LMFDB - Embedded newform 2.8.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,8,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	2.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:	$0.624770050968$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-8.00000 q^{2} +12.0000 q^{3} +64.0000 q^{4} -210.000 q^{5} -96.0000 q^{6} +1016.00 q^{7} -512.000 q^{8} -2043.00 q^{9} +O(q^{10})$

\(q-8.00000 q^{2} +12.0000 q^{3} +64.0000 q^{4} -210.000 q^{5} -96.0000 q^{6} +1016.00 q^{7} -512.000 q^{8} -2043.00 q^{9} +1680.00 q^{10} +1092.00 q^{11} +768.000 q^{12} +1382.00 q^{13} -8128.00 q^{14} -2520.00 q^{15} +4096.00 q^{16} +14706.0 q^{17} +16344.0 q^{18} -39940.0 q^{19} -13440.0 q^{20} +12192.0 q^{21} -8736.00 q^{22} +68712.0 q^{23} -6144.00 q^{24} -34025.0 q^{25} -11056.0 q^{26} -50760.0 q^{27} +65024.0 q^{28} -102570. q^{29} +20160.0 q^{30} +227552. q^{31} -32768.0 q^{32} +13104.0 q^{33} -117648. q^{34} -213360. q^{35} -130752. q^{36} +160526. q^{37} +319520. q^{38} +16584.0 q^{39} +107520. q^{40} +10842.0 q^{41} -97536.0 q^{42} -630748. q^{43} +69888.0 q^{44} +429030. q^{45} -549696. q^{46} +472656. q^{47} +49152.0 q^{48} +208713. q^{49} +272200. q^{50} +176472. q^{51} +88448.0 q^{52} -1.49402e6 q^{53} +406080. q^{54} -229320. q^{55} -520192. q^{56} -479280. q^{57} +820560. q^{58} +2.64066e6 q^{59} -161280. q^{60} +827702. q^{61} -1.82042e6 q^{62} -2.07569e6 q^{63} +262144. q^{64} -290220. q^{65} -104832. q^{66} -126004. q^{67} +941184. q^{68} +824544. q^{69} +1.70688e6 q^{70} -1.41473e6 q^{71} +1.04602e6 q^{72} +980282. q^{73} -1.28421e6 q^{74} -408300. q^{75} -2.55616e6 q^{76} +1.10947e6 q^{77} -132672. q^{78} -3.56680e6 q^{79} -860160. q^{80} +3.85892e6 q^{81} -86736.0 q^{82} +5.67289e6 q^{83} +780288. q^{84} -3.08826e6 q^{85} +5.04598e6 q^{86} -1.23084e6 q^{87} -559104. q^{88} -1.19512e7 q^{89} -3.43224e6 q^{90} +1.40411e6 q^{91} +4.39757e6 q^{92} +2.73062e6 q^{93} -3.78125e6 q^{94} +8.38740e6 q^{95} -393216. q^{96} +8.68215e6 q^{97} -1.66970e6 q^{98} -2.23096e6 q^{99} +O(q^{100})\)

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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	12.0000	0.256600	0.128300	−	0.991735i	$-0.459048\pi$
$3$	12.0000	0.256600	0.128300	+	0.991735i	$0.459048\pi$
$4$	64.0000	0.500000
$5$	−210.000	−0.751319	−0.375659	−	0.926758i	$-0.622584\pi$
$5$	−210.000	−0.751319	−0.375659	+	0.926758i	$0.622584\pi$
$6$	−96.0000	−0.181444
$7$	1016.00	1.11957	0.559784	−	0.828638i	$-0.310884\pi$
$7$	1016.00	1.11957	0.559784	+	0.828638i	$0.310884\pi$
$8$	−512.000	−0.353553
$9$	−2043.00	−0.934156
$10$	1680.00	0.531263
$11$	1092.00	0.247371	0.123685	−	0.992321i	$-0.460529\pi$
$11$	1092.00	0.247371	0.123685	+	0.992321i	$0.460529\pi$
$12$	768.000	0.128300
$13$	1382.00	0.174464	0.0872321	−	0.996188i	$-0.472198\pi$
$13$	1382.00	0.174464	0.0872321	+	0.996188i	$0.472198\pi$
$14$	−8128.00	−0.791654
$15$	−2520.00	−0.192789
$16$	4096.00	0.250000
$17$	14706.0	0.725978	0.362989	−	0.931793i	$-0.381756\pi$
$17$	14706.0	0.725978	0.362989	+	0.931793i	$0.381756\pi$
$18$	16344.0	0.660548
$19$	−39940.0	−1.33589	−0.667945	−	0.744211i	$-0.732826\pi$
$19$	−39940.0	−1.33589	−0.667945	+	0.744211i	$0.732826\pi$
$20$	−13440.0	−0.375659
$21$	12192.0	0.287281
$22$	−8736.00	−0.174917
$23$	68712.0	1.17757	0.588783	−	0.808291i	$-0.299607\pi$
$23$	68712.0	1.17757	0.588783	+	0.808291i	$0.299607\pi$
$24$	−6144.00	−0.0907218
$25$	−34025.0	−0.435520
$26$	−11056.0	−0.123365
$27$	−50760.0	−0.496305
$28$	65024.0	0.559784
$29$	−102570.	−0.780957	−0.390479	−	0.920612i	$-0.627690\pi$
$29$	−102570.	−0.780957	−0.390479	+	0.920612i	$0.627690\pi$
$30$	20160.0	0.136322
$31$	227552.	1.37188	0.685938	−	0.727660i	$-0.259392\pi$
$31$	227552.	1.37188	0.685938	+	0.727660i	$0.259392\pi$
$32$	−32768.0	−0.176777
$33$	13104.0	0.0634753
$34$	−117648.	−0.513344
$35$	−213360.	−0.841153
$36$	−130752.	−0.467078
$37$	160526.	0.521002	0.260501	−	0.965474i	$-0.416112\pi$
$37$	160526.	0.521002	0.260501	+	0.965474i	$0.416112\pi$
$38$	319520.	0.944616
$39$	16584.0	0.0447675
$40$	107520.	0.265631
$41$	10842.0	0.0245678	0.0122839	−	0.999925i	$-0.496090\pi$
$41$	10842.0	0.0245678	0.0122839	+	0.999925i	$0.496090\pi$
$42$	−97536.0	−0.203139
$43$	−630748.	−1.20981	−0.604904	−	0.796299i	$-0.706788\pi$
$43$	−630748.	−1.20981	−0.604904	+	0.796299i	$0.706788\pi$
$44$	69888.0	0.123685
$45$	429030.	0.701849
$46$	−549696.	−0.832665
$47$	472656.	0.664053	0.332026	−	0.943270i	$-0.392268\pi$
$47$	472656.	0.664053	0.332026	+	0.943270i	$0.392268\pi$
$48$	49152.0	0.0641500
$49$	208713.	0.253433
$50$	272200.	0.307959
$51$	176472.	0.186286
$52$	88448.0	0.0872321
$53$	−1.49402e6	−1.37845	−0.689224	−	0.724548i	$-0.742048\pi$
$53$	−1.49402e6	−1.37845	−0.689224	+	0.724548i	$0.742048\pi$
$54$	406080.	0.350940
$55$	−229320.	−0.185854
$56$	−520192.	−0.395827
$57$	−479280.	−0.342789
$58$	820560.	0.552220
$59$	2.64066e6	1.67390	0.836952	−	0.547277i	$-0.184335\pi$
$59$	2.64066e6	1.67390	0.836952	+	0.547277i	$0.184335\pi$
$60$	−161280.	−0.0963943
$61$	827702.	0.466895	0.233448	−	0.972369i	$-0.424999\pi$
$61$	827702.	0.466895	0.233448	+	0.972369i	$0.424999\pi$
$62$	−1.82042e6	−0.970063
$63$	−2.07569e6	−1.04585
$64$	262144.	0.125000
$65$	−290220.	−0.131078
$66$	−104832.	−0.0448838
$67$	−126004.	−0.0511826	−0.0255913	−	0.999672i	$-0.508147\pi$
$67$	−126004.	−0.0511826	−0.0255913	+	0.999672i	$0.508147\pi$
$68$	941184.	0.362989
$69$	824544.	0.302164
$70$	1.70688e6	0.594785
$71$	−1.41473e6	−0.469104	−0.234552	−	0.972104i	$-0.575362\pi$
$71$	−1.41473e6	−0.469104	−0.234552	+	0.972104i	$0.575362\pi$
$72$	1.04602e6	0.330274
$73$	980282.	0.294931	0.147466	−	0.989067i	$-0.452888\pi$
$73$	980282.	0.294931	0.147466	+	0.989067i	$0.452888\pi$
$74$	−1.28421e6	−0.368404
$75$	−408300.	−0.111754
$76$	−2.55616e6	−0.667945
$77$	1.10947e6	0.276948
$78$	−132672.	−0.0316554
$79$	−3.56680e6	−0.813924	−0.406962	−	0.913445i	$-0.633412\pi$
$79$	−3.56680e6	−0.813924	−0.406962	+	0.913445i	$0.633412\pi$
$80$	−860160.	−0.187830
$81$	3.85892e6	0.806805
$82$	−86736.0	−0.0173720
$83$	5.67289e6	1.08901	0.544504	−	0.838758i	$-0.316718\pi$
$83$	5.67289e6	1.08901	0.544504	+	0.838758i	$0.316718\pi$
$84$	780288.	0.143641
$85$	−3.08826e6	−0.545441
$86$	5.04598e6	0.855463
$87$	−1.23084e6	−0.200394
$88$	−559104.	−0.0874587
$89$	−1.19512e7	−1.79699	−0.898496	−	0.438982i	$-0.855339\pi$
$89$	−1.19512e7	−1.79699	−0.898496	+	0.438982i	$0.855339\pi$
$90$	−3.43224e6	−0.496282
$91$	1.40411e6	0.195325
$92$	4.39757e6	0.588783
$93$	2.73062e6	0.352023
$94$	−3.78125e6	−0.469556
$95$	8.38740e6	1.00368
$96$	−393216.	−0.0453609
$97$	8.68215e6	0.965886	0.482943	−	0.875652i	$-0.339568\pi$
$97$	8.68215e6	0.965886	0.482943	+	0.875652i	$0.339568\pi$
$98$	−1.66970e6	−0.179204
$99$	−2.23096e6	−0.231083
$100$	−2.17760e6	−0.217760
$101$	−1.00795e7	−0.973455	−0.486727	−	0.873554i	$-0.661810\pi$
$101$	−1.00795e7	−0.973455	−0.486727	+	0.873554i	$0.661810\pi$
$102$	−1.41178e6	−0.131724
$103$	3.74799e6	0.337962	0.168981	−	0.985619i	$-0.445952\pi$
$103$	3.74799e6	0.337962	0.168981	+	0.985619i	$0.445952\pi$
$104$	−707584.	−0.0616824
$105$	−2.56032e6	−0.215840
$106$	1.19521e7	0.974710
$107$	−1.79856e7	−1.41932	−0.709661	−	0.704543i	$-0.751152\pi$
$107$	−1.79856e7	−1.41932	−0.709661	+	0.704543i	$0.751152\pi$
$108$	−3.24864e6	−0.248152
$109$	1.22570e7	0.906552	0.453276	−	0.891370i	$-0.350255\pi$
$109$	1.22570e7	0.906552	0.453276	+	0.891370i	$0.350255\pi$
$110$	1.83456e6	0.131419
$111$	1.92631e6	0.133689
$112$	4.16154e6	0.279892
$113$	1.65950e7	1.08194	0.540968	−	0.841043i	$-0.318058\pi$
$113$	1.65950e7	1.08194	0.540968	+	0.841043i	$0.318058\pi$
$114$	3.83424e6	0.242389
$115$	−1.44295e7	−0.884727
$116$	−6.56448e6	−0.390479
$117$	−2.82343e6	−0.162977
$118$	−2.11253e7	−1.18363
$119$	1.49413e7	0.812782
$120$	1.29024e6	0.0681610
$121$	−1.82947e7	−0.938808
$122$	−6.62162e6	−0.330145
$123$	130104.	0.00630410
$124$	1.45633e7	0.685938
$125$	2.35515e7	1.07853
$126$	1.66055e7	0.739529
$127$	1.16826e6	0.0506087	0.0253043	−	0.999680i	$-0.491945\pi$
$127$	1.16826e6	0.0506087	0.0253043	+	0.999680i	$0.491945\pi$
$128$	−2.09715e6	−0.0883883
$129$	−7.56898e6	−0.310437
$130$	2.32176e6	0.0926863
$131$	−7.92383e6	−0.307954	−0.153977	−	0.988074i	$-0.549208\pi$
$131$	−7.92383e6	−0.307954	−0.153977	+	0.988074i	$0.549208\pi$
$132$	838656.	0.0317377
$133$	−4.05790e7	−1.49562
$134$	1.00803e6	0.0361916
$135$	1.06596e7	0.372883
$136$	−7.52947e6	−0.256672
$137$	−315654.	−0.0104879	−0.00524396	−	0.999986i	$-0.501669\pi$
$137$	−315654.	−0.0104879	−0.00524396	+	0.999986i	$0.501669\pi$
$138$	−6.59635e6	−0.213662
$139$	3.92038e7	1.23816	0.619079	−	0.785329i	$-0.287506\pi$
$139$	3.92038e7	1.23816	0.619079	+	0.785329i	$0.287506\pi$
$140$	−1.36550e7	−0.420576
$141$	5.67187e6	0.170396
$142$	1.13178e7	0.331706
$143$	1.50914e6	0.0431573
$144$	−8.36813e6	−0.233539
$145$	2.15397e7	0.586748
$146$	−7.84226e6	−0.208548
$147$	2.50456e6	0.0650309
$148$	1.02737e7	0.260501
$149$	−2.18860e7	−0.542020	−0.271010	−	0.962577i	$-0.587358\pi$
$149$	−2.18860e7	−0.542020	−0.271010	+	0.962577i	$0.587358\pi$
$150$	3.26640e6	0.0790224
$151$	−2.94154e7	−0.695274	−0.347637	−	0.937629i	$-0.613016\pi$
$151$	−2.94154e7	−0.695274	−0.347637	+	0.937629i	$0.613016\pi$
$152$	2.04493e7	0.472308
$153$	−3.00444e7	−0.678177
$154$	−8.87578e6	−0.195832
$155$	−4.77859e7	−1.03072
$156$	1.06138e6	0.0223838
$157$	6.05550e7	1.24882	0.624412	−	0.781095i	$-0.285339\pi$
$157$	6.05550e7	1.24882	0.624412	+	0.781095i	$0.285339\pi$
$158$	2.85344e7	0.575531
$159$	−1.79282e7	−0.353710
$160$	6.88128e6	0.132816
$161$	6.98114e7	1.31837
$162$	−3.08714e7	−0.570497
$163$	5.70853e7	1.03245	0.516223	−	0.856454i	$-0.327337\pi$
$163$	5.70853e7	1.03245	0.516223	+	0.856454i	$0.327337\pi$
$164$	693888.	0.0122839
$165$	−2.75184e6	−0.0476902
$166$	−4.53831e7	−0.770045
$167$	−8.77265e7	−1.45755	−0.728775	−	0.684754i	$-0.759910\pi$
$167$	−8.77265e7	−1.45755	−0.728775	+	0.684754i	$0.759910\pi$
$168$	−6.24230e6	−0.101569
$169$	−6.08386e7	−0.969562
$170$	2.47061e7	0.385685
$171$	8.15974e7	1.24793
$172$	−4.03679e7	−0.604904
$173$	8.56954e6	0.125833	0.0629167	−	0.998019i	$-0.479960\pi$
$173$	8.56954e6	0.125833	0.0629167	+	0.998019i	$0.479960\pi$
$174$	9.84672e6	0.141700
$175$	−3.45694e7	−0.487594
$176$	4.47283e6	0.0618427
$177$	3.16879e7	0.429524
$178$	9.56095e7	1.27067
$179$	1.88041e7	0.245056	0.122528	−	0.992465i	$-0.460900\pi$
$179$	1.88041e7	0.245056	0.122528	+	0.992465i	$0.460900\pi$
$180$	2.74579e7	0.350925
$181$	−5.99625e7	−0.751631	−0.375816	−	0.926694i	$-0.622637\pi$
$181$	−5.99625e7	−0.751631	−0.375816	+	0.926694i	$0.622637\pi$
$182$	−1.12329e7	−0.138115
$183$	9.93242e6	0.119805
$184$	−3.51805e7	−0.416332
$185$	−3.37105e7	−0.391439
$186$	−2.18450e7	−0.248918
$187$	1.60590e7	0.179586
$188$	3.02500e7	0.332026
$189$	−5.15722e7	−0.555647
$190$	−6.70992e7	−0.709708
$191$	9.39861e7	0.975993	0.487997	−	0.872845i	$-0.337728\pi$
$191$	9.39861e7	0.975993	0.487997	+	0.872845i	$0.337728\pi$
$192$	3.14573e6	0.0320750
$193$	−3.51946e7	−0.352391	−0.176196	−	0.984355i	$-0.556379\pi$
$193$	−3.51946e7	−0.352391	−0.176196	+	0.984355i	$0.556379\pi$
$194$	−6.94572e7	−0.682985
$195$	−3.48264e6	−0.0336347
$196$	1.33576e7	0.126717
$197$	1.02985e8	0.959718	0.479859	−	0.877346i	$-0.340688\pi$
$197$	1.02985e8	0.959718	0.479859	+	0.877346i	$0.340688\pi$
$198$	1.78476e7	0.163400
$199$	8.36376e7	0.752342	0.376171	−	0.926550i	$-0.377240\pi$
$199$	8.36376e7	0.752342	0.376171	+	0.926550i	$0.377240\pi$
$200$	1.74208e7	0.153980
$201$	−1.51205e6	−0.0131335
$202$	8.06363e7	0.688337
$203$	−1.04211e8	−0.874335
$204$	1.12942e7	0.0931430
$205$	−2.27682e6	−0.0184582
$206$	−2.99839e7	−0.238975
$207$	−1.40379e8	−1.10003
$208$	5.66067e6	0.0436160
$209$	−4.36145e7	−0.330460
$210$	2.04826e7	0.152622
$211$	−9.74010e7	−0.713797	−0.356899	−	0.934143i	$-0.616166\pi$
$211$	−9.74010e7	−0.713797	−0.356899	+	0.934143i	$0.616166\pi$
$212$	−9.56172e7	−0.689224
$213$	−1.69767e7	−0.120372
$214$	1.43885e8	1.00361
$215$	1.32457e8	0.908951
$216$	2.59891e7	0.175470
$217$	2.31193e8	1.53591
$218$	−9.80562e7	−0.641029
$219$	1.17634e7	0.0756794
$220$	−1.46765e7	−0.0929271
$221$	2.03237e7	0.126657
$222$	−1.54105e7	−0.0945325
$223$	−1.46457e7	−0.0884390	−0.0442195	−	0.999022i	$-0.514080\pi$
$223$	−1.46457e7	−0.0884390	−0.0442195	+	0.999022i	$0.514080\pi$
$224$	−3.32923e7	−0.197914
$225$	6.95131e7	0.406844
$226$	−1.32760e8	−0.765045
$227$	−1.84541e8	−1.04713	−0.523567	−	0.851985i	$-0.675399\pi$
$227$	−1.84541e8	−1.04713	−0.523567	+	0.851985i	$0.675399\pi$
$228$	−3.06739e7	−0.171395
$229$	−8.75461e6	−0.0481740	−0.0240870	−	0.999710i	$-0.507668\pi$
$229$	−8.75461e6	−0.0481740	−0.0240870	+	0.999710i	$0.507668\pi$
$230$	1.15436e8	0.625597
$231$	1.33137e7	0.0710650
$232$	5.25158e7	0.276110
$233$	−1.19556e8	−0.619193	−0.309597	−	0.950868i	$-0.600194\pi$
$233$	−1.19556e8	−0.619193	−0.309597	+	0.950868i	$0.600194\pi$
$234$	2.25874e7	0.115242
$235$	−9.92578e7	−0.498915
$236$	1.69002e8	0.836952
$237$	−4.28016e7	−0.208853
$238$	−1.19530e8	−0.574723
$239$	3.96209e8	1.87729	0.938646	−	0.344883i	$-0.112081\pi$
$239$	3.96209e8	1.87729	0.938646	+	0.344883i	$0.112081\pi$
$240$	−1.03219e7	−0.0481971
$241$	−2.56606e8	−1.18089	−0.590443	−	0.807080i	$-0.701047\pi$
$241$	−2.56606e8	−1.18089	−0.590443	+	0.807080i	$0.701047\pi$
$242$	1.46358e8	0.663837
$243$	1.57319e8	0.703331
$244$	5.29729e7	0.233448
$245$	−4.38297e7	−0.190409
$246$	−1.04083e6	−0.00445767
$247$	−5.51971e7	−0.233065
$248$	−1.16507e8	−0.485031
$249$	6.80747e7	0.279440
$250$	−1.88412e8	−0.762638
$251$	−7.34775e7	−0.293290	−0.146645	−	0.989189i	$-0.546847\pi$
$251$	−7.34775e7	−0.293290	−0.146645	+	0.989189i	$0.546847\pi$
$252$	−1.32844e8	−0.522926
$253$	7.50335e7	0.291295
$254$	−9.34605e6	−0.0357857
$255$	−3.70591e7	−0.139960
$256$	1.67772e7	0.0625000
$257$	−2.02701e8	−0.744886	−0.372443	−	0.928055i	$-0.621480\pi$
$257$	−2.02701e8	−0.744886	−0.372443	+	0.928055i	$0.621480\pi$
$258$	6.05518e7	0.219512
$259$	1.63094e8	0.583297
$260$	−1.85741e7	−0.0655391
$261$	2.09551e8	0.729536
$262$	6.33906e7	0.217756
$263$	1.54254e8	0.522867	0.261434	−	0.965221i	$-0.415805\pi$
$263$	1.54254e8	0.522867	0.261434	+	0.965221i	$0.415805\pi$
$264$	−6.70925e6	−0.0224419
$265$	3.13744e8	1.03565
$266$	3.24632e8	1.05756
$267$	−1.43414e8	−0.461108
$268$	−8.06426e6	−0.0255913
$269$	−6.24018e8	−1.95463	−0.977315	−	0.211793i	$-0.932070\pi$
$269$	−6.24018e8	−1.95463	−0.977315	+	0.211793i	$0.932070\pi$
$270$	−8.52768e7	−0.263668
$271$	−3.87983e8	−1.18419	−0.592094	−	0.805869i	$-0.701698\pi$
$271$	−3.87983e8	−1.18419	−0.592094	+	0.805869i	$0.701698\pi$
$272$	6.02358e7	0.181494
$273$	1.68493e7	0.0501203
$274$	2.52523e6	0.00741608
$275$	−3.71553e7	−0.107735
$276$	5.27708e7	0.151082
$277$	4.53952e8	1.28331	0.641654	−	0.766994i	$-0.278248\pi$
$277$	4.53952e8	1.28331	0.641654	+	0.766994i	$0.278248\pi$
$278$	−3.13630e8	−0.875510
$279$	−4.64889e8	−1.28155
$280$	1.09240e8	0.297392
$281$	3.33770e8	0.897377	0.448689	−	0.893688i	$-0.351891\pi$
$281$	3.33770e8	0.897377	0.448689	+	0.893688i	$0.351891\pi$
$282$	−4.53750e7	−0.120488
$283$	5.37695e8	1.41021	0.705104	−	0.709104i	$-0.250900\pi$
$283$	5.37695e8	1.41021	0.705104	+	0.709104i	$0.250900\pi$
$284$	−9.05426e7	−0.234552
$285$	1.00649e8	0.257544
$286$	−1.20732e7	−0.0305168
$287$	1.10155e7	0.0275053
$288$	6.69450e7	0.165137
$289$	−1.94072e8	−0.472956
$290$	−1.72318e8	−0.414894
$291$	1.04186e8	0.247847
$292$	6.27380e7	0.147466
$293$	3.35600e8	0.779445	0.389722	−	0.920932i	$-0.372571\pi$
$293$	3.35600e8	0.779445	0.389722	+	0.920932i	$0.372571\pi$
$294$	−2.00364e7	−0.0459838
$295$	−5.54539e8	−1.25764
$296$	−8.21893e7	−0.184202
$297$	−5.54299e7	−0.122771
$298$	1.75088e8	0.383266
$299$	9.49600e7	0.205443
$300$	−2.61312e7	−0.0558772
$301$	−6.40840e8	−1.35446
$302$	2.35324e8	0.491633
$303$	−1.20954e8	−0.249789
$304$	−1.63594e8	−0.333972
$305$	−1.73817e8	−0.350787
$306$	2.40355e8	0.479543
$307$	2.15029e8	0.424143	0.212072	−	0.977254i	$-0.431979\pi$
$307$	2.15029e8	0.424143	0.212072	+	0.977254i	$0.431979\pi$
$308$	7.10062e7	0.138474
$309$	4.49759e7	0.0867212
$310$	3.82287e8	0.728826
$311$	7.92062e8	1.49313	0.746565	−	0.665313i	$-0.231702\pi$
$311$	7.92062e8	1.49313	0.746565	+	0.665313i	$0.231702\pi$
$312$	−8.49101e6	−0.0158277
$313$	−1.18457e8	−0.218352	−0.109176	−	0.994022i	$-0.534821\pi$
$313$	−1.18457e8	−0.218352	−0.109176	+	0.994022i	$0.534821\pi$
$314$	−4.84440e8	−0.883051
$315$	4.35894e8	0.785768
$316$	−2.28275e8	−0.406962
$317$	−5.07310e7	−0.0894470	−0.0447235	−	0.998999i	$-0.514241\pi$
$317$	−5.07310e7	−0.0894470	−0.0447235	+	0.998999i	$0.514241\pi$
$318$	1.43426e8	0.250111
$319$	−1.12006e8	−0.193186
$320$	−5.50502e7	−0.0939149
$321$	−2.15827e8	−0.364198
$322$	−5.58491e8	−0.932225
$323$	−5.87358e8	−0.969826
$324$	2.46971e8	0.403402
$325$	−4.70226e7	−0.0759826
$326$	−4.56682e8	−0.730050
$327$	1.47084e8	0.232621
$328$	−5.55110e6	−0.00868602
$329$	4.80218e8	0.743453
$330$	2.20147e7	0.0337221
$331$	2.73757e8	0.414923	0.207461	−	0.978243i	$-0.433480\pi$
$331$	2.73757e8	0.414923	0.207461	+	0.978243i	$0.433480\pi$
$332$	3.63065e8	0.544504
$333$	−3.27955e8	−0.486697
$334$	7.01812e8	1.03064
$335$	2.64608e7	0.0384545
$336$	4.99384e7	0.0718203
$337$	−9.18512e7	−0.130732	−0.0653658	−	0.997861i	$-0.520821\pi$
$337$	−9.18512e7	−0.130732	−0.0653658	+	0.997861i	$0.520821\pi$
$338$	4.86709e8	0.685584
$339$	1.99140e8	0.277625
$340$	−1.97649e8	−0.272720
$341$	2.48487e8	0.339362
$342$	−6.52779e8	−0.882419
$343$	−6.24667e8	−0.835833
$344$	3.22943e8	0.427732
$345$	−1.73154e8	−0.227021
$346$	−6.85563e7	−0.0889777
$347$	−1.36700e9	−1.75637	−0.878187	−	0.478318i	$-0.841247\pi$
$347$	−1.36700e9	−1.75637	−0.878187	+	0.478318i	$0.841247\pi$
$348$	−7.87738e7	−0.100197
$349$	1.13143e9	1.42475	0.712377	−	0.701797i	$-0.247619\pi$
$349$	1.13143e9	1.42475	0.712377	+	0.701797i	$0.247619\pi$
$350$	2.76555e8	0.344781
$351$	−7.01503e7	−0.0865874
$352$	−3.57827e7	−0.0437294
$353$	−4.48395e7	−0.0542562	−0.0271281	−	0.999632i	$-0.508636\pi$
$353$	−4.48395e7	−0.0542562	−0.0271281	+	0.999632i	$0.508636\pi$
$354$	−2.53503e8	−0.303719
$355$	2.97093e8	0.352446
$356$	−7.64876e8	−0.898496
$357$	1.79296e8	0.208560
$358$	−1.50432e8	−0.173281
$359$	3.98281e8	0.454317	0.227158	−	0.973858i	$-0.427057\pi$
$359$	3.98281e8	0.454317	0.227158	+	0.973858i	$0.427057\pi$
$360$	−2.19663e8	−0.248141
$361$	7.01332e8	0.784600
$362$	4.79700e8	0.531483
$363$	−2.19536e8	−0.240898
$364$	8.98632e7	0.0976623
$365$	−2.05859e8	−0.221588
$366$	−7.94594e7	−0.0847152
$367$	1.63472e9	1.72628	0.863140	−	0.504964i	$-0.168494\pi$
$367$	1.63472e9	1.72628	0.863140	+	0.504964i	$0.168494\pi$
$368$	2.81444e8	0.294391
$369$	−2.21502e7	−0.0229501
$370$	2.69684e8	0.276789
$371$	−1.51792e9	−1.54327
$372$	1.74760e8	0.176012
$373$	−1.54633e9	−1.54284	−0.771421	−	0.636325i	$-0.780454\pi$
$373$	−1.54633e9	−1.54284	−0.771421	+	0.636325i	$0.780454\pi$
$374$	−1.28472e8	−0.126986
$375$	2.82618e8	0.276752
$376$	−2.42000e8	−0.234778
$377$	−1.41752e8	−0.136249
$378$	4.12577e8	0.392902
$379$	−1.05688e9	−0.997216	−0.498608	−	0.866828i	$-0.666155\pi$
$379$	−1.05688e9	−0.997216	−0.498608	+	0.866828i	$0.666155\pi$
$380$	5.36794e8	0.501839
$381$	1.40191e7	0.0129862
$382$	−7.51889e8	−0.690132
$383$	2.24910e8	0.204556	0.102278	−	0.994756i	$-0.467387\pi$
$383$	2.24910e8	0.204556	0.102278	+	0.994756i	$0.467387\pi$
$384$	−2.51658e7	−0.0226805
$385$	−2.32989e8	−0.208077
$386$	2.81556e8	0.249178
$387$	1.28862e9	1.13015
$388$	5.55657e8	0.482943
$389$	1.01788e9	0.876746	0.438373	−	0.898793i	$-0.355555\pi$
$389$	1.01788e9	0.876746	0.438373	+	0.898793i	$0.355555\pi$
$390$	2.78611e7	0.0237833
$391$	1.01048e9	0.854887
$392$	−1.06861e8	−0.0896021
$393$	−9.50859e7	−0.0790210
$394$	−8.23883e8	−0.678623
$395$	7.49028e8	0.611517
$396$	−1.42781e8	−0.115541
$397$	−1.47565e9	−1.18363	−0.591817	−	0.806072i	$-0.701589\pi$
$397$	−1.47565e9	−1.18363	−0.591817	+	0.806072i	$0.701589\pi$
$398$	−6.69100e8	−0.531986
$399$	−4.86948e8	−0.383776
$400$	−1.39366e8	−0.108880
$401$	2.74912e8	0.212906	0.106453	−	0.994318i	$-0.466051\pi$
$401$	2.74912e8	0.212906	0.106453	+	0.994318i	$0.466051\pi$
$402$	1.20964e7	0.00928676
$403$	3.14477e8	0.239343
$404$	−6.45090e8	−0.486727
$405$	−8.10373e8	−0.606167
$406$	8.33689e8	0.618248
$407$	1.75294e8	0.128881
$408$	−9.03537e7	−0.0658620
$409$	−1.63427e9	−1.18112	−0.590558	−	0.806995i	$-0.701092\pi$
$409$	−1.63427e9	−1.18112	−0.590558	+	0.806995i	$0.701092\pi$
$410$	1.82146e7	0.0130519
$411$	−3.78785e6	−0.00269120
$412$	2.39871e8	0.168981
$413$	2.68291e9	1.87405
$414$	1.12303e9	0.777839
$415$	−1.19131e9	−0.818192
$416$	−4.52854e7	−0.0308412
$417$	4.70445e8	0.317712
$418$	3.48916e8	0.233670
$419$	−1.11280e9	−0.739039	−0.369519	−	0.929223i	$-0.620478\pi$
$419$	−1.11280e9	−0.739039	−0.369519	+	0.929223i	$0.620478\pi$
$420$	−1.63860e8	−0.107920
$421$	9.22528e8	0.602549	0.301274	−	0.953537i	$-0.402588\pi$
$421$	9.22528e8	0.602549	0.301274	+	0.953537i	$0.402588\pi$
$422$	7.79208e8	0.504731
$423$	−9.65636e8	−0.620329
$424$	7.64937e8	0.487355
$425$	−5.00372e8	−0.316178
$426$	1.35814e8	0.0851159
$427$	8.40945e8	0.522721
$428$	−1.15108e9	−0.709661
$429$	1.81097e7	0.0110742
$430$	−1.05966e9	−0.642726
$431$	−9.81508e8	−0.590505	−0.295252	−	0.955419i	$-0.595404\pi$
$431$	−9.81508e8	−0.590505	−0.295252	+	0.955419i	$0.595404\pi$
$432$	−2.07913e8	−0.124076
$433$	2.84998e9	1.68707	0.843537	−	0.537071i	$-0.180469\pi$
$433$	2.84998e9	1.68707	0.843537	+	0.537071i	$0.180469\pi$
$434$	−1.84954e9	−1.08605
$435$	2.58476e8	0.150560
$436$	7.84450e8	0.453276
$437$	−2.74436e9	−1.57310
$438$	−9.41071e7	−0.0535134
$439$	−1.05622e9	−0.595838	−0.297919	−	0.954591i	$-0.596292\pi$
$439$	−1.05622e9	−0.595838	−0.297919	+	0.954591i	$0.596292\pi$
$440$	1.17412e8	0.0657094
$441$	−4.26401e8	−0.236746
$442$	−1.62590e8	−0.0895601
$443$	1.82325e9	0.996401	0.498201	−	0.867062i	$-0.333994\pi$
$443$	1.82325e9	0.996401	0.498201	+	0.867062i	$0.333994\pi$
$444$	1.23284e8	0.0668446
$445$	2.50975e9	1.35011
$446$	1.17166e8	0.0625358
$447$	−2.62633e8	−0.139082
$448$	2.66338e8	0.139946
$449$	1.84846e9	0.963713	0.481856	−	0.876250i	$-0.339963\pi$
$449$	1.84846e9	0.963713	0.481856	+	0.876250i	$0.339963\pi$
$450$	−5.56105e8	−0.287682
$451$	1.18395e7	0.00607735
$452$	1.06208e9	0.540968
$453$	−3.52985e8	−0.178407
$454$	1.47633e9	0.740435
$455$	−2.94864e8	−0.146751
$456$	2.45391e8	0.121194
$457$	−2.98066e9	−1.46085	−0.730425	−	0.682993i	$-0.760678\pi$
$457$	−2.98066e9	−1.46085	−0.730425	+	0.682993i	$0.760678\pi$
$458$	7.00369e7	0.0340642
$459$	−7.46477e8	−0.360306
$460$	−9.23489e8	−0.442364
$461$	−2.52781e9	−1.20169	−0.600843	−	0.799367i	$-0.705168\pi$
$461$	−2.52781e9	−1.20169	−0.600843	+	0.799367i	$0.705168\pi$
$462$	−1.06509e8	−0.0502505
$463$	−8.90291e8	−0.416868	−0.208434	−	0.978036i	$-0.566837\pi$
$463$	−8.90291e8	−0.416868	−0.208434	+	0.978036i	$0.566837\pi$
$464$	−4.20127e8	−0.195239
$465$	−5.73431e8	−0.264482
$466$	9.56450e8	0.437836
$467$	2.65667e9	1.20706	0.603529	−	0.797341i	$-0.293761\pi$
$467$	2.65667e9	1.20706	0.603529	+	0.797341i	$0.293761\pi$
$468$	−1.80699e8	−0.0814884
$469$	−1.28020e8	−0.0573024
$470$	7.94062e8	0.352786
$471$	7.26660e8	0.320448
$472$	−1.35202e9	−0.591814
$473$	−6.88777e8	−0.299271
$474$	3.42413e8	0.147681
$475$	1.35896e9	0.581806
$476$	9.56243e8	0.406391
$477$	3.05228e9	1.28769
$478$	−3.16967e9	−1.32745
$479$	1.30093e9	0.540855	0.270428	−	0.962740i	$-0.412835\pi$
$479$	1.30093e9	0.540855	0.270428	+	0.962740i	$0.412835\pi$
$480$	8.25754e7	0.0340805
$481$	2.21847e8	0.0908962
$482$	2.05285e9	0.835012
$483$	8.37737e8	0.338293
$484$	−1.17086e9	−0.469404
$485$	−1.82325e9	−0.725689
$486$	−1.25855e9	−0.497330
$487$	−1.07447e9	−0.421542	−0.210771	−	0.977535i	$-0.567598\pi$
$487$	−1.07447e9	−0.421542	−0.210771	+	0.977535i	$0.567598\pi$
$488$	−4.23783e8	−0.165072
$489$	6.85024e8	0.264926
$490$	3.50638e8	0.134640
$491$	−7.83344e8	−0.298653	−0.149327	−	0.988788i	$-0.547711\pi$
$491$	−7.83344e8	−0.298653	−0.149327	+	0.988788i	$0.547711\pi$
$492$	8.32666e6	0.00315205
$493$	−1.50839e9	−0.566958
$494$	4.41577e8	0.164802
$495$	4.68501e8	0.173617
$496$	9.32053e8	0.342969
$497$	−1.43736e9	−0.525193
$498$	−5.44598e8	−0.197594
$499$	−6.23188e8	−0.224526	−0.112263	−	0.993679i	$-0.535810\pi$
$499$	−6.23188e8	−0.224526	−0.112263	+	0.993679i	$0.535810\pi$
$500$	1.50730e9	0.539267
$501$	−1.05272e9	−0.374007
$502$	5.87820e8	0.207387
$503$	−2.70927e9	−0.949215	−0.474607	−	0.880198i	$-0.657410\pi$
$503$	−2.70927e9	−0.949215	−0.474607	+	0.880198i	$0.657410\pi$
$504$	1.06275e9	0.369764
$505$	2.11670e9	0.731375
$506$	−6.00268e8	−0.205977
$507$	−7.30063e8	−0.248790
$508$	7.47684e7	0.0253043
$509$	3.49943e9	1.17621	0.588106	−	0.808784i	$-0.299874\pi$
$509$	3.49943e9	1.17621	0.588106	+	0.808784i	$0.299874\pi$
$510$	2.96473e8	0.0989668
$511$	9.95967e8	0.330196
$512$	−1.34218e8	−0.0441942
$513$	2.02735e9	0.663008
$514$	1.62161e9	0.526714
$515$	−7.87078e8	−0.253918
$516$	−4.84414e8	−0.155218
$517$	5.16140e8	0.164267
$518$	−1.30476e9	−0.412453
$519$	1.02835e8	0.0322889
$520$	1.48593e8	0.0463432
$521$	−1.37683e9	−0.426530	−0.213265	−	0.976994i	$-0.568410\pi$
$521$	−1.37683e9	−0.426530	−0.213265	+	0.976994i	$0.568410\pi$
$522$	−1.67640e9	−0.515860
$523$	−2.86154e9	−0.874669	−0.437334	−	0.899299i	$-0.644077\pi$
$523$	−2.86154e9	−0.874669	−0.437334	+	0.899299i	$0.644077\pi$
$524$	−5.07125e8	−0.153977
$525$	−4.14833e8	−0.125117
$526$	−1.23403e9	−0.369723
$527$	3.34638e9	0.995951
$528$	5.36740e7	0.0158688
$529$	1.31651e9	0.386661
$530$	−2.50995e9	−0.732318
$531$	−5.39487e9	−1.56369
$532$	−2.59706e9	−0.747810
$533$	1.49836e7	0.00428620
$534$	1.14731e9	0.326053
$535$	3.77697e9	1.06636
$536$	6.45140e7	0.0180958
$537$	2.25649e8	0.0628815
$538$	4.99215e9	1.38213
$539$	2.27915e8	0.0626919
$540$	6.82214e8	0.186442
$541$	5.34467e9	1.45121	0.725605	−	0.688111i	$-0.241560\pi$
$541$	5.34467e9	1.45121	0.725605	+	0.688111i	$0.241560\pi$
$542$	3.10387e9	0.837347
$543$	−7.19550e8	−0.192869
$544$	−4.81886e8	−0.128336
$545$	−2.57398e9	−0.681109
$546$	−1.34795e8	−0.0354404
$547$	−3.37135e9	−0.880740	−0.440370	−	0.897816i	$-0.645153\pi$
$547$	−3.37135e9	−0.880740	−0.440370	+	0.897816i	$0.645153\pi$
$548$	−2.02019e7	−0.00524396
$549$	−1.69100e9	−0.436153
$550$	2.97242e8	0.0761801
$551$	4.09665e9	1.04327
$552$	−4.22167e8	−0.106831
$553$	−3.62387e9	−0.911244
$554$	−3.63162e9	−0.907436
$555$	−4.04526e8	−0.100443
$556$	2.50904e9	0.619079
$557$	−5.61106e9	−1.37579	−0.687894	−	0.725811i	$-0.741465\pi$
$557$	−5.61106e9	−1.37579	−0.687894	+	0.725811i	$0.741465\pi$
$558$	3.71911e9	0.906190
$559$	−8.71694e8	−0.211068
$560$	−8.73923e8	−0.210288
$561$	1.92707e8	0.0460817
$562$	−2.67016e9	−0.634542
$563$	6.69690e9	1.58159	0.790795	−	0.612081i	$-0.209667\pi$
$563$	6.69690e9	1.58159	0.790795	+	0.612081i	$0.209667\pi$
$564$	3.63000e8	0.0851980
$565$	−3.48494e9	−0.812879
$566$	−4.30156e9	−0.997168
$567$	3.92066e9	0.903273
$568$	7.24341e8	0.165853
$569$	1.96850e9	0.447964	0.223982	−	0.974593i	$-0.428094\pi$
$569$	1.96850e9	0.447964	0.223982	+	0.974593i	$0.428094\pi$
$570$	−8.05190e8	−0.182111
$571$	1.02926e9	0.231365	0.115682	−	0.993286i	$-0.463094\pi$
$571$	1.02926e9	0.231365	0.115682	+	0.993286i	$0.463094\pi$
$572$	9.65852e7	0.0215787
$573$	1.12783e9	0.250440
$574$	−8.81238e7	−0.0194492
$575$	−2.33793e9	−0.512853
$576$	−5.35560e8	−0.116770
$577$	3.31179e9	0.717708	0.358854	−	0.933394i	$-0.383168\pi$
$577$	3.31179e9	0.717708	0.358854	+	0.933394i	$0.383168\pi$
$578$	1.55258e9	0.334431
$579$	−4.22335e8	−0.0904236
$580$	1.37854e9	0.293374
$581$	5.76366e9	1.21922
$582$	−8.33486e8	−0.175254
$583$	−1.63147e9	−0.340988
$584$	−5.01904e8	−0.104274
$585$	5.92919e8	0.122448
$586$	−2.68480e9	−0.551151
$587$	−5.59411e8	−0.114156	−0.0570778	−	0.998370i	$-0.518178\pi$
$587$	−5.59411e8	−0.114156	−0.0570778	+	0.998370i	$0.518178\pi$
$588$	1.60292e8	0.0325155
$589$	−9.08843e9	−1.83267
$590$	4.43631e9	0.889282
$591$	1.23582e9	0.246264
$592$	6.57514e8	0.130250
$593$	−3.02459e9	−0.595628	−0.297814	−	0.954624i	$-0.596258\pi$
$593$	−3.02459e9	−0.595628	−0.297814	+	0.954624i	$0.596258\pi$
$594$	4.43439e8	0.0868124
$595$	−3.13767e9	−0.610658
$596$	−1.40071e9	−0.271010
$597$	1.00365e9	0.193051
$598$	−7.59680e8	−0.145270
$599$	−5.63246e9	−1.07079	−0.535395	−	0.844602i	$-0.679837\pi$
$599$	−5.63246e9	−1.07079	−0.535395	+	0.844602i	$0.679837\pi$
$600$	2.09050e8	0.0395112
$601$	3.40792e8	0.0640366	0.0320183	−	0.999487i	$-0.489807\pi$
$601$	3.40792e8	0.0640366	0.0320183	+	0.999487i	$0.489807\pi$
$602$	5.12672e9	0.957749
$603$	2.57426e8	0.0478126
$604$	−1.88259e9	−0.347637
$605$	3.84189e9	0.705344
$606$	9.67636e8	0.176627
$607$	3.85420e9	0.699477	0.349739	−	0.936847i	$-0.386270\pi$
$607$	3.85420e9	0.699477	0.349739	+	0.936847i	$0.386270\pi$
$608$	1.30875e9	0.236154
$609$	−1.25053e9	−0.224355
$610$	1.39054e9	0.248044
$611$	6.53211e8	0.115853
$612$	−1.92284e9	−0.339088
$613$	9.22245e9	1.61709	0.808545	−	0.588434i	$-0.200255\pi$
$613$	9.22245e9	1.61709	0.808545	+	0.588434i	$0.200255\pi$
$614$	−1.72023e9	−0.299915
$615$	−2.73218e7	−0.00473639
$616$	−5.68050e8	−0.0979160
$617$	6.53611e9	1.12027	0.560133	−	0.828402i	$-0.310750\pi$
$617$	6.53611e9	1.12027	0.560133	+	0.828402i	$0.310750\pi$
$618$	−3.59807e8	−0.0613211
$619$	1.36559e9	0.231420	0.115710	−	0.993283i	$-0.463086\pi$
$619$	1.36559e9	0.231420	0.115710	+	0.993283i	$0.463086\pi$
$620$	−3.05830e9	−0.515358
$621$	−3.48782e9	−0.584431
$622$	−6.33649e9	−1.05580
$623$	−1.21424e10	−2.01186
$624$	6.79281e7	0.0111919
$625$	−2.28761e9	−0.374802
$626$	9.47659e8	0.154398
$627$	−5.23374e8	−0.0847960
$628$	3.87552e9	0.624412
$629$	2.36070e9	0.378236
$630$	−3.48716e9	−0.555622
$631$	1.54079e9	0.244141	0.122070	−	0.992521i	$-0.461047\pi$
$631$	1.54079e9	0.244141	0.122070	+	0.992521i	$0.461047\pi$
$632$	1.82620e9	0.287766
$633$	−1.16881e9	−0.183160
$634$	4.05848e8	0.0632486
$635$	−2.45334e8	−0.0380233
$636$	−1.14741e9	−0.176855
$637$	2.88441e8	0.0442150
$638$	8.96052e8	0.136603
$639$	2.89029e9	0.438216
$640$	4.40402e8	0.0664078
$641$	−4.54018e9	−0.680879	−0.340440	−	0.940266i	$-0.610576\pi$
$641$	−4.54018e9	−0.680879	−0.340440	+	0.940266i	$0.610576\pi$
$642$	1.72661e9	0.257527
$643$	1.14054e10	1.69189	0.845944	−	0.533272i	$-0.179038\pi$
$643$	1.14054e10	1.69189	0.845944	+	0.533272i	$0.179038\pi$
$644$	4.46793e9	0.659183
$645$	1.58948e9	0.233237
$646$	4.69886e9	0.685770
$647$	−1.26393e10	−1.83468	−0.917338	−	0.398109i	$-0.869666\pi$
$647$	−1.26393e10	−1.83468	−0.917338	+	0.398109i	$0.869666\pi$
$648$	−1.97577e9	−0.285248
$649$	2.88360e9	0.414075
$650$	3.76180e8	0.0537278
$651$	2.77431e9	0.394114
$652$	3.65346e9	0.516223
$653$	−1.05004e10	−1.47575	−0.737873	−	0.674940i	$-0.764170\pi$
$653$	−1.05004e10	−1.47575	−0.737873	+	0.674940i	$0.764170\pi$
$654$	−1.17667e9	−0.164488
$655$	1.66400e9	0.231371
$656$	4.44088e7	0.00614194
$657$	−2.00272e9	−0.275512
$658$	−3.84175e9	−0.525700
$659$	9.64818e9	1.31325	0.656624	−	0.754219i	$-0.271984\pi$
$659$	9.64818e9	1.31325	0.656624	+	0.754219i	$0.271984\pi$
$660$	−1.76118e8	−0.0238451
$661$	−6.58299e9	−0.886580	−0.443290	−	0.896378i	$-0.646189\pi$
$661$	−6.58299e9	−0.886580	−0.443290	+	0.896378i	$0.646189\pi$
$662$	−2.19006e9	−0.293395
$663$	2.43884e8	0.0325002
$664$	−2.90452e9	−0.385023
$665$	8.52160e9	1.12369
$666$	2.62364e9	0.344147
$667$	−7.04779e9	−0.919629
$668$	−5.61450e9	−0.728775
$669$	−1.75749e8	−0.0226935
$670$	−2.11687e8	−0.0271914
$671$	9.03851e8	0.115496
$672$	−3.99507e8	−0.0507846
$673$	−8.54649e9	−1.08077	−0.540387	−	0.841416i	$-0.681722\pi$
$673$	−8.54649e9	−1.08077	−0.540387	+	0.841416i	$0.681722\pi$
$674$	7.34810e8	0.0924411
$675$	1.72711e9	0.216151
$676$	−3.89367e9	−0.484781
$677$	8.71305e9	1.07922	0.539610	−	0.841915i	$-0.318572\pi$
$677$	8.71305e9	1.07922	0.539610	+	0.841915i	$0.318572\pi$
$678$	−1.59312e9	−0.196311
$679$	8.82106e9	1.08138
$680$	1.58119e9	0.192842
$681$	−2.21449e9	−0.268695
$682$	−1.98789e9	−0.239965
$683$	1.46109e10	1.75470	0.877351	−	0.479849i	$-0.159308\pi$
$683$	1.46109e10	1.75470	0.877351	+	0.479849i	$0.159308\pi$
$684$	5.22223e9	0.623965
$685$	6.62873e7	0.00787977
$686$	4.99734e9	0.591023
$687$	−1.05055e8	−0.0123615
$688$	−2.58354e9	−0.302452
$689$	−2.06473e9	−0.240490
$690$	1.38523e9	0.160528
$691$	−1.47348e10	−1.69891	−0.849454	−	0.527662i	$-0.823069\pi$
$691$	−1.47348e10	−1.69891	−0.849454	+	0.527662i	$0.823069\pi$
$692$	5.48451e8	0.0629167
$693$	−2.26665e9	−0.258713
$694$	1.09360e10	1.24194
$695$	−8.23279e9	−0.930252
$696$	6.30190e8	0.0708499
$697$	1.59442e8	0.0178357
$698$	−9.05146e9	−1.00745
$699$	−1.43467e9	−0.158885
$700$	−2.21244e9	−0.243797
$701$	1.31502e9	0.144185	0.0720923	−	0.997398i	$-0.477032\pi$
$701$	1.31502e9	0.144185	0.0720923	+	0.997398i	$0.477032\pi$
$702$	5.61203e8	0.0612265
$703$	−6.41141e9	−0.696001
$704$	2.86261e8	0.0309213
$705$	−1.19109e9	−0.128022
$706$	3.58716e8	0.0383649
$707$	−1.02408e10	−1.08985
$708$	2.02803e9	0.214762
$709$	6.64028e8	0.0699721	0.0349860	−	0.999388i	$-0.488861\pi$
$709$	6.64028e8	0.0699721	0.0349860	+	0.999388i	$0.488861\pi$
$710$	−2.37674e9	−0.249217
$711$	7.28697e9	0.760332
$712$	6.11901e9	0.635333
$713$	1.56356e10	1.61547
$714$	−1.43436e9	−0.147474
$715$	−3.16920e8	−0.0324249
$716$	1.20346e9	0.122528
$717$	4.75451e9	0.481713
$718$	−3.18624e9	−0.321250
$719$	4.95034e9	0.496689	0.248344	−	0.968672i	$-0.420114\pi$
$719$	4.95034e9	0.496689	0.248344	+	0.968672i	$0.420114\pi$
$720$	1.75731e9	0.175462
$721$	3.80796e9	0.378372
$722$	−5.61065e9	−0.554796
$723$	−3.07928e9	−0.303015
$724$	−3.83760e9	−0.375816
$725$	3.48994e9	0.340123
$726$	1.75629e9	0.170341
$727$	8.81101e9	0.850463	0.425231	−	0.905085i	$-0.360193\pi$
$727$	8.81101e9	0.850463	0.425231	+	0.905085i	$0.360193\pi$
$728$	−7.18905e8	−0.0690577
$729$	−6.55163e9	−0.626330
$730$	1.64687e9	0.156686
$731$	−9.27578e9	−0.878293
$732$	6.35675e8	0.0599027
$733$	−1.49414e8	−0.0140129	−0.00700643	−	0.999975i	$-0.502230\pi$
$733$	−1.49414e8	−0.0140129	−0.00700643	+	0.999975i	$0.502230\pi$
$734$	−1.30777e10	−1.22066
$735$	−5.25957e8	−0.0488590
$736$	−2.25155e9	−0.208166
$737$	−1.37596e8	−0.0126611
$738$	1.77202e8	0.0162282
$739$	−4.70806e9	−0.429127	−0.214564	−	0.976710i	$-0.568833\pi$
$739$	−4.70806e9	−0.429127	−0.214564	+	0.976710i	$0.568833\pi$
$740$	−2.15747e9	−0.195719
$741$	−6.62365e8	−0.0598045
$742$	1.21434e10	1.09125
$743$	1.69676e9	0.151761	0.0758805	−	0.997117i	$-0.475823\pi$
$743$	1.69676e9	0.151761	0.0758805	+	0.997117i	$0.475823\pi$
$744$	−1.39808e9	−0.124459
$745$	4.59607e9	0.407230
$746$	1.23707e10	1.09095
$747$	−1.15897e10	−1.01730
$748$	1.02777e9	0.0897928
$749$	−1.82733e10	−1.58903
$750$	−2.26094e9	−0.195693
$751$	1.06650e10	0.918800	0.459400	−	0.888229i	$-0.348064\pi$
$751$	1.06650e10	0.918800	0.459400	+	0.888229i	$0.348064\pi$
$752$	1.93600e9	0.166013
$753$	−8.81731e8	−0.0752581
$754$	1.13401e9	0.0963427
$755$	6.17724e9	0.522373
$756$	−3.30062e9	−0.277824
$757$	6.22876e9	0.521874	0.260937	−	0.965356i	$-0.415968\pi$
$757$	6.22876e9	0.521874	0.260937	+	0.965356i	$0.415968\pi$
$758$	8.45506e9	0.705138
$759$	9.00402e8	0.0747464
$760$	−4.29435e9	−0.354854
$761$	−8.38334e9	−0.689558	−0.344779	−	0.938684i	$-0.612046\pi$
$761$	−8.38334e9	−0.689558	−0.344779	+	0.938684i	$0.612046\pi$
$762$	−1.12153e8	−0.00918263
$763$	1.24531e10	1.01495
$764$	6.01511e9	0.487997
$765$	6.30932e9	0.509527
$766$	−1.79928e9	−0.144643
$767$	3.64939e9	0.292036
$768$	2.01327e8	0.0160375
$769$	−1.18649e10	−0.940852	−0.470426	−	0.882439i	$-0.655900\pi$
$769$	−1.18649e10	−0.940852	−0.470426	+	0.882439i	$0.655900\pi$
$770$	1.86391e9	0.147132
$771$	−2.43241e9	−0.191138
$772$	−2.25245e9	−0.176196
$773$	5.56680e9	0.433488	0.216744	−	0.976228i	$-0.430456\pi$
$773$	5.56680e9	0.433488	0.216744	+	0.976228i	$0.430456\pi$
$774$	−1.03089e10	−0.799136
$775$	−7.74246e9	−0.597479
$776$	−4.44526e9	−0.341492
$777$	1.95713e9	0.149674
$778$	−8.14306e9	−0.619953
$779$	−4.33029e8	−0.0328198
$780$	−2.22889e8	−0.0168173
$781$	−1.54488e9	−0.116042
$782$	−8.08383e9	−0.604496
$783$	5.20645e9	0.387593
$784$	8.54888e8	0.0633583
$785$	−1.27165e10	−0.938264
$786$	7.60687e8	0.0558763
$787$	1.34611e8	0.00984395	0.00492198	−	0.999988i	$-0.498433\pi$
$787$	1.34611e8	0.00984395	0.00492198	+	0.999988i	$0.498433\pi$
$788$	6.59106e9	0.479859
$789$	1.85105e9	0.134168
$790$	−5.99222e9	−0.432408
$791$	1.68605e10	1.21130
$792$	1.14225e9	0.0817001
$793$	1.14388e9	0.0814565
$794$	1.18052e10	0.836955
$795$	3.76493e9	0.265749
$796$	5.35280e9	0.376171
$797$	−7.41548e9	−0.518842	−0.259421	−	0.965764i	$-0.583532\pi$
$797$	−7.41548e9	−0.518842	−0.259421	+	0.965764i	$0.583532\pi$
$798$	3.89559e9	0.271371
$799$	6.95088e9	0.482088
$800$	1.11493e9	0.0769898
$801$	2.44163e10	1.67867
$802$	−2.19930e9	−0.150548
$803$	1.07047e9	0.0729574
$804$	−9.67711e7	−0.00656673
$805$	−1.46604e10	−0.990513
$806$	−2.51581e9	−0.169241
$807$	−7.48822e9	−0.501558
$808$	5.16072e9	0.344168
$809$	−1.41542e10	−0.939863	−0.469932	−	0.882703i	$-0.655721\pi$
$809$	−1.41542e10	−0.939863	−0.469932	+	0.882703i	$0.655721\pi$
$810$	6.48299e9	0.428625
$811$	−2.63708e10	−1.73600	−0.868001	−	0.496563i	$-0.834595\pi$
$811$	−2.63708e10	−1.73600	−0.868001	+	0.496563i	$0.834595\pi$
$812$	−6.66951e9	−0.437168
$813$	−4.65580e9	−0.303863
$814$	−1.40236e9	−0.0911324
$815$	−1.19879e10	−0.775697
$816$	7.22829e8	0.0465715
$817$	2.51921e10	1.61617
$818$	1.30742e10	0.835176
$819$	−2.86860e9	−0.182464
$820$	−1.45716e8	−0.00922912
$821$	8.06264e9	0.508483	0.254241	−	0.967141i	$-0.418174\pi$
$821$	8.06264e9	0.508483	0.254241	+	0.967141i	$0.418174\pi$
$822$	3.03028e7	0.00190297
$823$	−2.34202e10	−1.46451	−0.732253	−	0.681033i	$-0.761531\pi$
$823$	−2.34202e10	−1.46451	−0.732253	+	0.681033i	$0.761531\pi$
$824$	−1.91897e9	−0.119488
$825$	−4.45864e8	−0.0276448
$826$	−2.14633e10	−1.32515
$827$	5.55722e9	0.341655	0.170828	−	0.985301i	$-0.445356\pi$
$827$	5.55722e9	0.341655	0.170828	+	0.985301i	$0.445356\pi$
$828$	−8.98423e9	−0.550015
$829$	2.84256e10	1.73288	0.866440	−	0.499281i	$-0.166403\pi$
$829$	2.84256e10	1.73288	0.866440	+	0.499281i	$0.166403\pi$
$830$	9.53046e9	0.578549
$831$	5.44743e9	0.329297
$832$	3.62283e8	0.0218080
$833$	3.06933e9	0.183987
$834$	−3.76356e9	−0.224656
$835$	1.84226e10	1.09508
$836$	−2.79133e9	−0.165230
$837$	−1.15505e10	−0.680868
$838$	8.90238e9	0.522579
$839$	1.04036e10	0.608156	0.304078	−	0.952647i	$-0.401652\pi$
$839$	1.04036e10	0.608156	0.304078	+	0.952647i	$0.401652\pi$
$840$	1.31088e9	0.0763109
$841$	−6.72927e9	−0.390105
$842$	−7.38023e9	−0.426066
$843$	4.00524e9	0.230267
$844$	−6.23367e9	−0.356899
$845$	1.27761e10	0.728450
$846$	7.72509e9	0.438639
$847$	−1.85874e10	−1.05106
$848$	−6.11950e9	−0.344612
$849$	6.45234e9	0.361860
$850$	4.00297e9	0.223572
$851$	1.10301e10	0.613514
$852$	−1.08651e9	−0.0601860
$853$	−1.80580e10	−0.996205	−0.498102	−	0.867118i	$-0.665970\pi$
$853$	−1.80580e10	−0.996205	−0.498102	+	0.867118i	$0.665970\pi$
$854$	−6.72756e9	−0.369620
$855$	−1.71355e10	−0.937593
$856$	9.20861e9	0.501806
$857$	−6.34034e9	−0.344096	−0.172048	−	0.985089i	$-0.555038\pi$
$857$	−6.34034e9	−0.344096	−0.172048	+	0.985089i	$0.555038\pi$
$858$	−1.44878e8	−0.00783062
$859$	1.21489e10	0.653973	0.326987	−	0.945029i	$-0.393967\pi$
$859$	1.21489e10	0.653973	0.326987	+	0.945029i	$0.393967\pi$
$860$	8.47725e9	0.454476
$861$	1.32186e8	0.00705786
$862$	7.85206e9	0.417550
$863$	−2.87111e10	−1.52059	−0.760295	−	0.649578i	$-0.774946\pi$
$863$	−2.87111e10	−1.52059	−0.760295	+	0.649578i	$0.774946\pi$
$864$	1.66330e9	0.0877351
$865$	−1.79960e9	−0.0945411
$866$	−2.27998e10	−1.19294
$867$	−2.32887e9	−0.121361
$868$	1.47963e10	0.767954
$869$	−3.89495e9	−0.201341
$870$	−2.06781e9	−0.106462
$871$	−1.74138e8	−0.00892953
$872$	−6.27560e9	−0.320514
$873$	−1.77376e10	−0.902289
$874$	2.19549e10	1.11235
$875$	2.39283e10	1.20749
$876$	7.52857e8	0.0378397
$877$	2.46021e10	1.23161	0.615806	−	0.787898i	$-0.288831\pi$
$877$	2.46021e10	1.23161	0.615806	+	0.787898i	$0.288831\pi$
$878$	8.44975e9	0.421321
$879$	4.02720e9	0.200006
$880$	−9.39295e8	−0.0464636
$881$	−1.25378e10	−0.617738	−0.308869	−	0.951105i	$-0.599951\pi$
$881$	−1.25378e10	−0.617738	−0.308869	+	0.951105i	$0.599951\pi$
$882$	3.41121e9	0.167405
$883$	1.93097e10	0.943873	0.471937	−	0.881633i	$-0.343555\pi$
$883$	1.93097e10	0.943873	0.471937	+	0.881633i	$0.343555\pi$
$884$	1.30072e9	0.0633286
$885$	−6.65446e9	−0.322709
$886$	−1.45860e10	−0.704562
$887$	3.20268e10	1.54092	0.770462	−	0.637486i	$-0.220026\pi$
$887$	3.20268e10	1.54092	0.770462	+	0.637486i	$0.220026\pi$
$888$	−9.86272e8	−0.0472663
$889$	1.18695e9	0.0566599
$890$	−2.00780e10	−0.954675
$891$	4.21394e9	0.199580
$892$	−9.37327e8	−0.0442195
$893$	−1.88779e10	−0.887101
$894$	2.10106e9	0.0983461
$895$	−3.94885e9	−0.184115
$896$	−2.13071e9	−0.0989568
$897$	1.13952e9	0.0527167
$898$	−1.47877e10	−0.681448
$899$	−2.33400e10	−1.07138
$900$	4.44884e9	0.203422
$901$	−2.19710e10	−1.00072
$902$	−9.47157e7	−0.00429733
$903$	−7.69008e9	−0.347555
$904$	−8.49662e9	−0.382522
$905$	1.25921e10	0.564715
$906$	2.82388e9	0.126153
$907$	2.33703e9	0.104002	0.0520008	−	0.998647i	$-0.483440\pi$
$907$	2.33703e9	0.104002	0.0520008	+	0.998647i	$0.483440\pi$
$908$	−1.18106e10	−0.523567
$909$	2.05925e10	0.909359
$910$	2.35891e9	0.103769
$911$	2.20343e10	0.965573	0.482786	−	0.875738i	$-0.339625\pi$
$911$	2.20343e10	0.965573	0.482786	+	0.875738i	$0.339625\pi$
$912$	−1.96313e9	−0.0856973
$913$	6.19480e9	0.269389
$914$	2.38453e10	1.03298
$915$	−2.08581e9	−0.0900121
$916$	−5.60295e8	−0.0240870
$917$	−8.05061e9	−0.344775
$918$	5.97181e9	0.254775
$919$	−1.43277e10	−0.608938	−0.304469	−	0.952522i	$-0.598479\pi$
$919$	−1.43277e10	−0.608938	−0.304469	+	0.952522i	$0.598479\pi$
$920$	7.38791e9	0.312798
$921$	2.58035e9	0.108835
$922$	2.02225e10	0.849720
$923$	−1.95515e9	−0.0818418
$924$	8.52074e8	0.0355325
$925$	−5.46190e9	−0.226907
$926$	7.12233e9	0.294770
$927$	−7.65715e9	−0.315710
$928$	3.36101e9	0.138055
$929$	1.31280e10	0.537208	0.268604	−	0.963251i	$-0.413438\pi$
$929$	1.31280e10	0.537208	0.268604	+	0.963251i	$0.413438\pi$
$930$	4.58745e9	0.187017
$931$	−8.33600e9	−0.338558
$932$	−7.65160e9	−0.309597
$933$	9.50474e9	0.383137
$934$	−2.12533e10	−0.853519
$935$	−3.37238e9	−0.134926
$936$	1.44559e9	0.0576210
$937$	−3.87626e10	−1.53930	−0.769652	−	0.638463i	$-0.779571\pi$
$937$	−3.87626e10	−1.53930	−0.769652	+	0.638463i	$0.779571\pi$
$938$	1.02416e9	0.0405189
$939$	−1.42149e9	−0.0560291
$940$	−6.35250e9	−0.249458
$941$	2.06279e10	0.807035	0.403517	−	0.914972i	$-0.367788\pi$
$941$	2.06279e10	0.807035	0.403517	+	0.914972i	$0.367788\pi$
$942$	−5.81328e9	−0.226591
$943$	7.44976e8	0.0289302
$944$	1.08161e10	0.418476
$945$	1.08302e10	0.417468
$946$	5.51021e9	0.211617
$947$	−2.11705e10	−0.810040	−0.405020	−	0.914308i	$-0.632736\pi$
$947$	−2.11705e10	−0.810040	−0.405020	+	0.914308i	$0.632736\pi$
$948$	−2.73930e9	−0.104427
$949$	1.35475e9	0.0514550
$950$	−1.08717e10	−0.411399
$951$	−6.08771e8	−0.0229521
$952$	−7.64994e9	−0.287362
$953$	2.14876e10	0.804196	0.402098	−	0.915597i	$-0.368281\pi$
$953$	2.14876e10	0.804196	0.402098	+	0.915597i	$0.368281\pi$
$954$	−2.44182e10	−0.910531
$955$	−1.97371e10	−0.733282
$956$	2.53574e10	0.938646
$957$	−1.34408e9	−0.0495715
$958$	−1.04075e10	−0.382442
$959$	−3.20704e8	−0.0117419
$960$	−6.60603e8	−0.0240986
$961$	2.42673e10	0.882043
$962$	−1.77478e9	−0.0642733
$963$	3.67445e10	1.32587
$964$	−1.64228e10	−0.590443
$965$	7.39086e9	0.264758
$966$	−6.70189e9	−0.239209
$967$	3.92625e10	1.39632	0.698161	−	0.715941i	$-0.254002\pi$
$967$	3.92625e10	1.39632	0.698161	+	0.715941i	$0.254002\pi$
$968$	9.36689e9	0.331919
$969$	−7.04829e9	−0.248857
$970$	1.45860e10	0.513139
$971$	−5.62647e10	−1.97228	−0.986140	−	0.165917i	$-0.946941\pi$
$971$	−5.62647e10	−1.97228	−0.986140	+	0.165917i	$0.946941\pi$
$972$	1.00684e10	0.351665
$973$	3.98310e10	1.38620
$974$	8.59573e9	0.298076
$975$	−5.64271e8	−0.0194972
$976$	3.39027e9	0.116724
$977$	−8.43437e9	−0.289349	−0.144674	−	0.989479i	$-0.546213\pi$
$977$	−8.43437e9	−0.289349	−0.144674	+	0.989479i	$0.546213\pi$
$978$	−5.48019e9	−0.187331
$979$	−1.30507e10	−0.444523
$980$	−2.80510e9	−0.0952045
$981$	−2.50411e10	−0.846861
$982$	6.26675e9	0.211180
$983$	−2.24230e10	−0.752932	−0.376466	−	0.926430i	$-0.622861\pi$
$983$	−2.24230e10	−0.752932	−0.376466	+	0.926430i	$0.622861\pi$
$984$	−6.66132e7	−0.00222883
$985$	−2.16269e10	−0.721054
$986$	1.20672e10	0.400900
$987$	5.76262e9	0.190770
$988$	−3.53261e9	−0.116532
$989$	−4.33400e10	−1.42463
$990$	−3.74801e9	−0.122766
$991$	3.46728e10	1.13170	0.565849	−	0.824509i	$-0.308548\pi$
$991$	3.46728e10	1.13170	0.565849	+	0.824509i	$0.308548\pi$
$992$	−7.45642e9	−0.242516
$993$	3.28508e9	0.106469
$994$	1.14989e10	0.371368
$995$	−1.75639e10	−0.565249
$996$	4.35678e9	0.139720
$997$	−2.96474e10	−0.947444	−0.473722	−	0.880674i	$-0.657090\pi$
$997$	−2.96474e10	−0.947444	−0.473722	+	0.880674i	$0.657090\pi$
$998$	4.98550e9	0.158764
$999$	−8.14830e9	−0.258576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.8.a.a.1.1	✓	1
3.2	odd	2		18.8.a.b.1.1		1
4.3	odd	2		16.8.a.b.1.1		1
5.2	odd	4		50.8.b.c.49.1		2
5.3	odd	4		50.8.b.c.49.2		2
5.4	even	2		50.8.a.g.1.1		1
7.2	even	3		98.8.c.d.67.1		2
7.3	odd	6		98.8.c.e.79.1		2
7.4	even	3		98.8.c.d.79.1		2
7.5	odd	6		98.8.c.e.67.1		2
7.6	odd	2		98.8.a.a.1.1		1
8.3	odd	2		64.8.a.e.1.1		1
8.5	even	2		64.8.a.c.1.1		1
9.2	odd	6		162.8.c.a.109.1		2
9.4	even	3		162.8.c.l.55.1		2
9.5	odd	6		162.8.c.a.55.1		2
9.7	even	3		162.8.c.l.109.1		2
11.10	odd	2		242.8.a.e.1.1		1
12.11	even	2		144.8.a.i.1.1		1
13.5	odd	4		338.8.b.d.337.2		2
13.8	odd	4		338.8.b.d.337.1		2
13.12	even	2		338.8.a.d.1.1		1
15.2	even	4		450.8.c.g.199.2		2
15.8	even	4		450.8.c.g.199.1		2
15.14	odd	2		450.8.a.c.1.1		1
16.3	odd	4		256.8.b.f.129.1		2
16.5	even	4		256.8.b.b.129.1		2
16.11	odd	4		256.8.b.f.129.2		2
16.13	even	4		256.8.b.b.129.2		2
17.16	even	2		578.8.a.b.1.1		1
20.3	even	4		400.8.c.j.49.1		2
20.7	even	4		400.8.c.j.49.2		2
20.19	odd	2		400.8.a.l.1.1		1
24.5	odd	2		576.8.a.g.1.1		1
24.11	even	2		576.8.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.8.a.a.1.1	✓	1	1.1	even	1	trivial
16.8.a.b.1.1		1	4.3	odd	2
18.8.a.b.1.1		1	3.2	odd	2
50.8.a.g.1.1		1	5.4	even	2
50.8.b.c.49.1		2	5.2	odd	4
50.8.b.c.49.2		2	5.3	odd	4
64.8.a.c.1.1		1	8.5	even	2
64.8.a.e.1.1		1	8.3	odd	2
98.8.a.a.1.1		1	7.6	odd	2
98.8.c.d.67.1		2	7.2	even	3
98.8.c.d.79.1		2	7.4	even	3
98.8.c.e.67.1		2	7.5	odd	6
98.8.c.e.79.1		2	7.3	odd	6
144.8.a.i.1.1		1	12.11	even	2
162.8.c.a.55.1		2	9.5	odd	6
162.8.c.a.109.1		2	9.2	odd	6
162.8.c.l.55.1		2	9.4	even	3
162.8.c.l.109.1		2	9.7	even	3
242.8.a.e.1.1		1	11.10	odd	2
256.8.b.b.129.1		2	16.5	even	4
256.8.b.b.129.2		2	16.13	even	4
256.8.b.f.129.1		2	16.3	odd	4
256.8.b.f.129.2		2	16.11	odd	4
338.8.a.d.1.1		1	13.12	even	2
338.8.b.d.337.1		2	13.8	odd	4
338.8.b.d.337.2		2	13.5	odd	4
400.8.a.l.1.1		1	20.19	odd	2
400.8.c.j.49.1		2	20.3	even	4
400.8.c.j.49.2		2	20.7	even	4
450.8.a.c.1.1		1	15.14	odd	2
450.8.c.g.199.1		2	15.8	even	4
450.8.c.g.199.2		2	15.2	even	4
576.8.a.f.1.1		1	24.11	even	2
576.8.a.g.1.1		1	24.5	odd	2
578.8.a.b.1.1		1	17.16	even	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

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