LMFDB - Embedded newform 322.2.i.d.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(29,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("322.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.i (of order $11$, degree $10$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	322.71
Dual form			322.2.i.d.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(-0.0270781 - 0.188333i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.254438 - 0.0747098i) q^{5} +(0.0790407 - 0.173075i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.84374 - 0.834998i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(-0.0270781 - 0.188333i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.254438 - 0.0747098i) q^{5} +(0.0790407 - 0.173075i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.84374 - 0.834998i) q^{9} +(-0.173656 - 0.200410i) q^{10} +(2.46873 - 1.58655i) q^{11} +(0.160065 - 0.102867i) q^{12} +(2.25238 + 2.59938i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.00718058 + 0.0499420i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.92216 + 6.39865i) q^{17} +(2.84374 + 0.834998i) q^{18} +(1.05049 + 2.30026i) q^{19} +(-0.0377390 - 0.262481i) q^{20} +(-0.160065 - 0.102867i) q^{21} +2.93458 q^{22} +(-3.69657 - 3.05539i) q^{23} +0.190269 q^{24} +(-4.14711 - 2.66519i) q^{25} +(0.489488 + 3.40446i) q^{26} +(-0.471383 - 1.03218i) q^{27} +(0.959493 + 0.281733i) q^{28} +(3.23284 - 7.07893i) q^{29} +(-0.0330414 + 0.0381318i) q^{30} +(0.292089 - 2.03153i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-0.365648 - 0.421980i) q^{33} +(-5.91765 + 3.80304i) q^{34} +(-0.223084 + 0.143367i) q^{35} +(1.94087 + 2.23989i) q^{36} +(-1.01568 + 0.298232i) q^{37} +(-0.359883 + 2.50304i) q^{38} +(0.428558 - 0.494582i) q^{39} +(0.110160 - 0.241216i) q^{40} +(-10.7954 - 3.16981i) q^{41} +(-0.0790407 - 0.173075i) q^{42} +(0.0614568 + 0.427442i) q^{43} +(2.46873 + 1.58655i) q^{44} -0.785940 q^{45} +(-1.45788 - 4.56887i) q^{46} +9.70311 q^{47} +(0.160065 + 0.102867i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-2.04786 - 4.48419i) q^{50} +(1.28420 + 0.377075i) q^{51} +(-1.42881 + 3.12866i) q^{52} +(-7.70500 + 8.89205i) q^{53} +(0.161488 - 1.12318i) q^{54} +(-0.746669 + 0.219242i) q^{55} +(0.654861 + 0.755750i) q^{56} +(0.404769 - 0.260129i) q^{57} +(6.54679 - 4.20737i) q^{58} +(-9.34925 - 10.7896i) q^{59} +(-0.0484118 + 0.0142150i) q^{60} +(-0.217805 + 1.51487i) q^{61} +(1.34405 - 1.55111i) q^{62} +(1.23121 - 2.69597i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.378892 - 0.829657i) q^{65} +(-0.0794629 - 0.552677i) q^{66} +(-9.37174 - 6.02285i) q^{67} -7.03432 q^{68} +(-0.475332 + 0.778918i) q^{69} -0.265180 q^{70} +(3.54061 + 2.27541i) q^{71} +(0.421792 + 2.93363i) q^{72} +(4.74539 + 10.3909i) q^{73} +(-1.01568 - 0.298232i) q^{74} +(-0.389645 + 0.853204i) q^{75} +(-1.65600 + 1.91113i) q^{76} +(0.417634 - 2.90471i) q^{77} +(0.627917 - 0.184373i) q^{78} +(5.57548 + 6.43445i) q^{79} +(0.223084 - 0.143367i) q^{80} +(7.29829 - 4.69032i) q^{81} +(-7.36793 - 8.50305i) q^{82} +(-9.76067 + 2.86599i) q^{83} +(0.0270781 - 0.188333i) q^{84} +(1.22155 - 1.40975i) q^{85} +(-0.179392 + 0.392813i) q^{86} +(-1.42073 - 0.417164i) q^{87} +(1.21907 + 2.66939i) q^{88} +(-0.679170 - 4.72373i) q^{89} +(-0.661175 - 0.424911i) q^{90} +3.43947 q^{91} +(1.24367 - 4.63177i) q^{92} -0.390512 q^{93} +(8.16278 + 5.24590i) q^{94} +(-0.0954338 - 0.663757i) q^{95} +(0.0790407 + 0.173075i) q^{96} +(-3.02715 - 0.888852i) q^{97} +(0.415415 - 0.909632i) q^{98} +(5.69565 - 6.57313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	−0.0270781	−	0.188333i	−0.0156336	−	0.108734i	0.980510	−	0.196467i	$-0.0629468\pi$
$3$	−0.0270781	−	0.188333i	−0.0156336	−	0.108734i	−0.996144	+	0.0877331i	$0.972038\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−0.254438	−	0.0747098i	−0.113788	−	0.0334113i	0.224343	−	0.974510i	$-0.427977\pi$
$5$	−0.254438	−	0.0747098i	−0.113788	−	0.0334113i	−0.338131	+	0.941099i	$0.609795\pi$
$6$	0.0790407	−	0.173075i	0.0322682	−	0.0706576i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	2.84374	−	0.834998i	0.947914	−	0.278333i
$10$	−0.173656	−	0.200410i	−0.0549148	−	0.0633751i
$11$	2.46873	−	1.58655i	0.744349	−	0.478364i	−0.112681	−	0.993631i	$-0.535944\pi$
$11$	2.46873	−	1.58655i	0.744349	−	0.478364i	0.857029	+	0.515267i	$0.172307\pi$
$12$	0.160065	−	0.102867i	0.0462067	−	0.0296952i
$13$	2.25238	+	2.59938i	0.624697	+	0.720939i	0.976592	−	0.215101i	$-0.0690081\pi$
$13$	2.25238	+	2.59938i	0.624697	+	0.720939i	−0.351895	+	0.936039i	$0.614463\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	−0.00718058	+	0.0499420i	−0.00185402	+	0.0128950i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−2.92216	+	6.39865i	−0.708729	+	1.55190i	0.120328	+	0.992734i	$0.461606\pi$
$17$	−2.92216	+	6.39865i	−0.708729	+	1.55190i	−0.829056	+	0.559165i	$0.811122\pi$
$18$	2.84374	+	0.834998i	0.670277	+	0.196811i
$19$	1.05049	+	2.30026i	0.241000	+	0.527716i	0.991022	−	0.133696i	$-0.0426847\pi$
$19$	1.05049	+	2.30026i	0.241000	+	0.527716i	−0.750023	+	0.661412i	$0.769957\pi$
$20$	−0.0377390	−	0.262481i	−0.00843871	−	0.0586925i
$21$	−0.160065	−	0.102867i	−0.0349290	−	0.0224475i
$22$	2.93458			0.625654
$23$	−3.69657	−	3.05539i	−0.770788	−	0.637092i
$23$	−3.69657	−	3.05539i	−0.770788	−	0.637092i
$24$	0.190269			0.0388385
$25$	−4.14711	−	2.66519i	−0.829422	−	0.533037i
$26$	0.489488	+	3.40446i	0.0959965	+	0.667670i
$27$	−0.471383	−	1.03218i	−0.0907176	−	0.198644i
$28$	0.959493	+	0.281733i	0.181327	+	0.0532424i
$29$	3.23284	−	7.07893i	0.600323	−	1.31452i	−0.328677	−	0.944443i	$-0.606603\pi$
$29$	3.23284	−	7.07893i	0.600323	−	1.31452i	0.928999	−	0.370081i	$-0.120670\pi$
$30$	−0.0330414	+	0.0381318i	−0.00603250	+	0.00696188i
$31$	0.292089	−	2.03153i	0.0524608	−	0.364873i	−0.946633	−	0.322313i	$-0.895540\pi$
$31$	0.292089	−	2.03153i	0.0524608	−	0.364873i	0.999094	−	0.0425597i	$-0.0135513\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−0.365648	−	0.421980i	−0.0636512	−	0.0734574i
$34$	−5.91765	+	3.80304i	−1.01487	+	0.652216i
$35$	−0.223084	+	0.143367i	−0.0377080	+	0.0242335i
$36$	1.94087	+	2.23989i	0.323479	+	0.373315i
$37$	−1.01568	+	0.298232i	−0.166978	+	0.0490290i	−0.364153	−	0.931339i	$-0.618641\pi$
$37$	−1.01568	+	0.298232i	−0.166978	+	0.0490290i	0.197175	+	0.980368i	$0.436823\pi$
$38$	−0.359883	+	2.50304i	−0.0583808	+	0.406047i
$39$	0.428558	−	0.494582i	0.0686242	−	0.0791965i
$40$	0.110160	−	0.241216i	0.0174178	−	0.0381396i
$41$	−10.7954	−	3.16981i	−1.68596	−	0.495042i	−0.708418	−	0.705793i	$-0.750591\pi$
$41$	−10.7954	−	3.16981i	−1.68596	−	0.495042i	−0.977540	+	0.210752i	$0.932409\pi$
$42$	−0.0790407	−	0.173075i	−0.0121962	−	0.0267060i
$43$	0.0614568	+	0.427442i	0.00937208	+	0.0651843i	0.993971	−	0.109646i	$-0.0349716\pi$
$43$	0.0614568	+	0.427442i	0.00937208	+	0.0651843i	−0.984599	+	0.174830i	$0.944062\pi$
$44$	2.46873	+	1.58655i	0.372174	+	0.239182i
$45$	−0.785940			−0.117161
$46$	−1.45788	−	4.56887i	−0.214953	−	0.673643i
$47$	9.70311			1.41534			0.707672	−	0.706541i	$-0.249745\pi$
$47$	9.70311			1.41534			0.707672	+	0.706541i	$0.249745\pi$
$48$	0.160065	+	0.102867i	0.0231033	+	0.0148476i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−2.04786	−	4.48419i	−0.289612	−	0.634161i
$51$	1.28420	+	0.377075i	0.179824	+	0.0528011i
$52$	−1.42881	+	3.12866i	−0.198140	+	0.433866i
$53$	−7.70500	+	8.89205i	−1.05836	+	1.22142i	−0.0839931	+	0.996466i	$0.526767\pi$
$53$	−7.70500	+	8.89205i	−1.05836	+	1.22142i	−0.974370	+	0.224950i	$0.927778\pi$
$54$	0.161488	−	1.12318i	0.0219758	−	0.152845i
$55$	−0.746669	+	0.219242i	−0.100681	+	0.0295626i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	0.404769	−	0.260129i	0.0536129	−	0.0344549i
$58$	6.54679	−	4.20737i	0.859636	−	0.552454i
$59$	−9.34925	−	10.7896i	−1.21717	−	1.40469i	−0.887638	−	0.460542i	$-0.847655\pi$
$59$	−9.34925	−	10.7896i	−1.21717	−	1.40469i	−0.329530	−	0.944145i	$-0.606890\pi$
$60$	−0.0484118	+	0.0142150i	−0.00624993	+	0.00183515i
$61$	−0.217805	+	1.51487i	−0.0278871	+	0.193959i	−0.999003	−	0.0446508i	$-0.985782\pi$
$61$	−0.217805	+	1.51487i	−0.0278871	+	0.193959i	0.971116	+	0.238609i	$0.0766916\pi$
$62$	1.34405	−	1.55111i	0.170694	−	0.196991i
$63$	1.23121	−	2.69597i	0.155117	−	0.339660i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−0.378892	−	0.829657i	−0.0469957	−	0.102906i
$66$	−0.0794629	−	0.552677i	−0.00978121	−	0.0680298i
$67$	−9.37174	−	6.02285i	−1.14494	−	0.735808i	−0.176314	−	0.984334i	$-0.556418\pi$
$67$	−9.37174	−	6.02285i	−1.14494	−	0.735808i	−0.968625	+	0.248526i	$0.920054\pi$
$68$	−7.03432			−0.853037
$69$	−0.475332	+	0.778918i	−0.0572233	+	0.0937707i
$70$	−0.265180			−0.0316951
$71$	3.54061	+	2.27541i	0.420193	+	0.270042i	0.733606	−	0.679575i	$-0.237836\pi$
$71$	3.54061	+	2.27541i	0.420193	+	0.270042i	−0.313413	+	0.949617i	$0.601472\pi$
$72$	0.421792	+	2.93363i	0.0497087	+	0.345732i
$73$	4.74539	+	10.3909i	0.555405	+	1.21617i	0.954211	+	0.299133i	$0.0966974\pi$
$73$	4.74539	+	10.3909i	0.555405	+	1.21617i	−0.398806	+	0.917035i	$0.630575\pi$
$74$	−1.01568	−	0.298232i	−0.118071	−	0.0346688i
$75$	−0.389645	+	0.853204i	−0.0449924	+	0.0985195i
$76$	−1.65600	+	1.91113i	−0.189956	+	0.219221i
$77$	0.417634	−	2.90471i	0.0475938	−	0.331022i
$78$	0.627917	−	0.184373i	0.0710976	−	0.0208761i
$79$	5.57548	+	6.43445i	0.627291	+	0.723932i	0.977074	−	0.212899i	$-0.0682904\pi$
$79$	5.57548	+	6.43445i	0.627291	+	0.723932i	−0.349784	+	0.936830i	$0.613745\pi$
$80$	0.223084	−	0.143367i	0.0249415	−	0.0160289i
$81$	7.29829	−	4.69032i	0.810921	−	0.521147i
$82$	−7.36793	−	8.50305i	−0.813652	−	0.939005i
$83$	−9.76067	+	2.86599i	−1.07137	+	0.314583i	−0.769422	−	0.638740i	$-0.779456\pi$
$83$	−9.76067	+	2.86599i	−1.07137	+	0.314583i	−0.301950	+	0.953324i	$0.597638\pi$
$84$	0.0270781	−	0.188333i	0.00295447	−	0.0205488i
$85$	1.22155	−	1.40975i	0.132496	−	0.152908i
$86$	−0.179392	+	0.392813i	−0.0193443	+	0.0423581i
$87$	−1.42073	−	0.417164i	−0.152318	−	0.0447247i
$88$	1.21907	+	2.66939i	0.129953	+	0.284558i
$89$	−0.679170	−	4.72373i	−0.0719918	−	0.500714i	−0.993632	−	0.112670i	$-0.964060\pi$
$89$	−0.679170	−	4.72373i	−0.0719918	−	0.500714i	0.921641	−	0.388045i	$-0.126849\pi$
$90$	−0.661175	−	0.424911i	−0.0696939	−	0.0447896i
$91$	3.43947			0.360555
$92$	1.24367	−	4.63177i	0.129661	−	0.482895i
$93$	−0.390512			−0.0404942
$94$	8.16278	+	5.24590i	0.841926	+	0.541073i
$95$	−0.0954338	−	0.663757i	−0.00979130	−	0.0681000i
$96$	0.0790407	+	0.173075i	0.00806706	+	0.0176644i
$97$	−3.02715	−	0.888852i	−0.307361	−	0.0902493i	0.124415	−	0.992230i	$-0.460295\pi$
$97$	−3.02715	−	0.888852i	−0.307361	−	0.0902493i	−0.431776	+	0.901981i	$0.642113\pi$
$98$	0.415415	−	0.909632i	0.0419633	−	0.0918867i
$99$	5.69565	−	6.57313i	0.572434	−	0.660625i
$100$	0.701567	−	4.87950i	0.0701567	−	0.487950i
$101$	−17.8253	+	5.23397i	−1.77368	+	0.520799i	−0.994382	−	0.105855i	$-0.966242\pi$
$101$	−17.8253	+	5.23397i	−1.77368	+	0.520799i	−0.779297	+	0.626654i	$0.784424\pi$
$102$	0.876475	+	1.01151i	0.0867840	+	0.100154i
$103$	6.76841	−	4.34979i	0.666911	−	0.428598i	−0.162900	−	0.986643i	$-0.552085\pi$
$103$	6.76841	−	4.34979i	0.666911	−	0.428598i	0.829811	+	0.558045i	$0.188448\pi$
$104$	−2.89347	+	1.85952i	−0.283728	+	0.182341i
$105$	0.0330414	+	0.0381318i	0.00322451	+	0.00372128i
$106$	−11.2893	+	3.31483i	−1.09651	+	0.321964i
$107$	1.54405	−	10.7391i	0.149269	−	1.03819i	−0.768151	−	0.640269i	$-0.778823\pi$
$107$	1.54405	−	10.7391i	0.149269	−	1.03819i	0.917420	−	0.397920i	$-0.130268\pi$
$108$	0.743088	−	0.857569i	0.0715037	−	0.0825197i
$109$	−4.15742	+	9.10348i	−0.398209	+	0.871956i	0.599240	+	0.800569i	$0.295470\pi$
$109$	−4.15742	+	9.10348i	−0.398209	+	0.871956i	−0.997449	+	0.0713862i	$0.977258\pi$
$110$	−0.746669	−	0.219242i	−0.0711921	−	0.0209039i
$111$	0.0836696	+	0.183211i	0.00794157	+	0.0173896i
$112$	0.142315	+	0.989821i	0.0134475	+	0.0935293i
$113$	16.6958	+	10.7297i	1.57061	+	1.00937i	0.979175	+	0.203017i	$0.0650746\pi$
$113$	16.6958	+	10.7297i	1.57061	+	1.00937i	0.591435	+	0.806353i	$0.298562\pi$
$114$	0.481149			0.0450638
$115$	0.712281	+	1.05358i	0.0664206	+	0.0982466i
$116$	7.78219			0.722558
$117$	8.57566	+	5.51124i	0.792820	+	0.509514i
$118$	−2.03179	−	14.1314i	−0.187041	−	1.30090i
$119$	2.92216	+	6.39865i	0.267874	+	0.586563i
$120$	−0.0484118	−	0.0142150i	−0.00441937	−	0.00129764i
$121$	−0.992112	+	2.17242i	−0.0901920	+	0.197493i
$122$	−1.00223	+	1.15663i	−0.0907374	+	0.104717i
$123$	−0.304660	+	2.11896i	−0.0274703	+	0.191060i
$124$	1.96928	−	0.578232i	0.176846	−	0.0519268i
$125$	1.72435	+	1.99000i	0.154230	+	0.177991i
$126$	2.49331	−	1.60235i	0.222121	−	0.142749i
$127$	7.02087	−	4.51204i	0.623002	−	0.400379i	−0.190711	−	0.981646i	$-0.561079\pi$
$127$	7.02087	−	4.51204i	0.623002	−	0.400379i	0.813713	+	0.581267i	$0.197443\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	0.0788370	−	0.0231486i	0.00694122	−	0.00203812i
$130$	0.129802	−	0.902796i	0.0113844	−	0.0791804i
$131$	6.22645	−	7.18571i	0.544008	−	0.627818i	−0.415469	−	0.909607i	$-0.636382\pi$
$131$	6.22645	−	7.18571i	0.544008	−	0.627818i	0.959476	+	0.281789i	$0.0909279\pi$
$132$	0.231951	−	0.507902i	0.0201888	−	0.0442072i
$133$	2.42635	+	0.712440i	0.210391	+	0.0617764i
$134$	−4.62781	−	10.1335i	−0.399782	−	0.875400i
$135$	0.0428235	+	0.297844i	0.00368566	+	0.0256343i
$136$	−5.91765	−	3.80304i	−0.507434	−	0.326108i
$137$	−15.3568			−1.31202			−0.656009	−	0.754753i	$-0.727757\pi$
$137$	−15.3568			−1.31202			−0.656009	+	0.754753i	$0.727757\pi$
$138$	−0.820990	+	0.398283i	−0.0698873	+	0.0339041i
$139$	−6.11932			−0.519034			−0.259517	−	0.965738i	$-0.583563\pi$
$139$	−6.11932			−0.519034			−0.259517	+	0.965738i	$0.583563\pi$
$140$	−0.223084	−	0.143367i	−0.0188540	−	0.0121167i
$141$	−0.262742	−	1.82741i	−0.0221269	−	0.153896i
$142$	1.74837	+	3.82840i	0.146720	+	0.321272i
$143$	9.68456	+	2.84364i	0.809863	+	0.237797i
$144$	−1.23121	+	2.69597i	−0.102601	+	0.224664i
$145$	−1.35142	+	1.55963i	−0.112230	+	0.129520i
$146$	−1.62570	+	11.3070i	−0.134544	+	0.935772i
$147$	−0.182562	+	0.0536050i	−0.0150575	+	0.00442127i
$148$	−0.693212	−	0.800009i	−0.0569817	−	0.0657604i
$149$	−5.50493	+	3.53780i	−0.450981	+	0.289828i	−0.746348	−	0.665556i	$-0.768194\pi$
$149$	−5.50493	+	3.53780i	−0.450981	+	0.289828i	0.295367	+	0.955384i	$0.404558\pi$
$150$	−0.789067	+	0.507103i	−0.0644271	+	0.0414048i
$151$	10.2906	+	11.8760i	0.837441	+	0.966458i	0.999794	−	0.0202746i	$-0.00645406\pi$
$151$	10.2906	+	11.8760i	0.837441	+	0.966458i	−0.162354	+	0.986733i	$0.551909\pi$
$152$	−2.42635	+	0.712440i	−0.196803	+	0.0577865i
$153$	−2.96702	+	20.6361i	−0.239870	+	1.66833i
$154$	1.92174	−	2.21781i	0.154858	−	0.178716i
$155$	−0.226094	+	0.495076i	−0.0181603	+	0.0397655i
$156$	0.627917	+	0.184373i	0.0502736	+	0.0147617i
$157$	−2.04404	−	4.47583i	−0.163132	−	0.357210i	0.810359	−	0.585934i	$-0.199272\pi$
$157$	−2.04404	−	4.47583i	−0.163132	−	0.357210i	−0.973491	+	0.228723i	$0.926545\pi$
$158$	1.21167	+	8.42733i	0.0963951	+	0.670443i
$159$	1.88330	+	1.21032i	0.149355	+	0.0959848i
$160$	0.265180			0.0209643
$161$	−4.72984	+	0.792827i	−0.372764	+	0.0624835i
$162$	8.67549			0.681611
$163$	9.96060	+	6.40129i	0.780175	+	0.501388i	0.869092	−	0.494651i	$-0.164704\pi$
$163$	9.96060	+	6.40129i	0.780175	+	0.501388i	−0.0889170	+	0.996039i	$0.528341\pi$
$164$	−1.60120	−	11.1366i	−0.125033	−	0.869624i
$165$	0.0615088	+	0.134685i	0.00478845	+	0.0104853i
$166$	−9.76067	−	2.86599i	−0.757575	−	0.222444i
$167$	0.482976	−	1.05757i	0.0373738	−	0.0818371i	−0.890024	−	0.455913i	$-0.849313\pi$
$167$	0.482976	−	1.05757i	0.0373738	−	0.0818371i	0.927398	+	0.374076i	$0.122040\pi$
$168$	0.124600	−	0.143796i	0.00961309	−	0.0110941i
$169$	0.166511	−	1.15811i	0.0128086	−	0.0890855i
$170$	1.78980	−	0.525533i	0.137272	−	0.0403065i
$171$	4.90805	+	5.66419i	0.375328	+	0.433151i
$172$	−0.363285	+	0.233469i	−0.0277002	+	0.0178018i
$173$	11.8351	−	7.60598i	0.899809	−	0.578272i	−0.00692448	−	0.999976i	$-0.502204\pi$
$173$	11.8351	−	7.60598i	0.899809	−	0.578272i	0.906734	+	0.421704i	$0.138568\pi$
$174$	−0.969659	−	1.11905i	−0.0735097	−	0.0848347i
$175$	−4.72999	+	1.38885i	−0.357554	+	0.104987i
$176$	−0.417634	+	2.90471i	−0.0314804	+	0.218951i
$177$	−1.77887	+	2.05293i	−0.133708	+	0.154308i
$178$	1.98249	−	4.34104i	0.148594	−	0.325375i
$179$	−15.7974	−	4.63853i	−1.18075	−	0.346700i	−0.368288	−	0.929712i	$-0.620056\pi$
$179$	−15.7974	−	4.63853i	−1.18075	−	0.346700i	−0.812464	+	0.583012i	$0.801874\pi$
$180$	−0.326491	−	0.714916i	−0.0243352	−	0.0532867i
$181$	1.34784	+	9.37446i	0.100184	+	0.696798i	0.976572	+	0.215191i	$0.0690375\pi$
$181$	1.34784	+	9.37446i	0.100184	+	0.696798i	−0.876387	+	0.481607i	$0.840053\pi$
$182$	2.89347	+	1.85952i	0.214478	+	0.137837i
$183$	0.291196			0.0215258
$184$	3.55036	−	3.22412i	0.261736	−	0.237685i
$185$	0.280710			0.0206382
$186$	−0.328519	−	0.211126i	−0.0240882	−	0.0154805i
$187$	2.93777	+	20.4327i	0.214831	+	1.49418i
$188$	4.03082	+	8.82626i	0.293978	+	0.643721i
$189$	−1.08876	−	0.319690i	−0.0791958	−	0.0232540i
$190$	0.278570	−	0.609983i	0.0202096	−	0.0442528i
$191$	11.3565	−	13.1060i	0.821724	−	0.948320i	−0.177636	−	0.984096i	$-0.556845\pi$
$191$	11.3565	−	13.1060i	0.821724	−	0.948320i	0.999360	+	0.0357762i	$0.0113903\pi$
$192$	−0.0270781	+	0.188333i	−0.00195420	+	0.0135917i
$193$	20.4261	−	5.99765i	1.47030	−	0.431720i	0.554106	−	0.832446i	$-0.313060\pi$
$193$	20.4261	−	5.99765i	1.47030	−	0.431720i	0.916198	+	0.400726i	$0.131242\pi$
$194$	−2.06605	−	2.38435i	−0.148334	−	0.171187i
$195$	−0.145992	+	0.0938232i	−0.0104547	+	0.00671882i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	−1.22813	−	1.41734i	−0.0875010	−	0.100982i	0.710311	−	0.703888i	$-0.248554\pi$
$197$	−1.22813	−	1.41734i	−0.0875010	−	0.100982i	−0.797812	+	0.602907i	$0.794009\pi$
$198$	8.34519	−	2.45037i	0.593067	−	0.174140i
$199$	0.740481	−	5.15016i	0.0524913	−	0.365085i	−0.946598	−	0.322416i	$-0.895505\pi$
$199$	0.740481	−	5.15016i	0.0524913	−	0.365085i	0.999089	−	0.0426688i	$-0.0135860\pi$
$200$	3.22825	−	3.72560i	0.228272	−	0.263440i
$201$	−0.880529	+	1.92809i	−0.0621077	+	0.135997i
$202$	−17.8253	−	5.23397i	−1.25418	−	0.368261i
$203$	−3.23284	−	7.07893i	−0.226901	−	0.496843i
$204$	0.190476	+	1.32479i	0.0133360	+	0.0927540i
$205$	2.50995	+	1.61304i	0.175302	+	0.112660i
$206$	8.04562			0.560565
$207$	−13.0633	−	5.60211i	−0.907964	−	0.389373i
$208$	−3.43947			−0.238485
$209$	6.24287	+	4.01205i	0.431828	+	0.277519i
$210$	0.00718058	+	0.0499420i	0.000495507	+	0.00344633i
$211$	11.2671	+	24.6714i	0.775656	+	1.69845i	0.713784	+	0.700366i	$0.246980\pi$
$211$	11.2671	+	24.6714i	0.775656	+	1.69845i	0.0618728	+	0.998084i	$0.480293\pi$
$212$	−11.2893	−	3.31483i	−0.775350	−	0.227663i
$213$	0.332661	−	0.728426i	0.0227936	−	0.0499109i
$214$	7.10494	−	8.19954i	0.485684	−	0.560509i
$215$	0.0162971	−	0.113349i	0.00111145	−	0.00773034i
$216$	1.08876	−	0.319690i	0.0740809	−	0.0217521i
$217$	−1.34405	−	1.55111i	−0.0912398	−	0.105296i
$218$	−8.41916	+	5.41067i	−0.570218	+	0.366457i
$219$	1.82846	−	1.17508i	0.123556	−	0.0794044i
$220$	−0.509607	−	0.588118i	−0.0343577	−	0.0396509i
$221$	−23.2143	+	6.81634i	−1.56156	+	0.458517i
$222$	−0.0286639	+	0.199362i	−0.00192380	+	0.0133803i
$223$	15.7832	−	18.2148i	1.05692	−	1.21976i	0.0821360	−	0.996621i	$-0.473826\pi$
$223$	15.7832	−	18.2148i	1.05692	−	1.21976i	0.974788	−	0.223134i	$-0.0716287\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	−14.0187	−	4.11627i	−0.934583	−	0.274418i
$226$	8.24447	+	18.0529i	0.548414	+	1.20086i
$227$	−1.66808	−	11.6018i	−0.110715	−	0.770037i	−0.967227	−	0.253912i	$-0.918283\pi$
$227$	−1.66808	−	11.6018i	−0.110715	−	0.770037i	0.856513	−	0.516126i	$-0.172626\pi$
$228$	0.404769	+	0.260129i	0.0268064	+	0.0172275i
$229$	23.8080			1.57328			0.786638	−	0.617415i	$-0.211820\pi$
$229$	23.8080			1.57328			0.786638	+	0.617415i	$0.211820\pi$
$230$	0.0296021	+	1.27141i	0.00195190	+	0.0838346i
$231$	−0.558360			−0.0367374
$232$	6.54679	+	4.20737i	0.429818	+	0.276227i
$233$	0.738046	+	5.13322i	0.0483510	+	0.336289i	0.999611	+	0.0278978i	$0.00888131\pi$
$233$	0.738046	+	5.13322i	0.0483510	+	0.336289i	−0.951260	+	0.308391i	$0.900210\pi$
$234$	4.23470	+	9.27270i	0.276831	+	0.606175i
$235$	−2.46884	−	0.724918i	−0.161050	−	0.0472884i
$236$	5.93075	−	12.9865i	0.386059	−	0.845352i
$237$	1.06084	−	1.22428i	0.0689091	−	0.0795254i
$238$	−1.00109	+	6.96272i	−0.0648909	+	0.451326i
$239$	1.00159	−	0.294093i	0.0647875	−	0.0190233i	−0.249178	−	0.968458i	$-0.580160\pi$
$239$	1.00159	−	0.294093i	0.0647875	−	0.0190233i	0.313966	+	0.949434i	$0.398342\pi$
$240$	−0.0330414	−	0.0381318i	−0.00213281	−	0.00246140i
$241$	11.1171	−	7.14453i	0.716116	−	0.460220i	−0.131168	−	0.991360i	$-0.541873\pi$
$241$	11.1171	−	7.14453i	0.716116	−	0.460220i	0.847284	+	0.531141i	$0.178236\pi$
$242$	−2.00912	+	1.29118i	−0.129151	+	0.0830003i
$243$	−3.31023	−	3.82021i	−0.212351	−	0.245066i
$244$	−1.46845	+	0.431176i	−0.0940079	+	0.0276032i
$245$	−0.0377390	+	0.262481i	−0.00241106	+	0.0167693i
$246$	−1.40189	+	1.61787i	−0.0893813	+	0.103152i
$247$	−3.61315	+	7.91169i	−0.229899	+	0.503409i
$248$	1.96928	+	0.578232i	0.125049	+	0.0367178i
$249$	0.804060	+	1.76065i	0.0509552	+	0.111576i
$250$	0.374737	+	2.60635i	0.0237004	+	0.164840i
$251$	−13.9903	−	8.99101i	−0.883059	−	0.567507i	0.0186623	−	0.999826i	$-0.494059\pi$
$251$	−13.9903	−	8.99101i	−0.883059	−	0.567507i	−0.901721	+	0.432318i	$0.857696\pi$
$252$	2.96380			0.186702
$253$	−13.9733	−	1.67811i	−0.878497	−	0.105502i
$254$	8.34573			0.523658
$255$	−0.298578	−	0.191885i	−0.0186977	−	0.0120163i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	1.05889	+	2.31865i	0.0660519	+	0.144633i	0.939779	−	0.341783i	$-0.111031\pi$
$257$	1.05889	+	2.31865i	0.0660519	+	0.144633i	−0.873727	+	0.486417i	$0.838304\pi$
$258$	0.0788370	+	0.0231486i	0.00490818	+	0.00144117i
$259$	−0.439743	+	0.962904i	−0.0273243	+	0.0598319i
$260$	0.597285	−	0.689304i	0.0370421	−	0.0427488i
$261$	3.28247	−	22.8301i	0.203180	−	1.41315i
$262$	9.12291	−	2.67873i	0.563615	−	0.165492i
$263$	7.32906	+	8.45819i	0.451929	+	0.521554i	0.935297	−	0.353863i	$-0.115132\pi$
$263$	7.32906	+	8.45819i	0.451929	+	0.521554i	−0.483368	+	0.875417i	$0.660587\pi$
$264$	0.469722	−	0.301872i	0.0289094	−	0.0185790i
$265$	2.62477	−	1.68684i	0.161238	−	0.103622i
$266$	1.65600	+	1.91113i	0.101536	+	0.117179i
$267$	−0.871241	+	0.255820i	−0.0533191	+	0.0156559i
$268$	1.58542	−	11.0268i	0.0968447	−	0.673570i
$269$	8.94319	−	10.3210i	0.545276	−	0.629282i	−0.414500	−	0.910049i	$-0.636044\pi$
$269$	8.94319	−	10.3210i	0.545276	−	0.629282i	0.959776	+	0.280768i	$0.0905890\pi$
$270$	−0.125001	+	0.273715i	−0.00760733	+	0.0166577i
$271$	−1.44372	−	0.423915i	−0.0876999	−	0.0257510i	0.237588	−	0.971366i	$-0.423643\pi$
$271$	−1.44372	−	0.423915i	−0.0876999	−	0.0257510i	−0.325288	+	0.945615i	$0.605461\pi$
$272$	−2.92216	−	6.39865i	−0.177182	−	0.387975i
$273$	−0.0931345	−	0.647765i	−0.00563676	−	0.0392045i
$274$	−12.9189	−	8.30250i	−0.780462	−	0.501573i
$275$	−14.4665			−0.872365
$276$	−0.905989	−	0.108803i	−0.0545341	−	0.00654919i
$277$	8.04602			0.483439			0.241719	−	0.970346i	$-0.422289\pi$
$277$	8.04602			0.483439			0.241719	+	0.970346i	$0.422289\pi$
$278$	−5.14790	−	3.30836i	−0.308751	−	0.198422i
$279$	−0.865693	−	6.02103i	−0.0518277	−	0.360470i
$280$	−0.110160	−	0.241216i	−0.00658330	−	0.0144154i
$281$	−4.08984	−	1.20089i	−0.243980	−	0.0716389i	0.157456	−	0.987526i	$-0.449671\pi$
$281$	−4.08984	−	1.20089i	−0.243980	−	0.0716389i	−0.401436	+	0.915887i	$0.631489\pi$
$282$	0.766940	−	1.67937i	0.0456706	−	0.100005i
$283$	−5.65187	+	6.52261i	−0.335969	+	0.387729i	−0.898446	−	0.439084i	$-0.855303\pi$
$283$	−5.65187	+	6.52261i	−0.335969	+	0.387729i	0.562477	+	0.826813i	$0.309848\pi$
$284$	−0.598965	+	4.16589i	−0.0355420	+	0.247200i
$285$	−0.122423	+	0.0359466i	−0.00725170	+	0.00212929i
$286$	6.60978	+	7.62809i	0.390844	+	0.451058i
$287$	−9.46507	+	6.08283i	−0.558705	+	0.359058i
$288$	−2.49331	+	1.60235i	−0.146919	+	0.0944194i
$289$	−21.2710	−	24.5480i	−1.25123	−	1.44400i
$290$	−1.98009	+	0.581406i	−0.116275	+	0.0341413i
$291$	−0.0854302	+	0.594180i	−0.00500800	+	0.0348314i
$292$	−7.48063	+	8.63311i	−0.437771	+	0.505215i
$293$	−11.4318	+	25.0321i	−0.667852	+	1.46239i	0.207169	+	0.978305i	$0.433575\pi$
$293$	−11.4318	+	25.0321i	−0.667852	+	1.46239i	−0.875020	+	0.484086i	$0.839152\pi$
$294$	−0.182562	−	0.0536050i	−0.0106472	−	0.00312631i
$295$	1.57272	+	3.44377i	0.0915671	+	0.200504i
$296$	−0.150649	−	1.04779i	−0.00875632	−	0.0609015i
$297$	−2.80133	−	1.80030i	−0.162550	−	0.104464i
$298$	−6.54372			−0.379067
$299$	−0.383949	−	16.4907i	−0.0222043	−	0.953680i
$300$	−0.937966			−0.0541535
$301$	0.363285	+	0.233469i	0.0209394	+	0.0134569i
$302$	2.23637	+	15.5543i	0.128689	+	0.895049i
$303$	1.46840	+	3.21535i	0.0843574	+	0.184717i
$304$	−2.42635	−	0.712440i	−0.139161	−	0.0408612i
$305$	0.168593	−	0.369168i	0.00965362	−	0.0211385i
$306$	−13.6527	+	15.7561i	−0.780475	+	0.900716i
$307$	1.34665	−	9.36614i	0.0768572	−	0.534554i	−0.914624	−	0.404305i	$-0.867513\pi$
$307$	1.34665	−	9.36614i	0.0768572	−	0.534554i	0.991481	−	0.130249i	$-0.0415775\pi$
$308$	2.81571	−	0.826767i	0.160440	−	0.0471094i
$309$	−1.00248	−	1.15693i	−0.0570292	−	0.0658153i
$310$	−0.457860	+	0.294249i	−0.0260047	+	0.0167122i
$311$	−1.69006	+	1.08614i	−0.0958345	+	0.0615891i	−0.587680	−	0.809093i	$-0.699959\pi$
$311$	−1.69006	+	1.08614i	−0.0958345	+	0.0615891i	0.491846	+	0.870682i	$0.336322\pi$
$312$	0.428558	+	0.494582i	0.0242623	+	0.0280002i
$313$	−14.9498	+	4.38965i	−0.845010	+	0.248117i	−0.675453	−	0.737403i	$-0.736052\pi$
$313$	−14.9498	+	4.38965i	−0.845010	+	0.248117i	−0.169557	+	0.985520i	$0.554234\pi$
$314$	0.700258	−	4.87040i	0.0395178	−	0.274853i
$315$	−0.514681	+	0.593974i	−0.0289990	+	0.0334666i
$316$	−3.53684	+	7.74460i	−0.198963	+	0.435668i
$317$	−9.43516	−	2.77041i	−0.529931	−	0.155602i	0.00581154	−	0.999983i	$-0.498150\pi$
$317$	−9.43516	−	2.77041i	−0.529931	−	0.155602i	−0.535743	+	0.844381i	$0.679968\pi$
$318$	0.929982	+	2.03638i	0.0521508	+	0.114194i
$319$	−3.25011	−	22.6050i	−0.181971	−	1.26564i
$320$	0.223084	+	0.143367i	0.0124708	+	0.00801447i
$321$	−2.06433			−0.115220
$322$	−4.40763	−	1.89018i	−0.245628	−	0.105336i
$323$	−17.7883			−0.989766
$324$	7.29829	+	4.69032i	0.405460	+	0.260574i
$325$	−2.41302	−	16.7829i	−0.133850	−	0.930949i
$326$	4.91859	+	10.7702i	0.272416	+	0.596507i
$327$	1.82706	+	0.536472i	0.101037	+	0.0296670i
$328$	4.67389	−	10.2344i	0.258073	−	0.565100i
$329$	6.35419	−	7.33312i	0.350318	−	0.404288i
$330$	−0.0210720	+	0.146559i	−0.00115997	+	0.00806780i
$331$	−13.4066	+	3.93654i	−0.736894	+	0.216372i	−0.628580	−	0.777745i	$-0.716363\pi$
$331$	−13.4066	+	3.93654i	−0.736894	+	0.216372i	−0.108314	+	0.994117i	$0.534545\pi$
$332$	−6.66173	−	7.68804i	−0.365610	−	0.421936i
$333$	−2.63932	+	1.69619i	−0.144634	+	0.0929507i
$334$	0.978070	−	0.628567i	0.0535176	−	0.0343937i
$335$	1.93456	+	2.23260i	0.105696	+	0.121980i
$336$	0.182562	−	0.0536050i	0.00995957	−	0.00292439i
$337$	−0.650904	+	4.52714i	−0.0354570	+	0.246609i	−0.999840	−	0.0179018i	$-0.994301\pi$
$337$	−0.650904	+	4.52714i	−0.0354570	+	0.246609i	0.964383	+	0.264511i	$0.0852105\pi$
$338$	0.766200	−	0.884242i	0.0416758	−	0.0480964i
$339$	1.56867	−	3.43491i	0.0851984	−	0.186558i
$340$	1.78980	+	0.525533i	0.0970656	+	0.0285010i
$341$	−2.50204	−	5.47869i	−0.135493	−	0.296688i
$342$	1.06662	+	7.41851i	0.0576763	+	0.401147i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	−0.431837			−0.0232831
$345$	0.179136	−	0.162675i	0.00964434	−	0.00875811i
$346$	14.0685			0.756325
$347$	−4.14289	−	2.66248i	−0.222402	−	0.142929i	0.424696	−	0.905336i	$-0.360381\pi$
$347$	−4.14289	−	2.66248i	−0.222402	−	0.142929i	−0.647098	+	0.762407i	$0.724017\pi$
$348$	−0.210727	−	1.46564i	−0.0112962	−	0.0785665i
$349$	−2.22995	−	4.88290i	−0.119366	−	0.261376i	0.840512	−	0.541793i	$-0.182254\pi$
$349$	−2.22995	−	4.88290i	−0.119366	−	0.261376i	−0.959878	+	0.280417i	$0.909527\pi$
$350$	−4.72999	−	1.38885i	−0.252829	−	0.0742372i
$351$	1.62131	−	3.55017i	0.0865390	−	0.189494i
$352$	−1.92174	+	2.21781i	−0.102429	+	0.118210i
$353$	−0.718711	+	4.99874i	−0.0382531	+	0.266056i	−0.999968	−	0.00799555i	$-0.997455\pi$
$353$	−0.718711	+	4.99874i	−0.0382531	+	0.266056i	0.961715	+	0.274052i	$0.0883640\pi$
$354$	−2.60638	+	0.765303i	−0.138528	+	0.0406754i
$355$	−0.730871	−	0.843470i	−0.0387906	−	0.0447668i
$356$	4.01472	−	2.58010i	0.212780	−	0.136745i
$357$	1.12595	−	0.723602i	0.0595914	−	0.0382971i
$358$	−10.7818	−	12.4429i	−0.569837	−	0.657627i
$359$	−29.6860	+	8.71660i	−1.56677	+	0.460045i	−0.946059	−	0.323996i	$-0.894974\pi$
$359$	−29.6860	+	8.71660i	−1.56677	+	0.460045i	−0.620710	+	0.784040i	$0.713155\pi$
$360$	0.111851	−	0.777940i	0.00589506	−	0.0410010i
$361$	8.25469	−	9.52642i	0.434457	−	0.501391i
$362$	−3.93434	+	8.61500i	−0.206784	+	0.452794i
$363$	0.436002	+	0.128022i	0.0228842	+	0.00671940i
$364$	1.42881	+	3.12866i	0.0748899	+	0.163986i
$365$	−0.431102	−	2.99838i	−0.0225649	−	0.156942i
$366$	0.244970	+	0.157433i	0.0128048	+	0.00822913i
$367$	−15.2900			−0.798131			−0.399066	−	0.916922i	$-0.630665\pi$
$367$	−15.2900			−0.798131			−0.399066	+	0.916922i	$0.630665\pi$
$368$	4.72984	−	0.792827i	0.246560	−	0.0413290i
$369$	−33.3461			−1.73593
$370$	0.236148	+	0.151763i	0.0122768	+	0.00788980i
$371$	1.67446	+	11.6461i	0.0869335	+	0.604636i
$372$	−0.162224	−	0.355222i	−0.00841094	−	0.0184174i
$373$	17.0988	+	5.02065i	0.885341	+	0.259959i	0.692627	−	0.721296i	$-0.256453\pi$
$373$	17.0988	+	5.02065i	0.885341	+	0.259959i	0.192713	+	0.981255i	$0.438271\pi$
$374$	−8.57532	+	18.7773i	−0.443419	+	0.970953i
$375$	0.328090	−	0.378636i	0.0169425	−	0.0195527i
$376$	−1.38090	+	9.60435i	−0.0712143	+	0.495306i
$377$	25.6824	−	7.54103i	1.32271	−	0.388383i
$378$	−0.743088	−	0.857569i	−0.0382203	−	0.0441086i
$379$	3.51564	−	2.25936i	0.180586	−	0.116056i	−0.447225	−	0.894422i	$-0.647588\pi$
$379$	3.51564	−	2.25936i	0.180586	−	0.116056i	0.627811	+	0.778366i	$0.283951\pi$
$380$	0.564130	−	0.362544i	0.0289392	−	0.0185981i
$381$	−1.03988	−	1.20008i	−0.0532745	−	0.0614820i
$382$	16.6393	−	4.88574i	0.851342	−	0.249976i
$383$	−4.27405	+	29.7267i	−0.218394	+	1.51896i	0.525575	+	0.850747i	$0.323850\pi$
$383$	−4.27405	+	29.7267i	−0.218394	+	1.51896i	−0.743968	+	0.668215i	$0.767059\pi$
$384$	−0.124600	+	0.143796i	−0.00635846	+	0.00733805i
$385$	−0.323273	+	0.707868i	−0.0164755	+	0.0360763i
$386$	20.4261	+	5.99765i	1.03966	+	0.305272i
$387$	0.531681	+	1.16422i	0.0270268	+	0.0591805i
$388$	−0.448996	−	3.12284i	−0.0227943	−	0.158538i
$389$	2.18927	+	1.40696i	0.111000	+	0.0713355i	0.594963	−	0.803753i	$-0.297167\pi$
$389$	2.18927	+	1.40696i	0.111000	+	0.0713355i	−0.483963	+	0.875089i	$0.660803\pi$
$390$	−0.173541			−0.00878757
$391$	30.3523	−	14.7247i	1.53498	−	0.744660i
$392$	1.00000			0.0505076
$393$	−1.52190	−	0.978068i	−0.0767699	−	0.0493370i
$394$	−0.266899	−	1.85632i	−0.0134462	−	0.0935203i
$395$	−0.937900	−	2.05371i	−0.0471908	−	0.103334i
$396$	8.34519	+	2.45037i	0.419362	+	0.123136i
$397$	−2.41660	+	5.29162i	−0.121286	+	0.265579i	−0.960530	−	0.278175i	$-0.910270\pi$
$397$	−2.41660	+	5.29162i	−0.121286	+	0.265579i	0.839245	+	0.543754i	$0.182998\pi$
$398$	3.40732	−	3.93226i	0.170794	−	0.197106i
$399$	0.0684747	−	0.476252i	0.00342802	−	0.0238424i
$400$	4.72999	−	1.38885i	0.236500	−	0.0694426i
$401$	5.71531	+	6.59582i	0.285409	+	0.329379i	0.880292	−	0.474433i	$-0.157347\pi$
$401$	5.71531	+	6.59582i	0.285409	+	0.329379i	−0.594883	+	0.803813i	$0.702801\pi$
$402$	−1.78315	+	1.14596i	−0.0889356	+	0.0571554i
$403$	5.93860	−	3.81651i	0.295823	−	0.190114i
$404$	−12.1659	−	14.0402i	−0.605274	−	0.698524i
$405$	−2.20738	+	0.648144i	−0.109685	+	0.0322066i
$406$	1.10752	−	7.70298i	0.0549653	−	0.382292i
$407$	−2.03429	+	2.34769i	−0.100836	+	0.116371i
$408$	−0.555998	+	1.21747i	−0.0275260	+	0.0602735i
$409$	−13.1262	−	3.85420i	−0.649049	−	0.190578i	−0.0593957	−	0.998235i	$-0.518917\pi$
$409$	−13.1262	−	3.85420i	−0.649049	−	0.190578i	−0.589653	+	0.807657i	$0.700736\pi$
$410$	1.23942	+	2.71396i	0.0612108	+	0.134033i
$411$	0.415833	+	2.89218i	0.0205115	+	0.142661i
$412$	6.76841	+	4.34979i	0.333455	+	0.214299i
$413$	−14.2767			−0.702510
$414$	−7.96085	−	11.7754i	−0.391254	−	0.578727i
$415$	2.69761			0.132420
$416$	−2.89347	−	1.85952i	−0.141864	−	0.0911705i
$417$	0.165700	+	1.15247i	0.00811436	+	0.0564366i
$418$	3.08276	+	6.75030i	0.150783	+	0.330168i
$419$	5.52921	+	1.62352i	0.270120	+	0.0793143i	0.413987	−	0.910283i	$-0.364136\pi$
$419$	5.52921	+	1.62352i	0.270120	+	0.0793143i	−0.143868	+	0.989597i	$0.545954\pi$
$420$	−0.0209600	+	0.0458960i	−0.00102274	+	0.00223950i
$421$	5.51013	−	6.35903i	0.268547	−	0.309920i	−0.605419	−	0.795907i	$-0.706994\pi$
$421$	5.51013	−	6.35903i	0.268547	−	0.309920i	0.873966	+	0.485987i	$0.161540\pi$
$422$	−3.85992	+	26.8463i	−0.187898	+	1.30686i
$423$	27.5932	−	8.10208i	1.34162	−	0.393937i
$424$	−7.70500	−	8.89205i	−0.374188	−	0.431836i
$425$	29.1721	−	18.7478i	1.41506	−	0.909401i
$426$	0.673669	−	0.432941i	0.0326394	−	0.0209761i
$427$	1.00223	+	1.15663i	0.0485012	+	0.0559733i
$428$	10.4101	−	3.05667i	0.503189	−	0.147750i
$429$	0.273311	−	1.90092i	0.0131956	−	0.0917771i
$430$	0.0749911	−	0.0865444i	0.00361639	−	0.00417354i
$431$	9.36167	−	20.4992i	0.450936	−	0.987412i	−0.538525	−	0.842610i	$-0.681018\pi$
$431$	9.36167	−	20.4992i	0.450936	−	0.987412i	0.989461	−	0.144802i	$-0.0462545\pi$
$432$	1.08876	+	0.319690i	0.0523831	+	0.0153811i
$433$	8.80405	+	19.2782i	0.423096	+	0.926450i	0.994397	+	0.105710i	$0.0337115\pi$
$433$	8.80405	+	19.2782i	0.423096	+	0.926450i	−0.571301	+	0.820740i	$0.693561\pi$
$434$	−0.292089	−	2.03153i	−0.0140207	−	0.0975163i
$435$	0.330322	+	0.212285i	0.0158377	+	0.0101783i
$436$	−10.0079			−0.479290
$437$	3.14496	−	11.7127i	0.150444	−	0.560296i
$438$	2.17349			0.103853
$439$	4.07389	+	2.61813i	0.194436	+	0.124957i	0.634237	−	0.773139i	$-0.281314\pi$
$439$	4.07389	+	2.61813i	0.194436	+	0.124957i	−0.439801	+	0.898095i	$0.644951\pi$
$440$	−0.110748	−	0.770271i	−0.00527971	−	0.0367212i
$441$	−1.23121	−	2.69597i	−0.0586289	−	0.128379i
$442$	−23.2143	−	6.81634i	−1.10419	−	0.324220i
$443$	−15.1414	+	33.1550i	−0.719389	+	1.57524i	0.0953695	+	0.995442i	$0.469597\pi$
$443$	−15.1414	+	33.1550i	−0.719389	+	1.57524i	−0.814759	+	0.579800i	$0.803131\pi$
$444$	−0.131897	+	0.152217i	−0.00625955	+	0.00722391i
$445$	−0.180102	+	1.25264i	−0.00853766	+	0.0593808i
$446$	23.1254	−	6.79023i	1.09502	−	0.321526i
$447$	0.815346	+	0.940960i	0.0385645	+	0.0445059i
$448$	−0.841254	+	0.540641i	−0.0397455	+	0.0255429i
$449$	16.1346	−	10.3690i	0.761437	−	0.489346i	−0.101389	−	0.994847i	$-0.532329\pi$
$449$	16.1346	−	10.3690i	0.761437	−	0.489346i	0.862826	+	0.505501i	$0.168692\pi$
$450$	−9.56789	−	11.0419i	−0.451035	−	0.520522i
$451$	−31.6799	+	9.30207i	−1.49175	+	0.438017i
$452$	−2.82443	+	19.6443i	−0.132850	+	0.923992i
$453$	1.95799	−	2.25964i	0.0919945	−	0.106167i
$454$	4.86911	−	10.6619i	0.228519	−	0.500387i
$455$	−0.875134	−	0.256963i	−0.0410269	−	0.0120466i
$456$	0.199877	+	0.437669i	0.00936008	+	0.0204957i
$457$	−4.35703	−	30.3038i	−0.203813	−	1.41755i	−0.792836	−	0.609435i	$-0.791396\pi$
$457$	−4.35703	−	30.3038i	−0.203813	−	1.41755i	0.589023	−	0.808116i	$-0.299513\pi$
$458$	20.0286	+	12.8716i	0.935873	+	0.601449i
$459$	7.98204			0.372570
$460$	−0.662475	+	1.08559i	−0.0308881	+	0.0506157i
$461$	41.9850			1.95543			0.977717	−	0.209927i	$-0.0673225\pi$
$461$	41.9850			1.95543			0.977717	+	0.209927i	$0.0673225\pi$
$462$	−0.469722	−	0.301872i	−0.0218535	−	0.0140444i
$463$	4.79619	+	33.3582i	0.222898	+	1.55029i	0.726996	+	0.686641i	$0.240916\pi$
$463$	4.79619	+	33.3582i	0.222898	+	1.55029i	−0.504099	+	0.863646i	$0.668175\pi$
$464$	3.23284	+	7.07893i	0.150081	+	0.328631i
$465$	0.0993611	+	0.0291751i	0.00460776	+	0.00135296i
$466$	−2.15435	+	4.71736i	−0.0997981	+	0.218527i
$467$	16.5194	−	19.0644i	0.764428	−	0.882197i	−0.231455	−	0.972846i	$-0.574348\pi$
$467$	16.5194	−	19.0644i	0.764428	−	0.882197i	0.995883	+	0.0906483i	$0.0288939\pi$
$468$	−1.45074	+	10.0901i	−0.0670607	+	0.466417i
$469$	−10.6889	+	3.13856i	−0.493570	+	0.144925i
$470$	−1.68500	−	1.94460i	−0.0777234	−	0.0896976i
$471$	−0.787596	+	0.506157i	−0.0362905	+	0.0233225i
$472$	12.0103	−	7.71856i	0.552820	−	0.355276i
$473$	0.829879	+	0.957732i	0.0381579	+	0.0440366i
$474$	1.55433	−	0.456393i	0.0713928	−	0.0209628i
$475$	1.77411	−	12.3392i	0.0814017	−	0.566161i
$476$	−4.60650	+	5.31619i	−0.211139	+	0.243667i
$477$	−14.4862	+	31.7204i	−0.663278	+	1.45238i
$478$	1.00159	+	0.294093i	0.0458117	+	0.0134515i
$479$	11.2640	+	24.6646i	0.514664	+	1.12696i	0.971421	+	0.237365i	$0.0762836\pi$
$479$	11.2640	+	24.6646i	0.514664	+	1.12696i	−0.456757	+	0.889591i	$0.650989\pi$
$480$	−0.00718058	−	0.0499420i	−0.000327747	−	0.00227953i
$481$	−3.06292	−	1.96842i	−0.139657	−	0.0897523i
$482$	13.2149			0.601923
$483$	0.277390	+	0.869315i	0.0126217	+	0.0395552i
$484$	−2.38824			−0.108557
$485$	0.703818	+	0.452316i	0.0319587	+	0.0205386i
$486$	−0.719381	−	5.00341i	−0.0326318	−	0.226959i
$487$	10.1381	+	22.1994i	0.459402	+	1.00595i	0.987624	+	0.156843i	$0.0501316\pi$
$487$	10.1381	+	22.1994i	0.459402	+	1.00595i	−0.528222	+	0.849106i	$0.677141\pi$
$488$	−1.46845	−	0.431176i	−0.0664736	−	0.0195184i
$489$	0.935857	−	2.04924i	0.0423209	−	0.0926698i
$490$	−0.173656	+	0.200410i	−0.00784498	+	0.00905359i
$491$	1.33159	−	9.26144i	0.0600940	−	0.417963i	−0.937462	−	0.348088i	$-0.886831\pi$
$491$	1.33159	−	9.26144i	0.0600940	−	0.417963i	0.997556	−	0.0698748i	$-0.0222600\pi$
$492$	−2.05403	+	0.603118i	−0.0926029	+	0.0271907i
$493$	35.8487	+	41.3716i	1.61454	+	1.86328i
$494$	−7.31695	+	4.70232i	−0.329205	+	0.211567i
$495$	−1.94027	+	1.24694i	−0.0872086	+	0.0560456i
$496$	1.34405	+	1.55111i	0.0603495	+	0.0696470i
$497$	4.03825	−	1.18574i	0.181140	−	0.0531876i
$498$	−0.275459	+	1.91586i	−0.0123436	+	0.0858516i
$499$	−3.99234	+	4.60741i	−0.178722	+	0.206256i	−0.838041	−	0.545607i	$-0.816299\pi$
$499$	−3.99234	+	4.60741i	−0.178722	+	0.206256i	0.659319	+	0.751863i	$0.270845\pi$
$500$	−1.09385	+	2.39520i	−0.0489185	+	0.107117i
$501$	−0.212253	−	0.0623230i	−0.00948275	−	0.00278439i
$502$	−6.90847	−	15.1274i	−0.308340	−	0.675170i
$503$	−0.798291	−	5.55224i	−0.0355940	−	0.247562i	0.964254	−	0.264979i	$-0.0853649\pi$
$503$	−0.798291	−	5.55224i	−0.0355940	−	0.247562i	−0.999848	+	0.0174167i	$0.994456\pi$
$504$	2.49331	+	1.60235i	0.111061	+	0.0713743i
$505$	4.92646			0.219224
$506$	−10.8479	−	8.96627i	−0.482247	−	0.398600i
$507$	−0.222619			−0.00988685
$508$	7.02087	+	4.51204i	0.311501	+	0.200189i
$509$	0.255129	+	1.77446i	0.0113084	+	0.0786515i	0.994694	−	0.102877i	$-0.0328047\pi$
$509$	0.255129	+	1.77446i	0.0113084	+	0.0786515i	−0.983386	+	0.181528i	$0.941896\pi$
$510$	−0.147439	−	0.322847i	−0.00652873	−	0.0142959i
$511$	10.9605	+	3.21830i	0.484865	+	0.142369i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	1.87911	−	2.16861i	0.0829646	−	0.0957463i
$514$	−0.362760	+	2.52305i	−0.0160007	+	0.111287i
$515$	−2.04711	+	0.601087i	−0.0902066	+	0.0264871i
$516$	0.0538068	+	0.0620964i	0.00236871	+	0.00273364i
$517$	23.9543	−	15.3945i	1.05351	−	0.677049i
$518$	−0.890521	+	0.572303i	−0.0391272	+	0.0251455i
$519$	−1.75293	−	2.02299i	−0.0769450	−	0.0887992i
$520$	0.875134	−	0.256963i	0.0383772	−	0.0112686i
$521$	−1.41122	+	9.81522i	−0.0618265	+	0.430013i	0.935274	+	0.353923i	$0.115153\pi$
$521$	−1.41122	+	9.81522i	−0.0618265	+	0.430013i	−0.997101	+	0.0760895i	$0.975757\pi$
$522$	15.1043	−	17.4312i	0.661095	−	0.762944i
$523$	−17.1020	+	37.4482i	−0.747818	+	1.63749i	0.0224290	+	0.999748i	$0.492860\pi$
$523$	−17.1020	+	37.4482i	−0.747818	+	1.63749i	−0.770247	+	0.637745i	$0.779867\pi$
$524$	9.12291	+	2.67873i	0.398536	+	0.117021i
$525$	0.389645	+	0.853204i	0.0170055	+	0.0372369i
$526$	1.59276	+	11.0779i	0.0694475	+	0.483018i
$527$	12.1455	+	7.80543i	0.529065	+	0.340010i
$528$	0.558360			0.0242995
$529$	4.32923	+	22.5889i	0.188227	+	0.982125i
$530$	3.12007			0.135527
$531$	−35.5962	−	22.8763i	−1.54474	−	0.992745i
$532$	0.359883	+	2.50304i	0.0156029	+	0.108521i
$533$	−16.0757	−	35.2010i	−0.696318	−	1.52472i
$534$	−0.871241	−	0.255820i	−0.0377023	−	0.0110704i
$535$	−1.19518	+	2.61709i	−0.0516723	+	0.113146i
$536$	7.29528	−	8.41920i	0.315108	−	0.363654i
$537$	−0.445823	+	3.10076i	−0.0192387	+	0.133808i
$538$	13.1034	−	3.84752i	0.564929	−	0.165878i
$539$	−1.92174	−	2.21781i	−0.0827752	−	0.0955277i
$540$	−0.253139	+	0.162683i	−0.0108934	+	0.00700074i
$541$	−14.7852	+	9.50188i	−0.635666	+	0.408518i	−0.818404	−	0.574644i	$-0.805141\pi$
$541$	−14.7852	+	9.50188i	−0.635666	+	0.408518i	0.182737	+	0.983162i	$0.441504\pi$
$542$	−0.985351	−	1.13716i	−0.0423244	−	0.0488450i
$543$	1.72902	−	0.507686i	0.0741993	−	0.0217869i
$544$	1.00109	−	6.96272i	0.0429213	−	0.298524i
$545$	1.73793	−	2.00567i	0.0744446	−	0.0859137i
$546$	0.271858	−	0.595287i	0.0116345	−	0.0254759i
$547$	−12.4533	−	3.65662i	−0.532464	−	0.156346i	0.00443788	−	0.999990i	$-0.498587\pi$
$547$	−12.4533	−	3.65662i	−0.532464	−	0.156346i	−0.536902	+	0.843645i	$0.680406\pi$
$548$	−6.37944	−	13.9690i	−0.272516	−	0.596727i
$549$	0.645529	+	4.48976i	0.0275505	+	0.191618i
$550$	−12.1700	−	7.82120i	−0.518932	−	0.333497i
$551$	19.6795			0.838373
$552$	−0.703343	−	0.581346i	−0.0299363	−	0.0247437i
$553$	8.51400			0.362052
$554$	6.76875	+	4.35001i	0.287576	+	0.184814i
$555$	−0.00760110	−	0.0528668i	−0.000322649	−	0.00224407i
$556$	−2.54206	−	5.56633i	−0.107807	−	0.236065i
$557$	24.2141	+	7.10991i	1.02599	+	0.301257i	0.751078	−	0.660214i	$-0.229534\pi$
$557$	24.2141	+	7.10991i	1.02599	+	0.301257i	0.274908	+	0.961470i	$0.411352\pi$
$558$	2.52695	−	5.53324i	0.106974	−	0.234241i
$559$	−0.972660	+	1.12251i	−0.0411391	+	0.0474771i
$560$	0.0377390	−	0.262481i	0.00159477	−	0.0110918i
$561$	3.76859	−	1.10656i	0.159110	−	0.0467189i
$562$	−2.79135	−	3.22139i	−0.117746	−	0.135886i
$563$	7.11400	−	4.57189i	0.299819	−	0.192682i	−0.382078	−	0.924130i	$-0.624791\pi$
$563$	7.11400	−	4.57189i	0.299819	−	0.192682i	0.681897	+	0.731448i	$0.261155\pi$
$564$	1.55312	−	0.998133i	0.0653983	−	0.0420290i
$565$	−3.44644	−	3.97740i	−0.144993	−	0.167330i
$566$	−8.28104	+	2.43153i	−0.348078	+	0.102205i
$567$	1.23465	−	8.58719i	0.0518505	−	0.360628i
$568$	−2.75613	+	3.18075i	−0.115645	+	0.133461i
$569$	5.38533	−	11.7922i	0.225765	−	0.494356i	−0.762522	−	0.646962i	$-0.776039\pi$
$569$	5.38533	−	11.7922i	0.225765	−	0.494356i	0.988287	+	0.152606i	$0.0487666\pi$
$570$	−0.122423	−	0.0359466i	−0.00512773	−	0.00150564i
$571$	−8.93194	−	19.5582i	−0.373790	−	0.818486i	−0.999268	−	0.0382445i	$-0.987823\pi$
$571$	−8.93194	−	19.5582i	−0.373790	−	0.818486i	0.625478	−	0.780242i	$-0.284904\pi$
$572$	1.43644	+	9.99067i	0.0600607	+	0.417731i
$573$	−2.77581	−	1.78390i	−0.115961	−	0.0745236i
$574$	−11.2511			−0.469614
$575$	7.18690	+	22.5231i	0.299715	+	0.939277i
$576$	−2.96380			−0.123492
$577$	−1.23145	−	0.791404i	−0.0512659	−	0.0329466i	0.514757	−	0.857336i	$-0.327882\pi$
$577$	−1.23145	−	0.791404i	−0.0512659	−	0.0329466i	−0.566023	+	0.824390i	$0.691519\pi$
$578$	−4.62263	−	32.1511i	−0.192276	−	1.33731i
$579$	−1.68265	−	3.68450i	−0.0699287	−	0.153122i
$580$	−1.98009	−	0.581406i	−0.0822186	−	0.0241416i
$581$	−4.22591	+	9.25345i	−0.175320	+	0.383898i
$582$	−0.393106	+	0.453669i	−0.0162948	+	0.0188052i
$583$	−4.91383	+	34.1764i	−0.203510	+	1.41544i
$584$	−10.9605	+	3.21830i	−0.453550	+	0.133174i
$585$	−1.77023	−	2.04296i	−0.0731901	−	0.0844659i
$586$	−23.1504	+	14.8779i	−0.956334	+	0.614599i
$587$	21.7530	−	13.9798i	0.897842	−	0.577008i	−0.00830750	−	0.999965i	$-0.502644\pi$
$587$	21.7530	−	13.9798i	0.897842	−	0.577008i	0.906150	+	0.422957i	$0.139008\pi$
$588$	−0.124600	−	0.143796i	−0.00513841	−	0.00593004i
$589$	4.97988	−	1.46222i	0.205192	−	0.0602499i
$590$	−0.538789	+	3.74736i	−0.0221816	+	0.154276i
$591$	−0.233676	+	0.269677i	−0.00961215	+	0.0110930i
$592$	0.439743	−	0.962904i	0.0180733	−	0.0395751i
$593$	−10.9772	−	3.22321i	−0.450782	−	0.132361i	0.0484584	−	0.998825i	$-0.484569\pi$
$593$	−10.9772	−	3.22321i	−0.450782	−	0.132361i	−0.499240	+	0.866464i	$0.666387\pi$
$594$	−1.38331	−	3.02903i	−0.0567579	−	0.124282i
$595$	−0.265469	−	1.84637i	−0.0108832	−	0.0756940i
$596$	−5.50493	−	3.53780i	−0.225491	−	0.144914i
$597$	−0.989994			−0.0405177
$598$	8.59253	−	14.0804i	0.351375	−	0.575791i
$599$	17.0514			0.696700			0.348350	−	0.937365i	$-0.386742\pi$
$599$	17.0514			0.696700			0.348350	+	0.937365i	$0.386742\pi$
$600$	−0.789067	−	0.507103i	−0.0322135	−	0.0207024i
$601$	−0.710940	−	4.94470i	−0.0289998	−	0.201698i	0.970171	−	0.242423i	$-0.0779423\pi$
$601$	−0.710940	−	4.94470i	−0.0289998	−	0.201698i	−0.999170	+	0.0407251i	$0.987033\pi$
$602$	0.179392	+	0.392813i	0.00731146	+	0.0160099i
$603$	−31.6799	−	9.30205i	−1.29010	−	0.378809i
$604$	−6.52793	+	14.2942i	−0.265618	+	0.581622i
$605$	0.414733	−	0.478627i	0.0168613	−	0.0194590i
$606$	−0.503052	+	3.49880i	−0.0204351	+	0.142129i
$607$	−33.7262	+	9.90292i	−1.36891	+	0.401947i	−0.881894	−	0.471448i	$-0.843731\pi$
$607$	−33.7262	+	9.90292i	−1.36891	+	0.401947i	−0.487012	+	0.873395i	$0.661913\pi$
$608$	−1.65600	−	1.91113i	−0.0671597	−	0.0775064i
$609$	−1.24565	+	0.800533i	−0.0504764	+	0.0324392i
$610$	0.341417	−	0.219415i	0.0138236	−	0.00888387i
$611$	21.8551	+	25.2221i	0.884161	+	1.02038i
$612$	−20.0038	+	5.87365i	−0.808606	+	0.237428i
$613$	3.16935	−	22.0433i	0.128009	−	0.890322i	−0.820065	−	0.572271i	$-0.806063\pi$
$613$	3.16935	−	22.0433i	0.128009	−	0.890322i	0.948074	−	0.318051i	$-0.103028\pi$
$614$	6.19659	−	7.15124i	0.250074	−	0.288601i
$615$	0.235824	−	0.516383i	0.00950934	−	0.0208226i
$616$	2.81571	+	0.826767i	0.113448	+	0.0333114i
$617$	−8.93692	−	19.5691i	−0.359787	−	0.787823i	−0.999810	−	0.0194679i	$-0.993803\pi$
$617$	−8.93692	−	19.5691i	−0.359787	−	0.787823i	0.640024	−	0.768355i	$-0.278924\pi$
$618$	−0.217860	−	1.51525i	−0.00876363	−	0.0609524i
$619$	−13.4236	−	8.62679i	−0.539538	−	0.346740i	0.242320	−	0.970196i	$-0.422092\pi$
$619$	−13.4236	−	8.62679i	−0.539538	−	0.346740i	−0.781858	+	0.623456i	$0.785728\pi$
$620$	−0.544260			−0.0218580
$621$	−1.41122	+	5.25579i	−0.0566304	+	0.210908i
$622$	−2.00898			−0.0805526
$623$	−4.01472	−	2.58010i	−0.160846	−	0.103370i
$624$	0.0931345	+	0.647765i	0.00372836	+	0.0259313i
$625$	9.94925	+	21.7858i	0.397970	+	0.871432i
$626$	−14.9498	−	4.38965i	−0.597513	−	0.175446i
$627$	0.586554	−	1.28437i	0.0234247	−	0.0512929i
$628$	3.22223	−	3.71865i	0.128581	−	0.148390i
$629$	1.05972	−	7.37049i	0.0422537	−	0.293881i
$630$	−0.754104	+	0.221425i	−0.0300442	+	0.00882178i
$631$	−7.12911	−	8.22743i	−0.283805	−	0.327529i	0.595890	−	0.803066i	$-0.296799\pi$
$631$	−7.12911	−	8.22743i	−0.283805	−	0.327529i	−0.879696	+	0.475537i	$0.842254\pi$
$632$	−7.16243	+	4.60301i	−0.284906	+	0.183098i
$633$	4.34134	−	2.79001i	0.172553	−	0.110893i
$634$	−6.43956	−	7.43165i	−0.255748	−	0.295148i
$635$	−2.12347	+	0.623508i	−0.0842675	+	0.0247432i
$636$	−0.318598	+	2.21589i	−0.0126332	+	0.0878659i
$637$	2.25238	−	2.59938i	0.0892424	−	0.102991i
$638$	9.48702	−	20.7737i	0.375595	−	0.822438i
$639$	11.9686	+	3.51428i	0.473469	+	0.139023i
$640$	0.110160	+	0.241216i	0.00435445	+	0.00953491i
$641$	4.45824	+	31.0078i	0.176090	+	1.22473i	0.865704	+	0.500556i	$0.166871\pi$
$641$	4.45824	+	31.0078i	0.176090	+	1.22473i	−0.689614	+	0.724177i	$0.742220\pi$
$642$	−1.73663	−	1.11606i	−0.0685392	−	0.0440475i
$643$	−8.95337			−0.353086			−0.176543	−	0.984293i	$-0.556492\pi$
$643$	−8.95337			−0.353086			−0.176543	+	0.984293i	$0.556492\pi$
$644$	−2.68603	−	3.97307i	−0.105844	−	0.156561i
$645$	−0.0217886			−0.000857925
$646$	−14.9644	−	9.61706i	−0.588768	−	0.378378i
$647$	3.11954	+	21.6969i	0.122642	+	0.852992i	0.954544	+	0.298070i	$0.0963429\pi$
$647$	3.11954	+	21.6969i	0.122642	+	0.852992i	−0.831902	+	0.554922i	$0.812748\pi$
$648$	3.60393	+	7.89150i	0.141576	+	0.310008i
$649$	−40.1990	−	11.8035i	−1.57795	−	0.463328i
$650$	7.04357	−	15.4233i	0.276272	−	0.604950i
$651$	−0.255731	+	0.295129i	−0.0100229	+	0.0115670i
$652$	−1.68503	+	11.7197i	−0.0659911	+	0.458978i
$653$	13.7917	−	4.04962i	0.539713	−	0.158474i	−0.000503994	−	1.00000i	$-0.500160\pi$
$653$	13.7917	−	4.04962i	0.539713	−	0.158474i	0.540217	+	0.841526i	$0.318342\pi$
$654$	1.24698	+	1.43909i	0.0487608	+	0.0562729i
$655$	−2.12109	+	1.36314i	−0.0828779	+	0.0532624i
$656$	9.46507	−	6.08283i	0.369549	−	0.237495i
$657$	22.1711	+	25.5868i	0.864976	+	0.998236i
$658$	9.31007	−	2.73368i	0.362944	−	0.106570i
$659$	−0.682370	+	4.74599i	−0.0265814	+	0.184877i	−0.998786	−	0.0492542i	$-0.984316\pi$
$659$	−0.682370	+	4.74599i	−0.0265814	+	0.184877i	0.972205	+	0.234132i	$0.0752247\pi$
$660$	−0.0969626	+	0.111901i	−0.00377426	+	0.00435573i
$661$	5.57169	−	12.2003i	0.216714	−	0.474537i	−0.769786	−	0.638303i	$-0.779637\pi$
$661$	5.57169	−	12.2003i	0.216714	−	0.474537i	0.986499	+	0.163766i	$0.0523642\pi$
$662$	−13.4066	−	3.93654i	−0.521063	−	0.152998i
$663$	1.91234	+	4.18744i	0.0742691	+	0.162627i
$664$	−1.44773	−	10.0692i	−0.0561829	−	0.390760i
$665$	−0.564130	−	0.362544i	−0.0218760	−	0.0140589i
$666$	−3.13737			−0.121571
$667$	−33.5793	+	16.2902i	−1.30019	+	0.630758i
$668$	1.16263			0.0449837
$669$	−3.85782	−	2.47927i	−0.149152	−	0.0958543i
$670$	0.420421	+	2.92409i	0.0162423	+	0.112967i
$671$	1.86572	+	4.08535i	0.0720251	+	0.157713i
$672$	0.182562	+	0.0536050i	0.00704248	+	0.00206786i
$673$	−1.93286	+	4.23237i	−0.0745062	+	0.163146i	−0.943220	−	0.332168i	$-0.892220\pi$
$673$	−1.93286	+	4.23237i	−0.0745062	+	0.163146i	0.868714	+	0.495314i	$0.164947\pi$
$674$	−2.99513	+	3.45656i	−0.115368	+	0.133142i
$675$	−0.796086	+	5.53690i	−0.0306414	+	0.213115i
$676$	1.12263	−	0.329633i	0.0431779	−	0.0126782i
$677$	−7.53054	−	8.69071i	−0.289422	−	0.334011i	0.592355	−	0.805677i	$-0.298198\pi$
$677$	−7.53054	−	8.69071i	−0.289422	−	0.334011i	−0.881777	+	0.471666i	$0.843653\pi$
$678$	3.17670	−	2.04154i	0.122000	−	0.0784049i
$679$	−2.65411	+	1.70570i	−0.101856	+	0.0654586i
$680$	1.22155	+	1.40975i	0.0468444	+	0.0540613i
$681$	−2.13982	+	0.628309i	−0.0819982	+	0.0240769i
$682$	0.857159	−	5.96167i	0.0328223	−	0.228284i
$683$	−24.7805	+	28.5982i	−0.948198	+	1.09428i	0.0472418	+	0.998883i	$0.484957\pi$
$683$	−24.7805	+	28.5982i	−0.948198	+	1.09428i	−0.995439	+	0.0953950i	$0.969589\pi$
$684$	−3.11345	+	6.81751i	−0.119046	+	0.260674i
$685$	3.90735	+	1.14730i	0.149292	+	0.0438362i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	−0.644676	−	4.48382i	−0.0245959	−	0.171068i
$688$	−0.363285	−	0.233469i	−0.0138501	−	0.00890092i
$689$	−40.4684			−1.54172
$690$	0.238647	−	0.0400025i	0.00908514	−	0.00152287i
$691$	−31.3101			−1.19109			−0.595547	−	0.803320i	$-0.703065\pi$
$691$	−31.3101			−1.19109			−0.595547	+	0.803320i	$0.703065\pi$
$692$	11.8351	+	7.60598i	0.449905	+	0.289136i
$693$	−1.23778	−	8.60897i	−0.0470195	−	0.327028i
$694$	−2.04578	−	4.47963i	−0.0776567	−	0.170045i
$695$	1.55699	+	0.457174i	0.0590600	+	0.0173416i
$696$	0.615109	−	1.34690i	0.0233157	−	0.0510542i
$697$	51.8284	−	59.8132i	1.96314	−	2.26559i
$698$	0.763946	−	5.31336i	0.0289158	−	0.201114i
$699$	0.946768	−	0.277996i	0.0358100	−	0.0105148i
$700$	−3.22825	−	3.72560i	−0.122017	−	0.140815i
$701$	1.85112	−	1.18964i	0.0699159	−	0.0449322i	−0.505216	−	0.862993i	$-0.668587\pi$
$701$	1.85112	−	1.18964i	0.0699159	−	0.0449322i	0.575132	+	0.818061i	$0.304951\pi$
$702$	3.28330	−	2.11005i	0.123920	−	0.0796386i
$703$	−1.75298	−	2.02305i	−0.0661150	−	0.0763007i
$704$	−2.81571	+	0.826767i	−0.106121	+	0.0311599i
$705$	−0.0696739	+	0.484593i	−0.00262407	+	0.0182508i
$706$	−3.30714	+	3.81665i	−0.124466	+	0.143641i
$707$	−7.71749	+	16.8989i	−0.290246	+	0.635550i
$708$	−2.60638	−	0.765303i	−0.0979538	−	0.0287618i
$709$	−19.8459	−	43.4565i	−0.745328	−	1.63204i	−0.774585	−	0.632469i	$-0.782041\pi$
$709$	−19.8459	−	43.4565i	−0.745328	−	1.63204i	0.0292571	−	0.999572i	$-0.490686\pi$
$710$	−0.158834	−	1.10471i	−0.00596092	−	0.0414591i
$711$	21.2280	+	13.6424i	0.796112	+	0.511630i
$712$	4.77230			0.178850
$713$	−7.28682	+	6.61723i	−0.272894	+	0.247817i
$714$	1.33841			0.0500889
$715$	−2.25167	−	1.44706i	−0.0842078	−	0.0541171i
$716$	−2.34312	−	16.2967i	−0.0875663	−	0.609037i
$717$	−0.0825085	−	0.180668i	−0.00308134	−	0.00674719i
$718$	−29.6860	−	8.71660i	−1.10787	−	0.325301i
$719$	15.1269	−	33.1234i	0.564140	−	1.23529i	−0.385719	−	0.922616i	$-0.626047\pi$
$719$	15.1269	−	33.1234i	0.564140	−	1.23529i	0.949859	−	0.312678i	$-0.101226\pi$
$720$	0.514681	−	0.593974i	0.0191810	−	0.0221361i
$721$	1.14501	−	7.96373i	0.0426424	−	0.296585i
$722$	12.0947	−	3.55131i	0.450117	−	0.132166i
$723$	−1.64658	−	1.90025i	−0.0612369	−	0.0706711i
$724$	−7.96739	+	5.12033i	−0.296106	+	0.190296i
$725$	−32.2736	+	20.7410i	−1.19861	+	0.770301i
$726$	0.297575	+	0.343420i	0.0110440	+	0.0127455i
$727$	−23.2467	+	6.82585i	−0.862173	+	0.253157i	−0.682783	−	0.730621i	$-0.739230\pi$
$727$	−23.2467	+	6.82585i	−0.862173	+	0.253157i	−0.179390	+	0.983778i	$0.557412\pi$
$728$	−0.489488	+	3.40446i	−0.0181416	+	0.126178i
$729$	16.4139	−	18.9426i	0.607921	−	0.701579i
$730$	1.25838	−	2.75547i	0.0465748	−	0.101985i
$731$	−2.91464	−	0.855814i	−0.107802	−	0.0316534i
$732$	0.120967	+	0.264881i	0.00447108	+	0.00979030i
$733$	−1.50183	−	10.4455i	−0.0554713	−	0.385812i	−0.998577	−	0.0533198i	$-0.983020\pi$
$733$	−1.50183	−	10.4455i	−0.0554713	−	0.385812i	0.943106	−	0.332492i	$-0.107889\pi$
$734$	−12.8628	−	8.26640i	−0.474773	−	0.305118i
$735$	0.0504556			0.00186108
$736$	4.40763	+	1.89018i	0.162467	+	0.0696729i
$737$	−32.6918			−1.20422
$738$	−28.0525	−	18.0283i	−1.03263	−	0.663630i
$739$	−5.59968	−	38.9467i	−0.205988	−	1.43268i	−0.786080	−	0.618125i	$-0.787892\pi$
$739$	−5.59968	−	38.9467i	−0.205988	−	1.43268i	0.580092	−	0.814551i	$-0.303017\pi$
$740$	0.116611	+	0.255343i	0.00428671	+	0.00938659i
$741$	1.58787	+	0.466239i	0.0583317	+	0.0171277i
$742$	−4.88772	+	10.7026i	−0.179434	+	0.392905i
$743$	4.99279	−	5.76198i	0.183168	−	0.211387i	−0.656739	−	0.754118i	$-0.728064\pi$
$743$	4.99279	−	5.76198i	0.183168	−	0.211387i	0.839906	+	0.542732i	$0.182610\pi$
$744$	0.0555756	−	0.386537i	0.00203750	−	0.0141711i
$745$	1.66497	−	0.488880i	0.0609999	−	0.0179112i
$746$	11.6700	+	13.4679i	0.427270	+	0.493096i
$747$	−25.3637	+	16.3003i	−0.928011	+	0.596396i
$748$	−17.3658	+	11.1603i	−0.634957	+	0.408062i
$749$	−7.10494	−	8.19954i	−0.259609	−	0.299605i
$750$	0.480713	−	0.141150i	0.0175532	−	0.00515408i
$751$	−2.10770	+	14.6594i	−0.0769109	+	0.534927i	0.914545	+	0.404484i	$0.132549\pi$
$751$	−2.10770	+	14.6594i	−0.0769109	+	0.534927i	−0.991456	+	0.130443i	$0.958360\pi$
$752$	−6.35419	+	7.33312i	−0.231713	+	0.267411i
$753$	−1.31447	+	2.87828i	−0.0479019	+	0.104891i
$754$	25.6824	+	7.54103i	0.935298	+	0.274628i
$755$	−1.73108	−	3.79053i	−0.0630004	−	0.137952i
$756$	−0.161488	−	1.12318i	−0.00587328	−	0.0408496i
$757$	4.78837	+	3.07730i	0.174036	+	0.111846i	0.624759	−	0.780818i	$-0.285197\pi$
$757$	4.78837	+	3.07730i	0.174036	+	0.111846i	−0.450723	+	0.892664i	$0.648834\pi$
$758$	4.17904			0.151790
$759$	0.0623298	+	2.67708i	0.00226243	+	0.0971717i
$760$	0.670582			0.0243246
$761$	35.6678	+	22.9223i	1.29296	+	0.830933i	0.992427	−	0.122839i	$-0.0391998\pi$
$761$	35.6678	+	22.9223i	1.29296	+	0.830933i	0.300531	+	0.953772i	$0.402836\pi$
$762$	−0.225987	−	1.57177i	−0.00818664	−	0.0569393i
$763$	4.15742	+	9.10348i	0.150509	+	0.329568i
$764$	16.6393	+	4.88574i	0.601989	+	0.176760i
$765$	2.29664	−	5.02895i	0.0830354	−	0.181822i
$766$	−19.6670	+	22.6969i	−0.710598	+	0.820074i
$767$	6.98827	−	48.6045i	0.252332	−	1.75501i
$768$	−0.182562	+	0.0536050i	−0.00658764	+	0.00193430i
$769$	11.2204	+	12.9491i	0.404619	+	0.466955i	0.921090	−	0.389349i	$-0.127300\pi$
$769$	11.2204	+	12.9491i	0.404619	+	0.466955i	−0.516471	+	0.856305i	$0.672755\pi$
$770$	−0.654657	+	0.420722i	−0.0235922	+	0.0151618i
$771$	0.408004	−	0.262208i	0.0146939	−	0.00944321i
$772$	13.9410	+	16.0887i	0.501747	+	0.579046i
$773$	38.7812	−	11.3872i	1.39486	−	0.409568i	0.503945	−	0.863736i	$-0.331881\pi$
$773$	38.7812	−	11.3872i	1.39486	−	0.409568i	0.890917	+	0.454167i	$0.150063\pi$
$774$	−0.182146	+	1.26685i	−0.00654709	+	0.0455360i
$775$	−6.62572	+	7.64649i	−0.238003	+	0.274670i
$776$	1.31061	−	2.86984i	0.0470483	−	0.103021i
$777$	0.193254	+	0.0567444i	0.00693293	+	0.00203569i
$778$	1.08107	+	2.36721i	0.0387582	+	0.0848687i
$779$	−4.04910	−	28.1621i	−0.145074	−	1.00901i
$780$	−0.145992	−	0.0938232i	−0.00522734	−	0.00335941i
$781$	12.3509			0.441948
$782$	33.4948	+	4.02250i	1.19777	+	0.143844i
$783$	−8.83066			−0.315582
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	0.185694	+	1.29153i	0.00662772	+	0.0460968i
$786$	−0.751523	−	1.64561i	−0.0268059	−	0.0586968i
$787$	34.5161	+	10.1348i	1.23037	+	0.361268i	0.831388	−	0.555692i	$-0.187547\pi$
$787$	34.5161	+	10.1348i	1.23037	+	0.361268i	0.398978	+	0.916960i	$0.369365\pi$
$788$	0.779075	−	1.70594i	0.0277534	−	0.0607715i
$789$	1.39449	−	1.60933i	0.0496453	−	0.0572938i
$790$	0.321310	−	2.23476i	0.0114317	−	0.0795092i
$791$	19.0424	−	5.59136i	0.677071	−	0.198806i
$792$	5.69565	+	6.57313i	0.202386	+	0.233566i
$793$	−4.42829	+	2.84589i	−0.157253	+	0.101061i
$794$	−4.89384	+	3.14508i	−0.173676	+	0.111615i
$795$	−0.388760	−	0.448653i	−0.0137879	−	0.0159121i
$796$	4.99236	−	1.46589i	0.176949	−	0.0519571i
$797$	−3.29713	+	22.9320i	−0.116790	+	0.812294i	0.844263	+	0.535930i	$0.180039\pi$
$797$	−3.29713	+	22.9320i	−0.116790	+	0.812294i	−0.961053	+	0.276365i	$0.910870\pi$
$798$	0.315086	−	0.363628i	0.0111539	−	0.0128723i
$799$	−28.3541	+	62.0868i	−1.00309	+	2.19647i
$800$	4.72999	+	1.38885i	0.167231	+	0.0491033i
$801$	−5.87569	−	12.8660i	−0.207607	−	0.454597i
$802$	1.24206	+	8.63868i	0.0438585	+	0.305043i
$803$	28.2008	+	18.1236i	0.995186	+	0.639567i
$804$	−2.11964			−0.0747539
$805$	1.26269	+	0.151640i	0.0445038	+	0.00534462i
$806$	7.05923			0.248651
$807$	−2.18594	−	1.40482i	−0.0769488	−	0.0494520i
$808$	−2.64389	−	18.3887i	−0.0930119	−	0.646912i
$809$	14.6113	+	31.9942i	0.513705	+	1.12486i	0.971768	+	0.235937i	$0.0758160\pi$
$809$	14.6113	+	31.9942i	0.513705	+	1.12486i	−0.458063	+	0.888920i	$0.651457\pi$
$810$	−2.20738	−	0.648144i	−0.0775593	−	0.0227735i
$811$	4.70611	−	10.3050i	0.165254	−	0.361856i	−0.808830	−	0.588043i	$-0.799899\pi$
$811$	4.70611	−	10.3050i	0.165254	−	0.361856i	0.974084	+	0.226187i	$0.0726260\pi$
$812$	5.09625	−	5.88138i	0.178843	−	0.206396i
$813$	−0.0407437	+	0.283379i	−0.00142894	+	0.00993853i
$814$	−2.98061	+	0.875185i	−0.104470	+	0.0306752i
$815$	−2.05612	−	2.37289i	−0.0720227	−	0.0831187i
$816$	−1.12595	+	0.723602i	−0.0394160	+	0.0253311i
$817$	−0.918667	+	0.590392i	−0.0321401	+	0.0206552i
$818$	−8.95873	−	10.3389i	−0.313234	−	0.361492i
$819$	9.78098	−	2.87195i	0.341775	−	0.100354i
$820$	−0.424608	+	2.95321i	−0.0148279	+	0.103131i
$821$	6.80291	−	7.85098i	0.237423	−	0.274001i	−0.624517	−	0.781011i	$-0.714704\pi$
$821$	6.80291	−	7.85098i	0.237423	−	0.274001i	0.861940	+	0.507010i	$0.169249\pi$
$822$	−1.21381	+	2.65787i	−0.0423365	+	0.0927040i
$823$	−20.5782	−	6.04230i	−0.717310	−	0.210621i	−0.0973449	−	0.995251i	$-0.531035\pi$
$823$	−20.5782	−	6.04230i	−0.717310	−	0.210621i	−0.619965	+	0.784630i	$0.712853\pi$
$824$	3.34227	+	7.31855i	0.116434	+	0.254954i
$825$	0.391727	+	2.72452i	0.0136382	+	0.0948556i
$826$	−12.0103	−	7.71856i	−0.417892	−	0.268563i
$827$	21.4977			0.747548			0.373774	−	0.927520i	$-0.378064\pi$
$827$	21.4977			0.747548			0.373774	+	0.927520i	$0.378064\pi$
$828$	−0.330849	−	14.2100i	−0.0114978	−	0.493832i
$829$	−14.1950			−0.493011			−0.246506	−	0.969141i	$-0.579282\pi$
$829$	−14.1950			−0.493011			−0.246506	+	0.969141i	$0.579282\pi$
$830$	2.26937	+	1.45844i	0.0787710	+	0.0506231i
$831$	−0.217871	−	1.51533i	−0.00755787	−	0.0525661i
$832$	−1.42881	−	3.12866i	−0.0495350	−	0.108467i
$833$	6.74938	+	1.98180i	0.233852	+	0.0686652i
$834$	−0.483676	+	1.05910i	−0.0167483	+	0.0366737i
$835$	−0.201898	+	0.233003i	−0.00698698	+	0.00806340i
$836$	−1.05611	+	7.34538i	−0.0365262	+	0.254045i
$837$	−2.23459	+	0.656136i	−0.0772389	+	0.0226794i
$838$	3.77373	+	4.35511i	0.130361	+	0.150445i
$839$	42.3779	−	27.2346i	1.46305	−	0.940244i	0.464545	−	0.885550i	$-0.346218\pi$
$839$	42.3779	−	27.2346i	1.46305	−	0.940244i	0.998503	−	0.0546940i	$-0.0174183\pi$
$840$	−0.0424459	+	0.0272783i	−0.00146452	+	0.000941192i
$841$	−20.6690	−	23.8533i	−0.712724	−	0.822528i
$842$	8.07337	−	2.37056i	0.278227	−	0.0816948i
$843$	−0.115421	+	0.802769i	−0.00397530	+	0.0276488i
$844$	−17.7614	+	20.4978i	−0.611373	+	0.705562i
$845$	−0.128889	+	0.282228i	−0.00443392	+	0.00970893i
$846$	27.5932	+	8.10208i	0.948672	+	0.278555i
$847$	0.992112	+	2.17242i	0.0340894	+	0.0746453i
$848$	−1.67446	−	11.6461i	−0.0575011	−	0.399929i
$849$	1.38146	+	0.887811i	0.0474116	+	0.0304696i
$850$	34.6770			1.18941
$851$	4.66576	+	2.00087i	0.159940	+	0.0685891i
$852$	0.800792			0.0274347
$853$	−26.2921	−	16.8969i	−0.900223	−	0.578538i	0.00663344	−	0.999978i	$-0.497888\pi$
$853$	−26.2921	−	16.8969i	−0.900223	−	0.578538i	−0.906856	+	0.421440i	$0.861525\pi$
$854$	0.217805	+	1.51487i	0.00745313	+	0.0518376i
$855$	−0.825625	−	1.80787i	−0.0282358	−	0.0618277i
$856$	10.4101	+	3.05667i	0.355809	+	0.104475i
$857$	−12.6700	+	27.7434i	−0.432798	+	0.947696i	0.560066	+	0.828448i	$0.310776\pi$
$857$	−12.6700	+	27.7434i	−0.432798	+	0.947696i	−0.992864	+	0.119248i	$0.961952\pi$
$858$	1.25764	−	1.45139i	0.0429350	−	0.0495497i
$859$	−0.560183	+	3.89616i	−0.0191132	+	0.132935i	−0.997144	−	0.0755260i	$-0.975936\pi$
$859$	−0.560183	+	3.89616i	−0.0191132	+	0.132935i	0.978031	+	0.208461i	$0.0668455\pi$
$860$	0.109876	−	0.0322625i	0.00374674	−	0.00110014i
$861$	1.40189	+	1.61787i	0.0477763	+	0.0551368i
$862$	18.9582	−	12.1837i	0.645720	−	0.414979i
$863$	28.3807	−	18.2392i	0.966091	−	0.620869i	0.0404140	−	0.999183i	$-0.487132\pi$
$863$	28.3807	−	18.2392i	0.966091	−	0.620869i	0.925677	+	0.378314i	$0.123496\pi$
$864$	0.743088	+	0.857569i	0.0252804	+	0.0291751i
$865$	−3.57956	+	1.05105i	−0.121709	+	0.0357369i
$866$	−3.01613	+	20.9777i	−0.102492	+	0.712850i
$867$	−4.04721	+	4.67073i	−0.137451	+	0.158626i
$868$	0.852604	−	1.86694i	0.0289393	−	0.0633682i
$869$	23.9729	+	7.03909i	0.813226	+	0.238785i
$870$	0.163115	+	0.357171i	0.00553011	+	0.0121092i
$871$	−5.45300	−	37.9264i	−0.184768	−	1.28509i
$872$	−8.41916	−	5.41067i	−0.285109	−	0.183228i
$873$	−9.35064			−0.316471
$874$	8.97809	−	8.15308i	0.303689	−	0.275782i
$875$	2.63315			0.0890168
$876$	1.82846	+	1.17508i	0.0617778	+	0.0397022i
$877$	0.113535	+	0.789657i	0.00383382	+	0.0266648i	0.991649	−	0.128970i	$-0.0411669\pi$
$877$	0.113535	+	0.789657i	0.00383382	+	0.0266648i	−0.987815	+	0.155634i	$0.950258\pi$
$878$	2.01171	+	4.40502i	0.0678918	+	0.148662i
$879$	5.02391	+	1.47515i	0.169452	+	0.0497557i
$880$	0.323273	−	0.707868i	0.0108975	−	0.0238622i
$881$	−15.1434	+	17.4764i	−0.510194	+	0.588795i	−0.951148	−	0.308734i	$-0.900095\pi$
$881$	−15.1434	+	17.4764i	−0.510194	+	0.588795i	0.440954	+	0.897530i	$0.354640\pi$
$882$	0.421792	−	2.93363i	0.0142025	−	0.0987805i
$883$	−35.8084	+	10.5143i	−1.20505	+	0.353835i	−0.821782	−	0.569803i	$-0.807020\pi$
$883$	−35.8084	+	10.5143i	−1.20505	+	0.353835i	−0.383268	+	0.923637i	$0.625201\pi$
$884$	−15.8439	−	18.2849i	−0.532889	−	0.614987i
$885$	0.605988	−	0.389445i	0.0203701	−	0.0130910i
$886$	−30.6627	+	19.7057i	−1.03013	+	0.662027i
$887$	−15.5152	−	17.9055i	−0.520949	−	0.601207i	0.432919	−	0.901433i	$-0.357484\pi$
$887$	−15.5152	−	17.9055i	−0.520949	−	0.601207i	−0.953868	+	0.300225i	$0.902938\pi$
$888$	−0.193254	+	0.0567444i	−0.00648516	+	0.00190422i
$889$	1.18772	−	8.26078i	0.0398349	−	0.277058i
$890$	−0.828739	+	0.956416i	−0.0277794	+	0.0320591i
$891$	10.5760	−	23.1582i	0.354310	−	0.775830i
$892$	23.1254	+	6.79023i	0.774295	+	0.227354i
$893$	10.1931	+	22.3197i	0.341098	+	0.746900i
$894$	0.177192	+	1.23239i	0.00592617	+	0.0412175i
$895$	3.67292	+	2.36044i	0.122772	+	0.0789008i
$896$	−1.00000			−0.0334077
$897$	−3.09533	+	0.518847i	−0.103350	+	0.0173238i
$898$	19.1792			0.640018
$899$	−13.4367	−	8.63527i	−0.448140	−	0.288002i
$900$	−2.07930	−	14.4619i	−0.0693100	−	0.482062i
$901$	−34.3818	−	75.2856i	−1.14542	−	2.50813i
$902$	−31.6799	−	9.30207i	−1.05483	−	0.309725i
$903$	0.0341327	−	0.0747402i	0.00113587	−	0.00248720i
$904$	−12.9966	+	14.9989i	−0.432260	+	0.498855i
$905$	0.357421	−	2.48592i	0.0118811	−	0.0826347i
$906$	2.86882	−	0.842363i	0.0953103	−	0.0279856i
$907$	31.7311	+	36.6197i	1.05361	+	1.21594i	0.975731	+	0.218974i	$0.0702710\pi$
$907$	31.7311	+	36.6197i	1.05361	+	1.21594i	0.0778842	+	0.996962i	$0.475184\pi$
$908$	9.86040	−	6.33690i	0.327229	−	0.210297i
$909$	−46.3201	+	29.7681i	−1.53634	+	0.987346i
$910$	−0.597285	−	0.689304i	−0.0197998	−	0.0228502i
$911$	30.2374	−	8.87851i	1.00181	−	0.294158i	0.260612	−	0.965444i	$-0.416076\pi$
$911$	30.2374	−	8.87851i	1.00181	−	0.294158i	0.741199	+	0.671286i	$0.234258\pi$
$912$	−0.0684747	+	0.476252i	−0.00226742	+	0.0157703i
$913$	−19.5494	+	22.5612i	−0.646989	+	0.746666i
$914$	12.7181	−	27.8488i	0.420677	−	0.921155i
$915$	−0.0740915	−	0.0217552i	−0.00244939	−	0.000719206i
$916$	9.89019	+	21.6565i	0.326781	+	0.715551i
$917$	−1.35314	−	9.41128i	−0.0446845	−	0.310788i
$918$	6.71492	+	4.31541i	0.221625	+	0.142430i
$919$	18.0774			0.596318			0.298159	−	0.954516i	$-0.403627\pi$
$919$	18.0774			0.596318			0.298159	+	0.954516i	$0.403627\pi$
$920$	−1.14422	+	0.555091i	−0.0377239	+	0.0183008i
$921$	−1.80041			−0.0593256
$922$	35.3200	+	22.6988i	1.16320	+	0.747545i
$923$	2.06012	+	14.3285i	0.0678098	+	0.471628i
$924$	−0.231951	−	0.507902i	−0.00763063	−	0.0167088i
$925$	5.00700	+	1.47019i	0.164629	+	0.0483395i
$926$	−14.0000	+	30.6557i	−0.460069	+	1.00741i
$927$	15.6155	−	18.0213i	0.512882	−	0.591897i
$928$	−1.10752	+	7.70298i	−0.0363561	+	0.252863i
$929$	24.6876	−	7.24893i	0.809973	−	0.237830i	0.149580	−	0.988750i	$-0.452208\pi$
$929$	24.6876	−	7.24893i	0.809973	−	0.237830i	0.660393	+	0.750920i	$0.270390\pi$
$930$	0.0678147	+	0.0782623i	0.00222373	+	0.00256632i
$931$	2.12735	−	1.36716i	0.0697210	−	0.0448069i
$932$	−4.36275	+	2.80377i	−0.142907	+	0.0918405i
$933$	0.250318	+	0.288883i	0.00819505	+	0.00945759i
$934$	24.2041	−	7.10695i	0.791981	−	0.232547i
$935$	0.779039	−	5.41833i	0.0254773	−	0.177198i
$936$	−6.67559	+	7.70404i	−0.218198	+	0.251814i
$937$	4.22165	−	9.24412i	0.137915	−	0.301992i	−0.828054	−	0.560648i	$-0.810552\pi$
$937$	4.22165	−	9.24412i	0.137915	−	0.301992i	0.965970	+	0.258656i	$0.0832795\pi$
$938$	−10.6889	−	3.13856i	−0.349006	−	0.102478i
$939$	1.23152	+	2.69666i	0.0401893	+	0.0880023i
$940$	−0.366186	−	2.54688i	−0.0119437	−	0.0830701i
$941$	29.2592	+	18.8038i	0.953824	+	0.612985i	0.922282	−	0.386517i	$-0.126322\pi$
$941$	29.2592	+	18.8038i	0.953824	+	0.612985i	0.0315415	+	0.999502i	$0.489958\pi$
$942$	−0.936217			−0.0305036
$943$	30.2209	+	44.7015i	0.984128	+	1.45568i
$944$	14.2767			0.464667
$945$	0.253139	+	0.162683i	0.00823461	+	0.00529206i
$946$	0.180350	+	1.25436i	0.00586368	+	0.0407828i
$947$	6.74222	+	14.7634i	0.219093	+	0.479746i	0.986981	−	0.160838i	$-0.0514197\pi$
$947$	6.74222	+	14.7634i	0.219093	+	0.479746i	−0.767888	+	0.640584i	$0.778692\pi$
$948$	1.55433	+	0.456393i	0.0504823	+	0.0148230i
$949$	−16.3216	+	35.7394i	−0.529823	+	1.16015i
$950$	8.16355	−	9.42124i	0.264860	−	0.305665i
$951$	−0.266272	+	1.85196i	−0.00863447	+	0.0600541i
$952$	−6.74938	+	1.98180i	−0.218749	+	0.0642304i
$953$	−14.7405	−	17.0114i	−0.477491	−	0.551053i	0.464989	−	0.885316i	$-0.346058\pi$
$953$	−14.7405	−	17.0114i	−0.477491	−	0.551053i	−0.942480	+	0.334263i	$0.891513\pi$
$954$	−29.3359	+	18.8530i	−0.949784	+	0.610389i
$955$	−3.86867	+	2.48624i	−0.125187	+	0.0804529i
$956$	0.683592	+	0.788908i	0.0221090	+	0.0255151i
$957$	−4.16925	+	1.22420i	−0.134773	+	0.0395728i
$958$	−3.85886	+	26.8390i	−0.124674	+	0.867128i
$959$	−10.0566	+	11.6059i	−0.324743	+	0.374773i
$960$	0.0209600	−	0.0458960i	0.000676481	−	0.00148129i
$961$	25.7025	+	7.54694i	0.829113	+	0.243450i
$962$	−1.51249	−	3.31188i	−0.0487645	−	0.106779i
$963$	−4.57625	−	31.8285i	−0.147468	−	1.02566i
$964$	11.1171	+	7.14453i	0.358058	+	0.230110i
$965$	−5.64527			−0.181728
$966$	−0.236632	+	0.881283i	−0.00761350	+	0.0283548i
$967$	24.3005			0.781451			0.390726	−	0.920507i	$-0.372224\pi$
$967$	24.3005			0.781451			0.390726	+	0.920507i	$0.372224\pi$
$968$	−2.00912	−	1.29118i	−0.0645755	−	0.0415002i
$969$	0.481673	+	3.35011i	0.0154736	+	0.107621i
$970$	0.347549	+	0.761025i	0.0111591	+	0.0244350i
$971$	−45.3111	−	13.3045i	−1.45410	−	0.426963i	−0.543206	−	0.839600i	$-0.682790\pi$
$971$	−45.3111	−	13.3045i	−1.45410	−	0.426963i	−0.910896	+	0.412637i	$0.864608\pi$
$972$	2.09986	−	4.59806i	0.0673532	−	0.147483i
$973$	−4.00731	+	4.62468i	−0.128468	+	0.148260i
$974$	−3.47316	+	24.1564i	−0.111287	+	0.774020i
$975$	−3.09543	+	0.908900i	−0.0991331	+	0.0291081i
$976$	−1.00223	−	1.15663i	−0.0320805	−	0.0370229i
$977$	−10.3145	+	6.62873i	−0.329990	+	0.212072i	−0.695136	−	0.718879i	$-0.744656\pi$
$977$	−10.3145	+	6.62873i	−0.329990	+	0.212072i	0.365145	+	0.930951i	$0.381019\pi$
$978$	1.89520	−	1.21797i	0.0606017	−	0.0389463i
$979$	−9.17113	−	10.5841i	−0.293111	−	0.338268i
$980$	−0.254438	+	0.0747098i	−0.00812773	+	0.00238652i
$981$	−4.22125	+	29.3594i	−0.134774	+	0.937374i
$982$	6.12732	−	7.07131i	0.195531	−	0.225655i
$983$	22.7175	−	49.7445i	0.724577	−	1.58660i	−0.0827998	−	0.996566i	$-0.526386\pi$
$983$	22.7175	−	49.7445i	0.724577	−	1.58660i	0.807377	−	0.590036i	$-0.200887\pi$
$984$	−2.05403	−	0.603118i	−0.0654801	−	0.0192267i
$985$	0.206595	+	0.452380i	0.00658267	+	0.0144140i
$986$	7.79066	+	54.1852i	0.248105	+	1.72561i
$987$	−1.55312	−	0.998133i	−0.0494365	−	0.0317709i
$988$	−8.69768			−0.276710
$989$	1.07882	−	1.76784i	0.0343045	−	0.0562141i
$990$	−2.30640			−0.0733023
$991$	−14.5736	−	9.36586i	−0.462944	−	0.297516i	0.288300	−	0.957540i	$-0.406910\pi$
$991$	−14.5736	−	9.36586i	−0.462944	−	0.297516i	−0.751245	+	0.660024i	$0.770546\pi$
$992$	0.292089	+	2.03153i	0.00927384	+	0.0645010i
$993$	1.10440	+	2.41831i	0.0350472	+	0.0767426i
$994$	4.03825	+	1.18574i	0.128085	+	0.0376093i
$995$	−0.573175	+	1.25508i	−0.0181709	+	0.0397886i
$996$	−1.26752	+	1.46280i	−0.0401629	+	0.0463505i
$997$	6.78234	−	47.1722i	0.214799	−	1.49396i	−0.542037	−	0.840355i	$-0.682347\pi$
$997$	6.78234	−	47.1722i	0.214799	−	1.49396i	0.756836	−	0.653605i	$-0.226744\pi$
$998$	−5.84953	+	1.71758i	−0.185163	+	0.0543689i
$999$	0.786606	+	0.907792i	0.0248871	+	0.0287213i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.i.d.71.3	✓	40
23.9	even	11		7406.2.a.bu.1.9		20
23.12	even	11	inner	322.2.i.d.127.3	yes	40
23.14	odd	22		7406.2.a.bv.1.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.d.71.3	✓	40	1.1	even	1	trivial
322.2.i.d.127.3	yes	40	23.12	even	11	inner
7406.2.a.bu.1.9		20	23.9	even	11
7406.2.a.bv.1.9		20	23.14	odd	22

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.0270781 - 0.188333i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.254438 - 0.0747098i) q^{5} +(0.0790407 - 0.173075i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.84374 - 0.834998i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.0270781 - 0.188333i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.254438 - 0.0747098i) q^{5} +(0.0790407 - 0.173075i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(2.84374 - 0.834998i) q^{9} +(-0.173656 - 0.200410i) q^{10} +(2.46873 - 1.58655i) q^{11} +(0.160065 - 0.102867i) q^{12} +(2.25238 + 2.59938i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-0.00718058 + 0.0499420i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.92216 + 6.39865i) q^{17} +(2.84374 + 0.834998i) q^{18} +(1.05049 + 2.30026i) q^{19} +(-0.0377390 - 0.262481i) q^{20} +(-0.160065 - 0.102867i) q^{21} +2.93458 q^{22} +(-3.69657 - 3.05539i) q^{23} +0.190269 q^{24} +(-4.14711 - 2.66519i) q^{25} +(0.489488 + 3.40446i) q^{26} +(-0.471383 - 1.03218i) q^{27} +(0.959493 + 0.281733i) q^{28} +(3.23284 - 7.07893i) q^{29} +(-0.0330414 + 0.0381318i) q^{30} +(0.292089 - 2.03153i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-0.365648 - 0.421980i) q^{33} +(-5.91765 + 3.80304i) q^{34} +(-0.223084 + 0.143367i) q^{35} +(1.94087 + 2.23989i) q^{36} +(-1.01568 + 0.298232i) q^{37} +(-0.359883 + 2.50304i) q^{38} +(0.428558 - 0.494582i) q^{39} +(0.110160 - 0.241216i) q^{40} +(-10.7954 - 3.16981i) q^{41} +(-0.0790407 - 0.173075i) q^{42} +(0.0614568 + 0.427442i) q^{43} +(2.46873 + 1.58655i) q^{44} -0.785940 q^{45} +(-1.45788 - 4.56887i) q^{46} +9.70311 q^{47} +(0.160065 + 0.102867i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-2.04786 - 4.48419i) q^{50} +(1.28420 + 0.377075i) q^{51} +(-1.42881 + 3.12866i) q^{52} +(-7.70500 + 8.89205i) q^{53} +(0.161488 - 1.12318i) q^{54} +(-0.746669 + 0.219242i) q^{55} +(0.654861 + 0.755750i) q^{56} +(0.404769 - 0.260129i) q^{57} +(6.54679 - 4.20737i) q^{58} +(-9.34925 - 10.7896i) q^{59} +(-0.0484118 + 0.0142150i) q^{60} +(-0.217805 + 1.51487i) q^{61} +(1.34405 - 1.55111i) q^{62} +(1.23121 - 2.69597i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.378892 - 0.829657i) q^{65} +(-0.0794629 - 0.552677i) q^{66} +(-9.37174 - 6.02285i) q^{67} -7.03432 q^{68} +(-0.475332 + 0.778918i) q^{69} -0.265180 q^{70} +(3.54061 + 2.27541i) q^{71} +(0.421792 + 2.93363i) q^{72} +(4.74539 + 10.3909i) q^{73} +(-1.01568 - 0.298232i) q^{74} +(-0.389645 + 0.853204i) q^{75} +(-1.65600 + 1.91113i) q^{76} +(0.417634 - 2.90471i) q^{77} +(0.627917 - 0.184373i) q^{78} +(5.57548 + 6.43445i) q^{79} +(0.223084 - 0.143367i) q^{80} +(7.29829 - 4.69032i) q^{81} +(-7.36793 - 8.50305i) q^{82} +(-9.76067 + 2.86599i) q^{83} +(0.0270781 - 0.188333i) q^{84} +(1.22155 - 1.40975i) q^{85} +(-0.179392 + 0.392813i) q^{86} +(-1.42073 - 0.417164i) q^{87} +(1.21907 + 2.66939i) q^{88} +(-0.679170 - 4.72373i) q^{89} +(-0.661175 - 0.424911i) q^{90} +3.43947 q^{91} +(1.24367 - 4.63177i) q^{92} -0.390512 q^{93} +(8.16278 + 5.24590i) q^{94} +(-0.0954338 - 0.663757i) q^{95} +(0.0790407 + 0.173075i) q^{96} +(-3.02715 - 0.888852i) q^{97} +(0.415415 - 0.909632i) q^{98} +(5.69565 - 6.57313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9	\( 40 q - 4 q^{2} - 4 q^{4} + 9 q^{5} + 4 q^{7} - 4 q^{8} - 8 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 13 q^{17} - 8 q^{18} - 22 q^{19} - 2 q^{20} - 16 q^{22} - 9 q^{23} + 22 q^{24} - 15 q^{25} - 9 q^{26} + 21 q^{27} + 4 q^{28} - 10 q^{29} - 14 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 2 q^{34} + 13 q^{35} - 8 q^{36} - 45 q^{37} + 11 q^{38} - 22 q^{39} + 9 q^{40} + 21 q^{41} + 31 q^{43} + 6 q^{44} + 2 q^{45} - 9 q^{46} + 64 q^{47} - 4 q^{49} + 7 q^{50} + 65 q^{51} + 2 q^{52} + 69 q^{53} + 21 q^{54} - 74 q^{55} + 4 q^{56} - 68 q^{57} + 12 q^{58} + 48 q^{59} - 3 q^{60} + 6 q^{61} - 13 q^{62} + 8 q^{63} - 4 q^{64} - 64 q^{65} - 69 q^{66} + 31 q^{67} - 2 q^{68} - 62 q^{69} + 2 q^{70} - 57 q^{71} - 19 q^{72} + 70 q^{73} - 45 q^{74} - 11 q^{75} + 22 q^{76} - 6 q^{77} + 33 q^{78} + 34 q^{79} - 13 q^{80} + 30 q^{81} - 12 q^{82} - 56 q^{83} - 17 q^{85} + 42 q^{86} - 3 q^{87} + 6 q^{88} + 16 q^{89} + 46 q^{90} - 46 q^{91} + 24 q^{92} + 48 q^{93} + 9 q^{94} - 42 q^{95} - 36 q^{97} - 4 q^{98} + 112 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^4 + 9 * q^5 + 4 * q^7 - 4 * q^8 - 8 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 - 13 * q^17 - 8 * q^18 - 22 * q^19 - 2 * q^20 - 16 * q^22 - 9 * q^23 + 22 * q^24 - 15 * q^25 - 9 * q^26 + 21 * q^27 + 4 * q^28 - 10 * q^29 - 14 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 2 * q^34 + 13 * q^35 - 8 * q^36 - 45 * q^37 + 11 * q^38 - 22 * q^39 + 9 * q^40 + 21 * q^41 + 31 * q^43 + 6 * q^44 + 2 * q^45 - 9 * q^46 + 64 * q^47 - 4 * q^49 + 7 * q^50 + 65 * q^51 + 2 * q^52 + 69 * q^53 + 21 * q^54 - 74 * q^55 + 4 * q^56 - 68 * q^57 + 12 * q^58 + 48 * q^59 - 3 * q^60 + 6 * q^61 - 13 * q^62 + 8 * q^63 - 4 * q^64 - 64 * q^65 - 69 * q^66 + 31 * q^67 - 2 * q^68 - 62 * q^69 + 2 * q^70 - 57 * q^71 - 19 * q^72 + 70 * q^73 - 45 * q^74 - 11 * q^75 + 22 * q^76 - 6 * q^77 + 33 * q^78 + 34 * q^79 - 13 * q^80 + 30 * q^81 - 12 * q^82 - 56 * q^83 - 17 * q^85 + 42 * q^86 - 3 * q^87 + 6 * q^88 + 16 * q^89 + 46 * q^90 - 46 * q^91 + 24 * q^92 + 48 * q^93 + 9 * q^94 - 42 * q^95 - 36 * q^97 - 4 * q^98 + 112 * q^99

Introduction

L-functions

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