LMFDB - Embedded newform 25.3.f.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, 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:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.4
Character	$\chi$	$=$	25.8
Dual form			25.3.f.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70026 + 1.37585i) q^{2} +(-4.42692 - 0.701156i) q^{3} +(3.04732 + 4.19427i) q^{4} +(1.95091 - 4.60369i) q^{5} +(-10.9892 - 7.98410i) q^{6} +(-4.77540 + 4.77540i) q^{7} +(0.561510 + 3.54523i) q^{8} +(10.5465 + 3.42677i) q^{9} +O(q^{10})$	\(q+(2.70026 + 1.37585i) q^{2} +(-4.42692 - 0.701156i) q^{3} +(3.04732 + 4.19427i) q^{4} +(1.95091 - 4.60369i) q^{5} +(-10.9892 - 7.98410i) q^{6} +(-4.77540 + 4.77540i) q^{7} +(0.561510 + 3.54523i) q^{8} +(10.5465 + 3.42677i) q^{9} +(11.6020 - 9.74701i) q^{10} +(3.84423 + 11.8313i) q^{11} +(-10.5494 - 20.7044i) q^{12} +(-1.05261 + 0.536333i) q^{13} +(-19.4651 + 6.32459i) q^{14} +(-11.8644 + 19.0123i) q^{15} +(3.04678 - 9.37702i) q^{16} +(-4.59461 + 0.727715i) q^{17} +(23.7637 + 23.7637i) q^{18} +(12.8564 - 17.6953i) q^{19} +(25.2542 - 5.84624i) q^{20} +(24.4886 - 17.7920i) q^{21} +(-5.89773 + 37.2368i) q^{22} +(-4.03970 + 7.92835i) q^{23} -16.0882i q^{24} +(-17.3879 - 17.9628i) q^{25} -3.58025 q^{26} +(-8.34369 - 4.25132i) q^{27} +(-34.5815 - 5.47717i) q^{28} +(5.42781 + 7.47074i) q^{29} +(-58.1952 + 35.0145i) q^{30} +(-25.3215 - 18.3971i) q^{31} +(31.2809 - 31.2809i) q^{32} +(-8.72252 - 55.0718i) q^{33} +(-13.4079 - 4.35649i) q^{34} +(12.6681 + 31.3008i) q^{35} +(17.7658 + 54.6774i) q^{36} +(6.47182 + 12.7017i) q^{37} +(59.0618 - 30.0935i) q^{38} +(5.03589 - 1.63626i) q^{39} +(17.4166 + 4.33142i) q^{40} +(-16.8825 + 51.9589i) q^{41} +(90.6050 - 14.3504i) q^{42} +(-36.1728 - 36.1728i) q^{43} +(-37.9092 + 52.1775i) q^{44} +(36.3511 - 41.8676i) q^{45} +(-21.8165 + 15.8506i) q^{46} +(-0.703158 + 4.43956i) q^{47} +(-20.0626 + 39.3751i) q^{48} +3.39110i q^{49} +(-22.2377 - 72.4274i) q^{50} +20.8502 q^{51} +(-5.45717 - 2.78057i) q^{52} +(69.2402 + 10.9666i) q^{53} +(-16.6810 - 22.9594i) q^{54} +(61.9675 + 5.38424i) q^{55} +(-19.6113 - 14.2485i) q^{56} +(-69.3215 + 69.3215i) q^{57} +(4.37788 + 27.6409i) q^{58} +(-67.9339 - 22.0730i) q^{59} +(-115.897 + 8.17375i) q^{60} +(15.0860 + 46.4300i) q^{61} +(-43.0629 - 84.5157i) q^{62} +(-66.7281 + 33.9997i) q^{63} +(89.9967 - 29.2417i) q^{64} +(0.415555 + 5.89224i) q^{65} +(52.2176 - 160.709i) q^{66} +(79.5063 - 12.5926i) q^{67} +(-17.0535 - 17.0535i) q^{68} +(23.4424 - 32.2657i) q^{69} +(-8.85824 + 101.950i) q^{70} +(-34.9284 + 25.3769i) q^{71} +(-6.22673 + 39.3140i) q^{72} +(27.3286 - 53.6354i) q^{73} +43.2021i q^{74} +(64.3801 + 91.7115i) q^{75} +113.396 q^{76} +(-74.8571 - 38.1416i) q^{77} +(15.8495 + 2.51031i) q^{78} +(-27.4839 - 37.8283i) q^{79} +(-37.2249 - 32.3202i) q^{80} +(-46.7867 - 33.9925i) q^{81} +(-117.075 + 117.075i) q^{82} +(17.1166 + 108.070i) q^{83} +(149.249 + 48.4940i) q^{84} +(-5.61351 + 22.5719i) q^{85} +(-47.9077 - 147.445i) q^{86} +(-18.7904 - 36.8782i) q^{87} +(-39.7862 + 20.2721i) q^{88} +(63.0322 - 20.4804i) q^{89} +(155.761 - 63.0397i) q^{90} +(2.46544 - 7.58786i) q^{91} +(-45.5639 + 7.21661i) q^{92} +(99.1969 + 99.1969i) q^{93} +(-8.00690 + 11.0206i) q^{94} +(-56.3820 - 93.7088i) q^{95} +(-160.411 + 116.546i) q^{96} +(8.99168 - 56.7712i) q^{97} +(-4.66566 + 9.15688i) q^{98} +137.953i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	2.70026	+	1.37585i	1.35013	+	0.687927i	0.971371	−	0.237568i	$-0.0763501\pi$
$2$	2.70026	+	1.37585i	1.35013	+	0.687927i	0.378761	+	0.925494i	$0.376350\pi$
$3$	−4.42692	−	0.701156i	−1.47564	−	0.233719i	−0.633822	−	0.773479i	$-0.718515\pi$
$3$	−4.42692	−	0.701156i	−1.47564	−	0.233719i	−0.841819	+	0.539760i	$0.818515\pi$
$4$	3.04732	+	4.19427i	0.761829	+	1.04857i
$5$	1.95091	−	4.60369i	0.390182	−	0.920738i
$5$	1.95091	−	4.60369i	0.390182	−	0.920738i
$6$	−10.9892	−	7.98410i	−1.83153	−	1.33068i
$7$	−4.77540	+	4.77540i	−0.682200	+	0.682200i	−0.960496	−	0.278295i	$-0.910231\pi$
$7$	−4.77540	+	4.77540i	−0.682200	+	0.682200i	0.278295	+	0.960496i	$0.410231\pi$
$8$	0.561510	+	3.54523i	0.0701887	+	0.443154i
$9$	10.5465	+	3.42677i	1.17184	+	0.380753i
$10$	11.6020	−	9.74701i	1.16020	−	0.974701i
$11$	3.84423	+	11.8313i	0.349476	+	1.07558i	0.959144	+	0.282919i	$0.0913027\pi$
$11$	3.84423	+	11.8313i	0.349476	+	1.07558i	−0.609668	+	0.792657i	$0.708697\pi$
$12$	−10.5494	−	20.7044i	−0.879116	−	1.72536i
$13$	−1.05261	+	0.536333i	−0.0809703	+	0.0412564i	−0.494007	−	0.869458i	$-0.664468\pi$
$13$	−1.05261	+	0.536333i	−0.0809703	+	0.0412564i	0.413036	+	0.910714i	$0.364468\pi$
$14$	−19.4651	+	6.32459i	−1.39036	+	0.451757i
$15$	−11.8644	+	19.0123i	−0.790963	+	1.26749i
$16$	3.04678	−	9.37702i	0.190424	−	0.586064i
$17$	−4.59461	+	0.727715i	−0.270271	+	0.0428067i	−0.290099	−	0.956997i	$-0.593688\pi$
$17$	−4.59461	+	0.727715i	−0.270271	+	0.0428067i	0.0198278	+	0.999803i	$0.493688\pi$
$18$	23.7637	+	23.7637i	1.32020	+	1.32020i
$19$	12.8564	−	17.6953i	0.676652	−	0.931332i	−0.323235	−	0.946319i	$-0.604771\pi$
$19$	12.8564	−	17.6953i	0.676652	−	0.931332i	0.999888	+	0.0149865i	$0.00477052\pi$
$20$	25.2542	−	5.84624i	1.26271	−	0.292312i
$21$	24.4886	−	17.7920i	1.16613	−	0.847240i
$22$	−5.89773	+	37.2368i	−0.268079	+	1.69258i
$23$	−4.03970	+	7.92835i	−0.175639	+	0.344711i	−0.961997	−	0.273060i	$-0.911964\pi$
$23$	−4.03970	+	7.92835i	−0.175639	+	0.344711i	0.786358	+	0.617771i	$0.211964\pi$
$24$		−	16.0882i		−	0.670341i
$25$	−17.3879	−	17.9628i	−0.695515	−	0.718511i
$26$	−3.58025			−0.137702
$27$	−8.34369	−	4.25132i	−0.309025	−	0.157456i
$28$	−34.5815	−	5.47717i	−1.23505	−	0.195613i
$29$	5.42781	+	7.47074i	0.187166	+	0.257612i	0.892280	−	0.451482i	$-0.149104\pi$
$29$	5.42781	+	7.47074i	0.187166	+	0.257612i	−0.705114	+	0.709094i	$0.749104\pi$
$30$	−58.1952	+	35.0145i	−1.93984	+	1.16715i
$31$	−25.3215	−	18.3971i	−0.816821	−	0.593456i	0.0989788	−	0.995090i	$-0.468442\pi$
$31$	−25.3215	−	18.3971i	−0.816821	−	0.593456i	−0.915800	+	0.401634i	$0.868442\pi$
$32$	31.2809	−	31.2809i	0.977529	−	0.977529i
$33$	−8.72252	−	55.0718i	−0.264319	−	1.66884i
$34$	−13.4079	−	4.35649i	−0.394350	−	0.128132i
$35$	12.6681	+	31.3008i	0.361945	+	0.894310i
$36$	17.7658	+	54.6774i	0.493494	+	1.51882i
$37$	6.47182	+	12.7017i	0.174914	+	0.343288i	0.961774	−	0.273843i	$-0.0882948\pi$
$37$	6.47182	+	12.7017i	0.174914	+	0.343288i	−0.786860	+	0.617131i	$0.788295\pi$
$38$	59.0618	−	30.0935i	1.55426	−	0.791934i
$39$	5.03589	−	1.63626i	0.129125	−	0.0419554i
$40$	17.4166	+	4.33142i	0.435415	+	0.108286i
$41$	−16.8825	+	51.9589i	−0.411767	+	1.26729i	0.503343	+	0.864086i	$0.332103\pi$
$41$	−16.8825	+	51.9589i	−0.411767	+	1.26729i	−0.915111	+	0.403203i	$0.867897\pi$
$42$	90.6050	−	14.3504i	2.15726	−	0.341677i
$43$	−36.1728	−	36.1728i	−0.841228	−	0.841228i	0.147791	−	0.989019i	$-0.452784\pi$
$43$	−36.1728	−	36.1728i	−0.841228	−	0.841228i	−0.989019	+	0.147791i	$0.952784\pi$
$44$	−37.9092	+	52.1775i	−0.861573	+	1.18585i
$45$	36.3511	−	41.8676i	0.807803	−	0.930390i
$46$	−21.8165	+	15.8506i	−0.474272	+	0.344579i
$47$	−0.703158	+	4.43956i	−0.0149608	+	0.0944588i	−0.994039	−	0.109026i	$-0.965227\pi$
$47$	−0.703158	+	4.43956i	−0.0149608	+	0.0944588i	0.979078	+	0.203485i	$0.0652268\pi$
$48$	−20.0626	+	39.3751i	−0.417971	+	0.820314i
$49$			3.39110i			0.0692062i
$50$	−22.2377	−	72.4274i	−0.444755	−	1.44855i
$51$	20.8502			0.408828
$52$	−5.45717	−	2.78057i	−0.104946	−	0.0534725i
$53$	69.2402	+	10.9666i	1.30642	+	0.206916i	0.770547	−	0.637383i	$-0.219983\pi$
$53$	69.2402	+	10.9666i	1.30642	+	0.206916i	0.535872	+	0.844299i	$0.319983\pi$
$54$	−16.6810	−	22.9594i	−0.308907	−	0.425174i
$55$	61.9675	+	5.38424i	1.12668	+	0.0978953i
$56$	−19.6113	−	14.2485i	−0.350202	−	0.254437i
$57$	−69.3215	+	69.3215i	−1.21617	+	1.21617i
$58$	4.37788	+	27.6409i	0.0754807	+	0.476567i
$59$	−67.9339	−	22.0730i	−1.15142	−	0.374119i	−0.329743	−	0.944071i	$-0.606962\pi$
$59$	−67.9339	−	22.0730i	−1.15142	−	0.374119i	−0.821678	+	0.569951i	$0.806962\pi$
$60$	−115.897	+	8.17375i	−1.93162	+	0.136229i
$61$	15.0860	+	46.4300i	0.247312	+	0.761148i	0.995248	+	0.0973769i	$0.0310452\pi$
$61$	15.0860	+	46.4300i	0.247312	+	0.761148i	−0.747936	+	0.663771i	$0.768955\pi$
$62$	−43.0629	−	84.5157i	−0.694563	−	1.36316i
$63$	−66.7281	+	33.9997i	−1.05918	+	0.539677i
$64$	89.9967	−	29.2417i	1.40620	−	0.456902i
$65$	0.415555	+	5.89224i	0.00639315	+	0.0906499i
$66$	52.2176	−	160.709i	0.791176	−	2.43499i
$67$	79.5063	−	12.5926i	1.18666	−	0.187949i	0.468268	−	0.883586i	$-0.344878\pi$
$67$	79.5063	−	12.5926i	1.18666	−	0.187949i	0.718393	+	0.695638i	$0.244878\pi$
$68$	−17.0535	−	17.0535i	−0.250786	−	0.250786i
$69$	23.4424	−	32.2657i	0.339745	−	0.467620i
$70$	−8.85824	+	101.950i	−0.126546	+	1.45643i
$71$	−34.9284	+	25.3769i	−0.491949	+	0.357422i	−0.805933	−	0.592006i	$-0.798336\pi$
$71$	−34.9284	+	25.3769i	−0.491949	+	0.357422i	0.313985	+	0.949428i	$0.398336\pi$
$72$	−6.22673	+	39.3140i	−0.0864824	+	0.546028i
$73$	27.3286	−	53.6354i	0.374364	−	0.734731i	−0.624566	−	0.780972i	$-0.714724\pi$
$73$	27.3286	−	53.6354i	0.374364	−	0.734731i	0.998930	+	0.0462407i	$0.0147241\pi$
$74$			43.2021i			0.583813i
$75$	64.3801	+	91.7115i	0.858402	+	1.22282i
$76$	113.396			1.49206
$77$	−74.8571	−	38.1416i	−0.972170	−	0.495345i
$78$	15.8495	+	2.51031i	0.203199	+	0.0321835i
$79$	−27.4839	−	37.8283i	−0.347898	−	0.478840i	0.598830	−	0.800876i	$-0.295633\pi$
$79$	−27.4839	−	37.8283i	−0.347898	−	0.478840i	−0.946727	+	0.322037i	$0.895633\pi$
$80$	−37.2249	−	32.3202i	−0.465311	−	0.404002i
$81$	−46.7867	−	33.9925i	−0.577613	−	0.419660i
$82$	−117.075	+	117.075i	−1.42774	+	1.42774i
$83$	17.1166	+	108.070i	0.206224	+	1.30205i	0.845874	+	0.533382i	$0.179079\pi$
$83$	17.1166	+	108.070i	0.206224	+	1.30205i	−0.639650	+	0.768666i	$0.720921\pi$
$84$	149.249	+	48.4940i	1.77678	+	0.577309i
$85$	−5.61351	+	22.5719i	−0.0660413	+	0.265551i
$86$	−47.9077	−	147.445i	−0.557066	−	1.71447i
$87$	−18.7904	−	36.8782i	−0.215981	−	0.423887i
$88$	−39.7862	+	20.2721i	−0.452116	+	0.230365i
$89$	63.0322	−	20.4804i	0.708227	−	0.230117i	0.0673154	−	0.997732i	$-0.478557\pi$
$89$	63.0322	−	20.4804i	0.708227	−	0.230117i	0.640911	+	0.767615i	$0.278557\pi$
$90$	155.761	−	63.0397i	1.73068	−	0.700441i
$91$	2.46544	−	7.58786i	0.0270928	−	0.0833830i
$92$	−45.5639	+	7.21661i	−0.495259	+	0.0784414i
$93$	99.1969	+	99.1969i	1.06663	+	1.06663i
$94$	−8.00690	+	11.0206i	−0.0851798	+	0.117240i
$95$	−56.3820	−	93.7088i	−0.593495	−	0.986409i
$96$	−160.411	+	116.546i	−1.67095	+	1.21402i
$97$	8.99168	−	56.7712i	0.0926977	−	0.585270i	−0.896993	−	0.442046i	$-0.854253\pi$
$97$	8.99168	−	56.7712i	0.0926977	−	0.585270i	0.989690	−	0.143225i	$-0.0457471\pi$
$98$	−4.66566	+	9.15688i	−0.0476088	+	0.0934375i
$99$			137.953i			1.39346i
$100$	22.3544	−	127.668i	0.223544	−	1.27668i
$101$	−4.10343			−0.0406280			−0.0203140	−	0.999794i	$-0.506467\pi$
$101$	−4.10343			−0.0406280			−0.0203140	+	0.999794i	$0.506467\pi$
$102$	56.3011	+	28.6869i	0.551972	+	0.281244i
$103$	−93.2854	−	14.7750i	−0.905683	−	0.143446i	−0.313818	−	0.949483i	$-0.601608\pi$
$103$	−93.2854	−	14.7750i	−0.905683	−	0.143446i	−0.591865	+	0.806037i	$0.701608\pi$
$104$	−2.49248	−	3.43060i	−0.0239661	−	0.0329866i
$105$	−34.1338	−	147.449i	−0.325084	−	1.40427i
$106$	171.878	+	124.877i	1.62149	+	1.17808i
$107$	142.289	−	142.289i	1.32980	−	1.32980i	0.424266	−	0.905538i	$-0.360532\pi$
$107$	142.289	−	142.289i	1.32980	−	1.32980i	0.905538	−	0.424266i	$-0.139468\pi$
$108$	−7.59466	−	47.9508i	−0.0703209	−	0.443989i
$109$	−129.134	−	41.9581i	−1.18471	−	0.384936i	−0.350597	−	0.936526i	$-0.614021\pi$
$109$	−129.134	−	41.9581i	−1.18471	−	0.384936i	−0.834115	+	0.551590i	$0.814021\pi$
$110$	159.921	+	99.7971i	1.45383	+	0.907246i
$111$	−19.7444	−	60.7671i	−0.177878	−	0.547451i
$112$	30.2294	+	59.3286i	0.269906	+	0.529720i
$113$	−82.9619	+	42.2712i	−0.734176	+	0.374081i	−0.780758	−	0.624833i	$-0.785167\pi$
$113$	−82.9619	+	42.2712i	−0.734176	+	0.374081i	0.0465823	+	0.998914i	$0.485167\pi$
$114$	−282.562	+	91.8101i	−2.47862	+	0.805352i
$115$	28.6186	+	34.0650i	0.248857	+	0.296218i
$116$	−14.7941	+	45.5314i	−0.127535	+	0.392512i
$117$	−12.9393	+	2.04938i	−0.110592	+	0.0175161i
$118$	−153.070	−	153.070i	−1.29720	−	1.29720i
$119$	18.4660	−	25.4162i	0.155176	−	0.213582i
$120$	−74.0649	−	31.3866i	−0.617208	−	0.261555i
$121$	−27.3112	+	19.8428i	−0.225713	+	0.163990i
$122$	−23.1447	+	146.130i	−0.189710	+	1.19778i
$123$	111.169	−	218.181i	0.903810	−	1.77383i
$124$		−	162.267i		−	1.30860i
$125$	−116.617	+	45.0046i	−0.932938	+	0.360037i
$126$	−226.962			−1.80129
$127$	−43.9744	−	22.4061i	−0.346255	−	0.176426i	0.272210	−	0.962238i	$-0.412245\pi$
$127$	−43.9744	−	22.4061i	−0.346255	−	0.176426i	−0.618465	+	0.785812i	$0.712245\pi$
$128$	108.474	+	17.1806i	0.847454	+	0.134224i
$129$	134.771	+	185.497i	1.04474	+	1.43796i
$130$	−6.98475	+	16.4824i	−0.0537289	+	0.126787i
$131$	109.772	+	79.7539i	0.837953	+	0.608809i	0.921798	−	0.387670i	$-0.126720\pi$
$131$	109.772	+	79.7539i	0.837953	+	0.608809i	−0.0838450	+	0.996479i	$0.526720\pi$
$132$	204.406	−	204.406i	1.54853	−	1.54853i
$133$	23.1078	+	145.897i	0.173743	+	1.09697i
$134$	232.014	+	75.3858i	1.73144	+	0.562580i
$135$	−35.8496	+	30.1178i	−0.265552	+	0.223095i
$136$	−5.15983	−	15.8803i	−0.0379400	−	0.116767i
$137$	84.2247	+	165.300i	0.614779	+	1.20657i	0.963087	+	0.269192i	$0.0867565\pi$
$137$	84.2247	+	165.300i	0.614779	+	1.20657i	−0.348308	+	0.937380i	$0.613243\pi$
$138$	107.694	−	54.8727i	0.780389	−	0.397628i
$139$	122.872	−	39.9236i	0.883973	−	0.287220i	0.168367	−	0.985724i	$-0.446151\pi$
$139$	122.872	−	39.9236i	0.883973	−	0.287220i	0.715606	+	0.698504i	$0.246151\pi$
$140$	−92.6806	+	148.517i	−0.662004	+	1.06083i
$141$	6.22565	−	19.1606i	0.0441535	−	0.135891i
$142$	−129.231	+	20.4681i	−0.910076	+	0.144142i
$143$	−10.3920	−	10.3920i	−0.0726715	−	0.0726715i
$144$	64.2658	−	88.4543i	0.446291	−	0.614266i
$145$	44.9822	−	10.4132i	0.310222	−	0.0718151i
$146$	147.589	−	107.230i	1.01088	−	0.734449i
$147$	2.37769	−	15.0122i	0.0161748	−	0.102123i
$148$	−33.5525	+	65.8506i	−0.226706	+	0.444936i
$149$		−	232.485i		−	1.56030i	−0.625592	−	0.780150i	$-0.715143\pi$
$149$		−	232.485i		−	1.56030i	0.625592	−	0.780150i	$-0.284857\pi$
$150$	47.6618	+	336.223i	0.317745	+	2.24149i
$151$	172.702			1.14372			0.571861	−	0.820351i	$-0.306222\pi$
$151$	172.702			1.14372			0.571861	+	0.820351i	$0.306222\pi$
$152$	69.9530	+	35.6428i	0.460217	+	0.234492i
$153$	−50.9509	−	8.06982i	−0.333012	−	0.0527439i
$154$	−149.657	−	205.985i	−0.971797	−	1.33756i
$155$	−134.095	+	80.6810i	−0.865126	+	0.520522i
$156$	22.2089	+	16.1357i	0.142365	+	0.103434i
$157$	−154.466	+	154.466i	−0.983858	+	0.983858i	−0.999872	−	0.0160139i	$-0.994902\pi$
$157$	−154.466	+	154.466i	−0.983858	+	0.983858i	0.0160139	+	0.999872i	$0.494902\pi$
$158$	−22.1675	−	139.960i	−0.140301	−	0.885825i
$159$	−298.832	−	97.0963i	−1.87945	−	0.610669i
$160$	−82.9813	−	205.034i	−0.518633	−	1.28146i
$161$	−18.5699	−	57.1522i	−0.115341	−	0.354983i
$162$	−79.5677	−	156.160i	−0.491158	−	0.963953i
$163$	32.1939	−	16.4036i	0.197508	−	0.100636i	−0.352439	−	0.935835i	$-0.614648\pi$
$163$	32.1939	−	16.4036i	0.197508	−	0.100636i	0.549948	+	0.835199i	$0.314648\pi$
$164$	−269.376	+	87.5254i	−1.64253	+	0.533692i
$165$	−270.550	−	67.2845i	−1.63970	−	0.407785i
$166$	−102.469	+	315.368i	−0.617284	+	1.89980i
$167$	−11.3916	+	1.80425i	−0.0682130	+	0.0108039i	−0.190448	−	0.981697i	$-0.560994\pi$
$167$	−11.3916	+	1.80425i	−0.0682130	+	0.0108039i	0.122235	+	0.992501i	$0.460994\pi$
$168$	76.8275	+	76.8275i	0.457306	+	0.457306i
$169$	−98.5154	+	135.595i	−0.582931	+	0.802336i
$170$	−46.2135	+	53.2266i	−0.271844	+	0.313098i
$171$	196.228	−	142.568i	1.14753	−	0.833731i
$172$	41.4886	−	261.948i	0.241213	−	1.52296i
$173$	−44.0149	+	86.3841i	−0.254421	+	0.499330i	−0.982523	−	0.186139i	$-0.940403\pi$
$173$	−44.0149	+	86.3841i	−0.254421	+	0.499330i	0.728102	+	0.685469i	$0.240403\pi$
$174$		−	125.434i		−	0.720883i
$175$	168.814	+	2.74537i	0.964649	+	0.0156878i
$176$	122.655			0.696904
$177$	285.261	+	145.348i	1.61165	+	0.821175i
$178$	198.382	+	31.4206i	1.11450	+	0.176520i
$179$	119.212	+	164.081i	0.665987	+	0.916653i	0.999661	−	0.0260360i	$-0.00828846\pi$
$179$	119.212	+	164.081i	0.665987	+	0.916653i	−0.333674	+	0.942689i	$0.608288\pi$
$180$	286.377	+	24.8828i	1.59098	+	0.138238i
$181$	−245.629	−	178.460i	−1.35707	−	0.985966i	−0.998625	−	0.0524129i	$-0.983309\pi$
$181$	−245.629	−	178.460i	−1.35707	−	0.985966i	−0.358440	−	0.933553i	$-0.616691\pi$
$182$	17.0971	−	17.0971i	0.0939403	−	0.0939403i
$183$	−34.2300	−	216.120i	−0.187049	−	1.18098i
$184$	−30.3762	−	9.86982i	−0.165088	−	0.0536403i
$185$	71.1005	−	5.01441i	0.384327	−	0.0271049i
$186$	131.378	+	404.338i	0.706331	+	2.17386i
$187$	−26.2726	−	51.5628i	−0.140495	−	0.275737i
$188$	−20.7635	+	10.5795i	−0.110444	+	0.0562740i
$189$	60.1462	−	19.5427i	0.318234	−	0.103400i
$190$	−23.3167	−	330.612i	−0.122719	−	1.74006i
$191$	28.3111	−	87.1326i	0.148226	−	0.456192i	−0.849186	−	0.528094i	$-0.822907\pi$
$191$	28.3111	−	87.1326i	0.148226	−	0.456192i	0.997412	+	0.0719021i	$0.0229069\pi$
$192$	−418.912	+	66.3491i	−2.18183	+	0.345568i
$193$	129.347	+	129.347i	0.670189	+	0.670189i	0.957760	−	0.287570i	$-0.0928475\pi$
$193$	129.347	+	129.347i	0.670189	+	0.670189i	−0.287570	+	0.957760i	$0.592847\pi$
$194$	102.389	−	140.926i	0.527777	−	0.726423i
$195$	2.29175	−	26.3759i	0.0117526	−	0.135261i
$196$	−14.2232	+	10.3338i	−0.0725673	+	0.0527233i
$197$	19.2400	−	121.476i	0.0976648	−	0.616631i	−0.889501	−	0.456933i	$-0.848948\pi$
$197$	19.2400	−	121.476i	0.0976648	−	0.616631i	0.987166	−	0.159698i	$-0.0510521\pi$
$198$	−189.803	+	372.509i	−0.958600	+	1.88136i
$199$			390.191i			1.96076i	0.197114	+	0.980381i	$0.436843\pi$
$199$			390.191i			1.96076i	−0.197114	+	0.980381i	$0.563157\pi$
$200$	53.9188	−	71.7304i	0.269594	−	0.358652i
$201$	−360.798			−1.79501
$202$	−11.0803	−	5.64572i	−0.0548532	−	0.0279491i
$203$	−61.5958	−	9.75581i	−0.303427	−	0.0480582i
$204$	63.5372	+	87.4515i	0.311457	+	0.428684i
$205$	206.266	+	179.089i	1.00618	+	0.873604i
$206$	−231.567	−	168.243i	−1.12411	−	0.816715i
$207$	−69.7734	+	69.7734i	−0.337070	+	0.337070i
$208$	1.82213	+	11.5045i	0.00876023	+	0.0553099i
$209$	258.782	+	84.0834i	1.23819	+	0.402313i
$210$	110.698	−	445.114i	0.527131	−	2.11959i
$211$	−34.5087	−	106.207i	−0.163548	−	0.503350i	0.835378	−	0.549676i	$-0.185249\pi$
$211$	−34.5087	−	106.207i	−0.163548	−	0.503350i	−0.998926	+	0.0463257i	$0.985249\pi$
$212$	165.000	+	323.831i	0.778302	+	1.52750i
$213$	172.418	−	87.8515i	0.809476	−	0.412449i
$214$	579.987	−	188.449i	2.71022	−	0.880603i
$215$	−237.098	+	95.9583i	−1.10278	+	0.446318i
$216$	10.3869	−	31.9675i	0.0480873	−	0.147998i
$217$	208.774	−	33.0665i	0.962091	−	0.152380i
$218$	−290.967	−	290.967i	−1.33471	−	1.33471i
$219$	−158.588	+	218.278i	−0.724148	+	0.996704i
$220$	166.252	+	276.316i	0.755689	+	1.25598i
$221$	4.44605	−	3.23024i	0.0201179	−	0.0146165i
$222$	30.2914	−	191.253i	0.136448	−	0.861498i
$223$	−20.5207	+	40.2741i	−0.0920209	+	0.180601i	−0.932429	−	0.361352i	$-0.882315\pi$
$223$	−20.5207	+	40.2741i	−0.0920209	+	0.180601i	0.840408	+	0.541954i	$0.182315\pi$
$224$			298.758i			1.33374i
$225$	−121.827	−	249.029i	−0.541455	−	1.10680i
$226$	−282.178			−1.24858
$227$	−107.017	−	54.5277i	−0.471439	−	0.240210i	0.202096	−	0.979366i	$-0.435225\pi$
$227$	−107.017	−	54.5277i	−0.471439	−	0.240210i	−0.673535	+	0.739156i	$0.735225\pi$
$228$	−501.997	−	79.5085i	−2.20174	−	0.348722i
$229$	−71.1775	−	97.9675i	−0.310819	−	0.427806i	0.624817	−	0.780771i	$-0.285173\pi$
$229$	−71.1775	−	97.9675i	−0.310819	−	0.427806i	−0.935636	+	0.352965i	$0.885173\pi$
$230$	30.4092	+	131.360i	0.132214	+	0.571128i
$231$	304.643	+	221.336i	1.31880	+	0.958166i
$232$	−23.4377	+	23.4377i	−0.101025	+	0.101025i
$233$	−30.8904	−	195.034i	−0.132577	−	0.837056i	−0.960918	−	0.276833i	$-0.910715\pi$
$233$	−30.8904	−	195.034i	−0.132577	−	0.837056i	0.828341	−	0.560224i	$-0.189285\pi$
$234$	−37.7592	−	12.2687i	−0.161364	−	0.0524304i
$235$	19.0666	+	11.8983i	0.0811343	+	0.0506311i
$236$	−114.436	−	352.196i	−0.484896	−	1.49236i
$237$	95.1456	+	186.734i	0.401458	+	0.787906i
$238$	84.8320	−	43.2241i	0.356437	−	0.181614i
$239$	−105.011	+	34.1201i	−0.439375	+	0.142762i	−0.520347	−	0.853955i	$-0.674198\pi$
$239$	−105.011	+	34.1201i	−0.439375	+	0.142762i	0.0809720	+	0.996716i	$0.474198\pi$
$240$	142.130	+	169.179i	0.592209	+	0.704914i
$241$	21.0011	−	64.6348i	0.0871416	−	0.268194i	−0.897985	−	0.440027i	$-0.854969\pi$
$241$	21.0011	−	64.6348i	0.0871416	−	0.268194i	0.985126	+	0.171833i	$0.0549689\pi$
$242$	−101.048	+	16.0045i	−0.417555	+	0.0661342i
$243$	242.881	+	242.881i	0.999511	+	0.999511i
$244$	−148.768	+	204.762i	−0.609706	+	0.839188i
$245$	15.6116	+	6.61574i	0.0637207	+	0.0270030i
$246$	600.369	−	436.194i	2.44053	−	1.77315i
$247$	−4.04223	+	25.5216i	−0.0163653	+	0.103326i
$248$	51.0038	−	100.101i	0.205661	−	0.403632i
$249$		−	490.419i		−	1.96955i
$250$	−376.817	−	38.9240i	−1.50727	−	0.155696i
$251$	−184.575			−0.735358			−0.367679	−	0.929953i	$-0.619847\pi$
$251$	−184.575			−0.735358			−0.367679	+	0.929953i	$0.619847\pi$
$252$	−345.945	−	176.268i	−1.37280	−	0.699476i
$253$	−109.332	−	17.3166i	−0.432144	−	0.0684449i
$254$	−87.9151	−	121.005i	−0.346122	−	0.476396i
$255$	40.6770	−	95.9879i	0.159517	−	0.376423i
$256$	−36.9523	−	26.8474i	−0.144345	−	0.104873i
$257$	110.251	−	110.251i	0.428992	−	0.428992i	−0.459293	−	0.888285i	$-0.651897\pi$
$257$	110.251	−	110.251i	0.428992	−	0.428992i	0.888285	+	0.459293i	$0.151897\pi$
$258$	108.702	+	686.317i	0.421325	+	2.66014i
$259$	−91.5611	−	29.7500i	−0.353518	−	0.114865i
$260$	−23.4473	+	19.6985i	−0.0901820	+	0.0757633i
$261$	31.6440	+	97.3903i	0.121241	+	0.373143i
$262$	186.683	+	366.387i	0.712532	+	1.39842i
$263$	−295.330	+	150.478i	−1.12293	+	0.572160i	−0.913977	−	0.405766i	$-0.867005\pi$
$263$	−295.330	+	150.478i	−1.12293	+	0.572160i	−0.208950	+	0.977926i	$0.567005\pi$
$264$	190.345	−	61.8467i	0.721002	−	0.234268i
$265$	185.568	−	297.365i	0.700257	−	1.12213i
$266$	−138.335	+	425.752i	−0.520058	+	1.60057i
$267$	−293.399	+	46.4698i	−1.09887	+	0.174044i
$268$	295.097	+	295.097i	1.10111	+	1.10111i
$269$	306.607	−	422.008i	1.13980	−	1.56880i	0.371857	−	0.928290i	$-0.378721\pi$
$269$	306.607	−	422.008i	1.13980	−	1.56880i	0.767946	−	0.640515i	$-0.221279\pi$
$270$	−138.241	+	32.0022i	−0.512003	+	0.118527i
$271$	33.2207	−	24.1363i	0.122586	−	0.0890638i	−0.524803	−	0.851224i	$-0.675861\pi$
$271$	33.2207	−	24.1363i	0.122586	−	0.0890638i	0.647389	+	0.762160i	$0.275861\pi$
$272$	−7.17496	+	45.3009i	−0.0263785	+	0.166547i
$273$	−16.2346	+	31.8622i	−0.0594674	+	0.116711i
$274$			562.236i			2.05195i
$275$	145.681	−	274.775i	0.529747	−	0.999182i
$276$	206.768			0.749159
$277$	−471.855	−	240.422i	−1.70345	−	0.867950i	−0.985040	−	0.172327i	$-0.944872\pi$
$277$	−471.855	−	240.422i	−1.70345	−	0.867950i	−0.718407	−	0.695623i	$-0.755128\pi$
$278$	386.717	+	61.2499i	1.39107	+	0.220323i
$279$	−204.011	−	280.797i	−0.731221	−	1.00644i
$280$	−103.855	+	62.4870i	−0.370912	+	0.223168i
$281$	130.914	+	95.1145i	0.465886	+	0.338486i	0.795836	−	0.605513i	$-0.207032\pi$
$281$	130.914	+	95.1145i	0.465886	+	0.338486i	−0.329950	+	0.943998i	$0.607032\pi$
$282$	43.1731	−	43.1731i	0.153096	−	0.153096i
$283$	−50.0186	−	315.805i	−0.176744	−	1.11592i	−0.903362	−	0.428878i	$-0.858909\pi$
$283$	−50.0186	−	315.805i	−0.176744	−	1.11592i	0.726618	−	0.687042i	$-0.241091\pi$
$284$	−212.875	−	69.1674i	−0.749561	−	0.243547i
$285$	183.894	+	454.374i	0.645243	+	1.59430i
$286$	−13.7633	−	42.3591i	−0.0481235	−	0.148109i
$287$	−167.504	−	328.745i	−0.583637	−	1.14545i
$288$	437.098	−	222.712i	1.51770	−	0.773307i
$289$	−254.274	+	82.6188i	−0.879842	+	0.285878i
$290$	135.791	+	33.7705i	0.468244	+	0.116450i
$291$	−79.6109	+	245.017i	−0.273577	+	0.841984i
$292$	308.240	−	48.8204i	1.05562	−	0.167193i
$293$	252.694	+	252.694i	0.862436	+	0.862436i	0.991621	−	0.129184i	$-0.0412359\pi$
$293$	252.694	+	252.694i	0.862436	+	0.862436i	−0.129184	+	0.991621i	$0.541236\pi$
$294$	27.0749	−	37.2654i	0.0920916	−	0.126753i
$295$	−234.150	+	269.684i	−0.793730	+	0.914182i
$296$	−41.3964	+	30.0762i	−0.139853	+	0.101609i
$297$	18.2237	−	115.060i	0.0613593	−	0.387407i
$298$	319.865	−	627.770i	1.07337	−	2.10661i
$299$		−	10.5121i		−	0.0351576i
$300$	−188.476	+	549.501i	−0.628254	+	1.83167i
$301$	345.479			1.14777
$302$	466.341	+	237.613i	1.54417	+	0.786796i
$303$	18.1656	+	2.87714i	0.0599524	+	0.00949552i
$304$	−126.759	−	174.468i	−0.416969	−	0.573909i
$305$	243.181	+	21.1295i	0.797315	+	0.0692772i
$306$	−126.478	−	91.8916i	−0.413327	−	0.300299i
$307$	260.783	−	260.783i	0.849457	−	0.849457i	−0.140609	−	0.990065i	$-0.544906\pi$
$307$	260.783	−	260.783i	0.849457	−	0.849457i	0.990065	+	0.140609i	$0.0449060\pi$
$308$	−68.1370	−	430.200i	−0.221224	−	1.39675i
$309$	402.608	+	130.815i	1.30294	+	0.423350i
$310$	−473.096	+	33.3655i	−1.52612	+	0.107630i
$311$	117.574	+	361.855i	0.378051	+	1.16352i	0.941397	+	0.337300i	$0.109514\pi$
$311$	117.574	+	361.855i	0.378051	+	1.16352i	−0.563347	+	0.826221i	$0.690486\pi$
$312$	8.62862	+	16.9346i	0.0276558	+	0.0542777i
$313$	−365.880	+	186.425i	−1.16895	+	0.595607i	−0.927139	−	0.374717i	$-0.877740\pi$
$313$	−365.880	+	186.425i	−1.16895	+	0.595607i	−0.241806	+	0.970325i	$0.577740\pi$
$314$	−629.620	+	204.576i	−2.00516	+	0.651516i
$315$	26.3432	+	373.526i	0.0836291	+	1.18580i
$316$	74.9102	−	230.550i	0.237058	−	0.729588i
$317$	−171.773	+	27.2062i	−0.541872	+	0.0858241i	−0.421370	−	0.906889i	$-0.638450\pi$
$317$	−171.773	+	27.2062i	−0.541872	+	0.0858241i	−0.120502	+	0.992713i	$0.538450\pi$
$318$	−673.335	−	673.335i	−2.11740	−	2.11740i
$319$	−67.5231	+	92.9375i	−0.211671	+	0.291340i
$320$	40.9560	−	471.365i	0.127988	−	1.47301i
$321$	−729.669	+	530.136i	−2.27311	+	1.65151i
$322$	28.4895	−	179.876i	0.0884767	−	0.558620i
$323$	−46.1930	+	90.6588i	−0.143012	+	0.280677i
$324$		−	299.822i		−	0.925376i
$325$	27.9368	+	9.58216i	0.0859592	+	0.0294836i
$326$	109.501			0.335892
$327$	542.246	+	276.288i	1.65824	+	0.844917i
$328$	−193.686	−	30.6768i	−0.590506	−	0.0935269i
$329$	−17.8428	−	24.5585i	−0.0542335	−	0.0746460i
$330$	−637.984	−	553.924i	−1.93328	−	1.67856i
$331$	31.9665	+	23.2250i	0.0965755	+	0.0701662i	0.635025	−	0.772492i	$-0.280990\pi$
$331$	31.9665	+	23.2250i	0.0965755	+	0.0701662i	−0.538450	+	0.842658i	$0.680990\pi$
$332$	−401.115	+	401.115i	−1.20818	+	1.20818i
$333$	24.7295	+	156.136i	0.0742628	+	0.468877i
$334$	−33.2426	−	10.8012i	−0.0995289	−	0.0323389i
$335$	97.1376	−	390.589i	0.289963	−	1.16594i
$336$	−92.2248	−	283.839i	−0.274479	−	0.844758i
$337$	53.9081	+	105.801i	0.159965	+	0.313948i	0.957052	−	0.289915i	$-0.0936271\pi$
$337$	53.9081	+	105.801i	0.159965	+	0.313948i	−0.797088	+	0.603864i	$0.793627\pi$
$338$	−452.576	+	230.599i	−1.33898	+	0.682246i
$339$	396.905	−	128.962i	1.17081	−	0.380419i
$340$	−111.779	+	45.2390i	−0.328760	+	0.133056i
$341$	120.321	−	370.309i	0.352847	−	1.08595i
$342$	726.021	−	114.990i	2.12287	−	0.336229i
$343$	−250.188	−	250.188i	−0.729413	−	0.729413i
$344$	107.930	−	148.552i	0.313749	−	0.431838i
$345$	−102.807	−	170.869i	−0.297992	−	0.495273i
$346$	−237.704	+	172.702i	−0.687005	+	0.499138i
$347$	−67.0138	+	423.108i	−0.193123	+	1.21933i	0.680507	+	0.732742i	$0.261760\pi$
$347$	−67.0138	+	423.108i	−0.193123	+	1.21933i	−0.873630	+	0.486591i	$0.838240\pi$
$348$	97.4168	−	191.191i	0.279933	−	0.549400i
$349$		−	111.740i		−	0.320171i	−0.987103	−	0.160085i	$-0.948823\pi$
$349$		−	111.740i		−	0.320171i	0.987103	−	0.160085i	$-0.0511769\pi$
$350$	452.064	+	239.676i	1.29161	+	0.684789i
$351$	11.0628			0.0315180
$352$	490.346	+	249.844i	1.39303	+	0.709784i
$353$	329.586	+	52.2014i	0.933673	+	0.147879i	0.604694	−	0.796458i	$-0.293295\pi$
$353$	329.586	+	52.2014i	0.933673	+	0.147879i	0.328979	+	0.944337i	$0.393295\pi$
$354$	570.304	+	784.956i	1.61103	+	2.21739i
$355$	48.6853	+	210.307i	0.137142	+	0.592415i
$356$	277.979	+	201.964i	0.780840	+	0.567314i
$357$	−99.5682	+	99.5682i	−0.278902	+	0.278902i
$358$	96.1519	+	607.079i	0.268581	+	1.69575i
$359$	−111.358	−	36.1824i	−0.310189	−	0.100787i	0.149786	−	0.988718i	$-0.452142\pi$
$359$	−111.358	−	36.1824i	−0.310189	−	0.100787i	−0.459975	+	0.887932i	$0.652142\pi$
$360$	168.842	+	105.364i	0.469005	+	0.292678i
$361$	−36.2820	−	111.664i	−0.100504	−	0.309320i
$362$	−417.728	−	819.838i	−1.15395	−	2.26475i
$363$	134.818	−	68.6930i	0.371398	−	0.189237i
$364$	39.3385	−	12.7819i	0.108073	−	0.0351150i
$365$	−193.605	−	230.450i	−0.530424	−	0.631370i
$366$	204.919	−	630.676i	0.559889	−	1.72316i
$367$	153.553	−	24.3204i	0.418401	−	0.0662682i	0.0563153	−	0.998413i	$-0.482065\pi$
$367$	153.553	−	24.3204i	0.418401	−	0.0662682i	0.362086	+	0.932145i	$0.382065\pi$
$368$	62.0362	+	62.0362i	0.168577	+	0.168577i
$369$	−356.102	+	490.133i	−0.965047	+	1.32827i
$370$	198.889	+	84.2836i	0.537538	+	0.227794i
$371$	−383.019	+	278.280i	−1.03240	+	0.750081i
$372$	−113.774	+	718.343i	−0.305845	+	1.93103i
$373$	160.733	−	315.456i	0.430919	−	0.845725i	−0.568811	−	0.822468i	$-0.692596\pi$
$373$	160.733	−	315.456i	0.430919	−	0.845725i	0.999730	−	0.0232570i	$-0.00740360\pi$
$374$		−	175.381i		−	0.468932i
$375$	547.811	−	117.465i	1.46083	−	0.313240i
$376$	−16.1341			−0.0429099
$377$	−9.72020	−	4.95269i	−0.0257830	−	0.0131371i
$378$	189.299	+	29.9819i	0.500790	+	0.0793173i
$379$	210.869	+	290.236i	0.556382	+	0.765794i	0.990861	−	0.134888i	$-0.0430674\pi$
$379$	210.869	+	290.236i	0.556382	+	0.765794i	−0.434479	+	0.900682i	$0.643067\pi$
$380$	221.226	−	522.042i	0.582175	−	1.37379i
$381$	178.961	+	130.023i	0.469714	+	0.341267i
$382$	196.329	−	196.329i	0.513951	−	0.513951i
$383$	−8.47845	−	53.5308i	−0.0221370	−	0.139767i	0.974144	−	0.225926i	$-0.0725408\pi$
$383$	−8.47845	−	53.5308i	−0.0221370	−	0.139767i	−0.996281	+	0.0861588i	$0.972541\pi$
$384$	−468.160	−	152.115i	−1.21917	−	0.396132i
$385$	−321.632	+	270.208i	−0.835407	+	0.701838i
$386$	171.308	+	527.232i	0.443803	+	1.36589i
$387$	−257.541	−	505.453i	−0.665482	−	1.30608i
$388$	265.514	−	135.286i	0.684315	−	0.348676i
$389$	−340.490	+	110.632i	−0.875296	+	0.284401i	−0.712003	−	0.702176i	$-0.752212\pi$
$389$	−340.490	+	110.632i	−0.875296	+	0.284401i	−0.163294	+	0.986578i	$0.552212\pi$
$390$	42.4777	−	68.0687i	0.108917	−	0.174535i
$391$	12.7912	−	39.3674i	0.0327142	−	0.100684i
$392$	−12.0222	+	1.90414i	−0.0306690	+	0.00485749i
$393$	−430.032	−	430.032i	−1.09423	−	1.09423i
$394$	219.087	−	301.547i	0.556057	−	0.765347i
$395$	−227.769	+	52.7275i	−0.576629	+	0.133487i
$396$	−578.611	+	420.386i	−1.46114	+	1.06158i
$397$	−8.95869	+	56.5629i	−0.0225660	+	0.142476i	−0.996399	−	0.0847891i	$-0.972978\pi$
$397$	−8.95869	+	56.5629i	−0.0225660	+	0.142476i	0.973833	+	0.227265i	$0.0729784\pi$
$398$	−536.846	+	1053.62i	−1.34886	+	2.64729i
$399$		−	662.075i		−	1.65934i
$400$	−221.414	+	108.318i	−0.553536	+	0.270795i
$401$	410.265			1.02310			0.511552	−	0.859252i	$-0.329071\pi$
$401$	410.265			1.02310			0.511552	+	0.859252i	$0.329071\pi$
$402$	−974.249	−	496.405i	−2.42351	−	1.23484i
$403$	36.5207	+	5.78431i	0.0906221	+	0.0143531i
$404$	−12.5044	−	17.2109i	−0.0309516	−	0.0426012i
$405$	−247.768	+	149.075i	−0.611772	+	0.368086i
$406$	−152.902	−	111.090i	−0.376607	−	0.273621i
$407$	−125.398	+	125.398i	−0.308104	+	0.308104i
$408$	11.7076	+	73.9189i	0.0286951	+	0.181174i
$409$	230.995	+	75.0548i	0.564780	+	0.183508i	0.577471	−	0.816411i	$-0.304040\pi$
$409$	230.995	+	75.0548i	0.564780	+	0.183508i	−0.0126910	+	0.999919i	$0.504040\pi$
$410$	310.573	+	767.379i	0.757496	+	1.87166i
$411$	−256.955	−	790.827i	−0.625195	−	1.92415i
$412$	−222.300	−	436.288i	−0.539563	−	1.05895i
$413$	429.819	−	219.004i	1.04072	−	0.530275i
$414$	−284.405	+	92.4087i	−0.686968	+	0.223209i
$415$	530.914	+	132.036i	1.27931	+	0.318158i
$416$	−16.1497	+	49.7037i	−0.0388215	+	0.119480i
$417$	−571.939	+	90.5862i	−1.37156	+	0.217233i
$418$	583.094	+	583.094i	1.39496	+	1.39496i
$419$	27.4988	−	37.8489i	0.0656296	−	0.0903314i	−0.774940	−	0.632034i	$-0.782220\pi$
$419$	27.4988	−	37.8489i	0.0656296	−	0.0903314i	0.840570	+	0.541703i	$0.182220\pi$
$420$	514.423	−	592.489i	1.22482	−	1.41069i
$421$	516.008	−	374.902i	1.22567	−	0.890503i	0.229114	−	0.973400i	$-0.426417\pi$
$421$	516.008	−	374.902i	1.22567	−	0.890503i	0.996558	+	0.0828969i	$0.0264172\pi$
$422$	52.9425	−	334.266i	0.125456	−	0.792099i
$423$	−22.6292	+	44.4124i	−0.0534970	+	0.104994i
$424$			251.630i			0.593468i
$425$	92.9623	+	69.8785i	0.218735	+	0.164420i
$426$	586.446			1.37663
$427$	−293.764	−	149.680i	−0.687972	−	0.350539i
$428$	1030.40	+	163.199i	2.40747	+	0.381306i
$429$	38.7183	+	53.2911i	0.0902524	+	0.124222i
$430$	−772.253	−	67.0996i	−1.79594	−	0.156046i
$431$	−126.852	−	92.1635i	−0.294321	−	0.213836i	0.430819	−	0.902438i	$-0.358225\pi$
$431$	−126.852	−	92.1635i	−0.294321	−	0.213836i	−0.725140	+	0.688602i	$0.758225\pi$
$432$	−65.2861	+	65.2861i	−0.151125	+	0.151125i
$433$	20.5870	+	129.981i	0.0475451	+	0.300188i	0.999990	−	0.00452353i	$-0.00143989\pi$
$433$	20.5870	+	129.981i	0.0475451	+	0.300188i	−0.952445	+	0.304712i	$0.901440\pi$
$434$	609.239	+	197.954i	1.40378	+	0.456115i
$435$	−206.434	+	14.5589i	−0.474561	+	0.0334687i
$436$	−217.528	−	669.481i	−0.498916	−	1.53551i
$437$	88.3587	+	173.414i	0.202194	+	0.396828i
$438$	−728.549	+	371.214i	−1.66335	+	0.847521i
$439$	648.563	−	210.731i	1.47736	−	0.480025i	0.544040	−	0.839059i	$-0.316894\pi$
$439$	648.563	−	210.731i	1.47736	−	0.480025i	0.933324	+	0.359034i	$0.116894\pi$
$440$	15.7070	+	222.713i	0.0356977	+	0.506165i
$441$	−11.6205	+	35.7644i	−0.0263504	+	0.0810983i
$442$	16.4499	−	2.60540i	0.0372169	−	0.00589457i
$443$	3.05272	+	3.05272i	0.00689102	+	0.00689102i	0.710544	−	0.703653i	$-0.248449\pi$
$443$	3.05272	+	3.05272i	0.00689102	+	0.00689102i	−0.703653	+	0.710544i	$0.748449\pi$
$444$	194.706	−	267.990i	0.438527	−	0.603581i
$445$	28.6849	−	330.136i	0.0644604	−	0.741878i
$446$	−110.822	+	80.5172i	−0.248481	+	0.180532i
$447$	−163.008	+	1029.19i	−0.364671	+	2.30244i
$448$	−290.130	+	569.411i	−0.647611	+	1.27101i
$449$		−	68.8584i		−	0.153359i	−0.997056	−	0.0766797i	$-0.975568\pi$
$449$		−	68.8584i		−	0.153359i	0.997056	−	0.0766797i	$-0.0244319\pi$
$450$	13.6617	−	840.061i	0.0303593	−	1.86680i
$451$	−679.643			−1.50697
$452$	−430.108	−	219.151i	−0.951566	−	0.484847i
$453$	−764.538	−	121.091i	−1.68772	−	0.267309i
$454$	−213.951	−	294.479i	−0.471258	−	0.648631i
$455$	−30.1223	−	26.1534i	−0.0662028	−	0.0574799i
$456$	−284.685	−	206.836i	−0.624310	−	0.453588i
$457$	−133.432	+	133.432i	−0.291974	+	0.291974i	−0.837860	−	0.545886i	$-0.816193\pi$
$457$	−133.432	+	133.432i	−0.291974	+	0.291974i	0.545886	+	0.837860i	$0.316193\pi$
$458$	−57.4093	−	362.468i	−0.125348	−	0.791415i
$459$	41.4297	+	13.4613i	0.0902608	+	0.0293275i
$460$	−55.6681	+	223.841i	−0.121018	+	0.486610i
$461$	141.436	+	435.294i	0.306802	+	0.944239i	0.978999	+	0.203866i	$0.0653508\pi$
$461$	141.436	+	435.294i	0.306802	+	0.944239i	−0.672197	+	0.740372i	$0.734649\pi$
$462$	518.091	+	1016.81i	1.12141	+	2.20089i
$463$	−210.502	+	107.256i	−0.454649	+	0.231655i	−0.666291	−	0.745692i	$-0.732119\pi$
$463$	−210.502	+	107.256i	−0.454649	+	0.231655i	0.211642	+	0.977347i	$0.432119\pi$
$464$	86.5907	−	28.1350i	0.186618	−	0.0606358i
$465$	650.196	−	263.147i	1.39827	−	0.565908i
$466$	184.926	−	569.144i	0.396837	−	1.22134i
$467$	375.182	−	59.4229i	0.803387	−	0.127244i	0.258781	−	0.965936i	$-0.416679\pi$
$467$	375.182	−	59.4229i	0.803387	−	0.127244i	0.544606	+	0.838692i	$0.316679\pi$
$468$	−48.0258	−	48.0258i	−0.102619	−	0.102619i
$469$	−319.540	+	439.809i	−0.681322	+	0.937759i
$470$	35.1144	+	58.3614i	0.0747115	+	0.124173i
$471$	792.112	−	575.503i	1.68177	−	1.22188i
$472$	40.1086	−	253.236i	0.0849758	−	0.536516i
$473$	288.916	−	567.029i	0.610816	−	1.19879i
$474$			635.137i			1.33995i
$475$	−541.403	+	76.7474i	−1.13979	+	0.161573i
$476$	162.874			0.342173
$477$	692.663	+	352.930i	1.45212	+	0.739894i
$478$	−330.501	−	52.3462i	−0.691425	−	0.109511i
$479$	−136.238	−	187.515i	−0.284421	−	0.391472i	0.642771	−	0.766058i	$-0.277785\pi$
$479$	−136.238	−	187.515i	−0.284421	−	0.391472i	−0.927192	+	0.374587i	$0.877785\pi$
$480$	223.591	+	965.853i	0.465815	+	2.01219i
$481$	−13.6247	−	9.89889i	−0.0283257	−	0.0205798i
$482$	145.637	−	145.637i	0.302151	−	0.302151i
$483$	42.1348	+	266.029i	0.0872357	+	0.550784i
$484$	−166.452	−	54.0835i	−0.343909	−	0.111743i
$485$	−243.815	−	152.151i	−0.502711	−	0.313712i
$486$	321.675	+	990.013i	0.661882	+	2.03706i
$487$	65.2171	+	127.996i	0.133916	+	0.262825i	0.948220	−	0.317613i	$-0.102881\pi$
$487$	65.2171	+	127.996i	0.133916	+	0.262825i	−0.814304	+	0.580438i	$0.802881\pi$
$488$	−156.134	+	79.5544i	−0.319947	+	0.163021i
$489$	−154.021	+	50.0446i	−0.314972	+	0.102341i
$490$	33.0531	+	39.3435i	0.0674553	+	0.0802929i
$491$	−37.0190	+	113.933i	−0.0753951	+	0.232042i	−0.981651	−	0.190688i	$-0.938928\pi$
$491$	−37.0190	+	113.933i	−0.0753951	+	0.232042i	0.906256	+	0.422730i	$0.138928\pi$
$492$	1253.87	−	198.594i	2.54852	−	0.403647i
$493$	−30.3752	−	30.3752i	−0.0616131	−	0.0616131i
$494$	−46.0291	+	63.3536i	−0.0931764	+	0.128246i
$495$	635.091	+	269.134i	1.28301	+	0.543704i
$496$	−249.659	+	181.388i	−0.503345	+	0.365701i
$497$	45.6119	−	287.982i	0.0917743	−	0.579440i
$498$	674.745	−	1324.26i	1.35491	−	2.65916i
$499$			274.256i			0.549612i	0.961500	+	0.274806i	$0.0886136\pi$
$499$			274.256i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$500$	−544.131	−	351.981i	−1.08826	−	0.703962i
$501$	51.6947			0.103183
$502$	−498.401	−	253.948i	−0.992831	−	0.505872i
$503$	−379.704	−	60.1392i	−0.754879	−	0.119561i	−0.232878	−	0.972506i	$-0.574814\pi$
$503$	−379.704	−	60.1392i	−0.754879	−	0.119561i	−0.522001	+	0.852945i	$0.674814\pi$
$504$	−158.005	−	217.475i	−0.313502	−	0.431499i
$505$	−8.00543	+	18.8909i	−0.0158523	+	0.0374077i
$506$	−271.402	−	197.185i	−0.536367	−	0.389693i
$507$	531.193	−	531.193i	1.04772	−	1.04772i
$508$	−40.0267	−	252.719i	−0.0787928	−	0.497478i
$509$	21.4135	+	6.95766i	0.0420697	+	0.0136693i	0.329976	−	0.943989i	$-0.392959\pi$
$509$	21.4135	+	6.95766i	0.0420697	+	0.0136693i	−0.287907	+	0.957659i	$0.592959\pi$
$510$	241.904	−	203.227i	0.474321	−	0.398485i
$511$	125.625	+	386.635i	0.245842	+	0.756625i
$512$	−262.283	−	514.760i	−0.512272	−	1.00539i
$513$	−182.498	+	92.9875i	−0.355747	+	0.181262i
$514$	449.396	−	146.018i	0.874312	−	0.284081i
$515$	−250.011	+	400.632i	−0.485458	+	0.777927i
$516$	−367.333	+	1130.54i	−0.711886	+	2.19096i
$517$	−55.2290	+	8.74742i	−0.106826	+	0.0169196i
$518$	−206.308	−	206.308i	−0.398277	−	0.398277i
$519$	255.419	−	351.554i	0.492137	−	0.677369i
$520$	−20.6560	+	4.78179i	−0.0397231	+	0.00919575i
$521$	−189.989	+	138.035i	−0.364663	+	0.264943i	−0.754994	−	0.655731i	$-0.772360\pi$
$521$	−189.989	+	138.035i	−0.364663	+	0.264943i	0.390332	+	0.920674i	$0.372360\pi$
$522$	−48.5475	+	306.517i	−0.0930029	+	0.587197i
$523$	27.0755	−	53.1387i	0.0517696	−	0.101604i	−0.863672	−	0.504054i	$-0.831841\pi$
$523$	27.0755	−	53.1387i	0.0517696	−	0.101604i	0.915442	+	0.402450i	$0.131841\pi$
$524$			703.448i			1.34246i
$525$	−745.400	−	130.518i	−1.41981	−	0.248606i
$526$	−1004.50			−1.90970
$527$	129.730	+	66.1008i	0.246167	+	0.125428i
$528$	−542.985	−	86.0004i	−1.02838	−	0.162880i
$529$	264.399	+	363.914i	0.499809	+	0.687928i
$530$	910.214	−	547.651i	1.71739	−	1.03330i
$531$	−640.827	−	465.588i	−1.20683	−	0.876813i
$532$	−541.513	+	541.513i	−1.01788	+	1.01788i
$533$	−10.0966	−	63.7472i	−0.0189429	−	0.119601i
$534$	−856.189	−	278.193i	−1.60335	−	0.520960i
$535$	−377.461	−	932.647i	−0.705534	−	1.74327i
$536$	89.2871	+	274.797i	0.166580	+	0.512682i
$537$	−412.695	−	809.959i	−0.768519	−	1.50830i
$538$	1408.54	−	717.688i	2.61811	−	1.33399i
$539$	−40.1213	+	13.0362i	−0.0744365	+	0.0241859i
$540$	−235.567	−	58.5843i	−0.436235	−	0.108490i
$541$	−127.378	+	392.030i	−0.235450	+	0.724640i	0.761612	+	0.648034i	$0.224408\pi$
$541$	−127.378	+	392.030i	−0.235450	+	0.724640i	−0.997061	+	0.0766062i	$0.975592\pi$
$542$	122.913	−	19.4675i	0.226776	−	0.0359178i
$543$	962.252	+	962.252i	1.77210	+	1.77210i
$544$	−120.960	+	166.487i	−0.222353	+	0.306043i
$545$	−445.090	+	512.635i	−0.816679	+	0.940614i
$546$	−87.6754	+	63.6999i	−0.160578	+	0.116667i
$547$	64.7443	−	408.779i	0.118362	−	0.747311i	−0.855100	−	0.518463i	$-0.826504\pi$
$547$	64.7443	−	408.779i	0.118362	−	0.747311i	0.973462	−	0.228848i	$-0.0734958\pi$
$548$	−436.655	+	856.984i	−0.796816	+	1.56384i
$549$			541.372i			0.986106i
$550$	771.426	−	541.530i	1.40259	−	0.984600i
$551$	201.979			0.366569
$552$	127.553	+	64.9914i	0.231074	+	0.117738i
$553$	311.892	+	49.3989i	0.564000	+	0.0893289i
$554$	−943.347	−	1298.41i	−1.70279	−	2.34369i
$555$	−318.272	−	27.6541i	−0.573464	−	0.0498272i
$556$	541.881	+	393.699i	0.974606	+	0.708092i
$557$	−364.882	+	364.882i	−0.655084	+	0.655084i	−0.954213	−	0.299129i	$-0.903304\pi$
$557$	−364.882	+	364.882i	−0.655084	+	0.655084i	0.299129	+	0.954213i	$0.403304\pi$
$558$	−164.548	−	1038.91i	−0.294889	−	1.86185i
$559$	57.4767	+	18.6753i	0.102820	+	0.0334084i
$560$	332.105	−	23.4220i	0.593045	−	0.0418250i
$561$	80.1531	+	246.686i	0.142875	+	0.439725i
$562$	222.638	+	436.953i	0.396154	+	0.777496i
$563$	453.798	−	231.222i	0.806036	−	0.410696i	−0.00187651	−	0.999998i	$-0.500597\pi$
$563$	453.798	−	231.222i	0.806036	−	0.410696i	0.807913	+	0.589302i	$0.200597\pi$
$564$	99.3362	−	32.2763i	0.176128	−	0.0572274i
$565$	32.7520	+	464.398i	0.0579682	+	0.821943i
$566$	299.438	−	921.576i	0.529043	−	1.62823i
$567$	385.753	−	61.0972i	0.680340	−	0.107755i
$568$	−109.580	−	109.580i	−0.192922	−	0.192922i
$569$	−282.994	+	389.508i	−0.497353	+	0.684548i	−0.981723	−	0.190315i	$-0.939049\pi$
$569$	−282.994	+	389.508i	−0.497353	+	0.684548i	0.484370	+	0.874863i	$0.339049\pi$
$570$	−128.589	+	1479.94i	−0.225596	+	2.59639i
$571$	501.209	−	364.150i	0.877775	−	0.637741i	−0.0548871	−	0.998493i	$-0.517480\pi$
$571$	501.209	−	364.150i	0.877775	−	0.637741i	0.932662	+	0.360752i	$0.117480\pi$
$572$	11.9192	−	75.2548i	0.0208377	−	0.131564i
$573$	−186.425	+	365.879i	−0.325349	+	0.638532i
$574$		−	1118.16i		−	1.94801i
$575$	212.657	−	65.2931i	0.369838	−	0.113553i
$576$	1049.36			1.82180
$577$	296.742	+	151.197i	0.514284	+	0.262041i	0.691815	−	0.722074i	$-0.256811\pi$
$577$	296.742	+	151.197i	0.514284	+	0.262041i	−0.177532	+	0.984115i	$0.556811\pi$
$578$	−800.280	−	126.752i	−1.38457	−	0.219294i
$579$	−481.915	−	663.299i	−0.832323	−	1.14559i
$580$	180.751	+	156.935i	0.311639	+	0.270578i
$581$	−597.816	−	434.339i	−1.02894	−	0.747571i
$582$	−552.078	+	552.078i	−0.948588	+	0.948588i
$583$	136.426	+	861.362i	0.234007	+	1.47746i
$584$	205.495	+	66.7694i	0.351875	+	0.114331i
$585$	−15.8087	+	63.5667i	−0.0270235	+	0.108661i
$586$	334.671	+	1030.01i	0.571110	+	1.75770i
$587$	313.341	+	614.967i	0.533801	+	1.04764i	0.987666	+	0.156573i	$0.0500448\pi$
$587$	313.341	+	614.967i	0.533801	+	1.04764i	−0.453865	+	0.891070i	$0.649955\pi$
$588$	70.2106	−	35.7741i	0.119406	−	0.0608403i
$589$	−651.086	+	211.551i	−1.10541	+	0.359169i
$590$	−1003.31	+	406.061i	−1.70053	+	0.688238i
$591$	−170.348	+	524.276i	−0.288236	+	0.887100i
$592$	138.822	−	21.9872i	0.234497	−	0.0371406i
$593$	−236.882	−	236.882i	−0.399464	−	0.399464i	0.478580	−	0.878044i	$-0.341152\pi$
$593$	−236.882	−	236.882i	−0.399464	−	0.399464i	−0.878044	+	0.478580i	$0.841152\pi$
$594$	207.515	−	285.619i	0.349351	−	0.480841i
$595$	−80.9829	−	134.596i	−0.136106	−	0.226212i
$596$	975.104	−	708.454i	1.63608	−	1.18868i
$597$	273.585	−	1727.35i	0.458266	−	2.89338i
$598$	14.4631	−	28.3855i	0.0241858	−	0.0474674i
$599$		−	120.628i		−	0.201382i	−0.994918	−	0.100691i	$-0.967895\pi$
$599$		−	120.628i		−	0.201382i	0.994918	−	0.100691i	$-0.0321053\pi$
$600$	−288.988	+	279.739i	−0.481647	+	0.466232i
$601$	1122.78			1.86819			0.934095	−	0.357025i	$-0.116209\pi$
$601$	1122.78			1.86819			0.934095	+	0.357025i	$0.116209\pi$
$602$	932.885	+	475.329i	1.54964	+	0.789583i
$603$	881.667	+	139.642i	1.46213	+	0.231579i
$604$	526.277	+	724.358i	0.871320	+	1.19927i
$605$	38.0681	+	164.444i	0.0629225	+	0.271808i
$606$	45.0933	+	32.7622i	0.0744114	+	0.0540630i
$607$	125.125	−	125.125i	0.206136	−	0.206136i	−0.596487	−	0.802623i	$-0.703437\pi$
$607$	125.125	−	125.125i	0.206136	−	0.206136i	0.802623	+	0.596487i	$0.203437\pi$
$608$	−151.366	−	955.686i	−0.248957	−	1.57185i
$609$	265.839	+	86.3765i	0.436518	+	0.141833i
$610$	627.582	+	391.637i	1.02882	+	0.642027i
$611$	−1.64093	−	5.05027i	−0.00268565	−	0.00826558i
$612$	−121.416	−	238.293i	−0.198393	−	0.389368i
$613$	−249.961	+	127.362i	−0.407767	+	0.207768i	−0.645829	−	0.763482i	$-0.723488\pi$
$613$	−249.961	+	127.362i	−0.407767	+	0.207768i	0.238062	+	0.971250i	$0.423488\pi$
$614$	1062.98	−	345.384i	1.73124	−	0.562515i
$615$	−787.555	−	937.437i	−1.28058	−	1.52429i
$616$	93.1878	−	286.803i	0.151279	−	0.465589i
$617$	−74.7801	+	11.8440i	−0.121200	+	0.0191961i	−0.216740	−	0.976229i	$-0.569542\pi$
$617$	−74.7801	+	11.8440i	−0.121200	+	0.0191961i	0.0955399	+	0.995426i	$0.469542\pi$
$618$	907.165	+	907.165i	1.46790	+	1.46790i
$619$	131.262	−	180.667i	0.212055	−	0.291868i	−0.689719	−	0.724078i	$-0.742266\pi$
$619$	131.262	−	180.667i	0.212055	−	0.291868i	0.901773	+	0.432209i	$0.142266\pi$
$620$	−747.026	−	316.568i	−1.20488	−	0.510594i
$621$	67.4119	−	48.9776i	0.108554	−	0.0788690i
$622$	−180.379	+	1138.87i	−0.289998	+	1.83098i
$623$	−203.202	+	398.806i	−0.326167	+	0.640138i
$624$		−	52.2070i		−	0.0836650i
$625$	−20.3230	+	624.669i	−0.0325168	+	0.999471i
$626$	−1244.47			−1.98796
$627$	−1086.65	−	553.677i	−1.73310	−	0.883058i
$628$	−1118.58	−	177.165i	−1.78117	−	0.282110i
$629$	−38.9787	−	53.6496i	−0.0619693	−	0.0852934i
$630$	−442.783	+	1044.86i	−0.702830	+	1.65851i
$631$	−292.773	−	212.712i	−0.463982	−	0.337103i	0.331109	−	0.943592i	$-0.392577\pi$
$631$	−292.773	−	212.712i	−0.463982	−	0.337103i	−0.795091	+	0.606490i	$0.792577\pi$
$632$	118.678	−	118.678i	0.187781	−	0.187781i
$633$	78.2999	+	494.366i	0.123696	+	0.780989i
$634$	−501.265	−	162.871i	−0.790639	−	0.256894i
$635$	−188.941	+	158.732i	−0.297545	+	0.249972i
$636$	−503.386	−	1549.26i	−0.791488	−	2.43595i
$637$	−1.81876	−	3.56952i	−0.00285520	−	0.00560364i
$638$	−310.199	+	158.054i	−0.486205	+	0.247734i
$639$	−455.334	+	147.947i	−0.712572	+	0.231529i
$640$	290.718	−	465.863i	0.454246	−	0.727911i
$641$	282.130	−	868.306i	0.440140	−	1.35461i	−0.447587	−	0.894241i	$-0.647716\pi$
$641$	282.130	−	868.306i	0.440140	−	1.35461i	0.887727	−	0.460371i	$-0.152284\pi$
$642$	−2699.69	+	427.589i	−4.20512	+	0.666026i
$643$	−520.582	−	520.582i	−0.809615	−	0.809615i	0.174960	−	0.984575i	$-0.444020\pi$
$643$	−520.582	−	520.582i	−0.809615	−	0.809615i	−0.984575	+	0.174960i	$0.944020\pi$
$644$	183.124	−	252.048i	0.284353	−	0.391379i
$645$	1116.90	−	258.557i	1.73162	−	0.400864i
$646$	−249.467	+	181.248i	−0.386171	+	0.280570i
$647$	−167.501	+	1057.56i	−0.258888	+	1.63456i	0.425159	+	0.905118i	$0.360218\pi$
$647$	−167.501	+	1057.56i	−0.258888	+	1.63456i	−0.684048	+	0.729437i	$0.739782\pi$
$648$	94.2401	−	184.957i	0.145432	−	0.285427i
$649$		−	888.602i		−	1.36919i
$650$	62.2530	+	64.3113i	0.0957738	+	0.0989404i
$651$	−947.410			−1.45532
$652$	166.906	+	85.0429i	0.255991	+	0.130434i
$653$	357.048	+	56.5509i	0.546781	+	0.0866016i	0.423713	−	0.905797i	$-0.360727\pi$
$653$	357.048	+	56.5509i	0.546781	+	0.0866016i	0.123068	+	0.992398i	$0.460727\pi$
$654$	1084.08	+	1492.10i	1.65761	+	2.28150i
$655$	581.317	−	349.762i	0.887508	−	0.533989i
$656$	435.782	+	316.614i	0.664302	+	0.482644i
$657$	472.018	−	472.018i	0.718444	−	0.718444i
$658$	−14.3914	−	90.8637i	−0.0218714	−	0.138091i
$659$	438.078	+	142.340i	0.664762	+	0.215994i	0.621912	−	0.783087i	$-0.286356\pi$
$659$	438.078	+	142.340i	0.664762	+	0.215994i	0.0428503	+	0.999082i	$0.486356\pi$
$660$	−542.243	−	1339.80i	−0.821580	−	2.03000i
$661$	42.7285	+	131.505i	0.0646422	+	0.198948i	0.978161	−	0.207848i	$-0.0666459\pi$
$661$	42.7285	+	131.505i	0.0646422	+	0.198948i	−0.913519	+	0.406796i	$0.866646\pi$
$662$	54.3638	+	106.695i	0.0821205	+	0.161171i
$663$	−21.9472	+	11.1827i	−0.0331029	+	0.0168668i
$664$	−373.522	+	121.365i	−0.562533	+	0.182778i
$665$	716.744	+	178.251i	1.07781	+	0.268046i
$666$	−148.044	+	455.633i	−0.222288	+	0.684133i
$667$	−81.1574	+	12.8541i	−0.121675	+	0.0192715i
$668$	−42.2812	−	42.2812i	−0.0632952	−	0.0632952i
$669$	119.082	−	163.902i	0.178000	−	0.244996i
$670$	799.691	−	921.047i	1.19357	−	1.37470i
$671$	−491.335	+	356.976i	−0.732243	+	0.532006i
$672$	209.476	−	1322.58i	0.311720	−	1.96812i
$673$	−274.452	+	538.642i	−0.407803	+	0.800359i	−0.999985	−	0.00544506i	$-0.998267\pi$
$673$	−274.452	+	538.642i	−0.407803	+	0.800359i	0.592182	+	0.805804i	$0.298267\pi$
$674$			359.859i			0.533916i
$675$	68.7135	+	223.797i	0.101798	+	0.331552i
$676$	−868.928			−1.28540
$677$	222.931	+	113.589i	0.329293	+	0.167783i	0.610819	−	0.791771i	$-0.290840\pi$
$677$	222.931	+	113.589i	0.329293	+	0.167783i	−0.281526	+	0.959554i	$0.590840\pi$
$678$	1249.18	+	197.851i	1.84245	+	0.291815i
$679$	228.166	+	314.044i	0.336033	+	0.462510i
$680$	−83.1745	−	7.22687i	−0.122315	−	0.0106278i
$681$	435.522	+	316.425i	0.639533	+	0.464648i
$682$	834.390	−	834.390i	1.22345	−	1.22345i
$683$	−59.7898	−	377.498i	−0.0875400	−	0.552706i	−0.992009	−	0.126167i	$-0.959733\pi$
$683$	−59.7898	−	377.498i	−0.0875400	−	0.552706i	0.904469	−	0.426539i	$-0.140267\pi$
$684$	1195.94	+	388.584i	1.74845	+	0.568105i
$685$	925.306	−	65.2579i	1.35081	−	0.0952671i
$686$	−331.352	−	1019.80i	−0.483021	−	1.48659i
$687$	246.407	+	483.601i	0.358671	+	0.703932i
$688$	−449.404	+	228.983i	−0.653203	+	0.332824i
$689$	−78.7649	+	25.5923i	−0.114318	+	0.0371441i
$690$	−42.5158	−	602.840i	−0.0616170	−	0.873681i
$691$	−328.195	+	1010.08i	−0.474957	+	1.46177i	0.371059	+	0.928609i	$0.378995\pi$
$691$	−328.195	+	1010.08i	−0.474957	+	1.46177i	−0.846016	+	0.533158i	$0.821005\pi$
$692$	−496.445	+	78.6292i	−0.717406	+	0.113626i
$693$	−658.780	−	658.780i	−0.950620	−	0.950620i
$694$	−763.090	+	1050.30i	−1.09955	+	1.51341i
$695$	55.9171	−	643.553i	0.0804562	−	0.925975i
$696$	120.191	−	87.3236i	0.172688	−	0.125465i
$697$	39.7571	−	251.016i	0.0570403	−	0.360138i
$698$	153.737	−	301.726i	0.220254	−	0.432273i
$699$			885.060i			1.26618i
$700$	502.913	+	716.416i	0.718448	+	1.02345i
$701$	−709.732			−1.01246			−0.506228	−	0.862400i	$-0.668961\pi$
$701$	−709.732			−1.01246			−0.506228	+	0.862400i	$0.668961\pi$
$702$	29.8725	+	15.2208i	0.0425534	+	0.0216820i
$703$	307.964	+	48.7768i	0.438072	+	0.0693837i
$704$	691.937	+	952.369i	0.982865	+	1.35280i
$705$	−76.0636	−	66.0416i	−0.107892	−	0.0936760i
$706$	818.149	+	594.420i	1.15885	+	0.841955i
$707$	19.5955	−	19.5955i	0.0277164	−	0.0277164i
$708$	259.653	+	1639.38i	0.366741	+	2.31551i
$709$	−1304.06	−	423.715i	−1.83930	−	0.597624i	−0.998407	−	0.0564168i	$-0.982032\pi$
$709$	−1304.06	−	423.715i	−1.83930	−	0.597624i	−0.840889	−	0.541207i	$-0.817968\pi$
$710$	−157.889	+	634.870i	−0.222379	+	0.894182i
$711$	−160.230	−	493.139i	−0.225359	−	0.693585i
$712$	108.001	+	211.964i	0.151687	+	0.297702i
$713$	248.150	−	126.439i	0.348036	−	0.177333i
$714$	−405.852	+	131.869i	−0.568420	+	0.184691i
$715$	−68.1156	+	27.5677i	−0.0952666	+	0.0385563i
$716$	−324.924	+	1000.01i	−0.453804	+	1.39666i
$717$	488.798	−	77.4180i	0.681727	−	0.107975i
$718$	−250.914	−	250.914i	−0.349463	−	0.349463i
$719$	182.262	−	250.863i	0.253494	−	0.348905i	−0.663237	−	0.748409i	$-0.730818\pi$
$719$	182.262	−	250.863i	0.253494	−	0.348905i	0.916731	+	0.399505i	$0.130818\pi$
$720$	−281.839	−	468.427i	−0.391443	−	0.650592i
$721$	516.031	−	374.919i	0.715716	−	0.519998i
$722$	55.6630	−	351.442i	0.0770956	−	0.486762i
$723$	−138.289	+	271.408i	−0.191272	+	0.375392i
$724$		−	1574.06i		−	2.17411i
$725$	39.8172	−	227.399i	0.0549202	−	0.313654i
$726$	458.555			0.631618
$727$	−573.466	−	292.196i	−0.788812	−	0.401920i	0.0126843	−	0.999920i	$-0.495962\pi$
$727$	−573.466	−	292.196i	−0.788812	−	0.401920i	−0.801496	+	0.598000i	$0.795962\pi$
$728$	28.2851	+	4.47992i	0.0388531	+	0.00615373i
$729$	−598.987	−	824.434i	−0.821655	−	1.13091i
$730$	−205.719	−	888.649i	−0.281806	−	1.21733i
$731$	192.523	+	139.876i	0.263370	+	0.191349i
$732$	802.155	−	802.155i	1.09584	−	1.09584i
$733$	−157.542	−	994.681i	−0.214928	−	1.35700i	−0.825214	−	0.564820i	$-0.808946\pi$
$733$	−157.542	−	994.681i	−0.214928	−	1.35700i	0.610287	−	0.792181i	$-0.291054\pi$
$734$	448.096	+	145.595i	0.610484	+	0.198358i
$735$	−64.4726	−	40.2335i	−0.0877178	−	0.0547395i
$736$	121.641	+	374.372i	0.165273	+	0.508657i
$737$	454.627	+	892.257i	0.616862	+	1.21066i
$738$	−1635.92	+	833.544i	−2.21670	+	1.12946i
$739$	−884.508	+	287.394i	−1.19690	+	0.388896i	−0.838619	−	0.544718i	$-0.816637\pi$
$739$	−884.508	+	287.394i	−1.19690	+	0.388896i	−0.358280	+	0.933614i	$0.616637\pi$
$740$	237.697	+	282.934i	0.321213	+	0.382343i
$741$	35.7893	−	110.148i	0.0482986	−	0.148648i
$742$	−1417.13	+	224.451i	−1.90987	+	0.302494i
$743$	−527.824	−	527.824i	−0.710395	−	0.710395i	0.256223	−	0.966618i	$-0.417522\pi$
$743$	−527.824	−	527.824i	−0.710395	−	0.710395i	−0.966618	+	0.256223i	$0.917522\pi$
$744$	−295.976	+	407.376i	−0.397817	+	0.547549i
$745$	−1070.29	−	453.557i	−1.43663	−	0.608802i
$746$	868.041	−	630.669i	1.16359	−	0.845401i
$747$	−189.811	+	1198.42i	−0.254097	+	1.60431i
$748$	136.208	−	267.322i	0.182096	−	0.357383i
$749$			1358.97i			1.81438i
$750$	1640.85	+	436.521i	2.18780	+	0.582028i
$751$	166.431			0.221612			0.110806	−	0.993842i	$-0.464657\pi$
$751$	166.431			0.221612			0.110806	+	0.993842i	$0.464657\pi$
$752$	39.4875	+	20.1199i	0.0525100	+	0.0267552i
$753$	817.099	+	129.416i	1.08512	+	0.171867i
$754$	−19.4329	−	26.7471i	−0.0257731	−	0.0354737i
$755$	336.926	−	795.066i	0.446260	−	1.05307i
$756$	265.252	+	192.717i	0.350862	+	0.254916i
$757$	317.868	−	317.868i	0.419905	−	0.419905i	−0.465266	−	0.885171i	$-0.654041\pi$
$757$	317.868	−	317.868i	0.419905	−	0.419905i	0.885171	+	0.465266i	$0.154041\pi$
$758$	170.079	+	1073.84i	0.224379	+	1.41667i
$759$	471.865	+	153.318i	0.621693	+	0.202000i
$760$	300.561	−	252.506i	0.395474	−	0.332244i
$761$	−371.860	−	1144.47i	−0.488646	−	1.50390i	−0.826629	−	0.562747i	$-0.809745\pi$
$761$	−371.860	−	1144.47i	−0.488646	−	1.50390i	0.337983	−	0.941152i	$-0.390255\pi$
$762$	304.350	+	597.321i	0.399410	+	0.783885i
$763$	817.032	−	416.298i	1.07081	−	0.545607i
$764$	451.731	−	146.776i	0.591271	−	0.192115i
$765$	−136.552	+	218.818i	−0.178499	+	0.286037i
$766$	50.7565	−	156.213i	0.0662618	−	0.203933i
$767$	83.3466	−	13.2008i	0.108666	−	0.0172110i
$768$	144.761	+	144.761i	0.188490	+	0.188490i
$769$	827.508	−	1138.97i	1.07608	−	1.48110i	0.212321	−	0.977200i	$-0.431898\pi$
$769$	827.508	−	1138.97i	1.07608	−	1.48110i	0.863761	−	0.503901i	$-0.168102\pi$
$770$	−1240.26	+	287.115i	−1.61072	+	0.372876i
$771$	−565.376	+	410.770i	−0.733302	+	0.532775i
$772$	−148.355	+	936.674i	−0.192169	+	1.21331i
$773$	−460.242	+	903.275i	−0.595397	+	1.16853i	0.375002	+	0.927024i	$0.377642\pi$
$773$	−460.242	+	903.275i	−0.595397	+	1.16853i	−0.970399	+	0.241508i	$0.922358\pi$
$774$		−	1719.20i		−	2.22119i
$775$	109.823	+	774.731i	0.141707	+	0.999653i
$776$	206.316			0.265871
$777$	384.475	+	195.900i	0.494819	+	0.252123i
$778$	−1071.63	−	169.729i	−1.37741	−	0.218161i
$779$	702.381	+	966.744i	0.901644	+	1.24101i
$780$	117.611	−	70.7634i	0.150784	−	0.0907223i
$781$	−434.516	−	315.694i	−0.556358	−	0.404218i
$782$	88.7036	−	88.7036i	0.113432	−	0.113432i
$783$	−13.5274	−	85.4089i	−0.0172764	−	0.109079i
$784$	31.7984	+	10.3319i	0.0405592	+	0.0131785i
$785$	409.763	+	1012.46i	0.521991	+	1.28976i
$786$	−569.539	−	1752.86i	−0.724604	−	2.23010i
$787$	−574.499	−	1127.52i	−0.729986	−	1.43268i	−0.894852	−	0.446363i	$-0.852719\pi$
$787$	−574.499	−	1127.52i	−0.729986	−	1.43268i	0.164866	−	0.986316i	$-0.447281\pi$
$788$	568.135	−	289.479i	0.720983	−	0.367359i
$789$	1412.91	−	459.083i	1.79076	−	0.581854i
$790$	−687.581	−	170.998i	−0.870356	−	0.216453i
$791$	194.314	−	598.038i	0.245657	−	0.756053i
$792$	−489.074	+	77.4618i	−0.617518	+	0.0978053i
$793$	−40.7817	−	40.7817i	−0.0514272	−	0.0514272i
$794$	−102.013	+	140.409i	−0.128480	+	0.176838i
$795$	−1030.00	+	1186.30i	−1.29559	+	1.49220i
$796$	−1636.57	+	1189.04i	−2.05599	+	1.49376i
$797$	153.706	−	970.462i	0.192856	−	1.21764i	−0.681302	−	0.732002i	$-0.738586\pi$
$797$	153.706	−	970.462i	0.192856	−	1.21764i	0.874158	−	0.485641i	$-0.161414\pi$
$798$	910.919	−	1787.78i	1.14150	−	2.24032i
$799$		−	20.9097i		−	0.0261699i
$800$	−1105.80	−	17.9833i	−1.38225	−	0.0224792i
$801$	734.952			0.917543
$802$	1107.82	+	564.464i	1.38133	+	0.703821i
$803$	739.636	+	117.147i	0.921090	+	0.145886i
$804$	−1099.46	−	1513.28i	−1.36749	−	1.88219i
$805$	−299.339	−	26.0090i	−0.371850	−	0.0323093i
$806$	90.6572	+	65.8663i	0.112478	+	0.0817200i
$807$	−1653.22	+	1653.22i	−2.04860	+	2.04860i
$808$	−2.30411	−	14.5476i	−0.00285163	−	0.0180045i
$809$	−748.876	−	243.325i	−0.925681	−	0.300772i	−0.192886	−	0.981221i	$-0.561785\pi$
$809$	−748.876	−	243.325i	−0.925681	−	0.300772i	−0.732795	+	0.680449i	$0.761785\pi$
$810$	−874.143	+	61.6496i	−1.07919	+	0.0761106i
$811$	−0.441685	−	1.35937i	−0.000544618	−	0.00167616i	0.950784	−	0.309855i	$-0.100280\pi$
$811$	−0.441685	−	1.35937i	−0.000544618	−	0.00167616i	−0.951328	+	0.308179i	$0.900280\pi$
$812$	−146.783	−	288.078i	−0.180768	−	0.354776i
$813$	−163.989	+	83.5565i	−0.201708	+	0.102776i
$814$	−511.139	+	166.079i	−0.627935	+	0.204028i
$815$	−12.7096	−	180.213i	−0.0155946	−	0.221120i
$816$	63.5260	−	195.513i	0.0778505	−	0.239599i
$817$	−1105.14	+	175.037i	−1.35268	+	0.214244i
$818$	520.483	+	520.483i	0.636287	+	0.636287i
$819$	52.0037	−	71.5770i	0.0634966	−	0.0873956i
$820$	−122.588	+	1410.88i	−0.149498	+	1.72058i
$821$	−266.252	+	193.444i	−0.324303	+	0.235620i	−0.738009	−	0.674791i	$-0.764234\pi$
$821$	−266.252	+	193.444i	−0.324303	+	0.235620i	0.413707	+	0.910410i	$0.364234\pi$
$822$	394.215	−	2488.97i	0.479580	−	3.02795i
$823$	384.423	−	754.474i	0.467100	−	0.916736i	−0.530512	−	0.847677i	$-0.678000\pi$
$823$	384.423	−	754.474i	0.467100	−	0.916736i	0.997613	−	0.0690586i	$-0.0219995\pi$
$824$		−	339.015i		−	0.411425i
$825$	−837.577	+	1114.26i	−1.01524	+	1.35062i
$826$	1461.94			1.76991
$827$	−308.853	−	157.369i	−0.373462	−	0.190289i	0.257177	−	0.966364i	$-0.417208\pi$
$827$	−308.853	−	157.369i	−0.373462	−	0.190289i	−0.630640	+	0.776076i	$0.717208\pi$
$828$	−505.270	−	80.0269i	−0.610230	−	0.0966509i
$829$	172.734	+	237.748i	0.208364	+	0.286789i	0.900390	−	0.435084i	$-0.143281\pi$
$829$	172.734	+	237.748i	0.208364	+	0.286789i	−0.692026	+	0.721873i	$0.743281\pi$
$830$	1251.95	+	1086.99i	1.50837	+	1.30963i
$831$	1920.29	+	1395.17i	2.31082	+	1.67891i
$832$	−79.0484	+	79.0484i	−0.0950102	+	0.0950102i
$833$	−2.46775	−	15.5808i	−0.00296249	−	0.0187044i
$834$	−1669.02	−	542.297i	−2.00122	−	0.650236i
$835$	−13.9178	+	55.9632i	−0.0166680	+	0.0670218i
$836$	435.922	+	1341.63i	0.521438	+	1.60482i
$837$	133.062	+	261.149i	0.158975	+	0.312007i
$838$	126.329	−	64.3676i	0.150750	−	0.0768110i
$839$	−613.225	+	199.249i	−0.730900	+	0.237484i	−0.650743	−	0.759298i	$-0.725542\pi$
$839$	−613.225	+	199.249i	−0.730900	+	0.237484i	−0.0801576	+	0.996782i	$0.525542\pi$
$840$	503.573	−	203.806i	0.599492	−	0.242626i
$841$	233.532	−	718.739i	0.277684	−	0.854624i
$842$	1909.17	−	302.382i	2.26742	−	0.359124i
$843$	−512.856	−	512.856i	−0.608370	−	0.608370i
$844$	340.301	−	468.385i	0.403201	−	0.554958i
$845$	432.041	+	718.067i	0.511291	+	0.849784i
$846$	−122.210	+	88.7907i	−0.144456	+	0.104954i
$847$	35.6649	−	225.179i	0.0421073	−	0.265855i
$848$	313.793	−	615.854i	0.370039	−	0.726243i
$849$			1433.12i			1.68801i
$850$	154.880	+	316.593i	0.182212	+	0.372462i
$851$	−126.847			−0.149057
$852$	893.886	+	455.458i	1.04916	+	0.534575i
$853$	−959.328	−	151.943i	−1.12465	−	0.178127i	−0.433720	−	0.901048i	$-0.642799\pi$
$853$	−959.328	−	151.943i	−1.12465	−	0.178127i	−0.690931	+	0.722920i	$0.742799\pi$
$854$	−587.302	−	808.352i	−0.687708	−	0.946548i
$855$	−273.515	−	1181.51i	−0.319901	−	1.38188i
$856$	584.344	+	424.551i	0.682645	+	0.495970i
$857$	−41.2739	+	41.2739i	−0.0481609	+	0.0481609i	−0.730777	−	0.682616i	$-0.760842\pi$
$857$	−41.2739	+	41.2739i	−0.0481609	+	0.0481609i	0.682616	+	0.730777i	$0.260842\pi$
$858$	31.2288	+	197.171i	0.0363972	+	0.229803i
$859$	1517.56	+	493.085i	1.76666	+	0.574023i	0.997855	−	0.0654608i	$-0.0208517\pi$
$859$	1517.56	+	493.085i	1.76666	+	0.574023i	0.768805	+	0.639483i	$0.220852\pi$
$860$	−1124.99	−	702.039i	−1.30813	−	0.816324i
$861$	511.025	+	1572.77i	0.593525	+	1.82668i
$862$	−215.731	−	423.396i	−0.250268	−	0.491179i
$863$	−179.583	+	91.5021i	−0.208092	+	0.106028i	−0.554930	−	0.831897i	$-0.687255\pi$
$863$	−179.583	+	91.5021i	−0.208092	+	0.106028i	0.346839	+	0.937925i	$0.387255\pi$
$864$	−393.984	+	128.013i	−0.456000	+	0.148163i
$865$	311.816	+	371.158i	0.360481	+	0.429085i
$866$	−123.245	+	379.309i	−0.142315	+	0.438001i
$867$	1183.58	−	187.461i	1.36515	−	0.216218i
$868$	774.889	+	774.889i	0.892730	+	0.892730i
$869$	341.905	−	470.592i	0.393447	−	0.541533i
$870$	−577.457	−	244.710i	−0.663744	−	0.281276i
$871$	−76.9356	+	55.8970i	−0.0883302	+	0.0641756i
$872$	76.2413	−	481.369i	0.0874327	−	0.552028i
$873$	289.373	−	567.927i	0.331470	−	0.650546i
$874$			589.832i			0.674864i
$875$	341.979	−	771.809i	0.390833	−	0.882067i
$876$	−1398.79			−1.59679
$877$	1256.66	+	640.303i	1.43291	+	0.730106i	0.986352	−	0.164647i	$-0.0526487\pi$
$877$	1256.66	+	640.303i	1.43291	+	0.730106i	0.446561	+	0.894753i	$0.352649\pi$
$878$	2041.23	+	323.299i	2.32486	+	0.368222i
$879$	−941.479	−	1295.83i	−1.07108	−	1.47421i
$880$	239.289	−	564.666i	0.271920	−	0.641666i
$881$	640.260	+	465.176i	0.726742	+	0.528009i	0.888531	−	0.458816i	$-0.151726\pi$
$881$	640.260	+	465.176i	0.726742	+	0.528009i	−0.161789	+	0.986825i	$0.551726\pi$
$882$	−80.5850	+	80.5850i	−0.0913663	+	0.0913663i
$883$	196.982	+	1243.69i	0.223082	+	1.40849i	0.804051	+	0.594560i	$0.202674\pi$
$883$	196.982	+	1243.69i	0.223082	+	1.40849i	−0.580969	+	0.813925i	$0.697326\pi$
$884$	27.0970	+	8.80436i	0.0306527	+	0.00995968i
$885$	1225.66	−	1029.69i	1.38492	−	1.16350i
$886$	4.04306	+	12.4433i	0.00456327	+	0.0140443i
$887$	417.143	+	818.690i	0.470286	+	0.922988i	0.997321	+	0.0731444i	$0.0233034\pi$
$887$	417.143	+	818.690i	0.470286	+	0.922988i	−0.527036	+	0.849843i	$0.676697\pi$
$888$	204.347	−	104.120i	0.230120	−	0.117252i
$889$	316.993	−	102.997i	0.356573	−	0.115858i
$890$	531.675	−	851.988i	0.597388	−	0.957290i
$891$	222.318	−	684.224i	0.249515	−	0.767928i
$892$	−231.453	+	36.6586i	−0.259477	+	0.0410971i
$893$	69.5194	+	69.5194i	0.0778492	+	0.0778492i
$894$	−1856.18	+	2554.82i	−2.07627	+	2.85774i
$895$	987.948	−	228.706i	1.10385	−	0.255538i
$896$	−600.052	+	435.963i	−0.669701	+	0.486566i
$897$	−7.37063	+	46.5363i	−0.00821698	+	0.0518800i
$898$	94.7391	−	185.936i	0.105500	−	0.207056i
$899$		−	289.026i		−	0.321498i
$900$	673.249	−	1269.85i	0.748055	−	1.41094i
$901$	−326.112			−0.361945
$902$	−1835.21	−	935.089i	−2.03461	−	1.03668i
$903$	−1529.41	−	242.235i	−1.69370	−	0.268256i
$904$	−196.445	−	270.383i	−0.217307	−	0.299097i
$905$	−1300.77	+	782.639i	−1.43732	+	0.864795i
$906$	−1897.85	−	1378.87i	−2.09476	−	1.52193i
$907$	−718.126	+	718.126i	−0.791759	+	0.791759i	−0.981780	−	0.190021i	$-0.939145\pi$
$907$	−718.126	+	718.126i	−0.791759	+	0.791759i	0.190021	+	0.981780i	$0.439145\pi$
$908$	−97.4096	−	615.020i	−0.107279	−	0.677335i
$909$	−43.2769	−	14.0615i	−0.0476094	−	0.0154692i
$910$	−45.3549	−	112.065i	−0.0498405	−	0.123148i
$911$	−253.082	−	778.907i	−0.277807	−	0.855002i	−0.988463	−	0.151462i	$-0.951602\pi$
$911$	−253.082	−	778.907i	−0.277807	−	0.855002i	0.710656	−	0.703540i	$-0.248398\pi$
$912$	438.822	+	861.236i	0.481164	+	0.944337i
$913$	−1212.81	+	617.959i	−1.32838	+	0.676844i
$914$	−543.885	+	176.719i	−0.595060	+	0.193347i
$915$	−1061.73	−	264.047i	−1.16036	−	0.288576i
$916$	194.002	−	597.076i	0.211792	−	0.651829i
$917$	−905.062	+	143.348i	−0.986981	+	0.156322i
$918$	93.3504	+	93.3504i	0.101689	+	0.101689i
$919$	879.635	−	1210.71i	0.957165	−	1.31742i	0.00889471	−	0.999960i	$-0.497169\pi$
$919$	879.635	−	1210.71i	0.957165	−	1.31742i	0.948270	−	0.317464i	$-0.102831\pi$
$920$	−104.699	+	120.587i	−0.113803	+	0.131073i
$921$	−1337.32	+	971.617i	−1.45203	+	1.05496i
$922$	−216.987	+	1370.00i	−0.235344	+	1.48590i
$923$	23.1556	−	45.4453i	0.0250873	−	0.0492366i
$924$			1952.24i			2.11281i
$925$	115.626	−	337.107i	0.125001	−	0.364440i
$926$	−715.981			−0.773197
$927$	−933.206	−	475.492i	−1.00669	−	0.512937i
$928$	403.479	+	63.9048i	0.434783	+	0.0688629i
$929$	−648.674	−	892.823i	−0.698250	−	0.961058i	−0.999971	−	0.00766213i	$-0.997561\pi$
$929$	−648.674	−	892.823i	−0.698250	−	0.961058i	0.301721	−	0.953396i	$-0.402439\pi$
$930$	2117.75	+	184.008i	2.27715	+	0.197858i
$931$	60.0066	+	43.5974i	0.0644539	+	0.0468285i
$932$	723.893	−	723.893i	0.776709	−	0.776709i
$933$	−266.773	−	1684.34i	−0.285931	−	1.80530i
$934$	1094.85	+	355.737i	1.17221	+	0.380875i
$935$	−288.635	+	20.3562i	−0.308700	+	0.0217713i
$936$	−14.5311	−	44.7221i	−0.0155247	−	0.0477800i
$937$	−26.6874	−	52.3769i	−0.0284817	−	0.0558985i	0.876327	−	0.481716i	$-0.159986\pi$
$937$	−26.6874	−	52.3769i	−0.0284817	−	0.0558985i	−0.904809	+	0.425818i	$0.859986\pi$
$938$	−1467.95	+	747.960i	−1.56498	+	0.797399i
$939$	1750.43	−	568.751i	1.86415	−	0.605698i
$940$	8.19708	+	116.228i	0.00872030	+	0.123647i
$941$	−455.101	+	1400.66i	−0.483635	+	1.48848i	0.350312	+	0.936633i	$0.386075\pi$
$941$	−455.101	+	1400.66i	−0.483635	+	1.48848i	−0.833948	+	0.551844i	$0.813925\pi$
$942$	2930.72	−	464.181i	3.11117	−	0.492761i
$943$	−343.748	−	343.748i	−0.364526	−	0.364526i
$944$	−413.959	+	569.765i	−0.438516	+	0.603565i
$945$	27.3715	−	315.020i	0.0289646	−	0.333355i
$946$	1560.30	−	1133.62i	1.64936	−	1.19833i
$947$	214.634	−	1355.15i	0.226646	−	1.43099i	−0.567555	−	0.823335i	$-0.692111\pi$
$947$	214.634	−	1355.15i	0.226646	−	1.43099i	0.794202	−	0.607654i	$-0.207889\pi$
$948$	−493.273	+	968.103i	−0.520330	+	1.02121i
$949$			71.1146i			0.0749363i
$950$	−1567.52	−	537.652i	−1.65002	−	0.565950i
$951$	779.503			0.819667
$952$	100.475	+	51.1947i	0.105541	+	0.0537759i
$953$	−1007.09	−	159.507i	−1.05676	−	0.167374i	−0.396211	−	0.918159i	$-0.629675\pi$
$953$	−1007.09	−	159.507i	−1.05676	−	0.167374i	−0.660546	+	0.750786i	$0.729675\pi$
$954$	1384.80	+	1906.01i	1.45157	+	1.99791i
$955$	−345.899	−	300.324i	−0.362198	−	0.314475i
$956$	−463.109	−	336.469i	−0.484424	−	0.351955i
$957$	364.083	−	364.083i	0.380442	−	0.380442i
$958$	−109.884	−	693.783i	−0.114702	−	0.724200i
$959$	−1191.58	−	387.169i	−1.24253	−	0.403721i
$960$	−511.809	+	2057.98i	−0.533135	+	2.14373i
$961$	5.75717	+	17.7188i	0.00599082	+	0.0184378i
$962$	−23.1708	−	45.4752i	−0.0240860	−	0.0472715i
$963$	1988.25	−	1013.06i	2.06464	−	1.05199i
$964$	335.093	−	108.878i	0.347607	−	0.112944i
$965$	847.815	−	343.127i	0.878565	−	0.355572i
$966$	−252.242	+	776.320i	−0.261120	+	0.803644i
$967$	461.511	−	73.0962i	0.477261	−	0.0755907i	0.0868303	−	0.996223i	$-0.472326\pi$
$967$	461.511	−	73.0962i	0.477261	−	0.0755907i	0.390430	+	0.920632i	$0.372326\pi$
$968$	−85.6828	−	85.6828i	−0.0885153	−	0.0885153i
$969$	268.059	−	368.951i	0.276634	−	0.380755i
$970$	−449.028	−	746.300i	−0.462916	−	0.769382i
$971$	805.523	−	585.247i	0.829581	−	0.602726i	−0.0898601	−	0.995954i	$-0.528642\pi$
$971$	805.523	−	585.247i	0.829581	−	0.602726i	0.919441	+	0.393229i	$0.128642\pi$
$972$	−278.574	+	1758.84i	−0.286598	+	1.80951i
$973$	−396.113	+	777.415i	−0.407105	+	0.798988i
$974$			435.351i			0.446973i
$975$	−116.955	−	62.0075i	−0.119954	−	0.0635975i
$976$	481.339			0.493175
$977$	−1580.72	−	805.418i	−1.61793	−	0.824378i	−0.999249	−	0.0387385i	$-0.987666\pi$
$977$	−1580.72	−	805.418i	−1.61793	−	0.824378i	−0.618684	−	0.785640i	$-0.712334\pi$
$978$	−484.752	−	76.7772i	−0.495657	−	0.0785043i
$979$	484.621	+	667.023i	0.495016	+	0.681331i
$980$	19.8252	+	85.6394i	0.0202298	+	0.0873872i
$981$	−1218.13	−	885.024i	−1.24172	−	0.902165i
$982$	−256.716	+	256.716i	−0.261421	+	0.261421i
$983$	−113.706	−	717.913i	−0.115673	−	0.730329i	−0.975542	−	0.219814i	$-0.929455\pi$
$983$	−113.706	−	717.913i	−0.115673	−	0.730329i	0.859869	−	0.510515i	$-0.170545\pi$
$984$	835.923	+	271.608i	0.849515	+	0.276024i
$985$	−521.704	−	325.564i	−0.529648	−	0.330522i
$986$	−40.2293	−	123.813i	−0.0408005	−	0.125571i
$987$	61.7695	+	121.229i	0.0625831	+	0.122826i
$988$	−119.363	+	60.8183i	−0.120812	+	0.0615569i
$989$	432.918	−	140.664i	0.437733	−	0.142228i
$990$	1344.63	+	1600.52i	1.35821	+	1.61669i
$991$	−468.726	+	1442.59i	−0.472983	+	1.45569i	0.375675	+	0.926751i	$0.377411\pi$
$991$	−468.726	+	1442.59i	−0.472983	+	1.45569i	−0.848658	+	0.528941i	$0.822589\pi$
$992$	−1367.56	+	216.600i	−1.37859	+	0.218347i
$993$	−125.229	−	125.229i	−0.126112	−	0.126112i
$994$	519.385	−	714.872i	0.522520	−	0.719187i
$995$	1796.32	+	761.229i	1.80535	+	0.765055i
$996$	2056.95	−	1494.46i	2.06521	−	1.50046i
$997$	−125.911	+	794.973i	−0.126290	+	0.797365i	0.840503	+	0.541806i	$0.182259\pi$
$997$	−125.911	+	794.973i	−0.126290	+	0.797365i	−0.966794	+	0.255559i	$0.917741\pi$
$998$	−377.336	+	740.565i	−0.378093	+	0.742049i
$999$		−	133.493i		−	0.133626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.8.4	✓	32
3.2	odd	2		225.3.r.a.208.1		32
4.3	odd	2		400.3.bg.c.33.4		32
5.2	odd	4		125.3.f.a.107.1		32
5.3	odd	4		125.3.f.b.107.4		32
5.4	even	2		125.3.f.c.18.1		32
25.3	odd	20		125.3.f.c.7.1		32
25.4	even	10		125.3.f.b.118.4		32
25.21	even	5		125.3.f.a.118.1		32
25.22	odd	20	inner	25.3.f.a.22.4	yes	32
75.47	even	20		225.3.r.a.172.1		32
100.47	even	20		400.3.bg.c.97.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.8.4	✓	32	1.1	even	1	trivial
25.3.f.a.22.4	yes	32	25.22	odd	20	inner
125.3.f.a.107.1		32	5.2	odd	4
125.3.f.a.118.1		32	25.21	even	5
125.3.f.b.107.4		32	5.3	odd	4
125.3.f.b.118.4		32	25.4	even	10
125.3.f.c.7.1		32	25.3	odd	20
125.3.f.c.18.1		32	5.4	even	2
225.3.r.a.172.1		32	75.47	even	20
225.3.r.a.208.1		32	3.2	odd	2
400.3.bg.c.33.4		32	4.3	odd	2
400.3.bg.c.97.4		32	100.47	even	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70026 + 1.37585i) q^{2} +(-4.42692 - 0.701156i) q^{3} +(3.04732 + 4.19427i) q^{4} +(1.95091 - 4.60369i) q^{5} +(-10.9892 - 7.98410i) q^{6} +(-4.77540 + 4.77540i) q^{7} +(0.561510 + 3.54523i) q^{8} +(10.5465 + 3.42677i) q^{9} +O(q^{10})\)	\(q+(2.70026 + 1.37585i) q^{2} +(-4.42692 - 0.701156i) q^{3} +(3.04732 + 4.19427i) q^{4} +(1.95091 - 4.60369i) q^{5} +(-10.9892 - 7.98410i) q^{6} +(-4.77540 + 4.77540i) q^{7} +(0.561510 + 3.54523i) q^{8} +(10.5465 + 3.42677i) q^{9} +(11.6020 - 9.74701i) q^{10} +(3.84423 + 11.8313i) q^{11} +(-10.5494 - 20.7044i) q^{12} +(-1.05261 + 0.536333i) q^{13} +(-19.4651 + 6.32459i) q^{14} +(-11.8644 + 19.0123i) q^{15} +(3.04678 - 9.37702i) q^{16} +(-4.59461 + 0.727715i) q^{17} +(23.7637 + 23.7637i) q^{18} +(12.8564 - 17.6953i) q^{19} +(25.2542 - 5.84624i) q^{20} +(24.4886 - 17.7920i) q^{21} +(-5.89773 + 37.2368i) q^{22} +(-4.03970 + 7.92835i) q^{23} -16.0882i q^{24} +(-17.3879 - 17.9628i) q^{25} -3.58025 q^{26} +(-8.34369 - 4.25132i) q^{27} +(-34.5815 - 5.47717i) q^{28} +(5.42781 + 7.47074i) q^{29} +(-58.1952 + 35.0145i) q^{30} +(-25.3215 - 18.3971i) q^{31} +(31.2809 - 31.2809i) q^{32} +(-8.72252 - 55.0718i) q^{33} +(-13.4079 - 4.35649i) q^{34} +(12.6681 + 31.3008i) q^{35} +(17.7658 + 54.6774i) q^{36} +(6.47182 + 12.7017i) q^{37} +(59.0618 - 30.0935i) q^{38} +(5.03589 - 1.63626i) q^{39} +(17.4166 + 4.33142i) q^{40} +(-16.8825 + 51.9589i) q^{41} +(90.6050 - 14.3504i) q^{42} +(-36.1728 - 36.1728i) q^{43} +(-37.9092 + 52.1775i) q^{44} +(36.3511 - 41.8676i) q^{45} +(-21.8165 + 15.8506i) q^{46} +(-0.703158 + 4.43956i) q^{47} +(-20.0626 + 39.3751i) q^{48} +3.39110i q^{49} +(-22.2377 - 72.4274i) q^{50} +20.8502 q^{51} +(-5.45717 - 2.78057i) q^{52} +(69.2402 + 10.9666i) q^{53} +(-16.6810 - 22.9594i) q^{54} +(61.9675 + 5.38424i) q^{55} +(-19.6113 - 14.2485i) q^{56} +(-69.3215 + 69.3215i) q^{57} +(4.37788 + 27.6409i) q^{58} +(-67.9339 - 22.0730i) q^{59} +(-115.897 + 8.17375i) q^{60} +(15.0860 + 46.4300i) q^{61} +(-43.0629 - 84.5157i) q^{62} +(-66.7281 + 33.9997i) q^{63} +(89.9967 - 29.2417i) q^{64} +(0.415555 + 5.89224i) q^{65} +(52.2176 - 160.709i) q^{66} +(79.5063 - 12.5926i) q^{67} +(-17.0535 - 17.0535i) q^{68} +(23.4424 - 32.2657i) q^{69} +(-8.85824 + 101.950i) q^{70} +(-34.9284 + 25.3769i) q^{71} +(-6.22673 + 39.3140i) q^{72} +(27.3286 - 53.6354i) q^{73} +43.2021i q^{74} +(64.3801 + 91.7115i) q^{75} +113.396 q^{76} +(-74.8571 - 38.1416i) q^{77} +(15.8495 + 2.51031i) q^{78} +(-27.4839 - 37.8283i) q^{79} +(-37.2249 - 32.3202i) q^{80} +(-46.7867 - 33.9925i) q^{81} +(-117.075 + 117.075i) q^{82} +(17.1166 + 108.070i) q^{83} +(149.249 + 48.4940i) q^{84} +(-5.61351 + 22.5719i) q^{85} +(-47.9077 - 147.445i) q^{86} +(-18.7904 - 36.8782i) q^{87} +(-39.7862 + 20.2721i) q^{88} +(63.0322 - 20.4804i) q^{89} +(155.761 - 63.0397i) q^{90} +(2.46544 - 7.58786i) q^{91} +(-45.5639 + 7.21661i) q^{92} +(99.1969 + 99.1969i) q^{93} +(-8.00690 + 11.0206i) q^{94} +(-56.3820 - 93.7088i) q^{95} +(-160.411 + 116.546i) q^{96} +(8.99168 - 56.7712i) q^{97} +(-4.66566 + 9.15688i) q^{98} +137.953i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

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