LMFDB - Embedded newform 363.6.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,6,Mod(1,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("363.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	363.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:	$58.2193265921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{177}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 44 $ x^2 - x - 44
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.15207$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.15207 q^{2} -9.00000 q^{3} +51.7603 q^{4} +95.5207 q^{5} -82.3686 q^{6} +209.521 q^{7} +180.848 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.15207 q^{2} -9.00000 q^{3} +51.7603 q^{4} +95.5207 q^{5} -82.3686 q^{6} +209.521 q^{7} +180.848 q^{8} +81.0000 q^{9} +874.212 q^{10} -465.843 q^{12} +335.779 q^{13} +1917.55 q^{14} -859.686 q^{15} -1.19832 q^{16} +799.124 q^{17} +741.317 q^{18} +658.175 q^{19} +4944.18 q^{20} -1885.69 q^{21} -4119.66 q^{23} -1627.63 q^{24} +5999.20 q^{25} +3073.07 q^{26} -729.000 q^{27} +10844.9 q^{28} -559.348 q^{29} -7867.90 q^{30} -6052.31 q^{31} -5798.10 q^{32} +7313.64 q^{34} +20013.6 q^{35} +4192.59 q^{36} -14053.3 q^{37} +6023.66 q^{38} -3022.01 q^{39} +17274.7 q^{40} -1846.27 q^{41} -17257.9 q^{42} -1623.49 q^{43} +7737.17 q^{45} -37703.4 q^{46} +20728.1 q^{47} +10.7848 q^{48} +27091.9 q^{49} +54905.1 q^{50} -7192.12 q^{51} +17380.0 q^{52} -7585.46 q^{53} -6671.86 q^{54} +37891.4 q^{56} -5923.58 q^{57} -5119.19 q^{58} +18468.5 q^{59} -44497.6 q^{60} +16972.3 q^{61} -55391.2 q^{62} +16971.2 q^{63} -53026.3 q^{64} +32073.8 q^{65} -5618.62 q^{67} +41362.9 q^{68} +37076.9 q^{69} +183165. q^{70} +3703.10 q^{71} +14648.7 q^{72} +19808.0 q^{73} -128617. q^{74} -53992.8 q^{75} +34067.4 q^{76} -27657.6 q^{78} -64009.9 q^{79} -114.464 q^{80} +6561.00 q^{81} -16897.2 q^{82} +46390.2 q^{83} -97603.7 q^{84} +76332.9 q^{85} -14858.3 q^{86} +5034.13 q^{87} -53959.5 q^{89} +70811.1 q^{90} +70352.5 q^{91} -213235. q^{92} +54470.8 q^{93} +189705. q^{94} +62869.3 q^{95} +52182.9 q^{96} +145249. q^{97} +247947. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} - 18 q^{3} + 37 q^{4} + 58 q^{5} - 45 q^{6} + 286 q^{7} + 375 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q + 5 * q^2 - 18 * q^3 + 37 * q^4 + 58 * q^5 - 45 * q^6 + 286 * q^7 + 375 * q^8 + 162 * q^9	\( 2 q + 5 q^{2} - 18 q^{3} + 37 q^{4} + 58 q^{5} - 45 q^{6} + 286 q^{7} + 375 q^{8} + 162 q^{9} + 1030 q^{10} - 333 q^{12} + 166 q^{13} + 1600 q^{14} - 522 q^{15} - 335 q^{16} + 800 q^{17} + 405 q^{18} + 1476 q^{19} + 5498 q^{20} - 2574 q^{21} - 3370 q^{23} - 3375 q^{24} + 4282 q^{25} + 3778 q^{26} - 1458 q^{27} + 9716 q^{28} - 6600 q^{29} - 9270 q^{30} - 7528 q^{31} - 10625 q^{32} + 7310 q^{34} + 17144 q^{35} + 2997 q^{36} - 29916 q^{37} + 2628 q^{38} - 1494 q^{39} + 9990 q^{40} + 5780 q^{41} - 14400 q^{42} + 16656 q^{43} + 4698 q^{45} - 40816 q^{46} + 7850 q^{47} + 3015 q^{48} + 16134 q^{49} + 62035 q^{50} - 7200 q^{51} + 19886 q^{52} + 14178 q^{53} - 3645 q^{54} + 52740 q^{56} - 13284 q^{57} + 19962 q^{58} + 17300 q^{59} - 49482 q^{60} + 2946 q^{61} - 49264 q^{62} + 23166 q^{63} - 22303 q^{64} + 38444 q^{65} + 31336 q^{67} + 41350 q^{68} + 30330 q^{69} + 195080 q^{70} - 33810 q^{71} + 30375 q^{72} - 60644 q^{73} - 62754 q^{74} - 38538 q^{75} + 21996 q^{76} - 34002 q^{78} - 1870 q^{79} + 12410 q^{80} + 13122 q^{81} - 48562 q^{82} + 58296 q^{83} - 87444 q^{84} + 76300 q^{85} - 90756 q^{86} + 59400 q^{87} + 92388 q^{89} + 83430 q^{90} + 57368 q^{91} - 224300 q^{92} + 67752 q^{93} + 243176 q^{94} + 32184 q^{95} + 95625 q^{96} + 7120 q^{97} + 293445 q^{98}+O(q^{100}) \) 2 * q + 5 * q^2 - 18 * q^3 + 37 * q^4 + 58 * q^5 - 45 * q^6 + 286 * q^7 + 375 * q^8 + 162 * q^9 + 1030 * q^10 - 333 * q^12 + 166 * q^13 + 1600 * q^14 - 522 * q^15 - 335 * q^16 + 800 * q^17 + 405 * q^18 + 1476 * q^19 + 5498 * q^20 - 2574 * q^21 - 3370 * q^23 - 3375 * q^24 + 4282 * q^25 + 3778 * q^26 - 1458 * q^27 + 9716 * q^28 - 6600 * q^29 - 9270 * q^30 - 7528 * q^31 - 10625 * q^32 + 7310 * q^34 + 17144 * q^35 + 2997 * q^36 - 29916 * q^37 + 2628 * q^38 - 1494 * q^39 + 9990 * q^40 + 5780 * q^41 - 14400 * q^42 + 16656 * q^43 + 4698 * q^45 - 40816 * q^46 + 7850 * q^47 + 3015 * q^48 + 16134 * q^49 + 62035 * q^50 - 7200 * q^51 + 19886 * q^52 + 14178 * q^53 - 3645 * q^54 + 52740 * q^56 - 13284 * q^57 + 19962 * q^58 + 17300 * q^59 - 49482 * q^60 + 2946 * q^61 - 49264 * q^62 + 23166 * q^63 - 22303 * q^64 + 38444 * q^65 + 31336 * q^67 + 41350 * q^68 + 30330 * q^69 + 195080 * q^70 - 33810 * q^71 + 30375 * q^72 - 60644 * q^73 - 62754 * q^74 - 38538 * q^75 + 21996 * q^76 - 34002 * q^78 - 1870 * q^79 + 12410 * q^80 + 13122 * q^81 - 48562 * q^82 + 58296 * q^83 - 87444 * q^84 + 76300 * q^85 - 90756 * q^86 + 59400 * q^87 + 92388 * q^89 + 83430 * q^90 + 57368 * q^91 - 224300 * q^92 + 67752 * q^93 + 243176 * q^94 + 32184 * q^95 + 95625 * q^96 + 7120 * q^97 + 293445 * q^98

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 $

$2$	9.15207	1.61787	0.808936	−	0.587897i	$-0.200044\pi$
$2$	9.15207	1.61787	0.808936	+	0.587897i	$0.200044\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	51.7603	1.61751
$5$	95.5207	1.70873	0.854363	−	0.519677i	$-0.173948\pi$
$5$	95.5207	1.70873	0.854363	+	0.519677i	$0.173948\pi$
$6$	−82.3686	−0.934079
$7$	209.521	1.61615	0.808075	−	0.589079i	$-0.200509\pi$
$7$	209.521	1.61615	0.808075	+	0.589079i	$0.200509\pi$
$8$	180.848	0.999053
$9$	81.0000	0.333333
$10$	874.212	2.76450
$11$	0	0
$11$	0	0
$12$	−465.843	−0.933870
$13$	335.779	0.551055	0.275527	−	0.961293i	$-0.411148\pi$
$13$	335.779	0.551055	0.275527	+	0.961293i	$0.411148\pi$
$14$	1917.55	2.61472
$15$	−859.686	−0.986533
$16$	−1.19832	−0.00117023
$17$	799.124	0.670644	0.335322	−	0.942104i	$-0.391155\pi$
$17$	799.124	0.670644	0.335322	+	0.942104i	$0.391155\pi$
$18$	741.317	0.539291
$19$	658.175	0.418271	0.209135	−	0.977887i	$-0.432935\pi$
$19$	658.175	0.418271	0.209135	+	0.977887i	$0.432935\pi$
$20$	4944.18	2.76388
$21$	−1885.69	−0.933085
$22$	0	0
$23$	−4119.66	−1.62383	−0.811917	−	0.583773i	$-0.801576\pi$
$23$	−4119.66	−1.62383	−0.811917	+	0.583773i	$0.801576\pi$
$24$	−1627.63	−0.576804
$25$	5999.20	1.91974
$26$	3073.07	0.891536
$27$	−729.000	−0.192450
$28$	10844.9	2.61414
$29$	−559.348	−0.123506	−0.0617529	−	0.998091i	$-0.519669\pi$
$29$	−559.348	−0.123506	−0.0617529	+	0.998091i	$0.519669\pi$
$30$	−7867.90	−1.59608
$31$	−6052.31	−1.13114	−0.565571	−	0.824700i	$-0.691344\pi$
$31$	−6052.31	−1.13114	−0.565571	+	0.824700i	$0.691344\pi$
$32$	−5798.10	−1.00095
$33$	0	0
$34$	7313.64	1.08502
$35$	20013.6	2.76156
$36$	4192.59	0.539170
$37$	−14053.3	−1.68762	−0.843810	−	0.536642i	$-0.819692\pi$
$37$	−14053.3	−1.68762	−0.843810	+	0.536642i	$0.819692\pi$
$38$	6023.66	0.676709
$39$	−3022.01	−0.318151
$40$	17274.7	1.70711
$41$	−1846.27	−0.171528	−0.0857642	−	0.996315i	$-0.527333\pi$
$41$	−1846.27	−0.171528	−0.0857642	+	0.996315i	$0.527333\pi$
$42$	−17257.9	−1.50961
$43$	−1623.49	−0.133900	−0.0669498	−	0.997756i	$-0.521327\pi$
$43$	−1623.49	−0.133900	−0.0669498	+	0.997756i	$0.521327\pi$
$44$	0	0
$45$	7737.17	0.569575
$46$	−37703.4	−2.62715
$47$	20728.1	1.36872	0.684361	−	0.729143i	$-0.260081\pi$
$47$	20728.1	1.36872	0.684361	+	0.729143i	$0.260081\pi$
$48$	10.7848	0.000675633 0
$49$	27091.9	1.61194
$50$	54905.1	3.10590
$51$	−7192.12	−0.387196
$52$	17380.0	0.891337
$53$	−7585.46	−0.370930	−0.185465	−	0.982651i	$-0.559379\pi$
$53$	−7585.46	−0.370930	−0.185465	+	0.982651i	$0.559379\pi$
$54$	−6671.86	−0.311360
$55$	0	0
$56$	37891.4	1.61462
$57$	−5923.58	−0.241489
$58$	−5119.19	−0.199817
$59$	18468.5	0.690717	0.345359	−	0.938471i	$-0.387757\pi$
$59$	18468.5	0.690717	0.345359	+	0.938471i	$0.387757\pi$
$60$	−44497.6	−1.59573
$61$	16972.3	0.584005	0.292002	−	0.956418i	$-0.405678\pi$
$61$	16972.3	0.584005	0.292002	+	0.956418i	$0.405678\pi$
$62$	−55391.2	−1.83004
$63$	16971.2	0.538717
$64$	−53026.3	−1.61823
$65$	32073.8	0.941601
$66$	0	0
$67$	−5618.62	−0.152912	−0.0764561	−	0.997073i	$-0.524361\pi$
$67$	−5618.62	−0.152912	−0.0764561	+	0.997073i	$0.524361\pi$
$68$	41362.9	1.08477
$69$	37076.9	0.937521
$70$	183165.	4.46785
$71$	3703.10	0.0871807	0.0435903	−	0.999049i	$-0.486120\pi$
$71$	3703.10	0.0871807	0.0435903	+	0.999049i	$0.486120\pi$
$72$	14648.7	0.333018
$73$	19808.0	0.435044	0.217522	−	0.976055i	$-0.430203\pi$
$73$	19808.0	0.435044	0.217522	+	0.976055i	$0.430203\pi$
$74$	−128617.	−2.73035
$75$	−53992.8	−1.10836
$76$	34067.4	0.676557
$77$	0	0
$78$	−27657.6	−0.514728
$79$	−64009.9	−1.15393	−0.576965	−	0.816769i	$-0.695763\pi$
$79$	−64009.9	−1.15393	−0.576965	+	0.816769i	$0.695763\pi$
$80$	−114.464	−0.00199960
$81$	6561.00	0.111111
$82$	−16897.2	−0.277511
$83$	46390.2	0.739147	0.369573	−	0.929202i	$-0.379504\pi$
$83$	46390.2	0.739147	0.369573	+	0.929202i	$0.379504\pi$
$84$	−97603.7	−1.50927
$85$	76332.9	1.14595
$86$	−14858.3	−0.216632
$87$	5034.13	0.0713061
$88$	0	0
$89$	−53959.5	−0.722093	−0.361046	−	0.932548i	$-0.617580\pi$
$89$	−53959.5	−0.722093	−0.361046	+	0.932548i	$0.617580\pi$
$90$	70811.1	0.921500
$91$	70352.5	0.890587
$92$	−213235.	−2.62657
$93$	54470.8	0.653065
$94$	189705.	2.21442
$95$	62869.3	0.714710
$96$	52182.9	0.577897
$97$	145249.	1.56741	0.783707	−	0.621130i	$-0.213326\pi$
$97$	145249.	1.56741	0.783707	+	0.621130i	$0.213326\pi$
$98$	247947.	2.60792
$99$	0	0
$100$	310521.	3.10521
$101$	77215.1	0.753180	0.376590	−	0.926380i	$-0.377097\pi$
$101$	77215.1	0.753180	0.376590	+	0.926380i	$0.377097\pi$
$102$	−65822.7	−0.626434
$103$	−106203.	−0.986374	−0.493187	−	0.869923i	$-0.664168\pi$
$103$	−106203.	−0.986374	−0.493187	+	0.869923i	$0.664168\pi$
$104$	60724.9	0.550533
$105$	−180122.	−1.59439
$106$	−69422.6	−0.600118
$107$	−33750.8	−0.284987	−0.142493	−	0.989796i	$-0.545512\pi$
$107$	−33750.8	−0.284987	−0.142493	+	0.989796i	$0.545512\pi$
$108$	−37733.3	−0.311290
$109$	37977.1	0.306165	0.153083	−	0.988213i	$-0.451080\pi$
$109$	37977.1	0.306165	0.153083	+	0.988213i	$0.451080\pi$
$110$	0	0
$111$	126480.	0.974348
$112$	−251.072	−0.00189127
$113$	239549.	1.76481	0.882407	−	0.470486i	$-0.155922\pi$
$113$	239549.	1.76481	0.882407	+	0.470486i	$0.155922\pi$
$114$	−54213.0	−0.390698
$115$	−393512.	−2.77469
$116$	−28952.1	−0.199772
$117$	27198.1	0.183685
$118$	169025.	1.11749
$119$	167433.	1.08386
$120$	−155472.	−0.985599
$121$	0	0
$122$	155332.	0.944845
$123$	16616.4	0.0990320
$124$	−313270.	−1.82963
$125$	274545.	1.57159
$126$	155321.	0.871575
$127$	−88793.2	−0.488507	−0.244253	−	0.969711i	$-0.578543\pi$
$127$	−88793.2	−0.488507	−0.244253	+	0.969711i	$0.578543\pi$
$128$	−299761.	−1.61715
$129$	14611.4	0.0773070
$130$	293542.	1.52339
$131$	−333640.	−1.69864	−0.849318	−	0.527881i	$-0.822987\pi$
$131$	−333640.	−1.69864	−0.849318	+	0.527881i	$0.822987\pi$
$132$	0	0
$133$	137901.	0.675988
$134$	−51421.9	−0.247392
$135$	−69634.6	−0.328844
$136$	144520.	0.670009
$137$	−377709.	−1.71932	−0.859659	−	0.510869i	$-0.829324\pi$
$137$	−377709.	−1.71932	−0.859659	+	0.510869i	$0.829324\pi$
$138$	339330.	1.51679
$139$	365308.	1.60370	0.801849	−	0.597527i	$-0.203850\pi$
$139$	365308.	1.60370	0.801849	+	0.597527i	$0.203850\pi$
$140$	1.03591e6	4.46685
$141$	−186553.	−0.790232
$142$	33891.1	0.141047
$143$	0	0
$144$	−97.0636	−0.000390077 0
$145$	−53429.3	−0.211038
$146$	181284.	0.703845
$147$	−243827.	−0.930655
$148$	−727405.	−2.72974
$149$	−297568.	−1.09805	−0.549023	−	0.835807i	$-0.685000\pi$
$149$	−297568.	−1.09805	−0.549023	+	0.835807i	$0.685000\pi$
$150$	−494146.	−1.79319
$151$	−318093.	−1.13530	−0.567651	−	0.823269i	$-0.692148\pi$
$151$	−318093.	−1.13530	−0.567651	+	0.823269i	$0.692148\pi$
$152$	119030.	0.417875
$153$	64729.0	0.223548
$154$	0	0
$155$	−578121.	−1.93281
$156$	−156420.	−0.514613
$157$	−34489.6	−0.111671	−0.0558353	−	0.998440i	$-0.517782\pi$
$157$	−34489.6	−0.111671	−0.0558353	+	0.998440i	$0.517782\pi$
$158$	−585823.	−1.86691
$159$	68269.1	0.214157
$160$	−553839.	−1.71034
$161$	−863153.	−2.62436
$162$	60046.7	0.179764
$163$	−45865.7	−0.135213	−0.0676067	−	0.997712i	$-0.521536\pi$
$163$	−45865.7	−0.135213	−0.0676067	+	0.997712i	$0.521536\pi$
$164$	−95563.7	−0.277449
$165$	0	0
$166$	424566.	1.19584
$167$	−290943.	−0.807265	−0.403633	−	0.914921i	$-0.632253\pi$
$167$	−290943.	−0.807265	−0.403633	+	0.914921i	$0.632253\pi$
$168$	−341022.	−0.932201
$169$	−258546.	−0.696339
$170$	698604.	1.85399
$171$	53312.2	0.139424
$172$	−84032.5	−0.216584
$173$	139360.	0.354016	0.177008	−	0.984209i	$-0.443358\pi$
$173$	139360.	0.354016	0.177008	+	0.984209i	$0.443358\pi$
$174$	46072.7	0.115364
$175$	1.25696e6	3.10259
$176$	0	0
$177$	−166216.	−0.398786
$178$	−493841.	−1.16825
$179$	−599556.	−1.39861	−0.699306	−	0.714823i	$-0.746507\pi$
$179$	−599556.	−1.39861	−0.699306	+	0.714823i	$0.746507\pi$
$180$	400479.	0.921294
$181$	130631.	0.296380	0.148190	−	0.988959i	$-0.452655\pi$
$181$	130631.	0.296380	0.148190	+	0.988959i	$0.452655\pi$
$182$	643871.	1.44086
$183$	−152751.	−0.337175
$184$	−745031.	−1.62230
$185$	−1.34238e6	−2.88368
$186$	498520.	1.05658
$187$	0	0
$188$	1.07289e6	2.21392
$189$	−152741.	−0.311028
$190$	575384.	1.15631
$191$	338243.	0.670882	0.335441	−	0.942061i	$-0.391115\pi$
$191$	338243.	0.670882	0.335441	+	0.942061i	$0.391115\pi$
$192$	477236.	0.934287
$193$	329094.	0.635955	0.317978	−	0.948098i	$-0.396996\pi$
$193$	329094.	0.635955	0.317978	+	0.948098i	$0.396996\pi$
$194$	1.32933e6	2.53588
$195$	−288664.	−0.543634
$196$	1.40229e6	2.60733
$197$	−517397.	−0.949858	−0.474929	−	0.880024i	$-0.657526\pi$
$197$	−517397.	−0.949858	−0.474929	+	0.880024i	$0.657526\pi$
$198$	0	0
$199$	−531436.	−0.951302	−0.475651	−	0.879634i	$-0.657788\pi$
$199$	−531436.	−0.951302	−0.475651	+	0.879634i	$0.657788\pi$
$200$	1.08494e6	1.91793
$201$	50567.5	0.0882839
$202$	706678.	1.21855
$203$	−117195.	−0.199604
$204$	−372266.	−0.626294
$205$	−176357.	−0.293095
$206$	−971973.	−1.59583
$207$	−333692.	−0.541278
$208$	−402.369	−0.000644861 0
$209$	0	0
$210$	−1.64849e6	−2.57951
$211$	−409913.	−0.633848	−0.316924	−	0.948451i	$-0.602650\pi$
$211$	−409913.	−0.633848	−0.316924	+	0.948451i	$0.602650\pi$
$212$	−392626.	−0.599984
$213$	−33327.9	−0.0503338
$214$	−308890.	−0.461072
$215$	−155077.	−0.228798
$216$	−131838.	−0.192268
$217$	−1.26808e6	−1.82810
$218$	347569.	0.495336
$219$	−178272.	−0.251173
$220$	0	0
$221$	268329.	0.369561
$222$	1.15755e6	1.57637
$223$	269898.	0.363444	0.181722	−	0.983350i	$-0.441833\pi$
$223$	269898.	0.363444	0.181722	+	0.983350i	$0.441833\pi$
$224$	−1.21482e6	−1.61768
$225$	485935.	0.639915
$226$	2.19237e6	2.85524
$227$	1.02146e6	1.31570	0.657852	−	0.753147i	$-0.271465\pi$
$227$	1.02146e6	1.31570	0.657852	+	0.753147i	$0.271465\pi$
$228$	−306606.	−0.390611
$229$	169276.	0.213307	0.106654	−	0.994296i	$-0.465986\pi$
$229$	169276.	0.213307	0.106654	+	0.994296i	$0.465986\pi$
$230$	−3.60145e6	−4.48909
$231$	0	0
$232$	−101157.	−0.123389
$233$	20445.6	0.0246723	0.0123361	−	0.999924i	$-0.496073\pi$
$233$	20445.6	0.0246723	0.0123361	+	0.999924i	$0.496073\pi$
$234$	248919.	0.297179
$235$	1.97996e6	2.33877
$236$	955933.	1.11724
$237$	576089.	0.666222
$238$	1.53236e6	1.75355
$239$	933552.	1.05717	0.528583	−	0.848881i	$-0.322723\pi$
$239$	933552.	1.05717	0.528583	+	0.848881i	$0.322723\pi$
$240$	1030.18	0.00115447
$241$	1.30259e6	1.44466	0.722331	−	0.691547i	$-0.243071\pi$
$241$	1.30259e6	1.44466	0.722331	+	0.691547i	$0.243071\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	878493.	0.944634
$245$	2.58784e6	2.75437
$246$	152075.	0.160221
$247$	221001.	0.230490
$248$	−1.09455e6	−1.13007
$249$	−417511.	−0.426747
$250$	2.51266e6	2.54263
$251$	−930872.	−0.932622	−0.466311	−	0.884621i	$-0.654417\pi$
$251$	−930872.	−0.932622	−0.466311	+	0.884621i	$0.654417\pi$
$252$	878434.	0.871380
$253$	0	0
$254$	−812642.	−0.790342
$255$	−686996.	−0.661612
$256$	−1.04659e6	−0.998106
$257$	−25313.6	−0.0239067	−0.0119534	−	0.999929i	$-0.503805\pi$
$257$	−25313.6	−0.0239067	−0.0119534	+	0.999929i	$0.503805\pi$
$258$	133725.	0.125073
$259$	−2.94446e6	−2.72745
$260$	1.66015e6	1.52305
$261$	−45307.2	−0.0411686
$262$	−3.05350e6	−2.74818
$263$	1.69322e6	1.50947	0.754735	−	0.656030i	$-0.227765\pi$
$263$	1.69322e6	1.50947	0.754735	+	0.656030i	$0.227765\pi$
$264$	0	0
$265$	−724568.	−0.633818
$266$	1.26208e6	1.09366
$267$	485636.	0.416901
$268$	−290821.	−0.247337
$269$	469365.	0.395485	0.197742	−	0.980254i	$-0.436639\pi$
$269$	469365.	0.395485	0.197742	+	0.980254i	$0.436639\pi$
$270$	−637300.	−0.532028
$271$	2.18341e6	1.80598	0.902988	−	0.429666i	$-0.141369\pi$
$271$	2.18341e6	1.80598	0.902988	+	0.429666i	$0.141369\pi$
$272$	−957.603	−0.000784808 0
$273$	−633173.	−0.514181
$274$	−3.45682e6	−2.78164
$275$	0	0
$276$	1.91911e6	1.51645
$277$	84280.4	0.0659974	0.0329987	−	0.999455i	$-0.489494\pi$
$277$	84280.4	0.0659974	0.0329987	+	0.999455i	$0.489494\pi$
$278$	3.34333e6	2.59458
$279$	−490237.	−0.377047
$280$	3.61941e6	2.75894
$281$	−649515.	−0.490708	−0.245354	−	0.969433i	$-0.578904\pi$
$281$	−649515.	−0.490708	−0.245354	+	0.969433i	$0.578904\pi$
$282$	−1.70735e6	−1.27849
$283$	−1.54893e6	−1.14965	−0.574826	−	0.818276i	$-0.694930\pi$
$283$	−1.54893e6	−1.14965	−0.574826	+	0.818276i	$0.694930\pi$
$284$	191674.	0.141016
$285$	−565824.	−0.412638
$286$	0	0
$287$	−386832.	−0.277216
$288$	−469646.	−0.333649
$289$	−781258.	−0.550237
$290$	−488989.	−0.341432
$291$	−1.30724e6	−0.904947
$292$	1.02527e6	0.703688
$293$	70276.6	0.0478236	0.0239118	−	0.999714i	$-0.492388\pi$
$293$	70276.6	0.0478236	0.0239118	+	0.999714i	$0.492388\pi$
$294$	−2.23152e6	−1.50568
$295$	1.76412e6	1.18025
$296$	−2.54151e6	−1.68602
$297$	0	0
$298$	−2.72336e6	−1.77650
$299$	−1.38329e6	−0.894821
$300$	−2.79469e6	−1.79279
$301$	−340155.	−0.216402
$302$	−2.91121e6	−1.83678
$303$	−694936.	−0.434849
$304$	−788.702	−0.000489473 0
$305$	1.62121e6	0.997904
$306$	592405.	0.361672
$307$	−1.43343e6	−0.868022	−0.434011	−	0.900908i	$-0.642902\pi$
$307$	−1.43343e6	−0.868022	−0.434011	+	0.900908i	$0.642902\pi$
$308$	0	0
$309$	955823.	0.569484
$310$	−5.29100e6	−3.12704
$311$	−227879.	−0.133599	−0.0667996	−	0.997766i	$-0.521279\pi$
$311$	−227879.	−0.133599	−0.0667996	+	0.997766i	$0.521279\pi$
$312$	−546524.	−0.317850
$313$	−723760.	−0.417574	−0.208787	−	0.977961i	$-0.566952\pi$
$313$	−723760.	−0.417574	−0.208787	+	0.977961i	$0.566952\pi$
$314$	−315651.	−0.180669
$315$	1.62110e6	0.920519
$316$	−3.31317e6	−1.86649
$317$	1.26086e6	0.704723	0.352362	−	0.935864i	$-0.385379\pi$
$317$	1.26086e6	0.704723	0.352362	+	0.935864i	$0.385379\pi$
$318$	624804.	0.346478
$319$	0	0
$320$	−5.06510e6	−2.76512
$321$	303757.	0.164537
$322$	−7.89964e6	−4.24588
$323$	525964.	0.280511
$324$	339600.	0.179723
$325$	2.01440e6	1.05788
$326$	−419766.	−0.218758
$327$	−341794.	−0.176765
$328$	−333894.	−0.171366
$329$	4.34297e6	2.21206
$330$	0	0
$331$	433444.	0.217452	0.108726	−	0.994072i	$-0.465323\pi$
$331$	433444.	0.217452	0.108726	+	0.994072i	$0.465323\pi$
$332$	2.40117e6	1.19558
$333$	−1.13832e6	−0.562540
$334$	−2.66273e6	−1.30605
$335$	−536694.	−0.261285
$336$	2259.65	0.00109192
$337$	−3.80554e6	−1.82533	−0.912666	−	0.408706i	$-0.865980\pi$
$337$	−3.80554e6	−1.82533	−0.912666	+	0.408706i	$0.865980\pi$
$338$	−2.36623e6	−1.12659
$339$	−2.15594e6	−1.01892
$340$	3.95101e6	1.85358
$341$	0	0
$342$	487917.	0.225570
$343$	2.15490e6	0.988991
$344$	−293605.	−0.133773
$345$	3.54161e6	1.60197
$346$	1.27543e6	0.572753
$347$	−2.91029e6	−1.29752	−0.648759	−	0.760994i	$-0.724712\pi$
$347$	−2.91029e6	−1.29752	−0.648759	+	0.760994i	$0.724712\pi$
$348$	260568.	0.115338
$349$	4.13500e6	1.81724	0.908620	−	0.417625i	$-0.137137\pi$
$349$	4.13500e6	1.81724	0.908620	+	0.417625i	$0.137137\pi$
$350$	1.15037e7	5.01960
$351$	−244783.	−0.106050
$352$	0	0
$353$	499935.	0.213539	0.106769	−	0.994284i	$-0.465949\pi$
$353$	499935.	0.213539	0.106769	+	0.994284i	$0.465949\pi$
$354$	−1.52122e6	−0.645185
$355$	353723.	0.148968
$356$	−2.79296e6	−1.16799
$357$	−1.50690e6	−0.625768
$358$	−5.48718e6	−2.26278
$359$	2.96365e6	1.21364	0.606822	−	0.794838i	$-0.292444\pi$
$359$	2.96365e6	1.21364	0.606822	+	0.794838i	$0.292444\pi$
$360$	1.39925e6	0.569036
$361$	−2.04290e6	−0.825050
$362$	1.19554e6	0.479504
$363$	0	0
$364$	3.64147e6	1.44053
$365$	1.89207e6	0.743371
$366$	−1.39799e6	−0.545507
$367$	257505.	0.0997976	0.0498988	−	0.998754i	$-0.484110\pi$
$367$	257505.	0.0997976	0.0498988	+	0.998754i	$0.484110\pi$
$368$	4936.65	0.00190026
$369$	−149548.	−0.0571761
$370$	−1.22856e7	−4.66542
$371$	−1.58931e6	−0.599479
$372$	2.81943e6	1.05634
$373$	1.28217e6	0.477169	0.238584	−	0.971122i	$-0.423317\pi$
$373$	1.28217e6	0.477169	0.238584	+	0.971122i	$0.423317\pi$
$374$	0	0
$375$	−2.47091e6	−0.907358
$376$	3.74864e6	1.36743
$377$	−187817.	−0.0680584
$378$	−1.39789e6	−0.503204
$379$	3.13440e6	1.12087	0.560436	−	0.828198i	$-0.310634\pi$
$379$	3.13440e6	1.12087	0.560436	+	0.828198i	$0.310634\pi$
$380$	3.25414e6	1.15605
$381$	799139.	0.282040
$382$	3.09563e6	1.08540
$383$	875781.	0.305069	0.152535	−	0.988298i	$-0.451256\pi$
$383$	875781.	0.305069	0.152535	+	0.988298i	$0.451256\pi$
$384$	2.69785e6	0.933661
$385$	0	0
$386$	3.01189e6	1.02889
$387$	−131503.	−0.0446332
$388$	7.51814e6	2.53531
$389$	−1.95280e6	−0.654312	−0.327156	−	0.944970i	$-0.606090\pi$
$389$	−1.95280e6	−0.654312	−0.327156	+	0.944970i	$0.606090\pi$
$390$	−2.64187e6	−0.879530
$391$	−3.29212e6	−1.08901
$392$	4.89952e6	1.61042
$393$	3.00276e6	0.980708
$394$	−4.73526e6	−1.53675
$395$	−6.11427e6	−1.97175
$396$	0	0
$397$	−1.70718e6	−0.543629	−0.271814	−	0.962350i	$-0.587624\pi$
$397$	−1.70718e6	−0.543629	−0.271814	+	0.962350i	$0.587624\pi$
$398$	−4.86374e6	−1.53909
$399$	−1.24111e6	−0.390282
$400$	−7188.94	−0.00224654
$401$	4.51630e6	1.40256	0.701280	−	0.712886i	$-0.252612\pi$
$401$	4.51630e6	1.40256	0.701280	+	0.712886i	$0.252612\pi$
$402$	462798.	0.142832
$403$	−2.03224e6	−0.623321
$404$	3.99668e6	1.21828
$405$	626711.	0.189858
$406$	−1.07258e6	−0.322934
$407$	0	0
$408$	−1.30068e6	−0.386830
$409$	721013.	0.213125	0.106563	−	0.994306i	$-0.466016\pi$
$409$	721013.	0.213125	0.106563	+	0.994306i	$0.466016\pi$
$410$	−1.61403e6	−0.474190
$411$	3.39938e6	0.992648
$412$	−5.49708e6	−1.59547
$413$	3.86952e6	1.11630
$414$	−3.05397e6	−0.875718
$415$	4.43122e6	1.26300
$416$	−1.94688e6	−0.551576
$417$	−3.28777e6	−0.925895
$418$	0	0
$419$	3.89904e6	1.08498	0.542491	−	0.840061i	$-0.317481\pi$
$419$	3.89904e6	1.08498	0.542491	+	0.840061i	$0.317481\pi$
$420$	−9.32318e6	−2.57894
$421$	−3.39665e6	−0.933996	−0.466998	−	0.884258i	$-0.654665\pi$
$421$	−3.39665e6	−0.933996	−0.466998	+	0.884258i	$0.654665\pi$
$422$	−3.75155e6	−1.02549
$423$	1.67898e6	0.456241
$424$	−1.37181e6	−0.370579
$425$	4.79410e6	1.28746
$426$	−305020.	−0.0814336
$427$	3.55605e6	0.943840
$428$	−1.74695e6	−0.460969
$429$	0	0
$430$	−1.41928e6	−0.370165
$431$	5.15196e6	1.33592	0.667958	−	0.744199i	$-0.267168\pi$
$431$	5.15196e6	1.33592	0.667958	+	0.744199i	$0.267168\pi$
$432$	873.573	0.000225211 0
$433$	−3.23450e6	−0.829063	−0.414531	−	0.910035i	$-0.636055\pi$
$433$	−3.23450e6	−0.829063	−0.414531	+	0.910035i	$0.636055\pi$
$434$	−1.16056e7	−2.95762
$435$	480864.	0.121843
$436$	1.96571e6	0.495226
$437$	−2.71146e6	−0.679202
$438$	−1.63156e6	−0.406365
$439$	−6.31060e6	−1.56282	−0.781411	−	0.624017i	$-0.785500\pi$
$439$	−6.31060e6	−1.56282	−0.781411	+	0.624017i	$0.785500\pi$
$440$	0	0
$441$	2.19444e6	0.537314
$442$	2.45576e6	0.597903
$443$	2.87512e6	0.696061	0.348030	−	0.937483i	$-0.386851\pi$
$443$	2.87512e6	0.696061	0.348030	+	0.937483i	$0.386851\pi$
$444$	6.54664e6	1.57602
$445$	−5.15425e6	−1.23386
$446$	2.47013e6	0.588006
$447$	2.67811e6	0.633957
$448$	−1.11101e7	−2.61531
$449$	−4.54361e6	−1.06362	−0.531809	−	0.846865i	$-0.678487\pi$
$449$	−4.54361e6	−1.06362	−0.531809	+	0.846865i	$0.678487\pi$
$450$	4.44731e6	1.03530
$451$	0	0
$452$	1.23992e7	2.85461
$453$	2.86284e6	0.655467
$454$	9.34850e6	2.12864
$455$	6.72012e6	1.52177
$456$	−1.07127e6	−0.241260
$457$	−2.78485e6	−0.623751	−0.311876	−	0.950123i	$-0.600957\pi$
$457$	−2.78485e6	−0.623751	−0.311876	+	0.950123i	$0.600957\pi$
$458$	1.54922e6	0.345104
$459$	−582561.	−0.129065
$460$	−2.03683e7	−4.48808
$461$	2.00495e6	0.439391	0.219695	−	0.975569i	$-0.429494\pi$
$461$	2.00495e6	0.439391	0.219695	+	0.975569i	$0.429494\pi$
$462$	0	0
$463$	−4.67402e6	−1.01330	−0.506650	−	0.862152i	$-0.669116\pi$
$463$	−4.67402e6	−1.01330	−0.506650	+	0.862152i	$0.669116\pi$
$464$	670.276	0.000144530 0
$465$	5.20309e6	1.11591
$466$	187119.	0.0399166
$467$	−1.41948e6	−0.301188	−0.150594	−	0.988596i	$-0.548119\pi$
$467$	−1.41948e6	−0.301188	−0.150594	+	0.988596i	$0.548119\pi$
$468$	1.40778e6	0.297112
$469$	−1.17722e6	−0.247129
$470$	1.81208e7	3.78383
$471$	310406.	0.0644731
$472$	3.33998e6	0.690063
$473$	0	0
$474$	5.27241e6	1.07786
$475$	3.94852e6	0.802973
$476$	8.66639e6	1.75316
$477$	−614422.	−0.123643
$478$	8.54393e6	1.71036
$479$	3.60077e6	0.717062	0.358531	−	0.933518i	$-0.383278\pi$
$479$	3.60077e6	0.717062	0.358531	+	0.933518i	$0.383278\pi$
$480$	4.98455e6	0.987467
$481$	−4.71880e6	−0.929970
$482$	1.19214e7	2.33728
$483$	7.76838e6	1.51517
$484$	0	0
$485$	1.38743e7	2.67828
$486$	−540420.	−0.103787
$487$	−5.57519e6	−1.06521	−0.532607	−	0.846363i	$-0.678788\pi$
$487$	−5.57519e6	−1.06521	−0.532607	+	0.846363i	$0.678788\pi$
$488$	3.06941e6	0.583452
$489$	412792.	0.0780654
$490$	2.36841e7	4.45621
$491$	1.80948e6	0.338728	0.169364	−	0.985554i	$-0.445829\pi$
$491$	1.80948e6	0.338728	0.169364	+	0.985554i	$0.445829\pi$
$492$	860073.	0.160185
$493$	−446989.	−0.0828284
$494$	2.02262e6	0.372903
$495$	0	0
$496$	7252.58	0.00132370
$497$	775877.	0.140897
$498$	−3.82109e6	−0.690421
$499$	−5.94504e6	−1.06882	−0.534409	−	0.845226i	$-0.679466\pi$
$499$	−5.94504e6	−1.06882	−0.534409	+	0.845226i	$0.679466\pi$
$500$	1.42106e7	2.54206
$501$	2.61848e6	0.466075
$502$	−8.51940e6	−1.50886
$503$	−6.57296e6	−1.15835	−0.579176	−	0.815202i	$-0.696626\pi$
$503$	−6.57296e6	−1.15835	−0.579176	+	0.815202i	$0.696626\pi$
$504$	3.06920e6	0.538207
$505$	7.37564e6	1.28698
$506$	0	0
$507$	2.32691e6	0.402031
$508$	−4.59597e6	−0.790165
$509$	1.76650e6	0.302218	0.151109	−	0.988517i	$-0.451716\pi$
$509$	1.76650e6	0.302218	0.151109	+	0.988517i	$0.451716\pi$
$510$	−6.28743e6	−1.07040
$511$	4.15018e6	0.703096
$512$	13882.8	0.00234046
$513$	−479810.	−0.0804962
$514$	−231671.	−0.0386780
$515$	−1.01445e7	−1.68544
$516$	756293.	0.125045
$517$	0	0
$518$	−2.69479e7	−4.41266
$519$	−1.25424e6	−0.204391
$520$	5.80048e6	0.940709
$521$	9.74164e6	1.57231	0.786154	−	0.618031i	$-0.212069\pi$
$521$	9.74164e6	1.57231	0.786154	+	0.618031i	$0.212069\pi$
$522$	−414655.	−0.0666055
$523$	−6.30069e6	−1.00724	−0.503621	−	0.863925i	$-0.667999\pi$
$523$	−6.30069e6	−1.00724	−0.503621	+	0.863925i	$0.667999\pi$
$524$	−1.72693e7	−2.74756
$525$	−1.13126e7	−1.79128
$526$	1.54965e7	2.44213
$527$	−4.83655e6	−0.758593
$528$	0	0
$529$	1.05352e7	1.63683
$530$	−6.63130e6	−1.02544
$531$	1.49594e6	0.230239
$532$	7.13782e6	1.09342
$533$	−619939.	−0.0945215
$534$	4.44457e6	0.674492
$535$	−3.22390e6	−0.486964
$536$	−1.01611e6	−0.152767
$537$	5.39600e6	0.807489
$538$	4.29566e6	0.639844
$539$	0	0
$540$	−3.60431e6	−0.531909
$541$	1.12441e7	1.65169	0.825847	−	0.563894i	$-0.190697\pi$
$541$	1.12441e7	1.65169	0.825847	+	0.563894i	$0.190697\pi$
$542$	1.99827e7	2.92184
$543$	−1.17567e6	−0.171115
$544$	−4.63340e6	−0.671278
$545$	3.62760e6	0.523153
$546$	−5.79484e6	−0.831879
$547$	−60699.0	−0.00867388	−0.00433694	−	0.999991i	$-0.501380\pi$
$547$	−60699.0	−0.00867388	−0.00433694	+	0.999991i	$0.501380\pi$
$548$	−1.95504e7	−2.78101
$549$	1.37476e6	0.194668
$550$	0	0
$551$	−368149.	−0.0516589
$552$	6.70528e6	0.936633
$553$	−1.34114e7	−1.86492
$554$	771340.	0.106775
$555$	1.20814e7	1.66489
$556$	1.89085e7	2.59400
$557$	−2.28778e6	−0.312447	−0.156224	−	0.987722i	$-0.549932\pi$
$557$	−2.28778e6	−0.312447	−0.156224	+	0.987722i	$0.549932\pi$
$558$	−4.48668e6	−0.610014
$559$	−545134.	−0.0737860
$560$	−23982.6	−0.00323166
$561$	0	0
$562$	−5.94441e6	−0.793904
$563$	5.37938e6	0.715256	0.357628	−	0.933864i	$-0.383586\pi$
$563$	5.37938e6	0.715256	0.357628	+	0.933864i	$0.383586\pi$
$564$	−9.65605e6	−1.27821
$565$	2.28819e7	3.01558
$566$	−1.41759e7	−1.85999
$567$	1.37467e6	0.179572
$568$	669699.	0.0870981
$569$	6.95488e6	0.900552	0.450276	−	0.892889i	$-0.351326\pi$
$569$	6.95488e6	0.900552	0.450276	+	0.892889i	$0.351326\pi$
$570$	−5.17846e6	−0.667596
$571$	3.19590e6	0.410206	0.205103	−	0.978740i	$-0.434247\pi$
$571$	3.19590e6	0.410206	0.205103	+	0.978740i	$0.434247\pi$
$572$	0	0
$573$	−3.04419e6	−0.387334
$574$	−3.54031e6	−0.448500
$575$	−2.47146e7	−3.11734
$576$	−4.29513e6	−0.539411
$577$	2.54992e6	0.318851	0.159425	−	0.987210i	$-0.449036\pi$
$577$	2.54992e6	0.318851	0.159425	+	0.987210i	$0.449036\pi$
$578$	−7.15012e6	−0.890213
$579$	−2.96184e6	−0.367169
$580$	−2.76552e6	−0.341355
$581$	9.71970e6	1.19457
$582$	−1.19640e7	−1.46409
$583$	0	0
$584$	3.58223e6	0.434632
$585$	2.59798e6	0.313867
$586$	643177.	0.0773724
$587$	−1.96757e6	−0.235687	−0.117843	−	0.993032i	$-0.537598\pi$
$587$	−1.96757e6	−0.235687	−0.117843	+	0.993032i	$0.537598\pi$
$588$	−1.26206e7	−1.50534
$589$	−3.98348e6	−0.473124
$590$	1.61453e7	1.90949
$591$	4.65658e6	0.548401
$592$	16840.3	0.00197490
$593$	8.41413e6	0.982590	0.491295	−	0.870993i	$-0.336524\pi$
$593$	8.41413e6	0.982590	0.491295	+	0.870993i	$0.336524\pi$
$594$	0	0
$595$	1.59933e7	1.85202
$596$	−1.54022e7	−1.77610
$597$	4.78293e6	0.549235
$598$	−1.26600e7	−1.44771
$599$	−1.00298e7	−1.14216	−0.571078	−	0.820896i	$-0.693475\pi$
$599$	−1.00298e7	−1.14216	−0.571078	+	0.820896i	$0.693475\pi$
$600$	−9.76448e6	−1.10732
$601$	1.42206e7	1.60595	0.802977	−	0.596010i	$-0.203248\pi$
$601$	1.42206e7	1.60595	0.802977	+	0.596010i	$0.203248\pi$
$602$	−3.11312e6	−0.350111
$603$	−455108.	−0.0509708
$604$	−1.64646e7	−1.83636
$605$	0	0
$606$	−6.36010e6	−0.703530
$607$	−1.51717e7	−1.67133	−0.835665	−	0.549240i	$-0.814917\pi$
$607$	−1.51717e7	−1.67133	−0.835665	+	0.549240i	$0.814917\pi$
$608$	−3.81617e6	−0.418667
$609$	1.05476e6	0.115241
$610$	1.48374e7	1.61448
$611$	6.96006e6	0.754241
$612$	3.35040e6	0.361591
$613$	1.52884e7	1.64328	0.821638	−	0.570010i	$-0.193061\pi$
$613$	1.52884e7	1.64328	0.821638	+	0.570010i	$0.193061\pi$
$614$	−1.31189e7	−1.40435
$615$	1.58721e6	0.169218
$616$	0	0
$617$	−1.81989e6	−0.192457	−0.0962284	−	0.995359i	$-0.530678\pi$
$617$	−1.81989e6	−0.192457	−0.0962284	+	0.995359i	$0.530678\pi$
$618$	8.74775e6	0.921352
$619$	1.39678e7	1.46521	0.732606	−	0.680653i	$-0.238304\pi$
$619$	1.39678e7	1.46521	0.732606	+	0.680653i	$0.238304\pi$
$620$	−2.99237e7	−3.12634
$621$	3.00323e6	0.312507
$622$	−2.08557e6	−0.216147
$623$	−1.13056e7	−1.16701
$624$	3621.32	0.000372311 0
$625$	7.47727e6	0.765672
$626$	−6.62390e6	−0.675582
$627$	0	0
$628$	−1.78519e6	−0.180628
$629$	−1.12303e7	−1.13179
$630$	1.48364e7	1.48928
$631$	−1.64990e7	−1.64962	−0.824808	−	0.565413i	$-0.808717\pi$
$631$	−1.64990e7	−1.64962	−0.824808	+	0.565413i	$0.808717\pi$
$632$	−1.15761e7	−1.15284
$633$	3.68921e6	0.365952
$634$	1.15395e7	1.14015
$635$	−8.48159e6	−0.834724
$636$	3.53363e6	0.346401
$637$	9.09688e6	0.888268
$638$	0	0
$639$	299951.	0.0290602
$640$	−2.86333e7	−2.76326
$641$	1.14852e7	1.10406	0.552030	−	0.833824i	$-0.313853\pi$
$641$	1.14852e7	1.10406	0.552030	+	0.833824i	$0.313853\pi$
$642$	2.78001e6	0.266200
$643$	−5.83065e6	−0.556147	−0.278073	−	0.960560i	$-0.589696\pi$
$643$	−5.83065e6	−0.556147	−0.278073	+	0.960560i	$0.589696\pi$
$644$	−4.46771e7	−4.24493
$645$	1.39569e6	0.132096
$646$	4.81365e6	0.453830
$647$	−1.27091e7	−1.19359	−0.596795	−	0.802394i	$-0.703559\pi$
$647$	−1.27091e7	−1.19359	−0.596795	+	0.802394i	$0.703559\pi$
$648$	1.18654e6	0.111006
$649$	0	0
$650$	1.84359e7	1.71152
$651$	1.14128e7	1.05545
$652$	−2.37403e6	−0.218709
$653$	−8.01118e6	−0.735214	−0.367607	−	0.929981i	$-0.619823\pi$
$653$	−8.01118e6	−0.735214	−0.367607	+	0.929981i	$0.619823\pi$
$654$	−3.12812e6	−0.285983
$655$	−3.18696e7	−2.90250
$656$	2212.42	0.000200728 0
$657$	1.60445e6	0.145015
$658$	3.97472e7	3.57883
$659$	−1.48896e7	−1.33558	−0.667790	−	0.744350i	$-0.732759\pi$
$659$	−1.48896e7	−1.33558	−0.667790	+	0.744350i	$0.732759\pi$
$660$	0	0
$661$	−1.15205e7	−1.02558	−0.512788	−	0.858515i	$-0.671387\pi$
$661$	−1.15205e7	−1.02558	−0.512788	+	0.858515i	$0.671387\pi$
$662$	3.96691e6	0.351809
$663$	−2.41496e6	−0.213366
$664$	8.38956e6	0.738447
$665$	1.31724e7	1.15508
$666$	−1.04180e7	−0.910118
$667$	2.30432e6	0.200553
$668$	−1.50593e7	−1.30576
$669$	−2.42908e6	−0.209835
$670$	−4.91186e6	−0.422726
$671$	0	0
$672$	1.09334e7	0.933968
$673$	1.68386e7	1.43308	0.716538	−	0.697548i	$-0.245726\pi$
$673$	1.68386e7	1.43308	0.716538	+	0.697548i	$0.245726\pi$
$674$	−3.48286e7	−2.95315
$675$	−4.37342e6	−0.369455
$676$	−1.33824e7	−1.12634
$677$	6.56811e6	0.550768	0.275384	−	0.961334i	$-0.411195\pi$
$677$	6.56811e6	0.550768	0.275384	+	0.961334i	$0.411195\pi$
$678$	−1.97314e7	−1.64848
$679$	3.04327e7	2.53318
$680$	1.38046e7	1.14486
$681$	−9.19317e6	−0.759622
$682$	0	0
$683$	−1.01525e7	−0.832761	−0.416381	−	0.909190i	$-0.636702\pi$
$683$	−1.01525e7	−0.832761	−0.416381	+	0.909190i	$0.636702\pi$
$684$	2.75946e6	0.225519
$685$	−3.60790e7	−2.93784
$686$	1.97218e7	1.60006
$687$	−1.52348e6	−0.123153
$688$	1945.46	0.000156693 0
$689$	−2.54704e6	−0.204403
$690$	3.24131e7	2.59178
$691$	−1.01356e7	−0.807521	−0.403760	−	0.914865i	$-0.632297\pi$
$691$	−1.01356e7	−0.807521	−0.403760	+	0.914865i	$0.632297\pi$
$692$	7.21332e6	0.572625
$693$	0	0
$694$	−2.66352e7	−2.09922
$695$	3.48945e7	2.74028
$696$	910413.	0.0712386
$697$	−1.47540e6	−0.115034
$698$	3.78438e7	2.94006
$699$	−184010.	−0.0142445
$700$	6.50605e7	5.01848
$701$	−9.16091e6	−0.704115	−0.352058	−	0.935978i	$-0.614518\pi$
$701$	−9.16091e6	−0.704115	−0.352058	+	0.935978i	$0.614518\pi$
$702$	−2.24027e6	−0.171576
$703$	−9.24955e6	−0.705882
$704$	0	0
$705$	−1.78197e7	−1.35029
$706$	4.57544e6	0.345478
$707$	1.61782e7	1.21725
$708$	−8.60340e6	−0.645040
$709$	−8.97668e6	−0.670656	−0.335328	−	0.942101i	$-0.608847\pi$
$709$	−8.97668e6	−0.670656	−0.335328	+	0.942101i	$0.608847\pi$
$710$	3.23730e6	0.241011
$711$	−5.18480e6	−0.384643
$712$	−9.75847e6	−0.721409
$713$	2.49334e7	1.83679
$714$	−1.37912e7	−1.01241
$715$	0	0
$716$	−3.10332e7	−2.26227
$717$	−8.40196e6	−0.610356
$718$	2.71235e7	1.96352
$719$	7.92637e6	0.571811	0.285905	−	0.958258i	$-0.407706\pi$
$719$	7.92637e6	0.571811	0.285905	+	0.958258i	$0.407706\pi$
$720$	−9271.58	−0.000666534 0
$721$	−2.22516e7	−1.59413
$722$	−1.86968e7	−1.33482
$723$	−1.17233e7	−0.834076
$724$	6.76148e6	0.479397
$725$	−3.35564e6	−0.237099
$726$	0	0
$727$	1.78172e7	1.25027	0.625135	−	0.780516i	$-0.285044\pi$
$727$	1.78172e7	1.25027	0.625135	+	0.780516i	$0.285044\pi$
$728$	1.27231e7	0.889744
$729$	531441.	0.0370370
$730$	1.73164e7	1.20268
$731$	−1.29737e6	−0.0897989
$732$	−7.90644e6	−0.545385
$733$	−1.81797e7	−1.24976	−0.624882	−	0.780719i	$-0.714853\pi$
$733$	−1.81797e7	−1.24976	−0.624882	+	0.780719i	$0.714853\pi$
$734$	2.35670e6	0.161460
$735$	−2.32905e7	−1.59023
$736$	2.38862e7	1.62537
$737$	0	0
$738$	−1.36867e6	−0.0925037
$739$	1.38291e7	0.931502	0.465751	−	0.884916i	$-0.345784\pi$
$739$	1.38291e7	0.931502	0.465751	+	0.884916i	$0.345784\pi$
$740$	−6.94822e7	−4.66438
$741$	−1.98901e6	−0.133073
$742$	−1.45455e7	−0.969881
$743$	7.07226e6	0.469987	0.234994	−	0.971997i	$-0.424493\pi$
$743$	7.07226e6	0.469987	0.234994	+	0.971997i	$0.424493\pi$
$744$	9.85093e6	0.652447
$745$	−2.84239e7	−1.87626
$746$	1.17345e7	0.771998
$747$	3.75760e6	0.246382
$748$	0	0
$749$	−7.07149e6	−0.460582
$750$	−2.26139e7	−1.46799
$751$	−653678.	−0.0422926	−0.0211463	−	0.999776i	$-0.506732\pi$
$751$	−653678.	−0.0422926	−0.0211463	+	0.999776i	$0.506732\pi$
$752$	−24838.8	−0.00160172
$753$	8.37785e6	0.538449
$754$	−1.71892e6	−0.110110
$755$	−3.03845e7	−1.93992
$756$	−7.90590e6	−0.503092
$757$	2.72250e7	1.72674	0.863372	−	0.504569i	$-0.168348\pi$
$757$	2.72250e7	1.72674	0.863372	+	0.504569i	$0.168348\pi$
$758$	2.86862e7	1.81343
$759$	0	0
$760$	1.13698e7	0.714033
$761$	5.41780e6	0.339126	0.169563	−	0.985519i	$-0.445764\pi$
$761$	5.41780e6	0.339126	0.169563	+	0.985519i	$0.445764\pi$
$762$	7.31378e6	0.456304
$763$	7.95700e6	0.494809
$764$	1.75076e7	1.08516
$765$	6.18296e6	0.381982
$766$	8.01521e6	0.493563
$767$	6.20131e6	0.380623
$768$	9.41931e6	0.576257
$769$	−2.96407e7	−1.80748	−0.903739	−	0.428084i	$-0.859189\pi$
$769$	−2.96407e7	−1.80748	−0.903739	+	0.428084i	$0.859189\pi$
$770$	0	0
$771$	227822.	0.0138026
$772$	1.70340e7	1.02866
$773$	1.87755e7	1.13017	0.565083	−	0.825034i	$-0.308844\pi$
$773$	1.87755e7	1.13017	0.565083	+	0.825034i	$0.308844\pi$
$774$	−1.20352e6	−0.0722108
$775$	−3.63090e7	−2.17150
$776$	2.62680e7	1.56593
$777$	2.65001e7	1.57469
$778$	−1.78722e7	−1.05859
$779$	−1.21517e6	−0.0717453
$780$	−1.49414e7	−0.879333
$781$	0	0
$782$	−3.01297e7	−1.76188
$783$	407765.	0.0237687
$784$	−32464.7	−0.00188634
$785$	−3.29447e6	−0.190814
$786$	2.74815e7	1.58666
$787$	1.54112e7	0.886951	0.443475	−	0.896286i	$-0.353745\pi$
$787$	1.54112e7	0.886951	0.443475	+	0.896286i	$0.353745\pi$
$788$	−2.67807e7	−1.53641
$789$	−1.52390e7	−0.871493
$790$	−5.59582e7	−3.19004
$791$	5.01906e7	2.85221
$792$	0	0
$793$	5.69894e6	0.321819
$794$	−1.56242e7	−0.879522
$795$	6.52111e6	0.365935
$796$	−2.75073e7	−1.53874
$797$	2.10597e7	1.17437	0.587186	−	0.809452i	$-0.300236\pi$
$797$	2.10597e7	1.17437	0.587186	+	0.809452i	$0.300236\pi$
$798$	−1.13587e7	−0.631427
$799$	1.65643e7	0.917925
$800$	−3.47840e7	−1.92156
$801$	−4.37072e6	−0.240698
$802$	4.13334e7	2.26916
$803$	0	0
$804$	2.61739e6	0.142800
$805$	−8.24490e7	−4.48431
$806$	−1.85992e7	−1.00845
$807$	−4.22428e6	−0.228333
$808$	1.39642e7	0.752467
$809$	−1.95659e7	−1.05106	−0.525532	−	0.850774i	$-0.676134\pi$
$809$	−1.95659e7	−1.05106	−0.525532	+	0.850774i	$0.676134\pi$
$810$	5.73570e6	0.307167
$811$	−1.29945e7	−0.693758	−0.346879	−	0.937910i	$-0.612759\pi$
$811$	−1.29945e7	−0.693758	−0.346879	+	0.937910i	$0.612759\pi$
$812$	−6.06605e6	−0.322861
$813$	−1.96507e7	−1.04268
$814$	0	0
$815$	−4.38113e6	−0.231042
$816$	8618.43	0.000453109 0
$817$	−1.06854e6	−0.0560063
$818$	6.59876e6	0.344809
$819$	5.69856e6	0.296862
$820$	−9.12830e6	−0.474084
$821$	3.50872e7	1.81673	0.908367	−	0.418175i	$-0.137330\pi$
$821$	3.50872e7	1.81673	0.908367	+	0.418175i	$0.137330\pi$
$822$	3.11114e7	1.60598
$823$	1.38494e7	0.712742	0.356371	−	0.934345i	$-0.384014\pi$
$823$	1.38494e7	0.712742	0.356371	+	0.934345i	$0.384014\pi$
$824$	−1.92065e7	−0.985440
$825$	0	0
$826$	3.54141e7	1.80604
$827$	−2.31031e7	−1.17464	−0.587322	−	0.809353i	$-0.699818\pi$
$827$	−2.31031e7	−1.17464	−0.587322	+	0.809353i	$0.699818\pi$
$828$	−1.72720e7	−0.875522
$829$	−1.28103e6	−0.0647401	−0.0323701	−	0.999476i	$-0.510306\pi$
$829$	−1.28103e6	−0.0647401	−0.0323701	+	0.999476i	$0.510306\pi$
$830$	4.05548e7	2.04337
$831$	−758523.	−0.0381036
$832$	−1.78051e7	−0.891735
$833$	2.16498e7	1.08104
$834$	−3.00899e7	−1.49798
$835$	−2.77910e7	−1.37939
$836$	0	0
$837$	4.41213e6	0.217688
$838$	3.56843e7	1.75536
$839$	1.98332e7	0.972721	0.486361	−	0.873758i	$-0.338324\pi$
$839$	1.98332e7	0.972721	0.486361	+	0.873758i	$0.338324\pi$
$840$	−3.25747e7	−1.59288
$841$	−2.01983e7	−0.984746
$842$	−3.10863e7	−1.51109
$843$	5.84564e6	0.283311
$844$	−2.12172e7	−1.02526
$845$	−2.46965e7	−1.18985
$846$	1.53661e7	0.738139
$847$	0	0
$848$	9089.78	0.000434074 0
$849$	1.39404e7	0.663751
$850$	4.38760e7	2.08295
$851$	5.78948e7	2.74041
$852$	−1.72507e6	−0.0814154
$853$	2.65097e7	1.24747	0.623737	−	0.781634i	$-0.285614\pi$
$853$	2.65097e7	1.24747	0.623737	+	0.781634i	$0.285614\pi$
$854$	3.25452e7	1.52701
$855$	5.09242e6	0.238237
$856$	−6.10376e6	−0.284717
$857$	1.96831e7	0.915465	0.457733	−	0.889090i	$-0.348662\pi$
$857$	1.96831e7	0.915465	0.457733	+	0.889090i	$0.348662\pi$
$858$	0	0
$859$	−1.74273e7	−0.805835	−0.402917	−	0.915236i	$-0.632004\pi$
$859$	−1.74273e7	−0.805835	−0.402917	+	0.915236i	$0.632004\pi$
$860$	−8.02684e6	−0.370083
$861$	3.48149e6	0.160051
$862$	4.71511e7	2.16134
$863$	−6.02685e6	−0.275463	−0.137732	−	0.990470i	$-0.543981\pi$
$863$	−6.02685e6	−0.275463	−0.137732	+	0.990470i	$0.543981\pi$
$864$	4.22682e6	0.192632
$865$	1.33118e7	0.604916
$866$	−2.96024e7	−1.34132
$867$	7.03132e6	0.317679
$868$	−6.56365e7	−2.95696
$869$	0	0
$870$	4.40090e6	0.197126
$871$	−1.88661e6	−0.0842630
$872$	6.86809e6	0.305875
$873$	1.17652e7	0.522472
$874$	−2.48154e7	−1.09886
$875$	5.75229e7	2.53993
$876$	−9.22741e6	−0.406274
$877$	5.71518e6	0.250917	0.125459	−	0.992099i	$-0.459960\pi$
$877$	5.71518e6	0.250917	0.125459	+	0.992099i	$0.459960\pi$
$878$	−5.77551e7	−2.52845
$879$	−632490.	−0.0276109
$880$	0	0
$881$	1.76619e7	0.766649	0.383324	−	0.923614i	$-0.374779\pi$
$881$	1.76619e7	0.766649	0.383324	+	0.923614i	$0.374779\pi$
$882$	2.00837e7	0.869306
$883$	2.70117e7	1.16587	0.582936	−	0.812518i	$-0.301904\pi$
$883$	2.70117e7	1.16587	0.582936	+	0.812518i	$0.301904\pi$
$884$	1.38888e7	0.597769
$885$	−1.58771e7	−0.681416
$886$	2.63133e7	1.12614
$887$	−1.30141e7	−0.555398	−0.277699	−	0.960668i	$-0.589572\pi$
$887$	−1.30141e7	−0.555398	−0.277699	+	0.960668i	$0.589572\pi$
$888$	2.28736e7	0.973425
$889$	−1.86040e7	−0.789500
$890$	−4.71720e7	−1.99623
$891$	0	0
$892$	1.39700e7	0.587875
$893$	1.36427e7	0.572496
$894$	2.45103e7	1.02566
$895$	−5.72700e7	−2.38984
$896$	−6.28061e7	−2.61355
$897$	1.24496e7	0.516625
$898$	−4.15834e7	−1.72080
$899$	3.38535e6	0.139703
$900$	2.51522e7	1.03507
$901$	−6.06172e6	−0.248762
$902$	0	0
$903$	3.06140e6	0.124940
$904$	4.33220e7	1.76314
$905$	1.24779e7	0.506431
$906$	2.62009e7	1.06046
$907$	9.84123e6	0.397220	0.198610	−	0.980079i	$-0.436357\pi$
$907$	9.84123e6	0.397220	0.198610	+	0.980079i	$0.436357\pi$
$908$	5.28713e7	2.12816
$909$	6.25442e6	0.251060
$910$	6.15030e7	2.46203
$911$	7.41735e6	0.296110	0.148055	−	0.988979i	$-0.452699\pi$
$911$	7.41735e6	0.296110	0.148055	+	0.988979i	$0.452699\pi$
$912$	7098.32	0.000282598 0
$913$	0	0
$914$	−2.54871e7	−1.00915
$915$	−1.45909e7	−0.576140
$916$	8.76177e6	0.345027
$917$	−6.99046e7	−2.74525
$918$	−5.33164e6	−0.208811
$919$	−1.15896e7	−0.452667	−0.226333	−	0.974050i	$-0.572674\pi$
$919$	−1.15896e7	−0.452667	−0.226333	+	0.974050i	$0.572674\pi$
$920$	−7.11659e7	−2.77206
$921$	1.29009e7	0.501153
$922$	1.83494e7	0.710878
$923$	1.24342e6	0.0480413
$924$	0	0
$925$	−8.43087e7	−3.23980
$926$	−4.27769e7	−1.63939
$927$	−8.60240e6	−0.328791
$928$	3.24316e6	0.123623
$929$	1.17151e7	0.445357	0.222679	−	0.974892i	$-0.428520\pi$
$929$	1.17151e7	0.445357	0.222679	+	0.974892i	$0.428520\pi$
$930$	4.76190e7	1.80540
$931$	1.78312e7	0.674228
$932$	1.05827e6	0.0399077
$933$	2.05091e6	0.0771336
$934$	−1.29912e7	−0.487284
$935$	0	0
$936$	4.91871e6	0.183511
$937$	−9.18288e6	−0.341688	−0.170844	−	0.985298i	$-0.554649\pi$
$937$	−9.18288e6	−0.341688	−0.170844	+	0.985298i	$0.554649\pi$
$938$	−1.07740e7	−0.399823
$939$	6.51384e6	0.241087
$940$	1.02484e8	3.78299
$941$	−3.24899e6	−0.119612	−0.0598059	−	0.998210i	$-0.519048\pi$
$941$	−3.24899e6	−0.119612	−0.0598059	+	0.998210i	$0.519048\pi$
$942$	2.84086e6	0.104309
$943$	7.60601e6	0.278534
$944$	−22131.0	−0.000808299 0
$945$	−1.45899e7	−0.531462
$946$	0	0
$947$	3.50906e7	1.27150	0.635750	−	0.771895i	$-0.280691\pi$
$947$	3.50906e7	1.27150	0.635750	+	0.771895i	$0.280691\pi$
$948$	2.98186e7	1.07762
$949$	6.65109e6	0.239733
$950$	3.61372e7	1.29911
$951$	−1.13477e7	−0.406872
$952$	3.02799e7	1.08283
$953$	3.27415e7	1.16780	0.583898	−	0.811827i	$-0.301527\pi$
$953$	3.27415e7	1.16780	0.583898	+	0.811827i	$0.301527\pi$
$954$	−5.62323e6	−0.200039
$955$	3.23092e7	1.14635
$956$	4.83209e7	1.70998
$957$	0	0
$958$	3.29545e7	1.16011
$959$	−7.91379e7	−2.77868
$960$	4.55859e7	1.59644
$961$	8.00132e6	0.279482
$962$	−4.31868e7	−1.50457
$963$	−2.73382e6	−0.0949956
$964$	6.74227e7	2.33676
$965$	3.14353e7	1.08667
$966$	7.10967e7	2.45136
$967$	3.94890e7	1.35803	0.679016	−	0.734124i	$-0.262407\pi$
$967$	3.94890e7	1.35803	0.679016	+	0.734124i	$0.262407\pi$
$968$	0	0
$969$	−4.73367e6	−0.161953
$970$	1.26978e8	4.33312
$971$	1.43971e7	0.490033	0.245017	−	0.969519i	$-0.421207\pi$
$971$	1.43971e7	0.490033	0.245017	+	0.969519i	$0.421207\pi$
$972$	−3.05640e6	−0.103763
$973$	7.65396e7	2.59182
$974$	−5.10245e7	−1.72338
$975$	−1.81296e7	−0.610769
$976$	−20338.2	−0.000683421 0
$977$	−4.55108e7	−1.52538	−0.762690	−	0.646764i	$-0.776122\pi$
$977$	−4.55108e7	−1.52538	−0.762690	+	0.646764i	$0.776122\pi$
$978$	3.77790e6	0.126300
$979$	0	0
$980$	1.33947e8	4.45522
$981$	3.07615e6	0.102055
$982$	1.65605e7	0.548018
$983$	−3.34028e7	−1.10255	−0.551276	−	0.834323i	$-0.685859\pi$
$983$	−3.34028e7	−1.10255	−0.551276	+	0.834323i	$0.685859\pi$
$984$	3.00505e6	0.0989382
$985$	−4.94222e7	−1.62305
$986$	−4.09087e6	−0.134006
$987$	−3.90867e7	−1.27713
$988$	1.14391e7	0.372820
$989$	6.68823e6	0.217431
$990$	0	0
$991$	4.23892e7	1.37111	0.685553	−	0.728023i	$-0.259560\pi$
$991$	4.23892e7	1.37111	0.685553	+	0.728023i	$0.259560\pi$
$992$	3.50919e7	1.13221
$993$	−3.90100e6	−0.125546
$994$	7.10088e6	0.227953
$995$	−5.07632e7	−1.62551
$996$	−2.16105e7	−0.690267
$997$	−3.39103e7	−1.08042	−0.540212	−	0.841529i	$-0.681656\pi$
$997$	−3.39103e7	−1.08042	−0.540212	+	0.841529i	$0.681656\pi$
$998$	−5.44094e7	−1.72921
$999$	1.02449e7	0.324783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.6.a.j.1.2		2
3.2	odd	2		1089.6.a.j.1.1		2
11.10	odd	2		33.6.a.c.1.1	✓	2
33.32	even	2		99.6.a.f.1.2		2
44.43	even	2		528.6.a.s.1.2		2
55.54	odd	2		825.6.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.a.c.1.1	✓	2	11.10	odd	2
99.6.a.f.1.2		2	33.32	even	2
363.6.a.j.1.2		2	1.1	even	1	trivial
528.6.a.s.1.2		2	44.43	even	2
825.6.a.e.1.2		2	55.54	odd	2
1089.6.a.j.1.1		2	3.2	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q+9.15207 q^{2} -9.00000 q^{3} +51.7603 q^{4} +95.5207 q^{5} -82.3686 q^{6} +209.521 q^{7} +180.848 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.15207 q^{2} -9.00000 q^{3} +51.7603 q^{4} +95.5207 q^{5} -82.3686 q^{6} +209.521 q^{7} +180.848 q^{8} +81.0000 q^{9} +874.212 q^{10} -465.843 q^{12} +335.779 q^{13} +1917.55 q^{14} -859.686 q^{15} -1.19832 q^{16} +799.124 q^{17} +741.317 q^{18} +658.175 q^{19} +4944.18 q^{20} -1885.69 q^{21} -4119.66 q^{23} -1627.63 q^{24} +5999.20 q^{25} +3073.07 q^{26} -729.000 q^{27} +10844.9 q^{28} -559.348 q^{29} -7867.90 q^{30} -6052.31 q^{31} -5798.10 q^{32} +7313.64 q^{34} +20013.6 q^{35} +4192.59 q^{36} -14053.3 q^{37} +6023.66 q^{38} -3022.01 q^{39} +17274.7 q^{40} -1846.27 q^{41} -17257.9 q^{42} -1623.49 q^{43} +7737.17 q^{45} -37703.4 q^{46} +20728.1 q^{47} +10.7848 q^{48} +27091.9 q^{49} +54905.1 q^{50} -7192.12 q^{51} +17380.0 q^{52} -7585.46 q^{53} -6671.86 q^{54} +37891.4 q^{56} -5923.58 q^{57} -5119.19 q^{58} +18468.5 q^{59} -44497.6 q^{60} +16972.3 q^{61} -55391.2 q^{62} +16971.2 q^{63} -53026.3 q^{64} +32073.8 q^{65} -5618.62 q^{67} +41362.9 q^{68} +37076.9 q^{69} +183165. q^{70} +3703.10 q^{71} +14648.7 q^{72} +19808.0 q^{73} -128617. q^{74} -53992.8 q^{75} +34067.4 q^{76} -27657.6 q^{78} -64009.9 q^{79} -114.464 q^{80} +6561.00 q^{81} -16897.2 q^{82} +46390.2 q^{83} -97603.7 q^{84} +76332.9 q^{85} -14858.3 q^{86} +5034.13 q^{87} -53959.5 q^{89} +70811.1 q^{90} +70352.5 q^{91} -213235. q^{92} +54470.8 q^{93} +189705. q^{94} +62869.3 q^{95} +52182.9 q^{96} +145249. q^{97} +247947. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} - 18 q^{3} + 37 q^{4} + 58 q^{5} - 45 q^{6} + 286 q^{7} + 375 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q + 5 * q^2 - 18 * q^3 + 37 * q^4 + 58 * q^5 - 45 * q^6 + 286 * q^7 + 375 * q^8 + 162 * q^9	\( 2 q + 5 q^{2} - 18 q^{3} + 37 q^{4} + 58 q^{5} - 45 q^{6} + 286 q^{7} + 375 q^{8} + 162 q^{9} + 1030 q^{10} - 333 q^{12} + 166 q^{13} + 1600 q^{14} - 522 q^{15} - 335 q^{16} + 800 q^{17} + 405 q^{18} + 1476 q^{19} + 5498 q^{20} - 2574 q^{21} - 3370 q^{23} - 3375 q^{24} + 4282 q^{25} + 3778 q^{26} - 1458 q^{27} + 9716 q^{28} - 6600 q^{29} - 9270 q^{30} - 7528 q^{31} - 10625 q^{32} + 7310 q^{34} + 17144 q^{35} + 2997 q^{36} - 29916 q^{37} + 2628 q^{38} - 1494 q^{39} + 9990 q^{40} + 5780 q^{41} - 14400 q^{42} + 16656 q^{43} + 4698 q^{45} - 40816 q^{46} + 7850 q^{47} + 3015 q^{48} + 16134 q^{49} + 62035 q^{50} - 7200 q^{51} + 19886 q^{52} + 14178 q^{53} - 3645 q^{54} + 52740 q^{56} - 13284 q^{57} + 19962 q^{58} + 17300 q^{59} - 49482 q^{60} + 2946 q^{61} - 49264 q^{62} + 23166 q^{63} - 22303 q^{64} + 38444 q^{65} + 31336 q^{67} + 41350 q^{68} + 30330 q^{69} + 195080 q^{70} - 33810 q^{71} + 30375 q^{72} - 60644 q^{73} - 62754 q^{74} - 38538 q^{75} + 21996 q^{76} - 34002 q^{78} - 1870 q^{79} + 12410 q^{80} + 13122 q^{81} - 48562 q^{82} + 58296 q^{83} - 87444 q^{84} + 76300 q^{85} - 90756 q^{86} + 59400 q^{87} + 92388 q^{89} + 83430 q^{90} + 57368 q^{91} - 224300 q^{92} + 67752 q^{93} + 243176 q^{94} + 32184 q^{95} + 95625 q^{96} + 7120 q^{97} + 293445 q^{98}+O(q^{100}) \) 2 * q + 5 * q^2 - 18 * q^3 + 37 * q^4 + 58 * q^5 - 45 * q^6 + 286 * q^7 + 375 * q^8 + 162 * q^9 + 1030 * q^10 - 333 * q^12 + 166 * q^13 + 1600 * q^14 - 522 * q^15 - 335 * q^16 + 800 * q^17 + 405 * q^18 + 1476 * q^19 + 5498 * q^20 - 2574 * q^21 - 3370 * q^23 - 3375 * q^24 + 4282 * q^25 + 3778 * q^26 - 1458 * q^27 + 9716 * q^28 - 6600 * q^29 - 9270 * q^30 - 7528 * q^31 - 10625 * q^32 + 7310 * q^34 + 17144 * q^35 + 2997 * q^36 - 29916 * q^37 + 2628 * q^38 - 1494 * q^39 + 9990 * q^40 + 5780 * q^41 - 14400 * q^42 + 16656 * q^43 + 4698 * q^45 - 40816 * q^46 + 7850 * q^47 + 3015 * q^48 + 16134 * q^49 + 62035 * q^50 - 7200 * q^51 + 19886 * q^52 + 14178 * q^53 - 3645 * q^54 + 52740 * q^56 - 13284 * q^57 + 19962 * q^58 + 17300 * q^59 - 49482 * q^60 + 2946 * q^61 - 49264 * q^62 + 23166 * q^63 - 22303 * q^64 + 38444 * q^65 + 31336 * q^67 + 41350 * q^68 + 30330 * q^69 + 195080 * q^70 - 33810 * q^71 + 30375 * q^72 - 60644 * q^73 - 62754 * q^74 - 38538 * q^75 + 21996 * q^76 - 34002 * q^78 - 1870 * q^79 + 12410 * q^80 + 13122 * q^81 - 48562 * q^82 + 58296 * q^83 - 87444 * q^84 + 76300 * q^85 - 90756 * q^86 + 59400 * q^87 + 92388 * q^89 + 83430 * q^90 + 57368 * q^91 - 224300 * q^92 + 67752 * q^93 + 243176 * q^94 + 32184 * q^95 + 95625 * q^96 + 7120 * q^97 + 293445 * q^98

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