LMFDB - Embedded newform 418.2.n.e.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	418.49
Dual form			418.2.n.e.273.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(2.70941 - 1.20631i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.53406 + 1.70375i) q^{5} +(-2.90101 + 0.616628i) q^{6} +(-1.86152 + 1.35247i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(3.87833 - 4.30732i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(2.70941 - 1.20631i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.53406 + 1.70375i) q^{5} +(-2.90101 + 0.616628i) q^{6} +(-1.86152 + 1.35247i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(3.87833 - 4.30732i) q^{9} +(-1.14631 - 1.98547i) q^{10} +(-0.183801 - 3.31153i) q^{11} +2.96582 q^{12} +(0.514478 - 0.571386i) q^{13} +(2.10204 - 0.935887i) q^{14} +(6.21165 + 2.76560i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.62736 + 1.80736i) q^{17} +(-4.68912 + 3.40685i) q^{18} +(3.60840 - 2.44530i) q^{19} +(0.708459 + 2.18041i) q^{20} +(-3.41212 + 5.90997i) q^{21} +(-0.508720 + 3.27738i) q^{22} +(2.57439 + 4.45897i) q^{23} +(-2.90101 - 0.616628i) q^{24} +(-0.0267706 + 0.254706i) q^{25} +(-0.622033 + 0.451933i) q^{26} +(2.56257 - 7.88678i) q^{27} +(-2.25068 + 0.478398i) q^{28} +(-6.14398 - 2.73548i) q^{29} +(-5.50091 - 3.99664i) q^{30} +(1.62114 + 4.98935i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.49271 - 8.75056i) q^{33} +(-1.21602 - 2.10622i) q^{34} +(-5.15996 - 1.09678i) q^{35} +(5.29498 - 2.35748i) q^{36} +(-5.51579 + 4.00746i) q^{37} +(-4.03795 + 1.64163i) q^{38} +(0.704665 - 2.16874i) q^{39} +(-0.239644 - 2.28006i) q^{40} +(3.45970 - 1.54036i) q^{41} +(4.56631 - 5.07140i) q^{42} +(-4.41306 + 7.64364i) q^{43} +(1.17901 - 3.09999i) q^{44} +13.2882 q^{45} +(-1.59106 - 4.89678i) q^{46} +(1.05533 - 10.0408i) q^{47} +(2.70941 + 1.20631i) q^{48} +(-0.527046 + 1.62208i) q^{49} +(0.0791419 - 0.243574i) q^{50} +(6.58942 + 2.93380i) q^{51} +(0.702402 - 0.312730i) q^{52} +(-5.59733 + 6.21647i) q^{53} +(-4.14633 + 7.18165i) q^{54} +(5.36005 - 5.39324i) q^{55} +2.30097 q^{56} +(6.82684 - 10.9781i) q^{57} +(5.44099 + 3.95311i) q^{58} +(-0.766440 - 7.29219i) q^{59} +(4.54975 + 5.05301i) q^{60} +(-8.62738 + 1.83381i) q^{61} +(-0.548368 - 5.21738i) q^{62} +(-1.39405 + 13.2635i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.76274 q^{65} +(2.57519 + 9.49343i) q^{66} +(-3.08653 - 5.34603i) q^{67} +(0.751544 + 2.31302i) q^{68} +(12.3540 + 8.97567i) q^{69} +(4.81917 + 2.14563i) q^{70} +(-4.59405 - 5.10220i) q^{71} +(-5.66942 + 1.20507i) q^{72} +(1.18350 + 11.2603i) q^{73} +(6.22846 - 2.77309i) q^{74} +(0.234721 + 0.722396i) q^{75} +(4.29103 - 0.766223i) q^{76} +(4.82090 + 5.91589i) q^{77} +(-1.14017 + 1.97484i) q^{78} +(-8.90982 - 1.89384i) q^{79} +(-0.239644 + 2.28006i) q^{80} +(-0.753261 - 7.16680i) q^{81} +(-3.70436 + 0.787386i) q^{82} +(3.95101 - 12.1600i) q^{83} +(-5.52093 + 4.01119i) q^{84} +(-0.582826 + 5.54522i) q^{85} +(5.90582 - 6.55908i) q^{86} -19.9464 q^{87} +(-1.79777 + 2.78712i) q^{88} +(-5.90976 - 10.2360i) q^{89} +(-12.9978 - 2.76277i) q^{90} +(-0.184927 + 1.75946i) q^{91} +(0.538193 + 5.12057i) q^{92} +(10.4110 + 11.5626i) q^{93} +(-3.11986 + 9.60195i) q^{94} +(9.70168 + 2.39656i) q^{95} +(-2.39940 - 1.74326i) q^{96} +(-12.9657 - 2.75594i) q^{97} +(0.852778 - 1.47706i) q^{98} +(-14.9767 - 12.0515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	2.70941	−	1.20631i	1.56428	−	0.696462i	0.571973	−	0.820273i	$-0.306178\pi$
$3$	2.70941	−	1.20631i	1.56428	−	0.696462i	0.992306	+	0.123811i	$0.0395117\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	1.53406	+	1.70375i	0.686054	+	0.761940i	0.981091	−	0.193546i	$-0.0619988\pi$
$5$	1.53406	+	1.70375i	0.686054	+	0.761940i	−0.295038	+	0.955486i	$0.595332\pi$
$6$	−2.90101	+	0.616628i	−1.18433	+	0.251737i
$7$	−1.86152	+	1.35247i	−0.703589	+	0.511187i	−0.881099	−	0.472932i	$-0.843196\pi$
$7$	−1.86152	+	1.35247i	−0.703589	+	0.511187i	0.177510	+	0.984119i	$0.443196\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	3.87833	−	4.30732i	1.29278	−	1.43577i
$10$	−1.14631	−	1.98547i	−0.362495	−	0.627860i
$11$	−0.183801	−	3.31153i	−0.0554182	−	0.998463i
$11$	−0.183801	−	3.31153i	−0.0554182	−	0.998463i
$12$	2.96582			0.856158
$13$	0.514478	−	0.571386i	0.142690	−	0.158474i	−0.667563	−	0.744553i	$-0.732663\pi$
$13$	0.514478	−	0.571386i	0.142690	−	0.158474i	0.810254	+	0.586079i	$0.199329\pi$
$14$	2.10204	−	0.935887i	0.561793	−	0.250126i
$15$	6.21165	+	2.76560i	1.60384	+	0.714076i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	1.62736	+	1.80736i	0.394692	+	0.438350i	0.907435	−	0.420192i	$-0.138037\pi$
$17$	1.62736	+	1.80736i	0.394692	+	0.438350i	−0.512743	+	0.858542i	$0.671371\pi$
$18$	−4.68912	+	3.40685i	−1.10524	+	0.803002i
$19$	3.60840	−	2.44530i	0.827823	−	0.560990i
$19$	3.60840	−	2.44530i	0.827823	−	0.560990i
$20$	0.708459	+	2.18041i	0.158416	+	0.487555i
$21$	−3.41212	+	5.90997i	−0.744586	+	1.28966i
$22$	−0.508720	+	3.27738i	−0.108460	+	0.698739i
$23$	2.57439	+	4.45897i	0.536797	+	0.929759i	0.999074	+	0.0430240i	$0.0136992\pi$
$23$	2.57439	+	4.45897i	0.536797	+	0.929759i	−0.462277	+	0.886735i	$0.652967\pi$
$24$	−2.90101	−	0.616628i	−0.592166	−	0.125869i
$25$	−0.0267706	+	0.254706i	−0.00535413	+	0.0509411i
$26$	−0.622033	+	0.451933i	−0.121991	+	0.0886314i
$27$	2.56257	−	7.88678i	0.493167	−	1.51781i
$28$	−2.25068	+	0.478398i	−0.425339	+	0.0904087i
$29$	−6.14398	−	2.73548i	−1.14091	−	0.507965i	−0.252764	−	0.967528i	$-0.581340\pi$
$29$	−6.14398	−	2.73548i	−1.14091	−	0.507965i	−0.888145	+	0.459563i	$0.848006\pi$
$30$	−5.50091	−	3.99664i	−1.00432	−	0.729684i
$31$	1.62114	+	4.98935i	0.291165	+	0.896114i	0.984483	+	0.175482i	$0.0561483\pi$
$31$	1.62114	+	4.98935i	0.291165	+	0.896114i	−0.693318	+	0.720632i	$0.743852\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.49271	−	8.75056i	−0.782081	−	1.52328i
$34$	−1.21602	−	2.10622i	−0.208546	−	0.361213i
$35$	−5.15996	−	1.09678i	−0.872193	−	0.185390i
$36$	5.29498	−	2.35748i	0.882497	−	0.392913i
$37$	−5.51579	+	4.00746i	−0.906791	+	0.658822i	−0.940201	−	0.340620i	$-0.889363\pi$
$37$	−5.51579	+	4.00746i	−0.906791	+	0.658822i	0.0334105	+	0.999442i	$0.489363\pi$
$38$	−4.03795	+	1.64163i	−0.655042	+	0.266308i
$39$	0.704665	−	2.16874i	0.112837	−	0.347276i
$40$	−0.239644	−	2.28006i	−0.0378911	−	0.360509i
$41$	3.45970	−	1.54036i	0.540315	−	0.240564i	−0.118387	−	0.992968i	$-0.537772\pi$
$41$	3.45970	−	1.54036i	0.540315	−	0.240564i	0.658702	+	0.752404i	$0.271106\pi$
$42$	4.56631	−	5.07140i	0.704597	−	0.782534i
$43$	−4.41306	+	7.64364i	−0.672985	+	1.16564i	0.304069	+	0.952650i	$0.401655\pi$
$43$	−4.41306	+	7.64364i	−0.672985	+	1.16564i	−0.977054	+	0.212994i	$0.931679\pi$
$44$	1.17901	−	3.09999i	0.177742	−	0.467341i
$45$	13.2882			1.98089
$46$	−1.59106	−	4.89678i	−0.234589	−	0.721990i
$47$	1.05533	−	10.0408i	0.153935	−	1.46460i	−0.595945	−	0.803025i	$-0.703222\pi$
$47$	1.05533	−	10.0408i	0.153935	−	1.46460i	0.749881	−	0.661573i	$-0.230111\pi$
$48$	2.70941	+	1.20631i	0.391070	+	0.174115i
$49$	−0.527046	+	1.62208i	−0.0752923	+	0.231726i
$50$	0.0791419	−	0.243574i	0.0111924	−	0.0344465i
$51$	6.58942	+	2.93380i	0.922703	+	0.410814i
$52$	0.702402	−	0.312730i	0.0974057	−	0.0433678i
$53$	−5.59733	+	6.21647i	−0.768853	+	0.853898i	−0.992685	−	0.120730i	$-0.961476\pi$
$53$	−5.59733	+	6.21647i	−0.768853	+	0.853898i	0.223833	+	0.974628i	$0.428143\pi$
$54$	−4.14633	+	7.18165i	−0.564244	+	0.977299i
$55$	5.36005	−	5.39324i	0.722749	−	0.727225i
$56$	2.30097			0.307479
$57$	6.82684	−	10.9781i	0.904238	−	1.45409i
$58$	5.44099	+	3.95311i	0.714436	+	0.519068i
$59$	−0.766440	−	7.29219i	−0.0997820	−	0.949362i	−0.923820	−	0.382827i	$-0.874950\pi$
$59$	−0.766440	−	7.29219i	−0.0997820	−	0.949362i	0.824038	−	0.566535i	$-0.191716\pi$
$60$	4.54975	+	5.05301i	0.587370	+	0.652341i
$61$	−8.62738	+	1.83381i	−1.10462	+	0.234795i	−0.723907	−	0.689897i	$-0.757656\pi$
$61$	−8.62738	+	1.83381i	−1.10462	+	0.234795i	−0.380716	+	0.924692i	$0.624322\pi$
$62$	−0.548368	−	5.21738i	−0.0696428	−	0.662607i
$63$	−1.39405	+	13.2635i	−0.175634	+	1.67105i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.76274			0.218641
$66$	2.57519	+	9.49343i	0.316984	+	1.16856i
$67$	−3.08653	−	5.34603i	−0.377080	−	0.653122i	0.613556	−	0.789651i	$-0.289739\pi$
$67$	−3.08653	−	5.34603i	−0.377080	−	0.653122i	−0.990636	+	0.136529i	$0.956405\pi$
$68$	0.751544	+	2.31302i	0.0911382	+	0.280494i
$69$	12.3540	+	8.97567i	1.48724	+	1.08054i
$70$	4.81917	+	2.14563i	0.576001	+	0.256452i
$71$	−4.59405	−	5.10220i	−0.545213	−	0.605520i	0.406069	−	0.913842i	$-0.366899\pi$
$71$	−4.59405	−	5.10220i	−0.545213	−	0.605520i	−0.951282	+	0.308322i	$0.900233\pi$
$72$	−5.66942	+	1.20507i	−0.668147	+	0.142019i
$73$	1.18350	+	11.2603i	0.138519	+	1.31792i	0.814140	+	0.580668i	$0.197209\pi$
$73$	1.18350	+	11.2603i	0.138519	+	1.31792i	−0.675622	+	0.737248i	$0.736125\pi$
$74$	6.22846	−	2.77309i	0.724043	−	0.322365i
$75$	0.234721	+	0.722396i	0.0271032	+	0.0834151i
$76$	4.29103	−	0.766223i	0.492214	−	0.0878918i
$77$	4.82090	+	5.91589i	0.549393	+	0.674178i
$78$	−1.14017	+	1.97484i	−0.129099	+	0.223606i
$79$	−8.90982	−	1.89384i	−1.00243	−	0.213074i	−0.322675	−	0.946510i	$-0.604582\pi$
$79$	−8.90982	−	1.89384i	−1.00243	−	0.213074i	−0.679758	+	0.733436i	$0.737915\pi$
$80$	−0.239644	+	2.28006i	−0.0267930	+	0.254919i
$81$	−0.753261	−	7.16680i	−0.0836956	−	0.796311i
$82$	−3.70436	+	0.787386i	−0.409078	+	0.0869522i
$83$	3.95101	−	12.1600i	0.433679	−	1.33473i	−0.460754	−	0.887528i	$-0.652421\pi$
$83$	3.95101	−	12.1600i	0.433679	−	1.33473i	0.894434	−	0.447200i	$-0.147579\pi$
$84$	−5.52093	+	4.01119i	−0.602383	+	0.437657i
$85$	−0.582826	+	5.54522i	−0.0632164	+	0.601464i
$86$	5.90582	−	6.55908i	0.636841	−	0.707284i
$87$	−19.9464			−2.13848
$88$	−1.79777	+	2.78712i	−0.191643	+	0.297108i
$89$	−5.90976	−	10.2360i	−0.626433	−	1.08501i	−0.988262	−	0.152769i	$-0.951181\pi$
$89$	−5.90976	−	10.2360i	−0.626433	−	1.08501i	0.361829	−	0.932245i	$-0.382152\pi$
$90$	−12.9978	−	2.76277i	−1.37009	−	0.291222i
$91$	−0.184927	+	1.75946i	−0.0193856	+	0.184442i
$92$	0.538193	+	5.12057i	0.0561106	+	0.533856i
$93$	10.4110	+	11.5626i	1.07957	+	1.19899i
$94$	−3.11986	+	9.60195i	−0.321789	+	0.990365i
$95$	9.70168	+	2.39656i	0.995371	+	0.245882i
$96$	−2.39940	−	1.74326i	−0.244887	−	0.177921i
$97$	−12.9657	−	2.75594i	−1.31647	−	0.279824i	−0.504442	−	0.863446i	$-0.668302\pi$
$97$	−12.9657	−	2.75594i	−1.31647	−	0.279824i	−0.812025	+	0.583622i	$0.801635\pi$
$98$	0.852778	−	1.47706i	0.0861436	−	0.149205i
$99$	−14.9767	−	12.0515i	−1.50521	−	1.21122i
$100$	−0.128054	+	0.221797i	−0.0128054	+	0.0221797i
$101$	−6.85358	+	7.61167i	−0.681957	+	0.757390i	−0.980396	−	0.197039i	$-0.936867\pi$
$101$	−6.85358	+	7.61167i	−0.681957	+	0.757390i	0.298439	+	0.954429i	$0.403534\pi$
$102$	−5.83545	−	4.23970i	−0.577796	−	0.419793i
$103$	−6.23152	+	4.52747i	−0.614010	+	0.446104i	−0.850824	−	0.525451i	$-0.823897\pi$
$103$	−6.23152	+	4.52747i	−0.614010	+	0.446104i	0.236814	+	0.971555i	$0.423897\pi$
$104$	−0.752073	+	0.159858i	−0.0737469	+	0.0156754i
$105$	−15.3035	+	3.25286i	−1.49347	+	0.317447i
$106$	6.76749	−	4.91687i	0.657317	−	0.477569i
$107$	3.90685	+	2.83849i	0.377689	+	0.274407i	0.760392	−	0.649464i	$-0.225007\pi$
$107$	3.90685	+	2.83849i	0.377689	+	0.274407i	−0.382703	+	0.923871i	$0.625007\pi$
$108$	5.54887	−	6.16264i	0.533940	−	0.593001i
$109$	0.113105	−	0.195903i	0.0108335	−	0.0187641i	−0.860558	−	0.509353i	$-0.829885\pi$
$109$	0.113105	−	0.195903i	0.0108335	−	0.0187641i	0.871391	+	0.490589i	$0.163218\pi$
$110$	−6.36424	+	4.16097i	−0.606806	+	0.396733i
$111$	−10.1103	+	17.5116i	−0.959629	+	1.66213i
$112$	−2.25068	−	0.478398i	−0.212670	−	0.0452043i
$113$	−1.99832	−	1.45187i	−0.187987	−	0.136580i	0.489811	−	0.871828i	$-0.337066\pi$
$113$	−1.99832	−	1.45187i	−0.187987	−	0.136580i	−0.677798	+	0.735248i	$0.737066\pi$
$114$	−8.96015	+	9.31886i	−0.839195	+	0.872792i
$115$	−3.64769	+	11.2264i	−0.340149	+	1.04687i
$116$	−4.50019	−	4.99797i	−0.417832	−	0.464050i
$117$	−0.465827	−	4.43205i	−0.0430657	−	0.409743i
$118$	−0.766440	+	7.29219i	−0.0705565	+	0.671300i
$119$	−5.47377	−	1.16349i	−0.501780	−	0.106657i
$120$	−3.39975	−	5.88854i	−0.310353	−	0.537547i
$121$	−10.9324	+	1.21733i	−0.993858	+	0.110666i
$122$	8.82012			0.798536
$123$	7.51561	−	8.34693i	0.677660	−	0.752617i
$124$	−0.548368	+	5.21738i	−0.0492449	+	0.468534i
$125$	8.79882	−	6.39272i	0.786991	−	0.571782i
$126$	4.12123	−	12.6838i	0.367148	−	1.12997i
$127$	20.7517	−	4.41091i	1.84141	−	0.391405i	0.850508	−	0.525961i	$-0.176294\pi$
$127$	20.7517	−	4.41091i	1.84141	−	0.391405i	0.990906	+	0.134557i	$0.0429610\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	−2.73620	+	26.0332i	−0.240909	+	2.29210i
$130$	−1.72422	−	0.366494i	−0.151224	−	0.0321437i
$131$	−5.36520	+	9.29281i	−0.468760	+	0.811916i	−0.999362	−	0.0357047i	$-0.988632\pi$
$131$	−5.36520	+	9.29281i	−0.468760	+	0.811916i	0.530602	+	0.847621i	$0.321966\pi$
$132$	−0.545122	−	9.82139i	−0.0474467	−	0.854842i
$133$	−3.40990	+	9.43223i	−0.295676	+	0.817878i
$134$	1.90758	+	5.87094i	0.164790	+	0.507172i
$135$	17.3682	−	7.73284i	1.49482	−	0.665537i
$136$	−0.254218	−	2.41873i	−0.0217990	−	0.207404i
$137$	1.79361	−	0.381244i	0.153239	−	0.0325718i	−0.130654	−	0.991428i	$-0.541708\pi$
$137$	1.79361	−	0.381244i	0.153239	−	0.0325718i	0.283892	+	0.958856i	$0.408374\pi$
$138$	−10.2178	−	11.3481i	−0.869801	−	0.966011i
$139$	7.43904	+	3.31207i	0.630971	+	0.280926i	0.697199	−	0.716878i	$-0.254430\pi$
$139$	7.43904	+	3.31207i	0.630971	+	0.280926i	−0.0662274	+	0.997805i	$0.521096\pi$
$140$	−4.26776	−	3.10071i	−0.360692	−	0.262058i
$141$	−9.25294	−	28.4776i	−0.779238	−	2.39825i
$142$	3.43285	+	5.94586i	0.288078	+	0.498966i
$143$	−1.98672	−	1.59869i	−0.166138	−	0.133689i
$144$	5.79608			0.483006
$145$	−4.76469	−	14.6642i	−0.395686	−	1.21780i
$146$	1.18350	−	11.2603i	0.0979475	−	0.931908i
$147$	0.528744	+	5.03066i	0.0436100	+	0.414922i
$148$	−6.66891	+	1.41752i	−0.548181	+	0.116519i
$149$	−0.984892	−	1.09383i	−0.0806855	−	0.0896103i	0.701450	−	0.712719i	$-0.252536\pi$
$149$	−0.984892	−	1.09383i	−0.0806855	−	0.0896103i	−0.782136	+	0.623108i	$0.785870\pi$
$150$	−0.0793969	−	0.755411i	−0.00648273	−	0.0616790i
$151$	11.9682	+	8.69544i	0.973962	+	0.707625i	0.956351	−	0.292220i	$-0.0943939\pi$
$151$	11.9682	+	8.69544i	0.973962	+	0.707625i	0.0176111	+	0.999845i	$0.494394\pi$
$152$	−4.35656	−	0.142675i	−0.353364	−	0.0115725i
$153$	14.0963			1.13962
$154$	−3.48557	−	6.78894i	−0.280876	−	0.547068i
$155$	−6.01367	+	10.4160i	−0.483030	+	0.836632i
$156$	1.52585	−	1.69463i	0.122166	−	0.135679i
$157$	15.9839	−	7.11648i	1.27565	−	0.567957i	0.346637	−	0.937999i	$-0.387324\pi$
$157$	15.9839	−	7.11648i	1.27565	−	0.567957i	0.929015	+	0.370043i	$0.120657\pi$
$158$	8.32137	+	3.70491i	0.662012	+	0.294747i
$159$	−7.66650	+	23.5951i	−0.607993	+	1.87121i
$160$	0.708459	−	2.18041i	0.0560086	−	0.172377i
$161$	−10.8229	−	4.81867i	−0.852965	−	0.379765i
$162$	−0.753261	+	7.16680i	−0.0591817	+	0.563077i
$163$	6.75669	+	20.7949i	0.529224	+	1.62879i	0.755808	+	0.654794i	$0.227244\pi$
$163$	6.75669	+	20.7949i	0.529224	+	1.62879i	−0.226583	+	0.973992i	$0.572756\pi$
$164$	3.78712			0.295724
$165$	8.01666	−	21.0784i	0.624096	−	1.64095i
$166$	−6.39287	+	11.0728i	−0.496183	+	0.859413i
$167$	9.43985	−	10.4840i	0.730477	−	0.811277i	−0.257434	−	0.966296i	$-0.582877\pi$
$167$	9.43985	−	10.4840i	0.730477	−	0.811277i	0.987912	+	0.155019i	$0.0495437\pi$
$168$	6.23426	−	2.77567i	0.480984	−	0.214148i
$169$	1.29708	+	12.3409i	0.0997751	+	0.949296i
$170$	1.72301	−	5.30287i	0.132149	−	0.406711i
$171$	3.46187	−	25.0262i	0.264736	−	1.91380i
$172$	−7.14047	+	5.18786i	−0.544456	+	0.395570i
$173$	−4.10315	+	1.82684i	−0.311957	+	0.138892i	−0.556743	−	0.830685i	$-0.687949\pi$
$173$	−4.10315	+	1.82684i	−0.311957	+	0.138892i	0.244786	+	0.969577i	$0.421282\pi$
$174$	19.5105	+	4.14709i	1.47909	+	0.314390i
$175$	−0.294649	−	0.510347i	−0.0222733	−	0.0385786i
$176$	2.33796	−	2.35244i	0.176230	−	0.177322i
$177$	−10.8732	−	18.8330i	−0.817281	−	1.41557i
$178$	3.65243	+	11.2410i	0.273761	+	0.842551i
$179$	−5.36373	−	3.89698i	−0.400904	−	0.291274i	0.369005	−	0.929427i	$-0.379698\pi$
$179$	−5.36373	−	3.89698i	−0.400904	−	0.291274i	−0.769909	+	0.638154i	$0.779698\pi$
$180$	12.1394	+	5.40480i	0.904816	+	0.402850i
$181$	−6.86688	+	1.45960i	−0.510411	+	0.108491i	−0.455916	−	0.890023i	$-0.650688\pi$
$181$	−6.86688	+	1.45960i	−0.510411	+	0.108491i	−0.0544951	+	0.998514i	$0.517355\pi$
$182$	0.546699	−	1.68257i	0.0405240	−	0.124720i
$183$	−21.1630	+	15.3758i	−1.56441	+	1.13661i
$184$	0.538193	−	5.12057i	0.0396762	−	0.377493i
$185$	−15.2893	−	3.24984i	−1.12409	−	0.238933i
$186$	−7.77951	−	13.4745i	−0.570421	−	0.987999i
$187$	5.68603	−	5.72124i	0.415804	−	0.418378i
$188$	5.04804	−	8.74347i	0.368166	−	0.637683i
$189$	5.89639	+	18.1472i	0.428899	+	1.32002i
$190$	−8.99140	−	4.36128i	−0.652305	−	0.316401i
$191$	7.56982	−	5.49980i	0.547733	−	0.397951i	−0.279216	−	0.960228i	$-0.590074\pi$
$191$	7.56982	−	5.49980i	0.547733	−	0.397951i	0.826949	+	0.562277i	$0.190074\pi$
$192$	1.98452	+	2.20403i	0.143220	+	0.159062i
$193$	−1.22058	−	1.35559i	−0.0878594	−	0.0975777i	0.697612	−	0.716476i	$-0.254246\pi$
$193$	−1.22058	−	1.35559i	−0.0878594	−	0.0975777i	−0.785471	+	0.618898i	$0.787579\pi$
$194$	12.1094	+	5.39144i	0.869402	+	0.387083i
$195$	4.77598	−	2.12640i	0.342015	−	0.152275i
$196$	−1.14124	+	1.26748i	−0.0815171	+	0.0905339i
$197$	7.05572			0.502700			0.251350	−	0.967896i	$-0.419126\pi$
$197$	7.05572			0.502700			0.251350	+	0.967896i	$0.419126\pi$
$198$	12.1437	+	14.9020i	0.863018	+	1.05904i
$199$	−6.18332	−	10.7098i	−0.438324	−	0.759199i	0.559236	−	0.829008i	$-0.311094\pi$
$199$	−6.18332	−	10.7098i	−0.438324	−	0.759199i	−0.997560	+	0.0698088i	$0.977761\pi$
$200$	0.171370	−	0.190326i	0.0121177	−	0.0134581i
$201$	−14.8116	−	10.7613i	−1.04473	−	0.759043i
$202$	8.28637	−	6.02040i	0.583027	−	0.423594i
$203$	15.1368	−	3.21743i	1.06240	−	0.225819i
$204$	4.82645	+	5.36031i	0.337919	+	0.375297i
$205$	7.93179	+	3.53146i	0.553980	+	0.246648i
$206$	7.03666	−	3.13292i	0.490267	−	0.218281i
$207$	29.1906	+	6.20464i	2.02888	+	0.431253i
$208$	0.768875			0.0533119
$209$	−8.76090	−	11.4999i	−0.606004	−	0.795462i
$210$	15.6454			1.07964
$211$	24.1280	+	5.12856i	1.66104	+	0.353064i	0.940353	−	0.340200i	$-0.110495\pi$
$211$	24.1280	+	5.12856i	1.66104	+	0.353064i	0.720684	+	0.693264i	$0.243828\pi$
$212$	−7.64188	+	3.40239i	−0.524847	+	0.233677i
$213$	−18.6020	−	8.28213i	−1.27459	−	0.567482i
$214$	−3.23132	−	3.58875i	−0.220889	−	0.245322i
$215$	−19.7927	+	4.20708i	−1.34985	+	0.286920i
$216$	−6.70890	+	4.87430i	−0.456483	+	0.331654i
$217$	−9.76575	−	7.09523i	−0.662942	−	0.481656i
$218$	−0.151364	+	0.168107i	−0.0102516	+	0.0113856i
$219$	16.7900	+	29.0811i	1.13456	+	1.96512i
$220$	7.09028	−	2.74684i	0.478026	−	0.185192i
$221$	1.86994			0.125786
$222$	13.5302	−	15.0269i	0.908091	−	1.00854i
$223$	15.2953	−	6.80993i	1.02425	−	0.456026i	0.175310	−	0.984513i	$-0.443907\pi$
$223$	15.2953	−	6.80993i	1.02425	−	0.456026i	0.848941	+	0.528487i	$0.177240\pi$
$224$	2.10204	+	0.935887i	0.140448	+	0.0625316i
$225$	0.993275	+	1.10314i	0.0662183	+	0.0735429i
$226$	1.65280	+	1.83562i	0.109942	+	0.122103i
$227$	6.46791	−	4.69921i	0.429291	−	0.311898i	−0.352075	−	0.935972i	$-0.614524\pi$
$227$	6.46791	−	4.69921i	0.429291	−	0.311898i	0.781365	+	0.624074i	$0.214524\pi$
$228$	10.7018	−	7.25231i	0.708747	−	0.480296i
$229$	6.71183	+	20.6569i	0.443530	+	1.36505i	0.884087	+	0.467322i	$0.154781\pi$
$229$	6.71183	+	20.6569i	0.443530	+	1.36505i	−0.440557	+	0.897725i	$0.645219\pi$
$230$	5.90209	−	10.2227i	0.389172	−	0.674067i
$231$	20.1982	+	10.2131i	1.32894	+	0.671971i
$232$	3.36271	+	5.82439i	0.220773	+	0.382390i
$233$	18.7816	+	3.99214i	1.23042	+	0.261534i	0.776850	−	0.629686i	$-0.216816\pi$
$233$	18.7816	+	3.99214i	1.23042	+	0.261534i	0.453571	+	0.891220i	$0.350150\pi$
$234$	−0.465827	+	4.43205i	−0.0304521	+	0.289732i
$235$	18.7259	−	13.6052i	1.22154	−	0.887503i
$236$	2.26582	−	6.97349i	0.147493	−	0.453935i
$237$	−26.4249	+	5.61679i	−1.71648	+	0.364849i
$238$	5.11226	+	2.27612i	0.331378	+	0.147539i
$239$	0.368892	+	0.268016i	0.0238617	+	0.0173365i	0.599652	−	0.800261i	$-0.295306\pi$
$239$	0.368892	+	0.268016i	0.0238617	+	0.0173365i	−0.575790	+	0.817597i	$0.695306\pi$
$240$	2.10116	+	6.46670i	0.135629	+	0.417424i
$241$	−10.8428	−	18.7802i	−0.698444	−	1.20974i	−0.969006	−	0.247037i	$-0.920543\pi$
$241$	−10.8428	−	18.7802i	−0.698444	−	1.20974i	0.270562	−	0.962702i	$-0.412790\pi$
$242$	10.9466	+	1.08226i	0.703676	+	0.0695700i
$243$	1.75273	+	3.03583i	0.112438	+	0.194748i
$244$	−8.62738	−	1.83381i	−0.552311	−	0.117397i
$245$	−3.57214	+	1.59042i	−0.228216	+	0.101608i
$246$	−9.08680	+	6.60195i	−0.579353	+	0.420925i
$247$	0.459232	−	3.31984i	0.0292203	−	0.211236i
$248$	1.62114	−	4.98935i	0.102942	−	0.316824i
$249$	−3.96373	−	37.7124i	−0.251191	−	2.38993i
$250$	−9.93567	+	4.42364i	−0.628387	+	0.279776i
$251$	−9.31074	+	10.3406i	−0.587688	+	0.652694i	−0.961498	−	0.274811i	$-0.911385\pi$
$251$	−9.31074	+	10.3406i	−0.587688	+	0.652694i	0.373810	+	0.927505i	$0.378051\pi$
$252$	−6.66829	+	11.5498i	−0.420063	+	0.727570i
$253$	14.2928	−	9.34472i	0.898582	−	0.587498i
$254$	−21.2153			−1.33117
$255$	5.11012	+	15.7273i	0.320008	+	0.984884i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	19.7156	+	8.77794i	1.22982	+	0.547553i	0.915713	−	0.401834i	$-0.131627\pi$
$257$	19.7156	+	8.77794i	1.22982	+	0.547553i	0.314111	+	0.949386i	$0.398294\pi$
$258$	8.08903	−	24.8955i	0.503601	−	1.54992i
$259$	4.84778	−	14.9199i	0.301226	−	0.927079i
$260$	1.61034	+	0.716971i	0.0998692	+	0.0444646i
$261$	−35.6110	+	15.8550i	−2.20427	+	0.981402i
$262$	7.18004	−	7.97425i	0.443585	−	0.492651i
$263$	13.8973	−	24.0709i	0.856946	−	1.48427i	−0.0178821	−	0.999840i	$-0.505692\pi$
$263$	13.8973	−	24.0709i	0.856946	−	1.48427i	0.874828	−	0.484434i	$-0.160974\pi$
$264$	−1.50877	+	9.72011i	−0.0928585	+	0.598231i
$265$	−19.1780			−1.17809
$266$	5.29646	−	8.51716i	0.324747	−	0.522220i
$267$	−28.3597	−	20.6045i	−1.73559	−	1.26098i
$268$	−0.645261	−	6.13925i	−0.0394156	−	0.375015i
$269$	11.0635	+	12.2873i	0.674555	+	0.749169i	0.979111	−	0.203325i	$-0.0651748\pi$
$269$	11.0635	+	12.2873i	0.674555	+	0.749169i	−0.304556	+	0.952494i	$0.598508\pi$
$270$	−18.5965	+	3.95280i	−1.13174	+	0.240560i
$271$	−0.630017	−	5.99421i	−0.0382708	−	0.364123i	−0.996851	−	0.0792993i	$-0.974732\pi$
$271$	−0.630017	−	5.99421i	−0.0382708	−	0.364123i	0.958580	−	0.284823i	$-0.0919349\pi$
$272$	−0.254218	+	2.41873i	−0.0154143	+	0.146657i
$273$	1.62141	+	4.99019i	0.0981322	+	0.302020i
$274$	−1.83368			−0.110777
$275$	0.848386	+	0.0418365i	0.0511596	+	0.00252283i
$276$	7.63516	+	13.2245i	0.459583	+	0.796021i
$277$	−7.20145	−	22.1638i	−0.432693	−	1.33169i	−0.895432	−	0.445199i	$-0.853133\pi$
$277$	−7.20145	−	22.1638i	−0.432693	−	1.33169i	0.462738	−	0.886495i	$-0.346867\pi$
$278$	−6.58786	−	4.78636i	−0.395114	−	0.287067i
$279$	27.7781	+	12.3676i	1.66303	+	0.740428i
$280$	3.52983	+	3.92027i	0.210947	+	0.234281i
$281$	1.82869	−	0.388700i	0.109091	−	0.0231879i	−0.153043	−	0.988220i	$-0.548907\pi$
$281$	1.82869	−	0.388700i	0.109091	−	0.0231879i	0.262133	+	0.965032i	$0.415574\pi$
$282$	3.12991	+	29.7791i	0.186384	+	1.77332i
$283$	−24.6603	+	10.9795i	−1.46590	+	0.652661i	−0.975732	−	0.218968i	$-0.929731\pi$
$283$	−24.6603	+	10.9795i	−1.46590	+	0.652661i	−0.490168	+	0.871628i	$0.663064\pi$
$284$	−2.12162	−	6.52966i	−0.125895	−	0.387464i
$285$	29.1768	−	5.20993i	1.72828	−	0.308610i
$286$	1.61092	+	1.97681i	0.0952557	+	0.116891i
$287$	−4.35701	+	7.54657i	−0.257186	+	0.445460i
$288$	−5.66942	−	1.20507i	−0.334074	−	0.0710096i
$289$	1.15871	−	11.0244i	0.0681596	−	0.648495i
$290$	1.61171	+	15.3344i	0.0946428	+	0.900466i
$291$	−38.4539	+	8.17363i	−2.25421	+	0.479147i
$292$	−3.49879	+	10.7682i	−0.204751	+	0.630159i
$293$	4.25617	−	3.09229i	0.248648	−	0.180653i	−0.456479	−	0.889734i	$-0.650890\pi$
$293$	4.25617	−	3.09229i	0.248648	−	0.180653i	0.705127	+	0.709081i	$0.250890\pi$
$294$	0.528744	−	5.03066i	0.0308370	−	0.293394i
$295$	11.2483	−	12.4925i	0.654901	−	0.727341i
$296$	6.81789			0.396282
$297$	−26.5883	−	7.03642i	−1.54281	−	0.408295i
$298$	0.735949	+	1.27470i	0.0426324	+	0.0738415i
$299$	3.87226	+	0.823074i	0.223938	+	0.0475996i
$300$	−0.0793969	+	0.755411i	−0.00458398	+	0.0436137i
$301$	−2.12282	−	20.1973i	−0.122358	−	1.16415i
$302$	−9.89883	−	10.9938i	−0.569614	−	0.632620i
$303$	−9.38715	+	28.8907i	−0.539277	+	1.65973i
$304$	4.23170	+	1.04534i	0.242705	+	0.0599542i
$305$	−16.3593	−	11.8857i	−0.936730	−	0.680574i
$306$	−13.7883	−	2.93079i	−0.788225	−	0.167542i
$307$	−0.0642989	+	0.111369i	−0.00366973	+	0.00635616i	−0.867854	−	0.496819i	$-0.834501\pi$
$307$	−0.0642989	+	0.111369i	−0.00366973	+	0.00635616i	0.864185	+	0.503175i	$0.167835\pi$
$308$	1.99791	+	7.36527i	0.113841	+	0.419675i
$309$	−11.4222	+	19.7839i	−0.649788	+	1.12547i
$310$	8.04787	−	8.93806i	0.457088	−	0.507648i
$311$	−18.2020	−	13.2245i	−1.03214	−	0.749894i	−0.0634050	−	0.997988i	$-0.520196\pi$
$311$	−18.2020	−	13.2245i	−1.03214	−	0.749894i	−0.968736	+	0.248093i	$0.920196\pi$
$312$	−1.84484	+	1.34035i	−0.104443	+	0.0758825i
$313$	−12.4103	+	2.63789i	−0.701471	+	0.149102i	−0.544821	−	0.838552i	$-0.683403\pi$
$313$	−12.4103	+	2.63789i	−0.701471	+	0.149102i	−0.156649	+	0.987654i	$0.550069\pi$
$314$	−17.1142	+	3.63773i	−0.965809	+	0.205289i
$315$	−24.7363	+	17.9719i	−1.39373	+	1.01260i
$316$	−7.36923	−	5.35406i	−0.414552	−	0.301189i
$317$	−21.2381	+	23.5873i	−1.19285	+	1.32479i	−0.259536	+	0.965733i	$0.583570\pi$
$317$	−21.2381	+	23.5873i	−1.19285	+	1.32479i	−0.933314	+	0.359061i	$0.883097\pi$
$318$	12.4047	−	21.4855i	0.695619	−	1.20485i
$319$	−7.92934	+	20.8488i	−0.443958	+	1.16731i
$320$	−1.14631	+	1.98547i	−0.0640807	+	0.110991i
$321$	14.0094	+	2.97778i	0.781926	+	0.166203i
$322$	9.58455	+	6.96358i	0.534126	+	0.388065i
$323$	10.2917	+	2.54231i	0.572645	+	0.141458i
$324$	2.22686	−	6.85357i	0.123714	−	0.380754i
$325$	0.131762	+	0.146337i	0.00730886	+	0.00811731i
$326$	−2.28552	−	21.7453i	−0.126583	−	1.20436i
$327$	0.0701278	−	0.667221i	0.00387808	−	0.0368974i
$328$	−3.70436	−	0.787386i	−0.204539	−	0.0434761i
$329$	11.6154	+	20.1184i	0.640376	+	1.10916i
$330$	−12.2239	+	18.9510i	−0.672905	+	1.04322i
$331$	−6.82872			−0.375340			−0.187670	−	0.982232i	$-0.560094\pi$
$331$	−6.82872			−0.375340			−0.187670	+	0.982232i	$0.560094\pi$
$332$	8.55532	−	9.50165i	0.469534	−	0.521471i
$333$	−4.13066	+	39.3006i	−0.226359	+	2.15366i
$334$	−11.4133	+	8.29226i	−0.624509	+	0.453732i
$335$	4.37336	−	13.4598i	0.238942	−	0.735389i
$336$	−6.67512	+	1.41884i	−0.364158	+	0.0774041i
$337$	−0.264631	−	2.51780i	−0.0144154	−	0.137153i	0.984947	−	0.172856i	$-0.0552996\pi$
$337$	−0.264631	−	2.51780i	−0.0144154	−	0.137153i	−0.999362	+	0.0357030i	$0.988633\pi$
$338$	1.29708	−	12.3409i	0.0705516	−	0.671254i
$339$	−7.16568	−	1.52311i	−0.389186	−	0.0827241i
$340$	−2.78788	+	4.82875i	−0.151194	+	0.261876i
$341$	16.2244	−	6.28549i	0.878601	−	0.340379i
$342$	−8.58946	+	23.7596i	−0.464465	+	1.28477i
$343$	−6.18998	−	19.0508i	−0.334227	−	1.02865i
$344$	8.06305	−	3.58990i	0.434731	−	0.193555i
$345$	3.65944	+	34.8173i	0.197018	+	1.87450i
$346$	4.39331	−	0.933826i	0.236186	−	0.0502028i
$347$	8.77084	+	9.74101i	0.470843	+	0.522925i	0.931052	−	0.364886i	$-0.118892\pi$
$347$	8.77084	+	9.74101i	0.470843	+	0.522925i	−0.460209	+	0.887811i	$0.652225\pi$
$348$	−18.2219	−	8.11293i	−0.976798	−	0.434899i
$349$	−4.91560	−	3.57139i	−0.263126	−	0.191172i	0.448398	−	0.893834i	$-0.351995\pi$
$349$	−4.91560	−	3.57139i	−0.263126	−	0.191172i	−0.711524	+	0.702662i	$0.751995\pi$
$350$	0.182103	+	0.560455i	0.00973381	+	0.0299576i
$351$	−3.18801	−	5.52179i	−0.170163	−	0.294731i
$352$	−2.77597	+	1.81494i	−0.147960	+	0.0967367i
$353$	2.23793			0.119113			0.0595565	−	0.998225i	$-0.481031\pi$
$353$	2.23793			0.119113			0.0595565	+	0.998225i	$0.481031\pi$
$354$	6.72002	+	20.6821i	0.357165	+	1.09924i
$355$	1.64532	−	15.6542i	0.0873247	−	0.830839i
$356$	−1.23548	−	11.7548i	−0.0654801	−	0.623001i
$357$	−16.2342	+	3.45069i	−0.859206	+	0.182630i
$358$	4.43629	+	4.92700i	0.234465	+	0.260400i
$359$	−0.248087	−	2.36039i	−0.0130935	−	0.124576i	0.986023	−	0.166611i	$-0.0532826\pi$
$359$	−0.248087	−	2.36039i	−0.0130935	−	0.124576i	−0.999116	+	0.0420350i	$0.986616\pi$
$360$	−10.7504	−	7.81061i	−0.566595	−	0.411655i
$361$	7.04104	−	17.6472i	0.370581	−	0.928800i
$362$	7.02029			0.368978
$363$	−28.1520	+	16.4861i	−1.47760	+	0.865296i
$364$	−0.884578	+	1.53213i	−0.0463645	+	0.0803056i
$365$	−17.3691	+	19.2904i	−0.909142	+	1.00970i
$366$	23.8973	−	10.6398i	1.24913	−	0.556150i
$367$	11.7601	+	5.23594i	0.613873	+	0.273314i	0.690028	−	0.723782i	$-0.257598\pi$
$367$	11.7601	+	5.23594i	0.613873	+	0.273314i	−0.0761559	+	0.997096i	$0.524265\pi$
$368$	−1.59106	+	4.89678i	−0.0829397	+	0.255262i
$369$	6.78305	−	20.8761i	0.353112	−	1.08677i
$370$	14.2795	+	6.35764i	0.742355	+	0.330518i
$371$	2.01194	−	19.1423i	0.104455	−	0.993820i
$372$	4.80800	+	14.7975i	0.249283	+	0.767215i
$373$	−5.89593			−0.305280			−0.152640	−	0.988282i	$-0.548777\pi$
$373$	−5.89593			−0.305280			−0.152640	+	0.988282i	$0.548777\pi$
$374$	−6.75129	+	4.41402i	−0.349101	+	0.228244i
$375$	16.1280	−	27.9346i	0.832848	−	1.44254i
$376$	−6.75560	+	7.50285i	−0.348394	+	0.386930i
$377$	−4.72396	+	2.10324i	−0.243296	+	0.108322i
$378$	−1.99452	−	18.9766i	−0.102587	−	0.976050i
$379$	10.4954	−	32.3016i	0.539114	−	1.65922i	−0.195474	−	0.980709i	$-0.562625\pi$
$379$	10.4954	−	32.3016i	0.539114	−	1.65922i	0.734588	−	0.678513i	$-0.237375\pi$
$380$	7.88815	+	6.13540i	0.404654	+	0.314739i
$381$	50.9039	−	36.9839i	2.60789	−	1.89474i
$382$	−8.54788	+	3.80576i	−0.437347	+	0.194720i
$383$	27.0662	+	5.75310i	1.38302	+	0.293970i	0.838556	−	0.544815i	$-0.183400\pi$
$383$	27.0662	+	5.75310i	1.38302	+	0.293970i	0.544463	+	0.838785i	$0.316733\pi$
$384$	−1.48291	−	2.56847i	−0.0756744	−	0.131072i
$385$	−2.68362	+	17.2890i	−0.136770	+	0.881127i
$386$	0.912065	+	1.57974i	0.0464229	+	0.0804068i
$387$	15.8083	+	48.6530i	0.803582	+	2.47317i
$388$	−10.7238	−	7.79130i	−0.544419	−	0.395544i
$389$	−29.2698	−	13.0318i	−1.48404	−	0.660736i	−0.504761	−	0.863259i	$-0.668419\pi$
$389$	−29.2698	−	13.0318i	−1.48404	−	0.660736i	−0.979278	+	0.202523i	$0.935086\pi$
$390$	−5.11372	+	1.08695i	−0.258943	+	0.0550401i
$391$	−3.86953	+	11.9092i	−0.195691	+	0.602274i
$392$	1.37982	−	1.00250i	0.0696916	−	0.0506339i
$393$	−3.32656	+	31.6501i	−0.167803	+	1.59654i
$394$	−6.90154	−	1.46697i	−0.347695	−	0.0739048i
$395$	−10.4416	−	18.0854i	−0.525373	−	0.909973i
$396$	−8.78007	−	17.1012i	−0.441215	−	0.859366i
$397$	−7.13212	+	12.3532i	−0.357951	+	0.619989i	−0.987618	−	0.156876i	$-0.949858\pi$
$397$	−7.13212	+	12.3532i	−0.357951	+	0.619989i	0.629668	+	0.776865i	$0.283191\pi$
$398$	3.82150	+	11.7614i	0.191555	+	0.589544i
$399$	2.13934	+	29.6692i	0.107101	+	1.48532i
$400$	−0.207196	+	0.150537i	−0.0103598	+	0.00752685i
$401$	6.50590	+	7.22554i	0.324889	+	0.360826i	0.883358	−	0.468700i	$-0.155277\pi$
$401$	6.50590	+	7.22554i	0.324889	+	0.360826i	−0.558468	+	0.829526i	$0.688611\pi$
$402$	12.2506	+	13.6056i	0.611003	+	0.678588i
$403$	3.68488	+	1.64062i	0.183557	+	0.0817249i
$404$	−9.35701	+	4.16601i	−0.465528	+	0.207267i
$405$	11.0549	−	12.2777i	0.549321	−	0.610083i
$406$	−15.4750			−0.768010
$407$	14.2846	+	17.5291i	0.708062	+	0.868886i
$408$	−3.60651	−	6.24665i	−0.178549	−	0.309255i
$409$	11.1616	−	12.3962i	0.551905	−	0.612952i	−0.401053	−	0.916055i	$-0.631356\pi$
$409$	11.1616	−	12.3962i	0.551905	−	0.612952i	0.952958	+	0.303103i	$0.0980225\pi$
$410$	−7.02423	−	5.10340i	−0.346902	−	0.252039i
$411$	4.39973	−	3.19659i	0.217023	−	0.157676i
$412$	−7.53427	+	1.60146i	−0.371187	+	0.0788982i
$413$	11.2892	+	12.5380i	0.555507	+	0.616953i
$414$	−27.2627	−	12.1381i	−1.33989	−	0.596556i
$415$	26.7786	−	11.9226i	1.31451	−	0.585257i
$416$	−0.752073	−	0.159858i	−0.0368734	−	0.00783769i
$417$	24.1508			1.18267
$418$	6.17850	+	13.0700i	0.302200	+	0.639277i
$419$	3.01107			0.147101			0.0735503	−	0.997292i	$-0.476567\pi$
$419$	3.01107			0.147101			0.0735503	+	0.997292i	$0.476567\pi$
$420$	−15.3035	−	3.25286i	−0.746735	−	0.158723i
$421$	19.8375	−	8.83222i	0.966821	−	0.430456i	0.138285	−	0.990392i	$-0.455841\pi$
$421$	19.8375	−	8.83222i	0.966821	−	0.430456i	0.828536	+	0.559936i	$0.189174\pi$
$422$	−22.5344	−	10.0330i	−1.09696	−	0.488397i
$423$	−39.1560	−	43.4871i	−1.90383	−	2.11442i
$424$	8.18229	−	1.73920i	0.397367	−	0.0844630i
$425$	−0.503912	+	0.366113i	−0.0244433	+	0.0177591i
$426$	16.4735	+	11.9687i	0.798145	+	0.579886i
$427$	13.5799	−	15.0820i	0.657176	−	0.729868i
$428$	2.41457	+	4.18215i	0.116712	+	0.202152i
$429$	−7.31135	−	1.93490i	−0.352995	−	0.0934179i
$430$	20.2349			0.975815
$431$	−19.8512	+	22.0470i	−0.956197	+	1.06196i	0.0418265	+	0.999125i	$0.486682\pi$
$431$	−19.8512	+	22.0470i	−0.956197	+	1.06196i	−0.998024	+	0.0628397i	$0.979984\pi$
$432$	7.57572	−	3.37293i	0.364487	−	0.162280i
$433$	−5.61024	−	2.49784i	−0.269611	−	0.120039i	0.267478	−	0.963564i	$-0.413810\pi$
$433$	−5.61024	−	2.49784i	−0.269611	−	0.120039i	−0.537090	+	0.843525i	$0.680476\pi$
$434$	8.07716	+	8.97060i	0.387716	+	0.430602i
$435$	−30.5990	−	33.9837i	−1.46711	−	1.62939i
$436$	0.183007	−	0.132963i	0.00876447	−	0.00636776i
$437$	20.1929	+	9.79459i	0.965958	+	0.468539i
$438$	−10.3768	−	31.9364i	−0.495821	−	1.52598i
$439$	5.93467	−	10.2792i	0.283246	−	0.490597i	−0.688936	−	0.724822i	$-0.741922\pi$
$439$	5.93467	−	10.2792i	0.283246	−	0.490597i	0.972182	+	0.234225i	$0.0752553\pi$
$440$	−7.50644	+	1.21267i	−0.357855	+	0.0578116i
$441$	4.94277	+	8.56112i	0.235370	+	0.407673i
$442$	−1.82908	−	0.388783i	−0.0870004	−	0.0184925i
$443$	−4.21131	+	40.0679i	−0.200085	+	1.90368i	0.188178	+	0.982135i	$0.439742\pi$
$443$	−4.21131	+	40.0679i	−0.200085	+	1.90368i	−0.388263	+	0.921549i	$0.626925\pi$
$444$	−16.3588	+	11.8854i	−0.776356	+	0.564056i
$445$	8.37364	−	25.7714i	0.396949	−	1.22168i
$446$	−16.3770	+	3.48103i	−0.775472	+	0.164832i
$447$	−3.98797	−	1.77556i	−0.188625	−	0.0839811i
$448$	−1.86152	−	1.35247i	−0.0879486	−	0.0638984i
$449$	1.17453	+	3.61482i	0.0554293	+	0.170594i	0.974938	−	0.222475i	$-0.0714135\pi$
$449$	1.17453	+	3.61482i	0.0554293	+	0.170594i	−0.919509	+	0.393069i	$0.871413\pi$
$450$	−0.742213	−	1.28555i	−0.0349882	−	0.0606014i
$451$	−5.73684	−	11.1738i	−0.270137	−	0.526153i
$452$	−1.23503	−	2.13914i	−0.0580910	−	0.100617i
$453$	42.9163	+	9.12213i	2.01638	+	0.428595i
$454$	−7.30360	+	3.25177i	−0.342775	+	0.152613i
$455$	−3.28137	+	2.38406i	−0.153833	+	0.111766i
$456$	−11.9758	+	4.86879i	−0.560819	+	0.228002i
$457$	−9.30353	+	28.6333i	−0.435201	+	1.33941i	0.457680	+	0.889117i	$0.348681\pi$
$457$	−9.30353	+	28.6333i	−0.435201	+	1.33941i	−0.892881	+	0.450293i	$0.851319\pi$
$458$	−2.27035	−	21.6010i	−0.106087	−	1.00935i
$459$	18.4245	−	8.20312i	0.859983	−	0.382889i
$460$	−7.89854	+	8.77222i	−0.368271	+	0.409007i
$461$	8.43933	−	14.6173i	0.393059	−	0.680798i	−0.599793	−	0.800156i	$-0.704750\pi$
$461$	8.43933	−	14.6173i	0.393059	−	0.680798i	0.992851	+	0.119358i	$0.0380835\pi$
$462$	−17.6334	−	14.1893i	−0.820379	−	0.660148i
$463$	24.8932			1.15689			0.578443	−	0.815723i	$-0.303660\pi$
$463$	24.8932			1.15689			0.578443	+	0.815723i	$0.303660\pi$
$464$	−2.07827	−	6.39626i	−0.0964813	−	0.296939i
$465$	−3.72863	+	35.4755i	−0.172911	+	1.64514i
$466$	−17.5411	−	7.80981i	−0.812577	−	0.361783i
$467$	11.8297	−	36.4081i	0.547414	−	1.68477i	−0.167768	−	0.985827i	$-0.553656\pi$
$467$	11.8297	−	36.4081i	0.547414	−	1.68477i	0.715181	−	0.698939i	$-0.246344\pi$
$468$	1.37712	−	4.23834i	0.0636575	−	0.195918i
$469$	12.9760	+	5.77730i	0.599177	+	0.266771i
$470$	−21.1454	+	9.41453i	−0.975363	+	0.434260i
$471$	34.7222	−	38.5629i	1.59991	−	1.77688i
$472$	−3.66618	+	6.35001i	−0.168750	+	0.292283i
$473$	26.1232	+	13.2090i	1.20115	+	0.607353i
$474$	27.0152			1.24085
$475$	0.526232	+	0.984541i	0.0241452	+	0.0451739i
$476$	−4.52731	−	3.28928i	−0.207509	−	0.150764i
$477$	5.06803	+	48.2191i	0.232049	+	2.20780i
$478$	−0.305108	−	0.338856i	−0.0139553	−	0.0154989i
$479$	5.93580	−	1.26169i	0.271214	−	0.0576482i	−0.0702972	−	0.997526i	$-0.522395\pi$
$479$	5.93580	−	1.26169i	0.271214	−	0.0576482i	0.341511	+	0.939878i	$0.389061\pi$
$480$	−0.710741	−	6.76225i	−0.0324407	−	0.308653i
$481$	−0.547950	+	5.21339i	−0.0249844	+	0.237710i
$482$	6.70120	+	20.6242i	0.305231	+	0.939405i
$483$	−35.1365			−1.59877
$484$	−10.4824	−	3.33454i	−0.476473	−	0.151570i
$485$	−15.1948	−	26.3181i	−0.689958	−	1.19504i
$486$	−1.08325	−	3.33390i	−0.0491372	−	0.151229i
$487$	0.663233	+	0.481867i	0.0300540	+	0.0218355i	0.602711	−	0.797960i	$-0.294087\pi$
$487$	0.663233	+	0.481867i	0.0300540	+	0.0218355i	−0.572657	+	0.819795i	$0.694087\pi$
$488$	8.05758	+	3.58747i	0.364750	+	0.162397i
$489$	43.3917	+	48.1914i	1.96224	+	2.17929i
$490$	3.82475	−	0.812975i	0.172784	−	0.0367265i
$491$	4.00442	+	38.0995i	0.180717	+	1.71941i	0.590341	+	0.807154i	$0.298993\pi$
$491$	4.00442	+	38.0995i	0.180717	+	1.71941i	−0.409624	+	0.912254i	$0.634340\pi$
$492$	10.2609	−	4.56843i	0.462595	−	0.205961i
$493$	−5.05446	−	15.5560i	−0.227641	−	0.700608i
$494$	−1.13943	+	3.15181i	−0.0512654	+	0.141807i
$495$	−2.44239	−	44.0043i	−0.109777	−	1.97784i
$496$	−2.62306	+	4.54327i	−0.117779	+	0.203999i
$497$	15.4525	+	3.28453i	0.693140	+	0.147331i
$498$	−3.96373	+	37.7124i	−0.177619	+	1.68993i
$499$	−0.897642	−	8.54050i	−0.0401840	−	0.382325i	−0.996069	−	0.0885833i	$-0.971766\pi$
$499$	−0.897642	−	8.54050i	−0.0401840	−	0.382325i	0.955885	−	0.293742i	$-0.0949006\pi$
$500$	10.6383	−	2.26124i	0.475758	−	0.101126i
$501$	12.9295	−	39.7928i	0.577646	−	1.77781i
$502$	11.2572	−	8.17884i	0.502434	−	0.365040i
$503$	−2.10918	+	20.0675i	−0.0940436	+	0.894765i	0.841191	+	0.540738i	$0.181855\pi$
$503$	−2.10918	+	20.0675i	−0.0940436	+	0.894765i	−0.935235	+	0.354028i	$0.884812\pi$
$504$	8.92391	−	9.91101i	0.397503	−	0.441471i
$505$	−23.4822			−1.04494
$506$	−15.9234	+	6.16887i	−0.707880	+	0.274240i
$507$	18.4012	+	31.8718i	0.817225	+	1.41547i
$508$	20.7517	+	4.41091i	0.920707	+	0.195702i
$509$	4.47070	−	42.5359i	0.198160	−	1.88537i	−0.217811	−	0.975991i	$-0.569892\pi$
$509$	4.47070	−	42.5359i	0.198160	−	1.88537i	0.415971	−	0.909378i	$-0.363442\pi$
$510$	−1.72856	−	16.4461i	−0.0765418	−	0.728246i
$511$	−17.4324	−	19.3606i	−0.771162	−	0.856462i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−10.0388	−	34.7249i	−0.443222	−	1.53314i
$514$	−17.4597	−	12.6852i	−0.770115	−	0.559521i
$515$	−17.2732	−	3.67153i	−0.761149	−	0.161787i
$516$	−13.0883	+	22.6696i	−0.576181	+	0.997975i
$517$	−33.4443	−	1.64924i	−1.47088	−	0.0725335i
$518$	−7.84387	+	13.5860i	−0.344640	+	0.596934i
$519$	−8.91338	+	9.89931i	−0.391254	+	0.434532i
$520$	−1.42609	−	1.03611i	−0.0625380	−	0.0454365i
$521$	14.8738	−	10.8064i	0.651633	−	0.473439i	−0.212194	−	0.977227i	$-0.568061\pi$
$521$	14.8738	−	10.8064i	0.651633	−	0.473439i	0.863827	+	0.503789i	$0.168061\pi$
$522$	38.1293	−	8.10462i	1.66887	−	0.354730i
$523$	−14.1811	+	3.01429i	−0.620097	+	0.131806i	−0.507239	−	0.861805i	$-0.669334\pi$
$523$	−14.1811	+	3.01429i	−0.620097	+	0.131806i	−0.112858	+	0.993611i	$0.536001\pi$
$524$	−8.68108	+	6.30718i	−0.379235	+	0.275530i
$525$	−1.41396	−	1.02730i	−0.0617102	−	0.0448351i
$526$	−18.5983	+	20.6555i	−0.810922	+	0.900621i
$527$	−6.37940	+	11.0495i	−0.277891	+	0.481322i
$528$	3.49673	−	9.19401i	0.152175	−	0.400118i
$529$	−1.75494	+	3.03965i	−0.0763017	+	0.132158i
$530$	18.7589	+	3.98732i	0.814834	+	0.173198i
$531$	−34.3823	−	24.9802i	−1.49207	−	1.08405i
$532$	−6.95154	+	7.22984i	−0.301387	+	0.313453i
$533$	0.899802	−	2.76931i	0.0389747	−	0.119952i
$534$	23.4561	+	26.0506i	1.01504	+	1.12732i
$535$	1.15727	+	11.0107i	0.0500333	+	0.476035i
$536$	−0.645261	+	6.13925i	−0.0278710	+	0.265175i
$537$	−19.2335	−	4.08821i	−0.829987	−	0.176419i
$538$	−8.26709	−	14.3190i	−0.356420	−	0.617337i
$539$	5.46844	+	1.44719i	0.235542	+	0.0623347i
$540$	19.0119			0.818142
$541$	−16.7167	+	18.5658i	−0.718708	+	0.798206i	−0.986236	−	0.165344i	$-0.947127\pi$
$541$	−16.7167	+	18.5658i	−0.718708	+	0.798206i	0.267528	+	0.963550i	$0.413793\pi$
$542$	−0.630017	+	5.99421i	−0.0270616	+	0.257474i
$543$	−16.8445	+	12.2382i	−0.722865	+	0.525192i
$544$	0.751544	−	2.31302i	0.0322222	−	0.0991697i
$545$	0.507280	−	0.107826i	0.0217295	−	0.00461874i
$546$	−0.548460	−	5.21825i	−0.0234719	−	0.223320i
$547$	−1.92603	+	18.3250i	−0.0823513	+	0.783520i	0.872935	+	0.487837i	$0.162214\pi$
$547$	−1.92603	+	18.3250i	−0.0823513	+	0.783520i	−0.955286	+	0.295683i	$0.904453\pi$
$548$	1.79361	+	0.381244i	0.0766193	+	0.0162859i
$549$	−25.5610	+	44.2730i	−1.09092	+	1.88953i
$550$	−0.821148	−	0.217312i	−0.0350139	−	0.00926620i
$551$	−28.8590	+	5.15318i	−1.22943	+	0.219533i
$552$	−4.71879	−	14.5229i	−0.200845	−	0.618138i
$553$	19.1472	−	8.52487i	0.814221	−	0.362514i
$554$	2.43597	+	23.1767i	0.103495	+	0.984685i
$555$	−45.3452	+	9.63842i	−1.92480	+	0.409128i
$556$	5.44876	+	6.05146i	0.231079	+	0.256639i
$557$	−4.35753	−	1.94010i	−0.184634	−	0.0822045i	0.312337	−	0.949971i	$-0.398888\pi$
$557$	−4.35753	−	1.94010i	−0.184634	−	0.0822045i	−0.496972	+	0.867767i	$0.665555\pi$
$558$	−24.5997	−	17.8727i	−1.04139	−	0.756612i
$559$	2.09704	+	6.45404i	0.0886955	+	0.272977i
$560$	−2.63762	−	4.56849i	−0.111460	−	0.193054i
$561$	8.50421	−	22.3603i	0.359048	−	0.944052i
$562$	−1.86955			−0.0788620
$563$	−8.18466	−	25.1898i	−0.344942	−	1.06162i	−0.961615	−	0.274403i	$-0.911520\pi$
$563$	−8.18466	−	25.1898i	−0.344942	−	1.06162i	0.616673	−	0.787220i	$-0.288480\pi$
$564$	3.12991	−	29.7791i	0.131793	−	1.25393i
$565$	−0.591936	−	5.63190i	−0.0249029	−	0.236936i
$566$	26.4041	−	5.61237i	1.10985	−	0.235905i
$567$	11.0951	+	12.3224i	0.465951	+	0.517491i
$568$	0.717660	+	6.82808i	0.0301124	+	0.286500i
$569$	−16.6551	−	12.1006i	−0.698218	−	0.507285i	0.181133	−	0.983459i	$-0.442023\pi$
$569$	−16.6551	−	12.1006i	−0.698218	−	0.507285i	−0.879351	+	0.476174i	$0.842023\pi$
$570$	−29.6224	−	0.970118i	−1.24075	−	0.0406338i
$571$	−14.8814			−0.622769			−0.311385	−	0.950284i	$-0.600793\pi$
$571$	−14.8814			−0.622769			−0.311385	+	0.950284i	$0.600793\pi$
$572$	−1.16472	−	2.26855i	−0.0486992	−	0.0948526i
$573$	13.8753	−	24.0327i	0.579649	−	1.00398i
$574$	5.83082	−	6.47578i	0.243374	−	0.270294i
$575$	−1.20464	+	0.536342i	−0.0502371	+	0.0223670i
$576$	5.29498	+	2.35748i	0.220624	+	0.0982282i
$577$	−14.7169	+	45.2940i	−0.612673	+	1.88561i	−0.181340	+	0.983420i	$0.558043\pi$
$577$	−14.7169	+	45.2940i	−0.612673	+	1.88561i	−0.431333	+	0.902193i	$0.641957\pi$
$578$	−3.42550	+	10.5426i	−0.142482	+	0.438514i
$579$	−4.94232	−	2.20046i	−0.205396	−	0.0914480i
$580$	1.61171	−	15.3344i	0.0669226	−	0.636726i
$581$	9.09113	+	27.9796i	0.377164	+	1.16079i
$582$	39.3130			1.62958
$583$	21.6148	+	17.3931i	0.895194	+	0.720350i
$584$	5.66115	−	9.80541i	0.234260	−	0.405751i
$585$	6.83649	−	7.59269i	0.282654	−	0.313919i
$586$	−4.80608	+	2.13981i	−0.198537	+	0.0883946i
$587$	−1.41982	−	13.5087i	−0.0586022	−	0.557563i	−0.983950	−	0.178444i	$-0.942894\pi$
$587$	−1.41982	−	13.5087i	−0.0586022	−	0.557563i	0.925348	−	0.379119i	$-0.123773\pi$
$588$	−1.56312	+	4.81080i	−0.0644621	+	0.198394i
$589$	18.0502	+	14.0394i	0.743744	+	0.578483i
$590$	−13.5998	+	9.88085i	−0.559896	+	0.406788i
$591$	19.1168	−	8.51137i	0.786362	−	0.350111i
$592$	−6.66891	−	1.41752i	−0.274090	−	0.0582597i
$593$	−3.19962	−	5.54191i	−0.131393	−	0.227579i	0.792821	−	0.609455i	$-0.208612\pi$
$593$	−3.19962	−	5.54191i	−0.131393	−	0.227579i	−0.924214	+	0.381876i	$0.875278\pi$
$594$	24.5443	+	12.4107i	1.00707	+	0.509216i
$595$	−6.41482	−	11.1108i	−0.262982	−	0.455498i
$596$	−0.454842	−	1.39986i	−0.0186310	−	0.0573404i
$597$	−29.6725	−	21.5583i	−1.21441	−	0.882323i
$598$	−3.61651	−	1.61017i	−0.147890	−	0.0658449i
$599$	−5.43341	+	1.15491i	−0.222003	+	0.0471882i	−0.317570	−	0.948235i	$-0.602867\pi$
$599$	−5.43341	+	1.15491i	−0.222003	+	0.0471882i	0.0955671	+	0.995423i	$0.469534\pi$
$600$	0.234721	−	0.722396i	0.00958243	−	0.0294917i
$601$	37.4441	−	27.2048i	1.52738	−	1.10971i	0.569705	−	0.821849i	$-0.307058\pi$
$601$	37.4441	−	27.2048i	1.52738	−	1.10971i	0.957674	−	0.287856i	$-0.0929424\pi$
$602$	−2.12282	+	20.1973i	−0.0865199	+	0.823182i
$603$	−34.9977	−	7.43899i	−1.42522	−	0.302939i
$604$	7.39678	+	12.8116i	0.300971	+	0.521297i
$605$	−18.8451	−	16.7587i	−0.766161	−	0.681337i
$606$	15.1887	−	26.3076i	0.617000	−	1.06867i
$607$	−9.12971	−	28.0983i	−0.370563	−	1.14048i	−0.946423	−	0.322928i	$-0.895333\pi$
$607$	−9.12971	−	28.0983i	−0.370563	−	1.14048i	0.575860	−	0.817548i	$-0.304667\pi$
$608$	−3.92189	−	1.90231i	−0.159054	−	0.0771490i
$609$	37.1306	−	26.9770i	1.50461	−	1.09316i
$610$	13.5306	+	15.0273i	0.547839	+	0.608436i
$611$	−5.19421	−	5.76876i	−0.210135	−	0.233379i
$612$	12.8776	+	5.73350i	0.520548	+	0.231763i
$613$	7.16897	−	3.19183i	0.289552	−	0.128917i	−0.256821	−	0.966459i	$-0.582675\pi$
$613$	7.16897	−	3.19183i	0.289552	−	0.128917i	0.546372	+	0.837542i	$0.316008\pi$
$614$	0.0860487	−	0.0955667i	0.00347264	−	0.00385676i
$615$	25.7505			1.03836
$616$	−0.422921	−	7.61971i	−0.0170400	−	0.307007i
$617$	−10.0896	−	17.4756i	−0.406191	−	0.703543i	0.588269	−	0.808666i	$-0.299810\pi$
$617$	−10.0896	−	17.4756i	−0.406191	−	0.703543i	−0.994459	+	0.105123i	$0.966476\pi$
$618$	15.2859	−	16.9767i	0.614890	−	0.682905i
$619$	18.9228	+	13.7482i	0.760571	+	0.552587i	0.899085	−	0.437774i	$-0.144233\pi$
$619$	18.9228	+	13.7482i	0.760571	+	0.552587i	−0.138515	+	0.990360i	$0.544233\pi$
$620$	−9.73033	+	7.06950i	−0.390779	+	0.283918i
$621$	41.7640	−	8.87721i	1.67593	−	0.356230i
$622$	15.0547	+	16.7200i	0.603639	+	0.670409i
$623$	24.8451	+	11.0617i	0.995396	+	0.443179i
$624$	2.08320	−	0.927499i	0.0833947	−	0.0371297i
$625$	25.6421	+	5.45039i	1.02568	+	0.218016i
$626$	12.6875			0.507096
$627$	−37.6092	−	20.5895i	−1.50197	−	0.822265i
$628$	17.4965			0.698187
$629$	−16.2191	−	3.44748i	−0.646698	−	0.137460i
$630$	27.9323	−	12.4363i	1.11285	−	0.495472i
$631$	−20.3223	−	9.04808i	−0.809019	−	0.360198i	−0.0398192	−	0.999207i	$-0.512678\pi$
$631$	−20.3223	−	9.04808i	−0.809019	−	0.360198i	−0.769200	+	0.639008i	$0.779345\pi$
$632$	6.09502	+	6.76921i	0.242447	+	0.269265i
$633$	71.5591	−	15.2104i	2.84422	−	0.604558i
$634$	25.6781	−	18.6562i	1.01981	−	0.740932i
$635$	39.3495	+	28.5891i	1.56154	+	1.13452i
$636$	−16.6007	+	18.4369i	−0.658259	+	0.731071i
$637$	0.655680	+	1.13567i	0.0259790	+	0.0449969i
$638$	12.0908	−	18.7446i	0.478678	−	0.742104i
$639$	−39.7941			−1.57423
$640$	1.53406	−	1.70375i	0.0606391	−	0.0673466i
$641$	−4.24001	+	1.88777i	−0.167470	+	0.0745626i	−0.488760	−	0.872418i	$-0.662550\pi$
$641$	−4.24001	+	1.88777i	−0.167470	+	0.0745626i	0.321289	+	0.946981i	$0.395884\pi$
$642$	−13.0841	−	5.82542i	−0.516388	−	0.229911i
$643$	−12.8340	−	14.2536i	−0.506123	−	0.562107i	0.434887	−	0.900485i	$-0.356788\pi$
$643$	−12.8340	−	14.2536i	−0.506123	−	0.562107i	−0.941010	+	0.338378i	$0.890122\pi$
$644$	−7.92729	−	8.80415i	−0.312379	−	0.346932i
$645$	−48.5516	+	35.2748i	−1.91172	+	1.38894i
$646$	−9.53822	−	4.62652i	−0.375276	−	0.182028i
$647$	3.98051	+	12.2507i	0.156490	+	0.481626i	0.998309	−	0.0581337i	$-0.0185150\pi$
$647$	3.98051	+	12.2507i	0.156490	+	0.481626i	−0.841819	+	0.539760i	$0.818515\pi$
$648$	−3.60314	+	6.24081i	−0.141545	+	0.245162i
$649$	−24.0074	+	3.87840i	−0.942374	+	0.152241i
$650$	−0.0984578	−	0.170534i	−0.00386183	−	0.00668889i
$651$	−35.0184	−	7.44340i	−1.37248	−	0.291730i
$652$	−2.28552	+	21.7453i	−0.0895080	+	0.851612i
$653$	−25.3125	+	18.3906i	−0.990554	+	0.719679i	−0.960042	−	0.279855i	$-0.909714\pi$
$653$	−25.3125	+	18.3906i	−0.990554	+	0.719679i	−0.0305113	+	0.999534i	$0.509714\pi$
$654$	−0.207318	+	0.638061i	−0.00810679	+	0.0249501i
$655$	−24.0632	+	5.11478i	−0.940226	+	0.199851i
$656$	3.45970	+	1.54036i	0.135079	+	0.0601409i
$657$	53.0917	+	38.5734i	2.07131	+	1.50489i
$658$	−7.17870	−	22.0938i	−0.279855	−	0.861304i
$659$	−4.10795	−	7.11517i	−0.160023	−	0.277168i	0.774854	−	0.632141i	$-0.217823\pi$
$659$	−4.10795	−	7.11517i	−0.160023	−	0.277168i	−0.934877	+	0.354973i	$0.884490\pi$
$660$	15.8969	−	15.9954i	0.618787	−	0.622619i
$661$	6.98955	+	12.1063i	0.271862	+	0.470879i	0.969339	−	0.245729i	$-0.0790272\pi$
$661$	6.98955	+	12.1063i	0.271862	+	0.470879i	−0.697477	+	0.716608i	$0.745694\pi$
$662$	6.67950	+	1.41977i	0.259606	+	0.0551810i
$663$	5.06644	−	2.25572i	0.196764	−	0.0876051i
$664$	−10.3439	+	7.51526i	−0.401420	+	0.291649i
$665$	−21.3012	+	8.66001i	−0.826024	+	0.335821i
$666$	12.2114	−	37.5829i	0.473184	−	1.45631i
$667$	−3.61958	−	34.4380i	−0.140151	−	1.33345i
$668$	12.8880	−	5.73809i	0.498650	−	0.222013i
$669$	33.2265	−	36.9018i	1.28461	−	1.42670i
$670$	−7.07625	+	12.2564i	−0.273379	+	0.473507i
$671$	7.65842	+	28.2328i	0.295650	+	1.08991i
$672$	6.82425			0.263251
$673$	10.8864	+	33.5047i	0.419638	+	1.29151i	0.908036	+	0.418892i	$0.137581\pi$
$673$	10.8864	+	33.5047i	0.419638	+	1.29151i	−0.488398	+	0.872621i	$0.662419\pi$
$674$	−0.264631	+	2.51780i	−0.0101932	+	0.0969820i
$675$	1.94021	+	0.863836i	0.0746786	+	0.0332491i
$676$	−3.83454	+	11.8015i	−0.147482	+	0.453904i
$677$	−2.52519	+	7.77172i	−0.0970508	+	0.298692i	−0.987783	−	0.155837i	$-0.950192\pi$
$677$	−2.52519	+	7.77172i	−0.0970508	+	0.298692i	0.890732	+	0.454529i	$0.150192\pi$
$678$	6.69242	+	2.97966i	0.257021	+	0.114433i
$679$	27.8633	−	12.4055i	1.06929	−	0.476080i
$680$	3.73092	−	4.14360i	0.143074	−	0.158900i
$681$	11.8555	−	20.5344i	0.454305	−	0.786879i
$682$	−17.1767	+	2.77490i	−0.657730	+	0.106256i
$683$	−40.5702			−1.55238			−0.776188	−	0.630502i	$-0.782849\pi$
$683$	−40.5702			−1.55238			−0.776188	+	0.630502i	$0.782849\pi$
$684$	13.3417	−	21.4545i	0.510131	−	0.820334i
$685$	3.40105	+	2.47101i	0.129948	+	0.0944125i
$686$	2.09383	+	19.9215i	0.0799428	+	0.760605i
$687$	43.1037	+	47.8715i	1.64451	+	1.82641i
$688$	−8.63324	+	1.83505i	−0.329139	+	0.0699607i
$689$	0.672296	+	6.39647i	0.0256124	+	0.243686i
$690$	3.65944	−	34.8173i	0.139313	−	1.32547i
$691$	15.6243	+	48.0865i	0.594375	+	1.82930i	0.557813	+	0.829967i	$0.311641\pi$
$691$	15.6243	+	48.0865i	0.594375	+	1.82930i	0.0365624	+	0.999331i	$0.488359\pi$
$692$	−4.49146			−0.170740
$693$	44.1787	+	2.17859i	1.67821	+	0.0827577i
$694$	−6.55391	−	11.3517i	−0.248783	−	0.430905i
$695$	5.76901	+	17.7552i	0.218831	+	0.673493i
$696$	16.1370	+	11.7242i	0.611670	+	0.444405i
$697$	8.41417	+	3.74623i	0.318709	+	0.141899i
$698$	4.06565	+	4.51536i	0.153887	+	0.170909i
$699$	55.7027	−	11.8400i	2.10687	−	0.447829i
$700$	−0.0615983	−	0.586069i	−0.00232820	−	0.0221513i
$701$	3.72726	−	1.65948i	0.140776	−	0.0626777i	−0.335139	−	0.942169i	$-0.608783\pi$
$701$	3.72726	−	1.65948i	0.140776	−	0.0626777i	0.475916	+	0.879491i	$0.342117\pi$
$702$	1.97030	+	6.06395i	0.0743641	+	0.228869i
$703$	−10.1037	+	27.9482i	−0.381070	+	1.05409i
$704$	3.09265	−	1.19812i	0.116559	−	0.0451560i
$705$	34.3241	−	59.4512i	1.29272	−	2.23906i
$706$	−2.18903	−	0.465292i	−0.0823851	−	0.0175115i
$707$	2.46349	−	23.4386i	0.0926492	−	0.881498i
$708$	−2.27312	−	21.6273i	−0.0854291	−	0.812804i
$709$	−7.78923	+	1.65565i	−0.292531	+	0.0621793i	−0.351839	−	0.936060i	$-0.614444\pi$
$709$	−7.78923	+	1.65565i	−0.292531	+	0.0621793i	0.0593087	+	0.998240i	$0.481110\pi$
$710$	−4.86406	+	14.9700i	−0.182545	+	0.561815i
$711$	−42.7126	+	31.0325i	−1.60185	+	1.16381i
$712$	−1.23548	+	11.7548i	−0.0463014	+	0.440529i
$713$	−18.0739	+	20.0731i	−0.676874	+	0.751745i
$714$	16.5969			0.621123
$715$	−0.323994	−	5.83736i	−0.0121167	−	0.218305i
$716$	−3.31497	−	5.74169i	−0.123886	−	0.214577i
$717$	1.32279	+	0.281168i	0.0494005	+	0.0105004i
$718$	−0.248087	+	2.36039i	−0.00925851	+	0.0880888i
$719$	2.67655	+	25.4657i	0.0998185	+	0.949710i	0.923744	+	0.383011i	$0.125113\pi$
$719$	2.67655	+	25.4657i	0.0998185	+	0.949710i	−0.823925	+	0.566699i	$0.808220\pi$
$720$	8.89154	+	9.87506i	0.331368	+	0.368022i
$721$	5.47683	−	16.8559i	0.203968	−	0.627748i
$722$	−10.5562	+	15.7977i	−0.392863	+	0.587928i
$723$	−52.0322	−	37.8036i	−1.93510	−	1.40593i
$724$	−6.86688	−	1.45960i	−0.255206	−	0.0542456i
$725$	0.861220	−	1.49168i	0.0319849	−	0.0553995i
$726$	30.9644	−	10.2727i	1.14920	−	0.381256i
$727$	7.68231	−	13.3062i	0.284921	−	0.493498i	−0.687669	−	0.726024i	$-0.741366\pi$
$727$	7.68231	−	13.3062i	0.284921	−	0.493498i	0.972590	+	0.232527i	$0.0746992\pi$
$728$	1.18380	−	1.31474i	0.0438744	−	0.0487275i
$729$	25.9010	+	18.8182i	0.959296	+	0.696970i
$730$	21.0003	−	15.2576i	0.777255	−	0.564709i
$731$	−20.9965	+	4.46294i	−0.776582	+	0.165068i
$732$	−25.5872	+	5.43873i	−0.945731	+	0.201021i
$733$	−17.9752	+	13.0597i	−0.663929	+	0.482373i	−0.867988	−	0.496586i	$-0.834587\pi$
$733$	−17.9752	+	13.0597i	−0.663929	+	0.482373i	0.204058	+	0.978959i	$0.434587\pi$
$734$	−10.4145	−	7.56658i	−0.384406	−	0.279288i
$735$	−7.75985	+	8.61819i	−0.286227	+	0.317887i
$736$	2.57439	−	4.45897i	0.0948932	−	0.164360i
$737$	−17.1362	+	11.2038i	−0.631221	+	0.412696i
$738$	−10.9752	+	19.0096i	−0.404003	+	0.699754i
$739$	−41.2504	−	8.76803i	−1.51742	−	0.322537i	−0.627486	−	0.778628i	$-0.715916\pi$
$739$	−41.2504	−	8.76803i	−1.51742	−	0.322537i	−0.889933	+	0.456091i	$0.849249\pi$
$740$	−12.6456	−	9.18758i	−0.464862	−	0.337742i
$741$	−2.76049	−	9.54877i	−0.101409	−	0.350783i
$742$	−5.94789	+	18.3057i	−0.218354	+	0.672024i
$743$	−2.39225	−	2.65686i	−0.0877631	−	0.0974708i	0.697664	−	0.716426i	$-0.254223\pi$
$743$	−2.39225	−	2.65686i	−0.0877631	−	0.0974708i	−0.785427	+	0.618955i	$0.787556\pi$
$744$	−1.62636	−	15.4738i	−0.0596253	−	0.567297i
$745$	0.352732	−	3.35602i	0.0129231	−	0.122955i
$746$	5.76709	+	1.22583i	0.211148	+	0.0448810i
$747$	−37.0535	−	64.1786i	−1.35572	−	2.34817i
$748$	7.52148	−	2.91390i	0.275013	−	0.106543i
$749$	−11.1117			−0.406012
$750$	−21.5835	+	23.9709i	−0.788119	+	0.875295i
$751$	−1.10023	+	10.4680i	−0.0401479	+	0.381982i	0.955936	+	0.293574i	$0.0948446\pi$
$751$	−1.10023	+	10.4680i	−0.0401479	+	0.381982i	−0.996084	+	0.0884081i	$0.971822\pi$
$752$	8.16791	−	5.93433i	0.297853	−	0.216403i
$753$	−12.7526	+	39.2486i	−0.464732	+	1.43030i
$754$	5.05802	−	1.07511i	0.184202	−	0.0391534i
$755$	3.54519	+	33.7302i	0.129023	+	1.22757i
$756$	−1.99452	+	18.9766i	−0.0725400	+	0.690172i
$757$	41.8219	+	8.88952i	1.52004	+	0.323095i	0.890902	−	0.454196i	$-0.150073\pi$
$757$	41.8219	+	8.88952i	1.52004	+	0.323095i	0.629141	+	0.777291i	$0.283407\pi$
$758$	−16.9820	+	29.4136i	−0.616813	+	1.06835i
$759$	27.4525	−	42.5602i	0.996463	−	1.54484i
$760$	−6.44016	−	7.64136i	−0.233609	−	0.277181i
$761$	−6.12820	−	18.8607i	−0.222147	−	0.683699i	−0.998569	−	0.0534848i	$-0.982967\pi$
$761$	−6.12820	−	18.8607i	−0.222147	−	0.683699i	0.776421	−	0.630214i	$-0.217033\pi$
$762$	−57.4809	+	25.5922i	−2.08231	+	0.927106i
$763$	0.0544071	+	0.517649i	0.00196967	+	0.0187402i
$764$	9.15235	−	1.94539i	0.331120	−	0.0703818i
$765$	21.6247	+	24.0166i	0.781842	+	0.868323i
$766$	−25.2786	−	11.2548i	−0.913354	−	0.406651i
$767$	−4.56097	−	3.31374i	−0.164687	−	0.119652i
$768$	0.916488	+	2.82066i	0.0330709	+	0.101782i
$769$	−6.09928	−	10.5643i	−0.219946	−	0.380957i	0.734845	−	0.678235i	$-0.237255\pi$
$769$	−6.09928	−	10.5643i	−0.219946	−	0.380957i	−0.954791	+	0.297278i	$0.903921\pi$
$770$	6.21956	−	16.3532i	0.224137	−	0.589328i
$771$	64.0064			2.30514
$772$	−0.563687	−	1.73485i	−0.0202875	−	0.0624386i
$773$	3.43119	−	32.6456i	0.123411	−	1.17418i	−0.741039	−	0.671462i	$-0.765667\pi$
$773$	3.43119	−	32.6456i	0.123411	−	1.17418i	0.864450	−	0.502718i	$-0.167667\pi$
$774$	−5.34734	−	50.8766i	−0.192206	−	1.82872i
$775$	−1.31422	+	0.279345i	−0.0472080	+	0.0100344i
$776$	8.86957	+	9.85065i	0.318399	+	0.353618i
$777$	−4.86339	−	46.2721i	−0.174473	−	1.66000i
$778$	25.9207	+	18.8325i	0.929303	+	0.675178i
$779$	8.71734	−	14.0182i	0.312331	−	0.502255i
$780$	5.22796			0.187191
$781$	−16.0517	+	16.1511i	−0.574375	+	0.577932i
$782$	6.26104	−	10.8444i	0.223894	−	0.387796i
$783$	−37.3185	+	41.4464i	−1.33365	+	1.48117i
$784$	−1.55810	+	0.693712i	−0.0556465	+	0.0247754i
$785$	36.6449	+	16.3154i	1.30791	+	0.582321i
$786$	9.83429	−	30.2668i	0.350778	−	1.07958i
$787$	−7.43859	+	22.8936i	−0.265157	+	0.816070i	0.726500	+	0.687166i	$0.241146\pi$
$787$	−7.43859	+	22.8936i	−0.265157	+	0.816070i	−0.991657	+	0.128903i	$0.958854\pi$
$788$	6.44573	+	2.86982i	0.229619	+	0.102233i
$789$	8.61669	−	81.9823i	0.306762	−	2.91865i
$790$	6.45326	+	19.8611i	0.229597	+	0.706626i
$791$	5.68353			0.202083
$792$	5.03268	+	18.5529i	0.178828	+	0.659250i
$793$	−3.39079	+	5.87301i	−0.120410	+	0.208557i
$794$	9.54464	−	10.6004i	0.338727	−	0.376194i
$795$	−51.9610	+	23.1345i	−1.84287	+	0.820496i
$796$	−1.29267	−	12.2989i	−0.0458173	−	0.435923i
$797$	−16.4163	+	50.5243i	−0.581496	+	1.78966i	0.0314101	+	0.999507i	$0.490000\pi$
$797$	−16.4163	+	50.5243i	−0.581496	+	1.78966i	−0.612907	+	0.790155i	$0.710000\pi$
$798$	4.07597	−	29.4656i	0.144288	−	1.04307i
$799$	19.8647	−	14.4326i	0.702764	−	0.510588i
$800$	0.233967	−	0.104169i	0.00827198	−	0.00368292i
$801$	−67.0098	−	14.2434i	−2.36767	−	0.503265i
$802$	−4.86146	−	8.42030i	−0.171664	−	0.297331i
$803$	37.0712	−	5.98886i	1.30821	−	0.211342i
$804$	−9.15410	−	15.8554i	−0.322840	−	0.559176i
$805$	−8.39322	−	25.8317i	−0.295822	−	0.910447i
$806$	−3.26326	−	2.37089i	−0.114943	−	0.0835112i
$807$	44.7979	+	19.9453i	1.57696	+	0.702108i
$808$	10.0187	−	2.12954i	0.352456	−	0.0749169i
$809$	12.7367	−	39.1994i	0.447797	−	1.37818i	−0.431590	−	0.902070i	$-0.642047\pi$
$809$	12.7367	−	39.1994i	0.447797	−	1.37818i	0.879387	−	0.476108i	$-0.157953\pi$
$810$	−13.3660	+	9.71095i	−0.469632	+	0.341208i
$811$	1.07140	−	10.1937i	0.0376221	−	0.357950i	−0.959474	−	0.281797i	$-0.909070\pi$
$811$	1.07140	−	10.1937i	0.0376221	−	0.357950i	0.997096	−	0.0761532i	$-0.0242638\pi$
$812$	15.1368	+	3.21743i	0.531198	+	0.112910i
$813$	−8.93784	−	15.4808i	−0.313464	−	0.542935i
$814$	−10.3280	−	20.1160i	−0.361995	−	0.705066i
$815$	−25.0642	+	43.4124i	−0.877960	+	1.52067i
$816$	2.22894	+	6.85998i	0.0780287	+	0.240147i
$817$	2.76691	+	38.3725i	0.0968019	+	1.34248i
$818$	−13.4950	+	9.80468i	−0.471841	+	0.342813i
$819$	6.86137	+	7.62033i	0.239756	+	0.266276i
$820$	5.80967	+	6.45230i	0.202883	+	0.225324i
$821$	42.1417	+	18.7627i	1.47075	+	0.654822i	0.976700	−	0.214609i	$-0.0688478\pi$
$821$	42.1417	+	18.7627i	1.47075	+	0.654822i	0.494054	+	0.869431i	$0.335514\pi$
$822$	−4.96819	+	2.21198i	−0.173286	+	0.0771517i
$823$	24.6417	−	27.3674i	0.858957	−	0.953969i	−0.140390	−	0.990096i	$-0.544836\pi$
$823$	24.6417	−	27.3674i	0.858957	−	0.953969i	0.999347	+	0.0361276i	$0.0115023\pi$
$824$	7.70259			0.268332
$825$	2.34909	−	0.910061i	0.0817849	−	0.0316843i
$826$	−8.43575	−	14.6112i	−0.293517	−	0.508387i
$827$	−12.7326	+	14.1410i	−0.442757	+	0.491731i	−0.922673	−	0.385583i	$-0.874000\pi$
$827$	−12.7326	+	14.1410i	−0.442757	+	0.491731i	0.479916	+	0.877314i	$0.340667\pi$
$828$	24.1432	+	17.5411i	0.839036	+	0.609595i
$829$	13.0353	−	9.47072i	0.452736	−	0.328932i	−0.337939	−	0.941168i	$-0.609730\pi$
$829$	13.0353	−	9.47072i	0.452736	−	0.328932i	0.790675	+	0.612236i	$0.209730\pi$
$830$	−28.6723	+	6.09448i	−0.995229	+	0.211542i
$831$	−46.2480	−	51.3636i	−1.60433	−	1.78178i
$832$	0.702402	+	0.312730i	0.0243514	+	0.0108420i
$833$	−3.78938	+	1.68714i	−0.131294	+	0.0584560i
$834$	−23.6230	−	5.02123i	−0.817999	−	0.173871i
$835$	32.3434			1.11929
$836$	−3.32607	−	14.0690i	−0.115034	−	0.486587i
$837$	43.5042			1.50373
$838$	−2.94528	−	0.626038i	−0.101743	−	0.0216261i
$839$	−30.3865	+	13.5290i	−1.04906	+	0.467071i	−0.857540	−	0.514417i	$-0.828008\pi$
$839$	−30.3865	+	13.5290i	−1.04906	+	0.467071i	−0.191520	+	0.981489i	$0.561342\pi$
$840$	14.2928	+	6.36356i	0.493148	+	0.219564i
$841$	10.8609	+	12.0623i	0.374514	+	0.415940i
$842$	−21.2403	+	4.51477i	−0.731990	+	0.155589i
$843$	4.48578	−	3.25911i	0.154499	−	0.112250i
$844$	19.9560	+	14.4989i	0.686914	+	0.499072i
$845$	−19.0359	+	21.1415i	−0.654856	+	0.727291i
$846$	29.2588	+	50.6778i	1.00594	+	1.74234i
$847$	18.7045	−	17.0519i	0.642696	−	0.585911i
$848$	−8.36508			−0.287258
$849$	−53.5701	+	59.4957i	−1.83852	+	2.04189i
$850$	0.569019	−	0.253344i	0.0195172	−	0.00868961i
$851$	−32.0689	−	14.2780i	−1.09931	−	0.489444i
$852$	−13.6251	−	15.1322i	−0.466788	−	0.518421i
$853$	6.47471	+	7.19089i	0.221690	+	0.246211i	0.843722	−	0.536780i	$-0.180359\pi$
$853$	6.47471	+	7.19089i	0.221690	+	0.246211i	−0.622032	+	0.782991i	$0.713693\pi$
$854$	−16.4188	+	11.9290i	−0.561841	+	0.408201i
$855$	47.9491	−	32.4936i	1.63982	−	1.11126i
$856$	−1.49228	−	4.59278i	−0.0510052	−	0.156978i
$857$	−1.37674	+	2.38458i	−0.0470284	+	0.0814555i	−0.888581	−	0.458719i	$-0.848308\pi$
$857$	−1.37674	+	2.38458i	−0.0470284	+	0.0814555i	0.841553	+	0.540175i	$0.181642\pi$
$858$	6.74929	+	3.41273i	0.230417	+	0.116509i
$859$	−18.2577	−	31.6232i	−0.622944	−	1.07897i	−0.988935	−	0.148352i	$-0.952603\pi$
$859$	−18.2577	−	31.6232i	−0.622944	−	1.07897i	0.365991	−	0.930619i	$-0.380730\pi$
$860$	−19.7927	−	4.20708i	−0.674927	−	0.143460i
$861$	−2.70146	+	25.7026i	−0.0920654	+	0.875944i
$862$	24.0012	−	17.4379i	0.817484	−	0.593937i
$863$	3.93968	−	12.1251i	0.134108	−	0.412743i	−0.861342	−	0.508026i	$-0.830376\pi$
$863$	3.93968	−	12.1251i	0.134108	−	0.412743i	0.995450	+	0.0952828i	$0.0303755\pi$
$864$	−8.11144	+	1.72414i	−0.275957	+	0.0586564i
$865$	−9.40696	−	4.18825i	−0.319846	−	0.142405i
$866$	4.96832	+	3.60969i	0.168830	+	0.122662i
$867$	−10.1594	−	31.2674i	−0.345031	−	1.06190i
$868$	−6.03556	−	10.4539i	−0.204860	−	0.354829i
$869$	−4.63387	+	29.8532i	−0.157193	+	1.01270i
$870$	22.8648	+	39.6029i	0.775188	+	1.34266i
$871$	−4.64260	−	0.986815i	−0.157309	−	0.0334370i
$872$	−0.206653	+	0.0920077i	−0.00699815	+	0.00311578i
$873$	−62.1560	+	45.1590i	−2.10366	+	1.52840i
$874$	−17.7152	−	13.7789i	−0.599227	−	0.466078i
$875$	−7.73320	+	23.8004i	−0.261430	+	0.804599i
$876$	3.51006	+	33.3960i	0.118594	+	1.12834i
$877$	−12.2811	+	5.46790i	−0.414704	+	0.184638i	−0.603473	−	0.797383i	$-0.706217\pi$
$877$	−12.2811	+	5.46790i	−0.414704	+	0.184638i	0.188769	+	0.982021i	$0.439550\pi$
$878$	−7.94214	+	8.82064i	−0.268034	+	0.297682i
$879$	7.80145	−	13.5125i	0.263136	−	0.455766i
$880$	7.59453	+	0.374510i	0.256012	+	0.0126247i
$881$	2.71986			0.0916344			0.0458172	−	0.998950i	$-0.485411\pi$
$881$	2.71986			0.0916344			0.0458172	+	0.998950i	$0.485411\pi$
$882$	−3.05480	−	9.40170i	−0.102860	−	0.316572i
$883$	−0.421496	+	4.01027i	−0.0141845	+	0.134956i	−0.999322	−	0.0368094i	$-0.988281\pi$
$883$	−0.421496	+	4.01027i	−0.0141845	+	0.134956i	0.985138	+	0.171766i	$0.0549472\pi$
$884$	1.70828	+	0.760574i	0.0574556	+	0.0255809i
$885$	15.4065	−	47.4162i	0.517882	−	1.59388i
$886$	12.4499	−	38.3167i	0.418261	−	1.28728i
$887$	−42.1854	−	18.7821i	−1.41645	−	0.630642i	−0.451304	−	0.892370i	$-0.649041\pi$
$887$	−42.1854	−	18.7821i	−1.41645	−	0.630642i	−0.965142	+	0.261728i	$0.915708\pi$
$888$	18.4725	−	8.22447i	0.619895	−	0.275995i
$889$	−32.6641	+	36.2771i	−1.09552	+	1.21670i
$890$	−13.5488	+	23.4673i	−0.454158	+	0.786625i
$891$	−23.5946	+	3.81171i	−0.790449	+	0.127697i
$892$	16.7428			0.560592
$893$	−20.7446	−	38.8117i	−0.694193	−	1.29878i
$894$	3.53167	+	2.56591i	0.118117	+	0.0858168i
$895$	−1.58883	−	15.1167i	−0.0531086	−	0.505294i
$896$	1.53965	+	1.70995i	0.0514360	+	0.0571254i
$897$	11.4844	−	2.44109i	0.383453	−	0.0815055i
$898$	−0.397297	−	3.78003i	−0.0132580	−	0.126141i
$899$	3.68801	−	35.0891i	0.123002	−	1.17029i
$900$	0.458713	+	1.41177i	0.0152904	+	0.0470591i
$901$	−20.3443			−0.677767
$902$	3.28832	+	12.1224i	0.109489	+	0.403631i
$903$	−30.1158	−	52.1621i	−1.00219	−	1.73584i
$904$	0.763292	+	2.34917i	0.0253867	+	0.0781323i
$905$	−13.0210	−	9.46032i	−0.432833	−	0.314472i
$906$	−40.0818	−	17.8456i	−1.33163	−	0.592880i
$907$	15.8968	+	17.6552i	0.527846	+	0.586232i	0.946819	−	0.321766i	$-0.104277\pi$
$907$	15.8968	+	17.6552i	0.527846	+	0.586232i	−0.418973	+	0.907999i	$0.637610\pi$
$908$	7.82008	−	1.66221i	0.259518	−	0.0551623i
$909$	6.20548	+	59.0412i	0.205823	+	1.95827i
$910$	3.70534	−	1.64972i	0.122831	−	0.0546878i
$911$	−7.17730	−	22.0895i	−0.237794	−	0.731856i	−0.996738	−	0.0807002i	$-0.974284\pi$
$911$	−7.17730	−	22.0895i	−0.237794	−	0.731856i	0.758944	−	0.651156i	$-0.225716\pi$
$912$	12.7264	−	2.27248i	0.421413	−	0.0752493i
$913$	−40.9942	−	10.8489i	−1.35671	−	0.359045i
$914$	15.0534	−	26.0733i	0.497923	−	0.862428i
$915$	−58.6618	−	12.4690i	−1.93930	−	0.412211i
$916$	−2.27035	+	21.6010i	−0.0750146	+	0.713716i
$917$	−2.58084	−	24.5550i	−0.0852268	−	0.810879i
$918$	−19.7274	+	4.19319i	−0.651102	+	0.138396i
$919$	−2.19721	+	6.76231i	−0.0724792	+	0.223068i	−0.980733	−	0.195351i	$-0.937416\pi$
$919$	−2.19721	+	6.76231i	−0.0724792	+	0.223068i	0.908254	+	0.418419i	$0.137416\pi$
$920$	9.54979	−	6.93833i	0.314847	−	0.228750i
$921$	−0.0398669	+	0.379308i	−0.00131366	+	0.0124986i
$922$	−11.2940	+	12.5433i	−0.371949	+	0.413091i
$923$	−5.27886			−0.173756
$924$	14.2979	+	17.5455i	0.470367	+	0.577203i
$925$	−0.873061	−	1.51219i	−0.0287061	−	0.0497204i
$926$	−24.3492	−	5.17559i	−0.800166	−	0.170081i
$927$	−4.66665	+	44.4002i	−0.153273	+	1.45829i
$928$	0.702999	+	6.68859i	0.0230771	+	0.219564i
$929$	27.2556	+	30.2704i	0.894228	+	0.993141i	0.999999	−	0.00124952i	$-0.000397735\pi$
$929$	27.2556	+	30.2704i	0.894228	+	0.993141i	−0.105771	+	0.994391i	$0.533731\pi$
$930$	11.0229	−	33.9251i	0.361456	−	1.11245i
$931$	2.06468	+	7.14189i	0.0676671	+	0.234066i
$932$	15.5341	+	11.2862i	0.508835	+	0.369690i
$933$	−65.2695	−	13.8735i	−2.13683	−	0.454197i
$934$	−19.1409	+	33.1530i	−0.626308	+	1.08480i
$935$	18.4703	+	0.910826i	0.604043	+	0.0297872i
$936$	−2.22823	+	3.85941i	−0.0728320	+	0.126149i
$937$	17.8031	−	19.7723i	0.581601	−	0.645933i	−0.378495	−	0.925603i	$-0.623558\pi$
$937$	17.8031	−	19.7723i	0.581601	−	0.645933i	0.960096	+	0.279670i	$0.0902251\pi$
$938$	−11.4913	−	8.34891i	−0.375204	−	0.272602i
$939$	−30.4424	+	22.1177i	−0.993451	+	0.721785i
$940$	22.6407	−	4.81243i	0.738458	−	0.156964i
$941$	32.9481	−	7.00334i	1.07408	−	0.228302i	0.363267	−	0.931685i	$-0.381661\pi$
$941$	32.9481	−	7.00334i	1.07408	−	0.228302i	0.710811	+	0.703383i	$0.248328\pi$
$942$	−41.9811	+	30.5011i	−1.36782	+	0.993778i
$943$	15.7750	+	11.4612i	0.513706	+	0.373229i
$944$	4.90630	−	5.44900i	0.159687	−	0.177350i
$945$	−21.8729	+	37.8849i	−0.711525	+	1.23240i
$946$	−22.8061	−	18.3517i	−0.741489	−	0.596666i
$947$	25.4136	−	44.0176i	0.825830	−	1.43038i	−0.0754536	−	0.997149i	$-0.524040\pi$
$947$	25.4136	−	44.0176i	0.825830	−	1.43038i	0.901283	−	0.433230i	$-0.142626\pi$
$948$	−26.4249	−	5.61679i	−0.858241	−	0.182425i
$949$	7.04285	+	5.11693i	0.228621	+	0.166103i
$950$	−0.310035	−	1.07244i	−0.0100589	−	0.0347944i
$951$	−29.0892	+	89.5273i	−0.943281	+	2.90312i
$952$	3.74450	+	4.15868i	0.121360	+	0.134784i
$953$	0.245058	+	2.33157i	0.00793820	+	0.0755269i	0.997774	−	0.0666896i	$-0.0212437\pi$
$953$	0.245058	+	2.33157i	0.00793820	+	0.0755269i	−0.989836	+	0.142217i	$0.954577\pi$
$954$	5.06803	−	48.2191i	0.164083	−	1.56115i
$955$	20.9829	+	4.46004i	0.678989	+	0.144324i
$956$	0.227988	+	0.394887i	0.00737366	+	0.0127716i
$957$	3.66618	+	66.0530i	0.118511	+	2.13519i
$958$	−6.06841			−0.196061
$959$	−2.82322	+	3.13550i	−0.0911666	+	0.101251i
$960$	−0.710741	+	6.76225i	−0.0229391	+	0.218251i
$961$	2.81399	−	2.04448i	0.0907739	−	0.0659511i
$962$	1.61990	−	4.98554i	0.0522277	−	0.160740i
$963$	27.3784	−	5.81945i	0.882256	−	0.187529i
$964$	−2.26675	−	21.5667i	−0.0730072	−	0.694618i
$965$	0.437142	−	4.15913i	0.0140721	−	0.133887i
$966$	34.3687	+	7.30529i	1.10579	+	0.235044i
$967$	17.2551	−	29.8867i	0.554886	−	0.961090i	−0.443027	−	0.896508i	$-0.646095\pi$
$967$	17.2551	−	29.8867i	0.554886	−	0.961090i	0.997912	−	0.0645818i	$-0.0205713\pi$
$968$	9.56005	+	5.44109i	0.307272	+	0.174883i
$969$	30.9512	−	5.52678i	0.994297	−	0.177546i
$970$	9.39087	+	28.9021i	0.301523	+	0.927992i
$971$	51.7294	−	23.0314i	1.66007	−	0.739113i	0.660147	−	0.751137i	$-0.270494\pi$
$971$	51.7294	−	23.0314i	1.66007	−	0.739113i	0.999928	+	0.0120239i	$0.00382743\pi$
$972$	0.366421	+	3.48627i	0.0117530	+	0.111822i
$973$	−18.3274	+	3.89561i	−0.587550	+	0.124888i
$974$	−0.548554	−	0.609231i	−0.0175768	−	0.0195210i
$975$	0.533525	+	0.237541i	0.0170865	+	0.00760739i
$976$	−7.13563	−	5.18434i	−0.228406	−	0.165947i
$977$	2.75040	+	8.46487i	0.0879932	+	0.270815i	0.985364	−	0.170461i	$-0.0545258\pi$
$977$	2.75040	+	8.46487i	0.0879932	+	0.270815i	−0.897371	+	0.441277i	$0.854526\pi$
$978$	−32.4239	−	56.1599i	−1.03680	−	1.79580i
$979$	−32.8106	+	21.4517i	−1.04863	+	0.685600i
$980$	−3.91019			−0.124907
$981$	−0.405161	−	1.24696i	−0.0129358	−	0.0398123i
$982$	4.00442	−	38.0995i	0.127786	−	1.21580i
$983$	2.54606	+	24.2242i	0.0812068	+	0.772631i	0.957028	+	0.289995i	$0.0936538\pi$
$983$	2.54606	+	24.2242i	0.0812068	+	0.772631i	−0.875821	+	0.482636i	$0.839680\pi$
$984$	−10.9865	+	2.33524i	−0.350235	+	0.0744448i
$985$	10.8239	+	12.0212i	0.344879	+	0.383027i
$986$	1.70973	+	16.2670i	0.0544488	+	0.518046i
$987$	55.7398	+	40.4973i	1.77422	+	1.28904i
$988$	1.76983	−	2.84604i	0.0563058	−	0.0905444i
$989$	−45.4437			−1.44502
$990$	−6.75998	+	43.5505i	−0.214846	+	1.38412i
$991$	0.253341	−	0.438800i	0.00804764	−	0.0139389i	−0.861974	−	0.506953i	$-0.830772\pi$
$991$	0.253341	−	0.438800i	0.00804764	−	0.0139389i	0.870021	+	0.493014i	$0.164105\pi$
$992$	3.51034	−	3.89862i	0.111453	−	0.123781i
$993$	−18.5018	+	8.23753i	−0.587137	+	0.261410i
$994$	−14.4319	−	6.42551i	−0.457753	−	0.203805i
$995$	8.76125	−	26.9644i	0.277750	−	0.854828i
$996$	11.7180	−	36.0642i	0.371298	−	1.14274i
$997$	4.29829	+	1.91372i	0.136128	+	0.0606082i	0.473670	−	0.880702i	$-0.342929\pi$
$997$	4.29829	+	1.91372i	0.136128	+	0.0606082i	−0.337542	+	0.941310i	$0.609596\pi$
$998$	−0.897642	+	8.54050i	−0.0284144	+	0.270345i
$999$	17.4713	+	53.7712i	0.552769	+	1.70125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.e.49.9	✓	72
11.9	even	5	inner	418.2.n.e.163.1	yes	72
19.7	even	3	inner	418.2.n.e.159.1	yes	72
209.64	even	15	inner	418.2.n.e.273.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.e.49.9	✓	72	1.1	even	1	trivial
418.2.n.e.159.1	yes	72	19.7	even	3	inner
418.2.n.e.163.1	yes	72	11.9	even	5	inner
418.2.n.e.273.9	yes	72	209.64	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(2.70941 - 1.20631i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.53406 + 1.70375i) q^{5} +(-2.90101 + 0.616628i) q^{6} +(-1.86152 + 1.35247i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(3.87833 - 4.30732i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(2.70941 - 1.20631i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.53406 + 1.70375i) q^{5} +(-2.90101 + 0.616628i) q^{6} +(-1.86152 + 1.35247i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(3.87833 - 4.30732i) q^{9} +(-1.14631 - 1.98547i) q^{10} +(-0.183801 - 3.31153i) q^{11} +2.96582 q^{12} +(0.514478 - 0.571386i) q^{13} +(2.10204 - 0.935887i) q^{14} +(6.21165 + 2.76560i) q^{15} +(0.669131 + 0.743145i) q^{16} +(1.62736 + 1.80736i) q^{17} +(-4.68912 + 3.40685i) q^{18} +(3.60840 - 2.44530i) q^{19} +(0.708459 + 2.18041i) q^{20} +(-3.41212 + 5.90997i) q^{21} +(-0.508720 + 3.27738i) q^{22} +(2.57439 + 4.45897i) q^{23} +(-2.90101 - 0.616628i) q^{24} +(-0.0267706 + 0.254706i) q^{25} +(-0.622033 + 0.451933i) q^{26} +(2.56257 - 7.88678i) q^{27} +(-2.25068 + 0.478398i) q^{28} +(-6.14398 - 2.73548i) q^{29} +(-5.50091 - 3.99664i) q^{30} +(1.62114 + 4.98935i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.49271 - 8.75056i) q^{33} +(-1.21602 - 2.10622i) q^{34} +(-5.15996 - 1.09678i) q^{35} +(5.29498 - 2.35748i) q^{36} +(-5.51579 + 4.00746i) q^{37} +(-4.03795 + 1.64163i) q^{38} +(0.704665 - 2.16874i) q^{39} +(-0.239644 - 2.28006i) q^{40} +(3.45970 - 1.54036i) q^{41} +(4.56631 - 5.07140i) q^{42} +(-4.41306 + 7.64364i) q^{43} +(1.17901 - 3.09999i) q^{44} +13.2882 q^{45} +(-1.59106 - 4.89678i) q^{46} +(1.05533 - 10.0408i) q^{47} +(2.70941 + 1.20631i) q^{48} +(-0.527046 + 1.62208i) q^{49} +(0.0791419 - 0.243574i) q^{50} +(6.58942 + 2.93380i) q^{51} +(0.702402 - 0.312730i) q^{52} +(-5.59733 + 6.21647i) q^{53} +(-4.14633 + 7.18165i) q^{54} +(5.36005 - 5.39324i) q^{55} +2.30097 q^{56} +(6.82684 - 10.9781i) q^{57} +(5.44099 + 3.95311i) q^{58} +(-0.766440 - 7.29219i) q^{59} +(4.54975 + 5.05301i) q^{60} +(-8.62738 + 1.83381i) q^{61} +(-0.548368 - 5.21738i) q^{62} +(-1.39405 + 13.2635i) q^{63} +(0.309017 + 0.951057i) q^{64} +1.76274 q^{65} +(2.57519 + 9.49343i) q^{66} +(-3.08653 - 5.34603i) q^{67} +(0.751544 + 2.31302i) q^{68} +(12.3540 + 8.97567i) q^{69} +(4.81917 + 2.14563i) q^{70} +(-4.59405 - 5.10220i) q^{71} +(-5.66942 + 1.20507i) q^{72} +(1.18350 + 11.2603i) q^{73} +(6.22846 - 2.77309i) q^{74} +(0.234721 + 0.722396i) q^{75} +(4.29103 - 0.766223i) q^{76} +(4.82090 + 5.91589i) q^{77} +(-1.14017 + 1.97484i) q^{78} +(-8.90982 - 1.89384i) q^{79} +(-0.239644 + 2.28006i) q^{80} +(-0.753261 - 7.16680i) q^{81} +(-3.70436 + 0.787386i) q^{82} +(3.95101 - 12.1600i) q^{83} +(-5.52093 + 4.01119i) q^{84} +(-0.582826 + 5.54522i) q^{85} +(5.90582 - 6.55908i) q^{86} -19.9464 q^{87} +(-1.79777 + 2.78712i) q^{88} +(-5.90976 - 10.2360i) q^{89} +(-12.9978 - 2.76277i) q^{90} +(-0.184927 + 1.75946i) q^{91} +(0.538193 + 5.12057i) q^{92} +(10.4110 + 11.5626i) q^{93} +(-3.11986 + 9.60195i) q^{94} +(9.70168 + 2.39656i) q^{95} +(-2.39940 - 1.74326i) q^{96} +(-12.9657 - 2.75594i) q^{97} +(0.852778 - 1.47706i) q^{98} +(-14.9767 - 12.0515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9	\( 72 q + 9 q^{2} - 2 q^{3} + 9 q^{4} + 8 q^{5} + 3 q^{6} - 20 q^{7} - 18 q^{8} + 9 q^{9} - 22 q^{10} + 10 q^{11} + 4 q^{12} + 15 q^{13} + 10 q^{14} + 9 q^{15} + 9 q^{16} + 6 q^{17} - 28 q^{18} + 7 q^{19} - 16 q^{20} + 48 q^{21} - 15 q^{22} - 20 q^{23} + 3 q^{24} + 7 q^{25} + 30 q^{26} - 56 q^{27} - 10 q^{28} + 35 q^{29} - 18 q^{30} + 52 q^{31} - 36 q^{32} - 12 q^{33} - 4 q^{34} - 9 q^{35} + 14 q^{36} - 52 q^{37} - 2 q^{38} - 42 q^{39} + 3 q^{40} + 41 q^{41} - 2 q^{42} + 14 q^{43} + 116 q^{45} - 50 q^{46} + 19 q^{47} - 2 q^{48} + 46 q^{49} - 44 q^{50} + 33 q^{51} - 15 q^{52} - 15 q^{53} - 2 q^{54} - 55 q^{55} - 33 q^{57} - 70 q^{58} - 13 q^{59} - 6 q^{60} + 8 q^{61} + 19 q^{62} + 40 q^{63} - 18 q^{64} + 120 q^{65} + 23 q^{66} + 2 q^{67} - 12 q^{68} - 194 q^{69} + q^{70} + 52 q^{71} + 9 q^{72} - 48 q^{73} + 26 q^{74} - 158 q^{75} + 20 q^{76} + 130 q^{77} + 46 q^{78} - 48 q^{79} + 3 q^{80} + 48 q^{81} - 14 q^{82} - 62 q^{83} + 44 q^{84} - 27 q^{85} - 16 q^{86} - 164 q^{87} + 10 q^{88} + 20 q^{89} + 52 q^{90} + 4 q^{91} - 15 q^{92} - 39 q^{93} - 8 q^{94} + 69 q^{95} + 4 q^{96} + 2 q^{97} - 48 q^{98} + 9 q^{99}+O(q^{100}) \) 72 * q + 9 * q^2 - 2 * q^3 + 9 * q^4 + 8 * q^5 + 3 * q^6 - 20 * q^7 - 18 * q^8 + 9 * q^9 - 22 * q^10 + 10 * q^11 + 4 * q^12 + 15 * q^13 + 10 * q^14 + 9 * q^15 + 9 * q^16 + 6 * q^17 - 28 * q^18 + 7 * q^19 - 16 * q^20 + 48 * q^21 - 15 * q^22 - 20 * q^23 + 3 * q^24 + 7 * q^25 + 30 * q^26 - 56 * q^27 - 10 * q^28 + 35 * q^29 - 18 * q^30 + 52 * q^31 - 36 * q^32 - 12 * q^33 - 4 * q^34 - 9 * q^35 + 14 * q^36 - 52 * q^37 - 2 * q^38 - 42 * q^39 + 3 * q^40 + 41 * q^41 - 2 * q^42 + 14 * q^43 + 116 * q^45 - 50 * q^46 + 19 * q^47 - 2 * q^48 + 46 * q^49 - 44 * q^50 + 33 * q^51 - 15 * q^52 - 15 * q^53 - 2 * q^54 - 55 * q^55 - 33 * q^57 - 70 * q^58 - 13 * q^59 - 6 * q^60 + 8 * q^61 + 19 * q^62 + 40 * q^63 - 18 * q^64 + 120 * q^65 + 23 * q^66 + 2 * q^67 - 12 * q^68 - 194 * q^69 + q^70 + 52 * q^71 + 9 * q^72 - 48 * q^73 + 26 * q^74 - 158 * q^75 + 20 * q^76 + 130 * q^77 + 46 * q^78 - 48 * q^79 + 3 * q^80 + 48 * q^81 - 14 * q^82 - 62 * q^83 + 44 * q^84 - 27 * q^85 - 16 * q^86 - 164 * q^87 + 10 * q^88 + 20 * q^89 + 52 * q^90 + 4 * q^91 - 15 * q^92 - 39 * q^93 - 8 * q^94 + 69 * q^95 + 4 * q^96 + 2 * q^97 - 48 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

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Database

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