LMFDB - Embedded newform 605.6.a.p.1.17

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			1.17
Root			$8.98229$ 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)

$f(q)$	$=$	$q+8.98229 q^{2} +23.5092 q^{3} +48.6815 q^{4} -25.0000 q^{5} +211.166 q^{6} -232.955 q^{7} +149.838 q^{8} +309.680 q^{9} +O(q^{10})$	\(q+8.98229 q^{2} +23.5092 q^{3} +48.6815 q^{4} -25.0000 q^{5} +211.166 q^{6} -232.955 q^{7} +149.838 q^{8} +309.680 q^{9} -224.557 q^{10} +1144.46 q^{12} -462.643 q^{13} -2092.47 q^{14} -587.729 q^{15} -211.920 q^{16} -154.921 q^{17} +2781.64 q^{18} -2263.23 q^{19} -1217.04 q^{20} -5476.58 q^{21} +2790.04 q^{23} +3522.57 q^{24} +625.000 q^{25} -4155.59 q^{26} +1567.60 q^{27} -11340.6 q^{28} -1620.83 q^{29} -5279.15 q^{30} -6968.54 q^{31} -6698.34 q^{32} -1391.54 q^{34} +5823.88 q^{35} +15075.7 q^{36} +2845.13 q^{37} -20329.0 q^{38} -10876.3 q^{39} -3745.95 q^{40} +11475.2 q^{41} -49192.2 q^{42} -16245.3 q^{43} -7742.01 q^{45} +25061.0 q^{46} +3990.75 q^{47} -4982.05 q^{48} +37461.0 q^{49} +5613.93 q^{50} -3642.05 q^{51} -22522.2 q^{52} +18802.7 q^{53} +14080.6 q^{54} -34905.5 q^{56} -53206.7 q^{57} -14558.8 q^{58} -6423.24 q^{59} -28611.5 q^{60} +42729.7 q^{61} -62593.4 q^{62} -72141.6 q^{63} -53385.0 q^{64} +11566.1 q^{65} +43869.0 q^{67} -7541.77 q^{68} +65591.5 q^{69} +52311.7 q^{70} -53143.8 q^{71} +46401.9 q^{72} -60573.1 q^{73} +25555.8 q^{74} +14693.2 q^{75} -110178. q^{76} -97694.5 q^{78} -34366.0 q^{79} +5297.99 q^{80} -38399.4 q^{81} +103074. q^{82} -51358.2 q^{83} -266608. q^{84} +3873.01 q^{85} -145920. q^{86} -38104.3 q^{87} -59529.5 q^{89} -69541.0 q^{90} +107775. q^{91} +135823. q^{92} -163824. q^{93} +35846.0 q^{94} +56580.8 q^{95} -157472. q^{96} +23866.3 q^{97} +336486. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.98229	1.58786	0.793930	−	0.608010i	$-0.208032\pi$
$2$	8.98229	1.58786	0.793930	+	0.608010i	$0.208032\pi$
$3$	23.5092	1.50811	0.754057	−	0.656810i	$-0.228094\pi$
$3$	23.5092	1.50811	0.754057	+	0.656810i	$0.228094\pi$
$4$	48.6815	1.52130
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	211.166	2.39467
$7$	−232.955	−1.79691	−0.898456	−	0.439063i	$-0.855310\pi$
$7$	−232.955	−1.79691	−0.898456	+	0.439063i	$0.855310\pi$
$8$	149.838	0.827746
$9$	309.680	1.27440
$10$	−224.557	−0.710112
$11$	0	0
$11$	0	0
$12$	1144.46	2.29429
$13$	−462.643	−0.759255	−0.379628	−	0.925139i	$-0.623948\pi$
$13$	−462.643	−0.759255	−0.379628	+	0.925139i	$0.623948\pi$
$14$	−2092.47	−2.85324
$15$	−587.729	−0.674449
$16$	−211.920	−0.206953
$17$	−154.921	−0.130013	−0.0650065	−	0.997885i	$-0.520707\pi$
$17$	−154.921	−0.130013	−0.0650065	+	0.997885i	$0.520707\pi$
$18$	2781.64	2.02358
$19$	−2263.23	−1.43829	−0.719143	−	0.694862i	$-0.755465\pi$
$19$	−2263.23	−1.43829	−0.719143	+	0.694862i	$0.755465\pi$
$20$	−1217.04	−0.680345
$21$	−5476.58	−2.70995
$22$	0	0
$23$	2790.04	1.09974	0.549871	−	0.835249i	$-0.314677\pi$
$23$	2790.04	1.09974	0.549871	+	0.835249i	$0.314677\pi$
$24$	3522.57	1.24833
$25$	625.000	0.200000
$26$	−4155.59	−1.20559
$27$	1567.60	0.413834
$28$	−11340.6	−2.73364
$29$	−1620.83	−0.357884	−0.178942	−	0.983860i	$-0.557267\pi$
$29$	−1620.83	−0.357884	−0.178942	+	0.983860i	$0.557267\pi$
$30$	−5279.15	−1.07093
$31$	−6968.54	−1.30238	−0.651190	−	0.758915i	$-0.725730\pi$
$31$	−6968.54	−1.30238	−0.651190	+	0.758915i	$0.725730\pi$
$32$	−6698.34	−1.15636
$33$	0	0
$34$	−1391.54	−0.206442
$35$	5823.88	0.803604
$36$	15075.7	1.93875
$37$	2845.13	0.341663	0.170832	−	0.985300i	$-0.445355\pi$
$37$	2845.13	0.341663	0.170832	+	0.985300i	$0.445355\pi$
$38$	−20329.0	−2.28379
$39$	−10876.3	−1.14504
$40$	−3745.95	−0.370179
$41$	11475.2	1.06611	0.533053	−	0.846082i	$-0.321044\pi$
$41$	11475.2	1.06611	0.533053	+	0.846082i	$0.321044\pi$
$42$	−49192.2	−4.30301
$43$	−16245.3	−1.33985	−0.669925	−	0.742429i	$-0.733674\pi$
$43$	−16245.3	−1.33985	−0.669925	+	0.742429i	$0.733674\pi$
$44$	0	0
$45$	−7742.01	−0.569931
$46$	25061.0	1.74624
$47$	3990.75	0.263518	0.131759	−	0.991282i	$-0.457938\pi$
$47$	3990.75	0.263518	0.131759	+	0.991282i	$0.457938\pi$
$48$	−4982.05	−0.312108
$49$	37461.0	2.22889
$50$	5613.93	0.317572
$51$	−3642.05	−0.196074
$52$	−22522.2	−1.15505
$53$	18802.7	0.919455	0.459727	−	0.888060i	$-0.347947\pi$
$53$	18802.7	0.919455	0.459727	+	0.888060i	$0.347947\pi$
$54$	14080.6	0.657109
$55$	0	0
$56$	−34905.5	−1.48739
$57$	−53206.7	−2.16910
$58$	−14558.8	−0.568270
$59$	−6423.24	−0.240228	−0.120114	−	0.992760i	$-0.538326\pi$
$59$	−6423.24	−0.240228	−0.120114	+	0.992760i	$0.538326\pi$
$60$	−28611.5	−1.02604
$61$	42729.7	1.47030	0.735149	−	0.677905i	$-0.237112\pi$
$61$	42729.7	1.47030	0.735149	+	0.677905i	$0.237112\pi$
$62$	−62593.4	−2.06800
$63$	−72141.6	−2.28999
$64$	−53385.0	−1.62918
$65$	11566.1	0.339549
$66$	0	0
$67$	43869.0	1.19391	0.596954	−	0.802276i	$-0.296378\pi$
$67$	43869.0	1.19391	0.596954	+	0.802276i	$0.296378\pi$
$68$	−7541.77	−0.197788
$69$	65591.5	1.65854
$70$	52311.7	1.27601
$71$	−53143.8	−1.25114	−0.625571	−	0.780167i	$-0.715134\pi$
$71$	−53143.8	−1.25114	−0.625571	+	0.780167i	$0.715134\pi$
$72$	46401.9	1.05488
$73$	−60573.1	−1.33037	−0.665186	−	0.746678i	$-0.731648\pi$
$73$	−60573.1	−1.33037	−0.665186	+	0.746678i	$0.731648\pi$
$74$	25555.8	0.542513
$75$	14693.2	0.301623
$76$	−110178.	−2.18806
$77$	0	0
$78$	−97694.5	−1.81817
$79$	−34366.0	−0.619529	−0.309765	−	0.950813i	$-0.600250\pi$
$79$	−34366.0	−0.619529	−0.309765	+	0.950813i	$0.600250\pi$
$80$	5297.99	0.0925521
$81$	−38399.4	−0.650297
$82$	103074.	1.69283
$83$	−51358.2	−0.818303	−0.409152	−	0.912466i	$-0.634175\pi$
$83$	−51358.2	−0.818303	−0.409152	+	0.912466i	$0.634175\pi$
$84$	−266608.	−4.12263
$85$	3873.01	0.0581436
$86$	−145920.	−2.12749
$87$	−38104.3	−0.539730
$88$	0	0
$89$	−59529.5	−0.796631	−0.398316	−	0.917248i	$-0.630405\pi$
$89$	−59529.5	−0.796631	−0.398316	+	0.917248i	$0.630405\pi$
$90$	−69541.0	−0.904970
$91$	107775.	1.36432
$92$	135823.	1.67303
$93$	−163824.	−1.96414
$94$	35846.0	0.418429
$95$	56580.8	0.643221
$96$	−157472.	−1.74392
$97$	23866.3	0.257547	0.128773	−	0.991674i	$-0.458896\pi$
$97$	23866.3	0.257547	0.128773	+	0.991674i	$0.458896\pi$
$98$	336486.	3.53917
$99$	0	0
$100$	30425.9	0.304259
$101$	100444.	0.979758	0.489879	−	0.871790i	$-0.337041\pi$
$101$	100444.	0.979758	0.489879	+	0.871790i	$0.337041\pi$
$102$	−32714.0	−0.311338
$103$	−91309.5	−0.848053	−0.424027	−	0.905650i	$-0.639384\pi$
$103$	−91309.5	−0.848053	−0.424027	+	0.905650i	$0.639384\pi$
$104$	−69321.5	−0.628470
$105$	136914.	1.21193
$106$	168891.	1.45996
$107$	129797.	1.09598	0.547992	−	0.836483i	$-0.315392\pi$
$107$	129797.	1.09598	0.547992	+	0.836483i	$0.315392\pi$
$108$	76313.1	0.629564
$109$	121212.	0.977188	0.488594	−	0.872511i	$-0.337510\pi$
$109$	121212.	0.977188	0.488594	+	0.872511i	$0.337510\pi$
$110$	0	0
$111$	66886.7	0.515267
$112$	49367.8	0.371876
$113$	−188446.	−1.38833	−0.694164	−	0.719817i	$-0.744226\pi$
$113$	−188446.	−1.38833	−0.694164	+	0.719817i	$0.744226\pi$
$114$	−477918.	−3.44422
$115$	−69751.0	−0.491820
$116$	−78904.4	−0.544448
$117$	−143272.	−0.967599
$118$	−57695.3	−0.381448
$119$	36089.5	0.233622
$120$	−88064.1	−0.558272
$121$	0	0
$122$	383811.	2.33463
$123$	269772.	1.60781
$124$	−339239.	−1.98131
$125$	−15625.0	−0.0894427
$126$	−647997.	−3.63619
$127$	−4072.26	−0.0224040	−0.0112020	−	0.999937i	$-0.503566\pi$
$127$	−4072.26	−0.0224040	−0.0112020	+	0.999937i	$0.503566\pi$
$128$	−265172.	−1.43055
$129$	−381913.	−2.02064
$130$	103890.	0.539156
$131$	−16319.8	−0.0830875	−0.0415437	−	0.999137i	$-0.513228\pi$
$131$	−16319.8	−0.0830875	−0.0415437	+	0.999137i	$0.513228\pi$
$132$	0	0
$133$	527231.	2.58447
$134$	394044.	1.89576
$135$	−39190.0	−0.185072
$136$	−23213.0	−0.107618
$137$	−61738.9	−0.281033	−0.140517	−	0.990078i	$-0.544876\pi$
$137$	−61738.9	−0.281033	−0.140517	+	0.990078i	$0.544876\pi$
$138$	589162.	2.63352
$139$	148046.	0.649921	0.324960	−	0.945728i	$-0.394649\pi$
$139$	148046.	0.649921	0.324960	+	0.945728i	$0.394649\pi$
$140$	283515.	1.22252
$141$	93819.1	0.397414
$142$	−477353.	−1.98664
$143$	0	0
$144$	−65627.4	−0.263742
$145$	40520.8	0.160051
$146$	−544085.	−2.11244
$147$	880677.	3.36143
$148$	138505.	0.519771
$149$	176434.	0.651054	0.325527	−	0.945533i	$-0.394458\pi$
$149$	176434.	0.651054	0.325527	+	0.945533i	$0.394458\pi$
$150$	131979.	0.478934
$151$	−162225.	−0.578994	−0.289497	−	0.957179i	$-0.593488\pi$
$151$	−162225.	−0.578994	−0.289497	+	0.957179i	$0.593488\pi$
$152$	−339118.	−1.19053
$153$	−47975.9	−0.165689
$154$	0	0
$155$	174213.	0.582442
$156$	−529477.	−1.74195
$157$	255949.	0.828714	0.414357	−	0.910115i	$-0.364007\pi$
$157$	255949.	0.828714	0.414357	+	0.910115i	$0.364007\pi$
$158$	−308686.	−0.983725
$159$	442036.	1.38664
$160$	167459.	0.517139
$161$	−649954.	−1.97614
$162$	−344914.	−1.03258
$163$	77938.6	0.229765	0.114882	−	0.993379i	$-0.463351\pi$
$163$	77938.6	0.229765	0.114882	+	0.993379i	$0.463351\pi$
$164$	558630.	1.62186
$165$	0	0
$166$	−461314.	−1.29935
$167$	−374513.	−1.03915	−0.519573	−	0.854426i	$-0.673909\pi$
$167$	−374513.	−1.03915	−0.519573	+	0.854426i	$0.673909\pi$
$168$	−820599.	−2.24315
$169$	−157254.	−0.423532
$170$	34788.5	0.0923238
$171$	−700879.	−1.83296
$172$	−790845.	−2.03831
$173$	267949.	0.680671	0.340336	−	0.940304i	$-0.389459\pi$
$173$	267949.	0.680671	0.340336	+	0.940304i	$0.389459\pi$
$174$	−342264.	−0.857015
$175$	−145597.	−0.359383
$176$	0	0
$177$	−151005.	−0.362291
$178$	−534711.	−1.26494
$179$	−47689.5	−0.111247	−0.0556237	−	0.998452i	$-0.517715\pi$
$179$	−47689.5	−0.111247	−0.0556237	+	0.998452i	$0.517715\pi$
$180$	−376893.	−0.867034
$181$	685564.	1.55543	0.777717	−	0.628615i	$-0.216378\pi$
$181$	685564.	1.55543	0.777717	+	0.628615i	$0.216378\pi$
$182$	968066.	2.16634
$183$	1.00454e6	2.21738
$184$	418054.	0.910307
$185$	−71128.3	−0.152796
$186$	−1.47152e6	−3.11877
$187$	0	0
$188$	194276.	0.400888
$189$	−365180.	−0.743623
$190$	508225.	1.02134
$191$	−746007.	−1.47965	−0.739826	−	0.672799i	$-0.765092\pi$
$191$	−746007.	−1.47965	−0.739826	+	0.672799i	$0.765092\pi$
$192$	−1.25504e6	−2.45699
$193$	−12854.7	−0.0248410	−0.0124205	−	0.999923i	$-0.503954\pi$
$193$	−12854.7	−0.0248410	−0.0124205	+	0.999923i	$0.503954\pi$
$194$	214374.	0.408948
$195$	271909.	0.512079
$196$	1.82366e6	3.39081
$197$	610189.	1.12021	0.560104	−	0.828422i	$-0.310761\pi$
$197$	610189.	1.12021	0.560104	+	0.828422i	$0.310761\pi$
$198$	0	0
$199$	766020.	1.37122	0.685610	−	0.727969i	$-0.259536\pi$
$199$	766020.	1.37122	0.685610	+	0.727969i	$0.259536\pi$
$200$	93648.8	0.165549
$201$	1.03132e6	1.80055
$202$	902213.	1.55572
$203$	377580.	0.643087
$204$	−177301.	−0.298287
$205$	−286880.	−0.476777
$206$	−820169.	−1.34659
$207$	864021.	1.40152
$208$	98043.2	0.157130
$209$	0	0
$210$	1.22980e6	1.92437
$211$	−1.13308e6	−1.75208	−0.876040	−	0.482238i	$-0.839824\pi$
$211$	−1.13308e6	−1.75208	−0.876040	+	0.482238i	$0.839824\pi$
$212$	915343.	1.39876
$213$	−1.24937e6	−1.88686
$214$	1.16587e6	1.74027
$215$	406132.	0.599199
$216$	234886.	0.342549
$217$	1.62336e6	2.34026
$218$	1.08876e6	1.55164
$219$	−1.42402e6	−2.00635
$220$	0	0
$221$	71672.9	0.0987130
$222$	600795.	0.818171
$223$	−274073.	−0.369066	−0.184533	−	0.982826i	$-0.559077\pi$
$223$	−274073.	−0.369066	−0.184533	+	0.982826i	$0.559077\pi$
$224$	1.56041e6	2.07787
$225$	193550.	0.254881
$226$	−1.69268e6	−2.20447
$227$	−525330.	−0.676656	−0.338328	−	0.941028i	$-0.609861\pi$
$227$	−525330.	−0.676656	−0.338328	+	0.941028i	$0.609861\pi$
$228$	−2.59018e6	−3.29984
$229$	−58584.9	−0.0738239	−0.0369119	−	0.999319i	$-0.511752\pi$
$229$	−58584.9	−0.0738239	−0.0369119	+	0.999319i	$0.511752\pi$
$230$	−626524.	−0.780941
$231$	0	0
$232$	−242862.	−0.296237
$233$	−1.41971e6	−1.71321	−0.856605	−	0.515973i	$-0.827431\pi$
$233$	−1.41971e6	−1.71321	−0.856605	+	0.515973i	$0.827431\pi$
$234$	−1.28691e6	−1.53641
$235$	−99768.7	−0.117849
$236$	−312693.	−0.365458
$237$	−807917.	−0.934320
$238$	324166.	0.370959
$239$	−907546.	−1.02772	−0.513859	−	0.857875i	$-0.671785\pi$
$239$	−907546.	−1.02772	−0.513859	+	0.857875i	$0.671785\pi$
$240$	124551.	0.139579
$241$	1.46429e6	1.62400	0.811998	−	0.583661i	$-0.198380\pi$
$241$	1.46429e6	1.62400	0.811998	+	0.583661i	$0.198380\pi$
$242$	0	0
$243$	−1.28366e6	−1.39456
$244$	2.08015e6	2.23676
$245$	−936526.	−0.996792
$246$	2.42317e6	2.55298
$247$	1.04707e6	1.09203
$248$	−1.04415e6	−1.07804
$249$	−1.20739e6	−1.23409
$250$	−140348.	−0.142022
$251$	−1.08612e6	−1.08817	−0.544083	−	0.839031i	$-0.683122\pi$
$251$	−1.08612e6	−1.08817	−0.544083	+	0.839031i	$0.683122\pi$
$252$	−3.51196e6	−3.48376
$253$	0	0
$254$	−36578.2	−0.0355744
$255$	91051.3	0.0876871
$256$	−673536.	−0.642334
$257$	458144.	0.432682	0.216341	−	0.976318i	$-0.430588\pi$
$257$	458144.	0.432682	0.216341	+	0.976318i	$0.430588\pi$
$258$	−3.43045e6	−3.20850
$259$	−662788.	−0.613939
$260$	563054.	0.516555
$261$	−501939.	−0.456089
$262$	−146589.	−0.131931
$263$	−841448.	−0.750132	−0.375066	−	0.926998i	$-0.622380\pi$
$263$	−841448.	−0.750132	−0.375066	+	0.926998i	$0.622380\pi$
$264$	0	0
$265$	−470067.	−0.411193
$266$	4.73574e6	4.10378
$267$	−1.39949e6	−1.20141
$268$	2.13561e6	1.81629
$269$	853344.	0.719024	0.359512	−	0.933140i	$-0.382943\pi$
$269$	853344.	0.719024	0.359512	+	0.933140i	$0.382943\pi$
$270$	−352016.	−0.293868
$271$	−1.32652e6	−1.09722	−0.548608	−	0.836080i	$-0.684842\pi$
$271$	−1.32652e6	−1.09722	−0.548608	+	0.836080i	$0.684842\pi$
$272$	32830.7	0.0269066
$273$	2.53370e6	2.05754
$274$	−554556.	−0.446241
$275$	0	0
$276$	3.19309e6	2.52313
$277$	−140375.	−0.109924	−0.0549618	−	0.998488i	$-0.517504\pi$
$277$	−140375.	−0.109924	−0.0549618	+	0.998488i	$0.517504\pi$
$278$	1.32979e6	1.03198
$279$	−2.15802e6	−1.65976
$280$	872638.	0.665180
$281$	−1.47455e6	−1.11402	−0.557010	−	0.830506i	$-0.688052\pi$
$281$	−1.47455e6	−1.11402	−0.557010	+	0.830506i	$0.688052\pi$
$282$	842710.	0.631038
$283$	−676251.	−0.501928	−0.250964	−	0.967996i	$-0.580748\pi$
$283$	−676251.	−0.501928	−0.250964	+	0.967996i	$0.580748\pi$
$284$	−2.58712e6	−1.90336
$285$	1.33017e6	0.970050
$286$	0	0
$287$	−2.67321e6	−1.91570
$288$	−2.07434e6	−1.47367
$289$	−1.39586e6	−0.983097
$290$	363969.	0.254138
$291$	561077.	0.388410
$292$	−2.94879e6	−2.02389
$293$	−964122.	−0.656089	−0.328044	−	0.944662i	$-0.606390\pi$
$293$	−964122.	−0.656089	−0.328044	+	0.944662i	$0.606390\pi$
$294$	7.91050e6	5.33747
$295$	160581.	0.107433
$296$	426309.	0.282810
$297$	0	0
$298$	1.58478e6	1.03378
$299$	−1.29079e6	−0.834985
$300$	715288.	0.458858
$301$	3.78442e6	2.40759
$302$	−1.45715e6	−0.919361
$303$	2.36134e6	1.47759
$304$	479623.	0.297657
$305$	−1.06824e6	−0.657538
$306$	−430933.	−0.263091
$307$	1.89223e6	1.14585	0.572925	−	0.819608i	$-0.305809\pi$
$307$	1.89223e6	1.14585	0.572925	+	0.819608i	$0.305809\pi$
$308$	0	0
$309$	−2.14661e6	−1.27896
$310$	1.56484e6	0.924836
$311$	1.18915e6	0.697164	0.348582	−	0.937278i	$-0.386663\pi$
$311$	1.18915e6	0.697164	0.348582	+	0.937278i	$0.386663\pi$
$312$	−1.62969e6	−0.947804
$313$	1.28524e6	0.741519	0.370760	−	0.928729i	$-0.379097\pi$
$313$	1.28524e6	0.741519	0.370760	+	0.928729i	$0.379097\pi$
$314$	2.29901e6	1.31588
$315$	1.80354e6	1.02412
$316$	−1.67299e6	−0.942488
$317$	911406.	0.509405	0.254703	−	0.967019i	$-0.418022\pi$
$317$	911406.	0.509405	0.254703	+	0.967019i	$0.418022\pi$
$318$	3.97049e6	2.20179
$319$	0	0
$320$	1.33462e6	0.728592
$321$	3.05141e6	1.65287
$322$	−5.83807e6	−3.13783
$323$	350621.	0.186996
$324$	−1.86934e6	−0.989295
$325$	−289152.	−0.151851
$326$	700067.	0.364834
$327$	2.84958e6	1.47371
$328$	1.71942e6	0.882466
$329$	−929664.	−0.473518
$330$	0	0
$331$	219870.	0.110305	0.0551527	−	0.998478i	$-0.482435\pi$
$331$	219870.	0.110305	0.0551527	+	0.998478i	$0.482435\pi$
$332$	−2.50019e6	−1.24488
$333$	881082.	0.435417
$334$	−3.36399e6	−1.65002
$335$	−1.09672e6	−0.533932
$336$	1.16059e6	0.560831
$337$	−2.77303e6	−1.33008	−0.665042	−	0.746806i	$-0.731586\pi$
$337$	−2.77303e6	−1.33008	−0.665042	+	0.746806i	$0.731586\pi$
$338$	−1.41250e6	−0.672508
$339$	−4.43022e6	−2.09375
$340$	188544.	0.0884536
$341$	0	0
$342$	−6.29549e6	−2.91048
$343$	−4.81146e6	−2.20822
$344$	−2.43416e6	−1.10906
$345$	−1.63979e6	−0.741720
$346$	2.40680e6	1.08081
$347$	1.62857e6	0.726079	0.363040	−	0.931774i	$-0.381739\pi$
$347$	1.62857e6	0.726079	0.363040	+	0.931774i	$0.381739\pi$
$348$	−1.85498e6	−0.821089
$349$	3.50001e6	1.53817	0.769087	−	0.639144i	$-0.220711\pi$
$349$	3.50001e6	1.53817	0.769087	+	0.639144i	$0.220711\pi$
$350$	−1.30779e6	−0.570649
$351$	−725239.	−0.314205
$352$	0	0
$353$	−626859.	−0.267752	−0.133876	−	0.990998i	$-0.542742\pi$
$353$	−626859.	−0.267752	−0.133876	+	0.990998i	$0.542742\pi$
$354$	−1.35637e6	−0.575267
$355$	1.32859e6	0.559528
$356$	−2.89799e6	−1.21191
$357$	848434.	0.352328
$358$	−428360.	−0.176645
$359$	−3.38152e6	−1.38476	−0.692381	−	0.721532i	$-0.743438\pi$
$359$	−3.38152e6	−1.38476	−0.692381	+	0.721532i	$0.743438\pi$
$360$	−1.16005e6	−0.471758
$361$	2.64612e6	1.06866
$362$	6.15793e6	2.46981
$363$	0	0
$364$	5.24665e6	2.07553
$365$	1.51433e6	0.594960
$366$	9.02307e6	3.52088
$367$	−1.02453e6	−0.397064	−0.198532	−	0.980094i	$-0.563617\pi$
$367$	−1.02453e6	−0.397064	−0.198532	+	0.980094i	$0.563617\pi$
$368$	−591265.	−0.227595
$369$	3.55365e6	1.35865
$370$	−638895.	−0.242619
$371$	−4.38018e6	−1.65218
$372$	−7.97522e6	−2.98803
$373$	−1.80401e6	−0.671379	−0.335689	−	0.941973i	$-0.608969\pi$
$373$	−1.80401e6	−0.671379	−0.335689	+	0.941973i	$0.608969\pi$
$374$	0	0
$375$	−367331.	−0.134890
$376$	597966.	0.218126
$377$	749866.	0.271725
$378$	−3.28015e6	−1.18077
$379$	−3.64434e6	−1.30323	−0.651615	−	0.758550i	$-0.725908\pi$
$379$	−3.64434e6	−1.30323	−0.651615	+	0.758550i	$0.725908\pi$
$380$	2.75444e6	0.978530
$381$	−95735.4	−0.0337878
$382$	−6.70085e6	−2.34948
$383$	2.55518e6	0.890070	0.445035	−	0.895513i	$-0.353191\pi$
$383$	2.55518e6	0.890070	0.445035	+	0.895513i	$0.353191\pi$
$384$	−6.23398e6	−2.15743
$385$	0	0
$386$	−115465.	−0.0394441
$387$	−5.03084e6	−1.70751
$388$	1.16185e6	0.391805
$389$	4.98926e6	1.67172	0.835858	−	0.548946i	$-0.184971\pi$
$389$	4.98926e6	1.67172	0.835858	+	0.548946i	$0.184971\pi$
$390$	2.44236e6	0.813109
$391$	−432235.	−0.142981
$392$	5.61309e6	1.84496
$393$	−383664.	−0.125305
$394$	5.48090e6	1.77873
$395$	859151.	0.277062
$396$	0	0
$397$	−3.32827e6	−1.05984	−0.529922	−	0.848046i	$-0.677779\pi$
$397$	−3.32827e6	−1.05984	−0.529922	+	0.848046i	$0.677779\pi$
$398$	6.88061e6	2.17730
$399$	1.23948e7	3.89768
$400$	−132450.	−0.0413906
$401$	−1.41300e6	−0.438814	−0.219407	−	0.975633i	$-0.570412\pi$
$401$	−1.41300e6	−0.438814	−0.219407	+	0.975633i	$0.570412\pi$
$402$	9.26364e6	2.85902
$403$	3.22395e6	0.988838
$404$	4.88975e6	1.49050
$405$	959985.	0.290822
$406$	3.39154e6	1.02113
$407$	0	0
$408$	−545718.	−0.162300
$409$	−5.01452e6	−1.48225	−0.741125	−	0.671367i	$-0.765707\pi$
$409$	−5.01452e6	−1.48225	−0.741125	+	0.671367i	$0.765707\pi$
$410$	−2.57684e6	−0.757055
$411$	−1.45143e6	−0.423830
$412$	−4.44508e6	−1.29014
$413$	1.49632e6	0.431669
$414$	7.76089e6	2.22541
$415$	1.28395e6	0.365956
$416$	3.09894e6	0.877971
$417$	3.48044e6	0.980154
$418$	0	0
$419$	1.86241e6	0.518252	0.259126	−	0.965844i	$-0.416566\pi$
$419$	1.86241e6	0.518252	0.259126	+	0.965844i	$0.416566\pi$
$420$	6.66520e6	1.84370
$421$	2.08177e6	0.572435	0.286218	−	0.958165i	$-0.407602\pi$
$421$	2.08177e6	0.572435	0.286218	+	0.958165i	$0.407602\pi$
$422$	−1.01776e7	−2.78206
$423$	1.23586e6	0.335828
$424$	2.81736e6	0.761075
$425$	−96825.4	−0.0260026
$426$	−1.12222e7	−2.99607
$427$	−9.95411e6	−2.64200
$428$	6.31870e6	1.66732
$429$	0	0
$430$	3.64799e6	0.951444
$431$	470131.	0.121906	0.0609531	−	0.998141i	$-0.480586\pi$
$431$	470131.	0.121906	0.0609531	+	0.998141i	$0.480586\pi$
$432$	−332205.	−0.0856440
$433$	773175.	0.198179	0.0990896	−	0.995079i	$-0.468407\pi$
$433$	773175.	0.198179	0.0990896	+	0.995079i	$0.468407\pi$
$434$	1.45815e7	3.71601
$435$	952609.	0.241375
$436$	5.90076e6	1.48659
$437$	−6.31451e6	−1.58174
$438$	−1.27910e7	−3.18580
$439$	1.06179e6	0.262951	0.131476	−	0.991319i	$-0.458028\pi$
$439$	1.06179e6	0.262951	0.131476	+	0.991319i	$0.458028\pi$
$440$	0	0
$441$	1.16009e7	2.84051
$442$	643787.	0.156742
$443$	−1.88015e6	−0.455180	−0.227590	−	0.973757i	$-0.573085\pi$
$443$	−1.88015e6	−0.455180	−0.227590	+	0.973757i	$0.573085\pi$
$444$	3.25614e6	0.783874
$445$	1.48824e6	0.356264
$446$	−2.46180e6	−0.586025
$447$	4.14782e6	0.981862
$448$	1.24363e7	2.92750
$449$	−5.82845e6	−1.36439	−0.682193	−	0.731172i	$-0.738974\pi$
$449$	−5.82845e6	−1.36439	−0.682193	+	0.731172i	$0.738974\pi$
$450$	1.73852e6	0.404715
$451$	0	0
$452$	−9.17386e6	−2.11206
$453$	−3.81376e6	−0.873189
$454$	−4.71867e6	−1.07443
$455$	−2.69438e6	−0.610140
$456$	−7.97238e6	−1.79546
$457$	−4.33894e6	−0.971836	−0.485918	−	0.874005i	$-0.661515\pi$
$457$	−4.33894e6	−0.971836	−0.485918	+	0.874005i	$0.661515\pi$
$458$	−526226.	−0.117222
$459$	−242853.	−0.0538037
$460$	−3.39558e6	−0.748204
$461$	3.56035e6	0.780262	0.390131	−	0.920759i	$-0.372430\pi$
$461$	3.56035e6	0.780262	0.390131	+	0.920759i	$0.372430\pi$
$462$	0	0
$463$	−3.86588e6	−0.838099	−0.419050	−	0.907963i	$-0.637637\pi$
$463$	−3.86588e6	−0.838099	−0.419050	+	0.907963i	$0.637637\pi$
$464$	343486.	0.0740652
$465$	4.09561e6	0.878388
$466$	−1.27523e7	−2.72034
$467$	−822913.	−0.174607	−0.0873035	−	0.996182i	$-0.527825\pi$
$467$	−822913.	−0.174607	−0.0873035	+	0.996182i	$0.527825\pi$
$468$	−6.97467e6	−1.47200
$469$	−1.02195e7	−2.14535
$470$	−896151.	−0.187127
$471$	6.01715e6	1.24979
$472$	−962445.	−0.198848
$473$	0	0
$474$	−7.25694e6	−1.48357
$475$	−1.41452e6	−0.287657
$476$	1.75689e6	0.355408
$477$	5.82283e6	1.17176
$478$	−8.15184e6	−1.63187
$479$	1.37321e6	0.273463	0.136731	−	0.990608i	$-0.456340\pi$
$479$	1.37321e6	0.273463	0.136731	+	0.990608i	$0.456340\pi$
$480$	3.93681e6	0.779904
$481$	−1.31628e6	−0.259410
$482$	1.31527e7	2.57868
$483$	−1.52799e7	−2.98024
$484$	0	0
$485$	−596658.	−0.115178
$486$	−1.15302e7	−2.21436
$487$	6.86918e6	1.31245	0.656224	−	0.754566i	$-0.272153\pi$
$487$	6.86918e6	1.31245	0.656224	+	0.754566i	$0.272153\pi$
$488$	6.40254e6	1.21703
$489$	1.83227e6	0.346511
$490$	−8.41214e6	−1.58277
$491$	5.44313e6	1.01893	0.509466	−	0.860491i	$-0.329843\pi$
$491$	5.44313e6	1.01893	0.509466	+	0.860491i	$0.329843\pi$
$492$	1.31329e7	2.44596
$493$	251100.	0.0465296
$494$	9.40507e6	1.73398
$495$	0	0
$496$	1.47677e6	0.269531
$497$	1.23801e7	2.24819
$498$	−1.08451e7	−1.95957
$499$	−7.72891e6	−1.38953	−0.694764	−	0.719238i	$-0.744491\pi$
$499$	−7.72891e6	−1.38953	−0.694764	+	0.719238i	$0.744491\pi$
$500$	−760648.	−0.136069
$501$	−8.80449e6	−1.56715
$502$	−9.75588e6	−1.72785
$503$	6.67639e6	1.17658	0.588291	−	0.808650i	$-0.299801\pi$
$503$	6.67639e6	1.17658	0.588291	+	0.808650i	$0.299801\pi$
$504$	−1.08096e7	−1.89553
$505$	−2.51109e6	−0.438161
$506$	0	0
$507$	−3.69692e6	−0.638733
$508$	−198244.	−0.0340832
$509$	−8.38953e6	−1.43530	−0.717651	−	0.696403i	$-0.754783\pi$
$509$	−8.38953e6	−1.43530	−0.717651	+	0.696403i	$0.754783\pi$
$510$	817849.	0.139235
$511$	1.41108e7	2.39056
$512$	2.43563e6	0.410616
$513$	−3.54784e6	−0.595211
$514$	4.11518e6	0.687039
$515$	2.28274e6	0.379261
$516$	−1.85921e7	−3.07400
$517$	0	0
$518$	−5.95335e6	−0.974849
$519$	6.29926e6	1.02653
$520$	1.73304e6	0.281060
$521$	1.82827e6	0.295084	0.147542	−	0.989056i	$-0.452864\pi$
$521$	1.82827e6	0.295084	0.147542	+	0.989056i	$0.452864\pi$
$522$	−4.50856e6	−0.724206
$523$	−2.32250e6	−0.371280	−0.185640	−	0.982618i	$-0.559436\pi$
$523$	−2.32250e6	−0.371280	−0.185640	+	0.982618i	$0.559436\pi$
$524$	−794470.	−0.126401
$525$	−3.42286e6	−0.541989
$526$	−7.55813e6	−1.19110
$527$	1.07957e6	0.169326
$528$	0	0
$529$	1.34799e6	0.209434
$530$	−4.22228e6	−0.652916
$531$	−1.98915e6	−0.306148
$532$	2.56664e7	3.93175
$533$	−5.30892e6	−0.809447
$534$	−1.25706e7	−1.90767
$535$	−3.24492e6	−0.490139
$536$	6.57324e6	0.988252
$537$	−1.12114e6	−0.167774
$538$	7.66498e6	1.14171
$539$	0	0
$540$	−1.90783e6	−0.281549
$541$	2.98144e6	0.437958	0.218979	−	0.975730i	$-0.429727\pi$
$541$	2.98144e6	0.437958	0.218979	+	0.975730i	$0.429727\pi$
$542$	−1.19152e7	−1.74222
$543$	1.61170e7	2.34577
$544$	1.03771e6	0.150342
$545$	−3.03029e6	−0.437012
$546$	2.27584e7	3.26709
$547$	7.68370e6	1.09800	0.548999	−	0.835823i	$-0.315009\pi$
$547$	7.68370e6	1.09800	0.548999	+	0.835823i	$0.315009\pi$
$548$	−3.00554e6	−0.427535
$549$	1.32326e7	1.87376
$550$	0	0
$551$	3.66831e6	0.514740
$552$	9.82810e6	1.37285
$553$	8.00574e6	1.11324
$554$	−1.26089e6	−0.174543
$555$	−1.67217e6	−0.230434
$556$	7.20712e6	0.988723
$557$	2.32103e6	0.316988	0.158494	−	0.987360i	$-0.449336\pi$
$557$	2.32103e6	0.316988	0.158494	+	0.987360i	$0.449336\pi$
$558$	−1.93840e7	−2.63546
$559$	7.51577e6	1.01729
$560$	−1.23419e6	−0.166308
$561$	0	0
$562$	−1.32448e7	−1.76891
$563$	1.16724e7	1.55199	0.775994	−	0.630740i	$-0.217248\pi$
$563$	1.16724e7	1.55199	0.775994	+	0.630740i	$0.217248\pi$
$564$	4.56725e6	0.604585
$565$	4.71116e6	0.620879
$566$	−6.07428e6	−0.796992
$567$	8.94533e6	1.16853
$568$	−7.96296e6	−1.03563
$569$	−1.23942e7	−1.60486	−0.802431	−	0.596745i	$-0.796460\pi$
$569$	−1.23942e7	−1.60486	−0.802431	+	0.596745i	$0.796460\pi$
$570$	1.19479e7	1.54030
$571$	9.76908e6	1.25390	0.626951	−	0.779059i	$-0.284303\pi$
$571$	9.76908e6	1.25390	0.626951	+	0.779059i	$0.284303\pi$
$572$	0	0
$573$	−1.75380e7	−2.23148
$574$	−2.40115e7	−3.04186
$575$	1.74378e6	0.219949
$576$	−1.65323e7	−2.07624
$577$	1.06661e7	1.33372	0.666862	−	0.745181i	$-0.267637\pi$
$577$	1.06661e7	1.33372	0.666862	+	0.745181i	$0.267637\pi$
$578$	−1.25380e7	−1.56102
$579$	−302204.	−0.0374631
$580$	1.97261e6	0.243485
$581$	1.19641e7	1.47042
$582$	5.03976e6	0.616740
$583$	0	0
$584$	−9.07616e6	−1.10121
$585$	3.58179e6	0.432723
$586$	−8.66002e6	−1.04178
$587$	−134855.	−0.0161537	−0.00807684	−	0.999967i	$-0.502571\pi$
$587$	−134855.	−0.0161537	−0.00807684	+	0.999967i	$0.502571\pi$
$588$	4.28727e7	5.11373
$589$	1.57714e7	1.87319
$590$	1.44238e6	0.170589
$591$	1.43450e7	1.68940
$592$	−602940.	−0.0707082
$593$	3.54302e6	0.413748	0.206874	−	0.978368i	$-0.433671\pi$
$593$	3.54302e6	0.413748	0.206874	+	0.978368i	$0.433671\pi$
$594$	0	0
$595$	−902238.	−0.104479
$596$	8.58907e6	0.990446
$597$	1.80085e7	2.06795
$598$	−1.15943e7	−1.32584
$599$	−5.88881e6	−0.670595	−0.335298	−	0.942112i	$-0.608837\pi$
$599$	−5.88881e6	−0.670595	−0.335298	+	0.942112i	$0.608837\pi$
$600$	2.20160e6	0.249667
$601$	2.42115e6	0.273423	0.136711	−	0.990611i	$-0.456347\pi$
$601$	2.42115e6	0.273423	0.136711	+	0.990611i	$0.456347\pi$
$602$	3.39927e7	3.82292
$603$	1.35854e7	1.52152
$604$	−7.89733e6	−0.880822
$605$	0	0
$606$	2.12103e7	2.34620
$607$	−6.95111e6	−0.765742	−0.382871	−	0.923802i	$-0.625065\pi$
$607$	−6.95111e6	−0.765742	−0.382871	+	0.923802i	$0.625065\pi$
$608$	1.51599e7	1.66317
$609$	8.87660e6	0.969847
$610$	−9.59527e6	−1.04408
$611$	−1.84629e6	−0.200077
$612$	−2.33554e6	−0.252062
$613$	−1.78765e6	−0.192146	−0.0960728	−	0.995374i	$-0.530628\pi$
$613$	−1.78765e6	−0.192146	−0.0960728	+	0.995374i	$0.530628\pi$
$614$	1.69965e7	1.81945
$615$	−6.74431e6	−0.719034
$616$	0	0
$617$	1.58089e7	1.67182	0.835910	−	0.548866i	$-0.184940\pi$
$617$	1.58089e7	1.67182	0.835910	+	0.548866i	$0.184940\pi$
$618$	−1.92815e7	−2.03081
$619$	−1.10016e7	−1.15406	−0.577029	−	0.816723i	$-0.695788\pi$
$619$	−1.10016e7	−1.15406	−0.577029	+	0.816723i	$0.695788\pi$
$620$	8.48097e6	0.886067
$621$	4.37367e6	0.455110
$622$	1.06813e7	1.10700
$623$	1.38677e7	1.43148
$624$	2.30491e6	0.236970
$625$	390625.	0.0400000
$626$	1.15444e7	1.17743
$627$	0	0
$628$	1.24600e7	1.26072
$629$	−440770.	−0.0444207
$630$	1.61999e7	1.62615
$631$	1.52738e7	1.52712	0.763559	−	0.645738i	$-0.223450\pi$
$631$	1.52738e7	1.52712	0.763559	+	0.645738i	$0.223450\pi$
$632$	−5.14934e6	−0.512813
$633$	−2.66377e7	−2.64234
$634$	8.18651e6	0.808864
$635$	101806.	0.0100194
$636$	2.15190e7	2.10949
$637$	−1.73311e7	−1.69230
$638$	0	0
$639$	−1.64576e7	−1.59446
$640$	6.62931e6	0.639762
$641$	7.84378e6	0.754015	0.377008	−	0.926210i	$-0.376953\pi$
$641$	7.84378e6	0.754015	0.377008	+	0.926210i	$0.376953\pi$
$642$	2.74087e7	2.62452
$643$	−1.47066e7	−1.40277	−0.701384	−	0.712783i	$-0.747434\pi$
$643$	−1.47066e7	−1.40277	−0.701384	+	0.712783i	$0.747434\pi$
$644$	−3.16407e7	−3.00630
$645$	9.54782e6	0.903660
$646$	3.14938e6	0.296923
$647$	−1.31105e7	−1.23129	−0.615643	−	0.788026i	$-0.711103\pi$
$647$	−1.31105e7	−1.23129	−0.615643	+	0.788026i	$0.711103\pi$
$648$	−5.75369e6	−0.538281
$649$	0	0
$650$	−2.59725e6	−0.241118
$651$	3.81637e7	3.52938
$652$	3.79417e6	0.349541
$653$	−2.82207e6	−0.258991	−0.129495	−	0.991580i	$-0.541336\pi$
$653$	−2.82207e6	−0.258991	−0.129495	+	0.991580i	$0.541336\pi$
$654$	2.55958e7	2.34004
$655$	407994.	0.0371578
$656$	−2.43182e6	−0.220634
$657$	−1.87583e7	−1.69543
$658$	−8.35051e6	−0.751880
$659$	−7.66311e6	−0.687372	−0.343686	−	0.939085i	$-0.611676\pi$
$659$	−7.66311e6	−0.687372	−0.343686	+	0.939085i	$0.611676\pi$
$660$	0	0
$661$	1.54115e6	0.137196	0.0685980	−	0.997644i	$-0.478147\pi$
$661$	1.54115e6	0.137196	0.0685980	+	0.997644i	$0.478147\pi$
$662$	1.97494e6	0.175149
$663$	1.68497e6	0.148870
$664$	−7.69540e6	−0.677347
$665$	−1.31808e7	−1.15581
$666$	7.91413e6	0.691381
$667$	−4.52218e6	−0.393580
$668$	−1.82319e7	−1.58085
$669$	−6.44323e6	−0.556594
$670$	−9.85110e6	−0.847808
$671$	0	0
$672$	3.66840e7	3.13367
$673$	−3.71406e6	−0.316090	−0.158045	−	0.987432i	$-0.550519\pi$
$673$	−3.71406e6	−0.316090	−0.158045	+	0.987432i	$0.550519\pi$
$674$	−2.49081e7	−2.11199
$675$	979750.	0.0827667
$676$	−7.65538e6	−0.644317
$677$	2.90006e6	0.243184	0.121592	−	0.992580i	$-0.461200\pi$
$677$	2.90006e6	0.243184	0.121592	+	0.992580i	$0.461200\pi$
$678$	−3.97935e7	−3.32459
$679$	−5.55978e6	−0.462789
$680$	580325.	0.0481281
$681$	−1.23501e7	−1.02047
$682$	0	0
$683$	4.71228e6	0.386526	0.193263	−	0.981147i	$-0.438093\pi$
$683$	4.71228e6	0.386526	0.193263	+	0.981147i	$0.438093\pi$
$684$	−3.41198e7	−2.78847
$685$	1.54347e6	0.125682
$686$	−4.32179e7	−3.50634
$687$	−1.37728e6	−0.111335
$688$	3.44269e6	0.277286
$689$	−8.69894e6	−0.698101
$690$	−1.47290e7	−1.17775
$691$	4.36271e6	0.347585	0.173792	−	0.984782i	$-0.444398\pi$
$691$	4.36271e6	0.347585	0.173792	+	0.984782i	$0.444398\pi$
$692$	1.30442e7	1.03550
$693$	0	0
$694$	1.46283e7	1.15291
$695$	−3.70116e6	−0.290653
$696$	−5.70948e6	−0.446759
$697$	−1.77774e6	−0.138608
$698$	3.14381e7	2.44240
$699$	−3.33762e7	−2.58371
$700$	−7.08787e6	−0.546727
$701$	−1.46747e7	−1.12791	−0.563955	−	0.825805i	$-0.690721\pi$
$701$	−1.46747e7	−1.12791	−0.563955	+	0.825805i	$0.690721\pi$
$702$	−6.51431e6	−0.498914
$703$	−6.43920e6	−0.491409
$704$	0	0
$705$	−2.34548e6	−0.177729
$706$	−5.63063e6	−0.425153
$707$	−2.33988e7	−1.76054
$708$	−7.35114e6	−0.551152
$709$	−8.89377e6	−0.664462	−0.332231	−	0.943198i	$-0.607801\pi$
$709$	−8.89377e6	−0.664462	−0.332231	+	0.943198i	$0.607801\pi$
$710$	1.19338e7	0.888451
$711$	−1.06425e7	−0.789531
$712$	−8.91978e6	−0.659408
$713$	−1.94425e7	−1.43228
$714$	7.62088e6	0.559448
$715$	0	0
$716$	−2.32159e6	−0.169240
$717$	−2.13356e7	−1.54991
$718$	−3.03738e7	−2.19881
$719$	−2.53780e7	−1.83078	−0.915389	−	0.402570i	$-0.868117\pi$
$719$	−2.53780e7	−1.83078	−0.915389	+	0.402570i	$0.868117\pi$
$720$	1.64068e6	0.117949
$721$	2.12710e7	1.52388
$722$	2.37682e7	1.69689
$723$	3.44242e7	2.44917
$724$	3.33743e7	2.36628
$725$	−1.01302e6	−0.0715768
$726$	0	0
$727$	−2.70910e7	−1.90103	−0.950515	−	0.310678i	$-0.899444\pi$
$727$	−2.70910e7	−1.90103	−0.950515	+	0.310678i	$0.899444\pi$
$728$	1.61488e7	1.12931
$729$	−2.08468e7	−1.45285
$730$	1.36021e7	0.944713
$731$	2.51673e6	0.174198
$732$	4.89025e7	3.37329
$733$	1.40924e7	0.968778	0.484389	−	0.874853i	$-0.339042\pi$
$733$	1.40924e7	0.968778	0.484389	+	0.874853i	$0.339042\pi$
$734$	−9.20263e6	−0.630481
$735$	−2.20169e7	−1.50327
$736$	−1.86886e7	−1.27170
$737$	0	0
$738$	3.19199e7	2.15735
$739$	2.18373e7	1.47091	0.735457	−	0.677572i	$-0.236968\pi$
$739$	2.18373e7	1.47091	0.735457	+	0.677572i	$0.236968\pi$
$740$	−3.46263e6	−0.232449
$741$	2.46157e7	1.64690
$742$	−3.93441e7	−2.62343
$743$	−1.22738e7	−0.815655	−0.407827	−	0.913059i	$-0.633714\pi$
$743$	−1.22738e7	−0.815655	−0.407827	+	0.913059i	$0.633714\pi$
$744$	−2.45471e7	−1.62581
$745$	−4.41085e6	−0.291160
$746$	−1.62042e7	−1.06606
$747$	−1.59046e7	−1.04285
$748$	0	0
$749$	−3.02368e7	−1.96939
$750$	−3.29947e6	−0.214186
$751$	8.10784e6	0.524572	0.262286	−	0.964990i	$-0.415524\pi$
$751$	8.10784e6	0.524572	0.262286	+	0.964990i	$0.415524\pi$
$752$	−845718.	−0.0545357
$753$	−2.55339e7	−1.64108
$754$	6.73551e6	0.431462
$755$	4.05561e6	0.258934
$756$	−1.77775e7	−1.13127
$757$	1.48213e7	0.940043	0.470021	−	0.882655i	$-0.344246\pi$
$757$	1.48213e7	0.940043	0.470021	+	0.882655i	$0.344246\pi$
$758$	−3.27345e7	−2.06935
$759$	0	0
$760$	8.47795e6	0.532423
$761$	−2.00756e7	−1.25663	−0.628315	−	0.777959i	$-0.716255\pi$
$761$	−2.00756e7	−1.25663	−0.628315	+	0.777959i	$0.716255\pi$
$762$	−859923.	−0.0536503
$763$	−2.82369e7	−1.75592
$764$	−3.63167e7	−2.25099
$765$	1.19940e6	0.0740985
$766$	2.29514e7	1.41331
$767$	2.97167e6	0.182394
$768$	−1.58343e7	−0.968712
$769$	2.84624e7	1.73562	0.867811	−	0.496895i	$-0.165527\pi$
$769$	2.84624e7	1.73562	0.867811	+	0.496895i	$0.165527\pi$
$770$	0	0
$771$	1.07706e7	0.652534
$772$	−625787.	−0.0377906
$773$	−2.53185e7	−1.52402	−0.762009	−	0.647567i	$-0.775787\pi$
$773$	−2.53185e7	−1.52402	−0.762009	+	0.647567i	$0.775787\pi$
$774$	−4.51885e7	−2.71129
$775$	−4.35534e6	−0.260476
$776$	3.57608e6	0.213183
$777$	−1.55816e7	−0.925889
$778$	4.48150e7	2.65445
$779$	−2.59710e7	−1.53337
$780$	1.32369e7	0.779024
$781$	0	0
$782$	−3.88246e6	−0.227033
$783$	−2.54081e6	−0.148104
$784$	−7.93873e6	−0.461276
$785$	−6.39873e6	−0.370612
$786$	−3.44618e6	−0.198967
$787$	−6.06464e6	−0.349035	−0.174517	−	0.984654i	$-0.555836\pi$
$787$	−6.06464e6	−0.349035	−0.174517	+	0.984654i	$0.555836\pi$
$788$	2.97049e7	1.70417
$789$	−1.97817e7	−1.13128
$790$	7.71714e6	0.439935
$791$	4.38996e7	2.49470
$792$	0	0
$793$	−1.97686e7	−1.11633
$794$	−2.98955e7	−1.68288
$795$	−1.10509e7	−0.620125
$796$	3.72910e7	2.08603
$797$	2.44749e6	0.136482	0.0682410	−	0.997669i	$-0.478261\pi$
$797$	2.44749e6	0.136482	0.0682410	+	0.997669i	$0.478261\pi$
$798$	1.11333e8	6.18896
$799$	−618249.	−0.0342607
$800$	−4.18646e6	−0.231272
$801$	−1.84351e7	−1.01523
$802$	−1.26919e7	−0.696774
$803$	0	0
$804$	5.02064e7	2.73917
$805$	1.62489e7	0.883757
$806$	2.89584e7	1.57014
$807$	2.00614e7	1.08437
$808$	1.50503e7	0.810991
$809$	−1.59076e7	−0.854545	−0.427272	−	0.904123i	$-0.640525\pi$
$809$	−1.59076e7	−0.854545	−0.427272	+	0.904123i	$0.640525\pi$
$810$	8.62286e6	0.461784
$811$	−1.36156e7	−0.726916	−0.363458	−	0.931611i	$-0.618404\pi$
$811$	−1.36156e7	−0.726916	−0.363458	+	0.931611i	$0.618404\pi$
$812$	1.83812e7	0.978326
$813$	−3.11855e7	−1.65473
$814$	0	0
$815$	−1.94847e6	−0.102754
$816$	771823.	0.0405781
$817$	3.67668e7	1.92709
$818$	−4.50419e7	−2.35360
$819$	3.33758e7	1.73869
$820$	−1.39658e7	−0.725320
$821$	−2.67354e7	−1.38430	−0.692148	−	0.721756i	$-0.743335\pi$
$821$	−2.67354e7	−1.38430	−0.692148	+	0.721756i	$0.743335\pi$
$822$	−1.30372e7	−0.672982
$823$	−1.40177e7	−0.721404	−0.360702	−	0.932681i	$-0.617463\pi$
$823$	−1.40177e7	−0.721404	−0.360702	+	0.932681i	$0.617463\pi$
$824$	−1.36816e7	−0.701972
$825$	0	0
$826$	1.34404e7	0.685429
$827$	1.07462e7	0.546375	0.273188	−	0.961961i	$-0.411922\pi$
$827$	1.07462e7	0.546375	0.273188	+	0.961961i	$0.411922\pi$
$828$	4.20618e7	2.13212
$829$	6.79092e6	0.343196	0.171598	−	0.985167i	$-0.445107\pi$
$829$	6.79092e6	0.343196	0.171598	+	0.985167i	$0.445107\pi$
$830$	1.15328e7	0.581087
$831$	−3.30010e6	−0.165777
$832$	2.46982e7	1.23696
$833$	−5.80348e6	−0.289785
$834$	3.12623e7	1.55635
$835$	9.36283e6	0.464720
$836$	0	0
$837$	−1.09239e7	−0.538968
$838$	1.67287e7	0.822911
$839$	1.63233e7	0.800575	0.400287	−	0.916390i	$-0.368910\pi$
$839$	1.63233e7	0.800575	0.400287	+	0.916390i	$0.368910\pi$
$840$	2.05150e7	1.00317
$841$	−1.78841e7	−0.871919
$842$	1.86990e7	0.908947
$843$	−3.46654e7	−1.68007
$844$	−5.51600e7	−2.66543
$845$	3.93136e6	0.189409
$846$	1.11008e7	0.533248
$847$	0	0
$848$	−3.98466e6	−0.190284
$849$	−1.58981e7	−0.756965
$850$	−869713.	−0.0412885
$851$	7.93804e6	0.375742
$852$	−6.08210e7	−2.87048
$853$	157775.	0.00742447	0.00371224	−	0.999993i	$-0.498818\pi$
$853$	157775.	0.00742447	0.00371224	+	0.999993i	$0.498818\pi$
$854$	−8.94106e7	−4.19512
$855$	1.75220e7	0.819724
$856$	1.94485e7	0.907197
$857$	−1.48800e7	−0.692070	−0.346035	−	0.938222i	$-0.612472\pi$
$857$	−1.48800e7	−0.692070	−0.346035	+	0.938222i	$0.612472\pi$
$858$	0	0
$859$	2.35044e7	1.08684	0.543420	−	0.839461i	$-0.317129\pi$
$859$	2.35044e7	1.08684	0.543420	+	0.839461i	$0.317129\pi$
$860$	1.97711e7	0.911559
$861$	−6.28448e7	−2.88909
$862$	4.22285e6	0.193570
$863$	1.04978e7	0.479814	0.239907	−	0.970796i	$-0.422883\pi$
$863$	1.04978e7	0.479814	0.239907	+	0.970796i	$0.422883\pi$
$864$	−1.05003e7	−0.478540
$865$	−6.69873e6	−0.304405
$866$	6.94488e6	0.314681
$867$	−3.28154e7	−1.48262
$868$	7.90274e7	3.56023
$869$	0	0
$870$	8.55661e6	0.383269
$871$	−2.02957e7	−0.906480
$872$	1.81621e7	0.808863
$873$	7.39093e6	0.328219
$874$	−5.67188e7	−2.51159
$875$	3.63992e6	0.160721
$876$	−6.93236e7	−3.05226
$877$	−1.00320e7	−0.440441	−0.220221	−	0.975450i	$-0.570678\pi$
$877$	−1.00320e7	−0.440441	−0.220221	+	0.975450i	$0.570678\pi$
$878$	9.53726e6	0.417530
$879$	−2.26657e7	−0.989456
$880$	0	0
$881$	−2.28260e7	−0.990808	−0.495404	−	0.868663i	$-0.664980\pi$
$881$	−2.28260e7	−0.990808	−0.495404	+	0.868663i	$0.664980\pi$
$882$	1.04203e8	4.51034
$883$	1.47296e7	0.635754	0.317877	−	0.948132i	$-0.397030\pi$
$883$	1.47296e7	0.635754	0.317877	+	0.948132i	$0.397030\pi$
$884$	3.48915e6	0.150172
$885$	3.77512e6	0.162022
$886$	−1.68880e7	−0.722762
$887$	−1.10653e7	−0.472229	−0.236114	−	0.971725i	$-0.575874\pi$
$887$	−1.10653e7	−0.472229	−0.236114	+	0.971725i	$0.575874\pi$
$888$	1.00222e7	0.426510
$889$	948653.	0.0402581
$890$	1.33678e7	0.565698
$891$	0	0
$892$	−1.33423e7	−0.561459
$893$	−9.03199e6	−0.379013
$894$	3.72569e7	1.55906
$895$	1.19224e6	0.0497513
$896$	6.17733e7	2.57058
$897$	−3.03455e7	−1.25925
$898$	−5.23528e7	−2.16645
$899$	1.12948e7	0.466101
$900$	9.42232e6	0.387750
$901$	−2.91292e6	−0.119541
$902$	0	0
$903$	8.89685e7	3.63092
$904$	−2.82364e7	−1.14918
$905$	−1.71391e7	−0.695611
$906$	−3.42563e7	−1.38650
$907$	1.21986e7	0.492369	0.246185	−	0.969223i	$-0.420823\pi$
$907$	1.21986e7	0.492369	0.246185	+	0.969223i	$0.420823\pi$
$908$	−2.55739e7	−1.02939
$909$	3.11054e7	1.24861
$910$	−2.42017e7	−0.968817
$911$	−2.63693e7	−1.05270	−0.526348	−	0.850269i	$-0.676439\pi$
$911$	−2.63693e7	−1.05270	−0.526348	+	0.850269i	$0.676439\pi$
$912$	1.12755e7	0.448901
$913$	0	0
$914$	−3.89736e7	−1.54314
$915$	−2.51135e7	−0.991641
$916$	−2.85200e6	−0.112308
$917$	3.80177e6	0.149301
$918$	−2.18138e6	−0.0854328
$919$	2.59281e7	1.01270	0.506351	−	0.862327i	$-0.330994\pi$
$919$	2.59281e7	1.01270	0.506351	+	0.862327i	$0.330994\pi$
$920$	−1.04514e7	−0.407102
$921$	4.44847e7	1.72807
$922$	3.19801e7	1.23895
$923$	2.45866e7	0.949936
$924$	0	0
$925$	1.77821e6	0.0683326
$926$	−3.47244e7	−1.33078
$927$	−2.82768e7	−1.08076
$928$	1.08569e7	0.413842
$929$	−9.33009e6	−0.354688	−0.177344	−	0.984149i	$-0.556751\pi$
$929$	−9.33009e6	−0.354688	−0.177344	+	0.984149i	$0.556751\pi$
$930$	3.67880e7	1.39476
$931$	−8.47830e7	−3.20579
$932$	−6.91137e7	−2.60630
$933$	2.79559e7	1.05140
$934$	−7.39164e6	−0.277251
$935$	0	0
$936$	−2.14675e7	−0.800926
$937$	1.71808e7	0.639286	0.319643	−	0.947538i	$-0.396437\pi$
$937$	1.71808e7	0.639286	0.319643	+	0.947538i	$0.396437\pi$
$938$	−9.17945e7	−3.40651
$939$	3.02149e7	1.11830
$940$	−4.85689e6	−0.179283
$941$	−1.60883e7	−0.592291	−0.296146	−	0.955143i	$-0.595701\pi$
$941$	−1.60883e7	−0.592291	−0.296146	+	0.955143i	$0.595701\pi$
$942$	5.40478e7	1.98450
$943$	3.20163e7	1.17244
$944$	1.36121e6	0.0497159
$945$	9.12950e6	0.332558
$946$	0	0
$947$	4.81230e6	0.174372	0.0871862	−	0.996192i	$-0.472212\pi$
$947$	4.81230e6	0.174372	0.0871862	+	0.996192i	$0.472212\pi$
$948$	−3.93306e7	−1.42138
$949$	2.80238e7	1.01009
$950$	−1.27056e7	−0.456759
$951$	2.14264e7	0.768241
$952$	5.40758e6	0.193380
$953$	3.25180e7	1.15982	0.579911	−	0.814680i	$-0.303087\pi$
$953$	3.25180e7	1.15982	0.579911	+	0.814680i	$0.303087\pi$
$954$	5.23023e7	1.86059
$955$	1.86502e7	0.661720
$956$	−4.41807e7	−1.56346
$957$	0	0
$958$	1.23346e7	0.434221
$959$	1.43824e7	0.504992
$960$	3.13759e7	1.09880
$961$	1.99314e7	0.696192
$962$	−1.18232e7	−0.411906
$963$	4.01955e7	1.39673
$964$	7.12839e7	2.47058
$965$	321368.	0.0111092
$966$	−1.37248e8	−4.73221
$967$	−1.13037e7	−0.388735	−0.194368	−	0.980929i	$-0.562265\pi$
$967$	−1.13037e7	−0.388735	−0.194368	+	0.980929i	$0.562265\pi$
$968$	0	0
$969$	8.24281e6	0.282011
$970$	−5.35935e6	−0.182887
$971$	7.34876e6	0.250130	0.125065	−	0.992149i	$-0.460086\pi$
$971$	7.34876e6	0.250130	0.125065	+	0.992149i	$0.460086\pi$
$972$	−6.24907e7	−2.12153
$973$	−3.44881e7	−1.16785
$974$	6.17009e7	2.08398
$975$	−6.79772e6	−0.229009
$976$	−9.05527e6	−0.304283
$977$	257689.	0.00863693	0.00431847	−	0.999991i	$-0.498625\pi$
$977$	257689.	0.00863693	0.00431847	+	0.999991i	$0.498625\pi$
$978$	1.64580e7	0.550211
$979$	0	0
$980$	−4.55915e7	−1.51642
$981$	3.75369e7	1.24533
$982$	4.88917e7	1.61792
$983$	−751872.	−0.0248176	−0.0124088	−	0.999923i	$-0.503950\pi$
$983$	−751872.	−0.0248176	−0.0124088	+	0.999923i	$0.503950\pi$
$984$	4.04221e7	1.33086
$985$	−1.52547e7	−0.500973
$986$	2.25545e6	0.0738824
$987$	−2.18556e7	−0.714119
$988$	5.09729e7	1.66130
$989$	−4.53250e7	−1.47349
$990$	0	0
$991$	−4.41087e7	−1.42672	−0.713362	−	0.700795i	$-0.752829\pi$
$991$	−4.41087e7	−1.42672	−0.713362	+	0.700795i	$0.752829\pi$
$992$	4.66777e7	1.50602
$993$	5.16897e6	0.166353
$994$	1.11202e8	3.56981
$995$	−1.91505e7	−0.613228
$996$	−5.87774e7	−1.87742
$997$	3.85351e7	1.22778	0.613888	−	0.789393i	$-0.289605\pi$
$997$	3.85351e7	1.22778	0.613888	+	0.789393i	$0.289605\pi$
$998$	−6.94233e7	−2.20637
$999$	4.46003e6	0.141392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.17		20
11.5	even	5		55.6.g.b.36.2	yes	40
11.9	even	5		55.6.g.b.26.2	✓	40
11.10	odd	2		605.6.a.o.1.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.26.2	✓	40	11.9	even	5
55.6.g.b.36.2	yes	40	11.5	even	5
605.6.a.o.1.4		20	11.10	odd	2
605.6.a.p.1.17		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)

\(f(q)\)	\(=\)	\(q+8.98229 q^{2} +23.5092 q^{3} +48.6815 q^{4} -25.0000 q^{5} +211.166 q^{6} -232.955 q^{7} +149.838 q^{8} +309.680 q^{9} +O(q^{10})\)	\(q+8.98229 q^{2} +23.5092 q^{3} +48.6815 q^{4} -25.0000 q^{5} +211.166 q^{6} -232.955 q^{7} +149.838 q^{8} +309.680 q^{9} -224.557 q^{10} +1144.46 q^{12} -462.643 q^{13} -2092.47 q^{14} -587.729 q^{15} -211.920 q^{16} -154.921 q^{17} +2781.64 q^{18} -2263.23 q^{19} -1217.04 q^{20} -5476.58 q^{21} +2790.04 q^{23} +3522.57 q^{24} +625.000 q^{25} -4155.59 q^{26} +1567.60 q^{27} -11340.6 q^{28} -1620.83 q^{29} -5279.15 q^{30} -6968.54 q^{31} -6698.34 q^{32} -1391.54 q^{34} +5823.88 q^{35} +15075.7 q^{36} +2845.13 q^{37} -20329.0 q^{38} -10876.3 q^{39} -3745.95 q^{40} +11475.2 q^{41} -49192.2 q^{42} -16245.3 q^{43} -7742.01 q^{45} +25061.0 q^{46} +3990.75 q^{47} -4982.05 q^{48} +37461.0 q^{49} +5613.93 q^{50} -3642.05 q^{51} -22522.2 q^{52} +18802.7 q^{53} +14080.6 q^{54} -34905.5 q^{56} -53206.7 q^{57} -14558.8 q^{58} -6423.24 q^{59} -28611.5 q^{60} +42729.7 q^{61} -62593.4 q^{62} -72141.6 q^{63} -53385.0 q^{64} +11566.1 q^{65} +43869.0 q^{67} -7541.77 q^{68} +65591.5 q^{69} +52311.7 q^{70} -53143.8 q^{71} +46401.9 q^{72} -60573.1 q^{73} +25555.8 q^{74} +14693.2 q^{75} -110178. q^{76} -97694.5 q^{78} -34366.0 q^{79} +5297.99 q^{80} -38399.4 q^{81} +103074. q^{82} -51358.2 q^{83} -266608. q^{84} +3873.01 q^{85} -145920. q^{86} -38104.3 q^{87} -59529.5 q^{89} -69541.0 q^{90} +107775. q^{91} +135823. q^{92} -163824. q^{93} +35846.0 q^{94} +56580.8 q^{95} -157472. q^{96} +23866.3 q^{97} +336486. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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