LMFDB - Embedded newform 448.2.bn.a.221.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(37,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 27, 16]))

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

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

chi := DirichletCharacter("448.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.bn (of order $48$, degree $16$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			221.3
Character	$\chi$	$=$	448.221
Dual form			448.2.bn.a.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40062 + 0.195640i) q^{2} +(1.89561 - 2.16153i) q^{3} +(1.92345 - 0.548033i) q^{4} +(-0.425845 - 0.0279114i) q^{5} +(-2.23214 + 3.39833i) q^{6} +(1.85929 - 1.88230i) q^{7} +(-2.58680 + 1.14389i) q^{8} +(-0.687295 - 5.22052i) q^{9} +O(q^{10})$	\(q+(-1.40062 + 0.195640i) q^{2} +(1.89561 - 2.16153i) q^{3} +(1.92345 - 0.548033i) q^{4} +(-0.425845 - 0.0279114i) q^{5} +(-2.23214 + 3.39833i) q^{6} +(1.85929 - 1.88230i) q^{7} +(-2.58680 + 1.14389i) q^{8} +(-0.687295 - 5.22052i) q^{9} +(0.601906 - 0.0442193i) q^{10} +(-5.02161 - 1.70461i) q^{11} +(2.46153 - 5.19646i) q^{12} +(-0.752891 - 1.12678i) q^{13} +(-2.23590 + 3.00013i) q^{14} +(-0.867569 + 0.867569i) q^{15} +(3.39932 - 2.10823i) q^{16} +(-0.593609 + 0.159057i) q^{17} +(1.98398 + 7.17748i) q^{18} +(4.31451 + 2.12768i) q^{19} +(-0.834389 + 0.179691i) q^{20} +(-0.544157 - 7.58702i) q^{21} +(7.36684 + 1.40507i) q^{22} +(2.02106 - 0.266077i) q^{23} +(-2.43102 + 7.75981i) q^{24} +(-4.77666 - 0.628859i) q^{25} +(1.27495 + 1.43089i) q^{26} +(-5.41577 - 3.61870i) q^{27} +(2.54469 - 4.63946i) q^{28} +(0.278277 - 1.39899i) q^{29} +(1.04540 - 1.38486i) q^{30} +(8.34875 + 4.82015i) q^{31} +(-4.34869 + 3.61786i) q^{32} +(-13.2036 + 7.62310i) q^{33} +(0.800300 - 0.338911i) q^{34} +(-0.844307 + 0.749673i) q^{35} +(-4.18300 - 9.66475i) q^{36} +(-0.126305 + 1.92704i) q^{37} +(-6.45923 - 2.13597i) q^{38} +(-3.86276 - 0.508542i) q^{39} +(1.13350 - 0.414918i) q^{40} +(1.97608 - 4.77068i) q^{41} +(2.24648 + 10.5200i) q^{42} +(-6.87655 + 1.36783i) q^{43} +(-10.5930 - 0.526718i) q^{44} +(0.146969 + 2.24232i) q^{45} +(-2.77867 + 0.768072i) q^{46} +(0.503610 - 1.87950i) q^{47} +(1.88679 - 11.3441i) q^{48} +(-0.0860931 - 6.99947i) q^{49} +(6.81329 - 0.0537156i) q^{50} +(-0.781446 + 1.58462i) q^{51} +(-2.06566 - 1.75470i) q^{52} +(10.7186 + 3.63846i) q^{53} +(8.29338 + 4.00887i) q^{54} +(2.09085 + 0.866059i) q^{55} +(-2.65647 + 6.99594i) q^{56} +(12.7777 - 5.29269i) q^{57} +(-0.116060 + 2.01389i) q^{58} +(0.839734 + 1.70281i) q^{59} +(-1.19327 + 2.14418i) q^{60} +(-3.40556 - 10.0325i) q^{61} +(-12.6364 - 5.11783i) q^{62} +(-11.1045 - 8.41276i) q^{63} +(5.38304 - 5.91801i) q^{64} +(0.289165 + 0.500849i) q^{65} +(17.0018 - 13.2602i) q^{66} +(-2.22171 + 2.53337i) q^{67} +(-1.05461 + 0.631256i) q^{68} +(3.25601 - 4.87296i) q^{69} +(1.03588 - 1.21518i) q^{70} +(12.5820 - 5.21163i) q^{71} +(7.74958 + 12.7182i) q^{72} +(9.50654 - 7.29463i) q^{73} +(-0.200102 - 2.72376i) q^{74} +(-10.4140 + 9.13283i) q^{75} +(9.46478 + 1.72799i) q^{76} +(-12.5452 + 6.28281i) q^{77} +(5.50974 - 0.0434384i) q^{78} +(-0.365624 - 0.0979688i) q^{79} +(-1.50643 + 0.802900i) q^{80} +(-2.82970 + 0.758215i) q^{81} +(-1.83439 + 7.06849i) q^{82} +(-13.5408 + 9.04769i) q^{83} +(-5.20460 - 14.2950i) q^{84} +(0.257225 - 0.0511653i) q^{85} +(9.36380 - 3.26113i) q^{86} +(-2.49646 - 3.25345i) q^{87} +(14.9398 - 1.33468i) q^{88} +(-7.94453 + 10.3535i) q^{89} +(-0.644535 - 3.11187i) q^{90} +(-3.52078 - 0.677845i) q^{91} +(3.74158 - 1.61939i) q^{92} +(26.2449 - 8.90895i) q^{93} +(-0.337659 + 2.73098i) q^{94} +(-1.77793 - 1.02649i) q^{95} +(-0.423305 + 16.2579i) q^{96} +14.7184i q^{97} +(1.48996 + 9.78673i) q^{98} +(-5.44761 + 27.3870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) $ 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 32 q^{13} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 32 q^{20} - 16 q^{21} - 16 q^{22} - 8 q^{23} - 88 q^{24} - 8 q^{25} - 8 q^{26} - 32 q^{27} - 56 q^{28} - 32 q^{29} - 88 q^{30} - 8 q^{32} - 32 q^{34} - 16 q^{35} + 128 q^{36} - 8 q^{37} - 88 q^{38} - 8 q^{39} - 8 q^{40} - 32 q^{41} - 56 q^{42} - 32 q^{43} - 16 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 32 q^{48} - 16 q^{49} + 16 q^{50} - 8 q^{51} - 56 q^{52} - 8 q^{53} - 8 q^{54} - 32 q^{55} - 16 q^{56} - 32 q^{57} - 8 q^{58} + 56 q^{59} + 88 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} + 160 q^{64} - 16 q^{65} - 136 q^{66} - 88 q^{67} - 8 q^{68} - 32 q^{69} - 16 q^{70} - 160 q^{71} - 8 q^{72} - 8 q^{73} + 48 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{77} + 64 q^{78} - 8 q^{79} - 32 q^{80} - 8 q^{81} + 72 q^{82} - 32 q^{83} - 128 q^{84} - 32 q^{85} - 8 q^{86} - 8 q^{87} - 8 q^{88} - 8 q^{89} - 320 q^{90} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 8 q^{94} + 128 q^{96} - 152 q^{98} - 80 q^{99}+O(q^{100}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 32 * q^13 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 32 * q^20 - 16 * q^21 - 16 * q^22 - 8 * q^23 - 88 * q^24 - 8 * q^25 - 8 * q^26 - 32 * q^27 - 56 * q^28 - 32 * q^29 - 88 * q^30 - 8 * q^32 - 32 * q^34 - 16 * q^35 + 128 * q^36 - 8 * q^37 - 88 * q^38 - 8 * q^39 - 8 * q^40 - 32 * q^41 - 56 * q^42 - 32 * q^43 - 16 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 32 * q^48 - 16 * q^49 + 16 * q^50 - 8 * q^51 - 56 * q^52 - 8 * q^53 - 8 * q^54 - 32 * q^55 - 16 * q^56 - 32 * q^57 - 8 * q^58 + 56 * q^59 + 88 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 + 160 * q^64 - 16 * q^65 - 136 * q^66 - 88 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 160 * q^71 - 8 * q^72 - 8 * q^73 + 48 * q^74 - 8 * q^75 - 32 * q^76 - 16 * q^77 + 64 * q^78 - 8 * q^79 - 32 * q^80 - 8 * q^81 + 72 * q^82 - 32 * q^83 - 128 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 - 320 * q^90 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 8 * q^94 + 128 * q^96 - 152 * q^98 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	−1.40062	+	0.195640i	−0.990385	+	0.138338i
$2$	−1.40062	+	0.195640i	−0.990385	+	0.138338i
$3$	1.89561	−	2.16153i	1.09443	−	1.24796i	0.127799	−	0.991800i	$-0.459209\pi$
$3$	1.89561	−	2.16153i	1.09443	−	1.24796i	0.966634	−	0.256161i	$-0.0824578\pi$
$4$	1.92345	−	0.548033i	0.961725	−	0.274017i
$5$	−0.425845	−	0.0279114i	−0.190444	−	0.0124823i	−0.0301173	−	0.999546i	$-0.509588\pi$
$5$	−0.425845	−	0.0279114i	−0.190444	−	0.0124823i	−0.160327	+	0.987064i	$0.551255\pi$
$6$	−2.23214	+	3.39833i	−0.911269	+	1.38736i
$7$	1.85929	−	1.88230i	0.702745	−	0.711442i
$7$	1.85929	−	1.88230i	0.702745	−	0.711442i
$8$	−2.58680	+	1.14389i	−0.914571	+	0.404425i
$9$	−0.687295	−	5.22052i	−0.229098	−	1.74017i
$10$	0.601906	−	0.0442193i	0.190340	−	0.0139834i
$11$	−5.02161	−	1.70461i	−1.51407	−	0.513958i	−0.563943	−	0.825814i	$-0.690716\pi$
$11$	−5.02161	−	1.70461i	−1.51407	−	0.513958i	−0.950130	+	0.311856i	$0.899050\pi$
$12$	2.46153	−	5.19646i	0.710581	−	1.50009i
$13$	−0.752891	−	1.12678i	−0.208814	−	0.312513i	0.712248	−	0.701928i	$-0.247677\pi$
$13$	−0.752891	−	1.12678i	−0.208814	−	0.312513i	−0.921062	+	0.389415i	$0.872677\pi$
$14$	−2.23590	+	3.00013i	−0.597568	+	0.801818i
$15$	−0.867569	+	0.867569i	−0.224005	+	0.224005i
$16$	3.39932	−	2.10823i	0.849830	−	0.527057i
$17$	−0.593609	+	0.159057i	−0.143971	+	0.0385770i	−0.330085	−	0.943951i	$-0.607077\pi$
$17$	−0.593609	+	0.159057i	−0.143971	+	0.0385770i	0.186114	+	0.982528i	$0.440411\pi$
$18$	1.98398	+	7.17748i	0.467628	+	1.69175i
$19$	4.31451	+	2.12768i	0.989817	+	0.488124i	0.863762	−	0.503900i	$-0.168102\pi$
$19$	4.31451	+	2.12768i	0.989817	+	0.488124i	0.126054	+	0.992023i	$0.459769\pi$
$20$	−0.834389	+	0.179691i	−0.186575	+	0.0401802i
$21$	−0.544157	−	7.58702i	−0.118745	−	1.65562i
$22$	7.36684	+	1.40507i	1.57061	+	0.299562i
$23$	2.02106	−	0.266077i	0.421420	−	0.0554809i	0.0831654	−	0.996536i	$-0.473497\pi$
$23$	2.02106	−	0.266077i	0.421420	−	0.0554809i	0.338254	+	0.941055i	$0.390164\pi$
$24$	−2.43102	+	7.75981i	−0.496229	+	1.58397i
$25$	−4.77666	−	0.628859i	−0.955332	−	0.125772i
$26$	1.27495	+	1.43089i	0.250039	+	0.280621i
$27$	−5.41577	−	3.61870i	−1.04227	−	0.696420i
$28$	2.54469	−	4.63946i	0.480901	−	0.876775i
$29$	0.278277	−	1.39899i	0.0516747	−	0.259786i	−0.946308	−	0.323265i	$-0.895219\pi$
$29$	0.278277	−	1.39899i	0.0516747	−	0.259786i	0.997983	+	0.0634787i	$0.0202195\pi$
$30$	1.04540	−	1.38486i	0.190863	−	0.252840i
$31$	8.34875	+	4.82015i	1.49948	+	0.865725i	1.00000		0.000600351i	$-0.000191098\pi$
$31$	8.34875	+	4.82015i	1.49948	+	0.865725i	0.499480	+	0.866325i	$0.333524\pi$
$32$	−4.34869	+	3.61786i	−0.768747	+	0.639554i
$33$	−13.2036	+	7.62310i	−2.29845	+	1.32701i
$34$	0.800300	−	0.338911i	0.137250	−	0.0581228i
$35$	−0.844307	+	0.749673i	−0.142714	+	0.126718i
$36$	−4.18300	−	9.66475i	−0.697166	−	1.61079i
$37$	−0.126305	+	1.92704i	−0.0207644	+	0.316804i	0.974824	+	0.222976i	$0.0715771\pi$
$37$	−0.126305	+	1.92704i	−0.0207644	+	0.316804i	−0.995588	+	0.0938283i	$0.970090\pi$
$38$	−6.45923	−	2.13597i	−1.04783	−	0.346501i
$39$	−3.86276	−	0.508542i	−0.618537	−	0.0814319i
$40$	1.13350	−	0.414918i	0.179223	−	0.0656043i
$41$	1.97608	−	4.77068i	0.308612	−	0.745055i	−0.691139	−	0.722722i	$-0.742891\pi$
$41$	1.97608	−	4.77068i	0.308612	−	0.745055i	0.999751	−	0.0223326i	$-0.00710929\pi$
$42$	2.24648	+	10.5200i	0.346639	+	1.62328i
$43$	−6.87655	+	1.36783i	−1.04866	+	0.208592i	−0.689203	−	0.724568i	$-0.742039\pi$
$43$	−6.87655	+	1.36783i	−1.04866	+	0.208592i	−0.359460	+	0.933160i	$0.617039\pi$
$44$	−10.5930	−	0.526718i	−1.59695	−	0.0794057i
$45$	0.146969	+	2.24232i	0.0219089	+	0.334265i
$46$	−2.77867	+	0.768072i	−0.409692	+	0.113246i
$47$	0.503610	−	1.87950i	0.0734591	−	0.274153i	−0.919420	−	0.393276i	$-0.871342\pi$
$47$	0.503610	−	1.87950i	0.0734591	−	0.274153i	0.992879	+	0.119123i	$0.0380083\pi$
$48$	1.88679	−	11.3441i	0.272335	−	1.63738i
$49$	−0.0860931	−	6.99947i	−0.0122990	−	0.999924i
$50$	6.81329	−	0.0537156i	0.963545	−	0.00759653i
$51$	−0.781446	+	1.58462i	−0.109424	+	0.221891i
$52$	−2.06566	−	1.75470i	−0.286456	−	0.243333i
$53$	10.7186	+	3.63846i	1.47231	+	0.499781i	0.938337	−	0.345721i	$-0.112366\pi$
$53$	10.7186	+	3.63846i	1.47231	+	0.499781i	0.533971	+	0.845503i	$0.320699\pi$
$54$	8.29338	+	4.00887i	1.12859	+	0.545538i
$55$	2.09085	+	0.866059i	0.281930	+	0.116779i
$56$	−2.65647	+	6.99594i	−0.354985	+	0.934872i
$57$	12.7777	−	5.29269i	1.69245	−	0.701034i
$58$	−0.116060	+	2.01389i	−0.0152394	+	0.264437i
$59$	0.839734	+	1.70281i	0.109324	+	0.221687i	0.944659	−	0.328054i	$-0.106393\pi$
$59$	0.839734	+	1.70281i	0.109324	+	0.221687i	−0.835335	+	0.549742i	$0.814726\pi$
$60$	−1.19327	+	2.14418i	−0.154050	+	0.276813i
$61$	−3.40556	−	10.0325i	−0.436038	−	1.28453i	−0.913846	−	0.406062i	$-0.866902\pi$
$61$	−3.40556	−	10.0325i	−0.436038	−	1.28453i	0.477808	−	0.878464i	$-0.341431\pi$
$62$	−12.6364	−	5.11783i	−1.60483	−	0.649966i
$63$	−11.1045	−	8.41276i	−1.39903	−	1.05991i
$64$	5.38304	−	5.91801i	0.672880	−	0.739751i
$65$	0.289165	+	0.500849i	0.0358665	+	0.0621226i
$66$	17.0018	−	13.2602i	2.09277	−	1.63222i
$67$	−2.22171	+	2.53337i	−0.271425	+	0.309501i	−0.871454	−	0.490478i	$-0.836822\pi$
$67$	−2.22171	+	2.53337i	−0.271425	+	0.309501i	0.600029	+	0.799978i	$0.295156\pi$
$68$	−1.05461	+	0.631256i	−0.127890	+	0.0765510i
$69$	3.25601	−	4.87296i	0.391977	−	0.586635i
$70$	1.03588	−	1.21518i	0.123812	−	0.145242i
$71$	12.5820	−	5.21163i	1.49321	−	0.618507i	0.521195	−	0.853438i	$-0.325486\pi$
$71$	12.5820	−	5.21163i	1.49321	−	0.618507i	0.972012	+	0.234931i	$0.0754864\pi$
$72$	7.74958	+	12.7182i	0.913297	+	1.49886i
$73$	9.50654	−	7.29463i	1.11266	−	0.853771i	0.122325	−	0.992490i	$-0.460965\pi$
$73$	9.50654	−	7.29463i	1.11266	−	0.853771i	0.990332	+	0.138719i	$0.0442984\pi$
$74$	−0.200102	−	2.72376i	−0.0232614	−	0.316631i
$75$	−10.4140	+	9.13283i	−1.20250	+	1.05457i
$76$	9.46478	+	1.72799i	1.08569	+	0.198215i
$77$	−12.5452	+	6.28281i	−1.42966	+	0.715993i
$78$	5.50974	−	0.0434384i	0.623855	−	0.00491843i
$79$	−0.365624	−	0.0979688i	−0.0411360	−	0.0110223i	0.238192	−	0.971218i	$-0.423445\pi$
$79$	−0.365624	−	0.0979688i	−0.0411360	−	0.0110223i	−0.279328	+	0.960196i	$0.590112\pi$
$80$	−1.50643	+	0.802900i	−0.168424	+	0.0897669i
$81$	−2.82970	+	0.758215i	−0.314411	+	0.0842461i
$82$	−1.83439	+	7.06849i	−0.202575	+	0.780584i
$83$	−13.5408	+	9.04769i	−1.48630	+	0.993113i	−0.493971	+	0.869478i	$0.664455\pi$
$83$	−13.5408	+	9.04769i	−1.48630	+	0.993113i	−0.992328	+	0.123635i	$0.960545\pi$
$84$	−5.20460	−	14.2950i	−0.567868	−	1.55972i
$85$	0.257225	−	0.0511653i	0.0279000	−	0.00554965i
$86$	9.36380	−	3.26113i	1.00972	−	0.351657i
$87$	−2.49646	−	3.25345i	−0.267649	−	0.348807i
$88$	14.9398	−	1.33468i	1.59258	−	0.142278i
$89$	−7.94453	+	10.3535i	−0.842118	+	1.09747i	0.151915	+	0.988394i	$0.451456\pi$
$89$	−7.94453	+	10.3535i	−0.842118	+	1.09747i	−0.994033	+	0.109077i	$0.965211\pi$
$90$	−0.644535	−	3.11187i	−0.0679399	−	0.328020i
$91$	−3.52078	−	0.677845i	−0.369078	−	0.0710575i
$92$	3.74158	−	1.61939i	0.390087	−	0.168833i
$93$	26.2449	−	8.90895i	2.72147	−	0.923815i
$94$	−0.337659	+	2.73098i	−0.0348269	+	0.281679i
$95$	−1.77793	−	1.02649i	−0.182412	−	0.105315i
$96$	−0.423305	+	16.2579i	−0.0432034	+	1.65931i
$97$			14.7184i			1.49443i	0.664583	+	0.747214i	$0.268609\pi$
$97$			14.7184i			1.49443i	−0.664583	+	0.747214i	$0.731391\pi$
$98$	1.48996	+	9.78673i	0.150509	+	0.988609i
$99$	−5.44761	+	27.3870i	−0.547506	+	2.75250i
$100$	−9.53230	+	1.40819i	−0.953230	+	0.140819i
$101$	7.35474	−	3.62695i	0.731824	−	0.360896i	−0.0378924	−	0.999282i	$-0.512064\pi$
$101$	7.35474	−	3.62695i	0.731824	−	0.360896i	0.769716	+	0.638386i	$0.220398\pi$
$102$	0.784491	−	2.37232i	0.0776762	−	0.234895i
$103$	1.24146	−	1.61791i	0.122325	−	0.159417i	−0.728176	−	0.685390i	$-0.759632\pi$
$103$	1.24146	−	1.61791i	0.122325	−	0.159417i	0.850502	+	0.525972i	$0.176299\pi$
$104$	3.23649	+	2.05353i	0.317364	+	0.201365i
$105$	0.0199626	+	3.24609i	0.00194815	+	0.316786i
$106$	−15.7244	−	2.99911i	−1.52729	−	0.291299i
$107$	0.657182	+	0.749373i	0.0635322	+	0.0724446i	0.782733	−	0.622358i	$-0.213825\pi$
$107$	0.657182	+	0.749373i	0.0635322	+	0.0724446i	−0.719201	+	0.694802i	$0.755492\pi$
$108$	−12.4001	−	3.99237i	−1.19320	−	0.384166i
$109$	1.13864	+	17.3722i	0.109062	+	1.66396i	0.605469	+	0.795869i	$0.292986\pi$
$109$	1.13864	+	17.3722i	0.109062	+	1.66396i	−0.496407	+	0.868090i	$0.665348\pi$
$110$	−3.09792	−	0.803962i	−0.295375	−	0.0766548i
$111$	3.92594	+	3.92594i	0.372634	+	0.372634i
$112$	2.35200	−	10.3183i	0.222243	−	0.974991i
$113$	10.1760	−	10.1760i	0.957277	−	0.957277i	−0.0418475	−	0.999124i	$-0.513324\pi$
$113$	10.1760	−	10.1760i	0.957277	−	0.957277i	0.999124	+	0.0418475i	$0.0133243\pi$
$114$	−16.8612	+	9.91286i	−1.57919	+	0.928424i
$115$	−0.868084	+	0.0568973i	−0.0809493	+	0.00530570i
$116$	−0.231442	−	2.84340i	−0.0214889	−	0.264003i
$117$	−5.36493	+	4.70491i	−0.495988	+	0.434969i
$118$	−1.50928	−	2.22070i	−0.138941	−	0.204432i
$119$	−0.804297	+	1.41308i	−0.0737298	+	0.129537i
$120$	1.25182	−	3.23663i	0.114275	−	0.295462i
$121$	13.5840	+	10.4234i	1.23491	+	0.947579i
$122$	6.73264	+	13.3854i	0.609545	+	1.21185i
$123$	−6.56609	−	13.3147i	−0.592045	−	1.20055i
$124$	18.7000	+	4.69593i	1.67931	+	0.421707i
$125$	4.10936	+	0.817403i	0.367552	+	0.0731107i
$126$	17.1990	+	9.61057i	1.53220	+	0.856178i
$127$	−5.03973			−0.447204			−0.223602	−	0.974681i	$-0.571782\pi$
$127$	−5.03973			−0.447204			−0.223602	+	0.974681i	$0.571782\pi$
$128$	−6.38178	+	9.34200i	−0.564075	+	0.825724i
$129$	−10.0787	+	17.4568i	−0.887377	+	1.53698i
$130$	−0.502995	−	0.644924i	−0.0441156	−	0.0565636i
$131$	4.17561	+	12.3010i	0.364825	+	1.07474i	0.962098	+	0.272702i	$0.0879174\pi$
$131$	4.17561	+	12.3010i	0.364825	+	1.07474i	−0.597273	+	0.802038i	$0.703749\pi$
$132$	−21.2187	+	21.8986i	−1.84685	+	1.90603i
$133$	12.0269	−	4.16522i	1.04286	−	0.361171i
$134$	2.61613	−	3.98294i	0.225999	−	0.344073i
$135$	2.20528	+	1.69217i	0.189800	+	0.145639i
$136$	1.35360	−	1.09047i	0.116070	−	0.0935071i
$137$	1.43503	−	1.10114i	0.122603	−	0.0940766i	−0.545640	−	0.838020i	$-0.683713\pi$
$137$	1.43503	−	1.10114i	0.122603	−	0.0940766i	0.668243	+	0.743943i	$0.267047\pi$
$138$	−3.60707	+	7.46215i	−0.307054	+	0.635220i
$139$	−1.25030	−	6.28569i	−0.106049	−	0.533145i	−0.996888	−	0.0788264i	$-0.974883\pi$
$139$	−1.25030	−	6.28569i	−0.106049	−	0.533145i	0.890839	−	0.454319i	$-0.150117\pi$
$140$	−1.21314	+	1.90467i	−0.102529	+	0.160974i
$141$	−3.10795	−	4.65137i	−0.261736	−	0.391716i
$142$	−16.6029	+	9.76103i	−1.39329	+	0.819128i
$143$	1.86001	+	6.94164i	0.155542	+	0.580489i
$144$	−13.3424	−	16.2972i	−1.11187	−	1.35810i
$145$	−0.157551	+	0.587987i	−0.0130839	+	0.0488297i
$146$	−11.8879	+	12.0768i	−0.983849	+	0.999486i
$147$	−15.2928	−	13.0822i	−1.26133	−	1.07900i
$148$	0.813142	+	3.77579i	0.0668399	+	0.310368i
$149$	3.68045	+	4.19675i	0.301515	+	0.343811i	0.882680	−	0.469974i	$-0.155737\pi$
$149$	3.68045	+	4.19675i	0.301515	+	0.343811i	−0.581166	+	0.813785i	$0.697403\pi$
$150$	12.7993	−	14.8290i	1.04506	−	1.21078i
$151$	8.59141	+	11.1965i	0.699159	+	0.911162i	0.999084	−	0.0428013i	$-0.0136282\pi$
$151$	8.59141	+	11.1965i	0.699159	+	0.911162i	−0.299925	+	0.953963i	$0.596962\pi$
$152$	−13.5946	−	0.568565i	−1.10267	−	0.0461167i
$153$	1.23835	+	2.98963i	0.100114	+	0.241697i
$154$	16.3418	−	11.2541i	1.31686	−	0.906885i
$155$	−3.42074	−	2.28567i	−0.274760	−	0.183589i
$156$	−7.70853	+	1.13877i	−0.617176	+	0.0911742i
$157$	−13.3714	−	11.7264i	−1.06715	−	0.935868i	−0.0690610	−	0.997612i	$-0.522000\pi$
$157$	−13.3714	−	11.7264i	−1.06715	−	0.935868i	−0.998092	+	0.0617443i	$0.980334\pi$
$158$	0.531266	+	0.0656858i	0.0422652	+	0.00522569i
$159$	28.1829	−	16.2714i	2.23505	−	1.29041i
$160$	1.95285	−	1.41927i	0.154386	−	0.112203i
$161$	3.25689	−	4.29895i	0.256679	−	0.338804i
$162$	3.81498	−	1.61557i	0.299733	−	0.126931i
$163$	13.6703	−	4.64046i	1.07074	−	0.363469i	0.270238	−	0.962794i	$-0.412898\pi$
$163$	13.6703	−	4.64046i	1.07074	−	0.363469i	0.800506	+	0.599325i	$0.204564\pi$
$164$	1.18640	−	10.2591i	0.0926423	−	0.801102i
$165$	5.83546	−	2.87773i	0.454290	−	0.224031i
$166$	17.1954	−	15.3215i	1.33462	−	1.18918i
$167$	1.61565	+	3.90052i	0.125023	+	0.301832i	0.973982	−	0.226628i	$-0.0727700\pi$
$167$	1.61565	+	3.90052i	0.125023	+	0.301832i	−0.848959	+	0.528459i	$0.822770\pi$
$168$	10.0863	+	19.0036i	0.778177	+	1.46616i
$169$	4.27209	−	10.3137i	0.328623	−	0.793365i
$170$	−0.350264	+	0.121986i	−0.0268640	+	0.00935593i
$171$	8.14227	−	23.9863i	0.622655	−	1.83428i
$172$	−12.4771	+	6.39953i	−0.951368	+	0.487959i
$173$	−12.5161	−	6.17227i	−0.951584	−	0.469269i	−0.100871	−	0.994900i	$-0.532163\pi$
$173$	−12.5161	−	6.17227i	−0.951584	−	0.469269i	−0.850713	+	0.525630i	$0.823829\pi$
$174$	4.13309	+	4.06843i	0.313329	+	0.308427i
$175$	−10.0649	+	7.82187i	−0.760834	+	0.591278i
$176$	−20.6638	+	4.79220i	−1.55759	+	0.361225i
$177$	5.27249	+	1.41276i	0.396305	+	0.106190i
$178$	9.10167	−	16.0556i	0.682199	−	1.20342i
$179$	3.22130	−	0.211135i	0.240771	−	0.0157810i	0.0554601	−	0.998461i	$-0.482337\pi$
$179$	3.22130	−	0.211135i	0.240771	−	0.0157810i	0.185311	+	0.982680i	$0.440671\pi$
$180$	1.51155	+	4.23244i	0.112665	+	0.315468i
$181$	0.175003	+	0.879801i	0.0130079	+	0.0653951i	0.986744	−	0.162284i	$-0.0518862\pi$
$181$	0.175003	+	0.879801i	0.0130079	+	0.0653951i	−0.973736	+	0.227679i	$0.926886\pi$
$182$	5.06387	+	0.260596i	0.375359	+	0.0193167i
$183$	−28.1411	−	11.6564i	−2.08025	−	0.861669i
$184$	−4.92370	+	3.00015i	−0.362980	+	0.221174i
$185$	0.107573	−	0.817098i	0.00790892	−	0.0600742i
$186$	−35.0161	+	17.6126i	−2.56751	+	1.29142i
$187$	3.25200	+	0.213147i	0.237810	+	0.0155869i
$188$	−0.0613584	−	3.89112i	−0.00447502	−	0.283789i
$189$	−16.8810	+	3.46588i	−1.22791	+	0.252106i
$190$	2.69102	+	1.08988i	0.195227	+	0.0790682i
$191$	12.7139	+	22.0211i	0.919946	+	1.59339i	0.799495	+	0.600673i	$0.205101\pi$
$191$	12.7139	+	22.0211i	0.919946	+	1.59339i	0.120451	+	0.992719i	$0.461566\pi$
$192$	−2.58781	−	22.8539i	−0.186759	−	1.64934i
$193$	10.3146	−	17.8654i	0.742459	−	1.28598i	−0.208914	−	0.977934i	$-0.566993\pi$
$193$	10.3146	−	17.8654i	0.742459	−	1.28598i	0.951373	−	0.308042i	$-0.0996738\pi$
$194$	−2.87951	−	20.6148i	−0.206737	−	1.48006i
$195$	1.63075	+	0.324375i	0.116780	+	0.0232290i
$196$	−4.00154	−	13.4159i	−0.285824	−	0.958282i
$197$	0.831392	−	1.24427i	0.0592342	−	0.0886503i	−0.800670	−	0.599105i	$-0.795523\pi$
$197$	0.831392	−	1.24427i	0.0592342	−	0.0886503i	0.859904	+	0.510455i	$0.170523\pi$
$198$	2.27202	−	39.4244i	0.161465	−	2.80177i
$199$	−1.93477	+	14.6960i	−0.137152	+	1.04177i	0.775012	+	0.631947i	$0.217744\pi$
$199$	−1.93477	+	14.6960i	−0.137152	+	1.04177i	−0.912164	+	0.409826i	$0.865590\pi$
$200$	13.0756	−	3.83723i	0.924584	−	0.271333i
$201$	1.26447	+	9.60459i	0.0891887	+	0.677455i
$202$	−9.59158	+	6.51885i	−0.674862	+	0.458665i
$203$	−2.11592	−	3.12493i	−0.148509	−	0.219327i
$204$	−0.634650	+	3.47619i	−0.0444344	+	0.243382i
$205$	−0.974660	+	1.97642i	−0.0680732	+	0.138039i
$206$	−1.42229	+	2.50895i	−0.0990955	+	0.174807i
$207$	−2.77812	−	10.3681i	−0.193093	−	0.720633i
$208$	−4.93483	−	2.24302i	−0.342169	−	0.155526i
$209$	−18.0389	−	18.0389i	−1.24778	−	1.24778i
$210$	−0.663024	−	4.54261i	−0.0457530	−	0.313470i
$211$	−12.1032	+	8.08713i	−0.833221	+	0.556741i	−0.897410	−	0.441197i	$-0.854554\pi$
$211$	−12.1032	+	8.08713i	−0.833221	+	0.556741i	0.0641889	+	0.997938i	$0.479554\pi$
$212$	22.6106	+	1.12427i	1.55290	+	0.0772154i
$213$	12.5855	−	37.0756i	0.862342	−	2.54038i
$214$	−1.06707	−	0.921012i	−0.0729432	−	0.0629591i
$215$	2.96652	−	0.390550i	0.202315	−	0.0266353i
$216$	18.1489	+	3.16582i	1.23488	+	0.215407i
$217$	24.5957	−	6.75278i	1.66966	−	0.458409i
$218$	−4.99350	−	24.1091i	−0.338202	−	1.63287i
$219$	2.25315	−	34.3765i	0.152254	−	2.32295i
$220$	4.49628	+	0.519966i	0.303139	+	0.0350561i
$221$	0.626145	+	0.549115i	0.0421191	+	0.0369374i
$222$	−6.26681	−	4.73067i	−0.420601	−	0.317502i
$223$			8.38442i			0.561462i	0.959786	+	0.280731i	$0.0905769\pi$
$223$			8.38442i			0.561462i	−0.959786	+	0.280731i	$0.909423\pi$
$224$	−1.27557	+	14.9122i	−0.0852277	+	0.996362i
$225$			25.3689i			1.69126i
$226$	−12.2618	+	16.2435i	−0.815644	+	1.08050i
$227$	−5.27111	−	4.62264i	−0.349856	−	0.306815i	0.466323	−	0.884614i	$-0.345578\pi$
$227$	−5.27111	−	4.62264i	−0.349856	−	0.306815i	−0.816179	+	0.577799i	$0.803912\pi$
$228$	21.6767	−	17.1828i	1.43557	−	1.13796i
$229$	0.778380	−	11.8758i	0.0514368	−	0.784774i	−0.891754	−	0.452521i	$-0.850525\pi$
$229$	0.778380	−	11.8758i	0.0514368	−	0.784774i	0.943190	−	0.332253i	$-0.107809\pi$
$230$	1.20472	−	0.249523i	0.0794370	−	0.0164531i
$231$	−10.2003	+	39.0266i	−0.671133	+	2.56776i
$232$	0.880444	+	3.93723i	0.0578040	+	0.258492i
$233$	−19.3917	+	2.55297i	−1.27039	+	0.167250i	−0.735416	−	0.677616i	$-0.763013\pi$
$233$	−19.3917	+	2.55297i	−1.27039	+	0.167250i	−0.534977	+	0.844866i	$0.679680\pi$
$234$	6.59373	−	7.63937i	0.431046	−	0.499401i
$235$	−0.266919	+	0.786319i	−0.0174119	+	0.0512938i
$236$	2.54838	+	2.81507i	0.165886	+	0.183246i
$237$	−0.904845	+	0.604598i	−0.0587760	+	0.0392729i
$238$	0.850056	−	2.13654i	0.0551010	−	0.138491i
$239$	9.96691	+	9.96691i	0.644706	+	0.644706i	0.951709	−	0.307003i	$-0.0993261\pi$
$239$	9.96691	+	9.96691i	0.644706	+	0.644706i	−0.307003	+	0.951709i	$0.599326\pi$
$240$	−1.12011	+	4.77818i	−0.0723029	+	0.308430i
$241$	5.75455	+	21.4763i	0.370683	+	1.38341i	0.859551	+	0.511050i	$0.170743\pi$
$241$	5.75455	+	21.4763i	0.370683	+	1.38341i	−0.488868	+	0.872358i	$0.662590\pi$
$242$	−21.0652	−	11.9416i	−1.35412	−	0.767633i
$243$	4.91743	−	9.97156i	0.315453	−	0.639676i
$244$	−12.0486	−	17.4306i	−0.771330	−	1.11588i
$245$	−0.158703	+	2.98310i	−0.0101391	+	0.190583i
$246$	11.8015	+	17.3642i	0.752434	+	1.10710i
$247$	−0.850925	−	6.46342i	−0.0541431	−	0.411258i
$248$	−27.1102	−	2.91873i	−1.72150	−	0.185339i
$249$	−6.11129	+	46.4199i	−0.387287	+	2.94174i
$250$	−5.91555	−	0.340912i	−0.374132	−	0.0215612i
$251$	7.00211	−	10.4794i	0.441969	−	0.661454i	−0.541879	−	0.840456i	$-0.682287\pi$
$251$	7.00211	−	10.4794i	0.441969	−	0.661454i	0.983849	+	0.179002i	$0.0572870\pi$
$252$	−25.9693	−	10.0959i	−1.63591	−	0.635983i
$253$	−10.6025	−	2.10897i	−0.666575	−	0.132590i
$254$	7.05872	−	0.985972i	0.442904	−	0.0618654i
$255$	0.377004	−	0.652990i	0.0236089	−	0.0408918i
$256$	7.11075	−	14.3331i	0.444422	−	0.895818i
$257$	3.53328	+	6.11982i	0.220400	+	0.381744i	0.954930	−	0.296833i	$-0.0959304\pi$
$257$	3.53328	+	6.11982i	0.220400	+	0.381744i	−0.734529	+	0.678577i	$0.762597\pi$
$258$	10.7011	−	26.4220i	0.666221	−	1.64496i
$259$	3.39243	+	3.82068i	0.210796	+	0.237405i
$260$	0.830676	+	0.804885i	0.0515164	+	0.0499169i
$261$	−7.49473	−	0.491230i	−0.463912	−	0.0304064i
$262$	−8.25499	−	16.4120i	−0.509995	−	1.01394i
$263$	−0.615911	+	4.67831i	−0.0379787	+	0.288477i	0.961907	+	0.273376i	$0.0881403\pi$
$263$	−0.615911	+	4.67831i	−0.0379787	+	0.288477i	−0.999886	+	0.0151010i	$0.995193\pi$
$264$	25.4351	−	34.8228i	1.56542	−	2.14320i
$265$	−4.46290	−	1.84859i	−0.274154	−	0.113558i
$266$	−16.0301	+	8.18681i	−0.982869	+	0.501966i
$267$	7.31970	+	36.7986i	0.447958	+	2.25204i
$268$	−2.88497	+	6.09039i	−0.176228	+	0.372029i
$269$	12.2118	−	0.800406i	0.744569	−	0.0488016i	0.311604	−	0.950212i	$-0.399134\pi$
$269$	12.2118	−	0.800406i	0.744569	−	0.0488016i	0.432965	+	0.901411i	$0.357467\pi$
$270$	−3.41980	−	1.93864i	−0.208123	−	0.117982i
$271$	−20.5850	−	5.51574i	−1.25045	−	0.335057i	−0.427940	−	0.903807i	$-0.640761\pi$
$271$	−20.5850	−	5.51574i	−1.25045	−	0.335057i	−0.822510	+	0.568750i	$0.807427\pi$
$272$	−1.68254	+	1.79215i	−0.102019	+	0.108665i
$273$	−8.13922	+	6.32534i	−0.492608	+	0.382827i
$274$	−1.79450	+	1.82302i	−0.108410	+	0.110133i
$275$	22.9146	+	11.3002i	1.38180	+	0.681428i
$276$	3.59222	−	11.1573i	0.216227	−	0.671590i
$277$	−2.56902	+	7.56808i	−0.154357	+	0.454722i	−0.996409	−	0.0846757i	$-0.973015\pi$
$277$	−2.56902	+	7.56808i	−0.154357	+	0.454722i	0.842051	+	0.539397i	$0.181348\pi$
$278$	2.98092	+	8.55923i	0.178784	+	0.513348i
$279$	19.4257	−	46.8977i	1.16298	−	2.80769i
$280$	1.32651	−	2.90504i	0.0792741	−	0.173610i
$281$	−2.04422	−	4.93518i	−0.121948	−	0.294408i	0.851103	−	0.524999i	$-0.175934\pi$
$281$	−2.04422	−	4.93518i	−0.121948	−	0.294408i	−0.973051	+	0.230591i	$0.925934\pi$
$282$	5.26303	+	5.90675i	0.313409	+	0.351742i
$283$	4.11671	−	2.03014i	0.244713	−	0.120679i	−0.315797	−	0.948827i	$-0.602272\pi$
$283$	4.11671	−	2.03014i	0.244713	−	0.120679i	0.560510	+	0.828148i	$0.310605\pi$
$284$	21.3447	−	16.9197i	1.26657	−	1.00400i
$285$	−5.58905	+	1.89723i	−0.331067	+	0.112382i
$286$	−3.96322	−	9.35868i	−0.234350	−	0.553390i
$287$	−5.30574	−	12.5896i	−0.313188	−	0.743143i
$288$	21.8760	+	20.2159i	1.28905	+	1.19123i
$289$	−14.3954	+	8.31116i	−0.846786	+	0.488892i
$290$	0.105634	−	0.854368i	0.00620305	−	0.0501702i
$291$	31.8143	+	27.9004i	1.86499	+	1.63555i
$292$	14.2877	−	19.2407i	0.836122	−	1.12598i
$293$	−14.4606	−	9.66230i	−0.844800	−	0.564477i	0.0561390	−	0.998423i	$-0.482121\pi$
$293$	−14.4606	−	9.66230i	−0.844800	−	0.564477i	−0.900939	+	0.433946i	$0.857121\pi$
$294$	23.9787	+	15.3312i	1.39847	+	0.894137i
$295$	−0.310069	−	0.748573i	−0.0180529	−	0.0435836i
$296$	−1.87760	−	5.12935i	−0.109133	−	0.298138i
$297$	21.0274	+	27.4035i	1.22013	+	1.59011i
$298$	−5.97596	−	5.15800i	−0.346178	−	0.298795i
$299$	−1.82145	−	2.07696i	−0.105337	−	0.120114i
$300$	−15.0257	+	23.2738i	−0.867510	+	1.34371i
$301$	−10.2108	+	15.4869i	−0.588542	+	0.892650i
$302$	−14.2238	−	14.0012i	−0.818485	−	0.805680i
$303$	6.10195	−	22.7728i	0.350548	−	1.30826i
$304$	19.1520	−	1.86330i	1.09844	−	0.106868i
$305$	1.17022	+	4.36733i	0.0670068	+	0.250073i
$306$	−2.31934	−	3.94505i	−0.132588	−	0.225524i
$307$	−10.9193	−	16.3419i	−0.623197	−	0.932681i	−0.999980	−	0.00637880i	$-0.997970\pi$
$307$	−10.9193	−	16.3419i	−0.623197	−	0.932681i	0.376782	−	0.926302i	$-0.377030\pi$
$308$	−20.6869	+	18.9599i	−1.17874	+	1.08034i
$309$	−1.14382	−	5.75039i	−0.0650699	−	0.327129i
$310$	5.23831	+	2.53211i	0.297516	+	0.143814i
$311$	−17.7730	+	13.6377i	−1.00781	+	0.773323i	−0.974102	−	0.226109i	$-0.927400\pi$
$311$	−17.7730	+	13.6377i	−1.00781	+	0.773323i	−0.0337120	+	0.999432i	$0.510733\pi$
$312$	10.5739	−	3.10307i	0.598629	−	0.175677i
$313$	−19.9632	−	15.3183i	−1.12839	−	0.865843i	−0.136211	−	0.990680i	$-0.543493\pi$
$313$	−19.9632	−	15.3183i	−1.12839	−	0.865843i	−0.992177	+	0.124837i	$0.960159\pi$
$314$	21.0223	+	13.8082i	1.18636	+	0.779242i
$315$	4.49397	+	3.89248i	0.253207	+	0.219316i
$316$	−0.756950	+	0.0119362i	−0.0425818	+	0.000671465i
$317$	1.01975	+	3.00409i	0.0572750	+	0.168727i	0.971802	−	0.235798i	$-0.0757703\pi$
$317$	1.01975	+	3.00409i	0.0572750	+	0.168727i	−0.914527	+	0.404525i	$0.867437\pi$
$318$	−36.2901	+	28.3037i	−2.03505	+	1.58719i
$319$	−3.78213	+	6.55084i	−0.211759	+	0.366777i
$320$	−2.45752	+	2.36991i	−0.137380	+	0.132482i
$321$	2.86556			0.159940
$322$	−3.72061	+	6.65835i	−0.207341	+	0.371055i
$323$	−2.89955	−	0.576757i	−0.161336	−	0.0320916i
$324$	−5.02725	+	3.00916i	−0.279292	+	0.167175i
$325$	2.88772	+	5.85571i	0.160182	+	0.324816i
$326$	−18.2390	+	9.17396i	−1.01017	+	0.508099i
$327$	39.7091	+	30.4698i	2.19592	+	1.68499i
$328$	0.345402	+	14.6012i	0.0190716	+	0.806216i
$329$	−2.60142	−	4.44247i	−0.143421	−	0.244922i
$330$	−7.61024	+	5.17224i	−0.418930	+	0.284723i
$331$	−17.9498	+	15.7416i	−0.986611	+	0.865235i	−0.990879	−	0.134756i	$-0.956975\pi$
$331$	−17.9498	+	15.7416i	−0.986611	+	0.865235i	0.00426769	+	0.999991i	$0.498642\pi$
$332$	−21.0867	+	24.8236i	−1.15728	+	1.36237i
$333$	10.1470	−	0.665069i	0.556052	−	0.0364455i
$334$	−3.02600	−	5.14705i	−0.165576	−	0.281634i
$335$	1.01681	−	1.01681i	0.0555545	−	0.0555545i
$336$	−17.8449	−	24.6435i	−0.973521	−	1.34441i
$337$	5.81598	+	5.81598i	0.316817	+	0.316817i	0.847543	−	0.530726i	$-0.178081\pi$
$337$	5.81598	+	5.81598i	0.316817	+	0.316817i	−0.530726	+	0.847543i	$0.678081\pi$
$338$	−3.96578	+	15.2814i	−0.215710	+	0.831198i
$339$	−2.70599	−	41.2855i	−0.146969	−	2.24232i
$340$	0.466719	−	0.239382i	0.0253114	−	0.0129823i
$341$	−33.7077	−	38.4363i	−1.82537	−	2.08144i
$342$	−6.71150	+	35.1886i	−0.362916	+	1.90278i
$343$	−13.3352	−	12.8520i	−0.720031	−	0.693942i
$344$	16.2236	−	11.4043i	0.874717	−	0.614878i
$345$	−1.52257	+	1.98425i	−0.0819722	+	0.106828i
$346$	18.7378	+	6.19633i	1.00735	+	0.333117i
$347$	−17.3421	+	8.55218i	−0.930973	+	0.459105i	−0.843541	−	0.537065i	$-0.819533\pi$
$347$	−17.3421	+	8.55218i	−0.930973	+	0.459105i	−0.0874323	+	0.996170i	$0.527866\pi$
$348$	−6.58482	−	4.88971i	−0.352983	−	0.262116i
$349$	−3.21746	+	16.1753i	−0.172227	+	0.865843i	0.793954	+	0.607978i	$0.208019\pi$
$349$	−3.21746	+	16.1753i	−0.172227	+	0.865843i	−0.966181	+	0.257865i	$0.916981\pi$
$350$	12.5668	−	12.9245i	0.671722	−	0.690845i
$351$			8.82687i			0.471144i
$352$	28.0044	−	10.7547i	1.49264	−	0.573227i
$353$	−15.8276	−	9.13804i	−0.842416	−	0.486369i	0.0156690	−	0.999877i	$-0.495012\pi$
$353$	−15.8276	−	9.13804i	−0.842416	−	0.486369i	−0.858085	+	0.513508i	$0.828346\pi$
$354$	−7.66113	−	0.947224i	−0.407185	−	0.0503444i
$355$	−5.50345	+	1.86817i	−0.292093	+	0.0991521i
$356$	−9.60684	+	24.2683i	−0.509161	+	1.28622i
$357$	1.52979	+	4.41717i	0.0809648	+	0.233781i
$358$	−4.47049	+	0.925933i	−0.236273	+	0.0489371i
$359$	−10.2350	+	13.3386i	−0.540184	+	0.703982i	−0.981086	−	0.193573i	$-0.937992\pi$
$359$	−10.2350	+	13.3386i	−0.540184	+	0.703982i	0.440901	+	0.897556i	$0.354659\pi$
$360$	−2.94514	−	5.63231i	−0.155223	−	0.296849i
$361$	2.52151	+	3.28609i	0.132711	+	0.172952i
$362$	−0.417237	−	1.19803i	−0.0219295	−	0.0629669i
$363$	48.2804	−	9.60358i	2.53407	−	0.504057i
$364$	−7.14352	+	0.625701i	−0.374422	+	0.0327957i
$365$	−4.25192	+	2.84104i	−0.222556	+	0.148707i
$366$	41.6954	+	10.8207i	2.17945	+	0.565605i
$367$	19.9941	−	5.35740i	1.04368	−	0.279654i	0.304045	−	0.952658i	$-0.401663\pi$
$367$	19.9941	−	5.35740i	1.04368	−	0.279654i	0.739639	+	0.673004i	$0.234996\pi$
$368$	6.30927	−	5.16533i	0.328893	−	0.269261i
$369$	−26.2636	−	7.03730i	−1.36723	−	0.366347i
$370$	0.00918861	+	1.16549i	0.000477693	+	0.0605907i
$371$	26.7776	−	13.4106i	1.39022	−	0.696243i
$372$	45.5984	−	31.5190i	2.36417	−	1.63418i
$373$	−25.1000	+	22.0121i	−1.29963	+	1.13974i	−0.318175	+	0.948032i	$0.603070\pi$
$373$	−25.1000	+	22.0121i	−1.29963	+	1.13974i	−0.981452	+	0.191710i	$0.938597\pi$
$374$	−4.59651	+	0.337684i	−0.237680	+	0.0174612i
$375$	9.55660	−	7.33304i	0.493501	−	0.378676i
$376$	0.847198	+	5.43796i	0.0436909	+	0.280441i
$377$	−1.78587	+	0.739731i	−0.0919770	+	0.0380981i
$378$	22.9657	−	8.15696i	1.18123	−	0.419549i
$379$	−6.21288	+	9.29824i	−0.319134	+	0.477618i	−0.956004	−	0.293353i	$-0.905229\pi$
$379$	−6.21288	+	9.29824i	−0.319134	+	0.477618i	0.636870	+	0.770971i	$0.280229\pi$
$380$	−3.98230	−	1.00003i	−0.204288	−	0.0513006i
$381$	−9.55337	+	10.8935i	−0.489434	+	0.558093i
$382$	−22.1155	−	28.3558i	−1.13153	−	1.45081i
$383$	6.31407	+	10.9363i	0.322634	+	0.558818i	0.981031	−	0.193853i	$-0.0620984\pi$
$383$	6.31407	+	10.9363i	0.322634	+	0.558818i	−0.658397	+	0.752671i	$0.728765\pi$
$384$	8.09566	+	31.5032i	0.413130	+	1.60764i
$385$	5.51768	−	2.32535i	0.281207	−	0.118511i
$386$	−10.9516	+	27.0404i	−0.557420	+	1.37632i
$387$	11.8670	+	34.9591i	0.603234	+	1.77707i
$388$	8.06618	+	28.3101i	0.409498	+	1.43723i
$389$	−14.4016	−	29.2036i	−0.730192	−	1.48068i	−0.871333	−	0.490693i	$-0.836744\pi$
$389$	−14.4016	−	29.2036i	−0.730192	−	1.48068i	0.141141	−	0.989989i	$-0.454923\pi$
$390$	−2.34751	−	0.135286i	−0.118871	−	0.00685049i
$391$	−1.15740	+	0.479409i	−0.0585320	+	0.0242448i
$392$	8.22931	+	18.0077i	0.415643	+	0.909528i
$393$	34.5043	+	14.2921i	1.74051	+	0.720943i
$394$	−0.921033	+	1.90539i	−0.0464010	+	0.0959923i
$395$	0.152965	+	0.0519246i	0.00769651	+	0.00261261i
$396$	4.53077	+	55.6630i	0.227680	+	2.79717i
$397$	−13.5656	+	27.5083i	−0.680838	+	1.38060i	0.232176	+	0.972674i	$0.425415\pi$
$397$	−13.5656	+	27.5083i	−0.680838	+	1.38060i	−0.913014	+	0.407929i	$0.866251\pi$
$398$	−0.165263	−	20.9620i	−0.00828388	−	1.05073i
$399$	13.7950	−	33.8921i	0.690613	−	1.69673i
$400$	−17.5632	+	7.93259i	−0.878158	+	0.396630i
$401$	1.31852	−	4.92079i	0.0658438	−	0.245732i	−0.925158	−	0.379583i	$-0.876068\pi$
$401$	1.31852	−	4.92079i	0.0658438	−	0.245732i	0.991002	+	0.133851i	$0.0427342\pi$
$402$	−3.65008	−	13.2050i	−0.182049	−	0.658603i
$403$	−0.854442	−	13.0363i	−0.0425628	−	0.649382i
$404$	12.1588	−	11.0069i	0.604922	−	0.547614i
$405$	1.22618	−	0.243902i	0.0609292	−	0.0121196i
$406$	3.57496	+	3.96287i	0.177422	+	0.196674i
$407$	3.91911	−	9.46157i	0.194263	−	0.468992i
$408$	0.208820	−	4.99297i	0.0103381	−	0.247189i
$409$	−7.24253	−	0.953497i	−0.358120	−	0.0471474i	−0.0506803	−	0.998715i	$-0.516139\pi$
$409$	−7.24253	−	0.953497i	−0.358120	−	0.0471474i	−0.307440	+	0.951568i	$0.599472\pi$
$410$	0.978459	−	2.95888i	0.0483226	−	0.146129i
$411$	0.340118	−	5.18920i	0.0167768	−	0.255964i
$412$	1.50123	−	3.79233i	0.0739602	−	0.186835i
$413$	4.76651	+	1.58539i	0.234545	+	0.0780119i
$414$	5.91950	+	13.9782i	0.290928	+	0.686992i
$415$	6.01883	−	3.47497i	0.295453	−	0.170580i
$416$	7.35062	+	2.17616i	0.360394	+	0.106695i
$417$	−15.9568	−	9.21266i	−0.781408	−	0.451146i
$418$	28.7947	+	21.7365i	1.40840	+	1.06317i
$419$	5.30855	−	26.6879i	0.259339	−	1.30379i	−0.603116	−	0.797654i	$-0.706074\pi$
$419$	5.30855	−	26.6879i	0.259339	−	1.30379i	0.862455	−	0.506134i	$-0.168926\pi$
$420$	1.81736	+	6.23274i	0.0886781	+	0.304127i
$421$	−25.8016	−	17.2401i	−1.25749	−	0.840230i	−0.265206	−	0.964192i	$-0.585440\pi$
$421$	−25.8016	−	17.2401i	−1.25749	−	0.840230i	−0.992287	+	0.123962i	$0.960440\pi$
$422$	15.3698	−	13.6948i	0.748191	−	0.666654i
$423$	−10.1581	−	1.33734i	−0.493903	−	0.0650236i
$424$	−31.8888	+	2.84887i	−1.54865	+	0.138353i
$425$	2.93549	−	0.386465i	0.142392	−	0.0187463i
$426$	−10.3739	+	54.3909i	−0.502619	+	2.63525i
$427$	−25.2160	−	12.2430i	−1.22029	−	0.592479i
$428$	1.67474	+	1.08122i	0.0809515	+	0.0522629i
$429$	18.5304	+	9.13819i	0.894657	+	0.441196i
$430$	−4.07855	+	1.12738i	−0.196685	+	0.0543672i
$431$	30.3906	−	8.14313i	1.46386	−	0.392241i	0.563041	−	0.826429i	$-0.309631\pi$
$431$	30.3906	−	8.14313i	1.46386	−	0.392241i	0.900822	+	0.434188i	$0.142965\pi$
$432$	−26.0390	−	0.883445i	−1.25280	−	0.0425048i
$433$	17.6528	−	17.6528i	0.848341	−	0.848341i	−0.141585	−	0.989926i	$-0.545220\pi$
$433$	17.6528	−	17.6528i	0.848341	−	0.848341i	0.989926	+	0.141585i	$0.0452200\pi$
$434$	−33.1280	+	14.2700i	−1.59020	+	0.684980i
$435$	0.972298	+	1.45515i	0.0466181	+	0.0697690i
$436$	11.7107	+	32.7906i	0.560839	+	1.57039i
$437$	9.28600	+	3.15217i	0.444210	+	0.150789i
$438$	3.56961	+	48.5891i	0.170563	+	2.32168i
$439$	0.0395474	+	0.300392i	0.00188749	+	0.0143369i	0.992363	−	0.123354i	$-0.0393652\pi$
$439$	0.0395474	+	0.300392i	0.00188749	+	0.0143369i	−0.990475	+	0.137691i	$0.956032\pi$
$440$	−6.39928	+	0.151380i	−0.305074	+	0.00721674i
$441$	−36.4817	+	5.26015i	−1.73722	+	0.250483i
$442$	−0.984418	−	0.646600i	−0.0468240	−	0.0307556i
$443$	−29.6811	−	1.94540i	−1.41019	−	0.0924287i	−0.658815	−	0.752305i	$-0.728942\pi$
$443$	−29.6811	−	1.94540i	−1.41019	−	0.0924287i	−0.751375	+	0.659876i	$0.770609\pi$
$444$	9.70290	+	5.39981i	0.460479	+	0.256264i
$445$	3.67212	−	4.18725i	0.174075	−	0.198495i
$446$	−1.64033	−	11.7434i	−0.0776718	−	0.556064i
$447$	16.0481			0.759051
$448$	−1.13083	−	21.1358i	−0.0534268	−	0.998572i
$449$	4.57716			0.216009			0.108005	−	0.994150i	$-0.465554\pi$
$449$	4.57716			0.216009			0.108005	+	0.994150i	$0.465554\pi$
$450$	−4.96317	−	35.5320i	−0.233966	−	1.67500i
$451$	−18.0552	+	20.5880i	−0.850188	+	0.969453i
$452$	13.9962	−	25.1498i	0.658327	−	1.18295i
$453$	40.4877	+	2.65370i	1.90228	+	0.124682i
$454$	8.28718	+	5.44330i	0.388936	+	0.255467i
$455$	1.48039	+	0.386927i	0.0694017	+	0.0181394i
$456$	−26.9991	+	28.3074i	−1.26435	+	1.32561i
$457$	−2.84165	−	21.5845i	−0.132927	−	1.00968i	−0.919751	−	0.392503i	$-0.871609\pi$
$457$	−2.84165	−	21.5845i	−0.132927	−	1.00968i	0.786824	−	0.617178i	$-0.211724\pi$
$458$	1.23317	+	16.7857i	0.0576221	+	0.784344i
$459$	3.79043	+	1.28668i	0.176922	+	0.0600570i
$460$	−1.63854	+	0.585178i	−0.0763971	+	0.0272841i
$461$	−1.16336	−	1.74109i	−0.0541829	−	0.0810905i	0.803389	−	0.595455i	$-0.203028\pi$
$461$	−1.16336	−	1.74109i	−0.0541829	−	0.0810905i	−0.857572	+	0.514364i	$0.828028\pi$
$462$	6.65159	−	56.6569i	0.309460	−	2.63592i
$463$	19.2855	−	19.2855i	0.896273	−	0.896273i	−0.0988315	−	0.995104i	$-0.531510\pi$
$463$	19.2855	−	19.2855i	0.896273	−	0.896273i	0.995104	+	0.0988315i	$0.0315105\pi$
$464$	−2.00344	−	5.34229i	−0.0930075	−	0.248010i
$465$	−11.4249	+	3.06130i	−0.529819	+	0.141965i
$466$	26.6609	−	7.36952i	1.23504	−	0.341386i
$467$	27.6362	+	13.6287i	1.27885	+	0.630659i	0.949565	−	0.313572i	$-0.101526\pi$
$467$	27.6362	+	13.6287i	1.27885	+	0.630659i	0.329285	+	0.944231i	$0.393192\pi$
$468$	−7.74072	+	11.9898i	−0.357815	+	0.554230i
$469$	0.637766	+	8.89219i	0.0294493	+	0.410603i
$470$	0.220016	−	1.15355i	0.0101486	−	0.0532094i
$471$	−50.6940	+	6.67399i	−2.33585	+	0.307521i
$472$	−4.12005	−	3.44427i	−0.189641	−	0.158535i
$473$	36.8629	+	4.85310i	1.69496	+	0.223146i
$474$	1.14906	−	1.02383i	0.0527779	−	0.0470262i
$475$	−19.2709	−	12.8764i	−0.884211	−	0.590811i
$476$	−0.772610	+	3.15877i	−0.0354125	+	0.144782i
$477$	11.6279	−	58.4572i	0.532403	−	2.67657i
$478$	−15.9097	−	12.0099i	−0.727694	−	0.549319i
$479$	3.75968	+	2.17065i	0.171784	+	0.0991797i	0.583427	−	0.812166i	$-0.301711\pi$
$479$	3.75968	+	2.17065i	0.171784	+	0.0991797i	−0.411643	+	0.911345i	$0.635045\pi$
$480$	0.634043	−	6.91153i	0.0289400	−	0.315467i
$481$	2.26645	−	1.30854i	0.103341	−	0.0596641i
$482$	−12.2615	−	28.9542i	−0.558497	−	1.31883i
$483$	−3.11851	−	15.1890i	−0.141897	−	0.691124i
$484$	31.8405	+	12.6043i	1.44729	+	0.572925i
$485$	0.410811	−	6.26777i	0.0186540	−	0.284605i
$486$	−4.93659	+	14.9284i	−0.223928	+	0.677165i
$487$	14.6743	+	1.93191i	0.664956	+	0.0875431i	0.455446	−	0.890263i	$-0.349480\pi$
$487$	14.6743	+	1.93191i	0.664956	+	0.0875431i	0.209510	+	0.977806i	$0.432813\pi$
$488$	20.2855	+	22.0564i	0.918282	+	0.998445i
$489$	15.8832	−	38.3454i	0.718262	−	1.73404i
$490$	−0.361331	−	4.20922i	−0.0163233	−	0.190153i
$491$	34.7622	−	6.91463i	1.56880	−	0.312053i	0.667283	−	0.744804i	$-0.267457\pi$
$491$	34.7622	−	6.91463i	1.56880	−	0.312053i	0.901514	+	0.432751i	$0.142457\pi$
$492$	−19.9265	−	22.0118i	−0.898354	−	0.992367i
$493$	0.0573319	+	0.874716i	0.00258210	+	0.0393952i
$494$	2.45632	+	8.88629i	0.110515	+	0.399813i
$495$	3.08425	−	11.5106i	0.138627	−	0.517362i
$496$	38.5421	−	1.21583i	1.73059	−	0.0545924i
$497$	13.5837	−	33.3730i	0.609312	−	1.49698i
$498$	−0.522011	−	66.2120i	−0.0233919	−	2.96703i
$499$	−5.39925	+	10.9486i	−0.241704	+	0.490126i	−0.983594	−	0.180394i	$-0.942263\pi$
$499$	−5.39925	+	10.9486i	−0.241704	+	0.490126i	0.741891	+	0.670521i	$0.233929\pi$
$500$	8.35211	−	0.679832i	0.373518	−	0.0304030i
$501$	11.4938	+	3.90160i	0.513503	+	0.174311i
$502$	−7.75708	+	16.0475i	−0.346215	+	0.716235i
$503$	−28.5371	−	11.8204i	−1.27241	−	0.527048i	−0.358711	−	0.933449i	$-0.616784\pi$
$503$	−28.5371	−	11.8204i	−1.27241	−	0.527048i	−0.913695	+	0.406401i	$0.866784\pi$
$504$	38.3482	+	9.05986i	1.70817	+	0.403558i
$505$	−3.23321	+	1.33924i	−0.143876	+	0.0595955i
$506$	15.2627	+	0.879583i	0.678508	+	0.0391022i
$507$	−14.1953	−	28.7851i	−0.630434	−	1.27839i
$508$	−9.69367	+	2.76194i	−0.430087	+	0.122541i
$509$	2.97759	+	8.77168i	0.131979	+	0.388798i	0.992750	−	0.120194i	$-0.0383516\pi$
$509$	2.97759	+	8.77168i	0.131979	+	0.388798i	−0.860771	+	0.508992i	$0.830018\pi$
$510$	−0.400287	+	0.988345i	−0.0177250	+	0.0437647i
$511$	3.94474	−	31.4570i	0.174505	−	1.39157i
$512$	−7.15530	+	21.4663i	−0.316223	+	0.948685i
$513$	−15.6670	−	27.1360i	−0.691713	−	1.19808i
$514$	−6.14605	−	7.88027i	−0.271091	−	0.347584i
$515$	−0.573830	+	0.654328i	−0.0252860	+	0.0288331i
$516$	−9.81892	+	39.1006i	−0.432254	+	1.72131i
$517$	−5.73274	+	8.57965i	−0.252126	+	0.377333i
$518$	−5.49898	−	4.68760i	−0.241611	−	0.205961i
$519$	−37.0673	+	15.3538i	−1.62707	+	0.673956i
$520$	−1.32093	−	0.964822i	−0.0579264	−	0.0423102i
$521$	0.247387	−	0.189826i	0.0108382	−	0.00831645i	−0.603328	−	0.797493i	$-0.706159\pi$
$521$	0.247387	−	0.189826i	0.0108382	−	0.00831645i	0.614166	+	0.789177i	$0.289492\pi$
$522$	10.5933	−	0.778243i	0.463658	−	0.0340628i
$523$	−10.5995	+	9.29550i	−0.463483	+	0.406464i	−0.858985	−	0.512002i	$-0.828904\pi$
$523$	−10.5995	+	9.29550i	−0.463483	+	0.406464i	0.395501	+	0.918465i	$0.370571\pi$
$524$	14.7729	+	21.3719i	0.645358	+	0.933636i
$525$	−2.17191	+	36.5828i	−0.0947901	+	1.59660i
$526$	−0.0526096	−	6.67301i	−0.00229389	−	0.290957i
$527$	−5.72257	−	1.53336i	−0.249279	−	0.0667941i
$528$	−28.8120	+	53.7495i	−1.25388	+	2.33915i
$529$	−18.2024	+	4.87732i	−0.791410	+	0.212058i
$530$	6.61246	+	1.71605i	0.287227	+	0.0745403i
$531$	8.31242	−	5.55418i	0.360728	−	0.241031i
$532$	20.8504	−	14.6027i	0.903978	−	0.633108i
$533$	−6.86328	+	1.36519i	−0.297282	+	0.0591330i
$534$	−17.4514	−	50.1087i	−0.755194	−	2.16842i
$535$	−0.258942	−	0.337460i	−0.0111950	−	0.0145897i
$536$	2.84922	−	9.09471i	0.123067	−	0.392831i
$537$	5.64996	−	7.36317i	0.243814	−	0.317744i
$538$	−16.9475	+	3.51019i	−0.730659	+	0.151335i
$539$	−11.4990	+	35.2954i	−0.495298	+	1.52028i
$540$	5.16911	+	2.04624i	0.222443	+	0.0880561i
$541$	16.0549	−	5.44989i	0.690253	−	0.234309i	0.0457969	−	0.998951i	$-0.485417\pi$
$541$	16.0549	−	5.44989i	0.690253	−	0.234309i	0.644456	+	0.764642i	$0.277084\pi$
$542$	29.9108	+	3.69818i	1.28478	+	0.158850i
$543$	2.23346	+	1.28949i	0.0958469	+	0.0553372i
$544$	2.00597	−	2.83928i	0.0860054	−	0.121733i
$545$		−	7.42967i		−	0.318252i
$546$	10.1624	−	10.4517i	0.434912	−	0.447293i
$547$	−0.571240	+	2.87182i	−0.0244245	+	0.122790i	−0.991074	−	0.133313i	$-0.957439\pi$
$547$	−0.571240	+	2.87182i	−0.0244245	+	0.122790i	0.966650	+	0.256103i	$0.0824386\pi$
$548$	2.15675	−	2.90443i	0.0921318	−	0.124071i
$549$	−50.0341	+	24.6741i	−2.13540	+	1.05306i
$550$	−34.3053	−	11.3443i	−1.46278	−	0.483720i
$551$	4.17724	−	5.44388i	0.177956	−	0.231917i
$552$	−2.84851	+	16.3299i	−0.121241	+	0.695045i
$553$	−0.864208	+	0.506062i	−0.0367498	+	0.0215199i
$554$	2.11759	−	11.1026i	0.0899676	−	0.471703i
$555$	−1.56227	−	1.78142i	−0.0663145	−	0.0756172i
$556$	−5.84966	−	11.4050i	−0.248081	−	0.483680i
$557$	1.05150	+	16.0428i	0.0445535	+	0.679755i	0.960469	+	0.278385i	$0.0897992\pi$
$557$	1.05150	+	16.0428i	0.0445535	+	0.679755i	−0.915916	+	0.401370i	$0.868534\pi$
$558$	−18.0328	+	69.4861i	−0.763390	+	2.94158i
$559$	6.71853	+	6.71853i	0.284164	+	0.284164i
$560$	−1.28959	+	4.32837i	−0.0544950	+	0.182907i
$561$	6.62526	−	6.62526i	0.279719	−	0.279719i
$562$	3.82868	+	6.51236i	0.161503	+	0.274707i
$563$	−14.5459	+	0.953386i	−0.613035	+	0.0401804i	−0.368758	−	0.929525i	$-0.620217\pi$
$563$	−14.5459	+	0.953386i	−0.613035	+	0.0401804i	−0.244276	+	0.969706i	$0.578550\pi$
$564$	−8.52709	−	7.24342i	−0.359055	−	0.305003i
$565$	−4.61742	+	4.04937i	−0.194256	+	0.170358i
$566$	−5.36876	+	3.64884i	−0.225666	+	0.153372i
$567$	−3.83403	+	6.73607i	−0.161014	+	0.282888i
$568$	−26.5855	+	27.8738i	−1.11550	+	1.16956i
$569$	−21.8946	−	16.8003i	−0.917867	−	0.704305i	0.0376337	−	0.999292i	$-0.488018\pi$
$569$	−21.8946	−	16.8003i	−0.917867	−	0.704305i	−0.955501	+	0.294987i	$0.904685\pi$
$570$	7.45694	−	3.75073i	0.312337	−	0.157101i
$571$	8.92625	+	18.1006i	0.373552	+	0.757488i	0.999754	−	0.0221723i	$-0.00705825\pi$
$571$	8.92625	+	18.1006i	0.373552	+	0.757488i	−0.626202	+	0.779661i	$0.715392\pi$
$572$	7.38187	+	12.3325i	0.308652	+	0.515650i
$573$	71.7000	+	14.2620i	2.99531	+	0.595804i
$574$	9.89434	+	16.5952i	0.412982	+	0.692672i
$575$	−9.82123			−0.409573
$576$	−34.5948	−	24.0349i	−1.44145	−	1.00145i
$577$	−19.5186	+	33.8072i	−0.812569	+	1.40741i	0.0984912	+	0.995138i	$0.468598\pi$
$577$	−19.5186	+	33.8072i	−0.812569	+	1.40741i	−0.911060	+	0.412273i	$0.864735\pi$
$578$	18.5364	−	14.4571i	0.771011	−	0.601334i
$579$	−19.0641	−	56.1611i	−0.792277	−	2.33397i
$580$	0.0191955	+	1.21731i	0.000797051	+	0.0505459i
$581$	−8.14585	+	42.3101i	−0.337947	+	1.75532i
$582$	−50.0181	−	32.8536i	−2.07332	−	1.36183i
$583$	−47.6223	−	36.5419i	−1.97231	−	1.51341i
$584$	−16.2473	+	29.7441i	−0.672317	+	1.23082i
$585$	2.41595	−	1.85382i	0.0998872	−	0.0766462i
$586$	22.1441	+	10.7041i	0.914766	+	0.442182i
$587$	5.15145	+	25.8981i	0.212623	+	1.06893i	0.928679	+	0.370885i	$0.120946\pi$
$587$	5.15145	+	25.8981i	0.212623	+	1.06893i	−0.716056	+	0.698043i	$0.754054\pi$
$588$	−36.5844	−	16.7820i	−1.50871	−	0.692078i
$589$	25.7650	+	38.5601i	1.06163	+	1.58884i
$590$	0.580738	+	0.987801i	0.0239086	+	0.0406671i
$591$	−1.11352	−	4.15573i	−0.0458042	−	0.170944i
$592$	3.63330	+	6.81692i	0.149328	+	0.280174i
$593$	−1.11480	+	4.16050i	−0.0457795	+	0.170851i	−0.985031	−	0.172379i	$-0.944855\pi$
$593$	−1.11480	+	4.16050i	−0.0457795	+	0.170851i	0.939251	+	0.343231i	$0.111521\pi$
$594$	−34.8126	−	34.2679i	−1.42838	−	1.40603i
$595$	0.381947	−	0.579305i	0.0156583	−	0.0237492i
$596$	9.37913	+	6.05524i	0.384184	+	0.248032i
$597$	28.0983	+	32.0400i	1.14999	+	1.31131i
$598$	2.95748	+	2.55268i	0.120940	+	0.104387i
$599$	27.5842	+	35.9485i	1.12706	+	1.46881i	0.863623	+	0.504139i	$0.168190\pi$
$599$	27.5842	+	35.9485i	1.12706	+	1.46881i	0.263439	+	0.964676i	$0.415143\pi$
$600$	16.4920	−	35.5372i	0.673282	−	1.45080i
$601$	5.63544	+	13.6052i	0.229874	+	0.554966i	0.996162	−	0.0875322i	$-0.0278981\pi$
$601$	5.63544	+	13.6052i	0.229874	+	0.554966i	−0.766287	+	0.642498i	$0.777898\pi$
$602$	11.2716	−	23.6888i	0.459395	−	0.965485i
$603$	14.7525	+	9.85730i	0.600768	+	0.401420i
$604$	22.6612	+	16.8276i	0.922072	+	0.684706i
$605$	−5.49375	−	4.81789i	−0.223353	−	0.195875i
$606$	−4.09122	+	33.0897i	−0.166195	+	1.34418i
$607$	−20.0417	+	11.5711i	−0.813468	+	0.469656i	−0.848159	−	0.529742i	$-0.822289\pi$
$607$	−20.0417	+	11.5711i	−0.813468	+	0.469656i	0.0346907	+	0.999398i	$0.488955\pi$
$608$	−26.4601	+	6.35668i	−1.07310	+	0.257797i
$609$	−10.7656	−	1.35002i	−0.436244	−	0.0547056i
$610$	−2.49346	−	5.88802i	−0.100957	−	0.238399i
$611$	−2.49695	+	0.847599i	−0.101016	+	0.0342902i
$612$	4.02031	+	5.07175i	0.162511	+	0.205013i
$613$	23.7904	−	11.7321i	0.960886	−	0.473857i	0.106967	−	0.994263i	$-0.465886\pi$
$613$	23.7904	−	11.7321i	0.960886	−	0.473857i	0.853919	+	0.520406i	$0.174219\pi$
$614$	18.4909	+	20.7525i	0.746231	+	0.837501i
$615$	2.42451	+	5.85328i	0.0977656	+	0.236027i
$616$	25.2651	−	30.6027i	1.01796	−	1.23302i
$617$	−17.5242	+	42.3073i	−0.705500	+	1.70323i	0.00545103	+	0.999985i	$0.498265\pi$
$617$	−17.5242	+	42.3073i	−0.705500	+	1.70323i	−0.710951	+	0.703242i	$0.751735\pi$
$618$	2.72707	+	7.83032i	0.109699	+	0.314982i
$619$	−2.30735	+	6.79723i	−0.0927402	+	0.273204i	−0.983396	−	0.181475i	$-0.941913\pi$
$619$	−2.30735	+	6.79723i	−0.0927402	+	0.273204i	0.890655	+	0.454679i	$0.150246\pi$
$620$	−7.83224	−	2.52168i	−0.314550	−	0.101273i
$621$	−11.9084	−	5.87259i	−0.477869	−	0.235659i
$622$	22.2251	−	22.5783i	0.891144	−	0.905307i
$623$	4.71723	+	34.2041i	0.188992	+	1.37036i
$624$	−14.2029	+	6.41489i	−0.568571	+	0.256801i
$625$	21.5414	+	5.77201i	0.861657	+	0.230880i
$626$	30.9577	+	17.5495i	1.23732	+	0.701418i
$627$	−73.1866	+	4.79690i	−2.92279	+	0.191570i
$628$	−32.1456	−	15.2272i	−1.28275	−	0.607630i
$629$	−0.231534	−	1.16400i	−0.00923187	−	0.0464117i
$630$	−7.05585	−	4.57267i	−0.281112	−	0.182179i
$631$	−1.85412	−	0.768003i	−0.0738115	−	0.0305737i	0.345472	−	0.938429i	$-0.387719\pi$
$631$	−1.85412	−	0.768003i	−0.0738115	−	0.0305737i	−0.419284	+	0.907855i	$0.637719\pi$
$632$	1.05786	−	0.164808i	0.0420795	−	0.00655570i
$633$	−5.46247	+	41.4916i	−0.217114	+	1.64914i
$634$	−2.01600	−	4.00808i	−0.0800656	−	0.159181i
$635$	2.14615	+	0.140666i	0.0851672	+	0.00558215i
$636$	45.2911	−	46.7424i	1.79591	−	1.85346i
$637$	−7.82205	+	5.36685i	−0.309921	+	0.212642i
$638$	4.01570	−	9.91515i	0.158983	−	0.392544i
$639$	−35.8550	−	62.1026i	−1.41840	−	2.45674i
$640$	2.97840	−	3.80012i	0.117732	−	0.150213i
$641$	20.7973	−	36.0219i	0.821442	−	1.42278i	−0.0831656	−	0.996536i	$-0.526503\pi$
$641$	20.7973	−	36.0219i	0.821442	−	1.42278i	0.904608	−	0.426244i	$-0.140164\pi$
$642$	−4.01354	+	0.560617i	−0.158402	+	0.0221258i
$643$	−33.7173	−	6.70679i	−1.32968	−	0.264490i	−0.521413	−	0.853305i	$-0.674595\pi$
$643$	−33.7173	−	6.70679i	−1.32968	−	0.264490i	−0.808268	+	0.588815i	$0.799595\pi$
$644$	3.90850	−	10.0537i	0.154017	−	0.396171i
$645$	4.77919	−	7.15257i	0.188181	−	0.281632i
$646$	4.17400	+	0.240547i	0.164224	+	0.00946418i
$647$	5.06465	−	38.4698i	0.199112	−	1.51241i	−0.541631	−	0.840616i	$-0.682193\pi$
$647$	5.06465	−	38.4698i	0.199112	−	1.51241i	0.740743	−	0.671789i	$-0.234474\pi$
$648$	6.45254	−	5.19820i	0.253480	−	0.204205i
$649$	−1.31419	−	9.98228i	−0.0515865	−	0.391839i
$650$	−5.19019	−	7.63665i	−0.203576	−	0.299534i
$651$	32.0276	−	65.9651i	1.25526	−	2.58537i
$652$	23.7511	−	16.4175i	0.930165	−	0.642958i
$653$	20.7865	−	42.1509i	0.813440	−	1.64949i	0.0543362	−	0.998523i	$-0.482696\pi$
$653$	20.7865	−	42.1509i	0.813440	−	1.64949i	0.759104	−	0.650970i	$-0.225638\pi$
$654$	−61.5783	−	34.9079i	−2.40790	−	1.36501i
$655$	−1.43483	−	5.35485i	−0.0560634	−	0.209231i
$656$	−3.34035	−	20.3831i	−0.130419	−	0.795826i
$657$	−44.6156	−	44.6156i	−1.74062	−	1.74062i
$658$	4.51272	+	5.71326i	0.175924	+	0.222726i
$659$	−1.69234	+	1.13079i	−0.0659242	+	0.0440492i	−0.588096	−	0.808791i	$-0.700122\pi$
$659$	−1.69234	+	1.13079i	−0.0659242	+	0.0440492i	0.522171	+	0.852841i	$0.325122\pi$
$660$	9.64712	−	8.73320i	0.375514	−	0.339939i
$661$	−0.632870	+	1.86437i	−0.0246158	+	0.0725158i	−0.958544	−	0.284946i	$-0.908024\pi$
$661$	−0.632870	+	1.86437i	−0.0246158	+	0.0725158i	0.933928	+	0.357462i	$0.116358\pi$
$662$	22.0611	−	25.5596i	0.857430	−	0.993402i
$663$	2.37386	−	0.312524i	0.0921930	−	0.0121374i
$664$	24.6778	−	38.8937i	0.957686	−	1.50937i
$665$	−5.23784	+	1.43805i	−0.203115	+	0.0557654i
$666$	−14.0819	+	2.91666i	−0.545663	+	0.113018i
$667$	0.190173	−	2.90149i	0.00736354	−	0.112346i
$668$	5.24524	+	6.61703i	0.202944	+	0.256021i
$669$	18.1232	+	15.8936i	0.700683	+	0.614483i
$670$	−1.22524	+	1.62310i	−0.0473350	+	0.0627057i
$671$			56.1843i			2.16897i
$672$	29.8152	+	31.0249i	1.15014	+	1.19681i
$673$		−	24.1250i		−	0.929949i	−0.885324	−	0.464974i	$-0.846063\pi$
$673$		−	24.1250i		−	0.929949i	0.885324	−	0.464974i	$-0.153937\pi$
$674$	−9.28380	−	7.00812i	−0.357599	−	0.269943i
$675$	23.5936	+	20.6911i	0.908119	+	0.796399i
$676$	2.56489	−	22.1792i	0.0986494	−	0.853047i
$677$	0.242955	−	3.70678i	0.00933753	−	0.142463i	−0.990645	−	0.136468i	$-0.956425\pi$
$677$	0.242955	−	3.70678i	0.00933753	−	0.142463i	0.999982	−	0.00599527i	$-0.00190837\pi$
$678$	11.8671	+	57.2957i	0.455755	+	2.20043i
$679$	27.7044	+	27.3658i	1.06320	+	1.05020i
$680$	−0.606862	+	0.426591i	−0.0232721	+	0.0163590i
$681$	−19.9840	+	2.63094i	−0.765787	+	0.100818i
$682$	54.7312	+	47.2399i	2.09577	+	1.80891i
$683$	5.93728	−	17.4907i	0.227184	−	0.669261i	−0.772241	−	0.635330i	$-0.780864\pi$
$683$	5.93728	−	17.4907i	0.227184	−	0.669261i	0.999424	−	0.0339310i	$-0.0108026\pi$
$684$	2.51593	−	50.5988i	0.0961991	−	1.93469i
$685$	−0.641836	+	0.428861i	−0.0245233	+	0.0163859i
$686$	21.1918	+	15.3918i	0.809107	+	0.587662i
$687$	−24.1944	−	24.1944i	−0.923073	−	0.923073i
$688$	−20.4919	+	19.1470i	−0.781246	+	0.729973i
$689$	−3.97016	−	14.8168i	−0.151251	−	0.564477i
$690$	1.74433	−	3.07704i	0.0664056	−	0.117141i
$691$	8.15891	−	16.5446i	0.310380	−	0.629388i	−0.684660	−	0.728862i	$-0.740049\pi$
$691$	8.15891	−	16.5446i	0.310380	−	0.629388i	0.995040	+	0.0994744i	$0.0317161\pi$
$692$	−27.4568	−	5.01280i	−1.04375	−	0.190558i
$693$	41.4218	+	61.1744i	1.57348	+	2.32382i
$694$	22.6165	−	15.3711i	0.858510	−	0.583480i
$695$	0.356993	+	2.71163i	0.0135415	+	0.102858i
$696$	10.1794	+	5.56035i	0.385850	+	0.210765i
$697$	−0.414209	+	3.14623i	−0.0156893	+	0.119172i
$698$	1.34190	−	23.2848i	0.0507916	−	0.881344i
$699$	−31.2409	+	46.7552i	−1.18164	+	1.76845i
$700$	−15.0727	+	20.5609i	−0.569693	+	0.777127i
$701$	−2.44787	−	0.486912i	−0.0924549	−	0.0183904i	0.148646	−	0.988890i	$-0.452508\pi$
$701$	−2.44787	−	0.486912i	−0.0924549	−	0.0183904i	−0.241101	+	0.970500i	$0.577508\pi$
$702$	−1.72689	−	12.3631i	−0.0651773	−	0.466614i
$703$	−4.64508	+	8.04552i	−0.175193	+	0.303442i
$704$	−37.1194	+	20.5420i	−1.39899	+	0.774205i
$705$	1.19368	+	2.06751i	0.0449565	+	0.0778670i
$706$	23.9561	+	9.70238i	0.901599	+	0.365154i
$707$	6.84757	−	20.5874i	0.257529	−	0.774267i
$708$	10.9156	−	0.172127i	0.410234	−	0.00646892i
$709$	−5.96106	−	0.390709i	−0.223872	−	0.0146734i	−0.0469459	−	0.998897i	$-0.514949\pi$
$709$	−5.96106	−	0.390709i	−0.223872	−	0.0146734i	−0.176927	+	0.984224i	$0.556615\pi$
$710$	7.34272	−	3.69328i	0.275568	−	0.138606i
$711$	−0.260156	+	1.97608i	−0.00975662	+	0.0741089i
$712$	8.70764	−	35.8701i	0.326332	−	1.34429i
$713$	18.1558	+	7.52039i	0.679941	+	0.281641i
$714$	−3.00682	−	5.88747i	−0.112527	−	0.220333i
$715$	−0.598324	−	3.00798i	−0.0223761	−	0.112492i
$716$	6.08029	−	2.17148i	0.227231	−	0.0811522i
$717$	40.4372	−	2.65039i	1.51015	−	0.0989808i
$718$	11.7258	−	20.6846i	0.437603	−	0.771942i
$719$	36.7975	+	9.85987i	1.37232	+	0.367711i	0.868324	−	0.495997i	$-0.165197\pi$
$719$	36.7975	+	9.85987i	1.37232	+	0.367711i	0.503992	+	0.863708i	$0.331864\pi$
$720$	5.22692	+	7.31251i	0.194796	+	0.272521i
$721$	−0.737145	−	5.34497i	−0.0274527	−	0.199057i
$722$	−4.17455	−	4.10925i	−0.155361	−	0.152930i
$723$	57.3301	+	28.2721i	2.13213	+	1.05145i
$724$	0.818771	+	1.59635i	0.0304294	+	0.0593278i
$725$	−2.20900	+	6.50751i	−0.0820403	+	0.241683i
$726$	−65.7435	+	22.8965i	−2.43997	+	0.849769i
$727$	−3.81468	+	9.20946i	−0.141479	+	0.341560i	−0.978697	−	0.205309i	$-0.934180\pi$
$727$	−3.81468	+	9.20946i	−0.141479	+	0.341560i	0.837219	+	0.546868i	$0.184180\pi$
$728$	9.88292	−	2.27393i	0.366285	−	0.0842773i
$729$	−15.5955	−	37.6510i	−0.577613	−	1.39448i
$730$	5.39949	−	4.81105i	0.199844	−	0.178065i
$731$	3.86442	−	1.90572i	0.142931	−	0.0704856i
$732$	−60.5162	−	6.99831i	−2.23674	−	0.258665i
$733$	−25.0899	+	8.51687i	−0.926716	+	0.314578i	−0.743686	−	0.668529i	$-0.766924\pi$
$733$	−25.0899	+	8.51687i	−0.926716	+	0.314578i	−0.183031	+	0.983107i	$0.558591\pi$
$734$	−26.9559	+	11.4153i	−0.994962	+	0.421347i
$735$	6.14722	+	5.99783i	0.226744	+	0.221233i
$736$	−7.82631	+	8.46899i	−0.288482	+	0.312171i
$737$	15.4750	−	8.93447i	0.570027	−	0.329105i
$738$	38.1620	+	4.71835i	1.40476	+	0.173685i
$739$	21.4553	+	18.8158i	0.789246	+	0.692150i	0.955844	−	0.293875i	$-0.0949448\pi$
$739$	21.4553	+	18.8158i	0.789246	+	0.692150i	−0.166598	+	0.986025i	$0.553278\pi$
$740$	−0.240885	−	1.63060i	−0.00885512	−	0.0599421i
$741$	−15.5839	−	10.4128i	−0.572489	−	0.382525i
$742$	−34.8815	+	24.0218i	−1.28054	+	0.881870i
$743$	−1.59087	−	3.84069i	−0.0583632	−	0.140901i	0.892008	−	0.452020i	$-0.149296\pi$
$743$	−1.59087	−	3.84069i	−0.0583632	−	0.140901i	−0.950371	+	0.311119i	$0.899296\pi$
$744$	−57.6994	+	53.0669i	−2.11536	+	1.94553i
$745$	−1.45017	−	1.88989i	−0.0531300	−	0.0692404i
$746$	30.8490	−	35.7410i	1.12946	−	1.30857i
$747$	56.5402	+	64.4718i	2.06870	+	2.35890i
$748$	6.37188	−	1.37223i	0.232979	−	0.0501736i
$749$	2.63243	+	0.156287i	0.0961870	+	0.00571060i
$750$	−11.9505	+	12.1404i	−0.436370	+	0.443306i
$751$	−4.47527	+	16.7020i	−0.163305	+	0.609463i	0.834945	+	0.550333i	$0.185499\pi$
$751$	−4.47527	+	16.7020i	−0.163305	+	0.609463i	−0.998250	+	0.0591298i	$0.981167\pi$
$752$	−2.25048	−	7.45074i	−0.0820666	−	0.271701i
$753$	−9.37827	−	35.0002i	−0.341763	−	1.27548i
$754$	2.35660	−	1.38547i	0.0858222	−	0.0504557i
$755$	−3.34610	−	5.00779i	−0.121777	−	0.182252i
$756$	−30.5703	+	15.9178i	−1.11183	+	0.578924i
$757$	−6.97235	−	35.0524i	−0.253414	−	1.27400i	−0.872476	−	0.488658i	$-0.837487\pi$
$757$	−6.97235	−	35.0524i	−0.253414	−	1.27400i	0.619061	−	0.785343i	$-0.287513\pi$
$758$	6.88276	−	14.2387i	0.249993	−	0.517175i
$759$	−24.6569	+	18.9199i	−0.894988	+	0.686748i
$760$	5.77333	+	0.621565i	0.209421	+	0.0225465i
$761$	−16.3728	−	12.5633i	−0.593514	−	0.455419i	0.267813	−	0.963471i	$-0.413699\pi$
$761$	−16.3728	−	12.5633i	−0.593514	−	0.455419i	−0.861326	+	0.508052i	$0.830366\pi$
$762$	11.2494	−	17.1267i	0.407523	−	0.620434i
$763$	34.8168	+	30.1567i	1.26045	+	1.09175i
$764$	36.5229	+	35.3889i	1.32135	+	1.28032i
$765$	−0.443899	−	1.30768i	−0.0160492	−	0.0472794i
$766$	−10.9832	−	14.0823i	−0.396838	−	0.508813i
$767$	1.28647	−	2.22823i	0.0464517	−	0.0804567i
$768$	−17.5022	−	42.5401i	−0.631556	−	1.53503i
$769$	−13.5162			−0.487407			−0.243703	−	0.969850i	$-0.578362\pi$
$769$	−13.5162			−0.487407			−0.243703	+	0.969850i	$0.578362\pi$
$770$	−7.27322	+	4.33640i	−0.262108	+	0.156273i
$771$	19.9259	+	3.96351i	0.717615	+	0.142743i
$772$	10.0487	−	40.0158i	0.361662	−	1.44020i
$773$	−8.45455	−	17.1441i	−0.304089	−	0.616631i	0.690168	−	0.723649i	$-0.257537\pi$
$773$	−8.45455	−	17.1441i	−0.304089	−	0.616631i	−0.994257	+	0.107018i	$0.965870\pi$
$774$	−23.4605	−	46.6426i	−0.843270	−	1.67653i
$775$	−36.8479	−	28.2744i	−1.32362	−	1.01565i
$776$	−16.8362	−	38.0736i	−0.604385	−	1.36676i
$777$	14.6893	−	0.0903351i	0.526974	−	0.00324075i
$778$	25.8845	+	38.0855i	0.928006	+	1.36543i
$779$	18.6763	−	16.3787i	0.669148	−	0.586827i
$780$	3.31443	−	0.269782i	0.118675	−	0.00965976i
$781$	−72.0656	+	4.72343i	−2.57871	+	0.169018i
$782$	1.52728	−	0.897901i	0.0546153	−	0.0321089i
$783$	−6.56962	+	6.56962i	−0.234779	+	0.234779i
$784$	−15.0491	−	23.6119i	−0.537469	−	0.843283i
$785$	5.36684	+	5.36684i	0.191551	+	0.191551i
$786$	−51.1233	−	13.2674i	−1.82351	−	0.473232i
$787$	2.04802	+	31.2467i	0.0730039	+	1.11382i	0.864494	+	0.502643i	$0.167639\pi$
$787$	2.04802	+	31.2467i	0.0730039	+	1.11382i	−0.791490	+	0.611182i	$0.790694\pi$
$788$	0.917242	−	2.84891i	0.0326754	−	0.101488i
$789$	8.94479	+	10.1996i	0.318443	+	0.363115i
$790$	−0.224404	−	0.0428004i	−0.00798393	−	0.00152277i
$791$	−0.234147	−	38.0743i	−0.00832532	−	1.35377i
$792$	−17.2358	−	77.0761i	−0.612447	−	2.73878i
$793$	−8.74037	+	11.3907i	−0.310380	+	0.404495i
$794$	13.6185	−	41.1825i	0.483301	−	1.46151i
$795$	−12.4557	+	6.14248i	−0.441759	+	0.217851i
$796$	4.33247	+	29.3273i	0.153560	+	1.03948i
$797$	−3.41900	+	17.1885i	−0.121107	+	0.608847i	0.871791	+	0.489878i	$0.162959\pi$
$797$	−3.41900	+	17.1885i	−0.121107	+	0.608847i	−0.992898	+	0.118969i	$0.962041\pi$
$798$	−12.6908	+	50.1686i	−0.449251	+	1.77595i
$799$			1.19579i			0.0423040i
$800$	23.0473	−	14.5466i	0.814846	−	0.514299i
$801$	59.5110	+	34.3587i	2.10272	+	1.21400i
$802$	−0.884038	+	7.15009i	−0.0312165	+	0.252478i
$803$	−60.1726	+	20.4259i	−2.12345	+	0.720813i
$804$	7.69577	+	17.7810i	0.271409	+	0.627087i
$805$	−1.50692	+	1.73978i	−0.0531120	+	0.0613193i
$806$	3.74716	+	18.0916i	0.131988	+	0.637251i
$807$	21.4188	−	27.9135i	0.753978	−	0.982603i
$808$	−14.8764	+	17.7952i	−0.523349	+	0.626033i
$809$	−16.7778	−	21.8653i	−0.589877	−	0.768742i	0.399085	−	0.916914i	$-0.369328\pi$
$809$	−16.7778	−	21.8653i	−0.589877	−	0.768742i	−0.988962	+	0.148172i	$0.952661\pi$
$810$	−1.66968	+	0.581501i	−0.0586667	+	0.0204319i
$811$	−11.5469	+	2.29682i	−0.405467	+	0.0806524i	−0.393610	−	0.919277i	$-0.628774\pi$
$811$	−11.5469	+	2.29682i	−0.405467	+	0.0806524i	−0.0118564	+	0.999930i	$0.503774\pi$
$812$	−5.78244	−	4.85105i	−0.202924	−	0.170238i
$813$	−50.9437	+	34.0395i	−1.78667	+	1.19382i
$814$	−3.63811	+	14.0188i	−0.127516	+	0.491357i
$815$	−5.95097	+	1.59456i	−0.208454	+	0.0558550i
$816$	0.684347	+	7.03408i	0.0239569	+	0.246242i
$817$	−32.5792	−	8.72958i	−1.13980	−	0.305409i
$818$	10.3305	−	0.0814453i	0.361199	−	0.00284767i
$819$	−1.11889	+	18.8462i	−0.0390973	+	0.658539i
$820$	−0.791569	+	4.33568i	−0.0276428	+	0.151409i
$821$	30.7528	−	26.9695i	1.07328	−	0.941242i	0.0748469	−	0.997195i	$-0.476153\pi$
$821$	30.7528	−	26.9695i	1.07328	−	0.941242i	0.998433	+	0.0559535i	$0.0178198\pi$
$822$	0.538840	+	7.33462i	0.0187942	+	0.255824i
$823$	−2.03175	+	1.55901i	−0.0708222	+	0.0543438i	−0.643566	−	0.765391i	$-0.722546\pi$
$823$	−2.03175	+	1.55901i	−0.0708222	+	0.0543438i	0.572744	+	0.819735i	$0.305879\pi$
$824$	−1.36071	+	5.60530i	−0.0474027	+	0.195270i
$825$	67.8629	−	28.1097i	2.36268	−	0.978655i
$826$	−6.98621	−	1.28800i	−0.243081	−	0.0448153i
$827$	23.6728	−	35.4289i	0.823185	−	1.23198i	−0.146884	−	0.989154i	$-0.546924\pi$
$827$	23.6728	−	35.4289i	0.823185	−	1.23198i	0.970069	−	0.242830i	$-0.0780757\pi$
$828$	−11.0256	−	18.4200i	−0.383168	−	0.640140i
$829$	17.1974	−	19.6099i	0.597292	−	0.681081i	−0.371649	−	0.928373i	$-0.621207\pi$
$829$	17.1974	−	19.6099i	0.597292	−	0.681081i	0.968941	+	0.247292i	$0.0795408\pi$
$830$	−7.75023	+	6.04463i	−0.269014	+	0.209812i
$831$	11.4888	+	19.8992i	0.398541	+	0.690294i
$832$	−10.7211	−	1.60989i	−0.371689	−	0.0558130i
$833$	1.16442	+	4.14125i	0.0403448	+	0.143486i
$834$	24.1517	+	9.78162i	0.836306	+	0.338710i
$835$	−0.579148	−	1.70611i	−0.0200422	−	0.0590425i
$836$	−44.5829	−	24.8110i	−1.54193	−	0.858108i
$837$	−27.7722	−	56.3165i	−0.959948	−	1.94658i
$838$	−2.21402	+	38.4180i	−0.0764821	+	1.32713i
$839$	−14.2965	+	5.92180i	−0.493570	+	0.204443i	−0.615563	−	0.788088i	$-0.711071\pi$
$839$	−14.2965	+	5.92180i	−0.493570	+	0.204443i	0.121993	+	0.992531i	$0.461071\pi$
$840$	−3.76480	−	8.37413i	−0.129898	−	0.288935i
$841$	24.9128	+	10.3192i	0.859061	+	0.355835i
$842$	39.5110	+	19.0989i	1.36164	+	0.658191i
$843$	−14.5426	−	4.93655i	−0.500874	−	0.170024i
$844$	−18.8480	+	22.1882i	−0.648774	+	0.763748i
$845$	−2.10712	+	4.27282i	−0.0724872	+	0.146990i
$846$	14.4892	−	0.114232i	0.498150	−	0.00392738i
$847$	44.8764	−	6.18909i	1.54197	−	0.212659i
$848$	44.1065	−	10.2289i	1.51462	−	0.351261i
$849$	3.41548	−	12.7468i	0.117219	−	0.437468i
$850$	−4.03589	+	1.11559i	−0.138430	+	0.0382644i
$851$	0.257473	+	3.92827i	0.00882605	+	0.134660i
$852$	3.88887	−	78.2103i	0.133230	−	2.67944i
$853$	8.79219	−	1.74888i	0.301039	−	0.0598804i	−0.0422597	−	0.999107i	$-0.513456\pi$
$853$	8.79219	−	1.74888i	0.301039	−	0.0598804i	0.343299	+	0.939226i	$0.388456\pi$
$854$	37.7132	+	12.2144i	1.29052	+	0.417969i
$855$	−4.13684	+	9.98721i	−0.141477	+	0.341555i
$856$	−2.55720	−	1.18673i	−0.0874031	−	0.0405617i
$857$	2.94506	+	0.387724i	0.100601	+	0.0132444i	0.180659	−	0.983546i	$-0.442177\pi$
$857$	2.94506	+	0.387724i	0.100601	+	0.0132444i	−0.0800575	+	0.996790i	$0.525510\pi$
$858$	−27.7418	−	9.17381i	−0.947089	−	0.313189i
$859$	−0.138567	+	2.11412i	−0.00472783	+	0.0721327i	−0.999571	−	0.0292940i	$-0.990674\pi$
$859$	−0.138567	+	2.11412i	−0.00472783	+	0.0721327i	0.994843	+	0.101427i	$0.0323408\pi$
$860$	5.49193	−	2.37696i	0.187273	−	0.0810536i
$861$	−37.2705	−	12.3966i	−1.27018	−	0.422474i
$862$	−40.9724	+	17.3510i	−1.39553	+	0.590978i
$863$	−13.6102	+	7.85787i	−0.463297	+	0.267485i	−0.713430	−	0.700727i	$-0.752859\pi$
$863$	−13.6102	+	7.85787i	−0.463297	+	0.267485i	0.250132	+	0.968212i	$0.419526\pi$
$864$	36.6435	−	3.85690i	1.24664	−	0.131214i
$865$	5.15766	+	2.97778i	0.175366	+	0.101247i
$866$	−21.2712	+	28.1784i	−0.722826	+	0.957542i
$867$	−9.32318	+	46.8708i	−0.316632	+	1.59182i
$868$	43.6079	−	26.4679i	1.48015	−	0.898379i
$869$	1.66902	+	1.11521i	0.0566178	+	0.0378308i
$870$	−1.64650	−	1.84788i	−0.0558216	−	0.0626491i
$871$	4.52726	+	0.596025i	0.153400	+	0.0201955i
$872$	−22.8173	−	43.6360i	−0.772692	−	1.47770i
$873$	76.8378	−	10.1159i	2.60057	−	0.342371i
$874$	−13.6228	−	2.59827i	−0.460798	−	0.0878878i
$875$	9.17908	−	6.21526i	0.310310	−	0.210114i
$876$	−14.5056	−	67.3563i	−0.490099	−	2.27576i
$877$	16.4393	+	8.10696i	0.555116	+	0.273753i	0.698134	−	0.715967i	$-0.254014\pi$
$877$	16.4393	+	8.10696i	0.555116	+	0.273753i	−0.143018	+	0.989720i	$0.545681\pi$
$878$	−0.114159	−	0.412997i	−0.00385269	−	0.0139380i
$879$	−48.2972	+	12.9412i	−1.62902	+	0.436495i
$880$	8.93332	−	1.46398i	0.301142	−	0.0493508i
$881$	−15.7460	+	15.7460i	−0.530496	+	0.530496i	−0.920720	−	0.390224i	$-0.872398\pi$
$881$	−15.7460	+	15.7460i	−0.530496	+	0.530496i	0.390224	+	0.920720i	$0.372398\pi$
$882$	50.0678	−	14.5047i	1.68587	−	0.488400i
$883$	−6.68096	−	9.99877i	−0.224832	−	0.336485i	0.701854	−	0.712321i	$-0.252356\pi$
$883$	−6.68096	−	9.99877i	−0.224832	−	0.336485i	−0.926686	+	0.375835i	$0.877356\pi$
$884$	1.50529	+	0.713046i	0.0506284	+	0.0239823i
$885$	−2.20584	−	0.748780i	−0.0741483	−	0.0251700i
$886$	41.9524	−	3.08205i	1.40942	−	0.103543i
$887$	1.27440	+	9.68004i	0.0427902	+	0.325024i	0.999430	+	0.0337511i	$0.0107454\pi$
$887$	1.27440	+	9.68004i	0.0427902	+	0.325024i	−0.956640	+	0.291273i	$0.905921\pi$
$888$	−14.6465	−	5.66478i	−0.491503	−	0.190098i
$889$	−9.37031	+	9.48627i	−0.314270	+	0.318159i
$890$	−4.32404	+	6.58315i	−0.144942	+	0.220668i
$891$	15.5021	+	1.01606i	0.519339	+	0.0340393i
$892$	4.59494	+	16.1270i	0.153850	+	0.539972i
$893$	6.17180	−	7.03759i	0.206532	−	0.235504i
$894$	−22.4773	+	3.13966i	−0.751753	+	0.105006i
$895$	−1.37767			−0.0460503
$896$	5.71887	+	29.3819i	0.191054	+	0.981580i
$897$	−7.94218			−0.265182
$898$	−6.41084	+	0.895475i	−0.213932	+	0.0298824i
$899$	9.06662	−	10.3385i	0.302389	−	0.344808i
$900$	13.9030	+	48.7957i	0.463433	+	1.62652i
$901$	−6.94136	−	0.454961i	−0.231250	−	0.0151569i
$902$	21.2606	−	32.3683i	0.707900	−	1.07775i
$903$	14.1197	+	51.4282i	0.469873	+	1.71142i
$904$	−14.6830	+	37.9634i	−0.488351	+	1.26264i
$905$	−0.0499679	−	0.379544i	−0.00166099	−	0.0126165i
$906$	−57.2268	+	4.20419i	−1.90123	+	0.139675i
$907$	38.6004	+	13.1031i	1.28171	+	0.435080i	0.877495	−	0.479586i	$-0.159213\pi$
$907$	38.6004	+	13.1031i	1.28171	+	0.435080i	0.404210	+	0.914666i	$0.367546\pi$
$908$	−12.6721	−	6.00267i	−0.420538	−	0.199206i
$909$	−23.9895	−	35.9028i	−0.795681	−	1.19082i
$910$	−2.14915	−	0.252313i	−0.0712437	−	0.00836410i
$911$	3.38337	−	3.38337i	0.112096	−	0.112096i	−0.648834	−	0.760930i	$-0.724743\pi$
$911$	3.38337	−	3.38337i	0.112096	−	0.112096i	0.760930	+	0.648834i	$0.224743\pi$
$912$	32.2773	−	44.9299i	1.06881	−	1.48778i
$913$	83.4195	−	22.3522i	2.76078	−	0.739750i
$914$	8.20286	+	29.6757i	0.271326	+	0.981584i
$915$	11.6584	+	5.74930i	0.385416	+	0.190066i
$916$	−5.01115	−	23.2691i	−0.165573	−	0.768831i
$917$	30.9177	+	15.0113i	1.02099	+	0.495716i
$918$	−5.56066	−	1.06058i	−0.183529	−	0.0350044i
$919$	−5.73626	+	0.755193i	−0.189222	+	0.0249115i	−0.224541	−	0.974465i	$-0.572088\pi$
$919$	−5.73626	+	0.755193i	−0.189222	+	0.0249115i	0.0353196	+	0.999376i	$0.488755\pi$
$920$	2.18047	−	1.14017i	0.0718881	−	0.0375904i
$921$	−56.0223	−	7.37547i	−1.84600	−	0.243030i
$922$	1.97004	+	2.21099i	0.0648799	+	0.0728152i
$923$	−15.3452	−	10.2534i	−0.505094	−	0.337493i
$924$	1.76803	+	80.6559i	0.0581641	+	2.65338i
$925$	1.81516	−	9.12541i	0.0596820	−	0.300042i
$926$	−23.2385	+	30.7846i	−0.763666	+	1.01164i
$927$	−9.29958	−	5.36911i	−0.305438	−	0.176345i
$928$	3.85122	+	7.09055i	0.126422	+	0.232759i
$929$	26.8572	−	15.5060i	0.881157	−	0.508736i	0.0101175	−	0.999949i	$-0.496779\pi$
$929$	26.8572	−	15.5060i	0.881157	−	0.508736i	0.871040	+	0.491212i	$0.163446\pi$
$930$	15.4030	−	6.52288i	0.505085	−	0.213894i
$931$	14.5212	−	30.3825i	0.475913	−	0.995745i
$932$	−35.8999	+	15.5378i	−1.17594	+	0.508958i
$933$	−4.21239	+	64.2687i	−0.137908	+	2.10406i
$934$	−41.3740	−	13.6818i	−1.35380	−	0.447681i
$935$	−1.37890	−	0.181536i	−0.0450949	−	0.00593685i
$936$	8.49609	−	18.3075i	0.277703	−	0.598400i
$937$	14.1511	−	34.1637i	0.462295	−	1.11608i	−0.505158	−	0.863027i	$-0.668566\pi$
$937$	14.1511	−	34.1637i	0.462295	−	1.11608i	0.967453	−	0.253051i	$-0.0814342\pi$
$938$	−2.63293	−	12.3298i	−0.0859683	−	0.402581i
$939$	−70.9536	+	14.1136i	−2.31548	+	0.460578i
$940$	−0.0824772	+	1.65873i	−0.00269011	+	0.0541017i
$941$	0.816474	+	12.4570i	0.0266163	+	0.406086i	0.990291	+	0.139008i	$0.0443914\pi$
$941$	0.816474	+	12.4570i	0.0266163	+	0.406086i	−0.963675	+	0.267078i	$0.913942\pi$
$942$	69.6971	−	19.2655i	2.27085	−	0.627703i
$943$	2.72440	−	10.1676i	0.0887187	−	0.331103i
$944$	6.44444	+	4.01805i	0.209749	+	0.130776i
$945$	7.28542	−	1.00476i	0.236995	−	0.0326848i
$946$	−52.5803	+	0.414539i	−1.70953	+	0.0134778i
$947$	−1.58685	+	3.21781i	−0.0515656	+	0.104565i	−0.921130	−	0.389254i	$-0.872733\pi$
$947$	−1.58685	+	3.21781i	−0.0515656	+	0.104565i	0.869565	+	0.493819i	$0.164399\pi$
$948$	−1.40908	+	1.65880i	−0.0457649	+	0.0538753i
$949$	−15.3768	−	5.21973i	−0.499153	−	0.169440i
$950$	29.5103	+	14.2648i	0.957441	+	0.462810i
$951$	8.42650	+	3.49037i	0.273248	+	0.113183i
$952$	0.464148	−	4.57538i	0.0150431	−	0.148289i
$953$	−43.2985	+	17.9348i	−1.40258	+	0.580966i	−0.950419	−	0.310971i	$-0.899346\pi$
$953$	−43.2985	+	17.9348i	−1.40258	+	0.580966i	−0.452158	+	0.891938i	$0.649346\pi$
$954$	−4.84960	+	84.1510i	−0.157012	+	2.72449i
$955$	−4.79952	−	9.73246i	−0.155309	−	0.314935i
$956$	24.6330	+	13.7087i	0.796690	+	0.443370i
$957$	6.99040	+	20.5931i	0.225968	+	0.665679i
$958$	−5.69054	−	2.30471i	−0.183853	−	0.0744617i
$959$	0.595467	−	4.74849i	0.0192286	−	0.153337i
$960$	0.464122	+	9.80445i	0.0149795	+	0.316437i
$961$	30.9678	+	53.6377i	0.998960	+	1.73025i
$962$	−2.91843	+	2.27616i	−0.0940938	+	0.0733865i
$963$	3.46044	−	3.94587i	0.111511	−	0.127154i
$964$	22.8383	+	38.1548i	0.735572	+	1.22888i
$965$	−4.89106	+	7.31998i	−0.157449	+	0.235639i
$966$	7.33941	+	20.6639i	0.236142	+	0.664849i
$967$	26.4494	−	10.9557i	0.850556	−	0.352312i	0.0855489	−	0.996334i	$-0.472736\pi$
$967$	26.4494	−	10.9557i	0.850556	−	0.352312i	0.765007	+	0.644022i	$0.222736\pi$
$968$	−47.0622	−	11.4246i	−1.51264	−	0.367200i
$969$	−6.74311	+	5.17417i	−0.216620	+	0.166218i
$970$	0.650837	+	8.85911i	0.0208971	+	0.284449i
$971$	17.0199	−	14.9260i	0.546193	−	0.478999i	−0.341214	−	0.939986i	$-0.610838\pi$
$971$	17.0199	−	14.9260i	0.546193	−	0.478999i	0.887407	+	0.460987i	$0.152505\pi$
$972$	3.99368	−	21.8747i	0.128097	−	0.701632i
$973$	−14.1562	−	9.33347i	−0.453827	−	0.299217i
$974$	−20.9310	+	0.165019i	−0.670673	+	0.00528754i
$975$	18.1313	+	4.85827i	0.580666	+	0.155589i
$976$	−32.7273	−	26.9239i	−1.04758	−	0.861812i
$977$	−13.7854	+	3.69380i	−0.441035	+	0.118175i	−0.472502	−	0.881330i	$-0.656649\pi$
$977$	−13.7854	+	3.69380i	−0.441035	+	0.118175i	0.0314664	+	0.999505i	$0.489982\pi$
$978$	−14.7443	+	56.8146i	−0.471472	+	1.81673i
$979$	57.5430	−	38.4490i	1.83908	−	1.22884i
$980$	1.32958	+	5.82481i	0.0424718	+	0.186067i
$981$	89.9096	−	17.8841i	2.87059	−	0.570996i
$982$	−47.3357	+	16.4856i	−1.51054	+	0.526077i
$983$	−0.254640	−	0.331854i	−0.00812177	−	0.0105845i	0.789275	−	0.614040i	$-0.210457\pi$
$983$	−0.254640	−	0.331854i	−0.00812177	−	0.0105845i	−0.797397	+	0.603456i	$0.793790\pi$
$984$	32.2157	+	26.9316i	1.02700	+	0.858548i
$985$	−0.388774	+	0.506660i	−0.0123874	+	0.0161435i
$986$	−0.251429	−	1.21392i	−0.00800715	−	0.0386592i
$987$	−14.5338	−	2.79816i	−0.462617	−	0.0890663i
$988$	−5.17888	−	11.9657i	−0.164762	−	0.380681i
$989$	−13.5339	+	4.59416i	−0.430354	+	0.146086i
$990$	−2.06792	+	16.7253i	−0.0657228	+	0.531565i
$991$	−48.7452	−	28.1431i	−1.54844	−	0.893994i	−0.998261	−	0.0589484i	$-0.981225\pi$
$991$	−48.7452	−	28.1431i	−1.54844	−	0.893994i	−0.550181	−	0.835045i	$-0.685441\pi$
$992$	−53.7447	+	9.24328i	−1.70640	+	0.293474i
$993$			68.6390i			2.17819i
$994$	−12.4965	+	49.4002i	−0.396364	+	1.56688i
$995$	1.23410	−	6.20422i	0.0391235	−	0.196687i
$996$	13.6849	+	92.6355i	0.433621	+	2.93527i
$997$	−25.2774	+	12.4654i	−0.800543	+	0.394784i	−0.796069	−	0.605206i	$-0.793091\pi$
$997$	−25.2774	+	12.4654i	−0.800543	+	0.394784i	−0.00447390	+	0.999990i	$0.501424\pi$
$998$	5.42029	−	16.3911i	0.171576	−	0.518851i
$999$	7.65744	−	9.97937i	0.242271	−	0.315733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.bn.a.221.3	yes	992
7.2	even	3	inner	448.2.bn.a.93.45	yes	992
64.53	even	16	inner	448.2.bn.a.53.45	✓	992
448.373	even	48	inner	448.2.bn.a.373.3	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.bn.a.53.45	✓	992	64.53	even	16	inner
448.2.bn.a.93.45	yes	992	7.2	even	3	inner
448.2.bn.a.221.3	yes	992	1.1	even	1	trivial
448.2.bn.a.373.3	yes	992	448.373	even	48	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.bn (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40062 + 0.195640i) q^{2} +(1.89561 - 2.16153i) q^{3} +(1.92345 - 0.548033i) q^{4} +(-0.425845 - 0.0279114i) q^{5} +(-2.23214 + 3.39833i) q^{6} +(1.85929 - 1.88230i) q^{7} +(-2.58680 + 1.14389i) q^{8} +(-0.687295 - 5.22052i) q^{9} +O(q^{10})\)	\(q+(-1.40062 + 0.195640i) q^{2} +(1.89561 - 2.16153i) q^{3} +(1.92345 - 0.548033i) q^{4} +(-0.425845 - 0.0279114i) q^{5} +(-2.23214 + 3.39833i) q^{6} +(1.85929 - 1.88230i) q^{7} +(-2.58680 + 1.14389i) q^{8} +(-0.687295 - 5.22052i) q^{9} +(0.601906 - 0.0442193i) q^{10} +(-5.02161 - 1.70461i) q^{11} +(2.46153 - 5.19646i) q^{12} +(-0.752891 - 1.12678i) q^{13} +(-2.23590 + 3.00013i) q^{14} +(-0.867569 + 0.867569i) q^{15} +(3.39932 - 2.10823i) q^{16} +(-0.593609 + 0.159057i) q^{17} +(1.98398 + 7.17748i) q^{18} +(4.31451 + 2.12768i) q^{19} +(-0.834389 + 0.179691i) q^{20} +(-0.544157 - 7.58702i) q^{21} +(7.36684 + 1.40507i) q^{22} +(2.02106 - 0.266077i) q^{23} +(-2.43102 + 7.75981i) q^{24} +(-4.77666 - 0.628859i) q^{25} +(1.27495 + 1.43089i) q^{26} +(-5.41577 - 3.61870i) q^{27} +(2.54469 - 4.63946i) q^{28} +(0.278277 - 1.39899i) q^{29} +(1.04540 - 1.38486i) q^{30} +(8.34875 + 4.82015i) q^{31} +(-4.34869 + 3.61786i) q^{32} +(-13.2036 + 7.62310i) q^{33} +(0.800300 - 0.338911i) q^{34} +(-0.844307 + 0.749673i) q^{35} +(-4.18300 - 9.66475i) q^{36} +(-0.126305 + 1.92704i) q^{37} +(-6.45923 - 2.13597i) q^{38} +(-3.86276 - 0.508542i) q^{39} +(1.13350 - 0.414918i) q^{40} +(1.97608 - 4.77068i) q^{41} +(2.24648 + 10.5200i) q^{42} +(-6.87655 + 1.36783i) q^{43} +(-10.5930 - 0.526718i) q^{44} +(0.146969 + 2.24232i) q^{45} +(-2.77867 + 0.768072i) q^{46} +(0.503610 - 1.87950i) q^{47} +(1.88679 - 11.3441i) q^{48} +(-0.0860931 - 6.99947i) q^{49} +(6.81329 - 0.0537156i) q^{50} +(-0.781446 + 1.58462i) q^{51} +(-2.06566 - 1.75470i) q^{52} +(10.7186 + 3.63846i) q^{53} +(8.29338 + 4.00887i) q^{54} +(2.09085 + 0.866059i) q^{55} +(-2.65647 + 6.99594i) q^{56} +(12.7777 - 5.29269i) q^{57} +(-0.116060 + 2.01389i) q^{58} +(0.839734 + 1.70281i) q^{59} +(-1.19327 + 2.14418i) q^{60} +(-3.40556 - 10.0325i) q^{61} +(-12.6364 - 5.11783i) q^{62} +(-11.1045 - 8.41276i) q^{63} +(5.38304 - 5.91801i) q^{64} +(0.289165 + 0.500849i) q^{65} +(17.0018 - 13.2602i) q^{66} +(-2.22171 + 2.53337i) q^{67} +(-1.05461 + 0.631256i) q^{68} +(3.25601 - 4.87296i) q^{69} +(1.03588 - 1.21518i) q^{70} +(12.5820 - 5.21163i) q^{71} +(7.74958 + 12.7182i) q^{72} +(9.50654 - 7.29463i) q^{73} +(-0.200102 - 2.72376i) q^{74} +(-10.4140 + 9.13283i) q^{75} +(9.46478 + 1.72799i) q^{76} +(-12.5452 + 6.28281i) q^{77} +(5.50974 - 0.0434384i) q^{78} +(-0.365624 - 0.0979688i) q^{79} +(-1.50643 + 0.802900i) q^{80} +(-2.82970 + 0.758215i) q^{81} +(-1.83439 + 7.06849i) q^{82} +(-13.5408 + 9.04769i) q^{83} +(-5.20460 - 14.2950i) q^{84} +(0.257225 - 0.0511653i) q^{85} +(9.36380 - 3.26113i) q^{86} +(-2.49646 - 3.25345i) q^{87} +(14.9398 - 1.33468i) q^{88} +(-7.94453 + 10.3535i) q^{89} +(-0.644535 - 3.11187i) q^{90} +(-3.52078 - 0.677845i) q^{91} +(3.74158 - 1.61939i) q^{92} +(26.2449 - 8.90895i) q^{93} +(-0.337659 + 2.73098i) q^{94} +(-1.77793 - 1.02649i) q^{95} +(-0.423305 + 16.2579i) q^{96} +14.7184i q^{97} +(1.48996 + 9.78673i) q^{98} +(-5.44761 + 27.3870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 32 q^{13} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 32 q^{20} - 16 q^{21} - 16 q^{22} - 8 q^{23} - 88 q^{24} - 8 q^{25} - 8 q^{26} - 32 q^{27} - 56 q^{28} - 32 q^{29} - 88 q^{30} - 8 q^{32} - 32 q^{34} - 16 q^{35} + 128 q^{36} - 8 q^{37} - 88 q^{38} - 8 q^{39} - 8 q^{40} - 32 q^{41} - 56 q^{42} - 32 q^{43} - 16 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 32 q^{48} - 16 q^{49} + 16 q^{50} - 8 q^{51} - 56 q^{52} - 8 q^{53} - 8 q^{54} - 32 q^{55} - 16 q^{56} - 32 q^{57} - 8 q^{58} + 56 q^{59} + 88 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} + 160 q^{64} - 16 q^{65} - 136 q^{66} - 88 q^{67} - 8 q^{68} - 32 q^{69} - 16 q^{70} - 160 q^{71} - 8 q^{72} - 8 q^{73} + 48 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{77} + 64 q^{78} - 8 q^{79} - 32 q^{80} - 8 q^{81} + 72 q^{82} - 32 q^{83} - 128 q^{84} - 32 q^{85} - 8 q^{86} - 8 q^{87} - 8 q^{88} - 8 q^{89} - 320 q^{90} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 8 q^{94} + 128 q^{96} - 152 q^{98} - 80 q^{99}+O(q^{100}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 32 * q^13 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 32 * q^20 - 16 * q^21 - 16 * q^22 - 8 * q^23 - 88 * q^24 - 8 * q^25 - 8 * q^26 - 32 * q^27 - 56 * q^28 - 32 * q^29 - 88 * q^30 - 8 * q^32 - 32 * q^34 - 16 * q^35 + 128 * q^36 - 8 * q^37 - 88 * q^38 - 8 * q^39 - 8 * q^40 - 32 * q^41 - 56 * q^42 - 32 * q^43 - 16 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 32 * q^48 - 16 * q^49 + 16 * q^50 - 8 * q^51 - 56 * q^52 - 8 * q^53 - 8 * q^54 - 32 * q^55 - 16 * q^56 - 32 * q^57 - 8 * q^58 + 56 * q^59 + 88 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 + 160 * q^64 - 16 * q^65 - 136 * q^66 - 88 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 160 * q^71 - 8 * q^72 - 8 * q^73 + 48 * q^74 - 8 * q^75 - 32 * q^76 - 16 * q^77 + 64 * q^78 - 8 * q^79 - 32 * q^80 - 8 * q^81 + 72 * q^82 - 32 * q^83 - 128 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 - 320 * q^90 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 8 * q^94 + 128 * q^96 - 152 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

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