LMFDB - Embedded newform 804.2.e.b.535.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(535,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("804.535");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.e (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			535.15
Character	$\chi$	$=$	804.535
Dual form			804.2.e.b.535.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.338334 - 1.37315i) q^{2} +1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} +0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} -3.75704 q^{7} +(1.87509 + 2.11755i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.338334 - 1.37315i) q^{2} +1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} +0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} -3.75704 q^{7} +(1.87509 + 2.11755i) q^{8} +1.00000 q^{9} +(0.0837203 - 0.0206282i) q^{10} +1.10283 q^{11} +(-1.77106 + 0.929165i) q^{12} +4.93979i q^{13} +(1.27114 + 5.15897i) q^{14} +0.0609697i q^{15} +(2.27330 - 3.29121i) q^{16} +6.72065 q^{17} +(-0.338334 - 1.37315i) q^{18} +1.13293i q^{19} +(-0.0566509 - 0.107981i) q^{20} -3.75704 q^{21} +(-0.373126 - 1.51435i) q^{22} +2.63987i q^{23} +(1.87509 + 2.11755i) q^{24} +4.99628 q^{25} +(6.78305 - 1.67130i) q^{26} +1.00000 q^{27} +(6.65395 - 3.49091i) q^{28} -1.58868 q^{29} +(0.0837203 - 0.0206282i) q^{30} +0.470277 q^{31} +(-5.28845 - 2.00805i) q^{32} +1.10283 q^{33} +(-2.27383 - 9.22844i) q^{34} -0.229066i q^{35} +(-1.77106 + 0.929165i) q^{36} +4.49393 q^{37} +(1.55567 - 0.383308i) q^{38} +4.93979i q^{39} +(-0.129107 + 0.114324i) q^{40} +1.53098i q^{41} +(1.27114 + 5.15897i) q^{42} +3.78361 q^{43} +(-1.95318 + 1.02471i) q^{44} +0.0609697i q^{45} +(3.62493 - 0.893161i) q^{46} +8.21552i q^{47} +(2.27330 - 3.29121i) q^{48} +7.11537 q^{49} +(-1.69041 - 6.86063i) q^{50} +6.72065 q^{51} +(-4.58988 - 8.74866i) q^{52} +2.81313i q^{53} +(-0.338334 - 1.37315i) q^{54} +0.0672393i q^{55} +(-7.04479 - 7.95574i) q^{56} +1.13293i q^{57} +(0.537506 + 2.18149i) q^{58} +8.36670i q^{59} +(-0.0566509 - 0.107981i) q^{60} -4.04264i q^{61} +(-0.159111 - 0.645759i) q^{62} -3.75704 q^{63} +(-0.968076 + 7.94121i) q^{64} -0.301178 q^{65} +(-0.373126 - 1.51435i) q^{66} +(-6.62825 - 4.80274i) q^{67} +(-11.9027 + 6.24460i) q^{68} +2.63987i q^{69} +(-0.314541 + 0.0775009i) q^{70} +8.01796i q^{71} +(1.87509 + 2.11755i) q^{72} +11.0563 q^{73} +(-1.52045 - 6.17082i) q^{74} +4.99628 q^{75} +(-1.05268 - 2.00648i) q^{76} -4.14339 q^{77} +(6.78305 - 1.67130i) q^{78} -4.16494 q^{79} +(0.200664 + 0.138603i) q^{80} +1.00000 q^{81} +(2.10226 - 0.517983i) q^{82} -0.0220613i q^{83} +(6.65395 - 3.49091i) q^{84} +0.409756i q^{85} +(-1.28013 - 5.19545i) q^{86} -1.58868 q^{87} +(2.06791 + 2.33531i) q^{88} -10.1973 q^{89} +(0.0837203 - 0.0206282i) q^{90} -18.5590i q^{91} +(-2.45288 - 4.67537i) q^{92} +0.470277 q^{93} +(11.2811 - 2.77959i) q^{94} -0.0690742 q^{95} +(-5.28845 - 2.00805i) q^{96} -3.14310i q^{97} +(-2.40738 - 9.77045i) q^{98} +1.10283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	$ 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) $ 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.338334	−	1.37315i	−0.239239	−	0.970961i
$2$	−0.338334	−	1.37315i	−0.239239	−	0.970961i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.77106	+	0.929165i	−0.885530	+	0.464583i
$5$			0.0609697i			0.0272665i	0.999907	+	0.0136332i	$0.00433973\pi$
$5$			0.0609697i			0.0272665i	−0.999907	+	0.0136332i	$0.995660\pi$
$6$	−0.338334	−	1.37315i	−0.138124	−	0.560584i
$7$	−3.75704			−1.42003			−0.710014	−	0.704187i	$-0.751312\pi$
$7$	−3.75704			−1.42003			−0.710014	+	0.704187i	$0.751312\pi$
$8$	1.87509	+	2.11755i	0.662944	+	0.748669i
$9$	1.00000			0.333333
$10$	0.0837203	−	0.0206282i	0.0264747	−	0.00652319i
$11$	1.10283			0.332516			0.166258	−	0.986082i	$-0.446831\pi$
$11$	1.10283			0.332516			0.166258	+	0.986082i	$0.446831\pi$
$12$	−1.77106	+	0.929165i	−0.511261	+	0.268227i
$13$			4.93979i			1.37005i	0.728519	+	0.685026i	$0.240209\pi$
$13$			4.93979i			1.37005i	−0.728519	+	0.685026i	$0.759791\pi$
$14$	1.27114	+	5.15897i	0.339726	+	1.37879i
$15$			0.0609697i			0.0157423i
$16$	2.27330	−	3.29121i	0.568326	−	0.822803i
$17$	6.72065			1.63000			0.814999	−	0.579462i	$-0.196737\pi$
$17$	6.72065			1.63000			0.814999	+	0.579462i	$0.196737\pi$
$18$	−0.338334	−	1.37315i	−0.0797462	−	0.323654i
$19$			1.13293i			0.259911i	0.991520	+	0.129956i	$0.0414835\pi$
$19$			1.13293i			0.259911i	−0.991520	+	0.129956i	$0.958517\pi$
$20$	−0.0566509	−	0.107981i	−0.0126675	−	0.0241453i
$21$	−3.75704			−0.819854
$22$	−0.373126	−	1.51435i	−0.0795507	−	0.322860i
$23$			2.63987i			0.550452i	0.961380	+	0.275226i	$0.0887527\pi$
$23$			2.63987i			0.550452i	−0.961380	+	0.275226i	$0.911247\pi$
$24$	1.87509	+	2.11755i	0.382751	+	0.432244i
$25$	4.99628			0.999257
$26$	6.78305	−	1.67130i	1.33027	−	0.327769i
$27$	1.00000			0.192450
$28$	6.65395	−	3.49091i	1.25748	−	0.659721i
$29$	−1.58868			−0.295011			−0.147505	−	0.989061i	$-0.547124\pi$
$29$	−1.58868			−0.295011			−0.147505	+	0.989061i	$0.547124\pi$
$30$	0.0837203	−	0.0206282i	0.0152852	−	0.00376617i
$31$	0.470277			0.0844643			0.0422322	−	0.999108i	$-0.486553\pi$
$31$	0.470277			0.0844643			0.0422322	+	0.999108i	$0.486553\pi$
$32$	−5.28845	−	2.00805i	−0.934875	−	0.354976i
$33$	1.10283			0.191978
$34$	−2.27383	−	9.22844i	−0.389958	−	1.58266i
$35$		−	0.229066i		−	0.0387192i
$36$	−1.77106	+	0.929165i	−0.295177	+	0.154861i
$37$	4.49393			0.738797			0.369399	−	0.929271i	$-0.379564\pi$
$37$	4.49393			0.738797			0.369399	+	0.929271i	$0.379564\pi$
$38$	1.55567	−	0.383308i	0.252363	−	0.0621808i
$39$			4.93979i			0.791000i
$40$	−0.129107	+	0.114324i	−0.0204136	+	0.0180762i
$41$			1.53098i			0.239099i	0.992828	+	0.119549i	$0.0381450\pi$
$41$			1.53098i			0.239099i	−0.992828	+	0.119549i	$0.961855\pi$
$42$	1.27114	+	5.15897i	0.196141	+	0.796046i
$43$	3.78361			0.576995			0.288498	−	0.957481i	$-0.406844\pi$
$43$	3.78361			0.576995			0.288498	+	0.957481i	$0.406844\pi$
$44$	−1.95318	+	1.02471i	−0.294453	+	0.154481i
$45$			0.0609697i			0.00908883i
$46$	3.62493	−	0.893161i	0.534467	−	0.131689i
$47$			8.21552i			1.19836i	0.800616	+	0.599178i	$0.204506\pi$
$47$			8.21552i			1.19836i	−0.800616	+	0.599178i	$0.795494\pi$
$48$	2.27330	−	3.29121i	0.328123	−	0.475046i
$49$	7.11537			1.01648
$50$	−1.69041	−	6.86063i	−0.239061	−	0.970239i
$51$	6.72065			0.941080
$52$	−4.58988	−	8.74866i	−0.636502	−	1.21322i
$53$			2.81313i			0.386414i	0.981158	+	0.193207i	$0.0618888\pi$
$53$			2.81313i			0.386414i	−0.981158	+	0.193207i	$0.938111\pi$
$54$	−0.338334	−	1.37315i	−0.0460415	−	0.186861i
$55$			0.0672393i			0.00906655i
$56$	−7.04479	−	7.95574i	−0.941400	−	1.06313i
$57$			1.13293i			0.150060i
$58$	0.537506	+	2.18149i	0.0705779	+	0.286444i
$59$			8.36670i			1.08925i	0.838679	+	0.544626i	$0.183328\pi$
$59$			8.36670i			1.08925i	−0.838679	+	0.544626i	$0.816672\pi$
$60$	−0.0566509	−	0.107981i	−0.00731360	−	0.0139403i
$61$		−	4.04264i		−	0.517607i	−0.965930	−	0.258803i	$-0.916672\pi$
$61$		−	4.04264i		−	0.517607i	0.965930	−	0.258803i	$-0.0833281\pi$
$62$	−0.159111	−	0.645759i	−0.0202071	−	0.0820115i
$63$	−3.75704			−0.473343
$64$	−0.968076	+	7.94121i	−0.121009	+	0.992651i
$65$	−0.301178			−0.0373565
$66$	−0.373126	−	1.51435i	−0.0459286	−	0.186403i
$67$	−6.62825	−	4.80274i	−0.809770	−	0.586747i
$67$	−6.62825	−	4.80274i	−0.809770	−	0.586747i
$68$	−11.9027	+	6.24460i	−1.44341	+	0.757269i
$69$			2.63987i			0.317804i
$70$	−0.314541	+	0.0775009i	−0.0375948	+	0.00926312i
$71$			8.01796i			0.951556i	0.879565	+	0.475778i	$0.157833\pi$
$71$			8.01796i			0.951556i	−0.879565	+	0.475778i	$0.842167\pi$
$72$	1.87509	+	2.11755i	0.220981	+	0.249556i
$73$	11.0563			1.29405			0.647023	−	0.762471i	$-0.276014\pi$
$73$	11.0563			1.29405			0.647023	+	0.762471i	$0.276014\pi$
$74$	−1.52045	−	6.17082i	−0.176749	−	0.717343i
$75$	4.99628			0.576921
$76$	−1.05268	−	2.00648i	−0.120750	−	0.230159i
$77$	−4.14339			−0.472183
$78$	6.78305	−	1.67130i	0.768030	−	0.189238i
$79$	−4.16494			−0.468592			−0.234296	−	0.972165i	$-0.575278\pi$
$79$	−4.16494			−0.468592			−0.234296	+	0.972165i	$0.575278\pi$
$80$	0.200664	+	0.138603i	0.0224350	+	0.0154963i
$81$	1.00000			0.111111
$82$	2.10226	−	0.517983i	0.232156	−	0.0572017i
$83$		−	0.0220613i		−	0.00242154i	−0.999999	−	0.00121077i	$-0.999615\pi$
$83$		−	0.0220613i		−	0.00242154i	0.999999	−	0.00121077i	$-0.000385401\pi$
$84$	6.65395	−	3.49091i	0.726005	−	0.380890i
$85$			0.409756i			0.0444443i
$86$	−1.28013	−	5.19545i	−0.138040	−	0.560240i
$87$	−1.58868			−0.170324
$88$	2.06791	+	2.33531i	0.220440	+	0.248945i
$89$	−10.1973			−1.08091			−0.540455	−	0.841373i	$-0.681748\pi$
$89$	−10.1973			−1.08091			−0.540455	+	0.841373i	$0.681748\pi$
$90$	0.0837203	−	0.0206282i	0.00882489	−	0.00217440i
$91$		−	18.5590i		−	1.94551i
$92$	−2.45288	−	4.67537i	−0.255730	−	0.487442i
$93$	0.470277			0.0487655
$94$	11.2811	−	2.77959i	1.16356	−	0.286693i
$95$	−0.0690742			−0.00708686
$96$	−5.28845	−	2.00805i	−0.539751	−	0.204945i
$97$		−	3.14310i		−	0.319133i	−0.987187	−	0.159567i	$-0.948990\pi$
$97$		−	3.14310i		−	0.319133i	0.987187	−	0.159567i	$-0.0510096\pi$
$98$	−2.40738	−	9.77045i	−0.243182	−	0.986964i
$99$	1.10283			0.110839
$100$	−8.84871	+	4.64237i	−0.884871	+	0.464237i
$101$		−	7.96684i		−	0.792730i	−0.918093	−	0.396365i	$-0.870271\pi$
$101$		−	7.96684i		−	0.792730i	0.918093	−	0.396365i	$-0.129729\pi$
$102$	−2.27383	−	9.22844i	−0.225143	−	0.913752i
$103$		−	16.4526i		−	1.62112i	−0.585655	−	0.810561i	$-0.699163\pi$
$103$		−	16.4526i		−	1.62112i	0.585655	−	0.810561i	$-0.300837\pi$
$104$	−10.4603	+	9.26255i	−1.02571	+	0.908268i
$105$		−	0.229066i		−	0.0223545i
$106$	3.86284	−	0.951780i	0.375192	−	0.0924450i
$107$		−	7.61778i		−	0.736439i	−0.929739	−	0.368219i	$-0.879968\pi$
$107$		−	7.61778i		−	0.736439i	0.929739	−	0.368219i	$-0.120032\pi$
$108$	−1.77106	+	0.929165i	−0.170420	+	0.0894090i
$109$			15.1979i			1.45570i	0.685737	+	0.727849i	$0.259480\pi$
$109$			15.1979i			1.45570i	−0.685737	+	0.727849i	$0.740520\pi$
$110$	0.0923294	−	0.0227494i	0.00880326	−	0.00216907i
$111$	4.49393			0.426545
$112$	−8.54090	+	12.3652i	−0.807039	+	1.16840i
$113$			18.0077i			1.69402i	0.531574	+	0.847012i	$0.321601\pi$
$113$			18.0077i			1.69402i	−0.531574	+	0.847012i	$0.678399\pi$
$114$	1.55567	−	0.383308i	0.145702	−	0.0359001i
$115$	−0.160952			−0.0150089
$116$	2.81365	−	1.47615i	0.261241	−	0.137057i
$117$			4.93979i			0.456684i
$118$	11.4887	−	2.83074i	1.05762	−	0.260591i
$119$	−25.2498			−2.31464
$120$	−0.129107	+	0.114324i	−0.0117858	+	0.0104363i
$121$	−9.78376			−0.889433
$122$	−5.55113	+	1.36776i	−0.502576	+	0.123831i
$123$			1.53098i			0.138044i
$124$	−0.832889	+	0.436965i	−0.0747957	+	0.0392406i
$125$			0.609470i			0.0545127i
$126$	1.27114	+	5.15897i	0.113242	+	0.459597i
$127$		−	13.1675i		−	1.16843i	−0.811600	−	0.584213i	$-0.801403\pi$
$127$		−	13.1675i		−	1.16843i	0.811600	−	0.584213i	$-0.198597\pi$
$128$	11.2320	−	1.35748i	0.992776	−	0.119985i
$129$	3.78361			0.333128
$130$	0.101899	+	0.413561i	0.00893711	+	0.0362717i
$131$		−	13.2574i		−	1.15831i	−0.815219	−	0.579153i	$-0.803383\pi$
$131$		−	13.2574i		−	1.15831i	0.815219	−	0.579153i	$-0.196617\pi$
$132$	−1.95318	+	1.02471i	−0.170003	+	0.0891898i
$133$		−	4.25645i		−	0.369081i
$134$	−4.35229	+	10.7265i	−0.375981	+	0.926628i
$135$			0.0609697i			0.00524744i
$136$	12.6018	+	14.2314i	1.08060	+	1.22033i
$137$			0.299850i			0.0256179i	0.999918	+	0.0128090i	$0.00407733\pi$
$137$			0.299850i			0.0256179i	−0.999918	+	0.0128090i	$0.995923\pi$
$138$	3.62493	−	0.893161i	0.308575	−	0.0760309i
$139$	4.27209			0.362354			0.181177	−	0.983451i	$-0.442009\pi$
$139$	4.27209			0.362354			0.181177	+	0.983451i	$0.442009\pi$
$140$	0.212840	+	0.405689i	0.0179883	+	0.0342870i
$141$			8.21552i			0.691871i
$142$	11.0098	−	2.71275i	0.923924	−	0.227649i
$143$			5.44776i			0.455565i
$144$	2.27330	−	3.29121i	0.189442	−	0.274268i
$145$		−	0.0968614i		−	0.00804390i
$146$	−3.74074	−	15.1820i	−0.309586	−	1.25647i
$147$	7.11537			0.586866
$148$	−7.95901	+	4.17560i	−0.654227	+	0.343232i
$149$	11.3899			0.933096			0.466548	−	0.884496i	$-0.345497\pi$
$149$	11.3899			0.933096			0.466548	+	0.884496i	$0.345497\pi$
$150$	−1.69041	−	6.86063i	−0.138022	−	0.560168i
$151$			5.92062i			0.481814i	0.970548	+	0.240907i	$0.0774448\pi$
$151$			5.92062i			0.481814i	−0.970548	+	0.240907i	$0.922555\pi$
$152$	−2.39903	+	2.12434i	−0.194587	+	0.172307i
$153$	6.72065			0.543333
$154$	1.40185	+	5.68948i	0.112964	+	0.458471i
$155$			0.0286727i			0.00230304i
$156$	−4.58988	−	8.74866i	−0.367485	−	0.700454i
$157$	5.21451			0.416163			0.208082	−	0.978111i	$-0.433278\pi$
$157$	5.21451			0.416163			0.208082	+	0.978111i	$0.433278\pi$
$158$	1.40914	+	5.71907i	0.112105	+	0.454984i
$159$			2.81313i			0.223096i
$160$	0.122430	−	0.322435i	0.00967894	−	0.0254908i
$161$		−	9.91812i		−	0.781658i
$162$	−0.338334	−	1.37315i	−0.0265821	−	0.107885i
$163$		−	0.859050i		−	0.0672860i	−0.999434	−	0.0336430i	$-0.989289\pi$
$163$		−	0.859050i		−	0.0672860i	0.999434	−	0.0336430i	$-0.0107109\pi$
$164$	−1.42253	−	2.71146i	−0.111081	−	0.211729i
$165$			0.0672393i			0.00523458i
$166$	−0.0302934	+	0.00746411i	−0.00235122	+	0.000579327i
$167$			13.4828i			1.04333i	0.853149	+	0.521667i	$0.174690\pi$
$167$			13.4828i			1.04333i	−0.853149	+	0.521667i	$0.825310\pi$
$168$	−7.04479	−	7.95574i	−0.543518	−	0.613799i
$169$	−11.4015			−0.877041
$170$	0.562655	−	0.138635i	0.0431537	−	0.0106328i
$171$			1.13293i			0.0866370i
$172$	−6.70100	+	3.51560i	−0.510947	+	0.268062i
$173$	3.37315			0.256456			0.128228	−	0.991745i	$-0.459071\pi$
$173$	3.37315			0.256456			0.128228	+	0.991745i	$0.459071\pi$
$174$	0.537506	+	2.18149i	0.0407482	+	0.165378i
$175$	−18.7713			−1.41897
$176$	2.50707	−	3.62966i	0.188978	−	0.273596i
$177$			8.36670i			0.628880i
$178$	3.45010	+	14.0024i	0.258596	+	1.04952i
$179$	−19.8446			−1.48326			−0.741629	−	0.670810i	$-0.765947\pi$
$179$	−19.8446			−1.48326			−0.741629	+	0.670810i	$0.765947\pi$
$180$	−0.0566509	−	0.107981i	−0.00422251	−	0.00804843i
$181$	−12.1020			−0.899535			−0.449767	−	0.893146i	$-0.648493\pi$
$181$	−12.1020			−0.899535			−0.449767	+	0.893146i	$0.648493\pi$
$182$	−25.4842	+	6.27915i	−1.88902	+	0.465442i
$183$		−	4.04264i		−	0.298840i
$184$	−5.59008	+	4.95000i	−0.412106	+	0.364919i
$185$			0.273993i			0.0201444i
$186$	−0.159111	−	0.645759i	−0.0116666	−	0.0473494i
$187$	7.41175			0.542001
$188$	−7.63357	−	14.5502i	−0.556736	−	1.06118i
$189$	−3.75704			−0.273285
$190$	0.0233702	+	0.0948489i	0.00169545	+	0.00688106i
$191$	19.4833			1.40976			0.704882	−	0.709325i	$-0.251000\pi$
$191$	19.4833			1.40976			0.704882	+	0.709325i	$0.251000\pi$
$192$	−0.968076	+	7.94121i	−0.0698648	+	0.573108i
$193$	−16.3459			−1.17661			−0.588303	−	0.808641i	$-0.700204\pi$
$193$	−16.3459			−1.17661			−0.588303	+	0.808641i	$0.700204\pi$
$194$	−4.31593	+	1.06342i	−0.309866	+	0.0763489i
$195$	−0.301178			−0.0215678
$196$	−12.6018	+	6.61136i	−0.900125	+	0.472240i
$197$		−	17.6850i		−	1.26000i	−0.776594	−	0.630001i	$-0.783054\pi$
$197$		−	17.6850i		−	1.26000i	0.776594	−	0.630001i	$-0.216946\pi$
$198$	−0.373126	−	1.51435i	−0.0265169	−	0.107620i
$199$			0.273537i			0.0193905i	0.999953	+	0.00969525i	$0.00308614\pi$
$199$			0.273537i			0.0193905i	−0.999953	+	0.00969525i	$0.996914\pi$
$200$	9.36848	+	10.5799i	0.662452	+	0.748112i
$201$	−6.62825	−	4.80274i	−0.467521	−	0.338759i
$202$	−10.9396	+	2.69546i	−0.769710	+	0.189652i
$203$	5.96874			0.418924
$204$	−11.9027	+	6.24460i	−0.833354	+	0.437209i
$205$	−0.0933434			−0.00651939
$206$	−22.5918	+	5.56648i	−1.57405	+	0.387835i
$207$			2.63987i			0.183484i
$208$	16.2579	+	11.2296i	1.12728	+	0.778636i
$209$			1.24943i			0.0864247i
$210$	−0.314541	+	0.0775009i	−0.0217054	+	0.00534807i
$211$			23.0337i			1.58570i	0.609415	+	0.792852i	$0.291405\pi$
$211$			23.0337i			1.58570i	−0.609415	+	0.792852i	$0.708595\pi$
$212$	−2.61387	−	4.98223i	−0.179521	−	0.342181i
$213$			8.01796i			0.549381i
$214$	−10.4603	+	2.57736i	−0.715053	+	0.176185i
$215$			0.230686i			0.0157326i
$216$	1.87509	+	2.11755i	0.127584	+	0.144081i
$217$	−1.76685			−0.119942
$218$	20.8690	−	5.14199i	1.41343	−	0.348259i
$219$	11.0563			0.747117
$220$	−0.0624764	−	0.119085i	−0.00421216	−	0.00802870i
$221$			33.1986i			2.23318i
$222$	−1.52045	−	6.17082i	−0.102046	−	0.414158i
$223$			0.306864i			0.0205491i	0.999947	+	0.0102746i	$0.00327055\pi$
$223$			0.306864i			0.0205491i	−0.999947	+	0.0102746i	$0.996729\pi$
$224$	19.8690	+	7.54432i	1.32755	+	0.504076i
$225$	4.99628			0.333086
$226$	24.7272	−	6.09263i	1.64483	−	0.405276i
$227$			25.5455i			1.69552i	0.530383	+	0.847758i	$0.322048\pi$
$227$			25.5455i			1.69552i	−0.530383	+	0.847758i	$0.677952\pi$
$228$	−1.05268	−	2.00648i	−0.0697151	−	0.132882i
$229$			0.674492i			0.0445717i	0.999752	+	0.0222858i	$0.00709439\pi$
$229$			0.674492i			0.0445717i	−0.999752	+	0.0222858i	$0.992906\pi$
$230$	0.0544557	+	0.221011i	0.00359070	+	0.0145730i
$231$	−4.14339			−0.272615
$232$	−2.97892	−	3.36412i	−0.195576	−	0.220865i
$233$		−	26.4164i		−	1.73059i	−0.501259	−	0.865297i	$-0.667130\pi$
$233$		−	26.4164i		−	1.73059i	0.501259	−	0.865297i	$-0.332870\pi$
$234$	6.78305	−	1.67130i	0.443422	−	0.109256i
$235$	−0.500898			−0.0326750
$236$	−7.77405	−	14.8179i	−0.506047	−	0.964565i
$237$	−4.16494			−0.270542
$238$	8.54287	+	34.6716i	0.553752	+	2.24743i
$239$	14.5374			0.940348			0.470174	−	0.882574i	$-0.344191\pi$
$239$	14.5374			0.940348			0.470174	+	0.882574i	$0.344191\pi$
$240$	0.200664	+	0.138603i	0.0129528	+	0.00894676i
$241$	25.6937			1.65507			0.827537	−	0.561411i	$-0.189741\pi$
$241$	25.6937			1.65507			0.827537	+	0.561411i	$0.189741\pi$
$242$	3.31018	+	13.4345i	0.212787	+	0.863604i
$243$	1.00000			0.0641500
$244$	3.75628	+	7.15975i	0.240471	+	0.458356i
$245$			0.433822i			0.0277159i
$246$	2.10226	−	0.517983i	0.134035	−	0.0330254i
$247$	−5.59642			−0.356092
$248$	0.881812	+	0.995838i	0.0559951	+	0.0632358i
$249$		−	0.0220613i		−	0.00139808i
$250$	0.836892	−	0.206205i	0.0529297	−	0.0130415i
$251$	10.6671			0.673298			0.336649	−	0.941630i	$-0.390706\pi$
$251$	10.6671			0.673298			0.336649	+	0.941630i	$0.390706\pi$
$252$	6.65395	−	3.49091i	0.419159	−	0.219907i
$253$			2.91134i			0.183034i
$254$	−18.0809	+	4.45502i	−1.13450	+	0.279533i
$255$			0.409756i			0.0256599i
$256$	−5.66418	−	14.9639i	−0.354011	−	0.935241i
$257$	−19.2696			−1.20200			−0.601002	−	0.799248i	$-0.705232\pi$
$257$	−19.2696			−1.20200			−0.601002	+	0.799248i	$0.705232\pi$
$258$	−1.28013	−	5.19545i	−0.0796972	−	0.323455i
$259$	−16.8839			−1.04911
$260$	0.533404	−	0.279844i	0.0330803	−	0.0173552i
$261$	−1.58868			−0.0983369
$262$	−18.2044	+	4.48544i	−1.12467	+	0.277112i
$263$		−	5.69061i		−	0.350898i	−0.984489	−	0.175449i	$-0.943862\pi$
$263$		−	5.69061i		−	0.350898i	0.984489	−	0.175449i	$-0.0561377\pi$
$264$	2.06791	+	2.33531i	0.127271	+	0.143728i
$265$	−0.171516			−0.0105361
$266$	−5.84473	+	1.44010i	−0.358363	+	0.0882985i
$267$	−10.1973			−0.624064
$268$	16.2016	+	2.34719i	0.989668	+	0.143377i
$269$	−28.6783			−1.74854			−0.874272	−	0.485436i	$-0.838661\pi$
$269$	−28.6783			−1.74854			−0.874272	+	0.485436i	$0.838661\pi$
$270$	0.0837203	−	0.0206282i	0.00509506	−	0.00125539i
$271$	3.65752			0.222179			0.111089	−	0.993810i	$-0.464566\pi$
$271$	3.65752			0.222179			0.111089	+	0.993810i	$0.464566\pi$
$272$	15.2781	−	22.1191i	0.926370	−	1.34117i
$273$		−	18.5590i		−	1.12324i
$274$	0.411738	−	0.101450i	0.0248740	−	0.00612880i
$275$	5.51006			0.332269
$276$	−2.45288	−	4.67537i	−0.147646	−	0.281424i
$277$	−24.8319			−1.49200			−0.746002	−	0.665943i	$-0.768029\pi$
$277$	−24.8319			−1.49200			−0.746002	+	0.665943i	$0.768029\pi$
$278$	−1.44540	−	5.86620i	−0.0866891	−	0.351831i
$279$	0.470277			0.0281548
$280$	0.485059	−	0.429519i	0.0289878	−	0.0256687i
$281$			27.2668i			1.62660i	0.581845	+	0.813300i	$0.302331\pi$
$281$			27.2668i			1.62660i	−0.581845	+	0.813300i	$0.697669\pi$
$282$	11.2811	−	2.77959i	0.671780	−	0.165522i
$283$		−	29.4074i		−	1.74809i	−0.485845	−	0.874045i	$-0.661488\pi$
$283$		−	29.4074i		−	1.74809i	0.485845	−	0.874045i	$-0.338512\pi$
$284$	−7.45001	−	14.2003i	−0.442077	−	0.842632i
$285$	−0.0690742			−0.00409160
$286$	7.48057	−	1.84316i	0.442335	−	0.108989i
$287$		−	5.75196i		−	0.339527i
$288$	−5.28845	−	2.00805i	−0.311625	−	0.118325i
$289$	28.1672			1.65689
$290$	−0.133005	+	0.0327716i	−0.00781031	+	0.00192441i
$291$		−	3.14310i		−	0.184252i
$292$	−19.5814	+	10.2732i	−1.14592	+	0.601191i
$293$	3.91718			0.228844			0.114422	−	0.993432i	$-0.463498\pi$
$293$	3.91718			0.228844			0.114422	+	0.993432i	$0.463498\pi$
$294$	−2.40738	−	9.77045i	−0.140401	−	0.569824i
$295$	−0.510115			−0.0297001
$296$	8.42652	+	9.51614i	0.489781	+	0.553114i
$297$	1.10283			0.0639928
$298$	−3.85359	−	15.6400i	−0.223233	−	0.906000i
$299$	−13.0404			−0.754147
$300$	−8.84871	+	4.64237i	−0.510881	+	0.268027i
$301$	−14.2152			−0.819350
$302$	8.12988	−	2.00315i	0.467822	−	0.115268i
$303$		−	7.96684i		−	0.457683i
$304$	3.72870	+	2.57549i	0.213856	+	0.147714i
$305$	0.246478			0.0141133
$306$	−2.27383	−	9.22844i	−0.129986	−	0.527555i
$307$		−	19.0966i		−	1.08990i	−0.838468	−	0.544951i	$-0.816548\pi$
$307$		−	19.0966i		−	1.08990i	0.838468	−	0.544951i	$-0.183452\pi$
$308$	7.33819	−	3.84989i	0.418132	−	0.219368i
$309$		−	16.4526i		−	0.935955i
$310$	0.0393718	−	0.00970095i	0.00223617	−	0.000550977i
$311$	16.1088			0.913448			0.456724	−	0.889609i	$-0.349023\pi$
$311$	16.1088			0.913448			0.456724	+	0.889609i	$0.349023\pi$
$312$	−10.4603	+	9.26255i	−0.592197	+	0.524389i
$313$		−	25.0638i		−	1.41669i	−0.705868	−	0.708344i	$-0.749443\pi$
$313$		−	25.0638i		−	1.41669i	0.705868	−	0.708344i	$-0.250557\pi$
$314$	−1.76425	−	7.16028i	−0.0995623	−	0.404078i
$315$		−	0.229066i		−	0.0129064i
$316$	7.37635	−	3.86991i	0.414952	−	0.217700i
$317$	5.89851			0.331293			0.165647	−	0.986185i	$-0.447029\pi$
$317$	5.89851			0.331293			0.165647	+	0.986185i	$0.447029\pi$
$318$	3.86284	−	0.951780i	0.216617	−	0.0533732i
$319$	−1.75205			−0.0980959
$320$	−0.484173	−	0.0590233i	−0.0270661	−	0.00329950i
$321$		−	7.61778i		−	0.425183i
$322$	−13.6190	+	3.35564i	−0.758959	+	0.187003i
$323$			7.61400i			0.423654i
$324$	−1.77106	+	0.929165i	−0.0983922	+	0.0516203i
$325$			24.6806i			1.36903i
$326$	−1.17960	+	0.290646i	−0.0653321	+	0.0160974i
$327$			15.1979i			0.840448i
$328$	−3.24193	+	2.87073i	−0.179006	+	0.158509i
$329$		−	30.8661i		−	1.70170i
$330$	0.0923294	−	0.0227494i	0.00508257	−	0.00125231i
$331$	−9.35027			−0.513937			−0.256969	−	0.966420i	$-0.582724\pi$
$331$	−9.35027			−0.513937			−0.256969	+	0.966420i	$0.582724\pi$
$332$	0.0204986	+	0.0390719i	0.00112501	+	0.00214435i
$333$	4.49393			0.246266
$334$	18.5139	−	4.56171i	1.01304	−	0.249606i
$335$	0.292821	−	0.404123i	0.0159985	−	0.0220796i
$336$	−8.54090	+	12.3652i	−0.465944	+	0.674579i
$337$		−	26.5945i		−	1.44869i	−0.689436	−	0.724346i	$-0.742142\pi$
$337$		−	26.5945i		−	1.44869i	0.689436	−	0.724346i	$-0.257858\pi$
$338$	3.85753	+	15.6560i	0.209822	+	0.851573i
$339$			18.0077i			0.978045i
$340$	−0.380731	−	0.725703i	−0.0206481	−	0.0393568i
$341$	0.518637			0.0280858
$342$	1.55567	−	0.383308i	0.0841211	−	0.0207269i
$343$	−0.433469			−0.0234051
$344$	7.09461	+	8.01200i	0.382516	+	0.431978i
$345$	−0.160952			−0.00866538
$346$	−1.14125	−	4.63183i	−0.0613542	−	0.249009i
$347$	−3.83875			−0.206075			−0.103038	−	0.994677i	$-0.532856\pi$
$347$	−3.83875			−0.206075			−0.103038	+	0.994677i	$0.532856\pi$
$348$	2.81365	−	1.47615i	0.150827	−	0.0791298i
$349$	−1.32332			−0.0708355			−0.0354178	−	0.999373i	$-0.511276\pi$
$349$	−1.32332			−0.0708355			−0.0354178	+	0.999373i	$0.511276\pi$
$350$	6.35096	+	25.7757i	0.339473	+	1.37777i
$351$			4.93979i			0.263667i
$352$	−5.83228	−	2.21454i	−0.310861	−	0.118035i
$353$		−	21.3119i		−	1.13432i	−0.823608	−	0.567160i	$-0.808042\pi$
$353$		−	21.3119i		−	1.13432i	0.823608	−	0.567160i	$-0.191958\pi$
$354$	11.4887	−	2.83074i	0.610618	−	0.150452i
$355$	−0.488852			−0.0259456
$356$	18.0600	−	9.47497i	0.957179	−	0.502172i
$357$	−25.2498			−1.33636
$358$	6.71413	+	27.2496i	0.354853	+	1.44019i
$359$		−	33.0334i		−	1.74344i	−0.490005	−	0.871719i	$-0.663005\pi$
$359$		−	33.0334i		−	1.74344i	0.490005	−	0.871719i	$-0.336995\pi$
$360$	−0.129107	+	0.114324i	−0.00680452	+	0.00602539i
$361$	17.7165			0.932446
$362$	4.09452	+	16.6178i	0.215203	+	0.873413i
$363$	−9.78376			−0.513514
$364$	17.2444	+	32.8691i	0.903851	+	1.72281i
$365$			0.674101i			0.0352841i
$366$	−5.55113	+	1.36776i	−0.290162	+	0.0714941i
$367$	21.1961			1.10643			0.553215	−	0.833039i	$-0.313401\pi$
$367$	21.1961			1.10643			0.553215	+	0.833039i	$0.313401\pi$
$368$	8.68839	+	6.00124i	0.452914	+	0.312836i
$369$			1.53098i			0.0796996i
$370$	0.376233	−	0.0927014i	0.0195594	−	0.00481932i
$371$		−	10.5691i		−	0.548718i
$372$	−0.832889	+	0.436965i	−0.0431833	+	0.0226556i
$373$		−	35.8774i		−	1.85766i	−0.370507	−	0.928830i	$-0.620816\pi$
$373$		−	35.8774i		−	1.85766i	0.370507	−	0.928830i	$-0.379184\pi$
$374$	−2.50765	−	10.1774i	−0.129668	−	0.526262i
$375$			0.609470i			0.0314729i
$376$	−17.3968	+	15.4048i	−0.897172	+	0.794444i
$377$		−	7.84775i		−	0.404180i
$378$	1.27114	+	5.15897i	0.0653802	+	0.265349i
$379$	30.5273			1.56808			0.784041	−	0.620710i	$-0.213155\pi$
$379$	30.5273			1.56808			0.784041	+	0.620710i	$0.213155\pi$
$380$	0.122334	−	0.0641813i	0.00627563	−	0.00329243i
$381$		−	13.1675i		−	0.674591i
$382$	−6.59188	−	26.7534i	−0.337270	−	1.36882i
$383$	15.2134			0.777368			0.388684	−	0.921371i	$-0.372930\pi$
$383$	15.2134			0.777368			0.388684	+	0.921371i	$0.372930\pi$
$384$	11.2320	−	1.35748i	0.573179	−	0.0692734i
$385$		−	0.252621i		−	0.0128748i
$386$	5.53039	+	22.4453i	0.281489	+	1.14244i
$387$	3.78361			0.192332
$388$	2.92046	+	5.56661i	0.148264	+	0.282602i
$389$	−1.67565			−0.0849590			−0.0424795	−	0.999097i	$-0.513526\pi$
$389$	−1.67565			−0.0849590			−0.0424795	+	0.999097i	$0.513526\pi$
$390$	0.101899	+	0.413561i	0.00515984	+	0.0209415i
$391$			17.7417i			0.897235i
$392$	13.3420	+	15.0672i	0.673871	+	0.761008i
$393$		−	13.2574i		−	0.668748i
$394$	−24.2841	+	5.98344i	−1.22341	+	0.301441i
$395$		−	0.253935i		−	0.0127769i
$396$	−1.95318	+	1.02471i	−0.0981510	+	0.0514938i
$397$	−25.6396			−1.28681			−0.643407	−	0.765524i	$-0.722480\pi$
$397$	−25.6396			−1.28681			−0.643407	+	0.765524i	$0.722480\pi$
$398$	0.375606	−	0.0925469i	0.0188274	−	0.00463896i
$399$		−	4.25645i		−	0.213089i
$400$	11.3581	−	16.4438i	0.567903	−	0.822192i
$401$			19.3773i			0.967657i	0.875163	+	0.483829i	$0.160754\pi$
$401$			19.3773i			0.967657i	−0.875163	+	0.483829i	$0.839246\pi$
$402$	−4.35229	+	10.7265i	−0.217072	+	0.534989i
$403$			2.32307i			0.115720i
$404$	7.40251	+	14.1097i	0.368289	+	0.701986i
$405$			0.0609697i			0.00302961i
$406$	−2.01943	−	8.19596i	−0.100223	−	0.406758i
$407$	4.95605			0.245662
$408$	12.6018	+	14.2314i	0.623884	+	0.704557i
$409$			15.0648i			0.744904i	0.928051	+	0.372452i	$0.121483\pi$
$409$			15.0648i			0.744904i	−0.928051	+	0.372452i	$0.878517\pi$
$410$	0.0315813	+	0.128174i	0.00155969	+	0.00633007i
$411$			0.299850i			0.0147905i
$412$	15.2872	+	29.1385i	0.753145	+	1.43555i
$413$		−	31.4341i		−	1.54677i
$414$	3.62493	−	0.893161i	0.178156	−	0.0438964i
$415$	0.00134507			6.60270e−5
$416$	9.91933	−	26.1239i	0.486335	−	1.28083i
$417$	4.27209			0.209205
$418$	1.71565	−	0.422724i	0.0839150	−	0.0206761i
$419$			9.77867i			0.477720i	0.971054	+	0.238860i	$0.0767736\pi$
$419$			9.77867i			0.477720i	−0.971054	+	0.238860i	$0.923226\pi$
$420$	0.212840	+	0.405689i	0.0103855	+	0.0197956i
$421$	4.19368			0.204388			0.102194	−	0.994765i	$-0.467414\pi$
$421$	4.19368			0.204388			0.102194	+	0.994765i	$0.467414\pi$
$422$	31.6286	−	7.79309i	1.53966	−	0.379361i
$423$			8.21552i			0.399452i
$424$	−5.95696	+	5.27488i	−0.289296	+	0.256171i
$425$	33.5783			1.62879
$426$	11.0098	−	2.71275i	0.533428	−	0.131433i
$427$			15.1884i			0.735016i
$428$	7.07818	+	13.4915i	0.342137	+	0.652138i
$429$			5.44776i			0.263020i
$430$	0.316765	−	0.0780489i	0.0152758	−	0.00376385i
$431$		−	29.5680i		−	1.42424i	−0.702057	−	0.712121i	$-0.747735\pi$
$431$		−	29.5680i		−	1.42424i	0.702057	−	0.712121i	$-0.252265\pi$
$432$	2.27330	−	3.29121i	0.109374	−	0.158349i
$433$		−	24.4560i		−	1.17528i	−0.809122	−	0.587641i	$-0.800057\pi$
$433$		−	24.4560i		−	1.17528i	0.809122	−	0.587641i	$-0.199943\pi$
$434$	0.597787	+	2.42615i	0.0286947	+	0.116459i
$435$		−	0.0968614i		−	0.00464415i
$436$	−14.1214	−	26.9165i	−0.676292	−	1.28906i
$437$	−2.99078			−0.143069
$438$	−3.74074	−	15.1820i	−0.178739	−	0.725422i
$439$		−	2.81752i		−	0.134473i	−0.997737	−	0.0672364i	$-0.978582\pi$
$439$		−	2.81752i		−	0.134473i	0.997737	−	0.0672364i	$-0.0214182\pi$
$440$	−0.142383	+	0.126080i	−0.00678784	+	0.00601062i
$441$	7.11537			0.338827
$442$	45.5866	−	11.2322i	2.16833	−	0.534263i
$443$	20.3857			0.968555			0.484278	−	0.874914i	$-0.339082\pi$
$443$	20.3857			0.968555			0.484278	+	0.874914i	$0.339082\pi$
$444$	−7.95901	+	4.17560i	−0.377718	+	0.198165i
$445$		−	0.621726i		−	0.0294726i
$446$	0.421369	−	0.103823i	0.0199524	−	0.00491614i
$447$	11.3899			0.538723
$448$	3.63710	−	29.8355i	0.171837	−	1.40959i
$449$	15.7872			0.745046			0.372523	−	0.928023i	$-0.378493\pi$
$449$	15.7872			0.745046			0.372523	+	0.928023i	$0.378493\pi$
$450$	−1.69041	−	6.86063i	−0.0796869	−	0.323413i
$451$			1.68841i			0.0795043i
$452$	−16.7321	−	31.8927i	−0.787014	−	1.50011i
$453$			5.92062i			0.278175i
$454$	35.0777	−	8.64293i	1.64628	−	0.405633i
$455$	1.13154			0.0530473
$456$	−2.39903	+	2.12434i	−0.112345	+	0.0994812i
$457$	−15.0733			−0.705098			−0.352549	−	0.935793i	$-0.614685\pi$
$457$	−15.0733			−0.705098			−0.352549	+	0.935793i	$0.614685\pi$
$458$	0.926175	−	0.228204i	0.0432773	−	0.0106633i
$459$	6.72065			0.313693
$460$	0.285056	−	0.149551i	0.0132908	−	0.00697287i
$461$	−6.00665			−0.279758			−0.139879	−	0.990169i	$-0.544671\pi$
$461$	−6.00665			−0.279758			−0.139879	+	0.990169i	$0.544671\pi$
$462$	1.40185	+	5.68948i	0.0652200	+	0.264698i
$463$	−27.9282			−1.29793			−0.648966	−	0.760817i	$-0.724798\pi$
$463$	−27.9282			−1.29793			−0.648966	+	0.760817i	$0.724798\pi$
$464$	−3.61155	+	5.22869i	−0.167662	+	0.242736i
$465$			0.0286727i			0.00132966i
$466$	−36.2735	+	8.93757i	−1.68034	+	0.414025i
$467$		−	8.56204i		−	0.396204i	−0.980181	−	0.198102i	$-0.936522\pi$
$467$		−	8.56204i		−	0.396204i	0.980181	−	0.198102i	$-0.0634778\pi$
$468$	−4.58988	−	8.74866i	−0.212167	−	0.404407i
$469$	24.9026	+	18.0441i	1.14990	+	0.833198i
$470$	0.169471	+	0.687806i	0.00781711	+	0.0317261i
$471$	5.21451			0.240272
$472$	−17.7170	+	15.6883i	−0.815489	+	0.722113i
$473$	4.17269			0.191860
$474$	1.40914	+	5.71907i	0.0647240	+	0.262685i
$475$			5.66042i			0.259718i
$476$	44.7189	−	23.4612i	2.04969	−	1.07534i
$477$			2.81313i			0.128805i
$478$	−4.91851	−	19.9620i	−0.224968	−	0.913041i
$479$			4.26200i			0.194736i	0.995248	+	0.0973679i	$0.0310424\pi$
$479$			4.26200i			0.194736i	−0.995248	+	0.0973679i	$0.968958\pi$
$480$	0.122430	−	0.322435i	0.00558814	−	0.0147171i
$481$			22.1991i			1.01219i
$482$	−8.69305	−	35.2811i	−0.395957	−	1.60701i
$483$		−	9.91812i		−	0.451290i
$484$	17.3276	−	9.09073i	0.787619	−	0.413215i
$485$	0.191634			0.00870164
$486$	−0.338334	−	1.37315i	−0.0153472	−	0.0622872i
$487$	27.6700			1.25385			0.626924	−	0.779080i	$-0.284314\pi$
$487$	27.6700			1.25385			0.626924	+	0.779080i	$0.284314\pi$
$488$	8.56050	−	7.58031i	0.387516	−	0.343144i
$489$		−	0.859050i		−	0.0388476i
$490$	0.595701	−	0.146777i	0.0269110	−	0.00663071i
$491$			37.3820i			1.68702i	0.537110	+	0.843512i	$0.319516\pi$
$491$			37.3820i			1.68702i	−0.537110	+	0.843512i	$0.680484\pi$
$492$	−1.42253	−	2.71146i	−0.0641328	−	0.122242i
$493$	−10.6770			−0.480867
$494$	1.89346	+	7.68470i	0.0851908	+	0.345751i
$495$			0.0672393i			0.00302218i
$496$	1.06908	−	1.54778i	0.0480033	−	0.0694975i
$497$		−	30.1238i		−	1.35124i
$498$	−0.0302934	+	0.00746411i	−0.00135748	+	0.000334475i
$499$	5.40037			0.241754			0.120877	−	0.992668i	$-0.461429\pi$
$499$	5.40037			0.241754			0.120877	+	0.992668i	$0.461429\pi$
$500$	−0.566299	−	1.07941i	−0.0253256	−	0.0482726i
$501$			13.4828i			0.602369i
$502$	−3.60903	−	14.6474i	−0.161079	−	0.653746i
$503$	32.7304			1.45938			0.729689	−	0.683779i	$-0.239665\pi$
$503$	32.7304			1.45938			0.729689	+	0.683779i	$0.239665\pi$
$504$	−7.04479	−	7.95574i	−0.313800	−	0.354377i
$505$	0.485736			0.0216150
$506$	3.99769	−	0.985006i	0.177719	−	0.0437889i
$507$	−11.4015			−0.506360
$508$	12.2348	+	23.3204i	0.542830	+	1.03468i
$509$	0.765912			0.0339485			0.0169742	−	0.999856i	$-0.494597\pi$
$509$	0.765912			0.0339485			0.0169742	+	0.999856i	$0.494597\pi$
$510$	0.562655	−	0.138635i	0.0249148	−	0.00613885i
$511$	−41.5391			−1.83758
$512$	−18.6312	+	12.8405i	−0.823389	+	0.567477i
$513$			1.13293i			0.0500199i
$514$	6.51957	+	26.4600i	0.287566	+	1.16710i
$515$	1.00311			0.0442023
$516$	−6.70100	+	3.51560i	−0.294995	+	0.154766i
$517$			9.06033i			0.398473i
$518$	5.71240	+	23.1840i	0.250988	+	1.01865i
$519$	3.37315			0.148065
$520$	−0.564735	−	0.637760i	−0.0247653	−	0.0279676i
$521$			33.7198i			1.47729i	0.674094	+	0.738646i	$0.264534\pi$
$521$			33.7198i			1.47729i	−0.674094	+	0.738646i	$0.735466\pi$
$522$	0.537506	+	2.18149i	0.0235260	+	0.0954813i
$523$		−	9.44525i		−	0.413012i	−0.978445	−	0.206506i	$-0.933791\pi$
$523$		−	9.44525i		−	0.413012i	0.978445	−	0.206506i	$-0.0662093\pi$
$524$	12.3183	+	23.4797i	0.538129	+	1.02571i
$525$	−18.7713			−0.819245
$526$	−7.81404	+	1.92533i	−0.340708	+	0.0839483i
$527$	3.16057			0.137677
$528$	2.50707	−	3.62966i	0.109106	−	0.157960i
$529$	16.0311			0.697003
$530$	0.0580297	+	0.235516i	0.00252065	+	0.0102302i
$531$			8.36670i			0.363084i
$532$	3.95495	+	7.53843i	0.171469	+	0.326832i
$533$	−7.56272			−0.327578
$534$	3.45010	+	14.0024i	0.149300	+	0.605942i
$535$	0.464454			0.0200801
$536$	−2.25852	−	23.0412i	−0.0975530	−	0.995230i
$537$	−19.8446			−0.856360
$538$	9.70285	+	39.3794i	0.418319	+	1.69777i
$539$	7.84706			0.337997
$540$	−0.0566509	−	0.107981i	−0.00243787	−	0.00464676i
$541$		−	34.1061i		−	1.46634i	−0.680047	−	0.733169i	$-0.738041\pi$
$541$		−	34.1061i		−	1.46634i	0.680047	−	0.733169i	$-0.261959\pi$
$542$	−1.23747	−	5.02231i	−0.0531537	−	0.215727i
$543$	−12.1020			−0.519347
$544$	−35.5419	−	13.4954i	−1.52385	−	0.578610i
$545$	−0.926614			−0.0396918
$546$	−25.4842	+	6.27915i	−1.09062	+	0.268723i
$547$	−42.8293			−1.83125			−0.915624	−	0.402036i	$-0.868303\pi$
$547$	−42.8293			−1.83125			−0.915624	+	0.402036i	$0.868303\pi$
$548$	−0.278610	−	0.531053i	−0.0119016	−	0.0226854i
$549$		−	4.04264i		−	0.172536i
$550$	−1.86424	−	7.56612i	−0.0794916	−	0.322620i
$551$		−	1.79986i		−	0.0766765i
$552$	−5.59008	+	4.95000i	−0.237930	+	0.210686i
$553$	15.6478			0.665414
$554$	8.40149	+	34.0978i	0.356945	+	1.44868i
$555$			0.273993i			0.0116304i
$556$	−7.56613	+	3.96948i	−0.320875	+	0.168343i
$557$	−10.7291			−0.454607			−0.227303	−	0.973824i	$-0.572991\pi$
$557$	−10.7291			−0.454607			−0.227303	+	0.973824i	$0.572991\pi$
$558$	−0.159111	−	0.645759i	−0.00673571	−	0.0273372i
$559$			18.6902i			0.790513i
$560$	−0.753905	−	0.520736i	−0.0318583	−	0.0220051i
$561$	7.41175			0.312924
$562$	37.4413	−	9.22529i	1.57936	−	0.389145i
$563$	−27.9704			−1.17881			−0.589405	−	0.807837i	$-0.700638\pi$
$563$	−27.9704			−1.17881			−0.589405	+	0.807837i	$0.700638\pi$
$564$	−7.63357	−	14.5502i	−0.321431	−	0.612673i
$565$	−1.09792			−0.0461901
$566$	−40.3807	+	9.94955i	−1.69733	+	0.418211i
$567$	−3.75704			−0.157781
$568$	−16.9785	+	15.0344i	−0.712400	+	0.630829i
$569$	−6.81343			−0.285634			−0.142817	−	0.989749i	$-0.545616\pi$
$569$	−6.81343			−0.285634			−0.142817	+	0.989749i	$0.545616\pi$
$570$	0.0233702	+	0.0948489i	0.000978869	+	0.00397278i
$571$		−	4.24888i		−	0.177810i	−0.996040	−	0.0889050i	$-0.971663\pi$
$571$		−	4.24888i		−	0.177810i	0.996040	−	0.0889050i	$-0.0283368\pi$
$572$	−5.06187	−	9.64831i	−0.211647	−	0.403416i
$573$	19.4833			0.813927
$574$	−7.89828	+	1.94609i	−0.329668	+	0.0812281i
$575$			13.1896i			0.550043i
$576$	−0.968076	+	7.94121i	−0.0403365	+	0.330884i
$577$		−	33.8937i		−	1.41101i	−0.708704	−	0.705506i	$-0.750720\pi$
$577$		−	33.8937i		−	1.41101i	0.708704	−	0.705506i	$-0.249280\pi$
$578$	−9.52993	−	38.6777i	−0.396393	−	1.60878i
$579$	−16.3459			−0.679314
$580$	0.0900003	+	0.171547i	0.00373706	+	0.00712312i
$581$			0.0828853i			0.00343866i
$582$	−4.31593	+	1.06342i	−0.178901	+	0.0440801i
$583$			3.10241i			0.128489i
$584$	20.7316	+	23.4124i	0.857880	+	0.968811i
$585$	−0.301178			−0.0124522
$586$	−1.32532	−	5.37887i	−0.0547484	−	0.222199i
$587$	20.6867			0.853831			0.426915	−	0.904292i	$-0.359600\pi$
$587$	20.6867			0.853831			0.426915	+	0.904292i	$0.359600\pi$
$588$	−12.6018	+	6.61136i	−0.519688	+	0.272648i
$589$			0.532789i			0.0219532i
$590$	0.172590	+	0.700463i	0.00710540	+	0.0288376i
$591$		−	17.6850i		−	0.727463i
$592$	10.2161	−	14.7905i	0.419878	−	0.607885i
$593$			33.6914i			1.38354i	0.722118	+	0.691770i	$0.243169\pi$
$593$			33.6914i			1.38354i	−0.722118	+	0.691770i	$0.756831\pi$
$594$	−0.373126	−	1.51435i	−0.0153095	−	0.0621345i
$595$		−	1.53947i		−	0.0631122i
$596$	−20.1722	+	10.5831i	−0.826284	+	0.433500i
$597$			0.273537i			0.0111951i
$598$	4.41203	+	17.9064i	0.180421	+	0.732248i
$599$	−34.3230			−1.40240			−0.701199	−	0.712966i	$-0.747352\pi$
$599$	−34.3230			−1.40240			−0.701199	+	0.712966i	$0.747352\pi$
$600$	9.36848	+	10.5799i	0.382467	+	0.431923i
$601$	−11.6051			−0.473383			−0.236691	−	0.971585i	$-0.576063\pi$
$601$	−11.6051			−0.473383			−0.236691	+	0.971585i	$0.576063\pi$
$602$	4.80949	+	19.5195i	0.196020	+	0.795557i
$603$	−6.62825	−	4.80274i	−0.269923	−	0.195582i
$604$	−5.50124	−	10.4858i	−0.223842	−	0.426660i
$605$		−	0.596513i		−	0.0242517i
$606$	−10.9396	+	2.69546i	−0.444392	+	0.109495i
$607$		−	36.1180i		−	1.46599i	−0.680236	−	0.732993i	$-0.738123\pi$
$607$		−	36.1180i		−	1.46599i	0.680236	−	0.732993i	$-0.261877\pi$
$608$	2.27497	−	5.99143i	0.0922622	−	0.242984i
$609$	5.96874			0.241866
$610$	−0.0833921	−	0.338451i	−0.00337645	−	0.0137035i
$611$	−40.5829			−1.64181
$612$	−11.9027	+	6.24460i	−0.481137	+	0.252423i
$613$	−22.2211			−0.897501			−0.448750	−	0.893657i	$-0.648131\pi$
$613$	−22.2211			−0.897501			−0.448750	+	0.893657i	$0.648131\pi$
$614$	−26.2224	+	6.46104i	−1.05825	+	0.260746i
$615$	−0.0933434			−0.00376397
$616$	−7.76922	−	8.77385i	−0.313031	−	0.353508i
$617$	1.45070			0.0584028			0.0292014	−	0.999574i	$-0.490704\pi$
$617$	1.45070			0.0584028			0.0292014	+	0.999574i	$0.490704\pi$
$618$	−22.5918	+	5.56648i	−0.908775	+	0.223917i
$619$		−	45.2790i		−	1.81992i	−0.414699	−	0.909958i	$-0.636113\pi$
$619$		−	45.2790i		−	1.81992i	0.414699	−	0.909958i	$-0.363887\pi$
$620$	−0.0266416	−	0.0507810i	−0.00106995	−	0.00203941i
$621$			2.63987i			0.105935i
$622$	−5.45017	−	22.1198i	−0.218532	−	0.886922i
$623$	38.3117			1.53492
$624$	16.2579	+	11.2296i	0.650837	+	0.449546i
$625$	24.9443			0.997770
$626$	−34.4162	+	8.47994i	−1.37555	+	0.338926i
$627$			1.24943i			0.0498973i
$628$	−9.23521	+	4.84514i	−0.368525	+	0.193342i
$629$	30.2021			1.20424
$630$	−0.314541	+	0.0775009i	−0.0125316	+	0.00308771i
$631$	−43.0310			−1.71304			−0.856518	−	0.516118i	$-0.827377\pi$
$631$	−43.0310			−1.71304			−0.856518	+	0.516118i	$0.827377\pi$
$632$	−7.80963	−	8.81948i	−0.310650	−	0.350820i
$633$			23.0337i			0.915506i
$634$	−1.99567	−	8.09951i	−0.0792581	−	0.321673i
$635$	0.802818			0.0318589
$636$	−2.61387	−	4.98223i	−0.103647	−	0.197558i
$637$			35.1485i			1.39263i
$638$	0.592778	+	2.40582i	0.0234683	+	0.0952472i
$639$			8.01796i			0.317185i
$640$	0.0827649	+	0.684810i	0.00327157	+	0.0270695i
$641$			8.27565i			0.326869i	0.986554	+	0.163434i	$0.0522572\pi$
$641$			8.27565i			0.326869i	−0.986554	+	0.163434i	$0.947743\pi$
$642$	−10.4603	+	2.57736i	−0.412836	+	0.101720i
$643$			44.9629i			1.77317i	0.462570	+	0.886583i	$0.346927\pi$
$643$			44.9629i			1.77317i	−0.462570	+	0.886583i	$0.653073\pi$
$644$	9.21557	+	17.5656i	0.363145	+	0.692181i
$645$			0.230686i			0.00908324i
$646$	10.4551	−	2.57608i	0.411352	−	0.101355i
$647$	16.8929			0.664127			0.332063	−	0.943257i	$-0.392255\pi$
$647$	16.8929			0.664127			0.332063	+	0.943257i	$0.392255\pi$
$648$	1.87509	+	2.11755i	0.0736605	+	0.0831854i
$649$			9.22707i			0.362194i
$650$	33.8901	−	8.35030i	1.32928	−	0.327526i
$651$	−1.76685			−0.0692484
$652$	0.798200	+	1.52143i	0.0312599	+	0.0595838i
$653$			14.8987i			0.583033i	0.956566	+	0.291516i	$0.0941598\pi$
$653$			14.8987i			0.583033i	−0.956566	+	0.291516i	$0.905840\pi$
$654$	20.8690	−	5.14199i	0.816042	−	0.201068i
$655$	0.808301			0.0315829
$656$	5.03878	+	3.48038i	0.196731	+	0.135886i
$657$	11.0563			0.431348
$658$	−42.3836	+	10.4431i	−1.65228	+	0.407112i
$659$		−	11.9371i		−	0.465003i	−0.972596	−	0.232502i	$-0.925309\pi$
$659$		−	11.9371i		−	0.465003i	0.972596	−	0.232502i	$-0.0746911\pi$
$660$	−0.0624764	−	0.119085i	−0.00243189	−	0.00463537i
$661$		−	27.4833i		−	1.06898i	−0.845176	−	0.534488i	$-0.820504\pi$
$661$		−	27.4833i		−	1.06898i	0.845176	−	0.534488i	$-0.179496\pi$
$662$	3.16352	+	12.8393i	0.122954	+	0.499013i
$663$			33.1986i			1.28933i
$664$	0.0467161	−	0.0413670i	0.00181293	−	0.00160535i
$665$	0.259515			0.0100635
$666$	−1.52045	−	6.17082i	−0.0589163	−	0.239114i
$667$		−	4.19392i		−	0.162389i
$668$	−12.5278	−	23.8789i	−0.484715	−	0.923903i
$669$			0.306864i			0.0118640i
$670$	−0.653991	−	0.265358i	−0.0252659	−	0.0102517i
$671$		−	4.45835i		−	0.172113i
$672$	19.8690	+	7.54432i	0.766461	+	0.291028i
$673$		−	39.3560i		−	1.51706i	−0.651638	−	0.758530i	$-0.725918\pi$
$673$		−	39.3560i		−	1.51706i	0.651638	−	0.758530i	$-0.274082\pi$
$674$	−36.5181	+	8.99782i	−1.40662	+	0.346583i
$675$	4.99628			0.192307
$676$	20.1928	−	10.5939i	0.776646	−	0.407458i
$677$			30.4168i			1.16901i	0.811390	+	0.584505i	$0.198711\pi$
$677$			30.4168i			1.16901i	−0.811390	+	0.584505i	$0.801289\pi$
$678$	24.7272	−	6.09263i	0.949643	−	0.233986i
$679$			11.8087i			0.453178i
$680$	−0.867681	+	0.768330i	−0.0332741	+	0.0294641i
$681$			25.5455i			0.978907i
$682$	−0.175473	−	0.712164i	−0.00671920	−	0.0272702i
$683$	−35.5098			−1.35874			−0.679372	−	0.733794i	$-0.737748\pi$
$683$	−35.5098			−1.35874			−0.679372	+	0.733794i	$0.737748\pi$
$684$	−1.05268	−	2.00648i	−0.0402500	−	0.0767197i
$685$	−0.0182818			−0.000698511
$686$	0.146657	+	0.595216i	0.00559941	+	0.0227255i
$687$			0.674492i			0.0257335i
$688$	8.60130	−	12.4527i	0.327921	−	0.474754i
$689$	−13.8963			−0.529407
$690$	0.0544557	+	0.221011i	0.00207309	+	0.00841375i
$691$			5.77351i			0.219635i	0.993952	+	0.109817i	$0.0350266\pi$
$691$			5.77351i			0.219635i	−0.993952	+	0.109817i	$0.964973\pi$
$692$	−5.97406	+	3.13422i	−0.227100	+	0.119145i
$693$	−4.14339			−0.157394
$694$	1.29878	+	5.27117i	0.0493011	+	0.200091i
$695$			0.260468i			0.00988012i
$696$	−2.97892	−	3.36412i	−0.112916	−	0.127517i
$697$			10.2892i			0.389731i
$698$	0.447724	+	1.81711i	0.0169466	+	0.0687785i
$699$		−	26.4164i		−	0.999159i
$700$	33.2450	−	17.4416i	1.25654	−	0.659230i
$701$			38.6943i			1.46146i	0.682666	+	0.730731i	$0.260821\pi$
$701$			38.6943i			1.46146i	−0.682666	+	0.730731i	$0.739179\pi$
$702$	6.78305	−	1.67130i	0.256010	−	0.0630792i
$703$			5.09129i			0.192021i
$704$	−1.06762	+	8.75782i	−0.0402376	+	0.330073i
$705$	−0.500898			−0.0188649
$706$	−29.2644	+	7.21056i	−1.10138	+	0.271373i
$707$			29.9318i			1.12570i
$708$	−7.77405	−	14.8179i	−0.292167	−	0.556892i
$709$	−6.14543			−0.230797			−0.115398	−	0.993319i	$-0.536814\pi$
$709$	−6.14543			−0.230797			−0.115398	+	0.993319i	$0.536814\pi$
$710$	0.165396	+	0.671266i	0.00620719	+	0.0251922i
$711$	−4.16494			−0.156197
$712$	−19.1208	−	21.5933i	−0.716584	−	0.809244i
$713$			1.24147i			0.0464935i
$714$	8.54287	+	34.6716i	0.319709	+	1.29755i
$715$	−0.332148			−0.0124216
$716$	35.1460	−	18.4390i	1.31347	−	0.689096i
$717$	14.5374			0.542910
$718$	−45.3597	+	11.1764i	−1.69281	+	0.417098i
$719$		−	27.3015i		−	1.01817i	−0.860715	−	0.509087i	$-0.829983\pi$
$719$		−	27.3015i		−	1.01817i	0.860715	−	0.509087i	$-0.170017\pi$
$720$	0.200664	+	0.138603i	0.00747832	+	0.00516542i
$721$			61.8131i			2.30204i
$722$	−5.99410	−	24.3273i	−0.223077	−	0.905369i
$723$	25.6937			0.955557
$724$	21.4334	−	11.2448i	0.796565	−	0.417908i
$725$	−7.93750			−0.294791
$726$	3.31018	+	13.4345i	0.122852	+	0.498602i
$727$	28.2755			1.04868			0.524340	−	0.851509i	$-0.324312\pi$
$727$	28.2755			1.04868			0.524340	+	0.851509i	$0.324312\pi$
$728$	39.2997	−	34.7998i	1.45654	−	1.28977i
$729$	1.00000			0.0370370
$730$	0.925639	−	0.228072i	0.0342594	−	0.00844131i
$731$	25.4283			0.940501
$732$	3.75628	+	7.15975i	0.138836	+	0.264632i
$733$		−	4.28232i		−	0.158171i	−0.996868	−	0.0790855i	$-0.974800\pi$
$733$		−	4.28232i		−	0.158171i	0.996868	−	0.0790855i	$-0.0252000\pi$
$734$	−7.17139	−	29.1054i	−0.264701	−	1.07430i
$735$			0.433822i			0.0160018i
$736$	5.30099	−	13.9609i	0.195397	−	0.514604i
$737$	−7.30985	−	5.29661i	−0.269262	−	0.195103i
$738$	2.10226	−	0.517983i	0.0773852	−	0.0190672i
$739$	50.2060			1.84686			0.923429	−	0.383769i	$-0.125374\pi$
$739$	50.2060			1.84686			0.923429	+	0.383769i	$0.125374\pi$
$740$	−0.254585	−	0.485259i	−0.00935874	−	0.0178385i
$741$	−5.59642			−0.205590
$742$	−14.5129	+	3.57588i	−0.532784	+	0.131275i
$743$		−	45.7389i		−	1.67800i	−0.544134	−	0.838998i	$-0.683142\pi$
$743$		−	45.7389i		−	1.67800i	0.544134	−	0.838998i	$-0.316858\pi$
$744$	0.881812	+	0.995838i	0.0323288	+	0.0365092i
$745$			0.694438i			0.0254422i
$746$	−49.2649	+	12.1386i	−1.80371	+	0.444424i
$747$		−	0.0220613i		−	0.000807182i
$748$	−13.1267	+	6.88674i	−0.479958	+	0.251804i
$749$			28.6203i			1.04576i
$750$	0.836892	−	0.206205i	0.0305590	−	0.00752954i
$751$			23.7461i			0.866507i	0.901272	+	0.433253i	$0.142634\pi$
$751$			23.7461i			0.866507i	−0.901272	+	0.433253i	$0.857366\pi$
$752$	27.0390	+	18.6764i	0.986012	+	0.681057i
$753$	10.6671			0.388729
$754$	−10.7761	+	2.65517i	−0.392443	+	0.0966954i
$755$	−0.360979			−0.0131374
$756$	6.65395	−	3.49091i	0.242002	−	0.126963i
$757$			49.3512i			1.79370i	0.442334	+	0.896850i	$0.354150\pi$
$757$			49.3512i			1.79370i	−0.442334	+	0.896850i	$0.645850\pi$
$758$	−10.3284	−	41.9184i	−0.375146	−	1.52255i
$759$			2.91134i			0.105675i
$760$	−0.129520	−	0.146268i	−0.00469819	−	0.00530571i
$761$	27.3276			0.990624			0.495312	−	0.868715i	$-0.335054\pi$
$761$	27.3276			0.990624			0.495312	+	0.868715i	$0.335054\pi$
$762$	−18.0809	+	4.45502i	−0.655002	+	0.161388i
$763$		−	57.0993i		−	2.06713i
$764$	−34.5061	+	18.1032i	−1.24839	+	0.654951i
$765$			0.409756i			0.0148148i
$766$	−5.14721	−	20.8902i	−0.185976	−	0.754793i
$767$	−41.3298			−1.49233
$768$	−5.66418	−	14.9639i	−0.204388	−	0.539962i
$769$		−	39.0002i		−	1.40638i	−0.711000	−	0.703192i	$-0.751757\pi$
$769$		−	39.0002i		−	1.40638i	0.711000	−	0.703192i	$-0.248243\pi$
$770$	−0.346886	+	0.0854704i	−0.0125009	+	0.00308014i
$771$	−19.2696			−0.693977
$772$	28.9496	−	15.1881i	1.04192	−	0.546631i
$773$	−15.8396			−0.569712			−0.284856	−	0.958570i	$-0.591946\pi$
$773$	−15.8396			−0.569712			−0.284856	+	0.958570i	$0.591946\pi$
$774$	−1.28013	−	5.19545i	−0.0460132	−	0.186747i
$775$	2.34964			0.0844015
$776$	6.65568	−	5.89359i	0.238925	−	0.211567i
$777$	−16.8839			−0.605706
$778$	0.566932	+	2.30092i	0.0203255	+	0.0824919i
$779$	−1.73449			−0.0621445
$780$	0.533404	−	0.279844i	0.0190989	−	0.0100200i
$781$			8.84246i			0.316408i
$782$	24.3619	−	6.00262i	0.871181	−	0.214653i
$783$	−1.58868			−0.0567748
$784$	16.1754	−	23.4182i	0.577693	−	0.836365i
$785$			0.317927i			0.0113473i
$786$	−18.2044	+	4.48544i	−0.649329	+	0.159990i
$787$	−8.86947			−0.316162			−0.158081	−	0.987426i	$-0.550531\pi$
$787$	−8.86947			−0.316162			−0.158081	+	0.987426i	$0.550531\pi$
$788$	16.4323	+	31.3211i	0.585375	+	1.11577i
$789$		−	5.69061i		−	0.202591i
$790$	−0.348690	+	0.0859149i	−0.0124058	+	0.00305672i
$791$		−	67.6558i		−	2.40556i
$792$	2.06791	+	2.33531i	0.0734799	+	0.0829815i
$793$	19.9698			0.709148
$794$	8.67476	+	35.2069i	0.307856	+	1.24945i
$795$	−0.171516			−0.00608304
$796$	−0.254161	−	0.484450i	−0.00900849	−	0.0171709i
$797$	−50.3078			−1.78199			−0.890997	−	0.454009i	$-0.849993\pi$
$797$	−50.3078			−1.78199			−0.890997	+	0.454009i	$0.849993\pi$
$798$	−5.84473	+	1.44010i	−0.206901	+	0.0509791i
$799$			55.2137i			1.95332i
$800$	−26.4226	−	10.0328i	−0.934180	−	0.354712i
$801$	−10.1973			−0.360304
$802$	26.6079	−	6.55602i	0.939557	−	0.231501i
$803$	12.1933			0.430291
$804$	16.2016	+	2.34719i	0.571385	+	0.0827789i
$805$	0.604705			0.0213131
$806$	3.18992	−	0.785975i	0.112360	−	0.0276848i
$807$	−28.6783			−1.00952
$808$	16.8702	−	14.9385i	0.593492	−	0.525536i
$809$		−	34.5157i		−	1.21351i	−0.794890	−	0.606754i	$-0.792471\pi$
$809$		−	34.5157i		−	1.21351i	0.794890	−	0.606754i	$-0.207529\pi$
$810$	0.0837203	−	0.0206282i	0.00294163	−	0.000724799i
$811$	31.4903			1.10578			0.552888	−	0.833256i	$-0.313526\pi$
$811$	31.4903			1.10578			0.552888	+	0.833256i	$0.313526\pi$
$812$	−10.5710	+	5.54595i	−0.370969	+	0.194625i
$813$	3.65752			0.128275
$814$	−1.67680	−	6.80537i	−0.0587718	−	0.238528i
$815$	0.0523761			0.00183465
$816$	15.2781	−	22.1191i	0.534840	−	0.774324i
$817$			4.28655i			0.149967i
$818$	20.6861	−	5.09693i	0.723273	−	0.178210i
$819$		−	18.5590i		−	0.648504i
$820$	0.165317	−	0.0867314i	0.00577311	−	0.00302879i
$821$	10.9479			0.382084			0.191042	−	0.981582i	$-0.438813\pi$
$821$	10.9479			0.382084			0.191042	+	0.981582i	$0.438813\pi$
$822$	0.411738	−	0.101450i	0.0143610	−	0.00353846i
$823$			48.8253i			1.70194i	0.525211	+	0.850972i	$0.323986\pi$
$823$			48.8253i			1.70194i	−0.525211	+	0.850972i	$0.676014\pi$
$824$	34.8392	−	30.8501i	1.21368	−	1.07471i
$825$	5.51006			0.191836
$826$	−43.1636	+	10.6352i	−1.50185	+	0.370047i
$827$			15.1710i			0.527546i	0.964585	+	0.263773i	$0.0849670\pi$
$827$			15.1710i			0.527546i	−0.964585	+	0.263773i	$0.915033\pi$
$828$	−2.45288	−	4.67537i	−0.0852435	−	0.162481i
$829$	−50.1705			−1.74249			−0.871246	−	0.490847i	$-0.836688\pi$
$829$	−50.1705			−1.74249			−0.871246	+	0.490847i	$0.836688\pi$
$830$	−0.000455084	−	0.00184698i	−1.57962e−5	−	6.41096e-5i
$831$	−24.8319			−0.861409
$832$	−39.2279	−	4.78209i	−1.35998	−	0.165789i
$833$	47.8200			1.65686
$834$	−1.44540	−	5.86620i	−0.0500499	−	0.203130i
$835$	−0.822045			−0.0284480
$836$	−1.16092	−	2.21281i	−0.0401514	−	0.0765316i
$837$	0.470277			0.0162552
$838$	13.4275	−	3.30846i	0.463847	−	0.114289i
$839$			29.6526i			1.02372i	0.859068	+	0.511861i	$0.171044\pi$
$839$			29.6526i			1.02372i	−0.859068	+	0.511861i	$0.828956\pi$
$840$	0.485059	−	0.429519i	0.0167361	−	0.0148198i
$841$	−26.4761			−0.912969
$842$	−1.41887	−	5.75854i	−0.0488974	−	0.198452i
$843$			27.2668i			0.939118i
$844$	−21.4021	−	40.7940i	−0.736690	−	1.40419i
$845$		−	0.695148i		−	0.0239138i
$846$	11.2811	−	2.77959i	0.387852	−	0.0955644i
$847$	36.7580			1.26302
$848$	9.25862	+	6.39511i	0.317942	+	0.219609i
$849$		−	29.4074i		−	1.00926i
$850$	−11.3607	−	46.1079i	−0.389669	−	1.58149i
$851$			11.8634i			0.406672i
$852$	−7.45001	−	14.2003i	−0.255233	−	0.486494i
$853$	0.559952			0.0191724			0.00958620	−	0.999954i	$-0.496949\pi$
$853$	0.559952			0.0191724			0.00958620	+	0.999954i	$0.496949\pi$
$854$	20.8558	−	5.13875i	0.713672	−	0.175844i
$855$	−0.0690742			−0.00236229
$856$	16.1311	−	14.2840i	0.551348	−	0.488218i
$857$		−	1.73577i		−	0.0592927i	−0.999560	−	0.0296464i	$-0.990562\pi$
$857$		−	1.73577i		−	0.0592927i	0.999560	−	0.0296464i	$-0.00943812\pi$
$858$	7.48057	−	1.84316i	0.255382	−	0.0629246i
$859$			32.0998i			1.09523i	0.836730	+	0.547616i	$0.184465\pi$
$859$			32.0998i			1.09523i	−0.836730	+	0.547616i	$0.815535\pi$
$860$	−0.214345	−	0.408558i	−0.00730911	−	0.0139317i
$861$		−	5.75196i		−	0.196026i
$862$	−40.6012	+	10.0039i	−1.38288	+	0.340733i
$863$			22.0871i			0.751854i	0.926649	+	0.375927i	$0.122676\pi$
$863$			22.0871i			0.751854i	−0.926649	+	0.375927i	$0.877324\pi$
$864$	−5.28845	−	2.00805i	−0.179917	−	0.0683152i
$865$			0.205660i			0.00699266i
$866$	−33.5817	+	8.27432i	−1.14115	+	0.281173i
$867$	28.1672			0.956608
$868$	3.12920	−	1.64170i	0.106212	−	0.0557228i
$869$	−4.59322			−0.155814
$870$	−0.133005	+	0.0327716i	−0.00450929	+	0.00111106i
$871$	23.7245	−	32.7422i	0.803874	−	1.10943i
$872$	−32.1825	+	28.4975i	−1.08984	+	0.965047i
$873$		−	3.14310i		−	0.106378i
$874$	1.01188	+	4.10678i	0.0342275	+	0.138914i
$875$		−	2.28981i		−	0.0774096i
$876$	−19.5814	+	10.2732i	−0.661595	+	0.347098i
$877$	42.7191			1.44252			0.721261	−	0.692664i	$-0.243563\pi$
$877$	42.7191			1.44252			0.721261	+	0.692664i	$0.243563\pi$
$878$	−3.86886	+	0.953264i	−0.130568	+	0.0321711i
$879$	3.91718			0.132123
$880$	0.221299	+	0.152855i	0.00745999	+	0.00515276i
$881$	12.3679			0.416686			0.208343	−	0.978056i	$-0.433193\pi$
$881$	12.3679			0.416686			0.208343	+	0.978056i	$0.433193\pi$
$882$	−2.40738	−	9.77045i	−0.0810606	−	0.328988i
$883$	17.3230			0.582964			0.291482	−	0.956576i	$-0.405852\pi$
$883$	17.3230			0.582964			0.291482	+	0.956576i	$0.405852\pi$
$884$	−30.8470	−	58.7968i	−1.03750	−	1.97755i
$885$	−0.510115			−0.0171473
$886$	−6.89719	−	27.9926i	−0.231716	−	0.940429i
$887$		−	16.9517i		−	0.569184i	−0.958649	−	0.284592i	$-0.908142\pi$
$887$		−	16.9517i		−	0.569184i	0.958649	−	0.284592i	$-0.0918581\pi$
$888$	8.42652	+	9.51614i	0.282775	+	0.319341i
$889$			49.4708i			1.65920i
$890$	−0.853720	+	0.210351i	−0.0286168	+	0.00705099i
$891$	1.10283			0.0369463
$892$	−0.285127	−	0.543474i	−0.00954676	−	0.0181969i
$893$	−9.30757			−0.311466
$894$	−3.85359	−	15.6400i	−0.128883	−	0.523079i
$895$		−	1.20992i		−	0.0404432i
$896$	−42.1990	+	5.10010i	−1.40977	+	0.170382i
$897$	−13.0404			−0.435407
$898$	−5.34137	−	21.6782i	−0.178244	−	0.723410i
$899$	−0.747121			−0.0249179
$900$	−8.84871	+	4.64237i	−0.294957	+	0.154746i
$901$			18.9061i			0.629853i
$902$	2.31844	−	0.571249i	0.0771956	−	0.0190205i
$903$	−14.2152			−0.473052
$904$	−38.1323	+	33.7661i	−1.26826	+	1.12304i
$905$		−	0.737855i		−	0.0245271i
$906$	8.12988	−	2.00315i	0.270097	−	0.0665502i
$907$			38.6115i			1.28208i	0.767510	+	0.641038i	$0.221496\pi$
$907$			38.6115i			1.28208i	−0.767510	+	0.641038i	$0.778504\pi$
$908$	−23.7360	−	45.2426i	−0.787707	−	1.50143i
$909$		−	7.96684i		−	0.264243i
$910$	−0.382838	−	1.55377i	−0.0126910	−	0.0515068i
$911$			5.06984i			0.167971i	0.996467	+	0.0839856i	$0.0267650\pi$
$911$			5.06984i			0.167971i	−0.996467	+	0.0839856i	$0.973235\pi$
$912$	3.72870	+	2.57549i	0.123470	+	0.0852828i
$913$		−	0.0243299i		−	0.000805203i
$914$	5.09981	+	20.6978i	0.168687	+	0.684623i
$915$	0.246478			0.00814832
$916$	−0.626714	−	1.19456i	−0.0207072	−	0.0394695i
$917$			49.8087i			1.64483i
$918$	−2.27383	−	9.22844i	−0.0750475	−	0.304584i
$919$	−29.8150			−0.983506			−0.491753	−	0.870735i	$-0.663644\pi$
$919$	−29.8150			−0.983506			−0.491753	+	0.870735i	$0.663644\pi$
$920$	−0.301800	−	0.340825i	−0.00995006	−	0.0112367i
$921$		−	19.0966i		−	0.629255i
$922$	2.03226	+	8.24801i	0.0669288	+	0.271634i
$923$	−39.6070			−1.30368
$924$	7.33819	−	3.84989i	0.241409	−	0.126652i
$925$	22.4529			0.738248
$926$	9.44906	+	38.3495i	0.310515	+	1.26024i
$927$		−	16.4526i		−	0.540374i
$928$	8.40167	+	3.19015i	0.275798	+	0.104722i
$929$		−	3.21339i		−	0.105428i	−0.998610	−	0.0527140i	$-0.983213\pi$
$929$		−	3.21339i		−	0.105428i	0.998610	−	0.0527140i	$-0.0167872\pi$
$930$	0.0393718	−	0.00970095i	0.00129105	−	0.000318107i
$931$			8.06119i			0.264195i
$932$	24.5452	+	46.7850i	0.804004	+	1.53249i
$933$	16.1088			0.527379
$934$	−11.7569	+	2.89683i	−0.384699	+	0.0947873i
$935$			0.451892i			0.0147785i
$936$	−10.4603	+	9.26255i	−0.341905	+	0.302756i
$937$		−	23.1966i		−	0.757801i	−0.925437	−	0.378901i	$-0.876302\pi$
$937$		−	23.1966i		−	0.757801i	0.925437	−	0.378901i	$-0.123698\pi$
$938$	16.3517	−	40.2999i	0.533903	−	1.31584i
$939$		−	25.0638i		−	0.817925i
$940$	0.887120	−	0.465417i	0.0289347	−	0.0151802i
$941$			10.4771i			0.341545i	0.985310	+	0.170773i	$0.0546263\pi$
$941$			10.4771i			0.341545i	−0.985310	+	0.170773i	$0.945374\pi$
$942$	−1.76425	−	7.16028i	−0.0574823	−	0.233295i
$943$	−4.04160			−0.131612
$944$	27.5366	+	19.0201i	0.896240	+	0.619050i
$945$		−	0.229066i		−	0.00745151i
$946$	−1.41176	−	5.72971i	−0.0459004	−	0.186289i
$947$			0.995538i			0.0323506i	0.999869	+	0.0161753i	$0.00514899\pi$
$947$			0.995538i			0.0323506i	−0.999869	+	0.0161753i	$0.994851\pi$
$948$	7.37635	−	3.86991i	0.239573	−	0.125689i
$949$			54.6160i			1.77291i
$950$	7.77258	−	1.91511i	0.252176	−	0.0621345i
$951$	5.89851			0.191272
$952$	−47.3456	−	53.4678i	−1.53448	−	1.73290i
$953$	46.4967			1.50618			0.753088	−	0.657920i	$-0.228563\pi$
$953$	46.4967			1.50618			0.753088	+	0.657920i	$0.228563\pi$
$954$	3.86284	−	0.951780i	0.125064	−	0.0308150i
$955$			1.18789i			0.0384393i
$956$	−25.7467	+	13.5077i	−0.832706	+	0.436869i
$957$	−1.75205			−0.0566357
$958$	5.85235	−	1.44198i	0.189081	−	0.0465883i
$959$		−	1.12655i		−	0.0363782i
$960$	−0.484173	−	0.0590233i	−0.0156266	−	0.00190497i
$961$	−30.7788			−0.992866
$962$	30.4825	−	7.51071i	0.982797	−	0.242155i
$963$		−	7.61778i		−	0.245480i
$964$	−45.5050	+	23.8736i	−1.46562	+	0.768918i
$965$		−	0.996606i		−	0.0320819i
$966$	−13.6190	+	3.35564i	−0.438185	+	0.107966i
$967$		−	24.1332i		−	0.776071i	−0.921644	−	0.388036i	$-0.873154\pi$
$967$		−	24.1332i		−	0.776071i	0.921644	−	0.388036i	$-0.126846\pi$
$968$	−18.3454	−	20.7177i	−0.589645	−	0.665891i
$969$			7.61400i			0.244597i
$970$	−0.0648363	−	0.263141i	−0.00208177	−	0.00844895i
$971$			12.8703i			0.413029i	0.978444	+	0.206515i	$0.0662121\pi$
$971$			12.8703i			0.413029i	−0.978444	+	0.206515i	$0.933788\pi$
$972$	−1.77106	+	0.929165i	−0.0568068	+	0.0298030i
$973$	−16.0504			−0.514553
$974$	−9.36172	−	37.9950i	−0.299969	−	1.21744i
$975$			24.6806i			0.790412i
$976$	−13.3052	−	9.19014i	−0.425888	−	0.294169i
$977$	16.2901			0.521168			0.260584	−	0.965451i	$-0.416085\pi$
$977$	16.2901			0.521168			0.260584	+	0.965451i	$0.416085\pi$
$978$	−1.17960	+	0.290646i	−0.0377195	+	0.00929385i
$979$	−11.2459			−0.359420
$980$	−0.403093	−	0.768325i	−0.0128763	−	0.0245432i
$981$			15.1979i			0.485233i
$982$	51.3309	−	12.6476i	1.63803	−	0.403601i
$983$	42.9400			1.36957			0.684786	−	0.728744i	$-0.259896\pi$
$983$	42.9400			1.36957			0.684786	+	0.728744i	$0.259896\pi$
$984$	−3.24193	+	2.87073i	−0.103349	+	0.0915154i
$985$	1.07825			0.0343558
$986$	3.61239	+	14.6610i	0.115042	+	0.466903i
$987$		−	30.8661i		−	0.982477i
$988$	9.91159	−	5.20000i	0.315330	−	0.165434i
$989$			9.98826i			0.317608i
$990$	0.0923294	−	0.0227494i	0.00293442	−	0.000723023i
$991$	23.7585			0.754712			0.377356	−	0.926068i	$-0.376833\pi$
$991$	23.7585			0.754712			0.377356	+	0.926068i	$0.376833\pi$
$992$	−2.48704	−	0.944339i	−0.0789636	−	0.0299828i
$993$	−9.35027			−0.296722
$994$	−41.3644	+	10.1919i	−1.31200	+	0.323268i
$995$	−0.0166774			−0.000528711
$996$	0.0204986	+	0.0390719i	0.000649523	+	0.00123804i
$997$	32.6064			1.03265			0.516327	−	0.856392i	$-0.327299\pi$
$997$	32.6064			1.03265			0.516327	+	0.856392i	$0.327299\pi$
$998$	−1.82713	−	7.41550i	−0.0578368	−	0.234733i
$999$	4.49393			0.142182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.b.535.15	yes	34
4.3	odd	2		804.2.e.a.535.19	✓	34
67.66	odd	2		804.2.e.a.535.20	yes	34
268.267	even	2	inner	804.2.e.b.535.16	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.19	✓	34	4.3	odd	2
804.2.e.a.535.20	yes	34	67.66	odd	2
804.2.e.b.535.15	yes	34	1.1	even	1	trivial
804.2.e.b.535.16	yes	34	268.267	even	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.338334 - 1.37315i) q^{2} +1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} +0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} -3.75704 q^{7} +(1.87509 + 2.11755i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.338334 - 1.37315i) q^{2} +1.00000 q^{3} +(-1.77106 + 0.929165i) q^{4} +0.0609697i q^{5} +(-0.338334 - 1.37315i) q^{6} -3.75704 q^{7} +(1.87509 + 2.11755i) q^{8} +1.00000 q^{9} +(0.0837203 - 0.0206282i) q^{10} +1.10283 q^{11} +(-1.77106 + 0.929165i) q^{12} +4.93979i q^{13} +(1.27114 + 5.15897i) q^{14} +0.0609697i q^{15} +(2.27330 - 3.29121i) q^{16} +6.72065 q^{17} +(-0.338334 - 1.37315i) q^{18} +1.13293i q^{19} +(-0.0566509 - 0.107981i) q^{20} -3.75704 q^{21} +(-0.373126 - 1.51435i) q^{22} +2.63987i q^{23} +(1.87509 + 2.11755i) q^{24} +4.99628 q^{25} +(6.78305 - 1.67130i) q^{26} +1.00000 q^{27} +(6.65395 - 3.49091i) q^{28} -1.58868 q^{29} +(0.0837203 - 0.0206282i) q^{30} +0.470277 q^{31} +(-5.28845 - 2.00805i) q^{32} +1.10283 q^{33} +(-2.27383 - 9.22844i) q^{34} -0.229066i q^{35} +(-1.77106 + 0.929165i) q^{36} +4.49393 q^{37} +(1.55567 - 0.383308i) q^{38} +4.93979i q^{39} +(-0.129107 + 0.114324i) q^{40} +1.53098i q^{41} +(1.27114 + 5.15897i) q^{42} +3.78361 q^{43} +(-1.95318 + 1.02471i) q^{44} +0.0609697i q^{45} +(3.62493 - 0.893161i) q^{46} +8.21552i q^{47} +(2.27330 - 3.29121i) q^{48} +7.11537 q^{49} +(-1.69041 - 6.86063i) q^{50} +6.72065 q^{51} +(-4.58988 - 8.74866i) q^{52} +2.81313i q^{53} +(-0.338334 - 1.37315i) q^{54} +0.0672393i q^{55} +(-7.04479 - 7.95574i) q^{56} +1.13293i q^{57} +(0.537506 + 2.18149i) q^{58} +8.36670i q^{59} +(-0.0566509 - 0.107981i) q^{60} -4.04264i q^{61} +(-0.159111 - 0.645759i) q^{62} -3.75704 q^{63} +(-0.968076 + 7.94121i) q^{64} -0.301178 q^{65} +(-0.373126 - 1.51435i) q^{66} +(-6.62825 - 4.80274i) q^{67} +(-11.9027 + 6.24460i) q^{68} +2.63987i q^{69} +(-0.314541 + 0.0775009i) q^{70} +8.01796i q^{71} +(1.87509 + 2.11755i) q^{72} +11.0563 q^{73} +(-1.52045 - 6.17082i) q^{74} +4.99628 q^{75} +(-1.05268 - 2.00648i) q^{76} -4.14339 q^{77} +(6.78305 - 1.67130i) q^{78} -4.16494 q^{79} +(0.200664 + 0.138603i) q^{80} +1.00000 q^{81} +(2.10226 - 0.517983i) q^{82} -0.0220613i q^{83} +(6.65395 - 3.49091i) q^{84} +0.409756i q^{85} +(-1.28013 - 5.19545i) q^{86} -1.58868 q^{87} +(2.06791 + 2.33531i) q^{88} -10.1973 q^{89} +(0.0837203 - 0.0206282i) q^{90} -18.5590i q^{91} +(-2.45288 - 4.67537i) q^{92} +0.470277 q^{93} +(11.2811 - 2.77959i) q^{94} -0.0690742 q^{95} +(-5.28845 - 2.00805i) q^{96} -3.14310i q^{97} +(-2.40738 - 9.77045i) q^{98} +1.10283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9	\( 34 q + 34 q^{3} + 2 q^{4} + 4 q^{7} - 6 q^{8} + 34 q^{9} - 6 q^{10} + 2 q^{12} - 4 q^{14} + 2 q^{16} - 12 q^{20} + 4 q^{21} - 8 q^{22} - 6 q^{24} - 34 q^{25} + 10 q^{26} + 34 q^{27} - 8 q^{28} - 16 q^{29} - 6 q^{30} - 4 q^{31} + 2 q^{36} + 12 q^{37} + 26 q^{38} - 18 q^{40} - 4 q^{42} - 4 q^{43} + 26 q^{44} - 4 q^{46} + 2 q^{48} + 46 q^{49} - 18 q^{50} + 32 q^{52} + 14 q^{56} + 4 q^{58} - 12 q^{60} - 2 q^{62} + 4 q^{63} + 26 q^{64} - 8 q^{66} - 18 q^{67} - 34 q^{68} + 56 q^{70} - 6 q^{72} + 12 q^{73} + 22 q^{74} - 34 q^{75} - 32 q^{76} - 8 q^{77} + 10 q^{78} - 12 q^{79} - 2 q^{80} + 34 q^{81} + 26 q^{82} - 8 q^{84} + 6 q^{86} - 16 q^{87} - 28 q^{88} - 6 q^{90} - 46 q^{92} - 4 q^{93} + 32 q^{94} - 40 q^{95} - 40 q^{98}+O(q^{100}) \) 34 * q + 34 * q^3 + 2 * q^4 + 4 * q^7 - 6 * q^8 + 34 * q^9 - 6 * q^10 + 2 * q^12 - 4 * q^14 + 2 * q^16 - 12 * q^20 + 4 * q^21 - 8 * q^22 - 6 * q^24 - 34 * q^25 + 10 * q^26 + 34 * q^27 - 8 * q^28 - 16 * q^29 - 6 * q^30 - 4 * q^31 + 2 * q^36 + 12 * q^37 + 26 * q^38 - 18 * q^40 - 4 * q^42 - 4 * q^43 + 26 * q^44 - 4 * q^46 + 2 * q^48 + 46 * q^49 - 18 * q^50 + 32 * q^52 + 14 * q^56 + 4 * q^58 - 12 * q^60 - 2 * q^62 + 4 * q^63 + 26 * q^64 - 8 * q^66 - 18 * q^67 - 34 * q^68 + 56 * q^70 - 6 * q^72 + 12 * q^73 + 22 * q^74 - 34 * q^75 - 32 * q^76 - 8 * q^77 + 10 * q^78 - 12 * q^79 - 2 * q^80 + 34 * q^81 + 26 * q^82 - 8 * q^84 + 6 * q^86 - 16 * q^87 - 28 * q^88 - 6 * q^90 - 46 * q^92 - 4 * q^93 + 32 * q^94 - 40 * q^95 - 40 * q^98

Introduction

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