LMFDB - Embedded newform 150.6.c.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(49,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("150.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.6.c.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} -176.000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} -176.000i q^{7} +64.0000i q^{8} -81.0000 q^{9} -60.0000 q^{11} +144.000i q^{12} -658.000i q^{13} -704.000 q^{14} +256.000 q^{16} +414.000i q^{17} +324.000i q^{18} -956.000 q^{19} -1584.00 q^{21} +240.000i q^{22} +600.000i q^{23} +576.000 q^{24} -2632.00 q^{26} +729.000i q^{27} +2816.00i q^{28} -5574.00 q^{29} -3592.00 q^{31} -1024.00i q^{32} +540.000i q^{33} +1656.00 q^{34} +1296.00 q^{36} +8458.00i q^{37} +3824.00i q^{38} -5922.00 q^{39} +19194.0 q^{41} +6336.00i q^{42} +13316.0i q^{43} +960.000 q^{44} +2400.00 q^{46} +19680.0i q^{47} -2304.00i q^{48} -14169.0 q^{49} +3726.00 q^{51} +10528.0i q^{52} -31266.0i q^{53} +2916.00 q^{54} +11264.0 q^{56} +8604.00i q^{57} +22296.0i q^{58} -26340.0 q^{59} -31090.0 q^{61} +14368.0i q^{62} +14256.0i q^{63} -4096.00 q^{64} +2160.00 q^{66} +16804.0i q^{67} -6624.00i q^{68} +5400.00 q^{69} +6120.00 q^{71} -5184.00i q^{72} -25558.0i q^{73} +33832.0 q^{74} +15296.0 q^{76} +10560.0i q^{77} +23688.0i q^{78} -74408.0 q^{79} +6561.00 q^{81} -76776.0i q^{82} -6468.00i q^{83} +25344.0 q^{84} +53264.0 q^{86} +50166.0i q^{87} -3840.00i q^{88} +32742.0 q^{89} -115808. q^{91} -9600.00i q^{92} +32328.0i q^{93} +78720.0 q^{94} -9216.00 q^{96} -166082. i q^{97} +56676.0i q^{98} +4860.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9}+O(q^{10}) $ 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9	$ 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9} - 120 q^{11} - 1408 q^{14} + 512 q^{16} - 1912 q^{19} - 3168 q^{21} + 1152 q^{24} - 5264 q^{26} - 11148 q^{29} - 7184 q^{31} + 3312 q^{34} + 2592 q^{36} - 11844 q^{39} + 38388 q^{41} + 1920 q^{44} + 4800 q^{46} - 28338 q^{49} + 7452 q^{51} + 5832 q^{54} + 22528 q^{56} - 52680 q^{59} - 62180 q^{61} - 8192 q^{64} + 4320 q^{66} + 10800 q^{69} + 12240 q^{71} + 67664 q^{74} + 30592 q^{76} - 148816 q^{79} + 13122 q^{81} + 50688 q^{84} + 106528 q^{86} + 65484 q^{89} - 231616 q^{91} + 157440 q^{94} - 18432 q^{96} + 9720 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9 - 120 * q^11 - 1408 * q^14 + 512 * q^16 - 1912 * q^19 - 3168 * q^21 + 1152 * q^24 - 5264 * q^26 - 11148 * q^29 - 7184 * q^31 + 3312 * q^34 + 2592 * q^36 - 11844 * q^39 + 38388 * q^41 + 1920 * q^44 + 4800 * q^46 - 28338 * q^49 + 7452 * q^51 + 5832 * q^54 + 22528 * q^56 - 52680 * q^59 - 62180 * q^61 - 8192 * q^64 + 4320 * q^66 + 10800 * q^69 + 12240 * q^71 + 67664 * q^74 + 30592 * q^76 - 148816 * q^79 + 13122 * q^81 + 50688 * q^84 + 106528 * q^86 + 65484 * q^89 - 231616 * q^91 + 157440 * q^94 - 18432 * q^96 + 9720 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 4.00000i	− 0.707107i
$2$	− 4.00000i	− 0.707107i
$3$	− 9.00000i	− 0.577350i
$3$	− 9.00000i	− 0.577350i
$4$	−16.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	−36.0000	−0.408248
$7$	− 176.000i	− 1.35759i	−0.734329	−	0.678793i	$-0.762503\pi$
$7$	− 176.000i	− 1.35759i	0.734329	−	0.678793i	$-0.237497\pi$
$8$	64.0000i	0.353553i
$9$	−81.0000	−0.333333
$10$	0	0
$11$	−60.0000	−0.149510	−0.0747549	−	0.997202i	$-0.523817\pi$
$11$	−60.0000	−0.149510	−0.0747549	+	0.997202i	$0.523817\pi$
$12$	144.000i	0.288675i
$13$	− 658.000i	− 1.07986i	−0.841710	−	0.539930i	$-0.818451\pi$
$13$	− 658.000i	− 1.07986i	0.841710	−	0.539930i	$-0.181549\pi$
$14$	−704.000	−0.959959
$15$	0	0
$16$	256.000	0.250000
$17$	414.000i	0.347439i	0.984795	+	0.173719i	$0.0555785\pi$
$17$	414.000i	0.347439i	−0.984795	+	0.173719i	$0.944421\pi$
$18$	324.000i	0.235702i
$19$	−956.000	−0.607539	−0.303769	−	0.952746i	$-0.598245\pi$
$19$	−956.000	−0.607539	−0.303769	+	0.952746i	$0.598245\pi$
$20$	0	0
$21$	−1584.00	−0.783803
$22$	240.000i	0.105719i
$23$	600.000i	0.236500i	0.992984	+	0.118250i	$0.0377285\pi$
$23$	600.000i	0.236500i	−0.992984	+	0.118250i	$0.962272\pi$
$24$	576.000	0.204124
$25$	0	0
$26$	−2632.00	−0.763576
$27$	729.000i	0.192450i
$28$	2816.00i	0.678793i
$29$	−5574.00	−1.23076	−0.615378	−	0.788232i	$-0.710997\pi$
$29$	−5574.00	−1.23076	−0.615378	+	0.788232i	$0.710997\pi$
$30$	0	0
$31$	−3592.00	−0.671324	−0.335662	−	0.941983i	$-0.608960\pi$
$31$	−3592.00	−0.671324	−0.335662	+	0.941983i	$0.608960\pi$
$32$	− 1024.00i	− 0.176777i
$33$	540.000i	0.0863195i
$34$	1656.00	0.245676
$35$	0	0
$36$	1296.00	0.166667
$37$	8458.00i	1.01570i	0.861447	+	0.507848i	$0.169559\pi$
$37$	8458.00i	1.01570i	−0.861447	+	0.507848i	$0.830441\pi$
$38$	3824.00i	0.429595i
$39$	−5922.00	−0.623458
$40$	0	0
$41$	19194.0	1.78322	0.891612	−	0.452800i	$-0.149575\pi$
$41$	19194.0	1.78322	0.891612	+	0.452800i	$0.149575\pi$
$42$	6336.00i	0.554232i
$43$	13316.0i	1.09825i	0.835739	+	0.549127i	$0.185040\pi$
$43$	13316.0i	1.09825i	−0.835739	+	0.549127i	$0.814960\pi$
$44$	960.000	0.0747549
$45$	0	0
$46$	2400.00	0.167231
$47$	19680.0i	1.29951i	0.760143	+	0.649756i	$0.225129\pi$
$47$	19680.0i	1.29951i	−0.760143	+	0.649756i	$0.774871\pi$
$48$	− 2304.00i	− 0.144338i
$49$	−14169.0	−0.843042
$50$	0	0
$51$	3726.00	0.200594
$52$	10528.0i	0.539930i
$53$	− 31266.0i	− 1.52891i	−0.644676	−	0.764456i	$-0.723008\pi$
$53$	− 31266.0i	− 1.52891i	0.644676	−	0.764456i	$-0.276992\pi$
$54$	2916.00	0.136083
$55$	0	0
$56$	11264.0	0.479979
$57$	8604.00i	0.350763i
$58$	22296.0i	0.870276i
$59$	−26340.0	−0.985112	−0.492556	−	0.870281i	$-0.663937\pi$
$59$	−26340.0	−0.985112	−0.492556	+	0.870281i	$0.663937\pi$
$60$	0	0
$61$	−31090.0	−1.06978	−0.534892	−	0.844920i	$-0.679648\pi$
$61$	−31090.0	−1.06978	−0.534892	+	0.844920i	$0.679648\pi$
$62$	14368.0i	0.474698i
$63$	14256.0i	0.452529i
$64$	−4096.00	−0.125000
$65$	0	0
$66$	2160.00	0.0610371
$67$	16804.0i	0.457326i	0.973506	+	0.228663i	$0.0734353\pi$
$67$	16804.0i	0.457326i	−0.973506	+	0.228663i	$0.926565\pi$
$68$	− 6624.00i	− 0.173719i
$69$	5400.00	0.136544
$70$	0	0
$71$	6120.00	0.144081	0.0720403	−	0.997402i	$-0.477049\pi$
$71$	6120.00	0.144081	0.0720403	+	0.997402i	$0.477049\pi$
$72$	− 5184.00i	− 0.117851i
$73$	− 25558.0i	− 0.561332i	−0.959806	−	0.280666i	$-0.909445\pi$
$73$	− 25558.0i	− 0.561332i	0.959806	−	0.280666i	$-0.0905553\pi$
$74$	33832.0	0.718205
$75$	0	0
$76$	15296.0	0.303769
$77$	10560.0i	0.202972i
$78$	23688.0i	0.440851i
$79$	−74408.0	−1.34138	−0.670690	−	0.741738i	$-0.734002\pi$
$79$	−74408.0	−1.34138	−0.670690	+	0.741738i	$0.734002\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	− 76776.0i	− 1.26093i
$83$	− 6468.00i	− 0.103056i	−0.998672	−	0.0515282i	$-0.983591\pi$
$83$	− 6468.00i	− 0.103056i	0.998672	−	0.0515282i	$-0.0164092\pi$
$84$	25344.0	0.391902
$85$	0	0
$86$	53264.0	0.776583
$87$	50166.0i	0.710577i
$88$	− 3840.00i	− 0.0528597i
$89$	32742.0	0.438157	0.219079	−	0.975707i	$-0.429695\pi$
$89$	32742.0	0.438157	0.219079	+	0.975707i	$0.429695\pi$
$90$	0	0
$91$	−115808.	−1.46600
$92$	− 9600.00i	− 0.118250i
$93$	32328.0i	0.387589i
$94$	78720.0	0.918894
$95$	0	0
$96$	−9216.00	−0.102062
$97$	− 166082.i	− 1.79223i	−0.443824	−	0.896114i	$-0.646378\pi$
$97$	− 166082.i	− 1.79223i	0.443824	−	0.896114i	$-0.353622\pi$
$98$	56676.0i	0.596120i
$99$	4860.00	0.0498366
$100$	0	0
$101$	−22002.0	−0.214614	−0.107307	−	0.994226i	$-0.534223\pi$
$101$	−22002.0	−0.214614	−0.107307	+	0.994226i	$0.534223\pi$
$102$	− 14904.0i	− 0.141841i
$103$	− 79264.0i	− 0.736178i	−0.929791	−	0.368089i	$-0.880012\pi$
$103$	− 79264.0i	− 0.736178i	0.929791	−	0.368089i	$-0.119988\pi$
$104$	42112.0	0.381788
$105$	0	0
$106$	−125064.	−1.08110
$107$	− 227988.i	− 1.92510i	−0.271110	−	0.962548i	$-0.587391\pi$
$107$	− 227988.i	− 1.92510i	0.271110	−	0.962548i	$-0.412609\pi$
$108$	− 11664.0i	− 0.0962250i
$109$	8530.00	0.0687674	0.0343837	−	0.999409i	$-0.489053\pi$
$109$	8530.00	0.0687674	0.0343837	+	0.999409i	$0.489053\pi$
$110$	0	0
$111$	76122.0	0.586412
$112$	− 45056.0i	− 0.339397i
$113$	− 195438.i	− 1.43984i	−0.694059	−	0.719918i	$-0.744179\pi$
$113$	− 195438.i	− 1.43984i	0.694059	−	0.719918i	$-0.255821\pi$
$114$	34416.0	0.248027
$115$	0	0
$116$	89184.0	0.615378
$117$	53298.0i	0.359953i
$118$	105360.i	0.696580i
$119$	72864.0	0.471678
$120$	0	0
$121$	−157451.	−0.977647
$122$	124360.i	0.756452i
$123$	− 172746.i	− 1.02954i
$124$	57472.0	0.335662
$125$	0	0
$126$	57024.0	0.319986
$127$	− 173000.i	− 0.951780i	−0.879505	−	0.475890i	$-0.842126\pi$
$127$	− 173000.i	− 0.951780i	0.879505	−	0.475890i	$-0.157874\pi$
$128$	16384.0i	0.0883883i
$129$	119844.	0.634077
$130$	0	0
$131$	151260.	0.770098	0.385049	−	0.922896i	$-0.374185\pi$
$131$	151260.	0.770098	0.385049	+	0.922896i	$0.374185\pi$
$132$	− 8640.00i	− 0.0431597i
$133$	168256.i	0.824786i
$134$	67216.0	0.323378
$135$	0	0
$136$	−26496.0	−0.122838
$137$	128454.i	0.584718i	0.956309	+	0.292359i	$0.0944402\pi$
$137$	128454.i	0.584718i	−0.956309	+	0.292359i	$0.905560\pi$
$138$	− 21600.0i	− 0.0965508i
$139$	−154196.	−0.676918	−0.338459	−	0.940981i	$-0.609906\pi$
$139$	−154196.	−0.676918	−0.338459	+	0.940981i	$0.609906\pi$
$140$	0	0
$141$	177120.	0.750274
$142$	− 24480.0i	− 0.101880i
$143$	39480.0i	0.161450i
$144$	−20736.0	−0.0833333
$145$	0	0
$146$	−102232.	−0.396922
$147$	127521.i	0.486730i
$148$	− 135328.i	− 0.507848i
$149$	−29454.0	−0.108687	−0.0543436	−	0.998522i	$-0.517307\pi$
$149$	−29454.0	−0.108687	−0.0543436	+	0.998522i	$0.517307\pi$
$150$	0	0
$151$	−203872.	−0.727638	−0.363819	−	0.931470i	$-0.618527\pi$
$151$	−203872.	−0.727638	−0.363819	+	0.931470i	$0.618527\pi$
$152$	− 61184.0i	− 0.214797i
$153$	− 33534.0i	− 0.115813i
$154$	42240.0	0.143523
$155$	0	0
$156$	94752.0	0.311729
$157$	− 136142.i	− 0.440801i	−0.975409	−	0.220401i	$-0.929263\pi$
$157$	− 136142.i	− 0.440801i	0.975409	−	0.220401i	$-0.0707365\pi$
$158$	297632.i	0.948499i
$159$	−281394.	−0.882718
$160$	0	0
$161$	105600.	0.321070
$162$	− 26244.0i	− 0.0785674i
$163$	− 171124.i	− 0.504478i	−0.967665	−	0.252239i	$-0.918833\pi$
$163$	− 171124.i	− 0.504478i	0.967665	−	0.252239i	$-0.0811669\pi$
$164$	−307104.	−0.891612
$165$	0	0
$166$	−25872.0	−0.0728718
$167$	676200.i	1.87622i	0.346336	+	0.938110i	$0.387426\pi$
$167$	676200.i	1.87622i	−0.346336	+	0.938110i	$0.612574\pi$
$168$	− 101376.i	− 0.277116i
$169$	−61671.0	−0.166098
$170$	0	0
$171$	77436.0	0.202513
$172$	− 213056.i	− 0.549127i
$173$	133158.i	0.338261i	0.985594	+	0.169131i	$0.0540959\pi$
$173$	133158.i	0.338261i	−0.985594	+	0.169131i	$0.945904\pi$
$174$	200664.	0.502454
$175$	0	0
$176$	−15360.0	−0.0373774
$177$	237060.i	0.568755i
$178$	− 130968.i	− 0.309824i
$179$	693396.	1.61752	0.808758	−	0.588141i	$-0.200140\pi$
$179$	693396.	1.61752	0.808758	+	0.588141i	$0.200140\pi$
$180$	0	0
$181$	377174.	0.855747	0.427873	−	0.903839i	$-0.359263\pi$
$181$	377174.	0.855747	0.427873	+	0.903839i	$0.359263\pi$
$182$	463232.i	1.03662i
$183$	279810.i	0.617640i
$184$	−38400.0	−0.0836155
$185$	0	0
$186$	129312.	0.274067
$187$	− 24840.0i	− 0.0519455i
$188$	− 314880.i	− 0.649756i
$189$	128304.	0.261268
$190$	0	0
$191$	−265344.	−0.526291	−0.263145	−	0.964756i	$-0.584760\pi$
$191$	−265344.	−0.526291	−0.263145	+	0.964756i	$0.584760\pi$
$192$	36864.0i	0.0721688i
$193$	295298.i	0.570647i	0.958431	+	0.285323i	$0.0921010\pi$
$193$	295298.i	0.570647i	−0.958431	+	0.285323i	$0.907899\pi$
$194$	−664328.	−1.26730
$195$	0	0
$196$	226704.	0.421521
$197$	− 201294.i	− 0.369543i	−0.982781	−	0.184772i	$-0.940845\pi$
$197$	− 201294.i	− 0.369543i	0.982781	−	0.184772i	$-0.0591545\pi$
$198$	− 19440.0i	− 0.0352398i
$199$	−652448.	−1.16792	−0.583960	−	0.811782i	$-0.698498\pi$
$199$	−652448.	−1.16792	−0.583960	+	0.811782i	$0.698498\pi$
$200$	0	0
$201$	151236.	0.264037
$202$	88008.0i	0.151755i
$203$	981024.i	1.67086i
$204$	−59616.0	−0.100297
$205$	0	0
$206$	−317056.	−0.520557
$207$	− 48600.0i	− 0.0788334i
$208$	− 168448.i	− 0.269965i
$209$	57360.0	0.0908330
$210$	0	0
$211$	−1.14706e6	−1.77370	−0.886850	−	0.462058i	$-0.847111\pi$
$211$	−1.14706e6	−1.77370	−0.886850	+	0.462058i	$0.847111\pi$
$212$	500256.i	0.764456i
$213$	− 55080.0i	− 0.0831850i
$214$	−911952.	−1.36125
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	632192.i	0.911380i
$218$	− 34120.0i	− 0.0486259i
$219$	−230022.	−0.324085
$220$	0	0
$221$	272412.	0.375185
$222$	− 304488.i	− 0.414656i
$223$	701960.i	0.945258i	0.881262	+	0.472629i	$0.156695\pi$
$223$	701960.i	0.945258i	−0.881262	+	0.472629i	$0.843305\pi$
$224$	−180224.	−0.239990
$225$	0	0
$226$	−781752.	−1.01812
$227$	− 1.23611e6i	− 1.59218i	−0.605179	−	0.796089i	$-0.706899\pi$
$227$	− 1.23611e6i	− 1.59218i	0.605179	−	0.796089i	$-0.293101\pi$
$228$	− 137664.i	− 0.175381i
$229$	−105830.	−0.133358	−0.0666792	−	0.997774i	$-0.521240\pi$
$229$	−105830.	−0.133358	−0.0666792	+	0.997774i	$0.521240\pi$
$230$	0	0
$231$	95040.0	0.117186
$232$	− 356736.i	− 0.435138i
$233$	− 438678.i	− 0.529366i	−0.964335	−	0.264683i	$-0.914733\pi$
$233$	− 438678.i	− 0.529366i	0.964335	−	0.264683i	$-0.0852673\pi$
$234$	213192.	0.254525
$235$	0	0
$236$	421440.	0.492556
$237$	669672.i	0.774446i
$238$	− 291456.i	− 0.333527i
$239$	−28464.0	−0.0322330	−0.0161165	−	0.999870i	$-0.505130\pi$
$239$	−28464.0	−0.0322330	−0.0161165	+	0.999870i	$0.505130\pi$
$240$	0	0
$241$	892562.	0.989910	0.494955	−	0.868919i	$-0.335185\pi$
$241$	892562.	0.989910	0.494955	+	0.868919i	$0.335185\pi$
$242$	629804.i	0.691301i
$243$	− 59049.0i	− 0.0641500i
$244$	497440.	0.534892
$245$	0	0
$246$	−690984.	−0.727998
$247$	629048.i	0.656057i
$248$	− 229888.i	− 0.237349i
$249$	−58212.0	−0.0594996
$250$	0	0
$251$	−110124.	−0.110331	−0.0551655	−	0.998477i	$-0.517569\pi$
$251$	−110124.	−0.110331	−0.0551655	+	0.998477i	$0.517569\pi$
$252$	− 228096.i	− 0.226264i
$253$	− 36000.0i	− 0.0353591i
$254$	−692000.	−0.673010
$255$	0	0
$256$	65536.0	0.0625000
$257$	− 140802.i	− 0.132977i	−0.997787	−	0.0664884i	$-0.978820\pi$
$257$	− 140802.i	− 0.132977i	0.997787	−	0.0664884i	$-0.0211795\pi$
$258$	− 479376.i	− 0.448360i
$259$	1.48861e6	1.37889
$260$	0	0
$261$	451494.	0.410252
$262$	− 605040.i	− 0.544541i
$263$	− 938760.i	− 0.836884i	−0.908244	−	0.418442i	$-0.862576\pi$
$263$	− 938760.i	− 0.836884i	0.908244	−	0.418442i	$-0.137424\pi$
$264$	−34560.0	−0.0305186
$265$	0	0
$266$	673024.	0.583212
$267$	− 294678.i	− 0.252970i
$268$	− 268864.i	− 0.228663i
$269$	1.11451e6	0.939078	0.469539	−	0.882912i	$-0.344420\pi$
$269$	1.11451e6	0.939078	0.469539	+	0.882912i	$0.344420\pi$
$270$	0	0
$271$	567704.	0.469568	0.234784	−	0.972048i	$-0.424562\pi$
$271$	567704.	0.469568	0.234784	+	0.972048i	$0.424562\pi$
$272$	105984.i	0.0868596i
$273$	1.04227e6i	0.846398i
$274$	513816.	0.413458
$275$	0	0
$276$	−86400.0	−0.0682718
$277$	1.21326e6i	0.950066i	0.879968	+	0.475033i	$0.157564\pi$
$277$	1.21326e6i	0.950066i	−0.879968	+	0.475033i	$0.842436\pi$
$278$	616784.i	0.478653i
$279$	290952.	0.223775
$280$	0	0
$281$	687738.	0.519586	0.259793	−	0.965664i	$-0.416346\pi$
$281$	687738.	0.519586	0.259793	+	0.965664i	$0.416346\pi$
$282$	− 708480.i	− 0.530524i
$283$	− 830908.i	− 0.616718i	−0.951270	−	0.308359i	$-0.900220\pi$
$283$	− 830908.i	− 0.616718i	0.951270	−	0.308359i	$-0.0997799\pi$
$284$	−97920.0	−0.0720403
$285$	0	0
$286$	157920.	0.114162
$287$	− 3.37814e6i	− 2.42088i
$288$	82944.0i	0.0589256i
$289$	1.24846e6	0.879286
$290$	0	0
$291$	−1.49474e6	−1.03474
$292$	408928.i	0.280666i
$293$	− 1.31263e6i	− 0.893248i	−0.894722	−	0.446624i	$-0.852626\pi$
$293$	− 1.31263e6i	− 0.893248i	0.894722	−	0.446624i	$-0.147374\pi$
$294$	510084.	0.344170
$295$	0	0
$296$	−541312.	−0.359102
$297$	− 43740.0i	− 0.0287732i
$298$	117816.i	0.0768535i
$299$	394800.	0.255387
$300$	0	0
$301$	2.34362e6	1.49097
$302$	815488.i	0.514518i
$303$	198018.i	0.123908i
$304$	−244736.	−0.151885
$305$	0	0
$306$	−134136.	−0.0818921
$307$	− 1.69022e6i	− 1.02352i	−0.859128	−	0.511761i	$-0.828993\pi$
$307$	− 1.69022e6i	− 1.02352i	0.859128	−	0.511761i	$-0.171007\pi$
$308$	− 168960.i	− 0.101486i
$309$	−713376.	−0.425033
$310$	0	0
$311$	−1.50204e6	−0.880604	−0.440302	−	0.897850i	$-0.645129\pi$
$311$	−1.50204e6	−0.880604	−0.440302	+	0.897850i	$0.645129\pi$
$312$	− 379008.i	− 0.220426i
$313$	810842.i	0.467816i	0.972259	+	0.233908i	$0.0751515\pi$
$313$	810842.i	0.467816i	−0.972259	+	0.233908i	$0.924848\pi$
$314$	−544568.	−0.311694
$315$	0	0
$316$	1.19053e6	0.670690
$317$	− 903558.i	− 0.505019i	−0.967594	−	0.252510i	$-0.918744\pi$
$317$	− 903558.i	− 0.505019i	0.967594	−	0.252510i	$-0.0812559\pi$
$318$	1.12558e6i	0.624176i
$319$	334440.	0.184010
$320$	0	0
$321$	−2.05189e6	−1.11146
$322$	− 422400.i	− 0.227031i
$323$	− 395784.i	− 0.211082i
$324$	−104976.	−0.0555556
$325$	0	0
$326$	−684496.	−0.356720
$327$	− 76770.0i	− 0.0397029i
$328$	1.22842e6i	0.630465i
$329$	3.46368e6	1.76420
$330$	0	0
$331$	1.12197e6	0.562875	0.281438	−	0.959580i	$-0.409189\pi$
$331$	1.12197e6	0.562875	0.281438	+	0.959580i	$0.409189\pi$
$332$	103488.i	0.0515282i
$333$	− 685098.i	− 0.338565i
$334$	2.70480e6	1.32669
$335$	0	0
$336$	−405504.	−0.195951
$337$	2.75217e6i	1.32008i	0.751229	+	0.660041i	$0.229461\pi$
$337$	2.75217e6i	1.32008i	−0.751229	+	0.660041i	$0.770539\pi$
$338$	246684.i	0.117449i
$339$	−1.75894e6	−0.831289
$340$	0	0
$341$	215520.	0.100369
$342$	− 309744.i	− 0.143198i
$343$	− 464288.i	− 0.213085i
$344$	−852224.	−0.388291
$345$	0	0
$346$	532632.	0.239187
$347$	− 1.91749e6i	− 0.854889i	−0.904042	−	0.427445i	$-0.859414\pi$
$347$	− 1.91749e6i	− 0.854889i	0.904042	−	0.427445i	$-0.140586\pi$
$348$	− 802656.i	− 0.355289i
$349$	−1.83659e6	−0.807140	−0.403570	−	0.914949i	$-0.632231\pi$
$349$	−1.83659e6	−0.807140	−0.403570	+	0.914949i	$0.632231\pi$
$350$	0	0
$351$	479682.	0.207819
$352$	61440.0i	0.0264298i
$353$	− 622014.i	− 0.265683i	−0.991137	−	0.132841i	$-0.957590\pi$
$353$	− 622014.i	− 0.265683i	0.991137	−	0.132841i	$-0.0424101\pi$
$354$	948240.	0.402170
$355$	0	0
$356$	−523872.	−0.219079
$357$	− 655776.i	− 0.272323i
$358$	− 2.77358e6i	− 1.14376i
$359$	−3.74062e6	−1.53182	−0.765909	−	0.642949i	$-0.777711\pi$
$359$	−3.74062e6	−1.53182	−0.765909	+	0.642949i	$0.777711\pi$
$360$	0	0
$361$	−1.56216e6	−0.630897
$362$	− 1.50870e6i	− 0.605104i
$363$	1.41706e6i	0.564445i
$364$	1.85293e6	0.733002
$365$	0	0
$366$	1.11924e6	0.436738
$367$	− 16232.0i	− 0.00629081i	−0.999995	−	0.00314541i	$-0.998999\pi$
$367$	− 16232.0i	− 0.00629081i	0.999995	−	0.00314541i	$-0.00100122\pi$
$368$	153600.i	0.0591251i
$369$	−1.55471e6	−0.594408
$370$	0	0
$371$	−5.50282e6	−2.07563
$372$	− 517248.i	− 0.193795i
$373$	293606.i	0.109268i	0.998506	+	0.0546340i	$0.0173992\pi$
$373$	293606.i	0.109268i	−0.998506	+	0.0546340i	$0.982601\pi$
$374$	−99360.0	−0.0367310
$375$	0	0
$376$	−1.25952e6	−0.459447
$377$	3.66769e6i	1.32904i
$378$	− 513216.i	− 0.184744i
$379$	−3.18012e6	−1.13722	−0.568611	−	0.822607i	$-0.692519\pi$
$379$	−3.18012e6	−1.13722	−0.568611	+	0.822607i	$0.692519\pi$
$380$	0	0
$381$	−1.55700e6	−0.549511
$382$	1.06138e6i	0.372144i
$383$	− 2.97984e6i	− 1.03800i	−0.854775	−	0.518998i	$-0.826305\pi$
$383$	− 2.97984e6i	− 1.03800i	0.854775	−	0.518998i	$-0.173695\pi$
$384$	147456.	0.0510310
$385$	0	0
$386$	1.18119e6	0.403508
$387$	− 1.07860e6i	− 0.366085i
$388$	2.65731e6i	0.896114i
$389$	−3.45977e6	−1.15924	−0.579620	−	0.814887i	$-0.696799\pi$
$389$	−3.45977e6	−1.15924	−0.579620	+	0.814887i	$0.696799\pi$
$390$	0	0
$391$	−248400.	−0.0821693
$392$	− 906816.i	− 0.298060i
$393$	− 1.36134e6i	− 0.444616i
$394$	−805176.	−0.261307
$395$	0	0
$396$	−77760.0	−0.0249183
$397$	3.90416e6i	1.24323i	0.783323	+	0.621615i	$0.213523\pi$
$397$	3.90416e6i	1.24323i	−0.783323	+	0.621615i	$0.786477\pi$
$398$	2.60979e6i	0.825844i
$399$	1.51430e6	0.476191
$400$	0	0
$401$	5.44115e6	1.68978	0.844890	−	0.534940i	$-0.179666\pi$
$401$	5.44115e6	1.68978	0.844890	+	0.534940i	$0.179666\pi$
$402$	− 604944.i	− 0.186702i
$403$	2.36354e6i	0.724936i
$404$	352032.	0.107307
$405$	0	0
$406$	3.92410e6	1.18148
$407$	− 507480.i	− 0.151856i
$408$	238464.i	0.0709206i
$409$	−1.96995e6	−0.582299	−0.291150	−	0.956678i	$-0.594038\pi$
$409$	−1.96995e6	−0.582299	−0.291150	+	0.956678i	$0.594038\pi$
$410$	0	0
$411$	1.15609e6	0.337587
$412$	1.26822e6i	0.368089i
$413$	4.63584e6i	1.33738i
$414$	−194400.	−0.0557437
$415$	0	0
$416$	−673792.	−0.190894
$417$	1.38776e6i	0.390819i
$418$	− 229440.i	− 0.0642286i
$419$	−139020.	−0.0386850	−0.0193425	−	0.999813i	$-0.506157\pi$
$419$	−139020.	−0.0386850	−0.0193425	+	0.999813i	$0.506157\pi$
$420$	0	0
$421$	4.32743e6	1.18994	0.594970	−	0.803748i	$-0.297164\pi$
$421$	4.32743e6	1.18994	0.594970	+	0.803748i	$0.297164\pi$
$422$	4.58824e6i	1.25419i
$423$	− 1.59408e6i	− 0.433171i
$424$	2.00102e6	0.540552
$425$	0	0
$426$	−220320.	−0.0588207
$427$	5.47184e6i	1.45232i
$428$	3.64781e6i	0.962548i
$429$	355320.	0.0932130
$430$	0	0
$431$	−2.79936e6	−0.725881	−0.362941	−	0.931812i	$-0.618227\pi$
$431$	−2.79936e6	−0.725881	−0.362941	+	0.931812i	$0.618227\pi$
$432$	186624.i	0.0481125i
$433$	− 5.90241e6i	− 1.51290i	−0.654052	−	0.756449i	$-0.726932\pi$
$433$	− 5.90241e6i	− 1.51290i	0.654052	−	0.756449i	$-0.273068\pi$
$434$	2.52877e6	0.644443
$435$	0	0
$436$	−136480.	−0.0343837
$437$	− 573600.i	− 0.143683i
$438$	920088.i	0.229163i
$439$	446512.	0.110579	0.0552894	−	0.998470i	$-0.482392\pi$
$439$	446512.	0.110579	0.0552894	+	0.998470i	$0.482392\pi$
$440$	0	0
$441$	1.14769e6	0.281014
$442$	− 1.08965e6i	− 0.265296i
$443$	3.49525e6i	0.846193i	0.906085	+	0.423096i	$0.139057\pi$
$443$	3.49525e6i	0.846193i	−0.906085	+	0.423096i	$0.860943\pi$
$444$	−1.21795e6	−0.293206
$445$	0	0
$446$	2.80784e6	0.668398
$447$	265086.i	0.0627506i
$448$	720896.i	0.169698i
$449$	1.20613e6	0.282343	0.141171	−	0.989985i	$-0.454913\pi$
$449$	1.20613e6	0.282343	0.141171	+	0.989985i	$0.454913\pi$
$450$	0	0
$451$	−1.15164e6	−0.266609
$452$	3.12701e6i	0.719918i
$453$	1.83485e6i	0.420102i
$454$	−4.94443e6	−1.12584
$455$	0	0
$456$	−550656.	−0.124013
$457$	− 233546.i	− 0.0523097i	−0.999658	−	0.0261548i	$-0.991674\pi$
$457$	− 233546.i	− 0.0523097i	0.999658	−	0.0261548i	$-0.00832629\pi$
$458$	423320.i	0.0942986i
$459$	−301806.	−0.0668646
$460$	0	0
$461$	−1.74489e6	−0.382398	−0.191199	−	0.981551i	$-0.561238\pi$
$461$	−1.74489e6	−0.382398	−0.191199	+	0.981551i	$0.561238\pi$
$462$	− 380160.i	− 0.0828632i
$463$	− 2.91786e6i	− 0.632576i	−0.948663	−	0.316288i	$-0.897563\pi$
$463$	− 2.91786e6i	− 0.632576i	0.948663	−	0.316288i	$-0.102437\pi$
$464$	−1.42694e6	−0.307689
$465$	0	0
$466$	−1.75471e6	−0.374318
$467$	5.31076e6i	1.12684i	0.826169	+	0.563422i	$0.190516\pi$
$467$	5.31076e6i	1.12684i	−0.826169	+	0.563422i	$0.809484\pi$
$468$	− 852768.i	− 0.179977i
$469$	2.95750e6	0.620859
$470$	0	0
$471$	−1.22528e6	−0.254497
$472$	− 1.68576e6i	− 0.348290i
$473$	− 798960.i	− 0.164200i
$474$	2.67869e6	0.547616
$475$	0	0
$476$	−1.16582e6	−0.235839
$477$	2.53255e6i	0.509638i
$478$	113856.i	0.0227922i
$479$	−2.34466e6	−0.466918	−0.233459	−	0.972367i	$-0.575004\pi$
$479$	−2.34466e6	−0.466918	−0.233459	+	0.972367i	$0.575004\pi$
$480$	0	0
$481$	5.56536e6	1.09681
$482$	− 3.57025e6i	− 0.699972i
$483$	− 950400.i	− 0.185370i
$484$	2.51922e6	0.488823
$485$	0	0
$486$	−236196.	−0.0453609
$487$	− 9.81531e6i	− 1.87535i	−0.347517	−	0.937674i	$-0.612975\pi$
$487$	− 9.81531e6i	− 1.87535i	0.347517	−	0.937674i	$-0.387025\pi$
$488$	− 1.98976e6i	− 0.378226i
$489$	−1.54012e6	−0.291260
$490$	0	0
$491$	−5.94520e6	−1.11292	−0.556458	−	0.830876i	$-0.687840\pi$
$491$	−5.94520e6	−1.11292	−0.556458	+	0.830876i	$0.687840\pi$
$492$	2.76394e6i	0.514772i
$493$	− 2.30764e6i	− 0.427612i
$494$	2.51619e6	0.463902
$495$	0	0
$496$	−919552.	−0.167831
$497$	− 1.07712e6i	− 0.195602i
$498$	232848.i	0.0420726i
$499$	−6.47832e6	−1.16469	−0.582346	−	0.812941i	$-0.697865\pi$
$499$	−6.47832e6	−1.16469	−0.582346	+	0.812941i	$0.697865\pi$
$500$	0	0
$501$	6.08580e6	1.08324
$502$	440496.i	0.0780158i
$503$	4.71794e6i	0.831444i	0.909492	+	0.415722i	$0.136471\pi$
$503$	4.71794e6i	0.831444i	−0.909492	+	0.415722i	$0.863529\pi$
$504$	−912384.	−0.159993
$505$	0	0
$506$	−144000.	−0.0250027
$507$	555039.i	0.0958967i
$508$	2.76800e6i	0.475890i
$509$	1.90771e6	0.326375	0.163188	−	0.986595i	$-0.447822\pi$
$509$	1.90771e6	0.326375	0.163188	+	0.986595i	$0.447822\pi$
$510$	0	0
$511$	−4.49821e6	−0.762057
$512$	− 262144.i	− 0.0441942i
$513$	− 696924.i	− 0.116921i
$514$	−563208.	−0.0940288
$515$	0	0
$516$	−1.91750e6	−0.317039
$517$	− 1.18080e6i	− 0.194290i
$518$	− 5.95443e6i	− 0.975025i
$519$	1.19842e6	0.195295
$520$	0	0
$521$	8.01974e6	1.29439	0.647196	−	0.762324i	$-0.275941\pi$
$521$	8.01974e6	1.29439	0.647196	+	0.762324i	$0.275941\pi$
$522$	− 1.80598e6i	− 0.290092i
$523$	1.91162e6i	0.305596i	0.988257	+	0.152798i	$0.0488284\pi$
$523$	1.91162e6i	0.305596i	−0.988257	+	0.152798i	$0.951172\pi$
$524$	−2.42016e6	−0.385049
$525$	0	0
$526$	−3.75504e6	−0.591766
$527$	− 1.48709e6i	− 0.233244i
$528$	138240.i	0.0215799i
$529$	6.07634e6	0.944068
$530$	0	0
$531$	2.13354e6	0.328371
$532$	− 2.69210e6i	− 0.412393i
$533$	− 1.26297e7i	− 1.92563i
$534$	−1.17871e6	−0.178877
$535$	0	0
$536$	−1.07546e6	−0.161689
$537$	− 6.24056e6i	− 0.933874i
$538$	− 4.45802e6i	− 0.664028i
$539$	850140.	0.126043
$540$	0	0
$541$	−1.19900e7	−1.76128	−0.880639	−	0.473788i	$-0.842886\pi$
$541$	−1.19900e7	−1.76128	−0.880639	+	0.473788i	$0.842886\pi$
$542$	− 2.27082e6i	− 0.332035i
$543$	− 3.39457e6i	− 0.494066i
$544$	423936.	0.0614190
$545$	0	0
$546$	4.16909e6	0.598494
$547$	− 4.45809e6i	− 0.637061i	−0.947913	−	0.318530i	$-0.896811\pi$
$547$	− 4.45809e6i	− 0.637061i	0.947913	−	0.318530i	$-0.103189\pi$
$548$	− 2.05526e6i	− 0.292359i
$549$	2.51829e6	0.356595
$550$	0	0
$551$	5.32874e6	0.747732
$552$	345600.i	0.0482754i
$553$	1.30958e7i	1.82104i
$554$	4.85303e6	0.671798
$555$	0	0
$556$	2.46714e6	0.338459
$557$	− 9.02612e6i	− 1.23272i	−0.787466	−	0.616358i	$-0.788607\pi$
$557$	− 9.02612e6i	− 1.23272i	0.787466	−	0.616358i	$-0.211393\pi$
$558$	− 1.16381e6i	− 0.158233i
$559$	8.76193e6	1.18596
$560$	0	0
$561$	−223560.	−0.0299907
$562$	− 2.75095e6i	− 0.367403i
$563$	6.84899e6i	0.910658i	0.890323	+	0.455329i	$0.150478\pi$
$563$	6.84899e6i	0.910658i	−0.890323	+	0.455329i	$0.849522\pi$
$564$	−2.83392e6	−0.375137
$565$	0	0
$566$	−3.32363e6	−0.436086
$567$	− 1.15474e6i	− 0.150843i
$568$	391680.i	0.0509402i
$569$	5.46322e6	0.707405	0.353703	−	0.935358i	$-0.384923\pi$
$569$	5.46322e6	0.707405	0.353703	+	0.935358i	$0.384923\pi$
$570$	0	0
$571$	−1.02324e7	−1.31337	−0.656684	−	0.754166i	$-0.728041\pi$
$571$	−1.02324e7	−1.31337	−0.656684	+	0.754166i	$0.728041\pi$
$572$	− 631680.i	− 0.0807248i
$573$	2.38810e6i	0.303854i
$574$	−1.35126e7	−1.71182
$575$	0	0
$576$	331776.	0.0416667
$577$	− 1.59437e7i	− 1.99365i	−0.0796186	−	0.996825i	$-0.525370\pi$
$577$	− 1.59437e7i	− 1.99365i	0.0796186	−	0.996825i	$-0.474630\pi$
$578$	− 4.99384e6i	− 0.621749i
$579$	2.65768e6	0.329463
$580$	0	0
$581$	−1.13837e6	−0.139908
$582$	5.97895e6i	0.731674i
$583$	1.87596e6i	0.228587i
$584$	1.63571e6	0.198461
$585$	0	0
$586$	−5.25050e6	−0.631622
$587$	9.47713e6i	1.13522i	0.823296	+	0.567612i	$0.192133\pi$
$587$	9.47713e6i	1.13522i	−0.823296	+	0.567612i	$0.807867\pi$
$588$	− 2.04034e6i	− 0.243365i
$589$	3.43395e6	0.407855
$590$	0	0
$591$	−1.81165e6	−0.213356
$592$	2.16525e6i	0.253924i
$593$	2.45349e6i	0.286515i	0.989685	+	0.143258i	$0.0457577\pi$
$593$	2.45349e6i	0.286515i	−0.989685	+	0.143258i	$0.954242\pi$
$594$	−174960.	−0.0203457
$595$	0	0
$596$	471264.	0.0543436
$597$	5.87203e6i	0.674299i
$598$	− 1.57920e6i	− 0.180586i
$599$	9.29978e6	1.05902	0.529512	−	0.848302i	$-0.322375\pi$
$599$	9.29978e6	1.05902	0.529512	+	0.848302i	$0.322375\pi$
$600$	0	0
$601$	−1.14617e7	−1.29438	−0.647192	−	0.762327i	$-0.724057\pi$
$601$	−1.14617e7	−1.29438	−0.647192	+	0.762327i	$0.724057\pi$
$602$	− 9.37446e6i	− 1.05428i
$603$	− 1.36112e6i	− 0.152442i
$604$	3.26195e6	0.363819
$605$	0	0
$606$	792072.	0.0876159
$607$	− 1.12784e7i	− 1.24244i	−0.783637	−	0.621219i	$-0.786638\pi$
$607$	− 1.12784e7i	− 1.24244i	0.783637	−	0.621219i	$-0.213362\pi$
$608$	978944.i	0.107399i
$609$	8.82922e6	0.964670
$610$	0	0
$611$	1.29494e7	1.40329
$612$	536544.i	0.0579064i
$613$	93782.0i	0.0100802i	0.999987	+	0.00504009i	$0.00160432\pi$
$613$	93782.0i	0.0100802i	−0.999987	+	0.00504009i	$0.998396\pi$
$614$	−6.76088e6	−0.723740
$615$	0	0
$616$	−675840.	−0.0717616
$617$	1.49642e7i	1.58248i	0.611504	+	0.791242i	$0.290565\pi$
$617$	1.49642e7i	1.58248i	−0.611504	+	0.791242i	$0.709435\pi$
$618$	2.85350e6i	0.300543i
$619$	5.06888e6	0.531723	0.265861	−	0.964011i	$-0.414344\pi$
$619$	5.06888e6	0.531723	0.265861	+	0.964011i	$0.414344\pi$
$620$	0	0
$621$	−437400.	−0.0455145
$622$	6.00816e6i	0.622681i
$623$	− 5.76259e6i	− 0.594837i
$624$	−1.51603e6	−0.155864
$625$	0	0
$626$	3.24337e6	0.330796
$627$	− 516240.i	− 0.0524424i
$628$	2.17827e6i	0.220401i
$629$	−3.50161e6	−0.352892
$630$	0	0
$631$	1.55919e7	1.55892	0.779462	−	0.626450i	$-0.215493\pi$
$631$	1.55919e7	1.55892	0.779462	+	0.626450i	$0.215493\pi$
$632$	− 4.76211e6i	− 0.474250i
$633$	1.03235e7i	1.02405i
$634$	−3.61423e6	−0.357102
$635$	0	0
$636$	4.50230e6	0.441359
$637$	9.32320e6i	0.910367i
$638$	− 1.33776e6i	− 0.130115i
$639$	−495720.	−0.0480269
$640$	0	0
$641$	1.09701e7	1.05455	0.527274	−	0.849695i	$-0.323214\pi$
$641$	1.09701e7	1.05455	0.527274	+	0.849695i	$0.323214\pi$
$642$	8.20757e6i	0.785917i
$643$	− 2.83704e6i	− 0.270607i	−0.990804	−	0.135303i	$-0.956799\pi$
$643$	− 2.83704e6i	− 0.270607i	0.990804	−	0.135303i	$-0.0432009\pi$
$644$	−1.68960e6	−0.160535
$645$	0	0
$646$	−1.58314e6	−0.149258
$647$	6.05686e6i	0.568835i	0.958700	+	0.284418i	$0.0918002\pi$
$647$	6.05686e6i	0.568835i	−0.958700	+	0.284418i	$0.908200\pi$
$648$	419904.i	0.0392837i
$649$	1.58040e6	0.147284
$650$	0	0
$651$	5.68973e6	0.526186
$652$	2.73798e6i	0.252239i
$653$	− 1.08892e6i	− 0.0999341i	−0.998751	−	0.0499671i	$-0.984088\pi$
$653$	− 1.08892e6i	− 0.0999341i	0.998751	−	0.0499671i	$-0.0159116\pi$
$654$	−307080.	−0.0280742
$655$	0	0
$656$	4.91366e6	0.445806
$657$	2.07020e6i	0.187111i
$658$	− 1.38547e7i	− 1.24748i
$659$	−7.41803e6	−0.665388	−0.332694	−	0.943035i	$-0.607958\pi$
$659$	−7.41803e6	−0.665388	−0.332694	+	0.943035i	$0.607958\pi$
$660$	0	0
$661$	767654.	0.0683379	0.0341690	−	0.999416i	$-0.489122\pi$
$661$	767654.	0.0683379	0.0341690	+	0.999416i	$0.489122\pi$
$662$	− 4.48789e6i	− 0.398013i
$663$	− 2.45171e6i	− 0.216613i
$664$	413952.	0.0364359
$665$	0	0
$666$	−2.74039e6	−0.239402
$667$	− 3.34440e6i	− 0.291074i
$668$	− 1.08192e7i	− 0.938110i
$669$	6.31764e6	0.545745
$670$	0	0
$671$	1.86540e6	0.159943
$672$	1.62202e6i	0.138558i
$673$	1.42263e6i	0.121075i	0.998166	+	0.0605373i	$0.0192814\pi$
$673$	1.42263e6i	0.121075i	−0.998166	+	0.0605373i	$0.980719\pi$
$674$	1.10087e7	0.933439
$675$	0	0
$676$	986736.	0.0830490
$677$	6.16231e6i	0.516739i	0.966046	+	0.258370i	$0.0831853\pi$
$677$	6.16231e6i	0.516739i	−0.966046	+	0.258370i	$0.916815\pi$
$678$	7.03577e6i	0.587810i
$679$	−2.92304e7	−2.43310
$680$	0	0
$681$	−1.11250e7	−0.919245
$682$	− 862080.i	− 0.0709719i
$683$	1.50621e7i	1.23548i	0.786383	+	0.617739i	$0.211951\pi$
$683$	1.50621e7i	1.23548i	−0.786383	+	0.617739i	$0.788049\pi$
$684$	−1.23898e6	−0.101256
$685$	0	0
$686$	−1.85715e6	−0.150674
$687$	952470.i	0.0769945i
$688$	3.40890e6i	0.274563i
$689$	−2.05730e7	−1.65101
$690$	0	0
$691$	−5.87636e6	−0.468180	−0.234090	−	0.972215i	$-0.575211\pi$
$691$	−5.87636e6	−0.468180	−0.234090	+	0.972215i	$0.575211\pi$
$692$	− 2.13053e6i	− 0.169131i
$693$	− 855360.i	− 0.0676575i
$694$	−7.66997e6	−0.604498
$695$	0	0
$696$	−3.21062e6	−0.251227
$697$	7.94632e6i	0.619561i
$698$	7.34636e6i	0.570734i
$699$	−3.94810e6	−0.305630
$700$	0	0
$701$	3.60077e6	0.276758	0.138379	−	0.990379i	$-0.455811\pi$
$701$	3.60077e6	0.276758	0.138379	+	0.990379i	$0.455811\pi$
$702$	− 1.91873e6i	− 0.146950i
$703$	− 8.08585e6i	− 0.617074i
$704$	245760.	0.0186887
$705$	0	0
$706$	−2.48806e6	−0.187866
$707$	3.87235e6i	0.291358i
$708$	− 3.79296e6i	− 0.284377i
$709$	−9.22516e6	−0.689221	−0.344610	−	0.938746i	$-0.611989\pi$
$709$	−9.22516e6	−0.689221	−0.344610	+	0.938746i	$0.611989\pi$
$710$	0	0
$711$	6.02705e6	0.447127
$712$	2.09549e6i	0.154912i
$713$	− 2.15520e6i	− 0.158768i
$714$	−2.62310e6	−0.192562
$715$	0	0
$716$	−1.10943e7	−0.808758
$717$	256176.i	0.0186098i
$718$	1.49625e7i	1.08316i
$719$	2.63923e7	1.90395	0.951975	−	0.306177i	$-0.0990500\pi$
$719$	2.63923e7	1.90395	0.951975	+	0.306177i	$0.0990500\pi$
$720$	0	0
$721$	−1.39505e7	−0.999426
$722$	6.24865e6i	0.446111i
$723$	− 8.03306e6i	− 0.571525i
$724$	−6.03478e6	−0.427873
$725$	0	0
$726$	5.66824e6	0.399123
$727$	9.79485e6i	0.687324i	0.939093	+	0.343662i	$0.111667\pi$
$727$	9.79485e6i	0.687324i	−0.939093	+	0.343662i	$0.888333\pi$
$728$	− 7.41171e6i	− 0.518311i
$729$	−531441.	−0.0370370
$730$	0	0
$731$	−5.51282e6	−0.381576
$732$	− 4.47696e6i	− 0.308820i
$733$	4.07584e6i	0.280193i	0.990138	+	0.140096i	$0.0447412\pi$
$733$	4.07584e6i	0.280193i	−0.990138	+	0.140096i	$0.955259\pi$
$734$	−64928.0	−0.00444828
$735$	0	0
$736$	614400.	0.0418077
$737$	− 1.00824e6i	− 0.0683747i
$738$	6.21886e6i	0.420310i
$739$	1.65709e7	1.11618	0.558089	−	0.829781i	$-0.311535\pi$
$739$	1.65709e7	1.11618	0.558089	+	0.829781i	$0.311535\pi$
$740$	0	0
$741$	5.66143e6	0.378775
$742$	2.20113e7i	1.46769i
$743$	1.44141e7i	0.957892i	0.877844	+	0.478946i	$0.158981\pi$
$743$	1.44141e7i	0.957892i	−0.877844	+	0.478946i	$0.841019\pi$
$744$	−2.06899e6	−0.137033
$745$	0	0
$746$	1.17442e6	0.0772641
$747$	523908.i	0.0343521i
$748$	397440.i	0.0259727i
$749$	−4.01259e7	−2.61349
$750$	0	0
$751$	1.67944e7	1.08659	0.543295	−	0.839542i	$-0.317177\pi$
$751$	1.67944e7	1.08659	0.543295	+	0.839542i	$0.317177\pi$
$752$	5.03808e6i	0.324878i
$753$	991116.i	0.0636997i
$754$	1.46708e7	0.939776
$755$	0	0
$756$	−2.05286e6	−0.130634
$757$	− 1.32943e7i	− 0.843188i	−0.906785	−	0.421594i	$-0.861471\pi$
$757$	− 1.32943e7i	− 0.843188i	0.906785	−	0.421594i	$-0.138529\pi$
$758$	1.27205e7i	0.804137i
$759$	−324000.	−0.0204146
$760$	0	0
$761$	−2.14786e6	−0.134445	−0.0672225	−	0.997738i	$-0.521414\pi$
$761$	−2.14786e6	−0.134445	−0.0672225	+	0.997738i	$0.521414\pi$
$762$	6.22800e6i	0.388563i
$763$	− 1.50128e6i	− 0.0933577i
$764$	4.24550e6	0.263145
$765$	0	0
$766$	−1.19194e7	−0.733975
$767$	1.73317e7i	1.06378i
$768$	− 589824.i	− 0.0360844i
$769$	1.31059e7	0.799193	0.399596	−	0.916691i	$-0.369150\pi$
$769$	1.31059e7	0.799193	0.399596	+	0.916691i	$0.369150\pi$
$770$	0	0
$771$	−1.26722e6	−0.0767742
$772$	− 4.72477e6i	− 0.285323i
$773$	− 2.37154e7i	− 1.42752i	−0.700392	−	0.713759i	$-0.746991\pi$
$773$	− 2.37154e7i	− 1.42752i	0.700392	−	0.713759i	$-0.253009\pi$
$774$	−4.31438e6	−0.258861
$775$	0	0
$776$	1.06292e7	0.633648
$777$	− 1.33975e7i	− 0.796105i
$778$	1.38391e7i	0.819707i
$779$	−1.83495e7	−1.08338
$780$	0	0
$781$	−367200.	−0.0215415
$782$	993600.i	0.0581025i
$783$	− 4.06345e6i	− 0.236859i
$784$	−3.62726e6	−0.210760
$785$	0	0
$786$	−5.44536e6	−0.314391
$787$	8.40048e6i	0.483468i	0.970343	+	0.241734i	$0.0777161\pi$
$787$	8.40048e6i	0.483468i	−0.970343	+	0.241734i	$0.922284\pi$
$788$	3.22070e6i	0.184772i
$789$	−8.44884e6	−0.483175
$790$	0	0
$791$	−3.43971e7	−1.95470
$792$	311040.i	0.0176199i
$793$	2.04572e7i	1.15522i
$794$	1.56166e7	0.879097
$795$	0	0
$796$	1.04392e7	0.583960
$797$	− 5.41023e6i	− 0.301696i	−0.988557	−	0.150848i	$-0.951800\pi$
$797$	− 5.41023e6i	− 0.301696i	0.988557	−	0.150848i	$-0.0482004\pi$
$798$	− 6.05722e6i	− 0.336718i
$799$	−8.14752e6	−0.451501
$800$	0	0
$801$	−2.65210e6	−0.146052
$802$	− 2.17646e7i	− 1.19485i
$803$	1.53348e6i	0.0839246i
$804$	−2.41978e6	−0.132019
$805$	0	0
$806$	9.45414e6	0.512607
$807$	− 1.00306e7i	− 0.542177i
$808$	− 1.40813e6i	− 0.0758776i
$809$	2.60777e7	1.40087	0.700436	−	0.713715i	$-0.252989\pi$
$809$	2.60777e7	1.40087	0.700436	+	0.713715i	$0.252989\pi$
$810$	0	0
$811$	1.90021e7	1.01449	0.507247	−	0.861800i	$-0.330663\pi$
$811$	1.90021e7	1.01449	0.507247	+	0.861800i	$0.330663\pi$
$812$	− 1.56964e7i	− 0.835429i
$813$	− 5.10934e6i	− 0.271105i
$814$	−2.02992e6	−0.107379
$815$	0	0
$816$	953856.	0.0501484
$817$	− 1.27301e7i	− 0.667231i
$818$	7.87978e6i	0.411748i
$819$	9.38045e6	0.488668
$820$	0	0
$821$	−3.10173e7	−1.60600	−0.803001	−	0.595978i	$-0.796764\pi$
$821$	−3.10173e7	−1.60600	−0.803001	+	0.595978i	$0.796764\pi$
$822$	− 4.62434e6i	− 0.238710i
$823$	− 1.56290e7i	− 0.804323i	−0.915569	−	0.402162i	$-0.868259\pi$
$823$	− 1.56290e7i	− 0.804323i	0.915569	−	0.402162i	$-0.131741\pi$
$824$	5.07290e6	0.260278
$825$	0	0
$826$	1.85434e7	0.945667
$827$	− 1.58421e7i	− 0.805467i	−0.915317	−	0.402733i	$-0.868060\pi$
$827$	− 1.58421e7i	− 0.805467i	0.915317	−	0.402733i	$-0.131940\pi$
$828$	777600.i	0.0394167i
$829$	−2.06176e6	−0.104196	−0.0520980	−	0.998642i	$-0.516591\pi$
$829$	−2.06176e6	−0.104196	−0.0520980	+	0.998642i	$0.516591\pi$
$830$	0	0
$831$	1.09193e7	0.548521
$832$	2.69517e6i	0.134983i
$833$	− 5.86597e6i	− 0.292905i
$834$	5.55106e6	0.276351
$835$	0	0
$836$	−917760.	−0.0454165
$837$	− 2.61857e6i	− 0.129196i
$838$	556080.i	0.0273544i
$839$	−3.03900e7	−1.49048	−0.745240	−	0.666796i	$-0.767665\pi$
$839$	−3.03900e7	−1.49048	−0.745240	+	0.666796i	$0.767665\pi$
$840$	0	0
$841$	1.05583e7	0.514760
$842$	− 1.73097e7i	− 0.841414i
$843$	− 6.18964e6i	− 0.299983i
$844$	1.83530e7	0.886850
$845$	0	0
$846$	−6.37632e6	−0.306298
$847$	2.77114e7i	1.32724i
$848$	− 8.00410e6i	− 0.382228i
$849$	−7.47817e6	−0.356062
$850$	0	0
$851$	−5.07480e6	−0.240212
$852$	881280.i	0.0415925i
$853$	− 2.97738e7i	− 1.40108i	−0.713615	−	0.700538i	$-0.752944\pi$
$853$	− 2.97738e7i	− 1.40108i	0.713615	−	0.700538i	$-0.247056\pi$
$854$	2.18874e7	1.02695
$855$	0	0
$856$	1.45912e7	0.680624
$857$	− 8.64100e6i	− 0.401894i	−0.979602	−	0.200947i	$-0.935598\pi$
$857$	− 8.64100e6i	− 0.401894i	0.979602	−	0.200947i	$-0.0644020\pi$
$858$	− 1.42128e6i	− 0.0659115i
$859$	3.35663e7	1.55210	0.776051	−	0.630670i	$-0.217220\pi$
$859$	3.35663e7	1.55210	0.776051	+	0.630670i	$0.217220\pi$
$860$	0	0
$861$	−3.04033e7	−1.39770
$862$	1.11974e7i	0.513276i
$863$	3.90191e7i	1.78341i	0.452621	+	0.891703i	$0.350489\pi$
$863$	3.90191e7i	1.78341i	−0.452621	+	0.891703i	$0.649511\pi$
$864$	746496.	0.0340207
$865$	0	0
$866$	−2.36097e7	−1.06978
$867$	− 1.12361e7i	− 0.507656i
$868$	− 1.01151e7i	− 0.455690i
$869$	4.46448e6	0.200549
$870$	0	0
$871$	1.10570e7	0.493848
$872$	545920.i	0.0243130i
$873$	1.34526e7i	0.597409i
$874$	−2.29440e6	−0.101599
$875$	0	0
$876$	3.68035e6	0.162043
$877$	1.81382e7i	0.796333i	0.917313	+	0.398166i	$0.130353\pi$
$877$	1.81382e7i	0.796333i	−0.917313	+	0.398166i	$0.869647\pi$
$878$	− 1.78605e6i	− 0.0781910i
$879$	−1.18136e7	−0.515717
$880$	0	0
$881$	3.05312e7	1.32527	0.662634	−	0.748943i	$-0.269438\pi$
$881$	3.05312e7	1.32527	0.662634	+	0.748943i	$0.269438\pi$
$882$	− 4.59076e6i	− 0.198707i
$883$	− 4.35533e7i	− 1.87983i	−0.341405	−	0.939916i	$-0.610903\pi$
$883$	− 4.35533e7i	− 1.87983i	0.341405	−	0.939916i	$-0.389097\pi$
$884$	−4.35859e6	−0.187593
$885$	0	0
$886$	1.39810e7	0.598348
$887$	1.34152e7i	0.572515i	0.958153	+	0.286257i	$0.0924113\pi$
$887$	1.34152e7i	0.572515i	−0.958153	+	0.286257i	$0.907589\pi$
$888$	4.87181e6i	0.207328i
$889$	−3.04480e7	−1.29212
$890$	0	0
$891$	−393660.	−0.0166122
$892$	− 1.12314e7i	− 0.472629i
$893$	− 1.88141e7i	− 0.789504i
$894$	1.06034e6	0.0443714
$895$	0	0
$896$	2.88358e6	0.119995
$897$	− 3.55320e6i	− 0.147448i
$898$	− 4.82450e6i	− 0.199647i
$899$	2.00218e7	0.826236
$900$	0	0
$901$	1.29441e7	0.531203
$902$	4.60656e6i	0.188521i
$903$	− 2.10925e7i	− 0.860815i
$904$	1.25080e7	0.509059
$905$	0	0
$906$	7.33939e6	0.297057
$907$	− 3.10816e6i	− 0.125454i	−0.998031	−	0.0627272i	$-0.980020\pi$
$907$	− 3.10816e6i	− 0.125454i	0.998031	−	0.0627272i	$-0.0199798\pi$
$908$	1.97777e7i	0.796089i
$909$	1.78216e6	0.0715381
$910$	0	0
$911$	1.19035e6	0.0475203	0.0237602	−	0.999718i	$-0.492436\pi$
$911$	1.19035e6	0.0475203	0.0237602	+	0.999718i	$0.492436\pi$
$912$	2.20262e6i	0.0876906i
$913$	388080.i	0.0154079i
$914$	−934184.	−0.0369885
$915$	0	0
$916$	1.69328e6	0.0666792
$917$	− 2.66218e7i	− 1.04547i
$918$	1.20722e6i	0.0472804i
$919$	4.71996e7	1.84353	0.921764	−	0.387752i	$-0.126748\pi$
$919$	4.71996e7	1.84353	0.921764	+	0.387752i	$0.126748\pi$
$920$	0	0
$921$	−1.52120e7	−0.590931
$922$	6.97956e6i	0.270396i
$923$	− 4.02696e6i	− 0.155587i
$924$	−1.52064e6	−0.0585931
$925$	0	0
$926$	−1.16715e7	−0.447299
$927$	6.42038e6i	0.245393i
$928$	5.70778e6i	0.217569i
$929$	−1.33595e6	−0.0507870	−0.0253935	−	0.999678i	$-0.508084\pi$
$929$	−1.33595e6	−0.0507870	−0.0253935	+	0.999678i	$0.508084\pi$
$930$	0	0
$931$	1.35456e7	0.512180
$932$	7.01885e6i	0.264683i
$933$	1.35184e7i	0.508417i
$934$	2.12430e7	0.796800
$935$	0	0
$936$	−3.41107e6	−0.127263
$937$	− 1.47238e7i	− 0.547861i	−0.961749	−	0.273931i	$-0.911676\pi$
$937$	− 1.47238e7i	− 0.547861i	0.961749	−	0.273931i	$-0.0883239\pi$
$938$	− 1.18300e7i	− 0.439014i
$939$	7.29758e6	0.270094
$940$	0	0
$941$	−2.69196e7	−0.991049	−0.495525	−	0.868594i	$-0.665024\pi$
$941$	−2.69196e7	−0.991049	−0.495525	+	0.868594i	$0.665024\pi$
$942$	4.90111e6i	0.179956i
$943$	1.15164e7i	0.421733i
$944$	−6.74304e6	−0.246278
$945$	0	0
$946$	−3.19584e6	−0.116107
$947$	3.73160e6i	0.135214i	0.997712	+	0.0676068i	$0.0215364\pi$
$947$	3.73160e6i	0.135214i	−0.997712	+	0.0676068i	$0.978464\pi$
$948$	− 1.07148e7i	− 0.387223i
$949$	−1.68172e7	−0.606160
$950$	0	0
$951$	−8.13202e6	−0.291573
$952$	4.66330e6i	0.166763i
$953$	2.18735e7i	0.780166i	0.920780	+	0.390083i	$0.127554\pi$
$953$	2.18735e7i	0.780166i	−0.920780	+	0.390083i	$0.872446\pi$
$954$	1.01302e7	0.360368
$955$	0	0
$956$	455424.	0.0161165
$957$	− 3.00996e6i	− 0.106238i
$958$	9.37862e6i	0.330161i
$959$	2.26079e7	0.793805
$960$	0	0
$961$	−1.57267e7	−0.549324
$962$	− 2.22615e7i	− 0.775561i
$963$	1.84670e7i	0.641699i
$964$	−1.42810e7	−0.494955
$965$	0	0
$966$	−3.80160e6	−0.131076
$967$	− 1.76025e7i	− 0.605352i	−0.953093	−	0.302676i	$-0.902120\pi$
$967$	− 1.76025e7i	− 0.605352i	0.953093	−	0.302676i	$-0.0978800\pi$
$968$	− 1.00769e7i	− 0.345650i
$969$	−3.56206e6	−0.121868
$970$	0	0
$971$	1.67317e7	0.569497	0.284749	−	0.958602i	$-0.408090\pi$
$971$	1.67317e7	0.569497	0.284749	+	0.958602i	$0.408090\pi$
$972$	944784.i	0.0320750i
$973$	2.71385e7i	0.918975i
$974$	−3.92612e7	−1.32607
$975$	0	0
$976$	−7.95904e6	−0.267446
$977$	− 5.55382e7i	− 1.86147i	−0.365699	−	0.930733i	$-0.619170\pi$
$977$	− 5.55382e7i	− 1.86147i	0.365699	−	0.930733i	$-0.380830\pi$
$978$	6.16046e6i	0.205952i
$979$	−1.96452e6	−0.0655088
$980$	0	0
$981$	−690930.	−0.0229225
$982$	2.37808e7i	0.786951i
$983$	− 3.86784e7i	− 1.27669i	−0.769751	−	0.638344i	$-0.779620\pi$
$983$	− 3.86784e7i	− 1.27669i	0.769751	−	0.638344i	$-0.220380\pi$
$984$	1.10557e7	0.363999
$985$	0	0
$986$	−9.23054e6	−0.302367
$987$	− 3.11731e7i	− 1.01856i
$988$	− 1.00648e7i	− 0.328028i
$989$	−7.98960e6	−0.259737
$990$	0	0
$991$	9.58498e6	0.310033	0.155016	−	0.987912i	$-0.450457\pi$
$991$	9.58498e6	0.310033	0.155016	+	0.987912i	$0.450457\pi$
$992$	3.67821e6i	0.118674i
$993$	− 1.00977e7i	− 0.324976i
$994$	−4.30848e6	−0.138311
$995$	0	0
$996$	931392.	0.0297498
$997$	1.03650e7i	0.330242i	0.986273	+	0.165121i	$0.0528015\pi$
$997$	1.03650e7i	0.330242i	−0.986273	+	0.165121i	$0.947198\pi$
$998$	2.59133e7i	0.823561i
$999$	−6.16588e6	−0.195471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.c.b.49.1		2
3.2	odd	2		450.6.c.j.199.2		2
5.2	odd	4		6.6.a.a.1.1	✓	1
5.3	odd	4		150.6.a.d.1.1		1
5.4	even	2	inner	150.6.c.b.49.2		2
15.2	even	4		18.6.a.b.1.1		1
15.8	even	4		450.6.a.m.1.1		1
15.14	odd	2		450.6.c.j.199.1		2
20.7	even	4		48.6.a.c.1.1		1
35.2	odd	12		294.6.e.g.67.1		2
35.12	even	12		294.6.e.a.67.1		2
35.17	even	12		294.6.e.a.79.1		2
35.27	even	4		294.6.a.m.1.1		1
35.32	odd	12		294.6.e.g.79.1		2
40.27	even	4		192.6.a.g.1.1		1
40.37	odd	4		192.6.a.o.1.1		1
45.2	even	12		162.6.c.h.109.1		2
45.7	odd	12		162.6.c.e.109.1		2
45.22	odd	12		162.6.c.e.55.1		2
45.32	even	12		162.6.c.h.55.1		2
55.32	even	4		726.6.a.a.1.1		1
60.47	odd	4		144.6.a.j.1.1		1
65.12	odd	4		1014.6.a.c.1.1		1
80.27	even	4		768.6.d.p.385.1		2
80.37	odd	4		768.6.d.c.385.2		2
80.67	even	4		768.6.d.p.385.2		2
80.77	odd	4		768.6.d.c.385.1		2
105.62	odd	4		882.6.a.a.1.1		1
120.77	even	4		576.6.a.j.1.1		1
120.107	odd	4		576.6.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.6.a.a.1.1	✓	1	5.2	odd	4
18.6.a.b.1.1		1	15.2	even	4
48.6.a.c.1.1		1	20.7	even	4
144.6.a.j.1.1		1	60.47	odd	4
150.6.a.d.1.1		1	5.3	odd	4
150.6.c.b.49.1		2	1.1	even	1	trivial
150.6.c.b.49.2		2	5.4	even	2	inner
162.6.c.e.55.1		2	45.22	odd	12
162.6.c.e.109.1		2	45.7	odd	12
162.6.c.h.55.1		2	45.32	even	12
162.6.c.h.109.1		2	45.2	even	12
192.6.a.g.1.1		1	40.27	even	4
192.6.a.o.1.1		1	40.37	odd	4
294.6.a.m.1.1		1	35.27	even	4
294.6.e.a.67.1		2	35.12	even	12
294.6.e.a.79.1		2	35.17	even	12
294.6.e.g.67.1		2	35.2	odd	12
294.6.e.g.79.1		2	35.32	odd	12
450.6.a.m.1.1		1	15.8	even	4
450.6.c.j.199.1		2	15.14	odd	2
450.6.c.j.199.2		2	3.2	odd	2
576.6.a.i.1.1		1	120.107	odd	4
576.6.a.j.1.1		1	120.77	even	4
726.6.a.a.1.1		1	55.32	even	4
768.6.d.c.385.1		2	80.77	odd	4
768.6.d.c.385.2		2	80.37	odd	4
768.6.d.p.385.1		2	80.27	even	4
768.6.d.p.385.2		2	80.67	even	4
882.6.a.a.1.1		1	105.62	odd	4
1014.6.a.c.1.1		1	65.12	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} -176.000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} -36.0000 q^{6} -176.000i q^{7} +64.0000i q^{8} -81.0000 q^{9} -60.0000 q^{11} +144.000i q^{12} -658.000i q^{13} -704.000 q^{14} +256.000 q^{16} +414.000i q^{17} +324.000i q^{18} -956.000 q^{19} -1584.00 q^{21} +240.000i q^{22} +600.000i q^{23} +576.000 q^{24} -2632.00 q^{26} +729.000i q^{27} +2816.00i q^{28} -5574.00 q^{29} -3592.00 q^{31} -1024.00i q^{32} +540.000i q^{33} +1656.00 q^{34} +1296.00 q^{36} +8458.00i q^{37} +3824.00i q^{38} -5922.00 q^{39} +19194.0 q^{41} +6336.00i q^{42} +13316.0i q^{43} +960.000 q^{44} +2400.00 q^{46} +19680.0i q^{47} -2304.00i q^{48} -14169.0 q^{49} +3726.00 q^{51} +10528.0i q^{52} -31266.0i q^{53} +2916.00 q^{54} +11264.0 q^{56} +8604.00i q^{57} +22296.0i q^{58} -26340.0 q^{59} -31090.0 q^{61} +14368.0i q^{62} +14256.0i q^{63} -4096.00 q^{64} +2160.00 q^{66} +16804.0i q^{67} -6624.00i q^{68} +5400.00 q^{69} +6120.00 q^{71} -5184.00i q^{72} -25558.0i q^{73} +33832.0 q^{74} +15296.0 q^{76} +10560.0i q^{77} +23688.0i q^{78} -74408.0 q^{79} +6561.00 q^{81} -76776.0i q^{82} -6468.00i q^{83} +25344.0 q^{84} +53264.0 q^{86} +50166.0i q^{87} -3840.00i q^{88} +32742.0 q^{89} -115808. q^{91} -9600.00i q^{92} +32328.0i q^{93} +78720.0 q^{94} -9216.00 q^{96} -166082. i q^{97} +56676.0i q^{98} +4860.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9}+O(q^{10}) \) 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9	\( 2 q - 32 q^{4} - 72 q^{6} - 162 q^{9} - 120 q^{11} - 1408 q^{14} + 512 q^{16} - 1912 q^{19} - 3168 q^{21} + 1152 q^{24} - 5264 q^{26} - 11148 q^{29} - 7184 q^{31} + 3312 q^{34} + 2592 q^{36} - 11844 q^{39} + 38388 q^{41} + 1920 q^{44} + 4800 q^{46} - 28338 q^{49} + 7452 q^{51} + 5832 q^{54} + 22528 q^{56} - 52680 q^{59} - 62180 q^{61} - 8192 q^{64} + 4320 q^{66} + 10800 q^{69} + 12240 q^{71} + 67664 q^{74} + 30592 q^{76} - 148816 q^{79} + 13122 q^{81} + 50688 q^{84} + 106528 q^{86} + 65484 q^{89} - 231616 q^{91} + 157440 q^{94} - 18432 q^{96} + 9720 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 - 72 * q^6 - 162 * q^9 - 120 * q^11 - 1408 * q^14 + 512 * q^16 - 1912 * q^19 - 3168 * q^21 + 1152 * q^24 - 5264 * q^26 - 11148 * q^29 - 7184 * q^31 + 3312 * q^34 + 2592 * q^36 - 11844 * q^39 + 38388 * q^41 + 1920 * q^44 + 4800 * q^46 - 28338 * q^49 + 7452 * q^51 + 5832 * q^54 + 22528 * q^56 - 52680 * q^59 - 62180 * q^61 - 8192 * q^64 + 4320 * q^66 + 10800 * q^69 + 12240 * q^71 + 67664 * q^74 + 30592 * q^76 - 148816 * q^79 + 13122 * q^81 + 50688 * q^84 + 106528 * q^86 + 65484 * q^89 - 231616 * q^91 + 157440 * q^94 - 18432 * q^96 + 9720 * q^99

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