LMFDB - Embedded newform 288.2.bf.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34246 - 0.444750i) q^{2} +(-0.318231 - 1.70257i) q^{3} +(1.60439 + 1.19412i) q^{4} +(0.201801 + 1.53283i) q^{5} +(-0.330005 + 2.42716i) q^{6} +(0.765564 + 2.85712i) q^{7} +(-1.62275 - 2.31661i) q^{8} +(-2.79746 + 1.08362i) q^{9} +O(q^{10})$	\(q+(-1.34246 - 0.444750i) q^{2} +(-0.318231 - 1.70257i) q^{3} +(1.60439 + 1.19412i) q^{4} +(0.201801 + 1.53283i) q^{5} +(-0.330005 + 2.42716i) q^{6} +(0.765564 + 2.85712i) q^{7} +(-1.62275 - 2.31661i) q^{8} +(-2.79746 + 1.08362i) q^{9} +(0.410817 - 2.14751i) q^{10} +(-2.13126 + 1.63537i) q^{11} +(1.52250 - 3.11159i) q^{12} +(-3.96131 + 5.16247i) q^{13} +(0.242968 - 4.17606i) q^{14} +(2.54552 - 0.831373i) q^{15} +(1.14816 + 3.83167i) q^{16} -4.99281 q^{17} +(4.23741 - 0.210541i) q^{18} +(1.11086 - 0.460133i) q^{19} +(-1.50661 + 2.70024i) q^{20} +(4.62082 - 2.21265i) q^{21} +(3.58847 - 1.24754i) q^{22} +(5.75268 + 1.54143i) q^{23} +(-3.42777 + 3.50005i) q^{24} +(2.52078 - 0.675442i) q^{25} +(7.61391 - 5.16862i) q^{26} +(2.73517 + 4.41802i) q^{27} +(-2.18348 + 5.49813i) q^{28} +(-2.24187 - 0.295148i) q^{29} +(-3.78702 - 0.0160388i) q^{30} +(6.12971 - 3.53899i) q^{31} +(0.162778 - 5.65451i) q^{32} +(3.46257 + 3.10819i) q^{33} +(6.70264 + 2.22055i) q^{34} +(-4.22500 + 1.75005i) q^{35} +(-5.78219 - 1.60195i) q^{36} +(-2.82618 + 6.82299i) q^{37} +(-1.69593 + 0.123655i) q^{38} +(10.0501 + 5.10153i) q^{39} +(3.22350 - 2.95489i) q^{40} +(-1.24802 + 4.65767i) q^{41} +(-7.18733 + 0.915280i) q^{42} +(-4.77531 - 6.22330i) q^{43} +(-5.37222 + 0.0788062i) q^{44} +(-2.22553 - 4.06935i) q^{45} +(-7.03719 - 4.62781i) q^{46} +(-5.05837 - 2.92045i) q^{47} +(6.15830 - 3.17418i) q^{48} +(-1.51489 + 0.874625i) q^{49} +(-3.68445 - 0.214366i) q^{50} +(1.58886 + 8.50058i) q^{51} +(-12.5201 + 3.55237i) q^{52} +(0.936950 - 2.26200i) q^{53} +(-1.70693 - 7.14747i) q^{54} +(-2.93684 - 2.93684i) q^{55} +(5.37653 - 6.40991i) q^{56} +(-1.13692 - 1.74488i) q^{57} +(2.87836 + 1.39330i) q^{58} +(9.62319 - 1.26692i) q^{59} +(5.07678 + 1.70581i) q^{60} +(0.825476 - 6.27012i) q^{61} +(-9.80285 + 2.02476i) q^{62} +(-5.23766 - 7.16311i) q^{63} +(-2.73337 + 7.51856i) q^{64} +(-8.71259 - 5.03022i) q^{65} +(-3.26599 - 5.71259i) q^{66} +(-6.82356 + 8.89264i) q^{67} +(-8.01043 - 5.96200i) q^{68} +(0.793700 - 10.2848i) q^{69} +(6.45022 - 0.470303i) q^{70} +(11.1140 + 11.1140i) q^{71} +(7.04989 + 4.72218i) q^{72} +(4.15800 - 4.15800i) q^{73} +(6.82856 - 7.90265i) q^{74} +(-1.95217 - 4.07685i) q^{75} +(2.33171 + 0.588263i) q^{76} +(-6.30409 - 4.83730i) q^{77} +(-11.2229 - 11.3184i) q^{78} +(2.07756 - 3.59845i) q^{79} +(-5.64161 + 2.53317i) q^{80} +(6.65155 - 6.06275i) q^{81} +(3.74691 - 5.69767i) q^{82} +(-1.51171 - 0.199020i) q^{83} +(10.0558 + 1.96784i) q^{84} +(-1.00755 - 7.65313i) q^{85} +(3.64284 + 10.4783i) q^{86} +(0.210924 + 3.91086i) q^{87} +(7.24703 + 2.28350i) q^{88} +(-6.21714 + 6.21714i) q^{89} +(1.17784 + 6.45275i) q^{90} +(-17.7825 - 7.36574i) q^{91} +(7.38892 + 9.34244i) q^{92} +(-7.97602 - 9.31001i) q^{93} +(5.49179 + 6.17030i) q^{94} +(0.929478 + 1.60990i) q^{95} +(-9.67898 + 1.52230i) q^{96} +(-0.292590 + 0.506782i) q^{97} +(2.42267 - 0.500398i) q^{98} +(4.19000 - 6.88436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.34246	−	0.444750i	−0.949262	−	0.314486i
$2$	−1.34246	−	0.444750i	−0.949262	−	0.314486i
$3$	−0.318231	−	1.70257i	−0.183731	−	0.982977i
$3$	−0.318231	−	1.70257i	−0.183731	−	0.982977i
$4$	1.60439	+	1.19412i	0.802197	+	0.597059i
$5$	0.201801	+	1.53283i	0.0902481	+	0.685503i	0.975438	+	0.220273i	$0.0706949\pi$
$5$	0.201801	+	1.53283i	0.0902481	+	0.685503i	−0.885190	+	0.465229i	$0.845972\pi$
$6$	−0.330005	+	2.42716i	−0.134724	+	0.990883i
$7$	0.765564	+	2.85712i	0.289356	+	1.07989i	0.945597	+	0.325340i	$0.105479\pi$
$7$	0.765564	+	2.85712i	0.289356	+	1.07989i	−0.656241	+	0.754551i	$0.727855\pi$
$8$	−1.62275	−	2.31661i	−0.573728	−	0.819046i
$9$	−2.79746	+	1.08362i	−0.932486	+	0.361206i
$10$	0.410817	−	2.14751i	0.129912	−	0.679103i
$11$	−2.13126	+	1.63537i	−0.642600	+	0.493084i	−0.877903	−	0.478838i	$-0.841058\pi$
$11$	−2.13126	+	1.63537i	−0.642600	+	0.493084i	0.235304	+	0.971922i	$0.424391\pi$
$12$	1.52250	−	3.11159i	0.439507	−	0.898239i
$13$	−3.96131	+	5.16247i	−1.09867	+	1.43181i	−0.207446	+	0.978246i	$0.566515\pi$
$13$	−3.96131	+	5.16247i	−1.09867	+	1.43181i	−0.891222	+	0.453566i	$0.850151\pi$
$14$	0.242968	−	4.17606i	0.0649360	−	1.11610i
$15$	2.54552	−	0.831373i	0.657252	−	0.214660i
$16$	1.14816	+	3.83167i	0.287040	+	0.957918i
$17$	−4.99281			−1.21093			−0.605467	−	0.795871i	$-0.707014\pi$
$17$	−4.99281			−1.21093			−0.605467	+	0.795871i	$0.707014\pi$
$18$	4.23741	−	0.210541i	0.998768	−	0.0496250i
$19$	1.11086	−	0.460133i	0.254849	−	0.105562i	−0.251602	−	0.967831i	$-0.580957\pi$
$19$	1.11086	−	0.460133i	0.254849	−	0.105562i	0.506450	+	0.862269i	$0.330957\pi$
$20$	−1.50661	+	2.70024i	−0.336889	+	0.603792i
$21$	4.62082	−	2.21265i	1.00834	−	0.482839i
$22$	3.58847	−	1.24754i	0.765063	−	0.265977i
$23$	5.75268	+	1.54143i	1.19952	+	0.321410i	0.802641	−	0.596463i	$-0.203428\pi$
$23$	5.75268	+	1.54143i	1.19952	+	0.321410i	0.396876	+	0.917872i	$0.370094\pi$
$24$	−3.42777	+	3.50005i	−0.699691	+	0.714445i
$25$	2.52078	−	0.675442i	0.504157	−	0.135088i
$26$	7.61391	−	5.16862i	1.49321	−	1.01365i
$27$	2.73517	+	4.41802i	0.526383	+	0.850248i
$28$	−2.18348	+	5.49813i	−0.412639	+	1.03905i
$29$	−2.24187	−	0.295148i	−0.416305	−	0.0548076i	−0.0805356	−	0.996752i	$-0.525663\pi$
$29$	−2.24187	−	0.295148i	−0.416305	−	0.0548076i	−0.335770	+	0.941944i	$0.608996\pi$
$30$	−3.78702	−	0.0160388i	−0.691412	−	0.00292827i
$31$	6.12971	−	3.53899i	1.10093	−	0.635621i	0.164463	−	0.986383i	$-0.447411\pi$
$31$	6.12971	−	3.53899i	1.10093	−	0.635621i	0.936464	+	0.350762i	$0.114078\pi$
$32$	0.162778	−	5.65451i	0.0287754	−	0.999586i
$33$	3.46257	+	3.10819i	0.602755	+	0.541066i
$34$	6.70264	+	2.22055i	1.14949	+	0.380822i
$35$	−4.22500	+	1.75005i	−0.714155	+	0.295813i
$36$	−5.78219	−	1.60195i	−0.963699	−	0.266991i
$37$	−2.82618	+	6.82299i	−0.464621	+	1.12169i	0.501859	+	0.864950i	$0.332650\pi$
$37$	−2.82618	+	6.82299i	−0.464621	+	1.12169i	−0.966479	+	0.256744i	$0.917350\pi$
$38$	−1.69593	+	0.123655i	−0.275116	+	0.0200594i
$39$	10.0501	+	5.10153i	1.60930	+	0.816898i
$40$	3.22350	−	2.95489i	0.509680	−	0.467210i
$41$	−1.24802	+	4.65767i	−0.194908	+	0.727405i	0.797383	+	0.603473i	$0.206217\pi$
$41$	−1.24802	+	4.65767i	−0.194908	+	0.727405i	−0.992291	+	0.123932i	$0.960450\pi$
$42$	−7.18733	+	0.915280i	−1.10903	+	0.141231i
$43$	−4.77531	−	6.22330i	−0.728228	−	0.949045i	0.271683	−	0.962387i	$-0.412420\pi$
$43$	−4.77531	−	6.22330i	−0.728228	−	0.949045i	−0.999911	+	0.0133421i	$0.995753\pi$
$44$	−5.37222	+	0.0788062i	−0.809892	+	0.0118805i
$45$	−2.22553	−	4.06935i	−0.331763	−	0.606624i
$46$	−7.03719	−	4.62781i	−1.03758	−	0.682333i
$47$	−5.05837	−	2.92045i	−0.737840	−	0.425992i	0.0834437	−	0.996512i	$-0.473408\pi$
$47$	−5.05837	−	2.92045i	−0.737840	−	0.425992i	−0.821283	+	0.570521i	$0.806741\pi$
$48$	6.15830	−	3.17418i	0.888873	−	0.458153i
$49$	−1.51489	+	0.874625i	−0.216413	+	0.124946i
$50$	−3.68445	−	0.214366i	−0.521060	−	0.0303160i
$51$	1.58886	+	8.50058i	0.222486	+	1.19032i
$52$	−12.5201	+	3.55237i	−1.73623	+	0.492626i
$53$	0.936950	−	2.26200i	0.128700	−	0.310709i	−0.846374	−	0.532589i	$-0.821219\pi$
$53$	0.936950	−	2.26200i	0.128700	−	0.310709i	0.975074	+	0.221880i	$0.0712192\pi$
$54$	−1.70693	−	7.14747i	−0.232284	−	0.972648i
$55$	−2.93684	−	2.93684i	−0.396004	−	0.396004i
$56$	5.37653	−	6.40991i	0.718469	−	0.856560i
$57$	−1.13692	−	1.74488i	−0.150588	−	0.231115i
$58$	2.87836	+	1.39330i	0.377947	+	0.182949i
$59$	9.62319	−	1.26692i	1.25283	−	0.164939i	0.525244	−	0.850952i	$-0.323974\pi$
$59$	9.62319	−	1.26692i	1.25283	−	0.164939i	0.727589	+	0.686013i	$0.240641\pi$
$60$	5.07678	+	1.70581i	0.655410	+	0.220219i
$61$	0.825476	−	6.27012i	0.105691	−	0.802806i	−0.853707	−	0.520753i	$-0.825651\pi$
$61$	0.825476	−	6.27012i	0.105691	−	0.802806i	0.959399	−	0.282053i	$-0.0910154\pi$
$62$	−9.80285	+	2.02476i	−1.24496	+	0.257144i
$63$	−5.23766	−	7.16311i	−0.659884	−	0.902467i
$64$	−2.73337	+	7.51856i	−0.341671	+	0.939820i
$65$	−8.71259	−	5.03022i	−1.08066	−	0.623922i
$66$	−3.26599	−	5.71259i	−0.402015	−	0.703171i
$67$	−6.82356	+	8.89264i	−0.833631	+	1.08641i	0.161404	+	0.986888i	$0.448398\pi$
$67$	−6.82356	+	8.89264i	−0.833631	+	1.08641i	−0.995035	+	0.0995208i	$0.968269\pi$
$68$	−8.01043	−	5.96200i	−0.971407	−	0.722999i
$69$	0.793700	−	10.2848i	0.0955502	−	1.23815i
$70$	6.45022	−	0.470303i	0.770949	−	0.0562120i
$71$	11.1140	+	11.1140i	1.31899	+	1.31899i	0.914579	+	0.404408i	$0.132522\pi$
$71$	11.1140	+	11.1140i	1.31899	+	1.31899i	0.404408	+	0.914579i	$0.367478\pi$
$72$	7.04989	+	4.72218i	0.830838	+	0.556515i
$73$	4.15800	−	4.15800i	0.486657	−	0.486657i	−0.420592	−	0.907250i	$-0.638178\pi$
$73$	4.15800	−	4.15800i	0.486657	−	0.486657i	0.907250	+	0.420592i	$0.138178\pi$
$74$	6.82856	−	7.90265i	0.793804	−	0.918664i
$75$	−1.95217	−	4.07685i	−0.225418	−	0.470754i
$76$	2.33171	+	0.588263i	0.267465	+	0.0674784i
$77$	−6.30409	−	4.83730i	−0.718417	−	0.551261i
$78$	−11.2229	−	11.3184i	−1.27074	−	1.28155i
$79$	2.07756	−	3.59845i	0.233744	−	0.404857i	−0.725163	−	0.688578i	$-0.758235\pi$
$79$	2.07756	−	3.59845i	0.233744	−	0.404857i	0.958907	+	0.283721i	$0.0915688\pi$
$80$	−5.64161	+	2.53317i	−0.630751	+	0.283217i
$81$	6.65155	−	6.06275i	0.739061	−	0.673639i
$82$	3.74691	−	5.69767i	0.413777	−	0.629202i
$83$	−1.51171	−	0.199020i	−0.165932	−	0.0218453i	0.0471025	−	0.998890i	$-0.485001\pi$
$83$	−1.51171	−	0.199020i	−0.165932	−	0.0218453i	−0.213034	+	0.977045i	$0.568335\pi$
$84$	10.0558	+	1.96784i	1.09717	+	0.214709i
$85$	−1.00755	−	7.65313i	−0.109284	−	0.830098i
$86$	3.64284	+	10.4783i	0.392818	+	1.12991i
$87$	0.210924	+	3.91086i	0.0226134	+	0.419288i
$88$	7.24703	+	2.28350i	0.772536	+	0.243422i
$89$	−6.21714	+	6.21714i	−0.659016	+	0.659016i	−0.955147	−	0.296132i	$-0.904303\pi$
$89$	−6.21714	+	6.21714i	−0.659016	+	0.659016i	0.296132	+	0.955147i	$0.404303\pi$
$90$	1.17784	+	6.45275i	0.124155	+	0.680179i
$91$	−17.7825	−	7.36574i	−1.86411	−	0.772139i
$92$	7.38892	+	9.34244i	0.770348	+	0.974017i
$93$	−7.97602	−	9.31001i	−0.827074	−	0.965403i
$94$	5.49179	+	6.17030i	0.566435	+	0.636418i
$95$	0.929478	+	1.60990i	0.0953624	+	0.165173i
$96$	−9.67898	+	1.52230i	−0.987857	+	0.155369i
$97$	−0.292590	+	0.506782i	−0.0297081	+	0.0514559i	−0.880497	−	0.474051i	$-0.842791\pi$
$97$	−0.292590	+	0.506782i	−0.0297081	+	0.0514559i	0.850789	+	0.525507i	$0.176124\pi$
$98$	2.42267	−	0.500398i	0.244727	−	0.0505479i
$99$	4.19000	−	6.88436i	0.421110	−	0.691905i
$100$	4.85089	+	1.92644i	0.485089	+	0.192644i
$101$	−2.99854	+	2.30086i	−0.298365	+	0.228944i	−0.747085	−	0.664729i	$-0.768547\pi$
$101$	−2.99854	+	2.30086i	−0.298365	+	0.228944i	0.448719	+	0.893673i	$0.351880\pi$
$102$	1.64765	−	12.1183i	0.163142	−	1.19989i
$103$	−11.0429	−	2.95894i	−1.08809	−	0.291553i	−0.330184	−	0.943917i	$-0.607111\pi$
$103$	−11.0429	−	2.95894i	−1.08809	−	0.291553i	−0.757906	+	0.652364i	$0.773777\pi$
$104$	18.3877	+	0.799402i	1.80306	+	0.0783878i
$105$	4.32410	+	6.63641i	0.421989	+	0.647648i
$106$	−2.26384	+	2.61993i	−0.219884	+	0.254470i
$107$	1.14688	+	0.475053i	0.110873	+	0.0459252i	0.437430	−	0.899252i	$-0.355889\pi$
$107$	1.14688	+	0.475053i	0.110873	+	0.0459252i	−0.326557	+	0.945177i	$0.605889\pi$
$108$	−0.887351	+	10.3544i	−0.0853854	+	0.996348i
$109$	−1.65254	−	3.98958i	−0.158284	−	0.382132i	0.824764	−	0.565476i	$-0.191308\pi$
$109$	−1.65254	−	3.98958i	−0.158284	−	0.382132i	−0.983049	+	0.183344i	$0.941308\pi$
$110$	2.63643	+	5.24875i	0.251374	+	0.500449i
$111$	12.5160	+	2.64047i	1.18796	+	0.250622i
$112$	−10.0686	+	6.21383i	−0.951391	+	0.587152i
$113$	8.82710	+	15.2890i	0.830384	+	1.43827i	0.897734	+	0.440537i	$0.145212\pi$
$113$	8.82710	+	15.2890i	0.830384	+	1.43827i	−0.0673509	+	0.997729i	$0.521455\pi$
$114$	0.750226	+	2.84808i	0.0702651	+	0.266747i
$115$	−1.20185	+	9.12895i	−0.112073	+	0.851279i
$116$	−3.24441	−	3.15060i	−0.301235	−	0.292525i
$117$	5.48744	−	18.7343i	0.507314	−	1.73199i
$118$	−13.4822	−	2.57913i	−1.24114	−	0.237428i
$119$	−3.82231	−	14.2651i	−0.350391	−	1.30768i
$120$	−6.05672	−	4.54788i	−0.552900	−	0.415163i
$121$	−0.979183	+	3.65436i	−0.0890167	+	0.332215i
$122$	−3.89680	+	8.05024i	−0.352800	+	0.728835i
$123$	8.32714	+	0.642620i	0.750833	+	0.0579431i
$124$	14.0604	+	1.64167i	1.26266	+	0.147426i
$125$	4.50229	+	10.8695i	0.402697	+	0.972196i
$126$	3.84555	+	11.9456i	0.342589	+	1.06420i
$127$			4.81135i			0.426938i	0.976950	+	0.213469i	$0.0684763\pi$
$127$			4.81135i			0.426938i	−0.976950	+	0.213469i	$0.931524\pi$
$128$	7.01332	−	8.87769i	0.619896	−	0.784684i
$129$	−9.07593	+	10.1107i	−0.799091	+	0.890199i
$130$	9.45911	+	10.6278i	0.829619	+	0.932119i
$131$	2.71450	+	2.08291i	0.237167	+	0.181985i	0.720506	−	0.693448i	$-0.243909\pi$
$131$	2.71450	+	2.08291i	0.237167	+	0.181985i	−0.483339	+	0.875433i	$0.660576\pi$
$132$	1.84378	+	9.12147i	0.160480	+	0.793922i
$133$	2.16509	+	2.82160i	0.187737	+	0.244664i
$134$	13.1154	−	8.90323i	1.13299	−	0.769122i
$135$	−6.22011	+	5.08411i	−0.535342	+	0.437570i
$136$	8.10207	+	11.5664i	0.694747	+	0.991810i
$137$	7.27729	−	1.94994i	0.621740	−	0.166595i	0.0658216	−	0.997831i	$-0.479033\pi$
$137$	7.27729	−	1.94994i	0.621740	−	0.166595i	0.555919	+	0.831237i	$0.312367\pi$
$138$	−5.63970	+	13.4540i	−0.480083	+	1.14528i
$139$	−0.660667	+	0.0869784i	−0.0560370	+	0.00737741i	−0.158493	−	0.987360i	$-0.550663\pi$
$139$	−0.660667	+	0.0869784i	−0.0560370	+	0.00737741i	0.102456	+	0.994738i	$0.467330\pi$
$140$	−8.86833	−	2.23738i	−0.749510	−	0.189093i
$141$	−3.36253	+	9.54159i	−0.283176	+	0.803547i
$142$	−9.97712	−	19.8630i	−0.837261	−	1.66687i
$143$		−	17.4808i		−	1.46182i
$144$	−7.36400	−	9.47478i	−0.613667	−	0.789565i
$145$		−	3.49597i		−	0.290325i
$146$	−7.43122	+	3.73268i	−0.615012	+	0.308919i
$147$	1.97119	+	2.30087i	0.162581	+	0.189773i
$148$	−12.6818	+	7.57198i	−1.04243	+	0.622413i
$149$	−9.21391	+	1.21303i	−0.754833	+	0.0993756i	−0.498115	−	0.867111i	$-0.665974\pi$
$149$	−9.21391	+	1.21303i	−0.754833	+	0.0993756i	−0.256718	+	0.966486i	$0.582641\pi$
$150$	0.807533	+	6.34124i	0.0659348	+	0.517760i
$151$	17.1036	−	4.58290i	1.39187	−	0.372951i	0.516454	−	0.856315i	$-0.327252\pi$
$151$	17.1036	−	4.58290i	1.39187	−	0.372951i	0.875420	+	0.483364i	$0.160585\pi$
$152$	−2.86859	−	1.82675i	−0.232674	−	0.148169i
$153$	13.9672	−	5.41029i	1.12918	−	0.437396i
$154$	6.31159	+	9.29762i	0.508602	+	0.749223i
$155$	6.66165	+	8.68163i	0.535076	+	0.697325i
$156$	10.0324	+	20.1858i	0.803237	+	1.61616i
$157$	−2.50403	−	1.92141i	−0.199843	−	0.153345i	0.503992	−	0.863708i	$-0.331864\pi$
$157$	−2.50403	−	1.92141i	−0.199843	−	0.153345i	−0.703835	+	0.710363i	$0.748531\pi$
$158$	−4.38946	+	3.90677i	−0.349206	+	0.310806i
$159$	−4.14936	−	0.875382i	−0.329066	−	0.0694223i
$160$	8.70026	−	0.891574i	0.687816	−	0.0704851i
$161$			17.6162i			1.38835i
$162$	−11.6258	+	5.18071i	−0.913412	+	0.407035i
$163$	−8.28458	−	20.0007i	−0.648898	−	1.56658i	−0.814358	−	0.580363i	$-0.802911\pi$
$163$	−8.28458	−	20.0007i	−0.648898	−	1.56658i	0.165460	−	0.986217i	$-0.447089\pi$
$164$	−7.56412	+	5.98245i	−0.590658	+	0.467151i
$165$	−4.06557	+	5.93476i	−0.316504	+	0.462020i
$166$	1.94089	+	0.939510i	0.150643	+	0.0729201i
$167$	0.799383	−	2.98334i	0.0618581	−	0.230858i	−0.928075	−	0.372393i	$-0.878537\pi$
$167$	0.799383	−	2.98334i	0.0618581	−	0.230858i	0.989933	+	0.141536i	$0.0452040\pi$
$168$	−12.6243	−	7.11406i	−0.973983	−	0.548862i
$169$	−7.59455	−	28.3433i	−0.584196	−	2.18025i
$170$	−2.05113	+	10.7221i	−0.157315	+	0.822349i
$171$	−2.60897	+	2.49095i	−0.199513	+	0.190488i
$172$	−0.230115	−	15.6869i	−0.0175461	−	1.19612i
$173$	−0.224937	+	1.70857i	−0.0171016	+	0.129900i	−0.997866	−	0.0652959i	$-0.979201\pi$
$173$	−0.224937	+	1.70857i	−0.0171016	+	0.129900i	0.980764	+	0.195196i	$0.0625342\pi$
$174$	1.45620	−	5.34398i	0.110394	−	0.405126i
$175$	3.85964	+	6.68510i	0.291762	+	0.505346i
$176$	−8.71325	−	6.28863i	−0.656786	−	0.474023i
$177$	−5.21940	−	15.9809i	−0.392314	−	1.20120i
$178$	11.1113	−	5.58118i	0.832830	−	0.418327i
$179$	1.10554	+	2.66901i	0.0826319	+	0.199491i	0.959795	−	0.280701i	$-0.0905670\pi$
$179$	1.10554	+	2.66901i	0.0826319	+	0.199491i	−0.877163	+	0.480192i	$0.840567\pi$
$180$	1.28866	−	9.18640i	0.0960513	−	0.684714i
$181$	20.2567	+	8.39058i	1.50567	+	0.623667i	0.974658	−	0.223700i	$-0.0718136\pi$
$181$	20.2567	+	8.39058i	1.50567	+	0.623667i	0.531007	+	0.847367i	$0.321814\pi$
$182$	20.5963	+	17.7970i	1.52670	+	1.31920i
$183$	−10.9380	+	0.589915i	−0.808558	+	0.0436078i
$184$	−5.76428	−	15.8281i	−0.424948	−	1.16686i
$185$	−11.0288	−	2.95516i	−0.810855	−	0.217268i
$186$	6.56685	+	16.0456i	0.481505	+	1.17652i
$187$	10.6410	−	8.16511i	0.778145	−	0.597092i
$188$	−4.62826	−	10.7259i	−0.337550	−	0.782263i
$189$	−10.5289	+	11.1970i	−0.765863	+	0.814461i
$190$	−0.531781	−	2.57462i	−0.0385795	−	0.186782i
$191$	0.988975	−	1.71295i	0.0715597	−	0.123945i	−0.828025	−	0.560691i	$-0.810536\pi$
$191$	0.988975	−	1.71295i	0.0715597	−	0.123945i	0.899585	+	0.436746i	$0.143869\pi$
$192$	13.6707	+	2.26111i	0.986596	+	0.163181i
$193$	13.4692	+	23.3294i	0.969538	+	1.67929i	0.696895	+	0.717173i	$0.254564\pi$
$193$	13.4692	+	23.3294i	0.969538	+	1.67929i	0.272643	+	0.962115i	$0.412102\pi$
$194$	0.618182	−	0.550204i	0.0443829	−	0.0395023i
$195$	−5.79166	+	16.4345i	−0.414749	+	1.17690i
$196$	−3.47489	−	0.405721i	−0.248207	−	0.0289801i
$197$	17.1270	+	7.09424i	1.22025	+	0.505443i	0.897489	−	0.441037i	$-0.145389\pi$
$197$	17.1270	+	7.09424i	1.22025	+	0.505443i	0.322760	+	0.946481i	$0.395389\pi$
$198$	−8.68672	+	7.37848i	−0.617339	+	0.524365i
$199$	−0.638740	+	0.638740i	−0.0452791	+	0.0452791i	−0.729384	−	0.684105i	$-0.760193\pi$
$199$	−0.638740	+	0.638740i	−0.0452791	+	0.0452791i	0.684105	+	0.729384i	$0.260193\pi$
$200$	−5.65534	−	4.74360i	−0.399893	−	0.335423i
$201$	17.3118	+	8.78765i	1.22108	+	0.619833i
$202$	5.04872	−	1.75521i	0.355227	−	0.123496i
$203$	−0.873022	−	6.63126i	−0.0612742	−	0.465424i
$204$	−7.60154	+	15.5356i	−0.532214	+	1.08771i
$205$	−7.39126	−	0.973078i	−0.516228	−	0.0679627i
$206$	13.5087	+	8.88359i	0.941193	+	0.618949i
$207$	−17.7632	+	1.92163i	−1.23463	+	0.133562i
$208$	−24.3291	−	9.25108i	−1.68692	−	0.641447i
$209$	−1.61504	+	2.79733i	−0.111715	+	0.193496i
$210$	−2.85338	−	10.8323i	−0.196902	−	0.747497i
$211$	−7.59881	−	5.83077i	−0.523124	−	0.401407i	0.313163	−	0.949699i	$-0.398611\pi$
$211$	−7.59881	−	5.83077i	−0.523124	−	0.401407i	−0.836287	+	0.548292i	$0.815278\pi$
$212$	4.20433	−	2.51031i	0.288755	−	0.172409i
$213$	15.3855	−	22.4591i	1.05420	−	1.53887i
$214$	−1.32836	−	1.14782i	−0.0908048	−	0.0784631i
$215$	8.57560	−	8.57560i	0.584851	−	0.584851i
$216$	5.79633	−	13.5056i	0.394391	−	0.918943i
$217$	14.8040	+	14.8040i	1.00496	+	1.00496i
$218$	0.444097	+	6.09081i	0.0300781	+	0.412522i
$219$	−8.40248	−	5.75607i	−0.567787	−	0.388959i
$220$	−1.20491	−	8.21879i	−0.0812353	−	0.554111i
$221$	19.7780	−	25.7752i	1.33041	−	1.73383i
$222$	−15.6278	−	9.11120i	−1.04887	−	0.611504i
$223$	−3.44361	−	1.98817i	−0.230601	−	0.133138i	0.380248	−	0.924884i	$-0.375839\pi$
$223$	−3.44361	−	1.98817i	−0.230601	−	0.133138i	−0.610849	+	0.791747i	$0.709172\pi$
$224$	16.2803	−	3.86381i	1.08777	−	0.258162i
$225$	−6.31987	+	4.62109i	−0.421325	+	0.308072i
$226$	−5.05024	−	24.4507i	−0.335937	−	1.62644i
$227$	−0.787474	+	5.98146i	−0.0522665	+	0.397004i	0.945237	+	0.326385i	$0.105831\pi$
$227$	−0.787474	+	5.98146i	−0.0522665	+	0.397004i	−0.997503	+	0.0706185i	$0.977503\pi$
$228$	0.259535	−	4.15709i	0.0171881	−	0.275310i
$229$	14.2553	−	1.87675i	0.942020	−	0.124019i	0.356154	−	0.934427i	$-0.384088\pi$
$229$	14.2553	−	1.87675i	0.942020	−	0.124019i	0.585866	+	0.810408i	$0.300755\pi$
$230$	5.67354	−	11.7207i	0.374102	−	0.772841i
$231$	−6.22966	+	12.2725i	−0.409881	+	0.807471i
$232$	2.95425	+	5.67250i	0.193956	+	0.372418i
$233$	−15.6057	−	15.6057i	−1.02236	−	1.02236i	−0.999744	−	0.0226194i	$-0.992799\pi$
$233$	−15.6057	−	15.6057i	−1.02236	−	1.02236i	−0.0226194	−	0.999744i	$-0.507201\pi$
$234$	−15.6988	+	22.7096i	−1.02626	+	1.48457i
$235$	3.45577	−	8.34298i	0.225430	−	0.544236i
$236$	16.9522	+	9.45859i	1.10350	+	0.615702i
$237$	−6.78774	−	2.39205i	−0.440911	−	0.155381i
$238$	−1.21309	+	20.8503i	−0.0786332	+	1.35152i
$239$	7.83827	−	4.52542i	0.507015	−	0.292725i	−0.224591	−	0.974453i	$-0.572104\pi$
$239$	7.83827	−	4.52542i	0.507015	−	0.292725i	0.731606	+	0.681728i	$0.238771\pi$
$240$	6.10822	+	8.79907i	0.394284	+	0.567978i
$241$	9.52404	+	5.49871i	0.613497	+	0.354203i	0.774333	−	0.632778i	$-0.218086\pi$
$241$	9.52404	+	5.49871i	0.613497	+	0.354203i	−0.160836	+	0.986981i	$0.551419\pi$
$242$	2.93979	−	4.47034i	0.188977	−	0.287364i
$243$	−12.4390	−	9.39534i	−0.797959	−	0.602712i
$244$	8.81165	−	9.07402i	0.564108	−	0.580905i
$245$	−1.64636	−	2.14558i	−0.105182	−	0.137076i
$246$	−10.8930	−	4.56619i	−0.694515	−	0.291130i
$247$	−2.02503	+	7.55751i	−0.128849	+	0.480873i
$248$	−18.1454	−	8.45725i	−1.15224	−	0.537036i
$249$	0.142227	+	2.63712i	0.00901328	+	0.167121i
$250$	−1.20993	−	16.5942i	−0.0765227	−	1.04951i
$251$	−1.33905	+	3.23276i	−0.0845203	+	0.204050i	−0.960489	−	0.278318i	$-0.910223\pi$
$251$	−1.33905	+	3.23276i	−0.0845203	+	0.204050i	0.875969	+	0.482368i	$0.160223\pi$
$252$	0.150326	−	17.7468i	0.00946963	−	1.11795i
$253$	−14.7813	+	6.12261i	−0.929291	+	0.384925i
$254$	2.13985	−	6.45904i	0.134266	−	0.405276i
$255$	−12.7093	+	4.15089i	−0.795888	+	0.259939i
$256$	−13.3635	+	8.79876i	−0.835216	+	0.549923i
$257$	−15.6978	+	9.06314i	−0.979204	+	0.565343i	−0.902030	−	0.431674i	$-0.857923\pi$
$257$	−15.6978	+	9.06314i	−0.979204	+	0.565343i	−0.0771740	+	0.997018i	$0.524590\pi$
$258$	16.6808	−	9.53671i	1.03850	−	0.593729i
$259$	−21.6578	−	2.85130i	−1.34575	−	0.177171i
$260$	−7.97176	−	18.4743i	−0.494387	−	1.14573i
$261$	6.59137	−	1.60367i	0.407996	−	0.0992645i
$262$	−2.71774	−	4.00350i	−0.167902	−	0.247337i
$263$	19.2026	−	5.14532i	1.18408	−	0.317274i	0.387538	−	0.921854i	$-0.373326\pi$
$263$	19.2026	−	5.14532i	1.18408	−	0.317274i	0.796544	+	0.604580i	$0.206659\pi$
$264$	1.58158	−	13.0652i	0.0973397	−	0.804109i
$265$	3.65634	+	0.979712i	0.224607	+	0.0601832i
$266$	−1.65164	−	4.75081i	−0.101268	−	0.291291i
$267$	12.5636	+	8.60660i	0.768878	+	0.526716i
$268$	−21.5666	+	6.11916i	−1.31739	+	0.373787i
$269$	−11.8080	+	4.89104i	−0.719948	+	0.298212i	−0.712414	−	0.701759i	$-0.752398\pi$
$269$	−11.8080	+	4.89104i	−0.719948	+	0.298212i	−0.00753398	+	0.999972i	$0.502398\pi$
$270$	10.6114	−	4.05881i	0.645789	−	0.247011i
$271$	−7.14125			−0.433800			−0.216900	−	0.976194i	$-0.569595\pi$
$271$	−7.14125			−0.433800			−0.216900	+	0.976194i	$0.569595\pi$
$272$	−5.73255	−	19.1308i	−0.347587	−	1.15998i
$273$	−6.88173	+	32.6198i	−0.416501	+	1.97424i
$274$	−10.6367	−	0.618857i	−0.642586	−	0.0373865i
$275$	−4.26785	+	5.56197i	−0.257361	+	0.335399i
$276$	13.5547	−	15.5532i	0.815899	−	0.936191i
$277$	−11.2759	+	8.65230i	−0.677503	+	0.519866i	−0.889229	−	0.457463i	$-0.848758\pi$
$277$	−11.2759	+	8.65230i	−0.677503	+	0.519866i	0.211726	+	0.977329i	$0.432092\pi$
$278$	0.925602	+	0.177067i	0.0555139	+	0.0106198i
$279$	−13.3127	+	16.5424i	−0.797010	+	0.990369i
$280$	10.9103	+	6.94778i	0.652015	+	0.415209i
$281$	−5.78495	−	21.5897i	−0.345101	−	1.28793i	−0.892494	−	0.451059i	$-0.851046\pi$
$281$	−5.78495	−	21.5897i	−0.345101	−	1.28793i	0.547393	−	0.836876i	$-0.315620\pi$
$282$	8.75769	−	11.3137i	0.521513	−	0.673722i
$283$	−3.43824	−	26.1160i	−0.204382	−	1.55244i	−0.718996	−	0.695014i	$-0.755398\pi$
$283$	−3.43824	−	26.1160i	−0.204382	−	1.55244i	0.514614	−	0.857422i	$-0.327935\pi$
$284$	4.55979	+	31.1026i	0.270574	+	1.84560i
$285$	2.44518	−	2.09482i	0.144840	−	0.124086i
$286$	−7.77459	+	23.4673i	−0.459721	+	1.38765i
$287$	−14.2630			−0.841917
$288$	5.67196	+	15.9947i	0.334223	+	0.942494i
$289$	7.92813			0.466360
$290$	−1.55483	+	4.69320i	−0.0913030	+	0.275594i
$291$	0.955940	+	0.336881i	0.0560382	+	0.0197483i
$292$	11.6362	−	1.70593i	0.680959	−	0.0998318i
$293$	−0.659021	−	5.00576i	−0.0385004	−	0.292440i	−0.999853	−	0.0171209i	$-0.994550\pi$
$293$	−0.659021	−	5.00576i	−0.0385004	−	0.292440i	0.961353	−	0.275319i	$-0.0887833\pi$
$294$	−1.62293	−	3.96552i	−0.0946512	−	0.231274i
$295$	3.88394	+	14.4951i	0.226132	+	0.843934i
$296$	20.3924	−	4.52486i	1.18528	−	0.263002i
$297$	−13.0545	−	4.94293i	−0.757497	−	0.286818i
$298$	12.9088	+	2.46944i	0.747787	+	0.143051i
$299$	−30.7457	+	23.5920i	−1.77807	+	1.36436i
$300$	1.73619	−	8.87201i	0.100239	−	0.512226i
$301$	14.1249	−	18.4080i	0.814148	−	1.06102i
$302$	−24.9992	−	1.45448i	−1.43854	−	0.0836961i
$303$	4.87159	+	4.37300i	0.279865	+	0.251222i
$304$	3.03853	+	3.72814i	0.174271	+	0.213824i
$305$	9.77761			0.559864
$306$	−21.1566	+	1.05119i	−1.20944	+	0.0600926i
$307$	4.85832	−	2.01238i	0.277279	−	0.114853i	−0.239711	−	0.970844i	$-0.577053\pi$
$307$	4.85832	−	2.01238i	0.277279	−	0.114853i	0.516990	+	0.855992i	$0.327053\pi$
$308$	−4.33793	−	15.2888i	−0.247177	−	0.871158i
$309$	−1.52359	+	19.7429i	−0.0866742	+	1.12313i
$310$	−5.08183	−	14.6175i	−0.288629	−	0.830218i
$311$	13.2455	+	3.54911i	0.751081	+	0.201252i	0.613998	−	0.789308i	$-0.289560\pi$
$311$	13.2455	+	3.54911i	0.751081	+	0.201252i	0.137083	+	0.990559i	$0.456227\pi$
$312$	−4.49048	−	31.5606i	−0.254223	−	1.78677i
$313$	−12.4095	+	3.32511i	−0.701426	+	0.187946i	−0.591869	−	0.806034i	$-0.701610\pi$
$313$	−12.4095	+	3.32511i	−0.701426	+	0.187946i	−0.109557	+	0.993981i	$0.534943\pi$
$314$	2.50701	+	3.69308i	0.141479	+	0.208412i
$315$	9.92287	−	9.47397i	0.559090	−	0.533798i
$316$	7.63020	−	3.29247i	0.429233	−	0.185216i
$317$	22.2519	+	2.92952i	1.24979	+	0.164538i	0.726232	−	0.687449i	$-0.241270\pi$
$317$	22.2519	+	2.92952i	1.24979	+	0.164538i	0.523561	+	0.851988i	$0.324603\pi$
$318$	5.18103	+	3.02060i	0.290538	+	0.169387i
$319$	5.26069	−	3.03726i	0.294542	−	0.170054i
$320$	−12.0763	−	2.67254i	−0.675084	−	0.149400i
$321$	0.443837	−	2.10382i	0.0247726	−	0.117424i
$322$	7.83481	−	23.6490i	0.436617	−	1.31791i
$323$	−5.54631	+	2.29736i	−0.308605	+	0.127828i
$324$	17.9113	−	1.78430i	0.995075	−	0.0991277i
$325$	−6.49864	+	15.6891i	−0.360480	+	0.870276i
$326$	2.22637	+	30.5348i	0.123307	+	1.69116i
$327$	−6.26663	+	4.08316i	−0.346545	+	0.225799i
$328$	12.8152	−	4.66705i	0.707602	−	0.257695i
$329$	4.47159	−	16.6882i	0.246527	−	0.920050i
$330$	8.09735	−	6.15901i	0.445745	−	0.339042i
$331$	14.5537	+	18.9667i	0.799942	+	1.04250i	0.998056	+	0.0623256i	$0.0198517\pi$
$331$	14.5537	+	18.9667i	0.799942	+	1.04250i	−0.198114	+	0.980179i	$0.563482\pi$
$332$	−2.18772	−	2.12447i	−0.120067	−	0.116595i
$333$	0.512599	−	22.1495i	0.0280903	−	1.21379i
$334$	−2.39998	+	3.64948i	−0.131321	+	0.199691i
$335$	−15.0079	−	8.66482i	−0.819970	−	0.473410i
$336$	13.7836	+	15.1650i	0.751956	+	0.827318i
$337$	28.2080	−	16.2859i	1.53659	−	0.887149i	0.537552	−	0.843230i	$-0.319349\pi$
$337$	28.2080	−	16.2859i	1.53659	−	0.887149i	0.999035	−	0.0439189i	$-0.0139843\pi$
$338$	−2.41030	+	41.4273i	−0.131103	+	2.25335i
$339$	23.2214	−	19.8941i	1.26122	−	1.08050i
$340$	7.52223	−	13.4818i	0.407950	−	0.731152i
$341$	−7.27644	+	17.5669i	−0.394041	+	0.951299i
$342$	4.61029	−	2.18365i	0.249296	−	0.118079i
$343$	10.9823	+	10.9823i	0.592986	+	0.592986i
$344$	−6.66784	+	21.1614i	−0.359506	+	1.14095i
$345$	15.9251	−	0.858885i	0.857378	−	0.0462408i
$346$	1.06185	−	2.19364i	0.0570856	−	0.117931i
$347$	28.9175	−	3.80706i	1.55237	−	0.204374i	0.694976	−	0.719033i	$-0.255415\pi$
$347$	28.9175	−	3.80706i	1.55237	−	0.204374i	0.857395	+	0.514659i	$0.172081\pi$
$348$	−4.33163	+	6.52643i	−0.232200	+	0.349853i
$349$	−1.85775	+	14.1110i	−0.0994431	+	0.755345i	0.866972	+	0.498358i	$0.166063\pi$
$349$	−1.85775	+	14.1110i	−0.0994431	+	0.755345i	−0.966415	+	0.256988i	$0.917270\pi$
$350$	−2.20821	−	10.6911i	−0.118034	−	0.571461i
$351$	−33.6427	−	3.38089i	−1.79572	−	0.180459i
$352$	8.90032	+	12.3174i	0.474389	+	0.656522i
$353$	1.76716	+	1.02027i	0.0940563	+	0.0543034i	0.546290	−	0.837596i	$-0.316040\pi$
$353$	1.76716	+	1.02027i	0.0940563	+	0.0543034i	−0.452234	+	0.891899i	$0.649373\pi$
$354$	−0.100692	+	23.7751i	−0.00535174	+	1.26363i
$355$	−14.7930	+	19.2787i	−0.785133	+	1.02320i
$356$	−17.3987	+	2.55074i	−0.922132	+	0.135189i
$357$	−23.0708	+	11.0473i	−1.22104	+	0.584686i
$358$	−0.297099	−	4.07472i	−0.0157022	−	0.215356i
$359$	−12.1288	−	12.1288i	−0.640134	−	0.640134i	0.310454	−	0.950588i	$-0.399519\pi$
$359$	−12.1288	−	12.1288i	−0.640134	−	0.640134i	−0.950588	+	0.310454i	$0.899519\pi$
$360$	−5.81563	+	11.7592i	−0.306511	+	0.619766i
$361$	−12.4127	+	12.4127i	−0.653302	+	0.653302i
$362$	−23.4620	−	20.2732i	−1.23314	−	1.06553i
$363$	6.53340	+	0.504194i	0.342914	+	0.0264633i
$364$	−19.7345	−	33.0519i	−1.03437	−	1.73239i
$365$	7.21260	+	5.53442i	0.377525	+	0.289685i
$366$	14.9462	+	4.07273i	0.781248	+	0.212885i
$367$	−1.49493	+	2.58930i	−0.0780349	+	0.135160i	−0.902402	−	0.430895i	$-0.858198\pi$
$367$	−1.49493	+	2.58930i	−0.0780349	+	0.135160i	0.824367	+	0.566055i	$0.191531\pi$
$368$	0.698764	+	23.8122i	0.0364256	+	1.24130i
$369$	−1.55585	−	14.3820i	−0.0809942	−	0.748697i
$370$	13.4914	+	8.87226i	0.701386	+	0.461247i
$371$	7.18010	+	0.945278i	0.372772	+	0.0490764i
$372$	−1.67942	−	24.4612i	−0.0870738	−	1.26826i
$373$	3.94516	+	29.9665i	0.204273	+	1.55161i	0.719463	+	0.694530i	$0.244388\pi$
$373$	3.94516	+	29.9665i	0.204273	+	1.55161i	−0.515190	+	0.857076i	$0.672279\pi$
$374$	−17.9165	+	6.22875i	−0.926441	+	0.322081i
$375$	17.0732	−	11.1244i	0.881658	−	0.574464i
$376$	1.44292	+	16.4574i	0.0744128	+	0.848728i
$377$	10.4044	−	10.4044i	0.535856	−	0.535856i
$378$	19.1145	−	10.3488i	0.983141	−	0.532284i
$379$	7.48322	+	3.09965i	0.384387	+	0.159218i	0.566505	−	0.824058i	$-0.308295\pi$
$379$	7.48322	+	3.09965i	0.384387	+	0.159218i	−0.182118	+	0.983277i	$0.558295\pi$
$380$	−0.431166	+	3.69283i	−0.0221184	+	0.189438i
$381$	8.19164	−	1.53112i	0.419670	−	0.0784416i
$382$	−2.08950	+	1.85973i	−0.106908	+	0.0951518i
$383$	0.257852	+	0.446612i	0.0131756	+	0.0228208i	0.872538	−	0.488546i	$-0.162473\pi$
$383$	0.257852	+	0.446612i	0.0131756	+	0.0228208i	−0.859362	+	0.511367i	$0.829139\pi$
$384$	−17.3467	−	9.11548i	−0.885220	−	0.465172i
$385$	6.14258	−	10.6393i	0.313055	−	0.542227i
$386$	−7.70615	−	37.3093i	−0.392233	−	1.89899i
$387$	20.1024	+	12.2348i	1.02186	+	0.621931i
$388$	−1.07459	+	0.463690i	−0.0545539	+	0.0235403i
$389$	13.0058	−	9.97970i	0.659420	−	0.505991i	−0.223990	−	0.974591i	$-0.571908\pi$
$389$	13.0058	−	9.97970i	0.659420	−	0.505991i	0.883410	+	0.468601i	$0.155242\pi$
$390$	15.0843	−	19.4868i	0.763825	−	0.986755i
$391$	−28.7220	−	7.69605i	−1.45254	−	0.389206i
$392$	4.48446	+	2.09012i	0.226499	+	0.105567i
$393$	2.68246	−	5.28447i	0.135312	−	0.266566i
$394$	−19.8371	−	17.1410i	−0.999381	−	0.863549i
$395$	5.93506	+	2.45838i	0.298625	+	0.123695i
$396$	14.9432	−	6.04188i	0.750922	−	0.303616i
$397$	8.66632	+	20.9223i	0.434950	+	1.05006i	0.977670	+	0.210148i	$0.0673947\pi$
$397$	8.66632	+	20.9223i	0.434950	+	1.05006i	−0.542719	+	0.839914i	$0.682605\pi$
$398$	1.14156	−	0.573402i	0.0572213	−	0.0287421i
$399$	4.11496	−	4.58413i	0.206006	−	0.229494i
$400$	5.48234	+	8.88331i	0.274117	+	0.444165i
$401$	−2.47477	−	4.28643i	−0.123584	−	0.214054i	0.797594	−	0.603194i	$-0.206106\pi$
$401$	−2.47477	−	4.28643i	−0.123584	−	0.214054i	−0.921179	+	0.389140i	$0.872772\pi$
$402$	−19.3320	−	19.4965i	−0.964194	−	0.972396i
$403$	−6.01171	+	45.6635i	−0.299465	+	2.27466i
$404$	−7.55833	+	0.110875i	−0.376041	+	0.00551623i
$405$	10.6355	+	8.97223i	0.528480	+	0.445834i
$406$	−1.77726	+	9.29048i	−0.0882039	+	0.461079i
$407$	−5.13483	−	19.1634i	−0.254524	−	0.949897i
$408$	17.1142	−	17.4751i	0.847280	−	0.865146i
$409$	−0.857913	+	3.20178i	−0.0424211	+	0.158318i	−0.983887	−	0.178790i	$-0.942782\pi$
$409$	−0.857913	+	3.20178i	−0.0424211	+	0.158318i	0.941466	+	0.337107i	$0.109449\pi$
$410$	9.48969	+	4.59359i	0.468663	+	0.226861i
$411$	−5.63576	−	11.7695i	−0.277992	−	0.580548i
$412$	−14.1838	−	17.9338i	−0.698788	−	0.883537i
$413$	10.9869	+	26.5247i	0.540630	+	1.30520i
$414$	24.7010	+	5.32049i	1.21399	+	0.261488i
$415$		−	2.35736i		−	0.115718i
$416$	28.5465	+	23.2396i	1.39961	+	1.13941i
$417$	0.358331	+	1.09715i	0.0175475	+	0.0537276i
$418$	3.41224	−	3.03702i	0.166898	−	0.148545i
$419$	−30.2660	−	23.2239i	−1.47859	−	1.13456i	−0.960164	−	0.279438i	$-0.909852\pi$
$419$	−30.2660	−	23.2239i	−1.47859	−	1.13456i	−0.518425	−	0.855123i	$-0.673482\pi$
$420$	−0.987104	+	15.8109i	−0.0481658	+	0.771493i
$421$	12.8717	+	16.7747i	0.627328	+	0.817549i	0.993600	−	0.112958i	$-0.0360327\pi$
$421$	12.8717	+	16.7747i	0.627328	+	0.817549i	−0.366272	+	0.930508i	$0.619366\pi$
$422$	7.60786	+	11.2072i	0.370345	+	0.545556i
$423$	17.3152	+	2.68851i	0.841896	+	0.130720i
$424$	−6.76060	+	1.50011i	−0.328324	+	0.0728516i
$425$	−12.5858	+	3.37235i	−0.610500	+	0.163583i
$426$	−30.6431	+	23.3077i	−1.48466	+	1.12926i
$427$	18.5465	−	2.44169i	0.897526	−	0.118162i
$428$	1.27278	+	2.13168i	0.0615221	+	0.103039i
$429$	−29.7622	+	5.56293i	−1.43693	+	0.268581i
$430$	−15.3264	+	7.69840i	−0.739105	+	0.371250i
$431$			35.6626i			1.71781i	0.512137	+	0.858904i	$0.328854\pi$
$431$			35.6626i			1.71781i	−0.512137	+	0.858904i	$0.671146\pi$
$432$	−13.7880	+	15.5529i	−0.663375	+	0.748287i
$433$		−	11.4762i		−	0.551512i	−0.961228	−	0.275756i	$-0.911072\pi$
$433$		−	11.4762i		−	0.551512i	0.961228	−	0.275756i	$-0.0889282\pi$
$434$	−13.2897	−	26.4579i	−0.637926	−	1.27002i
$435$	−5.95212	+	1.11253i	−0.285382	+	0.0533415i
$436$	2.11271	−	8.37418i	0.101180	−	0.401050i
$437$	7.09968	−	0.934691i	0.339624	−	0.0447123i
$438$	8.71997	+	11.4643i	0.416656	+	0.547785i
$439$	9.16729	−	2.45637i	0.437531	−	0.117236i	−0.0333283	−	0.999444i	$-0.510611\pi$
$439$	9.16729	−	2.45637i	0.437531	−	0.117236i	0.470859	+	0.882208i	$0.343944\pi$
$440$	−2.03776	+	11.5693i	−0.0971465	+	0.551544i
$441$	3.29010	−	4.08829i	0.156671	−	0.194681i
$442$	−38.0148	+	25.8059i	−1.80818	+	1.22746i
$443$	14.4580	+	18.8421i	0.686922	+	0.895215i	0.998486	−	0.0550108i	$-0.0175193\pi$
$443$	14.4580	+	18.8421i	0.686922	+	0.895215i	−0.311563	+	0.950225i	$0.600853\pi$
$444$	16.9275	+	19.1819i	0.803345	+	0.910333i
$445$	−10.7844	−	8.27520i	−0.511232	−	0.392282i
$446$	3.73867	+	4.20058i	0.177031	+	0.198903i
$447$	4.99742	+	15.3013i	0.236370	+	0.723725i
$448$	−23.5740	−	2.05364i	−1.11377	−	0.0970254i
$449$		−	34.6572i		−	1.63557i	−0.575522	−	0.817786i	$-0.695201\pi$
$449$		−	34.6572i		−	1.63557i	0.575522	−	0.817786i	$-0.304799\pi$
$450$	10.5394	−	3.39286i	0.496832	−	0.159941i
$451$	−4.95718	−	11.9677i	−0.233424	−	0.563536i
$452$	−4.09471	+	35.0702i	−0.192599	+	1.64956i
$453$	−13.2456	−	27.6616i	−0.622332	−	1.29966i
$454$	3.71741	−	7.67964i	0.174467	−	0.360423i
$455$	7.70191	−	28.7439i	0.361071	−	1.34754i
$456$	−2.19728	+	5.46530i	−0.102897	+	0.255936i
$457$	−7.24753	−	27.0481i	−0.339025	−	1.26526i	−0.899439	−	0.437046i	$-0.856025\pi$
$457$	−7.24753	−	27.0481i	−0.339025	−	1.26526i	0.560414	−	0.828213i	$-0.310642\pi$
$458$	−19.9719	−	3.82061i	−0.933226	−	0.178525i
$459$	−13.6562	−	22.0583i	−0.637415	−	1.02959i
$460$	−12.8293	+	13.2113i	−0.598168	+	0.615979i
$461$	−1.17429	+	8.91964i	−0.0546922	+	0.415429i	0.942096	+	0.335344i	$0.108853\pi$
$461$	−1.17429	+	8.91964i	−0.0546922	+	0.415429i	−0.996788	+	0.0800850i	$0.974481\pi$
$462$	13.8213	−	13.7047i	0.643023	−	0.637600i
$463$	6.30838	+	10.9264i	0.293175	+	0.507794i	0.974559	−	0.224132i	$-0.0719548\pi$
$463$	6.30838	+	10.9264i	0.293175	+	0.507794i	−0.681384	+	0.731926i	$0.738621\pi$
$464$	−1.44312	−	8.92900i	−0.0669952	−	0.414519i
$465$	12.6611	−	14.1047i	0.587144	−	0.654088i
$466$	14.0094	+	27.8907i	0.648972	+	1.29201i
$467$	−10.2089	−	24.6464i	−0.472411	−	1.14050i	−0.963095	−	0.269163i	$-0.913253\pi$
$467$	−10.2089	−	24.6464i	−0.472411	−	1.14050i	0.490684	−	0.871338i	$-0.336747\pi$
$468$	31.1751	−	23.5046i	1.44107	−	1.08650i
$469$	−30.6313	−	12.6879i	−1.41442	−	0.585872i
$470$	−8.34978	+	9.66315i	−0.385147	+	0.445728i
$471$	−2.47446	+	4.87472i	−0.114017	+	0.224615i
$472$	−18.5510	−	20.2373i	−0.853878	−	0.931497i
$473$	20.3549	+	5.45407i	0.935917	+	0.250778i
$474$	8.04839	+	6.23008i	0.369675	+	0.286157i
$475$	2.48944	−	1.91022i	0.114223	−	0.0876467i
$476$	10.9017	−	27.4511i	0.499678	−	1.25822i
$477$	−0.169940	+	7.34314i	−0.00778101	+	0.336219i
$478$	−12.5352	+	2.58913i	−0.573348	+	0.118424i
$479$	10.0972	−	17.4888i	0.461352	−	0.799086i	−0.537676	−	0.843151i	$-0.680698\pi$
$479$	10.0972	−	17.4888i	0.461352	−	0.799086i	0.999029	+	0.0440655i	$0.0140310\pi$
$480$	−4.28665	−	14.5290i	−0.195658	−	0.663156i
$481$	−24.0282	−	41.6180i	−1.09559	−	1.89762i
$482$	−10.3401	−	11.6176i	−0.470978	−	0.529168i
$483$	29.9927	−	5.60601i	1.36472	−	0.255082i
$484$	−5.93474	+	4.69378i	−0.269761	+	0.213353i
$485$	−0.835855	−	0.346223i	−0.0379542	−	0.0157212i
$486$	12.5202	+	18.1451i	0.567928	+	0.823078i
$487$	−2.14034	+	2.14034i	−0.0969880	+	0.0969880i	−0.753936	−	0.656948i	$-0.771847\pi$
$487$	−2.14034	+	2.14034i	−0.0969880	+	0.0969880i	0.656948	+	0.753936i	$0.271847\pi$
$488$	−15.8650	+	8.26252i	−0.718173	+	0.374027i
$489$	−31.4162	+	20.4699i	−1.42069	+	0.925680i
$490$	1.25592	+	3.61257i	0.0567368	+	0.163199i
$491$	2.00127	+	15.2012i	0.0903161	+	0.686019i	0.975377	+	0.220544i	$0.0707833\pi$
$491$	2.00127	+	15.2012i	0.0903161	+	0.686019i	−0.885061	+	0.465475i	$0.845883\pi$
$492$	12.5926	+	10.9746i	0.567720	+	0.494774i
$493$	11.1932	+	1.47362i	0.504118	+	0.0663684i
$494$	6.07972	−	9.24502i	0.273540	−	0.415953i
$495$	11.3981	+	5.03328i	0.512307	+	0.226229i
$496$	20.5981	+	19.4237i	0.924884	+	0.872150i
$497$	−23.2456	+	40.2625i	−1.04271	+	1.80602i
$498$	0.981925	−	3.60348i	0.0440011	−	0.161476i
$499$	11.8627	+	9.10255i	0.531046	+	0.407486i	0.839177	−	0.543858i	$-0.183037\pi$
$499$	11.8627	+	9.10255i	0.531046	+	0.407486i	−0.308131	+	0.951344i	$0.599704\pi$
$500$	−5.75601	+	22.8152i	−0.257417	+	1.02033i
$501$	−5.33372	−	0.411612i	−0.238293	−	0.0183895i
$502$	3.23540	−	3.74431i	0.144403	−	0.167117i
$503$	−21.7138	+	21.7138i	−0.968172	+	0.968172i	−0.999509	−	0.0313367i	$-0.990024\pi$
$503$	−21.7138	+	21.7138i	−0.968172	+	0.968172i	0.0313367	+	0.999509i	$0.490024\pi$
$504$	−8.09472	+	23.7576i	−0.360568	+	1.05825i
$505$	−4.13193	−	4.13193i	−0.183869	−	0.183869i
$506$	22.5663	−	1.64537i	1.00319	−	0.0731456i
$507$	−45.8394	+	21.9499i	−2.03580	+	0.974830i
$508$	−5.74532	+	7.71930i	−0.254908	+	0.342489i
$509$	6.80071	−	8.86285i	0.301436	−	0.392839i	−0.617936	−	0.786228i	$-0.712031\pi$
$509$	6.80071	−	8.86285i	0.301436	−	0.392839i	0.919372	+	0.393389i	$0.128698\pi$
$510$	18.9078	+	0.0800786i	0.837254	+	0.00354594i
$511$	15.0632	+	8.69671i	0.666355	+	0.384720i
$512$	21.8531	−	5.86858i	0.965782	−	0.259357i
$513$	5.07126	+	3.64925i	0.223902	+	0.161118i
$514$	25.1045	−	5.18529i	1.10731	−	0.228713i
$515$	2.30708	−	17.5240i	0.101662	−	0.772200i
$516$	−26.6348	+	5.38384i	−1.17253	+	0.237010i
$517$	15.5568	−	2.04809i	0.684185	−	0.0900747i
$518$	27.8066	+	13.4601i	1.22175	+	0.591401i
$519$	2.98053	−	0.160748i	0.130831	−	0.00705606i
$520$	2.48530	+	28.3465i	0.108987	+	1.24307i
$521$	−17.6069	−	17.6069i	−0.771373	−	0.771373i	0.206973	−	0.978347i	$-0.433639\pi$
$521$	−17.6069	−	17.6069i	−0.771373	−	0.771373i	−0.978347	+	0.206973i	$0.933639\pi$
$522$	−9.56188	−	0.778658i	−0.418512	−	0.0340809i
$523$	4.78488	−	11.5517i	0.209228	−	0.505122i	−0.784074	−	0.620668i	$-0.786862\pi$
$523$	4.78488	−	11.5517i	0.209228	−	0.505122i	0.993302	+	0.115546i	$0.0368617\pi$
$524$	1.86789	+	6.58325i	0.0815992	+	0.287591i
$525$	10.1536	−	8.69870i	0.443138	−	0.379642i
$526$	−28.0671	−	1.63298i	−1.22378	−	0.0712012i
$527$	−30.6044	+	17.6695i	−1.33315	+	0.769695i
$528$	−7.93397	+	16.8361i	−0.345282	+	0.732698i
$529$	10.7988	+	6.23467i	0.469512	+	0.271073i
$530$	−4.47275	−	2.94138i	−0.194284	−	0.127765i
$531$	−25.5476	+	13.9720i	−1.10867	+	0.606333i
$532$	0.104332	+	7.11234i	0.00452339	+	0.308359i
$533$	−19.1013	−	24.8933i	−0.827369	−	1.07825i
$534$	−13.0383	−	17.1417i	−0.564222	−	0.741793i
$535$	−0.496735	+	1.85384i	−0.0214757	+	0.0801485i
$536$	31.6737	+	1.37701i	1.36810	+	0.0594779i
$537$	4.19234	−	2.73161i	0.180913	−	0.117878i
$538$	18.0271	−	1.31440i	0.777203	−	0.0566680i
$539$	1.79830	−	4.34147i	0.0774582	−	0.187001i
$540$	−16.0505	+	0.729360i	−0.690705	+	0.0313866i
$541$	−21.2859	+	8.81690i	−0.915152	+	0.379068i	−0.790026	−	0.613073i	$-0.789933\pi$
$541$	−21.2859	+	8.81690i	−0.915152	+	0.379068i	−0.125125	+	0.992141i	$0.539933\pi$
$542$	9.58684	+	3.17607i	0.411790	+	0.136424i
$543$	7.83923	−	37.1584i	0.336413	−	1.59462i
$544$	−0.812722	+	28.2319i	−0.0348452	+	1.21043i
$545$	5.78186	−	3.33816i	0.247668	−	0.142991i
$546$	23.7461	−	40.7301i	1.01624	−	1.74309i
$547$	18.1443	+	2.38874i	0.775793	+	0.102135i	0.508018	−	0.861346i	$-0.330378\pi$
$547$	18.1443	+	2.38874i	0.775793	+	0.102135i	0.267775	+	0.963481i	$0.413712\pi$
$548$	14.0041	+	5.56147i	0.598225	+	0.237574i
$549$	4.48517	+	18.4349i	0.191422	+	0.786782i
$550$	8.20310	−	5.56859i	0.349781	−	0.237445i
$551$	−2.62621	+	0.703691i	−0.111880	+	0.0299783i
$552$	−25.1140	+	14.8510i	−1.06892	+	0.632102i
$553$	11.8717	+	3.18102i	0.504837	+	0.135271i
$554$	18.9855	−	6.60040i	0.806618	−	0.280424i
$555$	−1.52165	+	19.7177i	−0.0645905	+	0.836970i
$556$	−1.16383	−	0.649367i	−0.0493575	−	0.0275393i
$557$	0.459370	−	0.190277i	0.0194641	−	0.00806231i	−0.372930	−	0.927859i	$-0.621647\pi$
$557$	0.459370	−	0.190277i	0.0194641	−	0.00806231i	0.392394	+	0.919797i	$0.371647\pi$
$558$	25.2290	−	16.2867i	1.06803	−	0.689471i
$559$	51.0441			2.15894
$560$	−11.5566	−	14.1795i	−0.488355	−	0.599192i
$561$	−17.2879	−	15.5186i	−0.729897	−	0.655195i
$562$	−1.83598	+	31.5562i	−0.0774461	+	1.33112i
$563$	−13.4978	+	17.5907i	−0.568865	+	0.741360i	−0.985864	−	0.167547i	$-0.946415\pi$
$563$	−13.4978	+	17.5907i	−0.568865	+	0.741360i	0.416999	+	0.908907i	$0.363082\pi$
$564$	−16.7886	+	11.2932i	−0.706928	+	0.475530i
$565$	−21.6541	+	16.6158i	−0.910995	+	0.699031i
$566$	−6.99941	+	36.5888i	−0.294207	+	1.53794i
$567$	22.4142	+	14.3629i	0.941308	+	0.603184i
$568$	7.71156	−	43.7820i	0.323570	−	1.83705i
$569$	−8.45064	−	31.5382i	−0.354269	−	1.32215i	−0.881402	−	0.472368i	$-0.843399\pi$
$569$	−8.45064	−	31.5382i	−0.354269	−	1.32215i	0.527132	−	0.849783i	$-0.323267\pi$
$570$	−4.21422	+	1.72471i	−0.176514	+	0.0722403i
$571$	0.157240	+	1.19436i	0.00658028	+	0.0499822i	0.994420	−	0.105494i	$-0.0336423\pi$
$571$	0.157240	+	1.19436i	0.00658028	+	0.0499822i	−0.987840	+	0.155476i	$0.950309\pi$
$572$	20.8742	−	28.0461i	0.872792	−	1.17267i
$573$	−3.23114	−	1.13868i	−0.134983	−	0.0475690i
$574$	19.1475	+	6.34346i	0.799199	+	0.264771i
$575$	15.5424			0.648163
$576$	−0.500747	−	23.9948i	−0.0208645	−	0.999782i
$577$	20.7034			0.861892			0.430946	−	0.902378i	$-0.358180\pi$
$577$	20.7034			0.861892			0.430946	+	0.902378i	$0.358180\pi$
$578$	−10.6432	−	3.52604i	−0.442698	−	0.146664i
$579$	35.4335	−	30.3564i	1.47257	−	1.26157i
$580$	4.17460	−	5.60892i	0.173341	−	0.232898i
$581$	−0.588685	−	4.47150i	−0.0244228	−	0.185509i
$582$	−1.13348	−	0.877404i	−0.0469844	−	0.0363696i
$583$	1.70233	+	6.35317i	0.0705032	+	0.263121i
$584$	−16.3799	−	2.88508i	−0.677804	−	0.119385i
$585$	29.8239	+	4.63071i	1.23307	+	0.191456i
$586$	−1.34160	+	7.01313i	−0.0554212	+	0.289710i
$587$	36.2324	−	27.8021i	1.49547	−	1.14751i	0.544283	−	0.838902i	$-0.316802\pi$
$587$	36.2324	−	27.8021i	1.49547	−	1.14751i	0.951188	−	0.308613i	$-0.0998647\pi$
$588$	0.415051	+	6.04535i	0.0171164	+	0.249306i
$589$	5.18084	−	6.75180i	0.213473	−	0.278203i
$590$	1.23265	−	21.1864i	0.0507475	−	0.872230i
$591$	6.62807	−	31.4174i	0.272642	−	1.29234i
$592$	−29.3884	−	2.99509i	−1.20786	−	0.123097i
$593$	−46.2856			−1.90072			−0.950360	−	0.311153i	$-0.899285\pi$
$593$	−46.2856			−1.90072			−0.950360	+	0.311153i	$0.899285\pi$
$594$	15.3267	+	12.4417i	0.628863	+	0.510487i
$595$	21.0946	−	8.73767i	0.864794	−	0.358209i
$596$	−16.2313	−	9.05632i	−0.664858	−	0.370961i
$597$	1.29076	+	0.884230i	0.0528274	+	0.0361891i
$598$	51.7674	−	17.9972i	2.11693	−	0.735958i
$599$	−16.7892	−	4.49865i	−0.685988	−	0.183810i	−0.101042	−	0.994882i	$-0.532218\pi$
$599$	−16.7892	−	4.49865i	−0.685988	−	0.183810i	−0.584946	+	0.811072i	$0.698884\pi$
$600$	−6.27659	+	11.1381i	−0.256241	+	0.454713i
$601$	−29.0356	+	7.78007i	−1.18439	+	0.317356i	−0.796665	−	0.604421i	$-0.793405\pi$
$601$	−29.0356	+	7.78007i	−1.18439	+	0.317356i	−0.387722	+	0.921776i	$0.626738\pi$
$602$	−27.1491	+	18.4299i	−1.10652	+	0.751147i
$603$	9.45242	−	32.2709i	0.384932	−	1.31417i
$604$	32.9135	+	13.0710i	1.33923	+	0.531850i
$605$	−5.79912	−	0.763468i	−0.235768	−	0.0310394i
$606$	−4.59501	−	8.03721i	−0.186660	−	0.326490i
$607$	−4.39067	+	2.53496i	−0.178212	+	0.102891i	−0.586452	−	0.809984i	$-0.699476\pi$
$607$	−4.39067	+	2.53496i	−0.178212	+	0.102891i	0.408240	+	0.912874i	$0.366143\pi$
$608$	−2.42100	−	6.35627i	−0.0981846	−	0.257781i
$609$	−11.0123	+	3.59665i	−0.446242	+	0.145744i
$610$	−13.1260	−	4.34859i	−0.531458	−	0.176069i
$611$	35.1145	−	14.5449i	1.42058	−	0.588424i
$612$	28.8694	+	7.99822i	1.16698	+	0.323309i
$613$	8.99571	−	21.7176i	0.363333	−	0.877164i	−0.631475	−	0.775396i	$-0.717550\pi$
$613$	8.99571	−	21.7176i	0.363333	−	0.877164i	0.994808	−	0.101768i	$-0.0324499\pi$
$614$	−7.41710	+	0.540801i	−0.299330	+	0.0218250i
$615$	0.695397	+	12.8938i	0.0280411	+	0.519927i
$616$	−0.976179	+	22.4538i	−0.0393314	+	0.904691i
$617$	−2.49632	+	9.31640i	−0.100498	+	0.375064i	−0.997796	−	0.0663623i	$-0.978861\pi$
$617$	−2.49632	+	9.31640i	−0.100498	+	0.375064i	0.897297	+	0.441426i	$0.145527\pi$
$618$	10.8260	−	25.8264i	0.435486	−	1.03889i
$619$	−8.47699	−	11.0474i	−0.340719	−	0.444034i	0.591295	−	0.806455i	$-0.298617\pi$
$619$	−8.47699	−	11.0474i	−0.340719	−	0.444034i	−0.932014	+	0.362421i	$0.881950\pi$
$620$	0.321015	+	21.8836i	0.0128923	+	0.878865i
$621$	8.92449	+	29.6315i	0.358128	+	1.18907i
$622$	−16.2030	−	10.6555i	−0.649682	−	0.427245i
$623$	−22.5228	−	13.0035i	−0.902356	−	0.520975i
$624$	−8.00829	+	44.3659i	−0.320588	+	1.77606i
$625$	−4.45214	+	2.57044i	−0.178086	+	0.102818i
$626$	18.1381	+	1.05530i	0.724943	+	0.0421781i
$627$	5.27660	+	1.85952i	0.210727	+	0.0742620i
$628$	−1.72306	−	6.07280i	−0.0687575	−	0.242331i
$629$	14.1106	−	34.0659i	0.562625	−	1.35830i
$630$	−17.5346	+	8.30522i	−0.698595	+	0.330888i
$631$	−22.5108	−	22.5108i	−0.896142	−	0.896142i	0.0989505	−	0.995092i	$-0.468451\pi$
$631$	−22.5108	−	22.5108i	−0.896142	−	0.896142i	−0.995092	+	0.0989505i	$0.968451\pi$
$632$	−11.7076	+	1.02647i	−0.465702	+	0.0408308i
$633$	−7.50910	+	14.7930i	−0.298460	+	0.587969i
$634$	−28.5694	−	13.8293i	−1.13464	−	0.549233i
$635$	−7.37499	+	0.970935i	−0.292667	+	0.0385304i
$636$	−5.61191	−	6.35929i	−0.222527	−	0.252162i
$637$	1.48573	−	11.2853i	0.0588669	−	0.447138i
$638$	−8.41309	+	1.73771i	−0.333078	+	0.0687965i
$639$	−43.1342	−	19.0476i	−1.70636	−	0.753511i
$640$	15.0233	+	8.95870i	0.593847	+	0.354124i
$641$	9.65337	+	5.57338i	0.381285	+	0.220135i	0.678377	−	0.734714i	$-0.262684\pi$
$641$	9.65337	+	5.57338i	0.381285	+	0.220135i	−0.297092	+	0.954849i	$0.596017\pi$
$642$	−1.53151	+	2.62689i	−0.0604437	+	0.103675i
$643$	−6.54625	+	8.53124i	−0.258159	+	0.336439i	−0.904393	−	0.426700i	$-0.859676\pi$
$643$	−6.54625	+	8.53124i	−0.258159	+	0.336439i	0.646235	+	0.763139i	$0.276343\pi$
$644$	−21.0358	+	28.2633i	−0.828927	+	1.11373i
$645$	−17.3295	−	11.8715i	−0.682350	−	0.467440i
$646$	8.46744	−	0.617384i	0.333147	−	0.0242907i
$647$	1.36854	+	1.36854i	0.0538029	+	0.0538029i	0.733496	−	0.679693i	$-0.237887\pi$
$647$	1.36854	+	1.36854i	0.0538029	+	0.0538029i	−0.679693	+	0.733496i	$0.737887\pi$
$648$	−24.8388	−	5.57073i	−0.975761	−	0.218839i
$649$	−18.4376	+	18.4376i	−0.723741	+	0.723741i
$650$	15.7019	−	18.1717i	0.615879	−	0.712754i
$651$	20.4937	−	29.9159i	0.803212	−	1.17250i
$652$	10.5915	−	41.9818i	0.414796	−	1.64414i
$653$	5.04347	+	3.86999i	0.197366	+	0.151444i	0.702717	−	0.711470i	$-0.251970\pi$
$653$	5.04347	+	3.86999i	0.197366	+	0.151444i	−0.505351	+	0.862914i	$0.668637\pi$
$654$	10.2287	−	2.69439i	0.399973	−	0.105359i
$655$	−2.64496	+	4.58121i	−0.103347	+	0.179003i
$656$	−19.2796	+	0.565755i	−0.752741	+	0.0220890i
$657$	−7.12616	+	16.1375i	−0.278018	+	0.629585i
$658$	−13.4250	+	20.4145i	−0.523361	+	0.795840i
$659$	11.0059	+	1.44896i	0.428730	+	0.0564434i	0.341804	−	0.939771i	$-0.388962\pi$
$659$	11.0059	+	1.44896i	0.428730	+	0.0564434i	0.0869265	+	0.996215i	$0.472295\pi$
$660$	−13.6096	+	4.66692i	−0.529753	+	0.181660i
$661$	2.57392	+	19.5509i	0.100114	+	0.760441i	0.965696	+	0.259674i	$0.0836153\pi$
$661$	2.57392	+	19.5509i	0.100114	+	0.760441i	−0.865582	+	0.500767i	$0.833051\pi$
$662$	−11.1023	−	31.9348i	−0.431501	−	1.24118i
$663$	−50.1780	−	25.4709i	−1.94875	−	0.989209i
$664$	1.99207	+	3.82500i	0.0773074	+	0.148439i
$665$	−3.88812	+	3.88812i	−0.150775	+	0.150775i
$666$	−10.5392	+	29.5069i	−0.408384	+	1.14337i
$667$	−12.4418	−	5.15357i	−0.481750	−	0.199547i
$668$	4.84498	−	3.83189i	0.187458	−	0.148260i
$669$	−2.28913	+	6.49567i	−0.0885027	+	0.251137i
$670$	16.2938	+	18.3069i	0.629486	+	0.707259i
$671$	8.49468	+	14.7132i	0.327934	+	0.567998i
$672$	−11.7593	−	26.4886i	−0.453624	−	1.02182i
$673$	−15.3531	+	26.5923i	−0.591817	+	1.02506i	0.402170	+	0.915565i	$0.368256\pi$
$673$	−15.3531	+	26.5923i	−0.591817	+	1.02506i	−0.993988	+	0.109493i	$0.965077\pi$
$674$	−45.1112	+	9.31763i	−1.73762	+	0.358902i
$675$	9.87888	+	9.28942i	0.380238	+	0.357550i
$676$	21.6605	−	54.5425i	0.833098	−	2.09779i
$677$	−23.2383	+	17.8314i	−0.893119	+	0.685315i	−0.949726	−	0.313082i	$-0.898639\pi$
$677$	−23.2383	+	17.8314i	−0.893119	+	0.685315i	0.0566067	+	0.998397i	$0.481972\pi$
$678$	−40.0218	+	16.3793i	−1.53703	+	0.629044i
$679$	−1.67193	−	0.447994i	−0.0641630	−	0.0171924i
$680$	−16.0943	+	14.7532i	−0.617189	+	0.565760i
$681$	10.4344	−	0.562758i	0.399848	−	0.0215649i
$682$	17.5812	−	20.3466i	0.673219	−	0.779112i
$683$	−5.90737	−	2.44691i	−0.226039	−	0.0936285i	0.266790	−	0.963755i	$-0.414037\pi$
$683$	−5.90737	−	2.44691i	−0.226039	−	0.0936285i	−0.492829	+	0.870126i	$0.664037\pi$
$684$	−7.16031	+	0.881039i	−0.273781	+	0.0336874i
$685$	4.45749	+	10.7613i	0.170312	+	0.411170i
$686$	−9.85887	−	19.6276i	−0.376414	−	0.749385i
$687$	−7.73178	−	23.6734i	−0.294986	−	0.903197i
$688$	18.3628	−	25.4428i	0.700077	−	0.969997i
$689$	7.96596	+	13.7974i	0.303479	+	0.525641i
$690$	−21.7608	−	5.92967i	−0.828419	−	0.225739i
$691$	5.35080	−	40.6433i	0.203554	−	1.54615i	−0.518966	−	0.854795i	$-0.673683\pi$
$691$	5.35080	−	40.6433i	0.203554	−	1.54615i	0.722520	−	0.691350i	$-0.242984\pi$
$692$	−2.40112	+	2.47261i	−0.0912768	+	0.0939946i
$693$	22.8772	+	6.70092i	0.869033	+	0.254547i
$694$	−40.5137	−	7.75024i	−1.53788	−	0.294195i
$695$	−0.266646	−	0.995138i	−0.0101145	−	0.0377477i
$696$	8.71766	−	6.83497i	0.330442	−	0.259079i
$697$	6.23111	−	23.2548i	0.236020	−	0.880840i
$698$	8.76983	−	18.1172i	0.331943	−	0.685747i
$699$	−21.6035	+	31.5359i	−0.817120	+	1.19280i
$700$	−1.79041	+	15.3344i	−0.0676712	+	0.579586i
$701$	7.49793	+	18.1016i	0.283193	+	0.683688i	0.999906	−	0.0136798i	$-0.00435455\pi$
$701$	7.49793	+	18.1016i	0.283193	+	0.683688i	−0.716714	+	0.697368i	$0.754355\pi$
$702$	43.6603	+	19.5013i	1.64785	+	0.736030i
$703$			8.87980i			0.334908i
$704$	−6.47013	−	20.4941i	−0.243852	−	0.772400i
$705$	−15.3042	−	3.22869i	−0.576390	−	0.121600i
$706$	−1.91857	−	2.15561i	−0.0722064	−	0.0811275i
$707$	−8.86941	−	6.80574i	−0.333568	−	0.255956i
$708$	10.7092	−	31.8723i	0.402475	−	1.19783i
$709$	−21.2772	−	27.7289i	−0.799080	−	1.04138i	−0.998114	−	0.0613891i	$-0.980447\pi$
$709$	−21.2772	−	27.7289i	−0.799080	−	1.04138i	0.199034	−	0.979993i	$-0.436220\pi$
$710$	28.4332	−	19.3016i	1.06708	−	0.724376i
$711$	−1.91256	+	12.3178i	−0.0717267	+	0.461953i
$712$	24.4916	+	4.31383i	0.917860	+	0.161668i
$713$	40.7173	−	10.9102i	1.52488	−	0.408589i
$714$	35.8850	−	4.56982i	1.34296	−	0.171021i
$715$	26.7951	−	3.52764i	1.00208	−	0.131926i
$716$	−1.41339	+	5.60228i	−0.0528209	+	0.209367i
$717$	−10.1992	−	11.9050i	−0.380896	−	0.444602i
$718$	10.8881	+	21.6767i	0.406342	+	0.808969i
$719$			9.92272i			0.370055i	0.982733	+	0.185028i	$0.0592374\pi$
$719$			9.92272i			0.370055i	−0.982733	+	0.185028i	$0.940763\pi$
$720$	13.0372	−	13.1998i	0.485867	−	0.491927i
$721$		−	33.8162i		−	1.25938i
$722$	22.1842	−	11.1430i	0.825610	−	0.414701i
$723$	6.33107	−	17.9652i	0.235455	−	0.668131i
$724$	22.4803	+	37.6507i	0.835474	+	1.39928i
$725$	−5.85063	+	0.770250i	−0.217287	+	0.0286064i
$726$	−8.54658	−	3.58259i	−0.317193	−	0.132962i
$727$	−2.71569	+	0.727668i	−0.100720	+	0.0269877i	−0.308827	−	0.951118i	$-0.599936\pi$
$727$	−2.71569	+	0.727668i	−0.100720	+	0.0269877i	0.208107	+	0.978106i	$0.433270\pi$
$728$	11.7929	+	53.1478i	0.437075	+	1.96979i
$729$	−12.0377	+	24.1680i	−0.445842	+	0.895112i
$730$	−7.22119	−	10.6375i	−0.267268	−	0.393713i
$731$	23.8422	+	31.0717i	0.881835	+	1.14923i
$732$	−18.2533	−	12.1148i	−0.674660	−	0.447775i
$733$	−35.7393	−	27.4237i	−1.32006	−	1.01292i	−0.997802	−	0.0662654i	$-0.978892\pi$
$733$	−35.7393	−	27.4237i	−1.32006	−	1.01292i	−0.322258	−	0.946652i	$-0.604442\pi$
$734$	3.15848	−	2.81116i	0.116582	−	0.103762i
$735$	−3.12906	+	3.48582i	−0.115417	+	0.128576i
$736$	9.65243	−	32.2777i	0.355793	−	1.18977i
$737$		−	30.1116i		−	1.10918i
$738$	−4.30774	+	19.9992i	−0.158570	+	0.736181i
$739$	12.0702	+	29.1401i	0.444010	+	1.07194i	0.974529	+	0.224262i	$0.0719973\pi$
$739$	12.0702	+	29.1401i	0.444010	+	1.07194i	−0.530518	+	0.847673i	$0.678003\pi$
$740$	−14.1658	−	17.9110i	−0.520744	−	0.658420i
$741$	13.5116	+	1.04271i	0.496360	+	0.0383050i
$742$	−9.21858	−	4.46235i	−0.338425	−	0.163818i
$743$	2.44176	−	9.11278i	0.0895796	−	0.334316i	−0.906562	−	0.422072i	$-0.861303\pi$
$743$	2.44176	−	9.11278i	0.0895796	−	0.334316i	0.996142	+	0.0877563i	$0.0279697\pi$
$744$	−8.62459	+	33.5851i	−0.316193	+	1.23129i
$745$	−3.71875	−	13.8786i	−0.136245	−	0.508471i
$746$	8.03139	−	41.9834i	0.294050	−	1.53712i
$747$	4.44461	−	1.08136i	0.162620	−	0.0395650i
$748$	26.8224	−	0.393464i	0.980725	−	0.0143865i
$749$	−0.479276	+	3.64046i	−0.0175124	+	0.133020i
$750$	−27.8677	+	7.34078i	−1.01759	+	0.268047i
$751$	10.6806	+	18.4994i	0.389742	+	0.675053i	0.992415	−	0.122936i	$-0.0392308\pi$
$751$	10.6806	+	18.4994i	0.389742	+	0.675053i	−0.602673	+	0.797989i	$0.705898\pi$
$752$	5.38240	−	22.7352i	0.196276	−	0.829067i
$753$	5.93012	+	1.25106i	0.216105	+	0.0455913i
$754$	−18.5949	+	9.34016i	−0.677187	+	0.340148i
$755$	10.4763	+	25.2921i	0.381273	+	0.920475i
$756$	−30.2630	+	5.39165i	−1.10065	+	0.196092i
$757$	−10.3129	−	4.27173i	−0.374828	−	0.155259i	0.187313	−	0.982300i	$-0.440022\pi$
$757$	−10.3129	−	4.27173i	−0.374828	−	0.155259i	−0.562141	+	0.827042i	$0.690022\pi$
$758$	−8.66734	−	7.48932i	−0.314812	−	0.272024i
$759$	15.1280	+	23.2177i	0.549111	+	0.842749i
$760$	2.22121	−	4.76571i	0.0805717	−	0.172870i
$761$	2.24485	+	0.601506i	0.0813758	+	0.0218046i	0.299277	−	0.954166i	$-0.403254\pi$
$761$	2.24485	+	0.601506i	0.0813758	+	0.0218046i	−0.217901	+	0.975971i	$0.569921\pi$
$762$	−11.6779	−	1.58777i	−0.423046	−	0.0575188i
$763$	10.1336	−	7.77578i	0.366861	−	0.281502i
$764$	3.63218	−	1.56730i	0.131408	−	0.0567030i
$765$	11.1116	+	20.3175i	0.401742	+	0.734581i
$766$	−0.147524	−	0.714238i	−0.00533027	−	0.0258065i
$767$	−31.5800	+	54.6981i	−1.14029	+	1.97503i
$768$	19.2331	+	19.9521i	0.694016	+	0.719960i
$769$	−21.7094	−	37.6017i	−0.782860	−	1.35595i	−0.930269	−	0.366877i	$-0.880427\pi$
$769$	−21.7094	−	37.6017i	−0.782860	−	1.35595i	0.147410	−	0.989075i	$-0.452906\pi$
$770$	−12.9780	+	11.5509i	−0.467694	+	0.416264i
$771$	20.4261	+	23.8424i	0.735629	+	0.858663i
$772$	−6.24811	+	53.5135i	−0.224875	+	1.92599i
$773$	10.7482	+	4.45203i	0.386584	+	0.160128i	0.567506	−	0.823369i	$-0.307908\pi$
$773$	10.7482	+	4.45203i	0.386584	+	0.160128i	−0.180922	+	0.983497i	$0.557908\pi$
$774$	−21.5452	−	25.3653i	−0.774427	−	0.911737i
$775$	13.0613	−	13.0613i	0.469175	−	0.469175i
$776$	1.64882	−	0.144561i	0.0591891	−	0.00518944i
$777$	2.03764	+	37.7811i	0.0731000	+	1.35539i
$778$	−21.8982	+	7.61300i	−0.785089	+	0.272939i
$779$	0.756773	+	5.74827i	0.0271142	+	0.205953i
$780$	−28.9169	+	19.4515i	−1.03539	+	0.696477i
$781$	−41.8623	−	5.51128i	−1.49795	−	0.197209i
$782$	35.1353	+	23.1058i	1.25644	+	0.826260i
$783$	−4.82792	−	10.7119i	−0.172536	−	0.382812i
$784$	−5.09062	−	4.80037i	−0.181808	−	0.171442i
$785$	2.43988	−	4.22599i	0.0870829	−	0.150832i
$786$	−5.95136	+	5.90116i	−0.212278	+	0.210487i
$787$	−15.3583	−	11.7848i	−0.547463	−	0.420083i	0.297647	−	0.954676i	$-0.403798\pi$
$787$	−15.3583	−	11.7848i	−0.547463	−	0.420083i	−0.845110	+	0.534593i	$0.820465\pi$
$788$	19.0071	+	31.8336i	0.677100	+	1.13403i
$789$	−14.8711	−	31.0563i	−0.529425	−	1.10563i
$790$	−6.87421	−	5.93990i	−0.244574	−	0.211332i
$791$	−36.9248	+	36.9248i	−1.31290	+	1.31290i
$792$	−22.7477	+	1.46501i	−0.808304	+	0.0520567i
$793$	29.0993	+	29.0993i	1.03335	+	1.03335i
$794$	−2.32896	−	31.9417i	−0.0826517	−	1.13357i
$795$	0.504466	−	6.53692i	0.0178916	−	0.231841i
$796$	−1.78752	+	0.262059i	−0.0633570	+	0.00928844i
$797$	18.0969	−	23.5843i	0.641025	−	0.835400i	−0.353977	−	0.935254i	$-0.615171\pi$
$797$	18.0969	−	23.5843i	0.641025	−	0.835400i	0.995002	+	0.0998538i	$0.0318375\pi$
$798$	−7.56296	+	4.32388i	−0.267726	+	0.153064i
$799$	25.2555	+	14.5813i	0.893475	+	0.515848i
$800$	−3.40897	−	14.3637i	−0.120525	−	0.507835i
$801$	10.6552	−	24.1292i	0.376483	−	0.852563i
$802$	1.41589	+	6.85501i	0.0499967	+	0.242059i
$803$	−2.06190	+	15.6617i	−0.0727629	+	0.552689i
$804$	17.2814	+	34.7712i	0.609468	+	1.22628i
$805$	−27.0026	+	3.55496i	−0.951718	+	0.125296i
$806$	28.3793	−	58.6276i	0.999619	−	2.06507i
$807$	12.0850	+	18.5475i	0.425412	+	0.652901i
$808$	10.1961	+	3.21273i	0.358696	+	0.113023i
$809$	37.5254	+	37.5254i	1.31932	+	1.31932i	0.914310	+	0.405014i	$0.132733\pi$
$809$	37.5254	+	37.5254i	1.31932	+	1.31932i	0.405014	+	0.914310i	$0.367267\pi$
$810$	−10.2873	−	16.7750i	−0.361457	−	0.589412i
$811$	−14.5706	+	35.1764i	−0.511641	+	1.23521i	0.431287	+	0.902215i	$0.358060\pi$
$811$	−14.5706	+	35.1764i	−0.511641	+	1.23521i	−0.942928	+	0.332997i	$0.891940\pi$
$812$	6.51784	−	11.6817i	0.228731	−	0.409946i
$813$	2.27257	+	12.1584i	0.0797023	+	0.426415i
$814$	−1.62965	+	28.0099i	−0.0571192	+	0.981745i
$815$	28.9859	−	16.7350i	1.01533	−	0.586202i
$816$	−30.7472	+	15.8481i	−1.07637	+	0.554793i
$817$	−8.16824	−	4.71594i	−0.285771	−	0.164990i
$818$	2.57571	−	3.91670i	0.0900574	−	0.136944i
$819$	57.7274	+	1.33596i	2.01716	+	0.0466824i
$820$	−10.6965	−	10.3872i	−0.373539	−	0.362738i
$821$	16.4297	+	21.4116i	0.573401	+	0.747270i	0.986562	−	0.163388i	$-0.0522421\pi$
$821$	16.4297	+	21.4116i	0.573401	+	0.747270i	−0.413161	+	0.910658i	$0.635575\pi$
$822$	2.33128	+	18.3066i	0.0813127	+	0.638516i
$823$	−11.9283	+	44.5171i	−0.415795	+	1.55177i	0.367442	+	0.930046i	$0.380233\pi$
$823$	−11.9283	+	44.5171i	−0.415795	+	1.55177i	−0.783238	+	0.621722i	$0.786433\pi$
$824$	11.0652	+	30.3837i	0.385473	+	1.05847i
$825$	10.8278	+	5.49630i	0.376975	+	0.191357i
$826$	−2.95259	−	40.4948i	−0.102734	−	1.40899i
$827$	5.01593	−	12.1095i	0.174421	−	0.421090i	−0.812358	−	0.583159i	$-0.801817\pi$
$827$	5.01593	−	12.1095i	0.174421	−	0.421090i	0.986779	+	0.162069i	$0.0518166\pi$
$828$	−30.7938	−	18.1283i	−1.07016	−	0.630003i
$829$	33.0578	−	13.6930i	1.14814	−	0.475577i	0.274233	−	0.961663i	$-0.411576\pi$
$829$	33.0578	−	13.6930i	1.14814	−	0.475577i	0.873911	+	0.486086i	$0.161576\pi$
$830$	−1.04844	+	3.16466i	−0.0363917	+	0.109847i
$831$	18.3194	+	16.4445i	0.635494	+	0.570454i
$832$	−27.9866	−	43.8943i	−0.970262	−	1.52176i
$833$	7.56358	−	4.36683i	0.262062	−	0.151302i
$834$	0.00691290	−	1.63225i	0.000239374	−	0.0565201i
$835$	4.73427	+	0.623278i	0.163836	+	0.0215694i
$836$	−5.93151	+	2.55948i	−0.205146	+	0.0885213i
$837$	32.4011	+	17.4014i	1.11994	+	0.601481i
$838$	30.3020	+	44.6379i	1.04676	+	1.54199i
$839$	21.4577	−	5.74956i	0.740801	−	0.198497i	0.131367	−	0.991334i	$-0.458063\pi$
$839$	21.4577	−	5.74956i	0.740801	−	0.198497i	0.609434	+	0.792837i	$0.291397\pi$
$840$	8.35706	−	20.7865i	0.288346	−	0.717202i
$841$	−23.0730	−	6.18238i	−0.795620	−	0.213186i
$842$	−9.81916	−	28.2441i	−0.338391	−	0.973354i
$843$	−34.9170	+	16.7198i	−1.20260	+	0.575859i
$844$	−5.22885	−	18.4287i	−0.179985	−	0.634343i
$845$	41.9128	−	17.3609i	1.44184	−	0.597231i
$846$	−22.0493	−	11.3102i	−0.758070	−	0.388852i
$847$	−11.1906			−0.384513
$848$	9.74301	+	0.992949i	0.334576	+	0.0340980i
$849$	−43.3701	+	14.1647i	−1.48846	+	0.486133i
$850$	18.3958	+	1.07029i	0.630970	+	0.0367106i
$851$	−26.7752	+	34.8942i	−0.917843	+	1.19616i
$852$	51.5032	−	17.6612i	1.76447	−	0.605061i
$853$	27.3917	−	21.0184i	0.937875	−	0.719657i	−0.0220961	−	0.999756i	$-0.507034\pi$
$853$	27.3917	−	21.0184i	0.937875	−	0.719657i	0.959971	+	0.280099i	$0.0903673\pi$
$854$	−25.9838	−	4.97068i	−0.889148	−	0.170093i
$855$	−4.34470	−	3.49644i	−0.148585	−	0.119576i
$856$	−0.760586	−	3.42777i	−0.0259963	−	0.117159i
$857$	4.86221	+	18.1460i	0.166090	+	0.619856i	0.997899	+	0.0647934i	$0.0206389\pi$
$857$	4.86221	+	18.1460i	0.166090	+	0.619856i	−0.831809	+	0.555062i	$0.812694\pi$
$858$	42.4287	+	5.76875i	1.44849	+	0.196942i
$859$	1.40745	+	10.6906i	0.0480214	+	0.364759i	0.998537	+	0.0540806i	$0.0172228\pi$
$859$	1.40745	+	10.6906i	0.0480214	+	0.364759i	−0.950515	+	0.310678i	$0.899444\pi$
$860$	23.9989	−	3.51836i	0.818357	−	0.119975i
$861$	4.53891	+	24.2836i	0.154686	+	0.827584i
$862$	15.8610	−	47.8756i	0.540226	−	1.63065i
$863$	23.6325			0.804461			0.402231	−	0.915538i	$-0.368235\pi$
$863$	23.6325			0.804461			0.402231	+	0.915538i	$0.368235\pi$
$864$	25.4270	−	14.7469i	0.865042	−	0.501699i
$865$	−2.66433			−0.0905900
$866$	−5.10406	+	15.4064i	−0.173443	+	0.523530i
$867$	−2.52297	−	13.4982i	−0.0856847	−	0.458421i
$868$	6.07372	+	41.4292i	0.206156	+	1.40620i
$869$	1.45698	+	11.0668i	0.0494245	+	0.375416i
$870$	8.48528	+	1.15369i	0.287678	+	0.0391137i
$871$	−18.8778	−	70.4530i	−0.639650	−	2.38721i
$872$	−6.56064	+	10.3024i	−0.222171	+	0.348882i
$873$	0.269353	−	1.73476i	0.00911620	−	0.0587126i
$874$	−9.94674	−	1.90280i	−0.336453	−	0.0643632i
$875$	−27.6087	+	21.1849i	−0.933344	+	0.716180i
$876$	−6.60746	−	19.2686i	−0.223245	−	0.651024i
$877$	30.5610	−	39.8279i	1.03197	−	1.34489i	0.0950060	−	0.995477i	$-0.469713\pi$
$877$	30.5610	−	39.8279i	1.03197	−	1.34489i	0.936967	−	0.349417i	$-0.113620\pi$
$878$	−13.3992	−	0.779581i	−0.452200	−	0.0263096i
$879$	−8.31291	+	2.71501i	−0.280388	+	0.0915751i
$880$	7.88105	−	14.6250i	0.265670	−	0.493008i
$881$	28.1356			0.947912			0.473956	−	0.880548i	$-0.342826\pi$
$881$	28.1356			0.947912			0.473956	+	0.880548i	$0.342826\pi$
$882$	−6.23509	+	4.02509i	−0.209946	+	0.135532i
$883$	5.34397	−	2.21354i	0.179839	−	0.0744917i	−0.290947	−	0.956739i	$-0.593970\pi$
$883$	5.34397	−	2.21354i	0.179839	−	0.0744917i	0.470786	+	0.882247i	$0.343970\pi$
$884$	62.5105	−	17.7363i	2.10245	−	0.596537i
$885$	23.4428	−	11.2254i	0.788021	−	0.377339i
$886$	−11.0293	−	31.7250i	−0.370537	−	1.06582i
$887$	36.5727	+	9.79963i	1.22799	+	0.329039i	0.813797	−	0.581149i	$-0.197397\pi$
$887$	36.5727	+	9.79963i	1.22799	+	0.329039i	0.414194	+	0.910189i	$0.364063\pi$
$888$	−14.1934	−	33.2794i	−0.476298	−	1.11679i
$889$	−13.7466	+	3.68340i	−0.461047	+	0.123537i
$890$	10.7973	+	15.9055i	0.361926	+	0.533154i
$891$	−4.26133	+	23.7991i	−0.142760	+	0.797299i
$892$	−3.15080	−	7.30189i	−0.105497	−	0.244485i
$893$	−6.96294	−	0.916688i	−0.233006	−	0.0306758i
$894$	0.0964099	−	22.7639i	0.00322443	−	0.761340i
$895$	−3.86804	+	2.23321i	−0.129294	+	0.0746480i
$896$	30.7338	+	13.2415i	1.02674	+	0.442367i
$897$	49.9512	+	44.8389i	1.66782	+	1.49713i
$898$	−15.4138	+	46.5258i	−0.514365	+	1.55259i
$899$	−14.7865	+	6.12479i	−0.493159	+	0.204273i
$900$	−15.6577	−	0.132629i	−0.521923	−	0.00442098i
$901$	−4.67801	+	11.2937i	−0.155847	+	0.376248i
$902$	1.33218	+	18.2708i	0.0443566	+	0.608352i
$903$	−35.8358	−	18.1907i	−1.19254	−	0.605347i
$904$	21.0945	−	45.2591i	0.701591	−	1.50530i
$905$	−8.77353	+	32.7432i	−0.291642	+	1.08842i
$906$	5.47915	+	43.0256i	0.182033	+	1.42943i
$907$	−20.2191	−	26.3500i	−0.671364	−	0.874938i	0.326157	−	0.945316i	$-0.394246\pi$
$907$	−20.2191	−	26.3500i	−0.671364	−	0.874938i	−0.997520	+	0.0703775i	$0.977580\pi$
$908$	−8.40599	+	8.65628i	−0.278963	+	0.287269i
$909$	5.89503	−	9.68582i	0.195526	−	0.321258i
$910$	−23.1234	+	35.1621i	−0.766532	+	1.16561i
$911$	−23.9981	−	13.8553i	−0.795094	−	0.459048i	0.0466587	−	0.998911i	$-0.485143\pi$
$911$	−23.9981	−	13.8553i	−0.795094	−	0.459048i	−0.841753	+	0.539863i	$0.818476\pi$
$912$	5.38046	−	6.35970i	0.178165	−	0.210591i
$913$	3.54732	−	2.04805i	0.117399	−	0.0677805i
$914$	−2.30016	+	39.5344i	−0.0760825	+	1.30768i
$915$	−3.11153	−	16.6470i	−0.102864	−	0.550333i
$916$	25.1123	+	14.0115i	0.829732	+	0.462954i
$917$	−3.87301	+	9.35028i	−0.127898	+	0.308774i
$918$	8.52240	+	35.6860i	0.281281	+	1.17781i
$919$	23.8430	+	23.8430i	0.786507	+	0.786507i	0.980920	−	0.194413i	$-0.0622801\pi$
$919$	23.8430	+	23.8430i	0.786507	+	0.786507i	−0.194413	+	0.980920i	$0.562280\pi$
$920$	23.0985	−	12.0298i	0.761535	−	0.396610i
$921$	−4.97228	−	7.63120i	−0.163842	−	0.251457i
$922$	5.54345	−	11.4520i	0.182564	−	0.377151i
$923$	−101.402	+	13.3498i	−3.33767	+	0.439413i
$924$	−24.6496	+	12.2510i	−0.810914	+	0.403027i
$925$	−2.51564	+	19.1082i	−0.0827139	+	0.628274i
$926$	−3.60921	−	17.4739i	−0.118606	−	0.574229i
$927$	34.0984	−	3.68877i	1.11994	−	0.121155i
$928$	−2.03385	+	12.6287i	−0.0667643	+	0.414556i
$929$	11.1510	+	6.43802i	0.365852	+	0.211225i	0.671645	−	0.740873i	$-0.265588\pi$
$929$	11.1510	+	6.43802i	0.365852	+	0.211225i	−0.305793	+	0.952098i	$0.598922\pi$
$930$	−23.2701	+	13.3039i	−0.763055	+	0.436252i
$931$	−1.28039	+	1.66864i	−0.0419631	+	0.0546874i
$932$	−6.40264	−	43.6728i	−0.209725	−	1.43055i
$933$	1.82748	−	23.6807i	0.0598290	−	0.775271i
$934$	2.74350	+	37.6272i	0.0897702	+	1.23120i
$935$	14.6631	+	14.6631i	0.479534	+	0.479534i
$936$	−52.3049	+	17.6889i	−1.70964	+	0.578179i
$937$	−27.2540	+	27.2540i	−0.890348	+	0.890348i	−0.994556	−	0.104207i	$-0.966769\pi$
$937$	−27.2540	+	27.2540i	−0.890348	+	0.890348i	0.104207	+	0.994556i	$0.466769\pi$
$938$	35.4783	+	30.6562i	1.15841	+	1.00096i
$939$	9.61030	+	20.0698i	0.313620	+	0.654954i
$940$	15.5069	−	9.25882i	0.505780	−	0.301989i
$941$	−0.883622	−	0.678027i	−0.0288052	−	0.0221030i	0.594258	−	0.804274i	$-0.297446\pi$
$941$	−0.883622	−	0.678027i	−0.0288052	−	0.0221030i	−0.623064	+	0.782171i	$0.714112\pi$
$942$	5.48990	−	5.44359i	0.178871	−	0.177362i
$943$	−14.3589	+	24.8703i	−0.467590	+	0.809890i
$944$	15.9034	+	35.4183i	0.517611	+	1.15277i
$945$	−19.2878	−	13.8794i	−0.627433	−	0.451498i
$946$	−24.8999	−	16.3747i	−0.809565	−	0.532387i
$947$	−5.52250	−	0.727051i	−0.179457	−	0.0236260i	0.0402620	−	0.999189i	$-0.487181\pi$
$947$	−5.52250	−	0.727051i	−0.179457	−	0.0236260i	−0.219719	+	0.975563i	$0.570514\pi$
$948$	−8.03381	−	11.9432i	−0.260926	−	0.387896i
$949$	4.99446	+	37.9367i	0.162127	+	1.23148i
$950$	−4.19155	+	1.45721i	−0.135992	+	0.0472781i
$951$	−2.09354	−	38.8177i	−0.0678878	−	1.25875i
$952$	−26.8440	+	32.0035i	−0.870018	+	1.03724i
$953$	7.30358	−	7.30358i	0.236586	−	0.236586i	−0.578849	−	0.815435i	$-0.696498\pi$
$953$	7.30358	−	7.30358i	0.236586	−	0.236586i	0.815435	+	0.578849i	$0.196498\pi$
$954$	3.49400	−	9.78228i	0.113122	−	0.316713i
$955$	2.82525	+	1.17025i	0.0914228	+	0.0378686i
$956$	17.9796	+	2.09925i	0.581501	+	0.0678947i
$957$	−6.84525	−	7.99013i	−0.221276	−	0.258284i
$958$	−21.3332	+	18.9873i	−0.689246	+	0.613453i
$959$	11.1425	+	19.2993i	0.359809	+	0.623207i
$960$	−0.707136	+	21.4111i	−0.0228227	+	0.691041i
$961$	9.54886	−	16.5391i	0.308028	−	0.533520i
$962$	13.7472	+	66.5571i	0.443228	+	2.14589i
$963$	−3.72313	−	0.0861631i	−0.119976	−	0.00277657i
$964$	8.71420	+	20.1949i	0.280666	+	0.650435i
$965$	−33.0419	+	25.3540i	−1.06366	+	0.816173i
$966$	−42.7573	−	5.81343i	−1.37569	−	0.187044i
$967$	−29.5735	−	7.92419i	−0.951019	−	0.254825i	−0.250224	−	0.968188i	$-0.580504\pi$
$967$	−29.5735	−	7.92419i	−0.951019	−	0.254825i	−0.700795	+	0.713363i	$0.747171\pi$
$968$	10.0547	−	3.66173i	0.323170	−	0.117692i
$969$	5.67640	+	8.71186i	0.182352	+	0.279865i
$970$	0.968119	+	0.836537i	0.0310844	+	0.0268596i
$971$	−3.76295	−	1.55866i	−0.120759	−	0.0500199i	0.321486	−	0.946914i	$-0.395818\pi$
$971$	−3.76295	−	1.55866i	−0.120759	−	0.0500199i	−0.442245	+	0.896894i	$0.645818\pi$
$972$	−8.73783	−	29.9274i	−0.280266	−	0.959922i
$973$	−0.754291	−	1.82102i	−0.0241815	−	0.0583792i
$974$	3.82523	−	1.92140i	0.122568	−	0.0615657i
$975$	28.7798	+	6.07161i	0.921692	+	0.194447i
$976$	24.9728	−	4.03615i	0.799360	−	0.129194i
$977$	29.0456	+	50.3084i	0.929250	+	1.60951i	0.784579	+	0.620028i	$0.212879\pi$
$977$	29.0456	+	50.3084i	0.929250	+	1.60951i	0.144671	+	0.989480i	$0.453788\pi$
$978$	51.2789	−	13.5076i	1.63972	−	0.431927i
$979$	3.08300	−	23.4177i	0.0985331	−	0.748433i
$980$	−0.0793355	−	5.40830i	−0.00253428	−	0.172762i
$981$	8.94607	+	9.36995i	0.285626	+	0.299160i
$982$	4.07410	−	21.2970i	0.130010	−	0.679615i
$983$	−7.78645	−	29.0594i	−0.248349	−	0.926851i	−0.971670	−	0.236340i	$-0.924052\pi$
$983$	−7.78645	−	29.0594i	−0.248349	−	0.926851i	0.723321	−	0.690512i	$-0.242615\pi$
$984$	−12.0242	−	20.3336i	−0.383316	−	0.648210i
$985$	−7.41802	+	27.6844i	−0.236358	+	0.882099i
$986$	−14.3711	−	6.95647i	−0.457668	−	0.221539i
$987$	−29.8357	−	2.30248i	−0.949682	−	0.0732887i
$988$	−12.2735	+	9.70710i	−0.390472	+	0.308824i
$989$	−17.8781	−	43.1615i	−0.568489	−	1.37245i
$990$	−13.0629	−	11.8263i	−0.415168	−	0.375864i
$991$		−	16.9912i		−	0.539742i	−0.962896	−	0.269871i	$-0.913019\pi$
$991$		−	16.9912i		−	0.539742i	0.962896	−	0.269871i	$-0.0869811\pi$
$992$	−19.0135	−	35.2366i	−0.603678	−	1.11876i
$993$	27.6606	−	30.8144i	0.877784	−	0.977864i
$994$	49.1130	−	43.7123i	1.55777	−	1.38647i
$995$	−1.10798	−	0.850181i	−0.0351253	−	0.0269526i
$996$	−2.92084	+	4.40081i	−0.0925505	+	0.139445i
$997$	6.87065	+	8.95401i	0.217596	+	0.283576i	0.889378	−	0.457172i	$-0.151138\pi$
$997$	6.87065	+	8.95401i	0.217596	+	0.283576i	−0.671782	+	0.740749i	$0.734471\pi$
$998$	−11.8768	−	17.4957i	−0.375953	−	0.553818i
$999$	−37.8742	+	6.17593i	−1.19829	+	0.195398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.4	✓	368
3.2	odd	2		864.2.bn.a.683.43		368
9.4	even	3		864.2.bn.a.395.34		368
9.5	odd	6	inner	288.2.bf.a.203.13	yes	368
32.3	odd	8	inner	288.2.bf.a.227.13	yes	368
96.35	even	8		864.2.bn.a.35.34		368
288.67	odd	24		864.2.bn.a.611.43		368
288.131	even	24	inner	288.2.bf.a.131.4	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.4	✓	368	1.1	even	1	trivial
288.2.bf.a.131.4	yes	368	288.131	even	24	inner
288.2.bf.a.203.13	yes	368	9.5	odd	6	inner
288.2.bf.a.227.13	yes	368	32.3	odd	8	inner
864.2.bn.a.35.34		368	96.35	even	8
864.2.bn.a.395.34		368	9.4	even	3
864.2.bn.a.611.43		368	288.67	odd	24
864.2.bn.a.683.43		368	3.2	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34246 - 0.444750i) q^{2} +(-0.318231 - 1.70257i) q^{3} +(1.60439 + 1.19412i) q^{4} +(0.201801 + 1.53283i) q^{5} +(-0.330005 + 2.42716i) q^{6} +(0.765564 + 2.85712i) q^{7} +(-1.62275 - 2.31661i) q^{8} +(-2.79746 + 1.08362i) q^{9} +O(q^{10})\)	\(q+(-1.34246 - 0.444750i) q^{2} +(-0.318231 - 1.70257i) q^{3} +(1.60439 + 1.19412i) q^{4} +(0.201801 + 1.53283i) q^{5} +(-0.330005 + 2.42716i) q^{6} +(0.765564 + 2.85712i) q^{7} +(-1.62275 - 2.31661i) q^{8} +(-2.79746 + 1.08362i) q^{9} +(0.410817 - 2.14751i) q^{10} +(-2.13126 + 1.63537i) q^{11} +(1.52250 - 3.11159i) q^{12} +(-3.96131 + 5.16247i) q^{13} +(0.242968 - 4.17606i) q^{14} +(2.54552 - 0.831373i) q^{15} +(1.14816 + 3.83167i) q^{16} -4.99281 q^{17} +(4.23741 - 0.210541i) q^{18} +(1.11086 - 0.460133i) q^{19} +(-1.50661 + 2.70024i) q^{20} +(4.62082 - 2.21265i) q^{21} +(3.58847 - 1.24754i) q^{22} +(5.75268 + 1.54143i) q^{23} +(-3.42777 + 3.50005i) q^{24} +(2.52078 - 0.675442i) q^{25} +(7.61391 - 5.16862i) q^{26} +(2.73517 + 4.41802i) q^{27} +(-2.18348 + 5.49813i) q^{28} +(-2.24187 - 0.295148i) q^{29} +(-3.78702 - 0.0160388i) q^{30} +(6.12971 - 3.53899i) q^{31} +(0.162778 - 5.65451i) q^{32} +(3.46257 + 3.10819i) q^{33} +(6.70264 + 2.22055i) q^{34} +(-4.22500 + 1.75005i) q^{35} +(-5.78219 - 1.60195i) q^{36} +(-2.82618 + 6.82299i) q^{37} +(-1.69593 + 0.123655i) q^{38} +(10.0501 + 5.10153i) q^{39} +(3.22350 - 2.95489i) q^{40} +(-1.24802 + 4.65767i) q^{41} +(-7.18733 + 0.915280i) q^{42} +(-4.77531 - 6.22330i) q^{43} +(-5.37222 + 0.0788062i) q^{44} +(-2.22553 - 4.06935i) q^{45} +(-7.03719 - 4.62781i) q^{46} +(-5.05837 - 2.92045i) q^{47} +(6.15830 - 3.17418i) q^{48} +(-1.51489 + 0.874625i) q^{49} +(-3.68445 - 0.214366i) q^{50} +(1.58886 + 8.50058i) q^{51} +(-12.5201 + 3.55237i) q^{52} +(0.936950 - 2.26200i) q^{53} +(-1.70693 - 7.14747i) q^{54} +(-2.93684 - 2.93684i) q^{55} +(5.37653 - 6.40991i) q^{56} +(-1.13692 - 1.74488i) q^{57} +(2.87836 + 1.39330i) q^{58} +(9.62319 - 1.26692i) q^{59} +(5.07678 + 1.70581i) q^{60} +(0.825476 - 6.27012i) q^{61} +(-9.80285 + 2.02476i) q^{62} +(-5.23766 - 7.16311i) q^{63} +(-2.73337 + 7.51856i) q^{64} +(-8.71259 - 5.03022i) q^{65} +(-3.26599 - 5.71259i) q^{66} +(-6.82356 + 8.89264i) q^{67} +(-8.01043 - 5.96200i) q^{68} +(0.793700 - 10.2848i) q^{69} +(6.45022 - 0.470303i) q^{70} +(11.1140 + 11.1140i) q^{71} +(7.04989 + 4.72218i) q^{72} +(4.15800 - 4.15800i) q^{73} +(6.82856 - 7.90265i) q^{74} +(-1.95217 - 4.07685i) q^{75} +(2.33171 + 0.588263i) q^{76} +(-6.30409 - 4.83730i) q^{77} +(-11.2229 - 11.3184i) q^{78} +(2.07756 - 3.59845i) q^{79} +(-5.64161 + 2.53317i) q^{80} +(6.65155 - 6.06275i) q^{81} +(3.74691 - 5.69767i) q^{82} +(-1.51171 - 0.199020i) q^{83} +(10.0558 + 1.96784i) q^{84} +(-1.00755 - 7.65313i) q^{85} +(3.64284 + 10.4783i) q^{86} +(0.210924 + 3.91086i) q^{87} +(7.24703 + 2.28350i) q^{88} +(-6.21714 + 6.21714i) q^{89} +(1.17784 + 6.45275i) q^{90} +(-17.7825 - 7.36574i) q^{91} +(7.38892 + 9.34244i) q^{92} +(-7.97602 - 9.31001i) q^{93} +(5.49179 + 6.17030i) q^{94} +(0.929478 + 1.60990i) q^{95} +(-9.67898 + 1.52230i) q^{96} +(-0.292590 + 0.506782i) q^{97} +(2.42267 - 0.500398i) q^{98} +(4.19000 - 6.88436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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