LMFDB - Embedded newform 349.2.e.a.227.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.4
Character	$\chi$	$=$	349.227
Dual form			349.2.e.a.123.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00748 - 1.15902i) q^{2} +(1.04619 + 1.81206i) q^{3} +(1.68665 + 2.92136i) q^{4} +(-0.198863 - 0.344441i) q^{5} -4.85022i q^{6} +(-2.47763 - 1.43046i) q^{7} -3.18335i q^{8} +(-0.689035 + 1.19344i) q^{9} +O(q^{10})$	\(q+(-2.00748 - 1.15902i) q^{2} +(1.04619 + 1.81206i) q^{3} +(1.68665 + 2.92136i) q^{4} +(-0.198863 - 0.344441i) q^{5} -4.85022i q^{6} +(-2.47763 - 1.43046i) q^{7} -3.18335i q^{8} +(-0.689035 + 1.19344i) q^{9} +0.921944i q^{10} -4.98737i q^{11} +(-3.52911 + 6.11260i) q^{12} +(-4.31756 - 2.49274i) q^{13} +(3.31586 + 5.74324i) q^{14} +(0.416098 - 0.720703i) q^{15} +(-0.316264 + 0.547785i) q^{16} +5.93523 q^{17} +(2.76644 - 1.59721i) q^{18} +(2.37072 + 4.10621i) q^{19} +(0.670824 - 1.16190i) q^{20} -5.98615i q^{21} +(-5.78045 + 10.0120i) q^{22} +(3.98625 - 6.90439i) q^{23} +(5.76841 - 3.33039i) q^{24} +(2.42091 - 4.19313i) q^{25} +(5.77827 + 10.0083i) q^{26} +3.39370 q^{27} -9.65074i q^{28} +(2.59263 + 4.49057i) q^{29} +(-1.67062 + 0.964530i) q^{30} +2.42891 q^{31} +(-4.24393 + 2.45024i) q^{32} +(9.03739 - 5.21774i) q^{33} +(-11.9148 - 6.87904i) q^{34} +1.13786i q^{35} -4.64863 q^{36} -9.42659 q^{37} -10.9908i q^{38} -10.4316i q^{39} +(-1.09648 + 0.633050i) q^{40} -0.791646 q^{41} +(-6.93806 + 12.0171i) q^{42} +(-6.54900 + 3.78107i) q^{43} +(14.5699 - 8.41193i) q^{44} +0.548094 q^{45} +(-16.0046 + 9.24028i) q^{46} -5.81645i q^{47} -1.32349 q^{48} +(0.592443 + 1.02614i) q^{49} +(-9.71984 + 5.61175i) q^{50} +(6.20939 + 10.7550i) q^{51} -16.8175i q^{52} -7.68414i q^{53} +(-6.81278 - 3.93336i) q^{54} +(-1.71785 + 0.991803i) q^{55} +(-4.55366 + 7.88717i) q^{56} +(-4.96046 + 8.59177i) q^{57} -12.0196i q^{58} +(-1.17170 + 0.676479i) q^{59} +2.80724 q^{60} -5.58802i q^{61} +(-4.87598 - 2.81515i) q^{62} +(3.41435 - 1.97128i) q^{63} +12.6245 q^{64} +1.98286i q^{65} -24.1898 q^{66} -3.17102 q^{67} +(10.0106 + 17.3389i) q^{68} +16.6815 q^{69} +(1.31881 - 2.28424i) q^{70} +(7.05659 + 4.07413i) q^{71} +(3.79914 + 2.19344i) q^{72} +(-5.71174 - 9.89302i) q^{73} +(18.9237 + 10.9256i) q^{74} +10.1309 q^{75} +(-7.99715 + 13.8515i) q^{76} +(-7.13424 + 12.3569i) q^{77} +(-12.0904 + 20.9411i) q^{78} +5.40938i q^{79} +0.251573 q^{80} +(5.61757 + 9.72991i) q^{81} +(1.58921 + 0.917532i) q^{82} +(-2.71361 + 4.70010i) q^{83} +(17.4877 - 10.0965i) q^{84} +(-1.18030 - 2.04434i) q^{85} +17.5293 q^{86} +(-5.42478 + 9.39599i) q^{87} -15.8765 q^{88} +(-1.00312 + 0.579154i) q^{89} +(-1.10029 - 0.635251i) q^{90} +(7.13155 + 12.3522i) q^{91} +26.8936 q^{92} +(2.54111 + 4.40132i) q^{93} +(-6.74138 + 11.6764i) q^{94} +(0.942899 - 1.63315i) q^{95} +(-8.87994 - 5.12684i) q^{96} +(11.1772 + 6.45318i) q^{97} -2.74661i q^{98} +(5.95214 + 3.43647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.00748	−	1.15902i	−1.41950	−	0.819550i	−0.423247	−	0.906014i	$-0.639110\pi$
$2$	−2.00748	−	1.15902i	−1.41950	−	0.819550i	−0.996255	+	0.0864646i	$0.972443\pi$
$3$	1.04619	+	1.81206i	0.604019	+	1.04619i	0.992206	+	0.124611i	$0.0397683\pi$
$3$	1.04619	+	1.81206i	0.604019	+	1.04619i	−0.388187	+	0.921581i	$0.626898\pi$
$4$	1.68665	+	2.92136i	0.843324	+	1.46068i
$5$	−0.198863	−	0.344441i	−0.0889343	−	0.154039i	0.818127	−	0.575038i	$-0.195013\pi$
$5$	−0.198863	−	0.344441i	−0.0889343	−	0.154039i	−0.907061	+	0.420999i	$0.861679\pi$
$6$		−	4.85022i		−	1.98009i
$7$	−2.47763	−	1.43046i	−0.936457	−	0.540664i	−0.0476092	−	0.998866i	$-0.515160\pi$
$7$	−2.47763	−	1.43046i	−0.936457	−	0.540664i	−0.888848	+	0.458202i	$0.848494\pi$
$8$		−	3.18335i		−	1.12548i
$9$	−0.689035	+	1.19344i	−0.229678	+	0.397814i
$10$			0.921944i			0.291544i
$11$		−	4.98737i		−	1.50375i	−0.659307	−	0.751874i	$-0.729150\pi$
$11$		−	4.98737i		−	1.50375i	0.659307	−	0.751874i	$-0.270850\pi$
$12$	−3.52911	+	6.11260i	−1.01877	+	1.76456i
$13$	−4.31756	−	2.49274i	−1.19748	−	0.691363i	−0.237484	−	0.971392i	$-0.576323\pi$
$13$	−4.31756	−	2.49274i	−1.19748	−	0.691363i	−0.959992	+	0.280029i	$0.909656\pi$
$14$	3.31586	+	5.74324i	0.886202	+	1.53495i
$15$	0.416098	−	0.720703i	0.107436	−	0.186085i
$16$	−0.316264	+	0.547785i	−0.0790659	+	0.136946i
$17$	5.93523			1.43950			0.719752	−	0.694231i	$-0.244255\pi$
$17$	5.93523			1.43950			0.719752	+	0.694231i	$0.244255\pi$
$18$	2.76644	−	1.59721i	0.652057	−	0.376465i
$19$	2.37072	+	4.10621i	0.543881	+	0.942030i	0.998676	+	0.0514337i	$0.0163791\pi$
$19$	2.37072	+	4.10621i	0.543881	+	0.942030i	−0.454795	+	0.890596i	$0.650288\pi$
$20$	0.670824	−	1.16190i	0.150001	−	0.259809i
$21$		−	5.98615i		−	1.30629i
$22$	−5.78045	+	10.0120i	−1.23240	+	2.13457i
$23$	3.98625	−	6.90439i	0.831191	−	1.43967i	−0.0659030	−	0.997826i	$-0.520993\pi$
$23$	3.98625	−	6.90439i	0.831191	−	1.43967i	0.897094	−	0.441839i	$-0.145674\pi$
$24$	5.76841	−	3.33039i	1.17747	−	0.679813i
$25$	2.42091	−	4.19313i	0.484181	−	0.838627i
$26$	5.77827	+	10.0083i	1.13321	+	1.96278i
$27$	3.39370			0.653118
$28$		−	9.65074i		−	1.82382i
$29$	2.59263	+	4.49057i	0.481439	+	0.833877i	0.999773	−	0.0213010i	$-0.00678082\pi$
$29$	2.59263	+	4.49057i	0.481439	+	0.833877i	−0.518334	+	0.855178i	$0.673447\pi$
$30$	−1.67062	+	0.964530i	−0.305011	+	0.176098i
$31$	2.42891			0.436245			0.218123	−	0.975921i	$-0.430007\pi$
$31$	2.42891			0.436245			0.218123	+	0.975921i	$0.430007\pi$
$32$	−4.24393	+	2.45024i	−0.750229	+	0.433145i
$33$	9.03739	−	5.21774i	1.57321	−	0.908292i
$34$	−11.9148	−	6.87904i	−2.04338	−	1.17975i
$35$			1.13786i			0.192334i
$36$	−4.64863			−0.774772
$37$	−9.42659			−1.54972			−0.774861	−	0.632132i	$-0.782180\pi$
$37$	−9.42659			−1.54972			−0.774861	+	0.632132i	$0.782180\pi$
$38$		−	10.9908i		−	1.78295i
$39$		−	10.4316i		−	1.67038i
$40$	−1.09648	+	0.633050i	−0.173368	+	0.100094i
$41$	−0.791646			−0.123634			−0.0618172	−	0.998087i	$-0.519690\pi$
$41$	−0.791646			−0.123634			−0.0618172	+	0.998087i	$0.519690\pi$
$42$	−6.93806	+	12.0171i	−1.07057	+	1.85427i
$43$	−6.54900	+	3.78107i	−0.998713	+	0.576607i	−0.907867	−	0.419258i	$-0.862290\pi$
$43$	−6.54900	+	3.78107i	−0.998713	+	0.576607i	−0.0908457	+	0.995865i	$0.528957\pi$
$44$	14.5699	−	8.41193i	2.19649	−	1.26815i
$45$	0.548094			0.0817051
$46$	−16.0046	+	9.24028i	−2.35975	+	1.36241i
$47$		−	5.81645i		−	0.848417i	−0.905565	−	0.424208i	$-0.860552\pi$
$47$		−	5.81645i		−	0.848417i	0.905565	−	0.424208i	$-0.139448\pi$
$48$	−1.32349			−0.191029
$49$	0.592443	+	1.02614i	0.0846348	+	0.146592i
$50$	−9.71984	+	5.61175i	−1.37459	+	0.793621i
$51$	6.20939	+	10.7550i	0.869488	+	1.50600i
$52$		−	16.8175i		−	2.33217i
$53$		−	7.68414i		−	1.05550i	−0.849400	−	0.527749i	$-0.823036\pi$
$53$		−	7.68414i		−	1.05550i	0.849400	−	0.527749i	$-0.176964\pi$
$54$	−6.81278	−	3.93336i	−0.927102	−	0.535263i
$55$	−1.71785	+	0.991803i	−0.231635	+	0.133735i
$56$	−4.55366	+	7.88717i	−0.608508	+	1.05397i
$57$	−4.96046	+	8.59177i	−0.657029	+	1.13801i
$58$		−	12.0196i		−	1.57825i
$59$	−1.17170	+	0.676479i	−0.152542	+	0.0880700i	−0.574328	−	0.818625i	$-0.694737\pi$
$59$	−1.17170	+	0.676479i	−0.152542	+	0.0880700i	0.421786	+	0.906695i	$0.361403\pi$
$60$	2.80724			0.362413
$61$		−	5.58802i		−	0.715473i	−0.933823	−	0.357736i	$-0.883549\pi$
$61$		−	5.58802i		−	0.715473i	0.933823	−	0.357736i	$-0.116451\pi$
$62$	−4.87598	−	2.81515i	−0.619251	−	0.357525i
$63$	3.41435	−	1.97128i	0.430168	−	0.248357i
$64$	12.6245			1.57807
$65$			1.98286i			0.245943i
$66$	−24.1898			−2.97756
$67$	−3.17102			−0.387401			−0.193701	−	0.981061i	$-0.562049\pi$
$67$	−3.17102			−0.387401			−0.193701	+	0.981061i	$0.562049\pi$
$68$	10.0106	+	17.3389i	1.21397	+	2.10266i
$69$	16.6815			2.00822
$70$	1.31881	−	2.28424i	0.157627	−	0.273019i
$71$	7.05659	+	4.07413i	0.837464	+	0.483510i	0.856401	−	0.516311i	$-0.172695\pi$
$71$	7.05659	+	4.07413i	0.837464	+	0.483510i	−0.0189377	+	0.999821i	$0.506028\pi$
$72$	3.79914	+	2.19344i	0.447733	+	0.258499i
$73$	−5.71174	−	9.89302i	−0.668509	−	1.15789i	−0.978321	−	0.207093i	$-0.933600\pi$
$73$	−5.71174	−	9.89302i	−0.668509	−	1.15789i	0.309813	−	0.950798i	$-0.399734\pi$
$74$	18.9237	+	10.9256i	2.19983	+	1.27007i
$75$	10.1309			1.16982
$76$	−7.99715	+	13.8515i	−0.917336	+	1.58887i
$77$	−7.13424	+	12.3569i	−0.813022	+	1.40820i
$78$	−12.0904	+	20.9411i	−1.36896	+	2.37111i
$79$			5.40938i			0.608603i	0.952576	+	0.304301i	$0.0984230\pi$
$79$			5.40938i			0.608603i	−0.952576	+	0.304301i	$0.901577\pi$
$80$	0.251573			0.0281267
$81$	5.61757	+	9.72991i	0.624174	+	1.08110i
$82$	1.58921	+	0.917532i	0.175499	+	0.101325i
$83$	−2.71361	+	4.70010i	−0.297857	+	0.515903i	−0.975645	−	0.219354i	$-0.929605\pi$
$83$	−2.71361	+	4.70010i	−0.297857	+	0.515903i	0.677789	+	0.735257i	$0.262938\pi$
$84$	17.4877	−	10.0965i	1.90806	−	1.10162i
$85$	−1.18030	−	2.04434i	−0.128021	−	0.221739i
$86$	17.5293			1.89023
$87$	−5.42478	+	9.39599i	−0.581597	+	1.00736i
$88$	−15.8765			−1.69244
$89$	−1.00312	+	0.579154i	−0.106331	+	0.0613902i	−0.552222	−	0.833697i	$-0.686220\pi$
$89$	−1.00312	+	0.579154i	−0.106331	+	0.0613902i	0.445891	+	0.895087i	$0.352887\pi$
$90$	−1.10029	−	0.635251i	−0.115981	−	0.0669614i
$91$	7.13155	+	12.3522i	0.747590	+	1.29486i
$92$	26.8936			2.80385
$93$	2.54111	+	4.40132i	0.263500	+	0.456396i
$94$	−6.74138	+	11.6764i	−0.695320	+	1.20433i
$95$	0.942899	−	1.63315i	0.0967394	−	0.167558i
$96$	−8.87994	−	5.12684i	−0.906305	−	0.523255i
$97$	11.1772	+	6.45318i	1.13488	+	0.655221i	0.945157	−	0.326618i	$-0.105909\pi$
$97$	11.1772	+	6.45318i	1.13488	+	0.655221i	0.189719	+	0.981838i	$0.439242\pi$
$98$		−	2.74661i		−	0.277450i
$99$	5.95214	+	3.43647i	0.598212	+	0.345378i
$100$	16.3329			1.63329
$101$		−	19.1662i		−	1.90711i	−0.301222	−	0.953554i	$-0.597395\pi$
$101$		−	19.1662i		−	1.90711i	0.301222	−	0.953554i	$-0.402605\pi$
$102$		−	28.7872i		−	2.85036i
$103$			9.30686i			0.917032i	0.888686	+	0.458516i	$0.151619\pi$
$103$			9.30686i			0.917032i	−0.888686	+	0.458516i	$0.848381\pi$
$104$	−7.93527	+	13.7443i	−0.778117	+	1.34774i
$105$	−2.06188	+	1.19042i	−0.201219	+	0.116174i
$106$	−8.90606	+	15.4257i	−0.865033	+	1.49828i
$107$	−5.21561	−	3.01123i	−0.504212	−	0.291107i	0.226239	−	0.974072i	$-0.427357\pi$
$107$	−5.21561	−	3.01123i	−0.504212	−	0.291107i	−0.730451	+	0.682965i	$0.760690\pi$
$108$	5.72398	+	9.91422i	0.550790	+	0.953996i
$109$	−4.68912	−	8.12179i	−0.449136	−	0.777926i	0.549194	−	0.835695i	$-0.314935\pi$
$109$	−4.68912	−	8.12179i	−0.449136	−	0.777926i	−0.998330	+	0.0577687i	$0.981601\pi$
$110$	4.59807			0.438409
$111$	−9.86202	−	17.0815i	−0.936062	−	1.62131i
$112$	1.56717	−	0.904806i	0.148084	−	0.0854962i
$113$	−1.66450	−	0.960999i	−0.156583	−	0.0904032i	0.419661	−	0.907681i	$-0.362149\pi$
$113$	−1.66450	−	0.960999i	−0.156583	−	0.0904032i	−0.576244	+	0.817278i	$0.695482\pi$
$114$	19.9160	−	11.4985i	1.86531	−	1.07694i
$115$	−3.17088			−0.295686
$116$	−8.74571	+	15.1480i	−0.812018	+	1.40646i
$117$	5.94989	−	3.43517i	0.550068	−	0.317582i
$118$	3.13621			0.288711
$119$	−14.7053	−	8.49012i	−1.34803	−	0.778288i
$120$	−2.29425	−	1.32458i	−0.209435	−	0.120917i
$121$	−13.8738			−1.26126
$122$	−6.47662	+	11.2178i	−0.586365	+	1.01561i
$123$	−0.828214	−	1.43451i	−0.0746775	−	0.129345i
$124$	4.09671	+	7.09572i	0.367896	+	0.637214i
$125$	−3.91435			−0.350110
$126$	−9.13898			−0.814165
$127$			16.0745i			1.42638i	0.700971	+	0.713190i	$0.252750\pi$
$127$			16.0745i			1.42638i	−0.700971	+	0.713190i	$0.747250\pi$
$128$	−16.8556	−	9.73159i	−1.48984	−	0.860159i
$129$	−13.7030	−	7.91144i	−1.20648	−	0.696563i
$130$	2.29817	−	3.98055i	0.201563	−	0.349117i
$131$			0.743618i			0.0649702i	0.999472	+	0.0324851i	$0.0103421\pi$
$131$			0.743618i			0.0649702i	−0.999472	+	0.0324851i	$0.989658\pi$
$132$	30.4858	+	17.6010i	2.65345	+	1.53197i
$133$		−	13.5649i		−	1.17623i
$134$	6.36575	+	3.67526i	0.549917	+	0.317495i
$135$	−0.674882	−	1.16893i	−0.0580846	−	0.100605i
$136$		−	18.8939i		−	1.62014i
$137$	9.95475	−	5.74738i	0.850492	−	0.491032i	−0.0103251	−	0.999947i	$-0.503287\pi$
$137$	9.95475	−	5.74738i	0.850492	−	0.491032i	0.860817	+	0.508915i	$0.169953\pi$
$138$	−33.4878	−	19.3342i	−2.85067	−	1.64584i
$139$	1.46808			0.124521			0.0622605	−	0.998060i	$-0.480169\pi$
$139$	1.46808			0.124521			0.0622605	+	0.998060i	$0.480169\pi$
$140$	−3.32411	+	1.91918i	−0.280939	+	0.162200i
$141$	10.5397	−	6.08513i	0.887607	−	0.512460i
$142$	−9.44397	−	16.3574i	−0.792521	−	1.37269i
$143$	−12.4322	+	21.5332i	−1.03963	+	1.80070i
$144$	−0.435833	−	0.754885i	−0.0363194	−	0.0629071i
$145$	1.03116	−	1.78602i	0.0856329	−	0.148321i
$146$			26.4800i			2.19150i
$147$	−1.23962	+	2.14708i	−0.102242	+	0.177088i
$148$	−15.8993	−	27.5385i	−1.30692	−	2.26365i
$149$	7.74922	+	4.47402i	0.634841	+	0.366526i	0.782624	−	0.622494i	$-0.213881\pi$
$149$	7.74922	+	4.47402i	0.634841	+	0.366526i	−0.147783	+	0.989020i	$0.547214\pi$
$150$	−20.3376	−	11.7419i	−1.66056	−	0.958725i
$151$	−4.76085	−	8.24604i	−0.387433	−	0.671053i	0.604671	−	0.796475i	$-0.293305\pi$
$151$	−4.76085	−	8.24604i	−0.387433	−	0.671053i	−0.992103	+	0.125423i	$0.959971\pi$
$152$	13.0715	−	7.54683i	1.06024	−	0.612129i
$153$	−4.08958	+	7.08336i	−0.330623	+	0.572656i
$154$	28.6437	−	16.5374i	2.30817	−	1.33262i
$155$	−0.483021	−	0.836616i	−0.0387972	−	0.0671986i
$156$	30.4743	−	17.5943i	2.43990	−	1.40868i
$157$	0.464102	+	0.803848i	0.0370394	+	0.0641540i	0.883951	−	0.467580i	$-0.154874\pi$
$157$	0.464102	+	0.803848i	0.0370394	+	0.0641540i	−0.846911	+	0.531734i	$0.821541\pi$
$158$	6.26957	−	10.8592i	0.498780	−	0.863913i
$159$	13.9241	−	8.03908i	1.10425	−	0.637541i
$160$	1.68792	+	0.974524i	0.133442	+	0.0770428i
$161$	−19.7529	+	11.4044i	−1.55675	+	0.898790i
$162$		−	26.0435i		−	2.04617i
$163$			22.4570i			1.75897i	0.475930	+	0.879483i	$0.342112\pi$
$163$			22.4570i			1.75897i	−0.475930	+	0.879483i	$0.657888\pi$
$164$	−1.33523	−	2.31268i	−0.104264	−	0.180590i
$165$	−3.59441	−	2.07523i	−0.279824	−	0.161557i
$166$	10.8950	−	6.29024i	0.845617	−	0.488217i
$167$			9.38473i			0.726212i	0.931748	+	0.363106i	$0.118284\pi$
$167$			9.38473i			0.726212i	−0.931748	+	0.363106i	$0.881716\pi$
$168$	−19.0560			−1.47020
$169$	5.92754	+	10.2668i	0.455964	+	0.789754i
$170$			5.47195i			0.419680i
$171$	−6.53404			−0.499671
$172$	−22.0917	−	12.7546i	−1.68448	−	0.972533i
$173$	−2.49363	−	1.43970i	−0.189588	−	0.109458i	0.402202	−	0.915551i	$-0.368245\pi$
$173$	−2.49363	−	1.43970i	−0.189588	−	0.109458i	−0.591789	+	0.806093i	$0.701578\pi$
$174$	21.7803	−	12.5748i	1.65116	−	0.953296i
$175$	−11.9962	+	6.92603i	−0.906830	+	0.523559i
$176$	2.73200	+	1.57732i	0.205933	+	0.118895i
$177$	−2.45164	−	1.41545i	−0.184276	−	0.106392i
$178$	2.68500			0.201249
$179$			23.4052i			1.74938i	0.484680	+	0.874692i	$0.338936\pi$
$179$			23.4052i			1.74938i	−0.484680	+	0.874692i	$0.661064\pi$
$180$	0.924442	+	1.60118i	0.0689038	+	0.119345i
$181$	12.9310			0.961156			0.480578	−	0.876952i	$-0.340427\pi$
$181$	12.9310			0.961156			0.480578	+	0.876952i	$0.340427\pi$
$182$		−	33.0624i		−	2.45075i
$183$	10.1258	−	5.84614i	0.748522	−	0.432159i
$184$	−21.9791	−	12.6896i	−1.62032	−	0.935492i
$185$	1.87460	+	3.24690i	0.137823	+	0.238717i
$186$		−	11.7808i		−	0.863807i
$187$		−	29.6012i		−	2.16465i
$188$	16.9919	−	9.81031i	1.23927	−	0.715490i
$189$	−8.40835	−	4.85456i	−0.611617	−	0.353117i
$190$	−3.78570	+	2.18567i	−0.274643	+	0.158565i
$191$	−2.87935	+	4.98717i	−0.208342	+	0.360859i	−0.951192	−	0.308598i	$-0.900140\pi$
$191$	−2.87935	+	4.98717i	−0.208342	+	0.360859i	0.742850	+	0.669458i	$0.233473\pi$
$192$	13.2077	+	22.8764i	0.953182	+	1.65096i
$193$	18.5079	−	10.6855i	1.33223	−	0.769161i	0.346586	−	0.938018i	$-0.387341\pi$
$193$	18.5079	−	10.6855i	1.33223	−	0.769161i	0.985641	+	0.168857i	$0.0540076\pi$
$194$	−14.9587	−	25.9092i	−1.07397	−	1.86017i
$195$	−3.59305	+	2.07445i	−0.257304	+	0.148555i
$196$	−1.99849	+	3.46148i	−0.142749	+	0.247249i
$197$	−12.9195	+	7.45908i	−0.920477	+	0.531438i	−0.883787	−	0.467889i	$-0.845015\pi$
$197$	−12.9195	+	7.45908i	−0.920477	+	0.531438i	−0.0366899	+	0.999327i	$0.511681\pi$
$198$	−7.96586	−	13.7973i	−0.566109	−	0.980530i
$199$	15.7187	+	9.07521i	1.11427	+	0.643325i	0.939932	−	0.341361i	$-0.110888\pi$
$199$	15.7187	+	9.07521i	1.11427	+	0.643325i	0.174339	+	0.984686i	$0.444221\pi$
$200$	−13.3482	−	7.70659i	−0.943860	−	0.544938i
$201$	−3.31749	−	5.74606i	−0.233998	−	0.405296i
$202$	−22.2140	+	38.4757i	−1.56297	+	2.70714i
$203$		−	14.8346i		−	1.04119i
$204$	−20.9461	+	36.2797i	−1.46652	+	2.54009i
$205$	0.157429	+	0.272675i	0.0109953	+	0.0190445i
$206$	10.7868	−	18.6833i	0.751553	−	1.30173i
$207$	5.49333	+	9.51473i	0.381813	+	0.661320i
$208$	2.73097	−	1.57673i	0.189359	−	0.109326i
$209$	20.4792	−	11.8237i	1.41657	−	0.817860i
$210$	5.51890			0.380840
$211$	18.3501	+	10.5944i	1.26327	+	0.729349i	0.973706	−	0.227809i	$-0.0731562\pi$
$211$	18.3501	+	10.5944i	1.26327	+	0.729349i	0.289564	+	0.957159i	$0.406490\pi$
$212$	22.4481	−	12.9604i	1.54174	−	0.890126i
$213$			17.0493i			1.16820i
$214$	6.98015	+	12.0900i	0.477153	+	0.826454i
$215$	2.60471	+	1.50383i	0.177640	+	0.102560i
$216$		−	10.8033i		−	0.735074i
$217$	−6.01795	−	3.47446i	−0.408525	−	0.235862i
$218$			21.7391i			1.47236i
$219$	11.9512	−	20.7000i	0.807584	−	1.39878i
$220$	−5.79483	−	3.34565i	−0.390687	−	0.225563i
$221$	−25.6257	−	14.7950i	−1.72377	−	0.995220i
$222$			45.7211i			3.06860i
$223$	−8.91308			−0.596864			−0.298432	−	0.954431i	$-0.596464\pi$
$223$	−8.91308			−0.596864			−0.298432	+	0.954431i	$0.596464\pi$
$224$	14.0199			0.936743
$225$	3.33618	+	5.77843i	0.222412	+	0.385229i
$226$	2.22763	+	3.85837i	0.148180	+	0.256655i
$227$	12.1577	−	21.0578i	0.806937	−	1.39766i	−0.108039	−	0.994147i	$-0.534457\pi$
$227$	12.1577	−	21.0578i	0.806937	−	1.39766i	0.914976	−	0.403509i	$-0.132210\pi$
$228$	−33.4662			−2.21635
$229$	14.1713	+	8.18178i	0.936463	+	0.540667i	0.888850	−	0.458198i	$-0.151505\pi$
$229$	14.1713	+	8.18178i	0.936463	+	0.540667i	0.0476135	+	0.998866i	$0.484838\pi$
$230$	6.36546	+	3.67510i	0.419726	+	0.242329i
$231$	−29.8551			−1.96432
$232$	14.2950	−	8.25324i	0.938515	−	0.541852i
$233$	−6.63900	+	11.4991i	−0.434935	+	0.753330i	−0.997290	−	0.0735659i	$-0.976562\pi$
$233$	−6.63900	+	11.4991i	−0.434935	+	0.753330i	0.562355	+	0.826896i	$0.309895\pi$
$234$	−15.9257			−1.04110
$235$	−2.00343	+	1.15668i	−0.130689	+	0.0754534i
$236$	−3.95247	−	2.28196i	−0.257284	−	0.148543i
$237$	−9.80211	+	5.65925i	−0.636715	+	0.367608i
$238$	19.6804	+	34.0875i	1.27569	+	2.20956i
$239$	1.29712			0.0839035			0.0419517	−	0.999120i	$-0.486642\pi$
$239$	1.29712			0.0839035			0.0419517	+	0.999120i	$0.486642\pi$
$240$	0.263193	+	0.455864i	0.0169891	+	0.0294259i
$241$	3.07384	+	5.32404i	0.198003	+	0.342952i	0.947881	−	0.318625i	$-0.103221\pi$
$241$	3.07384	+	5.32404i	0.198003	+	0.342952i	−0.749878	+	0.661576i	$0.769888\pi$
$242$	27.8514	+	16.0800i	1.79036	+	1.03366i
$243$	−6.66355	+	11.5416i	−0.427467	+	0.740395i
$244$	16.3246	−	9.42502i	1.04508	−	0.603375i
$245$	0.235630	−	0.408124i	0.0150539	−	0.0260741i
$246$			3.83966i			0.244808i
$247$		−	23.6384i		−	1.50408i
$248$		−	7.73206i		−	0.490987i
$249$	−11.3558			−0.719645
$250$	7.85797	+	4.53680i	0.496982	+	0.286933i
$251$		−	17.4969i		−	1.10440i	−0.833713	−	0.552199i	$-0.813789\pi$
$251$		−	17.4969i		−	1.10440i	0.833713	−	0.552199i	$-0.186211\pi$
$252$	11.5176	+	6.64969i	0.725541	+	0.418891i
$253$	−34.4347	−	19.8809i	−2.16489	−	1.24990i
$254$	18.6306	−	32.2692i	1.16899	−	2.02475i
$255$	2.46964	−	4.27754i	0.154655	−	0.267870i
$256$	9.93366	+	17.2056i	0.620853	+	1.07535i
$257$	−6.05169			−0.377494			−0.188747	−	0.982026i	$-0.560443\pi$
$257$	−6.05169			−0.377494			−0.188747	+	0.982026i	$0.560443\pi$
$258$	18.3390	+	31.7641i	1.14174	+	1.97755i
$259$	23.3556	+	13.4844i	1.45125	+	0.837879i
$260$	−5.79264	+	3.34438i	−0.359244	+	0.207410i
$261$	−7.14565			−0.442305
$262$	0.861867	−	1.49280i	0.0532463	−	0.0922253i
$263$	25.9903			1.60263			0.801314	−	0.598244i	$-0.204135\pi$
$263$	25.9903			1.60263			0.801314	+	0.598244i	$0.204135\pi$
$264$	−16.6099	−	28.7692i	−1.02227	−	1.77062i
$265$	−2.64673	+	1.52809i	−0.162588	+	0.0938699i
$266$	−15.7220	+	27.2313i	−0.963977	+	1.66966i
$267$	−2.09892	−	1.21181i	−0.128452	−	0.0741618i
$268$	−5.34838	−	9.26367i	−0.326705	−	0.565869i
$269$	3.36461			0.205144			0.102572	−	0.994726i	$-0.467293\pi$
$269$	3.36461			0.205144			0.102572	+	0.994726i	$0.467293\pi$
$270$			3.12880i			0.190413i
$271$	−5.09181	+	8.81927i	−0.309305	+	0.535732i	−0.978211	−	0.207615i	$-0.933430\pi$
$271$	−5.09181	+	8.81927i	−0.309305	+	0.535732i	0.668905	+	0.743348i	$0.266763\pi$
$272$	−1.87710	+	3.25123i	−0.113816	+	0.197135i
$273$	−14.9219	+	25.8456i	−0.903117	+	1.56424i
$274$	−26.6453			−1.60970
$275$	−20.9127	−	12.0740i	−1.26108	−	0.728087i
$276$	28.1359	+	48.7328i	1.69358	+	2.93337i
$277$	−23.0308	−	13.2968i	−1.38379	−	0.798930i	−0.391181	−	0.920314i	$-0.627933\pi$
$277$	−23.0308	−	13.2968i	−1.38379	−	0.798930i	−0.992606	+	0.121384i	$0.961267\pi$
$278$	−2.94714	−	1.70153i	−0.176758	−	0.102051i
$279$	−1.67360	+	2.89877i	−0.100196	+	0.173545i
$280$	3.62222			0.216469
$281$	10.5331	+	18.2439i	0.628352	+	1.08834i	0.987882	+	0.155205i	$0.0496037\pi$
$281$	10.5331	+	18.2439i	0.628352	+	1.08834i	−0.359530	+	0.933134i	$0.617063\pi$
$282$	−28.2111			−1.67995
$283$	7.83319			0.465635			0.232817	−	0.972520i	$-0.425206\pi$
$283$	7.83319			0.465635			0.232817	+	0.972520i	$0.425206\pi$
$284$			27.4865i			1.63102i
$285$	3.94581			0.233730
$286$	49.9149	−	28.8184i	2.95153	−	1.70407i
$287$	1.96141	+	1.13242i	0.115778	+	0.0668446i
$288$		−	6.75319i		−	0.397936i
$289$	18.2270			1.07217
$290$	−4.14005	+	2.39026i	−0.243112	+	0.140361i
$291$			27.0050i			1.58306i
$292$	19.2674	−	33.3721i	1.12754	−	1.95295i
$293$	−0.475816	+	0.824137i	−0.0277974	+	0.0481466i	−0.879589	−	0.475733i	$-0.842183\pi$
$293$	−0.475816	+	0.824137i	−0.0277974	+	0.0481466i	0.851792	+	0.523880i	$0.175516\pi$
$294$	4.97702	−	2.87348i	0.290265	−	0.167585i
$295$	0.466014	+	0.269053i	0.0271324	+	0.0156649i
$296$			30.0081i			1.74419i
$297$		−	16.9256i		−	0.982125i
$298$	−10.3709	−	17.9630i	−0.600772	−	1.04057i
$299$	−34.4218	+	19.8734i	−1.99066	+	1.14931i
$300$	17.0873	+	29.5961i	0.986536	+	1.70873i
$301$	21.6347			1.24700
$302$			22.0717i			1.27008i
$303$	34.7302	−	20.0515i	1.99520	−	1.15193i
$304$	−2.99909			−0.172010
$305$	−1.92474	+	1.11125i	−0.110210	+	0.0636301i
$306$	16.4195	−	9.47980i	0.938640	−	0.541924i
$307$	3.05365	−	5.28908i	0.174281	−	0.301864i	−0.765631	−	0.643280i	$-0.777573\pi$
$307$	3.05365	−	5.28908i	0.174281	−	0.301864i	0.939912	+	0.341416i	$0.110906\pi$
$308$	−48.1318			−2.74256
$309$	−16.8646	+	9.73676i	−0.959391	+	0.553905i
$310$			2.23932i			0.127185i
$311$			2.13204i			0.120897i	0.998171	+	0.0604484i	$0.0192530\pi$
$311$			2.13204i			0.120897i	−0.998171	+	0.0604484i	$0.980747\pi$
$312$	−33.2073			−1.87999
$313$	16.0453			0.906932			0.453466	−	0.891274i	$-0.350187\pi$
$313$	16.0453			0.906932			0.453466	+	0.891274i	$0.350187\pi$
$314$		−	2.15161i		−	0.121422i
$315$	−1.35798	−	0.784028i	−0.0765133	−	0.0441750i
$316$	−15.8027	+	9.12371i	−0.888973	+	0.513249i
$317$	1.66090	−	0.958920i	0.0932854	−	0.0538583i	−0.452632	−	0.891698i	$-0.649515\pi$
$317$	1.66090	−	0.958920i	0.0932854	−	0.0538583i	0.545917	+	0.837839i	$0.316181\pi$
$318$	−37.2698			−2.08999
$319$	22.3961	−	12.9304i	1.25394	−	0.723963i
$320$	−2.51055	−	4.34841i	−0.140344	−	0.243083i
$321$		−	12.6013i		−	0.703337i
$322$	52.8715			2.94641
$323$	14.0708	+	24.3713i	0.782920	+	1.35606i
$324$	−18.9497	+	32.8219i	−1.05276	+	1.82344i
$325$	−20.9048	+	12.0694i	−1.15959	+	0.669490i
$326$	26.0281	−	45.0819i	1.44156	−	2.49686i
$327$	9.81143	−	16.9939i	0.542573	−	0.939764i
$328$			2.52008i			0.139148i
$329$	−8.32022	+	14.4110i	−0.458708	+	0.794506i
$330$	4.81047	+	8.33197i	0.264807	+	0.458660i
$331$	10.5231	−	6.07552i	0.578402	−	0.333941i	−0.182096	−	0.983281i	$-0.558288\pi$
$331$	10.5231	−	6.07552i	0.578402	−	0.333941i	0.760498	+	0.649340i	$0.224955\pi$
$332$	−18.3076			−1.00476
$333$	6.49525	−	11.2501i	0.355937	−	0.616502i
$334$	10.8771	−	18.8396i	0.595167	−	1.03086i
$335$	0.630598	+	1.09223i	0.0344533	+	0.0596748i
$336$	3.27912	+	1.89320i	0.178891	+	0.103283i
$337$	−10.8552	+	18.8018i	−0.591323	+	1.02420i	0.402732	+	0.915318i	$0.368061\pi$
$337$	−10.8552	+	18.8018i	−0.591323	+	1.02420i	−0.994055	+	0.108883i	$0.965273\pi$
$338$		−	27.4805i		−	1.49474i
$339$		−	4.02156i		−	0.218421i
$340$	3.98149	−	6.89615i	0.215927	−	0.373996i
$341$		−	12.1139i		−	0.656002i
$342$	13.1169	+	7.57307i	0.709283	+	0.409505i
$343$			16.6366i			0.898292i
$344$	12.0364	+	20.8477i	0.648962	+	1.12403i
$345$	−3.31734	−	5.74581i	−0.178600	−	0.309344i
$346$	3.33728	+	5.78034i	0.179413	+	0.310753i
$347$	1.14719	+	0.662333i	0.0615846	+	0.0355559i	0.530476	−	0.847700i	$-0.322013\pi$
$347$	1.14719	+	0.662333i	0.0615846	+	0.0355559i	−0.468892	+	0.883256i	$0.655346\pi$
$348$	−36.5987			−1.96190
$349$	−16.2365	+	9.23986i	−0.869122	+	0.494599i
$349$	−16.2365	+	9.23986i	−0.869122	+	0.494599i
$350$	32.1096			1.71633
$351$	−14.6525	−	8.45963i	−0.782093	−	0.451541i
$352$	12.2202	+	21.1661i	0.651340	+	1.12815i
$353$	1.35544	+	2.34769i	0.0721429	+	0.124955i	0.899840	−	0.436220i	$-0.143683\pi$
$353$	1.35544	+	2.34769i	0.0721429	+	0.124955i	−0.827697	+	0.561175i	$0.810350\pi$
$354$	3.28107	+	5.68298i	0.174387	+	0.302047i
$355$		−	3.24077i		−	0.172002i
$356$	−3.38384	−	1.95366i	−0.179343	−	0.103544i
$357$		−	35.5292i		−	1.88040i
$358$	27.1270	−	46.9854i	1.43371	−	2.48325i
$359$		−	30.1789i		−	1.59278i	−0.604783	−	0.796390i	$-0.706740\pi$
$359$		−	30.1789i		−	1.59278i	0.604783	−	0.796390i	$-0.293260\pi$
$360$		−	1.74477i		−	0.0919577i
$361$	−1.74065	+	3.01490i	−0.0916134	+	0.158679i
$362$	−25.9588	−	14.9873i	−1.36436	−	0.787715i
$363$	−14.5147	−	25.1402i	−0.761823	−	1.31952i
$364$	−24.0568	+	41.6676i	−1.26092	+	2.18398i
$365$	−2.27171	+	3.93472i	−0.118907	+	0.205952i
$366$	−27.1031			−1.41670
$367$	5.02994	−	2.90404i	0.262561	−	0.151590i	−0.362941	−	0.931812i	$-0.618227\pi$
$367$	5.02994	−	2.90404i	0.262561	−	0.151590i	0.625502	+	0.780222i	$0.284894\pi$
$368$	2.52141	+	4.36722i	0.131438	+	0.227657i
$369$	0.545472	−	0.944785i	0.0283961	−	0.0491835i
$370$		−	8.69079i		−	0.451813i
$371$	−10.9919	+	19.0385i	−0.570669	+	0.988428i
$372$	−8.57190	+	14.8470i	−0.444432	+	0.769779i
$373$	−32.7174	+	18.8894i	−1.69404	+	0.978056i	−0.742851	+	0.669456i	$0.766527\pi$
$373$	−32.7174	+	18.8894i	−1.69404	+	0.978056i	−0.951192	+	0.308600i	$0.900140\pi$
$374$	−34.3083	+	59.4237i	−1.77404	+	3.07273i
$375$	−4.09516	−	7.09302i	−0.211473	−	0.366282i
$376$	−18.5158			−0.954879
$377$		−	25.8510i		−	1.33140i
$378$	11.2531	+	19.4909i	0.578794	+	1.00250i
$379$	−7.80625	+	4.50694i	−0.400980	+	0.231506i	−0.686907	−	0.726746i	$-0.741032\pi$
$379$	−7.80625	+	4.50694i	−0.400980	+	0.231506i	0.285927	+	0.958251i	$0.407699\pi$
$380$	6.36135			0.326330
$381$	−29.1279	+	16.8170i	−1.49227	+	0.861561i
$382$	11.5604	−	6.67443i	0.591484	−	0.341493i
$383$	7.59605	+	4.38558i	0.388140	+	0.224093i	0.681354	−	0.731954i	$-0.261391\pi$
$383$	7.59605	+	4.38558i	0.388140	+	0.224093i	−0.293214	+	0.956047i	$0.594725\pi$
$384$		−	40.7244i		−	2.07821i
$385$	5.67495			0.289222
$386$	−49.5389			−2.52146
$387$		−	10.4211i		−	0.529736i
$388$			43.5369i			2.21025i
$389$	−4.48239	+	2.58791i	−0.227266	+	0.131212i	−0.609310	−	0.792932i	$-0.708554\pi$
$389$	−4.48239	+	2.58791i	−0.227266	+	0.131212i	0.382044	+	0.924144i	$0.375220\pi$
$390$	9.61731			0.486991
$391$	23.6593	−	40.9792i	1.19650	−	2.07241i
$392$	3.26657	−	1.88595i	0.164987	−	0.0952550i
$393$	−1.34748	+	0.777967i	−0.0679713	+	0.0392432i
$394$	34.5809			1.74216
$395$	1.86321	−	1.07573i	0.0937484	−	0.0541257i
$396$			23.1844i			1.16506i
$397$	15.5125			0.778550			0.389275	−	0.921121i	$-0.372726\pi$
$397$	15.5125			0.778550			0.389275	+	0.921121i	$0.372726\pi$
$398$	−21.0367	−	36.4366i	−1.05447	−	1.82640i
$399$	24.5804	−	14.1915i	1.23056	−	0.710464i
$400$	1.53129	+	2.65227i	0.0765645	+	0.132614i
$401$		−	32.4489i		−	1.62042i	−0.586140	−	0.810210i	$-0.699353\pi$
$401$		−	32.4489i		−	1.62042i	0.586140	−	0.810210i	$-0.300647\pi$
$402$			15.3801i			0.767091i
$403$	−10.4870	−	6.05465i	−0.522393	−	0.301604i
$404$	55.9913	−	32.3266i	2.78567	−	1.60831i
$405$	2.23425	−	3.86984i	0.111021	−	0.192294i
$406$	−17.1936	+	29.7802i	−0.853305	+	1.47797i
$407$			47.0139i			2.33039i
$408$	34.2368	−	19.7666i	1.69498	−	0.978595i
$409$	−4.73154			−0.233960			−0.116980	−	0.993134i	$-0.537321\pi$
$409$	−4.73154			−0.233960			−0.116980	+	0.993134i	$0.537321\pi$
$410$		−	0.729853i		−	0.0360449i
$411$	20.8292	+	12.0257i	1.02743	+	0.593185i
$412$	−27.1887	+	15.6974i	−1.33949	+	0.773355i
$413$	3.87071			0.190465
$414$		−	25.4675i		−	1.25166i
$415$	2.15854			0.105959
$416$	24.4312			1.19784
$417$	1.53590	+	2.66025i	0.0752131	+	0.130273i
$418$	−54.8154			−2.68111
$419$	−11.6265	+	20.1377i	−0.567991	+	0.983790i	0.428773	+	0.903412i	$0.358946\pi$
$419$	−11.6265	+	20.1377i	−0.567991	+	0.983790i	−0.996764	+	0.0803777i	$0.974387\pi$
$420$	−6.95532	−	4.01565i	−0.339385	−	0.195944i
$421$	−26.6962	−	15.4131i	−1.30109	−	0.751186i	−0.320501	−	0.947248i	$-0.603851\pi$
$421$	−26.6962	−	15.4131i	−1.30109	−	0.751186i	−0.980591	+	0.196062i	$0.937185\pi$
$422$	−24.5582	−	42.5361i	−1.19548	−	2.07063i
$423$	6.94161	+	4.00774i	0.337512	+	0.194863i
$424$	−24.4613			−1.18794
$425$	14.3686	−	24.8872i	0.696981	−	1.20721i
$426$	19.7604	−	34.2260i	0.957395	−	1.65826i
$427$	−7.99345	+	13.8451i	−0.386830	+	0.670009i
$428$		−	20.3156i		−	0.981990i
$429$	−52.0260			−2.51184
$430$	−3.48593	−	6.03781i	−0.168107	−	0.291169i
$431$	22.7086	+	13.1108i	1.09383	+	0.631526i	0.934595	−	0.355714i	$-0.115762\pi$
$431$	22.7086	+	13.1108i	1.09383	+	0.631526i	0.159240	+	0.987240i	$0.449096\pi$
$432$	−1.07330	+	1.85902i	−0.0516394	+	0.0894420i
$433$	2.61641	−	1.51059i	0.125737	−	0.0725942i	−0.435812	−	0.900038i	$-0.643539\pi$
$433$	2.61641	−	1.51059i	0.125737	−	0.0725942i	0.561549	+	0.827443i	$0.310206\pi$
$434$	8.05393	+	13.9498i	0.386601	+	0.669613i
$435$	4.31515			0.206896
$436$	15.8178	−	27.3972i	0.757534	−	1.31209i
$437$	37.8012			1.80828
$438$	−47.9834	+	27.7032i	−2.29273	+	1.32371i
$439$	4.32255	+	2.49562i	0.206304	+	0.119110i	0.599592	−	0.800305i	$-0.295329\pi$
$439$	4.32255	+	2.49562i	0.206304	+	0.119110i	−0.393289	+	0.919415i	$0.628663\pi$
$440$	3.15725	+	5.46853i	0.150516	+	0.260702i
$441$	−1.63286			−0.0777550
$442$	34.2954	+	59.4013i	1.63126	+	2.82543i
$443$	10.8276	−	18.7540i	0.514436	−	0.891029i	−0.485424	−	0.874279i	$-0.661335\pi$
$443$	10.8276	−	18.7540i	0.514436	−	0.891029i	0.999860	−	0.0167498i	$-0.00533188\pi$
$444$	33.2675	−	57.6210i	1.57881	−	2.73457i
$445$	0.398969	+	0.230345i	0.0189130	+	0.0109194i
$446$	17.8928	+	10.3304i	0.847250	+	0.489160i
$447$			18.7227i			0.885554i
$448$	−31.2790	−	18.0589i	−1.47779	−	0.853203i
$449$	−24.1837			−1.14130			−0.570649	−	0.821194i	$-0.693308\pi$
$449$	−24.1837			−1.14130			−0.570649	+	0.821194i	$0.693308\pi$
$450$		−	15.4668i		−	0.729110i
$451$			3.94823i			0.185915i
$452$		−	6.48347i		−	0.304957i
$453$	9.96153	−	17.2539i	0.468033	−	0.810658i
$454$	−48.8128	+	28.1821i	−2.29090	+	1.32265i
$455$	2.83640	−	4.91280i	0.132973	−	0.230315i
$456$	27.3506	+	15.7909i	1.28081	+	0.739475i
$457$	5.81820	+	10.0774i	0.272164	+	0.471401i	0.969416	−	0.245425i	$-0.0789274\pi$
$457$	5.81820	+	10.0774i	0.272164	+	0.471401i	−0.697252	+	0.716826i	$0.745594\pi$
$458$	−18.9657	−	32.8495i	−0.886208	−	1.53496i
$459$	20.1424			0.940167
$460$	−5.34815	−	9.26326i	−0.249359	−	0.431902i
$461$	35.1603	−	20.2998i	1.63758	−	0.945455i	0.655912	−	0.754838i	$-0.272284\pi$
$461$	35.1603	−	20.2998i	1.63758	−	0.945455i	0.981664	−	0.190617i	$-0.0610490\pi$
$462$	59.9335	+	34.6026i	2.78836	+	1.60986i
$463$	13.9011	−	8.02579i	0.646038	−	0.372990i	−0.140899	−	0.990024i	$-0.544999\pi$
$463$	13.9011	−	8.02579i	0.646038	−	0.372990i	0.786936	+	0.617034i	$0.211666\pi$
$464$	−3.27982			−0.152262
$465$	1.01066	−	1.75052i	0.0468684	−	0.0811785i
$466$	26.6553	−	15.3894i	1.23478	−	0.712902i
$467$	−3.18262			−0.147274			−0.0736369	−	0.997285i	$-0.523461\pi$
$467$	−3.18262			−0.147274			−0.0736369	+	0.997285i	$0.523461\pi$
$468$	20.0707	+	11.5879i	0.927771	+	0.535649i
$469$	7.85661	+	4.53602i	0.362785	+	0.209454i
$470$	5.36245			0.247351
$471$	−0.971079	+	1.68196i	−0.0447450	+	0.0775005i
$472$	2.15347	+	3.72991i	0.0991214	+	0.171683i
$473$	18.8576	+	32.6623i	0.867072	+	1.50181i
$474$	26.2367			1.20509
$475$	22.9572			1.05335
$476$		−	57.2794i		−	2.62540i
$477$	9.17058	+	5.29464i	0.419892	+	0.242425i
$478$	−2.60393	−	1.50338i	−0.119101	−	0.0687631i
$479$	−11.7583	+	20.3660i	−0.537252	+	0.930548i	0.461798	+	0.886985i	$0.347204\pi$
$479$	−11.7583	+	20.3660i	−0.537252	+	0.930548i	−0.999051	+	0.0435633i	$0.986129\pi$
$480$			4.07815i			0.186141i
$481$	40.6998	+	23.4981i	1.85575	+	1.07142i
$482$		−	14.2505i		−	0.649094i
$483$	−41.3307	−	23.8623i	−1.88061	−	1.08577i
$484$	−23.4003	−	40.5304i	−1.06365	−	1.84229i
$485$		−	5.13320i		−	0.233086i
$486$	26.7539	−	15.4464i	1.21358	−	0.700661i
$487$	1.38709	+	0.800836i	0.0628550	+	0.0362894i	0.531098	−	0.847310i	$-0.321780\pi$
$487$	1.38709	+	0.800836i	0.0628550	+	0.0362894i	−0.468243	+	0.883600i	$0.655113\pi$
$488$	−17.7886			−0.805252
$489$	−40.6933	+	23.4943i	−1.84022	+	1.06245i
$490$	−0.946046	+	0.546200i	−0.0427380	+	0.0246748i
$491$	14.9833	+	25.9519i	0.676189	+	1.17119i	0.976120	+	0.217233i	$0.0697031\pi$
$491$	14.9833	+	25.9519i	0.676189	+	1.17119i	−0.299931	+	0.953961i	$0.596964\pi$
$492$	2.79381	−	4.83902i	0.125955	−	0.218160i
$493$	15.3879	+	26.6526i	0.693034	+	1.20037i
$494$	−27.3974	+	47.4536i	−1.23267	+	2.13504i
$495$		−	2.73355i		−	0.122864i
$496$	−0.768176	+	1.33052i	−0.0344921	+	0.0597421i
$497$	−11.6558	−	20.1884i	−0.522833	−	0.905573i
$498$	22.7965	+	13.1616i	1.02154	+	0.589785i
$499$	14.7199	+	8.49856i	0.658955	+	0.380448i	0.791879	−	0.610678i	$-0.209103\pi$
$499$	14.7199	+	8.49856i	0.658955	+	0.380448i	−0.132924	+	0.991126i	$0.542436\pi$
$500$	−6.60212	−	11.4352i	−0.295256	−	0.511398i
$501$	−17.0057	+	9.81823i	−0.759757	+	0.438646i
$502$	−20.2793	+	35.1247i	−0.905109	+	1.56769i
$503$	−14.2162	+	8.20774i	−0.633870	+	0.365965i	−0.782249	−	0.622965i	$-0.785928\pi$
$503$	−14.2162	+	8.20774i	−0.633870	+	0.365965i	0.148379	+	0.988931i	$0.452594\pi$
$504$	−6.27526	−	10.8691i	−0.279522	−	0.484147i
$505$	−6.60163	+	3.81145i	−0.293768	+	0.169607i
$506$	46.0847	+	79.8210i	2.04871	+	3.54848i
$507$	−12.4027	+	21.4821i	−0.550823	+	0.954053i
$508$	−46.9593	+	27.1120i	−2.08348	+	1.20290i
$509$	−20.1416	−	11.6287i	−0.892760	−	0.515435i	−0.0179156	−	0.999840i	$-0.505703\pi$
$509$	−20.1416	−	11.6287i	−0.892760	−	0.515435i	−0.874844	+	0.484404i	$0.839036\pi$
$510$	−9.91549	+	5.72471i	−0.439065	+	0.253494i
$511$			32.6817i			1.44575i
$512$		−	7.12679i		−	0.314963i
$513$	8.04553	+	13.9353i	0.355219	+	0.615257i
$514$	12.1486	+	7.01402i	0.535853	+	0.309375i
$515$	3.20566	−	1.85079i	0.141258	−	0.0815556i
$516$		−	53.3752i		−	2.34971i
$517$	−29.0088			−1.27580
$518$	−31.2573	−	54.1392i	−1.37337	−	2.37874i
$519$		−	6.02481i		−	0.264460i
$520$	6.31213			0.276805
$521$	−13.3935	−	7.73274i	−0.586780	−	0.338778i	0.177043	−	0.984203i	$-0.443347\pi$
$521$	−13.3935	−	7.73274i	−0.586780	−	0.338778i	−0.763823	+	0.645425i	$0.776680\pi$
$522$	14.3447	+	8.28194i	0.627852	+	0.362491i
$523$	−30.2761	+	17.4799i	−1.32388	+	0.764344i	−0.984346	−	0.176249i	$-0.943604\pi$
$523$	−30.2761	+	17.4799i	−1.32388	+	0.764344i	−0.339537	+	0.940593i	$0.610270\pi$
$524$	−2.17237	+	1.25422i	−0.0949006	+	0.0547909i
$525$	−25.1007	−	14.4919i	−1.09549	−	0.632479i
$526$	−52.1749	−	30.1232i	−2.27493	−	1.31343i
$527$	14.4161			0.627977
$528$			6.60073i			0.287260i
$529$	−20.2804	−	35.1267i	−0.881758	−	1.52725i
$530$	7.08435			0.307724
$531$		−	1.86447i		−	0.0809111i
$532$	39.6280	−	22.8792i	1.71809	−	0.991940i
$533$	3.41798	+	1.97337i	0.148049	+	0.0854762i
$534$	2.80903	+	4.86538i	0.121559	+	0.210546i
$535$			2.39529i			0.103558i
$536$			10.0944i			0.436014i
$537$	−42.4115	+	24.4863i	−1.83019	+	1.05666i
$538$	−6.75438	−	3.89964i	−0.291202	−	0.168125i
$539$	5.11775	−	2.95473i	0.220437	−	0.127269i
$540$	2.27658	−	3.94315i	0.0979682	−	0.169686i
$541$	11.4665	+	19.8605i	0.492982	+	0.853869i	0.999967	−	0.00808526i	$-0.00257365\pi$
$541$	11.4665	+	19.8605i	0.492982	+	0.853869i	−0.506986	+	0.861954i	$0.669240\pi$
$542$	20.4434	−	11.8030i	0.878119	−	0.506982i
$543$	13.5283	+	23.4318i	0.580557	+	1.00555i
$544$	−25.1887	+	14.5427i	−1.07996	+	0.623514i
$545$	−1.86498	+	3.23025i	−0.0798872	+	0.138369i
$546$	59.9109	−	34.5896i	2.56395	−	1.48030i
$547$	−12.9726	−	22.4692i	−0.554667	−	0.960712i	−0.997929	−	0.0643201i	$-0.979512\pi$
$547$	−12.9726	−	22.4692i	−0.554667	−	0.960712i	0.443262	−	0.896392i	$-0.353821\pi$
$548$	33.5803	+	19.3876i	1.43448	+	0.828197i
$549$	6.66898	+	3.85034i	0.284625	+	0.164328i
$550$	27.9879	+	48.4764i	1.19341	+	2.06704i
$551$	−12.2928	+	21.2918i	−0.523692	+	0.907060i
$552$		−	53.1031i		−	2.26022i
$553$	7.73791	−	13.4025i	0.329049	−	0.569930i
$554$	30.8226	+	53.3862i	1.30953	+	2.26816i
$555$	−3.92238	+	6.79377i	−0.166496	+	0.288379i
$556$	2.47614	+	4.28879i	0.105012	+	0.181885i
$557$	14.0736	−	8.12542i	0.596319	−	0.344285i	−0.171273	−	0.985224i	$-0.554788\pi$
$557$	14.0736	−	8.12542i	0.596319	−	0.344285i	0.767592	+	0.640939i	$0.221455\pi$
$558$	6.71945	−	3.87947i	0.284457	−	0.164231i
$559$	37.7009			1.59458
$560$	−0.623305	−	0.359865i	−0.0263394	−	0.0152071i
$561$	53.6390	−	30.9685i	2.26464	−	1.30749i
$562$		−	48.8323i		−	2.05986i
$563$	1.34417	+	2.32817i	0.0566499	+	0.0981205i	0.892960	−	0.450137i	$-0.148625\pi$
$563$	1.34417	+	2.32817i	0.0566499	+	0.0981205i	−0.836310	+	0.548257i	$0.815291\pi$
$564$	35.5537	+	20.5269i	1.49708	+	0.864339i
$565$			0.764429i			0.0321598i
$566$	−15.7250	−	9.07881i	−0.660970	−	0.381611i
$567$		−	32.1429i		−	1.34987i
$568$	12.9694	−	22.4636i	0.544182	−	0.942551i
$569$	6.59339	+	3.80670i	0.276409	+	0.159585i	0.631797	−	0.775134i	$-0.282318\pi$
$569$	6.59339	+	3.80670i	0.276409	+	0.159585i	−0.355387	+	0.934719i	$0.615651\pi$
$570$	−7.92113	−	4.57327i	−0.331780	−	0.191553i
$571$			6.34067i			0.265349i	0.991160	+	0.132674i	$0.0423564\pi$
$571$			6.34067i			0.265349i	−0.991160	+	0.132674i	$0.957644\pi$
$572$	−83.8751			−3.50699
$573$	−12.0494			−0.503370
$574$	−2.62499	−	4.54662i	−0.109565	−	0.189772i
$575$	−19.3007	−	33.4298i	−0.804895	−	1.39412i
$576$	−8.69874	+	15.0667i	−0.362448	+	0.627778i
$577$	40.4615			1.68443			0.842216	−	0.539140i	$-0.181250\pi$
$577$	40.4615			1.68443			0.842216	+	0.539140i	$0.181250\pi$
$578$	−36.5902	−	21.1254i	−1.52195	−	0.878700i
$579$	38.7256	+	22.3582i	1.60938	+	0.929176i
$580$	6.95679			0.288865
$581$	13.4466	−	7.76342i	0.557860	−	0.322081i
$582$	31.2993	−	54.2120i	1.29740	−	2.24716i
$583$	−38.3236			−1.58720
$584$	−31.4929	+	18.1825i	−1.30319	+	0.752395i
$585$	−2.36643	−	1.36626i	−0.0978398	−	0.0564878i
$586$	1.91038	−	1.10296i	0.0789170	−	0.0455628i
$587$	11.5811	+	20.0591i	0.478005	+	0.827928i	0.999682	−	0.0252146i	$-0.00802692\pi$
$587$	11.5811	+	20.0591i	0.478005	+	0.827928i	−0.521678	+	0.853143i	$0.674694\pi$
$588$	−8.36320			−0.344892
$589$	5.75827	+	9.97362i	0.237265	+	0.410956i
$590$	−0.623676	−	1.08024i	−0.0256763	−	0.0444727i
$591$	−27.0326	−	15.6073i	−1.11197	−	0.641997i
$592$	2.98129	−	5.16374i	0.122530	−	0.212228i
$593$	35.6960	−	20.6091i	1.46586	−	0.846313i	0.466586	−	0.884476i	$-0.345484\pi$
$593$	35.6960	−	20.6091i	1.46586	−	0.846313i	0.999272	+	0.0381621i	$0.0121503\pi$
$594$	−19.6171	+	33.9778i	−0.804900	+	1.39413i
$595$			6.75349i			0.276866i
$596$			30.1843i			1.23640i
$597$			37.9777i			1.55432i
$598$	92.1346			3.76766
$599$	16.1762	+	9.33935i	0.660943	+	0.381596i	0.792636	−	0.609695i	$-0.208708\pi$
$599$	16.1762	+	9.33935i	0.660943	+	0.381596i	−0.131693	+	0.991291i	$0.542041\pi$
$600$		−	32.2503i		−	1.31661i
$601$	−21.4621	−	12.3911i	−0.875457	−	0.505445i	−0.00629885	−	0.999980i	$-0.502005\pi$
$601$	−21.4621	−	12.3911i	−0.875457	−	0.505445i	−0.869158	+	0.494535i	$0.835338\pi$
$602$	−43.4312	−	25.0750i	−1.77012	−	1.02198i
$603$	2.18494	−	3.78443i	0.0889776	−	0.154114i
$604$	16.0598	−	27.8163i	0.653462	−	1.13183i
$605$	2.75899	+	4.77872i	0.112169	+	0.194282i
$606$	−92.9603			−3.77625
$607$	−9.79430	−	16.9642i	−0.397539	−	0.688557i	0.595883	−	0.803071i	$-0.296802\pi$
$607$	−9.79430	−	16.9642i	−0.397539	−	0.688557i	−0.993422	+	0.114514i	$0.963469\pi$
$608$	−20.1224	−	11.6177i	−0.816070	−	0.471158i
$609$	26.8812	−	15.5199i	1.08928	−	0.628897i
$610$	5.15184			0.208592
$611$	−14.4989	+	25.1129i	−0.586564	+	1.01596i
$612$	−27.5907			−1.11529
$613$	4.87372	+	8.44153i	0.196848	+	0.340950i	0.947505	−	0.319742i	$-0.103596\pi$
$613$	4.87372	+	8.44153i	0.196848	+	0.340950i	−0.750657	+	0.660692i	$0.770263\pi$
$614$	−12.2603	+	7.07848i	−0.494785	+	0.285664i
$615$	−0.329402	+	0.570542i	−0.0132828	+	0.0230065i
$616$	39.3362	+	22.7108i	1.58490	+	0.915043i
$617$	8.52293	+	14.7622i	0.343120	+	0.594302i	0.985010	−	0.172495i	$-0.0551828\pi$
$617$	8.52293	+	14.7622i	0.343120	+	0.594302i	−0.641890	+	0.766797i	$0.721849\pi$
$618$	45.1403			1.81581
$619$		−	37.8201i		−	1.52012i	−0.649854	−	0.760059i	$-0.725170\pi$
$619$		−	37.8201i		−	1.52012i	0.649854	−	0.760059i	$-0.274830\pi$
$620$	1.62937	−	2.82215i	0.0654371	−	0.113340i
$621$	13.5282	−	23.4314i	0.542866	−	0.940271i
$622$	2.47107	−	4.28002i	0.0990809	−	0.171613i
$623$	3.31383			0.132766
$624$	5.71424	+	3.29912i	0.228753	+	0.132071i
$625$	−11.3261	−	19.6174i	−0.453045	−	0.784696i
$626$	−32.2105	−	18.5968i	−1.28739	−	0.743276i
$627$	42.8503	+	24.7396i	1.71128	+	0.988006i
$628$	−1.56555	+	2.71162i	−0.0624723	+	0.108205i
$629$	−55.9490			−2.23083
$630$	1.81741	+	3.14784i	0.0724072	+	0.125413i
$631$	−44.3622			−1.76603			−0.883016	−	0.469343i	$-0.844491\pi$
$631$	−44.3622			−1.76603			−0.883016	+	0.469343i	$0.844491\pi$
$632$	17.2199			0.684972
$633$			44.3351i			1.76216i
$634$	−4.44563			−0.176558
$635$	5.53671	−	3.19662i	0.219718	−	0.126854i
$636$	46.9701	+	27.1182i	1.86249	+	1.07531i
$637$		−	5.90724i		−	0.234053i
$638$	−59.9463			−2.37330
$639$	−9.72447	+	5.61443i	−0.384694	+	0.222103i
$640$			7.74102i			0.305991i
$641$	−8.25957	+	14.3060i	−0.326234	+	0.565053i	−0.981761	−	0.190118i	$-0.939113\pi$
$641$	−8.25957	+	14.3060i	−0.326234	+	0.565053i	0.655528	+	0.755171i	$0.272446\pi$
$642$	−14.6052	+	25.2969i	−0.576419	+	0.998388i
$643$	24.7008	−	14.2610i	0.974103	−	0.562399i	0.0736187	−	0.997286i	$-0.476545\pi$
$643$	24.7008	−	14.2610i	0.974103	−	0.562399i	0.900485	+	0.434888i	$0.143212\pi$
$644$	−66.6325	−	38.4703i	−2.62569	−	1.51594i
$645$			6.29318i			0.247794i
$646$		−	65.2332i		−	2.56657i
$647$	−19.5152	−	33.8013i	−0.767220	−	1.32886i	−0.939065	−	0.343740i	$-0.888306\pi$
$647$	−19.5152	−	33.8013i	−0.767220	−	1.32886i	0.171844	−	0.985124i	$-0.445027\pi$
$648$	30.9737	−	17.8827i	1.21676	−	0.702497i
$649$	3.37385	+	5.84368i	0.132435	+	0.229384i
$650$	55.9546			2.19472
$651$		−	14.5398i		−	0.569860i
$652$	−65.6049	+	37.8770i	−2.56929	+	1.48338i
$653$	−2.47715			−0.0969383			−0.0484691	−	0.998825i	$-0.515434\pi$
$653$	−2.47715			−0.0969383			−0.0484691	+	0.998825i	$0.515434\pi$
$654$	−39.3925	+	22.7433i	−1.54037	+	0.889332i
$655$	0.256133	−	0.147878i	0.0100079	−	0.00577808i
$656$	0.250369	−	0.433652i	0.00977526	−	0.0169313i
$657$	15.7423			0.614167
$658$	33.4053	−	19.2866i	1.30227	−	0.751869i
$659$		−	15.4194i		−	0.600653i	−0.953836	−	0.300326i	$-0.902904\pi$
$659$		−	15.4194i		−	0.600653i	0.953836	−	0.300326i	$-0.0970956\pi$
$660$		−	14.0007i		−	0.544978i
$661$	−37.1346			−1.44437			−0.722184	−	0.691701i	$-0.756862\pi$
$661$	−37.1346			−1.44437			−0.722184	+	0.691701i	$0.756862\pi$
$662$	−28.1666			−1.09472
$663$		−	61.9137i		−	2.40453i
$664$	14.9621	+	8.63835i	0.580640	+	0.335233i
$665$	−4.67231	+	2.69756i	−0.181185	+	0.104607i
$666$	−26.0781	+	15.0562i	−1.01051	+	0.583417i
$667$	41.3395			1.60067
$668$	−27.4162	+	15.8287i	−1.06076	+	0.612432i
$669$	−9.32479	−	16.1510i	−0.360517	−	0.624434i
$670$		−	2.92350i		−	0.112945i
$671$	−27.8695			−1.07589
$672$	14.6675	+	25.4048i	0.565811	+	0.980013i
$673$	−8.23652	+	14.2661i	−0.317495	+	0.549917i	−0.979965	−	0.199172i	$-0.936175\pi$
$673$	−8.23652	+	14.2661i	−0.317495	+	0.549917i	0.662470	+	0.749088i	$0.269508\pi$
$674$	43.5834	−	25.1629i	1.67877	−	0.969237i
$675$	8.21583	−	14.2302i	0.316228	−	0.547722i
$676$	−19.9953	+	34.6329i	−0.769051	+	1.33204i
$677$		−	15.7105i		−	0.603805i	−0.953339	−	0.301903i	$-0.902378\pi$
$677$		−	15.7105i		−	0.603805i	0.953339	−	0.301903i	$-0.0976218\pi$
$678$	−4.66106	+	8.07319i	−0.179007	+	0.310049i
$679$	−18.4620	−	31.9772i	−0.708508	−	1.22717i
$680$	−6.50784	+	3.75730i	−0.249564	+	0.144086i
$681$	50.8773			1.94962
$682$	−14.0402	+	24.3183i	−0.537627	+	0.931197i
$683$	11.9902	−	20.7676i	0.458792	−	0.794652i	−0.540105	−	0.841598i	$-0.681616\pi$
$683$	11.9902	−	20.7676i	0.458792	−	0.794652i	0.998897	+	0.0469460i	$0.0149489\pi$
$684$	−11.0206	−	19.0883i	−0.421384	−	0.729859i
$685$	−3.95927	−	2.28588i	−0.151276	−	0.0873391i
$686$	19.2821	−	33.3976i	0.736195	−	1.27513i
$687$			34.2389i			1.30629i
$688$		−	4.78326i		−	0.182360i
$689$	−19.1546	+	33.1767i	−0.729732	+	1.26393i
$690$			15.3794i			0.585486i
$691$	4.84757	+	2.79875i	0.184410	+	0.106469i	0.589363	−	0.807868i	$-0.299379\pi$
$691$	4.84757	+	2.79875i	0.184410	+	0.106469i	−0.404953	+	0.914338i	$0.632712\pi$
$692$		−	9.71307i		−	0.369235i
$693$	−9.83148	−	17.0286i	−0.373467	−	0.646864i
$694$	−1.53531	−	2.65924i	−0.0582796	−	0.100943i
$695$	−0.291947	−	0.505668i	−0.0110742	−	0.0191811i
$696$	29.9107	+	17.2690i	1.13376	+	0.654578i
$697$	−4.69860			−0.177972
$698$	43.3037	+	0.269607i	1.63907	+	0.0102048i
$699$	−27.7827			−1.05084
$700$	−40.4668	−	23.3635i	−1.52950	−	0.883059i
$701$	−10.0652	−	17.4335i	−0.380159	−	0.658455i	0.610926	−	0.791688i	$-0.290797\pi$
$701$	−10.0652	−	17.4335i	−0.380159	−	0.658455i	−0.991085	+	0.133233i	$0.957464\pi$
$702$	19.6097	+	33.9650i	0.740121	+	1.28193i
$703$	−22.3478	−	38.7076i	−0.842864	−	1.45988i
$704$		−	62.9632i		−	2.37301i
$705$	−4.19193	−	2.42021i	−0.157877	−	0.0911506i
$706$		−	6.28393i		−	0.236499i
$707$	−27.4165	+	47.4868i	−1.03110	+	1.78592i
$708$		−	9.54948i		−	0.358892i
$709$			43.9863i			1.65194i	0.563715	+	0.825969i	$0.309372\pi$
$709$			43.9863i			1.65194i	−0.563715	+	0.825969i	$0.690628\pi$
$710$	−3.75612	+	6.50579i	−0.140965	+	0.244158i
$711$	−6.45579	−	3.72725i	−0.242111	−	0.139783i
$712$	1.84365	+	3.19330i	0.0690937	+	0.119674i
$713$	9.68225	−	16.7701i	0.362603	−	0.628047i
$714$	−41.1790	+	71.3241i	−1.54108	+	2.66924i
$715$	9.88924			0.369837
$716$	−68.3749	+	39.4762i	−2.55529	+	1.47530i
$717$	1.35703	+	2.35045i	0.0506793	+	0.0877791i
$718$	−34.9779	+	60.5835i	−1.30536	+	2.26095i
$719$			4.12650i			0.153893i	0.997035	+	0.0769463i	$0.0245170\pi$
$719$			4.12650i			0.153893i	−0.997035	+	0.0769463i	$0.975483\pi$
$720$	−0.173342	+	0.300238i	−0.00646009	+	0.0111892i
$721$	13.3131	−	23.0590i	0.495806	−	0.858761i
$722$	6.98865	−	4.03490i	0.260091	−	0.150163i
$723$	−6.43164	+	11.1399i	−0.239195	+	0.414299i
$724$	21.8101	+	37.7762i	0.810566	+	1.40394i
$725$	25.1061			0.932416
$726$			67.2911i			2.49741i
$727$	−18.4204	−	31.9050i	−0.683174	−	1.18329i	−0.974007	−	0.226518i	$-0.927266\pi$
$727$	−18.4204	−	31.9050i	−0.683174	−	1.18329i	0.290833	−	0.956774i	$-0.406068\pi$
$728$	39.3214	−	22.7022i	1.45735	−	0.841399i
$729$	5.81998			0.215555
$730$	9.12082	−	5.26591i	0.337577	−	0.194900i
$731$	−38.8698	+	22.4415i	−1.43765	+	0.830029i
$732$	34.1573	+	19.7208i	1.26249	+	0.728900i
$733$			40.4803i			1.49517i	0.664164	+	0.747587i	$0.268788\pi$
$733$			40.4803i			1.49517i	−0.664164	+	0.747587i	$0.731212\pi$
$734$	−13.4633			−0.496941
$735$	0.986058			0.0363713
$736$			39.0691i			1.44010i
$737$			15.8150i			0.582554i
$738$	−2.19005	+	1.26442i	−0.0806167	+	0.0465441i
$739$	−21.8264			−0.802896			−0.401448	−	0.915882i	$-0.631493\pi$
$739$	−21.8264			−0.802896			−0.401448	+	0.915882i	$0.631493\pi$
$740$	−6.32358	+	10.9528i	−0.232460	+	0.402632i
$741$	42.8342	−	24.7303i	1.57355	−	0.908491i
$742$	44.1319	−	25.4796i	1.62013	−	0.935384i
$743$	6.79409			0.249251			0.124626	−	0.992204i	$-0.460227\pi$
$743$	6.79409			0.249251			0.124626	+	0.992204i	$0.460227\pi$
$744$	14.0109	−	8.08922i	0.513666	−	0.296565i
$745$		−	3.55887i		−	0.130387i
$746$	87.5727			3.20626
$747$	−3.73954	−	6.47707i	−0.136822	−	0.236983i
$748$	86.4756	−	49.9267i	3.16186	−	1.82550i
$749$	8.61491	+	14.9215i	0.314782	+	0.545218i
$750$			18.9855i			0.693251i
$751$			27.5941i			1.00692i	0.864017	+	0.503462i	$0.167941\pi$
$751$			27.5941i			1.00692i	−0.864017	+	0.503462i	$0.832059\pi$
$752$	3.18616	+	1.83953i	0.116187	+	0.0670809i
$753$	31.7055	−	18.3052i	1.15541	−	0.667077i
$754$	−29.9618	+	51.8954i	−1.09115	+	1.88992i
$755$	−1.89352	+	3.27967i	−0.0689121	+	0.119359i
$756$		−	32.7517i		−	1.19117i
$757$	24.6936	−	14.2568i	0.897503	−	0.518174i	0.0211137	−	0.999777i	$-0.493279\pi$
$757$	24.6936	−	14.2568i	0.897503	−	0.518174i	0.876389	+	0.481604i	$0.159945\pi$
$758$	20.8945			0.758922
$759$		−	83.1970i		−	3.01986i
$760$	−5.19888	−	3.00157i	−0.188583	−	0.108879i
$761$	26.6548	−	15.3891i	0.966234	−	0.557856i	0.0681482	−	0.997675i	$-0.478291\pi$
$761$	26.6548	−	15.3891i	0.966234	−	0.557856i	0.898086	+	0.439820i	$0.144958\pi$
$762$	77.9648			2.82437
$763$			26.8304i			0.971326i
$764$	−19.4258			−0.702799
$765$	3.25307			0.117615
$766$	−10.1659	−	17.6079i	−0.367310	−	0.636200i
$767$	6.74515			0.243553
$768$	−20.7850	+	36.0007i	−0.750015	+	1.29906i
$769$	13.6695	+	7.89210i	0.492935	+	0.284596i	0.725791	−	0.687915i	$-0.241474\pi$
$769$	13.6695	+	7.89210i	0.492935	+	0.284596i	−0.232856	+	0.972511i	$0.574807\pi$
$770$	−11.3923	−	6.57737i	−0.410551	−	0.237032i
$771$	−6.33123	−	10.9660i	−0.228014	−	0.394931i
$772$	62.4325	+	36.0454i	2.24700	+	1.29730i
$773$	17.4533			0.627753			0.313876	−	0.949464i	$-0.398372\pi$
$773$	17.4533			0.627753			0.313876	+	0.949464i	$0.398372\pi$
$774$	−12.0783	+	20.9202i	−0.434145	+	0.751962i
$775$	5.88016	−	10.1847i	0.211222	−	0.365847i
$776$	20.5427	−	35.5810i	0.737440	−	1.27728i
$777$			56.4290i			2.02438i
$778$	11.9977			0.430139
$779$	−1.87677	−	3.25067i	−0.0672424	−	0.116467i
$780$	−12.1204	−	6.99773i	−0.433981	−	0.250559i
$781$	20.3192	−	35.1938i	0.727077	−	1.25933i
$782$	−94.9912	+	54.8432i	−3.39688	+	1.96119i
$783$	8.79861	+	15.2396i	0.314437	+	0.544620i
$784$	−0.749473			−0.0267669
$785$	0.184585	−	0.319711i	0.00658814	−	0.0114110i
$786$	3.60671			0.128647
$787$	−9.84818	+	5.68585i	−0.351050	+	0.202679i	−0.665148	−	0.746712i	$-0.731631\pi$
$787$	−9.84818	+	5.68585i	−0.351050	+	0.202679i	0.314098	+	0.949391i	$0.398298\pi$
$788$	−43.5813	−	25.1617i	−1.55252	−	0.896348i
$789$	27.1908	+	47.0958i	0.968018	+	1.67666i
$790$	−4.98715			−0.177435
$791$	2.74935	+	4.76201i	0.0977555	+	0.169317i
$792$	10.9395	−	18.9477i	0.388717	−	0.673278i
$793$	−13.9295	+	24.1266i	−0.494651	+	0.856761i
$794$	−31.1410	−	17.9793i	−1.10515	−	0.638061i
$795$	−5.53798	−	3.19735i	−0.196412	−	0.113398i
$796$			61.2267i			2.17012i
$797$	22.9033	+	13.2232i	0.811275	+	0.468390i	0.847399	−	0.530957i	$-0.178168\pi$
$797$	22.9033	+	13.2232i	0.811275	+	0.468390i	−0.0361233	+	0.999347i	$0.511501\pi$
$798$	−65.7929			−2.32904
$799$		−	34.5220i		−	1.22130i
$800$			23.7272i			0.838882i
$801$		−	1.59623i		−	0.0564000i
$802$	−37.6088	+	65.1404i	−1.32801	+	2.30019i
$803$	−49.3401	+	28.4865i	−1.74118	+	1.00527i
$804$	11.1909	−	19.3832i	0.394672	−	0.683591i
$805$	7.85626	+	4.53582i	0.276897	+	0.159867i
$806$	14.0349	+	24.3092i	0.494358	+	0.856254i
$807$	3.52002	+	6.09686i	0.123911	+	0.214620i
$808$	−61.0127			−2.14642
$809$	−24.7905	−	42.9384i	−0.871587	−	1.50963i	−0.860354	−	0.509697i	$-0.829758\pi$
$809$	−24.7905	−	42.9384i	−0.871587	−	1.50963i	−0.0112331	−	0.999937i	$-0.503576\pi$
$810$	−8.97043	+	5.17908i	−0.315189	+	0.181974i
$811$	−25.7942	−	14.8923i	−0.905756	−	0.522938i	−0.0266926	−	0.999644i	$-0.508498\pi$
$811$	−25.7942	−	14.8923i	−0.905756	−	0.522938i	−0.879063	+	0.476705i	$0.841831\pi$
$812$	43.3373	−	25.0208i	1.52084	−	0.878058i
$813$	−21.3080			−0.747305
$814$	54.4899	−	94.3793i	1.90987	−	3.30799i
$815$	7.73511	−	4.46587i	0.270949	−	0.156432i
$816$	−7.85522			−0.274988
$817$	−31.0517	−	17.9277i	−1.08636	−	0.627211i
$818$	9.49847	+	5.48394i	0.332106	+	0.191742i
$819$	−19.6555			−0.686820
$820$	−0.531055	+	0.919815i	−0.0185453	+	0.0321213i
$821$	21.7173	+	37.6155i	0.757940	+	1.31279i	0.943900	+	0.330233i	$0.107127\pi$
$821$	21.7173	+	37.6155i	0.757940	+	1.31279i	−0.185960	+	0.982557i	$0.559539\pi$
$822$	−27.8761	−	48.2827i	−0.972289	−	1.68405i
$823$	17.0559			0.594532			0.297266	−	0.954795i	$-0.403925\pi$
$823$	17.0559			0.594532			0.297266	+	0.954795i	$0.403925\pi$
$824$	29.6270			1.03210
$825$		−	50.5267i		−	1.75911i
$826$	−7.77037	−	4.48622i	−0.270366	−	0.156096i
$827$	24.5835	+	14.1933i	0.854853	+	0.493550i	0.862285	−	0.506423i	$-0.169032\pi$
$827$	24.5835	+	14.1933i	0.854853	+	0.493550i	−0.00743202	+	0.999972i	$0.502366\pi$
$828$	−18.5306	+	32.0960i	−0.643984	+	1.11541i
$829$		−	34.4594i		−	1.19682i	−0.801189	−	0.598411i	$-0.795799\pi$
$829$		−	34.4594i		−	1.19682i	0.801189	−	0.598411i	$-0.204201\pi$
$830$	−4.33323	−	2.50179i	−0.150409	−	0.0868385i
$831$		−	55.6442i		−	1.93027i
$832$	−54.5072	−	31.4697i	−1.88970	−	1.09102i
$833$	3.51629	+	6.09039i	0.121832	+	0.211019i
$834$		−	7.12052i		−	0.246564i
$835$	3.23249	−	1.86628i	0.111865	−	0.0645852i
$836$	69.0823	+	39.8847i	2.38926	+	1.37944i
$837$	8.24299			0.284920
$838$	46.6799	−	26.9506i	1.61253	−	0.930994i
$839$	−11.1640	+	6.44554i	−0.385424	+	0.222525i	−0.680176	−	0.733049i	$-0.738096\pi$
$839$	−11.1640	+	6.44554i	−0.385424	+	0.222525i	0.294752	+	0.955574i	$0.404763\pi$
$840$	3.78954	+	6.56367i	0.130751	+	0.226468i
$841$	1.05654	−	1.82997i	0.0364323	−	0.0631025i
$842$	35.7280	+	61.8827i	1.23127	+	2.13262i
$843$	−22.0393	+	38.1732i	−0.759074	+	1.31475i
$844$			71.4761i			2.46031i
$845$	2.35754	−	4.08338i	0.0811018	−	0.140472i
$846$	−9.29008	−	16.0909i	−0.319400	−	0.553216i
$847$	34.3742	+	19.8460i	1.18111	+	0.681916i
$848$	4.20925	+	2.43021i	0.144546	+	0.0834539i
$849$	8.19502	+	14.1942i	0.281252	+	0.487143i
$850$	−57.6895	+	33.3070i	−1.97873	+	1.14242i
$851$	−37.5768	+	65.0849i	−1.28812	+	2.23108i
$852$	−49.8070	+	28.7561i	−1.70636	+	0.985168i
$853$	9.52412	+	16.4963i	0.326100	+	0.564821i	0.981734	−	0.190257i	$-0.0609321\pi$
$853$	9.52412	+	16.4963i	0.326100	+	0.564821i	−0.655635	+	0.755078i	$0.727599\pi$
$854$	32.0934	−	18.5291i	1.09821	−	0.634053i
$855$	1.29938	+	2.25059i	0.0444379	+	0.0769686i
$856$	−9.58580	+	16.6031i	−0.327636	+	0.567482i
$857$	10.4519	−	6.03438i	0.357029	−	0.206131i	−0.310748	−	0.950492i	$-0.600579\pi$
$857$	10.4519	−	6.03438i	0.357029	−	0.206131i	0.667777	+	0.744362i	$0.267246\pi$
$858$	104.441	+	60.2991i	3.56556	+	2.05858i
$859$	21.5510	−	12.4425i	0.735311	−	0.424532i	−0.0850512	−	0.996377i	$-0.527105\pi$
$859$	21.5510	−	12.4425i	0.735311	−	0.424532i	0.820362	+	0.571845i	$0.193772\pi$
$860$			10.1457i			0.345966i
$861$			4.73891i			0.161502i
$862$	−30.3913	−	52.6394i	−1.03513	−	1.79290i
$863$	10.3036	+	5.94876i	0.350737	+	0.202498i	0.665010	−	0.746835i	$-0.268427\pi$
$863$	10.3036	+	5.94876i	0.350737	+	0.202498i	−0.314273	+	0.949333i	$0.601761\pi$
$864$	−14.4026	+	8.31537i	−0.489988	+	0.282895i
$865$			1.14521i			0.0389384i
$866$	−7.00319			−0.237978
$867$	19.0689	+	33.0283i	0.647614	+	1.12170i
$868$		−	23.4408i		−	0.795632i
$869$	26.9786			0.915185
$870$	−8.66258	−	5.00134i	−0.293689	−	0.169561i
$871$	13.6910	+	7.90453i	0.463903	+	0.267835i
$872$	−25.8545	+	14.9271i	−0.875543	+	0.505495i
$873$	−15.4030	+	8.89292i	−0.521312	+	0.300980i
$874$	−75.8851	−	43.8123i	−2.56685	−	1.48197i
$875$	9.69832	+	5.59933i	0.327863	+	0.189292i
$876$	80.6295			2.72422
$877$		−	10.6519i		−	0.359688i	−0.983695	−	0.179844i	$-0.942441\pi$
$877$		−	10.6519i		−	0.359688i	0.983695	−	0.179844i	$-0.0575593\pi$
$878$	−5.78494	−	10.0198i	−0.195232	−	0.338152i
$879$	−1.99118			−0.0671607
$880$		−	1.25469i		−	0.0422954i
$881$	−30.1910	+	17.4308i	−1.01716	+	0.587259i	−0.913281	−	0.407331i	$-0.866460\pi$
$881$	−30.1910	+	17.4308i	−1.01716	+	0.587259i	−0.103881	+	0.994590i	$0.533126\pi$
$882$	3.27792	+	1.89251i	0.110373	+	0.0637241i
$883$	3.34515	+	5.79396i	0.112573	+	0.194982i	0.916807	−	0.399330i	$-0.130757\pi$
$883$	3.34515	+	5.79396i	0.112573	+	0.194982i	−0.804234	+	0.594313i	$0.797424\pi$
$884$		−	99.8158i		−	3.35717i
$885$			1.12593i			0.0378476i
$886$	−43.4724	+	25.0988i	−1.46048	+	0.843211i
$887$	−3.04331	−	1.75705i	−0.102184	−	0.0589961i	0.448037	−	0.894015i	$-0.352123\pi$
$887$	−3.04331	−	1.75705i	−0.102184	−	0.0589961i	−0.550221	+	0.835019i	$0.685457\pi$
$888$	−54.3764	+	31.3942i	−1.82475	+	1.05352i
$889$	22.9939	−	39.8267i	0.771192	−	1.33574i
$890$	−0.533948	−	0.924825i	−0.0178980	−	0.0310002i
$891$	48.5266	−	28.0169i	1.62570	−	0.938600i
$892$	−15.0332	−	26.0383i	−0.503350	−	0.871827i
$893$	23.8836	−	13.7892i	0.799234	−	0.461438i
$894$	21.7000	−	37.5854i	0.725756	−	1.25705i
$895$	8.06170	−	4.65442i	0.269473	−	0.155580i
$896$	27.8413	+	48.2226i	0.930114	+	1.61100i
$897$	−72.0235	−	41.5828i	−2.40480	−	1.38841i
$898$	48.5482	+	28.0293i	1.62007	+	0.935350i
$899$	6.29727	+	10.9072i	0.210026	+	0.363775i
$900$	−11.2539	+	19.4923i	−0.375130	+	0.649745i
$901$		−	45.6071i		−	1.51939i
$902$	4.57607	−	7.92599i	0.152366	−	0.263906i
$903$	22.6340	+	39.2033i	0.753213	+	1.30460i
$904$	−3.05919	+	5.29868i	−0.101747	+	0.176231i
$905$	−2.57151	−	4.45398i	−0.0854797	−	0.148055i
$906$	−39.9951	+	23.0912i	−1.32875	+	0.767153i
$907$	−21.3421	+	12.3218i	−0.708651	+	0.409140i	−0.810561	−	0.585654i	$-0.800838\pi$
$907$	−21.3421	+	12.3218i	−0.708651	+	0.409140i	0.101910	+	0.994794i	$0.467505\pi$
$908$	82.0232			2.72204
$909$	22.8738	+	13.2062i	0.758675	+	0.438021i
$910$	−11.3880	+	6.57489i	−0.377510	+	0.217955i
$911$		−	14.0484i		−	0.465445i	−0.972543	−	0.232723i	$-0.925237\pi$
$911$		−	14.0484i		−	0.465445i	0.972543	−	0.232723i	$-0.0747634\pi$
$912$	−3.13763	−	5.43453i	−0.103897	−	0.179955i
$913$	23.4411	+	13.5337i	0.775788	+	0.447902i
$914$		−	26.9736i		−	0.892207i
$915$	−4.02730	−	2.32516i	−0.133138	−	0.0768675i
$916$			55.1991i			1.82383i
$917$	1.06372	−	1.84241i	0.0351270	−	0.0608418i
$918$	−40.4354	−	23.3454i	−1.33457	−	0.770513i
$919$	17.1418	+	9.89681i	0.565455	+	0.326466i	0.755332	−	0.655342i	$-0.227476\pi$
$919$	17.1418	+	9.89681i	0.565455	+	0.326466i	−0.189877	+	0.981808i	$0.560809\pi$
$920$			10.0940i			0.332789i
$921$	12.7788			0.421077
$922$	−94.1113			−3.09939
$923$	−20.3115	−	35.1806i	−0.668561	−	1.15798i
$924$	−50.3551	−	87.2175i	−1.65656	−	2.86925i
$925$	−22.8209	+	39.5270i	−0.750346	+	1.29964i
$926$	−37.2081			−1.22274
$927$	−11.1072	−	6.41275i	−0.364808	−	0.210622i
$928$	−22.0059	−	12.7051i	−0.722379	−	0.417066i
$929$	−47.5783			−1.56099			−0.780496	−	0.625160i	$-0.785034\pi$
$929$	−47.5783			−1.56099			−0.780496	+	0.625160i	$0.785034\pi$
$930$	−4.05777	+	2.34276i	−0.133060	+	0.0768220i
$931$	−2.80904	+	4.86540i	−0.0920625	+	0.159457i
$932$	−44.7906			−1.46716
$933$	−3.86337	+	2.23052i	−0.126481	+	0.0730239i
$934$	6.38903	+	3.68871i	0.209056	+	0.120698i
$935$	−10.1959	+	5.88658i	−0.333440	+	0.192512i
$936$	−10.9353	−	18.9406i	−0.357433	−	0.619092i
$937$	13.9394			0.455379			0.227690	−	0.973734i	$-0.426883\pi$
$937$	13.9394			0.455379			0.227690	+	0.973734i	$0.426883\pi$
$938$	−10.5147	−	18.2119i	−0.343316	−	0.594640i
$939$	16.7864	+	29.0749i	0.547804	+	0.948825i
$940$	−6.75814	−	3.90182i	−0.220426	−	0.127263i
$941$	13.6264	−	23.6016i	0.444207	−	0.769389i	−0.553789	−	0.832657i	$-0.686819\pi$
$941$	13.6264	−	23.6016i	0.444207	−	0.769389i	0.997997	+	0.0632673i	$0.0201521\pi$
$942$	3.89884	−	2.25100i	0.127031	−	0.0733414i
$943$	−3.15570	+	5.46584i	−0.102764	+	0.177992i
$944$		−	0.855783i		−	0.0278534i
$945$			3.86157i			0.125617i
$946$		−	87.4250i		−	2.84243i
$947$	−4.35113			−0.141393			−0.0706963	−	0.997498i	$-0.522522\pi$
$947$	−4.35113			−0.141393			−0.0706963	+	0.997498i	$0.522522\pi$
$948$	−33.0654	−	19.0903i	−1.07391	−	0.620024i
$949$			56.9516i			1.84873i
$950$	−46.0861	−	26.6078i	−1.49523	−	0.863271i
$951$	3.47524	+	2.00643i	0.112692	+	0.0650629i
$952$	−27.0270	+	46.8122i	−0.875950	+	1.51719i
$953$	24.2119	−	41.9362i	0.784299	−	1.35845i	−0.145118	−	0.989414i	$-0.546356\pi$
$953$	24.2119	−	41.9362i	0.784299	−	1.35845i	0.929417	−	0.369032i	$-0.120311\pi$
$954$	−12.2732	−	21.2577i	−0.397358	−	0.688245i
$955$	2.29038			0.0741150
$956$	2.18778	+	3.78934i	0.0707578	+	0.122556i
$957$	46.8612	+	27.0554i	1.51481	+	0.874575i
$958$	47.2092	−	27.2563i	1.52526	−	0.880610i
$959$	−32.8856			−1.06193
$960$	5.25304	−	9.09854i	0.169541	−	0.293654i
$961$	−25.1004			−0.809690
$962$	−54.4694	−	94.3437i	−1.75616	−	3.04176i
$963$	7.18747	−	4.14969i	0.231613	−	0.133722i
$964$	−10.3690	+	17.9596i	−0.333962	+	0.578438i
$965$	−7.36107	−	4.24992i	−0.236961	−	0.136810i
$966$	55.3137	+	95.8062i	1.77969	+	3.08251i
$967$	37.1151			1.19354			0.596770	−	0.802412i	$-0.296451\pi$
$967$	37.1151			1.19354			0.596770	+	0.802412i	$0.296451\pi$
$968$			44.1652i			1.41952i
$969$	−29.4415	+	50.9941i	−0.945797	+	1.63817i
$970$	−5.94947	+	10.3048i	−0.191026	+	0.330867i
$971$	4.91551	−	8.51391i	0.157746	−	0.273224i	−0.776309	−	0.630352i	$-0.782911\pi$
$971$	4.91551	−	8.51391i	0.157746	−	0.273224i	0.934056	+	0.357128i	$0.116244\pi$
$972$	−44.9563			−1.44197
$973$	−3.63737	−	2.10004i	−0.116609	−	0.0673240i
$974$	−1.85637	−	3.21532i	−0.0594819	−	0.103026i
$975$	−43.7409	−	25.2538i	−1.40083	−	0.808769i
$976$	3.06103	+	1.76729i	0.0979812	+	0.0565695i
$977$	−21.1338	+	36.6049i	−0.676132	+	1.17109i	0.300005	+	0.953938i	$0.403012\pi$
$977$	−21.1338	+	36.6049i	−0.676132	+	1.17109i	−0.976137	+	0.217157i	$0.930322\pi$
$978$	108.921			3.48292
$979$	2.88846	+	5.00295i	0.0923154	+	0.159895i
$980$	1.58970			0.0507811
$981$	12.9239			0.412627
$982$		−	69.4639i		−	2.21668i
$983$	45.6747			1.45680			0.728399	−	0.685153i	$-0.240265\pi$
$983$	45.6747			1.45680			0.728399	+	0.685153i	$0.240265\pi$
$984$	−4.56654	+	2.63649i	−0.145576	+	0.0840483i
$985$	5.13843	+	2.96667i	0.163724	+	0.0945261i
$986$		−	71.3392i		−	2.27190i
$987$	−34.8182			−1.10827
$988$	69.0563	−	39.8697i	2.19697	−	1.26842i
$989$			60.2891i			1.91708i
$990$	−3.16823	+	5.48754i	−0.100693	+	0.174405i
$991$	8.24314	−	14.2775i	0.261852	−	0.453541i	−0.704882	−	0.709324i	$-0.749000\pi$
$991$	8.24314	−	14.2775i	0.261852	−	0.453541i	0.966734	+	0.255784i	$0.0823335\pi$
$992$	−10.3081	+	5.95140i	−0.327284	+	0.188957i
$993$	22.0184	+	12.7123i	0.698732	+	0.403413i
$994$			54.0370i			1.71395i
$995$		−	7.21890i		−	0.228855i
$996$	−19.1532	−	33.1744i	−0.606894	−	1.05117i
$997$	2.86841	−	1.65608i	0.0908434	−	0.0524485i	−0.453890	−	0.891058i	$-0.649964\pi$
$997$	2.86841	−	1.65608i	0.0908434	−	0.0524485i	0.544734	+	0.838609i	$0.316631\pi$
$998$	−19.7000	−	34.1214i	−0.623592	−	1.08009i
$999$	−31.9910			−1.01215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.227.4	yes	58
349.123	even	6	inner	349.2.e.a.123.4	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.4	✓	58	349.123	even	6	inner
349.2.e.a.227.4	yes	58	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00748 - 1.15902i) q^{2} +(1.04619 + 1.81206i) q^{3} +(1.68665 + 2.92136i) q^{4} +(-0.198863 - 0.344441i) q^{5} -4.85022i q^{6} +(-2.47763 - 1.43046i) q^{7} -3.18335i q^{8} +(-0.689035 + 1.19344i) q^{9} +O(q^{10})\)	\(q+(-2.00748 - 1.15902i) q^{2} +(1.04619 + 1.81206i) q^{3} +(1.68665 + 2.92136i) q^{4} +(-0.198863 - 0.344441i) q^{5} -4.85022i q^{6} +(-2.47763 - 1.43046i) q^{7} -3.18335i q^{8} +(-0.689035 + 1.19344i) q^{9} +0.921944i q^{10} -4.98737i q^{11} +(-3.52911 + 6.11260i) q^{12} +(-4.31756 - 2.49274i) q^{13} +(3.31586 + 5.74324i) q^{14} +(0.416098 - 0.720703i) q^{15} +(-0.316264 + 0.547785i) q^{16} +5.93523 q^{17} +(2.76644 - 1.59721i) q^{18} +(2.37072 + 4.10621i) q^{19} +(0.670824 - 1.16190i) q^{20} -5.98615i q^{21} +(-5.78045 + 10.0120i) q^{22} +(3.98625 - 6.90439i) q^{23} +(5.76841 - 3.33039i) q^{24} +(2.42091 - 4.19313i) q^{25} +(5.77827 + 10.0083i) q^{26} +3.39370 q^{27} -9.65074i q^{28} +(2.59263 + 4.49057i) q^{29} +(-1.67062 + 0.964530i) q^{30} +2.42891 q^{31} +(-4.24393 + 2.45024i) q^{32} +(9.03739 - 5.21774i) q^{33} +(-11.9148 - 6.87904i) q^{34} +1.13786i q^{35} -4.64863 q^{36} -9.42659 q^{37} -10.9908i q^{38} -10.4316i q^{39} +(-1.09648 + 0.633050i) q^{40} -0.791646 q^{41} +(-6.93806 + 12.0171i) q^{42} +(-6.54900 + 3.78107i) q^{43} +(14.5699 - 8.41193i) q^{44} +0.548094 q^{45} +(-16.0046 + 9.24028i) q^{46} -5.81645i q^{47} -1.32349 q^{48} +(0.592443 + 1.02614i) q^{49} +(-9.71984 + 5.61175i) q^{50} +(6.20939 + 10.7550i) q^{51} -16.8175i q^{52} -7.68414i q^{53} +(-6.81278 - 3.93336i) q^{54} +(-1.71785 + 0.991803i) q^{55} +(-4.55366 + 7.88717i) q^{56} +(-4.96046 + 8.59177i) q^{57} -12.0196i q^{58} +(-1.17170 + 0.676479i) q^{59} +2.80724 q^{60} -5.58802i q^{61} +(-4.87598 - 2.81515i) q^{62} +(3.41435 - 1.97128i) q^{63} +12.6245 q^{64} +1.98286i q^{65} -24.1898 q^{66} -3.17102 q^{67} +(10.0106 + 17.3389i) q^{68} +16.6815 q^{69} +(1.31881 - 2.28424i) q^{70} +(7.05659 + 4.07413i) q^{71} +(3.79914 + 2.19344i) q^{72} +(-5.71174 - 9.89302i) q^{73} +(18.9237 + 10.9256i) q^{74} +10.1309 q^{75} +(-7.99715 + 13.8515i) q^{76} +(-7.13424 + 12.3569i) q^{77} +(-12.0904 + 20.9411i) q^{78} +5.40938i q^{79} +0.251573 q^{80} +(5.61757 + 9.72991i) q^{81} +(1.58921 + 0.917532i) q^{82} +(-2.71361 + 4.70010i) q^{83} +(17.4877 - 10.0965i) q^{84} +(-1.18030 - 2.04434i) q^{85} +17.5293 q^{86} +(-5.42478 + 9.39599i) q^{87} -15.8765 q^{88} +(-1.00312 + 0.579154i) q^{89} +(-1.10029 - 0.635251i) q^{90} +(7.13155 + 12.3522i) q^{91} +26.8936 q^{92} +(2.54111 + 4.40132i) q^{93} +(-6.74138 + 11.6764i) q^{94} +(0.942899 - 1.63315i) q^{95} +(-8.87994 - 5.12684i) q^{96} +(11.1772 + 6.45318i) q^{97} -2.74661i q^{98} +(5.95214 + 3.43647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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