LMFDB - Embedded newform 6032.2.a.u.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6032,2,Mod(1,6032)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6032, 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("6032.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6032 = 2^{4} \cdot 13 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6032.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:	$48.1657624992$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 15x^{3} - 15x^{2} - 8x + 6 $ x^7 - 2x^6 - 7x^5 + 11x^4 + 15x^3 - 15x^2 - 8x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 377)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.05973$ of defining polynomial
Character	$\chi$	$=$	6032.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.182751 q^{3} +1.30841 q^{5} -4.37827 q^{7} -2.96660 q^{9} +O(q^{10})$	$q-0.182751 q^{3} +1.30841 q^{5} -4.37827 q^{7} -2.96660 q^{9} +6.13336 q^{11} -1.00000 q^{13} -0.239113 q^{15} +4.69496 q^{17} -4.05729 q^{19} +0.800135 q^{21} +4.43800 q^{23} -3.28807 q^{25} +1.09040 q^{27} +1.00000 q^{29} -5.70964 q^{31} -1.12088 q^{33} -5.72856 q^{35} +6.51879 q^{37} +0.182751 q^{39} -9.77623 q^{41} -3.97202 q^{43} -3.88152 q^{45} +6.34409 q^{47} +12.1693 q^{49} -0.858010 q^{51} -5.48828 q^{53} +8.02492 q^{55} +0.741476 q^{57} -0.0899747 q^{59} -10.2475 q^{61} +12.9886 q^{63} -1.30841 q^{65} +4.34415 q^{67} -0.811050 q^{69} -12.7962 q^{71} +7.05543 q^{73} +0.600900 q^{75} -26.8535 q^{77} +5.03346 q^{79} +8.70053 q^{81} -2.74656 q^{83} +6.14291 q^{85} -0.182751 q^{87} +15.5064 q^{89} +4.37827 q^{91} +1.04344 q^{93} -5.30859 q^{95} -3.20796 q^{97} -18.1952 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{3} - 2 q^{5} - 7 q^{7} + 5 q^{9}+O(q^{10}) $ 7 * q - 2 * q^3 - 2 * q^5 - 7 * q^7 + 5 * q^9	$ 7 q - 2 q^{3} - 2 q^{5} - 7 q^{7} + 5 q^{9} + 3 q^{11} - 7 q^{13} - 20 q^{15} + 14 q^{17} + 12 q^{19} + q^{21} - 5 q^{23} + 5 q^{25} - 14 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} + 6 q^{35} + 9 q^{37} + 2 q^{39} - 9 q^{41} - 24 q^{43} + 10 q^{45} + 9 q^{47} - 10 q^{49} - 5 q^{51} - 13 q^{53} - 7 q^{55} + 12 q^{57} - 13 q^{59} + 3 q^{61} - 2 q^{63} + 2 q^{65} + 7 q^{67} + 8 q^{69} - 22 q^{71} + 4 q^{73} + 29 q^{75} - 30 q^{77} - 48 q^{79} + 15 q^{81} + 30 q^{83} - 9 q^{85} - 2 q^{87} - 25 q^{89} + 7 q^{91} - 27 q^{93} - 23 q^{95} + 4 q^{97} + 25 q^{99}+O(q^{100}) $ 7 * q - 2 * q^3 - 2 * q^5 - 7 * q^7 + 5 * q^9 + 3 * q^11 - 7 * q^13 - 20 * q^15 + 14 * q^17 + 12 * q^19 + q^21 - 5 * q^23 + 5 * q^25 - 14 * q^27 + 7 * q^29 + 3 * q^31 - q^33 + 6 * q^35 + 9 * q^37 + 2 * q^39 - 9 * q^41 - 24 * q^43 + 10 * q^45 + 9 * q^47 - 10 * q^49 - 5 * q^51 - 13 * q^53 - 7 * q^55 + 12 * q^57 - 13 * q^59 + 3 * q^61 - 2 * q^63 + 2 * q^65 + 7 * q^67 + 8 * q^69 - 22 * q^71 + 4 * q^73 + 29 * q^75 - 30 * q^77 - 48 * q^79 + 15 * q^81 + 30 * q^83 - 9 * q^85 - 2 * q^87 - 25 * q^89 + 7 * q^91 - 27 * q^93 - 23 * q^95 + 4 * q^97 + 25 * 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
$3$	−0.182751	−0.105512	−0.0527558	−	0.998607i	$-0.516800\pi$
$3$	−0.182751	−0.105512	−0.0527558	+	0.998607i	$0.516800\pi$
$4$	0	0
$5$	1.30841	0.585137	0.292568	−	0.956245i	$-0.405490\pi$
$5$	1.30841	0.585137	0.292568	+	0.956245i	$0.405490\pi$
$6$	0	0
$7$	−4.37827	−1.65483	−0.827415	−	0.561590i	$-0.810190\pi$
$7$	−4.37827	−1.65483	−0.827415	+	0.561590i	$0.810190\pi$
$8$	0	0
$9$	−2.96660	−0.988867
$10$	0	0
$11$	6.13336	1.84928	0.924638	−	0.380846i	$-0.124367\pi$
$11$	6.13336	1.84928	0.924638	+	0.380846i	$0.124367\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	−0.239113	−0.0617387
$16$	0	0
$17$	4.69496	1.13870	0.569348	−	0.822097i	$-0.307196\pi$
$17$	4.69496	1.13870	0.569348	+	0.822097i	$0.307196\pi$
$18$	0	0
$19$	−4.05729	−0.930807	−0.465403	−	0.885099i	$-0.654091\pi$
$19$	−4.05729	−0.930807	−0.465403	+	0.885099i	$0.654091\pi$
$20$	0	0
$21$	0.800135	0.174604
$22$	0	0
$23$	4.43800	0.925387	0.462693	−	0.886518i	$-0.346883\pi$
$23$	4.43800	0.925387	0.462693	+	0.886518i	$0.346883\pi$
$24$	0	0
$25$	−3.28807	−0.657615
$26$	0	0
$27$	1.09040	0.209848
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−5.70964	−1.02548	−0.512741	−	0.858543i	$-0.671370\pi$
$31$	−5.70964	−1.02548	−0.512741	+	0.858543i	$0.671370\pi$
$32$	0	0
$33$	−1.12088	−0.195120
$34$	0	0
$35$	−5.72856	−0.968303
$36$	0	0
$37$	6.51879	1.07168	0.535842	−	0.844319i	$-0.319994\pi$
$37$	6.51879	1.07168	0.535842	+	0.844319i	$0.319994\pi$
$38$	0	0
$39$	0.182751	0.0292636
$40$	0	0
$41$	−9.77623	−1.52679	−0.763396	−	0.645931i	$-0.776469\pi$
$41$	−9.77623	−1.52679	−0.763396	+	0.645931i	$0.776469\pi$
$42$	0	0
$43$	−3.97202	−0.605728	−0.302864	−	0.953034i	$-0.597943\pi$
$43$	−3.97202	−0.605728	−0.302864	+	0.953034i	$0.597943\pi$
$44$	0	0
$45$	−3.88152	−0.578623
$46$	0	0
$47$	6.34409	0.925380	0.462690	−	0.886520i	$-0.346884\pi$
$47$	6.34409	0.925380	0.462690	+	0.886520i	$0.346884\pi$
$48$	0	0
$49$	12.1693	1.73846
$50$	0	0
$51$	−0.858010	−0.120145
$52$	0	0
$53$	−5.48828	−0.753873	−0.376936	−	0.926239i	$-0.623022\pi$
$53$	−5.48828	−0.753873	−0.376936	+	0.926239i	$0.623022\pi$
$54$	0	0
$55$	8.02492	1.08208
$56$	0	0
$57$	0.741476	0.0982108
$58$	0	0
$59$	−0.0899747	−0.0117137	−0.00585685	−	0.999983i	$-0.501864\pi$
$59$	−0.0899747	−0.0117137	−0.00585685	+	0.999983i	$0.501864\pi$
$60$	0	0
$61$	−10.2475	−1.31205	−0.656026	−	0.754738i	$-0.727764\pi$
$61$	−10.2475	−1.31205	−0.656026	+	0.754738i	$0.727764\pi$
$62$	0	0
$63$	12.9886	1.63641
$64$	0	0
$65$	−1.30841	−0.162288
$66$	0	0
$67$	4.34415	0.530723	0.265361	−	0.964149i	$-0.414509\pi$
$67$	4.34415	0.530723	0.265361	+	0.964149i	$0.414509\pi$
$68$	0	0
$69$	−0.811050	−0.0976389
$70$	0	0
$71$	−12.7962	−1.51863	−0.759316	−	0.650722i	$-0.774466\pi$
$71$	−12.7962	−1.51863	−0.759316	+	0.650722i	$0.774466\pi$
$72$	0	0
$73$	7.05543	0.825775	0.412888	−	0.910782i	$-0.364520\pi$
$73$	7.05543	0.825775	0.412888	+	0.910782i	$0.364520\pi$
$74$	0	0
$75$	0.600900	0.0693859
$76$	0	0
$77$	−26.8535	−3.06024
$78$	0	0
$79$	5.03346	0.566309	0.283154	−	0.959074i	$-0.408619\pi$
$79$	5.03346	0.566309	0.283154	+	0.959074i	$0.408619\pi$
$80$	0	0
$81$	8.70053	0.966726
$82$	0	0
$83$	−2.74656	−0.301475	−0.150737	−	0.988574i	$-0.548165\pi$
$83$	−2.74656	−0.301475	−0.150737	+	0.988574i	$0.548165\pi$
$84$	0	0
$85$	6.14291	0.666293
$86$	0	0
$87$	−0.182751	−0.0195930
$88$	0	0
$89$	15.5064	1.64367	0.821836	−	0.569725i	$-0.192950\pi$
$89$	15.5064	1.64367	0.821836	+	0.569725i	$0.192950\pi$
$90$	0	0
$91$	4.37827	0.458967
$92$	0	0
$93$	1.04344	0.108200
$94$	0	0
$95$	−5.30859	−0.544650
$96$	0	0
$97$	−3.20796	−0.325719	−0.162860	−	0.986649i	$-0.552072\pi$
$97$	−3.20796	−0.325719	−0.162860	+	0.986649i	$0.552072\pi$
$98$	0	0
$99$	−18.1952	−1.82869
$100$	0	0
$101$	10.5246	1.04724	0.523619	−	0.851952i	$-0.324581\pi$
$101$	10.5246	1.04724	0.523619	+	0.851952i	$0.324581\pi$
$102$	0	0
$103$	10.0836	0.993565	0.496782	−	0.867875i	$-0.334515\pi$
$103$	10.0836	0.993565	0.496782	+	0.867875i	$0.334515\pi$
$104$	0	0
$105$	1.04690	0.102167
$106$	0	0
$107$	−7.27190	−0.703001	−0.351500	−	0.936188i	$-0.614328\pi$
$107$	−7.27190	−0.703001	−0.351500	+	0.936188i	$0.614328\pi$
$108$	0	0
$109$	−0.290055	−0.0277822	−0.0138911	−	0.999904i	$-0.504422\pi$
$109$	−0.290055	−0.0277822	−0.0138911	+	0.999904i	$0.504422\pi$
$110$	0	0
$111$	−1.19132	−0.113075
$112$	0	0
$113$	−14.6497	−1.37813	−0.689065	−	0.724699i	$-0.741979\pi$
$113$	−14.6497	−1.37813	−0.689065	+	0.724699i	$0.741979\pi$
$114$	0	0
$115$	5.80670	0.541478
$116$	0	0
$117$	2.96660	0.274262
$118$	0	0
$119$	−20.5558	−1.88435
$120$	0	0
$121$	26.6181	2.41982
$122$	0	0
$123$	1.78662	0.161094
$124$	0	0
$125$	−10.8442	−0.969932
$126$	0	0
$127$	−12.2799	−1.08967	−0.544834	−	0.838544i	$-0.683407\pi$
$127$	−12.2799	−1.08967	−0.544834	+	0.838544i	$0.683407\pi$
$128$	0	0
$129$	0.725892	0.0639112
$130$	0	0
$131$	−10.8858	−0.951101	−0.475550	−	0.879689i	$-0.657751\pi$
$131$	−10.8858	−0.951101	−0.475550	+	0.879689i	$0.657751\pi$
$132$	0	0
$133$	17.7639	1.54033
$134$	0	0
$135$	1.42669	0.122790
$136$	0	0
$137$	17.5761	1.50163	0.750815	−	0.660512i	$-0.229661\pi$
$137$	17.5761	1.50163	0.750815	+	0.660512i	$0.229661\pi$
$138$	0	0
$139$	−8.64175	−0.732984	−0.366492	−	0.930421i	$-0.619441\pi$
$139$	−8.64175	−0.732984	−0.366492	+	0.930421i	$0.619441\pi$
$140$	0	0
$141$	−1.15939	−0.0976382
$142$	0	0
$143$	−6.13336	−0.512897
$144$	0	0
$145$	1.30841	0.108657
$146$	0	0
$147$	−2.22395	−0.183428
$148$	0	0
$149$	−14.7657	−1.20965	−0.604827	−	0.796357i	$-0.706758\pi$
$149$	−14.7657	−1.20965	−0.604827	+	0.796357i	$0.706758\pi$
$150$	0	0
$151$	−11.3034	−0.919856	−0.459928	−	0.887956i	$-0.652125\pi$
$151$	−11.3034	−0.919856	−0.459928	+	0.887956i	$0.652125\pi$
$152$	0	0
$153$	−13.9281	−1.12602
$154$	0	0
$155$	−7.47053	−0.600047
$156$	0	0
$157$	−16.2180	−1.29434	−0.647171	−	0.762345i	$-0.724048\pi$
$157$	−16.2180	−1.29434	−0.647171	+	0.762345i	$0.724048\pi$
$158$	0	0
$159$	1.00299	0.0795423
$160$	0	0
$161$	−19.4308	−1.53136
$162$	0	0
$163$	−7.79883	−0.610851	−0.305426	−	0.952216i	$-0.598799\pi$
$163$	−7.79883	−0.610851	−0.305426	+	0.952216i	$0.598799\pi$
$164$	0	0
$165$	−1.46656	−0.114172
$166$	0	0
$167$	−19.5066	−1.50947	−0.754733	−	0.656032i	$-0.772234\pi$
$167$	−19.5066	−1.50947	−0.754733	+	0.656032i	$0.772234\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	12.0364	0.920445
$172$	0	0
$173$	−20.6992	−1.57373	−0.786865	−	0.617125i	$-0.788297\pi$
$173$	−20.6992	−1.57373	−0.786865	+	0.617125i	$0.788297\pi$
$174$	0	0
$175$	14.3961	1.08824
$176$	0	0
$177$	0.0164430	0.00123593
$178$	0	0
$179$	8.25743	0.617189	0.308595	−	0.951194i	$-0.400141\pi$
$179$	8.25743	0.617189	0.308595	+	0.951194i	$0.400141\pi$
$180$	0	0
$181$	−1.81702	−0.135058	−0.0675289	−	0.997717i	$-0.521511\pi$
$181$	−1.81702	−0.135058	−0.0675289	+	0.997717i	$0.521511\pi$
$182$	0	0
$183$	1.87274	0.138437
$184$	0	0
$185$	8.52923	0.627081
$186$	0	0
$187$	28.7959	2.10576
$188$	0	0
$189$	−4.77408	−0.347264
$190$	0	0
$191$	−9.81383	−0.710104	−0.355052	−	0.934847i	$-0.615537\pi$
$191$	−9.81383	−0.710104	−0.355052	+	0.934847i	$0.615537\pi$
$192$	0	0
$193$	−1.91532	−0.137868	−0.0689339	−	0.997621i	$-0.521960\pi$
$193$	−1.91532	−0.137868	−0.0689339	+	0.997621i	$0.521960\pi$
$194$	0	0
$195$	0.239113	0.0171232
$196$	0	0
$197$	−26.0799	−1.85811	−0.929057	−	0.369936i	$-0.879380\pi$
$197$	−26.0799	−1.85811	−0.929057	+	0.369936i	$0.879380\pi$
$198$	0	0
$199$	−16.4593	−1.16677	−0.583383	−	0.812197i	$-0.698271\pi$
$199$	−16.4593	−1.16677	−0.583383	+	0.812197i	$0.698271\pi$
$200$	0	0
$201$	−0.793900	−0.0559974
$202$	0	0
$203$	−4.37827	−0.307294
$204$	0	0
$205$	−12.7913	−0.893382
$206$	0	0
$207$	−13.1658	−0.915085
$208$	0	0
$209$	−24.8848	−1.72132
$210$	0	0
$211$	3.55419	0.244680	0.122340	−	0.992488i	$-0.460960\pi$
$211$	3.55419	0.244680	0.122340	+	0.992488i	$0.460960\pi$
$212$	0	0
$213$	2.33853	0.160233
$214$	0	0
$215$	−5.19702	−0.354434
$216$	0	0
$217$	24.9983	1.69700
$218$	0	0
$219$	−1.28939	−0.0871288
$220$	0	0
$221$	−4.69496	−0.315817
$222$	0	0
$223$	−10.5580	−0.707015	−0.353508	−	0.935432i	$-0.615011\pi$
$223$	−10.5580	−0.707015	−0.353508	+	0.935432i	$0.615011\pi$
$224$	0	0
$225$	9.75441	0.650294
$226$	0	0
$227$	6.47498	0.429760	0.214880	−	0.976641i	$-0.431064\pi$
$227$	6.47498	0.429760	0.214880	+	0.976641i	$0.431064\pi$
$228$	0	0
$229$	2.01870	0.133400	0.0666998	−	0.997773i	$-0.478753\pi$
$229$	2.01870	0.133400	0.0666998	+	0.997773i	$0.478753\pi$
$230$	0	0
$231$	4.90751	0.322890
$232$	0	0
$233$	0.631863	0.0413947	0.0206974	−	0.999786i	$-0.493411\pi$
$233$	0.631863	0.0413947	0.0206974	+	0.999786i	$0.493411\pi$
$234$	0	0
$235$	8.30064	0.541474
$236$	0	0
$237$	−0.919871	−0.0597521
$238$	0	0
$239$	1.91133	0.123633	0.0618167	−	0.998088i	$-0.480311\pi$
$239$	1.91133	0.123633	0.0618167	+	0.998088i	$0.480311\pi$
$240$	0	0
$241$	−22.6798	−1.46093	−0.730466	−	0.682949i	$-0.760697\pi$
$241$	−22.6798	−1.46093	−0.730466	+	0.682949i	$0.760697\pi$
$242$	0	0
$243$	−4.86125	−0.311849
$244$	0	0
$245$	15.9223	1.01724
$246$	0	0
$247$	4.05729	0.258159
$248$	0	0
$249$	0.501938	0.0318090
$250$	0	0
$251$	−6.61614	−0.417607	−0.208803	−	0.977958i	$-0.566957\pi$
$251$	−6.61614	−0.417607	−0.208803	+	0.977958i	$0.566957\pi$
$252$	0	0
$253$	27.2198	1.71130
$254$	0	0
$255$	−1.12263	−0.0703015
$256$	0	0
$257$	4.83968	0.301891	0.150945	−	0.988542i	$-0.451768\pi$
$257$	4.83968	0.301891	0.150945	+	0.988542i	$0.451768\pi$
$258$	0	0
$259$	−28.5410	−1.77345
$260$	0	0
$261$	−2.96660	−0.183628
$262$	0	0
$263$	−10.4612	−0.645063	−0.322531	−	0.946559i	$-0.604534\pi$
$263$	−10.4612	−0.645063	−0.322531	+	0.946559i	$0.604534\pi$
$264$	0	0
$265$	−7.18090	−0.441119
$266$	0	0
$267$	−2.83381	−0.173426
$268$	0	0
$269$	4.46517	0.272246	0.136123	−	0.990692i	$-0.456536\pi$
$269$	4.46517	0.272246	0.136123	+	0.990692i	$0.456536\pi$
$270$	0	0
$271$	19.0288	1.15591	0.577957	−	0.816067i	$-0.303850\pi$
$271$	19.0288	1.15591	0.577957	+	0.816067i	$0.303850\pi$
$272$	0	0
$273$	−0.800135	−0.0484263
$274$	0	0
$275$	−20.1669	−1.21611
$276$	0	0
$277$	−14.6879	−0.882509	−0.441254	−	0.897382i	$-0.645466\pi$
$277$	−14.6879	−0.882509	−0.441254	+	0.897382i	$0.645466\pi$
$278$	0	0
$279$	16.9382	1.01407
$280$	0	0
$281$	−20.7484	−1.23774	−0.618872	−	0.785491i	$-0.712410\pi$
$281$	−20.7484	−1.23774	−0.618872	+	0.785491i	$0.712410\pi$
$282$	0	0
$283$	−11.3900	−0.677067	−0.338534	−	0.940954i	$-0.609931\pi$
$283$	−11.3900	−0.677067	−0.338534	+	0.940954i	$0.609931\pi$
$284$	0	0
$285$	0.970151	0.0574668
$286$	0	0
$287$	42.8030	2.52658
$288$	0	0
$289$	5.04265	0.296627
$290$	0	0
$291$	0.586260	0.0343671
$292$	0	0
$293$	25.4063	1.48425	0.742125	−	0.670262i	$-0.233818\pi$
$293$	25.4063	1.48425	0.742125	+	0.670262i	$0.233818\pi$
$294$	0	0
$295$	−0.117723	−0.00685412
$296$	0	0
$297$	6.68784	0.388068
$298$	0	0
$299$	−4.43800	−0.256656
$300$	0	0
$301$	17.3906	1.00238
$302$	0	0
$303$	−1.92339	−0.110496
$304$	0	0
$305$	−13.4078	−0.767731
$306$	0	0
$307$	7.63912	0.435988	0.217994	−	0.975950i	$-0.430049\pi$
$307$	7.63912	0.435988	0.217994	+	0.975950i	$0.430049\pi$
$308$	0	0
$309$	−1.84279	−0.104832
$310$	0	0
$311$	−25.4672	−1.44411	−0.722055	−	0.691835i	$-0.756802\pi$
$311$	−25.4672	−1.44411	−0.722055	+	0.691835i	$0.756802\pi$
$312$	0	0
$313$	8.59915	0.486053	0.243026	−	0.970020i	$-0.421860\pi$
$313$	8.59915	0.486053	0.243026	+	0.970020i	$0.421860\pi$
$314$	0	0
$315$	16.9943	0.957523
$316$	0	0
$317$	−28.3319	−1.59128	−0.795640	−	0.605769i	$-0.792865\pi$
$317$	−28.3319	−1.59128	−0.795640	+	0.605769i	$0.792865\pi$
$318$	0	0
$319$	6.13336	0.343402
$320$	0	0
$321$	1.32895	0.0741747
$322$	0	0
$323$	−19.0488	−1.05991
$324$	0	0
$325$	3.28807	0.182390
$326$	0	0
$327$	0.0530079	0.00293134
$328$	0	0
$329$	−27.7761	−1.53135
$330$	0	0
$331$	13.8113	0.759140	0.379570	−	0.925163i	$-0.376072\pi$
$331$	13.8113	0.759140	0.379570	+	0.925163i	$0.376072\pi$
$332$	0	0
$333$	−19.3387	−1.05975
$334$	0	0
$335$	5.68392	0.310545
$336$	0	0
$337$	5.42100	0.295301	0.147650	−	0.989040i	$-0.452829\pi$
$337$	5.42100	0.295301	0.147650	+	0.989040i	$0.452829\pi$
$338$	0	0
$339$	2.67726	0.145409
$340$	0	0
$341$	−35.0193	−1.89640
$342$	0	0
$343$	−22.6324	−1.22203
$344$	0	0
$345$	−1.06118	−0.0571321
$346$	0	0
$347$	−6.65245	−0.357122	−0.178561	−	0.983929i	$-0.557144\pi$
$347$	−6.65245	−0.357122	−0.178561	+	0.983929i	$0.557144\pi$
$348$	0	0
$349$	−22.6263	−1.21116	−0.605579	−	0.795785i	$-0.707058\pi$
$349$	−22.6263	−1.21116	−0.605579	+	0.795785i	$0.707058\pi$
$350$	0	0
$351$	−1.09040	−0.0582015
$352$	0	0
$353$	−12.2725	−0.653198	−0.326599	−	0.945163i	$-0.605903\pi$
$353$	−12.2725	−0.653198	−0.326599	+	0.945163i	$0.605903\pi$
$354$	0	0
$355$	−16.7426	−0.888607
$356$	0	0
$357$	3.75660	0.198820
$358$	0	0
$359$	22.9828	1.21299	0.606493	−	0.795089i	$-0.292576\pi$
$359$	22.9828	1.21299	0.606493	+	0.795089i	$0.292576\pi$
$360$	0	0
$361$	−2.53837	−0.133598
$362$	0	0
$363$	−4.86449	−0.255319
$364$	0	0
$365$	9.23136	0.483192
$366$	0	0
$367$	−5.79365	−0.302426	−0.151213	−	0.988501i	$-0.548318\pi$
$367$	−5.79365	−0.302426	−0.151213	+	0.988501i	$0.548318\pi$
$368$	0	0
$369$	29.0022	1.50979
$370$	0	0
$371$	24.0292	1.24753
$372$	0	0
$373$	−27.0146	−1.39876	−0.699380	−	0.714750i	$-0.746541\pi$
$373$	−27.0146	−1.39876	−0.699380	+	0.714750i	$0.746541\pi$
$374$	0	0
$375$	1.98179	0.102339
$376$	0	0
$377$	−1.00000	−0.0515026
$378$	0	0
$379$	−8.09669	−0.415899	−0.207950	−	0.978140i	$-0.566679\pi$
$379$	−8.09669	−0.415899	−0.207950	+	0.978140i	$0.566679\pi$
$380$	0	0
$381$	2.24417	0.114972
$382$	0	0
$383$	20.8138	1.06354	0.531768	−	0.846890i	$-0.321528\pi$
$383$	20.8138	1.06354	0.531768	+	0.846890i	$0.321528\pi$
$384$	0	0
$385$	−35.1353	−1.79066
$386$	0	0
$387$	11.7834	0.598984
$388$	0	0
$389$	38.3720	1.94554	0.972769	−	0.231777i	$-0.0744539\pi$
$389$	38.3720	1.94554	0.972769	+	0.231777i	$0.0744539\pi$
$390$	0	0
$391$	20.8362	1.05373
$392$	0	0
$393$	1.98940	0.100352
$394$	0	0
$395$	6.58581	0.331368
$396$	0	0
$397$	12.2896	0.616797	0.308398	−	0.951257i	$-0.400207\pi$
$397$	12.2896	0.616797	0.308398	+	0.951257i	$0.400207\pi$
$398$	0	0
$399$	−3.24638	−0.162522
$400$	0	0
$401$	−13.0223	−0.650304	−0.325152	−	0.945662i	$-0.605416\pi$
$401$	−13.0223	−0.650304	−0.325152	+	0.945662i	$0.605416\pi$
$402$	0	0
$403$	5.70964	0.284417
$404$	0	0
$405$	11.3838	0.565667
$406$	0	0
$407$	39.9821	1.98184
$408$	0	0
$409$	30.1658	1.49160	0.745802	−	0.666168i	$-0.232067\pi$
$409$	30.1658	1.49160	0.745802	+	0.666168i	$0.232067\pi$
$410$	0	0
$411$	−3.21206	−0.158439
$412$	0	0
$413$	0.393933	0.0193842
$414$	0	0
$415$	−3.59362	−0.176404
$416$	0	0
$417$	1.57929	0.0773382
$418$	0	0
$419$	27.4156	1.33934	0.669670	−	0.742658i	$-0.266435\pi$
$419$	27.4156	1.33934	0.669670	+	0.742658i	$0.266435\pi$
$420$	0	0
$421$	20.6598	1.00690	0.503448	−	0.864025i	$-0.332064\pi$
$421$	20.6598	1.00690	0.503448	+	0.864025i	$0.332064\pi$
$422$	0	0
$423$	−18.8204	−0.915078
$424$	0	0
$425$	−15.4374	−0.748823
$426$	0	0
$427$	44.8661	2.17123
$428$	0	0
$429$	1.12088	0.0541165
$430$	0	0
$431$	10.1212	0.487521	0.243760	−	0.969835i	$-0.421619\pi$
$431$	10.1212	0.487521	0.243760	+	0.969835i	$0.421619\pi$
$432$	0	0
$433$	32.0445	1.53996	0.769980	−	0.638068i	$-0.220266\pi$
$433$	32.0445	1.53996	0.769980	+	0.638068i	$0.220266\pi$
$434$	0	0
$435$	−0.239113	−0.0114646
$436$	0	0
$437$	−18.0063	−0.861356
$438$	0	0
$439$	2.42761	0.115864	0.0579318	−	0.998321i	$-0.481549\pi$
$439$	2.42761	0.115864	0.0579318	+	0.998321i	$0.481549\pi$
$440$	0	0
$441$	−36.1013	−1.71911
$442$	0	0
$443$	9.90253	0.470483	0.235242	−	0.971937i	$-0.424412\pi$
$443$	9.90253	0.470483	0.235242	+	0.971937i	$0.424412\pi$
$444$	0	0
$445$	20.2886	0.961773
$446$	0	0
$447$	2.69845	0.127632
$448$	0	0
$449$	−30.0913	−1.42010	−0.710048	−	0.704153i	$-0.751327\pi$
$449$	−30.0913	−1.42010	−0.710048	+	0.704153i	$0.751327\pi$
$450$	0	0
$451$	−59.9611	−2.82346
$452$	0	0
$453$	2.06571	0.0970554
$454$	0	0
$455$	5.72856	0.268559
$456$	0	0
$457$	−31.7704	−1.48616	−0.743079	−	0.669203i	$-0.766636\pi$
$457$	−31.7704	−1.48616	−0.743079	+	0.669203i	$0.766636\pi$
$458$	0	0
$459$	5.11940	0.238953
$460$	0	0
$461$	−2.05353	−0.0956426	−0.0478213	−	0.998856i	$-0.515228\pi$
$461$	−2.05353	−0.0956426	−0.0478213	+	0.998856i	$0.515228\pi$
$462$	0	0
$463$	−13.7494	−0.638990	−0.319495	−	0.947588i	$-0.603513\pi$
$463$	−13.7494	−0.638990	−0.319495	+	0.947588i	$0.603513\pi$
$464$	0	0
$465$	1.36525	0.0633119
$466$	0	0
$467$	−8.85610	−0.409811	−0.204906	−	0.978782i	$-0.565689\pi$
$467$	−8.85610	−0.409811	−0.204906	+	0.978782i	$0.565689\pi$
$468$	0	0
$469$	−19.0199	−0.878256
$470$	0	0
$471$	2.96387	0.136568
$472$	0	0
$473$	−24.3618	−1.12016
$474$	0	0
$475$	13.3407	0.612112
$476$	0	0
$477$	16.2815	0.745480
$478$	0	0
$479$	13.9990	0.639629	0.319815	−	0.947480i	$-0.396379\pi$
$479$	13.9990	0.639629	0.319815	+	0.947480i	$0.396379\pi$
$480$	0	0
$481$	−6.51879	−0.297231
$482$	0	0
$483$	3.55100	0.161576
$484$	0	0
$485$	−4.19732	−0.190590
$486$	0	0
$487$	−24.8097	−1.12423	−0.562117	−	0.827058i	$-0.690013\pi$
$487$	−24.8097	−1.12423	−0.562117	+	0.827058i	$0.690013\pi$
$488$	0	0
$489$	1.42525	0.0644518
$490$	0	0
$491$	10.3007	0.464864	0.232432	−	0.972613i	$-0.425332\pi$
$491$	10.3007	0.464864	0.232432	+	0.972613i	$0.425332\pi$
$492$	0	0
$493$	4.69496	0.211450
$494$	0	0
$495$	−23.8067	−1.07003
$496$	0	0
$497$	56.0253	2.51308
$498$	0	0
$499$	18.2579	0.817337	0.408668	−	0.912683i	$-0.365993\pi$
$499$	18.2579	0.817337	0.408668	+	0.912683i	$0.365993\pi$
$500$	0	0
$501$	3.56486	0.159266
$502$	0	0
$503$	1.77689	0.0792278	0.0396139	−	0.999215i	$-0.487387\pi$
$503$	1.77689	0.0792278	0.0396139	+	0.999215i	$0.487387\pi$
$504$	0	0
$505$	13.7705	0.612778
$506$	0	0
$507$	−0.182751	−0.00811627
$508$	0	0
$509$	−1.86113	−0.0824931	−0.0412466	−	0.999149i	$-0.513133\pi$
$509$	−1.86113	−0.0824931	−0.0412466	+	0.999149i	$0.513133\pi$
$510$	0	0
$511$	−30.8906	−1.36652
$512$	0	0
$513$	−4.42409	−0.195328
$514$	0	0
$515$	13.1934	0.581371
$516$	0	0
$517$	38.9105	1.71128
$518$	0	0
$519$	3.78280	0.166047
$520$	0	0
$521$	7.26113	0.318116	0.159058	−	0.987269i	$-0.449154\pi$
$521$	7.26113	0.318116	0.159058	+	0.987269i	$0.449154\pi$
$522$	0	0
$523$	16.1735	0.707216	0.353608	−	0.935394i	$-0.384955\pi$
$523$	16.1735	0.707216	0.353608	+	0.935394i	$0.384955\pi$
$524$	0	0
$525$	−2.63090	−0.114822
$526$	0	0
$527$	−26.8065	−1.16771
$528$	0	0
$529$	−3.30417	−0.143660
$530$	0	0
$531$	0.266919	0.0115833
$532$	0	0
$533$	9.77623	0.423456
$534$	0	0
$535$	−9.51459	−0.411352
$536$	0	0
$537$	−1.50906	−0.0651206
$538$	0	0
$539$	74.6384	3.21490
$540$	0	0
$541$	−17.5124	−0.752915	−0.376458	−	0.926434i	$-0.622858\pi$
$541$	−17.5124	−0.752915	−0.376458	+	0.926434i	$0.622858\pi$
$542$	0	0
$543$	0.332062	0.0142501
$544$	0	0
$545$	−0.379509	−0.0162564
$546$	0	0
$547$	−19.1339	−0.818105	−0.409052	−	0.912511i	$-0.634141\pi$
$547$	−19.1339	−0.818105	−0.409052	+	0.912511i	$0.634141\pi$
$548$	0	0
$549$	30.4001	1.29745
$550$	0	0
$551$	−4.05729	−0.172847
$552$	0	0
$553$	−22.0379	−0.937145
$554$	0	0
$555$	−1.55873	−0.0661643
$556$	0	0
$557$	−23.7295	−1.00545	−0.502726	−	0.864446i	$-0.667670\pi$
$557$	−23.7295	−1.00545	−0.502726	+	0.864446i	$0.667670\pi$
$558$	0	0
$559$	3.97202	0.167999
$560$	0	0
$561$	−5.26248	−0.222182
$562$	0	0
$563$	15.1293	0.637625	0.318812	−	0.947818i	$-0.396716\pi$
$563$	15.1293	0.637625	0.318812	+	0.947818i	$0.396716\pi$
$564$	0	0
$565$	−19.1678	−0.806395
$566$	0	0
$567$	−38.0933	−1.59977
$568$	0	0
$569$	25.6303	1.07448	0.537239	−	0.843430i	$-0.319467\pi$
$569$	25.6303	1.07448	0.537239	+	0.843430i	$0.319467\pi$
$570$	0	0
$571$	−11.2121	−0.469212	−0.234606	−	0.972091i	$-0.575380\pi$
$571$	−11.2121	−0.469212	−0.234606	+	0.972091i	$0.575380\pi$
$572$	0	0
$573$	1.79349	0.0749241
$574$	0	0
$575$	−14.5925	−0.608548
$576$	0	0
$577$	12.1757	0.506883	0.253441	−	0.967351i	$-0.418437\pi$
$577$	12.1757	0.506883	0.253441	+	0.967351i	$0.418437\pi$
$578$	0	0
$579$	0.350028	0.0145466
$580$	0	0
$581$	12.0252	0.498889
$582$	0	0
$583$	−33.6616	−1.39412
$584$	0	0
$585$	3.88152	0.160481
$586$	0	0
$587$	−2.17164	−0.0896332	−0.0448166	−	0.998995i	$-0.514270\pi$
$587$	−2.17164	−0.0896332	−0.0448166	+	0.998995i	$0.514270\pi$
$588$	0	0
$589$	23.1657	0.954525
$590$	0	0
$591$	4.76613	0.196052
$592$	0	0
$593$	−31.2492	−1.28325	−0.641625	−	0.767019i	$-0.721739\pi$
$593$	−31.2492	−1.28325	−0.641625	+	0.767019i	$0.721739\pi$
$594$	0	0
$595$	−26.8953	−1.10260
$596$	0	0
$597$	3.00795	0.123107
$598$	0	0
$599$	−10.5234	−0.429972	−0.214986	−	0.976617i	$-0.568971\pi$
$599$	−10.5234	−0.429972	−0.214986	+	0.976617i	$0.568971\pi$
$600$	0	0
$601$	−15.0448	−0.613691	−0.306846	−	0.951759i	$-0.599274\pi$
$601$	−15.0448	−0.613691	−0.306846	+	0.951759i	$0.599274\pi$
$602$	0	0
$603$	−12.8874	−0.524814
$604$	0	0
$605$	34.8272	1.41593
$606$	0	0
$607$	7.79470	0.316377	0.158189	−	0.987409i	$-0.449435\pi$
$607$	7.79470	0.316377	0.158189	+	0.987409i	$0.449435\pi$
$608$	0	0
$609$	0.800135	0.0324231
$610$	0	0
$611$	−6.34409	−0.256654
$612$	0	0
$613$	−11.8571	−0.478903	−0.239452	−	0.970908i	$-0.576968\pi$
$613$	−11.8571	−0.478903	−0.239452	+	0.970908i	$0.576968\pi$
$614$	0	0
$615$	2.33762	0.0942621
$616$	0	0
$617$	10.1008	0.406645	0.203322	−	0.979112i	$-0.434826\pi$
$617$	10.1008	0.406645	0.203322	+	0.979112i	$0.434826\pi$
$618$	0	0
$619$	38.9997	1.56753	0.783765	−	0.621057i	$-0.213296\pi$
$619$	38.9997	1.56753	0.783765	+	0.621057i	$0.213296\pi$
$620$	0	0
$621$	4.83921	0.194191
$622$	0	0
$623$	−67.8910	−2.72000
$624$	0	0
$625$	2.25180	0.0900719
$626$	0	0
$627$	4.54773	0.181619
$628$	0	0
$629$	30.6055	1.22032
$630$	0	0
$631$	−22.6127	−0.900195	−0.450098	−	0.892979i	$-0.648611\pi$
$631$	−22.6127	−0.900195	−0.450098	+	0.892979i	$0.648611\pi$
$632$	0	0
$633$	−0.649533	−0.0258166
$634$	0	0
$635$	−16.0671	−0.637605
$636$	0	0
$637$	−12.1693	−0.482163
$638$	0	0
$639$	37.9613	1.50173
$640$	0	0
$641$	−14.2308	−0.562081	−0.281041	−	0.959696i	$-0.590680\pi$
$641$	−14.2308	−0.562081	−0.281041	+	0.959696i	$0.590680\pi$
$642$	0	0
$643$	−26.5633	−1.04755	−0.523777	−	0.851855i	$-0.675477\pi$
$643$	−26.5633	−1.04755	−0.523777	+	0.851855i	$0.675477\pi$
$644$	0	0
$645$	0.949762	0.0373968
$646$	0	0
$647$	21.8363	0.858475	0.429237	−	0.903192i	$-0.358782\pi$
$647$	21.8363	0.858475	0.429237	+	0.903192i	$0.358782\pi$
$648$	0	0
$649$	−0.551847	−0.0216619
$650$	0	0
$651$	−4.56848	−0.179053
$652$	0	0
$653$	2.53370	0.0991513	0.0495756	−	0.998770i	$-0.484213\pi$
$653$	2.53370	0.0991513	0.0495756	+	0.998770i	$0.484213\pi$
$654$	0	0
$655$	−14.2431	−0.556524
$656$	0	0
$657$	−20.9306	−0.816582
$658$	0	0
$659$	23.2185	0.904463	0.452231	−	0.891901i	$-0.350628\pi$
$659$	23.2185	0.904463	0.452231	+	0.891901i	$0.350628\pi$
$660$	0	0
$661$	5.74211	0.223342	0.111671	−	0.993745i	$-0.464380\pi$
$661$	5.74211	0.223342	0.111671	+	0.993745i	$0.464380\pi$
$662$	0	0
$663$	0.858010	0.0333223
$664$	0	0
$665$	23.2424	0.901303
$666$	0	0
$667$	4.43800	0.171840
$668$	0	0
$669$	1.92949	0.0745983
$670$	0	0
$671$	−62.8513	−2.42635
$672$	0	0
$673$	−22.0176	−0.848718	−0.424359	−	0.905494i	$-0.639500\pi$
$673$	−22.0176	−0.848718	−0.424359	+	0.905494i	$0.639500\pi$
$674$	0	0
$675$	−3.58533	−0.137999
$676$	0	0
$677$	−6.40571	−0.246191	−0.123096	−	0.992395i	$-0.539282\pi$
$677$	−6.40571	−0.246191	−0.123096	+	0.992395i	$0.539282\pi$
$678$	0	0
$679$	14.0453	0.539010
$680$	0	0
$681$	−1.18331	−0.0453446
$682$	0	0
$683$	6.56249	0.251107	0.125553	−	0.992087i	$-0.459929\pi$
$683$	6.56249	0.251107	0.125553	+	0.992087i	$0.459929\pi$
$684$	0	0
$685$	22.9967	0.878660
$686$	0	0
$687$	−0.368921	−0.0140752
$688$	0	0
$689$	5.48828	0.209087
$690$	0	0
$691$	38.0793	1.44860	0.724302	−	0.689483i	$-0.242162\pi$
$691$	38.0793	1.44860	0.724302	+	0.689483i	$0.242162\pi$
$692$	0	0
$693$	79.6636	3.02617
$694$	0	0
$695$	−11.3069	−0.428896
$696$	0	0
$697$	−45.8990	−1.73855
$698$	0	0
$699$	−0.115474	−0.00436762
$700$	0	0
$701$	38.8752	1.46829	0.734147	−	0.678990i	$-0.237582\pi$
$701$	38.8752	1.46829	0.734147	+	0.678990i	$0.237582\pi$
$702$	0	0
$703$	−26.4487	−0.997530
$704$	0	0
$705$	−1.51695	−0.0571317
$706$	0	0
$707$	−46.0796	−1.73300
$708$	0	0
$709$	8.20526	0.308155	0.154077	−	0.988059i	$-0.450759\pi$
$709$	8.20526	0.308155	0.154077	+	0.988059i	$0.450759\pi$
$710$	0	0
$711$	−14.9323	−0.560004
$712$	0	0
$713$	−25.3394	−0.948967
$714$	0	0
$715$	−8.02492	−0.300115
$716$	0	0
$717$	−0.349297	−0.0130448
$718$	0	0
$719$	−18.3539	−0.684483	−0.342242	−	0.939612i	$-0.611186\pi$
$719$	−18.3539	−0.684483	−0.342242	+	0.939612i	$0.611186\pi$
$720$	0	0
$721$	−44.1486	−1.64418
$722$	0	0
$723$	4.14475	0.154145
$724$	0	0
$725$	−3.28807	−0.122116
$726$	0	0
$727$	14.5606	0.540024	0.270012	−	0.962857i	$-0.412972\pi$
$727$	14.5606	0.540024	0.270012	+	0.962857i	$0.412972\pi$
$728$	0	0
$729$	−25.2132	−0.933822
$730$	0	0
$731$	−18.6485	−0.689739
$732$	0	0
$733$	−7.10508	−0.262432	−0.131216	−	0.991354i	$-0.541888\pi$
$733$	−7.10508	−0.262432	−0.131216	+	0.991354i	$0.541888\pi$
$734$	0	0
$735$	−2.90982	−0.107331
$736$	0	0
$737$	26.6442	0.981453
$738$	0	0
$739$	1.66940	0.0614100	0.0307050	−	0.999528i	$-0.490225\pi$
$739$	1.66940	0.0614100	0.0307050	+	0.999528i	$0.490225\pi$
$740$	0	0
$741$	−0.741476	−0.0272388
$742$	0	0
$743$	−13.2181	−0.484926	−0.242463	−	0.970161i	$-0.577955\pi$
$743$	−13.2181	−0.484926	−0.242463	+	0.970161i	$0.577955\pi$
$744$	0	0
$745$	−19.3195	−0.707813
$746$	0	0
$747$	8.14796	0.298118
$748$	0	0
$749$	31.8383	1.16335
$750$	0	0
$751$	−39.3677	−1.43655	−0.718274	−	0.695760i	$-0.755068\pi$
$751$	−39.3677	−1.43655	−0.718274	+	0.695760i	$0.755068\pi$
$752$	0	0
$753$	1.20911	0.0440623
$754$	0	0
$755$	−14.7894	−0.538242
$756$	0	0
$757$	−23.6529	−0.859678	−0.429839	−	0.902906i	$-0.641430\pi$
$757$	−23.6529	−0.859678	−0.429839	+	0.902906i	$0.641430\pi$
$758$	0	0
$759$	−4.97446	−0.180561
$760$	0	0
$761$	−41.5503	−1.50620	−0.753099	−	0.657907i	$-0.771442\pi$
$761$	−41.5503	−1.50620	−0.753099	+	0.657907i	$0.771442\pi$
$762$	0	0
$763$	1.26994	0.0459748
$764$	0	0
$765$	−18.2236	−0.658875
$766$	0	0
$767$	0.0899747	0.00324880
$768$	0	0
$769$	17.0760	0.615775	0.307888	−	0.951423i	$-0.400378\pi$
$769$	17.0760	0.615775	0.307888	+	0.951423i	$0.400378\pi$
$770$	0	0
$771$	−0.884457	−0.0318529
$772$	0	0
$773$	−16.2751	−0.585373	−0.292687	−	0.956208i	$-0.594549\pi$
$773$	−16.2751	−0.585373	−0.292687	+	0.956208i	$0.594549\pi$
$774$	0	0
$775$	18.7737	0.674372
$776$	0	0
$777$	5.21591	0.187120
$778$	0	0
$779$	39.6651	1.42115
$780$	0	0
$781$	−78.4838	−2.80837
$782$	0	0
$783$	1.09040	0.0389679
$784$	0	0
$785$	−21.2198	−0.757367
$786$	0	0
$787$	20.0020	0.712995	0.356498	−	0.934296i	$-0.383971\pi$
$787$	20.0020	0.712995	0.356498	+	0.934296i	$0.383971\pi$
$788$	0	0
$789$	1.91179	0.0680616
$790$	0	0
$791$	64.1405	2.28057
$792$	0	0
$793$	10.2475	0.363898
$794$	0	0
$795$	1.31232	0.0465431
$796$	0	0
$797$	−20.7288	−0.734250	−0.367125	−	0.930172i	$-0.619658\pi$
$797$	−20.7288	−0.734250	−0.367125	+	0.930172i	$0.619658\pi$
$798$	0	0
$799$	29.7852	1.05373
$800$	0	0
$801$	−46.0012	−1.62537
$802$	0	0
$803$	43.2734	1.52709
$804$	0	0
$805$	−25.4233	−0.896054
$806$	0	0
$807$	−0.816015	−0.0287251
$808$	0	0
$809$	26.0269	0.915056	0.457528	−	0.889195i	$-0.348735\pi$
$809$	26.0269	0.915056	0.457528	+	0.889195i	$0.348735\pi$
$810$	0	0
$811$	33.9473	1.19205	0.596026	−	0.802965i	$-0.296746\pi$
$811$	33.9473	1.19205	0.596026	+	0.802965i	$0.296746\pi$
$812$	0	0
$813$	−3.47753	−0.121962
$814$	0	0
$815$	−10.2040	−0.357432
$816$	0	0
$817$	16.1157	0.563815
$818$	0	0
$819$	−12.9886	−0.453858
$820$	0	0
$821$	51.8615	1.80998	0.904990	−	0.425433i	$-0.139878\pi$
$821$	51.8615	1.80998	0.904990	+	0.425433i	$0.139878\pi$
$822$	0	0
$823$	−56.5300	−1.97051	−0.985256	−	0.171089i	$-0.945272\pi$
$823$	−56.5300	−1.97051	−0.985256	+	0.171089i	$0.945272\pi$
$824$	0	0
$825$	3.68553	0.128314
$826$	0	0
$827$	−21.2274	−0.738151	−0.369075	−	0.929399i	$-0.620326\pi$
$827$	−21.2274	−0.738151	−0.369075	+	0.929399i	$0.620326\pi$
$828$	0	0
$829$	46.1492	1.60283	0.801414	−	0.598110i	$-0.204081\pi$
$829$	46.1492	1.60283	0.801414	+	0.598110i	$0.204081\pi$
$830$	0	0
$831$	2.68423	0.0931148
$832$	0	0
$833$	57.1342	1.97958
$834$	0	0
$835$	−25.5226	−0.883244
$836$	0	0
$837$	−6.22582	−0.215196
$838$	0	0
$839$	−0.669985	−0.0231305	−0.0115652	−	0.999933i	$-0.503681\pi$
$839$	−0.669985	−0.0231305	−0.0115652	+	0.999933i	$0.503681\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	3.79179	0.130596
$844$	0	0
$845$	1.30841	0.0450105
$846$	0	0
$847$	−116.541	−4.00440
$848$	0	0
$849$	2.08154	0.0714384
$850$	0	0
$851$	28.9304	0.991721
$852$	0	0
$853$	28.9297	0.990535	0.495267	−	0.868741i	$-0.335070\pi$
$853$	28.9297	0.990535	0.495267	+	0.868741i	$0.335070\pi$
$854$	0	0
$855$	15.7485	0.538586
$856$	0	0
$857$	−25.0861	−0.856926	−0.428463	−	0.903559i	$-0.640945\pi$
$857$	−25.0861	−0.856926	−0.428463	+	0.903559i	$0.640945\pi$
$858$	0	0
$859$	48.7855	1.66454	0.832269	−	0.554372i	$-0.187041\pi$
$859$	48.7855	1.66454	0.832269	+	0.554372i	$0.187041\pi$
$860$	0	0
$861$	−7.82230	−0.266583
$862$	0	0
$863$	−5.83418	−0.198598	−0.0992990	−	0.995058i	$-0.531660\pi$
$863$	−5.83418	−0.198598	−0.0992990	+	0.995058i	$0.531660\pi$
$864$	0	0
$865$	−27.0829	−0.920847
$866$	0	0
$867$	−0.921551	−0.0312975
$868$	0	0
$869$	30.8720	1.04726
$870$	0	0
$871$	−4.34415	−0.147196
$872$	0	0
$873$	9.51675	0.322093
$874$	0	0
$875$	47.4787	1.60507
$876$	0	0
$877$	17.4119	0.587957	0.293978	−	0.955812i	$-0.405021\pi$
$877$	17.4119	0.587957	0.293978	+	0.955812i	$0.405021\pi$
$878$	0	0
$879$	−4.64303	−0.156605
$880$	0	0
$881$	−31.6817	−1.06738	−0.533691	−	0.845679i	$-0.679196\pi$
$881$	−31.6817	−1.06738	−0.533691	+	0.845679i	$0.679196\pi$
$882$	0	0
$883$	−47.9089	−1.61226	−0.806132	−	0.591736i	$-0.798443\pi$
$883$	−47.9089	−1.61226	−0.806132	+	0.591736i	$0.798443\pi$
$884$	0	0
$885$	0.0215141	0.000723189 0
$886$	0	0
$887$	−8.93377	−0.299967	−0.149983	−	0.988689i	$-0.547922\pi$
$887$	−8.93377	−0.299967	−0.149983	+	0.988689i	$0.547922\pi$
$888$	0	0
$889$	53.7648	1.80321
$890$	0	0
$891$	53.3635	1.78774
$892$	0	0
$893$	−25.7398	−0.861350
$894$	0	0
$895$	10.8041	0.361140
$896$	0	0
$897$	0.811050	0.0270802
$898$	0	0
$899$	−5.70964	−0.190427
$900$	0	0
$901$	−25.7672	−0.858431
$902$	0	0
$903$	−3.17815	−0.105762
$904$	0	0
$905$	−2.37739	−0.0790273
$906$	0	0
$907$	−49.3860	−1.63983	−0.819917	−	0.572482i	$-0.805981\pi$
$907$	−49.3860	−1.63983	−0.819917	+	0.572482i	$0.805981\pi$
$908$	0	0
$909$	−31.2224	−1.03558
$910$	0	0
$911$	−13.9711	−0.462884	−0.231442	−	0.972849i	$-0.574344\pi$
$911$	−13.9711	−0.462884	−0.231442	+	0.972849i	$0.574344\pi$
$912$	0	0
$913$	−16.8457	−0.557510
$914$	0	0
$915$	2.45030	0.0810044
$916$	0	0
$917$	47.6612	1.57391
$918$	0	0
$919$	9.14356	0.301618	0.150809	−	0.988563i	$-0.451812\pi$
$919$	9.14356	0.301618	0.150809	+	0.988563i	$0.451812\pi$
$920$	0	0
$921$	−1.39606	−0.0460017
$922$	0	0
$923$	12.7962	0.421193
$924$	0	0
$925$	−21.4343	−0.704755
$926$	0	0
$927$	−29.9140	−0.982504
$928$	0	0
$929$	45.3048	1.48640	0.743201	−	0.669069i	$-0.233307\pi$
$929$	45.3048	1.48640	0.743201	+	0.669069i	$0.233307\pi$
$930$	0	0
$931$	−49.3742	−1.61817
$932$	0	0
$933$	4.65416	0.152370
$934$	0	0
$935$	37.6767	1.23216
$936$	0	0
$937$	38.8009	1.26757	0.633786	−	0.773509i	$-0.281500\pi$
$937$	38.8009	1.26757	0.633786	+	0.773509i	$0.281500\pi$
$938$	0	0
$939$	−1.57151	−0.0512842
$940$	0	0
$941$	−42.4785	−1.38476	−0.692379	−	0.721534i	$-0.743437\pi$
$941$	−42.4785	−1.38476	−0.692379	+	0.721534i	$0.743437\pi$
$942$	0	0
$943$	−43.3869	−1.41287
$944$	0	0
$945$	−6.24644	−0.203197
$946$	0	0
$947$	−35.2492	−1.14544	−0.572722	−	0.819750i	$-0.694113\pi$
$947$	−35.2492	−1.14544	−0.572722	+	0.819750i	$0.694113\pi$
$948$	0	0
$949$	−7.05543	−0.229029
$950$	0	0
$951$	5.17770	0.167898
$952$	0	0
$953$	59.0365	1.91238	0.956189	−	0.292749i	$-0.0945701\pi$
$953$	59.0365	1.91238	0.956189	+	0.292749i	$0.0945701\pi$
$954$	0	0
$955$	−12.8405	−0.415508
$956$	0	0
$957$	−1.12088	−0.0362329
$958$	0	0
$959$	−76.9531	−2.48494
$960$	0	0
$961$	1.59999	0.0516125
$962$	0	0
$963$	21.5728	0.695175
$964$	0	0
$965$	−2.50602	−0.0806716
$966$	0	0
$967$	7.63614	0.245562	0.122781	−	0.992434i	$-0.460819\pi$
$967$	7.63614	0.245562	0.122781	+	0.992434i	$0.460819\pi$
$968$	0	0
$969$	3.48120	0.111832
$970$	0	0
$971$	9.87165	0.316796	0.158398	−	0.987375i	$-0.449367\pi$
$971$	9.87165	0.316796	0.158398	+	0.987375i	$0.449367\pi$
$972$	0	0
$973$	37.8359	1.21296
$974$	0	0
$975$	−0.600900	−0.0192442
$976$	0	0
$977$	−1.28007	−0.0409529	−0.0204765	−	0.999790i	$-0.506518\pi$
$977$	−1.28007	−0.0409529	−0.0204765	+	0.999790i	$0.506518\pi$
$978$	0	0
$979$	95.1061	3.03960
$980$	0	0
$981$	0.860477	0.0274729
$982$	0	0
$983$	26.5040	0.845345	0.422672	−	0.906283i	$-0.361092\pi$
$983$	26.5040	0.845345	0.422672	+	0.906283i	$0.361092\pi$
$984$	0	0
$985$	−34.1231	−1.08725
$986$	0	0
$987$	5.07612	0.161575
$988$	0	0
$989$	−17.6278	−0.560532
$990$	0	0
$991$	2.68527	0.0853004	0.0426502	−	0.999090i	$-0.486420\pi$
$991$	2.68527	0.0853004	0.0426502	+	0.999090i	$0.486420\pi$
$992$	0	0
$993$	−2.52404	−0.0800980
$994$	0	0
$995$	−21.5354	−0.682718
$996$	0	0
$997$	43.5172	1.37820	0.689102	−	0.724664i	$-0.258005\pi$
$997$	43.5172	1.37820	0.689102	+	0.724664i	$0.258005\pi$
$998$	0	0
$999$	7.10812	0.224891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6032.2.a.u.1.4		7
4.3	odd	2		377.2.a.e.1.5	✓	7
12.11	even	2		3393.2.a.o.1.3		7
20.19	odd	2		9425.2.a.s.1.3		7
52.51	odd	2		4901.2.a.k.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
377.2.a.e.1.5	✓	7	4.3	odd	2
3393.2.a.o.1.3		7	12.11	even	2
4901.2.a.k.1.3		7	52.51	odd	2
6032.2.a.u.1.4		7	1.1	even	1	trivial
9425.2.a.s.1.3		7	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:	\( N \)	\(=\)	\( 6032 = 2^{4} \cdot 13 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6032.a (trivial)

\(f(q)\)	\(=\)	\(q-0.182751 q^{3} +1.30841 q^{5} -4.37827 q^{7} -2.96660 q^{9} +O(q^{10})\)	\(q-0.182751 q^{3} +1.30841 q^{5} -4.37827 q^{7} -2.96660 q^{9} +6.13336 q^{11} -1.00000 q^{13} -0.239113 q^{15} +4.69496 q^{17} -4.05729 q^{19} +0.800135 q^{21} +4.43800 q^{23} -3.28807 q^{25} +1.09040 q^{27} +1.00000 q^{29} -5.70964 q^{31} -1.12088 q^{33} -5.72856 q^{35} +6.51879 q^{37} +0.182751 q^{39} -9.77623 q^{41} -3.97202 q^{43} -3.88152 q^{45} +6.34409 q^{47} +12.1693 q^{49} -0.858010 q^{51} -5.48828 q^{53} +8.02492 q^{55} +0.741476 q^{57} -0.0899747 q^{59} -10.2475 q^{61} +12.9886 q^{63} -1.30841 q^{65} +4.34415 q^{67} -0.811050 q^{69} -12.7962 q^{71} +7.05543 q^{73} +0.600900 q^{75} -26.8535 q^{77} +5.03346 q^{79} +8.70053 q^{81} -2.74656 q^{83} +6.14291 q^{85} -0.182751 q^{87} +15.5064 q^{89} +4.37827 q^{91} +1.04344 q^{93} -5.30859 q^{95} -3.20796 q^{97} -18.1952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{3} - 2 q^{5} - 7 q^{7} + 5 q^{9}+O(q^{10}) \) 7 * q - 2 * q^3 - 2 * q^5 - 7 * q^7 + 5 * q^9	\( 7 q - 2 q^{3} - 2 q^{5} - 7 q^{7} + 5 q^{9} + 3 q^{11} - 7 q^{13} - 20 q^{15} + 14 q^{17} + 12 q^{19} + q^{21} - 5 q^{23} + 5 q^{25} - 14 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} + 6 q^{35} + 9 q^{37} + 2 q^{39} - 9 q^{41} - 24 q^{43} + 10 q^{45} + 9 q^{47} - 10 q^{49} - 5 q^{51} - 13 q^{53} - 7 q^{55} + 12 q^{57} - 13 q^{59} + 3 q^{61} - 2 q^{63} + 2 q^{65} + 7 q^{67} + 8 q^{69} - 22 q^{71} + 4 q^{73} + 29 q^{75} - 30 q^{77} - 48 q^{79} + 15 q^{81} + 30 q^{83} - 9 q^{85} - 2 q^{87} - 25 q^{89} + 7 q^{91} - 27 q^{93} - 23 q^{95} + 4 q^{97} + 25 q^{99}+O(q^{100}) \) 7 * q - 2 * q^3 - 2 * q^5 - 7 * q^7 + 5 * q^9 + 3 * q^11 - 7 * q^13 - 20 * q^15 + 14 * q^17 + 12 * q^19 + q^21 - 5 * q^23 + 5 * q^25 - 14 * q^27 + 7 * q^29 + 3 * q^31 - q^33 + 6 * q^35 + 9 * q^37 + 2 * q^39 - 9 * q^41 - 24 * q^43 + 10 * q^45 + 9 * q^47 - 10 * q^49 - 5 * q^51 - 13 * q^53 - 7 * q^55 + 12 * q^57 - 13 * q^59 + 3 * q^61 - 2 * q^63 + 2 * q^65 + 7 * q^67 + 8 * q^69 - 22 * q^71 + 4 * q^73 + 29 * q^75 - 30 * q^77 - 48 * q^79 + 15 * q^81 + 30 * q^83 - 9 * q^85 - 2 * q^87 - 25 * q^89 + 7 * q^91 - 27 * q^93 - 23 * q^95 + 4 * q^97 + 25 * q^99

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