LMFDB - Embedded newform 342.2.u.a.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (of order $9$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	342.55
Dual form			342.2.u.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-3.20574 + 1.16679i) q^{5} +(1.43969 + 2.49362i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-3.20574 + 1.16679i) q^{5} +(1.43969 + 2.49362i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.592396 + 3.35965i) q^{10} +(-0.173648 + 0.300767i) q^{11} +(-1.26604 + 1.06234i) q^{13} +(2.70574 - 0.984808i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.20574 + 6.83807i) q^{17} +(-2.82635 + 3.31839i) q^{19} +3.41147 q^{20} +(0.266044 + 0.223238i) q^{22} +(6.39053 + 2.32596i) q^{23} +(5.08512 - 4.26692i) q^{25} +(0.826352 + 1.43128i) q^{26} +(-0.500000 - 2.83564i) q^{28} +(-1.10354 - 6.25849i) q^{29} +(-0.798133 - 1.38241i) q^{31} +(0.766044 - 0.642788i) q^{32} +(6.52481 + 2.37484i) q^{34} +(-7.52481 - 6.31407i) q^{35} -11.2121 q^{37} +(2.77719 + 3.35965i) q^{38} +(0.592396 - 3.35965i) q^{40} +(2.67365 + 2.24346i) q^{41} +(-2.14543 + 0.780873i) q^{43} +(0.266044 - 0.223238i) q^{44} +(3.40033 - 5.88954i) q^{46} +(-0.971782 - 5.51125i) q^{47} +(-0.645430 + 1.11792i) q^{49} +(-3.31908 - 5.74881i) q^{50} +(1.55303 - 0.565258i) q^{52} +(1.86097 + 0.677337i) q^{53} +(0.205737 - 1.16679i) q^{55} -2.87939 q^{56} -6.35504 q^{58} +(-0.0773815 + 0.438852i) q^{59} +(11.7763 + 4.28623i) q^{61} +(-1.50000 + 0.545955i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.81908 - 4.88279i) q^{65} +(-0.187319 - 1.06234i) q^{67} +(3.47178 - 6.01330i) q^{68} +(-7.52481 + 6.31407i) q^{70} +(-15.6211 + 5.68561i) q^{71} +(9.51367 + 7.98292i) q^{73} +(-1.94697 + 11.0418i) q^{74} +(3.79086 - 2.15160i) q^{76} -1.00000 q^{77} +(-8.36824 - 7.02179i) q^{79} +(-3.20574 - 1.16679i) q^{80} +(2.67365 - 2.24346i) q^{82} +(5.85844 + 10.1471i) q^{83} +(-4.11334 - 23.3279i) q^{85} +(0.396459 + 2.24843i) q^{86} +(-0.173648 - 0.300767i) q^{88} +(-1.37346 + 1.15247i) q^{89} +(-4.47178 - 1.62760i) q^{91} +(-5.20961 - 4.37138i) q^{92} -5.59627 q^{94} +(5.18866 - 13.9357i) q^{95} +(0.634285 - 3.59721i) q^{97} +(0.988856 + 0.829748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8	$ 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8} - 3 q^{13} + 6 q^{14} + 3 q^{17} - 18 q^{19} - 3 q^{22} + 21 q^{23} + 9 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 9 q^{31} + 12 q^{34} - 18 q^{35} - 18 q^{37} + 6 q^{38} + 15 q^{41} + 3 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 12 q^{49} - 3 q^{50} - 3 q^{52} - 12 q^{53} - 9 q^{55} - 6 q^{56} + 12 q^{58} - 27 q^{59} + 3 q^{61} - 9 q^{62} - 3 q^{64} + 21 q^{67} + 6 q^{68} - 18 q^{70} - 39 q^{71} + 36 q^{73} - 24 q^{74} - 9 q^{76} - 6 q^{77} - 45 q^{79} - 9 q^{80} + 15 q^{82} + 27 q^{83} - 18 q^{85} + 12 q^{86} + 30 q^{89} - 12 q^{91} + 3 q^{92} - 6 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) $ 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8 - 3 * q^13 + 6 * q^14 + 3 * q^17 - 18 * q^19 - 3 * q^22 + 21 * q^23 + 9 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 9 * q^31 + 12 * q^34 - 18 * q^35 - 18 * q^37 + 6 * q^38 + 15 * q^41 + 3 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 12 * q^49 - 3 * q^50 - 3 * q^52 - 12 * q^53 - 9 * q^55 - 6 * q^56 + 12 * q^58 - 27 * q^59 + 3 * q^61 - 9 * q^62 - 3 * q^64 + 21 * q^67 + 6 * q^68 - 18 * q^70 - 39 * q^71 + 36 * q^73 - 24 * q^74 - 9 * q^76 - 6 * q^77 - 45 * q^79 - 9 * q^80 + 15 * q^82 + 27 * q^83 - 18 * q^85 + 12 * q^86 + 30 * q^89 - 12 * q^91 + 3 * q^92 - 6 * q^94 - 6 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−3.20574	+	1.16679i	−1.43365	+	0.521806i	−0.937975	−	0.346703i	$-0.887301\pi$
$5$	−3.20574	+	1.16679i	−1.43365	+	0.521806i	−0.495674	+	0.868509i	$0.665079\pi$
$6$		0			0
$7$	1.43969	+	2.49362i	0.544153	+	0.942500i	0.998660	+	0.0517569i	$0.0164821\pi$
$7$	1.43969	+	2.49362i	0.544153	+	0.942500i	−0.454507	+	0.890743i	$0.650185\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	0.592396	+	3.35965i	0.187332	+	1.06241i
$11$	−0.173648	+	0.300767i	−0.0523569	+	0.0906848i	−0.891016	−	0.453972i	$-0.850007\pi$
$11$	−0.173648	+	0.300767i	−0.0523569	+	0.0906848i	0.838659	+	0.544657i	$0.183340\pi$
$12$		0			0
$13$	−1.26604	+	1.06234i	−0.351138	+	0.294639i	−0.801247	−	0.598334i	$-0.795830\pi$
$13$	−1.26604	+	1.06234i	−0.351138	+	0.294639i	0.450109	+	0.892974i	$0.351385\pi$
$14$	2.70574	−	0.984808i	0.723139	−	0.263201i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.20574	+	6.83807i	−0.292434	+	1.65848i	0.385017	+	0.922909i	$0.374195\pi$
$17$	−1.20574	+	6.83807i	−0.292434	+	1.65848i	−0.677452	+	0.735567i	$0.736916\pi$
$18$		0			0
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$20$	3.41147			0.762829
$21$		0			0
$22$	0.266044	+	0.223238i	0.0567209	+	0.0475945i
$23$	6.39053	+	2.32596i	1.33252	+	0.484997i	0.907448	−	0.420164i	$-0.138027\pi$
$23$	6.39053	+	2.32596i	1.33252	+	0.484997i	0.425069	+	0.905161i	$0.360250\pi$
$24$		0			0
$25$	5.08512	−	4.26692i	1.01702	−	0.853385i
$26$	0.826352	+	1.43128i	0.162061	+	0.280698i
$27$		0			0
$28$	−0.500000	−	2.83564i	−0.0944911	−	0.535886i
$29$	−1.10354	−	6.25849i	−0.204922	−	1.16217i	−0.897562	−	0.440888i	$-0.854663\pi$
$29$	−1.10354	−	6.25849i	−0.204922	−	1.16217i	0.692640	−	0.721284i	$-0.256448\pi$
$30$		0			0
$31$	−0.798133	−	1.38241i	−0.143349	−	0.248288i	0.785407	−	0.618980i	$-0.212454\pi$
$31$	−0.798133	−	1.38241i	−0.143349	−	0.248288i	−0.928756	+	0.370692i	$0.879120\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$		0			0
$34$	6.52481	+	2.37484i	1.11900	+	0.407281i
$35$	−7.52481	−	6.31407i	−1.27193	−	1.06727i
$36$		0			0
$37$	−11.2121			−1.84326			−0.921632	−	0.388066i	$-0.873143\pi$
$37$	−11.2121			−1.84326			−0.921632	+	0.388066i	$0.873143\pi$
$38$	2.77719	+	3.35965i	0.450520	+	0.545007i
$39$		0			0
$40$	0.592396	−	3.35965i	0.0936661	−	0.531207i
$41$	2.67365	+	2.24346i	0.417554	+	0.350369i	0.827232	−	0.561861i	$-0.189914\pi$
$41$	2.67365	+	2.24346i	0.417554	+	0.350369i	−0.409678	+	0.912230i	$0.634359\pi$
$42$		0			0
$43$	−2.14543	+	0.780873i	−0.327175	+	0.119082i	−0.500385	−	0.865803i	$-0.666808\pi$
$43$	−2.14543	+	0.780873i	−0.327175	+	0.119082i	0.173210	+	0.984885i	$0.444586\pi$
$44$	0.266044	−	0.223238i	0.0401077	−	0.0336544i
$45$		0			0
$46$	3.40033	−	5.88954i	0.501351	−	0.868366i
$47$	−0.971782	−	5.51125i	−0.141749	−	0.803898i	−0.969920	−	0.243423i	$-0.921730\pi$
$47$	−0.971782	−	5.51125i	−0.141749	−	0.803898i	0.828171	−	0.560475i	$-0.189381\pi$
$48$		0			0
$49$	−0.645430	+	1.11792i	−0.0922042	+	0.159702i
$50$	−3.31908	−	5.74881i	−0.469388	−	0.813005i
$51$		0			0
$52$	1.55303	−	0.565258i	0.215367	−	0.0783872i
$53$	1.86097	+	0.677337i	0.255623	+	0.0930393i	0.466653	−	0.884440i	$-0.345460\pi$
$53$	1.86097	+	0.677337i	0.255623	+	0.0930393i	−0.211030	+	0.977480i	$0.567682\pi$
$54$		0			0
$55$	0.205737	−	1.16679i	0.0277416	−	0.157330i
$56$	−2.87939			−0.384774
$57$		0			0
$58$	−6.35504			−0.834457
$59$	−0.0773815	+	0.438852i	−0.0100742	+	0.0571337i	−0.989430	−	0.145008i	$-0.953679\pi$
$59$	−0.0773815	+	0.438852i	−0.0100742	+	0.0571337i	0.979356	+	0.202142i	$0.0647902\pi$
$60$		0			0
$61$	11.7763	+	4.28623i	1.50780	+	0.548795i	0.958067	−	0.286544i	$-0.0925064\pi$
$61$	11.7763	+	4.28623i	1.50780	+	0.548795i	0.549735	+	0.835339i	$0.314729\pi$
$62$	−1.50000	+	0.545955i	−0.190500	+	0.0693364i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.81908	−	4.88279i	0.349664	−	0.605635i
$66$		0			0
$67$	−0.187319	−	1.06234i	−0.0228846	−	0.129785i	0.971225	−	0.238163i	$-0.0765454\pi$
$67$	−0.187319	−	1.06234i	−0.0228846	−	0.129785i	−0.994110	+	0.108378i	$0.965434\pi$
$68$	3.47178	−	6.01330i	0.421015	−	0.729220i
$69$		0			0
$70$	−7.52481	+	6.31407i	−0.899387	+	0.754676i
$71$	−15.6211	+	5.68561i	−1.85388	+	0.674758i	−0.870786	+	0.491662i	$0.836390\pi$
$71$	−15.6211	+	5.68561i	−1.85388	+	0.674758i	−0.983095	+	0.183096i	$0.941388\pi$
$72$		0			0
$73$	9.51367	+	7.98292i	1.11349	+	0.934330i	0.998257	−	0.0590086i	$-0.0187939\pi$
$73$	9.51367	+	7.98292i	1.11349	+	0.934330i	0.115233	+	0.993338i	$0.463238\pi$
$74$	−1.94697	+	11.0418i	−0.226330	+	1.28358i
$75$		0			0
$76$	3.79086	−	2.15160i	0.434841	−	0.246806i
$77$	−1.00000			−0.113961
$78$		0			0
$79$	−8.36824	−	7.02179i	−0.941501	−	0.790013i	0.0363452	−	0.999339i	$-0.488428\pi$
$79$	−8.36824	−	7.02179i	−0.941501	−	0.790013i	−0.977846	+	0.209326i	$0.932873\pi$
$80$	−3.20574	−	1.16679i	−0.358412	−	0.130451i
$81$		0			0
$82$	2.67365	−	2.24346i	0.295255	−	0.247748i
$83$	5.85844	+	10.1471i	0.643047	+	1.11379i	0.984749	+	0.173982i	$0.0556635\pi$
$83$	5.85844	+	10.1471i	0.643047	+	1.11379i	−0.341701	+	0.939809i	$0.611003\pi$
$84$		0			0
$85$	−4.11334	−	23.3279i	−0.446154	−	2.53027i
$86$	0.396459	+	2.24843i	0.0427513	+	0.242455i
$87$		0			0
$88$	−0.173648	−	0.300767i	−0.0185110	−	0.0320619i
$89$	−1.37346	+	1.15247i	−0.145586	+	0.122161i	−0.712672	−	0.701497i	$-0.752515\pi$
$89$	−1.37346	+	1.15247i	−0.145586	+	0.122161i	0.567086	+	0.823659i	$0.308071\pi$
$90$		0			0
$91$	−4.47178	−	1.62760i	−0.468770	−	0.170618i
$92$	−5.20961	−	4.37138i	−0.543139	−	0.455748i
$93$		0			0
$94$	−5.59627			−0.577211
$95$	5.18866	−	13.9357i	0.532346	−	1.42977i
$96$		0			0
$97$	0.634285	−	3.59721i	0.0644019	−	0.365241i	−0.935526	−	0.353257i	$-0.885074\pi$
$97$	0.634285	−	3.59721i	0.0644019	−	0.365241i	0.999928	−	0.0119843i	$-0.00381481\pi$
$98$	0.988856	+	0.829748i	0.0998895	+	0.0838172i
$99$		0			0
$100$	−6.23783	+	2.27038i	−0.623783	+	0.227038i
$101$	7.58899	−	6.36792i	0.755133	−	0.633632i	−0.181722	−	0.983350i	$-0.558167\pi$
$101$	7.58899	−	6.36792i	0.755133	−	0.633632i	0.936855	+	0.349718i	$0.113723\pi$
$102$		0			0
$103$	−3.92262	+	6.79417i	−0.386507	+	0.669450i	−0.991977	−	0.126418i	$-0.959652\pi$
$103$	−3.92262	+	6.79417i	−0.386507	+	0.669450i	0.605470	+	0.795868i	$0.292985\pi$
$104$	−0.286989	−	1.62760i	−0.0281416	−	0.159599i
$105$		0			0
$106$	0.990200	−	1.71508i	0.0961767	−	0.166583i
$107$	−0.0136706	−	0.0236781i	−0.00132158	−	0.00228905i	0.865364	−	0.501144i	$-0.167087\pi$
$107$	−0.0136706	−	0.0236781i	−0.00132158	−	0.00228905i	−0.866685	+	0.498855i	$0.833754\pi$
$108$		0			0
$109$	10.1236	−	3.68469i	0.969666	−	0.352929i	0.191852	−	0.981424i	$-0.438551\pi$
$109$	10.1236	−	3.68469i	0.969666	−	0.352929i	0.777814	+	0.628494i	$0.216329\pi$
$110$	−1.11334	−	0.405223i	−0.106153	−	0.0386365i
$111$		0			0
$112$	−0.500000	+	2.83564i	−0.0472456	+	0.267943i
$113$	11.6604			1.09692			0.548461	−	0.836176i	$-0.315214\pi$
$113$	11.6604			1.09692			0.548461	+	0.836176i	$0.315214\pi$
$114$		0			0
$115$	−23.2003			−2.16344
$116$	−1.10354	+	6.25849i	−0.102461	+	0.581086i
$117$		0			0
$118$	0.418748	+	0.152412i	0.0385489	+	0.0140306i
$119$	−18.7875	+	6.83807i	−1.72224	+	0.626845i
$120$		0			0
$121$	5.43969	+	9.42182i	0.494518	+	0.856529i
$122$	6.26604	−	10.8531i	0.567301	−	0.982594i
$123$		0			0
$124$	0.277189	+	1.57202i	0.0248923	+	0.141171i
$125$	−2.79426	+	4.83981i	−0.249926	+	0.432885i
$126$		0			0
$127$	12.4192	−	10.4210i	1.10203	−	0.924711i	0.104467	−	0.994528i	$-0.466686\pi$
$127$	12.4192	−	10.4210i	1.10203	−	0.924711i	0.997560	+	0.0698178i	$0.0222418\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$		0			0
$130$	−4.31908	−	3.62414i	−0.378808	−	0.317858i
$131$	0.486329	−	2.75811i	0.0424908	−	0.240977i	−0.956164	−	0.292832i	$-0.905402\pi$
$131$	0.486329	−	2.75811i	0.0424908	−	0.240977i	0.998655	+	0.0518550i	$0.0165134\pi$
$132$		0			0
$133$	−12.3439	−	2.27038i	−1.07035	−	0.196867i
$134$	−1.07873			−0.0931877
$135$		0			0
$136$	−5.31908	−	4.46324i	−0.456107	−	0.382719i
$137$	15.0680	+	5.48432i	1.28735	+	0.468557i	0.892856	−	0.450341i	$-0.148698\pi$
$137$	15.0680	+	5.48432i	1.28735	+	0.468557i	0.394494	+	0.918899i	$0.370920\pi$
$138$		0			0
$139$	−1.59240	+	1.33618i	−0.135065	+	0.113333i	−0.707818	−	0.706395i	$-0.750320\pi$
$139$	−1.59240	+	1.33618i	−0.135065	+	0.113333i	0.572752	+	0.819728i	$0.305876\pi$
$140$	4.91147	+	8.50692i	0.415095	+	0.718966i
$141$		0			0
$142$	2.88666	+	16.3711i	0.242243	+	1.37383i
$143$	−0.0996702	−	0.565258i	−0.00833484	−	0.0472692i
$144$		0			0
$145$	10.8400	+	18.7755i	0.900215	+	1.55922i
$146$	9.51367	−	7.98292i	0.787357	−	0.660671i
$147$		0			0
$148$	10.5360	+	3.83478i	0.866051	+	0.315217i
$149$	1.27719	+	1.07169i	0.104631	+	0.0877962i	0.693603	−	0.720358i	$-0.256022\pi$
$149$	1.27719	+	1.07169i	0.104631	+	0.0877962i	−0.588971	+	0.808154i	$0.700467\pi$
$150$		0			0
$151$	20.0523			1.63183			0.815917	−	0.578169i	$-0.196232\pi$
$151$	20.0523			1.63183			0.815917	+	0.578169i	$0.196232\pi$
$152$	−1.46064	−	4.10689i	−0.118473	−	0.333113i
$153$		0			0
$154$	−0.173648	+	0.984808i	−0.0139930	+	0.0793581i
$155$	4.17159	+	3.50038i	0.335070	+	0.281157i
$156$		0			0
$157$	3.85117	−	1.40171i	0.307357	−	0.111869i	−0.183737	−	0.982975i	$-0.558820\pi$
$157$	3.85117	−	1.40171i	0.307357	−	0.111869i	0.491094	+	0.871107i	$0.336597\pi$
$158$	−8.36824	+	7.02179i	−0.665741	+	0.558623i
$159$		0			0
$160$	−1.70574	+	2.95442i	−0.134850	+	0.233568i
$161$	3.40033	+	19.2842i	0.267984	+	1.51981i
$162$		0			0
$163$	4.06758	−	7.04526i	0.318598	−	0.551827i	−0.661598	−	0.749859i	$-0.730121\pi$
$163$	4.06758	−	7.04526i	0.318598	−	0.551827i	0.980196	+	0.198031i	$0.0634548\pi$
$164$	−1.74510	−	3.02260i	−0.136269	−	0.236026i
$165$		0			0
$166$	11.0103	−	4.00741i	0.854562	−	0.311035i
$167$	−12.5890	−	4.58202i	−0.974166	−	0.354567i	−0.194596	−	0.980883i	$-0.562340\pi$
$167$	−12.5890	−	4.58202i	−0.974166	−	0.354567i	−0.779569	+	0.626316i	$0.784562\pi$
$168$		0			0
$169$	−1.78312	+	10.1126i	−0.137163	+	0.777890i
$170$	−23.6878			−1.81677
$171$		0			0
$172$	2.28312			0.174086
$173$	0.177519	−	1.00676i	0.0134965	−	0.0765424i	−0.977316	−	0.211788i	$-0.932071\pi$
$173$	0.177519	−	1.00676i	0.0134965	−	0.0765424i	0.990812	+	0.135246i	$0.0431824\pi$
$174$		0			0
$175$	17.9611	+	6.53731i	1.35773	+	0.494174i
$176$	−0.326352	+	0.118782i	−0.0245997	+	0.00895356i
$177$		0			0
$178$	0.896459	+	1.55271i	0.0671925	+	0.116381i
$179$	1.01754	−	1.76243i	0.0760546	−	0.131730i	−0.825490	−	0.564417i	$-0.809101\pi$
$179$	1.01754	−	1.76243i	0.0760546	−	0.131730i	0.901544	+	0.432687i	$0.142434\pi$
$180$		0			0
$181$	3.87299	+	21.9648i	0.287877	+	1.63263i	0.694824	+	0.719180i	$0.255482\pi$
$181$	3.87299	+	21.9648i	0.287877	+	1.63263i	−0.406947	+	0.913452i	$0.633407\pi$
$182$	−2.37939	+	4.12122i	−0.176372	+	0.305485i
$183$		0			0
$184$	−5.20961	+	4.37138i	−0.384057	+	0.322262i
$185$	35.9432	−	13.0822i	2.64259	−	0.961825i
$186$		0			0
$187$	−1.84730	−	1.55007i	−0.135088	−	0.113352i
$188$	−0.971782	+	5.51125i	−0.0708745	+	0.401949i
$189$		0			0
$190$	−12.8229	−	7.52974i	−0.930274	−	0.546265i
$191$	−10.7861			−0.780456			−0.390228	−	0.920718i	$-0.627604\pi$
$191$	−10.7861			−0.780456			−0.390228	+	0.920718i	$0.627604\pi$
$192$		0			0
$193$	−2.19459	−	1.84148i	−0.157970	−	0.132553i	0.560377	−	0.828238i	$-0.310656\pi$
$193$	−2.19459	−	1.84148i	−0.157970	−	0.132553i	−0.718347	+	0.695685i	$0.755101\pi$
$194$	−3.43242	−	1.24930i	−0.246433	−	0.0896944i
$195$		0			0
$196$	0.988856	−	0.829748i	0.0706325	−	0.0592677i
$197$	−4.16772	−	7.21870i	−0.296938	−	0.514311i	0.678496	−	0.734604i	$-0.262632\pi$
$197$	−4.16772	−	7.21870i	−0.296938	−	0.514311i	−0.975434	+	0.220293i	$0.929299\pi$
$198$		0			0
$199$	−0.526874	−	2.98805i	−0.0373491	−	0.211817i	0.960422	−	0.278550i	$-0.0898537\pi$
$199$	−0.526874	−	2.98805i	−0.0373491	−	0.211817i	−0.997771	+	0.0667324i	$0.978743\pi$
$200$	1.15270	+	6.53731i	0.0815085	+	0.462257i
$201$		0			0
$202$	−4.95336	−	8.57948i	−0.348517	−	0.603650i
$203$	14.0175	−	11.7621i	0.983839	−	0.825539i
$204$		0			0
$205$	−11.1887	−	4.07234i	−0.781450	−	0.284425i
$206$	6.00980	+	5.04282i	0.418723	+	0.351350i
$207$		0			0
$208$	−1.65270			−0.114594
$209$	−0.507274	−	1.42631i	−0.0350889	−	0.0986598i
$210$		0			0
$211$	−2.88919	+	16.3854i	−0.198900	+	1.12802i	0.707855	+	0.706358i	$0.249663\pi$
$211$	−2.88919	+	16.3854i	−0.198900	+	1.12802i	−0.906755	+	0.421659i	$0.861448\pi$
$212$	−1.51707	−	1.27298i	−0.104193	−	0.0874284i
$213$		0			0
$214$	−0.0256923	+	0.00935122i	−0.00175629	+	0.000639236i
$215$	5.96657	−	5.00654i	0.406916	−	0.341443i
$216$		0			0
$217$	2.29813	−	3.98048i	0.156007	−	0.270213i
$218$	−1.87077	−	10.6096i	−0.126704	−	0.718576i
$219$		0			0
$220$	−0.592396	+	1.02606i	−0.0399393	+	0.0691770i
$221$	−5.73783	−	9.93821i	−0.385968	−	0.668516i
$222$		0			0
$223$	7.67752	−	2.79439i	0.514125	−	0.187126i	−0.0719114	−	0.997411i	$-0.522910\pi$
$223$	7.67752	−	2.79439i	0.514125	−	0.187126i	0.586036	+	0.810285i	$0.300688\pi$
$224$	2.70574	+	0.984808i	0.180785	+	0.0658002i
$225$		0			0
$226$	2.02481	−	11.4833i	0.134689	−	0.763857i
$227$	−1.80066			−0.119514			−0.0597570	−	0.998213i	$-0.519033\pi$
$227$	−1.80066			−0.119514			−0.0597570	+	0.998213i	$0.519033\pi$
$228$		0			0
$229$	−18.7392			−1.23832			−0.619160	−	0.785265i	$-0.712527\pi$
$229$	−18.7392			−1.23832			−0.619160	+	0.785265i	$0.712527\pi$
$230$	−4.02869	+	22.8478i	−0.265644	+	1.50654i
$231$		0			0
$232$	5.97178	+	2.17355i	0.392067	+	0.142701i
$233$	−3.85117	+	1.40171i	−0.252298	+	0.0918291i	−0.465073	−	0.885272i	$-0.653972\pi$
$233$	−3.85117	+	1.40171i	−0.252298	+	0.0918291i	0.212775	+	0.977101i	$0.431750\pi$
$234$		0			0
$235$	9.54576	+	16.5337i	0.622697	+	1.07854i
$236$	0.222811	−	0.385920i	0.0145038	−	0.0251213i
$237$		0			0
$238$	3.47178	+	19.6895i	0.225042	+	1.27628i
$239$	−14.1138	+	24.4458i	−0.912946	+	1.58127i	−0.103066	+	0.994675i	$0.532865\pi$
$239$	−14.1138	+	24.4458i	−0.912946	+	1.58127i	−0.809881	+	0.586595i	$0.800468\pi$
$240$		0			0
$241$	5.02687	−	4.21805i	0.323809	−	0.271708i	−0.466362	−	0.884594i	$-0.654436\pi$
$241$	5.02687	−	4.21805i	0.323809	−	0.271708i	0.790172	+	0.612885i	$0.209991\pi$
$242$	10.2233	−	3.72097i	0.657177	−	0.239193i
$243$		0			0
$244$	−9.60014	−	8.05547i	−0.614586	−	0.515699i
$245$	0.764700	−	4.33683i	0.0488549	−	0.277070i
$246$		0			0
$247$	0.0530334	−	7.20377i	0.00337444	−	0.458365i
$248$	1.59627			0.101363
$249$		0			0
$250$	4.28106	+	3.59224i	0.270758	+	0.227193i
$251$	8.35756	+	3.04190i	0.527525	+	0.192003i	0.592033	−	0.805914i	$-0.298326\pi$
$251$	8.35756	+	3.04190i	0.527525	+	0.192003i	−0.0645080	+	0.997917i	$0.520548\pi$
$252$		0			0
$253$	−1.80928	+	1.51816i	−0.113748	+	0.0954462i
$254$	−8.10607	−	14.0401i	−0.508620	−	0.880955i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	2.33837	+	13.2616i	0.145864	+	0.827234i	0.966670	+	0.256027i	$0.0824136\pi$
$257$	2.33837	+	13.2616i	0.145864	+	0.827234i	−0.820806	+	0.571207i	$0.806475\pi$
$258$		0			0
$259$	−16.1420	−	27.9588i	−1.00302	−	1.73728i
$260$	−4.31908	+	3.62414i	−0.267858	+	0.224759i
$261$		0			0
$262$	−2.63176	−	0.957882i	−0.162591	−	0.0591781i
$263$	12.8327	+	10.7680i	0.791301	+	0.663981i	0.946067	−	0.323971i	$-0.105018\pi$
$263$	12.8327	+	10.7680i	0.791301	+	0.663981i	−0.154766	+	0.987951i	$0.549462\pi$
$264$		0			0
$265$	−6.75608			−0.415023
$266$	−4.37939	+	11.7621i	−0.268517	+	0.721181i
$267$		0			0
$268$	−0.187319	+	1.06234i	−0.0114423	+	0.0648926i
$269$	−2.74969	−	2.30726i	−0.167651	−	0.140676i	0.555102	−	0.831782i	$-0.312679\pi$
$269$	−2.74969	−	2.30726i	−0.167651	−	0.140676i	−0.722753	+	0.691106i	$0.757124\pi$
$270$		0			0
$271$	−22.5141	+	8.19448i	−1.36764	+	0.497779i	−0.918407	−	0.395637i	$-0.870524\pi$
$271$	−22.5141	+	8.19448i	−1.36764	+	0.497779i	−0.449230	+	0.893416i	$0.648301\pi$
$272$	−5.31908	+	4.46324i	−0.322516	+	0.270623i
$273$		0			0
$274$	8.01754	−	13.8868i	0.484357	−	0.838932i
$275$	0.400330	+	2.27038i	0.0241408	+	0.136909i
$276$		0			0
$277$	9.36097	−	16.2137i	0.562446	−	0.974185i	−0.434836	−	0.900510i	$-0.643194\pi$
$277$	9.36097	−	16.2137i	0.562446	−	0.974185i	0.997282	−	0.0736755i	$-0.0234729\pi$
$278$	1.03936	+	1.80023i	0.0623368	+	0.107971i
$279$		0			0
$280$	9.23055	−	3.35965i	0.551631	−	0.200777i
$281$	−9.99660	−	3.63846i	−0.596347	−	0.217053i	0.0261718	−	0.999657i	$-0.491668\pi$
$281$	−9.99660	−	3.63846i	−0.596347	−	0.217053i	−0.622519	+	0.782605i	$0.713891\pi$
$282$		0			0
$283$	−2.43330	+	13.7999i	−0.144644	+	0.820319i	0.823008	+	0.568030i	$0.192294\pi$
$283$	−2.43330	+	13.7999i	−0.144644	+	0.820319i	−0.967652	+	0.252289i	$0.918817\pi$
$284$	16.6236			0.986430
$285$		0			0
$286$	−0.573978			−0.0339400
$287$	−1.74510	+	9.89695i	−0.103010	+	0.584199i
$288$		0			0
$289$	−29.3307	−	10.6755i	−1.72533	−	0.627970i
$290$	20.3726	−	7.41501i	1.19632	−	0.435424i
$291$		0			0
$292$	−6.20961	−	10.7554i	−0.363390	−	0.629410i
$293$	−5.76011	+	9.97681i	−0.336509	+	0.582852i	−0.983774	−	0.179414i	$-0.942580\pi$
$293$	−5.76011	+	9.97681i	−0.336509	+	0.582852i	0.647264	+	0.762266i	$0.275913\pi$
$294$		0			0
$295$	−0.263985	−	1.49713i	−0.0153698	−	0.0871665i
$296$	5.60607	−	9.70999i	0.325846	−	0.564382i
$297$		0			0
$298$	1.27719	−	1.07169i	0.0739856	−	0.0620813i
$299$	−10.5617	+	3.84413i	−0.610796	+	0.222312i
$300$		0			0
$301$	−5.03596	−	4.22567i	−0.290268	−	0.243564i
$302$	3.48205	−	19.7477i	0.200369	−	1.13635i
$303$		0			0
$304$	−4.29813	+	0.725293i	−0.246515	+	0.0415984i
$305$	−42.7529			−2.44802
$306$		0			0
$307$	3.29220	+	2.76249i	0.187896	+	0.157663i	0.731883	−	0.681430i	$-0.238642\pi$
$307$	3.29220	+	2.76249i	0.187896	+	0.157663i	−0.543987	+	0.839093i	$0.683086\pi$
$308$	0.939693	+	0.342020i	0.0535440	+	0.0194884i
$309$		0			0
$310$	4.17159	−	3.50038i	0.236930	−	0.198808i
$311$	−11.4966	−	19.9127i	−0.651912	−	1.12915i	−0.982658	−	0.185425i	$-0.940634\pi$
$311$	−11.4966	−	19.9127i	−0.651912	−	1.12915i	0.330746	−	0.943720i	$-0.392700\pi$
$312$		0			0
$313$	−1.59926	−	9.06985i	−0.0903955	−	0.512658i	−0.996061	−	0.0886663i	$-0.971740\pi$
$313$	−1.59926	−	9.06985i	−0.0903955	−	0.512658i	0.905666	−	0.423992i	$-0.139372\pi$
$314$	−0.711667	−	4.03606i	−0.0401617	−	0.227768i
$315$		0			0
$316$	5.46198	+	9.46043i	0.307260	+	0.532191i
$317$	−2.57011	+	2.15658i	−0.144352	+	0.121125i	−0.712104	−	0.702074i	$-0.752258\pi$
$317$	−2.57011	+	2.15658i	−0.144352	+	0.121125i	0.567752	+	0.823199i	$0.307813\pi$
$318$		0			0
$319$	2.07398	+	0.754866i	0.116120	+	0.0422644i
$320$	2.61334	+	2.19285i	0.146090	+	0.122584i
$321$		0			0
$322$	19.5817			1.09125
$323$	−19.2836	−	23.3279i	−1.07297	−	1.29800i
$324$		0			0
$325$	−1.90508	+	10.8042i	−0.105675	+	0.599311i
$326$	−6.23190	−	5.22918i	−0.345153	−	0.289618i
$327$		0			0
$328$	−3.27972	+	1.19372i	−0.181092	+	0.0659121i
$329$	12.3439	−	10.3578i	0.680541	−	0.571042i
$330$		0			0
$331$	11.0371	−	19.1169i	0.606656	−	1.05076i	−0.385131	−	0.922862i	$-0.625844\pi$
$331$	11.0371	−	19.1169i	0.606656	−	1.05076i	0.991787	−	0.127897i	$-0.0408228\pi$
$332$	−2.03462	−	11.5389i	−0.111664	−	0.633278i
$333$		0			0
$334$	−6.69846	+	11.6021i	−0.366524	+	0.634837i
$335$	1.84002	+	3.18701i	0.100531	+	0.174125i
$336$		0			0
$337$	12.3255	−	4.48611i	0.671411	−	0.244374i	0.0162559	−	0.999868i	$-0.494825\pi$
$337$	12.3255	−	4.48611i	0.671411	−	0.244374i	0.655155	+	0.755494i	$0.272603\pi$
$338$	9.64930	+	3.51206i	0.524853	+	0.191031i
$339$		0			0
$340$	−4.11334	+	23.3279i	−0.223077	+	1.26513i
$341$	0.554378			0.0300212
$342$		0			0
$343$	16.4388			0.887613
$344$	0.396459	−	2.24843i	0.0213757	−	0.121227i
$345$		0			0
$346$	−0.960637	−	0.349643i	−0.0516442	−	0.0187969i
$347$	8.23055	−	2.99568i	0.441839	−	0.160816i	−0.111514	−	0.993763i	$-0.535570\pi$
$347$	8.23055	−	2.99568i	0.441839	−	0.160816i	0.553354	+	0.832947i	$0.313348\pi$
$348$		0			0
$349$	−1.63176	−	2.82629i	−0.0873461	−	0.151288i	0.819042	−	0.573733i	$-0.194505\pi$
$349$	−1.63176	−	2.82629i	−0.0873461	−	0.151288i	−0.906389	+	0.422445i	$0.861172\pi$
$350$	9.55690	−	16.5530i	0.510838	−	0.884797i
$351$		0			0
$352$	0.0603074	+	0.342020i	0.00321439	+	0.0182297i
$353$	14.5419	−	25.1873i	0.773987	−	1.34058i	−0.161376	−	0.986893i	$-0.551593\pi$
$353$	14.5419	−	25.1873i	0.773987	−	1.34058i	0.935362	−	0.353691i	$-0.115074\pi$
$354$		0			0
$355$	43.4432	−	36.4531i	2.30572	−	1.93473i
$356$	1.68479	−	0.613214i	0.0892938	−	0.0325003i
$357$		0			0
$358$	−1.55896	−	1.30813i	−0.0823938	−	0.0691366i
$359$	−1.14796	+	6.51038i	−0.0605868	+	0.343605i	0.939413	+	0.342788i	$0.111371\pi$
$359$	−1.14796	+	6.51038i	−0.0605868	+	0.343605i	−1.00000		0.000817017i	$0.999740\pi$
$360$		0			0
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	22.3037			1.17225
$363$		0			0
$364$	3.64543	+	3.05888i	0.191072	+	0.160329i
$365$	−39.8127	−	14.4907i	−2.08389	−	0.758475i
$366$		0			0
$367$	−4.43969	+	3.72534i	−0.231750	+	0.194461i	−0.751266	−	0.659999i	$-0.770557\pi$
$367$	−4.43969	+	3.72534i	−0.231750	+	0.194461i	0.519516	+	0.854461i	$0.326112\pi$
$368$	3.40033	+	5.88954i	0.177254	+	0.307014i
$369$		0			0
$370$	−6.64203	−	37.6688i	−0.345302	−	1.95831i
$371$	0.990200	+	5.61570i	0.0514086	+	0.291553i
$372$		0			0
$373$	12.9449	+	22.4212i	0.670262	+	1.16093i	0.977830	+	0.209401i	$0.0671516\pi$
$373$	12.9449	+	22.4212i	0.670262	+	1.16093i	−0.307568	+	0.951526i	$0.599515\pi$
$374$	−1.84730	+	1.55007i	−0.0955214	+	0.0801520i
$375$		0			0
$376$	5.25877	+	1.91404i	0.271200	+	0.0987089i
$377$	8.04576	+	6.75119i	0.414378	+	0.347704i
$378$		0			0
$379$	−19.1557			−0.983962			−0.491981	−	0.870606i	$-0.663727\pi$
$379$	−19.1557			−0.983962			−0.491981	+	0.870606i	$0.663727\pi$
$380$	−9.64203	+	11.3206i	−0.494626	+	0.580735i
$381$		0			0
$382$	−1.87299	+	10.6222i	−0.0958304	+	0.543481i
$383$	7.42649	+	6.23156i	0.379476	+	0.318418i	0.812497	−	0.582966i	$-0.198108\pi$
$383$	7.42649	+	6.23156i	0.379476	+	0.318418i	−0.433021	+	0.901384i	$0.642552\pi$
$384$		0			0
$385$	3.20574	−	1.16679i	0.163379	−	0.0594653i
$386$	−2.19459	+	1.84148i	−0.111702	+	0.0937290i
$387$		0			0
$388$	−1.82635	+	3.16333i	−0.0927190	+	0.160594i
$389$	0.142026	+	0.805470i	0.00720101	+	0.0408390i	0.988197	−	0.153191i	$-0.0489551\pi$
$389$	0.142026	+	0.805470i	0.00720101	+	0.0408390i	−0.980996	+	0.194030i	$0.937844\pi$
$390$		0			0
$391$	−23.6104	+	40.8944i	−1.19403	+	2.06812i
$392$	−0.645430	−	1.11792i	−0.0325991	−	0.0564633i
$393$		0			0
$394$	−7.83275	+	2.85089i	−0.394608	+	0.143626i
$395$	35.0194	+	12.7460i	1.76201	+	0.641321i
$396$		0			0
$397$	−0.642026	+	3.64111i	−0.0322224	+	0.182742i	−0.996671	−	0.0815281i	$-0.974020\pi$
$397$	−0.642026	+	3.64111i	−0.0322224	+	0.182742i	0.964449	+	0.264270i	$0.0851311\pi$
$398$	−3.03415			−0.152088
$399$		0			0
$400$	6.63816			0.331908
$401$	3.77513	−	21.4098i	0.188521	−	1.06916i	−0.732827	−	0.680416i	$-0.761799\pi$
$401$	3.77513	−	21.4098i	0.188521	−	1.06916i	0.921347	−	0.388740i	$-0.127090\pi$
$402$		0			0
$403$	2.47906	+	0.902302i	0.123491	+	0.0449469i
$404$	−9.30928	+	3.38830i	−0.463154	+	0.168574i
$405$		0			0
$406$	−9.14930	−	15.8471i	−0.454072	−	0.786476i
$407$	1.94697	−	3.37225i	0.0965076	−	0.167156i
$408$		0			0
$409$	−0.704088	−	3.99308i	−0.0348149	−	0.197445i	0.962440	−	0.271496i	$-0.0875184\pi$
$409$	−0.704088	−	3.99308i	−0.0348149	−	0.197445i	−0.997254	+	0.0740509i	$0.976407\pi$
$410$	−5.95336	+	10.3115i	−0.294016	+	0.509250i
$411$		0			0
$412$	6.00980	−	5.04282i	0.296082	−	0.248442i
$413$	−1.20574	+	0.438852i	−0.0593304	+	0.0215945i
$414$		0			0
$415$	−30.6202	−	25.6934i	−1.50309	−	1.26124i
$416$	−0.286989	+	1.62760i	−0.0140708	+	0.0797994i
$417$		0			0
$418$	−1.49273	+	0.251892i	−0.0730116	+	0.0123204i
$419$	−23.4989			−1.14800			−0.573998	−	0.818857i	$-0.694608\pi$
$419$	−23.4989			−1.14800			−0.573998	+	0.818857i	$0.694608\pi$
$420$		0			0
$421$	−17.6748	−	14.8309i	−0.861419	−	0.722816i	0.100855	−	0.994901i	$-0.467842\pi$
$421$	−17.6748	−	14.8309i	−0.861419	−	0.722816i	−0.962273	+	0.272085i	$0.912287\pi$
$422$	15.6348	+	5.69058i	0.761088	+	0.277013i
$423$		0			0
$424$	−1.51707	+	1.27298i	−0.0736756	+	0.0618212i
$425$	23.0462	+	39.9172i	1.11791	+	1.93627i
$426$		0			0
$427$	6.26604	+	35.5365i	0.303235	+	1.71973i
$428$	0.00474774	+	0.0269258i	0.000229491	+	0.00130151i
$429$		0			0
$430$	−3.89440	−	6.74530i	−0.187805	−	0.325287i
$431$	2.69253	−	2.25930i	0.129695	−	0.108827i	−0.575633	−	0.817708i	$-0.695244\pi$
$431$	2.69253	−	2.25930i	0.129695	−	0.108827i	0.705328	+	0.708881i	$0.250800\pi$
$432$		0			0
$433$	32.0574	+	11.6679i	1.54058	+	0.560725i	0.966184	−	0.257853i	$-0.0830152\pi$
$433$	32.0574	+	11.6679i	1.54058	+	0.560725i	0.574395	+	0.818578i	$0.305237\pi$
$434$	−3.52094	−	2.95442i	−0.169011	−	0.141817i
$435$		0			0
$436$	−10.7733			−0.515948
$437$	−25.7803	+	14.6323i	−1.23324	+	0.699958i
$438$		0			0
$439$	1.68463	−	9.55401i	0.0804030	−	0.455988i	−0.917851	−	0.396925i	$-0.870077\pi$
$439$	1.68463	−	9.55401i	0.0804030	−	0.455988i	0.998254	−	0.0590636i	$-0.0188115\pi$
$440$	0.907604	+	0.761570i	0.0432683	+	0.0363064i
$441$		0			0
$442$	−10.7836	+	3.92490i	−0.512923	+	0.186689i
$443$	−11.6302	+	9.75887i	−0.552566	+	0.463658i	−0.875809	−	0.482658i	$-0.839671\pi$
$443$	−11.6302	+	9.75887i	−0.552566	+	0.463658i	0.323243	+	0.946316i	$0.395227\pi$
$444$		0			0
$445$	3.05825	−	5.29704i	0.144975	−	0.251104i
$446$	−1.41875	−	8.04612i	−0.0671797	−	0.380995i
$447$		0			0
$448$	1.43969	−	2.49362i	0.0680191	−	0.117813i
$449$	17.4192	+	30.1710i	0.822064	+	1.42386i	0.904143	+	0.427230i	$0.140511\pi$
$449$	17.4192	+	30.1710i	0.822064	+	1.42386i	−0.0820794	+	0.996626i	$0.526156\pi$
$450$		0			0
$451$	−1.13903	+	0.414574i	−0.0536350	+	0.0195215i
$452$	−10.9572	−	3.98811i	−0.515385	−	0.187585i
$453$		0			0
$454$	−0.312681	+	1.77330i	−0.0146749	+	0.0832253i
$455$	16.2344			0.761081
$456$		0			0
$457$	−31.8749			−1.49105			−0.745523	−	0.666479i	$-0.767800\pi$
$457$	−31.8749			−1.49105			−0.745523	+	0.666479i	$0.767800\pi$
$458$	−3.25402	+	18.4545i	−0.152050	+	0.862321i
$459$		0			0
$460$	21.8011	+	7.93496i	1.01648	+	0.369969i
$461$	−10.0449	+	3.65604i	−0.467837	+	0.170279i	−0.565172	−	0.824973i	$-0.691190\pi$
$461$	−10.0449	+	3.65604i	−0.467837	+	0.170279i	0.0973354	+	0.995252i	$0.468968\pi$
$462$		0			0
$463$	−7.65910	−	13.2660i	−0.355949	−	0.616521i	0.631331	−	0.775513i	$-0.282509\pi$
$463$	−7.65910	−	13.2660i	−0.355949	−	0.616521i	−0.987280	+	0.158992i	$0.949176\pi$
$464$	3.17752	−	5.50362i	0.147513	−	0.255499i
$465$		0			0
$466$	0.711667	+	4.03606i	0.0329673	+	0.186967i
$467$	14.2562	−	24.6925i	0.659700	−	1.14263i	−0.320993	−	0.947082i	$-0.604017\pi$
$467$	14.2562	−	24.6925i	0.659700	−	1.14263i	0.980693	−	0.195553i	$-0.0626501\pi$
$468$		0			0
$469$	2.37939	−	1.99654i	0.109870	−	0.0921917i
$470$	17.9402	−	6.52968i	0.827518	−	0.301192i
$471$		0			0
$472$	−0.341367	−	0.286441i	−0.0157127	−	0.0131845i
$473$	0.137689	−	0.780873i	0.00633094	−	0.0359046i
$474$		0			0
$475$	−0.213011	+	28.9343i	−0.00977362	+	1.32760i
$476$	19.9932			0.916386
$477$		0			0
$478$	21.6236	+	18.1444i	0.989041	+	0.829904i
$479$	7.56583	+	2.75374i	0.345691	+	0.125821i	0.509030	−	0.860749i	$-0.330004\pi$
$479$	7.56583	+	2.75374i	0.345691	+	0.125821i	−0.163339	+	0.986570i	$0.552226\pi$
$480$		0			0
$481$	14.1951	−	11.9111i	0.647239	−	0.543098i
$482$	−3.28106	−	5.68296i	−0.149448	−	0.258852i
$483$		0			0
$484$	−1.88919	−	10.7141i	−0.0858721	−	0.487005i
$485$	2.16385	+	12.2718i	0.0982553	+	0.557233i
$486$		0			0
$487$	−3.05778	−	5.29623i	−0.138561	−	0.239995i	0.788391	−	0.615175i	$-0.210914\pi$
$487$	−3.05778	−	5.29623i	−0.138561	−	0.239995i	−0.926952	+	0.375179i	$0.877581\pi$
$488$	−9.60014	+	8.05547i	−0.434578	+	0.364654i
$489$		0			0
$490$	−4.13816	−	1.50617i	−0.186943	−	0.0680416i
$491$	17.3778	+	14.5817i	0.784249	+	0.658063i	0.944315	−	0.329043i	$-0.106726\pi$
$491$	17.3778	+	14.5817i	0.784249	+	0.658063i	−0.160066	+	0.987106i	$0.551171\pi$
$492$		0			0
$493$	44.1266			1.98736
$494$	−7.08512	−	1.30315i	−0.318775	−	0.0586315i
$495$		0			0
$496$	0.277189	−	1.57202i	0.0124461	−	0.0705856i
$497$	−36.6673	−	30.7675i	−1.64475	−	1.38011i
$498$		0			0
$499$	−23.3567	+	8.50114i	−1.04559	+	0.380563i	−0.806996	−	0.590557i	$-0.798908\pi$
$499$	−23.3567	+	8.50114i	−1.04559	+	0.380563i	−0.238593	+	0.971120i	$0.576686\pi$
$500$	4.28106	−	3.59224i	0.191455	−	0.160650i
$501$		0			0
$502$	4.44697	−	7.70237i	0.198478	−	0.343774i
$503$	−4.34524	−	24.6431i	−0.193745	−	1.09878i	−0.914195	−	0.405274i	$-0.867176\pi$
$503$	−4.34524	−	24.6431i	−0.193745	−	1.09878i	0.720451	−	0.693506i	$-0.243935\pi$
$504$		0			0
$505$	−16.8983	+	29.2687i	−0.751963	+	1.30244i
$506$	1.18092	+	2.04542i	0.0524984	+	0.0909299i
$507$		0			0
$508$	−15.2344	+	5.54488i	−0.675918	+	0.246014i
$509$	0.845075	+	0.307582i	0.0374573	+	0.0136333i	0.360681	−	0.932689i	$-0.382544\pi$
$509$	0.845075	+	0.307582i	0.0374573	+	0.0136333i	−0.323224	+	0.946323i	$0.604767\pi$
$510$		0			0
$511$	−6.20961	+	35.2164i	−0.274697	+	1.55788i
$512$	1.00000			0.0441942
$513$		0			0
$514$	13.4662			0.593967
$515$	4.64749	−	26.3572i	0.204793	−	1.16144i
$516$		0			0
$517$	1.82635	+	0.664738i	0.0803229	+	0.0292351i
$518$	−30.3371	+	11.0418i	−1.33294	+	0.485149i
$519$		0			0
$520$	2.81908	+	4.88279i	0.123625	+	0.214124i
$521$	−3.31773	+	5.74648i	−0.145353	+	0.251758i	−0.929504	−	0.368811i	$-0.879765\pi$
$521$	−3.31773	+	5.74648i	−0.145353	+	0.251758i	0.784152	+	0.620569i	$0.213098\pi$
$522$		0			0
$523$	6.59034	+	37.3757i	0.288175	+	1.63432i	0.693718	+	0.720247i	$0.255972\pi$
$523$	6.59034	+	37.3757i	0.288175	+	1.63432i	−0.405542	+	0.914076i	$0.632917\pi$
$524$	−1.40033	+	2.42544i	−0.0611737	+	0.105956i
$525$		0			0
$526$	12.8327	−	10.7680i	0.559534	−	0.469505i
$527$	10.4153	−	3.79088i	0.453700	−	0.165133i
$528$		0			0
$529$	17.8097	+	14.9442i	0.774337	+	0.649746i
$530$	−1.17318	+	6.65344i	−0.0509597	+	0.289007i
$531$		0			0
$532$	10.8229	+	6.35532i	0.469234	+	0.275538i
$533$	−5.76827			−0.249851
$534$		0			0
$535$	0.0714517	+	0.0599551i	0.00308913	+	0.00259209i
$536$	1.01367	+	0.368946i	0.0437839	+	0.0159360i
$537$		0			0
$538$	−2.74969	+	2.30726i	−0.118547	+	0.0994730i
$539$	−0.224155	−	0.388249i	−0.00965506	−	0.0167230i
$540$		0			0
$541$	2.62742	+	14.9009i	0.112962	+	0.640638i	0.987739	+	0.156113i	$0.0498963\pi$
$541$	2.62742	+	14.9009i	0.112962	+	0.640638i	−0.874778	+	0.484525i	$0.838993\pi$
$542$	4.16044	+	23.5951i	0.178706	+	1.01349i
$543$		0			0
$544$	3.47178	+	6.01330i	0.148851	+	0.257818i
$545$	−28.1544	+	23.6243i	−1.20600	+	1.01195i
$546$		0			0
$547$	−30.6215	−	11.1453i	−1.30928	−	0.476540i	−0.409274	−	0.912412i	$-0.634218\pi$
$547$	−30.6215	−	11.1453i	−1.30928	−	0.476540i	−0.900009	+	0.435872i	$0.856440\pi$
$548$	−12.2836	−	10.3072i	−0.524729	−	0.440300i
$549$		0			0
$550$	2.30541			0.0983029
$551$	23.8871	+	14.0267i	1.01763	+	0.597558i
$552$		0			0
$553$	5.46198	−	30.9764i	0.232267	−	1.31725i
$554$	−14.3418	−	12.0342i	−0.609326	−	0.511285i
$555$		0			0
$556$	1.95336	−	0.710966i	0.0828411	−	0.0301517i
$557$	15.2777	−	12.8195i	0.647335	−	0.543179i	−0.258926	−	0.965897i	$-0.583369\pi$
$557$	15.2777	−	12.8195i	0.647335	−	0.543179i	0.906261	+	0.422719i	$0.138924\pi$
$558$		0			0
$559$	1.88666	−	3.26779i	0.0797972	−	0.138213i
$560$	−1.70574	−	9.67372i	−0.0720805	−	0.408789i
$561$		0			0
$562$	−5.31908	+	9.21291i	−0.224372	+	0.388623i
$563$	1.98411	+	3.43658i	0.0836202	+	0.144834i	0.904802	−	0.425832i	$-0.140018\pi$
$563$	1.98411	+	3.43658i	0.0836202	+	0.144834i	−0.821182	+	0.570666i	$0.806685\pi$
$564$		0			0
$565$	−37.3803	+	13.6053i	−1.57260	+	0.572380i
$566$	13.1677	+	4.79266i	0.553480	+	0.201450i
$567$		0			0
$568$	2.88666	−	16.3711i	0.121122	−	0.686914i
$569$	−14.8135			−0.621012			−0.310506	−	0.950571i	$-0.600499\pi$
$569$	−14.8135			−0.621012			−0.310506	+	0.950571i	$0.600499\pi$
$570$		0			0
$571$	21.0615			0.881396			0.440698	−	0.897655i	$-0.354731\pi$
$571$	21.0615			0.881396			0.440698	+	0.897655i	$0.354731\pi$
$572$	−0.0996702	+	0.565258i	−0.00416742	+	0.0236346i
$573$		0			0
$574$	9.44356	+	3.43718i	0.394167	+	0.143465i
$575$	42.4213	−	15.4401i	1.76909	−	0.643897i
$576$		0			0
$577$	22.1211	+	38.3148i	0.920913	+	1.59507i	0.798006	+	0.602649i	$0.205888\pi$
$577$	22.1211	+	38.3148i	0.920913	+	1.59507i	0.122907	+	0.992418i	$0.460778\pi$
$578$	−15.6065	+	27.0313i	−0.649146	+	1.12435i
$579$		0			0
$580$	−3.76470	−	21.3507i	−0.156321	−	0.886539i
$581$	−16.8687	+	29.2175i	−0.699832	+	1.21214i
$582$		0			0
$583$	−0.526874	+	0.442100i	−0.0218209	+	0.0183099i
$584$	−11.6702	+	4.24762i	−0.482918	+	0.175768i
$585$		0			0
$586$	8.82501	+	7.40506i	0.364558	+	0.305900i
$587$	−1.73689	+	9.85041i	−0.0716892	+	0.406570i	0.927754	+	0.373193i	$0.121737\pi$
$587$	−1.73689	+	9.85041i	−0.0716892	+	0.406570i	−0.999443	+	0.0333765i	$0.989374\pi$
$588$		0			0
$589$	6.84318	+	1.25865i	0.281968	+	0.0518617i
$590$	−1.52023			−0.0625869
$591$		0			0
$592$	−8.58899	−	7.20702i	−0.353005	−	0.296207i
$593$	−10.7981	−	3.93020i	−0.443426	−	0.161394i	0.110651	−	0.993859i	$-0.464706\pi$
$593$	−10.7981	−	3.93020i	−0.443426	−	0.161394i	−0.554077	+	0.832465i	$0.686929\pi$
$594$		0			0
$595$	52.2490	−	43.8421i	2.14200	−	1.79735i
$596$	−0.833626	−	1.44388i	−0.0341466	−	0.0591437i
$597$		0			0
$598$	1.95171	+	11.0687i	0.0798115	+	0.452634i
$599$	−1.11422	−	6.31905i	−0.0455257	−	0.258189i	0.953547	−	0.301244i	$-0.0974020\pi$
$599$	−1.11422	−	6.31905i	−0.0455257	−	0.258189i	−0.999073	+	0.0430552i	$0.986291\pi$
$600$		0			0
$601$	−15.7579	−	27.2935i	−0.642778	−	1.11332i	−0.984810	−	0.173636i	$-0.944448\pi$
$601$	−15.7579	−	27.2935i	−0.642778	−	1.11332i	0.342032	−	0.939688i	$-0.388885\pi$
$602$	−5.03596	+	4.22567i	−0.205250	+	0.172226i
$603$		0			0
$604$	−18.8430	−	6.85830i	−0.766711	−	0.279060i
$605$	−28.4315	−	23.8569i	−1.15591	−	0.969921i
$606$		0			0
$607$	0.748341			0.0303742			0.0151871	−	0.999885i	$-0.495166\pi$
$607$	0.748341			0.0303742			0.0151871	+	0.999885i	$0.495166\pi$
$608$	−0.0320889	+	4.35878i	−0.00130138	+	0.176772i
$609$		0			0
$610$	−7.42396	+	42.1034i	−0.300587	+	1.70472i
$611$	7.08512	+	5.94512i	0.286633	+	0.240514i
$612$		0			0
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.313938	−	0.949443i	$-0.398352\pi$
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.850781	+	0.525520i	$0.176129\pi$
$614$	3.29220	−	2.76249i	0.132863	−	0.111485i
$615$		0			0
$616$	0.500000	−	0.866025i	0.0201456	−	0.0348932i
$617$	4.73917	+	26.8772i	0.190792	+	1.08203i	0.918285	+	0.395919i	$0.129574\pi$
$617$	4.73917	+	26.8772i	0.190792	+	1.08203i	−0.727493	+	0.686115i	$0.759315\pi$
$618$		0			0
$619$	6.61856	−	11.4637i	0.266022	−	0.460764i	−0.701809	−	0.712365i	$-0.747624\pi$
$619$	6.61856	−	11.4637i	0.266022	−	0.460764i	0.967831	+	0.251601i	$0.0809572\pi$
$620$	−2.72281	−	4.71605i	−0.109351	−	0.189401i
$621$		0			0
$622$	−21.6065	+	7.86414i	−0.866343	+	0.315323i
$623$	−4.85117	−	1.76568i	−0.194358	−	0.0707405i
$624$		0			0
$625$	−2.45290	+	13.9111i	−0.0981159	+	0.556443i
$626$	−9.20977			−0.368096
$627$		0			0
$628$	−4.09833			−0.163541
$629$	13.5189	−	76.6694i	0.539033	−	3.05701i
$630$		0			0
$631$	11.5013	+	4.18615i	0.457861	+	0.166648i	0.560646	−	0.828056i	$-0.310553\pi$
$631$	11.5013	+	4.18615i	0.457861	+	0.166648i	−0.102784	+	0.994704i	$0.532775\pi$
$632$	10.2652	−	3.73622i	0.408326	−	0.148619i
$633$		0			0
$634$	1.67752	+	2.90555i	0.0666228	+	0.115394i
$635$	−27.6536	+	47.8975i	−1.09740	+	1.90075i
$636$		0			0
$637$	−0.370462	−	2.10100i	−0.0146783	−	0.0832445i
$638$	1.10354	−	1.91139i	0.0436896	−	0.0756726i
$639$		0			0
$640$	2.61334	−	2.19285i	0.103301	−	0.0866801i
$641$	8.41370	−	3.06233i	0.332321	−	0.120955i	−0.170470	−	0.985363i	$-0.554529\pi$
$641$	8.41370	−	3.06233i	0.332321	−	0.120955i	0.502791	+	0.864408i	$0.332306\pi$
$642$		0			0
$643$	−24.0305	−	20.1640i	−0.947670	−	0.795190i	0.0312334	−	0.999512i	$-0.490056\pi$
$643$	−24.0305	−	20.1640i	−0.947670	−	0.795190i	−0.978904	+	0.204322i	$0.934501\pi$
$644$	3.40033	−	19.2842i	0.133992	−	0.759905i
$645$		0			0
$646$	−26.3221	+	14.9398i	−1.03563	+	0.587798i
$647$	5.54933			0.218166			0.109083	−	0.994033i	$-0.465208\pi$
$647$	5.54933			0.218166			0.109083	+	0.994033i	$0.465208\pi$
$648$		0			0
$649$	−0.118555	−	0.0994798i	−0.00465371	−	0.00390492i
$650$	10.3093	+	3.75227i	0.404363	+	0.147176i
$651$		0			0
$652$	−6.23190	+	5.22918i	−0.244060	+	0.204791i
$653$	19.4552	+	33.6974i	0.761340	+	1.31868i	0.942160	+	0.335163i	$0.108791\pi$
$653$	19.4552	+	33.6974i	0.761340	+	1.31868i	−0.180820	+	0.983516i	$0.557875\pi$
$654$		0			0
$655$	1.65910	+	9.40923i	0.0648264	+	0.367649i
$656$	0.606067	+	3.43718i	0.0236629	+	0.134199i
$657$		0			0
$658$	−8.05690	−	13.9550i	−0.314091	−	0.544021i
$659$	30.2708	−	25.4003i	1.17918	−	0.989454i	0.179201	−	0.983813i	$-0.442649\pi$
$659$	30.2708	−	25.4003i	1.17918	−	0.989454i	0.999984	−	0.00564104i	$-0.00179561\pi$
$660$		0			0
$661$	0.0859997	+	0.0313013i	0.00334500	+	0.00121748i	0.343692	−	0.939082i	$-0.388322\pi$
$661$	0.0859997	+	0.0313013i	0.00334500	+	0.00121748i	−0.340347	+	0.940300i	$0.610545\pi$
$662$	−16.9099	−	14.1891i	−0.657221	−	0.551474i
$663$		0			0
$664$	−11.7169			−0.454703
$665$	42.2203	−	7.12452i	1.63723	−	0.276277i
$666$		0			0
$667$	7.50480	−	42.5619i	0.290587	−	1.64800i
$668$	10.2626	+	8.61138i	0.397073	+	0.333184i
$669$		0			0
$670$	3.45811	−	1.25865i	0.133598	−	0.0486259i
$671$	−3.33409	+	2.79764i	−0.128711	+	0.108002i
$672$		0			0
$673$	19.9281	−	34.5165i	0.768173	−	1.33052i	−0.170379	−	0.985379i	$-0.554499\pi$
$673$	19.9281	−	34.5165i	0.768173	−	1.33052i	0.938552	−	0.345137i	$-0.112167\pi$
$674$	−2.27766	−	12.9172i	−0.0877320	−	0.497553i
$675$		0			0
$676$	5.13429	−	8.89284i	0.197473	−	0.342032i
$677$	14.6912	+	25.4459i	0.564628	+	0.977965i	0.997084	+	0.0763098i	$0.0243138\pi$
$677$	14.6912	+	25.4459i	0.564628	+	0.977965i	−0.432456	+	0.901655i	$0.642353\pi$
$678$		0			0
$679$	9.88326	−	3.59721i	0.379285	−	0.138048i
$680$	22.2592	+	8.10170i	0.853603	+	0.310686i
$681$		0			0
$682$	0.0962667	−	0.545955i	0.00368624	−	0.0209057i
$683$	21.0933			0.807112			0.403556	−	0.914955i	$-0.367774\pi$
$683$	21.0933			0.807112			0.403556	+	0.914955i	$0.367774\pi$
$684$		0			0
$685$	−54.7033			−2.09010
$686$	2.85457	−	16.1891i	0.108988	−	0.618102i
$687$		0			0
$688$	−2.14543	−	0.780873i	−0.0817937	−	0.0297705i
$689$	−3.07563	+	1.11944i	−0.117172	+	0.0426471i
$690$		0			0
$691$	8.08172	+	13.9979i	0.307443	+	0.532507i	0.977802	−	0.209530i	$-0.0671933\pi$
$691$	8.08172	+	13.9979i	0.307443	+	0.532507i	−0.670359	+	0.742037i	$0.733860\pi$
$692$	−0.511144	+	0.885328i	−0.0194308	+	0.0336551i
$693$		0			0
$694$	−1.52094	−	8.62571i	−0.0577343	−	0.327427i
$695$	3.54576	−	6.14144i	0.134498	−	0.232958i
$696$		0			0
$697$	−18.5646	+	15.5776i	−0.703186	+	0.590043i
$698$	−3.06670	+	1.11619i	−0.116076	+	0.0422484i
$699$		0			0
$700$	−14.6420	−	12.2861i	−0.553417	−	0.464372i
$701$	3.48561	−	19.7679i	0.131650	−	0.746623i	−0.845484	−	0.534000i	$-0.820688\pi$
$701$	3.48561	−	19.7679i	0.131650	−	0.746623i	0.977134	−	0.212623i	$-0.0682007\pi$
$702$		0			0
$703$	31.6894	−	37.2063i	1.19519	−	1.40326i
$704$	0.347296			0.0130892
$705$		0			0
$706$	−22.2795	−	18.6947i	−0.838499	−	0.703584i
$707$	26.8050	+	9.75622i	1.00811	+	0.366920i
$708$		0			0
$709$	−29.7998	+	25.0050i	−1.11915	+	0.939082i	−0.998561	−	0.0536201i	$-0.982924\pi$
$709$	−29.7998	+	25.0050i	−1.11915	+	0.939082i	−0.120593	+	0.992702i	$0.538480\pi$
$710$	−28.3555	−	49.1132i	−1.06416	−	1.84318i
$711$		0			0
$712$	−0.311337	−	1.76568i	−0.0116679	−	0.0661717i
$713$	−1.88507	−	10.6907i	−0.0705963	−	0.400372i
$714$		0			0
$715$	0.979055	+	1.69577i	0.0366146	+	0.0634183i
$716$	−1.55896	+	1.30813i	−0.0582612	+	0.0488869i
$717$		0			0
$718$	6.21213	+	2.26103i	0.231835	+	0.0843810i
$719$	−2.34549	−	1.96810i	−0.0874718	−	0.0733976i	0.598003	−	0.801494i	$-0.295961\pi$
$719$	−2.34549	−	1.96810i	−0.0874718	−	0.0733976i	−0.685475	+	0.728096i	$0.740405\pi$
$720$		0			0
$721$	−22.5895			−0.841275
$722$	−18.9979	−	0.279737i	−0.707030	−	0.0104107i
$723$		0			0
$724$	3.87299	−	21.9648i	0.143938	−	0.816316i
$725$	−32.3161	−	27.1165i	−1.20019	−	1.00708i
$726$		0			0
$727$	16.4226	−	5.97734i	0.609081	−	0.221687i	−0.0190200	−	0.999819i	$-0.506055\pi$
$727$	16.4226	−	5.97734i	0.609081	−	0.221687i	0.628101	+	0.778132i	$0.283832\pi$
$728$	3.64543	−	3.05888i	0.135109	−	0.113370i
$729$		0			0
$730$	−21.1839	+	36.6916i	−0.784052	+	1.35802i
$731$	−2.75284	−	15.6121i	−0.101817	−	0.577436i
$732$		0			0
$733$	20.7087	−	35.8686i	0.764894	−	1.32484i	−0.175408	−	0.984496i	$-0.556124\pi$
$733$	20.7087	−	35.8686i	0.764894	−	1.32484i	0.940302	−	0.340340i	$-0.110542\pi$
$734$	2.89780	+	5.01914i	0.106960	+	0.185260i
$735$		0			0
$736$	6.39053	−	2.32596i	0.235558	−	0.0857361i
$737$	0.352044	+	0.128134i	0.0129677	+	0.00471986i
$738$		0			0
$739$	4.59358	−	26.0515i	0.168978	−	0.958319i	−0.775890	−	0.630868i	$-0.782699\pi$
$739$	4.59358	−	26.0515i	0.168978	−	0.958319i	0.944868	−	0.327451i	$-0.106190\pi$
$740$	−38.2499			−1.40609
$741$		0			0
$742$	5.70233			0.209339
$743$	2.61793	−	14.8470i	0.0960424	−	0.544684i	−0.898381	−	0.439218i	$-0.855256\pi$
$743$	2.61793	−	14.8470i	0.0960424	−	0.544684i	0.994423	−	0.105466i	$-0.0336333\pi$
$744$		0			0
$745$	−5.34477	−	1.94534i	−0.195817	−	0.0712716i
$746$	24.3285	−	8.85484i	0.890728	−	0.324199i
$747$		0			0
$748$	1.20574	+	2.08840i	0.0440861	+	0.0763594i
$749$	0.0393628	−	0.0681784i	0.00143829	−	0.00249119i
$750$		0			0
$751$	−0.921274	−	5.22481i	−0.0336178	−	0.190656i	0.963374	−	0.268161i	$-0.0864158\pi$
$751$	−0.921274	−	5.22481i	−0.0336178	−	0.190656i	−0.996992	+	0.0775048i	$0.975305\pi$
$752$	2.79813	−	4.84651i	0.102037	−	0.176734i
$753$		0			0
$754$	8.04576	−	6.75119i	0.293009	−	0.245864i
$755$	−64.2825	+	23.3969i	−2.33948	+	0.851500i
$756$		0			0
$757$	6.23442	+	5.23130i	0.226594	+	0.190135i	0.749016	−	0.662552i	$-0.230527\pi$
$757$	6.23442	+	5.23130i	0.226594	+	0.190135i	−0.522422	+	0.852687i	$0.674971\pi$
$758$	−3.32635	+	18.8647i	−0.120819	+	0.685196i
$759$		0			0
$760$	9.47431	+	11.4613i	0.343669	+	0.415747i
$761$	46.2113			1.67516			0.837579	−	0.546316i	$-0.183970\pi$
$761$	46.2113			1.67516			0.837579	+	0.546316i	$0.183970\pi$
$762$		0			0
$763$	23.7631	+	19.9396i	0.860282	+	0.721863i
$764$	10.1356	+	3.68907i	0.366694	+	0.133466i
$765$		0			0
$766$	7.42649	−	6.23156i	0.268330	−	0.225156i
$767$	−0.368241	−	0.637812i	−0.0132964	−	0.0230301i
$768$		0			0
$769$	−4.66132	−	26.4357i	−0.168092	−	0.953295i	−0.945819	−	0.324693i	$-0.894739\pi$
$769$	−4.66132	−	26.4357i	−0.168092	−	0.953295i	0.777728	−	0.628601i	$-0.216372\pi$
$770$	−0.592396	−	3.35965i	−0.0213485	−	0.121073i
$771$		0			0
$772$	1.43242	+	2.48102i	0.0515539	+	0.0892939i
$773$	16.1065	−	13.5150i	0.579312	−	0.486100i	−0.305409	−	0.952221i	$-0.598793\pi$
$773$	16.1065	−	13.5150i	0.579312	−	0.486100i	0.884721	+	0.466121i	$0.154349\pi$
$774$		0			0
$775$	−9.95723	−	3.62414i	−0.357674	−	0.130183i
$776$	2.79813	+	2.34791i	0.100447	+	0.0842852i
$777$		0			0
$778$	0.817896			0.0293230
$779$	−15.0013	+	2.53142i	−0.537479	+	0.0906974i
$780$		0			0
$781$	1.00253	−	5.68561i	0.0358732	−	0.203447i
$782$	36.1732	+	30.3530i	1.29355	+	1.08542i
$783$		0			0
$784$	−1.21301	+	0.441500i	−0.0433218	+	0.0157679i
$785$	−10.7103	+	8.98703i	−0.382268	+	0.320761i
$786$		0			0
$787$	−22.7656	+	39.4312i	−0.811507	+	1.40557i	0.100302	+	0.994957i	$0.468019\pi$
$787$	−22.7656	+	39.4312i	−0.811507	+	1.40557i	−0.911809	+	0.410615i	$0.865314\pi$
$788$	1.44743	+	8.20880i	0.0515627	+	0.292426i
$789$		0			0
$790$	18.6334	−	32.2740i	0.662947	−	1.14826i
$791$	16.7875	+	29.0767i	0.596893	+	1.03385i
$792$		0			0
$793$	−19.4628	+	7.08386i	−0.691143	+	0.251555i
$794$	3.47431	+	1.26454i	0.123299	+	0.0448770i
$795$		0			0
$796$	−0.526874	+	2.98805i	−0.0186746	+	0.105909i
$797$	−36.1780			−1.28149			−0.640745	−	0.767754i	$-0.721374\pi$
$797$	−36.1780			−1.28149			−0.640745	+	0.767754i	$0.721374\pi$
$798$		0			0
$799$	38.8580			1.37470
$800$	1.15270	−	6.53731i	0.0407542	−	0.231129i
$801$		0			0
$802$	−20.4290	−	7.43555i	−0.721374	−	0.262559i
$803$	−4.05303	+	1.47518i	−0.143028	+	0.0520581i
$804$		0			0
$805$	−33.4013	−	57.8527i	−1.17724	−	2.03904i
$806$	1.31908	−	2.28471i	0.0464625	−	0.0804755i
$807$		0			0
$808$	1.72028	+	9.75622i	0.0605194	+	0.343223i
$809$	1.18938	−	2.06006i	0.0418163	−	0.0724280i	−0.844360	−	0.535777i	$-0.820019\pi$
$809$	1.18938	−	2.06006i	0.0418163	−	0.0724280i	0.886176	+	0.463349i	$0.153352\pi$
$810$		0			0
$811$	−28.3904	+	23.8223i	−0.996921	+	0.836516i	−0.986555	−	0.163431i	$-0.947744\pi$
$811$	−28.3904	+	23.8223i	−0.996921	+	0.836516i	−0.0103658	+	0.999946i	$0.503300\pi$
$812$	−17.1951	+	6.25849i	−0.603428	+	0.219630i
$813$		0			0
$814$	−2.98293	−	2.50297i	−0.104551	−	0.0877291i
$815$	−4.81924	+	27.3313i	−0.168811	+	0.957373i
$816$		0			0
$817$	3.47250	−	9.32640i	0.121487	−	0.326289i
$818$	−4.05468			−0.141769
$819$		0			0
$820$	9.12108	+	7.65350i	0.318522	+	0.267272i
$821$	−24.3949	−	8.87901i	−0.851387	−	0.309879i	−0.120781	−	0.992679i	$-0.538540\pi$
$821$	−24.3949	−	8.87901i	−0.851387	−	0.309879i	−0.730606	+	0.682800i	$0.760762\pi$
$822$		0			0
$823$	−34.4805	+	28.9325i	−1.20191	+	1.00852i	−0.202340	+	0.979315i	$0.564855\pi$
$823$	−34.4805	+	28.9325i	−1.20191	+	1.00852i	−0.999573	+	0.0292095i	$0.990701\pi$
$824$	−3.92262	−	6.79417i	−0.136651	−	0.236686i
$825$		0			0
$826$	0.222811	+	1.26363i	0.00775259	+	0.0439671i
$827$	2.92473	+	16.5870i	0.101703	+	0.576786i	0.992486	+	0.122358i	$0.0390455\pi$
$827$	2.92473	+	16.5870i	0.101703	+	0.576786i	−0.890783	+	0.454429i	$0.849843\pi$
$828$		0			0
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	0.956545	−	0.291583i	$-0.0941820\pi$
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	−0.730791	+	0.682601i	$0.760849\pi$
$830$	−30.6202	+	25.6934i	−1.06284	+	0.891831i
$831$		0			0
$832$	1.55303	+	0.565258i	0.0538417	+	0.0195968i
$833$	−6.86618	−	5.76141i	−0.237899	−	0.199621i
$834$		0			0
$835$	45.7033			1.58163
$836$	−0.0111444	+	1.51379i	−0.000385436	+	0.0523555i
$837$		0			0
$838$	−4.08054	+	23.1419i	−0.140960	+	0.799423i
$839$	−1.02687	−	0.861650i	−0.0354516	−	0.0297475i	0.624890	−	0.780713i	$-0.285144\pi$
$839$	−1.02687	−	0.861650i	−0.0354516	−	0.0297475i	−0.660341	+	0.750966i	$0.729588\pi$
$840$		0			0
$841$	−10.6998	+	3.89441i	−0.368959	+	0.134290i
$842$	−17.6748	+	14.8309i	−0.609115	+	0.511108i
$843$		0			0
$844$	8.31908	−	14.4091i	0.286354	−	0.495980i
$845$	−6.08306	−	34.4988i	−0.209264	−	1.18679i
$846$		0			0
$847$	−15.6630	+	27.1291i	−0.538186	+	0.932166i
$848$	0.990200	+	1.71508i	0.0340036	+	0.0588960i
$849$		0			0
$850$	43.3127	−	15.7645i	1.48561	−	0.540720i
$851$	−71.6515	−	26.0790i	−2.45618	−	0.893977i
$852$		0			0
$853$	−1.37969	+	7.82461i	−0.0472397	+	0.267910i	−0.999275	−	0.0380795i	$-0.987876\pi$
$853$	−1.37969	+	7.82461i	−0.0472397	+	0.267910i	0.952035	+	0.305989i	$0.0989871\pi$
$854$	36.0847			1.23479
$855$		0			0
$856$	0.0273411			0.000934501
$857$	−8.31356	+	47.1485i	−0.283986	+	1.61056i	0.424900	+	0.905240i	$0.360309\pi$
$857$	−8.31356	+	47.1485i	−0.283986	+	1.61056i	−0.708886	+	0.705323i	$0.750802\pi$
$858$		0			0
$859$	−1.53849	−	0.559963i	−0.0524924	−	0.0191057i	0.315640	−	0.948879i	$-0.397781\pi$
$859$	−1.53849	−	0.559963i	−0.0524924	−	0.0191057i	−0.368133	+	0.929773i	$0.620003\pi$
$860$	−7.31908	+	2.66393i	−0.249578	+	0.0908391i
$861$		0			0
$862$	−1.75743	−	3.04395i	−0.0598582	−	0.103677i
$863$	17.4616	−	30.2443i	0.594399	−	1.02953i	−0.399233	−	0.916850i	$-0.630723\pi$
$863$	17.4616	−	30.2443i	0.594399	−	1.02953i	0.993631	−	0.112679i	$-0.0359432\pi$
$864$		0			0
$865$	0.605600	+	3.43453i	0.0205910	+	0.116777i
$866$	17.0574	−	29.5442i	0.579633	−	1.00395i
$867$		0			0
$868$	−3.52094	+	2.95442i	−0.119509	+	0.100280i
$869$	3.56506	−	1.29757i	0.120936	−	0.0440172i
$870$		0			0
$871$	1.36571	+	1.14597i	0.0462755	+	0.0388297i
$872$	−1.87077	+	10.6096i	−0.0633522	+	0.359288i
$873$		0			0
$874$	9.93330	+	27.9296i	0.335999	+	0.944731i
$875$	−16.0915			−0.543993
$876$		0			0
$877$	−4.88120	−	4.09581i	−0.164826	−	0.138306i	0.556644	−	0.830751i	$-0.312089\pi$
$877$	−4.88120	−	4.09581i	−0.164826	−	0.138306i	−0.721470	+	0.692446i	$0.756533\pi$
$878$	−9.11633	−	3.31807i	−0.307661	−	0.111980i
$879$		0			0
$880$	0.907604	−	0.761570i	0.0305953	−	0.0256725i
$881$	2.63697	+	4.56737i	0.0888419	+	0.153879i	0.907022	−	0.421084i	$-0.138350\pi$
$881$	2.63697	+	4.56737i	0.0888419	+	0.153879i	−0.818180	+	0.574962i	$0.805017\pi$
$882$		0			0
$883$	−0.564588	−	3.20194i	−0.0189999	−	0.107754i	0.973833	−	0.227265i	$-0.0729784\pi$
$883$	−0.564588	−	3.20194i	−0.0189999	−	0.107754i	−0.992833	+	0.119511i	$0.961867\pi$
$884$	1.99273	+	11.3013i	0.0670226	+	0.380104i
$885$		0			0
$886$	7.59105	+	13.1481i	0.255026	+	0.441719i
$887$	17.1368	−	14.3795i	0.575398	−	0.482816i	−0.308034	−	0.951375i	$-0.599671\pi$
$887$	17.1368	−	14.3795i	0.575398	−	0.482816i	0.883432	+	0.468559i	$0.155227\pi$
$888$		0			0
$889$	43.8658	+	15.9658i	1.47121	+	0.535477i
$890$	−4.68551	−	3.93161i	−0.157059	−	0.131788i
$891$		0			0
$892$	−8.17024			−0.273560
$893$	21.0351	+	12.3520i	0.703912	+	0.413343i
$894$		0			0
$895$	−1.20557	+	6.83716i	−0.0402979	+	0.228541i
$896$	−2.20574	−	1.85083i	−0.0736885	−	0.0618320i
$897$		0			0
$898$	32.7374	−	11.9154i	1.09246	−	0.397624i
$899$	−7.77101	+	6.52065i	−0.259178	+	0.217476i
$900$		0			0
$901$	−6.87551	+	11.9087i	−0.229057	+	0.396738i
$902$	0.210485	+	1.19372i	0.00700838	+	0.0397465i
$903$		0			0
$904$	−5.83022	+	10.0982i	−0.193910	+	0.335863i
$905$	−38.0442	−	65.8944i	−1.26463	−	2.19040i
$906$		0			0
$907$	−2.96703	+	1.07991i	−0.0985187	+	0.0358579i	−0.390809	−	0.920472i	$-0.627805\pi$
$907$	−2.96703	+	1.07991i	−0.0985187	+	0.0358579i	0.292291	+	0.956330i	$0.405583\pi$
$908$	1.69207	+	0.615862i	0.0561532	+	0.0204381i
$909$		0			0
$910$	2.81908	−	15.9878i	0.0934515	−	0.529990i
$911$	44.3387			1.46901			0.734504	−	0.678604i	$-0.237415\pi$
$911$	44.3387			1.46901			0.734504	+	0.678604i	$0.237415\pi$
$912$		0			0
$913$	−4.06923			−0.134672
$914$	−5.53503	+	31.3907i	−0.183082	+	1.03831i
$915$		0			0
$916$	17.6091	+	6.40917i	0.581820	+	0.211765i
$917$	7.57785	−	2.75811i	0.250243	−	0.0910809i
$918$		0			0
$919$	−7.10220	−	12.3014i	−0.234280	−	0.405785i	0.724783	−	0.688977i	$-0.241940\pi$
$919$	−7.10220	−	12.3014i	−0.234280	−	0.405785i	−0.959063	+	0.283192i	$0.908607\pi$
$920$	11.6001	−	20.0920i	0.382445	−	0.662415i
$921$		0			0
$922$	1.85622	+	10.5271i	0.0611313	+	0.346693i
$923$	13.7369	−	23.7931i	0.452157	−	0.783159i
$924$		0			0
$925$	−57.0151	+	47.8413i	−1.87464	+	1.57301i
$926$	−14.3944	+	5.23913i	−0.473029	+	0.172169i
$927$		0			0
$928$	−4.86824	−	4.08494i	−0.159808	−	0.134095i
$929$	2.67881	−	15.1923i	0.0878888	−	0.498442i	−0.908807	−	0.417217i	$-0.863006\pi$
$929$	2.67881	−	15.1923i	0.0878888	−	0.498442i	0.996696	−	0.0812253i	$-0.0258833\pi$
$930$		0			0
$931$	−1.88548	−	5.30142i	−0.0617940	−	0.173747i
$932$	4.09833			0.134245
$933$		0			0
$934$	−21.8418	−	18.3275i	−0.714687	−	0.599693i
$935$	7.73055	+	2.81369i	0.252816	+	0.0920175i
$936$		0			0
$937$	−7.42830	+	6.23308i	−0.242672	+	0.203626i	−0.756009	−	0.654561i	$-0.772853\pi$
$937$	−7.42830	+	6.23308i	−0.242672	+	0.203626i	0.513337	+	0.858187i	$0.328409\pi$
$938$	−1.55303	−	2.68993i	−0.0507083	−	0.0878294i
$939$		0			0
$940$	−3.31521	−	18.8015i	−0.108130	−	0.613237i
$941$	3.12314	+	17.7122i	0.101811	+	0.577402i	0.992446	+	0.122682i	$0.0391495\pi$
$941$	3.12314	+	17.7122i	0.101811	+	0.577402i	−0.890635	+	0.454720i	$0.849739\pi$
$942$		0			0
$943$	11.8678	+	20.5557i	0.386470	+	0.669385i
$944$	−0.341367	+	0.286441i	−0.0111105	+	0.00932285i
$945$		0			0
$946$	−0.745100	−	0.271194i	−0.0242253	−	0.00881728i
$947$	−1.68067	−	1.41025i	−0.0546146	−	0.0458271i	0.615072	−	0.788471i	$-0.289127\pi$
$947$	−1.68067	−	1.41025i	−0.0546146	−	0.0458271i	−0.669686	+	0.742644i	$0.733571\pi$
$948$		0			0
$949$	−20.5253			−0.666279
$950$	28.4577	+	5.23416i	0.923290	+	0.169818i
$951$		0			0
$952$	3.47178	−	19.6895i	0.112521	−	0.638139i
$953$	8.66456	+	7.27043i	0.280673	+	0.235512i	0.772246	−	0.635324i	$-0.219133\pi$
$953$	8.66456	+	7.27043i	0.280673	+	0.235512i	−0.491573	+	0.870836i	$0.663578\pi$
$954$		0			0
$955$	34.5774	−	12.5852i	1.11890	−	0.407246i
$956$	21.6236	−	18.1444i	0.699357	−	0.586831i
$957$		0			0
$958$	4.02569	−	6.97270i	0.130064	−	0.225278i
$959$	8.01754	+	45.4697i	0.258900	+	1.46829i
$960$		0			0
$961$	14.2260	−	24.6401i	0.458902	−	0.794842i
$962$	−9.26517	−	16.0477i	−0.298721	−	0.517400i
$963$		0			0
$964$	−6.16637	+	2.24438i	−0.198606	+	0.0722865i
$965$	9.18392	+	3.34267i	0.295641	+	0.107604i
$966$		0			0
$967$	8.12402	−	46.0736i	0.261251	−	1.48163i	−0.518252	−	0.855228i	$-0.673417\pi$
$967$	8.12402	−	46.0736i	0.261251	−	1.48163i	0.779503	−	0.626399i	$-0.215472\pi$
$968$	−10.8794			−0.349677
$969$		0			0
$970$	12.4611			0.400102
$971$	−10.4834	+	59.4543i	−0.336428	+	1.90798i	0.0762258	+	0.997091i	$0.475713\pi$
$971$	−10.4834	+	59.4543i	−0.336428	+	1.90798i	−0.412654	+	0.910888i	$0.635398\pi$
$972$		0			0
$973$	−5.62449	−	2.04715i	−0.180313	−	0.0656285i
$974$	−5.74675	+	2.09165i	−0.184138	+	0.0670206i
$975$		0			0
$976$	6.26604	+	10.8531i	0.200571	+	0.347400i
$977$	11.3978	−	19.7416i	0.364648	−	0.631589i	−0.624072	−	0.781367i	$-0.714523\pi$
$977$	11.3978	−	19.7416i	0.364648	−	0.631589i	0.988720	+	0.149778i	$0.0478560\pi$
$978$		0			0
$979$	−0.108126	−	0.613214i	−0.00345573	−	0.0195984i
$980$	−2.20187	+	3.81374i	−0.0703361	+	0.121826i
$981$		0			0
$982$	17.3778	−	14.5817i	0.554548	−	0.465321i
$983$	−28.9359	+	10.5318i	−0.922911	+	0.335912i	−0.759396	−	0.650629i	$-0.774505\pi$
$983$	−28.9359	+	10.5318i	−0.922911	+	0.335912i	−0.163515	+	0.986541i	$0.552283\pi$
$984$		0			0
$985$	21.7833	+	18.2784i	0.694075	+	0.582398i
$986$	7.66250	−	43.4562i	0.244024	−	1.38393i
$987$		0			0
$988$	−2.51367	+	6.75119i	−0.0799705	+	0.214784i
$989$	−15.5267			−0.493721
$990$		0			0
$991$	−29.2467	−	24.5409i	−0.929054	−	0.779569i	0.0465937	−	0.998914i	$-0.485163\pi$
$991$	−29.2467	−	24.5409i	−0.929054	−	0.779569i	−0.975647	+	0.219345i	$0.929608\pi$
$992$	−1.50000	−	0.545955i	−0.0476250	−	0.0173341i
$993$		0			0
$994$	−36.6673	+	30.7675i	−1.16302	+	0.975887i
$995$	5.17546	+	8.96416i	0.164073	+	0.284183i
$996$		0			0
$997$	5.37423	+	30.4788i	0.170203	+	0.965272i	0.943536	+	0.331271i	$0.107477\pi$
$997$	5.37423	+	30.4788i	0.170203	+	0.965272i	−0.773332	+	0.634001i	$0.781411\pi$
$998$	4.31614	+	24.4781i	0.136625	+	0.774839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.a.55.1		6
3.2	odd	2		114.2.i.d.55.1	✓	6
12.11	even	2		912.2.bo.f.625.1		6
19.3	odd	18		6498.2.a.bn.1.3		3
19.9	even	9	inner	342.2.u.a.199.1		6
19.16	even	9		6498.2.a.bs.1.3		3
57.35	odd	18		2166.2.a.o.1.1		3
57.41	even	18		2166.2.a.u.1.1		3
57.47	odd	18		114.2.i.d.85.1	yes	6
228.47	even	18		912.2.bo.f.769.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.55.1	✓	6	3.2	odd	2
114.2.i.d.85.1	yes	6	57.47	odd	18
342.2.u.a.55.1		6	1.1	even	1	trivial
342.2.u.a.199.1		6	19.9	even	9	inner
912.2.bo.f.625.1		6	12.11	even	2
912.2.bo.f.769.1		6	228.47	even	18
2166.2.a.o.1.1		3	57.35	odd	18
2166.2.a.u.1.1		3	57.41	even	18
6498.2.a.bn.1.3		3	19.3	odd	18
6498.2.a.bs.1.3		3	19.16	even	9

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-3.20574 + 1.16679i) q^{5} +(1.43969 + 2.49362i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(-3.20574 + 1.16679i) q^{5} +(1.43969 + 2.49362i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.592396 + 3.35965i) q^{10} +(-0.173648 + 0.300767i) q^{11} +(-1.26604 + 1.06234i) q^{13} +(2.70574 - 0.984808i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.20574 + 6.83807i) q^{17} +(-2.82635 + 3.31839i) q^{19} +3.41147 q^{20} +(0.266044 + 0.223238i) q^{22} +(6.39053 + 2.32596i) q^{23} +(5.08512 - 4.26692i) q^{25} +(0.826352 + 1.43128i) q^{26} +(-0.500000 - 2.83564i) q^{28} +(-1.10354 - 6.25849i) q^{29} +(-0.798133 - 1.38241i) q^{31} +(0.766044 - 0.642788i) q^{32} +(6.52481 + 2.37484i) q^{34} +(-7.52481 - 6.31407i) q^{35} -11.2121 q^{37} +(2.77719 + 3.35965i) q^{38} +(0.592396 - 3.35965i) q^{40} +(2.67365 + 2.24346i) q^{41} +(-2.14543 + 0.780873i) q^{43} +(0.266044 - 0.223238i) q^{44} +(3.40033 - 5.88954i) q^{46} +(-0.971782 - 5.51125i) q^{47} +(-0.645430 + 1.11792i) q^{49} +(-3.31908 - 5.74881i) q^{50} +(1.55303 - 0.565258i) q^{52} +(1.86097 + 0.677337i) q^{53} +(0.205737 - 1.16679i) q^{55} -2.87939 q^{56} -6.35504 q^{58} +(-0.0773815 + 0.438852i) q^{59} +(11.7763 + 4.28623i) q^{61} +(-1.50000 + 0.545955i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(2.81908 - 4.88279i) q^{65} +(-0.187319 - 1.06234i) q^{67} +(3.47178 - 6.01330i) q^{68} +(-7.52481 + 6.31407i) q^{70} +(-15.6211 + 5.68561i) q^{71} +(9.51367 + 7.98292i) q^{73} +(-1.94697 + 11.0418i) q^{74} +(3.79086 - 2.15160i) q^{76} -1.00000 q^{77} +(-8.36824 - 7.02179i) q^{79} +(-3.20574 - 1.16679i) q^{80} +(2.67365 - 2.24346i) q^{82} +(5.85844 + 10.1471i) q^{83} +(-4.11334 - 23.3279i) q^{85} +(0.396459 + 2.24843i) q^{86} +(-0.173648 - 0.300767i) q^{88} +(-1.37346 + 1.15247i) q^{89} +(-4.47178 - 1.62760i) q^{91} +(-5.20961 - 4.37138i) q^{92} -5.59627 q^{94} +(5.18866 - 13.9357i) q^{95} +(0.634285 - 3.59721i) q^{97} +(0.988856 + 0.829748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8	\( 6 q - 9 q^{5} + 3 q^{7} - 3 q^{8} - 3 q^{13} + 6 q^{14} + 3 q^{17} - 18 q^{19} - 3 q^{22} + 21 q^{23} + 9 q^{25} + 6 q^{26} - 3 q^{28} + 3 q^{29} + 9 q^{31} + 12 q^{34} - 18 q^{35} - 18 q^{37} + 6 q^{38} + 15 q^{41} + 3 q^{43} - 3 q^{44} + 6 q^{46} + 9 q^{47} + 12 q^{49} - 3 q^{50} - 3 q^{52} - 12 q^{53} - 9 q^{55} - 6 q^{56} + 12 q^{58} - 27 q^{59} + 3 q^{61} - 9 q^{62} - 3 q^{64} + 21 q^{67} + 6 q^{68} - 18 q^{70} - 39 q^{71} + 36 q^{73} - 24 q^{74} - 9 q^{76} - 6 q^{77} - 45 q^{79} - 9 q^{80} + 15 q^{82} + 27 q^{83} - 18 q^{85} + 12 q^{86} + 30 q^{89} - 12 q^{91} + 3 q^{92} - 6 q^{94} - 6 q^{97} + 12 q^{98}+O(q^{100}) \) 6 * q - 9 * q^5 + 3 * q^7 - 3 * q^8 - 3 * q^13 + 6 * q^14 + 3 * q^17 - 18 * q^19 - 3 * q^22 + 21 * q^23 + 9 * q^25 + 6 * q^26 - 3 * q^28 + 3 * q^29 + 9 * q^31 + 12 * q^34 - 18 * q^35 - 18 * q^37 + 6 * q^38 + 15 * q^41 + 3 * q^43 - 3 * q^44 + 6 * q^46 + 9 * q^47 + 12 * q^49 - 3 * q^50 - 3 * q^52 - 12 * q^53 - 9 * q^55 - 6 * q^56 + 12 * q^58 - 27 * q^59 + 3 * q^61 - 9 * q^62 - 3 * q^64 + 21 * q^67 + 6 * q^68 - 18 * q^70 - 39 * q^71 + 36 * q^73 - 24 * q^74 - 9 * q^76 - 6 * q^77 - 45 * q^79 - 9 * q^80 + 15 * q^82 + 27 * q^83 - 18 * q^85 + 12 * q^86 + 30 * q^89 - 12 * q^91 + 3 * q^92 - 6 * q^94 - 6 * q^97 + 12 * q^98

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