
$83$	13.9627	−	10.1445i	1.53261	−	1.11351i	0.954766	−	0.297357i	$-0.0961052\pi$
$84$	0.0756511	+	0.232830i	0.00825421	+	0.0254038i
$85$	0.753927	−	2.32035i	0.0817748	−	0.251677i
$86$	10.3333	+	7.50755i	1.11426	+	0.809559i
$87$	−4.40020			−0.471750
$88$	−8.20113	+	3.69034i	−0.874243	+	0.393392i
$89$	−8.91982			−0.945499			−0.472750	−	0.881197i	$-0.656738\pi$
$89$	−8.91982			−0.945499			−0.472750	+	0.881197i	$0.656738\pi$
$90$	−0.211544	−	0.153696i	−0.0222987	−	0.0162009i
$91$	0.488963	−	1.50487i	0.0512572	−	0.157753i
$92$	−0.0843952	−	0.259742i	−0.00879881	−	0.0270799i
$93$	1.69369	−	1.23053i	0.175627	−	0.127600i
$94$	−7.58873	+	5.51353i	−0.782718	+	0.568678i
$95$	0.608919	+	1.87406i	0.0624738	+	0.192275i
$96$	−0.427051	+	1.31433i	−0.0435857	+	0.134143i
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	0.693264	−	0.720684i	$-0.256172\pi$
$97$	2.18727	+	1.58915i	0.222084	+	0.161353i	−0.471180	+	0.882037i	$0.656172\pi$
$98$	−1.46673			−0.148162
$99$	−0.137407	−	1.25936i	−0.0138099	−	0.126571i
$100$	−0.723551			−0.0723551
$101$	−0.144637	−	0.105085i	−0.0143919	−	0.0104563i	0.580566	−	0.814213i	$-0.302831\pi$
$101$	−0.144637	−	0.105085i	−0.0143919	−	0.0104563i	−0.594958	+	0.803757i	$0.702831\pi$
$102$	3.83354	−	11.7984i	0.379577	−	1.16822i
$103$	5.21535	+	16.0512i	0.513884	+	1.58157i	0.785304	+	0.619111i	$0.212507\pi$
$103$	5.21535	+	16.0512i	0.513884	+	1.58157i	−0.271420	+	0.962461i	$0.587493\pi$
$104$	3.47110	−	2.52190i	0.340370	−	0.247293i
$105$	−0.610960	+	0.443888i	−0.0596236	+	0.0433191i
$106$	5.98484	+	18.4195i	0.581299	+	1.78906i
$107$	−4.78241	+	14.7188i	−0.462333	+	1.42292i	0.399972	+	0.916527i	$0.369020\pi$
$107$	−4.78241	+	14.7188i	−0.462333	+	1.42292i	−0.862305	+	0.506389i	$0.830980\pi$
$108$	−0.669822	−	0.486655i	−0.0644537	−	0.0468284i
$109$	11.0349			1.05695			0.528476	−	0.848948i	$-0.322764\pi$
$109$	11.0349			1.05695			0.528476	+	0.848948i	$0.322764\pi$
$110$	1.52590	+	1.68126i	0.145489	+	0.160301i
$111$	3.14256			0.298278
$112$	−3.46236	−	2.51555i	−0.327162	−	0.237697i
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	−0.922027	−	0.387127i	$-0.873468\pi$
$113$	0.546984	−	1.68344i	0.0514559	−	0.158365i	0.973482	+	0.228762i	$0.0734676\pi$
$114$	3.09621	+	9.52916i	0.289987	+	0.892488i
$115$	0.681577	−	0.495195i	0.0635574	−	0.0461772i
$116$	−0.332880	+	0.241851i	−0.0309071	+	0.0224553i
$117$	0.186767	+	0.574810i	0.0172666	+	0.0531412i
$118$	3.89967	−	12.0019i	0.358994	−	1.10487i
$119$	4.22899	+	3.07254i	0.387671	+	0.281660i
$120$	−2.04773			−0.186931
$121$	−1.06317	+	10.9485i	−0.0966521	+	0.995318i
$122$	22.3532			2.02376
$123$	−1.36285	−	0.990166i	−0.122884	−	0.0892802i
$124$	0.0604944	−	0.186183i	0.00543255	−	0.0167197i
$125$	−1.41086	−	4.34219i	−0.126191	−	0.388377i
$126$	0.453245	−	0.329302i	0.0403783	−	0.0293365i
$127$	6.90919	−	5.01982i	0.613092	−	0.445437i	−0.237410	−	0.971410i	$-0.576298\pi$
$127$	6.90919	−	5.01982i	0.613092	−	0.445437i	0.850502	+	0.525972i	$0.176298\pi$
$128$	−3.83958	−	11.8170i	−0.339374	−	1.04449i
$129$	−4.35410	+	13.4005i	−0.383357	+	1.17985i
$130$	−0.876333	−	0.636693i	−0.0768595	−	0.0558417i
$131$	−9.66708			−0.844617			−0.422308	−	0.906452i	$-0.638780\pi$
$131$	−9.66708			−0.844617			−0.422308	+	0.906452i	$0.638780\pi$
$132$	0.545685	+	0.601241i	0.0474957	+	0.0523313i
$133$	−4.22192			−0.366087
$134$	−5.54839	−	4.03114i	−0.479308	−	0.348237i
$135$	0.789236	−	2.42902i	0.0679266	−	0.209057i
$136$	4.38004	+	13.4804i	0.375586	+	1.15593i
$137$	11.3350	−	8.23535i	0.968413	−	0.703593i	0.0133236	−	0.999911i	$-0.495759\pi$
$137$	11.3350	−	8.23535i	0.968413	−	0.703593i	0.955089	+	0.296318i	$0.0957589\pi$
$138$	3.46566	−	2.51795i	0.295017	−	0.214342i
$139$	2.95966	+	9.10889i	0.251035	+	0.772606i	0.994585	+	0.103926i	$0.0331404\pi$
$139$	2.95966	+	9.10889i	0.251035	+	0.772606i	−0.743550	+	0.668680i	$0.766860\pi$
$140$	−0.0218220	+	0.0671613i	−0.00184430	+	0.00567616i
$141$	−8.37155	−	6.08229i	−0.705012	−	0.512221i
$142$	−14.2905			−1.19923
$143$	−0.569215	−	5.21699i	−0.0476001	−	0.436267i
$144$	1.63470			0.136225
$145$	−1.02686	−	0.746054i	−0.0852757	−	0.0619564i
$146$	6.03723	−	18.5807i	0.499645	−	1.53775i
$147$	−0.500000	−	1.53884i	−0.0412393	−	0.126922i
$148$	0.237738	−	0.172727i	0.0195419	−	0.0141980i
$149$	−12.1049	+	8.79474i	−0.991674	+	0.720493i	−0.960287	−	0.279014i	$-0.909992\pi$
$149$	−12.1049	+	8.79474i	−0.991674	+	0.720493i	−0.0313866	+	0.999507i	$0.509992\pi$
$150$	−3.50707	−	10.7937i	−0.286351	−	0.881299i
$151$	−0.887599	+	2.73175i	−0.0722318	+	0.222307i	−0.980655	−	0.195746i	$-0.937287\pi$
$151$	−0.887599	+	2.73175i	−0.0722318	+	0.222307i	0.908423	+	0.418053i	$0.137287\pi$
$152$	−9.26156	−	6.72892i	−0.751212	−	0.545787i
$153$	−1.99666			−0.161420
$154$	−4.43617	+	1.99619i	−0.357476	+	0.160857i
$155$	0.603886			0.0485053
$156$	−0.313389	−	0.227690i	−0.0250912	−	0.0182298i
$157$	−5.83496	+	17.9582i	−0.465680	+	1.43322i	0.392444	+	0.919776i	$0.371630\pi$
$157$	−5.83496	+	17.9582i	−0.465680	+	1.43322i	−0.858125	+	0.513441i	$0.828370\pi$
$158$	−1.62367	−	4.99713i	−0.129172	−	0.397551i
$159$	−17.2848	+	12.5582i	−1.37078	+	0.995927i
$160$	−0.322504	+	0.234313i	−0.0254962	+	0.0185240i
$161$	0.557792	+	1.71671i	0.0439602	+	0.135296i
$162$	3.49371	−	10.7525i	0.274491	−	0.844798i
$163$	−9.38067	−	6.81545i	−0.734751	−	0.533827i	0.156312	−	0.987708i	$-0.450039\pi$
$163$	−9.38067	−	6.81545i	−0.734751	−	0.533827i	−0.891063	+	0.453880i	$0.850039\pi$
$164$	−0.157524			−0.0123006
$165$	−1.24374	+	2.17405i	−0.0968252	+	0.169250i
$166$	25.3142			1.96476
$167$	−5.11696	−	3.71769i	−0.395963	−	0.287684i	0.371932	−	0.928260i	$-0.378695\pi$
$167$	−5.11696	−	3.71769i	−0.395963	−	0.287684i	−0.767894	+	0.640576i	$0.778695\pi$
$168$	1.35577	−	4.17264i	0.104600	−	0.321926i
$169$	−3.24353	−	9.98255i	−0.249502	−	0.767889i
$170$	2.89504	−	2.10337i	0.222040	−	0.161321i
$171$	1.30464	−	0.947880i	0.0997687	−	0.0724862i
$172$	0.407152	+	1.25308i	0.0310450	+	0.0955467i
$173$	0.413793	−	1.27352i	0.0314601	−	0.0968243i	−0.934093	−	0.357029i	$-0.883790\pi$
$173$	0.413793	−	1.27352i	0.0314601	−	0.0968243i	0.965554	+	0.260204i	$0.0837899\pi$
$174$	−5.22132	−	3.79351i	−0.395827	−	0.287585i
$175$	4.78216			0.361497
$176$	−13.8956	−	2.89616i	−1.04742	−	0.218306i
$177$	13.9214			1.04639
$178$	−10.5844	−	7.68999i	−0.793331	−	0.576389i
$179$	5.49705	−	16.9182i	0.410868	−	1.26452i	−0.505026	−	0.863104i	$-0.668517\pi$
$179$	5.49705	−	16.9182i	0.410868	−	1.26452i	0.915895	−	0.401419i	$-0.131483\pi$
$180$	−0.00833527	−	0.0256533i	−0.000621274	−	0.00191209i
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	−0.558430	−	0.829551i	$-0.688596\pi$
$181$	0.779712	−	0.566494i	0.0579555	−	0.0421072i	0.616386	+	0.787444i	$0.288596\pi$
$182$	1.87759	−	1.36415i	0.139177	−	0.101118i
$183$	7.62007	+	23.4522i	0.563292	+	1.73363i
$184$	−1.51248	+	4.65493i	−0.111501	+	0.343166i
$185$	0.733366	+	0.532822i	0.0539181	+	0.0391738i
$186$	3.07062			0.225149
$187$	16.9724	+	3.53743i	1.24114	+	0.258682i
$188$	−0.967622			−0.0705711
$189$	4.42705	+	3.21644i	0.322021	+	0.233962i
$190$	−0.893121	+	2.74874i	−0.0647938	+	0.199415i
$191$	−4.97173	−	15.3014i	−0.359742	−	1.10717i	−0.953209	−	0.302313i	$-0.902241\pi$
$191$	−4.97173	−	15.3014i	−0.359742	−	1.10717i	0.593467	−	0.804858i	$-0.297759\pi$
$192$	9.56458	−	6.94907i	0.690264	−	0.501506i
$193$	−9.82750	+	7.14010i	−0.707399	+	0.513955i	−0.882333	−	0.470625i	$-0.844029\pi$
$193$	−9.82750	+	7.14010i	−0.707399	+	0.513955i	0.174935	+	0.984580i	$0.444029\pi$
$194$	1.22540	+	3.77140i	0.0879787	+	0.270771i
$195$	0.369259	−	1.13646i	0.0264432	−	0.0813837i
$196$	−0.122406	−	0.0889332i	−0.00874329	−	0.00635237i
$197$	−2.30179			−0.163996			−0.0819978	−	0.996633i	$-0.526130\pi$
$197$	−2.30179			−0.163996			−0.0819978	+	0.996633i	$0.526130\pi$
$198$	0.922679	−	1.61284i	0.0655719	−	0.114619i
$199$	20.2797			1.43759			0.718795	−	0.695222i	$-0.244694\pi$
$199$	20.2797			1.43759			0.718795	+	0.695222i	$0.244694\pi$
$200$	10.4906	+	7.62184i	0.741794	+	0.538945i
$201$	2.33791	−	7.19536i	0.164904	−	0.507521i
$202$	−0.0810316	−	0.249390i	−0.00570136	−	0.0175470i
$203$	2.20010	−	1.59846i	0.154417	−	0.112190i
$204$	1.03531	−	0.752196i	0.0724861	−	0.0526642i
$205$	−0.150159	−	0.462142i	−0.0104876	−	0.0322774i
$206$	−7.64952	+	23.5428i	−0.532967	+	1.64030i
$207$	−0.557792	−	0.405260i	−0.0387692	−	0.0281675i
$208$	6.77186			0.469544
$209$	−12.7693	+	5.74593i	−0.883271	+	0.397454i
$210$	−1.10766			−0.0764357
$211$	−4.34062	−	3.15364i	−0.298820	−	0.217106i	0.428264	−	0.903654i	$-0.359125\pi$
$211$	−4.34062	−	3.15364i	−0.298820	−	0.217106i	−0.727085	+	0.686548i	$0.759125\pi$
$212$	−0.617372	+	1.90008i	−0.0424013	+	0.130498i
$213$	−4.87155	−	14.9931i	−0.333793	−	1.02731i
$214$	−18.3642	+	13.3424i	−1.25535	+	0.912068i
$215$	−3.28817	+	2.38899i	−0.224251	+	0.162928i
$216$	4.58517	+	14.1117i	0.311982	+	0.960181i
$217$	−0.399825	+	1.23053i	−0.0271419	+	0.0835341i
$218$	13.0941	+	9.51344i	0.886847	+	0.644332i
$219$	21.5522			1.45637
$220$	0.0254036	+	0.232830i	0.00171271	+	0.0156974i
$221$	−8.27128			−0.556387
$222$	3.72899	+	2.70927i	0.250274	+	0.181834i
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	0.236072	+	0.971736i	$0.424140\pi$
$223$	−7.85614	+	24.1787i	−0.526086	+	1.61913i	−0.762158	+	0.647391i	$0.775860\pi$
$224$	−0.263932	−	0.812299i	−0.0176347	−	0.0542740i
$225$	−1.47777	+	1.07366i	−0.0985179	+	0.0715775i
$226$	2.10039	−	1.52602i	0.139716	−	0.101510i
$227$	−6.70869	−	20.6472i	−0.445271	−	1.37040i	−0.882186	−	0.470901i	$-0.843929\pi$
$227$	−6.70869	−	20.6472i	−0.445271	−	1.37040i	0.436915	−	0.899503i	$-0.356071\pi$
$228$	−0.319393	+	0.982990i	−0.0211523	+	0.0651001i
$229$	−16.6097	−	12.0676i	−1.09760	−	0.797451i	−0.116931	−	0.993140i	$-0.537306\pi$
$229$	−16.6097	−	12.0676i	−1.09760	−	0.797451i	−0.980666	+	0.195689i	$0.937306\pi$
$230$	1.23569			0.0814787
$231$	−3.60659	−	3.97378i	−0.237296	−	0.261455i
$232$	7.37396			0.484124
$233$	−0.561503	−	0.407956i	−0.0367853	−	0.0267261i	0.569241	−	0.822171i	$-0.307237\pi$
$233$	−0.561503	−	0.407956i	−0.0367853	−	0.0267261i	−0.606026	+	0.795445i	$0.707237\pi$
$234$	−0.273937	+	0.843092i	−0.0179078	+	0.0551147i
$235$	−0.922381	−	2.83880i	−0.0601695	−	0.185183i
$236$	1.05317	−	0.765171i	0.0685554	−	0.0498084i
$237$	4.68931	−	3.40699i	0.304604	−	0.221307i
$238$	2.36926	+	7.29183i	0.153576	+	0.472659i
$239$	0.107093	−	0.329599i	0.00692728	−	0.0213200i	−0.947533	−	0.319658i	$-0.896432\pi$
$239$	0.107093	−	0.329599i	0.00692728	−	0.0213200i	0.954460	+	0.298338i	$0.0964321\pi$
$240$	−2.61473	−	1.89971i	−0.168780	−	0.122626i
$241$	−10.4372			−0.672317			−0.336158	−	0.941806i	$-0.609128\pi$
$241$	−10.4372			−0.672317			−0.336158	+	0.941806i	$0.609128\pi$
$242$	−10.7005	+	12.0750i	−0.687856	+	0.776212i
$243$	−3.94427			−0.253025
$244$	1.86549	+	1.35536i	0.119426	+	0.0867677i
$245$	0.144228	−	0.443888i	0.00921439	−	0.0283590i
$246$	−0.763523	−	2.34988i	−0.0486805	−	0.149823i
$247$	5.40457	−	3.92665i	0.343884	−	0.249847i
$248$	−2.83832	+	2.06216i	−0.180234	+	0.130947i
$249$	8.62944	+	26.5587i	0.546869	+	1.68309i
$250$	2.06936	−	6.36882i	0.130878	−	0.402800i
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	0.751883	−	0.659297i	$-0.229146\pi$
$251$	5.65909	+	4.11157i	0.357199	+	0.259520i	−0.394684	+	0.918817i	$0.629146\pi$
$252$	0.0577923			0.00364057
$253$	4.02345	+	4.43308i	0.252952	+	0.278706i
$254$	12.5262			0.785965
$255$	3.19369	+	2.32035i	0.199996	+	0.145306i
$256$	1.11586	−	3.43426i	0.0697412	−	0.214641i
$257$	−3.07423	−	9.46152i	−0.191765	−	0.590193i	−0.999999	−	0.00133144i	$-0.999576\pi$
$257$	−3.07423	−	9.46152i	−0.191765	−	0.590193i	0.808234	−	0.588862i	$-0.200424\pi$
$258$	−16.7196	+	12.1475i	−1.04091	+	0.756268i
$259$	−1.57128	+	1.14160i	−0.0976345	+	0.0709356i
$260$	−0.0345293	−	0.106270i	−0.00214142	−	0.00659061i
$261$	−0.320990	+	0.987905i	−0.0198688	+	0.0611498i
$262$	−11.4711	−	8.33422i	−0.708685	−	0.514890i
$263$	14.1803			0.874397			0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803			0.874397			0.437199	+	0.899365i	$0.355971\pi$
$264$	−1.57829	−	14.4654i	−0.0971371	−	0.890285i
$265$	−6.16293			−0.378586
$266$	−5.00978	−	3.63982i	−0.307169	−	0.223171i
$267$	4.45991	−	13.7262i	0.272942	−	0.840029i
$268$	−0.218618	−	0.672837i	−0.0133542	−	0.0411001i
$269$	14.8884	−	10.8171i	0.907762	−	0.659528i	−0.0326859	−	0.999466i	$-0.510406\pi$
$269$	14.8884	−	10.8171i	0.907762	−	0.659528i	0.940448	+	0.339938i	$0.110406\pi$
$270$	3.03063	−	2.20188i	0.184438	−	0.134002i
$271$	0.225765	+	0.694833i	0.0137142	+	0.0422081i	0.957679	−	0.287837i	$-0.0929361\pi$
$271$	0.225765	+	0.694833i	0.0137142	+	0.0422081i	−0.943965	+	0.330045i	$0.892936\pi$
$272$	−6.91316	+	21.2765i	−0.419172	+	1.29008i
$273$	2.07128	+	1.50487i	0.125360	+	0.0910790i
$274$	20.5501			1.24148
$275$	14.4638	−	6.50840i	0.872198	−	0.392472i
$276$	0.441899			0.0265992
$277$	−12.1874	−	8.85463i	−0.732267	−	0.532023i	0.158013	−	0.987437i	$-0.449491\pi$
$277$	−12.1874	−	8.85463i	−0.732267	−	0.532023i	−0.890280	+	0.455414i	$0.849491\pi$
$278$	−4.34102	+	13.3603i	−0.260357	+	0.801297i
$279$	−0.152719	−	0.470022i	−0.00914308	−	0.0281395i
$280$	1.02386	−	0.743880i	0.0611875	−	0.0444553i
$281$	8.65334	−	6.28702i	0.516215	−	0.375052i	−0.298961	−	0.954265i	$-0.596640\pi$
$281$	8.65334	−	6.28702i	0.516215	−	0.375052i	0.815176	+	0.579213i	$0.196640\pi$
$282$	−4.69009	−	14.4346i	−0.279291	−	0.859569i
$283$	2.81481	−	8.66308i	0.167323	−	0.514967i	−0.831877	−	0.554960i	$-0.812734\pi$
$283$	2.81481	−	8.66308i	0.167323	−	0.514967i	0.999200	+	0.0399931i	$0.0127336\pi$
$284$	−1.19261	−	0.866485i	−0.0707687	−	0.0514164i
$285$	−3.18834			−0.188861
$286$	3.82225	−	6.68127i	0.226014	−	0.395072i
$287$	1.04112			0.0614555
$288$	0.263932	+	0.191758i	0.0155523	+	0.0112994i
$289$	3.19057	−	9.81958i	0.187681	−	0.577622i
$290$	−0.575287	−	1.77055i	−0.0337820	−	0.103970i
$291$	−3.53908	+	2.57129i	−0.207465	+	0.150732i
$292$	1.63045	−	1.18459i	0.0954149	−	0.0693230i
$293$	3.67390	+	11.3071i	0.214632	+	0.660569i	0.999180	+	0.0405002i	$0.0128951\pi$
$293$	3.67390	+	11.3071i	0.214632	+	0.660569i	−0.784548	+	0.620068i	$0.787105\pi$
$294$	0.733366	−	2.25707i	0.0427708	−	0.131635i
$295$	3.24878	+	2.36037i	0.189151	+	0.137426i
$296$	−5.26638			−0.306102
$297$	17.7672	+	3.70310i	1.03096	+	0.214875i
$298$	−21.9460			−1.27130
$299$	−2.31069	−	1.67881i	−0.133630	−	0.0970882i
$300$	0.361776	−	1.11343i	0.0208871	−	0.0642840i
$301$	−2.69098	−	8.28199i	−0.155106	−	0.477366i
$302$	−3.40834	+	2.47630i	−0.196128	+	0.142495i
$303$	0.234027	−	0.170031i	0.0134445	−	0.00976802i
$304$	−5.58350	−	17.1843i	−0.320236	−	0.985585i
$305$	−2.19806	+	6.76492i	−0.125860	+	0.387358i
$306$	−2.36926	−	1.72137i	−0.135442	−	0.0984040i
$307$	2.22072			0.126743			0.0633716	−	0.997990i	$-0.479815\pi$
$307$	2.22072			0.126743			0.0633716	+	0.997990i	$0.479815\pi$
$308$	−0.491256	−	0.102389i	−0.0279919	−	0.00583415i
$309$	−27.3079			−1.55349
$310$	0.716577	+	0.520624i	0.0406989	+	0.0295695i
$311$	−6.61685	+	20.3646i	−0.375207	+	1.15477i	0.568132	+	0.822937i	$0.307666\pi$
$311$	−6.61685	+	20.3646i	−0.375207	+	1.15477i	−0.943339	+	0.331831i	$0.892334\pi$
$312$	2.14526	+	6.60243i	0.121451	+	0.373789i
$313$	25.5283	−	18.5474i	1.44295	−	1.04836i	0.455531	−	0.890220i	$-0.349450\pi$
$313$	25.5283	−	18.5474i	1.44295	−	1.04836i	0.987416	−	0.158142i	$-0.0505505\pi$
$314$	−22.4060	+	16.2789i	−1.26444	+	0.918671i
$315$	0.0550902	+	0.169550i	0.00310398	+	0.00955307i
$316$	0.167491	−	0.515484i	0.00942211	−	0.0289983i
$317$	10.6796	+	7.75915i	0.599824	+	0.435798i	0.845816	−	0.533474i	$-0.179114\pi$
$317$	10.6796	+	7.75915i	0.599824	+	0.435798i	−0.245992	+	0.969272i	$0.579114\pi$
$318$	−31.3370			−1.75729
$319$	4.47878	−	7.82887i	0.250763	−	0.438333i
$320$	3.41026			0.190639
$321$	−20.2586	−	14.7188i	−1.13073	−	0.821521i
$322$	−0.818132	+	2.51795i	−0.0455927	+	0.140320i
$323$	6.81980	+	20.9892i	0.379464	+	1.16787i
$324$	0.943531	−	0.685515i	0.0524184	−	0.0380842i
$325$	−6.12174	+	4.44771i	−0.339573	+	0.246714i
$326$	−5.25544	−	16.1746i	−0.291072	−	0.895827i
$327$	−5.51745	+	16.9810i	−0.305116	+	0.939050i
$328$	2.28389	+	1.65935i	0.126107	+	0.0916220i
$329$	6.39530			0.352584
$330$	−3.35014	+	1.50750i	−0.184419	+	0.0829849i
$331$	9.47653			0.520877			0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653			0.520877			0.260439	+	0.965490i	$0.416133\pi$
$332$	2.11259	+	1.53489i	0.115944	+	0.0842379i
$333$	0.229247	−	0.705548i	0.0125626	−	0.0386638i
$334$	−2.86674	−	8.82291i	−0.156861	−	0.482768i
$335$	1.76556	−	1.28276i	0.0964631	−	0.0700845i
$336$	5.60222	−	4.07025i	0.305626	−	0.222050i
$337$	−5.93346	−	18.2613i	−0.323216	−	0.994758i	−0.972239	−	0.233989i	$-0.924822\pi$
$337$	−5.93346	−	18.2613i	−0.323216	−	0.994758i	0.649023	−	0.760769i	$-0.275178\pi$
$338$	4.75738	−	14.6417i	0.258768	−	0.796405i
$339$	2.31706	+	1.68344i	0.125845	+	0.0914321i
$340$	0.369141			0.0200195
$341$	0.465447	+	4.26593i	0.0252054	+	0.231013i
$342$	2.36530			0.127901
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	7.29672	−	22.4570i	0.393413	−	1.21080i
$345$	0.421238	+	1.29644i	0.0226787	+	0.0697978i
$346$	1.58895	−	1.15444i	0.0854223	−	0.0620629i
$347$	−2.46613	+	1.79175i	−0.132389	+	0.0961862i	−0.652009	−	0.758211i	$-0.726074\pi$
$347$	−2.46613	+	1.79175i	−0.132389	+	0.0961862i	0.519620	+	0.854397i	$0.326074\pi$
$348$	−0.205731	−	0.633175i	−0.0110283	−	0.0339417i
$349$	5.99373	−	18.4468i	0.320837	−	0.987435i	−0.652448	−	0.757834i	$-0.726258\pi$
$349$	5.99373	−	18.4468i	0.320837	−	0.987435i	0.973285	−	0.229601i	$-0.0737421\pi$
$350$	5.67457	+	4.12281i	0.303318	+	0.220374i
$351$	−8.65865			−0.462165
$352$	−1.90379	−	2.09761i	−0.101472	−	0.111803i
$353$	−10.7585			−0.572619			−0.286309	−	0.958137i	$-0.592428\pi$
$353$	−10.7585			−0.572619			−0.286309	+	0.958137i	$0.592428\pi$
$354$	16.5193	+	12.0019i	0.877989	+	0.637896i
$355$	1.40523	−	4.32485i	0.0745818	−	0.229539i
$356$	−0.417046	−	1.28353i	−0.0221034	−	0.0680272i
$357$	−6.84266	+	4.97148i	−0.362152	+	0.263119i
$358$	21.1084	−	15.3361i	1.11561	−	0.810541i
$359$	0.187643	+	0.577506i	0.00990342	+	0.0304796i	0.955886	−	0.293738i	$-0.0948992\pi$
$359$	0.187643	+	0.577506i	0.00990342	+	0.0304796i	−0.945983	+	0.324217i	$0.894899\pi$
$360$	−0.149380	+	0.459743i	−0.00787299	+	0.0242306i
$361$	0.950914	+	0.690879i	0.0500481	+	0.0363621i
$362$	1.41360			0.0742973
$363$	−16.3164	−	7.11030i	−0.856390	−	0.373194i
$364$	0.239408			0.0125484
$365$	5.02956	+	3.65419i	0.263259	+	0.191269i
$366$	−11.1766	+	34.3981i	−0.584211	+	1.79802i
$367$	8.54829	+	26.3089i	0.446217	+	1.37332i	0.881143	+	0.472849i	$0.156774\pi$
$367$	8.54829	+	26.3089i	0.446217	+	1.37332i	−0.434926	+	0.900466i	$0.643226\pi$
$368$	−6.24975	+	4.54071i	−0.325791	+	0.236701i
$369$	−0.321724	+	0.233746i	−0.0167483	+	0.0121684i
$370$	0.410862	+	1.26450i	0.0213597	+	0.0657384i
$371$	4.08039	−	12.5582i	0.211843	−	0.651987i
$372$	0.256258	+	0.186183i	0.0132864	+	0.00965311i
$373$	−29.4513			−1.52493			−0.762465	−	0.647029i	$-0.776011\pi$
$373$	−29.4513			−1.52493			−0.762465	+	0.647029i	$0.776011\pi$
$374$	17.0899	+	18.8298i	0.883697	+	0.973666i
$375$	7.38737			0.381482
$376$	14.0293	+	10.1929i	0.723504	+	0.525657i
$377$	−1.32972	+	4.09246i	−0.0684840	+	0.210772i
$378$	2.48022	+	7.63333i	0.127569	+	0.392616i
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.972817	−	0.231577i	$-0.925612\pi$
$379$	−20.5034	+	14.8966i	−1.05319	+	0.765188i	−0.0803745	+	0.996765i	$0.525612\pi$
$380$	−0.241202	+	0.175243i	−0.0123734	+	0.00898979i
$381$	4.27012	+	13.1421i	0.218765	+	0.673288i
$382$	7.29219	−	22.4431i	0.373101	−	1.14829i
$383$	25.8337	+	18.7693i	1.32004	+	0.959065i	0.999932	+	0.0116837i	$0.00371913\pi$
$383$	25.8337	+	18.7693i	1.32004	+	0.959065i	0.320108	+	0.947381i	$0.396281\pi$
$384$	20.1043			1.02594
$385$	−0.167900	−	1.53884i	−0.00855697	−	0.0784266i
$386$	−17.8171			−0.906865
$387$	2.69098	+	1.95511i	0.136790	+	0.0993840i
$388$	−0.126407	+	0.389042i	−0.00641737	+	0.0197506i
$389$	5.48558	+	16.8829i	0.278130	+	0.855996i	0.988374	+	0.152040i	$0.0485844\pi$
$389$	5.48558	+	16.8829i	0.278130	+	0.855996i	−0.710244	+	0.703955i	$0.751416\pi$
$390$	1.41794	−	1.03019i	0.0718000	−	0.0521657i
$391$	7.63356	−	5.54611i	0.386046	−	0.280479i
$392$	0.837913	+	2.57883i	0.0423210	+	0.130251i
$393$	4.83354	−	14.8761i	0.243820	−	0.750400i
$394$	−2.73133	−	1.98442i	−0.137602	−	0.0999738i
$395$	1.67198			0.0841265
$396$	0.174794	−	0.0786539i	0.00878374	−	0.00395251i
$397$	−13.3047			−0.667742			−0.333871	−	0.942619i	$-0.608355\pi$
$397$	−13.3047			−0.667742			−0.333871	+	0.942619i	$0.608355\pi$
$398$	24.0641	+	17.4836i	1.20623	+	0.876374i
$399$	2.11096	−	6.49687i	0.105680	−	0.325250i
$400$	6.32443	+	19.4646i	0.316221	+	0.973229i
$401$	2.82317	−	2.05115i	0.140982	−	0.102430i	−0.515059	−	0.857155i	$-0.672230\pi$
$401$	2.82317	−	2.05115i	0.140982	−	0.102430i	0.656041	+	0.754725i	$0.272230\pi$
$402$	8.97748	−	6.52252i	0.447756	−	0.325314i
$403$	−0.632649	−	1.94709i	−0.0315145	−	0.0969917i
$404$	0.00835890	−	0.0257260i	0.000415871	−	0.00127992i
$405$	2.91057	+	2.11465i	0.144627	+	0.105078i
$406$	3.98873			0.197958
$407$	−3.19868	+	5.59127i	−0.158553	+	0.277149i
$408$	−22.9342			−1.13541
$409$	23.9675	+	17.4134i	1.18512	+	0.861039i	0.992740	−	0.120282i	$-0.0383799\pi$
$409$	23.9675	+	17.4134i	1.18512	+	0.861039i	0.192379	+	0.981321i	$0.438380\pi$
$410$	0.220243	−	0.677838i	0.0108770	−	0.0334760i
$411$	7.00540	+	21.5604i	0.345551	+	1.06350i
$412$	−2.06587	+	1.50095i	−0.101778	+	0.0739463i
$413$	−6.96069	+	5.05724i	−0.342513	+	0.248850i
$414$	−0.312499	−	0.961771i	−0.0153585	−	0.0472685i
$415$	−2.48922	+	7.66102i	−0.122191	+	0.376065i
$416$	1.09335	+	0.794368i	0.0536061	+	0.0389471i
$417$	−15.4970			−0.758890
$418$	−20.1059	−	4.19053i	−0.983411	−	0.204965i
$419$	−11.6452			−0.568907			−0.284454	−	0.958690i	$-0.591812\pi$
$419$	−11.6452			−0.568907			−0.284454	+	0.958690i	$0.591812\pi$
$420$	−0.0924396	−	0.0671613i	−0.00451059	−	0.00327713i
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	−0.682204	−	0.731162i	$-0.738978\pi$
$421$	6.14475	−	18.9116i	0.299477	−	0.921696i	0.981681	−	0.190533i	$-0.0610217\pi$
$422$	−2.43179	−	7.48429i	−0.118378	−	0.364330i
$423$	−1.97626	+	1.43583i	−0.0960888	+	0.0698126i
$424$	28.9664	−	21.0453i	1.40673	−	1.02205i
$425$	−7.72478	−	23.7744i	−0.374707	−	1.15323i
$426$	7.14526	−	21.9908i	0.346189	−	1.06546i
$427$	−12.3295	−	8.95793i	−0.596668	−	0.433505i
$428$	−2.34159			−0.113185
$429$	8.31273	+	1.73256i	0.401342	+	0.0836489i
$430$	−5.96138			−0.287483
$431$	−24.4698	−	17.7784i	−1.17867	−	0.856354i	−0.186649	−	0.982427i	$-0.559763\pi$
$431$	−24.4698	−	17.7784i	−1.17867	−	0.856354i	−0.992021	+	0.126073i	$0.959763\pi$
$432$	−7.23692	+	22.2730i	−0.348186	+	1.07161i
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	0.899694	−	0.436521i	$-0.143789\pi$
$433$	−1.76362	−	5.42786i	−0.0847542	−	0.260846i	−0.984448	+	0.175674i	$0.943789\pi$
$434$	−1.53531	+	1.11547i	−0.0736972	+	0.0535441i
$435$	1.66149	−	1.20714i	0.0796622	−	0.0578780i
$436$	0.515936	+	1.58789i	0.0247089	+	0.0760461i
$437$	−2.35495	+	7.24780i	−0.112653	+	0.346709i
$438$	25.5741	+	18.5807i	1.22198	+	0.887820i
$439$	6.84875			0.326873			0.163436	−	0.986554i	$-0.447742\pi$
$439$	6.84875			0.326873			0.163436	+	0.986554i	$0.447742\pi$
$440$	2.08430	−	3.64333i	0.0993649	−	0.173689i
$441$	−0.381966			−0.0181889
$442$	−9.81479	−	7.13086i	−0.466842	−	0.339181i
$443$	0.0311165	−	0.0957668i	0.00147839	−	0.00455002i	−0.950315	−	0.311291i	$-0.899239\pi$
$443$	0.0311165	−	0.0957668i	0.00147839	−	0.00455002i	0.951793	+	0.306741i	$0.0992386\pi$
$444$	0.146930	+	0.452204i	0.00697300	+	0.0214607i
$445$	3.36807	−	2.44705i	0.159662	−	0.116001i
$446$	−30.1672	+	21.9178i	−1.42846	+	1.03784i
$447$	−7.48125	−	23.0249i	−0.353851	−	1.08904i
$448$	−2.25789	+	6.94907i	−0.106675	+	0.328313i
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.991729	−	0.128351i	$-0.0409683\pi$
$449$	24.9216	+	18.1066i	1.17612	+	0.854502i	0.184392	+	0.982853i	$0.440968\pi$
$450$	−2.67917			−0.126297
$451$	3.14890	−	1.41694i	0.148276	−	0.0667211i
$452$	0.267817			0.0125970
$453$	−3.75993	−	2.73175i	−0.176657	−	0.128349i
$454$	9.83984	−	30.2839i	0.461807	−	1.42129i
$455$	0.228214	+	0.702372i	0.0106989	+	0.0329277i
$456$	14.9855	−	10.8876i	0.701761	−	0.509859i
$457$	−18.7171	+	13.5987i	−0.875547	+	0.636122i	−0.932070	−	0.362279i	$-0.881999\pi$
$457$	−18.7171	+	13.5987i	−0.875547	+	0.636122i	0.0565223	+	0.998401i	$0.481999\pi$
$458$	−9.30542	−	28.6392i	−0.434814	−	1.33822i
$459$	8.83932	−	27.2046i	0.412584	−	1.26980i
$460$	0.103124	+	0.0749241i	0.00480819	+	0.00349335i
$461$	−2.77839			−0.129403			−0.0647013	−	0.997905i	$-0.520609\pi$
$461$	−2.77839			−0.129403			−0.0647013	+	0.997905i	$0.520609\pi$
$462$	−0.853731	−	7.82465i	−0.0397192	−	0.364036i
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	9.41578	+	6.84097i	0.437117	+	0.317584i
$465$	−0.301943	+	0.929285i	−0.0140023	+	0.0430945i
$466$	−0.314577	−	0.968169i	−0.0145725	−	0.0448496i
$467$	2.15060	−	1.56250i	0.0995180	−	0.0723041i	−0.536913	−	0.843637i	$-0.680410\pi$
$467$	2.15060	−	1.56250i	0.0995180	−	0.0723041i	0.636431	+	0.771333i	$0.280410\pi$
$468$	−0.0739811	+	0.0537504i	−0.00341978	+	0.00248461i
$469$	1.44491	+	4.44698i	0.0667197	+	0.205342i
$470$	1.35289	−	4.16375i	0.0624040	−	0.192060i
$471$	−24.7173	−	17.9582i	−1.13891	−	0.827468i
$472$	−23.3298			−1.07384
$473$	−19.4105	−	21.3867i	−0.892497	−	0.983363i
$474$	8.50163			0.390493
$475$	16.3340	+	11.8673i	0.749454	+	0.544510i
$476$	−0.244403	+	0.752196i	−0.0112022	+	0.0344768i
$477$	1.55857	+	4.79679i	0.0713621	+	0.219630i
$478$	0.411233	−	0.298778i	0.0188093	−	0.0136658i
$479$	6.70047	−	4.86818i	0.306152	−	0.222433i	−0.424091	−	0.905619i	$-0.639407\pi$
$479$	6.70047	−	4.86818i	0.306152	−	0.222433i	0.730244	+	0.683187i	$0.239407\pi$
$480$	−0.199318	−	0.613439i	−0.00909759	−	0.0279995i
$481$	0.949667	−	2.92277i	0.0433011	−	0.133267i
$482$	−12.3848	−	8.99812i	−0.564114	−	0.409853i
$483$	−2.92064			−0.132894
$484$	−1.62516	+	0.358909i	−0.0738711	+	0.0163141i
$485$	−1.26186			−0.0572983
$486$	−4.68032	−	3.40045i	−0.212303	−	0.154247i
$487$	−6.05536	+	18.6365i	−0.274395	+	0.844500i	0.714984	+	0.699141i	$0.246434\pi$
$487$	−6.05536	+	18.6365i	−0.274395	+	0.844500i	−0.989379	+	0.145360i	$0.953566\pi$
$488$	−12.7699	−	39.3018i	−0.578067	−	1.77911i
$489$	15.1782	−	11.0276i	0.686384	−	0.498687i
$490$	0.553829	−	0.402380i	0.0250194	−	0.0181777i
$491$	−8.86312	−	27.2779i	−0.399987	−	1.23103i	−0.925009	−	0.379945i	$-0.875943\pi$
$491$	−8.86312	−	27.2779i	−0.399987	−	1.23103i	0.525022	−	0.851089i	$-0.324057\pi$
$492$	0.0787620	−	0.242405i	0.00355087	−	0.0109284i
$493$	−11.5006	−	8.35569i	−0.517962	−	0.376321i
$494$	9.79837			0.440850
$495$	0.397375	+	0.437832i	0.0178607	+	0.0196791i
$496$	−5.53735			−0.248634
$497$	7.88234	+	5.72685i	0.353571	+	0.256884i
$498$	−12.6571	+	38.9545i	−0.567177	+	1.74559i
$499$	8.63700	+	26.5819i	0.386645	+	1.18997i	0.935280	+	0.353909i	$0.115148\pi$
$499$	8.63700	+	26.5819i	0.386645	+	1.18997i	−0.548635	+	0.836062i	$0.684852\pi$
$500$	0.558863	−	0.406037i	0.0249931	−	0.0181585i
$501$	8.27942	−	6.01535i	0.369897	−	0.268746i
$502$	3.17046	+	9.75767i	0.141505	+	0.435506i
$503$	−2.50222	+	7.70104i	−0.111568	+	0.343373i	−0.991216	−	0.132254i	$-0.957779\pi$
$503$	−2.50222	+	7.70104i	−0.111568	+	0.343373i	0.879647	+	0.475626i	$0.157779\pi$
$504$	−0.837913	−	0.608780i	−0.0373236	−	0.0271172i
$505$	0.0834428			0.00371316
$506$	0.952410	+	8.72906i	0.0423398	+	0.388054i
$507$	16.9833			0.754256
$508$	1.04538	+	0.759510i	0.0463811	+	0.0336978i
$509$	5.03702	−	15.5024i	0.223262	−	0.687130i	−0.775201	−	0.631714i	$-0.782352\pi$
$509$	5.03702	−	15.5024i	0.223262	−	0.687130i	0.998463	−	0.0554159i	$-0.0176485\pi$
$510$	1.78924	+	5.50670i	0.0792287	+	0.243841i
$511$	−10.7761	+	7.82931i	−0.476707	+	0.346348i
$512$	−15.8195	+	11.4935i	−0.699129	+	0.507947i
$513$	7.13919	+	21.9722i	0.315203	+	0.970096i
$514$	4.50908	−	13.8775i	0.198887	−	0.612111i
$515$	−6.37274	−	4.63007i	−0.280816	−	0.204025i
$516$	−2.13187			−0.0938505
$517$	19.3427	−	8.70384i	0.850692	−	0.382795i
$518$	−2.84870			−0.125165
$519$	1.75286	+	1.27352i	0.0769419	+	0.0559015i
$520$	−0.618813	+	1.90451i	−0.0271368	+	0.0835184i
$521$	2.37512	+	7.30987i	0.104056	+	0.320251i	0.989508	−	0.144480i	$-0.0461509\pi$
$521$	2.37512	+	7.30987i	0.104056	+	0.320251i	−0.885452	+	0.464731i	$0.846151\pi$
$522$	−1.23259	+	0.895526i	−0.0539488	+	0.0391961i
$523$	−21.1339	+	15.3547i	−0.924121	+	0.671413i	−0.944546	−	0.328378i	$-0.893498\pi$
$523$	−21.1339	+	15.3547i	−0.924121	+	0.671413i	0.0204256	+	0.999791i	$0.493498\pi$
$524$	−0.451984	−	1.39106i	−0.0197450	−	0.0607689i
$525$	−2.39108	+	7.35899i	−0.104355	+	0.321173i
$526$	16.8265	+	12.2252i	0.733672	+	0.533044i
$527$	6.76343			0.294619
$528$	11.4045	−	19.9350i	0.496318	−	0.867561i
$529$	−19.7418			−0.858338
$530$	−7.31300	−	5.31320i	−0.317656	−	0.230791i
$531$	1.01555	−	3.12554i	0.0440712	−	0.135637i
$532$	−0.197396	−	0.607521i	−0.00855819	−	0.0263394i
$533$	−1.33276	+	0.968308i	−0.0577283	+	0.0419421i
$534$	17.1258	−	12.4427i	0.741108	−	0.538446i
$535$	−2.23210	−	6.86971i	−0.0965023	−	0.297004i
$536$	−3.91794	+	12.0582i	−0.169229	+	0.520834i
$537$	23.2859	+	16.9182i	1.00486	+	0.730073i
$538$	26.9924			1.16372
$539$	3.24685	+	0.676718i	0.139852	+	0.0291483i
$540$	0.386429			0.0166292
$541$	20.9355	+	15.2105i	0.900086	+	0.653951i	0.938488	−	0.345312i	$-0.112227\pi$
$541$	20.9355	+	15.2105i	0.900086	+	0.653951i	−0.0384021	+	0.999262i	$0.512227\pi$
$542$	−0.331137	+	1.01913i	−0.0142235	+	0.0437756i
$543$	0.481889	+	1.48310i	0.0206798	+	0.0636459i
$544$	−3.61199	+	2.62427i	−0.154863	+	0.112514i
$545$	−4.16671	+	3.02729i	−0.178482	+	0.129675i
$546$	1.16042	+	3.57140i	0.0496613	+	0.152842i
$547$	−11.7726	+	36.2322i	−0.503359	+	1.54918i	0.300154	+	0.953891i	$0.402962\pi$
$547$	−11.7726	+	36.2322i	−0.503359	+	1.54918i	−0.803513	+	0.595288i	$0.797038\pi$
$548$	1.71501	+	1.24603i	0.0732615	+	0.0532276i
$549$	5.82122			0.248444
$550$	22.7739	+	4.74660i	0.971083	+	0.202396i
$551$	11.4814			0.489123
$552$	−6.40696	−	4.65493i	−0.272698	−	0.198127i
$553$	−1.10700	+	3.40699i	−0.0470743	+	0.144880i
$554$	−6.82786	−	21.0140i	−0.290088	−	0.892799i
$555$	−1.18661	+	0.862123i	−0.0503688	+	0.0365951i
$556$	−1.17236	+	0.851771i	−0.0497192	+	0.0361231i
$557$	10.6741	+	32.8516i	0.452277	+	1.39197i	0.874303	+	0.485381i	$0.161319\pi$
$557$	10.6741	+	32.8516i	0.452277	+	1.39197i	−0.422026	+	0.906584i	$0.638681\pi$
$558$	0.223999	−	0.689397i	0.00948261	−	0.0291845i
$559$	11.1476	+	8.09917i	0.471491	+	0.342558i
$560$	1.99748			0.0844088
$561$	−13.9297	+	24.3490i	−0.588113	+	1.02802i
$562$	15.6883			0.661773
$563$	−15.7612	−	11.4512i	−0.664256	−	0.482610i	0.203842	−	0.979004i	$-0.434657\pi$
$563$	−15.7612	−	11.4512i	−0.664256	−	0.482610i	−0.868098	+	0.496394i	$0.834657\pi$
$564$	0.483811	−	1.48902i	0.0203721	−	0.0626990i
$565$	0.255295	+	0.785717i	0.0107403	+	0.0330553i
$566$	10.8087	−	7.85300i	0.454325	−	0.330086i
$567$	−6.23607	+	4.53077i	−0.261890	+	0.190274i
$568$	8.16387	+	25.1258i	0.342549	+	1.05426i
$569$	5.29308	−	16.2904i	0.221897	−	0.682930i	−0.776694	−	0.629878i	$-0.783105\pi$
$569$	5.29308	−	16.2904i	0.221897	−	0.682930i	0.998592	−	0.0530524i	$-0.0168950\pi$
$570$	−3.78332	−	2.74874i	−0.158466	−	0.115132i
$571$	−3.85581			−0.161360			−0.0806802	−	0.996740i	$-0.525709\pi$
$571$	−3.85581			−0.161360			−0.0806802	+	0.996740i	$0.525709\pi$
$572$	0.724095	−	0.325828i	0.0302759	−	0.0136236i
$573$	26.0323			1.08751
$574$	1.23541	+	0.897575i	0.0515649	+	0.0374641i
$575$	2.66745	−	8.20958i	0.111240	−	0.342363i
$576$	−0.862437	−	2.65431i	−0.0359349	−	0.110596i
$577$	7.91368	−	5.74963i	0.329451	−	0.239360i	−0.410747	−	0.911750i	$-0.634732\pi$
$577$	7.91368	−	5.74963i	0.329451	−	0.239360i	0.740198	+	0.672389i	$0.234732\pi$
$578$	12.2517	−	8.90135i	0.509602	−	0.370247i
$579$	−6.07373	−	18.6930i	−0.252416	−	0.776855i
$580$	0.0593443	−	0.182643i	0.00246414	−	0.00758384i
$581$	−13.9627	−	10.1445i	−0.579272	−	0.420865i
$582$	−6.41628			−0.265964
$583$	−4.75010	−	43.5358i	−0.196729	−	1.80307i
$584$	−36.1178			−1.49457
$585$	−0.228214	−	0.165807i	−0.00943551	−	0.00685530i
$586$	−5.38863	+	16.5845i	−0.222602	+	0.685099i
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	0.904599	−	0.426264i	$-0.140170\pi$
$587$	−1.88467	−	5.80041i	−0.0777886	−	0.239409i	−0.982387	+	0.186855i	$0.940170\pi$
$588$	0.198057	−	0.143897i	0.00816774	−	0.00593421i
$589$	−4.41932	+	3.21082i	−0.182095	+	0.132300i
$590$	1.82010	+	5.60169i	0.0749323	+	0.230618i
$591$	1.15089	−	3.54209i	0.0473414	−	0.145702i
$592$	−6.72462	−	4.88572i	−0.276380	−	0.200802i
$593$	13.2330			0.543413			0.271706	−	0.962380i	$-0.412412\pi$
$593$	13.2330			0.543413			0.271706	+	0.962380i	$0.412412\pi$
$594$	17.8903	+	19.7117i	0.734046	+	0.808780i
$595$	−2.43976			−0.100020
$596$	−1.83150	−	1.33066i	−0.0750212	−	0.0545061i
$597$	−10.1399	+	31.2073i	−0.414997	+	1.27723i
$598$	−1.29454	−	3.98419i	−0.0529378	−	0.162926i
$599$	4.79355	−	3.48271i	0.195859	−	0.142300i	−0.485534	−	0.874218i	$-0.661375\pi$
$599$	4.79355	−	3.48271i	0.195859	−	0.142300i	0.681393	+	0.731918i	$0.261375\pi$
$600$	−16.9741	+	12.3324i	−0.692964	+	0.503468i
$601$	3.93712	+	12.1172i	0.160599	+	0.494272i	0.998685	−	0.0512657i	$-0.0163255\pi$
$601$	3.93712	+	12.1172i	0.160599	+	0.494272i	−0.838086	+	0.545538i	$0.816326\pi$
$602$	3.94695	−	12.1475i	0.160866	−	0.495094i
$603$	−1.44491	−	1.04979i	−0.0588413	−	0.0427507i
$604$	−0.434590			−0.0176832
$605$	−2.60214	−	4.42576i	−0.105792	−	0.179933i
$606$	0.424287			0.0172355
$607$	−6.76452	−	4.91471i	−0.274563	−	0.199482i	0.441979	−	0.897025i	$-0.354276\pi$
$607$	−6.76452	−	4.91471i	−0.274563	−	0.199482i	−0.716543	+	0.697543i	$0.754276\pi$
$608$	1.11430	−	3.42946i	0.0451908	−	0.139083i
$609$	1.35974	+	4.18483i	0.0550992	+	0.169578i
$610$	−8.44044	+	6.13234i	−0.341743	+	0.248291i
$611$	−8.18675	+	5.94802i	−0.331201	+	0.240631i
$612$	−0.0933537	−	0.287313i	−0.00377360	−	0.0116139i
$613$	−2.06514	+	6.35585i	−0.0834102	+	0.256710i	−0.984060	−	0.177835i	$-0.943091\pi$
$613$	−2.06514	+	6.35585i	−0.0834102	+	0.256710i	0.900650	+	0.434545i	$0.143091\pi$
$614$	2.63513	+	1.91453i	0.106345	+	0.0772643i
$615$	0.786243			0.0317044
$616$	6.04401	+	6.65936i	0.243520	+	0.268313i
$617$	11.8669			0.477741			0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669			0.477741			0.238871	+	0.971051i	$0.423223\pi$
$618$	−32.4039	−	23.5428i	−1.30348	−	0.947031i
$619$	6.37213	−	19.6114i	0.256118	−	0.788249i	−0.737490	−	0.675358i	$-0.763989\pi$
$619$	6.37213	−	19.6114i	0.256118	−	0.788249i	0.993607	−	0.112891i	$-0.0360109\pi$
$620$	0.0282346	+	0.0868973i	0.00113393	+	0.00348988i
$621$	7.99107	−	5.80585i	0.320670	−	0.232981i
$622$	−25.4084	+	18.4603i	−1.01878	+	0.740189i
$623$	2.75638	+	8.48325i	0.110432	+	0.339874i
$624$	−3.38593	+	10.4208i	−0.135546	+	0.417167i
$625$	−17.6203	−	12.8019i	−0.704812	−	0.512076i
$626$	46.2824			1.84982
$627$	−2.45743	−	22.5229i	−0.0981402	−	0.899478i
$628$	−2.85694			−0.114004
$629$	8.21358	+	5.96752i	0.327497	+	0.237941i
$630$	−0.0808026	+	0.248685i	−0.00321925	+	0.00990784i
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	0.809575	−	0.587017i	$-0.199698\pi$
$631$	−4.78342	−	14.7219i	−0.190425	−	0.586068i	−1.00000		0.000949112i	$0.999698\pi$
$632$	−7.85847	+	5.70952i	−0.312593	+	0.227112i
$633$	7.02326	−	5.10270i	0.279150	−	0.202814i
$634$	5.98314	+	18.4142i	0.237621	+	0.731321i
$635$	−1.23174	+	3.79091i	−0.0488801	+	0.150438i
$636$	−2.61523	−	1.90008i	−0.103701	−	0.0753430i
$637$	−1.58232			−0.0626937
$638$	12.0640	−	5.42857i	0.477619	−	0.214919i
$639$	−3.72153			−0.147222
$640$	4.69166	+	3.40869i	0.185454	+	0.134740i
$641$	−7.28615	+	22.4245i	−0.287786	+	0.885713i	0.697764	+	0.716327i	$0.254178\pi$
$641$	−7.28615	+	22.4245i	−0.287786	+	0.885713i	−0.985550	+	0.169385i	$0.945822\pi$
$642$	−11.3497	−	34.9309i	−0.447938	−	1.37861i
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	−0.942285	−	0.334812i	$-0.891327\pi$
$643$	−23.2031	+	16.8581i	−0.915042	+	0.664817i	0.0272428	+	0.999629i	$0.491327\pi$
$644$	−0.220949	+	0.160529i	−0.00870663	+	0.00632574i
$645$	−2.03220	−	6.25446i	−0.0800177	−	0.246269i
$646$	−10.0028	+	30.7855i	−0.393556	+	1.21124i
$647$	−4.39104	−	3.19028i	−0.172630	−	0.125423i	0.498115	−	0.867111i	$-0.334026\pi$
$647$	−4.39104	−	3.19028i	−0.172630	−	0.125423i	−0.670745	+	0.741688i	$0.734026\pi$
$648$	−20.9011			−0.821074
$649$	−14.1700	+	24.7691i	−0.556221	+	0.972271i
$650$	−11.0986			−0.435323
$651$	−1.69369	−	1.23053i	−0.0663808	−	0.0482284i
$652$	0.542130	−	1.66851i	0.0212315	−	0.0653437i
$653$	−3.81392	−	11.7380i	−0.149250	−	0.459344i	0.848283	−	0.529543i	$-0.177637\pi$
$653$	−3.81392	−	11.7380i	−0.149250	−	0.459344i	−0.997533	+	0.0701988i	$0.977637\pi$
$654$	−21.1868	+	15.3931i	−0.828468	+	0.601917i
$655$	3.65023	−	2.65205i	0.142626	−	0.103624i
$656$	1.37689	+	4.23762i	0.0537584	+	0.165451i
$657$	1.57221	−	4.83878i	0.0613379	−	0.188779i
$658$	7.58873	+	5.51353i	0.295839	+	0.214940i
$659$	16.2115			0.631512			0.315756	−	0.948840i	$-0.397742\pi$
$659$	16.2115			0.631512			0.315756	+	0.948840i	$0.397742\pi$
$660$	−0.370991	−	0.0773229i	−0.0144408	−	0.00300979i
$661$	43.7050			1.69993			0.849964	−	0.526840i	$-0.176623\pi$
$661$	43.7050			1.69993			0.849964	+	0.526840i	$0.176623\pi$
$662$	11.2450	+	8.16994i	0.437048	+	0.317534i
$663$	4.13564	−	12.7282i	0.160615	−	0.494322i
$664$	−14.4614	−	44.5078i	−0.561213	−	1.72724i
$665$	1.59417	−	1.15823i	0.0618193	−	0.0449144i
$666$	0.880296	−	0.639573i	0.0341108	−	0.0247829i
$667$	−1.51690	−	4.66854i	−0.0587346	−	0.180766i
$668$	0.295721	−	0.910136i	0.0114418	−	0.0352142i
$669$	−33.2792	−	24.1787i	−1.28665	−	0.934803i
$670$	3.20093			0.123663
$671$	−49.4825	−	10.3133i	−1.91025	−	0.398140i
$672$	1.38197			0.0533105
$673$	4.74166	+	3.44502i	0.182778	+	0.132796i	0.675412	−	0.737441i	$-0.263966\pi$
$673$	4.74166	+	3.44502i	0.182778	+	0.132796i	−0.492634	+	0.870237i	$0.663966\pi$
$674$	8.70280	−	26.7845i	0.335219	−	1.03170i
$675$	−8.08655	−	24.8879i	−0.311252	−	0.957934i
$676$	1.28481	−	0.933467i	0.0494157	−	0.0359026i
$677$	16.6074	−	12.0660i	0.638275	−	0.463734i	−0.220982	−	0.975278i	$-0.570926\pi$
$677$	16.6074	−	12.0660i	0.638275	−	0.463734i	0.859257	+	0.511544i	$0.170926\pi$
$678$	1.29811	+	3.99519i	0.0498538	+	0.153434i
$679$	0.835464	−	2.57129i	0.0320622	−	0.0986772i
$680$	−5.35206	−	3.88850i	−0.205242	−	0.149117i
$681$	35.1271			1.34607
$682$	−3.12546	+	5.46327i	−0.119680	+	0.209200i
$683$	38.7055			1.48103			0.740513	−	0.672042i	$-0.234583\pi$
$683$	38.7055			1.48103			0.740513	+	0.672042i	$0.234583\pi$
$684$	0.197396	+	0.143416i	0.00754761	+	0.00548366i
$685$	−2.02075	+	6.21923i	−0.0772090	+	0.237625i
$686$	0.453245	+	1.39494i	0.0173050	+	0.0532592i
$687$	26.8750	−	19.5258i	1.02535	−	0.744957i
$688$	30.1509	−	21.9059i	1.14949	−	0.835156i
$689$	6.45647	+	19.8710i	0.245972	+	0.757024i
$690$	−0.617843	+	1.90153i	−0.0235209	+	0.0723898i
$691$	18.7126	+	13.5955i	0.711860	+	0.517197i	0.883773	−	0.467916i	$-0.154995\pi$
$691$	18.7126	+	13.5955i	0.711860	+	0.517197i	−0.171913	+	0.985112i	$0.554995\pi$
$692$	0.202603			0.00770182
$693$	−1.15527	+	0.519846i	−0.0438849	+	0.0197473i
$694$	−4.47105			−0.169719
$695$	−3.61646	−	2.62751i	−0.137180	−	0.0996673i
$696$	−3.68698	+	11.3474i	−0.139755	+	0.430121i
$697$	−1.68176	−	5.17592i	−0.0637011	−	0.196052i
$698$	23.0156	−	16.7218i	0.871155	−	0.632931i
$699$	0.908531	−	0.660086i	0.0343638	−	0.0249668i
$700$	0.223590	+	0.688138i	0.00845090	+	0.0260092i
$701$	10.9734	−	33.7727i	0.414460	−	1.27558i	−0.498273	−	0.867020i	$-0.666032\pi$
$701$	10.9734	−	33.7727i	0.414460	−	1.27558i	0.912733	−	0.408557i	$-0.133968\pi$
$702$	−10.2744	−	7.46482i	−0.387784	−	0.281742i
$703$	−8.19985			−0.309263
$704$	2.62847	+	24.0906i	0.0990643	+	0.907947i
$705$	4.82965			0.181895
$706$	−12.7662	−	9.27518i	−0.480462	−	0.349076i
$707$	−0.0552464	+	0.170031i	−0.00207775	+	0.00639467i
$708$	0.650893	+	2.00324i	0.0244621	+	0.0752865i
$709$	−35.4386	+	25.7476i	−1.33092	+	0.966972i	−0.331197	+	0.943562i	$0.607453\pi$
$709$	−35.4386	+	25.7476i	−1.33092	+	0.966972i	−0.999726	+	0.0234107i	$0.992547\pi$
$710$	5.39601	−	3.92043i	0.202509	−	0.147131i
$711$	−0.422835	−	1.30135i	−0.0158576	−	0.0488045i
$712$	−7.47403	+	23.0027i	−0.280101	+	0.862063i
$713$	1.88945	+	1.37277i	0.0707604	+	0.0514105i
$714$	−12.4056			−0.464268
$715$	1.64615	+	1.81375i	0.0615625	+	0.0678303i
$716$	2.69149			0.100586
$717$	0.453654	+	0.329599i	0.0169420	+	0.0123091i
$718$	−0.275222	+	0.847046i	−0.0102712	+	0.0316115i
$719$	4.90115	+	15.0842i	0.182782	+	0.562546i	0.999903	−	0.0139205i	$-0.00443118\pi$
$719$	4.90115	+	15.0842i	0.182782	+	0.562546i	−0.817121	+	0.576466i	$0.804431\pi$
$720$	−0.617255	+	0.448462i	−0.0230037	+	0.0167132i
$721$	13.6540	−	9.92019i	0.508500	−	0.369447i
$722$	0.532741	+	1.63961i	0.0198266	+	0.0610199i
$723$	5.21858	−	16.0611i	0.194081	−	0.597320i
$724$	0.117972	+	0.0857118i	0.00438440	+	0.00318545i
$725$	−13.0049			−0.482992
$726$	−13.2313	−	22.5039i	−0.491059	−	0.835199i
$727$	13.7719			0.510770			0.255385	−	0.966839i	$-0.417798\pi$
$727$	13.7719			0.510770			0.255385	+	0.966839i	$0.417798\pi$
$728$	−3.47110	−	2.52190i	−0.128648	−	0.0934680i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$	2.81777	+	8.67220i	0.104290	+	0.320972i
$731$	−36.8269	+	26.7563i	−1.36209	+	0.989619i
$732$	−3.01842	+	2.19301i	−0.111564	+	0.0810560i
$733$	−6.04675	−	18.6100i	−0.223342	−	0.687376i	−0.998456	−	0.0555542i	$-0.982307\pi$
$733$	−6.04675	−	18.6100i	−0.223342	−	0.687376i	0.775114	−	0.631822i	$-0.217693\pi$
$734$	−12.5380	+	38.5881i	−0.462788	+	1.42431i
$735$	0.610960	+	0.443888i	0.0225356	+	0.0163731i
$736$	−1.54170			−0.0568278
$737$	10.4224	+	11.4835i	0.383914	+	0.423000i
$738$	−0.583280			−0.0214708
$739$	9.02392	+	6.55626i	0.331950	+	0.241176i	0.741258	−	0.671220i	$-0.234230\pi$
$739$	9.02392	+	6.55626i	0.331950	+	0.241176i	−0.409307	+	0.912397i	$0.634230\pi$
$740$	−0.0423829	+	0.130441i	−0.00155803	+	0.00479511i
$741$	3.34021	+	10.2801i	0.122706	+	0.377649i
$742$	15.6685	−	11.3838i	0.575210	−	0.417914i
$743$	−16.7102	+	12.1407i	−0.613038	+	0.445398i	−0.850483	−	0.526003i	$-0.823690\pi$
$743$	−16.7102	+	12.1407i	−0.613038	+	0.445398i	0.237445	+	0.971401i	$0.423690\pi$
$744$	−1.75418	−	5.39881i	−0.0643113	−	0.197930i
$745$	2.15801	−	6.64168i	0.0790635	−	0.243332i
$746$	−34.9472	−	25.3907i	−1.27951	−	0.929618i
$747$	6.59231			0.241200
$748$	0.284517	+	2.60766i	0.0104030	+	0.0953455i
$749$	15.4762			0.565489
$750$	8.76593	+	6.36882i	0.320087	+	0.232557i
$751$	8.21957	−	25.2972i	0.299936	−	0.923109i	−0.681582	−	0.731742i	$-0.738708\pi$
$751$	8.21957	−	25.2972i	0.299936	−	0.923109i	0.981518	−	0.191367i	$-0.0612922\pi$
$752$	8.45780	+	26.0304i	0.308424	+	0.949233i
$753$	−9.15661	+	6.65266i	−0.333685	+	0.242437i
$754$	−5.10606	+	3.70977i	−0.185952	+	0.135102i
$755$	−0.414271	−	1.27499i	−0.0150769	−	0.0464018i
$756$	−0.255849	+	0.787424i	−0.00930515	+	0.0286383i
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	0.232644	−	0.972562i	$-0.425262\pi$
$757$	−17.0702	−	12.4022i	−0.620427	−	0.450767i	−0.853071	+	0.521796i	$0.825262\pi$
$758$	−37.1723			−1.35016
$759$	−8.83354	+	3.97492i	−0.320637	+	0.144280i
$760$	5.34311			0.193815
$761$	6.47006	+	4.70077i	0.234539	+	0.170403i	0.698847	−	0.715271i	$-0.253697\pi$
$761$	6.47006	+	4.70077i	0.234539	+	0.170403i	−0.464308	+	0.885674i	$0.653697\pi$
$762$	−6.26311	+	19.2759i	−0.226889	+	0.698292i
$763$	−3.40997	−	10.4948i	−0.123449	−	0.379938i
$764$	1.96937	−	1.43083i	0.0712494	−	0.0517657i
$765$	0.753927	−	0.547760i	0.0272583	−	0.0198043i
$766$	14.4731	+	44.5436i	0.522935	+	1.60943i
$767$	4.20698	−	12.9477i	0.151905	−	0.467516i
$768$	4.72685	+	3.43426i	0.170566	+	0.123923i
$769$	−52.0476			−1.87689			−0.938443	−	0.345435i	$-0.887731\pi$
$769$	−52.0476			−1.87689			−0.938443	+	0.345435i	$0.887731\pi$
$770$	1.12744	−	1.97076i	0.0406301	−	0.0710211i
$771$	16.0969			0.579716
$772$	−1.48692	−	1.08031i	−0.0535155	−	0.0388813i
$773$	−0.488554	+	1.50361i	−0.0175721	+	0.0540812i	−0.959458	−	0.281851i	$-0.909051\pi$
$773$	−0.488554	+	1.50361i	−0.0175721	+	0.0540812i	0.941886	+	0.335933i	$0.109051\pi$
$774$	1.50760	+	4.63992i	0.0541896	+	0.166778i
$775$	5.00575	−	3.63689i	0.179812	−	0.130641i
$776$	5.93089	−	4.30904i	0.212906	−	0.154686i
$777$	−0.971104	−	2.98875i	−0.0348382	−	0.107221i
$778$	−8.04587	+	24.7626i	−0.288458	+	0.887784i
$779$	3.55606	+	2.58363i	0.127409	+	0.0925681i
$780$	0.180798			0.00647361
$781$	31.6344	+	6.59334i	1.13197	+	0.235928i
$782$	13.8395			0.494899
$783$	−12.0392	−	8.74702i	−0.430247	−	0.312593i
$784$	−1.32250	+	4.07025i	−0.0472323	+	0.145366i
$785$	−2.72336	−	8.38164i	−0.0972009	−	0.299154i
$786$	18.5606	−	13.4850i	0.662034	−	0.480996i
$787$	−18.9235	+	13.7487i	−0.674549	+	0.490089i	−0.871545	−	0.490316i	$-0.836882\pi$
$787$	−18.9235	+	13.7487i	−0.674549	+	0.490089i	0.196996	+	0.980404i	$0.436882\pi$
$788$	−0.107620	−	0.331220i	−0.00383380	−	0.0117992i
$789$	−7.09017	+	21.8213i	−0.252417	+	0.776859i
$790$	1.98399	+	1.44145i	0.0705872	+	0.0512846i
$791$	−1.77008			−0.0629367
$792$	−3.36282	−	0.700889i	−0.119493	−	0.0249050i
$793$	24.1147			0.856339
$794$	−15.7875	−	11.4703i	−0.560276	−	0.407064i
$795$	3.08146	−	9.48377i	0.109288	−	0.336355i
$796$	0.948177	+	2.91819i	0.0336072	+	0.103432i
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.322669	−	0.946512i	$-0.395420\pi$
$797$	37.3376	−	27.1274i	1.32257	−	0.960900i	0.999896	−	0.0143887i	$-0.00458021\pi$
$798$	8.10599	−	5.88935i	0.286949	−	0.208481i
$799$	−10.3305	−	31.7941i	−0.365468	−	1.12479i
$800$	−1.26217	+	3.88455i	−0.0446243	+	0.137339i
$801$	−2.75638	−	2.00262i	−0.0973918	−	0.0707593i
$802$	5.11834			0.180735
$803$	−21.9371	+	38.3460i	−0.774145	+	1.35320i
$804$	1.14470			0.0403704
$805$	−0.681577	−	0.495195i	−0.0240224	−	0.0174533i
$806$	0.927927	−	2.85587i	0.0326848	−	0.100594i
$807$	9.20154	+	28.3194i	0.323910	+	0.996891i
$808$	−0.392189	+	0.284942i	−0.0137972	+	0.0100242i
$809$	−27.3044	+	19.8378i	−0.959972	+	0.697461i	−0.953144	−	0.302516i	$-0.902173\pi$
$809$	−27.3044	+	19.8378i	−0.959972	+	0.697461i	−0.00682787	+	0.999977i	$0.502173\pi$
$810$	1.63062	+	5.01854i	0.0572943	+	0.176334i
$811$	−9.50690	+	29.2592i	−0.333833	+	1.02743i	0.633462	+	0.773774i	$0.281633\pi$
$811$	−9.50690	+	29.2592i	−0.333833	+	1.02743i	−0.967294	+	0.253657i	$0.918367\pi$
$812$	0.332880	+	0.241851i	0.0116818	+	0.00848731i
$813$	−1.18212			−0.0414588
$814$	−8.61596	+	3.87701i	−0.301989	+	0.135889i
$815$	5.41182			0.189568
$816$	−29.2846	−	21.2765i	−1.02517	−	0.744827i
$817$	11.3611	−	34.9659i	0.397475	−	1.22330i
$818$	13.4276	+	41.3259i	0.469485	+	1.44493i
$819$	0.488963	−	0.355252i	0.0170857	−	0.0124135i
$820$	0.0594801	−	0.0432148i	0.00207714	−	0.00150913i
$821$	3.73242	+	11.4872i	0.130262	+	0.400906i	0.994823	−	0.101622i	$-0.0324033\pi$
$821$	3.73242	+	11.4872i	0.130262	+	0.400906i	−0.864561	+	0.502528i	$0.832403\pi$
$822$	−10.2750	+	31.6233i	−0.358383	+	1.10299i
$823$	20.0787	+	14.5880i	0.699900	+	0.508507i	0.879900	−	0.475159i	$-0.157610\pi$
$823$	20.0787	+	14.5880i	0.699900	+	0.508507i	−0.179999	+	0.983667i	$0.557610\pi$
$824$	45.7634			1.59424
$825$	2.78352	+	25.5116i	0.0969098	+	0.888201i
$826$	−12.6196			−0.439092
$827$	−4.18529	−	3.04079i	−0.145537	−	0.105739i	0.512634	−	0.858607i	$-0.328670\pi$
$827$	−4.18529	−	3.04079i	−0.145537	−	0.105739i	−0.658171	+	0.752868i	$0.728670\pi$
$828$	0.0322361	−	0.0992125i	0.00112028	−	0.00344787i
$829$	9.75057	+	30.0092i	0.338651	+	1.04226i	0.964895	+	0.262635i	$0.0845914\pi$
$829$	9.75057	+	30.0092i	0.338651	+	1.04226i	−0.626244	+	0.779627i	$0.715409\pi$
$830$	−9.55847	+	6.94464i	−0.331779	+	0.241052i
$831$	19.7196	−	14.3271i	0.684064	−	0.497001i
$832$	−3.57270	−	10.9956i	−0.123861	−	0.381205i
$833$	1.61533	−	4.97148i	0.0559679	−	0.172252i
$834$	−18.3889	−	13.3603i	−0.636755	−	0.462629i
$835$	2.95204			0.102160
$836$	−1.42385	−	1.56881i	−0.0492449	−	0.0542585i
$837$	7.08018			0.244727
$838$	−13.8184	−	10.0396i	−0.477348	−	0.346813i
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	−0.977350	−	0.211628i	$-0.932124\pi$
$839$	−1.80355	+	5.55077i	−0.0622656	+	0.191634i	0.915085	+	0.403262i	$0.132124\pi$
$840$	0.632782	+	1.94750i	0.0218330	+	0.0671952i
$841$	17.4784	−	12.6988i	0.602703	−	0.437889i
$842$	23.5956	−	17.1432i	0.813157	−	0.590793i
$843$	5.34806	+	16.4596i	0.184197	+	0.566900i
$844$	0.250854	−	0.772050i	0.00863475	−	0.0265750i
$845$	3.96333	+	2.87953i	0.136343	+	0.0990588i
$846$	−3.58291			−0.123183
$847$	10.7412	−	2.37214i	0.369071	−	0.0815075i
$848$	56.5112			1.94060
$849$	11.9237	+	8.66308i	0.409221	+	0.297316i
$850$	11.3302	−	34.8707i	0.388622	−	1.19606i
$851$	1.08335	+	3.33420i	0.0371367	+	0.114295i
$852$	1.92969	−	1.40200i	0.0661101	−	0.0480318i
$853$	16.4604	−	11.9592i	0.563593	−	0.409475i	−0.269179	−	0.963090i	$-0.586752\pi$
$853$	16.4604	−	11.9592i	0.563593	−	0.409475i	0.832772	+	0.553616i	$0.186752\pi$
$854$	−6.90752	−	21.2592i	−0.236371	−	0.727474i
$855$	−0.232586	+	0.715828i	−0.00795429	+	0.0244808i
$856$	33.9499	+	24.6661i	1.16039	+	0.843069i
$857$	−15.1087			−0.516104			−0.258052	−	0.966131i	$-0.583081\pi$
$857$	−15.1087			−0.516104			−0.258052	+	0.966131i	$0.583081\pi$
$858$	8.37029	+	9.22247i	0.285757	+	0.314850i
$859$	−33.9641			−1.15884			−0.579420	−	0.815029i	$-0.696721\pi$
$859$	−33.9641			−1.15884			−0.579420	+	0.815029i	$0.696721\pi$
$860$	−0.497507	−	0.361460i	−0.0169648	−	0.0123257i
$861$	−0.520561	+	1.60212i	−0.0177407	+	0.0546002i
$862$	−13.7090	−	42.1920i	−0.466931	−	1.43707i
$863$	2.24691	−	1.63248i	0.0764859	−	0.0555702i	−0.548885	−	0.835898i	$-0.684948\pi$
$863$	2.24691	−	1.63248i	0.0764859	−	0.0555702i	0.625371	+	0.780327i	$0.284948\pi$
$864$	−3.78115	+	2.74717i	−0.128637	+	0.0934606i
$865$	0.193130	+	0.594395i	0.00656663	+	0.0202100i
$866$	2.58676	−	7.96122i	0.0879016	−	0.270533i
$867$	13.5155	+	9.81958i	0.459010	+	0.333490i
$868$	−0.195764			−0.00664466
$869$	1.28869	+	11.8111i	0.0437156	+	0.400664i
$870$	3.01224			0.102125
$871$	−5.98562	−	4.34881i	−0.202815	−	0.147354i
$872$	9.24629	−	28.4571i	0.313119	−	0.963681i
$873$	0.319119	+	0.982147i	0.0108005	+	0.0332406i
$874$	−9.04292	+	6.57006i	−0.305881	+	0.222236i
$875$	−3.69369	+	2.68362i	−0.124869	+	0.0907229i
$876$	1.00767	+	3.10130i	0.0340461	+	0.104783i
$877$	15.3514	−	47.2469i	0.518381	−	1.59541i	−0.258662	−	0.965968i	$-0.583282\pi$
$877$	15.3514	−	47.2469i	0.518381	−	1.59541i	0.777044	−	0.629446i	$-0.216718\pi$
$878$	8.12680	+	5.90446i	0.274266	+	0.199266i
$879$	−19.2368			−0.648841
$880$	6.04142	−	2.71852i	0.203656	−	0.0916412i
$881$	−27.3064			−0.919975			−0.459988	−	0.887925i	$-0.652146\pi$
$881$	−27.3064			−0.919975			−0.459988	+	0.887925i	$0.652146\pi$
$882$	−0.453245	−	0.329302i	−0.0152616	−	0.0110882i
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	−0.999952	−	0.00978852i	$-0.996884\pi$
$883$	−5.50388	+	16.9392i	−0.185220	+	0.570049i	0.814732	+	0.579838i	$0.196884\pi$
$884$	−0.386723	−	1.19021i	−0.0130069	−	0.0400312i
$885$	−5.25663	+	3.81916i	−0.176700	+	0.128380i
$886$	0.119486	−	0.0868116i	0.00401421	−	0.00291649i
$887$	−5.09040	−	15.6666i	−0.170919	−	0.526034i	0.828505	−	0.559982i	$-0.189192\pi$
$887$	−5.09040	−	15.6666i	−0.170919	−	0.526034i	−0.999424	+	0.0339479i	$0.989192\pi$
$888$	2.63319	−	8.10413i	0.0883641	−	0.271957i
$889$	−6.90919	−	5.01982i	−0.231727	−	0.168359i
$890$	6.10625			0.204682
$891$	−12.6949	+	22.1906i	−0.425294	+	0.743412i
$892$	−3.84656			−0.128792
$893$	21.8438	+	15.8705i	0.730975	+	0.531084i
$894$	10.9730	−	33.7714i	0.366992	−	1.12948i
$895$	2.56565	+	7.89625i	0.0857601	+	0.263942i
$896$	−10.0522	+	7.30332i	−0.335819	+	0.243987i
$897$	3.73877	−	2.71638i	0.124834	−	0.0906971i
$898$	13.9621	+	42.9709i	0.465921	+	1.43396i
$899$	1.08731	−	3.34640i	0.0362639	−	0.111609i
$900$	−0.223590	−	0.162447i	−0.00745299	−	0.00541491i
$901$	−69.0238			−2.29952
$902$	4.95809	+	1.03338i	0.165086	+	0.0344078i
$903$	14.0902			0.468891
$904$	−3.88299	−	2.82116i	−0.129146	−	0.0938304i
$905$	−0.139004	+	0.427809i	−0.00462064	+	0.0142209i
$906$	−2.10647	−	6.48305i	−0.0699828	−	0.215385i
$907$	−23.0470	+	16.7446i	−0.765264	+	0.555997i	−0.900520	−	0.434814i	$-0.856814\pi$
$907$	−23.0470	+	16.7446i	−0.765264	+	0.555997i	0.135257	+	0.990811i	$0.456814\pi$
$908$	2.65741	−	1.93072i	0.0881891	−	0.0640731i
$909$	−0.0211022	−	0.0649460i	−0.000699917	−	0.00215412i
$910$	−0.334729	+	1.03019i	−0.0110962	+	0.0341505i
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	0.728090	−	0.685482i	$-0.240408\pi$
$911$	9.08955	+	6.60394i	0.301150	+	0.218798i	−0.426940	+	0.904280i	$0.640408\pi$
$912$	29.2356			0.968088
$913$	−56.0371	−	11.6794i	−1.85456	−	0.386532i
$914$	−33.9337			−1.12243
$915$	−9.31112	−	6.76492i	−0.307816	−	0.223641i
$916$	0.959910	−	2.95430i	0.0317163	−	0.0976128i
$917$	2.98729	+	9.19394i	0.0986491	+	0.303611i
$918$	33.9426	−	24.6607i	1.12027	−	0.813925i
$919$	−0.631403	+	0.458741i	−0.0208281	+	0.0151325i	−0.598151	−	0.801384i	$-0.704098\pi$
$919$	−0.631403	+	0.458741i	−0.0208281	+	0.0151325i	0.577323	+	0.816516i	$0.304098\pi$
$920$	−0.705922	−	2.17260i	−0.0232735	−	0.0716286i
$921$	−1.11036	+	3.41734i	−0.0365876	+	0.112605i
$922$	−3.29687	−	2.39532i	−0.108577	−	0.0788856i
$923$	−15.4167			−0.507446
$924$	0.403188	−	0.704771i	0.0132639	−	0.0231853i
$925$	9.28795			0.305386
$926$	−30.9646	−	22.4971i	−1.01756	−	0.739301i
$927$	−1.99209	+	6.13101i	−0.0654287	+	0.201369i
$928$	0.717755	+	2.20902i	0.0235615	+	0.0725148i
$929$	−21.5169	+	15.6329i	−0.705946	+	0.512899i	−0.881863	−	0.471505i	$-0.843711\pi$
$929$	−21.5169	+	15.6329i	−0.705946	+	0.512899i	0.175918	+	0.984405i	$0.443711\pi$
$930$	−1.15945	+	0.842387i	−0.0380198	+	0.0276230i
$931$	1.30464	+	4.01528i	0.0427580	+	0.131596i
$932$	0.0324505	−	0.0998725i	0.00106295	−	0.00327143i
$933$	−28.0294	−	20.3646i	−0.917642	−	0.666706i
$934$	3.89900			0.127579
$935$	−7.37911	+	3.32045i	−0.241323	+	0.108590i
$936$	1.63883			0.0535669
$937$	−33.9542	−	24.6691i	−1.10923	−	0.805906i	−0.126691	−	0.991942i	$-0.540436\pi$
$937$	−33.9542	−	24.6691i	−1.10923	−	0.805906i	−0.982543	+	0.186036i	$0.940436\pi$
$938$	−2.11930	+	6.52252i	−0.0691974	+	0.212968i
$939$	15.7774	+	48.5578i	0.514875	+	1.58462i
$940$	0.365368	−	0.265456i	0.0119170	−	0.00865821i
$941$	39.6685	−	28.8209i	1.29316	−	0.939533i	0.293292	−	0.956023i	$-0.405249\pi$
$941$	39.6685	−	28.8209i	1.29316	−	0.939533i	0.999864	+	0.0164899i	$0.00524912\pi$
$942$	−13.8477	−	42.6187i	−0.451181	−	1.38859i
$943$	0.580730	−	1.78730i	0.0189112	−	0.0582026i
$944$	−29.7897	−	21.6435i	−0.969574	−	0.704437i
$945$	−2.55402			−0.0830823
$946$	−4.59475	−	42.1120i	−0.149388	−	1.36918i
$947$	−27.2953			−0.886978			−0.443489	−	0.896280i	$-0.646259\pi$
$947$	−27.2953			−0.886978			−0.443489	+	0.896280i	$0.646259\pi$
$948$	0.709503	+	0.515484i	0.0230436	+	0.0167422i
$949$	6.51299	−	20.0449i	0.211421	−	0.650686i
$950$	9.15097	+	28.1638i	0.296897	+	0.913754i
$951$	−17.2799	+	12.5546i	−0.560339	+	0.407110i
$952$	11.4671	−	8.33134i	0.371651	−	0.270020i
$953$	6.10023	+	18.7746i	0.197606	+	0.608169i	0.999936	+	0.0112883i	$0.00359326\pi$
$953$	6.10023	+	18.7746i	0.197606	+	0.608169i	−0.802330	+	0.596880i	$0.796407\pi$
$954$	−2.28601	+	7.03561i	−0.0740122	+	0.227786i
$955$	6.07505	+	4.41378i	0.196584	+	0.142827i
$956$	0.0524354			0.00169588
$957$	9.80801	+	10.8066i	0.317048	+	0.349327i
$958$	12.1478			0.392478
$959$	−11.3350	−	8.23535i	−0.366026	−	0.265933i
$960$	−1.70513	+	5.24785i	−0.0550329	+	0.169374i
$961$	−9.06221	−	27.8906i	−0.292329	−	0.899697i
$962$	3.64668	−	2.64947i	0.117574	−	0.0854222i
$963$	−4.78241	+	3.47463i	−0.154111	+	0.111968i
$964$	−0.487989	−	1.50188i	−0.0157171	−	0.0483721i
$965$	1.75200	−	5.39211i	0.0563990	−	0.173578i
$966$	−3.46566	−	2.51795i	−0.111506	−	0.0810137i
$967$	−12.6734			−0.407551			−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734			−0.407551			−0.203775	+	0.979018i	$0.565321\pi$
$968$	27.3435	+	11.9156i	0.878853	+	0.382983i
$969$	−35.7089			−1.14714
$970$	−1.49734	−	1.08788i	−0.0480768	−	0.0349298i
$971$	5.16170	−	15.8861i	0.165647	−	0.509809i	−0.833436	−	0.552615i	$-0.813630\pi$
$971$	5.16170	−	15.8861i	0.165647	−	0.509809i	0.999083	+	0.0428065i	$0.0136299\pi$
$972$	−0.184414	−	0.567569i	−0.00591509	−	0.0182048i
$973$	7.74848	−	5.62960i	0.248405	−	0.180477i
$974$	−23.2523	+	16.8938i	−0.745052	+	0.541312i
$975$	−3.78345	−	11.6443i	−0.121167	−	0.372914i
$976$	20.1552	−	62.0312i	0.645151	−	1.98557i
$977$	−22.1227	−	16.0731i	−0.707769	−	0.514224i	0.174684	−	0.984625i	$-0.444110\pi$
$977$	−22.1227	−	16.0731i	−0.707769	−	0.514224i	−0.882453	+	0.470400i	$0.844110\pi$
$978$	27.5178			0.879924
$979$	19.8822	+	21.9064i	0.635439	+	0.700133i
$980$	0.0706175			0.00225579
$981$	3.40997	+	2.47749i	0.108872	+	0.0791001i
$982$	12.9998	−	40.0093i	0.414841	−	1.27675i
$983$	−16.9979	−	52.3143i	−0.542150	−	1.66857i	−0.727671	−	0.685926i	$-0.759397\pi$
$983$	−16.9979	−	52.3143i	−0.542150	−	1.66857i	0.185521	−	0.982640i	$-0.440603\pi$
$984$	−3.69542	+	2.68488i	−0.117806	+	0.0855908i
$985$	0.869141	−	0.631468i	0.0276931	−	0.0201202i
$986$	−6.44313	−	19.8299i	−0.205191	−	0.631513i
$987$	−3.19765	+	9.84135i	−0.101782	+	0.313254i
$988$	0.817723	+	0.594110i	0.0260152	+	0.0189012i
$989$	−15.7188			−0.499828
$990$	0.0940645	+	0.862123i	0.00298957	+	0.0274001i
$991$	53.2327			1.69099			0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327			1.69099			0.845497	+	0.533980i	$0.179304\pi$
$992$	−0.894035	−	0.649555i	−0.0283857	−	0.0206234i
$993$	−4.73826	+	14.5829i	−0.150364	+	0.462774i
$994$	4.41601	+	13.5911i	0.140067	+	0.431083i
$995$	−7.65750	+	5.56350i	−0.242759	+	0.176375i
$996$	−3.41825	+	2.48350i	−0.108311	+	0.0786927i
$997$	10.1217	+	31.1515i	0.320558	+	0.986577i	0.973406	+	0.229087i	$0.0735742\pi$
$997$	10.1217	+	31.1515i	0.320558	+	0.986577i	−0.652848	+	0.757489i	$0.726426\pi$
$998$	−12.6682	+	38.9886i	−0.401004	+	1.23416i
$999$	8.59825	+	6.24700i	0.272037	+	0.197646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.a.15.2	✓	8
3.2	odd	2		693.2.m.g.631.1		8
7.2	even	3		539.2.q.c.312.2		16
7.3	odd	6		539.2.q.b.422.1		16
7.4	even	3		539.2.q.c.422.1		16
7.5	odd	6		539.2.q.b.312.2		16
7.6	odd	2		539.2.f.d.246.2		8
11.2	odd	10		847.2.f.s.148.2		8
11.3	even	5	inner	77.2.f.a.36.2	yes	8
11.4	even	5		847.2.f.p.372.1		8
11.5	even	5		847.2.a.l.1.1		4
11.6	odd	10		847.2.a.k.1.4		4
11.7	odd	10		847.2.f.s.372.2		8
11.8	odd	10		847.2.f.q.729.1		8
11.9	even	5		847.2.f.p.148.1		8
11.10	odd	2		847.2.f.q.323.1		8
33.5	odd	10		7623.2.a.ch.1.4		4
33.14	odd	10		693.2.m.g.190.1		8
33.17	even	10		7623.2.a.co.1.1		4
77.3	odd	30		539.2.q.b.520.2		16
77.6	even	10		5929.2.a.bb.1.4		4
77.25	even	15		539.2.q.c.520.2		16
77.27	odd	10		5929.2.a.bi.1.1		4
77.47	odd	30		539.2.q.b.410.1		16
77.58	even	15		539.2.q.c.410.1		16
77.69	odd	10		539.2.f.d.344.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	1.1	even	1	trivial
77.2.f.a.36.2	yes	8	11.3	even	5	inner
539.2.f.d.246.2		8	7.6	odd	2
539.2.f.d.344.2		8	77.69	odd	10
539.2.q.b.312.2		16	7.5	odd	6
539.2.q.b.410.1		16	77.47	odd	30
539.2.q.b.422.1		16	7.3	odd	6
539.2.q.b.520.2		16	77.3	odd	30
539.2.q.c.312.2		16	7.2	even	3
539.2.q.c.410.1		16	77.58	even	15
539.2.q.c.422.1		16	7.4	even	3
539.2.q.c.520.2		16	77.25	even	15
693.2.m.g.190.1		8	33.14	odd	10
693.2.m.g.631.1		8	3.2	odd	2
847.2.a.k.1.4		4	11.6	odd	10
847.2.a.l.1.1		4	11.5	even	5
847.2.f.p.148.1		8	11.9	even	5
847.2.f.p.372.1		8	11.4	even	5
847.2.f.q.323.1		8	11.10	odd	2
847.2.f.q.729.1		8	11.8	odd	10
847.2.f.s.148.2		8	11.2	odd	10
847.2.f.s.372.2		8	11.7	odd	10
5929.2.a.bb.1.4		4	77.6	even	10
5929.2.a.bi.1.1		4	77.27	odd	10
7623.2.a.ch.1.4		4	33.5	odd	10
7623.2.a.co.1.1		4	33.17	even	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18661 + 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.837913 - 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(1.18661 + 0.862123i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.0467549 + 0.143897i) q^{4} +(-0.377594 + 0.274338i) q^{5} +(-1.91998 + 1.39494i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.837913 - 2.57883i) q^{8} +(0.309017 + 0.224514i) q^{9} -0.684570 q^{10} +(-2.22899 - 2.45593i) q^{11} -0.244812 q^{12} +(1.28012 + 0.930062i) q^{13} +(0.453245 - 1.39494i) q^{14} +(-0.233366 - 0.718226i) q^{15} +(3.46236 - 2.51555i) q^{16} +(-4.22899 + 3.07254i) q^{17} +(0.173124 + 0.532822i) q^{18} +(1.30464 - 4.01528i) q^{19} +(-0.0571308 - 0.0415079i) q^{20} +1.61803 q^{21} +(-0.527635 - 4.83590i) q^{22} -1.80505 q^{23} +(3.54946 + 2.57883i) q^{24} +(-1.47777 + 4.54811i) q^{25} +(0.717177 + 2.20724i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(0.122406 - 0.0889332i) q^{28} +(0.840363 + 2.58637i) q^{29} +(0.342285 - 1.05345i) q^{30} +(-1.04675 - 0.760512i) q^{31} +0.854102 q^{32} +(4.89378 - 2.20210i) q^{33} -7.66708 q^{34} +(0.377594 + 0.274338i) q^{35} +(-0.0178588 + 0.0549637i) q^{36} +(-0.600175 - 1.84715i) q^{37} +(5.00978 - 3.63982i) q^{38} +(-2.07128 + 1.50487i) q^{39} +(0.391081 + 1.20362i) q^{40} +(-0.321724 + 0.990166i) q^{41} +(1.91998 + 1.39494i) q^{42} +8.70820 q^{43} +(0.249184 - 0.435572i) q^{44} -0.178276 q^{45} +(-2.14190 - 1.55618i) q^{46} +(-1.97626 + 6.08229i) q^{47} +(2.13986 + 6.58580i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-5.67457 + 4.12281i) q^{50} +(-2.61366 - 8.04402i) q^{51} +(-0.0739811 + 0.227690i) q^{52} +(10.6826 + 7.76137i) q^{53} -8.02616 q^{54} +(1.51541 + 0.315846i) q^{55} -2.71154 q^{56} +(5.52656 + 4.01528i) q^{57} +(-1.23259 + 3.79351i) q^{58} +(-2.65875 - 8.18278i) q^{59} +(0.0924396 - 0.0671613i) q^{60} +(12.3295 - 8.95793i) q^{61} +(-0.586436 - 1.80486i) q^{62} +(0.118034 - 0.363271i) q^{63} +(-5.91123 - 4.29476i) q^{64} -0.738517 q^{65} +(7.70550 + 1.60600i) q^{66} -4.67583 q^{67} +(-0.639856 - 0.464883i) q^{68} +(0.902527 - 2.77769i) q^{69} +(0.211544 + 0.651065i) q^{70} +(-7.88234 + 5.72685i) q^{71} +(0.837913 - 0.608780i) q^{72} +(-4.11611 - 12.6681i) q^{73} +(0.880296 - 2.70927i) q^{74} +(-6.25993 - 4.54811i) q^{75} +0.638786 q^{76} +(-1.64693 + 2.87882i) q^{77} -3.75519 q^{78} +(-2.89815 - 2.10563i) q^{79} +(-0.617255 + 1.89971i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-1.23541 + 0.897575i) q^{82} +(13.9627 - 10.1445i) q^{83} +(0.0756511 + 0.232830i) q^{84} +(0.753927 - 2.32035i) q^{85} +(10.3333 + 7.50755i) q^{86} -4.40020 q^{87} +(-8.20113 + 3.69034i) q^{88} -8.91982 q^{89} +(-0.211544 - 0.153696i) q^{90} +(0.488963 - 1.50487i) q^{91} +(-0.0843952 - 0.259742i) q^{92} +(1.69369 - 1.23053i) q^{93} +(-7.58873 + 5.51353i) q^{94} +(0.608919 + 1.87406i) q^{95} +(-0.427051 + 1.31433i) q^{96} +(2.18727 + 1.58915i) q^{97} -1.46673 q^{98} +(-0.137407 - 1.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9	\( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20} + 4 q^{21} - q^{22} - 16 q^{23} + 21 q^{24} + 5 q^{25} + 21 q^{26} - 22 q^{27} + 7 q^{28} - 9 q^{29} + 14 q^{30} - 11 q^{31} - 20 q^{32} + 10 q^{33} - 24 q^{34} - 3 q^{35} - 2 q^{36} + 6 q^{37} + 35 q^{38} - 5 q^{39} - 16 q^{40} - 22 q^{41} - 3 q^{42} + 16 q^{43} + 29 q^{44} + 18 q^{45} + 29 q^{46} + 7 q^{47} + 4 q^{48} - 2 q^{49} - 34 q^{50} + 3 q^{51} + 21 q^{52} + 2 q^{53} + 4 q^{54} + 26 q^{55} - 18 q^{56} - 3 q^{57} - 39 q^{58} + 25 q^{59} - 38 q^{60} + 7 q^{61} - 5 q^{62} - 8 q^{63} + q^{64} + 24 q^{65} + 18 q^{66} - 30 q^{67} + 8 q^{68} + 8 q^{69} - 2 q^{70} - 14 q^{71} + 3 q^{72} + 3 q^{73} - 9 q^{74} + 5 q^{75} - 52 q^{76} - 5 q^{77} - 18 q^{78} - 9 q^{79} - 33 q^{80} - 28 q^{81} + 31 q^{82} + 23 q^{83} + 4 q^{84} - 10 q^{85} - 17 q^{86} + 12 q^{87} - 7 q^{88} - 34 q^{89} + 2 q^{90} + 5 q^{91} - 34 q^{92} + 8 q^{93} - 30 q^{94} + 24 q^{95} + 10 q^{96} + 30 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more