LMFDB - Embedded newform 425.2.k.c.86.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.18
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03533 - 1.47876i) q^{2} +(0.0964356 - 0.296798i) q^{3} +(1.33783 - 4.11742i) q^{4} +(1.48564 - 1.67119i) q^{5} +(-0.242614 - 0.746689i) q^{6} -1.80284 q^{7} +(-1.81087 - 5.57328i) q^{8} +(2.34826 + 1.70611i) q^{9} +(0.552492 - 5.59833i) q^{10} +(-4.16934 + 3.02920i) q^{11} +(-1.09303 - 0.794131i) q^{12} +(0.440376 + 0.319952i) q^{13} +(-3.66939 + 2.66597i) q^{14} +(-0.352737 - 0.602098i) q^{15} +(-4.92229 - 3.57625i) q^{16} +(-0.309017 - 0.951057i) q^{17} +7.30242 q^{18} +(2.19606 + 6.75877i) q^{19} +(-4.89345 - 8.35276i) q^{20} +(-0.173858 + 0.535081i) q^{21} +(-4.00654 + 12.3309i) q^{22} +(1.92137 - 1.39596i) q^{23} -1.82877 q^{24} +(-0.585745 - 4.96557i) q^{25} +1.36944 q^{26} +(1.49024 - 1.08272i) q^{27} +(-2.41190 + 7.42306i) q^{28} +(0.304113 - 0.935963i) q^{29} +(-1.60829 - 0.703857i) q^{30} +(-0.561979 - 1.72959i) q^{31} -3.58672 q^{32} +(0.496989 + 1.52958i) q^{33} +(-2.03533 - 1.47876i) q^{34} +(-2.67838 + 3.01289i) q^{35} +(10.1663 - 7.38628i) q^{36} +(-3.79807 - 2.75946i) q^{37} +(14.4643 + 10.5089i) q^{38} +(0.137429 - 0.0998481i) q^{39} +(-12.0043 - 5.25359i) q^{40} +(-3.84387 - 2.79274i) q^{41} +(0.437395 + 1.34616i) q^{42} -0.257786 q^{43} +(6.89462 + 21.2195i) q^{44} +(6.33991 - 1.38972i) q^{45} +(1.84635 - 5.68248i) q^{46} +(-2.88783 + 8.88784i) q^{47} +(-1.53611 + 1.11605i) q^{48} -3.74976 q^{49} +(-8.53506 - 9.24042i) q^{50} -0.312072 q^{51} +(1.90652 - 1.38517i) q^{52} +(1.23913 - 3.81366i) q^{53} +(1.43206 - 4.40741i) q^{54} +(-1.13177 + 11.4681i) q^{55} +(3.26471 + 10.0478i) q^{56} +2.21777 q^{57} +(-0.765090 - 2.35471i) q^{58} +(3.17556 + 2.30718i) q^{59} +(-2.95099 + 0.646863i) q^{60} +(11.4705 - 8.33382i) q^{61} +(-3.70147 - 2.68927i) q^{62} +(-4.23355 - 3.07585i) q^{63} +(2.54441 - 1.84862i) q^{64} +(1.18894 - 0.260618i) q^{65} +(3.27341 + 2.37827i) q^{66} +(1.13202 + 3.48399i) q^{67} -4.32931 q^{68} +(-0.229029 - 0.704879i) q^{69} +(-0.996057 + 10.0929i) q^{70} +(-2.72344 + 8.38190i) q^{71} +(5.25625 - 16.1771i) q^{72} +(3.33963 - 2.42638i) q^{73} -11.8109 q^{74} +(-1.53026 - 0.305010i) q^{75} +30.7666 q^{76} +(7.51666 - 5.46118i) q^{77} +(0.132063 - 0.406449i) q^{78} +(-1.51457 + 4.66138i) q^{79} +(-13.2893 + 2.91305i) q^{80} +(2.51323 + 7.73493i) q^{81} -11.9533 q^{82} +(-2.08681 - 6.42254i) q^{83} +(1.97056 + 1.43169i) q^{84} +(-2.04848 - 0.896502i) q^{85} +(-0.524681 + 0.381203i) q^{86} +(-0.248465 - 0.180520i) q^{87} +(24.4327 + 17.7514i) q^{88} +(-13.8721 + 10.0787i) q^{89} +(10.8488 - 12.2037i) q^{90} +(-0.793929 - 0.576823i) q^{91} +(-3.17727 - 9.77863i) q^{92} -0.567536 q^{93} +(7.26525 + 22.3601i) q^{94} +(14.5577 + 6.37108i) q^{95} +(-0.345888 + 1.06453i) q^{96} +(-5.88349 + 18.1075i) q^{97} +(-7.63201 + 5.54498i) q^{98} -14.9589 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	2.03533	−	1.47876i	1.43920	−	1.04564i	0.450989	−	0.892529i	$-0.351071\pi$
$2$	2.03533	−	1.47876i	1.43920	−	1.04564i	0.988209	−	0.153110i	$-0.0489288\pi$
$3$	0.0964356	−	0.296798i	0.0556771	−	0.171357i	−0.919351	−	0.393439i	$-0.871285\pi$
$3$	0.0964356	−	0.296798i	0.0556771	−	0.171357i	0.975028	+	0.222082i	$0.0712853\pi$
$4$	1.33783	−	4.11742i	0.668915	−	2.05871i
$5$	1.48564	−	1.67119i	0.664399	−	0.747378i
$5$	1.48564	−	1.67119i	0.664399	−	0.747378i
$6$	−0.242614	−	0.746689i	−0.0990467	−	0.304834i
$7$	−1.80284			−0.681411			−0.340705	−	0.940170i	$-0.610666\pi$
$7$	−1.80284			−0.681411			−0.340705	+	0.940170i	$0.610666\pi$
$8$	−1.81087	−	5.57328i	−0.640239	−	1.97045i
$9$	2.34826	+	1.70611i	0.782754	+	0.568704i
$10$	0.552492	−	5.59833i	0.174713	−	1.77035i
$11$	−4.16934	+	3.02920i	−1.25710	+	0.913339i	−0.998612	−	0.0526751i	$-0.983225\pi$
$11$	−4.16934	+	3.02920i	−1.25710	+	0.913339i	−0.258491	+	0.966014i	$0.583225\pi$
$12$	−1.09303	−	0.794131i	−0.315530	−	0.229246i
$13$	0.440376	+	0.319952i	0.122138	+	0.0887387i	0.647177	−	0.762339i	$-0.275949\pi$
$13$	0.440376	+	0.319952i	0.122138	+	0.0887387i	−0.525039	+	0.851078i	$0.675949\pi$
$14$	−3.66939	+	2.66597i	−0.980685	+	0.712510i
$15$	−0.352737	−	0.602098i	−0.0910764	−	0.155461i
$16$	−4.92229	−	3.57625i	−1.23057	−	0.894063i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	7.30242			1.72120
$19$	2.19606	+	6.75877i	0.503810	+	1.55057i	0.802762	+	0.596300i	$0.203363\pi$
$19$	2.19606	+	6.75877i	0.503810	+	1.55057i	−0.298951	+	0.954268i	$0.596637\pi$
$20$	−4.89345	−	8.35276i	−1.09421	−	1.86774i
$21$	−0.173858	+	0.535081i	−0.0379390	+	0.116764i
$22$	−4.00654	+	12.3309i	−0.854198	+	2.62895i
$23$	1.92137	−	1.39596i	0.400633	−	0.291077i	−0.369166	−	0.929364i	$-0.620356\pi$
$23$	1.92137	−	1.39596i	0.400633	−	0.291077i	0.769799	+	0.638287i	$0.220356\pi$
$24$	−1.82877			−0.373297
$25$	−0.585745	−	4.96557i	−0.117149	−	0.993114i
$26$	1.36944			0.268570
$27$	1.49024	−	1.08272i	0.286797	−	0.208370i
$28$	−2.41190	+	7.42306i	−0.455806	+	1.40283i
$29$	0.304113	−	0.935963i	0.0564723	−	0.173804i	−0.918842	−	0.394626i	$-0.870874\pi$
$29$	0.304113	−	0.935963i	0.0564723	−	0.173804i	0.975314	+	0.220822i	$0.0708741\pi$
$30$	−1.60829	−	0.703857i	−0.293633	−	0.128506i
$31$	−0.561979	−	1.72959i	−0.100934	−	0.310644i	0.887820	−	0.460190i	$-0.152219\pi$
$31$	−0.561979	−	1.72959i	−0.100934	−	0.310644i	−0.988755	+	0.149546i	$0.952219\pi$
$32$	−3.58672			−0.634049
$33$	0.496989	+	1.52958i	0.0865147	+	0.266265i
$34$	−2.03533	−	1.47876i	−0.349057	−	0.253605i
$35$	−2.67838	+	3.01289i	−0.452728	+	0.509272i
$36$	10.1663	−	7.38628i	1.69439	−	1.23105i
$37$	−3.79807	−	2.75946i	−0.624399	−	0.453653i	0.230056	−	0.973177i	$-0.426109\pi$
$37$	−3.79807	−	2.75946i	−0.624399	−	0.453653i	−0.854455	+	0.519525i	$0.826109\pi$
$38$	14.4643	+	10.5089i	2.34642	+	1.70477i
$39$	0.137429	−	0.0998481i	0.0220063	−	0.0159885i
$40$	−12.0043	−	5.25359i	−1.89805	−	0.830665i
$41$	−3.84387	−	2.79274i	−0.600312	−	0.436152i	0.245678	−	0.969352i	$-0.420989\pi$
$41$	−3.84387	−	2.79274i	−0.600312	−	0.436152i	−0.845989	+	0.533200i	$0.820989\pi$
$42$	0.437395	+	1.34616i	0.0674915	+	0.207717i
$43$	−0.257786			−0.0393120			−0.0196560	−	0.999807i	$-0.506257\pi$
$43$	−0.257786			−0.0393120			−0.0196560	+	0.999807i	$0.506257\pi$
$44$	6.89462	+	21.2195i	1.03940	+	3.19895i
$45$	6.33991	−	1.38972i	0.945098	−	0.207167i
$46$	1.84635	−	5.68248i	0.272229	−	0.837836i
$47$	−2.88783	+	8.88784i	−0.421234	+	1.29643i	0.485321	+	0.874336i	$0.338703\pi$
$47$	−2.88783	+	8.88784i	−0.421234	+	1.29643i	−0.906555	+	0.422089i	$0.861297\pi$
$48$	−1.53611	+	1.11605i	−0.221718	+	0.161088i
$49$	−3.74976			−0.535679
$50$	−8.53506	−	9.24042i	−1.20704	−	1.30679i
$51$	−0.312072			−0.0436989
$52$	1.90652	−	1.38517i	0.264387	−	0.192089i
$53$	1.23913	−	3.81366i	0.170208	−	0.523846i	−0.829174	−	0.558990i	$-0.811189\pi$
$53$	1.23913	−	3.81366i	0.170208	−	0.523846i	0.999382	+	0.0351438i	$0.0111889\pi$
$54$	1.43206	−	4.40741i	0.194878	−	0.599773i
$55$	−1.13177	+	11.4681i	−0.152608	+	1.54635i
$56$	3.26471	+	10.0478i	0.436266	+	1.34269i
$57$	2.21777			0.293751
$58$	−0.765090	−	2.35471i	−0.100461	−	0.309188i
$59$	3.17556	+	2.30718i	0.413423	+	0.300370i	0.774986	−	0.631978i	$-0.217757\pi$
$59$	3.17556	+	2.30718i	0.413423	+	0.300370i	−0.361563	+	0.932348i	$0.617757\pi$
$60$	−2.95099	+	0.646863i	−0.380971	+	0.0835096i
$61$	11.4705	−	8.33382i	1.46865	−	1.06704i	0.487647	−	0.873041i	$-0.337855\pi$
$61$	11.4705	−	8.33382i	1.46865	−	1.06704i	0.981002	−	0.193995i	$-0.0621446\pi$
$62$	−3.70147	−	2.68927i	−0.470087	−	0.341538i
$63$	−4.23355	−	3.07585i	−0.533377	−	0.387521i
$64$	2.54441	−	1.84862i	0.318051	−	0.231077i
$65$	1.18894	−	0.260618i	0.147470	−	0.0323257i
$66$	3.27341	+	2.37827i	0.402929	+	0.292745i
$67$	1.13202	+	3.48399i	0.138298	+	0.425638i	0.996088	−	0.0883621i	$-0.0281633\pi$
$67$	1.13202	+	3.48399i	0.138298	+	0.425638i	−0.857790	+	0.514000i	$0.828163\pi$
$68$	−4.32931			−0.525006
$69$	−0.229029	−	0.704879i	−0.0275719	−	0.0848575i
$70$	−0.996057	+	10.0929i	−0.119052	+	1.20633i
$71$	−2.72344	+	8.38190i	−0.323213	+	0.994748i	0.649027	+	0.760765i	$0.275176\pi$
$71$	−2.72344	+	8.38190i	−0.323213	+	0.994748i	−0.972241	+	0.233983i	$0.924824\pi$
$72$	5.25625	−	16.1771i	0.619455	−	1.90649i
$73$	3.33963	−	2.42638i	0.390874	−	0.283987i	−0.374940	−	0.927049i	$-0.622337\pi$
$73$	3.33963	−	2.42638i	0.390874	−	0.283987i	0.765814	+	0.643063i	$0.222337\pi$
$74$	−11.8109			−1.37299
$75$	−1.53026	−	0.305010i	−0.176699	−	0.0352195i
$76$	30.7666			3.52917
$77$	7.51666	−	5.46118i	0.856603	−	0.622359i
$78$	0.132063	−	0.406449i	0.0149532	−	0.0460212i
$79$	−1.51457	+	4.66138i	−0.170403	+	0.524446i	−0.999394	−	0.0348162i	$-0.988915\pi$
$79$	−1.51457	+	4.66138i	−0.170403	+	0.524446i	0.828991	+	0.559262i	$0.188915\pi$
$80$	−13.2893	+	2.91305i	−1.48579	+	0.325689i
$81$	2.51323	+	7.73493i	0.279248	+	0.859436i
$82$	−11.9533			−1.32003
$83$	−2.08681	−	6.42254i	−0.229057	−	0.704966i	−0.997854	−	0.0654729i	$-0.979144\pi$
$83$	−2.08681	−	6.42254i	−0.229057	−	0.704966i	0.768797	−	0.639493i	$-0.220856\pi$
$84$	1.97056	+	1.43169i	0.215005	+	0.156211i
$85$	−2.04848	−	0.896502i	−0.222189	−	0.0972393i
$86$	−0.524681	+	0.381203i	−0.0565778	+	0.0411062i
$87$	−0.248465	−	0.180520i	−0.0266382	−	0.0193538i
$88$	24.4327	+	17.7514i	2.60454	+	1.89231i
$89$	−13.8721	+	10.0787i	−1.47044	+	1.06834i	−0.489956	+	0.871747i	$0.662987\pi$
$89$	−13.8721	+	10.0787i	−1.47044	+	1.06834i	−0.980485	+	0.196591i	$0.937013\pi$
$90$	10.8488	−	12.2037i	1.14356	−	1.28639i
$91$	−0.793929	−	0.576823i	−0.0832264	−	0.0604675i
$92$	−3.17727	−	9.77863i	−0.331253	−	1.01949i
$93$	−0.567536			−0.0588507
$94$	7.26525	+	22.3601i	0.749353	+	2.30627i
$95$	14.5577	+	6.37108i	1.49359	+	0.653659i
$96$	−0.345888	+	1.06453i	−0.0353020	+	0.108648i
$97$	−5.88349	+	18.1075i	−0.597378	+	1.83854i	−0.0548647	+	0.998494i	$0.517473\pi$
$97$	−5.88349	+	18.1075i	−0.597378	+	1.83854i	−0.542513	+	0.840047i	$0.682527\pi$
$98$	−7.63201	+	5.54498i	−0.770949	+	0.560127i
$99$	−14.9589			−1.50342
$100$	−21.2290	−	4.23133i	−2.12290	−	0.423133i
$101$	−16.2144			−1.61339			−0.806697	−	0.590965i	$-0.798747\pi$
$101$	−16.2144			−1.61339			−0.806697	+	0.590965i	$0.798747\pi$
$102$	−0.635171	+	0.461479i	−0.0628913	+	0.0456932i
$103$	4.08638	−	12.5766i	0.402643	−	1.23921i	−0.520205	−	0.854041i	$-0.674145\pi$
$103$	4.08638	−	12.5766i	0.402643	−	1.23921i	0.922848	−	0.385165i	$-0.125855\pi$
$104$	0.985719	−	3.03373i	0.0966577	−	0.297482i
$105$	0.635930	+	1.08549i	0.0620604	+	0.105933i
$106$	−3.11742	−	9.59445i	−0.302791	−	0.931895i
$107$	5.06536			0.489687			0.244844	−	0.969563i	$-0.421263\pi$
$107$	5.06536			0.489687			0.244844	+	0.969563i	$0.421263\pi$
$108$	−2.46434	−	7.58445i	−0.237131	−	0.729814i
$109$	−5.21971	−	3.79234i	−0.499957	−	0.363240i	0.309043	−	0.951048i	$-0.399991\pi$
$109$	−5.21971	−	3.79234i	−0.499957	−	0.363240i	−0.809001	+	0.587808i	$0.799991\pi$
$110$	14.6549	+	25.0149i	1.39729	+	2.38508i
$111$	−1.18527	+	0.861151i	−0.112501	+	0.0817369i
$112$	8.87412	+	6.44742i	0.838525	+	0.609224i
$113$	−6.94391	−	5.04505i	−0.653228	−	0.474598i	0.211141	−	0.977456i	$-0.432282\pi$
$113$	−6.94391	−	5.04505i	−0.653228	−	0.474598i	−0.864369	+	0.502858i	$0.832282\pi$
$114$	4.51390	−	3.27954i	0.422766	−	0.307157i
$115$	0.521557	−	5.28486i	0.0486354	−	0.492816i
$116$	−3.44690	−	2.50432i	−0.320036	−	0.232520i
$117$	0.488244	+	1.50266i	0.0451382	+	0.138921i
$118$	9.87510			0.909076
$119$	0.557109	+	1.71461i	0.0510701	+	0.157178i
$120$	−2.71690	+	3.05623i	−0.248018	+	0.278994i
$121$	4.80813	−	14.7979i	0.437103	−	1.34526i
$122$	11.0226	−	33.9242i	0.997943	−	3.07135i
$123$	−1.19957	+	0.871535i	−0.108161	+	0.0785837i
$124$	−7.87329			−0.707043
$125$	−9.16862	−	6.39816i	−0.820066	−	0.572269i
$126$	−13.1651			−1.17284
$127$	11.6627	−	8.47346i	1.03490	−	0.751898i	0.0656152	−	0.997845i	$-0.479099\pi$
$127$	11.6627	−	8.47346i	1.03490	−	0.751898i	0.969283	+	0.245947i	$0.0790990\pi$
$128$	4.66177	−	14.3475i	0.412046	−	1.26815i
$129$	−0.0248598	+	0.0765105i	−0.00218878	+	0.00673637i
$130$	2.03450	−	2.28860i	0.178438	−	0.200723i
$131$	0.168160	+	0.517544i	0.0146922	+	0.0452181i	0.958134	−	0.286321i	$-0.0924323\pi$
$131$	0.168160	+	0.517544i	0.0146922	+	0.0452181i	−0.943442	+	0.331539i	$0.892432\pi$
$132$	6.96279			0.606033
$133$	−3.95915	−	12.1850i	−0.343302	−	1.05657i
$134$	7.45602	+	5.41711i	0.644102	+	0.467967i
$135$	0.404527	−	4.09902i	0.0348161	−	0.352787i
$136$	−4.74092	+	3.44448i	−0.406530	+	0.295362i
$137$	15.4550	+	11.2287i	1.32041	+	0.959332i	0.999927	+	0.0120770i	$0.00384431\pi$
$137$	15.4550	+	11.2287i	1.32041	+	0.959332i	0.320480	+	0.947255i	$0.396156\pi$
$138$	−1.50850	−	1.09599i	−0.128412	−	0.0932966i
$139$	−13.9947	+	10.1677i	−1.18701	+	0.862416i	−0.992945	−	0.118572i	$-0.962168\pi$
$139$	−13.9947	+	10.1677i	−1.18701	+	0.862416i	−0.194069	+	0.980988i	$0.562168\pi$
$140$	8.82212	+	15.0587i	0.745605	+	1.27269i
$141$	2.35941	+	1.71421i	0.198698	+	0.144362i
$142$	6.85167	+	21.0873i	0.574979	+	1.76960i
$143$	−2.80528			−0.234589
$144$	−5.45734	−	16.7960i	−0.454778	−	1.39966i
$145$	−1.11237	−	1.89873i	−0.0923772	−	0.157681i
$146$	3.20923	−	9.87700i	0.265598	−	0.817426i
$147$	−0.361610	+	1.11292i	−0.0298251	+	0.0917922i
$148$	−16.4430	+	11.9466i	−1.35161	+	0.982001i
$149$	12.4600			1.02077			0.510383	−	0.859947i	$-0.329504\pi$
$149$	12.4600			1.02077			0.510383	+	0.859947i	$0.329504\pi$
$150$	−3.56563	+	1.64209i	−0.291132	+	0.134076i
$151$	3.63955			0.296183			0.148091	−	0.988974i	$-0.452687\pi$
$151$	3.63955			0.296183			0.148091	+	0.988974i	$0.452687\pi$
$152$	33.6918	−	24.4785i	2.73276	−	1.98547i
$153$	0.896956	−	2.76055i	0.0725146	−	0.223177i
$154$	7.22317	−	22.2306i	0.582060	−	1.79140i
$155$	−3.72538	−	1.63038i	−0.299230	−	0.130955i
$156$	−0.227259	−	0.699433i	−0.0181953	−	0.0559994i
$157$	0.816243			0.0651433			0.0325717	−	0.999469i	$-0.489630\pi$
$157$	0.816243			0.0651433			0.0325717	+	0.999469i	$0.489630\pi$
$158$	3.81038	+	11.7271i	0.303138	+	0.932961i
$159$	−1.01239	−	0.735545i	−0.0802878	−	0.0583325i
$160$	−5.32858	+	5.99409i	−0.421261	+	0.473874i
$161$	−3.46393	+	2.51669i	−0.272996	+	0.198343i
$162$	16.5533	+	12.0267i	1.30055	+	0.944907i
$163$	−14.7611	−	10.7246i	−1.15618	−	0.840013i	−0.166889	−	0.985976i	$-0.553372\pi$
$163$	−14.7611	−	10.7246i	−1.15618	−	0.840013i	−0.989290	+	0.145962i	$0.953372\pi$
$164$	−16.6413	+	12.0906i	−1.29947	+	0.944118i
$165$	3.29456	+	1.44184i	0.256481	+	0.112247i
$166$	−13.7447	−	9.98614i	−1.06680	−	0.775074i
$167$	−7.24650	−	22.3024i	−0.560751	−	1.72582i	−0.680250	−	0.732981i	$-0.738129\pi$
$167$	−7.24650	−	22.3024i	−0.560751	−	1.72582i	0.119498	−	0.992834i	$-0.461871\pi$
$168$	3.29699			0.254368
$169$	−3.92566	−	12.0819i	−0.301974	−	0.929380i
$170$	−5.49506	+	1.20453i	−0.421452	+	0.0923830i
$171$	−6.37430	+	19.6181i	−0.487455	+	1.50023i
$172$	−0.344874	+	1.06141i	−0.0262964	+	0.0809319i
$173$	−7.10537	+	5.16235i	−0.540211	+	0.392486i	−0.824163	−	0.566352i	$-0.808354\pi$
$173$	−7.10537	+	5.16235i	−0.540211	+	0.392486i	0.283952	+	0.958838i	$0.408354\pi$
$174$	−0.772655			−0.0585748
$175$	1.05601	+	8.95215i	0.0798266	+	0.676719i
$176$	31.3559			2.36354
$177$	0.991006	−	0.720008i	0.0744885	−	0.0541191i
$178$	−13.3305	+	41.0270i	−0.999161	+	3.07510i
$179$	7.02850	−	21.6315i	0.525335	−	1.61681i	−0.238318	−	0.971187i	$-0.576596\pi$
$179$	7.02850	−	21.6315i	0.525335	−	1.61681i	0.763653	−	0.645627i	$-0.223404\pi$
$180$	2.75966	−	27.9632i	0.205693	−	2.08426i
$181$	3.34609	+	10.2982i	0.248713	+	0.765459i	0.995004	+	0.0998391i	$0.0318328\pi$
$181$	3.34609	+	10.2982i	0.248713	+	0.765459i	−0.746291	+	0.665620i	$0.768167\pi$
$182$	−2.46889			−0.183006
$183$	−1.36730	−	4.20811i	−0.101074	−	0.311072i
$184$	−11.2594	−	8.18044i	−0.830055	−	0.603070i
$185$	−10.2542	+	2.24773i	−0.753900	+	0.165256i
$186$	−1.15512	+	0.839247i	−0.0846979	+	0.0615366i
$187$	4.16934	+	3.02920i	0.304892	+	0.221517i
$188$	32.7315	+	23.7808i	2.38719	+	1.73440i
$189$	−2.68667	+	1.95198i	−0.195427	+	0.141986i
$190$	39.0511	−	8.56009i	2.83307	−	0.621014i
$191$	−18.0706	−	13.1290i	−1.30754	−	0.949984i	−0.307542	−	0.951534i	$-0.599507\pi$
$191$	−18.0706	−	13.1290i	−1.30754	−	0.949984i	−0.999999	+	0.00155022i	$0.999507\pi$
$192$	−0.303296	−	0.933448i	−0.0218885	−	0.0673658i
$193$	10.5299			0.757957			0.378978	−	0.925406i	$-0.376275\pi$
$193$	10.5299			0.757957			0.378978	+	0.925406i	$0.376275\pi$
$194$	14.8018	+	45.5551i	1.06270	+	3.27067i
$195$	0.0373052	−	0.378008i	0.00267148	−	0.0270697i
$196$	−5.01653	+	15.4393i	−0.358324	+	1.10281i
$197$	−0.626160	+	1.92712i	−0.0446121	+	0.137302i	−0.970882	−	0.239560i	$-0.922997\pi$
$197$	−0.626160	+	1.92712i	−0.0446121	+	0.137302i	0.926269	+	0.376862i	$0.122997\pi$
$198$	−30.4463	+	22.1205i	−2.16372	+	1.57204i
$199$	5.28623			0.374731			0.187365	−	0.982290i	$-0.440005\pi$
$199$	5.28623			0.374731			0.187365	+	0.982290i	$0.440005\pi$
$200$	−26.6138	+	12.2565i	−1.88188	+	0.866667i
$201$	1.14321			0.0806358
$202$	−33.0018	+	23.9772i	−2.32200	+	1.68703i
$203$	−0.548268	+	1.68739i	−0.0384808	+	0.118432i
$204$	−0.417499	+	1.28493i	−0.0292308	+	0.0899632i
$205$	−10.3778	+	2.27483i	−0.724817	+	0.158881i
$206$	−10.2805	−	31.6403i	−0.716280	−	2.20448i
$207$	6.89354			0.479134
$208$	−1.02343	−	3.14979i	−0.0709621	−	0.218399i
$209$	−29.6298	−	21.5273i	−2.04954	−	1.48907i
$210$	2.89950	+	1.26894i	0.200085	+	0.0875655i
$211$	1.91946	−	1.39457i	0.132141	−	0.0960063i	−0.519751	−	0.854318i	$-0.673975\pi$
$211$	1.91946	−	1.39457i	0.132141	−	0.0960063i	0.651892	+	0.758311i	$0.273975\pi$
$212$	−14.0447	−	10.2041i	−0.964592	−	0.700817i
$213$	2.22510	+	1.61663i	0.152461	+	0.110769i
$214$	10.3097	−	7.49044i	0.704757	−	0.512036i
$215$	−0.382977	+	0.430809i	−0.0261188	+	0.0293809i
$216$	−8.73297	−	6.34487i	−0.594203	−	0.431714i
$217$	1.01316	+	3.11819i	0.0687778	+	0.211676i
$218$	−16.2318			−1.09936
$219$	−0.398087	−	1.22519i	−0.0269002	−	0.0827904i
$220$	45.7046	+	20.0023i	3.08141	+	1.34855i
$221$	0.168209	−	0.517693i	0.0113149	−	0.0348238i
$222$	−1.13899	+	3.50546i	−0.0764442	+	0.235271i
$223$	−0.540700	+	0.392841i	−0.0362079	+	0.0263066i	−0.605742	−	0.795661i	$-0.707124\pi$
$223$	−0.540700	+	0.392841i	−0.0362079	+	0.0263066i	0.569534	+	0.821968i	$0.307124\pi$
$224$	6.46630			0.432048
$225$	7.09634	−	12.6598i	0.473089	−	0.843987i
$226$	−21.5936			−1.43638
$227$	−18.4504	+	13.4050i	−1.22460	+	0.889721i	−0.996473	−	0.0839114i	$-0.973259\pi$
$227$	−18.4504	+	13.4050i	−1.22460	+	0.889721i	−0.228123	+	0.973632i	$0.573259\pi$
$228$	2.96700	−	9.13148i	0.196494	−	0.604747i
$229$	−2.83352	+	8.72066i	−0.187244	+	0.576278i	−0.999980	−	0.00635463i	$-0.997977\pi$
$229$	−2.83352	+	8.72066i	−0.187244	+	0.576278i	0.812736	+	0.582632i	$0.197977\pi$
$230$	−6.75348	−	11.5277i	−0.445311	−	0.760115i
$231$	−0.895994	−	2.75758i	−0.0589521	−	0.181436i
$232$	−5.76709			−0.378628
$233$	−2.74258	−	8.44081i	−0.179673	−	0.552976i	0.820143	−	0.572158i	$-0.193894\pi$
$233$	−2.74258	−	8.44081i	−0.179673	−	0.552976i	−0.999816	+	0.0191825i	$0.993894\pi$
$234$	3.21581	+	2.33642i	0.210224	+	0.152737i
$235$	10.5630	+	18.0303i	0.689053	+	1.17616i
$236$	13.7480	−	9.98850i	0.894918	−	0.650196i
$237$	1.23743	+	0.899045i	0.0803797	+	0.0583993i
$238$	3.66939	+	2.66597i	0.237851	+	0.172809i
$239$	2.40501	−	1.74734i	0.155567	−	0.113026i	−0.507279	−	0.861782i	$-0.669349\pi$
$239$	2.40501	−	1.74734i	0.155567	−	0.113026i	0.662846	+	0.748756i	$0.269349\pi$
$240$	−0.416978	+	4.22518i	−0.0269158	+	0.272734i
$241$	20.5417	+	14.9244i	1.32321	+	0.961366i	0.999886	+	0.0150758i	$0.00479896\pi$
$241$	20.5417	+	14.9244i	1.32321	+	0.961366i	0.323320	+	0.946290i	$0.395201\pi$
$242$	−12.0964	−	37.2287i	−0.777583	−	2.39315i
$243$	8.06420			0.517319
$244$	−18.9682	−	58.3781i	−1.21431	−	3.73728i
$245$	−5.57079	+	6.26655i	−0.355905	+	0.400355i
$246$	−1.15273	+	3.54773i	−0.0734952	+	0.226195i
$247$	−1.19539	+	3.67903i	−0.0760609	+	0.234091i
$248$	−8.62185	+	6.26414i	−0.547488	+	0.397773i
$249$	−2.10744			−0.133554
$250$	−28.1225	+	0.535755i	−1.77862	+	0.0338841i
$251$	−19.2425			−1.21457			−0.607287	−	0.794483i	$-0.707742\pi$
$251$	−19.2425			−1.21457			−0.607287	+	0.794483i	$0.707742\pi$
$252$	−18.3283	+	13.3163i	−1.15458	+	0.838849i
$253$	−3.78221	+	11.6404i	−0.237785	+	0.731828i
$254$	11.2073	−	34.4926i	0.703211	−	2.16426i
$255$	−0.463627	+	0.521532i	−0.0290335	+	0.0326596i
$256$	−9.78439	−	30.1133i	−0.611524	−	1.88208i
$257$	9.96594			0.621658			0.310829	−	0.950466i	$-0.399393\pi$
$257$	9.96594			0.621658			0.310829	+	0.950466i	$0.399393\pi$
$258$	0.0625425	+	0.192486i	0.00389372	+	0.0119836i
$259$	6.84733	+	4.97488i	0.425472	+	0.309124i
$260$	0.517527	−	5.24403i	0.0320956	−	0.325221i
$261$	2.31099	−	1.67903i	0.143047	−	0.103930i
$262$	1.10758	+	0.804707i	0.0684268	+	0.0497150i
$263$	8.13258	+	5.90866i	0.501476	+	0.364344i	0.809581	−	0.587009i	$-0.199695\pi$
$263$	8.13258	+	5.90866i	0.501476	+	0.364344i	−0.308104	+	0.951353i	$0.599695\pi$
$264$	7.62478	−	5.53972i	0.469273	−	0.340946i
$265$	−4.53244	−	7.73655i	−0.278426	−	0.475253i
$266$	−26.0769	−	18.9459i	−1.59887	−	1.16165i
$267$	1.65357	+	5.08917i	0.101197	+	0.311452i
$268$	15.8595			0.968773
$269$	5.39941	+	16.6177i	0.329208	+	1.01320i	0.969505	+	0.245070i	$0.0788110\pi$
$269$	5.39941	+	16.6177i	0.329208	+	1.01320i	−0.640298	+	0.768127i	$0.721189\pi$
$270$	−5.23810	−	8.94106i	−0.318781	−	0.544136i
$271$	−3.21697	+	9.90082i	−0.195417	+	0.601432i	0.804554	+	0.593879i	$0.202404\pi$
$271$	−3.21697	+	9.90082i	−0.195417	+	0.601432i	−0.999971	+	0.00755294i	$0.997596\pi$
$272$	−1.88015	+	5.78650i	−0.114001	+	0.350858i
$273$	−0.247763	+	0.180011i	−0.0149953	+	0.0108947i
$274$	48.0605			2.90344
$275$	17.4839	+	18.9288i	1.05432	+	1.14145i
$276$	−3.20868			−0.193140
$277$	13.4302	−	9.75758i	0.806940	−	0.586276i	−0.106002	−	0.994366i	$-0.533805\pi$
$277$	13.4302	−	9.75758i	0.806940	−	0.586276i	0.912942	+	0.408090i	$0.133805\pi$
$278$	−13.4483	+	41.3895i	−0.806573	+	2.48238i
$279$	1.63121	−	5.02034i	0.0976578	−	0.300560i
$280$	21.6419	+	9.47140i	1.29335	+	0.566024i
$281$	−8.51376	−	26.2027i	−0.507888	−	1.56312i	−0.795860	−	0.605480i	$-0.792981\pi$
$281$	−8.51376	−	26.2027i	−0.507888	−	1.56312i	0.287972	−	0.957639i	$-0.407019\pi$
$282$	7.33708			0.436917
$283$	1.82492	+	5.61651i	0.108480	+	0.333867i	0.990531	−	0.137286i	$-0.0438379\pi$
$283$	1.82492	+	5.61651i	0.108480	+	0.333867i	−0.882051	+	0.471153i	$0.843838\pi$
$284$	30.8682	+	22.4271i	1.83169	+	1.33080i
$285$	3.29481	−	3.70631i	0.195168	−	0.219543i
$286$	−5.70967	+	4.14832i	−0.337620	+	0.245295i
$287$	6.92990	+	5.03486i	0.409059	+	0.297199i
$288$	−8.42256	−	6.11935i	−0.496304	−	0.360586i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−5.07181	−	2.21964i	−0.297827	−	0.130341i
$291$	4.80691	+	3.49242i	0.281786	+	0.204729i
$292$	−5.52257	−	16.9967i	−0.323184	−	0.994658i
$293$	14.0256			0.819384			0.409692	−	0.912224i	$-0.365636\pi$
$293$	14.0256			0.819384			0.409692	+	0.912224i	$0.365636\pi$
$294$	0.909743	+	2.79990i	0.0530573	+	0.163293i
$295$	8.57349	−	1.87933i	0.499168	−	0.109419i
$296$	−8.50145	+	26.1648i	−0.494137	+	1.52080i
$297$	−2.93353	+	9.02849i	−0.170221	+	0.523886i
$298$	25.3603	−	18.4254i	1.46908	−	1.06735i
$299$	1.29276			0.0747625
$300$	−3.30308	+	5.89267i	−0.190703	+	0.340213i
$301$	0.464748			0.0267876
$302$	7.40771	−	5.38202i	0.426266	−	0.309700i
$303$	−1.56365	+	4.81241i	−0.0898292	+	0.276466i
$304$	13.3614	−	41.1223i	0.766331	−	2.35853i
$305$	3.11368	−	31.5505i	0.178289	−	1.80657i
$306$	−2.25657	−	6.94502i	−0.129000	−	0.397020i
$307$	−0.978219			−0.0558299			−0.0279149	−	0.999610i	$-0.508887\pi$
$307$	−0.978219			−0.0558299			−0.0279149	+	0.999610i	$0.508887\pi$
$308$	−12.4299	−	38.2553i	−0.708260	−	2.17980i
$309$	−3.33863	−	2.42566i	−0.189928	−	0.137991i
$310$	−9.99333	+	2.19056i	−0.567583	+	0.124415i
$311$	4.16461	−	3.02577i	0.236153	−	0.171576i	−0.463414	−	0.886142i	$-0.653376\pi$
$311$	4.16461	−	3.02577i	0.236153	−	0.171576i	0.699568	+	0.714566i	$0.253376\pi$
$312$	−0.805348	−	0.585120i	−0.0455939	−	0.0331259i
$313$	11.1738	+	8.11828i	0.631583	+	0.458872i	0.856948	−	0.515402i	$-0.172358\pi$
$313$	11.1738	+	8.11828i	0.631583	+	0.458872i	−0.225365	+	0.974274i	$0.572358\pi$
$314$	1.66133	−	1.20703i	0.0937542	−	0.0681164i
$315$	−11.4299	+	2.50545i	−0.644000	+	0.141166i
$316$	17.1666	+	12.4723i	0.965696	+	0.701619i
$317$	−9.09212	−	27.9827i	−0.510664	−	1.57166i	−0.791035	−	0.611771i	$-0.790457\pi$
$317$	−9.09212	−	27.9827i	−0.510664	−	1.57166i	0.280370	−	0.959892i	$-0.409543\pi$
$318$	−3.14825			−0.176545
$319$	1.56727	+	4.82356i	0.0877503	+	0.270068i
$320$	0.690680	−	6.99856i	0.0386102	−	0.391232i
$321$	0.488481	−	1.50339i	0.0272644	−	0.0839111i
$322$	−3.32868	+	10.2446i	−0.185500	+	0.570910i
$323$	5.74935	−	4.17715i	0.319903	−	0.232423i
$324$	35.2102			1.95612
$325$	1.33080	−	2.37413i	0.0738193	−	0.131693i
$326$	−45.9028			−2.54232
$327$	−1.62893	+	1.18348i	−0.0900798	+	0.0654468i
$328$	−8.60396	+	26.4803i	−0.475074	+	1.46213i
$329$	5.20631	−	16.0234i	0.287033	−	0.883398i
$330$	8.83765	−	1.93723i	0.486497	−	0.106641i
$331$	−8.79416	−	27.0656i	−0.483371	−	1.48766i	−0.834327	−	0.551270i	$-0.814143\pi$
$331$	−8.79416	−	27.0656i	−0.483371	−	1.48766i	0.350956	−	0.936392i	$-0.385857\pi$
$332$	−29.2361			−1.60454
$333$	−4.21092	−	12.9599i	−0.230757	−	0.710197i
$334$	−47.7290	−	34.6771i	−2.61161	−	1.89745i
$335$	7.50418	+	3.28415i	0.409997	+	0.179432i
$336$	2.76937	−	2.01206i	0.151081	−	0.109767i
$337$	22.5499	+	16.3834i	1.22837	+	0.892463i	0.996767	−	0.0803471i	$-0.0256029\pi$
$337$	22.5499	+	16.3834i	1.22837	+	0.892463i	0.231603	+	0.972810i	$0.425603\pi$
$338$	−25.8563	−	18.7857i	−1.40640	−	1.02181i
$339$	−2.16700	+	1.57442i	−0.117695	+	0.0855107i
$340$	−6.43179	+	7.23509i	−0.348813	+	0.392378i
$341$	7.58237	+	5.50892i	0.410609	+	0.298325i
$342$	16.0365	+	49.3554i	0.867157	+	2.66883i
$343$	19.3801			1.04643
$344$	0.466817	+	1.43671i	0.0251691	+	0.0774625i
$345$	−1.51824	−	0.664446i	−0.0817394	−	0.0357726i
$346$	−6.82793	+	21.0142i	−0.367072	+	1.12973i
$347$	7.63721	−	23.5049i	0.409987	−	1.26181i	−0.506672	−	0.862139i	$-0.669125\pi$
$347$	7.63721	−	23.5049i	0.409987	−	1.26181i	0.916659	−	0.399670i	$-0.130875\pi$
$348$	−1.07568	+	0.781528i	−0.0576625	+	0.0418943i
$349$	−16.5397			−0.885351			−0.442676	−	0.896682i	$-0.645971\pi$
$349$	−16.5397			−0.885351			−0.442676	+	0.896682i	$0.645971\pi$
$350$	15.3874	+	16.6590i	0.822490	+	0.890463i
$351$	1.00269			0.0535195
$352$	14.9543	−	10.8649i	0.797064	−	0.579101i
$353$	8.85290	−	27.2464i	0.471192	−	1.45018i	−0.379833	−	0.925055i	$-0.624018\pi$
$353$	8.85290	−	27.2464i	0.471192	−	1.45018i	0.851025	−	0.525125i	$-0.175982\pi$
$354$	0.952311	−	2.93091i	0.0506148	−	0.155776i
$355$	9.96167	+	17.0039i	0.528711	+	0.902472i
$356$	22.9396	+	70.6008i	1.21580	+	3.74184i
$357$	0.562617			0.0297769
$358$	−17.6824	−	54.4208i	−0.934543	−	2.87623i
$359$	23.8972	+	17.3623i	1.26125	+	0.916349i	0.998818	−	0.0486027i	$-0.0154768\pi$
$359$	23.8972	+	17.3623i	1.26125	+	0.916349i	0.262428	+	0.964952i	$0.415477\pi$
$360$	−19.2261	−	32.8175i	−1.01330	−	1.72963i
$361$	−25.4870	+	18.5174i	−1.34142	+	0.974600i
$362$	22.0389	+	16.0122i	1.15834	+	0.841584i
$363$	−3.92832	−	2.85409i	−0.206183	−	0.149801i
$364$	−3.43716	+	2.49724i	−0.180156	+	0.130891i
$365$	0.906544	−	9.18588i	0.0474507	−	0.480811i
$366$	−9.00567	−	6.54301i	−0.470734	−	0.342008i
$367$	1.61649	+	4.97504i	0.0843800	+	0.259695i	0.984341	−	0.176276i	$-0.0564051\pi$
$367$	1.61649	+	4.97504i	0.0843800	+	0.259695i	−0.899961	+	0.435971i	$0.856405\pi$
$368$	−14.4498			−0.753250
$369$	−4.26169	−	13.1161i	−0.221855	−	0.682799i
$370$	−17.5468	+	19.7383i	−0.912214	+	1.02614i
$371$	−2.23396	+	6.87543i	−0.115982	+	0.356955i
$372$	−0.759266	+	2.33678i	−0.0393661	+	0.121156i
$373$	10.7512	−	7.81122i	0.556677	−	0.404449i	−0.273564	−	0.961854i	$-0.588203\pi$
$373$	10.7512	−	7.81122i	0.556677	−	0.404449i	0.830241	+	0.557404i	$0.188203\pi$
$374$	12.9654			0.670427
$375$	−2.78315	+	2.10422i	−0.143721	+	0.108661i
$376$	54.7640			2.82424
$377$	0.433387	−	0.314874i	0.0223206	−	0.0162168i
$378$	−2.58177	+	7.94587i	−0.132792	+	0.408692i
$379$	−9.29608	+	28.6104i	−0.477508	+	1.46962i	0.365038	+	0.930993i	$0.381056\pi$
$379$	−9.29608	+	28.6104i	−0.477508	+	1.46962i	−0.842546	+	0.538625i	$0.818944\pi$
$380$	45.7081	−	51.4168i	2.34478	−	2.63763i
$381$	−1.39021	−	4.27862i	−0.0712225	−	0.219200i
$382$	−56.1943			−2.87515
$383$	−2.39746	−	7.37861i	−0.122504	−	0.377030i	0.870934	−	0.491400i	$-0.163515\pi$
$383$	−2.39746	−	7.37861i	−0.122504	−	0.377030i	−0.993438	+	0.114371i	$0.963515\pi$
$384$	−3.80874	−	2.76721i	−0.194364	−	0.141214i
$385$	2.04040	−	20.6751i	0.103989	−	1.05370i
$386$	21.4318	−	15.5711i	1.09085	−	0.792549i
$387$	−0.605349	−	0.439812i	−0.0307716	−	0.0223569i
$388$	66.6851	+	48.4496i	3.38542	+	2.45965i
$389$	−16.6799	+	12.1186i	−0.845703	+	0.614439i	−0.923958	−	0.382494i	$-0.875065\pi$
$389$	−16.6799	+	12.1186i	−0.845703	+	0.614439i	0.0782551	+	0.996933i	$0.475065\pi$
$390$	−0.483054	−	0.824539i	−0.0244604	−	0.0417522i
$391$	−1.92137	−	1.39596i	−0.0971678	−	0.0705966i
$392$	6.79032	+	20.8985i	0.342963	+	1.05553i
$393$	0.169823			0.00856643
$394$	1.57530	+	4.84828i	0.0793625	+	0.244253i
$395$	5.53993	+	9.45627i	0.278744	+	0.475796i
$396$	−20.0124	+	61.5918i	−1.00566	+	3.09511i
$397$	−4.23653	+	13.0387i	−0.212625	+	0.654393i	0.786689	+	0.617350i	$0.211794\pi$
$397$	−4.23653	+	13.0387i	−0.212625	+	0.654393i	−0.999314	+	0.0370428i	$0.988206\pi$
$398$	10.7592	−	7.81704i	0.539312	−	0.391833i
$399$	−3.99829			−0.200165
$400$	−14.8749	+	26.5368i	−0.743747	+	1.32684i
$401$	21.7983			1.08856			0.544278	−	0.838905i	$-0.316804\pi$
$401$	21.7983			1.08856			0.544278	+	0.838905i	$0.316804\pi$
$402$	2.32682	−	1.69053i	0.116051	−	0.0843160i
$403$	0.305905	−	0.941479i	0.0152382	−	0.0468984i
$404$	−21.6921	+	66.7615i	−1.07922	+	3.32151i
$405$	16.6603	+	7.29124i	0.827856	+	0.362304i
$406$	1.37934	+	4.24517i	0.0684554	+	0.210684i
$407$	24.1944			1.19927
$408$	0.565122	+	1.73927i	0.0279777	+	0.0861066i
$409$	16.3527	+	11.8810i	0.808590	+	0.587475i	0.913422	−	0.407015i	$-0.133430\pi$
$409$	16.3527	+	11.8810i	0.808590	+	0.587475i	−0.104831	+	0.994490i	$0.533430\pi$
$410$	−17.7584	+	19.9763i	−0.877023	+	0.986558i
$411$	4.82307	−	3.50416i	0.237904	−	0.172848i
$412$	−46.3161	−	33.6506i	−2.28183	−	1.65785i
$413$	−5.72505	−	4.15949i	−0.281711	−	0.204675i
$414$	14.0307	−	10.1939i	0.689569	−	0.501001i
$415$	−13.8335	−	6.05413i	−0.679061	−	0.297186i
$416$	−1.57951	−	1.14758i	−0.0774417	−	0.0562647i
$417$	1.66818	+	5.13413i	0.0816912	+	0.251420i
$418$	−92.1402			−4.50672
$419$	−1.92297	−	5.91829i	−0.0939432	−	0.289127i	0.893034	−	0.449990i	$-0.148572\pi$
$419$	−1.92297	−	5.91829i	−0.0939432	−	0.289127i	−0.986977	+	0.160862i	$0.948572\pi$
$420$	5.32017	−	1.16619i	0.259598	−	0.0569043i
$421$	3.89329	−	11.9823i	0.189747	−	0.583982i	−0.810251	−	0.586084i	$-0.800669\pi$
$421$	3.89329	−	11.9823i	0.189747	−	0.583982i	0.999998	+	0.00210163i	$0.000668969\pi$
$422$	1.84452	−	5.67684i	0.0897897	−	0.276344i
$423$	−21.9450	+	15.9440i	−1.06700	+	0.775224i
$424$	−23.4985			−1.14119
$425$	−4.54153	+	2.09152i	−0.220297	+	0.101454i
$426$	6.91941			0.335247
$427$	−20.6795	+	15.0246i	−1.00075	+	0.727090i
$428$	6.77659	−	20.8562i	0.327559	−	1.00812i
$429$	−0.270529	+	0.832601i	−0.0130612	+	0.0401984i
$430$	−0.142425	+	1.44317i	−0.00686834	+	0.0695959i
$431$	9.12609	+	28.0872i	0.439588	+	1.35291i	0.888311	+	0.459243i	$0.151879\pi$
$431$	9.12609	+	28.0872i	0.439588	+	1.35291i	−0.448722	+	0.893671i	$0.648121\pi$
$432$	−11.2075			−0.539221
$433$	−0.443244	−	1.36417i	−0.0213010	−	0.0655576i	0.939841	−	0.341612i	$-0.110973\pi$
$433$	−0.443244	−	1.36417i	−0.0213010	−	0.0655576i	−0.961142	+	0.276055i	$0.910973\pi$
$434$	6.67316	+	4.84834i	0.320322	+	0.232728i
$435$	−0.670813	+	0.147044i	−0.0321630	+	0.00705020i
$436$	−22.5977	+	16.4182i	−1.08223	+	0.786289i
$437$	13.6544	+	9.92050i	0.653178	+	0.474562i
$438$	−2.62199	−	1.90499i	−0.125284	−	0.0910239i
$439$	13.2416	−	9.62058i	0.631987	−	0.459165i	−0.225101	−	0.974335i	$-0.572271\pi$
$439$	13.2416	−	9.62058i	0.631987	−	0.459165i	0.857088	+	0.515170i	$0.172271\pi$
$440$	65.9642	−	14.4595i	3.14472	−	0.689329i
$441$	−8.80541	−	6.39750i	−0.419305	−	0.304643i
$442$	−0.423181	−	1.30242i	−0.0201287	−	0.0619497i
$443$	−20.0416			−0.952207			−0.476103	−	0.879389i	$-0.657951\pi$
$443$	−20.0416			−0.952207			−0.476103	+	0.879389i	$0.657951\pi$
$444$	1.96002	+	6.03234i	0.0930187	+	0.286282i
$445$	−3.76559	+	38.1562i	−0.178506	+	1.80878i
$446$	−0.519588	+	1.59913i	−0.0246032	+	0.0757209i
$447$	1.20159	−	3.69812i	0.0568333	−	0.174915i
$448$	−4.58716	+	3.33277i	−0.216723	+	0.157459i
$449$	15.3939			0.726483			0.363241	−	0.931695i	$-0.381670\pi$
$449$	15.3939			0.726483			0.363241	+	0.931695i	$0.381670\pi$
$450$	−4.27736	−	36.2607i	−0.201637	−	1.70935i
$451$	24.4862			1.15301
$452$	−30.0623	+	21.8416i	−1.41401	+	1.02734i
$453$	0.350983	−	1.08021i	0.0164906	−	0.0507529i
$454$	−17.7300	+	54.5673i	−0.832110	+	2.56097i
$455$	−2.14347	+	0.469854i	−0.100488	+	0.0220271i
$456$	−4.01609	−	12.3603i	−0.188071	−	0.578822i
$457$	32.9755			1.54253			0.771264	−	0.636515i	$-0.219625\pi$
$457$	32.9755			1.54253			0.771264	+	0.636515i	$0.219625\pi$
$458$	7.12859	+	21.9395i	0.333097	+	1.02517i
$459$	−1.49024	−	1.08272i	−0.0695586	−	0.0505373i
$460$	−21.0622	−	9.21771i	−0.982031	−	0.429778i
$461$	18.9799	−	13.7897i	0.883984	−	0.642252i	−0.0503183	−	0.998733i	$-0.516024\pi$
$461$	18.9799	−	13.7897i	0.883984	−	0.642252i	0.934303	+	0.356481i	$0.116024\pi$
$462$	−5.90144	−	4.28765i	−0.274560	−	0.199480i
$463$	15.5261	+	11.2804i	0.721561	+	0.524245i	0.886883	−	0.461995i	$-0.152866\pi$
$463$	15.5261	+	11.2804i	0.721561	+	0.524245i	−0.165321	+	0.986240i	$0.552866\pi$
$464$	−4.84417	+	3.51950i	−0.224885	+	0.163389i
$465$	−0.843154	+	0.948459i	−0.0391003	+	0.0439838i
$466$	−18.0640	−	13.1242i	−0.836798	−	0.607969i
$467$	9.18947	+	28.2823i	0.425238	+	1.30875i	0.902766	+	0.430132i	$0.141533\pi$
$467$	9.18947	+	28.2823i	0.425238	+	1.30875i	−0.477528	+	0.878616i	$0.658467\pi$
$468$	6.84027			0.316192
$469$	−2.04085	−	6.28109i	−0.0942378	−	0.290034i
$470$	48.1616	+	21.0775i	2.22153	+	0.972233i
$471$	0.0787149	−	0.242260i	0.00362699	−	0.0111627i
$472$	7.10805	−	21.8763i	0.327175	−	1.00694i
$473$	1.07480	−	0.780886i	0.0494192	−	0.0359052i
$474$	3.84805			0.176747
$475$	32.2748	−	14.8636i	1.48087	−	0.681989i
$476$	7.80506			0.357744
$477$	9.41634	−	6.84137i	0.431144	−	0.313245i
$478$	2.31110	−	7.11284i	0.105707	−	0.325334i
$479$	−5.03528	+	15.4970i	−0.230068	+	0.708077i	0.767669	+	0.640846i	$0.221416\pi$
$479$	−5.03528	+	15.4970i	−0.230068	+	0.708077i	−0.997737	+	0.0672305i	$0.978584\pi$
$480$	1.26517	+	2.15956i	0.0577469	+	0.0985698i
$481$	−0.789685	−	2.43040i	−0.0360066	−	0.110817i
$482$	63.8788			2.90960
$483$	0.412904	+	1.27079i	0.0187878	+	0.0578228i
$484$	−54.4967	−	39.5942i	−2.47712	−	1.79973i
$485$	21.5203	+	36.7337i	0.977189	+	1.66799i
$486$	16.4133	−	11.9250i	0.744524	−	0.540929i
$487$	9.27696	+	6.74010i	0.420379	+	0.305423i	0.777790	−	0.628524i	$-0.216341\pi$
$487$	9.27696	+	6.74010i	0.420379	+	0.305423i	−0.357411	+	0.933947i	$0.616341\pi$
$488$	−67.2184	−	48.8370i	−3.04283	−	2.21075i
$489$	−4.60653	+	3.34684i	−0.208315	+	0.151349i
$490$	−2.07171	+	20.9924i	−0.0935904	+	0.948339i
$491$	17.6538	+	12.8262i	0.796705	+	0.578840i	0.909946	−	0.414728i	$-0.136123\pi$
$491$	17.6538	+	12.8262i	0.796705	+	0.578840i	−0.113241	+	0.993568i	$0.536123\pi$
$492$	1.98366	+	6.10507i	0.0894302	+	0.275238i
$493$	−0.984129			−0.0443230
$494$	3.00738	+	9.25576i	0.135308	+	0.416436i
$495$	−22.2235	+	24.9991i	−0.998871	+	1.12362i
$496$	−3.41924	+	10.5233i	−0.153529	+	0.472512i
$497$	4.90994	−	15.1112i	0.220241	−	0.677832i
$498$	−4.28935	+	3.11640i	−0.192210	+	0.139649i
$499$	−21.5224			−0.963476			−0.481738	−	0.876315i	$-0.659994\pi$
$499$	−21.5224			−0.963476			−0.481738	+	0.876315i	$0.659994\pi$
$500$	−38.6099	+	29.1914i	−1.72669	+	1.30548i
$501$	−7.31815			−0.326951
$502$	−39.1648	+	28.4549i	−1.74801	+	1.27001i
$503$	10.9790	−	33.7899i	0.489529	−	1.50662i	−0.335783	−	0.941939i	$-0.609001\pi$
$503$	10.9790	−	33.7899i	0.489529	−	1.50662i	0.825312	−	0.564677i	$-0.190999\pi$
$504$	−9.47620	+	29.1647i	−0.422103	+	1.29910i
$505$	−24.0888	+	27.0974i	−1.07194	+	1.20582i
$506$	9.51532	+	29.2851i	0.423007	+	1.30188i
$507$	−3.96447			−0.176068
$508$	−19.2860	−	59.3563i	−0.855679	−	2.63351i
$509$	−9.12632	−	6.63066i	−0.404517	−	0.293899i	0.366861	−	0.930276i	$-0.380432\pi$
$509$	−9.12632	−	6.63066i	−0.404517	−	0.293899i	−0.771378	+	0.636377i	$0.780432\pi$
$510$	−0.172418	+	1.74708i	−0.00763478	+	0.0773621i
$511$	−6.02083	+	4.37439i	−0.266346	+	0.193512i
$512$	−40.0353	−	29.0874i	−1.76933	−	1.28549i
$513$	10.5905	+	7.69448i	0.467584	+	0.339720i
$514$	20.2840	−	14.7372i	0.894689	−	0.650030i
$515$	−14.9469	−	25.5134i	−0.658641	−	1.12425i
$516$	0.281767	+	0.204716i	0.0124041	+	0.00901212i
$517$	−14.8827	−	45.8043i	−0.654541	−	2.01447i
$518$	21.2932			0.935571
$519$	0.846967	+	2.60670i	0.0371777	+	0.114421i
$520$	−3.60552	−	6.15436i	−0.158112	−	0.269886i
$521$	−0.796699	+	2.45199i	−0.0349040	+	0.107423i	−0.966991	−	0.254812i	$-0.917986\pi$
$521$	−0.796699	+	2.45199i	−0.0349040	+	0.107423i	0.932087	+	0.362236i	$0.117986\pi$
$522$	2.22076	−	6.83479i	0.0972000	−	0.299151i
$523$	−15.1172	+	10.9833i	−0.661027	+	0.480265i	−0.867010	−	0.498291i	$-0.833961\pi$
$523$	−15.1172	+	10.9833i	−0.661027	+	0.480265i	0.205982	+	0.978556i	$0.433961\pi$
$524$	2.35591			0.102919
$525$	2.75882	+	0.549885i	0.120405	+	0.0239989i
$526$	25.2900			1.10270
$527$	−1.47128	+	1.06895i	−0.0640900	+	0.0465641i
$528$	3.02382	−	9.30637i	0.131595	−	0.405008i
$529$	−5.36442	+	16.5100i	−0.233236	+	0.717826i
$530$	−20.6655	−	9.04409i	−0.897652	−	0.392850i
$531$	3.52074	+	10.8357i	0.152787	+	0.470231i
$532$	−55.4674			−2.40482
$533$	−0.799207	−	2.45971i	−0.0346175	−	0.106542i
$534$	10.8912	+	7.91293i	0.471309	+	0.342426i
$535$	7.52531	−	8.46518i	0.325347	−	0.365982i
$536$	17.3673	−	12.6181i	0.750155	−	0.545020i
$537$	−5.74240	−	4.17209i	−0.247803	−	0.180039i
$538$	35.5631	+	25.8381i	1.53323	+	1.11396i
$539$	15.6340	−	11.3588i	0.673404	−	0.489257i
$540$	−16.3362	−	7.14939i	−0.702997	−	0.307661i
$541$	28.7067	+	20.8566i	1.23420	+	0.896696i	0.997198	−	0.0748136i	$-0.0238362\pi$
$541$	28.7067	+	20.8566i	1.23420	+	0.896696i	0.236999	+	0.971510i	$0.423836\pi$
$542$	8.09329	+	24.9086i	0.347637	+	1.06992i
$543$	3.37917			0.145014
$544$	1.10836	+	3.41117i	0.0475204	+	0.146253i
$545$	−14.0923	+	3.08906i	−0.603649	+	0.132321i
$546$	−0.238089	+	0.732763i	−0.0101893	+	0.0313594i
$547$	4.02413	−	12.3850i	0.172059	−	0.529545i	−0.827427	−	0.561573i	$-0.810197\pi$
$547$	4.02413	−	12.3850i	0.172059	−	0.529545i	0.999487	+	0.0320279i	$0.0101966\pi$
$548$	66.9093	−	48.6125i	2.85822	−	2.07662i
$549$	41.1542			1.75642
$550$	63.5767	+	12.6720i	2.71092	+	0.540337i
$551$	6.99381			0.297946
$552$	−3.51375	+	2.55289i	−0.149555	+	0.108658i
$553$	2.73054	−	8.40373i	0.116114	−	0.357363i
$554$	12.9058	−	39.7199i	0.548314	−	1.68754i
$555$	−0.321743	+	3.26018i	−0.0136572	+	0.138387i
$556$	23.1423	+	71.2247i	0.981452	+	3.02060i
$557$	−30.4575			−1.29053			−0.645264	−	0.763960i	$-0.723252\pi$
$557$	−30.4575			−1.29053			−0.645264	+	0.763960i	$0.723252\pi$
$558$	−4.10381	−	12.6302i	−0.173728	−	0.534680i
$559$	−0.113523	−	0.0824792i	−0.00480150	−	0.00348850i
$560$	23.9586	−	5.25178i	1.01244	−	0.221928i
$561$	1.30113	−	0.945330i	0.0549339	−	0.0399118i
$562$	−56.0757	−	40.7414i	−2.36541	−	1.71857i
$563$	−22.7848	−	16.5541i	−0.960265	−	0.697673i	−0.00705255	−	0.999975i	$-0.502245\pi$
$563$	−22.7848	−	16.5541i	−0.960265	−	0.697673i	−0.953212	+	0.302302i	$0.902245\pi$
$564$	10.2146	−	7.42134i	0.430112	−	0.312495i
$565$	−18.7474	+	4.10946i	−0.788708	+	0.172886i
$566$	12.0198	+	8.73287i	0.505229	+	0.367070i
$567$	−4.53096	−	13.9449i	−0.190282	−	0.585629i
$568$	51.6465			2.16704
$569$	−9.75981	−	30.0376i	−0.409153	−	1.25924i	−0.917378	−	0.398018i	$-0.869698\pi$
$569$	−9.75981	−	30.0376i	−0.409153	−	1.25924i	0.508225	−	0.861224i	$-0.330302\pi$
$570$	1.22530	−	12.4158i	0.0513222	−	0.520041i
$571$	4.96779	−	15.2893i	0.207896	−	0.639837i	−0.791686	−	0.610928i	$-0.790797\pi$
$571$	4.96779	−	15.2893i	0.207896	−	0.639837i	0.999582	−	0.0289095i	$-0.00920345\pi$
$572$	−3.75298	+	11.5505i	−0.156920	+	0.482950i
$573$	−5.63933	+	4.09721i	−0.235586	+	0.171163i
$574$	21.5500			0.899479
$575$	−8.05716	−	8.72302i	−0.336007	−	0.363775i
$576$	9.12888			0.380370
$577$	2.03301	−	1.47707i	0.0846354	−	0.0614912i	−0.544663	−	0.838655i	$-0.683342\pi$
$577$	2.03301	−	1.47707i	0.0846354	−	0.0614912i	0.629298	+	0.777164i	$0.283342\pi$
$578$	−0.777428	+	2.39268i	−0.0323368	+	0.0995223i
$579$	1.01545	−	3.12525i	0.0422008	−	0.129881i
$580$	−9.30604	+	2.03990i	−0.386412	+	0.0847023i
$581$	3.76219	+	11.5788i	0.156082	+	0.480371i
$582$	14.9481			0.619619
$583$	6.38598	+	19.6540i	0.264480	+	0.813986i
$584$	−19.5706	−	14.2188i	−0.809835	−	0.588380i
$585$	3.23659	+	1.41647i	0.133816	+	0.0585637i
$586$	28.5468	−	20.7404i	1.17926	−	0.856780i
$587$	−36.7158	−	26.6756i	−1.51542	−	1.10102i	−0.963699	−	0.266990i	$-0.913971\pi$
$587$	−36.7158	−	26.6756i	−1.51542	−	1.10102i	−0.551722	−	0.834028i	$-0.686029\pi$
$588$	4.09859	+	2.97780i	0.169023	+	0.122802i
$589$	10.4558	−	7.59658i	0.430824	−	0.313012i
$590$	14.6708	−	16.5032i	0.603989	−	0.679424i
$591$	0.511583	+	0.371687i	0.0210437	+	0.0152891i
$592$	8.82669	+	27.1657i	0.362775	+	1.11651i
$593$	−5.30745			−0.217951			−0.108975	−	0.994044i	$-0.534757\pi$
$593$	−5.30745			−0.217951			−0.108975	+	0.994044i	$0.534757\pi$
$594$	7.38022	+	22.7140i	0.302814	+	0.931966i
$595$	3.69309	+	1.61625i	0.151402	+	0.0662599i
$596$	16.6694	−	51.3031i	0.682805	−	2.10146i
$597$	0.509780	−	1.56894i	0.0208639	−	0.0642126i
$598$	2.63121	−	1.91168i	0.107598	−	0.0781746i
$599$	−14.1092			−0.576486			−0.288243	−	0.957557i	$-0.593071\pi$
$599$	−14.1092			−0.576486			−0.288243	+	0.957557i	$0.593071\pi$
$600$	1.07120	+	9.08091i	0.0437314	+	0.370726i
$601$	24.1056			0.983289			0.491644	−	0.870796i	$-0.336396\pi$
$601$	24.1056			0.983289			0.491644	+	0.870796i	$0.336396\pi$
$602$	0.945917	−	0.687249i	0.0385527	−	0.0280102i
$603$	−3.28581	+	10.1127i	−0.133808	+	0.411820i
$604$	4.86910	−	14.9856i	0.198121	−	0.609754i
$605$	−17.5869	−	30.0197i	−0.715011	−	1.22047i
$606$	3.93384	+	12.1071i	0.159801	+	0.491818i
$607$	−10.3849			−0.421508			−0.210754	−	0.977539i	$-0.567592\pi$
$607$	−10.3849			−0.421508			−0.210754	+	0.977539i	$0.567592\pi$
$608$	−7.87665	−	24.2418i	−0.319440	−	0.983136i
$609$	0.447943	+	0.325450i	0.0181516	+	0.0131879i
$610$	−40.3181	−	68.8201i	−1.63243	−	2.78644i
$611$	−4.11542	+	2.99002i	−0.166492	+	0.120963i
$612$	−10.1663	−	7.38628i	−0.410950	−	0.298573i
$613$	1.97123	+	1.43218i	0.0796173	+	0.0578454i	0.626882	−	0.779114i	$-0.284331\pi$
$613$	1.97123	+	1.43218i	0.0796173	+	0.0578454i	−0.547265	+	0.836960i	$0.684331\pi$
$614$	−1.99100	+	1.44655i	−0.0803503	+	0.0583779i
$615$	−0.325622	+	3.29949i	−0.0131304	+	0.133048i
$616$	−44.0484	−	32.0030i	−1.77476	−	1.28944i
$617$	−2.83955	−	8.73924i	−0.114316	−	0.351829i	0.877488	−	0.479599i	$-0.159218\pi$
$617$	−2.83955	−	8.73924i	−0.114316	−	0.351829i	−0.991804	+	0.127770i	$0.959218\pi$
$618$	−10.3822			−0.417633
$619$	−0.334959	−	1.03090i	−0.0134631	−	0.0414353i	0.944099	−	0.329661i	$-0.106935\pi$
$619$	−0.334959	−	1.03090i	−0.0134631	−	0.0414353i	−0.957562	+	0.288226i	$0.906935\pi$
$620$	−11.6969	+	13.1578i	−0.469758	+	0.528428i
$621$	1.35187	−	4.16063i	0.0542487	−	0.166960i
$622$	4.00200	−	12.3169i	0.160466	−	0.493863i
$623$	25.0093	−	18.1703i	1.00197	−	0.727977i
$624$	−1.03355			−0.0413751
$625$	−24.3138	+	5.81712i	−0.972552	+	0.232685i
$626$	34.7475			1.38879
$627$	−9.24663	+	6.71807i	−0.369275	+	0.268294i
$628$	1.09199	−	3.36081i	0.0435753	−	0.134111i
$629$	−1.45073	+	4.46490i	−0.0578446	+	0.178027i
$630$	−19.5586	+	22.0014i	−0.779235	+	0.876557i
$631$	4.44672	+	13.6856i	0.177021	+	0.544815i	0.999720	−	0.0236624i	$-0.00753268\pi$
$631$	4.44672	+	13.6856i	0.177021	+	0.544815i	−0.822699	+	0.568477i	$0.807533\pi$
$632$	28.7219			1.14249
$633$	−0.228802	−	0.704180i	−0.00909406	−	0.0279886i
$634$	−59.8851	−	43.5090i	−2.37834	−	1.72796i
$635$	3.16585	−	32.0791i	0.125633	−	1.27302i
$636$	−4.38295	+	3.18440i	−0.173795	+	0.126270i
$637$	−1.65130	−	1.19974i	−0.0654270	−	0.0475355i
$638$	10.3228	+	7.49995i	0.408683	+	0.296926i
$639$	−20.6958	+	15.0364i	−0.818713	+	0.594830i
$640$	−17.0516	−	29.1059i	−0.674024	−	1.15051i
$641$	−14.9310	−	10.8480i	−0.589740	−	0.428471i	0.252482	−	0.967601i	$-0.418753\pi$
$641$	−14.9310	−	10.8480i	−0.589740	−	0.428471i	−0.842222	+	0.539130i	$0.818753\pi$
$642$	−1.22893	−	3.78225i	−0.0485019	−	0.149273i
$643$	−31.9211			−1.25885			−0.629423	−	0.777063i	$-0.716709\pi$
$643$	−31.9211			−1.25885			−0.629423	+	0.777063i	$0.716709\pi$
$644$	5.72812	+	17.6293i	0.225720	+	0.694693i
$645$	0.0909308	+	0.155212i	0.00358040	+	0.00611148i
$646$	5.52487	−	17.0038i	0.217373	−	0.669005i
$647$	−7.98704	+	24.5816i	−0.314003	+	0.966402i	0.662160	+	0.749363i	$0.269640\pi$
$647$	−7.98704	+	24.5816i	−0.314003	+	0.966402i	−0.976163	+	0.217039i	$0.930360\pi$
$648$	38.5578	−	28.0139i	1.51469	−	1.10049i
$649$	−20.2289			−0.794055
$650$	−0.802145	−	6.80007i	−0.0314627	−	0.266721i
$651$	1.02318			0.0401015
$652$	−63.9054	+	46.4300i	−2.50273	+	1.81834i
$653$	−6.38219	+	19.6424i	−0.249754	+	0.768665i	0.745064	+	0.666993i	$0.232419\pi$
$653$	−6.38219	+	19.6424i	−0.249754	+	0.768665i	−0.994818	+	0.101671i	$0.967581\pi$
$654$	−1.56532	+	4.81757i	−0.0612090	+	0.188382i
$655$	1.11474	+	0.487857i	0.0435565	+	0.0190621i
$656$	8.93312	+	27.4933i	0.348780	+	1.07343i
$657$	11.9820			0.467462
$658$	−13.0981	−	40.3118i	−0.510617	−	1.57152i
$659$	−2.14272	−	1.55678i	−0.0834686	−	0.0606435i	0.545268	−	0.838262i	$-0.316428\pi$
$659$	−2.14272	−	1.55678i	−0.0834686	−	0.0606435i	−0.628737	+	0.777618i	$0.716428\pi$
$660$	10.3442	−	11.6361i	0.402647	−	0.452936i
$661$	−0.835766	+	0.607220i	−0.0325075	+	0.0236181i	−0.603920	−	0.797045i	$-0.706396\pi$
$661$	−0.835766	+	0.607220i	−0.0325075	+	0.0236181i	0.571413	+	0.820663i	$0.306396\pi$
$662$	−57.9225	−	42.0832i	−2.25122	−	1.63561i
$663$	−0.137429	−	0.0998481i	−0.00533731	−	0.00387778i
$664$	−32.0157	+	23.2608i	−1.24245	+	0.902693i
$665$	−26.2453	−	11.4861i	−1.01775	−	0.445410i
$666$	−27.7351	−	20.1508i	−1.07471	−	0.780826i
$667$	−0.722251	−	2.22286i	−0.0279657	−	0.0860694i
$668$	−101.523			−3.92804
$669$	0.0644520	+	0.198363i	0.00249186	+	0.00766915i
$670$	20.1300	−	4.41253i	0.777689	−	0.170471i
$671$	−22.5796	+	69.4930i	−0.871678	+	2.68275i
$672$	0.623581	−	1.91919i	0.0240552	−	0.0740342i
$673$	6.65631	−	4.83609i	0.256582	−	0.186418i	−0.452057	−	0.891989i	$-0.649310\pi$
$673$	6.65631	−	4.83609i	0.256582	−	0.186418i	0.708639	+	0.705571i	$0.249310\pi$
$674$	70.1237			2.70106
$675$	−6.24925	−	6.76570i	−0.240534	−	0.260412i
$676$	−54.9982			−2.11532
$677$	−1.02693	+	0.746106i	−0.0394680	+	0.0286752i	−0.607344	−	0.794439i	$-0.707765\pi$
$677$	−1.02693	+	0.746106i	−0.0394680	+	0.0286752i	0.567876	+	0.823114i	$0.307765\pi$
$678$	−2.08239	+	6.40894i	−0.0799737	+	0.246134i
$679$	10.6070	−	32.6450i	0.407060	−	1.25280i
$680$	−1.28692	+	13.0402i	−0.0493513	+	0.500070i
$681$	2.19931	+	6.76877i	0.0842776	+	0.259380i
$682$	23.5790			0.902887
$683$	−6.09940	−	18.7720i	−0.233387	−	0.718291i	−0.997331	−	0.0730091i	$-0.976740\pi$
$683$	−6.09940	−	18.7720i	−0.233387	−	0.718291i	0.763944	−	0.645282i	$-0.223260\pi$
$684$	72.2481	+	52.4913i	2.76247	+	2.00706i
$685$	41.7258	−	9.14638i	1.59426	−	0.349465i
$686$	39.4450	−	28.6585i	1.50602	−	1.09419i
$687$	2.31503	+	1.68197i	0.0883238	+	0.0641710i
$688$	1.26890	+	0.921908i	0.0483763	+	0.0351474i
$689$	1.76587	−	1.28298i	0.0672744	−	0.0488777i
$690$	−4.07268	+	0.892740i	−0.155044	+	0.0339860i
$691$	20.5024	+	14.8959i	0.779947	+	0.566665i	0.904963	−	0.425490i	$-0.139898\pi$
$691$	20.5024	+	14.8959i	0.779947	+	0.566665i	−0.125016	+	0.992155i	$0.539898\pi$
$692$	11.7498	+	36.1621i	0.446660	+	1.37468i
$693$	26.9685			1.02445
$694$	−19.2138	−	59.1339i	−0.729345	−	2.24469i
$695$	−3.79887	+	38.4934i	−0.144099	+	1.46014i
$696$	−0.556153	+	1.71166i	−0.0210809	+	0.0648805i
$697$	−1.46823	+	4.51874i	−0.0556131	+	0.171159i
$698$	−33.6639	+	24.4582i	−1.27420	+	0.925758i
$699$	−2.76970			−0.104760
$700$	38.2725	+	7.62843i	1.44656	+	0.288327i
$701$	−2.52366			−0.0953171			−0.0476586	−	0.998864i	$-0.515176\pi$
$701$	−2.52366			−0.0953171			−0.0476586	+	0.998864i	$0.515176\pi$
$702$	2.04080	−	1.48273i	0.0770251	−	0.0559620i
$703$	10.3098	−	31.7302i	0.388841	−	1.19673i
$704$	−5.00865	+	15.4150i	−0.188771	+	0.580976i
$705$	6.37000	−	1.39632i	0.239908	−	0.0525883i
$706$	−22.2722	−	68.5469i	−0.838226	−	2.57980i
$707$	29.2321			1.09938
$708$	−1.63877	−	5.04363i	−0.0615889	−	0.189551i
$709$	12.5000	+	9.08176i	0.469446	+	0.341073i	0.797225	−	0.603682i	$-0.206300\pi$
$709$	12.5000	+	9.08176i	0.469446	+	0.341073i	−0.327779	+	0.944754i	$0.606300\pi$
$710$	45.4199	+	19.8777i	1.70458	+	0.745995i
$711$	−11.5094	+	8.36210i	−0.431638	+	0.313603i
$712$	81.2920	+	59.0621i	3.04655	+	2.21344i
$713$	−3.49421	−	2.53869i	−0.130859	−	0.0950748i
$714$	1.14511	−	0.831974i	0.0428548	−	0.0311359i
$715$	−4.16763	+	4.68815i	−0.155861	+	0.175327i
$716$	−79.6630	−	57.8785i	−2.97714	−	2.16302i
$717$	−0.286679	−	0.882308i	−0.0107062	−	0.0329504i
$718$	74.3135			2.77335
$719$	−10.7699	−	33.1465i	−0.401651	−	1.23615i	−0.923659	−	0.383215i	$-0.874817\pi$
$719$	−10.7699	−	33.1465i	−0.401651	−	1.23615i	0.522008	−	0.852940i	$-0.325183\pi$
$720$	−36.1769	−	15.8325i	−1.34823	−	0.590043i
$721$	−7.36709	+	22.6736i	−0.274365	+	0.844408i
$722$	−24.4918	+	75.3782i	−0.911492	+	2.80528i
$723$	6.41049	−	4.65749i	0.238409	−	0.173214i
$724$	46.8785			1.74222
$725$	−4.82572	−	0.961858i	−0.179223	−	0.0357225i
$726$	−12.2159			−0.453376
$727$	9.07878	−	6.59612i	0.336713	−	0.244637i	−0.406560	−	0.913624i	$-0.633272\pi$
$727$	9.07878	−	6.59612i	0.336713	−	0.244637i	0.743274	+	0.668987i	$0.233272\pi$
$728$	−1.77710	+	5.46934i	−0.0658636	+	0.202707i
$729$	−6.76201	+	20.8113i	−0.250445	+	0.770790i
$730$	−11.7386	−	20.0369i	−0.434464	−	0.741599i
$731$	0.0796603	+	0.245169i	0.00294634	+	0.00906791i
$732$	−19.1557			−0.708016
$733$	4.18069	+	12.8669i	0.154417	+	0.475248i	0.998101	−	0.0615921i	$-0.0196178\pi$
$733$	4.18069	+	12.8669i	0.154417	+	0.475248i	−0.843684	+	0.536840i	$0.819618\pi$
$734$	10.6470	+	7.73547i	0.392987	+	0.285522i
$735$	1.32268	+	2.25772i	0.0487878	+	0.0832772i
$736$	−6.89142	+	5.00691i	−0.254021	+	0.184557i
$737$	−15.2735	−	11.0968i	−0.562606	−	0.408757i
$738$	−28.0696	−	20.3937i	−1.03325	−	0.750704i
$739$	18.0828	−	13.1380i	0.665188	−	0.483287i	−0.203223	−	0.979132i	$-0.565142\pi$
$739$	18.0828	−	13.1380i	0.665188	−	0.483287i	0.868411	+	0.495845i	$0.165142\pi$
$740$	−4.46347	+	45.2277i	−0.164080	+	1.66260i
$741$	0.976653	+	0.709580i	0.0358782	+	0.0260671i
$742$	5.62023	+	17.2973i	0.206325	+	0.635003i
$743$	10.9327			0.401082			0.200541	−	0.979685i	$-0.435730\pi$
$743$	10.9327			0.401082			0.200541	+	0.979685i	$0.435730\pi$
$744$	1.02773	+	3.16304i	0.0376785	+	0.115963i
$745$	18.5111	−	20.8231i	0.678195	−	0.762898i
$746$	10.3314	−	31.7969i	0.378261	−	1.16417i
$747$	6.05720	−	18.6421i	0.221621	−	0.682080i
$748$	18.0503	−	13.1143i	0.659986	−	0.479508i
$749$	−9.13206			−0.333678
$750$	−2.55300	+	8.39838i	−0.0932224	+	0.306666i
$751$	−21.5897			−0.787820			−0.393910	−	0.919149i	$-0.628878\pi$
$751$	−21.5897			−0.787820			−0.393910	+	0.919149i	$0.628878\pi$
$752$	45.9999	−	33.4209i	1.67745	−	1.21874i
$753$	−1.85566	+	5.71113i	−0.0676240	+	0.208125i
$754$	0.416465	−	1.28175i	0.0151668	−	0.0466785i
$755$	5.40707	−	6.08238i	0.196783	−	0.221361i
$756$	4.44281	+	13.6736i	0.161584	+	0.497303i
$757$	5.71049			0.207551			0.103776	−	0.994601i	$-0.466908\pi$
$757$	5.71049			0.207551			0.103776	+	0.994601i	$0.466908\pi$
$758$	23.3872	+	71.9784i	0.849461	+	2.61437i
$759$	3.09012	+	2.24510i	0.112164	+	0.0814921i
$760$	9.14565	−	92.6716i	0.331748	−	3.36155i
$761$	20.7590	−	15.0823i	0.752514	−	0.546733i	−0.144091	−	0.989564i	$-0.546026\pi$
$761$	20.7590	−	15.0823i	0.752514	−	0.546733i	0.896605	+	0.442831i	$0.146026\pi$
$762$	−9.15657	−	6.65264i	−0.331707	−	0.241000i
$763$	9.41031	+	6.83699i	0.340676	+	0.247516i
$764$	−78.2331	+	56.8397i	−2.83037	+	2.05639i
$765$	−3.28084	−	5.60016i	−0.118619	−	0.202474i
$766$	−15.7908	−	11.4727i	−0.570545	−	0.414525i
$767$	0.660255	+	2.03206i	0.0238404	+	0.0733733i
$768$	−9.88113			−0.356554
$769$	−0.146243	−	0.450091i	−0.00527367	−	0.0162307i	0.948385	−	0.317121i	$-0.102716\pi$
$769$	−0.146243	−	0.450091i	−0.00527367	−	0.0162307i	−0.953659	+	0.300890i	$0.902716\pi$
$770$	−26.4206	−	45.0980i	−0.952131	−	1.62522i
$771$	0.961071	−	2.95787i	0.0346121	−	0.106525i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03533 - 1.47876i) q^{2} +(0.0964356 - 0.296798i) q^{3} +(1.33783 - 4.11742i) q^{4} +(1.48564 - 1.67119i) q^{5} +(-0.242614 - 0.746689i) q^{6} -1.80284 q^{7} +(-1.81087 - 5.57328i) q^{8} +(2.34826 + 1.70611i) q^{9} +(0.552492 - 5.59833i) q^{10} +(-4.16934 + 3.02920i) q^{11} +(-1.09303 - 0.794131i) q^{12} +(0.440376 + 0.319952i) q^{13} +(-3.66939 + 2.66597i) q^{14} +(-0.352737 - 0.602098i) q^{15} +(-4.92229 - 3.57625i) q^{16} +(-0.309017 - 0.951057i) q^{17} +7.30242 q^{18} +(2.19606 + 6.75877i) q^{19} +(-4.89345 - 8.35276i) q^{20} +(-0.173858 + 0.535081i) q^{21} +(-4.00654 + 12.3309i) q^{22} +(1.92137 - 1.39596i) q^{23} -1.82877 q^{24} +(-0.585745 - 4.96557i) q^{25} +1.36944 q^{26} +(1.49024 - 1.08272i) q^{27} +(-2.41190 + 7.42306i) q^{28} +(0.304113 - 0.935963i) q^{29} +(-1.60829 - 0.703857i) q^{30} +(-0.561979 - 1.72959i) q^{31} -3.58672 q^{32} +(0.496989 + 1.52958i) q^{33} +(-2.03533 - 1.47876i) q^{34} +(-2.67838 + 3.01289i) q^{35} +(10.1663 - 7.38628i) q^{36} +(-3.79807 - 2.75946i) q^{37} +(14.4643 + 10.5089i) q^{38} +(0.137429 - 0.0998481i) q^{39} +(-12.0043 - 5.25359i) q^{40} +(-3.84387 - 2.79274i) q^{41} +(0.437395 + 1.34616i) q^{42} -0.257786 q^{43} +(6.89462 + 21.2195i) q^{44} +(6.33991 - 1.38972i) q^{45} +(1.84635 - 5.68248i) q^{46} +(-2.88783 + 8.88784i) q^{47} +(-1.53611 + 1.11605i) q^{48} -3.74976 q^{49} +(-8.53506 - 9.24042i) q^{50} -0.312072 q^{51} +(1.90652 - 1.38517i) q^{52} +(1.23913 - 3.81366i) q^{53} +(1.43206 - 4.40741i) q^{54} +(-1.13177 + 11.4681i) q^{55} +(3.26471 + 10.0478i) q^{56} +2.21777 q^{57} +(-0.765090 - 2.35471i) q^{58} +(3.17556 + 2.30718i) q^{59} +(-2.95099 + 0.646863i) q^{60} +(11.4705 - 8.33382i) q^{61} +(-3.70147 - 2.68927i) q^{62} +(-4.23355 - 3.07585i) q^{63} +(2.54441 - 1.84862i) q^{64} +(1.18894 - 0.260618i) q^{65} +(3.27341 + 2.37827i) q^{66} +(1.13202 + 3.48399i) q^{67} -4.32931 q^{68} +(-0.229029 - 0.704879i) q^{69} +(-0.996057 + 10.0929i) q^{70} +(-2.72344 + 8.38190i) q^{71} +(5.25625 - 16.1771i) q^{72} +(3.33963 - 2.42638i) q^{73} -11.8109 q^{74} +(-1.53026 - 0.305010i) q^{75} +30.7666 q^{76} +(7.51666 - 5.46118i) q^{77} +(0.132063 - 0.406449i) q^{78} +(-1.51457 + 4.66138i) q^{79} +(-13.2893 + 2.91305i) q^{80} +(2.51323 + 7.73493i) q^{81} -11.9533 q^{82} +(-2.08681 - 6.42254i) q^{83} +(1.97056 + 1.43169i) q^{84} +(-2.04848 - 0.896502i) q^{85} +(-0.524681 + 0.381203i) q^{86} +(-0.248465 - 0.180520i) q^{87} +(24.4327 + 17.7514i) q^{88} +(-13.8721 + 10.0787i) q^{89} +(10.8488 - 12.2037i) q^{90} +(-0.793929 - 0.576823i) q^{91} +(-3.17727 - 9.77863i) q^{92} -0.567536 q^{93} +(7.26525 + 22.3601i) q^{94} +(14.5577 + 6.37108i) q^{95} +(-0.345888 + 1.06453i) q^{96} +(-5.88349 + 18.1075i) q^{97} +(-7.63201 + 5.54498i) q^{98} -14.9589 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more