LMFDB - Embedded newform 1960.2.q.c.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (of order $3$, degree $2$, not 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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.00000 q^{13} +2.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} -6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(1.00000 - 1.73205i) q^{33} +(2.50000 - 4.33013i) q^{37} +(-3.00000 - 5.19615i) q^{39} +5.00000 q^{41} +6.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-4.50000 + 7.79423i) q^{47} +(-2.00000 + 3.46410i) q^{51} +(-5.50000 - 9.52628i) q^{53} -1.00000 q^{55} +10.0000 q^{57} +(4.00000 + 6.92820i) q^{59} +(-6.00000 + 10.3923i) q^{61} +(-1.50000 + 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +14.0000 q^{69} -4.00000 q^{71} +(6.00000 + 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(-7.00000 + 12.1244i) q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +2.00000 q^{85} +(6.00000 + 10.3923i) q^{87} +(3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{93} +(-2.50000 - 4.33013i) q^{95} -6.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - q^{5} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - q^5 - q^9	$ 2 q - 2 q^{3} - q^{5} - q^{9} + q^{11} + 6 q^{13} + 4 q^{15} - 2 q^{17} - 5 q^{19} - 7 q^{23} - q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 2 q^{33} + 5 q^{37} - 6 q^{39} + 10 q^{41} + 12 q^{43} - q^{45} - 9 q^{47} - 4 q^{51} - 11 q^{53} - 2 q^{55} + 20 q^{57} + 8 q^{59} - 12 q^{61} - 3 q^{65} + 4 q^{67} + 28 q^{69} - 8 q^{71} + 12 q^{73} - 2 q^{75} - 14 q^{79} + 11 q^{81} + 8 q^{83} + 4 q^{85} + 12 q^{87} + 6 q^{89} + 8 q^{93} - 5 q^{95} - 12 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - q^5 - q^9 + q^11 + 6 * q^13 + 4 * q^15 - 2 * q^17 - 5 * q^19 - 7 * q^23 - q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 2 * q^33 + 5 * q^37 - 6 * q^39 + 10 * q^41 + 12 * q^43 - q^45 - 9 * q^47 - 4 * q^51 - 11 * q^53 - 2 * q^55 + 20 * q^57 + 8 * q^59 - 12 * q^61 - 3 * q^65 + 4 * q^67 + 28 * q^69 - 8 * q^71 + 12 * q^73 - 2 * q^75 - 14 * q^79 + 11 * q^81 + 8 * q^83 + 4 * q^85 + 12 * q^87 + 6 * q^89 + 8 * q^93 - 5 * q^95 - 12 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	−0.584002	−	0.811752i	$-0.698514\pi$
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	0.994999	+	0.0998840i	$0.0318472\pi$
$38$		0			0
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$		0			0
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	−0.945134	−	0.326683i	$-0.894069\pi$
$53$	−5.50000	−	9.52628i	−0.755483	−	1.30854i	0.189651	−	0.981852i	$-0.439264\pi$
$54$		0			0
$55$	−1.00000			−0.134840
$56$		0			0
$57$	10.0000			1.32453
$58$		0			0
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	0.170305	+	0.985391i	$0.445525\pi$
$61$	−6.00000	+	10.3923i	−0.768221	+	1.33060i	−0.938527	+	0.345207i	$0.887809\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$	14.0000			1.68540
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	0.967676	+	0.252197i	$0.0811531\pi$
$73$	6.00000	+	10.3923i	0.702247	+	1.21633i	−0.265429	+	0.964130i	$0.585514\pi$
$74$		0			0
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	10.0000	−	17.3205i	0.985329	−	1.70664i	0.344865	−	0.938652i	$-0.387925\pi$
$103$	10.0000	−	17.3205i	0.985329	−	1.70664i	0.640464	−	0.767988i	$-0.278742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$		0			0
$111$	−10.0000			−0.949158
$112$		0			0
$113$	20.0000			1.88144			0.940721	−	0.339182i	$-0.110150\pi$
$113$	20.0000			1.88144			0.940721	+	0.339182i	$0.110150\pi$
$114$		0			0
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$		0			0
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−5.00000	−	8.66025i	−0.450835	−	0.780869i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$		0			0
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$		0			0
$131$	3.50000	−	6.06218i	0.305796	−	0.529655i	−0.671642	−	0.740876i	$-0.734411\pi$
$131$	3.50000	−	6.06218i	0.305796	−	0.529655i	0.977438	+	0.211221i	$0.0677440\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	3.00000	−	5.19615i	0.249136	−	0.431517i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$		0			0
$159$	−11.0000	+	19.0526i	−0.872357	+	1.51097i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$		0			0
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$		0			0
$167$	−5.00000			−0.386912			−0.193456	−	0.981109i	$-0.561970\pi$
$167$	−5.00000			−0.386912			−0.193456	+	0.981109i	$0.561970\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$		0			0
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	−0.237816	−	0.971310i	$-0.576431\pi$
$173$	9.50000	−	16.4545i	0.722272	−	1.25101i	0.960087	−	0.279701i	$-0.0902353\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.00000	−	13.8564i	0.601317	−	1.04151i
$178$		0			0
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	24.0000			1.77413
$184$		0			0
$185$	2.50000	+	4.33013i	0.183804	+	0.318357i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$		0			0
$193$	10.0000	+	17.3205i	0.719816	+	1.24676i	0.961073	+	0.276296i	$0.0891071\pi$
$193$	10.0000	+	17.3205i	0.719816	+	1.24676i	−0.241257	+	0.970461i	$0.577560\pi$
$194$		0			0
$195$	6.00000			0.429669
$196$		0			0
$197$	−27.0000			−1.92367			−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000			−1.92367			−0.961835	+	0.273629i	$0.911776\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	4.00000	−	6.92820i	0.282138	−	0.488678i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$		0			0
$207$	−3.50000	−	6.06218i	−0.243267	−	0.421350i
$208$		0			0
$209$	−5.00000			−0.345857
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$		0			0
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$		0			0
$215$	−3.00000	+	5.19615i	−0.204598	+	0.354375i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	12.0000	−	20.7846i	0.810885	−	1.40449i
$220$		0			0
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	0.702202	−	0.711977i	$-0.252200\pi$
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	−0.967692	+	0.252136i	$0.918867\pi$
$228$		0			0
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.133820	+	0.991006i	$0.542724\pi$
$229$	−14.0000	+	24.2487i	−0.925146	+	1.60240i	−0.791326	+	0.611394i	$0.790609\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	−0.896921	−	0.442191i	$-0.854201\pi$
$233$	−1.00000	+	1.73205i	−0.0655122	+	0.113470i	0.831409	+	0.555661i	$0.187535\pi$
$234$		0			0
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$		0			0
$237$	28.0000			1.81880
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$		0			0
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.50000	+	12.9904i	−0.477214	+	0.826558i
$248$		0			0
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$		0			0
$251$	−29.0000			−1.83046			−0.915232	−	0.402928i	$-0.867993\pi$
$251$	−29.0000			−1.83046			−0.915232	+	0.402928i	$0.867993\pi$
$252$		0			0
$253$	−7.00000			−0.440086
$254$		0			0
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$		0			0
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$		0			0
$265$	11.0000			0.675725
$266$		0			0
$267$	−12.0000			−0.734388
$268$		0			0
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	−0.982173	−	0.187980i	$-0.939806\pi$
$283$	−11.0000	−	19.0526i	−0.653882	−	1.13256i	0.328291	−	0.944577i	$-0.393527\pi$
$284$		0			0
$285$	−5.00000	+	8.66025i	−0.296174	+	0.512989i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	6.00000	+	10.3923i	0.351726	+	0.609208i
$292$		0			0
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$		0			0
$299$	−10.5000	+	18.1865i	−0.607231	+	1.05175i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	12.0000	−	20.7846i	0.689382	−	1.19404i
$304$		0			0
$305$	−6.00000	−	10.3923i	−0.343559	−	0.595062i
$306$		0			0
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$		0			0
$309$	−40.0000			−2.27552
$310$		0			0
$311$	−2.00000	−	3.46410i	−0.113410	−	0.196431i	0.803733	−	0.594990i	$-0.202844\pi$
$311$	−2.00000	−	3.46410i	−0.113410	−	0.196431i	−0.917143	+	0.398559i	$0.869511\pi$
$312$		0			0
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	−0.546335	−	0.837567i	$-0.683977\pi$
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	0.998522	+	0.0543564i	$0.0173107\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	−0.892741	−	0.450570i	$-0.851221\pi$
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	0.836576	+	0.547852i	$0.184554\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	24.0000			1.33955
$322$		0			0
$323$	10.0000			0.556415
$324$		0			0
$325$	−1.50000	−	2.59808i	−0.0832050	−	0.144115i
$326$		0			0
$327$	4.00000	−	6.92820i	0.221201	−	0.383131i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	−0.209544	−	0.977799i	$-0.567198\pi$
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	0.951571	−	0.307429i	$-0.0994688\pi$
$332$		0			0
$333$	2.50000	+	4.33013i	0.136999	+	0.237289i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$		0			0
$339$	−20.0000	−	34.6410i	−1.08625	−	1.88144i
$340$		0			0
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−7.00000	+	12.1244i	−0.376867	+	0.652753i
$346$		0			0
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	0.738458	−	0.674299i	$-0.235554\pi$
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	−0.953189	+	0.302374i	$0.902221\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−12.0000			−0.640513
$352$		0			0
$353$	10.0000	+	17.3205i	0.532246	+	0.921878i	0.999291	+	0.0376440i	$0.0119853\pi$
$353$	10.0000	+	17.3205i	0.532246	+	0.921878i	−0.467045	+	0.884234i	$0.654681\pi$
$354$		0			0
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$	−20.0000			−1.04973
$364$		0			0
$365$	−12.0000			−0.628109
$366$		0			0
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$		0			0
$369$	−2.50000	+	4.33013i	−0.130145	+	0.225417i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	−1.00000	−	1.73205i	−0.0516398	−	0.0894427i
$376$		0			0
$377$	−18.0000			−0.927047
$378$		0			0
$379$	−21.0000			−1.07870			−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000			−1.07870			−0.539349	+	0.842082i	$0.681330\pi$
$380$		0			0
$381$	−17.0000	−	29.4449i	−0.870936	−	1.50851i
$382$		0			0
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$		0			0
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337237\pi$
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$		0			0
$393$	−14.0000			−0.706207
$394$		0			0
$395$	−7.00000	−	12.1244i	−0.352208	−	0.610043i
$396$		0			0
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	−0.546795	−	0.837267i	$-0.684152\pi$
$397$	9.00000	−	15.5885i	0.451697	−	0.782362i	0.998492	+	0.0549046i	$0.0174855\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	−0.981430	−	0.191820i	$-0.938561\pi$
$401$	−6.50000	+	11.2583i	−0.324595	+	0.562214i	0.656836	+	0.754034i	$0.271895\pi$
$402$		0			0
$403$	6.00000	+	10.3923i	0.298881	+	0.517678i
$404$		0			0
$405$	−11.0000			−0.546594
$406$		0			0
$407$	5.00000			0.247841
$408$		0			0
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$		0			0
$411$	12.0000	−	20.7846i	0.591916	−	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.00000	+	3.46410i	−0.0981761	+	0.170046i
$416$		0			0
$417$	4.00000	+	6.92820i	0.195881	+	0.339276i
$418$		0			0
$419$	5.00000			0.244266			0.122133	−	0.992514i	$-0.461027\pi$
$419$	5.00000			0.244266			0.122133	+	0.992514i	$0.461027\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$		0			0
$423$	−4.50000	−	7.79423i	−0.218797	−	0.378968i
$424$		0			0
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$		0			0
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$		0			0
$433$	−24.0000			−1.15337			−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−24.0000			−1.15337			−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$		0			0
$437$	−17.5000	−	30.3109i	−0.837139	−	1.44997i
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	−0.182573	−	0.983192i	$-0.558443\pi$
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	0.942756	−	0.333483i	$-0.108224\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$	20.0000			0.945968
$448$		0			0
$449$	13.0000			0.613508			0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000			0.613508			0.306754	+	0.951789i	$0.400757\pi$
$450$		0			0
$451$	2.50000	+	4.33013i	0.117720	+	0.203898i
$452$		0			0
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	−0.485299	−	0.874348i	$-0.661289\pi$
$457$	11.0000	−	19.0526i	0.514558	−	0.891241i	0.999857	−	0.0168929i	$-0.00537742\pi$
$458$		0			0
$459$	4.00000	+	6.92820i	0.186704	+	0.323381i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	9.00000			0.418265			0.209133	−	0.977887i	$-0.432936\pi$
$463$	9.00000			0.418265			0.209133	+	0.977887i	$0.432936\pi$
$464$		0			0
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$		0			0
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	−0.958212	−	0.286058i	$-0.907655\pi$
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	0.726840	+	0.686807i	$0.240988\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$		0			0
$475$	5.00000			0.229416
$476$		0			0
$477$	11.0000			0.503655
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$	7.50000	−	12.9904i	0.341971	−	0.592310i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$		0			0
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$		0			0
$489$	8.00000			0.361773
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$		0			0
$495$	0.500000	−	0.866025i	0.0224733	−	0.0389249i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$		0			0
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$		0			0
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$		0			0
$507$	4.00000	+	6.92820i	0.177646	+	0.307692i
$508$		0			0
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	10.0000	−	17.3205i	0.441511	−	0.764719i
$514$		0			0
$515$	10.0000	+	17.3205i	0.440653	+	0.763233i
$516$		0			0
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−38.0000			−1.66801
$520$		0			0
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$		0			0
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	−0.378695	−	0.925521i	$-0.623627\pi$
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	0.990873	−	0.134801i	$-0.0430394\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$		0			0
$531$	−8.00000			−0.347170
$532$		0			0
$533$	15.0000			0.649722
$534$		0			0
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	−0.0121878	−	0.999926i	$-0.503880\pi$
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	0.872055	−	0.489408i	$-0.162787\pi$
$542$		0			0
$543$	2.00000	+	3.46410i	0.0858282	+	0.148659i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$		0			0
$549$	−6.00000	−	10.3923i	−0.256074	−	0.443533i
$550$		0			0
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	5.00000	−	8.66025i	0.212238	−	0.367607i
$556$		0			0
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	0.553146	−	0.833084i	$-0.313427\pi$
$557$	−10.5000	−	18.1865i	−0.444899	−	0.770588i	−0.998045	+	0.0624962i	$0.980094\pi$
$558$		0			0
$559$	18.0000			0.761319
$560$		0			0
$561$	−4.00000			−0.168880
$562$		0			0
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	0.922293	−	0.386492i	$-0.126313\pi$
$563$	3.00000	+	5.19615i	0.126435	+	0.218992i	−0.795858	+	0.605483i	$0.792980\pi$
$564$		0			0
$565$	−10.0000	+	17.3205i	−0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	−0.727405	−	0.686209i	$-0.759274\pi$
$569$	5.50000	−	9.52628i	0.230572	−	0.399362i	0.957977	+	0.286846i	$0.0926069\pi$
$570$		0			0
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	0.408883	−	0.912587i	$-0.365918\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$	7.00000			0.291920
$576$		0			0
$577$	−2.00000	−	3.46410i	−0.0832611	−	0.144212i	0.821388	−	0.570370i	$-0.193200\pi$
$577$	−2.00000	−	3.46410i	−0.0832611	−	0.144212i	−0.904649	+	0.426158i	$0.859867\pi$
$578$		0			0
$579$	20.0000	−	34.6410i	0.831172	−	1.43963i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	5.50000	−	9.52628i	0.227787	−	0.394538i
$584$		0			0
$585$	−1.50000	−	2.59808i	−0.0620174	−	0.107417i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−20.0000			−0.824086
$590$		0			0
$591$	27.0000	+	46.7654i	1.11063	+	1.92367i
$592$		0			0
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	−0.962522	−	0.271205i	$-0.912578\pi$
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	0.716131	+	0.697966i	$0.245911\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$		0			0
$599$	−17.0000	−	29.4449i	−0.694601	−	1.20308i	−0.970315	−	0.241845i	$-0.922248\pi$
$599$	−17.0000	−	29.4449i	−0.694601	−	1.20308i	0.275714	−	0.961240i	$-0.411086\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$		0			0
$607$	16.5000	−	28.5788i	0.669714	−	1.15998i	−0.308270	−	0.951299i	$-0.599750\pi$
$607$	16.5000	−	28.5788i	0.669714	−	1.15998i	0.977984	−	0.208680i	$-0.0669168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.5000	+	23.3827i	−0.546152	+	0.945962i
$612$		0			0
$613$	20.5000	+	35.5070i	0.827987	+	1.43412i	0.899615	+	0.436684i	$0.143847\pi$
$613$	20.5000	+	35.5070i	0.827987	+	1.43412i	−0.0716275	+	0.997431i	$0.522819\pi$
$614$		0			0
$615$	10.0000			0.403239
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$		0			0
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	0.967271	+	0.253744i	$0.0816620\pi$
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	−0.263887	+	0.964554i	$0.585005\pi$
$620$		0			0
$621$	14.0000	−	24.2487i	0.561801	−	0.973067i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	5.00000	+	8.66025i	0.199681	+	0.345857i
$628$		0			0
$629$	−10.0000			−0.398726
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$	13.0000	+	22.5167i	0.516704	+	0.894957i
$634$		0			0
$635$	−8.50000	+	14.7224i	−0.337312	+	0.584242i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$		0			0
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	−0.971442	−	0.237276i	$-0.923745\pi$
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	0.280234	−	0.959932i	$-0.409588\pi$
$642$		0			0
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$	12.0000			0.472500
$646$		0			0
$647$	11.5000	+	19.9186i	0.452112	+	0.783080i	0.998517	−	0.0544405i	$-0.0173375\pi$
$647$	11.5000	+	19.9186i	0.452112	+	0.783080i	−0.546405	+	0.837521i	$0.684004\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.5000	+	38.9711i	−0.880493	+	1.52506i	−0.0296993	+	0.999559i	$0.509455\pi$
$653$	−22.5000	+	38.9711i	−0.880493	+	1.52506i	−0.850794	+	0.525500i	$0.823878\pi$
$654$		0			0
$655$	3.50000	+	6.06218i	0.136756	+	0.236869i
$656$		0			0
$657$	−12.0000			−0.468165
$658$		0			0
$659$	−16.0000			−0.623272			−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000			−0.623272			−0.311636	+	0.950202i	$0.600877\pi$
$660$		0			0
$661$	−18.0000	−	31.1769i	−0.700119	−	1.21264i	−0.968424	−	0.249308i	$-0.919797\pi$
$661$	−18.0000	−	31.1769i	−0.700119	−	1.21264i	0.268306	−	0.963334i	$-0.413536\pi$
$662$		0			0
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.0000	−	36.3731i	0.813123	−	1.40837i
$668$		0			0
$669$	−16.0000	−	27.7128i	−0.618596	−	1.07144i
$670$		0			0
$671$	−12.0000			−0.463255
$672$		0			0
$673$	−42.0000			−1.61898			−0.809491	−	0.587133i	$-0.800257\pi$
$673$	−42.0000			−1.61898			−0.809491	+	0.587133i	$0.800257\pi$
$674$		0			0
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$		0			0
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	−0.590603	−	0.806962i	$-0.701110\pi$
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	0.994151	+	0.107997i	$0.0344436\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−8.00000	+	13.8564i	−0.306561	+	0.530979i
$682$		0			0
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	56.0000			2.13653
$688$		0			0
$689$	−16.5000	−	28.5788i	−0.628600	−	1.08877i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$		0			0
$697$	−5.00000	−	8.66025i	−0.189389	−	0.328031i
$698$		0			0
$699$	4.00000			0.151294
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	12.5000	+	21.6506i	0.471446	+	0.816569i
$704$		0			0
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	−0.646055	−	0.763291i	$-0.723582\pi$
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	0.984057	+	0.177854i	$0.0569156\pi$
$710$		0			0
$711$	−7.00000	−	12.1244i	−0.262521	−	0.454699i
$712$		0			0
$713$	−28.0000			−1.04861
$714$		0			0
$715$	−3.00000			−0.112194
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$		0			0
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	23.0000	−	39.8372i	0.855379	−	1.48156i
$724$		0			0
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−41.0000			−1.52061			−0.760303	−	0.649569i	$-0.774949\pi$
$727$	−41.0000			−1.52061			−0.760303	+	0.649569i	$0.774949\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	−0.423802	−	0.905755i	$-0.639305\pi$
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	0.996308	−	0.0858539i	$-0.0273618\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$		0			0
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	0.945818	+	0.324697i	$0.105262\pi$
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	−0.191714	+	0.981451i	$0.561404\pi$
$740$		0			0
$741$	30.0000			1.10208
$742$		0			0
$743$	−3.00000			−0.110059			−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000			−0.110059			−0.0550297	+	0.998485i	$0.517525\pi$
$744$		0			0
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$		0			0
$747$	−2.00000	+	3.46410i	−0.0731762	+	0.126745i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	−0.982197	−	0.187851i	$-0.939848\pi$
$751$	−9.00000	+	15.5885i	−0.328415	+	0.568831i	0.653783	+	0.756682i	$0.273181\pi$
$752$		0			0
$753$	29.0000	+	50.2295i	1.05682	+	1.83046i
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	−6.00000			−0.218074			−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000			−0.218074			−0.109037	+	0.994038i	$0.534777\pi$
$758$		0			0
$759$	7.00000	+	12.1244i	0.254084	+	0.440086i
$760$		0			0
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$		0			0
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$		0			0
$769$	41.0000			1.47850			0.739249	−	0.673432i	$-0.235181\pi$
$769$	41.0000			1.47850			0.739249	+	0.673432i	$0.235181\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	7.50000	+	12.9904i	0.269756	+	0.467232i	0.968799	−	0.247849i	$-0.0797235\pi$
$773$	7.50000	+	12.9904i	0.269756	+	0.467232i	−0.699043	+	0.715080i	$0.746390\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.5000	+	21.6506i	−0.447859	+	0.775715i
$780$		0			0
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$		0			0
$783$	24.0000			0.857690
$784$		0			0
$785$	−5.00000			−0.178458
$786$		0			0
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	0.659841	−	0.751405i	$-0.270624\pi$
$787$	−9.00000	−	15.5885i	−0.320815	−	0.555668i	−0.980656	+	0.195737i	$0.937290\pi$
$788$		0			0
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−18.0000	+	31.1769i	−0.639199	+	1.10712i
$794$		0			0
$795$	−11.0000	−	19.0526i	−0.390130	−	0.675725i
$796$		0			0
$797$	−2.00000			−0.0708436			−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000			−0.0708436			−0.0354218	+	0.999372i	$0.511277\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$		0			0
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.0000	+	20.7846i	−0.422420	+	0.731653i
$808$		0			0
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.704564	−	0.709640i	$-0.748858\pi$
$809$	−27.5000	−	47.6314i	−0.966849	−	1.67463i	−0.262284	−	0.964991i	$-0.584476\pi$
$810$		0			0
$811$	5.00000			0.175574			0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000			0.175574			0.0877869	+	0.996139i	$0.472021\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	−15.0000	+	25.9808i	−0.524784	+	0.908952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$		0			0
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−14.0000			−0.486828			−0.243414	−	0.969923i	$-0.578267\pi$
$827$	−14.0000			−0.486828			−0.243414	+	0.969923i	$0.578267\pi$
$828$		0			0
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	0.980642	+	0.195810i	$0.0627335\pi$
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	−0.320745	+	0.947166i	$0.603933\pi$
$830$		0			0
$831$	−2.00000	+	3.46410i	−0.0693792	+	0.120168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.50000	−	4.33013i	0.0865161	−	0.149850i
$836$		0			0
$837$	−8.00000	−	13.8564i	−0.276520	−	0.478947i
$838$		0			0
$839$	14.0000			0.483334			0.241667	−	0.970359i	$-0.422306\pi$
$839$	14.0000			0.483334			0.241667	+	0.970359i	$0.422306\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$		0			0
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−22.0000	+	38.1051i	−0.755038	+	1.30776i
$850$		0			0
$851$	17.5000	+	30.3109i	0.599892	+	1.03904i
$852$		0			0
$853$	−23.0000			−0.787505			−0.393753	−	0.919216i	$-0.628823\pi$
$853$	−23.0000			−0.787505			−0.393753	+	0.919216i	$0.628823\pi$
$854$		0			0
$855$	5.00000			0.170996
$856$		0			0
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	6.50000	−	11.2583i	0.221263	−	0.383238i	−0.733929	−	0.679226i	$-0.762316\pi$
$863$	6.50000	−	11.2583i	0.221263	−	0.383238i	0.955192	+	0.295988i	$0.0956489\pi$
$864$		0			0
$865$	9.50000	+	16.4545i	0.323010	+	0.559469i
$866$		0			0
$867$	−26.0000			−0.883006
$868$		0			0
$869$	−14.0000			−0.474917
$870$		0			0
$871$	6.00000	+	10.3923i	0.203302	+	0.352130i
$872$		0			0
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.50000	+	7.79423i	−0.151954	+	0.263192i	−0.931946	−	0.362598i	$-0.881890\pi$
$877$	−4.50000	+	7.79423i	−0.151954	+	0.263192i	0.779992	+	0.625790i	$0.215223\pi$
$878$		0			0
$879$	21.0000	+	36.3731i	0.708312	+	1.22683i
$880$		0			0
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$		0			0
$885$	8.00000	+	13.8564i	0.268917	+	0.465778i
$886$		0			0
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.50000	+	9.52628i	−0.184257	+	0.319142i
$892$		0			0
$893$	−22.5000	−	38.9711i	−0.752934	−	1.30412i
$894$		0			0
$895$	9.00000			0.300837
$896$		0			0
$897$	42.0000			1.40234
$898$		0			0
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$	−11.0000	+	19.0526i	−0.366463	+	0.634733i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$		0			0
$907$	−11.0000	−	19.0526i	−0.365249	−	0.632630i	0.623567	−	0.781770i	$-0.285683\pi$
$907$	−11.0000	−	19.0526i	−0.365249	−	0.632630i	−0.988816	+	0.149140i	$0.952349\pi$
$908$		0			0
$909$	−12.0000			−0.398015
$910$		0			0
$911$	42.0000			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$911$	42.0000			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$		0			0
$915$	−12.0000	+	20.7846i	−0.396708	+	0.687118i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.00000	−	15.5885i	0.296883	−	0.514216i	−0.678538	−	0.734565i	$-0.737386\pi$
$919$	9.00000	−	15.5885i	0.296883	−	0.514216i	0.975421	+	0.220349i	$0.0707197\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$		0			0
$923$	−12.0000			−0.394985
$924$		0			0
$925$	−5.00000			−0.164399
$926$		0			0
$927$	10.0000	+	17.3205i	0.328443	+	0.568880i
$928$		0			0
$929$	−15.5000	+	26.8468i	−0.508539	+	0.880815i	0.491413	+	0.870927i	$0.336481\pi$
$929$	−15.5000	+	26.8468i	−0.508539	+	0.880815i	−0.999951	+	0.00988764i	$0.996853\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.00000	+	6.92820i	−0.130954	+	0.226819i
$934$		0			0
$935$	1.00000	+	1.73205i	0.0327035	+	0.0566441i
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$	−32.0000			−1.04428
$940$		0			0
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$		0			0
$943$	−17.5000	+	30.3109i	−0.569878	+	0.987058i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.00000	+	12.1244i	−0.227469	+	0.393989i	−0.957057	−	0.289898i	$-0.906379\pi$
$947$	−7.00000	+	12.1244i	−0.227469	+	0.393989i	0.729588	+	0.683887i	$0.239712\pi$
$948$		0			0
$949$	18.0000	+	31.1769i	0.584305	+	1.01205i
$950$		0			0
$951$	4.00000			0.129709
$952$		0			0
$953$	−20.0000			−0.647864			−0.323932	−	0.946080i	$-0.605005\pi$
$953$	−20.0000			−0.647864			−0.323932	+	0.946080i	$0.605005\pi$
$954$		0			0
$955$	−6.00000	−	10.3923i	−0.194155	−	0.336287i
$956$		0			0
$957$	−6.00000	+	10.3923i	−0.193952	+	0.335936i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$		0			0
$965$	−20.0000			−0.643823
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$	−10.0000	−	17.3205i	−0.321246	−	0.556415i
$970$		0			0
$971$	3.50000	−	6.06218i	0.112320	−	0.194545i	−0.804385	−	0.594108i	$-0.797505\pi$
$971$	3.50000	−	6.06218i	0.112320	−	0.194545i	0.916705	+	0.399564i	$0.130838\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−3.00000	+	5.19615i	−0.0960769	+	0.166410i
$976$		0			0
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−4.00000			−0.127710
$982$		0			0
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	0.841112	−	0.540860i	$-0.181901\pi$
$983$	−1.50000	−	2.59808i	−0.0478426	−	0.0828658i	−0.888955	+	0.457995i	$0.848568\pi$
$984$		0			0
$985$	13.5000	−	23.3827i	0.430146	−	0.745034i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.0000	+	36.3731i	−0.667761	+	1.15660i
$990$		0			0
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$		0			0
$993$	−54.0000			−1.71364
$994$		0			0
$995$	4.00000			0.126809
$996$		0			0
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	0.957552	+	0.288261i	$0.0930771\pi$
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	−0.229135	+	0.973395i	$0.573590\pi$
$998$		0			0
$999$	−10.0000	+	17.3205i	−0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.c.961.1		2
7.2	even	3		1960.2.a.m.1.1		1
7.3	odd	6		280.2.q.c.81.1	✓	2
7.4	even	3	inner	1960.2.q.c.361.1		2
7.5	odd	6		1960.2.a.a.1.1		1
7.6	odd	2		280.2.q.c.121.1	yes	2
21.17	even	6		2520.2.bi.e.361.1		2
21.20	even	2		2520.2.bi.e.1801.1		2
28.3	even	6		560.2.q.c.81.1		2
28.19	even	6		3920.2.a.bf.1.1		1
28.23	odd	6		3920.2.a.i.1.1		1
28.27	even	2		560.2.q.c.401.1		2
35.3	even	12		1400.2.bh.e.249.2		4
35.9	even	6		9800.2.a.g.1.1		1
35.13	even	4		1400.2.bh.e.849.1		4
35.17	even	12		1400.2.bh.e.249.1		4
35.19	odd	6		9800.2.a.bi.1.1		1
35.24	odd	6		1400.2.q.a.1201.1		2
35.27	even	4		1400.2.bh.e.849.2		4
35.34	odd	2		1400.2.q.a.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.c.81.1	✓	2	7.3	odd	6
280.2.q.c.121.1	yes	2	7.6	odd	2
560.2.q.c.81.1		2	28.3	even	6
560.2.q.c.401.1		2	28.27	even	2
1400.2.q.a.401.1		2	35.34	odd	2
1400.2.q.a.1201.1		2	35.24	odd	6
1400.2.bh.e.249.1		4	35.17	even	12
1400.2.bh.e.249.2		4	35.3	even	12
1400.2.bh.e.849.1		4	35.13	even	4
1400.2.bh.e.849.2		4	35.27	even	4
1960.2.a.a.1.1		1	7.5	odd	6
1960.2.a.m.1.1		1	7.2	even	3
1960.2.q.c.361.1		2	7.4	even	3	inner
1960.2.q.c.961.1		2	1.1	even	1	trivial
2520.2.bi.e.361.1		2	21.17	even	6
2520.2.bi.e.1801.1		2	21.20	even	2
3920.2.a.i.1.1		1	28.23	odd	6
3920.2.a.bf.1.1		1	28.19	even	6
9800.2.a.g.1.1		1	35.9	even	6
9800.2.a.bi.1.1		1	35.19	odd	6

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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} +3.00000 q^{13} +2.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-3.50000 + 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} -6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(1.00000 - 1.73205i) q^{33} +(2.50000 - 4.33013i) q^{37} +(-3.00000 - 5.19615i) q^{39} +5.00000 q^{41} +6.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-4.50000 + 7.79423i) q^{47} +(-2.00000 + 3.46410i) q^{51} +(-5.50000 - 9.52628i) q^{53} -1.00000 q^{55} +10.0000 q^{57} +(4.00000 + 6.92820i) q^{59} +(-6.00000 + 10.3923i) q^{61} +(-1.50000 + 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +14.0000 q^{69} -4.00000 q^{71} +(6.00000 + 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(-7.00000 + 12.1244i) q^{79} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +2.00000 q^{85} +(6.00000 + 10.3923i) q^{87} +(3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{93} +(-2.50000 - 4.33013i) q^{95} -6.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - q^5 - q^9	\( 2 q - 2 q^{3} - q^{5} - q^{9} + q^{11} + 6 q^{13} + 4 q^{15} - 2 q^{17} - 5 q^{19} - 7 q^{23} - q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 2 q^{33} + 5 q^{37} - 6 q^{39} + 10 q^{41} + 12 q^{43} - q^{45} - 9 q^{47} - 4 q^{51} - 11 q^{53} - 2 q^{55} + 20 q^{57} + 8 q^{59} - 12 q^{61} - 3 q^{65} + 4 q^{67} + 28 q^{69} - 8 q^{71} + 12 q^{73} - 2 q^{75} - 14 q^{79} + 11 q^{81} + 8 q^{83} + 4 q^{85} + 12 q^{87} + 6 q^{89} + 8 q^{93} - 5 q^{95} - 12 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - q^5 - q^9 + q^11 + 6 * q^13 + 4 * q^15 - 2 * q^17 - 5 * q^19 - 7 * q^23 - q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 2 * q^33 + 5 * q^37 - 6 * q^39 + 10 * q^41 + 12 * q^43 - q^45 - 9 * q^47 - 4 * q^51 - 11 * q^53 - 2 * q^55 + 20 * q^57 + 8 * q^59 - 12 * q^61 - 3 * q^65 + 4 * q^67 + 28 * q^69 - 8 * q^71 + 12 * q^73 - 2 * q^75 - 14 * q^79 + 11 * q^81 + 8 * q^83 + 4 * q^85 + 12 * q^87 + 6 * q^89 + 8 * q^93 - 5 * q^95 - 12 * q^97 - 2 * q^99

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