LMFDB - Embedded newform 2960.2.a.bc.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2960,2,Mod(1,2960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2960, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2960.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2960 = 2^{4} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2960.a (trivial)

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:	yes
Analytic conductor:	$23.6357189983$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.693982032.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 16x^{4} + 12x^{3} + 60x^{2} - 18x - 44 $ x^6 - x^5 - 16x^4 + 12x^3 + 60x^2 - 18x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1480)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-3.26341$ of defining polynomial
Character	$\chi$	$=$	2960.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.26341 q^{3} +1.00000 q^{5} -1.62704 q^{7} +7.64987 q^{9} +O(q^{10})$	$q+3.26341 q^{3} +1.00000 q^{5} -1.62704 q^{7} +7.64987 q^{9} +3.45670 q^{11} +3.89604 q^{13} +3.26341 q^{15} -1.19317 q^{17} -0.150240 q^{19} -5.30970 q^{21} -8.16748 q^{23} +1.00000 q^{25} +15.1745 q^{27} -5.82395 q^{29} +8.17296 q^{31} +11.2807 q^{33} -1.62704 q^{35} -1.00000 q^{37} +12.7144 q^{39} +7.37060 q^{41} +6.34329 q^{43} +7.64987 q^{45} -7.46218 q^{47} -4.35275 q^{49} -3.89381 q^{51} +5.07012 q^{53} +3.45670 q^{55} -0.490295 q^{57} -0.0485215 q^{59} +0.702875 q^{61} -12.4466 q^{63} +3.89604 q^{65} -14.8446 q^{67} -26.6539 q^{69} -11.2807 q^{71} +3.47252 q^{73} +3.26341 q^{75} -5.62419 q^{77} +7.74357 q^{79} +26.5709 q^{81} -10.3096 q^{83} -1.19317 q^{85} -19.0060 q^{87} +14.9022 q^{89} -6.33901 q^{91} +26.6717 q^{93} -0.150240 q^{95} -8.30310 q^{97} +26.4434 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 6 q^{5} - 8 q^{7} + 15 q^{9}+O(q^{10}) $ 6 * q - q^3 + 6 * q^5 - 8 * q^7 + 15 * q^9	$ 6 q - q^{3} + 6 q^{5} - 8 q^{7} + 15 q^{9} + 10 q^{13} - q^{15} + 3 q^{17} + 6 q^{19} + 9 q^{21} - 4 q^{23} + 6 q^{25} - 7 q^{27} + 3 q^{29} + 3 q^{31} + 9 q^{33} - 8 q^{35} - 6 q^{37} + 16 q^{39} + 10 q^{41} + 11 q^{43} + 15 q^{45} - 23 q^{47} + 8 q^{49} + 16 q^{51} + 10 q^{53} + 4 q^{57} - 6 q^{59} + q^{61} - 23 q^{63} + 10 q^{65} + 4 q^{67} - 2 q^{69} - 9 q^{71} + 11 q^{73} - q^{75} + 32 q^{77} + 14 q^{79} + 46 q^{81} - 11 q^{83} + 3 q^{85} - 32 q^{87} + 30 q^{89} + 4 q^{91} + 2 q^{93} + 6 q^{95} + 29 q^{97} + 39 q^{99}+O(q^{100}) $ 6 * q - q^3 + 6 * q^5 - 8 * q^7 + 15 * q^9 + 10 * q^13 - q^15 + 3 * q^17 + 6 * q^19 + 9 * q^21 - 4 * q^23 + 6 * q^25 - 7 * q^27 + 3 * q^29 + 3 * q^31 + 9 * q^33 - 8 * q^35 - 6 * q^37 + 16 * q^39 + 10 * q^41 + 11 * q^43 + 15 * q^45 - 23 * q^47 + 8 * q^49 + 16 * q^51 + 10 * q^53 + 4 * q^57 - 6 * q^59 + q^61 - 23 * q^63 + 10 * q^65 + 4 * q^67 - 2 * q^69 - 9 * q^71 + 11 * q^73 - q^75 + 32 * q^77 + 14 * q^79 + 46 * q^81 - 11 * q^83 + 3 * q^85 - 32 * q^87 + 30 * q^89 + 4 * q^91 + 2 * q^93 + 6 * q^95 + 29 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

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
$3$	3.26341	1.88413	0.942067	−	0.335426i	$-0.108880\pi$
$3$	3.26341	1.88413	0.942067	+	0.335426i	$0.108880\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.62704	−0.614962	−0.307481	−	0.951554i	$-0.599486\pi$
$7$	−1.62704	−0.614962	−0.307481	+	0.951554i	$0.599486\pi$
$8$	0	0
$9$	7.64987	2.54996
$10$	0	0
$11$	3.45670	1.04224	0.521118	−	0.853485i	$-0.325515\pi$
$11$	3.45670	1.04224	0.521118	+	0.853485i	$0.325515\pi$
$12$	0	0
$13$	3.89604	1.08057	0.540284	−	0.841483i	$-0.318317\pi$
$13$	3.89604	1.08057	0.540284	+	0.841483i	$0.318317\pi$
$14$	0	0
$15$	3.26341	0.842610
$16$	0	0
$17$	−1.19317	−0.289386	−0.144693	−	0.989477i	$-0.546219\pi$
$17$	−1.19317	−0.289386	−0.144693	+	0.989477i	$0.546219\pi$
$18$	0	0
$19$	−0.150240	−0.0344674	−0.0172337	−	0.999851i	$-0.505486\pi$
$19$	−0.150240	−0.0344674	−0.0172337	+	0.999851i	$0.505486\pi$
$20$	0	0
$21$	−5.30970	−1.15867
$22$	0	0
$23$	−8.16748	−1.70304	−0.851519	−	0.524324i	$-0.824318\pi$
$23$	−8.16748	−1.70304	−0.851519	+	0.524324i	$0.824318\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	15.1745	2.92033
$28$	0	0
$29$	−5.82395	−1.08148	−0.540741	−	0.841189i	$-0.681856\pi$
$29$	−5.82395	−1.08148	−0.540741	+	0.841189i	$0.681856\pi$
$30$	0	0
$31$	8.17296	1.46791	0.733953	−	0.679200i	$-0.237673\pi$
$31$	8.17296	1.46791	0.733953	+	0.679200i	$0.237673\pi$
$32$	0	0
$33$	11.2807	1.96371
$34$	0	0
$35$	−1.62704	−0.275020
$36$	0	0
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0	0
$39$	12.7144	2.03593
$40$	0	0
$41$	7.37060	1.15109	0.575547	−	0.817768i	$-0.304789\pi$
$41$	7.37060	1.15109	0.575547	+	0.817768i	$0.304789\pi$
$42$	0	0
$43$	6.34329	0.967342	0.483671	−	0.875250i	$-0.339303\pi$
$43$	6.34329	0.967342	0.483671	+	0.875250i	$0.339303\pi$
$44$	0	0
$45$	7.64987	1.14038
$46$	0	0
$47$	−7.46218	−1.08847	−0.544235	−	0.838933i	$-0.683180\pi$
$47$	−7.46218	−1.08847	−0.544235	+	0.838933i	$0.683180\pi$
$48$	0	0
$49$	−4.35275	−0.621821
$50$	0	0
$51$	−3.89381	−0.545242
$52$	0	0
$53$	5.07012	0.696435	0.348218	−	0.937414i	$-0.386787\pi$
$53$	5.07012	0.696435	0.348218	+	0.937414i	$0.386787\pi$
$54$	0	0
$55$	3.45670	0.466102
$56$	0	0
$57$	−0.490295	−0.0649411
$58$	0	0
$59$	−0.0485215	−0.00631697	−0.00315848	−	0.999995i	$-0.501005\pi$
$59$	−0.0485215	−0.00631697	−0.00315848	+	0.999995i	$0.501005\pi$
$60$	0	0
$61$	0.702875	0.0899939	0.0449969	−	0.998987i	$-0.485672\pi$
$61$	0.702875	0.0899939	0.0449969	+	0.998987i	$0.485672\pi$
$62$	0	0
$63$	−12.4466	−1.56813
$64$	0	0
$65$	3.89604	0.483245
$66$	0	0
$67$	−14.8446	−1.81355	−0.906775	−	0.421614i	$-0.861464\pi$
$67$	−14.8446	−1.81355	−0.906775	+	0.421614i	$0.861464\pi$
$68$	0	0
$69$	−26.6539	−3.20875
$70$	0	0
$71$	−11.2807	−1.33877	−0.669384	−	0.742917i	$-0.733442\pi$
$71$	−11.2807	−1.33877	−0.669384	+	0.742917i	$0.733442\pi$
$72$	0	0
$73$	3.47252	0.406428	0.203214	−	0.979134i	$-0.434861\pi$
$73$	3.47252	0.406428	0.203214	+	0.979134i	$0.434861\pi$
$74$	0	0
$75$	3.26341	0.376827
$76$	0	0
$77$	−5.62419	−0.640936
$78$	0	0
$79$	7.74357	0.871219	0.435610	−	0.900136i	$-0.356533\pi$
$79$	7.74357	0.871219	0.435610	+	0.900136i	$0.356533\pi$
$80$	0	0
$81$	26.5709	2.95233
$82$	0	0
$83$	−10.3096	−1.13162	−0.565812	−	0.824535i	$-0.691437\pi$
$83$	−10.3096	−1.13162	−0.565812	+	0.824535i	$0.691437\pi$
$84$	0	0
$85$	−1.19317	−0.129417
$86$	0	0
$87$	−19.0060	−2.03765
$88$	0	0
$89$	14.9022	1.57963	0.789816	−	0.613343i	$-0.210176\pi$
$89$	14.9022	1.57963	0.789816	+	0.613343i	$0.210176\pi$
$90$	0	0
$91$	−6.33901	−0.664509
$92$	0	0
$93$	26.6717	2.76573
$94$	0	0
$95$	−0.150240	−0.0154143
$96$	0	0
$97$	−8.30310	−0.843052	−0.421526	−	0.906816i	$-0.638505\pi$
$97$	−8.30310	−0.843052	−0.421526	+	0.906816i	$0.638505\pi$
$98$	0	0
$99$	26.4434	2.65766
$100$	0	0
$101$	4.85779	0.483368	0.241684	−	0.970355i	$-0.422300\pi$
$101$	4.85779	0.483368	0.241684	+	0.970355i	$0.422300\pi$
$102$	0	0
$103$	1.91390	0.188582	0.0942911	−	0.995545i	$-0.469942\pi$
$103$	1.91390	0.188582	0.0942911	+	0.995545i	$0.469942\pi$
$104$	0	0
$105$	−5.30970	−0.518173
$106$	0	0
$107$	−14.3453	−1.38681	−0.693407	−	0.720546i	$-0.743891\pi$
$107$	−14.3453	−1.38681	−0.693407	+	0.720546i	$0.743891\pi$
$108$	0	0
$109$	13.6433	1.30679	0.653394	−	0.757018i	$-0.273344\pi$
$109$	13.6433	1.30679	0.653394	+	0.757018i	$0.273344\pi$
$110$	0	0
$111$	−3.26341	−0.309750
$112$	0	0
$113$	1.55251	0.146048	0.0730241	−	0.997330i	$-0.476735\pi$
$113$	1.55251	0.146048	0.0730241	+	0.997330i	$0.476735\pi$
$114$	0	0
$115$	−8.16748	−0.761622
$116$	0	0
$117$	29.8042	2.75540
$118$	0	0
$119$	1.94133	0.177962
$120$	0	0
$121$	0.948804	0.0862549
$122$	0	0
$123$	24.0533	2.16882
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−13.9121	−1.23450	−0.617248	−	0.786769i	$-0.711752\pi$
$127$	−13.9121	−1.23450	−0.617248	+	0.786769i	$0.711752\pi$
$128$	0	0
$129$	20.7008	1.82260
$130$	0	0
$131$	0.669575	0.0585010	0.0292505	−	0.999572i	$-0.490688\pi$
$131$	0.669575	0.0585010	0.0292505	+	0.999572i	$0.490688\pi$
$132$	0	0
$133$	0.244446	0.0211961
$134$	0	0
$135$	15.1745	1.30601
$136$	0	0
$137$	20.0457	1.71262	0.856309	−	0.516464i	$-0.172752\pi$
$137$	20.0457	1.71262	0.856309	+	0.516464i	$0.172752\pi$
$138$	0	0
$139$	3.95719	0.335645	0.167822	−	0.985817i	$-0.446327\pi$
$139$	3.95719	0.335645	0.167822	+	0.985817i	$0.446327\pi$
$140$	0	0
$141$	−24.3522	−2.05082
$142$	0	0
$143$	13.4675	1.12621
$144$	0	0
$145$	−5.82395	−0.483653
$146$	0	0
$147$	−14.2048	−1.17159
$148$	0	0
$149$	−21.1363	−1.73155	−0.865776	−	0.500433i	$-0.833174\pi$
$149$	−21.1363	−1.73155	−0.865776	+	0.500433i	$0.833174\pi$
$150$	0	0
$151$	−3.49161	−0.284143	−0.142072	−	0.989856i	$-0.545376\pi$
$151$	−3.49161	−0.284143	−0.142072	+	0.989856i	$0.545376\pi$
$152$	0	0
$153$	−9.12760	−0.737922
$154$	0	0
$155$	8.17296	0.656468
$156$	0	0
$157$	−11.1515	−0.889987	−0.444994	−	0.895534i	$-0.646794\pi$
$157$	−11.1515	−0.889987	−0.444994	+	0.895534i	$0.646794\pi$
$158$	0	0
$159$	16.5459	1.31218
$160$	0	0
$161$	13.2888	1.04730
$162$	0	0
$163$	6.41845	0.502731	0.251366	−	0.967892i	$-0.419120\pi$
$163$	6.41845	0.502731	0.251366	+	0.967892i	$0.419120\pi$
$164$	0	0
$165$	11.2807	0.878198
$166$	0	0
$167$	23.5486	1.82225	0.911123	−	0.412134i	$-0.135216\pi$
$167$	23.5486	1.82225	0.911123	+	0.412134i	$0.135216\pi$
$168$	0	0
$169$	2.17916	0.167628
$170$	0	0
$171$	−1.14932	−0.0878904
$172$	0	0
$173$	6.35119	0.482872	0.241436	−	0.970417i	$-0.422382\pi$
$173$	6.35119	0.482872	0.241436	+	0.970417i	$0.422382\pi$
$174$	0	0
$175$	−1.62704	−0.122992
$176$	0	0
$177$	−0.158346	−0.0119020
$178$	0	0
$179$	−13.6287	−1.01865	−0.509327	−	0.860573i	$-0.670106\pi$
$179$	−13.6287	−1.01865	−0.509327	+	0.860573i	$0.670106\pi$
$180$	0	0
$181$	9.57447	0.711664	0.355832	−	0.934550i	$-0.384197\pi$
$181$	9.57447	0.711664	0.355832	+	0.934550i	$0.384197\pi$
$182$	0	0
$183$	2.29377	0.169560
$184$	0	0
$185$	−1.00000	−0.0735215
$186$	0	0
$187$	−4.12443	−0.301608
$188$	0	0
$189$	−24.6894	−1.79589
$190$	0	0
$191$	−17.1340	−1.23978	−0.619888	−	0.784690i	$-0.712822\pi$
$191$	−17.1340	−1.23978	−0.619888	+	0.784690i	$0.712822\pi$
$192$	0	0
$193$	9.73401	0.700669	0.350335	−	0.936625i	$-0.386068\pi$
$193$	9.73401	0.700669	0.350335	+	0.936625i	$0.386068\pi$
$194$	0	0
$195$	12.7144	0.910498
$196$	0	0
$197$	−22.5130	−1.60398	−0.801992	−	0.597335i	$-0.796226\pi$
$197$	−22.5130	−1.60398	−0.801992	+	0.597335i	$0.796226\pi$
$198$	0	0
$199$	6.52077	0.462245	0.231123	−	0.972925i	$-0.425760\pi$
$199$	6.52077	0.462245	0.231123	+	0.972925i	$0.425760\pi$
$200$	0	0
$201$	−48.4439	−3.41697
$202$	0	0
$203$	9.47579	0.665070
$204$	0	0
$205$	7.37060	0.514785
$206$	0	0
$207$	−62.4802	−4.34268
$208$	0	0
$209$	−0.519335	−0.0359231
$210$	0	0
$211$	1.80856	0.124506	0.0622530	−	0.998060i	$-0.480171\pi$
$211$	1.80856	0.124506	0.0622530	+	0.998060i	$0.480171\pi$
$212$	0	0
$213$	−36.8135	−2.52242
$214$	0	0
$215$	6.34329	0.432609
$216$	0	0
$217$	−13.2977	−0.902707
$218$	0	0
$219$	11.3323	0.765764
$220$	0	0
$221$	−4.64864	−0.312701
$222$	0	0
$223$	−25.6479	−1.71751	−0.858755	−	0.512386i	$-0.828762\pi$
$223$	−25.6479	−1.71751	−0.858755	+	0.512386i	$0.828762\pi$
$224$	0	0
$225$	7.64987	0.509992
$226$	0	0
$227$	12.3508	0.819750	0.409875	−	0.912142i	$-0.365572\pi$
$227$	12.3508	0.819750	0.409875	+	0.912142i	$0.365572\pi$
$228$	0	0
$229$	−3.33952	−0.220682	−0.110341	−	0.993894i	$-0.535194\pi$
$229$	−3.33952	−0.220682	−0.110341	+	0.993894i	$0.535194\pi$
$230$	0	0
$231$	−18.3541	−1.20761
$232$	0	0
$233$	16.7018	1.09417	0.547086	−	0.837076i	$-0.315737\pi$
$233$	16.7018	1.09417	0.547086	+	0.837076i	$0.315737\pi$
$234$	0	0
$235$	−7.46218	−0.486779
$236$	0	0
$237$	25.2705	1.64149
$238$	0	0
$239$	7.82276	0.506012	0.253006	−	0.967465i	$-0.418581\pi$
$239$	7.82276	0.506012	0.253006	+	0.967465i	$0.418581\pi$
$240$	0	0
$241$	12.0457	0.775930	0.387965	−	0.921674i	$-0.373178\pi$
$241$	12.0457	0.775930	0.387965	+	0.921674i	$0.373178\pi$
$242$	0	0
$243$	41.1886	2.64225
$244$	0	0
$245$	−4.35275	−0.278087
$246$	0	0
$247$	−0.585341	−0.0372444
$248$	0	0
$249$	−33.6444	−2.13213
$250$	0	0
$251$	−0.774353	−0.0488767	−0.0244383	−	0.999701i	$-0.507780\pi$
$251$	−0.774353	−0.0488767	−0.0244383	+	0.999701i	$0.507780\pi$
$252$	0	0
$253$	−28.2326	−1.77497
$254$	0	0
$255$	−3.89381	−0.243840
$256$	0	0
$257$	0.263946	0.0164645	0.00823224	−	0.999966i	$-0.497380\pi$
$257$	0.263946	0.0164645	0.00823224	+	0.999966i	$0.497380\pi$
$258$	0	0
$259$	1.62704	0.101099
$260$	0	0
$261$	−44.5525	−2.75773
$262$	0	0
$263$	−8.59872	−0.530220	−0.265110	−	0.964218i	$-0.585408\pi$
$263$	−8.59872	−0.530220	−0.265110	+	0.964218i	$0.585408\pi$
$264$	0	0
$265$	5.07012	0.311455
$266$	0	0
$267$	48.6321	2.97624
$268$	0	0
$269$	7.46928	0.455410	0.227705	−	0.973730i	$-0.426878\pi$
$269$	7.46928	0.455410	0.227705	+	0.973730i	$0.426878\pi$
$270$	0	0
$271$	−1.41365	−0.0858734	−0.0429367	−	0.999078i	$-0.513671\pi$
$271$	−1.41365	−0.0858734	−0.0429367	+	0.999078i	$0.513671\pi$
$272$	0	0
$273$	−20.6868	−1.25202
$274$	0	0
$275$	3.45670	0.208447
$276$	0	0
$277$	−22.6608	−1.36156	−0.680778	−	0.732490i	$-0.738358\pi$
$277$	−22.6608	−1.36156	−0.680778	+	0.732490i	$0.738358\pi$
$278$	0	0
$279$	62.5221	3.74310
$280$	0	0
$281$	11.5543	0.689273	0.344636	−	0.938736i	$-0.388002\pi$
$281$	11.5543	0.689273	0.344636	+	0.938736i	$0.388002\pi$
$282$	0	0
$283$	−21.4737	−1.27648	−0.638239	−	0.769838i	$-0.720337\pi$
$283$	−21.4737	−1.27648	−0.638239	+	0.769838i	$0.720337\pi$
$284$	0	0
$285$	−0.490295	−0.0290426
$286$	0	0
$287$	−11.9923	−0.707880
$288$	0	0
$289$	−15.5763	−0.916256
$290$	0	0
$291$	−27.0965	−1.58842
$292$	0	0
$293$	−22.6632	−1.32400	−0.662000	−	0.749504i	$-0.730292\pi$
$293$	−22.6632	−1.32400	−0.662000	+	0.749504i	$0.730292\pi$
$294$	0	0
$295$	−0.0485215	−0.00282503
$296$	0	0
$297$	52.4536	3.04367
$298$	0	0
$299$	−31.8209	−1.84025
$300$	0	0
$301$	−10.3208	−0.594879
$302$	0	0
$303$	15.8530	0.910729
$304$	0	0
$305$	0.702875	0.0402465
$306$	0	0
$307$	11.3574	0.648201	0.324100	−	0.946023i	$-0.394938\pi$
$307$	11.3574	0.648201	0.324100	+	0.946023i	$0.394938\pi$
$308$	0	0
$309$	6.24585	0.355314
$310$	0	0
$311$	2.52481	0.143169	0.0715843	−	0.997435i	$-0.477194\pi$
$311$	2.52481	0.143169	0.0715843	+	0.997435i	$0.477194\pi$
$312$	0	0
$313$	25.9266	1.46546	0.732730	−	0.680519i	$-0.238246\pi$
$313$	25.9266	1.46546	0.732730	+	0.680519i	$0.238246\pi$
$314$	0	0
$315$	−12.4466	−0.701288
$316$	0	0
$317$	33.4674	1.87972	0.939858	−	0.341566i	$-0.110957\pi$
$317$	33.4674	1.87972	0.939858	+	0.341566i	$0.110957\pi$
$318$	0	0
$319$	−20.1317	−1.12716
$320$	0	0
$321$	−46.8147	−2.61294
$322$	0	0
$323$	0.179262	0.00997438
$324$	0	0
$325$	3.89604	0.216114
$326$	0	0
$327$	44.5237	2.46216
$328$	0	0
$329$	12.1412	0.669368
$330$	0	0
$331$	−23.7697	−1.30650	−0.653250	−	0.757142i	$-0.726595\pi$
$331$	−23.7697	−1.30650	−0.653250	+	0.757142i	$0.726595\pi$
$332$	0	0
$333$	−7.64987	−0.419210
$334$	0	0
$335$	−14.8446	−0.811045
$336$	0	0
$337$	7.99594	0.435566	0.217783	−	0.975997i	$-0.430117\pi$
$337$	7.99594	0.435566	0.217783	+	0.975997i	$0.430117\pi$
$338$	0	0
$339$	5.06650	0.275174
$340$	0	0
$341$	28.2515	1.52990
$342$	0	0
$343$	18.4713	0.997359
$344$	0	0
$345$	−26.6539	−1.43500
$346$	0	0
$347$	−23.4398	−1.25831	−0.629156	−	0.777279i	$-0.716599\pi$
$347$	−23.4398	−1.25831	−0.629156	+	0.777279i	$0.716599\pi$
$348$	0	0
$349$	−12.4503	−0.666452	−0.333226	−	0.942847i	$-0.608137\pi$
$349$	−12.4503	−0.666452	−0.333226	+	0.942847i	$0.608137\pi$
$350$	0	0
$351$	59.1204	3.15561
$352$	0	0
$353$	−33.2408	−1.76923	−0.884615	−	0.466323i	$-0.845578\pi$
$353$	−33.2408	−1.76923	−0.884615	+	0.466323i	$0.845578\pi$
$354$	0	0
$355$	−11.2807	−0.598715
$356$	0	0
$357$	6.33537	0.335303
$358$	0	0
$359$	−5.80023	−0.306125	−0.153062	−	0.988217i	$-0.548914\pi$
$359$	−5.80023	−0.306125	−0.153062	+	0.988217i	$0.548914\pi$
$360$	0	0
$361$	−18.9774	−0.998812
$362$	0	0
$363$	3.09634	0.162516
$364$	0	0
$365$	3.47252	0.181760
$366$	0	0
$367$	33.7528	1.76188	0.880942	−	0.473224i	$-0.156910\pi$
$367$	33.7528	1.76188	0.880942	+	0.473224i	$0.156910\pi$
$368$	0	0
$369$	56.3842	2.93524
$370$	0	0
$371$	−8.24928	−0.428281
$372$	0	0
$373$	21.8702	1.13240	0.566198	−	0.824269i	$-0.308414\pi$
$373$	21.8702	1.13240	0.566198	+	0.824269i	$0.308414\pi$
$374$	0	0
$375$	3.26341	0.168522
$376$	0	0
$377$	−22.6904	−1.16861
$378$	0	0
$379$	−36.1130	−1.85500	−0.927499	−	0.373825i	$-0.878046\pi$
$379$	−36.1130	−1.85500	−0.927499	+	0.373825i	$0.878046\pi$
$380$	0	0
$381$	−45.4008	−2.32595
$382$	0	0
$383$	14.4348	0.737583	0.368792	−	0.929512i	$-0.379772\pi$
$383$	14.4348	0.737583	0.368792	+	0.929512i	$0.379772\pi$
$384$	0	0
$385$	−5.62419	−0.286635
$386$	0	0
$387$	48.5254	2.46668
$388$	0	0
$389$	−17.2275	−0.873467	−0.436733	−	0.899591i	$-0.643865\pi$
$389$	−17.2275	−0.873467	−0.436733	+	0.899591i	$0.643865\pi$
$390$	0	0
$391$	9.74519	0.492836
$392$	0	0
$393$	2.18510	0.110224
$394$	0	0
$395$	7.74357	0.389621
$396$	0	0
$397$	0.460059	0.0230897	0.0115448	−	0.999933i	$-0.496325\pi$
$397$	0.460059	0.0230897	0.0115448	+	0.999933i	$0.496325\pi$
$398$	0	0
$399$	0.797728	0.0399364
$400$	0	0
$401$	−23.8044	−1.18874	−0.594369	−	0.804193i	$-0.702598\pi$
$401$	−23.8044	−1.18874	−0.594369	+	0.804193i	$0.702598\pi$
$402$	0	0
$403$	31.8422	1.58617
$404$	0	0
$405$	26.5709	1.32032
$406$	0	0
$407$	−3.45670	−0.171342
$408$	0	0
$409$	−9.43921	−0.466739	−0.233369	−	0.972388i	$-0.574975\pi$
$409$	−9.43921	−0.466739	−0.233369	+	0.972388i	$0.574975\pi$
$410$	0	0
$411$	65.4173	3.22680
$412$	0	0
$413$	0.0789464	0.00388470
$414$	0	0
$415$	−10.3096	−0.506077
$416$	0	0
$417$	12.9140	0.632399
$418$	0	0
$419$	9.19927	0.449414	0.224707	−	0.974426i	$-0.427858\pi$
$419$	9.19927	0.449414	0.224707	+	0.974426i	$0.427858\pi$
$420$	0	0
$421$	11.7524	0.572779	0.286390	−	0.958113i	$-0.407545\pi$
$421$	11.7524	0.572779	0.286390	+	0.958113i	$0.407545\pi$
$422$	0	0
$423$	−57.0847	−2.77555
$424$	0	0
$425$	−1.19317	−0.0578772
$426$	0	0
$427$	−1.14360	−0.0553429
$428$	0	0
$429$	43.9499	2.12192
$430$	0	0
$431$	−41.2051	−1.98478	−0.992390	−	0.123134i	$-0.960705\pi$
$431$	−41.2051	−1.98478	−0.992390	+	0.123134i	$0.960705\pi$
$432$	0	0
$433$	36.2302	1.74111	0.870555	−	0.492071i	$-0.163760\pi$
$433$	36.2302	1.74111	0.870555	+	0.492071i	$0.163760\pi$
$434$	0	0
$435$	−19.0060	−0.911267
$436$	0	0
$437$	1.22708	0.0586993
$438$	0	0
$439$	6.67691	0.318672	0.159336	−	0.987224i	$-0.449065\pi$
$439$	6.67691	0.318672	0.159336	+	0.987224i	$0.449065\pi$
$440$	0	0
$441$	−33.2980	−1.58562
$442$	0	0
$443$	−37.1992	−1.76739	−0.883694	−	0.468066i	$-0.844951\pi$
$443$	−37.1992	−1.76739	−0.883694	+	0.468066i	$0.844951\pi$
$444$	0	0
$445$	14.9022	0.706433
$446$	0	0
$447$	−68.9764	−3.26247
$448$	0	0
$449$	−31.1977	−1.47231	−0.736156	−	0.676811i	$-0.763361\pi$
$449$	−31.1977	−1.47231	−0.736156	+	0.676811i	$0.763361\pi$
$450$	0	0
$451$	25.4780	1.19971
$452$	0	0
$453$	−11.3946	−0.535363
$454$	0	0
$455$	−6.33901	−0.297177
$456$	0	0
$457$	−33.9414	−1.58771	−0.793856	−	0.608105i	$-0.791930\pi$
$457$	−33.9414	−1.58771	−0.793856	+	0.608105i	$0.791930\pi$
$458$	0	0
$459$	−18.1057	−0.845102
$460$	0	0
$461$	12.6176	0.587658	0.293829	−	0.955858i	$-0.405070\pi$
$461$	12.6176	0.587658	0.293829	+	0.955858i	$0.405070\pi$
$462$	0	0
$463$	−1.59601	−0.0741728	−0.0370864	−	0.999312i	$-0.511808\pi$
$463$	−1.59601	−0.0741728	−0.0370864	+	0.999312i	$0.511808\pi$
$464$	0	0
$465$	26.6717	1.23687
$466$	0	0
$467$	−27.7478	−1.28402	−0.642008	−	0.766698i	$-0.721898\pi$
$467$	−27.7478	−1.28402	−0.642008	+	0.766698i	$0.721898\pi$
$468$	0	0
$469$	24.1526	1.11527
$470$	0	0
$471$	−36.3920	−1.67685
$472$	0	0
$473$	21.9269	1.00820
$474$	0	0
$475$	−0.150240	−0.00689348
$476$	0	0
$477$	38.7858	1.77588
$478$	0	0
$479$	29.9993	1.37070	0.685352	−	0.728212i	$-0.259648\pi$
$479$	29.9993	1.37070	0.685352	+	0.728212i	$0.259648\pi$
$480$	0	0
$481$	−3.89604	−0.177644
$482$	0	0
$483$	43.3669	1.97326
$484$	0	0
$485$	−8.30310	−0.377024
$486$	0	0
$487$	−22.3192	−1.01138	−0.505689	−	0.862716i	$-0.668762\pi$
$487$	−22.3192	−1.01138	−0.505689	+	0.862716i	$0.668762\pi$
$488$	0	0
$489$	20.9460	0.947213
$490$	0	0
$491$	−9.63721	−0.434921	−0.217461	−	0.976069i	$-0.569777\pi$
$491$	−9.63721	−0.434921	−0.217461	+	0.976069i	$0.569777\pi$
$492$	0	0
$493$	6.94896	0.312966
$494$	0	0
$495$	26.4434	1.18854
$496$	0	0
$497$	18.3541	0.823292
$498$	0	0
$499$	31.0163	1.38848	0.694241	−	0.719743i	$-0.255740\pi$
$499$	31.0163	1.38848	0.694241	+	0.719743i	$0.255740\pi$
$500$	0	0
$501$	76.8489	3.43336
$502$	0	0
$503$	−22.5156	−1.00392	−0.501961	−	0.864890i	$-0.667388\pi$
$503$	−22.5156	−1.00392	−0.501961	+	0.864890i	$0.667388\pi$
$504$	0	0
$505$	4.85779	0.216169
$506$	0	0
$507$	7.11150	0.315833
$508$	0	0
$509$	3.97890	0.176362	0.0881809	−	0.996104i	$-0.471895\pi$
$509$	3.97890	0.176362	0.0881809	+	0.996104i	$0.471895\pi$
$510$	0	0
$511$	−5.64992	−0.249938
$512$	0	0
$513$	−2.27981	−0.100656
$514$	0	0
$515$	1.91390	0.0843365
$516$	0	0
$517$	−25.7945	−1.13444
$518$	0	0
$519$	20.7266	0.909796
$520$	0	0
$521$	3.35028	0.146779	0.0733893	−	0.997303i	$-0.476618\pi$
$521$	3.35028	0.146779	0.0733893	+	0.997303i	$0.476618\pi$
$522$	0	0
$523$	18.4373	0.806206	0.403103	−	0.915155i	$-0.367932\pi$
$523$	18.4373	0.806206	0.403103	+	0.915155i	$0.367932\pi$
$524$	0	0
$525$	−5.30970	−0.231734
$526$	0	0
$527$	−9.75172	−0.424792
$528$	0	0
$529$	43.7078	1.90034
$530$	0	0
$531$	−0.371184	−0.0161080
$532$	0	0
$533$	28.7162	1.24384
$534$	0	0
$535$	−14.3453	−0.620202
$536$	0	0
$537$	−44.4759	−1.91928
$538$	0	0
$539$	−15.0462	−0.648084
$540$	0	0
$541$	19.2753	0.828709	0.414355	−	0.910115i	$-0.364007\pi$
$541$	19.2753	0.828709	0.414355	+	0.910115i	$0.364007\pi$
$542$	0	0
$543$	31.2455	1.34087
$544$	0	0
$545$	13.6433	0.584414
$546$	0	0
$547$	13.8719	0.593119	0.296559	−	0.955014i	$-0.404161\pi$
$547$	13.8719	0.593119	0.296559	+	0.955014i	$0.404161\pi$
$548$	0	0
$549$	5.37690	0.229481
$550$	0	0
$551$	0.874990	0.0372758
$552$	0	0
$553$	−12.5991	−0.535767
$554$	0	0
$555$	−3.26341	−0.138524
$556$	0	0
$557$	28.8738	1.22342	0.611711	−	0.791081i	$-0.290481\pi$
$557$	28.8738	1.22342	0.611711	+	0.791081i	$0.290481\pi$
$558$	0	0
$559$	24.7137	1.04528
$560$	0	0
$561$	−13.4597	−0.568271
$562$	0	0
$563$	43.5520	1.83550	0.917749	−	0.397160i	$-0.130004\pi$
$563$	43.5520	1.83550	0.917749	+	0.397160i	$0.130004\pi$
$564$	0	0
$565$	1.55251	0.0653148
$566$	0	0
$567$	−43.2319	−1.81557
$568$	0	0
$569$	11.7180	0.491242	0.245621	−	0.969366i	$-0.421008\pi$
$569$	11.7180	0.491242	0.245621	+	0.969366i	$0.421008\pi$
$570$	0	0
$571$	34.0270	1.42398	0.711992	−	0.702188i	$-0.247793\pi$
$571$	34.0270	1.42398	0.711992	+	0.702188i	$0.247793\pi$
$572$	0	0
$573$	−55.9155	−2.33590
$574$	0	0
$575$	−8.16748	−0.340608
$576$	0	0
$577$	−45.8974	−1.91073	−0.955366	−	0.295425i	$-0.904539\pi$
$577$	−45.8974	−1.91073	−0.955366	+	0.295425i	$0.904539\pi$
$578$	0	0
$579$	31.7661	1.32015
$580$	0	0
$581$	16.7741	0.695906
$582$	0	0
$583$	17.5259	0.725849
$584$	0	0
$585$	29.8042	1.23225
$586$	0	0
$587$	−8.67363	−0.357999	−0.179000	−	0.983849i	$-0.557286\pi$
$587$	−8.67363	−0.357999	−0.179000	+	0.983849i	$0.557286\pi$
$588$	0	0
$589$	−1.22790	−0.0505949
$590$	0	0
$591$	−73.4692	−3.02212
$592$	0	0
$593$	−29.2400	−1.20074	−0.600371	−	0.799721i	$-0.704980\pi$
$593$	−29.2400	−1.20074	−0.600371	+	0.799721i	$0.704980\pi$
$594$	0	0
$595$	1.94133	0.0795868
$596$	0	0
$597$	21.2800	0.870931
$598$	0	0
$599$	−43.0568	−1.75926	−0.879628	−	0.475663i	$-0.842208\pi$
$599$	−43.0568	−1.75926	−0.879628	+	0.475663i	$0.842208\pi$
$600$	0	0
$601$	−7.86865	−0.320969	−0.160485	−	0.987038i	$-0.551306\pi$
$601$	−7.86865	−0.320969	−0.160485	+	0.987038i	$0.551306\pi$
$602$	0	0
$603$	−113.559	−4.62448
$604$	0	0
$605$	0.948804	0.0385744
$606$	0	0
$607$	9.69304	0.393428	0.196714	−	0.980461i	$-0.436973\pi$
$607$	9.69304	0.393428	0.196714	+	0.980461i	$0.436973\pi$
$608$	0	0
$609$	30.9234	1.25308
$610$	0	0
$611$	−29.0730	−1.17617
$612$	0	0
$613$	−16.5187	−0.667183	−0.333592	−	0.942718i	$-0.608261\pi$
$613$	−16.5187	−0.667183	−0.333592	+	0.942718i	$0.608261\pi$
$614$	0	0
$615$	24.0533	0.969924
$616$	0	0
$617$	−9.03457	−0.363718	−0.181859	−	0.983325i	$-0.558211\pi$
$617$	−9.03457	−0.363718	−0.181859	+	0.983325i	$0.558211\pi$
$618$	0	0
$619$	20.4178	0.820660	0.410330	−	0.911937i	$-0.365413\pi$
$619$	20.4178	0.820660	0.410330	+	0.911937i	$0.365413\pi$
$620$	0	0
$621$	−123.937	−4.97343
$622$	0	0
$623$	−24.2465	−0.971415
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−1.69480	−0.0676840
$628$	0	0
$629$	1.19317	0.0475748
$630$	0	0
$631$	9.85214	0.392208	0.196104	−	0.980583i	$-0.437171\pi$
$631$	9.85214	0.392208	0.196104	+	0.980583i	$0.437171\pi$
$632$	0	0
$633$	5.90206	0.234586
$634$	0	0
$635$	−13.9121	−0.552083
$636$	0	0
$637$	−16.9585	−0.671920
$638$	0	0
$639$	−86.2956	−3.41380
$640$	0	0
$641$	−26.7261	−1.05562	−0.527809	−	0.849363i	$-0.676986\pi$
$641$	−26.7261	−1.05562	−0.527809	+	0.849363i	$0.676986\pi$
$642$	0	0
$643$	36.5476	1.44130	0.720649	−	0.693300i	$-0.243844\pi$
$643$	36.5476	1.44130	0.720649	+	0.693300i	$0.243844\pi$
$644$	0	0
$645$	20.7008	0.815092
$646$	0	0
$647$	7.79910	0.306614	0.153307	−	0.988179i	$-0.451008\pi$
$647$	7.79910	0.306614	0.153307	+	0.988179i	$0.451008\pi$
$648$	0	0
$649$	−0.167725	−0.00658377
$650$	0	0
$651$	−43.3959	−1.70082
$652$	0	0
$653$	−23.0918	−0.903653	−0.451827	−	0.892106i	$-0.649227\pi$
$653$	−23.0918	−0.903653	−0.451827	+	0.892106i	$0.649227\pi$
$654$	0	0
$655$	0.669575	0.0261624
$656$	0	0
$657$	26.5643	1.03637
$658$	0	0
$659$	37.9410	1.47797	0.738986	−	0.673721i	$-0.235305\pi$
$659$	37.9410	1.47797	0.738986	+	0.673721i	$0.235305\pi$
$660$	0	0
$661$	23.7096	0.922198	0.461099	−	0.887349i	$-0.347455\pi$
$661$	23.7096	0.922198	0.461099	+	0.887349i	$0.347455\pi$
$662$	0	0
$663$	−15.1704	−0.589171
$664$	0	0
$665$	0.244446	0.00947920
$666$	0	0
$667$	47.5671	1.84180
$668$	0	0
$669$	−83.6997	−3.23602
$670$	0	0
$671$	2.42963	0.0937948
$672$	0	0
$673$	−41.8519	−1.61327	−0.806635	−	0.591050i	$-0.798714\pi$
$673$	−41.8519	−1.61327	−0.806635	+	0.591050i	$0.798714\pi$
$674$	0	0
$675$	15.1745	0.584065
$676$	0	0
$677$	−17.1914	−0.660717	−0.330359	−	0.943855i	$-0.607170\pi$
$677$	−17.1914	−0.660717	−0.330359	+	0.943855i	$0.607170\pi$
$678$	0	0
$679$	13.5095	0.518445
$680$	0	0
$681$	40.3057	1.54452
$682$	0	0
$683$	−2.64705	−0.101286	−0.0506432	−	0.998717i	$-0.516127\pi$
$683$	−2.64705	−0.101286	−0.0506432	+	0.998717i	$0.516127\pi$
$684$	0	0
$685$	20.0457	0.765906
$686$	0	0
$687$	−10.8983	−0.415794
$688$	0	0
$689$	19.7534	0.752546
$690$	0	0
$691$	−1.59112	−0.0605291	−0.0302645	−	0.999542i	$-0.509635\pi$
$691$	−1.59112	−0.0605291	−0.0302645	+	0.999542i	$0.509635\pi$
$692$	0	0
$693$	−43.0243	−1.63436
$694$	0	0
$695$	3.95719	0.150105
$696$	0	0
$697$	−8.79438	−0.333111
$698$	0	0
$699$	54.5049	2.06157
$700$	0	0
$701$	1.07541	0.0406176	0.0203088	−	0.999794i	$-0.493535\pi$
$701$	1.07541	0.0406176	0.0203088	+	0.999794i	$0.493535\pi$
$702$	0	0
$703$	0.150240	0.00566640
$704$	0	0
$705$	−24.3522	−0.917156
$706$	0	0
$707$	−7.90380	−0.297253
$708$	0	0
$709$	−8.00847	−0.300764	−0.150382	−	0.988628i	$-0.548050\pi$
$709$	−8.00847	−0.300764	−0.150382	+	0.988628i	$0.548050\pi$
$710$	0	0
$711$	59.2373	2.22157
$712$	0	0
$713$	−66.7525	−2.49990
$714$	0	0
$715$	13.4675	0.503655
$716$	0	0
$717$	25.5289	0.953395
$718$	0	0
$719$	−16.5683	−0.617893	−0.308946	−	0.951079i	$-0.599976\pi$
$719$	−16.5683	−0.617893	−0.308946	+	0.951079i	$0.599976\pi$
$720$	0	0
$721$	−3.11399	−0.115971
$722$	0	0
$723$	39.3100	1.46196
$724$	0	0
$725$	−5.82395	−0.216296
$726$	0	0
$727$	−40.5861	−1.50525	−0.752627	−	0.658447i	$-0.771214\pi$
$727$	−40.5861	−1.50525	−0.752627	+	0.658447i	$0.771214\pi$
$728$	0	0
$729$	54.7027	2.02603
$730$	0	0
$731$	−7.56862	−0.279935
$732$	0	0
$733$	−14.6895	−0.542569	−0.271285	−	0.962499i	$-0.587449\pi$
$733$	−14.6895	−0.542569	−0.271285	+	0.962499i	$0.587449\pi$
$734$	0	0
$735$	−14.2048	−0.523953
$736$	0	0
$737$	−51.3132	−1.89015
$738$	0	0
$739$	27.2057	1.00078	0.500390	−	0.865800i	$-0.333190\pi$
$739$	27.2057	1.00078	0.500390	+	0.865800i	$0.333190\pi$
$740$	0	0
$741$	−1.91021	−0.0701733
$742$	0	0
$743$	12.9407	0.474750	0.237375	−	0.971418i	$-0.423713\pi$
$743$	12.9407	0.474750	0.237375	+	0.971418i	$0.423713\pi$
$744$	0	0
$745$	−21.1363	−0.774373
$746$	0	0
$747$	−78.8670	−2.88559
$748$	0	0
$749$	23.3404	0.852838
$750$	0	0
$751$	32.1077	1.17163	0.585814	−	0.810446i	$-0.300775\pi$
$751$	32.1077	1.17163	0.585814	+	0.810446i	$0.300775\pi$
$752$	0	0
$753$	−2.52703	−0.0920902
$754$	0	0
$755$	−3.49161	−0.127073
$756$	0	0
$757$	24.5455	0.892122	0.446061	−	0.895003i	$-0.352827\pi$
$757$	24.5455	0.892122	0.446061	+	0.895003i	$0.352827\pi$
$758$	0	0
$759$	−92.1346	−3.34427
$760$	0	0
$761$	10.1368	0.367459	0.183730	−	0.982977i	$-0.441183\pi$
$761$	10.1368	0.367459	0.183730	+	0.982977i	$0.441183\pi$
$762$	0	0
$763$	−22.1981	−0.803626
$764$	0	0
$765$	−9.12760	−0.330009
$766$	0	0
$767$	−0.189042	−0.00682591
$768$	0	0
$769$	−24.5691	−0.885983	−0.442991	−	0.896526i	$-0.646083\pi$
$769$	−24.5691	−0.885983	−0.442991	+	0.896526i	$0.646083\pi$
$770$	0	0
$771$	0.861364	0.0310213
$772$	0	0
$773$	−25.1444	−0.904381	−0.452190	−	0.891921i	$-0.649357\pi$
$773$	−25.1444	−0.904381	−0.452190	+	0.891921i	$0.649357\pi$
$774$	0	0
$775$	8.17296	0.293581
$776$	0	0
$777$	5.30970	0.190484
$778$	0	0
$779$	−1.10736	−0.0396752
$780$	0	0
$781$	−38.9939	−1.39531
$782$	0	0
$783$	−88.3754	−3.15828
$784$	0	0
$785$	−11.1515	−0.398014
$786$	0	0
$787$	−4.37829	−0.156069	−0.0780346	−	0.996951i	$-0.524864\pi$
$787$	−4.37829	−0.156069	−0.0780346	+	0.996951i	$0.524864\pi$
$788$	0	0
$789$	−28.0612	−0.999004
$790$	0	0
$791$	−2.52600	−0.0898142
$792$	0	0
$793$	2.73843	0.0972445
$794$	0	0
$795$	16.5459	0.586823
$796$	0	0
$797$	−29.4715	−1.04393	−0.521967	−	0.852966i	$-0.674802\pi$
$797$	−29.4715	−1.04393	−0.521967	+	0.852966i	$0.674802\pi$
$798$	0	0
$799$	8.90364	0.314988
$800$	0	0
$801$	114.000	4.02800
$802$	0	0
$803$	12.0035	0.423593
$804$	0	0
$805$	13.2888	0.468369
$806$	0	0
$807$	24.3753	0.858053
$808$	0	0
$809$	23.5056	0.826415	0.413207	−	0.910637i	$-0.364408\pi$
$809$	23.5056	0.826415	0.413207	+	0.910637i	$0.364408\pi$
$810$	0	0
$811$	−23.0398	−0.809037	−0.404519	−	0.914530i	$-0.632561\pi$
$811$	−23.0398	−0.809037	−0.404519	+	0.914530i	$0.632561\pi$
$812$	0	0
$813$	−4.61334	−0.161797
$814$	0	0
$815$	6.41845	0.224828
$816$	0	0
$817$	−0.953015	−0.0333418
$818$	0	0
$819$	−48.4926	−1.69447
$820$	0	0
$821$	26.6048	0.928513	0.464257	−	0.885701i	$-0.346322\pi$
$821$	26.6048	0.928513	0.464257	+	0.885701i	$0.346322\pi$
$822$	0	0
$823$	5.84716	0.203819	0.101910	−	0.994794i	$-0.467505\pi$
$823$	5.84716	0.203819	0.101910	+	0.994794i	$0.467505\pi$
$824$	0	0
$825$	11.2807	0.392742
$826$	0	0
$827$	9.38863	0.326475	0.163237	−	0.986587i	$-0.447806\pi$
$827$	9.38863	0.326475	0.163237	+	0.986587i	$0.447806\pi$
$828$	0	0
$829$	36.2250	1.25815	0.629073	−	0.777346i	$-0.283435\pi$
$829$	36.2250	1.25815	0.629073	+	0.777346i	$0.283435\pi$
$830$	0	0
$831$	−73.9516	−2.56535
$832$	0	0
$833$	5.19357	0.179946
$834$	0	0
$835$	23.5486	0.814933
$836$	0	0
$837$	124.020	4.28677
$838$	0	0
$839$	38.8036	1.33965	0.669825	−	0.742519i	$-0.266369\pi$
$839$	38.8036	1.33965	0.669825	+	0.742519i	$0.266369\pi$
$840$	0	0
$841$	4.91844	0.169601
$842$	0	0
$843$	37.7065	1.29868
$844$	0	0
$845$	2.17916	0.0749654
$846$	0	0
$847$	−1.54374	−0.0530435
$848$	0	0
$849$	−70.0776	−2.40506
$850$	0	0
$851$	8.16748	0.279978
$852$	0	0
$853$	4.06343	0.139129	0.0695646	−	0.997577i	$-0.477839\pi$
$853$	4.06343	0.139129	0.0695646	+	0.997577i	$0.477839\pi$
$854$	0	0
$855$	−1.14932	−0.0393058
$856$	0	0
$857$	45.6860	1.56060	0.780302	−	0.625403i	$-0.215065\pi$
$857$	45.6860	1.56060	0.780302	+	0.625403i	$0.215065\pi$
$858$	0	0
$859$	12.3340	0.420830	0.210415	−	0.977612i	$-0.432519\pi$
$859$	12.3340	0.420830	0.210415	+	0.977612i	$0.432519\pi$
$860$	0	0
$861$	−39.1357	−1.33374
$862$	0	0
$863$	−28.4877	−0.969732	−0.484866	−	0.874588i	$-0.661132\pi$
$863$	−28.4877	−0.969732	−0.484866	+	0.874588i	$0.661132\pi$
$864$	0	0
$865$	6.35119	0.215947
$866$	0	0
$867$	−50.8321	−1.72635
$868$	0	0
$869$	26.7672	0.908016
$870$	0	0
$871$	−57.8350	−1.95967
$872$	0	0
$873$	−63.5177	−2.14975
$874$	0	0
$875$	−1.62704	−0.0550039
$876$	0	0
$877$	45.2388	1.52760	0.763802	−	0.645451i	$-0.223330\pi$
$877$	45.2388	1.52760	0.763802	+	0.645451i	$0.223330\pi$
$878$	0	0
$879$	−73.9595	−2.49459
$880$	0	0
$881$	5.22089	0.175896	0.0879481	−	0.996125i	$-0.471969\pi$
$881$	5.22089	0.175896	0.0879481	+	0.996125i	$0.471969\pi$
$882$	0	0
$883$	−44.0900	−1.48375	−0.741874	−	0.670539i	$-0.766063\pi$
$883$	−44.0900	−1.48375	−0.741874	+	0.670539i	$0.766063\pi$
$884$	0	0
$885$	−0.158346	−0.00532274
$886$	0	0
$887$	14.7720	0.495997	0.247998	−	0.968760i	$-0.420227\pi$
$887$	14.7720	0.495997	0.247998	+	0.968760i	$0.420227\pi$
$888$	0	0
$889$	22.6354	0.759168
$890$	0	0
$891$	91.8479	3.07702
$892$	0	0
$893$	1.12112	0.0375167
$894$	0	0
$895$	−13.6287	−0.455556
$896$	0	0
$897$	−103.845	−3.46727
$898$	0	0
$899$	−47.5989	−1.58751
$900$	0	0
$901$	−6.04952	−0.201539
$902$	0	0
$903$	−33.6810	−1.12083
$904$	0	0
$905$	9.57447	0.318266
$906$	0	0
$907$	23.4760	0.779509	0.389754	−	0.920919i	$-0.372560\pi$
$907$	23.4760	0.779509	0.389754	+	0.920919i	$0.372560\pi$
$908$	0	0
$909$	37.1614	1.23257
$910$	0	0
$911$	24.0035	0.795270	0.397635	−	0.917544i	$-0.369831\pi$
$911$	24.0035	0.795270	0.397635	+	0.917544i	$0.369831\pi$
$912$	0	0
$913$	−35.6372	−1.17942
$914$	0	0
$915$	2.29377	0.0758297
$916$	0	0
$917$	−1.08942	−0.0359759
$918$	0	0
$919$	22.8880	0.755004	0.377502	−	0.926009i	$-0.376783\pi$
$919$	22.8880	0.755004	0.377502	+	0.926009i	$0.376783\pi$
$920$	0	0
$921$	37.0639	1.22130
$922$	0	0
$923$	−43.9499	−1.44663
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	0	0
$927$	14.6411	0.480877
$928$	0	0
$929$	−3.91166	−0.128337	−0.0641686	−	0.997939i	$-0.520440\pi$
$929$	−3.91166	−0.128337	−0.0641686	+	0.997939i	$0.520440\pi$
$930$	0	0
$931$	0.653956	0.0214325
$932$	0	0
$933$	8.23949	0.269749
$934$	0	0
$935$	−4.12443	−0.134883
$936$	0	0
$937$	18.4611	0.603099	0.301549	−	0.953451i	$-0.402496\pi$
$937$	18.4611	0.603099	0.301549	+	0.953451i	$0.402496\pi$
$938$	0	0
$939$	84.6094	2.76112
$940$	0	0
$941$	33.0853	1.07855	0.539275	−	0.842130i	$-0.318698\pi$
$941$	33.0853	1.07855	0.539275	+	0.842130i	$0.318698\pi$
$942$	0	0
$943$	−60.1993	−1.96036
$944$	0	0
$945$	−24.6894	−0.803147
$946$	0	0
$947$	−23.9447	−0.778098	−0.389049	−	0.921217i	$-0.627196\pi$
$947$	−23.9447	−0.778098	−0.389049	+	0.921217i	$0.627196\pi$
$948$	0	0
$949$	13.5291	0.439173
$950$	0	0
$951$	109.218	3.54163
$952$	0	0
$953$	−22.9547	−0.743576	−0.371788	−	0.928318i	$-0.621255\pi$
$953$	−22.9547	−0.743576	−0.371788	+	0.928318i	$0.621255\pi$
$954$	0	0
$955$	−17.1340	−0.554445
$956$	0	0
$957$	−65.6980	−2.12372
$958$	0	0
$959$	−32.6151	−1.05320
$960$	0	0
$961$	35.7972	1.15475
$962$	0	0
$963$	−109.740	−3.53632
$964$	0	0
$965$	9.73401	0.313349
$966$	0	0
$967$	15.6148	0.502139	0.251069	−	0.967969i	$-0.419218\pi$
$967$	15.6148	0.502139	0.251069	+	0.967969i	$0.419218\pi$
$968$	0	0
$969$	0.585005	0.0187931
$970$	0	0
$971$	−4.21823	−0.135369	−0.0676846	−	0.997707i	$-0.521561\pi$
$971$	−4.21823	−0.135369	−0.0676846	+	0.997707i	$0.521561\pi$
$972$	0	0
$973$	−6.43850	−0.206409
$974$	0	0
$975$	12.7144	0.407187
$976$	0	0
$977$	−37.9179	−1.21310	−0.606551	−	0.795045i	$-0.707447\pi$
$977$	−37.9179	−1.21310	−0.606551	+	0.795045i	$0.707447\pi$
$978$	0	0
$979$	51.5126	1.64635
$980$	0	0
$981$	104.369	3.33226
$982$	0	0
$983$	17.4064	0.555177	0.277588	−	0.960700i	$-0.410465\pi$
$983$	17.4064	0.555177	0.277588	+	0.960700i	$0.410465\pi$
$984$	0	0
$985$	−22.5130	−0.717323
$986$	0	0
$987$	39.6219	1.26118
$988$	0	0
$989$	−51.8087	−1.64742
$990$	0	0
$991$	34.4446	1.09417	0.547085	−	0.837077i	$-0.315738\pi$
$991$	34.4446	1.09417	0.547085	+	0.837077i	$0.315738\pi$
$992$	0	0
$993$	−77.5703	−2.46162
$994$	0	0
$995$	6.52077	0.206722
$996$	0	0
$997$	34.5294	1.09356	0.546778	−	0.837278i	$-0.315854\pi$
$997$	34.5294	1.09356	0.546778	+	0.837278i	$0.315854\pi$
$998$	0	0
$999$	−15.1745	−0.480099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2960.2.a.bc.1.6		6
4.3	odd	2		1480.2.a.k.1.1	✓	6
20.19	odd	2		7400.2.a.s.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1480.2.a.k.1.1	✓	6	4.3	odd	2
2960.2.a.bc.1.6		6	1.1	even	1	trivial
7400.2.a.s.1.6		6	20.19	odd	2

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:	\( N \)	\(=\)	\( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2960.a (trivial)

\(f(q)\)	\(=\)	\(q+3.26341 q^{3} +1.00000 q^{5} -1.62704 q^{7} +7.64987 q^{9} +O(q^{10})\)	\(q+3.26341 q^{3} +1.00000 q^{5} -1.62704 q^{7} +7.64987 q^{9} +3.45670 q^{11} +3.89604 q^{13} +3.26341 q^{15} -1.19317 q^{17} -0.150240 q^{19} -5.30970 q^{21} -8.16748 q^{23} +1.00000 q^{25} +15.1745 q^{27} -5.82395 q^{29} +8.17296 q^{31} +11.2807 q^{33} -1.62704 q^{35} -1.00000 q^{37} +12.7144 q^{39} +7.37060 q^{41} +6.34329 q^{43} +7.64987 q^{45} -7.46218 q^{47} -4.35275 q^{49} -3.89381 q^{51} +5.07012 q^{53} +3.45670 q^{55} -0.490295 q^{57} -0.0485215 q^{59} +0.702875 q^{61} -12.4466 q^{63} +3.89604 q^{65} -14.8446 q^{67} -26.6539 q^{69} -11.2807 q^{71} +3.47252 q^{73} +3.26341 q^{75} -5.62419 q^{77} +7.74357 q^{79} +26.5709 q^{81} -10.3096 q^{83} -1.19317 q^{85} -19.0060 q^{87} +14.9022 q^{89} -6.33901 q^{91} +26.6717 q^{93} -0.150240 q^{95} -8.30310 q^{97} +26.4434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 6 q^{5} - 8 q^{7} + 15 q^{9}+O(q^{10}) \) 6 * q - q^3 + 6 * q^5 - 8 * q^7 + 15 * q^9	\( 6 q - q^{3} + 6 q^{5} - 8 q^{7} + 15 q^{9} + 10 q^{13} - q^{15} + 3 q^{17} + 6 q^{19} + 9 q^{21} - 4 q^{23} + 6 q^{25} - 7 q^{27} + 3 q^{29} + 3 q^{31} + 9 q^{33} - 8 q^{35} - 6 q^{37} + 16 q^{39} + 10 q^{41} + 11 q^{43} + 15 q^{45} - 23 q^{47} + 8 q^{49} + 16 q^{51} + 10 q^{53} + 4 q^{57} - 6 q^{59} + q^{61} - 23 q^{63} + 10 q^{65} + 4 q^{67} - 2 q^{69} - 9 q^{71} + 11 q^{73} - q^{75} + 32 q^{77} + 14 q^{79} + 46 q^{81} - 11 q^{83} + 3 q^{85} - 32 q^{87} + 30 q^{89} + 4 q^{91} + 2 q^{93} + 6 q^{95} + 29 q^{97} + 39 q^{99}+O(q^{100}) \) 6 * q - q^3 + 6 * q^5 - 8 * q^7 + 15 * q^9 + 10 * q^13 - q^15 + 3 * q^17 + 6 * q^19 + 9 * q^21 - 4 * q^23 + 6 * q^25 - 7 * q^27 + 3 * q^29 + 3 * q^31 + 9 * q^33 - 8 * q^35 - 6 * q^37 + 16 * q^39 + 10 * q^41 + 11 * q^43 + 15 * q^45 - 23 * q^47 + 8 * q^49 + 16 * q^51 + 10 * q^53 + 4 * q^57 - 6 * q^59 + q^61 - 23 * q^63 + 10 * q^65 + 4 * q^67 - 2 * q^69 - 9 * q^71 + 11 * q^73 - q^75 + 32 * q^77 + 14 * q^79 + 46 * q^81 - 11 * q^83 + 3 * q^85 - 32 * q^87 + 30 * q^89 + 4 * q^91 + 2 * q^93 + 6 * q^95 + 29 * q^97 + 39 * q^99

Introduction

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