LMFDB - Embedded newform 349.2.c.a.122.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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([4]))

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (of order $3$, 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:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.5
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10993 + 1.92246i) q^{2} +(-0.792401 - 1.37248i) q^{3} +(-1.46391 - 2.53556i) q^{4} +(-0.325113 - 0.563112i) q^{5} +3.51805 q^{6} +(-2.07452 + 3.59318i) q^{7} +2.05963 q^{8} +(0.244201 - 0.422969i) q^{9} +O(q^{10})$	\(q+(-1.10993 + 1.92246i) q^{2} +(-0.792401 - 1.37248i) q^{3} +(-1.46391 - 2.53556i) q^{4} +(-0.325113 - 0.563112i) q^{5} +3.51805 q^{6} +(-2.07452 + 3.59318i) q^{7} +2.05963 q^{8} +(0.244201 - 0.422969i) q^{9} +1.44342 q^{10} -1.43391 q^{11} +(-2.32001 + 4.01837i) q^{12} +(2.14822 - 3.72083i) q^{13} +(-4.60517 - 7.97639i) q^{14} +(-0.515240 + 0.892421i) q^{15} +(0.641760 - 1.11156i) q^{16} +7.36678 q^{17} +(0.542095 + 0.938936i) q^{18} +(0.958725 + 1.66056i) q^{19} +(-0.951871 + 1.64869i) q^{20} +6.57542 q^{21} +(1.59155 - 2.75664i) q^{22} +(3.49959 - 6.06146i) q^{23} +(-1.63206 - 2.82680i) q^{24} +(2.28860 - 3.96398i) q^{25} +(4.76877 + 8.25975i) q^{26} -5.52843 q^{27} +12.1477 q^{28} +(-2.96126 - 5.12905i) q^{29} +(-1.14376 - 1.98106i) q^{30} +2.41439 q^{31} +(3.48426 + 6.03491i) q^{32} +(1.13623 + 1.96801i) q^{33} +(-8.17664 + 14.1624i) q^{34} +2.69782 q^{35} -1.42995 q^{36} +9.07279 q^{37} -4.25649 q^{38} -6.80901 q^{39} +(-0.669613 - 1.15980i) q^{40} -12.6768 q^{41} +(-7.29828 + 12.6410i) q^{42} +(2.93743 + 5.08778i) q^{43} +(2.09911 + 3.63577i) q^{44} -0.317572 q^{45} +(7.76863 + 13.4557i) q^{46} -0.246077 q^{47} -2.03412 q^{48} +(-5.10730 - 8.84610i) q^{49} +(5.08040 + 8.79951i) q^{50} +(-5.83744 - 10.1107i) q^{51} -12.5792 q^{52} -5.42587 q^{53} +(6.13619 - 10.6282i) q^{54} +(0.466182 + 0.807452i) q^{55} +(-4.27276 + 7.40064i) q^{56} +(1.51939 - 2.63166i) q^{57} +13.1472 q^{58} +(-3.33460 - 5.77569i) q^{59} +3.01705 q^{60} +8.31899 q^{61} +(-2.67981 + 4.64157i) q^{62} +(1.01320 + 1.75492i) q^{63} -12.9021 q^{64} -2.79366 q^{65} -5.04457 q^{66} +7.90916 q^{67} +(-10.7843 - 18.6789i) q^{68} -11.0923 q^{69} +(-2.99440 + 5.18645i) q^{70} +(0.0471509 - 0.0816678i) q^{71} +(0.502965 - 0.871161i) q^{72} +(4.44594 + 7.70060i) q^{73} +(-10.0702 + 17.4421i) q^{74} -7.25397 q^{75} +(2.80697 - 4.86182i) q^{76} +(2.97468 - 5.15230i) q^{77} +(7.55756 - 13.0901i) q^{78} -0.515524 q^{79} -0.834577 q^{80} +(3.64813 + 6.31874i) q^{81} +(14.0705 - 24.3708i) q^{82} +(8.59984 - 14.8954i) q^{83} +(-9.62581 - 16.6724i) q^{84} +(-2.39504 - 4.14832i) q^{85} -13.0414 q^{86} +(-4.69301 + 8.12853i) q^{87} -2.95333 q^{88} +(-3.40998 - 5.90626i) q^{89} +(0.352484 - 0.610520i) q^{90} +(8.91307 + 15.4379i) q^{91} -20.4923 q^{92} +(-1.91316 - 3.31370i) q^{93} +(0.273129 - 0.473073i) q^{94} +(0.623388 - 1.07974i) q^{95} +(5.52186 - 9.56413i) q^{96} +(4.38506 - 7.59515i) q^{97} +22.6751 q^{98} +(-0.350163 + 0.606499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.10993	+	1.92246i	−0.784842	+	1.35939i	0.144251	+	0.989541i	$0.453923\pi$
$2$	−1.10993	+	1.92246i	−0.784842	+	1.35939i	−0.929093	+	0.369845i	$0.879411\pi$
$3$	−0.792401	−	1.37248i	−0.457493	−	0.792401i	0.541335	−	0.840807i	$-0.317919\pi$
$3$	−0.792401	−	1.37248i	−0.457493	−	0.792401i	−0.998828	+	0.0484061i	$0.984586\pi$
$4$	−1.46391	−	2.53556i	−0.731954	−	1.26778i
$5$	−0.325113	−	0.563112i	−0.145395	−	0.251831i	0.784125	−	0.620603i	$-0.213112\pi$
$5$	−0.325113	−	0.563112i	−0.145395	−	0.251831i	−0.929520	+	0.368771i	$0.879779\pi$
$6$	3.51805			1.43624
$7$	−2.07452	+	3.59318i	−0.784096	+	1.35809i	0.145441	+	0.989367i	$0.453540\pi$
$7$	−2.07452	+	3.59318i	−0.784096	+	1.35809i	−0.929537	+	0.368728i	$0.879793\pi$
$8$	2.05963			0.728190
$9$	0.244201	−	0.422969i	0.0814005	−	0.140990i
$10$	1.44342			0.456448
$11$	−1.43391			−0.432340			−0.216170	−	0.976356i	$-0.569357\pi$
$11$	−1.43391			−0.432340			−0.216170	+	0.976356i	$0.569357\pi$
$12$	−2.32001	+	4.01837i	−0.669728	+	1.16000i
$13$	2.14822	−	3.72083i	0.595809	−	1.03197i	−0.397623	−	0.917549i	$-0.630165\pi$
$13$	2.14822	−	3.72083i	0.595809	−	1.03197i	0.993432	−	0.114423i	$-0.0365020\pi$
$14$	−4.60517	−	7.97639i	−1.23078	−	2.13178i
$15$	−0.515240	+	0.892421i	−0.133034	+	0.230422i
$16$	0.641760	−	1.11156i	0.160440	−	0.277890i
$17$	7.36678			1.78671			0.893353	−	0.449355i	$-0.148346\pi$
$17$	7.36678			1.78671			0.893353	+	0.449355i	$0.148346\pi$
$18$	0.542095	+	0.938936i	0.127773	+	0.221309i
$19$	0.958725	+	1.66056i	0.219947	+	0.380959i	0.954791	−	0.297277i	$-0.0960784\pi$
$19$	0.958725	+	1.66056i	0.219947	+	0.380959i	−0.734845	+	0.678235i	$0.762745\pi$
$20$	−0.951871	+	1.64869i	−0.212845	+	0.368658i
$21$	6.57542			1.43487
$22$	1.59155	−	2.75664i	0.339319	−	0.587717i
$23$	3.49959	−	6.06146i	0.729715	−	1.26390i	−0.227289	−	0.973827i	$-0.572986\pi$
$23$	3.49959	−	6.06146i	0.729715	−	1.26390i	0.957004	−	0.290075i	$-0.0936804\pi$
$24$	−1.63206	−	2.82680i	−0.333142	−	0.577019i
$25$	2.28860	−	3.96398i	0.457721	−	0.792795i
$26$	4.76877	+	8.25975i	0.935233	+	1.61987i
$27$	−5.52843			−1.06395
$28$	12.1477			2.29569
$29$	−2.96126	−	5.12905i	−0.549892	−	0.952440i	−0.998281	−	0.0586023i	$-0.981336\pi$
$29$	−2.96126	−	5.12905i	−0.549892	−	0.952440i	0.448390	−	0.893838i	$-0.351998\pi$
$30$	−1.14376	−	1.98106i	−0.208822	−	0.361690i
$31$	2.41439			0.433637			0.216818	−	0.976212i	$-0.430432\pi$
$31$	2.41439			0.433637			0.216818	+	0.976212i	$0.430432\pi$
$32$	3.48426	+	6.03491i	0.615935	+	1.06683i
$33$	1.13623	+	1.96801i	0.197792	+	0.342587i
$34$	−8.17664	+	14.1624i	−1.40228	+	2.42882i
$35$	2.69782			0.456014
$36$	−1.42995			−0.238326
$37$	9.07279			1.49156			0.745779	−	0.666194i	$-0.232078\pi$
$37$	9.07279			1.49156			0.745779	+	0.666194i	$0.232078\pi$
$38$	−4.25649			−0.690493
$39$	−6.80901			−1.09031
$40$	−0.669613	−	1.15980i	−0.105875	−	0.183381i
$41$	−12.6768			−1.97979			−0.989895	−	0.141799i	$-0.954711\pi$
$41$	−12.6768			−1.97979			−0.989895	+	0.141799i	$0.954711\pi$
$42$	−7.29828	+	12.6410i	−1.12615	+	1.95055i
$43$	2.93743	+	5.08778i	0.447954	+	0.775880i	0.998253	−	0.0590885i	$-0.0188194\pi$
$43$	2.93743	+	5.08778i	0.447954	+	0.775880i	−0.550298	+	0.834968i	$0.685486\pi$
$44$	2.09911	+	3.63577i	0.316453	+	0.548113i
$45$	−0.317572			−0.0473408
$46$	7.76863	+	13.4557i	1.14542	+	1.98393i
$47$	−0.246077			−0.0358940			−0.0179470	−	0.999839i	$-0.505713\pi$
$47$	−0.246077			−0.0358940			−0.0179470	+	0.999839i	$0.505713\pi$
$48$	−2.03412			−0.293600
$49$	−5.10730	−	8.84610i	−0.729614	−	1.26373i
$50$	5.08040	+	8.79951i	0.718477	+	1.24444i
$51$	−5.83744	−	10.1107i	−0.817406	−	1.41579i
$52$	−12.5792			−1.74442
$53$	−5.42587			−0.745300			−0.372650	−	0.927972i	$-0.621551\pi$
$53$	−5.42587			−0.745300			−0.372650	+	0.927972i	$0.621551\pi$
$54$	6.13619	−	10.6282i	0.835030	−	1.44631i
$55$	0.466182	+	0.807452i	0.0628600	+	0.108877i
$56$	−4.27276	+	7.40064i	−0.570971	+	0.988951i
$57$	1.51939	−	2.63166i	0.201248	−	0.348572i
$58$	13.1472			1.72631
$59$	−3.33460	−	5.77569i	−0.434128	−	0.751931i	0.563096	−	0.826391i	$-0.309610\pi$
$59$	−3.33460	−	5.77569i	−0.434128	−	0.751931i	−0.997224	+	0.0744602i	$0.976277\pi$
$60$	3.01705			0.389500
$61$	8.31899			1.06514			0.532569	−	0.846387i	$-0.321227\pi$
$61$	8.31899			1.06514			0.532569	+	0.846387i	$0.321227\pi$
$62$	−2.67981	+	4.64157i	−0.340337	+	0.589480i
$63$	1.01320	+	1.75492i	0.127652	+	0.221099i
$64$	−12.9021			−1.61277
$65$	−2.79366			−0.346511
$66$	−5.04457			−0.620943
$67$	7.90916			0.966258			0.483129	−	0.875549i	$-0.339500\pi$
$67$	7.90916			0.966258			0.483129	+	0.875549i	$0.339500\pi$
$68$	−10.7843	−	18.6789i	−1.30779	−	2.26515i
$69$	−11.0923			−1.33536
$70$	−2.99440	+	5.18645i	−0.357899	+	0.619900i
$71$	0.0471509	−	0.0816678i	0.00559578	−	0.00969218i	−0.863214	−	0.504838i	$-0.831552\pi$
$71$	0.0471509	−	0.0816678i	0.00559578	−	0.00969218i	0.868810	+	0.495146i	$0.164885\pi$
$72$	0.502965	−	0.871161i	0.0592750	−	0.102667i
$73$	4.44594	+	7.70060i	0.520358	+	0.901287i	0.999720	+	0.0236692i	$0.00753484\pi$
$73$	4.44594	+	7.70060i	0.520358	+	0.901287i	−0.479362	+	0.877617i	$0.659132\pi$
$74$	−10.0702	+	17.4421i	−1.17064	+	2.02760i
$75$	−7.25397			−0.837616
$76$	2.80697	−	4.86182i	0.321982	−	0.557689i
$77$	2.97468	−	5.15230i	0.338996	−	0.587159i
$78$	7.55756	−	13.0901i	0.855725	−	1.48216i
$79$	−0.515524			−0.0580010			−0.0290005	−	0.999579i	$-0.509232\pi$
$79$	−0.515524			−0.0580010			−0.0290005	+	0.999579i	$0.509232\pi$
$80$	−0.834577			−0.0933086
$81$	3.64813	+	6.31874i	0.405347	+	0.702082i
$82$	14.0705	−	24.3708i	1.55382	−	2.69130i
$83$	8.59984	−	14.8954i	0.943955	−	1.63498i	0.186125	−	0.982526i	$-0.440407\pi$
$83$	8.59984	−	14.8954i	0.943955	−	1.63498i	0.757830	−	0.652452i	$-0.226260\pi$
$84$	−9.62581	−	16.6724i	−1.05026	−	1.81911i
$85$	−2.39504	−	4.14832i	−0.259778	−	0.449949i
$86$	−13.0414			−1.40629
$87$	−4.69301	+	8.12853i	−0.503143	+	0.871470i
$88$	−2.95333			−0.314826
$89$	−3.40998	−	5.90626i	−0.361457	−	0.626062i	0.626744	−	0.779225i	$-0.284387\pi$
$89$	−3.40998	−	5.90626i	−0.361457	−	0.626062i	−0.988201	+	0.153163i	$0.951054\pi$
$90$	0.352484	−	0.610520i	0.0371551	−	0.0643545i
$91$	8.91307	+	15.4379i	0.934344	+	1.61833i
$92$	−20.4923			−2.13647
$93$	−1.91316	−	3.31370i	−0.198386	−	0.343614i
$94$	0.273129	−	0.473073i	0.0281711	−	0.0487938i
$95$	0.623388	−	1.07974i	0.0639582	−	0.110779i
$96$	5.52186	−	9.56413i	0.563572	−	0.976135i
$97$	4.38506	−	7.59515i	0.445235	−	0.771170i	−0.552833	−	0.833292i	$-0.686453\pi$
$97$	4.38506	−	7.59515i	0.445235	−	0.771170i	0.998069	+	0.0621215i	$0.0197866\pi$
$98$	22.6751			2.29053
$99$	−0.350163	+	0.606499i	−0.0351927	+	0.0609555i
$100$	−13.4012			−1.34012
$101$	−6.06351			−0.603342			−0.301671	−	0.953412i	$-0.597544\pi$
$101$	−6.06351			−0.603342			−0.301671	+	0.953412i	$0.597544\pi$
$102$	25.9167			2.56614
$103$	−6.74207			−0.664316			−0.332158	−	0.943224i	$-0.607777\pi$
$103$	−6.74207			−0.664316			−0.332158	+	0.943224i	$0.607777\pi$
$104$	4.42455	−	7.66354i	0.433863	−	0.751472i
$105$	−2.13775	−	3.70270i	−0.208623	−	0.361346i
$106$	6.02236	−	10.4310i	0.584943	−	1.01315i
$107$	−0.300617	+	0.520685i	−0.0290618	+	0.0503365i	−0.880190	−	0.474621i	$-0.842585\pi$
$107$	−0.300617	+	0.520685i	−0.0290618	+	0.0503365i	0.851129	+	0.524957i	$0.175919\pi$
$108$	8.09311	+	14.0177i	0.778760	+	1.34885i
$109$	−4.50795	−	7.80801i	−0.431784	−	0.747871i	0.565243	−	0.824924i	$-0.308782\pi$
$109$	−4.50795	−	7.80801i	−0.431784	−	0.747871i	−0.997027	+	0.0770529i	$0.975449\pi$
$110$	−2.06973			−0.197341
$111$	−7.18929	−	12.4522i	−0.682377	−	1.18191i
$112$	2.66269	+	4.61192i	0.251601	+	0.435785i
$113$	−9.34147	+	16.1799i	−0.878772	+	1.52208i	−0.0260823	+	0.999660i	$0.508303\pi$
$113$	−9.34147	+	16.1799i	−0.878772	+	1.52208i	−0.852690	+	0.522418i	$0.825030\pi$
$114$	3.37284	+	5.84194i	0.315896	+	0.547148i
$115$	−4.55105			−0.424387
$116$	−8.67002	+	15.0169i	−0.804991	+	1.39429i
$117$	−1.04920	−	1.81726i	−0.0969983	−	0.168006i
$118$	14.8047			1.36289
$119$	−15.2826	+	26.4702i	−1.40095	+	2.42652i
$120$	−1.06120	+	1.83806i	−0.0968743	+	0.167791i
$121$	−8.94390			−0.813082
$122$	−9.23354	+	15.9930i	−0.835965	+	1.44793i
$123$	10.0451	+	17.3987i	0.905740	+	1.56879i
$124$	−3.53444	−	6.12184i	−0.317402	−	0.549757i
$125$	−6.22735			−0.556991
$126$	−4.49836			−0.400745
$127$	−9.44580			−0.838179			−0.419090	−	0.907945i	$-0.637651\pi$
$127$	−9.44580			−0.838179			−0.419090	+	0.907945i	$0.637651\pi$
$128$	7.35202	−	12.7341i	0.649833	−	1.12554i
$129$	4.65525	−	8.06313i	0.409872	−	0.709919i
$130$	3.10078	−	5.37070i	0.271956	−	0.471042i
$131$	11.4357			0.999138			0.499569	−	0.866274i	$-0.333492\pi$
$131$	11.4357			0.999138			0.499569	+	0.866274i	$0.333492\pi$
$132$	3.32668	−	5.76197i	0.289550	−	0.501516i
$133$	−7.95559			−0.689837
$134$	−8.77865	+	15.2051i	−0.758360	+	1.31352i
$135$	1.79736	+	3.11312i	0.154692	+	0.267935i
$136$	15.1729			1.30106
$137$	3.91169	+	6.77524i	0.334198	+	0.578848i	0.983330	−	0.181828i	$-0.0582013\pi$
$137$	3.91169	+	6.77524i	0.334198	+	0.578848i	−0.649133	+	0.760675i	$0.724868\pi$
$138$	12.3117	−	21.3246i	1.04804	−	1.81527i
$139$	13.0332			1.10546			0.552732	−	0.833359i	$-0.313585\pi$
$139$	13.0332			1.10546			0.552732	+	0.833359i	$0.313585\pi$
$140$	−3.94936	−	6.84049i	−0.333782	−	0.578127i
$141$	0.194991	+	0.337735i	0.0164212	+	0.0284424i
$142$	0.104669	+	0.181292i	0.00878361	+	0.0152137i
$143$	−3.08036	+	5.33533i	−0.257592	+	0.446163i
$144$	−0.313437	−	0.542889i	−0.0261198	−	0.0452408i
$145$	−1.92549	+	3.33504i	−0.159903	+	0.276960i
$146$	−19.7388			−1.63360
$147$	−8.09406	+	14.0193i	−0.667587	+	1.15629i
$148$	−13.2817	−	23.0046i	−1.09175	−	1.89097i
$149$	10.8594	−	18.8089i	0.889633	−	1.54089i	0.0493229	−	0.998783i	$-0.484294\pi$
$149$	10.8594	−	18.8089i	0.889633	−	1.54089i	0.840310	−	0.542106i	$-0.182373\pi$
$150$	8.05143	−	13.9455i	0.657396	−	1.13864i
$151$	−0.0677500	−	0.117346i	−0.00551342	−	0.00954952i	0.863256	−	0.504767i	$-0.168422\pi$
$151$	−0.0677500	−	0.117346i	−0.00551342	−	0.00954952i	−0.868769	+	0.495218i	$0.835088\pi$
$152$	1.97462	+	3.42015i	0.160163	+	0.277410i
$153$	1.79898	−	3.11592i	0.145439	−	0.251907i
$154$	6.60340	+	11.4374i	0.532117	+	0.921654i
$155$	−0.784949	−	1.35957i	−0.0630486	−	0.109203i
$156$	9.96777	+	17.2647i	0.798060	+	1.38228i
$157$	−2.78031	−	4.81565i	−0.221893	−	0.384330i	0.733490	−	0.679701i	$-0.237890\pi$
$157$	−2.78031	−	4.81565i	−0.221893	−	0.384330i	−0.955383	+	0.295370i	$0.904557\pi$
$158$	0.572198	−	0.991076i	0.0455216	−	0.0788457i
$159$	4.29946	+	7.44689i	0.340970	+	0.590577i
$160$	2.26555	−	3.92405i	0.179108	−	0.310224i
$161$	14.5200	+	25.1493i	1.14433	+	1.98204i
$162$	−16.1967			−1.27254
$163$	−13.6488			−1.06906			−0.534530	−	0.845149i	$-0.679511\pi$
$163$	−13.6488			−1.06906			−0.534530	+	0.845149i	$0.679511\pi$
$164$	18.5577	+	32.1430i	1.44912	+	2.50994i
$165$	0.738807	−	1.27965i	0.0575160	−	0.0996207i
$166$	19.0905	+	33.0657i	1.48171	+	2.56640i
$167$	17.3514			1.34269			0.671346	−	0.741144i	$-0.265717\pi$
$167$	17.3514			1.34269			0.671346	+	0.741144i	$0.265717\pi$
$168$	13.5430			1.04486
$169$	−2.72971	−	4.72800i	−0.209978	−	0.363692i
$170$	10.6333			0.815539
$171$	0.936488			0.0716150
$172$	8.60027	−	14.8961i	0.655764	−	1.13582i
$173$	3.86241	−	6.68990i	0.293654	−	0.508624i	−0.681017	−	0.732268i	$-0.738462\pi$
$173$	3.86241	−	6.68990i	0.293654	−	0.508624i	0.974671	+	0.223644i	$0.0717953\pi$
$174$	−10.4179	−	18.0443i	−0.789776	−	1.36793i
$175$	9.49552	+	16.4467i	0.717794	+	1.24326i
$176$	−0.920225	+	1.59388i	−0.0693646	+	0.120143i
$177$	−5.28468	+	9.15333i	−0.397221	+	0.688006i
$178$	15.1394			1.13475
$179$	−1.35054			−0.100944			−0.0504720	−	0.998725i	$-0.516073\pi$
$179$	−1.35054			−0.100944			−0.0504720	+	0.998725i	$0.516073\pi$
$180$	0.464897	+	0.805224i	0.0346513	+	0.0600179i
$181$	8.79439			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$181$	8.79439			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$182$	−39.5717			−2.93325
$183$	−6.59198	−	11.4176i	−0.487293	−	0.844016i
$184$	7.20787	−	12.4844i	0.531371	−	0.920362i
$185$	−2.94968	−	5.10900i	−0.216865	−	0.375621i
$186$	8.49395			0.622806
$187$	−10.5633			−0.772465
$188$	0.360234	+	0.623943i	0.0262727	+	0.0455057i
$189$	11.4689	−	19.8646i	0.834236	−	1.44494i
$190$	1.38384	+	2.39688i	0.100394	+	0.173888i
$191$	−3.93124	+	6.80912i	−0.284455	+	0.492690i	−0.972477	−	0.233000i	$-0.925146\pi$
$191$	−3.93124	+	6.80912i	−0.284455	+	0.492690i	0.688022	+	0.725690i	$0.258479\pi$
$192$	10.2237	+	17.7079i	0.737830	+	1.27796i
$193$	12.6956	+	21.9895i	0.913852	+	1.58284i	0.808574	+	0.588395i	$0.200240\pi$
$193$	12.6956	+	21.9895i	0.913852	+	1.58284i	0.105278	+	0.994443i	$0.466427\pi$
$194$	9.73426	+	16.8602i	0.698879	+	1.21049i
$195$	2.21370	+	3.83424i	0.158526	+	0.274575i
$196$	−14.9532	+	25.8998i	−1.06809	+	1.84998i
$197$	−2.13630	−	3.70018i	−0.152205	−	0.263627i	0.779833	−	0.625988i	$-0.215304\pi$
$197$	−2.13630	−	3.70018i	−0.152205	−	0.263627i	−0.932038	+	0.362361i	$0.881971\pi$
$198$	−0.777315	−	1.34635i	−0.0552414	−	0.0956809i
$199$	2.89780	−	5.01914i	0.205420	−	0.355798i	−0.744847	−	0.667236i	$-0.767477\pi$
$199$	2.89780	−	5.01914i	0.205420	−	0.355798i	0.950266	+	0.311438i	$0.100811\pi$
$200$	4.71368	−	8.16434i	0.333308	−	0.577306i
$201$	−6.26723	−	10.8552i	−0.442056	−	0.765664i
$202$	6.73010	−	11.6569i	0.473528	−	0.820175i
$203$	24.5728			1.72467
$204$	−17.0910	+	29.6024i	−1.19661	+	2.07258i
$205$	4.12141	+	7.13849i	0.287852	+	0.498573i
$206$	7.48325	−	12.9614i	0.521383	−	0.903062i
$207$	−1.70921	−	2.96044i	−0.118798	−	0.205765i
$208$	−2.75728	−	4.77576i	−0.191183	−	0.331139i
$209$	−1.37472	−	2.38109i	−0.0950917	−	0.164704i
$210$	9.49107			0.654946
$211$	−2.28644	+	3.96023i	−0.157405	+	0.272633i	−0.933932	−	0.357450i	$-0.883646\pi$
$211$	−2.28644	+	3.96023i	−0.157405	+	0.272633i	0.776527	+	0.630084i	$0.216979\pi$
$212$	7.94298	+	13.7576i	0.545526	+	0.944879i
$213$	−0.149450			−0.0102401
$214$	−0.667331	−	1.15585i	−0.0456178	−	0.0790124i
$215$	1.90999	−	3.30821i	0.130261	−	0.225618i
$216$	−11.3865			−0.774755
$217$	−5.00871	+	8.67533i	−0.340013	+	0.588920i
$218$	20.0141			1.35553
$219$	7.04594	−	12.2039i	0.476120	−	0.824664i
$220$	1.36490	−	2.36407i	0.0920213	−	0.159386i
$221$	15.8255	−	27.4105i	1.06454	−	1.84383i
$222$	31.9185			2.14223
$223$	−24.6642			−1.65164			−0.825819	−	0.563935i	$-0.809287\pi$
$223$	−24.6642			−1.65164			−0.825819	+	0.563935i	$0.809287\pi$
$224$	−28.9127			−1.93181
$225$	−1.11776	−	1.93602i	−0.0745173	−	0.129068i
$226$	−20.7368	−	35.9173i	−1.37939	−	2.38918i
$227$	−0.771678	+	1.33658i	−0.0512180	+	0.0887123i	−0.890498	−	0.454988i	$-0.849644\pi$
$227$	−0.771678	+	1.33658i	−0.0512180	+	0.0887123i	0.839280	+	0.543700i	$0.182977\pi$
$228$	−8.89699			−0.589218
$229$	3.73574	−	6.47050i	0.246865	−	0.427583i	−0.715789	−	0.698316i	$-0.753933\pi$
$229$	3.73574	−	6.47050i	0.246865	−	0.427583i	0.962654	+	0.270734i	$0.0872663\pi$
$230$	5.05136	−	8.74922i	0.333077	−	0.576906i
$231$	−9.42856			−0.620353
$232$	−6.09911	−	10.5640i	−0.400426	−	0.693558i
$233$	1.11711	−	1.93490i	0.0731845	−	0.126759i	−0.827111	−	0.562039i	$-0.810017\pi$
$233$	1.11711	−	1.93490i	0.0731845	−	0.126759i	0.900295	+	0.435280i	$0.143350\pi$
$234$	4.65816			0.304513
$235$	0.0800027	+	0.138569i	0.00521880	+	0.00903923i
$236$	−9.76309	+	16.9102i	−0.635523	+	1.10076i
$237$	0.408502	+	0.707546i	0.0265350	+	0.0459600i
$238$	−33.9253	−	58.7603i	−2.19905	−	3.80887i
$239$	7.89628			0.510768			0.255384	−	0.966840i	$-0.417798\pi$
$239$	7.89628			0.510768			0.255384	+	0.966840i	$0.417798\pi$
$240$	0.661320	+	1.14544i	0.0426880	+	0.0739378i
$241$	8.23459	+	14.2627i	0.530436	+	0.918743i	0.999369	+	0.0355090i	$0.0113053\pi$
$241$	8.23459	+	14.2627i	0.530436	+	0.918743i	−0.468933	+	0.883234i	$0.655361\pi$
$242$	9.92715	−	17.1943i	0.638141	−	1.10529i
$243$	−2.51108	+	4.34932i	−0.161086	+	0.279009i
$244$	−12.1782	−	21.0933i	−0.779632	−	1.35036i
$245$	−3.32090	+	5.75196i	−0.212164	+	0.367479i
$246$	−44.5978			−2.84345
$247$	8.23822			0.524185
$248$	4.97276			0.315770
$249$	−27.2581			−1.72741
$250$	6.91195	−	11.9718i	0.437150	−	0.757166i
$251$	3.63343			0.229340			0.114670	−	0.993404i	$-0.463419\pi$
$251$	3.63343			0.229340			0.114670	+	0.993404i	$0.463419\pi$
$252$	2.96647	−	5.13808i	0.186870	−	0.323669i
$253$	−5.01809	+	8.69159i	−0.315485	+	0.546436i
$254$	10.4842	−	18.1592i	0.657838	−	1.13941i
$255$	−3.79566	+	6.57427i	−0.237693	+	0.411697i
$256$	3.41838	+	5.92081i	0.213649	+	0.370050i
$257$	8.20829			0.512019			0.256010	−	0.966674i	$-0.417592\pi$
$257$	8.20829			0.512019			0.256010	+	0.966674i	$0.417592\pi$
$258$	10.3340	+	17.8991i	0.643369	+	1.11435i
$259$	−18.8217	+	32.6002i	−1.16952	+	2.02568i
$260$	4.08966	+	7.08350i	0.253630	+	0.439300i
$261$	−2.89257			−0.179046
$262$	−12.6928	+	21.9846i	−0.784166	+	1.35821i
$263$	4.09061			0.252238			0.126119	−	0.992015i	$-0.459748\pi$
$263$	4.09061			0.252238			0.126119	+	0.992015i	$0.459748\pi$
$264$	2.34022	+	4.05338i	0.144031	+	0.249468i
$265$	1.76402	+	3.05537i	0.108363	+	0.187690i
$266$	8.83019	−	15.2943i	0.541413	−	0.937756i
$267$	−5.40414	+	9.36025i	−0.330728	+	0.572838i
$268$	−11.5783	−	20.0542i	−0.707257	−	1.22500i
$269$	−12.8810			−0.785370			−0.392685	−	0.919673i	$-0.628454\pi$
$269$	−12.8810			−0.785370			−0.392685	+	0.919673i	$0.628454\pi$
$270$	−7.97982			−0.485636
$271$	−1.50898	+	2.61362i	−0.0916638	+	0.158766i	−0.908211	−	0.418512i	$-0.862552\pi$
$271$	−1.50898	+	2.61362i	−0.0916638	+	0.158766i	0.816548	+	0.577278i	$0.195885\pi$
$272$	4.72770	−	8.18862i	0.286659	−	0.496508i
$273$	14.1255	−	24.4660i	0.854912	−	1.48075i
$274$	−17.3669			−1.04917
$275$	−3.28165	+	5.68398i	−0.197891	+	0.342757i
$276$	16.2381	+	28.1253i	0.977420	+	1.69294i
$277$	3.37266	−	5.84162i	0.202644	−	0.350989i	−0.746736	−	0.665121i	$-0.768380\pi$
$277$	3.37266	−	5.84162i	0.202644	−	0.350989i	0.949379	+	0.314132i	$0.101713\pi$
$278$	−14.4660	+	25.0559i	−0.867615	+	1.50275i
$279$	0.589597	−	1.02121i	0.0352982	−	0.0611384i
$280$	5.55652			0.332065
$281$	10.6820	+	18.5018i	0.637234	+	1.10372i	0.986037	+	0.166526i	$0.0532550\pi$
$281$	10.6820	+	18.5018i	0.637234	+	1.10372i	−0.348803	+	0.937196i	$0.613412\pi$
$282$	−0.865711			−0.0515523
$283$	−13.8903			−0.825694			−0.412847	−	0.910800i	$-0.635466\pi$
$283$	−13.8903			−0.825694			−0.412847	+	0.910800i	$0.635466\pi$
$284$	−0.276098			−0.0163834
$285$	−1.97589			−0.117042
$286$	−6.83798	−	11.8437i	−0.404339	−	0.700335i
$287$	26.2984	−	45.5502i	1.55235	−	2.68874i
$288$	3.40344			0.200550
$289$	37.2695			2.19232
$290$	−4.27433	−	7.40335i	−0.250997	−	0.434740i
$291$	−13.8989			−0.814768
$292$	13.0169	−	22.5459i	0.761757	−	1.31940i
$293$	2.55441	−	4.42437i	0.149230	−	0.258474i	−0.781713	−	0.623638i	$-0.785654\pi$
$293$	2.55441	−	4.42437i	0.149230	−	0.258474i	0.930943	+	0.365164i	$0.118987\pi$
$294$	−17.9677	−	31.1211i	−1.04790	−	1.81502i
$295$	−2.16824	+	3.75550i	−0.126240	+	0.218654i
$296$	18.6866			1.08614
$297$	7.92726			0.459987
$298$	24.1063	+	41.7534i	1.39644	+	2.41871i
$299$	−15.0358	−	26.0427i	−0.869542	−	1.50609i
$300$	10.6191	+	18.3929i	0.613097	+	1.06191i
$301$	−24.3751			−1.40496
$302$	0.300792			0.0173087
$303$	4.80473	+	8.32204i	0.276025	+	0.478089i
$304$	2.46108			0.141153
$305$	−2.70461	−	4.68452i	−0.154866	−	0.268235i
$306$	3.99349	+	6.91694i	0.228293	+	0.395415i
$307$	12.5844	−	21.7968i	0.718230	−	1.24401i	−0.243470	−	0.969908i	$-0.578286\pi$
$307$	12.5844	−	21.7968i	0.718230	−	1.24401i	0.961700	−	0.274103i	$-0.0883809\pi$
$308$	−17.4186			−0.992519
$309$	5.34242	+	9.25334i	0.303920	+	0.526404i
$310$	3.48497			0.197933
$311$	−12.0246			−0.681852			−0.340926	−	0.940090i	$-0.610741\pi$
$311$	−12.0246			−0.681852			−0.340926	+	0.940090i	$0.610741\pi$
$312$	−14.0241			−0.793957
$313$	−3.73568			−0.211153			−0.105577	−	0.994411i	$-0.533669\pi$
$313$	−3.73568			−0.211153			−0.105577	+	0.994411i	$0.533669\pi$
$314$	12.3439			0.696605
$315$	0.658811	−	1.14109i	0.0371198	−	0.0642934i
$316$	0.754680	+	1.30714i	0.0424541	+	0.0735326i
$317$	13.0153	+	22.5431i	0.731011	+	1.26615i	0.956452	+	0.291891i	$0.0942845\pi$
$317$	13.0153	+	22.5431i	0.731011	+	1.26615i	−0.225441	+	0.974257i	$0.572382\pi$
$318$	−19.0885			−1.07043
$319$	4.24618	+	7.35459i	0.237740	+	0.411778i
$320$	4.19465	+	7.26535i	0.234488	+	0.406146i
$321$	0.952838			0.0531822
$322$	−64.4648			−3.59248
$323$	7.06272	+	12.2330i	0.392980	+	0.680661i
$324$	10.6811	−	18.5001i	0.593392	−	1.02778i
$325$	−9.83285	−	17.0310i	−0.545429	−	0.944710i
$326$	15.1493	−	26.2394i	0.839043	−	1.45327i
$327$	−7.14421	+	12.3741i	−0.395076	+	0.684292i
$328$	−26.1097			−1.44166
$329$	0.510492	−	0.884198i	0.0281443	−	0.0487474i
$330$	1.64005	+	2.84066i	0.0902820	+	0.156373i
$331$	−7.30508	−	12.6528i	−0.401523	−	0.695459i	0.592387	−	0.805654i	$-0.298186\pi$
$331$	−7.30508	−	12.6528i	−0.401523	−	0.695459i	−0.993910	+	0.110195i	$0.964852\pi$
$332$	−50.3575			−2.76373
$333$	2.21559	−	3.83751i	0.121413	−	0.210294i
$334$	−19.2589	+	33.3574i	−1.05380	+	1.82524i
$335$	−2.57137	−	4.45374i	−0.140489	−	0.243334i
$336$	4.21984	−	7.30898i	0.230211	−	0.398737i
$337$	−3.84997	+	6.66835i	−0.209721	+	0.363248i	−0.951627	−	0.307257i	$-0.900589\pi$
$337$	−3.84997	+	6.66835i	−0.209721	+	0.363248i	0.741905	+	0.670505i	$0.233922\pi$
$338$	12.1192			0.659198
$339$	29.6088			1.60813
$340$	−7.01223	+	12.1455i	−0.380291	+	0.658684i
$341$	−3.46201			−0.187479
$342$	−1.03944	+	1.80036i	−0.0562065	+	0.0973525i
$343$	13.3375			0.720159
$344$	6.05003	+	10.4790i	0.326196	+	0.564988i
$345$	3.60625	+	6.24621i	0.194154	+	0.336285i
$346$	8.57405	+	14.8507i	0.460944	+	0.798378i
$347$	−13.6391	+	23.6237i	−0.732186	+	1.26818i	0.223760	+	0.974644i	$0.428167\pi$
$347$	−13.6391	+	23.6237i	−0.732186	+	1.26818i	−0.955947	+	0.293540i	$0.905167\pi$
$348$	27.4805			1.47311
$349$	−18.4641	+	2.84219i	−0.988359	+	0.152139i
$349$	−18.4641	+	2.84219i	−0.988359	+	0.152139i
$350$	−42.1576			−2.25342
$351$	−11.8763	+	20.5703i	−0.633909	+	1.09796i
$352$	−4.99611	−	8.65351i	−0.266293	−	0.461234i
$353$	11.1099	+	19.2429i	0.591321	+	1.02420i	0.994055	+	0.108880i	$0.0347265\pi$
$353$	11.1099	+	19.2429i	0.591321	+	1.02420i	−0.402734	+	0.915317i	$0.631940\pi$
$354$	−11.7313	−	20.3192i	−0.623511	−	1.07995i
$355$	−0.0613175			−0.00325439
$356$	−9.98380	+	17.2924i	−0.529140	+	0.916498i
$357$	48.4397			2.56370
$358$	1.49901	−	2.59636i	0.0792251	−	0.137222i
$359$	−20.1890			−1.06554			−0.532768	−	0.846261i	$-0.678848\pi$
$359$	−20.1890			−1.06554			−0.532768	+	0.846261i	$0.678848\pi$
$360$	−0.654082			−0.0344731
$361$	7.66169	−	13.2704i	0.403247	−	0.698444i
$362$	−9.76120	+	16.9069i	−0.513037	+	0.888606i
$363$	7.08716	+	12.2753i	0.371979	+	0.644287i
$364$	26.0959	−	45.1994i	1.36779	−	2.36909i
$365$	2.89087	−	5.00713i	0.151315	−	0.262085i
$366$	29.2666			1.52979
$367$	−8.37570	−	14.5071i	−0.437208	−	0.757266i	0.560265	−	0.828313i	$-0.310699\pi$
$367$	−8.37570	−	14.5071i	−0.437208	−	0.757266i	−0.997473	+	0.0710470i	$0.977366\pi$
$368$	−4.49179	−	7.78001i	−0.234151	−	0.405561i
$369$	−3.09570	+	5.36192i	−0.161156	+	0.279130i
$370$	13.0958			0.680819
$371$	11.2561	−	19.4961i	0.584387	−	1.01219i
$372$	−5.60139	+	9.70190i	−0.290419	+	0.503020i
$373$	1.60754	+	2.78434i	0.0832352	+	0.144168i	0.904638	−	0.426181i	$-0.140141\pi$
$373$	1.60754	+	2.78434i	0.0832352	+	0.144168i	−0.821403	+	0.570349i	$0.806808\pi$
$374$	11.7246	−	20.3075i	0.606263	−	1.05008i
$375$	4.93456	+	8.54690i	0.254819	+	0.441360i
$376$	−0.506828			−0.0261376
$377$	−25.4458			−1.31052
$378$	25.4594	+	44.0969i	1.30949	+	2.26810i
$379$	13.6918	+	23.7149i	0.703301	+	1.21815i	0.967301	+	0.253630i	$0.0816246\pi$
$379$	13.6918	+	23.7149i	0.703301	+	1.21815i	−0.264001	+	0.964523i	$0.585042\pi$
$380$	−3.65033			−0.187258
$381$	7.48486	+	12.9642i	0.383461	+	0.664174i
$382$	−8.72685	−	15.1153i	−0.446504	−	0.773368i
$383$	−14.3553	+	24.8642i	−0.733524	+	1.27050i	0.221844	+	0.975082i	$0.428792\pi$
$383$	−14.3553	+	24.8642i	−0.733524	+	1.27050i	−0.955368	+	0.295419i	$0.904541\pi$
$384$	−23.3030			−1.18918
$385$	−3.86843			−0.197153
$386$	−56.3653			−2.86892
$387$	2.86930			0.145855
$388$	−25.6773			−1.30357
$389$	12.0085	+	20.7993i	0.608853	+	1.05457i	0.991430	+	0.130641i	$0.0417036\pi$
$389$	12.0085	+	20.7993i	0.608853	+	1.05457i	−0.382576	+	0.923924i	$0.624963\pi$
$390$	−9.82824			−0.497672
$391$	25.7807	−	44.6535i	1.30379	−	2.25822i
$392$	−10.5192	−	18.2197i	−0.531298	−	0.920235i
$393$	−9.06163	−	15.6952i	−0.457099	−	0.791718i
$394$	9.48462			0.477828
$395$	0.167603	+	0.290298i	0.00843305	+	0.0146065i
$396$	2.05042			0.103038
$397$	14.8554			0.745570			0.372785	−	0.927918i	$-0.378403\pi$
$397$	14.8554			0.745570			0.372785	+	0.927918i	$0.378403\pi$
$398$	6.43274	+	11.1418i	0.322444	+	0.558490i
$399$	6.30402	+	10.9189i	0.315596	+	0.546628i
$400$	−2.93747	−	5.08784i	−0.146873	−	0.254392i
$401$	−25.9359			−1.29518			−0.647589	−	0.761990i	$-0.724223\pi$
$401$	−25.9359			−1.29518			−0.647589	+	0.761990i	$0.724223\pi$
$402$	27.8248			1.38778
$403$	5.18664	−	8.98353i	0.258365	−	0.447501i
$404$	8.87643	+	15.3744i	0.441619	+	0.764906i
$405$	2.37211	−	4.10861i	0.117871	−	0.204158i
$406$	−27.2742	+	47.2403i	−1.35360	+	2.34450i
$407$	−13.0096			−0.644860
$408$	−12.0230	−	20.8244i	−0.595227	−	1.03096i
$409$	11.2551			0.556531			0.278265	−	0.960504i	$-0.410241\pi$
$409$	11.2551			0.556531			0.278265	+	0.960504i	$0.410241\pi$
$410$	−18.2980			−0.903672
$411$	6.19925	−	10.7374i	0.305786	−	0.529637i
$412$	9.86977	+	17.0949i	0.486249	+	0.842208i
$413$	27.6708			1.36159
$414$	7.58844			0.372951
$415$	−11.1837			−0.548985
$416$	29.9398			1.46792
$417$	−10.3275	−	17.8878i	−0.505742	−	0.875971i
$418$	6.10342			0.298528
$419$	15.0730	−	26.1071i	0.736362	−	1.27542i	−0.217761	−	0.976002i	$-0.569875\pi$
$419$	15.0730	−	26.1071i	0.736362	−	1.27542i	0.954123	−	0.299414i	$-0.0967913\pi$
$420$	−6.25895	+	10.8408i	−0.305406	+	0.528978i
$421$	5.02999	−	8.71220i	0.245147	−	0.424607i	−0.717026	−	0.697046i	$-0.754497\pi$
$421$	5.02999	−	8.71220i	0.245147	−	0.424607i	0.962173	+	0.272440i	$0.0878305\pi$
$422$	−5.07559	−	8.79119i	−0.247076	−	0.427948i
$423$	−0.0600922	+	0.104083i	−0.00292178	+	0.00506068i
$424$	−11.1753			−0.542721
$425$	16.8596	−	29.2017i	0.817813	−	1.41649i
$426$	0.165879	−	0.287311i	0.00803688	−	0.0139203i
$427$	−17.2579	+	29.8916i	−0.835171	+	1.44656i
$428$	1.76031			0.0850876
$429$	9.76351			0.471387
$430$	4.23994	+	7.34379i	0.204468	+	0.354149i
$431$	−3.52908	+	6.11254i	−0.169990	+	0.294431i	−0.938416	−	0.345508i	$-0.887707\pi$
$431$	−3.52908	+	6.11254i	−0.169990	+	0.294431i	0.768426	+	0.639938i	$0.221040\pi$
$432$	−3.54792	+	6.14518i	−0.170699	+	0.295660i
$433$	14.1341	+	24.4809i	0.679240	+	1.17648i	0.975210	+	0.221281i	$0.0710238\pi$
$433$	14.1341	+	24.4809i	0.679240	+	1.17648i	−0.295970	+	0.955197i	$0.595643\pi$
$434$	−11.1187	−	19.2581i	−0.533713	−	0.924419i
$435$	6.10303			0.292618
$436$	−13.1985	+	22.8604i	−0.632092	+	1.09482i
$437$	13.4206			0.641993
$438$	15.6411	+	27.0911i	0.747358	+	1.29446i
$439$	−10.1894	+	17.6486i	−0.486315	+	0.842323i	−0.999876	−	0.0157302i	$-0.994993\pi$
$439$	−10.1894	+	17.6486i	−0.486315	+	0.842323i	0.513561	+	0.858053i	$0.328326\pi$
$440$	0.960165	+	1.66305i	0.0457741	+	0.0792830i
$441$	−4.98884			−0.237564
$442$	35.1305	+	60.8478i	1.67099	+	2.89423i
$443$	8.75507	−	15.1642i	0.415966	−	0.720474i	−0.579563	−	0.814927i	$-0.696777\pi$
$443$	8.75507	−	15.1642i	0.415966	−	0.720474i	0.995529	+	0.0944529i	$0.0301102\pi$
$444$	−21.0489	+	36.4578i	−0.998937	+	1.73021i
$445$	−2.21726	+	3.84040i	−0.105108	+	0.182052i
$446$	27.3757	−	47.4160i	1.29628	−	2.24521i
$447$	−34.4198			−1.62800
$448$	26.7658	−	46.3597i	1.26457	−	2.19029i
$449$	−26.0489			−1.22932			−0.614662	−	0.788791i	$-0.710708\pi$
$449$	−26.0489			−1.22932			−0.614662	+	0.788791i	$0.710708\pi$
$450$	4.96256			0.233937
$451$	18.1775			0.855943
$452$	54.7003			2.57288
$453$	−0.107370	+	0.185971i	−0.00504470	+	0.00873768i
$454$	−1.71302	−	2.96704i	−0.0803962	−	0.139250i
$455$	5.79551	−	10.0381i	0.271698	−	0.470594i
$456$	3.12938	−	5.42025i	0.146547	−	0.253827i
$457$	3.82692	+	6.62843i	0.179016	+	0.310065i	0.941544	−	0.336891i	$-0.109375\pi$
$457$	3.82692	+	6.62843i	0.179016	+	0.310065i	−0.762528	+	0.646955i	$0.776042\pi$
$458$	8.29286	+	14.3637i	0.387500	+	0.671170i
$459$	−40.7267			−1.90096
$460$	6.66232	+	11.5395i	0.310632	+	0.538030i
$461$	9.22097	+	15.9712i	0.429464	+	0.743853i	0.996826	−	0.0796158i	$-0.0253693\pi$
$461$	9.22097	+	15.9712i	0.429464	+	0.743853i	−0.567362	+	0.823468i	$0.692036\pi$
$462$	10.4651	−	18.1260i	0.486880	−	0.843300i
$463$	−16.2741	−	28.1875i	−0.756320	−	1.30999i	−0.944715	−	0.327892i	$-0.893662\pi$
$463$	−16.2741	−	28.1875i	−0.756320	−	1.30999i	0.188395	−	0.982093i	$-0.439672\pi$
$464$	−7.60166			−0.352898
$465$	−1.24399	+	2.15465i	−0.0576886	+	0.0999196i
$466$	2.47984	+	4.29522i	0.114877	+	0.198972i
$467$	6.73953			0.311868			0.155934	−	0.987767i	$-0.450161\pi$
$467$	6.73953			0.311868			0.155934	+	0.987767i	$0.450161\pi$
$468$	−3.07186	+	5.32061i	−0.141997	+	0.245945i
$469$	−16.4077	+	28.4190i	−0.757639	+	1.31227i
$470$	−0.355191			−0.0163837
$471$	−4.40625	+	7.63185i	−0.203029	+	0.351657i
$472$	−6.86805	−	11.8958i	−0.316128	−	0.547549i
$473$	−4.21201	−	7.29542i	−0.193669	−	0.335444i
$474$	−1.81364			−0.0833033
$475$	8.77656			0.402696
$476$	89.4891			4.10173
$477$	−1.32500	+	2.29497i	−0.0606678	+	0.105080i
$478$	−8.76435	+	15.1803i	−0.400872	+	0.694331i
$479$	−21.4941	+	37.2288i	−0.982089	+	1.70103i	−0.327872	+	0.944722i	$0.606332\pi$
$479$	−21.4941	+	37.2288i	−0.982089	+	1.70103i	−0.654217	+	0.756307i	$0.727002\pi$
$480$	−7.18091			−0.327762
$481$	19.4904	−	33.7583i	0.888684	−	1.53925i
$482$	−36.5594			−1.66524
$483$	23.0113	−	39.8567i	1.04705	−	1.81354i
$484$	13.0931	+	22.6778i	0.595139	+	1.03081i
$485$	−5.70256			−0.258940
$486$	−5.57427	−	9.65492i	−0.252854	−	0.437956i
$487$	8.01612	−	13.8843i	0.363245	−	0.629159i	−0.625248	−	0.780426i	$-0.715002\pi$
$487$	8.01612	−	13.8843i	0.363245	−	0.629159i	0.988493	+	0.151267i	$0.0483355\pi$
$488$	17.1341			0.775623
$489$	10.8154	+	18.7328i	0.489087	+	0.847124i
$490$	−7.37196	−	12.7686i	−0.333031	−	0.576827i
$491$	0.640356	+	1.10913i	0.0288989	+	0.0500543i	0.880113	−	0.474764i	$-0.157467\pi$
$491$	0.640356	+	1.10913i	0.0288989	+	0.0500543i	−0.851214	+	0.524818i	$0.824133\pi$
$492$	29.4104	−	50.9402i	1.32592	−	2.29656i
$493$	−21.8149	−	37.7846i	−0.982495	−	1.70173i
$494$	−9.14388	+	15.8377i	−0.411403	+	0.712570i
$495$	0.455370			0.0204673
$496$	1.54946	−	2.68374i	0.0695727	−	0.120503i
$497$	0.195631	+	0.338843i	0.00877527	+	0.0151992i
$498$	30.2547	−	52.4027i	1.35575	−	2.34822i
$499$	−11.2335	+	19.4570i	−0.502882	+	0.871017i	0.497113	+	0.867686i	$0.334394\pi$
$499$	−11.2335	+	19.4570i	−0.502882	+	0.871017i	−0.999994	+	0.00333076i	$0.998940\pi$
$500$	9.11627	+	15.7898i	0.407692	+	0.706143i
$501$	−13.7493	−	23.8144i	−0.614272	−	1.06395i
$502$	−4.03287	+	6.98513i	−0.179996	+	0.311762i
$503$	−18.5987	−	32.2140i	−0.829277	−	1.43635i	−0.898606	−	0.438756i	$-0.855419\pi$
$503$	−18.5987	−	32.2140i	−0.829277	−	1.43635i	0.0693297	−	0.997594i	$-0.477914\pi$
$504$	2.08683	+	3.61449i	0.0929547	+	0.161002i
$505$	1.97133	+	3.41444i	0.0877228	+	0.151940i
$506$	−11.1395	−	19.2942i	−0.495212	−	0.857731i
$507$	−4.32605	+	7.49295i	−0.192127	+	0.332773i
$508$	13.8278	+	23.9504i	0.613509	+	1.06263i
$509$	17.7749	−	30.7870i	0.787858	−	1.36461i	−0.139419	−	0.990234i	$-0.544523\pi$
$509$	17.7749	−	30.7870i	0.787858	−	1.36461i	0.927277	−	0.374377i	$-0.122143\pi$
$510$	−8.42586	−	14.5940i	−0.373103	−	0.646234i
$511$	−36.8928			−1.63204
$512$	14.2314			0.628944
$513$	−5.30024	−	9.18029i	−0.234011	−	0.405320i
$514$	−9.11067	+	15.7801i	−0.401854	+	0.696032i
$515$	2.19193	+	3.79654i	0.0965881	+	0.167296i
$516$	−27.2594			−1.20003
$517$	0.352852			0.0155184
$518$	−41.7817	−	72.3681i	−1.83578	−	3.17967i
$519$	−12.2423			−0.537378
$520$	−5.75391			−0.252326
$521$	5.08211	−	8.80247i	0.222651	−	0.385643i	−0.732961	−	0.680271i	$-0.761862\pi$
$521$	5.08211	−	8.80247i	0.222651	−	0.385643i	0.955612	+	0.294628i	$0.0951956\pi$
$522$	3.21057	−	5.56086i	0.140523	−	0.243392i
$523$	−2.98021	−	5.16188i	−0.130316	−	0.225713i	0.793483	−	0.608593i	$-0.208266\pi$
$523$	−2.98021	−	5.16188i	−0.130316	−	0.225713i	−0.923798	+	0.382880i	$0.874932\pi$
$524$	−16.7408	−	28.9958i	−0.731324	−	1.26669i
$525$	15.0485	−	26.0648i	0.656772	−	1.13756i
$526$	−4.54031	+	7.86405i	−0.197967	+	0.342889i
$527$	17.7863			0.774782
$528$	2.91675			0.126935
$529$	−12.9942	−	22.5067i	−0.564967	−	0.978551i
$530$	−7.83179			−0.340191
$531$	−3.25725			−0.141353
$532$	11.6463	+	20.1719i	0.504929	+	0.874563i
$533$	−27.2327	+	47.1684i	−1.17958	+	2.04309i
$534$	−11.9965	−	20.7785i	−0.519139	−	0.899175i
$535$	0.390938			0.0169017
$536$	16.2900			0.703620
$537$	1.07017	+	1.85358i	0.0461811	+	0.0799881i
$538$	14.2971	−	24.7633i	0.616392	−	1.06762i
$539$	7.32340	+	12.6845i	0.315441	+	0.546360i
$540$	5.26235	−	9.11466i	0.226456	−	0.392233i
$541$	−13.2324	−	22.9193i	−0.568907	−	0.985376i	−0.996674	−	0.0814868i	$-0.974033\pi$
$541$	−13.2324	−	22.9193i	−0.568907	−	0.985376i	0.427768	−	0.903889i	$-0.359300\pi$
$542$	−3.34973	−	5.80190i	−0.143883	−	0.249213i
$543$	−6.96868	−	12.0701i	−0.299055	−	0.517978i
$544$	25.6677	+	44.4578i	1.10050	+	1.90611i
$545$	−2.93119	+	5.07697i	−0.125558	+	0.217473i
$546$	31.3567	+	54.3113i	1.34194	+	2.32431i
$547$	4.16395	+	7.21218i	0.178038	+	0.308370i	0.941208	−	0.337827i	$-0.109692\pi$
$547$	4.16395	+	7.21218i	0.178038	+	0.308370i	−0.763171	+	0.646197i	$0.776358\pi$
$548$	11.4527	−	19.8367i	0.489235	−	0.847380i
$549$	2.03151	−	3.51868i	0.0867027	−	0.150173i
$550$	−7.28483	−	12.6177i	−0.310626	−	0.538020i
$551$	5.67806	−	9.83469i	0.241894	−	0.418972i
$552$	−22.8461			−0.972394
$553$	1.06947	−	1.85237i	0.0454784	−	0.0787708i
$554$	7.48687	+	12.9676i	0.318087	+	0.550942i
$555$	−4.67466	+	8.09675i	−0.198428	+	0.343688i
$556$	−19.0795	−	33.0466i	−0.809150	−	1.40149i
$557$	5.62036	+	9.73474i	0.238142	+	0.412474i	0.960181	−	0.279378i	$-0.0901283\pi$
$557$	5.62036	+	9.73474i	0.238142	+	0.412474i	−0.722039	+	0.691852i	$0.756795\pi$
$558$	1.30883	+	2.26696i	0.0554071	+	0.0959679i
$559$	25.2410			1.06758
$560$	1.73135	−	2.99879i	0.0731629	−	0.126722i
$561$	8.37037	+	14.4979i	0.353397	+	0.612102i
$562$	−47.4253			−2.00051
$563$	7.16771	+	12.4148i	0.302083	+	0.523223i	0.976608	−	0.215030i	$-0.0689848\pi$
$563$	7.16771	+	12.4148i	0.302083	+	0.523223i	−0.674525	+	0.738252i	$0.735651\pi$
$564$	0.570899	−	0.988826i	0.0240392	−	0.0416371i
$565$	12.1481			0.511076
$566$	15.4174	−	26.7036i	0.648040	−	1.12244i
$567$	−30.2725			−1.27133
$568$	0.0971136	−	0.168206i	0.00407480	−	0.00705775i
$569$	−5.32016	+	9.21479i	−0.223033	+	0.386304i	−0.955727	−	0.294253i	$-0.904929\pi$
$569$	−5.32016	+	9.21479i	−0.223033	+	0.386304i	0.732695	+	0.680558i	$0.238262\pi$
$570$	2.19311	−	3.79858i	0.0918593	−	0.159105i
$571$	−12.6404			−0.528985			−0.264492	−	0.964388i	$-0.585204\pi$
$571$	−12.6404			−0.528985			−0.264492	+	0.964388i	$0.585204\pi$
$572$	18.0374			0.754183
$573$	12.4605			0.520544
$574$	58.3791	+	101.115i	2.43669	+	4.22048i
$575$	−16.0183	−	27.7446i	−0.668011	−	1.15703i
$576$	−3.15072	+	5.45721i	−0.131280	+	0.227384i
$577$	−26.0741			−1.08548			−0.542739	−	0.839902i	$-0.682613\pi$
$577$	−26.0741			−1.08548			−0.542739	+	0.839902i	$0.682613\pi$
$578$	−41.3666	+	71.6491i	−1.72063	+	2.98021i
$579$	20.1201	−	34.8490i	0.836162	−	1.44827i
$580$	11.2749			0.468167
$581$	35.6812	+	61.8016i	1.48030	+	2.56396i
$582$	15.4269	−	26.7201i	0.639465	−	1.10759i
$583$	7.78020			0.322223
$584$	9.15701	+	15.8604i	0.378920	+	0.656308i
$585$	−0.682215	+	1.18163i	−0.0282061	+	0.0488544i
$586$	5.67046	+	9.82152i	0.234244	+	0.405723i
$587$	−0.947131	−	1.64048i	−0.0390923	−	0.0677098i	0.845817	−	0.533473i	$-0.179113\pi$
$587$	−0.947131	−	1.64048i	−0.0390923	−	0.0677098i	−0.884910	+	0.465763i	$0.845780\pi$
$588$	47.3959			1.95457
$589$	2.31473	+	4.00924i	0.0953770	+	0.165198i
$590$	−4.81321	−	8.33673i	−0.198157	−	0.343218i
$591$	−3.38561	+	5.86406i	−0.139266	+	0.241215i
$592$	5.82255	−	10.0850i	0.239305	−	0.414489i
$593$	−12.2451	−	21.2091i	−0.502845	−	0.870953i	−0.999995	−	0.00328826i	$-0.998953\pi$
$593$	−12.2451	−	21.2091i	−0.502845	−	0.870953i	0.497150	−	0.867665i	$-0.334380\pi$
$594$	−8.79874	+	15.2399i	−0.361017	+	0.625299i
$595$	19.8742			0.814764
$596$	−63.5884			−2.60468
$597$	−9.18489			−0.375912
$598$	66.7549			2.72981
$599$	−1.15944	+	2.00822i	−0.0473736	+	0.0820535i	−0.888740	−	0.458412i	$-0.848418\pi$
$599$	−1.15944	+	2.00822i	−0.0473736	+	0.0820535i	0.841366	+	0.540465i	$0.181752\pi$
$600$	−14.9405			−0.609944
$601$	−19.4339	+	33.6606i	−0.792727	+	1.37304i	0.131546	+	0.991310i	$0.458006\pi$
$601$	−19.4339	+	33.6606i	−0.792727	+	1.37304i	−0.924273	+	0.381733i	$0.875327\pi$
$602$	27.0548	−	46.8602i	1.10267	−	1.90988i
$603$	1.93143	−	3.34533i	0.0786538	−	0.136232i
$604$	−0.198360	+	0.343569i	−0.00807114	+	0.0139796i
$605$	2.90778	+	5.03642i	0.118218	+	0.204760i
$606$	−21.3317			−0.866543
$607$	−10.8166	−	18.7349i	−0.439032	−	0.760425i	0.558583	−	0.829448i	$-0.311345\pi$
$607$	−10.8166	−	18.7349i	−0.439032	−	0.760425i	−0.997615	+	0.0690233i	$0.978012\pi$
$608$	−6.68089	+	11.5716i	−0.270946	+	0.469292i
$609$	−19.4715	−	33.7256i	−0.789025	−	1.36663i
$610$	12.0078			0.486180
$611$	−0.528627	+	0.915609i	−0.0213860	+	0.0370416i
$612$	−10.5342			−0.425818
$613$	23.3906	+	40.5137i	0.944737	+	1.63633i	0.756277	+	0.654251i	$0.227016\pi$
$613$	23.3906	+	40.5137i	0.944737	+	1.63633i	0.188460	+	0.982081i	$0.439650\pi$
$614$	27.9357	+	48.3861i	1.12739	+	1.95271i
$615$	6.53161	−	11.3131i	0.263380	−	0.456188i
$616$	6.12675	−	10.6118i	0.246854	−	0.427563i
$617$	24.0480	+	41.6524i	0.968138	+	1.67686i	0.700937	+	0.713224i	$0.252766\pi$
$617$	24.0480	+	41.6524i	0.968138	+	1.67686i	0.267201	+	0.963641i	$0.413901\pi$
$618$	−23.7189			−0.954116
$619$	20.0572			0.806169			0.403084	−	0.915163i	$-0.367938\pi$
$619$	20.0572			0.806169			0.403084	+	0.915163i	$0.367938\pi$
$620$	−2.29819	+	3.98058i	−0.0922974	+	0.159864i
$621$	−19.3472	+	33.5104i	−0.776377	+	1.34472i
$622$	13.3465	−	23.1168i	0.535146	−	0.926901i
$623$	28.2963			1.13367
$624$	−4.36975	+	7.56863i	−0.174930	+	0.302988i
$625$	−9.41843	−	16.3132i	−0.376737	−	0.652528i
$626$	4.14636	−	7.18170i	0.165722	−	0.287039i
$627$	−2.17867	+	3.77356i	−0.0870076	+	0.150702i
$628$	−8.14025	+	14.0993i	−0.324832	+	0.562625i
$629$	66.8372			2.66497
$630$	1.46247	+	2.53308i	0.0582663	+	0.100920i
$631$	−9.63454			−0.383545			−0.191772	−	0.981439i	$-0.561424\pi$
$631$	−9.63454			−0.383545			−0.191772	+	0.981439i	$0.561424\pi$
$632$	−1.06179			−0.0422358
$633$	7.24710			0.288047
$634$	−57.7844			−2.29491
$635$	3.07095	+	5.31904i	0.121867	+	0.211080i
$636$	12.5880	−	21.8031i	0.499148	−	0.864550i
$637$	−43.8864			−1.73884
$638$	−18.8519			−0.746354
$639$	−0.0230286	−	0.0398868i	−0.000910998	−	0.00157790i
$640$	−9.56095			−0.377930
$641$	−2.71766	+	4.70712i	−0.107341	+	0.185920i	−0.914692	−	0.404151i	$-0.867567\pi$
$641$	−2.71766	+	4.70712i	−0.107341	+	0.185920i	0.807351	+	0.590071i	$0.200900\pi$
$642$	−1.05759	+	1.83180i	−0.0417397	+	0.0722952i
$643$	16.3039	+	28.2391i	0.642962	+	1.11364i	0.984768	+	0.173872i	$0.0556280\pi$
$643$	16.3039	+	28.2391i	0.642962	+	1.11364i	−0.341806	+	0.939770i	$0.611039\pi$
$644$	42.5118	−	73.6326i	1.67520	−	2.90153i
$645$	−6.05393			−0.238373
$646$	−31.3566			−1.23371
$647$	1.44966	+	2.51089i	0.0569921	+	0.0987133i	0.893114	−	0.449831i	$-0.148516\pi$
$647$	1.44966	+	2.51089i	0.0569921	+	0.0987133i	−0.836122	+	0.548544i	$0.815182\pi$
$648$	7.51380	+	13.0143i	0.295170	+	0.511250i
$649$	4.78151	+	8.28182i	0.187691	+	0.325090i
$650$	43.6553			1.71230
$651$	15.8756			0.622214
$652$	19.9807	+	34.6075i	0.782503	+	1.35534i
$653$	−9.14279			−0.357785			−0.178892	−	0.983869i	$-0.557251\pi$
$653$	−9.14279			−0.357785			−0.178892	+	0.983869i	$0.557251\pi$
$654$	−15.8592	−	27.4690i	−0.620145	−	1.07412i
$655$	−3.71788	−	6.43956i	−0.145270	−	0.251614i
$656$	−8.13549	+	14.0911i	−0.317637	+	0.550164i
$657$	4.34282			0.169430
$658$	1.13322	+	1.96280i	0.0441777	+	0.0765180i
$659$	−17.8380			−0.694870			−0.347435	−	0.937704i	$-0.612947\pi$
$659$	−17.8380			−0.694870			−0.347435	+	0.937704i	$0.612947\pi$
$660$	−4.32618			−0.168396
$661$	−26.1554			−1.01733			−0.508663	−	0.860966i	$-0.669860\pi$
$661$	−26.1554			−1.01733			−0.508663	+	0.860966i	$0.669860\pi$
$662$	32.4326			1.26053
$663$	−50.1605			−1.94807
$664$	17.7125	−	30.6790i	0.687379	−	1.19058i
$665$	2.58647	+	4.47989i	0.100299	+	0.173723i
$666$	4.91831	+	8.51877i	0.190581	+	0.330096i
$667$	−41.4527			−1.60506
$668$	−25.4009	−	43.9956i	−0.982789	−	1.70224i
$669$	19.5439	+	33.8511i	0.755613	+	1.30876i
$670$	11.4162			0.441047
$671$	−11.9287			−0.460502
$672$	22.9104	+	39.6820i	0.883789	+	1.53077i
$673$	−1.03478	+	1.79229i	−0.0398878	+	0.0690877i	−0.885280	−	0.465058i	$-0.846033\pi$
$673$	−1.03478	+	1.79229i	−0.0398878	+	0.0690877i	0.845392	+	0.534146i	$0.179367\pi$
$674$	−8.54643	−	14.8029i	−0.329196	−	0.570185i
$675$	−12.6524	+	21.9146i	−0.486990	+	0.843492i
$676$	−7.99210	+	13.8427i	−0.307388	+	0.532412i
$677$	3.76288			0.144619			0.0723096	−	0.997382i	$-0.476963\pi$
$677$	3.76288			0.144619			0.0723096	+	0.997382i	$0.476963\pi$
$678$	−32.8638	+	56.9218i	−1.26213	+	2.18607i
$679$	18.1938	+	31.5126i	0.698215	+	1.20934i
$680$	−4.93289	−	8.54402i	−0.189168	−	0.327648i
$681$	2.44591			0.0937276
$682$	3.84261	−	6.65559i	0.147141	−	0.254856i
$683$	1.55280	−	2.68952i	0.0594161	−	0.102912i	−0.834787	−	0.550573i	$-0.814409\pi$
$683$	1.55280	−	2.68952i	0.0594161	−	0.102912i	0.894203	+	0.447661i	$0.147743\pi$
$684$	−1.37093	−	2.37453i	−0.0524189	−	0.0907922i
$685$	2.54348	−	4.40543i	0.0971813	−	0.168323i
$686$	−14.8038	+	25.6409i	−0.565211	+	0.978974i
$687$	−11.8408			−0.451756
$688$	7.54050			0.287479
$689$	−11.6560	+	20.1887i	−0.444057	+	0.769129i
$690$	−16.0108			−0.609521
$691$	−21.0092	+	36.3889i	−0.799226	+	1.38430i	0.120894	+	0.992665i	$0.461424\pi$
$691$	−21.0092	+	36.3889i	−0.799226	+	1.38430i	−0.920121	+	0.391635i	$0.871910\pi$
$692$	−22.6169			−0.859765
$693$	−1.45284	−	2.51640i	−0.0551889	−	0.0955900i
$694$	−30.2771	−	52.4414i	−1.14930	−	1.99065i
$695$	−4.23727	−	7.33917i	−0.160729	−	0.278391i
$696$	−9.66587	+	16.7418i	−0.366384	+	0.634596i
$697$	−93.3876			−3.53731
$698$	15.0299	−	38.6511i	0.568890	−	1.46297i
$699$	−3.54081			−0.133926
$700$	27.8012	−	48.1530i	1.05079	−	1.82001i
$701$	−20.5602	−	35.6113i	−0.776548	−	1.34502i	−0.933920	−	0.357481i	$-0.883636\pi$
$701$	−20.5602	−	35.6113i	−0.776548	−	1.34502i	0.157372	−	0.987539i	$-0.449698\pi$
$702$	−26.3638	−	45.6634i	−0.995038	−	1.72346i
$703$	8.69831	+	15.0659i	0.328063	+	0.568222i
$704$	18.5005			0.697264
$705$	0.126788	−	0.219604i	0.00477513	−	0.00827076i
$706$	−49.3251			−1.85637
$707$	12.5789	−	21.7873i	0.473078	−	0.819395i
$708$	30.9451			1.16299
$709$	11.9903			0.450306			0.225153	−	0.974323i	$-0.427712\pi$
$709$	11.9903			0.450306			0.225153	+	0.974323i	$0.427712\pi$
$710$	0.0680584	−	0.117881i	0.00255419	−	0.00442398i
$711$	−0.125892	+	0.218051i	−0.00472131	+	0.00817754i
$712$	−7.02331	−	12.1647i	−0.263210	−	0.455892i
$713$	8.44937	−	14.6347i	0.316431	−	0.548075i
$714$	−53.7649	+	93.1235i	−2.01210	+	3.48506i
$715$	4.00585			0.149810
$716$	1.97706	+	3.42438i	0.0738864	+	0.127975i
$717$	−6.25702	−	10.8375i	−0.233673	−	0.404733i
$718$	22.4085	−	38.8126i	0.836277	−	1.44847i
$719$	34.8952			1.30137			0.650685	−	0.759348i	$-0.274482\pi$
$719$	34.8952			1.30137			0.650685	+	0.759348i	$0.274482\pi$
$720$	−0.203805	+	0.353000i	−0.00759536	+	0.0131556i
$721$	13.9866	−	24.2255i	0.520887	−	0.902204i
$722$	17.0080	+	29.4586i	0.632970	+	1.09634i
$723$	13.0502	−	22.6036i	0.485342	−	0.840637i
$724$	−12.8742	−	22.2987i	−0.478465	−	0.828726i
$725$	−27.1086			−1.00679
$726$	−31.4651			−1.16778
$727$	14.0448	+	24.3263i	0.520893	+	0.902214i	0.999705	+	0.0242959i	$0.00773437\pi$
$727$	14.0448	+	24.3263i	0.520893	+	0.902214i	−0.478812	+	0.877918i	$0.658932\pi$
$728$	18.3577	+	31.7964i	0.680380	+	1.17845i
$729$	29.8479			1.10548
$730$	6.41734	+	11.1152i	0.237516	+	0.411391i
$731$	21.6394	+	37.4806i	0.800363	+	1.38627i
$732$	−19.3001	+	33.4288i	−0.713352	+	1.23556i
$733$	−8.48950			−0.313567			−0.156783	−	0.987633i	$-0.550112\pi$
$733$	−8.48950			−0.313567			−0.156783	+	0.987633i	$0.550112\pi$
$734$	37.1859			1.37256
$735$	10.5259			0.388255
$736$	48.7738			1.79783
$737$	−11.3410			−0.417752
$738$	−6.87206	−	11.9027i	−0.252964	−	0.438146i
$739$	51.4101			1.89115			0.945576	−	0.325402i	$-0.105500\pi$
$739$	51.4101			1.89115			0.945576	+	0.325402i	$0.105500\pi$
$740$	−8.63613	+	14.9582i	−0.317470	+	0.549875i
$741$	−6.52797	−	11.3068i	−0.239811	−	0.415365i
$742$	24.9871	+	43.2788i	0.917304	+	1.58882i
$743$	9.02940			0.331257			0.165628	−	0.986188i	$-0.447035\pi$
$743$	9.02940			0.331257			0.165628	+	0.986188i	$0.447035\pi$
$744$	−3.94042	−	6.82500i	−0.144463	−	0.250217i
$745$	−14.1221			−0.517392
$746$	−7.13705			−0.261306
$747$	−4.20019	−	7.27494i	−0.153677	−	0.266176i
$748$	15.4637	+	26.7839i	0.565409	+	0.979317i
$749$	−1.24728	−	2.16035i	−0.0455745	−	0.0789373i
$750$	−21.9081			−0.799972
$751$	43.5011			1.58738			0.793689	−	0.608324i	$-0.208158\pi$
$751$	43.5011			1.58738			0.793689	+	0.608324i	$0.208158\pi$
$752$	−0.157922	+	0.273529i	−0.00575882	+	0.00997458i
$753$	−2.87913	−	4.98680i	−0.104921	−	0.181729i
$754$	28.2431	−	48.9185i	1.02855	−	1.78151i
$755$	−0.0440528	+	0.0763017i	−0.00160325	+	0.00277690i
$756$	−67.1574			−2.44249
$757$	−12.3094	−	21.3205i	−0.447392	−	0.774905i	0.550824	−	0.834622i	$-0.314314\pi$
$757$	−12.3094	−	21.3205i	−0.447392	−	0.774905i	−0.998215	+	0.0597163i	$0.980980\pi$
$758$	−60.7880			−2.20792
$759$	15.9054			0.577328
$760$	1.28395	−	2.22387i	0.0465738	−	0.0806681i
$761$	−1.45363	−	2.51777i	−0.0526941	−	0.0912689i	0.838475	−	0.544940i	$-0.183448\pi$
$761$	−1.45363	−	2.51777i	−0.0526941	−	0.0912689i	−0.891169	+	0.453671i	$0.850114\pi$
$762$	−33.2308			−1.20383
$763$	37.4074			1.35424
$764$	23.0199			0.832832
$765$	−2.33948			−0.0845842
$766$	−31.8670	−	55.1952i	−1.15140	−	1.99429i
$767$	−28.6538			−1.03463
$768$	5.41745	−	9.38330i	0.195486	−	0.338591i
$769$	18.7073	−	32.4020i	0.674602	−	1.16844i	−0.301984	−	0.953313i	$-0.597649\pi$
$769$	18.7073	−	32.4020i	0.674602	−	1.16844i	0.976585	−	0.215131i	$-0.0690179\pi$
$770$	4.29370	−	7.43691i	0.154734	−	0.268008i
$771$	−6.50426	−	11.2657i	−0.234245	−	0.405725i
$772$	37.1705	−	64.3812i	1.33780	−	2.31713i
$773$	−49.3948			−1.77661			−0.888304	−	0.459255i	$-0.848116\pi$
$773$	−49.3948			−1.77661			−0.888304	+	0.459255i	$0.848116\pi$
$774$	−3.18473	+	5.51612i	−0.114473	+	0.198273i
$775$	5.52558	−	9.57058i	0.198485	−	0.343785i
$776$	9.03162	−	15.6432i	0.324216	−	0.561559i
$777$	59.6574			2.14020
$778$	−53.3144			−1.91142
$779$	−12.1536	−	21.0507i	−0.435448	−	0.754219i
$780$	6.48130	−	11.2259i	0.232068	−	0.401953i
$781$	−0.0676101	+	0.117104i	−0.00241928	+	0.00419032i
$782$	57.2298	+	99.1249i	2.04653	+	3.54470i
$783$	16.3711	+	28.3556i	0.585055	+	1.01335i
$784$	−13.1106			−0.468237
$785$	−1.80783	+	3.13126i	−0.0645243	+	0.111759i
$786$	40.2312			1.43500
$787$	14.9238	+	25.8488i	0.531977	+	0.921410i	0.999303	+	0.0373257i	$0.0118839\pi$
$787$	14.9238	+	25.8488i	0.531977	+	0.921410i	−0.467327	+	0.884085i	$0.654783\pi$
$788$	−6.25470	+	10.8335i	−0.222814	+	0.385926i
$789$	−3.24141	−	5.61428i	−0.115397	−	0.199874i
$790$	−0.744115			−0.0264744
$791$	−38.7582	−	67.1312i	−1.37808	−	2.38691i
$792$	−0.721207	+	1.24917i	−0.0256270	+	0.0443872i
$793$	17.8710	−	30.9535i	0.634619	−	1.09919i
$794$	−16.4885	+	28.5589i	−0.585154	+	1.01352i
$795$	2.79562	−	4.84216i	0.0991505	−	0.171734i
$796$	−16.9685			−0.601432
$797$	7.37480	−	12.7735i	0.261229	−	0.452462i	−0.705340	−	0.708869i	$-0.749206\pi$
$797$	7.37480	−	12.7735i	0.261229	−	0.452462i	0.966569	+	0.256408i	$0.0825389\pi$
$798$	−27.9882			−0.990771
$799$	−1.81279			−0.0641320
$800$	31.8963			1.12771
$801$	−3.33089			−0.117691
$802$	28.7872	−	49.8609i	1.01651	−	1.76065i
$803$	−6.37508	−	11.0420i	−0.224972	−	0.389662i
$804$	−18.3493	+	31.7819i	−0.647130	+	1.12086i
$805$	9.44125	−	16.3527i	0.332760	−	0.576358i
$806$	11.5137	+	19.9423i	0.405552	+	0.702436i
$807$	10.2069	+	17.6789i	0.359301	+	0.622328i
$808$	−12.4886			−0.439348
$809$	3.49436	+	6.05240i	0.122855	+	0.212791i	0.920892	−	0.389817i	$-0.127462\pi$
$809$	3.49436	+	6.05240i	0.122855	+	0.212791i	−0.798037	+	0.602608i	$0.794128\pi$
$810$	5.26577	+	9.12057i	0.185020	+	0.320464i
$811$	0.648176	−	1.12267i	0.0227605	−	0.0394224i	−0.854421	−	0.519582i	$-0.826088\pi$
$811$	0.648176	−	1.12267i	0.0227605	−	0.0394224i	0.877181	+	0.480159i	$0.159421\pi$
$812$	−35.9723	−	62.3059i	−1.26238	−	2.18651i
$813$	4.78286			0.167742
$814$	14.4398	−	25.0104i	0.506113	−	0.876614i
$815$	4.43742	+	7.68583i	0.155436	+	0.269223i
$816$	−14.9849			−0.524578
$817$	−5.63238	+	9.75557i	−0.197052	+	0.341304i
$818$	−12.4925	+	21.6376i	−0.436789	+	0.756540i
$819$	8.70634			0.304224
$820$	12.0667	−	20.9002i	0.421388	−	0.729866i
$821$	13.9546	+	24.1701i	0.487020	+	0.843543i	0.999889	−	0.0149240i	$-0.00475065\pi$
$821$	13.9546	+	24.1701i	0.487020	+	0.843543i	−0.512869	+	0.858467i	$0.671417\pi$
$822$	13.7615	+	23.8356i	0.479988	+	0.831363i
$823$	−48.4775			−1.68982			−0.844910	−	0.534908i	$-0.820346\pi$
$823$	−48.4775			−1.68982			−0.844910	+	0.534908i	$0.820346\pi$
$824$	−13.8862			−0.483748
$825$	10.4015			0.362135
$826$	−30.7128	+	53.1961i	−1.06863	+	1.85093i
$827$	−22.1653	+	38.3914i	−0.770763	+	1.33500i	0.166383	+	0.986061i	$0.446791\pi$
$827$	−22.1653	+	38.3914i	−0.770763	+	1.33500i	−0.937145	+	0.348939i	$0.886542\pi$
$828$	−5.00425	+	8.66762i	−0.173910	+	0.301220i
$829$	−7.36764			−0.255889			−0.127944	−	0.991781i	$-0.540838\pi$
$829$	−7.36764			−0.255889			−0.127944	+	0.991781i	$0.540838\pi$
$830$	12.4131	−	21.5002i	0.430867	−	0.746283i
$831$	−10.6900			−0.370832
$832$	−27.7167	+	48.0067i	−0.960902	+	1.66433i
$833$	−37.6244	−	65.1673i	−1.30361	−	2.25791i
$834$	45.8516			1.58771
$835$	−5.64116	−	9.77078i	−0.195220	−	0.338132i
$836$	−4.02494	+	6.97141i	−0.139206	+	0.241111i
$837$	−13.3478			−0.461366
$838$	33.4600	+	57.9544i	1.15586	+	2.00200i
$839$	2.47101	+	4.27991i	0.0853087	+	0.147759i	0.905523	−	0.424298i	$-0.139479\pi$
$839$	2.47101	+	4.27991i	0.0853087	+	0.147759i	−0.820214	+	0.572057i	$0.806146\pi$
$840$	−4.40299	−	7.62620i	−0.151918	−	0.263129i
$841$	−3.03810	+	5.26214i	−0.104762	+	0.181453i
$842$	11.1659	+	19.3399i	0.384803	+	0.666498i
$843$	16.9288	−	29.3216i	0.583060	−	1.00989i
$844$	13.3886			0.460853
$845$	−1.77493	+	3.07427i	−0.0610594	+	0.105758i
$846$	−0.133397	−	0.231050i	−0.00458628	−	0.00794367i
$847$	18.5543	−	32.1371i	0.637535	−	1.10424i
$848$	−3.48210	+	6.03118i	−0.119576	+	0.207112i
$849$	11.0067	+	19.0642i	0.377749	+	0.654281i
$850$	37.4262	+	64.8240i	1.28371	+	2.22345i
$851$	31.7510	−	54.9944i	1.08841	−	1.88518i
$852$	0.218781	+	0.378939i	0.00749530	+	0.0129822i
$853$	−0.0919293	−	0.159226i	−0.00314760	−	0.00545180i	0.864447	−	0.502723i	$-0.167669\pi$
$853$	−0.0919293	−	0.159226i	−0.00314760	−	0.00545180i	−0.867595	+	0.497272i	$0.834335\pi$
$854$	−38.3104	−	66.3555i	−1.31095	−	2.27064i
$855$	−0.304464	−	0.527348i	−0.0104125	−	0.0180349i
$856$	−0.619162	+	1.07242i	−0.0211625	+	0.0366545i
$857$	15.8042	+	27.3737i	0.539861	+	0.935067i	0.998911	+	0.0466564i	$0.0148566\pi$
$857$	15.8042	+	27.3737i	0.539861	+	0.935067i	−0.459050	+	0.888410i	$0.651810\pi$
$858$	−10.8369	+	18.7700i	−0.369964	+	0.640796i
$859$	−2.80439	−	4.85735i	−0.0956847	−	0.165731i	0.814209	−	0.580571i	$-0.197171\pi$
$859$	−2.80439	−	4.85735i	−0.0956847	−	0.165731i	−0.909894	+	0.414840i	$0.863837\pi$
$860$	−11.1842			−0.381379
$861$	−83.3556			−2.84075
$862$	−7.83409	−	13.5690i	−0.266830	−	0.462163i
$863$	−8.76034	+	15.1734i	−0.298205	+	0.516507i	−0.975725	−	0.218997i	$-0.929721\pi$
$863$	−8.76034	+	15.1734i	−0.298205	+	0.516507i	0.677520	+	0.735504i	$0.263055\pi$
$864$	−19.2625	−	33.3635i	−0.655322	−	1.13505i
$865$	−5.02288			−0.170783
$866$	−62.7516			−2.13238
$867$	−29.5323	−	51.1515i	−1.00297	−	1.73720i
$868$	29.3292			0.995497
$869$	0.739215			0.0250761
$870$	−6.77396	+	11.7328i	−0.229659	+	0.397781i
$871$	16.9906	−	29.4286i	0.575706	−	0.997151i
$872$	−9.28473	−	16.0816i	−0.314421	−	0.544593i
$873$	−2.14168	−	3.70949i	−0.0724847	−	0.125547i
$874$	−14.8960	+	25.8005i	−0.503863	+	0.872717i
$875$	12.9188	−	22.3760i	0.436734	−	0.756446i
$876$	−41.2584			−1.39399
$877$	−31.9671			−1.07945			−0.539726	−	0.841841i	$-0.681472\pi$
$877$	−31.9671			−1.07945			−0.539726	+	0.841841i	$0.681472\pi$
$878$	−22.6192	−	39.1776i	−0.763362	−	1.32218i
$879$	−8.09647			−0.273087
$880$	1.19671			0.0403410
$881$	−11.5062	−	19.9294i	−0.387654	−	0.671437i	0.604479	−	0.796621i	$-0.293381\pi$
$881$	−11.5062	−	19.9294i	−0.387654	−	0.671437i	−0.992134	+	0.125184i	$0.960048\pi$
$882$	5.53728	−	9.59085i	0.186450	−	0.322941i
$883$	16.5497	+	28.6649i	0.556941	+	0.964650i	0.997750	+	0.0670488i	$0.0213583\pi$
$883$	16.5497	+	28.6649i	0.556941	+	0.964650i	−0.440809	+	0.897601i	$0.645308\pi$
$884$	−92.6682			−3.11677
$885$	6.87247			0.231015
$886$	19.4351	+	33.6626i	0.652935	+	1.13092i
$887$	17.4282	−	30.1866i	0.585183	−	1.01357i	−0.409669	−	0.912234i	$-0.634356\pi$
$887$	17.4282	−	30.1866i	0.585183	−	1.01357i	0.994853	−	0.101333i	$-0.0323108\pi$
$888$	−14.8073	−	25.6470i	−0.496900	−	0.860656i
$889$	19.5955	−	33.9405i	0.657213	−	1.13833i
$890$	−4.92202	−	8.52519i	−0.164986	−	0.285765i
$891$	−5.23108	−	9.06050i	−0.175248	−	0.303538i
$892$	36.1062	+	62.5377i	1.20892	+	2.09392i
$893$	−0.235920	−	0.408625i	−0.00789476	−	0.0136741i
$894$	38.2038	−	66.1709i	1.27773	−	2.21309i
$895$	0.439077	+	0.760504i	0.0146767	+	0.0254208i
$896$	30.5039	+	52.8343i	1.01906	+	1.76507i
$897$	−23.8287	+	41.2726i	−0.795618	+	1.37805i
$898$	28.9126	−	50.0781i	0.964825	−	1.67113i
$899$	−7.14963	−	12.3835i	−0.238453	−	0.413013i
$900$	−3.27260	+	5.66830i	−0.109087	+	0.188943i
$901$	−39.9712			−1.33163
$902$	−20.1758	+	34.9455i	−0.671780	+	1.16356i
$903$	19.3149	+	33.4543i	0.642758	+	1.11329i
$904$	−19.2400	+	33.3247i	−0.639913	+	1.10836i
$905$	−2.85917	−	4.95223i	−0.0950420	−	0.164618i
$906$	−0.238348	−	0.412831i	−0.00791858	−	0.0137154i
$907$	3.83801	+	6.64763i	0.127439	+	0.220731i	0.922684	−	0.385558i	$-0.125991\pi$
$907$	3.83801	+	6.64763i	0.127439	+	0.220731i	−0.795245	+	0.606289i	$0.792658\pi$
$908$	4.51866			0.149957
$909$	−1.48072	+	2.56468i	−0.0491123	+	0.0850650i
$910$	12.8653	+	22.2833i	0.426480	+	0.738684i
$911$	35.8352			1.18727			0.593637	−	0.804733i	$-0.297691\pi$
$911$	35.8352			1.18727			0.593637	+	0.804733i	$0.297691\pi$
$912$	−1.95017	−	3.37779i	−0.0645764	−	0.111850i
$913$	−12.3314	+	21.3586i	−0.408110	+	0.706866i
$914$	−16.9905			−0.561997
$915$	−4.28627	+	7.42404i	−0.141700	+	0.245431i
$916$	−21.8752			−0.722775
$917$	−23.7235	+	41.0904i	−0.783421	+	1.35692i
$918$	45.2040	−	78.2956i	1.49195	−	2.58414i
$919$	−10.2646	+	17.7788i	−0.338598	+	0.586468i	−0.984169	−	0.177231i	$-0.943286\pi$
$919$	−10.2646	+	17.7788i	−0.338598	+	0.586468i	0.645572	+	0.763700i	$0.276619\pi$
$920$	−9.37348			−0.309035
$921$	−39.8876			−1.31434
$922$	−40.9387			−1.34824
$923$	−0.202581	−	0.350881i	−0.00666804	−	0.0115494i
$924$	13.8025	+	23.9067i	0.454070	+	0.786473i
$925$	20.7640	−	35.9643i	0.682716	−	1.18250i
$926$	72.2526			2.37437
$927$	−1.64642	+	2.85169i	−0.0540756	+	0.0936617i
$928$	20.6356	−	35.7418i	0.677395	−	1.17328i
$929$	25.3522			0.831780			0.415890	−	0.909415i	$-0.363470\pi$
$929$	25.3522			0.831780			0.415890	+	0.909415i	$0.363470\pi$
$930$	−2.76149	−	4.78304i	−0.0905529	−	0.156842i
$931$	9.79299	−	16.9620i	0.320952	−	0.555906i
$932$	−6.54140			−0.214271
$933$	9.52830	+	16.5035i	0.311943	+	0.540300i
$934$	−7.48044	+	12.9565i	−0.244767	+	0.423950i
$935$	3.43426	+	5.94832i	0.112312	+	0.194531i
$936$	−2.16096	−	3.74290i	−0.0706332	−	0.122340i
$937$	38.9034			1.27092			0.635459	−	0.772134i	$-0.280811\pi$
$937$	38.9034			1.27092			0.635459	+	0.772134i	$0.280811\pi$
$938$	−36.4230	−	63.0866i	−1.18925	−	2.05985i
$939$	2.96016	+	5.12714i	0.0966010	+	0.167318i
$940$	0.234233	−	0.405704i	0.00763985	−	0.0132326i
$941$	10.2794	−	17.8045i	0.335100	−	0.580411i	−0.648404	−	0.761297i	$-0.724563\pi$
$941$	10.2794	−	17.8045i	0.335100	−	0.580411i	0.983504	+	0.180886i	$0.0578964\pi$
$942$	−9.78129	−	16.9417i	−0.318692	−	0.551990i
$943$	−44.3637	+	76.8403i	−1.44468	+	2.50226i
$944$	−8.56004			−0.278606
$945$	−14.9147			−0.485175
$946$	18.7002			0.607997
$947$	26.8889			0.873771			0.436886	−	0.899517i	$-0.356081\pi$
$947$	26.8889			0.873771			0.436886	+	0.899517i	$0.356081\pi$
$948$	1.19602	−	2.07156i	0.0388449	−	0.0672813i
$949$	38.2035			1.24014
$950$	−9.74141	+	16.8726i	−0.316053	+	0.547420i
$951$	20.6266	−	35.7264i	0.668865	−	1.15851i
$952$	−31.4765	+	54.5189i	−1.02016	+	1.76697i
$953$	11.3736	−	19.6997i	0.368427	−	0.638135i	−0.620893	−	0.783896i	$-0.713230\pi$
$953$	11.3736	−	19.6997i	0.368427	−	0.638135i	0.989320	+	0.145761i	$0.0465631\pi$
$954$	−2.94134	−	5.09454i	−0.0952293	−	0.164942i
$955$	5.11239			0.165433
$956$	−11.5594	−	20.0215i	−0.373859	−	0.647542i
$957$	6.72935	−	11.6556i	0.217529	−	0.376771i
$958$	−47.7140	−	82.6431i	−1.54157	−	2.67008i
$959$	−32.4595			−1.04817
$960$	6.64769	−	11.5141i	0.214553	−	0.371617i
$961$	−25.1707			−0.811959
$962$	43.2660	+	74.9390i	1.39495	+	2.41613i
$963$	0.146822	+	0.254304i	0.00473128	+	0.00819482i
$964$	24.1094	−	41.7587i	0.776511	−	1.34496i
$965$	8.25503	−	14.2981i	0.265739	−	0.460273i
$966$	51.0820	+	88.4766i	1.64354	+	2.84669i
$967$	15.3582			0.493887			0.246943	−	0.969030i	$-0.420574\pi$
$967$	15.3582			0.493887			0.246943	+	0.969030i	$0.420574\pi$
$968$	−18.4212			−0.592079
$969$	11.1930	−	19.3869i	0.359571	−	0.622796i
$970$	6.32947	−	10.9630i	0.203227	−	0.351999i
$971$	−0.245300	+	0.424872i	−0.00787205	+	0.0136348i	−0.869935	−	0.493167i	$-0.835839\pi$
$971$	−0.245300	+	0.424872i	−0.00787205	+	0.0136348i	0.862063	+	0.506802i	$0.169172\pi$
$972$	14.7040			0.471630
$973$	−27.0378	+	46.8308i	−0.866791	+	1.50133i
$974$	17.7947	+	30.8214i	0.570180	+	0.987581i
$975$	−15.5831	+	26.9908i	−0.499059	+	0.864396i
$976$	5.33879	−	9.24706i	0.170891	−	0.295991i
$977$	−19.5691	+	33.8947i	−0.626071	+	1.08439i	0.362261	+	0.932077i	$0.382005\pi$
$977$	−19.5691	+	33.8947i	−0.626071	+	1.08439i	−0.988333	+	0.152311i	$0.951329\pi$
$978$	−48.0174			−1.53543
$979$	4.88960	+	8.46904i	0.156272	+	0.270672i
$980$	19.4460			0.621179
$981$	−4.40339			−0.140590
$982$	−2.84301			−0.0907242
$983$	18.6202			0.593893			0.296947	−	0.954894i	$-0.404032\pi$
$983$	18.6202			0.593893			0.296947	+	0.954894i	$0.404032\pi$
$984$	20.6893	+	35.8350i	0.659551	+	1.14238i
$985$	−1.38908	+	2.40595i	−0.0442597	+	0.0766601i
$986$	96.8526			3.08441
$987$	−1.61806			−0.0515033
$988$	−12.0600	−	20.8885i	−0.383680	−	0.664553i
$989$	41.1192			1.30752
$990$	−0.505430	+	0.875431i	−0.0160636	+	0.0278230i
$991$	−16.6322	+	28.8078i	−0.528338	+	0.915109i	0.471116	+	0.882071i	$0.343851\pi$
$991$	−16.6322	+	28.8078i	−0.528338	+	0.915109i	−0.999454	+	0.0330375i	$0.989482\pi$
$992$	8.41235	+	14.5706i	0.267092	+	0.462617i
$993$	−11.5771	+	20.0521i	−0.367388	+	0.636335i
$994$	−0.868552			−0.0275488
$995$	−3.76845			−0.119468
$996$	39.9034	+	69.1146i	1.26439	+	2.18998i
$997$	−1.89664	−	3.28507i	−0.0600671	−	0.104039i	0.834428	−	0.551117i	$-0.185798\pi$
$997$	−1.89664	−	3.28507i	−0.0600671	−	0.104039i	−0.894495	+	0.447078i	$0.852465\pi$
$998$	−24.9370	−	43.1921i	−0.789366	−	1.36722i
$999$	−50.1582			−1.58694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.5	✓	56
349.226	even	3	inner	349.2.c.a.226.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.5	✓	56	1.1	even	1	trivial
349.2.c.a.226.5	yes	56	349.226	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10993 + 1.92246i) q^{2} +(-0.792401 - 1.37248i) q^{3} +(-1.46391 - 2.53556i) q^{4} +(-0.325113 - 0.563112i) q^{5} +3.51805 q^{6} +(-2.07452 + 3.59318i) q^{7} +2.05963 q^{8} +(0.244201 - 0.422969i) q^{9} +O(q^{10})\)	\(q+(-1.10993 + 1.92246i) q^{2} +(-0.792401 - 1.37248i) q^{3} +(-1.46391 - 2.53556i) q^{4} +(-0.325113 - 0.563112i) q^{5} +3.51805 q^{6} +(-2.07452 + 3.59318i) q^{7} +2.05963 q^{8} +(0.244201 - 0.422969i) q^{9} +1.44342 q^{10} -1.43391 q^{11} +(-2.32001 + 4.01837i) q^{12} +(2.14822 - 3.72083i) q^{13} +(-4.60517 - 7.97639i) q^{14} +(-0.515240 + 0.892421i) q^{15} +(0.641760 - 1.11156i) q^{16} +7.36678 q^{17} +(0.542095 + 0.938936i) q^{18} +(0.958725 + 1.66056i) q^{19} +(-0.951871 + 1.64869i) q^{20} +6.57542 q^{21} +(1.59155 - 2.75664i) q^{22} +(3.49959 - 6.06146i) q^{23} +(-1.63206 - 2.82680i) q^{24} +(2.28860 - 3.96398i) q^{25} +(4.76877 + 8.25975i) q^{26} -5.52843 q^{27} +12.1477 q^{28} +(-2.96126 - 5.12905i) q^{29} +(-1.14376 - 1.98106i) q^{30} +2.41439 q^{31} +(3.48426 + 6.03491i) q^{32} +(1.13623 + 1.96801i) q^{33} +(-8.17664 + 14.1624i) q^{34} +2.69782 q^{35} -1.42995 q^{36} +9.07279 q^{37} -4.25649 q^{38} -6.80901 q^{39} +(-0.669613 - 1.15980i) q^{40} -12.6768 q^{41} +(-7.29828 + 12.6410i) q^{42} +(2.93743 + 5.08778i) q^{43} +(2.09911 + 3.63577i) q^{44} -0.317572 q^{45} +(7.76863 + 13.4557i) q^{46} -0.246077 q^{47} -2.03412 q^{48} +(-5.10730 - 8.84610i) q^{49} +(5.08040 + 8.79951i) q^{50} +(-5.83744 - 10.1107i) q^{51} -12.5792 q^{52} -5.42587 q^{53} +(6.13619 - 10.6282i) q^{54} +(0.466182 + 0.807452i) q^{55} +(-4.27276 + 7.40064i) q^{56} +(1.51939 - 2.63166i) q^{57} +13.1472 q^{58} +(-3.33460 - 5.77569i) q^{59} +3.01705 q^{60} +8.31899 q^{61} +(-2.67981 + 4.64157i) q^{62} +(1.01320 + 1.75492i) q^{63} -12.9021 q^{64} -2.79366 q^{65} -5.04457 q^{66} +7.90916 q^{67} +(-10.7843 - 18.6789i) q^{68} -11.0923 q^{69} +(-2.99440 + 5.18645i) q^{70} +(0.0471509 - 0.0816678i) q^{71} +(0.502965 - 0.871161i) q^{72} +(4.44594 + 7.70060i) q^{73} +(-10.0702 + 17.4421i) q^{74} -7.25397 q^{75} +(2.80697 - 4.86182i) q^{76} +(2.97468 - 5.15230i) q^{77} +(7.55756 - 13.0901i) q^{78} -0.515524 q^{79} -0.834577 q^{80} +(3.64813 + 6.31874i) q^{81} +(14.0705 - 24.3708i) q^{82} +(8.59984 - 14.8954i) q^{83} +(-9.62581 - 16.6724i) q^{84} +(-2.39504 - 4.14832i) q^{85} -13.0414 q^{86} +(-4.69301 + 8.12853i) q^{87} -2.95333 q^{88} +(-3.40998 - 5.90626i) q^{89} +(0.352484 - 0.610520i) q^{90} +(8.91307 + 15.4379i) q^{91} -20.4923 q^{92} +(-1.91316 - 3.31370i) q^{93} +(0.273129 - 0.473073i) q^{94} +(0.623388 - 1.07974i) q^{95} +(5.52186 - 9.56413i) q^{96} +(4.38506 - 7.59515i) q^{97} +22.6751 q^{98} +(-0.350163 + 0.606499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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