LMFDB - Embedded newform 671.2.i.b.34.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(34,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("671.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.i (of order $5$, degree $4$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			34.13
Character	$\chi$	$=$	671.34
Dual form			671.2.i.b.375.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.200295 + 0.145523i) q^{2} +(-0.573642 + 0.416776i) q^{3} +(-0.599093 + 1.84382i) q^{4} +(1.29845 - 3.99621i) q^{5} +(0.0542474 - 0.166956i) q^{6} +(-0.123158 - 0.0894793i) q^{7} +(-0.301334 - 0.927412i) q^{8} +(-0.771687 + 2.37501i) q^{9} +O(q^{10})$	\(q+(-0.200295 + 0.145523i) q^{2} +(-0.573642 + 0.416776i) q^{3} +(-0.599093 + 1.84382i) q^{4} +(1.29845 - 3.99621i) q^{5} +(0.0542474 - 0.166956i) q^{6} +(-0.123158 - 0.0894793i) q^{7} +(-0.301334 - 0.927412i) q^{8} +(-0.771687 + 2.37501i) q^{9} +(0.321467 + 0.989375i) q^{10} -1.00000 q^{11} +(-0.424793 - 1.30738i) q^{12} +3.24702 q^{13} +0.0376892 q^{14} +(0.920678 + 2.83356i) q^{15} +(-2.94158 - 2.13718i) q^{16} +(1.30533 - 4.01740i) q^{17} +(-0.191053 - 0.588001i) q^{18} +(3.20787 - 2.33065i) q^{19} +(6.59039 + 4.78820i) q^{20} +0.107941 q^{21} +(0.200295 - 0.145523i) q^{22} +(1.14558 - 3.52573i) q^{23} +(0.559381 + 0.406414i) q^{24} +(-10.2386 - 7.43881i) q^{25} +(-0.650361 + 0.472515i) q^{26} +(-1.20451 - 3.70710i) q^{27} +(0.238766 - 0.173474i) q^{28} +1.10100 q^{29} +(-0.596755 - 0.433568i) q^{30} +(6.04360 + 4.39093i) q^{31} +2.85047 q^{32} +(0.573642 - 0.416776i) q^{33} +(0.323172 + 0.994621i) q^{34} +(-0.517492 + 0.375980i) q^{35} +(-3.91677 - 2.84570i) q^{36} +(-2.77332 - 2.01494i) q^{37} +(-0.303357 + 0.933636i) q^{38} +(-1.86263 + 1.35328i) q^{39} -4.09740 q^{40} +(6.63157 + 4.81812i) q^{41} +(-0.0216201 + 0.0157079i) q^{42} +(-2.48160 - 7.63757i) q^{43} +(0.599093 - 1.84382i) q^{44} +(8.48904 + 6.16765i) q^{45} +(0.283620 + 0.872893i) q^{46} +12.0933 q^{47} +2.57814 q^{48} +(-2.15596 - 6.63536i) q^{49} +3.13327 q^{50} +(0.925559 + 2.84858i) q^{51} +(-1.94526 + 5.98691i) q^{52} +(-1.36640 - 4.20535i) q^{53} +(0.780725 + 0.567230i) q^{54} +(-1.29845 + 3.99621i) q^{55} +(-0.0458725 + 0.141181i) q^{56} +(-0.868810 + 2.67392i) q^{57} +(-0.220525 + 0.160221i) q^{58} +(10.6227 - 7.71784i) q^{59} -5.77613 q^{60} +(1.97078 + 7.55752i) q^{61} -1.84949 q^{62} +(0.307553 - 0.223451i) q^{63} +(5.31222 - 3.85955i) q^{64} +(4.21608 - 12.9758i) q^{65} +(-0.0542474 + 0.166956i) q^{66} +(-3.20655 + 9.86876i) q^{67} +(6.62533 + 4.81359i) q^{68} +(0.812284 + 2.49995i) q^{69} +(0.0489374 - 0.150614i) q^{70} +(2.61461 + 8.04694i) q^{71} +2.43515 q^{72} +(-4.83154 - 14.8700i) q^{73} +0.848703 q^{74} +8.97363 q^{75} +(2.37549 + 7.31100i) q^{76} +(0.123158 + 0.0894793i) q^{77} +(0.176142 - 0.542110i) q^{78} +(3.41992 + 10.5254i) q^{79} +(-12.3601 + 8.98014i) q^{80} +(-3.82493 - 2.77897i) q^{81} -2.02942 q^{82} +(-9.59803 + 6.97337i) q^{83} +(-0.0646668 + 0.199024i) q^{84} +(-14.3595 - 10.4328i) q^{85} +(1.60849 + 1.16864i) q^{86} +(-0.631580 + 0.458870i) q^{87} +(0.301334 + 0.927412i) q^{88} +(2.52217 - 1.83246i) q^{89} -2.59785 q^{90} +(-0.399895 - 0.290541i) q^{91} +(5.81449 + 4.22447i) q^{92} -5.29690 q^{93} +(-2.42222 + 1.75985i) q^{94} +(-5.14853 - 15.8455i) q^{95} +(-1.63515 + 1.18801i) q^{96} +(-3.05786 - 2.22167i) q^{97} +(1.39742 + 1.01529i) q^{98} +(0.771687 - 2.37501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) $ 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.200295	+	0.145523i	−0.141630	+	0.102900i	−0.656344	−	0.754462i	$-0.727898\pi$
$2$	−0.200295	+	0.145523i	−0.141630	+	0.102900i	0.514714	+	0.857362i	$0.327898\pi$
$3$	−0.573642	+	0.416776i	−0.331193	+	0.240625i	−0.740936	−	0.671575i	$-0.765618\pi$
$3$	−0.573642	+	0.416776i	−0.331193	+	0.240625i	0.409744	+	0.912201i	$0.365618\pi$
$4$	−0.599093	+	1.84382i	−0.299546	+	0.921909i
$5$	1.29845	−	3.99621i	0.580683	−	1.78716i	−0.0352716	−	0.999378i	$-0.511230\pi$
$5$	1.29845	−	3.99621i	0.580683	−	1.78716i	0.615955	−	0.787781i	$-0.288770\pi$
$6$	0.0542474	−	0.166956i	0.0221464	−	0.0681596i
$7$	−0.123158	−	0.0894793i	−0.0465492	−	0.0338200i	0.564267	−	0.825592i	$-0.309159\pi$
$7$	−0.123158	−	0.0894793i	−0.0465492	−	0.0338200i	−0.610817	+	0.791772i	$0.709159\pi$
$8$	−0.301334	−	0.927412i	−0.106538	−	0.327890i
$9$	−0.771687	+	2.37501i	−0.257229	+	0.791670i
$10$	0.321467	+	0.989375i	0.101657	+	0.312868i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−0.424793	−	1.30738i	−0.122627	−	0.377408i
$13$	3.24702			0.900560			0.450280	−	0.892887i	$-0.351324\pi$
$13$	3.24702			0.900560			0.450280	+	0.892887i	$0.351324\pi$
$14$	0.0376892			0.0100729
$15$	0.920678	+	2.83356i	0.237718	+	0.731621i
$16$	−2.94158	−	2.13718i	−0.735394	−	0.534295i
$17$	1.30533	−	4.01740i	0.316589	−	0.974362i	−0.658506	−	0.752576i	$-0.728811\pi$
$17$	1.30533	−	4.01740i	0.316589	−	0.974362i	0.975095	−	0.221786i	$-0.0711888\pi$
$18$	−0.191053	−	0.588001i	−0.0450317	−	0.138593i
$19$	3.20787	−	2.33065i	0.735935	−	0.534688i	−0.155500	−	0.987836i	$-0.549699\pi$
$19$	3.20787	−	2.33065i	0.735935	−	0.534688i	0.891435	+	0.453148i	$0.149699\pi$
$20$	6.59039	+	4.78820i	1.47366	+	1.07067i
$21$	0.107941			0.0235547
$22$	0.200295	−	0.145523i	0.0427031	−	0.0310256i
$23$	1.14558	−	3.52573i	0.238869	−	0.735165i	−0.757715	−	0.652586i	$-0.773684\pi$
$23$	1.14558	−	3.52573i	0.238869	−	0.735165i	0.996585	−	0.0825790i	$-0.0263157\pi$
$24$	0.559381	+	0.406414i	0.114183	+	0.0829589i
$25$	−10.2386	−	7.43881i	−2.04773	−	1.48776i
$26$	−0.650361	+	0.472515i	−0.127546	+	0.0926679i
$27$	−1.20451	−	3.70710i	−0.231808	−	0.713431i
$28$	0.238766	−	0.173474i	0.0451226	−	0.0327835i
$29$	1.10100			0.204451			0.102225	−	0.994761i	$-0.467404\pi$
$29$	1.10100			0.204451			0.102225	+	0.994761i	$0.467404\pi$
$30$	−0.596755	−	0.433568i	−0.108952	−	0.0791583i
$31$	6.04360	+	4.39093i	1.08546	+	0.788635i	0.978627	−	0.205641i	$-0.0659281\pi$
$31$	6.04360	+	4.39093i	1.08546	+	0.788635i	0.106836	+	0.994277i	$0.465928\pi$
$32$	2.85047			0.503896
$33$	0.573642	−	0.416776i	0.0998583	−	0.0725513i
$34$	0.323172	+	0.994621i	0.0554235	+	0.170576i
$35$	−0.517492	+	0.375980i	−0.0874721	+	0.0635522i
$36$	−3.91677	−	2.84570i	−0.652795	−	0.474284i
$37$	−2.77332	−	2.01494i	−0.455932	−	0.331254i	0.336002	−	0.941861i	$-0.390925\pi$
$37$	−2.77332	−	2.01494i	−0.455932	−	0.331254i	−0.791933	+	0.610608i	$0.790925\pi$
$38$	−0.303357	+	0.933636i	−0.0492110	+	0.151456i
$39$	−1.86263	+	1.35328i	−0.298259	+	0.216698i
$40$	−4.09740			−0.647855
$41$	6.63157	+	4.81812i	1.03568	+	0.752463i	0.969437	−	0.245340i	$-0.0788997\pi$
$41$	6.63157	+	4.81812i	1.03568	+	0.752463i	0.0662399	+	0.997804i	$0.478900\pi$
$42$	−0.0216201	+	0.0157079i	−0.00333606	+	0.00242379i
$43$	−2.48160	−	7.63757i	−0.378440	−	1.16472i	−0.941128	−	0.338049i	$-0.890233\pi$
$43$	−2.48160	−	7.63757i	−0.378440	−	1.16472i	0.562688	−	0.826669i	$-0.309767\pi$
$44$	0.599093	−	1.84382i	0.0903166	−	0.277966i
$45$	8.48904	+	6.16765i	1.26547	+	0.919419i
$46$	0.283620	+	0.872893i	0.0418175	+	0.128701i
$47$	12.0933			1.76399			0.881993	−	0.471263i	$-0.156202\pi$
$47$	12.0933			1.76399			0.881993	+	0.471263i	$0.156202\pi$
$48$	2.57814			0.372122
$49$	−2.15596	−	6.63536i	−0.307994	−	0.947908i
$50$	3.13327			0.443111
$51$	0.925559	+	2.84858i	0.129604	+	0.398881i
$52$	−1.94526	+	5.98691i	−0.269760	+	0.830234i
$53$	−1.36640	−	4.20535i	−0.187690	−	0.577649i	0.812295	−	0.583247i	$-0.198218\pi$
$53$	−1.36640	−	4.20535i	−0.187690	−	0.577649i	−0.999984	+	0.00559796i	$0.998218\pi$
$54$	0.780725	+	0.567230i	0.106243	+	0.0771902i
$55$	−1.29845	+	3.99621i	−0.175083	+	0.538849i
$56$	−0.0458725	+	0.141181i	−0.00612997	+	0.0188661i
$57$	−0.868810	+	2.67392i	−0.115077	+	0.354169i
$58$	−0.220525	+	0.160221i	−0.0289563	+	0.0210380i
$59$	10.6227	−	7.71784i	1.38296	−	1.00478i	0.386360	−	0.922348i	$-0.373732\pi$
$59$	10.6227	−	7.71784i	1.38296	−	1.00478i	0.996597	−	0.0824293i	$-0.0262679\pi$
$60$	−5.77613			−0.745696
$61$	1.97078	+	7.55752i	0.252332	+	0.967641i
$61$	1.97078	+	7.55752i	0.252332	+	0.967641i
$62$	−1.84949			−0.234885
$63$	0.307553	−	0.223451i	0.0387481	−	0.0281521i
$64$	5.31222	−	3.85955i	0.664027	−	0.482444i
$65$	4.21608	−	12.9758i	0.522940	−	1.60944i
$66$	−0.0542474	+	0.166956i	−0.00667739	+	0.0205509i
$67$	−3.20655	+	9.86876i	−0.391743	+	1.20566i	0.539726	+	0.841841i	$0.318528\pi$
$67$	−3.20655	+	9.86876i	−0.391743	+	1.20566i	−0.931469	+	0.363820i	$0.881472\pi$
$68$	6.62533	+	4.81359i	0.803440	+	0.583733i
$69$	0.812284	+	2.49995i	0.0977875	+	0.300959i
$70$	0.0489374	−	0.150614i	0.00584914	−	0.0180018i
$71$	2.61461	+	8.04694i	0.310297	+	0.954997i	0.977647	+	0.210252i	$0.0674285\pi$
$71$	2.61461	+	8.04694i	0.310297	+	0.954997i	−0.667350	+	0.744744i	$0.732571\pi$
$72$	2.43515			0.286985
$73$	−4.83154	−	14.8700i	−0.565489	−	1.74040i	−0.666493	−	0.745511i	$-0.732206\pi$
$73$	−4.83154	−	14.8700i	−0.565489	−	1.74040i	0.101004	−	0.994886i	$-0.467794\pi$
$74$	0.848703			0.0986597
$75$	8.97363			1.03619
$76$	2.37549	+	7.31100i	0.272487	+	0.838629i
$77$	0.123158	+	0.0894793i	0.0140351	+	0.0101971i
$78$	0.176142	−	0.542110i	0.0199442	−	0.0613818i
$79$	3.41992	+	10.5254i	0.384771	+	1.18420i	0.936646	+	0.350277i	$0.113913\pi$
$79$	3.41992	+	10.5254i	0.384771	+	1.18420i	−0.551875	+	0.833927i	$0.686087\pi$
$80$	−12.3601	+	8.98014i	−1.38190	+	1.00401i
$81$	−3.82493	−	2.77897i	−0.424992	−	0.308775i
$82$	−2.02942			−0.224112
$83$	−9.59803	+	6.97337i	−1.05352	+	0.765427i	−0.972879	−	0.231316i	$-0.925697\pi$
$83$	−9.59803	+	6.97337i	−1.05352	+	0.765427i	−0.0806416	+	0.996743i	$0.525697\pi$
$84$	−0.0646668	+	0.199024i	−0.00705573	+	0.0217153i
$85$	−14.3595	−	10.4328i	−1.55750	−	1.13159i
$86$	1.60849	+	1.16864i	0.173448	+	0.126018i
$87$	−0.631580	+	0.458870i	−0.0677125	+	0.0491960i
$88$	0.301334	+	0.927412i	0.0321223	+	0.0988624i
$89$	2.52217	−	1.83246i	0.267350	−	0.194241i	−0.446031	−	0.895017i	$-0.647163\pi$
$89$	2.52217	−	1.83246i	0.267350	−	0.194241i	0.713381	+	0.700776i	$0.247163\pi$
$90$	−2.59785			−0.273837
$91$	−0.399895	−	0.290541i	−0.0419204	−	0.0304569i
$92$	5.81449	+	4.22447i	0.606202	+	0.440432i
$93$	−5.29690			−0.549263
$94$	−2.42222	+	1.75985i	−0.249833	+	0.181515i
$95$	−5.14853	−	15.8455i	−0.528228	−	1.62572i
$96$	−1.63515	+	1.18801i	−0.166887	+	0.121250i
$97$	−3.05786	−	2.22167i	−0.310479	−	0.225576i	0.421623	−	0.906771i	$-0.361461\pi$
$97$	−3.05786	−	2.22167i	−0.310479	−	0.225576i	−0.732102	+	0.681195i	$0.761461\pi$
$98$	1.39742	+	1.01529i	0.141161	+	0.102560i
$99$	0.771687	−	2.37501i	0.0775575	−	0.238697i
$100$	19.8497	−	14.4217i	1.98497	−	1.44217i
$101$	−17.2098			−1.71244			−0.856222	−	0.516608i	$-0.827194\pi$
$101$	−17.2098			−1.71244			−0.856222	+	0.516608i	$0.827194\pi$
$102$	−0.599919	−	0.435866i	−0.0594008	−	0.0431572i
$103$	4.77063	−	3.46607i	0.470064	−	0.341522i	−0.327402	−	0.944885i	$-0.606173\pi$
$103$	4.77063	−	3.46607i	0.470064	−	0.341522i	0.797466	+	0.603363i	$0.206173\pi$
$104$	−0.978437	−	3.01132i	−0.0959437	−	0.295284i
$105$	0.140156	−	0.431356i	0.0136778	−	0.0420960i
$106$	0.885658	+	0.643468i	0.0860227	+	0.0624992i
$107$	0.139075	+	0.428030i	0.0134449	+	0.0413792i	0.957554	−	0.288254i	$-0.0930748\pi$
$107$	0.139075	+	0.428030i	0.0134449	+	0.0413792i	−0.944109	+	0.329633i	$0.893075\pi$
$108$	7.55683			0.727156
$109$	−20.7169			−1.98432			−0.992162	−	0.124960i	$-0.960120\pi$
$109$	−20.7169			−1.98432			−0.992162	+	0.124960i	$0.960120\pi$
$110$	−0.321467	−	0.989375i	−0.0306507	−	0.0943332i
$111$	2.43067			0.230709
$112$	0.171044	+	0.526420i	0.0161622	+	0.0497420i
$113$	0.511192	−	1.57329i	0.0480889	−	0.148002i	−0.924129	−	0.382081i	$-0.875207\pi$
$113$	0.511192	−	1.57329i	0.0480889	−	0.148002i	0.972218	+	0.234079i	$0.0752074\pi$
$114$	−0.215098	−	0.662005i	−0.0201458	−	0.0620025i
$115$	−12.6021	−	9.15594i	−1.17515	−	0.853795i
$116$	−0.659601	+	2.03004i	−0.0612424	+	0.188485i
$117$	−2.50568	+	7.71169i	−0.231650	+	0.712946i
$118$	−1.00455	+	3.09169i	−0.0924765	+	0.284613i
$119$	−0.520236	+	0.377973i	−0.0476899	+	0.0346488i
$120$	2.35044	−	1.70770i	0.214565	−	0.155891i
$121$	1.00000			0.0909091
$122$	−1.49453	−	1.22694i	−0.135308	−	0.111082i
$123$	−5.81222			−0.524070
$124$	−11.7168	+	8.51273i	−1.05220	+	0.764465i
$125$	−26.0245	+	18.9079i	−2.32770	+	1.69117i
$126$	−0.0290843	+	0.0895122i	−0.00259103	+	0.00797438i
$127$	−1.15632	+	3.55878i	−0.102607	+	0.315790i	−0.989161	−	0.146833i	$-0.953092\pi$
$127$	−1.15632	+	3.55878i	−0.102607	+	0.315790i	0.886555	+	0.462624i	$0.153092\pi$
$128$	−2.26404	+	6.96801i	−0.200115	+	0.615891i
$129$	4.60670	+	3.34696i	0.405597	+	0.294684i
$130$	1.04381	+	3.21252i	0.0915482	+	0.281756i
$131$	2.61181	−	8.03833i	0.228195	−	0.702312i	−0.769757	−	0.638338i	$-0.779622\pi$
$131$	2.61181	−	8.03833i	0.228195	−	0.702312i	0.997952	−	0.0639744i	$-0.0203776\pi$
$132$	0.424793	+	1.30738i	0.0369735	+	0.113793i
$133$	−0.603619			−0.0523404
$134$	−0.793873	−	2.44329i	−0.0685802	−	0.211068i
$135$	−16.3783			−1.40962
$136$	−4.11912			−0.353212
$137$	2.43645	+	7.49863i	0.208160	+	0.640651i	0.999569	+	0.0293638i	$0.00934814\pi$
$137$	2.43645	+	7.49863i	0.208160	+	0.640651i	−0.791409	+	0.611288i	$0.790652\pi$
$138$	−0.526497	−	0.382523i	−0.0448184	−	0.0325625i
$139$	−5.55070	+	17.0833i	−0.470804	+	1.44899i	0.380729	+	0.924687i	$0.375673\pi$
$139$	−5.55070	+	17.0833i	−0.470804	+	1.44899i	−0.851534	+	0.524300i	$0.824327\pi$
$140$	−0.383213	−	1.17941i	−0.0323874	−	0.0996781i
$141$	−6.93721	+	5.04018i	−0.584219	+	0.424460i
$142$	−1.69471	−	1.23128i	−0.142217	−	0.103327i
$143$	−3.24702			−0.271529
$144$	7.34580	−	5.33703i	0.612150	−	0.444753i
$145$	1.42959	−	4.39983i	0.118721	−	0.365386i
$146$	3.13165	+	2.27528i	0.259178	+	0.188304i
$147$	4.00220	+	2.90777i	0.330096	+	0.239829i
$148$	5.37666	−	3.90637i	0.441958	−	0.321102i
$149$	−1.58201	−	4.86894i	−0.129604	−	0.398879i	0.865108	−	0.501585i	$-0.167250\pi$
$149$	−1.58201	−	4.86894i	−0.129604	−	0.398879i	−0.994712	+	0.102707i	$0.967250\pi$
$150$	−1.79737	+	1.30587i	−0.146755	+	0.106624i
$151$	4.97883			0.405171			0.202586	−	0.979265i	$-0.435066\pi$
$151$	4.97883			0.405171			0.202586	+	0.979265i	$0.435066\pi$
$152$	−3.12811	−	2.27271i	−0.253724	−	0.184341i
$153$	8.53405	+	6.20035i	0.689937	+	0.501268i
$154$	−0.0376892			−0.00303708
$155$	25.3944	−	18.4501i	2.03973	−	1.48195i
$156$	−1.37931	−	4.24508i	−0.110433	−	0.339878i
$157$	4.65079	−	3.37900i	0.371174	−	0.269674i	−0.386524	−	0.922279i	$-0.626324\pi$
$157$	4.65079	−	3.37900i	0.371174	−	0.269674i	0.757698	+	0.652606i	$0.226324\pi$
$158$	−2.21669	−	1.61052i	−0.176350	−	0.128126i
$159$	2.53651	+	1.84288i	0.201159	+	0.146150i
$160$	3.70118	−	11.3911i	0.292604	−	0.900543i
$161$	−0.456566	+	0.331715i	−0.0359825	+	0.0261428i
$162$	1.17052			0.0919646
$163$	−3.06983	−	2.23036i	−0.240448	−	0.174696i	0.461035	−	0.887382i	$-0.347478\pi$
$163$	−3.06983	−	2.23036i	−0.240448	−	0.174696i	−0.701483	+	0.712686i	$0.747478\pi$
$164$	−12.8567	+	9.34091i	−1.00394	+	0.729402i
$165$	−0.920678	−	2.83356i	−0.0716747	−	0.220592i
$166$	0.907652	−	2.79347i	0.0704475	−	0.216815i
$167$	12.8035	+	9.30227i	0.990763	+	0.719832i	0.960088	−	0.279698i	$-0.0902343\pi$
$167$	12.8035	+	9.30227i	0.990763	+	0.719832i	0.0306751	+	0.999529i	$0.490234\pi$
$168$	−0.0325264	−	0.100106i	−0.00250947	−	0.00772334i
$169$	−2.45689			−0.188991
$170$	4.39433			0.337030
$171$	3.05985	+	9.41725i	0.233993	+	0.720155i
$172$	15.5690			1.18712
$173$	−5.87742	−	18.0888i	−0.446852	−	1.37527i	−0.880440	−	0.474158i	$-0.842752\pi$
$173$	−5.87742	−	18.0888i	−0.446852	−	1.37527i	0.433587	−	0.901111i	$-0.357248\pi$
$174$	0.0597263	−	0.183819i	0.00452784	−	0.0139353i
$175$	0.595348	+	1.83229i	0.0450041	+	0.138508i
$176$	2.94158	+	2.13718i	0.221730	+	0.161096i
$177$	−2.87702	+	8.85456i	−0.216250	+	0.665549i
$178$	−0.238513	+	0.734068i	−0.0178773	+	0.0550207i
$179$	−4.50938	+	13.8785i	−0.337047	+	1.03732i	0.628658	+	0.777682i	$0.283605\pi$
$179$	−4.50938	+	13.8785i	−0.337047	+	1.03732i	−0.965705	+	0.259642i	$0.916395\pi$
$180$	−16.4577	+	11.9573i	−1.22669	+	0.891241i
$181$	11.0652	−	8.03936i	0.822472	−	0.597561i	−0.0949474	−	0.995482i	$-0.530268\pi$
$181$	11.0652	−	8.03936i	0.822472	−	0.597561i	0.917420	+	0.397921i	$0.130268\pi$
$182$	0.122377			0.00907121
$183$	−4.28031	−	3.51394i	−0.316410	−	0.259758i
$184$	−3.61500			−0.266501
$185$	−11.6531	+	8.46649i	−0.856755	+	0.622469i
$186$	1.06094	−	0.770821i	0.0777922	−	0.0565193i
$187$	−1.30533	+	4.01740i	−0.0954553	+	0.293781i
$188$	−7.24499	+	22.2978i	−0.528396	+	1.62623i
$189$	−0.183364	+	0.564336i	−0.0133378	+	0.0410494i
$190$	3.33711	+	2.42456i	0.242100	+	0.175896i
$191$	1.25450	+	3.86097i	0.0907727	+	0.279370i	0.986129	−	0.165981i	$-0.0530790\pi$
$191$	1.25450	+	3.86097i	0.0907727	+	0.279370i	−0.895356	+	0.445351i	$0.853079\pi$
$192$	−1.43875	+	4.42800i	−0.103832	+	0.319564i
$193$	7.43244	+	22.8747i	0.534999	+	1.64656i	0.743652	+	0.668567i	$0.233092\pi$
$193$	7.43244	+	22.8747i	0.534999	+	1.64656i	−0.208653	+	0.977990i	$0.566908\pi$
$194$	0.935779			0.0671850
$195$	2.98946	+	9.20060i	0.214079	+	0.658869i
$196$	13.5260			0.966143
$197$	11.5768			0.824815			0.412407	−	0.911000i	$-0.364688\pi$
$197$	11.5768			0.824815			0.412407	+	0.911000i	$0.364688\pi$
$198$	0.191053	+	0.588001i	0.0135776	+	0.0417874i
$199$	−5.56578	−	4.04377i	−0.394548	−	0.286656i	0.372769	−	0.927924i	$-0.378408\pi$
$199$	−5.56578	−	4.04377i	−0.394548	−	0.286656i	−0.767316	+	0.641269i	$0.778408\pi$
$200$	−3.81358	+	11.7370i	−0.269661	+	0.829931i
$201$	−2.27364	−	6.99755i	−0.160370	−	0.493569i
$202$	3.44705	−	2.50443i	0.242533	−	0.176211i
$203$	−0.135597	−	0.0985167i	−0.00951702	−	0.00691452i
$204$	−5.80676			−0.406554
$205$	27.8649	−	20.2451i	1.94617	−	1.41398i
$206$	−0.451142	+	1.38847i	−0.0314326	+	0.0967395i
$207$	7.48960	+	5.44152i	0.520563	+	0.378211i
$208$	−9.55134	−	6.93946i	−0.662266	−	0.481165i
$209$	−3.20787	+	2.33065i	−0.221893	+	0.161215i
$210$	0.0346996	+	0.106794i	0.00239450	+	0.00736951i
$211$	−21.0793	+	15.3150i	−1.45116	+	1.05433i	−0.465600	+	0.884995i	$0.654161\pi$
$211$	−21.0793	+	15.3150i	−1.45116	+	1.05433i	−0.985559	+	0.169333i	$0.945839\pi$
$212$	8.57250			0.588762
$213$	−4.85362	−	3.52636i	−0.332565	−	0.241622i
$214$	−0.0901442	−	0.0654936i	−0.00616213	−	0.00447705i
$215$	−33.7436			−2.30129
$216$	−3.07505	+	2.23415i	−0.209230	+	0.152015i
$217$	−0.351419	−	1.08155i	−0.0238558	−	0.0734207i
$218$	4.14950	−	3.01479i	0.281040	−	0.204187i
$219$	8.96901	+	6.51637i	0.606070	+	0.440335i
$220$	−6.59039	−	4.78820i	−0.444324	−	0.322820i
$221$	4.23843	−	13.0446i	0.285108	−	0.877472i
$222$	−0.486852	+	0.353719i	−0.0326754	+	0.0237400i
$223$	3.45518			0.231376			0.115688	−	0.993286i	$-0.463093\pi$
$223$	3.45518			0.231376			0.115688	+	0.993286i	$0.463093\pi$
$224$	−0.351057	−	0.255058i	−0.0234560	−	0.0170418i
$225$	25.5683	−	18.5764i	1.70455	−	1.23843i
$226$	0.126560	+	0.389512i	0.00841865	+	0.0259100i
$227$	−1.91159	+	5.88326i	−0.126876	+	0.390486i	−0.994238	−	0.107192i	$-0.965814\pi$
$227$	−1.91159	+	5.88326i	−0.126876	+	0.390486i	0.867362	+	0.497678i	$0.165814\pi$
$228$	−4.40973	−	3.20385i	−0.292041	−	0.212180i
$229$	−5.08553	−	15.6517i	−0.336062	−	1.03429i	−0.966197	−	0.257806i	$-0.917001\pi$
$229$	−5.08553	−	15.6517i	−0.336062	−	1.03429i	0.630135	−	0.776485i	$-0.282999\pi$
$230$	3.85653			0.254292
$231$	−0.107941			−0.00710201
$232$	−0.331769	−	1.02108i	−0.0217817	−	0.0670372i
$233$	−26.9452			−1.76524			−0.882620	−	0.470088i	$-0.844222\pi$
$233$	−26.9452			−1.76524			−0.882620	+	0.470088i	$0.844222\pi$
$234$	−0.620353	−	1.90925i	−0.0405537	−	0.124811i
$235$	15.7025	−	48.3273i	1.02432	−	3.15252i
$236$	7.86631	+	24.2100i	0.512053	+	1.57594i
$237$	−6.34856	−	4.61250i	−0.412383	−	0.299614i
$238$	0.0491969	−	0.151412i	0.00318896	−	0.00981461i
$239$	−2.72173	+	8.37663i	−0.176054	+	0.541839i	−0.999680	−	0.0252944i	$-0.991948\pi$
$239$	−2.72173	+	8.37663i	−0.176054	+	0.541839i	0.823626	+	0.567134i	$0.191948\pi$
$240$	3.34757	−	10.3028i	0.216085	−	0.665041i
$241$	11.7533	−	8.53925i	0.757094	−	0.550061i	−0.140923	−	0.990020i	$-0.545007\pi$
$241$	11.7533	−	8.53925i	0.757094	−	0.550061i	0.898018	+	0.439959i	$0.145007\pi$
$242$	−0.200295	+	0.145523i	−0.0128755	+	0.00935457i
$243$	15.0460			0.965199
$244$	−15.1154	−	0.893899i	−0.967662	−	0.0572260i
$245$	−29.3157			−1.87291
$246$	1.16416	−	0.845811i	0.0742241	−	0.0539270i
$247$	10.4160	−	7.56766i	0.662754	−	0.481519i
$248$	2.25106	−	6.92805i	0.142942	−	0.439931i
$249$	2.59950	−	8.00045i	0.164737	−	0.507008i
$250$	2.46104	−	7.57432i	0.155650	−	0.479042i
$251$	3.38323	+	2.45806i	0.213548	+	0.155151i	0.689417	−	0.724364i	$-0.257867\pi$
$251$	3.38323	+	2.45806i	0.213548	+	0.155151i	−0.475870	+	0.879516i	$0.657867\pi$
$252$	0.227749	+	0.700940i	0.0143469	+	0.0441551i
$253$	−1.14558	+	3.52573i	−0.0720218	+	0.221660i
$254$	−0.286279	−	0.881077i	−0.0179628	−	0.0552837i
$255$	12.5853			0.788123
$256$	3.49764	+	10.7646i	0.218603	+	0.672790i
$257$	11.4480			0.714109			0.357055	−	0.934084i	$-0.383781\pi$
$257$	11.4480			0.714109			0.357055	+	0.934084i	$0.383781\pi$
$258$	−1.40976			−0.0877678
$259$	0.161261	+	0.496310i	0.0100203	+	0.0308392i
$260$	21.3991	+	15.5474i	1.32712	+	0.964207i
$261$	−0.849628	+	2.61489i	−0.0525906	+	0.161857i
$262$	0.646628	+	1.99012i	0.0399488	+	0.122950i
$263$	6.03019	−	4.38119i	0.371838	−	0.270156i	−0.386135	−	0.922442i	$-0.626190\pi$
$263$	6.03019	−	4.38119i	0.371838	−	0.270156i	0.757973	+	0.652286i	$0.226190\pi$
$264$	−0.559381	−	0.406414i	−0.0344275	−	0.0250130i
$265$	−18.5797			−1.14134
$266$	0.120902	−	0.0878404i	0.00741297	−	0.00538584i
$267$	−0.683098	+	2.10236i	−0.0418049	+	0.128662i
$268$	−16.2752	−	11.8246i	−0.994164	−	0.722303i
$269$	−5.73566	−	4.16720i	−0.349709	−	0.254079i	0.399038	−	0.916935i	$-0.369344\pi$
$269$	−5.73566	−	4.16720i	−0.349709	−	0.254079i	−0.748747	+	0.662856i	$0.769344\pi$
$270$	3.28050	−	2.38342i	0.199645	−	0.145050i
$271$	−3.17791	−	9.78060i	−0.193044	−	0.594129i	−0.999994	−	0.00350888i	$-0.998883\pi$
$271$	−3.17791	−	9.78060i	−0.193044	−	0.594129i	0.806950	−	0.590620i	$-0.201117\pi$
$272$	−12.4256	+	9.02775i	−0.753414	+	0.547388i
$273$	0.350487			0.0212124
$274$	−1.57923	−	1.14738i	−0.0954050	−	0.0693158i
$275$	10.2386	+	7.43881i	0.617413	+	0.448577i
$276$	−5.09609			−0.306749
$277$	2.45987	−	1.78720i	0.147799	−	0.107382i	−0.511428	−	0.859326i	$-0.670883\pi$
$277$	2.45987	−	1.78720i	0.147799	−	0.107382i	0.659227	+	0.751944i	$0.270883\pi$
$278$	−1.37423	−	4.22946i	−0.0824211	−	0.253666i
$279$	−15.0923	+	10.9652i	−0.903551	+	0.656469i
$280$	0.504626	+	0.366632i	0.0301572	+	0.0219105i
$281$	8.23275	+	5.98144i	0.491124	+	0.356823i	0.805617	−	0.592437i	$-0.201834\pi$
$281$	8.23275	+	5.98144i	0.491124	+	0.356823i	−0.314492	+	0.949260i	$0.601834\pi$
$282$	0.656028	−	2.01905i	0.0390659	−	0.120233i
$283$	−2.38180	+	1.73048i	−0.141583	+	0.102866i	−0.656322	−	0.754481i	$-0.727889\pi$
$283$	−2.38180	+	1.73048i	−0.141583	+	0.102866i	0.514739	+	0.857347i	$0.327889\pi$
$284$	−16.4035			−0.973368
$285$	9.55744	+	6.94389i	0.566134	+	0.411321i
$286$	0.650361	−	0.472515i	0.0384567	−	0.0279404i
$287$	−0.385607	−	1.18678i	−0.0227617	−	0.0700532i
$288$	−2.19967	+	6.76989i	−0.129617	+	0.398920i
$289$	−0.682301	−	0.495720i	−0.0401353	−	0.0291600i
$290$	0.353936	+	1.08930i	0.0207838	+	0.0639660i
$291$	2.68006			0.157108
$292$	30.3120			1.77388
$293$	8.14710	+	25.0742i	0.475958	+	1.46485i	0.844661	+	0.535302i	$0.179802\pi$
$293$	8.14710	+	25.0742i	0.475958	+	1.46485i	−0.368702	+	0.929548i	$0.620198\pi$
$294$	−1.22477			−0.0714300
$295$	−17.0491	−	52.4717i	−0.992637	−	3.05502i
$296$	−1.03298	+	3.17918i	−0.0600407	+	0.184786i
$297$	1.20451	+	3.70710i	0.0698927	+	0.215108i
$298$	1.02541	+	0.745005i	0.0594005	+	0.0431570i
$299$	3.71971	−	11.4481i	0.215116	−	0.662060i
$300$	−5.37604	+	16.5457i	−0.310386	+	0.955269i
$301$	−0.377777	+	1.16268i	−0.0217747	+	0.0670156i
$302$	−0.997235	+	0.724534i	−0.0573844	+	0.0416922i
$303$	9.87230	−	7.17264i	0.567149	−	0.412058i
$304$	−14.4172			−0.826883
$305$	32.7604	+	1.93740i	1.87585	+	0.110935i
$306$	−2.61162			−0.149296
$307$	−0.00195509	+	0.00142046i	−0.000111583	+	8.10697e-5i	−0.587841	−	0.808976i	$-0.700022\pi$
$307$	−0.00195509	+	0.00142046i	−0.000111583	+	8.10697e-5i	0.587729	+	0.809058i	$0.300022\pi$
$308$	−0.238766	+	0.173474i	−0.0136050	+	0.00988460i
$309$	−1.29206	+	3.97657i	−0.0735030	+	0.226219i
$310$	−2.40146	+	7.39093i	−0.136394	+	0.419777i
$311$	−2.55220	+	7.85486i	−0.144722	+	0.445408i	−0.996975	−	0.0777212i	$-0.975236\pi$
$311$	−2.55220	+	7.85486i	−0.144722	+	0.445408i	0.852253	+	0.523130i	$0.175236\pi$
$312$	1.81632	+	1.31963i	0.102829	+	0.0747095i
$313$	−1.19724	−	3.68471i	−0.0676718	−	0.208272i	0.911502	−	0.411295i	$-0.134923\pi$
$313$	−1.19724	−	3.68471i	−0.0676718	−	0.208272i	−0.979174	+	0.203023i	$0.934923\pi$
$314$	−0.439810	+	1.35359i	−0.0248199	+	0.0763878i
$315$	−0.493614	−	1.51919i	−0.0278120	−	0.0855965i
$316$	−21.4558			−1.20699
$317$	0.903892	+	2.78189i	0.0507676	+	0.156247i	0.973226	−	0.229849i	$-0.0738233\pi$
$317$	0.903892	+	2.78189i	0.0507676	+	0.156247i	−0.922459	+	0.386096i	$0.873823\pi$
$318$	−0.776233			−0.0435290
$319$	−1.10100			−0.0616442
$320$	−8.52594	−	26.2401i	−0.476615	−	1.46687i
$321$	−0.258172	−	0.187573i	−0.0144097	−	0.0104693i
$322$	0.0431759	−	0.132882i	0.00240610	−	0.00740521i
$323$	−5.17582	−	15.9295i	−0.287991	−	0.886344i
$324$	7.41540	−	5.38761i	0.411967	−	0.299311i
$325$	−33.2450	−	24.1539i	−1.84410	−	1.33982i
$326$	0.939442			0.0520309
$327$	11.8841	−	8.63432i	0.657193	−	0.477479i
$328$	2.47006	−	7.60206i	0.136386	−	0.419753i
$329$	−1.48938	−	1.08210i	−0.0821122	−	0.0596580i
$330$	0.596755	+	0.433568i	0.0328503	+	0.0238671i
$331$	−9.78063	+	7.10605i	−0.537592	+	0.390584i	−0.823190	−	0.567766i	$-0.807808\pi$
$331$	−9.78063	+	7.10605i	−0.537592	+	0.390584i	0.285598	+	0.958350i	$0.407808\pi$
$332$	−7.10752	−	21.8747i	−0.390076	−	1.20053i
$333$	6.92563	−	5.03177i	0.379522	−	0.275739i
$334$	−3.91817			−0.214393
$335$	35.2741	+	25.6281i	1.92723	+	1.40021i
$336$	−0.317517	−	0.230690i	−0.0173220	−	0.0125852i
$337$	20.0389			1.09159			0.545794	−	0.837919i	$-0.316228\pi$
$337$	20.0389			1.09159			0.545794	+	0.837919i	$0.316228\pi$
$338$	0.492103	−	0.357534i	0.0267669	−	0.0194473i
$339$	0.362466	+	1.11556i	0.0196865	+	0.0605887i
$340$	27.8387	−	20.2260i	1.50977	−	1.09691i
$341$	−6.04360	−	4.39093i	−0.327279	−	0.237782i
$342$	−1.98330	−	1.44095i	−0.107245	−	0.0779177i
$343$	−0.657499	+	2.02357i	−0.0355016	+	0.109263i
$344$	−6.33538	+	4.60292i	−0.341581	+	0.248173i
$345$	11.0450			0.594645
$346$	3.80956	+	2.76781i	0.204803	+	0.148798i
$347$	−20.1231	+	14.6203i	−1.08026	+	0.784858i	−0.977729	−	0.209871i	$-0.932696\pi$
$347$	−20.1231	+	14.6203i	−1.08026	+	0.784858i	−0.102536	+	0.994729i	$0.532696\pi$
$348$	−0.467697	−	1.43942i	−0.0250712	−	0.0771612i
$349$	−3.45818	+	10.6432i	−0.185112	+	0.569717i	−0.999950	−	0.00997160i	$-0.996826\pi$
$349$	−3.45818	+	10.6432i	−0.185112	+	0.569717i	0.814838	+	0.579689i	$0.196826\pi$
$350$	−0.385886	−	0.280363i	−0.0206265	−	0.0149860i
$351$	−3.91106	−	12.0370i	−0.208757	−	0.642488i
$352$	−2.85047			−0.151930
$353$	33.3409			1.77456			0.887280	−	0.461232i	$-0.152592\pi$
$353$	33.3409			1.77456			0.887280	+	0.461232i	$0.152592\pi$
$354$	−0.712288	−	2.19220i	−0.0378577	−	0.116514i
$355$	35.5522			1.88692
$356$	1.86772	+	5.74824i	0.0989888	+	0.304656i
$357$	0.140899	−	0.433643i	0.00745717	−	0.0229508i
$358$	−1.11643	−	3.43601i	−0.0590050	−	0.181599i
$359$	6.15510	+	4.47194i	0.324854	+	0.236020i	0.738244	−	0.674534i	$-0.235655\pi$
$359$	6.15510	+	4.47194i	0.324854	+	0.236020i	−0.413390	+	0.910554i	$0.635655\pi$
$360$	3.16191	−	9.73136i	0.166647	−	0.512888i
$361$	−1.01285	+	3.11723i	−0.0533079	+	0.164065i
$362$	−1.04640	+	3.22049i	−0.0549976	+	0.169265i
$363$	−0.573642	+	0.416776i	−0.0301084	+	0.0218750i
$364$	0.775278	−	0.563273i	0.0406356	−	0.0295235i
$365$	−65.6970			−3.43874
$366$	1.36868	+	0.0809419i	0.0715422	+	0.00423090i
$367$	31.1362			1.62530			0.812648	−	0.582755i	$-0.198025\pi$
$367$	31.1362			1.62530			0.812648	+	0.582755i	$0.198025\pi$
$368$	−10.9049	+	7.92288i	−0.568458	+	0.413009i
$369$	−16.5606	+	12.0320i	−0.862109	+	0.626359i
$370$	1.10200	−	3.39159i	0.0572900	−	0.176321i
$371$	−0.208009	+	0.640186i	−0.0107993	+	0.0332368i
$372$	3.17334	−	9.76652i	0.164530	−	0.506371i
$373$	24.6771	+	17.9290i	1.27773	+	0.928328i	0.999482	−	0.0321799i	$-0.0102449\pi$
$373$	24.6771	+	17.9290i	1.27773	+	0.928328i	0.278252	+	0.960508i	$0.410245\pi$
$374$	−0.323172	−	0.994621i	−0.0167108	−	0.0514306i
$375$	7.04839	−	21.6927i	0.363978	−	1.12021i
$376$	−3.64412	−	11.2154i	−0.187931	−	0.578392i
$377$	3.57496			0.184120
$378$	−0.0453970	−	0.139717i	−0.00233497	−	0.00718629i
$379$	30.0773			1.54497			0.772484	−	0.635034i	$-0.219014\pi$
$379$	30.0773			1.54497			0.772484	+	0.635034i	$0.219014\pi$
$380$	32.3007			1.65699
$381$	−0.819899	−	2.52339i	−0.0420047	−	0.129277i
$382$	−0.813130	−	0.590774i	−0.0416034	−	0.0302266i
$383$	−1.39965	+	4.30767i	−0.0715187	+	0.220112i	−0.980427	−	0.196885i	$-0.936917\pi$
$383$	−1.39965	+	4.30767i	−0.0715187	+	0.220112i	0.908908	+	0.416997i	$0.136917\pi$
$384$	−1.60535	−	4.94074i	−0.0819224	−	0.252131i
$385$	0.517492	−	0.375980i	0.0263738	−	0.0191617i
$386$	−4.81747	−	3.50010i	−0.245203	−	0.178150i
$387$	20.0543			1.01942
$388$	5.92830	−	4.30716i	0.300964	−	0.218663i
$389$	−2.00243	+	6.16285i	−0.101527	+	0.312469i	−0.988900	−	0.148584i	$-0.952528\pi$
$389$	−2.00243	+	6.16285i	−0.101527	+	0.312469i	0.887372	+	0.461053i	$0.152528\pi$
$390$	−1.93767	−	1.40780i	−0.0981178	−	0.0712868i
$391$	−12.6689	−	9.20448i	−0.640693	−	0.465491i
$392$	−5.50404	+	3.99892i	−0.277996	+	0.201976i
$393$	1.85193	+	5.69966i	0.0934177	+	0.287510i
$394$	−2.31878	+	1.68469i	−0.116819	+	0.0848736i
$395$	46.5024			2.33979
$396$	3.91677	+	2.84570i	0.196825	+	0.143002i
$397$	5.22402	+	3.79547i	0.262186	+	0.190489i	0.711110	−	0.703081i	$-0.248193\pi$
$397$	5.22402	+	3.79547i	0.262186	+	0.190489i	−0.448924	+	0.893570i	$0.648193\pi$
$398$	1.70326			0.0853767
$399$	0.346261	−	0.251573i	0.0173347	−	0.0125944i
$400$	14.2197	+	43.7636i	0.710983	+	2.18818i
$401$	−7.04437	+	5.11804i	−0.351779	+	0.255583i	−0.749615	−	0.661874i	$-0.769761\pi$
$401$	−7.04437	+	5.11804i	−0.351779	+	0.255583i	0.397836	+	0.917457i	$0.369761\pi$
$402$	1.47370	+	1.07071i	0.0735016	+	0.0534021i
$403$	19.6237	+	14.2574i	0.977525	+	0.710213i
$404$	10.3103	−	31.7318i	0.512956	−	1.57872i
$405$	−16.0718	+	11.6769i	−0.798615	+	0.580228i
$406$	0.0414958			0.00205940
$407$	2.77332	+	2.01494i	0.137469	+	0.0998767i
$408$	2.36290	−	1.71675i	0.116981	−	0.0849918i
$409$	3.47387	+	10.6915i	0.171772	+	0.528660i	0.999471	−	0.0325121i	$-0.0103508\pi$
$409$	3.47387	+	10.6915i	0.171772	+	0.528660i	−0.827699	+	0.561172i	$0.810351\pi$
$410$	−2.63509	+	8.10998i	−0.130138	+	0.400523i
$411$	−4.52290	−	3.28608i	−0.223098	−	0.162090i
$412$	3.53275	+	10.8727i	0.174046	+	0.535658i
$413$	−1.99885			−0.0983572
$414$	−2.29200			−0.112645
$415$	15.4045	+	47.4103i	0.756179	+	2.32728i
$416$	9.25552			0.453789
$417$	−3.93578	−	12.1131i	−0.192736	−	0.593181i
$418$	0.303357	−	0.933636i	0.0148377	−	0.0456656i
$419$	−2.52160	−	7.76068i	−0.123188	−	0.379134i	0.870378	−	0.492383i	$-0.163874\pi$
$419$	−2.52160	−	7.76068i	−0.123188	−	0.379134i	−0.993567	+	0.113249i	$0.963874\pi$
$420$	0.711375	+	0.516844i	0.0347116	+	0.0252194i
$421$	1.80252	−	5.54759i	0.0878495	−	0.270373i	−0.897475	−	0.441066i	$-0.854601\pi$
$421$	1.80252	−	5.54759i	0.0878495	−	0.270373i	0.985324	+	0.170693i	$0.0546006\pi$
$422$	1.99340	−	6.13504i	0.0970370	−	0.298649i
$423$	−9.33223	+	28.7216i	−0.453748	+	1.39649i
$424$	−3.48835	+	2.53443i	−0.169409	+	0.123083i
$425$	−43.2495	+	31.4226i	−2.09791	+	1.52422i
$426$	1.48532			0.0719641
$427$	0.433525	−	1.10711i	0.0209797	−	0.0535768i
$428$	−0.872527			−0.0421752
$429$	1.86263	−	1.35328i	0.0899284	−	0.0653368i
$430$	6.75867	−	4.91046i	0.325932	−	0.236803i
$431$	−1.05546	+	3.24838i	−0.0508398	+	0.156469i	−0.973253	−	0.229735i	$-0.926214\pi$
$431$	−1.05546	+	3.24838i	−0.0508398	+	0.156469i	0.922413	+	0.386204i	$0.126214\pi$
$432$	−4.37958	+	13.4790i	−0.210713	+	0.648507i
$433$	−4.82193	+	14.8404i	−0.231727	+	0.713183i	0.765812	+	0.643065i	$0.222338\pi$
$433$	−4.82193	+	14.8404i	−0.231727	+	0.713183i	−0.997539	+	0.0701179i	$0.977662\pi$
$434$	0.227778	+	0.165491i	0.0109337	+	0.00794381i
$435$	1.01367	+	3.11974i	0.0486016	+	0.149580i
$436$	12.4114	−	38.1983i	0.594397	−	1.82937i
$437$	−4.54238	−	13.9800i	−0.217291	−	0.668754i
$438$	−2.74473			−0.131148
$439$	−5.00202	−	15.3946i	−0.238733	−	0.734746i	−0.996604	−	0.0823411i	$-0.973760\pi$
$439$	−5.00202	−	15.3946i	−0.238733	−	0.734746i	0.757871	−	0.652405i	$-0.226240\pi$
$440$	4.09740			0.195336
$441$	17.4228			0.829655
$442$	1.04934	+	3.22955i	0.0499122	+	0.153614i
$443$	−15.7827	−	11.4668i	−0.749857	−	0.544803i	0.145926	−	0.989296i	$-0.453384\pi$
$443$	−15.7827	−	11.4668i	−0.749857	−	0.544803i	−0.895782	+	0.444493i	$0.853384\pi$
$444$	−1.45620	+	4.48172i	−0.0691081	+	0.212693i
$445$	−4.04801	−	12.4585i	−0.191894	−	0.590589i
$446$	−0.692056	+	0.502808i	−0.0327698	+	0.0238086i
$447$	2.93676	+	2.13368i	0.138904	+	0.100920i
$448$	−0.999590			−0.0472262
$449$	20.5425	−	14.9250i	0.969463	−	0.704356i	0.0141335	−	0.999900i	$-0.495501\pi$
$449$	20.5425	−	14.9250i	0.969463	−	0.704356i	0.955329	+	0.295544i	$0.0955010\pi$
$450$	−2.41790	+	7.44154i	−0.113981	+	0.350798i
$451$	−6.63157	−	4.81812i	−0.312268	−	0.226876i
$452$	2.59460	+	1.88509i	0.122040	+	0.0886672i
$453$	−2.85607	+	2.07505i	−0.134190	+	0.0974945i
$454$	−0.473268	−	1.45657i	−0.0222115	−	0.0683601i
$455$	−1.68030	+	1.22081i	−0.0787739	+	0.0572326i
$456$	2.74163			0.128388
$457$	−13.3025	−	9.66482i	−0.622264	−	0.452101i	0.231447	−	0.972847i	$-0.425654\pi$
$457$	−13.3025	−	9.66482i	−0.622264	−	0.452101i	−0.853712	+	0.520746i	$0.825654\pi$
$458$	3.29628	+	2.39489i	0.154025	+	0.111906i
$459$	−16.4652			−0.768528
$460$	24.4317	−	17.7507i	1.13913	−	0.827629i
$461$	−4.63616	−	14.2686i	−0.215927	−	0.664556i	−0.999086	−	0.0427348i	$-0.986393\pi$
$461$	−4.63616	−	14.2686i	−0.215927	−	0.664556i	0.783159	−	0.621821i	$-0.213607\pi$
$462$	0.0216201	−	0.0157079i	0.00100586	−	0.000730799i
$463$	−13.5011	−	9.80913i	−0.627450	−	0.455869i	0.228066	−	0.973646i	$-0.426760\pi$
$463$	−13.5011	−	9.80913i	−0.627450	−	0.455869i	−0.855516	+	0.517777i	$0.826760\pi$
$464$	−3.23867	−	2.35303i	−0.150352	−	0.109237i
$465$	−6.87775	+	21.1675i	−0.318948	+	0.981621i
$466$	5.39699	−	3.92115i	0.250011	−	0.181644i
$467$	10.0310			0.464181			0.232091	−	0.972694i	$-0.425443\pi$
$467$	10.0310			0.464181			0.232091	+	0.972694i	$0.425443\pi$
$468$	−12.7178	−	9.24004i	−0.587882	−	0.427121i
$469$	1.27796	−	0.928493i	0.0590108	−	0.0428738i
$470$	3.88760	+	11.9648i	0.179321	+	0.551894i
$471$	−1.25961	+	3.87668i	−0.0580397	+	0.178628i
$472$	−10.3586	−	7.52596i	−0.476793	−	0.346410i
$473$	2.48160	+	7.63757i	0.114104	+	0.351176i
$474$	1.94281			0.0892362
$475$	−50.1815			−2.30248
$476$	−0.385245	−	1.18566i	−0.0176577	−	0.0543447i
$477$	11.0422			0.505587
$478$	−0.673842	−	2.07387i	−0.0308208	−	0.0948567i
$479$	7.02497	−	21.6206i	0.320979	−	0.987872i	−0.652244	−	0.758009i	$-0.726172\pi$
$479$	7.02497	−	21.6206i	0.320979	−	0.987872i	0.973223	−	0.229863i	$-0.0738278\pi$
$480$	2.62436	+	8.07696i	0.119785	+	0.368661i
$481$	−9.00502	−	6.54253i	−0.410594	−	0.298314i
$482$	−1.11147	+	3.42074i	−0.0506259	+	0.155810i
$483$	0.123655	−	0.380571i	0.00562650	−	0.0173166i
$484$	−0.599093	+	1.84382i	−0.0272315	+	0.0838099i
$485$	−12.8487	+	9.33515i	−0.583431	+	0.423887i
$486$	−3.01363	+	2.18953i	−0.136701	+	0.0993192i
$487$	3.73495			0.169247			0.0846234	−	0.996413i	$-0.473031\pi$
$487$	3.73495			0.169247			0.0846234	+	0.996413i	$0.473031\pi$
$488$	6.41507	−	4.10506i	0.290396	−	0.185827i
$489$	2.69055			0.121671
$490$	5.87179	−	4.26610i	0.265260	−	0.192723i
$491$	13.9692	−	10.1492i	0.630423	−	0.458029i	−0.226124	−	0.974099i	$-0.572605\pi$
$491$	13.9692	−	10.1492i	0.630423	−	0.458029i	0.856547	+	0.516069i	$0.172605\pi$
$492$	3.48206	−	10.7167i	0.156983	−	0.483145i
$493$	1.43717	−	4.42315i	0.0647269	−	0.199209i
$494$	−0.985004	+	3.03153i	−0.0443174	+	0.136395i
$495$	−8.48904	−	6.16765i	−0.381554	−	0.277215i
$496$	−8.39350	−	25.8325i	−0.376879	−	1.15991i
$497$	0.398026	−	1.22500i	0.0178539	−	0.0549486i
$498$	0.643581	+	1.98074i	0.0288395	+	0.0887590i
$499$	−18.5139			−0.828794			−0.414397	−	0.910096i	$-0.636008\pi$
$499$	−18.5139			−0.828794			−0.414397	+	0.910096i	$0.636008\pi$
$500$	−19.2716	−	59.3120i	−0.861853	−	2.65251i
$501$	−11.2216			−0.501343
$502$	−1.03535			−0.0462099
$503$	1.10352	+	3.39627i	0.0492033	+	0.151432i	0.972639	−	0.232320i	$-0.0746317\pi$
$503$	1.10352	+	3.39627i	0.0492033	+	0.151432i	−0.923436	+	0.383752i	$0.874632\pi$
$504$	−0.299907	−	0.217895i	−0.0133589	−	0.00970583i
$505$	−22.3461	+	68.7741i	−0.994387	+	3.06041i
$506$	−0.283620	−	0.872893i	−0.0126085	−	0.0388048i
$507$	1.40938	−	1.02397i	0.0625925	−	0.0454761i
$508$	−5.86900	−	4.26408i	−0.260395	−	0.189188i
$509$	−14.7422			−0.653436			−0.326718	−	0.945122i	$-0.605943\pi$
$509$	−14.7422			−0.653436			−0.326718	+	0.945122i	$0.605943\pi$
$510$	−2.52078	+	1.83145i	−0.111622	+	0.0810980i
$511$	−0.735512	+	2.26367i	−0.0325371	+	0.100139i
$512$	−14.1218	−	10.2601i	−0.624099	−	0.453435i
$513$	−12.5039	−	9.08458i	−0.552059	−	0.401094i
$514$	−2.29299	+	1.66595i	−0.101139	+	0.0734820i
$515$	−7.65672	−	23.5650i	−0.337395	−	1.03840i
$516$	−8.93104	+	6.48878i	−0.393167	+	0.285652i
$517$	−12.0933			−0.531862
$518$	−0.104524	−	0.0759413i	−0.00459253	−	0.00333667i
$519$	10.9105	+	7.92696i	0.478919	+	0.347955i
$520$	−13.3043			−0.583433
$521$	26.6211	−	19.3414i	1.16629	−	0.847361i	0.175732	−	0.984438i	$-0.443771\pi$
$521$	26.6211	−	19.3414i	1.16629	−	0.847361i	0.990560	+	0.137077i	$0.0437706\pi$
$522$	−0.210349	−	0.647389i	−0.00920675	−	0.0283355i
$523$	−0.973598	+	0.707360i	−0.0425725	+	0.0309307i	−0.608868	−	0.793272i	$-0.708376\pi$
$523$	−0.973598	+	0.707360i	−0.0425725	+	0.0309307i	0.566296	+	0.824202i	$0.308376\pi$
$524$	13.2565	+	9.63141i	0.579113	+	0.420750i
$525$	−1.10517	−	0.802954i	−0.0482337	−	0.0350438i
$526$	−0.570255	+	1.75506i	−0.0248643	+	0.0765244i
$527$	25.5290	−	18.5479i	1.11206	−	0.807961i
$528$	−2.57814			−0.112199
$529$	7.48900	+	5.44108i	0.325609	+	0.236569i
$530$	3.72142	−	2.70377i	0.161648	−	0.117444i
$531$	10.1325	+	31.1848i	0.439715	+	1.35330i
$532$	0.361624	−	1.11296i	0.0156784	−	0.0482531i
$533$	21.5328	+	15.6445i	0.932689	+	0.677638i
$534$	−0.169120	−	0.520499i	−0.00731855	−	0.0225242i
$535$	1.89108			0.0817584
$536$	10.1186			0.437059
$537$	−3.19743	−	9.84067i	−0.137979	−	0.424656i
$538$	1.75525			0.0756741
$539$	2.15596	+	6.63536i	0.0928637	+	0.285805i
$540$	9.81214	−	30.1987i	0.422247	−	1.29954i
$541$	−1.99148	−	6.12915i	−0.0856205	−	0.263513i	0.899076	−	0.437794i	$-0.144240\pi$
$541$	−1.99148	−	6.12915i	−0.0856205	−	0.263513i	−0.984696	+	0.174281i	$0.944240\pi$
$542$	2.05982	+	1.49655i	0.0884769	+	0.0642823i
$543$	−2.99688	+	9.22344i	−0.128608	+	0.395816i
$544$	3.72081	−	11.4515i	0.159528	−	0.490977i
$545$	−26.8999	+	82.7893i	−1.15226	+	3.54630i
$546$	−0.0702008	+	0.0510039i	−0.00300432	+	0.00218277i
$547$	−30.9185	+	22.4636i	−1.32198	+	0.960473i	−0.322072	+	0.946715i	$0.604379\pi$
$547$	−30.9185	+	22.4636i	−1.32198	+	0.960473i	−0.999905	+	0.0137579i	$0.995621\pi$
$548$	−15.2858			−0.652976
$549$	−19.4700	−	1.15143i	−0.830959	−	0.0491417i
$550$	−3.13327			−0.133603
$551$	3.53186	−	2.56605i	0.150462	−	0.109317i
$552$	2.07372	−	1.50664i	0.0882633	−	0.0641270i
$553$	0.520619	−	1.60230i	0.0221390	−	0.0681368i
$554$	−0.232621	+	0.715934i	−0.00988313	+	0.0304171i
$555$	3.15610	−	9.71348i	0.133969	−	0.412314i
$556$	−28.1731	−	20.4690i	−1.19481	−	0.868077i
$557$	−5.06508	−	15.5887i	−0.214614	−	0.660515i	−0.999181	−	0.0404702i	$-0.987114\pi$
$557$	−5.06508	−	15.5887i	−0.214614	−	0.660515i	0.784566	−	0.620045i	$-0.212886\pi$
$558$	1.42723	−	4.39255i	0.0604193	−	0.185951i
$559$	−8.05779	−	24.7993i	−0.340808	−	1.04890i
$560$	2.32578			0.0982820
$561$	−0.925559	−	2.84858i	−0.0390772	−	0.120267i
$562$	−2.51942			−0.106275
$563$	11.6334			0.490289			0.245145	−	0.969487i	$-0.421165\pi$
$563$	11.6334			0.490289			0.245145	+	0.969487i	$0.421165\pi$
$564$	−5.13714	−	15.8105i	−0.216313	−	0.665742i
$565$	−5.62343	−	4.08566i	−0.236580	−	0.171885i
$566$	0.225238	−	0.693213i	0.00946748	−	0.0291379i
$567$	0.222409	+	0.684504i	0.00934029	+	0.0287464i
$568$	6.67496	−	4.84964i	0.280075	−	0.203486i
$569$	−8.04660	−	5.84620i	−0.337331	−	0.245085i	0.406204	−	0.913783i	$-0.366852\pi$
$569$	−8.04660	−	5.84620i	−0.337331	−	0.245085i	−0.743535	+	0.668697i	$0.766852\pi$
$570$	−2.92480			−0.122507
$571$	−7.43741	+	5.40360i	−0.311246	+	0.226133i	−0.732431	−	0.680841i	$-0.761614\pi$
$571$	−7.43741	+	5.40360i	−0.311246	+	0.226133i	0.421185	+	0.906975i	$0.361614\pi$
$572$	1.94526	−	5.98691i	0.0813356	−	0.250325i
$573$	−2.32879	−	1.69197i	−0.0972867	−	0.0706829i
$574$	0.249938	+	0.181591i	0.0104322	+	0.00757946i
$575$	−37.9564	+	27.5769i	−1.58289	+	1.15004i
$576$	5.06710	+	15.5949i	0.211129	+	0.649789i
$577$	−15.9713	+	11.6038i	−0.664892	+	0.483072i	−0.868312	−	0.496019i	$-0.834795\pi$
$577$	−15.9713	+	11.6038i	−0.664892	+	0.483072i	0.203419	+	0.979092i	$0.434795\pi$
$578$	0.208800			0.00868494
$579$	−13.7972	−	10.0242i	−0.573391	−	0.416593i
$580$	7.25602	+	5.27181i	0.301290	+	0.218900i
$581$	1.80604			0.0749273
$582$	−0.536802	+	0.390010i	−0.0222512	+	0.0161664i
$583$	1.36640	+	4.20535i	0.0565905	+	0.174168i
$584$	−12.3347	+	8.96166i	−0.510412	+	0.370836i
$585$	27.5640	+	20.0265i	1.13963	+	0.827992i
$586$	−5.28069	−	3.83665i	−0.218143	−	0.158490i
$587$	8.76765	−	26.9841i	0.361880	−	1.11375i	−0.590032	−	0.807380i	$-0.700885\pi$
$587$	8.76765	−	26.9841i	0.361880	−	1.11375i	0.951912	−	0.306371i	$-0.0991149\pi$
$588$	−7.75909	+	5.63731i	−0.319979	+	0.232479i
$589$	29.6208			1.22050
$590$	11.0507	+	8.02880i	0.454950	+	0.330540i
$591$	−6.64096	+	4.82494i	−0.273172	+	0.198471i
$592$	3.85166	+	11.8542i	0.158302	+	0.487204i
$593$	0.580315	−	1.78603i	0.0238307	−	0.0733433i	−0.938434	−	0.345459i	$-0.887723\pi$
$593$	0.580315	−	1.78603i	0.0238307	−	0.0733433i	0.962265	+	0.272116i	$0.0877233\pi$
$594$	−0.780725	−	0.567230i	−0.0320335	−	0.0232737i
$595$	0.834962	+	2.56975i	0.0342301	+	0.105349i
$596$	9.92521			0.406552
$597$	4.87811			0.199648
$598$	0.920920	+	2.83430i	0.0376592	+	0.115903i
$599$	−19.5785			−0.799955			−0.399978	−	0.916525i	$-0.630982\pi$
$599$	−19.5785			−0.799955			−0.399978	+	0.916525i	$0.630982\pi$
$600$	−2.70406	−	8.32225i	−0.110393	−	0.339754i
$601$	−5.72881	+	17.6315i	−0.233683	+	0.719203i	0.763610	+	0.645678i	$0.223425\pi$
$601$	−5.72881	+	17.6315i	−0.233683	+	0.719203i	−0.997293	+	0.0735253i	$0.976575\pi$
$602$	−0.0935294	−	0.287854i	−0.00381197	−	0.0117320i
$603$	−20.9639	−	15.2312i	−0.853717	−	0.620262i
$604$	−2.98278	+	9.18005i	−0.121368	+	0.373531i
$605$	1.29845	−	3.99621i	0.0527894	−	0.162469i
$606$	−0.933589	+	2.87329i	−0.0379245	+	0.116719i
$607$	−27.1913	+	19.7556i	−1.10366	+	0.801857i	−0.981654	−	0.190672i	$-0.938933\pi$
$607$	−27.1913	+	19.7556i	−1.10366	+	0.801857i	−0.122008	+	0.992529i	$0.538933\pi$
$608$	9.14392	−	6.64345i	0.370835	−	0.269427i
$609$	0.118843			0.00481577
$610$	−6.84368	+	4.37933i	−0.277092	+	0.177314i
$611$	39.2671			1.58858
$612$	−16.5450	+	12.0206i	−0.668792	+	0.485906i
$613$	−29.5890	+	21.4977i	−1.19509	+	0.868282i	−0.993793	−	0.111249i	$-0.964515\pi$
$613$	−29.5890	+	21.4977i	−1.19509	+	0.868282i	−0.201295	+	0.979531i	$0.564515\pi$
$614$	0.000184886	0	0.000569021i	7.46139e−6	0	2.29638e-5i
$615$	−7.54686	+	23.2269i	−0.304319	+	0.936597i
$616$	0.0458725	−	0.141181i	0.00184826	−	0.00568835i
$617$	18.6561	+	13.5545i	0.751068	+	0.545683i	0.896158	−	0.443736i	$-0.146347\pi$
$617$	18.6561	+	13.5545i	0.751068	+	0.545683i	−0.145090	+	0.989418i	$0.546347\pi$
$618$	−0.319887	−	0.984512i	−0.0128678	−	0.0396029i
$619$	13.0464	−	40.1528i	0.524381	−	1.61388i	−0.241156	−	0.970486i	$-0.577526\pi$
$619$	13.0464	−	40.1528i	0.524381	−	1.61388i	0.765537	−	0.643392i	$-0.222474\pi$
$620$	18.8050	+	57.8760i	0.755229	+	2.32435i
$621$	−14.4501			−0.579861
$622$	−0.631869	−	1.94469i	−0.0253357	−	0.0779751i
$623$	−0.474593			−0.0190142
$624$	8.37125			0.335118
$625$	22.2144	+	68.3689i	0.888576	+	2.73476i
$626$	0.776011	+	0.563805i	0.0310156	+	0.0225342i
$627$	0.868810	−	2.67392i	0.0346969	−	0.106786i
$628$	3.44400	+	10.5996i	0.137431	+	0.422968i
$629$	−11.7149	+	8.51138i	−0.467104	+	0.339371i
$630$	0.319945	+	0.232454i	0.0127469	+	0.00926117i
$631$	−27.8080			−1.10702			−0.553509	−	0.832843i	$-0.686712\pi$
$631$	−27.8080			−1.10702			−0.553509	+	0.832843i	$0.686712\pi$
$632$	8.73087	−	6.34335i	0.347296	−	0.252325i
$633$	5.70906	−	17.5707i	0.226915	−	0.698371i
$634$	−0.585874	−	0.425663i	−0.0232680	−	0.0169052i
$635$	12.7202	+	9.24177i	0.504786	+	0.366748i
$636$	−4.91755	+	3.57281i	−0.194994	+	0.141671i
$637$	−7.00043	−	21.5451i	−0.277367	−	0.853648i
$638$	0.220525	−	0.160221i	0.00873067	−	0.00634320i
$639$	−21.1292			−0.835859
$640$	24.9059	+	18.0952i	0.984492	+	0.715275i
$641$	1.91671	+	1.39257i	0.0757057	+	0.0550034i	0.624994	−	0.780629i	$-0.285101\pi$
$641$	1.91671	+	1.39257i	0.0757057	+	0.0550034i	−0.549289	+	0.835633i	$0.685101\pi$
$642$	0.0790067			0.00311814
$643$	32.3393	−	23.4959i	1.27534	−	0.926587i	0.275935	−	0.961176i	$-0.411012\pi$
$643$	32.3393	−	23.4959i	1.27534	−	0.926587i	0.999402	+	0.0345896i	$0.0110124\pi$
$644$	−0.338096	−	1.04055i	−0.0133229	−	0.0410035i
$645$	19.3567	−	14.0635i	0.762171	−	0.553749i
$646$	3.35481	+	2.43741i	0.131993	+	0.0958986i
$647$	21.5913	+	15.6870i	0.848842	+	0.616720i	0.924826	−	0.380389i	$-0.124210\pi$
$647$	21.5913	+	15.6870i	0.848842	+	0.616720i	−0.0759847	+	0.997109i	$0.524210\pi$
$648$	−1.42467	+	4.38468i	−0.0559663	+	0.172247i
$649$	−10.6227	+	7.71784i	−0.416977	+	0.302952i
$650$	10.1738			0.399048
$651$	0.652354	+	0.473963i	0.0255678	+	0.0185761i
$652$	5.95150	−	4.32402i	0.233079	−	0.169342i
$653$	−14.5922	−	44.9102i	−0.571038	−	1.75747i	−0.649292	−	0.760539i	$-0.724935\pi$
$653$	−14.5922	−	44.9102i	−0.571038	−	1.75747i	0.0782542	−	0.996933i	$-0.475065\pi$
$654$	−1.12384	+	3.45882i	−0.0439456	+	0.135251i
$655$	−28.7315	−	20.8747i	−1.12263	−	0.815642i
$656$	−9.21008	−	28.3457i	−0.359593	−	1.10671i
$657$	39.0447			1.52328
$658$	0.455786			0.0177684
$659$	−9.51066	−	29.2708i	−0.370483	−	1.14023i	−0.946476	−	0.322774i	$-0.895385\pi$
$659$	−9.51066	−	29.2708i	−0.370483	−	1.14023i	0.575993	−	0.817455i	$-0.304615\pi$
$660$	5.77613			0.224836
$661$	10.6026	+	32.6313i	0.412392	+	1.26921i	0.914563	+	0.404443i	$0.132535\pi$
$661$	10.6026	+	32.6313i	0.412392	+	1.26921i	−0.502171	+	0.864768i	$0.667465\pi$
$662$	0.924921	−	2.84661i	0.0359481	−	0.110637i
$663$	3.00531	+	9.24938i	0.116716	+	0.359216i
$664$	9.35940	+	6.80000i	0.363215	+	0.263891i
$665$	−0.783767	+	2.41219i	−0.0303932	+	0.0935406i
$666$	−0.654933	+	2.01568i	−0.0253781	+	0.0781059i
$667$	1.26128	−	3.88182i	0.0488370	−	0.150305i
$668$	−24.8222	+	18.0344i	−0.960399	+	0.697771i
$669$	−1.98204	+	1.44003i	−0.0766300	+	0.0556750i
$670$	−10.7947			−0.417036
$671$	−1.97078	−	7.55752i	−0.0760810	−	0.291755i
$672$	0.307683			0.0118691
$673$	−11.3367	+	8.23663i	−0.436999	+	0.317499i	−0.784442	−	0.620203i	$-0.787050\pi$
$673$	−11.3367	+	8.23663i	−0.436999	+	0.317499i	0.347442	+	0.937701i	$0.387050\pi$
$674$	−4.01369	+	2.91612i	−0.154602	+	0.112325i
$675$	−15.2439	+	46.9157i	−0.586736	+	1.80579i
$676$	1.47190	−	4.53005i	0.0566117	−	0.174233i
$677$	−7.03283	+	21.6448i	−0.270294	+	0.831879i	0.720133	+	0.693837i	$0.244081\pi$
$677$	−7.03283	+	21.6448i	−0.270294	+	0.831879i	−0.990426	+	0.138042i	$0.955919\pi$
$678$	−0.234939	−	0.170693i	−0.00902279	−	0.00655544i
$679$	0.177806	+	0.547231i	0.00682357	+	0.0210008i
$680$	−5.34846	+	16.4609i	−0.205104	+	0.631246i
$681$	−1.35543	−	4.17159i	−0.0519402	−	0.159856i
$682$	1.84949			0.0708205
$683$	−4.40172	−	13.5471i	−0.168427	−	0.518365i	0.830845	−	0.556503i	$-0.187857\pi$
$683$	−4.40172	−	13.5471i	−0.168427	−	0.518365i	−0.999272	+	0.0381380i	$0.987857\pi$
$684$	−19.1968			−0.734009
$685$	33.1297			1.26582
$686$	−0.162782	−	0.500993i	−0.00621506	−	0.0191280i
$687$	9.44051	+	6.85893i	0.360178	+	0.261685i
$688$	−9.02305	+	27.7701i	−0.344001	+	1.05873i
$689$	−4.43673	−	13.6548i	−0.169026	−	0.520208i
$690$	−2.21227	+	1.60731i	−0.0842197	+	0.0611892i
$691$	36.4800	+	26.5043i	1.38777	+	1.00827i	0.996106	+	0.0881611i	$0.0280990\pi$
$691$	36.4800	+	26.5043i	1.38777	+	1.00827i	0.391660	+	0.920110i	$0.371901\pi$
$692$	36.8737			1.40173
$693$	−0.307553	+	0.223451i	−0.0116830	+	0.00848819i
$694$	1.90297	−	5.85675i	0.0722358	−	0.222319i
$695$	61.0612	+	44.3635i	2.31618	+	1.68280i
$696$	0.615878	+	0.447462i	0.0233448	+	0.0169610i
$697$	28.0127	−	20.3524i	1.06106	−	0.770902i
$698$	−0.856172	−	2.63503i	−0.0324066	−	0.0997372i
$699$	15.4569	−	11.2301i	0.584634	−	0.424762i
$700$	−3.73508			−0.141173
$701$	−5.28562	−	3.84022i	−0.199635	−	0.145043i	0.483477	−	0.875357i	$-0.339374\pi$
$701$	−5.28562	−	3.84022i	−0.199635	−	0.145043i	−0.683112	+	0.730314i	$0.739374\pi$
$702$	2.53503	+	1.84180i	0.0956784	+	0.0695144i
$703$	−13.5926			−0.512653
$704$	−5.31222	+	3.85955i	−0.200212	+	0.145462i
$705$	11.1340	+	34.2670i	0.419331	+	1.29057i
$706$	−6.67803	+	4.85187i	−0.251331	+	0.182603i
$707$	2.11953	+	1.53993i	0.0797129	+	0.0579148i
$708$	−14.6026	−	10.6094i	−0.548799	−	0.398726i
$709$	−12.3250	+	37.9323i	−0.462873	+	1.42458i	0.398764	+	0.917053i	$0.369439\pi$
$709$	−12.3250	+	37.9323i	−0.462873	+	1.42458i	−0.861638	+	0.507524i	$0.830561\pi$
$710$	−7.12093	+	5.17366i	−0.267244	+	0.194164i
$711$	−27.6371			−1.03647
$712$	−2.45947	−	1.78691i	−0.0921724	−	0.0669672i
$713$	22.4046	−	16.2779i	0.839061	−	0.609613i
$714$	0.0348836	+	0.107361i	0.00130549	+	0.00401787i
$715$	−4.21608	+	12.9758i	−0.157672	+	0.485266i
$716$	−22.8878	−	16.6290i	−0.855358	−	0.621454i
$717$	−1.92987	−	5.93954i	−0.0720725	−	0.221816i
$718$	−1.88361			−0.0702956
$719$	1.63546			0.0609925			0.0304963	−	0.999535i	$-0.490291\pi$
$719$	1.63546			0.0609925			0.0304963	+	0.999535i	$0.490291\pi$
$720$	−11.7898	−	36.2852i	−0.439379	−	1.35227i
$721$	−0.897682			−0.0334314
$722$	−0.250760	−	0.771760i	−0.00933232	−	0.0287219i
$723$	−3.18322	+	9.79695i	−0.118385	+	0.364352i
$724$	8.19402	+	25.2186i	0.304528	+	0.937242i
$725$	−11.2727	−	8.19013i	−0.418659	−	0.304174i
$726$	0.0542474	−	0.166956i	0.00201331	−	0.00619633i
$727$	−4.60114	+	14.1609i	−0.170647	+	0.525197i	−0.999408	−	0.0344056i	$-0.989046\pi$
$727$	−4.60114	+	14.1609i	−0.170647	+	0.525197i	0.828761	+	0.559603i	$0.189046\pi$
$728$	−0.148949	+	0.458417i	−0.00552041	+	0.0169901i
$729$	2.84378	−	2.06612i	0.105325	−	0.0765231i
$730$	13.1588	−	9.56042i	0.487028	−	0.353847i
$731$	−33.9225			−1.25467
$732$	9.04337	−	5.78693i	0.334252	−	0.213891i
$733$	−38.6918			−1.42911			−0.714557	−	0.699577i	$-0.753372\pi$
$733$	−38.6918			−1.42911			−0.714557	+	0.699577i	$0.753372\pi$
$734$	−6.23643	+	4.53103i	−0.230191	+	0.167243i
$735$	16.8167	−	12.2181i	0.620294	−	0.450670i
$736$	3.26543	−	10.0500i	0.120365	−	0.370447i
$737$	3.20655	−	9.86876i	0.118115	−	0.363520i
$738$	1.56608	−	4.81989i	0.0576480	−	0.177422i
$739$	10.9168	+	7.93149i	0.401579	+	0.291765i	0.770184	−	0.637822i	$-0.220164\pi$
$739$	10.9168	+	7.93149i	0.401579	+	0.291765i	−0.368605	+	0.929586i	$0.620164\pi$
$740$	−8.62937	−	26.5585i	−0.317222	−	0.976308i
$741$	−2.82104	+	8.68226i	−0.103633	+	0.318951i
$742$	−0.0514985	−	0.158496i	−0.00189057	−	0.00581858i
$743$	10.9024			0.399972			0.199986	−	0.979799i	$-0.435910\pi$
$743$	10.9024			0.399972			0.199986	+	0.979799i	$0.435910\pi$
$744$	1.59614	+	4.91241i	0.0585173	+	0.180098i
$745$	−21.5115			−0.788119
$746$	−7.55179			−0.276491
$747$	−9.15515	−	28.1767i	−0.334970	−	1.03093i
$748$	−6.62533	−	4.81359i	−0.242246	−	0.176002i
$749$	0.0211716	−	0.0651595i	0.000773594	−	0.00238088i
$750$	1.74503	+	5.37065i	0.0637195	+	0.196108i
$751$	−5.93198	+	4.30983i	−0.216461	+	0.157268i	−0.690732	−	0.723111i	$-0.742712\pi$
$751$	−5.93198	+	4.30983i	−0.216461	+	0.157268i	0.474271	+	0.880379i	$0.342712\pi$
$752$	−35.5733	−	25.8455i	−1.29722	−	0.942488i
$753$	−2.96523			−0.108059
$754$	−0.716048	+	0.520239i	−0.0260769	+	0.0189460i
$755$	6.46475	−	19.8964i	0.235276	−	0.724106i
$756$	−0.930681	−	0.676180i	−0.0338486	−	0.0245924i
$757$	34.0387	+	24.7305i	1.23716	+	0.898847i	0.997406	−	0.0719875i	$-0.0229342\pi$
$757$	34.0387	+	24.7305i	1.23716	+	0.898847i	0.239751	+	0.970834i	$0.422934\pi$
$758$	−6.02434	+	4.37694i	−0.218814	+	0.158978i
$759$	−0.812284	−	2.49995i	−0.0294841	−	0.0907426i
$760$	−13.1439	+	9.54961i	−0.476780	+	0.346401i
$761$	27.6553			1.00250			0.501251	−	0.865302i	$-0.332873\pi$
$761$	27.6553			1.00250			0.501251	+	0.865302i	$0.332873\pi$
$762$	0.531433	+	0.386109i	0.0192518	+	0.0139872i
$763$	2.55145	+	1.85374i	0.0923688	+	0.0671098i
$764$	−7.87048			−0.284744
$765$	35.8589	−	26.0530i	1.29648	−	0.941949i
$766$	−0.346523	−	1.06649i	−0.0125204	−	0.0385337i
$767$	34.4921	−	25.0599i	1.24544	−	0.904862i
$768$	−6.49283	−	4.71732i	−0.234290	−	0.170222i
$769$	0.126027	+	0.0915638i	0.00454464	+	0.00330188i	0.590055	−	0.807363i	$-0.299106\pi$
$769$	0.126027	+	0.0915638i	0.00454464	+	0.00330188i	−0.585511	+	0.810665i	$0.699106\pi$
$770$	−0.0489374	+	0.150614i	−0.00176358	+	0.00542775i
$771$	−6.56708	+	4.77126i	−0.236508	+	0.171833i
$772$	−46.6295			−1.67823
$773$	−8.84556	−	6.42668i	−0.318153	−	0.231152i	0.417234	−	0.908799i	$-0.363000\pi$
$773$	−8.84556	−	6.42668i	−0.318153	−	0.231152i	−0.735387	+	0.677648i	$0.763000\pi$
$774$	−4.01678	+	2.91836i	−0.144380	+	0.104898i
$775$	−29.2150	−	89.9144i	−1.04943	−	3.22982i
$776$	−1.13896	+	3.50536i	−0.0408863	+	0.125835i
$777$	−0.299356	−	0.217495i	−0.0107393	−	0.00780259i
$778$	−0.495759	−	1.52579i	−0.0177738	−	0.0547022i
$779$	32.5025			1.16452
$780$	−18.7552			−0.671544
$781$	−2.61461	−	8.04694i	−0.0935581	−	0.287942i
$782$	3.87698			0.138640
$783$	−1.32616	−	4.08151i	−0.0473932	−	0.145861i
$784$	−7.83903	+	24.1261i	−0.279965	+	0.861645i
$785$	−7.46438	−	22.9730i	−0.266415	−	0.819942i
$786$	−1.20037	−	0.872116i	−0.0428156	−	0.0311074i
$787$	−11.6949	+	35.9931i	−0.416877	+	1.28302i	0.493684	+	0.869641i	$0.335650\pi$
$787$	−11.6949	+	35.9931i	−0.416877	+	1.28302i	−0.910561	+	0.413374i	$0.864350\pi$
$788$	−6.93559	+	21.3456i	−0.247070	+	0.760404i
$789$	−1.63320	+	5.02647i	−0.0581435	+	0.178947i
$790$	−9.31421	+	6.76717i	−0.331385	+	0.240765i
$791$	−0.203734	+	0.148021i	−0.00724395	+	0.00526303i
$792$	−2.43515			−0.0865292
$793$	6.39914	+	24.5394i	0.227240	+	0.871419i
$794$	−1.59867			−0.0567348
$795$	10.6581	−	7.74355i	0.378003	−	0.274635i
$796$	10.7904	−	7.83968i	0.382456	−	0.277870i
$797$	−2.89395	+	8.90668i	−0.102509	+	0.315491i	−0.989138	−	0.146991i	$-0.953041\pi$
$797$	−2.89395	+	8.90668i	−0.102509	+	0.315491i	0.886629	+	0.462482i	$0.153041\pi$
$798$	−0.0327447	+	0.100778i	−0.00115915	+	0.00356750i
$799$	15.7857	−	48.5835i	0.558459	−	1.71876i
$800$	−29.1849	−	21.2041i	−1.03184	−	0.749678i
$801$	2.40579	+	7.40427i	0.0850045	+	0.261617i
$802$	0.666162	−	2.05024i	0.0235230	−	0.0723964i
$803$	4.83154	+	14.8700i	0.170501	+	0.524749i
$804$	14.2643			0.503064
$805$	0.732775	+	2.25525i	0.0258269	+	0.0794871i
$806$	−6.00531			−0.211528
$807$	5.02701			0.176959
$808$	5.18592	+	15.9606i	0.182440	+	0.561492i
$809$	5.69691	+	4.13905i	0.200293	+	0.145521i	0.683411	−	0.730034i	$-0.260496\pi$
$809$	5.69691	+	4.13905i	0.200293	+	0.145521i	−0.483118	+	0.875555i	$0.660496\pi$
$810$	1.51986	−	4.67764i	0.0534023	−	0.164355i
$811$	−15.5422	−	47.8341i	−0.545762	−	1.67968i	−0.719172	−	0.694832i	$-0.755479\pi$
$811$	−15.5422	−	47.8341i	−0.545762	−	1.67968i	0.173410	−	0.984850i	$-0.444521\pi$
$812$	0.262882	−	0.190995i	0.00922534	−	0.00670261i
$813$	5.89930	+	4.28609i	0.206897	+	0.150320i
$814$	−0.848703			−0.0297470
$815$	−12.8990	+	9.37169i	−0.451833	+	0.328276i
$816$	3.36532	−	10.3574i	0.117810	−	0.362581i
$817$	−25.7611	−	18.7166i	−0.901269	−	0.654810i
$818$	−2.25165	−	1.63592i	−0.0787273	−	0.0571987i
$819$	0.998631	−	0.725548i	0.0348950	−	0.0253527i
$820$	20.6345	+	63.5066i	0.720589	+	2.21775i
$821$	−17.5270	+	12.7341i	−0.611698	+	0.444425i	−0.850012	−	0.526764i	$-0.823405\pi$
$821$	−17.5270	+	12.7341i	−0.611698	+	0.444425i	0.238314	+	0.971188i	$0.423405\pi$
$822$	1.38411			0.0482765
$823$	−27.2705	−	19.8132i	−0.950591	−	0.690645i	0.000355371	−	1.00000i	$-0.499887\pi$
$823$	−27.2705	−	19.8132i	−0.950591	−	0.690645i	−0.950947	+	0.309355i	$0.899887\pi$
$824$	−4.65203	−	3.37990i	−0.162061	−	0.117744i
$825$	−8.97363			−0.312422
$826$	0.400361	−	0.290879i	0.0139303	−	0.0101210i
$827$	7.81574	+	24.0544i	0.271780	+	0.836453i	0.990053	+	0.140692i	$0.0449327\pi$
$827$	7.81574	+	24.0544i	0.271780	+	0.836453i	−0.718273	+	0.695761i	$0.755067\pi$
$828$	−14.5201	+	10.5495i	−0.504609	+	0.366620i
$829$	−14.7148	−	10.6910i	−0.511068	−	0.371312i	0.302161	−	0.953257i	$-0.402292\pi$
$829$	−14.7148	−	10.6910i	−0.511068	−	0.371312i	−0.813228	+	0.581945i	$0.802292\pi$
$830$	−9.98474	−	7.25434i	−0.346575	−	0.251802i
$831$	−0.666224	+	2.05043i	−0.0231110	+	0.0711285i
$832$	17.2488	−	12.5320i	0.597996	−	0.434470i
$833$	−29.4711			−1.02111
$834$	2.55105	+	1.85345i	0.0883357	+	0.0641797i
$835$	53.7985	−	39.0869i	1.86177	−	1.35266i
$836$	−2.37549	−	7.31100i	−0.0821580	−	0.252856i
$837$	8.99805	−	27.6931i	0.311018	−	0.957215i
$838$	1.63442	+	1.18748i	0.0564602	+	0.0410207i
$839$	14.0725	+	43.3107i	0.485837	+	1.49525i	0.830765	+	0.556624i	$0.187903\pi$
$839$	14.0725	+	43.3107i	0.485837	+	1.49525i	−0.344928	+	0.938629i	$0.612097\pi$
$840$	−0.442278			−0.0152601
$841$	−27.7878			−0.958200
$842$	0.446265	+	1.37346i	0.0153793	+	0.0473327i
$843$	−7.21557			−0.248517
$844$	−15.6096	−	48.0415i	−0.537306	−	1.65366i
$845$	−3.19014	+	9.81824i	−0.109744	+	0.337758i
$846$	−2.31046	−	7.11086i	−0.0794352	−	0.244476i
$847$	−0.123158	−	0.0894793i	−0.00423175	−	0.00307455i
$848$	−4.96822	+	15.2906i	−0.170609	+	0.525081i
$849$	0.645079	−	1.98535i	0.0221391	−	0.0681371i
$850$	4.08995	−	12.5876i	0.140284	−	0.431750i
$851$	−10.2812	+	7.46971i	−0.352434	+	0.256058i
$852$	9.40974	−	6.83658i	0.322372	−	0.234217i
$853$	45.7022			1.56481			0.782406	−	0.622768i	$-0.213992\pi$
$853$	45.7022			1.56481			0.782406	+	0.622768i	$0.213992\pi$
$854$	0.0742770	+	0.284837i	0.00254171	+	0.00974691i
$855$	41.6063			1.42291
$856$	0.355051	−	0.257960i	0.0121354	−	0.00881689i
$857$	−3.88990	+	2.82617i	−0.132876	+	0.0965403i	−0.652238	−	0.758014i	$-0.726170\pi$
$857$	−3.88990	+	2.82617i	−0.132876	+	0.0965403i	0.519362	+	0.854555i	$0.326170\pi$
$858$	−0.176142	+	0.542110i	−0.00601339	+	0.0185073i
$859$	−10.0134	+	30.8181i	−0.341653	+	1.05150i	0.621699	+	0.783256i	$0.286443\pi$
$859$	−10.0134	+	30.8181i	−0.341653	+	1.05150i	−0.963351	+	0.268242i	$0.913557\pi$
$860$	20.2155	−	62.2170i	0.689344	−	2.12158i
$861$	0.715820	+	0.520074i	0.0243951	+	0.0177241i
$862$	−0.261309	−	0.804228i	−0.00890023	−	0.0273921i
$863$	−1.23105	+	3.78877i	−0.0419053	+	0.128971i	−0.969820	−	0.243820i	$-0.921599\pi$
$863$	−1.23105	+	3.78877i	−0.0419053	+	0.128971i	0.927915	+	0.372791i	$0.121599\pi$
$864$	−3.43341	−	10.5670i	−0.116807	−	0.359495i
$865$	−79.9184			−2.71731
$866$	−1.19381	−	3.67416i	−0.0405672	−	0.124853i
$867$	0.598001			0.0203092
$868$	2.20472			0.0748332
$869$	−3.41992	−	10.5254i	−0.116013	−	0.357051i
$870$	−0.657027	−	0.477358i	−0.0222753	−	0.0161840i
$871$	−10.4117	+	32.0440i	−0.352788	+	1.08577i
$872$	6.24273	+	19.2131i	0.211405	+	0.650639i
$873$	7.63620	−	5.54802i	0.258446	−	0.187772i
$874$	2.94423	+	2.13911i	0.0995900	+	0.0723563i
$875$	4.89698			0.165548
$876$	−17.3883	+	12.6333i	−0.587495	+	0.426840i
$877$	0.340958	−	1.04936i	0.0115133	−	0.0354344i	−0.945135	−	0.326681i	$-0.894070\pi$
$877$	0.340958	−	1.04936i	0.0115133	−	0.0354344i	0.956648	+	0.291246i	$0.0940699\pi$
$878$	3.24215	+	2.35556i	0.109417	+	0.0794963i
$879$	−15.1238	−	10.9881i	−0.510114	−	0.370620i
$880$	12.3601	−	8.98014i	0.416659	−	0.302720i
$881$	−6.36062	−	19.5760i	−0.214295	−	0.659531i	−0.999203	−	0.0399191i	$-0.987290\pi$
$881$	−6.36062	−	19.5760i	−0.214295	−	0.659531i	0.784908	−	0.619612i	$-0.212710\pi$
$882$	−3.48969	+	2.53541i	−0.117504	+	0.0853717i
$883$	−27.7622			−0.934274			−0.467137	−	0.884185i	$-0.654715\pi$
$883$	−27.7622			−0.934274			−0.467137	+	0.884185i	$0.654715\pi$
$884$	21.5126	+	15.6298i	0.723546	+	0.525687i
$885$	31.6490	+	22.9944i	1.06387	+	0.772947i
$886$	4.82987			0.162263
$887$	3.06837	−	2.22930i	0.103026	−	0.0748526i	−0.535080	−	0.844802i	$-0.679718\pi$
$887$	3.06837	−	2.22930i	0.103026	−	0.0748526i	0.638105	+	0.769949i	$0.279718\pi$
$888$	−0.732445	−	2.25423i	−0.0245792	−	0.0756471i
$889$	0.460846	−	0.334824i	0.0154563	−	0.0112297i
$890$	2.62379	+	1.90630i	0.0879497	+	0.0638992i
$891$	3.82493	+	2.77897i	0.128140	+	0.0930991i
$892$	−2.06997	+	6.37072i	−0.0693078	+	0.213308i
$893$	38.7936	−	28.1852i	1.29818	−	0.943182i
$894$	−0.898719			−0.0300577
$895$	49.6060	+	36.0409i	1.65815	+	1.20471i
$896$	0.902327	−	0.655579i	0.0301446	−	0.0219014i
$897$	2.63750	+	8.11739i	0.0880636	+	0.271032i
$898$	−1.94264	+	5.97882i	−0.0648266	+	0.199516i
$899$	6.65401	+	4.83442i	0.221924	+	0.161237i
$900$	18.9338	+	58.2722i	0.631127	+	1.94241i
$901$	−18.6782			−0.622260
$902$	2.02942			0.0675722
$903$	−0.267867	−	0.824409i	−0.00891405	−	0.0274346i
$904$	−1.61312			−0.0536517
$905$	−17.7594	−	54.6577i	−0.590341	−	1.81688i
$906$	0.270088	−	0.831246i	0.00897308	−	0.0276163i
$907$	−7.72626	−	23.7790i	−0.256546	−	0.789568i	−0.993521	−	0.113648i	$-0.963746\pi$
$907$	−7.72626	−	23.7790i	−0.256546	−	0.789568i	0.736975	−	0.675920i	$-0.236254\pi$
$908$	−9.70244	−	7.04923i	−0.321987	−	0.233937i
$909$	13.2806	−	40.8735i	0.440490	−	1.35569i
$910$	0.158901	−	0.489046i	0.00526750	−	0.0162117i
$911$	13.4974	−	41.5408i	0.447189	−	1.37631i	−0.432876	−	0.901454i	$-0.642501\pi$
$911$	13.4974	−	41.5408i	0.447189	−	1.37631i	0.880065	−	0.474854i	$-0.157499\pi$
$912$	8.27032	−	6.00874i	0.273858	−	0.198969i
$913$	9.59803	−	6.97337i	0.317648	−	0.230785i
$914$	4.07088			0.134653
$915$	−19.6002	+	12.5423i	−0.647962	+	0.414637i
$916$	31.9055			1.05419
$917$	−1.04093	+	0.756279i	−0.0343745	+	0.0249745i
$918$	3.29789	−	2.39606i	0.108847	−	0.0790817i
$919$	0.818140	−	2.51798i	0.0269879	−	0.0830603i	−0.936655	−	0.350252i	$-0.886096\pi$
$919$	0.818140	−	2.51798i	0.0269879	−	0.0830603i	0.963643	+	0.267192i	$0.0860958\pi$
$920$	−4.69389	+	14.4463i	−0.154753	+	0.476280i
$921$	0.000529511	−	0.00162967i	1.74480e−5	−	5.36993e-5i
$922$	3.00501	+	2.18327i	0.0989648	+	0.0719021i
$923$	8.48968	+	26.1286i	0.279441	+	0.860032i
$924$	0.0646668	−	0.199024i	0.00212738	−	0.00654741i
$925$	13.4063	+	41.2604i	0.440797	+	1.35663i
$926$	4.13166			0.135775
$927$	4.55051	+	14.0050i	0.149458	+	0.459985i
$928$	3.13837			0.103022
$929$	−30.3664			−0.996288			−0.498144	−	0.867094i	$-0.665985\pi$
$929$	−30.3664			−0.996288			−0.498144	+	0.867094i	$0.665985\pi$
$930$	−1.70278	−	5.24062i	−0.0558364	−	0.171847i
$931$	−22.3807	−	16.2605i	−0.733499	−	0.532918i
$932$	16.1427	−	49.6821i	0.528771	−	1.62739i
$933$	−1.80966	−	5.56958i	−0.0592458	−	0.182340i
$934$	−2.00917	+	1.45975i	−0.0657420	+	0.0477644i
$935$	14.3595	+	10.4328i	0.469604	+	0.341188i
$936$	7.90696			0.258447
$937$	−1.35041	+	0.981129i	−0.0441159	+	0.0320521i	−0.609625	−	0.792690i	$-0.708680\pi$
$937$	−1.35041	+	0.981129i	−0.0441159	+	0.0320521i	0.565509	+	0.824742i	$0.308680\pi$
$938$	−0.120852	+	0.371945i	−0.00394597	+	0.0121444i
$939$	2.22248	+	1.61473i	0.0725280	+	0.0526947i
$940$	79.6994	+	57.9050i	2.59951	+	1.88865i
$941$	29.4404	−	21.3897i	0.959730	−	0.697284i	0.00664162	−	0.999978i	$-0.497886\pi$
$941$	29.4404	−	21.3897i	0.959730	−	0.697284i	0.953088	+	0.302694i	$0.0978859\pi$
$942$	−0.311852	−	0.959781i	−0.0101607	−	0.0312714i
$943$	24.5843	−	17.8616i	0.800576	−	0.581652i
$944$	−47.7419			−1.55387
$945$	2.01712	+	1.46552i	0.0656168	+	0.0476734i
$946$	−1.60849	−	1.16864i	−0.0522966	−	0.0379957i
$947$	27.2719			0.886219			0.443110	−	0.896467i	$-0.353875\pi$
$947$	27.2719			0.886219			0.443110	+	0.896467i	$0.353875\pi$
$948$	12.3080	−	8.94227i	0.399745	−	0.290431i
$949$	−15.6881	−	48.2830i	−0.509257	−	1.56733i
$950$	10.0511	−	7.30255i	0.326101	−	0.236926i
$951$	−1.67794	−	1.21909i	−0.0544108	−	0.0395318i
$952$	0.507302	+	0.368576i	0.0164417	+	0.0119456i
$953$	−13.2725	+	40.8487i	−0.429940	+	1.32322i	0.468244	+	0.883599i	$0.344887\pi$
$953$	−13.2725	+	40.8487i	−0.429940	+	1.32322i	−0.898184	+	0.439620i	$0.855113\pi$
$954$	−2.21169	+	1.60689i	−0.0716063	+	0.0520250i
$955$	17.0581			0.551988
$956$	−13.8144	−	10.0368i	−0.446790	−	0.324612i
$957$	0.631580	−	0.458870i	0.0204161	−	0.0148332i
$958$	1.73923	+	5.35280i	0.0561920	+	0.172941i
$959$	0.370905	−	1.14153i	0.0119771	−	0.0368618i
$960$	15.8271	+	11.4991i	0.510817	+	0.371130i
$961$	7.66531	+	23.5914i	0.247268	+	0.761012i
$962$	2.75575			0.0888490
$963$	−1.12390			−0.0362171
$964$	8.70352	+	26.7867i	0.280321	+	0.862741i
$965$	101.063			3.25332
$966$	0.0306143	+	0.0942212i	0.000985000	+	0.00303152i
$967$	−0.485691	+	1.49480i	−0.0156188	+	0.0480696i	−0.958562	−	0.284883i	$-0.908045\pi$
$967$	−0.485691	+	1.49480i	−0.0156188	+	0.0480696i	0.942943	+	0.332953i	$0.108045\pi$
$968$	−0.301334	−	0.927412i	−0.00968525	−	0.0298081i
$969$	9.60812	+	6.98071i	0.308657	+	0.224253i
$970$	1.21506	−	3.73957i	0.0390132	−	0.120070i
$971$	−13.7712	+	42.3835i	−0.441940	+	1.36015i	0.443865	+	0.896094i	$0.353607\pi$
$971$	−13.7712	+	42.3835i	−0.441940	+	1.36015i	−0.885805	+	0.464058i	$0.846393\pi$
$972$	−9.01393	+	27.7420i	−0.289122	+	0.889826i
$973$	2.21221	−	1.60727i	0.0709203	−	0.0515266i
$974$	−0.748093	+	0.543521i	−0.0239704	+	0.0174155i
$975$	29.1375			0.933147
$976$	10.3546	−	26.4429i	0.331442	−	0.846417i
$977$	20.8199			0.666087			0.333044	−	0.942911i	$-0.391924\pi$
$977$	20.8199			0.666087			0.333044	+	0.942911i	$0.391924\pi$
$978$	−0.538904	+	0.391536i	−0.0172322	+	0.0125200i
$979$	−2.52217	+	1.83246i	−0.0806090	+	0.0585658i
$980$	17.5628	−	54.0528i	0.561023	−	1.72665i
$981$	15.9870	−	49.2029i	0.510426	−	1.57093i
$982$	−1.32102	+	4.06569i	−0.0421555	+	0.129741i
$983$	−39.1749	−	28.4623i	−1.24949	−	0.907805i	−0.251295	−	0.967911i	$-0.580856\pi$
$983$	−39.1749	−	28.4623i	−1.24949	−	0.907805i	−0.998192	+	0.0601054i	$0.980856\pi$
$984$	1.75142	+	5.39032i	0.0558333	+	0.171837i
$985$	15.0319	−	46.2634i	0.478956	−	1.47407i
$986$	0.355812	+	1.09508i	0.0113314	+	0.0348744i
$987$	1.30536			0.0415502
$988$	7.71325	+	23.7389i	0.245391	+	0.755236i
$989$	−29.7708			−0.946658
$990$	2.59785			0.0825650
$991$	1.25155	+	3.85188i	0.0397568	+	0.122359i	0.968965	−	0.247197i	$-0.0795096\pi$
$991$	1.25155	+	3.85188i	0.0397568	+	0.122359i	−0.929208	+	0.369556i	$0.879510\pi$
$992$	17.2271	+	12.5162i	0.546961	+	0.397390i
$993$	2.64896	−	8.15266i	0.0840622	−	0.258717i
$994$	0.0985425	+	0.303283i	0.00312558	+	0.00961954i
$995$	−23.3866	+	16.9914i	−0.741406	+	0.538663i
$996$	13.1940	+	9.58602i	0.418069	+	0.303745i
$997$	−6.40616			−0.202885			−0.101443	−	0.994841i	$-0.532346\pi$
$997$	−6.40616			−0.202885			−0.101443	+	0.994841i	$0.532346\pi$
$998$	3.70824	−	2.69419i	0.117382	−	0.0852831i
$999$	−4.12908	+	12.7080i	−0.130638	+	0.402063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.i.b.34.13	✓	108
61.9	even	5	inner	671.2.i.b.375.13	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.i.b.34.13	✓	108	1.1	even	1	trivial
671.2.i.b.375.13	yes	108	61.9	even	5	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.200295 + 0.145523i) q^{2} +(-0.573642 + 0.416776i) q^{3} +(-0.599093 + 1.84382i) q^{4} +(1.29845 - 3.99621i) q^{5} +(0.0542474 - 0.166956i) q^{6} +(-0.123158 - 0.0894793i) q^{7} +(-0.301334 - 0.927412i) q^{8} +(-0.771687 + 2.37501i) q^{9} +O(q^{10})\)	\(q+(-0.200295 + 0.145523i) q^{2} +(-0.573642 + 0.416776i) q^{3} +(-0.599093 + 1.84382i) q^{4} +(1.29845 - 3.99621i) q^{5} +(0.0542474 - 0.166956i) q^{6} +(-0.123158 - 0.0894793i) q^{7} +(-0.301334 - 0.927412i) q^{8} +(-0.771687 + 2.37501i) q^{9} +(0.321467 + 0.989375i) q^{10} -1.00000 q^{11} +(-0.424793 - 1.30738i) q^{12} +3.24702 q^{13} +0.0376892 q^{14} +(0.920678 + 2.83356i) q^{15} +(-2.94158 - 2.13718i) q^{16} +(1.30533 - 4.01740i) q^{17} +(-0.191053 - 0.588001i) q^{18} +(3.20787 - 2.33065i) q^{19} +(6.59039 + 4.78820i) q^{20} +0.107941 q^{21} +(0.200295 - 0.145523i) q^{22} +(1.14558 - 3.52573i) q^{23} +(0.559381 + 0.406414i) q^{24} +(-10.2386 - 7.43881i) q^{25} +(-0.650361 + 0.472515i) q^{26} +(-1.20451 - 3.70710i) q^{27} +(0.238766 - 0.173474i) q^{28} +1.10100 q^{29} +(-0.596755 - 0.433568i) q^{30} +(6.04360 + 4.39093i) q^{31} +2.85047 q^{32} +(0.573642 - 0.416776i) q^{33} +(0.323172 + 0.994621i) q^{34} +(-0.517492 + 0.375980i) q^{35} +(-3.91677 - 2.84570i) q^{36} +(-2.77332 - 2.01494i) q^{37} +(-0.303357 + 0.933636i) q^{38} +(-1.86263 + 1.35328i) q^{39} -4.09740 q^{40} +(6.63157 + 4.81812i) q^{41} +(-0.0216201 + 0.0157079i) q^{42} +(-2.48160 - 7.63757i) q^{43} +(0.599093 - 1.84382i) q^{44} +(8.48904 + 6.16765i) q^{45} +(0.283620 + 0.872893i) q^{46} +12.0933 q^{47} +2.57814 q^{48} +(-2.15596 - 6.63536i) q^{49} +3.13327 q^{50} +(0.925559 + 2.84858i) q^{51} +(-1.94526 + 5.98691i) q^{52} +(-1.36640 - 4.20535i) q^{53} +(0.780725 + 0.567230i) q^{54} +(-1.29845 + 3.99621i) q^{55} +(-0.0458725 + 0.141181i) q^{56} +(-0.868810 + 2.67392i) q^{57} +(-0.220525 + 0.160221i) q^{58} +(10.6227 - 7.71784i) q^{59} -5.77613 q^{60} +(1.97078 + 7.55752i) q^{61} -1.84949 q^{62} +(0.307553 - 0.223451i) q^{63} +(5.31222 - 3.85955i) q^{64} +(4.21608 - 12.9758i) q^{65} +(-0.0542474 + 0.166956i) q^{66} +(-3.20655 + 9.86876i) q^{67} +(6.62533 + 4.81359i) q^{68} +(0.812284 + 2.49995i) q^{69} +(0.0489374 - 0.150614i) q^{70} +(2.61461 + 8.04694i) q^{71} +2.43515 q^{72} +(-4.83154 - 14.8700i) q^{73} +0.848703 q^{74} +8.97363 q^{75} +(2.37549 + 7.31100i) q^{76} +(0.123158 + 0.0894793i) q^{77} +(0.176142 - 0.542110i) q^{78} +(3.41992 + 10.5254i) q^{79} +(-12.3601 + 8.98014i) q^{80} +(-3.82493 - 2.77897i) q^{81} -2.02942 q^{82} +(-9.59803 + 6.97337i) q^{83} +(-0.0646668 + 0.199024i) q^{84} +(-14.3595 - 10.4328i) q^{85} +(1.60849 + 1.16864i) q^{86} +(-0.631580 + 0.458870i) q^{87} +(0.301334 + 0.927412i) q^{88} +(2.52217 - 1.83246i) q^{89} -2.59785 q^{90} +(-0.399895 - 0.290541i) q^{91} +(5.81449 + 4.22447i) q^{92} -5.29690 q^{93} +(-2.42222 + 1.75985i) q^{94} +(-5.14853 - 15.8455i) q^{95} +(-1.63515 + 1.18801i) q^{96} +(-3.05786 - 2.22167i) q^{97} +(1.39742 + 1.01529i) q^{98} +(0.771687 - 2.37501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9}+O(q^{10}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9	\( 108 q - 2 q^{3} - 34 q^{4} + 4 q^{5} + 6 q^{6} + 10 q^{7} - 18 q^{8} - 25 q^{9} + 6 q^{10} - 108 q^{11} - 15 q^{12} - 26 q^{13} + 2 q^{14} + 8 q^{15} - 40 q^{16} + 4 q^{17} + 50 q^{18} + 8 q^{19} + 8 q^{20} - 64 q^{21} - 3 q^{23} + 71 q^{24} - 7 q^{25} + 29 q^{26} - 8 q^{27} + 42 q^{28} - 40 q^{29} - 36 q^{30} - 7 q^{31} - 6 q^{32} + 2 q^{33} - 4 q^{34} + 2 q^{35} + 30 q^{36} - 32 q^{37} - 3 q^{38} + 10 q^{39} - 154 q^{40} + 10 q^{41} - 36 q^{42} - 29 q^{43} + 34 q^{44} - 23 q^{45} + 45 q^{46} + 40 q^{47} + 140 q^{48} - 15 q^{49} + 6 q^{50} - 25 q^{51} - 7 q^{52} + 15 q^{53} - 2 q^{54} - 4 q^{55} + 35 q^{56} + 20 q^{57} + 77 q^{58} + 22 q^{59} + 72 q^{60} + 20 q^{61} + 80 q^{62} - 6 q^{63} - 30 q^{64} + 56 q^{65} - 6 q^{66} - 4 q^{67} - 109 q^{68} - 46 q^{69} + 41 q^{70} + 7 q^{71} - 264 q^{72} - 16 q^{73} - 44 q^{74} - 6 q^{75} + 22 q^{76} - 10 q^{77} - 60 q^{78} + 79 q^{79} + 57 q^{80} - 25 q^{81} - 28 q^{82} + 2 q^{83} + 87 q^{84} + 30 q^{85} - 10 q^{86} - 38 q^{87} + 18 q^{88} + 18 q^{89} + 62 q^{90} - 30 q^{91} - 6 q^{92} - 24 q^{93} - 16 q^{94} - 10 q^{95} + 65 q^{96} + 16 q^{97} + 9 q^{98} + 25 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 34 * q^4 + 4 * q^5 + 6 * q^6 + 10 * q^7 - 18 * q^8 - 25 * q^9 + 6 * q^10 - 108 * q^11 - 15 * q^12 - 26 * q^13 + 2 * q^14 + 8 * q^15 - 40 * q^16 + 4 * q^17 + 50 * q^18 + 8 * q^19 + 8 * q^20 - 64 * q^21 - 3 * q^23 + 71 * q^24 - 7 * q^25 + 29 * q^26 - 8 * q^27 + 42 * q^28 - 40 * q^29 - 36 * q^30 - 7 * q^31 - 6 * q^32 + 2 * q^33 - 4 * q^34 + 2 * q^35 + 30 * q^36 - 32 * q^37 - 3 * q^38 + 10 * q^39 - 154 * q^40 + 10 * q^41 - 36 * q^42 - 29 * q^43 + 34 * q^44 - 23 * q^45 + 45 * q^46 + 40 * q^47 + 140 * q^48 - 15 * q^49 + 6 * q^50 - 25 * q^51 - 7 * q^52 + 15 * q^53 - 2 * q^54 - 4 * q^55 + 35 * q^56 + 20 * q^57 + 77 * q^58 + 22 * q^59 + 72 * q^60 + 20 * q^61 + 80 * q^62 - 6 * q^63 - 30 * q^64 + 56 * q^65 - 6 * q^66 - 4 * q^67 - 109 * q^68 - 46 * q^69 + 41 * q^70 + 7 * q^71 - 264 * q^72 - 16 * q^73 - 44 * q^74 - 6 * q^75 + 22 * q^76 - 10 * q^77 - 60 * q^78 + 79 * q^79 + 57 * q^80 - 25 * q^81 - 28 * q^82 + 2 * q^83 + 87 * q^84 + 30 * q^85 - 10 * q^86 - 38 * q^87 + 18 * q^88 + 18 * q^89 + 62 * q^90 - 30 * q^91 - 6 * q^92 - 24 * q^93 - 16 * q^94 - 10 * q^95 + 65 * q^96 + 16 * q^97 + 9 * q^98 + 25 * q^99

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