LMFDB - Embedded newform 429.2.j.a.122.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.3
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84950 - 1.84950i) q^{2} +(-1.73089 - 0.0633404i) q^{3} +4.84133i q^{4} +(2.48780 + 2.48780i) q^{5} +(3.08414 + 3.31844i) q^{6} +(-2.91775 - 2.91775i) q^{7} +(5.25505 - 5.25505i) q^{8} +(2.99198 + 0.219271i) q^{9} +O(q^{10})$	\(q+(-1.84950 - 1.84950i) q^{2} +(-1.73089 - 0.0633404i) q^{3} +4.84133i q^{4} +(2.48780 + 2.48780i) q^{5} +(3.08414 + 3.31844i) q^{6} +(-2.91775 - 2.91775i) q^{7} +(5.25505 - 5.25505i) q^{8} +(2.99198 + 0.219271i) q^{9} -9.20239i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.306652 - 8.37982i) q^{12} +(-3.37519 + 1.26812i) q^{13} +10.7928i q^{14} +(-4.14853 - 4.46369i) q^{15} -9.75582 q^{16} +2.42581 q^{17} +(-5.12813 - 5.93921i) q^{18} +(-2.47137 + 2.47137i) q^{19} +(-12.0443 + 12.0443i) q^{20} +(4.86549 + 5.23512i) q^{21} -2.61559 q^{22} -3.76979 q^{23} +(-9.42879 + 8.76307i) q^{24} +7.37828i q^{25} +(8.58781 + 3.89703i) q^{26} +(-5.16490 - 0.569047i) q^{27} +(14.1258 - 14.1258i) q^{28} +1.90780i q^{29} +(-0.582883 + 15.9283i) q^{30} +(-1.28575 + 1.28575i) q^{31} +(7.53332 + 7.53332i) q^{32} +(-1.26871 + 1.17914i) q^{33} +(-4.48654 - 4.48654i) q^{34} -14.5175i q^{35} +(-1.06156 + 14.4851i) q^{36} +(-5.53463 - 5.53463i) q^{37} +9.14163 q^{38} +(5.92241 - 1.98119i) q^{39} +26.1470 q^{40} +(-0.696716 - 0.696716i) q^{41} +(0.683618 - 18.6811i) q^{42} +8.91072i q^{43} +(3.42334 + 3.42334i) q^{44} +(6.89793 + 7.98894i) q^{45} +(6.97225 + 6.97225i) q^{46} +(-2.35138 + 2.35138i) q^{47} +(16.8863 + 0.617938i) q^{48} +10.0265i q^{49} +(13.6462 - 13.6462i) q^{50} +(-4.19881 - 0.153652i) q^{51} +(-6.13937 - 16.3404i) q^{52} +13.6591i q^{53} +(8.50005 + 10.6050i) q^{54} +3.51828 q^{55} -30.6658 q^{56} +(4.43422 - 4.12114i) q^{57} +(3.52849 - 3.52849i) q^{58} +(-0.0963120 + 0.0963120i) q^{59} +(21.6102 - 20.0844i) q^{60} -2.90103 q^{61} +4.75599 q^{62} +(-8.09005 - 9.36960i) q^{63} -8.35419i q^{64} +(-11.5516 - 5.24197i) q^{65} +(4.52731 + 0.165673i) q^{66} +(-6.45845 + 6.45845i) q^{67} +11.7441i q^{68} +(6.52511 + 0.238780i) q^{69} +(-26.8502 + 26.8502i) q^{70} +(-2.49321 - 2.49321i) q^{71} +(16.8753 - 14.5707i) q^{72} +(-4.61531 - 4.61531i) q^{73} +20.4726i q^{74} +(0.467344 - 12.7710i) q^{75} +(-11.9647 - 11.9647i) q^{76} -4.12632 q^{77} +(-14.6177 - 7.28930i) q^{78} -11.0517 q^{79} +(-24.2705 - 24.2705i) q^{80} +(8.90384 + 1.31211i) q^{81} +2.57716i q^{82} +(6.77757 + 6.77757i) q^{83} +(-25.3449 + 23.5555i) q^{84} +(6.03492 + 6.03492i) q^{85} +(16.4804 - 16.4804i) q^{86} +(0.120841 - 3.30220i) q^{87} -7.43177i q^{88} +(-4.21431 + 4.21431i) q^{89} +(2.01782 - 27.5333i) q^{90} +(13.5480 + 6.14790i) q^{91} -18.2508i q^{92} +(2.30693 - 2.14405i) q^{93} +8.69778 q^{94} -12.2966 q^{95} +(-12.5622 - 13.5165i) q^{96} +(7.53673 - 7.53673i) q^{97} +(18.5440 - 18.5440i) q^{98} +(2.27069 - 1.96060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.84950	−	1.84950i	−1.30780	−	1.30780i	−0.923002	−	0.384795i	$-0.874272\pi$
$2$	−1.84950	−	1.84950i	−1.30780	−	1.30780i	−0.384795	−	0.923002i	$-0.625728\pi$
$3$	−1.73089	−	0.0633404i	−0.999331	−	0.0365696i
$3$	−1.73089	−	0.0633404i	−0.999331	−	0.0365696i
$4$			4.84133i			2.42067i
$5$	2.48780	+	2.48780i	1.11258	+	1.11258i	0.992801	+	0.119777i	$0.0382178\pi$
$5$	2.48780	+	2.48780i	1.11258	+	1.11258i	0.119777	+	0.992801i	$0.461782\pi$
$6$	3.08414	+	3.31844i	1.25910	+	1.35475i
$7$	−2.91775	−	2.91775i	−1.10280	−	1.10280i	−0.994071	−	0.108733i	$-0.965321\pi$
$7$	−2.91775	−	2.91775i	−1.10280	−	1.10280i	−0.108733	−	0.994071i	$-0.534679\pi$
$8$	5.25505	−	5.25505i	1.85794	−	1.85794i
$9$	2.99198	+	0.219271i	0.997325	+	0.0730903i
$10$		−	9.20239i		−	2.91005i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	0.306652	−	8.37982i	0.0885228	−	2.41905i
$13$	−3.37519	+	1.26812i	−0.936108	+	0.351712i
$13$	−3.37519	+	1.26812i	−0.936108	+	0.351712i
$14$			10.7928i			2.88449i
$15$	−4.14853	−	4.46369i	−1.07115	−	1.15252i
$16$	−9.75582			−2.43895
$17$	2.42581			0.588345			0.294173	−	0.955752i	$-0.404956\pi$
$17$	2.42581			0.588345			0.294173	+	0.955752i	$0.404956\pi$
$18$	−5.12813	−	5.93921i	−1.20871	−	1.39989i
$19$	−2.47137	+	2.47137i	−0.566972	+	0.566972i	−0.931279	−	0.364307i	$-0.881306\pi$
$19$	−2.47137	+	2.47137i	−0.566972	+	0.566972i	0.364307	+	0.931279i	$0.381306\pi$
$20$	−12.0443	+	12.0443i	−2.69318	+	2.69318i
$21$	4.86549	+	5.23512i	1.06174	+	1.14240i
$22$	−2.61559			−0.557646
$23$	−3.76979			−0.786056			−0.393028	−	0.919526i	$-0.628572\pi$
$23$	−3.76979			−0.786056			−0.393028	+	0.919526i	$0.628572\pi$
$24$	−9.42879	+	8.76307i	−1.92464	+	1.78875i
$25$			7.37828i			1.47566i
$26$	8.58781	+	3.89703i	1.68421	+	0.764271i
$27$	−5.16490	−	0.569047i	−0.993985	−	0.109513i
$28$	14.1258	−	14.1258i	2.66952	−	2.66952i
$29$			1.90780i			0.354270i	0.984187	+	0.177135i	$0.0566830\pi$
$29$			1.90780i			0.354270i	−0.984187	+	0.177135i	$0.943317\pi$
$30$	−0.582883	+	15.9283i	−0.106419	+	2.90810i
$31$	−1.28575	+	1.28575i	−0.230927	+	0.230927i	−0.813080	−	0.582153i	$-0.802211\pi$
$31$	−1.28575	+	1.28575i	−0.230927	+	0.230927i	0.582153	+	0.813080i	$0.302211\pi$
$32$	7.53332	+	7.53332i	1.33172	+	1.33172i
$33$	−1.26871	+	1.17914i	−0.220855	+	0.205261i
$34$	−4.48654	−	4.48654i	−0.769436	−	0.769436i
$35$		−	14.5175i		−	2.45391i
$36$	−1.06156	+	14.4851i	−0.176927	+	2.41419i
$37$	−5.53463	−	5.53463i	−0.909888	−	0.909888i	0.0863749	−	0.996263i	$-0.472472\pi$
$37$	−5.53463	−	5.53463i	−0.909888	−	0.909888i	−0.996263	+	0.0863749i	$0.972472\pi$
$38$	9.14163			1.48297
$39$	5.92241	−	1.98119i	0.948344	−	0.317244i
$40$	26.1470			4.13421
$41$	−0.696716	−	0.696716i	−0.108809	−	0.108809i	0.650606	−	0.759415i	$-0.274515\pi$
$41$	−0.696716	−	0.696716i	−0.108809	−	0.108809i	−0.759415	+	0.650606i	$0.774515\pi$
$42$	0.683618	−	18.6811i	0.105485	−	2.88256i
$43$			8.91072i			1.35887i	0.733734	+	0.679436i	$0.237776\pi$
$43$			8.91072i			1.35887i	−0.733734	+	0.679436i	$0.762224\pi$
$44$	3.42334	+	3.42334i	0.516088	+	0.516088i
$45$	6.89793	+	7.98894i	1.02828	+	1.19092i
$46$	6.97225	+	6.97225i	1.02800	+	1.02800i
$47$	−2.35138	+	2.35138i	−0.342984	+	0.342984i	−0.857488	−	0.514504i	$-0.827976\pi$
$47$	−2.35138	+	2.35138i	−0.342984	+	0.342984i	0.514504	+	0.857488i	$0.327976\pi$
$48$	16.8863	+	0.617938i	2.43732	+	0.0891916i
$49$			10.0265i			1.43236i
$50$	13.6462	−	13.6462i	1.92986	−	1.92986i
$51$	−4.19881	−	0.153652i	−0.587951	−	0.0215155i
$52$	−6.13937	−	16.3404i	−0.851377	−	2.26600i
$53$			13.6591i			1.87622i	0.346334	+	0.938111i	$0.387426\pi$
$53$			13.6591i			1.87622i	−0.346334	+	0.938111i	$0.612574\pi$
$54$	8.50005	+	10.6050i	1.15671	+	1.44315i
$55$	3.51828			0.474405
$56$	−30.6658			−4.09789
$57$	4.43422	−	4.12114i	0.587327	−	0.545859i
$58$	3.52849	−	3.52849i	0.463313	−	0.463313i
$59$	−0.0963120	+	0.0963120i	−0.0125388	+	0.0125388i	−0.713348	−	0.700810i	$-0.752822\pi$
$59$	−0.0963120	+	0.0963120i	−0.0125388	+	0.0125388i	0.700810	+	0.713348i	$0.252822\pi$
$60$	21.6102	−	20.0844i	2.78986	−	2.59289i
$61$	−2.90103			−0.371439			−0.185720	−	0.982603i	$-0.559462\pi$
$61$	−2.90103			−0.371439			−0.185720	+	0.982603i	$0.559462\pi$
$62$	4.75599			0.604011
$63$	−8.09005	−	9.36960i	−1.01925	−	1.18046i
$64$		−	8.35419i		−	1.04427i
$65$	−11.5516	−	5.24197i	−1.43280	−	0.650186i
$66$	4.52731	+	0.165673i	0.557273	+	0.0203929i
$67$	−6.45845	+	6.45845i	−0.789025	+	0.789025i	−0.981334	−	0.192309i	$-0.938402\pi$
$67$	−6.45845	+	6.45845i	−0.789025	+	0.789025i	0.192309	+	0.981334i	$0.438402\pi$
$68$			11.7441i			1.42419i
$69$	6.52511	+	0.238780i	0.785530	+	0.0287458i
$70$	−26.8502	+	26.8502i	−3.20922	+	3.20922i
$71$	−2.49321	−	2.49321i	−0.295890	−	0.295890i	0.543512	−	0.839402i	$-0.317094\pi$
$71$	−2.49321	−	2.49321i	−0.295890	−	0.295890i	−0.839402	+	0.543512i	$0.817094\pi$
$72$	16.8753	−	14.5707i	1.98877	−	1.71717i
$73$	−4.61531	−	4.61531i	−0.540181	−	0.540181i	0.383401	−	0.923582i	$-0.374753\pi$
$73$	−4.61531	−	4.61531i	−0.540181	−	0.540181i	−0.923582	+	0.383401i	$0.874753\pi$
$74$			20.4726i			2.37990i
$75$	0.467344	−	12.7710i	0.0539642	−	1.47467i
$76$	−11.9647	−	11.9647i	−1.37245	−	1.37245i
$77$	−4.12632			−0.470237
$78$	−14.6177	−	7.28930i	−1.65513	−	0.825351i
$79$	−11.0517			−1.24341			−0.621707	−	0.783250i	$-0.713561\pi$
$79$	−11.0517			−1.24341			−0.621707	+	0.783250i	$0.713561\pi$
$80$	−24.2705	−	24.2705i	−2.71353	−	2.71353i
$81$	8.90384	+	1.31211i	0.989316	+	0.145790i
$82$			2.57716i			0.284600i
$83$	6.77757	+	6.77757i	0.743935	+	0.743935i	0.973333	−	0.229398i	$-0.0736757\pi$
$83$	6.77757	+	6.77757i	0.743935	+	0.743935i	−0.229398	+	0.973333i	$0.573676\pi$
$84$	−25.3449	+	23.5555i	−2.76536	+	2.57011i
$85$	6.03492	+	6.03492i	0.654579	+	0.654579i
$86$	16.4804	−	16.4804i	1.77713	−	1.77713i
$87$	0.120841	−	3.30220i	0.0129555	−	0.354033i
$88$		−	7.43177i		−	0.792229i
$89$	−4.21431	+	4.21431i	−0.446716	+	0.446716i	−0.894261	−	0.447545i	$-0.852298\pi$
$89$	−4.21431	+	4.21431i	−0.446716	+	0.446716i	0.447545	+	0.894261i	$0.352298\pi$
$90$	2.01782	−	27.5333i	0.212696	−	2.90227i
$91$	13.5480	+	6.14790i	1.42021	+	0.644475i
$92$		−	18.2508i		−	1.90278i
$93$	2.30693	−	2.14405i	0.239217	−	0.222328i
$94$	8.69778			0.897108
$95$	−12.2966			−1.26160
$96$	−12.5622	−	13.5165i	−1.28212	−	1.37953i
$97$	7.53673	−	7.53673i	0.765239	−	0.765239i	−0.212025	−	0.977264i	$-0.568006\pi$
$97$	7.53673	−	7.53673i	0.765239	−	0.765239i	0.977264	+	0.212025i	$0.0680058\pi$
$98$	18.5440	−	18.5440i	1.87323	−	1.87323i
$99$	2.27069	−	1.96060i	0.228213	−	0.197048i
$100$	−35.7207			−3.57207
$101$	−15.3211			−1.52450			−0.762251	−	0.647281i	$-0.775906\pi$
$101$	−15.3211			−1.52450			−0.762251	+	0.647281i	$0.775906\pi$
$102$	7.48154	+	8.04990i	0.740783	+	0.797059i
$103$			3.50034i			0.344899i	0.985018	+	0.172449i	$0.0551681\pi$
$103$			3.50034i			0.344899i	−0.985018	+	0.172449i	$0.944832\pi$
$104$	−11.0728	+	24.4008i	−1.08577	+	2.39269i
$105$	−0.919546	+	25.1283i	−0.0897385	+	2.45227i
$106$	25.2626	−	25.2626i	2.45372	−	2.45372i
$107$			6.65207i			0.643080i	0.946896	+	0.321540i	$0.104200\pi$
$107$			6.65207i			0.643080i	−0.946896	+	0.321540i	$0.895800\pi$
$108$	2.75495	−	25.0050i	0.265095	−	2.40611i
$109$	−3.59949	+	3.59949i	−0.344769	+	0.344769i	−0.858157	−	0.513388i	$-0.828390\pi$
$109$	−3.59949	+	3.59949i	−0.344769	+	0.344769i	0.513388	+	0.858157i	$0.328390\pi$
$110$	−6.50707	−	6.50707i	−0.620425	−	0.620425i
$111$	9.22929	+	9.93042i	0.876005	+	0.942553i
$112$	28.4650	+	28.4650i	2.68969	+	2.68969i
$113$		−	6.66989i		−	0.627450i	−0.949514	−	0.313725i	$-0.898423\pi$
$113$		−	6.66989i		−	0.627450i	0.949514	−	0.313725i	$-0.101577\pi$
$114$	−15.8232	−	0.579035i	−1.48198	−	0.0542316i
$115$	−9.37849	−	9.37849i	−0.874548	−	0.874548i
$116$	−9.23631			−0.857570
$117$	−10.3765	+	3.05409i	−0.959311	+	0.282351i
$118$	0.356259			0.0327963
$119$	−7.07789	−	7.07789i	−0.648829	−	0.648829i
$120$	−45.2577	−	1.65616i	−4.13144	−	0.151186i
$121$		−	1.00000i		−	0.0909091i
$122$	5.36548	+	5.36548i	0.485767	+	0.485767i
$123$	1.16181	+	1.25007i	0.104757	+	0.112715i
$124$	−6.22473	−	6.22473i	−0.558997	−	0.558997i
$125$	−5.91669	+	5.91669i	−0.529205	+	0.529205i
$126$	−2.36654	+	32.2917i	−0.210828	+	2.87677i
$127$			7.15583i			0.634978i	0.948262	+	0.317489i	$0.102840\pi$
$127$			7.15583i			0.634978i	−0.948262	+	0.317489i	$0.897160\pi$
$128$	−0.384453	+	0.384453i	−0.0339811	+	0.0339811i
$129$	0.564409	−	15.4235i	0.0496934	−	1.35796i
$130$	11.6697	+	31.0598i	1.02350	+	2.72412i
$131$		−	20.9981i		−	1.83461i	−0.398181	−	0.917307i	$-0.630358\pi$
$131$		−	20.9981i		−	1.83461i	0.398181	−	0.917307i	$-0.369642\pi$
$132$	−5.70859	−	6.14226i	−0.496869	−	0.534615i
$133$	14.4217			1.25052
$134$	23.8899			2.06377
$135$	−11.4336	−	14.2649i	−0.984044	−	1.22773i
$136$	12.7478	−	12.7478i	1.09311	−	1.09311i
$137$	2.43623	−	2.43623i	0.208141	−	0.208141i	−0.595336	−	0.803477i	$-0.702981\pi$
$137$	2.43623	−	2.43623i	0.208141	−	0.208141i	0.803477	+	0.595336i	$0.202981\pi$
$138$	−11.6266	−	12.5098i	−0.989721	−	1.06491i
$139$	7.36071			0.624327			0.312163	−	0.950028i	$-0.398946\pi$
$139$	7.36071			0.624327			0.312163	+	0.950028i	$0.398946\pi$
$140$	70.2842			5.94010
$141$	4.21893	−	3.92105i	0.355298	−	0.330212i
$142$			9.22242i			0.773928i
$143$	−1.48992	+	3.28331i	−0.124594	+	0.274564i
$144$	−29.1892	−	2.13917i	−2.43243	−	0.178264i
$145$	−4.74623	+	4.74623i	−0.394153	+	0.394153i
$146$			17.0721i			1.41290i
$147$	0.635082	−	17.3548i	0.0523807	−	1.43140i
$148$	26.7950	−	26.7950i	2.20253	−	2.20253i
$149$	10.0696	+	10.0696i	0.824933	+	0.824933i	0.986811	−	0.161878i	$-0.0517550\pi$
$149$	10.0696	+	10.0696i	0.824933	+	0.824933i	−0.161878	+	0.986811i	$0.551755\pi$
$150$	−24.4844	+	22.7557i	−1.99914	+	1.85799i
$151$	−6.01973	−	6.01973i	−0.489878	−	0.489878i	0.418389	−	0.908268i	$-0.362595\pi$
$151$	−6.01973	−	6.01973i	−0.489878	−	0.489878i	−0.908268	+	0.418389i	$0.862595\pi$
$152$			25.9744i			2.10680i
$153$	7.25796	+	0.531909i	0.586771	+	0.0430023i
$154$	7.63164	+	7.63164i	0.614975	+	0.614975i
$155$	−6.39736			−0.513848
$156$	9.59158	+	28.6723i	0.767941	+	2.29562i
$157$	−18.1931			−1.45197			−0.725986	−	0.687710i	$-0.758616\pi$
$157$	−18.1931			−1.45197			−0.725986	+	0.687710i	$0.758616\pi$
$158$	20.4402	+	20.4402i	1.62613	+	1.62613i
$159$	0.865173	−	23.6424i	0.0686127	−	1.87497i
$160$			37.4828i			2.96327i
$161$	10.9993	+	10.9993i	0.866866	+	0.866866i
$162$	−14.0409	−	18.8944i	−1.10316	−	1.48449i
$163$	5.61651	+	5.61651i	0.439919	+	0.439919i	0.891985	−	0.452065i	$-0.149313\pi$
$163$	5.61651	+	5.61651i	0.439919	+	0.439919i	−0.452065	+	0.891985i	$0.649313\pi$
$164$	3.37303	−	3.37303i	0.263390	−	0.263390i
$165$	−6.08976	−	0.222849i	−0.474087	−	0.0173488i
$166$		−	25.0703i		−	1.94583i
$167$	14.8175	−	14.8175i	1.14661	−	1.14661i	0.159397	−	0.987215i	$-0.449045\pi$
$167$	14.8175	−	14.8175i	1.14661	−	1.14661i	0.987215	−	0.159397i	$-0.0509549\pi$
$168$	53.0792	+	1.94239i	4.09515	+	0.149858i
$169$	9.78376	−	8.56025i	0.752597	−	0.658481i
$170$		−	22.3232i		−	1.71211i
$171$	−7.93619	+	6.85239i	−0.606896	+	0.524015i
$172$	−43.1398			−3.28938
$173$	−15.8588			−1.20572			−0.602862	−	0.797845i	$-0.705973\pi$
$173$	−15.8588			−1.20572			−0.602862	+	0.797845i	$0.705973\pi$
$174$	−6.33093	+	5.88394i	−0.479947	+	0.446060i
$175$	21.5280	−	21.5280i	1.62736	−	1.62736i
$176$	−6.89841	+	6.89841i	−0.519987	+	0.519987i
$177$	0.172806	−	0.160605i	0.0129889	−	0.0120718i
$178$	15.5888			1.16843
$179$	3.07224			0.229630			0.114815	−	0.993387i	$-0.463372\pi$
$179$	3.07224			0.229630			0.114815	+	0.993387i	$0.463372\pi$
$180$	−38.6771	+	33.3952i	−2.88282	+	2.48913i
$181$		−	3.51749i		−	0.261453i	−0.991418	−	0.130726i	$-0.958269\pi$
$181$		−	3.51749i		−	0.261453i	0.991418	−	0.130726i	$-0.0417309\pi$
$182$	−13.6865	−	36.4276i	−1.01451	−	2.70019i
$183$	5.02138	+	0.183753i	0.371191	+	0.0135834i
$184$	−19.8105	+	19.8105i	−1.46045	+	1.46045i
$185$		−	27.5381i		−	2.02464i
$186$	−8.23210	−	0.301246i	−0.603607	−	0.0220884i
$187$	1.71531	−	1.71531i	0.125436	−	0.125436i
$188$	−11.3838	−	11.3838i	−0.830250	−	0.830250i
$189$	13.4095	+	16.7302i	0.975400	+	1.21694i
$190$	22.7425	+	22.7425i	1.64992	+	1.64992i
$191$			8.41909i			0.609184i	0.952483	+	0.304592i	$0.0985201\pi$
$191$			8.41909i			0.609184i	−0.952483	+	0.304592i	$0.901480\pi$
$192$	−0.529157	+	14.4602i	−0.0381887	+	1.04357i
$193$	−9.22687	−	9.22687i	−0.664165	−	0.664165i	0.292194	−	0.956359i	$-0.405615\pi$
$193$	−9.22687	−	9.22687i	−0.664165	−	0.664165i	−0.956359	+	0.292194i	$0.905615\pi$
$194$	−27.8784			−2.00156
$195$	19.6625	+	9.80496i	1.40806	+	0.702148i
$196$	−48.5415			−3.46725
$197$	7.07326	+	7.07326i	0.503949	+	0.503949i	0.912663	−	0.408714i	$-0.134023\pi$
$197$	7.07326	+	7.07326i	0.503949	+	0.503949i	−0.408714	+	0.912663i	$0.634023\pi$
$198$	−7.82579	−	0.573523i	−0.556155	−	0.0407585i
$199$		−	2.79254i		−	0.197958i	−0.995090	−	0.0989790i	$-0.968442\pi$
$199$		−	2.79254i		−	0.197958i	0.995090	−	0.0989790i	$-0.0315577\pi$
$200$	38.7733	+	38.7733i	2.74168	+	2.74168i
$201$	11.5880	−	10.7698i	0.817352	−	0.759643i
$202$	28.3364	+	28.3364i	1.99374	+	1.99374i
$203$	5.56649	−	5.56649i	0.390691	−	0.390691i
$204$	0.743879	−	20.3278i	0.0520819	−	1.42323i
$205$		−	3.46658i		−	0.242116i
$206$	6.47389	−	6.47389i	0.451057	−	0.451057i
$207$	−11.2791	−	0.826606i	−0.783954	−	0.0574531i
$208$	32.9277	−	12.3715i	2.28313	−	0.857810i
$209$			3.49505i			0.241758i
$210$	48.1756	−	44.7742i	3.32443	−	3.08971i
$211$	−6.34836			−0.437039			−0.218519	−	0.975833i	$-0.570123\pi$
$211$	−6.34836			−0.437039			−0.218519	+	0.975833i	$0.570123\pi$
$212$	−66.1283			−4.54171
$213$	4.15756	+	4.47341i	0.284872	+	0.306513i
$214$	12.3030	−	12.3030i	0.841018	−	0.841018i
$215$	−22.1681	+	22.1681i	−1.51185	+	1.51185i
$216$	−30.1322	+	24.1514i	−2.05024	+	1.64330i
$217$	7.50297			0.509335
$218$	13.3145			0.901775
$219$	7.69627	+	8.28094i	0.520066	+	0.559574i
$220$			17.0331i			1.14837i
$221$	−8.18756	+	3.07621i	−0.550755	+	0.206928i
$222$	1.29675	−	35.4359i	0.0870319	−	2.37831i
$223$	17.5776	−	17.5776i	1.17708	−	1.17708i	0.196596	−	0.980485i	$-0.437011\pi$
$223$	17.5776	−	17.5776i	1.17708	−	1.17708i	0.980485	−	0.196596i	$-0.0629886\pi$
$224$		−	43.9607i		−	2.93724i
$225$	−1.61784	+	22.0757i	−0.107856	+	1.47171i
$226$	−12.3360	+	12.3360i	−0.820578	+	0.820578i
$227$	16.5159	+	16.5159i	1.09620	+	1.09620i	0.994851	+	0.101348i	$0.0323155\pi$
$227$	16.5159	+	16.5159i	1.09620	+	1.09620i	0.101348	+	0.994851i	$0.467684\pi$
$228$	19.9518	+	21.4675i	1.32134	+	1.42172i
$229$	3.41139	+	3.41139i	0.225431	+	0.225431i	0.810781	−	0.585350i	$-0.199043\pi$
$229$	3.41139	+	3.41139i	0.225431	+	0.225431i	−0.585350	+	0.810781i	$0.699043\pi$
$230$			34.6911i			2.28746i
$231$	7.14221	+	0.261363i	0.469923	+	0.0171964i
$232$	10.0256	+	10.0256i	0.658213	+	0.658213i
$233$	−8.14586			−0.533653			−0.266827	−	0.963745i	$-0.585975\pi$
$233$	−8.14586			−0.533653			−0.266827	+	0.963745i	$0.585975\pi$
$234$	24.8400	+	13.5429i	1.62384	+	0.885326i
$235$	−11.6995			−0.763193
$236$	−0.466278	−	0.466278i	−0.0303521	−	0.0303521i
$237$	19.1293	+	0.700020i	1.24258	+	0.0454712i
$238$			26.1812i			1.69707i
$239$	−7.12344	−	7.12344i	−0.460777	−	0.460777i	0.438133	−	0.898910i	$-0.355640\pi$
$239$	−7.12344	−	7.12344i	−0.460777	−	0.460777i	−0.898910	+	0.438133i	$0.855640\pi$
$240$	40.4723	+	43.5470i	2.61248	+	2.81094i
$241$	−12.1166	−	12.1166i	−0.780498	−	0.780498i	0.199417	−	0.979915i	$-0.436095\pi$
$241$	−12.1166	−	12.1166i	−0.780498	−	0.780498i	−0.979915	+	0.199417i	$0.936095\pi$
$242$	−1.84950	+	1.84950i	−0.118891	+	0.118891i
$243$	−15.3285	−	2.83509i	−0.983322	−	0.181871i
$244$		−	14.0449i		−	0.899130i
$245$	−24.9439	+	24.9439i	−1.59361	+	1.59361i
$246$	0.163238	−	4.46079i	0.0104077	−	0.284409i
$247$	5.20736	−	11.4753i	0.331336	−	0.730158i
$248$			13.5133i			0.858098i
$249$	−11.3019	−	12.1605i	−0.716232	−	0.770643i
$250$	21.8859			1.38419
$251$	15.2417			0.962047			0.481024	−	0.876708i	$-0.340265\pi$
$251$	15.2417			0.962047			0.481024	+	0.876708i	$0.340265\pi$
$252$	45.3613	−	39.1666i	2.85750	−	2.46726i
$253$	−2.66565	+	2.66565i	−0.167588	+	0.167588i
$254$	13.2347	−	13.2347i	0.830422	−	0.830422i
$255$	−10.0635	−	10.8281i	−0.630204	−	0.678079i
$256$	−15.2863			−0.955392
$257$	10.2912			0.641950			0.320975	−	0.947088i	$-0.395989\pi$
$257$	10.2912			0.641950			0.320975	+	0.947088i	$0.395989\pi$
$258$	−29.5697	+	27.4820i	−1.84093	+	1.71095i
$259$			32.2973i			2.00686i
$260$	25.3781	−	55.9251i	1.57388	−	3.46833i
$261$	−0.418326	+	5.70810i	−0.0258937	+	0.353323i
$262$	−38.8361	+	38.8361i	−2.39930	+	2.39930i
$263$			24.8500i			1.53232i	0.642652	+	0.766158i	$0.277834\pi$
$263$			24.8500i			1.53232i	−0.642652	+	0.766158i	$0.722166\pi$
$264$	−0.470731	+	12.8636i	−0.0289715	+	0.791699i
$265$	−33.9811	+	33.9811i	−2.08744	+	2.08744i
$266$	−26.6730	−	26.6730i	−1.63542	−	1.63542i
$267$	7.56146	−	7.02758i	0.462754	−	0.430081i
$268$	−31.2675	−	31.2675i	−1.90997	−	1.90997i
$269$		−	20.4390i		−	1.24619i	−0.782147	−	0.623094i	$-0.785876\pi$
$269$		−	20.4390i		−	1.24619i	0.782147	−	0.623094i	$-0.214124\pi$
$270$	−5.23659	+	47.5294i	−0.318689	+	2.89255i
$271$	14.6033	+	14.6033i	0.887088	+	0.887088i	0.994242	−	0.107155i	$-0.0341740\pi$
$271$	14.6033	+	14.6033i	0.887088	+	0.887088i	−0.107155	+	0.994242i	$0.534174\pi$
$272$	−23.6658			−1.43495
$273$	−23.0607	−	11.4995i	−1.39570	−	0.695980i
$274$	−9.01164			−0.544413
$275$	5.21724	+	5.21724i	0.314611	+	0.314611i
$276$	−1.15601	+	31.5902i	−0.0695839	+	1.90151i
$277$		−	5.13491i		−	0.308527i	−0.988030	−	0.154263i	$-0.950700\pi$
$277$		−	5.13491i		−	0.308527i	0.988030	−	0.154263i	$-0.0493005\pi$
$278$	−13.6137	−	13.6137i	−0.816493	−	0.816493i
$279$	−4.12885	+	3.56500i	−0.247188	+	0.213431i
$280$	−76.2904	−	76.2904i	−4.55922	−	4.55922i
$281$	−6.57348	+	6.57348i	−0.392141	+	0.392141i	−0.875450	−	0.483309i	$-0.839435\pi$
$281$	−6.57348	+	6.57348i	−0.392141	+	0.392141i	0.483309	+	0.875450i	$0.339435\pi$
$282$	−15.0549	−	0.550921i	−0.896508	−	0.0328069i
$283$			30.2874i			1.80040i	0.435476	+	0.900200i	$0.356580\pi$
$283$			30.2874i			1.80040i	−0.435476	+	0.900200i	$0.643420\pi$
$284$	12.0705	−	12.0705i	0.716251	−	0.716251i
$285$	21.2840	+	0.778869i	1.26076	+	0.0461362i
$286$	8.82812	−	3.31688i	0.522017	−	0.196131i
$287$			4.06568i			0.239990i
$288$	20.8877	+	24.1914i	1.23082	+	1.42549i
$289$	−11.1155			−0.653850
$290$	17.5563			1.03094
$291$	−13.5227	+	12.5679i	−0.792712	+	0.736743i
$292$	22.3443	−	22.3443i	1.30760	−	1.30760i
$293$	13.6009	−	13.6009i	0.794575	−	0.794575i	−0.187659	−	0.982234i	$-0.560090\pi$
$293$	13.6009	−	13.6009i	0.794575	−	0.794575i	0.982234	+	0.187659i	$0.0600901\pi$
$294$	−33.2723	+	30.9231i	−1.94048	+	1.80347i
$295$	−0.479210			−0.0279007
$296$	−58.1696			−3.38104
$297$	−4.05451	+	3.24976i	−0.235267	+	0.188570i
$298$		−	37.2475i		−	2.15769i
$299$	12.7238	−	4.78054i	0.735834	−	0.276465i
$300$	61.8287	+	2.26256i	3.56968	+	0.130629i
$301$	25.9992	−	25.9992i	1.49857	−	1.49857i
$302$			22.2670i			1.28132i
$303$	26.5191	+	0.970442i	1.52348	+	0.0557504i
$304$	24.1103	−	24.1103i	1.38282	−	1.38282i
$305$	−7.21719	−	7.21719i	−0.413255	−	0.413255i
$306$	−12.4399	−	14.4074i	−0.711140	−	0.823616i
$307$	−6.64137	−	6.64137i	−0.379043	−	0.379043i	0.491714	−	0.870757i	$-0.336371\pi$
$307$	−6.64137	−	6.64137i	−0.379043	−	0.379043i	−0.870757	+	0.491714i	$0.836371\pi$
$308$		−	19.9769i		−	1.13829i
$309$	0.221713	−	6.05871i	0.0126128	−	0.344668i
$310$	11.8319	+	11.8319i	0.672009	+	0.672009i
$311$	27.4085			1.55419			0.777096	−	0.629383i	$-0.216692\pi$
$311$	27.4085			1.55419			0.777096	+	0.629383i	$0.216692\pi$
$312$	20.7113	−	41.5338i	1.17255	−	2.35139i
$313$	26.8621			1.51834			0.759169	−	0.650894i	$-0.225606\pi$
$313$	26.8621			1.51834			0.759169	+	0.650894i	$0.225606\pi$
$314$	33.6483	+	33.6483i	1.89888	+	1.89888i
$315$	3.18327	−	43.4361i	0.179357	−	2.44735i
$316$		−	53.5050i		−	3.00989i
$317$	6.34235	+	6.34235i	0.356222	+	0.356222i	0.862418	−	0.506196i	$-0.168949\pi$
$317$	6.34235	+	6.34235i	0.356222	+	0.356222i	−0.506196	+	0.862418i	$0.668949\pi$
$318$	−45.3269	+	42.1267i	−2.54181	+	2.36235i
$319$	1.34902	+	1.34902i	0.0755307	+	0.0755307i
$320$	20.7835	−	20.7835i	1.16183	−	1.16183i
$321$	0.421345	−	11.5140i	0.0235172	−	0.642649i
$322$		−	40.6865i		−	2.26737i
$323$	−5.99508	+	5.99508i	−0.333575	+	0.333575i
$324$	−6.35234	+	43.1064i	−0.352908	+	2.39480i
$325$	−9.35652	−	24.9031i	−0.519006	−	1.38137i
$326$		−	20.7755i		−	1.15065i
$327$	6.45832	−	6.00234i	0.357146	−	0.331930i
$328$	−7.32256			−0.404321
$329$	13.7215			0.756489
$330$	10.8509	+	11.6752i	0.597321	+	0.642699i
$331$	7.83817	−	7.83817i	0.430825	−	0.430825i	−0.458084	−	0.888909i	$-0.651464\pi$
$331$	7.83817	−	7.83817i	0.430825	−	0.430825i	0.888909	+	0.458084i	$0.151464\pi$
$332$	−32.8124	+	32.8124i	−1.80082	+	1.80082i
$333$	−15.3459	−	17.7731i	−0.840950	−	0.973958i
$334$	−54.8100			−2.99907
$335$	−32.1346			−1.75570
$336$	−47.4669	−	51.0728i	−2.58953	−	2.78625i
$337$		−	14.6634i		−	0.798768i	−0.916784	−	0.399384i	$-0.869224\pi$
$337$		−	14.6634i		−	0.798768i	0.916784	−	0.399384i	$-0.130776\pi$
$338$	−33.9273	−	2.26288i	−1.84540	−	0.123085i
$339$	−0.422473	+	11.5449i	−0.0229456	+	0.627031i
$340$	−29.2171	+	29.2171i	−1.58452	+	1.58452i
$341$			1.81832i			0.0984676i
$342$	27.3515	+	2.00449i	1.47900	+	0.108391i
$343$	8.83052	−	8.83052i	0.476803	−	0.476803i
$344$	46.8263	+	46.8263i	2.52471	+	2.52471i
$345$	15.6391	+	16.8272i	0.841982	+	0.905945i
$346$	29.3310	+	29.3310i	1.57684	+	1.57684i
$347$			5.57001i			0.299014i	0.988761	+	0.149507i	$0.0477686\pi$
$347$			5.57001i			0.299014i	−0.988761	+	0.149507i	$0.952231\pi$
$348$	15.9871	+	0.585031i	0.856996	+	0.0313610i
$349$	−4.65972	−	4.65972i	−0.249429	−	0.249429i	0.571307	−	0.820736i	$-0.306436\pi$
$349$	−4.65972	−	4.65972i	−0.249429	−	0.249429i	−0.820736	+	0.571307i	$0.806436\pi$
$350$	−79.6321			−4.25652
$351$	18.1541	−	4.62905i	0.968995	−	0.247080i
$352$	10.6537			0.567846
$353$	9.48875	+	9.48875i	0.505035	+	0.505035i	0.912998	−	0.407963i	$-0.133761\pi$
$353$	9.48875	+	9.48875i	0.505035	+	0.505035i	−0.407963	+	0.912998i	$0.633761\pi$
$354$	−0.616646	−	0.0225656i	−0.0327743	−	0.00119935i
$355$		−	12.4052i		−	0.658401i
$356$	−20.4029	−	20.4029i	−1.08135	−	1.08135i
$357$	11.8028	+	12.6994i	0.624668	+	0.672123i
$358$	−5.68212	−	5.68212i	−0.300309	−	0.300309i
$359$	−2.67973	+	2.67973i	−0.141431	+	0.141431i	−0.774277	−	0.632847i	$-0.781886\pi$
$359$	−2.67973	+	2.67973i	−0.141431	+	0.141431i	0.632847	+	0.774277i	$0.281886\pi$
$360$	78.2313	+	5.73328i	4.12315	+	0.302170i
$361$			6.78462i			0.357085i
$362$	−6.50560	+	6.50560i	−0.341927	+	0.341927i
$363$	−0.0633404	+	1.73089i	−0.00332451	+	0.0908483i
$364$	−29.7640	+	65.5902i	−1.56006	+	3.43786i
$365$		−	22.9639i		−	1.20199i
$366$	−8.94721	−	9.62691i	−0.467678	−	0.503207i
$367$	9.90918			0.517255			0.258628	−	0.965977i	$-0.416730\pi$
$367$	9.90918			0.517255			0.258628	+	0.965977i	$0.416730\pi$
$368$	36.7774			1.91716
$369$	−1.93179	−	2.23733i	−0.100565	−	0.116471i
$370$	−50.9318	+	50.9318i	−2.64782	+	2.64782i
$371$	39.8538	−	39.8538i	2.06911	−	2.06911i
$372$	10.3801	+	11.1686i	0.538181	+	0.579065i
$373$	4.70529			0.243631			0.121815	−	0.992553i	$-0.461128\pi$
$373$	4.70529			0.243631			0.121815	+	0.992553i	$0.461128\pi$
$374$	−6.34493			−0.328089
$375$	10.6159	−	9.86639i	0.548204	−	0.509498i
$376$			24.7133i			1.27449i
$377$	−2.41932	−	6.43919i	−0.124601	−	0.331635i
$378$	6.14159	−	55.7436i	0.315889	−	2.86714i
$379$	0.814279	−	0.814279i	0.0418267	−	0.0418267i	−0.685884	−	0.727711i	$-0.740584\pi$
$379$	0.814279	−	0.814279i	0.0418267	−	0.0418267i	0.727711	+	0.685884i	$0.240584\pi$
$380$		−	59.5317i		−	3.05391i
$381$	0.453253	−	12.3860i	0.0232209	−	0.634553i
$382$	15.5711	−	15.5711i	0.796689	−	0.796689i
$383$	−25.2680	−	25.2680i	−1.29114	−	1.29114i	−0.934085	−	0.357051i	$-0.883782\pi$
$383$	−25.2680	−	25.2680i	−1.29114	−	1.29114i	−0.357051	−	0.934085i	$-0.616218\pi$
$384$	0.689797	−	0.641095i	0.0352011	−	0.0327157i
$385$	−10.2654	−	10.2654i	−0.523175	−	0.523175i
$386$			34.1303i			1.73718i
$387$	−1.95386	+	26.6607i	−0.0993204	+	1.35524i
$388$	36.4878	+	36.4878i	1.85239	+	1.85239i
$389$	37.4037			1.89644			0.948222	−	0.317608i	$-0.102880\pi$
$389$	37.4037			1.89644			0.948222	+	0.317608i	$0.102880\pi$
$390$	−18.2316	−	54.5003i	−0.923195	−	2.75973i
$391$	−9.14480			−0.462472
$392$	52.6897	+	52.6897i	2.66123	+	2.66123i
$393$	−1.33003	+	36.3455i	−0.0670911	+	1.83339i
$394$		−	26.1640i		−	1.31813i
$395$	−27.4944	−	27.4944i	−1.38340	−	1.38340i
$396$	9.49191	+	10.9932i	0.476986	+	0.552428i
$397$	−15.8092	−	15.8092i	−0.793442	−	0.793442i	0.188610	−	0.982052i	$-0.439602\pi$
$397$	−15.8092	−	15.8092i	−0.793442	−	0.793442i	−0.982052	+	0.188610i	$0.939602\pi$
$398$	−5.16482	+	5.16482i	−0.258889	+	0.258889i
$399$	−24.9624	−	0.913475i	−1.24968	−	0.0457310i
$400$		−	71.9812i		−	3.59906i
$401$	−6.96285	+	6.96285i	−0.347708	+	0.347708i	−0.859255	−	0.511547i	$-0.829073\pi$
$401$	−6.96285	+	6.96285i	−0.347708	+	0.347708i	0.511547	+	0.859255i	$0.329073\pi$
$402$	−41.3508	−	1.51319i	−2.06239	−	0.0754712i
$403$	2.70916	−	5.97011i	0.134953	−	0.297392i
$404$		−	74.1743i		−	3.69031i
$405$	18.8867	+	25.4152i	0.938488	+	1.26289i
$406$	−20.5905			−1.02189
$407$	−7.82715			−0.387977
$408$	−22.8724	+	21.2575i	−1.13235	+	1.05240i
$409$	−3.07427	+	3.07427i	−0.152013	+	0.152013i	−0.779017	−	0.627003i	$-0.784281\pi$
$409$	−3.07427	+	3.07427i	−0.152013	+	0.152013i	0.627003	+	0.779017i	$0.284281\pi$
$410$	−6.41145	+	6.41145i	−0.316639	+	0.316639i
$411$	−4.37117	+	4.06254i	−0.215614	+	0.200390i
$412$	−16.9463			−0.834884
$413$	0.562028			0.0276556
$414$	19.3320	+	22.3896i	0.950115	+	1.10039i
$415$			33.7224i			1.65537i
$416$	−34.9795	−	15.8732i	−1.71501	−	0.778250i
$417$	−12.7406	−	0.466230i	−0.623909	−	0.0228314i
$418$	6.46411	−	6.46411i	0.316170	−	0.316170i
$419$			15.2378i			0.744417i	0.928149	+	0.372209i	$0.121399\pi$
$419$			15.2378i			0.744417i	−0.928149	+	0.372209i	$0.878601\pi$
$420$	−121.654	−	4.45183i	−5.93612	−	0.217227i
$421$	−11.3901	+	11.3901i	−0.555122	+	0.555122i	−0.927915	−	0.372793i	$-0.878400\pi$
$421$	−11.3901	+	11.3901i	−0.555122	+	0.555122i	0.372793	+	0.927915i	$0.378400\pi$
$422$	11.7413	+	11.7413i	0.571558	+	0.571558i
$423$	−7.55087	+	6.51969i	−0.367136	+	0.316998i
$424$	71.7793	+	71.7793i	3.48591	+	3.48591i
$425$			17.8983i			0.868195i
$426$	0.584152	−	15.9630i	0.0283022	−	0.773410i
$427$	8.46448	+	8.46448i	0.409625	+	0.409625i
$428$	−32.2049			−1.55668
$429$	2.78686	−	5.58868i	0.134551	−	0.269824i
$430$	81.9999			3.95439
$431$	−15.5745	−	15.5745i	−0.750199	−	0.750199i	0.224317	−	0.974516i	$-0.427985\pi$
$431$	−15.5745	−	15.5745i	−0.750199	−	0.750199i	−0.974516	+	0.224317i	$0.927985\pi$
$432$	50.3878	+	5.55152i	2.42429	+	0.267098i
$433$			22.4344i			1.07813i	0.842264	+	0.539065i	$0.181222\pi$
$433$			22.4344i			1.07813i	−0.842264	+	0.539065i	$0.818778\pi$
$434$	−13.8768	−	13.8768i	−0.666106	−	0.666106i
$435$	8.51584	−	7.91459i	0.408303	−	0.379475i
$436$	−17.4263	−	17.4263i	−0.834569	−	0.834569i
$437$	9.31657	−	9.31657i	0.445672	−	0.445672i
$438$	1.08135	−	29.5499i	0.0516690	−	1.41195i
$439$			8.52557i			0.406903i	0.979085	+	0.203452i	$0.0652160\pi$
$439$			8.52557i			0.406903i	−0.979085	+	0.203452i	$0.934784\pi$
$440$	18.4887	−	18.4887i	0.881416	−	0.881416i
$441$	−2.19852	+	29.9990i	−0.104691	+	1.42852i
$442$	20.8324	+	9.45346i	0.990895	+	0.449655i
$443$		−	10.8283i		−	0.514468i	−0.966349	−	0.257234i	$-0.917189\pi$
$443$		−	10.8283i		−	0.514468i	0.966349	−	0.257234i	$-0.0828111\pi$
$444$	−48.0764	+	44.6820i	−2.28161	+	2.12051i
$445$	−20.9687			−0.994013
$446$	−65.0195			−3.07876
$447$	−16.7916	−	18.0672i	−0.794214	−	0.854549i
$448$	−24.3754	+	24.3754i	−1.15163	+	1.15163i
$449$	8.74457	−	8.74457i	0.412682	−	0.412682i	−0.469990	−	0.882672i	$-0.655742\pi$
$449$	8.74457	−	8.74457i	0.412682	−	0.412682i	0.882672	+	0.469990i	$0.155742\pi$
$450$	43.8212	−	37.8368i	2.06575	−	1.78364i
$451$	−0.985306			−0.0463962
$452$	32.2911			1.51885
$453$	10.0382	+	10.8008i	0.471636	+	0.507465i
$454$		−	61.0925i		−	2.86721i
$455$	18.4099	+	48.9994i	0.863070	+	2.29713i
$456$	1.64523	−	44.9589i	0.0770449	−	2.10539i
$457$	−29.1192	+	29.1192i	−1.36214	+	1.36214i	−0.490950	+	0.871188i	$0.663350\pi$
$457$	−29.1192	+	29.1192i	−1.36214	+	1.36214i	−0.871188	+	0.490950i	$0.836650\pi$
$458$		−	12.6188i		−	0.589636i
$459$	−12.5291	−	1.38040i	−0.584806	−	0.0644315i
$460$	45.4044	−	45.4044i	2.11699	−	2.11699i
$461$	−9.85739	−	9.85739i	−0.459105	−	0.459105i	0.439257	−	0.898362i	$-0.355242\pi$
$461$	−9.85739	−	9.85739i	−0.459105	−	0.459105i	−0.898362	+	0.439257i	$0.855242\pi$
$462$	−12.7262	−	13.6929i	−0.592074	−	0.637053i
$463$	0.690377	+	0.690377i	0.0320845	+	0.0320845i	0.722967	−	0.690883i	$-0.242778\pi$
$463$	0.690377	+	0.690377i	0.0320845	+	0.0320845i	−0.690883	+	0.722967i	$0.742778\pi$
$464$		−	18.6122i		−	0.864049i
$465$	11.0731	+	0.405211i	0.513504	+	0.0187912i
$466$	15.0658	+	15.0658i	0.697910	+	0.697910i
$467$	12.6120			0.583613			0.291807	−	0.956477i	$-0.405744\pi$
$467$	12.6120			0.583613			0.291807	+	0.956477i	$0.405744\pi$
$468$	−14.7859	−	50.2362i	−0.683477	−	2.32217i
$469$	37.6882			1.74028
$470$	21.6383	+	21.6383i	0.998102	+	0.998102i
$471$	31.4904	+	1.15236i	1.45100	+	0.0530980i
$472$			1.01225i			0.0465925i
$473$	6.30083	+	6.30083i	0.289713	+	0.289713i
$474$	−34.0851	−	36.6745i	−1.56558	−	1.68451i
$475$	−18.2345	−	18.2345i	−0.836656	−	0.836656i
$476$	34.2664	−	34.2664i	1.57060	−	1.57060i
$477$	−2.99504	+	40.8677i	−0.137134	+	1.87120i
$478$			26.3497i			1.20521i
$479$	15.0783	−	15.0783i	0.688946	−	0.688946i	−0.273053	−	0.961999i	$-0.588033\pi$
$479$	15.0783	−	15.0783i	0.688946	−	0.688946i	0.961999	+	0.273053i	$0.0880334\pi$
$480$	2.37417	−	64.8787i	0.108366	−	2.96129i
$481$	25.6990	+	11.6619i	1.17177	+	0.531735i
$482$			44.8194i			2.04147i
$483$	−18.3419	−	19.7353i	−0.834585	−	0.897987i
$484$	4.84133			0.220060
$485$	37.4998			1.70278
$486$	23.1066	+	33.5936i	1.04814	+	1.52384i
$487$	−9.29743	+	9.29743i	−0.421307	+	0.421307i	−0.885654	−	0.464347i	$-0.846289\pi$
$487$	−9.29743	+	9.29743i	−0.421307	+	0.421307i	0.464347	+	0.885654i	$0.346289\pi$
$488$	−15.2451	+	15.2451i	−0.690113	+	0.690113i
$489$	−9.36583	−	10.0773i	−0.423537	−	0.455713i
$490$	92.2676			4.16823
$491$	−7.89768			−0.356417			−0.178209	−	0.983993i	$-0.557030\pi$
$491$	−7.89768			−0.356417			−0.178209	+	0.983993i	$0.557030\pi$
$492$	−6.05201	+	5.62471i	−0.272846	+	0.253581i
$493$			4.62797i			0.208433i
$494$	−30.8547	+	11.5926i	−1.38822	+	0.521578i
$495$	10.5266	+	0.771456i	0.473136	+	0.0346744i
$496$	12.5435	−	12.5435i	0.563220	−	0.563220i
$497$			14.5491i			0.652618i
$498$	−1.58796	+	43.3940i	−0.0711583	+	1.94453i
$499$	6.55211	−	6.55211i	0.293313	−	0.293313i	−0.545075	−	0.838388i	$-0.683499\pi$
$499$	6.55211	−	6.55211i	0.293313	−	0.293313i	0.838388	+	0.545075i	$0.183499\pi$
$500$	−28.6447	−	28.6447i	−1.28103	−	1.28103i
$501$	−26.5860	+	24.7089i	−1.18778	+	1.10391i
$502$	−28.1896	−	28.1896i	−1.25816	−	1.25816i
$503$			10.4264i			0.464891i	0.972609	+	0.232445i	$0.0746727\pi$
$503$			10.4264i			0.464891i	−0.972609	+	0.232445i	$0.925327\pi$
$504$	−91.7514	−	6.72412i	−4.08693	−	0.299516i
$505$	−38.1157	−	38.1157i	−1.69613	−	1.69613i
$506$	9.86025			0.438341
$507$	−17.4769	+	14.1972i	−0.776174	+	0.630519i
$508$	−34.6438			−1.53707
$509$	−15.5511	−	15.5511i	−0.689291	−	0.689291i	0.272785	−	0.962075i	$-0.412055\pi$
$509$	−15.5511	−	15.5511i	−0.689291	−	0.689291i	−0.962075	+	0.272785i	$0.912055\pi$
$510$	−1.41396	+	38.6391i	−0.0626113	+	1.71097i
$511$			26.9326i			1.19143i
$512$	29.0409	+	29.0409i	1.28344	+	1.28344i
$513$	14.1707	−	11.3581i	0.625653	−	0.501471i
$514$	−19.0337	−	19.0337i	−0.839540	−	0.839540i
$515$	−8.70814	+	8.70814i	−0.383727	+	0.383727i
$516$	74.6703	+	2.73249i	3.28718	+	0.120291i
$517$			3.32536i			0.146249i
$518$	59.7340	−	59.7340i	2.62456	−	2.62456i
$519$	27.4499	+	1.00450i	1.20492	+	0.0440929i
$520$	−88.2511	+	33.1575i	−3.87007	+	1.45405i
$521$			23.4342i			1.02667i	0.858188	+	0.513336i	$0.171590\pi$
$521$			23.4342i			1.02667i	−0.858188	+	0.513336i	$0.828410\pi$
$522$	11.3309	−	9.78346i	0.495938	−	0.428211i
$523$	13.1862			0.576592			0.288296	−	0.957541i	$-0.406911\pi$
$523$	13.1862			0.576592			0.288296	+	0.957541i	$0.406911\pi$
$524$	101.659			4.44099
$525$	−38.6262	+	35.8990i	−1.68578	+	1.56676i
$526$	45.9602	−	45.9602i	2.00396	−	2.00396i
$527$	−3.11898	+	3.11898i	−0.135865	+	0.135865i
$528$	12.3773	−	11.5034i	0.538655	−	0.500623i
$529$	−8.78866			−0.382116
$530$	125.696			5.45990
$531$	−0.309282	+	0.267045i	−0.0134217	+	0.0115888i
$532$			69.8201i			3.02709i
$533$	3.23506	+	1.46803i	0.140126	+	0.0635875i
$534$	−26.9825	−	0.987399i	−1.16765	−	0.0427289i
$535$	−16.5490	+	16.5490i	−0.715476	+	0.715476i
$536$			67.8790i			2.93193i
$537$	−5.31771	−	0.194597i	−0.229476	−	0.00839747i
$538$	−37.8020	+	37.8020i	−1.62976	+	1.62976i
$539$	7.08980	+	7.08980i	0.305379	+	0.305379i
$540$	69.0611	−	55.3536i	2.97192	−	2.38204i
$541$	20.7059	+	20.7059i	0.890214	+	0.890214i	0.994543	−	0.104329i	$-0.0332694\pi$
$541$	20.7059	+	20.7059i	0.890214	+	0.890214i	−0.104329	+	0.994543i	$0.533269\pi$
$542$		−	54.0178i		−	2.32026i
$543$	−0.222799	+	6.08839i	−0.00956122	+	0.261278i
$544$	18.2744	+	18.2744i	0.783508	+	0.783508i
$545$	−17.9096			−0.767164
$546$	21.3825	+	63.9192i	0.915086	+	2.73549i
$547$	−20.7868			−0.888778			−0.444389	−	0.895834i	$-0.646579\pi$
$547$	−20.7868			−0.888778			−0.444389	+	0.895834i	$0.646579\pi$
$548$	11.7946	+	11.7946i	0.503840	+	0.503840i
$549$	−8.67983	−	0.636112i	−0.370446	−	0.0271486i
$550$		−	19.2986i		−	0.822895i
$551$	−4.71490	−	4.71490i	−0.200861	−	0.200861i
$552$	35.5446	−	33.0350i	1.51288	−	1.40606i
$553$	32.2461	+	32.2461i	1.37124	+	1.37124i
$554$	−9.49704	+	9.49704i	−0.403491	+	0.403491i
$555$	−1.74427	+	47.6655i	−0.0740403	+	2.02329i
$556$			35.6356i			1.51129i
$557$	−17.4294	+	17.4294i	−0.738506	+	0.738506i	−0.972289	−	0.233783i	$-0.924889\pi$
$557$	−17.4294	+	17.4294i	−0.738506	+	0.738506i	0.233783	+	0.972289i	$0.424889\pi$
$558$	14.2298	+	1.04285i	0.602396	+	0.0441473i
$559$	−11.2998	−	30.0754i	−0.477932	−	1.27205i
$560$			141.630i			5.98498i
$561$	−3.07766	+	2.86036i	−0.129939	+	0.120765i
$562$	24.3153			1.02568
$563$	7.22746			0.304601			0.152301	−	0.988334i	$-0.451332\pi$
$563$	7.22746			0.304601			0.152301	+	0.988334i	$0.451332\pi$
$564$	18.9831	+	20.4252i	0.799333	+	0.860057i
$565$	16.5933	−	16.5933i	0.698087	−	0.698087i
$566$	56.0167	−	56.0167i	2.35456	−	2.35456i
$567$	−22.1508	−	29.8075i	−0.930244	−	1.25180i
$568$	−26.2039			−1.09949
$569$	−36.4459			−1.52789			−0.763945	−	0.645281i	$-0.776740\pi$
$569$	−36.4459			−1.52789			−0.763945	+	0.645281i	$0.776740\pi$
$570$	−37.9244	−	40.8054i	−1.58848	−	1.70915i
$571$			15.4673i			0.647285i	0.946179	+	0.323643i	$0.104908\pi$
$571$			15.4673i			0.647285i	−0.946179	+	0.323643i	$0.895092\pi$
$572$	−15.8956	−	7.21321i	−0.664628	−	0.301600i
$573$	0.533268	−	14.5725i	0.0222776	−	0.608776i
$574$	7.51950	−	7.51950i	0.313858	−	0.313858i
$575$		−	27.8146i		−	1.15995i
$576$	1.83183	−	24.9955i	0.0763262	−	1.04148i
$577$	6.50979	−	6.50979i	0.271006	−	0.271006i	−0.558499	−	0.829505i	$-0.688623\pi$
$577$	6.50979	−	6.50979i	0.271006	−	0.271006i	0.829505	+	0.558499i	$0.188623\pi$
$578$	20.5581	+	20.5581i	0.855103	+	0.855103i
$579$	15.3863	+	16.5552i	0.639432	+	0.688009i
$580$	−22.9781	−	22.9781i	−0.954113	−	0.954113i
$581$		−	39.5504i		−	1.64083i
$582$	48.2546	+	1.76583i	2.00022	+	0.0731961i
$583$	9.65845	+	9.65845i	0.400012	+	0.400012i
$584$	−48.5074			−2.00725
$585$	−33.4127	−	18.2168i	−1.38145	−	0.753171i
$586$	−50.3100			−2.07828
$587$	−27.7929	−	27.7929i	−1.14714	−	1.14714i	−0.987113	−	0.160022i	$-0.948843\pi$
$587$	−27.7929	−	27.7929i	−1.14714	−	1.14714i	−0.160022	−	0.987113i	$-0.551157\pi$
$588$	84.0202	+	3.07464i	3.46493	+	0.126796i
$589$		−	6.35512i		−	0.261858i
$590$	0.886300	+	0.886300i	0.0364884	+	0.0364884i
$591$	−11.7950	−	12.6911i	−0.485183	−	0.522041i
$592$	53.9949	+	53.9949i	2.21918	+	2.21918i
$593$	6.72323	−	6.72323i	0.276090	−	0.276090i	−0.555456	−	0.831546i	$-0.687456\pi$
$593$	6.72323	−	6.72323i	0.276090	−	0.276090i	0.831546	+	0.555456i	$0.187456\pi$
$594$	13.5093	+	1.48840i	0.554292	+	0.0610696i
$595$		−	35.2168i		−	1.44375i
$596$	−48.7502	+	48.7502i	−1.99689	+	1.99689i
$597$	−0.176881	+	4.83359i	−0.00723925	+	0.197826i
$598$	−32.3743	−	14.6910i	−1.32388	−	0.600760i
$599$			40.0248i			1.63537i	0.575668	+	0.817684i	$0.304742\pi$
$599$			40.0248i			1.63537i	−0.575668	+	0.817684i	$0.695258\pi$
$600$	−64.6564	−	69.5683i	−2.63959	−	2.84011i
$601$	25.1913			1.02757			0.513787	−	0.857918i	$-0.328242\pi$
$601$	25.1913			1.02757			0.513787	+	0.857918i	$0.328242\pi$
$602$	−96.1714			−3.91965
$603$	−20.7397	+	17.9074i	−0.844585	+	0.729245i
$604$	29.1435	−	29.1435i	1.18583	−	1.18583i
$605$	2.48780	−	2.48780i	0.101143	−	0.101143i
$606$	−47.2523	−	50.8420i	−1.91950	−	2.06532i
$607$	−29.0276			−1.17819			−0.589096	−	0.808063i	$-0.700516\pi$
$607$	−29.0276			−1.17819			−0.589096	+	0.808063i	$0.700516\pi$
$608$	−37.2353			−1.51009
$609$	−9.98757	+	9.28241i	−0.404717	+	0.376142i
$610$			26.6964i			1.08091i
$611$	4.95453	−	10.9182i	0.200439	−	0.441702i
$612$	−2.57515	+	35.1382i	−0.104094	+	1.42038i
$613$	10.5391	−	10.5391i	0.425672	−	0.425672i	−0.461479	−	0.887151i	$-0.652681\pi$
$613$	10.5391	−	10.5391i	0.425672	−	0.425672i	0.887151	+	0.461479i	$0.152681\pi$
$614$			24.5665i			0.991422i
$615$	−0.219575	+	6.00028i	−0.00885410	+	0.241955i
$616$	−21.6840	+	21.6840i	−0.873674	+	0.873674i
$617$	26.8722	+	26.8722i	1.08183	+	1.08183i	0.996339	+	0.0854948i	$0.0272471\pi$
$617$	26.8722	+	26.8722i	1.08183	+	1.08183i	0.0854948	+	0.996339i	$0.472753\pi$
$618$	−11.6157	+	10.7956i	−0.467251	+	0.434261i
$619$	−16.1660	−	16.1660i	−0.649766	−	0.649766i	0.303171	−	0.952936i	$-0.401955\pi$
$619$	−16.1660	−	16.1660i	−0.649766	−	0.649766i	−0.952936	+	0.303171i	$0.901955\pi$
$620$		−	30.9717i		−	1.24385i
$621$	19.4706	+	2.14519i	0.781328	+	0.0860835i
$622$	−50.6921	−	50.6921i	−2.03257	−	2.03257i
$623$	24.5926			0.985281
$624$	−57.7779	+	19.3281i	−2.31297	+	0.773743i
$625$	7.45234			0.298094
$626$	−49.6816	−	49.6816i	−1.98568	−	1.98568i
$627$	0.221378	−	6.04956i	0.00884098	−	0.241596i
$628$		−	88.0790i		−	3.51474i
$629$	−13.4260	−	13.4260i	−0.535328	−	0.535328i
$630$	−86.2227	+	74.4478i	−3.43520	+	2.96607i
$631$	−16.2804	−	16.2804i	−0.648114	−	0.648114i	0.304423	−	0.952537i	$-0.401536\pi$
$631$	−16.2804	−	16.2804i	−0.648114	−	0.648114i	−0.952537	+	0.304423i	$0.901536\pi$
$632$	−58.0773	+	58.0773i	−2.31019	+	2.31019i
$633$	10.9883	+	0.402108i	0.436747	+	0.0159823i
$634$		−	23.4604i		−	0.931731i
$635$	−17.8023	+	17.8023i	−0.706462	+	0.706462i
$636$	114.461	+	4.18859i	4.53867	+	0.166088i
$637$	−12.7147	−	33.8413i	−0.503777	−	1.34084i
$638$		−	4.99004i		−	0.197558i
$639$	−6.91295	−	8.00632i	−0.273472	−	0.316725i
$640$	−1.91288			−0.0756133
$641$	−28.1326			−1.11117			−0.555585	−	0.831460i	$-0.687506\pi$
$641$	−28.1326			−1.11117			−0.555585	+	0.831460i	$0.687506\pi$
$642$	−22.0745	+	20.5159i	−0.871211	+	0.809699i
$643$	−5.04176	+	5.04176i	−0.198827	+	0.198827i	−0.799497	−	0.600670i	$-0.794901\pi$
$643$	−5.04176	+	5.04176i	−0.198827	+	0.198827i	0.600670	+	0.799497i	$0.294901\pi$
$644$	−53.2512	+	53.2512i	−2.09839	+	2.09839i
$645$	39.7747	−	36.9664i	1.56613	−	1.45555i
$646$	22.1758			0.872497
$647$	−46.3828			−1.82350			−0.911748	−	0.410749i	$-0.865267\pi$
$647$	−46.3828			−1.82350			−0.911748	+	0.410749i	$0.865267\pi$
$648$	53.6853	−	39.8950i	2.10896	−	1.56722i
$649$			0.136206i			0.00534654i
$650$	−28.7534	+	63.3633i	−1.12780	+	2.48531i
$651$	−12.9868	−	0.475241i	−0.508994	−	0.0186262i
$652$	−27.1914	+	27.1914i	−1.06490	+	1.06490i
$653$		−	17.2337i		−	0.674408i	−0.941432	−	0.337204i	$-0.890519\pi$
$653$		−	17.2337i		−	0.674408i	0.941432	−	0.337204i	$-0.109481\pi$
$654$	−23.0460	−	0.843349i	−0.901171	−	0.0329775i
$655$	52.2391	−	52.2391i	2.04115	−	2.04115i
$656$	6.79704	+	6.79704i	0.265380	+	0.265380i
$657$	−12.7969	−	14.8209i	−0.499255	−	0.578219i
$658$	−25.3779	−	25.3779i	−0.989334	−	0.989334i
$659$		−	29.0675i		−	1.13231i	−0.824300	−	0.566154i	$-0.808431\pi$
$659$		−	29.0675i		−	1.13231i	0.824300	−	0.566154i	$-0.191569\pi$
$660$	1.07889	−	29.4825i	0.0419956	−	1.14761i
$661$	30.6333	+	30.6333i	1.19150	+	1.19150i	0.976647	+	0.214852i	$0.0689268\pi$
$661$	30.6333	+	30.6333i	1.19150	+	1.19150i	0.214852	+	0.976647i	$0.431073\pi$
$662$	−28.9934			−1.12686
$663$	14.3666	−	4.80598i	0.557953	−	0.186649i
$664$	71.2329			2.76437
$665$	35.8782	+	35.8782i	1.39130	+	1.39130i
$666$	−4.48905	+	61.2537i	−0.173947	+	2.37353i
$667$		−	7.19203i		−	0.278476i
$668$	71.7363	+	71.7363i	2.77556	+	2.77556i
$669$	−31.5382	+	29.3115i	−1.21934	+	1.13325i
$670$	59.4332	+	59.4332i	2.29610	+	2.29610i
$671$	−2.05134	+	2.05134i	−0.0791911	+	0.0791911i
$672$	−2.78449	+	76.0912i	−0.107414	+	2.93528i
$673$		−	4.66411i		−	0.179788i	−0.995951	−	0.0898942i	$-0.971347\pi$
$673$		−	4.66411i		−	0.179788i	0.995951	−	0.0898942i	$-0.0286529\pi$
$674$	−27.1201	+	27.1201i	−1.04463	+	1.04463i
$675$	4.19859	−	38.1081i	0.161604	−	1.46678i
$676$	41.4430	+	47.3664i	1.59396	+	1.82179i
$677$		−	9.06630i		−	0.348446i	−0.984706	−	0.174223i	$-0.944259\pi$
$677$		−	9.06630i		−	0.348446i	0.984706	−	0.174223i	$-0.0557414\pi$
$678$	22.1336	−	20.5709i	0.850037	−	0.790021i
$679$	−43.9806			−1.68782
$680$	63.4277			2.43234
$681$	−27.5411	−	29.6334i	−1.05538	−	1.13555i
$682$	3.36299	−	3.36299i	0.128776	−	0.128776i
$683$	−30.9320	+	30.9320i	−1.18358	+	1.18358i	−0.204771	+	0.978810i	$0.565645\pi$
$683$	−30.9320	+	30.9320i	−1.18358	+	1.18358i	−0.978810	+	0.204771i	$0.934355\pi$
$684$	−33.1747	−	38.4217i	−1.26847	−	1.46909i
$685$	12.1217			0.463147
$686$	−32.6642			−1.24712
$687$	−5.68867	−	6.12083i	−0.217036	−	0.233524i
$688$		−	86.9314i		−	3.31423i
$689$	−17.3213	−	46.1020i	−0.659890	−	1.75635i
$690$	2.19735	−	60.0466i	0.0836516	−	2.28593i
$691$	1.19286	−	1.19286i	0.0453787	−	0.0453787i	−0.684053	−	0.729432i	$-0.739784\pi$
$691$	1.19286	−	1.19286i	0.0453787	−	0.0453787i	0.729432	+	0.684053i	$0.239784\pi$
$692$		−	76.7778i		−	2.91866i
$693$	−12.3458	−	0.904781i	−0.468980	−	0.0343698i
$694$	10.3018	−	10.3018i	0.391049	−	0.391049i
$695$	18.3120	+	18.3120i	0.694612	+	0.694612i
$696$	−16.7182	−	17.9883i	−0.633702	−	0.681844i
$697$	−1.69010	−	1.69010i	−0.0640171	−	0.0640171i
$698$			17.2363i			0.652405i
$699$	14.0996	+	0.515962i	0.533296	+	0.0195155i
$700$	104.224	+	104.224i	3.93930	+	3.93930i
$701$	40.4009			1.52592			0.762961	−	0.646445i	$-0.223745\pi$
$701$	40.4009			1.52592			0.762961	+	0.646445i	$0.223745\pi$
$702$	−42.1376	−	25.0147i	−1.59038	−	0.944118i
$703$	27.3563			1.03176
$704$	−5.90730	−	5.90730i	−0.222640	−	0.222640i
$705$	20.2506	+	0.741053i	0.762683	+	0.0279097i
$706$		−	35.0990i		−	1.32097i
$707$	44.7030	+	44.7030i	1.68123	+	1.68123i
$708$	0.777543	+	0.836611i	0.0292219	+	0.0314418i
$709$	5.44302	+	5.44302i	0.204417	+	0.204417i	0.801889	−	0.597472i	$-0.203828\pi$
$709$	5.44302	+	5.44302i	0.204417	+	0.204417i	−0.597472	+	0.801889i	$0.703828\pi$
$710$	−22.9435	+	22.9435i	−0.861055	+	0.861055i
$711$	−33.0665	−	2.42332i	−1.24009	−	0.0908815i
$712$			44.2929i			1.65994i
$713$	4.84700	−	4.84700i	0.181522	−	0.181522i
$714$	1.65833	−	45.3168i	0.0620613	−	1.69594i
$715$	−11.8748	+	4.46159i	−0.444094	+	0.166854i
$716$			14.8737i			0.555857i
$717$	11.8787	+	12.7811i	0.443618	+	0.477319i
$718$	9.91234			0.369925
$719$	−9.46821			−0.353105			−0.176552	−	0.984291i	$-0.556494\pi$
$719$	−9.46821			−0.353105			−0.176552	+	0.984291i	$0.556494\pi$
$720$	−67.2950	−	77.9386i	−2.50794	−	2.90460i
$721$	10.2131	−	10.2131i	0.380356	−	0.380356i
$722$	12.5482	−	12.5482i	0.466995	−	0.466995i
$723$	20.2050	+	21.7400i	0.751434	+	0.808519i
$724$	17.0293			0.632889
$725$	−14.0763			−0.522781
$726$	3.31844	−	3.08414i	0.123159	−	0.114463i
$727$			1.49573i			0.0554735i	0.999615	+	0.0277367i	$0.00883001\pi$
$727$			1.49573i			0.0554735i	−0.999615	+	0.0277367i	$0.991170\pi$
$728$	103.503	−	38.8878i	3.83607	−	1.44128i
$729$	26.3524	+	5.87814i	0.976014	+	0.217709i
$730$	−42.4719	+	42.4719i	−1.57196	+	1.57196i
$731$			21.6157i			0.799486i
$732$	−0.889608	+	24.3102i	−0.0328808	+	0.898529i
$733$	−0.423830	+	0.423830i	−0.0156545	+	0.0156545i	−0.714891	−	0.699236i	$-0.753524\pi$
$733$	−0.423830	+	0.423830i	−0.0156545	+	0.0156545i	0.699236	+	0.714891i	$0.253524\pi$
$734$	−18.3271	−	18.3271i	−0.676465	−	0.676465i
$735$	44.7551	−	41.5952i	1.65082	−	1.53426i
$736$	−28.3991	−	28.3991i	−1.04680	−	1.04680i
$737$			9.13363i			0.336442i
$738$	−0.565096	+	7.71080i	−0.0208015	+	0.283838i
$739$	−12.4017	−	12.4017i	−0.456204	−	0.456204i	0.441203	−	0.897407i	$-0.354552\pi$
$739$	−12.4017	−	12.4017i	−0.456204	−	0.456204i	−0.897407	+	0.441203i	$0.854552\pi$
$740$	133.321			4.90098
$741$	−9.74023	+	19.5327i	−0.357816	+	0.717553i
$742$	−147.420			−5.41194
$743$	−14.8803	−	14.8803i	−0.545906	−	0.545906i	0.379348	−	0.925254i	$-0.376148\pi$
$743$	−14.8803	−	14.8803i	−0.545906	−	0.545906i	−0.925254	+	0.379348i	$0.876148\pi$
$744$	0.855940	−	23.3901i	0.0313803	−	0.857524i
$745$			50.1022i			1.83560i
$746$	−8.70245	−	8.70245i	−0.318619	−	0.318619i
$747$	18.7922	+	21.7644i	0.687571	+	0.796319i
$748$	8.30436	+	8.30436i	0.303638	+	0.303638i
$749$	19.4090	−	19.4090i	0.709191	−	0.709191i
$750$	−37.8821	−	1.38626i	−1.38326	−	0.0506191i
$751$			30.1772i			1.10118i	0.834775	+	0.550592i	$0.185598\pi$
$751$			30.1772i			1.10118i	−0.834775	+	0.550592i	$0.814402\pi$
$752$	22.9397	−	22.9397i	0.836523	−	0.836523i
$753$	−26.3817	−	0.965415i	−0.961404	−	0.0351817i
$754$	−7.43478	+	16.3838i	−0.270759	+	0.596665i
$755$		−	29.9517i		−	1.09006i
$756$	−80.9964	+	64.9200i	−2.94581	+	2.36112i
$757$	52.3615			1.90311			0.951555	−	0.307479i	$-0.0994854\pi$
$757$	52.3615			1.90311			0.951555	+	0.307479i	$0.0994854\pi$
$758$	−3.01202			−0.109402
$759$	4.78279	−	4.44510i	0.173604	−	0.161347i
$760$	−64.6191	+	64.6191i	−2.34398	+	2.34398i
$761$	−13.0760	+	13.0760i	−0.474005	+	0.474005i	−0.903208	−	0.429203i	$-0.858794\pi$
$761$	−13.0760	+	13.0760i	−0.474005	+	0.474005i	0.429203	+	0.903208i	$0.358794\pi$
$762$	−23.7462	+	22.0696i	−0.860234	+	0.799498i
$763$	21.0048			0.760425
$764$	−40.7596			−1.47463
$765$	16.7331	+	19.3796i	0.604985	+	0.700672i
$766$			93.4666i			3.37709i
$767$	0.202936	−	0.447206i	0.00732760	−	0.0161477i
$768$	26.4589	+	0.968239i	0.954753	+	0.0349383i
$769$	−13.3384	+	13.3384i	−0.480995	+	0.480995i	−0.905449	−	0.424454i	$-0.860466\pi$
$769$	−13.3384	+	13.3384i	−0.480995	+	0.480995i	0.424454	+	0.905449i	$0.360466\pi$
$770$			37.9720i			1.36841i
$771$	−17.8130	−	0.651852i	−0.641521	−	0.0234759i
$772$	44.6703	−	44.6703i	1.60772	−	1.60772i
$773$	9.19335	+	9.19335i	0.330662	+	0.330662i	0.852838	−	0.522176i	$-0.174880\pi$
$773$	9.19335	+	9.19335i	0.330662	+	0.330662i	−0.522176	+	0.852838i	$0.674880\pi$
$774$	52.9227	−	45.6953i	1.90227	−	1.64249i
$775$	−9.48661	−	9.48661i	−0.340769	−	0.340769i
$776$		−	79.2119i		−	2.84354i
$777$	2.04572	−	55.9031i	0.0733899	−	2.00551i
$778$	−69.1783	−	69.1783i	−2.48016	−	2.48016i
$779$	3.44369			0.123383
$780$	−47.4691	+	95.1929i	−1.69967	+	3.40845i
$781$	−3.52594			−0.126168
$782$	16.9133	+	16.9133i	0.604820	+	0.604820i
$783$	1.08563	−	9.85361i	0.0387973	−	0.352139i
$784$		−	97.8166i		−	3.49345i
$785$	−45.2609	−	45.2609i	−1.61543	−	1.61543i
$786$	69.6810	−	64.7612i	2.48544	−	2.30996i
$787$	−16.0719	−	16.0719i	−0.572900	−	0.572900i	0.360038	−	0.932938i	$-0.382764\pi$
$787$	−16.0719	−	16.0719i	−0.572900	−	0.572900i	−0.932938	+	0.360038i	$0.882764\pi$
$788$	−34.2440	+	34.2440i	−1.21989	+	1.21989i
$789$	1.57401	−	43.0127i	0.0560362	−	1.53129i
$790$			101.702i			3.61840i
$791$	−19.4610	+	19.4610i	−0.691955	+	0.691955i
$792$	1.62957	−	22.2357i	0.0579042	−	0.790110i
$793$	9.79153	−	3.67885i	0.347707	−	0.130640i
$794$			58.4785i			2.07532i
$795$	60.9700	−	56.6653i	2.16238	−	2.00971i
$796$	13.5196			0.479190
$797$	−0.0322862			−0.00114364			−0.000571818	−	1.00000i	$-0.500182\pi$
$797$	−0.0322862			−0.00114364			−0.000571818		1.00000i	$0.500182\pi$
$798$	44.4785	+	47.8575i	1.57452	+	1.69414i
$799$	−5.70400	+	5.70400i	−0.201793	+	0.201793i
$800$	−55.5830	+	55.5830i	−1.96516	+	1.96516i
$801$	−13.5332	+	11.6850i	−0.478172	+	0.412871i
$802$	25.7556			0.909463
$803$	−6.52704			−0.230334
$804$	52.1402	+	56.1012i	1.83884	+	1.97854i
$805$			54.7281i			1.92891i
$806$	−16.0523	+	6.03114i	−0.565420	+	0.212438i
$807$	−1.29461	+	35.3777i	−0.0455726	+	1.24535i
$808$	−80.5130	+	80.5130i	−2.83244	+	2.83244i
$809$		−	47.8551i		−	1.68250i	−0.540650	−	0.841248i	$-0.681822\pi$
$809$		−	47.8551i		−	1.68250i	0.540650	−	0.841248i	$-0.318178\pi$
$810$	12.0745	−	81.9366i	0.424255	−	2.87896i
$811$	19.5080	−	19.5080i	0.685018	−	0.685018i	−0.276109	−	0.961126i	$-0.589045\pi$
$811$	19.5080	−	19.5080i	0.685018	−	0.685018i	0.961126	+	0.276109i	$0.0890450\pi$
$812$	26.9492	+	26.9492i	0.945732	+	0.945732i
$813$	−24.3518	−	26.2017i	−0.854054	−	0.918935i
$814$	14.4763	+	14.4763i	0.507396	+	0.507396i
$815$			27.9455i			0.978889i
$816$	40.9629	+	1.49900i	1.43399	+	0.0524754i
$817$	−22.0217	−	22.0217i	−0.770443	−	0.770443i
$818$	11.3718			0.397604
$819$	39.1872	+	21.3650i	1.36931	+	0.746555i
$820$	16.7829			0.586083
$821$	13.4723	+	13.4723i	0.470188	+	0.470188i	0.901975	−	0.431788i	$-0.142117\pi$
$821$	13.4723	+	13.4723i	0.470188	+	0.470188i	−0.431788	+	0.901975i	$0.642117\pi$
$822$	15.5982	+	0.570801i	0.544049	+	0.0199090i
$823$		−	54.0953i		−	1.88564i	−0.333299	−	0.942821i	$-0.608162\pi$
$823$		−	54.0953i		−	1.88564i	0.333299	−	0.942821i	$-0.391838\pi$
$824$	18.3945	+	18.3945i	0.640802	+	0.640802i
$825$	−8.70001	−	9.36093i	−0.302895	−	0.325906i
$826$	−1.03947	−	1.03947i	−0.0361679	−	0.0361679i
$827$	−0.146101	+	0.146101i	−0.00508042	+	0.00508042i	−0.709642	−	0.704562i	$-0.751143\pi$
$827$	−0.146101	+	0.146101i	−0.00508042	+	0.00508042i	0.704562	+	0.709642i	$0.251143\pi$
$828$	4.00187	−	54.6060i	0.139075	−	1.89769i
$829$		−	48.7796i		−	1.69419i	−0.531445	−	0.847093i	$-0.678351\pi$
$829$		−	48.7796i		−	1.69419i	0.531445	−	0.847093i	$-0.321649\pi$
$830$	62.3698	−	62.3698i	2.16489	−	2.16489i
$831$	−0.325247	+	8.88798i	−0.0112827	+	0.308321i
$832$	10.5941	+	28.1969i	0.367283	+	0.977553i
$833$			24.3223i			0.842719i
$834$	22.7015	+	24.4261i	0.786088	+	0.845805i
$835$	73.7258			2.55139
$836$	−16.9207			−0.585214
$837$	7.37240	−	5.90910i	0.254828	−	0.204248i
$838$	28.1825	−	28.1825i	0.973547	−	0.973547i
$839$	−29.9897	+	29.9897i	−1.03536	+	1.03536i	−0.0360082	+	0.999351i	$0.511464\pi$
$839$	−29.9897	+	29.9897i	−1.03536	+	1.03536i	−0.999351	+	0.0360082i	$0.988536\pi$
$840$	127.218	+	136.883i	4.38944	+	4.72290i
$841$	25.3603			0.874493
$842$	42.1322			1.45197
$843$	11.7943	−	10.9616i	0.406219	−	0.377538i
$844$		−	30.7345i		−	1.05793i
$845$	45.6362	+	3.04384i	1.56993	+	0.104711i
$846$	26.0236	+	1.90717i	0.894708	+	0.0655698i
$847$	−2.91775	+	2.91775i	−0.100255	+	0.100255i
$848$		−	133.256i		−	4.57602i
$849$	1.91842	−	52.4243i	0.0658399	−	1.79920i
$850$	33.1030	−	33.1030i	1.13542	−	1.13542i
$851$	20.8644	+	20.8644i	0.715223	+	0.715223i
$852$	−21.6572	+	20.1281i	−0.741965	+	0.689579i
$853$	−2.18285	−	2.18285i	−0.0747394	−	0.0747394i	0.668749	−	0.743488i	$-0.266830\pi$
$853$	−2.18285	−	2.18285i	−0.0747394	−	0.0747394i	−0.743488	+	0.668749i	$0.766830\pi$
$854$		−	31.3102i		−	1.07141i
$855$	−36.7910	−	2.69628i	−1.25823	−	0.0922107i
$856$	34.9570	+	34.9570i	1.19480	+	1.19480i
$857$	41.6162			1.42158			0.710791	−	0.703404i	$-0.248337\pi$
$857$	41.6162			1.42158			0.710791	+	0.703404i	$0.248337\pi$
$858$	−15.4906	+	5.18198i	−0.528841	+	0.176910i
$859$	−32.8728			−1.12161			−0.560803	−	0.827949i	$-0.689508\pi$
$859$	−32.8728			−1.12161			−0.560803	+	0.827949i	$0.689508\pi$
$860$	−107.323	−	107.323i	−3.65969	−	3.65969i
$861$	0.257522	−	7.03726i	0.00877633	−	0.239829i
$862$			57.6103i			1.96222i
$863$	−3.84905	−	3.84905i	−0.131023	−	0.131023i	0.638554	−	0.769577i	$-0.279533\pi$
$863$	−3.84905	−	3.84905i	−0.131023	−	0.131023i	−0.769577	+	0.638554i	$0.779533\pi$
$864$	−34.6220	−	43.1957i	−1.17787	−	1.46955i
$865$	−39.4536	−	39.4536i	−1.34146	−	1.34146i
$866$	41.4926	−	41.4926i	1.40997	−	1.40997i
$867$	19.2397	+	0.704057i	0.653413	+	0.0239110i
$868$			36.3243i			1.23293i
$869$	−7.81474	+	7.81474i	−0.265097	+	0.265097i
$870$	−30.3881	−	1.11203i	−1.03025	−	0.0377012i
$871$	13.6084	−	29.9885i	0.461103	−	1.01612i
$872$			37.8310i			1.28112i
$873$	24.2023	−	20.8971i	0.819124	−	0.707261i
$874$	−34.4621			−1.16570
$875$	34.5268			1.16722
$876$	−40.0908	+	37.2602i	−1.35454	+	1.25891i
$877$	−7.47983	+	7.47983i	−0.252576	+	0.252576i	−0.822026	−	0.569450i	$-0.807156\pi$
$877$	−7.47983	+	7.47983i	−0.252576	+	0.252576i	0.569450	+	0.822026i	$0.307156\pi$
$878$	15.7681	−	15.7681i	0.532147	−	0.532147i
$879$	−24.4032	+	22.6803i	−0.823101	+	0.764986i
$880$	−34.3237			−1.15705
$881$	12.9893			0.437622			0.218811	−	0.975767i	$-0.429782\pi$
$881$	12.9893			0.437622			0.218811	+	0.975767i	$0.429782\pi$
$882$	59.5494	−	51.4171i	2.00513	−	1.73130i
$883$		−	33.1975i		−	1.11718i	−0.829443	−	0.558592i	$-0.811342\pi$
$883$		−	33.1975i		−	1.11718i	0.829443	−	0.558592i	$-0.188658\pi$
$884$	−14.8929	−	39.6387i	−0.500904	−	1.33319i
$885$	0.829460	+	0.0303533i	0.0278820	+	0.00102032i
$886$	−20.0270	+	20.0270i	−0.672819	+	0.672819i
$887$			9.98206i			0.335165i	0.985858	+	0.167582i	$0.0535960\pi$
$887$			9.98206i			0.335165i	−0.985858	+	0.167582i	$0.946404\pi$
$888$	100.685	+	3.68448i	3.37878	+	0.123643i
$889$	20.8789	−	20.8789i	0.700256	−	0.700256i
$890$	38.7817	+	38.7817i	1.29997	+	1.29997i
$891$	7.22377	−	5.36817i	0.242005	−	0.179840i
$892$	85.0988	+	85.0988i	2.84932	+	2.84932i
$893$		−	11.6223i		−	0.388925i
$894$	−2.35927	+	64.4714i	−0.0789058	+	2.15625i
$895$	7.64311	+	7.64311i	0.255481	+	0.255481i
$896$	2.24347			0.0749491
$897$	−22.3262	+	7.46866i	−0.745452	+	0.249371i
$898$	−32.3462			−1.07941
$899$	−2.45295	−	2.45295i	−0.0818105	−	0.0818105i
$900$	−106.876	−	7.83251i	−3.56252	−	0.261084i
$901$			33.1344i			1.10387i
$902$	1.82233	+	1.82233i	0.0606769	+	0.0606769i
$903$	−46.6487	+	43.3551i	−1.55237	+	1.44277i
$904$	−35.0506	−	35.0506i	−1.16577	−	1.16577i
$905$	8.75080	−	8.75080i	0.290886	−	0.290886i
$906$	1.41040	−	38.5418i	0.0468575	−	1.28047i
$907$			13.6962i			0.454775i	0.973804	+	0.227387i	$0.0730184\pi$
$907$			13.6962i			0.454775i	−0.973804	+	0.227387i	$0.926982\pi$
$908$	−79.9589	+	79.9589i	−2.65353	+	2.65353i
$909$	−45.8402	−	3.35946i	−1.52042	−	0.111426i
$910$	56.5753	−	124.674i	1.87545	−	4.13289i
$911$			28.4013i			0.940978i	0.882406	+	0.470489i	$0.155923\pi$
$911$			28.4013i			0.940978i	−0.882406	+	0.470489i	$0.844077\pi$
$912$	−43.2594	+	40.2051i	−1.43246	+	1.33133i
$913$	9.58493			0.317215
$914$	107.712			3.56280
$915$	12.0350	+	12.9493i	0.397866	+	0.428091i
$916$	−16.5157	+	16.5157i	−0.545693	+	0.545693i
$917$	−61.2672	+	61.2672i	−2.02322	+	2.02322i
$918$	20.6195	+	25.7256i	0.680545	+	0.849071i
$919$	18.1630			0.599143			0.299571	−	0.954074i	$-0.403156\pi$
$919$	18.1630			0.599143			0.299571	+	0.954074i	$0.403156\pi$
$920$	−98.5689			−3.24972
$921$	11.0748	+	11.9162i	0.364928	+	0.392651i
$922$			36.4626i			1.20083i
$923$	11.5767	+	5.25338i	0.381053	+	0.172917i
$924$	−1.26534	+	34.5778i	−0.0416267	+	1.13753i
$925$	40.8361	−	40.8361i	1.34268	−	1.34268i
$926$		−	2.55371i		−	0.0839201i
$927$	−0.767522	+	10.4729i	−0.0252087	+	0.343976i
$928$	−14.3721	+	14.3721i	−0.471787	+	0.471787i
$929$	1.55936	+	1.55936i	0.0511610	+	0.0511610i	0.732224	−	0.681063i	$-0.238482\pi$
$929$	1.55936	+	1.55936i	0.0511610	+	0.0511610i	−0.681063	+	0.732224i	$0.738482\pi$
$930$	−19.7304	−	21.2293i	−0.646984	−	0.696135i
$931$	−24.7792	−	24.7792i	−0.812105	−	0.812105i
$932$		−	39.4368i		−	1.29180i
$933$	−47.4411	−	1.73606i	−1.55315	−	0.0568362i
$934$	−23.3259	−	23.3259i	−0.763247	−	0.763247i
$935$	8.53467			0.279114
$936$	−38.4798	+	70.5787i	−1.25775	+	2.30694i
$937$	30.5479			0.997958			0.498979	−	0.866614i	$-0.333709\pi$
$937$	30.5479			0.997958			0.498979	+	0.866614i	$0.333709\pi$
$938$	−69.7046	−	69.7046i	−2.27593	−	2.27593i
$939$	−46.4954	−	1.70146i	−1.51732	−	0.0555250i
$940$		−	56.6413i		−	1.84744i
$941$	5.89068	+	5.89068i	0.192031	+	0.192031i	0.796573	−	0.604542i	$-0.206644\pi$
$941$	5.89068	+	5.89068i	0.192031	+	0.192031i	−0.604542	+	0.796573i	$0.706644\pi$
$942$	−56.1103	−	60.3729i	−1.82817	−	1.96705i
$943$	2.62648	+	2.62648i	0.0855299	+	0.0855299i
$944$	0.939602	−	0.939602i	0.0305814	−	0.0305814i
$945$	−8.26116	+	74.9816i	−0.268736	+	2.43915i
$946$		−	23.3068i		−	0.757770i
$947$	1.46880	−	1.46880i	0.0477295	−	0.0477295i	−0.682839	−	0.730569i	$-0.739255\pi$
$947$	1.46880	−	1.46880i	0.0477295	−	0.0477295i	0.730569	+	0.682839i	$0.239255\pi$
$948$	−3.38903	+	92.6114i	−0.110071	+	3.00788i
$949$	21.4303	+	9.72479i	0.695657	+	0.315680i
$950$			67.4496i			2.18835i
$951$	−10.5762	−	11.3796i	−0.342957	−	0.369010i
$952$	−74.3894			−2.41097
$953$	−42.4769			−1.37596			−0.687981	−	0.725729i	$-0.741503\pi$
$953$	−42.4769			−1.37596			−0.687981	+	0.725729i	$0.741503\pi$
$954$	81.1244	−	70.0457i	2.62650	−	2.26781i
$955$	−20.9450	+	20.9450i	−0.677764	+	0.677764i
$956$	34.4869	−	34.4869i	1.11539	−	1.11539i
$957$	−2.24956	−	2.42046i	−0.0727180	−	0.0782423i
$958$	−55.7748			−1.80200
$959$	−14.2166			−0.459078
$960$	−37.2905	+	34.6576i	−1.20355	+	1.11857i
$961$			27.6937i			0.893345i
$962$	−25.9617	−	69.0990i	−0.837039	−	2.22784i
$963$	−1.45860	+	19.9028i	−0.0470029	+	0.641360i
$964$	58.6604	−	58.6604i	1.88933	−	1.88933i
$965$		−	45.9092i		−	1.47787i
$966$	−2.57710	+	70.4239i	−0.0829168	+	2.26585i
$967$	−22.7476	+	22.7476i	−0.731513	+	0.731513i	−0.970920	−	0.239406i	$-0.923047\pi$
$967$	−22.7476	+	22.7476i	−0.731513	+	0.731513i	0.239406	+	0.970920i	$0.423047\pi$
$968$	−5.25505	−	5.25505i	−0.168904	−	0.168904i
$969$	10.7566	−	9.99711i	0.345551	−	0.321153i
$970$	−69.3559	−	69.3559i	−2.22689	−	2.22689i
$971$			34.0987i			1.09428i	0.837042	+	0.547139i	$0.184283\pi$
$971$			34.0987i			1.09428i	−0.837042	+	0.547139i	$0.815717\pi$
$972$	13.7256	−	74.2102i	0.440249	−	2.38029i
$973$	−21.4767	−	21.4767i	−0.688510	−	0.688510i
$974$	34.3913			1.10197
$975$	14.6178	+	43.6972i	0.468143	+	1.39943i
$976$	28.3020			0.905924
$977$	−5.43379	−	5.43379i	−0.173842	−	0.173842i	0.614823	−	0.788665i	$-0.289227\pi$
$977$	−5.43379	−	5.43379i	−0.173842	−	0.173842i	−0.788665	+	0.614823i	$0.789227\pi$
$978$	−1.31593	+	35.9602i	−0.0420788	+	1.14988i
$979$			5.95994i			0.190480i
$980$	−120.762	−	120.762i	−3.85759	−	3.85759i
$981$	−11.5589	+	9.98032i	−0.369046	+	0.318647i
$982$	14.6068	+	14.6068i	0.466122	+	0.466122i
$983$	15.0657	−	15.0657i	0.480521	−	0.480521i	−0.424777	−	0.905298i	$-0.639647\pi$
$983$	15.0657	−	15.0657i	0.480521	−	0.480521i	0.905298	+	0.424777i	$0.139647\pi$
$984$	12.6746	+	0.463814i	0.404050	+	0.0147859i
$985$			35.1937i			1.12136i
$986$	8.55944	−	8.55944i	0.272588	−	0.272588i
$987$	−23.7504	−	0.869124i	−0.755983	−	0.0276645i
$988$	55.5559	+	25.2105i	1.76747	+	0.802054i
$989$		−	33.5916i		−	1.06815i
$990$	−18.0422	−	20.8958i	−0.573418	−	0.664112i
$991$	−55.4273			−1.76071			−0.880353	−	0.474318i	$-0.842695\pi$
$991$	−55.4273			−1.76071			−0.880353	+	0.474318i	$0.842695\pi$
$992$	−19.3719			−0.615058
$993$	−14.0635	+	13.0706i	−0.446292	+	0.414781i
$994$	26.9087	−	26.9087i	0.853491	−	0.853491i
$995$	6.94728	−	6.94728i	0.220244	−	0.220244i
$996$	58.8732	−	54.7165i	1.86547	−	1.73376i
$997$	−50.9539			−1.61373			−0.806863	−	0.590738i	$-0.798837\pi$
$997$	−50.9539			−1.61373			−0.806863	+	0.590738i	$0.798837\pi$
$998$	−24.2363			−0.767187
$999$	25.4363	+	31.7353i	0.804770	+	1.00406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.3	✓	96
3.2	odd	2	inner	429.2.j.a.122.46	yes	96
13.8	odd	4	inner	429.2.j.a.320.46	yes	96
39.8	even	4	inner	429.2.j.a.320.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.3	✓	96	1.1	even	1	trivial
429.2.j.a.122.46	yes	96	3.2	odd	2	inner
429.2.j.a.320.3	yes	96	39.8	even	4	inner
429.2.j.a.320.46	yes	96	13.8	odd	4	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84950 - 1.84950i) q^{2} +(-1.73089 - 0.0633404i) q^{3} +4.84133i q^{4} +(2.48780 + 2.48780i) q^{5} +(3.08414 + 3.31844i) q^{6} +(-2.91775 - 2.91775i) q^{7} +(5.25505 - 5.25505i) q^{8} +(2.99198 + 0.219271i) q^{9} +O(q^{10})\)	\(q+(-1.84950 - 1.84950i) q^{2} +(-1.73089 - 0.0633404i) q^{3} +4.84133i q^{4} +(2.48780 + 2.48780i) q^{5} +(3.08414 + 3.31844i) q^{6} +(-2.91775 - 2.91775i) q^{7} +(5.25505 - 5.25505i) q^{8} +(2.99198 + 0.219271i) q^{9} -9.20239i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.306652 - 8.37982i) q^{12} +(-3.37519 + 1.26812i) q^{13} +10.7928i q^{14} +(-4.14853 - 4.46369i) q^{15} -9.75582 q^{16} +2.42581 q^{17} +(-5.12813 - 5.93921i) q^{18} +(-2.47137 + 2.47137i) q^{19} +(-12.0443 + 12.0443i) q^{20} +(4.86549 + 5.23512i) q^{21} -2.61559 q^{22} -3.76979 q^{23} +(-9.42879 + 8.76307i) q^{24} +7.37828i q^{25} +(8.58781 + 3.89703i) q^{26} +(-5.16490 - 0.569047i) q^{27} +(14.1258 - 14.1258i) q^{28} +1.90780i q^{29} +(-0.582883 + 15.9283i) q^{30} +(-1.28575 + 1.28575i) q^{31} +(7.53332 + 7.53332i) q^{32} +(-1.26871 + 1.17914i) q^{33} +(-4.48654 - 4.48654i) q^{34} -14.5175i q^{35} +(-1.06156 + 14.4851i) q^{36} +(-5.53463 - 5.53463i) q^{37} +9.14163 q^{38} +(5.92241 - 1.98119i) q^{39} +26.1470 q^{40} +(-0.696716 - 0.696716i) q^{41} +(0.683618 - 18.6811i) q^{42} +8.91072i q^{43} +(3.42334 + 3.42334i) q^{44} +(6.89793 + 7.98894i) q^{45} +(6.97225 + 6.97225i) q^{46} +(-2.35138 + 2.35138i) q^{47} +(16.8863 + 0.617938i) q^{48} +10.0265i q^{49} +(13.6462 - 13.6462i) q^{50} +(-4.19881 - 0.153652i) q^{51} +(-6.13937 - 16.3404i) q^{52} +13.6591i q^{53} +(8.50005 + 10.6050i) q^{54} +3.51828 q^{55} -30.6658 q^{56} +(4.43422 - 4.12114i) q^{57} +(3.52849 - 3.52849i) q^{58} +(-0.0963120 + 0.0963120i) q^{59} +(21.6102 - 20.0844i) q^{60} -2.90103 q^{61} +4.75599 q^{62} +(-8.09005 - 9.36960i) q^{63} -8.35419i q^{64} +(-11.5516 - 5.24197i) q^{65} +(4.52731 + 0.165673i) q^{66} +(-6.45845 + 6.45845i) q^{67} +11.7441i q^{68} +(6.52511 + 0.238780i) q^{69} +(-26.8502 + 26.8502i) q^{70} +(-2.49321 - 2.49321i) q^{71} +(16.8753 - 14.5707i) q^{72} +(-4.61531 - 4.61531i) q^{73} +20.4726i q^{74} +(0.467344 - 12.7710i) q^{75} +(-11.9647 - 11.9647i) q^{76} -4.12632 q^{77} +(-14.6177 - 7.28930i) q^{78} -11.0517 q^{79} +(-24.2705 - 24.2705i) q^{80} +(8.90384 + 1.31211i) q^{81} +2.57716i q^{82} +(6.77757 + 6.77757i) q^{83} +(-25.3449 + 23.5555i) q^{84} +(6.03492 + 6.03492i) q^{85} +(16.4804 - 16.4804i) q^{86} +(0.120841 - 3.30220i) q^{87} -7.43177i q^{88} +(-4.21431 + 4.21431i) q^{89} +(2.01782 - 27.5333i) q^{90} +(13.5480 + 6.14790i) q^{91} -18.2508i q^{92} +(2.30693 - 2.14405i) q^{93} +8.69778 q^{94} -12.2966 q^{95} +(-12.5622 - 13.5165i) q^{96} +(7.53673 - 7.53673i) q^{97} +(18.5440 - 18.5440i) q^{98} +(2.27069 - 1.96060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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