LMFDB - Embedded newform 890.2.o.a.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [890,2,Mod(91,890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(890, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("890.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 890 = 2 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	890.o (of order $11$, degree $10$, 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:	$7.10668577989$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.3
Character	$\chi$	$=$	890.271
Dual form			890.2.o.a.601.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841254 - 0.540641i) q^{2} +(0.249407 + 0.546126i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.505073 + 0.324591i) q^{6} +(-0.576031 - 4.00638i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(1.72853 - 1.99483i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.724517 + 5.03912i) q^{11} +0.600381 q^{12} +(-1.01250 - 2.21706i) q^{13} +(-2.65060 - 3.05896i) q^{14} +(0.505073 - 0.324591i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-6.33590 - 4.07183i) q^{17} +(0.375646 - 2.61268i) q^{18} +(-1.94414 + 2.24365i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(2.04432 - 1.31381i) q^{21} +(2.11485 + 4.63088i) q^{22} +(2.48507 - 2.86793i) q^{23} +(0.505073 - 0.324591i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-2.05040 - 1.31771i) q^{26} +(3.24872 + 0.953912i) q^{27} +(-3.88363 - 1.14034i) q^{28} +(-0.844171 - 5.87134i) q^{29} +(0.249407 - 0.546126i) q^{30} +(5.79879 + 6.69217i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-2.93270 + 0.861118i) q^{33} -7.53150 q^{34} +(-3.88363 + 1.14034i) q^{35} +(-1.09651 - 2.40101i) q^{36} +3.13112 q^{37} +(-0.422501 + 2.93856i) q^{38} +(0.958272 - 1.10590i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(-3.24125 + 7.09734i) q^{41} +(1.00950 - 2.21049i) q^{42} +(0.923100 - 6.42030i) q^{43} +(4.28277 + 2.75237i) q^{44} +(-2.22052 - 1.42704i) q^{45} +(0.540058 - 3.75619i) q^{46} +(2.23467 - 4.89324i) q^{47} +(0.249407 - 0.546126i) q^{48} +(-9.00284 + 2.64347i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(0.643515 - 4.47575i) q^{51} -2.43732 q^{52} +(-1.60613 - 3.51693i) q^{53} +(3.24872 - 0.953912i) q^{54} +5.09094 q^{55} +(-3.88363 + 1.14034i) q^{56} +(-1.71020 - 0.502160i) q^{57} +(-3.88445 - 4.48289i) q^{58} +(4.65825 - 10.2001i) q^{59} +(-0.0854432 - 0.594270i) q^{60} +(7.28591 + 2.13934i) q^{61} +(8.49631 + 2.49474i) q^{62} +(-8.98775 - 5.77608i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.05040 + 1.31771i) q^{65} +(-2.00159 + 2.30995i) q^{66} +(1.42794 + 3.12675i) q^{67} +(-6.33590 + 4.07183i) q^{68} +(2.18605 + 0.641881i) q^{69} +(-2.65060 + 3.05896i) q^{70} +(0.938588 - 6.52802i) q^{71} +(-2.22052 - 1.42704i) q^{72} +(9.74027 + 11.2409i) q^{73} +(2.63406 - 1.69281i) q^{74} +(-0.393166 - 0.453738i) q^{75} +(1.23328 + 2.70050i) q^{76} +20.6060 q^{77} +(0.208252 - 1.44843i) q^{78} +(0.354422 + 0.409025i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.837638 - 5.82590i) q^{81} +(1.11040 + 7.72301i) q^{82} +(9.04024 + 5.80981i) q^{83} +(-0.345838 - 2.40536i) q^{84} +(-3.12870 + 6.85089i) q^{85} +(-2.69452 - 5.90017i) q^{86} +(2.99595 - 1.92538i) q^{87} +5.09094 q^{88} +(5.02196 - 7.98624i) q^{89} -2.63954 q^{90} +(-8.29918 + 5.33356i) q^{91} +(-1.57642 - 3.45188i) q^{92} +(-2.20850 + 4.83595i) q^{93} +(-0.765563 - 5.32461i) q^{94} +(2.49750 + 1.60504i) q^{95} +(-0.0854432 - 0.594270i) q^{96} +(1.94575 + 13.5330i) q^{97} +(-6.14450 + 7.09113i) q^{98} +(8.79986 + 10.1556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} - 30 q^{13} + 6 q^{14} + 4 q^{15} - 6 q^{16} - 10 q^{17} + 6 q^{18} + 7 q^{19} - 6 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) $ 60 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 - 30 * q^13 + 6 * q^14 + 4 * q^15 - 6 * q^16 - 10 * q^17 + 6 * q^18 + 7 * q^19 - 6 * q^20 - 8 * q^21 + 16 * q^22 - 9 * q^23 + 4 * q^24 - 6 * q^25 + 3 * q^26 + 13 * q^27 - 16 * q^28 + q^29 + 4 * q^30 - 10 * q^31 - 6 * q^32 - 10 * q^33 - 54 * q^34 - 16 * q^35 - 16 * q^36 - 4 * q^37 - 26 * q^38 + 11 * q^39 - 6 * q^40 + 30 * q^41 - 19 * q^42 + 34 * q^43 - 6 * q^44 - 5 * q^45 + 13 * q^46 + 38 * q^47 + 4 * q^48 + 14 * q^49 - 6 * q^50 - 6 * q^51 + 14 * q^52 + 38 * q^53 + 13 * q^54 - 28 * q^55 - 16 * q^56 + 54 * q^57 - 10 * q^58 + 16 * q^59 - 7 * q^60 + 7 * q^61 + 34 * q^62 - 77 * q^63 - 6 * q^64 + 3 * q^65 + 12 * q^66 - 4 * q^67 - 10 * q^68 + 12 * q^69 + 6 * q^70 + 17 * q^71 - 5 * q^72 + 25 * q^73 + 18 * q^74 + 4 * q^75 - 15 * q^76 - 46 * q^77 + 11 * q^78 + 85 * q^79 - 6 * q^80 + 18 * q^81 - 14 * q^82 + 9 * q^83 + 3 * q^84 + 12 * q^85 + 12 * q^86 - 31 * q^87 - 28 * q^88 - 37 * q^89 + 28 * q^90 + 16 * q^91 + 2 * q^92 - 85 * q^93 + 16 * q^94 + 7 * q^95 - 7 * q^96 - 77 * q^97 + 14 * q^98 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/890\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.249407	+	0.546126i	0.143995	+	0.315306i	0.967864	−	0.251475i	$-0.0809157\pi$
$3$	0.249407	+	0.546126i	0.143995	+	0.315306i	−0.823868	+	0.566781i	$0.808188\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	0.505073	+	0.324591i	0.206195	+	0.132514i
$7$	−0.576031	−	4.00638i	−0.217719	−	1.51427i	−0.746428	−	0.665467i	$-0.768233\pi$
$7$	−0.576031	−	4.00638i	−0.217719	−	1.51427i	0.528708	−	0.848804i	$-0.322677\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	1.72853	−	1.99483i	0.576177	−	0.664944i
$10$	−0.654861	−	0.755750i	−0.207085	−	0.238989i
$11$	−0.724517	+	5.03912i	−0.218450	+	1.51935i	0.525313	+	0.850909i	$0.323948\pi$
$11$	−0.724517	+	5.03912i	−0.218450	+	1.51935i	−0.743763	+	0.668444i	$0.766961\pi$
$12$	0.600381			0.173315
$13$	−1.01250	−	2.21706i	−0.280817	−	0.614903i	0.715690	−	0.698418i	$-0.246112\pi$
$13$	−1.01250	−	2.21706i	−0.280817	−	0.614903i	−0.996506	+	0.0835154i	$0.973385\pi$
$14$	−2.65060	−	3.05896i	−0.708403	−	0.817541i
$15$	0.505073	−	0.324591i	0.130409	−	0.0838090i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−6.33590	−	4.07183i	−1.53668	−	0.987565i	−0.988503	−	0.151203i	$-0.951685\pi$
$17$	−6.33590	−	4.07183i	−1.53668	−	0.987565i	−0.548178	−	0.836362i	$-0.684678\pi$
$18$	0.375646	−	2.61268i	0.0885406	−	0.615813i
$19$	−1.94414	+	2.24365i	−0.446016	+	0.514729i	−0.933586	−	0.358354i	$-0.883338\pi$
$19$	−1.94414	+	2.24365i	−0.446016	+	0.514729i	0.487570	+	0.873084i	$0.337883\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	2.04432	−	1.31381i	0.446108	−	0.286696i
$22$	2.11485	+	4.63088i	0.450888	+	0.987308i
$23$	2.48507	−	2.86793i	0.518174	−	0.598004i	−0.434999	−	0.900431i	$-0.643251\pi$
$23$	2.48507	−	2.86793i	0.518174	−	0.598004i	0.953173	+	0.302427i	$0.0977968\pi$
$24$	0.505073	−	0.324591i	0.103098	−	0.0662568i
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−2.05040	−	1.31771i	−0.402117	−	0.258425i
$27$	3.24872	+	0.953912i	0.625217	+	0.183580i
$28$	−3.88363	−	1.14034i	−0.733936	−	0.215503i
$29$	−0.844171	−	5.87134i	−0.156759	−	1.09028i	−0.904556	−	0.426354i	$-0.859798\pi$
$29$	−0.844171	−	5.87134i	−0.156759	−	1.09028i	0.747798	−	0.663927i	$-0.231111\pi$
$30$	0.249407	−	0.546126i	0.0455354	−	0.0997085i
$31$	5.79879	+	6.69217i	1.04149	+	1.20195i	0.978991	+	0.203904i	$0.0653630\pi$
$31$	5.79879	+	6.69217i	1.04149	+	1.20195i	0.0625034	+	0.998045i	$0.480092\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−2.93270	+	0.861118i	−0.510517	+	0.149901i
$34$	−7.53150			−1.29164
$35$	−3.88363	+	1.14034i	−0.656452	+	0.192752i
$36$	−1.09651	−	2.40101i	−0.182751	−	0.400169i
$37$	3.13112			0.514753			0.257376	−	0.966311i	$-0.417142\pi$
$37$	3.13112			0.514753			0.257376	+	0.966311i	$0.417142\pi$
$38$	−0.422501	+	2.93856i	−0.0685388	+	0.476698i
$39$	0.958272	−	1.10590i	0.153446	−	0.177086i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	−3.24125	+	7.09734i	−0.506198	+	1.10842i	0.468207	+	0.883619i	$0.344900\pi$
$41$	−3.24125	+	7.09734i	−0.506198	+	1.10842i	−0.974405	+	0.224800i	$0.927827\pi$
$42$	1.00950	−	2.21049i	0.155769	−	0.341086i
$43$	0.923100	−	6.42030i	0.140771	−	0.979087i	−0.789901	−	0.613234i	$-0.789868\pi$
$43$	0.923100	−	6.42030i	0.140771	−	0.979087i	0.930673	−	0.365853i	$-0.119223\pi$
$44$	4.28277	+	2.75237i	0.645652	+	0.414936i
$45$	−2.22052	−	1.42704i	−0.331016	−	0.212731i
$46$	0.540058	−	3.75619i	0.0796272	−	0.553819i
$47$	2.23467	−	4.89324i	0.325960	−	0.713752i	−0.673722	−	0.738985i	$-0.735305\pi$
$47$	2.23467	−	4.89324i	0.325960	−	0.713752i	0.999682	+	0.0252326i	$0.00803264\pi$
$48$	0.249407	−	0.546126i	0.0359989	−	0.0788265i
$49$	−9.00284	+	2.64347i	−1.28612	+	0.377639i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	0.643515	−	4.47575i	0.0901101	−	0.626730i
$52$	−2.43732			−0.337995
$53$	−1.60613	−	3.51693i	−0.220619	−	0.483087i	0.766667	−	0.642045i	$-0.221914\pi$
$53$	−1.60613	−	3.51693i	−0.220619	−	0.483087i	−0.987285	+	0.158958i	$0.949187\pi$
$54$	3.24872	−	0.953912i	0.442095	−	0.129811i
$55$	5.09094			0.686462
$56$	−3.88363	+	1.14034i	−0.518971	+	0.152384i
$57$	−1.71020	−	0.502160i	−0.226522	−	0.0665127i
$58$	−3.88445	−	4.48289i	−0.510053	−	0.588633i
$59$	4.65825	−	10.2001i	0.606452	−	1.32795i	−0.318522	−	0.947915i	$-0.603186\pi$
$59$	4.65825	−	10.2001i	0.606452	−	1.32795i	0.924974	−	0.380030i	$-0.124086\pi$
$60$	−0.0854432	−	0.594270i	−0.0110307	−	0.0767200i
$61$	7.28591	+	2.13934i	0.932866	+	0.273914i	0.712636	−	0.701534i	$-0.247501\pi$
$61$	7.28591	+	2.13934i	0.932866	+	0.273914i	0.220230	+	0.975448i	$0.429319\pi$
$62$	8.49631	+	2.49474i	1.07903	+	0.316833i
$63$	−8.98775	−	5.77608i	−1.13235	−	0.727717i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−2.05040	+	1.31771i	−0.254321	+	0.163442i
$66$	−2.00159	+	2.30995i	−0.246378	+	0.284336i
$67$	1.42794	+	3.12675i	0.174451	+	0.381993i	0.976579	−	0.215158i	$-0.0690265\pi$
$67$	1.42794	+	3.12675i	0.174451	+	0.381993i	−0.802129	+	0.597151i	$0.796299\pi$
$68$	−6.33590	+	4.07183i	−0.768340	+	0.493782i
$69$	2.18605	+	0.641881i	0.263169	+	0.0772734i
$70$	−2.65060	+	3.05896i	−0.316807	+	0.365615i
$71$	0.938588	−	6.52802i	0.111390	−	0.774734i	−0.855180	−	0.518331i	$-0.826554\pi$
$71$	0.938588	−	6.52802i	0.111390	−	0.774734i	0.966570	−	0.256403i	$-0.0825374\pi$
$72$	−2.22052	−	1.42704i	−0.261691	−	0.168179i
$73$	9.74027	+	11.2409i	1.14001	+	1.31565i	0.942064	+	0.335433i	$0.108883\pi$
$73$	9.74027	+	11.2409i	1.14001	+	1.31565i	0.197949	+	0.980212i	$0.436572\pi$
$74$	2.63406	−	1.69281i	0.306204	−	0.196785i
$75$	−0.393166	−	0.453738i	−0.0453989	−	0.0523932i
$76$	1.23328	+	2.70050i	0.141466	+	0.309768i
$77$	20.6060			2.34827
$78$	0.208252	−	1.44843i	0.0235799	−	0.164002i
$79$	0.354422	+	0.409025i	0.0398756	+	0.0460189i	0.775337	−	0.631548i	$-0.217580\pi$
$79$	0.354422	+	0.409025i	0.0398756	+	0.0460189i	−0.735461	+	0.677567i	$0.763035\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	−0.837638	−	5.82590i	−0.0930709	−	0.647322i
$82$	1.11040	+	7.72301i	0.122623	+	0.852864i
$83$	9.04024	+	5.80981i	0.992295	+	0.637709i	0.932753	−	0.360516i	$-0.117400\pi$
$83$	9.04024	+	5.80981i	0.992295	+	0.637709i	0.0595422	+	0.998226i	$0.481036\pi$
$84$	−0.345838	−	2.40536i	−0.0377340	−	0.262446i
$85$	−3.12870	+	6.85089i	−0.339355	+	0.743083i
$86$	−2.69452	−	5.90017i	−0.290557	−	0.636231i
$87$	2.99595	−	1.92538i	0.321200	−	0.206422i
$88$	5.09094			0.542696
$89$	5.02196	−	7.98624i	0.532326	−	0.846539i
$89$	5.02196	−	7.98624i	0.532326	−	0.846539i
$90$	−2.63954			−0.278232
$91$	−8.29918	+	5.33356i	−0.869990	+	0.559109i
$92$	−1.57642	−	3.45188i	−0.164353	−	0.359884i
$93$	−2.20850	+	4.83595i	−0.229011	+	0.501465i
$94$	−0.765563	−	5.32461i	−0.0789618	−	0.549191i
$95$	2.49750	+	1.60504i	0.256238	+	0.164674i
$96$	−0.0854432	−	0.594270i	−0.00872051	−	0.0606525i
$97$	1.94575	+	13.5330i	0.197561	+	1.37406i	0.811334	+	0.584582i	$0.198742\pi$
$97$	1.94575	+	13.5330i	0.197561	+	1.37406i	−0.613774	+	0.789482i	$0.710349\pi$
$98$	−6.14450	+	7.09113i	−0.620688	+	0.716312i
$99$	8.79986	+	10.1556i	0.884419	+	1.02067i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	−4.78596			−0.476221			−0.238111	−	0.971238i	$-0.576528\pi$
$101$	−4.78596			−0.476221			−0.238111	+	0.971238i	$0.576528\pi$
$102$	−1.87841	−	4.11315i	−0.185990	−	0.407262i
$103$	−0.152513	−	0.176010i	−0.0150276	−	0.0173428i	0.748186	−	0.663489i	$-0.230925\pi$
$103$	−0.152513	−	0.176010i	−0.0150276	−	0.0173428i	−0.763214	+	0.646146i	$0.776380\pi$
$104$	−2.05040	+	1.31771i	−0.201059	+	0.129213i
$105$	−1.59137	−	1.83654i	−0.155302	−	0.179228i
$106$	−3.25256	−	2.09029i	−0.315916	−	0.203027i
$107$	2.39118	−	16.6310i	0.231164	−	1.60778i	−0.461920	−	0.886921i	$-0.652839\pi$
$107$	2.39118	−	16.6310i	0.231164	−	1.60778i	0.693084	−	0.720857i	$-0.256252\pi$
$108$	2.21728	−	2.55887i	0.213358	−	0.246228i
$109$	3.75680	+	1.10310i	0.359836	+	0.105657i	0.456653	−	0.889645i	$-0.349048\pi$
$109$	3.75680	+	1.10310i	0.359836	+	0.105657i	−0.0968170	+	0.995302i	$0.530866\pi$
$110$	4.28277	−	2.75237i	0.408346	−	0.262428i
$111$	0.780924	+	1.70999i	0.0741220	+	0.162305i
$112$	−2.65060	+	3.05896i	−0.250458	+	0.289044i
$113$	−12.2927	+	7.90005i	−1.15640	+	0.743175i	−0.970904	−	0.239470i	$-0.923026\pi$
$113$	−12.2927	+	7.90005i	−1.15640	+	0.743175i	−0.185498	+	0.982645i	$0.559390\pi$
$114$	−1.71020	+	0.502160i	−0.160175	+	0.0470316i
$115$	−3.19240	−	2.05163i	−0.297693	−	0.191315i
$116$	−5.69144	−	1.67116i	−0.528437	−	0.155163i
$117$	−6.17281	−	1.81250i	−0.570676	−	0.167566i
$118$	−1.59584	−	11.0993i	−0.146909	−	1.02178i
$119$	−12.6637	+	27.7295i	−1.16088	+	2.54196i
$120$	−0.393166	−	0.453738i	−0.0358910	−	0.0414204i
$121$	−14.3134	−	4.20280i	−1.30122	−	0.382073i
$122$	7.28591	−	2.13934i	0.659636	−	0.193686i
$123$	−4.68443			−0.422381
$124$	8.49631	−	2.49474i	0.762992	−	0.224035i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	−10.6838			−0.951785
$127$	−0.599461	+	4.16934i	−0.0531936	+	0.369969i	0.945785	+	0.324792i	$0.105294\pi$
$127$	−0.599461	+	4.16934i	−0.0531936	+	0.369969i	−0.998979	+	0.0451772i	$0.985615\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	3.73652	−	1.09714i	0.328983	−	0.0965980i
$130$	−1.01250	+	2.21706i	−0.0888021	+	0.194449i
$131$	−4.09087	+	8.95775i	−0.357421	+	0.782642i	0.642446	+	0.766331i	$0.277920\pi$
$131$	−4.09087	+	8.95775i	−0.357421	+	0.782642i	−0.999867	+	0.0163114i	$0.994808\pi$
$132$	−0.434986	+	3.02540i	−0.0378607	+	0.263327i
$133$	10.1088	+	6.49654i	0.876545	+	0.563322i
$134$	2.89171	+	1.85839i	0.249806	+	0.160540i
$135$	0.481860	−	3.35141i	0.0414719	−	0.288444i
$136$	−3.12870	+	6.85089i	−0.268284	+	0.587459i
$137$	−9.26092	+	20.2786i	−0.791214	+	1.73252i	−0.118069	+	0.993005i	$0.537670\pi$
$137$	−9.26092	+	20.2786i	−0.791214	+	1.73252i	−0.673145	+	0.739511i	$0.735057\pi$
$138$	2.18605	−	0.641881i	0.186089	−	0.0546405i
$139$	3.33500	−	3.84880i	0.282871	−	0.326451i	−0.596477	−	0.802630i	$-0.703433\pi$
$139$	3.33500	−	3.84880i	0.282871	−	0.326451i	0.879348	+	0.476179i	$0.157979\pi$
$140$	−0.576031	+	4.00638i	−0.0486835	+	0.338601i
$141$	3.22967			0.271987
$142$	−2.73973	−	5.99916i	−0.229913	−	0.503438i
$143$	11.9056	−	3.49581i	0.995599	−	0.292334i
$144$	−2.63954			−0.219962
$145$	−5.69144	+	1.67116i	−0.472648	+	0.138782i
$146$	14.2713	+	4.19044i	1.18110	+	0.346803i
$147$	−3.68904	−	4.25738i	−0.304267	−	0.351143i
$148$	1.30071	−	2.84816i	0.106918	−	0.234118i
$149$	0.176041	+	1.22439i	0.0144218	+	0.100306i	0.995761	−	0.0919790i	$-0.0293193\pi$
$149$	0.176041	+	1.22439i	0.0144218	+	0.100306i	−0.981339	+	0.192285i	$0.938410\pi$
$150$	−0.576062	−	0.169147i	−0.0470352	−	0.0138108i
$151$	3.51281	+	1.03146i	0.285869	+	0.0839386i	0.421523	−	0.906818i	$-0.361496\pi$
$151$	3.51281	+	1.03146i	0.285869	+	0.0839386i	−0.135655	+	0.990756i	$0.543314\pi$
$152$	2.49750	+	1.60504i	0.202574	+	0.130186i
$153$	−19.0744	+	5.60076i	−1.54208	+	0.452795i
$154$	17.3349	−	11.1404i	1.39688	−	0.897723i
$155$	5.79879	−	6.69217i	0.465770	−	0.537528i
$156$	−0.607886	−	1.33108i	−0.0486698	−	0.106572i
$157$	19.4310	−	12.4876i	1.55076	−	0.996615i	0.565663	−	0.824637i	$-0.308620\pi$
$157$	19.4310	−	12.4876i	1.55076	−	0.996615i	0.985101	−	0.171979i	$-0.0550160\pi$
$158$	0.519294	+	0.152479i	0.0413128	+	0.0121305i
$159$	1.52011	−	1.75430i	0.120552	−	0.139125i
$160$	−0.142315	+	0.989821i	−0.0112510	+	0.0782523i
$161$	−12.9215	−	8.30414i	−1.01836	−	0.654458i
$162$	−3.85439	−	4.44820i	−0.302829	−	0.349483i
$163$	9.32975	−	5.99586i	0.730762	−	0.469632i	−0.121603	−	0.992579i	$-0.538804\pi$
$163$	9.32975	−	5.99586i	0.730762	−	0.469632i	0.852366	+	0.522946i	$0.175167\pi$
$164$	5.10950	+	5.89668i	0.398985	+	0.460454i
$165$	1.26972	+	2.78030i	0.0988475	+	0.216446i
$166$	10.7462			0.834063
$167$	−3.27726	+	22.7938i	−0.253602	+	1.76384i	0.322602	+	0.946535i	$0.395443\pi$
$167$	−3.27726	+	22.7938i	−0.253602	+	1.76384i	−0.576204	+	0.817306i	$0.695466\pi$
$168$	−1.59137	−	1.83654i	−0.122777	−	0.141692i
$169$	4.62297	−	5.33519i	0.355613	−	0.410399i
$170$	1.07184	+	7.45484i	0.0822067	+	0.571760i
$171$	1.11521	+	7.75646i	0.0852822	+	0.593151i
$172$	−5.45664	−	3.50677i	−0.416065	−	0.267389i
$173$	2.28199	+	15.8716i	0.173497	+	1.20670i	0.871425	+	0.490529i	$0.163196\pi$
$173$	2.28199	+	15.8716i	0.173497	+	1.20670i	−0.697928	+	0.716168i	$0.745895\pi$
$174$	1.47941	−	3.23947i	0.112154	−	0.245583i
$175$	1.68143	+	3.68181i	0.127104	+	0.278319i
$176$	4.28277	−	2.75237i	0.322826	−	0.207468i
$177$	6.73237			0.506036
$178$	−0.0929462	−	9.43352i	−0.00696661	−	0.707072i
$179$	3.97499			0.297105			0.148552	−	0.988905i	$-0.452539\pi$
$179$	3.97499			0.297105			0.148552	+	0.988905i	$0.452539\pi$
$180$	−2.22052	+	1.42704i	−0.165508	+	0.106366i
$181$	6.95903	+	15.2381i	0.517260	+	1.13264i	0.970466	+	0.241236i	$0.0775529\pi$
$181$	6.95903	+	15.2381i	0.517260	+	1.13264i	−0.453206	+	0.891406i	$0.649720\pi$
$182$	−4.09817	+	8.97375i	−0.303777	+	0.665178i
$183$	0.648813	+	4.51260i	0.0479617	+	0.333581i
$184$	−3.19240	−	2.05163i	−0.235347	−	0.151248i
$185$	−0.445604	−	3.09925i	−0.0327615	−	0.227861i
$186$	0.756600	+	5.26227i	0.0554766	+	0.385848i
$187$	25.1089	−	28.9773i	1.83615	−	2.11903i
$188$	−3.52273	−	4.06545i	−0.256922	−	0.296503i
$189$	1.95037	−	13.5651i	0.141868	−	0.986717i
$190$	2.96878			0.215378
$191$	−0.372653	−	0.815996i	−0.0269642	−	0.0590434i	0.895671	−	0.444718i	$-0.146696\pi$
$191$	−0.372653	−	0.815996i	−0.0269642	−	0.0590434i	−0.922635	+	0.385674i	$0.873969\pi$
$192$	−0.393166	−	0.453738i	−0.0283743	−	0.0327457i
$193$	−6.30592	+	4.05257i	−0.453910	+	0.291710i	−0.747550	−	0.664206i	$-0.768770\pi$
$193$	−6.30592	+	4.05257i	−0.453910	+	0.291710i	0.293640	+	0.955916i	$0.405133\pi$
$194$	8.95334	+	10.3327i	0.642812	+	0.741845i
$195$	−1.23102	−	0.791131i	−0.0881555	−	0.0566541i
$196$	−1.33533	+	9.28741i	−0.0953805	+	0.663386i
$197$	4.75037	−	5.48222i	0.338450	−	0.390592i	−0.560855	−	0.827914i	$-0.689527\pi$
$197$	4.75037	−	5.48222i	0.338450	−	0.390592i	0.899305	+	0.437322i	$0.144073\pi$
$198$	12.8934	+	3.78585i	0.916296	+	0.269049i
$199$	−22.0992	+	14.2023i	−1.56657	+	1.00677i	−0.586067	+	0.810262i	$0.699325\pi$
$199$	−22.0992	+	14.2023i	−1.56657	+	1.00677i	−0.980502	+	0.196511i	$0.937039\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	−1.35146	+	1.55967i	−0.0953248	+	0.110011i
$202$	−4.02621	+	2.58749i	−0.283283	+	0.182055i
$203$	−23.0366	+	6.76415i	−1.61685	+	0.474750i
$204$	−3.80396	−	2.44465i	−0.266330	−	0.171160i
$205$	7.48638	+	2.19820i	0.522871	+	0.153529i
$206$	−0.223461	−	0.0656139i	−0.0155692	−	0.00457154i
$207$	−1.42551	−	9.91461i	−0.0990795	−	0.689113i
$208$	−1.01250	+	2.21706i	−0.0702042	+	0.153726i
$209$	−9.89749	−	11.4223i	−0.684624	−	0.790098i
$210$	−2.33166	−	0.684636i	−0.160900	−	0.0472444i
$211$	−1.01280	+	0.297384i	−0.0697239	+	0.0204728i	−0.316408	−	0.948623i	$-0.602477\pi$
$211$	−1.01280	+	0.297384i	−0.0697239	+	0.0204728i	0.246685	+	0.969096i	$0.420659\pi$
$212$	−3.86632			−0.265540
$213$	3.79922	−	1.11555i	0.260318	−	0.0764362i
$214$	−6.97981	−	15.2836i	−0.477130	−	1.04477i
$215$	−6.48632			−0.442364
$216$	0.481860	−	3.35141i	0.0327865	−	0.228035i
$217$	23.4711	−	27.0871i	1.59332	−	1.83879i
$218$	3.75680	−	1.10310i	0.254443	−	0.0747111i
$219$	−3.70964	+	8.12298i	−0.250674	+	0.548900i
$220$	2.11485	−	4.63088i	0.142583	−	0.312214i
$221$	−2.61243	+	18.1698i	−0.175731	+	1.22223i
$222$	1.58144	+	1.01633i	0.106140	+	0.0682117i
$223$	5.77312	+	3.71016i	0.386597	+	0.248451i	0.719474	−	0.694520i	$-0.244383\pi$
$223$	5.77312	+	3.71016i	0.386597	+	0.248451i	−0.332877	+	0.942970i	$0.608019\pi$
$224$	−0.576031	+	4.00638i	−0.0384877	+	0.267688i
$225$	−1.09651	+	2.40101i	−0.0731004	+	0.160067i
$226$	−6.07021	+	13.2919i	−0.403784	+	0.884164i
$227$	9.01107	−	2.64589i	0.598085	−	0.175614i	0.0313429	−	0.999509i	$-0.490022\pi$
$227$	9.01107	−	2.64589i	0.598085	−	0.175614i	0.566743	+	0.823895i	$0.308203\pi$
$228$	−1.16722	+	1.34705i	−0.0773013	+	0.0892104i
$229$	−0.156654	+	1.08955i	−0.0103520	+	0.0719996i	−0.994343	−	0.106221i	$-0.966125\pi$
$229$	−0.156654	+	1.08955i	−0.0103520	+	0.0719996i	0.983991	+	0.178220i	$0.0570340\pi$
$230$	−3.79481			−0.250222
$231$	5.13929	+	11.2535i	0.338140	+	0.740424i
$232$	−5.69144	+	1.67116i	−0.373661	+	0.109717i
$233$	−12.8620			−0.842621			−0.421310	−	0.906916i	$-0.638430\pi$
$233$	−12.8620			−0.842621			−0.421310	+	0.906916i	$0.638430\pi$
$234$	−6.17281	+	1.81250i	−0.403529	+	0.118487i
$235$	−5.16146	−	1.51554i	−0.336697	−	0.0988630i
$236$	−7.34327	−	8.47458i	−0.478006	−	0.551648i
$237$	−0.134984	+	0.295573i	−0.00876813	+	0.0191995i
$238$	4.33837	+	30.1741i	0.281215	+	1.95589i
$239$	0.0252035	+	0.00740041i	0.00163028	+	0.000478693i	0.282548	−	0.959253i	$-0.408820\pi$
$239$	0.0252035	+	0.00740041i	0.00163028	+	0.000478693i	−0.280917	+	0.959732i	$0.590639\pi$
$240$	−0.576062	−	0.169147i	−0.0371846	−	0.0109184i
$241$	−4.07697	−	2.62011i	−0.262621	−	0.168776i	0.402704	−	0.915330i	$-0.368070\pi$
$241$	−4.07697	−	2.62011i	−0.262621	−	0.168776i	−0.665325	+	0.746554i	$0.731707\pi$
$242$	−14.3134	+	4.20280i	−0.920101	+	0.270166i
$243$	11.5179	−	7.40211i	0.738874	−	0.474845i
$244$	4.97269	−	5.73879i	0.318344	−	0.367388i
$245$	3.89780	+	8.53500i	0.249021	+	0.545281i
$246$	−3.94080	+	2.53260i	−0.251256	+	0.161472i
$247$	6.94276	+	2.03858i	0.441757	+	0.129712i
$248$	5.79879	−	6.69217i	0.368224	−	0.424953i
$249$	−0.918186	+	6.38612i	−0.0581876	+	0.404704i
$250$	0.841254	+	0.540641i	0.0532055	+	0.0341931i
$251$	13.1019	+	15.1204i	0.826983	+	0.954390i	0.999531	−	0.0306114i	$-0.00974542\pi$
$251$	13.1019	+	15.1204i	0.826983	+	0.954390i	−0.172548	+	0.985001i	$0.555200\pi$
$252$	−8.98775	+	5.77608i	−0.566175	+	0.363859i
$253$	12.6514	+	14.6005i	0.795384	+	0.917922i
$254$	1.74982	+	3.83157i	0.109793	+	0.240414i
$255$	−4.52177			−0.283164
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−12.0941	−	13.9573i	−0.754407	−	0.870633i	0.240580	−	0.970629i	$-0.422662\pi$
$257$	−12.0941	−	13.9573i	−0.754407	−	0.870633i	−0.994988	+	0.0999967i	$0.968117\pi$
$258$	2.55020	−	2.94309i	0.158769	−	0.183229i
$259$	−1.80362	−	12.5445i	−0.112072	−	0.779474i
$260$	0.346867	+	2.41251i	0.0215118	+	0.149618i
$261$	−13.1715	−	8.46482i	−0.815297	−	0.523959i
$262$	1.40147	+	9.74743i	0.0865830	+	0.602198i
$263$	0.936414	−	2.05046i	0.0577418	−	0.126437i	−0.878562	−	0.477629i	$-0.841496\pi$
$263$	0.936414	−	2.05046i	0.0577418	−	0.126437i	0.936303	+	0.351192i	$0.114224\pi$
$264$	1.26972	+	2.78030i	0.0781458	+	0.171115i
$265$	−3.25256	+	2.09029i	−0.199803	+	0.128406i
$266$	12.0164			0.736771
$267$	5.61401	+	0.750795i	0.343572	+	0.0459479i
$268$	3.43738			0.209971
$269$	7.53278	−	4.84103i	0.459282	−	0.295163i	−0.290467	−	0.956885i	$-0.593811\pi$
$269$	7.53278	−	4.84103i	0.459282	−	0.295163i	0.749749	+	0.661722i	$0.230174\pi$
$270$	−1.40654	−	3.07990i	−0.0855995	−	0.187437i
$271$	13.1906	−	28.8834i	0.801272	−	1.75454i	0.160166	−	0.987090i	$-0.448797\pi$
$271$	13.1906	−	28.8834i	0.801272	−	1.75454i	0.641107	−	0.767452i	$-0.278476\pi$
$272$	1.07184	+	7.45484i	0.0649901	+	0.452016i
$273$	−4.98267	−	3.20217i	−0.301565	−	0.193804i
$274$	3.17265	+	22.0663i	0.191667	+	1.33307i
$275$	−0.724517	−	5.03912i	−0.0436900	−	0.303871i
$276$	1.49199	−	1.72185i	0.0898074	−	0.103643i
$277$	−17.7010	−	20.4281i	−1.06355	−	1.22740i	−0.972828	−	0.231529i	$-0.925627\pi$
$277$	−17.7010	−	20.4281i	−1.06355	−	1.22740i	−0.0907243	−	0.995876i	$-0.528918\pi$
$278$	0.724765	−	5.04085i	0.0434685	−	0.302330i
$279$	23.3732			1.39931
$280$	1.68143	+	3.68181i	0.100484	+	0.220030i
$281$	−5.72537	−	6.60743i	−0.341547	−	0.394166i	0.558826	−	0.829285i	$-0.311252\pi$
$281$	−5.72537	−	6.60743i	−0.341547	−	0.394166i	−0.900373	+	0.435119i	$0.856706\pi$
$282$	2.71697	−	1.74609i	0.161793	−	0.103978i
$283$	−12.9150	−	14.9047i	−0.767717	−	0.885993i	0.228442	−	0.973558i	$-0.426637\pi$
$283$	−12.9150	−	14.9047i	−0.767717	−	0.885993i	−0.996159	+	0.0875648i	$0.972092\pi$
$284$	−5.54820	−	3.56561i	−0.329225	−	0.211580i
$285$	−0.253662	+	1.76426i	−0.0150256	+	0.104506i
$286$	8.12568	−	9.37753i	0.480481	−	0.554505i
$287$	30.3017	+	8.89738i	1.78865	+	0.525196i
$288$	−2.22052	+	1.42704i	−0.130846	+	0.0840894i
$289$	16.5017	+	36.1337i	0.970689	+	2.12551i
$290$	−3.88445	+	4.48289i	−0.228103	+	0.263244i
$291$	−6.90542	+	4.43785i	−0.404803	+	0.260151i
$292$	14.2713	−	4.19044i	0.835166	−	0.245227i
$293$	−23.6237	−	15.1821i	−1.38011	−	0.886945i	−0.380824	−	0.924647i	$-0.624360\pi$
$293$	−23.6237	−	15.1821i	−1.38011	−	0.886945i	−0.999289	+	0.0377026i	$0.987996\pi$
$294$	−5.40514	−	1.58709i	−0.315234	−	0.0925610i
$295$	−10.7593	−	3.15920i	−0.626428	−	0.183936i
$296$	−0.445604	−	3.09925i	−0.0259002	−	0.180140i
$297$	−7.16063	+	15.6796i	−0.415502	+	0.909823i
$298$	0.810051	+	0.934849i	0.0469250	+	0.0541544i
$299$	−8.87451	−	2.60579i	−0.513226	−	0.150697i
$300$	−0.576062	+	0.169147i	−0.0332589	+	0.00976571i
$301$	−26.2539			−1.51325
$302$	3.51281	−	1.03146i	0.202140	−	0.0593536i
$303$	−1.19365	−	2.61374i	−0.0685737	−	0.150155i
$304$	2.96878			0.170271
$305$	1.08067	−	7.51621i	0.0618789	−	0.430377i
$306$	−13.0184	+	15.0241i	−0.744214	+	0.858869i
$307$	−13.5932	+	3.99132i	−0.775805	+	0.227797i	−0.645585	−	0.763688i	$-0.723386\pi$
$307$	−13.5932	+	3.99132i	−0.775805	+	0.227797i	−0.130220	+	0.991485i	$0.541568\pi$
$308$	8.56004	−	18.7439i	0.487754	−	1.06803i
$309$	0.0580856	−	0.127190i	0.00330437	−	0.00723557i
$310$	1.26020	−	8.76487i	0.0715745	−	0.497811i
$311$	2.41296	+	1.55071i	0.136826	+	0.0879330i	0.607263	−	0.794501i	$-0.292267\pi$
$311$	2.41296	+	1.55071i	0.136826	+	0.0879330i	−0.470437	+	0.882434i	$0.655904\pi$
$312$	−1.23102	−	0.791131i	−0.0696930	−	0.0447890i
$313$	3.57482	−	24.8634i	0.202061	−	1.40536i	−0.596095	−	0.802914i	$-0.703282\pi$
$313$	3.57482	−	24.8634i	0.202061	−	1.40536i	0.798156	−	0.602451i	$-0.205809\pi$
$314$	9.59513	−	21.0104i	0.541484	−	1.18569i
$315$	−4.43819	+	9.71829i	−0.250064	+	0.547564i
$316$	0.519294	−	0.152479i	0.0292126	−	0.00857759i
$317$	13.1182	−	15.1392i	0.736792	−	0.850303i	−0.256427	−	0.966564i	$-0.582545\pi$
$317$	13.1182	−	15.1392i	0.736792	−	0.850303i	0.993219	+	0.116260i	$0.0370907\pi$
$318$	0.330351	−	2.29764i	0.0185252	−	0.128845i
$319$	30.1980			1.69076
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	9.67900	−	2.84201i	0.540229	−	0.158625i
$322$	−15.3598			−0.855969
$323$	21.4536	−	6.29936i	1.19371	−	0.350506i
$324$	−5.64739	−	1.65822i	−0.313744	−	0.0921236i
$325$	1.59611	+	1.84200i	0.0885360	+	0.102176i
$326$	4.60707	−	10.0881i	0.255162	−	0.558727i
$327$	0.334545	+	2.32681i	0.0185004	+	0.128673i
$328$	7.48638	+	2.19820i	0.413366	+	0.121375i
$329$	−20.8914	−	6.13428i	−1.15178	−	0.338194i
$330$	2.57130	+	1.65247i	0.141545	+	0.0909656i
$331$	19.6345	−	5.76519i	1.07921	−	0.316884i	0.306646	−	0.951824i	$-0.400793\pi$
$331$	19.6345	−	5.76519i	1.07921	−	0.316884i	0.772561	+	0.634940i	$0.218975\pi$
$332$	9.04024	−	5.80981i	0.496148	−	0.318855i
$333$	5.41224	−	6.24606i	0.296589	−	0.342282i
$334$	9.56628	+	20.9472i	0.523443	+	1.14618i
$335$	2.89171	−	1.85839i	0.157991	−	0.101535i
$336$	−2.33166	−	0.684636i	−0.127202	−	0.0373500i
$337$	14.8736	−	17.1651i	0.810219	−	0.935042i	−0.188676	−	0.982039i	$-0.560420\pi$
$337$	14.8736	−	17.1651i	0.810219	−	0.935042i	0.998895	+	0.0469970i	$0.0149651\pi$
$338$	1.00467	−	6.98762i	0.0546467	−	0.380076i
$339$	−7.38032	−	4.74305i	−0.400844	−	0.257607i
$340$	4.93208	+	5.69193i	0.267480	+	0.308688i
$341$	−37.9240	+	24.3723i	−2.05370	+	1.31983i
$342$	5.13163	+	5.92222i	0.277487	+	0.320237i
$343$	4.00669	+	8.77342i	0.216341	+	0.473720i
$344$	−6.48632			−0.349719
$345$	0.324241	−	2.25514i	0.0174565	−	0.121413i
$346$	10.5006	+	12.1183i	0.564515	+	0.651485i
$347$	−0.772754	+	0.891806i	−0.0414836	+	0.0478747i	−0.776112	−	0.630595i	$-0.782811\pi$
$347$	−0.772754	+	0.891806i	−0.0414836	+	0.0478747i	0.734629	+	0.678469i	$0.237356\pi$
$348$	−0.506825	−	3.52504i	−0.0271687	−	0.188962i
$349$	2.45930	+	17.1048i	0.131643	+	0.915598i	0.943413	+	0.331620i	$0.107595\pi$
$349$	2.45930	+	17.1048i	0.131643	+	0.915598i	−0.811770	+	0.583978i	$0.801496\pi$
$350$	3.40504	+	2.18829i	0.182007	+	0.116969i
$351$	−1.17445	−	8.16847i	−0.0626874	−	0.436000i
$352$	2.11485	−	4.63088i	0.112722	−	0.246827i
$353$	6.34231	+	13.8877i	0.337567	+	0.739169i	0.999950	−	0.00999642i	$-0.00318201\pi$
$353$	6.34231	+	13.8877i	0.337567	+	0.739169i	−0.662383	+	0.749166i	$0.730455\pi$
$354$	5.66363	−	3.63979i	0.301018	−	0.193453i
$355$	−6.59515			−0.350034
$356$	−5.17834	−	7.88573i	−0.274451	−	0.417943i
$357$	−18.3022			−0.968657
$358$	3.34397	−	2.14904i	0.176734	−	0.113580i
$359$	−1.71343	−	3.75189i	−0.0904315	−	0.198017i	0.859012	−	0.511956i	$-0.171079\pi$
$359$	−1.71343	−	3.75189i	−0.0904315	−	0.198017i	−0.949443	+	0.313938i	$0.898351\pi$
$360$	−1.09651	+	2.40101i	−0.0577909	+	0.126544i
$361$	1.44967	+	10.0827i	0.0762984	+	0.530667i
$362$	14.0927	+	9.05681i	0.740694	+	0.476015i
$363$	−1.27462	−	8.86514i	−0.0668999	−	0.465299i
$364$	1.40397	+	9.76483i	0.0735881	+	0.511816i
$365$	9.74027	−	11.2409i	0.509829	−	0.588374i
$366$	2.98551	+	3.44546i	0.156055	+	0.180097i
$367$	−2.29558	+	15.9661i	−0.119828	+	0.833424i	0.837915	+	0.545800i	$0.183774\pi$
$367$	−2.29558	+	15.9661i	−0.119828	+	0.833424i	−0.957744	+	0.287623i	$0.907135\pi$
$368$	−3.79481			−0.197818
$369$	8.55541	+	18.7337i	0.445377	+	0.975239i
$370$	−2.05045	−	2.36634i	−0.106598	−	0.123020i
$371$	−13.1650	+	8.46062i	−0.683492	+	0.439254i
$372$	3.48149	+	4.01785i	0.180507	+	0.208316i
$373$	10.9369	+	7.02870i	0.566290	+	0.363933i	0.792243	−	0.610206i	$-0.208913\pi$
$373$	10.9369	+	7.02870i	0.566290	+	0.363933i	−0.225953	+	0.974138i	$0.572550\pi$
$374$	5.45669	−	37.9521i	0.282159	−	1.96246i
$375$	−0.393166	+	0.453738i	−0.0203030	+	0.0234309i
$376$	−5.16146	−	1.51554i	−0.266182	−	0.0781581i
$377$	−12.1624	+	7.81631i	−0.626396	+	0.402560i
$378$	−5.69310	−	12.4662i	−0.292821	−	0.641190i
$379$	−8.60749	+	9.93357i	−0.442137	+	0.510253i	−0.932453	−	0.361291i	$-0.882336\pi$
$379$	−8.60749	+	9.93357i	−0.442137	+	0.510253i	0.490316	+	0.871545i	$0.336881\pi$
$380$	2.49750	−	1.60504i	0.128119	−	0.0823370i
$381$	−2.42650	+	0.712484i	−0.124313	+	0.0365017i
$382$	−0.754656	−	0.484988i	−0.0386116	−	0.0248141i
$383$	1.28095	+	0.376121i	0.0654535	+	0.0192189i	0.314295	−	0.949325i	$-0.398232\pi$
$383$	1.28095	+	0.376121i	0.0654535	+	0.0192189i	−0.248842	+	0.968544i	$0.580050\pi$
$384$	−0.576062	−	0.169147i	−0.0293970	−	0.00863175i
$385$	−2.93254	−	20.3963i	−0.149456	−	1.03949i
$386$	−3.11389	+	6.81848i	−0.158493	+	0.347051i
$387$	−11.2118	−	12.9391i	−0.569929	−	0.657733i
$388$	13.1183	+	3.85188i	0.665981	+	0.195550i
$389$	−5.41994	+	1.59144i	−0.274802	+	0.0806891i	−0.416230	−	0.909259i	$-0.636649\pi$
$389$	−5.41994	+	1.59144i	−0.274802	+	0.0806891i	0.141428	+	0.989949i	$0.454831\pi$
$390$	−1.46332			−0.0740982
$391$	−27.4229	+	8.05209i	−1.38684	+	0.407212i
$392$	3.89780	+	8.53500i	0.196869	+	0.431082i
$393$	−5.91235			−0.298239
$394$	1.03235	−	7.18018i	0.0520093	−	0.361732i
$395$	0.354422	−	0.409025i	0.0178329	−	0.0205803i
$396$	12.8934	−	3.78585i	0.647919	−	0.190246i
$397$	2.71743	−	5.95035i	0.136384	−	0.298639i	−0.829101	−	0.559099i	$-0.811147\pi$
$397$	2.71743	−	5.95035i	0.136384	−	0.298639i	0.965485	+	0.260460i	$0.0838743\pi$
$398$	−10.9127	+	23.8954i	−0.547003	+	1.19777i
$399$	−1.02672	+	7.14097i	−0.0514001	+	0.357496i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−20.6165	−	13.2494i	−1.02954	−	0.661646i	−0.0871625	−	0.996194i	$-0.527780\pi$
$401$	−20.6165	−	13.2494i	−1.02954	−	0.661646i	−0.942379	+	0.334548i	$0.891416\pi$
$402$	−0.293701	+	2.04273i	−0.0146485	+	0.101882i
$403$	8.96569	−	19.6321i	0.446613	−	0.977945i
$404$	−1.98816	+	4.35346i	−0.0989147	+	0.216593i
$405$	−5.64739	+	1.65822i	−0.280621	+	0.0823978i
$406$	−15.7226	+	18.1449i	−0.780300	+	0.900515i
$407$	−2.26855	+	15.7781i	−0.112448	+	0.782091i
$408$	−4.52177			−0.223861
$409$	−3.71200	−	8.12814i	−0.183547	−	0.401911i	0.795384	−	0.606106i	$-0.207269\pi$
$409$	−3.71200	−	8.12814i	−0.183547	−	0.401911i	−0.978930	+	0.204196i	$0.934542\pi$
$410$	7.48638	−	2.19820i	0.369726	−	0.108561i
$411$	−13.3844			−0.660204
$412$	−0.223461	+	0.0656139i	−0.0110091	+	0.00323257i
$413$	−43.5490	−	12.7871i	−2.14290	−	0.629213i
$414$	−6.55945	−	7.57001i	−0.322380	−	0.372046i
$415$	4.46411	−	9.77504i	0.219135	−	0.479838i
$416$	0.346867	+	2.41251i	0.0170065	+	0.118283i
$417$	2.93370	+	0.861413i	0.143664	+	0.0421836i
$418$	−14.5017	−	4.25807i	−0.709300	−	0.208269i
$419$	16.1478	+	10.3776i	0.788874	+	0.506978i	0.871968	−	0.489563i	$-0.162844\pi$
$419$	16.1478	+	10.3776i	0.788874	+	0.506978i	−0.0830941	+	0.996542i	$0.526480\pi$
$420$	−2.33166	+	0.684636i	−0.113773	+	0.0334068i
$421$	−14.1985	+	9.12482i	−0.691992	+	0.444717i	−0.838794	−	0.544449i	$-0.816739\pi$
$421$	−14.1985	+	9.12482i	−0.691992	+	0.444717i	0.146801	+	0.989166i	$0.453102\pi$
$422$	−0.691241	+	0.797735i	−0.0336491	+	0.0388331i
$423$	−5.89850	−	12.9159i	−0.286795	−	0.627993i
$424$	−3.25256	+	2.09029i	−0.157958	+	0.101513i
$425$	7.22642	+	2.12187i	0.350533	+	0.102926i
$426$	2.59299	−	2.99247i	0.125631	−	0.144986i
$427$	4.37409	−	30.4225i	0.211677	−	1.47225i
$428$	−14.1347	−	9.08385i	−0.683229	−	0.439085i
$429$	4.87851	+	5.63010i	0.235537	+	0.271824i
$430$	−5.45664	+	3.50677i	−0.263143	+	0.169112i
$431$	9.05350	+	10.4483i	0.436092	+	0.503277i	0.930672	−	0.365855i	$-0.119224\pi$
$431$	9.05350	+	10.4483i	0.436092	+	0.503277i	−0.494580	+	0.869132i	$0.664678\pi$
$432$	−1.40654	−	3.07990i	−0.0676724	−	0.148182i
$433$	24.5157			1.17815			0.589075	−	0.808078i	$-0.299492\pi$
$433$	24.5157			1.17815			0.589075	+	0.808078i	$0.299492\pi$
$434$	5.10076	−	35.4765i	0.244844	−	1.70293i
$435$	−2.33215	−	2.69145i	−0.111818	−	0.129045i
$436$	2.56404	−	2.95906i	0.122795	−	0.141713i
$437$	1.60331	+	11.1513i	0.0766968	+	0.533438i
$438$	1.27087	+	8.83907i	0.0607243	+	0.422347i
$439$	−2.70038	−	1.73543i	−0.128882	−	0.0828276i	0.474611	−	0.880196i	$-0.342589\pi$
$439$	−2.70038	−	1.73543i	−0.128882	−	0.0828276i	−0.603493	+	0.797368i	$0.706225\pi$
$440$	−0.724517	−	5.03912i	−0.0345400	−	0.240231i
$441$	−10.2884	+	22.5285i	−0.489924	+	1.07278i
$442$	7.62563	+	16.6978i	0.362714	+	0.794234i
$443$	17.0353	−	10.9479i	0.809369	−	0.520150i	−0.0692915	−	0.997596i	$-0.522074\pi$
$443$	17.0353	−	10.9479i	0.809369	−	0.520150i	0.878661	+	0.477446i	$0.158437\pi$
$444$	1.87986			0.0892144
$445$	−8.61965	−	3.83428i	−0.408610	−	0.181762i
$446$	6.86252			0.324950
$447$	−0.624767	+	0.401513i	−0.0295504	+	0.0189909i
$448$	1.68143	+	3.68181i	0.0794399	+	0.173949i
$449$	−1.72245	+	3.77164i	−0.0812875	+	0.177995i	−0.945912	−	0.324425i	$-0.894829\pi$
$449$	−1.72245	+	3.77164i	−0.0812875	+	0.177995i	0.864624	+	0.502419i	$0.167557\pi$
$450$	0.375646	+	2.61268i	0.0177081	+	0.123163i
$451$	−33.4160	−	21.4752i	−1.57350	−	1.01123i
$452$	2.07956	+	14.4637i	0.0978143	+	0.680313i
$453$	0.312817	+	2.17569i	0.0146974	+	0.102223i
$454$	6.15012	−	7.09761i	0.288639	−	0.333107i
$455$	6.46036	+	7.45566i	0.302867	+	0.349527i
$456$	−0.253662	+	1.76426i	−0.0118788	+	0.0826189i
$457$	−27.1145			−1.26836			−0.634182	−	0.773183i	$-0.718663\pi$
$457$	−27.1145			−1.26836			−0.634182	+	0.773183i	$0.718663\pi$
$458$	0.457271	+	1.00128i	0.0213669	+	0.0467869i
$459$	−16.6994	−	19.2722i	−0.779462	−	0.899547i
$460$	−3.19240	+	2.05163i	−0.148846	+	0.0956577i
$461$	−13.9768	−	16.1301i	−0.650964	−	0.751252i	0.330310	−	0.943873i	$-0.392847\pi$
$461$	−13.9768	−	16.1301i	−0.650964	−	0.751252i	−0.981273	+	0.192621i	$0.938301\pi$
$462$	10.4075	+	6.68852i	0.484202	+	0.311178i
$463$	−1.34229	+	9.33582i	−0.0623815	+	0.433873i	0.934566	+	0.355791i	$0.115789\pi$
$463$	−1.34229	+	9.33582i	−0.0623815	+	0.433873i	−0.996947	+	0.0780815i	$0.975121\pi$
$464$	−3.88445	+	4.48289i	−0.180331	+	0.208113i
$465$	5.10103	+	1.49780i	0.236555	+	0.0694587i
$466$	−10.8202	+	6.95375i	−0.501238	+	0.322126i
$467$	−7.17852	−	15.7188i	−0.332182	−	0.727377i	0.667672	−	0.744456i	$-0.267291\pi$
$467$	−7.17852	−	15.7188i	−0.332182	−	0.727377i	−0.999854	+	0.0170781i	$0.994564\pi$
$468$	−4.21299	+	4.86205i	−0.194745	+	0.224748i
$469$	11.7044	−	7.52198i	0.540460	−	0.347333i
$470$	−5.16146	+	1.51554i	−0.238080	+	0.0699067i
$471$	11.6660	+	7.49730i	0.537542	+	0.345457i
$472$	−10.7593	−	3.15920i	−0.495235	−	0.145414i
$473$	31.6839	+	9.30323i	1.45683	+	0.427763i
$474$	0.0462433	+	0.321629i	0.00212403	+	0.0147729i
$475$	1.23328	−	2.70050i	0.0565866	−	0.123907i
$476$	19.9630	+	23.0385i	0.915002	+	1.05597i
$477$	−9.79193	−	2.87517i	−0.448342	−	0.131645i
$478$	0.0252035	−	0.00740041i	0.00115278	−	0.000338487i
$479$	−31.7885			−1.45245			−0.726227	−	0.687455i	$-0.758728\pi$
$479$	−31.7885			−1.45245			−0.726227	+	0.687455i	$0.758728\pi$
$480$	−0.576062	+	0.169147i	−0.0262935	+	0.00772047i
$481$	−3.17025	−	6.94189i	−0.144551	−	0.316523i
$482$	−4.84630			−0.220743
$483$	1.31239	−	9.12788i	0.0597158	−	0.415333i
$484$	−9.76901	+	11.2740i	−0.444046	+	0.512456i
$485$	13.1183	−	3.85188i	0.595672	−	0.174905i
$486$	5.68760	−	12.4541i	0.257995	−	0.564929i
$487$	8.27645	−	18.1229i	0.375042	−	0.821226i	−0.624161	−	0.781296i	$-0.714559\pi$
$487$	8.27645	−	18.1229i	0.375042	−	0.821226i	0.999202	−	0.0399306i	$-0.0127137\pi$
$488$	1.08067	−	7.51621i	0.0489196	−	0.340243i
$489$	5.60141	+	3.59981i	0.253304	+	0.162789i
$490$	7.89341	+	5.07278i	0.356588	+	0.229165i
$491$	4.11757	−	28.6383i	0.185823	−	1.29243i	−0.656857	−	0.754015i	$-0.728115\pi$
$491$	4.11757	−	28.6383i	0.185823	−	1.29243i	0.842680	−	0.538414i	$-0.180976\pi$
$492$	−1.94598	+	4.26111i	−0.0877317	+	0.192106i
$493$	−18.5585	+	40.6375i	−0.835835	+	1.83022i
$494$	6.94276	−	2.03858i	0.312370	−	0.0917200i
$495$	8.79986	−	10.1556i	0.395524	−	0.456459i
$496$	1.26020	−	8.76487i	0.0565846	−	0.393554i
$497$	−26.6944			−1.19741
$498$	2.68017	+	5.86876i	0.120101	+	0.262985i
$499$	−23.4555	+	6.88717i	−1.05001	+	0.308312i	−0.760823	−	0.648959i	$-0.775204\pi$
$499$	−23.4555	+	6.88717i	−1.05001	+	0.308312i	−0.289191	+	0.957271i	$0.593386\pi$
$500$	1.00000			0.0447214
$501$	−13.2657	+	3.89516i	−0.592667	+	0.174023i
$502$	19.1967	+	5.63666i	0.856791	+	0.251576i
$503$	−4.66795	−	5.38711i	−0.208134	−	0.240199i	0.642079	−	0.766639i	$-0.278072\pi$
$503$	−4.66795	−	5.38711i	−0.208134	−	0.240199i	−0.850213	+	0.526439i	$0.823527\pi$
$504$	−4.43819	+	9.71829i	−0.197693	+	0.432887i
$505$	0.681113	+	4.73725i	0.0303092	+	0.210805i
$506$	18.5366	+	5.44284i	0.824053	+	0.241964i
$507$	4.06669	+	1.19409i	0.180608	+	0.0530313i
$508$	3.54354	+	2.27730i	0.157219	+	0.101039i
$509$	6.20117	−	1.82083i	0.274862	−	0.0807068i	−0.141397	−	0.989953i	$-0.545159\pi$
$509$	6.20117	−	1.82083i	0.274862	−	0.0807068i	0.416259	+	0.909246i	$0.363341\pi$
$510$	−3.80396	+	2.44465i	−0.168442	+	0.108251i
$511$	39.4245	−	45.4984i	1.74404	−	2.01273i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−8.45621	+	5.43448i	−0.373351	+	0.239938i
$514$	−17.7201	−	5.20308i	−0.781599	−	0.229498i
$515$	−0.152513	+	0.176010i	−0.00672054	+	0.00775592i
$516$	0.554212	−	3.85463i	0.0243978	−	0.169691i
$517$	23.0386	+	14.8060i	1.01324	+	0.651167i
$518$	−8.29935	−	9.57796i	−0.364652	−	0.420831i
$519$	−8.09876	+	5.20476i	−0.355496	+	0.228463i
$520$	1.59611	+	1.84200i	0.0699938	+	0.0807772i
$521$	8.14877	+	17.8433i	0.357004	+	0.781730i	0.999876	+	0.0157563i	$0.00501560\pi$
$521$	8.14877	+	17.8433i	0.357004	+	0.781730i	−0.642872	+	0.765974i	$0.722257\pi$
$522$	−15.6570			−0.685289
$523$	−1.87486	+	13.0399i	−0.0819818	+	0.570196i	0.906883	+	0.421382i	$0.138455\pi$
$523$	−1.87486	+	13.0399i	−0.0819818	+	0.570196i	−0.988865	+	0.148814i	$0.952454\pi$
$524$	6.44885	+	7.44237i	0.281719	+	0.325121i
$525$	−1.59137	+	1.83654i	−0.0694532	+	0.0801532i
$526$	−0.320801	−	2.23122i	−0.0139876	−	0.0972858i
$527$	−9.49118	−	66.0126i	−0.413442	−	2.87555i
$528$	2.57130	+	1.65247i	0.111901	+	0.0719146i
$529$	1.22382	+	8.51188i	0.0532097	+	0.370082i
$530$	−1.60613	+	3.51693i	−0.0697657	+	0.152766i
$531$	−12.2956	−	26.9237i	−0.533585	−	1.16839i
$532$	10.1088	−	6.49654i	0.438273	−	0.281661i
$533$	19.0170			0.823718
$534$	5.12871	−	2.40355i	0.221941	−	0.104012i
$535$	−16.8020			−0.726414
$536$	2.89171	−	1.85839i	0.124903	−	0.0802701i
$537$	0.991392	+	2.17085i	0.0427817	+	0.0936789i
$538$	3.71972	−	8.14506i	0.160369	−	0.351159i
$539$	−6.79807	−	47.2816i	−0.292814	−	2.03656i
$540$	−2.84838	−	1.83054i	−0.122575	−	0.0787740i
$541$	0.626102	+	4.35464i	0.0269182	+	0.187220i	0.998844	−	0.0480667i	$-0.0153060\pi$
$541$	0.626102	+	4.35464i	0.0269182	+	0.187220i	−0.971926	+	0.235287i	$0.924397\pi$
$542$	−4.51890	−	31.4296i	−0.194103	−	1.35002i
$543$	−6.58632	+	7.60101i	−0.282646	+	0.326191i
$544$	4.93208	+	5.69193i	0.211461	+	0.244039i
$545$	0.557220	−	3.87555i	0.0238687	−	0.166010i
$546$	−5.92291			−0.253477
$547$	−6.80548	−	14.9019i	−0.290981	−	0.637160i	0.706529	−	0.707684i	$-0.250260\pi$
$547$	−6.80548	−	14.9019i	−0.290981	−	0.637160i	−0.997510	+	0.0705240i	$0.977533\pi$
$548$	14.5989	+	16.8481i	0.623635	+	0.719713i
$549$	16.8616	−	10.8363i	0.719634	−	0.462481i
$550$	−3.33386	−	3.84748i	−0.142156	−	0.164057i
$551$	14.8144	+	9.52066i	0.631116	+	0.405594i
$552$	0.324241	−	2.25514i	0.0138006	−	0.0959853i
$553$	1.43455	−	1.65556i	0.0610033	−	0.0704016i
$554$	−25.9353	−	7.61530i	−1.10189	−	0.323543i
$555$	1.58144	−	1.01633i	0.0671285	−	0.0431409i
$556$	−2.11558	−	4.63247i	−0.0897206	−	0.196461i
$557$	−23.1619	+	26.7302i	−0.981401	+	1.13260i	0.00976289	+	0.999952i	$0.496892\pi$
$557$	−23.1619	+	26.7302i	−0.981401	+	1.13260i	−0.991164	+	0.132645i	$0.957653\pi$
$558$	19.6628	−	12.6365i	0.832391	−	0.534945i
$559$	−15.1689	+	4.45398i	−0.641574	+	0.188383i
$560$	3.40504	+	2.18829i	0.143889	+	0.0924720i
$561$	22.0876	+	6.48550i	0.932539	+	0.273818i
$562$	−8.38873	−	2.46315i	−0.353857	−	0.103902i
$563$	5.62737	+	39.1392i	0.237165	+	1.64952i	0.665864	+	0.746073i	$0.268063\pi$
$563$	5.62737	+	39.1392i	0.237165	+	1.64952i	−0.428699	+	0.903447i	$0.641028\pi$
$564$	1.34165	−	2.93781i	0.0564938	−	0.123704i
$565$	9.56908	+	11.0433i	0.402574	+	0.464595i
$566$	−18.9229	−	5.55626i	−0.795388	−	0.233547i
$567$	−22.8583	+	6.71180i	−0.959957	+	0.281869i
$568$	−6.59515			−0.276726
$569$	−10.0769	+	2.95883i	−0.422444	+	0.124041i	−0.486043	−	0.873935i	$-0.661560\pi$
$569$	−10.0769	+	2.95883i	−0.422444	+	0.124041i	0.0635993	+	0.997976i	$0.479742\pi$
$570$	0.740436	+	1.62133i	0.0310134	+	0.0679100i
$571$	33.9297			1.41991			0.709957	−	0.704245i	$-0.248714\pi$
$571$	33.9297			1.41991			0.709957	+	0.704245i	$0.248714\pi$
$572$	1.76588	−	12.2820i	0.0738351	−	0.513534i
$573$	0.352694	−	0.407031i	0.0147340	−	0.0170040i
$574$	30.3017	−	8.89738i	1.26477	−	0.371370i
$575$	−1.57642	+	3.45188i	−0.0657413	+	0.143953i
$576$	−1.09651	+	2.40101i	−0.0456877	+	0.100042i
$577$	1.26052	−	8.76712i	0.0524762	−	0.364980i	−0.946615	−	0.322365i	$-0.895522\pi$
$577$	1.26052	−	8.76712i	0.0524762	−	0.364980i	0.999092	−	0.0426148i	$-0.0135688\pi$
$578$	33.4175	+	21.4761i	1.38998	+	0.893288i
$579$	−3.78596	−	2.43309i	−0.157339	−	0.101116i
$580$	−0.844171	+	5.87134i	−0.0350523	+	0.243794i
$581$	18.0689	−	39.5653i	0.749623	−	1.64144i
$582$	−3.40993	+	7.46671i	−0.141346	+	0.309505i
$583$	18.8859	−	5.54540i	0.782174	−	0.229667i
$584$	9.74027	−	11.2409i	0.403055	−	0.465151i
$585$	−0.915569	+	6.36793i	−0.0378541	+	0.263281i
$586$	−28.0816			−1.16004
$587$	15.5810	+	34.1176i	0.643095	+	1.40818i	0.897469	+	0.441077i	$0.145403\pi$
$587$	15.5810	+	34.1176i	0.643095	+	1.40818i	−0.254374	+	0.967106i	$0.581869\pi$
$588$	−5.40514	+	1.58709i	−0.222904	+	0.0654505i
$589$	−26.2886			−1.08320
$590$	−10.7593	+	3.15920i	−0.442952	+	0.130062i
$591$	4.17876	+	1.22700i	0.171891	+	0.0504719i
$592$	−2.05045	−	2.36634i	−0.0842728	−	0.0972560i
$593$	−15.8636	+	34.7364i	−0.651439	+	1.42645i	0.238850	+	0.971057i	$0.423230\pi$
$593$	−15.8636	+	34.7364i	−0.651439	+	1.42645i	−0.890289	+	0.455396i	$0.849498\pi$
$594$	2.45312	+	17.0619i	0.100653	+	0.700056i
$595$	29.2495	+	8.58843i	1.19911	+	0.352091i
$596$	1.18688	+	0.348498i	0.0486163	+	0.0142750i
$597$	−13.2679	−	8.52678i	−0.543020	−	0.348978i
$598$	−8.87451	+	2.60579i	−0.362906	+	0.106559i
$599$	30.1886	−	19.4010i	1.23347	−	0.792705i	0.249044	−	0.968492i	$-0.419884\pi$
$599$	30.1886	−	19.4010i	1.23347	−	0.792705i	0.984428	+	0.175788i	$0.0562472\pi$
$600$	−0.393166	+	0.453738i	−0.0160509	+	0.0185238i
$601$	−9.94155	−	21.7690i	−0.405524	−	0.887974i	−0.996680	−	0.0814168i	$-0.974056\pi$
$601$	−9.94155	−	21.7690i	−0.405524	−	0.887974i	0.591156	−	0.806557i	$-0.298672\pi$
$602$	−22.0862	+	14.1939i	−0.900166	+	0.578502i
$603$	8.70558	+	2.55619i	0.354519	+	0.104096i
$604$	2.39752	−	2.76689i	0.0975537	−	0.112583i
$605$	−2.12301	+	14.7659i	−0.0863126	+	0.600317i
$606$	−2.41726	−	1.55348i	−0.0981945	−	0.0631058i
$607$	13.4318	+	15.5011i	0.545179	+	0.629170i	0.959753	−	0.280845i	$-0.0906148\pi$
$607$	13.4318	+	15.5011i	0.545179	+	0.629170i	−0.414574	+	0.910016i	$0.636069\pi$
$608$	2.49750	−	1.60504i	0.101287	−	0.0650931i
$609$	−9.43957	−	10.8938i	−0.382511	−	0.441441i
$610$	−3.15446	−	6.90729i	−0.127720	−	0.279668i
$611$	−13.1112			−0.530423
$612$	−2.82918	+	19.6774i	−0.114363	+	0.795410i
$613$	7.70623	+	8.89346i	0.311252	+	0.359204i	0.889724	−	0.456498i	$-0.150896\pi$
$613$	7.70623	+	8.89346i	0.311252	+	0.359204i	−0.578473	+	0.815702i	$0.696351\pi$
$614$	−9.27745	+	10.7068i	−0.374408	+	0.432089i
$615$	0.666664	+	4.63675i	0.0268825	+	0.186972i
$616$	−2.93254	−	20.3963i	−0.118155	−	0.821789i
$617$	−26.2530	−	16.8718i	−1.05691	−	0.679233i	−0.107796	−	0.994173i	$-0.534379\pi$
$617$	−26.2530	−	16.8718i	−1.05691	−	0.679233i	−0.949112	+	0.314940i	$0.898016\pi$
$618$	−0.0198992	−	0.138402i	−0.000800465	−	0.00556736i
$619$	−19.4996	+	42.6982i	−0.783756	+	1.71619i	−0.0900383	+	0.995938i	$0.528699\pi$
$619$	−19.4996	+	42.6982i	−0.783756	+	1.71619i	−0.693717	+	0.720247i	$0.744028\pi$
$620$	−3.67850	−	8.05480i	−0.147732	−	0.323488i
$621$	10.8091	−	6.94657i	0.433753	−	0.278756i
$622$	2.86829			0.115008
$623$	−34.8887	−	15.5196i	−1.39779	−	0.621778i
$624$	−1.46332			−0.0585797
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	−10.4349	−	22.8492i	−0.417061	−	0.913236i
$627$	3.76951	−	8.25409i	0.150540	−	0.329636i
$628$	−3.28714	−	22.8626i	−0.131171	−	0.912317i
$629$	−19.8384	−	12.7494i	−0.791010	−	0.508352i
$630$	1.52046	+	10.5750i	0.0605765	+	0.421319i
$631$	5.80654	+	40.3853i	0.231155	+	1.60772i	0.693123	+	0.720819i	$0.256234\pi$
$631$	5.80654	+	40.3853i	0.231155	+	1.60772i	−0.461969	+	0.886896i	$0.652857\pi$
$632$	0.354422	−	0.409025i	0.0140981	−	0.0162701i
$633$	−0.415009	−	0.478945i	−0.0164951	−	0.0190364i
$634$	2.85086	−	19.8282i	0.113222	−	0.787477i
$635$	4.21222			0.167157
$636$	−0.964289	−	2.11150i	−0.0382366	−	0.0837264i
$637$	14.9761	+	17.2834i	0.593375	+	0.684791i
$638$	25.4042	−	16.3263i	1.00576	−	0.646364i
$639$	−11.3999	−	13.1562i	−0.450974	−	0.520452i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	4.40125	−	30.6114i	0.173839	−	1.20908i	−0.696841	−	0.717226i	$-0.745411\pi$
$641$	4.40125	−	30.6114i	0.173839	−	1.20908i	0.870680	−	0.491851i	$-0.163679\pi$
$642$	6.60598	−	7.62371i	0.260717	−	0.300884i
$643$	9.17008	+	2.69258i	0.361633	+	0.106185i	0.457501	−	0.889209i	$-0.348745\pi$
$643$	9.17008	+	2.69258i	0.361633	+	0.106185i	−0.0958684	+	0.995394i	$0.530563\pi$
$644$	−12.9215	+	8.30414i	−0.509178	+	0.327229i
$645$	−1.61774	−	3.54235i	−0.0636984	−	0.139480i
$646$	14.6423	−	16.8981i	0.576092	−	0.664846i
$647$	−6.29553	+	4.04589i	−0.247503	+	0.159060i	−0.658511	−	0.752571i	$-0.728813\pi$
$647$	−6.29553	+	4.04589i	−0.247503	+	0.159060i	0.411008	+	0.911632i	$0.365177\pi$
$648$	−5.64739	+	1.65822i	−0.221851	+	0.0651412i
$649$	48.0248	+	30.8637i	1.88514	+	1.21150i
$650$	2.33859	+	0.686672i	0.0917271	+	0.0269335i
$651$	20.6468	+	6.06246i	0.809213	+	0.237606i
$652$	−1.57831	−	10.9774i	−0.0618115	−	0.429909i
$653$	5.53129	−	12.1118i	0.216456	−	0.473972i	−0.769991	−	0.638055i	$-0.779739\pi$
$653$	5.53129	−	12.1118i	0.216456	−	0.473972i	0.986447	+	0.164083i	$0.0524664\pi$
$654$	1.53940	+	1.77657i	0.0601955	+	0.0694693i
$655$	9.44876	+	2.77441i	0.369194	+	0.108405i
$656$	7.48638	−	2.19820i	0.292294	−	0.0858252i
$657$	39.2600			1.53168
$658$	−20.8914	+	6.13428i	−0.814433	+	0.239139i
$659$	−10.4233	−	22.8238i	−0.406034	−	0.889090i	−0.996623	−	0.0821173i	$-0.973832\pi$
$659$	−10.4233	−	22.8238i	−0.406034	−	0.889090i	0.590589	−	0.806973i	$-0.298895\pi$
$660$	3.05651			0.118974
$661$	1.46565	−	10.1938i	0.0570071	−	0.396493i	−0.941262	−	0.337678i	$-0.890359\pi$
$661$	1.46565	−	10.1938i	0.0570071	−	0.396493i	0.998269	−	0.0588155i	$-0.0187324\pi$
$662$	13.4007	−	15.4652i	0.520831	−	0.601071i
$663$	−10.5746	+	3.10497i	−0.410682	+	0.120587i
$664$	4.46411	−	9.77504i	0.173241	−	0.379345i
$665$	4.99178	−	10.9305i	0.193573	−	0.423866i
$666$	1.17619	−	8.18059i	0.0455765	−	0.316992i
$667$	−18.9364	−	12.1697i	−0.733220	−	0.471212i
$668$	19.3726	+	12.4500i	0.749548	+	0.481705i
$669$	−0.586356	+	4.07819i	−0.0226698	+	0.157672i
$670$	1.42794	−	3.12675i	0.0551661	−	0.120797i
$671$	−16.0592	+	35.1646i	−0.619957	+	1.35752i
$672$	−2.33166	+	0.684636i	−0.0899456	+	0.0264104i
$673$	7.93306	−	9.15524i	0.305797	−	0.352909i	−0.581963	−	0.813215i	$-0.697715\pi$
$673$	7.93306	−	9.15524i	0.305797	−	0.352909i	0.887760	+	0.460307i	$0.152261\pi$
$674$	3.23235	−	22.4815i	0.124506	−	0.865955i
$675$	−3.38588			−0.130322
$676$	−2.93261	−	6.42152i	−0.112793	−	0.246982i
$677$	−20.1073	+	5.90403i	−0.772786	+	0.226910i	−0.644271	−	0.764797i	$-0.722839\pi$
$677$	−20.1073	+	5.90403i	−0.772786	+	0.226910i	−0.128515	+	0.991708i	$0.541021\pi$
$678$	−8.77301			−0.336925
$679$	53.0974	−	15.5908i	2.03769	−	0.598320i
$680$	7.22642	+	2.12187i	0.277120	+	0.0813699i
$681$	3.69242	+	4.26128i	0.141494	+	0.163292i
$682$	−18.7270	+	41.0065i	−0.717095	+	1.57022i
$683$	−1.00012	−	6.95598i	−0.0382685	−	0.266163i	0.961700	−	0.274104i	$-0.0883813\pi$
$683$	−1.00012	−	6.95598i	−0.0382685	−	0.266163i	−0.999968	+	0.00794106i	$0.997472\pi$
$684$	7.51880	+	2.20772i	0.287488	+	0.0844142i
$685$	21.3901	+	6.28071i	0.817275	+	0.239974i
$686$	8.11391	+	5.21449i	0.309790	+	0.199090i
$687$	−0.634103	+	0.186190i	−0.0241926	+	0.00710358i
$688$	−5.45664	+	3.50677i	−0.208033	+	0.133694i
$689$	−6.17105	+	7.12178i	−0.235098	+	0.271318i
$690$	−0.946454	−	2.07245i	−0.0360309	−	0.0788967i
$691$	−14.0450	+	9.02614i	−0.534295	+	0.343371i	−0.779804	−	0.626024i	$-0.784681\pi$
$691$	−14.0450	+	9.02614i	−0.534295	+	0.343371i	0.245509	+	0.969394i	$0.421045\pi$
$692$	15.3853	+	4.51753i	0.584862	+	0.171731i
$693$	35.6181	−	41.1055i	1.35302	−	1.56147i
$694$	−0.167936	+	1.16802i	−0.00637475	+	0.0443373i
$695$	−4.28424	−	2.75332i	−0.162511	−	0.104439i
$696$	−2.33215	−	2.69145i	−0.0883999	−	0.102019i
$697$	49.4354	−	31.7702i	1.87250	−	1.20338i
$698$	11.3164	+	13.0599i	0.428333	+	0.494323i
$699$	−3.20789	−	7.02430i	−0.121334	−	0.265683i
$700$	4.04758			0.152984
$701$	−3.77543	+	26.2587i	−0.142596	+	0.991777i	0.785347	+	0.619055i	$0.212484\pi$
$701$	−3.77543	+	26.2587i	−0.142596	+	0.991777i	−0.927943	+	0.372721i	$0.878425\pi$
$702$	−5.40421	−	6.23680i	−0.203969	−	0.235393i
$703$	−6.08732	+	7.02514i	−0.229588	+	0.264958i
$704$	−0.724517	−	5.03912i	−0.0273062	−	0.189919i
$705$	−0.459630	−	3.19680i	−0.0173107	−	0.120398i
$706$	12.8438	+	8.25419i	0.483381	+	0.310650i
$707$	2.75686	+	19.1744i	0.103682	+	0.721127i
$708$	2.79673	−	6.12398i	0.105107	−	0.230153i
$709$	10.4115	+	22.7979i	0.391011	+	0.856194i	0.998103	+	0.0615626i	$0.0196084\pi$
$709$	10.4115	+	22.7979i	0.391011	+	0.856194i	−0.607093	+	0.794631i	$0.707664\pi$
$710$	−5.54820	+	3.56561i	−0.208220	+	0.133815i
$711$	1.42857			0.0535754
$712$	−8.61965	−	3.83428i	−0.323035	−	0.143696i
$713$	33.6031			1.25844
$714$	−15.3968	+	9.89493i	−0.576211	+	0.370309i
$715$	−5.15457	−	11.2869i	−0.192770	−	0.422108i
$716$	1.65127	−	3.61578i	0.0617108	−	0.135128i
$717$	0.00224438	+	0.0156100i	8.38179e−5	+	0.000582966i
$718$	−3.46986	−	2.22994i	−0.129494	−	0.0832207i
$719$	0.499565	+	3.47455i	0.0186306	+	0.129579i	0.997014	−	0.0772202i	$-0.0246044\pi$
$719$	0.499565	+	3.47455i	0.0186306	+	0.129579i	−0.978383	+	0.206799i	$0.933695\pi$
$720$	0.375646	+	2.61268i	0.0139995	+	0.0973687i
$721$	−0.617310	+	0.712414i	−0.0229898	+	0.0265317i
$722$	6.67064	+	7.69833i	0.248256	+	0.286502i
$723$	0.414084	−	2.88001i	0.0153999	−	0.107109i
$724$	16.7520			0.622583
$725$	2.46412	+	5.39568i	0.0915153	+	0.200390i
$726$	−5.86513	−	6.76872i	−0.217675	−	0.251211i
$727$	−16.7384	+	10.7571i	−0.620792	+	0.398959i	−0.812890	−	0.582417i	$-0.802107\pi$
$727$	−16.7384	+	10.7571i	−0.620792	+	0.398959i	0.192098	+	0.981376i	$0.438471\pi$
$728$	6.46036	+	7.45566i	0.239437	+	0.276325i
$729$	−7.93924	−	5.10224i	−0.294046	−	0.188972i
$730$	2.11676	−	14.7224i	0.0783449	−	0.544901i
$731$	−31.9911	+	36.9197i	−1.18323	+	1.36552i
$732$	4.37433	+	1.28442i	0.161680	+	0.0474735i
$733$	10.3856	−	6.67445i	0.383603	−	0.246526i	−0.334600	−	0.942360i	$-0.608601\pi$
$733$	10.3856	−	6.67445i	0.383603	−	0.246526i	0.718203	+	0.695834i	$0.244965\pi$
$734$	6.70076	+	14.6726i	0.247330	+	0.541576i
$735$	−3.68904	+	4.25738i	−0.136072	+	0.157036i
$736$	−3.19240	+	2.05163i	−0.117673	+	0.0756241i
$737$	−16.7906	+	4.93018i	−0.618492	+	0.181605i
$738$	17.3255	+	11.1344i	0.637760	+	0.409863i
$739$	8.33952	+	2.44870i	0.306774	+	0.0900770i	0.431496	−	0.902115i	$-0.357986\pi$
$739$	8.33952	+	2.44870i	0.306774	+	0.0900770i	−0.124722	+	0.992192i	$0.539804\pi$
$740$	−3.00429	−	0.882138i	−0.110440	−	0.0324280i
$741$	0.618255	+	4.30006i	0.0227122	+	0.157967i
$742$	−6.50093	+	14.2351i	−0.238657	+	0.522585i
$743$	5.44424	+	6.28299i	0.199730	+	0.230501i	0.846775	−	0.531951i	$-0.178541\pi$
$743$	5.44424	+	6.28299i	0.199730	+	0.230501i	−0.647045	+	0.762452i	$0.723996\pi$
$744$	5.10103	+	1.49780i	0.187013	+	0.0549119i
$745$	1.18688	−	0.348498i	0.0434838	−	0.0127680i
$746$	13.0007			0.475989
$747$	27.2159	−	7.99132i	0.995779	−	0.292387i
$748$	−15.9280	−	34.8775i	−0.582386	−	1.27525i
$749$	−68.0075			−2.48494
$750$	−0.0854432	+	0.594270i	−0.00311994	+	0.0216997i
$751$	25.5040	−	29.4332i	0.930655	−	1.07403i	−0.0664344	−	0.997791i	$-0.521162\pi$
$751$	25.5040	−	29.4332i	0.930655	−	1.07403i	0.997089	−	0.0762423i	$-0.0242922\pi$
$752$	−5.16146	+	1.51554i	−0.188219	+	0.0552661i
$753$	−4.98993	+	10.9264i	−0.181843	+	0.398181i
$754$	−6.00586	+	13.1510i	−0.218720	+	0.478931i
$755$	0.521031	−	3.62385i	0.0189623	−	0.131885i
$756$	−11.5291	−	7.40927i	−0.419308	−	0.269473i
$757$	−38.0343	−	24.4432i	−1.38238	−	0.888402i	−0.383005	−	0.923746i	$-0.625111\pi$
$757$	−38.0343	−	24.4432i	−1.38238	−	0.888402i	−0.999375	+	0.0353442i	$0.988747\pi$
$758$	−1.87059	+	13.0102i	−0.0679428	+	0.472552i
$759$	−4.81834	+	10.5507i	−0.174895	+	0.382966i
$760$	1.23328	−	2.70050i	0.0447356	−	0.0979573i
$761$	46.3797	−	13.6183i	1.68126	−	0.493664i	0.704811	−	0.709395i	$-0.251032\pi$
$761$	46.3797	−	13.6183i	1.68126	−	0.493664i	0.976453	+	0.215732i	$0.0692136\pi$
$762$	−1.65610	+	1.91124i	−0.0599942	+	0.0692370i
$763$	2.25539	−	15.6866i	0.0816507	−	0.567893i
$764$	−0.897062			−0.0324545
$765$	8.25833	+	18.0832i	0.298580	+	0.653800i
$766$	1.28095	−	0.376121i	0.0462826	−	0.0135898i
$767$	−27.3308			−0.986859
$768$	−0.576062	+	0.169147i	−0.0207868	+	0.00610357i
$769$	−39.6550	−	11.6438i	−1.43000	−	0.419885i	−0.527122	−	0.849790i	$-0.676729\pi$
$769$	−39.6550	−	11.6438i	−1.43000	−	0.419885i	−0.902874	+	0.429905i	$0.858547\pi$
$770$	−13.4941	−	15.5730i	−0.486292	−	0.561211i
$771$	4.60610	−	10.0859i	0.165885	−	0.363236i
$772$	1.06677	+	7.41957i	0.0383940	+	0.267036i
$773$	−48.2586	−	14.1700i	−1.73574	−	0.509660i	−0.747725	−	0.664008i	$-0.768854\pi$
$773$	−48.2586	−	14.1700i	−1.73574	−	0.509660i	−0.988017	+	0.154348i	$0.950672\pi$
$774$	−16.4274	−	4.82352i	−0.590471	−	0.173378i
$775$	−7.44930	−	4.78738i	−0.267587	−	0.171968i
$776$	13.1183	−	3.85188i	0.470920	−	0.138275i
$777$	6.40102	−	4.11368i	0.229635	−	0.147578i
$778$	−3.69915	+	4.26904i	−0.132621	+	0.153053i
$779$	−9.62254	−	21.0704i	−0.344763	−	0.754926i
$780$	−1.23102	+	0.791131i	−0.0440777	+	0.0283270i
$781$	32.2155	+	9.45932i	1.15276	+	0.338481i
$782$	−18.7163	+	21.5998i	−0.669294	+	0.772407i
$783$	2.85826	−	19.8796i	0.102146	−	0.710440i
$784$	7.89341	+	5.07278i	0.281907	+	0.181171i
$785$	−15.1258	−	17.4561i	−0.539862	−	0.623034i
$786$	−4.97379	+	3.19646i	−0.177409	+	0.114014i
$787$	4.55658	+	5.25857i	0.162424	+	0.187448i	0.831128	−	0.556082i	$-0.187696\pi$
$787$	4.55658	+	5.25857i	0.162424	+	0.187448i	−0.668703	+	0.743529i	$0.733150\pi$
$788$	−3.01343	−	6.59849i	−0.107349	−	0.235061i
$789$	1.35336			0.0481808
$790$	0.0770233	−	0.535709i	0.00274036	−	0.0190597i
$791$	38.7316	+	44.6987i	1.37714	+	1.58930i
$792$	8.79986	−	10.1556i	0.312689	−	0.360863i
$793$	−2.63393	−	18.3194i	−0.0935337	−	0.650541i
$794$	−0.930951	−	6.47490i	−0.0330382	−	0.229786i
$795$	−1.95277	−	1.25497i	−0.0692578	−	0.0445093i
$796$	3.73852	+	26.0020i	0.132508	+	0.921615i
$797$	2.82770	−	6.19180i	0.100162	−	0.219325i	−0.852916	−	0.522048i	$-0.825168\pi$
$797$	2.82770	−	6.19180i	0.100162	−	0.219325i	0.953079	+	0.302723i	$0.0978956\pi$
$798$	2.99697	+	6.56246i	0.106092	+	0.232308i
$799$	−34.0831	+	21.9039i	−1.20577	+	0.774903i
$800$	1.00000			0.0353553
$801$	−7.25059	−	23.8224i	−0.256187	−	0.841724i
$802$	−24.5069			−0.865370
$803$	−63.7012	+	40.9382i	−2.24796	+	1.44468i
$804$	0.857308	+	1.87724i	0.0302349	+	0.0662053i
$805$	−6.38069	+	13.9718i	−0.224890	+	0.492440i
$806$	−3.07151	−	21.3628i	−0.108189	−	0.752473i
$807$	4.52254	+	2.90646i	0.159201	+	0.102312i
$808$	0.681113	+	4.73725i	0.0239615	+	0.166656i
$809$	7.21470	+	50.1794i	0.253655	+	1.76421i	0.575866	+	0.817544i	$0.304665\pi$
$809$	7.21470	+	50.1794i	0.253655	+	1.76421i	−0.322210	+	0.946668i	$0.604426\pi$
$810$	−3.85439	+	4.44820i	−0.135429	+	0.156294i
$811$	10.0778	+	11.6304i	0.353879	+	0.408398i	0.904580	−	0.426304i	$-0.140185\pi$
$811$	10.0778	+	11.6304i	0.353879	+	0.408398i	−0.550700	+	0.834703i	$0.685639\pi$
$812$	−3.41685	+	23.7647i	−0.119908	+	0.833978i
$813$	19.0638			0.668597
$814$	6.62186	+	14.4998i	0.232096	+	0.508219i
$815$	−7.26260	−	8.38148i	−0.254398	−	0.293591i
$816$	−3.80396	+	2.44465i	−0.133165	+	0.0855800i
$817$	12.6103	+	14.5531i	0.441179	+	0.509147i
$818$	−7.51714	−	4.83097i	−0.262831	−	0.168911i
$819$	−3.70584	+	25.7747i	−0.129493	+	0.900641i
$820$	5.10950	−	5.89668i	0.178432	−	0.205921i
$821$	24.1790	+	7.09960i	0.843853	+	0.247778i	0.674958	−	0.737856i	$-0.264162\pi$
$821$	24.1790	+	7.09960i	0.843853	+	0.247778i	0.168896	+	0.985634i	$0.445980\pi$
$822$	−11.2597	+	7.23616i	−0.392726	+	0.252390i
$823$	1.89685	+	4.15353i	0.0661201	+	0.144783i	0.939807	−	0.341706i	$-0.111005\pi$
$823$	1.89685	+	4.15353i	0.0661201	+	0.144783i	−0.873687	+	0.486489i	$0.838277\pi$
$824$	−0.152513	+	0.176010i	−0.00531306	+	0.00613159i
$825$	2.57130	−	1.65247i	0.0895211	−	0.0575317i
$826$	−43.5490	+	12.7871i	−1.51526	+	0.444921i
$827$	19.0106	+	12.2174i	0.661063	+	0.424840i	0.827694	−	0.561180i	$-0.189652\pi$
$827$	19.0106	+	12.2174i	0.661063	+	0.424840i	−0.166631	+	0.986019i	$0.553289\pi$
$828$	−9.61082	−	2.82199i	−0.333999	−	0.0980710i
$829$	−41.4926	−	12.1833i	−1.44110	−	0.423145i	−0.534511	−	0.845161i	$-0.679504\pi$
$829$	−41.4926	−	12.1833i	−1.44110	−	0.423145i	−0.906588	+	0.422017i	$0.861322\pi$
$830$	−1.52934	−	10.6368i	−0.0530841	−	0.369208i
$831$	6.74154	−	14.7619i	0.233862	−	0.512085i
$832$	1.59611	+	1.84200i	0.0553350	+	0.0638600i
$833$	67.8048	+	19.9093i	2.34930	+	0.689816i
$834$	2.93370	−	0.861413i	0.101586	−	0.0298283i
$835$	23.0282			0.796925
$836$	−14.5017	+	4.25807i	−0.501550	+	0.147269i
$837$	12.4550	+	27.2725i	0.430506	+	0.942677i
$838$	19.1950			0.663079
$839$	−3.91498	+	27.2293i	−0.135160	+	0.940059i	0.803522	+	0.595275i	$0.202957\pi$
$839$	−3.91498	+	27.2293i	−0.135160	+	0.940059i	−0.938682	+	0.344784i	$0.887952\pi$
$840$	−1.59137	+	1.83654i	−0.0549076	+	0.0633667i
$841$	−5.93471	+	1.74259i	−0.204645	+	0.0600893i
$842$	−7.01129	+	15.3526i	−0.241625	+	0.529085i
$843$	2.18054	−	4.77472i	0.0751018	−	0.164450i
$844$	−0.150221	+	1.04481i	−0.00517082	+	0.0359639i
$845$	−5.93881	−	3.81664i	−0.204301	−	0.131296i
$846$	−11.9450	−	7.67659i	−0.410678	−	0.263927i
$847$	−8.59305	+	59.7660i	−0.295261	+	2.05358i
$848$	−1.60613	+	3.51693i	−0.0551546	+	0.120772i
$849$	4.91875	−	10.7706i	0.168811	−	0.369645i
$850$	7.22642	−	2.12187i	0.247864	−	0.0727795i
$851$	7.78106	−	8.97982i	0.266731	−	0.307824i
$852$	0.563511	−	3.91930i	0.0193056	−	0.134273i
$853$	13.8586			0.474509			0.237255	−	0.971447i	$-0.423752\pi$
$853$	13.8586			0.474509			0.237255	+	0.971447i	$0.423752\pi$
$854$	−12.7679	−	27.9578i	−0.436909	−	0.956697i
$855$	7.51880	−	2.20772i	0.257137	−	0.0755023i
$856$	−16.8020			−0.574281
$857$	−47.9571	+	14.0815i	−1.63818	+	0.481014i	−0.965822	−	0.259207i	$-0.916539\pi$
$857$	−47.9571	+	14.0815i	−1.63818	+	0.481014i	−0.672363	+	0.740222i	$0.734721\pi$
$858$	7.14792	+	2.09882i	0.244026	+	0.0716525i
$859$	27.9224	+	32.2242i	0.952701	+	1.09948i	0.994950	+	0.100368i	$0.0320021\pi$
$859$	27.9224	+	32.2242i	0.952701	+	1.09948i	−0.0422497	+	0.999107i	$0.513452\pi$
$860$	−2.69452	+	5.90017i	−0.0918822	+	0.201194i
$861$	2.69838	+	18.7676i	0.0919605	+	0.639599i
$862$	13.2651	+	3.89498i	0.451810	+	0.132663i
$863$	−55.2245	−	16.2154i	−1.87987	−	0.551978i	−0.996530	−	0.0832366i	$-0.973474\pi$
$863$	−55.2245	−	16.2154i	−1.87987	−	0.551978i	−0.883335	−	0.468742i	$-0.844708\pi$
$864$	−2.84838	−	1.83054i	−0.0969039	−	0.0622763i
$865$	15.3853	−	4.51753i	0.523116	−	0.153601i
$866$	20.6239	−	13.2542i	0.700830	−	0.450396i
$867$	−15.6179	+	18.0240i	−0.530412	+	0.612128i
$868$	−14.8890	−	32.6024i	−0.505367	−	1.10660i
$869$	−2.31791	+	1.48963i	−0.0786297	+	0.0505323i
$870$	−3.41704	−	1.00333i	−0.115848	−	0.0340161i
$871$	5.48642	−	6.33167i	0.185900	−	0.214540i
$872$	0.557220	−	3.87555i	0.0188698	−	0.131243i
$873$	30.3593	+	19.5107i	1.02751	+	0.660338i
$874$	7.37763	+	8.51424i	0.249552	+	0.287999i
$875$	3.40504	−	2.18829i	0.115111	−	0.0739776i
$876$	5.84788	+	6.74881i	0.197582	+	0.228021i
$877$	5.35050	+	11.7160i	0.180673	+	0.395620i	0.978200	−	0.207664i	$-0.0665860\pi$
$877$	5.35050	+	11.7160i	0.180673	+	0.395620i	−0.797527	+	0.603283i	$0.793859\pi$
$878$	−3.20995			−0.108331
$879$	2.39938	−	16.6881i	0.0809291	−	0.562874i
$880$	−3.33386	−	3.84748i	−0.112384	−	0.129698i
$881$	5.75670	−	6.64358i	0.193948	−	0.223828i	−0.650443	−	0.759555i	$-0.725417\pi$
$881$	5.75670	−	6.64358i	0.193948	−	0.223828i	0.844391	+	0.535727i	$0.179962\pi$
$882$	3.52465	+	24.5145i	0.118681	+	0.825446i
$883$	0.516695	+	3.59369i	0.0173882	+	0.120937i	0.996667	−	0.0815804i	$-0.0259967\pi$
$883$	0.516695	+	3.59369i	0.0173882	+	0.120937i	−0.979279	+	0.202518i	$0.935088\pi$
$884$	15.4426	+	9.92436i	0.519391	+	0.333792i
$885$	−0.958116	−	6.66384i	−0.0322067	−	0.224003i
$886$	8.41209	−	18.4199i	0.282610	−	0.618829i
$887$	19.2947	+	42.2495i	0.647852	+	1.41860i	0.893422	+	0.449219i	$0.148298\pi$
$887$	19.2947	+	42.2495i	0.647852	+	1.41860i	−0.245569	+	0.969379i	$0.578975\pi$
$888$	1.58144	−	1.01633i	0.0530698	−	0.0341059i
$889$	17.0493			0.571815
$890$	−9.32428	+	1.43453i	−0.312550	+	0.0480856i
$891$	29.9643			1.00384
$892$	5.77312	−	3.71016i	0.193298	−	0.124225i
$893$	6.63424	+	14.5269i	0.222006	+	0.486126i
$894$	−0.308513	+	0.675549i	−0.0103182	+	0.0225937i
$895$	−0.565700	−	3.93453i	−0.0189093	−	0.131517i
$896$	3.40504	+	2.18829i	0.113754	+	0.0731055i
$897$	−0.790279	−	5.49651i	−0.0263866	−	0.183523i
$898$	0.590085	+	4.10413i	0.0196914	+	0.136957i
$899$	34.3968	−	39.6960i	1.14720	−	1.32394i
$900$	1.72853	+	1.99483i	0.0576177	+	0.0664944i
$901$	−4.14409	+	28.8228i	−0.138060	+	0.960226i
$902$	−39.7217			−1.32259
$903$	−6.54792	−	14.3380i	−0.217901	−	0.477137i
$904$	9.56908	+	11.0433i	0.318263	+	0.367295i
$905$	14.0927	−	9.05681i	0.468456	−	0.301058i
$906$	1.43943	+	1.66119i	0.0478218	+	0.0551892i
$907$	15.4187	+	9.90899i	0.511969	+	0.329023i	0.770988	−	0.636850i	$-0.219763\pi$
$907$	15.4187	+	9.90899i	0.511969	+	0.329023i	−0.259019	+	0.965872i	$0.583399\pi$
$908$	1.33655	−	9.29590i	0.0443549	−	0.308495i
$909$	−8.27269	+	9.54720i	−0.274388	+	0.316660i
$910$	9.46564	+	2.77936i	0.313783	+	0.0921349i
$911$	18.4293	−	11.8438i	0.610589	−	0.392402i	−0.198489	−	0.980103i	$-0.563603\pi$
$911$	18.4293	−	11.8438i	0.610589	−	0.392402i	0.809078	+	0.587701i	$0.199967\pi$
$912$	0.740436	+	1.62133i	0.0245183	+	0.0536875i
$913$	−35.8261	+	41.3456i	−1.18567	+	1.36834i
$914$	−22.8102	+	14.6592i	−0.754495	+	0.484884i
$915$	4.37433	−	1.28442i	0.144611	−	0.0424616i
$916$	0.926015	+	0.595114i	0.0305964	+	0.0196631i
$917$	38.2446	+	11.2296i	1.26295	+	0.370835i
$918$	−24.4678	−	7.18438i	−0.807556	−	0.237120i
$919$	6.15160	+	42.7853i	0.202922	+	1.41136i	0.795554	+	0.605883i	$0.207180\pi$
$919$	6.15160	+	42.7853i	0.202922	+	1.41136i	−0.592631	+	0.805474i	$0.701911\pi$
$920$	−1.57642	+	3.45188i	−0.0519731	+	0.113805i
$921$	−5.57001	−	6.42814i	−0.183538	−	0.211814i
$922$	−20.4786	−	6.01306i	−0.674426	−	0.198029i
$923$	−15.4234	+	4.52871i	−0.507666	+	0.149064i
$924$	12.3715			0.406991
$925$	−3.00429	+	0.882138i	−0.0987803	+	0.0290045i
$926$	3.91812	+	8.57949i	0.128757	+	0.281940i
$927$	−0.614735			−0.0201905
$928$	−0.844171	+	5.87134i	−0.0277113	+	0.192736i
$929$	8.10085	−	9.34888i	0.265780	−	0.306727i	−0.607135	−	0.794599i	$-0.707681\pi$
$929$	8.10085	−	9.34888i	0.265780	−	0.306727i	0.872915	+	0.487872i	$0.162227\pi$
$930$	5.10103	−	1.49780i	0.167269	−	0.0491147i
$931$	11.5717	−	25.3385i	0.379248	−	0.830436i
$932$	−5.34309	+	11.6997i	−0.175019	+	0.383237i
$933$	−0.245076	+	1.70454i	−0.00802342	+	0.0558041i
$934$	−14.5372	−	9.34246i	−0.475670	−	0.305695i
$935$	−32.2557	−	20.7295i	−1.05487	−	0.677926i
$936$	−0.915569	+	6.36793i	−0.0299263	+	0.208142i
$937$	−8.09502	+	17.7256i	−0.264453	+	0.579071i	−0.994549	−	0.104274i	$-0.966748\pi$
$937$	−8.09502	+	17.7256i	−0.264453	+	0.579071i	0.730096	+	0.683345i	$0.239475\pi$
$938$	5.77970	−	12.6558i	0.188714	−	0.413226i
$939$	14.4702	−	4.24882i	0.472216	−	0.138655i
$940$	−3.52273	+	4.06545i	−0.114899	+	0.132600i
$941$	7.47560	−	51.9940i	0.243698	−	1.69495i	−0.389550	−	0.921005i	$-0.627369\pi$
$941$	7.47560	−	51.9940i	0.243698	−	1.69495i	0.633247	−	0.773949i	$-0.281722\pi$
$942$	13.8674			0.451825
$943$	12.2999	+	26.9331i	0.400540	+	0.877061i
$944$	−10.7593	+	3.15920i	−0.350184	+	0.102823i
$945$	−13.7046			−0.445811
$946$	31.6839	−	9.30323i	1.03013	−	0.302474i
$947$	45.1229	+	13.2493i	1.46630	+	0.430544i	0.914894	−	0.403694i	$-0.132274\pi$
$947$	45.1229	+	13.2493i	1.46630	+	0.430544i	0.551404	+	0.834238i	$0.314092\pi$
$948$	0.212788	+	0.245571i	0.00691105	+	0.00797577i
$949$	15.0597	−	32.9762i	0.488859	−	1.07045i
$950$	−0.422501	−	2.93856i	−0.0137078	−	0.0953395i
$951$	11.5397	+	3.38836i	0.374201	+	0.109875i
$952$	29.2495	+	8.58843i	0.947982	+	0.278353i
$953$	10.1662	+	6.53342i	0.329316	+	0.211638i	0.694842	−	0.719163i	$-0.255474\pi$
$953$	10.1662	+	6.53342i	0.329316	+	0.211638i	−0.365526	+	0.930801i	$0.619111\pi$
$954$	−9.79193	+	2.87517i	−0.317025	+	0.0930871i
$955$	−0.754656	+	0.484988i	−0.0244201	+	0.0156938i
$956$	0.0172016	−	0.0198517i	0.000556338	−	0.000642049i
$957$	7.53161	+	16.4919i	0.243462	+	0.533108i
$958$	−26.7422	+	17.1862i	−0.864001	+	0.555260i
$959$	86.5783	+	25.4217i	2.79576	+	0.820909i
$960$	−0.393166	+	0.453738i	−0.0126894	+	0.0146443i
$961$	−6.74730	+	46.9285i	−0.217655	+	1.51382i
$962$	−6.42006	−	4.12592i	−0.206991	−	0.133025i
$963$	−29.0428	−	33.5172i	−0.935892	−	1.08008i
$964$	−4.07697	+	2.62011i	−0.131310	+	0.0843880i
$965$	4.90875	+	5.66500i	0.158018	+	0.182363i
$966$	−3.83085	−	8.38839i	−0.123256	−	0.269892i
$967$	13.2284			0.425397			0.212699	−	0.977118i	$-0.431775\pi$
$967$	13.2284			0.425397			0.212699	+	0.977118i	$0.431775\pi$
$968$	−2.12301	+	14.7659i	−0.0682361	+	0.474592i
$969$	8.79094	+	10.1453i	0.282406	+	0.325914i
$970$	8.95334	−	10.3327i	0.287474	−	0.331763i
$971$	−2.28842	−	15.9163i	−0.0734388	−	0.510778i	−0.993026	−	0.117893i	$-0.962386\pi$
$971$	−2.28842	−	15.9163i	−0.0734388	−	0.510778i	0.919588	−	0.392885i	$-0.128523\pi$
$972$	−1.94848	−	13.5520i	−0.0624976	−	0.434681i
$973$	−17.3408	−	11.1443i	−0.555921	−	0.357269i
$974$	−2.83538	−	19.7205i	−0.0908516	−	0.631886i
$975$	−0.607886	+	1.33108i	−0.0194679	+	0.0426288i
$976$	−3.15446	−	6.90729i	−0.100972	−	0.221097i
$977$	0.175175	−	0.112578i	0.00560435	−	0.00360170i	−0.537836	−	0.843050i	$-0.680758\pi$
$977$	0.175175	−	0.112578i	0.00560435	−	0.00360170i	0.543440	+	0.839448i	$0.317122\pi$
$978$	6.65841			0.212912
$979$	36.6051	+	31.0924i	1.16991	+	0.993718i
$980$	9.38291			0.299726
$981$	8.69425	−	5.58745i	0.277586	−	0.178394i
$982$	−12.0191	−	26.3182i	−0.383546	−	0.839848i
$983$	7.03248	−	15.3990i	0.224301	−	0.491152i	−0.763705	−	0.645566i	$-0.776622\pi$
$983$	7.03248	−	15.3990i	0.224301	−	0.491152i	0.988006	+	0.154414i	$0.0493490\pi$
$984$	0.666664	+	4.63675i	0.0212525	+	0.147814i
$985$	−6.10247	−	3.92182i	−0.194441	−	0.124960i
$986$	6.35787	+	44.2200i	0.202476	+	1.40825i
$987$	−1.86039	−	12.9393i	−0.0592168	−	0.411862i
$988$	4.73848	−	5.46850i	0.150751	−	0.173976i
$989$	−16.1190	−	18.6023i	−0.512554	−	0.591519i
$990$	1.91239	−	13.3010i	0.0607798	−	0.422733i
$991$	−19.7094			−0.626090			−0.313045	−	0.949738i	$-0.601349\pi$
$991$	−19.7094			−0.626090			−0.313045	+	0.949738i	$0.601349\pi$
$992$	−3.67850	−	8.05480i	−0.116793	−	0.255740i
$993$	8.04550	+	9.28501i	0.255316	+	0.294651i
$994$	−22.4568	+	14.4321i	−0.712285	+	0.457758i
$995$	17.2028	+	19.8530i	0.545364	+	0.629384i
$996$	5.42759	+	3.48810i	0.171980	+	0.110525i
$997$	6.09680	−	42.4042i	0.193088	−	1.34295i	−0.630687	−	0.776037i	$-0.717227\pi$
$997$	6.09680	−	42.4042i	0.193088	−	1.34295i	0.823775	−	0.566917i	$-0.191864\pi$
$998$	−16.0086	+	18.4749i	−0.506742	+	0.584812i
$999$	10.1721	+	2.98681i	0.321832	+	0.0944985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	890.2.o.a.271.3	✓	60
89.67	even	11	inner	890.2.o.a.601.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
890.2.o.a.271.3	✓	60	1.1	even	1	trivial
890.2.o.a.601.3	yes	60	89.67	even	11	inner

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:	\( N \)	\(=\)	\( 890 = 2 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	890.o (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.249407 + 0.546126i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.505073 + 0.324591i) q^{6} +(-0.576031 - 4.00638i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(1.72853 - 1.99483i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.724517 + 5.03912i) q^{11} +0.600381 q^{12} +(-1.01250 - 2.21706i) q^{13} +(-2.65060 - 3.05896i) q^{14} +(0.505073 - 0.324591i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-6.33590 - 4.07183i) q^{17} +(0.375646 - 2.61268i) q^{18} +(-1.94414 + 2.24365i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(2.04432 - 1.31381i) q^{21} +(2.11485 + 4.63088i) q^{22} +(2.48507 - 2.86793i) q^{23} +(0.505073 - 0.324591i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-2.05040 - 1.31771i) q^{26} +(3.24872 + 0.953912i) q^{27} +(-3.88363 - 1.14034i) q^{28} +(-0.844171 - 5.87134i) q^{29} +(0.249407 - 0.546126i) q^{30} +(5.79879 + 6.69217i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-2.93270 + 0.861118i) q^{33} -7.53150 q^{34} +(-3.88363 + 1.14034i) q^{35} +(-1.09651 - 2.40101i) q^{36} +3.13112 q^{37} +(-0.422501 + 2.93856i) q^{38} +(0.958272 - 1.10590i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(-3.24125 + 7.09734i) q^{41} +(1.00950 - 2.21049i) q^{42} +(0.923100 - 6.42030i) q^{43} +(4.28277 + 2.75237i) q^{44} +(-2.22052 - 1.42704i) q^{45} +(0.540058 - 3.75619i) q^{46} +(2.23467 - 4.89324i) q^{47} +(0.249407 - 0.546126i) q^{48} +(-9.00284 + 2.64347i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(0.643515 - 4.47575i) q^{51} -2.43732 q^{52} +(-1.60613 - 3.51693i) q^{53} +(3.24872 - 0.953912i) q^{54} +5.09094 q^{55} +(-3.88363 + 1.14034i) q^{56} +(-1.71020 - 0.502160i) q^{57} +(-3.88445 - 4.48289i) q^{58} +(4.65825 - 10.2001i) q^{59} +(-0.0854432 - 0.594270i) q^{60} +(7.28591 + 2.13934i) q^{61} +(8.49631 + 2.49474i) q^{62} +(-8.98775 - 5.77608i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-2.05040 + 1.31771i) q^{65} +(-2.00159 + 2.30995i) q^{66} +(1.42794 + 3.12675i) q^{67} +(-6.33590 + 4.07183i) q^{68} +(2.18605 + 0.641881i) q^{69} +(-2.65060 + 3.05896i) q^{70} +(0.938588 - 6.52802i) q^{71} +(-2.22052 - 1.42704i) q^{72} +(9.74027 + 11.2409i) q^{73} +(2.63406 - 1.69281i) q^{74} +(-0.393166 - 0.453738i) q^{75} +(1.23328 + 2.70050i) q^{76} +20.6060 q^{77} +(0.208252 - 1.44843i) q^{78} +(0.354422 + 0.409025i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(-0.837638 - 5.82590i) q^{81} +(1.11040 + 7.72301i) q^{82} +(9.04024 + 5.80981i) q^{83} +(-0.345838 - 2.40536i) q^{84} +(-3.12870 + 6.85089i) q^{85} +(-2.69452 - 5.90017i) q^{86} +(2.99595 - 1.92538i) q^{87} +5.09094 q^{88} +(5.02196 - 7.98624i) q^{89} -2.63954 q^{90} +(-8.29918 + 5.33356i) q^{91} +(-1.57642 - 3.45188i) q^{92} +(-2.20850 + 4.83595i) q^{93} +(-0.765563 - 5.32461i) q^{94} +(2.49750 + 1.60504i) q^{95} +(-0.0854432 - 0.594270i) q^{96} +(1.94575 + 13.5330i) q^{97} +(-6.14450 + 7.09113i) q^{98} +(8.79986 + 10.1556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} - 30 q^{13} + 6 q^{14} + 4 q^{15} - 6 q^{16} - 10 q^{17} + 6 q^{18} + 7 q^{19} - 6 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 60 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 - 30 * q^13 + 6 * q^14 + 4 * q^15 - 6 * q^16 - 10 * q^17 + 6 * q^18 + 7 * q^19 - 6 * q^20 - 8 * q^21 + 16 * q^22 - 9 * q^23 + 4 * q^24 - 6 * q^25 + 3 * q^26 + 13 * q^27 - 16 * q^28 + q^29 + 4 * q^30 - 10 * q^31 - 6 * q^32 - 10 * q^33 - 54 * q^34 - 16 * q^35 - 16 * q^36 - 4 * q^37 - 26 * q^38 + 11 * q^39 - 6 * q^40 + 30 * q^41 - 19 * q^42 + 34 * q^43 - 6 * q^44 - 5 * q^45 + 13 * q^46 + 38 * q^47 + 4 * q^48 + 14 * q^49 - 6 * q^50 - 6 * q^51 + 14 * q^52 + 38 * q^53 + 13 * q^54 - 28 * q^55 - 16 * q^56 + 54 * q^57 - 10 * q^58 + 16 * q^59 - 7 * q^60 + 7 * q^61 + 34 * q^62 - 77 * q^63 - 6 * q^64 + 3 * q^65 + 12 * q^66 - 4 * q^67 - 10 * q^68 + 12 * q^69 + 6 * q^70 + 17 * q^71 - 5 * q^72 + 25 * q^73 + 18 * q^74 + 4 * q^75 - 15 * q^76 - 46 * q^77 + 11 * q^78 + 85 * q^79 - 6 * q^80 + 18 * q^81 - 14 * q^82 + 9 * q^83 + 3 * q^84 + 12 * q^85 + 12 * q^86 - 31 * q^87 - 28 * q^88 - 37 * q^89 + 28 * q^90 + 16 * q^91 + 2 * q^92 - 85 * q^93 + 16 * q^94 + 7 * q^95 - 7 * q^96 - 77 * q^97 + 14 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more