LMFDB - Embedded newform 129.2.i.c.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [129,2,Mod(4,129)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(129, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("129.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 129 = 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	129.i (of order $7$, degree $6$, 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:	$1.03007018607$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	129.64
Dual form			129.2.i.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18675 - 1.05308i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(2.42592 + 3.04201i) q^{4} +(-0.134341 - 0.588587i) q^{5} +2.42711 q^{6} +1.28895 q^{7} +(-1.02123 - 4.47429i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})$	\(q+(-2.18675 - 1.05308i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(2.42592 + 3.04201i) q^{4} +(-0.134341 - 0.588587i) q^{5} +2.42711 q^{6} +1.28895 q^{7} +(-1.02123 - 4.47429i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-0.326061 + 1.42857i) q^{10} +(2.17885 - 2.73219i) q^{11} +(-3.50556 - 1.68819i) q^{12} +(-1.30661 - 5.72462i) q^{13} +(-2.81861 - 1.35737i) q^{14} +(0.376416 + 0.472010i) q^{15} +(-0.747035 + 3.27297i) q^{16} +(0.0519955 - 0.227807i) q^{17} +(-2.18675 + 1.05308i) q^{18} +(0.427017 + 0.535462i) q^{19} +(1.46459 - 1.83653i) q^{20} +(-1.16130 + 0.559253i) q^{21} +(-7.64182 + 3.68011i) q^{22} +(1.58112 - 1.98267i) q^{23} +(2.86142 + 3.58811i) q^{24} +(4.17646 - 2.01128i) q^{25} +(-3.17128 + 13.8943i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(3.12688 + 3.92098i) q^{28} +(6.96448 + 3.35392i) q^{29} +(-0.326061 - 1.42857i) q^{30} +(7.14176 + 3.43929i) q^{31} +(-0.642539 + 0.805719i) q^{32} +(-0.777621 + 3.40698i) q^{33} +(-0.353602 + 0.443403i) q^{34} +(-0.173159 - 0.758657i) q^{35} +3.89087 q^{36} -11.9564 q^{37} +(-0.369893 - 1.62061i) q^{38} +(3.66103 + 4.59079i) q^{39} +(-2.49632 + 1.20216i) q^{40} +(-9.02624 - 4.34681i) q^{41} +3.12842 q^{42} +(0.599960 - 6.52993i) q^{43} +13.5970 q^{44} +(-0.543936 - 0.261946i) q^{45} +(-5.54544 + 2.67054i) q^{46} +(4.81683 + 6.04011i) q^{47} +(-0.747035 - 3.27297i) q^{48} -5.33862 q^{49} -11.2509 q^{50} +(0.0519955 + 0.227807i) q^{51} +(14.2446 - 17.8622i) q^{52} +(0.537519 - 2.35503i) q^{53} +(1.51328 - 1.89759i) q^{54} +(-1.90084 - 0.915396i) q^{55} +(-1.31631 - 5.76713i) q^{56} +(-0.617057 - 0.297159i) q^{57} +(-11.6976 - 14.6684i) q^{58} +(-2.29067 + 10.0361i) q^{59} +(-0.522705 + 2.29012i) q^{60} +(0.457977 - 0.220550i) q^{61} +(-11.9954 - 15.0418i) q^{62} +(0.803645 - 1.00774i) q^{63} +(8.30293 - 3.99848i) q^{64} +(-3.19391 + 1.53811i) q^{65} +(5.28830 - 6.63132i) q^{66} +(1.88403 + 2.36251i) q^{67} +(0.819128 - 0.394471i) q^{68} +(-0.564296 + 2.47234i) q^{69} +(-0.420275 + 1.84135i) q^{70} +(-1.26928 - 1.59162i) q^{71} +(-4.13487 - 1.99125i) q^{72} +(1.32313 + 5.79702i) q^{73} +(26.1456 + 12.5911i) q^{74} +(-2.89020 + 3.62419i) q^{75} +(-0.592971 + 2.59798i) q^{76} +(2.80841 - 3.52164i) q^{77} +(-3.17128 - 13.8943i) q^{78} +2.96949 q^{79} +2.02679 q^{80} +(-0.222521 - 0.974928i) q^{81} +(15.1606 + 19.0108i) q^{82} +(0.0585069 - 0.0281755i) q^{83} +(-4.51847 - 2.17598i) q^{84} -0.141070 q^{85} +(-8.18854 + 13.6475i) q^{86} -7.72999 q^{87} +(-14.4497 - 6.95861i) q^{88} +(4.53211 - 2.18255i) q^{89} +(0.913603 + 1.14562i) q^{90} +(-1.68415 - 7.37873i) q^{91} +9.86696 q^{92} -7.92676 q^{93} +(-4.17246 - 18.2808i) q^{94} +(0.257800 - 0.323271i) q^{95} +(0.229320 - 1.00472i) q^{96} +(-5.60727 + 7.03130i) q^{97} +(11.6742 + 5.62202i) q^{98} +(-0.777621 - 3.40698i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 5 q^{3} - 14 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} + 8 q^{8} - 5 q^{9}+O(q^{10}) $ 30 * q - 2 * q^2 - 5 * q^3 - 14 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 + 8 * q^8 - 5 * q^9	\( 30 q - 2 q^{2} - 5 q^{3} - 14 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} + 8 q^{8} - 5 q^{9} - 10 q^{10} - 6 q^{11} - 7 q^{12} - 14 q^{13} + 9 q^{14} + 3 q^{15} + 16 q^{16} - 6 q^{17} - 2 q^{18} - 20 q^{19} + 22 q^{20} - 5 q^{21} - 4 q^{22} - 10 q^{23} + q^{24} + 9 q^{25} - 6 q^{26} - 5 q^{27} - 8 q^{28} + 16 q^{29} - 10 q^{30} + 14 q^{31} - 20 q^{32} + q^{33} - 10 q^{34} + 4 q^{35} + 42 q^{36} - 16 q^{37} - 4 q^{38} + 14 q^{39} + 14 q^{40} - q^{41} - 12 q^{42} + 3 q^{43} + 186 q^{44} + 3 q^{45} - 51 q^{46} - 15 q^{47} + 16 q^{48} + 40 q^{49} - 80 q^{50} - 6 q^{51} - 12 q^{52} + 23 q^{53} - 2 q^{54} - 25 q^{55} - 87 q^{56} + 29 q^{57} - 26 q^{59} + q^{60} - 4 q^{61} - 44 q^{62} - 12 q^{63} - 70 q^{64} - 5 q^{65} + 3 q^{66} + q^{67} - 48 q^{68} + 11 q^{69} - 33 q^{70} - 60 q^{71} - 6 q^{72} - 25 q^{73} + 144 q^{74} - 12 q^{75} + q^{76} - 6 q^{77} - 6 q^{78} + 142 q^{79} - 98 q^{80} - 5 q^{81} + 140 q^{82} + 7 q^{83} - 15 q^{84} - 20 q^{85} - 4 q^{86} + 2 q^{87} + 8 q^{88} + 4 q^{89} + 4 q^{90} - 40 q^{91} + 122 q^{92} - 14 q^{93} + 38 q^{94} + 140 q^{95} - 6 q^{96} + 6 q^{97} + 23 q^{98} + q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 5 * q^3 - 14 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 + 8 * q^8 - 5 * q^9 - 10 * q^10 - 6 * q^11 - 7 * q^12 - 14 * q^13 + 9 * q^14 + 3 * q^15 + 16 * q^16 - 6 * q^17 - 2 * q^18 - 20 * q^19 + 22 * q^20 - 5 * q^21 - 4 * q^22 - 10 * q^23 + q^24 + 9 * q^25 - 6 * q^26 - 5 * q^27 - 8 * q^28 + 16 * q^29 - 10 * q^30 + 14 * q^31 - 20 * q^32 + q^33 - 10 * q^34 + 4 * q^35 + 42 * q^36 - 16 * q^37 - 4 * q^38 + 14 * q^39 + 14 * q^40 - q^41 - 12 * q^42 + 3 * q^43 + 186 * q^44 + 3 * q^45 - 51 * q^46 - 15 * q^47 + 16 * q^48 + 40 * q^49 - 80 * q^50 - 6 * q^51 - 12 * q^52 + 23 * q^53 - 2 * q^54 - 25 * q^55 - 87 * q^56 + 29 * q^57 - 26 * q^59 + q^60 - 4 * q^61 - 44 * q^62 - 12 * q^63 - 70 * q^64 - 5 * q^65 + 3 * q^66 + q^67 - 48 * q^68 + 11 * q^69 - 33 * q^70 - 60 * q^71 - 6 * q^72 - 25 * q^73 + 144 * q^74 - 12 * q^75 + q^76 - 6 * q^77 - 6 * q^78 + 142 * q^79 - 98 * q^80 - 5 * q^81 + 140 * q^82 + 7 * q^83 - 15 * q^84 - 20 * q^85 - 4 * q^86 + 2 * q^87 + 8 * q^88 + 4 * q^89 + 4 * q^90 - 40 * q^91 + 122 * q^92 - 14 * q^93 + 38 * q^94 + 140 * q^95 - 6 * q^96 + 6 * q^97 + 23 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/129\mathbb{Z}\right)^\times$.

$n$	$44$	$46$
$\chi(n)$	$1$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−2.18675	−	1.05308i	−1.54627	−	0.744643i	−0.550352	−	0.834933i	$-0.685506\pi$
$2$	−2.18675	−	1.05308i	−1.54627	−	0.744643i	−0.995916	+	0.0902897i	$0.971221\pi$
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$3$	−0.900969	+	0.433884i	−0.520175	+	0.250503i
$4$	2.42592	+	3.04201i	1.21296	+	1.52100i
$5$	−0.134341	−	0.588587i	−0.0600792	−	0.263224i	0.935964	−	0.352096i	$-0.114531\pi$
$5$	−0.134341	−	0.588587i	−0.0600792	−	0.263224i	−0.996043	+	0.0888719i	$0.971674\pi$
$6$	2.42711			0.990864
$7$	1.28895			0.487176			0.243588	−	0.969879i	$-0.421676\pi$
$7$	1.28895			0.487176			0.243588	+	0.969879i	$0.421676\pi$
$8$	−1.02123	−	4.47429i	−0.361059	−	1.58190i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	−0.326061	+	1.42857i	−0.103110	+	0.451753i
$11$	2.17885	−	2.73219i	0.656947	−	0.823785i	−0.336060	−	0.941840i	$-0.609095\pi$
$11$	2.17885	−	2.73219i	0.656947	−	0.823785i	0.993007	+	0.118055i	$0.0376661\pi$
$12$	−3.50556	−	1.68819i	−1.01197	−	0.487337i
$13$	−1.30661	−	5.72462i	−0.362388	−	1.58772i	−0.747116	−	0.664694i	$-0.768562\pi$
$13$	−1.30661	−	5.72462i	−0.362388	−	1.58772i	0.384728	−	0.923030i	$-0.374295\pi$
$14$	−2.81861	−	1.35737i	−0.753304	−	0.362772i
$15$	0.376416	+	0.472010i	0.0971901	+	0.121873i
$16$	−0.747035	+	3.27297i	−0.186759	+	0.818244i
$17$	0.0519955	−	0.227807i	0.0126108	−	0.0552514i	−0.968231	−	0.250057i	$-0.919551\pi$
$17$	0.0519955	−	0.227807i	0.0126108	−	0.0552514i	0.980842	+	0.194806i	$0.0624077\pi$
$18$	−2.18675	+	1.05308i	−0.515422	+	0.248214i
$19$	0.427017	+	0.535462i	0.0979644	+	0.122843i	0.828397	−	0.560141i	$-0.189253\pi$
$19$	0.427017	+	0.535462i	0.0979644	+	0.122843i	−0.730433	+	0.682984i	$0.760682\pi$
$20$	1.46459	−	1.83653i	0.327491	−	0.410661i
$21$	−1.16130	+	0.559253i	−0.253417	+	0.122039i
$22$	−7.64182	+	3.68011i	−1.62924	+	0.784601i
$23$	1.58112	−	1.98267i	0.329687	−	0.413414i	−0.589168	−	0.808011i	$-0.700544\pi$
$23$	1.58112	−	1.98267i	0.329687	−	0.413414i	0.918854	+	0.394597i	$0.129116\pi$
$24$	2.86142	+	3.58811i	0.584085	+	0.732419i
$25$	4.17646	−	2.01128i	0.835291	−	0.402255i
$26$	−3.17128	+	13.8943i	−0.621940	+	2.72490i
$27$	−0.222521	+	0.974928i	−0.0428242	+	0.187625i
$28$	3.12688	+	3.92098i	0.590925	+	0.740996i
$29$	6.96448	+	3.35392i	1.29327	+	0.622807i	0.948766	−	0.315978i	$-0.102333\pi$
$29$	6.96448	+	3.35392i	1.29327	+	0.622807i	0.344505	+	0.938785i	$0.388047\pi$
$30$	−0.326061	−	1.42857i	−0.0595304	−	0.260820i
$31$	7.14176	+	3.43929i	1.28270	+	0.617715i	0.946082	−	0.323927i	$-0.105003\pi$
$31$	7.14176	+	3.43929i	1.28270	+	0.617715i	0.336616	+	0.941642i	$0.390718\pi$
$32$	−0.642539	+	0.805719i	−0.113586	+	0.142432i
$33$	−0.777621	+	3.40698i	−0.135366	+	0.593079i
$34$	−0.353602	+	0.443403i	−0.0606422	+	0.0760429i
$35$	−0.173159	−	0.758657i	−0.0292691	−	0.128237i
$36$	3.89087			0.648479
$37$	−11.9564			−1.96562			−0.982808	−	0.184632i	$-0.940891\pi$
$37$	−11.9564			−1.96562			−0.982808	+	0.184632i	$0.940891\pi$
$38$	−0.369893	−	1.62061i	−0.0600046	−	0.262897i
$39$	3.66103	+	4.59079i	0.586234	+	0.735115i
$40$	−2.49632	+	1.20216i	−0.394703	+	0.190079i
$41$	−9.02624	−	4.34681i	−1.40966	−	0.678857i	−0.434565	−	0.900640i	$-0.643098\pi$
$41$	−9.02624	−	4.34681i	−1.40966	−	0.678857i	−0.975096	+	0.221783i	$0.928812\pi$
$42$	3.12842			0.482725
$43$	0.599960	−	6.52993i	0.0914930	−	0.995806i
$43$	0.599960	−	6.52993i	0.0914930	−	0.995806i
$44$	13.5970			2.04983
$45$	−0.543936	−	0.261946i	−0.0810853	−	0.0390486i
$46$	−5.54544	+	2.67054i	−0.817630	+	0.393750i
$47$	4.81683	+	6.04011i	0.702607	+	0.881041i	0.997215	−	0.0745772i	$-0.0237607\pi$
$47$	4.81683	+	6.04011i	0.702607	+	0.881041i	−0.294609	+	0.955618i	$0.595189\pi$
$48$	−0.747035	−	3.27297i	−0.107825	−	0.472413i
$49$	−5.33862			−0.762660
$50$	−11.2509			−1.59112
$51$	0.0519955	+	0.227807i	0.00728083	+	0.0318994i
$52$	14.2446	−	17.8622i	1.97537	−	2.47704i
$53$	0.537519	−	2.35503i	0.0738340	−	0.323488i	−0.924500	−	0.381181i	$-0.875517\pi$
$53$	0.537519	−	2.35503i	0.0738340	−	0.323488i	0.998334	+	0.0576934i	$0.0183746\pi$
$54$	1.51328	−	1.89759i	0.205931	−	0.258230i
$55$	−1.90084	−	0.915396i	−0.256309	−	0.123432i
$56$	−1.31631	−	5.76713i	−0.175899	−	0.770665i
$57$	−0.617057	−	0.297159i	−0.0817312	−	0.0393597i
$58$	−11.6976	−	14.6684i	−1.53597	−	1.92605i
$59$	−2.29067	+	10.0361i	−0.298219	+	1.30658i	0.574557	+	0.818465i	$0.305174\pi$
$59$	−2.29067	+	10.0361i	−0.298219	+	1.30658i	−0.872776	+	0.488120i	$0.837683\pi$
$60$	−0.522705	+	2.29012i	−0.0674809	+	0.295653i
$61$	0.457977	−	0.220550i	0.0586379	−	0.0282385i	−0.404335	−	0.914611i	$-0.632497\pi$
$61$	0.457977	−	0.220550i	0.0586379	−	0.0282385i	0.462973	+	0.886372i	$0.346783\pi$
$62$	−11.9954	−	15.0418i	−1.52342	−	1.91030i
$63$	0.803645	−	1.00774i	0.101250	−	0.126963i
$64$	8.30293	−	3.99848i	1.03787	−	0.499810i
$65$	−3.19391	+	1.53811i	−0.396156	+	0.190778i
$66$	5.28830	−	6.63132i	0.650945	−	0.816259i
$67$	1.88403	+	2.36251i	0.230172	+	0.288626i	0.883483	−	0.468463i	$-0.155192\pi$
$67$	1.88403	+	2.36251i	0.230172	+	0.288626i	−0.653311	+	0.757089i	$0.726621\pi$
$68$	0.819128	−	0.394471i	0.0993339	−	0.0478367i
$69$	−0.564296	+	2.47234i	−0.0679333	+	0.297635i
$70$	−0.420275	+	1.84135i	−0.0502325	+	0.220083i
$71$	−1.26928	−	1.59162i	−0.150636	−	0.188891i	0.700788	−	0.713369i	$-0.252832\pi$
$71$	−1.26928	−	1.59162i	−0.150636	−	0.188891i	−0.851424	+	0.524478i	$0.824260\pi$
$72$	−4.13487	−	1.99125i	−0.487299	−	0.234671i
$73$	1.32313	+	5.79702i	0.154861	+	0.678490i	0.991431	+	0.130630i	$0.0417000\pi$
$73$	1.32313	+	5.79702i	0.154861	+	0.678490i	−0.836570	+	0.547860i	$0.815443\pi$
$74$	26.1456	+	12.5911i	3.03937	+	1.46368i
$75$	−2.89020	+	3.62419i	−0.333731	+	0.418486i
$76$	−0.592971	+	2.59798i	−0.0680184	+	0.298008i
$77$	2.80841	−	3.52164i	0.320049	−	0.401328i
$78$	−3.17128	−	13.8943i	−0.359077	−	1.57322i
$79$	2.96949			0.334094			0.167047	−	0.985949i	$-0.446577\pi$
$79$	2.96949			0.334094			0.167047	+	0.985949i	$0.446577\pi$
$80$	2.02679			0.226602
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	15.1606	+	19.0108i	1.67421	+	2.09939i
$83$	0.0585069	−	0.0281755i	0.00642197	−	0.00309266i	−0.430670	−	0.902509i	$-0.641723\pi$
$83$	0.0585069	−	0.0281755i	0.00642197	−	0.00309266i	0.437092	+	0.899417i	$0.356008\pi$
$84$	−4.51847	−	2.17598i	−0.493006	−	0.237419i
$85$	−0.141070			−0.0153012
$86$	−8.18854	+	13.6475i	−0.882993	+	1.47165i
$87$	−7.72999			−0.828742
$88$	−14.4497	−	6.95861i	−1.54034	−	0.741790i
$89$	4.53211	−	2.18255i	0.480402	−	0.231350i	−0.177979	−	0.984034i	$-0.556956\pi$
$89$	4.53211	−	2.18255i	0.480402	−	0.231350i	0.658381	+	0.752685i	$0.271242\pi$
$90$	0.913603	+	1.14562i	0.0963022	+	0.120759i
$91$	−1.68415	−	7.37873i	−0.176547	−	0.773501i
$92$	9.86696			1.02870
$93$	−7.92676			−0.821966
$94$	−4.17246	−	18.2808i	−0.430357	−	1.88552i
$95$	0.257800	−	0.323271i	0.0264497	−	0.0331669i
$96$	0.229320	−	1.00472i	0.0234048	−	0.102543i
$97$	−5.60727	+	7.03130i	−0.569332	+	0.713920i	−0.980252	−	0.197751i	$-0.936636\pi$
$97$	−5.60727	+	7.03130i	−0.569332	+	0.713920i	0.410920	+	0.911671i	$0.365208\pi$
$98$	11.6742	+	5.62202i	1.17928	+	0.567909i
$99$	−0.777621	−	3.40698i	−0.0781538	−	0.342414i
$100$	16.2501	+	7.82562i	1.62501	+	0.782562i
$101$	−6.68184	−	8.37876i	−0.664868	−	0.833718i	0.328996	−	0.944331i	$-0.393290\pi$
$101$	−6.68184	−	8.37876i	−0.664868	−	0.833718i	−0.993863	+	0.110614i	$0.964718\pi$
$102$	0.126199	−	0.552914i	0.0124956	−	0.0547466i
$103$	−3.97731	+	17.4257i	−0.391896	+	1.71701i	0.266065	+	0.963955i	$0.414276\pi$
$103$	−3.97731	+	17.4257i	−0.391896	+	1.71701i	−0.657961	+	0.753052i	$0.728581\pi$
$104$	−24.2793	+	11.6923i	−2.38078	+	1.14652i
$105$	0.485180	+	0.608396i	0.0473487	+	0.0593734i
$106$	−3.65546	+	4.58381i	−0.355050	+	0.445219i
$107$	11.0619	−	5.32715i	1.06940	−	0.514995i	0.185485	−	0.982647i	$-0.440614\pi$
$107$	11.0619	−	5.32715i	1.06940	−	0.514995i	0.883912	+	0.467652i	$0.154900\pi$
$108$	−3.50556	+	1.68819i	−0.337322	+	0.162446i
$109$	−3.90471	+	4.89635i	−0.374003	+	0.468986i	−0.932839	−	0.360293i	$-0.882677\pi$
$109$	−3.90471	+	4.89635i	−0.374003	+	0.468986i	0.558836	+	0.829278i	$0.311248\pi$
$110$	3.19267	+	4.00349i	0.304410	+	0.381718i
$111$	10.7723	−	5.18767i	1.02246	−	0.492392i
$112$	−0.962888	+	4.21869i	−0.0909844	+	0.398628i
$113$	0.804259	−	3.52369i	0.0756584	−	0.331481i	−0.922907	−	0.385022i	$-0.874194\pi$
$113$	0.804259	−	3.52369i	0.0756584	−	0.331481i	0.998566	+	0.0535414i	$0.0170509\pi$
$114$	1.03642	+	1.29963i	0.0970694	+	0.121721i
$115$	−1.37938	−	0.664275i	−0.128628	−	0.0619440i
$116$	6.69263	+	29.3223i	0.621395	+	2.72251i
$117$	−5.29035	−	2.54770i	−0.489093	−	0.235535i
$118$	15.5779	−	19.5341i	1.43407	−	1.79826i
$119$	0.0670194	−	0.293631i	0.00614366	−	0.0269171i
$120$	1.72751	−	2.16623i	0.157699	−	0.197748i
$121$	−0.269741	−	1.18181i	−0.0245219	−	0.107438i
$122$	−1.23374			−0.111698
$123$	10.0184			0.903326
$124$	6.86299	+	30.0687i	0.616315	+	2.70025i
$125$	−3.62696	−	4.54806i	−0.324405	−	0.406791i
$126$	−2.81861	+	1.35737i	−0.251101	+	0.120924i
$127$	6.64287	+	3.19904i	0.589459	+	0.283869i	0.704742	−	0.709464i	$-0.251063\pi$
$127$	6.64287	+	3.19904i	0.589459	+	0.283869i	−0.115282	+	0.993333i	$0.536777\pi$
$128$	−20.3061			−1.79482
$129$	2.29269	+	6.14358i	0.201860	+	0.540912i
$130$	8.60404			0.754624
$131$	−9.03772	−	4.35233i	−0.789629	−	0.380265i	−0.00480846	−	0.999988i	$-0.501531\pi$
$131$	−9.03772	−	4.35233i	−0.789629	−	0.380265i	−0.784820	+	0.619723i	$0.787245\pi$
$132$	−12.2505	+	5.89953i	−1.06627	+	0.513488i
$133$	0.550402	+	0.690182i	0.0477259	+	0.0598464i
$134$	−1.63200	−	7.15026i	−0.140983	−	0.617689i
$135$	0.603724			0.0519603
$136$	−1.07238			−0.0919555
$137$	3.15789	+	13.8356i	0.269797	+	1.18206i	0.910250	+	0.414059i	$0.135889\pi$
$137$	3.15789	+	13.8356i	0.269797	+	1.18206i	−0.640453	+	0.767997i	$0.721254\pi$
$138$	3.83756	−	4.81215i	0.326675	−	0.409637i
$139$	0.409958	−	1.79615i	0.0347722	−	0.152347i	−0.954561	−	0.298014i	$-0.903676\pi$
$139$	0.409958	−	1.79615i	0.0347722	−	0.152347i	0.989334	+	0.145667i	$0.0465329\pi$
$140$	1.88777	−	2.36719i	0.159546	−	0.200064i
$141$	−6.96052	−	3.35201i	−0.586181	−	0.282290i
$142$	1.09948	+	4.81715i	0.0922665	+	0.404246i
$143$	−18.4876	−	8.90317i	−1.54601	−	0.744520i
$144$	2.09315	+	2.62472i	0.174429	+	0.218727i
$145$	1.03846	−	4.54977i	0.0862391	−	0.377838i
$146$	3.21139	−	14.0700i	0.265776	−	1.16444i
$147$	4.80993	−	2.31634i	0.396716	−	0.191048i
$148$	−29.0052	−	36.3714i	−2.38421	−	2.98971i
$149$	8.18703	−	10.2662i	0.670708	−	0.841041i	−0.323754	−	0.946141i	$-0.604945\pi$
$149$	8.18703	−	10.2662i	0.670708	−	0.841041i	0.994462	+	0.105101i	$0.0335165\pi$
$150$	10.1367	−	4.88159i	0.827660	−	0.398580i
$151$	−2.87277	+	1.38345i	−0.233782	+	0.112584i	−0.547108	−	0.837062i	$-0.684271\pi$
$151$	−2.87277	+	1.38345i	−0.233782	+	0.112584i	0.313325	+	0.949646i	$0.398557\pi$
$152$	1.95973	−	2.45743i	0.158955	−	0.199324i
$153$	−0.145688	−	0.182687i	−0.0117782	−	0.0147694i
$154$	−9.84989	+	4.74346i	−0.793727	+	0.382239i
$155$	1.06489	−	4.66559i	0.0855340	−	0.374749i
$156$	−5.08384	+	22.2738i	−0.407033	+	1.78333i
$157$	6.17675	+	7.74540i	0.492958	+	0.618150i	0.964625	−	0.263627i	$-0.0849188\pi$
$157$	6.17675	+	7.74540i	0.492958	+	0.618150i	−0.471666	+	0.881777i	$0.656347\pi$
$158$	−6.49354	−	3.12712i	−0.516598	−	0.248780i
$159$	0.537519	+	2.35503i	0.0426281	+	0.186766i
$160$	0.560555	+	0.269949i	0.0443158	+	0.0213414i
$161$	2.03798	−	2.55555i	0.160615	−	0.201405i
$162$	−0.540083	+	2.36626i	−0.0424329	+	0.185911i
$163$	9.39654	−	11.7829i	0.735994	−	0.922907i	−0.263130	−	0.964760i	$-0.584755\pi$
$163$	9.39654	−	11.7829i	0.735994	−	0.922907i	0.999124	+	0.0418535i	$0.0133263\pi$
$164$	−8.67391	−	38.0029i	−0.677318	−	2.96753i
$165$	2.10977			0.164245
$166$	−0.157611			−0.0122330
$167$	1.16490	+	5.10377i	0.0901429	+	0.394942i	0.999791	−	0.0204376i	$-0.00650593\pi$
$167$	1.16490	+	5.10377i	0.0901429	+	0.394942i	−0.909648	+	0.415380i	$0.863649\pi$
$168$	3.68822	+	4.62488i	0.284552	+	0.356817i
$169$	−19.3515	+	9.31918i	−1.48857	+	0.716860i
$170$	0.308484	+	0.148558i	0.0236597	+	0.0113939i
$171$	0.684882			0.0523742
$172$	21.3196	−	14.0160i	1.62560	−	1.06871i
$173$	21.5266			1.63664			0.818320	−	0.574763i	$-0.194906\pi$
$173$	21.5266			1.63664			0.818320	+	0.574763i	$0.194906\pi$
$174$	16.9036	+	8.14033i	1.28146	+	0.617117i
$175$	5.38323	−	2.59243i	0.406934	−	0.195969i
$176$	7.31470	+	9.17234i	0.551366	+	0.691391i
$177$	−2.29067	−	10.0361i	−0.172177	−	0.754357i
$178$	−12.2090			−0.915103
$179$	−21.0844			−1.57592			−0.787960	−	0.615726i	$-0.788863\pi$
$179$	−21.0844			−1.57592			−0.787960	+	0.615726i	$0.788863\pi$
$180$	−0.522705	−	2.29012i	−0.0389601	−	0.170695i
$181$	10.6807	−	13.3932i	0.793893	−	0.995510i	−0.205964	−	0.978560i	$-0.566033\pi$
$181$	10.6807	−	13.3932i	0.793893	−	0.995510i	0.999856	−	0.0169502i	$-0.00539567\pi$
$182$	−4.08761	+	17.9090i	−0.302994	+	1.32750i
$183$	−0.316930	+	0.397417i	−0.0234281	+	0.0293779i
$184$	−10.4857	−	5.04966i	−0.773017	−	0.372266i
$185$	1.60623	+	7.03737i	0.118093	+	0.517398i
$186$	17.3339	+	8.34754i	1.27098	+	0.612072i
$187$	−0.509122	−	0.638418i	−0.0372307	−	0.0466858i
$188$	−6.68882	+	29.3056i	−0.487833	+	2.13733i
$189$	−0.286818	+	1.25663i	−0.0208629	+	0.0914064i
$190$	−0.904177	+	0.435429i	−0.0655959	+	0.0315893i
$191$	15.1544	+	19.0031i	1.09654	+	1.37501i	0.920552	+	0.390621i	$0.127740\pi$
$191$	15.1544	+	19.0031i	1.09654	+	1.37501i	0.175985	+	0.984393i	$0.443689\pi$
$192$	−5.74581	+	7.20501i	−0.414668	+	0.519977i
$193$	−17.5619	+	8.45734i	−1.26413	+	0.608773i	−0.941264	−	0.337672i	$-0.890361\pi$
$193$	−17.5619	+	8.45734i	−1.26413	+	0.608773i	−0.322866	+	0.946445i	$0.604646\pi$
$194$	19.6663	−	9.47077i	1.41196	−	0.679962i
$195$	2.21025	−	2.77157i	0.158280	−	0.198476i
$196$	−12.9511	−	16.2401i	−0.925075	−	1.16001i
$197$	6.32793	−	3.04737i	0.450847	−	0.217116i	−0.194660	−	0.980871i	$-0.562360\pi$
$197$	6.32793	−	3.04737i	0.450847	−	0.217116i	0.645507	+	0.763754i	$0.276646\pi$
$198$	−1.88737	+	8.26912i	−0.134130	+	0.587661i
$199$	−2.65430	+	11.6292i	−0.188158	+	0.824376i	0.789428	+	0.613843i	$0.210377\pi$
$199$	−2.65430	+	11.6292i	−0.188158	+	0.824376i	−0.977587	+	0.210533i	$0.932480\pi$
$200$	−13.2642	−	16.6327i	−0.937918	−	1.17611i
$201$	−2.72251	−	1.31109i	−0.192031	−	0.0924773i
$202$	5.78798	+	25.3588i	0.407241	+	1.78424i
$203$	8.97684	+	4.32302i	0.630050	+	0.303416i
$204$	−0.566854	+	0.710813i	−0.0396878	+	0.0497669i
$205$	−1.34588	+	5.89668i	−0.0940003	+	0.411842i
$206$	27.0481	−	33.9173i	1.88453	−	2.36313i
$207$	−0.564296	−	2.47234i	−0.0392213	−	0.171840i
$208$	19.7126			1.36682
$209$	2.39339			0.165554
$210$	−0.420275	−	1.84135i	−0.0290018	−	0.127065i
$211$	7.94650	+	9.96460i	0.547060	+	0.685991i	0.976107	−	0.217291i	$-0.0697220\pi$
$211$	7.94650	+	9.96460i	0.547060	+	0.685991i	−0.429047	+	0.903282i	$0.641151\pi$
$212$	8.46798	−	4.07797i	0.581583	−	0.280076i
$213$	1.83416	+	0.883285i	0.125675	+	0.0605217i
$214$	−29.7996			−2.03706
$215$	−3.92404	+	0.524110i	−0.267617	+	0.0357440i
$216$	4.58936			0.312266
$217$	9.20535	+	4.43306i	0.624900	+	0.300936i
$218$	13.6949	−	6.59512i	0.927536	−	0.446678i
$219$	−3.70733	−	4.64885i	−0.250518	−	0.314140i
$220$	−1.82664	−	8.00304i	−0.123152	−	0.539565i
$221$	−1.37205			−0.0922940
$222$	−29.0195			−1.94766
$223$	−0.375082	−	1.64334i	−0.0251174	−	0.110046i	0.960815	−	0.277189i	$-0.0894030\pi$
$223$	−0.375082	−	1.64334i	−0.0251174	−	0.110046i	−0.985933	+	0.167143i	$0.946546\pi$
$224$	−0.828199	+	1.03853i	−0.0553364	+	0.0693896i
$225$	1.03150	−	4.51930i	0.0687666	−	0.301286i
$226$	−5.46946	+	6.85849i	−0.363823	+	0.456220i
$227$	−6.89413	−	3.32004i	−0.457580	−	0.220359i	0.190871	−	0.981615i	$-0.438869\pi$
$227$	−6.89413	−	3.32004i	−0.457580	−	0.220359i	−0.648451	+	0.761256i	$0.724583\pi$
$228$	−0.592971	−	2.59798i	−0.0392705	−	0.172055i
$229$	−10.4681	−	5.04116i	−0.691750	−	0.333129i	0.0547637	−	0.998499i	$-0.482559\pi$
$229$	−10.4681	−	5.04116i	−0.691750	−	0.333129i	−0.746514	+	0.665370i	$0.768274\pi$
$230$	2.31683	+	2.90521i	0.152767	+	0.191564i
$231$	−1.00231	+	4.39141i	−0.0659473	+	0.288934i
$232$	7.89408	−	34.5862i	0.518272	−	2.27070i
$233$	−0.0342195	+	0.0164792i	−0.00224179	+	0.00107959i	−0.435004	−	0.900428i	$-0.643253\pi$
$233$	−0.0342195	+	0.0164792i	−0.00224179	+	0.00107959i	0.432763	+	0.901508i	$0.357539\pi$
$234$	8.88574	+	11.1424i	0.580879	+	0.728399i
$235$	2.90803	−	3.64656i	0.189699	−	0.237875i
$236$	−36.0868	+	17.3785i	−2.34905	+	1.13124i
$237$	−2.67542	+	1.28841i	−0.173787	+	0.0836914i
$238$	−0.455774	+	0.571522i	−0.0295434	+	0.0370463i
$239$	−8.33582	−	10.4528i	−0.539200	−	0.676135i	0.435362	−	0.900256i	$-0.356620\pi$
$239$	−8.33582	−	10.4528i	−0.539200	−	0.676135i	−0.974561	+	0.224121i	$0.928049\pi$
$240$	−1.82607	+	0.879391i	−0.117873	+	0.0567644i
$241$	4.70290	−	20.6047i	0.302940	−	1.32727i	−0.562725	−	0.826644i	$-0.690247\pi$
$241$	4.70290	−	20.6047i	0.302940	−	1.32727i	0.865665	−	0.500624i	$-0.166896\pi$
$242$	−0.654692	+	2.86839i	−0.0420852	+	0.184387i
$243$	0.623490	+	0.781831i	0.0399969	+	0.0501545i
$244$	1.78193	+	0.858132i	0.114076	+	0.0549363i
$245$	0.717196	+	3.14224i	0.0458200	+	0.200751i
$246$	−21.9077	−	10.5502i	−1.39678	−	0.672655i
$247$	2.50737	−	3.14415i	0.159540	−	0.200057i
$248$	8.09503	−	35.4666i	0.514035	−	2.25213i
$249$	−0.0404881	+	0.0507704i	−0.00256583	+	0.00321744i
$250$	3.14177	+	13.7650i	0.198703	+	0.870574i
$251$	−15.6582			−0.988336			−0.494168	−	0.869367i	$-0.664527\pi$
$251$	−15.6582			−0.988336			−0.494168	+	0.869367i	$0.664527\pi$
$252$	5.01513			0.315923
$253$	−1.97199	−	8.63984i	−0.123978	−	0.543182i
$254$	−11.1575	−	13.9910i	−0.700081	−	0.877874i
$255$	0.127099	−	0.0612078i	0.00795927	−	0.00383298i
$256$	27.7985	+	13.3871i	1.73741	+	0.836691i
$257$	−8.95238			−0.558434			−0.279217	−	0.960228i	$-0.590075\pi$
$257$	−8.95238			−0.558434			−0.279217	+	0.960228i	$0.590075\pi$
$258$	1.45617	−	15.8489i	0.0906572	−	0.986708i
$259$	−15.4111			−0.957600
$260$	−12.4271	−	5.98457i	−0.770695	−	0.371147i
$261$	6.96448	−	3.35392i	0.431090	−	0.207602i
$262$	15.1799	+	19.0350i	0.937816	+	1.17598i
$263$	2.55184	+	11.1803i	0.157353	+	0.689408i	0.990632	+	0.136556i	$0.0436034\pi$
$263$	2.55184	+	11.1803i	0.157353	+	0.689408i	−0.833279	+	0.552852i	$0.813539\pi$
$264$	16.0380			0.987068
$265$	−1.45835			−0.0895857
$266$	−0.476772	−	2.08888i	−0.0292328	−	0.128077i
$267$	−3.13631	+	3.93281i	−0.191939	+	0.240684i
$268$	−2.61624	+	11.4625i	−0.159812	+	0.700183i
$269$	−18.9500	+	23.7626i	−1.15540	+	1.44883i	−0.283621	+	0.958936i	$0.591536\pi$
$269$	−18.9500	+	23.7626i	−1.15540	+	1.44883i	−0.871782	+	0.489894i	$0.837036\pi$
$270$	−1.32019	−	0.635772i	−0.0803445	−	0.0386919i
$271$	6.30768	+	27.6358i	0.383165	+	1.67875i	0.687497	+	0.726188i	$0.258710\pi$
$271$	6.30768	+	27.6358i	0.383165	+	1.67875i	−0.304332	+	0.952566i	$0.598433\pi$
$272$	0.706765	+	0.340360i	0.0428539	+	0.0206374i
$273$	4.71887	+	5.91728i	0.285599	+	0.358130i
$274$	7.66455	−	33.5806i	0.463032	−	2.02868i
$275$	3.60468	−	15.7931i	0.217370	−	0.952361i
$276$	−8.88982	+	4.28111i	−0.535104	+	0.257693i
$277$	13.0160	+	16.3215i	0.782054	+	0.980664i	0.999989	+	0.00470090i	$0.00149635\pi$
$277$	13.0160	+	16.3215i	0.782054	+	0.980664i	−0.217935	+	0.975963i	$0.569932\pi$
$278$	−2.78797	+	3.49600i	−0.167211	+	0.209676i
$279$	7.14176	−	3.43929i	0.427566	−	0.205905i
$280$	−3.21762	+	1.54953i	−0.192290	+	0.0926018i
$281$	19.0145	−	23.8435i	1.13431	−	1.42238i	0.242398	−	0.970177i	$-0.422066\pi$
$281$	19.0145	−	23.8435i	1.13431	−	1.42238i	0.891914	−	0.452205i	$-0.149363\pi$
$282$	11.6910	+	14.6600i	0.696188	+	0.872992i
$283$	0.0695944	−	0.0335149i	0.00413696	−	0.00199225i	−0.431814	−	0.901963i	$-0.642126\pi$
$283$	0.0695944	−	0.0335149i	0.00413696	−	0.00199225i	0.435951	+	0.899970i	$0.356412\pi$
$284$	1.76257	−	7.72231i	0.104589	−	0.458235i
$285$	−0.0920078	+	0.403113i	−0.00545007	+	0.0238783i
$286$	31.0521	+	38.9381i	1.83615	+	2.30246i
$287$	−11.6343	−	5.60280i	−0.686753	−	0.330723i
$288$	0.229320	+	1.00472i	0.0135128	+	0.0592034i
$289$	15.2673	+	7.35233i	0.898075	+	0.432490i
$290$	−7.06214	+	8.85564i	−0.414703	+	0.520021i
$291$	2.00121	−	8.76788i	0.117313	−	0.513982i
$292$	−14.4248	+	18.0881i	−0.844145	+	1.05852i
$293$	5.82095	+	25.5032i	0.340063	+	1.48992i	0.798937	+	0.601414i	$0.205396\pi$
$293$	5.82095	+	25.5032i	0.340063	+	1.48992i	−0.458874	+	0.888501i	$0.651747\pi$
$294$	−12.9574			−0.755692
$295$	6.21483			0.361842
$296$	12.2102	+	53.4963i	0.709703	+	3.10941i
$297$	2.17885	+	2.73219i	0.126429	+	0.158537i
$298$	−28.7142	+	13.8280i	−1.66337	+	0.801036i
$299$	−13.4159	−	6.46076i	−0.775862	−	0.373636i
$300$	−18.0362			−1.04132
$301$	0.773316	−	8.41673i	0.0445732	−	0.485133i
$302$	7.73892			0.445325
$303$	9.65553	+	4.64986i	0.554696	+	0.267127i
$304$	−2.07155	+	0.997606i	−0.118812	+	0.0572166i
$305$	−0.191338	−	0.239930i	−0.0109560	−	0.0137384i
$306$	0.126199	+	0.552914i	0.00721432	+	0.0316080i
$307$	−0.0523766			−0.00298929			−0.00149465	−	0.999999i	$-0.500476\pi$
$307$	−0.0523766			−0.00298929			−0.00149465	+	0.999999i	$0.500476\pi$
$308$	17.5258			0.998627
$309$	−3.97731	−	17.4257i	−0.226261	−	0.991315i
$310$	−7.24191	+	9.08107i	−0.411313	+	0.515770i
$311$	−0.900686	+	3.94616i	−0.0510732	+	0.223766i	−0.994023	−	0.109168i	$-0.965181\pi$
$311$	−0.900686	+	3.94616i	−0.0510732	+	0.223766i	0.942950	+	0.332934i	$0.108039\pi$
$312$	16.8018	−	21.0688i	0.951214	−	1.19279i
$313$	−3.77254	−	1.81676i	−0.213237	−	0.102689i	0.324217	−	0.945983i	$-0.394899\pi$
$313$	−3.77254	−	1.81676i	−0.213237	−	0.102689i	−0.537453	+	0.843293i	$0.680614\pi$
$314$	−5.35046	−	23.4419i	−0.301944	−	1.32290i
$315$	−0.701105	−	0.337634i	−0.0395028	−	0.0190235i
$316$	7.20374	+	9.03320i	0.405242	+	0.508157i
$317$	−5.80704	+	25.4423i	−0.326156	+	1.42898i	0.500237	+	0.865888i	$0.333246\pi$
$317$	−5.80704	+	25.4423i	−0.326156	+	1.42898i	−0.826393	+	0.563094i	$0.809611\pi$
$318$	1.30462	−	5.71591i	0.0731594	−	0.320532i
$319$	24.3380	−	11.7206i	1.36267	−	0.656227i
$320$	−3.46888	−	4.34984i	−0.193916	−	0.243163i
$321$	−7.65509	+	9.59919i	−0.427266	+	0.535774i
$322$	−7.14777	+	3.44219i	−0.398330	+	0.191825i
$323$	0.144185	−	0.0694359i	0.00802268	−	0.00386352i
$324$	2.42592	−	3.04201i	0.134773	−	0.169000i
$325$	−16.9708	−	21.2807i	−0.941370	−	1.18044i
$326$	−32.9563	+	15.8709i	−1.82528	+	0.879008i
$327$	1.39358	−	6.10565i	0.0770649	−	0.337643i
$328$	−10.2310	+	44.8251i	−0.564915	+	2.47505i
$329$	6.20863	+	7.78538i	0.342293	+	0.429222i
$330$	−4.61355	−	2.22177i	−0.253967	−	0.122304i
$331$	−5.23491	−	22.9356i	−0.287737	−	1.26066i	−0.887623	−	0.460571i	$-0.847645\pi$
$331$	−5.23491	−	22.9356i	−0.287737	−	1.26066i	0.599886	−	0.800085i	$-0.295213\pi$
$332$	0.227643	+	0.109627i	0.0124935	+	0.00601657i
$333$	−7.45468	+	9.34787i	−0.408514	+	0.512260i
$334$	2.82735	−	12.3874i	0.154706	−	0.677810i
$335$	1.13744	−	1.42630i	0.0621448	−	0.0779271i
$336$	−0.962888	−	4.21869i	−0.0525298	−	0.230148i
$337$	20.2197			1.10144			0.550719	−	0.834691i	$-0.314354\pi$
$337$	20.2197			1.10144			0.550719	+	0.834691i	$0.314354\pi$
$338$	52.1307			2.83554
$339$	0.804259	+	3.52369i	0.0436814	+	0.191381i
$340$	−0.342224	−	0.429135i	−0.0185597	−	0.0232731i
$341$	24.9576	−	12.0189i	1.35153	−	0.650862i
$342$	−1.49767	−	0.721238i	−0.0809845	−	0.0390001i
$343$	−15.9038			−0.858725
$344$	−29.8296	+	3.98416i	−1.60830	+	0.214811i
$345$	1.53100			0.0824262
$346$	−47.0734	−	22.6694i	−2.53068	−	1.21871i
$347$	6.33661	−	3.05155i	0.340167	−	0.163816i	−0.255999	−	0.966677i	$-0.582404\pi$
$347$	6.33661	−	3.05155i	0.340167	−	0.163816i	0.596166	+	0.802861i	$0.296690\pi$
$348$	−18.7523	−	23.5147i	−1.00523	−	1.26052i
$349$	−2.37532	−	10.4069i	−0.127148	−	0.557071i	−0.997866	−	0.0652894i	$-0.979203\pi$
$349$	−2.37532	−	10.4069i	−0.127148	−	0.557071i	0.870719	−	0.491782i	$-0.163654\pi$
$350$	−14.5018			−0.775155
$351$	5.87184			0.313416
$352$	0.801380	+	3.51107i	0.0427137	+	0.187141i
$353$	−5.11348	+	6.41210i	−0.272163	+	0.341282i	−0.899064	−	0.437817i	$-0.855752\pi$
$353$	−5.11348	+	6.41210i	−0.272163	+	0.341282i	0.626901	+	0.779099i	$0.284323\pi$
$354$	−5.55971	+	24.3587i	−0.295495	+	1.29465i
$355$	−0.766294	+	0.960902i	−0.0406707	+	0.0509994i
$356$	17.6338	+	8.49201i	0.934592	+	0.450076i
$357$	0.0670194	+	0.293631i	0.00354705	+	0.0155406i
$358$	46.1063	+	22.2036i	2.43679	+	1.17350i
$359$	13.8257	+	17.3369i	0.729694	+	0.915007i	0.998843	−	0.0480912i	$-0.0153138\pi$
$359$	13.8257	+	17.3369i	0.729694	+	0.915007i	−0.269149	+	0.963099i	$0.586742\pi$
$360$	−0.616540	+	2.70124i	−0.0324945	+	0.142368i
$361$	4.12352	−	18.0663i	0.217027	−	0.950859i
$362$	−37.4603	+	18.0399i	−1.96887	+	0.948158i
$363$	0.755798	+	0.947740i	0.0396691	+	0.0497435i
$364$	18.3605	−	23.0234i	0.962354	−	1.20675i
$365$	3.23430	−	1.55756i	0.169291	−	0.0815263i
$366$	1.11156	−	0.535299i	0.0581022	−	0.0279806i
$367$	9.51757	−	11.9347i	0.496813	−	0.622984i	−0.468694	−	0.883361i	$-0.655275\pi$
$367$	9.51757	−	11.9347i	0.496813	−	0.622984i	0.965507	+	0.260377i	$0.0838467\pi$
$368$	5.30806	+	6.65609i	0.276702	+	0.346973i
$369$	−9.02624	+	4.34681i	−0.469887	+	0.226286i
$370$	3.89851	−	17.0805i	0.202674	−	0.887972i
$371$	0.692833	−	3.03550i	0.0359701	−	0.157595i
$372$	−19.2297	−	24.1132i	−0.997012	−	1.25021i
$373$	−5.11559	−	2.46354i	−0.264875	−	0.127557i	0.296733	−	0.954960i	$-0.404103\pi$
$373$	−5.11559	−	2.46354i	−0.264875	−	0.127557i	−0.561608	+	0.827403i	$0.689817\pi$
$374$	0.441015	+	1.93221i	0.0228043	+	0.0999123i
$375$	5.24111	+	2.52399i	0.270650	+	0.130338i
$376$	22.1062	−	27.7202i	1.14004	−	1.42956i
$377$	10.1001	−	44.2512i	0.520179	−	2.27906i
$378$	1.95054	−	2.44589i	0.100325	−	0.125803i
$379$	2.16669	+	9.49288i	0.111295	+	0.487616i	0.999598	+	0.0283577i	$0.00902773\pi$
$379$	2.16669	+	9.49288i	0.111295	+	0.487616i	−0.888303	+	0.459259i	$0.848115\pi$
$380$	1.60880			0.0825295
$381$	−7.37303			−0.377732
$382$	−13.1272	−	57.5139i	−0.671645	−	2.94267i
$383$	−1.13845	−	1.42757i	−0.0581719	−	0.0729453i	0.751894	−	0.659284i	$-0.229140\pi$
$383$	−1.13845	−	1.42757i	−0.0581719	−	0.0729453i	−0.810066	+	0.586338i	$0.800569\pi$
$384$	18.2951	−	8.81048i	0.933620	−	0.449608i
$385$	−2.45008	−	1.17990i	−0.124868	−	0.0601331i
$386$	47.3097			2.40800
$387$	−4.73124	−	4.54042i	−0.240502	−	0.230802i
$388$	−34.9920			−1.77645
$389$	23.4685	+	11.3018i	1.18990	+	0.573026i	0.920781	−	0.390081i	$-0.127553\pi$
$389$	23.4685	+	11.3018i	1.18990	+	0.573026i	0.269120	+	0.963107i	$0.413267\pi$
$390$	−7.75197	+	3.73315i	−0.392536	+	0.189036i
$391$	−0.369454	−	0.463281i	−0.0186841	−	0.0234291i
$392$	5.45195	+	23.8866i	0.275365	+	1.20645i
$393$	10.0311			0.506002
$394$	−17.0468			−0.858803
$395$	−0.398925	−	1.74780i	−0.0200721	−	0.0879415i
$396$	8.47761	−	10.6306i	0.426016	−	0.534207i
$397$	1.70751	−	7.48109i	0.0856974	−	0.375465i	−0.913834	−	0.406089i	$-0.866892\pi$
$397$	1.70751	−	7.48109i	0.0856974	−	0.375465i	0.999531	+	0.0306240i	$0.00974945\pi$
$398$	18.0509	−	22.6351i	0.904809	−	1.13459i
$399$	−0.795353	−	0.383022i	−0.0398175	−	0.0191751i
$400$	3.46289	+	15.1719i	0.173145	+	0.758596i
$401$	−1.12895	−	0.543673i	−0.0563770	−	0.0271497i	0.405483	−	0.914103i	$-0.367103\pi$
$401$	−1.12895	−	0.543673i	−0.0563770	−	0.0271497i	−0.461860	+	0.886953i	$0.652818\pi$
$402$	4.57276	+	5.73406i	0.228069	+	0.285989i
$403$	10.3572	−	45.3777i	0.515927	−	2.26042i
$404$	9.27864	−	40.6524i	0.461630	−	2.02253i
$405$	−0.543936	+	0.261946i	−0.0270284	+	0.0130162i
$406$	−15.0776	−	18.9067i	−0.748290	−	0.938325i
$407$	−26.0511	+	32.6670i	−1.29130	+	1.61924i
$408$	0.966178	−	0.465287i	0.0478329	−	0.0230351i
$409$	−14.6839	+	7.07139i	−0.726072	+	0.349658i	−0.760138	−	0.649762i	$-0.774869\pi$
$409$	−14.6839	+	7.07139i	−0.726072	+	0.349658i	0.0340660	+	0.999420i	$0.489154\pi$
$410$	9.15281	−	11.4773i	0.452025	−	0.566822i
$411$	−8.84821	−	11.0953i	−0.436450	−	0.547291i
$412$	−62.6578	+	30.1744i	−3.08693	+	1.48659i
$413$	−2.95255	+	12.9360i	−0.145285	+	0.636537i
$414$	−1.36961	+	6.00065i	−0.0673127	+	0.294916i
$415$	−0.0244436	−	0.0306513i	−0.00119989	−	0.00150461i
$416$	5.45198	+	2.62554i	0.267305	+	0.128728i
$417$	0.409958	+	1.79615i	0.0200757	+	0.0879576i
$418$	−5.23374	−	2.52044i	−0.255991	−	0.123279i
$419$	−18.7535	+	23.5161i	−0.916167	+	1.14884i	0.0722973	+	0.997383i	$0.476967\pi$
$419$	−18.7535	+	23.5161i	−0.916167	+	1.14884i	−0.988464	+	0.151454i	$0.951604\pi$
$420$	−0.673738	+	2.95184i	−0.0328751	+	0.144035i
$421$	−11.8273	+	14.8309i	−0.576425	+	0.722815i	−0.981499	−	0.191470i	$-0.938675\pi$
$421$	−11.8273	+	14.8309i	−0.576425	+	0.722815i	0.405073	+	0.914284i	$0.367246\pi$
$422$	−6.88347	−	30.1585i	−0.335082	−	1.46809i
$423$	7.72559			0.375631
$424$	−11.0860			−0.538384
$425$	−0.241026	−	1.05600i	−0.0116915	−	0.0512238i
$426$	−3.08068	−	3.86305i	−0.149259	−	0.187165i
$427$	0.590307	−	0.284277i	0.0285670	−	0.0137571i
$428$	43.0406	+	20.7272i	2.08044	+	1.00189i
$429$	20.5197			0.990701
$430$	9.13283	+	2.98624i	0.440424	+	0.144009i
$431$	−24.8768			−1.19827			−0.599136	−	0.800648i	$-0.704489\pi$
$431$	−24.8768			−1.19827			−0.599136	+	0.800648i	$0.704489\pi$
$432$	−3.02468	−	1.45661i	−0.145525	−	0.0700812i
$433$	12.1754	−	5.86337i	0.585113	−	0.281775i	−0.117816	−	0.993035i	$-0.537589\pi$
$433$	12.1754	−	5.86337i	0.585113	−	0.281775i	0.702929	+	0.711260i	$0.251875\pi$
$434$	−15.4614	−	19.3880i	−0.742172	−	0.930654i
$435$	1.03846	+	4.54977i	0.0497901	+	0.218145i
$436$	−24.3673			−1.16698
$437$	1.73681			0.0830828
$438$	3.21139	+	14.0700i	0.153446	+	0.672291i
$439$	15.5411	−	19.4880i	0.741738	−	0.930110i	−0.257609	−	0.966249i	$-0.582935\pi$
$439$	15.5411	−	19.4880i	0.741738	−	0.930110i	0.999347	+	0.0361396i	$0.0115061\pi$
$440$	−2.15456	+	9.43974i	−0.102715	+	0.450022i
$441$	−3.32857	+	4.17390i	−0.158504	+	0.198757i
$442$	3.00033	+	1.44488i	0.142711	+	0.0687261i
$443$	−0.712663	−	3.12238i	−0.0338596	−	0.148349i	0.955172	−	0.296050i	$-0.0956696\pi$
$443$	−0.712663	−	3.12238i	−0.0338596	−	0.148349i	−0.989032	+	0.147702i	$0.952812\pi$
$444$	41.9137	+	20.1846i	1.98914	+	0.957918i
$445$	−1.89347	−	2.37433i	−0.0897590	−	0.112554i
$446$	−0.910367	+	3.98858i	−0.0431071	+	0.188865i
$447$	−2.92192	+	12.8018i	−0.138202	+	0.605502i
$448$	10.7020	−	5.15383i	0.505623	−	0.243495i
$449$	7.72284	+	9.68413i	0.364463	+	0.457022i	0.929923	−	0.367753i	$-0.119873\pi$
$449$	7.72284	+	9.68413i	0.364463	+	0.457022i	−0.565460	+	0.824776i	$0.691301\pi$
$450$	−7.01483	+	8.79632i	−0.330682	+	0.414663i
$451$	−31.5431	+	15.1903i	−1.48530	+	0.715285i
$452$	12.6702	−	6.10163i	0.595954	−	0.286996i
$453$	1.98802	−	2.49289i	0.0934051	−	0.117126i
$454$	11.5795	+	14.5202i	0.543452	+	0.681467i
$455$	−4.11678	+	1.98253i	−0.192997	+	0.0929427i
$456$	−0.699421	+	3.06436i	−0.0327534	+	0.143502i
$457$	7.08284	−	31.0319i	0.331321	−	1.45161i	−0.485254	−	0.874373i	$-0.661273\pi$
$457$	7.08284	−	31.0319i	0.331321	−	1.45161i	0.816575	−	0.577239i	$-0.195870\pi$
$458$	17.5823	+	22.0475i	0.821568	+	1.03021i
$459$	0.210526	+	0.101384i	0.00982650	+	0.00473219i
$460$	−1.32554	−	5.80757i	−0.0618036	−	0.270779i
$461$	−6.39575	−	3.08003i	−0.297880	−	0.143451i	0.278974	−	0.960299i	$-0.410006\pi$
$461$	−6.39575	−	3.08003i	−0.297880	−	0.143451i	−0.576854	+	0.816847i	$0.695720\pi$
$462$	6.81634	−	8.54742i	0.317125	−	0.397662i
$463$	−2.94797	+	12.9159i	−0.137004	+	0.600253i	0.859080	+	0.511841i	$0.171036\pi$
$463$	−2.94797	+	12.9159i	−0.137004	+	0.600253i	−0.996084	+	0.0884120i	$0.971821\pi$
$464$	−16.1800	+	20.2891i	−0.751137	+	0.941896i
$465$	1.06489	+	4.66559i	0.0493831	+	0.216361i
$466$	0.0921835			0.00427032
$467$	−36.2037			−1.67531			−0.837654	−	0.546201i	$-0.816073\pi$
$467$	−36.2037			−1.67531			−0.837654	+	0.546201i	$0.816073\pi$
$468$	−5.08384	−	22.2738i	−0.235001	−	1.02961i
$469$	2.42842	+	3.04514i	0.112134	+	0.140612i
$470$	−10.1993	+	4.91172i	−0.470458	+	0.226561i
$471$	−8.92566	−	4.29837i	−0.411273	−	0.198059i
$472$	47.2436			2.17456
$473$	−16.5338	−	15.8669i	−0.760224	−	0.729562i
$474$	7.20728			0.331041
$475$	2.86038	+	1.37749i	0.131243	+	0.0632034i
$476$	1.05581	−	0.508452i	0.0483931	−	0.0233049i
$477$	−1.50610	−	1.88858i	−0.0689594	−	0.0864723i
$478$	7.22071	+	31.6360i	0.330268	+	1.44700i
$479$	−13.8858			−0.634460			−0.317230	−	0.948349i	$-0.602753\pi$
$479$	−13.8858			−0.634460			−0.317230	+	0.948349i	$0.602753\pi$
$480$	−0.622170			−0.0283980
$481$	15.6223	+	68.4457i	0.712315	+	3.12085i
$482$	−31.9826	+	40.1049i	−1.45677	+	1.82673i
$483$	−0.727347	+	3.18672i	−0.0330955	+	0.145001i
$484$	2.94071	−	3.68754i	0.133669	−	0.167615i
$485$	4.89182	+	2.35578i	0.222126	+	0.106970i
$486$	−0.540083	−	2.36626i	−0.0244987	−	0.107336i
$487$	−28.0348	−	13.5008i	−1.27038	−	0.611781i	−0.327478	−	0.944859i	$-0.606199\pi$
$487$	−28.0348	−	13.5008i	−1.27038	−	0.611781i	−0.942899	+	0.333078i	$0.891913\pi$
$488$	−1.45450	−	1.82389i	−0.0658423	−	0.0825637i
$489$	−3.35359	+	14.6930i	−0.151654	+	0.664441i
$490$	1.74072	−	7.62657i	0.0786375	−	0.344534i
$491$	32.5423	−	15.6716i	1.46861	−	0.707247i	0.482900	−	0.875675i	$-0.339583\pi$
$491$	32.5423	−	15.6716i	1.46861	−	0.707247i	0.985714	+	0.168428i	$0.0538692\pi$
$492$	24.3037	+	30.4759i	1.09570	+	1.37396i
$493$	1.12617	−	1.41217i	0.0507201	−	0.0636010i
$494$	−8.79406	+	4.23500i	−0.395663	+	0.190541i
$495$	−1.90084	+	0.915396i	−0.0854363	+	0.0411440i
$496$	−16.5919	+	20.8055i	−0.744996	+	0.934196i
$497$	−1.63603	−	2.05152i	−0.0733861	−	0.0920232i
$498$	0.142003	−	0.0683850i	0.00636330	−	0.00306440i
$499$	0.953165	−	4.17609i	0.0426695	−	0.186947i	−0.949102	−	0.314970i	$-0.898006\pi$
$499$	0.953165	−	4.17609i	0.0426695	−	0.186947i	0.991771	+	0.128022i	$0.0408628\pi$
$500$	5.03653	−	22.0665i	0.225240	−	0.986843i
$501$	−3.26399	−	4.09291i	−0.145824	−	0.182858i
$502$	34.2406	+	16.4894i	1.52823	+	0.735957i
$503$	4.25460	+	18.6406i	0.189703	+	0.831145i	0.976772	+	0.214280i	$0.0687404\pi$
$503$	4.25460	+	18.6406i	0.189703	+	0.831145i	−0.787069	+	0.616865i	$0.788402\pi$
$504$	−5.32963	−	2.56661i	−0.237400	−	0.114326i
$505$	−4.03398	+	5.05846i	−0.179510	+	0.225098i
$506$	−4.78623	+	20.9699i	−0.212774	+	0.932224i
$507$	13.3916	−	16.7926i	0.594743	−	0.745784i
$508$	6.38357	+	27.9683i	0.283225	+	1.24089i
$509$	3.37397			0.149548			0.0747742	−	0.997200i	$-0.476176\pi$
$509$	3.37397			0.149548			0.0747742	+	0.997200i	$0.476176\pi$
$510$	−0.342392			−0.0151614
$511$	1.70545	+	7.47204i	0.0754445	+	0.330544i
$512$	−21.3695	−	26.7965i	−0.944407	−	1.18425i
$513$	−0.617057	+	0.297159i	−0.0272437	+	0.0131199i
$514$	19.5766	+	9.42761i	0.863488	+	0.415834i
$515$	10.7909			0.475503
$516$	−13.1269	+	21.8782i	−0.577881	+	0.963134i
$517$	26.9978			1.18736
$518$	33.7003	+	16.2292i	1.48071	+	0.713071i
$519$	−19.3948	+	9.34006i	−0.851338	+	0.409983i
$520$	10.1436	+	12.7197i	0.444828	+	0.557797i
$521$	−5.82226	−	25.5090i	−0.255078	−	1.11757i	−0.926441	−	0.376440i	$-0.877148\pi$
$521$	−5.82226	−	25.5090i	−0.255078	−	1.11757i	0.671363	−	0.741128i	$-0.265709\pi$
$522$	−18.7615			−0.821170
$523$	4.05163			0.177166			0.0885828	−	0.996069i	$-0.471766\pi$
$523$	4.05163			0.177166			0.0885828	+	0.996069i	$0.471766\pi$
$524$	−8.68494	−	38.0512i	−0.379403	−	1.66227i
$525$	−3.72531	+	4.67139i	−0.162586	+	0.203876i
$526$	6.19359	−	27.1359i	0.270053	−	1.18318i
$527$	1.15484	−	1.44812i	0.0503054	−	0.0630810i
$528$	−10.5700	−	5.09027i	−0.460002	−	0.221525i
$529$	3.68697	+	16.1537i	0.160303	+	0.702333i
$530$	3.18905	+	1.53577i	0.138523	+	0.0667094i
$531$	6.41831	+	8.04830i	0.278531	+	0.349267i
$532$	−0.764308	+	3.34865i	−0.0331369	+	0.145182i
$533$	−13.0901	+	57.3513i	−0.566994	+	2.48416i
$534$	10.9999	−	5.29729i	0.476013	−	0.229236i
$535$	−4.62156	−	5.79526i	−0.199808	−	0.250551i
$536$	8.64651	−	10.8424i	0.373473	−	0.468320i
$537$	18.9964	−	9.14817i	0.819754	−	0.394773i
$538$	66.4630	−	32.0069i	2.86542	−	1.37992i
$539$	−11.6320	+	14.5861i	−0.501027	+	0.628268i
$540$	1.46459	+	1.83653i	0.0630257	+	0.0790318i
$541$	−6.85690	+	3.30211i	−0.294801	+	0.141969i	−0.575438	−	0.817845i	$-0.695169\pi$
$541$	−6.85690	+	3.30211i	−0.294801	+	0.141969i	0.280637	+	0.959814i	$0.409454\pi$
$542$	15.3095	−	67.0751i	0.657598	−	2.88112i
$543$	−3.81191	+	16.7011i	−0.163585	+	0.716711i
$544$	0.150139	+	0.188269i	0.00643718	+	0.00807197i
$545$	3.40649	+	1.64048i	0.145918	+	0.0702705i
$546$	−4.08761	−	17.9090i	−0.174934	−	0.766434i
$547$	−4.33784	−	2.08899i	−0.185473	−	0.0893189i	0.338843	−	0.940843i	$-0.389964\pi$
$547$	−4.33784	−	2.08899i	−0.185473	−	0.0893189i	−0.524316	+	0.851524i	$0.675679\pi$
$548$	−34.4272	+	43.1704i	−1.47066	+	1.84415i
$549$	0.113111	−	0.495571i	0.00482746	−	0.0211505i
$550$	−24.5140	+	30.7396i	−1.04528	+	1.31074i
$551$	1.17805	+	5.16139i	0.0501868	+	0.219883i
$552$	11.6383			0.495358
$553$	3.82751			0.162762
$554$	−11.2748	−	49.3980i	−0.479019	−	2.09872i
$555$	−4.50057	−	5.64353i	−0.191038	−	0.239555i
$556$	6.45841	−	3.11021i	0.273898	−	0.131902i
$557$	6.11556	+	2.94510i	0.259125	+	0.124788i	0.558936	−	0.829211i	$-0.311210\pi$
$557$	6.11556	+	2.94510i	0.259125	+	0.124788i	−0.299812	+	0.953998i	$0.596924\pi$
$558$	−19.2391			−0.814457
$559$	−38.1653	+	5.09752i	−1.61422	+	0.215602i
$560$	2.61242			0.110395
$561$	0.735702	+	0.354295i	0.0310614	+	0.0149584i
$562$	−66.6893	+	32.1159i	−2.81312	+	1.35473i
$563$	2.31095	+	2.89784i	0.0973949	+	0.122129i	0.828141	−	0.560520i	$-0.189399\pi$
$563$	2.31095	+	2.89784i	0.0973949	+	0.122129i	−0.730746	+	0.682650i	$0.760827\pi$
$564$	−6.68882	−	29.3056i	−0.281650	−	1.23399i
$565$	−2.18204			−0.0917993
$566$	−0.187480			−0.00788036
$567$	−0.286818	−	1.25663i	−0.0120452	−	0.0527735i
$568$	−5.82518	+	7.30454i	−0.244419	+	0.306492i
$569$	4.90984	−	21.5114i	0.205831	−	0.901805i	−0.761475	−	0.648194i	$-0.775525\pi$
$569$	4.90984	−	21.5114i	0.205831	−	0.901805i	0.967306	−	0.253611i	$-0.0816183\pi$
$570$	0.625710	−	0.784616i	0.0262081	−	0.0328639i
$571$	−33.8330	−	16.2931i	−1.41587	−	0.681845i	−0.439555	−	0.898216i	$-0.644864\pi$
$571$	−33.8330	−	16.2931i	−1.41587	−	0.681845i	−0.976311	+	0.216370i	$0.930578\pi$
$572$	−17.7660	−	77.8378i	−0.742833	−	3.25456i
$573$	−21.8988	−	10.5459i	−0.914835	−	0.440562i
$574$	19.5412	+	24.5039i	0.815633	+	1.02277i
$575$	2.61580	−	11.4606i	0.109087	−	0.477940i
$576$	2.05065	−	8.98450i	0.0854439	−	0.374354i
$577$	−10.0787	+	4.85365i	−0.419582	+	0.202060i	−0.631749	−	0.775173i	$-0.717662\pi$
$577$	−10.0787	+	4.85365i	−0.419582	+	0.202060i	0.212166	+	0.977234i	$0.431948\pi$
$578$	−25.6431	−	32.1555i	−1.06661	−	1.33749i
$579$	12.1532	−	15.2396i	0.505069	−	0.633336i
$580$	16.3596	−	7.87839i	0.679297	−	0.327132i
$581$	0.0754123	−	0.0363166i	0.00312863	−	0.00150667i
$582$	−13.6095	+	17.0657i	−0.564131	+	0.707398i
$583$	−5.26320	−	6.59984i	−0.217979	−	0.273337i
$584$	24.5863	−	11.8402i	1.01739	−	0.489949i
$585$	−0.788830	+	3.45609i	−0.0326141	+	0.142892i
$586$	14.1281	−	61.8992i	0.583626	−	2.55703i
$587$	−16.4896	−	20.6773i	−0.680599	−	0.853444i	0.314810	−	0.949155i	$-0.398059\pi$
$587$	−16.4896	−	20.6773i	−0.680599	−	0.853444i	−0.995409	+	0.0957103i	$0.969488\pi$
$588$	18.7148	+	9.01258i	0.771786	+	0.371673i
$589$	1.20804	+	5.29278i	0.0497765	+	0.218085i
$590$	−13.5903	−	6.54474i	−0.559504	−	0.269443i
$591$	−4.37907	+	5.49117i	−0.180131	+	0.225877i
$592$	8.93183	−	39.1329i	0.367096	−	1.60835i
$593$	−17.4957	+	21.9389i	−0.718463	+	0.900924i	−0.998250	−	0.0591381i	$-0.981165\pi$
$593$	−17.4957	+	21.9389i	−0.718463	+	0.900924i	0.279787	+	0.960062i	$0.409736\pi$
$594$	−1.88737	−	8.26912i	−0.0774399	−	0.339286i
$595$	−0.181831			−0.00745435
$596$	51.0910			2.09277
$597$	−2.65430	−	11.6292i	−0.108633	−	0.475953i
$598$	22.5336	+	28.2562i	0.921465	+	1.15548i
$599$	−0.681530	+	0.328207i	−0.0278465	+	0.0134102i	−0.447755	−	0.894156i	$-0.647776\pi$
$599$	−0.681530	+	0.328207i	−0.0278465	+	0.0134102i	0.419909	+	0.907566i	$0.362062\pi$
$600$	19.1673	+	9.23047i	0.782500	+	0.376832i
$601$	−10.6136			−0.432939			−0.216469	−	0.976289i	$-0.569454\pi$
$601$	−10.6136			−0.432939			−0.216469	+	0.976289i	$0.569454\pi$
$602$	−10.5546	+	17.5909i	−0.430173	+	0.716953i
$603$	3.02176			0.123055
$604$	−11.1776	−	5.38283i	−0.454809	−	0.219024i
$605$	−0.659363	+	0.317532i	−0.0268069	+	0.0129095i
$606$	−16.2176	−	20.3362i	−0.658794	−	0.826101i
$607$	2.82679	+	12.3850i	0.114736	+	0.502690i	0.999339	+	0.0363462i	$0.0115719\pi$
$607$	2.82679	+	12.3850i	0.114736	+	0.502690i	−0.884604	+	0.466344i	$0.845571\pi$
$608$	−0.705807			−0.0286243
$609$	−9.96354			−0.403743
$610$	0.165742	+	0.726163i	0.00671070	+	0.0294015i
$611$	28.2836	−	35.4666i	1.14423	−	1.43482i
$612$	0.202308	−	0.886369i	0.00817782	−	0.0358294i
$613$	7.12109	−	8.92956i	0.287618	−	0.360662i	−0.616941	−	0.787009i	$-0.711628\pi$
$613$	7.12109	−	8.92956i	0.287618	−	0.360662i	0.904560	+	0.426347i	$0.140200\pi$
$614$	0.114535	+	0.0551570i	0.00462224	+	0.00222596i
$615$	−1.34588	−	5.89668i	−0.0542711	−	0.237777i
$616$	−18.6249	−	8.96927i	−0.750418	−	0.361382i
$617$	5.68254	+	7.12567i	0.228770	+	0.286869i	0.882947	−	0.469473i	$-0.155556\pi$
$617$	5.68254	+	7.12567i	0.228770	+	0.286869i	−0.654177	+	0.756342i	$0.726985\pi$
$618$	−9.65337	+	42.2942i	−0.388316	+	1.70132i
$619$	−7.88337	+	34.5393i	−0.316859	+	1.38825i	0.526168	+	0.850381i	$0.323628\pi$
$619$	−7.88337	+	34.5393i	−0.316859	+	1.38825i	−0.843027	+	0.537871i	$0.819229\pi$
$620$	16.7761	−	8.07894i	0.673744	−	0.324458i
$621$	1.58112	+	1.98267i	0.0634483	+	0.0795616i
$622$	6.12522	−	7.68079i	0.245599	−	0.307971i
$623$	5.84164	−	2.81319i	0.234040	−	0.112708i
$624$	−17.7605	+	8.55298i	−0.710987	+	0.342393i
$625$	12.2613	−	15.3752i	0.490452	−	0.615008i
$626$	6.33641	+	7.94561i	0.253254	+	0.317570i
$627$	−2.15637	+	1.03845i	−0.0861170	+	0.0414717i
$628$	−8.57726	+	37.5794i	−0.342270	+	1.49958i
$629$	−0.621678	+	2.72375i	−0.0247879	+	0.108603i
$630$	1.17759	+	1.47665i	0.0469161	+	0.0588310i
$631$	21.5423	+	10.3742i	0.857584	+	0.412991i	0.810387	−	0.585895i	$-0.199257\pi$
$631$	21.5423	+	10.3742i	0.857584	+	0.412991i	0.0471972	+	0.998886i	$0.484971\pi$
$632$	−3.03253	−	13.2864i	−0.120627	−	0.528503i
$633$	−11.4830	−	5.52994i	−0.456410	−	0.219795i
$634$	39.4914	−	49.5207i	1.56841	−	1.96672i
$635$	0.990502	−	4.33967i	0.0393069	−	0.172215i
$636$	−5.86003	+	7.34824i	−0.232365	+	0.291377i
$637$	6.97548	+	30.5616i	0.276378	+	1.21089i
$638$	−65.5640			−2.59570
$639$	−2.03576			−0.0805336
$640$	2.72794	+	11.9519i	0.107831	+	0.472440i
$641$	12.8799	+	16.1509i	0.508726	+	0.637923i	0.968173	−	0.250283i	$-0.0805236\pi$
$641$	12.8799	+	16.1509i	0.508726	+	0.637923i	−0.459446	+	0.888205i	$0.651952\pi$
$642$	26.8485	−	12.9296i	1.05963	−	0.510290i
$643$	22.8623	+	11.0099i	0.901601	+	0.434188i	0.826467	−	0.562985i	$-0.190347\pi$
$643$	22.8623	+	11.0099i	0.901601	+	0.434188i	0.0751340	+	0.997173i	$0.476062\pi$
$644$	12.7180			0.501159
$645$	3.30803	−	2.17478i	0.130254	−	0.0856320i
$646$	−0.388419			−0.0152821
$647$	37.0032	+	17.8198i	1.45475	+	0.700569i	0.983412	−	0.181386i	$-0.0580583\pi$
$647$	37.0032	+	17.8198i	1.45475	+	0.700569i	0.471334	+	0.881955i	$0.343773\pi$
$648$	−4.13487	+	1.99125i	−0.162433	+	0.0782236i
$649$	22.4294	+	28.1256i	0.880431	+	1.10403i
$650$	14.7005	+	64.4073i	0.576602	+	2.52626i
$651$	−10.2172			−0.400442
$652$	58.6389			2.29648
$653$	−4.32492	−	18.9487i	−0.169247	−	0.741520i	−0.986301	−	0.164958i	$-0.947251\pi$
$653$	−4.32492	−	18.9487i	−0.169247	−	0.741520i	0.817053	−	0.576562i	$-0.195606\pi$
$654$	−9.47717	+	11.8840i	−0.370587	+	0.464701i
$655$	−1.34759	+	5.90418i	−0.0526547	+	0.230696i
$656$	20.9699	−	26.2954i	0.818737	−	1.02666i
$657$	5.35725	+	2.57992i	0.209006	+	0.100652i
$658$	−5.37808	−	23.5629i	−0.209659	−	0.918578i
$659$	−22.5641	−	10.8663i	−0.878971	−	0.423290i	−0.0607224	−	0.998155i	$-0.519340\pi$
$659$	−22.5641	−	10.8663i	−0.878971	−	0.423290i	−0.818249	+	0.574865i	$0.805055\pi$
$660$	5.11814	+	6.41794i	0.199223	+	0.249818i
$661$	−6.19106	+	27.1248i	−0.240804	+	1.05503i	0.699482	+	0.714650i	$0.253414\pi$
$661$	−6.19106	+	27.1248i	−0.240804	+	1.05503i	−0.940287	+	0.340383i	$0.889443\pi$
$662$	−12.7057	+	55.6674i	−0.493822	+	2.16357i
$663$	1.23617	−	0.595309i	0.0480090	−	0.0231199i
$664$	−0.185814	−	0.233004i	−0.00721099	−	0.00904230i
$665$	0.332291	−	0.416679i	0.0128857	−	0.0161581i
$666$	26.1456	−	12.5911i	1.01312	−	0.487894i
$667$	17.6614	−	8.50528i	0.683852	−	0.329326i
$668$	−12.6998	+	15.9250i	−0.491368	+	0.616156i
$669$	1.05096	+	1.31786i	0.0406324	+	0.0509514i
$670$	−3.98931	+	1.92115i	−0.154120	+	0.0742205i
$671$	0.395277	−	1.73182i	0.0152595	−	0.0668562i
$672$	0.295581	−	1.29502i	0.0114023	−	0.0499566i
$673$	−24.3299	−	30.5087i	−0.937847	−	1.17602i	−0.984193	−	0.177098i	$-0.943329\pi$
$673$	−24.3299	−	30.5087i	−0.937847	−	1.17602i	0.0463460	−	0.998925i	$-0.485242\pi$
$674$	−44.2155	−	21.2931i	−1.70312	−	0.820178i
$675$	1.03150	+	4.51930i	0.0397024	+	0.173948i
$676$	−75.2941	−	36.2597i	−2.89593	−	1.39460i
$677$	15.3954	−	19.3053i	0.591694	−	0.741961i	−0.392364	−	0.919810i	$-0.628342\pi$
$677$	15.3954	−	19.3053i	0.591694	−	0.741961i	0.984058	+	0.177849i	$0.0569139\pi$
$678$	1.95203	−	8.55239i	0.0749672	−	0.328453i
$679$	−7.22747	+	9.06296i	−0.277365	+	0.347805i
$680$	0.144064	+	0.631187i	0.00552462	+	0.0242049i
$681$	7.65191			0.293222
$682$	−67.2330			−2.57448
$683$	−6.57942	−	28.8263i	−0.251754	−	1.10301i	−0.929822	−	0.368009i	$-0.880040\pi$
$683$	−6.57942	−	28.8263i	−0.251754	−	1.10301i	0.678068	−	0.734999i	$-0.262818\pi$
$684$	1.66147	+	2.08341i	0.0635278	+	0.0796614i
$685$	7.71923	−	3.71739i	0.294937	−	0.142034i
$686$	34.7777	+	16.7481i	1.32782	+	0.639444i
$687$	11.6187			0.443281
$688$	20.9241	+	6.84174i	0.797724	+	0.260839i
$689$	−14.1840			−0.540366
$690$	−3.34791	−	1.61227i	−0.127453	−	0.0613781i
$691$	20.4965	−	9.87058i	0.779722	−	0.375494i	−0.00129883	−	0.999999i	$-0.500413\pi$
$691$	20.4965	−	9.87058i	0.779722	−	0.375494i	0.781021	+	0.624505i	$0.214699\pi$
$692$	52.2219	+	65.4842i	1.98518	+	2.48933i
$693$	−1.00231	−	4.39141i	−0.0380747	−	0.166816i
$694$	−17.0701			−0.647974
$695$	−1.11226			−0.0421905
$696$	7.89408	+	34.5862i	0.299224	+	1.31099i
$697$	−1.45956	+	1.83023i	−0.0552847	+	0.0693248i
$698$	−5.76516	+	25.2588i	−0.218215	+	0.956061i
$699$	0.0236806	−	0.0296945i	0.000895683	−	0.00112315i
$700$	20.9455	+	10.0868i	0.791664	+	0.381245i
$701$	−6.60532	−	28.9398i	−0.249480	−	1.09304i	−0.932081	−	0.362250i	$-0.882009\pi$
$701$	−6.60532	−	28.9398i	−0.249480	−	1.09304i	0.682601	−	0.730791i	$-0.260849\pi$
$702$	−12.8403	−	6.18354i	−0.484624	−	0.233383i
$703$	−5.10557	−	6.40218i	−0.192560	−	0.241463i
$704$	7.16621	−	31.3972i	0.270087	−	1.18333i
$705$	−1.03787	+	4.54719i	−0.0390883	+	0.171257i
$706$	17.9344	−	8.63675i	0.674970	−	0.325048i
$707$	−8.61253	−	10.7998i	−0.323907	−	0.406167i
$708$	24.9728	−	31.3149i	0.938536	−	1.17689i
$709$	8.81409	−	4.24464i	0.331020	−	0.159411i	−0.260990	−	0.965342i	$-0.584049\pi$
$709$	8.81409	−	4.24464i	0.331020	−	0.159411i	0.592010	+	0.805931i	$0.298335\pi$
$710$	2.68761	−	1.29428i	0.100864	−	0.0485736i
$711$	1.85145	−	2.32164i	0.0694346	−	0.0870683i
$712$	−14.3937	−	18.0491i	−0.539426	−	0.676419i
$713$	18.1110	−	8.72178i	0.678261	−	0.326633i
$714$	0.162664	−	0.712676i	0.00608754	−	0.0266712i
$715$	−2.75664	+	12.0776i	−0.103093	+	0.451678i
$716$	−51.1490	−	64.1388i	−1.91153	−	2.39698i
$717$	12.0456	+	5.80086i	0.449852	+	0.216637i
$718$	−11.9762	−	52.4712i	−0.446948	−	1.95821i
$719$	−7.98019	−	3.84306i	−0.297611	−	0.143322i	0.279120	−	0.960256i	$-0.409957\pi$
$719$	−7.98019	−	3.84306i	−0.297611	−	0.143322i	−0.576730	+	0.816934i	$0.695672\pi$
$720$	1.26368	−	1.58461i	0.0470946	−	0.0590548i
$721$	−5.12654	+	22.4608i	−0.190922	+	0.836485i
$722$	−28.0425	+	35.1642i	−1.04363	+	1.30867i
$723$	4.70290	+	20.6047i	0.174903	+	0.766299i
$724$	66.6528			2.47713
$725$	35.8325			1.33079
$726$	−0.654692	−	2.86839i	−0.0242979	−	0.106456i
$727$	−6.95276	−	8.71849i	−0.257864	−	0.323351i	0.636001	−	0.771689i	$-0.280588\pi$
$727$	−6.95276	−	8.71849i	−0.257864	−	0.323351i	−0.893864	+	0.448338i	$0.852016\pi$
$728$	−31.2947	+	15.0707i	−1.15986	+	0.558559i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−8.71285			−0.322477
$731$	−1.45637	−	0.476203i	−0.0538659	−	0.0176130i
$732$	−1.97779			−0.0731013
$733$	−17.7914	−	8.56787i	−0.657139	−	0.316462i	0.0754329	−	0.997151i	$-0.475966\pi$
$733$	−17.7914	−	8.56787i	−0.657139	−	0.316462i	−0.732572	+	0.680689i	$0.761680\pi$
$734$	−33.3808	+	16.0753i	−1.23211	+	0.593351i
$735$	−2.00954	−	2.51988i	−0.0741230	−	0.0929473i
$736$	0.581537	+	2.54788i	0.0214357	+	0.0939161i
$737$	10.5598			0.388976
$738$	24.3157			0.895073
$739$	−0.200575	−	0.878775i	−0.00737826	−	0.0323263i	0.971105	−	0.238653i	$-0.0767060\pi$
$739$	−0.200575	−	0.878775i	−0.00737826	−	0.0323263i	−0.978483	+	0.206327i	$0.933849\pi$
$740$	−17.5111	+	21.9583i	−0.643722	+	0.807202i
$741$	−0.894872	+	3.92069i	−0.0328739	+	0.144030i
$742$	−4.71169	+	5.90828i	−0.172972	+	0.216900i
$743$	−25.3526	−	12.2092i	−0.930096	−	0.447911i	−0.0934311	−	0.995626i	$-0.529783\pi$
$743$	−25.3526	−	12.2092i	−0.930096	−	0.447911i	−0.836665	+	0.547715i	$0.815498\pi$
$744$	8.09503	+	35.4666i	0.296778	+	1.30027i
$745$	−7.14242	−	3.43961i	−0.261678	−	0.126017i
$746$	8.59221	+	10.7743i	0.314583	+	0.394475i
$747$	0.0144500	−	0.0633097i	0.000528699	−	0.00231638i
$748$	0.706985	−	3.09750i	0.0258499	−	0.113256i
$749$	14.2582	−	6.86640i	0.520985	−	0.250893i
$750$	−8.80304	−	11.0387i	−0.321442	−	0.403075i
$751$	2.13972	−	2.68312i	0.0780794	−	0.0979085i	−0.741258	−	0.671221i	$-0.765770\pi$
$751$	2.13972	−	2.68312i	0.0780794	−	0.0979085i	0.819337	+	0.573312i	$0.194342\pi$
$752$	−23.3675	+	11.2532i	−0.852124	+	0.410361i
$753$	14.1075	−	6.79383i	0.514107	−	0.247581i
$754$	−68.6866	+	86.1303i	−2.50142	+	3.13668i
$755$	1.20021	+	1.50502i	0.0436802	+	0.0547733i
$756$	−4.51847	+	2.17598i	−0.164335	+	0.0791397i
$757$	10.4149	−	45.6305i	0.378535	−	1.65847i	−0.323427	−	0.946253i	$-0.604835\pi$
$757$	10.4149	−	45.6305i	0.378535	−	1.65847i	0.701961	−	0.712215i	$-0.252308\pi$
$758$	5.25879	−	23.0403i	0.191008	−	0.836860i
$759$	5.52539	+	6.92862i	0.200559	+	0.251493i
$760$	−1.70968	−	0.823340i	−0.0620168	−	0.0298657i
$761$	−8.70663	−	38.1462i	−0.315615	−	1.38280i	−0.845158	−	0.534517i	$-0.820494\pi$
$761$	−8.70663	−	38.1462i	−0.315615	−	1.38280i	0.529543	−	0.848283i	$-0.322364\pi$
$762$	16.1230	+	7.76442i	0.584074	+	0.281275i
$763$	−5.03296	+	6.31114i	−0.182205	+	0.228478i
$764$	−21.0440	+	92.1998i	−0.761345	+	3.33567i
$765$	−0.0879555	+	0.110293i	−0.00318004	+	0.00398764i
$766$	0.986152	+	4.32062i	0.0356311	+	0.156110i
$767$	60.4457			2.18257
$768$	−30.8540			−1.11335
$769$	−6.30076	−	27.6054i	−0.227211	−	0.995478i	−0.951902	−	0.306403i	$-0.900874\pi$
$769$	−6.30076	−	27.6054i	−0.227211	−	0.995478i	0.724691	−	0.689074i	$-0.241983\pi$
$770$	4.11519	+	5.16028i	0.148301	+	0.185964i
$771$	8.06581	−	3.88429i	0.290483	−	0.139889i
$772$	−68.3309	−	32.9064i	−2.45928	−	1.18433i
$773$	22.8502			0.821864			0.410932	−	0.911666i	$-0.365203\pi$
$773$	22.8502			0.821864			0.410932	+	0.911666i	$0.365203\pi$
$774$	5.56461	+	14.9112i	0.200016	+	0.535971i
$775$	36.7446			1.31991
$776$	37.1864	+	17.9080i	1.33491	+	0.642861i
$777$	13.8849	−	6.68663i	0.498119	−	0.239882i
$778$	−39.4180	−	49.4286i	−1.41320	−	1.77210i
$779$	−1.52680	−	6.68937i	−0.0547034	−	0.239671i
$780$	13.7930			0.493870
$781$	−7.11418			−0.254565
$782$	0.320031	+	1.40215i	0.0114443	+	0.0501407i
$783$	−4.81957	+	6.04355i	−0.172237	+	0.215979i
$784$	3.98813	−	17.4732i	0.142433	−	0.624041i
$785$	3.72905	−	4.67608i	0.133096	−	0.166897i
$786$	−21.9355	−	10.5636i	−0.782415	−	0.376791i
$787$	6.33933	+	27.7744i	0.225973	+	0.990051i	0.952888	+	0.303324i	$0.0980964\pi$
$787$	6.33933	+	27.7744i	0.225973	+	0.990051i	−0.726915	+	0.686728i	$0.759046\pi$
$788$	24.6212	+	11.8569i	0.877093	+	0.422386i
$789$	−7.15008	−	8.96592i	−0.254550	−	0.319195i
$790$	−0.968235	+	4.24211i	−0.0344482	+	0.150928i
$791$	1.03665	−	4.54185i	0.0368589	−	0.161490i
$792$	−14.4497	+	6.95861i	−0.513448	+	0.247263i
$793$	−1.86096	−	2.33357i	−0.0660847	−	0.0828675i
$794$	−11.6121	+	14.5611i	−0.412099	+	0.516755i
$795$	1.31393	−	0.632754i	0.0466002	−	0.0224415i
$796$	−41.8154	+	20.1372i	−1.48211	+	0.713745i
$797$	−7.20408	+	9.03363i	−0.255182	+	0.319988i	−0.892877	−	0.450301i	$-0.851317\pi$
$797$	−7.20408	+	9.03363i	−0.255182	+	0.319988i	0.637695	+	0.770289i	$0.279888\pi$
$798$	1.33589	+	1.67515i	0.0472899	+	0.0592996i
$799$	1.62644	−	0.783250i	0.0575391	−	0.0277094i
$800$	−1.06302	+	4.65737i	−0.0375833	+	0.164663i
$801$	1.11934	−	4.90414i	0.0395499	−	0.173279i
$802$	1.89620	+	2.37775i	0.0669570	+	0.0839614i
$803$	18.7214	+	9.01577i	0.660665	+	0.318159i
$804$	−2.61624	−	11.4625i	−0.0922677	−	0.404251i
$805$	−1.77795	−	0.856215i	−0.0626645	−	0.0301776i
$806$	−70.4351	+	88.3228i	−2.48097	+	3.11104i
$807$	6.76319	−	29.6315i	0.238075	−	1.04308i
$808$	−30.6654	+	38.4531i	−1.07880	+	1.35278i
$809$	0.434540	+	1.90384i	0.0152776	+	0.0669355i	0.981992	−	0.188922i	$-0.0604993\pi$
$809$	0.434540	+	1.90384i	0.0152776	+	0.0669355i	−0.966714	+	0.255858i	$0.917642\pi$
$810$	1.46531			0.0514856
$811$	−7.25920			−0.254905			−0.127453	−	0.991845i	$-0.540680\pi$
$811$	−7.25920			−0.254905			−0.127453	+	0.991845i	$0.540680\pi$
$812$	8.62644	+	37.7949i	0.302729	+	1.32634i
$813$	−17.6737	−	22.1622i	−0.619845	−	0.777261i
$814$	91.3684	−	44.0007i	3.20246	−	1.54222i
$815$	−8.19760	−	3.94776i	−0.287149	−	0.138284i
$816$	−0.784450			−0.0274612
$817$	3.75273	−	2.46714i	0.131291	−	0.0863142i
$818$	39.5568			1.38307
$819$	−6.81897	−	3.28384i	−0.238274	−	0.114747i
$820$	−21.2027	+	10.2107i	−0.740432	+	0.356573i
$821$	−9.15305	−	11.4776i	−0.319444	−	0.400570i	0.596020	−	0.802969i	$-0.296748\pi$
$821$	−9.15305	−	11.4776i	−0.319444	−	0.400570i	−0.915464	+	0.402399i	$0.868176\pi$
$822$	7.66455	+	33.5806i	0.267332	+	1.17126i
$823$	6.47362			0.225656			0.112828	−	0.993615i	$-0.464009\pi$
$823$	6.47362			0.225656			0.112828	+	0.993615i	$0.464009\pi$
$824$	82.0296			2.85764
$825$	3.60468	+	15.7931i	0.125499	+	0.549846i
$826$	20.0791	−	25.1784i	0.698643	−	0.876070i
$827$	5.85234	−	25.6408i	0.203506	−	0.891616i	−0.765276	−	0.643702i	$-0.777398\pi$
$827$	5.85234	−	25.6408i	0.203506	−	0.891616i	0.968782	−	0.247914i	$-0.0797452\pi$
$828$	6.15195	−	7.71430i	0.213795	−	0.268090i
$829$	−6.15006	−	2.96171i	−0.213600	−	0.102865i	0.324024	−	0.946049i	$-0.394964\pi$
$829$	−6.15006	−	2.96171i	−0.213600	−	0.102865i	−0.537625	+	0.843184i	$0.680678\pi$
$830$	0.0211737	+	0.0927680i	0.000734950	+	0.00322003i
$831$	−18.8086	−	9.05775i	−0.652464	−	0.314210i
$832$	−33.7385	−	42.3067i	−1.16967	−	1.46672i
$833$	−0.277584	+	1.21618i	−0.00961773	+	0.0421380i
$834$	0.995015	−	4.35945i	0.0344546	−	0.150955i
$835$	2.84752	−	1.37129i	0.0985426	−	0.0474556i
$836$	5.80616	+	7.28069i	0.200810	+	0.251808i
$837$	−4.94225	+	6.19739i	−0.170829	+	0.214213i
$838$	65.7736	−	31.6749i	2.27211	−	1.09419i
$839$	28.1822	−	13.5718i	0.972956	−	0.468551i	0.121279	−	0.992618i	$-0.461300\pi$
$839$	28.1822	−	13.5718i	0.972956	−	0.468551i	0.851677	+	0.524067i	$0.175586\pi$
$840$	2.22666	−	2.79215i	0.0768272	−	0.0963383i
$841$	19.1740	+	24.0434i	0.661172	+	0.829084i
$842$	41.4815	−	19.9764i	1.42955	−	0.688433i
$843$	−6.78621	+	29.7323i	−0.233729	+	1.02404i
$844$	−11.0348	+	48.3466i	−0.379834	+	1.66416i
$845$	8.08485	+	10.1381i	0.278127	+	0.348761i
$846$	−16.8940	−	8.13570i	−0.580826	−	0.279711i
$847$	−0.347682	−	1.52329i	−0.0119465	−	0.0523410i
$848$	7.30639	+	3.51857i	0.250903	+	0.120828i
$849$	−0.0481608	+	0.0603918i	−0.00165288	+	0.00207264i
$850$	−0.584998	+	2.56304i	−0.0200653	+	0.0879116i
$851$	−18.9045	+	23.7055i	−0.648038	+	0.812613i
$852$	1.76257	+	7.72231i	0.0603845	+	0.264562i
$853$	−41.0779			−1.40648			−0.703240	−	0.710953i	$-0.748264\pi$
$853$	−41.0779			−1.40648			−0.703240	+	0.710953i	$0.748264\pi$
$854$	−1.59022			−0.0544163
$855$	−0.0920078	−	0.403113i	−0.00314660	−	0.0137862i
$856$	−35.1320	−	44.0541i	−1.20079	−	1.50574i
$857$	−17.9188	+	8.62924i	−0.612095	+	0.294769i	−0.714132	−	0.700011i	$-0.753178\pi$
$857$	−17.9188	+	8.62924i	−0.612095	+	0.294769i	0.102037	+	0.994781i	$0.467464\pi$
$858$	−44.8715	−	21.6090i	−1.53189	−	0.737719i
$859$	−0.965426			−0.0329399			−0.0164700	−	0.999864i	$-0.505243\pi$
$859$	−0.965426			−0.0329399			−0.0164700	+	0.999864i	$0.505243\pi$
$860$	−11.1137	−	10.6655i	−0.378975	−	0.363690i
$861$	12.9131			0.440078
$862$	54.3993	+	26.1973i	1.85285	+	0.892284i
$863$	35.3820	−	17.0391i	1.20442	−	0.580017i	0.279487	−	0.960150i	$-0.409836\pi$
$863$	35.3820	−	17.0391i	1.20442	−	0.580017i	0.924932	+	0.380132i	$0.124121\pi$
$864$	−0.642539	−	0.805719i	−0.0218596	−	0.0274111i
$865$	−2.89191	−	12.6703i	−0.0983280	−	0.430803i
$866$	−32.7992			−1.11456
$867$	−16.9454			−0.575496
$868$	8.84603	+	38.7570i	0.300254	+	1.31550i
$869$	6.47006	−	8.11319i	0.219482	−	0.275221i
$870$	2.52045	−	11.0428i	0.0854512	−	0.374386i
$871$	11.0628	−	13.8723i	0.374847	−	0.470043i
$872$	25.8953	+	12.4705i	0.876926	+	0.422306i
$873$	2.00121	+	8.76788i	0.0677308	+	0.296748i
$874$	−3.79797	−	1.82901i	−0.128468	−	0.0618670i
$875$	−4.67496	−	5.86221i	−0.158042	−	0.198179i
$876$	5.14814	−	22.5555i	0.173939	−	0.762078i
$877$	−7.85052	+	34.3954i	−0.265093	+	1.16145i	0.650552	+	0.759462i	$0.274538\pi$
$877$	−7.85052	+	34.3954i	−0.265093	+	1.16145i	−0.915645	+	0.401988i	$0.868319\pi$
$878$	−54.5071	+	26.2492i	−1.83952	+	0.885868i
$879$	−16.3099	−	20.4520i	−0.550121	−	0.689829i
$880$	4.41606	−	5.53756i	0.148865	−	0.186671i
$881$	−31.0281	+	14.9423i	−1.04536	+	0.503420i	−0.876089	−	0.482150i	$-0.839856\pi$
$881$	−31.0281	+	14.9423i	−1.04536	+	0.503420i	−0.169273	+	0.985569i	$0.554142\pi$
$882$	11.6742	−	5.62202i	0.393092	−	0.189303i
$883$	−7.79412	+	9.77352i	−0.262293	+	0.328905i	−0.895487	−	0.445088i	$-0.853172\pi$
$883$	−7.79412	+	9.77352i	−0.262293	+	0.328905i	0.633194	+	0.773993i	$0.281744\pi$
$884$	−3.32848	−	4.17378i	−0.111949	−	0.140379i
$885$	−5.59937	+	2.69652i	−0.188221	+	0.0906424i
$886$	−1.72971	+	7.57837i	−0.0581109	+	0.254600i
$887$	−3.44581	+	15.0971i	−0.115699	+	0.506910i	0.883556	+	0.468325i	$0.155142\pi$
$887$	−3.44581	+	15.0971i	−0.115699	+	0.506910i	−0.999255	+	0.0385855i	$0.987715\pi$
$888$	−34.2122	−	42.9007i	−1.14809	−	1.43965i
$889$	8.56230	+	4.12339i	0.287170	+	0.138294i
$890$	1.64017	+	7.18606i	0.0549787	+	0.240877i
$891$	−3.14852	−	1.51625i	−0.105479	−	0.0507962i
$892$	4.08914	−	5.12762i	0.136915	−	0.171685i
$893$	−1.17738	+	5.15846i	−0.0393997	+	0.172621i
$894$	19.8708	−	24.9172i	0.664580	−	0.833357i
$895$	2.83250	+	12.4100i	0.0946801	+	0.414820i
$896$	−26.1734			−0.874394
$897$	14.8905			0.497181
$898$	−6.68972	−	29.3096i	−0.223239	−	0.978074i
$899$	38.2035	+	47.9057i	1.27416	+	1.59775i
$900$	16.2501	−	7.82562i	0.541669	−	0.260854i
$901$	−0.508544	−	0.244902i	−0.0169420	−	0.00815886i
$902$	84.9735			2.82931
$903$	2.95515	+	7.91874i	0.0983412	+	0.263519i
$904$	−16.5874			−0.551687
$905$	−9.31794	−	4.48728i	−0.309739	−	0.149162i
$906$	−6.97253	+	3.35779i	−0.231647	+	0.111555i
$907$	5.17208	+	6.48559i	0.171736	+	0.215350i	0.860249	−	0.509873i	$-0.170308\pi$
$907$	5.17208	+	6.48559i	0.171736	+	0.215350i	−0.688513	+	0.725224i	$0.741736\pi$
$908$	−6.62503	−	29.0261i	−0.219859	−	0.963266i
$909$	−10.7168			−0.355455
$910$	11.0901			0.367635
$911$	−9.65302	−	42.2926i	−0.319819	−	1.40122i	−0.837871	−	0.545869i	$-0.816200\pi$
$911$	−9.65302	−	42.2926i	−0.319819	−	1.40122i	0.518052	−	0.855349i	$-0.326657\pi$
$912$	1.43356	−	1.79762i	0.0474698	−	0.0595253i
$913$	0.0504970	−	0.221242i	0.00167121	−	0.00732203i
$914$	−48.1677	+	60.4003i	−1.59324	+	1.99787i
$915$	0.276492	+	0.133151i	0.00914053	+	0.00440185i
$916$	−10.0595	−	44.0734i	−0.332374	−	1.45623i
$917$	−11.6491	−	5.60993i	−0.384688	−	0.185256i
$918$	−0.353602	−	0.443403i	−0.0116706	−	0.0146345i
$919$	−4.63253	+	20.2965i	−0.152813	+	0.669518i	0.839247	+	0.543751i	$0.182996\pi$
$919$	−4.63253	+	20.2965i	−0.152813	+	0.669518i	−0.992060	+	0.125767i	$0.959861\pi$
$920$	−1.56350	+	6.85014i	−0.0515470	+	0.225842i
$921$	0.0471897	−	0.0227254i	0.00155495	−	0.000748826i
$922$	10.7424	+	13.4705i	0.353782	+	0.443628i
$923$	−7.45300	+	9.34577i	−0.245319	+	0.307620i
$924$	−15.7902	+	7.60418i	−0.519461	+	0.250159i
$925$	−49.9353	+	24.0476i	−1.64186	+	0.790679i
$926$	20.0480	−	25.1394i	0.658819	−	0.826133i
$927$	11.1442	+	13.9743i	0.366022	+	0.458978i
$928$	−7.17726	+	3.45639i	−0.235605	+	0.113462i
$929$	2.68860	−	11.7795i	0.0882101	−	0.386474i	−0.911481	−	0.411343i	$-0.865060\pi$
$929$	2.68860	−	11.7795i	0.0882101	−	0.386474i	0.999691	+	0.0248692i	$0.00791694\pi$
$930$	2.58461	−	11.3239i	0.0847526	−	0.371326i
$931$	−2.27968	−	2.85863i	−0.0747135	−	0.0936877i
$932$	−0.133144	−	0.0641186i	−0.00436126	−	0.00210027i
$933$	−0.900686	−	3.94616i	−0.0294871	−	0.129192i
$934$	79.1685	+	38.1256i	2.59047	+	1.24751i
$935$	−0.307369	+	0.385428i	−0.0100520	+	0.0126049i
$936$	−5.99649	+	26.2723i	−0.196001	+	0.858738i
$937$	17.2327	−	21.6091i	0.562968	−	0.705939i	−0.416135	−	0.909303i	$-0.636616\pi$
$937$	17.2327	−	21.6091i	0.562968	−	0.705939i	0.979103	+	0.203363i	$0.0651872\pi$
$938$	−2.10356	−	9.21630i	−0.0686837	−	0.300923i
$939$	4.18720			0.136644
$940$	18.1475			0.591907
$941$	11.1538	+	48.8682i	0.363605	+	1.59306i	0.743965	+	0.668218i	$0.232943\pi$
$941$	11.1538	+	48.8682i	0.363605	+	1.59306i	−0.380360	+	0.924838i	$0.624200\pi$
$942$	14.9917	+	18.7990i	0.488455	+	0.612503i
$943$	−22.8898	+	11.0232i	−0.745396	+	0.358964i
$944$	−31.1366	−	14.9946i	−1.01341	−	0.488032i
$945$	0.778168			0.0253138
$946$	19.4461	+	52.1085i	0.632246	+	1.69419i
$947$	−27.4950			−0.893467			−0.446733	−	0.894667i	$-0.647413\pi$
$947$	−27.4950			−0.893467			−0.446733	+	0.894667i	$0.647413\pi$
$948$	−10.4097	−	5.01305i	−0.338091	−	0.162816i
$949$	31.4569	−	15.1489i	1.02113	−	0.491753i
$950$	−4.80433	−	6.02444i	−0.155873	−	0.195459i
$951$	−5.80704	−	25.4423i	−0.188306	−	0.825023i
$952$	−1.38224			−0.0447985
$953$	−38.1257			−1.23501			−0.617505	−	0.786567i	$-0.711857\pi$
$953$	−38.1257			−1.23501			−0.617505	+	0.786567i	$0.711857\pi$
$954$	1.30462	+	5.71591i	0.0422386	+	0.185059i
$955$	9.14910	−	11.4726i	0.296058	−	0.371245i
$956$	11.5754	−	50.7153i	0.374376	−	1.64025i
$957$	−16.8424	+	21.1198i	−0.544439	+	0.682705i
$958$	30.3649	+	14.6230i	0.981045	+	0.472446i
$959$	4.07035	+	17.8334i	0.131438	+	0.575869i
$960$	5.01268	+	2.41398i	0.161783	+	0.0779108i
$961$	19.8478	+	24.8884i	0.640253	+	0.802852i
$962$	37.9170	−	166.125i	1.22249	−	5.35610i
$963$	2.73207	−	11.9700i	0.0880398	−	0.385727i
$964$	74.0886	−	35.6792i	2.38623	−	1.14915i
$965$	7.33716	+	9.20051i	0.236192	+	0.296175i
$966$	4.94641	−	6.20260i	0.159148	−	0.199565i
$967$	−30.9639	+	14.9114i	−0.995732	+	0.479519i	−0.859488	−	0.511156i	$-0.829217\pi$
$967$	−30.9639	+	14.9114i	−0.995732	+	0.479519i	−0.136244	+	0.990675i	$0.543503\pi$
$968$	−5.01231	+	2.41380i	−0.161102	+	0.0775825i
$969$	−0.0997792	+	0.125119i	−0.00320537	+	0.00401941i
$970$	−8.21637	−	10.3030i	−0.263812	−	0.330809i
$971$	35.7634	−	17.2227i	1.14770	−	0.552704i	0.239360	−	0.970931i	$-0.423063\pi$
$971$	35.7634	−	17.2227i	1.14770	−	0.552704i	0.908343	+	0.418227i	$0.137348\pi$
$972$	−0.865801	+	3.79332i	−0.0277706	+	0.121671i
$973$	0.528414	−	2.31513i	0.0169402	−	0.0742198i
$974$	47.0876	+	59.0460i	1.50878	+	1.89195i
$975$	24.5235	+	11.8099i	0.785380	+	0.378219i
$976$	0.379730	+	1.66370i	0.0121549	+	0.0532539i
$977$	−31.4352	−	15.1384i	−1.00570	−	0.484321i	−0.142832	−	0.989747i	$-0.545621\pi$
$977$	−31.4352	−	15.1384i	−1.00570	−	0.484321i	−0.862870	+	0.505426i	$0.831335\pi$
$978$	22.8065	−	28.5984i	0.729270	−	0.914475i
$979$	3.91163	−	17.1380i	0.125016	−	0.547732i
$980$	−7.81886	+	9.80454i	−0.249764	+	0.313195i
$981$	1.39358	+	6.10565i	0.0444934	+	0.194938i
$982$	−87.6654			−2.79752
$983$	26.7005			0.851612			0.425806	−	0.904814i	$-0.359991\pi$
$983$	26.7005			0.851612			0.425806	+	0.904814i	$0.359991\pi$
$984$	−10.2310	−	44.8251i	−0.326154	−	1.42897i
$985$	−2.64375	−	3.31515i	−0.0842368	−	0.105630i
$986$	−3.94979	+	1.90212i	−0.125787	+	0.0605757i
$987$	−8.97173	−	4.32056i	−0.285573	−	0.137525i
$988$	15.6472			0.497804
$989$	−11.9981	−	11.5141i	−0.381516	−	0.366129i
$990$	5.12065			0.162745
$991$	−12.6191	−	6.07702i	−0.400858	−	0.193043i	0.222583	−	0.974914i	$-0.428551\pi$
$991$	−12.6191	−	6.07702i	−0.400858	−	0.193043i	−0.623440	+	0.781871i	$0.714266\pi$
$992$	−7.35996	+	3.54437i	−0.233679	+	0.112534i
$993$	14.6679	+	18.3930i	0.465471	+	0.583683i
$994$	1.41717	+	6.20904i	0.0449500	+	0.196939i
$995$	7.20141			0.228300
$996$	−0.252665			−0.00800599
$997$	−3.03585	−	13.3009i	−0.0961462	−	0.421244i	0.903832	−	0.427888i	$-0.140742\pi$
$997$	−3.03585	−	13.3009i	−0.0961462	−	0.421244i	−0.999978	+	0.00664401i	$0.997885\pi$
$998$	−6.48211	+	8.12831i	−0.205188	+	0.257297i
$999$	2.66054	−	11.6566i	0.0841758	−	0.368798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	129.2.i.c.64.1	✓	30
3.2	odd	2		387.2.u.e.64.5		30
43.16	even	7		5547.2.a.u.1.14		15
43.27	odd	14		5547.2.a.v.1.2		15
43.41	even	7	inner	129.2.i.c.127.1	yes	30
129.41	odd	14		387.2.u.e.127.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.i.c.64.1	✓	30	1.1	even	1	trivial
129.2.i.c.127.1	yes	30	43.41	even	7	inner
387.2.u.e.64.5		30	3.2	odd	2
387.2.u.e.127.5		30	129.41	odd	14
5547.2.a.u.1.14		15	43.16	even	7
5547.2.a.v.1.2		15	43.27	odd	14

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:	\( N \)	\(=\)	\( 129 = 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	129.i (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18675 - 1.05308i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(2.42592 + 3.04201i) q^{4} +(-0.134341 - 0.588587i) q^{5} +2.42711 q^{6} +1.28895 q^{7} +(-1.02123 - 4.47429i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(-2.18675 - 1.05308i) q^{2} +(-0.900969 + 0.433884i) q^{3} +(2.42592 + 3.04201i) q^{4} +(-0.134341 - 0.588587i) q^{5} +2.42711 q^{6} +1.28895 q^{7} +(-1.02123 - 4.47429i) q^{8} +(0.623490 - 0.781831i) q^{9} +(-0.326061 + 1.42857i) q^{10} +(2.17885 - 2.73219i) q^{11} +(-3.50556 - 1.68819i) q^{12} +(-1.30661 - 5.72462i) q^{13} +(-2.81861 - 1.35737i) q^{14} +(0.376416 + 0.472010i) q^{15} +(-0.747035 + 3.27297i) q^{16} +(0.0519955 - 0.227807i) q^{17} +(-2.18675 + 1.05308i) q^{18} +(0.427017 + 0.535462i) q^{19} +(1.46459 - 1.83653i) q^{20} +(-1.16130 + 0.559253i) q^{21} +(-7.64182 + 3.68011i) q^{22} +(1.58112 - 1.98267i) q^{23} +(2.86142 + 3.58811i) q^{24} +(4.17646 - 2.01128i) q^{25} +(-3.17128 + 13.8943i) q^{26} +(-0.222521 + 0.974928i) q^{27} +(3.12688 + 3.92098i) q^{28} +(6.96448 + 3.35392i) q^{29} +(-0.326061 - 1.42857i) q^{30} +(7.14176 + 3.43929i) q^{31} +(-0.642539 + 0.805719i) q^{32} +(-0.777621 + 3.40698i) q^{33} +(-0.353602 + 0.443403i) q^{34} +(-0.173159 - 0.758657i) q^{35} +3.89087 q^{36} -11.9564 q^{37} +(-0.369893 - 1.62061i) q^{38} +(3.66103 + 4.59079i) q^{39} +(-2.49632 + 1.20216i) q^{40} +(-9.02624 - 4.34681i) q^{41} +3.12842 q^{42} +(0.599960 - 6.52993i) q^{43} +13.5970 q^{44} +(-0.543936 - 0.261946i) q^{45} +(-5.54544 + 2.67054i) q^{46} +(4.81683 + 6.04011i) q^{47} +(-0.747035 - 3.27297i) q^{48} -5.33862 q^{49} -11.2509 q^{50} +(0.0519955 + 0.227807i) q^{51} +(14.2446 - 17.8622i) q^{52} +(0.537519 - 2.35503i) q^{53} +(1.51328 - 1.89759i) q^{54} +(-1.90084 - 0.915396i) q^{55} +(-1.31631 - 5.76713i) q^{56} +(-0.617057 - 0.297159i) q^{57} +(-11.6976 - 14.6684i) q^{58} +(-2.29067 + 10.0361i) q^{59} +(-0.522705 + 2.29012i) q^{60} +(0.457977 - 0.220550i) q^{61} +(-11.9954 - 15.0418i) q^{62} +(0.803645 - 1.00774i) q^{63} +(8.30293 - 3.99848i) q^{64} +(-3.19391 + 1.53811i) q^{65} +(5.28830 - 6.63132i) q^{66} +(1.88403 + 2.36251i) q^{67} +(0.819128 - 0.394471i) q^{68} +(-0.564296 + 2.47234i) q^{69} +(-0.420275 + 1.84135i) q^{70} +(-1.26928 - 1.59162i) q^{71} +(-4.13487 - 1.99125i) q^{72} +(1.32313 + 5.79702i) q^{73} +(26.1456 + 12.5911i) q^{74} +(-2.89020 + 3.62419i) q^{75} +(-0.592971 + 2.59798i) q^{76} +(2.80841 - 3.52164i) q^{77} +(-3.17128 - 13.8943i) q^{78} +2.96949 q^{79} +2.02679 q^{80} +(-0.222521 - 0.974928i) q^{81} +(15.1606 + 19.0108i) q^{82} +(0.0585069 - 0.0281755i) q^{83} +(-4.51847 - 2.17598i) q^{84} -0.141070 q^{85} +(-8.18854 + 13.6475i) q^{86} -7.72999 q^{87} +(-14.4497 - 6.95861i) q^{88} +(4.53211 - 2.18255i) q^{89} +(0.913603 + 1.14562i) q^{90} +(-1.68415 - 7.37873i) q^{91} +9.86696 q^{92} -7.92676 q^{93} +(-4.17246 - 18.2808i) q^{94} +(0.257800 - 0.323271i) q^{95} +(0.229320 - 1.00472i) q^{96} +(-5.60727 + 7.03130i) q^{97} +(11.6742 + 5.62202i) q^{98} +(-0.777621 - 3.40698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 5 q^{3} - 14 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} + 8 q^{8} - 5 q^{9}+O(q^{10}) \) 30 * q - 2 * q^2 - 5 * q^3 - 14 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 + 8 * q^8 - 5 * q^9	\( 30 q - 2 q^{2} - 5 q^{3} - 14 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} + 8 q^{8} - 5 q^{9} - 10 q^{10} - 6 q^{11} - 7 q^{12} - 14 q^{13} + 9 q^{14} + 3 q^{15} + 16 q^{16} - 6 q^{17} - 2 q^{18} - 20 q^{19} + 22 q^{20} - 5 q^{21} - 4 q^{22} - 10 q^{23} + q^{24} + 9 q^{25} - 6 q^{26} - 5 q^{27} - 8 q^{28} + 16 q^{29} - 10 q^{30} + 14 q^{31} - 20 q^{32} + q^{33} - 10 q^{34} + 4 q^{35} + 42 q^{36} - 16 q^{37} - 4 q^{38} + 14 q^{39} + 14 q^{40} - q^{41} - 12 q^{42} + 3 q^{43} + 186 q^{44} + 3 q^{45} - 51 q^{46} - 15 q^{47} + 16 q^{48} + 40 q^{49} - 80 q^{50} - 6 q^{51} - 12 q^{52} + 23 q^{53} - 2 q^{54} - 25 q^{55} - 87 q^{56} + 29 q^{57} - 26 q^{59} + q^{60} - 4 q^{61} - 44 q^{62} - 12 q^{63} - 70 q^{64} - 5 q^{65} + 3 q^{66} + q^{67} - 48 q^{68} + 11 q^{69} - 33 q^{70} - 60 q^{71} - 6 q^{72} - 25 q^{73} + 144 q^{74} - 12 q^{75} + q^{76} - 6 q^{77} - 6 q^{78} + 142 q^{79} - 98 q^{80} - 5 q^{81} + 140 q^{82} + 7 q^{83} - 15 q^{84} - 20 q^{85} - 4 q^{86} + 2 q^{87} + 8 q^{88} + 4 q^{89} + 4 q^{90} - 40 q^{91} + 122 q^{92} - 14 q^{93} + 38 q^{94} + 140 q^{95} - 6 q^{96} + 6 q^{97} + 23 q^{98} + q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 5 * q^3 - 14 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 + 8 * q^8 - 5 * q^9 - 10 * q^10 - 6 * q^11 - 7 * q^12 - 14 * q^13 + 9 * q^14 + 3 * q^15 + 16 * q^16 - 6 * q^17 - 2 * q^18 - 20 * q^19 + 22 * q^20 - 5 * q^21 - 4 * q^22 - 10 * q^23 + q^24 + 9 * q^25 - 6 * q^26 - 5 * q^27 - 8 * q^28 + 16 * q^29 - 10 * q^30 + 14 * q^31 - 20 * q^32 + q^33 - 10 * q^34 + 4 * q^35 + 42 * q^36 - 16 * q^37 - 4 * q^38 + 14 * q^39 + 14 * q^40 - q^41 - 12 * q^42 + 3 * q^43 + 186 * q^44 + 3 * q^45 - 51 * q^46 - 15 * q^47 + 16 * q^48 + 40 * q^49 - 80 * q^50 - 6 * q^51 - 12 * q^52 + 23 * q^53 - 2 * q^54 - 25 * q^55 - 87 * q^56 + 29 * q^57 - 26 * q^59 + q^60 - 4 * q^61 - 44 * q^62 - 12 * q^63 - 70 * q^64 - 5 * q^65 + 3 * q^66 + q^67 - 48 * q^68 + 11 * q^69 - 33 * q^70 - 60 * q^71 - 6 * q^72 - 25 * q^73 + 144 * q^74 - 12 * q^75 + q^76 - 6 * q^77 - 6 * q^78 + 142 * q^79 - 98 * q^80 - 5 * q^81 + 140 * q^82 + 7 * q^83 - 15 * q^84 - 20 * q^85 - 4 * q^86 + 2 * q^87 + 8 * q^88 + 4 * q^89 + 4 * q^90 - 40 * q^91 + 122 * q^92 - 14 * q^93 + 38 * q^94 + 140 * q^95 - 6 * q^96 + 6 * q^97 + 23 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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