LMFDB - Embedded newform 153.2.s.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34092 + 1.74752i) q^{2} +(1.37706 + 1.05057i) q^{3} +(-0.738117 + 2.75469i) q^{4} +(-1.77127 - 0.116095i) q^{5} +(0.0106286 + 3.81516i) q^{6} +(-0.295171 - 4.50344i) q^{7} +(-1.73356 + 0.718065i) q^{8} +(0.792591 + 2.89341i) q^{9} +O(q^{10})$	\(q+(1.34092 + 1.74752i) q^{2} +(1.37706 + 1.05057i) q^{3} +(-0.738117 + 2.75469i) q^{4} +(-1.77127 - 0.116095i) q^{5} +(0.0106286 + 3.81516i) q^{6} +(-0.295171 - 4.50344i) q^{7} +(-1.73356 + 0.718065i) q^{8} +(0.792591 + 2.89341i) q^{9} +(-2.17224 - 3.25099i) q^{10} +(-3.64040 - 3.19255i) q^{11} +(-3.91043 + 3.01793i) q^{12} +(3.24185 + 0.868651i) q^{13} +(7.47403 - 6.55454i) q^{14} +(-2.31718 - 2.02072i) q^{15} +(1.36018 + 0.785301i) q^{16} +(-1.37232 + 3.88803i) q^{17} +(-3.99347 + 5.26488i) q^{18} +(-2.09469 - 0.867648i) q^{19} +(1.62721 - 4.79360i) q^{20} +(4.32472 - 6.51160i) q^{21} +(0.697553 - 10.6426i) q^{22} +(1.20194 + 3.54079i) q^{23} +(-3.14160 - 0.832416i) q^{24} +(-1.83331 - 0.241360i) q^{25} +(2.82906 + 6.82997i) q^{26} +(-1.94829 + 4.81707i) q^{27} +(12.6234 + 2.51096i) q^{28} +(-3.39484 + 1.67415i) q^{29} +(0.424096 - 6.75891i) q^{30} +(-0.656322 - 0.748392i) q^{31} +(0.941400 + 7.15064i) q^{32} +(-1.65905 - 8.22084i) q^{33} +(-8.63455 + 2.81537i) q^{34} +8.01106i q^{35} +(-8.55546 + 0.0476692i) q^{36} +(0.0324450 + 0.163112i) q^{37} +(-1.29257 - 4.82394i) q^{38} +(3.55164 + 4.60198i) q^{39} +(3.15397 - 1.07063i) q^{40} +(1.80981 - 3.66994i) q^{41} +(17.1782 - 1.17399i) q^{42} +(1.31010 - 9.95119i) q^{43} +(11.4815 - 7.67170i) q^{44} +(-1.06798 - 5.21701i) q^{45} +(-4.57589 + 6.84831i) q^{46} +(7.98124 - 2.13857i) q^{47} +(1.04804 + 2.51038i) q^{48} +(-13.2537 + 1.74488i) q^{49} +(-2.03654 - 3.52739i) q^{50} +(-5.97442 + 3.91232i) q^{51} +(-4.78572 + 8.28912i) q^{52} +(1.75702 - 4.24182i) q^{53} +(-11.0304 + 3.05462i) q^{54} +(6.07749 + 6.07749i) q^{55} +(3.74546 + 7.59504i) q^{56} +(-1.97298 - 3.39543i) q^{57} +(-7.47779 - 3.68764i) q^{58} +(2.19280 + 1.68260i) q^{59} +(7.27679 - 4.89157i) q^{60} +(7.16122 - 0.469371i) q^{61} +(0.427754 - 2.15046i) q^{62} +(12.7963 - 4.42343i) q^{63} +(-9.01235 + 9.01235i) q^{64} +(-5.64134 - 1.91498i) q^{65} +(12.1414 - 13.9227i) q^{66} +(-0.191282 + 0.110437i) q^{67} +(-9.69737 - 6.65013i) q^{68} +(-2.06472 + 6.13861i) q^{69} +(-13.9995 + 10.7422i) q^{70} +(-4.68313 + 0.931533i) q^{71} +(-3.45166 - 4.44677i) q^{72} +(3.14851 + 2.10376i) q^{73} +(-0.241535 + 0.275417i) q^{74} +(-2.27102 - 2.25840i) q^{75} +(3.93622 - 5.12978i) q^{76} +(-13.3029 + 17.3367i) q^{77} +(-3.27959 + 12.3774i) q^{78} +(-6.37354 + 7.26763i) q^{79} +(-2.31808 - 1.54889i) q^{80} +(-7.74360 + 4.58657i) q^{81} +(8.84008 - 1.75840i) q^{82} +(-1.15581 + 0.886882i) q^{83} +(14.7453 + 16.7196i) q^{84} +(2.88212 - 6.72741i) q^{85} +(19.1466 - 11.0543i) q^{86} +(-6.43371 - 1.26112i) q^{87} +(8.60333 + 2.92044i) q^{88} +(-9.41257 + 9.41257i) q^{89} +(7.68474 - 8.86189i) q^{90} +(2.95501 - 14.8559i) q^{91} +(-10.6410 + 0.697445i) q^{92} +(-0.117554 - 1.72009i) q^{93} +(14.4394 + 11.0797i) q^{94} +(3.60952 + 1.78002i) q^{95} +(-6.21591 + 10.8359i) q^{96} +(6.36781 + 12.9126i) q^{97} +(-20.8213 - 20.8213i) q^{98} +(6.35199 - 13.0635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.34092	+	1.74752i	0.948170	+	1.23568i	0.971763	+	0.235958i	$0.0758228\pi$
$2$	1.34092	+	1.74752i	0.948170	+	1.23568i	−0.0235928	+	0.999722i	$0.507511\pi$
$3$	1.37706	+	1.05057i	0.795046	+	0.606549i
$3$	1.37706	+	1.05057i	0.795046	+	0.606549i
$4$	−0.738117	+	2.75469i	−0.369058	+	1.37734i
$5$	−1.77127	−	0.116095i	−0.792135	−	0.0519193i	−0.336037	−	0.941849i	$-0.609087\pi$
$5$	−1.77127	−	0.116095i	−0.792135	−	0.0519193i	−0.456098	+	0.889930i	$0.650753\pi$
$6$	0.0106286	+	3.81516i	0.00433909	+	1.55753i
$7$	−0.295171	−	4.50344i	−0.111564	−	1.70214i	−0.576745	−	0.816924i	$-0.695678\pi$
$7$	−0.295171	−	4.50344i	−0.111564	−	1.70214i	0.465181	−	0.885215i	$-0.345989\pi$
$8$	−1.73356	+	0.718065i	−0.612907	+	0.253874i
$9$	0.792591	+	2.89341i	0.264197	+	0.964469i
$10$	−2.17224	−	3.25099i	−0.686923	−	1.02805i
$11$	−3.64040	−	3.19255i	−1.09762	−	0.962589i	−0.0981538	−	0.995171i	$-0.531294\pi$
$11$	−3.64040	−	3.19255i	−1.09762	−	0.962589i	−0.999469	+	0.0325818i	$0.989627\pi$
$12$	−3.91043	+	3.01793i	−1.12885	+	0.871200i
$13$	3.24185	+	0.868651i	0.899127	+	0.240920i	0.678641	−	0.734470i	$-0.262569\pi$
$13$	3.24185	+	0.868651i	0.899127	+	0.240920i	0.220486	+	0.975390i	$0.429236\pi$
$14$	7.47403	−	6.55454i	1.99752	−	1.75178i
$15$	−2.31718	−	2.02072i	−0.598292	−	0.521747i
$16$	1.36018	+	0.785301i	0.340045	+	0.196325i
$17$	−1.37232	+	3.88803i	−0.332836	+	0.942985i
$17$	−1.37232	+	3.88803i	−0.332836	+	0.942985i
$18$	−3.99347	+	5.26488i	−0.941271	+	1.24094i
$19$	−2.09469	−	0.867648i	−0.480554	−	0.199052i	0.129238	−	0.991614i	$-0.458747\pi$
$19$	−2.09469	−	0.867648i	−0.480554	−	0.199052i	−0.609792	+	0.792562i	$0.708747\pi$
$20$	1.62721	−	4.79360i	0.363855	−	1.07188i
$21$	4.32472	−	6.51160i	0.943732	−	1.42095i
$22$	0.697553	−	10.6426i	0.148719	−	2.26901i
$23$	1.20194	+	3.54079i	0.250621	+	0.738306i	0.997321	+	0.0731454i	$0.0233037\pi$
$23$	1.20194	+	3.54079i	0.250621	+	0.738306i	−0.746700	+	0.665161i	$0.768363\pi$
$24$	−3.14160	−	0.832416i	−0.641277	−	0.169916i
$25$	−1.83331	−	0.241360i	−0.366663	−	0.0482720i
$26$	2.82906	+	6.82997i	0.554825	+	1.33947i
$27$	−1.94829	+	4.81707i	−0.374949	+	0.927046i
$28$	12.6234	+	2.51096i	2.38561	+	0.474526i
$29$	−3.39484	+	1.67415i	−0.630405	+	0.310882i	−0.729277	−	0.684219i	$-0.760143\pi$
$29$	−3.39484	+	1.67415i	−0.630405	+	0.310882i	0.0988715	+	0.995100i	$0.468477\pi$
$30$	0.424096	−	6.75891i	0.0774289	−	1.23400i
$31$	−0.656322	−	0.748392i	−0.117879	−	0.134415i	0.689890	−	0.723914i	$-0.257659\pi$
$31$	−0.656322	−	0.748392i	−0.117879	−	0.134415i	−0.807769	+	0.589499i	$0.799325\pi$
$32$	0.941400	+	7.15064i	0.166418	+	1.26407i
$33$	−1.65905	−	8.22084i	−0.288803	−	1.43106i
$34$	−8.63455	+	2.81537i	−1.48081	+	0.482831i
$35$			8.01106i			1.35412i
$36$	−8.55546	+	0.0476692i	−1.42591	+	0.00794487i
$37$	0.0324450	+	0.163112i	0.00533392	+	0.0268154i	0.983361	−	0.181664i	$-0.0581484\pi$
$37$	0.0324450	+	0.163112i	0.00533392	+	0.0268154i	−0.978027	+	0.208480i	$0.933148\pi$
$38$	−1.29257	−	4.82394i	−0.209683	−	0.782546i
$39$	3.55164	+	4.60198i	0.568717	+	0.736907i
$40$	3.15397	−	1.07063i	0.498686	−	0.169281i
$41$	1.80981	−	3.66994i	0.282645	−	0.573148i	−0.708534	−	0.705677i	$-0.750643\pi$
$41$	1.80981	−	3.66994i	0.282645	−	0.573148i	0.991179	+	0.132529i	$0.0423097\pi$
$42$	17.1782	−	1.17399i	2.65066	−	0.181151i
$43$	1.31010	−	9.95119i	0.199788	−	1.51754i	−0.538251	−	0.842784i	$-0.680915\pi$
$43$	1.31010	−	9.95119i	0.199788	−	1.51754i	0.738039	−	0.674758i	$-0.235752\pi$
$44$	11.4815	−	7.67170i	1.73090	−	1.15655i
$45$	−1.06798	−	5.21701i	−0.159205	−	0.777706i
$46$	−4.57589	+	6.84831i	−0.674679	+	1.00973i
$47$	7.98124	−	2.13857i	1.16418	−	0.311942i	0.375548	−	0.926803i	$-0.377454\pi$
$47$	7.98124	−	2.13857i	1.16418	−	0.311942i	0.788636	+	0.614861i	$0.210788\pi$
$48$	1.04804	+	2.51038i	0.151271	+	0.362342i
$49$	−13.2537	+	1.74488i	−1.89339	+	0.249269i
$50$	−2.03654	−	3.52739i	−0.288010	−	0.498848i
$51$	−5.97442	+	3.91232i	−0.836586	+	0.547835i
$52$	−4.78572	+	8.28912i	−0.663660	+	1.14949i
$53$	1.75702	−	4.24182i	0.241345	−	0.582659i	−0.756072	−	0.654489i	$-0.772884\pi$
$53$	1.75702	−	4.24182i	0.241345	−	0.582659i	0.997417	+	0.0718300i	$0.0228839\pi$
$54$	−11.0304	+	3.05462i	−1.50105	+	0.415681i
$55$	6.07749	+	6.07749i	0.819489	+	0.819489i
$56$	3.74546	+	7.59504i	0.500508	+	1.01493i
$57$	−1.97298	−	3.39543i	−0.261328	−	0.449735i
$58$	−7.47779	−	3.68764i	−0.981882	−	0.484210i
$59$	2.19280	+	1.68260i	0.285478	+	0.219055i	0.741567	−	0.670879i	$-0.234083\pi$
$59$	2.19280	+	1.68260i	0.285478	+	0.219055i	−0.456088	+	0.889935i	$0.650750\pi$
$60$	7.27679	−	4.89157i	0.939430	−	0.631500i
$61$	7.16122	−	0.469371i	0.916901	−	0.0600969i	0.400359	−	0.916359i	$-0.368886\pi$
$61$	7.16122	−	0.469371i	0.916901	−	0.0600969i	0.516542	+	0.856262i	$0.327219\pi$
$62$	0.427754	−	2.15046i	0.0543248	−	0.273109i
$63$	12.7963	−	4.42343i	1.61219	−	0.557300i
$64$	−9.01235	+	9.01235i	−1.12654	+	1.12654i
$65$	−5.64134	−	1.91498i	−0.699722	−	0.237523i
$66$	12.1414	−	13.9227i	1.49450	−	1.71376i
$67$	−0.191282	+	0.110437i	−0.0233688	+	0.0134920i	−0.511639	−	0.859201i	$-0.670961\pi$
$67$	−0.191282	+	0.110437i	−0.0233688	+	0.0134920i	0.488270	+	0.872693i	$0.337628\pi$
$68$	−9.69737	−	6.65013i	−1.17598	−	0.806446i
$69$	−2.06472	+	6.13861i	−0.248563	+	0.739002i
$70$	−13.9995	+	10.7422i	−1.67325	+	1.28393i
$71$	−4.68313	+	0.931533i	−0.555786	+	0.110553i	−0.464988	−	0.885317i	$-0.653942\pi$
$71$	−4.68313	+	0.931533i	−0.555786	+	0.110553i	−0.0907972	+	0.995869i	$0.528942\pi$
$72$	−3.45166	−	4.44677i	−0.406782	−	0.524057i
$73$	3.14851	+	2.10376i	0.368505	+	0.246227i	0.726010	−	0.687684i	$-0.241373\pi$
$73$	3.14851	+	2.10376i	0.368505	+	0.246227i	−0.357505	+	0.933911i	$0.616373\pi$
$74$	−0.241535	+	0.275417i	−0.0280778	+	0.0320166i
$75$	−2.27102	−	2.25840i	−0.262234	−	0.260777i
$76$	3.93622	−	5.12978i	0.451516	−	0.588427i
$77$	−13.3029	+	17.3367i	−1.51601	+	1.97570i
$78$	−3.27959	+	12.3774i	−0.371340	+	1.40147i
$79$	−6.37354	+	7.26763i	−0.717080	+	0.817673i	−0.989504	−	0.144504i	$-0.953841\pi$
$79$	−6.37354	+	7.26763i	−0.717080	+	0.817673i	0.272424	+	0.962177i	$0.412175\pi$
$80$	−2.31808	−	1.54889i	−0.259169	−	0.173171i
$81$	−7.74360	+	4.58657i	−0.860400	+	0.509619i
$82$	8.84008	−	1.75840i	0.976223	−	0.194183i
$83$	−1.15581	+	0.886882i	−0.126866	+	0.0973479i	−0.670246	−	0.742139i	$-0.733811\pi$
$83$	−1.15581	+	0.886882i	−0.126866	+	0.0973479i	0.543379	+	0.839487i	$0.317145\pi$
$84$	14.7453	+	16.7196i	1.60884	+	1.82426i
$85$	2.88212	−	6.72741i	0.312610	−	0.729691i
$86$	19.1466	−	11.0543i	2.06463	−	1.19201i
$87$	−6.43371	−	1.26112i	−0.689766	−	0.135207i
$88$	8.60333	+	2.92044i	0.917118	+	0.311319i
$89$	−9.41257	+	9.41257i	−0.997730	+	0.997730i	−0.999997	−	0.00226751i	$-0.999278\pi$
$89$	−9.41257	+	9.41257i	−0.997730	+	0.997730i	0.00226751	+	0.999997i	$0.499278\pi$
$90$	7.68474	−	8.86189i	0.810043	−	0.934125i
$91$	2.95501	−	14.8559i	0.309770	−	1.55732i
$92$	−10.6410	+	0.697445i	−1.10940	+	0.0727136i
$93$	−0.117554	−	1.72009i	−0.0121898	−	0.178366i
$94$	14.4394	+	11.0797i	1.48931	+	1.14278i
$95$	3.60952	+	1.78002i	0.370329	+	0.182626i
$96$	−6.21591	+	10.8359i	−0.634409	+	1.10593i
$97$	6.36781	+	12.9126i	0.646553	+	1.31108i	0.935362	+	0.353693i	$0.115074\pi$
$97$	6.36781	+	12.9126i	0.646553	+	1.31108i	−0.288809	+	0.957387i	$0.593259\pi$
$98$	−20.8213	−	20.8213i	−2.10327	−	2.10327i
$99$	6.35199	−	13.0635i	0.638399	−	1.31294i
$100$	2.01807	−	4.87205i	0.201807	−	0.487205i
$101$	0.803282	−	1.39133i	0.0799296	−	0.138442i	−0.823290	−	0.567621i	$-0.807864\pi$
$101$	0.803282	−	1.39133i	0.0799296	−	0.138442i	0.903219	+	0.429179i	$0.141197\pi$
$102$	−14.8480	−	5.19430i	−1.47018	−	0.514312i
$103$	0.664114	+	1.15028i	0.0654371	+	0.113340i	0.896888	−	0.442258i	$-0.145823\pi$
$103$	0.664114	+	1.15028i	0.0654371	+	0.113340i	−0.831451	+	0.555599i	$0.812489\pi$
$104$	−6.24370	+	0.821998i	−0.612245	+	0.0806035i
$105$	−8.41621	+	11.0317i	−0.821338	+	1.07659i
$106$	9.76866	−	2.61750i	0.948816	−	0.254235i
$107$	−1.19178	+	1.78362i	−0.115213	+	0.172429i	−0.884594	−	0.466361i	$-0.845565\pi$
$107$	−1.19178	+	1.78362i	−0.115213	+	0.172429i	0.769381	+	0.638790i	$0.220565\pi$
$108$	−11.8315	−	8.92249i	−1.13848	−	0.858567i
$109$	3.50804	−	2.34400i	0.336009	−	0.224514i	−0.376106	−	0.926577i	$-0.622737\pi$
$109$	3.50804	−	2.34400i	0.336009	−	0.224514i	0.712116	+	0.702062i	$0.247737\pi$
$110$	−2.47111	+	18.7699i	−0.235611	+	1.78964i
$111$	−0.126682	+	0.258701i	−0.0120242	+	0.0245548i
$112$	3.13507	−	6.35729i	0.296236	−	0.600707i
$113$	−1.83941	+	0.624396i	−0.173037	+	0.0587382i	−0.406614	−	0.913600i	$-0.633290\pi$
$113$	−1.83941	+	0.624396i	−0.173037	+	0.0587382i	0.233576	+	0.972338i	$0.424957\pi$
$114$	3.28795	−	8.00080i	0.307945	−	0.749343i
$115$	−1.71788	−	6.41123i	−0.160194	−	0.597850i
$116$	−2.10597	−	10.5874i	−0.195535	−	0.983019i
$117$	0.0560994	+	10.0685i	0.00518639	+	0.930830i
$118$			6.08817i			0.560462i
$119$	17.9145	+	5.03252i	1.64222	+	0.461330i
$120$	5.46798	+	1.83916i	0.499156	+	0.167891i
$121$	1.62439	+	12.3384i	0.147671	+	1.12168i
$122$	10.4228	+	11.8850i	0.943639	+	1.07601i
$123$	6.34776	−	3.15238i	0.572358	−	0.284241i
$124$	2.54603	−	1.25556i	0.228640	−	0.112753i
$125$	11.9241	+	2.37185i	1.06652	+	0.212144i
$126$	24.8888	+	16.4303i	2.21727	+	1.46373i
$127$	1.71483	+	4.13997i	0.152167	+	0.367363i	0.981519	−	0.191362i	$-0.0612906\pi$
$127$	1.71483	+	4.13997i	0.152167	+	0.367363i	−0.829353	+	0.558725i	$0.811291\pi$
$128$	−13.5327	−	1.78162i	−1.19614	−	0.157474i
$129$	12.2585	−	12.3270i	1.07930	−	1.08533i
$130$	−4.21811	−	12.4261i	−0.369952	−	1.08984i
$131$	0.137249	−	2.09401i	0.0119915	−	0.182955i	−0.987661	−	0.156605i	$-0.949945\pi$
$131$	0.137249	−	2.09401i	0.0119915	−	0.182955i	0.999653	−	0.0263496i	$-0.00838830\pi$
$132$	23.8704	+	1.49778i	2.07765	+	0.130365i
$133$	−3.28911	+	9.68939i	−0.285202	+	0.840177i
$134$	−0.449483	−	0.186182i	−0.0388294	−	0.0160837i
$135$	4.01018	−	8.30613i	0.345142	−	0.714878i
$136$	−0.412855	−	7.72555i	−0.0354020	−	0.662461i
$137$	−17.1862	−	9.92247i	−1.46832	−	0.847734i	−0.468949	−	0.883225i	$-0.655367\pi$
$137$	−17.1862	−	9.92247i	−1.46832	−	0.847734i	−0.999370	+	0.0354914i	$0.988700\pi$
$138$	−13.4959	+	4.62322i	−1.14885	+	0.393555i
$139$	16.4547	−	14.4304i	1.39567	−	1.22397i	0.452454	−	0.891788i	$-0.350549\pi$
$139$	16.4547	−	14.4304i	1.39567	−	1.22397i	0.943215	−	0.332182i	$-0.107785\pi$
$140$	−22.0680	−	5.91310i	−1.86508	−	0.499748i
$141$	13.2374	+	5.43995i	1.11479	+	0.458126i
$142$	−7.90755	−	6.93474i	−0.663587	−	0.581950i
$143$	−9.02843	−	13.5120i	−0.754995	−	1.12993i
$144$	−1.19413	+	4.55798i	−0.0995106	+	0.379832i
$145$	6.20753	−	2.57124i	0.515507	−	0.213530i
$146$	0.545520	+	8.32303i	0.0451476	+	0.688819i
$147$	−20.0843	−	11.5212i	−1.65652	−	0.950251i
$148$	−0.473271	−	0.0310198i	−0.0389026	−	0.00254981i
$149$	5.21859	−	19.4761i	0.427524	−	1.59554i	−0.330826	−	0.943692i	$-0.607327\pi$
$149$	5.21859	−	19.4761i	0.427524	−	1.59554i	0.758349	−	0.651848i	$-0.226006\pi$
$150$	0.901343	−	6.99695i	0.0735944	−	0.571299i
$151$	10.2545	+	13.3640i	0.834503	+	1.08755i	0.994937	+	0.100499i	$0.0320439\pi$
$151$	10.2545	+	13.3640i	0.834503	+	1.08755i	−0.160434	+	0.987047i	$0.551289\pi$
$152$	4.25430			0.345069
$153$	−12.3373	−	0.889063i	−0.997414	−	0.0718765i
$154$	−48.1342			−3.87876
$155$	1.07564	+	1.40180i	0.0863973	+	0.112595i
$156$	−15.2986	+	6.38686i	−1.22486	+	0.511358i
$157$	−4.45654	+	16.6320i	−0.355671	+	1.32738i	0.523968	+	0.851738i	$0.324451\pi$
$157$	−4.45654	+	16.6320i	−0.355671	+	1.32738i	−0.879639	+	0.475643i	$0.842216\pi$
$158$	−21.2467	−	1.39258i	−1.69030	−	0.110788i
$159$	6.87587	−	3.99536i	0.545292	−	0.316853i
$160$	−0.837318	−	12.7750i	−0.0661958	−	1.00995i
$161$	15.5910	−	6.45799i	1.22874	−	0.508961i
$162$	−18.3986	−	7.38185i	−1.44553	−	0.579973i
$163$	−11.1398	−	16.6719i	−0.872538	−	1.30585i	−0.951083	−	0.308935i	$-0.900027\pi$
$163$	−11.1398	−	16.6719i	−0.872538	−	1.30585i	0.0785451	−	0.996911i	$-0.474973\pi$
$164$	8.77368	+	7.69431i	0.685109	+	0.600825i
$165$	1.98422	+	14.7539i	0.154471	+	1.14859i
$166$	−3.09968	−	0.830556i	−0.240582	−	0.0644637i
$167$	3.88841	−	3.41004i	0.300894	−	0.263877i	−0.495563	−	0.868572i	$-0.665038\pi$
$167$	3.88841	−	3.41004i	0.300894	−	0.263877i	0.796457	+	0.604695i	$0.206705\pi$
$168$	−2.82142	+	14.3937i	−0.217678	+	1.11050i
$169$	−1.50331	−	0.867934i	−0.115639	−	0.0667641i
$170$	15.6209	−	3.98434i	1.19807	−	0.305585i
$171$	0.850228	−	6.74847i	0.0650186	−	0.516068i
$172$	26.4454	+	10.9541i	2.01644	+	0.835239i
$173$	4.23690	−	12.4815i	0.322126	−	0.948951i	−0.658418	−	0.752652i	$-0.728774\pi$
$173$	4.23690	−	12.4815i	0.322126	−	0.948951i	0.980544	−	0.196299i	$-0.0628924\pi$
$174$	−6.42323	−	12.9341i	−0.486944	−	0.980529i
$175$	−0.545810	+	8.32745i	−0.0412594	+	0.629496i
$176$	−2.44450	−	7.20125i	−0.184261	−	0.542815i
$177$	1.25193	+	4.62074i	0.0941008	+	0.347316i
$178$	−29.0701	−	3.82715i	−2.17889	−	0.286857i
$179$	−1.82943	−	4.41664i	−0.136738	−	0.330115i	0.840646	−	0.541584i	$-0.182175\pi$
$179$	−1.82943	−	4.41664i	−0.136738	−	0.330115i	−0.977385	+	0.211469i	$0.932175\pi$
$180$	15.1595	+	0.908811i	1.12993	+	0.0677388i
$181$	12.0979	+	2.40641i	0.899227	+	0.178867i	0.622997	−	0.782224i	$-0.285915\pi$
$181$	12.0979	+	2.40641i	0.899227	+	0.178867i	0.276230	+	0.961092i	$0.410915\pi$
$182$	29.9233	−	14.7565i	2.21806	−	1.09383i
$183$	10.3545	+	6.87704i	0.765430	+	0.508365i
$184$	−4.62615	−	5.27512i	−0.341045	−	0.388887i
$185$	−0.0385323	−	0.292682i	−0.00283295	−	0.0215184i
$186$	2.84826	−	2.51193i	0.208845	−	0.184184i
$187$	17.4085	−	9.77279i	1.27304	−	0.714657i
$188$			23.5643i			1.71861i
$189$	22.2685	+	7.35215i	1.61979	+	0.534790i
$190$	1.72945	+	8.69455i	0.125468	+	0.630769i
$191$	−1.09493	−	4.08635i	−0.0792266	−	0.295678i	0.914932	−	0.403608i	$-0.132244\pi$
$191$	−1.09493	−	4.08635i	−0.0792266	−	0.295678i	−0.994158	+	0.107931i	$0.965578\pi$
$192$	−21.8787	+	2.94242i	−1.57896	+	0.212351i
$193$	−13.4254	+	4.55731i	−0.966382	+	0.328043i	−0.759633	−	0.650352i	$-0.774622\pi$
$193$	−13.4254	+	4.55731i	−0.966382	+	0.328043i	−0.206749	+	0.978394i	$0.566288\pi$
$194$	−14.0263	+	28.4426i	−1.00703	+	2.04206i
$195$	−5.75664	−	8.56367i	−0.412241	−	0.613257i
$196$	4.97617	−	37.7978i	0.355441	−	2.69984i
$197$	−2.47427	+	1.65326i	−0.176285	+	0.117790i	−0.640582	−	0.767890i	$-0.721307\pi$
$197$	−2.47427	+	1.65326i	−0.176285	+	0.117790i	0.464297	+	0.885679i	$0.346307\pi$
$198$	31.3462	−	6.41692i	2.22768	−	0.456031i
$199$	−12.6286	+	18.9000i	−0.895215	+	1.33978i	0.0449235	+	0.998990i	$0.485696\pi$
$199$	−12.6286	+	18.9000i	−0.895215	+	1.33978i	−0.940138	+	0.340793i	$0.889304\pi$
$200$	3.35148	−	0.898025i	0.236985	−	0.0635000i
$201$	−0.379429	−	0.0488778i	−0.0267629	−	0.00344757i
$202$	3.50850	−	0.461902i	0.246857	−	0.0324993i
$203$	8.54148	+	14.7943i	0.599494	+	1.03835i
$204$	−6.36741	−	19.3454i	−0.445808	−	1.35445i
$205$	−3.63173	+	6.29033i	−0.253651	+	0.439336i
$206$	−1.11961	+	2.70298i	−0.0780069	+	0.188325i
$207$	−9.29231	+	6.28409i	−0.645860	+	0.436775i
$208$	3.72735	+	3.72735i	0.258445	+	0.258445i
$209$	4.85550	+	9.84598i	0.335862	+	0.681060i
$210$	−30.5635	+	0.0851461i	−2.10908	+	0.00587564i
$211$	7.03564	+	3.46959i	0.484353	+	0.238857i	0.668036	−	0.744129i	$-0.267135\pi$
$211$	7.03564	+	3.46959i	0.484353	+	0.238857i	−0.183683	+	0.982986i	$0.558802\pi$
$212$	10.3880	+	7.97100i	0.713451	+	0.547450i
$213$	−7.42760	−	3.63720i	−0.508931	−	0.249217i
$214$	−4.71497	+	0.309036i	−0.322309	+	0.0211252i
$215$	−3.47582	+	17.4741i	−0.237049	+	1.19173i
$216$	−0.0814859	−	9.74969i	−0.00554441	−	0.663383i
$217$	−3.17661	+	3.17661i	−0.215642	+	0.215642i
$218$	8.80016	+	2.98725i	0.596022	+	0.202322i
$219$	2.12552	+	6.20475i	0.143630	+	0.419278i
$220$	−21.2275	+	12.2557i	−1.43116	+	0.826279i
$221$	−7.82618	+	11.4123i	−0.526446	+	0.767676i
$222$	−0.621954	+	0.125517i	−0.0417428	+	0.00842412i
$223$	20.8267	−	15.9809i	1.39466	−	1.07016i	0.407017	−	0.913421i	$-0.366569\pi$
$223$	20.8267	−	15.9809i	1.39466	−	1.07016i	0.987640	−	0.156738i	$-0.0500977\pi$
$224$	31.9246	−	6.35020i	2.13305	−	0.424290i
$225$	−0.754713	−	5.49582i	−0.0503142	−	0.366388i
$226$	−3.55764	−	2.37714i	−0.236651	−	0.158125i
$227$	−1.58518	+	1.80755i	−0.105212	+	0.119971i	−0.802049	−	0.597258i	$-0.796257\pi$
$227$	−1.58518	+	1.80755i	−0.105212	+	0.119971i	0.696837	+	0.717229i	$0.254590\pi$
$228$	10.8096	−	2.92873i	0.715885	−	0.193960i
$229$	3.10723	−	4.04942i	0.205331	−	0.267593i	−0.679324	−	0.733838i	$-0.737727\pi$
$229$	3.10723	−	4.04942i	0.205331	−	0.267593i	0.884655	+	0.466245i	$0.154394\pi$
$230$	8.90019	−	11.5989i	0.586861	−	0.764812i
$231$	−36.5323	+	9.89798i	−2.40365	+	0.651239i
$232$	4.68302	−	5.33996i	0.307455	−	0.350585i
$233$	−3.76513	−	2.51578i	−0.246662	−	0.164814i	0.426094	−	0.904679i	$-0.359889\pi$
$233$	−3.76513	−	2.51578i	−0.246662	−	0.164814i	−0.672756	+	0.739865i	$0.734889\pi$
$234$	−17.5196	+	13.5990i	−1.14529	+	0.888994i
$235$	−14.3852	+	2.86139i	−0.938387	+	0.186657i
$236$	−6.25357	+	4.79853i	−0.407073	+	0.312358i
$237$	−16.4119	+	3.31209i	−1.06607	+	0.215144i
$238$	15.2275	+	38.0541i	0.987052	+	2.46668i
$239$	15.7473	−	9.09168i	1.01861	−	0.588092i	0.104906	−	0.994482i	$-0.466546\pi$
$239$	15.7473	−	9.09168i	1.01861	−	0.588092i	0.913700	+	0.406390i	$0.133213\pi$
$240$	−1.56491	−	4.56822i	−0.101014	−	0.294877i
$241$	−6.82375	−	2.31635i	−0.439557	−	0.149209i	0.0928836	−	0.995677i	$-0.470392\pi$
$241$	−6.82375	−	2.31635i	−0.439557	−	0.149209i	−0.532440	+	0.846468i	$0.678725\pi$
$242$	−19.3834	+	19.3834i	−1.24601	+	1.24601i
$243$	−15.4819	−	1.81923i	−0.993167	−	0.116704i
$244$	−3.99285	+	20.0734i	−0.255616	+	1.28507i
$245$	23.6784	−	1.55197i	1.51276	−	0.0991515i
$246$	14.0207	+	6.86573i	0.893924	+	0.437743i
$247$	−6.03697	−	4.63233i	−0.384123	−	0.294748i
$248$	1.67517	+	0.826102i	0.106373	+	0.0524575i
$249$	−2.52335	+	0.00702973i	−0.159911	+	0.000445491i
$250$	11.8443	+	24.0179i	0.749102	+	1.51903i
$251$	−2.54375	−	2.54375i	−0.160560	−	0.160560i	0.622255	−	0.782815i	$-0.286217\pi$
$251$	−2.54375	−	2.54375i	−0.160560	−	0.160560i	−0.782815	+	0.622255i	$0.786217\pi$
$252$	2.74000	+	38.5149i	0.172604	+	2.42621i
$253$	6.92861	−	16.7272i	0.435598	−	1.05163i
$254$	−4.93522	+	8.54805i	−0.309663	+	0.536352i
$255$	11.0365	−	6.23617i	0.691133	−	0.390524i
$256$	−2.28746	−	3.96200i	−0.142966	−	0.247625i
$257$	19.6917	−	2.59245i	1.22833	−	0.161713i	0.511699	−	0.859164i	$-0.329016\pi$
$257$	19.6917	−	2.59245i	1.22833	−	0.161713i	0.716632	+	0.697452i	$0.245683\pi$
$258$	37.9793	+	4.89248i	2.36449	+	0.304592i
$259$	0.724988	−	0.194260i	0.0450485	−	0.0120707i
$260$	9.43912	−	14.1266i	0.585390	−	0.876097i
$261$	−7.53471	−	8.49573i	−0.466387	−	0.525872i
$262$	3.84335	−	2.56805i	0.237443	−	0.158655i
$263$	−0.696416	+	5.28980i	−0.0429428	+	0.326183i	0.956467	+	0.291840i	$0.0942674\pi$
$263$	−0.696416	+	5.28980i	−0.0429428	+	0.326183i	−0.999410	+	0.0343435i	$0.989066\pi$
$264$	8.77917	+	13.0600i	0.540320	+	0.803790i
$265$	−3.60461	+	7.30942i	−0.221429	+	0.449014i
$266$	−21.3428	+	7.24490i	−1.30861	+	0.444213i
$267$	−22.8503	+	3.07308i	−1.39841	+	0.188069i
$268$	−0.163030	−	0.608438i	−0.00995867	−	0.0371663i
$269$	0.519457	+	2.61148i	0.0316718	+	0.159225i	0.993385	−	0.114834i	$-0.0366336\pi$
$269$	0.519457	+	2.61148i	0.0316718	+	0.159225i	−0.961713	+	0.274059i	$0.911634\pi$
$270$	19.8924	−	4.12997i	1.21061	−	0.251342i
$271$		−	32.3652i		−	1.96605i	−0.183479	−	0.983024i	$-0.558736\pi$
$271$		−	32.3652i		−	1.96605i	0.183479	−	0.983024i	$-0.441264\pi$
$272$	−4.91987	+	4.21074i	−0.298311	+	0.255313i
$273$	19.6764	−	17.3530i	1.19087	−	1.05025i
$274$	−5.70561	−	43.3384i	−0.344688	−	2.61817i
$275$	5.90344	+	6.73159i	0.355991	+	0.405930i
$276$	−15.3859	−	10.2187i	−0.926125	−	0.615092i
$277$	−17.6709	+	8.71433i	−1.06174	+	0.523593i	−0.887356	−	0.461084i	$-0.847461\pi$
$277$	−17.6709	+	8.71433i	−1.06174	+	0.523593i	−0.174386	+	0.984677i	$0.555794\pi$
$278$	47.2817	+	9.40491i	2.83577	+	0.564069i
$279$	1.64521	−	2.49217i	0.0984959	−	0.149203i
$280$	−5.75247	−	13.8877i	−0.343776	−	0.829948i
$281$	−3.48088	−	0.458266i	−0.207652	−	0.0273379i	0.0259826	−	0.999662i	$-0.491729\pi$
$281$	−3.48088	−	0.458266i	−0.207652	−	0.0273379i	−0.233634	+	0.972325i	$0.575062\pi$
$282$	8.24382	+	30.4270i	0.490912	+	1.81190i
$283$	3.41787	+	10.0687i	0.203171	+	0.598523i	0.999984	−	0.00570383i	$-0.00181560\pi$
$283$	3.41787	+	10.0687i	0.203171	+	0.598523i	−0.796813	+	0.604226i	$0.793482\pi$
$284$	0.890615	−	13.5882i	0.0528483	−	0.806309i
$285$	3.10049	+	6.24326i	0.183657	+	0.369819i
$286$	11.5061	−	33.8958i	0.680367	−	2.00430i
$287$	−17.0615	−	7.06712i	−1.00711	−	0.417159i
$288$	−19.9436	+	8.39139i	−1.17519	+	0.494467i
$289$	−13.2335	−	10.6712i	−0.778440	−	0.627719i
$290$	12.8170	+	7.39993i	0.752643	+	0.434539i
$291$	−4.79682	+	24.4713i	−0.281194	+	1.43453i
$292$	−8.11918	+	7.12033i	−0.475139	+	0.416686i
$293$	−21.1563	−	5.66881i	−1.23596	−	0.331175i	−0.419065	−	0.907956i	$-0.637642\pi$
$293$	−21.1563	−	5.66881i	−1.23596	−	0.331175i	−0.816899	+	0.576781i	$0.804309\pi$
$294$	−6.79789	−	50.5465i	−0.396461	−	2.94793i
$295$	−3.68870	−	3.23490i	−0.214764	−	0.188343i
$296$	−0.173370	−	0.259467i	−0.0100770	−	0.0150812i
$297$	22.4713	−	11.3161i	1.30392	−	0.656625i
$298$	41.0324	−	16.9962i	2.37694	−	0.984562i
$299$	0.820786	+	12.5228i	0.0474673	+	0.724211i
$300$	7.89746	−	4.58898i	0.455960	−	0.264945i
$301$	−45.2013	−	2.96265i	−2.60536	−	0.170764i
$302$	−9.60328	+	35.8399i	−0.552607	+	2.06236i
$303$	2.56786	−	1.07203i	0.147520	−	0.0615867i
$304$	−2.16779	−	2.82512i	−0.124331	−	0.162032i
$305$	−12.7389			−0.729430
$306$	−14.9897	−	22.7518i	−0.856902	−	1.30063i
$307$	−9.28181			−0.529741			−0.264870	−	0.964284i	$-0.585329\pi$
$307$	−9.28181			−0.529741			−0.264870	+	0.964284i	$0.585329\pi$
$308$	−37.9381	−	49.4418i	−2.16172	−	2.81721i
$309$	−0.293928	+	2.28170i	−0.0167210	+	0.129802i
$310$	−1.00732	+	3.75938i	−0.0572122	+	0.213519i
$311$	14.8685	+	0.974536i	0.843118	+	0.0552609i	0.480839	−	0.876809i	$-0.340332\pi$
$311$	14.8685	+	0.974536i	0.843118	+	0.0552609i	0.362279	+	0.932070i	$0.381999\pi$
$312$	−9.46152	−	5.42752i	−0.535653	−	0.307273i
$313$	1.11274	+	16.9771i	0.0628956	+	0.959602i	0.906384	+	0.422455i	$0.138831\pi$
$313$	1.11274	+	16.9771i	0.0628956	+	0.959602i	−0.843488	+	0.537147i	$0.819502\pi$
$314$	−35.0406	+	14.5143i	−1.97745	+	0.819088i
$315$	−23.1793	+	6.34949i	−1.30600	+	0.357753i
$316$	−15.3157	−	22.9215i	−0.861573	−	1.28943i
$317$	−21.7420	−	19.0672i	−1.22115	−	1.07092i	−0.995308	−	0.0967600i	$-0.969152\pi$
$317$	−21.7420	−	19.0672i	−1.22115	−	1.07092i	−0.225846	−	0.974163i	$-0.572515\pi$
$318$	16.2019	+	6.65823i	0.908558	+	0.373375i
$319$	17.7034	+	4.74360i	0.991199	+	0.265591i
$320$	17.0096	−	14.9170i	0.950864	−	0.833886i
$321$	−3.51497	+	1.20410i	−0.196187	+	0.0672065i
$322$	32.1916	+	18.5858i	1.79397	+	1.03575i
$323$	6.24801	−	6.95351i	0.347649	−	0.386903i
$324$	−6.91890	−	24.7166i	−0.384383	−	1.37315i
$325$	−5.73366	−	2.37496i	−0.318046	−	0.131739i
$326$	14.1969	−	41.8226i	0.786292	−	2.31634i
$327$	7.29333	+	0.457628i	0.403322	+	0.0253069i
$328$	−0.502170	+	7.66163i	−0.0277277	+	0.423043i
$329$	−11.9867	−	35.3118i	−0.660850	−	1.94680i
$330$	−23.1220	+	23.2512i	−1.27283	+	1.27994i
$331$	6.05088	+	0.796613i	0.332586	+	0.0437858i	0.294970	−	0.955506i	$-0.404690\pi$
$331$	6.05088	+	0.796613i	0.332586	+	0.0437858i	0.0376161	+	0.999292i	$0.488024\pi$
$332$	−1.58996	−	3.83851i	−0.0872605	−	0.210666i
$333$	−0.446234	+	0.223158i	−0.0244534	+	0.0122290i
$334$	11.1731	+	2.22247i	0.611366	+	0.121608i
$335$	0.351633	−	0.173406i	0.0192118	−	0.00947419i
$336$	10.9960	−	5.46075i	0.599880	−	0.297908i
$337$	−5.21884	−	5.95094i	−0.284288	−	0.324168i	0.592017	−	0.805926i	$-0.298332\pi$
$337$	−5.21884	−	5.95094i	−0.284288	−	0.324168i	−0.876305	+	0.481757i	$0.839999\pi$
$338$	−0.499078	−	3.79087i	−0.0271463	−	0.206196i
$339$	−3.18895	−	1.07261i	−0.173200	−	0.0582560i
$340$	16.4046	+	12.9050i	0.889664	+	0.699870i
$341$			4.81979i			0.261006i
$342$	12.9331	−	7.56334i	0.699344	−	0.408979i
$343$	5.60685	+	28.1875i	0.302741	+	1.52198i
$344$	4.87446	+	18.1917i	0.262814	+	0.980833i
$345$	4.36984	−	10.6334i	0.235264	−	0.572484i
$346$	27.4929	−	9.33260i	1.47803	−	0.501724i
$347$	8.93445	−	18.1173i	0.479627	−	0.972587i	−0.513778	−	0.857923i	$-0.671754\pi$
$347$	8.93445	−	18.1173i	0.479627	−	0.972587i	0.993404	−	0.114663i	$-0.0365789\pi$
$348$	8.22283	−	16.7920i	0.440790	−	0.900146i
$349$	−2.81515	+	21.3832i	−0.150692	+	1.14462i	0.734238	+	0.678892i	$0.237540\pi$
$349$	−2.81515	+	21.3832i	−0.150692	+	1.14462i	−0.884930	+	0.465725i	$0.845794\pi$
$350$	−15.2842	+	10.2126i	−0.816977	+	0.545886i
$351$	−10.5004	+	13.9238i	−0.560471	+	0.743199i
$352$	19.4017	−	29.0367i	1.03411	−	1.54766i
$353$	−15.2322	+	4.08144i	−0.810726	+	0.217233i	−0.640288	−	0.768135i	$-0.721185\pi$
$353$	−15.2322	+	4.08144i	−0.810726	+	0.217233i	−0.170438	+	0.985368i	$0.554518\pi$
$354$	−6.39607	+	8.38378i	−0.339947	+	0.445593i
$355$	8.40323	−	1.10631i	0.445997	−	0.0587166i
$356$	−18.9811	−	32.8763i	−1.00600	−	1.74244i
$357$	19.3824	+	25.7506i	1.02582	+	1.36287i
$358$	5.26503	−	9.11930i	0.278266	−	0.481970i
$359$	−2.97148	+	7.17379i	−0.156829	+	0.378618i	−0.982691	−	0.185254i	$-0.940689\pi$
$359$	−2.97148	+	7.17379i	−0.156829	+	0.378618i	0.825862	+	0.563873i	$0.190689\pi$
$360$	5.59757	+	8.27714i	0.295018	+	0.436244i
$361$	−9.80013	−	9.80013i	−0.515796	−	0.515796i
$362$	12.0170	+	24.3680i	0.631598	+	1.28075i
$363$	−10.7256	+	18.6973i	−0.562945	+	0.981354i
$364$	38.7421	+	19.1055i	2.03064	+	1.00140i
$365$	−5.33261	−	4.09186i	−0.279122	−	0.214178i
$366$	1.86684	+	27.3163i	0.0975814	+	1.42784i
$367$	−24.4182	+	1.60045i	−1.27462	+	0.0835429i	−0.687635	−	0.726056i	$-0.741351\pi$
$367$	−24.4182	+	1.60045i	−1.27462	+	0.0835429i	−0.586983	+	0.809599i	$0.699684\pi$
$368$	−1.14574	+	5.76000i	−0.0597256	+	0.300261i
$369$	12.0531	+	2.32777i	0.627457	+	0.121179i
$370$	0.459797	−	0.459797i	0.0239037	−	0.0239037i
$371$	−19.6214	−	6.66057i	−1.01869	−	0.345799i
$372$	4.82509	+	0.945805i	0.250169	+	0.0490377i
$373$	3.39921	−	1.96253i	0.176004	−	0.101616i	−0.409410	−	0.912351i	$-0.634265\pi$
$373$	3.39921	−	1.96253i	0.176004	−	0.101616i	0.585414	+	0.810735i	$0.300932\pi$
$374$	40.4214	+	17.3171i	2.09014	+	0.895448i
$375$	13.9284	+	15.7933i	0.719258	+	0.815562i
$376$	−12.3004	+	9.43839i	−0.634342	+	0.486748i
$377$	−12.4598	+	2.47841i	−0.641712	+	0.127644i
$378$	17.0121	+	48.7731i	0.875009	+	2.50862i
$379$	21.8032	+	14.5684i	1.11996	+	0.748331i	0.970659	−	0.240462i	$-0.0772988\pi$
$379$	21.8032	+	14.5684i	1.11996	+	0.748331i	0.149297	+	0.988792i	$0.452299\pi$
$380$	−7.56765	+	8.62925i	−0.388212	+	0.442671i
$381$	−1.98792	+	7.50255i	−0.101844	+	0.384367i
$382$	5.67274	−	7.39286i	0.290243	−	0.378252i
$383$	−5.09431	+	6.63903i	−0.260307	+	0.339239i	−0.905162	−	0.425066i	$-0.860251\pi$
$383$	−5.09431	+	6.63903i	−0.260307	+	0.339239i	0.644855	+	0.764305i	$0.276918\pi$
$384$	−16.7637	−	16.6705i	−0.855468	−	0.850715i
$385$	25.5757	−	29.1635i	1.30346	−	1.48631i
$386$	−25.9663	−	17.3501i	−1.32165	−	0.883099i
$387$	29.8312	−	4.09657i	1.51641	−	0.208240i
$388$	−40.2705	+	8.01030i	−2.04442	+	0.406661i
$389$	16.6930	−	12.8090i	0.846370	−	0.649443i	−0.0917388	−	0.995783i	$-0.529242\pi$
$389$	16.6930	−	12.8090i	0.846370	−	0.649443i	0.938109	+	0.346341i	$0.112576\pi$
$390$	7.24599	−	21.5430i	0.366915	−	1.09087i
$391$	−15.4161	−	0.185934i	−0.779627	−	0.00940309i
$392$	21.7232	−	12.5419i	1.09719	−	0.633461i
$393$	2.38891	−	2.73939i	0.120505	−	0.138184i
$394$	−6.20688	−	2.10695i	−0.312698	−	0.106147i
$395$	12.1330	−	12.1330i	0.610477	−	0.610477i
$396$	31.2975	+	27.1402i	1.57276	+	1.36385i
$397$	−0.764252	+	3.84216i	−0.0383567	+	0.192832i	−0.995213	−	0.0977292i	$-0.968842\pi$
$397$	−0.764252	+	3.84216i	−0.0383567	+	0.192832i	0.956856	+	0.290562i	$0.0938421\pi$
$398$	−49.9618	+	3.27467i	−2.50436	+	0.164144i
$399$	−14.7087	+	9.88743i	−0.736357	+	0.494991i
$400$	−2.30410	−	1.76800i	−0.115205	−	0.0883998i
$401$	31.3908	+	15.4802i	1.56758	+	0.773045i	0.998778	−	0.0494298i	$-0.0157404\pi$
$401$	31.3908	+	15.4802i	1.56758	+	0.773045i	0.568802	+	0.822474i	$0.307407\pi$
$402$	−0.423368	−	0.728599i	−0.0211157	−	0.0363392i
$403$	−1.47760	−	2.99629i	−0.0736047	−	0.149256i
$404$	3.23975	+	3.23975i	0.161184	+	0.161184i
$405$	14.2485	−	7.22506i	0.708012	−	0.359016i
$406$	−14.3998	+	34.7642i	−0.714651	+	1.72532i
$407$	0.402630	−	0.697375i	0.0199576	−	0.0345676i
$408$	7.54773	−	11.0723i	0.373668	−	0.548160i
$409$	13.7720	+	23.8538i	0.680980	+	1.17949i	0.974682	+	0.223595i	$0.0717794\pi$
$409$	13.7720	+	23.8538i	0.680980	+	1.17949i	−0.293702	+	0.955897i	$0.594887\pi$
$410$	−15.8623	+	2.08831i	−0.783383	+	0.103134i
$411$	−13.2422	−	31.7192i	−0.653189	−	1.56459i
$412$	−3.65885	+	0.980387i	−0.180259	+	0.0483002i
$413$	6.93021	−	10.3718i	0.341014	−	0.510363i
$414$	−23.4417	−	7.81201i	−1.15210	−	0.383939i
$415$	2.15021	−	1.43672i	0.105549	−	0.0705259i
$416$	−3.15953	+	23.9990i	−0.154909	+	1.17665i
$417$	37.8193	−	2.58464i	1.85202	−	0.126570i
$418$	−10.6952	+	21.6877i	−0.523118	+	1.06078i
$419$	−4.60408	+	1.56288i	−0.224924	+	0.0763515i	−0.431627	−	0.902052i	$-0.642060\pi$
$419$	−4.60408	+	1.56288i	−0.224924	+	0.0763515i	0.206702	+	0.978404i	$0.433727\pi$
$420$	−24.1768	−	31.3267i	−1.17971	−	1.52859i
$421$	−4.53863	−	16.9384i	−0.221199	−	0.825528i	−0.983892	−	0.178766i	$-0.942790\pi$
$421$	−4.53863	−	16.9384i	−0.221199	−	0.825528i	0.762692	−	0.646762i	$-0.223877\pi$
$422$	3.37103	+	16.9473i	0.164099	+	0.824982i
$423$	12.5136	+	21.3980i	0.608432	+	1.04040i
$424$			8.61512i			0.418387i
$425$	3.45430	−	6.79674i	0.167558	−	0.329690i
$426$	−3.60373	−	17.8570i	−0.174601	−	0.865176i
$427$	−4.22757	−	32.1116i	−0.204586	−	1.55399i
$428$	−4.03365	−	4.59949i	−0.194974	−	0.222325i
$429$	1.76266	−	28.0919i	0.0851018	−	1.35629i
$430$	−35.1971	+	17.3573i	−1.69735	+	0.837042i
$431$	−6.18897	−	1.23106i	−0.298112	−	0.0592982i	0.0437682	−	0.999042i	$-0.486064\pi$
$431$	−6.18897	−	1.23106i	−0.298112	−	0.0592982i	−0.341880	+	0.939744i	$0.611064\pi$
$432$	−6.43288	+	5.02209i	−0.309502	+	0.241626i
$433$	0.562141	+	1.35713i	0.0270148	+	0.0652194i	0.936811	−	0.349835i	$-0.113762\pi$
$433$	0.562141	+	1.35713i	0.0270148	+	0.0652194i	−0.909796	+	0.415055i	$0.863762\pi$
$434$	−9.81073	−	1.29161i	−0.470930	−	0.0619991i
$435$	11.2494	+	2.98071i	0.539368	+	0.142914i
$436$	3.86764	+	11.3937i	0.185226	+	0.545660i
$437$	0.554479	−	8.45971i	0.0265243	−	0.404683i
$438$	−7.99274	+	12.0344i	−0.381908	+	0.575027i
$439$	−3.52241	+	10.3767i	−0.168116	+	0.495252i	−0.998037	−	0.0626280i	$-0.980052\pi$
$439$	−3.52241	+	10.3767i	−0.168116	+	0.495252i	0.829921	+	0.557880i	$0.188385\pi$
$440$	−14.8997	−	6.17168i	−0.710318	−	0.294223i
$441$	−15.5534	−	36.9654i	−0.740639	−	1.76026i
$442$	−30.4375	+	1.62658i	−1.44776	+	0.0773687i
$443$	−7.97096	−	4.60204i	−0.378712	−	0.218649i	0.298546	−	0.954395i	$-0.403498\pi$
$443$	−7.97096	−	4.60204i	−0.378712	−	0.218649i	−0.677258	+	0.735746i	$0.736832\pi$
$444$	−0.619134	−	0.539922i	−0.0293828	−	0.0256236i
$445$	17.7649	−	15.5794i	0.842138	−	0.738535i
$446$	55.8536	+	14.9659i	2.64475	+	0.708657i
$447$	27.6473	−	21.3372i	1.30767	−	1.00921i
$448$	43.2468	+	37.9264i	2.04322	+	1.79185i
$449$	18.6058	+	27.8456i	0.878063	+	1.31411i	0.948558	+	0.316602i	$0.102542\pi$
$449$	18.6058	+	27.8456i	0.878063	+	1.31411i	−0.0704951	+	0.997512i	$0.522458\pi$
$450$	8.59202	−	8.68830i	0.405032	−	0.409570i
$451$	−18.3049	+	7.58214i	−0.861944	+	0.357029i
$452$	−0.362317	−	5.52788i	−0.0170419	−	0.260010i
$453$	0.0812811	+	29.1762i	0.00381892	+	1.37082i
$454$	−5.28430	−	0.346351i	−0.248005	−	0.0162551i
$455$	−6.95881	+	25.9706i	−0.326234	+	1.21752i
$456$	5.85843	+	4.46945i	0.274346	+	0.209301i
$457$	5.41808	+	7.06098i	0.253447	+	0.330299i	0.902697	−	0.430276i	$-0.141584\pi$
$457$	5.41808	+	7.06098i	0.253447	+	0.330299i	−0.649250	+	0.760575i	$0.724917\pi$
$458$	11.2429			0.525348
$459$	−16.0552	−	14.1856i	−0.749393	−	0.662125i
$460$	18.9289			0.882567
$461$	6.84015	+	8.91425i	0.318577	+	0.415178i	0.925002	−	0.379963i	$-0.124063\pi$
$461$	6.84015	+	8.91425i	0.318577	+	0.415178i	−0.606424	+	0.795141i	$0.707397\pi$
$462$	−66.2837	−	50.5685i	−3.08379	−	2.35266i
$463$	5.71367	−	21.3237i	0.265537	−	0.990997i	−0.696384	−	0.717669i	$-0.745209\pi$
$463$	5.71367	−	21.3237i	0.265537	−	0.990997i	0.961921	−	0.273328i	$-0.0881244\pi$
$464$	−5.93230	−	0.388824i	−0.275400	−	0.0180507i
$465$	0.00852587	+	3.06040i	0.000395378	+	0.141922i
$466$	−0.652359	−	9.95307i	−0.0302199	−	0.461067i
$467$	4.81567	−	1.99472i	0.222843	−	0.0923045i	−0.268469	−	0.963288i	$-0.586518\pi$
$467$	4.81567	−	1.99472i	0.222843	−	0.0923045i	0.491312	+	0.870984i	$0.336518\pi$
$468$	−27.7769	−	7.27717i	−1.28399	−	0.336387i
$469$	0.553806	+	0.828829i	0.0255724	+	0.0382718i
$470$	−24.2897	−	21.3015i	−1.12040	−	0.982563i
$471$	−23.6101	+	18.2214i	−1.08790	+	0.839597i
$472$	−5.00957	−	1.34231i	−0.230584	−	0.0617849i
$473$	−36.5389	+	32.0438i	−1.68006	+	1.47337i
$474$	−27.7950	−	24.2389i	−1.27666	−	1.11333i
$475$	3.63080	+	2.09624i	0.166593	+	0.0961822i
$476$	−27.0860	+	45.6344i	−1.24149	+	2.09165i
$477$	13.6659	+	1.72174i	0.625719	+	0.0788333i
$478$	37.0036	+	15.3274i	1.69250	+	0.701058i
$479$	−9.84878	+	29.0136i	−0.450002	+	1.32566i	0.451261	+	0.892392i	$0.350974\pi$
$479$	−9.84878	+	29.0136i	−0.450002	+	1.32566i	−0.901263	+	0.433272i	$0.857359\pi$
$480$	12.2680	−	18.4716i	0.559957	−	0.843110i
$481$	−0.0365056	+	0.556968i	−0.00166451	+	0.0253955i
$482$	−5.10222	−	15.0306i	−0.232400	−	0.684627i
$483$	28.2543	+	7.48641i	1.28561	+	0.340644i
$484$	−35.1875	−	4.63252i	−1.59943	−	0.210569i
$485$	−9.78000	−	23.6110i	−0.444087	−	1.07212i
$486$	−17.5808	−	29.4944i	−0.797483	−	1.33789i
$487$	−32.4289	−	6.45052i	−1.46950	−	0.292301i	−0.605518	−	0.795831i	$-0.707034\pi$
$487$	−32.4289	−	6.45052i	−1.46950	−	0.292301i	−0.863977	+	0.503531i	$0.832034\pi$
$488$	−12.0774	+	5.95591i	−0.546718	+	0.269611i
$489$	2.17487	−	34.6614i	0.0983511	−	1.56744i
$490$	34.4629	+	39.2974i	1.55687	+	1.77527i
$491$	−0.508600	−	3.86320i	−0.0229528	−	0.174344i	0.976129	−	0.217193i	$-0.0696900\pi$
$491$	−0.508600	−	3.86320i	−0.0229528	−	0.174344i	−0.999082	+	0.0428488i	$0.986357\pi$
$492$	3.99845	+	19.8129i	0.180264	+	0.893236i
$493$	−1.85033	−	15.4967i	−0.0833348	−	0.697935i
$494$		−	16.7613i		−	0.754125i
$495$	−12.7677	+	22.4016i	−0.573865	+	1.00688i
$496$	−0.305004	−	1.53336i	−0.0136951	−	0.0688498i
$497$	5.57743	+	20.8152i	0.250182	+	0.933691i
$498$	−3.39588	−	4.40017i	−0.152173	−	0.197176i
$499$	−24.7376	+	8.39728i	−1.10741	+	0.375914i	−0.814463	−	0.580216i	$-0.802968\pi$
$499$	−24.7376	+	8.39728i	−1.10741	+	0.375914i	−0.292943	+	0.956130i	$0.594635\pi$
$500$	−15.3351	+	31.0964i	−0.685804	+	1.39067i
$501$	8.93707	−	0.610776i	0.399279	−	0.0272875i
$502$	1.03429	−	7.85620i	0.0461625	−	0.350639i
$503$	29.6123	−	19.7863i	1.32035	−	0.882229i	0.322423	−	0.946596i	$-0.395503\pi$
$503$	29.6123	−	19.7863i	1.32035	−	0.882229i	0.997926	+	0.0643664i	$0.0205026\pi$
$504$	−19.0069	+	16.8569i	−0.846636	+	0.750866i
$505$	−1.58435	+	2.37115i	−0.0705028	+	0.105515i
$506$	38.5216	−	10.3218i	1.71250	−	0.458862i
$507$	−1.15831	−	2.77453i	−0.0514425	−	0.123221i
$508$	−12.6701	+	1.66805i	−0.562144	+	0.0740076i
$509$	−7.27561	−	12.6017i	−0.322486	−	0.558562i	0.658514	−	0.752568i	$-0.271185\pi$
$509$	−7.27561	−	12.6017i	−0.322486	−	0.558562i	−0.981000	+	0.194006i	$0.937852\pi$
$510$	25.6968	+	10.9243i	1.13787	+	0.483735i
$511$	8.54482	−	14.8001i	0.378001	−	0.654717i
$512$	−6.59052	+	15.9109i	−0.291263	+	0.703170i
$513$	8.26058	−	8.39982i	0.364713	−	0.370861i
$514$	30.9352	+	30.9352i	1.36449	+	1.36449i
$515$	−1.04278	−	2.11455i	−0.0459505	−	0.0931783i
$516$	24.9089	+	42.8673i	1.09655	+	1.88713i
$517$	−35.8824	−	17.6953i	−1.57811	−	0.778236i
$518$	1.31162	+	1.00644i	0.0576292	+	0.0442205i
$519$	18.9472	−	12.7366i	0.831690	−	0.559075i
$520$	11.1547	−	0.731117i	0.489165	−	0.0320616i
$521$	7.35708	−	36.9866i	0.322320	−	1.62041i	−0.391567	−	0.920149i	$-0.628067\pi$
$521$	7.35708	−	36.9866i	0.322320	−	1.62041i	0.713887	−	0.700261i	$-0.246933\pi$
$522$	4.74301	−	24.5591i	0.207596	−	1.07492i
$523$	−24.1651	+	24.1651i	−1.05666	+	1.05666i	−0.0583688	+	0.998295i	$0.518590\pi$
$523$	−24.1651	+	24.1651i	−1.05666	+	1.05666i	−0.998295	+	0.0583688i	$0.981410\pi$
$524$	5.66704	+	1.92370i	0.247566	+	0.0840373i
$525$	−9.50021	+	10.8940i	−0.414623	+	0.475453i
$526$	−10.1778	+	5.87618i	−0.443775	+	0.256214i
$527$	3.81045	−	1.52476i	0.165986	−	0.0664198i
$528$	4.19923	−	12.4847i	0.182748	−	0.543326i
$529$	7.15457	−	5.48989i	0.311068	−	0.238691i
$530$	−17.6068	+	3.50221i	−0.764790	+	0.152126i
$531$	−3.13044	+	7.67828i	−0.135849	+	0.333209i
$532$	−24.2635	−	16.2124i	−1.05196	−	0.702895i
$533$	9.05503	−	10.3253i	0.392217	−	0.447238i
$534$	−36.0105	−	35.8104i	−1.55833	−	1.54967i
$535$	2.31802	−	3.02091i	0.100217	−	0.130605i
$536$	0.252299	−	0.328802i	0.0108976	−	0.0142021i
$537$	2.12077	−	8.00394i	0.0915179	−	0.345395i
$538$	−3.86706	+	4.40954i	−0.166721	+	0.190109i
$539$	53.8195	+	35.9610i	2.31817	+	1.54895i
$540$	19.9208	+	17.1777i	0.857256	+	0.739211i
$541$	26.1766	−	5.20685i	1.12542	−	0.223860i	0.402923	−	0.915234i	$-0.367994\pi$
$541$	26.1766	−	5.20685i	1.12542	−	0.223860i	0.722497	+	0.691374i	$0.242994\pi$
$542$	56.5587	−	43.3990i	2.42940	−	1.86415i
$543$	14.1314	+	16.0235i	0.606435	+	0.687633i
$544$	−29.0938	−	6.15277i	−1.24739	−	0.263798i
$545$	−6.48581	+	3.74458i	−0.277821	+	0.160400i
$546$	56.7090	+	11.1160i	2.42692	+	0.475720i
$547$	7.05300	+	2.39417i	0.301564	+	0.102367i	0.468120	−	0.883665i	$-0.344931\pi$
$547$	7.05300	+	2.39417i	0.301564	+	0.102367i	−0.166556	+	0.986032i	$0.553265\pi$
$548$	40.0188	−	40.0188i	1.70952	−	1.70952i
$549$	7.03400	+	20.3483i	0.300204	+	0.868445i
$550$	−3.84753	+	19.3428i	−0.164059	+	0.824782i
$551$	8.56369	−	0.561294i	0.364825	−	0.0239119i
$552$	−0.828595	−	12.1243i	−0.0352673	−	0.516043i
$553$	34.6106	+	26.5577i	1.47179	+	1.12935i
$554$	−38.9236	−	19.1950i	−1.65371	−	0.815518i
$555$	0.254422	−	0.443521i	0.0107996	−	0.0188264i
$556$	27.6057	+	55.9789i	1.17074	+	2.37403i
$557$	6.25238	+	6.25238i	0.264922	+	0.264922i	0.827050	−	0.562128i	$-0.190017\pi$
$557$	6.25238	+	6.25238i	0.264922	+	0.264922i	−0.562128	+	0.827050i	$0.690017\pi$
$558$	6.56119	−	0.466771i	0.277757	−	0.0197600i
$559$	12.8912	−	31.1222i	0.545242	−	1.31633i
$560$	−6.29109	+	10.8965i	−0.265847	+	0.460461i
$561$	34.2396	+	4.83119i	1.44560	+	0.203973i
$562$	−3.86674	−	6.69739i	−0.163108	−	0.282512i
$563$	−5.29216	+	0.696726i	−0.223038	+	0.0293635i	−0.241217	−	0.970471i	$-0.577546\pi$
$563$	−5.29216	+	0.696726i	−0.223038	+	0.0293635i	0.0181790	+	0.999835i	$0.494213\pi$
$564$	−24.7561	+	32.4495i	−1.04242	+	1.36637i
$565$	3.33058	−	0.892426i	0.140119	−	0.0375447i
$566$	−13.0121	+	19.4741i	−0.546941	+	0.818556i
$567$	22.9410	+	33.5190i	0.963433	+	1.40767i
$568$	7.44960	−	4.97767i	0.312578	−	0.208858i
$569$	−5.45708	+	41.4506i	−0.228773	+	1.73770i	0.363172	+	0.931722i	$0.381694\pi$
$569$	−5.45708	+	41.4506i	−0.228773	+	1.73770i	−0.591945	+	0.805979i	$0.701640\pi$
$570$	−6.75270	+	13.7898i	−0.282840	+	0.577593i
$571$	−2.12298	+	4.30499i	−0.0888441	+	0.180158i	−0.936760	−	0.349973i	$-0.886191\pi$
$571$	−2.12298	+	4.30499i	−0.0888441	+	0.180158i	0.847916	+	0.530131i	$0.177857\pi$
$572$	43.8854	−	14.8971i	1.83494	−	0.622878i
$573$	2.78522	−	6.77746i	0.116354	−	0.283132i
$574$	−10.5282	−	39.2917i	−0.439438	−	1.64000i
$575$	−1.34892	−	6.78148i	−0.0562539	−	0.282807i
$576$	−33.2195	−	18.9333i	−1.38415	−	0.788887i
$577$			1.52901i			0.0636535i	0.999493	+	0.0318268i	$0.0101325\pi$
$577$			1.52901i			0.0636535i	−0.999493	+	0.0318268i	$0.989868\pi$
$578$	0.903137	−	37.4349i	0.0375655	−	1.55709i
$579$	−23.2754	−	7.82868i	−0.967292	−	0.325349i
$580$	2.50109	+	18.9977i	0.103852	+	0.788836i
$581$	4.33518	+	4.94332i	0.179853	+	0.205084i
$582$	−49.1961	+	24.4315i	−2.03925	+	1.01272i
$583$	−19.9385	+	9.83257i	−0.825767	+	0.407223i
$584$	−6.96877	−	1.38618i	−0.288370	−	0.0573603i
$585$	1.06953	−	17.8405i	0.0442197	−	0.737613i
$586$	−18.4625	−	44.5723i	−0.762677	−	1.84127i
$587$	−11.1452	−	1.46730i	−0.460013	−	0.0605618i	−0.103041	−	0.994677i	$-0.532857\pi$
$587$	−11.1452	−	1.46730i	−0.460013	−	0.0605618i	−0.356972	+	0.934115i	$0.616191\pi$
$588$	46.5618	−	46.8220i	1.92018	−	1.93091i
$589$	0.725448	+	2.13710i	0.0298916	+	0.0880578i
$590$	0.706807	−	10.7838i	0.0290988	−	0.443961i
$591$	−5.14409	−	0.322772i	−0.211600	−	0.0132771i
$592$	−0.0839609	+	0.247341i	−0.00345077	+	0.0101656i
$593$	−23.4096	−	9.69659i	−0.961319	−	0.398191i	−0.153845	−	0.988095i	$-0.549166\pi$
$593$	−23.4096	−	9.69659i	−0.961319	−	0.398191i	−0.807474	+	0.589904i	$0.799166\pi$
$594$	49.9071	+	24.0950i	2.04771	+	0.988631i
$595$	−31.1472	−	10.9937i	−1.27691	−	0.450699i
$596$	49.7985	+	28.7512i	2.03983	+	1.17769i
$597$	−37.2461	+	12.7592i	−1.52438	+	0.522198i
$598$	−20.7831	+	18.2263i	−0.849886	+	0.745330i
$599$	−19.8536	−	5.31976i	−0.811197	−	0.217359i	−0.170703	−	0.985323i	$-0.554604\pi$
$599$	−19.8536	−	5.31976i	−0.811197	−	0.217359i	−0.640494	+	0.767963i	$0.721270\pi$
$600$	5.55863	+	2.28434i	0.226930	+	0.0932576i
$601$	26.0453	+	22.8411i	1.06241	+	0.931708i	0.997806	−	0.0662028i	$-0.0210884\pi$
$601$	26.0453	+	22.8411i	1.06241	+	0.931708i	0.0646034	+	0.997911i	$0.479422\pi$
$602$	−55.4338	−	82.9625i	−2.25931	−	3.38130i
$603$	−0.471147	−	0.465926i	−0.0191866	−	0.0189740i
$604$	−44.3827	+	18.3839i	−1.80590	+	0.748030i
$605$	−1.44479	−	22.0432i	−0.0587391	−	0.896185i
$606$	5.31667	+	3.04987i	0.215975	+	0.123892i
$607$	−3.92665	−	0.257366i	−0.159378	−	0.0104462i	−0.0144946	−	0.999895i	$-0.504614\pi$
$607$	−3.92665	−	0.257366i	−0.159378	−	0.0104462i	−0.144883	+	0.989449i	$0.546281\pi$
$608$	4.23230	−	15.7952i	0.171642	−	0.640578i
$609$	−3.78034	+	29.3461i	−0.153187	+	1.18916i
$610$	−17.0818	−	22.2615i	−0.691623	−	0.901341i
$611$	27.7316			1.12190
$612$	11.5555	−	33.3293i	0.467102	−	1.34726i
$613$	11.8284			0.477747			0.238873	−	0.971051i	$-0.423222\pi$
$613$	11.8284			0.477747			0.238873	+	0.971051i	$0.423222\pi$
$614$	−12.4461	−	16.2201i	−0.502285	−	0.654590i
$615$	−11.6096	+	4.84677i	−0.468143	+	0.195441i
$616$	10.6125	−	39.6066i	0.427592	−	1.59579i
$617$	−25.9252	−	1.69923i	−1.04371	−	0.0684083i	−0.466108	−	0.884728i	$-0.654344\pi$
$617$	−25.9252	−	1.69923i	−1.04371	−	0.0684083i	−0.577601	+	0.816319i	$0.696011\pi$
$618$	−4.38144	+	2.54593i	−0.176248	+	0.102412i
$619$	−1.98966	−	30.3563i	−0.0799710	−	1.22012i	−0.829636	−	0.558304i	$-0.811452\pi$
$619$	−1.98966	−	30.3563i	−0.0799710	−	1.22012i	0.749665	−	0.661817i	$-0.230215\pi$
$620$	−4.65546	+	1.92836i	−0.186968	+	0.0774446i
$621$	−19.3980	−	1.10868i	−0.778414	−	0.0444897i
$622$	18.2344	+	27.2898i	0.731135	+	1.09422i
$623$	45.1672	+	39.6106i	1.80959	+	1.58696i
$624$	1.21693	+	9.04864i	0.0487162	+	0.362235i
$625$	−11.9147	−	3.19255i	−0.476590	−	0.127702i
$626$	−28.1756	+	24.7094i	−1.12613	+	0.987585i
$627$	−3.65761	+	18.6596i	−0.146071	+	0.745191i
$628$	−42.5266	−	24.5528i	−1.69700	−	0.979762i
$629$	−0.678708	−	0.0976947i	−0.0270619	−	0.00389534i
$630$	−42.1773	−	31.9920i	−1.68038	−	1.27459i
$631$	39.6115	+	16.4076i	1.57691	+	0.653177i	0.987920	−	0.154965i	$-0.0495265\pi$
$631$	39.6115	+	16.4076i	1.57691	+	0.653177i	0.588988	+	0.808142i	$0.299526\pi$
$632$	5.83030	−	17.1755i	0.231917	−	0.683206i
$633$	6.04344	+	12.1693i	0.240205	+	0.483686i
$634$	4.16608	−	63.5621i	0.165456	−	2.52437i
$635$	−2.55680	−	7.53208i	−0.101463	−	0.298901i
$636$	5.93079	+	21.8899i	0.235171	+	0.867992i
$637$	−44.4822	−	5.85619i	−1.76245	−	0.232031i
$638$	15.4492	+	37.2977i	0.611640	+	1.47663i
$639$	−6.40711	−	12.8119i	−0.253461	−	0.506830i
$640$	23.7633	+	4.72681i	0.939326	+	0.186844i
$641$	−0.0374861	+	0.0184861i	−0.00148061	+	0.000730157i	−0.443029	−	0.896507i	$-0.646096\pi$
$641$	−0.0374861	+	0.0184861i	−0.00148061	+	0.000730157i	0.441548	+	0.897238i	$0.354429\pi$
$642$	−6.81747	−	4.52786i	−0.269064	−	0.178701i
$643$	−13.6969	−	15.6183i	−0.540154	−	0.615927i	0.415796	−	0.909458i	$-0.363503\pi$
$643$	−13.6969	−	15.6183i	−0.540154	−	0.615927i	−0.955950	+	0.293531i	$0.905170\pi$
$644$	6.28180	+	47.7150i	0.247537	+	1.88023i
$645$	−23.1443	+	20.4113i	−0.911305	+	0.803695i
$646$	20.5294	+	1.59443i	0.807719	+	0.0627322i
$647$			4.44704i			0.174831i	0.996172	+	0.0874156i	$0.0278608\pi$
$647$			4.44704i			0.174831i	−0.996172	+	0.0874156i	$0.972139\pi$
$648$	10.1306	−	13.5115i	0.397966	−	0.530783i
$649$	−2.61091	−	13.1260i	−0.102487	−	0.515239i
$650$	−3.53808	−	13.2043i	−0.138775	−	0.517915i
$651$	−7.71164	+	1.03712i	−0.302243	+	0.0406480i
$652$	54.1484	−	18.3809i	2.12062	−	0.719852i
$653$	3.91465	−	7.93812i	0.153192	−	0.310643i	−0.806725	−	0.590927i	$-0.798762\pi$
$653$	3.91465	−	7.93812i	0.153192	−	0.310643i	0.959917	+	0.280284i	$0.0904288\pi$
$654$	8.98002	+	13.3588i	0.351147	+	0.522372i
$655$	−0.486209	+	3.69312i	−0.0189977	+	0.144302i
$656$	5.34368	−	3.57053i	0.208636	−	0.139406i
$657$	−3.59157	+	10.7773i	−0.140120	+	0.420464i
$658$	45.6347	−	68.2971i	1.77902	−	2.66250i
$659$	−39.4808	+	10.5788i	−1.53795	+	0.412093i	−0.925604	−	0.378494i	$-0.876442\pi$
$659$	−39.4808	+	10.5788i	−1.53795	+	0.412093i	−0.612349	+	0.790587i	$0.709775\pi$
$660$	−42.1070	−	5.42420i	−1.63901	−	0.211137i
$661$	−7.06533	+	0.930168i	−0.274809	+	0.0361793i	−0.266671	−	0.963788i	$-0.585924\pi$
$661$	−7.06533	+	0.930168i	−0.274809	+	0.0361793i	−0.00813806	+	0.999967i	$0.502590\pi$
$662$	6.72162	+	11.6422i	0.261243	+	0.452487i
$663$	−22.7666	+	7.49347i	−0.884182	+	0.291022i
$664$	1.36682	−	2.36741i	0.0530431	−	0.0918733i
$665$	6.95078	−	16.7807i	0.269540	−	0.650726i
$666$	−0.988333	−	0.480564i	−0.0382971	−	0.0186215i
$667$	−10.0082	−	10.0082i	−0.387519	−	0.387519i
$668$	6.52351	+	13.2284i	0.252402	+	0.511821i
$669$	45.4687	−	0.126670i	1.75792	−	0.00489734i
$670$	0.774540	+	0.381961i	0.0299231	+	0.0147564i
$671$	−27.5682	−	21.1539i	−1.06426	−	0.816635i
$672$	50.6335	+	24.7945i	1.95323	+	0.956470i
$673$	49.8014	−	3.26416i	1.91970	−	0.125824i	0.941974	−	0.335687i	$-0.108968\pi$
$673$	49.8014	−	3.26416i	1.91970	−	0.125824i	0.977731	+	0.209863i	$0.0673016\pi$
$674$	3.40134	−	17.0997i	0.131015	−	0.658656i
$675$	4.73448	−	8.36096i	0.182230	−	0.321813i
$676$	3.50050	−	3.50050i	0.134635	−	0.134635i
$677$	3.02793	+	1.02784i	0.116373	+	0.0395032i	0.379018	−	0.925389i	$-0.376262\pi$
$677$	3.02793	+	1.02784i	0.116373	+	0.0395032i	−0.262646	+	0.964892i	$0.584595\pi$
$678$	−2.40172	−	7.01102i	−0.0922377	−	0.269257i
$679$	56.2717	−	32.4885i	2.15951	−	1.24679i
$680$	−0.165621	+	13.7320i	−0.00635128	+	0.526596i
$681$	−4.08184	+	0.823757i	−0.156417	+	0.0315664i
$682$	−8.42265	+	6.46293i	−0.322520	+	0.247478i
$683$	−44.9817	+	8.94742i	−1.72118	+	0.342364i	−0.954168	−	0.299272i	$-0.903256\pi$
$683$	−44.9817	+	8.94742i	−1.72118	+	0.342364i	−0.767010	+	0.641635i	$0.778256\pi$
$684$	17.9624	+	7.32327i	0.686808	+	0.280012i
$685$	29.2895	+	19.5706i	1.11909	+	0.747754i
$686$	−41.7398	+	47.5951i	−1.59363	+	1.81719i
$687$	8.53305	−	2.31192i	0.325556	−	0.0882053i
$688$	9.59665	−	12.5066i	0.365869	−	0.476810i
$689$	9.38065	−	12.2251i	0.357374	−	0.465739i
$690$	24.4416	−	6.62215i	0.930477	−	0.252101i
$691$	−26.0511	+	29.7056i	−0.991031	+	1.13005i	0.000476258		1.00000i	$0.499848\pi$
$691$	−26.0511	+	29.7056i	−0.991031	+	1.13005i	−0.991507	+	0.130054i	$0.958485\pi$
$692$	31.2553	+	20.8841i	1.18815	+	0.793896i
$693$	−60.7058	−	24.7498i	−2.30602	−	0.940167i
$694$	43.6406	−	8.68065i	1.65657	−	0.329513i
$695$	−30.8210	+	23.6498i	−1.16911	+	0.897087i
$696$	12.0588	−	2.43359i	0.457088	−	0.0922450i
$697$	11.7852	+	12.0729i	0.446395	+	0.457295i
$698$	−41.1424	+	23.7536i	−1.55726	+	0.899085i
$699$	−2.54180	−	7.41993i	−0.0961398	−	0.280648i
$700$	−22.5367	−	7.65017i	−0.851806	−	0.289149i
$701$	19.0349	−	19.0349i	0.718939	−	0.718939i	−0.249449	−	0.968388i	$-0.580249\pi$
$701$	19.0349	−	19.0349i	0.718939	−	0.718939i	0.968388	+	0.249449i	$0.0802495\pi$
$702$	−38.4123	+	0.321042i	−1.44978	+	0.0121169i
$703$	0.0735616	−	0.369819i	0.00277443	−	0.0139480i
$704$	61.5810	−	4.03623i	2.32092	−	0.152121i
$705$	−22.8154	−	11.1724i	−0.859277	−	0.420777i
$706$	−27.5574	−	21.1455i	−1.03714	−	0.795823i
$707$	−6.50285	−	3.20685i	−0.244565	−	0.120606i
$708$	−13.6528	+	0.0380348i	−0.513102	+	0.00142944i
$709$	−9.05223	−	18.3561i	−0.339964	−	0.689378i	0.658010	−	0.753009i	$-0.271399\pi$
$709$	−9.05223	−	18.3561i	−0.339964	−	0.689378i	−0.997973	+	0.0636312i	$0.979732\pi$
$710$	13.2013	+	13.2013i	0.495436	+	0.495436i
$711$	−26.0798	−	12.6810i	−0.978070	−	0.475574i
$712$	9.55844	−	23.0761i	0.358218	−	0.864814i
$713$	1.86104	−	3.22342i	0.0696966	−	0.120718i
$714$	−19.0095	+	68.4004i	−0.711412	+	2.55982i
$715$	14.4231	+	24.9815i	0.539393	+	0.934256i
$716$	13.5168	−	1.77952i	0.505147	−	0.0665038i
$717$	31.2364	+	4.02385i	1.16654	+	0.150274i
$718$	−16.5208	+	4.42674i	−0.616551	+	0.165204i
$719$	−0.397661	+	0.595142i	−0.0148303	+	0.0221951i	−0.838811	−	0.544423i	$-0.816749\pi$
$719$	−0.397661	+	0.595142i	−0.0148303	+	0.0221951i	0.823980	+	0.566618i	$0.191749\pi$
$720$	2.64428	−	7.93477i	0.0985464	−	0.295711i
$721$	4.98418	−	3.33032i	0.185621	−	0.124028i
$722$	3.98473	−	30.2670i	0.148296	−	1.12642i
$723$	−6.96322	−	10.3586i	−0.258965	−	0.385241i
$724$	−15.5586	+	31.5496i	−0.578229	+	1.17253i
$725$	6.62787	−	2.24986i	0.246153	−	0.0835577i
$726$	−47.0559	+	6.32844i	−1.74641	+	0.234870i
$727$	1.12545	+	4.20024i	0.0417407	+	0.155778i	0.983651	−	0.180087i	$-0.0576379\pi$
$727$	1.12545	+	4.20024i	0.0417407	+	0.155778i	−0.941910	+	0.335865i	$0.890971\pi$
$728$	5.54477	+	27.8755i	0.205503	+	1.03313i
$729$	−19.4083	−	18.7701i	−0.718827	−	0.695189i
$730$		−	14.8057i		−	0.547982i
$731$	36.8926	+	18.7499i	1.36452	+	0.693490i
$732$	−26.5870	+	23.4475i	−0.982683	+	0.866644i
$733$	1.71135	+	12.9990i	0.0632102	+	0.480129i	0.993547	+	0.113422i	$0.0361814\pi$
$733$	1.71135	+	12.9990i	0.0632102	+	0.480129i	−0.930337	+	0.366707i	$0.880485\pi$
$734$	−35.5395	−	40.5251i	−1.31179	−	1.49581i
$735$	34.2371	+	22.7388i	1.26285	+	0.838733i
$736$	−24.1874	+	11.9279i	−0.891561	+	0.439669i
$737$	1.04892	+	0.208643i	0.0386374	+	0.00768546i
$738$	12.0943	+	24.1842i	0.445198	+	0.890234i
$739$	4.16111	+	10.0458i	0.153069	+	0.369541i	0.981749	−	0.190182i	$-0.0609077\pi$
$739$	4.16111	+	10.0458i	0.153069	+	0.369541i	−0.828680	+	0.559722i	$0.810908\pi$
$740$	0.834688	+	0.109889i	0.0306837	+	0.00403959i
$741$	−3.44667	−	12.7213i	−0.126617	−	0.467328i
$742$	−14.6712	−	43.2199i	−0.538596	−	1.58665i
$743$	0.974537	−	14.8686i	0.0357523	−	0.545475i	−0.941987	−	0.335650i	$-0.891044\pi$
$743$	0.974537	−	14.8686i	0.0357523	−	0.545475i	0.977739	−	0.209825i	$-0.0672893\pi$
$744$	1.43893	+	2.89748i	0.0527537	+	0.106227i
$745$	−11.5046	+	33.8914i	−0.421496	+	1.24169i
$746$	7.98761	+	3.30858i	0.292447	+	0.121136i
$747$	−3.48219	−	2.64128i	−0.127407	−	0.0966395i
$748$	14.0715	+	55.1685i	0.514504	+	2.01716i
$749$	8.38419	+	4.84062i	0.306352	+	0.176872i
$750$	−8.92224	+	45.5175i	−0.325794	+	1.66206i
$751$	−18.2721	+	16.0242i	−0.666759	+	0.584732i	−0.924361	−	0.381519i	$-0.875401\pi$
$751$	−18.2721	+	16.0242i	−0.666759	+	0.584732i	0.257602	+	0.966251i	$0.417068\pi$
$752$	12.5354	+	3.35884i	0.457117	+	0.122484i
$753$	−0.830501	−	6.17530i	−0.0302651	−	0.225040i
$754$	−21.0386	−	18.4503i	−0.766180	−	0.671922i
$755$	−16.6121	−	24.8617i	−0.604574	−	0.904810i
$756$	−36.6896	+	55.9159i	−1.33439	+	2.03364i
$757$	−15.4730	+	6.40913i	−0.562376	+	0.232944i	−0.645716	−	0.763577i	$-0.723441\pi$
$757$	−15.4730	+	6.40913i	−0.562376	+	0.232944i	0.0833402	+	0.996521i	$0.473441\pi$
$758$	3.77770	+	57.6365i	0.137212	+	2.09345i
$759$	27.1142	−	15.7553i	0.984184	−	0.571881i
$760$	−7.53550	−	0.493903i	−0.273341	−	0.0179157i
$761$	−4.41082	+	16.4614i	−0.159892	+	0.596725i	0.838745	+	0.544525i	$0.183290\pi$
$761$	−4.41082	+	16.4614i	−0.159892	+	0.596725i	−0.998637	+	0.0522004i	$0.983377\pi$
$762$	−15.7764	+	6.58637i	−0.571520	+	0.238599i
$763$	−11.5915	−	15.1064i	−0.419641	−	0.546887i
$764$	12.0648			0.436489
$765$	21.7495	+	3.00707i	0.786354	+	0.108721i
$766$	−18.4328			−0.666006
$767$	5.64714	+	7.35950i	0.203906	+	0.265736i
$768$	1.01240	−	7.85907i	0.0365318	−	0.283590i
$769$	1.25461	−	4.68225i	0.0452422	−	0.168846i	−0.939608	−	0.342252i	$-0.888810\pi$
$769$	1.25461	−	4.68225i	0.0452422	−	0.168846i	0.984851	+	0.173405i	$0.0554771\pi$
$770$	85.2585	+	5.58814i	3.07250	+	0.201382i
$771$	29.8402	+	17.1176i	1.07467	+	0.616474i
$772$	−2.64446	−	40.3466i	−0.0951762	−	1.45211i
$773$	−8.61545	+	3.56864i	−0.309876	+	0.128355i	−0.532202	−	0.846618i	$-0.678635\pi$
$773$	−8.61545	+	3.56864i	−0.309876	+	0.128355i	0.222326	+	0.974972i	$0.428635\pi$
$774$	47.1599	+	46.6373i	1.69513	+	1.67634i
$775$	1.02261	+	1.53045i	0.0367333	+	0.0549752i
$776$	−20.3111	−	17.8124i	−0.729126	−	0.639427i
$777$	1.20244	+	0.494145i	0.0431372	+	0.0177274i
$778$	44.7679	+	11.9955i	1.60501	+	0.430060i
$779$	−6.97520	+	6.11709i	−0.249913	+	0.219167i
$780$	27.8393	−	9.53675i	0.996808	−	0.341471i
$781$	20.0225	+	11.5600i	0.716460	+	0.413648i
$782$	−20.3468	−	27.1892i	−0.727600	−	0.972285i
$783$	−1.45036	−	19.6149i	−0.0518316	−	0.700979i
$784$	−19.3977	−	8.03479i	−0.692775	−	0.286957i
$785$	9.82462	−	28.9424i	0.350656	−	1.03300i
$786$	7.99045	+	0.501370i	0.285010	+	0.0178833i
$787$	1.51021	−	23.0413i	0.0538331	−	0.821334i	−0.882520	−	0.470275i	$-0.844155\pi$
$787$	1.51021	−	23.0413i	0.0538331	−	0.821334i	0.936353	−	0.351060i	$-0.114179\pi$
$788$	−2.72790	−	8.03614i	−0.0971775	−	0.286276i
$789$	−6.51633	+	6.55274i	−0.231988	+	0.233284i
$790$	37.4719	+	4.93327i	1.33319	+	0.175518i
$791$	3.35487	+	8.09937i	0.119285	+	0.287980i
$792$	−1.63109	+	27.2076i	−0.0579583	+	0.966781i
$793$	23.6233	+	4.69897i	0.838889	+	0.166865i
$794$	−7.73902	+	3.81646i	−0.274648	+	0.135441i
$795$	−12.6428	+	6.27861i	−0.448395	+	0.222679i
$796$	−42.7422	−	48.7381i	−1.51496	−	1.72748i
$797$	3.77764	+	28.6941i	0.133811	+	1.01640i	0.918197	+	0.396123i	$0.129645\pi$
$797$	3.77764	+	28.6941i	0.133811	+	1.01640i	−0.784386	+	0.620272i	$0.787022\pi$
$798$	−37.0016	−	12.4455i	−1.30984	−	0.440566i
$799$	−2.63800	+	33.9661i	−0.0933259	+	1.20163i
$800$		−	13.3366i		−	0.471519i
$801$	−34.6947	−	19.7741i	−1.22588	−	0.698682i
$802$	15.0405	+	75.6135i	0.531097	+	2.67000i
$803$	−4.74546	−	17.7103i	−0.167464	−	0.624983i
$804$	0.414706	−	1.00913i	0.0146256	−	0.0355893i
$805$	−28.3655	+	9.62879i	−0.999753	+	0.339370i
$806$	3.25471	−	6.59990i	0.114642	−	0.232472i
$807$	−2.02823	+	4.14190i	−0.0713972	+	0.145802i
$808$	−0.393478	+	2.98876i	−0.0138425	+	0.105144i
$809$	−40.9691	+	27.3747i	−1.44040	+	0.962442i	−0.442557	+	0.896740i	$0.645929\pi$
$809$	−40.9691	+	27.3747i	−1.44040	+	0.962442i	−0.997839	+	0.0657015i	$0.979071\pi$
$810$	31.7319	+	15.2112i	1.11494	+	0.534468i
$811$	−8.55044	+	12.7966i	−0.300247	+	0.449351i	−0.950662	−	0.310228i	$-0.899595\pi$
$811$	−8.55044	+	12.7966i	−0.300247	+	0.449351i	0.650416	+	0.759578i	$0.274595\pi$
$812$	−47.0582	+	12.6092i	−1.65142	+	0.442497i
$813$	34.0020	−	44.5689i	1.19250	−	1.56310i
$814$	1.75857	−	0.231520i	0.0616377	−	0.00811476i
$815$	17.7961	+	30.8237i	0.623369	+	1.07971i
$816$	−11.1986	+	0.629750i	−0.392031	+	0.0220457i
$817$	−11.3784	+	19.7079i	−0.398079	+	0.689493i
$818$	−23.2178	+	56.0526i	−0.811790	+	1.95983i
$819$	45.3262	−	3.22456i	1.58382	−	0.112675i
$820$	−14.6473	−	14.6473i	−0.511505	−	0.511505i
$821$	1.52252	+	3.08736i	0.0531362	+	0.107750i	0.921821	−	0.387615i	$-0.126701\pi$
$821$	1.52252	+	3.08736i	0.0531362	+	0.107750i	−0.868685	+	0.495365i	$0.835034\pi$
$822$	37.6732	−	65.6737i	1.31400	−	2.29063i
$823$	−19.5008	−	9.61674i	−0.679756	−	0.335218i	0.0694221	−	0.997587i	$-0.477884\pi$
$823$	−19.5008	−	9.61674i	−0.679756	−	0.335218i	−0.749178	+	0.662369i	$0.769551\pi$
$824$	−1.97726	−	1.51720i	−0.0688811	−	0.0528543i
$825$	1.05737	+	15.4718i	0.0368129	+	0.538659i
$826$	27.4177	−	1.79705i	0.953984	−	0.0625274i
$827$	0.995877	−	5.00661i	0.0346300	−	0.174097i	−0.959600	−	0.281369i	$-0.909212\pi$
$827$	0.995877	−	5.00661i	0.0346300	−	0.174097i	0.994230	+	0.107272i	$0.0342115\pi$
$828$	−10.4519	−	30.2358i	−0.363229	−	1.05077i
$829$	29.8068	−	29.8068i	1.03523	−	1.03523i	0.0358785	−	0.999356i	$-0.488577\pi$
$829$	29.8068	−	29.8068i	1.03523	−	1.03523i	0.999356	−	0.0358785i	$-0.0114229\pi$
$830$	5.39394	+	1.83100i	0.187226	+	0.0635548i
$831$	−33.4890	−	6.56443i	−1.16172	−	0.227718i
$832$	−37.0453	+	21.3881i	−1.28431	+	0.741499i
$833$	11.4042	−	53.9253i	0.395131	−	1.86840i
$834$	55.2292	+	62.6240i	1.91243	+	2.16849i
$835$	−7.28330	+	5.58867i	−0.252049	+	0.193404i
$836$	−30.7065	+	6.10791i	−1.06201	+	0.211246i
$837$	4.88376	−	1.70346i	0.168807	−	0.0588803i
$838$	−8.90483	−	5.95002i	−0.307612	−	0.205540i
$839$	28.9947	−	33.0621i	1.00101	−	1.14143i	0.0110670	−	0.999939i	$-0.496477\pi$
$839$	28.9947	−	33.0621i	1.00101	−	1.14143i	0.989940	−	0.141491i	$-0.0451895\pi$
$840$	6.66854	−	25.1676i	0.230086	−	0.868363i
$841$	−8.93194	+	11.6403i	−0.307998	+	0.401391i
$842$	23.5142	−	30.6443i	0.810353	−	1.05607i
$843$	−4.31194	−	4.28798i	−0.148511	−	0.147686i
$844$	−14.7508	+	16.8200i	−0.507742	+	0.578969i
$845$	2.56199	+	1.71187i	0.0881352	+	0.0588901i
$846$	−20.6136	+	50.5606i	−0.708710	+	1.73831i
$847$	55.0859	−	10.9573i	1.89277	−	0.376496i
$848$	5.72097	−	4.38985i	0.196459	−	0.150748i
$849$	−5.87131	+	17.4559i	−0.201503	+	0.599086i
$850$	16.5093	−	3.07741i	0.566266	−	0.105554i
$851$	−0.538549	+	0.310931i	−0.0184612	+	0.0106586i
$852$	15.5018	−	17.7761i	0.531082	−	0.608998i
$853$	−37.5519	−	12.7471i	−1.28575	−	0.436454i	−0.406867	−	0.913488i	$-0.633379\pi$
$853$	−37.5519	−	12.7471i	−1.28575	−	0.436454i	−0.878885	+	0.477034i	$0.841712\pi$
$854$	50.4467	−	50.4467i	1.72625	−	1.72625i
$855$	−2.28945	+	11.8546i	−0.0782974	+	0.405420i
$856$	0.785264	−	3.94779i	0.0268398	−	0.134933i
$857$	39.0035	−	2.55642i	1.33233	−	0.0873258i	0.617473	−	0.786592i	$-0.288157\pi$
$857$	39.0035	−	2.55642i	1.33233	−	0.0873258i	0.714861	+	0.699266i	$0.246490\pi$
$858$	51.4545	−	34.5885i	1.75663	−	1.18083i
$859$	−4.42883	−	3.39836i	−0.151110	−	0.115951i	0.530440	−	0.847723i	$-0.322027\pi$
$859$	−4.42883	−	3.39836i	−0.151110	−	0.115951i	−0.681549	+	0.731772i	$0.738694\pi$
$860$	−45.5702	−	22.4727i	−1.55393	−	0.766314i
$861$	−16.0702	−	27.6563i	−0.547672	−	0.942523i
$862$	−6.14758	−	12.4661i	−0.209387	−	0.424596i
$863$	35.6092	+	35.6092i	1.21215	+	1.21215i	0.970318	+	0.241832i	$0.0777481\pi$
$863$	35.6092	+	35.6092i	1.21215	+	1.21215i	0.241832	+	0.970318i	$0.422252\pi$
$864$	−36.2793	−	9.39674i	−1.23425	−	0.319684i
$865$	−8.95373	+	21.6162i	−0.304436	+	0.734973i
$866$	−1.61782	+	2.80214i	−0.0549757	+	0.0952207i
$867$	−7.01240	−	28.5977i	−0.238154	−	0.971227i
$868$	−6.40586	−	11.0953i	−0.217429	−	0.376598i
$869$	46.4045	−	6.10927i	1.57417	−	0.207243i
$870$	9.87568	+	23.6554i	0.334817	+	0.801993i
$871$	−0.716039	+	0.191862i	−0.0242620	+	0.00650099i
$872$	−4.39827	+	6.58247i	−0.148944	+	0.222911i
$873$	−32.3144	+	28.6591i	−1.09368	+	0.969963i
$874$	15.5270	−	10.3748i	0.525208	−	0.350933i
$875$	7.16182	−	54.3994i	0.242114	−	1.83904i
$876$	−18.6610	+	1.27533i	−0.630498	+	0.0430894i
$877$	−3.30568	+	6.70325i	−0.111625	+	0.226353i	−0.945516	−	0.325577i	$-0.894442\pi$
$877$	−3.30568	+	6.70325i	−0.111625	+	0.226353i	0.833891	+	0.551929i	$0.186108\pi$
$878$	−22.8567	+	7.75880i	−0.771375	+	0.261847i
$879$	−23.1780	−	30.0325i	−0.781774	−	1.01297i
$880$	3.49383	+	13.0391i	0.117777	+	0.439549i
$881$	1.61626	+	8.12548i	0.0544532	+	0.273755i	0.998414	−	0.0563039i	$-0.0179316\pi$
$881$	1.61626	+	8.12548i	0.0544532	+	0.273755i	−0.943961	+	0.330058i	$0.892932\pi$
$882$	43.7417	−	76.7473i	1.47286	−	2.58422i
$883$			18.4652i			0.621403i	0.950508	+	0.310701i	$0.100564\pi$
$883$			18.4652i			0.621403i	−0.950508	+	0.310701i	$0.899436\pi$
$884$	−25.6608	−	29.9823i	−0.863065	−	1.00841i
$885$	−1.68106	−	8.32990i	−0.0565082	−	0.280007i
$886$	−2.64626	−	20.1003i	−0.0889028	−	0.675284i
$887$	−5.13859	−	5.85944i	−0.172537	−	0.196741i	0.659108	−	0.752048i	$-0.270934\pi$
$887$	−5.13859	−	5.85944i	−0.172537	−	0.196741i	−0.831645	+	0.555307i	$0.812601\pi$
$888$	0.0338478	−	0.539440i	0.00113586	−	0.0181024i
$889$	18.1379	−	8.94464i	0.608327	−	0.299994i
$890$	51.0465	+	10.1538i	1.71108	+	0.340356i
$891$	42.8327	+	8.02484i	1.43495	+	0.268842i
$892$	28.6498	+	69.1667i	0.959266	+	2.31587i
$893$	−18.5737	−	2.44528i	−0.621546	−	0.0818281i
$894$	74.3598	+	19.7028i	2.48696	+	0.658960i
$895$	2.72767	+	8.03544i	0.0911758	+	0.268595i
$896$	−4.02894	+	61.4697i	−0.134597	+	2.05356i
$897$	−12.0258	+	18.1069i	−0.401531	+	0.604572i
$898$	−23.7117	+	69.8525i	−0.791271	+	2.33101i
$899$	3.48102	+	1.44189i	0.116099	+	0.0480896i
$900$	15.6963	+	1.97755i	0.523211	+	0.0659185i
$901$	14.0811	+	12.6525i	0.469110	+	0.421515i
$902$	−37.7952	−	21.8211i	−1.25844	−	0.726563i
$903$	−59.1324	−	51.5670i	−1.96780	−	1.71604i
$904$	2.74038	−	2.40325i	0.0911436	−	0.0799308i
$905$	−21.1492	−	5.66691i	−0.703023	−	0.188374i
$906$	−50.8768	+	39.2648i	−1.69027	+	1.30449i
$907$	−11.9341	−	10.4659i	−0.396264	−	0.347515i	0.437907	−	0.899021i	$-0.355720\pi$
$907$	−11.9341	−	10.4659i	−0.396264	−	0.347515i	−0.834171	+	0.551506i	$0.814053\pi$
$908$	−3.80918	−	5.70085i	−0.126412	−	0.189189i
$909$	4.66234	+	1.22147i	0.154640	+	0.0405136i
$910$	−54.7153	+	22.6638i	−1.81379	+	0.751298i
$911$	−0.610681	−	9.31719i	−0.0202328	−	0.308692i	−0.995966	−	0.0897301i	$-0.971400\pi$
$911$	−0.610681	−	9.31719i	−0.0202328	−	0.308692i	0.975733	−	0.218962i	$-0.0702671\pi$
$912$	−0.0171826	−	6.16778i	−0.000568974	−	0.204236i
$913$	7.03902	+	0.461361i	0.232957	+	0.0152688i
$914$	−5.07398	+	18.9364i	−0.167832	+	0.626359i
$915$	−17.5423	−	13.3832i	−0.579930	−	0.442435i
$916$	8.86139	+	11.5484i	0.292788	+	0.381569i
$917$	−9.47076			−0.312752
$918$	3.26079	−	47.0784i	0.107622	−	1.55382i
$919$	−1.14722			−0.0378433			−0.0189216	−	0.999821i	$-0.506023\pi$
$919$	−1.14722			−0.0378433			−0.0189216	+	0.999821i	$0.506023\pi$
$920$	7.58174	+	9.88072i	0.249963	+	0.325758i
$921$	−12.7816	−	9.75122i	−0.421168	−	0.321314i
$922$	−6.40573	+	23.9065i	−0.210962	+	0.787319i
$923$	−15.9912	−	1.04812i	−0.526356	−	0.0344992i
$924$	−0.300710	−	107.941i	−0.00989264	−	3.55100i
$925$	−0.0201131	−	0.306866i	−0.000661314	−	0.0100897i
$926$	44.9251	−	18.6086i	1.47633	−	0.611516i
$927$	−2.80185	+	2.83325i	−0.0920250	+	0.0930562i
$928$	−15.1671	−	22.6992i	−0.497886	−	0.745139i
$929$	−33.7462	−	29.5946i	−1.10718	−	0.970967i	−0.107446	−	0.994211i	$-0.534267\pi$
$929$	−33.7462	−	29.5946i	−1.10718	−	0.970967i	−0.999730	+	0.0232440i	$0.992601\pi$
$930$	−5.33666	+	4.11863i	−0.174996	+	0.135055i
$931$	29.2763	+	7.84456i	0.959492	+	0.257095i
$932$	9.70930	−	8.51483i	0.318039	−	0.278912i
$933$	19.4511	+	16.9625i	0.636799	+	0.555327i
$934$	9.94321	+	5.74071i	0.325352	+	0.187842i
$935$	−31.9697	+	15.2892i	−1.04552	+	0.500010i
$936$	−7.32707	−	17.4140i	−0.239493	−	0.569196i
$937$	−29.9281	−	12.3966i	−0.977709	−	0.404980i	−0.164133	−	0.986438i	$-0.552482\pi$
$937$	−29.9281	−	12.3966i	−0.977709	−	0.404980i	−0.813576	+	0.581458i	$0.802482\pi$
$938$	−0.705785	+	2.07917i	−0.0230447	+	0.0678875i
$939$	−16.3034	+	24.5475i	−0.532041	+	0.801077i
$940$	2.73570	−	41.7388i	0.0892288	−	1.36137i
$941$	7.01543	+	20.6668i	0.228697	+	0.673718i	0.999336	+	0.0364464i	$0.0116038\pi$
$941$	7.01543	+	20.6668i	0.228697	+	0.673718i	−0.770639	+	0.637272i	$0.780063\pi$
$942$	−63.5013	−	16.8257i	−2.06898	−	0.548209i
$943$	15.1698	+	1.99714i	0.493996	+	0.0650358i
$944$	1.66126	+	4.01064i	0.0540695	+	0.130535i
$945$	−38.5898	−	15.6079i	−1.25533	−	0.507724i
$946$	−104.993	−	20.8843i	−3.41360	−	0.679008i
$947$	5.82798	−	2.87404i	0.189384	−	0.0933938i	−0.345125	−	0.938557i	$-0.612163\pi$
$947$	5.82798	−	2.87404i	0.189384	−	0.0933938i	0.534509	+	0.845163i	$0.320497\pi$
$948$	2.99014	−	47.6545i	0.0971151	−	1.54775i
$949$	8.37954	+	9.55504i	0.272011	+	0.310170i
$950$	1.20538	+	9.15576i	0.0391077	+	0.297052i
$951$	−9.90854	−	49.0983i	−0.321306	−	1.59212i
$952$	−34.6697	+	4.13962i	−1.12365	+	0.134166i
$953$			25.3918i			0.822521i	0.911518	+	0.411261i	$0.134911\pi$
$953$			25.3918i			0.822521i	−0.911518	+	0.411261i	$0.865089\pi$
$954$	15.3161	+	26.1901i	0.495875	+	0.847936i
$955$	1.46502	+	7.36513i	0.0474068	+	0.238330i
$956$	13.4214	+	50.0895i	0.434080	+	1.62001i
$957$	19.3951	+	25.1309i	0.626955	+	0.812367i
$958$	−63.9081	+	21.6939i	−2.06478	+	0.700897i
$959$	−39.6124	+	80.3259i	−1.27915	+	2.59386i
$960$	39.0946	−	2.67180i	1.26177	−	0.0862319i
$961$	3.91698	−	29.7524i	0.126354	−	0.959755i
$962$	−1.02226	+	0.683052i	−0.0329590	+	0.0220225i
$963$	−6.10532	−	2.03461i	−0.196741	−	0.0655645i
$964$	11.4176	−	17.0876i	0.367735	−	0.550354i
$965$	24.3091	−	6.51360i	0.782537	−	0.209680i
$966$	24.8040	+	59.4134i	0.798055	+	1.91160i
$967$	59.1608	−	7.78867i	1.90248	−	0.250467i	0.914449	−	0.404702i	$-0.132625\pi$
$967$	59.1608	−	7.78867i	1.90248	−	0.250467i	0.988034	+	0.154235i	$0.0492914\pi$
$968$	−11.6758	−	20.2230i	−0.375274	−	0.649993i
$969$	15.9091	−	3.01140i	0.511073	−	0.0967401i
$970$	28.1464	−	48.7511i	0.903728	−	1.56530i
$971$	23.4487	−	56.6102i	0.752504	−	1.81671i	0.207587	−	0.978216i	$-0.433439\pi$
$971$	23.4487	−	56.6102i	0.752504	−	1.81671i	0.544917	−	0.838490i	$-0.316561\pi$
$972$	16.4389	−	41.3051i	0.527278	−	1.32486i
$973$	−69.8433	−	69.8433i	−2.23907	−	2.23907i
$974$	−32.2121	−	65.3197i	−1.03214	−	2.09298i
$975$	−5.40053	−	9.29410i	−0.172955	−	0.297649i
$976$	10.1092	+	4.98529i	0.323586	+	0.159575i
$977$	23.1770	+	17.7843i	0.741497	+	0.568971i	0.908948	−	0.416909i	$-0.136887\pi$
$977$	23.1770	+	17.7843i	0.741497	+	0.568971i	−0.167451	+	0.985880i	$0.553553\pi$
$978$	63.4877	−	42.6774i	2.03011	−	1.36467i
$979$	64.3156	−	4.21547i	2.05554	−	0.134727i
$980$	−13.2023	+	66.3723i	−0.421731	+	2.12018i
$981$	9.56258	+	8.29236i	0.305310	+	0.264755i
$982$	6.06901	−	6.06901i	0.193670	−	0.193670i
$983$	14.6023	+	4.95680i	0.465740	+	0.158097i	0.544438	−	0.838801i	$-0.316743\pi$
$983$	14.6023	+	4.95680i	0.465740	+	0.158097i	−0.0786981	+	0.996898i	$0.525076\pi$
$984$	−8.74063	+	10.0230i	−0.278641	+	0.319520i
$985$	4.57453	−	2.64111i	0.145757	−	0.0841527i
$986$	24.5995	−	24.0132i	0.783409	−	0.764737i
$987$	20.5912	−	61.2194i	0.655424	−	1.94864i
$988$	17.2166	−	13.2108i	0.547734	−	0.420291i
$989$	36.8098	−	7.32191i	1.17048	−	0.232823i
$990$	−56.2675	+	7.72694i	−1.78830	+	0.245578i
$991$	9.53304	+	6.36978i	0.302827	+	0.202343i	0.697694	−	0.716396i	$-0.254209\pi$
$991$	9.53304	+	6.36978i	0.302827	+	0.202343i	−0.394867	+	0.918738i	$0.629209\pi$
$992$	4.73362	−	5.39766i	0.150293	−	0.171376i
$993$	7.49552	+	7.45388i	0.237863	+	0.236542i
$994$	−28.8961	+	37.6581i	−0.916528	+	1.19444i
$995$	24.5628	−	32.0108i	0.778692	−	1.01481i
$996$	1.84316	−	6.95623i	0.0584028	−	0.220417i
$997$	8.71107	−	9.93307i	0.275882	−	0.314584i	−0.597261	−	0.802047i	$-0.703744\pi$
$997$	8.71107	−	9.93307i	0.275882	−	0.314584i	0.873143	+	0.487463i	$0.162078\pi$
$998$	−47.8454	−	31.9693i	−1.51452	−	1.01197i
$999$	−0.848934	−	0.161500i	−0.0268591	−	0.00510963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.15	✓	256
3.2	odd	2		459.2.y.a.62.2		256
9.4	even	3		459.2.y.a.368.2		256
9.5	odd	6	inner	153.2.s.a.113.15	yes	256
17.14	odd	16	inner	153.2.s.a.65.15	yes	256
51.14	even	16		459.2.y.a.116.2		256
153.14	even	48	inner	153.2.s.a.14.15	yes	256
153.31	odd	48		459.2.y.a.422.2		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.15	✓	256	1.1	even	1	trivial
153.2.s.a.14.15	yes	256	153.14	even	48	inner
153.2.s.a.65.15	yes	256	17.14	odd	16	inner
153.2.s.a.113.15	yes	256	9.5	odd	6	inner
459.2.y.a.62.2		256	3.2	odd	2
459.2.y.a.116.2		256	51.14	even	16
459.2.y.a.368.2		256	9.4	even	3
459.2.y.a.422.2		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34092 + 1.74752i) q^{2} +(1.37706 + 1.05057i) q^{3} +(-0.738117 + 2.75469i) q^{4} +(-1.77127 - 0.116095i) q^{5} +(0.0106286 + 3.81516i) q^{6} +(-0.295171 - 4.50344i) q^{7} +(-1.73356 + 0.718065i) q^{8} +(0.792591 + 2.89341i) q^{9} +O(q^{10})\)	\(q+(1.34092 + 1.74752i) q^{2} +(1.37706 + 1.05057i) q^{3} +(-0.738117 + 2.75469i) q^{4} +(-1.77127 - 0.116095i) q^{5} +(0.0106286 + 3.81516i) q^{6} +(-0.295171 - 4.50344i) q^{7} +(-1.73356 + 0.718065i) q^{8} +(0.792591 + 2.89341i) q^{9} +(-2.17224 - 3.25099i) q^{10} +(-3.64040 - 3.19255i) q^{11} +(-3.91043 + 3.01793i) q^{12} +(3.24185 + 0.868651i) q^{13} +(7.47403 - 6.55454i) q^{14} +(-2.31718 - 2.02072i) q^{15} +(1.36018 + 0.785301i) q^{16} +(-1.37232 + 3.88803i) q^{17} +(-3.99347 + 5.26488i) q^{18} +(-2.09469 - 0.867648i) q^{19} +(1.62721 - 4.79360i) q^{20} +(4.32472 - 6.51160i) q^{21} +(0.697553 - 10.6426i) q^{22} +(1.20194 + 3.54079i) q^{23} +(-3.14160 - 0.832416i) q^{24} +(-1.83331 - 0.241360i) q^{25} +(2.82906 + 6.82997i) q^{26} +(-1.94829 + 4.81707i) q^{27} +(12.6234 + 2.51096i) q^{28} +(-3.39484 + 1.67415i) q^{29} +(0.424096 - 6.75891i) q^{30} +(-0.656322 - 0.748392i) q^{31} +(0.941400 + 7.15064i) q^{32} +(-1.65905 - 8.22084i) q^{33} +(-8.63455 + 2.81537i) q^{34} +8.01106i q^{35} +(-8.55546 + 0.0476692i) q^{36} +(0.0324450 + 0.163112i) q^{37} +(-1.29257 - 4.82394i) q^{38} +(3.55164 + 4.60198i) q^{39} +(3.15397 - 1.07063i) q^{40} +(1.80981 - 3.66994i) q^{41} +(17.1782 - 1.17399i) q^{42} +(1.31010 - 9.95119i) q^{43} +(11.4815 - 7.67170i) q^{44} +(-1.06798 - 5.21701i) q^{45} +(-4.57589 + 6.84831i) q^{46} +(7.98124 - 2.13857i) q^{47} +(1.04804 + 2.51038i) q^{48} +(-13.2537 + 1.74488i) q^{49} +(-2.03654 - 3.52739i) q^{50} +(-5.97442 + 3.91232i) q^{51} +(-4.78572 + 8.28912i) q^{52} +(1.75702 - 4.24182i) q^{53} +(-11.0304 + 3.05462i) q^{54} +(6.07749 + 6.07749i) q^{55} +(3.74546 + 7.59504i) q^{56} +(-1.97298 - 3.39543i) q^{57} +(-7.47779 - 3.68764i) q^{58} +(2.19280 + 1.68260i) q^{59} +(7.27679 - 4.89157i) q^{60} +(7.16122 - 0.469371i) q^{61} +(0.427754 - 2.15046i) q^{62} +(12.7963 - 4.42343i) q^{63} +(-9.01235 + 9.01235i) q^{64} +(-5.64134 - 1.91498i) q^{65} +(12.1414 - 13.9227i) q^{66} +(-0.191282 + 0.110437i) q^{67} +(-9.69737 - 6.65013i) q^{68} +(-2.06472 + 6.13861i) q^{69} +(-13.9995 + 10.7422i) q^{70} +(-4.68313 + 0.931533i) q^{71} +(-3.45166 - 4.44677i) q^{72} +(3.14851 + 2.10376i) q^{73} +(-0.241535 + 0.275417i) q^{74} +(-2.27102 - 2.25840i) q^{75} +(3.93622 - 5.12978i) q^{76} +(-13.3029 + 17.3367i) q^{77} +(-3.27959 + 12.3774i) q^{78} +(-6.37354 + 7.26763i) q^{79} +(-2.31808 - 1.54889i) q^{80} +(-7.74360 + 4.58657i) q^{81} +(8.84008 - 1.75840i) q^{82} +(-1.15581 + 0.886882i) q^{83} +(14.7453 + 16.7196i) q^{84} +(2.88212 - 6.72741i) q^{85} +(19.1466 - 11.0543i) q^{86} +(-6.43371 - 1.26112i) q^{87} +(8.60333 + 2.92044i) q^{88} +(-9.41257 + 9.41257i) q^{89} +(7.68474 - 8.86189i) q^{90} +(2.95501 - 14.8559i) q^{91} +(-10.6410 + 0.697445i) q^{92} +(-0.117554 - 1.72009i) q^{93} +(14.4394 + 11.0797i) q^{94} +(3.60952 + 1.78002i) q^{95} +(-6.21591 + 10.8359i) q^{96} +(6.36781 + 12.9126i) q^{97} +(-20.8213 - 20.8213i) q^{98} +(6.35199 - 13.0635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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