LMFDB - Embedded newform 425.2.k.c.341.18

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			341.18
Character	$\chi$	$=$	425.341
Dual form			425.2.k.c.86.18

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

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

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	0.988209	+	0.153110i	$0.0489288\pi$
$2$	2.03533	+	1.47876i	1.43920	+	1.04564i	0.450989	+	0.892529i	$0.351071\pi$
$3$	0.0964356	+	0.296798i	0.0556771	+	0.171357i	0.975028	−	0.222082i	$-0.0712853\pi$
$3$	0.0964356	+	0.296798i	0.0556771	+	0.171357i	−0.919351	+	0.393439i	$0.871285\pi$
$4$	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	−0.258491	−	0.966014i	$-0.583225\pi$
$11$	−4.16934	−	3.02920i	−1.25710	−	0.913339i	−0.998612	+	0.0526751i	$0.983225\pi$
$12$	−1.09303	+	0.794131i	−0.315530	+	0.229246i
$13$	0.440376	−	0.319952i	0.122138	−	0.0887387i	−0.525039	−	0.851078i	$-0.675949\pi$
$13$	0.440376	−	0.319952i	0.122138	−	0.0887387i	0.647177	+	0.762339i	$0.275949\pi$
$14$	−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	−0.298951	−	0.954268i	$-0.596637\pi$
$19$	2.19606	−	6.75877i	0.503810	−	1.55057i	0.802762	−	0.596300i	$-0.203363\pi$
$20$	−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	0.769799	−	0.638287i	$-0.220356\pi$
$23$	1.92137	+	1.39596i	0.400633	+	0.291077i	−0.369166	+	0.929364i	$0.620356\pi$
$24$	−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	0.975314	−	0.220822i	$-0.0708741\pi$
$29$	0.304113	+	0.935963i	0.0564723	+	0.173804i	−0.918842	+	0.394626i	$0.870874\pi$
$30$	−1.60829	+	0.703857i	−0.293633	+	0.128506i
$31$	−0.561979	+	1.72959i	−0.100934	+	0.310644i	−0.988755	−	0.149546i	$-0.952219\pi$
$31$	−0.561979	+	1.72959i	−0.100934	+	0.310644i	0.887820	+	0.460190i	$0.152219\pi$
$32$	−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	−0.854455	−	0.519525i	$-0.826109\pi$
$37$	−3.79807	+	2.75946i	−0.624399	+	0.453653i	0.230056	+	0.973177i	$0.426109\pi$
$38$	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	−0.845989	−	0.533200i	$-0.820989\pi$
$41$	−3.84387	+	2.79274i	−0.600312	+	0.436152i	0.245678	+	0.969352i	$0.420989\pi$
$42$	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	−0.906555	−	0.422089i	$-0.861297\pi$
$47$	−2.88783	−	8.88784i	−0.421234	−	1.29643i	0.485321	−	0.874336i	$-0.338703\pi$
$48$	−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	0.999382	−	0.0351438i	$-0.0111889\pi$
$53$	1.23913	+	3.81366i	0.170208	+	0.523846i	−0.829174	+	0.558990i	$0.811189\pi$
$54$	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	−0.361563	−	0.932348i	$-0.617757\pi$
$59$	3.17556	−	2.30718i	0.413423	−	0.300370i	0.774986	+	0.631978i	$0.217757\pi$
$60$	−2.95099	−	0.646863i	−0.380971	−	0.0835096i
$61$	11.4705	+	8.33382i	1.46865	+	1.06704i	0.981002	+	0.193995i	$0.0621446\pi$
$61$	11.4705	+	8.33382i	1.46865	+	1.06704i	0.487647	+	0.873041i	$0.337855\pi$
$62$	−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	−0.857790	−	0.514000i	$-0.828163\pi$
$67$	1.13202	−	3.48399i	0.138298	−	0.425638i	0.996088	+	0.0883621i	$0.0281633\pi$
$68$	−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	−0.972241	−	0.233983i	$-0.924824\pi$
$71$	−2.72344	−	8.38190i	−0.323213	−	0.994748i	0.649027	−	0.760765i	$-0.275176\pi$
$72$	5.25625	+	16.1771i	0.619455	+	1.90649i
$73$	3.33963	+	2.42638i	0.390874	+	0.283987i	0.765814	−	0.643063i	$-0.222337\pi$
$73$	3.33963	+	2.42638i	0.390874	+	0.283987i	−0.374940	+	0.927049i	$0.622337\pi$
$74$	−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	0.828991	−	0.559262i	$-0.188915\pi$
$79$	−1.51457	−	4.66138i	−0.170403	−	0.524446i	−0.999394	+	0.0348162i	$0.988915\pi$
$80$	−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	0.768797	+	0.639493i	$0.220856\pi$
$83$	−2.08681	+	6.42254i	−0.229057	+	0.704966i	−0.997854	+	0.0654729i	$0.979144\pi$
$84$	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	−0.980485	−	0.196591i	$-0.937013\pi$
$89$	−13.8721	−	10.0787i	−1.47044	−	1.06834i	−0.489956	−	0.871747i	$-0.662987\pi$
$90$	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	−0.542513	−	0.840047i	$-0.682527\pi$
$97$	−5.88349	−	18.1075i	−0.597378	−	1.83854i	−0.0548647	−	0.998494i	$-0.517473\pi$
$98$	−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	0.922848	+	0.385165i	$0.125855\pi$
$103$	4.08638	+	12.5766i	0.402643	+	1.23921i	−0.520205	+	0.854041i	$0.674145\pi$
$104$	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	−0.809001	−	0.587808i	$-0.799991\pi$
$109$	−5.21971	+	3.79234i	−0.499957	+	0.363240i	0.309043	+	0.951048i	$0.399991\pi$
$110$	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	−0.864369	−	0.502858i	$-0.832282\pi$
$113$	−6.94391	+	5.04505i	−0.653228	+	0.474598i	0.211141	+	0.977456i	$0.432282\pi$
$114$	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	0.969283	−	0.245947i	$-0.0790990\pi$
$127$	11.6627	+	8.47346i	1.03490	+	0.751898i	0.0656152	+	0.997845i	$0.479099\pi$
$128$	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	−0.943442	−	0.331539i	$-0.892432\pi$
$131$	0.168160	−	0.517544i	0.0146922	−	0.0452181i	0.958134	+	0.286321i	$0.0924323\pi$
$132$	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	0.320480	−	0.947255i	$-0.396156\pi$
$137$	15.4550	−	11.2287i	1.32041	−	0.959332i	0.999927	−	0.0120770i	$-0.00384431\pi$
$138$	−1.50850	+	1.09599i	−0.128412	+	0.0932966i
$139$	−13.9947	−	10.1677i	−1.18701	−	0.862416i	−0.194069	−	0.980988i	$-0.562168\pi$
$139$	−13.9947	−	10.1677i	−1.18701	−	0.862416i	−0.992945	+	0.118572i	$0.962168\pi$
$140$	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	−0.989290	−	0.145962i	$-0.953372\pi$
$163$	−14.7611	+	10.7246i	−1.15618	+	0.840013i	−0.166889	+	0.985976i	$0.553372\pi$
$164$	−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	0.119498	+	0.992834i	$0.461871\pi$
$167$	−7.24650	+	22.3024i	−0.560751	+	1.72582i	−0.680250	+	0.732981i	$0.738129\pi$
$168$	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	0.283952	−	0.958838i	$-0.408354\pi$
$173$	−7.10537	−	5.16235i	−0.540211	−	0.392486i	−0.824163	+	0.566352i	$0.808354\pi$
$174$	−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	0.763653	+	0.645627i	$0.223404\pi$
$179$	7.02850	+	21.6315i	0.525335	+	1.61681i	−0.238318	+	0.971187i	$0.576596\pi$
$180$	2.75966	+	27.9632i	0.205693	+	2.08426i
$181$	3.34609	−	10.2982i	0.248713	−	0.765459i	−0.746291	−	0.665620i	$-0.768167\pi$
$181$	3.34609	−	10.2982i	0.248713	−	0.765459i	0.995004	−	0.0998391i	$-0.0318328\pi$
$182$	−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	−0.999999	−	0.00155022i	$-0.999507\pi$
$191$	−18.0706	+	13.1290i	−1.30754	+	0.949984i	−0.307542	+	0.951534i	$0.599507\pi$
$192$	−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	0.926269	−	0.376862i	$-0.122997\pi$
$197$	−0.626160	−	1.92712i	−0.0446121	−	0.137302i	−0.970882	+	0.239560i	$0.922997\pi$
$198$	−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	0.651892	−	0.758311i	$-0.273975\pi$
$211$	1.91946	+	1.39457i	0.132141	+	0.0960063i	−0.519751	+	0.854318i	$0.673975\pi$
$212$	−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	0.569534	−	0.821968i	$-0.307124\pi$
$223$	−0.540700	−	0.392841i	−0.0362079	−	0.0263066i	−0.605742	+	0.795661i	$0.707124\pi$
$224$	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	−0.228123	−	0.973632i	$-0.573259\pi$
$227$	−18.4504	−	13.4050i	−1.22460	−	0.889721i	−0.996473	+	0.0839114i	$0.973259\pi$
$228$	2.96700	+	9.13148i	0.196494	+	0.604747i
$229$	−2.83352	−	8.72066i	−0.187244	−	0.576278i	0.812736	−	0.582632i	$-0.197977\pi$
$229$	−2.83352	−	8.72066i	−0.187244	−	0.576278i	−0.999980	+	0.00635463i	$0.997977\pi$
$230$	−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	−0.999816	−	0.0191825i	$-0.993894\pi$
$233$	−2.74258	+	8.44081i	−0.179673	+	0.552976i	0.820143	+	0.572158i	$0.193894\pi$
$234$	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	0.662846	−	0.748756i	$-0.269349\pi$
$239$	2.40501	+	1.74734i	0.155567	+	0.113026i	−0.507279	+	0.861782i	$0.669349\pi$
$240$	−0.416978	−	4.22518i	−0.0269158	−	0.272734i
$241$	20.5417	−	14.9244i	1.32321	−	0.961366i	0.323320	−	0.946290i	$-0.395201\pi$
$241$	20.5417	−	14.9244i	1.32321	−	0.961366i	0.999886	−	0.0150758i	$-0.00479896\pi$
$242$	−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	−0.308104	−	0.951353i	$-0.599695\pi$
$263$	8.13258	−	5.90866i	0.501476	−	0.364344i	0.809581	+	0.587009i	$0.199695\pi$
$264$	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	−0.640298	−	0.768127i	$-0.721189\pi$
$269$	5.39941	−	16.6177i	0.329208	−	1.01320i	0.969505	−	0.245070i	$-0.0788110\pi$
$270$	−5.23810	+	8.94106i	−0.318781	+	0.544136i
$271$	−3.21697	−	9.90082i	−0.195417	−	0.601432i	−0.999971	−	0.00755294i	$-0.997596\pi$
$271$	−3.21697	−	9.90082i	−0.195417	−	0.601432i	0.804554	−	0.593879i	$-0.202404\pi$
$272$	−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	0.912942	−	0.408090i	$-0.133805\pi$
$277$	13.4302	+	9.75758i	0.806940	+	0.586276i	−0.106002	+	0.994366i	$0.533805\pi$
$278$	−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	0.287972	+	0.957639i	$0.407019\pi$
$281$	−8.51376	+	26.2027i	−0.507888	+	1.56312i	−0.795860	+	0.605480i	$0.792981\pi$
$282$	7.33708			0.436917
$283$	1.82492	−	5.61651i	0.108480	−	0.333867i	−0.882051	−	0.471153i	$-0.843838\pi$
$283$	1.82492	−	5.61651i	0.108480	−	0.333867i	0.990531	+	0.137286i	$0.0438379\pi$
$284$	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	0.699568	−	0.714566i	$-0.253376\pi$
$311$	4.16461	+	3.02577i	0.236153	+	0.171576i	−0.463414	+	0.886142i	$0.653376\pi$
$312$	−0.805348	+	0.585120i	−0.0455939	+	0.0331259i
$313$	11.1738	−	8.11828i	0.631583	−	0.458872i	−0.225365	−	0.974274i	$-0.572358\pi$
$313$	11.1738	−	8.11828i	0.631583	−	0.458872i	0.856948	+	0.515402i	$0.172358\pi$
$314$	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	0.280370	+	0.959892i	$0.409543\pi$
$317$	−9.09212	+	27.9827i	−0.510664	+	1.57166i	−0.791035	+	0.611771i	$0.790457\pi$
$318$	−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	0.350956	+	0.936392i	$0.385857\pi$
$331$	−8.79416	+	27.0656i	−0.483371	+	1.48766i	−0.834327	+	0.551270i	$0.814143\pi$
$332$	−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	0.231603	−	0.972810i	$-0.425603\pi$
$337$	22.5499	−	16.3834i	1.22837	−	0.892463i	0.996767	+	0.0803471i	$0.0256029\pi$
$338$	−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	0.916659	+	0.399670i	$0.130875\pi$
$347$	7.63721	+	23.5049i	0.409987	+	1.26181i	−0.506672	+	0.862139i	$0.669125\pi$
$348$	−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	0.851025	+	0.525125i	$0.175982\pi$
$353$	8.85290	+	27.2464i	0.471192	+	1.45018i	−0.379833	+	0.925055i	$0.624018\pi$
$354$	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	0.262428	−	0.964952i	$-0.415477\pi$
$359$	23.8972	−	17.3623i	1.26125	−	0.916349i	0.998818	+	0.0486027i	$0.0154768\pi$
$360$	−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	−0.899961	−	0.435971i	$-0.856405\pi$
$367$	1.61649	−	4.97504i	0.0843800	−	0.259695i	0.984341	+	0.176276i	$0.0564051\pi$
$368$	−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	0.830241	−	0.557404i	$-0.188203\pi$
$373$	10.7512	+	7.81122i	0.556677	+	0.404449i	−0.273564	+	0.961854i	$0.588203\pi$
$374$	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	−0.842546	−	0.538625i	$-0.818944\pi$
$379$	−9.29608	−	28.6104i	−0.477508	−	1.46962i	0.365038	−	0.930993i	$-0.381056\pi$
$380$	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	−0.993438	−	0.114371i	$-0.963515\pi$
$383$	−2.39746	+	7.37861i	−0.122504	+	0.377030i	0.870934	+	0.491400i	$0.163515\pi$
$384$	−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	0.0782551	−	0.996933i	$-0.475065\pi$
$389$	−16.6799	−	12.1186i	−0.845703	−	0.614439i	−0.923958	+	0.382494i	$0.875065\pi$
$390$	−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	−0.999314	−	0.0370428i	$-0.988206\pi$
$397$	−4.23653	−	13.0387i	−0.212625	−	0.654393i	0.786689	−	0.617350i	$-0.211794\pi$
$398$	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	−0.104831	−	0.994490i	$-0.533430\pi$
$409$	16.3527	−	11.8810i	0.808590	−	0.587475i	0.913422	+	0.407015i	$0.133430\pi$
$410$	−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	−0.986977	−	0.160862i	$-0.948572\pi$
$419$	−1.92297	+	5.91829i	−0.0939432	+	0.289127i	0.893034	+	0.449990i	$0.148572\pi$
$420$	5.32017	+	1.16619i	0.259598	+	0.0569043i
$421$	3.89329	+	11.9823i	0.189747	+	0.583982i	0.999998	−	0.00210163i	$-0.000668969\pi$
$421$	3.89329	+	11.9823i	0.189747	+	0.583982i	−0.810251	+	0.586084i	$0.800669\pi$
$422$	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	−0.448722	−	0.893671i	$-0.648121\pi$
$431$	9.12609	−	28.0872i	0.439588	−	1.35291i	0.888311	−	0.459243i	$-0.151879\pi$
$432$	−11.2075			−0.539221
$433$	−0.443244	+	1.36417i	−0.0213010	+	0.0655576i	−0.961142	−	0.276055i	$-0.910973\pi$
$433$	−0.443244	+	1.36417i	−0.0213010	+	0.0655576i	0.939841	+	0.341612i	$0.110973\pi$
$434$	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	0.857088	−	0.515170i	$-0.172271\pi$
$439$	13.2416	+	9.62058i	0.631987	+	0.459165i	−0.225101	+	0.974335i	$0.572271\pi$
$440$	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	0.934303	−	0.356481i	$-0.116024\pi$
$461$	18.9799	+	13.7897i	0.883984	+	0.642252i	−0.0503183	+	0.998733i	$0.516024\pi$
$462$	−5.90144	+	4.28765i	−0.274560	+	0.199480i
$463$	15.5261	−	11.2804i	0.721561	−	0.524245i	−0.165321	−	0.986240i	$-0.552866\pi$
$463$	15.5261	−	11.2804i	0.721561	−	0.524245i	0.886883	+	0.461995i	$0.152866\pi$
$464$	−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	−0.477528	−	0.878616i	$-0.658467\pi$
$467$	9.18947	−	28.2823i	0.425238	−	1.30875i	0.902766	−	0.430132i	$-0.141533\pi$
$468$	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	−0.997737	−	0.0672305i	$-0.978584\pi$
$479$	−5.03528	−	15.4970i	−0.230068	−	0.708077i	0.767669	−	0.640846i	$-0.221416\pi$
$480$	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	−0.357411	−	0.933947i	$-0.616341\pi$
$487$	9.27696	−	6.74010i	0.420379	−	0.305423i	0.777790	+	0.628524i	$0.216341\pi$
$488$	−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	−0.113241	−	0.993568i	$-0.536123\pi$
$491$	17.6538	−	12.8262i	0.796705	−	0.578840i	0.909946	+	0.414728i	$0.136123\pi$
$492$	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	0.825312	+	0.564677i	$0.190999\pi$
$503$	10.9790	+	33.7899i	0.489529	+	1.50662i	−0.335783	+	0.941939i	$0.609001\pi$
$504$	−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	−0.771378	−	0.636377i	$-0.780432\pi$
$509$	−9.12632	+	6.63066i	−0.404517	+	0.293899i	0.366861	+	0.930276i	$0.380432\pi$
$510$	−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	0.932087	−	0.362236i	$-0.117986\pi$
$521$	−0.796699	−	2.45199i	−0.0349040	−	0.107423i	−0.966991	+	0.254812i	$0.917986\pi$
$522$	2.22076	+	6.83479i	0.0972000	+	0.299151i
$523$	−15.1172	−	10.9833i	−0.661027	−	0.480265i	0.205982	−	0.978556i	$-0.433961\pi$
$523$	−15.1172	−	10.9833i	−0.661027	−	0.480265i	−0.867010	+	0.498291i	$0.833961\pi$
$524$	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	0.236999	−	0.971510i	$-0.423836\pi$
$541$	28.7067	−	20.8566i	1.23420	−	0.896696i	0.997198	+	0.0748136i	$0.0238362\pi$
$542$	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	0.999487	−	0.0320279i	$-0.0101966\pi$
$547$	4.02413	+	12.3850i	0.172059	+	0.529545i	−0.827427	+	0.561573i	$0.810197\pi$
$548$	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	−0.953212	−	0.302302i	$-0.902245\pi$
$563$	−22.7848	+	16.5541i	−0.960265	+	0.697673i	−0.00705255	+	0.999975i	$0.502245\pi$
$564$	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	0.508225	+	0.861224i	$0.330302\pi$
$569$	−9.75981	+	30.0376i	−0.409153	+	1.25924i	−0.917378	+	0.398018i	$0.869698\pi$
$570$	1.22530	+	12.4158i	0.0513222	+	0.520041i
$571$	4.96779	+	15.2893i	0.207896	+	0.639837i	0.999582	+	0.0289095i	$0.00920345\pi$
$571$	4.96779	+	15.2893i	0.207896	+	0.639837i	−0.791686	+	0.610928i	$0.790797\pi$
$572$	−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	0.629298	−	0.777164i	$-0.283342\pi$
$577$	2.03301	+	1.47707i	0.0846354	+	0.0614912i	−0.544663	+	0.838655i	$0.683342\pi$
$578$	−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	−0.551722	+	0.834028i	$0.686029\pi$
$587$	−36.7158	+	26.6756i	−1.51542	+	1.10102i	−0.963699	+	0.266990i	$0.913971\pi$
$588$	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	−0.547265	−	0.836960i	$-0.684331\pi$
$613$	1.97123	−	1.43218i	0.0796173	−	0.0578454i	0.626882	+	0.779114i	$0.284331\pi$
$614$	−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	−0.991804	−	0.127770i	$-0.959218\pi$
$617$	−2.83955	+	8.73924i	−0.114316	+	0.351829i	0.877488	+	0.479599i	$0.159218\pi$
$618$	−10.3822			−0.417633
$619$	−0.334959	+	1.03090i	−0.0134631	+	0.0414353i	−0.957562	−	0.288226i	$-0.906935\pi$
$619$	−0.334959	+	1.03090i	−0.0134631	+	0.0414353i	0.944099	+	0.329661i	$0.106935\pi$
$620$	−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	−0.822699	−	0.568477i	$-0.807533\pi$
$631$	4.44672	−	13.6856i	0.177021	−	0.544815i	0.999720	+	0.0236624i	$0.00753268\pi$
$632$	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	−0.842222	−	0.539130i	$-0.818753\pi$
$641$	−14.9310	+	10.8480i	−0.589740	+	0.428471i	0.252482	+	0.967601i	$0.418753\pi$
$642$	−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	−0.976163	−	0.217039i	$-0.930360\pi$
$647$	−7.98704	−	24.5816i	−0.314003	−	0.966402i	0.662160	−	0.749363i	$-0.269640\pi$
$648$	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	−0.994818	−	0.101671i	$-0.967581\pi$
$653$	−6.38219	−	19.6424i	−0.249754	−	0.768665i	0.745064	−	0.666993i	$-0.232419\pi$
$654$	−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	−0.628737	−	0.777618i	$-0.716428\pi$
$659$	−2.14272	+	1.55678i	−0.0834686	+	0.0606435i	0.545268	+	0.838262i	$0.316428\pi$
$660$	10.3442	+	11.6361i	0.402647	+	0.452936i
$661$	−0.835766	−	0.607220i	−0.0325075	−	0.0236181i	0.571413	−	0.820663i	$-0.306396\pi$
$661$	−0.835766	−	0.607220i	−0.0325075	−	0.0236181i	−0.603920	+	0.797045i	$0.706396\pi$
$662$	−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	0.708639	−	0.705571i	$-0.249310\pi$
$673$	6.65631	+	4.83609i	0.256582	+	0.186418i	−0.452057	+	0.891989i	$0.649310\pi$
$674$	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	0.567876	−	0.823114i	$-0.307765\pi$
$677$	−1.02693	−	0.746106i	−0.0394680	−	0.0286752i	−0.607344	+	0.794439i	$0.707765\pi$
$678$	−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	0.763944	+	0.645282i	$0.223260\pi$
$683$	−6.09940	+	18.7720i	−0.233387	+	0.718291i	−0.997331	+	0.0730091i	$0.976740\pi$
$684$	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	−0.125016	−	0.992155i	$-0.539898\pi$
$691$	20.5024	−	14.8959i	0.779947	−	0.566665i	0.904963	+	0.425490i	$0.139898\pi$
$692$	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	−0.327779	−	0.944754i	$-0.606300\pi$
$709$	12.5000	−	9.08176i	0.469446	−	0.341073i	0.797225	+	0.603682i	$0.206300\pi$
$710$	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	0.522008	+	0.852940i	$0.325183\pi$
$719$	−10.7699	+	33.1465i	−0.401651	+	1.23615i	−0.923659	+	0.383215i	$0.874817\pi$
$720$	−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	0.743274	−	0.668987i	$-0.233272\pi$
$727$	9.07878	+	6.59612i	0.336713	+	0.244637i	−0.406560	+	0.913624i	$0.633272\pi$
$728$	−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	−0.843684	−	0.536840i	$-0.819618\pi$
$733$	4.18069	−	12.8669i	0.154417	−	0.475248i	0.998101	+	0.0615921i	$0.0196178\pi$
$734$	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	0.868411	−	0.495845i	$-0.165142\pi$
$739$	18.0828	+	13.1380i	0.665188	+	0.483287i	−0.203223	+	0.979132i	$0.565142\pi$
$740$	−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	0.896605	−	0.442831i	$-0.146026\pi$
$761$	20.7590	+	15.0823i	0.752514	+	0.546733i	−0.144091	+	0.989564i	$0.546026\pi$
$762$	−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	−0.953659	−	0.300890i	$-0.902716\pi$
$769$	−0.146243	+	0.450091i	−0.00527367	+	0.0162307i	0.948385	+	0.317121i	$0.102716\pi$
$770$	−26.4206	+	45.0980i	−0.952131	+	1.62522i
$771$	0.961071	+	2.95787i	0.0346121	+	0.106525i
$772$	14.0872	+	43.3559i	0.507008	+	1.56041i
$773$	−18.7298	−	13.6080i	−0.673663	−	0.489444i	0.197587	−	0.980285i	$-0.436690\pi$
$773$	−18.7298	−	13.6080i	−0.673663	−	0.489444i	−0.871249	+	0.490841i	$0.836690\pi$
$774$	−1.88246			−0.0676637
$775$	−8.25925	−	3.80365i	−0.296681	−	0.136631i
$776$	111.573			4.00522
$777$	2.13686	+	1.55252i	0.0766595	+	0.0556964i
$778$	−16.0286	−	49.3309i	−0.574653	−	1.76860i
$779$	10.4341	+	32.1128i	0.373840	+	1.15056i
$780$	−1.50651	+	0.659312i	−0.0539417	+	0.0236072i
$781$	−14.0355	+	43.1968i	−0.502229	+	1.54570i
$782$	−5.97491			−0.213662
$783$	−0.560188	+	1.72408i	−0.0200195	+	0.0616136i
$784$	18.4574	−	13.4101i	0.659192	−	0.478931i
$785$	1.21264	+	1.36410i	0.0432811	+	0.0486867i
$786$	0.345646	+	0.251127i	0.0123288	+	0.00895740i
$787$	−25.3265	+	18.4008i	−0.902792	+	0.655916i	−0.939182	−	0.343421i	$-0.888414\pi$
$787$	−25.3265	+	18.4008i	−0.902792	+	0.655916i	0.0363899	+	0.999338i	$0.488414\pi$
$788$	7.09707	−	5.15633i	0.252823	−	0.183686i
$789$	2.53795	+	1.84393i	0.0903534	+	0.0656456i
$790$	25.2591	−	11.0545i	0.898679	−	0.393300i
$791$	12.5188	−	9.09543i	0.445117	−	0.323396i
$792$	27.0885	−	83.3699i	0.962549	−	2.96242i
$793$	7.71776			0.274066
$794$	10.6583	−	32.8029i	0.378249	−	1.16413i
$795$	−2.73328	−	0.599141i	−0.0969396	−	0.0212494i
$796$	7.07207	+	21.7656i	0.250663	+	0.771461i
$797$	−2.01719	−	6.20828i	−0.0714526	−	0.219908i	0.908953	−	0.416899i	$-0.136883\pi$
$797$	−2.01719	−	6.20828i	−0.0714526	−	0.219908i	−0.980405	+	0.196991i	$0.936883\pi$
$798$	−8.13786	−	5.91250i	−0.288077	−	0.209300i
$799$	9.34523			0.330610
$800$	2.10091	−	17.8101i	0.0742782	−	0.629683i
$801$	−49.7707			−1.75856
$802$	44.3669	+	32.2344i	1.56665	+	1.13824i
$803$	−6.57404	−	20.2328i	−0.231993	−	0.714001i
$804$	1.52942	+	4.70707i	0.0539385	+	0.166006i
$805$	−0.940285	−	9.52778i	−0.0331407	−	0.335810i
$806$	−0.769599	+	2.36858i	−0.0271080	+	0.0834298i
$807$	5.45279			0.191947
$808$	29.3622	−	90.3675i	1.03296	−	3.17912i
$809$	8.05101	−	5.84940i	0.283058	−	0.205654i	−0.437192	−	0.899368i	$-0.644027\pi$
$809$	8.05101	−	5.84940i	0.283058	−	0.205654i	0.720250	+	0.693714i	$0.244027\pi$
$810$	44.6912	+	9.79640i	1.57029	+	0.344210i
$811$	−12.9920	−	9.43921i	−0.456209	−	0.331455i	0.335833	−	0.941921i	$-0.390982\pi$
$811$	−12.9920	−	9.43921i	−0.456209	−	0.331455i	−0.792042	+	0.610466i	$0.790982\pi$
$812$	6.21421	−	4.51489i	0.218076	−	0.158442i
$813$	2.62832	−	1.90958i	0.0921791	−	0.0669720i
$814$	49.2437	+	35.7777i	1.72599	+	1.25401i
$815$	−39.8525	−	8.73574i	−1.39597	−	0.306000i
$816$	1.53611	−	1.11605i	0.0537746	−	0.0390695i
$817$	−0.566113	+	1.74232i	−0.0198058	+	0.0609560i
$818$	50.8523			1.77801
$819$	−0.880228	+	2.70906i	−0.0307577	+	0.0946623i
$820$	−4.51729	−	45.7730i	−0.157751	−	1.59846i
$821$	10.6928	+	32.9092i	0.373183	+	1.14854i	0.944697	+	0.327945i	$0.106356\pi$
$821$	10.6928	+	32.9092i	0.373183	+	1.14854i	−0.571514	+	0.820592i	$0.693644\pi$
$822$	4.63475	+	14.2643i	0.161655	+	0.497524i
$823$	38.8704	+	28.2410i	1.35494	+	0.984419i	0.998749	+	0.0500040i	$0.0159234\pi$
$823$	38.8704	+	28.2410i	1.35494	+	0.984419i	0.356187	+	0.934415i	$0.384077\pi$
$824$	−77.4927			−2.69959
$825$	7.30411	+	3.36378i	0.254296	+	0.117112i
$826$	−17.8033			−0.619454
$827$	−14.0935	−	10.2395i	−0.490078	−	0.356063i	0.315136	−	0.949046i	$-0.397950\pi$
$827$	−14.0935	−	10.2395i	−0.490078	−	0.356063i	−0.805214	+	0.592984i	$0.797950\pi$
$828$	9.22238	+	28.3836i	0.320500	+	0.986397i
$829$	−11.7529	−	36.1716i	−0.408194	−	1.25629i	−0.918199	−	0.396119i	$-0.870357\pi$
$829$	−11.7529	−	36.1716i	−0.408194	−	1.25629i	0.510006	−	0.860171i	$-0.329643\pi$
$830$	−37.1085	−	8.13425i	−1.28805	−	0.282344i
$831$	−1.60089	+	4.92703i	−0.0555342	+	0.170917i
$832$	1.71196			0.0593517
$833$	1.15874	−	3.56623i	0.0401479	−	0.123563i
$834$	10.9874	−	7.98284i	0.380464	−	0.276423i
$835$	−48.0373	+	21.0231i	−1.66240	+	0.727536i
$836$	−128.276	−	93.1983i	−4.43653	−	3.22333i
$837$	−2.71016	+	1.96905i	−0.0936768	+	0.0680602i
$838$	−12.6656	+	9.20210i	−0.437526	+	0.317881i
$839$	−28.3582	−	20.6035i	−0.979035	−	0.711310i	−0.0215421	−	0.999768i	$-0.506858\pi$
$839$	−28.3582	−	20.6035i	−0.979035	−	0.711310i	−0.957493	+	0.288458i	$0.906858\pi$
$840$	4.89814	+	5.50990i	0.169002	+	0.190110i
$841$	22.6780	−	16.4765i	0.781998	−	0.568155i
$842$	−9.79478	+	30.1452i	−0.337550	+	1.03887i
$843$	−8.59793			−0.296129
$844$	−3.17412	+	9.76893i	−0.109258	+	0.336260i
$845$	−26.0233	+	11.3889i	−0.895229	+	0.391790i
$846$	−21.0882	−	64.9028i	−0.725027	−	2.23140i
$847$	−8.66831	−	26.6783i	−0.297847	−	0.916678i
$848$	−19.7380	−	14.3405i	−0.677805	−	0.492454i
$849$	1.84296			0.0632502
$850$	−6.15069	−	10.9728i	−0.210967	−	0.376363i
$851$	−11.1496			−0.382203
$852$	9.63312	+	6.99887i	0.330025	+	0.239777i
$853$	−13.5759	−	41.7824i	−0.464831	−	1.43060i	−0.859195	−	0.511648i	$-0.829035\pi$
$853$	−13.5759	−	41.7824i	−0.464831	−	1.43060i	0.394365	−	0.918954i	$-0.370965\pi$
$854$	−19.8721	−	61.1600i	−0.680009	−	2.09285i
$855$	23.3156	−	39.7981i	0.797377	−	1.36107i
$856$	−9.17271	+	28.2307i	−0.313517	+	0.964906i
$857$	38.8380			1.32668			0.663341	−	0.748317i	$-0.269138\pi$
$857$	38.8380			1.32668			0.663341	+	0.748317i	$0.269138\pi$
$858$	0.680599	−	2.09467i	0.0232353	−	0.0715108i
$859$	3.44687	−	2.50430i	0.117606	−	0.0854456i	−0.527428	−	0.849600i	$-0.676843\pi$
$859$	3.44687	−	2.50430i	0.117606	−	0.0854456i	0.645033	+	0.764154i	$0.276843\pi$
$860$	1.26146	−	2.15323i	0.0430155	−	0.0734244i
$861$	2.16263	+	1.57124i	0.0737022	+	0.0535478i
$862$	60.1088	−	43.6716i	2.04731	−	1.48746i
$863$	−29.1237	+	21.1596i	−0.991382	+	0.720281i	−0.960223	−	0.279234i	$-0.909920\pi$
$863$	−29.1237	+	21.1596i	−0.991382	+	0.720281i	−0.0311584	+	0.999514i	$0.509920\pi$
$864$	−5.34508	−	3.88343i	−0.181843	−	0.132117i
$865$	−1.92876	−	19.5438i	−0.0655797	−	0.664510i
$866$	−2.91942	+	2.12108i	−0.0992059	+	0.0720773i
$867$	0.0964356	−	0.296798i	0.00327513	−	0.0100798i
$868$	14.1943			0.481786
$869$	−7.80548	+	24.0228i	−0.264783	+	0.814918i
$870$	−1.14789	−	1.29125i	−0.0389170	−	0.0437775i
$871$	−0.616197	−	1.89646i	−0.0208790	−	0.0642591i
$872$	−11.6836	−	35.9583i	−0.395656	−	1.21770i
$873$	−44.7094	−	32.4833i	−1.51319	−	1.09939i
$874$	42.4613			1.43627
$875$	16.5296	−	11.5349i	0.558802	−	0.389950i
$876$	−5.57717			−0.188435
$877$	−11.5455	−	8.38833i	−0.389865	−	0.283254i	0.375535	−	0.926808i	$-0.377459\pi$
$877$	−11.5455	−	8.38833i	−0.389865	−	0.283254i	−0.765400	+	0.643554i	$0.777459\pi$
$878$	12.7246	+	39.1622i	0.429434	+	1.32166i
$879$	1.35257	+	4.16277i	0.0456210	+	0.140407i
$880$	46.5836	+	52.4016i	1.57033	+	1.76646i
$881$	−10.9909	+	33.8267i	−0.370294	+	1.13965i	0.576304	+	0.817235i	$0.304494\pi$
$881$	−10.9909	+	33.8267i	−0.370294	+	1.13965i	−0.946599	+	0.322414i	$0.895506\pi$
$882$	−27.3823			−0.922010
$883$	11.6966	−	35.9983i	0.393621	−	1.21144i	−0.536410	−	0.843958i	$-0.680220\pi$
$883$	11.6966	−	35.9983i	0.393621	−	1.21144i	0.930030	−	0.367483i	$-0.119780\pi$
$884$	−1.90652	+	1.38517i	−0.0641233	+	0.0465883i
$885$	0.269009	+	2.72583i	0.00904264	+	0.0916278i
$886$	−40.7914	−	29.6367i	−1.37041	−	0.995665i
$887$	−16.2608	+	11.8142i	−0.545986	+	0.396682i	−0.826303	−	0.563226i	$-0.809560\pi$
$887$	−16.2608	+	11.8142i	−0.545986	+	0.396682i	0.280318	+	0.959907i	$0.409560\pi$
$888$	6.94582	−	5.04643i	0.233086	−	0.169347i
$889$	−21.0260	−	15.2763i	−0.705191	−	0.512351i
$890$	48.7596	−	83.2291i	1.63442	−	2.78985i
$891$	−33.9092	+	24.6364i	−1.13600	+	0.825352i
$892$	0.894127	−	2.75184i	0.0299376	−	0.0921385i
$893$	−66.4128			−2.22242
$894$	−3.02298	+	9.30377i	−0.101103	+	0.311165i
$895$	−25.7085	+	43.8826i	−0.859341	+	1.46683i
$896$	−8.40445	−	25.8662i	−0.280773	−	0.864130i
$897$	0.124669	+	0.383690i	0.00416256	+	0.0128110i
$898$	31.3317	+	22.7638i	1.04555	+	0.759639i
$899$	−1.78974			−0.0596912
$900$	−42.6320	+	46.1552i	−1.42107	+	1.53851i
$901$	−4.00992			−0.133590
$902$	49.8375	+	36.2091i	1.65941	+	1.20563i
$903$	0.0448183	+	0.137936i	0.00149146	+	0.00459024i
$904$	−15.5430	−	47.8363i	−0.516951	−	1.59101i
$905$	22.1813	−	9.70747i	0.737332	−	0.322687i
$906$	−0.883006	+	2.71761i	−0.0293359	+	0.0902867i
$907$	−14.0125			−0.465276			−0.232638	−	0.972563i	$-0.574736\pi$
$907$	−14.0125			−0.465276			−0.232638	+	0.972563i	$0.574736\pi$
$908$	30.5105	−	93.9016i	1.01253	−	3.11623i
$909$	−38.0757	+	27.6636i	−1.26289	+	0.917544i
$910$	−3.66789	−	4.12599i	−0.121589	−	0.136775i
$911$	−4.14577	−	3.01208i	−0.137356	−	0.0997946i	0.516986	−	0.855994i	$-0.327054\pi$
$911$	−4.14577	−	3.01208i	−0.137356	−	0.0997946i	−0.654341	+	0.756199i	$0.727054\pi$
$912$	−10.9165	+	7.93131i	−0.361482	+	0.262632i
$913$	28.1558	−	20.4564i	0.931821	−	0.677007i
$914$	67.1161	+	48.7627i	2.22000	+	1.61293i
$915$	−9.06385	+	3.96672i	−0.299642	+	0.131136i
$916$	32.1158	−	23.3335i	1.06114	−	0.770961i
$917$	−0.303167	+	0.933051i	−0.0100114	+	0.0308121i
$918$	−4.63423			−0.152952
$919$	12.2582	−	37.7270i	0.404362	−	1.24450i	−0.517065	−	0.855946i	$-0.672975\pi$
$919$	12.2582	−	37.7270i	0.404362	−	1.24450i	0.921427	−	0.388552i	$-0.127025\pi$
$920$	−30.3985	−	6.66341i	−1.00221	−	0.219686i
$921$	−0.0943351	−	0.290334i	−0.00310845	−	0.00956682i
$922$	18.2389	+	56.1335i	0.600665	+	1.84866i
$923$	−3.88114	−	2.81982i	−0.127749	−	0.0928154i
$924$	−12.5528			−0.412957
$925$	−11.4776	−	20.4759i	−0.377381	−	0.673245i
$926$	48.2819			1.58664
$927$	31.0529	+	22.5613i	1.01991	+	0.741009i
$928$	−1.09077	−	3.35704i	−0.0358062	−	0.110200i
$929$	11.6468	+	35.8453i	0.382120	+	1.17604i	0.938548	+	0.345149i	$0.112172\pi$
$929$	11.6468	+	35.8453i	0.382120	+	1.17604i	−0.556428	+	0.830896i	$0.687828\pi$
$930$	−0.313559	−	3.17725i	−0.0102820	−	0.104186i
$931$	−8.23468	+	25.3437i	−0.269881	+	0.830608i
$932$	−38.4234			−1.25860
$933$	−0.496426	+	1.52784i	−0.0162523	+	0.0500193i
$934$	60.5263	−	43.9749i	1.98048	−	1.43890i
$935$	11.2565	+	2.46745i	0.368127	+	0.0806942i
$936$	7.49061	+	5.44225i	0.244838	+	0.177885i
$937$	−2.22359	+	1.61553i	−0.0726416	+	0.0527772i	−0.623513	−	0.781813i	$-0.714295\pi$
$937$	−2.22359	+	1.61553i	−0.0726416	+	0.0527772i	0.550872	+	0.834590i	$0.314295\pi$
$938$	−13.4420	+	9.76620i	−0.438898	+	0.318878i
$939$	3.48705	+	2.53349i	0.113795	+	0.0826773i
$940$	88.3695	+	19.3708i	2.88230	+	0.631805i
$941$	14.9963	−	10.8954i	0.488865	−	0.355181i	−0.315883	−	0.948798i	$-0.602301\pi$
$941$	14.9963	−	10.8954i	0.488865	−	0.355181i	0.804748	+	0.593617i	$0.202301\pi$
$942$	−0.198032	+	0.609480i	−0.00645223	+	0.0198579i
$943$	−11.2840			−0.367459
$944$	−7.37998	+	22.7132i	−0.240198	+	0.739253i
$945$	−0.729299	−	7.38988i	−0.0237241	−	0.240393i
$946$	1.03283	+	3.17873i	0.0335802	+	0.103349i
$947$	−18.4146	−	56.6744i	−0.598395	−	1.84167i	−0.537043	−	0.843555i	$-0.680459\pi$
$947$	−18.4146	−	56.6744i	−0.598395	−	1.84167i	−0.0613517	−	0.998116i	$-0.519541\pi$
$948$	5.35721	+	3.89224i	0.173994	+	0.126414i
$949$	2.24702			0.0729413
$950$	43.7104	+	77.9790i	1.41815	+	2.52997i
$951$	−9.18201			−0.297747
$952$	8.54713	+	6.20986i	0.277014	+	0.201263i
$953$	−18.3565	−	56.4955i	−0.594625	−	1.83007i	−0.556582	−	0.830792i	$-0.687888\pi$
$953$	−18.3565	−	56.4955i	−0.594625	−	1.83007i	−0.0380429	−	0.999276i	$-0.512112\pi$
$954$	9.04867	+	27.8489i	0.292962	+	0.901643i
$955$	−48.7875	−	10.6943i	−1.57873	−	0.346060i
$956$	−3.97703	+	12.2401i	−0.128626	+	0.395872i
$957$	1.58277			0.0511636
$958$	12.6678	−	38.9876i	0.409279	−	1.25963i
$959$	−27.8629	+	20.2436i	−0.899740	+	0.653699i
$960$	−2.01056	+	0.879904i	−0.0648904	+	0.0283988i
$961$	22.4038	+	16.2773i	0.722705	+	0.525076i
$962$	−5.20125	+	3.77893i	−0.167695	+	0.121838i
$963$	11.8948	−	8.64208i	0.383305	−	0.278487i
$964$	88.9313	+	64.6123i	2.86428	+	2.08102i
$965$	15.6436	+	17.5974i	0.503585	+	0.566480i
$966$	2.71958	−	1.97589i	0.0875011	−	0.0635733i
$967$	−6.01205	+	18.5032i	−0.193334	+	0.595022i	0.806658	+	0.591019i	$0.201274\pi$
$967$	−6.01205	+	18.5032i	−0.193334	+	0.595022i	−0.999992	+	0.00400311i	$0.998726\pi$
$968$	−91.1798			−2.93063
$969$	−0.685329	+	2.10922i	−0.0220159	+	0.0677581i
$970$	98.1213	−	42.9420i	3.15049	−	1.37878i
$971$	−0.967020	−	2.97618i	−0.0310332	−	0.0955103i	0.934340	−	0.356382i	$-0.115990\pi$
$971$	−0.967020	−	2.97618i	−0.0310332	−	0.0955103i	−0.965373	+	0.260872i	$0.915990\pi$
$972$	10.7885	+	33.2037i	0.346042	+	1.06501i
$973$	25.2302	+	18.3308i	0.808844	+	0.587660i
$974$	28.8487			0.924371
$975$	−0.576302	+	0.623929i	−0.0184564	+	0.0199817i
$976$	−86.2651			−2.76128
$977$	−21.7239	−	15.7833i	−0.695009	−	0.504953i	0.183294	−	0.983058i	$-0.441324\pi$
$977$	−21.7239	−	15.7833i	−0.695009	−	0.504953i	−0.878303	+	0.478105i	$0.841324\pi$
$978$	−4.42667	−	13.6239i	−0.141549	−	0.435644i
$979$	27.3072	+	84.0429i	0.872742	+	2.68602i
$980$	18.3492	−	31.3208i	0.586145	−	1.00051i
$981$	−5.78708	+	17.8108i	−0.184767	+	0.568655i
$982$	54.8983			1.75187
$983$	−0.203260	+	0.625571i	−0.00648300	+	0.0199526i	−0.954246	−	0.299024i	$-0.903339\pi$
$983$	−0.203260	+	0.625571i	−0.00648300	+	0.0199526i	0.947763	+	0.318976i	$0.103339\pi$
$984$	7.02957	−	5.10728i	0.224094	−	0.162814i
$985$	2.29034	−	3.90945i	0.0729763	−	0.124565i
$986$	−2.00303	−	1.45529i	−0.0637895	−	0.0463458i
$987$	−4.25364	+	3.09045i	−0.135395	+	0.0983701i
$988$	13.5489	−	9.84384i	0.431047	−	0.313174i
$989$	−0.495302	−	0.359858i	−0.0157497	−	0.0114428i
$990$	−8.26465	−	83.7446i	−0.262668	−	2.66158i
$991$	20.9490	−	15.2203i	0.665467	−	0.483490i	−0.203038	−	0.979171i	$-0.565082\pi$
$991$	20.9490	−	15.2203i	0.665467	−	0.483490i	0.868505	+	0.495681i	$0.165082\pi$
$992$	2.01566	−	6.20357i	0.0639974	−	0.196964i
$993$	−8.88110			−0.281833
$994$	−12.3525	+	38.0170i	−0.391797	+	1.20583i
$995$	7.85343	+	8.83428i	0.248970	+	0.280066i
$996$	−2.81940	−	8.67722i	−0.0893361	−	0.274948i
$997$	−5.94355	−	18.2924i	−0.188234	−	0.579325i	0.811755	−	0.583998i	$-0.198512\pi$
$997$	−5.94355	−	18.2924i	−0.188234	−	0.579325i	−0.999989	+	0.00467313i	$0.998512\pi$
$998$	−43.8053	−	31.8264i	−1.38663	−	1.00745i
$999$	−8.64779			−0.273604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.c.341.18	yes	80
25.11	even	5	inner	425.2.k.c.86.18	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.c.86.18	✓	80	25.11	even	5	inner
425.2.k.c.341.18	yes	80	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
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

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