LMFDB - Embedded newform 170.2.b.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(101,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("170.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.b (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:	$1.35745683436$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.101
Dual form			170.2.b.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{10} +6.00000i q^{11} +1.00000i q^{12} -5.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} -2.00000 q^{18} +3.00000 q^{19} +1.00000i q^{20} -6.00000i q^{22} +2.00000i q^{23} -1.00000i q^{24} -1.00000 q^{25} +5.00000 q^{26} +5.00000i q^{27} -1.00000i q^{29} +1.00000 q^{30} -7.00000i q^{31} -1.00000 q^{32} -6.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} +2.00000 q^{36} -10.0000i q^{37} -3.00000 q^{38} -5.00000i q^{39} -1.00000i q^{40} -12.0000i q^{41} -4.00000 q^{43} +6.00000i q^{44} +2.00000i q^{45} -2.00000i q^{46} +7.00000 q^{47} +1.00000i q^{48} +7.00000 q^{49} +1.00000 q^{50} +(-1.00000 + 4.00000i) q^{51} -5.00000 q^{52} -1.00000 q^{53} -5.00000i q^{54} -6.00000 q^{55} +3.00000i q^{57} +1.00000i q^{58} -9.00000 q^{59} -1.00000 q^{60} +3.00000i q^{61} +7.00000i q^{62} +1.00000 q^{64} -5.00000i q^{65} +6.00000 q^{66} +10.0000 q^{67} +(4.00000 + 1.00000i) q^{68} -2.00000 q^{69} +9.00000i q^{71} -2.00000 q^{72} -7.00000i q^{73} +10.0000i q^{74} -1.00000i q^{75} +3.00000 q^{76} +5.00000i q^{78} +8.00000i q^{79} +1.00000i q^{80} +1.00000 q^{81} +12.0000i q^{82} +2.00000 q^{83} +(-1.00000 + 4.00000i) q^{85} +4.00000 q^{86} +1.00000 q^{87} -6.00000i q^{88} -1.00000 q^{89} -2.00000i q^{90} +2.00000i q^{92} +7.00000 q^{93} -7.00000 q^{94} +3.00000i q^{95} -1.00000i q^{96} -1.00000i q^{97} -7.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} - 10 q^{13} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{25} + 10 q^{26} + 2 q^{30} - 2 q^{32} - 12 q^{33} - 8 q^{34} + 4 q^{36} - 6 q^{38} - 8 q^{43} + 14 q^{47} + 14 q^{49} + 2 q^{50} - 2 q^{51} - 10 q^{52} - 2 q^{53} - 12 q^{55} - 18 q^{59} - 2 q^{60} + 2 q^{64} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} - 4 q^{72} + 6 q^{76} + 2 q^{81} + 4 q^{83} - 2 q^{85} + 8 q^{86} + 2 q^{87} - 2 q^{89} + 14 q^{93} - 14 q^{94} - 14 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 - 10 * q^13 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^25 + 10 * q^26 + 2 * q^30 - 2 * q^32 - 12 * q^33 - 8 * q^34 + 4 * q^36 - 6 * q^38 - 8 * q^43 + 14 * q^47 + 14 * q^49 + 2 * q^50 - 2 * q^51 - 10 * q^52 - 2 * q^53 - 12 * q^55 - 18 * q^59 - 2 * q^60 + 2 * q^64 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 - 4 * q^72 + 6 * q^76 + 2 * q^81 + 4 * q^83 - 2 * q^85 + 8 * q^86 + 2 * q^87 - 2 * q^89 + 14 * q^93 - 14 * q^94 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$-1$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			1.00000i			0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	1.00000			0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		−	1.00000i		−	0.408248i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$	−1.00000			−0.353553
$9$	2.00000			0.666667
$10$		−	1.00000i		−	0.316228i
$11$			6.00000i			1.80907i	0.426401	+	0.904534i	$0.359781\pi$
$11$			6.00000i			1.80907i	−0.426401	+	0.904534i	$0.640219\pi$
$12$			1.00000i			0.288675i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$17$	4.00000	+	1.00000i	0.970143	+	0.242536i
$18$	−2.00000			−0.471405
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$			1.00000i			0.223607i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$			2.00000i			0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$			2.00000i			0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.00000			−0.200000
$26$	5.00000			0.980581
$27$			5.00000i			0.962250i
$28$		0			0
$29$		−	1.00000i		−	0.185695i	−0.995680	−	0.0928477i	$-0.970403\pi$
$29$		−	1.00000i		−	0.185695i	0.995680	−	0.0928477i	$-0.0295970\pi$
$30$	1.00000			0.182574
$31$		−	7.00000i		−	1.25724i	−0.777714	−	0.628619i	$-0.783621\pi$
$31$		−	7.00000i		−	1.25724i	0.777714	−	0.628619i	$-0.216379\pi$
$32$	−1.00000			−0.176777
$33$	−6.00000			−1.04447
$34$	−4.00000	−	1.00000i	−0.685994	−	0.171499i
$35$		0			0
$36$	2.00000			0.333333
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$	−3.00000			−0.486664
$39$		−	5.00000i		−	0.800641i
$40$		−	1.00000i		−	0.158114i
$41$		−	12.0000i		−	1.87409i	−0.349215	−	0.937043i	$-0.613552\pi$
$41$		−	12.0000i		−	1.87409i	0.349215	−	0.937043i	$-0.386448\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$			6.00000i			0.904534i
$45$			2.00000i			0.298142i
$46$		−	2.00000i		−	0.294884i
$47$	7.00000			1.02105			0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000			1.02105			0.510527	+	0.859861i	$0.329450\pi$
$48$			1.00000i			0.144338i
$49$	7.00000			1.00000
$50$	1.00000			0.141421
$51$	−1.00000	+	4.00000i	−0.140028	+	0.560112i
$52$	−5.00000			−0.693375
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$		−	5.00000i		−	0.680414i
$55$	−6.00000			−0.809040
$56$		0			0
$57$			3.00000i			0.397360i
$58$			1.00000i			0.131306i
$59$	−9.00000			−1.17170			−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000			−1.17170			−0.585850	+	0.810419i	$0.699239\pi$
$60$	−1.00000			−0.129099
$61$			3.00000i			0.384111i	0.981384	+	0.192055i	$0.0615153\pi$
$61$			3.00000i			0.384111i	−0.981384	+	0.192055i	$0.938485\pi$
$62$			7.00000i			0.889001i
$63$		0			0
$64$	1.00000			0.125000
$65$		−	5.00000i		−	0.620174i
$66$	6.00000			0.738549
$67$	10.0000			1.22169			0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000			1.22169			0.610847	+	0.791748i	$0.290829\pi$
$68$	4.00000	+	1.00000i	0.485071	+	0.121268i
$69$	−2.00000			−0.240772
$70$		0			0
$71$			9.00000i			1.06810i	0.845452	+	0.534052i	$0.179331\pi$
$71$			9.00000i			1.06810i	−0.845452	+	0.534052i	$0.820669\pi$
$72$	−2.00000			−0.235702
$73$		−	7.00000i		−	0.819288i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$		−	7.00000i		−	0.819288i	0.912245	−	0.409644i	$-0.134347\pi$
$74$			10.0000i			1.16248i
$75$		−	1.00000i		−	0.115470i
$76$	3.00000			0.344124
$77$		0			0
$78$			5.00000i			0.566139i
$79$			8.00000i			0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$			8.00000i			0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$			1.00000i			0.111803i
$81$	1.00000			0.111111
$82$			12.0000i			1.32518i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$		0			0
$85$	−1.00000	+	4.00000i	−0.108465	+	0.433861i
$86$	4.00000			0.431331
$87$	1.00000			0.107211
$88$		−	6.00000i		−	0.639602i
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		−	2.00000i		−	0.210819i
$91$		0			0
$92$			2.00000i			0.208514i
$93$	7.00000			0.725866
$94$	−7.00000			−0.721995
$95$			3.00000i			0.307794i
$96$		−	1.00000i		−	0.102062i
$97$		−	1.00000i		−	0.101535i	−0.998711	−	0.0507673i	$-0.983833\pi$
$97$		−	1.00000i		−	0.101535i	0.998711	−	0.0507673i	$-0.0161667\pi$
$98$	−7.00000			−0.707107
$99$			12.0000i			1.20605i
$100$	−1.00000			−0.100000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	1.00000	−	4.00000i	0.0990148	−	0.396059i
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	1.00000			0.0971286
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$			5.00000i			0.481125i
$109$		−	17.0000i		−	1.62830i	−0.580651	−	0.814152i	$-0.697202\pi$
$109$		−	17.0000i		−	1.62830i	0.580651	−	0.814152i	$-0.302798\pi$
$110$	6.00000			0.572078
$111$	10.0000			0.949158
$112$		0			0
$113$			17.0000i			1.59923i	0.600516	+	0.799613i	$0.294962\pi$
$113$			17.0000i			1.59923i	−0.600516	+	0.799613i	$0.705038\pi$
$114$		−	3.00000i		−	0.280976i
$115$	−2.00000			−0.186501
$116$		−	1.00000i		−	0.0928477i
$117$	−10.0000			−0.924500
$118$	9.00000			0.828517
$119$		0			0
$120$	1.00000			0.0912871
$121$	−25.0000			−2.27273
$122$		−	3.00000i		−	0.271607i
$123$	12.0000			1.08200
$124$		−	7.00000i		−	0.628619i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−9.00000			−0.798621			−0.399310	−	0.916816i	$-0.630750\pi$
$127$	−9.00000			−0.798621			−0.399310	+	0.916816i	$0.630750\pi$
$128$	−1.00000			−0.0883883
$129$		−	4.00000i		−	0.352180i
$130$			5.00000i			0.438529i
$131$		−	8.00000i		−	0.698963i	−0.936943	−	0.349482i	$-0.886358\pi$
$131$		−	8.00000i		−	0.698963i	0.936943	−	0.349482i	$-0.113642\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	−10.0000			−0.863868
$135$	−5.00000			−0.430331
$136$	−4.00000	−	1.00000i	−0.342997	−	0.0857493i
$137$	−4.00000			−0.341743			−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000			−0.341743			−0.170872	+	0.985293i	$0.554658\pi$
$138$	2.00000			0.170251
$139$			10.0000i			0.848189i	0.905618	+	0.424094i	$0.139408\pi$
$139$			10.0000i			0.848189i	−0.905618	+	0.424094i	$0.860592\pi$
$140$		0			0
$141$			7.00000i			0.589506i
$142$		−	9.00000i		−	0.755263i
$143$		−	30.0000i		−	2.50873i
$144$	2.00000			0.166667
$145$	1.00000			0.0830455
$146$			7.00000i			0.579324i
$147$			7.00000i			0.577350i
$148$		−	10.0000i		−	0.821995i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$			1.00000i			0.0816497i
$151$	−6.00000			−0.488273			−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000			−0.488273			−0.244137	+	0.969741i	$0.578505\pi$
$152$	−3.00000			−0.243332
$153$	8.00000	+	2.00000i	0.646762	+	0.161690i
$154$		0			0
$155$	7.00000			0.562254
$156$		−	5.00000i		−	0.400320i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		−	8.00000i		−	0.636446i
$159$		−	1.00000i		−	0.0793052i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		−	12.0000i		−	0.937043i
$165$		−	6.00000i		−	0.467099i
$166$	−2.00000			−0.155230
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	1.00000	−	4.00000i	0.0766965	−	0.306786i
$171$	6.00000			0.458831
$172$	−4.00000			−0.304997
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	−1.00000			−0.0758098
$175$		0			0
$176$			6.00000i			0.452267i
$177$		−	9.00000i		−	0.676481i
$178$	1.00000			0.0749532
$179$	−16.0000			−1.19590			−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000			−1.19590			−0.597948	+	0.801535i	$0.704017\pi$
$180$			2.00000i			0.149071i
$181$			10.0000i			0.743294i	0.928374	+	0.371647i	$0.121207\pi$
$181$			10.0000i			0.743294i	−0.928374	+	0.371647i	$0.878793\pi$
$182$		0			0
$183$	−3.00000			−0.221766
$184$		−	2.00000i		−	0.147442i
$185$	10.0000			0.735215
$186$	−7.00000			−0.513265
$187$	−6.00000	+	24.0000i	−0.438763	+	1.75505i
$188$	7.00000			0.510527
$189$		0			0
$190$		−	3.00000i		−	0.217643i
$191$	−14.0000			−1.01300			−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000			−1.01300			−0.506502	+	0.862239i	$0.669062\pi$
$192$			1.00000i			0.0721688i
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$			1.00000i			0.0717958i
$195$	5.00000			0.358057
$196$	7.00000			0.500000
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		−	12.0000i		−	0.852803i
$199$		−	13.0000i		−	0.921546i	−0.887518	−	0.460773i	$-0.847572\pi$
$199$		−	13.0000i		−	0.921546i	0.887518	−	0.460773i	$-0.152428\pi$
$200$	1.00000			0.0707107
$201$			10.0000i			0.705346i
$202$	6.00000			0.422159
$203$		0			0
$204$	−1.00000	+	4.00000i	−0.0700140	+	0.280056i
$205$	12.0000			0.838116
$206$	−8.00000			−0.557386
$207$			4.00000i			0.278019i
$208$	−5.00000			−0.346688
$209$			18.0000i			1.24509i
$210$		0			0
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	−1.00000			−0.0686803
$213$	−9.00000			−0.616670
$214$			8.00000i			0.546869i
$215$		−	4.00000i		−	0.272798i
$216$		−	5.00000i		−	0.340207i
$217$		0			0
$218$			17.0000i			1.15139i
$219$	7.00000			0.473016
$220$	−6.00000			−0.404520
$221$	−20.0000	−	5.00000i	−1.34535	−	0.336336i
$222$	−10.0000			−0.671156
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		−	17.0000i		−	1.13082i
$227$		−	7.00000i		−	0.464606i	−0.972643	−	0.232303i	$-0.925374\pi$
$227$		−	7.00000i		−	0.464606i	0.972643	−	0.232303i	$-0.0746261\pi$
$228$			3.00000i			0.198680i
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$			1.00000i			0.0656532i
$233$		−	13.0000i		−	0.851658i	−0.904804	−	0.425829i	$-0.859982\pi$
$233$		−	13.0000i		−	0.851658i	0.904804	−	0.425829i	$-0.140018\pi$
$234$	10.0000			0.653720
$235$			7.00000i			0.456630i
$236$	−9.00000			−0.585850
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−28.0000			−1.81117			−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000			−1.81117			−0.905585	+	0.424165i	$0.860568\pi$
$240$	−1.00000			−0.0645497
$241$		−	8.00000i		−	0.515325i	−0.966235	−	0.257663i	$-0.917048\pi$
$241$		−	8.00000i		−	0.515325i	0.966235	−	0.257663i	$-0.0829523\pi$
$242$	25.0000			1.60706
$243$			16.0000i			1.02640i
$244$			3.00000i			0.192055i
$245$			7.00000i			0.447214i
$246$	−12.0000			−0.765092
$247$	−15.0000			−0.954427
$248$			7.00000i			0.444500i
$249$			2.00000i			0.126745i
$250$			1.00000i			0.0632456i
$251$	16.0000			1.00991			0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000			1.00991			0.504956	+	0.863145i	$0.331509\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	9.00000			0.564710
$255$	−4.00000	−	1.00000i	−0.250490	−	0.0626224i
$256$	1.00000			0.0625000
$257$	20.0000			1.24757			0.623783	−	0.781598i	$-0.285595\pi$
$257$	20.0000			1.24757			0.623783	+	0.781598i	$0.285595\pi$
$258$			4.00000i			0.249029i
$259$		0			0
$260$		−	5.00000i		−	0.310087i
$261$		−	2.00000i		−	0.123797i
$262$			8.00000i			0.494242i
$263$	17.0000			1.04826			0.524132	−	0.851637i	$-0.324390\pi$
$263$	17.0000			1.04826			0.524132	+	0.851637i	$0.324390\pi$
$264$	6.00000			0.369274
$265$		−	1.00000i		−	0.0614295i
$266$		0			0
$267$		−	1.00000i		−	0.0611990i
$268$	10.0000			0.610847
$269$		−	3.00000i		−	0.182913i	−0.995809	−	0.0914566i	$-0.970848\pi$
$269$		−	3.00000i		−	0.182913i	0.995809	−	0.0914566i	$-0.0291523\pi$
$270$	5.00000			0.304290
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	4.00000	+	1.00000i	0.242536	+	0.0606339i
$273$		0			0
$274$	4.00000			0.241649
$275$		−	6.00000i		−	0.361814i
$276$	−2.00000			−0.120386
$277$			26.0000i			1.56219i	0.624413	+	0.781094i	$0.285338\pi$
$277$			26.0000i			1.56219i	−0.624413	+	0.781094i	$0.714662\pi$
$278$		−	10.0000i		−	0.599760i
$279$		−	14.0000i		−	0.838158i
$280$		0			0
$281$	25.0000			1.49137			0.745687	−	0.666296i	$-0.232121\pi$
$281$	25.0000			1.49137			0.745687	+	0.666296i	$0.232121\pi$
$282$		−	7.00000i		−	0.416844i
$283$		−	11.0000i		−	0.653882i	−0.945045	−	0.326941i	$-0.893982\pi$
$283$		−	11.0000i		−	0.653882i	0.945045	−	0.326941i	$-0.106018\pi$
$284$			9.00000i			0.534052i
$285$	−3.00000			−0.177705
$286$			30.0000i			1.77394i
$287$		0			0
$288$	−2.00000			−0.117851
$289$	15.0000	+	8.00000i	0.882353	+	0.470588i
$290$	−1.00000			−0.0587220
$291$	1.00000			0.0586210
$292$		−	7.00000i		−	0.409644i
$293$	−15.0000			−0.876309			−0.438155	−	0.898900i	$-0.644368\pi$
$293$	−15.0000			−0.876309			−0.438155	+	0.898900i	$0.644368\pi$
$294$		−	7.00000i		−	0.408248i
$295$		−	9.00000i		−	0.524000i
$296$			10.0000i			0.581238i
$297$	−30.0000			−1.74078
$298$	−6.00000			−0.347571
$299$		−	10.0000i		−	0.578315i
$300$		−	1.00000i		−	0.0577350i
$301$		0			0
$302$	6.00000			0.345261
$303$		−	6.00000i		−	0.344691i
$304$	3.00000			0.172062
$305$	−3.00000			−0.171780
$306$	−8.00000	−	2.00000i	−0.457330	−	0.114332i
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$			8.00000i			0.455104i
$310$	−7.00000			−0.397573
$311$		−	32.0000i		−	1.81455i	−0.420534	−	0.907277i	$-0.638157\pi$
$311$		−	32.0000i		−	1.81455i	0.420534	−	0.907277i	$-0.361843\pi$
$312$			5.00000i			0.283069i
$313$			22.0000i			1.24351i	0.783210	+	0.621757i	$0.213581\pi$
$313$			22.0000i			1.24351i	−0.783210	+	0.621757i	$0.786419\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$			8.00000i			0.450035i
$317$			20.0000i			1.12331i	0.827371	+	0.561656i	$0.189836\pi$
$317$			20.0000i			1.12331i	−0.827371	+	0.561656i	$0.810164\pi$
$318$			1.00000i			0.0560772i
$319$	6.00000			0.335936
$320$			1.00000i			0.0559017i
$321$	8.00000			0.446516
$322$		0			0
$323$	12.0000	+	3.00000i	0.667698	+	0.166924i
$324$	1.00000			0.0555556
$325$	5.00000			0.277350
$326$		−	4.00000i		−	0.221540i
$327$	17.0000			0.940102
$328$			12.0000i			0.662589i
$329$		0			0
$330$			6.00000i			0.330289i
$331$	17.0000			0.934405			0.467202	−	0.884150i	$-0.345262\pi$
$331$	17.0000			0.934405			0.467202	+	0.884150i	$0.345262\pi$
$332$	2.00000			0.109764
$333$		−	20.0000i		−	1.09599i
$334$			18.0000i			0.984916i
$335$			10.0000i			0.546358i
$336$		0			0
$337$		−	7.00000i		−	0.381314i	−0.981657	−	0.190657i	$-0.938938\pi$
$337$		−	7.00000i		−	0.381314i	0.981657	−	0.190657i	$-0.0610619\pi$
$338$	−12.0000			−0.652714
$339$	−17.0000			−0.923313
$340$	−1.00000	+	4.00000i	−0.0542326	+	0.216930i
$341$	42.0000			2.27443
$342$	−6.00000			−0.324443
$343$		0			0
$344$	4.00000			0.215666
$345$		−	2.00000i		−	0.107676i
$346$		−	6.00000i		−	0.322562i
$347$		−	9.00000i		−	0.483145i	−0.970383	−	0.241573i	$-0.922337\pi$
$347$		−	9.00000i		−	0.483145i	0.970383	−	0.241573i	$-0.0776632\pi$
$348$	1.00000			0.0536056
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$		0			0
$351$		−	25.0000i		−	1.33440i
$352$		−	6.00000i		−	0.319801i
$353$	−34.0000			−1.80964			−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000			−1.80964			−0.904819	+	0.425797i	$0.859994\pi$
$354$			9.00000i			0.478345i
$355$	−9.00000			−0.477670
$356$	−1.00000			−0.0529999
$357$		0			0
$358$	16.0000			0.845626
$359$	−32.0000			−1.68890			−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000			−1.68890			−0.844448	+	0.535638i	$0.820071\pi$
$360$		−	2.00000i		−	0.105409i
$361$	−10.0000			−0.526316
$362$		−	10.0000i		−	0.525588i
$363$		−	25.0000i		−	1.31216i
$364$		0			0
$365$	7.00000			0.366397
$366$	3.00000			0.156813
$367$		−	22.0000i		−	1.14839i	−0.818718	−	0.574195i	$-0.805315\pi$
$367$		−	22.0000i		−	1.14839i	0.818718	−	0.574195i	$-0.194685\pi$
$368$			2.00000i			0.104257i
$369$		−	24.0000i		−	1.24939i
$370$	−10.0000			−0.519875
$371$		0			0
$372$	7.00000			0.362933
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$	6.00000	−	24.0000i	0.310253	−	1.24101i
$375$	1.00000			0.0516398
$376$	−7.00000			−0.360997
$377$			5.00000i			0.257513i
$378$		0			0
$379$			16.0000i			0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$			16.0000i			0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$			3.00000i			0.153897i
$381$		−	9.00000i		−	0.461084i
$382$	14.0000			0.716302
$383$	−21.0000			−1.07305			−0.536525	−	0.843884i	$-0.680263\pi$
$383$	−21.0000			−1.07305			−0.536525	+	0.843884i	$0.680263\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$		−	6.00000i		−	0.305392i
$387$	−8.00000			−0.406663
$388$		−	1.00000i		−	0.0507673i
$389$	−20.0000			−1.01404			−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000			−1.01404			−0.507020	+	0.861934i	$0.669253\pi$
$390$	−5.00000			−0.253185
$391$	−2.00000	+	8.00000i	−0.101144	+	0.404577i
$392$	−7.00000			−0.353553
$393$	8.00000			0.403547
$394$		−	6.00000i		−	0.302276i
$395$	−8.00000			−0.402524
$396$			12.0000i			0.603023i
$397$		−	32.0000i		−	1.60603i	−0.595956	−	0.803017i	$-0.703227\pi$
$397$		−	32.0000i		−	1.60603i	0.595956	−	0.803017i	$-0.296773\pi$
$398$			13.0000i			0.651631i
$399$		0			0
$400$	−1.00000			−0.0500000
$401$			4.00000i			0.199750i	0.995000	+	0.0998752i	$0.0318444\pi$
$401$			4.00000i			0.199750i	−0.995000	+	0.0998752i	$0.968156\pi$
$402$		−	10.0000i		−	0.498755i
$403$			35.0000i			1.74347i
$404$	−6.00000			−0.298511
$405$			1.00000i			0.0496904i
$406$		0			0
$407$	60.0000			2.97409
$408$	1.00000	−	4.00000i	0.0495074	−	0.198030i
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$	−12.0000			−0.592638
$411$		−	4.00000i		−	0.197305i
$412$	8.00000			0.394132
$413$		0			0
$414$		−	4.00000i		−	0.196589i
$415$			2.00000i			0.0981761i
$416$	5.00000			0.245145
$417$	−10.0000			−0.489702
$418$		−	18.0000i		−	0.880409i
$419$		−	30.0000i		−	1.46560i	−0.680446	−	0.732798i	$-0.738214\pi$
$419$		−	30.0000i		−	1.46560i	0.680446	−	0.732798i	$-0.261786\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		−	10.0000i		−	0.486792i
$423$	14.0000			0.680703
$424$	1.00000			0.0485643
$425$	−4.00000	−	1.00000i	−0.194029	−	0.0485071i
$426$	9.00000			0.436051
$427$		0			0
$428$		−	8.00000i		−	0.386695i
$429$	30.0000			1.44841
$430$			4.00000i			0.192897i
$431$			16.0000i			0.770693i	0.922772	+	0.385346i	$0.125918\pi$
$431$			16.0000i			0.770693i	−0.922772	+	0.385346i	$0.874082\pi$
$432$			5.00000i			0.240563i
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$			1.00000i			0.0479463i
$436$		−	17.0000i		−	0.814152i
$437$			6.00000i			0.287019i
$438$	−7.00000			−0.334473
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$	6.00000			0.286039
$441$	14.0000			0.666667
$442$	20.0000	+	5.00000i	0.951303	+	0.237826i
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$	10.0000			0.474579
$445$		−	1.00000i		−	0.0474045i
$446$	−19.0000			−0.899676
$447$			6.00000i			0.283790i
$448$		0			0
$449$			30.0000i			1.41579i	0.706319	+	0.707894i	$0.250354\pi$
$449$			30.0000i			1.41579i	−0.706319	+	0.707894i	$0.749646\pi$
$450$	2.00000			0.0942809
$451$	72.0000			3.39035
$452$			17.0000i			0.799613i
$453$		−	6.00000i		−	0.281905i
$454$			7.00000i			0.328526i
$455$		0			0
$456$		−	3.00000i		−	0.140488i
$457$	−24.0000			−1.12267			−0.561336	−	0.827588i	$-0.689713\pi$
$457$	−24.0000			−1.12267			−0.561336	+	0.827588i	$0.689713\pi$
$458$	−20.0000			−0.934539
$459$	−5.00000	+	20.0000i	−0.233380	+	0.933520i
$460$	−2.00000			−0.0932505
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$		−	1.00000i		−	0.0464238i
$465$			7.00000i			0.324617i
$466$			13.0000i			0.602213i
$467$	−22.0000			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$467$	−22.0000			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$468$	−10.0000			−0.462250
$469$		0			0
$470$		−	7.00000i		−	0.322886i
$471$			14.0000i			0.645086i
$472$	9.00000			0.414259
$473$		−	24.0000i		−	1.10352i
$474$	8.00000			0.367452
$475$	−3.00000			−0.137649
$476$		0			0
$477$	−2.00000			−0.0915737
$478$	28.0000			1.28069
$479$			23.0000i			1.05090i	0.850825	+	0.525448i	$0.176102\pi$
$479$			23.0000i			1.05090i	−0.850825	+	0.525448i	$0.823898\pi$
$480$	1.00000			0.0456435
$481$			50.0000i			2.27980i
$482$			8.00000i			0.364390i
$483$		0			0
$484$	−25.0000			−1.13636
$485$	1.00000			0.0454077
$486$		−	16.0000i		−	0.725775i
$487$		−	8.00000i		−	0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$		−	8.00000i		−	0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$		−	3.00000i		−	0.135804i
$489$	−4.00000			−0.180886
$490$		−	7.00000i		−	0.316228i
$491$	37.0000			1.66979			0.834893	−	0.550412i	$-0.185529\pi$
$491$	37.0000			1.66979			0.834893	+	0.550412i	$0.185529\pi$
$492$	12.0000			0.541002
$493$	1.00000	−	4.00000i	0.0450377	−	0.180151i
$494$	15.0000			0.674882
$495$	−12.0000			−0.539360
$496$		−	7.00000i		−	0.314309i
$497$		0			0
$498$		−	2.00000i		−	0.0896221i
$499$		−	16.0000i		−	0.716258i	−0.933672	−	0.358129i	$-0.883415\pi$
$499$		−	16.0000i		−	0.716258i	0.933672	−	0.358129i	$-0.116585\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	18.0000			0.804181
$502$	−16.0000			−0.714115
$503$			32.0000i			1.42681i	0.700752	+	0.713405i	$0.252848\pi$
$503$			32.0000i			1.42681i	−0.700752	+	0.713405i	$0.747152\pi$
$504$		0			0
$505$		−	6.00000i		−	0.266996i
$506$	12.0000			0.533465
$507$			12.0000i			0.532939i
$508$	−9.00000			−0.399310
$509$	−4.00000			−0.177297			−0.0886484	−	0.996063i	$-0.528255\pi$
$509$	−4.00000			−0.177297			−0.0886484	+	0.996063i	$0.528255\pi$
$510$	4.00000	+	1.00000i	0.177123	+	0.0442807i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$			15.0000i			0.662266i
$514$	−20.0000			−0.882162
$515$			8.00000i			0.352522i
$516$		−	4.00000i		−	0.176090i
$517$			42.0000i			1.84716i
$518$		0			0
$519$	−6.00000			−0.263371
$520$			5.00000i			0.219265i
$521$			16.0000i			0.700973i	0.936568	+	0.350486i	$0.113984\pi$
$521$			16.0000i			0.700973i	−0.936568	+	0.350486i	$0.886016\pi$
$522$			2.00000i			0.0875376i
$523$	6.00000			0.262362			0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000			0.262362			0.131181	+	0.991358i	$0.458123\pi$
$524$		−	8.00000i		−	0.349482i
$525$		0			0
$526$	−17.0000			−0.741235
$527$	7.00000	−	28.0000i	0.304925	−	1.21970i
$528$	−6.00000			−0.261116
$529$	19.0000			0.826087
$530$			1.00000i			0.0434372i
$531$	−18.0000			−0.781133
$532$		0			0
$533$			60.0000i			2.59889i
$534$			1.00000i			0.0432742i
$535$	8.00000			0.345870
$536$	−10.0000			−0.431934
$537$		−	16.0000i		−	0.690451i
$538$			3.00000i			0.129339i
$539$			42.0000i			1.80907i
$540$	−5.00000			−0.215166
$541$		−	38.0000i		−	1.63375i	−0.576816	−	0.816874i	$-0.695705\pi$
$541$		−	38.0000i		−	1.63375i	0.576816	−	0.816874i	$-0.304295\pi$
$542$	16.0000			0.687259
$543$	−10.0000			−0.429141
$544$	−4.00000	−	1.00000i	−0.171499	−	0.0428746i
$545$	17.0000			0.728200
$546$		0			0
$547$			29.0000i			1.23995i	0.784621	+	0.619975i	$0.212857\pi$
$547$			29.0000i			1.23995i	−0.784621	+	0.619975i	$0.787143\pi$
$548$	−4.00000			−0.170872
$549$			6.00000i			0.256074i
$550$			6.00000i			0.255841i
$551$		−	3.00000i		−	0.127804i
$552$	2.00000			0.0851257
$553$		0			0
$554$		−	26.0000i		−	1.10463i
$555$			10.0000i			0.424476i
$556$			10.0000i			0.424094i
$557$	39.0000			1.65248			0.826242	−	0.563316i	$-0.190475\pi$
$557$	39.0000			1.65248			0.826242	+	0.563316i	$0.190475\pi$
$558$			14.0000i			0.592667i
$559$	20.0000			0.845910
$560$		0			0
$561$	−24.0000	−	6.00000i	−1.01328	−	0.253320i
$562$	−25.0000			−1.05456
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$			7.00000i			0.294753i
$565$	−17.0000			−0.715195
$566$			11.0000i			0.462364i
$567$		0			0
$568$		−	9.00000i		−	0.377632i
$569$	1.00000			0.0419222			0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000			0.0419222			0.0209611	+	0.999780i	$0.493327\pi$
$570$	3.00000			0.125656
$571$		−	40.0000i		−	1.67395i	−0.547243	−	0.836974i	$-0.684323\pi$
$571$		−	40.0000i		−	1.67395i	0.547243	−	0.836974i	$-0.315677\pi$
$572$		−	30.0000i		−	1.25436i
$573$		−	14.0000i		−	0.584858i
$574$		0			0
$575$		−	2.00000i		−	0.0834058i
$576$	2.00000			0.0833333
$577$	24.0000			0.999133			0.499567	−	0.866276i	$-0.333493\pi$
$577$	24.0000			0.999133			0.499567	+	0.866276i	$0.333493\pi$
$578$	−15.0000	−	8.00000i	−0.623918	−	0.332756i
$579$	−6.00000			−0.249351
$580$	1.00000			0.0415227
$581$		0			0
$582$	−1.00000			−0.0414513
$583$		−	6.00000i		−	0.248495i
$584$			7.00000i			0.289662i
$585$		−	10.0000i		−	0.413449i
$586$	15.0000			0.619644
$587$	−26.0000			−1.07313			−0.536567	−	0.843857i	$-0.680279\pi$
$587$	−26.0000			−1.07313			−0.536567	+	0.843857i	$0.680279\pi$
$588$			7.00000i			0.288675i
$589$		−	21.0000i		−	0.865290i
$590$			9.00000i			0.370524i
$591$	−6.00000			−0.246807
$592$		−	10.0000i		−	0.410997i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	6.00000			0.245770
$597$	13.0000			0.532055
$598$			10.0000i			0.408930i
$599$	38.0000			1.55264			0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000			1.55264			0.776319	+	0.630340i	$0.217085\pi$
$600$			1.00000i			0.0408248i
$601$		−	28.0000i		−	1.14214i	−0.820900	−	0.571072i	$-0.806528\pi$
$601$		−	28.0000i		−	1.14214i	0.820900	−	0.571072i	$-0.193472\pi$
$602$		0			0
$603$	20.0000			0.814463
$604$	−6.00000			−0.244137
$605$		−	25.0000i		−	1.01639i
$606$			6.00000i			0.243733i
$607$			16.0000i			0.649420i	0.945814	+	0.324710i	$0.105267\pi$
$607$			16.0000i			0.649420i	−0.945814	+	0.324710i	$0.894733\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$	3.00000			0.121466
$611$	−35.0000			−1.41595
$612$	8.00000	+	2.00000i	0.323381	+	0.0808452i
$613$	−17.0000			−0.686624			−0.343312	−	0.939222i	$-0.611549\pi$
$613$	−17.0000			−0.686624			−0.343312	+	0.939222i	$0.611549\pi$
$614$	22.0000			0.887848
$615$			12.0000i			0.483887i
$616$		0			0
$617$		−	25.0000i		−	1.00646i	−0.864152	−	0.503231i	$-0.832144\pi$
$617$		−	25.0000i		−	1.00646i	0.864152	−	0.503231i	$-0.167856\pi$
$618$		−	8.00000i		−	0.321807i
$619$			18.0000i			0.723481i	0.932279	+	0.361741i	$0.117817\pi$
$619$			18.0000i			0.723481i	−0.932279	+	0.361741i	$0.882183\pi$
$620$	7.00000			0.281127
$621$	−10.0000			−0.401286
$622$			32.0000i			1.28308i
$623$		0			0
$624$		−	5.00000i		−	0.200160i
$625$	1.00000			0.0400000
$626$		−	22.0000i		−	0.879297i
$627$	−18.0000			−0.718851
$628$	14.0000			0.558661
$629$	10.0000	−	40.0000i	0.398726	−	1.59490i
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$		−	8.00000i		−	0.318223i
$633$	−10.0000			−0.397464
$634$		−	20.0000i		−	0.794301i
$635$		−	9.00000i		−	0.357154i
$636$		−	1.00000i		−	0.0396526i
$637$	−35.0000			−1.38675
$638$	−6.00000			−0.237542
$639$			18.0000i			0.712069i
$640$		−	1.00000i		−	0.0395285i
$641$			30.0000i			1.18493i	0.805597	+	0.592464i	$0.201845\pi$
$641$			30.0000i			1.18493i	−0.805597	+	0.592464i	$0.798155\pi$
$642$	−8.00000			−0.315735
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$	−12.0000	−	3.00000i	−0.472134	−	0.118033i
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$	−1.00000			−0.0392837
$649$		−	54.0000i		−	2.11969i
$650$	−5.00000			−0.196116
$651$		0			0
$652$			4.00000i			0.156652i
$653$		−	16.0000i		−	0.626128i	−0.949732	−	0.313064i	$-0.898644\pi$
$653$		−	16.0000i		−	0.626128i	0.949732	−	0.313064i	$-0.101356\pi$
$654$	−17.0000			−0.664753
$655$	8.00000			0.312586
$656$		−	12.0000i		−	0.468521i
$657$		−	14.0000i		−	0.546192i
$658$		0			0
$659$	−33.0000			−1.28550			−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000			−1.28550			−0.642749	+	0.766077i	$0.722206\pi$
$660$		−	6.00000i		−	0.233550i
$661$	4.00000			0.155582			0.0777910	−	0.996970i	$-0.475213\pi$
$661$	4.00000			0.155582			0.0777910	+	0.996970i	$0.475213\pi$
$662$	−17.0000			−0.660724
$663$	5.00000	−	20.0000i	0.194184	−	0.776736i
$664$	−2.00000			−0.0776151
$665$		0			0
$666$			20.0000i			0.774984i
$667$	2.00000			0.0774403
$668$		−	18.0000i		−	0.696441i
$669$			19.0000i			0.734582i
$670$		−	10.0000i		−	0.386334i
$671$	−18.0000			−0.694882
$672$		0			0
$673$		−	41.0000i		−	1.58043i	−0.612827	−	0.790217i	$-0.709968\pi$
$673$		−	41.0000i		−	1.58043i	0.612827	−	0.790217i	$-0.290032\pi$
$674$			7.00000i			0.269630i
$675$		−	5.00000i		−	0.192450i
$676$	12.0000			0.461538
$677$			12.0000i			0.461197i	0.973049	+	0.230599i	$0.0740685\pi$
$677$			12.0000i			0.461197i	−0.973049	+	0.230599i	$0.925932\pi$
$678$	17.0000			0.652881
$679$		0			0
$680$	1.00000	−	4.00000i	0.0383482	−	0.153393i
$681$	7.00000			0.268241
$682$	−42.0000			−1.60826
$683$		−	7.00000i		−	0.267848i	−0.990992	−	0.133924i	$-0.957242\pi$
$683$		−	7.00000i		−	0.267848i	0.990992	−	0.133924i	$-0.0427577\pi$
$684$	6.00000			0.229416
$685$		−	4.00000i		−	0.152832i
$686$		0			0
$687$			20.0000i			0.763048i
$688$	−4.00000			−0.152499
$689$	5.00000			0.190485
$690$			2.00000i			0.0761387i
$691$		−	18.0000i		−	0.684752i	−0.939563	−	0.342376i	$-0.888768\pi$
$691$		−	18.0000i		−	0.684752i	0.939563	−	0.342376i	$-0.111232\pi$
$692$			6.00000i			0.228086i
$693$		0			0
$694$			9.00000i			0.341635i
$695$	−10.0000			−0.379322
$696$	−1.00000			−0.0379049
$697$	12.0000	−	48.0000i	0.454532	−	1.81813i
$698$	−8.00000			−0.302804
$699$	13.0000			0.491705
$700$		0			0
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$			25.0000i			0.943564i
$703$		−	30.0000i		−	1.13147i
$704$			6.00000i			0.226134i
$705$	−7.00000			−0.263635
$706$	34.0000			1.27961
$707$		0			0
$708$		−	9.00000i		−	0.338241i
$709$			3.00000i			0.112667i	0.998412	+	0.0563337i	$0.0179411\pi$
$709$			3.00000i			0.112667i	−0.998412	+	0.0563337i	$0.982059\pi$
$710$	9.00000			0.337764
$711$			16.0000i			0.600047i
$712$	1.00000			0.0374766
$713$	14.0000			0.524304
$714$		0			0
$715$	30.0000			1.12194
$716$	−16.0000			−0.597948
$717$		−	28.0000i		−	1.04568i
$718$	32.0000			1.19423
$719$		−	7.00000i		−	0.261056i	−0.991445	−	0.130528i	$-0.958333\pi$
$719$		−	7.00000i		−	0.261056i	0.991445	−	0.130528i	$-0.0416672\pi$
$720$			2.00000i			0.0745356i
$721$		0			0
$722$	10.0000			0.372161
$723$	8.00000			0.297523
$724$			10.0000i			0.371647i
$725$			1.00000i			0.0371391i
$726$			25.0000i			0.927837i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	−7.00000			−0.259082
$731$	−16.0000	−	4.00000i	−0.591781	−	0.147945i
$732$	−3.00000			−0.110883
$733$	−14.0000			−0.517102			−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000			−0.517102			−0.258551	+	0.965998i	$0.583245\pi$
$734$			22.0000i			0.812035i
$735$	−7.00000			−0.258199
$736$		−	2.00000i		−	0.0737210i
$737$			60.0000i			2.21013i
$738$			24.0000i			0.883452i
$739$	9.00000			0.331070			0.165535	−	0.986204i	$-0.447065\pi$
$739$	9.00000			0.331070			0.165535	+	0.986204i	$0.447065\pi$
$740$	10.0000			0.367607
$741$		−	15.0000i		−	0.551039i
$742$		0			0
$743$			24.0000i			0.880475i	0.897881	+	0.440237i	$0.145106\pi$
$743$			24.0000i			0.880475i	−0.897881	+	0.440237i	$0.854894\pi$
$744$	−7.00000			−0.256632
$745$			6.00000i			0.219823i
$746$	−6.00000			−0.219676
$747$	4.00000			0.146352
$748$	−6.00000	+	24.0000i	−0.219382	+	0.877527i
$749$		0			0
$750$	−1.00000			−0.0365148
$751$			43.0000i			1.56909i	0.620070	+	0.784546i	$0.287104\pi$
$751$			43.0000i			1.56909i	−0.620070	+	0.784546i	$0.712896\pi$
$752$	7.00000			0.255264
$753$			16.0000i			0.583072i
$754$		−	5.00000i		−	0.182089i
$755$		−	6.00000i		−	0.218362i
$756$		0			0
$757$	−15.0000			−0.545184			−0.272592	−	0.962130i	$-0.587881\pi$
$757$	−15.0000			−0.545184			−0.272592	+	0.962130i	$0.587881\pi$
$758$		−	16.0000i		−	0.581146i
$759$		−	12.0000i		−	0.435572i
$760$		−	3.00000i		−	0.108821i
$761$	−26.0000			−0.942499			−0.471250	−	0.882000i	$-0.656197\pi$
$761$	−26.0000			−0.942499			−0.471250	+	0.882000i	$0.656197\pi$
$762$			9.00000i			0.326036i
$763$		0			0
$764$	−14.0000			−0.506502
$765$	−2.00000	+	8.00000i	−0.0723102	+	0.289241i
$766$	21.0000			0.758761
$767$	45.0000			1.62486
$768$			1.00000i			0.0360844i
$769$	25.0000			0.901523			0.450762	−	0.892644i	$-0.351152\pi$
$769$	25.0000			0.901523			0.450762	+	0.892644i	$0.351152\pi$
$770$		0			0
$771$			20.0000i			0.720282i
$772$			6.00000i			0.215945i
$773$	30.0000			1.07903			0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000			1.07903			0.539513	+	0.841978i	$0.318609\pi$
$774$	8.00000			0.287554
$775$			7.00000i			0.251447i
$776$			1.00000i			0.0358979i
$777$		0			0
$778$	20.0000			0.717035
$779$		−	36.0000i		−	1.28983i
$780$	5.00000			0.179029
$781$	−54.0000			−1.93227
$782$	2.00000	−	8.00000i	0.0715199	−	0.286079i
$783$	5.00000			0.178685
$784$	7.00000			0.250000
$785$			14.0000i			0.499681i
$786$	−8.00000			−0.285351
$787$		−	27.0000i		−	0.962446i	−0.876598	−	0.481223i	$-0.840193\pi$
$787$		−	27.0000i		−	0.962446i	0.876598	−	0.481223i	$-0.159807\pi$
$788$			6.00000i			0.213741i
$789$			17.0000i			0.605216i
$790$	8.00000			0.284627
$791$		0			0
$792$		−	12.0000i		−	0.426401i
$793$		−	15.0000i		−	0.532666i
$794$			32.0000i			1.13564i
$795$	1.00000			0.0354663
$796$		−	13.0000i		−	0.460773i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	28.0000	+	7.00000i	0.990569	+	0.247642i
$800$	1.00000			0.0353553
$801$	−2.00000			−0.0706665
$802$		−	4.00000i		−	0.141245i
$803$	42.0000			1.48215
$804$			10.0000i			0.352673i
$805$		0			0
$806$		−	35.0000i		−	1.23282i
$807$	3.00000			0.105605
$808$	6.00000			0.211079
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		−	1.00000i		−	0.0351364i
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$	−60.0000			−2.10300
$815$	−4.00000			−0.140114
$816$	−1.00000	+	4.00000i	−0.0350070	+	0.140028i
$817$	−12.0000			−0.419827
$818$	19.0000			0.664319
$819$		0			0
$820$	12.0000			0.419058
$821$			17.0000i			0.593304i	0.954986	+	0.296652i	$0.0958702\pi$
$821$			17.0000i			0.593304i	−0.954986	+	0.296652i	$0.904130\pi$
$822$			4.00000i			0.139516i
$823$			50.0000i			1.74289i	0.490493	+	0.871445i	$0.336817\pi$
$823$			50.0000i			1.74289i	−0.490493	+	0.871445i	$0.663183\pi$
$824$	−8.00000			−0.278693
$825$	6.00000			0.208893
$826$		0			0
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$			4.00000i			0.139010i
$829$	−20.0000			−0.694629			−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000			−0.694629			−0.347314	+	0.937749i	$0.612906\pi$
$830$		−	2.00000i		−	0.0694210i
$831$	−26.0000			−0.901930
$832$	−5.00000			−0.173344
$833$	28.0000	+	7.00000i	0.970143	+	0.242536i
$834$	10.0000			0.346272
$835$	18.0000			0.622916
$836$			18.0000i			0.622543i
$837$	35.0000			1.20978
$838$			30.0000i			1.03633i
$839$			5.00000i			0.172619i	0.996268	+	0.0863096i	$0.0275074\pi$
$839$			5.00000i			0.172619i	−0.996268	+	0.0863096i	$0.972493\pi$
$840$		0			0
$841$	28.0000			0.965517
$842$	2.00000			0.0689246
$843$			25.0000i			0.861046i
$844$			10.0000i			0.344214i
$845$			12.0000i			0.412813i
$846$	−14.0000			−0.481330
$847$		0			0
$848$	−1.00000			−0.0343401
$849$	11.0000			0.377519
$850$	4.00000	+	1.00000i	0.137199	+	0.0342997i
$851$	20.0000			0.685591
$852$	−9.00000			−0.308335
$853$		−	44.0000i		−	1.50653i	−0.657716	−	0.753266i	$-0.728477\pi$
$853$		−	44.0000i		−	1.50653i	0.657716	−	0.753266i	$-0.271523\pi$
$854$		0			0
$855$			6.00000i			0.205196i
$856$			8.00000i			0.273434i
$857$		−	31.0000i		−	1.05894i	−0.848329	−	0.529470i	$-0.822391\pi$
$857$		−	31.0000i		−	1.05894i	0.848329	−	0.529470i	$-0.177609\pi$
$858$	−30.0000			−1.02418
$859$	−53.0000			−1.80834			−0.904168	−	0.427176i	$-0.859508\pi$
$859$	−53.0000			−1.80834			−0.904168	+	0.427176i	$0.859508\pi$
$860$		−	4.00000i		−	0.136399i
$861$		0			0
$862$		−	16.0000i		−	0.544962i
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		−	5.00000i		−	0.170103i
$865$	−6.00000			−0.204006
$866$	28.0000			0.951479
$867$	−8.00000	+	15.0000i	−0.271694	+	0.509427i
$868$		0			0
$869$	−48.0000			−1.62829
$870$		−	1.00000i		−	0.0339032i
$871$	−50.0000			−1.69419
$872$			17.0000i			0.575693i
$873$		−	2.00000i		−	0.0676897i
$874$		−	6.00000i		−	0.202953i
$875$		0			0
$876$	7.00000			0.236508
$877$			18.0000i			0.607817i	0.952701	+	0.303908i	$0.0982917\pi$
$877$			18.0000i			0.607817i	−0.952701	+	0.303908i	$0.901708\pi$
$878$			8.00000i			0.269987i
$879$		−	15.0000i		−	0.505937i
$880$	−6.00000			−0.202260
$881$		−	30.0000i		−	1.01073i	−0.862907	−	0.505363i	$-0.831359\pi$
$881$		−	30.0000i		−	1.01073i	0.862907	−	0.505363i	$-0.168641\pi$
$882$	−14.0000			−0.471405
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$	−20.0000	−	5.00000i	−0.672673	−	0.168168i
$885$	9.00000			0.302532
$886$	12.0000			0.403148
$887$			28.0000i			0.940148i	0.882627	+	0.470074i	$0.155773\pi$
$887$			28.0000i			0.940148i	−0.882627	+	0.470074i	$0.844227\pi$
$888$	−10.0000			−0.335578
$889$		0			0
$890$			1.00000i			0.0335201i
$891$			6.00000i			0.201008i
$892$	19.0000			0.636167
$893$	21.0000			0.702738
$894$		−	6.00000i		−	0.200670i
$895$		−	16.0000i		−	0.534821i
$896$		0			0
$897$	10.0000			0.333890
$898$		−	30.0000i		−	1.00111i
$899$	−7.00000			−0.233463
$900$	−2.00000			−0.0666667
$901$	−4.00000	−	1.00000i	−0.133259	−	0.0333148i
$902$	−72.0000			−2.39734
$903$		0			0
$904$		−	17.0000i		−	0.565412i
$905$	−10.0000			−0.332411
$906$			6.00000i			0.199337i
$907$			1.00000i			0.0332045i	0.999862	+	0.0166022i	$0.00528490\pi$
$907$			1.00000i			0.0332045i	−0.999862	+	0.0166022i	$0.994715\pi$
$908$		−	7.00000i		−	0.232303i
$909$	−12.0000			−0.398015
$910$		0			0
$911$			48.0000i			1.59031i	0.606406	+	0.795155i	$0.292611\pi$
$911$			48.0000i			1.59031i	−0.606406	+	0.795155i	$0.707389\pi$
$912$			3.00000i			0.0993399i
$913$			12.0000i			0.397142i
$914$	24.0000			0.793849
$915$		−	3.00000i		−	0.0991769i
$916$	20.0000			0.660819
$917$		0			0
$918$	5.00000	−	20.0000i	0.165025	−	0.660098i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	2.00000			0.0659380
$921$		−	22.0000i		−	0.724925i
$922$	18.0000			0.592798
$923$		−	45.0000i		−	1.48119i
$924$		0			0
$925$			10.0000i			0.328798i
$926$	17.0000			0.558655
$927$	16.0000			0.525509
$928$			1.00000i			0.0328266i
$929$			44.0000i			1.44359i	0.692105	+	0.721797i	$0.256683\pi$
$929$			44.0000i			1.44359i	−0.692105	+	0.721797i	$0.743317\pi$
$930$		−	7.00000i		−	0.229539i
$931$	21.0000			0.688247
$932$		−	13.0000i		−	0.425829i
$933$	32.0000			1.04763
$934$	22.0000			0.719862
$935$	−24.0000	−	6.00000i	−0.784884	−	0.196221i
$936$	10.0000			0.326860
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$		0			0
$939$	−22.0000			−0.717943
$940$			7.00000i			0.228315i
$941$			29.0000i			0.945373i	0.881231	+	0.472686i	$0.156716\pi$
$941$			29.0000i			0.945373i	−0.881231	+	0.472686i	$0.843284\pi$
$942$		−	14.0000i		−	0.456145i
$943$	24.0000			0.781548
$944$	−9.00000			−0.292925
$945$		0			0
$946$			24.0000i			0.780307i
$947$			27.0000i			0.877382i	0.898638	+	0.438691i	$0.144558\pi$
$947$			27.0000i			0.877382i	−0.898638	+	0.438691i	$0.855442\pi$
$948$	−8.00000			−0.259828
$949$			35.0000i			1.13615i
$950$	3.00000			0.0973329
$951$	−20.0000			−0.648544
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	2.00000			0.0647524
$955$		−	14.0000i		−	0.453029i
$956$	−28.0000			−0.905585
$957$			6.00000i			0.193952i
$958$		−	23.0000i		−	0.743096i
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−18.0000			−0.580645
$962$		−	50.0000i		−	1.61206i
$963$		−	16.0000i		−	0.515593i
$964$		−	8.00000i		−	0.257663i
$965$	−6.00000			−0.193147
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	25.0000			0.803530
$969$	−3.00000	+	12.0000i	−0.0963739	+	0.385496i
$970$	−1.00000			−0.0321081
$971$	−9.00000			−0.288824			−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000			−0.288824			−0.144412	+	0.989518i	$0.546129\pi$
$972$			16.0000i			0.513200i
$973$		0			0
$974$			8.00000i			0.256337i
$975$			5.00000i			0.160128i
$976$			3.00000i			0.0960277i
$977$	−10.0000			−0.319928			−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−10.0000			−0.319928			−0.159964	+	0.987123i	$0.551138\pi$
$978$	4.00000			0.127906
$979$		−	6.00000i		−	0.191761i
$980$			7.00000i			0.223607i
$981$		−	34.0000i		−	1.08554i
$982$	−37.0000			−1.18072
$983$		−	12.0000i		−	0.382741i	−0.981518	−	0.191370i	$-0.938707\pi$
$983$		−	12.0000i		−	0.382741i	0.981518	−	0.191370i	$-0.0612931\pi$
$984$	−12.0000			−0.382546
$985$	−6.00000			−0.191176
$986$	−1.00000	+	4.00000i	−0.0318465	+	0.127386i
$987$		0			0
$988$	−15.0000			−0.477214
$989$		−	8.00000i		−	0.254385i
$990$	12.0000			0.381385
$991$		−	39.0000i		−	1.23888i	−0.785046	−	0.619438i	$-0.787361\pi$
$991$		−	39.0000i		−	1.23888i	0.785046	−	0.619438i	$-0.212639\pi$
$992$			7.00000i			0.222250i
$993$			17.0000i			0.539479i
$994$		0			0
$995$	13.0000			0.412128
$996$			2.00000i			0.0633724i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$			16.0000i			0.506471i
$999$	50.0000			1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.b.a.101.2	yes	2
3.2	odd	2		1530.2.c.d.271.1		2
4.3	odd	2		1360.2.c.b.1121.1		2
5.2	odd	4		850.2.d.g.849.1		2
5.3	odd	4		850.2.d.b.849.2		2
5.4	even	2		850.2.b.j.101.1		2
17.4	even	4		2890.2.a.q.1.1		1
17.13	even	4		2890.2.a.m.1.1		1
17.16	even	2	inner	170.2.b.a.101.1	✓	2
51.50	odd	2		1530.2.c.d.271.2		2
68.67	odd	2		1360.2.c.b.1121.2		2
85.33	odd	4		850.2.d.g.849.2		2
85.67	odd	4		850.2.d.b.849.1		2
85.84	even	2		850.2.b.j.101.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.b.a.101.1	✓	2	17.16	even	2	inner
170.2.b.a.101.2	yes	2	1.1	even	1	trivial
850.2.b.j.101.1		2	5.4	even	2
850.2.b.j.101.2		2	85.84	even	2
850.2.d.b.849.1		2	85.67	odd	4
850.2.d.b.849.2		2	5.3	odd	4
850.2.d.g.849.1		2	5.2	odd	4
850.2.d.g.849.2		2	85.33	odd	4
1360.2.c.b.1121.1		2	4.3	odd	2
1360.2.c.b.1121.2		2	68.67	odd	2
1530.2.c.d.271.1		2	3.2	odd	2
1530.2.c.d.271.2		2	51.50	odd	2
2890.2.a.m.1.1		1	17.13	even	4
2890.2.a.q.1.1		1	17.4	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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{8} +2.00000 q^{9} -1.00000i q^{10} +6.00000i q^{11} +1.00000i q^{12} -5.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +(4.00000 + 1.00000i) q^{17} -2.00000 q^{18} +3.00000 q^{19} +1.00000i q^{20} -6.00000i q^{22} +2.00000i q^{23} -1.00000i q^{24} -1.00000 q^{25} +5.00000 q^{26} +5.00000i q^{27} -1.00000i q^{29} +1.00000 q^{30} -7.00000i q^{31} -1.00000 q^{32} -6.00000 q^{33} +(-4.00000 - 1.00000i) q^{34} +2.00000 q^{36} -10.0000i q^{37} -3.00000 q^{38} -5.00000i q^{39} -1.00000i q^{40} -12.0000i q^{41} -4.00000 q^{43} +6.00000i q^{44} +2.00000i q^{45} -2.00000i q^{46} +7.00000 q^{47} +1.00000i q^{48} +7.00000 q^{49} +1.00000 q^{50} +(-1.00000 + 4.00000i) q^{51} -5.00000 q^{52} -1.00000 q^{53} -5.00000i q^{54} -6.00000 q^{55} +3.00000i q^{57} +1.00000i q^{58} -9.00000 q^{59} -1.00000 q^{60} +3.00000i q^{61} +7.00000i q^{62} +1.00000 q^{64} -5.00000i q^{65} +6.00000 q^{66} +10.0000 q^{67} +(4.00000 + 1.00000i) q^{68} -2.00000 q^{69} +9.00000i q^{71} -2.00000 q^{72} -7.00000i q^{73} +10.0000i q^{74} -1.00000i q^{75} +3.00000 q^{76} +5.00000i q^{78} +8.00000i q^{79} +1.00000i q^{80} +1.00000 q^{81} +12.0000i q^{82} +2.00000 q^{83} +(-1.00000 + 4.00000i) q^{85} +4.00000 q^{86} +1.00000 q^{87} -6.00000i q^{88} -1.00000 q^{89} -2.00000i q^{90} +2.00000i q^{92} +7.00000 q^{93} -7.00000 q^{94} +3.00000i q^{95} -1.00000i q^{96} -1.00000i q^{97} -7.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + 4 q^{9} - 10 q^{13} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} - 2 q^{25} + 10 q^{26} + 2 q^{30} - 2 q^{32} - 12 q^{33} - 8 q^{34} + 4 q^{36} - 6 q^{38} - 8 q^{43} + 14 q^{47} + 14 q^{49} + 2 q^{50} - 2 q^{51} - 10 q^{52} - 2 q^{53} - 12 q^{55} - 18 q^{59} - 2 q^{60} + 2 q^{64} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} - 4 q^{72} + 6 q^{76} + 2 q^{81} + 4 q^{83} - 2 q^{85} + 8 q^{86} + 2 q^{87} - 2 q^{89} + 14 q^{93} - 14 q^{94} - 14 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 + 4 * q^9 - 10 * q^13 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 4 * q^18 + 6 * q^19 - 2 * q^25 + 10 * q^26 + 2 * q^30 - 2 * q^32 - 12 * q^33 - 8 * q^34 + 4 * q^36 - 6 * q^38 - 8 * q^43 + 14 * q^47 + 14 * q^49 + 2 * q^50 - 2 * q^51 - 10 * q^52 - 2 * q^53 - 12 * q^55 - 18 * q^59 - 2 * q^60 + 2 * q^64 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 - 4 * q^72 + 6 * q^76 + 2 * q^81 + 4 * q^83 - 2 * q^85 + 8 * q^86 + 2 * q^87 - 2 * q^89 + 14 * q^93 - 14 * q^94 - 14 * q^98

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