LMFDB - Embedded newform 207.2.o.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.28767 + 0.108975i) q^{2} +(1.58319 - 0.702495i) q^{3} +(3.23063 - 0.308488i) q^{4} +(-0.595980 - 0.568266i) q^{5} +(-3.54528 + 1.77961i) q^{6} +(-0.645310 - 3.34819i) q^{7} +(-2.82310 + 0.405901i) q^{8} +(2.01300 - 2.22437i) q^{9} +O(q^{10})$	\(q+(-2.28767 + 0.108975i) q^{2} +(1.58319 - 0.702495i) q^{3} +(3.23063 - 0.308488i) q^{4} +(-0.595980 - 0.568266i) q^{5} +(-3.54528 + 1.77961i) q^{6} +(-0.645310 - 3.34819i) q^{7} +(-2.82310 + 0.405901i) q^{8} +(2.01300 - 2.22437i) q^{9} +(1.42534 + 1.23506i) q^{10} +(-3.24423 + 1.67252i) q^{11} +(4.89800 - 2.75790i) q^{12} +(1.19920 + 0.231127i) q^{13} +(1.84113 + 7.58924i) q^{14} +(-1.34276 - 0.481002i) q^{15} +(0.0407460 - 0.00785315i) q^{16} +(-1.97606 - 4.32697i) q^{17} +(-4.36269 + 5.30800i) q^{18} +(1.51046 + 0.689803i) q^{19} +(-2.10070 - 1.65201i) q^{20} +(-3.37373 - 4.84750i) q^{21} +(7.23948 - 4.17971i) q^{22} +(4.57336 - 1.44374i) q^{23} +(-4.18437 + 2.62583i) q^{24} +(-0.205643 - 4.31699i) q^{25} +(-2.76857 - 0.398061i) q^{26} +(1.62436 - 4.93573i) q^{27} +(-3.11764 - 10.6177i) q^{28} +(0.595424 - 6.23556i) q^{29} +(3.12420 + 0.954048i) q^{30} +(-1.18134 + 0.929013i) q^{31} +(5.45112 - 1.32243i) q^{32} +(-3.96131 + 4.92697i) q^{33} +(4.99212 + 9.68335i) q^{34} +(-1.51807 + 2.36216i) q^{35} +(5.81708 - 7.80711i) q^{36} +(-2.51221 + 8.55582i) q^{37} +(-3.53060 - 1.41344i) q^{38} +(2.06094 - 0.476515i) q^{39} +(1.91317 + 1.36236i) q^{40} +(-1.38614 + 1.45375i) q^{41} +(8.24626 + 10.7218i) q^{42} +(1.04336 - 1.32674i) q^{43} +(-9.96496 + 6.40409i) q^{44} +(-2.46374 + 0.181760i) q^{45} +(-10.3050 + 3.80119i) q^{46} +(9.52963 + 5.50193i) q^{47} +(0.0589920 - 0.0410569i) q^{48} +(-4.29535 + 1.71960i) q^{49} +(0.940890 + 9.85345i) q^{50} +(-6.16816 - 5.46226i) q^{51} +(3.94548 + 0.376748i) q^{52} +(4.16607 + 4.80790i) q^{53} +(-3.17814 + 11.4684i) q^{54} +(2.88393 + 0.846798i) q^{55} +(3.18081 + 9.19035i) q^{56} +(2.87593 + 0.0310027i) q^{57} +(-0.682614 + 14.3298i) q^{58} +(0.504712 - 2.61869i) q^{59} +(-4.48633 - 1.13972i) q^{60} +(-4.17874 + 10.4380i) q^{61} +(2.60127 - 2.25402i) q^{62} +(-8.74662 - 5.30450i) q^{63} +(-12.4059 + 3.64270i) q^{64} +(-0.583360 - 0.819214i) q^{65} +(8.52526 - 11.7030i) q^{66} +(-3.30135 + 6.40373i) q^{67} +(-7.71875 - 13.3693i) q^{68} +(6.22629 - 5.49848i) q^{69} +(3.21543 - 5.56929i) q^{70} +(6.72112 + 10.4583i) q^{71} +(-4.78004 + 7.09671i) q^{72} +(5.56880 - 12.1940i) q^{73} +(4.81475 - 19.8467i) q^{74} +(-3.35823 - 6.69016i) q^{75} +(5.09253 + 1.76254i) q^{76} +(7.69343 + 9.78299i) q^{77} +(-4.66282 + 1.31470i) q^{78} +(8.56154 - 2.96318i) q^{79} +(-0.0287465 - 0.0184742i) q^{80} +(-0.895644 - 8.95532i) q^{81} +(3.01262 - 3.47675i) q^{82} +(-4.58096 + 4.36793i) q^{83} +(-12.3947 - 14.6197i) q^{84} +(-1.28118 + 3.70172i) q^{85} +(-2.24229 + 3.14886i) q^{86} +(-3.43778 - 10.2904i) q^{87} +(8.47992 - 6.03852i) q^{88} +(-0.898270 + 6.24760i) q^{89} +(5.61643 - 0.684295i) q^{90} -4.16431i q^{91} +(14.3295 - 6.07502i) q^{92} +(-1.21766 + 2.30069i) q^{93} +(-22.4003 - 11.5481i) q^{94} +(-0.508211 - 1.26945i) q^{95} +(7.70117 - 5.92304i) q^{96} +(13.9326 + 3.38001i) q^{97} +(9.63898 - 4.40197i) q^{98} +(-2.81034 + 10.5831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.28767	+	0.108975i	−1.61763	+	0.0770572i	−0.836736	−	0.547607i	$-0.815539\pi$
$2$	−2.28767	+	0.108975i	−1.61763	+	0.0770572i	−0.780894	+	0.624664i	$0.785236\pi$
$3$	1.58319	−	0.702495i	0.914057	−	0.405586i
$3$	1.58319	−	0.702495i	0.914057	−	0.405586i
$4$	3.23063	−	0.308488i	1.61532	−	0.154244i
$5$	−0.595980	−	0.568266i	−0.266530	−	0.254136i	0.545014	−	0.838427i	$-0.316524\pi$
$5$	−0.595980	−	0.568266i	−0.266530	−	0.254136i	−0.811544	+	0.584291i	$0.801373\pi$
$6$	−3.54528	+	1.77961i	−1.44735	+	0.726522i
$7$	−0.645310	−	3.34819i	−0.243904	−	1.26550i	−0.872828	−	0.488028i	$-0.837716\pi$
$7$	−0.645310	−	3.34819i	−0.243904	−	1.26550i	0.628923	−	0.777467i	$-0.283496\pi$
$8$	−2.82310	+	0.405901i	−0.998118	+	0.143508i
$9$	2.01300	−	2.22437i	0.671001	−	0.741457i
$10$	1.42534	+	1.23506i	0.450731	+	0.390560i
$11$	−3.24423	+	1.67252i	−0.978172	+	0.504283i	−0.871704	−	0.490033i	$-0.836985\pi$
$11$	−3.24423	+	1.67252i	−0.978172	+	0.504283i	−0.106468	+	0.994316i	$0.533954\pi$
$12$	4.89800	−	2.75790i	1.41393	−	0.796137i
$13$	1.19920	+	0.231127i	0.332599	+	0.0641032i	0.352817	−	0.935692i	$-0.385224\pi$
$13$	1.19920	+	0.231127i	0.332599	+	0.0641032i	−0.0202178	+	0.999796i	$0.506436\pi$
$14$	1.84113	+	7.58924i	0.492062	+	2.02831i
$15$	−1.34276	−	0.481002i	−0.346698	−	0.124194i
$16$	0.0407460	−	0.00785315i	0.0101865	−	0.00196329i
$17$	−1.97606	−	4.32697i	−0.479265	−	1.04944i	−0.982665	−	0.185391i	$-0.940645\pi$
$17$	−1.97606	−	4.32697i	−0.479265	−	1.04944i	0.503400	−	0.864054i	$-0.332082\pi$
$18$	−4.36269	+	5.30800i	−1.02830	+	1.25111i
$19$	1.51046	+	0.689803i	0.346523	+	0.158252i	0.581071	−	0.813853i	$-0.302634\pi$
$19$	1.51046	+	0.689803i	0.346523	+	0.158252i	−0.234548	+	0.972104i	$0.575361\pi$
$20$	−2.10070	−	1.65201i	−0.469730	−	0.369400i
$21$	−3.37373	−	4.84750i	−0.736209	−	1.05781i
$22$	7.23948	−	4.17971i	1.54346	−	0.891118i
$23$	4.57336	−	1.44374i	0.953611	−	0.301041i
$23$	4.57336	−	1.44374i	0.953611	−	0.301041i
$24$	−4.18437	+	2.62583i	−0.854132	+	0.535996i
$25$	−0.205643	−	4.31699i	−0.0411287	−	0.863397i
$26$	−2.76857	−	0.398061i	−0.542962	−	0.0780661i
$27$	1.62436	−	4.93573i	0.312609	−	0.949882i
$28$	−3.11764	−	10.6177i	−0.589178	−	2.00655i
$29$	0.595424	−	6.23556i	0.110567	−	1.15792i	−0.754514	−	0.656284i	$-0.772127\pi$
$29$	0.595424	−	6.23556i	0.110567	−	1.15792i	0.865082	−	0.501631i	$-0.167267\pi$
$30$	3.12420	+	0.954048i	0.570399	+	0.174185i
$31$	−1.18134	+	0.929013i	−0.212174	+	0.166856i	−0.718590	−	0.695433i	$-0.755212\pi$
$31$	−1.18134	+	0.929013i	−0.212174	+	0.166856i	0.506416	+	0.862289i	$0.330970\pi$
$32$	5.45112	−	1.32243i	0.963630	−	0.233774i
$33$	−3.96131	+	4.92697i	−0.689575	+	0.857675i
$34$	4.99212	+	9.68335i	0.856141	+	1.66068i
$35$	−1.51807	+	2.36216i	−0.256600	+	0.399278i
$36$	5.81708	−	7.80711i	0.969513	−	1.30118i
$37$	−2.51221	+	8.55582i	−0.413006	+	1.40657i	0.446198	+	0.894934i	$0.352778\pi$
$37$	−2.51221	+	8.55582i	−0.413006	+	1.40657i	−0.859204	+	0.511634i	$0.829041\pi$
$38$	−3.53060	−	1.41344i	−0.572740	−	0.229290i
$39$	2.06094	−	0.476515i	0.330014	−	0.0763034i
$40$	1.91317	+	1.36236i	0.302499	+	0.215409i
$41$	−1.38614	+	1.45375i	−0.216479	+	0.227037i	−0.823015	−	0.568019i	$-0.807710\pi$
$41$	−1.38614	+	1.45375i	−0.216479	+	0.227037i	0.606536	+	0.795056i	$0.292559\pi$
$42$	8.24626	+	10.7218i	1.27243	+	1.65442i
$43$	1.04336	−	1.32674i	0.159111	−	0.202326i	−0.699961	−	0.714181i	$-0.746799\pi$
$43$	1.04336	−	1.32674i	0.159111	−	0.202326i	0.859072	+	0.511855i	$0.171042\pi$
$44$	−9.96496	+	6.40409i	−1.50227	+	0.965453i
$45$	−2.46374	+	0.181760i	−0.367273	+	0.0270952i
$46$	−10.3050	+	3.80119i	−1.51939	+	0.560455i
$47$	9.52963	+	5.50193i	1.39004	+	0.802539i	0.993319	−	0.115400i	$-0.0368151\pi$
$47$	9.52963	+	5.50193i	1.39004	+	0.802539i	0.396720	+	0.917940i	$0.370148\pi$
$48$	0.0589920	−	0.0410569i	0.00851476	−	0.00592605i
$49$	−4.29535	+	1.71960i	−0.613622	+	0.245657i
$50$	0.940890	+	9.85345i	0.133062	+	1.39349i
$51$	−6.16816	−	5.46226i	−0.863715	−	0.764869i
$52$	3.94548	+	0.376748i	0.547140	+	0.0522456i
$53$	4.16607	+	4.80790i	0.572254	+	0.660416i	0.965921	−	0.258837i	$-0.0833393\pi$
$53$	4.16607	+	4.80790i	0.572254	+	0.660416i	−0.393667	+	0.919253i	$0.628794\pi$
$54$	−3.17814	+	11.4684i	−0.432490	+	1.56065i
$55$	2.88393	+	0.846798i	0.388869	+	0.114182i
$56$	3.18081	+	9.19035i	0.425054	+	1.22811i
$57$	2.87593	+	0.0310027i	0.380926	+	0.00410641i
$58$	−0.682614	+	14.3298i	−0.0896316	+	1.88160i
$59$	0.504712	−	2.61869i	0.0657079	−	0.340925i	−0.934165	−	0.356840i	$-0.883854\pi$
$59$	0.504712	−	2.61869i	0.0657079	−	0.340925i	0.999873	+	0.0159153i	$0.00506621\pi$
$60$	−4.48633	−	1.13972i	−0.579183	−	0.147137i
$61$	−4.17874	+	10.4380i	−0.535033	+	1.33645i	0.376955	+	0.926232i	$0.376971\pi$
$61$	−4.17874	+	10.4380i	−0.535033	+	1.33645i	−0.911988	+	0.410216i	$0.865453\pi$
$62$	2.60127	−	2.25402i	0.330362	−	0.286260i
$63$	−8.74662	−	5.30450i	−1.10197	−	0.668304i
$64$	−12.4059	+	3.64270i	−1.55074	+	0.455337i
$65$	−0.583360	−	0.819214i	−0.0723568	−	0.101611i
$66$	8.52526	−	11.7030i	1.04939	−	1.44054i
$67$	−3.30135	+	6.40373i	−0.403324	+	0.782340i	−0.999794	−	0.0202956i	$-0.993539\pi$
$67$	−3.30135	+	6.40373i	−0.403324	+	0.782340i	0.596470	+	0.802636i	$0.296570\pi$
$68$	−7.71875	−	13.3693i	−0.936035	−	1.62126i
$69$	6.22629	−	5.49848i	0.749557	−	0.661939i
$70$	3.21543	−	5.56929i	0.384317	−	0.665657i
$71$	6.72112	+	10.4583i	0.797651	+	1.24117i	0.966789	+	0.255576i	$0.0822652\pi$
$71$	6.72112	+	10.4583i	0.797651	+	1.24117i	−0.169138	+	0.985592i	$0.554098\pi$
$72$	−4.78004	+	7.09671i	−0.563333	+	0.836355i
$73$	5.56880	−	12.1940i	0.651778	−	1.42720i	−0.238211	−	0.971213i	$-0.576561\pi$
$73$	5.56880	−	12.1940i	0.651778	−	1.42720i	0.889989	−	0.455982i	$-0.150712\pi$
$74$	4.81475	−	19.8467i	0.559704	−	2.30713i
$75$	−3.35823	−	6.69016i	−0.387775	−	0.772513i
$76$	5.09253	+	1.76254i	0.584153	+	0.202177i
$77$	7.69343	+	9.78299i	0.876748	+	1.11488i
$78$	−4.66282	+	1.31470i	−0.527961	+	0.148861i
$79$	8.56154	−	2.96318i	0.963248	−	0.333383i	0.200222	−	0.979751i	$-0.435834\pi$
$79$	8.56154	−	2.96318i	0.963248	−	0.333383i	0.763026	+	0.646367i	$0.223713\pi$
$80$	−0.0287465	−	0.0184742i	−0.00321395	−	0.00206548i
$81$	−0.895644	−	8.95532i	−0.0995160	−	0.995036i
$82$	3.01262	−	3.47675i	0.332688	−	0.383943i
$83$	−4.58096	+	4.36793i	−0.502825	+	0.479443i	−0.898516	−	0.438941i	$-0.855354\pi$
$83$	−4.58096	+	4.36793i	−0.502825	+	0.479443i	0.395691	+	0.918384i	$0.370505\pi$
$84$	−12.3947	−	14.6197i	−1.35237	−	1.59514i
$85$	−1.28118	+	3.70172i	−0.138963	+	0.401508i
$86$	−2.24229	+	3.14886i	−0.241792	+	0.339550i
$87$	−3.43778	−	10.2904i	−0.368569	−	1.10325i
$88$	8.47992	−	6.03852i	0.903962	−	0.643709i
$89$	−0.898270	+	6.24760i	−0.0952164	+	0.662245i	0.885186	+	0.465238i	$0.154031\pi$
$89$	−0.898270	+	6.24760i	−0.0952164	+	0.662245i	−0.980402	+	0.197007i	$0.936878\pi$
$90$	5.61643	−	0.684295i	0.592024	−	0.0721310i
$91$		−	4.16431i		−	0.436538i
$92$	14.3295	−	6.07502i	1.49395	−	0.633365i
$93$	−1.21766	+	2.30069i	−0.126265	+	0.238570i
$94$	−22.4003	−	11.5481i	−2.31041	−	1.19110i
$95$	−0.508211	−	1.26945i	−0.0521414	−	0.130243i
$96$	7.70117	−	5.92304i	0.785998	−	0.604517i
$97$	13.9326	+	3.38001i	1.41464	+	0.343188i	0.868992	−	0.494826i	$-0.164768\pi$
$97$	13.9326	+	3.38001i	1.41464	+	0.343188i	0.545649	+	0.838014i	$0.316283\pi$
$98$	9.63898	−	4.40197i	0.973684	−	0.444666i
$99$	−2.81034	+	10.5831i	−0.282450	+	1.06365i
$100$	−1.99610	−	13.8832i	−0.199610	−	1.38832i
$101$	−9.46068	−	9.92208i	−0.941373	−	0.987284i	0.0585662	−	0.998284i	$-0.481347\pi$
$101$	−9.46068	−	9.92208i	−0.941373	−	0.987284i	−0.999940	+	0.0109996i	$0.996499\pi$
$102$	14.7060	+	11.8237i	1.45611	+	1.17072i
$103$	−0.838685	−	0.0399515i	−0.0826381	−	0.00393654i	0.00622215	−	0.999981i	$-0.498019\pi$
$103$	−0.838685	−	0.0399515i	−0.0826381	−	0.00393654i	−0.0888602	+	0.996044i	$0.528322\pi$
$104$	−3.47929	−	0.165739i	−0.341172	−	0.0162520i
$105$	−0.743990	+	4.80619i	−0.0726060	+	0.469036i
$106$	−10.0546	−	10.5449i	−0.976584	−	1.02421i
$107$	0.225373	+	1.56751i	0.0217877	+	0.151537i	0.997811	−	0.0661290i	$-0.0210649\pi$
$107$	0.225373	+	1.56751i	0.0217877	+	0.151537i	−0.976023	+	0.217666i	$0.930156\pi$
$108$	3.72511	−	16.4466i	0.358449	−	1.58258i
$109$	−14.0826	+	6.43130i	−1.34887	+	0.616006i	−0.953187	−	0.302382i	$-0.902218\pi$
$109$	−14.0826	+	6.43130i	−1.34887	+	0.616006i	−0.395679	+	0.918389i	$0.629491\pi$
$110$	−6.68977	−	1.62292i	−0.637845	−	0.154739i
$111$	2.03310	+	15.3103i	0.192973	+	1.45319i
$112$	−0.0525876	−	0.131357i	−0.00496906	−	0.0124121i
$113$	−4.08845	−	2.10774i	−0.384609	−	0.198279i	0.255069	−	0.966923i	$-0.417902\pi$
$113$	−4.08845	−	2.10774i	−0.384609	−	0.198279i	−0.639678	+	0.768643i	$0.720932\pi$
$114$	−6.58257	+	0.242481i	−0.616514	+	0.0227104i
$115$	−3.54606	−	1.73844i	−0.330672	−	0.162111i
$116$		−	20.3285i		−	1.88745i
$117$	2.92811	−	2.20221i	0.270704	−	0.203595i
$118$	−0.869243	+	6.04572i	−0.0800203	+	0.556553i
$119$	−13.2123	+	9.40846i	−1.21117	+	0.862472i
$120$	3.98598	+	0.812892i	0.363868	+	0.0742066i
$121$	1.34709	−	1.89172i	0.122462	−	0.171974i
$122$	8.42211	−	24.3341i	0.762502	−	2.20311i
$123$	−1.17328	+	3.27532i	−0.105792	+	0.295326i
$124$	−3.52987	+	3.36573i	−0.316992	+	0.302251i
$125$	−5.02696	+	5.80142i	−0.449625	+	0.518895i
$126$	20.5875	+	11.1818i	1.83408	+	0.996154i
$127$	8.43831	+	5.42297i	0.748779	+	0.481211i	0.858540	−	0.512747i	$-0.171372\pi$
$127$	8.43831	+	5.42297i	0.748779	+	0.481211i	−0.109761	+	0.993958i	$0.535008\pi$
$128$	17.3822	−	6.01604i	1.53639	−	0.531748i
$129$	0.719814	−	2.83345i	0.0633761	−	0.249471i
$130$	1.42381	+	1.81052i	0.124876	+	0.158793i
$131$	11.3990	+	3.94523i	0.995936	+	0.344697i	0.775942	−	0.630805i	$-0.217275\pi$
$131$	11.3990	+	3.94523i	0.995936	+	0.344697i	0.219994	+	0.975501i	$0.429396\pi$
$132$	−11.2776	+	17.1392i	−0.981591	+	1.49178i
$133$	1.33487	−	5.50243i	0.115748	−	0.477121i
$134$	6.85457	−	15.0094i	0.592144	−	1.29662i
$135$	−3.77290	+	2.01853i	−0.324719	+	0.173727i
$136$	7.33495	+	11.4134i	0.628966	+	0.978691i
$137$	8.50971	−	14.7392i	0.727033	−	1.25926i	−0.231098	−	0.972930i	$-0.574232\pi$
$137$	8.50971	−	14.7392i	0.727033	−	1.25926i	0.958132	−	0.286328i	$-0.0924348\pi$
$138$	−13.6445	+	13.2572i	−1.16150	+	1.12853i
$139$	0.953387	+	1.65131i	0.0808652	+	0.140063i	0.903622	−	0.428331i	$-0.140898\pi$
$139$	0.953387	+	1.65131i	0.0808652	+	0.140063i	−0.822757	+	0.568394i	$0.807565\pi$
$140$	−4.17562	+	8.09958i	−0.352905	+	0.684539i
$141$	18.9523	+	2.01611i	1.59607	+	0.169787i
$142$	−16.5154	−	23.1927i	−1.38594	−	1.94629i
$143$	−4.27705	+	1.25586i	−0.357665	+	0.105020i
$144$	0.0645535	−	0.106443i	0.00537945	−	0.00887021i
$145$	−3.89832	+	3.37791i	−0.323738	+	0.280520i
$146$	−11.4107	+	28.5027i	−0.944360	+	2.35890i
$147$	−5.59237	+	5.73992i	−0.461251	+	0.473421i
$148$	−5.47668	+	28.4157i	−0.450180	+	2.33576i
$149$	1.06520	−	22.3613i	0.0872645	−	1.83191i	−0.354821	−	0.934934i	$-0.615458\pi$
$149$	1.06520	−	22.3613i	0.0872645	−	1.83191i	0.442086	−	0.896973i	$-0.354239\pi$
$150$	8.41161	+	14.9389i	0.686805	+	1.21976i
$151$	5.81654	+	16.8058i	0.473343	+	1.36764i	0.888914	+	0.458075i	$0.151461\pi$
$151$	5.81654	+	16.8058i	0.473343	+	1.36764i	−0.415570	+	0.909561i	$0.636418\pi$
$152$	−4.54417	−	1.33429i	−0.368581	−	0.108225i
$153$	−13.6026	−	4.31471i	−1.09970	−	0.348824i
$154$	−18.6662	−	21.5419i	−1.50416	−	1.73590i
$155$	1.23198	+	0.117640i	0.0989550	+	0.00944906i
$156$	6.51113	−	2.17522i	0.521308	−	0.174157i
$157$	−0.739777	−	7.74729i	−0.0590406	−	0.618301i	−0.975771	−	0.218795i	$-0.929787\pi$
$157$	−0.739777	−	7.74729i	−0.0590406	−	0.618301i	0.916730	−	0.399507i	$-0.130819\pi$
$158$	−19.2631	+	7.71178i	−1.53249	+	0.613516i
$159$	9.97322	+	4.68519i	0.790928	+	0.371560i
$160$	−4.00025	−	2.30954i	−0.316247	−	0.182585i
$161$	−7.78515	−	14.3808i	−0.613556	−	1.13337i
$162$	3.02485	+	20.3893i	0.237655	+	1.60193i
$163$	12.3097	−	7.91093i	0.964167	−	0.619632i	0.0390184	−	0.999238i	$-0.487577\pi$
$163$	12.3097	−	7.91093i	0.964167	−	0.619632i	0.925148	+	0.379606i	$0.123941\pi$
$164$	−4.02966	+	5.12413i	−0.314663	+	0.400127i
$165$	5.16069	−	0.685301i	0.401759	−	0.0533506i
$166$	10.0037	−	10.4916i	0.776441	−	0.814308i
$167$	−2.00521	−	1.42790i	−0.155168	−	0.110494i	0.499836	−	0.866120i	$-0.333394\pi$
$167$	−2.00521	−	1.42790i	−0.155168	−	0.110494i	−0.655004	+	0.755626i	$0.727333\pi$
$168$	11.4920	+	12.3156i	0.886627	+	0.950168i
$169$	−10.6841	−	4.27727i	−0.821855	−	0.329021i
$170$	2.52752	−	8.60794i	0.193852	−	0.660199i
$171$	4.57493	−	1.97124i	0.349854	−	0.150745i
$172$	2.96144	−	4.60808i	0.225807	−	0.351363i
$173$	8.93927	+	17.3398i	0.679640	+	1.31832i	0.936090	+	0.351760i	$0.114417\pi$
$173$	8.93927	+	17.3398i	0.679640	+	1.31832i	−0.256450	+	0.966557i	$0.582553\pi$
$174$	8.98592	+	23.1664i	0.681221	+	1.75624i
$175$	−14.3214	+	3.47433i	−1.08259	+	0.262634i
$176$	−0.119055	+	0.0936257i	−0.00897409	+	0.00705730i
$177$	−1.04056	−	4.50046i	−0.0782134	−	0.338275i
$178$	1.37411	−	14.3904i	0.102994	−	1.07860i
$179$	4.02968	+	13.7238i	0.301193	+	1.02577i	0.961507	+	0.274779i	$0.0886047\pi$
$179$	4.02968	+	13.7238i	0.301193	+	1.02577i	−0.660315	+	0.750989i	$0.729577\pi$
$180$	−7.90338	+	1.34723i	−0.589083	+	0.100417i
$181$	9.25811	+	1.33111i	0.688150	+	0.0989410i	0.477515	−	0.878624i	$-0.341538\pi$
$181$	9.25811	+	1.33111i	0.688150	+	0.0989410i	0.210635	+	0.977565i	$0.432447\pi$
$182$	0.453807	+	9.52657i	0.0336384	+	0.706157i
$183$	0.716879	+	19.4609i	0.0529932	+	1.43859i
$184$	−12.3250	+	5.93216i	−0.908615	+	0.437325i
$185$	6.35921	−	3.67149i	0.467538	−	0.269933i
$186$	2.53488	−	5.39592i	0.185867	−	0.395648i
$187$	13.6477	+	10.7327i	0.998020	+	0.784852i
$188$	32.4840	+	14.8349i	2.36914	+	1.08195i
$189$	−17.5740	−	2.25359i	−1.27832	−	0.163925i
$190$	1.30096	+	2.84871i	0.0943816	+	0.206667i
$191$	−11.7370	+	2.26212i	−0.849259	+	0.163681i	−0.595270	−	0.803526i	$-0.702955\pi$
$191$	−11.7370	+	2.26212i	−0.849259	+	0.163681i	−0.253989	+	0.967207i	$0.581743\pi$
$192$	−17.0820	+	14.4822i	−1.23278	+	1.04516i
$193$	−5.78344	−	23.8397i	−0.416301	−	1.71602i	−0.664484	−	0.747303i	$-0.731349\pi$
$193$	−5.78344	−	23.8397i	−0.416301	−	1.71602i	0.248183	−	0.968713i	$-0.420167\pi$
$194$	−32.2416	−	6.21405i	−2.31481	−	0.446143i
$195$	−1.49906	−	0.887167i	−0.107350	−	0.0635313i
$196$	−13.3462	+	6.88046i	−0.953302	+	0.491462i
$197$	−1.35838	−	1.17704i	−0.0967802	−	0.0838605i	0.605127	−	0.796129i	$-0.293122\pi$
$197$	−1.35838	−	1.17704i	−0.0967802	−	0.0838605i	−0.701907	+	0.712269i	$0.747668\pi$
$198$	5.27585	−	24.5170i	0.374938	−	1.74235i
$199$	19.1909	−	2.75924i	1.36041	−	0.195597i	0.576817	−	0.816874i	$-0.304295\pi$
$199$	19.1909	−	2.75924i	1.36041	−	0.195597i	0.783591	+	0.621276i	$0.213386\pi$
$200$	2.33282	+	12.1038i	0.164955	+	0.855870i
$201$	−0.728092	+	12.4575i	−0.0513556	+	0.878686i
$202$	22.7242	+	21.6675i	1.59887	+	1.52452i
$203$	−21.2621	+	2.03028i	−1.49230	+	0.142498i
$204$	−21.6121	−	15.7437i	−1.51315	−	1.10228i
$205$	1.65223	−	0.0787053i	0.115397	−	0.00549702i
$206$	1.92299			0.133981
$207$	5.99477	−	13.0791i	0.416665	−	0.909060i
$208$	0.0506778			0.00351387
$209$	−6.05398	+	0.288386i	−0.418762	+	0.0199481i
$210$	1.17825	−	11.0761i	0.0813070	−	0.764322i
$211$	1.75455	−	0.167539i	0.120788	−	0.0115338i	−0.0344870	−	0.999405i	$-0.510980\pi$
$211$	1.75455	−	0.167539i	0.120788	−	0.0115338i	0.155275	+	0.987871i	$0.450374\pi$
$212$	14.9422	+	14.2474i	1.02624	+	0.978514i
$213$	17.9877	+	11.8359i	1.23250	+	0.810983i
$214$	−0.686400	−	3.56138i	−0.0469214	−	0.243451i
$215$	−1.37577	+	0.197805i	−0.0938265	+	0.0134902i
$216$	−2.58233	+	14.5934i	−0.175705	+	0.992956i
$217$	3.87284	+	3.35583i	0.262905	+	0.227809i
$218$	31.5155	−	16.2474i	2.13450	−	1.10041i
$219$	0.250286	−	23.2174i	0.0169128	−	1.56889i
$220$	9.57815	+	1.84604i	0.645759	+	0.124460i
$221$	−1.36962	−	5.64564i	−0.0921304	−	0.379767i
$222$	−6.31951	−	34.8035i	−0.424138	−	2.33586i
$223$	−13.9573	+	2.69005i	−0.934650	+	0.180139i	−0.633769	−	0.773523i	$-0.718493\pi$
$223$	−13.9573	+	2.69005i	−0.934650	+	0.180139i	−0.300881	+	0.953662i	$0.597281\pi$
$224$	−7.94539	−	17.3980i	−0.530874	−	1.16245i
$225$	−10.0165	−	8.23268i	−0.667769	−	0.548845i
$226$	9.58272	+	4.37628i	0.637433	+	0.291106i
$227$	−11.2166	−	8.82086i	−0.744474	−	0.585461i	0.172216	−	0.985059i	$-0.444907\pi$
$227$	−11.2166	−	8.82086i	−0.744474	−	0.585461i	−0.916690	+	0.399598i	$0.869150\pi$
$228$	9.30063	−	0.787031i	0.615949	−	0.0521224i
$229$	17.0418	−	9.83909i	1.12615	−	0.650185i	0.183189	−	0.983078i	$-0.441358\pi$
$229$	17.0418	−	9.83909i	1.12615	−	0.650185i	0.942965	+	0.332893i	$0.108025\pi$
$230$	8.30168	+	3.59056i	0.547396	+	0.236754i
$231$	19.0527	+	10.0838i	1.25357	+	0.663464i
$232$	0.850078	+	17.8453i	0.0558103	+	1.17160i
$233$	12.5399	+	1.80297i	0.821517	+	0.118116i	0.540241	−	0.841511i	$-0.318333\pi$
$233$	12.5399	+	1.80297i	0.821517	+	0.118116i	0.281276	+	0.959627i	$0.409242\pi$
$234$	−6.45858	+	5.35703i	−0.422210	+	0.350200i
$235$	−2.55291	−	8.69441i	−0.166533	−	0.567160i
$236$	0.822703	−	8.61573i	0.0535534	−	0.560836i
$237$	11.4730	−	10.7057i	0.745248	−	0.695411i
$238$	29.2002	−	22.9633i	1.89277	−	1.48849i
$239$	−21.2745	+	5.16114i	−1.37613	+	0.333846i	−0.854557	−	0.519358i	$-0.826171\pi$
$239$	−21.2745	+	5.16114i	−1.37613	+	0.333846i	−0.521577	+	0.853204i	$0.674656\pi$
$240$	−0.0584893	−	0.00905404i	−0.00377547	−	0.000584436i
$241$	−11.4411	−	22.1927i	−0.736988	−	1.42956i	−0.896812	−	0.442412i	$-0.854123\pi$
$241$	−11.4411	−	22.1927i	−0.736988	−	1.42956i	0.159824	−	0.987145i	$-0.448907\pi$
$242$	−2.87554	+	4.47443i	−0.184847	+	0.287627i
$243$	−7.70905	−	13.5488i	−0.494536	−	0.869157i
$244$	−10.2800	+	35.0104i	−0.658108	+	2.24131i
$245$	3.53714	+	1.41606i	0.225979	+	0.0904685i
$246$	2.32716	−	7.62072i	0.148375	−	0.485879i
$247$	1.65191	+	1.17632i	0.105109	+	0.0748476i
$248$	2.95795	−	3.10221i	0.187830	−	0.196990i
$249$	−4.18409	+	10.1334i	−0.265156	+	0.642177i
$250$	10.8678	−	13.8196i	0.687342	−	0.874027i
$251$	−6.71604	+	4.31613i	−0.423912	+	0.272432i	−0.735156	−	0.677898i	$-0.762891\pi$
$251$	−6.71604	+	4.31613i	−0.423912	+	0.272432i	0.311243	+	0.950330i	$0.399255\pi$
$252$	−29.8935	−	14.4387i	−1.88311	−	0.909550i
$253$	−12.4223	+	12.3328i	−0.780986	+	0.775359i
$254$	−19.8951	−	11.4864i	−1.24833	−	0.720723i
$255$	0.572086	+	6.76055i	0.0358254	+	0.423362i
$256$	−15.1023	+	6.04606i	−0.943896	+	0.377879i
$257$	0.567957	+	5.94792i	0.0354282	+	0.371021i	0.995748	+	0.0921196i	$0.0293642\pi$
$257$	0.567957	+	5.94792i	0.0354282	+	0.371021i	−0.960320	+	0.278901i	$0.910030\pi$
$258$	−1.33792	+	6.56044i	−0.0832955	+	0.408435i
$259$	30.2676	+	2.89021i	1.88074	+	0.179589i
$260$	−2.13734	−	2.46662i	−0.132552	−	0.152973i
$261$	−12.6716	−	13.8766i	−0.784353	−	0.858943i
$262$	−26.5071	−	7.78320i	−1.63762	−	0.480848i
$263$	1.03881	+	3.00146i	0.0640560	+	0.185078i	0.972487	−	0.232957i	$-0.0748402\pi$
$263$	1.03881	+	3.00146i	0.0640560	+	0.185078i	−0.908431	+	0.418035i	$0.862719\pi$
$264$	9.18332	−	15.5172i	0.565194	−	0.955020i
$265$	0.249271	−	5.23285i	0.0153126	−	0.321451i
$266$	−2.45413	+	12.7332i	−0.150472	+	0.780725i
$267$	2.96677	+	10.5222i	0.181564	+	0.643948i
$268$	−8.68998	+	21.7065i	−0.530825	+	1.32594i
$269$	−15.9594	+	13.8289i	−0.973061	+	0.843162i	−0.987641	−	0.156731i	$-0.949904\pi$
$269$	−15.9594	+	13.8289i	−0.973061	+	0.843162i	0.0145802	+	0.999894i	$0.495359\pi$
$270$	8.41119	−	5.02889i	0.511889	−	0.306048i
$271$	0.594331	−	0.174511i	0.0361031	−	0.0106008i	−0.263631	−	0.964624i	$-0.584920\pi$
$271$	0.594331	−	0.174511i	0.0361031	−	0.0106008i	0.299734	+	0.954023i	$0.403102\pi$
$272$	−0.114497	−	0.160788i	−0.00694239	−	0.00974923i
$273$	−2.92540	−	6.59290i	−0.177053	−	0.399020i
$274$	−17.8612	+	34.6459i	−1.07904	+	2.09304i
$275$	7.88738	+	13.6613i	0.475627	+	0.823810i
$276$	18.4186	−	19.6843i	1.10867	−	1.18486i
$277$	−11.5102	+	19.9362i	−0.691578	+	1.19785i	0.279743	+	0.960075i	$0.409751\pi$
$277$	−11.5102	+	19.9362i	−0.691578	+	1.19785i	−0.971321	+	0.237773i	$0.923582\pi$
$278$	−2.36099	−	3.67377i	−0.141603	−	0.220338i
$279$	−0.311564	+	4.49783i	−0.0186528	+	0.269278i
$280$	3.32686	−	7.28481i	0.198818	−	0.435351i
$281$	−5.73956	+	23.6588i	−0.342393	+	1.41136i	0.496958	+	0.867774i	$0.334450\pi$
$281$	−5.73956	+	23.6588i	−0.342393	+	1.41136i	−0.839351	+	0.543589i	$0.817065\pi$
$282$	−43.5764	−	2.54687i	−2.59494	−	0.151664i
$283$	−4.28851	−	1.48427i	−0.254925	−	0.0882305i	0.196617	−	0.980480i	$-0.437005\pi$
$283$	−4.28851	−	1.48427i	−0.254925	−	0.0882305i	−0.451542	+	0.892250i	$0.649126\pi$
$284$	24.9397	+	31.7134i	1.47990	+	1.88185i
$285$	−1.69638	−	1.65277i	−0.100485	−	0.0979016i
$286$	9.64765	−	3.33908i	0.570477	−	0.197444i
$287$	5.76190	+	3.70295i	0.340114	+	0.218578i
$288$	8.03154	−	14.7873i	0.473263	−	0.871353i
$289$	−3.68522	+	4.25297i	−0.216778	+	0.250175i
$290$	8.54998	−	8.15239i	0.502072	−	0.478725i
$291$	24.4324	−	4.43636i	1.43225	−	0.260064i
$292$	14.2290	−	41.1121i	0.832692	−	2.40590i
$293$	12.8860	−	18.0959i	0.752811	−	1.05717i	−0.243376	−	0.969932i	$-0.578255\pi$
$293$	12.8860	−	18.0959i	0.752811	−	1.05717i	0.996187	−	0.0872427i	$-0.0278056\pi$
$294$	12.1680	−	13.7405i	0.709652	−	0.801362i
$295$	−1.78891	+	1.27388i	−0.104155	+	0.0741681i
$296$	3.61943	−	25.1737i	0.210375	−	1.46319i
$297$	2.98528	+	18.7294i	0.173224	+	1.08679i
$298$			51.2714i			2.97007i
$299$	5.81808	−	0.674310i	0.336468	−	0.0389963i
$300$	−12.9131	−	20.5775i	−0.745535	−	1.18804i
$301$	−5.11547	−	2.63721i	−0.294851	−	0.152006i
$302$	−15.1378	−	37.8123i	−0.871081	−	2.17585i
$303$	−21.9483	−	9.06249i	−1.26090	−	0.520626i
$304$	0.0669622	+	0.0162449i	0.00384054	+	0.000931706i
$305$	8.42200	−	3.84620i	0.482243	−	0.220233i
$306$	31.5885	+	8.38830i	1.80579	+	0.479527i
$307$	−2.89633	−	20.1444i	−0.165302	−	1.14970i	−0.888438	−	0.458997i	$-0.848209\pi$
$307$	−2.89633	−	20.1444i	−0.165302	−	1.14970i	0.723135	−	0.690706i	$-0.242700\pi$
$308$	27.8726	+	29.2319i	1.58819	+	1.66564i
$309$	−1.35587	+	0.525921i	−0.0771325	+	0.0299186i
$310$	−2.83119	−	0.134866i	−0.160801	−	0.00765988i
$311$	−0.890115	−	0.0424014i	−0.0504738	−	0.00240436i	0.0223298	−	0.999751i	$-0.492892\pi$
$311$	−0.890115	−	0.0424014i	−0.0504738	−	0.00240436i	−0.0728036	+	0.997346i	$0.523195\pi$
$312$	−5.62482	+	2.18179i	−0.318443	+	0.123519i
$313$	−7.32734	−	7.68470i	−0.414166	−	0.434365i	0.483296	−	0.875457i	$-0.339440\pi$
$313$	−7.32734	−	7.68470i	−0.414166	−	0.434365i	−0.897462	+	0.441092i	$0.854591\pi$
$314$	2.53663	+	17.6427i	0.143150	+	0.995633i
$315$	2.19844	+	8.13178i	0.123868	+	0.458174i
$316$	26.7451	−	12.2141i	1.50453	−	0.687095i
$317$	7.39060	+	1.79294i	0.415097	+	0.100702i	0.437868	−	0.899039i	$-0.355734\pi$
$317$	7.39060	+	1.79294i	0.415097	+	0.100702i	−0.0227708	+	0.999741i	$0.507249\pi$
$318$	−23.3260	−	9.63136i	−1.30806	−	0.540100i
$319$	8.49739	+	21.2255i	0.475762	+	1.18840i
$320$	9.46369	+	4.87887i	0.529036	+	0.272737i
$321$	1.45797	+	2.32334i	0.0813762	+	0.129676i
$322$	19.3770	+	32.0502i	1.07984	+	1.78609i
$323$		−	7.89880i		−	0.439501i
$324$	−5.65611	−	28.6551i	−0.314228	−	1.59195i
$325$	0.751166	−	5.22447i	0.0416672	−	0.289802i
$326$	−27.2984	+	19.4391i	−1.51192	+	1.07663i
$327$	−17.7775	+	20.0749i	−0.983097	+	1.11015i
$328$	3.32315	−	4.66671i	0.183490	−	0.257676i
$329$	12.2719	−	35.4574i	0.676574	−	1.95483i
$330$	−11.7313	+	2.13013i	−0.645787	+	0.117260i
$331$	−11.3562	+	10.8281i	−0.624195	+	0.595168i	−0.934715	−	0.355398i	$-0.884345\pi$
$331$	−11.3562	+	10.8281i	−0.624195	+	0.595168i	0.310520	+	0.950567i	$0.399497\pi$
$332$	−13.4519	+	15.5244i	−0.738271	+	0.852010i
$333$	13.9742	+	22.8110i	0.765782	+	1.25003i
$334$	4.74287	+	3.04806i	0.259518	+	0.166782i
$335$	5.60656	−	1.94045i	0.306319	−	0.106018i
$336$	−0.175534	−	0.171022i	−0.00957618	−	0.00933000i
$337$	−7.10882	−	9.03960i	−0.387242	−	0.492418i	0.552878	−	0.833262i	$-0.313530\pi$
$337$	−7.10882	−	9.03960i	−0.387242	−	0.492418i	−0.940120	+	0.340844i	$0.889287\pi$
$338$	24.9079	+	8.62070i	1.35481	+	0.468904i
$339$	−7.95348	−	0.464848i	−0.431973	−	0.0252471i
$340$	−2.99708	+	12.3541i	−0.162539	+	0.669996i
$341$	2.27874	−	4.98974i	0.123400	−	0.270209i
$342$	−10.2511	+	5.00811i	−0.554318	+	0.270808i
$343$	−4.37498	−	6.80761i	−0.236227	−	0.367576i
$344$	−2.40699	+	4.16903i	−0.129776	+	0.224779i
$345$	−6.83535	−	0.261203i	−0.368003	−	0.0140627i
$346$	−22.3397	−	38.6936i	−1.20099	−	2.08018i
$347$	−1.96109	+	3.80399i	−0.105277	+	0.204209i	−0.935590	−	0.353089i	$-0.885131\pi$
$347$	−1.96109	+	3.80399i	−0.105277	+	0.204209i	0.830313	+	0.557298i	$0.188162\pi$
$348$	−14.2807	−	32.1839i	−0.765524	−	1.72524i
$349$	17.9279	+	25.1762i	0.959659	+	1.34765i	0.937533	+	0.347897i	$0.113104\pi$
$349$	17.9279	+	25.1762i	0.959659	+	1.34765i	0.0221258	+	0.999755i	$0.492957\pi$
$350$	32.3840	−	9.50880i	1.73100	−	0.508267i
$351$	3.08872	−	5.54351i	0.164864	−	0.295891i
$352$	−15.4729	+	13.4073i	−0.824708	+	0.714613i
$353$	−1.16049	+	2.89876i	−0.0617666	+	0.154286i	−0.956041	−	0.293234i	$-0.905268\pi$
$353$	−1.16049	+	2.89876i	−0.0617666	+	0.154286i	0.894274	+	0.447520i	$0.147693\pi$
$354$	2.87091	+	10.1822i	0.152587	+	0.541177i
$355$	1.93742	−	10.0523i	0.102828	−	0.533521i
$356$	−0.974669	+	20.4608i	−0.0516573	+	1.08442i
$357$	−14.3083	+	24.1770i	−0.757275	+	1.27958i
$358$	−10.7142	−	30.9565i	−0.566261	−	1.63610i
$359$	−2.62796	−	0.771639i	−0.138698	−	0.0407255i	0.211647	−	0.977346i	$-0.432117\pi$
$359$	−2.62796	−	0.771639i	−0.138698	−	0.0407255i	−0.350345	+	0.936621i	$0.613936\pi$
$360$	6.88163	−	1.51316i	0.362694	−	0.0797507i
$361$	−10.6367	−	12.2754i	−0.559826	−	0.646074i
$362$	−21.3246	−	2.03625i	−1.12080	−	0.107023i
$363$	0.803775	−	3.94127i	0.0421873	−	0.206863i
$364$	−1.28464	−	13.4533i	−0.0673333	−	0.705147i
$365$	−10.2483	+	4.10280i	−0.536421	+	0.214750i
$366$	−3.76074	−	44.4421i	−0.196577	−	2.32302i
$367$	9.16318	+	5.29037i	0.478314	+	0.276155i	0.719714	−	0.694271i	$-0.244273\pi$
$367$	9.16318	+	5.29037i	0.478314	+	0.276155i	−0.241399	+	0.970426i	$0.577606\pi$
$368$	0.175008	−	0.0947419i	0.00912293	−	0.00493876i
$369$	0.443358	+	6.00969i	0.0230803	+	0.312852i
$370$	−14.1477	+	9.09217i	−0.735504	+	0.472680i
$371$	13.4093	−	17.0514i	0.696178	−	0.885263i
$372$	−3.22407	+	7.80832i	−0.167160	+	0.404842i
$373$	6.42026	−	6.73338i	0.332429	−	0.348641i	−0.536212	−	0.844083i	$-0.680145\pi$
$373$	6.42026	−	6.73338i	0.332429	−	0.348641i	0.868641	+	0.495442i	$0.164994\pi$
$374$	−32.3911	−	23.0656i	−1.67491	−	1.19270i
$375$	−3.88318	+	12.7162i	−0.200527	+	0.656661i
$376$	−29.1364	−	11.6644i	−1.50259	−	0.601548i
$377$	2.15524	−	7.34009i	0.111001	−	0.378034i
$378$	40.4491	+	3.24036i	2.08048	+	0.166666i
$379$	0.632891	−	0.984798i	0.0325094	−	0.0505857i	−0.824619	−	0.565689i	$-0.808610\pi$
$379$	0.632891	−	0.984798i	0.0325094	−	0.0505857i	0.857128	+	0.515104i	$0.172247\pi$
$380$	−2.03345	−	3.94435i	−0.104314	−	0.202341i
$381$	17.1691	+	2.65775i	0.879599	+	0.136160i
$382$	26.6039	−	6.45403i	1.36117	−	0.330217i
$383$	−12.4534	+	9.79345i	−0.636338	+	0.500422i	−0.883426	−	0.468571i	$-0.844769\pi$
$383$	−12.4534	+	9.79345i	−0.636338	+	0.500422i	0.247087	+	0.968993i	$0.420527\pi$
$384$	23.2932	−	21.7355i	1.18867	−	1.10918i
$385$	0.974210	−	10.2024i	0.0496503	−	0.519962i
$386$	15.8286	+	53.9071i	0.805652	+	2.74380i
$387$	−0.850877	−	4.99156i	−0.0432525	−	0.253735i
$388$	46.0538	+	6.62154i	2.33803	+	0.336158i
$389$	−0.733287	−	15.3936i	−0.0371791	−	0.780486i	−0.938071	−	0.346443i	$-0.887389\pi$
$389$	−0.733287	−	15.3936i	−0.0371791	−	0.780486i	0.900892	−	0.434043i	$-0.142914\pi$
$390$	3.52605	+	1.86619i	0.178548	+	0.0944981i
$391$	−15.2843	−	16.9359i	−0.772958	−	0.856484i
$392$	11.4282	−	6.59810i	0.577213	−	0.333254i
$393$	20.8183	−	1.76167i	1.05015	−	0.0888647i
$394$	3.23579	+	2.54465i	0.163017	+	0.128198i
$395$	−6.78638	−	3.09924i	−0.341460	−	0.155939i
$396$	−5.81442	+	35.0572i	−0.292186	+	1.76169i
$397$	−8.76579	−	19.1944i	−0.439942	−	0.963339i	−0.991609	−	0.129274i	$-0.958735\pi$
$397$	−8.76579	−	19.1944i	−0.439942	−	0.963339i	0.551667	−	0.834065i	$-0.313992\pi$
$398$	−43.6019	+	8.40357i	−2.18556	+	0.421233i
$399$	−1.75206	−	9.64915i	−0.0877129	−	0.483062i
$400$	−0.0422811	−	0.174285i	−0.00211405	−	0.00871425i
$401$	−5.95942	−	1.14858i	−0.297599	−	0.0573575i	0.0382661	−	0.999268i	$-0.487817\pi$
$401$	−5.95942	−	1.14858i	−0.297599	−	0.0573575i	−0.335865	+	0.941910i	$0.609029\pi$
$402$	0.308074	−	28.5781i	0.0153653	−	1.42535i
$403$	−1.63138	+	0.841036i	−0.0812650	+	0.0418950i
$404$	−33.6248	−	29.1361i	−1.67290	−	1.44957i
$405$	−4.55522	+	5.84616i	−0.226351	+	0.290498i
$406$	48.4194	−	6.96166i	2.40302	−	0.345501i
$407$	−6.15954	−	31.9588i	−0.305317	−	1.58414i
$408$	19.6305	+	12.9169i	0.971854	+	0.639480i
$409$	5.01382	+	4.78067i	0.247917	+	0.236389i	0.803840	−	0.594845i	$-0.202787\pi$
$409$	5.01382	+	4.78067i	0.247917	+	0.236389i	−0.555923	+	0.831234i	$0.687635\pi$
$410$	−3.77118	+	0.360104i	−0.186245	+	0.0177843i
$411$	3.11827	−	29.3131i	0.153813	−	1.44591i
$412$	−2.72181	+	0.129656i	−0.134094	+	0.00638768i
$413$	−9.09357			−0.447465
$414$	−12.2888	+	30.5740i	−0.603960	+	1.50263i
$415$	5.21231			0.255862
$416$	6.84264	−	0.325955i	0.335488	−	0.0159813i
$417$	2.66944	+	1.94460i	0.130723	+	0.0952275i
$418$	13.8181	−	1.31947i	0.675865	−	0.0645373i
$419$	18.8812	+	18.0032i	0.922409	+	0.879515i	0.993015	−	0.117989i	$-0.0376447\pi$
$419$	18.8812	+	18.0032i	0.922409	+	0.879515i	−0.0706057	+	0.997504i	$0.522493\pi$
$420$	−0.920907	+	15.7566i	−0.0449357	+	0.768841i
$421$	−1.63350	−	8.47540i	−0.0796119	−	0.413066i	−0.999769	−	0.0215152i	$-0.993151\pi$
$421$	−1.63350	−	8.47540i	−0.0796119	−	0.413066i	0.920157	−	0.391550i	$-0.128061\pi$
$422$	−3.99557	+	0.574476i	−0.194501	+	0.0279651i
$423$	31.4215	−	10.1220i	1.52777	−	0.492149i
$424$	−13.7128	−	11.8822i	−0.665951	−	0.577050i
$425$	−18.2731	+	9.42044i	−0.886376	+	0.456959i
$426$	−42.4399	−	25.1165i	−2.05622	−	1.21690i
$427$	37.6449	+	7.25547i	1.82177	+	0.351117i
$428$	1.21166	+	4.99451i	0.0585676	+	0.241419i
$429$	−5.88917	+	4.99287i	−0.284332	+	0.241058i
$430$	3.12575	−	0.602439i	0.150737	−	0.0290522i
$431$	4.48180	+	9.81378i	0.215881	+	0.472713i	0.986329	−	0.164790i	$-0.0526946\pi$
$431$	4.48180	+	9.81378i	0.215881	+	0.472713i	−0.770448	+	0.637503i	$0.779967\pi$
$432$	0.0274253	−	0.213868i	0.00131950	−	0.0102897i
$433$	8.19641	+	3.74317i	0.393894	+	0.179886i	0.602508	−	0.798113i	$-0.294168\pi$
$433$	8.19641	+	3.74317i	0.393894	+	0.179886i	−0.208614	+	0.977998i	$0.566895\pi$
$434$	−9.22549	−	7.25501i	−0.442838	−	0.348252i
$435$	−3.79883	+	8.08644i	−0.182140	+	0.387715i
$436$	−43.5116	+	25.1215i	−2.08383	+	1.20310i
$437$	7.90376	+	0.974007i	0.378088	+	0.0465931i
$438$	1.95756	+	53.1412i	0.0935357	+	2.53919i
$439$	0.269055	+	5.64817i	0.0128413	+	0.269572i	0.996152	+	0.0876395i	$0.0279324\pi$
$439$	0.269055	+	5.64817i	0.0128413	+	0.269572i	−0.983311	+	0.181933i	$0.941765\pi$
$440$	−8.48535	−	1.22001i	−0.404523	−	0.0581617i
$441$	−4.82153	+	13.0160i	−0.229597	+	0.619810i
$442$	3.74847	+	12.7661i	0.178297	+	0.607223i
$443$	−2.05179	+	21.4873i	−0.0974833	+	1.02089i	0.805898	+	0.592054i	$0.201683\pi$
$443$	−2.05179	+	21.4873i	−0.0974833	+	1.02089i	−0.903382	+	0.428838i	$0.858923\pi$
$444$	11.2912	+	48.8349i	0.535858	+	2.31760i
$445$	4.08565	−	3.21299i	0.193678	−	0.152310i
$446$	31.6366	−	7.67496i	1.49804	−	0.363420i
$447$	−14.0223	−	36.1505i	−0.663230	−	1.70986i
$448$	20.2021	+	39.1866i	0.954459	+	1.85139i
$449$	12.1697	−	18.9363i	0.574321	−	0.893662i	−0.425615	−	0.904904i	$-0.639942\pi$
$449$	12.1697	−	18.9363i	0.574321	−	0.893662i	0.999937	+	0.0112426i	$0.00357871\pi$
$450$	23.8117	+	17.7421i	1.12250	+	0.836372i
$451$	2.06555	−	7.03463i	0.0972631	−	0.331248i
$452$	−13.8585	−	5.54810i	−0.651848	−	0.260961i
$453$	21.0147	+	22.5207i	0.987356	+	1.05812i
$454$	26.6213	+	18.9569i	1.24940	+	0.889692i
$455$	−2.36643	+	2.48184i	−0.110940	+	0.116351i
$456$	−8.13163	+	1.07982i	−0.380798	+	0.0505671i
$457$	−11.3475	+	14.4295i	−0.530812	+	0.674983i	−0.975321	−	0.220792i	$-0.929136\pi$
$457$	−11.3475	+	14.4295i	−0.530812	+	0.674983i	0.444509	+	0.895775i	$0.353378\pi$
$458$	−37.9139	+	24.3658i	−1.77160	+	1.13854i
$459$	−24.5666	+	2.72473i	−1.14667	+	0.127180i
$460$	−11.9923	−	4.52235i	−0.559144	−	0.210856i
$461$	−8.01373	−	4.62673i	−0.373236	−	0.215488i	0.301635	−	0.953423i	$-0.402468\pi$
$461$	−8.01373	−	4.62673i	−0.373236	−	0.215488i	−0.674871	+	0.737935i	$0.735801\pi$
$462$	−44.6852	−	20.9921i	−2.07894	−	0.976642i
$463$	−24.3098	+	9.73218i	−1.12977	+	0.452293i	−0.859828	−	0.510583i	$-0.829430\pi$
$463$	−24.3098	+	9.73218i	−1.12977	+	0.452293i	−0.269944	+	0.962876i	$0.587005\pi$
$464$	−0.0247076	−	0.258750i	−0.00114702	−	0.0120122i
$465$	2.03310	−	0.679213i	0.0942829	−	0.0314977i
$466$	−28.8837	−	2.75806i	−1.33801	−	0.127765i
$467$	−14.9393	−	17.2409i	−0.691308	−	0.797812i	0.296243	−	0.955113i	$-0.404266\pi$
$467$	−14.9393	−	17.2409i	−0.691308	−	0.797812i	−0.987551	+	0.157301i	$0.949721\pi$
$468$	8.78030	−	8.01782i	0.405869	−	0.370624i
$469$	23.5713	+	6.92115i	1.08842	+	0.319589i
$470$	6.78770	+	19.6118i	0.313093	+	0.904623i
$471$	−6.61364	−	11.7458i	−0.304741	−	0.541217i
$472$	−0.361923	+	7.59770i	−0.0166589	+	0.349713i
$473$	−1.16591	+	6.04930i	−0.0536084	+	0.278147i
$474$	−25.0797	+	25.7415i	−1.15195	+	1.18234i
$475$	2.66725	−	6.66248i	0.122382	−	0.305695i
$476$	−39.7818	+	34.4711i	−1.82340	+	1.57998i
$477$	19.0809	+	0.411434i	0.873652	+	0.0188383i
$478$	48.1067	−	14.1254i	2.20035	−	0.646081i
$479$	−3.01132	−	4.22880i	−0.137591	−	0.193219i	0.740031	−	0.672572i	$-0.234811\pi$
$479$	−3.01132	−	4.22880i	−0.137591	−	0.193219i	−0.877622	+	0.479353i	$0.840871\pi$
$480$	−7.95561	−	0.846302i	−0.363122	−	0.0386282i
$481$	−4.99014	+	9.67952i	−0.227531	+	0.441348i
$482$	28.5920	+	49.5228i	1.30233	+	2.25570i
$483$	−22.4278	−	17.2986i	−1.02050	−	0.787112i
$484$	3.76837	−	6.52700i	0.171289	−	0.296682i
$485$	−6.38281	−	9.93184i	−0.289828	−	0.450982i
$486$	19.1123	+	30.1552i	0.866950	+	1.36787i
$487$	10.1403	−	22.2042i	0.459501	−	1.00617i	−0.528100	−	0.849182i	$-0.677095\pi$
$487$	10.1403	−	22.2042i	0.459501	−	1.00617i	0.987601	−	0.156985i	$-0.0501773\pi$
$488$	7.56023	−	31.1637i	0.342235	−	1.41071i
$489$	13.9312	−	21.1720i	0.629989	−	0.957431i
$490$	−8.24613	−	2.85401i	−0.372522	−	0.128931i
$491$	9.28904	+	11.8120i	0.419209	+	0.533067i	0.949090	−	0.315005i	$-0.102006\pi$
$491$	9.28904	+	11.8120i	0.419209	+	0.533067i	−0.529882	+	0.848072i	$0.677764\pi$
$492$	−2.78005	+	10.9433i	−0.125335	+	0.493362i
$493$	−28.1577	+	9.74547i	−1.26816	+	0.438914i
$494$	−3.90723	−	2.51102i	−0.175794	−	0.112976i
$495$	7.68895	−	4.71032i	0.345593	−	0.211713i
$496$	−0.0408390	+	0.0471308i	−0.00183373	+	0.00211623i
$497$	30.6790	−	29.2524i	1.37614	−	1.31215i
$498$	8.46755	−	23.6378i	0.379440	−	1.05924i
$499$	−13.3525	+	38.5794i	−0.597738	+	1.72705i	0.0849932	+	0.996382i	$0.472913\pi$
$499$	−13.3525	+	38.5794i	−0.597738	+	1.72705i	−0.682731	+	0.730669i	$0.739208\pi$
$500$	−14.4506	+	20.2930i	−0.646250	+	0.907531i
$501$	−4.17773	−	0.851998i	−0.186647	−	0.0380644i
$502$	14.8937	−	10.6058i	0.664740	−	0.473360i
$503$	−1.35192	+	9.40282i	−0.0602792	+	0.419251i	0.937230	+	0.348712i	$0.113381\pi$
$503$	−1.35192	+	9.40282i	−0.0602792	+	0.419251i	−0.997509	+	0.0705387i	$0.977528\pi$
$504$	26.8457	+	11.4249i	1.19580	+	0.508905i
$505$			11.2895i			0.502378i
$506$	27.0743	−	29.5673i	1.20360	−	1.31442i
$507$	−19.9198	+	0.733783i	−0.884669	+	0.0325884i
$508$	28.9340	+	14.9165i	1.28374	+	0.661813i
$509$	2.57133	+	6.42286i	0.113972	+	0.284688i	0.974376	−	0.224923i	$-0.0722132\pi$
$509$	2.57133	+	6.42286i	0.113972	+	0.284688i	−0.860404	+	0.509612i	$0.829789\pi$
$510$	−2.04548	−	15.4036i	−0.0905754	−	0.682083i
$511$	−44.4213	−	10.7765i	−1.96508	−	0.476723i
$512$	0.427039	−	0.195022i	0.0188726	−	0.00861884i
$513$	5.85821	−	6.33472i	0.258646	−	0.279685i
$514$	−1.94748	−	13.5450i	−0.0858996	−	0.597445i
$515$	0.477137	+	0.500406i	0.0210251	+	0.0220505i
$516$	1.45137	−	9.37588i	0.0638930	−	0.412750i
$517$	−40.1184	−	1.91107i	−1.76440	−	0.0840489i
$518$	−69.5574	−	3.31343i	−3.05618	−	0.145584i
$519$	26.3337	+	21.1724i	1.15592	+	0.929366i
$520$	1.97940	+	2.07594i	0.0868026	+	0.0910359i
$521$	4.26639	+	29.6734i	0.186914	+	1.30001i	0.839940	+	0.542679i	$0.182590\pi$
$521$	4.26639	+	29.6734i	0.186914	+	1.30001i	−0.653026	+	0.757335i	$0.726501\pi$
$522$	30.5007	+	30.3644i	1.33498	+	1.32901i
$523$	0.126289	−	0.0576744i	0.00552225	−	0.00252193i	−0.412652	−	0.910889i	$-0.635397\pi$
$523$	0.126289	−	0.0576744i	0.00552225	−	0.00252193i	0.418174	+	0.908367i	$0.362670\pi$
$524$	38.0431	+	9.22914i	1.66192	+	0.403177i
$525$	−20.2328	+	15.5612i	−0.883032	+	0.679147i
$526$	−2.70355	−	6.75315i	−0.117880	−	0.294451i
$527$	6.35420	+	3.27582i	0.276794	+	0.142697i
$528$	−0.122715	+	0.231863i	−0.00534049	+	0.0100905i
$529$	18.8312	−	13.2055i	0.818749	−	0.574152i
$530$			11.9982i			0.521169i
$531$	−4.80896	−	6.39410i	−0.208691	−	0.277480i
$532$	2.61506	−	18.1881i	0.113377	−	0.788555i
$533$	−1.99827	+	1.42296i	−0.0865546	+	0.0616353i
$534$	−7.93367	−	23.7480i	−0.343324	−	1.02768i
$535$	0.756442	−	1.06227i	0.0327039	−	0.0459261i
$536$	6.72078	−	19.4184i	0.290293	−	0.838748i
$537$	16.0207	+	18.8967i	0.691344	+	0.815451i
$538$	35.0029	−	33.3752i	1.50908	−	1.43891i
$539$	11.0591	−	12.7628i	0.476347	−	0.549734i
$540$	−11.5662	+	7.68501i	−0.497728	+	0.330710i
$541$	17.1010	+	10.9902i	0.735231	+	0.472504i	0.853905	−	0.520429i	$-0.174228\pi$
$541$	17.1010	+	10.9902i	0.735231	+	0.472504i	−0.118674	+	0.992933i	$0.537864\pi$
$542$	−1.34062	+	0.463993i	−0.0575845	+	0.0199302i
$543$	15.5925	−	4.39636i	0.669137	−	0.188666i
$544$	−16.4938	−	20.9736i	−0.707167	−	0.899237i
$545$	12.0476	+	4.16972i	0.516063	+	0.178611i
$546$	7.41083	+	14.7636i	0.317154	+	0.631824i
$547$	2.78652	−	11.4862i	0.119143	−	0.491114i	−0.880705	−	0.473666i	$-0.842931\pi$
$547$	2.78652	−	11.4862i	0.119143	−	0.491114i	0.999848	−	0.0174484i	$-0.00555429\pi$
$548$	22.9449	−	50.2422i	0.980156	−	2.14624i
$549$	14.8061	+	30.3068i	0.631911	+	1.29346i
$550$	−19.5325	−	30.3932i	−0.832869	−	1.29597i
$551$	5.20067	−	9.00783i	0.221556	−	0.383746i
$552$	−15.3456	+	18.0500i	−0.653153	+	0.768261i
$553$	−15.4461	−	26.7535i	−0.656836	−	1.13767i
$554$	24.1589	−	46.8618i	1.02641	−	1.99097i
$555$	7.48866	−	10.2800i	0.317876	−	0.436361i
$556$	3.58945	+	5.04068i	0.152227	+	0.213772i
$557$	−24.6668	+	7.24284i	−1.04517	+	0.306889i	−0.758863	−	0.651250i	$-0.774245\pi$
$557$	−24.6668	+	7.24284i	−1.04517	+	0.306889i	−0.286304	+	0.958139i	$0.592427\pi$
$558$	0.222603	−	10.3235i	0.00942353	−	0.437030i
$559$	1.55785	−	1.34988i	0.0658900	−	0.0570940i
$560$	−0.0433048	+	0.108170i	−0.00182996	+	0.00457102i
$561$	29.1466	+	7.40447i	1.23057	+	0.312617i
$562$	10.5520	−	54.7490i	0.445110	−	2.30945i
$563$	0.867469	−	18.2104i	0.0365595	−	0.767477i	−0.903935	−	0.427669i	$-0.859335\pi$
$563$	0.867469	−	18.2104i	0.0365595	−	0.767477i	0.940495	−	0.339808i	$-0.110362\pi$
$564$	61.8499	+	0.666747i	2.60435	+	0.0280751i
$565$	1.23888	+	3.57950i	0.0521199	+	0.150591i
$566$	9.97245	+	2.92818i	0.419174	+	0.123080i
$567$	−29.4061	+	8.77775i	−1.23494	+	0.368631i
$568$	−23.2194	−	26.7967i	−0.974266	−	1.12436i
$569$	6.86408	+	0.655440i	0.287757	+	0.0274775i	0.237936	−	0.971281i	$-0.423529\pi$
$569$	6.86408	+	0.655440i	0.287757	+	0.0274775i	0.0498206	+	0.998758i	$0.484135\pi$
$570$	4.06087	+	3.59613i	0.170091	+	0.150625i
$571$	2.57253	+	26.9408i	0.107657	+	1.12744i	0.874308	+	0.485371i	$0.161316\pi$
$571$	2.57253	+	26.9408i	0.107657	+	1.12744i	−0.766651	+	0.642064i	$0.778078\pi$
$572$	−13.4302	+	5.37663i	−0.561544	+	0.224808i
$573$	−16.9928	+	11.8265i	−0.709884	+	0.494061i
$574$	−13.5849	−	7.84324i	−0.567022	−	0.327370i
$575$	−7.17309	−	19.4462i	−0.299139	−	0.810964i
$576$	−16.8704	+	34.9281i	−0.702932	+	1.45534i
$577$	−39.4310	+	25.3408i	−1.64153	+	1.05495i	−0.702182	+	0.711998i	$0.747791\pi$
$577$	−39.4310	+	25.3408i	−1.64153	+	1.05495i	−0.939353	+	0.342953i	$0.888573\pi$
$578$	7.96711	−	10.1310i	0.331388	−	0.421394i
$579$	−25.9035	−	33.6799i	−1.07651	−	1.39969i
$580$	−11.5520	+	12.1154i	−0.479670	+	0.503064i
$581$	17.5808	+	12.5192i	0.729374	+	0.519385i
$582$	−55.4100	+	12.8115i	−2.29682	+	0.531053i
$583$	−21.5570	−	8.63011i	−0.892799	−	0.357423i
$584$	−10.7717	+	36.6852i	−0.445738	+	1.51804i
$585$	−2.99654	−	0.351472i	−0.123892	−	0.0145316i
$586$	−27.5071	+	42.8018i	−1.13631	+	1.76813i
$587$	−8.12137	−	15.7533i	−0.335205	−	0.650207i	0.659644	−	0.751578i	$-0.270707\pi$
$587$	−8.12137	−	15.7533i	−0.335205	−	0.650207i	−0.994849	+	0.101372i	$0.967677\pi$
$588$	−16.2962	+	20.2688i	−0.672043	+	0.835870i
$589$	−2.42519	+	0.588346i	−0.0999284	+	0.0242424i
$590$	3.95363	−	3.10917i	0.162768	−	0.128002i
$591$	−2.97743	−	0.909229i	−0.122475	−	0.0374007i
$592$	−0.0351726	+	0.368344i	−0.00144558	+	0.0151388i
$593$	−9.55874	−	32.5541i	−0.392531	−	1.33684i	−0.884628	−	0.466297i	$-0.845588\pi$
$593$	−9.55874	−	32.5541i	−0.392531	−	1.33684i	0.492098	−	0.870540i	$-0.336230\pi$
$594$	−8.87040	−	42.5215i	−0.363957	−	1.74468i
$595$	13.2208	+	1.90086i	0.542000	+	0.0779278i
$596$	−3.45692	−	72.5697i	−0.141601	−	2.97257i
$597$	28.4446	−	17.8499i	1.16416	−	0.730549i
$598$	−13.2364	+	2.17663i	−0.541276	+	0.0890089i
$599$	4.49961	−	2.59785i	0.183849	−	0.106145i	−0.405251	−	0.914206i	$-0.632816\pi$
$599$	4.49961	−	2.59785i	0.183849	−	0.106145i	0.589100	+	0.808060i	$0.299482\pi$
$600$	12.1962	+	17.5239i	0.497907	+	0.715410i
$601$	9.54259	+	7.50437i	0.389250	+	0.306110i	0.793536	−	0.608523i	$-0.208238\pi$
$601$	9.54259	+	7.50437i	0.389250	+	0.306110i	−0.404286	+	0.914633i	$0.632480\pi$
$602$	11.9899	+	5.47562i	0.488673	+	0.223169i
$603$	7.59863	+	20.2341i	0.309440	+	0.823998i
$604$	23.9755	+	52.4990i	0.975549	+	2.13615i
$605$	−1.87783	+	0.361923i	−0.0763448	+	0.0147143i
$606$	51.1981	+	18.3402i	2.07978	+	0.745020i
$607$	4.22514	+	17.4162i	0.171493	+	0.706904i	0.991003	+	0.133839i	$0.0427305\pi$
$607$	4.22514	+	17.4162i	0.171493	+	0.706904i	−0.819510	+	0.573065i	$0.805754\pi$
$608$	9.14589	+	1.76273i	0.370915	+	0.0714880i
$609$	−32.2357	+	18.1508i	−1.30626	+	0.735508i
$610$	−18.8477	+	9.71664i	−0.763119	+	0.393415i
$611$	10.1563	+	8.80049i	0.410880	+	0.356030i
$612$	−45.2760	−	9.74300i	−1.83018	−	0.393838i
$613$	−30.5912	+	4.39836i	−1.23557	+	0.177648i	−0.728977	−	0.684538i	$-0.760004\pi$
$613$	−30.5912	+	4.39836i	−1.23557	+	0.177648i	−0.506591	+	0.862186i	$0.669095\pi$
$614$	8.82111	+	45.7683i	0.355991	+	1.84706i
$615$	2.56051	−	1.28529i	0.103250	−	0.0518278i
$616$	−25.6903	−	24.4956i	−1.03509	−	0.986957i
$617$	6.20202	−	0.592221i	0.249684	−	0.0238419i	0.0305363	−	0.999534i	$-0.490278\pi$
$617$	6.20202	−	0.592221i	0.249684	−	0.0238419i	0.219147	+	0.975692i	$0.429672\pi$
$618$	3.04447	−	1.35089i	0.122466	−	0.0543408i
$619$	45.2187	−	2.15403i	1.81749	−	0.0865779i	0.888995	−	0.457916i	$-0.151404\pi$
$619$	45.2187	−	2.15403i	1.81749	−	0.0865779i	0.928498	+	0.371338i	$0.121101\pi$
$620$	4.01636			0.161301
$621$	0.302880	−	24.9180i	0.0121542	−	0.999926i
$622$	2.04091			0.0818332
$623$	21.4978	−	1.02407i	0.861292	−	0.0410284i
$624$	0.0802327	−	0.0356009i	0.00321188	−	0.00142518i
$625$	−15.2188	+	1.45322i	−0.608754	+	0.0581289i
$626$	17.6000	+	16.7816i	0.703438	+	0.670727i
$627$	−9.38202	+	4.70946i	−0.374682	+	0.188078i
$628$	−4.77989	−	24.8004i	−0.190739	−	0.989646i
$629$	41.9851	−	6.03654i	1.67405	−	0.240693i
$630$	−5.91549	−	18.3633i	−0.235679	−	0.731611i
$631$	−13.1130	−	11.3625i	−0.522021	−	0.452333i	0.353556	−	0.935414i	$-0.384973\pi$
$631$	−13.1130	−	11.3625i	−0.522021	−	0.452333i	−0.875576	+	0.483080i	$0.839518\pi$
$632$	−22.9673	+	11.8405i	−0.913592	+	0.470989i
$633$	2.66009	−	1.49780i	0.105729	−	0.0595324i
$634$	−17.1027	−	3.29627i	−0.679234	−	0.130912i
$635$	−1.94738	−	8.02719i	−0.0772792	−	0.318549i
$636$	33.6651	+	12.0595i	1.33491	+	0.478191i
$637$	−5.54845	+	1.06938i	−0.219838	+	0.0423702i
$638$	−21.7523	−	47.6309i	−0.861182	−	1.88573i
$639$	36.7927	+	6.10226i	1.45550	+	0.241402i
$640$	−13.7782	−	6.29228i	−0.544630	−	0.248724i
$641$	−12.4186	−	9.76607i	−0.490504	−	0.385737i	0.342049	−	0.939682i	$-0.388879\pi$
$641$	−12.4186	−	9.76607i	−0.490504	−	0.385737i	−0.832553	+	0.553946i	$0.813122\pi$
$642$	−3.58856	−	5.15616i	−0.141629	−	0.203498i
$643$	2.88529	−	1.66582i	0.113785	−	0.0656937i	−0.442028	−	0.897001i	$-0.645741\pi$
$643$	2.88529	−	1.66582i	0.113785	−	0.0656937i	0.555812	+	0.831308i	$0.312407\pi$
$644$	−29.5873	−	44.0575i	−1.16590	−	1.73611i
$645$	−2.03915	+	1.27963i	−0.0802913	+	0.0503855i
$646$	0.860774	+	18.0699i	0.0338667	+	0.710949i
$647$	40.0121	+	5.75287i	1.57304	+	0.226168i	0.872921	−	0.487861i	$-0.162223\pi$
$647$	40.0121	+	5.75287i	1.57304	+	0.226168i	0.700115	+	0.714030i	$0.253132\pi$
$648$	6.16347	+	24.9183i	0.242124	+	0.978882i
$649$	2.74241	+	9.33978i	0.107649	+	0.366618i
$650$	−1.14908	+	12.0338i	−0.0450708	+	0.472003i
$651$	8.48891	+	2.59228i	0.332706	+	0.101600i
$652$	37.3275	−	29.3547i	1.46186	−	1.14962i
$653$	20.7896	−	5.04351i	0.813561	−	0.197368i	0.192669	−	0.981264i	$-0.438286\pi$
$653$	20.7896	−	5.04351i	0.813561	−	0.197368i	0.620892	+	0.783896i	$0.286771\pi$
$654$	38.4814	−	47.8622i	1.50474	−	1.87156i
$655$	−4.55164	−	8.82895i	−0.177847	−	0.344976i
$656$	−0.0450633	+	0.0701199i	−0.00175943	+	0.00273772i
$657$	−15.9139	−	36.9335i	−0.620860	−	1.44091i
$658$	−24.2102	+	82.4524i	−0.943812	+	3.21433i
$659$	−2.34651	−	0.939400i	−0.0914070	−	0.0365938i	0.325508	−	0.945539i	$-0.394465\pi$
$659$	−2.34651	−	0.939400i	−0.0914070	−	0.0365938i	−0.416915	+	0.908945i	$0.636889\pi$
$660$	16.4609	−	3.80597i	0.640739	−	0.148147i
$661$	2.68296	+	1.91053i	0.104355	+	0.0743110i	0.631043	−	0.775748i	$-0.282627\pi$
$661$	2.68296	+	1.91053i	0.104355	+	0.0743110i	−0.526688	+	0.850059i	$0.676566\pi$
$662$	24.7993	−	26.0088i	0.963854	−	1.01086i
$663$	−6.13440	−	7.97599i	−0.238240	−	0.309762i
$664$	11.1596	−	14.1905i	0.433075	−	0.550700i
$665$	−3.92240	+	2.52078i	−0.152104	+	0.0977515i
$666$	−34.4543	−	50.6612i	−1.33508	−	1.96308i
$667$	−6.27945	−	29.3771i	−0.243141	−	1.13749i
$668$	−6.91859	−	3.99445i	−0.267688	−	0.154550i
$669$	−20.2074	+	14.0638i	−0.781262	+	0.543738i
$670$	−12.6145	+	5.05009i	−0.487342	+	0.195102i
$671$	−3.90092	−	40.8523i	−0.150593	−	1.57708i
$672$	−24.8011	−	21.9628i	−0.956722	−	0.847232i
$673$	−4.58002	−	0.437339i	−0.176547	−	0.0168582i	0.00640810	−	0.999979i	$-0.497960\pi$
$673$	−4.58002	−	0.437339i	−0.176547	−	0.0168582i	−0.182955	+	0.983121i	$0.558566\pi$
$674$	17.2477	+	19.9050i	0.664358	+	0.766710i
$675$	−21.6415	−	5.99735i	−0.832983	−	0.230838i
$676$	−35.8359	−	10.5224i	−1.37831	−	0.404707i
$677$	10.1525	+	29.3338i	0.390193	+	1.12739i	0.953566	+	0.301185i	$0.0973822\pi$
$677$	10.1525	+	29.3338i	0.390193	+	1.12739i	−0.563373	+	0.826203i	$0.690497\pi$
$678$	18.2456	+	0.196689i	0.700719	+	0.00755380i
$679$	2.32606	−	48.8301i	0.0892661	−	1.87393i
$680$	2.11436	−	10.9704i	0.0810821	−	0.420694i
$681$	−23.9547	−	6.08550i	−0.917947	−	0.233197i
$682$	−4.66925	+	11.6632i	−0.178795	+	0.446608i
$683$	3.80767	−	3.29936i	0.145696	−	0.126247i	−0.578963	−	0.815354i	$-0.696542\pi$
$683$	3.80767	−	3.29936i	0.145696	−	0.126247i	0.724660	+	0.689107i	$0.241997\pi$
$684$	14.1718	−	7.77967i	0.541873	−	0.297463i
$685$	−13.4474	+	3.94852i	−0.513800	+	0.150865i
$686$	10.7504	+	15.0968i	0.410452	+	0.576399i
$687$	20.0686	−	27.5489i	0.765663	−	1.05106i
$688$	0.0320937	−	0.0622531i	0.00122356	−	0.00237338i
$689$	3.88473	+	6.72854i	0.147996	+	0.256337i
$690$	15.6655	−	0.147336i	0.596376	−	0.00560900i
$691$	−2.89867	+	5.02064i	−0.110271	+	0.190994i	−0.915879	−	0.401454i	$-0.868505\pi$
$691$	−2.89867	+	5.02064i	−0.110271	+	0.190994i	0.805609	+	0.592448i	$0.201838\pi$
$692$	34.2286	+	53.2607i	1.30118	+	2.02467i
$693$	37.2479	+	2.58015i	1.41493	+	0.0980118i
$694$	4.07180	−	8.91601i	0.154564	−	0.338447i
$695$	0.370186	−	1.52593i	0.0140420	−	0.0578817i
$696$	13.8821	+	27.6554i	0.526199	+	1.04828i
$697$	9.02942	+	3.12511i	0.342014	+	0.118372i
$698$	−43.7568	−	55.6413i	−1.65622	−	2.10605i
$699$	21.1197	−	5.95478i	0.798820	−	0.225230i
$700$	−45.1953	+	15.6422i	−1.70822	+	0.591221i
$701$	10.1837	+	6.54467i	0.384633	+	0.247189i	0.718641	−	0.695382i	$-0.244765\pi$
$701$	10.1837	+	6.54467i	0.384633	+	0.247189i	−0.334007	+	0.942570i	$0.608401\pi$
$702$	−6.46189	+	13.0183i	−0.243888	+	0.491346i
$703$	−9.69642	+	11.1903i	−0.365707	+	0.422049i
$704$	34.1551	−	32.5668i	1.28727	−	1.22741i
$705$	−10.1495	−	11.9715i	−0.382253	−	0.450874i
$706$	2.33893	−	6.75789i	0.0880267	−	0.254337i
$707$	−27.1159	+	38.0790i	−1.01980	+	1.43211i
$708$	−4.75001	−	14.2183i	−0.178516	−	0.534357i
$709$	−30.0293	+	21.3837i	−1.12777	+	0.803083i	−0.982492	−	0.186307i	$-0.940348\pi$
$709$	−30.0293	+	21.3837i	−1.12777	+	0.803083i	−0.145281	+	0.989390i	$0.546409\pi$
$710$	−3.33674	+	23.2075i	−0.125226	+	0.870963i
$711$	10.6432	−	25.0089i	0.399151	−	0.937907i
$712$		−	18.0022i		−	0.674662i
$713$	−4.06142	+	5.95425i	−0.152101	+	0.222989i
$714$	30.0980	−	56.8684i	1.12639	−	2.12824i
$715$	3.26270	+	1.68204i	0.122018	+	0.0629047i
$716$	17.2521	+	43.0936i	0.644740	+	1.61048i
$717$	−30.0560	+	23.1163i	−1.12246	+	0.863295i
$718$	6.09600	+	1.47887i	0.227501	+	0.0551911i
$719$	31.4071	−	14.3431i	1.17129	−	0.534909i	0.267779	−	0.963480i	$-0.413710\pi$
$719$	31.4071	−	14.3431i	1.17129	−	0.534909i	0.903508	+	0.428572i	$0.140983\pi$
$720$	−0.0989603	+	0.0267541i	−0.00368803	+	0.000997067i
$721$	0.407447	+	2.83385i	0.0151741	+	0.105538i
$722$	25.6710	+	26.9230i	0.955376	+	1.00197i
$723$	−33.7038	−	27.0980i	−1.25346	−	1.00779i
$724$	30.3202	+	1.44433i	1.12684	+	0.0536780i
$725$	−27.0413	−	1.28814i	−1.00429	−	0.0478401i
$726$	−1.40927	+	9.10394i	−0.0523031	+	0.337879i
$727$	7.79060	+	8.17055i	0.288938	+	0.303029i	0.852165	−	0.523273i	$-0.175289\pi$
$727$	7.79060	+	8.17055i	0.288938	+	0.303029i	−0.563228	+	0.826302i	$0.690441\pi$
$728$	1.69030	+	11.7563i	0.0626465	+	0.435716i
$729$	−21.7229	−	16.0348i	−0.804551	−	0.593883i
$730$	22.9977	−	10.5027i	0.851182	−	0.388722i
$731$	−7.80252	−	1.89287i	−0.288587	−	0.0700104i
$732$	8.31943	+	62.6499i	0.307495	+	2.31561i
$733$	11.8323	+	29.5555i	0.437034	+	1.09166i	0.969475	+	0.245191i	$0.0788507\pi$
$733$	11.8323	+	29.5555i	0.437034	+	1.09166i	−0.532441	+	0.846467i	$0.678725\pi$
$734$	−21.5389	−	11.1041i	−0.795015	−	0.409859i
$735$	6.59474	−	0.242930i	0.243251	−	0.00896060i
$736$	23.0207	−	13.9179i	0.848553	−	0.513022i
$737$		−	26.2967i		−	0.968652i
$738$	−1.66917	−	13.6999i	−0.0614429	−	0.504300i
$739$	0.777887	−	5.41032i	0.0286150	−	0.199022i	−0.970499	−	0.241105i	$-0.922490\pi$
$739$	0.777887	−	5.41032i	0.0286150	−	0.199022i	0.999114	+	0.0420828i	$0.0133993\pi$
$740$	19.4117	−	13.8230i	0.713587	−	0.508143i
$741$	3.44166	+	0.701885i	0.126432	+	0.0257844i
$742$	−28.8180	+	40.4693i	−1.05794	+	1.48567i
$743$	−8.68354	+	25.0895i	−0.318568	+	0.920443i	0.666078	+	0.745882i	$0.267972\pi$
$743$	−8.68354	+	25.0895i	−0.318568	+	0.920443i	−0.984646	+	0.174561i	$0.944149\pi$
$744$	2.50372	−	6.98933i	0.0917908	−	0.256241i
$745$	−13.3420	+	12.7216i	−0.488813	+	0.466082i
$746$	−13.9537	+	16.1034i	−0.510881	+	0.589588i
$747$	0.494425	+	18.9824i	0.0180900	+	0.694530i
$748$	47.4017	+	30.4632i	1.73318	+	1.11385i
$749$	5.10287	−	1.76612i	0.186455	−	0.0645326i
$750$	7.49770	−	29.5136i	0.273777	−	1.07769i
$751$	−3.13001	−	3.98013i	−0.114216	−	0.145237i	0.725584	−	0.688134i	$-0.241570\pi$
$751$	−3.13001	−	3.98013i	−0.114216	−	0.145237i	−0.839799	+	0.542897i	$0.817327\pi$
$752$	0.431502	+	0.149344i	0.0157352	+	0.00544602i
$753$	−7.60072	+	11.5513i	−0.276986	+	0.420951i
$754$	−4.13061	+	17.0266i	−0.150428	+	0.620072i
$755$	6.08362	−	13.3213i	0.221406	−	0.484810i
$756$	−57.4702	−	1.85918i	−2.09017	−	0.0676176i
$757$	18.0026	+	28.0126i	0.654315	+	1.01813i	0.996902	+	0.0786481i	$0.0250603\pi$
$757$	18.0026	+	28.0126i	0.654315	+	1.01813i	−0.342587	+	0.939486i	$0.611303\pi$
$758$	−1.34053	+	2.32187i	−0.0486902	+	0.0843340i
$759$	−11.0032	+	28.2519i	−0.399391	+	1.02548i
$760$	1.95000	+	3.37751i	0.0707341	+	0.122515i
$761$	2.72885	−	5.29322i	0.0989206	−	0.191879i	−0.834182	−	0.551489i	$-0.814060\pi$
$761$	2.72885	−	5.29322i	0.0989206	−	0.191879i	0.933103	+	0.359610i	$0.117090\pi$
$762$	−39.5669	−	4.20905i	−1.43336	−	0.152478i
$763$	30.6208	+	43.0009i	1.10855	+	1.55674i
$764$	−37.2201	+	10.9288i	−1.34657	+	0.395390i
$765$	5.65498	+	10.3014i	0.204456	+	0.372447i
$766$	27.4220	−	23.7613i	0.990799	−	0.858532i
$767$	1.21050	−	3.02369i	0.0437088	−	0.109179i
$768$	−19.6626	+	20.1814i	−0.709512	+	0.728233i
$769$	−9.77905	+	50.7385i	−0.352641	+	1.82968i	0.180406	+	0.983592i	$0.442259\pi$
$769$	−9.77905	+	50.7385i	−0.352641	+	1.82968i	−0.533047	+	0.846085i	$0.678953\pi$
$770$	−1.11687	+	23.4459i	−0.0402490	+	0.844931i
$771$	5.07757	+	9.01772i	0.182864	+	0.324765i
$772$	−26.0384	−	75.2330i	−0.937143	−	2.70770i
$773$	−4.77710	−	1.40268i	−0.171820	−	0.0504510i	0.194691	−	0.980865i	$-0.437630\pi$
$773$	−4.77710	−	1.40268i	−0.171820	−	0.0504510i	−0.366511	+	0.930414i	$0.619448\pi$
$774$	2.49049	+	11.3263i	0.0895187	+	0.407117i
$775$	4.25347	+	4.90877i	0.152789	+	0.176328i
$776$	−40.7051	−	3.88687i	−1.46123	−	0.139530i
$777$	49.9499	−	16.6871i	1.79194	−	0.598646i
$778$	3.35504	+	35.1356i	0.120284	+	1.25967i
$779$	−3.09651	+	1.23965i	−0.110944	+	0.0444152i
$780$	−5.11661	−	2.40367i	−0.183204	−	0.0860651i
$781$	−39.2965	−	22.6878i	−1.40614	−	0.811835i
$782$	36.8110	+	37.0781i	1.31636	+	1.32591i
$783$	−29.8099	−	13.0677i	−1.06532	−	0.467001i
$784$	−0.161514	+	0.103799i	−0.00576836	+	0.00370710i
$785$	−3.96163	+	5.03762i	−0.141397	+	0.179801i
$786$	−47.4336	+	6.29882i	−1.69190	+	0.224671i
$787$	35.9788	−	37.7335i	1.28251	−	1.34505i	0.373860	−	0.927485i	$-0.378034\pi$
$787$	35.9788	−	37.7335i	1.28251	−	1.34505i	0.908646	−	0.417568i	$-0.137117\pi$
$788$	−4.75151	−	3.38354i	−0.169266	−	0.120534i
$789$	3.75315	+	4.02212i	0.133616	+	0.143191i
$790$	15.8628	+	6.35049i	0.564372	+	0.225940i
$791$	−4.41879	+	15.0490i	−0.157114	+	0.535082i
$792$	3.63819	−	31.0180i	0.129277	−	1.10218i
$793$	−7.42367	+	11.5515i	−0.263622	+	0.410204i
$794$	22.1450	+	42.9553i	0.785896	+	1.52443i
$795$	−3.28140	−	8.45972i	−0.116379	−	0.300035i
$796$	61.1476	−	14.8343i	2.16732	−	0.525786i
$797$	−21.8460	+	17.1799i	−0.773824	+	0.608542i	−0.925001	−	0.379965i	$-0.875936\pi$
$797$	−21.8460	+	17.1799i	−0.773824	+	0.608542i	0.151177	+	0.988507i	$0.451694\pi$
$798$	5.05967	+	21.8832i	0.179110	+	0.774656i
$799$	4.97557	−	52.1066i	0.176023	−	1.84340i
$800$	−6.82988	−	23.2604i	−0.241473	−	0.822381i
$801$	12.0888	+	14.5745i	0.427135	+	0.514966i
$802$	13.7584	+	1.97815i	0.485825	+	0.0698511i
$803$	2.32815	+	48.8739i	0.0821587	+	1.72472i
$804$	1.49080	+	40.4703i	0.0525764	+	1.42728i
$805$	−3.53232	+	12.9947i	−0.124498	+	0.458003i
$806$	3.64042	−	2.10180i	0.128228	−	0.0740327i
$807$	−15.5521	+	33.1052i	−0.547459	+	1.16536i
$808$	30.7359	+	24.1710i	1.08128	+	0.850331i
$809$	1.18423	+	0.540818i	0.0416352	+	0.0190142i	0.436124	−	0.899887i	$-0.356351\pi$
$809$	1.18423	+	0.540818i	0.0416352	+	0.0190142i	−0.394489	+	0.918901i	$0.629078\pi$
$810$	9.78377	−	13.8705i	0.343767	−	0.487360i
$811$	8.72972	+	19.1154i	0.306542	+	0.671233i	0.998725	−	0.0504893i	$-0.0160781\pi$
$811$	8.72972	+	19.1154i	0.306542	+	0.671233i	−0.692183	+	0.721722i	$0.743351\pi$
$812$	−68.0636	+	13.1182i	−2.38856	+	0.460358i
$813$	0.818348	−	0.693800i	0.0287007	−	0.0243326i
$814$	17.5737	+	72.4400i	0.615959	+	2.53902i
$815$	−11.8318	−	2.28040i	−0.414451	−	0.0798788i
$816$	−0.294224	−	0.174126i	−0.0102999	−	0.00609562i
$817$	2.49114	−	1.28427i	0.0871541	−	0.0449311i
$818$	−11.9910	−	10.3902i	−0.419254	−	0.363286i
$819$	−9.26296	−	8.38276i	−0.323674	−	0.292917i
$820$	5.31346	−	0.763961i	0.185554	−	0.0266787i
$821$	1.63050	+	8.45983i	0.0569048	+	0.295250i	0.999221	−	0.0394752i	$-0.0125686\pi$
$821$	1.63050	+	8.45983i	0.0569048	+	0.295250i	−0.942316	+	0.334725i	$0.891356\pi$
$822$	−3.93918	+	67.3986i	−0.137395	+	2.35080i
$823$	−15.1253	−	14.4219i	−0.527234	−	0.502717i	0.379055	−	0.925374i	$-0.376249\pi$
$823$	−15.1253	−	14.4219i	−0.527234	−	0.502717i	−0.906290	+	0.422657i	$0.861098\pi$
$824$	2.38391	−	0.227636i	0.0830475	−	0.00793007i
$825$	22.0843	+	16.0877i	0.768876	+	0.560102i
$826$	20.8031	−	0.990975i	0.723833	−	0.0344804i
$827$	0.162395			0.00564701			0.00282351	−	0.999996i	$-0.499101\pi$
$827$	0.162395			0.00564701			0.00282351	+	0.999996i	$0.499101\pi$
$828$	15.3321	−	44.1031i	0.532829	−	1.53269i
$829$	51.8376			1.80039			0.900197	−	0.435482i	$-0.143422\pi$
$829$	51.8376			1.80039			0.900197	+	0.435482i	$0.143422\pi$
$830$	−11.9241	+	0.568013i	−0.413890	+	0.0197160i
$831$	−4.21774	+	39.6486i	−0.146312	+	1.37540i
$832$	−15.7191	+	1.50099i	−0.544962	+	0.0520376i
$833$	15.9285	+	15.1878i	0.551891	+	0.526227i
$834$	−6.31871	−	4.15771i	−0.218799	−	0.143970i
$835$	0.383636	+	1.99049i	0.0132763	+	0.0688839i
$836$	−19.4692	+	2.79925i	−0.673357	+	0.0968141i
$837$	2.66644	+	7.33981i	0.0921657	+	0.253701i
$838$	−45.1560	−	39.1279i	−1.55989	−	1.35165i
$839$	8.64645	−	4.45756i	0.298509	−	0.153892i	−0.302466	−	0.953160i	$-0.597810\pi$
$839$	8.64645	−	4.45756i	0.298509	−	0.153892i	0.600974	+	0.799268i	$0.294779\pi$
$840$	0.149524	−	13.8704i	0.00515905	−	0.478573i
$841$	−10.0518	−	1.93732i	−0.346614	−	0.0668043i
$842$	4.66052	+	19.2109i	0.160612	+	0.662052i
$843$	7.53334	+	41.4884i	0.259462	+	1.42894i
$844$	5.61661	−	1.08251i	0.193332	−	0.0372616i
$845$	3.93689	+	8.62059i	0.135433	+	0.296557i
$846$	−70.7791	+	26.5800i	−2.43343	+	0.913840i
$847$	−7.20311	−	3.28955i	−0.247502	−	0.113030i
$848$	0.207508	+	0.163186i	0.00712584	+	0.00560383i
$849$	−7.83223	+	0.662773i	−0.268801	+	0.0227463i
$850$	40.7763	−	23.5422i	1.39862	−	0.807491i
$851$	0.863123	+	42.7558i	0.0295875	+	1.46565i
$852$	61.7629	+	32.6885i	2.11596	+	1.11989i
$853$	1.00923	+	21.1863i	0.0345553	+	0.725405i	0.947967	+	0.318368i	$0.103135\pi$
$853$	1.00923	+	21.1863i	0.0345553	+	0.725405i	−0.913412	+	0.407037i	$0.866562\pi$
$854$	−86.9100	−	12.4958i	−2.97400	−	0.427596i
$855$	−3.84676	−	1.42496i	−0.131556	−	0.0487325i
$856$	−1.27250	−	4.33375i	−0.0434933	−	0.148125i
$857$	−2.70085	+	28.2846i	−0.0922593	+	0.966183i	0.824265	+	0.566204i	$0.191589\pi$
$857$	−2.70085	+	28.2846i	−0.0922593	+	0.966183i	−0.916524	+	0.399979i	$0.869017\pi$
$858$	12.9284	−	12.0638i	0.441368	−	0.411853i
$859$	−15.9310	+	12.5283i	−0.543559	+	0.427460i	−0.851814	−	0.523844i	$-0.824497\pi$
$859$	−15.9310	+	12.5283i	−0.543559	+	0.427460i	0.308255	+	0.951304i	$0.400255\pi$
$860$	−4.38357	+	1.06344i	−0.149479	+	0.0362631i
$861$	11.7235	+	1.81478i	0.399536	+	0.0618475i
$862$	−11.3224	−	21.9623i	−0.385641	−	0.748040i
$863$	20.4029	−	31.7475i	0.694521	−	1.08070i	−0.297512	−	0.954718i	$-0.596157\pi$
$863$	20.4029	−	31.7475i	0.694521	−	1.08070i	0.992033	−	0.125978i	$-0.0402070\pi$
$864$	2.32745	−	29.0533i	0.0791815	−	0.988415i
$865$	4.52597	−	15.4140i	0.153888	−	0.524093i
$866$	−19.1586	−	7.66996i	−0.651037	−	0.260636i
$867$	−2.84673	+	9.32212i	−0.0966799	+	0.316596i
$868$	13.5470	+	9.64674i	0.459813	+	0.327432i
$869$	−22.8196	+	23.9325i	−0.774103	+	0.811856i
$870$	7.80926	−	18.9131i	0.264759	−	0.641215i
$871$	−5.43907	+	6.91634i	−0.184296	+	0.234351i
$872$	37.1461	−	23.8723i	1.25793	−	0.808420i
$873$	35.5647	−	24.1873i	1.20368	−	0.818615i
$874$	−18.1874	−	1.36689i	−0.615197	−	0.0462359i
$875$	22.6682	+	13.0875i	0.766325	+	0.442438i
$876$	−6.35372	−	75.0842i	−0.214672	−	2.53686i
$877$	10.1756	−	4.07368i	0.343604	−	0.137558i	−0.193441	−	0.981112i	$-0.561965\pi$
$877$	10.1756	−	4.07368i	0.343604	−	0.137558i	0.537045	+	0.843554i	$0.319541\pi$
$878$	−1.23102	−	12.8919i	−0.0415450	−	0.435079i
$879$	7.68881	−	37.7017i	0.259337	−	1.27165i
$880$	0.124159	+	0.0118557i	0.00418539	+	0.000399656i
$881$	−5.30482	−	6.12209i	−0.178724	−	0.206259i	0.659318	−	0.751864i	$-0.270845\pi$
$881$	−5.30482	−	6.12209i	−0.178724	−	0.206259i	−0.838042	+	0.545606i	$0.816300\pi$
$882$	9.61166	−	30.3018i	0.323642	−	1.02032i
$883$	−53.2966	−	15.6493i	−1.79357	−	0.526641i	−0.796608	−	0.604496i	$-0.793375\pi$
$883$	−53.2966	−	15.6493i	−1.79357	−	0.526641i	−0.996965	+	0.0778554i	$0.975193\pi$
$884$	−6.16634	−	17.8165i	−0.207396	−	0.599233i
$885$	−1.93730	+	3.27350i	−0.0651217	+	0.110037i
$886$	2.35224	−	49.3795i	0.0790249	−	1.65894i
$887$	−2.78842	+	14.4677i	−0.0936259	+	0.485777i	0.904601	+	0.426259i	$0.140169\pi$
$887$	−2.78842	+	14.4677i	−0.0936259	+	0.485777i	−0.998227	+	0.0595186i	$0.981043\pi$
$888$	−11.9541	−	42.3974i	−0.401154	−	1.42276i
$889$	12.7118	−	31.7525i	0.426340	−	1.06495i
$890$	−8.99650	+	7.79551i	−0.301563	+	0.261306i
$891$	17.8836	+	27.5551i	0.599123	+	0.923132i
$892$	−44.2611	+	12.9962i	−1.48197	+	0.435146i
$893$	10.5988	+	14.8840i	0.354677	+	0.498074i
$894$	36.0179	+	81.1725i	1.20462	+	2.71481i
$895$	5.39718	−	10.4691i	0.180408	−	0.349942i
$896$	−31.3598	−	54.3167i	−1.04766	−	1.81459i
$897$	8.73744	−	5.15473i	0.291735	−	0.172111i
$898$	−25.7766	+	44.6464i	−0.860176	+	1.48987i
$899$	5.08952	+	7.91946i	0.169745	+	0.264129i
$900$	−34.8994	−	23.5068i	−1.16331	−	0.783559i
$901$	12.5712	−	27.5272i	0.418809	−	0.917063i
$902$	−3.95871	+	16.3180i	−0.131811	+	0.543331i
$903$	−9.95141	−	0.581620i	−0.331162	−	0.0193551i
$904$	12.3976	+	4.29086i	0.412339	+	0.142712i
$905$	−4.76122	−	6.05439i	−0.158268	−	0.201255i
$906$	−50.5290	−	49.2300i	−1.67871	−	1.63556i
$907$	0.681309	−	0.235803i	0.0226225	−	0.00782972i	−0.315733	−	0.948848i	$-0.602250\pi$
$907$	0.681309	−	0.235803i	0.0226225	−	0.00782972i	0.338356	+	0.941018i	$0.390129\pi$
$908$	−38.9580	−	25.0368i	−1.29287	−	0.830874i
$909$	−41.1148	+	1.07089i	−1.36369	+	0.0355193i
$910$	5.14317	−	5.93553i	0.170494	−	0.196761i
$911$	18.0177	−	17.1799i	0.596954	−	0.569195i	−0.330183	−	0.943917i	$-0.607110\pi$
$911$	18.0177	−	17.1799i	0.596954	−	0.569195i	0.927137	+	0.374722i	$0.122262\pi$
$912$	0.117426	−	0.0213218i	0.00388836	−	0.000706037i
$913$	7.55624	−	21.8323i	0.250075	−	0.722544i
$914$	24.3869	−	34.2465i	0.806646	−	1.13278i
$915$	10.6317	−	12.0057i	0.351474	−	0.396896i
$916$	52.0205	−	37.0437i	1.71881	−	1.22396i
$917$	5.85349	−	40.7119i	0.193299	−	1.34443i
$918$	55.9034	−	8.91046i	1.84509	−	0.294089i
$919$		−	1.33479i		−	0.0440305i	−0.999758	−	0.0220153i	$-0.992992\pi$
$919$		−	1.33479i		−	0.0440305i	0.999758	−	0.0220153i	$-0.00700825\pi$
$920$	10.7165	+	3.46846i	0.353314	+	0.114352i
$921$	−18.7368	−	29.8579i	−0.617399	−	0.983850i
$922$	18.8370	+	9.71114i	0.620363	+	0.319819i
$923$	5.64280	+	14.0950i	0.185735	+	0.463944i
$924$	64.6630	+	26.6994i	2.12726	+	0.878347i
$925$	37.4520	+	9.08575i	1.23141	+	0.298738i
$926$	54.5524	−	24.9132i	1.79270	−	0.818700i
$927$	−1.77714	+	1.78512i	−0.0583690	+	0.0586311i
$928$	−5.00035	−	34.7782i	−0.164144	−	1.14165i
$929$	−24.7251	−	25.9310i	−0.811205	−	0.850767i	0.179923	−	0.983681i	$-0.442415\pi$
$929$	−24.7251	−	25.9310i	−0.811205	−	0.850767i	−0.991128	+	0.132914i	$0.957567\pi$
$930$	−4.57706	+	1.77538i	−0.150088	+	0.0582169i
$931$	−7.67413	−	0.365564i	−0.251510	−	0.0119809i
$932$	41.0680	+	1.95631i	1.34523	+	0.0640811i
$933$	−1.43901	+	0.558172i	−0.0471111	+	0.0182737i
$934$	36.0550	+	37.8134i	1.17976	+	1.23729i
$935$	−2.03475	−	14.1520i	−0.0665435	−	0.462820i
$936$	−7.37248	+	7.40559i	−0.240977	+	0.242059i
$937$	−14.8468	+	6.78029i	−0.485022	+	0.221502i	−0.642891	−	0.765958i	$-0.722265\pi$
$937$	−14.8468	+	6.78029i	−0.485022	+	0.221502i	0.157868	+	0.987460i	$0.449538\pi$
$938$	−54.6776	−	13.2646i	−1.78529	−	0.433106i
$939$	−16.9991	−	7.01894i	−0.554743	−	0.229054i
$940$	−10.9296	−	27.3009i	−0.356485	−	0.890457i
$941$	13.4427	+	6.93021i	0.438221	+	0.225919i	0.663196	−	0.748446i	$-0.269200\pi$
$941$	13.4427	+	6.93021i	0.438221	+	0.225919i	−0.224975	+	0.974365i	$0.572230\pi$
$942$	16.4099	+	26.1498i	0.534662	+	0.852006i
$943$	−4.24050	+	8.64973i	−0.138090	+	0.281674i
$944$		−	0.110665i		−	0.00360183i
$945$	9.19310	+	11.3298i	0.299051	+	0.368558i
$946$	2.00799	−	13.9659i	0.0652854	−	0.454070i
$947$	−4.02585	+	2.86680i	−0.130823	+	0.0931584i	−0.643595	−	0.765366i	$-0.722558\pi$
$947$	−4.02585	+	2.86680i	−0.130823	+	0.0931584i	0.512772	+	0.858525i	$0.328618\pi$
$948$	33.7623	−	38.1255i	1.09655	−	1.23826i
$949$	9.49648	−	13.3359i	0.308269	−	0.432903i
$950$	−5.37576	+	15.5322i	−0.174413	+	0.503932i
$951$	12.9603	−	2.35329i	0.420266	−	0.0763106i
$952$	33.4809	−	31.9239i	1.08512	−	1.03466i
$953$	8.32954	−	9.61281i	0.269820	−	0.311389i	−0.604628	−	0.796508i	$-0.706678\pi$
$953$	8.32954	−	9.61281i	0.269820	−	0.311389i	0.874448	+	0.485119i	$0.161224\pi$
$954$	−43.6956	+	1.13812i	−1.41470	+	0.0368479i
$955$	8.28050	+	5.32155i	0.267951	+	0.172201i
$956$	−67.1380	+	23.2367i	−2.17140	+	0.751528i
$957$	28.3638	+	27.6346i	0.916871	+	0.893301i
$958$	7.34974	+	9.34596i	0.237459	+	0.301954i
$959$	−54.8411	−	18.9807i	−1.77091	−	0.612919i
$960$	18.4102	+	1.07600i	0.594188	+	0.0347279i
$961$	−6.77604	+	27.9312i	−0.218582	+	0.901007i
$962$	10.3610	−	22.6874i	0.334052	−	0.731471i
$963$	3.94039	+	2.65408i	0.126977	+	0.0855265i
$964$	−43.8083	−	68.1670i	−1.41097	−	2.19551i
$965$	−10.1004	+	17.4945i	−0.325145	+	0.563168i
$966$	53.1927	+	37.1294i	1.71145	+	1.19462i
$967$	11.6905	+	20.2486i	0.375941	+	0.651150i	0.990467	−	0.137747i	$-0.0439860\pi$
$967$	11.6905	+	20.2486i	0.375941	+	0.651150i	−0.614526	+	0.788897i	$0.710653\pi$
$968$	−3.03511	+	5.88729i	−0.0975522	+	0.189225i
$969$	−5.54886	−	12.5053i	−0.178255	−	0.401729i
$970$	15.6841	+	22.0252i	0.503586	+	0.707188i
$971$	−49.4889	+	14.5313i	−1.58817	+	0.466330i	−0.952224	−	0.305400i	$-0.901210\pi$
$971$	−49.4889	+	14.5313i	−1.58817	+	0.466330i	−0.635950	+	0.771730i	$0.719392\pi$
$972$	−29.0847	−	41.3931i	−0.932894	−	1.32768i
$973$	4.91368	−	4.25773i	0.157525	−	0.136496i
$974$	−20.7780	+	51.9009i	−0.665770	+	1.66301i
$975$	−2.48092	−	8.79904i	−0.0794532	−	0.281795i
$976$	−0.0882959	+	0.458123i	−0.00282628	+	0.0146641i
$977$	2.82620	−	59.3292i	0.0904180	−	1.89811i	−0.266291	−	0.963893i	$-0.585798\pi$
$977$	2.82620	−	59.3292i	0.0904180	−	1.89811i	0.356709	−	0.934216i	$-0.383899\pi$
$978$	−29.5628	+	49.9528i	−0.945313	+	1.59731i
$979$	−7.53503	−	21.7710i	−0.240820	−	0.695805i
$980$	11.8640	+	3.48359i	0.378982	+	0.111279i
$981$	−14.0427	+	44.2711i	−0.448348	+	1.41347i
$982$	−22.5375	−	26.0097i	−0.719201	−	0.830002i
$983$	16.0347	+	1.53113i	0.511429	+	0.0488355i	0.347581	−	0.937650i	$-0.387003\pi$
$983$	16.0347	+	1.53113i	0.511429	+	0.0488355i	0.163848	+	0.986486i	$0.447609\pi$
$984$	1.98285	−	9.72280i	0.0632109	−	0.309952i
$985$	0.140694	+	1.47341i	0.00448287	+	0.0469468i
$986$	63.3536	−	25.3630i	2.01759	−	0.807721i
$987$	−5.47981	−	64.7569i	−0.174424	−	2.06124i
$988$	5.69960	+	3.29067i	0.181329	+	0.104690i
$989$	2.85620	−	7.57402i	0.0908218	−	0.240840i
$990$	−17.0765	+	11.6136i	−0.542727	+	0.369104i
$991$	16.2185	−	10.4230i	0.515197	−	0.331097i	−0.257072	−	0.966392i	$-0.582758\pi$
$991$	16.2185	−	10.4230i	0.515197	−	0.331097i	0.772269	+	0.635295i	$0.219122\pi$
$992$	−5.21105	+	6.62639i	−0.165451	+	0.210388i
$993$	−10.3724	+	25.1207i	−0.329158	+	0.797182i
$994$	−66.9958	+	70.2632i	−2.12498	+	2.22861i
$995$	−13.0054	−	9.26110i	−0.412299	−	0.293596i
$996$	−10.3912	+	34.0280i	−0.329259	+	1.07822i
$997$	10.6261	+	4.25405i	0.336532	+	0.134727i	0.533773	−	0.845628i	$-0.320774\pi$
$997$	10.6261	+	4.25405i	0.336532	+	0.134727i	−0.197241	+	0.980355i	$0.563198\pi$
$998$	26.3419	−	89.7122i	0.833837	−	2.83979i
$999$	38.1485	+	26.2974i	1.20696	+	0.832012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.4	✓	440
3.2	odd	2		621.2.s.a.494.19		440
9.4	even	3		621.2.s.a.287.19		440
9.5	odd	6	inner	207.2.o.a.149.4	yes	440
23.21	odd	22	inner	207.2.o.a.182.4	yes	440
69.44	even	22		621.2.s.a.251.19		440
207.67	odd	66		621.2.s.a.44.19		440
207.113	even	66	inner	207.2.o.a.113.4	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.4	✓	440	1.1	even	1	trivial
207.2.o.a.113.4	yes	440	207.113	even	66	inner
207.2.o.a.149.4	yes	440	9.5	odd	6	inner
207.2.o.a.182.4	yes	440	23.21	odd	22	inner
621.2.s.a.44.19		440	207.67	odd	66
621.2.s.a.251.19		440	69.44	even	22
621.2.s.a.287.19		440	9.4	even	3
621.2.s.a.494.19		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28767 + 0.108975i) q^{2} +(1.58319 - 0.702495i) q^{3} +(3.23063 - 0.308488i) q^{4} +(-0.595980 - 0.568266i) q^{5} +(-3.54528 + 1.77961i) q^{6} +(-0.645310 - 3.34819i) q^{7} +(-2.82310 + 0.405901i) q^{8} +(2.01300 - 2.22437i) q^{9} +O(q^{10})\)	\(q+(-2.28767 + 0.108975i) q^{2} +(1.58319 - 0.702495i) q^{3} +(3.23063 - 0.308488i) q^{4} +(-0.595980 - 0.568266i) q^{5} +(-3.54528 + 1.77961i) q^{6} +(-0.645310 - 3.34819i) q^{7} +(-2.82310 + 0.405901i) q^{8} +(2.01300 - 2.22437i) q^{9} +(1.42534 + 1.23506i) q^{10} +(-3.24423 + 1.67252i) q^{11} +(4.89800 - 2.75790i) q^{12} +(1.19920 + 0.231127i) q^{13} +(1.84113 + 7.58924i) q^{14} +(-1.34276 - 0.481002i) q^{15} +(0.0407460 - 0.00785315i) q^{16} +(-1.97606 - 4.32697i) q^{17} +(-4.36269 + 5.30800i) q^{18} +(1.51046 + 0.689803i) q^{19} +(-2.10070 - 1.65201i) q^{20} +(-3.37373 - 4.84750i) q^{21} +(7.23948 - 4.17971i) q^{22} +(4.57336 - 1.44374i) q^{23} +(-4.18437 + 2.62583i) q^{24} +(-0.205643 - 4.31699i) q^{25} +(-2.76857 - 0.398061i) q^{26} +(1.62436 - 4.93573i) q^{27} +(-3.11764 - 10.6177i) q^{28} +(0.595424 - 6.23556i) q^{29} +(3.12420 + 0.954048i) q^{30} +(-1.18134 + 0.929013i) q^{31} +(5.45112 - 1.32243i) q^{32} +(-3.96131 + 4.92697i) q^{33} +(4.99212 + 9.68335i) q^{34} +(-1.51807 + 2.36216i) q^{35} +(5.81708 - 7.80711i) q^{36} +(-2.51221 + 8.55582i) q^{37} +(-3.53060 - 1.41344i) q^{38} +(2.06094 - 0.476515i) q^{39} +(1.91317 + 1.36236i) q^{40} +(-1.38614 + 1.45375i) q^{41} +(8.24626 + 10.7218i) q^{42} +(1.04336 - 1.32674i) q^{43} +(-9.96496 + 6.40409i) q^{44} +(-2.46374 + 0.181760i) q^{45} +(-10.3050 + 3.80119i) q^{46} +(9.52963 + 5.50193i) q^{47} +(0.0589920 - 0.0410569i) q^{48} +(-4.29535 + 1.71960i) q^{49} +(0.940890 + 9.85345i) q^{50} +(-6.16816 - 5.46226i) q^{51} +(3.94548 + 0.376748i) q^{52} +(4.16607 + 4.80790i) q^{53} +(-3.17814 + 11.4684i) q^{54} +(2.88393 + 0.846798i) q^{55} +(3.18081 + 9.19035i) q^{56} +(2.87593 + 0.0310027i) q^{57} +(-0.682614 + 14.3298i) q^{58} +(0.504712 - 2.61869i) q^{59} +(-4.48633 - 1.13972i) q^{60} +(-4.17874 + 10.4380i) q^{61} +(2.60127 - 2.25402i) q^{62} +(-8.74662 - 5.30450i) q^{63} +(-12.4059 + 3.64270i) q^{64} +(-0.583360 - 0.819214i) q^{65} +(8.52526 - 11.7030i) q^{66} +(-3.30135 + 6.40373i) q^{67} +(-7.71875 - 13.3693i) q^{68} +(6.22629 - 5.49848i) q^{69} +(3.21543 - 5.56929i) q^{70} +(6.72112 + 10.4583i) q^{71} +(-4.78004 + 7.09671i) q^{72} +(5.56880 - 12.1940i) q^{73} +(4.81475 - 19.8467i) q^{74} +(-3.35823 - 6.69016i) q^{75} +(5.09253 + 1.76254i) q^{76} +(7.69343 + 9.78299i) q^{77} +(-4.66282 + 1.31470i) q^{78} +(8.56154 - 2.96318i) q^{79} +(-0.0287465 - 0.0184742i) q^{80} +(-0.895644 - 8.95532i) q^{81} +(3.01262 - 3.47675i) q^{82} +(-4.58096 + 4.36793i) q^{83} +(-12.3947 - 14.6197i) q^{84} +(-1.28118 + 3.70172i) q^{85} +(-2.24229 + 3.14886i) q^{86} +(-3.43778 - 10.2904i) q^{87} +(8.47992 - 6.03852i) q^{88} +(-0.898270 + 6.24760i) q^{89} +(5.61643 - 0.684295i) q^{90} -4.16431i q^{91} +(14.3295 - 6.07502i) q^{92} +(-1.21766 + 2.30069i) q^{93} +(-22.4003 - 11.5481i) q^{94} +(-0.508211 - 1.26945i) q^{95} +(7.70117 - 5.92304i) q^{96} +(13.9326 + 3.38001i) q^{97} +(9.63898 - 4.40197i) q^{98} +(-2.81034 + 10.5831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

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Database

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