LMFDB - Embedded newform 804.2.e.a.535.11

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			535.11
Character	$\chi$	$=$	804.535
Dual form			804.2.e.a.535.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.921850 - 1.07247i) q^{2} -1.00000 q^{3} +(-0.300386 + 1.97731i) q^{4} -1.54735i q^{5} +(0.921850 + 1.07247i) q^{6} +4.78228 q^{7} +(2.39752 - 1.50063i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.921850 - 1.07247i) q^{2} -1.00000 q^{3} +(-0.300386 + 1.97731i) q^{4} -1.54735i q^{5} +(0.921850 + 1.07247i) q^{6} +4.78228 q^{7} +(2.39752 - 1.50063i) q^{8} +1.00000 q^{9} +(-1.65949 + 1.42642i) q^{10} +3.05580 q^{11} +(0.300386 - 1.97731i) q^{12} +3.50455i q^{13} +(-4.40854 - 5.12886i) q^{14} +1.54735i q^{15} +(-3.81954 - 1.18791i) q^{16} -4.48195 q^{17} +(-0.921850 - 1.07247i) q^{18} +6.47223i q^{19} +(3.05959 + 0.464802i) q^{20} -4.78228 q^{21} +(-2.81698 - 3.27725i) q^{22} +5.90022i q^{23} +(-2.39752 + 1.50063i) q^{24} +2.60571 q^{25} +(3.75853 - 3.23067i) q^{26} -1.00000 q^{27} +(-1.43653 + 9.45607i) q^{28} +5.56432 q^{29} +(1.65949 - 1.42642i) q^{30} -8.11655 q^{31} +(2.24704 + 5.19142i) q^{32} -3.05580 q^{33} +(4.13168 + 4.80676i) q^{34} -7.39986i q^{35} +(-0.300386 + 1.97731i) q^{36} +2.86229 q^{37} +(6.94127 - 5.96642i) q^{38} -3.50455i q^{39} +(-2.32200 - 3.70980i) q^{40} -5.82224i q^{41} +(4.40854 + 5.12886i) q^{42} +8.69388 q^{43} +(-0.917918 + 6.04227i) q^{44} -1.54735i q^{45} +(6.32781 - 5.43911i) q^{46} -3.02486i q^{47} +(3.81954 + 1.18791i) q^{48} +15.8702 q^{49} +(-2.40207 - 2.79455i) q^{50} +4.48195 q^{51} +(-6.92960 - 1.05272i) q^{52} -5.29439i q^{53} +(0.921850 + 1.07247i) q^{54} -4.72838i q^{55} +(11.4656 - 7.17644i) q^{56} -6.47223i q^{57} +(-5.12946 - 5.96756i) q^{58} +14.0544i q^{59} +(-3.05959 - 0.464802i) q^{60} -0.366956i q^{61} +(7.48224 + 8.70476i) q^{62} +4.78228 q^{63} +(3.49622 - 7.19559i) q^{64} +5.42277 q^{65} +(2.81698 + 3.27725i) q^{66} +(-2.49611 + 7.79547i) q^{67} +(1.34631 - 8.86222i) q^{68} -5.90022i q^{69} +(-7.93613 + 6.82156i) q^{70} -4.06493i q^{71} +(2.39752 - 1.50063i) q^{72} -14.7237 q^{73} +(-2.63860 - 3.06973i) q^{74} -2.60571 q^{75} +(-12.7976 - 1.94417i) q^{76} +14.6137 q^{77} +(-3.75853 + 3.23067i) q^{78} +12.4188 q^{79} +(-1.83812 + 5.91016i) q^{80} +1.00000 q^{81} +(-6.24418 + 5.36723i) q^{82} -7.10690i q^{83} +(1.43653 - 9.45607i) q^{84} +6.93514i q^{85} +(-8.01445 - 9.32393i) q^{86} -5.56432 q^{87} +(7.32633 - 4.58562i) q^{88} +4.89866 q^{89} +(-1.65949 + 1.42642i) q^{90} +16.7598i q^{91} +(-11.6666 - 1.77234i) q^{92} +8.11655 q^{93} +(-3.24407 + 2.78847i) q^{94} +10.0148 q^{95} +(-2.24704 - 5.19142i) q^{96} -5.71259i q^{97} +(-14.6299 - 17.0203i) q^{98} +3.05580 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 $

$2$	−0.921850	−	1.07247i	−0.651846	−	0.758351i
$2$	−0.921850	−	1.07247i	−0.651846	−	0.758351i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.300386	+	1.97731i	−0.150193	+	0.988657i
$5$		−	1.54735i		−	0.691995i	−0.938235	−	0.345998i	$-0.887540\pi$
$5$		−	1.54735i		−	0.691995i	0.938235	−	0.345998i	$-0.112460\pi$
$6$	0.921850	+	1.07247i	0.376344	+	0.437834i
$7$	4.78228			1.80753			0.903766	−	0.428027i	$-0.140791\pi$
$7$	4.78228			1.80753			0.903766	+	0.428027i	$0.140791\pi$
$8$	2.39752	−	1.50063i	0.847652	−	0.530553i
$9$	1.00000			0.333333
$10$	−1.65949	+	1.42642i	−0.524776	+	0.451075i
$11$	3.05580			0.921357			0.460678	−	0.887567i	$-0.347606\pi$
$11$	3.05580			0.921357			0.460678	+	0.887567i	$0.347606\pi$
$12$	0.300386	−	1.97731i	0.0867140	−	0.570801i
$13$			3.50455i			0.971988i	0.873962	+	0.485994i	$0.161542\pi$
$13$			3.50455i			0.971988i	−0.873962	+	0.485994i	$0.838458\pi$
$14$	−4.40854	−	5.12886i	−1.17823	−	1.37074i
$15$			1.54735i			0.399524i
$16$	−3.81954	−	1.18791i	−0.954884	−	0.296979i
$17$	−4.48195			−1.08703			−0.543516	−	0.839399i	$-0.682907\pi$
$17$	−4.48195			−1.08703			−0.543516	+	0.839399i	$0.682907\pi$
$18$	−0.921850	−	1.07247i	−0.217282	−	0.252784i
$19$			6.47223i			1.48483i	0.669940	+	0.742415i	$0.266320\pi$
$19$			6.47223i			1.48483i	−0.669940	+	0.742415i	$0.733680\pi$
$20$	3.05959	+	0.464802i	0.684146	+	0.103933i
$21$	−4.78228			−1.04358
$22$	−2.81698	−	3.27725i	−0.600583	−	0.698712i
$23$			5.90022i			1.23028i	0.788418	+	0.615140i	$0.210901\pi$
$23$			5.90022i			1.23028i	−0.788418	+	0.615140i	$0.789099\pi$
$24$	−2.39752	+	1.50063i	−0.489392	+	0.306315i
$25$	2.60571			0.521142
$26$	3.75853	−	3.23067i	0.737108	−	0.633587i
$27$	−1.00000			−0.192450
$28$	−1.43653	+	9.45607i	−0.271479	+	1.78703i
$29$	5.56432			1.03327			0.516634	−	0.856207i	$-0.327185\pi$
$29$	5.56432			1.03327			0.516634	+	0.856207i	$0.327185\pi$
$30$	1.65949	−	1.42642i	0.302979	−	0.260428i
$31$	−8.11655			−1.45777			−0.728887	−	0.684634i	$-0.759962\pi$
$31$	−8.11655			−1.45777			−0.728887	+	0.684634i	$0.759962\pi$
$32$	2.24704	+	5.19142i	0.397223	+	0.917722i
$33$	−3.05580			−0.531946
$34$	4.13168	+	4.80676i	0.708578	+	0.824352i
$35$		−	7.39986i		−	1.25080i
$36$	−0.300386	+	1.97731i	−0.0500643	+	0.329552i
$37$	2.86229			0.470558			0.235279	−	0.971928i	$-0.424400\pi$
$37$	2.86229			0.470558			0.235279	+	0.971928i	$0.424400\pi$
$38$	6.94127	−	5.96642i	1.12602	−	0.967881i
$39$		−	3.50455i		−	0.561178i
$40$	−2.32200	−	3.70980i	−0.367140	−	0.586571i
$41$		−	5.82224i		−	0.909282i	−0.890675	−	0.454641i	$-0.849768\pi$
$41$		−	5.82224i		−	0.909282i	0.890675	−	0.454641i	$-0.150232\pi$
$42$	4.40854	+	5.12886i	0.680253	+	0.791400i
$43$	8.69388			1.32580			0.662902	−	0.748706i	$-0.269324\pi$
$43$	8.69388			1.32580			0.662902	+	0.748706i	$0.269324\pi$
$44$	−0.917918	+	6.04227i	−0.138381	+	0.910906i
$45$		−	1.54735i		−	0.230665i
$46$	6.32781	−	5.43911i	0.932984	−	0.801953i
$47$		−	3.02486i		−	0.441221i	−0.975362	−	0.220611i	$-0.929195\pi$
$47$		−	3.02486i		−	0.441221i	0.975362	−	0.220611i	$-0.0708050\pi$
$48$	3.81954	+	1.18791i	0.551303	+	0.171461i
$49$	15.8702			2.26717
$50$	−2.40207	−	2.79455i	−0.339705	−	0.395209i
$51$	4.48195			0.627598
$52$	−6.92960	−	1.05272i	−0.960962	−	0.145986i
$53$		−	5.29439i		−	0.727241i	−0.931547	−	0.363620i	$-0.881541\pi$
$53$		−	5.29439i		−	0.727241i	0.931547	−	0.363620i	$-0.118459\pi$
$54$	0.921850	+	1.07247i	0.125448	+	0.145945i
$55$		−	4.72838i		−	0.637575i
$56$	11.4656	−	7.17644i	1.53216	−	0.958992i
$57$		−	6.47223i		−	0.857267i
$58$	−5.12946	−	5.96756i	−0.673531	−	0.783580i
$59$			14.0544i			1.82973i	0.403760	+	0.914865i	$0.367703\pi$
$59$			14.0544i			1.82973i	−0.403760	+	0.914865i	$0.632297\pi$
$60$	−3.05959	−	0.464802i	−0.394992	−	0.0600057i
$61$		−	0.366956i		−	0.0469839i	−0.999724	−	0.0234919i	$-0.992522\pi$
$61$		−	0.366956i		−	0.0469839i	0.999724	−	0.0234919i	$-0.00747840\pi$
$62$	7.48224	+	8.70476i	0.950245	+	1.10551i
$63$	4.78228			0.602511
$64$	3.49622	−	7.19559i	0.437027	−	0.899448i
$65$	5.42277			0.672611
$66$	2.81698	+	3.27725i	0.346747	+	0.403402i
$67$	−2.49611	+	7.79547i	−0.304949	+	0.952369i
$67$	−2.49611	+	7.79547i	−0.304949	+	0.952369i
$68$	1.34631	−	8.86222i	0.163265	−	1.07470i
$69$		−	5.90022i		−	0.710303i
$70$	−7.93613	+	6.82156i	−0.948549	+	0.815332i
$71$		−	4.06493i		−	0.482418i	−0.970473	−	0.241209i	$-0.922456\pi$
$71$		−	4.06493i		−	0.482418i	0.970473	−	0.241209i	$-0.0775440\pi$
$72$	2.39752	−	1.50063i	0.282551	−	0.176851i
$73$	−14.7237			−1.72328			−0.861638	−	0.507523i	$-0.830561\pi$
$73$	−14.7237			−1.72328			−0.861638	+	0.507523i	$0.830561\pi$
$74$	−2.63860	−	3.06973i	−0.306732	−	0.356848i
$75$	−2.60571			−0.300882
$76$	−12.7976	−	1.94417i	−1.46799	−	0.223011i
$77$	14.6137			1.66538
$78$	−3.75853	+	3.23067i	−0.425570	+	0.365801i
$79$	12.4188			1.39722			0.698611	−	0.715502i	$-0.253802\pi$
$79$	12.4188			1.39722			0.698611	+	0.715502i	$0.253802\pi$
$80$	−1.83812	+	5.91016i	−0.205508	+	0.660775i
$81$	1.00000			0.111111
$82$	−6.24418	+	5.36723i	−0.689555	+	0.592712i
$83$		−	7.10690i		−	0.780084i	−0.920797	−	0.390042i	$-0.872460\pi$
$83$		−	7.10690i		−	0.780084i	0.920797	−	0.390042i	$-0.127540\pi$
$84$	1.43653	−	9.45607i	0.156738	−	1.03174i
$85$			6.93514i			0.752221i
$86$	−8.01445	−	9.32393i	−0.864221	−	1.00543i
$87$	−5.56432			−0.596557
$88$	7.32633	−	4.58562i	0.780990	−	0.488829i
$89$	4.89866			0.519257			0.259628	−	0.965709i	$-0.416400\pi$
$89$	4.89866			0.519257			0.259628	+	0.965709i	$0.416400\pi$
$90$	−1.65949	+	1.42642i	−0.174925	+	0.150358i
$91$			16.7598i			1.75690i
$92$	−11.6666	−	1.77234i	−1.21632	−	0.184779i
$93$	8.11655			0.841647
$94$	−3.24407	+	2.78847i	−0.334601	+	0.287608i
$95$	10.0148			1.02750
$96$	−2.24704	−	5.19142i	−0.229337	−	0.529847i
$97$		−	5.71259i		−	0.580026i	−0.957023	−	0.290013i	$-0.906340\pi$
$97$		−	5.71259i		−	0.580026i	0.957023	−	0.290013i	$-0.0936596\pi$
$98$	−14.6299	−	17.0203i	−1.47785	−	1.71931i
$99$	3.05580			0.307119
$100$	−0.782719	+	5.15231i	−0.0782719	+	0.515231i
$101$			0.0467073i			0.00464755i	0.999997	+	0.00232378i	$0.000739682\pi$
$101$			0.0467073i			0.00464755i	−0.999997	+	0.00232378i	$0.999260\pi$
$102$	−4.13168	−	4.80676i	−0.409098	−	0.475940i
$103$		−	18.4162i		−	1.81460i	−0.420482	−	0.907301i	$-0.638139\pi$
$103$		−	18.4162i		−	1.81460i	0.420482	−	0.907301i	$-0.361861\pi$
$104$	5.25904	+	8.40224i	0.515691	+	0.823907i
$105$			7.39986i			0.722152i
$106$	−5.67808	+	4.88063i	−0.551504	+	0.474049i
$107$			11.8686i			1.14738i	0.819072	+	0.573691i	$0.194489\pi$
$107$			11.8686i			1.14738i	−0.819072	+	0.573691i	$0.805511\pi$
$108$	0.300386	−	1.97731i	0.0289047	−	0.190267i
$109$			7.02149i			0.672536i	0.941766	+	0.336268i	$0.109165\pi$
$109$			7.02149i			0.672536i	−0.941766	+	0.336268i	$0.890835\pi$
$110$	−5.07105	+	4.35886i	−0.483506	+	0.415601i
$111$	−2.86229			−0.271677
$112$	−18.2661	−	5.68094i	−1.72598	−	0.536799i
$113$			3.48144i			0.327506i	0.986501	+	0.163753i	$0.0523600\pi$
$113$			3.48144i			0.327506i	−0.986501	+	0.163753i	$0.947640\pi$
$114$	−6.94127	+	5.96642i	−0.650110	+	0.558806i
$115$	9.12969			0.851348
$116$	−1.67144	+	11.0024i	−0.155190	+	1.02155i
$117$			3.50455i			0.323996i
$118$	15.0730	−	12.9561i	1.38758	−	1.19270i
$119$	−21.4339			−1.96485
$120$	2.32200	+	3.70980i	0.211969	+	0.338657i
$121$	−1.66211			−0.151101
$122$	−0.393549	+	0.338278i	−0.0356303	+	0.0306263i
$123$			5.82224i			0.524974i
$124$	2.43810	−	16.0490i	0.218948	−	1.44124i
$125$		−	11.7687i		−	1.05262i
$126$	−4.40854	−	5.12886i	−0.392744	−	0.456915i
$127$		−	16.7166i		−	1.48336i	−0.670756	−	0.741678i	$-0.734030\pi$
$127$		−	16.7166i		−	1.48336i	0.670756	−	0.741678i	$-0.265970\pi$
$128$	−10.9400	+	2.88366i	−0.966972	+	0.254882i
$129$	−8.69388			−0.765454
$130$	−4.99897	−	5.81576i	−0.438439	−	0.510076i
$131$		−	13.6516i		−	1.19274i	−0.802708	−	0.596372i	$-0.796608\pi$
$131$		−	13.6516i		−	1.19274i	0.802708	−	0.596372i	$-0.203392\pi$
$132$	0.917918	−	6.04227i	0.0798945	−	0.525912i
$133$			30.9520i			2.68388i
$134$	10.6615	−	4.50925i	0.921010	−	0.389540i
$135$			1.54735i			0.133175i
$136$	−10.7456	+	6.72575i	−0.921425	+	0.576728i
$137$		−	18.2998i		−	1.56346i	−0.623616	−	0.781731i	$-0.714337\pi$
$137$		−	18.2998i		−	1.56346i	0.623616	−	0.781731i	$-0.285663\pi$
$138$	−6.32781	+	5.43911i	−0.538659	+	0.463008i
$139$	−0.810802			−0.0687713			−0.0343857	−	0.999409i	$-0.510947\pi$
$139$	−0.810802			−0.0687713			−0.0343857	+	0.999409i	$0.510947\pi$
$140$	14.6318	+	2.22281i	1.23662	+	0.187862i
$141$			3.02486i			0.254739i
$142$	−4.35952	+	3.74725i	−0.365843	+	0.314463i
$143$			10.7092i			0.895548i
$144$	−3.81954	−	1.18791i	−0.318295	−	0.0989929i
$145$		−	8.60994i		−	0.715016i
$146$	13.5730	+	15.7907i	1.12331	+	1.30685i
$147$	−15.8702			−1.30895
$148$	−0.859793	+	5.65965i	−0.0706746	+	0.465220i
$149$	5.89971			0.483323			0.241662	−	0.970361i	$-0.422308\pi$
$149$	5.89971			0.483323			0.241662	+	0.970361i	$0.422308\pi$
$150$	2.40207	+	2.79455i	0.196129	+	0.228174i
$151$			14.6810i			1.19473i	0.801971	+	0.597363i	$0.203785\pi$
$151$			14.6810i			1.19473i	−0.801971	+	0.597363i	$0.796215\pi$
$152$	9.71242	+	15.5173i	0.787781	+	1.25862i
$153$	−4.48195			−0.362344
$154$	−13.4716	−	15.6727i	−1.08557	−	1.26294i
$155$			12.5591i			1.00877i
$156$	6.92960	+	1.05272i	0.554812	+	0.0842850i
$157$	−3.07058			−0.245059			−0.122529	−	0.992465i	$-0.539101\pi$
$157$	−3.07058			−0.245059			−0.122529	+	0.992465i	$0.539101\pi$
$158$	−11.4482	−	13.3188i	−0.910773	−	1.05958i
$159$			5.29439i			0.419873i
$160$	8.03294	−	3.47695i	0.635059	−	0.274877i
$161$			28.2165i			2.22377i
$162$	−0.921850	−	1.07247i	−0.0724274	−	0.0842612i
$163$		−	23.3234i		−	1.82683i	−0.407033	−	0.913414i	$-0.633436\pi$
$163$		−	23.3234i		−	1.82683i	0.407033	−	0.913414i	$-0.366564\pi$
$164$	11.5124	+	1.74892i	0.898967	+	0.136568i
$165$			4.72838i			0.368104i
$166$	−7.62194	+	6.55150i	−0.591578	+	0.508495i
$167$			10.8381i			0.838675i	0.907830	+	0.419337i	$0.137738\pi$
$167$			10.8381i			0.838675i	−0.907830	+	0.419337i	$0.862262\pi$
$168$	−11.4656	+	7.17644i	−0.884592	+	0.553674i
$169$	0.718110			0.0552392
$170$	7.43773	−	6.39316i	0.570448	−	0.490333i
$171$			6.47223i			0.494943i
$172$	−2.61152	+	17.1905i	−0.199127	+	1.31077i
$173$	14.4691			1.10006			0.550031	−	0.835144i	$-0.314616\pi$
$173$	14.4691			1.10006			0.550031	+	0.835144i	$0.314616\pi$
$174$	5.12946	+	5.96756i	0.388864	+	0.452400i
$175$	12.4612			0.941982
$176$	−11.6717	−	3.63002i	−0.879789	−	0.273623i
$177$		−	14.0544i		−	1.05640i
$178$	−4.51583	−	5.25367i	−0.338476	−	0.393779i
$179$	−8.10870			−0.606073			−0.303036	−	0.952979i	$-0.598000\pi$
$179$	−8.10870			−0.606073			−0.303036	+	0.952979i	$0.598000\pi$
$180$	3.05959	+	0.464802i	0.228049	+	0.0346443i
$181$	6.85919			0.509840			0.254920	−	0.966962i	$-0.417951\pi$
$181$	6.85919			0.509840			0.254920	+	0.966962i	$0.417951\pi$
$182$	17.9743	−	15.4500i	1.33235	−	1.14523i
$183$			0.366956i			0.0271262i
$184$	8.85405	+	14.1459i	0.652729	+	1.04285i
$185$		−	4.42897i		−	0.325624i
$186$	−7.48224	−	8.70476i	−0.548624	−	0.638264i
$187$	−13.6959			−1.00154
$188$	5.98110	+	0.908626i	0.436216	+	0.0662684i
$189$	−4.78228			−0.347860
$190$	−9.23213	−	10.7406i	−0.669769	−	0.779203i
$191$	−23.6446			−1.71086			−0.855432	−	0.517916i	$-0.826708\pi$
$191$	−23.6446			−1.71086			−0.855432	+	0.517916i	$0.826708\pi$
$192$	−3.49622	+	7.19559i	−0.252318	+	0.519297i
$193$	4.17460			0.300494			0.150247	−	0.988648i	$-0.451993\pi$
$193$	4.17460			0.300494			0.150247	+	0.988648i	$0.451993\pi$
$194$	−6.12658	+	5.26615i	−0.439863	+	0.378087i
$195$	−5.42277			−0.388332
$196$	−4.76719	+	31.3804i	−0.340514	+	2.24146i
$197$		−	0.313467i		−	0.0223336i	−0.999938	−	0.0111668i	$-0.996445\pi$
$197$		−	0.313467i		−	0.0223336i	0.999938	−	0.0111668i	$-0.00355458\pi$
$198$	−2.81698	−	3.27725i	−0.200194	−	0.232904i
$199$		−	12.6145i		−	0.894220i	−0.894479	−	0.447110i	$-0.852453\pi$
$199$		−	12.6145i		−	0.894220i	0.894479	−	0.447110i	$-0.147547\pi$
$200$	6.24725	−	3.91021i	0.441747	−	0.276494i
$201$	2.49611	−	7.79547i	0.176062	−	0.549850i
$202$	0.0500922	−	0.0430571i	0.00352448	−	0.00302949i
$203$	26.6101			1.86766
$204$	−1.34631	+	8.86222i	−0.0942609	+	0.620479i
$205$	−9.00904			−0.629219
$206$	−19.7508	+	16.9770i	−1.37611	+	1.18284i
$207$			5.90022i			0.410093i
$208$	4.16311	−	13.3858i	0.288660	−	0.928136i
$209$			19.7778i			1.36806i
$210$	7.93613	−	6.82156i	0.547645	−	0.470732i
$211$			20.0804i			1.38239i	0.722667	+	0.691196i	$0.242916\pi$
$211$			20.0804i			1.38239i	−0.722667	+	0.691196i	$0.757084\pi$
$212$	10.4687	+	1.59036i	0.718991	+	0.109226i
$213$			4.06493i			0.278524i
$214$	12.7287	−	10.9411i	0.870119	−	0.747917i
$215$		−	13.4525i		−	0.917451i
$216$	−2.39752	+	1.50063i	−0.163131	+	0.102105i
$217$	−38.8156			−2.63498
$218$	7.53034	−	6.47276i	0.510019	−	0.438390i
$219$	14.7237			0.994934
$220$	9.34949	+	1.42034i	0.630343	+	0.0957593i
$221$		−	15.7072i		−	1.05658i
$222$	2.63860	+	3.06973i	0.177092	+	0.206026i
$223$			9.08725i			0.608528i	0.952588	+	0.304264i	$0.0984104\pi$
$223$			9.08725i			0.608528i	−0.952588	+	0.304264i	$0.901590\pi$
$224$	10.7460	+	24.8268i	0.717994	+	1.65881i
$225$	2.60571			0.173714
$226$	3.73374	−	3.20936i	0.248364	−	0.213483i
$227$			6.05853i			0.402119i	0.979579	+	0.201059i	$0.0644385\pi$
$227$			6.05853i			0.402119i	−0.979579	+	0.201059i	$0.935562\pi$
$228$	12.7976	+	1.94417i	0.847543	+	0.128756i
$229$			0.968935i			0.0640290i	0.999487	+	0.0320145i	$0.0101923\pi$
$229$			0.968935i			0.0640290i	−0.999487	+	0.0320145i	$0.989808\pi$
$230$	−8.41620	−	9.79133i	−0.554948	−	0.645621i
$231$	−14.6137			−0.961509
$232$	13.3406	−	8.34998i	0.875851	−	0.548203i
$233$		−	10.3828i		−	0.680202i	−0.940389	−	0.340101i	$-0.889539\pi$
$233$		−	10.3828i		−	0.680202i	0.940389	−	0.340101i	$-0.110461\pi$
$234$	3.75853	−	3.23067i	0.245703	−	0.211196i
$235$	−4.68052			−0.305323
$236$	−27.7900	−	4.22175i	−1.80897	−	0.274813i
$237$	−12.4188			−0.806686
$238$	19.7589	+	22.9873i	1.28078	+	1.49004i
$239$	−14.1843			−0.917509			−0.458754	−	0.888563i	$-0.651704\pi$
$239$	−14.1843			−0.917509			−0.458754	+	0.888563i	$0.651704\pi$
$240$	1.83812	−	5.91016i	0.118650	−	0.381499i
$241$	−1.62279			−0.104533			−0.0522664	−	0.998633i	$-0.516645\pi$
$241$	−1.62279			−0.104533			−0.0522664	+	0.998633i	$0.516645\pi$
$242$	1.53222	+	1.78257i	0.0984948	+	0.114588i
$243$	−1.00000			−0.0641500
$244$	0.725587	+	0.110228i	0.0464509	+	0.00705665i
$245$		−	24.5568i		−	1.56887i
$246$	6.24418	−	5.36723i	0.398115	−	0.342202i
$247$	−22.6823			−1.44324
$248$	−19.4596	+	12.1799i	−1.23569	+	0.773427i
$249$			7.10690i			0.450382i
$250$	−12.6216	+	10.8490i	−0.798258	+	0.686149i
$251$	−13.1758			−0.831648			−0.415824	−	0.909445i	$-0.636507\pi$
$251$	−13.1758			−0.831648			−0.415824	+	0.909445i	$0.636507\pi$
$252$	−1.43653	+	9.45607i	−0.0904929	+	0.595676i
$253$			18.0299i			1.13353i
$254$	−17.9280	+	15.4102i	−1.12490	+	0.966920i
$255$		−	6.93514i		−	0.434295i
$256$	13.1777	+	9.07457i	0.823607	+	0.567160i
$257$	−0.163214			−0.0101810			−0.00509052	−	0.999987i	$-0.501620\pi$
$257$	−0.163214			−0.0101810			−0.00509052	+	0.999987i	$0.501620\pi$
$258$	8.01445	+	9.32393i	0.498958	+	0.580483i
$259$	13.6883			0.850549
$260$	−1.62892	+	10.7225i	−0.101022	+	0.664982i
$261$	5.56432			0.344422
$262$	−14.6409	+	12.5847i	−0.904519	+	0.777486i
$263$			8.85763i			0.546185i	0.961988	+	0.273092i	$0.0880465\pi$
$263$			8.85763i			0.546185i	−0.961988	+	0.273092i	$0.911954\pi$
$264$	−7.32633	+	4.58562i	−0.450905	+	0.282225i
$265$	−8.19227			−0.503247
$266$	33.1951	−	28.5331i	2.03532	−	1.74948i
$267$	−4.89866			−0.299793
$268$	−14.6643	−	7.27725i	−0.895764	−	0.444529i
$269$	−14.9333			−0.910497			−0.455248	−	0.890364i	$-0.650450\pi$
$269$	−14.9333			−0.910497			−0.455248	+	0.890364i	$0.650450\pi$
$270$	1.65949	−	1.42642i	0.100993	−	0.0868093i
$271$	−0.559494			−0.0339869			−0.0169934	−	0.999856i	$-0.505409\pi$
$271$	−0.559494			−0.0339869			−0.0169934	+	0.999856i	$0.505409\pi$
$272$	17.1190	+	5.32417i	1.03799	+	0.322825i
$273$		−	16.7598i		−	1.01435i
$274$	−19.6260	+	16.8697i	−1.18565	+	1.01914i
$275$	7.96252			0.480158
$276$	11.6666	+	1.77234i	0.702245	+	0.106682i
$277$	2.73938			0.164593			0.0822966	−	0.996608i	$-0.473775\pi$
$277$	2.73938			0.164593			0.0822966	+	0.996608i	$0.473775\pi$
$278$	0.747437	+	0.869561i	0.0448283	+	0.0521528i
$279$	−8.11655			−0.485925
$280$	−11.1045	−	17.7413i	−0.663618	−	1.06025i
$281$			18.4418i			1.10014i	0.835118	+	0.550071i	$0.185399\pi$
$281$			18.4418i			1.10014i	−0.835118	+	0.550071i	$0.814601\pi$
$282$	3.24407	−	2.78847i	0.193182	−	0.166051i
$283$		−	5.42691i		−	0.322596i	−0.986906	−	0.161298i	$-0.948432\pi$
$283$		−	5.42691i		−	0.322596i	0.986906	−	0.161298i	$-0.0515681\pi$
$284$	8.03764	+	1.22105i	0.476946	+	0.0724559i
$285$	−10.0148			−0.593225
$286$	11.4853	−	9.87227i	0.679140	−	0.583760i
$287$		−	27.8436i		−	1.64356i
$288$	2.24704	+	5.19142i	0.132408	+	0.305907i
$289$	3.08787			0.181639
$290$	−9.23390	+	7.93707i	−0.542233	+	0.466081i
$291$			5.71259i			0.334878i
$292$	4.42279	−	29.1133i	0.258824	−	1.70373i
$293$	−13.8229			−0.807540			−0.403770	−	0.914860i	$-0.632300\pi$
$293$	−13.8229			−0.807540			−0.403770	+	0.914860i	$0.632300\pi$
$294$	14.6299	+	17.0203i	0.853236	+	0.992646i
$295$	21.7471			1.26616
$296$	6.86241	−	4.29525i	0.398869	−	0.249656i
$297$	−3.05580			−0.177315
$298$	−5.43865	−	6.32726i	−0.315052	−	0.366529i
$299$	−20.6776			−1.19582
$300$	0.782719	−	5.15231i	0.0451903	−	0.297469i
$301$	41.5766			2.39644
$302$	15.7450	−	13.5337i	0.906022	−	0.778777i
$303$		−	0.0467073i		−	0.00268327i
$304$	7.68845	−	24.7209i	0.440963	−	1.41784i
$305$	−0.567809			−0.0325126
$306$	4.13168	+	4.80676i	0.236193	+	0.274784i
$307$		−	1.98977i		−	0.113562i	−0.998387	−	0.0567811i	$-0.981916\pi$
$307$		−	1.98977i		−	0.113562i	0.998387	−	0.0567811i	$-0.0180837\pi$
$308$	−4.38974	+	28.8958i	−0.250129	+	1.64649i
$309$			18.4162i			1.04766i
$310$	13.4693	−	11.5776i	0.765005	−	0.657565i
$311$	11.1604			0.632850			0.316425	−	0.948618i	$-0.397518\pi$
$311$	11.1604			0.632850			0.316425	+	0.948618i	$0.397518\pi$
$312$	−5.25904	−	8.40224i	−0.297734	−	0.475683i
$313$		−	13.7215i		−	0.775582i	−0.921747	−	0.387791i	$-0.873238\pi$
$313$		−	13.7215i		−	0.775582i	0.921747	−	0.387791i	$-0.126762\pi$
$314$	2.83061	+	3.29310i	0.159741	+	0.185841i
$315$		−	7.39986i		−	0.416935i
$316$	−3.73043	+	24.5558i	−0.209853	+	1.38137i
$317$	−6.57889			−0.369507			−0.184754	−	0.982785i	$-0.559149\pi$
$317$	−6.57889			−0.369507			−0.184754	+	0.982785i	$0.559149\pi$
$318$	5.67808	−	4.88063i	0.318411	−	0.273692i
$319$	17.0034			0.952008
$320$	−11.1341	−	5.40986i	−0.622414	−	0.302421i
$321$		−	11.8686i		−	0.662442i
$322$	30.2614	−	26.0114i	1.68640	−	1.44956i
$323$		−	29.0082i		−	1.61406i
$324$	−0.300386	+	1.97731i	−0.0166881	+	0.109851i
$325$			9.13185i			0.506544i
$326$	−25.0136	+	21.5006i	−1.38538	+	1.19081i
$327$		−	7.02149i		−	0.388289i
$328$	−8.73704	−	13.9590i	−0.482422	−	0.770754i
$329$		−	14.4657i		−	0.797522i
$330$	5.07105	−	4.35886i	0.279152	−	0.239947i
$331$	5.83274			0.320596			0.160298	−	0.987069i	$-0.448754\pi$
$331$	5.83274			0.320596			0.160298	+	0.987069i	$0.448754\pi$
$332$	14.0526	+	2.13481i	0.771235	+	0.117163i
$333$	2.86229			0.156853
$334$	11.6235	−	9.99107i	0.636010	−	0.546687i
$335$	12.0623	+	3.86236i	0.659035	+	0.211023i
$336$	18.2661	+	5.68094i	0.996497	+	0.309921i
$337$		−	32.0283i		−	1.74469i	−0.488889	−	0.872346i	$-0.662598\pi$
$337$		−	32.0283i		−	1.74469i	0.488889	−	0.872346i	$-0.337402\pi$
$338$	−0.661990	−	0.770152i	−0.0360075	−	0.0418907i
$339$		−	3.48144i		−	0.189086i
$340$	−13.7129	−	2.08322i	−0.743689	−	0.112978i
$341$	−24.8025			−1.34313
$342$	6.94127	−	5.96642i	0.375341	−	0.322627i
$343$	42.4198			2.29046
$344$	20.8438	−	13.0463i	1.12382	−	0.703410i
$345$	−9.12969			−0.491526
$346$	−13.3383	−	15.5176i	−0.717071	−	0.834233i
$347$	−30.8069			−1.65380			−0.826900	−	0.562349i	$-0.809898\pi$
$347$	−30.8069			−1.65380			−0.826900	+	0.562349i	$0.809898\pi$
$348$	1.67144	−	11.0024i	0.0895987	−	0.589790i
$349$	20.4980			1.09723			0.548617	−	0.836074i	$-0.315154\pi$
$349$	20.4980			1.09723			0.548617	+	0.836074i	$0.315154\pi$
$350$	−11.4874	−	13.3643i	−0.614027	−	0.714353i
$351$		−	3.50455i		−	0.187059i
$352$	6.86648	+	15.8639i	0.365985	+	0.845549i
$353$		−	3.46688i		−	0.184523i	−0.995735	−	0.0922616i	$-0.970590\pi$
$353$		−	3.46688i		−	0.184523i	0.995735	−	0.0922616i	$-0.0294096\pi$
$354$	−15.0730	+	12.9561i	−0.801118	+	0.688607i
$355$	−6.28986			−0.333831
$356$	−1.47149	+	9.68619i	−0.0779888	+	0.513367i
$357$	21.4339			1.13440
$358$	7.47501	+	8.69634i	0.395066	+	0.459616i
$359$		−	10.6674i		−	0.563005i	−0.959560	−	0.281503i	$-0.909167\pi$
$359$		−	10.6674i		−	0.563005i	0.959560	−	0.281503i	$-0.0908328\pi$
$360$	−2.32200	−	3.70980i	−0.122380	−	0.195524i
$361$	−22.8897			−1.20472
$362$	−6.32314	−	7.35628i	−0.332337	−	0.386637i
$363$	1.66211			0.0872384
$364$	−33.1393	−	5.03440i	−1.73697	−	0.263874i
$365$			22.7827i			1.19250i
$366$	0.393549	−	0.338278i	0.0205711	−	0.0176821i
$367$	8.98002			0.468753			0.234377	−	0.972146i	$-0.424695\pi$
$367$	8.98002			0.468753			0.234377	+	0.972146i	$0.424695\pi$
$368$	7.00895	−	22.5361i	0.365367	−	1.17477i
$369$		−	5.82224i		−	0.303094i
$370$	−4.74994	+	4.08284i	−0.246937	+	0.212257i
$371$		−	25.3193i		−	1.31451i
$372$	−2.43810	+	16.0490i	−0.126409	+	0.832100i
$373$		−	3.14024i		−	0.162595i	−0.996690	−	0.0812977i	$-0.974094\pi$
$373$		−	3.14024i		−	0.162595i	0.996690	−	0.0812977i	$-0.0259065\pi$
$374$	12.6256	+	14.6885i	0.652853	+	0.759523i
$375$			11.7687i			0.607732i
$376$	−4.53920	−	7.25217i	−0.234091	−	0.374002i
$377$			19.5004i			1.00432i
$378$	4.40854	+	5.12886i	0.226751	+	0.263800i
$379$	16.5187			0.848510			0.424255	−	0.905543i	$-0.360536\pi$
$379$	16.5187			0.848510			0.424255	+	0.905543i	$0.360536\pi$
$380$	−3.00830	+	19.8024i	−0.154323	+	1.01584i
$381$			16.7166i			0.856416i
$382$	21.7968	+	25.3581i	1.11522	+	1.29744i
$383$	−18.5644			−0.948597			−0.474298	−	0.880364i	$-0.657298\pi$
$383$	−18.5644			−0.948597			−0.474298	+	0.880364i	$0.657298\pi$
$384$	10.9400	−	2.88366i	0.558282	−	0.147156i
$385$		−	22.6124i		−	1.15244i
$386$	−3.84835	−	4.47713i	−0.195876	−	0.227880i
$387$	8.69388			0.441935
$388$	11.2956	+	1.71598i	0.573446	+	0.0871158i
$389$	−30.0217			−1.52216			−0.761081	−	0.648657i	$-0.775331\pi$
$389$	−30.0217			−1.52216			−0.761081	+	0.648657i	$0.775331\pi$
$390$	4.99897	+	5.81576i	0.253133	+	0.294492i
$391$		−	26.4445i		−	1.33735i
$392$	38.0492	−	23.8153i	1.92177	−	1.20286i
$393$			13.6516i			0.688631i
$394$	−0.336184	+	0.288970i	−0.0169367	+	0.0145581i
$395$		−	19.2162i		−	0.966871i
$396$	−0.917918	+	6.04227i	−0.0461271	+	0.303635i
$397$	3.19630			0.160418			0.0802088	−	0.996778i	$-0.474441\pi$
$397$	3.19630			0.160418			0.0802088	+	0.996778i	$0.474441\pi$
$398$	−13.5287	+	11.6287i	−0.678133	+	0.582894i
$399$		−	30.9520i		−	1.54954i
$400$	−9.95261	−	3.09536i	−0.497631	−	0.154768i
$401$		−	35.3660i		−	1.76609i	−0.469284	−	0.883047i	$-0.655488\pi$
$401$		−	35.3660i		−	1.76609i	0.469284	−	0.883047i	$-0.344512\pi$
$402$	−10.6615	+	4.50925i	−0.531745	+	0.224901i
$403$		−	28.4449i		−	1.41694i
$404$	−0.0923550	−	0.0140302i	−0.00459483	−	0.000698030i
$405$		−	1.54735i		−	0.0768884i
$406$	−24.5305	−	28.5386i	−1.21743	−	1.41635i
$407$	8.74658			0.433552
$408$	10.7456	−	6.72575i	0.531985	−	0.332974i
$409$			18.5775i			0.918598i	0.888282	+	0.459299i	$0.151899\pi$
$409$			18.5775i			0.918598i	−0.888282	+	0.459299i	$0.848101\pi$
$410$	8.30498	+	9.66193i	0.410154	+	0.477169i
$411$			18.2998i			0.902665i
$412$	36.4146	+	5.53197i	1.79402	+	0.272540i
$413$			67.2122i			3.30730i
$414$	6.32781	−	5.43911i	0.310995	−	0.267318i
$415$	−10.9969			−0.539815
$416$	−18.1936	+	7.87485i	−0.892015	+	0.386096i
$417$	0.810802			0.0397051
$418$	21.2111	−	18.2322i	1.03747	−	0.891764i
$419$		−	7.83168i		−	0.382603i	−0.981531	−	0.191301i	$-0.938729\pi$
$419$		−	7.83168i		−	0.382603i	0.981531	−	0.191301i	$-0.0612708\pi$
$420$	−14.6318	−	2.22281i	−0.713960	−	0.108462i
$421$	−2.30475			−0.112327			−0.0561633	−	0.998422i	$-0.517887\pi$
$421$	−2.30475			−0.112327			−0.0561633	+	0.998422i	$0.517887\pi$
$422$	21.5357	−	18.5111i	1.04834	−	0.901108i
$423$		−	3.02486i		−	0.147074i
$424$	−7.94493	−	12.6934i	−0.385840	−	0.616447i
$425$	−11.6787			−0.566499
$426$	4.35952	−	3.74725i	0.211219	−	0.181555i
$427$		−	1.75489i		−	0.0849249i
$428$	−23.4680	−	3.56517i	−1.13437	−	0.172329i
$429$		−	10.7092i		−	0.517045i
$430$	−14.4274	+	12.4012i	−0.695750	+	0.598037i
$431$			20.9734i			1.01025i	0.863045	+	0.505127i	$0.168554\pi$
$431$			20.9734i			1.01025i	−0.863045	+	0.505127i	$0.831446\pi$
$432$	3.81954	+	1.18791i	0.183768	+	0.0571536i
$433$			20.8670i			1.00280i	0.865214	+	0.501402i	$0.167182\pi$
$433$			20.8670i			1.00280i	−0.865214	+	0.501402i	$0.832818\pi$
$434$	35.7822	+	41.6286i	1.71760	+	1.99824i
$435$			8.60994i			0.412815i
$436$	−13.8837	−	2.10916i	−0.664908	−	0.101010i
$437$	−38.1875			−1.82676
$438$	−13.5730	−	15.7907i	−0.648544	−	0.754510i
$439$			31.6980i			1.51286i	0.654074	+	0.756431i	$0.273059\pi$
$439$			31.6980i			1.51286i	−0.654074	+	0.756431i	$0.726941\pi$
$440$	−7.09555	−	11.3364i	−0.338267	−	0.540441i
$441$	15.8702			0.755724
$442$	−16.8455	+	14.4797i	−0.801260	+	0.688729i
$443$	21.5765			1.02513			0.512565	−	0.858648i	$-0.328695\pi$
$443$	21.5765			1.02513			0.512565	+	0.858648i	$0.328695\pi$
$444$	0.859793	−	5.65965i	0.0408040	−	0.268595i
$445$		−	7.57994i		−	0.359323i
$446$	9.74581	−	8.37708i	0.461478	−	0.396666i
$447$	−5.89971			−0.279047
$448$	16.7199	−	34.4113i	0.789940	−	1.62578i
$449$	−22.2551			−1.05028			−0.525142	−	0.851014i	$-0.675988\pi$
$449$	−22.2551			−1.05028			−0.525142	+	0.851014i	$0.675988\pi$
$450$	−2.40207	−	2.79455i	−0.113235	−	0.131736i
$451$		−	17.7916i		−	0.837773i
$452$	−6.88389	−	1.04577i	−0.323791	−	0.0491891i
$453$		−	14.6810i		−	0.689775i
$454$	6.49760	−	5.58506i	0.304947	−	0.262120i
$455$	25.9332			1.21577
$456$	−9.71242	−	15.5173i	−0.454826	−	0.726664i
$457$	30.8118			1.44131			0.720657	−	0.693291i	$-0.243840\pi$
$457$	30.8118			1.44131			0.720657	+	0.693291i	$0.243840\pi$
$458$	1.03915	−	0.893213i	0.0485565	−	0.0417371i
$459$	4.48195			0.209199
$460$	−2.74243	+	18.0523i	−0.127867	+	0.841691i
$461$	−2.05285			−0.0956107			−0.0478053	−	0.998857i	$-0.515223\pi$
$461$	−2.05285			−0.0956107			−0.0478053	+	0.998857i	$0.515223\pi$
$462$	13.4716	+	15.6727i	0.626756	+	0.729162i
$463$	36.3808			1.69076			0.845379	−	0.534167i	$-0.179375\pi$
$463$	36.3808			1.69076			0.845379	+	0.534167i	$0.179375\pi$
$464$	−21.2531	−	6.60993i	−0.986651	−	0.306858i
$465$		−	12.5591i		−	0.582416i
$466$	−11.1353	+	9.57142i	−0.515832	+	0.443387i
$467$		−	3.74702i		−	0.173392i	−0.996235	−	0.0866958i	$-0.972369\pi$
$467$		−	3.74702i		−	0.173392i	0.996235	−	0.0866958i	$-0.0276308\pi$
$468$	−6.92960	−	1.05272i	−0.320321	−	0.0486619i
$469$	−11.9371	+	37.2801i	−0.551205	+	1.72144i
$470$	4.31473	+	5.01971i	0.199024	+	0.231542i
$471$	3.07058			0.141485
$472$	21.0905	+	33.6958i	0.970769	+	1.55097i
$473$	26.5667			1.22154
$474$	11.4482	+	13.3188i	0.525835	+	0.611751i
$475$			16.8648i			0.773808i
$476$	6.43846	−	42.3816i	0.295106	−	1.94256i
$477$		−	5.29439i		−	0.242414i
$478$	13.0758	+	15.2123i	0.598075	+	0.695794i
$479$			40.6636i			1.85797i	0.370122	+	0.928983i	$0.379316\pi$
$479$			40.6636i			1.85797i	−0.370122	+	0.928983i	$0.620684\pi$
$480$	−8.03294	+	3.47695i	−0.366652	+	0.158700i
$481$			10.0311i			0.457377i
$482$	1.49597	+	1.74039i	0.0681394	+	0.0792726i
$483$		−	28.2165i		−	1.28389i
$484$	0.499276	−	3.28652i	0.0226944	−	0.149387i
$485$	−8.83937			−0.401375
$486$	0.921850	+	1.07247i	0.0418160	+	0.0486483i
$487$	−23.9829			−1.08677			−0.543384	−	0.839484i	$-0.682857\pi$
$487$	−23.9829			−1.08677			−0.543384	+	0.839484i	$0.682857\pi$
$488$	−0.550665	−	0.879784i	−0.0249274	−	0.0398260i
$489$			23.3234i			1.05472i
$490$	−26.3364	+	22.6376i	−1.18976	+	1.02266i
$491$			7.18064i			0.324058i	0.986786	+	0.162029i	$0.0518037\pi$
$491$			7.18064i			0.324058i	−0.986786	+	0.162029i	$0.948196\pi$
$492$	−11.5124	−	1.74892i	−0.519019	−	0.0788474i
$493$	−24.9390			−1.12320
$494$	20.9096	+	24.3261i	0.940769	+	1.09448i
$495$		−	4.72838i		−	0.212525i
$496$	31.0014	+	9.64177i	1.39201	+	0.432928i
$497$		−	19.4396i		−	0.871987i
$498$	7.62194	−	6.55150i	0.341548	−	0.293580i
$499$	−6.49435			−0.290727			−0.145364	−	0.989378i	$-0.546435\pi$
$499$	−6.49435			−0.290727			−0.145364	+	0.989378i	$0.546435\pi$
$500$	23.2704	+	3.53515i	1.04068	+	0.158097i
$501$		−	10.8381i		−	0.484209i
$502$	12.1461	+	14.1306i	0.542107	+	0.630681i
$503$	−9.35791			−0.417248			−0.208624	−	0.977996i	$-0.566899\pi$
$503$	−9.35791			−0.417248			−0.208624	+	0.977996i	$0.566899\pi$
$504$	11.4656	−	7.17644i	0.510719	−	0.319664i
$505$	0.0722725			0.00321609
$506$	19.3365	−	16.6208i	0.859612	−	0.738885i
$507$	−0.718110			−0.0318924
$508$	33.0539	+	5.02143i	1.46653	+	0.222790i
$509$	14.8534			0.658367			0.329184	−	0.944266i	$-0.393226\pi$
$509$	14.8534			0.658367			0.329184	+	0.944266i	$0.393226\pi$
$510$	−7.43773	+	6.39316i	−0.329348	+	0.283094i
$511$	−70.4128			−3.11488
$512$	−2.41567	−	22.4981i	−0.106759	−	0.994285i
$513$		−	6.47223i		−	0.285756i
$514$	0.150459	+	0.175043i	0.00663647	+	0.00772080i
$515$	−28.4963			−1.25570
$516$	2.61152	−	17.1905i	0.114966	−	0.756771i
$517$		−	9.24336i		−	0.406522i
$518$	−12.6185	−	14.6803i	−0.554427	−	0.645015i
$519$	−14.4691			−0.635121
$520$	13.0012	−	8.13757i	0.570140	−	0.356856i
$521$			16.2467i			0.711782i	0.934527	+	0.355891i	$0.115823\pi$
$521$			16.2467i			0.711782i	−0.934527	+	0.355891i	$0.884177\pi$
$522$	−5.12946	−	5.96756i	−0.224510	−	0.261193i
$523$		−	20.8966i		−	0.913744i	−0.889532	−	0.456872i	$-0.848970\pi$
$523$		−	20.8966i		−	0.913744i	0.889532	−	0.456872i	$-0.151030\pi$
$524$	26.9935	+	4.10074i	1.17921	+	0.179142i
$525$	−12.4612			−0.543853
$526$	9.49954	−	8.16540i	0.414200	−	0.356028i
$527$	36.3780			1.58465
$528$	11.6717	+	3.63002i	0.507946	+	0.157977i
$529$	−11.8126			−0.513589
$530$	7.55204	+	8.78597i	0.328040	+	0.381638i
$531$			14.0544i			0.609910i
$532$	−61.2018	−	9.29755i	−2.65343	−	0.403100i
$533$	20.4044			0.883811
$534$	4.51583	+	5.25367i	0.195419	+	0.227348i
$535$	18.3649			0.793984
$536$	5.71364	+	22.4356i	0.246792	+	0.969069i
$537$	8.10870			0.349916
$538$	13.7662	+	16.0155i	0.593504	+	0.690476i
$539$	48.4961			2.08888
$540$	−3.05959	−	0.464802i	−0.131664	−	0.0200019i
$541$		−	0.771147i		−	0.0331542i	−0.999863	−	0.0165771i	$-0.994723\pi$
$541$		−	0.771147i		−	0.0331542i	0.999863	−	0.0165771i	$-0.00527690\pi$
$542$	0.515770	+	0.600041i	0.0221542	+	0.0257740i
$543$	−6.85919			−0.294356
$544$	−10.0711	−	23.2677i	−0.431795	−	0.997593i
$545$	10.8647			0.465392
$546$	−17.9743	+	15.4500i	−0.769231	+	0.661198i
$547$	−40.4316			−1.72873			−0.864366	−	0.502864i	$-0.832280\pi$
$547$	−40.4316			−1.72873			−0.864366	+	0.502864i	$0.832280\pi$
$548$	36.1845	+	5.49702i	1.54573	+	0.234821i
$549$		−	0.366956i		−	0.0156613i
$550$	−7.34025	−	8.53957i	−0.312989	−	0.364128i
$551$			36.0135i			1.53423i
$552$	−8.85405	−	14.1459i	−0.376853	−	0.602089i
$553$	59.3901			2.52552
$554$	−2.52529	−	2.93790i	−0.107289	−	0.124819i
$555$			4.42897i			0.187999i
$556$	0.243554	−	1.60321i	0.0103290	−	0.0679912i
$557$	5.15579			0.218458			0.109229	−	0.994017i	$-0.465162\pi$
$557$	5.15579			0.218458			0.109229	+	0.994017i	$0.465162\pi$
$558$	7.48224	+	8.70476i	0.316748	+	0.368502i
$559$			30.4682i			1.28867i
$560$	−8.79040	+	28.2640i	−0.371462	+	1.19437i
$561$	13.6959			0.578242
$562$	19.7782	−	17.0005i	0.834295	−	0.717124i
$563$	11.8933			0.501244			0.250622	−	0.968085i	$-0.419365\pi$
$563$	11.8933			0.501244			0.250622	+	0.968085i	$0.419365\pi$
$564$	−5.98110	−	0.908626i	−0.251850	−	0.0382601i
$565$	5.38700			0.226633
$566$	−5.82020	+	5.00280i	−0.244641	+	0.210283i
$567$	4.78228			0.200837
$568$	−6.09996	−	9.74575i	−0.255949	−	0.408923i
$569$	−28.8824			−1.21081			−0.605407	−	0.795916i	$-0.706990\pi$
$569$	−28.8824			−1.21081			−0.605407	+	0.795916i	$0.706990\pi$
$570$	9.23213	+	10.7406i	0.386691	+	0.449873i
$571$		−	29.5258i		−	1.23561i	−0.786330	−	0.617807i	$-0.788021\pi$
$571$		−	29.5258i		−	1.23561i	0.786330	−	0.617807i	$-0.211979\pi$
$572$	−21.1754	−	3.21689i	−0.885389	−	0.134505i
$573$	23.6446			0.987767
$574$	−29.8614	+	25.6676i	−1.24639	+	1.07135i
$575$			15.3743i			0.641151i
$576$	3.49622	−	7.19559i	0.145676	−	0.299816i
$577$		−	11.3610i		−	0.472967i	−0.971636	−	0.236483i	$-0.924005\pi$
$577$		−	11.3610i		−	0.472967i	0.971636	−	0.236483i	$-0.0759949\pi$
$578$	−2.84655	−	3.31165i	−0.118401	−	0.137746i
$579$	−4.17460			−0.173490
$580$	17.0245	+	2.58630i	0.706906	+	0.107390i
$581$		−	33.9872i		−	1.41003i
$582$	6.12658	−	5.26615i	0.253955	−	0.218289i
$583$		−	16.1786i		−	0.670048i
$584$	−35.3003	+	22.0948i	−1.46074	+	0.914290i
$585$	5.42277			0.224204
$586$	12.7426	+	14.8246i	0.526392	+	0.612399i
$587$	−13.6819			−0.564711			−0.282356	−	0.959310i	$-0.591116\pi$
$587$	−13.6819			−0.564711			−0.282356	+	0.959310i	$0.591116\pi$
$588$	4.76719	−	31.3804i	0.196596	−	1.29411i
$589$		−	52.5321i		−	2.16455i
$590$	−20.0476	−	23.3231i	−0.825345	−	0.960197i
$591$			0.313467i			0.0128943i
$592$	−10.9326	−	3.40016i	−0.449328	−	0.139746i
$593$		−	35.0111i		−	1.43773i	−0.695147	−	0.718867i	$-0.744661\pi$
$593$		−	35.0111i		−	1.43773i	0.695147	−	0.718867i	$-0.255339\pi$
$594$	2.81698	+	3.27725i	0.115582	+	0.134467i
$595$			33.1658i			1.35966i
$596$	−1.77219	+	11.6656i	−0.0725917	+	0.477841i
$597$			12.6145i			0.516278i
$598$	19.0617	+	22.1761i	0.779489	+	0.906850i
$599$	0.821520			0.0335664			0.0167832	−	0.999859i	$-0.494657\pi$
$599$	0.821520			0.0335664			0.0167832	+	0.999859i	$0.494657\pi$
$600$	−6.24725	+	3.91021i	−0.255043	+	0.159634i
$601$	2.63598			0.107524			0.0537620	−	0.998554i	$-0.482879\pi$
$601$	2.63598			0.107524			0.0537620	+	0.998554i	$0.482879\pi$
$602$	−38.3274	−	44.5897i	−1.56211	−	1.81734i
$603$	−2.49611	+	7.79547i	−0.101650	+	0.317456i
$604$	−29.0290	−	4.40998i	−1.18117	−	0.179439i
$605$			2.57187i			0.104561i
$606$	−0.0500922	+	0.0430571i	−0.00203486	+	0.00174908i
$607$		−	7.51090i		−	0.304858i	−0.988314	−	0.152429i	$-0.951290\pi$
$607$		−	7.51090i		−	0.304858i	0.988314	−	0.152429i	$-0.0487095\pi$
$608$	−33.6000	+	14.5433i	−1.36266	+	0.589809i
$609$	−26.6101			−1.07830
$610$	0.523434	+	0.608958i	0.0211932	+	0.0246560i
$611$	10.6008			0.428862
$612$	1.34631	−	8.86222i	0.0544216	−	0.358234i
$613$	3.33725			0.134790			0.0673951	−	0.997726i	$-0.478531\pi$
$613$	3.33725			0.134790			0.0673951	+	0.997726i	$0.478531\pi$
$614$	−2.13397	+	1.83427i	−0.0861200	+	0.0740251i
$615$	9.00904			0.363280
$616$	35.0366	−	21.9297i	1.41166	−	0.883574i
$617$	−46.5581			−1.87436			−0.937179	−	0.348849i	$-0.886573\pi$
$617$	−46.5581			−1.87436			−0.937179	+	0.348849i	$0.886573\pi$
$618$	19.7508	−	16.9770i	0.794495	−	0.682914i
$619$			9.13260i			0.367070i	0.983013	+	0.183535i	$0.0587541\pi$
$619$			9.13260i			0.367070i	−0.983013	+	0.183535i	$0.941246\pi$
$620$	−24.8333	−	3.77259i	−0.997331	−	0.151511i
$621$		−	5.90022i		−	0.236768i
$622$	−10.2882	−	11.9692i	−0.412521	−	0.479922i
$623$	23.4268			0.938574
$624$	−4.16311	+	13.3858i	−0.166658	+	0.535860i
$625$	−5.18171			−0.207268
$626$	−14.7159	+	12.6491i	−0.588164	+	0.505560i
$627$		−	19.7778i		−	0.789849i
$628$	0.922358	−	6.07149i	0.0368061	−	0.242279i
$629$	−12.8287			−0.511512
$630$	−7.93613	+	6.82156i	−0.316183	+	0.271777i
$631$	−11.4976			−0.457712			−0.228856	−	0.973460i	$-0.573498\pi$
$631$	−11.4976			−0.457712			−0.228856	+	0.973460i	$0.573498\pi$
$632$	29.7743	−	18.6360i	1.18436	−	0.741300i
$633$		−	20.0804i		−	0.798125i
$634$	6.06475	+	7.05567i	0.240862	+	0.280216i
$635$	−25.8664			−1.02648
$636$	−10.4687	−	1.59036i	−0.415110	−	0.0630619i
$637$			55.6180i			2.20366i
$638$	−15.6746	−	18.2357i	−0.620563	−	0.721957i
$639$		−	4.06493i		−	0.160806i
$640$	4.46203	+	16.9281i	0.176377	+	0.669140i
$641$		−	15.6618i		−	0.618603i	−0.950964	−	0.309301i	$-0.899905\pi$
$641$		−	15.6618i		−	0.618603i	0.950964	−	0.309301i	$-0.100095\pi$
$642$	−12.7287	+	10.9411i	−0.502364	+	0.431810i
$643$		−	42.5747i		−	1.67898i	−0.543372	−	0.839492i	$-0.682853\pi$
$643$		−	42.5747i		−	1.67898i	0.543372	−	0.839492i	$-0.317147\pi$
$644$	−55.7928	−	8.47584i	−2.19855	−	0.333995i
$645$			13.4525i			0.529691i
$646$	−31.1104	+	26.7412i	−1.22402	+	1.05212i
$647$	27.1445			1.06716			0.533580	−	0.845750i	$-0.320846\pi$
$647$	27.1445			1.06716			0.533580	+	0.845750i	$0.320846\pi$
$648$	2.39752	−	1.50063i	0.0941835	−	0.0589503i
$649$			42.9474i			1.68583i
$650$	9.79364	−	8.41820i	0.384138	−	0.330189i
$651$	38.8156			1.52130
$652$	46.1176	+	7.00601i	1.80611	+	0.274377i
$653$			12.4622i			0.487684i	0.969815	+	0.243842i	$0.0784078\pi$
$653$			12.4622i			0.487684i	−0.969815	+	0.243842i	$0.921592\pi$
$654$	−7.53034	+	6.47276i	−0.294459	+	0.253105i
$655$	−21.1238			−0.825374
$656$	−6.91633	+	22.2383i	−0.270037	+	0.868259i
$657$	−14.7237			−0.574426
$658$	−15.5141	+	13.3352i	−0.604802	+	0.519862i
$659$			14.3892i			0.560523i	0.959924	+	0.280261i	$0.0904212\pi$
$659$			14.3892i			0.560523i	−0.959924	+	0.280261i	$0.909579\pi$
$660$	−9.34949	−	1.42034i	−0.363928	−	0.0552866i
$661$			24.3443i			0.946884i	0.880825	+	0.473442i	$0.156989\pi$
$661$			24.3443i			0.946884i	−0.880825	+	0.473442i	$0.843011\pi$
$662$	−5.37691	−	6.25544i	−0.208979	−	0.243124i
$663$			15.7072i			0.610018i
$664$	−10.6648	−	17.0390i	−0.413876	−	0.661240i
$665$	47.8935			1.85723
$666$	−2.63860	−	3.06973i	−0.102244	−	0.118949i
$667$			32.8307i			1.27121i
$668$	−21.4303	−	3.25560i	−0.829161	−	0.125963i
$669$		−	9.08725i		−	0.351334i
$670$	−6.97738	−	16.4970i	−0.269560	−	0.637335i
$671$		−	1.12134i		−	0.0432889i
$672$	−10.7460	−	24.8268i	−0.414534	−	0.957716i
$673$		−	20.9565i		−	0.807816i	−0.914800	−	0.403908i	$-0.867652\pi$
$673$		−	20.9565i		−	0.807816i	0.914800	−	0.403908i	$-0.132348\pi$
$674$	−34.3494	+	29.5253i	−1.32309	+	1.13727i
$675$	−2.60571			−0.100294
$676$	−0.215710	+	1.41993i	−0.00829655	+	0.0546127i
$677$			21.6203i			0.830934i	0.909608	+	0.415467i	$0.136382\pi$
$677$			21.6203i			0.830934i	−0.909608	+	0.415467i	$0.863618\pi$
$678$	−3.73374	+	3.20936i	−0.143393	+	0.123255i
$679$		−	27.3192i		−	1.04841i
$680$	10.4071	+	16.6271i	0.399093	+	0.637622i
$681$		−	6.05853i		−	0.232163i
$682$	22.8642	+	26.6000i	0.875515	+	1.01857i
$683$	−1.26213			−0.0482940			−0.0241470	−	0.999708i	$-0.507687\pi$
$683$	−1.26213			−0.0482940			−0.0241470	+	0.999708i	$0.507687\pi$
$684$	−12.7976	−	1.94417i	−0.489329	−	0.0743371i
$685$	−28.3162			−1.08191
$686$	−39.1047	−	45.4940i	−1.49303	−	1.73697i
$687$		−	0.968935i		−	0.0369672i
$688$	−33.2066	−	10.3276i	−1.26599	−	0.393736i
$689$	18.5545			0.706869
$690$	8.41620	+	9.79133i	0.320399	+	0.372749i
$691$			0.518528i			0.0197257i	0.999951	+	0.00986286i	$0.00313950\pi$
$691$			0.518528i			0.0197257i	−0.999951	+	0.00986286i	$0.996861\pi$
$692$	−4.34630	+	28.6099i	−0.165222	+	1.08758i
$693$	14.6137			0.555127
$694$	28.3993	+	33.0395i	1.07802	+	1.25416i
$695$			1.25459i			0.0475894i
$696$	−13.3406	+	8.34998i	−0.505673	+	0.316505i
$697$			26.0950i			0.988419i
$698$	−18.8961	−	21.9835i	−0.715228	−	0.832089i
$699$			10.3828i			0.392715i
$700$	−3.74318	+	24.6398i	−0.141479	+	0.931296i
$701$			46.7136i			1.76435i	0.470924	+	0.882174i	$0.343921\pi$
$701$			46.7136i			1.76435i	−0.470924	+	0.882174i	$0.656079\pi$
$702$	−3.75853	+	3.23067i	−0.141857	+	0.121934i
$703$			18.5254i			0.698699i
$704$	10.6837	−	21.9882i	0.402658	−	0.828713i
$705$	4.68052			0.176278
$706$	−3.71812	+	3.19594i	−0.139933	+	0.120281i
$707$			0.223368i			0.00840060i
$708$	27.7900	+	4.22175i	1.04441	+	0.158663i
$709$	−44.2361			−1.66132			−0.830661	−	0.556778i	$-0.812037\pi$
$709$	−44.2361			−1.66132			−0.830661	+	0.556778i	$0.812037\pi$
$710$	5.79831	+	6.74569i	0.217607	+	0.253161i
$711$	12.4188			0.465740
$712$	11.7446	−	7.35108i	0.440149	−	0.275493i
$713$		−	47.8894i		−	1.79347i
$714$	−19.7589	−	22.9873i	−0.739457	−	0.860277i
$715$	16.5709			0.619715
$716$	2.43574	−	16.0334i	0.0910279	−	0.599198i
$717$	14.1843			0.529724
$718$	−11.4405	+	9.83376i	−0.426956	+	0.366993i
$719$			11.7106i			0.436732i	0.975867	+	0.218366i	$0.0700726\pi$
$719$			11.7106i			0.436732i	−0.975867	+	0.218366i	$0.929927\pi$
$720$	−1.83812	+	5.91016i	−0.0685026	+	0.220258i
$721$		−	88.0714i		−	3.27995i
$722$	21.1009	+	24.5485i	0.785293	+	0.913602i
$723$	1.62279			0.0603521
$724$	−2.06041	+	13.5628i	−0.0765744	+	0.504056i
$725$	14.4990			0.538479
$726$	−1.53222	−	1.78257i	−0.0568660	−	0.0661573i
$727$	0.0298100			0.00110559			0.000552796	−	1.00000i	$-0.499824\pi$
$727$	0.0298100			0.00110559			0.000552796		1.00000i	$0.499824\pi$
$728$	25.1502	+	40.1819i	0.932129	+	1.48924i
$729$	1.00000			0.0370370
$730$	24.4337	−	21.0022i	0.904333	−	0.777326i
$731$	−38.9655			−1.44119
$732$	−0.725587	−	0.110228i	−0.0268185	−	0.00407416i
$733$		−	9.73688i		−	0.359640i	−0.983700	−	0.179820i	$-0.942449\pi$
$733$		−	9.73688i		−	0.359640i	0.983700	−	0.179820i	$-0.0575515\pi$
$734$	−8.27823	−	9.63081i	−0.305555	−	0.355480i
$735$			24.5568i			0.905789i
$736$	−30.6305	+	13.2580i	−1.12906	+	0.488696i
$737$	−7.62762	+	23.8214i	−0.280967	+	0.877472i
$738$	−6.24418	+	5.36723i	−0.229852	+	0.197571i
$739$	40.6562			1.49556			0.747782	−	0.663945i	$-0.231119\pi$
$739$	40.6562			1.49556			0.747782	+	0.663945i	$0.231119\pi$
$740$	8.75745	+	1.33040i	0.321930	+	0.0489065i
$741$	22.6823			0.833253
$742$	−27.1542	+	23.3406i	−0.996861	+	0.856859i
$743$			32.2166i			1.18191i	0.806704	+	0.590956i	$0.201249\pi$
$743$			32.2166i			1.18191i	−0.806704	+	0.590956i	$0.798751\pi$
$744$	19.4596	−	12.1799i	0.713423	−	0.446538i
$745$		−	9.12891i		−	0.334457i
$746$	−3.36781	+	2.89483i	−0.123304	+	0.105987i
$747$		−	7.10690i		−	0.260028i
$748$	4.11406	−	27.0811i	0.150425	−	0.990184i
$749$			56.7591i			2.07393i
$750$	12.6216	−	10.8490i	0.460875	−	0.396148i
$751$		−	18.4253i		−	0.672348i	−0.941800	−	0.336174i	$-0.890867\pi$
$751$		−	18.4253i		−	0.672348i	0.941800	−	0.336174i	$-0.109133\pi$
$752$	−3.59328	+	11.5536i	−0.131033	+	0.421315i
$753$	13.1758			0.480152
$754$	20.9136	−	17.9765i	0.761630	−	0.654665i
$755$	22.7167			0.826745
$756$	1.43653	−	9.45607i	0.0522461	−	0.343914i
$757$		−	3.11832i		−	0.113337i	−0.998393	−	0.0566687i	$-0.981952\pi$
$757$		−	3.11832i		−	0.113337i	0.998393	−	0.0566687i	$-0.0180479\pi$
$758$	−15.2278	−	17.7158i	−0.553098	−	0.643469i
$759$		−	18.0299i		−	0.654442i
$760$	24.0107	−	15.0285i	0.870959	−	0.545141i
$761$	12.0775			0.437808			0.218904	−	0.975746i	$-0.429752\pi$
$761$	12.0775			0.437808			0.218904	+	0.975746i	$0.429752\pi$
$762$	17.9280	−	15.4102i	0.649464	−	0.558252i
$763$			33.5787i			1.21563i
$764$	7.10251	−	46.7528i	0.256960	−	1.69146i
$765$			6.93514i			0.250740i
$766$	17.1136	+	19.9098i	0.618339	+	0.719370i
$767$	−49.2545			−1.77848
$768$	−13.1777	−	9.07457i	−0.475510	−	0.327450i
$769$			8.75910i			0.315861i	0.987450	+	0.157931i	$0.0504822\pi$
$769$			8.75910i			0.315861i	−0.987450	+	0.157931i	$0.949518\pi$
$770$	−24.2512	+	20.8453i	−0.873952	+	0.751212i
$771$	0.163214			0.00587802
$772$	−1.25399	+	8.25449i	−0.0451321	+	0.297085i
$773$	40.6121			1.46072			0.730359	−	0.683064i	$-0.239353\pi$
$773$	40.6121			1.46072			0.730359	+	0.683064i	$0.239353\pi$
$774$	−8.01445	−	9.32393i	−0.288074	−	0.335142i
$775$	−21.1494			−0.759708
$776$	−8.57249	−	13.6961i	−0.307734	−	0.491660i
$777$	−13.6883			−0.491065
$778$	27.6755	+	32.1974i	0.992216	+	1.15433i
$779$	37.6829			1.35013
$780$	1.62892	−	10.7225i	0.0583248	−	0.383927i
$781$		−	12.4216i		−	0.444480i
$782$	−28.3609	+	24.3778i	−1.01418	+	0.871749i
$783$	−5.56432			−0.198852
$784$	−60.6168	−	18.8525i	−2.16489	−	0.673302i
$785$			4.75125i			0.169579i
$786$	14.6409	−	12.5847i	0.522224	−	0.448882i
$787$	−44.8417			−1.59843			−0.799217	−	0.601043i	$-0.794752\pi$
$787$	−44.8417			−1.59843			−0.799217	+	0.601043i	$0.794752\pi$
$788$	0.619823	+	0.0941612i	0.0220803	+	0.00335435i
$789$		−	8.85763i		−	0.315340i
$790$	−20.6088	+	17.7144i	−0.733227	+	0.630251i
$791$			16.6492i			0.591978i
$792$	7.32633	−	4.58562i	0.260330	−	0.162943i
$793$	1.28602			0.0456678
$794$	−2.94651	−	3.42793i	−0.104568	−	0.121653i
$795$	8.19227			0.290550
$796$	24.9429	+	3.78923i	0.884077	+	0.134306i
$797$	42.9144			1.52011			0.760053	−	0.649861i	$-0.225173\pi$
$797$	42.9144			1.52011			0.760053	+	0.649861i	$0.225173\pi$
$798$	−33.1951	+	28.5331i	−1.17509	+	1.01006i
$799$			13.5573i			0.479622i
$800$	5.85513	+	13.5273i	0.207010	+	0.478264i
$801$	4.89866			0.173086
$802$	−37.9290	+	32.6022i	−1.33932	+	1.15122i
$803$	−44.9926			−1.58775
$804$	14.6643	+	7.27725i	0.517170	+	0.256649i
$805$	43.6608			1.53884
$806$	−30.5063	+	26.2219i	−1.07454	+	0.923627i
$807$	14.9333			0.525676
$808$	0.0700904	+	0.111982i	0.00246577	+	0.00393951i
$809$		−	38.3795i		−	1.34935i	−0.738115	−	0.674675i	$-0.764284\pi$
$809$		−	38.3795i		−	1.34935i	0.738115	−	0.674675i	$-0.235716\pi$
$810$	−1.65949	+	1.42642i	−0.0583084	+	0.0501194i
$811$	−36.4651			−1.28046			−0.640232	−	0.768181i	$-0.721162\pi$
$811$	−36.4651			−1.28046			−0.640232	+	0.768181i	$0.721162\pi$
$812$	−7.99331	+	52.6165i	−0.280510	+	1.84648i
$813$	0.559494			0.0196223
$814$	−8.06304	−	9.38045i	−0.282609	−	0.328785i
$815$	−36.0894			−1.26416
$816$	−17.1190	−	5.32417i	−0.599284	−	0.186383i
$817$			56.2688i			1.96860i
$818$	19.9238	−	17.1257i	0.696620	−	0.598785i
$819$			16.7598i			0.585633i
$820$	2.70619	−	17.8137i	0.0945043	−	0.622081i
$821$	−14.7331			−0.514188			−0.257094	−	0.966386i	$-0.582765\pi$
$821$	−14.7331			−0.514188			−0.257094	+	0.966386i	$0.582765\pi$
$822$	19.6260	−	16.8697i	0.684537	−	0.588399i
$823$			30.2507i			1.05447i	0.849719	+	0.527236i	$0.176772\pi$
$823$			30.2507i			1.05447i	−0.849719	+	0.527236i	$0.823228\pi$
$824$	−27.6359	−	44.1532i	−0.962742	−	1.53815i
$825$	−7.96252			−0.277219
$826$	72.0831	−	61.9595i	2.50809	−	2.15585i
$827$			9.90648i			0.344482i	0.985055	+	0.172241i	$0.0551008\pi$
$827$			9.90648i			0.344482i	−0.985055	+	0.172241i	$0.944899\pi$
$828$	−11.6666	−	1.77234i	−0.405442	−	0.0615932i
$829$	0.604977			0.0210117			0.0105059	−	0.999945i	$-0.496656\pi$
$829$	0.604977			0.0210117			0.0105059	+	0.999945i	$0.496656\pi$
$830$	10.1375	+	11.7938i	0.351876	+	0.409369i
$831$	−2.73938			−0.0950279
$832$	25.2173	+	12.2527i	0.874253	+	0.424785i
$833$	−71.1295			−2.46449
$834$	−0.747437	−	0.869561i	−0.0258816	−	0.0301104i
$835$	16.7703			0.580359
$836$	−39.1069	−	5.94097i	−1.35254	−	0.205473i
$837$	8.11655			0.280549
$838$	−8.39925	+	7.21963i	−0.290147	+	0.249398i
$839$		−	43.0944i		−	1.48778i	−0.668301	−	0.743891i	$-0.732978\pi$
$839$		−	43.0944i		−	1.48778i	0.668301	−	0.743891i	$-0.267022\pi$
$840$	11.1045	+	17.7413i	0.383140	+	0.612133i
$841$	1.96161			0.0676416
$842$	2.12463	+	2.47178i	0.0732197	+	0.0851831i
$843$		−	18.4418i		−	0.635168i
$844$	−39.7053	−	6.03188i	−1.36671	−	0.207626i
$845$		−	1.11117i		−	0.0382253i
$846$	−3.24407	+	2.78847i	−0.111534	+	0.0958695i
$847$	−7.94870			−0.273120
$848$	−6.28929	+	20.2221i	−0.215975	+	0.694431i
$849$			5.42691i			0.186251i
$850$	10.7660	+	12.5250i	0.369270	+	0.429605i
$851$			16.8882i			0.578918i
$852$	−8.03764	−	1.22105i	−0.275365	−	0.0418324i
$853$	16.6821			0.571184			0.285592	−	0.958351i	$-0.407810\pi$
$853$	16.6821			0.571184			0.285592	+	0.958351i	$0.407810\pi$
$854$	−1.88206	+	1.61774i	−0.0644029	+	0.0553580i
$855$	10.0148			0.342499
$856$	17.8104	+	28.4553i	0.608748	+	0.972581i
$857$			4.46983i			0.152686i	0.997082	+	0.0763432i	$0.0243244\pi$
$857$			4.46983i			0.152686i	−0.997082	+	0.0763432i	$0.975676\pi$
$858$	−11.4853	+	9.87227i	−0.392102	+	0.337034i
$859$			42.9943i			1.46695i	0.679718	+	0.733474i	$0.262102\pi$
$859$			42.9943i			1.46695i	−0.679718	+	0.733474i	$0.737898\pi$
$860$	26.5998	+	4.04093i	0.907044	+	0.137795i
$861$			27.8436i			0.948907i
$862$	22.4934	−	19.3344i	0.766128	−	0.658531i
$863$			17.2498i			0.587189i	0.955930	+	0.293595i	$0.0948516\pi$
$863$			17.2498i			0.587189i	−0.955930	+	0.293595i	$0.905148\pi$
$864$	−2.24704	−	5.19142i	−0.0764457	−	0.176616i
$865$		−	22.3887i		−	0.761238i
$866$	22.3793	−	19.2363i	0.760478	−	0.653675i
$867$	−3.08787			−0.104869
$868$	11.6597	−	76.7506i	0.395755	−	2.60509i
$869$	37.9492			1.28734
$870$	9.23390	−	7.93707i	0.313059	−	0.269092i
$871$	−27.3196	−	8.74776i	−0.925691	−	0.296407i
$872$	10.5367	+	16.8342i	0.356816	+	0.570077i
$873$		−	5.71259i		−	0.193342i
$874$	35.2032	+	40.9550i	1.19076	+	1.38532i
$875$		−	56.2812i		−	1.90265i
$876$	−4.42279	+	29.1133i	−0.149432	+	0.983648i
$877$	19.6475			0.663448			0.331724	−	0.943377i	$-0.392370\pi$
$877$	19.6475			0.663448			0.331724	+	0.943377i	$0.392370\pi$
$878$	33.9951	−	29.2208i	1.14728	−	0.986153i
$879$	13.8229			0.466234
$880$	−5.61691	+	18.0602i	−0.189346	+	0.608810i
$881$	44.8142			1.50983			0.754914	−	0.655824i	$-0.227679\pi$
$881$	44.8142			1.50983			0.754914	+	0.655824i	$0.227679\pi$
$882$	−14.6299	−	17.0203i	−0.492616	−	0.573104i
$883$	−20.5967			−0.693133			−0.346567	−	0.938025i	$-0.612653\pi$
$883$	−20.5967			−0.693133			−0.346567	+	0.938025i	$0.612653\pi$
$884$	31.0581	+	4.71823i	1.04460	+	0.158691i
$885$	−21.7471			−0.731021
$886$	−19.8903	−	23.1402i	−0.668228	−	0.777409i
$887$		−	36.5355i		−	1.22674i	−0.789794	−	0.613372i	$-0.789813\pi$
$887$		−	36.5355i		−	1.22674i	0.789794	−	0.613372i	$-0.210187\pi$
$888$	−6.86241	+	4.29525i	−0.230287	+	0.144139i
$889$		−	79.9434i		−	2.68121i
$890$	−8.12926	+	6.98756i	−0.272493	+	0.234224i
$891$	3.05580			0.102373
$892$	−17.9683	−	2.72968i	−0.601625	−	0.0913966i
$893$	19.5776			0.655139
$894$	5.43865	+	6.32726i	0.181896	+	0.211615i
$895$			12.5470i			0.419400i
$896$	−52.3183	+	13.7905i	−1.74783	+	0.460708i
$897$	20.6776			0.690406
$898$	20.5159	+	23.8680i	0.684624	+	0.796485i
$899$	−45.1630			−1.50627
$900$	−0.782719	+	5.15231i	−0.0260906	+	0.171744i
$901$			23.7292i			0.790534i
$902$	−19.0810	+	16.4012i	−0.635326	+	0.546099i
$903$	−41.5766			−1.38358
$904$	5.22435	+	8.34682i	0.173759	+	0.277611i
$905$		−	10.6136i		−	0.352807i
$906$	−15.7450	+	13.5337i	−0.523092	+	0.449627i
$907$		−	0.123449i		−	0.00409906i	−0.999998	−	0.00204953i	$-0.999348\pi$
$907$		−	0.123449i		−	0.00409906i	0.999998	−	0.00204953i	$-0.000652386\pi$
$908$	−11.9796	−	1.81990i	−0.397558	−	0.0603955i
$909$			0.0467073i			0.00154918i
$910$	−23.9065	−	27.8126i	−0.792493	−	0.921978i
$911$			3.37113i			0.111691i	0.998439	+	0.0558453i	$0.0177854\pi$
$911$			3.37113i			0.111691i	−0.998439	+	0.0558453i	$0.982215\pi$
$912$	−7.68845	+	24.7209i	−0.254590	+	0.818591i
$913$		−	21.7172i		−	0.718736i
$914$	−28.4038	−	33.0447i	−0.939516	−	1.09302i
$915$	0.567809			0.0187712
$916$	−1.91589	−	0.291055i	−0.0633027	−	0.00961671i
$917$		−	65.2857i		−	2.15592i
$918$	−4.13168	−	4.80676i	−0.136366	−	0.158647i
$919$	−33.2454			−1.09666			−0.548332	−	0.836261i	$-0.684737\pi$
$919$	−33.2454			−1.09666			−0.548332	+	0.836261i	$0.684737\pi$
$920$	21.8886	−	13.7003i	0.721647	−	0.451685i
$921$			1.98977i			0.0655652i
$922$	1.89242	+	2.20162i	0.0623235	+	0.0725065i
$923$	14.2458			0.468905
$924$	4.38974	−	28.8958i	0.144412	−	0.950602i
$925$	7.45831			0.245228
$926$	−33.5376	−	39.0173i	−1.10211	−	1.28219i
$927$		−	18.4162i		−	0.604867i
$928$	12.5032	+	28.8867i	0.410438	+	0.948252i
$929$		−	53.7450i		−	1.76331i	−0.471890	−	0.881657i	$-0.656428\pi$
$929$		−	53.7450i		−	1.76331i	0.471890	−	0.881657i	$-0.343572\pi$
$930$	−13.4693	+	11.5776i	−0.441676	+	0.379645i
$931$			102.716i			3.36637i
$932$	20.5301	+	3.11886i	0.672487	+	0.102162i
$933$	−11.1604			−0.365376
$934$	−4.01857	+	3.45419i	−0.131492	+	0.113025i
$935$			21.1924i			0.693064i
$936$	5.25904	+	8.40224i	0.171897	+	0.274636i
$937$		−	22.6711i		−	0.740634i	−0.928905	−	0.370317i	$-0.879249\pi$
$937$		−	22.6711i		−	0.740634i	0.928905	−	0.370317i	$-0.120751\pi$
$938$	50.9861	−	21.5645i	1.66475	−	0.704105i
$939$			13.7215i			0.447783i
$940$	1.40596	−	9.25485i	0.0458574	−	0.301860i
$941$		−	22.6073i		−	0.736978i	−0.929632	−	0.368489i	$-0.879875\pi$
$941$		−	22.6073i		−	0.736978i	0.929632	−	0.368489i	$-0.120125\pi$
$942$	−2.83061	−	3.29310i	−0.0922263	−	0.107295i
$943$	34.3525			1.11867
$944$	16.6955	−	53.6814i	0.543391	−	1.74718i
$945$			7.39986i			0.240717i
$946$	−24.4905	−	28.4920i	−0.796256	−	0.926356i
$947$		−	39.4953i		−	1.28342i	−0.766946	−	0.641712i	$-0.778225\pi$
$947$		−	39.4953i		−	1.28342i	0.766946	−	0.641712i	$-0.221775\pi$
$948$	3.73043	−	24.5558i	0.121159	−	0.797536i
$949$		−	51.5999i		−	1.67500i
$950$	18.0870	−	15.5468i	0.586818	−	0.504404i
$951$	6.57889			0.213335
$952$	−51.3883	+	32.1644i	−1.66551	+	1.04246i
$953$	−52.4094			−1.69771			−0.848853	−	0.528628i	$-0.822707\pi$
$953$	−52.4094			−1.69771			−0.848853	+	0.528628i	$0.822707\pi$
$954$	−5.67808	+	4.88063i	−0.183835	+	0.158016i
$955$			36.5864i			1.18391i
$956$	4.26078	−	28.0469i	0.137803	−	0.907101i
$957$	−17.0034			−0.549642
$958$	43.6105	−	37.4857i	1.40899	−	1.21111i
$959$		−	87.5150i		−	2.82601i
$960$	11.1341	+	5.40986i	0.359351	+	0.174603i
$961$	34.8783			1.12511
$962$	10.7580	−	9.24713i	0.346852	−	0.298139i
$963$			11.8686i			0.382461i
$964$	0.487462	−	3.20876i	0.0157001	−	0.103347i
$965$		−	6.45956i		−	0.207940i
$966$	−30.2614	+	26.0114i	−0.973643	+	0.836902i
$967$		−	3.79429i		−	0.122016i	−0.998137	−	0.0610080i	$-0.980568\pi$
$967$		−	3.79429i		−	0.122016i	0.998137	−	0.0610080i	$-0.0194315\pi$
$968$	−3.98495	+	2.49422i	−0.128081	+	0.0801673i
$969$			29.0082i			0.931877i
$970$	8.14857	+	9.47996i	0.261635	+	0.304383i
$971$		−	3.30522i		−	0.106070i	−0.998593	−	0.0530348i	$-0.983111\pi$
$971$		−	3.30522i		−	0.106070i	0.998593	−	0.0530348i	$-0.0168894\pi$
$972$	0.300386	−	1.97731i	0.00963489	−	0.0634224i
$973$	−3.87748			−0.124306
$974$	22.1086	+	25.7209i	0.708406	+	0.824152i
$975$		−	9.13185i		−	0.292453i
$976$	−0.435912	+	1.40160i	−0.0139532	+	0.0448642i
$977$	25.9922			0.831564			0.415782	−	0.909464i	$-0.363508\pi$
$977$	25.9922			0.831564			0.415782	+	0.909464i	$0.363508\pi$
$978$	25.0136	−	21.5006i	0.799848	−	0.687515i
$979$	14.9693			0.478421
$980$	48.5564	+	7.37651i	1.55108	+	0.235634i
$981$			7.02149i			0.224179i
$982$	7.70102	−	6.61947i	0.245749	−	0.211236i
$983$	30.1713			0.962315			0.481157	−	0.876634i	$-0.340217\pi$
$983$	30.1713			0.962315			0.481157	+	0.876634i	$0.340217\pi$
$984$	8.73704	+	13.9590i	0.278527	+	0.444995i
$985$	−0.485043			−0.0154548
$986$	22.9900	+	26.7463i	0.732150	+	0.851776i
$987$			14.4657i			0.460449i
$988$	6.81343	−	44.8499i	0.216764	−	1.42687i
$989$			51.2958i			1.63111i
$990$	−5.07105	+	4.35886i	−0.161169	+	0.138534i
$991$	21.2569			0.675248			0.337624	−	0.941281i	$-0.390377\pi$
$991$	21.2569			0.675248			0.337624	+	0.941281i	$0.390377\pi$
$992$	−18.2382	−	42.1364i	−0.579062	−	1.33783i
$993$	−5.83274			−0.185096
$994$	−20.8484	+	17.9204i	−0.661272	+	0.568401i
$995$	−19.5191			−0.618796
$996$	−14.0526	−	2.13481i	−0.445273	−	0.0676442i
$997$	−14.0203			−0.444027			−0.222014	−	0.975044i	$-0.571263\pi$
$997$	−14.0203			−0.444027			−0.222014	+	0.975044i	$0.571263\pi$
$998$	5.98682	+	6.96500i	0.189509	+	0.220473i
$999$	−2.86229			−0.0905590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.e.a.535.11	✓	34
4.3	odd	2		804.2.e.b.535.23	yes	34
67.66	odd	2		804.2.e.b.535.24	yes	34
268.267	even	2	inner	804.2.e.a.535.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.e.a.535.11	✓	34	1.1	even	1	trivial
804.2.e.a.535.12	yes	34	268.267	even	2	inner
804.2.e.b.535.23	yes	34	4.3	odd	2
804.2.e.b.535.24	yes	34	67.66	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.921850 - 1.07247i) q^{2} -1.00000 q^{3} +(-0.300386 + 1.97731i) q^{4} -1.54735i q^{5} +(0.921850 + 1.07247i) q^{6} +4.78228 q^{7} +(2.39752 - 1.50063i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.921850 - 1.07247i) q^{2} -1.00000 q^{3} +(-0.300386 + 1.97731i) q^{4} -1.54735i q^{5} +(0.921850 + 1.07247i) q^{6} +4.78228 q^{7} +(2.39752 - 1.50063i) q^{8} +1.00000 q^{9} +(-1.65949 + 1.42642i) q^{10} +3.05580 q^{11} +(0.300386 - 1.97731i) q^{12} +3.50455i q^{13} +(-4.40854 - 5.12886i) q^{14} +1.54735i q^{15} +(-3.81954 - 1.18791i) q^{16} -4.48195 q^{17} +(-0.921850 - 1.07247i) q^{18} +6.47223i q^{19} +(3.05959 + 0.464802i) q^{20} -4.78228 q^{21} +(-2.81698 - 3.27725i) q^{22} +5.90022i q^{23} +(-2.39752 + 1.50063i) q^{24} +2.60571 q^{25} +(3.75853 - 3.23067i) q^{26} -1.00000 q^{27} +(-1.43653 + 9.45607i) q^{28} +5.56432 q^{29} +(1.65949 - 1.42642i) q^{30} -8.11655 q^{31} +(2.24704 + 5.19142i) q^{32} -3.05580 q^{33} +(4.13168 + 4.80676i) q^{34} -7.39986i q^{35} +(-0.300386 + 1.97731i) q^{36} +2.86229 q^{37} +(6.94127 - 5.96642i) q^{38} -3.50455i q^{39} +(-2.32200 - 3.70980i) q^{40} -5.82224i q^{41} +(4.40854 + 5.12886i) q^{42} +8.69388 q^{43} +(-0.917918 + 6.04227i) q^{44} -1.54735i q^{45} +(6.32781 - 5.43911i) q^{46} -3.02486i q^{47} +(3.81954 + 1.18791i) q^{48} +15.8702 q^{49} +(-2.40207 - 2.79455i) q^{50} +4.48195 q^{51} +(-6.92960 - 1.05272i) q^{52} -5.29439i q^{53} +(0.921850 + 1.07247i) q^{54} -4.72838i q^{55} +(11.4656 - 7.17644i) q^{56} -6.47223i q^{57} +(-5.12946 - 5.96756i) q^{58} +14.0544i q^{59} +(-3.05959 - 0.464802i) q^{60} -0.366956i q^{61} +(7.48224 + 8.70476i) q^{62} +4.78228 q^{63} +(3.49622 - 7.19559i) q^{64} +5.42277 q^{65} +(2.81698 + 3.27725i) q^{66} +(-2.49611 + 7.79547i) q^{67} +(1.34631 - 8.86222i) q^{68} -5.90022i q^{69} +(-7.93613 + 6.82156i) q^{70} -4.06493i q^{71} +(2.39752 - 1.50063i) q^{72} -14.7237 q^{73} +(-2.63860 - 3.06973i) q^{74} -2.60571 q^{75} +(-12.7976 - 1.94417i) q^{76} +14.6137 q^{77} +(-3.75853 + 3.23067i) q^{78} +12.4188 q^{79} +(-1.83812 + 5.91016i) q^{80} +1.00000 q^{81} +(-6.24418 + 5.36723i) q^{82} -7.10690i q^{83} +(1.43653 - 9.45607i) q^{84} +6.93514i q^{85} +(-8.01445 - 9.32393i) q^{86} -5.56432 q^{87} +(7.32633 - 4.58562i) q^{88} +4.89866 q^{89} +(-1.65949 + 1.42642i) q^{90} +16.7598i q^{91} +(-11.6666 - 1.77234i) q^{92} +8.11655 q^{93} +(-3.24407 + 2.78847i) q^{94} +10.0148 q^{95} +(-2.24704 - 5.19142i) q^{96} -5.71259i q^{97} +(-14.6299 - 17.0203i) q^{98} +3.05580 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

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