LMFDB - Embedded newform 605.6.a.p.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,6,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.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:	$97.0322109869$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 523 x^{18} + 521 x^{17} + 115018 x^{16} - 115347 x^{15} - 13821739 x^{14} + \cdots - 32708279373824 $ x^20 - x^19 - 523x^18 + 521x^17 + 115018x^16 - 115347x^15 - 13821739x^14 + 14112735x^13 + 987264735x^12 - 1043264932x^11 - 42703408468x^10 + 48021607312x^9 + 1089062915552x^8 - 1362443421632x^7 - 15019635572992x^6 + 22119016261376x^5 + 88321308161536x^4 - 163614980036608x^3 - 51220983567360x^2 + 157475390795776x - 32708279373824
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Root			$10.8658$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.8658 q^{2} -20.9346 q^{3} +86.0646 q^{4} -25.0000 q^{5} -227.471 q^{6} -150.113 q^{7} +587.453 q^{8} +195.259 q^{9} +O(q^{10})$	\(q+10.8658 q^{2} -20.9346 q^{3} +86.0646 q^{4} -25.0000 q^{5} -227.471 q^{6} -150.113 q^{7} +587.453 q^{8} +195.259 q^{9} -271.644 q^{10} -1801.73 q^{12} +871.590 q^{13} -1631.09 q^{14} +523.366 q^{15} +3629.05 q^{16} +650.781 q^{17} +2121.64 q^{18} -403.748 q^{19} -2151.61 q^{20} +3142.56 q^{21} -3566.39 q^{23} -12298.1 q^{24} +625.000 q^{25} +9470.49 q^{26} +999.432 q^{27} -12919.4 q^{28} -685.737 q^{29} +5686.77 q^{30} -2696.70 q^{31} +20633.9 q^{32} +7071.23 q^{34} +3752.82 q^{35} +16804.9 q^{36} +94.4665 q^{37} -4387.02 q^{38} -18246.4 q^{39} -14686.3 q^{40} -15328.4 q^{41} +34146.3 q^{42} -20658.0 q^{43} -4881.49 q^{45} -38751.6 q^{46} -21257.8 q^{47} -75972.8 q^{48} +5726.88 q^{49} +6791.10 q^{50} -13623.9 q^{51} +75013.1 q^{52} +692.105 q^{53} +10859.6 q^{54} -88184.2 q^{56} +8452.32 q^{57} -7451.05 q^{58} -28351.0 q^{59} +45043.3 q^{60} +30614.3 q^{61} -29301.7 q^{62} -29311.0 q^{63} +108073. q^{64} -21789.8 q^{65} -4920.71 q^{67} +56009.2 q^{68} +74661.2 q^{69} +40777.2 q^{70} -26751.8 q^{71} +114706. q^{72} -1241.48 q^{73} +1026.45 q^{74} -13084.2 q^{75} -34748.4 q^{76} -198261. q^{78} -66952.7 q^{79} -90726.2 q^{80} -68370.8 q^{81} -166554. q^{82} +34582.8 q^{83} +270463. q^{84} -16269.5 q^{85} -224465. q^{86} +14355.7 q^{87} +73789.4 q^{89} -53041.0 q^{90} -130837. q^{91} -306940. q^{92} +56454.6 q^{93} -230982. q^{94} +10093.7 q^{95} -431963. q^{96} -122834. q^{97} +62226.8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) $ 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * 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 $

$2$	10.8658	1.92081	0.960406	−	0.278604i	$-0.0898718\pi$
$2$	10.8658	1.92081	0.960406	+	0.278604i	$0.0898718\pi$
$3$	−20.9346	−1.34296	−0.671479	−	0.741023i	$-0.734341\pi$
$3$	−20.9346	−1.34296	−0.671479	+	0.741023i	$0.734341\pi$
$4$	86.0646	2.68952
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−227.471	−2.57957
$7$	−150.113	−1.15790	−0.578952	−	0.815361i	$-0.696538\pi$
$7$	−150.113	−1.15790	−0.578952	+	0.815361i	$0.696538\pi$
$8$	587.453	3.24525
$9$	195.259	0.803537
$10$	−271.644	−0.859013
$11$	0	0
$11$	0	0
$12$	−1801.73	−3.61191
$13$	871.590	1.43039	0.715194	−	0.698926i	$-0.246338\pi$
$13$	871.590	1.43039	0.715194	+	0.698926i	$0.246338\pi$
$14$	−1631.09	−2.22412
$15$	523.366	0.600589
$16$	3629.05	3.54399
$17$	650.781	0.546151	0.273076	−	0.961993i	$-0.411959\pi$
$17$	650.781	0.546151	0.273076	+	0.961993i	$0.411959\pi$
$18$	2121.64	1.54344
$19$	−403.748	−0.256582	−0.128291	−	0.991737i	$-0.540949\pi$
$19$	−403.748	−0.256582	−0.128291	+	0.991737i	$0.540949\pi$
$20$	−2151.61	−1.20279
$21$	3142.56	1.55502
$22$	0	0
$23$	−3566.39	−1.40576	−0.702878	−	0.711311i	$-0.748102\pi$
$23$	−3566.39	−1.40576	−0.702878	+	0.711311i	$0.748102\pi$
$24$	−12298.1	−4.35823
$25$	625.000	0.200000
$26$	9470.49	2.74751
$27$	999.432	0.263842
$28$	−12919.4	−3.11421
$29$	−685.737	−0.151413	−0.0757064	−	0.997130i	$-0.524121\pi$
$29$	−685.737	−0.151413	−0.0757064	+	0.997130i	$0.524121\pi$
$30$	5686.77	1.15362
$31$	−2696.70	−0.503998	−0.251999	−	0.967727i	$-0.581088\pi$
$31$	−2696.70	−0.503998	−0.251999	+	0.967727i	$0.581088\pi$
$32$	20633.9	3.56210
$33$	0	0
$34$	7071.23	1.04905
$35$	3752.82	0.517831
$36$	16804.9	2.16113
$37$	94.4665	0.0113442	0.00567210	−	0.999984i	$-0.498195\pi$
$37$	94.4665	0.0113442	0.00567210	+	0.999984i	$0.498195\pi$
$38$	−4387.02	−0.492846
$39$	−18246.4	−1.92095
$40$	−14686.3	−1.45132
$41$	−15328.4	−1.42409	−0.712044	−	0.702135i	$-0.752230\pi$
$41$	−15328.4	−1.42409	−0.712044	+	0.702135i	$0.752230\pi$
$42$	34146.3	2.98690
$43$	−20658.0	−1.70380	−0.851898	−	0.523708i	$-0.824548\pi$
$43$	−20658.0	−1.70380	−0.851898	+	0.523708i	$0.824548\pi$
$44$	0	0
$45$	−4881.49	−0.359353
$46$	−38751.6	−2.70019
$47$	−21257.8	−1.40370	−0.701848	−	0.712327i	$-0.747642\pi$
$47$	−21257.8	−1.40370	−0.701848	+	0.712327i	$0.747642\pi$
$48$	−75972.8	−4.75943
$49$	5726.88	0.340744
$50$	6791.10	0.384162
$51$	−13623.9	−0.733458
$52$	75013.1	3.84706
$53$	692.105	0.0338440	0.0169220	−	0.999857i	$-0.494613\pi$
$53$	692.105	0.0338440	0.0169220	+	0.999857i	$0.494613\pi$
$54$	10859.6	0.506791
$55$	0	0
$56$	−88184.2	−3.75769
$57$	8452.32	0.344579
$58$	−7451.05	−0.290836
$59$	−28351.0	−1.06032	−0.530162	−	0.847896i	$-0.677869\pi$
$59$	−28351.0	−1.06032	−0.530162	+	0.847896i	$0.677869\pi$
$60$	45043.3	1.61530
$61$	30614.3	1.05341	0.526707	−	0.850047i	$-0.323426\pi$
$61$	30614.3	1.05341	0.526707	+	0.850047i	$0.323426\pi$
$62$	−29301.7	−0.968086
$63$	−29311.0	−0.930419
$64$	108073.	3.29812
$65$	−21789.8	−0.639689
$66$	0	0
$67$	−4920.71	−0.133919	−0.0669593	−	0.997756i	$-0.521330\pi$
$67$	−4920.71	−0.133919	−0.0669593	+	0.997756i	$0.521330\pi$
$68$	56009.2	1.46888
$69$	74661.2	1.88787
$70$	40777.2	0.994656
$71$	−26751.8	−0.629807	−0.314903	−	0.949124i	$-0.601972\pi$
$71$	−26751.8	−0.629807	−0.314903	+	0.949124i	$0.601972\pi$
$72$	114706.	2.60768
$73$	−1241.48	−0.0272666	−0.0136333	−	0.999907i	$-0.504340\pi$
$73$	−1241.48	−0.0272666	−0.0136333	+	0.999907i	$0.504340\pi$
$74$	1026.45	0.0217901
$75$	−13084.2	−0.268592
$76$	−34748.4	−0.690082
$77$	0	0
$78$	−198261.	−3.68979
$79$	−66952.7	−1.20698	−0.603491	−	0.797370i	$-0.706224\pi$
$79$	−66952.7	−1.20698	−0.603491	+	0.797370i	$0.706224\pi$
$80$	−90726.2	−1.58492
$81$	−68370.8	−1.15787
$82$	−166554.	−2.73540
$83$	34582.8	0.551016	0.275508	−	0.961299i	$-0.411154\pi$
$83$	34582.8	0.551016	0.275508	+	0.961299i	$0.411154\pi$
$84$	270463.	4.18225
$85$	−16269.5	−0.244246
$86$	−224465.	−3.27267
$87$	14355.7	0.203341
$88$	0	0
$89$	73789.4	0.987459	0.493730	−	0.869615i	$-0.335633\pi$
$89$	73789.4	0.987459	0.493730	+	0.869615i	$0.335633\pi$
$90$	−53041.0	−0.690249
$91$	−130837.	−1.65625
$92$	−306940.	−3.78080
$93$	56454.6	0.676849
$94$	−230982.	−2.69624
$95$	10093.7	0.114747
$96$	−431963.	−4.78374
$97$	−122834.	−1.32553	−0.662766	−	0.748827i	$-0.730617\pi$
$97$	−122834.	−1.32553	−0.662766	+	0.748827i	$0.730617\pi$
$98$	62226.8	0.654504
$99$	0	0
$100$	53790.4	0.537904
$101$	114691.	1.11873	0.559364	−	0.828922i	$-0.311045\pi$
$101$	114691.	1.11873	0.559364	+	0.828922i	$0.311045\pi$
$102$	−148034.	−1.40884
$103$	−79175.5	−0.735356	−0.367678	−	0.929953i	$-0.619847\pi$
$103$	−79175.5	−0.735356	−0.367678	+	0.929953i	$0.619847\pi$
$104$	512018.	4.64197
$105$	−78564.0	−0.695425
$106$	7520.24	0.0650080
$107$	169903.	1.43463	0.717316	−	0.696748i	$-0.245371\pi$
$107$	169903.	1.43463	0.717316	+	0.696748i	$0.245371\pi$
$108$	86015.7	0.709608
$109$	−84632.9	−0.682296	−0.341148	−	0.940010i	$-0.610816\pi$
$109$	−84632.9	−0.682296	−0.341148	+	0.940010i	$0.610816\pi$
$110$	0	0
$111$	−1977.62	−0.0152348
$112$	−544767.	−4.10361
$113$	−35761.9	−0.263466	−0.131733	−	0.991285i	$-0.542054\pi$
$113$	−35761.9	−0.263466	−0.131733	+	0.991285i	$0.542054\pi$
$114$	91840.8	0.661871
$115$	89159.8	0.628673
$116$	−59017.7	−0.407228
$117$	170186.	1.14937
$118$	−308055.	−2.03668
$119$	−97690.7	−0.632391
$120$	307453.	1.94906
$121$	0	0
$122$	332647.	2.02341
$123$	320894.	1.91249
$124$	−232091.	−1.35551
$125$	−15625.0	−0.0894427
$126$	−318486.	−1.78716
$127$	−58744.5	−0.323190	−0.161595	−	0.986857i	$-0.551664\pi$
$127$	−58744.5	−0.323190	−0.161595	+	0.986857i	$0.551664\pi$
$128$	514010.	2.77298
$129$	432468.	2.28813
$130$	−236762.	−1.22872
$131$	−178508.	−0.908821	−0.454410	−	0.890792i	$-0.650150\pi$
$131$	−178508.	−0.908821	−0.454410	+	0.890792i	$0.650150\pi$
$132$	0	0
$133$	60607.7	0.297098
$134$	−53467.3	−0.257233
$135$	−24985.8	−0.117994
$136$	382303.	1.77240
$137$	−206329.	−0.939200	−0.469600	−	0.882879i	$-0.655602\pi$
$137$	−206329.	−0.939200	−0.469600	+	0.882879i	$0.655602\pi$
$138$	811250.	3.62624
$139$	311463.	1.36732	0.683658	−	0.729802i	$-0.260388\pi$
$139$	311463.	1.36732	0.683658	+	0.729802i	$0.260388\pi$
$140$	322985.	1.39272
$141$	445024.	1.88511
$142$	−290679.	−1.20974
$143$	0	0
$144$	708606.	2.84773
$145$	17143.4	0.0677139
$146$	−13489.6	−0.0523741
$147$	−119890.	−0.457604
$148$	8130.22	0.0305104
$149$	−26398.0	−0.0974102	−0.0487051	−	0.998813i	$-0.515509\pi$
$149$	−26398.0	−0.0974102	−0.0487051	+	0.998813i	$0.515509\pi$
$150$	−142169.	−0.515914
$151$	92876.1	0.331483	0.165742	−	0.986169i	$-0.446998\pi$
$151$	92876.1	0.331483	0.165742	+	0.986169i	$0.446998\pi$
$152$	−237183.	−0.832672
$153$	127071.	0.438852
$154$	0	0
$155$	67417.6	0.225395
$156$	−1.57037e6	−5.16644
$157$	47891.6	0.155064	0.0775319	−	0.996990i	$-0.475296\pi$
$157$	47891.6	0.155064	0.0775319	+	0.996990i	$0.475296\pi$
$158$	−727492.	−2.31838
$159$	−14489.0	−0.0454511
$160$	−515846.	−1.59302
$161$	535362.	1.62773
$162$	−742900.	−2.22404
$163$	−4149.83	−0.0122338	−0.00611690	−	0.999981i	$-0.501947\pi$
$163$	−4149.83	−0.0122338	−0.00611690	+	0.999981i	$0.501947\pi$
$164$	−1.31923e6	−3.83011
$165$	0	0
$166$	375768.	1.05840
$167$	258551.	0.717388	0.358694	−	0.933455i	$-0.383222\pi$
$167$	258551.	0.717388	0.358694	+	0.933455i	$0.383222\pi$
$168$	1.84611e6	5.04642
$169$	388377.	1.04601
$170$	−176781.	−0.469151
$171$	−78835.6	−0.206173
$172$	−1.77792e6	−4.58239
$173$	11813.7	0.0300103	0.0150051	−	0.999887i	$-0.495224\pi$
$173$	11813.7	0.0300103	0.0150051	+	0.999887i	$0.495224\pi$
$174$	155985.	0.390580
$175$	−93820.6	−0.231581
$176$	0	0
$177$	593518.	1.42397
$178$	801778.	1.89672
$179$	534441.	1.24672	0.623358	−	0.781937i	$-0.285768\pi$
$179$	534441.	1.24672	0.623358	+	0.781937i	$0.285768\pi$
$180$	−420123.	−0.966485
$181$	67088.6	0.152213	0.0761066	−	0.997100i	$-0.475751\pi$
$181$	67088.6	0.152213	0.0761066	+	0.997100i	$0.475751\pi$
$182$	−1.42164e6	−3.18135
$183$	−640899.	−1.41469
$184$	−2.09509e6	−4.56202
$185$	−2361.66	−0.00507328
$186$	613421.	1.30010
$187$	0	0
$188$	−1.82954e6	−3.77527
$189$	−150028.	−0.305504
$190$	109676.	0.220407
$191$	−883689.	−1.75273	−0.876367	−	0.481644i	$-0.840040\pi$
$191$	−883689.	−1.75273	−0.876367	+	0.481644i	$0.840040\pi$
$192$	−2.26247e6	−4.42924
$193$	−861121.	−1.66407	−0.832034	−	0.554725i	$-0.812823\pi$
$193$	−861121.	−1.66407	−0.832034	+	0.554725i	$0.812823\pi$
$194$	−1.33469e6	−2.54610
$195$	456161.	0.859076
$196$	492881.	0.916436
$197$	−12317.4	−0.0226127	−0.0113063	−	0.999936i	$-0.503599\pi$
$197$	−12317.4	−0.0226127	−0.0113063	+	0.999936i	$0.503599\pi$
$198$	0	0
$199$	−664090.	−1.18876	−0.594380	−	0.804184i	$-0.702603\pi$
$199$	−664090.	−1.18876	−0.594380	+	0.804184i	$0.702603\pi$
$200$	367158.	0.649050
$201$	103013.	0.179847
$202$	1.24620e6	2.14887
$203$	102938.	0.175322
$204$	−1.17253e6	−1.97265
$205$	383210.	0.636871
$206$	−860301.	−1.41248
$207$	−696372.	−1.12958
$208$	3.16304e6	5.06929
$209$	0	0
$210$	−853657.	−1.33578
$211$	−1.13800e6	−1.75969	−0.879843	−	0.475265i	$-0.842352\pi$
$211$	−1.13800e6	−1.75969	−0.879843	+	0.475265i	$0.842352\pi$
$212$	59565.7	0.0910242
$213$	560040.	0.845804
$214$	1.84612e6	2.75566
$215$	516450.	0.761961
$216$	587119.	0.856232
$217$	404810.	0.583582
$218$	−919600.	−1.31056
$219$	25989.9	0.0366180
$220$	0	0
$221$	567215.	0.781208
$222$	−21488.4	−0.0292631
$223$	−144798.	−0.194984	−0.0974921	−	0.995236i	$-0.531082\pi$
$223$	−144798.	−0.194984	−0.0974921	+	0.995236i	$0.531082\pi$
$224$	−3.09741e6	−4.12457
$225$	122037.	0.160707
$226$	−388580.	−0.506068
$227$	−247926.	−0.319343	−0.159672	−	0.987170i	$-0.551044\pi$
$227$	−247926.	−0.319343	−0.159672	+	0.987170i	$0.551044\pi$
$228$	727445.	0.926751
$229$	525696.	0.662439	0.331219	−	0.943554i	$-0.392540\pi$
$229$	525696.	0.662439	0.331219	+	0.943554i	$0.392540\pi$
$230$	968789.	1.20756
$231$	0	0
$232$	−402838.	−0.491372
$233$	−365575.	−0.441151	−0.220575	−	0.975370i	$-0.570793\pi$
$233$	−365575.	−0.441151	−0.220575	+	0.975370i	$0.570793\pi$
$234$	1.84920e6	2.20772
$235$	531444.	0.627752
$236$	−2.44002e6	−2.85176
$237$	1.40163e6	1.62093
$238$	−1.06148e6	−1.21470
$239$	441488.	0.499948	0.249974	−	0.968253i	$-0.419578\pi$
$239$	441488.	0.499948	0.249974	+	0.968253i	$0.419578\pi$
$240$	1.89932e6	2.12848
$241$	129855.	0.144017	0.0720086	−	0.997404i	$-0.477059\pi$
$241$	129855.	0.144017	0.0720086	+	0.997404i	$0.477059\pi$
$242$	0	0
$243$	1.18846e6	1.29112
$244$	2.63481e6	2.83318
$245$	−143172.	−0.152385
$246$	3.48676e6	3.67353
$247$	−351903.	−0.367012
$248$	−1.58419e6	−1.63560
$249$	−723978.	−0.739992
$250$	−169777.	−0.171803
$251$	−745528.	−0.746929	−0.373465	−	0.927644i	$-0.621830\pi$
$251$	−745528.	−0.746929	−0.373465	+	0.927644i	$0.621830\pi$
$252$	−2.52264e6	−2.50238
$253$	0	0
$254$	−638303.	−0.620787
$255$	340597.	0.328012
$256$	2.12677e6	2.02825
$257$	1.39979e6	1.32200	0.660999	−	0.750387i	$-0.270133\pi$
$257$	1.39979e6	1.32200	0.660999	+	0.750387i	$0.270133\pi$
$258$	4.69909e6	4.39506
$259$	−14180.6	−0.0131355
$260$	−1.87533e6	−1.72046
$261$	−133897.	−0.121666
$262$	−1.93962e6	−1.74567
$263$	1.44410e6	1.28738	0.643690	−	0.765286i	$-0.277402\pi$
$263$	1.44410e6	1.28738	0.643690	+	0.765286i	$0.277402\pi$
$264$	0	0
$265$	−17302.6	−0.0151355
$266$	658549.	0.570668
$267$	−1.54476e6	−1.32612
$268$	−423499.	−0.360177
$269$	−1.78058e6	−1.50031	−0.750156	−	0.661260i	$-0.770022\pi$
$269$	−1.78058e6	−1.50031	−0.750156	+	0.661260i	$0.770022\pi$
$270$	−271489.	−0.226644
$271$	−6207.65	−0.00513457	−0.00256728	−	0.999997i	$-0.500817\pi$
$271$	−6207.65	−0.00513457	−0.00256728	+	0.999997i	$0.500817\pi$
$272$	2.36172e6	1.93556
$273$	2.73903e6	2.22428
$274$	−2.24192e6	−1.80403
$275$	0	0
$276$	6.42569e6	5.07746
$277$	781154.	0.611699	0.305849	−	0.952080i	$-0.401060\pi$
$277$	781154.	0.611699	0.305849	+	0.952080i	$0.401060\pi$
$278$	3.38428e6	2.62636
$279$	−526557.	−0.404981
$280$	2.20461e6	1.68049
$281$	−792551.	−0.598772	−0.299386	−	0.954132i	$-0.596782\pi$
$281$	−792551.	−0.598772	−0.299386	+	0.954132i	$0.596782\pi$
$282$	4.83552e6	3.62093
$283$	2.28175e6	1.69356	0.846781	−	0.531942i	$-0.178537\pi$
$283$	2.28175e6	1.69356	0.846781	+	0.531942i	$0.178537\pi$
$284$	−2.30238e6	−1.69388
$285$	−211308.	−0.154100
$286$	0	0
$287$	2.30099e6	1.64896
$288$	4.02896e6	2.86227
$289$	−996341.	−0.701719
$290$	186276.	0.130066
$291$	2.57149e6	1.78013
$292$	−106847.	−0.0733342
$293$	1.96386e6	1.33641	0.668207	−	0.743976i	$-0.267062\pi$
$293$	1.96386e6	1.33641	0.668207	+	0.743976i	$0.267062\pi$
$294$	−1.30270e6	−0.878972
$295$	708775.	0.474191
$296$	55494.6	0.0368147
$297$	0	0
$298$	−286834.	−0.187107
$299$	−3.10843e6	−2.01078
$300$	−1.12608e6	−0.722382
$301$	3.10103e6	1.97283
$302$	1.00917e6	0.636717
$303$	−2.40101e6	−1.50240
$304$	−1.46522e6	−0.909325
$305$	−765357.	−0.471101
$306$	1.38072e6	0.842953
$307$	1.90716e6	1.15489	0.577445	−	0.816429i	$-0.304050\pi$
$307$	1.90716e6	1.15489	0.577445	+	0.816429i	$0.304050\pi$
$308$	0	0
$309$	1.65751e6	0.987553
$310$	732543.	0.432941
$311$	−1.27752e6	−0.748976	−0.374488	−	0.927232i	$-0.622181\pi$
$311$	−1.27752e6	−0.748976	−0.374488	+	0.927232i	$0.622181\pi$
$312$	−1.07189e7	−6.23397
$313$	1.74151e6	1.00477	0.502384	−	0.864645i	$-0.332456\pi$
$313$	1.74151e6	1.00477	0.502384	+	0.864645i	$0.332456\pi$
$314$	520379.	0.297848
$315$	732774.	0.416096
$316$	−5.76226e6	−3.24620
$317$	−505854.	−0.282733	−0.141367	−	0.989957i	$-0.545150\pi$
$317$	−505854.	−0.282733	−0.141367	+	0.989957i	$0.545150\pi$
$318$	−157434.	−0.0873031
$319$	0	0
$320$	−2.70182e6	−1.47497
$321$	−3.55685e6	−1.92665
$322$	5.81711e6	3.12656
$323$	−262752.	−0.140133
$324$	−5.88431e6	−3.11410
$325$	544744.	0.286078
$326$	−45091.1	−0.0234988
$327$	1.77176e6	0.916295
$328$	−9.00470e6	−4.62152
$329$	3.19107e6	1.62535
$330$	0	0
$331$	−1.33818e6	−0.671342	−0.335671	−	0.941979i	$-0.608963\pi$
$331$	−1.33818e6	−0.671342	−0.335671	+	0.941979i	$0.608963\pi$
$332$	2.97635e6	1.48197
$333$	18445.5	0.00911548
$334$	2.80935e6	1.37797
$335$	123018.	0.0598902
$336$	1.14045e7	5.51097
$337$	2.27649e6	1.09192	0.545961	−	0.837811i	$-0.316165\pi$
$337$	2.27649e6	1.09192	0.545961	+	0.837811i	$0.316165\pi$
$338$	4.22001e6	2.00919
$339$	748662.	0.353823
$340$	−1.40023e6	−0.656905
$341$	0	0
$342$	−856608.	−0.396020
$343$	1.66327e6	0.763356
$344$	−1.21356e7	−5.52924
$345$	−1.86653e6	−0.844281
$346$	128365.	0.0576441
$347$	−3.68426e6	−1.64258	−0.821289	−	0.570512i	$-0.806745\pi$
$347$	−3.68426e6	−1.64258	−0.821289	+	0.570512i	$0.806745\pi$
$348$	1.23551e6	0.546890
$349$	−60252.4	−0.0264795	−0.0132398	−	0.999912i	$-0.504214\pi$
$349$	−60252.4	−0.0264795	−0.0132398	+	0.999912i	$0.504214\pi$
$350$	−1.01943e6	−0.444823
$351$	871095.	0.377396
$352$	0	0
$353$	2.61432e6	1.11666	0.558332	−	0.829618i	$-0.311442\pi$
$353$	2.61432e6	1.11666	0.558332	+	0.829618i	$0.311442\pi$
$354$	6.44902e6	2.73518
$355$	668795.	0.281658
$356$	6.35066e6	2.65579
$357$	2.04512e6	0.849275
$358$	5.80711e6	2.39471
$359$	865420.	0.354397	0.177199	−	0.984175i	$-0.443296\pi$
$359$	865420.	0.354397	0.177199	+	0.984175i	$0.443296\pi$
$360$	−2.86764e6	−1.16619
$361$	−2.31309e6	−0.934166
$362$	728968.	0.292373
$363$	0	0
$364$	−1.12604e7	−4.45453
$365$	31036.9	0.0121940
$366$	−6.96385e6	−2.71736
$367$	1.30881e6	0.507237	0.253619	−	0.967304i	$-0.418379\pi$
$367$	1.30881e6	0.507237	0.253619	+	0.967304i	$0.418379\pi$
$368$	−1.29426e7	−4.98199
$369$	−2.99301e6	−1.14431
$370$	−25661.2	−0.00974481
$371$	−103894.	−0.0391882
$372$	4.85874e6	1.82040
$373$	−3.84707e6	−1.43172	−0.715861	−	0.698243i	$-0.753965\pi$
$373$	−3.84707e6	−1.43172	−0.715861	+	0.698243i	$0.753965\pi$
$374$	0	0
$375$	327104.	0.120118
$376$	−1.24879e7	−4.55534
$377$	−597682.	−0.216579
$378$	−1.63016e6	−0.586815
$379$	1.98853e6	0.711107	0.355553	−	0.934656i	$-0.384292\pi$
$379$	1.98853e6	0.711107	0.355553	+	0.934656i	$0.384292\pi$
$380$	868710.	0.308614
$381$	1.22979e6	0.434030
$382$	−9.60195e6	−3.36667
$383$	4.51043e6	1.57116	0.785581	−	0.618758i	$-0.212364\pi$
$383$	4.51043e6	1.57116	0.785581	+	0.618758i	$0.212364\pi$
$384$	−1.07606e7	−3.72399
$385$	0	0
$386$	−9.35673e6	−3.19636
$387$	−4.03367e6	−1.36906
$388$	−1.05717e7	−3.56504
$389$	−3.49699e6	−1.17171	−0.585855	−	0.810416i	$-0.699241\pi$
$389$	−3.49699e6	−1.17171	−0.585855	+	0.810416i	$0.699241\pi$
$390$	4.95653e6	1.65012
$391$	−2.32094e6	−0.767755
$392$	3.36427e6	1.10580
$393$	3.73699e6	1.22051
$394$	−133837.	−0.0434347
$395$	1.67382e6	0.539779
$396$	0	0
$397$	1.24286e6	0.395773	0.197886	−	0.980225i	$-0.436592\pi$
$397$	1.24286e6	0.395773	0.197886	+	0.980225i	$0.436592\pi$
$398$	−7.21584e6	−2.28338
$399$	−1.26880e6	−0.398990
$400$	2.26816e6	0.708798
$401$	2.12608e6	0.660267	0.330133	−	0.943934i	$-0.392906\pi$
$401$	2.12608e6	0.660267	0.330133	+	0.943934i	$0.392906\pi$
$402$	1.11932e6	0.345453
$403$	−2.35042e6	−0.720914
$404$	9.87080e6	3.00884
$405$	1.70927e6	0.517813
$406$	1.11850e6	0.336760
$407$	0	0
$408$	−8.00338e6	−2.38025
$409$	−3.07823e6	−0.909898	−0.454949	−	0.890518i	$-0.650342\pi$
$409$	−3.07823e6	−0.909898	−0.454949	+	0.890518i	$0.650342\pi$
$410$	4.16386e6	1.22331
$411$	4.31942e6	1.26131
$412$	−6.81421e6	−1.97775
$413$	4.25585e6	1.22775
$414$	−7.56661e6	−2.16970
$415$	−864569.	−0.246422
$416$	1.79843e7	5.09518
$417$	−6.52036e6	−1.83625
$418$	0	0
$419$	3.45869e6	0.962446	0.481223	−	0.876598i	$-0.340193\pi$
$419$	3.45869e6	0.962446	0.481223	+	0.876598i	$0.340193\pi$
$420$	−6.76158e6	−1.87036
$421$	6.84842e6	1.88315	0.941576	−	0.336800i	$-0.109345\pi$
$421$	6.84842e6	1.88315	0.941576	+	0.336800i	$0.109345\pi$
$422$	−1.23652e7	−3.38003
$423$	−4.15078e6	−1.12792
$424$	406579.	0.109832
$425$	406738.	0.109230
$426$	6.08525e6	1.62463
$427$	−4.59560e6	−1.21975
$428$	1.46226e7	3.85847
$429$	0	0
$430$	5.61162e6	1.46358
$431$	−584938.	−0.151676	−0.0758379	−	0.997120i	$-0.524163\pi$
$431$	−584938.	−0.151676	−0.0758379	+	0.997120i	$0.524163\pi$
$432$	3.62699e6	0.935054
$433$	1.88418e6	0.482951	0.241475	−	0.970407i	$-0.422369\pi$
$433$	1.88418e6	0.482951	0.241475	+	0.970407i	$0.422369\pi$
$434$	4.39857e6	1.12095
$435$	−358892.	−0.0909369
$436$	−7.28390e6	−1.83505
$437$	1.43992e6	0.360691
$438$	282400.	0.0703362
$439$	−4.45783e6	−1.10398	−0.551991	−	0.833850i	$-0.686132\pi$
$439$	−4.45783e6	−1.10398	−0.551991	+	0.833850i	$0.686132\pi$
$440$	0	0
$441$	1.11823e6	0.273800
$442$	6.16322e6	1.50055
$443$	7.54878e6	1.82754	0.913772	−	0.406228i	$-0.133156\pi$
$443$	7.54878e6	1.82754	0.913772	+	0.406228i	$0.133156\pi$
$444$	−170203.	−0.0409742
$445$	−1.84474e6	−0.441605
$446$	−1.57334e6	−0.374528
$447$	552632.	0.130818
$448$	−1.62231e7	−3.81891
$449$	−974601.	−0.228145	−0.114073	−	0.993472i	$-0.536390\pi$
$449$	−974601.	−0.228145	−0.114073	+	0.993472i	$0.536390\pi$
$450$	1.32603e6	0.308689
$451$	0	0
$452$	−3.07783e6	−0.708596
$453$	−1.94433e6	−0.445168
$454$	−2.69391e6	−0.613399
$455$	3.27092e6	0.740699
$456$	4.96534e6	1.11824
$457$	−1.97927e6	−0.443317	−0.221658	−	0.975124i	$-0.571147\pi$
$457$	−1.97927e6	−0.443317	−0.221658	+	0.975124i	$0.571147\pi$
$458$	5.71208e6	1.27242
$459$	650412.	0.144098
$460$	7.67351e6	1.69083
$461$	4.23075e6	0.927182	0.463591	−	0.886049i	$-0.346561\pi$
$461$	4.23075e6	0.927182	0.463591	+	0.886049i	$0.346561\pi$
$462$	0	0
$463$	1.49642e6	0.324415	0.162207	−	0.986757i	$-0.448139\pi$
$463$	1.49642e6	0.324415	0.162207	+	0.986757i	$0.448139\pi$
$464$	−2.48857e6	−0.536606
$465$	−1.41136e6	−0.302696
$466$	−3.97225e6	−0.847367
$467$	7.17230e6	1.52183	0.760916	−	0.648851i	$-0.224750\pi$
$467$	7.17230e6	1.52183	0.760916	+	0.648851i	$0.224750\pi$
$468$	1.46470e7	3.09125
$469$	738663.	0.155065
$470$	5.77454e6	1.20579
$471$	−1.00259e6	−0.208244
$472$	−1.66549e7	−3.44101
$473$	0	0
$474$	1.52298e7	3.11349
$475$	−252342.	−0.0513164
$476$	−8.40771e6	−1.70083
$477$	135140.	0.0271949
$478$	4.79710e6	0.960306
$479$	−1.27629e6	−0.254163	−0.127081	−	0.991892i	$-0.540561\pi$
$479$	−1.27629e6	−0.254163	−0.127081	+	0.991892i	$0.540561\pi$
$480$	1.07991e7	2.13936
$481$	82336.1	0.0162266
$482$	1.41097e6	0.276630
$483$	−1.12076e7	−2.18597
$484$	0	0
$485$	3.07085e6	0.592796
$486$	1.29135e7	2.48000
$487$	−7.66808e6	−1.46509	−0.732545	−	0.680719i	$-0.761667\pi$
$487$	−7.66808e6	−1.46509	−0.732545	+	0.680719i	$0.761667\pi$
$488$	1.79844e7	3.41859
$489$	86875.3	0.0164295
$490$	−1.55567e6	−0.292703
$491$	−649153.	−0.121519	−0.0607593	−	0.998152i	$-0.519352\pi$
$491$	−649153.	−0.121519	−0.0607593	+	0.998152i	$0.519352\pi$
$492$	2.76176e7	5.14368
$493$	−446265.	−0.0826943
$494$	−3.82369e6	−0.704961
$495$	0	0
$496$	−9.78647e6	−1.78617
$497$	4.01579e6	0.729256
$498$	−7.86657e6	−1.42139
$499$	899636.	0.161739	0.0808696	−	0.996725i	$-0.474230\pi$
$499$	899636.	0.161739	0.0808696	+	0.996725i	$0.474230\pi$
$500$	−1.34476e6	−0.240558
$501$	−5.41267e6	−0.963423
$502$	−8.10072e6	−1.43471
$503$	−9.63165e6	−1.69739	−0.848693	−	0.528886i	$-0.822610\pi$
$503$	−9.63165e6	−1.69739	−0.848693	+	0.528886i	$0.822610\pi$
$504$	−1.72188e7	−3.01944
$505$	−2.86727e6	−0.500310
$506$	0	0
$507$	−8.13053e6	−1.40475
$508$	−5.05582e6	−0.869225
$509$	−4.42944e6	−0.757800	−0.378900	−	0.925438i	$-0.623698\pi$
$509$	−4.42944e6	−0.757800	−0.378900	+	0.925438i	$0.623698\pi$
$510$	3.70084e6	0.630050
$511$	186362.	0.0315722
$512$	6.66067e6	1.12290
$513$	−403518.	−0.0676971
$514$	1.52098e7	2.53931
$515$	1.97939e6	0.328861
$516$	3.72202e7	6.15396
$517$	0	0
$518$	−154083.	−0.0252308
$519$	−247315.	−0.0403026
$520$	−1.28005e7	−2.07595
$521$	−5.72201e6	−0.923537	−0.461768	−	0.887001i	$-0.652785\pi$
$521$	−5.72201e6	−0.923537	−0.461768	+	0.887001i	$0.652785\pi$
$522$	−1.45489e6	−0.233697
$523$	−4.76420e6	−0.761616	−0.380808	−	0.924654i	$-0.624354\pi$
$523$	−4.76420e6	−0.761616	−0.380808	+	0.924654i	$0.624354\pi$
$524$	−1.53632e7	−2.44429
$525$	1.96410e6	0.311004
$526$	1.56912e7	2.47282
$527$	−1.75497e6	−0.275259
$528$	0	0
$529$	6.28282e6	0.976147
$530$	−188006.	−0.0290725
$531$	−5.53580e6	−0.852009
$532$	5.21618e6	0.799049
$533$	−1.33601e7	−2.03700
$534$	−1.67849e7	−2.54722
$535$	−4.24756e6	−0.641587
$536$	−2.89069e6	−0.434599
$537$	−1.11883e7	−1.67429
$538$	−1.93474e7	−2.88182
$539$	0	0
$540$	−2.15039e6	−0.317346
$541$	6.00205e6	0.881671	0.440836	−	0.897588i	$-0.354682\pi$
$541$	6.00205e6	0.881671	0.440836	+	0.897588i	$0.354682\pi$
$542$	−67450.8	−0.00986254
$543$	−1.40448e6	−0.204416
$544$	1.34281e7	1.94544
$545$	2.11582e6	0.305132
$546$	2.97616e7	4.27242
$547$	−7.24503e6	−1.03531	−0.517657	−	0.855588i	$-0.673196\pi$
$547$	−7.24503e6	−1.03531	−0.517657	+	0.855588i	$0.673196\pi$
$548$	−1.77576e7	−2.52600
$549$	5.97773e6	0.846458
$550$	0	0
$551$	276865.	0.0388498
$552$	4.38599e7	6.12661
$553$	1.00505e7	1.39757
$554$	8.48783e6	1.17496
$555$	49440.6	0.00681320
$556$	2.68059e7	3.67742
$557$	−3.61977e6	−0.494360	−0.247180	−	0.968970i	$-0.579504\pi$
$557$	−3.61977e6	−0.494360	−0.247180	+	0.968970i	$0.579504\pi$
$558$	−5.72144e6	−0.777893
$559$	−1.80053e7	−2.43709
$560$	1.36192e7	1.83519
$561$	0	0
$562$	−8.61167e6	−1.15013
$563$	−86116.5	−0.0114503	−0.00572513	−	0.999984i	$-0.501822\pi$
$563$	−86116.5	−0.0114503	−0.00572513	+	0.999984i	$0.501822\pi$
$564$	3.83008e7	5.07003
$565$	894046.	0.117825
$566$	2.47929e7	3.25301
$567$	1.02633e7	1.34070
$568$	−1.57154e7	−2.04388
$569$	−4.89811e6	−0.634231	−0.317116	−	0.948387i	$-0.602714\pi$
$569$	−4.89811e6	−0.634231	−0.317116	+	0.948387i	$0.602714\pi$
$570$	−2.29602e6	−0.295998
$571$	4.12939e6	0.530024	0.265012	−	0.964245i	$-0.414624\pi$
$571$	4.12939e6	0.530024	0.265012	+	0.964245i	$0.414624\pi$
$572$	0	0
$573$	1.84997e7	2.35385
$574$	2.50020e7	3.16734
$575$	−2.22900e6	−0.281151
$576$	2.11023e7	2.65016
$577$	−6.75382e6	−0.844520	−0.422260	−	0.906475i	$-0.638763\pi$
$577$	−6.75382e6	−0.844520	−0.422260	+	0.906475i	$0.638763\pi$
$578$	−1.08260e7	−1.34787
$579$	1.80273e7	2.23477
$580$	1.47544e6	0.182118
$581$	−5.19132e6	−0.638024
$582$	2.79412e7	3.41930
$583$	0	0
$584$	−729309.	−0.0884870
$585$	−4.25466e6	−0.514014
$586$	2.13388e7	2.56700
$587$	3.65329e6	0.437612	0.218806	−	0.975768i	$-0.429784\pi$
$587$	3.65329e6	0.437612	0.218806	+	0.975768i	$0.429784\pi$
$588$	−1.03183e7	−1.23074
$589$	1.08879e6	0.129317
$590$	7.70138e6	0.910832
$591$	257860.	0.0303679
$592$	342824.	0.0402037
$593$	−9.86114e6	−1.15157	−0.575785	−	0.817601i	$-0.695304\pi$
$593$	−9.86114e6	−1.15157	−0.575785	+	0.817601i	$0.695304\pi$
$594$	0	0
$595$	2.44227e6	0.282814
$596$	−2.27193e6	−0.261987
$597$	1.39025e7	1.59646
$598$	−3.37755e7	−3.86232
$599$	−1.31890e6	−0.150192	−0.0750959	−	0.997176i	$-0.523926\pi$
$599$	−1.31890e6	−0.150192	−0.0750959	+	0.997176i	$0.523926\pi$
$600$	−7.68632e6	−0.871646
$601$	−1.41061e6	−0.159302	−0.0796510	−	0.996823i	$-0.525381\pi$
$601$	−1.41061e6	−0.159302	−0.0796510	+	0.996823i	$0.525381\pi$
$602$	3.36951e7	3.78944
$603$	−960816.	−0.107609
$604$	7.99334e6	0.891530
$605$	0	0
$606$	−2.60888e7	−2.88584
$607$	−2.20277e6	−0.242660	−0.121330	−	0.992612i	$-0.538716\pi$
$607$	−2.20277e6	−0.242660	−0.121330	+	0.992612i	$0.538716\pi$
$608$	−8.33088e6	−0.913969
$609$	−2.15497e6	−0.235450
$610$	−8.31618e6	−0.904897
$611$	−1.85281e7	−2.00783
$612$	1.09363e7	1.18030
$613$	−6.53943e6	−0.702892	−0.351446	−	0.936208i	$-0.614310\pi$
$613$	−6.53943e6	−0.702892	−0.351446	+	0.936208i	$0.614310\pi$
$614$	2.07227e7	2.21833
$615$	−8.02236e6	−0.855291
$616$	0	0
$617$	5.87322e6	0.621103	0.310551	−	0.950557i	$-0.399486\pi$
$617$	5.87322e6	0.621103	0.310551	+	0.950557i	$0.399486\pi$
$618$	1.80101e7	1.89690
$619$	−1.08700e7	−1.14026	−0.570129	−	0.821555i	$-0.693107\pi$
$619$	−1.08700e7	−1.14026	−0.570129	+	0.821555i	$0.693107\pi$
$620$	5.80227e6	0.606204
$621$	−3.56437e6	−0.370897
$622$	−1.38812e7	−1.43864
$623$	−1.10767e7	−1.14338
$624$	−6.62172e7	−6.80784
$625$	390625.	0.0400000
$626$	1.89228e7	1.92997
$627$	0	0
$628$	4.12177e6	0.417047
$629$	61477.1	0.00619564
$630$	7.96214e6	0.799242
$631$	9.68665e6	0.968501	0.484251	−	0.874929i	$-0.339092\pi$
$631$	9.68665e6	0.968501	0.484251	+	0.874929i	$0.339092\pi$
$632$	−3.93316e7	−3.91695
$633$	2.38236e7	2.36318
$634$	−5.49648e6	−0.543077
$635$	1.46861e6	0.144535
$636$	−1.24699e6	−0.122242
$637$	4.99149e6	0.487396
$638$	0	0
$639$	−5.22354e6	−0.506073
$640$	−1.28502e7	−1.24011
$641$	−1.06690e6	−0.102560	−0.0512801	−	0.998684i	$-0.516330\pi$
$641$	−1.06690e6	−0.102560	−0.0512801	+	0.998684i	$0.516330\pi$
$642$	−3.86478e7	−3.70073
$643$	1.70562e7	1.62688	0.813440	−	0.581649i	$-0.197592\pi$
$643$	1.70562e7	1.62688	0.813440	+	0.581649i	$0.197592\pi$
$644$	4.60757e7	4.37781
$645$	−1.08117e7	−1.02328
$646$	−2.85499e6	−0.269168
$647$	1.63618e7	1.53663	0.768316	−	0.640070i	$-0.221095\pi$
$647$	1.63618e7	1.53663	0.768316	+	0.640070i	$0.221095\pi$
$648$	−4.01646e7	−3.75756
$649$	0	0
$650$	5.91905e6	0.549502
$651$	−8.47456e6	−0.783727
$652$	−357154.	−0.0329031
$653$	9.66423e6	0.886920	0.443460	−	0.896294i	$-0.353751\pi$
$653$	9.66423e6	0.886920	0.443460	+	0.896294i	$0.353751\pi$
$654$	1.92515e7	1.76003
$655$	4.46269e6	0.406437
$656$	−5.56274e7	−5.04695
$657$	−242410.	−0.0219098
$658$	3.46733e7	3.12199
$659$	−2.09239e7	−1.87684	−0.938422	−	0.345490i	$-0.887713\pi$
$659$	−2.09239e7	−1.87684	−0.938422	+	0.345490i	$0.887713\pi$
$660$	0	0
$661$	−4.95730e6	−0.441308	−0.220654	−	0.975352i	$-0.570819\pi$
$661$	−4.95730e6	−0.441308	−0.220654	+	0.975352i	$0.570819\pi$
$662$	−1.45403e7	−1.28952
$663$	−1.18744e7	−1.04913
$664$	2.03157e7	1.78818
$665$	−1.51519e6	−0.132866
$666$	200424.	0.0175091
$667$	2.44561e6	0.212849
$668$	2.22521e7	1.92943
$669$	3.03129e6	0.261856
$670$	1.33668e6	0.115038
$671$	0	0
$672$	6.48431e7	5.53912
$673$	−64946.6	−0.00552737	−0.00276369	−	0.999996i	$-0.500880\pi$
$673$	−64946.6	−0.00552737	−0.00276369	+	0.999996i	$0.500880\pi$
$674$	2.47358e7	2.09738
$675$	624645.	0.0527684
$676$	3.34255e7	2.81327
$677$	−1.34416e7	−1.12714	−0.563571	−	0.826068i	$-0.690573\pi$
$677$	−1.34416e7	−1.12714	−0.563571	+	0.826068i	$0.690573\pi$
$678$	8.13478e6	0.679628
$679$	1.84390e7	1.53484
$680$	−9.55758e6	−0.792639
$681$	5.19025e6	0.428865
$682$	0	0
$683$	2.24331e7	1.84008	0.920040	−	0.391823i	$-0.128156\pi$
$683$	2.24331e7	1.84008	0.920040	+	0.391823i	$0.128156\pi$
$684$	−6.78495e6	−0.554506
$685$	5.15822e6	0.420023
$686$	1.80727e7	1.46626
$687$	−1.10053e7	−0.889627
$688$	−7.49689e7	−6.03824
$689$	603232.	0.0484101
$690$	−2.02813e7	−1.62171
$691$	−7.31560e6	−0.582847	−0.291424	−	0.956594i	$-0.594129\pi$
$691$	−7.31560e6	−0.582847	−0.291424	+	0.956594i	$0.594129\pi$
$692$	1.01674e6	0.0807132
$693$	0	0
$694$	−4.00322e7	−3.15508
$695$	−7.78657e6	−0.611482
$696$	8.43327e6	0.659892
$697$	−9.97542e6	−0.777767
$698$	−654687.	−0.0508622
$699$	7.65319e6	0.592447
$700$	−8.07463e6	−0.622841
$701$	−1.38947e6	−0.106796	−0.0533981	−	0.998573i	$-0.517005\pi$
$701$	−1.38947e6	−0.106796	−0.0533981	+	0.998573i	$0.517005\pi$
$702$	9.46510e6	0.724908
$703$	−38140.6	−0.00291072
$704$	0	0
$705$	−1.11256e7	−0.843045
$706$	2.84066e7	2.14490
$707$	−1.72165e7	−1.29538
$708$	5.10809e7	3.82980
$709$	−1.87207e6	−0.139864	−0.0699322	−	0.997552i	$-0.522278\pi$
$709$	−1.87207e6	−0.139864	−0.0699322	+	0.997552i	$0.522278\pi$
$710$	7.26697e6	0.541012
$711$	−1.30732e7	−0.969854
$712$	4.33478e7	3.20455
$713$	9.61751e6	0.708498
$714$	2.22218e7	1.63130
$715$	0	0
$716$	4.59965e7	3.35307
$717$	−9.24241e6	−0.671409
$718$	9.40344e6	0.680731
$719$	−5.62171e6	−0.405552	−0.202776	−	0.979225i	$-0.564996\pi$
$719$	−5.62171e6	−0.405552	−0.202776	+	0.979225i	$0.564996\pi$
$720$	−1.77151e7	−1.27354
$721$	1.18853e7	0.851472
$722$	−2.51334e7	−1.79436
$723$	−2.71846e6	−0.193409
$724$	5.77396e6	0.409380
$725$	−428586.	−0.0302826
$726$	0	0
$727$	−9.85889e6	−0.691818	−0.345909	−	0.938268i	$-0.612429\pi$
$727$	−9.85889e6	−0.691818	−0.345909	+	0.938268i	$0.612429\pi$
$728$	−7.68605e7	−5.37495
$729$	−8.26581e6	−0.576059
$730$	337240.	0.0234224
$731$	−1.34439e7	−0.930530
$732$	−5.51587e7	−3.80484
$733$	6.60728e6	0.454216	0.227108	−	0.973870i	$-0.427073\pi$
$733$	6.60728e6	0.454216	0.227108	+	0.973870i	$0.427073\pi$
$734$	1.42212e7	0.974307
$735$	2.99725e6	0.204647
$736$	−7.35885e7	−5.00743
$737$	0	0
$738$	−3.25213e7	−2.19800
$739$	1.10206e7	0.742324	0.371162	−	0.928568i	$-0.378959\pi$
$739$	1.10206e7	0.742324	0.371162	+	0.928568i	$0.378959\pi$
$740$	−203256.	−0.0136447
$741$	7.36696e6	0.492882
$742$	−1.12888e6	−0.0752731
$743$	1.42654e7	0.948010	0.474005	−	0.880522i	$-0.342808\pi$
$743$	1.42654e7	0.948010	0.474005	+	0.880522i	$0.342808\pi$
$744$	3.31644e7	2.19654
$745$	659949.	0.0435632
$746$	−4.18014e7	−2.75007
$747$	6.75261e6	0.442762
$748$	0	0
$749$	−2.55046e7	−1.66117
$750$	3.55423e6	0.230724
$751$	−1.21939e7	−0.788941	−0.394470	−	0.918909i	$-0.629072\pi$
$751$	−1.21939e7	−0.788941	−0.394470	+	0.918909i	$0.629072\pi$
$752$	−7.71455e7	−4.97469
$753$	1.56074e7	1.00309
$754$	−6.49426e6	−0.416008
$755$	−2.32190e6	−0.148244
$756$	−1.29121e7	−0.821658
$757$	−2.69916e7	−1.71194	−0.855969	−	0.517026i	$-0.827039\pi$
$757$	−2.69916e7	−1.71194	−0.855969	+	0.517026i	$0.827039\pi$
$758$	2.16069e7	1.36590
$759$	0	0
$760$	5.92957e6	0.372382
$761$	−1.41491e7	−0.885658	−0.442829	−	0.896606i	$-0.646025\pi$
$761$	−1.41491e7	−0.885658	−0.442829	+	0.896606i	$0.646025\pi$
$762$	1.33626e7	0.833691
$763$	1.27045e7	0.790034
$764$	−7.60543e7	−4.71401
$765$	−3.17678e6	−0.196261
$766$	4.90092e7	3.01791
$767$	−2.47105e7	−1.51668
$768$	−4.45232e7	−2.72385
$769$	1.34923e7	0.822755	0.411377	−	0.911465i	$-0.365048\pi$
$769$	1.34923e7	0.822755	0.411377	+	0.911465i	$0.365048\pi$
$770$	0	0
$771$	−2.93041e7	−1.77539
$772$	−7.41120e7	−4.47554
$773$	1.93885e7	1.16707	0.583533	−	0.812090i	$-0.301670\pi$
$773$	1.93885e7	1.16707	0.583533	+	0.812090i	$0.301670\pi$
$774$	−4.38289e7	−2.62971
$775$	−1.68544e6	−0.100800
$776$	−7.21593e7	−4.30168
$777$	296867.	0.0176404
$778$	−3.79974e7	−2.25064
$779$	6.18880e6	0.365395
$780$	3.92593e7	2.31050
$781$	0	0
$782$	−2.52188e7	−1.47471
$783$	−685348.	−0.0399490
$784$	2.07831e7	1.20759
$785$	−1.19729e6	−0.0693466
$786$	4.06052e7	2.34437
$787$	−1.73832e7	−1.00044	−0.500222	−	0.865897i	$-0.666748\pi$
$787$	−1.73832e7	−1.00044	−0.500222	+	0.865897i	$0.666748\pi$
$788$	−1.06009e6	−0.0608172
$789$	−3.02317e7	−1.72890
$790$	1.81873e7	1.03681
$791$	5.36832e6	0.305068
$792$	0	0
$793$	2.66831e7	1.50679
$794$	1.35046e7	0.760205
$795$	362224.	0.0203264
$796$	−5.71546e7	−3.19719
$797$	−2.97383e6	−0.165833	−0.0829163	−	0.996557i	$-0.526423\pi$
$797$	−2.97383e6	−0.165833	−0.0829163	+	0.996557i	$0.526423\pi$
$798$	−1.37865e7	−0.766384
$799$	−1.38342e7	−0.766630
$800$	1.28962e7	0.712419
$801$	1.44081e7	0.793460
$802$	2.31015e7	1.26825
$803$	0	0
$804$	8.86581e6	0.483702
$805$	−1.33840e7	−0.727943
$806$	−2.55391e7	−1.38474
$807$	3.72759e7	2.01486
$808$	6.73753e7	3.63055
$809$	1.31720e6	0.0707586	0.0353793	−	0.999374i	$-0.488736\pi$
$809$	1.31720e6	0.0707586	0.0353793	+	0.999374i	$0.488736\pi$
$810$	1.85725e7	0.994622
$811$	−2.49896e7	−1.33416	−0.667079	−	0.744987i	$-0.732456\pi$
$811$	−2.49896e7	−1.33416	−0.667079	+	0.744987i	$0.732456\pi$
$812$	8.85932e6	0.471531
$813$	129955.	0.00689551
$814$	0	0
$815$	103746.	0.00547112
$816$	−4.94417e7	−2.59937
$817$	8.34063e6	0.437163
$818$	−3.34473e7	−1.74774
$819$	−2.55471e7	−1.33086
$820$	3.29808e7	1.71288
$821$	−1.85221e6	−0.0959028	−0.0479514	−	0.998850i	$-0.515269\pi$
$821$	−1.85221e6	−0.0959028	−0.0479514	+	0.998850i	$0.515269\pi$
$822$	4.69337e7	2.42273
$823$	1.80264e7	0.927707	0.463853	−	0.885912i	$-0.346466\pi$
$823$	1.80264e7	0.927707	0.463853	+	0.885912i	$0.346466\pi$
$824$	−4.65119e7	−2.38641
$825$	0	0
$826$	4.62430e7	2.35828
$827$	3.22579e7	1.64011	0.820055	−	0.572285i	$-0.193943\pi$
$827$	3.22579e7	1.64011	0.820055	+	0.572285i	$0.193943\pi$
$828$	−5.99330e7	−3.03802
$829$	2.40335e7	1.21459	0.607297	−	0.794475i	$-0.292254\pi$
$829$	2.40335e7	1.21459	0.607297	+	0.794475i	$0.292254\pi$
$830$	−9.39419e6	−0.473330
$831$	−1.63532e7	−0.821486
$832$	9.41953e7	4.71760
$833$	3.72695e6	0.186097
$834$	−7.08486e7	−3.52709
$835$	−6.46377e6	−0.320826
$836$	0	0
$837$	−2.69517e6	−0.132976
$838$	3.75813e7	1.84868
$839$	−465951.	−0.0228526	−0.0114263	−	0.999935i	$-0.503637\pi$
$839$	−465951.	−0.0228526	−0.0114263	+	0.999935i	$0.503637\pi$
$840$	−4.61526e7	−2.25683
$841$	−2.00409e7	−0.977074
$842$	7.44133e7	3.61718
$843$	1.65918e7	0.804126
$844$	−9.79413e7	−4.73271
$845$	−9.70942e6	−0.467791
$846$	−4.51014e7	−2.16653
$847$	0	0
$848$	2.51168e6	0.119943
$849$	−4.77675e7	−2.27438
$850$	4.41952e6	0.209811
$851$	−336905.	−0.0159472
$852$	4.81996e7	2.27481
$853$	1.42564e7	0.670870	0.335435	−	0.942063i	$-0.391117\pi$
$853$	1.42564e7	0.670870	0.335435	+	0.942063i	$0.391117\pi$
$854$	−4.99346e7	−2.34292
$855$	1.97089e6	0.0922034
$856$	9.98097e7	4.65573
$857$	−9.63660e6	−0.448200	−0.224100	−	0.974566i	$-0.571944\pi$
$857$	−9.63660e6	−0.448200	−0.224100	+	0.974566i	$0.571944\pi$
$858$	0	0
$859$	3.59880e7	1.66408	0.832040	−	0.554715i	$-0.187173\pi$
$859$	3.59880e7	1.66408	0.832040	+	0.554715i	$0.187173\pi$
$860$	4.44481e7	2.04931
$861$	−4.81704e7	−2.21448
$862$	−6.35579e6	−0.291341
$863$	−1.08792e7	−0.497246	−0.248623	−	0.968600i	$-0.579978\pi$
$863$	−1.08792e7	−0.497246	−0.248623	+	0.968600i	$0.579978\pi$
$864$	2.06221e7	0.939830
$865$	−295342.	−0.0134210
$866$	2.04731e7	0.927658
$867$	2.08580e7	0.942379
$868$	3.48398e7	1.56956
$869$	0	0
$870$	−3.89963e6	−0.174673
$871$	−4.28885e6	−0.191556
$872$	−4.97178e7	−2.21422
$873$	−2.39845e7	−1.06511
$874$	1.56459e7	0.692820
$875$	2.34551e6	0.103566
$876$	2.23681e6	0.0984847
$877$	−2.75771e7	−1.21074	−0.605368	−	0.795946i	$-0.706974\pi$
$877$	−2.75771e7	−1.21074	−0.605368	+	0.795946i	$0.706974\pi$
$878$	−4.84377e7	−2.12054
$879$	−4.11126e7	−1.79475
$880$	0	0
$881$	−4.51614e7	−1.96032	−0.980162	−	0.198199i	$-0.936491\pi$
$881$	−4.51614e7	−1.96032	−0.980162	+	0.198199i	$0.936491\pi$
$882$	1.21504e7	0.525918
$883$	2.40879e7	1.03968	0.519838	−	0.854265i	$-0.325992\pi$
$883$	2.40879e7	1.03968	0.519838	+	0.854265i	$0.325992\pi$
$884$	4.88171e7	2.10107
$885$	−1.48380e7	−0.636819
$886$	8.20232e7	3.51037
$887$	6.56722e6	0.280267	0.140134	−	0.990133i	$-0.455247\pi$
$887$	6.56722e6	0.280267	0.140134	+	0.990133i	$0.455247\pi$
$888$	−1.16176e6	−0.0494406
$889$	8.81830e6	0.374223
$890$	−2.00444e7	−0.848241
$891$	0	0
$892$	−1.24619e7	−0.524413
$893$	8.58278e6	0.360163
$894$	6.00476e6	0.251277
$895$	−1.33610e7	−0.557548
$896$	−7.71595e7	−3.21085
$897$	6.50740e7	2.70039
$898$	−1.05898e7	−0.438224
$899$	1.84923e6	0.0763118
$900$	1.05031e7	0.432225
$901$	450409.	0.0184840
$902$	0	0
$903$	−6.49191e7	−2.64943
$904$	−2.10084e7	−0.855011
$905$	−1.67722e6	−0.0680718
$906$	−2.11266e7	−0.855084
$907$	2.04406e7	0.825041	0.412521	−	0.910948i	$-0.364648\pi$
$907$	2.04406e7	0.825041	0.412521	+	0.910948i	$0.364648\pi$
$908$	−2.13377e7	−0.858880
$909$	2.23944e7	0.898939
$910$	3.55410e7	1.42274
$911$	3.43087e6	0.136965	0.0684824	−	0.997652i	$-0.478184\pi$
$911$	3.43087e6	0.136965	0.0684824	+	0.997652i	$0.478184\pi$
$912$	3.06739e7	1.22118
$913$	0	0
$914$	−2.15062e7	−0.851528
$915$	1.60225e7	0.632670
$916$	4.52438e7	1.78164
$917$	2.67963e7	1.05233
$918$	7.06721e6	0.276784
$919$	4.02569e7	1.57236	0.786179	−	0.617998i	$-0.212056\pi$
$919$	4.02569e7	1.57236	0.786179	+	0.617998i	$0.212056\pi$
$920$	5.23772e7	2.04020
$921$	−3.99257e7	−1.55097
$922$	4.59703e7	1.78094
$923$	−2.33166e7	−0.900869
$924$	0	0
$925$	59041.6	0.00226884
$926$	1.62597e7	0.623140
$927$	−1.54598e7	−0.590886
$928$	−1.41494e7	−0.539347
$929$	−2.47212e7	−0.939790	−0.469895	−	0.882722i	$-0.655708\pi$
$929$	−2.47212e7	−0.939790	−0.469895	+	0.882722i	$0.655708\pi$
$930$	−1.53355e7	−0.581422
$931$	−2.31221e6	−0.0874287
$932$	−3.14631e7	−1.18648
$933$	2.67445e7	1.00584
$934$	7.79325e7	2.92315
$935$	0	0
$936$	9.99764e7	3.72999
$937$	−1.46333e7	−0.544493	−0.272246	−	0.962228i	$-0.587767\pi$
$937$	−1.46333e7	−0.544493	−0.272246	+	0.962228i	$0.587767\pi$
$938$	8.02613e6	0.297851
$939$	−3.64579e7	−1.34936
$940$	4.57386e7	1.68835
$941$	2.63065e7	0.968475	0.484238	−	0.874937i	$-0.339097\pi$
$941$	2.63065e7	0.968475	0.484238	+	0.874937i	$0.339097\pi$
$942$	−1.08939e7	−0.399998
$943$	5.46670e7	2.00192
$944$	−1.02887e8	−3.75778
$945$	3.75069e6	0.136625
$946$	0	0
$947$	2.69513e7	0.976574	0.488287	−	0.872683i	$-0.337622\pi$
$947$	2.69513e7	0.976574	0.488287	+	0.872683i	$0.337622\pi$
$948$	1.20631e8	4.35951
$949$	−1.08206e6	−0.0390019
$950$	−2.74189e6	−0.0985692
$951$	1.05899e7	0.379699
$952$	−5.73886e7	−2.05227
$953$	−2.66994e6	−0.0952290	−0.0476145	−	0.998866i	$-0.515162\pi$
$953$	−2.66994e6	−0.0952290	−0.0476145	+	0.998866i	$0.515162\pi$
$954$	1.46840e6	0.0522363
$955$	2.20922e7	0.783847
$956$	3.79965e7	1.34462
$957$	0	0
$958$	−1.38679e7	−0.488199
$959$	3.09726e7	1.08750
$960$	5.65617e7	1.98082
$961$	−2.13569e7	−0.745986
$962$	894644.	0.0311683
$963$	3.31751e7	1.15278
$964$	1.11759e7	0.387337
$965$	2.15280e7	0.744194
$966$	−1.21779e8	−4.19885
$967$	−3.77329e7	−1.29764	−0.648819	−	0.760943i	$-0.724737\pi$
$967$	−3.77329e7	−1.29764	−0.648819	+	0.760943i	$0.724737\pi$
$968$	0	0
$969$	5.50061e6	0.188192
$970$	3.33671e7	1.13865
$971$	4.74227e7	1.61413	0.807065	−	0.590463i	$-0.201055\pi$
$971$	4.74227e7	1.61413	0.807065	+	0.590463i	$0.201055\pi$
$972$	1.02284e8	3.47250
$973$	−4.67546e7	−1.58322
$974$	−8.33194e7	−2.81416
$975$	−1.14040e7	−0.384190
$976$	1.11101e8	3.73329
$977$	−3.75646e7	−1.25905	−0.629524	−	0.776981i	$-0.716750\pi$
$977$	−3.75646e7	−1.25905	−0.629524	+	0.776981i	$0.716750\pi$
$978$	943965.	0.0315580
$979$	0	0
$980$	−1.23220e7	−0.409843
$981$	−1.65254e7	−0.548250
$982$	−7.05353e6	−0.233415
$983$	−4.76230e7	−1.57193	−0.785965	−	0.618271i	$-0.787834\pi$
$983$	−4.76230e7	−1.57193	−0.785965	+	0.618271i	$0.787834\pi$
$984$	1.88510e8	6.20650
$985$	307934.	0.0101127
$986$	−4.84901e6	−0.158840
$987$	−6.68038e7	−2.18277
$988$	−3.02864e7	−0.987085
$989$	7.36746e7	2.39512
$990$	0	0
$991$	4.20336e7	1.35960	0.679801	−	0.733396i	$-0.262066\pi$
$991$	4.20336e7	1.35960	0.679801	+	0.733396i	$0.262066\pi$
$992$	−5.56434e7	−1.79529
$993$	2.80143e7	0.901584
$994$	4.36346e7	1.40076
$995$	1.66022e7	0.531630
$996$	−6.23089e7	−1.99022
$997$	2.59536e7	0.826912	0.413456	−	0.910524i	$-0.364322\pi$
$997$	2.59536e7	0.826912	0.413456	+	0.910524i	$0.364322\pi$
$998$	9.77522e6	0.310671
$999$	94412.8	0.00299307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.20		20
11.3	even	5		55.6.g.b.31.10	yes	40
11.4	even	5		55.6.g.b.16.10	✓	40
11.10	odd	2		605.6.a.o.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.10	✓	40	11.4	even	5
55.6.g.b.31.10	yes	40	11.3	even	5
605.6.a.o.1.1		20	11.10	odd	2
605.6.a.p.1.20		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+10.8658 q^{2} -20.9346 q^{3} +86.0646 q^{4} -25.0000 q^{5} -227.471 q^{6} -150.113 q^{7} +587.453 q^{8} +195.259 q^{9} +O(q^{10})\)	\(q+10.8658 q^{2} -20.9346 q^{3} +86.0646 q^{4} -25.0000 q^{5} -227.471 q^{6} -150.113 q^{7} +587.453 q^{8} +195.259 q^{9} -271.644 q^{10} -1801.73 q^{12} +871.590 q^{13} -1631.09 q^{14} +523.366 q^{15} +3629.05 q^{16} +650.781 q^{17} +2121.64 q^{18} -403.748 q^{19} -2151.61 q^{20} +3142.56 q^{21} -3566.39 q^{23} -12298.1 q^{24} +625.000 q^{25} +9470.49 q^{26} +999.432 q^{27} -12919.4 q^{28} -685.737 q^{29} +5686.77 q^{30} -2696.70 q^{31} +20633.9 q^{32} +7071.23 q^{34} +3752.82 q^{35} +16804.9 q^{36} +94.4665 q^{37} -4387.02 q^{38} -18246.4 q^{39} -14686.3 q^{40} -15328.4 q^{41} +34146.3 q^{42} -20658.0 q^{43} -4881.49 q^{45} -38751.6 q^{46} -21257.8 q^{47} -75972.8 q^{48} +5726.88 q^{49} +6791.10 q^{50} -13623.9 q^{51} +75013.1 q^{52} +692.105 q^{53} +10859.6 q^{54} -88184.2 q^{56} +8452.32 q^{57} -7451.05 q^{58} -28351.0 q^{59} +45043.3 q^{60} +30614.3 q^{61} -29301.7 q^{62} -29311.0 q^{63} +108073. q^{64} -21789.8 q^{65} -4920.71 q^{67} +56009.2 q^{68} +74661.2 q^{69} +40777.2 q^{70} -26751.8 q^{71} +114706. q^{72} -1241.48 q^{73} +1026.45 q^{74} -13084.2 q^{75} -34748.4 q^{76} -198261. q^{78} -66952.7 q^{79} -90726.2 q^{80} -68370.8 q^{81} -166554. q^{82} +34582.8 q^{83} +270463. q^{84} -16269.5 q^{85} -224465. q^{86} +14355.7 q^{87} +73789.4 q^{89} -53041.0 q^{90} -130837. q^{91} -306940. q^{92} +56454.6 q^{93} -230982. q^{94} +10093.7 q^{95} -431963. q^{96} -122834. q^{97} +62226.8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

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