LMFDB - Embedded newform 490.2.c.d.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(99,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("490.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.2.c.d.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{8} +3.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} +3.00000 q^{11} +5.00000i q^{13} +1.00000 q^{16} -2.00000i q^{17} -3.00000i q^{18} -5.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -3.00000i q^{22} -7.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +5.00000 q^{26} +4.00000 q^{29} +2.00000 q^{31} -1.00000i q^{32} -2.00000 q^{34} -3.00000 q^{36} -1.00000i q^{37} +5.00000i q^{38} +(1.00000 + 2.00000i) q^{40} -3.00000 q^{41} +2.00000i q^{43} -3.00000 q^{44} +(6.00000 - 3.00000i) q^{45} -7.00000 q^{46} -7.00000i q^{47} +(-4.00000 - 3.00000i) q^{50} -5.00000i q^{52} +9.00000i q^{53} +(6.00000 - 3.00000i) q^{55} -4.00000i q^{58} -4.00000 q^{59} -6.00000 q^{61} -2.00000i q^{62} -1.00000 q^{64} +(5.00000 + 10.0000i) q^{65} -2.00000i q^{67} +2.00000i q^{68} -6.00000 q^{71} +3.00000i q^{72} +16.0000i q^{73} -1.00000 q^{74} +5.00000 q^{76} -14.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +9.00000 q^{81} +3.00000i q^{82} +6.00000i q^{83} +(-2.00000 - 4.00000i) q^{85} +2.00000 q^{86} +3.00000i q^{88} +2.00000 q^{89} +(-3.00000 - 6.00000i) q^{90} +7.00000i q^{92} -7.00000 q^{94} +(-10.0000 + 5.00000i) q^{95} -12.0000i q^{97} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 4 * q^5 + 6 * q^9	$ 2 q - 2 q^{4} + 4 q^{5} + 6 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{16} - 10 q^{19} - 4 q^{20} + 6 q^{25} + 10 q^{26} + 8 q^{29} + 4 q^{31} - 4 q^{34} - 6 q^{36} + 2 q^{40} - 6 q^{41} - 6 q^{44} + 12 q^{45} - 14 q^{46} - 8 q^{50} + 12 q^{55} - 8 q^{59} - 12 q^{61} - 2 q^{64} + 10 q^{65} - 12 q^{71} - 2 q^{74} + 10 q^{76} - 28 q^{79} + 4 q^{80} + 18 q^{81} - 4 q^{85} + 4 q^{86} + 4 q^{89} - 6 q^{90} - 14 q^{94} - 20 q^{95} + 18 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 6 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^16 - 10 * q^19 - 4 * q^20 + 6 * q^25 + 10 * q^26 + 8 * q^29 + 4 * q^31 - 4 * q^34 - 6 * q^36 + 2 * q^40 - 6 * q^41 - 6 * q^44 + 12 * q^45 - 14 * q^46 - 8 * q^50 + 12 * q^55 - 8 * q^59 - 12 * q^61 - 2 * q^64 + 10 * q^65 - 12 * q^71 - 2 * q^74 + 10 * q^76 - 28 * q^79 + 4 * q^80 + 18 * q^81 - 4 * q^85 + 4 * q^86 + 4 * q^89 - 6 * q^90 - 14 * q^94 - 20 * q^95 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	−1.00000			−0.500000
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	3.00000			1.00000
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		−	3.00000i		−	0.707107i
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	−2.00000	+	1.00000i	−0.447214	+	0.223607i
$21$		0			0
$22$		−	3.00000i		−	0.639602i
$23$		−	7.00000i		−	1.45960i	−0.683660	−	0.729800i	$-0.739613\pi$
$23$		−	7.00000i		−	1.45960i	0.683660	−	0.729800i	$-0.260387\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	5.00000			0.980581
$27$		0			0
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−3.00000			−0.500000
$37$		−	1.00000i		−	0.164399i	−0.996616	−	0.0821995i	$-0.973806\pi$
$37$		−	1.00000i		−	0.164399i	0.996616	−	0.0821995i	$-0.0261945\pi$
$38$			5.00000i			0.811107i
$39$		0			0
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−3.00000			−0.452267
$45$	6.00000	−	3.00000i	0.894427	−	0.447214i
$46$	−7.00000			−1.03209
$47$		−	7.00000i		−	1.02105i	−0.859861	−	0.510527i	$-0.829450\pi$
$47$		−	7.00000i		−	1.02105i	0.859861	−	0.510527i	$-0.170550\pi$
$48$		0			0
$49$		0			0
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$		−	5.00000i		−	0.693375i
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$	6.00000	−	3.00000i	0.809040	−	0.404520i
$56$		0			0
$57$		0			0
$58$		−	4.00000i		−	0.525226i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$		−	2.00000i		−	0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.00000	+	10.0000i	0.620174	+	1.24035i
$66$		0			0
$67$		−	2.00000i		−	0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$		−	2.00000i		−	0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$			2.00000i			0.242536i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$			3.00000i			0.353553i
$73$			16.0000i			1.87266i	0.351123	+	0.936329i	$0.385800\pi$
$73$			16.0000i			1.87266i	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	5.00000			0.573539
$77$		0			0
$78$		0			0
$79$	−14.0000			−1.57512			−0.787562	−	0.616236i	$-0.788657\pi$
$79$	−14.0000			−1.57512			−0.787562	+	0.616236i	$0.788657\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$	9.00000			1.00000
$82$			3.00000i			0.331295i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		0			0
$85$	−2.00000	−	4.00000i	−0.216930	−	0.433861i
$86$	2.00000			0.215666
$87$		0			0
$88$			3.00000i			0.319801i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−3.00000	−	6.00000i	−0.316228	−	0.632456i
$91$		0			0
$92$			7.00000i			0.729800i
$93$		0			0
$94$	−7.00000			−0.721995
$95$	−10.0000	+	5.00000i	−1.02598	+	0.512989i
$96$		0			0
$97$		−	12.0000i		−	1.21842i	−0.793011	−	0.609208i	$-0.791488\pi$
$97$		−	12.0000i		−	1.21842i	0.793011	−	0.609208i	$-0.208512\pi$
$98$		0			0
$99$	9.00000			0.904534
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			8.00000i			0.788263i	0.919054	+	0.394132i	$0.128955\pi$
$103$			8.00000i			0.788263i	−0.919054	+	0.394132i	$0.871045\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	9.00000			0.874157
$107$			16.0000i			1.54678i	0.633932	+	0.773389i	$0.281440\pi$
$107$			16.0000i			1.54678i	−0.633932	+	0.773389i	$0.718560\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−3.00000	−	6.00000i	−0.286039	−	0.572078i
$111$		0			0
$112$		0			0
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−7.00000	−	14.0000i	−0.652753	−	1.30551i
$116$	−4.00000			−0.371391
$117$			15.0000i			1.38675i
$118$			4.00000i			0.368230i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$			6.00000i			0.543214i
$123$		0			0
$124$	−2.00000			−0.179605
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		−	7.00000i		−	0.621150i	−0.950549	−	0.310575i	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	10.0000	−	5.00000i	0.877058	−	0.438529i
$131$	1.00000			0.0873704			0.0436852	−	0.999045i	$-0.486090\pi$
$131$	1.00000			0.0873704			0.0436852	+	0.999045i	$0.486090\pi$
$132$		0			0
$133$		0			0
$134$	−2.00000			−0.172774
$135$		0			0
$136$	2.00000			0.171499
$137$			8.00000i			0.683486i	0.939793	+	0.341743i	$0.111017\pi$
$137$			8.00000i			0.683486i	−0.939793	+	0.341743i	$0.888983\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$			6.00000i			0.503509i
$143$			15.0000i			1.25436i
$144$	3.00000			0.250000
$145$	8.00000	−	4.00000i	0.664364	−	0.332182i
$146$	16.0000			1.32417
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$		−	5.00000i		−	0.405554i
$153$		−	6.00000i		−	0.485071i
$154$		0			0
$155$	4.00000	−	2.00000i	0.321288	−	0.160644i
$156$		0			0
$157$		−	9.00000i		−	0.718278i	−0.933284	−	0.359139i	$-0.883070\pi$
$157$		−	9.00000i		−	0.718278i	0.933284	−	0.359139i	$-0.116930\pi$
$158$			14.0000i			1.11378i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		0			0
$162$		−	9.00000i		−	0.707107i
$163$		−	12.0000i		−	0.939913i	−0.882690	−	0.469956i	$-0.844270\pi$
$163$		−	12.0000i		−	0.939913i	0.882690	−	0.469956i	$-0.155730\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	6.00000			0.465690
$167$			15.0000i			1.16073i	0.814355	+	0.580367i	$0.197091\pi$
$167$			15.0000i			1.16073i	−0.814355	+	0.580367i	$0.802909\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−4.00000	+	2.00000i	−0.306786	+	0.153393i
$171$	−15.0000			−1.14708
$172$		−	2.00000i		−	0.152499i
$173$		−	9.00000i		−	0.684257i	−0.939653	−	0.342129i	$-0.888852\pi$
$173$		−	9.00000i		−	0.684257i	0.939653	−	0.342129i	$-0.111148\pi$
$174$		0			0
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$		−	2.00000i		−	0.149906i
$179$	−13.0000			−0.971666			−0.485833	−	0.874052i	$-0.661484\pi$
$179$	−13.0000			−0.971666			−0.485833	+	0.874052i	$0.661484\pi$
$180$	−6.00000	+	3.00000i	−0.447214	+	0.223607i
$181$	−26.0000			−1.93256			−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000			−1.93256			−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$		0			0
$184$	7.00000			0.516047
$185$	−1.00000	−	2.00000i	−0.0735215	−	0.147043i
$186$		0			0
$187$		−	6.00000i		−	0.438763i
$188$			7.00000i			0.510527i
$189$		0			0
$190$	5.00000	+	10.0000i	0.362738	+	0.725476i
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$		0			0
$197$			5.00000i			0.356235i	0.984009	+	0.178118i	$0.0570008\pi$
$197$			5.00000i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$198$		−	9.00000i		−	0.639602i
$199$	18.0000			1.27599			0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000			1.27599			0.637993	+	0.770042i	$0.279765\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.00000	+	3.00000i	−0.419058	+	0.209529i
$206$	8.00000			0.557386
$207$		−	21.0000i		−	1.45960i
$208$			5.00000i			0.346688i
$209$	−15.0000			−1.03757
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$		−	9.00000i		−	0.618123i
$213$		0			0
$214$	16.0000			1.09374
$215$	2.00000	+	4.00000i	0.136399	+	0.272798i
$216$		0			0
$217$		0			0
$218$			2.00000i			0.135457i
$219$		0			0
$220$	−6.00000	+	3.00000i	−0.404520	+	0.202260i
$221$	10.0000			0.672673
$222$		0			0
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$		0			0
$225$	9.00000	−	12.0000i	0.600000	−	0.800000i
$226$	14.0000			0.931266
$227$		−	6.00000i		−	0.398234i	−0.979976	−	0.199117i	$-0.936193\pi$
$227$		−	6.00000i		−	0.398234i	0.979976	−	0.199117i	$-0.0638074\pi$
$228$		0			0
$229$	16.0000			1.05731			0.528655	−	0.848837i	$-0.322697\pi$
$229$	16.0000			1.05731			0.528655	+	0.848837i	$0.322697\pi$
$230$	−14.0000	+	7.00000i	−0.923133	+	0.461566i
$231$		0			0
$232$			4.00000i			0.262613i
$233$		−	8.00000i		−	0.524097i	−0.965055	−	0.262049i	$-0.915602\pi$
$233$		−	8.00000i		−	0.524097i	0.965055	−	0.262049i	$-0.0843981\pi$
$234$	15.0000			0.980581
$235$	−7.00000	−	14.0000i	−0.456630	−	0.913259i
$236$	4.00000			0.260378
$237$		0			0
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	9.00000			0.579741			0.289870	−	0.957066i	$-0.406388\pi$
$241$	9.00000			0.579741			0.289870	+	0.957066i	$0.406388\pi$
$242$			2.00000i			0.128565i
$243$		0			0
$244$	6.00000			0.384111
$245$		0			0
$246$		0			0
$247$		−	25.0000i		−	1.59071i
$248$			2.00000i			0.127000i
$249$		0			0
$250$	−11.0000	−	2.00000i	−0.695701	−	0.126491i
$251$	−5.00000			−0.315597			−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000			−0.315597			−0.157799	+	0.987471i	$0.550440\pi$
$252$		0			0
$253$		−	21.0000i		−	1.32026i
$254$	−7.00000			−0.439219
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	6.00000i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$257$		−	6.00000i		−	0.374270i	0.982334	−	0.187135i	$-0.0599201\pi$
$258$		0			0
$259$		0			0
$260$	−5.00000	−	10.0000i	−0.310087	−	0.620174i
$261$	12.0000			0.742781
$262$		−	1.00000i		−	0.0617802i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	9.00000	+	18.0000i	0.552866	+	1.10573i
$266$		0			0
$267$		0			0
$268$			2.00000i			0.122169i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	−24.0000			−1.45790			−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000			−1.45790			−0.728948	+	0.684569i	$0.759990\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	8.00000			0.483298
$275$	9.00000	−	12.0000i	0.542720	−	0.723627i
$276$		0			0
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$		−	16.0000i		−	0.959616i
$279$	6.00000			0.359211
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		0			0
$283$		−	14.0000i		−	0.832214i	−0.909316	−	0.416107i	$-0.863394\pi$
$283$		−	14.0000i		−	0.832214i	0.909316	−	0.416107i	$-0.136606\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	15.0000			0.886969
$287$		0			0
$288$		−	3.00000i		−	0.176777i
$289$	13.0000			0.764706
$290$	−4.00000	−	8.00000i	−0.234888	−	0.469776i
$291$		0			0
$292$		−	16.0000i		−	0.936329i
$293$			9.00000i			0.525786i	0.964825	+	0.262893i	$0.0846766\pi$
$293$			9.00000i			0.525786i	−0.964825	+	0.262893i	$0.915323\pi$
$294$		0			0
$295$	−8.00000	+	4.00000i	−0.465778	+	0.232889i
$296$	1.00000			0.0581238
$297$		0			0
$298$		−	18.0000i		−	1.04271i
$299$	35.0000			2.02410
$300$		0			0
$301$		0			0
$302$			6.00000i			0.345261i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−12.0000	+	6.00000i	−0.687118	+	0.343559i
$306$	−6.00000			−0.342997
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$		0			0
$309$		0			0
$310$	−2.00000	−	4.00000i	−0.113592	−	0.227185i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$		0			0
$313$			22.0000i			1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$313$			22.0000i			1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$314$	−9.00000			−0.507899
$315$		0			0
$316$	14.0000			0.787562
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$		0			0
$319$	12.0000			0.671871
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		0			0
$322$		0			0
$323$			10.0000i			0.556415i
$324$	−9.00000			−0.500000
$325$	20.0000	+	15.0000i	1.10940	+	0.832050i
$326$	−12.0000			−0.664619
$327$		0			0
$328$		−	3.00000i		−	0.165647i
$329$		0			0
$330$		0			0
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$		−	6.00000i		−	0.329293i
$333$		−	3.00000i		−	0.164399i
$334$	15.0000			0.820763
$335$	−2.00000	−	4.00000i	−0.109272	−	0.218543i
$336$		0			0
$337$		−	10.0000i		−	0.544735i	−0.962193	−	0.272367i	$-0.912193\pi$
$337$		−	10.0000i		−	0.544735i	0.962193	−	0.272367i	$-0.0878066\pi$
$338$			12.0000i			0.652714i
$339$		0			0
$340$	2.00000	+	4.00000i	0.108465	+	0.216930i
$341$	6.00000			0.324918
$342$			15.0000i			0.811107i
$343$		0			0
$344$	−2.00000			−0.107833
$345$		0			0
$346$	−9.00000			−0.483843
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$		0			0
$349$	−12.0000			−0.642345			−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000			−0.642345			−0.321173	+	0.947021i	$0.604077\pi$
$350$		0			0
$351$		0			0
$352$		−	3.00000i		−	0.159901i
$353$		−	24.0000i		−	1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$		−	24.0000i		−	1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$		0			0
$355$	−12.0000	+	6.00000i	−0.636894	+	0.318447i
$356$	−2.00000			−0.106000
$357$		0			0
$358$			13.0000i			0.687071i
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$	3.00000	+	6.00000i	0.158114	+	0.316228i
$361$	6.00000			0.315789
$362$			26.0000i			1.36653i
$363$		0			0
$364$		0			0
$365$	16.0000	+	32.0000i	0.837478	+	1.67496i
$366$		0			0
$367$			13.0000i			0.678594i	0.940679	+	0.339297i	$0.110189\pi$
$367$			13.0000i			0.678594i	−0.940679	+	0.339297i	$0.889811\pi$
$368$		−	7.00000i		−	0.364900i
$369$	−9.00000			−0.468521
$370$	−2.00000	+	1.00000i	−0.103975	+	0.0519875i
$371$		0			0
$372$		0			0
$373$			26.0000i			1.34623i	0.739538	+	0.673114i	$0.235044\pi$
$373$			26.0000i			1.34623i	−0.739538	+	0.673114i	$0.764956\pi$
$374$	−6.00000			−0.310253
$375$		0			0
$376$	7.00000			0.360997
$377$			20.0000i			1.03005i
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	10.0000	−	5.00000i	0.512989	−	0.256495i
$381$		0			0
$382$			20.0000i			1.02329i
$383$		−	21.0000i		−	1.07305i	−0.843884	−	0.536525i	$-0.819737\pi$
$383$		−	21.0000i		−	1.07305i	0.843884	−	0.536525i	$-0.180263\pi$
$384$		0			0
$385$		0			0
$386$	−10.0000			−0.508987
$387$			6.00000i			0.304997i
$388$			12.0000i			0.609208i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−14.0000			−0.708010
$392$		0			0
$393$		0			0
$394$	5.00000			0.251896
$395$	−28.0000	+	14.0000i	−1.40883	+	0.704416i
$396$	−9.00000			−0.452267
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$		−	18.0000i		−	0.902258i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−15.0000			−0.749064			−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000			−0.749064			−0.374532	+	0.927214i	$0.622197\pi$
$402$		0			0
$403$			10.0000i			0.498135i
$404$		0			0
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$		0			0
$407$		−	3.00000i		−	0.148704i
$408$		0			0
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	3.00000	+	6.00000i	0.148159	+	0.296319i
$411$		0			0
$412$		−	8.00000i		−	0.394132i
$413$		0			0
$414$	−21.0000			−1.03209
$415$	6.00000	+	12.0000i	0.294528	+	0.589057i
$416$	5.00000			0.245145
$417$		0			0
$418$			15.0000i			0.733674i
$419$	35.0000			1.70986			0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000			1.70986			0.854931	+	0.518742i	$0.173599\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$			9.00000i			0.438113i
$423$		−	21.0000i		−	1.02105i
$424$	−9.00000			−0.437079
$425$	−8.00000	−	6.00000i	−0.388057	−	0.291043i
$426$		0			0
$427$		0			0
$428$		−	16.0000i		−	0.773389i
$429$		0			0
$430$	4.00000	−	2.00000i	0.192897	−	0.0964486i
$431$	2.00000			0.0963366			0.0481683	−	0.998839i	$-0.484662\pi$
$431$	2.00000			0.0963366			0.0481683	+	0.998839i	$0.484662\pi$
$432$		0			0
$433$		−	28.0000i		−	1.34559i	−0.739827	−	0.672797i	$-0.765093\pi$
$433$		−	28.0000i		−	1.34559i	0.739827	−	0.672797i	$-0.234907\pi$
$434$		0			0
$435$		0			0
$436$	2.00000			0.0957826
$437$			35.0000i			1.67428i
$438$		0			0
$439$	−28.0000			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$440$	3.00000	+	6.00000i	0.143019	+	0.286039i
$441$		0			0
$442$		−	10.0000i		−	0.475651i
$443$			30.0000i			1.42534i	0.701498	+	0.712672i	$0.252515\pi$
$443$			30.0000i			1.42534i	−0.701498	+	0.712672i	$0.747485\pi$
$444$		0			0
$445$	4.00000	−	2.00000i	0.189618	−	0.0948091i
$446$	8.00000			0.378811
$447$		0			0
$448$		0			0
$449$	−5.00000			−0.235965			−0.117982	−	0.993016i	$-0.537643\pi$
$449$	−5.00000			−0.235965			−0.117982	+	0.993016i	$0.537643\pi$
$450$	−12.0000	−	9.00000i	−0.565685	−	0.424264i
$451$	−9.00000			−0.423793
$452$		−	14.0000i		−	0.658505i
$453$		0			0
$454$	−6.00000			−0.281594
$455$		0			0
$456$		0			0
$457$			10.0000i			0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$			10.0000i			0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$		−	16.0000i		−	0.747631i
$459$		0			0
$460$	7.00000	+	14.0000i	0.326377	+	0.652753i
$461$	32.0000			1.49039			0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000			1.49039			0.745194	+	0.666847i	$0.232357\pi$
$462$		0			0
$463$		−	17.0000i		−	0.790057i	−0.918669	−	0.395029i	$-0.870735\pi$
$463$		−	17.0000i		−	0.790057i	0.918669	−	0.395029i	$-0.129265\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	−8.00000			−0.370593
$467$			34.0000i			1.57333i	0.617379	+	0.786666i	$0.288195\pi$
$467$			34.0000i			1.57333i	−0.617379	+	0.786666i	$0.711805\pi$
$468$		−	15.0000i		−	0.693375i
$469$		0			0
$470$	−14.0000	+	7.00000i	−0.645772	+	0.322886i
$471$		0			0
$472$		−	4.00000i		−	0.184115i
$473$			6.00000i			0.275880i
$474$		0			0
$475$	−15.0000	+	20.0000i	−0.688247	+	0.917663i
$476$		0			0
$477$			27.0000i			1.23625i
$478$			20.0000i			0.914779i
$479$	36.0000			1.64488			0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000			1.64488			0.822441	+	0.568850i	$0.192612\pi$
$480$		0			0
$481$	5.00000			0.227980
$482$		−	9.00000i		−	0.409939i
$483$		0			0
$484$	2.00000			0.0909091
$485$	−12.0000	−	24.0000i	−0.544892	−	1.08978i
$486$		0			0
$487$			32.0000i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$			32.0000i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$		−	6.00000i		−	0.271607i
$489$		0			0
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$		0			0
$493$		−	8.00000i		−	0.360302i
$494$	−25.0000			−1.12480
$495$	18.0000	−	9.00000i	0.809040	−	0.404520i
$496$	2.00000			0.0898027
$497$		0			0
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$		0			0
$502$			5.00000i			0.223161i
$503$		−	40.0000i		−	1.78351i	−0.452517	−	0.891756i	$-0.649474\pi$
$503$		−	40.0000i		−	1.78351i	0.452517	−	0.891756i	$-0.350526\pi$
$504$		0			0
$505$		0			0
$506$	−21.0000			−0.933564
$507$		0			0
$508$			7.00000i			0.310575i
$509$	−34.0000			−1.50702			−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−6.00000			−0.264649
$515$	8.00000	+	16.0000i	0.352522	+	0.705044i
$516$		0			0
$517$		−	21.0000i		−	0.923579i
$518$		0			0
$519$		0			0
$520$	−10.0000	+	5.00000i	−0.438529	+	0.219265i
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		−	12.0000i		−	0.525226i
$523$		−	16.0000i		−	0.699631i	−0.936819	−	0.349816i	$-0.886244\pi$
$523$		−	16.0000i		−	0.699631i	0.936819	−	0.349816i	$-0.113756\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$		0			0
$527$		−	4.00000i		−	0.174243i
$528$		0			0
$529$	−26.0000			−1.13043
$530$	18.0000	−	9.00000i	0.781870	−	0.390935i
$531$	−12.0000			−0.520756
$532$		0			0
$533$		−	15.0000i		−	0.649722i
$534$		0			0
$535$	16.0000	+	32.0000i	0.691740	+	1.38348i
$536$	2.00000			0.0863868
$537$		0			0
$538$			10.0000i			0.431131i
$539$		0			0
$540$		0			0
$541$	−16.0000			−0.687894			−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000			−0.687894			−0.343947	+	0.938989i	$0.611764\pi$
$542$			24.0000i			1.03089i
$543$		0			0
$544$	−2.00000			−0.0857493
$545$	−4.00000	+	2.00000i	−0.171341	+	0.0856706i
$546$		0			0
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$		−	8.00000i		−	0.341743i
$549$	−18.0000			−0.768221
$550$	−12.0000	−	9.00000i	−0.511682	−	0.383761i
$551$	−20.0000			−0.852029
$552$		0			0
$553$		0			0
$554$	2.00000			0.0849719
$555$		0			0
$556$	−16.0000			−0.678551
$557$		−	23.0000i		−	0.974541i	−0.873251	−	0.487271i	$-0.837993\pi$
$557$		−	23.0000i		−	0.974541i	0.873251	−	0.487271i	$-0.162007\pi$
$558$		−	6.00000i		−	0.254000i
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$		−	9.00000i		−	0.379642i
$563$		−	2.00000i		−	0.0842900i	−0.999112	−	0.0421450i	$-0.986581\pi$
$563$		−	2.00000i		−	0.0842900i	0.999112	−	0.0421450i	$-0.0134191\pi$
$564$		0			0
$565$	14.0000	+	28.0000i	0.588984	+	1.17797i
$566$	−14.0000			−0.588464
$567$		0			0
$568$		−	6.00000i		−	0.251754i
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		−	15.0000i		−	0.627182i
$573$		0			0
$574$		0			0
$575$	−28.0000	−	21.0000i	−1.16768	−	0.875761i
$576$	−3.00000			−0.125000
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$		−	13.0000i		−	0.540729i
$579$		0			0
$580$	−8.00000	+	4.00000i	−0.332182	+	0.166091i
$581$		0			0
$582$		0			0
$583$			27.0000i			1.11823i
$584$	−16.0000			−0.662085
$585$	15.0000	+	30.0000i	0.620174	+	1.24035i
$586$	9.00000			0.371787
$587$			34.0000i			1.40333i	0.712507	+	0.701665i	$0.247560\pi$
$587$			34.0000i			1.40333i	−0.712507	+	0.701665i	$0.752440\pi$
$588$		0			0
$589$	−10.0000			−0.412043
$590$	4.00000	+	8.00000i	0.164677	+	0.329355i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$		−	35.0000i		−	1.43126i
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		−	6.00000i		−	0.244339i
$604$	6.00000			0.244137
$605$	−4.00000	+	2.00000i	−0.162623	+	0.0813116i
$606$		0			0
$607$		−	13.0000i		−	0.527654i	−0.964570	−	0.263827i	$-0.915015\pi$
$607$		−	13.0000i		−	0.527654i	0.964570	−	0.263827i	$-0.0849848\pi$
$608$			5.00000i			0.202777i
$609$		0			0
$610$	6.00000	+	12.0000i	0.242933	+	0.485866i
$611$	35.0000			1.41595
$612$			6.00000i			0.242536i
$613$		−	15.0000i		−	0.605844i	−0.953015	−	0.302922i	$-0.902038\pi$
$613$		−	15.0000i		−	0.605844i	0.953015	−	0.302922i	$-0.0979622\pi$
$614$	−22.0000			−0.887848
$615$		0			0
$616$		0			0
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$		0			0
$619$	19.0000			0.763674			0.381837	−	0.924230i	$-0.375291\pi$
$619$	19.0000			0.763674			0.381837	+	0.924230i	$0.375291\pi$
$620$	−4.00000	+	2.00000i	−0.160644	+	0.0803219i
$621$		0			0
$622$			6.00000i			0.240578i
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	22.0000			0.879297
$627$		0			0
$628$			9.00000i			0.359139i
$629$	−2.00000			−0.0797452
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$		−	14.0000i		−	0.556890i
$633$		0			0
$634$	2.00000			0.0794301
$635$	−7.00000	−	14.0000i	−0.277787	−	0.555573i
$636$		0			0
$637$		0			0
$638$		−	12.0000i		−	0.475085i
$639$	−18.0000			−0.712069
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	−5.00000			−0.197488			−0.0987441	−	0.995113i	$-0.531483\pi$
$641$	−5.00000			−0.197488			−0.0987441	+	0.995113i	$0.531483\pi$
$642$		0			0
$643$			14.0000i			0.552106i	0.961142	+	0.276053i	$0.0890266\pi$
$643$			14.0000i			0.552106i	−0.961142	+	0.276053i	$0.910973\pi$
$644$		0			0
$645$		0			0
$646$	10.0000			0.393445
$647$		−	27.0000i		−	1.06148i	−0.847535	−	0.530740i	$-0.821914\pi$
$647$		−	27.0000i		−	1.06148i	0.847535	−	0.530740i	$-0.178086\pi$
$648$			9.00000i			0.353553i
$649$	−12.0000			−0.471041
$650$	15.0000	−	20.0000i	0.588348	−	0.784465i
$651$		0			0
$652$			12.0000i			0.469956i
$653$			3.00000i			0.117399i	0.998276	+	0.0586995i	$0.0186954\pi$
$653$			3.00000i			0.117399i	−0.998276	+	0.0586995i	$0.981305\pi$
$654$		0			0
$655$	2.00000	−	1.00000i	0.0781465	−	0.0390732i
$656$	−3.00000			−0.117130
$657$			48.0000i			1.87266i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−16.0000			−0.622328			−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000			−0.622328			−0.311164	+	0.950356i	$0.600719\pi$
$662$		−	5.00000i		−	0.194331i
$663$		0			0
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−3.00000			−0.116248
$667$		−	28.0000i		−	1.08416i
$668$		−	15.0000i		−	0.580367i
$669$		0			0
$670$	−4.00000	+	2.00000i	−0.154533	+	0.0772667i
$671$	−18.0000			−0.694882
$672$		0			0
$673$			32.0000i			1.23351i	0.787155	+	0.616755i	$0.211553\pi$
$673$			32.0000i			1.23351i	−0.787155	+	0.616755i	$0.788447\pi$
$674$	−10.0000			−0.385186
$675$		0			0
$676$	12.0000			0.461538
$677$		−	17.0000i		−	0.653363i	−0.945134	−	0.326682i	$-0.894070\pi$
$677$		−	17.0000i		−	0.653363i	0.945134	−	0.326682i	$-0.105930\pi$
$678$		0			0
$679$		0			0
$680$	4.00000	−	2.00000i	0.153393	−	0.0766965i
$681$		0			0
$682$		−	6.00000i		−	0.229752i
$683$		−	44.0000i		−	1.68361i	−0.539779	−	0.841807i	$-0.681492\pi$
$683$		−	44.0000i		−	1.68361i	0.539779	−	0.841807i	$-0.318508\pi$
$684$	15.0000			0.573539
$685$	8.00000	+	16.0000i	0.305664	+	0.611329i
$686$		0			0
$687$		0			0
$688$			2.00000i			0.0762493i
$689$	−45.0000			−1.71436
$690$		0			0
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$			9.00000i			0.342129i
$693$		0			0
$694$	12.0000			0.455514
$695$	32.0000	−	16.0000i	1.21383	−	0.606915i
$696$		0			0
$697$			6.00000i			0.227266i
$698$			12.0000i			0.454207i
$699$		0			0
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$			5.00000i			0.188579i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$		0			0
$709$	−12.0000			−0.450669			−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000			−0.450669			−0.225335	+	0.974281i	$0.572348\pi$
$710$	6.00000	+	12.0000i	0.225176	+	0.450352i
$711$	−42.0000			−1.57512
$712$			2.00000i			0.0749532i
$713$		−	14.0000i		−	0.524304i
$714$		0			0
$715$	15.0000	+	30.0000i	0.560968	+	1.12194i
$716$	13.0000			0.485833
$717$		0			0
$718$			16.0000i			0.597115i
$719$	26.0000			0.969636			0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000			0.969636			0.484818	+	0.874615i	$0.338886\pi$
$720$	6.00000	−	3.00000i	0.223607	−	0.111803i
$721$		0			0
$722$		−	6.00000i		−	0.223297i
$723$		0			0
$724$	26.0000			0.966282
$725$	12.0000	−	16.0000i	0.445669	−	0.594225i
$726$		0			0
$727$		−	29.0000i		−	1.07555i	−0.843088	−	0.537775i	$-0.819265\pi$
$727$		−	29.0000i		−	1.07555i	0.843088	−	0.537775i	$-0.180735\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	32.0000	−	16.0000i	1.18437	−	0.592187i
$731$	4.00000			0.147945
$732$		0			0
$733$		−	41.0000i		−	1.51437i	−0.653201	−	0.757185i	$-0.726574\pi$
$733$		−	41.0000i		−	1.51437i	0.653201	−	0.757185i	$-0.273426\pi$
$734$	13.0000			0.479839
$735$		0			0
$736$	−7.00000			−0.258023
$737$		−	6.00000i		−	0.221013i
$738$			9.00000i			0.331295i
$739$	29.0000			1.06678			0.533391	−	0.845869i	$-0.320917\pi$
$739$	29.0000			1.06678			0.533391	+	0.845869i	$0.320917\pi$
$740$	1.00000	+	2.00000i	0.0367607	+	0.0735215i
$741$		0			0
$742$		0			0
$743$		−	21.0000i		−	0.770415i	−0.922830	−	0.385208i	$-0.874130\pi$
$743$		−	21.0000i		−	0.770415i	0.922830	−	0.385208i	$-0.125870\pi$
$744$		0			0
$745$	36.0000	−	18.0000i	1.31894	−	0.659469i
$746$	26.0000			0.951928
$747$			18.0000i			0.658586i
$748$			6.00000i			0.219382i
$749$		0			0
$750$		0			0
$751$	28.0000			1.02173			0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000			1.02173			0.510867	+	0.859660i	$0.329324\pi$
$752$		−	7.00000i		−	0.255264i
$753$		0			0
$754$	20.0000			0.728357
$755$	−12.0000	+	6.00000i	−0.436725	+	0.218362i
$756$		0			0
$757$		−	42.0000i		−	1.52652i	−0.646094	−	0.763258i	$-0.723599\pi$
$757$		−	42.0000i		−	1.52652i	0.646094	−	0.763258i	$-0.276401\pi$
$758$		−	29.0000i		−	1.05333i
$759$		0			0
$760$	−5.00000	−	10.0000i	−0.181369	−	0.362738i
$761$	−1.00000			−0.0362500			−0.0181250	−	0.999836i	$-0.505770\pi$
$761$	−1.00000			−0.0362500			−0.0181250	+	0.999836i	$0.505770\pi$
$762$		0			0
$763$		0			0
$764$	20.0000			0.723575
$765$	−6.00000	−	12.0000i	−0.216930	−	0.433861i
$766$	−21.0000			−0.758761
$767$		−	20.0000i		−	0.722158i
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$		0			0
$771$		0			0
$772$			10.0000i			0.359908i
$773$		−	45.0000i		−	1.61854i	−0.587439	−	0.809269i	$-0.699864\pi$
$773$		−	45.0000i		−	1.61854i	0.587439	−	0.809269i	$-0.300136\pi$
$774$	6.00000			0.215666
$775$	6.00000	−	8.00000i	0.215526	−	0.287368i
$776$	12.0000			0.430775
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$	15.0000			0.537431
$780$		0			0
$781$	−18.0000			−0.644091
$782$			14.0000i			0.500639i
$783$		0			0
$784$		0			0
$785$	−9.00000	−	18.0000i	−0.321224	−	0.642448i
$786$		0			0
$787$			18.0000i			0.641631i	0.947142	+	0.320815i	$0.103957\pi$
$787$			18.0000i			0.641631i	−0.947142	+	0.320815i	$0.896043\pi$
$788$		−	5.00000i		−	0.178118i
$789$		0			0
$790$	14.0000	+	28.0000i	0.498098	+	0.996195i
$791$		0			0
$792$			9.00000i			0.319801i
$793$		−	30.0000i		−	1.06533i
$794$	−14.0000			−0.496841
$795$		0			0
$796$	−18.0000			−0.637993
$797$		−	2.00000i		−	0.0708436i	−0.999372	−	0.0354218i	$-0.988723\pi$
$797$		−	2.00000i		−	0.0708436i	0.999372	−	0.0354218i	$-0.0112775\pi$
$798$		0			0
$799$	−14.0000			−0.495284
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	6.00000			0.212000
$802$			15.0000i			0.529668i
$803$			48.0000i			1.69388i
$804$		0			0
$805$		0			0
$806$	10.0000			0.352235
$807$		0			0
$808$		0			0
$809$	5.00000			0.175791			0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000			0.175791			0.0878953	+	0.996130i	$0.471986\pi$
$810$	−9.00000	−	18.0000i	−0.316228	−	0.632456i
$811$	33.0000			1.15879			0.579393	−	0.815048i	$-0.303290\pi$
$811$	33.0000			1.15879			0.579393	+	0.815048i	$0.303290\pi$
$812$		0			0
$813$		0			0
$814$	−3.00000			−0.105150
$815$	−12.0000	−	24.0000i	−0.420342	−	0.840683i
$816$		0			0
$817$		−	10.0000i		−	0.349856i
$818$			14.0000i			0.489499i
$819$		0			0
$820$	6.00000	−	3.00000i	0.209529	−	0.104765i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$		0			0
$823$		−	24.0000i		−	0.836587i	−0.908312	−	0.418294i	$-0.862628\pi$
$823$		−	24.0000i		−	0.836587i	0.908312	−	0.418294i	$-0.137372\pi$
$824$	−8.00000			−0.278693
$825$		0			0
$826$		0			0
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$			21.0000i			0.729800i
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$	12.0000	−	6.00000i	0.416526	−	0.208263i
$831$		0			0
$832$		−	5.00000i		−	0.173344i
$833$		0			0
$834$		0			0
$835$	15.0000	+	30.0000i	0.519096	+	1.03819i
$836$	15.0000			0.518786
$837$		0			0
$838$		−	35.0000i		−	1.20905i
$839$	−34.0000			−1.17381			−0.586905	−	0.809656i	$-0.699654\pi$
$839$	−34.0000			−1.17381			−0.586905	+	0.809656i	$0.699654\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$			20.0000i			0.689246i
$843$		0			0
$844$	9.00000			0.309793
$845$	−24.0000	+	12.0000i	−0.825625	+	0.412813i
$846$	−21.0000			−0.721995
$847$		0			0
$848$			9.00000i			0.309061i
$849$		0			0
$850$	−6.00000	+	8.00000i	−0.205798	+	0.274398i
$851$	−7.00000			−0.239957
$852$		0			0
$853$			43.0000i			1.47229i	0.676823	+	0.736146i	$0.263356\pi$
$853$			43.0000i			1.47229i	−0.676823	+	0.736146i	$0.736644\pi$
$854$		0			0
$855$	−30.0000	+	15.0000i	−1.02598	+	0.512989i
$856$	−16.0000			−0.546869
$857$			8.00000i			0.273275i	0.990621	+	0.136637i	$0.0436295\pi$
$857$			8.00000i			0.273275i	−0.990621	+	0.136637i	$0.956370\pi$
$858$		0			0
$859$	−12.0000			−0.409435			−0.204717	−	0.978821i	$-0.565628\pi$
$859$	−12.0000			−0.409435			−0.204717	+	0.978821i	$0.565628\pi$
$860$	−2.00000	−	4.00000i	−0.0681994	−	0.136399i
$861$		0			0
$862$		−	2.00000i		−	0.0681203i
$863$		−	11.0000i		−	0.374444i	−0.982318	−	0.187222i	$-0.940052\pi$
$863$		−	11.0000i		−	0.374444i	0.982318	−	0.187222i	$-0.0599484\pi$
$864$		0			0
$865$	−9.00000	−	18.0000i	−0.306009	−	0.612018i
$866$	−28.0000			−0.951479
$867$		0			0
$868$		0			0
$869$	−42.0000			−1.42475
$870$		0			0
$871$	10.0000			0.338837
$872$		−	2.00000i		−	0.0677285i
$873$		−	36.0000i		−	1.21842i
$874$	35.0000			1.18389
$875$		0			0
$876$		0			0
$877$		−	31.0000i		−	1.04680i	−0.852088	−	0.523398i	$-0.824664\pi$
$877$		−	31.0000i		−	1.04680i	0.852088	−	0.523398i	$-0.175336\pi$
$878$			28.0000i			0.944954i
$879$		0			0
$880$	6.00000	−	3.00000i	0.202260	−	0.101130i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$	−10.0000			−0.336336
$885$		0			0
$886$	30.0000			1.00787
$887$			36.0000i			1.20876i	0.796696	+	0.604381i	$0.206579\pi$
$887$			36.0000i			1.20876i	−0.796696	+	0.604381i	$0.793421\pi$
$888$		0			0
$889$		0			0
$890$	−2.00000	−	4.00000i	−0.0670402	−	0.134080i
$891$	27.0000			0.904534
$892$		−	8.00000i		−	0.267860i
$893$			35.0000i			1.17123i
$894$		0			0
$895$	−26.0000	+	13.0000i	−0.869084	+	0.434542i
$896$		0			0
$897$		0			0
$898$			5.00000i			0.166852i
$899$	8.00000			0.266815
$900$	−9.00000	+	12.0000i	−0.300000	+	0.400000i
$901$	18.0000			0.599667
$902$			9.00000i			0.299667i
$903$		0			0
$904$	−14.0000			−0.465633
$905$	−52.0000	+	26.0000i	−1.72854	+	0.864269i
$906$		0			0
$907$			40.0000i			1.32818i	0.747653	+	0.664089i	$0.231180\pi$
$907$			40.0000i			1.32818i	−0.747653	+	0.664089i	$0.768820\pi$
$908$			6.00000i			0.199117i
$909$		0			0
$910$		0			0
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$		0			0
$913$			18.0000i			0.595713i
$914$	10.0000			0.330771
$915$		0			0
$916$	−16.0000			−0.528655
$917$		0			0
$918$		0			0
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	14.0000	−	7.00000i	0.461566	−	0.230783i
$921$		0			0
$922$		−	32.0000i		−	1.05386i
$923$		−	30.0000i		−	0.987462i
$924$		0			0
$925$	−4.00000	−	3.00000i	−0.131519	−	0.0986394i
$926$	−17.0000			−0.558655
$927$			24.0000i			0.788263i
$928$		−	4.00000i		−	0.131306i
$929$	21.0000			0.688988			0.344494	−	0.938789i	$-0.388051\pi$
$929$	21.0000			0.688988			0.344494	+	0.938789i	$0.388051\pi$
$930$		0			0
$931$		0			0
$932$			8.00000i			0.262049i
$933$		0			0
$934$	34.0000			1.11251
$935$	−6.00000	−	12.0000i	−0.196221	−	0.392442i
$936$	−15.0000			−0.490290
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		0			0
$939$		0			0
$940$	7.00000	+	14.0000i	0.228315	+	0.456630i
$941$	28.0000			0.912774			0.456387	−	0.889781i	$-0.349143\pi$
$941$	28.0000			0.912774			0.456387	+	0.889781i	$0.349143\pi$
$942$		0			0
$943$			21.0000i			0.683854i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	6.00000			0.195077
$947$			12.0000i			0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$			12.0000i			0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$		0			0
$949$	−80.0000			−2.59691
$950$	20.0000	+	15.0000i	0.648886	+	0.486664i
$951$		0			0
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$	27.0000			0.874157
$955$	−40.0000	+	20.0000i	−1.29437	+	0.647185i
$956$	20.0000			0.646846
$957$		0			0
$958$		−	36.0000i		−	1.16311i
$959$		0			0
$960$		0			0
$961$	−27.0000			−0.870968
$962$		−	5.00000i		−	0.161206i
$963$			48.0000i			1.54678i
$964$	−9.00000			−0.289870
$965$	−10.0000	−	20.0000i	−0.321911	−	0.643823i
$966$		0			0
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$		−	2.00000i		−	0.0642824i
$969$		0			0
$970$	−24.0000	+	12.0000i	−0.770594	+	0.385297i
$971$	33.0000			1.05902			0.529510	−	0.848304i	$-0.322376\pi$
$971$	33.0000			1.05902			0.529510	+	0.848304i	$0.322376\pi$
$972$		0			0
$973$		0			0
$974$	32.0000			1.02535
$975$		0			0
$976$	−6.00000			−0.192055
$977$		−	54.0000i		−	1.72761i	−0.503824	−	0.863807i	$-0.668074\pi$
$977$		−	54.0000i		−	1.72761i	0.503824	−	0.863807i	$-0.331926\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−6.00000			−0.191565
$982$		−	24.0000i		−	0.765871i
$983$			29.0000i			0.924956i	0.886631	+	0.462478i	$0.153040\pi$
$983$			29.0000i			0.924956i	−0.886631	+	0.462478i	$0.846960\pi$
$984$		0			0
$985$	5.00000	+	10.0000i	0.159313	+	0.318626i
$986$	−8.00000			−0.254772
$987$		0			0
$988$			25.0000i			0.795356i
$989$	14.0000			0.445174
$990$	−9.00000	−	18.0000i	−0.286039	−	0.572078i
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$		−	2.00000i		−	0.0635001i
$993$		0			0
$994$		0			0
$995$	36.0000	−	18.0000i	1.14128	−	0.570638i
$996$		0			0
$997$		−	38.0000i		−	1.20347i	−0.798695	−	0.601736i	$-0.794476\pi$
$997$		−	38.0000i		−	1.20347i	0.798695	−	0.601736i	$-0.205524\pi$
$998$			4.00000i			0.126618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.c.d.99.1		2
5.2	odd	4		2450.2.a.bb.1.1		1
5.3	odd	4		2450.2.a.j.1.1		1
5.4	even	2	inner	490.2.c.d.99.2		2
7.2	even	3		490.2.i.a.459.1		4
7.3	odd	6		70.2.i.b.9.2	yes	4
7.4	even	3		490.2.i.a.79.2		4
7.5	odd	6		70.2.i.b.39.1	yes	4
7.6	odd	2		490.2.c.a.99.1		2
21.5	even	6		630.2.u.a.109.2		4
21.17	even	6		630.2.u.a.289.1		4
28.3	even	6		560.2.bw.d.289.1		4
28.19	even	6		560.2.bw.d.529.2		4
35.3	even	12		350.2.e.j.51.1		2
35.4	even	6		490.2.i.a.79.1		4
35.9	even	6		490.2.i.a.459.2		4
35.12	even	12		350.2.e.c.151.1		2
35.13	even	4		2450.2.a.k.1.1		1
35.17	even	12		350.2.e.c.51.1		2
35.19	odd	6		70.2.i.b.39.2	yes	4
35.24	odd	6		70.2.i.b.9.1	✓	4
35.27	even	4		2450.2.a.ba.1.1		1
35.33	even	12		350.2.e.j.151.1		2
35.34	odd	2		490.2.c.a.99.2		2
105.59	even	6		630.2.u.a.289.2		4
105.89	even	6		630.2.u.a.109.1		4
140.19	even	6		560.2.bw.d.529.1		4
140.59	even	6		560.2.bw.d.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.b.9.1	✓	4	35.24	odd	6
70.2.i.b.9.2	yes	4	7.3	odd	6
70.2.i.b.39.1	yes	4	7.5	odd	6
70.2.i.b.39.2	yes	4	35.19	odd	6
350.2.e.c.51.1		2	35.17	even	12
350.2.e.c.151.1		2	35.12	even	12
350.2.e.j.51.1		2	35.3	even	12
350.2.e.j.151.1		2	35.33	even	12
490.2.c.a.99.1		2	7.6	odd	2
490.2.c.a.99.2		2	35.34	odd	2
490.2.c.d.99.1		2	1.1	even	1	trivial
490.2.c.d.99.2		2	5.4	even	2	inner
490.2.i.a.79.1		4	35.4	even	6
490.2.i.a.79.2		4	7.4	even	3
490.2.i.a.459.1		4	7.2	even	3
490.2.i.a.459.2		4	35.9	even	6
560.2.bw.d.289.1		4	28.3	even	6
560.2.bw.d.289.2		4	140.59	even	6
560.2.bw.d.529.1		4	140.19	even	6
560.2.bw.d.529.2		4	28.19	even	6
630.2.u.a.109.1		4	105.89	even	6
630.2.u.a.109.2		4	21.5	even	6
630.2.u.a.289.1		4	21.17	even	6
630.2.u.a.289.2		4	105.59	even	6
2450.2.a.j.1.1		1	5.3	odd	4
2450.2.a.k.1.1		1	35.13	even	4
2450.2.a.ba.1.1		1	35.27	even	4
2450.2.a.bb.1.1		1	5.2	odd	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{8} +3.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} +3.00000 q^{11} +5.00000i q^{13} +1.00000 q^{16} -2.00000i q^{17} -3.00000i q^{18} -5.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} -3.00000i q^{22} -7.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +5.00000 q^{26} +4.00000 q^{29} +2.00000 q^{31} -1.00000i q^{32} -2.00000 q^{34} -3.00000 q^{36} -1.00000i q^{37} +5.00000i q^{38} +(1.00000 + 2.00000i) q^{40} -3.00000 q^{41} +2.00000i q^{43} -3.00000 q^{44} +(6.00000 - 3.00000i) q^{45} -7.00000 q^{46} -7.00000i q^{47} +(-4.00000 - 3.00000i) q^{50} -5.00000i q^{52} +9.00000i q^{53} +(6.00000 - 3.00000i) q^{55} -4.00000i q^{58} -4.00000 q^{59} -6.00000 q^{61} -2.00000i q^{62} -1.00000 q^{64} +(5.00000 + 10.0000i) q^{65} -2.00000i q^{67} +2.00000i q^{68} -6.00000 q^{71} +3.00000i q^{72} +16.0000i q^{73} -1.00000 q^{74} +5.00000 q^{76} -14.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +9.00000 q^{81} +3.00000i q^{82} +6.00000i q^{83} +(-2.00000 - 4.00000i) q^{85} +2.00000 q^{86} +3.00000i q^{88} +2.00000 q^{89} +(-3.00000 - 6.00000i) q^{90} +7.00000i q^{92} -7.00000 q^{94} +(-10.0000 + 5.00000i) q^{95} -12.0000i q^{97} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 4 * q^5 + 6 * q^9	\( 2 q - 2 q^{4} + 4 q^{5} + 6 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{16} - 10 q^{19} - 4 q^{20} + 6 q^{25} + 10 q^{26} + 8 q^{29} + 4 q^{31} - 4 q^{34} - 6 q^{36} + 2 q^{40} - 6 q^{41} - 6 q^{44} + 12 q^{45} - 14 q^{46} - 8 q^{50} + 12 q^{55} - 8 q^{59} - 12 q^{61} - 2 q^{64} + 10 q^{65} - 12 q^{71} - 2 q^{74} + 10 q^{76} - 28 q^{79} + 4 q^{80} + 18 q^{81} - 4 q^{85} + 4 q^{86} + 4 q^{89} - 6 q^{90} - 14 q^{94} - 20 q^{95} + 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 6 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^16 - 10 * q^19 - 4 * q^20 + 6 * q^25 + 10 * q^26 + 8 * q^29 + 4 * q^31 - 4 * q^34 - 6 * q^36 + 2 * q^40 - 6 * q^41 - 6 * q^44 + 12 * q^45 - 14 * q^46 - 8 * q^50 + 12 * q^55 - 8 * q^59 - 12 * q^61 - 2 * q^64 + 10 * q^65 - 12 * q^71 - 2 * q^74 + 10 * q^76 - 28 * q^79 + 4 * q^80 + 18 * q^81 - 4 * q^85 + 4 * q^86 + 4 * q^89 - 6 * q^90 - 14 * q^94 - 20 * q^95 + 18 * q^99

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