LMFDB - Embedded newform 170.2.c.a.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(69,170)]

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([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("170.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.35745683436$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.69
Dual form			170.2.c.a.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +3.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +2.00000i q^{18} +7.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -6.00000i q^{22} -8.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -3.00000 q^{26} +5.00000i q^{27} +5.00000 q^{29} +(-1.00000 - 2.00000i) q^{30} +5.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.00000 q^{34} -2.00000 q^{36} -8.00000i q^{37} +7.00000i q^{38} -3.00000 q^{39} +(2.00000 - 1.00000i) q^{40} -4.00000i q^{43} +6.00000 q^{44} +(2.00000 + 4.00000i) q^{45} +8.00000 q^{46} -3.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +1.00000 q^{51} -3.00000i q^{52} +9.00000i q^{53} -5.00000 q^{54} +(-6.00000 - 12.0000i) q^{55} +7.00000i q^{57} +5.00000i q^{58} -5.00000 q^{59} +(2.00000 - 1.00000i) q^{60} -3.00000 q^{61} +5.00000i q^{62} -1.00000 q^{64} +(-6.00000 + 3.00000i) q^{65} +6.00000 q^{66} +2.00000i q^{67} +1.00000i q^{68} +8.00000 q^{69} -15.0000 q^{71} -2.00000i q^{72} -11.0000i q^{73} +8.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -7.00000 q^{76} -3.00000i q^{78} -8.00000 q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +4.00000i q^{83} +(2.00000 - 1.00000i) q^{85} +4.00000 q^{86} +5.00000i q^{87} +6.00000i q^{88} +1.00000 q^{89} +(-4.00000 + 2.00000i) q^{90} +8.00000i q^{92} +5.00000i q^{93} +3.00000 q^{94} +(7.00000 + 14.0000i) q^{95} -1.00000 q^{96} +9.00000i q^{97} +7.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^9	$ 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{9} - 4 q^{10} - 12 q^{11} - 4 q^{15} + 2 q^{16} + 14 q^{19} - 2 q^{20} + 2 q^{24} - 6 q^{25} - 6 q^{26} + 10 q^{29} - 2 q^{30} + 10 q^{31} + 2 q^{34} - 4 q^{36} - 6 q^{39} + 4 q^{40} + 12 q^{44} + 4 q^{45} + 16 q^{46} + 14 q^{49} - 8 q^{50} + 2 q^{51} - 10 q^{54} - 12 q^{55} - 10 q^{59} + 4 q^{60} - 6 q^{61} - 2 q^{64} - 12 q^{65} + 12 q^{66} + 16 q^{69} - 30 q^{71} + 16 q^{74} - 8 q^{75} - 14 q^{76} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{85} + 8 q^{86} + 2 q^{89} - 8 q^{90} + 6 q^{94} + 14 q^{95} - 2 q^{96} - 24 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^9 - 4 * q^10 - 12 * q^11 - 4 * q^15 + 2 * q^16 + 14 * q^19 - 2 * q^20 + 2 * q^24 - 6 * q^25 - 6 * q^26 + 10 * q^29 - 2 * q^30 + 10 * q^31 + 2 * q^34 - 4 * q^36 - 6 * q^39 + 4 * q^40 + 12 * q^44 + 4 * q^45 + 16 * q^46 + 14 * q^49 - 8 * q^50 + 2 * q^51 - 10 * q^54 - 12 * q^55 - 10 * q^59 + 4 * q^60 - 6 * q^61 - 2 * q^64 - 12 * q^65 + 12 * q^66 + 16 * q^69 - 30 * q^71 + 16 * q^74 - 8 * q^75 - 14 * q^76 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^85 + 8 * q^86 + 2 * q^89 - 8 * q^90 + 6 * q^94 + 14 * q^95 - 2 * q^96 - 24 * q^99

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$			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
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	−1.00000			−0.408248
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.00000			0.666667
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$		−	1.00000i		−	0.288675i
$13$			3.00000i			0.832050i	0.909353	+	0.416025i	$0.136577\pi$
$13$			3.00000i			0.832050i	−0.909353	+	0.416025i	$0.863423\pi$
$14$		0			0
$15$	−2.00000	+	1.00000i	−0.516398	+	0.258199i
$16$	1.00000			0.250000
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$			2.00000i			0.471405i
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$		−	6.00000i		−	1.27920i
$23$		−	8.00000i		−	1.66812i	−0.551677	−	0.834058i	$-0.686012\pi$
$23$		−	8.00000i		−	1.66812i	0.551677	−	0.834058i	$-0.313988\pi$
$24$	1.00000			0.204124
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	−3.00000			−0.588348
$27$			5.00000i			0.962250i
$28$		0			0
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	−1.00000	−	2.00000i	−0.182574	−	0.365148i
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$			1.00000i			0.176777i
$33$		−	6.00000i		−	1.04447i
$34$	1.00000			0.171499
$35$		0			0
$36$	−2.00000			−0.333333
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$			7.00000i			1.13555i
$39$	−3.00000			−0.480384
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$	6.00000			0.904534
$45$	2.00000	+	4.00000i	0.298142	+	0.596285i
$46$	8.00000			1.17954
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$			1.00000i			0.144338i
$49$	7.00000			1.00000
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	1.00000			0.140028
$52$		−	3.00000i		−	0.416025i
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$	−5.00000			−0.680414
$55$	−6.00000	−	12.0000i	−0.809040	−	1.61808i
$56$		0			0
$57$			7.00000i			0.927173i
$58$			5.00000i			0.656532i
$59$	−5.00000			−0.650945			−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000			−0.650945			−0.325472	+	0.945552i	$0.605523\pi$
$60$	2.00000	−	1.00000i	0.258199	−	0.129099i
$61$	−3.00000			−0.384111			−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000			−0.384111			−0.192055	+	0.981384i	$0.561515\pi$
$62$			5.00000i			0.635001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.00000	+	3.00000i	−0.744208	+	0.372104i
$66$	6.00000			0.738549
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$			1.00000i			0.121268i
$69$	8.00000			0.963087
$70$		0			0
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$		−	2.00000i		−	0.235702i
$73$		−	11.0000i		−	1.28745i	−0.765256	−	0.643726i	$-0.777388\pi$
$73$		−	11.0000i		−	1.28745i	0.765256	−	0.643726i	$-0.222612\pi$
$74$	8.00000			0.929981
$75$	−4.00000	−	3.00000i	−0.461880	−	0.346410i
$76$	−7.00000			−0.802955
$77$		0			0
$78$		−	3.00000i		−	0.339683i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$	1.00000			0.111111
$82$		0			0
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$		0			0
$85$	2.00000	−	1.00000i	0.216930	−	0.108465i
$86$	4.00000			0.431331
$87$			5.00000i			0.536056i
$88$			6.00000i			0.639602i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$	−4.00000	+	2.00000i	−0.421637	+	0.210819i
$91$		0			0
$92$			8.00000i			0.834058i
$93$			5.00000i			0.518476i
$94$	3.00000			0.309426
$95$	7.00000	+	14.0000i	0.718185	+	1.43637i
$96$	−1.00000			−0.102062
$97$			9.00000i			0.913812i	0.889515	+	0.456906i	$0.151042\pi$
$97$			9.00000i			0.913812i	−0.889515	+	0.456906i	$0.848958\pi$
$98$			7.00000i			0.707107i
$99$	−12.0000			−1.20605
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$			1.00000i			0.0990148i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	3.00000			0.294174
$105$		0			0
$106$	−9.00000			−0.874157
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		−	5.00000i		−	0.481125i
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$	12.0000	−	6.00000i	1.14416	−	0.572078i
$111$	8.00000			0.759326
$112$		0			0
$113$		−	13.0000i		−	1.22294i	−0.791269	−	0.611469i	$-0.790579\pi$
$113$		−	13.0000i		−	1.22294i	0.791269	−	0.611469i	$-0.209421\pi$
$114$	−7.00000			−0.655610
$115$	16.0000	−	8.00000i	1.49201	−	0.746004i
$116$	−5.00000			−0.464238
$117$			6.00000i			0.554700i
$118$		−	5.00000i		−	0.460287i
$119$		0			0
$120$	1.00000	+	2.00000i	0.0912871	+	0.182574i
$121$	25.0000			2.27273
$122$		−	3.00000i		−	0.271607i
$123$		0			0
$124$	−5.00000			−0.449013
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$		−	1.00000i		−	0.0887357i	−0.999015	−	0.0443678i	$-0.985873\pi$
$127$		−	1.00000i		−	0.0887357i	0.999015	−	0.0443678i	$-0.0141274\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	4.00000			0.352180
$130$	−3.00000	−	6.00000i	−0.263117	−	0.526235i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$			6.00000i			0.522233i
$133$		0			0
$134$	−2.00000			−0.172774
$135$	−10.0000	+	5.00000i	−0.860663	+	0.430331i
$136$	−1.00000			−0.0857493
$137$		−	12.0000i		−	1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$		−	12.0000i		−	1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$			8.00000i			0.681005i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$		−	15.0000i		−	1.25877i
$143$		−	18.0000i		−	1.50524i
$144$	2.00000			0.166667
$145$	5.00000	+	10.0000i	0.415227	+	0.830455i
$146$	11.0000			0.910366
$147$			7.00000i			0.577350i
$148$			8.00000i			0.657596i
$149$	2.00000			0.163846			0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000			0.163846			0.0819232	+	0.996639i	$0.473894\pi$
$150$	3.00000	−	4.00000i	0.244949	−	0.326599i
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$		−	7.00000i		−	0.567775i
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	5.00000	+	10.0000i	0.401610	+	0.803219i
$156$	3.00000			0.240192
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$		−	8.00000i		−	0.636446i
$159$	−9.00000			−0.713746
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$		0			0
$165$	12.0000	−	6.00000i	0.934199	−	0.467099i
$166$	−4.00000			−0.310460
$167$			6.00000i			0.464294i	0.972681	+	0.232147i	$0.0745750\pi$
$167$			6.00000i			0.464294i	−0.972681	+	0.232147i	$0.925425\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$	1.00000	+	2.00000i	0.0766965	+	0.153393i
$171$	14.0000			1.07061
$172$			4.00000i			0.304997i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	−5.00000			−0.379049
$175$		0			0
$176$	−6.00000			−0.452267
$177$		−	5.00000i		−	0.375823i
$178$			1.00000i			0.0749532i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−2.00000	−	4.00000i	−0.149071	−	0.298142i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$		−	3.00000i		−	0.221766i
$184$	−8.00000			−0.589768
$185$	16.0000	−	8.00000i	1.17634	−	0.588172i
$186$	−5.00000			−0.366618
$187$			6.00000i			0.438763i
$188$			3.00000i			0.218797i
$189$		0			0
$190$	−14.0000	+	7.00000i	−1.01567	+	0.507833i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			26.0000i			1.87152i	0.352636	+	0.935760i	$0.385285\pi$
$193$			26.0000i			1.87152i	−0.352636	+	0.935760i	$0.614715\pi$
$194$	−9.00000			−0.646162
$195$	−3.00000	−	6.00000i	−0.214834	−	0.429669i
$196$	−7.00000			−0.500000
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	12.0000i		−	0.852803i
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$	−2.00000			−0.141069
$202$		−	12.0000i		−	0.844317i
$203$		0			0
$204$	−1.00000			−0.0700140
$205$		0			0
$206$		0			0
$207$		−	16.0000i		−	1.11208i
$208$			3.00000i			0.208013i
$209$	−42.0000			−2.90520
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$		−	9.00000i		−	0.618123i
$213$		−	15.0000i		−	1.02778i
$214$	−4.00000			−0.273434
$215$	8.00000	−	4.00000i	0.545595	−	0.272798i
$216$	5.00000			0.340207
$217$		0			0
$218$		−	9.00000i		−	0.609557i
$219$	11.0000			0.743311
$220$	6.00000	+	12.0000i	0.404520	+	0.809040i
$221$	3.00000			0.201802
$222$			8.00000i			0.536925i
$223$		−	15.0000i		−	1.00447i	−0.864730	−	0.502237i	$-0.832510\pi$
$223$		−	15.0000i		−	1.00447i	0.864730	−	0.502237i	$-0.167490\pi$
$224$		0			0
$225$	−6.00000	+	8.00000i	−0.400000	+	0.533333i
$226$	13.0000			0.864747
$227$			9.00000i			0.597351i	0.954355	+	0.298675i	$0.0965448\pi$
$227$			9.00000i			0.597351i	−0.954355	+	0.298675i	$0.903455\pi$
$228$		−	7.00000i		−	0.463586i
$229$	−18.0000			−1.18947			−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000			−1.18947			−0.594737	+	0.803921i	$0.702744\pi$
$230$	8.00000	+	16.0000i	0.527504	+	1.05501i
$231$		0			0
$232$		−	5.00000i		−	0.328266i
$233$			27.0000i			1.76883i	0.466702	+	0.884414i	$0.345442\pi$
$233$			27.0000i			1.76883i	−0.466702	+	0.884414i	$0.654558\pi$
$234$	−6.00000			−0.392232
$235$	6.00000	−	3.00000i	0.391397	−	0.195698i
$236$	5.00000			0.325472
$237$		−	8.00000i		−	0.519656i
$238$		0			0
$239$	−10.0000			−0.646846			−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000			−0.646846			−0.323423	+	0.946254i	$0.604834\pi$
$240$	−2.00000	+	1.00000i	−0.129099	+	0.0645497i
$241$	−20.0000			−1.28831			−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000			−1.28831			−0.644157	+	0.764894i	$0.722792\pi$
$242$			25.0000i			1.60706i
$243$			16.0000i			1.02640i
$244$	3.00000			0.192055
$245$	7.00000	+	14.0000i	0.447214	+	0.894427i
$246$		0			0
$247$			21.0000i			1.33620i
$248$		−	5.00000i		−	0.317500i
$249$	−4.00000			−0.253490
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$			48.0000i			3.01773i
$254$	1.00000			0.0627456
$255$	1.00000	+	2.00000i	0.0626224	+	0.125245i
$256$	1.00000			0.0625000
$257$		−	28.0000i		−	1.74659i	−0.487190	−	0.873296i	$-0.661978\pi$
$257$		−	28.0000i		−	1.74659i	0.487190	−	0.873296i	$-0.338022\pi$
$258$			4.00000i			0.249029i
$259$		0			0
$260$	6.00000	−	3.00000i	0.372104	−	0.186052i
$261$	10.0000			0.618984
$262$			6.00000i			0.370681i
$263$			27.0000i			1.66489i	0.554107	+	0.832446i	$0.313060\pi$
$263$			27.0000i			1.66489i	−0.554107	+	0.832446i	$0.686940\pi$
$264$	−6.00000			−0.369274
$265$	−18.0000	+	9.00000i	−1.10573	+	0.552866i
$266$		0			0
$267$			1.00000i			0.0611990i
$268$		−	2.00000i		−	0.122169i
$269$	19.0000			1.15845			0.579225	−	0.815168i	$-0.303355\pi$
$269$	19.0000			1.15845			0.579225	+	0.815168i	$0.303355\pi$
$270$	−5.00000	−	10.0000i	−0.304290	−	0.608581i
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$		−	1.00000i		−	0.0606339i
$273$		0			0
$274$	12.0000			0.724947
$275$	18.0000	−	24.0000i	1.08544	−	1.44725i
$276$	−8.00000			−0.481543
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$		0			0
$279$	10.0000			0.598684
$280$		0			0
$281$	−33.0000			−1.96861			−0.984307	−	0.176462i	$-0.943535\pi$
$281$	−33.0000			−1.96861			−0.984307	+	0.176462i	$0.943535\pi$
$282$			3.00000i			0.178647i
$283$			11.0000i			0.653882i	0.945045	+	0.326941i	$0.106018\pi$
$283$			11.0000i			0.653882i	−0.945045	+	0.326941i	$0.893982\pi$
$284$	15.0000			0.890086
$285$	−14.0000	+	7.00000i	−0.829288	+	0.414644i
$286$	18.0000			1.06436
$287$		0			0
$288$			2.00000i			0.117851i
$289$	−1.00000			−0.0588235
$290$	−10.0000	+	5.00000i	−0.587220	+	0.293610i
$291$	−9.00000			−0.527589
$292$			11.0000i			0.643726i
$293$		−	19.0000i		−	1.10999i	−0.831853	−	0.554996i	$-0.812720\pi$
$293$		−	19.0000i		−	1.10999i	0.831853	−	0.554996i	$-0.187280\pi$
$294$	−7.00000			−0.408248
$295$	−5.00000	−	10.0000i	−0.291111	−	0.582223i
$296$	−8.00000			−0.464991
$297$		−	30.0000i		−	1.74078i
$298$			2.00000i			0.115857i
$299$	24.0000			1.38796
$300$	4.00000	+	3.00000i	0.230940	+	0.173205i
$301$		0			0
$302$		−	8.00000i		−	0.460348i
$303$		−	12.0000i		−	0.689382i
$304$	7.00000			0.401478
$305$	−3.00000	−	6.00000i	−0.171780	−	0.343559i
$306$	2.00000			0.114332
$307$			24.0000i			1.36975i	0.728659	+	0.684876i	$0.240144\pi$
$307$			24.0000i			1.36975i	−0.728659	+	0.684876i	$0.759856\pi$
$308$		0			0
$309$		0			0
$310$	−10.0000	+	5.00000i	−0.567962	+	0.283981i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$			3.00000i			0.169842i
$313$		−	22.0000i		−	1.24351i	−0.783210	−	0.621757i	$-0.786419\pi$
$313$		−	22.0000i		−	1.24351i	0.783210	−	0.621757i	$-0.213581\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		−	9.00000i		−	0.504695i
$319$	−30.0000			−1.67968
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$	−4.00000			−0.223258
$322$		0			0
$323$		−	7.00000i		−	0.389490i
$324$	−1.00000			−0.0555556
$325$	−12.0000	−	9.00000i	−0.665640	−	0.499230i
$326$	4.00000			0.221540
$327$		−	9.00000i		−	0.497701i
$328$		0			0
$329$		0			0
$330$	6.00000	+	12.0000i	0.330289	+	0.660578i
$331$	7.00000			0.384755			0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000			0.384755			0.192377	+	0.981321i	$0.438380\pi$
$332$		−	4.00000i		−	0.219529i
$333$		−	16.0000i		−	0.876795i
$334$	−6.00000			−0.328305
$335$	−4.00000	+	2.00000i	−0.218543	+	0.109272i
$336$		0			0
$337$		−	13.0000i		−	0.708155i	−0.935216	−	0.354078i	$-0.884795\pi$
$337$		−	13.0000i		−	0.708155i	0.935216	−	0.354078i	$-0.115205\pi$
$338$			4.00000i			0.217571i
$339$	13.0000			0.706063
$340$	−2.00000	+	1.00000i	−0.108465	+	0.0542326i
$341$	−30.0000			−1.62459
$342$			14.0000i			0.757033i
$343$		0			0
$344$	−4.00000			−0.215666
$345$	8.00000	+	16.0000i	0.430706	+	0.861411i
$346$		0			0
$347$		−	5.00000i		−	0.268414i	−0.990953	−	0.134207i	$-0.957151\pi$
$347$		−	5.00000i		−	0.268414i	0.990953	−	0.134207i	$-0.0428487\pi$
$348$		−	5.00000i		−	0.268028i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	−15.0000			−0.800641
$352$		−	6.00000i		−	0.319801i
$353$		−	8.00000i		−	0.425797i	−0.977074	−	0.212899i	$-0.931710\pi$
$353$		−	8.00000i		−	0.425797i	0.977074	−	0.212899i	$-0.0682904\pi$
$354$	5.00000			0.265747
$355$	−15.0000	−	30.0000i	−0.796117	−	1.59223i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$			12.0000i			0.634220i
$359$	28.0000			1.47778			0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000			1.47778			0.738892	+	0.673824i	$0.235349\pi$
$360$	4.00000	−	2.00000i	0.210819	−	0.105409i
$361$	30.0000			1.57895
$362$			2.00000i			0.105118i
$363$			25.0000i			1.31216i
$364$		0			0
$365$	22.0000	−	11.0000i	1.15153	−	0.575766i
$366$	3.00000			0.156813
$367$			10.0000i			0.521996i	0.965339	+	0.260998i	$0.0840516\pi$
$367$			10.0000i			0.521996i	−0.965339	+	0.260998i	$0.915948\pi$
$368$		−	8.00000i		−	0.417029i
$369$		0			0
$370$	8.00000	+	16.0000i	0.415900	+	0.831800i
$371$		0			0
$372$		−	5.00000i		−	0.259238i
$373$		−	14.0000i		−	0.724893i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$		−	14.0000i		−	0.724893i	0.932005	−	0.362446i	$-0.118058\pi$
$374$	−6.00000			−0.310253
$375$	2.00000	−	11.0000i	0.103280	−	0.568038i
$376$	−3.00000			−0.154713
$377$			15.0000i			0.772539i
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−7.00000	−	14.0000i	−0.359092	−	0.718185i
$381$	1.00000			0.0512316
$382$		0			0
$383$		−	27.0000i		−	1.37964i	−0.723983	−	0.689818i	$-0.757691\pi$
$383$		−	27.0000i		−	1.37964i	0.723983	−	0.689818i	$-0.242309\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−26.0000			−1.32337
$387$		−	8.00000i		−	0.406663i
$388$		−	9.00000i		−	0.456906i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	6.00000	−	3.00000i	0.303822	−	0.151911i
$391$	−8.00000			−0.404577
$392$		−	7.00000i		−	0.353553i
$393$			6.00000i			0.302660i
$394$	2.00000			0.100759
$395$	−8.00000	−	16.0000i	−0.402524	−	0.805047i
$396$	12.0000			0.603023
$397$			2.00000i			0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$			2.00000i			0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$		−	7.00000i		−	0.350878i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$		−	2.00000i		−	0.0997509i
$403$			15.0000i			0.747203i
$404$	12.0000			0.597022
$405$	1.00000	+	2.00000i	0.0496904	+	0.0993808i
$406$		0			0
$407$			48.0000i			2.37927i
$408$		−	1.00000i		−	0.0495074i
$409$	31.0000			1.53285			0.766426	−	0.642333i	$-0.222033\pi$
$409$	31.0000			1.53285			0.766426	+	0.642333i	$0.222033\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$		0			0
$413$		0			0
$414$	16.0000			0.786357
$415$	−8.00000	+	4.00000i	−0.392705	+	0.196352i
$416$	−3.00000			−0.147087
$417$		0			0
$418$		−	42.0000i		−	2.05429i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$			16.0000i			0.778868i
$423$		−	6.00000i		−	0.291730i
$424$	9.00000			0.437079
$425$	4.00000	+	3.00000i	0.194029	+	0.145521i
$426$	15.0000			0.726752
$427$		0			0
$428$		−	4.00000i		−	0.193347i
$429$	18.0000			0.869048
$430$	4.00000	+	8.00000i	0.192897	+	0.385794i
$431$	−16.0000			−0.770693			−0.385346	−	0.922772i	$-0.625918\pi$
$431$	−16.0000			−0.770693			−0.385346	+	0.922772i	$0.625918\pi$
$432$			5.00000i			0.240563i
$433$			20.0000i			0.961139i	0.876957	+	0.480569i	$0.159570\pi$
$433$			20.0000i			0.961139i	−0.876957	+	0.480569i	$0.840430\pi$
$434$		0			0
$435$	−10.0000	+	5.00000i	−0.479463	+	0.239732i
$436$	9.00000			0.431022
$437$		−	56.0000i		−	2.67884i
$438$			11.0000i			0.525600i
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$	−12.0000	+	6.00000i	−0.572078	+	0.286039i
$441$	14.0000			0.666667
$442$			3.00000i			0.142695i
$443$			10.0000i			0.475114i	0.971374	+	0.237557i	$0.0763467\pi$
$443$			10.0000i			0.475114i	−0.971374	+	0.237557i	$0.923653\pi$
$444$	−8.00000			−0.379663
$445$	1.00000	+	2.00000i	0.0474045	+	0.0948091i
$446$	15.0000			0.710271
$447$			2.00000i			0.0945968i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−8.00000	−	6.00000i	−0.377124	−	0.282843i
$451$		0			0
$452$			13.0000i			0.611469i
$453$		−	8.00000i		−	0.375873i
$454$	−9.00000			−0.422391
$455$		0			0
$456$	7.00000			0.327805
$457$			12.0000i			0.561336i	0.959805	+	0.280668i	$0.0905560\pi$
$457$			12.0000i			0.561336i	−0.959805	+	0.280668i	$0.909444\pi$
$458$		−	18.0000i		−	0.841085i
$459$	5.00000			0.233380
$460$	−16.0000	+	8.00000i	−0.746004	+	0.373002i
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$			31.0000i			1.44069i	0.693615	+	0.720346i	$0.256017\pi$
$463$			31.0000i			1.44069i	−0.693615	+	0.720346i	$0.743983\pi$
$464$	5.00000			0.232119
$465$	−10.0000	+	5.00000i	−0.463739	+	0.231869i
$466$	−27.0000			−1.25075
$467$			14.0000i			0.647843i	0.946084	+	0.323921i	$0.105001\pi$
$467$			14.0000i			0.647843i	−0.946084	+	0.323921i	$0.894999\pi$
$468$		−	6.00000i		−	0.277350i
$469$		0			0
$470$	3.00000	+	6.00000i	0.138380	+	0.276759i
$471$	14.0000			0.645086
$472$			5.00000i			0.230144i
$473$			24.0000i			1.10352i
$474$	8.00000			0.367452
$475$	−21.0000	+	28.0000i	−0.963546	+	1.28473i
$476$		0			0
$477$			18.0000i			0.824163i
$478$		−	10.0000i		−	0.457389i
$479$	37.0000			1.69057			0.845287	−	0.534313i	$-0.179430\pi$
$479$	37.0000			1.69057			0.845287	+	0.534313i	$0.179430\pi$
$480$	−1.00000	−	2.00000i	−0.0456435	−	0.0912871i
$481$	24.0000			1.09431
$482$		−	20.0000i		−	0.910975i
$483$		0			0
$484$	−25.0000			−1.13636
$485$	−18.0000	+	9.00000i	−0.817338	+	0.408669i
$486$	−16.0000			−0.725775
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$			3.00000i			0.135804i
$489$	4.00000			0.180886
$490$	−14.0000	+	7.00000i	−0.632456	+	0.316228i
$491$	−13.0000			−0.586682			−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000			−0.586682			−0.293341	+	0.956008i	$0.594767\pi$
$492$		0			0
$493$		−	5.00000i		−	0.225189i
$494$	−21.0000			−0.944835
$495$	−12.0000	−	24.0000i	−0.539360	−	1.07872i
$496$	5.00000			0.224507
$497$		0			0
$498$		−	4.00000i		−	0.179244i
$499$	28.0000			1.25345			0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000			1.25345			0.626726	+	0.779240i	$0.284395\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$	−6.00000			−0.268060
$502$			12.0000i			0.535586i
$503$		−	42.0000i		−	1.87269i	−0.351085	−	0.936344i	$-0.614187\pi$
$503$		−	42.0000i		−	1.87269i	0.351085	−	0.936344i	$-0.385813\pi$
$504$		0			0
$505$	−12.0000	−	24.0000i	−0.533993	−	1.06799i
$506$	−48.0000			−2.13386
$507$			4.00000i			0.177646i
$508$			1.00000i			0.0443678i
$509$	12.0000			0.531891			0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000			0.531891			0.265945	+	0.963988i	$0.414316\pi$
$510$	−2.00000	+	1.00000i	−0.0885615	+	0.0442807i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			35.0000i			1.54529i
$514$	28.0000			1.23503
$515$		0			0
$516$	−4.00000			−0.176090
$517$			18.0000i			0.791639i
$518$		0			0
$519$		0			0
$520$	3.00000	+	6.00000i	0.131559	+	0.263117i
$521$	28.0000			1.22670			0.613351	−	0.789810i	$-0.289821\pi$
$521$	28.0000			1.22670			0.613351	+	0.789810i	$0.289821\pi$
$522$			10.0000i			0.437688i
$523$			14.0000i			0.612177i	0.952003	+	0.306089i	$0.0990204\pi$
$523$			14.0000i			0.612177i	−0.952003	+	0.306089i	$0.900980\pi$
$524$	−6.00000			−0.262111
$525$		0			0
$526$	−27.0000			−1.17726
$527$		−	5.00000i		−	0.217803i
$528$		−	6.00000i		−	0.261116i
$529$	−41.0000			−1.78261
$530$	−9.00000	−	18.0000i	−0.390935	−	0.781870i
$531$	−10.0000			−0.433963
$532$		0			0
$533$		0			0
$534$	−1.00000			−0.0432742
$535$	−8.00000	+	4.00000i	−0.345870	+	0.172935i
$536$	2.00000			0.0863868
$537$			12.0000i			0.517838i
$538$			19.0000i			0.819148i
$539$	−42.0000			−1.80907
$540$	10.0000	−	5.00000i	0.430331	−	0.215166i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$		−	6.00000i		−	0.257722i
$543$			2.00000i			0.0858282i
$544$	1.00000			0.0428746
$545$	−9.00000	−	18.0000i	−0.385518	−	0.771035i
$546$		0			0
$547$		−	13.0000i		−	0.555840i	−0.960604	−	0.277920i	$-0.910355\pi$
$547$		−	13.0000i		−	0.555840i	0.960604	−	0.277920i	$-0.0896450\pi$
$548$			12.0000i			0.512615i
$549$	−6.00000			−0.256074
$550$	24.0000	+	18.0000i	1.02336	+	0.767523i
$551$	35.0000			1.49105
$552$		−	8.00000i		−	0.340503i
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	8.00000	+	16.0000i	0.339581	+	0.679162i
$556$		0			0
$557$		−	11.0000i		−	0.466085i	−0.972467	−	0.233042i	$-0.925132\pi$
$557$		−	11.0000i		−	0.466085i	0.972467	−	0.233042i	$-0.0748681\pi$
$558$			10.0000i			0.423334i
$559$	12.0000			0.507546
$560$		0			0
$561$	−6.00000			−0.253320
$562$		−	33.0000i		−	1.39202i
$563$			32.0000i			1.34864i	0.738440	+	0.674320i	$0.235563\pi$
$563$			32.0000i			1.34864i	−0.738440	+	0.674320i	$0.764437\pi$
$564$	−3.00000			−0.126323
$565$	26.0000	−	13.0000i	1.09383	−	0.546914i
$566$	−11.0000			−0.462364
$567$		0			0
$568$			15.0000i			0.629386i
$569$	21.0000			0.880366			0.440183	−	0.897908i	$-0.354914\pi$
$569$	21.0000			0.880366			0.440183	+	0.897908i	$0.354914\pi$
$570$	−7.00000	−	14.0000i	−0.293198	−	0.586395i
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$			18.0000i			0.752618i
$573$		0			0
$574$		0			0
$575$	32.0000	+	24.0000i	1.33449	+	1.00087i
$576$	−2.00000			−0.0833333
$577$		−	16.0000i		−	0.666089i	−0.942911	−	0.333044i	$-0.891924\pi$
$577$		−	16.0000i		−	0.666089i	0.942911	−	0.333044i	$-0.108076\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	−26.0000			−1.08052
$580$	−5.00000	−	10.0000i	−0.207614	−	0.415227i
$581$		0			0
$582$		−	9.00000i		−	0.373062i
$583$		−	54.0000i		−	2.23645i
$584$	−11.0000			−0.455183
$585$	−12.0000	+	6.00000i	−0.496139	+	0.248069i
$586$	19.0000			0.784883
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		−	7.00000i		−	0.288675i
$589$	35.0000			1.44215
$590$	10.0000	−	5.00000i	0.411693	−	0.205847i
$591$	2.00000			0.0822690
$592$		−	8.00000i		−	0.328798i
$593$			22.0000i			0.903432i	0.892162	+	0.451716i	$0.149188\pi$
$593$			22.0000i			0.903432i	−0.892162	+	0.451716i	$0.850812\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	−2.00000			−0.0819232
$597$		−	7.00000i		−	0.286491i
$598$			24.0000i			0.981433i
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$	−3.00000	+	4.00000i	−0.122474	+	0.163299i
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$	8.00000			0.325515
$605$	25.0000	+	50.0000i	1.01639	+	2.03279i
$606$	12.0000			0.487467
$607$			12.0000i			0.487065i	0.969893	+	0.243532i	$0.0783062\pi$
$607$			12.0000i			0.487065i	−0.969893	+	0.243532i	$0.921694\pi$
$608$			7.00000i			0.283887i
$609$		0			0
$610$	6.00000	−	3.00000i	0.242933	−	0.121466i
$611$	9.00000			0.364101
$612$			2.00000i			0.0808452i
$613$		−	17.0000i		−	0.686624i	−0.939222	−	0.343312i	$-0.888451\pi$
$613$		−	17.0000i		−	0.686624i	0.939222	−	0.343312i	$-0.111549\pi$
$614$	−24.0000			−0.968561
$615$		0			0
$616$		0			0
$617$			29.0000i			1.16750i	0.811935	+	0.583748i	$0.198414\pi$
$617$			29.0000i			1.16750i	−0.811935	+	0.583748i	$0.801586\pi$
$618$		0			0
$619$	−14.0000			−0.562708			−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000			−0.562708			−0.281354	+	0.959604i	$0.590783\pi$
$620$	−5.00000	−	10.0000i	−0.200805	−	0.401610i
$621$	40.0000			1.60514
$622$		−	4.00000i		−	0.160385i
$623$		0			0
$624$	−3.00000			−0.120096
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	22.0000			0.879297
$627$		−	42.0000i		−	1.67732i
$628$			14.0000i			0.558661i
$629$	−8.00000			−0.318981
$630$		0			0
$631$	−42.0000			−1.67199			−0.835997	−	0.548734i	$-0.815110\pi$
$631$	−42.0000			−1.67199			−0.835997	+	0.548734i	$0.815110\pi$
$632$			8.00000i			0.318223i
$633$			16.0000i			0.635943i
$634$		0			0
$635$	2.00000	−	1.00000i	0.0793676	−	0.0396838i
$636$	9.00000			0.356873
$637$			21.0000i			0.832050i
$638$		−	30.0000i		−	1.18771i
$639$	−30.0000			−1.18678
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$		−	4.00000i		−	0.157867i
$643$		−	44.0000i		−	1.73519i	−0.497271	−	0.867595i	$-0.665665\pi$
$643$		−	44.0000i		−	1.73519i	0.497271	−	0.867595i	$-0.334335\pi$
$644$		0			0
$645$	4.00000	+	8.00000i	0.157500	+	0.315000i
$646$	7.00000			0.275411
$647$		−	17.0000i		−	0.668339i	−0.942513	−	0.334169i	$-0.891544\pi$
$647$		−	17.0000i		−	0.668339i	0.942513	−	0.334169i	$-0.108456\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	30.0000			1.17760
$650$	9.00000	−	12.0000i	0.353009	−	0.470679i
$651$		0			0
$652$			4.00000i			0.156652i
$653$			30.0000i			1.17399i	0.809590	+	0.586995i	$0.199689\pi$
$653$			30.0000i			1.17399i	−0.809590	+	0.586995i	$0.800311\pi$
$654$	9.00000			0.351928
$655$	6.00000	+	12.0000i	0.234439	+	0.468879i
$656$		0			0
$657$		−	22.0000i		−	0.858302i
$658$		0			0
$659$	−19.0000			−0.740135			−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000			−0.740135			−0.370067	+	0.929005i	$0.620665\pi$
$660$	−12.0000	+	6.00000i	−0.467099	+	0.233550i
$661$	−16.0000			−0.622328			−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000			−0.622328			−0.311164	+	0.950356i	$0.600719\pi$
$662$			7.00000i			0.272063i
$663$			3.00000i			0.116510i
$664$	4.00000			0.155230
$665$		0			0
$666$	16.0000			0.619987
$667$		−	40.0000i		−	1.54881i
$668$		−	6.00000i		−	0.232147i
$669$	15.0000			0.579934
$670$	−2.00000	−	4.00000i	−0.0772667	−	0.154533i
$671$	18.0000			0.694882
$672$		0			0
$673$		−	35.0000i		−	1.34915i	−0.738206	−	0.674575i	$-0.764327\pi$
$673$		−	35.0000i		−	1.34915i	0.738206	−	0.674575i	$-0.235673\pi$
$674$	13.0000			0.500741
$675$	−20.0000	−	15.0000i	−0.769800	−	0.577350i
$676$	−4.00000			−0.153846
$677$			24.0000i			0.922395i	0.887298	+	0.461197i	$0.152580\pi$
$677$			24.0000i			0.922395i	−0.887298	+	0.461197i	$0.847420\pi$
$678$			13.0000i			0.499262i
$679$		0			0
$680$	−1.00000	−	2.00000i	−0.0383482	−	0.0766965i
$681$	−9.00000			−0.344881
$682$		−	30.0000i		−	1.14876i
$683$			45.0000i			1.72188i	0.508709	+	0.860939i	$0.330123\pi$
$683$			45.0000i			1.72188i	−0.508709	+	0.860939i	$0.669877\pi$
$684$	−14.0000			−0.535303
$685$	24.0000	−	12.0000i	0.916993	−	0.458496i
$686$		0			0
$687$		−	18.0000i		−	0.686743i
$688$		−	4.00000i		−	0.152499i
$689$	−27.0000			−1.02862
$690$	−16.0000	+	8.00000i	−0.609110	+	0.304555i
$691$	−16.0000			−0.608669			−0.304334	−	0.952565i	$-0.598434\pi$
$691$	−16.0000			−0.608669			−0.304334	+	0.952565i	$0.598434\pi$
$692$		0			0
$693$		0			0
$694$	5.00000			0.189797
$695$		0			0
$696$	5.00000			0.189525
$697$		0			0
$698$			2.00000i			0.0757011i
$699$	−27.0000			−1.02123
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		−	15.0000i		−	0.566139i
$703$		−	56.0000i		−	2.11208i
$704$	6.00000			0.226134
$705$	3.00000	+	6.00000i	0.112987	+	0.225973i
$706$	8.00000			0.301084
$707$		0			0
$708$			5.00000i			0.187912i
$709$	−23.0000			−0.863783			−0.431892	−	0.901926i	$-0.642154\pi$
$709$	−23.0000			−0.863783			−0.431892	+	0.901926i	$0.642154\pi$
$710$	30.0000	−	15.0000i	1.12588	−	0.562940i
$711$	−16.0000			−0.600047
$712$		−	1.00000i		−	0.0374766i
$713$		−	40.0000i		−	1.49801i
$714$		0			0
$715$	36.0000	−	18.0000i	1.34632	−	0.673162i
$716$	−12.0000			−0.448461
$717$		−	10.0000i		−	0.373457i
$718$			28.0000i			1.04495i
$719$	27.0000			1.00693			0.503465	−	0.864016i	$-0.332058\pi$
$719$	27.0000			1.00693			0.503465	+	0.864016i	$0.332058\pi$
$720$	2.00000	+	4.00000i	0.0745356	+	0.149071i
$721$		0			0
$722$			30.0000i			1.11648i
$723$		−	20.0000i		−	0.743808i
$724$	−2.00000			−0.0743294
$725$	−15.0000	+	20.0000i	−0.557086	+	0.742781i
$726$	−25.0000			−0.927837
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	11.0000	+	22.0000i	0.407128	+	0.814257i
$731$	−4.00000			−0.147945
$732$			3.00000i			0.110883i
$733$		−	14.0000i		−	0.517102i	−0.965998	−	0.258551i	$-0.916755\pi$
$733$		−	14.0000i		−	0.517102i	0.965998	−	0.258551i	$-0.0832450\pi$
$734$	−10.0000			−0.369107
$735$	−14.0000	+	7.00000i	−0.516398	+	0.258199i
$736$	8.00000			0.294884
$737$		−	12.0000i		−	0.442026i
$738$		0			0
$739$	1.00000			0.0367856			0.0183928	−	0.999831i	$-0.494145\pi$
$739$	1.00000			0.0367856			0.0183928	+	0.999831i	$0.494145\pi$
$740$	−16.0000	+	8.00000i	−0.588172	+	0.294086i
$741$	−21.0000			−0.771454
$742$		0			0
$743$			24.0000i			0.880475i	0.897881	+	0.440237i	$0.145106\pi$
$743$			24.0000i			0.880475i	−0.897881	+	0.440237i	$0.854894\pi$
$744$	5.00000			0.183309
$745$	2.00000	+	4.00000i	0.0732743	+	0.146549i
$746$	14.0000			0.512576
$747$			8.00000i			0.292705i
$748$		−	6.00000i		−	0.219382i
$749$		0			0
$750$	11.0000	+	2.00000i	0.401663	+	0.0730297i
$751$	11.0000			0.401396			0.200698	−	0.979653i	$-0.435679\pi$
$751$	11.0000			0.401396			0.200698	+	0.979653i	$0.435679\pi$
$752$		−	3.00000i		−	0.109399i
$753$			12.0000i			0.437304i
$754$	−15.0000			−0.546268
$755$	−8.00000	−	16.0000i	−0.291150	−	0.582300i
$756$		0			0
$757$			45.0000i			1.63555i	0.575536	+	0.817776i	$0.304793\pi$
$757$			45.0000i			1.63555i	−0.575536	+	0.817776i	$0.695207\pi$
$758$			20.0000i			0.726433i
$759$	−48.0000			−1.74229
$760$	14.0000	−	7.00000i	0.507833	−	0.253917i
$761$	14.0000			0.507500			0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000			0.507500			0.253750	+	0.967270i	$0.418336\pi$
$762$			1.00000i			0.0362262i
$763$		0			0
$764$		0			0
$765$	4.00000	−	2.00000i	0.144620	−	0.0723102i
$766$	27.0000			0.975550
$767$		−	15.0000i		−	0.541619i
$768$			1.00000i			0.0360844i
$769$	−37.0000			−1.33425			−0.667127	−	0.744944i	$-0.732476\pi$
$769$	−37.0000			−1.33425			−0.667127	+	0.744944i	$0.732476\pi$
$770$		0			0
$771$	28.0000			1.00840
$772$		−	26.0000i		−	0.935760i
$773$		−	6.00000i		−	0.215805i	−0.994161	−	0.107903i	$-0.965587\pi$
$773$		−	6.00000i		−	0.215805i	0.994161	−	0.107903i	$-0.0344134\pi$
$774$	8.00000			0.287554
$775$	−15.0000	+	20.0000i	−0.538816	+	0.718421i
$776$	9.00000			0.323081
$777$		0			0
$778$		−	30.0000i		−	1.07555i
$779$		0			0
$780$	3.00000	+	6.00000i	0.107417	+	0.214834i
$781$	90.0000			3.22045
$782$		−	8.00000i		−	0.286079i
$783$			25.0000i			0.893427i
$784$	7.00000			0.250000
$785$	28.0000	−	14.0000i	0.999363	−	0.499681i
$786$	−6.00000			−0.214013
$787$			47.0000i			1.67537i	0.546154	+	0.837685i	$0.316091\pi$
$787$			47.0000i			1.67537i	−0.546154	+	0.837685i	$0.683909\pi$
$788$			2.00000i			0.0712470i
$789$	−27.0000			−0.961225
$790$	16.0000	−	8.00000i	0.569254	−	0.284627i
$791$		0			0
$792$			12.0000i			0.426401i
$793$		−	9.00000i		−	0.319599i
$794$	−2.00000			−0.0709773
$795$	−9.00000	−	18.0000i	−0.319197	−	0.638394i
$796$	7.00000			0.248108
$797$		−	54.0000i		−	1.91278i	−0.292096	−	0.956389i	$-0.594353\pi$
$797$		−	54.0000i		−	1.91278i	0.292096	−	0.956389i	$-0.405647\pi$
$798$		0			0
$799$	−3.00000			−0.106132
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$	2.00000			0.0706665
$802$		−	10.0000i		−	0.353112i
$803$			66.0000i			2.32909i
$804$	2.00000			0.0705346
$805$		0			0
$806$	−15.0000			−0.528352
$807$			19.0000i			0.668832i
$808$			12.0000i			0.422159i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$	−2.00000	+	1.00000i	−0.0702728	+	0.0351364i
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$		−	6.00000i		−	0.210429i
$814$	−48.0000			−1.68240
$815$	8.00000	−	4.00000i	0.280228	−	0.140114i
$816$	1.00000			0.0350070
$817$		−	28.0000i		−	0.979596i
$818$			31.0000i			1.08389i
$819$		0			0
$820$		0			0
$821$	−27.0000			−0.942306			−0.471153	−	0.882051i	$-0.656162\pi$
$821$	−27.0000			−0.942306			−0.471153	+	0.882051i	$0.656162\pi$
$822$			12.0000i			0.418548i
$823$		−	54.0000i		−	1.88232i	−0.337959	−	0.941161i	$-0.609737\pi$
$823$		−	54.0000i		−	1.88232i	0.337959	−	0.941161i	$-0.390263\pi$
$824$		0			0
$825$	24.0000	+	18.0000i	0.835573	+	0.626680i
$826$		0			0
$827$			32.0000i			1.11275i	0.830932	+	0.556375i	$0.187808\pi$
$827$			32.0000i			1.11275i	−0.830932	+	0.556375i	$0.812192\pi$
$828$			16.0000i			0.556038i
$829$	−18.0000			−0.625166			−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000			−0.625166			−0.312583	+	0.949890i	$0.601194\pi$
$830$	−4.00000	−	8.00000i	−0.138842	−	0.277684i
$831$	−2.00000			−0.0693792
$832$		−	3.00000i		−	0.104006i
$833$		−	7.00000i		−	0.242536i
$834$		0			0
$835$	−12.0000	+	6.00000i	−0.415277	+	0.207639i
$836$	42.0000			1.45260
$837$			25.0000i			0.864126i
$838$		0			0
$839$	−31.0000			−1.07024			−0.535119	−	0.844776i	$-0.679733\pi$
$839$	−31.0000			−1.07024			−0.535119	+	0.844776i	$0.679733\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$			20.0000i			0.689246i
$843$		−	33.0000i		−	1.13658i
$844$	−16.0000			−0.550743
$845$	4.00000	+	8.00000i	0.137604	+	0.275208i
$846$	6.00000			0.206284
$847$		0			0
$848$			9.00000i			0.309061i
$849$	−11.0000			−0.377519
$850$	−3.00000	+	4.00000i	−0.102899	+	0.137199i
$851$	−64.0000			−2.19389
$852$			15.0000i			0.513892i
$853$			30.0000i			1.02718i	0.858036	+	0.513590i	$0.171685\pi$
$853$			30.0000i			1.02718i	−0.858036	+	0.513590i	$0.828315\pi$
$854$		0			0
$855$	14.0000	+	28.0000i	0.478790	+	0.957580i
$856$	4.00000			0.136717
$857$			57.0000i			1.94708i	0.228510	+	0.973541i	$0.426614\pi$
$857$			57.0000i			1.94708i	−0.228510	+	0.973541i	$0.573386\pi$
$858$			18.0000i			0.614510i
$859$	−33.0000			−1.12595			−0.562973	−	0.826475i	$-0.690342\pi$
$859$	−33.0000			−1.12595			−0.562973	+	0.826475i	$0.690342\pi$
$860$	−8.00000	+	4.00000i	−0.272798	+	0.136399i
$861$		0			0
$862$		−	16.0000i		−	0.544962i
$863$		−	8.00000i		−	0.272323i	−0.990687	−	0.136162i	$-0.956523\pi$
$863$		−	8.00000i		−	0.272323i	0.990687	−	0.136162i	$-0.0434766\pi$
$864$	−5.00000			−0.170103
$865$		0			0
$866$	−20.0000			−0.679628
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	48.0000			1.62829
$870$	−5.00000	−	10.0000i	−0.169516	−	0.339032i
$871$	−6.00000			−0.203302
$872$			9.00000i			0.304778i
$873$			18.0000i			0.609208i
$874$	56.0000			1.89423
$875$		0			0
$876$	−11.0000			−0.371656
$877$			10.0000i			0.337676i	0.985644	+	0.168838i	$0.0540015\pi$
$877$			10.0000i			0.337676i	−0.985644	+	0.168838i	$0.945999\pi$
$878$		−	16.0000i		−	0.539974i
$879$	19.0000			0.640854
$880$	−6.00000	−	12.0000i	−0.202260	−	0.404520i
$881$	38.0000			1.28025			0.640126	−	0.768270i	$-0.278882\pi$
$881$	38.0000			1.28025			0.640126	+	0.768270i	$0.278882\pi$
$882$			14.0000i			0.471405i
$883$		−	26.0000i		−	0.874970i	−0.899226	−	0.437485i	$-0.855869\pi$
$883$		−	26.0000i		−	0.874970i	0.899226	−	0.437485i	$-0.144131\pi$
$884$	−3.00000			−0.100901
$885$	10.0000	−	5.00000i	0.336146	−	0.168073i
$886$	−10.0000			−0.335957
$887$			14.0000i			0.470074i	0.971986	+	0.235037i	$0.0755211\pi$
$887$			14.0000i			0.470074i	−0.971986	+	0.235037i	$0.924479\pi$
$888$		−	8.00000i		−	0.268462i
$889$		0			0
$890$	−2.00000	+	1.00000i	−0.0670402	+	0.0335201i
$891$	−6.00000			−0.201008
$892$			15.0000i			0.502237i
$893$		−	21.0000i		−	0.702738i
$894$	−2.00000			−0.0668900
$895$	12.0000	+	24.0000i	0.401116	+	0.802232i
$896$		0			0
$897$			24.0000i			0.801337i
$898$			6.00000i			0.200223i
$899$	25.0000			0.833797
$900$	6.00000	−	8.00000i	0.200000	−	0.266667i
$901$	9.00000			0.299833
$902$		0			0
$903$		0			0
$904$	−13.0000			−0.432374
$905$	2.00000	+	4.00000i	0.0664822	+	0.132964i
$906$	8.00000			0.265782
$907$		−	27.0000i		−	0.896520i	−0.893903	−	0.448260i	$-0.852044\pi$
$907$		−	27.0000i		−	0.896520i	0.893903	−	0.448260i	$-0.147956\pi$
$908$		−	9.00000i		−	0.298675i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$			7.00000i			0.231793i
$913$		−	24.0000i		−	0.794284i
$914$	−12.0000			−0.396925
$915$	6.00000	−	3.00000i	0.198354	−	0.0991769i
$916$	18.0000			0.594737
$917$		0			0
$918$			5.00000i			0.165025i
$919$	6.00000			0.197922			0.0989609	−	0.995091i	$-0.468448\pi$
$919$	6.00000			0.197922			0.0989609	+	0.995091i	$0.468448\pi$
$920$	−8.00000	−	16.0000i	−0.263752	−	0.527504i
$921$	−24.0000			−0.790827
$922$		−	20.0000i		−	0.658665i
$923$		−	45.0000i		−	1.48119i
$924$		0			0
$925$	32.0000	+	24.0000i	1.05215	+	0.789115i
$926$	−31.0000			−1.01872
$927$		0			0
$928$			5.00000i			0.164133i
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$	−5.00000	−	10.0000i	−0.163956	−	0.327913i
$931$	49.0000			1.60591
$932$		−	27.0000i		−	0.884414i
$933$		−	4.00000i		−	0.130954i
$934$	−14.0000			−0.458094
$935$	−12.0000	+	6.00000i	−0.392442	+	0.196221i
$936$	6.00000			0.196116
$937$			44.0000i			1.43742i	0.695311	+	0.718709i	$0.255266\pi$
$937$			44.0000i			1.43742i	−0.695311	+	0.718709i	$0.744734\pi$
$938$		0			0
$939$	22.0000			0.717943
$940$	−6.00000	+	3.00000i	−0.195698	+	0.0978492i
$941$	−5.00000			−0.162995			−0.0814977	−	0.996674i	$-0.525970\pi$
$941$	−5.00000			−0.162995			−0.0814977	+	0.996674i	$0.525970\pi$
$942$			14.0000i			0.456145i
$943$		0			0
$944$	−5.00000			−0.162736
$945$		0			0
$946$	−24.0000			−0.780307
$947$			9.00000i			0.292461i	0.989251	+	0.146230i	$0.0467141\pi$
$947$			9.00000i			0.292461i	−0.989251	+	0.146230i	$0.953286\pi$
$948$			8.00000i			0.259828i
$949$	33.0000			1.07123
$950$	−28.0000	−	21.0000i	−0.908440	−	0.681330i
$951$		0			0
$952$		0			0
$953$		−	44.0000i		−	1.42530i	−0.701520	−	0.712650i	$-0.747495\pi$
$953$		−	44.0000i		−	1.42530i	0.701520	−	0.712650i	$-0.252505\pi$
$954$	−18.0000			−0.582772
$955$		0			0
$956$	10.0000			0.323423
$957$		−	30.0000i		−	0.969762i
$958$			37.0000i			1.19542i
$959$		0			0
$960$	2.00000	−	1.00000i	0.0645497	−	0.0322749i
$961$	−6.00000			−0.193548
$962$			24.0000i			0.773791i
$963$			8.00000i			0.257796i
$964$	20.0000			0.644157
$965$	−52.0000	+	26.0000i	−1.67394	+	0.836970i
$966$		0			0
$967$			16.0000i			0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$967$			16.0000i			0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$968$		−	25.0000i		−	0.803530i
$969$	7.00000			0.224872
$970$	−9.00000	−	18.0000i	−0.288973	−	0.577945i
$971$	37.0000			1.18739			0.593693	−	0.804691i	$-0.297669\pi$
$971$	37.0000			1.18739			0.593693	+	0.804691i	$0.297669\pi$
$972$		−	16.0000i		−	0.513200i
$973$		0			0
$974$	−2.00000			−0.0640841
$975$	9.00000	−	12.0000i	0.288231	−	0.384308i
$976$	−3.00000			−0.0960277
$977$		−	38.0000i		−	1.21573i	−0.794041	−	0.607864i	$-0.792027\pi$
$977$		−	38.0000i		−	1.21573i	0.794041	−	0.607864i	$-0.207973\pi$
$978$			4.00000i			0.127906i
$979$	−6.00000			−0.191761
$980$	−7.00000	−	14.0000i	−0.223607	−	0.447214i
$981$	−18.0000			−0.574696
$982$		−	13.0000i		−	0.414847i
$983$			30.0000i			0.956851i	0.878128	+	0.478426i	$0.158792\pi$
$983$			30.0000i			0.956851i	−0.878128	+	0.478426i	$0.841208\pi$
$984$		0			0
$985$	4.00000	−	2.00000i	0.127451	−	0.0637253i
$986$	5.00000			0.159232
$987$		0			0
$988$		−	21.0000i		−	0.668099i
$989$	−32.0000			−1.01754
$990$	24.0000	−	12.0000i	0.762770	−	0.381385i
$991$	−19.0000			−0.603555			−0.301777	−	0.953378i	$-0.597580\pi$
$991$	−19.0000			−0.603555			−0.301777	+	0.953378i	$0.597580\pi$
$992$			5.00000i			0.158750i
$993$			7.00000i			0.222138i
$994$		0			0
$995$	−7.00000	−	14.0000i	−0.221915	−	0.443830i
$996$	4.00000			0.126745
$997$		−	28.0000i		−	0.886769i	−0.896332	−	0.443384i	$-0.853778\pi$
$997$		−	28.0000i		−	0.886769i	0.896332	−	0.443384i	$-0.146222\pi$
$998$			28.0000i			0.886325i
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.c.a.69.2	yes	2
3.2	odd	2		1530.2.d.b.919.1		2
4.3	odd	2		1360.2.e.b.1089.1		2
5.2	odd	4		850.2.a.d.1.1		1
5.3	odd	4		850.2.a.h.1.1		1
5.4	even	2	inner	170.2.c.a.69.1	✓	2
15.2	even	4		7650.2.a.cb.1.1		1
15.8	even	4		7650.2.a.s.1.1		1
15.14	odd	2		1530.2.d.b.919.2		2
20.3	even	4		6800.2.a.r.1.1		1
20.7	even	4		6800.2.a.g.1.1		1
20.19	odd	2		1360.2.e.b.1089.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.c.a.69.1	✓	2	5.4	even	2	inner
170.2.c.a.69.2	yes	2	1.1	even	1	trivial
850.2.a.d.1.1		1	5.2	odd	4
850.2.a.h.1.1		1	5.3	odd	4
1360.2.e.b.1089.1		2	4.3	odd	2
1360.2.e.b.1089.2		2	20.19	odd	2
1530.2.d.b.919.1		2	3.2	odd	2
1530.2.d.b.919.2		2	15.14	odd	2
6800.2.a.g.1.1		1	20.7	even	4
6800.2.a.r.1.1		1	20.3	even	4
7650.2.a.s.1.1		1	15.8	even	4
7650.2.a.cb.1.1		1	15.2	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +2.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} -6.00000 q^{11} -1.00000i q^{12} +3.00000i q^{13} +(-2.00000 + 1.00000i) q^{15} +1.00000 q^{16} -1.00000i q^{17} +2.00000i q^{18} +7.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -6.00000i q^{22} -8.00000i q^{23} +1.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -3.00000 q^{26} +5.00000i q^{27} +5.00000 q^{29} +(-1.00000 - 2.00000i) q^{30} +5.00000 q^{31} +1.00000i q^{32} -6.00000i q^{33} +1.00000 q^{34} -2.00000 q^{36} -8.00000i q^{37} +7.00000i q^{38} -3.00000 q^{39} +(2.00000 - 1.00000i) q^{40} -4.00000i q^{43} +6.00000 q^{44} +(2.00000 + 4.00000i) q^{45} +8.00000 q^{46} -3.00000i q^{47} +1.00000i q^{48} +7.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +1.00000 q^{51} -3.00000i q^{52} +9.00000i q^{53} -5.00000 q^{54} +(-6.00000 - 12.0000i) q^{55} +7.00000i q^{57} +5.00000i q^{58} -5.00000 q^{59} +(2.00000 - 1.00000i) q^{60} -3.00000 q^{61} +5.00000i q^{62} -1.00000 q^{64} +(-6.00000 + 3.00000i) q^{65} +6.00000 q^{66} +2.00000i q^{67} +1.00000i q^{68} +8.00000 q^{69} -15.0000 q^{71} -2.00000i q^{72} -11.0000i q^{73} +8.00000 q^{74} +(-4.00000 - 3.00000i) q^{75} -7.00000 q^{76} -3.00000i q^{78} -8.00000 q^{79} +(1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +4.00000i q^{83} +(2.00000 - 1.00000i) q^{85} +4.00000 q^{86} +5.00000i q^{87} +6.00000i q^{88} +1.00000 q^{89} +(-4.00000 + 2.00000i) q^{90} +8.00000i q^{92} +5.00000i q^{93} +3.00000 q^{94} +(7.00000 + 14.0000i) q^{95} -1.00000 q^{96} +9.00000i q^{97} +7.00000i q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^9	\( 2 q - 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{9} - 4 q^{10} - 12 q^{11} - 4 q^{15} + 2 q^{16} + 14 q^{19} - 2 q^{20} + 2 q^{24} - 6 q^{25} - 6 q^{26} + 10 q^{29} - 2 q^{30} + 10 q^{31} + 2 q^{34} - 4 q^{36} - 6 q^{39} + 4 q^{40} + 12 q^{44} + 4 q^{45} + 16 q^{46} + 14 q^{49} - 8 q^{50} + 2 q^{51} - 10 q^{54} - 12 q^{55} - 10 q^{59} + 4 q^{60} - 6 q^{61} - 2 q^{64} - 12 q^{65} + 12 q^{66} + 16 q^{69} - 30 q^{71} + 16 q^{74} - 8 q^{75} - 14 q^{76} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 4 q^{85} + 8 q^{86} + 2 q^{89} - 8 q^{90} + 6 q^{94} + 14 q^{95} - 2 q^{96} - 24 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^9 - 4 * q^10 - 12 * q^11 - 4 * q^15 + 2 * q^16 + 14 * q^19 - 2 * q^20 + 2 * q^24 - 6 * q^25 - 6 * q^26 + 10 * q^29 - 2 * q^30 + 10 * q^31 + 2 * q^34 - 4 * q^36 - 6 * q^39 + 4 * q^40 + 12 * q^44 + 4 * q^45 + 16 * q^46 + 14 * q^49 - 8 * q^50 + 2 * q^51 - 10 * q^54 - 12 * q^55 - 10 * q^59 + 4 * q^60 - 6 * q^61 - 2 * q^64 - 12 * q^65 + 12 * q^66 + 16 * q^69 - 30 * q^71 + 16 * q^74 - 8 * q^75 - 14 * q^76 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 4 * q^85 + 8 * q^86 + 2 * q^89 - 8 * q^90 + 6 * q^94 + 14 * q^95 - 2 * q^96 - 24 * q^99

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