LMFDB - Embedded newform 1710.2.d.h.1369.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.180227832610816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + x^{10} - 8x^{6} + 16x^{2} + 64 $ x^12 + x^10 - 8x^6 + 16x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.3
Root			$-1.37729 + 0.321037i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.h.1369.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-0.726062 - 2.11491i) q^{5} +4.05705i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.726062 - 2.11491i) q^{5} +4.05705i q^{7} +1.00000i q^{8} +(-2.11491 + 0.726062i) q^{10} +0.466185 q^{11} -0.985939i q^{13} +4.05705 q^{14} +1.00000 q^{16} -4.94567i q^{17} -1.00000 q^{19} +(0.726062 + 2.11491i) q^{20} -0.466185i q^{22} -2.22982i q^{23} +(-3.94567 + 3.07111i) q^{25} -0.985939 q^{26} -4.05705i q^{28} +2.43806 q^{29} +0.715853 q^{31} -1.00000i q^{32} -4.94567 q^{34} +(8.58028 - 2.94567i) q^{35} -10.0324i q^{37} +1.00000i q^{38} +(2.11491 - 0.726062i) q^{40} -10.1993 q^{41} -0.466185i q^{43} -0.466185 q^{44} -2.22982 q^{46} -8.79811i q^{47} -9.45963 q^{49} +(3.07111 + 3.94567i) q^{50} +0.985939i q^{52} -3.89134i q^{53} +(-0.338479 - 0.985939i) q^{55} -4.05705 q^{56} -2.43806i q^{58} +7.42748 q^{59} -6.45963 q^{61} -0.715853i q^{62} -1.00000 q^{64} +(-2.08517 + 0.715853i) q^{65} -13.9226i q^{67} +4.94567i q^{68} +(-2.94567 - 8.58028i) q^{70} -6.14222 q^{71} -7.07459i q^{73} -10.0324 q^{74} +1.00000 q^{76} +1.89134i q^{77} -1.85244 q^{79} +(-0.726062 - 2.11491i) q^{80} +10.1993i q^{82} +4.37737i q^{83} +(-10.4596 + 3.59086i) q^{85} -0.466185 q^{86} +0.466185i q^{88} -6.02892 q^{89} +4.00000 q^{91} +2.22982i q^{92} -8.79811 q^{94} +(0.726062 + 2.11491i) q^{95} +6.60840i q^{97} +9.45963i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 12 q^{16} - 12 q^{19} - 4 q^{25} + 16 q^{31} - 16 q^{34} + 24 q^{46} - 12 q^{49} - 40 q^{55} + 24 q^{61} - 12 q^{64} + 8 q^{70} + 12 q^{76} - 24 q^{85} + 48 q^{91} - 40 q^{94}+O(q^{100}) $ 12 * q - 12 * q^4 + 12 * q^16 - 12 * q^19 - 4 * q^25 + 16 * q^31 - 16 * q^34 + 24 * q^46 - 12 * q^49 - 40 * q^55 + 24 * q^61 - 12 * q^64 + 8 * q^70 + 12 * q^76 - 24 * q^85 + 48 * q^91 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.726062	−	2.11491i	−0.324705	−	0.945815i
$5$	−0.726062	−	2.11491i	−0.324705	−	0.945815i
$6$		0			0
$7$			4.05705i			1.53342i	0.641994	+	0.766710i	$0.278107\pi$
$7$			4.05705i			1.53342i	−0.641994	+	0.766710i	$0.721893\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.11491	+	0.726062i	−0.668792	+	0.229601i
$11$	0.466185			0.140560			0.0702801	−	0.997527i	$-0.477611\pi$
$11$	0.466185			0.140560			0.0702801	+	0.997527i	$0.477611\pi$
$12$		0			0
$13$		−	0.985939i		−	0.273450i	−0.990609	−	0.136725i	$-0.956342\pi$
$13$		−	0.985939i		−	0.273450i	0.990609	−	0.136725i	$-0.0436577\pi$
$14$	4.05705			1.08429
$15$		0			0
$16$	1.00000			0.250000
$17$		−	4.94567i		−	1.19950i	−0.800187	−	0.599750i	$-0.795267\pi$
$17$		−	4.94567i		−	1.19950i	0.800187	−	0.599750i	$-0.204733\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.726062	+	2.11491i	0.162352	+	0.472908i
$21$		0			0
$22$		−	0.466185i		−	0.0993910i
$23$		−	2.22982i		−	0.464949i	−0.972603	−	0.232474i	$-0.925318\pi$
$23$		−	2.22982i		−	0.464949i	0.972603	−	0.232474i	$-0.0746822\pi$
$24$		0			0
$25$	−3.94567	+	3.07111i	−0.789134	+	0.614222i
$26$	−0.985939			−0.193359
$27$		0			0
$28$		−	4.05705i		−	0.766710i
$29$	2.43806			0.452737			0.226368	−	0.974042i	$-0.427315\pi$
$29$	2.43806			0.452737			0.226368	+	0.974042i	$0.427315\pi$
$30$		0			0
$31$	0.715853			0.128571			0.0642855	−	0.997932i	$-0.479523\pi$
$31$	0.715853			0.128571			0.0642855	+	0.997932i	$0.479523\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−4.94567			−0.848175
$35$	8.58028	−	2.94567i	1.45033	−	0.497909i
$36$		0			0
$37$		−	10.0324i		−	1.64932i	−0.565631	−	0.824658i	$-0.691367\pi$
$37$		−	10.0324i		−	1.64932i	0.565631	−	0.824658i	$-0.308633\pi$
$38$			1.00000i			0.162221i
$39$		0			0
$40$	2.11491	−	0.726062i	0.334396	−	0.114800i
$41$	−10.1993			−1.59286			−0.796429	−	0.604732i	$-0.793280\pi$
$41$	−10.1993			−1.59286			−0.796429	+	0.604732i	$0.793280\pi$
$42$		0			0
$43$		−	0.466185i		−	0.0710926i	−0.999368	−	0.0355463i	$-0.988683\pi$
$43$		−	0.466185i		−	0.0710926i	0.999368	−	0.0355463i	$-0.0113171\pi$
$44$	−0.466185			−0.0702801
$45$		0			0
$46$	−2.22982			−0.328768
$47$		−	8.79811i		−	1.28334i	−0.766982	−	0.641668i	$-0.778243\pi$
$47$		−	8.79811i		−	1.28334i	0.766982	−	0.641668i	$-0.221757\pi$
$48$		0			0
$49$	−9.45963			−1.35138
$50$	3.07111	+	3.94567i	0.434320	+	0.558002i
$51$		0			0
$52$			0.985939i			0.136725i
$53$		−	3.89134i		−	0.534516i	−0.963625	−	0.267258i	$-0.913882\pi$
$53$		−	3.89134i		−	0.534516i	0.963625	−	0.267258i	$-0.0861176\pi$
$54$		0			0
$55$	−0.338479	−	0.985939i	−0.0456406	−	0.132944i
$56$	−4.05705			−0.542146
$57$		0			0
$58$		−	2.43806i		−	0.320133i
$59$	7.42748			0.966976			0.483488	−	0.875351i	$-0.339370\pi$
$59$	7.42748			0.966976			0.483488	+	0.875351i	$0.339370\pi$
$60$		0			0
$61$	−6.45963			−0.827071			−0.413535	−	0.910488i	$-0.635706\pi$
$61$	−6.45963			−0.827071			−0.413535	+	0.910488i	$0.635706\pi$
$62$		−	0.715853i		−	0.0909134i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.08517	+	0.715853i	−0.258633	+	0.0887906i
$66$		0			0
$67$		−	13.9226i		−	1.70092i	−0.526044	−	0.850458i	$-0.676325\pi$
$67$		−	13.9226i		−	1.70092i	0.526044	−	0.850458i	$-0.323675\pi$
$68$			4.94567i			0.599750i
$69$		0			0
$70$	−2.94567	−	8.58028i	−0.352075	−	1.02554i
$71$	−6.14222			−0.728947			−0.364473	−	0.931214i	$-0.618751\pi$
$71$	−6.14222			−0.728947			−0.364473	+	0.931214i	$0.618751\pi$
$72$		0			0
$73$		−	7.07459i		−	0.828018i	−0.910273	−	0.414009i	$-0.864128\pi$
$73$		−	7.07459i		−	0.828018i	0.910273	−	0.414009i	$-0.135872\pi$
$74$	−10.0324			−1.16624
$75$		0			0
$76$	1.00000			0.114708
$77$			1.89134i			0.215538i
$78$		0			0
$79$	−1.85244			−0.208416			−0.104208	−	0.994556i	$-0.533231\pi$
$79$	−1.85244			−0.208416			−0.104208	+	0.994556i	$0.533231\pi$
$80$	−0.726062	−	2.11491i	−0.0811762	−	0.236454i
$81$		0			0
$82$			10.1993i			1.12632i
$83$			4.37737i			0.480479i	0.970714	+	0.240240i	$0.0772260\pi$
$83$			4.37737i			0.480479i	−0.970714	+	0.240240i	$0.922774\pi$
$84$		0			0
$85$	−10.4596	+	3.59086i	−1.13451	+	0.389484i
$86$	−0.466185			−0.0502701
$87$		0			0
$88$			0.466185i			0.0496955i
$89$	−6.02892			−0.639065			−0.319532	−	0.947575i	$-0.603526\pi$
$89$	−6.02892			−0.639065			−0.319532	+	0.947575i	$0.603526\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$			2.22982i			0.232474i
$93$		0			0
$94$	−8.79811			−0.907456
$95$	0.726062	+	2.11491i	0.0744924	+	0.216985i
$96$		0			0
$97$			6.60840i			0.670982i	0.942043	+	0.335491i	$0.108902\pi$
$97$			6.60840i			0.670982i	−0.942043	+	0.335491i	$0.891098\pi$
$98$			9.45963i			0.955567i
$99$		0			0
$100$	3.94567	−	3.07111i	0.394567	−	0.307111i
$101$	5.62246			0.559456			0.279728	−	0.960079i	$-0.409756\pi$
$101$	5.62246			0.559456			0.279728	+	0.960079i	$0.409756\pi$
$102$		0			0
$103$			18.9464i			1.86684i	0.358780	+	0.933422i	$0.383193\pi$
$103$			18.9464i			1.86684i	−0.358780	+	0.933422i	$0.616807\pi$
$104$	0.985939			0.0966793
$105$		0			0
$106$	−3.89134			−0.377960
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$		0			0
$109$	−4.60719			−0.441289			−0.220644	−	0.975354i	$-0.570816\pi$
$109$	−4.60719			−0.441289			−0.220644	+	0.975354i	$0.570816\pi$
$110$	−0.985939	+	0.338479i	−0.0940056	+	0.0322727i
$111$		0			0
$112$			4.05705i			0.383355i
$113$			14.4596i			1.36025i	0.733097	+	0.680124i	$0.238074\pi$
$113$			14.4596i			1.36025i	−0.733097	+	0.680124i	$0.761926\pi$
$114$		0			0
$115$	−4.71585	+	1.61898i	−0.439756	+	0.150971i
$116$	−2.43806			−0.226368
$117$		0			0
$118$		−	7.42748i		−	0.683755i
$119$	20.0648			1.83934
$120$		0			0
$121$	−10.7827			−0.980243
$122$			6.45963i			0.584827i
$123$		0			0
$124$	−0.715853			−0.0642855
$125$	9.35991	+	6.11491i	0.837176	+	0.546934i
$126$		0			0
$127$		−	4.69009i		−	0.416178i	−0.978110	−	0.208089i	$-0.933276\pi$
$127$		−	4.69009i		−	0.416178i	0.978110	−	0.208089i	$-0.0667244\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	0.715853	+	2.08517i	0.0627844	+	0.182881i
$131$	9.61979			0.840485			0.420242	−	0.907412i	$-0.361945\pi$
$131$	9.61979			0.840485			0.420242	+	0.907412i	$0.361945\pi$
$132$		0			0
$133$		−	4.05705i		−	0.351791i
$134$	−13.9226			−1.20273
$135$		0			0
$136$	4.94567			0.424088
$137$		−	18.8370i		−	1.60935i	−0.593713	−	0.804677i	$-0.702339\pi$
$137$		−	18.8370i		−	1.60935i	0.593713	−	0.804677i	$-0.297661\pi$
$138$		0			0
$139$	−14.3510			−1.21723			−0.608617	−	0.793465i	$-0.708275\pi$
$139$	−14.3510			−1.21723			−0.608617	+	0.793465i	$0.708275\pi$
$140$	−8.58028	+	2.94567i	−0.725166	+	0.248954i
$141$		0			0
$142$			6.14222i			0.515443i
$143$		−	0.459630i		−	0.0384362i
$144$		0			0
$145$	−1.77018	−	5.15628i	−0.147006	−	0.428206i
$146$	−7.07459			−0.585497
$147$		0			0
$148$			10.0324i			0.824658i
$149$	−15.3747			−1.25955			−0.629773	−	0.776779i	$-0.716852\pi$
$149$	−15.3747			−1.25955			−0.629773	+	0.776779i	$0.716852\pi$
$150$		0			0
$151$	−5.17548			−0.421175			−0.210587	−	0.977575i	$-0.567538\pi$
$151$	−5.17548			−0.421175			−0.210587	+	0.977575i	$0.567538\pi$
$152$		−	1.00000i		−	0.0811107i
$153$		0			0
$154$	1.89134			0.152408
$155$	−0.519753	−	1.51396i	−0.0417476	−	0.121604i
$156$		0			0
$157$		−	11.7050i		−	0.934157i	−0.884216	−	0.467079i	$-0.845307\pi$
$157$		−	11.7050i		−	0.934157i	0.884216	−	0.467079i	$-0.154693\pi$
$158$			1.85244i			0.147372i
$159$		0			0
$160$	−2.11491	+	0.726062i	−0.167198	+	0.0574002i
$161$	9.04646			0.712961
$162$		0			0
$163$			16.6944i			1.30760i	0.756666	+	0.653802i	$0.226827\pi$
$163$			16.6944i			1.30760i	−0.756666	+	0.653802i	$0.773173\pi$
$164$	10.1993			0.796429
$165$		0			0
$166$	4.37737			0.339750
$167$		−	19.7827i		−	1.53083i	−0.643538	−	0.765415i	$-0.722534\pi$
$167$		−	19.7827i		−	1.53083i	0.643538	−	0.765415i	$-0.277466\pi$
$168$		0			0
$169$	12.0279			0.925225
$170$	3.59086	+	10.4596i	0.275407	+	0.802217i
$171$		0			0
$172$			0.466185i			0.0355463i
$173$		−	12.3510i		−	0.939027i	−0.882925	−	0.469513i	$-0.844429\pi$
$173$		−	12.3510i		−	0.939027i	0.882925	−	0.469513i	$-0.155571\pi$
$174$		0			0
$175$	−12.4596	−	16.0078i	−0.941860	−	1.21007i
$176$	0.466185			0.0351400
$177$		0			0
$178$			6.02892i			0.451887i
$179$	4.52323			0.338082			0.169041	−	0.985609i	$-0.445933\pi$
$179$	4.52323			0.338082			0.169041	+	0.985609i	$0.445933\pi$
$180$		0			0
$181$	0.147558			0.0109679			0.00548396	−	0.999985i	$-0.498254\pi$
$181$	0.147558			0.0109679			0.00548396	+	0.999985i	$0.498254\pi$
$182$		−	4.00000i		−	0.296500i
$183$		0			0
$184$	2.22982			0.164384
$185$	−21.2176	+	7.28415i	−1.55995	+	0.535541i
$186$		0			0
$187$		−	2.30560i		−	0.168602i
$188$			8.79811i			0.641668i
$189$		0			0
$190$	2.11491	−	0.726062i	0.153432	−	0.0526741i
$191$	1.91831			0.138804			0.0694020	−	0.997589i	$-0.477891\pi$
$191$	1.91831			0.138804			0.0694020	+	0.997589i	$0.477891\pi$
$192$		0			0
$193$		−	26.6732i		−	1.91998i	−0.280035	−	0.959990i	$-0.590346\pi$
$193$		−	26.6732i		−	1.91998i	0.280035	−	0.959990i	$-0.409654\pi$
$194$	6.60840			0.474456
$195$		0			0
$196$	9.45963			0.675688
$197$			6.58078i			0.468861i	0.972133	+	0.234431i	$0.0753226\pi$
$197$			6.58078i			0.468861i	−0.972133	+	0.234431i	$0.924677\pi$
$198$		0			0
$199$	12.4596			0.883240			0.441620	−	0.897202i	$-0.354404\pi$
$199$	12.4596			0.883240			0.441620	+	0.897202i	$0.354404\pi$
$200$	−3.07111	−	3.94567i	−0.217160	−	0.279001i
$201$		0			0
$202$		−	5.62246i		−	0.395595i
$203$			9.89134i			0.694236i
$204$		0			0
$205$	7.40530	+	21.5705i	0.517208	+	1.50655i
$206$	18.9464			1.32006
$207$		0			0
$208$		−	0.985939i		−	0.0683626i
$209$	−0.466185			−0.0322467
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			3.89134i			0.267258i
$213$		0			0
$214$	−8.00000			−0.546869
$215$	−0.985939	+	0.338479i	−0.0672405	+	0.0230841i
$216$		0			0
$217$			2.90425i			0.197153i
$218$			4.60719i			0.312038i
$219$		0			0
$220$	0.338479	+	0.985939i	0.0228203	+	0.0664720i
$221$	−4.87613			−0.328004
$222$		0			0
$223$		−	3.75772i		−	0.251636i	−0.992053	−	0.125818i	$-0.959845\pi$
$223$		−	3.75772i		−	0.251636i	0.992053	−	0.125818i	$-0.0401555\pi$
$224$	4.05705			0.271073
$225$		0			0
$226$	14.4596			0.961840
$227$		−	17.8913i		−	1.18749i	−0.804653	−	0.593745i	$-0.797649\pi$
$227$		−	17.8913i		−	1.18749i	0.804653	−	0.593745i	$-0.202351\pi$
$228$		0			0
$229$	5.32304			0.351756			0.175878	−	0.984412i	$-0.443724\pi$
$229$	5.32304			0.351756			0.175878	+	0.984412i	$0.443724\pi$
$230$	1.61898	+	4.71585i	0.106753	+	0.310954i
$231$		0			0
$232$			2.43806i			0.160067i
$233$		−	3.51396i		−	0.230207i	−0.993353	−	0.115104i	$-0.963280\pi$
$233$		−	3.51396i		−	0.230207i	0.993353	−	0.115104i	$-0.0367200\pi$
$234$		0			0
$235$	−18.6072	+	6.38797i	−1.21380	+	0.416705i
$236$	−7.42748			−0.483488
$237$		0			0
$238$		−	20.0648i		−	1.30061i
$239$	−29.4986			−1.90810			−0.954052	−	0.299642i	$-0.903133\pi$
$239$	−29.4986			−1.90810			−0.954052	+	0.299642i	$0.903133\pi$
$240$		0			0
$241$	29.2702			1.88546			0.942731	−	0.333555i	$-0.108248\pi$
$241$	29.2702			1.88546			0.942731	+	0.333555i	$0.108248\pi$
$242$			10.7827i			0.693136i
$243$		0			0
$244$	6.45963			0.413535
$245$	6.86828	+	20.0062i	0.438798	+	1.27815i
$246$		0			0
$247$			0.985939i			0.0627338i
$248$			0.715853i			0.0454567i
$249$		0			0
$250$	6.11491	−	9.35991i	0.386741	−	0.591973i
$251$	13.7901			0.870425			0.435212	−	0.900328i	$-0.356673\pi$
$251$	13.7901			0.870425			0.435212	+	0.900328i	$0.356673\pi$
$252$		0			0
$253$		−	1.03951i		−	0.0653532i
$254$	−4.69009			−0.294283
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	4.10866i		−	0.256291i	−0.991755	−	0.128146i	$-0.959097\pi$
$257$		−	4.10866i		−	0.256291i	0.991755	−	0.128146i	$-0.0409025\pi$
$258$		0			0
$259$	40.7019			2.52909
$260$	2.08517	−	0.715853i	0.129317	−	0.0443953i
$261$		0			0
$262$		−	9.61979i		−	0.594312i
$263$			2.90677i			0.179239i	0.995976	+	0.0896197i	$0.0285652\pi$
$263$			2.90677i			0.179239i	−0.995976	+	0.0896197i	$0.971435\pi$
$264$		0			0
$265$	−8.22982	+	2.82535i	−0.505554	+	0.173560i
$266$	−4.05705			−0.248754
$267$		0			0
$268$			13.9226i			0.850458i
$269$	−6.60840			−0.402921			−0.201461	−	0.979497i	$-0.564569\pi$
$269$	−6.60840			−0.402921			−0.201461	+	0.979497i	$0.564569\pi$
$270$		0			0
$271$	29.3789			1.78464			0.892320	−	0.451403i	$-0.149076\pi$
$271$	29.3789			1.78464			0.892320	+	0.451403i	$0.149076\pi$
$272$		−	4.94567i		−	0.299875i
$273$		0			0
$274$	−18.8370			−1.13798
$275$	−1.83941	+	1.43171i	−0.110921	+	0.0863351i
$276$		0			0
$277$			17.8472i			1.07233i	0.844112	+	0.536166i	$0.180128\pi$
$277$			17.8472i			1.07233i	−0.844112	+	0.536166i	$0.819872\pi$
$278$			14.3510i			0.860714i
$279$		0			0
$280$	2.94567	+	8.58028i	0.176037	+	0.512770i
$281$	10.9051			0.650541			0.325270	−	0.945621i	$-0.394545\pi$
$281$	10.9051			0.650541			0.325270	+	0.945621i	$0.394545\pi$
$282$		0			0
$283$			6.27468i			0.372991i	0.982456	+	0.186496i	$0.0597130\pi$
$283$			6.27468i			0.372991i	−0.982456	+	0.186496i	$0.940287\pi$
$284$	6.14222			0.364473
$285$		0			0
$286$	−0.459630			−0.0271785
$287$		−	41.3789i		−	2.44252i
$288$		0			0
$289$	−7.45963			−0.438802
$290$	−5.15628	+	1.77018i	−0.302787	+	0.103949i
$291$		0			0
$292$			7.07459i			0.414009i
$293$			22.9193i			1.33896i	0.742831	+	0.669479i	$0.233482\pi$
$293$			22.9193i			1.33896i	−0.742831	+	0.669479i	$0.766518\pi$
$294$		0			0
$295$	−5.39281	−	15.7084i	−0.313982	−	0.914580i
$296$	10.0324			0.583122
$297$		0			0
$298$			15.3747i			0.890633i
$299$	−2.19846			−0.127140
$300$		0			0
$301$	1.89134			0.109015
$302$			5.17548i			0.297816i
$303$		0			0
$304$	−1.00000			−0.0573539
$305$	4.69009	+	13.6615i	0.268554	+	0.782256i
$306$		0			0
$307$			4.17034i			0.238014i	0.992893	+	0.119007i	$0.0379711\pi$
$307$			4.17034i			0.238014i	−0.992893	+	0.119007i	$0.962029\pi$
$308$		−	1.89134i		−	0.107769i
$309$		0			0
$310$	−1.51396	+	0.519753i	−0.0859873	+	0.0295200i
$311$	−12.2309			−0.693549			−0.346774	−	0.937949i	$-0.612723\pi$
$311$	−12.2309			−0.693549			−0.346774	+	0.937949i	$0.612723\pi$
$312$		0			0
$313$			8.71274i			0.492473i	0.969210	+	0.246237i	$0.0791941\pi$
$313$			8.71274i			0.492473i	−0.969210	+	0.246237i	$0.920806\pi$
$314$	−11.7050			−0.660549
$315$		0			0
$316$	1.85244			0.104208
$317$			9.78267i			0.549450i	0.961523	+	0.274725i	$0.0885867\pi$
$317$			9.78267i			0.549450i	−0.961523	+	0.274725i	$0.911413\pi$
$318$		0			0
$319$	1.13659			0.0636368
$320$	0.726062	+	2.11491i	0.0405881	+	0.118227i
$321$		0			0
$322$		−	9.04646i		−	0.504140i
$323$			4.94567i			0.275184i
$324$		0			0
$325$	3.02792	+	3.89019i	0.167959	+	0.215789i
$326$	16.6944			0.924616
$327$		0			0
$328$		−	10.1993i		−	0.563160i
$329$	35.6943			1.96789
$330$		0			0
$331$	12.4596			0.684843			0.342422	−	0.939546i	$-0.388753\pi$
$331$	12.4596			0.684843			0.342422	+	0.939546i	$0.388753\pi$
$332$		−	4.37737i		−	0.240240i
$333$		0			0
$334$	−19.7827			−1.08246
$335$	−29.4450	+	10.1087i	−1.60875	+	0.552295i
$336$		0			0
$337$			10.5522i			0.574813i	0.957809	+	0.287406i	$0.0927930\pi$
$337$			10.5522i			0.574813i	−0.957809	+	0.287406i	$0.907207\pi$
$338$		−	12.0279i		−	0.654233i
$339$		0			0
$340$	10.4596	−	3.59086i	0.567253	−	0.194742i
$341$	0.333720			0.0180720
$342$		0			0
$343$		−	9.97884i		−	0.538806i
$344$	0.466185			0.0251350
$345$		0			0
$346$	−12.3510			−0.663992
$347$		−	19.8649i		−	1.06641i	−0.845988	−	0.533203i	$-0.820988\pi$
$347$		−	19.8649i		−	1.06641i	0.845988	−	0.533203i	$-0.179012\pi$
$348$		0			0
$349$	32.3510			1.73171			0.865854	−	0.500297i	$-0.166776\pi$
$349$	32.3510			1.73171			0.865854	+	0.500297i	$0.166776\pi$
$350$	−16.0078	+	12.4596i	−0.855651	+	0.665995i
$351$		0			0
$352$		−	0.466185i		−	0.0248478i
$353$		−	17.4053i		−	0.926391i	−0.886256	−	0.463195i	$-0.846703\pi$
$353$		−	17.4053i		−	0.926391i	0.886256	−	0.463195i	$-0.153297\pi$
$354$		0			0
$355$	4.45963	+	12.9902i	0.236693	+	0.689449i
$356$	6.02892			0.319532
$357$		0			0
$358$		−	4.52323i		−	0.239060i
$359$	−32.5099			−1.71581			−0.857905	−	0.513809i	$-0.828234\pi$
$359$	−32.5099			−1.71581			−0.857905	+	0.513809i	$0.828234\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	0.147558i		−	0.00775549i
$363$		0			0
$364$	−4.00000			−0.209657
$365$	−14.9621	+	5.13659i	−0.783152	+	0.268861i
$366$		0			0
$367$			35.2473i			1.83990i	0.392041	+	0.919948i	$0.371769\pi$
$367$			35.2473i			1.83990i	−0.392041	+	0.919948i	$0.628231\pi$
$368$		−	2.22982i		−	0.116237i
$369$		0			0
$370$	7.28415	+	21.2176i	0.378685	+	1.10305i
$371$	15.7873			0.819637
$372$		0			0
$373$			16.0675i			0.831943i	0.909378	+	0.415971i	$0.136558\pi$
$373$			16.0675i			0.831943i	−0.909378	+	0.415971i	$0.863442\pi$
$374$	−2.30560			−0.119220
$375$		0			0
$376$	8.79811			0.453728
$377$		−	2.40378i		−	0.123801i
$378$		0			0
$379$	−8.24230			−0.423379			−0.211689	−	0.977337i	$-0.567896\pi$
$379$	−8.24230			−0.423379			−0.211689	+	0.977337i	$0.567896\pi$
$380$	−0.726062	−	2.11491i	−0.0372462	−	0.108492i
$381$		0			0
$382$		−	1.91831i		−	0.0981492i
$383$		−	12.9193i		−	0.660143i	−0.943956	−	0.330072i	$-0.892927\pi$
$383$		−	12.9193i		−	0.660143i	0.943956	−	0.330072i	$-0.107073\pi$
$384$		0			0
$385$	4.00000	−	1.37323i	0.203859	−	0.0699861i
$386$	−26.6732			−1.35763
$387$		0			0
$388$		−	6.60840i		−	0.335491i
$389$	−22.7830			−1.15515			−0.577573	−	0.816339i	$-0.696000\pi$
$389$	−22.7830			−1.15515			−0.577573	+	0.816339i	$0.696000\pi$
$390$		0			0
$391$	−11.0279			−0.557706
$392$		−	9.45963i		−	0.477783i
$393$		0			0
$394$	6.58078			0.331535
$395$	1.34499	+	3.91774i	0.0676737	+	0.197123i
$396$		0			0
$397$			20.4177i			1.02473i	0.858766	+	0.512367i	$0.171231\pi$
$397$			20.4177i			1.02473i	−0.858766	+	0.512367i	$0.828769\pi$
$398$		−	12.4596i		−	0.624545i
$399$		0			0
$400$	−3.94567	+	3.07111i	−0.197283	+	0.153555i
$401$	21.8163			1.08945			0.544726	−	0.838614i	$-0.316634\pi$
$401$	21.8163			1.08945			0.544726	+	0.838614i	$0.316634\pi$
$402$		0			0
$403$		−	0.705787i		−	0.0351578i
$404$	−5.62246			−0.279728
$405$		0			0
$406$	9.89134			0.490899
$407$		−	4.67696i		−	0.231828i
$408$		0			0
$409$	−19.3789			−0.958224			−0.479112	−	0.877754i	$-0.659041\pi$
$409$	−19.3789			−0.958224			−0.479112	+	0.877754i	$0.659041\pi$
$410$	21.5705	−	7.40530i	1.06529	−	0.365722i
$411$		0			0
$412$		−	18.9464i		−	0.933422i
$413$			30.1336i			1.48278i
$414$		0			0
$415$	9.25774	−	3.17824i	0.454445	−	0.156014i
$416$	−0.985939			−0.0483396
$417$		0			0
$418$			0.466185i			0.0228019i
$419$	28.7522			1.40464			0.702319	−	0.711862i	$-0.252148\pi$
$419$	28.7522			1.40464			0.702319	+	0.711862i	$0.252148\pi$
$420$		0			0
$421$	−14.7159			−0.717207			−0.358603	−	0.933490i	$-0.616747\pi$
$421$	−14.7159			−0.717207			−0.358603	+	0.933490i	$0.616747\pi$
$422$		−	12.0000i		−	0.584151i
$423$		0			0
$424$	3.89134			0.188980
$425$	15.1887	+	19.5140i	0.736759	+	0.946566i
$426$		0			0
$427$		−	26.2070i		−	1.26825i
$428$			8.00000i			0.386695i
$429$		0			0
$430$	0.338479	+	0.985939i	0.0163229	+	0.0475462i
$431$	18.2001			0.876666			0.438333	−	0.898813i	$-0.355569\pi$
$431$	18.2001			0.876666			0.438333	+	0.898813i	$0.355569\pi$
$432$		0			0
$433$		−	2.77178i		−	0.133203i	−0.997780	−	0.0666017i	$-0.978784\pi$
$433$		−	2.77178i		−	0.133203i	0.997780	−	0.0666017i	$-0.0212157\pi$
$434$	2.90425			0.139408
$435$		0			0
$436$	4.60719			0.220644
$437$			2.22982i			0.106667i
$438$		0			0
$439$	12.2034			0.582437			0.291218	−	0.956657i	$-0.405939\pi$
$439$	12.2034			0.582437			0.291218	+	0.956657i	$0.405939\pi$
$440$	0.985939	−	0.338479i	0.0470028	−	0.0161364i
$441$		0			0
$442$			4.87613i			0.231934i
$443$		−	21.9736i		−	1.04400i	−0.852946	−	0.521998i	$-0.825187\pi$
$443$		−	21.9736i		−	1.04400i	0.852946	−	0.521998i	$-0.174813\pi$
$444$		0			0
$445$	4.37737	+	12.7506i	0.207507	+	0.604437i
$446$	−3.75772			−0.177933
$447$		0			0
$448$		−	4.05705i		−	0.191677i
$449$	23.1895			1.09438			0.547190	−	0.837009i	$-0.315698\pi$
$449$	23.1895			1.09438			0.547190	+	0.837009i	$0.315698\pi$
$450$		0			0
$451$	−4.75475			−0.223892
$452$		−	14.4596i		−	0.680124i
$453$		0			0
$454$	−17.8913			−0.839682
$455$	−2.90425	−	8.45963i	−0.136153	−	0.396594i
$456$		0			0
$457$		−	34.3211i		−	1.60547i	−0.596333	−	0.802737i	$-0.703376\pi$
$457$		−	34.3211i		−	1.60547i	0.596333	−	0.802737i	$-0.296624\pi$
$458$		−	5.32304i		−	0.248729i
$459$		0			0
$460$	4.71585	−	1.61898i	0.219878	−	0.0754855i
$461$	−23.5959			−1.09897			−0.549486	−	0.835503i	$-0.685177\pi$
$461$	−23.5959			−1.09897			−0.549486	+	0.835503i	$0.685177\pi$
$462$		0			0
$463$		−	3.94991i		−	0.183568i	−0.995779	−	0.0917840i	$-0.970743\pi$
$463$		−	3.94991i		−	0.183568i	0.995779	−	0.0917840i	$-0.0292569\pi$
$464$	2.43806			0.113184
$465$		0			0
$466$	−3.51396			−0.162781
$467$		−	9.51396i		−	0.440254i	−0.975471	−	0.220127i	$-0.929353\pi$
$467$		−	9.51396i		−	0.440254i	0.975471	−	0.220127i	$-0.0706471\pi$
$468$		0			0
$469$	56.4846			2.60822
$470$	6.38797	+	18.6072i	0.294655	+	0.858286i
$471$		0			0
$472$			7.42748i			0.341877i
$473$		−	0.217329i		−	0.00999279i
$474$		0			0
$475$	3.94567	−	3.07111i	0.181040	−	0.140912i
$476$	−20.0648			−0.919669
$477$		0			0
$478$			29.4986i			1.34923i
$479$	28.4591			1.30033			0.650164	−	0.759794i	$-0.274700\pi$
$479$	28.4591			1.30033			0.650164	+	0.759794i	$0.274700\pi$
$480$		0			0
$481$	−9.89134			−0.451006
$482$		−	29.2702i		−	1.33322i
$483$		0			0
$484$	10.7827			0.490121
$485$	13.9762	−	4.79811i	0.634625	−	0.217871i
$486$		0			0
$487$			21.5169i			0.975025i	0.873116	+	0.487513i	$0.162096\pi$
$487$			21.5169i			0.975025i	−0.873116	+	0.487513i	$0.837904\pi$
$488$		−	6.45963i		−	0.292414i
$489$		0			0
$490$	20.0062	−	6.86828i	0.903790	−	0.310277i
$491$	−20.3044			−0.916325			−0.458163	−	0.888868i	$-0.651492\pi$
$491$	−20.3044			−0.916325			−0.458163	+	0.888868i	$0.651492\pi$
$492$		0			0
$493$		−	12.0578i		−	0.543058i
$494$	0.985939			0.0443595
$495$		0			0
$496$	0.715853			0.0321427
$497$		−	24.9193i		−	1.11778i
$498$		0			0
$499$	12.9193			0.578346			0.289173	−	0.957277i	$-0.406620\pi$
$499$	12.9193			0.578346			0.289173	+	0.957277i	$0.406620\pi$
$500$	−9.35991	−	6.11491i	−0.418588	−	0.273467i
$501$		0			0
$502$		−	13.7901i		−	0.615483i
$503$		−	18.4721i		−	0.823631i	−0.911267	−	0.411815i	$-0.864895\pi$
$503$		−	18.4721i		−	0.823631i	0.911267	−	0.411815i	$-0.135105\pi$
$504$		0			0
$505$	−4.08226	−	11.8910i	−0.181658	−	0.529142i
$506$	−1.03951			−0.0462117
$507$		0			0
$508$			4.69009i			0.208089i
$509$	41.2632			1.82896			0.914480	−	0.404630i	$-0.132600\pi$
$509$	41.2632			1.82896			0.914480	+	0.404630i	$0.132600\pi$
$510$		0			0
$511$	28.7019			1.26970
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−4.10866			−0.181225
$515$	40.0699	−	13.7563i	1.76569	−	0.606173i
$516$		0			0
$517$		−	4.10155i		−	0.180386i
$518$		−	40.7019i		−	1.78834i
$519$		0			0
$520$	−0.715853	−	2.08517i	−0.0313922	−	0.0914407i
$521$	−27.3598			−1.19866			−0.599328	−	0.800504i	$-0.704565\pi$
$521$	−27.3598			−1.19866			−0.599328	+	0.800504i	$0.704565\pi$
$522$		0			0
$523$			5.31698i			0.232495i	0.993220	+	0.116248i	$0.0370866\pi$
$523$			5.31698i			0.232495i	−0.993220	+	0.116248i	$0.962913\pi$
$524$	−9.61979			−0.420242
$525$		0			0
$526$	2.90677			0.126741
$527$		−	3.54037i		−	0.154221i
$528$		0			0
$529$	18.0279			0.783823
$530$	2.82535	+	8.22982i	0.122725	+	0.357480i
$531$		0			0
$532$			4.05705i			0.175895i
$533$			10.0558i			0.435567i
$534$		0			0
$535$	−16.9193	+	5.80850i	−0.731483	+	0.251123i
$536$	13.9226			0.601364
$537$		0			0
$538$			6.60840i			0.284908i
$539$	−4.40994			−0.189950
$540$		0			0
$541$	−10.2951			−0.442622			−0.221311	−	0.975203i	$-0.571034\pi$
$541$	−10.2951			−0.442622			−0.221311	+	0.975203i	$0.571034\pi$
$542$		−	29.3789i		−	1.26193i
$543$		0			0
$544$	−4.94567			−0.212044
$545$	3.34510	+	9.74378i	0.143289	+	0.417378i
$546$		0			0
$547$			3.50290i			0.149773i	0.997192	+	0.0748866i	$0.0238595\pi$
$547$			3.50290i			0.149773i	−0.997192	+	0.0748866i	$0.976141\pi$
$548$			18.8370i			0.804677i
$549$		0			0
$550$	1.43171	+	1.83941i	0.0610481	+	0.0784328i
$551$	−2.43806			−0.103865
$552$		0			0
$553$		−	7.51544i		−	0.319589i
$554$	17.8472			0.758254
$555$		0			0
$556$	14.3510			0.608617
$557$			15.2577i			0.646491i	0.946315	+	0.323246i	$0.104774\pi$
$557$			15.2577i			0.646491i	−0.946315	+	0.323246i	$0.895226\pi$
$558$		0			0
$559$	−0.459630			−0.0194403
$560$	8.58028	−	2.94567i	0.362583	−	0.124477i
$561$		0			0
$562$		−	10.9051i		−	0.460002i
$563$		−	27.5653i		−	1.16174i	−0.813996	−	0.580870i	$-0.802712\pi$
$563$		−	27.5653i		−	1.16174i	0.813996	−	0.580870i	$-0.197288\pi$
$564$		0			0
$565$	30.5808	−	10.4986i	1.28654	−	0.441679i
$566$	6.27468			0.263745
$567$		0			0
$568$		−	6.14222i		−	0.257722i
$569$	−27.3598			−1.14698			−0.573492	−	0.819211i	$-0.694412\pi$
$569$	−27.3598			−1.14698			−0.573492	+	0.819211i	$0.694412\pi$
$570$		0			0
$571$	−40.1895			−1.68188			−0.840939	−	0.541130i	$-0.817997\pi$
$571$	−40.1895			−1.68188			−0.840939	+	0.541130i	$0.817997\pi$
$572$			0.459630i			0.0192181i
$573$		0			0
$574$	−41.3789			−1.72712
$575$	6.84800	+	8.79811i	0.285581	+	0.366907i
$576$		0			0
$577$			18.7987i			0.782601i	0.920263	+	0.391300i	$0.127975\pi$
$577$			18.7987i			0.782601i	−0.920263	+	0.391300i	$0.872025\pi$
$578$			7.45963i			0.310280i
$579$		0			0
$580$	1.77018	+	5.15628i	0.0735029	+	0.214103i
$581$	−17.7592			−0.736776
$582$		0			0
$583$		−	1.81408i		−	0.0751317i
$584$	7.07459			0.292748
$585$		0			0
$586$	22.9193			0.946786
$587$			25.7563i			1.06307i	0.847035	+	0.531537i	$0.178385\pi$
$587$			25.7563i			1.06307i	−0.847035	+	0.531537i	$0.821615\pi$
$588$		0			0
$589$	−0.715853			−0.0294962
$590$	−15.7084	+	5.39281i	−0.646706	+	0.222019i
$591$		0			0
$592$		−	10.0324i		−	0.412329i
$593$			36.4332i			1.49613i	0.663624	+	0.748067i	$0.269018\pi$
$593$			36.4332i			1.49613i	−0.663624	+	0.748067i	$0.730982\pi$
$594$		0			0
$595$	−14.5683	−	42.4352i	−0.597242	−	1.73967i
$596$	15.3747			0.629773
$597$		0			0
$598$			2.19846i			0.0899018i
$599$	−11.3521			−0.463833			−0.231916	−	0.972736i	$-0.574500\pi$
$599$	−11.3521			−0.463833			−0.231916	+	0.972736i	$0.574500\pi$
$600$		0			0
$601$	−14.9721			−0.610724			−0.305362	−	0.952236i	$-0.598777\pi$
$601$	−14.9721			−0.610724			−0.305362	+	0.952236i	$0.598777\pi$
$602$		−	1.89134i		−	0.0770851i
$603$		0			0
$604$	5.17548			0.210587
$605$	7.82889	+	22.8044i	0.318290	+	0.927129i
$606$		0			0
$607$		−	28.3649i		−	1.15130i	−0.817697	−	0.575649i	$-0.804750\pi$
$607$		−	28.3649i		−	1.15130i	0.817697	−	0.575649i	$-0.195250\pi$
$608$			1.00000i			0.0405554i
$609$		0			0
$610$	13.6615	−	4.69009i	0.553139	−	0.189896i
$611$	−8.67440			−0.350929
$612$		0			0
$613$			22.8304i			0.922113i	0.887371	+	0.461056i	$0.152529\pi$
$613$			22.8304i			0.922113i	−0.887371	+	0.461056i	$0.847471\pi$
$614$	4.17034			0.168301
$615$		0			0
$616$	−1.89134			−0.0762041
$617$			9.62263i			0.387392i	0.981062	+	0.193696i	$0.0620476\pi$
$617$			9.62263i			0.387392i	−0.981062	+	0.193696i	$0.937952\pi$
$618$		0			0
$619$	−2.56829			−0.103228			−0.0516142	−	0.998667i	$-0.516437\pi$
$619$	−2.56829			−0.103228			−0.0516142	+	0.998667i	$0.516437\pi$
$620$	0.519753	+	1.51396i	0.0208738	+	0.0608022i
$621$		0			0
$622$			12.2309i			0.490413i
$623$		−	24.4596i		−	0.979954i
$624$		0			0
$625$	6.13659	−	24.2351i	0.245464	−	0.969406i
$626$	8.71274			0.348231
$627$		0			0
$628$			11.7050i			0.467079i
$629$	−49.6169			−1.97836
$630$		0			0
$631$	−20.6241			−0.821034			−0.410517	−	0.911853i	$-0.634652\pi$
$631$	−20.6241			−0.821034			−0.410517	+	0.911853i	$0.634652\pi$
$632$		−	1.85244i		−	0.0736862i
$633$		0			0
$634$	9.78267			0.388520
$635$	−9.91911	+	3.40530i	−0.393628	+	0.135135i
$636$		0			0
$637$			9.32662i			0.369534i
$638$		−	1.13659i		−	0.0449980i
$639$		0			0
$640$	2.11491	−	0.726062i	0.0835991	−	0.0287001i
$641$	−27.1332			−1.07170			−0.535849	−	0.844314i	$-0.680008\pi$
$641$	−27.1332			−1.07170			−0.535849	+	0.844314i	$0.680008\pi$
$642$		0			0
$643$			35.0016i			1.38033i	0.723653	+	0.690164i	$0.242461\pi$
$643$			35.0016i			1.38033i	−0.723653	+	0.690164i	$0.757539\pi$
$644$	−9.04646			−0.356481
$645$		0			0
$646$	4.94567			0.194585
$647$		−	5.77018i		−	0.226849i	−0.993547	−	0.113425i	$-0.963818\pi$
$647$		−	5.77018i		−	0.226849i	0.993547	−	0.113425i	$-0.0361821\pi$
$648$		0			0
$649$	3.46258			0.135918
$650$	3.89019	−	3.02792i	0.152586	−	0.118765i
$651$		0			0
$652$		−	16.6944i		−	0.653802i
$653$			41.6087i			1.62827i	0.580673	+	0.814137i	$0.302790\pi$
$653$			41.6087i			1.62827i	−0.580673	+	0.814137i	$0.697210\pi$
$654$		0			0
$655$	−6.98456	−	20.3450i	−0.272909	−	0.794943i
$656$	−10.1993			−0.398214
$657$		0			0
$658$		−	35.6943i		−	1.39151i
$659$	−6.16139			−0.240014			−0.120007	−	0.992773i	$-0.538292\pi$
$659$	−6.16139			−0.240014			−0.120007	+	0.992773i	$0.538292\pi$
$660$		0			0
$661$	33.3091			1.29557			0.647787	−	0.761821i	$-0.275695\pi$
$661$	33.3091			1.29557			0.647787	+	0.761821i	$0.275695\pi$
$662$		−	12.4596i		−	0.484257i
$663$		0			0
$664$	−4.37737			−0.169875
$665$	−8.58028	+	2.94567i	−0.332729	+	0.114228i
$666$		0			0
$667$		−	5.43643i		−	0.210499i
$668$			19.7827i			0.765415i
$669$		0			0
$670$	10.1087	+	29.4450i	0.390532	+	1.13756i
$671$	−3.01138			−0.116253
$672$		0			0
$673$		−	20.7576i		−	0.800146i	−0.916483	−	0.400073i	$-0.868985\pi$
$673$		−	20.7576i		−	0.800146i	0.916483	−	0.400073i	$-0.131015\pi$
$674$	10.5522			0.406454
$675$		0			0
$676$	−12.0279			−0.462612
$677$		−	0.403781i		−	0.0155186i	−0.999970	−	0.00775928i	$-0.997530\pi$
$677$		−	0.403781i		−	0.0155186i	0.999970	−	0.00775928i	$-0.00246988\pi$
$678$		0			0
$679$	−26.8106			−1.02890
$680$	−3.59086	−	10.4596i	−0.137703	−	0.401109i
$681$		0			0
$682$		−	0.333720i		−	0.0127788i
$683$			29.8913i			1.14376i	0.820337	+	0.571880i	$0.193786\pi$
$683$			29.8913i			1.14376i	−0.820337	+	0.571880i	$0.806214\pi$
$684$		0			0
$685$	−39.8385	+	13.6768i	−1.52215	+	0.522565i
$686$	−9.97884			−0.380994
$687$		0			0
$688$		−	0.466185i		−	0.0177731i
$689$	−3.83662			−0.146164
$690$		0			0
$691$	18.1336			0.689836			0.344918	−	0.938633i	$-0.387907\pi$
$691$	18.1336			0.689836			0.344918	+	0.938633i	$0.387907\pi$
$692$			12.3510i			0.469513i
$693$		0			0
$694$	−19.8649			−0.754062
$695$	10.4197	+	30.3510i	0.395241	+	1.15128i
$696$		0			0
$697$			50.4422i			1.91063i
$698$		−	32.3510i		−	1.22450i
$699$		0			0
$700$	12.4596	+	16.0078i	0.470930	+	0.605036i
$701$	27.1676			1.02611			0.513054	−	0.858357i	$-0.328514\pi$
$701$	27.1676			1.02611			0.513054	+	0.858357i	$0.328514\pi$
$702$		0			0
$703$			10.0324i			0.378379i
$704$	−0.466185			−0.0175700
$705$		0			0
$706$	−17.4053			−0.655057
$707$			22.8106i			0.857881i
$708$		0			0
$709$	16.1087			0.604974			0.302487	−	0.953154i	$-0.402183\pi$
$709$	16.1087			0.604974			0.302487	+	0.953154i	$0.402183\pi$
$710$	12.9902	−	4.45963i	0.487514	−	0.167367i
$711$		0			0
$712$		−	6.02892i		−	0.225944i
$713$		−	1.59622i		−	0.0597789i
$714$		0			0
$715$	−0.972075	+	0.333720i	−0.0363536	+	0.0124804i
$716$	−4.52323			−0.169041
$717$		0			0
$718$			32.5099i			1.21326i
$719$	−38.2113			−1.42504			−0.712521	−	0.701651i	$-0.752446\pi$
$719$	−38.2113			−1.42504			−0.712521	+	0.701651i	$0.752446\pi$
$720$		0			0
$721$	−76.8664			−2.86266
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	−0.147558			−0.00548396
$725$	−9.61979	+	7.48755i	−0.357270	+	0.278081i
$726$		0			0
$727$			26.3203i			0.976166i	0.872797	+	0.488083i	$0.162304\pi$
$727$			26.3203i			0.976166i	−0.872797	+	0.488083i	$0.837696\pi$
$728$			4.00000i			0.148250i
$729$		0			0
$730$	5.13659	+	14.9621i	0.190114	+	0.553772i
$731$	−2.30560			−0.0852756
$732$		0			0
$733$		−	31.1023i		−	1.14879i	−0.818578	−	0.574395i	$-0.805237\pi$
$733$		−	31.1023i		−	1.14879i	0.818578	−	0.574395i	$-0.194763\pi$
$734$	35.2473			1.30100
$735$		0			0
$736$	−2.22982			−0.0821921
$737$		−	6.49051i		−	0.239081i
$738$		0			0
$739$	6.86341			0.252475			0.126237	−	0.992000i	$-0.459710\pi$
$739$	6.86341			0.252475			0.126237	+	0.992000i	$0.459710\pi$
$740$	21.2176	−	7.28415i	0.779975	−	0.267771i
$741$		0			0
$742$		−	15.7873i		−	0.579571i
$743$			14.1865i			0.520450i	0.965548	+	0.260225i	$0.0837968\pi$
$743$			14.1865i			0.520450i	−0.965548	+	0.260225i	$0.916203\pi$
$744$		0			0
$745$	11.1630	+	32.5161i	0.408981	+	1.19130i
$746$	16.0675			0.588272
$747$		0			0
$748$			2.30560i			0.0843010i
$749$	32.4564			1.18593
$750$		0			0
$751$	−27.3091			−0.996524			−0.498262	−	0.867027i	$-0.666028\pi$
$751$	−27.3091			−0.996524			−0.498262	+	0.867027i	$0.666028\pi$
$752$		−	8.79811i		−	0.320834i
$753$		0			0
$754$	−2.40378			−0.0875405
$755$	3.75772	+	10.9457i	0.136757	+	0.398354i
$756$		0			0
$757$		−	1.72612i		−	0.0627369i	−0.999508	−	0.0313685i	$-0.990013\pi$
$757$		−	1.72612i		−	0.0627369i	0.999508	−	0.0313685i	$-0.00998653\pi$
$758$			8.24230i			0.299374i
$759$		0			0
$760$	−2.11491	+	0.726062i	−0.0767158	+	0.0263370i
$761$	2.63932			0.0956752			0.0478376	−	0.998855i	$-0.484767\pi$
$761$	2.63932			0.0956752			0.0478376	+	0.998855i	$0.484767\pi$
$762$		0			0
$763$		−	18.6916i		−	0.676681i
$764$	−1.91831			−0.0694020
$765$		0			0
$766$	−12.9193			−0.466792
$767$		−	7.32304i		−	0.264420i
$768$		0			0
$769$	−26.6241			−0.960091			−0.480046	−	0.877244i	$-0.659380\pi$
$769$	−26.6241			−0.960091			−0.480046	+	0.877244i	$0.659380\pi$
$770$	−1.37323	−	4.00000i	−0.0494877	−	0.144150i
$771$		0			0
$772$			26.6732i			0.959990i
$773$			10.1645i			0.365592i	0.983151	+	0.182796i	$0.0585148\pi$
$773$			10.1645i			0.365592i	−0.983151	+	0.182796i	$0.941485\pi$
$774$		0			0
$775$	−2.82452	+	2.19846i	−0.101460	+	0.0789711i
$776$	−6.60840			−0.237228
$777$		0			0
$778$			22.7830i			0.816811i
$779$	10.1993			0.365427
$780$		0			0
$781$	−2.86341			−0.102461
$782$			11.0279i			0.394358i
$783$		0			0
$784$	−9.45963			−0.337844
$785$	−24.7549	+	8.49852i	−0.883540	+	0.303325i
$786$		0			0
$787$		−	20.1719i		−	0.719052i	−0.933135	−	0.359526i	$-0.882938\pi$
$787$		−	20.1719i		−	0.719052i	0.933135	−	0.359526i	$-0.117062\pi$
$788$		−	6.58078i		−	0.234431i
$789$		0			0
$790$	3.91774	−	1.34499i	0.139387	−	0.0478525i
$791$	−58.6634			−2.08583
$792$		0			0
$793$			6.36880i			0.226163i
$794$	20.4177			0.724597
$795$		0			0
$796$	−12.4596			−0.441620
$797$			52.0808i			1.84480i	0.386239	+	0.922399i	$0.373774\pi$
$797$			52.0808i			1.84480i	−0.386239	+	0.922399i	$0.626226\pi$
$798$		0			0
$799$	−43.5125			−1.53936
$800$	3.07111	+	3.94567i	0.108580	+	0.139500i
$801$		0			0
$802$		−	21.8163i		−	0.770359i
$803$		−	3.29807i		−	0.116386i
$804$		0			0
$805$	−6.56829	−	19.1324i	−0.231502	−	0.674330i
$806$	−0.705787			−0.0248603
$807$		0			0
$808$			5.62246i			0.197798i
$809$	−11.4592			−0.402884			−0.201442	−	0.979500i	$-0.564563\pi$
$809$	−11.4592			−0.402884			−0.201442	+	0.979500i	$0.564563\pi$
$810$		0			0
$811$	13.5962			0.477428			0.238714	−	0.971090i	$-0.423274\pi$
$811$	13.5962			0.477428			0.238714	+	0.971090i	$0.423274\pi$
$812$		−	9.89134i		−	0.347118i
$813$		0			0
$814$	−4.67696			−0.163927
$815$	35.3071	−	12.1212i	1.23675	−	0.424585i
$816$		0			0
$817$			0.466185i			0.0163098i
$818$			19.3789i			0.677567i
$819$		0			0
$820$	−7.40530	−	21.5705i	−0.258604	−	0.753274i
$821$	−43.6731			−1.52420			−0.762100	−	0.647459i	$-0.775832\pi$
$821$	−43.6731			−1.52420			−0.762100	+	0.647459i	$0.775832\pi$
$822$		0			0
$823$		−	42.2148i		−	1.47151i	−0.677245	−	0.735757i	$-0.736826\pi$
$823$		−	42.2148i		−	1.47151i	0.677245	−	0.735757i	$-0.263174\pi$
$824$	−18.9464			−0.660029
$825$		0			0
$826$	30.1336			1.04848
$827$		−	53.8385i		−	1.87215i	−0.351802	−	0.936074i	$-0.614431\pi$
$827$		−	53.8385i		−	1.87215i	0.351802	−	0.936074i	$-0.385569\pi$
$828$		0			0
$829$	55.1755			1.91632			0.958162	−	0.286227i	$-0.0924011\pi$
$829$	55.1755			1.91632			0.958162	+	0.286227i	$0.0924011\pi$
$830$	−3.17824	−	9.25774i	−0.110318	−	0.321341i
$831$		0			0
$832$			0.985939i			0.0341813i
$833$			46.7842i			1.62098i
$834$		0			0
$835$	−41.8385	+	14.3634i	−1.44788	+	0.497068i
$836$	0.466185			0.0161234
$837$		0			0
$838$		−	28.7522i		−	0.993229i
$839$	17.0534			0.588750			0.294375	−	0.955690i	$-0.404889\pi$
$839$	17.0534			0.588750			0.294375	+	0.955690i	$0.404889\pi$
$840$		0			0
$841$	−23.0558			−0.795029
$842$			14.7159i			0.507142i
$843$		0			0
$844$	−12.0000			−0.413057
$845$	−8.73302	−	25.4379i	−0.300425	−	0.875092i
$846$		0			0
$847$		−	43.7458i		−	1.50312i
$848$		−	3.89134i		−	0.133629i
$849$		0			0
$850$	19.5140	−	15.1887i	0.669323	−	0.520967i
$851$	−22.3704			−0.766848
$852$		0			0
$853$		−	14.0106i		−	0.479712i	−0.970808	−	0.239856i	$-0.922900\pi$
$853$		−	14.0106i		−	0.479712i	0.970808	−	0.239856i	$-0.0771003\pi$
$854$	−26.2070			−0.896786
$855$		0			0
$856$	8.00000			0.273434
$857$		−	48.5933i		−	1.65991i	−0.557827	−	0.829957i	$-0.688365\pi$
$857$		−	48.5933i		−	1.65991i	0.557827	−	0.829957i	$-0.311635\pi$
$858$		0			0
$859$	−57.5434			−1.96336			−0.981678	−	0.190548i	$-0.938973\pi$
$859$	−57.5434			−1.96336			−0.981678	+	0.190548i	$0.938973\pi$
$860$	0.985939	−	0.338479i	0.0336202	−	0.0115421i
$861$		0			0
$862$		−	18.2001i		−	0.619897i
$863$			30.8634i			1.05060i	0.850916	+	0.525301i	$0.176047\pi$
$863$			30.8634i			1.05060i	−0.850916	+	0.525301i	$0.823953\pi$
$864$		0			0
$865$	−26.1212	+	8.96757i	−0.888146	+	0.304906i
$866$	−2.77178			−0.0941890
$867$		0			0
$868$		−	2.90425i		−	0.0985766i
$869$	−0.863581			−0.0292950
$870$		0			0
$871$	−13.7268			−0.465116
$872$		−	4.60719i		−	0.156019i
$873$		0			0
$874$	2.22982			0.0754246
$875$	−24.8085	+	37.9736i	−0.838679	+	1.28374i
$876$		0			0
$877$			42.4888i			1.43474i	0.696690	+	0.717372i	$0.254655\pi$
$877$			42.4888i			1.43474i	−0.696690	+	0.717372i	$0.745345\pi$
$878$		−	12.2034i		−	0.411845i
$879$		0			0
$880$	−0.338479	−	0.985939i	−0.0114101	−	0.0332360i
$881$	30.8182			1.03829			0.519146	−	0.854686i	$-0.326250\pi$
$881$	30.8182			1.03829			0.519146	+	0.854686i	$0.326250\pi$
$882$		0			0
$883$			39.8900i			1.34241i	0.741274	+	0.671203i	$0.234222\pi$
$883$			39.8900i			1.34241i	−0.741274	+	0.671203i	$0.765778\pi$
$884$	4.87613			0.164002
$885$		0			0
$886$	−21.9736			−0.738217
$887$			39.1924i			1.31595i	0.753038	+	0.657977i	$0.228587\pi$
$887$			39.1924i			1.31595i	−0.753038	+	0.657977i	$0.771413\pi$
$888$		0			0
$889$	19.0279			0.638176
$890$	12.7506	−	4.37737i	0.427402	−	0.146730i
$891$		0			0
$892$			3.75772i			0.125818i
$893$			8.79811i			0.294418i
$894$		0			0
$895$	−3.28415	−	9.56622i	−0.109777	−	0.319763i
$896$	−4.05705			−0.135536
$897$		0			0
$898$		−	23.1895i		−	0.773843i
$899$	1.74529			0.0582088
$900$		0			0
$901$	−19.2453			−0.641152
$902$			4.75475i			0.158316i
$903$		0			0
$904$	−14.4596			−0.480920
$905$	−0.107136	−	0.312072i	−0.00356133	−	0.0103736i
$906$		0			0
$907$		−	49.5098i		−	1.64395i	−0.569527	−	0.821973i	$-0.692873\pi$
$907$		−	49.5098i		−	1.64395i	0.569527	−	0.821973i	$-0.307127\pi$
$908$			17.8913i			0.593745i
$909$		0			0
$910$	−8.45963	+	2.90425i	−0.280434	+	0.0962749i
$911$	14.3634			0.475882			0.237941	−	0.971280i	$-0.423527\pi$
$911$	14.3634			0.475882			0.237941	+	0.971280i	$0.423527\pi$
$912$		0			0
$913$			2.04067i			0.0675362i
$914$	−34.3211			−1.13524
$915$		0			0
$916$	−5.32304			−0.175878
$917$			39.0279i			1.28882i
$918$		0			0
$919$	54.1336			1.78570			0.892852	−	0.450350i	$-0.148701\pi$
$919$	54.1336			1.78570			0.892852	+	0.450350i	$0.148701\pi$
$920$	−1.61898	−	4.71585i	−0.0533763	−	0.155477i
$921$		0			0
$922$			23.5959i			0.777091i
$923$			6.05585i			0.199331i
$924$		0			0
$925$	30.8106	+	39.5845i	1.01305	+	1.30153i
$926$	−3.94991			−0.129802
$927$		0			0
$928$		−	2.43806i		−	0.0800333i
$929$	−30.2579			−0.992730			−0.496365	−	0.868114i	$-0.665332\pi$
$929$	−30.2579			−0.992730			−0.496365	+	0.868114i	$0.665332\pi$
$930$		0			0
$931$	9.45963			0.310027
$932$			3.51396i			0.115104i
$933$		0			0
$934$	−9.51396			−0.311306
$935$	−4.87613	+	1.67401i	−0.159466	+	0.0547459i
$936$		0			0
$937$		−	49.7747i		−	1.62607i	−0.582215	−	0.813035i	$-0.697814\pi$
$937$		−	49.7747i		−	1.62607i	0.582215	−	0.813035i	$-0.302186\pi$
$938$		−	56.4846i		−	1.84429i
$939$		0			0
$940$	18.6072	−	6.38797i	0.606900	−	0.208353i
$941$	9.51265			0.310104			0.155052	−	0.987906i	$-0.450446\pi$
$941$	9.51265			0.310104			0.155052	+	0.987906i	$0.450446\pi$
$942$		0			0
$943$			22.7425i			0.740597i
$944$	7.42748			0.241744
$945$		0			0
$946$	−0.217329			−0.00706597
$947$			2.26871i			0.0737231i	0.999320	+	0.0368616i	$0.0117361\pi$
$947$			2.26871i			0.0737231i	−0.999320	+	0.0368616i	$0.988264\pi$
$948$		0			0
$949$	−6.97511			−0.226422
$950$	−3.07111	−	3.94567i	−0.0996399	−	0.128014i
$951$		0			0
$952$			20.0648i			0.650304i
$953$			1.75770i			0.0569374i	0.999595	+	0.0284687i	$0.00906310\pi$
$953$			1.75770i			0.0569374i	−0.999595	+	0.0284687i	$0.990937\pi$
$954$		0			0
$955$	−1.39281	−	4.05705i	−0.0450703	−	0.131283i
$956$	29.4986			0.954052
$957$		0			0
$958$		−	28.4591i		−	0.919470i
$959$	76.4226			2.46781
$960$		0			0
$961$	−30.4876			−0.983470
$962$			9.89134i			0.318909i
$963$		0			0
$964$	−29.2702			−0.942731
$965$	−56.4114	+	19.3664i	−1.81595	+	0.623427i
$966$		0			0
$967$			9.60061i			0.308735i	0.988014	+	0.154367i	$0.0493340\pi$
$967$			9.60061i			0.308735i	−0.988014	+	0.154367i	$0.950666\pi$
$968$		−	10.7827i		−	0.346568i
$969$		0			0
$970$	−4.79811	−	13.9762i	−0.154058	−	0.448747i
$971$	48.8232			1.56681			0.783405	−	0.621511i	$-0.213481\pi$
$971$	48.8232			1.56681			0.783405	+	0.621511i	$0.213481\pi$
$972$		0			0
$973$		−	58.2225i		−	1.86653i
$974$	21.5169			0.689447
$975$		0			0
$976$	−6.45963			−0.206768
$977$		−	25.1057i		−	0.803203i	−0.915815	−	0.401601i	$-0.868454\pi$
$977$		−	25.1057i		−	0.803203i	0.915815	−	0.401601i	$-0.131546\pi$
$978$		0			0
$979$	−2.81060			−0.0898270
$980$	−6.86828	−	20.0062i	−0.219399	−	0.639076i
$981$		0			0
$982$			20.3044i			0.647940i
$983$		−	27.7827i		−	0.886130i	−0.896490	−	0.443065i	$-0.853891\pi$
$983$		−	27.7827i		−	0.886130i	0.896490	−	0.443065i	$-0.146109\pi$
$984$		0			0
$985$	13.9177	−	4.77806i	0.443456	−	0.152241i
$986$	−12.0578			−0.384000
$987$		0			0
$988$		−	0.985939i		−	0.0313669i
$989$	−1.03951			−0.0330544
$990$		0			0
$991$	−51.0140			−1.62051			−0.810257	−	0.586075i	$-0.800672\pi$
$991$	−51.0140			−1.62051			−0.810257	+	0.586075i	$0.800672\pi$
$992$		−	0.715853i		−	0.0227283i
$993$		0			0
$994$	−24.9193			−0.790391
$995$	−9.04646	−	26.3510i	−0.286792	−	0.835382i
$996$		0			0
$997$		−	14.2371i		−	0.450895i	−0.974255	−	0.225447i	$-0.927616\pi$
$997$		−	14.2371i		−	0.450895i	0.974255	−	0.225447i	$-0.0723844\pi$
$998$		−	12.9193i		−	0.408952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.h.1369.3	✓	12
3.2	odd	2	inner	1710.2.d.h.1369.10	yes	12
5.2	odd	4		8550.2.a.cx.1.1		6
5.3	odd	4		8550.2.a.cw.1.6		6
5.4	even	2	inner	1710.2.d.h.1369.9	yes	12
15.2	even	4		8550.2.a.cw.1.1		6
15.8	even	4		8550.2.a.cx.1.6		6
15.14	odd	2	inner	1710.2.d.h.1369.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.d.h.1369.3	✓	12	1.1	even	1	trivial
1710.2.d.h.1369.4	yes	12	15.14	odd	2	inner
1710.2.d.h.1369.9	yes	12	5.4	even	2	inner
1710.2.d.h.1369.10	yes	12	3.2	odd	2	inner
8550.2.a.cw.1.1		6	15.2	even	4
8550.2.a.cw.1.6		6	5.3	odd	4
8550.2.a.cx.1.1		6	5.2	odd	4
8550.2.a.cx.1.6		6	15.8	even	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.726062 - 2.11491i) q^{5} +4.05705i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.726062 - 2.11491i) q^{5} +4.05705i q^{7} +1.00000i q^{8} +(-2.11491 + 0.726062i) q^{10} +0.466185 q^{11} -0.985939i q^{13} +4.05705 q^{14} +1.00000 q^{16} -4.94567i q^{17} -1.00000 q^{19} +(0.726062 + 2.11491i) q^{20} -0.466185i q^{22} -2.22982i q^{23} +(-3.94567 + 3.07111i) q^{25} -0.985939 q^{26} -4.05705i q^{28} +2.43806 q^{29} +0.715853 q^{31} -1.00000i q^{32} -4.94567 q^{34} +(8.58028 - 2.94567i) q^{35} -10.0324i q^{37} +1.00000i q^{38} +(2.11491 - 0.726062i) q^{40} -10.1993 q^{41} -0.466185i q^{43} -0.466185 q^{44} -2.22982 q^{46} -8.79811i q^{47} -9.45963 q^{49} +(3.07111 + 3.94567i) q^{50} +0.985939i q^{52} -3.89134i q^{53} +(-0.338479 - 0.985939i) q^{55} -4.05705 q^{56} -2.43806i q^{58} +7.42748 q^{59} -6.45963 q^{61} -0.715853i q^{62} -1.00000 q^{64} +(-2.08517 + 0.715853i) q^{65} -13.9226i q^{67} +4.94567i q^{68} +(-2.94567 - 8.58028i) q^{70} -6.14222 q^{71} -7.07459i q^{73} -10.0324 q^{74} +1.00000 q^{76} +1.89134i q^{77} -1.85244 q^{79} +(-0.726062 - 2.11491i) q^{80} +10.1993i q^{82} +4.37737i q^{83} +(-10.4596 + 3.59086i) q^{85} -0.466185 q^{86} +0.466185i q^{88} -6.02892 q^{89} +4.00000 q^{91} +2.22982i q^{92} -8.79811 q^{94} +(0.726062 + 2.11491i) q^{95} +6.60840i q^{97} +9.45963i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 12 q^{16} - 12 q^{19} - 4 q^{25} + 16 q^{31} - 16 q^{34} + 24 q^{46} - 12 q^{49} - 40 q^{55} + 24 q^{61} - 12 q^{64} + 8 q^{70} + 12 q^{76} - 24 q^{85} + 48 q^{91} - 40 q^{94}+O(q^{100}) \) 12 * q - 12 * q^4 + 12 * q^16 - 12 * q^19 - 4 * q^25 + 16 * q^31 - 16 * q^34 + 24 * q^46 - 12 * q^49 - 40 * q^55 + 24 * q^61 - 12 * q^64 + 8 * q^70 + 12 * q^76 - 24 * q^85 + 48 * q^91 - 40 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more