LMFDB - Embedded newform 847.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,6,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("847.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	847.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:	$135.845095382$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{57}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 14 $ x^2 - x - 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.27492$ of defining polynomial
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.27492 q^{2} -25.6495 q^{3} +36.4743 q^{4} +28.7492 q^{5} +212.248 q^{6} -49.0000 q^{7} -37.0241 q^{8} +414.897 q^{9} +O(q^{10})$	\(q-8.27492 q^{2} -25.6495 q^{3} +36.4743 q^{4} +28.7492 q^{5} +212.248 q^{6} -49.0000 q^{7} -37.0241 q^{8} +414.897 q^{9} -237.897 q^{10} -935.547 q^{12} -300.640 q^{13} +405.471 q^{14} -737.402 q^{15} -860.805 q^{16} -613.106 q^{17} -3433.24 q^{18} +1700.95 q^{19} +1048.60 q^{20} +1256.83 q^{21} +3188.15 q^{23} +949.650 q^{24} -2298.49 q^{25} +2487.77 q^{26} -4409.07 q^{27} -1787.24 q^{28} -4299.28 q^{29} +6101.94 q^{30} +2028.46 q^{31} +8307.86 q^{32} +5073.40 q^{34} -1408.71 q^{35} +15133.1 q^{36} +5154.46 q^{37} -14075.2 q^{38} +7711.26 q^{39} -1064.41 q^{40} +7146.21 q^{41} -10400.1 q^{42} +19584.3 q^{43} +11927.9 q^{45} -26381.7 q^{46} +19998.4 q^{47} +22079.2 q^{48} +2401.00 q^{49} +19019.8 q^{50} +15725.9 q^{51} -10965.6 q^{52} +3948.82 q^{53} +36484.7 q^{54} +1814.18 q^{56} -43628.5 q^{57} +35576.2 q^{58} -29707.6 q^{59} -26896.2 q^{60} +50519.3 q^{61} -16785.3 q^{62} -20330.0 q^{63} -41201.1 q^{64} -8643.14 q^{65} +5053.56 q^{67} -22362.6 q^{68} -81774.5 q^{69} +11657.0 q^{70} +32853.3 q^{71} -15361.2 q^{72} +11115.0 q^{73} -42652.7 q^{74} +58955.0 q^{75} +62040.8 q^{76} -63810.0 q^{78} -81889.4 q^{79} -24747.4 q^{80} +12270.6 q^{81} -59134.3 q^{82} -118234. q^{83} +45841.8 q^{84} -17626.3 q^{85} -162058. q^{86} +110274. q^{87} -41695.4 q^{89} -98702.8 q^{90} +14731.3 q^{91} +116286. q^{92} -52028.9 q^{93} -165485. q^{94} +48900.9 q^{95} -213092. q^{96} +43682.8 q^{97} -19868.1 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 9 q^{2} - 6 q^{3} + 5 q^{4} - 18 q^{5} + 198 q^{6} - 98 q^{7} + 9 q^{8} + 558 q^{9}+O(q^{10}) $ 2 * q - 9 * q^2 - 6 * q^3 + 5 * q^4 - 18 * q^5 + 198 * q^6 - 98 * q^7 + 9 * q^8 + 558 * q^9	\( 2 q - 9 q^{2} - 6 q^{3} + 5 q^{4} - 18 q^{5} + 198 q^{6} - 98 q^{7} + 9 q^{8} + 558 q^{9} - 204 q^{10} - 1554 q^{12} + 350 q^{13} + 441 q^{14} - 1656 q^{15} + 113 q^{16} - 1800 q^{17} - 3537 q^{18} + 3266 q^{19} + 2520 q^{20} + 294 q^{21} + 2088 q^{23} + 1854 q^{24} - 3238 q^{25} + 2016 q^{26} - 6372 q^{27} - 245 q^{28} - 6696 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 5934 q^{34} + 882 q^{35} + 10629 q^{36} + 6232 q^{37} - 15210 q^{38} + 20496 q^{39} - 3216 q^{40} + 6048 q^{41} - 9702 q^{42} + 3020 q^{43} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} + 41214 q^{48} + 4802 q^{49} + 19701 q^{50} - 7596 q^{51} - 31444 q^{52} + 9468 q^{53} + 37908 q^{54} - 441 q^{56} - 12876 q^{57} + 37314 q^{58} - 43938 q^{59} + 2016 q^{60} + 64754 q^{61} - 15300 q^{62} - 27342 q^{63} - 70783 q^{64} - 39060 q^{65} + 24784 q^{67} + 14994 q^{68} - 103392 q^{69} + 9996 q^{70} + 97416 q^{71} - 8775 q^{72} - 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 12782 q^{76} - 73080 q^{78} - 51256 q^{79} - 70272 q^{80} - 61074 q^{81} - 58338 q^{82} - 117558 q^{83} + 76146 q^{84} + 37860 q^{85} - 150048 q^{86} + 63180 q^{87} + 84276 q^{89} - 93852 q^{90} - 17150 q^{91} + 150912 q^{92} - 92280 q^{93} - 159468 q^{94} - 24264 q^{95} - 255906 q^{96} + 20776 q^{97} - 21609 q^{98}+O(q^{100}) \) 2 * q - 9 * q^2 - 6 * q^3 + 5 * q^4 - 18 * q^5 + 198 * q^6 - 98 * q^7 + 9 * q^8 + 558 * q^9 - 204 * q^10 - 1554 * q^12 + 350 * q^13 + 441 * q^14 - 1656 * q^15 + 113 * q^16 - 1800 * q^17 - 3537 * q^18 + 3266 * q^19 + 2520 * q^20 + 294 * q^21 + 2088 * q^23 + 1854 * q^24 - 3238 * q^25 + 2016 * q^26 - 6372 * q^27 - 245 * q^28 - 6696 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 5934 * q^34 + 882 * q^35 + 10629 * q^36 + 6232 * q^37 - 15210 * q^38 + 20496 * q^39 - 3216 * q^40 + 6048 * q^41 - 9702 * q^42 + 3020 * q^43 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 + 41214 * q^48 + 4802 * q^49 + 19701 * q^50 - 7596 * q^51 - 31444 * q^52 + 9468 * q^53 + 37908 * q^54 - 441 * q^56 - 12876 * q^57 + 37314 * q^58 - 43938 * q^59 + 2016 * q^60 + 64754 * q^61 - 15300 * q^62 - 27342 * q^63 - 70783 * q^64 - 39060 * q^65 + 24784 * q^67 + 14994 * q^68 - 103392 * q^69 + 9996 * q^70 + 97416 * q^71 - 8775 * q^72 - 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 12782 * q^76 - 73080 * q^78 - 51256 * q^79 - 70272 * q^80 - 61074 * q^81 - 58338 * q^82 - 117558 * q^83 + 76146 * q^84 + 37860 * q^85 - 150048 * q^86 + 63180 * q^87 + 84276 * q^89 - 93852 * q^90 - 17150 * q^91 + 150912 * q^92 - 92280 * q^93 - 159468 * q^94 - 24264 * q^95 - 255906 * q^96 + 20776 * q^97 - 21609 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−8.27492	−1.46281	−0.731406	−	0.681942i	$-0.761136\pi$
$2$	−8.27492	−1.46281	−0.731406	+	0.681942i	$0.761136\pi$
$3$	−25.6495	−1.64542	−0.822708	−	0.568464i	$-0.807538\pi$
$3$	−25.6495	−1.64542	−0.822708	+	0.568464i	$0.807538\pi$
$4$	36.4743	1.13982
$5$	28.7492	0.514281	0.257140	−	0.966374i	$-0.417220\pi$
$5$	28.7492	0.514281	0.257140	+	0.966374i	$0.417220\pi$
$6$	212.248	2.40694
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−37.0241	−0.204531
$9$	414.897	1.70740
$10$	−237.897	−0.752296
$11$	0	0
$11$	0	0
$12$	−935.547	−1.87548
$13$	−300.640	−0.493387	−0.246694	−	0.969094i	$-0.579344\pi$
$13$	−300.640	−0.493387	−0.246694	+	0.969094i	$0.579344\pi$
$14$	405.471	0.552891
$15$	−737.402	−0.846206
$16$	−860.805	−0.840630
$17$	−613.106	−0.514533	−0.257267	−	0.966340i	$-0.582822\pi$
$17$	−613.106	−0.514533	−0.257267	+	0.966340i	$0.582822\pi$
$18$	−3433.24	−2.49760
$19$	1700.95	1.08095	0.540477	−	0.841359i	$-0.318244\pi$
$19$	1700.95	1.08095	0.540477	+	0.841359i	$0.318244\pi$
$20$	1048.60	0.586188
$21$	1256.83	0.621909
$22$	0	0
$23$	3188.15	1.25667	0.628333	−	0.777945i	$-0.283738\pi$
$23$	3188.15	1.25667	0.628333	+	0.777945i	$0.283738\pi$
$24$	949.650	0.336539
$25$	−2298.49	−0.735515
$26$	2487.77	0.721733
$27$	−4409.07	−1.16396
$28$	−1787.24	−0.430812
$29$	−4299.28	−0.949294	−0.474647	−	0.880176i	$-0.657424\pi$
$29$	−4299.28	−0.949294	−0.474647	+	0.880176i	$0.657424\pi$
$30$	6101.94	1.23784
$31$	2028.46	0.379106	0.189553	−	0.981870i	$-0.439296\pi$
$31$	2028.46	0.379106	0.189553	+	0.981870i	$0.439296\pi$
$32$	8307.86	1.43421
$33$	0	0
$34$	5073.40	0.752666
$35$	−1408.71	−0.194380
$36$	15133.1	1.94612
$37$	5154.46	0.618983	0.309491	−	0.950902i	$-0.399841\pi$
$37$	5154.46	0.618983	0.309491	+	0.950902i	$0.399841\pi$
$38$	−14075.2	−1.58123
$39$	7711.26	0.811827
$40$	−1064.41	−0.105186
$41$	7146.21	0.663921	0.331960	−	0.943293i	$-0.392290\pi$
$41$	7146.21	0.663921	0.331960	+	0.943293i	$0.392290\pi$
$42$	−10400.1	−0.909736
$43$	19584.3	1.61524	0.807620	−	0.589703i	$-0.200755\pi$
$43$	19584.3	1.61524	0.807620	+	0.589703i	$0.200755\pi$
$44$	0	0
$45$	11927.9	0.878081
$46$	−26381.7	−1.83827
$47$	19998.4	1.32054	0.660268	−	0.751030i	$-0.270443\pi$
$47$	19998.4	1.32054	0.660268	+	0.751030i	$0.270443\pi$
$48$	22079.2	1.38319
$49$	2401.00	0.142857
$50$	19019.8	1.07592
$51$	15725.9	0.846621
$52$	−10965.6	−0.562373
$53$	3948.82	0.193098	0.0965489	−	0.995328i	$-0.469220\pi$
$53$	3948.82	0.193098	0.0965489	+	0.995328i	$0.469220\pi$
$54$	36484.7	1.70265
$55$	0	0
$56$	1814.18	0.0773055
$57$	−43628.5	−1.77862
$58$	35576.2	1.38864
$59$	−29707.6	−1.11106	−0.555530	−	0.831497i	$-0.687484\pi$
$59$	−29707.6	−1.11106	−0.555530	+	0.831497i	$0.687484\pi$
$60$	−26896.2	−0.964523
$61$	50519.3	1.73833	0.869165	−	0.494522i	$-0.164657\pi$
$61$	50519.3	1.73833	0.869165	+	0.494522i	$0.164657\pi$
$62$	−16785.3	−0.554562
$63$	−20330.0	−0.645335
$64$	−41201.1	−1.25736
$65$	−8643.14	−0.253740
$66$	0	0
$67$	5053.56	0.137534	0.0687671	−	0.997633i	$-0.478093\pi$
$67$	5053.56	0.137534	0.0687671	+	0.997633i	$0.478093\pi$
$68$	−22362.6	−0.586476
$69$	−81774.5	−2.06774
$70$	11657.0	0.284341
$71$	32853.3	0.773453	0.386726	−	0.922195i	$-0.373606\pi$
$71$	32853.3	0.773453	0.386726	+	0.922195i	$0.373606\pi$
$72$	−15361.2	−0.349215
$73$	11115.0	0.244119	0.122059	−	0.992523i	$-0.461050\pi$
$73$	11115.0	0.244119	0.122059	+	0.992523i	$0.461050\pi$
$74$	−42652.7	−0.905456
$75$	58955.0	1.21023
$76$	62040.8	1.23209
$77$	0	0
$78$	−63810.0	−1.18755
$79$	−81889.4	−1.47625	−0.738125	−	0.674664i	$-0.764288\pi$
$79$	−81889.4	−1.47625	−0.738125	+	0.674664i	$0.764288\pi$
$80$	−24747.4	−0.432320
$81$	12270.6	0.207803
$82$	−59134.3	−0.971191
$83$	−118234.	−1.88385	−0.941926	−	0.335819i	$-0.890987\pi$
$83$	−118234.	−1.88385	−0.941926	+	0.335819i	$0.890987\pi$
$84$	45841.8	0.708865
$85$	−17626.3	−0.264615
$86$	−162058.	−2.36279
$87$	110274.	1.56198
$88$	0	0
$89$	−41695.4	−0.557972	−0.278986	−	0.960295i	$-0.589998\pi$
$89$	−41695.4	−0.557972	−0.278986	+	0.960295i	$0.589998\pi$
$90$	−98702.8	−1.28447
$91$	14731.3	0.186483
$92$	116286.	1.43237
$93$	−52028.9	−0.623788
$94$	−165485.	−1.93170
$95$	48900.9	0.555914
$96$	−213092.	−2.35988
$97$	43682.8	0.471391	0.235695	−	0.971827i	$-0.424263\pi$
$97$	43682.8	0.471391	0.235695	+	0.971827i	$0.424263\pi$
$98$	−19868.1	−0.208973
$99$	0	0
$100$	−83835.5	−0.838355
$101$	−25648.1	−0.250179	−0.125090	−	0.992145i	$-0.539922\pi$
$101$	−25648.1	−0.250179	−0.125090	+	0.992145i	$0.539922\pi$
$102$	−130130.	−1.23845
$103$	−14320.0	−0.133000	−0.0664999	−	0.997786i	$-0.521183\pi$
$103$	−14320.0	−0.133000	−0.0664999	+	0.997786i	$0.521183\pi$
$104$	11130.9	0.100913
$105$	36132.7	0.319836
$106$	−32676.1	−0.282466
$107$	−17201.8	−0.145249	−0.0726247	−	0.997359i	$-0.523138\pi$
$107$	−17201.8	−0.145249	−0.0726247	+	0.997359i	$0.523138\pi$
$108$	−160818.	−1.32670
$109$	86017.6	0.693459	0.346730	−	0.937965i	$-0.387292\pi$
$109$	86017.6	0.693459	0.346730	+	0.937965i	$0.387292\pi$
$110$	0	0
$111$	−132209.	−1.01848
$112$	42179.4	0.317728
$113$	137568.	1.01349	0.506745	−	0.862096i	$-0.330848\pi$
$113$	137568.	1.01349	0.506745	+	0.862096i	$0.330848\pi$
$114$	361022.	2.60179
$115$	91656.8	0.646279
$116$	−156813.	−1.08202
$117$	−124734.	−0.842407
$118$	245828.	1.62527
$119$	30042.2	0.194475
$120$	27301.6	0.173075
$121$	0	0
$122$	−418043.	−2.54285
$123$	−183297.	−1.09243
$124$	73986.4	0.432113
$125$	−155921.	−0.892542
$126$	168229.	0.944004
$127$	70567.1	0.388233	0.194117	−	0.980978i	$-0.437816\pi$
$127$	70567.1	0.388233	0.194117	+	0.980978i	$0.437816\pi$
$128$	75084.2	0.405064
$129$	−502328.	−2.65774
$130$	71521.3	0.371173
$131$	173712.	0.884408	0.442204	−	0.896914i	$-0.354197\pi$
$131$	173712.	0.884408	0.442204	+	0.896914i	$0.354197\pi$
$132$	0	0
$133$	−83346.5	−0.408562
$134$	−41817.8	−0.201187
$135$	−126757.	−0.598602
$136$	22699.7	0.105238
$137$	−1989.94	−0.00905813	−0.00452907	−	0.999990i	$-0.501442\pi$
$137$	−1989.94	−0.00905813	−0.00452907	+	0.999990i	$0.501442\pi$
$138$	676678.	3.02471
$139$	−366409.	−1.60853	−0.804264	−	0.594272i	$-0.797440\pi$
$139$	−366409.	−1.60853	−0.804264	+	0.594272i	$0.797440\pi$
$140$	−51381.6	−0.221558
$141$	−512949.	−2.17283
$142$	−271859.	−1.13142
$143$	0	0
$144$	−357145.	−1.43529
$145$	−123601.	−0.488204
$146$	−91975.4	−0.357100
$147$	−61584.5	−0.235059
$148$	188005.	0.705529
$149$	−140719.	−0.519261	−0.259631	−	0.965708i	$-0.583601\pi$
$149$	−140719.	−0.519261	−0.259631	+	0.965708i	$0.583601\pi$
$150$	−487848.	−1.77034
$151$	−50064.6	−0.178685	−0.0893425	−	0.996001i	$-0.528477\pi$
$151$	−50064.6	−0.178685	−0.0893425	+	0.996001i	$0.528477\pi$
$152$	−62976.1	−0.221089
$153$	−254376.	−0.878512
$154$	0	0
$155$	58316.4	0.194967
$156$	281262.	0.925337
$157$	−89794.6	−0.290738	−0.145369	−	0.989378i	$-0.546437\pi$
$157$	−89794.6	−0.290738	−0.145369	+	0.989378i	$0.546437\pi$
$158$	677628.	2.15948
$159$	−101285.	−0.317726
$160$	238844.	0.737589
$161$	−156219.	−0.474975
$162$	−101538.	−0.303977
$163$	−481230.	−1.41868	−0.709339	−	0.704867i	$-0.751006\pi$
$163$	−481230.	−1.41868	−0.709339	+	0.704867i	$0.751006\pi$
$164$	260653.	0.756750
$165$	0	0
$166$	978376.	2.75572
$167$	86572.7	0.240209	0.120105	−	0.992761i	$-0.461677\pi$
$167$	86572.7	0.240209	0.120105	+	0.992761i	$0.461677\pi$
$168$	−46532.8	−0.127200
$169$	−280909.	−0.756569
$170$	145856.	0.387082
$171$	705718.	1.84562
$172$	714323.	1.84108
$173$	58137.4	0.147686	0.0738432	−	0.997270i	$-0.476474\pi$
$173$	58137.4	0.147686	0.0738432	+	0.997270i	$0.476474\pi$
$174$	−912511.	−2.28489
$175$	112626.	0.277999
$176$	0	0
$177$	761985.	1.82816
$178$	345026.	0.816209
$179$	−209380.	−0.488431	−0.244215	−	0.969721i	$-0.578530\pi$
$179$	−209380.	−0.488431	−0.244215	+	0.969721i	$0.578530\pi$
$180$	435063.	1.00085
$181$	278996.	0.632996	0.316498	−	0.948593i	$-0.397493\pi$
$181$	278996.	0.632996	0.316498	+	0.948593i	$0.397493\pi$
$182$	−121901.	−0.272789
$183$	−1.29579e6	−2.86028
$184$	−118038.	−0.257027
$185$	148186.	0.318331
$186$	430535.	0.912485
$187$	0	0
$188$	729426.	1.50517
$189$	216045.	0.439935
$190$	−404651.	−0.813198
$191$	−445132.	−0.882888	−0.441444	−	0.897289i	$-0.645534\pi$
$191$	−445132.	−0.882888	−0.441444	+	0.897289i	$0.645534\pi$
$192$	1.05679e6	2.06888
$193$	726811.	1.40452	0.702260	−	0.711920i	$-0.252174\pi$
$193$	726811.	1.40452	0.702260	+	0.711920i	$0.252174\pi$
$194$	−361471.	−0.689556
$195$	221692.	0.417507
$196$	87574.7	0.162831
$197$	364897.	0.669892	0.334946	−	0.942237i	$-0.391282\pi$
$197$	364897.	0.669892	0.334946	+	0.942237i	$0.391282\pi$
$198$	0	0
$199$	289307.	0.517877	0.258938	−	0.965894i	$-0.416627\pi$
$199$	289307.	0.517877	0.258938	+	0.965894i	$0.416627\pi$
$200$	85099.3	0.150436
$201$	−129621.	−0.226301
$202$	212236.	0.365965
$203$	210665.	0.358799
$204$	573589.	0.964997
$205$	205448.	0.341442
$206$	118497.	0.194554
$207$	1.32276e6	2.14562
$208$	258792.	0.414756
$209$	0	0
$210$	−298995.	−0.467860
$211$	−750147.	−1.15995	−0.579976	−	0.814633i	$-0.696938\pi$
$211$	−750147.	−1.15995	−0.579976	+	0.814633i	$0.696938\pi$
$212$	144030.	0.220097
$213$	−842672.	−1.27265
$214$	142343.	0.212473
$215$	563033.	0.830687
$216$	163242.	0.238066
$217$	−99394.3	−0.143289
$218$	−711788.	−1.01440
$219$	−285093.	−0.401677
$220$	0	0
$221$	184324.	0.253864
$222$	1.09402e6	1.48985
$223$	534398.	0.719619	0.359810	−	0.933026i	$-0.382842\pi$
$223$	534398.	0.719619	0.359810	+	0.933026i	$0.382842\pi$
$224$	−407085.	−0.542082
$225$	−953635.	−1.25582
$226$	−1.13836e6	−1.48255
$227$	410624.	0.528907	0.264453	−	0.964398i	$-0.414808\pi$
$227$	410624.	0.528907	0.264453	+	0.964398i	$0.414808\pi$
$228$	−1.59132e6	−2.02731
$229$	1.03036e6	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$229$	1.03036e6	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$230$	−758452.	−0.945385
$231$	0	0
$232$	159177.	0.194160
$233$	119211.	0.143856	0.0719278	−	0.997410i	$-0.477085\pi$
$233$	119211.	0.143856	0.0719278	+	0.997410i	$0.477085\pi$
$234$	1.03217e6	1.23228
$235$	574937.	0.679127
$236$	−1.08356e6	−1.26641
$237$	2.10042e6	2.42905
$238$	−248597.	−0.284481
$239$	254090.	0.287735	0.143868	−	0.989597i	$-0.454046\pi$
$239$	254090.	0.287735	0.143868	+	0.989597i	$0.454046\pi$
$240$	634759.	0.711346
$241$	−1.41251e6	−1.56656	−0.783282	−	0.621667i	$-0.786456\pi$
$241$	−1.41251e6	−1.56656	−0.783282	+	0.621667i	$0.786456\pi$
$242$	0	0
$243$	756671.	0.822037
$244$	1.84265e6	1.98138
$245$	69026.8	0.0734687
$246$	1.51677e6	1.59801
$247$	−511372.	−0.533329
$248$	−75101.7	−0.0775391
$249$	3.03264e6	3.09972
$250$	1.29023e6	1.30562
$251$	−1.67542e6	−1.67857	−0.839286	−	0.543690i	$-0.817027\pi$
$251$	−1.67542e6	−1.67857	−0.839286	+	0.543690i	$0.817027\pi$
$252$	−741520.	−0.735566
$253$	0	0
$254$	−583937.	−0.567913
$255$	452106.	0.435401
$256$	697120.	0.664825
$257$	726996.	0.686593	0.343296	−	0.939227i	$-0.388456\pi$
$257$	726996.	0.686593	0.343296	+	0.939227i	$0.388456\pi$
$258$	4.15672e6	3.88778
$259$	−252568.	−0.233953
$260$	−315252.	−0.289217
$261$	−1.78376e6	−1.62082
$262$	−1.43746e6	−1.29372
$263$	225880.	0.201367	0.100684	−	0.994918i	$-0.467897\pi$
$263$	225880.	0.201367	0.100684	+	0.994918i	$0.467897\pi$
$264$	0	0
$265$	113525.	0.0993065
$266$	689685.	0.597650
$267$	1.06947e6	0.918097
$268$	184325.	0.156764
$269$	1.80527e6	1.52111	0.760557	−	0.649272i	$-0.224926\pi$
$269$	1.80527e6	1.52111	0.760557	+	0.649272i	$0.224926\pi$
$270$	1.04891e6	0.875643
$271$	1.71380e6	1.41754	0.708771	−	0.705439i	$-0.249250\pi$
$271$	1.71380e6	1.41754	0.708771	+	0.705439i	$0.249250\pi$
$272$	527765.	0.432532
$273$	−377852.	−0.306842
$274$	16466.6	0.0132504
$275$	0	0
$276$	−2.98267e6	−2.35685
$277$	−2.23055e6	−1.74668	−0.873338	−	0.487115i	$-0.838049\pi$
$277$	−2.23055e6	−1.74668	−0.873338	+	0.487115i	$0.838049\pi$
$278$	3.03200e6	2.35298
$279$	841600.	0.647285
$280$	52156.2	0.0397567
$281$	−1.67140e6	−1.26274	−0.631371	−	0.775481i	$-0.717507\pi$
$281$	−1.67140e6	−1.26274	−0.631371	+	0.775481i	$0.717507\pi$
$282$	4.24461e6	3.17845
$283$	396152.	0.294033	0.147016	−	0.989134i	$-0.453033\pi$
$283$	396152.	0.294033	0.147016	+	0.989134i	$0.453033\pi$
$284$	1.19830e6	0.881597
$285$	−1.25428e6	−0.914710
$286$	0	0
$287$	−350164.	−0.250938
$288$	3.44691e6	2.44877
$289$	−1.04396e6	−0.735256
$290$	1.02279e6	0.714150
$291$	−1.12044e6	−0.775634
$292$	405410.	0.278251
$293$	929465.	0.632505	0.316252	−	0.948675i	$-0.397575\pi$
$293$	929465.	0.632505	0.316252	+	0.948675i	$0.397575\pi$
$294$	509606.	0.343848
$295$	−854068.	−0.571397
$296$	−190839.	−0.126601
$297$	0	0
$298$	1.16443e6	0.759582
$299$	−958485.	−0.620022
$300$	2.15034e6	1.37944
$301$	−959631.	−0.610503
$302$	414280.	0.261383
$303$	657860.	0.411649
$304$	−1.46418e6	−0.908682
$305$	1.45239e6	0.893990
$306$	2.10494e6	1.28510
$307$	−1.83295e6	−1.10995	−0.554976	−	0.831866i	$-0.687273\pi$
$307$	−1.83295e6	−1.10995	−0.554976	+	0.831866i	$0.687273\pi$
$308$	0	0
$309$	367302.	0.218840
$310$	−482563.	−0.285200
$311$	−2.29685e6	−1.34658	−0.673289	−	0.739379i	$-0.735119\pi$
$311$	−2.29685e6	−1.34658	−0.673289	+	0.739379i	$0.735119\pi$
$312$	−285502.	−0.166044
$313$	−3.42470e6	−1.97589	−0.987943	−	0.154817i	$-0.950521\pi$
$313$	−3.42470e6	−1.97589	−0.987943	+	0.154817i	$0.950521\pi$
$314$	743043.	0.425295
$315$	−584469.	−0.331883
$316$	−2.98685e6	−1.68266
$317$	2.94305e6	1.64494	0.822470	−	0.568808i	$-0.192595\pi$
$317$	2.94305e6	1.64494	0.822470	+	0.568808i	$0.192595\pi$
$318$	838127.	0.464774
$319$	0	0
$320$	−1.18450e6	−0.646635
$321$	441217.	0.238996
$322$	1.29270e6	0.694799
$323$	−1.04286e6	−0.556187
$324$	447560.	0.236858
$325$	691016.	0.362894
$326$	3.98214e6	2.07526
$327$	−2.20631e6	−1.14103
$328$	−264582.	−0.135792
$329$	−979921.	−0.499116
$330$	0	0
$331$	966164.	0.484709	0.242354	−	0.970188i	$-0.422080\pi$
$331$	966164.	0.484709	0.242354	+	0.970188i	$0.422080\pi$
$332$	−4.31250e6	−2.14725
$333$	2.13857e6	1.05685
$334$	−716382.	−0.351381
$335$	145286.	0.0707312
$336$	−1.08188e6	−0.522795
$337$	−136417.	−0.0654327	−0.0327163	−	0.999465i	$-0.510416\pi$
$337$	−136417.	−0.0654327	−0.0327163	+	0.999465i	$0.510416\pi$
$338$	2.32450e6	1.10672
$339$	−3.52854e6	−1.66761
$340$	−642906.	−0.301613
$341$	0	0
$342$	−5.83976e6	−2.69979
$343$	−117649.	−0.0539949
$344$	−725091.	−0.330367
$345$	−2.35095e6	−1.06340
$346$	−481082.	−0.216038
$347$	−355408.	−0.158454	−0.0792270	−	0.996857i	$-0.525245\pi$
$347$	−355408.	−0.158454	−0.0792270	+	0.996857i	$0.525245\pi$
$348$	4.02218e6	1.78038
$349$	140128.	0.0615830	0.0307915	−	0.999526i	$-0.490197\pi$
$349$	140128.	0.0615830	0.0307915	+	0.999526i	$0.490197\pi$
$350$	−931969.	−0.406660
$351$	1.32554e6	0.574283
$352$	0	0
$353$	3.48141e6	1.48703	0.743514	−	0.668721i	$-0.233158\pi$
$353$	3.48141e6	1.48703	0.743514	+	0.668721i	$0.233158\pi$
$354$	−6.30536e6	−2.67425
$355$	944507.	0.397772
$356$	−1.52081e6	−0.635988
$357$	−770568.	−0.319993
$358$	1.73260e6	0.714482
$359$	−1.75285e6	−0.717810	−0.358905	−	0.933374i	$-0.616850\pi$
$359$	−1.75285e6	−0.717810	−0.358905	+	0.933374i	$0.616850\pi$
$360$	−441621.	−0.179595
$361$	417127.	0.168461
$362$	−2.30867e6	−0.925955
$363$	0	0
$364$	537315.	0.212557
$365$	319546.	0.125546
$366$	1.07226e7	4.18405
$367$	−1.76939e6	−0.685738	−0.342869	−	0.939383i	$-0.611399\pi$
$367$	−1.76939e6	−0.685738	−0.342869	+	0.939383i	$0.611399\pi$
$368$	−2.74438e6	−1.05639
$369$	2.96494e6	1.13357
$370$	−1.22623e6	−0.465658
$371$	−193492.	−0.0729841
$372$	−1.89771e6	−0.711006
$373$	4.16212e6	1.54897	0.774485	−	0.632592i	$-0.218009\pi$
$373$	4.16212e6	1.54897	0.774485	+	0.632592i	$0.218009\pi$
$374$	0	0
$375$	3.99929e6	1.46860
$376$	−740422.	−0.270091
$377$	1.29253e6	0.468369
$378$	−1.78775e6	−0.643543
$379$	618163.	0.221057	0.110529	−	0.993873i	$-0.464746\pi$
$379$	618163.	0.221057	0.110529	+	0.993873i	$0.464746\pi$
$380$	1.78362e6	0.633642
$381$	−1.81001e6	−0.638805
$382$	3.68343e6	1.29150
$383$	−4.11163e6	−1.43225	−0.716123	−	0.697974i	$-0.754085\pi$
$383$	−4.11163e6	−1.43225	−0.716123	+	0.697974i	$0.754085\pi$
$384$	−1.92587e6	−0.666498
$385$	0	0
$386$	−6.01430e6	−2.05455
$387$	8.12547e6	2.75785
$388$	1.59330e6	0.537301
$389$	4.62076e6	1.54824	0.774122	−	0.633037i	$-0.218192\pi$
$389$	4.62076e6	1.54824	0.774122	+	0.633037i	$0.218192\pi$
$390$	−1.83448e6	−0.610735
$391$	−1.95468e6	−0.646596
$392$	−88894.8	−0.0292187
$393$	−4.45564e6	−1.45522
$394$	−3.01949e6	−0.979926
$395$	−2.35425e6	−0.759207
$396$	0	0
$397$	5.07349e6	1.61559	0.807794	−	0.589465i	$-0.200661\pi$
$397$	5.07349e6	1.61559	0.807794	+	0.589465i	$0.200661\pi$
$398$	−2.39399e6	−0.757557
$399$	2.13780e6	0.672255
$400$	1.97855e6	0.618296
$401$	−1.48056e6	−0.459795	−0.229898	−	0.973215i	$-0.573839\pi$
$401$	−1.48056e6	−0.459795	−0.229898	+	0.973215i	$0.573839\pi$
$402$	1.07261e6	0.331036
$403$	−609834.	−0.187046
$404$	−935495.	−0.285160
$405$	352768.	0.106869
$406$	−1.74323e6	−0.524856
$407$	0	0
$408$	−582236.	−0.173160
$409$	4.53379e6	1.34015	0.670075	−	0.742294i	$-0.266262\pi$
$409$	4.53379e6	1.34015	0.670075	+	0.742294i	$0.266262\pi$
$410$	−1.70006e6	−0.499465
$411$	51041.0	0.0149044
$412$	−522313.	−0.151596
$413$	1.45567e6	0.419941
$414$	−1.09457e7	−3.13865
$415$	−3.39913e6	−0.968829
$416$	−2.49767e6	−0.707623
$417$	9.39820e6	2.64670
$418$	0	0
$419$	111026.	0.0308952	0.0154476	−	0.999881i	$-0.495083\pi$
$419$	111026.	0.0308952	0.0154476	+	0.999881i	$0.495083\pi$
$420$	1.31791e6	0.364555
$421$	−1.41151e6	−0.388132	−0.194066	−	0.980988i	$-0.562168\pi$
$421$	−1.41151e6	−0.388132	−0.194066	+	0.980988i	$0.562168\pi$
$422$	6.20740e6	1.69679
$423$	8.29727e6	2.25468
$424$	−146201.	−0.0394945
$425$	1.40922e6	0.378447
$426$	6.97304e6	1.86165
$427$	−2.47544e6	−0.657027
$428$	−627422.	−0.165558
$429$	0	0
$430$	−4.65905e6	−1.21514
$431$	−1.07640e6	−0.279113	−0.139557	−	0.990214i	$-0.544568\pi$
$431$	−1.07640e6	−0.279113	−0.139557	+	0.990214i	$0.544568\pi$
$432$	3.79535e6	0.978459
$433$	−310172.	−0.0795029	−0.0397515	−	0.999210i	$-0.512657\pi$
$433$	−310172.	−0.0795029	−0.0397515	+	0.999210i	$0.512657\pi$
$434$	822480.	0.209605
$435$	3.17030e6	0.803298
$436$	3.13743e6	0.790419
$437$	5.42288e6	1.35840
$438$	2.35912e6	0.587578
$439$	−5.67650e6	−1.40579	−0.702893	−	0.711296i	$-0.748109\pi$
$439$	−5.67650e6	−1.40579	−0.702893	+	0.711296i	$0.748109\pi$
$440$	0	0
$441$	996168.	0.243914
$442$	−1.52527e6	−0.371356
$443$	4.05966e6	0.982834	0.491417	−	0.870924i	$-0.336479\pi$
$443$	4.05966e6	0.982834	0.491417	+	0.870924i	$0.336479\pi$
$444$	−4.82223e6	−1.16089
$445$	−1.19871e6	−0.286955
$446$	−4.42210e6	−1.05267
$447$	3.60936e6	0.854401
$448$	2.01885e6	0.475237
$449$	−6.96544e6	−1.63054	−0.815272	−	0.579078i	$-0.803413\pi$
$449$	−6.96544e6	−1.63054	−0.815272	+	0.579078i	$0.803413\pi$
$450$	7.89125e6	1.83702
$451$	0	0
$452$	5.01767e6	1.15520
$453$	1.28413e6	0.294011
$454$	−3.39788e6	−0.773692
$455$	423514.	0.0959045
$456$	1.61530e6	0.363783
$457$	−1.79523e6	−0.402096	−0.201048	−	0.979581i	$-0.564435\pi$
$457$	−1.79523e6	−0.402096	−0.201048	+	0.979581i	$0.564435\pi$
$458$	−8.52616e6	−1.89928
$459$	2.70323e6	0.598896
$460$	3.34311e6	0.736642
$461$	2.11294e6	0.463058	0.231529	−	0.972828i	$-0.425627\pi$
$461$	2.11294e6	0.463058	0.231529	+	0.972828i	$0.425627\pi$
$462$	0	0
$463$	1.26223e6	0.273643	0.136822	−	0.990596i	$-0.456311\pi$
$463$	1.26223e6	0.273643	0.136822	+	0.990596i	$0.456311\pi$
$464$	3.70084e6	0.798005
$465$	−1.49579e6	−0.320802
$466$	−986462.	−0.210434
$467$	−3.58926e6	−0.761576	−0.380788	−	0.924662i	$-0.624347\pi$
$467$	−3.58926e6	−0.761576	−0.380788	+	0.924662i	$0.624347\pi$
$468$	−4.54960e6	−0.960192
$469$	−247624.	−0.0519830
$470$	−4.75756e6	−0.993435
$471$	2.30319e6	0.478384
$472$	1.09990e6	0.227246
$473$	0	0
$474$	−1.73808e7	−3.55324
$475$	−3.90960e6	−0.795058
$476$	1.09577e6	0.221667
$477$	1.63835e6	0.329694
$478$	−2.10257e6	−0.420903
$479$	2.41693e6	0.481311	0.240655	−	0.970611i	$-0.422638\pi$
$479$	2.41693e6	0.481311	0.240655	+	0.970611i	$0.422638\pi$
$480$	−6.12623e6	−1.21364
$481$	−1.54963e6	−0.305398
$482$	1.16884e7	2.29159
$483$	4.00695e6	0.781531
$484$	0	0
$485$	1.25584e6	0.242427
$486$	−6.26139e6	−1.20249
$487$	−5.19403e6	−0.992388	−0.496194	−	0.868212i	$-0.665270\pi$
$487$	−5.19403e6	−0.992388	−0.496194	+	0.868212i	$0.665270\pi$
$488$	−1.87043e6	−0.355543
$489$	1.23433e7	2.33432
$490$	−571191.	−0.107471
$491$	−5.38961e6	−1.00891	−0.504456	−	0.863437i	$-0.668307\pi$
$491$	−5.38961e6	−1.00891	−0.504456	+	0.863437i	$0.668307\pi$
$492$	−6.68561e6	−1.24517
$493$	2.63592e6	0.488443
$494$	4.23156e6	0.780160
$495$	0	0
$496$	−1.74610e6	−0.318688
$497$	−1.60981e6	−0.292338
$498$	−2.50949e7	−4.53431
$499$	−3.29606e6	−0.592576	−0.296288	−	0.955099i	$-0.595749\pi$
$499$	−3.29606e6	−0.592576	−0.296288	+	0.955099i	$0.595749\pi$
$500$	−5.68709e6	−1.01734
$501$	−2.22055e6	−0.395244
$502$	1.38640e7	2.45544
$503$	1.06512e7	1.87706	0.938528	−	0.345204i	$-0.112190\pi$
$503$	1.06512e7	1.87706	0.938528	+	0.345204i	$0.112190\pi$
$504$	752698.	0.131991
$505$	−737361.	−0.128662
$506$	0	0
$507$	7.20517e6	1.24487
$508$	2.57388e6	0.442516
$509$	−2.74268e6	−0.469225	−0.234612	−	0.972089i	$-0.575382\pi$
$509$	−2.74268e6	−0.469225	−0.234612	+	0.972089i	$0.575382\pi$
$510$	−3.74114e6	−0.636910
$511$	−544633.	−0.0922682
$512$	−8.17130e6	−1.37758
$513$	−7.49961e6	−1.25819
$514$	−6.01583e6	−1.00436
$515$	−411689.	−0.0683992
$516$	−1.83220e7	−3.02935
$517$	0	0
$518$	2.08998e6	0.342230
$519$	−1.49120e6	−0.243006
$520$	320004.	0.0518976
$521$	4.97077e6	0.802286	0.401143	−	0.916015i	$-0.368613\pi$
$521$	4.97077e6	0.802286	0.401143	+	0.916015i	$0.368613\pi$
$522$	1.47605e7	2.37096
$523$	−2.41579e6	−0.386193	−0.193096	−	0.981180i	$-0.561853\pi$
$523$	−2.41579e6	−0.386193	−0.193096	+	0.981180i	$0.561853\pi$
$524$	6.33603e6	1.00807
$525$	−2.88880e6	−0.457424
$526$	−1.86914e6	−0.294563
$527$	−1.24366e6	−0.195063
$528$	0	0
$529$	3.72798e6	0.579207
$530$	−939412.	−0.145267
$531$	−1.23256e7	−1.89702
$532$	−3.04000e6	−0.465688
$533$	−2.14843e6	−0.327570
$534$	−8.84974e6	−1.34300
$535$	−494537.	−0.0746989
$536$	−187103.	−0.0281300
$537$	5.37050e6	0.803672
$538$	−1.49385e7	−2.22510
$539$	0	0
$540$	−4.62337e6	−0.682299
$541$	−472165.	−0.0693587	−0.0346794	−	0.999398i	$-0.511041\pi$
$541$	−472165.	−0.0693587	−0.0346794	+	0.999398i	$0.511041\pi$
$542$	−1.41815e7	−2.07360
$543$	−7.15610e6	−1.04154
$544$	−5.09360e6	−0.737951
$545$	2.47293e6	0.356633
$546$	3.12669e6	0.448852
$547$	−7.63716e6	−1.09135	−0.545675	−	0.837997i	$-0.683727\pi$
$547$	−7.63716e6	−1.09135	−0.545675	+	0.837997i	$0.683727\pi$
$548$	−72581.6	−0.0103246
$549$	2.09603e7	2.96802
$550$	0	0
$551$	−7.31285e6	−1.02614
$552$	3.02763e6	0.422917
$553$	4.01258e6	0.557970
$554$	1.84576e7	2.55506
$555$	−3.80091e6	−0.523787
$556$	−1.33645e7	−1.83343
$557$	4.48807e6	0.612946	0.306473	−	0.951879i	$-0.400851\pi$
$557$	4.48807e6	0.612946	0.306473	+	0.951879i	$0.400851\pi$
$558$	−6.96417e6	−0.946856
$559$	−5.88782e6	−0.796938
$560$	1.21262e6	0.163402
$561$	0	0
$562$	1.38307e7	1.84715
$563$	2.16500e6	0.287864	0.143932	−	0.989588i	$-0.454025\pi$
$563$	2.16500e6	0.287864	0.143932	+	0.989588i	$0.454025\pi$
$564$	−1.87094e7	−2.47664
$565$	3.95495e6	0.521219
$566$	−3.27812e6	−0.430115
$567$	−601258.	−0.0785422
$568$	−1.21637e6	−0.158195
$569$	1.13325e7	1.46739	0.733696	−	0.679478i	$-0.237794\pi$
$569$	1.13325e7	1.46739	0.733696	+	0.679478i	$0.237794\pi$
$570$	1.03791e7	1.33805
$571$	843773.	0.108302	0.0541509	−	0.998533i	$-0.482755\pi$
$571$	843773.	0.108302	0.0541509	+	0.998533i	$0.482755\pi$
$572$	0	0
$573$	1.14174e7	1.45272
$574$	2.89758e6	0.367076
$575$	−7.32792e6	−0.924296
$576$	−1.70942e7	−2.14681
$577$	−2.23784e6	−0.279827	−0.139914	−	0.990164i	$-0.544682\pi$
$577$	−2.23784e6	−0.279827	−0.139914	+	0.990164i	$0.544682\pi$
$578$	8.63866e6	1.07554
$579$	−1.86423e7	−2.31102
$580$	−4.50824e6	−0.556464
$581$	5.79346e6	0.712029
$582$	9.27156e6	1.13461
$583$	0	0
$584$	−411521.	−0.0499299
$585$	−3.58601e6	−0.433234
$586$	−7.69124e6	−0.925236
$587$	1.21190e7	1.45168	0.725839	−	0.687864i	$-0.241452\pi$
$587$	1.21190e7	1.45168	0.725839	+	0.687864i	$0.241452\pi$
$588$	−2.24625e6	−0.267926
$589$	3.45030e6	0.409797
$590$	7.06734e6	0.835846
$591$	−9.35942e6	−1.10225
$592$	−4.43698e6	−0.520335
$593$	−8.00167e6	−0.934424	−0.467212	−	0.884145i	$-0.654742\pi$
$593$	−8.00167e6	−0.934424	−0.467212	+	0.884145i	$0.654742\pi$
$594$	0	0
$595$	863689.	0.100015
$596$	−5.13261e6	−0.591865
$597$	−7.42058e6	−0.852123
$598$	7.93138e6	0.906976
$599$	1.45899e7	1.66144	0.830719	−	0.556692i	$-0.187930\pi$
$599$	1.45899e7	1.66144	0.830719	+	0.556692i	$0.187930\pi$
$600$	−2.18276e6	−0.247529
$601$	8.67178e6	0.979314	0.489657	−	0.871915i	$-0.337122\pi$
$601$	8.67178e6	0.979314	0.489657	+	0.871915i	$0.337122\pi$
$602$	7.94087e6	0.893052
$603$	2.09671e6	0.234825
$604$	−1.82607e6	−0.203669
$605$	0	0
$606$	−5.44374e6	−0.602166
$607$	1.33059e7	1.46580	0.732898	−	0.680339i	$-0.238167\pi$
$607$	1.33059e7	1.46580	0.732898	+	0.680339i	$0.238167\pi$
$608$	1.41312e7	1.55032
$609$	−5.40344e6	−0.590374
$610$	−1.20184e7	−1.30774
$611$	−6.01231e6	−0.651536
$612$	−9.27817e6	−1.00135
$613$	−2.35101e6	−0.252699	−0.126350	−	0.991986i	$-0.540326\pi$
$613$	−2.35101e6	−0.252699	−0.126350	+	0.991986i	$0.540326\pi$
$614$	1.51675e7	1.62365
$615$	−5.26963e6	−0.561814
$616$	0	0
$617$	9.63523e6	1.01894	0.509470	−	0.860488i	$-0.329841\pi$
$617$	9.63523e6	1.01894	0.509470	+	0.860488i	$0.329841\pi$
$618$	−3.03939e6	−0.320122
$619$	−4.86148e6	−0.509967	−0.254983	−	0.966945i	$-0.582070\pi$
$619$	−4.86148e6	−0.509967	−0.254983	+	0.966945i	$0.582070\pi$
$620$	2.12705e6	0.222228
$621$	−1.40568e7	−1.46271
$622$	1.90062e7	1.96979
$623$	2.04307e6	0.210894
$624$	−6.63789e6	−0.682446
$625$	2.70017e6	0.276498
$626$	2.83391e7	2.89035
$627$	0	0
$628$	−3.27519e6	−0.331389
$629$	−3.16023e6	−0.318487
$630$	4.83644e6	0.485483
$631$	−6.59770e6	−0.659659	−0.329829	−	0.944041i	$-0.606991\pi$
$631$	−6.59770e6	−0.659659	−0.329829	+	0.944041i	$0.606991\pi$
$632$	3.03188e6	0.301939
$633$	1.92409e7	1.90860
$634$	−2.43535e7	−2.40624
$635$	2.02874e6	0.199661
$636$	−3.69430e6	−0.362151
$637$	−721836.	−0.0704839
$638$	0	0
$639$	1.36308e7	1.32059
$640$	2.15861e6	0.208317
$641$	1.44525e7	1.38930	0.694651	−	0.719347i	$-0.255559\pi$
$641$	1.44525e7	1.38930	0.694651	+	0.719347i	$0.255559\pi$
$642$	−3.65104e6	−0.349606
$643$	−1.54720e7	−1.47577	−0.737886	−	0.674926i	$-0.764176\pi$
$643$	−1.54720e7	−1.47577	−0.737886	+	0.674926i	$0.764176\pi$
$644$	−5.69799e6	−0.541386
$645$	−1.44415e7	−1.36683
$646$	8.62960e6	0.813597
$647$	1.66647e7	1.56508	0.782540	−	0.622601i	$-0.213924\pi$
$647$	1.66647e7	1.56508	0.782540	+	0.622601i	$0.213924\pi$
$648$	−454306.	−0.0425022
$649$	0	0
$650$	−5.71810e6	−0.530845
$651$	2.54941e6	0.235770
$652$	−1.75525e7	−1.61704
$653$	−1.33451e7	−1.22472	−0.612361	−	0.790578i	$-0.709780\pi$
$653$	−1.33451e7	−1.22472	−0.612361	+	0.790578i	$0.709780\pi$
$654$	1.82570e7	1.66911
$655$	4.99409e6	0.454834
$656$	−6.15149e6	−0.558111
$657$	4.61157e6	0.416807
$658$	8.10877e6	0.730113
$659$	4.00667e6	0.359393	0.179697	−	0.983722i	$-0.442488\pi$
$659$	4.00667e6	0.359393	0.179697	+	0.983722i	$0.442488\pi$
$660$	0	0
$661$	1.08005e7	0.961478	0.480739	−	0.876864i	$-0.340368\pi$
$661$	1.08005e7	0.961478	0.480739	+	0.876864i	$0.340368\pi$
$662$	−7.99493e6	−0.709038
$663$	−4.72782e6	−0.417712
$664$	4.37750e6	0.385307
$665$	−2.39614e6	−0.210116
$666$	−1.76965e7	−1.54597
$667$	−1.37068e7	−1.19294
$668$	3.15767e6	0.273795
$669$	−1.37070e7	−1.18407
$670$	−1.20223e6	−0.103466
$671$	0	0
$672$	1.04415e7	0.891951
$673$	−1.09119e7	−0.928676	−0.464338	−	0.885658i	$-0.653708\pi$
$673$	−1.09119e7	−0.928676	−0.464338	+	0.885658i	$0.653708\pi$
$674$	1.12884e6	0.0957158
$675$	1.01342e7	0.856110
$676$	−1.02459e7	−0.862353
$677$	1.35765e7	1.13846	0.569229	−	0.822179i	$-0.307242\pi$
$677$	1.35765e7	1.13846	0.569229	+	0.822179i	$0.307242\pi$
$678$	2.91984e7	2.43941
$679$	−2.14046e6	−0.178169
$680$	652598.	0.0541219
$681$	−1.05323e7	−0.870272
$682$	0	0
$683$	−1.26726e7	−1.03948	−0.519738	−	0.854326i	$-0.673970\pi$
$683$	−1.26726e7	−1.03948	−0.519738	+	0.854326i	$0.673970\pi$
$684$	2.57406e7	2.10367
$685$	−57209.2	−0.00465843
$686$	973536.	0.0789845
$687$	−2.64283e7	−2.13637
$688$	−1.68583e7	−1.35782
$689$	−1.18717e6	−0.0952720
$690$	1.94539e7	1.55555
$691$	7.11964e6	0.567235	0.283617	−	0.958938i	$-0.408465\pi$
$691$	7.11964e6	0.567235	0.283617	+	0.958938i	$0.408465\pi$
$692$	2.12052e6	0.168336
$693$	0	0
$694$	2.94097e6	0.231789
$695$	−1.05339e7	−0.827235
$696$	−4.08281e6	−0.319474
$697$	−4.38139e6	−0.341609
$698$	−1.15955e6	−0.0900844
$699$	−3.05770e6	−0.236702
$700$	4.10794e6	0.316869
$701$	1.00155e7	0.769803	0.384902	−	0.922958i	$-0.374235\pi$
$701$	1.00155e7	0.769803	0.384902	+	0.922958i	$0.374235\pi$
$702$	−1.09687e7	−0.840068
$703$	8.76746e6	0.669092
$704$	0	0
$705$	−1.47469e7	−1.11745
$706$	−2.88084e7	−2.17524
$707$	1.25676e6	0.0945589
$708$	2.77928e7	2.08377
$709$	−8.84454e6	−0.660784	−0.330392	−	0.943844i	$-0.607181\pi$
$709$	−8.84454e6	−0.660784	−0.330392	+	0.943844i	$0.607181\pi$
$710$	−7.81571e6	−0.581866
$711$	−3.39757e7	−2.52054
$712$	1.54373e6	0.114123
$713$	6.46703e6	0.476410
$714$	6.37638e6	0.468090
$715$	0	0
$716$	−7.63698e6	−0.556723
$717$	−6.51728e6	−0.473444
$718$	1.45047e7	1.05002
$719$	6.58086e6	0.474745	0.237373	−	0.971419i	$-0.423714\pi$
$719$	6.58086e6	0.474745	0.237373	+	0.971419i	$0.423714\pi$
$720$	−1.02676e7	−0.738141
$721$	701682.	0.0502692
$722$	−3.45169e6	−0.246427
$723$	3.62301e7	2.57765
$724$	1.01762e7	0.721502
$725$	9.88183e6	0.698220
$726$	0	0
$727$	1.88401e7	1.32205	0.661023	−	0.750365i	$-0.270122\pi$
$727$	1.88401e7	1.32205	0.661023	+	0.750365i	$0.270122\pi$
$728$	−545414.	−0.0381415
$729$	−2.23900e7	−1.56040
$730$	−2.64422e6	−0.183650
$731$	−1.20073e7	−0.831095
$732$	−4.72631e7	−3.26020
$733$	2.78330e6	0.191337	0.0956687	−	0.995413i	$-0.469501\pi$
$733$	2.78330e6	0.191337	0.0956687	+	0.995413i	$0.469501\pi$
$734$	1.46416e7	1.00311
$735$	−1.77050e6	−0.120887
$736$	2.64867e7	1.80233
$737$	0	0
$738$	−2.45346e7	−1.65821
$739$	2.48970e7	1.67701	0.838505	−	0.544894i	$-0.183430\pi$
$739$	2.48970e7	1.67701	0.838505	+	0.544894i	$0.183430\pi$
$740$	5.40499e6	0.362840
$741$	1.31164e7	0.877548
$742$	1.60113e6	0.106762
$743$	3.86085e6	0.256573	0.128286	−	0.991737i	$-0.459052\pi$
$743$	3.86085e6	0.256573	0.128286	+	0.991737i	$0.459052\pi$
$744$	1.92632e6	0.127584
$745$	−4.04554e6	−0.267046
$746$	−3.44412e7	−2.26585
$747$	−4.90549e7	−3.21648
$748$	0	0
$749$	842888.	0.0548991
$750$	−3.30938e7	−2.14829
$751$	6.72737e6	0.435257	0.217628	−	0.976032i	$-0.430168\pi$
$751$	6.72737e6	0.435257	0.217628	+	0.976032i	$0.430168\pi$
$752$	−1.72147e7	−1.11008
$753$	4.29737e7	2.76195
$754$	−1.06956e7	−0.685136
$755$	−1.43932e6	−0.0918943
$756$	7.88007e6	0.501447
$757$	2.17782e7	1.38128	0.690642	−	0.723197i	$-0.257328\pi$
$757$	2.17782e7	1.38128	0.690642	+	0.723197i	$0.257328\pi$
$758$	−5.11525e6	−0.323366
$759$	0	0
$760$	−1.81051e6	−0.113702
$761$	2.57074e7	1.60915	0.804575	−	0.593851i	$-0.202393\pi$
$761$	2.57074e7	1.60915	0.804575	+	0.593851i	$0.202393\pi$
$762$	1.49777e7	0.934453
$763$	−4.21486e6	−0.262103
$764$	−1.62359e7	−1.00633
$765$	−7.31310e6	−0.451802
$766$	3.40234e7	2.09511
$767$	8.93127e6	0.548182
$768$	−1.78808e7	−1.09391
$769$	1.34375e7	0.819413	0.409706	−	0.912217i	$-0.365631\pi$
$769$	1.34375e7	0.819413	0.409706	+	0.912217i	$0.365631\pi$
$770$	0	0
$771$	−1.86471e7	−1.12973
$772$	2.65099e7	1.60090
$773$	3.05572e7	1.83935	0.919674	−	0.392682i	$-0.128453\pi$
$773$	3.05572e7	1.83935	0.919674	+	0.392682i	$0.128453\pi$
$774$	−6.72376e7	−4.03422
$775$	−4.66237e6	−0.278839
$776$	−1.61731e6	−0.0964140
$777$	6.47825e6	0.384951
$778$	−3.82364e7	−2.26479
$779$	1.21553e7	0.717667
$780$	8.08606e6	0.475883
$781$	0	0
$782$	1.61748e7	0.945849
$783$	1.89558e7	1.10494
$784$	−2.06679e6	−0.120090
$785$	−2.58152e6	−0.149521
$786$	3.68700e7	2.12871
$787$	2.07672e6	0.119520	0.0597602	−	0.998213i	$-0.480966\pi$
$787$	2.07672e6	0.119520	0.0597602	+	0.998213i	$0.480966\pi$
$788$	1.33093e7	0.763556
$789$	−5.79372e6	−0.331333
$790$	1.94812e7	1.11058
$791$	−6.74081e6	−0.383064
$792$	0	0
$793$	−1.51881e7	−0.857670
$794$	−4.19827e7	−2.36330
$795$	−2.91187e6	−0.163401
$796$	1.05523e7	0.590286
$797$	−5.98563e6	−0.333783	−0.166892	−	0.985975i	$-0.553373\pi$
$797$	−5.98563e6	−0.333783	−0.166892	+	0.985975i	$0.553373\pi$
$798$	−1.76901e7	−0.983383
$799$	−1.22611e7	−0.679460
$800$	−1.90955e7	−1.05489
$801$	−1.72993e7	−0.952679
$802$	1.22515e7	0.672594
$803$	0	0
$804$	−4.72784e6	−0.257942
$805$	−4.49118e6	−0.244270
$806$	5.04633e6	0.273614
$807$	−4.63043e7	−2.50286
$808$	949597.	0.0511695
$809$	−1.96864e7	−1.05754	−0.528769	−	0.848766i	$-0.677346\pi$
$809$	−1.96864e7	−1.05754	−0.528769	+	0.848766i	$0.677346\pi$
$810$	−2.91913e6	−0.156329
$811$	−8.50101e6	−0.453856	−0.226928	−	0.973912i	$-0.572868\pi$
$811$	−8.50101e6	−0.453856	−0.226928	+	0.973912i	$0.572868\pi$
$812$	7.68384e6	0.408967
$813$	−4.39580e7	−2.33245
$814$	0	0
$815$	−1.38350e7	−0.729599
$816$	−1.35369e7	−0.711695
$817$	3.33119e7	1.74600
$818$	−3.75168e7	−1.96039
$819$	6.11199e6	0.318400
$820$	7.49355e6	0.389182
$821$	1.36199e6	0.0705204	0.0352602	−	0.999378i	$-0.488774\pi$
$821$	1.36199e6	0.0705204	0.0352602	+	0.999378i	$0.488774\pi$
$822$	−422360.	−0.0218023
$823$	−1.35934e6	−0.0699566	−0.0349783	−	0.999388i	$-0.511136\pi$
$823$	−1.35934e6	−0.0699566	−0.0349783	+	0.999388i	$0.511136\pi$
$824$	530186.	0.0272026
$825$	0	0
$826$	−1.20456e7	−0.614295
$827$	−1.00727e7	−0.512132	−0.256066	−	0.966659i	$-0.582426\pi$
$827$	−1.00727e7	−0.512132	−0.256066	+	0.966659i	$0.582426\pi$
$828$	4.82465e7	2.44563
$829$	−5.63984e6	−0.285023	−0.142512	−	0.989793i	$-0.545518\pi$
$829$	−5.63984e6	−0.285023	−0.142512	+	0.989793i	$0.545518\pi$
$830$	2.81275e7	1.41722
$831$	5.72125e7	2.87401
$832$	1.23867e7	0.620364
$833$	−1.47207e6	−0.0735048
$834$	−7.77693e7	−3.87163
$835$	2.48889e6	0.123535
$836$	0	0
$837$	−8.94361e6	−0.441265
$838$	−918733.	−0.0451938
$839$	−1.16351e7	−0.570642	−0.285321	−	0.958432i	$-0.592100\pi$
$839$	−1.16351e7	−0.570642	−0.285321	+	0.958432i	$0.592100\pi$
$840$	−1.33778e6	−0.0654164
$841$	−2.02735e6	−0.0988413
$842$	1.16801e7	0.567764
$843$	4.28706e7	2.07774
$844$	−2.73610e7	−1.32214
$845$	−8.07590e6	−0.389089
$846$	−6.86592e7	−3.29817
$847$	0	0
$848$	−3.39916e6	−0.162324
$849$	−1.01611e7	−0.483806
$850$	−1.16611e7	−0.553597
$851$	1.64332e7	0.777854
$852$	−3.07358e7	−1.45059
$853$	−2.85205e7	−1.34210	−0.671049	−	0.741413i	$-0.734156\pi$
$853$	−2.85205e7	−1.34210	−0.671049	+	0.741413i	$0.734156\pi$
$854$	2.04841e7	0.961108
$855$	2.02888e7	0.949165
$856$	636880.	0.0297080
$857$	9.95725e6	0.463113	0.231557	−	0.972821i	$-0.425618\pi$
$857$	9.95725e6	0.463113	0.231557	+	0.972821i	$0.425618\pi$
$858$	0	0
$859$	−1.49322e7	−0.690463	−0.345232	−	0.938517i	$-0.612200\pi$
$859$	−1.49322e7	−0.690463	−0.345232	+	0.938517i	$0.612200\pi$
$860$	2.05362e7	0.946834
$861$	8.98154e6	0.412898
$862$	8.90711e6	0.408290
$863$	3.84933e7	1.75937	0.879687	−	0.475553i	$-0.157752\pi$
$863$	3.84933e7	1.75937	0.879687	+	0.475553i	$0.157752\pi$
$864$	−3.66300e7	−1.66937
$865$	1.67140e6	0.0759523
$866$	2.56665e6	0.116298
$867$	2.67770e7	1.20980
$868$	−3.62533e6	−0.163323
$869$	0	0
$870$	−2.62339e7	−1.17507
$871$	−1.51930e6	−0.0678576
$872$	−3.18472e6	−0.141834
$873$	1.81239e7	0.804850
$874$	−4.48739e7	−1.98708
$875$	7.64011e6	0.337349
$876$	−1.03986e7	−0.457839
$877$	−9.40311e6	−0.412831	−0.206416	−	0.978464i	$-0.566180\pi$
$877$	−9.40311e6	−0.412831	−0.206416	+	0.978464i	$0.566180\pi$
$878$	4.69726e7	2.05640
$879$	−2.38403e7	−1.04073
$880$	0	0
$881$	1.10395e6	0.0479194	0.0239597	−	0.999713i	$-0.492373\pi$
$881$	1.10395e6	0.0479194	0.0239597	+	0.999713i	$0.492373\pi$
$882$	−8.24321e6	−0.356800
$883$	8.06579e6	0.348133	0.174067	−	0.984734i	$-0.444309\pi$
$883$	8.06579e6	0.348133	0.174067	+	0.984734i	$0.444309\pi$
$884$	6.72308e6	0.289359
$885$	2.19064e7	0.940185
$886$	−3.35933e7	−1.43770
$887$	1.49902e7	0.639732	0.319866	−	0.947463i	$-0.396362\pi$
$887$	1.49902e7	0.639732	0.319866	+	0.947463i	$0.396362\pi$
$888$	4.89493e6	0.208312
$889$	−3.45779e6	−0.146738
$890$	9.91920e6	0.419761
$891$	0	0
$892$	1.94918e7	0.820237
$893$	3.40162e7	1.42744
$894$	−2.98672e7	−1.24983
$895$	−6.01950e6	−0.251190
$896$	−3.67912e6	−0.153100
$897$	2.45847e7	1.02019
$898$	5.76384e7	2.38518
$899$	−8.72090e6	−0.359883
$900$	−3.47831e7	−1.43140
$901$	−2.42104e6	−0.0993553
$902$	0	0
$903$	2.46141e7	1.00453
$904$	−5.09331e6	−0.207290
$905$	8.02089e6	0.325538
$906$	−1.06261e7	−0.430083
$907$	4.12622e6	0.166546	0.0832730	−	0.996527i	$-0.473463\pi$
$907$	4.12622e6	0.166546	0.0832730	+	0.996527i	$0.473463\pi$
$908$	1.49772e7	0.602859
$909$	−1.06413e7	−0.427155
$910$	−3.50454e6	−0.140290
$911$	4.04272e7	1.61391	0.806953	−	0.590616i	$-0.201115\pi$
$911$	4.04272e7	1.61391	0.806953	+	0.590616i	$0.201115\pi$
$912$	3.75556e7	1.49516
$913$	0	0
$914$	1.48554e7	0.588191
$915$	−3.72530e7	−1.47099
$916$	3.75817e7	1.47992
$917$	−8.51191e6	−0.334275
$918$	−2.23690e7	−0.876072
$919$	−2.18546e7	−0.853600	−0.426800	−	0.904346i	$-0.640359\pi$
$919$	−2.18546e7	−0.853600	−0.426800	+	0.904346i	$0.640359\pi$
$920$	−3.39351e6	−0.132184
$921$	4.70142e7	1.82633
$922$	−1.74844e7	−0.677366
$923$	−9.87702e6	−0.381612
$924$	0	0
$925$	−1.18474e7	−0.455271
$926$	−1.04448e7	−0.400289
$927$	−5.94134e6	−0.227083
$928$	−3.57178e7	−1.36149
$929$	1.06843e7	0.406169	0.203085	−	0.979161i	$-0.434903\pi$
$929$	1.06843e7	0.406169	0.203085	+	0.979161i	$0.434903\pi$
$930$	1.23775e7	0.469274
$931$	4.08398e6	0.154422
$932$	4.34813e6	0.163970
$933$	5.89130e7	2.21568
$934$	2.97009e7	1.11404
$935$	0	0
$936$	4.61818e6	0.172298
$937$	3.99105e7	1.48504	0.742521	−	0.669823i	$-0.233630\pi$
$937$	3.99105e7	1.48504	0.742521	+	0.669823i	$0.233630\pi$
$938$	2.04907e6	0.0760414
$939$	8.78419e7	3.25116
$940$	2.09704e7	0.774082
$941$	−1.32350e6	−0.0487248	−0.0243624	−	0.999703i	$-0.507756\pi$
$941$	−1.32350e6	−0.0487248	−0.0243624	+	0.999703i	$0.507756\pi$
$942$	−1.90587e7	−0.699787
$943$	2.27832e7	0.834326
$944$	2.55724e7	0.933990
$945$	6.21110e6	0.226250
$946$	0	0
$947$	−2.76322e7	−1.00124	−0.500622	−	0.865666i	$-0.666895\pi$
$947$	−2.76322e7	−1.00124	−0.500622	+	0.865666i	$0.666895\pi$
$948$	7.66113e7	2.76868
$949$	−3.34160e6	−0.120445
$950$	3.23517e7	1.16302
$951$	−7.54879e7	−2.70661
$952$	−1.11229e6	−0.0397763
$953$	3.07901e7	1.09819	0.549096	−	0.835759i	$-0.314972\pi$
$953$	3.07901e7	1.09819	0.549096	+	0.835759i	$0.314972\pi$
$954$	−1.35572e7	−0.482281
$955$	−1.27972e7	−0.454053
$956$	9.26775e6	0.327966
$957$	0	0
$958$	−1.99999e7	−0.704068
$959$	97507.1	0.00342365
$960$	3.03818e7	1.06398
$961$	−2.45145e7	−0.856278
$962$	1.28231e7	0.446740
$963$	−7.13697e6	−0.247998
$964$	−5.15202e7	−1.78560
$965$	2.08952e7	0.722318
$966$	−3.31572e7	−1.14323
$967$	−2.92557e6	−0.100611	−0.0503055	−	0.998734i	$-0.516019\pi$
$967$	−2.92557e6	−0.100611	−0.0503055	+	0.998734i	$0.516019\pi$
$968$	0	0
$969$	2.67489e7	0.915159
$970$	−1.03920e7	−0.354625
$971$	2.78109e6	0.0946601	0.0473301	−	0.998879i	$-0.484929\pi$
$971$	2.78109e6	0.0946601	0.0473301	+	0.998879i	$0.484929\pi$
$972$	2.75990e7	0.936975
$973$	1.79540e7	0.607967
$974$	4.29801e7	1.45168
$975$	−1.77242e7	−0.597111
$976$	−4.34872e7	−1.46129
$977$	7.48673e6	0.250932	0.125466	−	0.992098i	$-0.459957\pi$
$977$	7.48673e6	0.250932	0.125466	+	0.992098i	$0.459957\pi$
$978$	−1.02140e8	−3.41467
$979$	0	0
$980$	2.51770e6	0.0837411
$981$	3.56884e7	1.18401
$982$	4.45985e7	1.47585
$983$	1.79815e7	0.593528	0.296764	−	0.954951i	$-0.404093\pi$
$983$	1.79815e7	0.593528	0.296764	+	0.954951i	$0.404093\pi$
$984$	6.78639e6	0.223435
$985$	1.04905e7	0.344512
$986$	−2.18120e7	−0.714501
$987$	2.51345e7	0.821253
$988$	−1.86519e7	−0.607899
$989$	6.24378e7	2.02982
$990$	0	0
$991$	3.72778e7	1.20578	0.602888	−	0.797826i	$-0.294017\pi$
$991$	3.72778e7	1.20578	0.602888	+	0.797826i	$0.294017\pi$
$992$	1.68521e7	0.543720
$993$	−2.47816e7	−0.797548
$994$	1.33211e7	0.427635
$995$	8.31734e6	0.266334
$996$	1.10613e8	3.53313
$997$	−4.87422e7	−1.55298	−0.776492	−	0.630128i	$-0.783003\pi$
$997$	−4.87422e7	−1.55298	−0.776492	+	0.630128i	$0.783003\pi$
$998$	2.72747e7	0.866828
$999$	−2.27264e7	−0.720471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.6.a.c.1.1		2
11.10	odd	2		7.6.a.b.1.2	✓	2
33.32	even	2		63.6.a.f.1.1		2
44.43	even	2		112.6.a.h.1.2		2
55.32	even	4		175.6.b.c.99.4		4
55.43	even	4		175.6.b.c.99.1		4
55.54	odd	2		175.6.a.c.1.1		2
77.10	even	6		49.6.c.d.30.1		4
77.32	odd	6		49.6.c.e.30.1		4
77.54	even	6		49.6.c.d.18.1		4
77.65	odd	6		49.6.c.e.18.1		4
77.76	even	2		49.6.a.f.1.2		2
88.21	odd	2		448.6.a.w.1.2		2
88.43	even	2		448.6.a.u.1.1		2
132.131	odd	2		1008.6.a.bq.1.1		2
231.230	odd	2		441.6.a.l.1.1		2
308.307	odd	2		784.6.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.a.b.1.2	✓	2	11.10	odd	2
49.6.a.f.1.2		2	77.76	even	2
49.6.c.d.18.1		4	77.54	even	6
49.6.c.d.30.1		4	77.10	even	6
49.6.c.e.18.1		4	77.65	odd	6
49.6.c.e.30.1		4	77.32	odd	6
63.6.a.f.1.1		2	33.32	even	2
112.6.a.h.1.2		2	44.43	even	2
175.6.a.c.1.1		2	55.54	odd	2
175.6.b.c.99.1		4	55.43	even	4
175.6.b.c.99.4		4	55.32	even	4
441.6.a.l.1.1		2	231.230	odd	2
448.6.a.u.1.1		2	88.43	even	2
448.6.a.w.1.2		2	88.21	odd	2
784.6.a.v.1.1		2	308.307	odd	2
847.6.a.c.1.1		2	1.1	even	1	trivial
1008.6.a.bq.1.1		2	132.131	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

\(f(q)\)	\(=\)	\(q-8.27492 q^{2} -25.6495 q^{3} +36.4743 q^{4} +28.7492 q^{5} +212.248 q^{6} -49.0000 q^{7} -37.0241 q^{8} +414.897 q^{9} +O(q^{10})\)	\(q-8.27492 q^{2} -25.6495 q^{3} +36.4743 q^{4} +28.7492 q^{5} +212.248 q^{6} -49.0000 q^{7} -37.0241 q^{8} +414.897 q^{9} -237.897 q^{10} -935.547 q^{12} -300.640 q^{13} +405.471 q^{14} -737.402 q^{15} -860.805 q^{16} -613.106 q^{17} -3433.24 q^{18} +1700.95 q^{19} +1048.60 q^{20} +1256.83 q^{21} +3188.15 q^{23} +949.650 q^{24} -2298.49 q^{25} +2487.77 q^{26} -4409.07 q^{27} -1787.24 q^{28} -4299.28 q^{29} +6101.94 q^{30} +2028.46 q^{31} +8307.86 q^{32} +5073.40 q^{34} -1408.71 q^{35} +15133.1 q^{36} +5154.46 q^{37} -14075.2 q^{38} +7711.26 q^{39} -1064.41 q^{40} +7146.21 q^{41} -10400.1 q^{42} +19584.3 q^{43} +11927.9 q^{45} -26381.7 q^{46} +19998.4 q^{47} +22079.2 q^{48} +2401.00 q^{49} +19019.8 q^{50} +15725.9 q^{51} -10965.6 q^{52} +3948.82 q^{53} +36484.7 q^{54} +1814.18 q^{56} -43628.5 q^{57} +35576.2 q^{58} -29707.6 q^{59} -26896.2 q^{60} +50519.3 q^{61} -16785.3 q^{62} -20330.0 q^{63} -41201.1 q^{64} -8643.14 q^{65} +5053.56 q^{67} -22362.6 q^{68} -81774.5 q^{69} +11657.0 q^{70} +32853.3 q^{71} -15361.2 q^{72} +11115.0 q^{73} -42652.7 q^{74} +58955.0 q^{75} +62040.8 q^{76} -63810.0 q^{78} -81889.4 q^{79} -24747.4 q^{80} +12270.6 q^{81} -59134.3 q^{82} -118234. q^{83} +45841.8 q^{84} -17626.3 q^{85} -162058. q^{86} +110274. q^{87} -41695.4 q^{89} -98702.8 q^{90} +14731.3 q^{91} +116286. q^{92} -52028.9 q^{93} -165485. q^{94} +48900.9 q^{95} -213092. q^{96} +43682.8 q^{97} -19868.1 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 9 q^{2} - 6 q^{3} + 5 q^{4} - 18 q^{5} + 198 q^{6} - 98 q^{7} + 9 q^{8} + 558 q^{9}+O(q^{10}) \) 2 * q - 9 * q^2 - 6 * q^3 + 5 * q^4 - 18 * q^5 + 198 * q^6 - 98 * q^7 + 9 * q^8 + 558 * q^9	\( 2 q - 9 q^{2} - 6 q^{3} + 5 q^{4} - 18 q^{5} + 198 q^{6} - 98 q^{7} + 9 q^{8} + 558 q^{9} - 204 q^{10} - 1554 q^{12} + 350 q^{13} + 441 q^{14} - 1656 q^{15} + 113 q^{16} - 1800 q^{17} - 3537 q^{18} + 3266 q^{19} + 2520 q^{20} + 294 q^{21} + 2088 q^{23} + 1854 q^{24} - 3238 q^{25} + 2016 q^{26} - 6372 q^{27} - 245 q^{28} - 6696 q^{29} + 6768 q^{30} - 20 q^{31} + 6129 q^{32} + 5934 q^{34} + 882 q^{35} + 10629 q^{36} + 6232 q^{37} - 15210 q^{38} + 20496 q^{39} - 3216 q^{40} + 6048 q^{41} - 9702 q^{42} + 3020 q^{43} + 5238 q^{45} - 25584 q^{46} + 11700 q^{47} + 41214 q^{48} + 4802 q^{49} + 19701 q^{50} - 7596 q^{51} - 31444 q^{52} + 9468 q^{53} + 37908 q^{54} - 441 q^{56} - 12876 q^{57} + 37314 q^{58} - 43938 q^{59} + 2016 q^{60} + 64754 q^{61} - 15300 q^{62} - 27342 q^{63} - 70783 q^{64} - 39060 q^{65} + 24784 q^{67} + 14994 q^{68} - 103392 q^{69} + 9996 q^{70} + 97416 q^{71} - 8775 q^{72} - 17452 q^{73} - 43434 q^{74} + 40494 q^{75} + 12782 q^{76} - 73080 q^{78} - 51256 q^{79} - 70272 q^{80} - 61074 q^{81} - 58338 q^{82} - 117558 q^{83} + 76146 q^{84} + 37860 q^{85} - 150048 q^{86} + 63180 q^{87} + 84276 q^{89} - 93852 q^{90} - 17150 q^{91} + 150912 q^{92} - 92280 q^{93} - 159468 q^{94} - 24264 q^{95} - 255906 q^{96} + 20776 q^{97} - 21609 q^{98}+O(q^{100}) \) 2 * q - 9 * q^2 - 6 * q^3 + 5 * q^4 - 18 * q^5 + 198 * q^6 - 98 * q^7 + 9 * q^8 + 558 * q^9 - 204 * q^10 - 1554 * q^12 + 350 * q^13 + 441 * q^14 - 1656 * q^15 + 113 * q^16 - 1800 * q^17 - 3537 * q^18 + 3266 * q^19 + 2520 * q^20 + 294 * q^21 + 2088 * q^23 + 1854 * q^24 - 3238 * q^25 + 2016 * q^26 - 6372 * q^27 - 245 * q^28 - 6696 * q^29 + 6768 * q^30 - 20 * q^31 + 6129 * q^32 + 5934 * q^34 + 882 * q^35 + 10629 * q^36 + 6232 * q^37 - 15210 * q^38 + 20496 * q^39 - 3216 * q^40 + 6048 * q^41 - 9702 * q^42 + 3020 * q^43 + 5238 * q^45 - 25584 * q^46 + 11700 * q^47 + 41214 * q^48 + 4802 * q^49 + 19701 * q^50 - 7596 * q^51 - 31444 * q^52 + 9468 * q^53 + 37908 * q^54 - 441 * q^56 - 12876 * q^57 + 37314 * q^58 - 43938 * q^59 + 2016 * q^60 + 64754 * q^61 - 15300 * q^62 - 27342 * q^63 - 70783 * q^64 - 39060 * q^65 + 24784 * q^67 + 14994 * q^68 - 103392 * q^69 + 9996 * q^70 + 97416 * q^71 - 8775 * q^72 - 17452 * q^73 - 43434 * q^74 + 40494 * q^75 + 12782 * q^76 - 73080 * q^78 - 51256 * q^79 - 70272 * q^80 - 61074 * q^81 - 58338 * q^82 - 117558 * q^83 + 76146 * q^84 + 37860 * q^85 - 150048 * q^86 + 63180 * q^87 + 84276 * q^89 - 93852 * q^90 - 17150 * q^91 + 150912 * q^92 - 92280 * q^93 - 159468 * q^94 - 24264 * q^95 - 255906 * q^96 + 20776 * q^97 - 21609 * q^98

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