LMFDB - Embedded newform 350.2.h.c.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 241x^{12} + 1145x^{10} + 2841x^{8} + 3600x^{6} + 2156x^{4} + 480x^{2} + 16 $ x^16 + 25x^14 + 241x^12 + 1145x^10 + 2841x^8 + 3600x^6 + 2156x^4 + 480*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.2
Root			$-2.94531i$ of defining polynomial
Character	$\chi$	$=$	350.211
Dual form			350.2.h.c.141.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.0305168 + 0.0939212i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.05684 - 1.97056i) q^{5} +(-0.0305168 - 0.0939212i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(2.41916 + 1.75762i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.0305168 + 0.0939212i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.05684 - 1.97056i) q^{5} +(-0.0305168 - 0.0939212i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(2.41916 + 1.75762i) q^{9} +(2.01326 + 0.973023i) q^{10} +(0.490697 - 0.356512i) q^{11} +(0.0798941 + 0.0580465i) q^{12} +(-4.37894 - 3.18148i) q^{13} +(0.809017 - 0.587785i) q^{14} +(0.217328 - 0.0391240i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.55478 - 4.78513i) q^{17} -2.99025 q^{18} +(-2.40462 - 7.40066i) q^{19} +(-2.20069 + 0.396174i) q^{20} +(0.0305168 - 0.0939212i) q^{21} +(-0.187429 + 0.576849i) q^{22} +(5.59313 - 4.06365i) q^{23} -0.0987546 q^{24} +(-2.76620 + 4.16511i) q^{25} +5.41266 q^{26} +(-0.478586 + 0.347713i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(1.53328 - 4.71895i) q^{29} +(-0.152826 + 0.159394i) q^{30} +(2.84806 + 8.76544i) q^{31} +1.00000 q^{32} +(0.0185095 + 0.0569664i) q^{33} +(4.07048 + 2.95737i) q^{34} +(1.05684 + 1.97056i) q^{35} +(2.41916 - 1.75762i) q^{36} +(-6.70119 - 4.86870i) q^{37} +(6.29538 + 4.57386i) q^{38} +(0.432440 - 0.314186i) q^{39} +(1.54753 - 1.61405i) q^{40} +(1.64685 + 1.19651i) q^{41} +(0.0305168 + 0.0939212i) q^{42} +1.49575 q^{43} +(-0.187429 - 0.576849i) q^{44} +(0.906844 - 6.62462i) q^{45} +(-2.13639 + 6.57512i) q^{46} +(1.09893 - 3.38217i) q^{47} +(0.0798941 - 0.0580465i) q^{48} +1.00000 q^{49} +(-0.210289 - 4.99558i) q^{50} +0.496872 q^{51} +(-4.37894 + 3.18148i) q^{52} +(-1.59916 + 4.92170i) q^{53} +(0.182803 - 0.562611i) q^{54} +(-1.22111 - 0.590172i) q^{55} +(-0.309017 - 0.951057i) q^{56} +0.768460 q^{57} +(1.53328 + 4.71895i) q^{58} +(-2.05938 - 1.49623i) q^{59} +(0.0299490 - 0.218782i) q^{60} +(2.31563 - 1.68241i) q^{61} +(-7.45633 - 5.41734i) q^{62} +(-2.41916 - 1.75762i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.64148 + 11.9913i) q^{65} +(-0.0484585 - 0.0352072i) q^{66} +(1.70088 + 5.23476i) q^{67} -5.03138 q^{68} +(0.210978 + 0.649323i) q^{69} +(-2.01326 - 0.973023i) q^{70} +(2.27553 - 7.00336i) q^{71} +(-0.924037 + 2.84389i) q^{72} +(-12.6649 + 9.20156i) q^{73} +8.28312 q^{74} +(-0.306777 - 0.386911i) q^{75} -7.78152 q^{76} +(-0.490697 + 0.356512i) q^{77} +(-0.165177 + 0.508364i) q^{78} +(0.348205 - 1.07167i) q^{79} +(-0.303267 + 2.21541i) q^{80} +(2.75406 + 8.47612i) q^{81} -2.03562 q^{82} +(5.03013 + 15.4811i) q^{83} +(-0.0798941 - 0.0580465i) q^{84} +(-7.78623 + 8.12089i) q^{85} +(-1.21008 + 0.879178i) q^{86} +(0.396419 + 0.288015i) q^{87} +(0.490697 + 0.356512i) q^{88} +(10.3157 - 7.49479i) q^{89} +(3.16020 + 5.89246i) q^{90} +(4.37894 + 3.18148i) q^{91} +(-2.13639 - 6.57512i) q^{92} -0.910175 q^{93} +(1.09893 + 3.38217i) q^{94} +(-12.0421 + 12.5597i) q^{95} +(-0.0305168 + 0.0939212i) q^{96} +(-1.85365 + 5.70494i) q^{97} +(-0.809017 + 0.587785i) q^{98} +1.81369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.0305168	+	0.0939212i	−0.0176189	+	0.0542254i	−0.959479	−	0.281779i	$-0.909076\pi$
$3$	−0.0305168	+	0.0939212i	−0.0176189	+	0.0542254i	0.941861	+	0.336004i	$0.109076\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.05684	−	1.97056i	−0.472631	−	0.881260i
$5$	−1.05684	−	1.97056i	−0.472631	−	0.881260i
$6$	−0.0305168	−	0.0939212i	−0.0124585	−	0.0383432i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.41916	+	1.75762i	0.806387	+	0.585874i
$10$	2.01326	+	0.973023i	0.636650	+	0.307697i
$11$	0.490697	−	0.356512i	0.147951	−	0.107492i	−0.511348	−	0.859374i	$-0.670854\pi$
$11$	0.490697	−	0.356512i	0.147951	−	0.107492i	0.659298	+	0.751882i	$0.270854\pi$
$12$	0.0798941	+	0.0580465i	0.0230635	+	0.0167566i
$13$	−4.37894	−	3.18148i	−1.21450	−	0.882385i	−0.218867	−	0.975755i	$-0.570236\pi$
$13$	−4.37894	−	3.18148i	−1.21450	−	0.882385i	−0.995631	+	0.0933698i	$0.970236\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	0.217328	−	0.0391240i	0.0561140	−	0.0101018i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.55478	−	4.78513i	−0.377090	−	1.16056i	−0.942058	−	0.335451i	$-0.891111\pi$
$17$	−1.55478	−	4.78513i	−0.377090	−	1.16056i	0.564967	−	0.825113i	$-0.308889\pi$
$18$	−2.99025			−0.704808
$19$	−2.40462	−	7.40066i	−0.551658	−	1.69783i	−0.704610	−	0.709595i	$-0.748878\pi$
$19$	−2.40462	−	7.40066i	−0.551658	−	1.69783i	0.152952	−	0.988234i	$-0.451122\pi$
$20$	−2.20069	+	0.396174i	−0.492090	+	0.0885872i
$21$	0.0305168	−	0.0939212i	0.00665932	−	0.0204953i
$22$	−0.187429	+	0.576849i	−0.0399601	+	0.122985i
$23$	5.59313	−	4.06365i	1.16625	−	0.847329i	0.175693	−	0.984445i	$-0.443783\pi$
$23$	5.59313	−	4.06365i	1.16625	−	0.847329i	0.990555	+	0.137116i	$0.0437833\pi$
$24$	−0.0987546			−0.0201582
$25$	−2.76620	+	4.16511i	−0.553240	+	0.833022i
$26$	5.41266			1.06151
$27$	−0.478586	+	0.347713i	−0.0921039	+	0.0669174i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	1.53328	−	4.71895i	0.284723	−	0.876288i	−0.701758	−	0.712415i	$-0.747601\pi$
$29$	1.53328	−	4.71895i	0.284723	−	0.876288i	0.986482	−	0.163873i	$-0.0523986\pi$
$30$	−0.152826	+	0.159394i	−0.0279021	+	0.0291013i
$31$	2.84806	+	8.76544i	0.511527	+	1.57432i	0.789513	+	0.613734i	$0.210333\pi$
$31$	2.84806	+	8.76544i	0.511527	+	1.57432i	−0.277985	+	0.960585i	$0.589667\pi$
$32$	1.00000			0.176777
$33$	0.0185095	+	0.0569664i	0.00322209	+	0.00991658i
$34$	4.07048	+	2.95737i	0.698081	+	0.507185i
$35$	1.05684	+	1.97056i	0.178638	+	0.333085i
$36$	2.41916	−	1.75762i	0.403194	−	0.292937i
$37$	−6.70119	−	4.86870i	−1.10167	−	0.800409i	−0.120337	−	0.992733i	$-0.538398\pi$
$37$	−6.70119	−	4.86870i	−1.10167	−	0.800409i	−0.981331	+	0.192324i	$0.938398\pi$
$38$	6.29538	+	4.57386i	1.02125	+	0.741978i
$39$	0.432440	−	0.314186i	0.0692458	−	0.0503100i
$40$	1.54753	−	1.61405i	0.244686	−	0.255203i
$41$	1.64685	+	1.19651i	0.257195	+	0.186863i	0.708910	−	0.705299i	$-0.249187\pi$
$41$	1.64685	+	1.19651i	0.257195	+	0.186863i	−0.451714	+	0.892163i	$0.649187\pi$
$42$	0.0305168	+	0.0939212i	0.00470885	+	0.0144924i
$43$	1.49575			0.228099			0.114050	−	0.993475i	$-0.463618\pi$
$43$	1.49575			0.228099			0.114050	+	0.993475i	$0.463618\pi$
$44$	−0.187429	−	0.576849i	−0.0282561	−	0.0869632i
$45$	0.906844	−	6.62462i	0.135184	−	0.987539i
$46$	−2.13639	+	6.57512i	−0.314993	+	0.969448i
$47$	1.09893	−	3.38217i	0.160296	−	0.493341i	−0.838363	−	0.545113i	$-0.816487\pi$
$47$	1.09893	−	3.38217i	0.160296	−	0.493341i	0.998659	+	0.0517720i	$0.0164869\pi$
$48$	0.0798941	−	0.0580465i	0.0115317	−	0.00837829i
$49$	1.00000			0.142857
$50$	−0.210289	−	4.99558i	−0.0297394	−	0.706481i
$51$	0.496872			0.0695760
$52$	−4.37894	+	3.18148i	−0.607249	+	0.441192i
$53$	−1.59916	+	4.92170i	−0.219661	+	0.676048i	0.779129	+	0.626864i	$0.215662\pi$
$53$	−1.59916	+	4.92170i	−0.219661	+	0.676048i	−0.998790	+	0.0491834i	$0.984338\pi$
$54$	0.182803	−	0.562611i	0.0248764	−	0.0765617i
$55$	−1.22111	−	0.590172i	−0.164655	−	0.0795788i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$	0.768460			0.101785
$58$	1.53328	+	4.71895i	0.201330	+	0.619629i
$59$	−2.05938	−	1.49623i	−0.268108	−	0.194792i	0.445606	−	0.895229i	$-0.352988\pi$
$59$	−2.05938	−	1.49623i	−0.268108	−	0.194792i	−0.713714	+	0.700437i	$0.752988\pi$
$60$	0.0299490	−	0.218782i	0.00386640	−	0.0282446i
$61$	2.31563	−	1.68241i	0.296486	−	0.215410i	−0.429590	−	0.903024i	$-0.641342\pi$
$61$	2.31563	−	1.68241i	0.296486	−	0.215410i	0.726076	+	0.687614i	$0.241342\pi$
$62$	−7.45633	−	5.41734i	−0.946955	−	0.688003i
$63$	−2.41916	−	1.75762i	−0.304786	−	0.221440i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.64148	+	11.9913i	−0.203601	+	1.48733i
$66$	−0.0484585	−	0.0352072i	−0.00596484	−	0.00433371i
$67$	1.70088	+	5.23476i	0.207795	+	0.639528i	0.999587	+	0.0287370i	$0.00914854\pi$
$67$	1.70088	+	5.23476i	0.207795	+	0.639528i	−0.791792	+	0.610791i	$0.790851\pi$
$68$	−5.03138			−0.610145
$69$	0.210978	+	0.649323i	0.0253988	+	0.0781693i
$70$	−2.01326	−	0.973023i	−0.240631	−	0.116298i
$71$	2.27553	−	7.00336i	0.270056	−	0.831146i	−0.720429	−	0.693528i	$-0.756055\pi$
$71$	2.27553	−	7.00336i	0.270056	−	0.831146i	0.990485	−	0.137618i	$-0.0439447\pi$
$72$	−0.924037	+	2.84389i	−0.108899	+	0.335156i
$73$	−12.6649	+	9.20156i	−1.48231	+	1.07696i	−0.505505	+	0.862823i	$0.668694\pi$
$73$	−12.6649	+	9.20156i	−1.48231	+	1.07696i	−0.976804	+	0.214137i	$0.931306\pi$
$74$	8.28312			0.962894
$75$	−0.306777	−	0.386911i	−0.0354235	−	0.0446766i
$76$	−7.78152			−0.892601
$77$	−0.490697	+	0.356512i	−0.0559201	+	0.0406283i
$78$	−0.165177	+	0.508364i	−0.0187027	+	0.0575609i
$79$	0.348205	−	1.07167i	0.0391762	−	0.120572i	−0.929556	−	0.368681i	$-0.879809\pi$
$79$	0.348205	−	1.07167i	0.0391762	−	0.120572i	0.968732	+	0.248110i	$0.0798093\pi$
$80$	−0.303267	+	2.21541i	−0.0339063	+	0.247690i
$81$	2.75406	+	8.47612i	0.306007	+	0.941791i
$82$	−2.03562			−0.224797
$83$	5.03013	+	15.4811i	0.552128	+	1.69928i	0.703409	+	0.710786i	$0.251660\pi$
$83$	5.03013	+	15.4811i	0.552128	+	1.69928i	−0.151280	+	0.988491i	$0.548340\pi$
$84$	−0.0798941	−	0.0580465i	−0.00871717	−	0.00633339i
$85$	−7.78623	+	8.12089i	−0.844535	+	0.880834i
$86$	−1.21008	+	0.879178i	−0.130487	+	0.0948042i
$87$	0.396419	+	0.288015i	0.0425006	+	0.0308785i
$88$	0.490697	+	0.356512i	0.0523084	+	0.0380043i
$89$	10.3157	−	7.49479i	1.09346	−	0.794446i	0.113481	−	0.993540i	$-0.463800\pi$
$89$	10.3157	−	7.49479i	1.09346	−	0.794446i	0.979980	+	0.199094i	$0.0638000\pi$
$90$	3.16020	+	5.89246i	0.333114	+	0.621119i
$91$	4.37894	+	3.18148i	0.459037	+	0.333510i
$92$	−2.13639	−	6.57512i	−0.222734	−	0.685504i
$93$	−0.910175			−0.0943807
$94$	1.09893	+	3.38217i	0.113346	+	0.348844i
$95$	−12.0421	+	12.5597i	−1.23550	+	1.28860i
$96$	−0.0305168	+	0.0939212i	−0.00311461	+	0.00958579i
$97$	−1.85365	+	5.70494i	−0.188209	+	0.579249i	−0.999989	−	0.00471507i	$-0.998499\pi$
$97$	−1.85365	+	5.70494i	−0.188209	+	0.579249i	0.811779	+	0.583964i	$0.198499\pi$
$98$	−0.809017	+	0.587785i	−0.0817231	+	0.0593753i
$99$	1.81369			0.182283
$100$	3.10645	+	3.91790i	0.310645	+	0.391790i
$101$	4.76510			0.474145			0.237073	−	0.971492i	$-0.423812\pi$
$101$	4.76510			0.474145			0.237073	+	0.971492i	$0.423812\pi$
$102$	−0.401978	+	0.292054i	−0.0398018	+	0.0289177i
$103$	2.75177	−	8.46908i	0.271140	−	0.834483i	−0.719075	−	0.694933i	$-0.755434\pi$
$103$	2.75177	−	8.46908i	0.271140	−	0.834483i	0.990215	−	0.139551i	$-0.0445658\pi$
$104$	1.67261	−	5.14775i	0.164012	−	0.504778i
$105$	−0.217328	+	0.0391240i	−0.0212091	+	0.00381811i
$106$	−1.59916	−	4.92170i	−0.155324	−	0.478038i
$107$	13.5809			1.31292			0.656460	−	0.754361i	$-0.272053\pi$
$107$	13.5809			1.31292			0.656460	+	0.754361i	$0.272053\pi$
$108$	0.182803	+	0.562611i	0.0175903	+	0.0541373i
$109$	−14.4359	−	10.4883i	−1.38271	−	1.00460i	−0.996621	−	0.0821360i	$-0.973826\pi$
$109$	−14.4359	−	10.4883i	−1.38271	−	1.00460i	−0.386089	−	0.922462i	$-0.626174\pi$
$110$	1.33480	−	0.240293i	0.127268	−	0.0229111i
$111$	0.661773	−	0.480806i	0.0628127	−	0.0456361i
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	−0.835694	−	0.607167i	−0.0786155	−	0.0571175i	0.547783	−	0.836620i	$-0.315472\pi$
$113$	−0.835694	−	0.607167i	−0.0786155	−	0.0571175i	−0.626399	+	0.779503i	$0.715472\pi$
$114$	−0.621698	+	0.451690i	−0.0582273	+	0.0423046i
$115$	−13.9187	−	6.72698i	−1.29792	−	0.627294i
$116$	−4.01418	−	2.91647i	−0.372707	−	0.270788i
$117$	−5.00150	−	15.3930i	−0.462389	−	1.42309i
$118$	2.54553			0.234335
$119$	1.55478	+	4.78513i	0.142527	+	0.438652i
$120$	0.104367	+	0.194602i	0.00952739	+	0.0177646i
$121$	−3.28550	+	10.1117i	−0.298682	+	0.919249i
$122$	−0.884493	+	2.72219i	−0.0800782	+	0.246455i
$123$	−0.162634	+	0.118161i	−0.0146643	+	0.0106542i
$124$	9.21653			0.827669
$125$	11.1310	+	1.04912i	0.995588	+	0.0938360i
$126$	2.99025			0.266392
$127$	7.40399	−	5.37931i	0.656997	−	0.477337i	−0.208650	−	0.977990i	$-0.566907\pi$
$127$	7.40399	−	5.37931i	0.656997	−	0.477337i	0.865648	+	0.500654i	$0.166907\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.0456455	+	0.140482i	−0.00401886	+	0.0123688i
$130$	−5.72029	−	10.6660i	−0.501703	−	0.935467i
$131$	4.50999	+	13.8803i	0.394040	+	1.21273i	0.929707	+	0.368301i	$0.120060\pi$
$131$	4.50999	+	13.8803i	0.394040	+	1.21273i	−0.535667	+	0.844429i	$0.679940\pi$
$132$	0.0598981			0.00521346
$133$	2.40462	+	7.40066i	0.208507	+	0.641719i
$134$	−4.45296	−	3.23526i	−0.384677	−	0.279484i
$135$	1.19097	+	0.575606i	0.102503	+	0.0495402i
$136$	4.07048	−	2.95737i	0.349040	−	0.253593i
$137$	5.96460	+	4.33354i	0.509590	+	0.370239i	0.812668	−	0.582727i	$-0.198014\pi$
$137$	5.96460	+	4.33354i	0.509590	+	0.370239i	−0.303078	+	0.952966i	$0.598014\pi$
$138$	−0.552347	−	0.401304i	−0.0470189	−	0.0341613i
$139$	−2.11470	+	1.53642i	−0.179367	+	0.130318i	−0.673846	−	0.738872i	$-0.735359\pi$
$139$	−2.11470	+	1.53642i	−0.179367	+	0.130318i	0.494479	+	0.869189i	$0.335359\pi$
$140$	2.20069	−	0.396174i	0.185992	−	0.0334828i
$141$	0.284122	+	0.206427i	0.0239274	+	0.0173842i
$142$	2.27553	+	7.00336i	0.190958	+	0.587709i
$143$	−3.28297			−0.274535
$144$	−0.924037	−	2.84389i	−0.0770031	−	0.236991i
$145$	−10.9194	+	1.96574i	−0.906807	+	0.163246i
$146$	4.83754	−	14.8884i	0.400358	−	1.23218i
$147$	−0.0305168	+	0.0939212i	−0.00251699	+	0.00774649i
$148$	−6.70119	+	4.86870i	−0.550834	+	0.400205i
$149$	−19.8469			−1.62592			−0.812960	−	0.582320i	$-0.802145\pi$
$149$	−19.8469			−1.62592			−0.812960	+	0.582320i	$0.802145\pi$
$150$	0.475608	+	0.132699i	0.0388332	+	0.0108348i
$151$	21.7106			1.76678			0.883390	−	0.468638i	$-0.155255\pi$
$151$	21.7106			1.76678			0.883390	+	0.468638i	$0.155255\pi$
$152$	6.29538	−	4.57386i	0.510623	−	0.370989i
$153$	4.64919	−	14.3087i	0.375865	−	1.15679i
$154$	0.187429	−	0.576849i	0.0151035	−	0.0464838i
$155$	14.2629	−	14.8759i	1.14562	−	1.19486i
$156$	−0.165177	−	0.508364i	−0.0132248	−	0.0407017i
$157$	−4.82608			−0.385163			−0.192582	−	0.981281i	$-0.561686\pi$
$157$	−4.82608			−0.385163			−0.192582	+	0.981281i	$0.561686\pi$
$158$	0.348205	+	1.07167i	0.0277017	+	0.0852571i
$159$	−0.413451	−	0.300390i	−0.0327888	−	0.0238224i
$160$	−1.05684	−	1.97056i	−0.0835502	−	0.155786i
$161$	−5.59313	+	4.06365i	−0.440800	+	0.320260i
$162$	−7.21022	−	5.23853i	−0.566488	−	0.411578i
$163$	4.04486	+	2.93876i	0.316818	+	0.230181i	0.734816	−	0.678266i	$-0.237268\pi$
$163$	4.04486	+	2.93876i	0.316818	+	0.230181i	−0.417999	+	0.908448i	$0.637268\pi$
$164$	1.64685	−	1.19651i	0.128598	−	0.0934317i
$165$	0.0926942	−	0.0966782i	0.00721623	−	0.00752639i
$166$	−13.1691	−	9.56788i	−1.02212	−	0.742611i
$167$	−5.30352	−	16.3226i	−0.410399	−	1.26308i	−0.916302	−	0.400487i	$-0.868841\pi$
$167$	−5.30352	−	16.3226i	−0.410399	−	1.26308i	0.505904	−	0.862590i	$-0.331159\pi$
$168$	0.0987546			0.00761908
$169$	5.03603	+	15.4993i	0.387387	+	1.19225i
$170$	1.52585	−	11.1466i	0.117028	−	0.854903i
$171$	7.19041	−	22.1298i	0.549865	−	1.69231i
$172$	0.462211	−	1.42254i	0.0352433	−	0.108468i
$173$	12.1189	−	8.80489i	0.921383	−	0.669424i	−0.0224852	−	0.999747i	$-0.507158\pi$
$173$	12.1189	−	8.80489i	0.921383	−	0.669424i	0.943868	+	0.330324i	$0.107158\pi$
$174$	−0.490001			−0.0371469
$175$	2.76620	−	4.16511i	0.209105	−	0.314853i
$176$	−0.606534			−0.0457193
$177$	0.203373	−	0.147759i	0.0152865	−	0.0111063i
$178$	−3.94024	+	12.1268i	−0.295334	+	0.908944i
$179$	0.752606	−	2.31628i	0.0562524	−	0.173127i	−0.918983	−	0.394298i	$-0.870988\pi$
$179$	0.752606	−	2.31628i	0.0562524	−	0.173127i	0.975235	+	0.221171i	$0.0709878\pi$
$180$	−6.02015	−	2.90958i	−0.448716	−	0.216867i
$181$	−1.65059	−	5.07999i	−0.122687	−	0.377592i	0.870785	−	0.491663i	$-0.163611\pi$
$181$	−1.65059	−	5.07999i	−0.122687	−	0.377592i	−0.993473	+	0.114071i	$0.963611\pi$
$182$	−5.41266			−0.401213
$183$	0.0873477	+	0.268829i	0.00645693	+	0.0198724i
$184$	5.59313	+	4.06365i	0.412331	+	0.299576i
$185$	−2.51200	+	18.3505i	−0.184686	+	1.34916i
$186$	0.736347	−	0.534987i	0.0539916	−	0.0392272i
$187$	−2.46888	−	1.79375i	−0.180543	−	0.131172i
$188$	−2.87705	−	2.09030i	−0.209830	−	0.152451i
$189$	0.478586	−	0.347713i	0.0348120	−	0.0252924i
$190$	2.35988	−	17.2392i	0.171204	−	1.25067i
$191$	−14.0574	−	10.2133i	−1.01716	−	0.739010i	−0.0514612	−	0.998675i	$-0.516388\pi$
$191$	−14.0574	−	10.2133i	−1.01716	−	0.739010i	−0.965699	+	0.259665i	$0.916388\pi$
$192$	−0.0305168	−	0.0939212i	−0.00220236	−	0.00677818i
$193$	18.0469			1.29904			0.649522	−	0.760343i	$-0.274969\pi$
$193$	18.0469			1.29904			0.649522	+	0.760343i	$0.274969\pi$
$194$	−1.85365	−	5.70494i	−0.133084	−	0.409591i
$195$	−1.07614	−	0.520105i	−0.0770640	−	0.0372455i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−3.52694	+	10.8548i	−0.251284	+	0.773372i	0.743255	+	0.669008i	$0.233281\pi$
$197$	−3.52694	+	10.8548i	−0.251284	+	0.773372i	−0.994539	+	0.104364i	$0.966719\pi$
$198$	−1.46730	+	1.06606i	−0.104277	+	0.0757615i
$199$	16.9958			1.20480			0.602401	−	0.798193i	$-0.294211\pi$
$199$	16.9958			1.20480			0.602401	+	0.798193i	$0.294211\pi$
$200$	−4.81606	−	1.34372i	−0.340547	−	0.0950154i
$201$	−0.543561			−0.0383398
$202$	−3.85505	+	2.80086i	−0.271240	+	0.197067i
$203$	−1.53328	+	4.71895i	−0.107615	+	0.331206i
$204$	0.153542	−	0.472554i	0.0107501	−	0.0330854i
$205$	0.617338	−	4.50974i	0.0431168	−	0.314974i
$206$	2.75177	+	8.46908i	0.191725	+	0.590069i
$207$	20.6730			1.43688
$208$	1.67261	+	5.14775i	0.115974	+	0.356932i
$209$	−3.81836	−	2.77420i	−0.264122	−	0.191896i
$210$	0.152826	−	0.159394i	0.0105460	−	0.0109993i
$211$	2.34697	−	1.70517i	0.161572	−	0.117389i	−0.504061	−	0.863668i	$-0.668161\pi$
$211$	2.34697	−	1.70517i	0.161572	−	0.117389i	0.665633	+	0.746279i	$0.268161\pi$
$212$	4.18665	+	3.04178i	0.287540	+	0.208910i
$213$	0.588322	+	0.427441i	0.0403112	+	0.0292878i
$214$	−10.9872	+	7.98268i	−0.751071	+	0.545685i
$215$	−1.58076	−	2.94746i	−0.107807	−	0.201015i
$216$	−0.478586	−	0.347713i	−0.0325636	−	0.0236589i
$217$	−2.84806	−	8.76544i	−0.193339	−	0.595037i
$218$	17.8438			1.20853
$219$	−0.477730	−	1.47030i	−0.0322820	−	0.0993537i
$220$	−0.938631	+	0.978975i	−0.0632825	+	0.0660024i
$221$	−8.41552	+	25.9003i	−0.566089	+	1.74224i
$222$	−0.252775	+	0.777961i	−0.0169651	+	0.0522133i
$223$	−2.45060	+	1.78047i	−0.164105	+	0.119229i	−0.666807	−	0.745231i	$-0.732339\pi$
$223$	−2.45060	+	1.78047i	−0.164105	+	0.119229i	0.502702	+	0.864460i	$0.332339\pi$
$224$	−1.00000			−0.0668153
$225$	−14.0126	+	5.21414i	−0.934172	+	0.347609i
$226$	1.03297			0.0687125
$227$	13.2984	−	9.66185i	0.882646	−	0.641280i	−0.0513042	−	0.998683i	$-0.516338\pi$
$227$	13.2984	−	9.66185i	0.882646	−	0.641280i	0.933950	+	0.357403i	$0.116338\pi$
$228$	0.237467	−	0.730849i	0.0157267	−	0.0484017i
$229$	1.54977	−	4.76969i	0.102411	−	0.315190i	−0.886703	−	0.462340i	$-0.847010\pi$
$229$	1.54977	−	4.76969i	0.102411	−	0.315190i	0.989114	+	0.147150i	$0.0470100\pi$
$230$	15.2145	−	2.73895i	1.00321	−	0.180601i
$231$	−0.0185095	−	0.0569664i	−0.00121784	−	0.00374812i
$232$	4.96180			0.325758
$233$	−8.08617	−	24.8867i	−0.529742	−	1.63038i	−0.754743	−	0.656021i	$-0.772238\pi$
$233$	−8.08617	−	24.8867i	−0.529742	−	1.63038i	0.225000	−	0.974359i	$-0.427762\pi$
$234$	13.0941	+	9.51342i	0.855988	+	0.621912i
$235$	−7.82616	+	1.40889i	−0.510522	+	0.0919055i
$236$	−2.05938	+	1.49623i	−0.134054	+	0.0973961i
$237$	0.0900260	+	0.0654077i	0.00584782	+	0.00424869i
$238$	−4.07048	−	2.95737i	−0.263850	−	0.191698i
$239$	−10.8091	+	7.85328i	−0.699183	+	0.507987i	−0.879666	−	0.475592i	$-0.842234\pi$
$239$	−10.8091	+	7.85328i	−0.699183	+	0.507987i	0.180483	+	0.983578i	$0.442234\pi$
$240$	−0.198819	−	0.0960905i	−0.0128337	−	0.00620261i
$241$	−22.2513	−	16.1665i	−1.43333	−	1.04138i	−0.989384	−	0.145326i	$-0.953577\pi$
$241$	−22.2513	−	16.1665i	−1.43333	−	1.04138i	−0.443950	−	0.896052i	$-0.646423\pi$
$242$	−3.28550	−	10.1117i	−0.211200	−	0.650007i
$243$	−2.65483			−0.170307
$244$	−0.884493	−	2.72219i	−0.0566238	−	0.174270i
$245$	−1.05684	−	1.97056i	−0.0675187	−	0.125894i
$246$	0.0621208	−	0.191188i	0.00396068	−	0.0121897i
$247$	−13.0154	+	40.0573i	−0.828150	+	2.54878i
$248$	−7.45633	+	5.41734i	−0.473477	+	0.344001i
$249$	−1.60751			−0.101872
$250$	−9.62183	+	5.69389i	−0.608538	+	0.360113i
$251$	5.95489			0.375869			0.187935	−	0.982182i	$-0.439821\pi$
$251$	5.95489			0.375869			0.187935	+	0.982182i	$0.439821\pi$
$252$	−2.41916	+	1.75762i	−0.152393	+	0.110720i
$253$	1.29579	−	3.98804i	0.0814657	−	0.250726i
$254$	−2.82807	+	8.70391i	−0.177449	+	0.546132i
$255$	−0.525112	−	0.979116i	−0.0328838	−	0.0613146i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	20.5420			1.28137			0.640686	−	0.767803i	$-0.278650\pi$
$257$	20.5420			1.28137			0.640686	+	0.767803i	$0.278650\pi$
$258$	−0.0456455	−	0.140482i	−0.00284176	−	0.00874605i
$259$	6.70119	+	4.86870i	0.416392	+	0.302526i
$260$	10.8971	+	5.26664i	0.675810	+	0.326623i
$261$	12.0034	−	8.72098i	0.742992	−	0.539815i
$262$	−11.8073	−	8.57852i	−0.729458	−	0.529983i
$263$	4.52411	+	3.28696i	0.278968	+	0.202682i	0.718467	−	0.695561i	$-0.244844\pi$
$263$	4.52411	+	3.28696i	0.278968	+	0.202682i	−0.439499	+	0.898243i	$0.644844\pi$
$264$	−0.0484585	+	0.0352072i	−0.00298242	+	0.00216685i
$265$	11.3885	−	2.05019i	0.699593	−	0.125942i
$266$	−6.29538	−	4.57386i	−0.385994	−	0.280441i
$267$	0.389117	+	1.19758i	0.0238136	+	0.0732907i
$268$	5.50416			0.336220
$269$	1.58880	+	4.88981i	0.0968706	+	0.298137i	0.987737	−	0.156129i	$-0.0499016\pi$
$269$	1.58880	+	4.88981i	0.0968706	+	0.298137i	−0.890866	+	0.454266i	$0.849902\pi$
$270$	−1.30185	+	0.234363i	−0.0792281	+	0.0142629i
$271$	−2.20735	+	6.79352i	−0.134087	+	0.412677i	−0.995447	−	0.0953181i	$-0.969613\pi$
$271$	−2.20735	+	6.79352i	−0.134087	+	0.412677i	0.861360	+	0.507995i	$0.169613\pi$
$272$	−1.55478	+	4.78513i	−0.0942726	+	0.290141i
$273$	−0.432440	+	0.314186i	−0.0261725	+	0.0190154i
$274$	−7.37265			−0.445398
$275$	0.127548	+	3.02999i	0.00769142	+	0.182715i
$276$	0.682739			0.0410961
$277$	2.34766	−	1.70568i	0.141057	−	0.102484i	−0.515019	−	0.857179i	$-0.672215\pi$
$277$	2.34766	−	1.70568i	0.141057	−	0.102484i	0.656076	+	0.754695i	$0.272215\pi$
$278$	0.807744	−	2.48598i	0.0484453	−	0.149099i
$279$	−8.51642	+	26.2108i	−0.509865	+	1.56920i
$280$	−1.54753	+	1.61405i	−0.0924827	+	0.0964577i
$281$	−2.11627	−	6.51321i	−0.126246	−	0.388546i	0.867880	−	0.496774i	$-0.165482\pi$
$281$	−2.11627	−	6.51321i	−0.126246	−	0.388546i	−0.994126	+	0.108228i	$0.965482\pi$
$282$	−0.351194			−0.0209133
$283$	−2.20066	−	6.77292i	−0.130815	−	0.402608i	0.864100	−	0.503320i	$-0.167888\pi$
$283$	−2.20066	−	6.77292i	−0.130815	−	0.402608i	−0.994916	+	0.100711i	$0.967888\pi$
$284$	−5.95742	−	4.32832i	−0.353508	−	0.256838i
$285$	−0.812136	−	1.51430i	−0.0481068	−	0.0896992i
$286$	2.65598	−	1.92968i	0.157051	−	0.114104i
$287$	−1.64685	−	1.19651i	−0.0972107	−	0.0706277i
$288$	2.41916	+	1.75762i	0.142550	+	0.103569i
$289$	−6.72684	+	4.88734i	−0.395697	+	0.287490i
$290$	7.67855	−	8.00858i	0.450900	−	0.470280i
$291$	−0.479247	−	0.348194i	−0.0280940	−	0.0204115i
$292$	4.83754	+	14.8884i	0.283096	+	0.871279i
$293$	−5.78926			−0.338212			−0.169106	−	0.985598i	$-0.554088\pi$
$293$	−5.78926			−0.338212			−0.169106	+	0.985598i	$0.554088\pi$
$294$	−0.0305168	−	0.0939212i	−0.00177978	−	0.00547760i
$295$	−0.771977	+	5.63939i	−0.0449462	+	0.328338i
$296$	2.55963	−	7.87772i	0.148775	−	0.457883i
$297$	−0.110877	+	0.341243i	−0.00643371	+	0.0198009i
$298$	16.0565	−	11.6657i	0.930126	−	0.675776i
$299$	−37.4204			−2.16408
$300$	−0.462773	+	0.172200i	−0.0267182	+	0.00994196i
$301$	−1.49575			−0.0862134
$302$	−17.5642	+	12.7612i	−1.01071	+	0.734322i
$303$	−0.145416	+	0.447544i	−0.00835392	+	0.0257107i
$304$	−2.40462	+	7.40066i	−0.137914	+	0.424457i
$305$	−5.76252	−	2.78506i	−0.329961	−	0.159472i
$306$	4.64919	+	14.3087i	0.265776	+	0.817976i
$307$	10.3305			0.589591			0.294795	−	0.955560i	$-0.404749\pi$
$307$	10.3305			0.589591			0.294795	+	0.955560i	$0.404749\pi$
$308$	0.187429	+	0.576849i	0.0106798	+	0.0328690i
$309$	0.711451	+	0.516899i	0.0404730	+	0.0294054i
$310$	−2.79507	+	20.4184i	−0.158749	+	1.15969i
$311$	−0.102017	+	0.0741194i	−0.00578483	+	0.00420293i	−0.590674	−	0.806910i	$-0.701138\pi$
$311$	−0.102017	+	0.0741194i	−0.00578483	+	0.00420293i	0.584889	+	0.811113i	$0.301138\pi$
$312$	0.432440	+	0.314186i	0.0244821	+	0.0177873i
$313$	−13.4848	−	9.79730i	−0.762208	−	0.553776i	0.137379	−	0.990519i	$-0.456132\pi$
$313$	−13.4848	−	9.79730i	−0.762208	−	0.553776i	−0.899587	+	0.436742i	$0.856132\pi$
$314$	3.90438	−	2.83670i	0.220337	−	0.160084i
$315$	−0.906844	+	6.62462i	−0.0510949	+	0.373255i
$316$	−0.911613	−	0.662326i	−0.0512823	−	0.0372587i
$317$	−0.230137	−	0.708288i	−0.0129258	−	0.0397814i	0.944386	−	0.328840i	$-0.106658\pi$
$317$	−0.230137	−	0.708288i	−0.0129258	−	0.0397814i	−0.957311	+	0.289059i	$0.906658\pi$
$318$	0.511053			0.0286584
$319$	−0.929988	−	2.86221i	−0.0520693	−	0.160253i
$320$	2.01326	+	0.973023i	0.112545	+	0.0543936i
$321$	−0.414448	+	1.27554i	−0.0231322	+	0.0711936i
$322$	2.13639	−	6.57512i	0.119056	−	0.366417i
$323$	−31.6745	+	23.0129i	−1.76242	+	1.28047i
$324$	8.91232			0.495129
$325$	25.3642	−	9.43814i	1.40695	−	0.523534i
$326$	−4.99972			−0.276909
$327$	1.42561	−	1.03577i	0.0788366	−	0.0572781i
$328$	−0.629042	+	1.93599i	−0.0347331	+	0.106897i
$329$	−1.09893	+	3.38217i	−0.0605862	+	0.186465i
$330$	−0.0181651	+	0.132699i	−0.000999957	+	0.00730482i
$331$	2.42219	+	7.45474i	0.133136	+	0.409750i	0.995295	−	0.0968870i	$-0.0308886\pi$
$331$	2.42219	+	7.45474i	0.133136	+	0.409750i	−0.862160	+	0.506637i	$0.830889\pi$
$332$	16.2778			0.893363
$333$	−7.65392	−	23.5563i	−0.419432	−	1.29088i
$334$	13.8848	+	10.0879i	0.759742	+	0.551985i
$335$	8.51786	−	8.88396i	0.465380	−	0.485383i
$336$	−0.0798941	+	0.0580465i	−0.00435858	+	0.00316670i
$337$	17.4059	+	12.6462i	0.948162	+	0.688880i	0.950372	−	0.311117i	$-0.100703\pi$
$337$	17.4059	+	12.6462i	0.948162	+	0.688880i	−0.00220919	+	0.999998i	$0.500703\pi$
$338$	−13.1845	−	9.57909i	−0.717142	−	0.521034i
$339$	0.0825286	−	0.0599606i	0.00448234	−	0.00325661i
$340$	5.31735	+	9.91464i	0.288374	+	0.537697i
$341$	4.52252	+	3.28580i	0.244908	+	0.177936i
$342$	7.19041	+	22.1298i	0.388813	+	1.19664i
$343$	−1.00000			−0.0539949
$344$	0.462211	+	1.42254i	0.0249208	+	0.0766982i
$345$	1.05656	−	1.10197i	0.0568833	−	0.0593282i
$346$	−4.62901	+	14.2466i	−0.248857	+	0.765903i
$347$	1.74345	−	5.36578i	0.0935932	−	0.288050i	−0.893291	−	0.449478i	$-0.851610\pi$
$347$	1.74345	−	5.36578i	0.0935932	−	0.288050i	0.986884	+	0.161428i	$0.0516100\pi$
$348$	0.396419	−	0.288015i	0.0212503	−	0.0154392i
$349$	22.6817			1.21412			0.607061	−	0.794656i	$-0.292349\pi$
$349$	22.6817			1.21412			0.607061	+	0.794656i	$0.292349\pi$
$350$	0.210289	+	4.99558i	0.0112404	+	0.267025i
$351$	3.20194			0.170907
$352$	0.490697	−	0.356512i	0.0261542	−	0.0190022i
$353$	−0.815322	+	2.50930i	−0.0433952	+	0.133557i	−0.970407	−	0.241476i	$-0.922369\pi$
$353$	−0.815322	+	2.50930i	−0.0433952	+	0.133557i	0.927012	+	0.375033i	$0.122369\pi$
$354$	−0.0776817	+	0.239080i	−0.00412873	+	0.0127069i
$355$	−16.2054	+	2.91734i	−0.860093	+	0.154836i
$356$	−3.94024	−	12.1268i	−0.208832	−	0.642720i
$357$	−0.496872			−0.0262973
$358$	0.752606	+	2.31628i	0.0397765	+	0.122419i
$359$	−26.9828	−	19.6042i	−1.42410	−	1.03467i	−0.991078	−	0.133284i	$-0.957448\pi$
$359$	−26.9828	−	19.6042i	−1.42410	−	1.03467i	−0.433021	−	0.901384i	$-0.642552\pi$
$360$	6.58061	−	1.18466i	0.346829	−	0.0624370i
$361$	−33.6163	+	24.4237i	−1.76928	+	1.28546i
$362$	4.32129	+	3.13960i	0.227122	+	0.165014i
$363$	−0.849444	−	0.617157i	−0.0445842	−	0.0323923i
$364$	4.37894	−	3.18148i	0.229519	−	0.166755i
$365$	31.5169	+	15.2323i	1.64967	+	0.797295i
$366$	−0.228679	−	0.166145i	−0.0119533	−	0.00868455i
$367$	1.25720	+	3.86926i	0.0656252	+	0.201974i	0.978492	−	0.206283i	$-0.0661368\pi$
$367$	1.25720	+	3.86926i	0.0656252	+	0.201974i	−0.912867	+	0.408257i	$0.866137\pi$
$368$	−6.91349			−0.360391
$369$	1.88099	+	5.78910i	0.0979206	+	0.301368i
$370$	−8.75390	−	16.3224i	−0.455094	−	0.848560i
$371$	1.59916	−	4.92170i	0.0830241	−	0.255522i
$372$	−0.281259	+	0.865628i	−0.0145826	+	0.0448807i
$373$	22.6643	−	16.4666i	1.17351	−	0.852608i	0.182088	−	0.983282i	$-0.441714\pi$
$373$	22.6643	−	16.4666i	1.17351	−	0.852608i	0.991425	+	0.130675i	$0.0417143\pi$
$374$	3.05171			0.157800
$375$	−0.438218	+	1.01342i	−0.0226295	+	0.0523329i
$376$	3.55623			0.183398
$377$	−21.7274	+	15.7859i	−1.11902	+	0.813015i
$378$	−0.182803	+	0.562611i	−0.00940240	+	0.0289376i
$379$	0.492967	−	1.51720i	0.0253220	−	0.0779332i	−0.937597	−	0.347724i	$-0.886955\pi$
$379$	0.492967	−	1.51720i	0.0253220	−	0.0779332i	0.962919	+	0.269791i	$0.0869546\pi$
$380$	8.22378	+	15.3339i	0.421871	+	0.786614i
$381$	0.279285	+	0.859551i	0.0143082	+	0.0440361i
$382$	17.3759			0.889030
$383$	6.76535	+	20.8216i	0.345693	+	1.06393i	0.961212	+	0.275812i	$0.0889466\pi$
$383$	6.76535	+	20.8216i	0.345693	+	1.06393i	−0.615518	+	0.788122i	$0.711053\pi$
$384$	0.0798941	+	0.0580465i	0.00407708	+	0.00296217i
$385$	1.22111	+	0.590172i	0.0622337	+	0.0300779i
$386$	−14.6002	+	10.6077i	−0.743133	+	0.539917i
$387$	3.61845	+	2.62896i	0.183936	+	0.133637i
$388$	4.85291	+	3.52585i	0.246369	+	0.178998i
$389$	17.3486	−	12.6045i	0.879609	−	0.639074i	−0.0535386	−	0.998566i	$-0.517050\pi$
$389$	17.3486	−	12.6045i	0.879609	−	0.639074i	0.933148	+	0.359492i	$0.117050\pi$
$390$	1.17633	−	0.211765i	0.0595656	−	0.0107231i
$391$	−28.1412	−	20.4458i	−1.42316	−	1.03399i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	−1.44129			−0.0727034
$394$	−3.52694	−	10.8548i	−0.177684	−	0.546856i
$395$	−2.47978	+	0.446415i	−0.124771	+	0.0224616i
$396$	0.560460	−	1.72492i	0.0281642	−	0.0866805i
$397$	−5.92042	+	18.2212i	−0.297137	+	0.914495i	0.685358	+	0.728206i	$0.259646\pi$
$397$	−5.92042	+	18.2212i	−0.297137	+	0.914495i	−0.982495	+	0.186288i	$0.940354\pi$
$398$	−13.7499	+	9.98990i	−0.689221	+	0.500749i
$399$	−0.768460			−0.0384711
$400$	4.68609	−	1.74371i	0.234305	−	0.0871857i
$401$	−6.23910			−0.311566			−0.155783	−	0.987791i	$-0.549790\pi$
$401$	−6.23910			−0.311566			−0.155783	+	0.987791i	$0.549790\pi$
$402$	0.439750	−	0.319497i	0.0219327	−	0.0159351i
$403$	15.4156	−	47.4444i	0.767906	−	2.36337i
$404$	1.47250	−	4.53188i	0.0732595	−	0.225469i
$405$	13.7921	−	14.3849i	0.685335	−	0.714791i
$406$	−1.53328	−	4.71895i	−0.0760955	−	0.234198i
$407$	−5.02400			−0.249030
$408$	0.153542	+	0.472554i	0.00760146	+	0.0233949i
$409$	2.53779	+	1.84381i	0.125486	+	0.0911707i	0.648758	−	0.760995i	$-0.275289\pi$
$409$	2.53779	+	1.84381i	0.125486	+	0.0911707i	−0.523272	+	0.852166i	$0.675289\pi$
$410$	2.15132	+	4.01132i	0.106246	+	0.198105i
$411$	−0.589032	+	0.427957i	−0.0290548	+	0.0211095i
$412$	−7.20423	−	5.23418i	−0.354927	−	0.257869i
$413$	2.05938	+	1.49623i	0.101335	+	0.0736245i
$414$	−16.7248	+	12.1513i	−0.821981	+	0.597204i
$415$	25.1905	−	26.2732i	1.23655	−	1.28970i
$416$	−4.37894	−	3.18148i	−0.214695	−	0.155985i
$417$	−0.0797685	−	0.245502i	−0.00390628	−	0.0120223i
$418$	4.71976			0.230851
$419$	2.77122	+	8.52893i	0.135383	+	0.416666i	0.995649	−	0.0931789i	$-0.0297029\pi$
$419$	2.77122	+	8.52893i	0.135383	+	0.416666i	−0.860266	+	0.509845i	$0.829703\pi$
$420$	−0.0299490	+	0.218782i	−0.00146136	+	0.0106755i
$421$	6.33574	−	19.4994i	0.308785	−	0.950343i	−0.669452	−	0.742855i	$-0.733471\pi$
$421$	6.33574	−	19.4994i	0.308785	−	0.950343i	0.978238	−	0.207488i	$-0.0665288\pi$
$422$	−0.896463	+	2.75903i	−0.0436391	+	0.134307i
$423$	8.60309	−	6.25051i	0.418296	−	0.303910i
$424$	−5.17498			−0.251319
$425$	24.2314	+	6.76078i	1.17540	+	0.327946i
$426$	−0.727206			−0.0352333
$427$	−2.31563	+	1.68241i	−0.112061	+	0.0814173i
$428$	4.19674	−	12.9162i	0.202857	−	0.624330i
$429$	0.100186	−	0.308340i	0.00483702	−	0.0148868i
$430$	3.01133	+	1.45540i	0.145219	+	0.0701854i
$431$	1.58558	+	4.87992i	0.0763749	+	0.235058i	0.981954	−	0.189120i	$-0.0605634\pi$
$431$	1.58558	+	4.87992i	0.0763749	+	0.235058i	−0.905579	+	0.424177i	$0.860563\pi$
$432$	0.591564			0.0284617
$433$	−1.04514	−	3.21660i	−0.0502261	−	0.154580i	0.922798	−	0.385285i	$-0.125897\pi$
$433$	−1.04514	−	3.21660i	−0.0502261	−	0.154580i	−0.973024	+	0.230705i	$0.925897\pi$
$434$	7.45633	+	5.41734i	0.357915	+	0.260041i
$435$	0.148601	−	1.08555i	0.00712488	−	0.0520482i
$436$	−14.4359	+	10.4883i	−0.691355	+	0.502299i
$437$	−43.5230	−	31.6213i	−2.08199	−	1.51265i
$438$	1.25071	+	0.908696i	0.0597614	+	0.0434192i
$439$	−9.16080	+	6.65571i	−0.437221	+	0.317660i	−0.784530	−	0.620091i	$-0.787096\pi$
$439$	−9.16080	+	6.65571i	−0.437221	+	0.317660i	0.347309	+	0.937751i	$0.387096\pi$
$440$	0.183942	−	1.34372i	0.00876909	−	0.0640594i
$441$	2.41916	+	1.75762i	0.115198	+	0.0836964i
$442$	−8.41552	−	25.9003i	−0.400285	−	1.23195i
$443$	11.7342			0.557508			0.278754	−	0.960363i	$-0.410079\pi$
$443$	11.7342			0.557508			0.278754	+	0.960363i	$0.410079\pi$
$444$	−0.252775	−	0.777961i	−0.0119962	−	0.0369204i
$445$	−25.6709	−	12.4069i	−1.21692	−	0.588144i
$446$	0.936048	−	2.88086i	0.0443231	−	0.136413i
$447$	0.605664	−	1.86404i	0.0286469	−	0.0881662i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	7.06516			0.333425			0.166713	−	0.986006i	$-0.446685\pi$
$449$	7.06516			0.333425			0.166713	+	0.986006i	$0.446685\pi$
$450$	8.27162	−	12.4547i	0.389928	−	0.587121i
$451$	1.23468			0.0581386
$452$	−0.835694	+	0.607167i	−0.0393077	+	0.0285588i
$453$	−0.662538	+	2.03908i	−0.0311288	+	0.0958044i
$454$	−5.07954	+	15.6332i	−0.238395	+	0.733703i
$455$	1.64148	−	11.9913i	0.0769539	−	0.562159i
$456$	0.237467	+	0.730849i	0.0111204	+	0.0342252i
$457$	−1.59433			−0.0745797			−0.0372898	−	0.999304i	$-0.511872\pi$
$457$	−1.59433			−0.0745797			−0.0372898	+	0.999304i	$0.511872\pi$
$458$	1.54977	+	4.76969i	0.0724158	+	0.222873i
$459$	2.40795	+	1.74948i	0.112393	+	0.0816586i
$460$	−10.6988	+	11.1587i	−0.498836	+	0.520277i
$461$	−5.24210	+	3.80861i	−0.244149	+	0.177385i	−0.703130	−	0.711062i	$-0.748215\pi$
$461$	−5.24210	+	3.80861i	−0.244149	+	0.177385i	0.458981	+	0.888446i	$0.348215\pi$
$462$	0.0484585	+	0.0352072i	0.00225450	+	0.00163799i
$463$	−13.9315	−	10.1218i	−0.647453	−	0.470402i	0.214950	−	0.976625i	$-0.431041\pi$
$463$	−13.9315	−	10.1218i	−0.647453	−	0.470402i	−0.862403	+	0.506223i	$0.831041\pi$
$464$	−4.01418	+	2.91647i	−0.186354	+	0.135394i
$465$	0.961905	+	1.79355i	0.0446073	+	0.0831740i
$466$	21.1699	+	15.3808i	0.980675	+	0.712502i
$467$	0.454976	+	1.40027i	0.0210538	+	0.0647969i	0.961031	−	0.276439i	$-0.0891544\pi$
$467$	0.454976	+	1.40027i	0.0210538	+	0.0647969i	−0.939978	+	0.341236i	$0.889154\pi$
$468$	−16.1852			−0.748161
$469$	−1.70088	−	5.23476i	−0.0785393	−	0.241719i
$470$	5.50338	−	5.73991i	0.253852	−	0.264762i
$471$	0.147277	−	0.453271i	0.00678616	−	0.0208856i
$472$	0.786613	−	2.42095i	0.0362068	−	0.111433i
$473$	0.733958	−	0.533252i	0.0337474	−	0.0245189i
$474$	−0.111278			−0.00511118
$475$	37.4762	+	10.4562i	1.71953	+	0.479763i
$476$	5.03138			0.230613
$477$	−12.5191	+	9.09567i	−0.573211	+	0.416462i
$478$	4.12871	−	12.7069i	0.188843	−	0.581199i
$479$	2.09363	−	6.44352i	0.0956603	−	0.294412i	−0.891765	−	0.452499i	$-0.850533\pi$
$479$	2.09363	−	6.44352i	0.0956603	−	0.294412i	0.987425	+	0.158087i	$0.0505326\pi$
$480$	0.217328	−	0.0391240i	0.00991964	−	0.00178576i
$481$	13.8544	+	42.6394i	0.631706	+	1.94419i
$482$	27.5041			1.25278
$483$	−0.210978	−	0.649323i	−0.00959983	−	0.0295452i
$484$	8.60156	+	6.24940i	0.390980	+	0.284064i
$485$	13.2009	−	2.37646i	0.599423	−	0.107910i
$486$	2.14780	−	1.56047i	0.0974262	−	0.0707843i
$487$	25.7281	+	18.6925i	1.16585	+	0.847040i	0.990506	−	0.137468i	$-0.0438963\pi$
$487$	25.7281	+	18.6925i	1.16585	+	0.847040i	0.175344	+	0.984507i	$0.443896\pi$
$488$	2.31563	+	1.68241i	0.104824	+	0.0761589i
$489$	−0.399448	+	0.290216i	−0.0180637	+	0.0131240i
$490$	2.01326	+	0.973023i	0.0909499	+	0.0439567i
$491$	−20.9887	−	15.2492i	−0.947205	−	0.688185i	0.00293915	−	0.999996i	$-0.499064\pi$
$491$	−20.9887	−	15.2492i	−0.947205	−	0.688185i	−0.950144	+	0.311811i	$0.899064\pi$
$492$	0.0621208	+	0.191188i	0.00280062	+	0.00861943i
$493$	−24.9647			−1.12435
$494$	−13.0154	−	40.0573i	−0.585591	−	1.80226i
$495$	−1.91677	−	3.57398i	−0.0861524	−	0.160638i
$496$	2.84806	−	8.76544i	0.127882	−	0.393580i
$497$	−2.27553	+	7.00336i	−0.102072	+	0.314144i
$498$	1.30050	−	0.944872i	0.0582770	−	0.0423407i
$499$	−22.0077			−0.985202			−0.492601	−	0.870255i	$-0.663954\pi$
$499$	−22.0077			−0.985202			−0.492601	+	0.870255i	$0.663954\pi$
$500$	4.43744	−	10.2620i	0.198448	−	0.458932i
$501$	1.69488			0.0757217
$502$	−4.81760	+	3.50019i	−0.215020	+	0.156221i
$503$	−8.06098	+	24.8092i	−0.359421	+	1.10619i	0.593980	+	0.804480i	$0.297556\pi$
$503$	−8.06098	+	24.8092i	−0.359421	+	1.10619i	−0.953401	+	0.301705i	$0.902444\pi$
$504$	0.924037	−	2.84389i	0.0411599	−	0.126677i
$505$	−5.03593	−	9.38991i	−0.224096	−	0.417845i
$506$	1.29579	+	3.98804i	0.0576050	+	0.177290i
$507$	−1.60940			−0.0714758
$508$	−2.82807	−	8.70391i	−0.125475	−	0.386173i
$509$	10.1158	+	7.34954i	0.448374	+	0.325763i	0.788953	−	0.614453i	$-0.210623\pi$
$509$	10.1158	+	7.34954i	0.448374	+	0.325763i	−0.340580	+	0.940216i	$0.610623\pi$
$510$	1.00033	+	0.483468i	0.0442956	+	0.0214083i
$511$	12.6649	−	9.20156i	0.560260	−	0.407053i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	3.72412	+	2.70573i	0.164424	+	0.119461i
$514$	−16.6188	+	12.0743i	−0.733024	+	0.532573i
$515$	−19.5970	+	3.52790i	−0.863546	+	0.155458i
$516$	0.119501	+	0.0868228i	0.00526076	+	0.00382216i
$517$	−0.666542	−	2.05140i	−0.0293145	−	0.0902207i
$518$	−8.28312			−0.363940
$519$	0.457136	+	1.40692i	0.0200660	+	0.0617569i
$520$	−11.9116	+	2.14436i	−0.522359	+	0.0940363i
$521$	4.23515	−	13.0345i	0.185545	−	0.571050i	−0.814412	−	0.580287i	$-0.802940\pi$
$521$	4.23515	−	13.0345i	0.185545	−	0.571050i	0.999957	+	0.00923716i	$0.00294032\pi$
$522$	−4.58489	+	14.1108i	−0.200675	+	0.617615i
$523$	−1.19834	+	0.870642i	−0.0523996	+	0.0380705i	−0.613677	−	0.789557i	$-0.710310\pi$
$523$	−1.19834	+	0.870642i	−0.0523996	+	0.0380705i	0.561277	+	0.827628i	$0.310310\pi$
$524$	14.5946			0.637570
$525$	0.306777	+	0.386911i	0.0133888	+	0.0168862i
$526$	−5.59210			−0.243827
$527$	37.5157	−	27.2567i	1.63421	−	1.18732i
$528$	0.0185095	−	0.0569664i	0.000805523	−	0.00247915i
$529$	7.66249	−	23.5827i	0.333152	−	1.02534i
$530$	−8.00845	+	8.35266i	−0.347865	+	0.362816i
$531$	−2.35217	−	7.23923i	−0.102075	−	0.314156i
$532$	7.78152			0.337372
$533$	−3.40480	−	10.4789i	−0.147478	−	0.453891i
$534$	−1.01872	−	0.740145i	−0.0440844	−	0.0320292i
$535$	−14.3528	−	26.7620i	−0.620527	−	1.15702i
$536$	−4.45296	+	3.23526i	−0.192338	+	0.139742i
$537$	0.194581	+	0.141371i	0.00839679	+	0.00610062i
$538$	−4.15952	−	3.02207i	−0.179330	−	0.130291i
$539$	0.490697	−	0.356512i	0.0211358	−	0.0153561i
$540$	0.915465	−	0.954812i	0.0393953	−	0.0410886i
$541$	−11.9862	−	8.70849i	−0.515327	−	0.374407i	0.299513	−	0.954092i	$-0.403176\pi$
$541$	−11.9862	−	8.70849i	−0.515327	−	0.374407i	−0.814841	+	0.579685i	$0.803176\pi$
$542$	−2.20735	−	6.79352i	−0.0948137	−	0.291807i
$543$	0.527489			0.0226367
$544$	−1.55478	−	4.78513i	−0.0666608	−	0.205161i
$545$	−5.41143	+	39.5312i	−0.231800	+	1.69333i
$546$	0.165177	−	0.508364i	0.00706894	−	0.0217560i
$547$	−10.6127	+	32.6625i	−0.453765	+	1.39655i	0.418813	+	0.908072i	$0.362446\pi$
$547$	−10.6127	+	32.6625i	−0.453765	+	1.39655i	−0.872579	+	0.488474i	$0.837554\pi$
$548$	5.96460	−	4.33354i	0.254795	−	0.185119i
$549$	8.55892			0.365286
$550$	−1.88417	−	2.37634i	−0.0803413	−	0.101328i
$551$	−38.6103			−1.64486
$552$	−0.552347	+	0.401304i	−0.0235095	+	0.0170806i
$553$	−0.348205	+	1.07167i	−0.0148072	+	0.0455719i
$554$	−0.896727	+	2.75984i	−0.0380983	+	0.117254i
$555$	−1.64684	−	0.795929i	−0.0699046	−	0.0337853i
$556$	0.807744	+	2.48598i	0.0342560	+	0.105429i
$557$	30.8069			1.30533			0.652664	−	0.757647i	$-0.273651\pi$
$557$	30.8069			1.30533			0.652664	+	0.757647i	$0.273651\pi$
$558$	−8.51642	−	26.2108i	−0.360529	−	1.10959i
$559$	−6.54978	−	4.75869i	−0.277026	−	0.201271i
$560$	0.303267	−	2.21541i	0.0128154	−	0.0936180i
$561$	0.243814	−	0.177141i	0.0102938	−	0.00747890i
$562$	5.54047	+	4.02539i	0.233711	+	0.169801i
$563$	−7.17904	−	5.21588i	−0.302560	−	0.219823i	0.426137	−	0.904658i	$-0.359874\pi$
$563$	−7.17904	−	5.21588i	−0.302560	−	0.219823i	−0.728698	+	0.684836i	$0.759874\pi$
$564$	0.284122	−	0.206427i	0.0119637	−	0.00869212i
$565$	−0.313267	+	2.28846i	−0.0131793	+	0.0962762i
$566$	5.76139	+	4.18590i	0.242169	+	0.175946i
$567$	−2.75406	−	8.47612i	−0.115660	−	0.355964i
$568$	7.36377			0.308977
$569$	6.13667	+	18.8867i	0.257263	+	0.791773i	0.993375	+	0.114914i	$0.0366594\pi$
$569$	6.13667	+	18.8867i	0.257263	+	0.791773i	−0.736113	+	0.676859i	$0.763341\pi$
$570$	1.54711	+	0.747730i	0.0648014	+	0.0313189i
$571$	7.45052	−	22.9304i	0.311795	−	0.959605i	−0.665259	−	0.746613i	$-0.731679\pi$
$571$	7.45052	−	22.9304i	0.311795	−	0.959605i	0.977054	−	0.212993i	$-0.0683211\pi$
$572$	−1.01449	+	3.12229i	−0.0424181	+	0.130549i
$573$	1.38824	−	1.00861i	0.0579944	−	0.0421354i
$574$	2.03562			0.0849653
$575$	1.45383	+	34.5369i	0.0606290	+	1.44029i
$576$	−2.99025			−0.124594
$577$	−6.42832	+	4.67044i	−0.267614	+	0.194433i	−0.713497	−	0.700658i	$-0.752890\pi$
$577$	−6.42832	+	4.67044i	−0.267614	+	0.194433i	0.445883	+	0.895091i	$0.352890\pi$
$578$	2.56943	−	7.90788i	0.106874	−	0.328924i
$579$	−0.550734	+	1.69499i	−0.0228877	+	0.0704412i
$580$	−1.50475	+	10.9924i	−0.0624814	+	0.456435i
$581$	−5.03013	−	15.4811i	−0.208685	−	0.642266i
$582$	0.592382			0.0245550
$583$	0.969944	+	2.98518i	0.0401710	+	0.123634i
$584$	−12.6649	−	9.20156i	−0.524075	−	0.380763i
$585$	−25.0471	+	26.1237i	−1.03557	+	1.08008i
$586$	4.68361	−	3.40284i	0.193478	−	0.140570i
$587$	−16.3200	−	11.8571i	−0.673597	−	0.489397i	0.197630	−	0.980277i	$-0.436675\pi$
$587$	−16.3200	−	11.8571i	−0.673597	−	0.489397i	−0.871227	+	0.490880i	$0.836675\pi$
$588$	0.0798941	+	0.0580465i	0.00329478	+	0.00239380i
$589$	58.0215	−	42.1551i	2.39074	−	1.73697i
$590$	−2.69021	−	5.01612i	−0.110754	−	0.206511i
$591$	−0.911864	−	0.662508i	−0.0375091	−	0.0272519i
$592$	2.55963	+	7.87772i	0.105200	+	0.323772i
$593$	35.5527			1.45998			0.729988	−	0.683460i	$-0.239526\pi$
$593$	35.5527			1.45998			0.729988	+	0.683460i	$0.239526\pi$
$594$	−0.110877	−	0.341243i	−0.00454932	−	0.0140014i
$595$	7.78623	−	8.12089i	0.319204	−	0.332924i
$596$	−6.13302	+	18.8755i	−0.251218	+	0.773171i
$597$	−0.518659	+	1.59627i	−0.0212273	+	0.0653310i
$598$	30.2737	−	21.9952i	1.23799	−	0.899449i
$599$	−39.8279			−1.62732			−0.813662	−	0.581339i	$-0.802529\pi$
$599$	−39.8279			−1.62732			−0.813662	+	0.581339i	$0.802529\pi$
$600$	0.273175	−	0.411324i	0.0111523	−	0.0167922i
$601$	19.4394			0.792950			0.396475	−	0.918046i	$-0.370233\pi$
$601$	19.4394			0.792950			0.396475	+	0.918046i	$0.370233\pi$
$602$	1.21008	−	0.879178i	0.0493194	−	0.0358326i
$603$	−5.08605	+	15.6532i	−0.207120	+	0.637449i
$604$	6.70893	−	20.6480i	0.272983	−	0.840154i
$605$	23.3980	−	4.21217i	0.951265	−	0.171249i
$606$	−0.145416	−	0.447544i	−0.00590711	−	0.0181802i
$607$	−3.33371			−0.135311			−0.0676555	−	0.997709i	$-0.521552\pi$
$607$	−3.33371			−0.135311			−0.0676555	+	0.997709i	$0.521552\pi$
$608$	−2.40462	−	7.40066i	−0.0975203	−	0.300136i
$609$	−0.396419	−	0.288015i	−0.0160637	−	0.0116710i
$610$	6.29899	−	1.13396i	0.255039	−	0.0459127i
$611$	−15.5725	+	11.3141i	−0.629996	+	0.457719i
$612$	−12.1717	−	8.84328i	−0.492013	−	0.357468i
$613$	−18.1470	−	13.1846i	−0.732952	−	0.532520i	0.157544	−	0.987512i	$-0.449642\pi$
$613$	−18.1470	−	13.1846i	−0.732952	−	0.532520i	−0.890496	+	0.454991i	$0.849642\pi$
$614$	−8.35752	+	6.07209i	−0.337282	+	0.245050i
$615$	0.404721	+	0.195604i	0.0163199	+	0.00788752i
$616$	−0.490697	−	0.356512i	−0.0197707	−	0.0143643i
$617$	−1.63256	−	5.02450i	−0.0657244	−	0.202279i	0.912801	−	0.408404i	$-0.133915\pi$
$617$	−1.63256	−	5.02450i	−0.0657244	−	0.202279i	−0.978526	+	0.206125i	$0.933915\pi$
$618$	−0.879401			−0.0353747
$619$	7.94660	+	24.4571i	0.319401	+	0.983015i	0.973905	+	0.226956i	$0.0728775\pi$
$619$	7.94660	+	24.4571i	0.319401	+	0.983015i	−0.654504	+	0.756058i	$0.727123\pi$
$620$	−9.74035	−	18.1617i	−0.391182	−	0.729392i
$621$	−1.26381	+	3.88961i	−0.0507149	+	0.156085i
$622$	0.0389669	−	0.119928i	0.00156243	−	0.00480866i
$623$	−10.3157	+	7.49479i	−0.413289	+	0.300272i
$624$	−0.534525			−0.0213981
$625$	−9.69630	−	23.0430i	−0.387852	−	0.921722i
$626$	16.6682			0.666194
$627$	0.377081	−	0.273965i	0.0150592	−	0.0109411i
$628$	−1.49134	+	4.58988i	−0.0595110	+	0.183156i
$629$	−12.8785	+	39.6358i	−0.513498	+	1.58038i
$630$	−3.16020	−	5.89246i	−0.125905	−	0.234761i
$631$	−4.23986	−	13.0489i	−0.168786	−	0.519470i	0.830509	−	0.557005i	$-0.188050\pi$
$631$	−4.23986	−	13.0489i	−0.168786	−	0.519470i	−0.999295	+	0.0375346i	$0.988050\pi$
$632$	1.12682			0.0448223
$633$	0.0885298	+	0.272467i	0.00351874	+	0.0108296i
$634$	0.602506	+	0.437746i	0.0239286	+	0.0173851i
$635$	−18.4250	−	8.90494i	−0.731175	−	0.353382i
$636$	−0.413451	+	0.300390i	−0.0163944	+	0.0119112i
$637$	−4.37894	−	3.18148i	−0.173500	−	0.126055i
$638$	2.43474	+	1.76894i	0.0963923	+	0.0700331i
$639$	17.8142	−	12.9427i	0.704717	−	0.512007i
$640$	−2.20069	+	0.396174i	−0.0869900	+	0.0156602i
$641$	24.9534	+	18.1297i	0.985599	+	0.716079i	0.958953	−	0.283566i	$-0.0915174\pi$
$641$	24.9534	+	18.1297i	0.985599	+	0.716079i	0.0266457	+	0.999645i	$0.491517\pi$
$642$	−0.414448	−	1.27554i	−0.0163569	−	0.0503415i
$643$	7.26438			0.286479			0.143240	−	0.989688i	$-0.454248\pi$
$643$	7.26438			0.286479			0.143240	+	0.989688i	$0.454248\pi$
$644$	2.13639	+	6.57512i	0.0841854	+	0.259096i
$645$	0.325068	−	0.0585196i	0.0127996	−	0.00230421i
$646$	12.0986	−	37.2356i	0.476012	−	1.46501i
$647$	−11.5169	+	35.4455i	−0.452777	+	1.39350i	0.420948	+	0.907085i	$0.361697\pi$
$647$	−11.5169	+	35.4455i	−0.452777	+	1.39350i	−0.873725	+	0.486420i	$0.838303\pi$
$648$	−7.21022	+	5.23853i	−0.283244	+	0.205789i
$649$	−1.54395			−0.0606055
$650$	−14.9725	+	22.5443i	−0.587270	+	0.884262i
$651$	0.910175			0.0356726
$652$	4.04486	−	2.93876i	0.158409	−	0.115091i
$653$	−3.32586	+	10.2359i	−0.130151	+	0.400563i	−0.994804	−	0.101805i	$-0.967538\pi$
$653$	−3.32586	+	10.2359i	−0.130151	+	0.400563i	0.864653	+	0.502369i	$0.167538\pi$
$654$	−0.544536	+	1.67591i	−0.0212930	+	0.0655332i
$655$	22.5857	−	23.5564i	0.882496	−	0.920426i
$656$	−0.629042	−	1.93599i	−0.0245600	−	0.0755878i
$657$	−46.8112			−1.82628
$658$	−1.09893	−	3.38217i	−0.0428409	−	0.131851i
$659$	38.7327	+	28.1409i	1.50881	+	1.09621i	0.966702	+	0.255906i	$0.0823737\pi$
$659$	38.7327	+	28.1409i	1.50881	+	1.09621i	0.542108	+	0.840309i	$0.317626\pi$
$660$	−0.0633024	−	0.118033i	−0.00246404	−	0.00459441i
$661$	−2.65233	+	1.92703i	−0.103164	+	0.0749529i	−0.638171	−	0.769894i	$-0.720309\pi$
$661$	−2.65233	+	1.92703i	−0.103164	+	0.0749529i	0.535007	+	0.844847i	$0.320309\pi$
$662$	−6.34138	−	4.60728i	−0.246465	−	0.179067i
$663$	−2.17577	−	1.58079i	−0.0845000	−	0.0613929i
$664$	−13.1691	+	9.56788i	−0.511058	+	0.371306i
$665$	12.0421	−	12.5597i	0.466974	−	0.487045i
$666$	20.0382	+	14.5586i	0.776465	+	0.564135i
$667$	−10.6003	−	32.6244i	−0.410446	−	1.26322i
$668$	−17.1626			−0.664039
$669$	−0.0924390	−	0.284498i	−0.00357390	−	0.0109993i
$670$	−1.66923	+	12.1939i	−0.0644880	+	0.471093i
$671$	0.536475	−	1.65110i	0.0207104	−	0.0637401i
$672$	0.0305168	−	0.0939212i	0.00117721	−	0.00362309i
$673$	28.5825	−	20.7664i	1.10178	−	0.800487i	0.120427	−	0.992722i	$-0.461574\pi$
$673$	28.5825	−	20.7664i	1.10178	−	0.800487i	0.981349	+	0.192235i	$0.0615736\pi$
$674$	−21.5149			−0.828724
$675$	−0.124400	−	2.95521i	−0.00478815	−	0.113746i
$676$	16.2969			0.626805
$677$	35.3229	−	25.6636i	1.35757	−	0.986332i	0.358975	−	0.933347i	$-0.383126\pi$
$677$	35.3229	−	25.6636i	1.35757	−	0.986332i	0.998595	−	0.0529851i	$-0.0168736\pi$
$678$	−0.0315231	+	0.0970182i	−0.00121064	+	0.00372596i
$679$	1.85365	−	5.70494i	0.0711365	−	0.218936i
$680$	−10.1295	−	4.89565i	−0.388449	−	0.187740i
$681$	0.501628	+	1.54385i	0.0192224	+	0.0591605i
$682$	−5.59014			−0.214058
$683$	6.10520	+	18.7899i	0.233609	+	0.718974i	0.997303	+	0.0733959i	$0.0233837\pi$
$683$	6.10520	+	18.7899i	0.233609	+	0.718974i	−0.763694	+	0.645578i	$0.776616\pi$
$684$	−18.8247	−	13.6770i	−0.719782	−	0.522952i
$685$	2.23588	−	16.3334i	0.0854287	−	0.624068i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	0.400681	+	0.291112i	0.0152869	+	0.0111066i
$688$	−1.21008	−	0.879178i	−0.0461340	−	0.0335183i
$689$	22.6609	−	16.4641i	0.863312	−	0.627233i
$690$	−0.207052	+	1.51254i	−0.00788235	+	0.0575816i
$691$	29.5565	+	21.4741i	1.12438	+	0.816913i	0.984868	−	0.173307i	$-0.0554454\pi$
$691$	29.5565	+	21.4741i	1.12438	+	0.816913i	0.139516	+	0.990220i	$0.455445\pi$
$692$	−4.62901	−	14.2466i	−0.175968	−	0.541575i
$693$	−1.81369			−0.0688963
$694$	1.74345	+	5.36578i	0.0661804	+	0.203682i
$695$	5.26250	+	2.54340i	0.199618	+	0.0964766i
$696$	−0.151419	+	0.466018i	−0.00573950	+	0.0176644i
$697$	3.16495	−	9.74073i	0.119881	−	0.368956i
$698$	−18.3498	+	13.3319i	−0.694552	+	0.504621i
$699$	2.58415			0.0977415
$700$	−3.10645	−	3.91790i	−0.117413	−	0.148083i
$701$	−8.24513			−0.311414			−0.155707	−	0.987803i	$-0.549766\pi$
$701$	−8.24513			−0.311414			−0.155707	+	0.987803i	$0.549766\pi$
$702$	−2.59042	+	1.88205i	−0.0977692	+	0.0710335i
$703$	−19.9178	+	61.3006i	−0.751213	+	2.31200i
$704$	−0.187429	+	0.576849i	−0.00706401	+	0.0217408i
$705$	0.106506	−	0.778037i	0.00401123	−	0.0293026i
$706$	−0.815322	−	2.50930i	−0.0306850	−	0.0944389i
$707$	−4.76510			−0.179210
$708$	−0.0776817	−	0.239080i	−0.00291946	−	0.00898516i
$709$	25.8675	+	18.7938i	0.971475	+	0.705818i	0.955787	−	0.294059i	$-0.0950063\pi$
$709$	25.8675	+	18.7938i	0.971475	+	0.705818i	0.0156876	+	0.999877i	$0.495006\pi$
$710$	11.3957	−	11.8855i	0.427672	−	0.446054i
$711$	2.72595	−	1.98052i	0.102231	−	0.0742752i
$712$	10.3157	+	7.49479i	0.386597	+	0.280879i
$713$	51.5493	+	37.4527i	1.93053	+	1.40262i
$714$	0.401978	−	0.292054i	0.0150437	−	0.0109299i
$715$	3.46956	+	6.46928i	0.129754	+	0.241937i
$716$	−1.97035	−	1.43154i	−0.0736354	−	0.0534992i
$717$	−0.407730	−	1.25486i	−0.0152269	−	0.0468637i
$718$	33.3526			1.24471
$719$	6.85143	+	21.0865i	0.255515	+	0.786395i	0.993728	+	0.111827i	$0.0356702\pi$
$719$	6.85143	+	21.0865i	0.255515	+	0.786395i	−0.738213	+	0.674568i	$0.764330\pi$
$720$	−4.62750	+	4.82640i	−0.172457	+	0.179869i
$721$	−2.75177	+	8.46908i	−0.102481	+	0.315405i
$722$	12.8403	−	39.5183i	0.477866	−	1.47072i
$723$	2.19742	−	1.59652i	0.0817229	−	0.0593752i
$724$	−5.34141			−0.198512
$725$	15.4136	+	19.4398i	0.572447	+	0.721978i
$726$	1.04997			0.0389681
$727$	−32.5322	+	23.6360i	−1.20655	+	0.876612i	−0.994913	−	0.100735i	$-0.967881\pi$
$727$	−32.5322	+	23.6360i	−1.20655	+	0.876612i	−0.211640	+	0.977348i	$0.567881\pi$
$728$	−1.67261	+	5.14775i	−0.0619909	+	0.190788i
$729$	−8.18116	+	25.1790i	−0.303006	+	0.932556i
$730$	−34.4510	+	6.20196i	−1.27509	+	0.229545i
$731$	−2.32556	−	7.15734i	−0.0860140	−	0.264724i
$732$	0.282663			0.0104475
$733$	5.14950	+	15.8485i	0.190201	+	0.585378i	0.999999	−	0.00133019i	$-0.000423414\pi$
$733$	5.14950	+	15.8485i	0.190201	+	0.585378i	−0.809798	+	0.586709i	$0.800423\pi$
$734$	−3.29139	−	2.39133i	−0.121487	−	0.0882657i
$735$	0.217328	−	0.0391240i	0.00801628	−	0.00144311i
$736$	5.59313	−	4.06365i	0.206166	−	0.149788i
$737$	2.70087	+	1.96230i	0.0994879	+	0.0722822i
$738$	−4.92450	−	3.57786i	−0.181273	−	0.131703i
$739$	4.32501	−	3.14230i	0.159098	−	0.115591i	−0.505388	−	0.862892i	$-0.668651\pi$
$739$	4.32501	−	3.14230i	0.159098	−	0.115591i	0.664486	+	0.747301i	$0.268651\pi$
$740$	16.6761	+	8.05967i	0.613026	+	0.296279i
$741$	−3.36504	−	2.44484i	−0.123618	−	0.0898136i
$742$	1.59916	+	4.92170i	0.0587069	+	0.180681i
$743$	−18.6992			−0.686007			−0.343003	−	0.939334i	$-0.611444\pi$
$743$	−18.6992			−0.686007			−0.343003	+	0.939334i	$0.611444\pi$
$744$	−0.281259	−	0.865628i	−0.0103115	−	0.0317354i
$745$	20.9749	+	39.1094i	0.768460	+	1.43286i
$746$	−8.65700	+	26.6435i	−0.316955	+	0.975488i
$747$	−15.0413	+	46.2925i	−0.550334	+	1.69375i
$748$	−2.46888	+	1.79375i	−0.0902713	+	0.0655860i
$749$	−13.5809			−0.496237
$750$	−0.241149	−	1.07745i	−0.00880551	−	0.0393430i
$751$	49.3643			1.80133			0.900665	−	0.434514i	$-0.143080\pi$
$751$	49.3643			1.80133			0.900665	+	0.434514i	$0.143080\pi$
$752$	−2.87705	+	2.09030i	−0.104915	+	0.0762253i
$753$	−0.181724	+	0.559290i	−0.00662240	+	0.0203817i
$754$	8.29913	−	25.5421i	0.302237	−	0.930189i
$755$	−22.9445	−	42.7819i	−0.835036	−	1.55699i
$756$	−0.182803	−	0.562611i	−0.00664850	−	0.0204620i
$757$	−16.4889			−0.599299			−0.299650	−	0.954049i	$-0.596870\pi$
$757$	−16.4889			−0.599299			−0.299650	+	0.954049i	$0.596870\pi$
$758$	0.492967	+	1.51720i	0.0179054	+	0.0551071i
$759$	0.335018	+	0.243405i	0.0121604	+	0.00883503i
$760$	−15.6662	−	7.57159i	−0.568274	−	0.274651i
$761$	−27.8671	+	20.2467i	−1.01018	+	0.733941i	−0.964247	−	0.265004i	$-0.914627\pi$
$761$	−27.8671	+	20.2467i	−1.01018	+	0.733941i	−0.0459354	+	0.998944i	$0.514627\pi$
$762$	−0.731178	−	0.531232i	−0.0264878	−	0.0192445i
$763$	14.4359	+	10.4883i	0.522615	+	0.379702i
$764$	−14.0574	+	10.2133i	−0.508580	+	0.369505i
$765$	−33.1096	+	5.96048i	−1.19708	+	0.215501i
$766$	−17.7119	−	12.8685i	−0.639957	−	0.464956i
$767$	4.25767	+	13.1038i	0.153736	+	0.473150i
$768$	−0.0987546			−0.00356350
$769$	−7.28167	−	22.4107i	−0.262584	−	0.808150i	−0.992240	−	0.124336i	$-0.960320\pi$
$769$	−7.28167	−	22.4107i	−0.262584	−	0.808150i	0.729656	−	0.683814i	$-0.239680\pi$
$770$	−1.33480	+	0.240293i	−0.0481027	+	0.00865957i
$771$	−0.626876	+	1.92933i	−0.0225764	+	0.0694830i
$772$	5.57679	−	17.1636i	0.200713	−	0.617732i
$773$	−12.9599	+	9.41592i	−0.466135	+	0.338667i	−0.795933	−	0.605384i	$-0.793019\pi$
$773$	−12.9599	+	9.41592i	−0.466135	+	0.338667i	0.329798	+	0.944052i	$0.393019\pi$
$774$	−4.47265			−0.160766
$775$	−44.3873	−	12.3844i	−1.59444	−	0.444862i
$776$	−5.99853			−0.215335
$777$	−0.661773	+	0.480806i	−0.0237410	+	0.0172488i
$778$	−6.62658	+	20.3945i	−0.237574	+	0.731179i
$779$	4.89490	−	15.0650i	0.175378	−	0.539758i
$780$	−0.827195	+	0.862749i	−0.0296183	+	0.0308914i
$781$	−1.38019	−	4.24778i	−0.0493870	−	0.151998i
$782$	34.7844			1.24389
$783$	0.907034	+	2.79157i	0.0324148	+	0.0997624i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	5.10037	+	9.51008i	0.182040	+	0.339429i
$786$	1.16603	−	0.847168i	0.0415908	−	0.0302175i
$787$	9.04345	+	6.57045i	0.322364	+	0.234211i	0.737184	−	0.675692i	$-0.236155\pi$
$787$	9.04345	+	6.57045i	0.322364	+	0.234211i	−0.414819	+	0.909904i	$0.636155\pi$
$788$	9.23364	+	6.70863i	0.328935	+	0.238985i
$789$	−0.446776	+	0.324602i	−0.0159057	+	0.0115561i
$790$	1.74378	−	1.81873i	0.0620410	−	0.0647076i
$791$	0.835694	+	0.607167i	0.0297139	+	0.0215884i
$792$	0.560460	+	1.72492i	0.0199151	+	0.0612924i
$793$	−15.4926			−0.550157
$794$	−5.92042	−	18.2212i	−0.210108	−	0.646645i
$795$	−0.154986	+	1.13219i	−0.00549678	+	0.0401547i
$796$	5.25200	−	16.1640i	0.186152	−	0.572918i
$797$	12.4342	−	38.2685i	0.440441	−	1.35554i	−0.446966	−	0.894551i	$-0.647495\pi$
$797$	12.4342	−	38.2685i	0.440441	−	1.35554i	0.887407	−	0.460987i	$-0.152505\pi$
$798$	0.621698	−	0.451690i	0.0220079	−	0.0159896i
$799$	−17.8927			−0.633000
$800$	−2.76620	+	4.16511i	−0.0977999	+	0.147259i
$801$	38.1283			1.34720
$802$	5.04754	−	3.66725i	0.178235	−	0.129495i
$803$	−2.93414	+	9.03035i	−0.103543	+	0.318674i
$804$	−0.167970	+	0.516957i	−0.00592383	+	0.0182317i
$805$	13.9187	+	6.72698i	0.490569	+	0.237095i
$806$	15.4156	+	47.4444i	0.542992	+	1.67116i
$807$	−0.507742			−0.0178734
$808$	1.47250	+	4.53188i	0.0518023	+	0.159431i
$809$	−39.1170	−	28.4201i	−1.37528	−	0.999199i	−0.997304	−	0.0733834i	$-0.976620\pi$
$809$	−39.1170	−	28.4201i	−1.37528	−	0.999199i	−0.377976	−	0.925816i	$-0.623380\pi$
$810$	−2.70282	+	19.7444i	−0.0949673	+	0.693748i
$811$	10.6796	−	7.75918i	0.375012	−	0.272462i	−0.384274	−	0.923219i	$-0.625548\pi$
$811$	10.6796	−	7.75918i	0.375012	−	0.272462i	0.759286	+	0.650757i	$0.225548\pi$
$812$	4.01418	+	2.91647i	0.140870	+	0.102348i
$813$	−0.570694	−	0.414634i	−0.0200151	−	0.0145418i
$814$	4.06450	−	2.95303i	0.142461	−	0.103504i
$815$	1.51625	−	11.0764i	0.0531119	−	0.387990i
$816$	−0.401978	−	0.292054i	−0.0140721	−	0.0102239i
$817$	−3.59670	−	11.0695i	−0.125833	−	0.387273i
$818$	−3.13688			−0.109679
$819$	5.00150	+	15.3930i	0.174767	+	0.537876i
$820$	−4.09825	−	1.98071i	−0.143117	−	0.0691693i
$821$	−0.0980336	+	0.301716i	−0.00342140	+	0.0105300i	−0.952753	−	0.303747i	$-0.901762\pi$
$821$	−0.0980336	+	0.301716i	−0.00342140	+	0.0105300i	0.949331	+	0.314277i	$0.101762\pi$
$822$	0.224990	−	0.692448i	0.00784743	−	0.0241519i
$823$	15.4214	−	11.2043i	0.537558	−	0.390559i	−0.285619	−	0.958343i	$-0.592199\pi$
$823$	15.4214	−	11.2043i	0.537558	−	0.390559i	0.823177	+	0.567785i	$0.192199\pi$
$824$	8.90492			0.310217
$825$	−0.288473	−	0.0804863i	−0.0100433	−	0.00280217i
$826$	−2.54553			−0.0885705
$827$	−0.468081	+	0.340081i	−0.0162768	+	0.0118258i	−0.595894	−	0.803063i	$-0.703202\pi$
$827$	−0.468081	+	0.340081i	−0.0162768	+	0.0118258i	0.579617	+	0.814889i	$0.303202\pi$
$828$	6.38832	−	19.6612i	0.222010	−	0.683275i
$829$	−4.78160	+	14.7162i	−0.166072	+	0.511116i	−0.999114	−	0.0420936i	$-0.986597\pi$
$829$	−4.78160	+	14.7162i	−0.166072	+	0.511116i	0.833042	+	0.553210i	$0.186597\pi$
$830$	−4.93654	+	36.0620i	−0.171350	+	1.25173i
$831$	0.0885559	+	0.272547i	0.00307197	+	0.00945456i
$832$	5.41266			0.187650
$833$	−1.55478	−	4.78513i	−0.0538701	−	0.165795i
$834$	0.208837	+	0.151729i	0.00723142	+	0.00525393i
$835$	−26.5596	+	27.7011i	−0.919133	+	0.958638i
$836$	−3.81836	+	2.77420i	−0.132061	+	0.0959479i
$837$	−4.41090	−	3.20471i	−0.152463	−	0.110771i
$838$	−7.25515	−	5.27117i	−0.250625	−	0.182090i
$839$	−12.9375	+	9.39965i	−0.446652	+	0.324512i	−0.788273	−	0.615326i	$-0.789024\pi$
$839$	−12.9375	+	9.39965i	−0.446652	+	0.324512i	0.341620	+	0.939838i	$0.389024\pi$
$840$	−0.104367	−	0.194602i	−0.00360102	−	0.00671440i
$841$	3.54392	+	2.57481i	0.122204	+	0.0887866i
$842$	6.33574	+	19.4994i	0.218344	+	0.671994i
$843$	0.676311			0.0232934
$844$	−0.896463	−	2.75903i	−0.0308575	−	0.0949697i
$845$	25.2200	−	26.3040i	0.867595	−	0.904885i
$846$	−3.28609	+	10.1135i	−0.112978	+	0.347710i
$847$	3.28550	−	10.1117i	0.112891	−	0.347444i
$848$	4.18665	−	3.04178i	0.143770	−	0.104455i
$849$	0.703278			0.0241364
$850$	−23.5775	+	8.77330i	−0.808703	+	0.300922i
$851$	−57.2653			−1.96303
$852$	0.588322	−	0.427441i	0.0201556	−	0.0146439i
$853$	−10.7047	+	32.9457i	−0.366523	+	1.12804i	0.582500	+	0.812831i	$0.302075\pi$
$853$	−10.7047	+	32.9457i	−0.366523	+	1.12804i	−0.949022	+	0.315209i	$0.897925\pi$
$854$	0.884493	−	2.72219i	0.0302667	−	0.0931514i
$855$	−51.2072	+	9.21844i	−1.75125	+	0.315264i
$856$	4.19674	+	12.9162i	0.143442	+	0.441468i
$857$	16.2819			0.556181			0.278090	−	0.960555i	$-0.410299\pi$
$857$	16.2819			0.556181			0.278090	+	0.960555i	$0.410299\pi$
$858$	0.100186	+	0.308340i	0.00342029	+	0.0105266i
$859$	−47.0525	−	34.1857i	−1.60541	−	1.16640i	−0.875983	−	0.482342i	$-0.839786\pi$
$859$	−47.0525	−	34.1857i	−1.60541	−	1.16640i	−0.729428	−	0.684057i	$-0.760214\pi$
$860$	−3.29168	+	0.592576i	−0.112245	+	0.0202067i
$861$	0.162634	−	0.118161i	0.00554257	−	0.00402691i
$862$	−4.15111	−	3.01596i	−0.141387	−	0.102724i
$863$	22.4160	+	16.2862i	0.763051	+	0.554389i	0.899845	−	0.436211i	$-0.143680\pi$
$863$	22.4160	+	16.2862i	0.763051	+	0.554389i	−0.136794	+	0.990600i	$0.543680\pi$
$864$	−0.478586	+	0.347713i	−0.0162818	+	0.0118294i
$865$	−30.1582	−	14.5757i	−1.02541	−	0.495588i
$866$	2.73621	+	1.98797i	0.0929801	+	0.0675540i
$867$	−0.253743	−	0.780939i	−0.00861755	−	0.0265221i
$868$	−9.21653			−0.312829
$869$	−0.211199	−	0.650002i	−0.00716442	−	0.0220498i
$870$	0.517850	+	0.965575i	0.0175568	+	0.0327360i
$871$	9.20628	−	28.3340i	0.311943	−	0.960062i
$872$	5.51403	−	16.9704i	0.186729	−	0.574692i
$873$	−14.5114	+	10.5432i	−0.491137	+	0.356832i
$874$	53.7974			1.81973
$875$	−11.1310	−	1.04912i	−0.376297	−	0.0354667i
$876$	−1.54597			−0.0522333
$877$	−15.5648	+	11.3085i	−0.525586	+	0.381860i	−0.818704	−	0.574216i	$-0.805307\pi$
$877$	−15.5648	+	11.3085i	−0.525586	+	0.381860i	0.293118	+	0.956076i	$0.405307\pi$
$878$	3.49911	−	10.7692i	0.118089	−	0.363442i
$879$	0.176670	−	0.543734i	0.00595893	−	0.0183397i
$880$	0.641007	+	1.19521i	0.0216083	+	0.0402906i
$881$	−0.435613	−	1.34068i	−0.0146762	−	0.0451686i	0.943450	−	0.331514i	$-0.107559\pi$
$881$	−0.435613	−	1.34068i	−0.0146762	−	0.0451686i	−0.958126	+	0.286346i	$0.907559\pi$
$882$	−2.99025			−0.100687
$883$	7.76119	+	23.8865i	0.261185	+	0.803845i	0.992548	+	0.121856i	$0.0388847\pi$
$883$	7.76119	+	23.8865i	0.261185	+	0.803845i	−0.731363	+	0.681989i	$0.761115\pi$
$884$	22.0321	+	16.0073i	0.741020	+	0.538383i
$885$	−0.506100	−	0.244602i	−0.0170124	−	0.00822219i
$886$	−9.49316	+	6.89718i	−0.318929	+	0.231715i
$887$	−4.58267	−	3.32951i	−0.153871	−	0.111794i	0.508186	−	0.861247i	$-0.330316\pi$
$887$	−4.58267	−	3.32951i	−0.153871	−	0.111794i	−0.662057	+	0.749454i	$0.730316\pi$
$888$	0.661773	+	0.480806i	0.0222077	+	0.0161348i
$889$	−7.40399	+	5.37931i	−0.248322	+	0.180416i
$890$	28.0608	−	5.05157i	0.940600	−	0.169329i
$891$	4.37325	+	3.17735i	0.146509	+	0.106445i
$892$	0.936048	+	2.88086i	0.0313412	+	0.0964583i
$893$	−27.6728			−0.926036
$894$	0.605664	+	1.86404i	0.0202564	+	0.0623429i
$895$	−5.35975	+	0.964876i	−0.179157	+	0.0322523i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	1.14195	−	3.51457i	0.0381287	−	0.117348i
$898$	−5.71583	+	4.15280i	−0.190740	+	0.138581i
$899$	45.7306			1.52520
$900$	0.628817	+	14.9380i	0.0209606	+	0.497934i
$901$	26.0373			0.867429
$902$	−0.998874	+	0.725724i	−0.0332589	+	0.0241640i
$903$	0.0456455	−	0.140482i	0.00151899	−	0.00467496i
$904$	0.319207	−	0.982417i	0.0106167	−	0.0326747i
$905$	−8.26601	+	8.62129i	−0.274771	+	0.286581i
$906$	−0.662538	−	2.03908i	−0.0220114	−	0.0677440i
$907$	−6.15492			−0.204371			−0.102185	−	0.994765i	$-0.532583\pi$
$907$	−6.15492			−0.204371			−0.102185	+	0.994765i	$0.532583\pi$
$908$	−5.07954	−	15.6332i	−0.168570	−	0.518806i
$909$	11.5275	+	8.37525i	0.382345	+	0.277790i
$910$	5.72029	+	10.6660i	0.189626	+	0.353573i
$911$	32.1218	−	23.3379i	1.06424	−	0.773218i	0.0893741	−	0.995998i	$-0.471513\pi$
$911$	32.1218	−	23.3379i	1.06424	−	0.773218i	0.974869	+	0.222781i	$0.0715133\pi$
$912$	−0.621698	−	0.451690i	−0.0205865	−	0.0149569i
$913$	7.98748	+	5.80325i	0.264347	+	0.192059i
$914$	1.28984	−	0.937125i	0.0426642	−	0.0309973i
$915$	0.437430	−	0.456231i	0.0144610	−	0.0150825i
$916$	−4.05734	−	2.94783i	−0.134058	−	0.0973990i
$917$	−4.50999	−	13.8803i	−0.148933	−	0.458369i
$918$	−2.97639			−0.0982355
$919$	8.90780	+	27.4154i	0.293841	+	0.904351i	0.983608	+	0.180319i	$0.0577130\pi$
$919$	8.90780	+	27.4154i	0.293841	+	0.904351i	−0.689767	+	0.724032i	$0.742287\pi$
$920$	2.09663	−	15.3162i	0.0691240	−	0.504960i
$921$	−0.315253	+	0.970250i	−0.0103879	+	0.0319708i
$922$	2.00231	−	6.16246i	0.0659424	−	0.202950i
$923$	−32.2455	+	23.4277i	−1.06137	+	0.771133i
$924$	−0.0598981			−0.00197050
$925$	38.8155	−	14.4434i	1.27625	−	0.474896i
$926$	17.2203			0.565895
$927$	21.5424	−	15.6515i	0.707546	−	0.514062i
$928$	1.53328	−	4.71895i	0.0503324	−	0.154907i
$929$	10.5761	−	32.5498i	0.346989	−	1.06792i	−0.613521	−	0.789678i	$-0.710247\pi$
$929$	10.5761	−	32.5498i	0.346989	−	1.06792i	0.960510	−	0.278245i	$-0.0897526\pi$
$930$	−1.83242	−	0.885621i	−0.0600874	−	0.0290406i
$931$	−2.40462	−	7.40066i	−0.0788083	−	0.242547i
$932$	−26.1674			−0.857141
$933$	−0.00384816	−	0.0118434i	−0.000125983	−	0.000387736i
$934$	−1.19114	−	0.865417i	−0.0389754	−	0.0283173i
$935$	−0.925483	+	6.76078i	−0.0302665	+	0.221101i
$936$	13.0941	−	9.51342i	0.427994	−	0.310956i
$937$	−13.1462	−	9.55124i	−0.429466	−	0.312026i	0.351969	−	0.936012i	$-0.385512\pi$
$937$	−13.1462	−	9.55124i	−0.429466	−	0.312026i	−0.781435	+	0.623986i	$0.785512\pi$
$938$	4.45296	+	3.23526i	0.145394	+	0.105635i
$939$	1.33169	−	0.967529i	0.0434580	−	0.0315741i
$940$	−1.07849	+	7.87849i	−0.0351764	+	0.256968i
$941$	−22.2690	−	16.1794i	−0.725949	−	0.527433i	0.162330	−	0.986736i	$-0.448099\pi$
$941$	−22.2690	−	16.1794i	−0.725949	−	0.527433i	−0.888279	+	0.459304i	$0.848099\pi$
$942$	0.147277	+	0.453271i	0.00479854	+	0.0147684i
$943$	14.0733			0.458289
$944$	0.786613	+	2.42095i	0.0256021	+	0.0787951i
$945$	−1.19097	−	0.575606i	−0.0387424	−	0.0187245i
$946$	−0.280347	+	0.862819i	−0.00911487	+	0.0280527i
$947$	12.3481	−	38.0036i	0.401260	−	1.23495i	−0.522719	−	0.852505i	$-0.675082\pi$
$947$	12.3481	−	38.0036i	0.401260	−	1.23495i	0.923978	−	0.382445i	$-0.124918\pi$
$948$	0.0900260	−	0.0654077i	0.00292391	−	0.00212434i
$949$	84.7332			2.75056
$950$	−36.4649	+	13.5687i	−1.18308	+	0.440228i
$951$	0.0735463			0.00238490
$952$	−4.07048	+	2.95737i	−0.131925	+	0.0958490i
$953$	−2.62461	+	8.07771i	−0.0850193	+	0.261663i	−0.984524	−	0.175248i	$-0.943927\pi$
$953$	−2.62461	+	8.07771i	−0.0850193	+	0.261663i	0.899505	+	0.436910i	$0.143927\pi$
$954$	4.78188	−	14.7171i	0.154819	−	0.476484i
$955$	−5.26955	+	38.4948i	−0.170519	+	1.24566i
$956$	4.12871	+	12.7069i	0.133532	+	0.410970i
$957$	0.297202			0.00960718
$958$	2.09363	+	6.44352i	0.0676420	+	0.208181i
$959$	−5.96460	−	4.33354i	−0.192607	−	0.139937i
$960$	−0.152826	+	0.159394i	−0.00493243	+	0.00514443i
$961$	−43.6420	+	31.7077i	−1.40780	+	1.02283i
$962$	−36.2713	−	26.3526i	−1.16943	−	0.849643i
$963$	32.8545	+	23.8702i	1.05872	+	0.769206i
$964$	−22.2513	+	16.1665i	−0.716667	+	0.520689i
$965$	−19.0726	−	35.5624i	−0.613968	−	1.14480i
$966$	0.552347	+	0.401304i	0.0177715	+	0.0129117i
$967$	−15.1500	−	46.6269i	−0.487192	−	1.49942i	−0.828782	−	0.559572i	$-0.810965\pi$
$967$	−15.1500	−	46.6269i	−0.487192	−	1.49942i	0.341590	−	0.939849i	$-0.389035\pi$
$968$	−10.6321			−0.341729
$969$	−1.19479	−	3.67718i	−0.0383822	−	0.118128i
$970$	−9.28292	+	9.68190i	−0.298057	+	0.310867i
$971$	16.6594	−	51.2725i	0.534627	−	1.64541i	−0.209827	−	0.977739i	$-0.567290\pi$
$971$	16.6594	−	51.2725i	0.534627	−	1.64541i	0.744454	−	0.667674i	$-0.232710\pi$
$972$	−0.820386	+	2.52489i	−0.0263139	+	0.0809859i
$973$	2.11470	−	1.53642i	0.0677942	−	0.0492554i
$974$	−31.8016			−1.01899
$975$	0.112405	+	2.67026i	0.00359984	+	0.0855168i
$976$	−2.86228			−0.0916193
$977$	−6.27349	+	4.55796i	−0.200707	+	0.145822i	−0.683599	−	0.729858i	$-0.739586\pi$
$977$	−6.27349	+	4.55796i	−0.200707	+	0.145822i	0.482892	+	0.875680i	$0.339586\pi$
$978$	0.152576	−	0.469579i	0.00487883	−	0.0150155i
$979$	2.38989	−	7.35533i	0.0763813	−	0.235077i
$980$	−2.20069	+	0.396174i	−0.0702985	+	0.0126553i
$981$	−16.4883	−	50.7458i	−0.526431	−	1.62019i
$982$	25.9434			0.827888
$983$	3.07426	+	9.46159i	0.0980536	+	0.301778i	0.988037	−	0.154214i	$-0.0492846\pi$
$983$	3.07426	+	9.46159i	0.0980536	+	0.301778i	−0.889984	+	0.455992i	$0.849285\pi$
$984$	−0.162634	−	0.118161i	−0.00518460	−	0.00376683i
$985$	25.1174	−	4.52170i	0.800306	−	0.144073i
$986$	20.1969	−	14.6739i	0.643200	−	0.467312i
$987$	−0.284122	−	0.206427i	−0.00904369	−	0.00657063i
$988$	34.0748	+	24.7568i	1.08406	+	0.787618i
$989$	8.36591	−	6.07819i	0.266020	−	0.193275i
$990$	3.65143	+	1.76476i	0.116050	+	0.0560877i
$991$	46.3880	+	33.7028i	1.47356	+	1.07061i	0.979562	+	0.201143i	$0.0644657\pi$
$991$	46.3880	+	33.7028i	1.47356	+	1.07061i	0.494000	+	0.869462i	$0.335534\pi$
$992$	2.84806	+	8.76544i	0.0904261	+	0.278303i
$993$	−0.774076			−0.0245646
$994$	−2.27553	−	7.00336i	−0.0721755	−	0.222133i
$995$	−17.9618	−	33.4913i	−0.569427	−	1.06175i
$996$	−0.496748	+	1.52883i	−0.0157401	+	0.0484430i
$997$	−12.0555	+	37.1031i	−0.381802	+	1.17507i	0.556972	+	0.830531i	$0.311963\pi$
$997$	−12.0555	+	37.1031i	−0.381802	+	1.17507i	−0.938774	+	0.344534i	$0.888037\pi$
$998$	17.8046	−	12.9358i	0.563596	−	0.409477i
$999$	4.90000			0.155029

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.c.211.2	yes	16
25.4	even	10		8750.2.a.s.1.5		8
25.16	even	5	inner	350.2.h.c.141.2	✓	16
25.21	even	5		8750.2.a.u.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.c.141.2	✓	16	25.16	even	5	inner
350.2.h.c.211.2	yes	16	1.1	even	1	trivial
8750.2.a.s.1.5		8	25.4	even	10
8750.2.a.u.1.4		8	25.21	even	5

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.0305168 + 0.0939212i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.05684 - 1.97056i) q^{5} +(-0.0305168 - 0.0939212i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(2.41916 + 1.75762i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.0305168 + 0.0939212i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.05684 - 1.97056i) q^{5} +(-0.0305168 - 0.0939212i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(2.41916 + 1.75762i) q^{9} +(2.01326 + 0.973023i) q^{10} +(0.490697 - 0.356512i) q^{11} +(0.0798941 + 0.0580465i) q^{12} +(-4.37894 - 3.18148i) q^{13} +(0.809017 - 0.587785i) q^{14} +(0.217328 - 0.0391240i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.55478 - 4.78513i) q^{17} -2.99025 q^{18} +(-2.40462 - 7.40066i) q^{19} +(-2.20069 + 0.396174i) q^{20} +(0.0305168 - 0.0939212i) q^{21} +(-0.187429 + 0.576849i) q^{22} +(5.59313 - 4.06365i) q^{23} -0.0987546 q^{24} +(-2.76620 + 4.16511i) q^{25} +5.41266 q^{26} +(-0.478586 + 0.347713i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(1.53328 - 4.71895i) q^{29} +(-0.152826 + 0.159394i) q^{30} +(2.84806 + 8.76544i) q^{31} +1.00000 q^{32} +(0.0185095 + 0.0569664i) q^{33} +(4.07048 + 2.95737i) q^{34} +(1.05684 + 1.97056i) q^{35} +(2.41916 - 1.75762i) q^{36} +(-6.70119 - 4.86870i) q^{37} +(6.29538 + 4.57386i) q^{38} +(0.432440 - 0.314186i) q^{39} +(1.54753 - 1.61405i) q^{40} +(1.64685 + 1.19651i) q^{41} +(0.0305168 + 0.0939212i) q^{42} +1.49575 q^{43} +(-0.187429 - 0.576849i) q^{44} +(0.906844 - 6.62462i) q^{45} +(-2.13639 + 6.57512i) q^{46} +(1.09893 - 3.38217i) q^{47} +(0.0798941 - 0.0580465i) q^{48} +1.00000 q^{49} +(-0.210289 - 4.99558i) q^{50} +0.496872 q^{51} +(-4.37894 + 3.18148i) q^{52} +(-1.59916 + 4.92170i) q^{53} +(0.182803 - 0.562611i) q^{54} +(-1.22111 - 0.590172i) q^{55} +(-0.309017 - 0.951057i) q^{56} +0.768460 q^{57} +(1.53328 + 4.71895i) q^{58} +(-2.05938 - 1.49623i) q^{59} +(0.0299490 - 0.218782i) q^{60} +(2.31563 - 1.68241i) q^{61} +(-7.45633 - 5.41734i) q^{62} +(-2.41916 - 1.75762i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.64148 + 11.9913i) q^{65} +(-0.0484585 - 0.0352072i) q^{66} +(1.70088 + 5.23476i) q^{67} -5.03138 q^{68} +(0.210978 + 0.649323i) q^{69} +(-2.01326 - 0.973023i) q^{70} +(2.27553 - 7.00336i) q^{71} +(-0.924037 + 2.84389i) q^{72} +(-12.6649 + 9.20156i) q^{73} +8.28312 q^{74} +(-0.306777 - 0.386911i) q^{75} -7.78152 q^{76} +(-0.490697 + 0.356512i) q^{77} +(-0.165177 + 0.508364i) q^{78} +(0.348205 - 1.07167i) q^{79} +(-0.303267 + 2.21541i) q^{80} +(2.75406 + 8.47612i) q^{81} -2.03562 q^{82} +(5.03013 + 15.4811i) q^{83} +(-0.0798941 - 0.0580465i) q^{84} +(-7.78623 + 8.12089i) q^{85} +(-1.21008 + 0.879178i) q^{86} +(0.396419 + 0.288015i) q^{87} +(0.490697 + 0.356512i) q^{88} +(10.3157 - 7.49479i) q^{89} +(3.16020 + 5.89246i) q^{90} +(4.37894 + 3.18148i) q^{91} +(-2.13639 - 6.57512i) q^{92} -0.910175 q^{93} +(1.09893 + 3.38217i) q^{94} +(-12.0421 + 12.5597i) q^{95} +(-0.0305168 + 0.0939212i) q^{96} +(-1.85365 + 5.70494i) q^{97} +(-0.809017 + 0.587785i) q^{98} +1.81369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more