LMFDB - Embedded newform 430.2.k.d.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	430.41
Dual form			430.2.k.d.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(1.64572 + 0.792535i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.222521 - 0.974928i) q^{5} +1.82661 q^{6} +2.16285 q^{7} +(0.222521 - 0.974928i) q^{8} +(0.209800 + 0.263080i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(1.64572 + 0.792535i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.222521 - 0.974928i) q^{5} +1.82661 q^{6} +2.16285 q^{7} +(0.222521 - 0.974928i) q^{8} +(0.209800 + 0.263080i) q^{9} +(-0.222521 - 0.974928i) q^{10} +(-2.92074 - 3.66249i) q^{11} +(1.64572 - 0.792535i) q^{12} +(0.0888771 - 0.389396i) q^{13} +(1.94866 - 0.938427i) q^{14} +(1.13887 - 1.42810i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.13677 + 4.98050i) q^{17} +(0.303169 + 0.145999i) q^{18} +(-3.97575 + 4.98543i) q^{19} +(-0.623490 - 0.781831i) q^{20} +(3.55944 + 1.71414i) q^{21} +(-4.22059 - 2.03253i) q^{22} +(5.66069 + 7.09829i) q^{23} +(1.13887 - 1.42810i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.0888771 - 0.389396i) q^{26} +(-1.08260 - 4.74320i) q^{27} +(1.34852 - 1.69099i) q^{28} +(0.498844 - 0.240231i) q^{29} +(0.406458 - 1.78081i) q^{30} +(-2.34381 + 1.12872i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.90406 - 8.34221i) q^{33} +(3.18515 + 3.99405i) q^{34} +(0.481280 - 2.10863i) q^{35} +0.336492 q^{36} -11.8437 q^{37} +(-1.41893 + 6.21673i) q^{38} +(0.454876 - 0.570397i) q^{39} +(-0.900969 - 0.433884i) q^{40} +(4.86102 - 2.34094i) q^{41} +3.95069 q^{42} +(2.74127 + 5.95697i) q^{43} -4.68450 q^{44} +(0.303169 - 0.145999i) q^{45} +(8.17994 + 3.93925i) q^{46} +(6.18181 - 7.75175i) q^{47} +(0.406458 - 1.78081i) q^{48} -2.32206 q^{49} -1.00000 q^{50} +(-2.07643 + 9.09742i) q^{51} +(-0.249028 - 0.312271i) q^{52} +(2.27155 + 9.95232i) q^{53} +(-3.03339 - 3.80375i) q^{54} +(-4.22059 + 2.03253i) q^{55} +(0.481280 - 2.10863i) q^{56} +(-10.4941 + 5.05368i) q^{57} +(0.345211 - 0.432880i) q^{58} +(-0.164063 - 0.718806i) q^{59} +(-0.406458 - 1.78081i) q^{60} +(-11.5405 - 5.55763i) q^{61} +(-1.62196 + 2.03388i) q^{62} +(0.453766 + 0.569005i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.359856 - 0.173298i) q^{65} +(-5.33504 - 6.68993i) q^{66} +(4.92309 - 6.17336i) q^{67} +(4.60267 + 2.21653i) q^{68} +(3.69025 + 16.1681i) q^{69} +(-0.481280 - 2.10863i) q^{70} +(0.987929 - 1.23882i) q^{71} +(0.303169 - 0.145999i) q^{72} +(0.397529 - 1.74169i) q^{73} +(-10.6708 + 5.13881i) q^{74} +(-1.13887 - 1.42810i) q^{75} +(1.41893 + 6.21673i) q^{76} +(-6.31714 - 7.92144i) q^{77} +(0.162344 - 0.711273i) q^{78} +4.74409 q^{79} -1.00000 q^{80} +(2.20212 - 9.64813i) q^{81} +(3.36393 - 4.21823i) q^{82} +(-14.8187 - 7.13632i) q^{83} +(3.55944 - 1.71414i) q^{84} +5.10858 q^{85} +(5.05443 + 4.17765i) q^{86} +1.01135 q^{87} +(-4.22059 + 2.03253i) q^{88} +(3.01856 + 1.45366i) q^{89} +(0.209800 - 0.263080i) q^{90} +(0.192228 - 0.842207i) q^{91} +9.07905 q^{92} -4.75179 q^{93} +(2.20626 - 9.66627i) q^{94} +(3.97575 + 4.98543i) q^{95} +(-0.406458 - 1.78081i) q^{96} +(7.88404 + 9.88628i) q^{97} +(-2.09210 + 1.00750i) q^{98} +(0.350760 - 1.53678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 12 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 12 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 12 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 9 q^{11} + 2 q^{12} - 2 q^{13} - 5 q^{14} - 2 q^{15} - 4 q^{16} + 13 q^{17} - 10 q^{18} - 3 q^{19} + 4 q^{20} - 14 q^{21} - 5 q^{22} + 11 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 13 q^{27} + 5 q^{28} + 20 q^{29} + 2 q^{30} - 5 q^{31} + 4 q^{32} + 15 q^{33} + q^{34} + 9 q^{35} + 24 q^{36} - 38 q^{37} - 18 q^{38} + 5 q^{39} - 4 q^{40} - 2 q^{41} - 14 q^{42} - 2 q^{43} - 2 q^{44} - 10 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 50 q^{49} - 24 q^{50} - 42 q^{51} - 2 q^{52} + 22 q^{53} - 29 q^{54} - 5 q^{55} + 9 q^{56} - 67 q^{57} + 22 q^{58} - 44 q^{59} - 2 q^{60} - 26 q^{61} - 2 q^{62} + 37 q^{63} - 4 q^{64} + 2 q^{65} - 8 q^{66} + 37 q^{67} - 15 q^{68} + 88 q^{69} - 9 q^{70} + 19 q^{71} - 10 q^{72} + 22 q^{73} - 4 q^{74} + 2 q^{75} + 18 q^{76} + 28 q^{77} + 23 q^{78} + 30 q^{79} - 24 q^{80} - 26 q^{81} + 37 q^{82} - 11 q^{83} - 14 q^{84} - 6 q^{85} + 16 q^{86} - 26 q^{87} - 5 q^{88} + 30 q^{89} - 4 q^{90} + 36 q^{91} - 10 q^{92} - 98 q^{93} + 4 q^{94} + 3 q^{95} - 2 q^{96} - 39 q^{97} + 41 q^{98} - 31 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 12 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 9 * q^11 + 2 * q^12 - 2 * q^13 - 5 * q^14 - 2 * q^15 - 4 * q^16 + 13 * q^17 - 10 * q^18 - 3 * q^19 + 4 * q^20 - 14 * q^21 - 5 * q^22 + 11 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 13 * q^27 + 5 * q^28 + 20 * q^29 + 2 * q^30 - 5 * q^31 + 4 * q^32 + 15 * q^33 + q^34 + 9 * q^35 + 24 * q^36 - 38 * q^37 - 18 * q^38 + 5 * q^39 - 4 * q^40 - 2 * q^41 - 14 * q^42 - 2 * q^43 - 2 * q^44 - 10 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 50 * q^49 - 24 * q^50 - 42 * q^51 - 2 * q^52 + 22 * q^53 - 29 * q^54 - 5 * q^55 + 9 * q^56 - 67 * q^57 + 22 * q^58 - 44 * q^59 - 2 * q^60 - 26 * q^61 - 2 * q^62 + 37 * q^63 - 4 * q^64 + 2 * q^65 - 8 * q^66 + 37 * q^67 - 15 * q^68 + 88 * q^69 - 9 * q^70 + 19 * q^71 - 10 * q^72 + 22 * q^73 - 4 * q^74 + 2 * q^75 + 18 * q^76 + 28 * q^77 + 23 * q^78 + 30 * q^79 - 24 * q^80 - 26 * q^81 + 37 * q^82 - 11 * q^83 - 14 * q^84 - 6 * q^85 + 16 * q^86 - 26 * q^87 - 5 * q^88 + 30 * q^89 - 4 * q^90 + 36 * q^91 - 10 * q^92 - 98 * q^93 + 4 * q^94 + 3 * q^95 - 2 * q^96 - 39 * q^97 + 41 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	1.64572	+	0.792535i	0.950155	+	0.457570i	0.843740	−	0.536752i	$-0.180349\pi$
$3$	1.64572	+	0.792535i	0.950155	+	0.457570i	0.106414	+	0.994322i	$0.466063\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.222521	−	0.974928i	0.0995144	−	0.436001i
$5$	0.222521	−	0.974928i	0.0995144	−	0.436001i
$6$	1.82661			0.745709
$7$	2.16285			0.817482			0.408741	−	0.912650i	$-0.365968\pi$
$7$	2.16285			0.817482			0.408741	+	0.912650i	$0.365968\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	0.209800	+	0.263080i	0.0699332	+	0.0876935i
$10$	−0.222521	−	0.974928i	−0.0703673	−	0.308299i
$11$	−2.92074	−	3.66249i	−0.880636	−	1.10428i	−0.993852	−	0.110713i	$-0.964687\pi$
$11$	−2.92074	−	3.66249i	−0.880636	−	1.10428i	0.113216	−	0.993570i	$-0.463885\pi$
$12$	1.64572	−	0.792535i	0.475077	−	0.228785i
$13$	0.0888771	−	0.389396i	0.0246501	−	0.107999i	−0.961106	−	0.276179i	$-0.910932\pi$
$13$	0.0888771	−	0.389396i	0.0246501	−	0.107999i	0.985756	+	0.168180i	$0.0537889\pi$
$14$	1.94866	−	0.938427i	0.520803	−	0.250805i
$15$	1.13887	−	1.42810i	0.294055	−	0.368734i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	1.13677	+	4.98050i	0.275706	+	1.20795i	0.903163	+	0.429297i	$0.141239\pi$
$17$	1.13677	+	4.98050i	0.275706	+	1.20795i	−0.627457	+	0.778651i	$0.715904\pi$
$18$	0.303169	+	0.145999i	0.0714577	+	0.0344122i
$19$	−3.97575	+	4.98543i	−0.912100	+	1.14374i	0.0770798	+	0.997025i	$0.475440\pi$
$19$	−3.97575	+	4.98543i	−0.912100	+	1.14374i	−0.989179	+	0.146712i	$0.953131\pi$
$20$	−0.623490	−	0.781831i	−0.139417	−	0.174823i
$21$	3.55944	+	1.71414i	0.776734	+	0.374056i
$22$	−4.22059	−	2.03253i	−0.899833	−	0.433337i
$23$	5.66069	+	7.09829i	1.18034	+	1.48009i	0.842339	+	0.538948i	$0.181178\pi$
$23$	5.66069	+	7.09829i	1.18034	+	1.48009i	0.337997	+	0.941147i	$0.390251\pi$
$24$	1.13887	−	1.42810i	0.232471	−	0.291509i
$25$	−0.900969	−	0.433884i	−0.180194	−	0.0867767i
$26$	−0.0888771	−	0.389396i	−0.0174302	−	0.0763668i
$27$	−1.08260	−	4.74320i	−0.208347	−	0.912829i
$28$	1.34852	−	1.69099i	0.254846	−	0.319567i
$29$	0.498844	−	0.240231i	0.0926330	−	0.0446097i	−0.386994	−	0.922082i	$-0.626486\pi$
$29$	0.498844	−	0.240231i	0.0926330	−	0.0446097i	0.479627	+	0.877473i	$0.340772\pi$
$30$	0.406458	−	1.78081i	0.0742088	−	0.325130i
$31$	−2.34381	+	1.12872i	−0.420960	+	0.202724i	−0.632358	−	0.774676i	$-0.717913\pi$
$31$	−2.34381	+	1.12872i	−0.420960	+	0.202724i	0.211398	+	0.977400i	$0.432198\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−1.90406	−	8.34221i	−0.331454	−	1.45219i
$34$	3.18515	+	3.99405i	0.546249	+	0.684974i
$35$	0.481280	−	2.10863i	0.0813512	−	0.356423i
$36$	0.336492			0.0560821
$37$	−11.8437			−1.94710			−0.973550	−	0.228474i	$-0.926627\pi$
$37$	−11.8437			−1.94710			−0.973550	+	0.228474i	$0.926627\pi$
$38$	−1.41893	+	6.21673i	−0.230181	+	1.00849i
$39$	0.454876	−	0.570397i	0.0728385	−	0.0913366i
$40$	−0.900969	−	0.433884i	−0.142456	−	0.0686030i
$41$	4.86102	−	2.34094i	0.759164	−	0.365594i	−0.0139158	−	0.999903i	$-0.504430\pi$
$41$	4.86102	−	2.34094i	0.759164	−	0.365594i	0.773079	+	0.634309i	$0.218715\pi$
$42$	3.95069			0.609604
$43$	2.74127	+	5.95697i	0.418040	+	0.908429i
$43$	2.74127	+	5.95697i	0.418040	+	0.908429i
$44$	−4.68450			−0.706216
$45$	0.303169	−	0.145999i	0.0451938	−	0.0217642i
$46$	8.17994	+	3.93925i	1.20607	+	0.580811i
$47$	6.18181	−	7.75175i	0.901710	−	1.13071i	−0.0891773	−	0.996016i	$-0.528424\pi$
$47$	6.18181	−	7.75175i	0.901710	−	1.13071i	0.990887	−	0.134693i	$-0.0430048\pi$
$48$	0.406458	−	1.78081i	0.0586672	−	0.257038i
$49$	−2.32206			−0.331723
$50$	−1.00000			−0.141421
$51$	−2.07643	+	9.09742i	−0.290758	+	1.27389i
$52$	−0.249028	−	0.312271i	−0.0345340	−	0.0433042i
$53$	2.27155	+	9.95232i	0.312022	+	1.36706i	0.851190	+	0.524858i	$0.175882\pi$
$53$	2.27155	+	9.95232i	0.312022	+	1.36706i	−0.539168	+	0.842198i	$0.681261\pi$
$54$	−3.03339	−	3.80375i	−0.412792	−	0.517625i
$55$	−4.22059	+	2.03253i	−0.569105	+	0.274066i
$56$	0.481280	−	2.10863i	0.0643138	−	0.281777i
$57$	−10.4941	+	5.05368i	−1.38998	+	0.669377i
$58$	0.345211	−	0.432880i	0.0453284	−	0.0568400i
$59$	−0.164063	−	0.718806i	−0.0213591	−	0.0935805i	0.963125	−	0.269055i	$-0.0867113\pi$
$59$	−0.164063	−	0.718806i	−0.0213591	−	0.0935805i	−0.984484	+	0.175474i	$0.943854\pi$
$60$	−0.406458	−	1.78081i	−0.0524735	−	0.229902i
$61$	−11.5405	−	5.55763i	−1.47762	−	0.711582i	−0.490478	−	0.871454i	$-0.663178\pi$
$61$	−11.5405	−	5.55763i	−1.47762	−	0.711582i	−0.987138	+	0.159872i	$0.948892\pi$
$62$	−1.62196	+	2.03388i	−0.205990	+	0.258303i
$63$	0.453766	+	0.569005i	0.0571692	+	0.0716878i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−0.359856	−	0.173298i	−0.0446346	−	0.0214949i
$66$	−5.33504	−	6.68993i	−0.656699	−	0.823474i
$67$	4.92309	−	6.17336i	0.601451	−	0.754196i	−0.384152	−	0.923270i	$-0.625506\pi$
$67$	4.92309	−	6.17336i	0.601451	−	0.754196i	0.985603	+	0.169074i	$0.0540776\pi$
$68$	4.60267	+	2.21653i	0.558156	+	0.268794i
$69$	3.69025	+	16.1681i	0.444254	+	1.94641i
$70$	−0.481280	−	2.10863i	−0.0575240	−	0.252029i
$71$	0.987929	−	1.23882i	0.117246	−	0.147021i	−0.719745	−	0.694238i	$-0.755741\pi$
$71$	0.987929	−	1.23882i	0.117246	−	0.147021i	0.836991	+	0.547217i	$0.184313\pi$
$72$	0.303169	−	0.145999i	0.0357288	−	0.0172061i
$73$	0.397529	−	1.74169i	0.0465272	−	0.203849i	−0.946322	−	0.323226i	$-0.895233\pi$
$73$	0.397529	−	1.74169i	0.0465272	−	0.203849i	0.992849	+	0.119377i	$0.0380897\pi$
$74$	−10.6708	+	5.13881i	−1.24046	+	0.597374i
$75$	−1.13887	−	1.42810i	−0.131505	−	0.164903i
$76$	1.41893	+	6.21673i	0.162762	+	0.713108i
$77$	−6.31714	−	7.92144i	−0.719905	−	0.902732i
$78$	0.162344	−	0.711273i	0.0183818	−	0.0805358i
$79$	4.74409			0.533752			0.266876	−	0.963731i	$-0.414009\pi$
$79$	4.74409			0.533752			0.266876	+	0.963731i	$0.414009\pi$
$80$	−1.00000			−0.111803
$81$	2.20212	−	9.64813i	0.244680	−	1.07201i
$82$	3.36393	−	4.21823i	0.371484	−	0.465826i
$83$	−14.8187	−	7.13632i	−1.62657	−	0.783313i	−0.999992	−	0.00395032i	$-0.998743\pi$
$83$	−14.8187	−	7.13632i	−1.62657	−	0.783313i	−0.626573	−	0.779362i	$-0.715543\pi$
$84$	3.55944	−	1.71414i	0.388367	−	0.187028i
$85$	5.10858			0.554104
$86$	5.05443	+	4.17765i	0.545033	+	0.450487i
$87$	1.01135			0.108428
$88$	−4.22059	+	2.03253i	−0.449917	+	0.216668i
$89$	3.01856	+	1.45366i	0.319967	+	0.154088i	0.586972	−	0.809607i	$-0.300320\pi$
$89$	3.01856	+	1.45366i	0.319967	+	0.154088i	−0.267005	+	0.963695i	$0.586034\pi$
$90$	0.209800	−	0.263080i	0.0221148	−	0.0277311i
$91$	0.192228	−	0.842207i	0.0201510	−	0.0882873i
$92$	9.07905			0.946556
$93$	−4.75179			−0.492737
$94$	2.20626	−	9.66627i	0.227559	−	0.997000i
$95$	3.97575	+	4.98543i	0.407903	+	0.511495i
$96$	−0.406458	−	1.78081i	−0.0414840	−	0.181753i
$97$	7.88404	+	9.88628i	0.800503	+	1.00380i	0.999716	+	0.0238429i	$0.00759014\pi$
$97$	7.88404	+	9.88628i	0.800503	+	1.00380i	−0.199213	+	0.979956i	$0.563838\pi$
$98$	−2.09210	+	1.00750i	−0.211334	+	0.101773i
$99$	0.350760	−	1.53678i	0.0352527	−	0.154452i
$100$	−0.900969	+	0.433884i	−0.0900969	+	0.0433884i
$101$	−3.05137	+	3.82629i	−0.303622	+	0.380730i	−0.910113	−	0.414360i	$-0.864005\pi$
$101$	−3.05137	+	3.82629i	−0.303622	+	0.380730i	0.606491	+	0.795091i	$0.292577\pi$
$102$	2.07643	+	9.09742i	0.205597	+	0.900778i
$103$	−2.72102	−	11.9216i	−0.268110	−	1.17467i	−0.912209	−	0.409725i	$-0.865625\pi$
$103$	−2.72102	−	11.9216i	−0.268110	−	1.17467i	0.644099	−	0.764942i	$-0.277232\pi$
$104$	−0.359856	−	0.173298i	−0.0352868	−	0.0169932i
$105$	2.46321	−	3.08877i	0.240385	−	0.301433i
$106$	6.36475	+	7.98114i	0.618199	+	0.775197i
$107$	−6.51907	−	3.13942i	−0.630223	−	0.303499i	0.0913701	−	0.995817i	$-0.470875\pi$
$107$	−6.51907	−	3.13942i	−0.630223	−	0.303499i	−0.721593	+	0.692318i	$0.756590\pi$
$108$	−4.38338	−	2.11092i	−0.421791	−	0.203124i
$109$	1.82590	+	2.28961i	0.174890	+	0.219305i	0.861549	−	0.507675i	$-0.169495\pi$
$109$	1.82590	+	2.28961i	0.174890	+	0.219305i	−0.686659	+	0.726980i	$0.740923\pi$
$110$	−2.92074	+	3.66249i	−0.278482	+	0.349205i
$111$	−19.4914	−	9.38658i	−1.85005	−	0.890935i
$112$	−0.481280	−	2.10863i	−0.0454767	−	0.199247i
$113$	1.88384	+	8.25364i	0.177217	+	0.776437i	0.982907	+	0.184101i	$0.0589373\pi$
$113$	1.88384	+	8.25364i	0.177217	+	0.776437i	−0.805691	+	0.592337i	$0.798206\pi$
$114$	−7.26213	+	9.10642i	−0.680161	+	0.852895i
$115$	8.17994	−	3.93925i	0.762783	−	0.367337i
$116$	0.123204	−	0.539793i	0.0114392	−	0.0501185i
$117$	0.121089	−	0.0583133i	0.0111947	−	0.00539107i
$118$	−0.459693	−	0.576437i	−0.0423182	−	0.0530654i
$119$	2.45866	+	10.7721i	0.225385	+	0.987477i
$120$	−1.13887	−	1.42810i	−0.103964	−	0.130367i
$121$	−2.43540	+	10.6702i	−0.221400	+	0.970016i
$122$	−12.8090			−1.15968
$123$	9.85513			0.888608
$124$	−0.578872	+	2.53621i	−0.0519843	+	0.227758i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	0.655711	+	0.315774i	0.0584154	+	0.0281314i
$127$	−12.4796	+	6.00985i	−1.10738	+	0.533288i	−0.895973	−	0.444109i	$-0.853520\pi$
$127$	−12.4796	+	6.00985i	−1.10738	+	0.533288i	−0.211412	+	0.977397i	$0.567806\pi$
$128$	−1.00000			−0.0883883
$129$	−0.209754	+	11.9760i	−0.0184678	+	1.05443i
$130$	−0.399410			−0.0350306
$131$	12.2722	−	5.90999i	1.07223	−	0.516359i	0.187405	−	0.982283i	$-0.439992\pi$
$131$	12.2722	−	5.90999i	1.07223	−	0.516359i	0.884825	+	0.465924i	$0.154278\pi$
$132$	−7.70936	−	3.71263i	−0.671014	−	0.323143i
$133$	−8.59897	+	10.7828i	−0.745625	+	0.934984i
$134$	1.75703	−	7.69805i	0.151784	−	0.665011i
$135$	−4.86518			−0.418728
$136$	5.10858			0.438057
$137$	4.09923	−	17.9599i	0.350221	−	1.53442i	−0.426449	−	0.904512i	$-0.640236\pi$
$137$	4.09923	−	17.9599i	0.350221	−	1.53442i	0.776670	−	0.629907i	$-0.216907\pi$
$138$	10.3399	+	12.9658i	0.880188	+	1.10372i
$139$	0.887800	+	3.88971i	0.0753022	+	0.329921i	0.998522	−	0.0543522i	$-0.0173094\pi$
$139$	0.887800	+	3.88971i	0.0753022	+	0.329921i	−0.923220	+	0.384273i	$0.874452\pi$
$140$	−1.34852	−	1.69099i	−0.113971	−	0.142915i
$141$	16.3170	−	7.85787i	1.37414	−	0.661752i
$142$	0.352588	−	1.54479i	0.0295885	−	0.129636i
$143$	−1.68575	+	0.811813i	−0.140969	+	0.0678872i
$144$	0.209800	−	0.263080i	0.0174833	−	0.0219234i
$145$	−0.123204	−	0.539793i	−0.0102316	−	0.0448274i
$146$	−0.397529	−	1.74169i	−0.0328997	−	0.144143i
$147$	−3.82145	−	1.84031i	−0.315188	−	0.151787i
$148$	−7.38446	+	9.25982i	−0.606999	+	0.761152i
$149$	10.6623	+	13.3701i	0.873489	+	1.09532i	0.994713	+	0.102696i	$0.0327468\pi$
$149$	10.6623	+	13.3701i	0.873489	+	1.09532i	−0.121224	+	0.992625i	$0.538682\pi$
$150$	−1.64572	−	0.792535i	−0.134372	−	0.0647102i
$151$	−15.8243	−	7.62058i	−1.28776	−	0.620154i	−0.340389	−	0.940285i	$-0.610559\pi$
$151$	−15.8243	−	7.62058i	−1.28776	−	0.620154i	−0.947373	+	0.320131i	$0.896273\pi$
$152$	3.97575	+	4.98543i	0.322476	+	0.404372i
$153$	−1.07178	+	1.34397i	−0.0866482	+	0.108653i
$154$	−9.12853	−	4.39607i	−0.735598	−	0.354245i
$155$	0.578872	+	2.53621i	0.0464961	+	0.203713i
$156$	−0.162344	−	0.711273i	−0.0129979	−	0.0569474i
$157$	8.39484	−	10.5268i	0.669981	−	0.840130i	−0.324407	−	0.945917i	$-0.605165\pi$
$157$	8.39484	−	10.5268i	0.669981	−	0.840130i	0.994389	+	0.105787i	$0.0337363\pi$
$158$	4.27428	−	2.05838i	0.340043	−	0.163756i
$159$	−4.14923	+	18.1790i	−0.329056	+	1.44169i
$160$	−0.900969	+	0.433884i	−0.0712278	+	0.0343015i
$161$	12.2433	+	15.3526i	0.964904	+	1.20995i
$162$	−2.20212	−	9.64813i	−0.173015	−	0.758029i
$163$	−0.0312603	−	0.0391991i	−0.00244849	−	0.00307031i	0.780606	−	0.625024i	$-0.214911\pi$
$163$	−0.0312603	−	0.0391991i	−0.00244849	−	0.00307031i	−0.783054	+	0.621953i	$0.786339\pi$
$164$	1.20057	−	5.26005i	0.0937490	−	0.410741i
$165$	−8.55675			−0.666142
$166$	−16.4475			−1.27658
$167$	3.62721	−	15.8918i	0.280682	−	1.22975i	−0.616240	−	0.787558i	$-0.711345\pi$
$167$	3.62721	−	15.8918i	0.280682	−	1.22975i	0.896922	−	0.442189i	$-0.145798\pi$
$168$	2.46321	−	3.08877i	0.190041	−	0.238304i
$169$	11.5689	+	5.57127i	0.889913	+	0.428559i
$170$	4.60267	−	2.21653i	0.353009	−	0.170000i
$171$	−2.14568			−0.164084
$172$	6.36650	+	1.57090i	0.485441	+	0.119780i
$173$	−0.897799			−0.0682584			−0.0341292	−	0.999417i	$-0.510866\pi$
$173$	−0.897799			−0.0682584			−0.0341292	+	0.999417i	$0.510866\pi$
$174$	0.911191	−	0.438807i	0.0690772	−	0.0332658i
$175$	−1.94866	−	0.938427i	−0.147305	−	0.0709384i
$176$	−2.92074	+	3.66249i	−0.220159	+	0.276071i
$177$	0.299678	−	1.31298i	0.0225252	−	0.0986893i
$178$	3.35035			0.251119
$179$	16.1052			1.20376			0.601881	−	0.798585i	$-0.294418\pi$
$179$	16.1052			1.20376			0.601881	+	0.798585i	$0.294418\pi$
$180$	0.0748766	−	0.328056i	0.00558097	−	0.0244518i
$181$	−1.23028	−	1.54272i	−0.0914456	−	0.114669i	0.734004	−	0.679146i	$-0.237650\pi$
$181$	−1.23028	−	1.54272i	−0.0914456	−	0.114669i	−0.825449	+	0.564476i	$0.809078\pi$
$182$	−0.192228	−	0.842207i	−0.0142489	−	0.0624285i
$183$	−14.5878	−	18.2926i	−1.07836	−	1.35223i
$184$	8.17994	−	3.93925i	0.603033	−	0.290405i
$185$	−2.63548	+	11.5468i	−0.193764	+	0.848938i
$186$	−4.28121	+	2.06172i	−0.313914	+	0.151173i
$187$	14.9208	−	18.7102i	1.09112	−	1.36822i
$188$	−2.20626	−	9.66627i	−0.160908	−	0.704985i
$189$	−2.34152	−	10.2589i	−0.170320	−	0.746222i
$190$	5.74512	+	2.76671i	0.416795	+	0.200718i
$191$	−5.51217	+	6.91204i	−0.398847	+	0.500138i	−0.940184	−	0.340668i	$-0.889347\pi$
$191$	−5.51217	+	6.91204i	−0.398847	+	0.500138i	0.541337	+	0.840806i	$0.317918\pi$
$192$	−1.13887	−	1.42810i	−0.0821909	−	0.103064i
$193$	1.97998	+	0.953510i	0.142522	+	0.0686351i	0.503786	−	0.863829i	$-0.331940\pi$
$193$	1.97998	+	0.953510i	0.142522	+	0.0686351i	−0.361263	+	0.932464i	$0.617654\pi$
$194$	11.3928	+	5.48647i	0.817953	+	0.393906i
$195$	−0.454876	−	0.570397i	−0.0325744	−	0.0408470i
$196$	−1.44778	+	1.81546i	−0.103413	+	0.129676i
$197$	−13.9539	−	6.71987i	−0.994178	−	0.478771i	−0.135219	−	0.990816i	$-0.543174\pi$
$197$	−13.9539	−	6.71987i	−0.994178	−	0.478771i	−0.858959	+	0.512045i	$0.828888\pi$
$198$	−0.350760	−	1.53678i	−0.0249274	−	0.109214i
$199$	−0.494605	−	2.16701i	−0.0350616	−	0.153615i	0.954367	−	0.298637i	$-0.0965319\pi$
$199$	−0.494605	−	2.16701i	−0.0350616	−	0.153615i	−0.989428	+	0.145022i	$0.953675\pi$
$200$	−0.623490	+	0.781831i	−0.0440874	+	0.0552838i
$201$	12.9946	−	6.25787i	0.916569	−	0.441396i
$202$	−1.08902	+	4.77131i	−0.0766232	+	0.335708i
$203$	1.07893	−	0.519584i	0.0757258	−	0.0364676i
$204$	5.81802	+	7.29556i	0.407343	+	0.510791i
$205$	−1.20057	−	5.26005i	−0.0838516	−	0.367378i
$206$	−7.62413	−	9.56035i	−0.531198	−	0.666101i
$207$	−0.679808	+	2.97844i	−0.0472500	+	0.207016i
$208$	−0.399410			−0.0276941
$209$	29.8712			2.06624
$210$	0.879110	−	3.85163i	0.0606644	−	0.265788i
$211$	0.450579	−	0.565008i	0.0310191	−	0.0388968i	−0.766080	−	0.642745i	$-0.777795\pi$
$211$	0.450579	−	0.565008i	0.0310191	−	0.0388968i	0.797099	+	0.603848i	$0.206367\pi$
$212$	9.19733	+	4.42920i	0.631675	+	0.304199i
$213$	2.60766	−	1.25578i	0.178674	−	0.0860449i
$214$	−7.23563			−0.494617
$215$	6.41760	−	1.34699i	0.437677	−	0.0918639i
$216$	−4.86518			−0.331034
$217$	−5.06931	+	2.44125i	−0.344127	+	0.165723i
$218$	2.63850	+	1.27064i	0.178702	+	0.0860584i
$219$	2.03457	−	2.55127i	0.137483	−	0.172399i
$220$	−1.04240	+	4.56705i	−0.0702786	+	0.307911i
$221$	2.04042			0.137253
$222$	−21.6339			−1.45197
$223$	5.04674	−	22.1112i	0.337955	−	1.48068i	−0.465359	−	0.885122i	$-0.654075\pi$
$223$	5.04674	−	22.1112i	0.337955	−	1.48068i	0.803314	−	0.595555i	$-0.203068\pi$
$224$	−1.34852	−	1.69099i	−0.0901016	−	0.112984i
$225$	−0.0748766	−	0.328056i	−0.00499177	−	0.0218704i
$226$	5.27840	+	6.61891i	0.351114	+	0.440283i
$227$	11.7173	−	5.64276i	0.777706	−	0.374523i	−0.00253960	−	0.999997i	$-0.500808\pi$
$227$	11.7173	−	5.64276i	0.777706	−	0.374523i	0.780246	+	0.625473i	$0.215094\pi$
$228$	−2.59182	+	11.3555i	−0.171648	+	0.752038i
$229$	−10.7434	+	5.17373i	−0.709941	+	0.341890i	−0.753760	−	0.657150i	$-0.771762\pi$
$229$	−10.7434	+	5.17373i	−0.709941	+	0.341890i	0.0438186	+	0.999040i	$0.486048\pi$
$230$	5.66069	−	7.09829i	0.373255	−	0.468047i
$231$	−4.11820	−	18.0430i	−0.270957	−	1.18714i
$232$	−0.123204	−	0.539793i	−0.00808875	−	0.0354391i
$233$	5.60314	+	2.69833i	0.367074	+	0.176774i	0.608323	−	0.793690i	$-0.291843\pi$
$233$	5.60314	+	2.69833i	0.367074	+	0.176774i	−0.241249	+	0.970463i	$0.577557\pi$
$234$	0.0837961	−	0.105077i	0.00547792	−	0.00686910i
$235$	−6.18181	−	7.75175i	−0.403257	−	0.505668i
$236$	−0.664276	−	0.319899i	−0.0432407	−	0.0208236i
$237$	7.80743	+	3.75986i	0.507147	+	0.244229i
$238$	6.88902	+	8.63855i	0.446549	+	0.559954i
$239$	14.0430	−	17.6094i	0.908366	−	1.13905i	−0.0814466	−	0.996678i	$-0.525954\pi$
$239$	14.0430	−	17.6094i	0.908366	−	1.13905i	0.989812	−	0.142377i	$-0.0454746\pi$
$240$	−1.64572	−	0.792535i	−0.106231	−	0.0511579i
$241$	2.78291	+	12.1927i	0.179263	+	0.785402i	0.981971	+	0.189030i	$0.0605345\pi$
$241$	2.78291	+	12.1927i	0.179263	+	0.785402i	−0.802708	+	0.596372i	$0.796608\pi$
$242$	2.43540	+	10.6702i	0.156553	+	0.685905i
$243$	2.17038	−	2.72157i	0.139230	−	0.174589i
$244$	−11.5405	+	5.55763i	−0.738808	+	0.355791i
$245$	−0.516707	+	2.26384i	−0.0330112	+	0.144631i
$246$	8.87917	−	4.27598i	0.566115	−	0.272627i
$247$	1.58795	+	1.99123i	0.101039	+	0.126699i
$248$	0.578872	+	2.53621i	0.0367584	+	0.161049i
$249$	−18.7316	−	23.4887i	−1.18707	−	1.48854i
$250$	−0.222521	+	0.974928i	−0.0140735	+	0.0616599i
$251$	−2.95806			−0.186711			−0.0933555	−	0.995633i	$-0.529759\pi$
$251$	−2.95806			−0.186711			−0.0933555	+	0.995633i	$0.529759\pi$
$252$	0.727784			0.0458461
$253$	9.46400	−	41.4645i	0.594997	−	2.60685i
$254$	−8.63614	+	10.8294i	−0.541880	+	0.679496i
$255$	8.40728	+	4.04873i	0.526484	+	0.253541i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−3.90177			−0.243385			−0.121693	−	0.992568i	$-0.538832\pi$
$257$	−3.90177			−0.243385			−0.121693	+	0.992568i	$0.538832\pi$
$258$	5.00722	+	10.8810i	0.311736	+	0.677424i
$259$	−25.6163			−1.59172
$260$	−0.359856	+	0.173298i	−0.0223173	+	0.0107475i
$261$	0.167857	+	0.0808358i	0.0103901	+	0.00500361i
$262$	8.49265	−	10.6494i	0.524677	−	0.657925i
$263$	2.09185	−	9.16500i	0.128989	−	0.565138i	−0.868586	−	0.495539i	$-0.834971\pi$
$263$	2.09185	−	9.16500i	0.128989	−	0.565138i	0.997575	−	0.0695995i	$-0.0221721\pi$
$264$	−8.55675			−0.526631
$265$	10.2083			0.627089
$266$	−3.06894	+	13.4459i	−0.188169	+	0.824420i
$267$	3.81561	+	4.78463i	0.233512	+	0.292815i
$268$	−1.75703	−	7.69805i	−0.107328	−	0.470233i
$269$	−0.226753	−	0.284340i	−0.0138254	−	0.0173365i	0.774871	−	0.632120i	$-0.217815\pi$
$269$	−0.226753	−	0.284340i	−0.0138254	−	0.0173365i	−0.788696	+	0.614783i	$0.789243\pi$
$270$	−4.38338	+	2.11092i	−0.266764	+	0.128467i
$271$	−5.25909	+	23.0416i	−0.319467	+	1.39968i	0.519024	+	0.854760i	$0.326295\pi$
$271$	−5.25909	+	23.0416i	−0.319467	+	1.39968i	−0.838491	+	0.544916i	$0.816562\pi$
$272$	4.60267	−	2.21653i	0.279078	−	0.134397i
$273$	0.983832	−	1.23369i	0.0595442	−	0.0746661i
$274$	−4.09923	−	17.9599i	−0.247644	−	1.08500i
$275$	1.04240	+	4.56705i	0.0628591	+	0.275404i
$276$	14.9415	+	7.19546i	0.899375	+	0.433116i
$277$	−8.01648	+	10.0523i	−0.481664	+	0.603987i	−0.961984	−	0.273106i	$-0.911949\pi$
$277$	−8.01648	+	10.0523i	−0.481664	+	0.603987i	0.480320	+	0.877093i	$0.340520\pi$
$278$	2.48756	+	3.11930i	0.149194	+	0.187083i
$279$	−0.788673	−	0.379805i	−0.0472166	−	0.0227383i
$280$	−1.94866	−	0.938427i	−0.116455	−	0.0560818i
$281$	11.5851	+	14.5273i	0.691111	+	0.866626i	0.996325	−	0.0856580i	$-0.0272992\pi$
$281$	11.5851	+	14.5273i	0.691111	+	0.866626i	−0.305213	+	0.952284i	$0.598728\pi$
$282$	11.2917	−	14.1594i	0.672413	−	0.843180i
$283$	24.1715	+	11.6404i	1.43685	+	0.691950i	0.980257	−	0.197727i	$-0.0633560\pi$
$283$	24.1715	+	11.6404i	1.43685	+	0.691950i	0.456591	+	0.889677i	$0.349070\pi$
$284$	−0.352588	−	1.54479i	−0.0209222	−	0.0916663i
$285$	2.59182	+	11.3555i	0.153526	+	0.672643i
$286$	−1.16657	+	1.46284i	−0.0689809	+	0.0864993i
$287$	10.5137	−	5.06312i	0.620603	−	0.298867i
$288$	0.0748766	−	0.328056i	0.00441215	−	0.0193309i
$289$	−8.19668	+	3.94731i	−0.482157	+	0.232195i
$290$	−0.345211	−	0.432880i	−0.0202715	−	0.0254196i
$291$	5.13967	+	22.5184i	0.301293	+	1.32005i
$292$	−1.11385	−	1.39672i	−0.0651831	−	0.0817371i
$293$	−1.22421	+	5.36363i	−0.0715193	+	0.313347i	−0.998016	−	0.0629555i	$-0.979947\pi$
$293$	−1.22421	+	5.36363i	−0.0715193	+	0.313347i	0.926497	+	0.376302i	$0.122805\pi$
$294$	−4.24149			−0.247369
$295$	−0.737291			−0.0429267
$296$	−2.63548	+	11.5468i	−0.153184	+	0.671144i
$297$	−14.2099	+	17.8187i	−0.824544	+	1.03395i
$298$	15.4075	+	7.41984i	0.892530	+	0.429820i
$299$	3.26715	−	1.57338i	0.188944	−	0.0909907i
$300$	−1.82661			−0.105459
$301$	5.92897	+	12.8841i	0.341740	+	0.742624i
$302$	−17.5636			−1.01067
$303$	−8.05415	+	3.87867i	−0.462699	+	0.222824i
$304$	5.74512	+	2.76671i	0.329505	+	0.158681i
$305$	−7.98631	+	10.0145i	−0.457295	+	0.573429i
$306$	−0.382513	+	1.67590i	−0.0218668	+	0.0958049i
$307$	6.78592			0.387293			0.193647	−	0.981071i	$-0.437969\pi$
$307$	6.78592			0.387293			0.193647	+	0.981071i	$0.437969\pi$
$308$	−10.1319			−0.577319
$309$	4.97023	−	21.7760i	0.282747	−	1.23879i
$310$	1.62196	+	2.03388i	0.0921214	+	0.115517i
$311$	−4.18505	−	18.3359i	−0.237313	−	1.03973i	−0.943412	−	0.331622i	$-0.892404\pi$
$311$	−4.18505	−	18.3359i	−0.237313	−	1.03973i	0.706100	−	0.708112i	$-0.250453\pi$
$312$	−0.454876	−	0.570397i	−0.0257523	−	0.0322924i
$313$	−11.1504	+	5.36976i	−0.630259	+	0.303517i	−0.721608	−	0.692302i	$-0.756597\pi$
$313$	−11.1504	+	5.36976i	−0.630259	+	0.303517i	0.0913485	+	0.995819i	$0.470882\pi$
$314$	2.99608	−	13.1267i	0.169079	−	0.740783i
$315$	0.655711	−	0.315774i	0.0369451	−	0.0177918i
$316$	2.95789	−	3.70908i	0.166394	−	0.208652i
$317$	2.92939	+	12.8345i	0.164531	+	0.720858i	0.988122	+	0.153673i	$0.0491104\pi$
$317$	2.92939	+	12.8345i	0.164531	+	0.720858i	−0.823591	+	0.567185i	$0.808033\pi$
$318$	4.14923	+	18.1790i	0.232678	+	1.01943i
$319$	−2.33684	−	1.12536i	−0.130838	−	0.0630081i
$320$	−0.623490	+	0.781831i	−0.0348541	+	0.0437057i
$321$	−8.24044	−	10.3332i	−0.459937	−	0.576742i
$322$	17.6920	+	8.52003i	0.985938	+	0.474803i
$323$	−29.3494	−	14.1339i	−1.63305	−	0.786434i
$324$	−6.17021	−	7.73720i	−0.342790	−	0.429844i
$325$	−0.249028	+	0.312271i	−0.0138136	+	0.0173217i
$326$	−0.0451724	−	0.0217539i	−0.00250187	−	0.00120484i
$327$	1.19032	+	5.21514i	0.0658249	+	0.288398i
$328$	−1.20057	−	5.26005i	−0.0662905	−	0.290438i
$329$	13.3704	−	16.7659i	0.737132	−	0.924334i
$330$	−7.70936	+	3.71263i	−0.424386	+	0.204374i
$331$	6.84821	−	30.0040i	0.376412	−	1.64917i	−0.331935	−	0.943302i	$-0.607702\pi$
$331$	6.84821	−	30.0040i	0.376412	−	1.64917i	0.708347	−	0.705865i	$-0.249441\pi$
$332$	−14.8187	+	7.13632i	−0.813283	+	0.391656i
$333$	−2.48481	−	3.11586i	−0.136167	−	0.170748i
$334$	−3.62721	−	15.8918i	−0.198472	−	0.869562i
$335$	−4.92309	−	6.17336i	−0.268977	−	0.337287i
$336$	0.879110	−	3.85163i	0.0479594	−	0.210124i
$337$	9.60533			0.523236			0.261618	−	0.965172i	$-0.415744\pi$
$337$	9.60533			0.523236			0.261618	+	0.965172i	$0.415744\pi$
$338$	12.8405			0.698430
$339$	−3.44103	+	15.0762i	−0.186891	+	0.818824i
$340$	3.18515	−	3.99405i	0.172739	−	0.216608i
$341$	10.9796	+	5.28748i	0.594577	+	0.286333i
$342$	−1.93319	+	0.930976i	−0.104535	+	0.0503414i
$343$	−20.1623			−1.08866
$344$	6.41760	−	1.34699i	0.346014	−	0.0726248i
$345$	16.5839			0.892845
$346$	−0.808888	+	0.389540i	−0.0434861	+	0.0209418i
$347$	31.7639	+	15.2967i	1.70517	+	0.821169i	0.992857	+	0.119311i	$0.0380684\pi$
$347$	31.7639	+	15.2967i	1.70517	+	0.821169i	0.712317	+	0.701858i	$0.247646\pi$
$348$	0.630564	−	0.790702i	0.0338018	−	0.0423861i
$349$	−0.500397	+	2.19238i	−0.0267856	+	0.117356i	−0.986553	−	0.163440i	$-0.947741\pi$
$349$	−0.500397	+	2.19238i	−0.0267856	+	0.117356i	0.959768	+	0.280795i	$0.0905982\pi$
$350$	−2.16285			−0.115609
$351$	−1.94320			−0.103720
$352$	−1.04240	+	4.56705i	−0.0555601	+	0.243425i
$353$	6.74583	+	8.45900i	0.359044	+	0.450227i	0.928244	−	0.371972i	$-0.121318\pi$
$353$	6.74583	+	8.45900i	0.359044	+	0.450227i	−0.569200	+	0.822199i	$0.692747\pi$
$354$	−0.299678	−	1.31298i	−0.0159277	−	0.0697838i
$355$	−0.987929	−	1.23882i	−0.0524338	−	0.0657499i
$356$	3.01856	−	1.45366i	0.159983	−	0.0770439i
$357$	−4.49101	+	19.6764i	−0.237689	+	1.04138i
$358$	14.5103	−	6.98781i	0.766895	−	0.369317i
$359$	−6.55240	+	8.21645i	−0.345823	+	0.433648i	−0.924076	−	0.382210i	$-0.875163\pi$
$359$	−6.55240	+	8.21645i	−0.345823	+	0.433648i	0.578253	+	0.815857i	$0.303735\pi$
$360$	−0.0748766	−	0.328056i	−0.00394634	−	0.0172901i
$361$	−4.82005	−	21.1180i	−0.253687	−	1.11148i
$362$	−1.77780	−	0.856143i	−0.0934391	−	0.0449979i
$363$	−12.4645	+	15.6299i	−0.654215	+	0.820359i
$364$	−0.538612	−	0.675398i	−0.0282309	−	0.0354004i
$365$	−1.60956	−	0.775123i	−0.0842482	−	0.0405718i
$366$	−21.0800	−	10.1516i	−1.10187	−	0.530633i
$367$	−9.88527	−	12.3957i	−0.516007	−	0.647052i	0.453749	−	0.891130i	$-0.350086\pi$
$367$	−9.88527	−	12.3957i	−0.516007	−	0.647052i	−0.969756	+	0.244078i	$0.921515\pi$
$368$	5.66069	−	7.09829i	0.295084	−	0.370024i
$369$	1.63570	+	0.787710i	0.0851509	+	0.0410065i
$370$	2.63548	+	11.5468i	0.137012	+	0.600290i
$371$	4.91304	+	21.5254i	0.255072	+	1.11754i
$372$	−2.96269	+	3.71510i	−0.153608	+	0.192619i
$373$	−28.6699	+	13.8067i	−1.48447	+	0.714884i	−0.988184	−	0.153274i	$-0.951018\pi$
$373$	−28.6699	+	13.8067i	−1.48447	+	0.714884i	−0.496288	+	0.868158i	$0.665304\pi$
$374$	5.32519	−	23.3312i	0.275359	−	1.20643i
$375$	−1.64572	+	0.792535i	−0.0849844	+	0.0409263i
$376$	−6.18181	−	7.75175i	−0.318803	−	0.399766i
$377$	−0.0492090	−	0.215599i	−0.00253439	−	0.0111039i
$378$	−6.56078	−	8.22696i	−0.337450	−	0.423149i
$379$	3.40327	−	14.9107i	0.174814	−	0.765912i	−0.809158	−	0.587591i	$-0.800076\pi$
$379$	3.40327	−	14.9107i	0.174814	−	0.765912i	0.983972	−	0.178321i	$-0.0570664\pi$
$380$	6.37661			0.327113
$381$	−25.3009			−1.29620
$382$	−1.96727	+	8.61918i	−0.100654	+	0.440995i
$383$	−6.87109	+	8.61608i	−0.351097	+	0.440261i	−0.925750	−	0.378136i	$-0.876565\pi$
$383$	−6.87109	+	8.61608i	−0.351097	+	0.440261i	0.574654	+	0.818397i	$0.305137\pi$
$384$	−1.64572	−	0.792535i	−0.0839826	−	0.0404439i
$385$	−9.12853	+	4.39607i	−0.465233	+	0.224044i
$386$	2.19762			0.111856
$387$	−0.992044	+	1.97094i	−0.0504284	+	0.100189i
$388$	12.6450			0.641954
$389$	9.33328	−	4.49467i	0.473216	−	0.227889i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	9.33328	−	4.49467i	0.473216	−	0.227889i	0.655263	+	0.755401i	$0.272558\pi$
$390$	−0.657315	−	0.316546i	−0.0332845	−	0.0160290i
$391$	−28.9181	+	36.2622i	−1.46245	+	1.83386i
$392$	−0.516707	+	2.26384i	−0.0260976	+	0.114341i
$393$	24.8805			1.25505
$394$	−15.4877			−0.780260
$395$	1.05566	−	4.62515i	0.0531160	−	0.232716i
$396$	−0.982807	−	1.23240i	−0.0493879	−	0.0619305i
$397$	0.914852	+	4.00823i	0.0459151	+	0.201167i	0.992683	−	0.120750i	$-0.0385299\pi$
$397$	0.914852	+	4.00823i	0.0459151	+	0.201167i	−0.946768	+	0.321917i	$0.895673\pi$
$398$	−1.38585	−	1.73780i	−0.0694665	−	0.0871082i
$399$	−22.6972	+	10.9304i	−1.13628	+	0.547204i
$400$	−0.222521	+	0.974928i	−0.0111260	+	0.0487464i
$401$	−10.0249	+	4.82773i	−0.500619	+	0.241085i	−0.667112	−	0.744957i	$-0.732470\pi$
$401$	−10.0249	+	4.82773i	−0.500619	+	0.241085i	0.166494	+	0.986043i	$0.446756\pi$
$402$	8.99255	−	11.2763i	0.448508	−	0.562411i
$403$	0.231207	+	1.01299i	0.0115173	+	0.0504604i
$404$	1.08902	+	4.77131i	0.0541808	+	0.237381i
$405$	−8.91621	−	4.29382i	−0.443050	−	0.213362i
$406$	0.746640	−	0.936257i	0.0370551	−	0.0464657i
$407$	34.5925	+	43.3776i	1.71469	+	2.15015i
$408$	8.40728	+	4.04873i	0.416222	+	0.200442i
$409$	−15.3958	−	7.41421i	−0.761271	−	0.366609i	0.0126258	−	0.999920i	$-0.495981\pi$
$409$	−15.3958	−	7.41421i	−0.761271	−	0.366609i	−0.773897	+	0.633311i	$0.781695\pi$
$410$	−3.36393	−	4.21823i	−0.166133	−	0.208324i
$411$	20.9800	−	26.3081i	1.03487	−	1.29768i
$412$	−11.0172	−	5.30559i	−0.542778	−	0.261388i
$413$	−0.354844	−	1.55467i	−0.0174607	−	0.0765004i
$414$	0.679808	+	2.97844i	0.0334108	+	0.146382i
$415$	−10.2549	+	12.8592i	−0.503392	+	0.631233i
$416$	−0.359856	+	0.173298i	−0.0176434	+	0.00849661i
$417$	−1.62166	+	7.10496i	−0.0794131	+	0.347932i
$418$	26.9131	−	12.9606i	1.31636	−	0.633926i
$419$	−24.1338	−	30.2628i	−1.17901	−	1.47844i	−0.844098	−	0.536189i	$-0.819864\pi$
$419$	−24.1338	−	30.2628i	−1.17901	−	1.47844i	−0.334916	−	0.942248i	$-0.608708\pi$
$420$	−0.879110	−	3.85163i	−0.0428962	−	0.187940i
$421$	18.7651	+	23.5307i	0.914554	+	1.14681i	0.988751	+	0.149571i	$0.0477893\pi$
$421$	18.7651	+	23.5307i	0.914554	+	1.14681i	−0.0741966	+	0.997244i	$0.523639\pi$
$422$	0.160810	−	0.704554i	0.00782810	−	0.0342971i
$423$	3.33628			0.162215
$424$	10.2083			0.495757
$425$	1.13677	−	4.98050i	0.0551413	−	0.241590i
$426$	1.80456	−	2.26284i	0.0874311	−	0.109635i
$427$	−24.9605	−	12.0204i	−1.20792	−	0.581706i
$428$	−6.51907	+	3.13942i	−0.315111	+	0.151750i
$429$	−3.41765			−0.165006
$430$	5.19762	−	3.99809i	0.250652	−	0.192805i
$431$	16.9105			0.814548			0.407274	−	0.913306i	$-0.366479\pi$
$431$	16.9105			0.814548			0.407274	+	0.913306i	$0.366479\pi$
$432$	−4.38338	+	2.11092i	−0.210895	+	0.101562i
$433$	−9.94955	−	4.79145i	−0.478145	−	0.230262i	0.179257	−	0.983802i	$-0.442631\pi$
$433$	−9.94955	−	4.79145i	−0.478145	−	0.230262i	−0.657402	+	0.753540i	$0.728345\pi$
$434$	−3.50807	+	4.39898i	−0.168393	+	0.211158i
$435$	0.225046	−	0.985990i	0.0107901	−	0.0472746i
$436$	2.92852			0.140251
$437$	−57.8935			−2.76942
$438$	0.726128	−	3.18138i	0.0346958	−	0.152012i
$439$	−0.306604	−	0.384470i	−0.0146334	−	0.0183497i	0.774461	−	0.632622i	$-0.218021\pi$
$439$	−0.306604	−	0.384470i	−0.0146334	−	0.0183497i	−0.789094	+	0.614272i	$0.789450\pi$
$440$	1.04240	+	4.56705i	0.0496945	+	0.217726i
$441$	−0.487167	−	0.610888i	−0.0231984	−	0.0290899i
$442$	1.83835	−	0.885305i	0.0874416	−	0.0421097i
$443$	−5.01488	+	21.9716i	−0.238264	+	1.04390i	0.704306	+	0.709896i	$0.251258\pi$
$443$	−5.01488	+	21.9716i	−0.238264	+	1.04390i	−0.942571	+	0.334007i	$0.891599\pi$
$444$	−19.4914	+	9.38658i	−0.925023	+	0.445468i
$445$	2.08891	−	2.61941i	0.0990238	−	0.124172i
$446$	−5.04674	−	22.1112i	−0.238970	−	1.04700i
$447$	6.95084	+	30.4536i	0.328763	+	1.44041i
$448$	−1.94866	−	0.938427i	−0.0920658	−	0.0443365i
$449$	−11.4008	+	14.2962i	−0.538039	+	0.674680i	−0.974330	−	0.225126i	$-0.927721\pi$
$449$	−11.4008	+	14.2962i	−0.538039	+	0.674680i	0.436290	+	0.899806i	$0.356292\pi$
$450$	−0.209800	−	0.263080i	−0.00989005	−	0.0124017i
$451$	−22.7715	−	10.9662i	−1.07227	−	0.516376i
$452$	7.62751	+	3.67322i	0.358768	+	0.172774i
$453$	−20.0027	−	25.0826i	−0.939809	−	1.17848i
$454$	8.10864	−	10.1679i	0.380557	−	0.477204i
$455$	−0.778316	−	0.374817i	−0.0364880	−	0.0175717i
$456$	2.59182	+	11.3555i	0.121373	+	0.531771i
$457$	4.30617	+	18.8666i	0.201434	+	0.882541i	0.970064	+	0.242848i	$0.0780815\pi$
$457$	4.30617	+	18.8666i	0.201434	+	0.882541i	−0.768630	+	0.639693i	$0.779061\pi$
$458$	−7.43464	+	9.32274i	−0.347398	+	0.435623i
$459$	22.3928	−	10.7838i	1.04521	−	0.503346i
$460$	2.02028	−	8.85142i	0.0941960	−	0.412699i
$461$	−15.7408	+	7.58038i	−0.733123	+	0.353054i	−0.762912	−	0.646503i	$-0.776231\pi$
$461$	−15.7408	+	7.58038i	−0.733123	+	0.353054i	0.0297885	+	0.999556i	$0.490517\pi$
$462$	−11.5389	−	14.4694i	−0.536839	−	0.673175i
$463$	−4.42834	−	19.4018i	−0.205802	−	0.901679i	−0.967325	−	0.253540i	$-0.918405\pi$
$463$	−4.42834	−	19.4018i	−0.205802	−	0.901679i	0.761523	−	0.648138i	$-0.224452\pi$
$464$	−0.345211	−	0.432880i	−0.0160260	−	0.0200960i
$465$	−1.05737	+	4.63265i	−0.0490345	+	0.214834i
$466$	6.21902			0.288091
$467$	9.11102			0.421608			0.210804	−	0.977528i	$-0.432392\pi$
$467$	9.11102			0.421608			0.210804	+	0.977528i	$0.432392\pi$
$468$	0.0299065	−	0.131029i	0.00138243	−	0.00605681i
$469$	10.6479	−	13.3521i	0.491676	−	0.616542i
$470$	−8.93298	−	4.30190i	−0.412048	−	0.198432i
$471$	22.1584	−	10.6709i	1.02100	−	0.491690i
$472$	−0.737291			−0.0339366
$473$	13.8108	−	27.4386i	0.635022	−	1.26163i
$474$	8.66559			0.398024
$475$	5.74512	−	2.76671i	0.263604	−	0.126945i
$476$	9.95492	+	4.79403i	0.456283	+	0.219734i
$477$	−2.14169	+	2.68559i	−0.0980613	+	0.122965i
$478$	5.01189	−	21.9585i	0.229238	−	1.00436i
$479$	−0.567103			−0.0259116			−0.0129558	−	0.999916i	$-0.504124\pi$
$479$	−0.567103			−0.0259116			−0.0129558	+	0.999916i	$0.504124\pi$
$480$	−1.82661			−0.0833728
$481$	−1.05264	+	4.61191i	−0.0479962	+	0.210285i
$482$	7.79754	+	9.77780i	0.355168	+	0.445367i
$483$	7.98148	+	34.9692i	0.363170	+	1.59115i
$484$	6.82383	+	8.55682i	0.310174	+	0.388946i
$485$	11.3928	−	5.48647i	0.517319	−	0.249128i
$486$	0.774599	−	3.39374i	0.0351365	−	0.153943i
$487$	−18.6244	+	8.96902i	−0.843950	+	0.406425i	−0.805329	−	0.592829i	$-0.798011\pi$
$487$	−18.6244	+	8.96902i	−0.843950	+	0.406425i	−0.0386219	+	0.999254i	$0.512297\pi$
$488$	−7.98631	+	10.0145i	−0.361523	+	0.453336i
$489$	−0.0203788	−	0.0892855i	−0.000921563	−	0.00403763i
$490$	0.516707	+	2.26384i	0.0233424	+	0.102270i
$491$	−19.3695	−	9.32784i	−0.874131	−	0.420959i	−0.0576538	−	0.998337i	$-0.518362\pi$
$491$	−19.3695	−	9.32784i	−0.874131	−	0.420959i	−0.816478	+	0.577377i	$0.804076\pi$
$492$	6.14458	−	7.70505i	0.277019	−	0.347371i
$493$	1.76354	+	2.21141i	0.0794257	+	0.0995967i
$494$	2.29466	+	1.10505i	0.103242	+	0.0497186i
$495$	−1.42020	−	0.683931i	−0.0638331	−	0.0307404i
$496$	1.62196	+	2.03388i	0.0728283	+	0.0913239i
$497$	2.13675	−	2.67940i	0.0958462	−	0.120187i
$498$	−27.0680	−	13.0352i	−1.21294	−	0.584123i
$499$	−3.23837	−	14.1882i	−0.144970	−	0.635153i	−0.994238	−	0.107192i	$-0.965814\pi$
$499$	−3.23837	−	14.1882i	−0.144970	−	0.635153i	0.849269	−	0.527961i	$-0.177043\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	18.5642	−	23.2788i	0.829387	−	1.04002i
$502$	−2.66512	+	1.28345i	−0.118950	+	0.0572833i
$503$	−5.93410	+	25.9990i	−0.264588	+	1.15924i	0.651623	+	0.758543i	$0.274088\pi$
$503$	−5.93410	+	25.9990i	−0.264588	+	1.15924i	−0.916212	+	0.400695i	$0.868769\pi$
$504$	0.655711	−	0.315774i	0.0292077	−	0.0140657i
$505$	3.05137	+	3.82629i	0.135784	+	0.170268i
$506$	−9.46400	−	41.4645i	−0.420726	−	1.84332i
$507$	14.6236	+	18.3375i	0.649459	+	0.814395i
$508$	−3.08220	+	13.5040i	−0.136751	+	0.599144i
$509$	−22.6383			−1.00343			−0.501713	−	0.865034i	$-0.667297\pi$
$509$	−22.6383			−1.00343			−0.501713	+	0.865034i	$0.667297\pi$
$510$	9.33137			0.413200
$511$	0.859796	−	3.76701i	0.0380352	−	0.166643i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	27.9511	+	13.4605i	1.23407	+	0.594297i
$514$	−3.51537	+	1.69291i	−0.155056	+	0.0746712i
$515$	−12.2281			−0.538837
$516$	9.23245	+	7.63092i	0.406436	+	0.335933i
$517$	−46.4462			−2.04270
$518$	−23.0795	+	11.1145i	−1.01405	+	0.488343i
$519$	−1.47752	−	0.711537i	−0.0648560	−	0.0312330i
$520$	−0.249028	+	0.312271i	−0.0109206	+	0.0136940i
$521$	−0.125602	+	0.550299i	−0.00550273	+	0.0241090i	−0.977605	−	0.210449i	$-0.932507\pi$
$521$	−0.125602	+	0.550299i	−0.00550273	+	0.0241090i	0.972102	+	0.234558i	$0.0753644\pi$
$522$	0.186307			0.00815445
$523$	15.2018			0.664726			0.332363	−	0.943151i	$-0.392154\pi$
$523$	15.2018			0.664726			0.332363	+	0.943151i	$0.392154\pi$
$524$	3.03099	−	13.2796i	0.132409	−	0.580124i
$525$	−2.46321	−	3.08877i	−0.107503	−	0.134805i
$526$	−2.09185	−	9.16500i	−0.0912091	−	0.399613i
$527$	−8.28594	−	10.3902i	−0.360941	−	0.452606i
$528$	−7.70936	+	3.71263i	−0.335507	+	0.161572i
$529$	−13.2242	+	57.9391i	−0.574966	+	2.51909i
$530$	9.19733	−	4.42920i	0.399507	−	0.192392i
$531$	0.154683	−	0.193967i	0.00671269	−	0.00841744i
$532$	3.06894	+	13.4459i	0.133055	+	0.582953i
$533$	−0.479521	−	2.10092i	−0.0207703	−	0.0910008i
$534$	5.51372	+	2.65527i	0.238602	+	0.114905i
$535$	−4.51134	+	5.65704i	−0.195042	+	0.244575i
$536$	−4.92309	−	6.17336i	−0.212645	−	0.266649i
$537$	26.5047	+	12.7640i	1.14376	+	0.550806i
$538$	−0.327668	−	0.157797i	−0.0141268	−	0.00680310i
$539$	6.78213	+	8.50453i	0.292127	+	0.366316i
$540$	−3.03339	+	3.80375i	−0.130536	+	0.163687i
$541$	−7.28191	−	3.50678i	−0.313074	−	0.150768i	0.270748	−	0.962650i	$-0.412729\pi$
$541$	−7.28191	−	3.50678i	−0.313074	−	0.150768i	−0.583822	+	0.811882i	$0.698443\pi$
$542$	5.25909	+	23.0416i	0.225897	+	0.989720i
$543$	−0.802027	−	3.51391i	−0.0344183	−	0.150796i
$544$	3.18515	−	3.99405i	0.136562	−	0.171244i
$545$	2.63850	−	1.27064i	0.113021	−	0.0544281i
$546$	0.351125	−	1.53838i	0.0150268	−	0.0658366i
$547$	28.3184	−	13.6374i	1.21081	−	0.583095i	0.284071	−	0.958803i	$-0.408315\pi$
$547$	28.3184	−	13.6374i	1.21081	−	0.583095i	0.926738	+	0.375709i	$0.122601\pi$
$548$	−11.4858	−	14.4027i	−0.490649	−	0.615254i
$549$	−0.959098	−	4.20208i	−0.0409333	−	0.179340i
$550$	2.92074	+	3.66249i	0.124541	+	0.156169i
$551$	−0.785625	+	3.44205i	−0.0334688	+	0.146636i
$552$	16.5839			0.705856
$553$	10.2608			0.436333
$554$	−2.86105	+	12.5351i	−0.121554	+	0.532564i
$555$	−13.4885	+	16.9140i	−0.572555	+	0.717961i
$556$	3.59463	+	1.73108i	0.152446	+	0.0734142i
$557$	5.55371	−	2.67452i	0.235318	−	0.113323i	−0.312509	−	0.949915i	$-0.601169\pi$
$557$	5.55371	−	2.67452i	0.235318	−	0.113323i	0.547827	+	0.836592i	$0.315455\pi$
$558$	−0.875361			−0.0370570
$559$	2.56325	−	0.538001i	0.108414	−	0.0227550i
$560$	−2.16285			−0.0913973
$561$	39.3839	−	18.9663i	1.66279	−	0.800758i
$562$	16.7410	+	8.06204i	0.706177	+	0.340077i
$563$	−18.9490	+	23.7613i	−0.798607	+	1.00142i	0.201154	+	0.979560i	$0.435531\pi$
$563$	−18.9490	+	23.7613i	−0.798607	+	1.00142i	−0.999761	+	0.0218618i	$0.993041\pi$
$564$	4.02998	−	17.6565i	0.169693	−	0.743472i
$565$	8.46590			0.356163
$566$	26.8284			1.12768
$567$	4.76287	−	20.8675i	0.200022	−	0.876353i
$568$	−0.987929	−	1.23882i	−0.0414526	−	0.0519799i
$569$	1.78697	+	7.82922i	0.0749136	+	0.328218i	0.998473	−	0.0552368i	$-0.0175914\pi$
$569$	1.78697	+	7.82922i	0.0749136	+	0.328218i	−0.923560	+	0.383455i	$0.874734\pi$
$570$	7.26213	+	9.10642i	0.304177	+	0.381426i
$571$	−14.0309	+	6.75693i	−0.587175	+	0.282769i	−0.703789	−	0.710409i	$-0.748510\pi$
$571$	−14.0309	+	6.75693i	−0.587175	+	0.282769i	0.116614	+	0.993177i	$0.462796\pi$
$572$	−0.416345	+	1.82413i	−0.0174083	+	0.0762706i
$573$	−14.5495	+	7.00667i	−0.607814	+	0.292708i
$574$	7.27569	−	9.12343i	0.303681	−	0.380804i
$575$	−2.02028	−	8.85142i	−0.0842514	−	0.369130i
$576$	−0.0748766	−	0.328056i	−0.00311986	−	0.0136690i
$577$	−29.3060	−	14.1130i	−1.22002	−	0.587532i	−0.290706	−	0.956813i	$-0.593890\pi$
$577$	−29.3060	−	14.1130i	−1.22002	−	0.587532i	−0.929318	+	0.369280i	$0.879604\pi$
$578$	−5.67228	+	7.11281i	−0.235936	+	0.295854i
$579$	2.50280	+	3.13841i	0.104013	+	0.130428i
$580$	−0.498844	−	0.240231i	−0.0207134	−	0.00997503i
$581$	−32.0507	−	15.4348i	−1.32969	−	0.640344i
$582$	14.4010	+	18.0583i	0.596942	+	0.748542i
$583$	29.8157	−	37.3877i	1.23484	−	1.54844i
$584$	−1.60956	−	0.775123i	−0.0666041	−	0.0320748i
$585$	−0.0299065	−	0.131029i	−0.00123648	−	0.00541737i
$586$	1.22421	+	5.36363i	0.0505718	+	0.221570i
$587$	−10.2785	+	12.8888i	−0.424239	+	0.531979i	−0.947313	−	0.320308i	$-0.896214\pi$
$587$	−10.2785	+	12.8888i	−0.424239	+	0.531979i	0.523074	+	0.852287i	$0.324785\pi$
$588$	−3.82145	+	1.84031i	−0.157594	+	0.0758933i
$589$	3.69124	−	16.1724i	0.152095	−	0.666372i
$590$	−0.664276	+	0.319899i	−0.0273478	+	0.0131700i
$591$	−17.6385	−	22.1180i	−0.725551	−	0.909812i
$592$	2.63548	+	11.5468i	0.108318	+	0.474571i
$593$	−12.2688	−	15.3847i	−0.503821	−	0.631772i	0.463265	−	0.886220i	$-0.346678\pi$
$593$	−12.2688	−	15.3847i	−0.503821	−	0.631772i	−0.967087	+	0.254448i	$0.918106\pi$
$594$	−5.07147	+	22.2195i	−0.208085	+	0.911679i
$595$	11.0491			0.452970
$596$	17.1010			0.700484
$597$	0.903449	−	3.95827i	0.0369757	−	0.162001i
$598$	2.26094	−	2.83513i	0.0924566	−	0.115937i
$599$	10.4807	+	5.04726i	0.428232	+	0.206225i	0.635569	−	0.772044i	$-0.280766\pi$
$599$	10.4807	+	5.04726i	0.428232	+	0.206225i	−0.207337	+	0.978269i	$0.566480\pi$
$600$	−1.64572	+	0.792535i	−0.0671861	+	0.0323551i
$601$	13.1416			0.536059			0.268029	−	0.963411i	$-0.413628\pi$
$601$	13.1416			0.536059			0.268029	+	0.963411i	$0.413628\pi$
$602$	10.9320	+	9.03565i	0.445555	+	0.368265i
$603$	2.65695			0.108199
$604$	−15.8243	+	7.62058i	−0.643881	+	0.310077i
$605$	9.86073	+	4.74868i	0.400896	+	0.193061i
$606$	−5.57364	+	6.98913i	−0.226414	+	0.283914i
$607$	−9.20119	+	40.3131i	−0.373465	+	1.63626i	0.343504	+	0.939151i	$0.388386\pi$
$607$	−9.20119	+	40.3131i	−0.373465	+	1.63626i	−0.716969	+	0.697105i	$0.754471\pi$
$608$	6.37661			0.258606
$609$	2.18739			0.0886377
$610$	−2.85028	+	12.4879i	−0.115404	+	0.505620i
$611$	−2.46908	−	3.09613i	−0.0998882	−	0.125256i
$612$	0.382513	+	1.67590i	0.0154622	+	0.0677443i
$613$	5.66026	+	7.09774i	0.228616	+	0.286675i	0.882888	−	0.469584i	$-0.155596\pi$
$613$	5.66026	+	7.09774i	0.228616	+	0.286675i	−0.654272	+	0.756259i	$0.727025\pi$
$614$	6.11390	−	2.94430i	0.246737	−	0.118822i
$615$	2.19297	−	9.60805i	0.0884292	−	0.387434i
$616$	−9.12853	+	4.39607i	−0.367799	+	0.177123i
$617$	29.6540	−	37.1850i	1.19383	−	1.49701i	0.371079	−	0.928601i	$-0.378988\pi$
$617$	29.6540	−	37.1850i	1.19383	−	1.49701i	0.822747	−	0.568408i	$-0.192441\pi$
$618$	−4.97023	−	21.7760i	−0.199932	−	0.875960i
$619$	3.95110	+	17.3109i	0.158808	+	0.695785i	0.990149	+	0.140021i	$0.0447170\pi$
$619$	3.95110	+	17.3109i	0.158808	+	0.695785i	−0.831340	+	0.555764i	$0.812426\pi$
$620$	2.34381	+	1.12872i	0.0941295	+	0.0453304i
$621$	27.5403	−	34.5344i	1.10515	−	1.38582i
$622$	−11.7263	−	14.7043i	−0.470180	−	0.589587i
$623$	6.52871	+	3.14406i	0.261567	+	0.125964i
$624$	−0.657315	−	0.316546i	−0.0263137	−	0.0126720i
$625$	0.623490	+	0.781831i	0.0249396	+	0.0312733i
$626$	−7.71633	+	9.67598i	−0.308407	+	0.386730i
$627$	49.1596	+	23.6740i	1.96324	+	0.945449i
$628$	−2.99608	−	13.1267i	−0.119557	−	0.523812i
$629$	−13.4636	−	58.9878i	−0.536828	−	2.35200i
$630$	0.453766	−	0.569005i	0.0180785	−	0.0226697i
$631$	11.4365	−	5.50751i	0.455279	−	0.219251i	−0.192167	−	0.981362i	$-0.561552\pi$
$631$	11.4365	−	5.50751i	0.455279	−	0.219251i	0.647446	+	0.762112i	$0.275837\pi$
$632$	1.05566	−	4.62515i	0.0419919	−	0.183978i
$633$	1.18931	−	0.572743i	0.0472710	−	0.0227645i
$634$	8.20798	+	10.2925i	0.325981	+	0.408767i
$635$	3.08220	+	13.5040i	0.122314	+	0.535891i
$636$	11.6259	+	14.5784i	0.460997	+	0.578072i
$637$	−0.206378	+	0.904201i	−0.00817699	+	0.0358257i
$638$	−2.59369			−0.102685
$639$	0.533177			0.0210922
$640$	−0.222521	+	0.974928i	−0.00879591	+	0.0385374i
$641$	7.31092	−	9.16760i	0.288764	−	0.362098i	−0.616198	−	0.787591i	$-0.711328\pi$
$641$	7.31092	−	9.16760i	0.288764	−	0.362098i	0.904962	+	0.425493i	$0.139899\pi$
$642$	−11.9078	−	5.73449i	−0.469963	−	0.226322i
$643$	3.16356	−	1.52349i	0.124759	−	0.0600806i	−0.370463	−	0.928847i	$-0.620801\pi$
$643$	3.16356	−	1.52349i	0.124759	−	0.0600806i	0.495222	+	0.868767i	$0.335087\pi$
$644$	19.6367			0.773793
$645$	11.6291	+	2.86941i	0.457895	+	0.112983i
$646$	−32.5754			−1.28166
$647$	20.5375	−	9.89033i	0.807412	−	0.388829i	0.0158168	−	0.999875i	$-0.494965\pi$
$647$	20.5375	−	9.89033i	0.807412	−	0.388829i	0.791595	+	0.611046i	$0.209251\pi$
$648$	−8.91621	−	4.29382i	−0.350262	−	0.168677i
$649$	−2.15344	+	2.70032i	−0.0845298	+	0.105997i
$650$	−0.0888771	+	0.389396i	−0.00348605	+	0.0152734i
$651$	−10.2774			−0.402804
$652$	−0.0501376			−0.00196354
$653$	0.428468	−	1.87724i	0.0167673	−	0.0734622i	−0.965852	−	0.259094i	$-0.916576\pi$
$653$	0.428468	−	1.87724i	0.0167673	−	0.0734622i	0.982619	+	0.185632i	$0.0594332\pi$
$654$	3.33520	+	4.18221i	0.130417	+	0.163538i
$655$	−3.03099	−	13.2796i	−0.118431	−	0.518878i
$656$	−3.36393	−	4.21823i	−0.131339	−	0.164694i
$657$	0.541605	−	0.260823i	0.0211300	−	0.0101757i
$658$	4.77183	−	20.9067i	0.186025	−	0.815030i
$659$	20.1824	−	9.71934i	0.786195	−	0.378612i	0.00268947	−	0.999996i	$-0.499144\pi$
$659$	20.1824	−	9.71934i	0.786195	−	0.378612i	0.783506	+	0.621385i	$0.213430\pi$
$660$	−5.33504	+	6.68993i	−0.207666	+	0.260405i
$661$	2.17869	+	9.54548i	0.0847414	+	0.371276i	0.999462	−	0.0328116i	$-0.0104461\pi$
$661$	2.17869	+	9.54548i	0.0847414	+	0.371276i	−0.914720	+	0.404088i	$0.867589\pi$
$662$	−6.84821	−	30.0040i	−0.266163	−	1.16614i
$663$	3.35795	+	1.61710i	0.130412	+	0.0628031i
$664$	−10.2549	+	12.8592i	−0.397966	+	0.499034i
$665$	8.59897	+	10.7828i	0.333454	+	0.418138i
$666$	−3.59066	−	1.72917i	−0.139135	−	0.0670040i
$667$	4.52903	+	2.18106i	0.175365	+	0.0844511i
$668$	−10.1632	−	12.7443i	−0.393226	−	0.493090i
$669$	25.8294	−	32.3891i	0.998623	−	1.25223i
$670$	−7.11407	−	3.42596i	−0.274841	−	0.132356i
$671$	13.3521	+	58.4996i	0.515454	+	2.25835i
$672$	−0.879110	−	3.85163i	−0.0339124	−	0.148580i
$673$	22.3540	−	28.0311i	0.861684	−	1.08052i	−0.134296	−	0.990941i	$-0.542877\pi$
$673$	22.3540	−	28.0311i	0.861684	−	1.08052i	0.995980	−	0.0895767i	$-0.0285514\pi$
$674$	8.65410	−	4.16760i	0.333344	−	0.160530i
$675$	−1.08260	+	4.74320i	−0.0416695	+	0.182566i
$676$	11.5689	−	5.57127i	0.444956	−	0.214280i
$677$	−7.78751	−	9.76523i	−0.299298	−	0.375308i	0.609328	−	0.792918i	$-0.291439\pi$
$677$	−7.78751	−	9.76523i	−0.299298	−	0.375308i	−0.908626	+	0.417610i	$0.862868\pi$
$678$	3.44103	+	15.0762i	0.132152	+	0.578996i
$679$	17.0520	+	21.3826i	0.654397	+	0.820588i
$680$	1.13677	−	4.98050i	0.0435930	−	0.190993i
$681$	23.7555			0.910312
$682$	12.1864			0.466642
$683$	−7.22369	+	31.6491i	−0.276407	+	1.21102i	0.625893	+	0.779909i	$0.284735\pi$
$683$	−7.22369	+	31.6491i	−0.276407	+	1.21102i	−0.902300	+	0.431109i	$0.858122\pi$
$684$	−1.33781	+	1.67756i	−0.0511524	+	0.0641431i
$685$	−16.5975	−	7.99291i	−0.634156	−	0.305394i
$686$	−18.1656	+	8.74808i	−0.693565	+	0.334003i
$687$	−21.7809			−0.830993
$688$	5.19762	−	3.99809i	0.198158	−	0.152426i
$689$	4.07728			0.155332
$690$	14.9415	−	7.19546i	0.568814	−	0.273927i
$691$	−13.5095	−	6.50583i	−0.513925	−	0.247493i	0.158900	−	0.987295i	$-0.449205\pi$
$691$	−13.5095	−	6.50583i	−0.513925	−	0.247493i	−0.672825	+	0.739801i	$0.734919\pi$
$692$	−0.559768	+	0.701927i	−0.0212792	+	0.0266833i
$693$	0.758643	−	3.32383i	0.0288184	−	0.126262i
$694$	35.2552			1.33827
$695$	3.98974			0.151339
$696$	0.225046	−	0.985990i	0.00853034	−	0.0373738i
$697$	17.1849	+	21.5492i	0.650925	+	0.816234i
$698$	0.500397	+	2.19238i	0.0189403	+	0.0829829i
$699$	7.08266	+	8.88138i	0.267891	+	0.335924i
$700$	−1.94866	+	0.938427i	−0.0736526	+	0.0354692i
$701$	6.91608	−	30.3013i	0.261217	−	1.14447i	−0.658716	−	0.752391i	$-0.728900\pi$
$701$	6.91608	−	30.3013i	0.261217	−	1.14447i	0.919933	−	0.392075i	$-0.128243\pi$
$702$	−1.75076	+	0.843124i	−0.0660784	+	0.0318217i
$703$	47.0878	−	59.0462i	1.77595	−	2.22697i
$704$	1.04240	+	4.56705i	0.0392869	+	0.172127i
$705$	−4.02998	−	17.6565i	−0.151778	−	0.664981i
$706$	9.74800	+	4.69439i	0.366871	+	0.176676i
$707$	−6.59966	+	8.27571i	−0.248206	+	0.311240i
$708$	−0.839679	−	1.05292i	−0.0315571	−	0.0395713i
$709$	−46.4984	−	22.3925i	−1.74628	−	0.840966i	−0.980142	−	0.198296i	$-0.936459\pi$
$709$	−46.4984	−	22.3925i	−1.74628	−	0.840966i	−0.766143	−	0.642670i	$-0.777826\pi$
$710$	−1.42760	−	0.687495i	−0.0535768	−	0.0258012i
$711$	0.995308	+	1.24808i	0.0373270	+	0.0468066i
$712$	2.08891	−	2.61941i	0.0782851	−	0.0981665i
$713$	−21.2795	−	10.2477i	−0.796925	−	0.383779i
$714$	4.49101	+	19.6764i	0.168072	+	0.736370i
$715$	0.416345	+	1.82413i	0.0155704	+	0.0682185i
$716$	10.0415	−	12.5916i	0.375267	−	0.470570i
$717$	37.0668	−	17.8504i	1.38429	−	0.666637i
$718$	−2.33853	+	10.2457i	−0.0872730	+	0.382368i
$719$	−4.50162	+	2.16786i	−0.167882	+	0.0808477i	−0.515937	−	0.856626i	$-0.672556\pi$
$719$	−4.50162	+	2.16786i	−0.167882	+	0.0808477i	0.348056	+	0.937474i	$0.386842\pi$
$720$	−0.209800	−	0.263080i	−0.00781877	−	0.00980443i
$721$	−5.88517	−	25.7846i	−0.219175	−	0.960269i
$722$	−13.5055	−	16.9353i	−0.502622	−	0.630268i
$723$	−5.08328	+	22.2713i	−0.189049	+	0.828279i
$724$	−1.97321			−0.0733337
$725$	−0.553675			−0.0205630
$726$	−4.44852	+	19.4902i	−0.165100	+	0.723350i
$727$	3.62931	−	4.55101i	0.134604	−	0.168788i	−0.709961	−	0.704241i	$-0.751288\pi$
$727$	3.62931	−	4.55101i	0.134604	−	0.168788i	0.844565	+	0.535453i	$0.179859\pi$
$728$	−0.778316	−	0.374817i	−0.0288463	−	0.0138917i
$729$	−21.0199	+	10.1226i	−0.778514	+	0.374913i
$730$	−1.78648			−0.0661205
$731$	−26.5525	+	20.4246i	−0.982079	+	0.755430i
$732$	−23.3971			−0.864781
$733$	20.0213	−	9.64177i	0.739505	−	0.356127i	−0.0259098	−	0.999664i	$-0.508248\pi$
$733$	20.0213	−	9.64177i	0.739505	−	0.356127i	0.765415	+	0.643538i	$0.222534\pi$
$734$	−14.2846	−	6.87911i	−0.527255	−	0.253913i
$735$	−2.64453	+	3.31613i	−0.0975448	+	0.122317i
$736$	2.02028	−	8.85142i	0.0744684	−	0.326268i
$737$	−36.9890			−1.36251
$738$	1.81549			0.0668290
$739$	−4.26393	+	18.6815i	−0.156851	+	0.687210i	0.833945	+	0.551848i	$0.186077\pi$
$739$	−4.26393	+	18.6815i	−0.156851	+	0.687210i	−0.990796	+	0.135363i	$0.956780\pi$
$740$	7.38446	+	9.25982i	0.271458	+	0.340398i
$741$	1.03520	+	4.53551i	0.0380291	+	0.166616i
$742$	13.7660	+	17.2621i	0.505367	+	0.633710i
$743$	29.0713	−	14.0000i	1.06652	−	0.513610i	0.183538	−	0.983013i	$-0.441245\pi$
$743$	29.0713	−	14.0000i	1.06652	−	0.513610i	0.882984	+	0.469403i	$0.155531\pi$
$744$	−1.05737	+	4.63265i	−0.0387651	+	0.169841i
$745$	15.4075	−	7.41984i	0.564486	−	0.271842i
$746$	−19.8402	+	24.8788i	−0.726401	+	0.910878i
$747$	−1.23154	−	5.39571i	−0.0450595	−	0.197419i
$748$	−5.32519	−	23.3312i	−0.194708	−	0.853072i
$749$	−14.0998	−	6.79011i	−0.515196	−	0.248105i
$750$	−1.13887	+	1.42810i	−0.0415857	+	0.0521468i
$751$	32.5032	+	40.7577i	1.18606	+	1.48727i	0.834416	+	0.551135i	$0.185805\pi$
$751$	32.5032	+	40.7577i	1.18606	+	1.48727i	0.351642	+	0.936135i	$0.385624\pi$
$752$	−8.93298	−	4.30190i	−0.325752	−	0.156874i
$753$	−4.86812	−	2.34436i	−0.177404	−	0.0854334i
$754$	−0.137881	−	0.172897i	−0.00502131	−	0.00629653i
$755$	−10.9507	+	13.7318i	−0.398539	+	0.499752i
$756$	−9.48061	−	4.56562i	−0.344806	−	0.166050i
$757$	4.66408	+	20.4347i	0.169519	+	0.742711i	0.986191	+	0.165609i	$0.0529591\pi$
$757$	4.66408	+	20.4347i	0.169519	+	0.742711i	−0.816672	+	0.577101i	$0.804184\pi$
$758$	−3.40327	−	14.9107i	−0.123612	−	0.541581i
$759$	48.4371	−	60.7382i	1.75816	−	2.20466i
$760$	5.74512	−	2.76671i	0.208398	−	0.100359i
$761$	5.81799	−	25.4903i	0.210902	−	0.924021i	−0.753054	−	0.657959i	$-0.771420\pi$
$761$	5.81799	−	25.4903i	0.210902	−	0.924021i	0.963956	−	0.266063i	$-0.0857228\pi$
$762$	−22.7953	+	10.9776i	−0.825787	+	0.397678i
$763$	3.94916	+	4.95209i	0.142969	+	0.179278i
$764$	1.96727	+	8.61918i	0.0711734	+	0.311831i
$765$	1.07178	+	1.34397i	0.0387502	+	0.0485913i
$766$	−2.45227	+	10.7441i	−0.0886039	+	0.388199i
$767$	−0.294481			−0.0106331
$768$	−1.82661			−0.0659120
$769$	−0.887842	+	3.88989i	−0.0320164	+	0.140273i	−0.988410	−	0.151808i	$-0.951490\pi$
$769$	−0.887842	+	3.88989i	−0.0320164	+	0.140273i	0.956394	+	0.292081i	$0.0943476\pi$
$770$	−6.31714	+	7.92144i	−0.227654	+	0.285469i
$771$	−6.42120	−	3.09229i	−0.231254	−	0.111366i
$772$	1.97998	−	0.953510i	0.0712612	−	0.0343176i
$773$	12.4625			0.448246			0.224123	−	0.974561i	$-0.428048\pi$
$773$	12.4625			0.448246			0.224123	+	0.974561i	$0.428048\pi$
$774$	−0.0386404	+	2.20619i	−0.00138890	+	0.0792999i
$775$	2.60143			0.0934461
$776$	11.3928	−	5.48647i	0.408977	−	0.196953i
$777$	−42.1572	−	20.3018i	−1.51238	−	0.728324i
$778$	6.45883	−	8.09912i	0.231560	−	0.290367i
$779$	−7.65558	+	33.5413i	−0.274290	+	1.20174i
$780$	−0.729565			−0.0261226
$781$	−7.42267			−0.265604
$782$	−10.3208	+	45.2182i	−0.369070	+	1.61700i
$783$	−1.67951	−	2.10604i	−0.0600209	−	0.0752638i
$784$	0.516707	+	2.26384i	0.0184538	+	0.0808515i
$785$	−8.39484	−	10.5268i	−0.299625	−	0.375718i
$786$	22.4165	−	10.7952i	0.799571	−	0.385053i
$787$	11.1233	−	48.7345i	0.396504	−	1.73720i	−0.244490	−	0.969652i	$-0.578621\pi$
$787$	11.1233	−	48.7345i	0.396504	−	1.73720i	0.640994	−	0.767546i	$-0.278522\pi$
$788$	−13.9539	+	6.71987i	−0.497089	+	0.239385i
$789$	10.7062	−	13.4251i	0.381150	−	0.477947i
$790$	−1.05566	−	4.62515i	−0.0375587	−	0.164555i
$791$	4.07447	+	17.8514i	0.144872	+	0.634724i
$792$	−1.42020	−	0.683931i	−0.0504645	−	0.0243024i
$793$	−3.18981	+	3.99990i	−0.113273	+	0.142040i
$794$	2.56336	+	3.21435i	0.0909702	+	0.114073i
$795$	16.7999	+	8.09041i	0.595831	+	0.286937i
$796$	−2.00261	−	0.964408i	−0.0709808	−	0.0341826i
$797$	−28.8615	−	36.1911i	−1.02233	−	1.28196i	−0.958832	−	0.283973i	$-0.908347\pi$
$797$	−28.8615	−	36.1911i	−1.02233	−	1.28196i	−0.0634930	−	0.997982i	$-0.520224\pi$
$798$	−15.7069	+	19.6959i	−0.556019	+	0.697226i
$799$	45.6349	+	21.9766i	1.61445	+	0.777476i
$800$	0.222521	+	0.974928i	0.00786730	+	0.0344689i
$801$	0.250863	+	1.09910i	0.00886380	+	0.0388348i
$802$	−6.93743	+	8.69926i	−0.244969	+	0.307182i
$803$	−7.53999	+	3.63107i	−0.266081	+	0.128138i
$804$	3.20940	−	14.0613i	0.113187	−	0.495904i
$805$	17.6920	−	8.52003i	0.623562	−	0.300292i
$806$	0.647829	+	0.812352i	0.0228188	+	0.0286139i
$807$	−0.147822	−	0.647652i	−0.00520359	−	0.0227984i
$808$	3.05137	+	3.82629i	0.107347	+	0.134608i
$809$	1.29909	−	5.69170i	0.0456737	−	0.200110i	−0.946943	−	0.321401i	$-0.895846\pi$
$809$	1.29909	−	5.69170i	0.0456737	−	0.200110i	0.992617	+	0.121291i	$0.0387035\pi$
$810$	−9.89625			−0.347719
$811$	29.5089			1.03620			0.518099	−	0.855321i	$-0.326640\pi$
$811$	29.5089			1.03620			0.518099	+	0.855321i	$0.326640\pi$
$812$	0.266473	−	1.16749i	0.00935136	−	0.0409710i
$813$	−26.9162	+	33.7519i	−0.943992	+	1.18373i
$814$	49.9876	+	24.0728i	1.75207	+	0.843750i
$815$	−0.0451724	+	0.0217539i	−0.00158232	+	0.000762005i
$816$	9.33137			0.326663
$817$	−40.5966	−	10.0170i	−1.42030	−	0.350450i
$818$	−17.0880			−0.597468
$819$	0.261898	−	0.126123i	0.00915144	−	0.00440710i
$820$	−4.86102	−	2.34094i	−0.169754	−	0.0817493i
$821$	−23.5882	+	29.5786i	−0.823232	+	1.03230i	0.175622	+	0.984458i	$0.443806\pi$
$821$	−23.5882	+	29.5786i	−0.823232	+	1.03230i	−0.998855	+	0.0478433i	$0.984765\pi$
$822$	7.48769	−	32.8057i	0.261163	−	1.14423i
$823$	17.9753			0.626579			0.313289	−	0.949658i	$-0.398569\pi$
$823$	17.9753			0.626579			0.313289	+	0.949658i	$0.398569\pi$
$824$	−12.2281			−0.425988
$825$	−1.90406	+	8.34221i	−0.0662907	+	0.290439i
$826$	−0.994250	−	1.24675i	−0.0345944	−	0.0433800i
$827$	−4.07919	−	17.8721i	−0.141847	−	0.621474i	−0.995005	−	0.0998213i	$-0.968173\pi$
$827$	−4.07919	−	17.8721i	−0.141847	−	0.621474i	0.853158	−	0.521653i	$-0.174684\pi$
$828$	1.90478	+	2.38852i	0.0661957	+	0.0830068i
$829$	−5.24149	+	2.52417i	−0.182044	+	0.0876680i	−0.522686	−	0.852525i	$-0.675070\pi$
$829$	−5.24149	+	2.52417i	−0.182044	+	0.0876680i	0.340642	+	0.940193i	$0.389356\pi$
$830$	−3.65992	+	16.0352i	−0.127038	+	0.556589i
$831$	−21.1597	+	10.1900i	−0.734021	+	0.353486i
$832$	−0.249028	+	0.312271i	−0.00863350	+	0.0108261i
$833$	−2.63964	−	11.5650i	−0.0914581	−	0.400704i
$834$	1.62166	+	7.10496i	0.0561536	+	0.246025i
$835$	−14.6863	−	7.07253i	−0.508239	−	0.244755i
$836$	18.6244	−	23.3543i	0.644139	−	0.807725i
$837$	7.89115	+	9.89519i	0.272758	+	0.342028i
$838$	−34.8744	−	16.7946i	−1.20472	−	0.580160i
$839$	−21.7492	−	10.4739i	−0.750866	−	0.361598i	0.0189863	−	0.999820i	$-0.493956\pi$
$839$	−21.7492	−	10.4739i	−0.750866	−	0.361598i	−0.769853	+	0.638222i	$0.779670\pi$
$840$	−2.46321	−	3.08877i	−0.0849889	−	0.106573i
$841$	−17.8901	+	22.4334i	−0.616899	+	0.773567i
$842$	27.1163	+	13.0585i	0.934491	+	0.450027i
$843$	7.55245	+	33.0894i	0.260120	+	1.13966i
$844$	−0.160810	−	0.704554i	−0.00553530	−	0.0242517i
$845$	8.00590	−	10.0391i	0.275411	−	0.345355i
$846$	3.00588	−	1.44756i	0.103344	−	0.0497680i
$847$	−5.26741	+	23.0780i	−0.180990	+	0.792971i
$848$	9.19733	−	4.42920i	0.315838	−	0.152099i
$849$	30.5540	+	38.3136i	1.04861	+	1.31492i
$850$	−1.13677	−	4.98050i	−0.0389908	−	0.170830i
$851$	−67.0438	−	84.0703i	−2.29823	−	2.88189i
$852$	0.644039	−	2.82172i	0.0220644	−	0.0966705i
$853$	−32.1817			−1.10188			−0.550940	−	0.834545i	$-0.685731\pi$
$853$	−32.1817			−1.10188			−0.550940	+	0.834545i	$0.685731\pi$
$854$	−27.7041			−0.948015
$855$	−0.477459	+	2.09188i	−0.0163287	+	0.0715409i
$856$	−4.51134	+	5.65704i	−0.154194	+	0.193354i
$857$	18.1459	+	8.73861i	0.619852	+	0.298505i	0.717331	−	0.696732i	$-0.245364\pi$
$857$	18.1459	+	8.73861i	0.619852	+	0.298505i	−0.0974788	+	0.995238i	$0.531078\pi$
$858$	−3.07920	+	1.48286i	−0.105122	+	0.0506241i
$859$	−29.2560			−0.998202			−0.499101	−	0.866544i	$-0.666336\pi$
$859$	−29.2560			−0.998202			−0.499101	+	0.866544i	$0.666336\pi$
$860$	2.94819	−	5.85732i	0.100532	−	0.199733i
$861$	21.3152			0.726421
$862$	15.2358	−	7.33717i	0.518933	−	0.249905i
$863$	−39.3524	−	18.9511i	−1.33957	−	0.645104i	−0.379588	−	0.925156i	$-0.623934\pi$
$863$	−39.3524	−	18.9511i	−1.33957	−	0.645104i	−0.959985	+	0.280051i	$0.909648\pi$
$864$	−3.03339	+	3.80375i	−0.103198	+	0.129406i
$865$	−0.199779	+	0.875289i	−0.00679269	+	0.0297607i
$866$	−11.0432			−0.375262
$867$	−16.6178			−0.564370
$868$	−1.25202	+	5.48544i	−0.0424962	+	0.186188i
$869$	−13.8563	−	17.3752i	−0.470041	−	0.589413i
$870$	−0.225046	−	0.985990i	−0.00762976	−	0.0334282i
$871$	−1.96633	−	2.46570i	−0.0666266	−	0.0835471i
$872$	2.63850	−	1.27064i	0.0893510	−	0.0430292i
$873$	−0.946816	+	4.14827i	−0.0320449	+	0.140398i
$874$	−52.1603	+	25.1191i	−1.76435	+	0.849665i
$875$	−1.34852	+	1.69099i	−0.0455882	+	0.0571658i
$876$	−0.726128	−	3.18138i	−0.0245336	−	0.107489i
$877$	11.7887	+	51.6495i	0.398075	+	1.74408i	0.634962	+	0.772543i	$0.281016\pi$
$877$	11.7887	+	51.6495i	0.398075	+	1.74408i	−0.236887	+	0.971537i	$0.576127\pi$
$878$	−0.443056	−	0.213364i	−0.0149524	−	0.00720070i
$879$	−6.26557	+	7.85678i	−0.211333	+	0.265003i
$880$	2.92074	+	3.66249i	0.0984581	+	0.123463i
$881$	31.5276	+	15.1829i	1.06219	+	0.511525i	0.881583	−	0.472029i	$-0.156478\pi$
$881$	31.5276	+	15.1829i	1.06219	+	0.511525i	0.180611	+	0.983555i	$0.442193\pi$
$882$	−0.703977	−	0.339018i	−0.0237041	−	0.0114153i
$883$	−23.5100	−	29.4806i	−0.791174	−	0.992100i	−0.999900	−	0.0141262i	$-0.995503\pi$
$883$	−23.5100	−	29.4806i	−0.791174	−	0.992100i	0.208727	−	0.977974i	$-0.433068\pi$
$884$	1.27218	−	1.59526i	0.0427881	−	0.0536545i
$885$	−1.21337	−	0.584329i	−0.0407870	−	0.0196420i
$886$	5.01488	+	21.9716i	0.168478	+	0.738151i
$887$	3.64281	+	15.9602i	0.122314	+	0.535891i	0.998541	+	0.0539934i	$0.0171950\pi$
$887$	3.64281	+	15.9602i	0.122314	+	0.535891i	−0.876228	+	0.481897i	$0.839948\pi$
$888$	−13.4885	+	16.9140i	−0.452644	+	0.567598i
$889$	−26.9915	+	12.9984i	−0.905267	+	0.435954i
$890$	0.745523	−	3.26635i	0.0249900	−	0.109488i
$891$	−41.7680	+	20.1144i	−1.39928	+	0.673859i
$892$	−14.1407	−	17.7318i	−0.473464	−	0.593705i
$893$	14.0685	+	61.6380i	0.470784	+	2.06264i
$894$	19.4758	+	24.4219i	0.651369	+	0.816791i
$895$	3.58376	−	15.7015i	0.119792	−	0.524842i
$896$	−2.16285			−0.0722559
$897$	6.62376			0.221161
$898$	−4.06892	+	17.8271i	−0.135781	+	0.594898i
$899$	−0.898041	+	1.12611i	−0.0299513	+	0.0375578i
$900$	−0.303169	−	0.145999i	−0.0101056	−	0.00486662i
$901$	−46.9853	+	22.6269i	−1.56531	+	0.753813i
$902$	−25.2744			−0.841546
$903$	−0.453668	+	25.9024i	−0.0150971	+	0.861978i
$904$	8.46590			0.281572
$905$	−1.77780	+	0.856143i	−0.0590960	+	0.0284592i
$906$	−28.9048	−	13.9198i	−0.960296	−	0.462454i
$907$	−14.8193	+	18.5828i	−0.492068	+	0.617033i	−0.964419	−	0.264377i	$-0.914834\pi$
$907$	−14.8193	+	18.5828i	−0.492068	+	0.617033i	0.472352	+	0.881410i	$0.343405\pi$
$908$	2.89394	−	12.6792i	0.0960388	−	0.420773i
$909$	−1.64680			−0.0546208
$910$	−0.863866			−0.0286369
$911$	−6.79803	+	29.7841i	−0.225229	+	0.986792i	0.728245	+	0.685317i	$0.240336\pi$
$911$	−6.79803	+	29.7841i	−0.225229	+	0.986792i	−0.953474	+	0.301475i	$0.902521\pi$
$912$	7.26213	+	9.10642i	0.240473	+	0.301544i
$913$	17.1449	+	75.1168i	0.567414	+	2.48600i
$914$	12.0656	+	15.1298i	0.399095	+	0.500450i
$915$	−21.0800	+	10.1516i	−0.696885	+	0.335602i
$916$	−2.65339	+	11.6253i	−0.0876705	+	0.384110i
$917$	26.5430	−	12.7825i	0.876529	−	0.422114i
$918$	15.4963	−	19.4318i	0.511455	−	0.641344i
$919$	−7.50794	−	32.8945i	−0.247664	−	1.08509i	−0.933851	−	0.357662i	$-0.883574\pi$
$919$	−7.50794	−	32.8945i	−0.247664	−	1.08509i	0.686187	−	0.727425i	$-0.259283\pi$
$920$	−2.02028	−	8.85142i	−0.0666066	−	0.291823i
$921$	11.1677	+	5.37808i	0.367988	+	0.177214i
$922$	−10.8930	+	13.6594i	−0.358741	+	0.449848i
$923$	−0.394589	−	0.494799i	−0.0129880	−	0.0162865i
$924$	−16.6742	−	8.02989i	−0.548542	−	0.264164i
$925$	10.6708	+	5.13881i	0.350855	+	0.168963i
$926$	−12.4079	−	15.5590i	−0.407750	−	0.511302i
$927$	2.56546	−	3.21699i	0.0842608	−	0.105660i
$928$	−0.498844	−	0.240231i	−0.0163753	−	0.00788595i
$929$	2.03493	+	8.91560i	0.0667638	+	0.292511i	0.997277	−	0.0737471i	$-0.0234958\pi$
$929$	2.03493	+	8.91560i	0.0667638	+	0.292511i	−0.930513	+	0.366258i	$0.880639\pi$
$930$	1.05737	+	4.63265i	0.0346726	+	0.151911i
$931$	9.23193	−	11.5765i	0.302564	−	0.379404i
$932$	5.60314	−	2.69833i	0.183537	−	0.0883868i
$933$	7.64445	−	33.4925i	0.250268	−	1.09650i
$934$	8.20875	−	3.95312i	0.268598	−	0.129350i
$935$	−14.9208	−	18.7102i	−0.487964	−	0.611887i
$936$	−0.0299065	−	0.131029i	−0.000977524	−	0.00428281i
$937$	−3.47739	−	4.36051i	−0.113601	−	0.142452i	0.721780	−	0.692123i	$-0.243324\pi$
$937$	−3.47739	−	4.36051i	−0.113601	−	0.142452i	−0.835381	+	0.549671i	$0.814753\pi$
$938$	3.80020	−	16.6498i	0.124081	−	0.543634i
$939$	−22.6062			−0.737724
$940$	−9.91486			−0.323387
$941$	8.47913	−	37.1495i	0.276412	−	1.21104i	−0.625882	−	0.779918i	$-0.715261\pi$
$941$	8.47913	−	37.1495i	0.276412	−	1.21104i	0.902294	−	0.431121i	$-0.141882\pi$
$942$	15.3341	−	19.2283i	0.499611	−	0.626493i
$943$	44.1334	+	21.2535i	1.43718	+	0.692110i
$944$	−0.664276	+	0.319899i	−0.0216204	+	0.0104118i
$945$	−10.5227			−0.342303
$946$	0.537935	−	30.7136i	0.0174898	−	0.998587i
$947$	−39.0062			−1.26753			−0.633766	−	0.773525i	$-0.718492\pi$
$947$	−39.0062			−1.26753			−0.633766	+	0.773525i	$0.718492\pi$
$948$	7.80743	−	3.75986i	0.253573	−	0.122115i
$949$	−0.642874	−	0.309592i	−0.0208686	−	0.0100498i
$950$	3.97575	−	4.98543i	0.128990	−	0.161749i
$951$	−5.35085	+	23.4436i	−0.173513	+	0.760211i
$952$	11.0491			0.358104
$953$	16.5088			0.534771			0.267386	−	0.963590i	$-0.413840\pi$
$953$	16.5088			0.534771			0.267386	+	0.963590i	$0.413840\pi$
$954$	−0.764360	+	3.34888i	−0.0247471	+	0.108424i
$955$	5.51217	+	6.91204i	0.178370	+	0.223668i
$956$	−5.01189	−	21.9585i	−0.162096	−	0.710189i
$957$	−2.95388	−	3.70405i	−0.0954854	−	0.119735i
$958$	−0.510942	+	0.246057i	−0.0165078	+	0.00794973i
$959$	8.86605	−	38.8447i	0.286300	−	1.25436i
$960$	−1.64572	+	0.792535i	−0.0531153	+	0.0255790i
$961$	−15.1088	+	18.9458i	−0.487379	+	0.611154i
$962$	1.05264	+	4.61191i	0.0339384	+	0.148694i
$963$	−0.541779	−	2.37369i	−0.0174586	−	0.0764911i
$964$	11.2678	+	5.42627i	0.362910	+	0.174768i
$965$	1.37019	−	1.71817i	0.0441080	−	0.0553097i
$966$	22.3636	+	28.0431i	0.719538	+	0.902272i
$967$	55.1267	+	26.5476i	1.77275	+	0.853713i	0.964149	+	0.265361i	$0.0854913\pi$
$967$	55.1267	+	26.5476i	1.77275	+	0.853713i	0.808605	+	0.588352i	$0.200223\pi$
$968$	9.86073	+	4.74868i	0.316936	+	0.152628i
$969$	−37.0992	−	46.5209i	−1.19180	−	1.49447i
$970$	7.88404	−	9.88628i	0.253141	−	0.317429i
$971$	−16.5361	−	7.96336i	−0.530668	−	0.255556i	0.149308	−	0.988791i	$-0.452295\pi$
$971$	−16.5361	−	7.96336i	−0.530668	−	0.255556i	−0.679976	+	0.733235i	$0.738010\pi$
$972$	−0.774599	−	3.39374i	−0.0248453	−	0.108854i
$973$	1.92018	+	8.41287i	0.0615582	+	0.269704i
$974$	−12.8885	+	16.1616i	−0.412973	+	0.517852i
$975$	−0.657315	+	0.316546i	−0.0210509	+	0.0101376i
$976$	−2.85028	+	12.4879i	−0.0912352	+	0.399728i
$977$	47.1214	−	22.6925i	1.50755	−	0.725996i	0.516103	−	0.856527i	$-0.327382\pi$
$977$	47.1214	−	22.6925i	1.50755	−	0.725996i	0.991444	+	0.130531i	$0.0416681\pi$
$978$	−0.0571002	−	0.0716014i	−0.00182586	−	0.00228956i
$979$	−3.49240	−	15.3012i	−0.111618	−	0.489029i
$980$	1.44778	+	1.81546i	0.0462477	+	0.0579927i
$981$	−0.219278	+	0.960718i	−0.00700099	+	0.0306734i
$982$	−21.4985			−0.686044
$983$	−40.6245			−1.29572			−0.647860	−	0.761759i	$-0.724336\pi$
$983$	−40.6245			−1.29572			−0.647860	+	0.761759i	$0.724336\pi$
$984$	2.19297	−	9.60805i	0.0699095	−	0.306293i
$985$	−9.65643	+	12.1088i	−0.307679	+	0.385818i
$986$	2.54839	+	1.22724i	0.0811571	+	0.0390832i
$987$	35.2914	−	16.9954i	1.12334	−	0.540971i
$988$	2.54688			0.0810271
$989$	−26.7668	+	53.1789i	−0.851134	+	1.69099i
$990$	−1.57630			−0.0500981
$991$	−13.1993	+	6.35646i	−0.419290	+	0.201920i	−0.631619	−	0.775279i	$-0.717609\pi$
$991$	−13.1993	+	6.35646i	−0.419290	+	0.201920i	0.212329	+	0.977198i	$0.431895\pi$
$992$	2.34381	+	1.12872i	0.0744159	+	0.0358368i
$993$	35.0494	−	43.9505i	1.11226	−	1.39473i
$994$	0.762596	−	3.34115i	0.0241881	−	0.105975i
$995$	−2.22273			−0.0704654
$996$	−30.0432			−0.951955
$997$	7.03974	−	30.8431i	0.222951	−	0.976812i	−0.732292	−	0.680990i	$-0.761550\pi$
$997$	7.03974	−	30.8431i	0.222951	−	0.976812i	0.955243	−	0.295821i	$-0.0955933\pi$
$998$	−9.07372	−	11.3781i	−0.287224	−	0.360167i
$999$	12.8221	+	56.1773i	0.405673	+	1.77737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.d.41.3	yes	24
43.21	even	7	inner	430.2.k.d.21.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.d.21.3	✓	24	43.21	even	7	inner
430.2.k.d.41.3	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(1.64572 + 0.792535i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.222521 - 0.974928i) q^{5} +1.82661 q^{6} +2.16285 q^{7} +(0.222521 - 0.974928i) q^{8} +(0.209800 + 0.263080i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(1.64572 + 0.792535i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.222521 - 0.974928i) q^{5} +1.82661 q^{6} +2.16285 q^{7} +(0.222521 - 0.974928i) q^{8} +(0.209800 + 0.263080i) q^{9} +(-0.222521 - 0.974928i) q^{10} +(-2.92074 - 3.66249i) q^{11} +(1.64572 - 0.792535i) q^{12} +(0.0888771 - 0.389396i) q^{13} +(1.94866 - 0.938427i) q^{14} +(1.13887 - 1.42810i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.13677 + 4.98050i) q^{17} +(0.303169 + 0.145999i) q^{18} +(-3.97575 + 4.98543i) q^{19} +(-0.623490 - 0.781831i) q^{20} +(3.55944 + 1.71414i) q^{21} +(-4.22059 - 2.03253i) q^{22} +(5.66069 + 7.09829i) q^{23} +(1.13887 - 1.42810i) q^{24} +(-0.900969 - 0.433884i) q^{25} +(-0.0888771 - 0.389396i) q^{26} +(-1.08260 - 4.74320i) q^{27} +(1.34852 - 1.69099i) q^{28} +(0.498844 - 0.240231i) q^{29} +(0.406458 - 1.78081i) q^{30} +(-2.34381 + 1.12872i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.90406 - 8.34221i) q^{33} +(3.18515 + 3.99405i) q^{34} +(0.481280 - 2.10863i) q^{35} +0.336492 q^{36} -11.8437 q^{37} +(-1.41893 + 6.21673i) q^{38} +(0.454876 - 0.570397i) q^{39} +(-0.900969 - 0.433884i) q^{40} +(4.86102 - 2.34094i) q^{41} +3.95069 q^{42} +(2.74127 + 5.95697i) q^{43} -4.68450 q^{44} +(0.303169 - 0.145999i) q^{45} +(8.17994 + 3.93925i) q^{46} +(6.18181 - 7.75175i) q^{47} +(0.406458 - 1.78081i) q^{48} -2.32206 q^{49} -1.00000 q^{50} +(-2.07643 + 9.09742i) q^{51} +(-0.249028 - 0.312271i) q^{52} +(2.27155 + 9.95232i) q^{53} +(-3.03339 - 3.80375i) q^{54} +(-4.22059 + 2.03253i) q^{55} +(0.481280 - 2.10863i) q^{56} +(-10.4941 + 5.05368i) q^{57} +(0.345211 - 0.432880i) q^{58} +(-0.164063 - 0.718806i) q^{59} +(-0.406458 - 1.78081i) q^{60} +(-11.5405 - 5.55763i) q^{61} +(-1.62196 + 2.03388i) q^{62} +(0.453766 + 0.569005i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.359856 - 0.173298i) q^{65} +(-5.33504 - 6.68993i) q^{66} +(4.92309 - 6.17336i) q^{67} +(4.60267 + 2.21653i) q^{68} +(3.69025 + 16.1681i) q^{69} +(-0.481280 - 2.10863i) q^{70} +(0.987929 - 1.23882i) q^{71} +(0.303169 - 0.145999i) q^{72} +(0.397529 - 1.74169i) q^{73} +(-10.6708 + 5.13881i) q^{74} +(-1.13887 - 1.42810i) q^{75} +(1.41893 + 6.21673i) q^{76} +(-6.31714 - 7.92144i) q^{77} +(0.162344 - 0.711273i) q^{78} +4.74409 q^{79} -1.00000 q^{80} +(2.20212 - 9.64813i) q^{81} +(3.36393 - 4.21823i) q^{82} +(-14.8187 - 7.13632i) q^{83} +(3.55944 - 1.71414i) q^{84} +5.10858 q^{85} +(5.05443 + 4.17765i) q^{86} +1.01135 q^{87} +(-4.22059 + 2.03253i) q^{88} +(3.01856 + 1.45366i) q^{89} +(0.209800 - 0.263080i) q^{90} +(0.192228 - 0.842207i) q^{91} +9.07905 q^{92} -4.75179 q^{93} +(2.20626 - 9.66627i) q^{94} +(3.97575 + 4.98543i) q^{95} +(-0.406458 - 1.78081i) q^{96} +(7.88404 + 9.88628i) q^{97} +(-2.09210 + 1.00750i) q^{98} +(0.350760 - 1.53678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 12 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 12 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 12 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 9 q^{11} + 2 q^{12} - 2 q^{13} - 5 q^{14} - 2 q^{15} - 4 q^{16} + 13 q^{17} - 10 q^{18} - 3 q^{19} + 4 q^{20} - 14 q^{21} - 5 q^{22} + 11 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{26} - 13 q^{27} + 5 q^{28} + 20 q^{29} + 2 q^{30} - 5 q^{31} + 4 q^{32} + 15 q^{33} + q^{34} + 9 q^{35} + 24 q^{36} - 38 q^{37} - 18 q^{38} + 5 q^{39} - 4 q^{40} - 2 q^{41} - 14 q^{42} - 2 q^{43} - 2 q^{44} - 10 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 50 q^{49} - 24 q^{50} - 42 q^{51} - 2 q^{52} + 22 q^{53} - 29 q^{54} - 5 q^{55} + 9 q^{56} - 67 q^{57} + 22 q^{58} - 44 q^{59} - 2 q^{60} - 26 q^{61} - 2 q^{62} + 37 q^{63} - 4 q^{64} + 2 q^{65} - 8 q^{66} + 37 q^{67} - 15 q^{68} + 88 q^{69} - 9 q^{70} + 19 q^{71} - 10 q^{72} + 22 q^{73} - 4 q^{74} + 2 q^{75} + 18 q^{76} + 28 q^{77} + 23 q^{78} + 30 q^{79} - 24 q^{80} - 26 q^{81} + 37 q^{82} - 11 q^{83} - 14 q^{84} - 6 q^{85} + 16 q^{86} - 26 q^{87} - 5 q^{88} + 30 q^{89} - 4 q^{90} + 36 q^{91} - 10 q^{92} - 98 q^{93} + 4 q^{94} + 3 q^{95} - 2 q^{96} - 39 q^{97} + 41 q^{98} - 31 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 12 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 9 * q^11 + 2 * q^12 - 2 * q^13 - 5 * q^14 - 2 * q^15 - 4 * q^16 + 13 * q^17 - 10 * q^18 - 3 * q^19 + 4 * q^20 - 14 * q^21 - 5 * q^22 + 11 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^26 - 13 * q^27 + 5 * q^28 + 20 * q^29 + 2 * q^30 - 5 * q^31 + 4 * q^32 + 15 * q^33 + q^34 + 9 * q^35 + 24 * q^36 - 38 * q^37 - 18 * q^38 + 5 * q^39 - 4 * q^40 - 2 * q^41 - 14 * q^42 - 2 * q^43 - 2 * q^44 - 10 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 50 * q^49 - 24 * q^50 - 42 * q^51 - 2 * q^52 + 22 * q^53 - 29 * q^54 - 5 * q^55 + 9 * q^56 - 67 * q^57 + 22 * q^58 - 44 * q^59 - 2 * q^60 - 26 * q^61 - 2 * q^62 + 37 * q^63 - 4 * q^64 + 2 * q^65 - 8 * q^66 + 37 * q^67 - 15 * q^68 + 88 * q^69 - 9 * q^70 + 19 * q^71 - 10 * q^72 + 22 * q^73 - 4 * q^74 + 2 * q^75 + 18 * q^76 + 28 * q^77 + 23 * q^78 + 30 * q^79 - 24 * q^80 - 26 * q^81 + 37 * q^82 - 11 * q^83 - 14 * q^84 - 6 * q^85 + 16 * q^86 - 26 * q^87 - 5 * q^88 + 30 * q^89 - 4 * q^90 + 36 * q^91 - 10 * q^92 - 98 * q^93 + 4 * q^94 + 3 * q^95 - 2 * q^96 - 39 * q^97 + 41 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more