LMFDB - Embedded newform 950.2.l.l.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.3
Character	$\chi$	$=$	950.251
Dual form			950.2.l.l.651.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.0989733 - 0.561305i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0989733 - 0.561305i) q^{6} +(-2.10163 + 3.64013i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.51381 - 0.914952i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0989733 - 0.561305i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0989733 - 0.561305i) q^{6} +(-2.10163 + 3.64013i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.51381 - 0.914952i) q^{9} +(-1.66241 - 2.87938i) q^{11} +(0.284982 - 0.493604i) q^{12} +(-0.485193 + 2.75167i) q^{13} +(-3.21988 + 2.70180i) q^{14} +(0.173648 + 0.984808i) q^{16} +(4.32594 + 1.57451i) q^{17} +2.67514 q^{18} +(-0.508740 + 4.32911i) q^{19} +(2.25123 + 0.819381i) q^{21} +(-0.577349 - 3.27431i) q^{22} +(6.48241 + 5.43938i) q^{23} +(0.436618 - 0.366366i) q^{24} +(-1.39706 + 2.41977i) q^{26} +(-1.61731 - 2.80127i) q^{27} +(-3.94977 + 1.43760i) q^{28} +(-0.414225 + 0.150766i) q^{29} +(-4.93377 + 8.54554i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.45168 + 1.21810i) q^{33} +(3.52654 + 2.95912i) q^{34} +(2.51381 + 0.914952i) q^{36} +4.04577 q^{37} +(-1.95870 + 3.89403i) q^{38} +1.59255 q^{39} +(-1.90718 - 10.8162i) q^{41} +(1.83522 + 1.53993i) q^{42} +(1.03613 - 0.869414i) q^{43} +(0.577349 - 3.27431i) q^{44} +(4.23109 + 7.32846i) q^{46} +(-5.39446 + 1.96342i) q^{47} +(0.535591 - 0.194939i) q^{48} +(-5.33369 - 9.23823i) q^{49} +(0.455630 - 2.58401i) q^{51} +(-2.14042 + 1.79602i) q^{52} +(0.586495 + 0.492128i) q^{53} +(-0.561687 - 3.18549i) q^{54} -4.20326 q^{56} +(2.48030 - 0.142908i) q^{57} -0.440809 q^{58} +(5.17799 + 1.88463i) q^{59} +(5.05034 + 4.23774i) q^{61} +(-7.55897 + 6.34273i) q^{62} +(-1.95255 + 11.0735i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.78074 + 0.648138i) q^{66} +(-3.77939 + 1.37558i) q^{67} +(2.30178 + 3.98681i) q^{68} +(2.41157 - 4.17696i) q^{69} +(7.41755 - 6.22406i) q^{71} +(2.04928 + 1.71955i) q^{72} +(0.578974 + 3.28353i) q^{73} +(3.80178 + 1.38373i) q^{74} +(-3.17241 + 2.98928i) q^{76} +13.9751 q^{77} +(1.49650 + 0.544683i) q^{78} +(-0.964498 - 5.46994i) q^{79} +(4.73553 - 3.97358i) q^{81} +(1.90718 - 10.8162i) q^{82} +(3.75655 - 6.50654i) q^{83} +(1.19785 + 2.07474i) q^{84} +(1.27100 - 0.462606i) q^{86} +(0.125623 + 0.217585i) q^{87} +(1.66241 - 2.87938i) q^{88} +(-1.91958 + 10.8865i) q^{89} +(-8.99673 - 7.54915i) q^{91} +(1.46944 + 8.33362i) q^{92} +(5.28497 + 1.92357i) q^{93} -5.74067 q^{94} +0.569964 q^{96} +(-13.3547 - 4.86070i) q^{97} +(-1.85237 - 10.5053i) q^{98} +(-6.81347 - 5.71718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.0989733	−	0.561305i	−0.0571423	−	0.324070i	0.942815	−	0.333316i	$-0.108168\pi$
$3$	−0.0989733	−	0.561305i	−0.0571423	−	0.324070i	−0.999957	+	0.00924667i	$0.997057\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	0.0989733	−	0.561305i	0.0404057	−	0.229152i
$7$	−2.10163	+	3.64013i	−0.794341	+	1.37584i	0.128915	+	0.991656i	$0.458850\pi$
$7$	−2.10163	+	3.64013i	−0.794341	+	1.37584i	−0.923257	+	0.384184i	$0.874483\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.51381	−	0.914952i	0.837937	−	0.304984i
$10$		0			0
$11$	−1.66241	−	2.87938i	−0.501235	−	0.868165i	−0.999999	−	0.00142683i	$-0.999546\pi$
$11$	−1.66241	−	2.87938i	−0.501235	−	0.868165i	0.498764	−	0.866738i	$-0.333788\pi$
$12$	0.284982	−	0.493604i	0.0822673	−	0.142491i
$13$	−0.485193	+	2.75167i	−0.134568	+	0.763175i	0.840591	+	0.541670i	$0.182208\pi$
$13$	−0.485193	+	2.75167i	−0.134568	+	0.763175i	−0.975159	+	0.221505i	$0.928903\pi$
$14$	−3.21988	+	2.70180i	−0.860550	+	0.722087i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	4.32594	+	1.57451i	1.04919	+	0.381876i	0.808359	−	0.588690i	$-0.200356\pi$
$17$	4.32594	+	1.57451i	1.04919	+	0.381876i	0.240836	+	0.970566i	$0.422578\pi$
$18$	2.67514			0.630537
$19$	−0.508740	+	4.32911i	−0.116713	+	0.993166i
$19$	−0.508740	+	4.32911i	−0.116713	+	0.993166i
$20$		0			0
$21$	2.25123	+	0.819381i	0.491259	+	0.178803i
$22$	−0.577349	−	3.27431i	−0.123091	−	0.698084i
$23$	6.48241	+	5.43938i	1.35168	+	1.13419i	0.978458	+	0.206446i	$0.0661898\pi$
$23$	6.48241	+	5.43938i	1.35168	+	1.13419i	0.373217	+	0.927744i	$0.378255\pi$
$24$	0.436618	−	0.366366i	0.0891243	−	0.0747842i
$25$		0			0
$26$	−1.39706	+	2.41977i	−0.273986	+	0.474557i
$27$	−1.61731	−	2.80127i	−0.311252	−	0.539105i
$28$	−3.94977	+	1.43760i	−0.746437	+	0.271681i
$29$	−0.414225	+	0.150766i	−0.0769196	+	0.0279965i	−0.380193	−	0.924907i	$-0.624143\pi$
$29$	−0.414225	+	0.150766i	−0.0769196	+	0.0279965i	0.303274	+	0.952903i	$0.401920\pi$
$30$		0			0
$31$	−4.93377	+	8.54554i	−0.886131	+	1.53482i	−0.0417198	+	0.999129i	$0.513284\pi$
$31$	−4.93377	+	8.54554i	−0.886131	+	1.53482i	−0.844411	+	0.535695i	$0.820050\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−1.45168	+	1.21810i	−0.252704	+	0.212044i
$34$	3.52654	+	2.95912i	0.604796	+	0.507484i
$35$		0			0
$36$	2.51381	+	0.914952i	0.418968	+	0.152492i
$37$	4.04577			0.665120			0.332560	−	0.943082i	$-0.392088\pi$
$37$	4.04577			0.665120			0.332560	+	0.943082i	$0.392088\pi$
$38$	−1.95870	+	3.89403i	−0.317743	+	0.631695i
$39$	1.59255			0.255012
$40$		0			0
$41$	−1.90718	−	10.8162i	−0.297852	−	1.68920i	−0.655381	−	0.755298i	$-0.727492\pi$
$41$	−1.90718	−	10.8162i	−0.297852	−	1.68920i	0.357530	−	0.933902i	$-0.383619\pi$
$42$	1.83522	+	1.53993i	0.283180	+	0.237617i
$43$	1.03613	−	0.869414i	0.158008	−	0.132584i	−0.560356	−	0.828252i	$-0.689336\pi$
$43$	1.03613	−	0.869414i	0.158008	−	0.132584i	0.718364	+	0.695667i	$0.244891\pi$
$44$	0.577349	−	3.27431i	0.0870386	−	0.493620i
$45$		0			0
$46$	4.23109	+	7.32846i	0.623840	+	1.08052i
$47$	−5.39446	+	1.96342i	−0.786863	+	0.286395i	−0.704031	−	0.710169i	$-0.748619\pi$
$47$	−5.39446	+	1.96342i	−0.786863	+	0.286395i	−0.0828316	+	0.996564i	$0.526396\pi$
$48$	0.535591	−	0.194939i	0.0773060	−	0.0281371i
$49$	−5.33369	−	9.23823i	−0.761956	−	1.31975i
$50$		0			0
$51$	0.455630	−	2.58401i	0.0638010	−	0.361833i
$52$	−2.14042	+	1.79602i	−0.296822	+	0.249064i
$53$	0.586495	+	0.492128i	0.0805613	+	0.0675990i	0.682179	−	0.731185i	$-0.261032\pi$
$53$	0.586495	+	0.492128i	0.0805613	+	0.0675990i	−0.601618	+	0.798784i	$0.705477\pi$
$54$	−0.561687	−	3.18549i	−0.0764360	−	0.433490i
$55$		0			0
$56$	−4.20326			−0.561684
$57$	2.48030	−	0.142908i	0.328524	−	0.0189286i
$58$	−0.440809			−0.0578810
$59$	5.17799	+	1.88463i	0.674116	+	0.245358i	0.656319	−	0.754483i	$-0.272112\pi$
$59$	5.17799	+	1.88463i	0.674116	+	0.245358i	0.0177971	+	0.999842i	$0.494335\pi$
$60$		0			0
$61$	5.05034	+	4.23774i	0.646630	+	0.542587i	0.906046	−	0.423179i	$-0.139086\pi$
$61$	5.05034	+	4.23774i	0.646630	+	0.542587i	−0.259416	+	0.965766i	$0.583530\pi$
$62$	−7.55897	+	6.34273i	−0.959991	+	0.805528i
$63$	−1.95255	+	11.0735i	−0.245999	+	1.39513i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−1.78074	+	0.648138i	−0.219194	+	0.0797802i
$67$	−3.77939	+	1.37558i	−0.461725	+	0.168054i	−0.562400	−	0.826865i	$-0.690122\pi$
$67$	−3.77939	+	1.37558i	−0.461725	+	0.168054i	0.100675	+	0.994919i	$0.467900\pi$
$68$	2.30178	+	3.98681i	0.279132	+	0.483471i
$69$	2.41157	−	4.17696i	0.290319	−	0.502847i
$70$		0			0
$71$	7.41755	−	6.22406i	0.880301	−	0.738660i	−0.0859398	−	0.996300i	$-0.527389\pi$
$71$	7.41755	−	6.22406i	0.880301	−	0.738660i	0.966241	+	0.257640i	$0.0829448\pi$
$72$	2.04928	+	1.71955i	0.241510	+	0.202651i
$73$	0.578974	+	3.28353i	0.0677638	+	0.384308i	0.999761	+	0.0218432i	$0.00695347\pi$
$73$	0.578974	+	3.28353i	0.0677638	+	0.384308i	−0.931998	+	0.362464i	$0.881935\pi$
$74$	3.80178	+	1.38373i	0.441948	+	0.160856i
$75$		0			0
$76$	−3.17241	+	2.98928i	−0.363901	+	0.342894i
$77$	13.9751			1.59261
$78$	1.49650	+	0.544683i	0.169446	+	0.0616732i
$79$	−0.964498	−	5.46994i	−0.108515	−	0.615416i	−0.989758	−	0.142754i	$-0.954404\pi$
$79$	−0.964498	−	5.46994i	−0.108515	−	0.615416i	0.881244	−	0.472662i	$-0.156707\pi$
$80$		0			0
$81$	4.73553	−	3.97358i	0.526170	−	0.441509i
$82$	1.90718	−	10.8162i	0.210613	−	1.19444i
$83$	3.75655	−	6.50654i	0.412335	−	0.714186i	−0.582809	−	0.812609i	$-0.698047\pi$
$83$	3.75655	−	6.50654i	0.412335	−	0.714186i	0.995145	+	0.0984231i	$0.0313799\pi$
$84$	1.19785	+	2.07474i	0.130697	+	0.226373i
$85$		0			0
$86$	1.27100	−	0.462606i	0.137055	−	0.0498841i
$87$	0.125623	+	0.217585i	0.0134682	+	0.0233275i
$88$	1.66241	−	2.87938i	0.177213	−	0.306943i
$89$	−1.91958	+	10.8865i	−0.203475	+	1.15396i	0.696347	+	0.717705i	$0.254807\pi$
$89$	−1.91958	+	10.8865i	−0.203475	+	1.15396i	−0.899822	+	0.436258i	$0.856304\pi$
$90$		0			0
$91$	−8.99673	−	7.54915i	−0.943113	−	0.791366i
$92$	1.46944	+	8.33362i	0.153200	+	0.868840i
$93$	5.28497	+	1.92357i	0.548026	+	0.199465i
$94$	−5.74067			−0.592104
$95$		0			0
$96$	0.569964			0.0581718
$97$	−13.3547	−	4.86070i	−1.35596	−	0.493530i	−0.441158	−	0.897429i	$-0.645432\pi$
$97$	−13.3547	−	4.86070i	−1.35596	−	0.493530i	−0.914803	+	0.403900i	$0.867655\pi$
$98$	−1.85237	−	10.5053i	−0.187118	−	1.06120i
$99$	−6.81347	−	5.71718i	−0.684780	−	0.574598i
$100$		0			0
$101$	2.62836	−	14.9062i	0.261531	−	1.48322i	−0.517202	−	0.855863i	$-0.673026\pi$
$101$	2.62836	−	14.9062i	0.261531	−	1.48322i	0.778734	−	0.627355i	$-0.215862\pi$
$102$	1.31194	−	2.27234i	0.129901	−	0.224995i
$103$	−0.381449	−	0.660689i	−0.0375853	−	0.0650996i	0.846621	−	0.532197i	$-0.178633\pi$
$103$	−0.381449	−	0.660689i	−0.0375853	−	0.0650996i	−0.884206	+	0.467097i	$0.845300\pi$
$104$	−2.62561	+	0.955644i	−0.257462	+	0.0937086i
$105$		0			0
$106$	0.382808	+	0.663042i	0.0371816	+	0.0644004i
$107$	5.08947	−	8.81522i	0.492018	−	0.852199i	−0.507940	−	0.861392i	$-0.669593\pi$
$107$	5.08947	−	8.81522i	0.492018	−	0.852199i	0.999958	+	0.00919292i	$0.00292624\pi$
$108$	0.561687	−	3.18549i	0.0540484	−	0.306524i
$109$	4.37537	−	3.67138i	0.419085	−	0.351654i	−0.408730	−	0.912655i	$-0.634028\pi$
$109$	4.37537	−	3.67138i	0.419085	−	0.351654i	0.827815	+	0.561001i	$0.189584\pi$
$110$		0			0
$111$	−0.400423	−	2.27091i	−0.0380065	−	0.215545i
$112$	−3.94977	−	1.43760i	−0.373218	−	0.135840i
$113$	−10.2959			−0.968557			−0.484278	−	0.874914i	$-0.660918\pi$
$113$	−10.2959			−0.968557			−0.484278	+	0.874914i	$0.660918\pi$
$114$	2.37960	+	0.714024i	0.222870	+	0.0668745i
$115$		0			0
$116$	−0.414225	−	0.150766i	−0.0384598	−	0.0139982i
$117$	1.29796	+	7.36109i	0.119996	+	0.680533i
$118$	4.22113	+	3.54195i	0.388587	+	0.326063i
$119$	−14.8230	+	12.4379i	−1.35882	+	1.14018i
$120$		0			0
$121$	−0.0272071	+	0.0471242i	−0.00247338	+	0.00428401i
$122$	3.29637	+	5.70949i	0.298440	+	0.516913i
$123$	−5.88241	+	2.14102i	−0.530399	+	0.193049i
$124$	−9.27246	+	3.37490i	−0.832691	+	0.303075i
$125$		0			0
$126$	−5.62215	+	9.73786i	−0.500861	+	0.867517i
$127$	−0.894029	+	5.07029i	−0.0793323	+	0.449916i	0.919104	+	0.394015i	$0.128914\pi$
$127$	−0.894029	+	5.07029i	−0.0793323	+	0.449916i	−0.998436	+	0.0559007i	$0.982197\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−0.590556	−	0.495535i	−0.0519955	−	0.0436294i
$130$		0			0
$131$	3.41904	+	1.24443i	0.298723	+	0.108726i	0.487034	−	0.873383i	$-0.338079\pi$
$131$	3.41904	+	1.24443i	0.298723	+	0.108726i	−0.188311	+	0.982110i	$0.560301\pi$
$132$	−1.89503			−0.164941
$133$	−14.6893	−	10.9501i	−1.27373	−	0.949491i
$134$	−4.02194			−0.347442
$135$		0			0
$136$	0.799401	+	4.53363i	0.0685481	+	0.388756i
$137$	0.0803376	+	0.0674112i	0.00686370	+	0.00575933i	0.646213	−	0.763157i	$-0.276352\pi$
$137$	0.0803376	+	0.0674112i	0.00686370	+	0.00575933i	−0.639349	+	0.768916i	$0.720796\pi$
$138$	3.69474	−	3.10026i	0.314517	−	0.263911i
$139$	1.06327	−	6.03011i	0.0901855	−	0.511467i	−0.905931	−	0.423425i	$-0.860828\pi$
$139$	1.06327	−	6.03011i	0.0901855	−	0.511467i	0.996117	−	0.0880426i	$-0.0280611\pi$
$140$		0			0
$141$	1.63599	+	2.83361i	0.137775	+	0.238633i
$142$	9.09897	−	3.31175i	0.763569	−	0.277916i
$143$	8.72967	−	3.17734i	0.730012	−	0.265703i
$144$	1.33757	+	2.31674i	0.111464	+	0.193062i
$145$		0			0
$146$	−0.578974	+	3.28353i	−0.0479163	+	0.271747i
$147$	−4.65758	+	3.90817i	−0.384150	+	0.322340i
$148$	3.09924	+	2.60057i	0.254756	+	0.213765i
$149$	−2.78680	−	15.8047i	−0.228304	−	1.29477i	−0.856268	−	0.516532i	$-0.827223\pi$
$149$	−2.78680	−	15.8047i	−0.228304	−	1.29477i	0.627964	−	0.778242i	$-0.283888\pi$
$150$		0			0
$151$	−10.6769			−0.868873			−0.434436	−	0.900703i	$-0.643052\pi$
$151$	−10.6769			−0.868873			−0.434436	+	0.900703i	$0.643052\pi$
$152$	−4.00349	+	1.72397i	−0.324726	+	0.139833i
$153$	12.3152			0.995624
$154$	13.1323	+	4.77976i	1.05823	+	0.385164i
$155$		0			0
$156$	1.21996	+	1.02367i	0.0976751	+	0.0819591i
$157$	−1.42292	+	1.19397i	−0.113561	+	0.0952892i	−0.697800	−	0.716293i	$-0.745838\pi$
$157$	−1.42292	+	1.19397i	−0.113561	+	0.0952892i	0.584239	+	0.811582i	$0.301393\pi$
$158$	0.964498	−	5.46994i	0.0767313	−	0.435165i
$159$	0.218187	−	0.377911i	0.0173033	−	0.0299703i
$160$		0			0
$161$	−33.4237	+	12.1652i	−2.63415	+	0.958754i
$162$	5.80899	−	2.11430i	0.456397	−	0.166115i
$163$	−7.22285	−	12.5103i	−0.565737	−	0.979885i	−0.996981	−	0.0776498i	$-0.975258\pi$
$163$	−7.22285	−	12.5103i	−0.565737	−	0.979885i	0.431244	−	0.902236i	$-0.358075\pi$
$164$	5.49151	−	9.51157i	0.428815	−	0.742729i
$165$		0			0
$166$	5.75537	−	4.82933i	0.446704	−	0.374829i
$167$	−1.89231	−	1.58784i	−0.146431	−	0.122871i	0.566629	−	0.823973i	$-0.308247\pi$
$167$	−1.89231	−	1.58784i	−0.146431	−	0.122871i	−0.713061	+	0.701102i	$0.752692\pi$
$168$	0.416010	+	2.35931i	0.0320959	+	0.182025i
$169$	4.87975	+	1.77608i	0.375365	+	0.136622i
$170$		0			0
$171$	2.68205	+	11.3480i	0.205102	+	0.867805i
$172$	1.35257			0.103132
$173$	−10.0285	−	3.65007i	−0.762452	−	0.277510i	−0.0686160	−	0.997643i	$-0.521858\pi$
$173$	−10.0285	−	3.65007i	−0.762452	−	0.277510i	−0.693836	+	0.720133i	$0.744081\pi$
$174$	0.0436283	+	0.247428i	0.00330745	+	0.0187575i
$175$		0			0
$176$	2.54696	−	2.13715i	0.191984	−	0.161094i
$177$	0.545372	−	3.09296i	0.0409927	−	0.232481i
$178$	−5.52720	+	9.57340i	−0.414281	+	0.717556i
$179$	0.694503	+	1.20291i	0.0519096	+	0.0899101i	0.890813	−	0.454371i	$-0.150136\pi$
$179$	0.694503	+	1.20291i	0.0519096	+	0.0899101i	−0.838903	+	0.544281i	$0.816803\pi$
$180$		0			0
$181$	24.5561	−	8.93769i	1.82524	−	0.664334i	0.831116	−	0.556099i	$-0.187702\pi$
$181$	24.5561	−	8.93769i	1.82524	−	0.664334i	0.994125	−	0.108234i	$-0.0345197\pi$
$182$	−5.87220	−	10.1709i	−0.435276	−	0.753920i
$183$	1.87882	−	3.25421i	0.138886	−	0.240558i
$184$	−1.46944	+	8.33362i	−0.108329	+	0.614363i
$185$		0			0
$186$	4.30835	+	3.61513i	0.315903	+	0.265074i
$187$	−2.65786	−	15.0735i	−0.194362	−	1.10228i
$188$	−5.39446	−	1.96342i	−0.393431	−	0.143197i
$189$	13.5960			0.988962
$190$		0			0
$191$	−5.82059			−0.421163			−0.210581	−	0.977576i	$-0.567536\pi$
$191$	−5.82059			−0.421163			−0.210581	+	0.977576i	$0.567536\pi$
$192$	0.535591	+	0.194939i	0.0386530	+	0.0140685i
$193$	0.337712	+	1.91526i	0.0243090	+	0.137863i	0.994547	−	0.104291i	$-0.0332572\pi$
$193$	0.337712	+	1.91526i	0.0243090	+	0.137863i	−0.970238	+	0.242154i	$0.922146\pi$
$194$	−10.8868	−	9.13513i	−0.781629	−	0.655864i
$195$		0			0
$196$	1.85237	−	10.5053i	0.132312	−	0.750381i
$197$	−5.52244	+	9.56515i	−0.393458	+	0.681489i	−0.992903	−	0.118927i	$-0.962055\pi$
$197$	−5.52244	+	9.56515i	−0.393458	+	0.681489i	0.599445	+	0.800416i	$0.295388\pi$
$198$	−4.44718	−	7.70274i	−0.316047	−	0.547410i
$199$	−0.838010	+	0.305011i	−0.0594050	+	0.0216216i	−0.371552	−	0.928412i	$-0.621174\pi$
$199$	−0.838010	+	0.305011i	−0.0594050	+	0.0216216i	0.312147	+	0.950034i	$0.398952\pi$
$200$		0			0
$201$	1.14618	+	1.98524i	0.0808454	+	0.140028i
$202$	7.56805	−	13.1083i	0.532486	−	0.922294i
$203$	0.321741	−	1.82469i	0.0225818	−	0.128068i
$204$	2.01000	−	1.68659i	0.140728	−	0.118085i
$205$		0			0
$206$	−0.132476	−	0.751308i	−0.00923003	−	0.0523461i
$207$	21.2723	+	7.74249i	1.47853	+	0.538140i
$208$	−2.79412			−0.193737
$209$	13.3109	−	5.73190i	0.920732	−	0.396484i
$210$		0			0
$211$	13.9109	+	5.06316i	0.957666	+	0.348562i	0.773119	−	0.634261i	$-0.218696\pi$
$211$	13.9109	+	5.06316i	0.957666	+	0.348562i	0.184548	+	0.982824i	$0.440918\pi$
$212$	0.132948	+	0.753984i	0.00913088	+	0.0517838i
$213$	−4.22774	−	3.54749i	−0.289680	−	0.243070i
$214$	7.79752	−	6.54290i	0.533027	−	0.447263i
$215$		0			0
$216$	1.61731	−	2.80127i	0.110044	−	0.190602i
$217$	−20.7379	−	35.9191i	−1.40778	−	2.43835i
$218$	5.36719	−	1.95350i	0.363512	−	0.132308i
$219$	1.78576	−	0.649963i	0.120670	−	0.0439204i
$220$		0			0
$221$	−6.43145	+	11.1396i	−0.432626	+	0.749330i
$222$	0.400423	−	2.27091i	0.0268746	−	0.152414i
$223$	7.31353	−	6.13678i	0.489750	−	0.410949i	−0.364187	−	0.931326i	$-0.618653\pi$
$223$	7.31353	−	6.13678i	0.489750	−	0.410949i	0.853937	+	0.520377i	$0.174209\pi$
$224$	−3.21988	−	2.70180i	−0.215138	−	0.180522i
$225$		0			0
$226$	−9.67498	−	3.52140i	−0.643570	−	0.234240i
$227$	−3.28772			−0.218214			−0.109107	−	0.994030i	$-0.534799\pi$
$227$	−3.28772			−0.218214			−0.109107	+	0.994030i	$0.534799\pi$
$228$	1.99188	+	1.48483i	0.131916	+	0.0983356i
$229$	5.64170			0.372814			0.186407	−	0.982473i	$-0.440316\pi$
$229$	5.64170			0.372814			0.186407	+	0.982473i	$0.440316\pi$
$230$		0			0
$231$	−1.38316	−	7.84428i	−0.0910052	−	0.516116i
$232$	−0.337679	−	0.283346i	−0.0221697	−	0.0186026i
$233$	10.9994	−	9.22957i	0.720593	−	0.604649i	−0.206956	−	0.978350i	$-0.566356\pi$
$233$	10.9994	−	9.22957i	0.720593	−	0.604649i	0.927549	+	0.373701i	$0.121911\pi$
$234$	−1.29796	+	7.36109i	−0.0848503	+	0.481210i
$235$		0			0
$236$	2.75515	+	4.77206i	0.179345	+	0.310634i
$237$	−2.97485	+	1.08276i	−0.193237	+	0.0703326i
$238$	−18.1830	+	6.61809i	−1.17863	+	0.428987i
$239$	2.90592	+	5.03319i	0.187968	+	0.325570i	0.944573	−	0.328302i	$-0.106477\pi$
$239$	2.90592	+	5.03319i	0.187968	+	0.325570i	−0.756605	+	0.653873i	$0.773143\pi$
$240$		0			0
$241$	1.06017	−	6.01250i	0.0682913	−	0.387299i	−0.931435	−	0.363908i	$-0.881442\pi$
$241$	1.06017	−	6.01250i	0.0682913	−	0.387299i	0.999726	−	0.0233916i	$-0.00744647\pi$
$242$	−0.0416838	+	0.0349768i	−0.00267953	+	0.00224840i
$243$	−10.1327	−	8.50234i	−0.650013	−	0.545425i
$244$	1.14482	+	6.49259i	0.0732895	+	0.415646i
$245$		0			0
$246$	−6.25993			−0.399118
$247$	−11.6654	−	3.50034i	−0.742253	−	0.222721i
$248$	−9.86754			−0.626589
$249$	−4.02396	−	1.46460i	−0.255008	−	0.0928153i
$250$		0			0
$251$	6.14499	+	5.15626i	0.387868	+	0.325460i	0.815782	−	0.578359i	$-0.196307\pi$
$251$	6.14499	+	5.15626i	0.387868	+	0.325460i	−0.427914	+	0.903820i	$0.640751\pi$
$252$	−8.61364	+	7.22770i	−0.542608	+	0.455302i
$253$	4.88563	−	27.7078i	0.307157	−	1.74197i
$254$	−2.57425	+	4.45874i	−0.161523	+	0.279766i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−19.0006	+	6.91564i	−1.18522	+	0.431386i	−0.858043	−	0.513577i	$-0.828320\pi$
$257$	−19.0006	+	6.91564i	−1.18522	+	0.431386i	−0.327178	+	0.944963i	$0.606098\pi$
$258$	−0.385458	−	0.667633i	−0.0239976	−	0.0415650i
$259$	−8.50271	+	14.7271i	−0.528332	+	0.915099i
$260$		0			0
$261$	−0.903339	+	0.757992i	−0.0559153	+	0.0469185i
$262$	2.78723	+	2.33876i	0.172195	+	0.144489i
$263$	0.968214	+	5.49102i	0.0597027	+	0.338591i	0.999998	−	0.00176780i	$-0.000562709\pi$
$263$	0.968214	+	5.49102i	0.0597027	+	0.338591i	−0.940296	+	0.340358i	$0.889452\pi$
$264$	−1.78074	−	0.648138i	−0.109597	−	0.0398901i
$265$		0			0
$266$	−10.0583	−	15.3137i	−0.616715	−	0.938946i
$267$	6.30062			0.385592
$268$	−3.77939	−	1.37558i	−0.230863	−	0.0840271i
$269$	2.27698	+	12.9134i	0.138830	+	0.787344i	0.972116	+	0.234501i	$0.0753457\pi$
$269$	2.27698	+	12.9134i	0.138830	+	0.787344i	−0.833286	+	0.552842i	$0.813543\pi$
$270$		0			0
$271$	7.00589	−	5.87864i	0.425577	−	0.357102i	−0.404703	−	0.914448i	$-0.632625\pi$
$271$	7.00589	−	5.87864i	0.425577	−	0.357102i	0.830280	+	0.557347i	$0.188181\pi$
$272$	−0.799401	+	4.53363i	−0.0484708	+	0.274892i
$273$	−3.34694	+	5.79707i	−0.202566	+	0.350855i
$274$	0.0524366	+	0.0908229i	0.00316781	+	0.00548681i
$275$		0			0
$276$	4.53227	−	1.64961i	0.272811	−	0.0992949i
$277$	1.70008	+	2.94462i	0.102148	+	0.176925i	0.912569	−	0.408922i	$-0.134095\pi$
$277$	1.70008	+	2.94462i	0.102148	+	0.176925i	−0.810422	+	0.585847i	$0.800762\pi$
$278$	3.06157	−	5.30279i	0.183621	−	0.318040i
$279$	−4.58380	+	25.9960i	−0.274425	+	1.55634i
$280$		0			0
$281$	5.35122	+	4.49021i	0.319227	+	0.267863i	0.788293	−	0.615300i	$-0.210965\pi$
$281$	5.35122	+	4.49021i	0.319227	+	0.267863i	−0.469066	+	0.883163i	$0.655409\pi$
$282$	0.568173	+	3.22227i	0.0338342	+	0.191883i
$283$	−4.09218	−	1.48943i	−0.243255	−	0.0885375i	0.217516	−	0.976057i	$-0.430205\pi$
$283$	−4.09218	−	1.48943i	−0.243255	−	0.0885375i	−0.460771	+	0.887519i	$0.652427\pi$
$284$	9.68292			0.574576
$285$		0			0
$286$	9.28992			0.549325
$287$	43.3804	+	15.7892i	2.56066	+	0.932005i
$288$	0.464533	+	2.63450i	0.0273729	+	0.155239i
$289$	3.21190	+	2.69511i	0.188935	+	0.158536i
$290$		0			0
$291$	−1.40658	+	7.97713i	−0.0824554	+	0.467628i
$292$	−1.66709	+	2.88748i	−0.0975591	+	0.168977i
$293$	−3.43895	−	5.95643i	−0.200905	−	0.347978i	0.747915	−	0.663794i	$-0.231055\pi$
$293$	−3.43895	−	5.95643i	−0.200905	−	0.347978i	−0.948820	+	0.315816i	$0.897722\pi$
$294$	−5.71336	+	2.07949i	−0.333210	+	0.121279i
$295$		0			0
$296$	2.02288	+	3.50374i	0.117578	+	0.203651i
$297$	−5.37728	+	9.31371i	−0.312021	+	0.540436i
$298$	2.78680	−	15.8047i	0.161435	−	0.915544i
$299$	−18.1126	+	15.1983i	−1.04748	+	0.878938i
$300$		0			0
$301$	0.987224	+	5.59883i	0.0569026	+	0.322711i
$302$	−10.0330	−	3.65171i	−0.577334	−	0.210132i
$303$	−8.62704			−0.495611
$304$	−4.35168	+	0.250731i	−0.249586	+	0.0143804i
$305$		0			0
$306$	11.5725	+	4.21204i	0.661556	+	0.240787i
$307$	4.03494	+	22.8833i	0.230286	+	1.30602i	0.852317	+	0.523026i	$0.175197\pi$
$307$	4.03494	+	22.8833i	0.230286	+	1.30602i	−0.622031	+	0.782993i	$0.713692\pi$
$308$	10.7055	+	8.98300i	0.610004	+	0.511854i
$309$	−0.333095	+	0.279500i	−0.0189491	+	0.0159002i
$310$		0			0
$311$	−9.60580	+	16.6377i	−0.544695	+	0.943440i	0.453931	+	0.891037i	$0.350021\pi$
$311$	−9.60580	+	16.6377i	−0.544695	+	0.943440i	−0.998626	+	0.0524028i	$0.983312\pi$
$312$	0.796273	+	1.37919i	0.0450801	+	0.0780810i
$313$	15.5548	−	5.66149i	0.879210	−	0.320006i	0.137319	−	0.990527i	$-0.456151\pi$
$313$	15.5548	−	5.66149i	0.879210	−	0.320006i	0.741891	+	0.670521i	$0.233929\pi$
$314$	−1.74547	+	0.635299i	−0.0985025	+	0.0358520i
$315$		0			0
$316$	2.77716	−	4.81018i	0.156228	−	0.270594i
$317$	3.42163	−	19.4050i	0.192178	−	1.08990i	−0.724203	−	0.689587i	$-0.757792\pi$
$317$	3.42163	−	19.4050i	0.192178	−	1.08990i	0.916381	−	0.400308i	$-0.131097\pi$
$318$	0.334281	−	0.280495i	0.0187456	−	0.0157294i
$319$	1.12272	+	0.942075i	0.0628603	+	0.0527461i
$320$		0			0
$321$	−5.45175	−	1.98428i	−0.304287	−	0.110751i
$322$	−35.5687			−1.98217
$323$	−9.01702	+	17.9264i	−0.501720	+	0.997454i
$324$	6.18180			0.343433
$325$		0			0
$326$	−2.50847	−	14.2262i	−0.138931	−	0.787918i
$327$	−2.49381	−	2.09255i	−0.137908	−	0.115718i
$328$	8.41348	−	7.05975i	0.464557	−	0.389809i
$329$	4.19004	−	23.7629i	0.231005	−	1.31009i
$330$		0			0
$331$	−10.7770	−	18.6663i	−0.592358	−	1.02599i	−0.993914	−	0.110160i	$-0.964864\pi$
$331$	−10.7770	−	18.6663i	−0.592358	−	1.02599i	0.401556	−	0.915835i	$-0.368470\pi$
$332$	7.06001	−	2.56963i	0.387469	−	0.141027i
$333$	10.1703	−	3.70168i	0.557328	−	0.202851i
$334$	−1.23512	−	2.13929i	−0.0675826	−	0.117057i
$335$		0			0
$336$	−0.416010	+	2.35931i	−0.0226952	+	0.128711i
$337$	0.835081	−	0.700716i	0.0454898	−	0.0381704i	−0.619759	−	0.784792i	$-0.712770\pi$
$337$	0.835081	−	0.700716i	0.0454898	−	0.0381704i	0.665249	+	0.746621i	$0.268325\pi$
$338$	3.97801	+	3.33794i	0.216375	+	0.181560i
$339$	1.01902	+	5.77914i	0.0553455	+	0.313880i
$340$		0			0
$341$	32.8078			1.77664
$342$	−1.36095	+	11.5810i	−0.0735918	+	0.626227i
$343$	15.4150			0.832331
$344$	1.27100	+	0.462606i	0.0685277	+	0.0249420i
$345$		0			0
$346$	−8.17530	−	6.85989i	−0.439507	−	0.368790i
$347$	17.1622	−	14.4008i	0.921316	−	0.773076i	−0.0529220	−	0.998599i	$-0.516853\pi$
$347$	17.1622	−	14.4008i	0.921316	−	0.773076i	0.974238	+	0.225523i	$0.0724090\pi$
$348$	−0.0436283	+	0.247428i	−0.00233872	+	0.0132636i
$349$	2.69782	−	4.67276i	0.144411	−	0.250127i	−0.784742	−	0.619822i	$-0.787205\pi$
$349$	2.69782	−	4.67276i	0.144411	−	0.250127i	0.929153	+	0.369695i	$0.120538\pi$
$350$		0			0
$351$	8.49287	−	3.09115i	0.453316	−	0.164993i
$352$	3.12431	−	1.13715i	0.166526	−	0.0606105i
$353$	9.67513	+	16.7578i	0.514955	+	0.891928i	0.999849	+	0.0173555i	$0.00552471\pi$
$353$	9.67513	+	16.7578i	0.514955	+	0.891928i	−0.484894	+	0.874573i	$0.661142\pi$
$354$	1.57034	−	2.71990i	0.0834625	−	0.144561i
$355$		0			0
$356$	−8.46817	+	7.10563i	−0.448812	+	0.376598i
$357$	8.44856	+	7.08918i	0.447145	+	0.375199i
$358$	0.241198	+	1.36790i	0.0127477	+	0.0722960i
$359$	5.81891	+	2.11791i	0.307110	+	0.111779i	0.490978	−	0.871172i	$-0.336640\pi$
$359$	5.81891	+	2.11791i	0.307110	+	0.111779i	−0.183868	+	0.982951i	$0.558862\pi$
$360$		0			0
$361$	−18.4824	−	4.40478i	−0.972756	−	0.231830i
$362$	26.1321			1.37347
$363$	0.0291438	+	0.0106075i	0.00152965	+	0.000556749i
$364$	−2.03939	−	11.5660i	−0.106893	−	0.606221i
$365$		0			0
$366$	2.87851	−	2.41536i	0.150462	−	0.126253i
$367$	3.37441	−	19.1372i	0.176143	−	0.998955i	−0.760674	−	0.649134i	$-0.775131\pi$
$367$	3.37441	−	19.1372i	0.176143	−	0.998955i	0.936817	−	0.349821i	$-0.113758\pi$
$368$	−4.23109	+	7.32846i	−0.220561	+	0.382023i
$369$	−14.6906	−	25.4448i	−0.764760	−	1.32460i
$370$		0			0
$371$	−3.02401	+	1.10065i	−0.156999	+	0.0571428i
$372$	2.81207	+	4.87065i	0.145799	+	0.252532i
$373$	−18.9996	+	32.9083i	−0.983762	+	1.70393i	−0.336448	+	0.941702i	$0.609226\pi$
$373$	−18.9996	+	32.9083i	−0.983762	+	1.70393i	−0.647314	+	0.762223i	$0.724108\pi$
$374$	2.65786	−	15.0735i	0.137435	−	0.779432i
$375$		0			0
$376$	−4.39760	−	3.69003i	−0.226789	−	0.190299i
$377$	−0.213877	−	1.21296i	−0.0110152	−	0.0624706i
$378$	12.7760	+	4.65010i	0.657129	+	0.239175i
$379$	−14.6383			−0.751917			−0.375959	−	0.926636i	$-0.622687\pi$
$379$	−14.6383			−0.751917			−0.375959	+	0.926636i	$0.622687\pi$
$380$		0			0
$381$	2.93447			0.150337
$382$	−5.46956	−	1.99076i	−0.279847	−	0.101856i
$383$	5.13902	+	29.1448i	0.262592	+	1.48923i	0.775806	+	0.630971i	$0.217343\pi$
$383$	5.13902	+	29.1448i	0.262592	+	1.48923i	−0.513215	+	0.858260i	$0.671546\pi$
$384$	0.436618	+	0.366366i	0.0222811	+	0.0186960i
$385$		0			0
$386$	−0.337712	+	1.91526i	−0.0171891	+	0.0974842i
$387$	1.80916	−	3.13355i	0.0919645	−	0.159287i
$388$	−7.10587	−	12.3077i	−0.360746	−	0.624831i
$389$	20.9656	−	7.63087i	1.06300	−	0.386900i	0.249445	−	0.968389i	$-0.419752\pi$
$389$	20.9656	−	7.63087i	1.06300	−	0.386900i	0.813555	+	0.581488i	$0.197529\pi$
$390$		0			0
$391$	19.4781	+	33.7371i	0.985050	+	1.70616i
$392$	5.33369	−	9.23823i	0.269392	−	0.466601i
$393$	0.360111	−	2.04229i	0.0181652	−	0.103020i
$394$	−8.46087	+	7.09952i	−0.426253	+	0.357668i
$395$		0			0
$396$	−1.54449	−	8.75923i	−0.0776135	−	0.440168i
$397$	−0.450859	−	0.164099i	−0.0226279	−	0.00823590i	0.330681	−	0.943742i	$-0.392721\pi$
$397$	−0.450859	−	0.164099i	−0.0226279	−	0.00823590i	−0.353309	+	0.935507i	$0.614944\pi$
$398$	−0.891792			−0.0447015
$399$	−4.69248	+	9.32897i	−0.234918	+	0.467032i
$400$		0			0
$401$	−0.604768	−	0.220117i	−0.0302007	−	0.0109921i	0.326876	−	0.945067i	$-0.394004\pi$
$401$	−0.604768	−	0.220117i	−0.0302007	−	0.0109921i	−0.357076	+	0.934075i	$0.616226\pi$
$402$	0.398064	+	2.25754i	0.0198536	+	0.112596i
$403$	−21.1206	−	17.7223i	−1.05209	−	0.882812i
$404$	11.5949	−	9.72930i	0.576869	−	0.484051i
$405$		0			0
$406$	0.926417	−	1.60460i	0.0459773	−	0.0796350i
$407$	−6.72572	−	11.6493i	−0.333382	−	0.577434i
$408$	2.46563	−	0.897416i	0.122067	−	0.0444287i
$409$	30.3879	−	11.0603i	1.50258	−	0.546896i	0.545856	−	0.837879i	$-0.316204\pi$
$409$	30.3879	−	11.0603i	1.50258	−	0.546896i	0.956728	+	0.290983i	$0.0939822\pi$
$410$		0			0
$411$	0.0298870	−	0.0517658i	0.00147422	−	0.00255342i
$412$	0.132476	−	0.751308i	0.00652662	−	0.0370143i
$413$	−17.7425	+	14.8877i	−0.873052	+	0.732578i
$414$	17.3413	+	14.5511i	0.852281	+	0.715148i
$415$		0			0
$416$	−2.62561	−	0.955644i	−0.128731	−	0.0468543i
$417$	−3.48997			−0.170905
$418$	14.4685	−	0.833635i	0.707680	−	0.0407744i
$419$	5.41894			0.264732			0.132366	−	0.991201i	$-0.457743\pi$
$419$	5.41894			0.264732			0.132366	+	0.991201i	$0.457743\pi$
$420$		0			0
$421$	−1.32792	−	7.53101i	−0.0647189	−	0.367039i	−0.999917	−	0.0129130i	$-0.995890\pi$
$421$	−1.32792	−	7.53101i	−0.0647189	−	0.367039i	0.935198	−	0.354126i	$-0.115222\pi$
$422$	11.3403	+	9.51562i	0.552036	+	0.463213i
$423$	−11.7642	+	9.87134i	−0.571995	+	0.479961i
$424$	−0.132948	+	0.753984i	−0.00645651	+	0.0366167i
$425$		0			0
$426$	−2.75946	−	4.77953i	−0.133696	−	0.231569i
$427$	−26.0399	+	9.47773i	−1.26016	+	0.458660i
$428$	9.56507	−	3.48140i	0.462345	−	0.168280i
$429$	−2.64746	−	4.58554i	−0.127821	−	0.221392i
$430$		0			0
$431$	−5.11819	+	29.0267i	−0.246535	+	1.39817i	0.570367	+	0.821390i	$0.306801\pi$
$431$	−5.11819	+	29.0267i	−0.246535	+	1.39817i	−0.816901	+	0.576777i	$0.804310\pi$
$432$	2.47787	−	2.07918i	0.119217	−	0.100035i
$433$	16.8815	+	14.1653i	0.811274	+	0.680740i	0.950912	−	0.309463i	$-0.100149\pi$
$433$	16.8815	+	14.1653i	0.811274	+	0.680740i	−0.139637	+	0.990203i	$0.544594\pi$
$434$	−7.20220	−	40.8457i	−0.345717	−	1.96066i
$435$		0			0
$436$	5.71165			0.273538
$437$	−26.8455	+	25.2958i	−1.28420	+	1.21006i
$438$	1.90036			0.0908029
$439$	−23.3981	−	8.51622i	−1.11673	−	0.406457i	−0.283273	−	0.959039i	$-0.591420\pi$
$439$	−23.3981	−	8.51622i	−1.11673	−	0.406457i	−0.833458	+	0.552582i	$0.813643\pi$
$440$		0			0
$441$	−21.8604	−	18.3431i	−1.04097	−	0.873480i
$442$	−9.85355	+	8.26811i	−0.468686	+	0.393274i
$443$	−0.255117	+	1.44684i	−0.0121210	+	0.0687415i	−0.990268	−	0.139172i	$-0.955556\pi$
$443$	−0.255117	+	1.44684i	−0.0121210	+	0.0687415i	0.978147	+	0.207913i	$0.0666671\pi$
$444$	1.15297	−	1.99701i	0.0547176	−	0.0947737i
$445$		0			0
$446$	8.97137	−	3.26531i	0.424807	−	0.154617i
$447$	−8.59546	+	3.12849i	−0.406551	+	0.147973i
$448$	−2.10163	−	3.64013i	−0.0992927	−	0.171980i
$449$	−13.8101	+	23.9197i	−0.651737	+	1.12884i	0.330964	+	0.943643i	$0.392626\pi$
$449$	−13.8101	+	23.9197i	−0.651737	+	1.12884i	−0.982701	+	0.185198i	$0.940707\pi$
$450$		0			0
$451$	−27.9733	+	23.4724i	−1.31721	+	1.10527i
$452$	−7.88712	−	6.61808i	−0.370979	−	0.311288i
$453$	1.05673	+	5.99300i	0.0496494	+	0.281575i
$454$	−3.08945	−	1.12447i	−0.144995	−	0.0527739i
$455$		0			0
$456$	1.36391	+	2.07655i	0.0638711	+	0.0972435i
$457$	39.9872			1.87052			0.935262	−	0.353956i	$-0.115164\pi$
$457$	39.9872			1.87052			0.935262	+	0.353956i	$0.115164\pi$
$458$	5.30146	+	1.92958i	0.247721	+	0.0901631i
$459$	−2.58577	−	14.6646i	−0.120693	−	0.684485i
$460$		0			0
$461$	−10.7520	+	9.02198i	−0.500769	+	0.420195i	−0.857867	−	0.513872i	$-0.828211\pi$
$461$	−10.7520	+	9.02198i	−0.500769	+	0.420195i	0.357098	+	0.934067i	$0.383766\pi$
$462$	1.38316	−	7.84428i	0.0643504	−	0.364949i
$463$	−3.37472	+	5.84519i	−0.156837	+	0.271649i	−0.933726	−	0.357988i	$-0.883463\pi$
$463$	−3.37472	+	5.84519i	−0.156837	+	0.271649i	0.776890	+	0.629637i	$0.216796\pi$
$464$	−0.220404	−	0.381752i	−0.0102320	−	0.0177224i
$465$		0			0
$466$	13.4927	−	4.91095i	0.625039	−	0.227495i
$467$	3.13130	+	5.42358i	0.144899	+	0.250973i	0.929335	−	0.369237i	$-0.120381\pi$
$467$	3.13130	+	5.42358i	0.144899	+	0.250973i	−0.784436	+	0.620210i	$0.787047\pi$
$468$	−3.73733	+	6.47324i	−0.172758	+	0.299226i
$469$	2.93557	−	16.6484i	0.135552	−	0.768753i
$470$		0			0
$471$	0.811013	+	0.680521i	0.0373695	+	0.0313567i
$472$	0.956853	+	5.42658i	0.0440427	+	0.249779i
$473$	−4.22584	−	1.53808i	−0.194304	−	0.0707210i
$474$	−3.16577			−0.145408
$475$		0			0
$476$	−19.3500			−0.886905
$477$	1.92461	+	0.700501i	0.0881219	+	0.0320737i
$478$	1.00921	+	5.72354i	0.0461604	+	0.261789i
$479$	−10.1109	−	8.48408i	−0.461980	−	0.387647i	0.381879	−	0.924212i	$-0.375277\pi$
$479$	−10.1109	−	8.48408i	−0.461980	−	0.387647i	−0.843859	+	0.536565i	$0.819722\pi$
$480$		0			0
$481$	−1.96298	+	11.1326i	−0.0895041	+	0.507603i
$482$	3.05263	−	5.28730i	0.139043	−	0.240830i
$483$	10.1365	+	17.5569i	0.461225	+	0.798865i
$484$	−0.0511327	+	0.0186108i	−0.00232421	+	0.000845945i
$485$		0			0
$486$	−6.61365	−	11.4552i	−0.300001	−	0.519617i
$487$	14.7500	−	25.5477i	0.668386	−	1.15768i	−0.309970	−	0.950746i	$-0.600319\pi$
$487$	14.7500	−	25.5477i	0.668386	−	1.15768i	0.978355	−	0.206931i	$-0.0663477\pi$
$488$	−1.14482	+	6.49259i	−0.0518235	+	0.293906i
$489$	−6.30725	+	5.29241i	−0.285224	+	0.239331i
$490$		0			0
$491$	−2.15858	−	12.2419i	−0.0974154	−	0.552470i	−0.993980	−	0.109558i	$-0.965056\pi$
$491$	−2.15858	−	12.2419i	−0.0974154	−	0.552470i	0.896565	−	0.442912i	$-0.146055\pi$
$492$	−5.88241	−	2.14102i	−0.265199	−	0.0965247i
$493$	−2.02929			−0.0913948
$494$	−9.76473	−	7.27905i	−0.439336	−	0.327500i
$495$		0			0
$496$	−9.27246	−	3.37490i	−0.416346	−	0.151537i
$497$	7.06745	+	40.0815i	0.317019	+	1.79790i
$498$	−3.28036	−	2.75255i	−0.146996	−	0.123345i
$499$	−4.67880	+	3.92598i	−0.209452	+	0.175751i	−0.741478	−	0.670977i	$-0.765875\pi$
$499$	−4.67880	+	3.92598i	−0.209452	+	0.175751i	0.532027	+	0.846728i	$0.321431\pi$
$500$		0			0
$501$	−0.703973	+	1.21932i	−0.0314512	+	0.0544751i
$502$	4.01086	+	6.94701i	0.179013	+	0.310060i
$503$	−10.3322	+	3.76063i	−0.460692	+	0.167678i	−0.561931	−	0.827184i	$-0.689941\pi$
$503$	−10.3322	+	3.76063i	−0.460692	+	0.167678i	0.101239	+	0.994862i	$0.467719\pi$
$504$	−10.5662	+	3.84578i	−0.470656	+	0.171305i
$505$		0			0
$506$	14.0676	−	24.3658i	0.625381	−	1.08319i
$507$	0.513960	−	2.91481i	0.0228258	−	0.129451i
$508$	−3.94399	+	3.30940i	−0.174986	+	0.146831i
$509$	−14.3219	−	12.0175i	−0.634808	−	0.532667i	0.267611	−	0.963527i	$-0.413766\pi$
$509$	−14.3219	−	12.0175i	−0.634808	−	0.532667i	−0.902419	+	0.430860i	$0.858210\pi$
$510$		0			0
$511$	−13.1692	−	4.79321i	−0.582573	−	0.212039i
$512$	−1.00000			−0.0441942
$513$	12.9498	−	5.57641i	0.571747	−	0.246205i
$514$	−20.2200			−0.891864
$515$		0			0
$516$	−0.133868	−	0.759204i	−0.00589322	−	0.0334221i
$517$	14.6212	+	12.2687i	0.643041	+	0.539576i
$518$	−13.0269	+	10.9309i	−0.572369	+	0.480275i
$519$	−1.05625	+	5.99030i	−0.0463643	+	0.262945i
$520$		0			0
$521$	3.56772	+	6.17947i	0.156305	+	0.270727i	0.933533	−	0.358491i	$-0.116709\pi$
$521$	3.56772	+	6.17947i	0.156305	+	0.270727i	−0.777229	+	0.629218i	$0.783375\pi$
$522$	−1.10811	+	0.403319i	−0.0485006	+	0.0176528i
$523$	25.3481	−	9.22597i	1.10840	−	0.403424i	0.277992	−	0.960583i	$-0.410331\pi$
$523$	25.3481	−	9.22597i	1.10840	−	0.403424i	0.830405	+	0.557160i	$0.188109\pi$
$524$	1.81923	+	3.15100i	0.0794736	+	0.137652i
$525$		0			0
$526$	−0.968214	+	5.49102i	−0.0422162	+	0.239420i
$527$	−34.7983	+	29.1992i	−1.51584	+	1.27194i
$528$	−1.45168	−	1.21810i	−0.0631761	−	0.0530110i
$529$	8.44077	+	47.8700i	0.366990	+	2.08130i
$530$		0			0
$531$	14.7408			0.639697
$532$	−4.21412	−	17.8304i	−0.182705	−	0.773044i
$533$	30.6878			1.32924
$534$	5.92064	+	2.15494i	0.256211	+	0.0932533i
$535$		0			0
$536$	−3.08098	−	2.58525i	−0.133078	−	0.111666i
$537$	0.606465	−	0.508885i	0.0261709	−	0.0219600i
$538$	−2.27698	+	12.9134i	−0.0981676	+	0.556736i
$539$	−17.7336	+	30.7154i	−0.763839	+	1.32301i
$540$		0			0
$541$	40.1017	−	14.5958i	1.72411	−	0.627523i	0.725923	−	0.687776i	$-0.241413\pi$
$541$	40.1017	−	14.5958i	1.72411	−	0.627523i	0.998183	+	0.0602532i	$0.0191908\pi$
$542$	8.59399	−	3.12796i	0.369144	−	0.134357i
$543$	−7.44717	−	12.8989i	−0.319589	−	0.553544i
$544$	−2.30178	+	3.98681i	−0.0986882	+	0.170933i
$545$		0			0
$546$	−5.12781	+	4.30275i	−0.219450	+	0.184141i
$547$	−27.9599	−	23.4611i	−1.19548	−	1.00313i	−0.999748	−	0.0224681i	$-0.992848\pi$
$547$	−27.9599	−	23.4611i	−1.19548	−	1.00313i	−0.195731	−	0.980658i	$-0.562708\pi$
$548$	0.0182110	+	0.103280i	0.000777937	+	0.00441190i
$549$	16.5729	+	6.03205i	0.707315	+	0.257442i
$550$		0			0
$551$	−0.441948	−	1.86992i	−0.0188276	−	0.0796615i
$552$	4.82314			0.205287
$553$	21.9383	+	7.98489i	0.932912	+	0.339552i
$554$	0.590431	+	3.34850i	0.0250850	+	0.142264i
$555$		0			0
$556$	4.69059	−	3.93588i	0.198926	−	0.166918i
$557$	5.11574	−	29.0128i	0.216761	−	1.22931i	−0.661064	−	0.750330i	$-0.729895\pi$
$557$	5.11574	−	29.0128i	0.216761	−	1.22931i	0.877825	−	0.478982i	$-0.158994\pi$
$558$	−13.1985	+	22.8605i	−0.558738	+	0.967763i
$559$	1.88962	+	3.27291i	0.0799222	+	0.138429i
$560$		0			0
$561$	−8.19778	+	2.98375i	−0.346110	+	0.125974i
$562$	3.49276	+	6.04964i	0.147333	+	0.255189i
$563$	17.0407	−	29.5154i	0.718181	−	1.24393i	−0.243538	−	0.969891i	$-0.578308\pi$
$563$	17.0407	−	29.5154i	0.718181	−	1.24393i	0.961720	−	0.274035i	$-0.0883585\pi$
$564$	−0.568173	+	3.22227i	−0.0239244	+	0.135682i
$565$		0			0
$566$	−3.33598	−	2.79922i	−0.140222	−	0.117660i
$567$	4.51202	+	25.5890i	0.189487	+	1.07463i
$568$	9.09897	+	3.31175i	0.381784	+	0.138958i
$569$	24.7957			1.03949			0.519744	−	0.854322i	$-0.326027\pi$
$569$	24.7957			1.03949			0.519744	+	0.854322i	$0.326027\pi$
$570$		0			0
$571$	6.59096			0.275823			0.137912	−	0.990445i	$-0.455961\pi$
$571$	6.59096			0.275823			0.137912	+	0.990445i	$0.455961\pi$
$572$	8.72967	+	3.17734i	0.365006	+	0.132851i
$573$	0.576083	+	3.26713i	0.0240662	+	0.136486i
$574$	35.3640	+	29.6739i	1.47607	+	1.23857i
$575$		0			0
$576$	−0.464533	+	2.63450i	−0.0193556	+	0.109771i
$577$	−9.19106	+	15.9194i	−0.382629	+	0.662733i	−0.991437	−	0.130585i	$-0.958315\pi$
$577$	−9.19106	+	15.9194i	−0.382629	+	0.662733i	0.608808	+	0.793317i	$0.291648\pi$
$578$	2.09642	+	3.63111i	0.0871996	+	0.151034i
$579$	1.04162	−	0.379119i	0.0432883	−	0.0157557i
$580$		0			0
$581$	15.7898	+	27.3487i	0.655070	+	1.13461i
$582$	−4.05010	+	7.01497i	−0.167882	+	0.290780i
$583$	0.442027	−	2.50686i	0.0183069	−	0.103823i
$584$	−2.55413	+	2.14317i	−0.105691	+	0.0886850i
$585$		0			0
$586$	−1.19433	−	6.77340i	−0.0493375	−	0.279807i
$587$	5.63029	+	2.04926i	0.232387	+	0.0845819i	0.455589	−	0.890190i	$-0.349429\pi$
$587$	5.63029	+	2.04926i	0.232387	+	0.0845819i	−0.223202	+	0.974772i	$0.571651\pi$
$588$	−6.08003			−0.250736
$589$	−34.4846	−	25.7063i	−1.42091	−	1.05921i
$590$		0			0
$591$	5.91555	+	2.15308i	0.243333	+	0.0885660i
$592$	0.702540	+	3.98430i	0.0288742	+	0.163754i
$593$	31.1391	+	26.1288i	1.27873	+	1.07298i	0.993418	+	0.114549i	$0.0365422\pi$
$593$	31.1391	+	26.1288i	1.27873	+	1.07298i	0.285314	+	0.958434i	$0.407902\pi$
$594$	−8.23846	+	6.91289i	−0.338028	+	0.283639i
$595$		0			0
$596$	8.02427	−	13.8984i	0.328687	−	0.569303i
$597$	0.254145	+	0.440192i	0.0104015	+	0.0180159i
$598$	−22.2184	+	8.08683i	−0.908577	+	0.330695i
$599$	−0.731966	+	0.266414i	−0.0299073	+	0.0108854i	−0.356930	−	0.934131i	$-0.616177\pi$
$599$	−0.731966	+	0.266414i	−0.0299073	+	0.0108854i	0.327023	+	0.945016i	$0.393954\pi$
$600$		0			0
$601$	1.90179	−	3.29399i	0.0775755	−	0.134365i	−0.824628	−	0.565676i	$-0.808615\pi$
$601$	1.90179	−	3.29399i	0.0775755	−	0.134365i	0.902203	+	0.431311i	$0.141949\pi$
$602$	−0.987224	+	5.59883i	−0.0402362	+	0.228191i
$603$	−8.24206	+	6.91591i	−0.335643	+	0.281638i
$604$	−8.17897	−	6.86297i	−0.332798	−	0.279250i
$605$		0			0
$606$	−8.10677	−	2.95062i	−0.329315	−	0.119861i
$607$	−22.8747			−0.928456			−0.464228	−	0.885716i	$-0.653668\pi$
$607$	−22.8747			−0.928456			−0.464228	+	0.885716i	$0.653668\pi$
$608$	−4.17500	−	1.25275i	−0.169319	−	0.0508058i
$609$	−1.05605			−0.0427933
$610$		0			0
$611$	−2.78533	−	15.7964i	−0.112682	−	0.639054i
$612$	9.43398	+	7.91605i	0.381346	+	0.319987i
$613$	−29.1510	+	24.4606i	−1.17740	+	0.987955i	−0.177407	+	0.984138i	$0.556771\pi$
$613$	−29.1510	+	24.4606i	−1.17740	+	0.987955i	−0.999993	+	0.00381789i	$0.998785\pi$
$614$	−4.03494	+	22.8833i	−0.162837	+	0.923494i
$615$		0			0
$616$	6.98754	+	12.1028i	0.281536	+	0.487634i
$617$	−0.206525	+	0.0751690i	−0.00831438	+	0.00302619i	−0.346174	−	0.938170i	$-0.612519\pi$
$617$	−0.206525	+	0.0751690i	−0.00831438	+	0.00302619i	0.337860	+	0.941197i	$0.390297\pi$
$618$	−0.408602	+	0.148719i	−0.0164364	+	0.00598235i
$619$	22.6847	+	39.2911i	0.911777	+	1.57924i	0.811553	+	0.584279i	$0.198623\pi$
$619$	22.6847	+	39.2911i	0.911777	+	1.57924i	0.100224	+	0.994965i	$0.468044\pi$
$620$		0			0
$621$	4.75310	−	26.9562i	0.190735	−	1.08171i
$622$	−14.7169	+	12.3490i	−0.590096	+	0.495149i
$623$	−35.5939	−	29.8668i	−1.42604	−	1.19659i
$624$	0.276543	+	1.56835i	0.0110706	+	0.0627843i
$625$		0			0
$626$	16.5531			0.661594
$627$	−4.53476	−	6.90416i	−0.181101	−	0.275726i
$628$	−1.85749			−0.0741219
$629$	17.5017	+	6.37011i	0.697840	+	0.253993i
$630$		0			0
$631$	−23.4179	−	19.6499i	−0.932250	−	0.782251i	0.0439699	−	0.999033i	$-0.485999\pi$
$631$	−23.4179	−	19.6499i	−0.932250	−	0.782251i	−0.976220	+	0.216782i	$0.930444\pi$
$632$	4.25486	−	3.57025i	0.169249	−	0.142017i
$633$	1.46517	−	8.30938i	0.0582352	−	0.330268i
$634$	9.85219	−	17.0645i	0.391281	−	0.677718i
$635$		0			0
$636$	0.410057	−	0.149249i	0.0162598	−	0.00591809i
$637$	28.0084	−	10.1942i	1.10973	−	0.403910i
$638$	0.732805	+	1.26925i	0.0290120	+	0.0502503i
$639$	12.9516	−	22.4328i	0.512357	−	0.887428i
$640$		0			0
$641$	−14.2870	+	11.9882i	−0.564304	+	0.473507i	−0.879750	−	0.475436i	$-0.842290\pi$
$641$	−14.2870	+	11.9882i	−0.564304	+	0.473507i	0.315446	+	0.948943i	$0.397846\pi$
$642$	−4.44431	−	3.72922i	−0.175403	−	0.147180i
$643$	3.05256	+	17.3119i	0.120381	+	0.682716i	0.983944	+	0.178475i	$0.0571164\pi$
$643$	3.05256	+	17.3119i	0.120381	+	0.682716i	−0.863563	+	0.504241i	$0.831772\pi$
$644$	−33.4237	−	12.1652i	−1.31708	−	0.479377i
$645$		0			0
$646$	−14.6044	+	13.7613i	−0.574604	+	0.541433i
$647$	−13.1634			−0.517507			−0.258754	−	0.965943i	$-0.583312\pi$
$647$	−13.1634			−0.517507			−0.258754	+	0.965943i	$0.583312\pi$
$648$	5.80899	+	2.11430i	0.228199	+	0.0830575i
$649$	−3.18136	−	18.0424i	−0.124879	−	0.708226i
$650$		0			0
$651$	−18.1091	+	15.1953i	−0.709752	+	0.595552i
$652$	2.50847	−	14.2262i	0.0982392	−	0.557142i
$653$	15.2104	−	26.3451i	0.595227	−	1.03096i	−0.398288	−	0.917261i	$-0.630395\pi$
$653$	15.2104	−	26.3451i	0.595227	−	1.03096i	0.993515	−	0.113703i	$-0.0362712\pi$
$654$	−1.62772	−	2.81929i	−0.0636488	−	0.110243i
$655$		0			0
$656$	10.3207	−	3.75641i	0.402954	−	0.146663i
$657$	4.45970	+	7.72443i	0.173989	+	0.301359i
$658$	12.0648	−	20.8968i	0.470333	−	0.814641i
$659$	5.59080	−	31.7070i	0.217787	−	1.23513i	−0.658218	−	0.752828i	$-0.728689\pi$
$659$	5.59080	−	31.7070i	0.217787	−	1.23513i	0.876005	−	0.482303i	$-0.160200\pi$
$660$		0			0
$661$	3.51893	+	2.95274i	0.136871	+	0.114848i	0.708653	−	0.705557i	$-0.249303\pi$
$661$	3.51893	+	2.95274i	0.136871	+	0.114848i	−0.571782	+	0.820405i	$0.693748\pi$
$662$	−3.74282	−	21.2266i	−0.145469	−	0.824994i
$663$	6.88926	+	2.50749i	0.267557	+	0.0973826i
$664$	7.51311			0.291565
$665$		0			0
$666$	10.8230			0.419383
$667$	−3.50524	−	1.27580i	−0.135724	−	0.0493994i
$668$	−0.428952	−	2.43271i	−0.0165966	−	0.0941243i
$669$	−4.16845	−	3.49775i	−0.161162	−	0.135231i
$670$		0			0
$671$	3.80631	−	21.5867i	0.146941	−	0.833345i
$672$	−1.19785	+	2.07474i	−0.0462082	+	0.0800350i
$673$	−18.3364	−	31.7595i	−0.706815	−	1.22424i	−0.966033	−	0.258421i	$-0.916798\pi$
$673$	−18.3364	−	31.7595i	−0.706815	−	1.22424i	0.259218	−	0.965819i	$-0.416535\pi$
$674$	1.02438	−	0.372843i	0.0394576	−	0.0143614i
$675$		0			0
$676$	2.59646	+	4.49720i	0.0998639	+	0.172969i
$677$	10.5012	−	18.1886i	0.403593	−	0.699043i	−0.590564	−	0.806991i	$-0.701095\pi$
$677$	10.5012	−	18.1886i	0.403593	−	0.699043i	0.994157	+	0.107948i	$0.0344280\pi$
$678$	−1.01902	+	5.77914i	−0.0391352	+	0.221947i
$679$	45.7602	−	38.3973i	1.75611	−	1.47355i
$680$		0			0
$681$	0.325397	+	1.84542i	0.0124692	+	0.0707166i
$682$	30.8292	+	11.2209i	1.18051	+	0.429671i
$683$	30.4055			1.16343			0.581716	−	0.813392i	$-0.302381\pi$
$683$	30.4055			1.16343			0.581716	+	0.813392i	$0.302381\pi$
$684$	−5.23980	+	10.4171i	−0.200349	+	0.398307i
$685$		0			0
$686$	14.4854	+	5.27224i	0.553053	+	0.201295i
$687$	−0.558378	−	3.16672i	−0.0213034	−	0.120818i
$688$	1.03613	+	0.869414i	0.0395020	+	0.0331461i
$689$	−1.63874	+	1.37506i	−0.0624308	+	0.0523857i
$690$		0			0
$691$	−16.2986	+	28.2299i	−0.620026	+	1.07392i	0.369454	+	0.929249i	$0.379545\pi$
$691$	−16.2986	+	28.2299i	−0.620026	+	1.07392i	−0.989480	+	0.144668i	$0.953789\pi$
$692$	−5.33605	−	9.24230i	−0.202846	−	0.351340i
$693$	35.1307	−	12.7865i	1.33450	−	0.485720i
$694$	21.0526	−	7.66251i	0.799145	−	0.290865i
$695$		0			0
$696$	−0.125623	+	0.217585i	−0.00476172	+	0.00824753i
$697$	8.77984	−	49.7929i	0.332560	−	1.88604i
$698$	4.13330	−	3.46825i	0.156448	−	0.131275i
$699$	−6.26925	−	5.26053i	−0.237125	−	0.198971i
$700$		0			0
$701$	46.7242	+	17.0062i	1.76475	+	0.642316i	0.999998	−	0.00201130i	$-0.000640217\pi$
$701$	46.7242	+	17.0062i	1.76475	+	0.642316i	0.764750	+	0.644327i	$0.222862\pi$
$702$	9.03792			0.341114
$703$	−2.05824	+	17.5146i	−0.0776281	+	0.660574i
$704$	3.32482			0.125309
$705$		0			0
$706$	3.36014	+	19.0563i	0.126460	+	0.717193i
$707$	48.7365	+	40.8948i	1.83292	+	1.53801i
$708$	2.40590	−	2.01879i	0.0904191	−	0.0758706i
$709$	3.57210	−	20.2584i	0.134153	−	0.760820i	−0.841293	−	0.540580i	$-0.818205\pi$
$709$	3.57210	−	20.2584i	0.134153	−	0.760820i	0.975446	−	0.220240i	$-0.0706841\pi$
$710$		0			0
$711$	−7.42930	−	12.8679i	−0.278620	−	0.482585i
$712$	−10.3877	+	3.78083i	−0.389297	+	0.141693i
$713$	−78.4652	+	28.5590i	−2.93854	+	1.06954i
$714$	5.51440	+	9.55123i	0.206371	+	0.357446i
$715$		0			0
$716$	−0.241198	+	1.36790i	−0.00901401	+	0.0511210i
$717$	2.53755	−	2.12926i	0.0947666	−	0.0795186i
$718$	4.74362	+	3.98037i	0.177030	+	0.148546i
$719$	8.39163	+	47.5913i	0.312955	+	1.77486i	0.583465	+	0.812138i	$0.301696\pi$
$719$	8.39163	+	47.5913i	0.312955	+	1.77486i	−0.270511	+	0.962717i	$0.587193\pi$
$720$		0			0
$721$	3.20666			0.119422
$722$	−15.8612	−	10.4605i	−0.590294	−	0.389299i
$723$	−3.47978			−0.129414
$724$	24.5561	+	8.93769i	0.912621	+	0.332167i
$725$		0			0
$726$	0.0237583	+	0.0199355i	0.000881752	+	0.000739878i
$727$	−31.8410	+	26.7178i	−1.18092	+	0.990909i	−0.180947	+	0.983493i	$0.557916\pi$
$727$	−31.8410	+	26.7178i	−1.18092	+	0.990909i	−0.999973	+	0.00741587i	$0.997639\pi$
$728$	2.03939	−	11.5660i	0.0755849	−	0.428663i
$729$	5.50315	−	9.53174i	0.203821	−	0.353028i
$730$		0			0
$731$	5.85113	−	2.12964i	0.216412	−	0.0787675i
$732$	3.53102	−	1.28519i	0.130510	−	0.0475018i
$733$	−8.80966	−	15.2588i	−0.325392	−	0.563596i	0.656199	−	0.754588i	$-0.272163\pi$
$733$	−8.80966	−	15.2588i	−0.325392	−	0.563596i	−0.981592	+	0.190992i	$0.938830\pi$
$734$	9.71622	−	16.8290i	0.358632	−	0.621169i
$735$		0			0
$736$	−6.48241	+	5.43938i	−0.238945	+	0.200498i
$737$	10.2437	+	8.59549i	0.377332	+	0.316619i
$738$	−5.10198	−	28.9347i	−0.187806	−	1.06510i
$739$	−30.6448	−	11.1538i	−1.12729	−	0.410299i	−0.289981	−	0.957032i	$-0.593649\pi$
$739$	−30.6448	−	11.1538i	−1.12729	−	0.410299i	−0.837307	+	0.546733i	$0.815871\pi$
$740$		0			0
$741$	−0.810191	+	6.89431i	−0.0297631	+	0.253269i
$742$	−3.21808			−0.118139
$743$	−1.73353	−	0.630953i	−0.0635970	−	0.0231474i	0.310026	−	0.950728i	$-0.399662\pi$
$743$	−1.73353	−	0.630953i	−0.0635970	−	0.0231474i	−0.373623	+	0.927581i	$0.621885\pi$
$744$	0.976623	+	5.53870i	0.0358047	+	0.203059i
$745$		0			0
$746$	−29.1091	+	24.4254i	−1.06576	+	0.894278i
$747$	3.49009	−	19.7933i	0.127696	−	0.724198i
$748$	7.65301	−	13.2554i	0.279822	−	0.484666i
$749$	21.3924	+	37.0527i	0.781660	+	1.35387i
$750$		0			0
$751$	23.3704	−	8.50613i	0.852798	−	0.310393i	0.121617	−	0.992577i	$-0.461192\pi$
$751$	23.3704	−	8.50613i	0.852798	−	0.310393i	0.731181	+	0.682184i	$0.238970\pi$
$752$	−2.87033	−	4.97156i	−0.104670	−	0.181294i
$753$	2.28605	−	3.95955i	0.0833081	−	0.144294i
$754$	0.213877	−	1.21296i	0.00778895	−	0.0441734i
$755$		0			0
$756$	10.4151	+	8.73933i	0.378794	+	0.317846i
$757$	1.01187	+	5.73859i	0.0367770	+	0.208573i	0.997659	−	0.0683854i	$-0.0217848\pi$
$757$	1.01187	+	5.73859i	0.0367770	+	0.208573i	−0.960882	+	0.276958i	$0.910674\pi$
$758$	−13.7555	−	5.00658i	−0.499621	−	0.181847i
$759$	−16.0361			−0.582072
$760$		0			0
$761$	−4.83084			−0.175118			−0.0875589	−	0.996159i	$-0.527907\pi$
$761$	−4.83084			−0.175118			−0.0875589	+	0.996159i	$0.527907\pi$
$762$	2.75750	+	1.00365i	0.0998936	+	0.0363583i
$763$	4.16886	+	23.6428i	0.150923	+	0.855927i
$764$	−4.45883	−	3.74140i	−0.161315	−	0.135359i
$765$		0			0
$766$	−5.13902	+	29.1448i	−0.185680	+	1.05305i
$767$	−7.69820	+	13.3337i	−0.277966	+	0.481451i
$768$	0.284982	+	0.493604i	0.0102834	+	0.0178114i
$769$	−23.8584	+	8.68376i	−0.860358	+	0.313145i	−0.734256	−	0.678873i	$-0.762469\pi$
$769$	−23.8584	+	8.68376i	−0.860358	+	0.313145i	−0.126102	+	0.992017i	$0.540247\pi$
$770$		0			0
$771$	5.76233	+	9.98065i	0.207525	+	0.359444i
$772$	−0.972403	+	1.68425i	−0.0349976	+	0.0606175i
$773$	−4.55702	+	25.8442i	−0.163905	+	0.929550i	0.786282	+	0.617868i	$0.212003\pi$
$773$	−4.55702	+	25.8442i	−0.163905	+	0.929550i	−0.950187	+	0.311682i	$0.899108\pi$
$774$	2.77179	−	2.32581i	0.0996298	−	0.0835994i
$775$		0			0
$776$	−2.46784	−	13.9958i	−0.0885904	−	0.502421i
$777$	9.10795	+	3.31502i	0.326746	+	0.118926i
$778$	22.3112			0.799894
$779$	47.7946	−	2.75378i	1.71242	−	0.0986645i
$780$		0			0
$781$	−30.2524	−	11.0110i	−1.08252	−	0.394004i
$782$	6.76468	+	38.3644i	0.241904	+	1.37191i
$783$	1.09227	+	0.916520i	0.0390344	+	0.0327538i
$784$	8.17169	−	6.85687i	0.291846	−	0.244888i
$785$		0			0
$786$	1.03690	−	1.79596i	0.0369849	−	0.0640598i
$787$	−22.9615	−	39.7705i	−0.818490	−	1.41767i	−0.906794	−	0.421573i	$-0.861478\pi$
$787$	−22.9615	−	39.7705i	−0.818490	−	1.41767i	0.0883044	−	0.996094i	$-0.471855\pi$
$788$	−10.3788	+	3.77757i	−0.369729	+	0.134571i
$789$	2.98631	−	1.08693i	0.106315	−	0.0386957i
$790$		0			0
$791$	21.6382	−	37.4784i	0.769365	−	1.33258i
$792$	1.54449	−	8.75923i	0.0548810	−	0.311246i
$793$	−14.1112	+	11.8407i	−0.501104	+	0.420477i
$794$	−0.367543	−	0.308405i	−0.0130436	−	0.0109449i
$795$		0			0
$796$	−0.838010	−	0.305011i	−0.0297025	−	0.0108108i
$797$	−37.3026			−1.32132			−0.660662	−	0.750683i	$-0.729725\pi$
$797$	−37.3026			−1.32132			−0.660662	+	0.750683i	$0.729725\pi$
$798$	−7.60018	+	7.16144i	−0.269043	+	0.253512i
$799$	−26.4275			−0.934939
$800$		0			0
$801$	5.13514	+	29.1228i	0.181441	+	1.02900i
$802$	−0.493011	−	0.413685i	−0.0174088	−	0.0146077i
$803$	8.49202	−	7.12565i	0.299677	−	0.251459i
$804$	−0.398064	+	2.25754i	−0.0140386	+	0.0796171i
$805$		0			0
$806$	−13.7855	−	23.8772i	−0.485574	−	0.841039i
$807$	7.02300	−	2.55616i	0.247221	−	0.0899812i
$808$	14.2233	−	5.17685i	0.500374	−	0.182121i
$809$	9.05057	+	15.6760i	0.318201	+	0.551140i	0.980113	−	0.198441i	$-0.0635879\pi$
$809$	9.05057	+	15.6760i	0.318201	+	0.551140i	−0.661912	+	0.749582i	$0.730255\pi$
$810$		0			0
$811$	−2.56132	+	14.5260i	−0.0899402	+	0.510076i	0.906241	+	0.422762i	$0.138939\pi$
$811$	−2.56132	+	14.5260i	−0.0899402	+	0.510076i	−0.996181	+	0.0873139i	$0.972172\pi$
$812$	1.41935	−	1.19098i	0.0498095	−	0.0417952i
$813$	−3.99311	−	3.35061i	−0.140044	−	0.117511i
$814$	−2.33582	−	13.2471i	−0.0818704	−	0.464310i
$815$		0			0
$816$	2.62387			0.0918538
$817$	3.23667	+	4.92781i	0.113237	+	0.172402i
$818$	32.3381			1.13068
$819$	−29.5232	−	10.7456i	−1.03162	−	0.375480i
$820$		0			0
$821$	−33.7753	−	28.3408i	−1.17877	−	0.989102i	−0.999986	−	0.00521253i	$-0.998341\pi$
$821$	−33.7753	−	28.3408i	−1.17877	−	0.989102i	−0.178779	−	0.983889i	$-0.557215\pi$
$822$	0.0457895	−	0.0384220i	0.00159709	−	0.00134012i
$823$	2.24581	−	12.7366i	0.0782840	−	0.443971i	−0.920321	−	0.391165i	$-0.872072\pi$
$823$	2.24581	−	12.7366i	0.0782840	−	0.443971i	0.998605	−	0.0528062i	$-0.0168165\pi$
$824$	0.381449	−	0.660689i	0.0132884	−	0.0230162i
$825$		0			0
$826$	−21.7644	+	7.92160i	−0.757281	+	0.275628i
$827$	−2.31311	+	0.841902i	−0.0804346	+	0.0292758i	−0.381924	−	0.924194i	$-0.624738\pi$
$827$	−2.31311	+	0.841902i	−0.0804346	+	0.0292758i	0.301489	+	0.953470i	$0.402516\pi$
$828$	11.3188	+	19.6047i	0.393354	+	0.681309i
$829$	−26.9311	+	46.6461i	−0.935356	+	1.62008i	−0.161359	+	0.986896i	$0.551588\pi$
$829$	−26.9311	+	46.6461i	−0.935356	+	1.62008i	−0.773998	+	0.633189i	$0.781746\pi$
$830$		0			0
$831$	1.48457	−	1.24570i	0.0514992	−	0.0432129i
$832$	−2.14042	−	1.79602i	−0.0742056	−	0.0622659i
$833$	−8.52752	−	48.3620i	−0.295461	−	1.67564i
$834$	−3.27950	−	1.19364i	−0.113560	−	0.0413324i
$835$		0			0
$836$	13.8811	+	4.16517i	0.480088	+	0.144056i
$837$	31.9178			1.10324
$838$	5.09213	+	1.85339i	0.175905	+	0.0640241i
$839$	0.116023	+	0.658002i	0.00400557	+	0.0227167i	0.986745	−	0.162278i	$-0.0518842\pi$
$839$	0.116023	+	0.658002i	0.00400557	+	0.0227167i	−0.982739	+	0.184995i	$0.940773\pi$
$840$		0			0
$841$	−22.0664	+	18.5159i	−0.760912	+	0.638481i
$842$	1.32792	−	7.53101i	0.0457632	−	0.259536i
$843$	1.99075	−	3.44808i	0.0685651	−	0.118758i
$844$	7.40184	+	12.8204i	0.254782	+	0.441295i
$845$		0			0
$846$	−14.4309	+	5.25243i	−0.496146	+	0.180582i
$847$	−0.114359	−	0.198075i	−0.00392941	−	0.00680594i
$848$	−0.382808	+	0.663042i	−0.0131457	+	0.0227690i
$849$	−0.431010	+	2.44438i	−0.0147922	+	0.0838908i
$850$		0			0
$851$	26.2263	+	22.0065i	0.899026	+	0.754373i
$852$	−0.958351	−	5.43508i	−0.0328326	−	0.186203i
$853$	−17.5406	−	6.38427i	−0.600580	−	0.218593i	0.0237964	−	0.999717i	$-0.492425\pi$
$853$	−17.5406	−	6.38427i	−0.600580	−	0.218593i	−0.624376	+	0.781124i	$0.714647\pi$
$854$	−27.7110			−0.948252
$855$		0			0
$856$	10.1789			0.347909
$857$	−27.5462	−	10.0260i	−0.940962	−	0.342482i	−0.174416	−	0.984672i	$-0.555804\pi$
$857$	−27.5462	−	10.0260i	−0.940962	−	0.342482i	−0.766546	+	0.642190i	$0.778026\pi$
$858$	−0.919454	−	5.21448i	−0.0313897	−	0.178020i
$859$	29.0276	+	24.3570i	0.990409	+	0.831052i	0.985627	−	0.168937i	$-0.0540335\pi$
$859$	29.0276	+	24.3570i	0.990409	+	0.831052i	0.00478180	+	0.999989i	$0.498478\pi$
$860$		0			0
$861$	4.56905	−	25.9124i	0.155713	−	0.883091i
$862$	−14.7372	+	25.5257i	−0.501953	+	0.869408i
$863$	−12.2950	−	21.2955i	−0.418525	−	0.724907i	0.577266	−	0.816556i	$-0.304119\pi$
$863$	−12.2950	−	21.2955i	−0.418525	−	0.724907i	−0.995791	+	0.0916493i	$0.970786\pi$
$864$	3.03956	−	1.10631i	0.103408	−	0.0376374i
$865$		0			0
$866$	11.0186	+	19.0848i	0.374428	+	0.648529i
$867$	1.19489	−	2.06960i	0.0405804	−	0.0702874i
$868$	7.20220	−	40.8457i	0.244459	−	1.38639i
$869$	−14.1466	+	11.8704i	−0.479892	+	0.402677i
$870$		0			0
$871$	−1.95142	−	11.0670i	−0.0661212	−	0.374992i
$872$	5.36719	+	1.95350i	0.181756	+	0.0661538i
$873$	−38.0184			−1.28673
$874$	−33.8782	+	14.5886i	−1.14595	+	0.493466i
$875$		0			0
$876$	1.78576	+	0.649963i	0.0603352	+	0.0219602i
$877$	−6.48351	−	36.7698i	−0.218933	−	1.24163i	−0.873950	−	0.486015i	$-0.838450\pi$
$877$	−6.48351	−	36.7698i	−0.218933	−	1.24163i	0.655018	−	0.755614i	$-0.272661\pi$
$878$	−19.0743	−	16.0053i	−0.643727	−	0.540151i
$879$	−3.00301	+	2.51983i	−0.101289	+	0.0849916i
$880$		0			0
$881$	23.3697	−	40.4774i	0.787344	−	1.36372i	−0.140245	−	0.990117i	$-0.544789\pi$
$881$	23.3697	−	40.4774i	0.787344	−	1.36372i	0.927589	−	0.373603i	$-0.121878\pi$
$882$	−14.2684	−	24.7136i	−0.480441	−	0.832149i
$883$	−42.9592	+	15.6359i	−1.44569	+	0.526189i	−0.941385	−	0.337334i	$-0.890475\pi$
$883$	−42.9592	+	15.6359i	−1.44569	+	0.526189i	−0.504309	+	0.863524i	$0.668253\pi$
$884$	−12.0872	+	4.39937i	−0.406536	+	0.147967i
$885$		0			0
$886$	−0.734580	+	1.27233i	−0.0246787	+	0.0427448i
$887$	6.59212	−	37.3858i	0.221342	−	1.25529i	−0.648214	−	0.761458i	$-0.724484\pi$
$887$	6.59212	−	37.3858i	0.221342	−	1.25529i	0.869556	−	0.493834i	$-0.164405\pi$
$888$	1.76646	−	1.48223i	0.0592784	−	0.0497405i
$889$	−16.5776	−	13.9103i	−0.555995	−	0.466535i
$890$		0			0
$891$	−19.3138	−	7.02966i	−0.647038	−	0.235503i
$892$	9.54714			0.319662
$893$	−5.75550	−	24.3521i	−0.192600	−	0.814911i
$894$	−9.14710			−0.305925
$895$		0			0
$896$	−0.729888	−	4.13940i	−0.0243839	−	0.138288i
$897$	10.3235	+	8.66247i	0.344693	+	0.289232i
$898$	−21.1582	+	17.7539i	−0.706060	+	0.592454i
$899$	0.755317	−	4.28362i	0.0251912	−	0.142867i
$900$		0			0
$901$	1.76228	+	3.05236i	0.0587101	+	0.101689i
$902$	−34.3143	+	12.4894i	−1.14254	+	0.415851i
$903$	3.04494	−	1.10827i	0.101329	−	0.0368809i
$904$	−5.14795	−	8.91651i	−0.171218	−	0.296559i
$905$		0			0
$906$	−1.05673	+	5.99300i	−0.0351074	+	0.199104i
$907$	31.3817	−	26.3324i	1.04201	−	0.874352i	0.0497806	−	0.998760i	$-0.484148\pi$
$907$	31.3817	−	26.3324i	1.04201	−	0.874352i	0.992231	+	0.124409i	$0.0397033\pi$
$908$	−2.51854	−	2.11331i	−0.0835808	−	0.0701326i
$909$	−7.03123	−	39.8761i	−0.233211	−	1.32261i
$910$		0			0
$911$	−6.34997			−0.210384			−0.105192	−	0.994452i	$-0.533546\pi$
$911$	−6.34997			−0.210384			−0.105192	+	0.994452i	$0.533546\pi$
$912$	0.571437	+	2.41781i	0.0189222	+	0.0800616i
$913$	−24.9797			−0.826708
$914$	37.5757	+	13.6764i	1.24289	+	0.452376i
$915$		0			0
$916$	4.32179	+	3.62642i	0.142796	+	0.119820i
$917$	−11.7154	+	9.83042i	−0.386878	+	0.324629i
$918$	2.58577	−	14.6646i	0.0853430	−	0.484004i
$919$	2.59985	−	4.50307i	0.0857611	−	0.148543i	−0.819954	−	0.572429i	$-0.806001\pi$
$919$	2.59985	−	4.50307i	0.0857611	−	0.148543i	0.905715	+	0.423887i	$0.139334\pi$
$920$		0			0
$921$	12.4452	−	4.52967i	0.410082	−	0.149258i
$922$	−13.1892	+	4.80049i	−0.434365	+	0.158096i
$923$	13.5276	+	23.4305i	0.445266	+	0.771224i
$924$	3.98265	−	6.89815i	0.131019	−	0.226932i
$925$		0			0
$926$	−5.17037	+	4.33846i	−0.169909	+	0.142571i
$927$	−1.56339	−	1.31184i	−0.0513484	−	0.0430864i
$928$	−0.0765457	−	0.434112i	−0.00251273	−	0.0142504i
$929$	−1.32791	−	0.483321i	−0.0435674	−	0.0158572i	0.320145	−	0.947369i	$-0.396269\pi$
$929$	−1.32791	−	0.483321i	−0.0435674	−	0.0158572i	−0.363712	+	0.931511i	$0.618491\pi$
$930$		0			0
$931$	42.7068	−	18.3903i	1.39966	−	0.602717i
$932$	14.3587			0.470334
$933$	10.2896	+	3.74510i	0.336865	+	0.122609i
$934$	1.08749	+	6.16746i	0.0355838	+	0.201806i
$935$		0			0
$936$	−5.72591	+	4.80461i	−0.187157	+	0.157044i
$937$	0.686832	−	3.89522i	0.0224378	−	0.127251i	−0.971531	−	0.236911i	$-0.923865\pi$
$937$	0.686832	−	3.89522i	0.0224378	−	0.127251i	0.993969	+	0.109660i	$0.0349761\pi$
$938$	8.45262	−	14.6404i	0.275988	−	0.478025i
$939$	−4.71733	−	8.17066i	−0.153944	−	0.266639i
$940$		0			0
$941$	−13.1193	+	4.77504i	−0.427677	+	0.155662i	−0.546885	−	0.837208i	$-0.684187\pi$
$941$	−13.1193	+	4.77504i	−0.427677	+	0.155662i	0.119208	+	0.992869i	$0.461964\pi$
$942$	0.529351	+	0.916863i	0.0172472	+	0.0298730i
$943$	46.4701	−	80.4886i	1.51328	−	2.62107i
$944$	−0.956853	+	5.42658i	−0.0311429	+	0.176620i
$945$		0			0
$946$	−3.44494	−	2.89064i	−0.112005	−	0.0939830i
$947$	1.15959	+	6.57634i	0.0376815	+	0.213702i	0.997835	−	0.0657719i	$-0.0209510\pi$
$947$	1.15959	+	6.57634i	0.0376815	+	0.213702i	−0.960153	+	0.279474i	$0.909840\pi$
$948$	−2.97485	−	1.08276i	−0.0966186	−	0.0351663i
$949$	−9.31608			−0.302413
$950$		0			0
$951$	−11.2308			−0.364184
$952$	−18.1830	−	6.61809i	−0.589316	−	0.214493i
$953$	−5.59154	−	31.7112i	−0.181128	−	1.02723i	−0.930830	−	0.365452i	$-0.880915\pi$
$953$	−5.59154	−	31.7112i	−0.181128	−	1.02723i	0.749702	−	0.661775i	$-0.230197\pi$
$954$	1.56896	+	1.31651i	0.0507969	+	0.0426236i
$955$		0			0
$956$	−1.00921	+	5.72354i	−0.0326403	+	0.185112i
$957$	0.417673	−	0.723430i	0.0135014	−	0.0233852i
$958$	−6.59944	−	11.4306i	−0.213218	−	0.369305i
$959$	−0.414225	+	0.150766i	−0.0133760	+	0.00486848i
$960$		0			0
$961$	−33.1842	−	57.4767i	−1.07046	−	1.85409i
$962$	−5.65217	+	9.78985i	−0.182233	+	0.315637i
$963$	4.72846	−	26.8164i	0.152372	−	0.864147i
$964$	4.67689	−	3.92438i	0.150633	−	0.126396i
$965$		0			0
$966$	3.52035	+	19.9649i	0.113266	+	0.642361i
$967$	5.86880	+	2.13607i	0.188728	+	0.0686913i	0.434655	−	0.900597i	$-0.356870\pi$
$967$	5.86880	+	2.13607i	0.188728	+	0.0686913i	−0.245927	+	0.969288i	$0.579092\pi$
$968$	−0.0544143			−0.00174894
$969$	10.9547	+	3.28706i	0.351914	+	0.105596i
$970$		0			0
$971$	−7.13562	−	2.59715i	−0.228993	−	0.0833466i	0.224975	−	0.974364i	$-0.427770\pi$
$971$	−7.13562	−	2.59715i	−0.228993	−	0.0833466i	−0.453968	+	0.891018i	$0.649992\pi$
$972$	−2.29689	−	13.0263i	−0.0736729	−	0.417820i
$973$	19.7158	+	16.5435i	0.632059	+	0.530361i
$974$	22.5983	−	18.9622i	0.724096	−	0.607589i
$975$		0			0
$976$	−3.29637	+	5.70949i	−0.105514	+	0.182756i
$977$	7.91748	+	13.7135i	0.253303	+	0.438733i	0.964433	−	0.264327i	$-0.0851498\pi$
$977$	7.91748	+	13.7135i	0.253303	+	0.438733i	−0.711130	+	0.703060i	$0.751816\pi$
$978$	−7.73699	+	2.81603i	−0.247402	+	0.0900468i
$979$	34.5374	−	12.5706i	1.10382	−	0.401757i
$980$		0			0
$981$	7.63973	−	13.2324i	0.243918	−	0.422478i
$982$	2.15858	−	12.2419i	0.0688831	−	0.390655i
$983$	32.3221	−	27.1214i	1.03091	−	0.865039i	0.0399543	−	0.999202i	$-0.487279\pi$
$983$	32.3221	−	27.1214i	1.03091	−	0.865039i	0.990959	+	0.134162i	$0.0428343\pi$
$984$	−4.79538	−	4.02380i	−0.152871	−	0.128274i
$985$		0			0
$986$	−1.90691	−	0.694059i	−0.0607285	−	0.0221034i
$987$	−13.7530			−0.437762
$988$	−6.68626	−	10.1798i	−0.212718	−	0.323863i
$989$	11.4457			0.363951
$990$		0			0
$991$	−3.30182	−	18.7256i	−0.104886	−	0.594837i	−0.991266	−	0.131879i	$-0.957899\pi$
$991$	−3.30182	−	18.7256i	−0.104886	−	0.594837i	0.886380	−	0.462958i	$-0.153212\pi$
$992$	−7.55897	−	6.34273i	−0.239998	−	0.201382i
$993$	−9.41088	+	7.89666i	−0.298645	+	0.250593i
$994$	−7.06745	+	40.0815i	−0.224166	+	1.27131i
$995$		0			0
$996$	−2.14110	−	3.70850i	−0.0678434	−	0.117508i
$997$	−45.7119	+	16.6378i	−1.44771	+	0.526923i	−0.941950	−	0.335752i	$-0.891010\pi$
$997$	−45.7119	+	16.6378i	−1.44771	+	0.526923i	−0.505759	+	0.862675i	$0.668787\pi$
$998$	−5.73940	+	2.08897i	−0.181677	+	0.0661252i
$999$	−6.54328	−	11.3333i	−0.207020	−	0.358569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.251.3		30
5.2	odd	4		190.2.p.a.99.3	✓	60
5.3	odd	4		190.2.p.a.99.8	yes	60
5.4	even	2		950.2.l.m.251.3		30
19.5	even	9	inner	950.2.l.l.651.3		30
95.24	even	18		950.2.l.m.651.3		30
95.43	odd	36		190.2.p.a.119.3	yes	60
95.62	odd	36		190.2.p.a.119.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.99.3	✓	60	5.2	odd	4
190.2.p.a.99.8	yes	60	5.3	odd	4
190.2.p.a.119.3	yes	60	95.43	odd	36
190.2.p.a.119.8	yes	60	95.62	odd	36
950.2.l.l.251.3		30	1.1	even	1	trivial
950.2.l.l.651.3		30	19.5	even	9	inner
950.2.l.m.251.3		30	5.4	even	2
950.2.l.m.651.3		30	95.24	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0989733 - 0.561305i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0989733 - 0.561305i) q^{6} +(-2.10163 + 3.64013i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.51381 - 0.914952i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.0989733 - 0.561305i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0989733 - 0.561305i) q^{6} +(-2.10163 + 3.64013i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.51381 - 0.914952i) q^{9} +(-1.66241 - 2.87938i) q^{11} +(0.284982 - 0.493604i) q^{12} +(-0.485193 + 2.75167i) q^{13} +(-3.21988 + 2.70180i) q^{14} +(0.173648 + 0.984808i) q^{16} +(4.32594 + 1.57451i) q^{17} +2.67514 q^{18} +(-0.508740 + 4.32911i) q^{19} +(2.25123 + 0.819381i) q^{21} +(-0.577349 - 3.27431i) q^{22} +(6.48241 + 5.43938i) q^{23} +(0.436618 - 0.366366i) q^{24} +(-1.39706 + 2.41977i) q^{26} +(-1.61731 - 2.80127i) q^{27} +(-3.94977 + 1.43760i) q^{28} +(-0.414225 + 0.150766i) q^{29} +(-4.93377 + 8.54554i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.45168 + 1.21810i) q^{33} +(3.52654 + 2.95912i) q^{34} +(2.51381 + 0.914952i) q^{36} +4.04577 q^{37} +(-1.95870 + 3.89403i) q^{38} +1.59255 q^{39} +(-1.90718 - 10.8162i) q^{41} +(1.83522 + 1.53993i) q^{42} +(1.03613 - 0.869414i) q^{43} +(0.577349 - 3.27431i) q^{44} +(4.23109 + 7.32846i) q^{46} +(-5.39446 + 1.96342i) q^{47} +(0.535591 - 0.194939i) q^{48} +(-5.33369 - 9.23823i) q^{49} +(0.455630 - 2.58401i) q^{51} +(-2.14042 + 1.79602i) q^{52} +(0.586495 + 0.492128i) q^{53} +(-0.561687 - 3.18549i) q^{54} -4.20326 q^{56} +(2.48030 - 0.142908i) q^{57} -0.440809 q^{58} +(5.17799 + 1.88463i) q^{59} +(5.05034 + 4.23774i) q^{61} +(-7.55897 + 6.34273i) q^{62} +(-1.95255 + 11.0735i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.78074 + 0.648138i) q^{66} +(-3.77939 + 1.37558i) q^{67} +(2.30178 + 3.98681i) q^{68} +(2.41157 - 4.17696i) q^{69} +(7.41755 - 6.22406i) q^{71} +(2.04928 + 1.71955i) q^{72} +(0.578974 + 3.28353i) q^{73} +(3.80178 + 1.38373i) q^{74} +(-3.17241 + 2.98928i) q^{76} +13.9751 q^{77} +(1.49650 + 0.544683i) q^{78} +(-0.964498 - 5.46994i) q^{79} +(4.73553 - 3.97358i) q^{81} +(1.90718 - 10.8162i) q^{82} +(3.75655 - 6.50654i) q^{83} +(1.19785 + 2.07474i) q^{84} +(1.27100 - 0.462606i) q^{86} +(0.125623 + 0.217585i) q^{87} +(1.66241 - 2.87938i) q^{88} +(-1.91958 + 10.8865i) q^{89} +(-8.99673 - 7.54915i) q^{91} +(1.46944 + 8.33362i) q^{92} +(5.28497 + 1.92357i) q^{93} -5.74067 q^{94} +0.569964 q^{96} +(-13.3547 - 4.86070i) q^{97} +(-1.85237 - 10.5053i) q^{98} +(-6.81347 - 5.71718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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