LMFDB - Embedded newform 605.6.a.p.1.5

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			1.5
Root			$-6.92807$ 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)

$f(q)$	$=$	$q-6.92807 q^{2} -8.76999 q^{3} +15.9982 q^{4} -25.0000 q^{5} +60.7591 q^{6} -97.5351 q^{7} +110.862 q^{8} -166.087 q^{9} +O(q^{10})$	\(q-6.92807 q^{2} -8.76999 q^{3} +15.9982 q^{4} -25.0000 q^{5} +60.7591 q^{6} -97.5351 q^{7} +110.862 q^{8} -166.087 q^{9} +173.202 q^{10} -140.304 q^{12} -412.700 q^{13} +675.730 q^{14} +219.250 q^{15} -1280.00 q^{16} +329.194 q^{17} +1150.67 q^{18} +745.181 q^{19} -399.955 q^{20} +855.382 q^{21} -2741.44 q^{23} -972.255 q^{24} +625.000 q^{25} +2859.22 q^{26} +3587.69 q^{27} -1560.39 q^{28} -4357.38 q^{29} -1518.98 q^{30} +6527.19 q^{31} +5320.36 q^{32} -2280.68 q^{34} +2438.38 q^{35} -2657.10 q^{36} -11198.5 q^{37} -5162.67 q^{38} +3619.37 q^{39} -2771.54 q^{40} -7013.72 q^{41} -5926.15 q^{42} +16616.6 q^{43} +4152.18 q^{45} +18992.9 q^{46} +25547.9 q^{47} +11225.6 q^{48} -7293.90 q^{49} -4330.05 q^{50} -2887.02 q^{51} -6602.46 q^{52} +3028.86 q^{53} -24855.8 q^{54} -10812.9 q^{56} -6535.23 q^{57} +30188.3 q^{58} +25868.1 q^{59} +3507.60 q^{60} -31259.7 q^{61} -45220.9 q^{62} +16199.3 q^{63} +4100.14 q^{64} +10317.5 q^{65} +52903.1 q^{67} +5266.51 q^{68} +24042.4 q^{69} -16893.3 q^{70} +22810.8 q^{71} -18412.7 q^{72} -26483.2 q^{73} +77584.0 q^{74} -5481.24 q^{75} +11921.6 q^{76} -25075.3 q^{78} +96132.1 q^{79} +32000.0 q^{80} +8895.24 q^{81} +48591.6 q^{82} -12714.3 q^{83} +13684.6 q^{84} -8229.84 q^{85} -115121. q^{86} +38214.2 q^{87} +60525.7 q^{89} -28766.6 q^{90} +40252.7 q^{91} -43858.2 q^{92} -57243.4 q^{93} -176998. q^{94} -18629.5 q^{95} -46659.5 q^{96} +74280.4 q^{97} +50532.7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.92807	−1.22472	−0.612361	−	0.790578i	$-0.709780\pi$
$2$	−6.92807	−1.22472	−0.612361	+	0.790578i	$0.709780\pi$
$3$	−8.76999	−0.562595	−0.281297	−	0.959621i	$-0.590765\pi$
$3$	−8.76999	−0.562595	−0.281297	+	0.959621i	$0.590765\pi$
$4$	15.9982	0.499944
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	60.7591	0.689022
$7$	−97.5351	−0.752343	−0.376172	−	0.926550i	$-0.622760\pi$
$7$	−97.5351	−0.752343	−0.376172	+	0.926550i	$0.622760\pi$
$8$	110.862	0.612430
$9$	−166.087	−0.683487
$10$	173.202	0.547712
$11$	0	0
$11$	0	0
$12$	−140.304	−0.281266
$13$	−412.700	−0.677292	−0.338646	−	0.940914i	$-0.609969\pi$
$13$	−412.700	−0.677292	−0.338646	+	0.940914i	$0.609969\pi$
$14$	675.730	0.921411
$15$	219.250	0.251600
$16$	−1280.00	−1.25000
$17$	329.194	0.276267	0.138134	−	0.990414i	$-0.455890\pi$
$17$	329.194	0.276267	0.138134	+	0.990414i	$0.455890\pi$
$18$	1150.67	0.837082
$19$	745.181	0.473563	0.236782	−	0.971563i	$-0.423907\pi$
$19$	745.181	0.473563	0.236782	+	0.971563i	$0.423907\pi$
$20$	−399.955	−0.223582
$21$	855.382	0.423264
$22$	0	0
$23$	−2741.44	−1.08059	−0.540294	−	0.841477i	$-0.681687\pi$
$23$	−2741.44	−1.08059	−0.540294	+	0.841477i	$0.681687\pi$
$24$	−972.255	−0.344550
$25$	625.000	0.200000
$26$	2859.22	0.829494
$27$	3587.69	0.947121
$28$	−1560.39	−0.376129
$29$	−4357.38	−0.962123	−0.481061	−	0.876687i	$-0.659749\pi$
$29$	−4357.38	−0.962123	−0.481061	+	0.876687i	$0.659749\pi$
$30$	−1518.98	−0.308140
$31$	6527.19	1.21989	0.609947	−	0.792442i	$-0.291191\pi$
$31$	6527.19	1.21989	0.609947	+	0.792442i	$0.291191\pi$
$32$	5320.36	0.918473
$33$	0	0
$34$	−2280.68	−0.338350
$35$	2438.38	0.336458
$36$	−2657.10	−0.341705
$37$	−11198.5	−1.34479	−0.672396	−	0.740192i	$-0.734735\pi$
$37$	−11198.5	−1.34479	−0.672396	+	0.740192i	$0.734735\pi$
$38$	−5162.67	−0.579983
$39$	3619.37	0.381041
$40$	−2771.54	−0.273887
$41$	−7013.72	−0.651612	−0.325806	−	0.945437i	$-0.605636\pi$
$41$	−7013.72	−0.651612	−0.325806	+	0.945437i	$0.605636\pi$
$42$	−5926.15	−0.518381
$43$	16616.6	1.37047	0.685236	−	0.728321i	$-0.259699\pi$
$43$	16616.6	1.37047	0.685236	+	0.728321i	$0.259699\pi$
$44$	0	0
$45$	4152.18	0.305665
$46$	18992.9	1.32342
$47$	25547.9	1.68698	0.843491	−	0.537143i	$-0.180496\pi$
$47$	25547.9	1.68698	0.843491	+	0.537143i	$0.180496\pi$
$48$	11225.6	0.703244
$49$	−7293.90	−0.433980
$50$	−4330.05	−0.244944
$51$	−2887.02	−0.155426
$52$	−6602.46	−0.338608
$53$	3028.86	0.148112	0.0740559	−	0.997254i	$-0.476406\pi$
$53$	3028.86	0.148112	0.0740559	+	0.997254i	$0.476406\pi$
$54$	−24855.8	−1.15996
$55$	0	0
$56$	−10812.9	−0.460757
$57$	−6535.23	−0.266424
$58$	30188.3	1.17833
$59$	25868.1	0.967463	0.483731	−	0.875217i	$-0.339281\pi$
$59$	25868.1	0.967463	0.483731	+	0.875217i	$0.339281\pi$
$60$	3507.60	0.125786
$61$	−31259.7	−1.07562	−0.537812	−	0.843065i	$-0.680749\pi$
$61$	−31259.7	−1.07562	−0.537812	+	0.843065i	$0.680749\pi$
$62$	−45220.9	−1.49403
$63$	16199.3	0.514217
$64$	4100.14	0.125126
$65$	10317.5	0.302894
$66$	0	0
$67$	52903.1	1.43977	0.719887	−	0.694091i	$-0.244194\pi$
$67$	52903.1	1.43977	0.719887	+	0.694091i	$0.244194\pi$
$68$	5266.51	0.138118
$69$	24042.4	0.607933
$70$	−16893.3	−0.412068
$71$	22810.8	0.537026	0.268513	−	0.963276i	$-0.413468\pi$
$71$	22810.8	0.537026	0.268513	+	0.963276i	$0.413468\pi$
$72$	−18412.7	−0.418588
$73$	−26483.2	−0.581653	−0.290827	−	0.956776i	$-0.593930\pi$
$73$	−26483.2	−0.581653	−0.290827	+	0.956776i	$0.593930\pi$
$74$	77584.0	1.64700
$75$	−5481.24	−0.112519
$76$	11921.6	0.236755
$77$	0	0
$78$	−25075.3	−0.466669
$79$	96132.1	1.73301	0.866504	−	0.499170i	$-0.166362\pi$
$79$	96132.1	1.73301	0.866504	+	0.499170i	$0.166362\pi$
$80$	32000.0	0.559017
$81$	8895.24	0.150642
$82$	48591.6	0.798043
$83$	−12714.3	−0.202580	−0.101290	−	0.994857i	$-0.532297\pi$
$83$	−12714.3	−0.202580	−0.101290	+	0.994857i	$0.532297\pi$
$84$	13684.6	0.211608
$85$	−8229.84	−0.123550
$86$	−115121.	−1.67845
$87$	38214.2	0.541285
$88$	0	0
$89$	60525.7	0.809962	0.404981	−	0.914325i	$-0.367278\pi$
$89$	60525.7	0.809962	0.404981	+	0.914325i	$0.367278\pi$
$90$	−28766.6	−0.374354
$91$	40252.7	0.509556
$92$	−43858.2	−0.540233
$93$	−57243.4	−0.686306
$94$	−176998.	−2.06609
$95$	−18629.5	−0.211784
$96$	−46659.5	−0.516728
$97$	74280.4	0.801577	0.400788	−	0.916171i	$-0.368736\pi$
$97$	74280.4	0.801577	0.400788	+	0.916171i	$0.368736\pi$
$98$	50532.7	0.531505
$99$	0	0
$100$	9998.88	0.0999888
$101$	−14762.0	−0.143993	−0.0719965	−	0.997405i	$-0.522937\pi$
$101$	−14762.0	−0.143993	−0.0719965	+	0.997405i	$0.522937\pi$
$102$	20001.5	0.190354
$103$	80663.3	0.749175	0.374587	−	0.927192i	$-0.377784\pi$
$103$	80663.3	0.749175	0.374587	+	0.927192i	$0.377784\pi$
$104$	−45752.6	−0.414794
$105$	−21384.5	−0.189290
$106$	−20984.2	−0.181396
$107$	−141191.	−1.19220	−0.596098	−	0.802912i	$-0.703283\pi$
$107$	−141191.	−1.19220	−0.596098	+	0.802912i	$0.703283\pi$
$108$	57396.6	0.473507
$109$	59489.5	0.479595	0.239797	−	0.970823i	$-0.422919\pi$
$109$	59489.5	0.479595	0.239797	+	0.970823i	$0.422919\pi$
$110$	0	0
$111$	98210.6	0.756573
$112$	124845.	0.940429
$113$	177366.	1.30669	0.653347	−	0.757059i	$-0.273364\pi$
$113$	177366.	1.30669	0.653347	+	0.757059i	$0.273364\pi$
$114$	45276.5	0.326296
$115$	68536.1	0.483253
$116$	−69710.3	−0.481007
$117$	68544.2	0.462920
$118$	−179216.	−1.18487
$119$	−32108.0	−0.207848
$120$	24306.4	0.154087
$121$	0	0
$122$	216570.	1.31734
$123$	61510.2	0.366593
$124$	104423.	0.609879
$125$	−15625.0	−0.0894427
$126$	−112230.	−0.629773
$127$	178298.	0.980928	0.490464	−	0.871462i	$-0.336827\pi$
$127$	178298.	0.980928	0.490464	+	0.871462i	$0.336827\pi$
$128$	−198658.	−1.07172
$129$	−145727.	−0.771020
$130$	−71480.4	−0.370961
$131$	−26376.2	−0.134287	−0.0671435	−	0.997743i	$-0.521389\pi$
$131$	−26376.2	−0.134287	−0.0671435	+	0.997743i	$0.521389\pi$
$132$	0	0
$133$	−72681.3	−0.356282
$134$	−366517.	−1.76332
$135$	−89692.3	−0.423565
$136$	36495.0	0.169194
$137$	49019.8	0.223136	0.111568	−	0.993757i	$-0.464413\pi$
$137$	49019.8	0.223136	0.111568	+	0.993757i	$0.464413\pi$
$138$	−166568.	−0.744549
$139$	−92410.2	−0.405679	−0.202840	−	0.979212i	$-0.565017\pi$
$139$	−92410.2	−0.405679	−0.202840	+	0.979212i	$0.565017\pi$
$140$	39009.7	0.168210
$141$	−224055.	−0.949088
$142$	−158035.	−0.657707
$143$	0	0
$144$	212592.	0.854359
$145$	108935.	0.430274
$146$	183478.	0.712363
$147$	63967.4	0.244155
$148$	−179156.	−0.672320
$149$	−152564.	−0.562971	−0.281485	−	0.959566i	$-0.590827\pi$
$149$	−152564.	−0.562971	−0.281485	+	0.959566i	$0.590827\pi$
$150$	37974.4	0.137804
$151$	−143009.	−0.510413	−0.255206	−	0.966887i	$-0.582143\pi$
$151$	−143009.	−0.510413	−0.255206	+	0.966887i	$0.582143\pi$
$152$	82612.0	0.290024
$153$	−54674.9	−0.188825
$154$	0	0
$155$	−163180.	−0.545553
$156$	57903.4	0.190499
$157$	542247.	1.75569	0.877846	−	0.478944i	$-0.158980\pi$
$157$	542247.	1.75569	0.877846	+	0.478944i	$0.158980\pi$
$158$	−666010.	−2.12245
$159$	−26563.1	−0.0833270
$160$	−133009.	−0.410753
$161$	267387.	0.812972
$162$	−61626.9	−0.184494
$163$	−174131.	−0.513344	−0.256672	−	0.966499i	$-0.582626\pi$
$163$	−174131.	−0.513344	−0.256672	+	0.966499i	$0.582626\pi$
$164$	−112207.	−0.325769
$165$	0	0
$166$	88085.6	0.248104
$167$	−480769.	−1.33397	−0.666984	−	0.745072i	$-0.732415\pi$
$167$	−480769.	−1.33397	−0.666984	+	0.745072i	$0.732415\pi$
$168$	94829.0	0.259220
$169$	−200972.	−0.541276
$170$	57017.0	0.151315
$171$	−123765.	−0.323674
$172$	265835.	0.685159
$173$	153661.	0.390345	0.195173	−	0.980769i	$-0.437473\pi$
$173$	153661.	0.390345	0.195173	+	0.980769i	$0.437473\pi$
$174$	−264751.	−0.662924
$175$	−60959.4	−0.150469
$176$	0	0
$177$	−226863.	−0.544290
$178$	−419326.	−0.991978
$179$	−264186.	−0.616279	−0.308139	−	0.951341i	$-0.599706\pi$
$179$	−264186.	−0.616279	−0.308139	+	0.951341i	$0.599706\pi$
$180$	66427.5	0.152815
$181$	−782425.	−1.77520	−0.887598	−	0.460620i	$-0.847627\pi$
$181$	−782425.	−1.77520	−0.887598	+	0.460620i	$0.847627\pi$
$182$	−278874.	−0.624064
$183$	274147.	0.605140
$184$	−303921.	−0.661784
$185$	279962.	0.601409
$186$	396586.	0.840534
$187$	0	0
$188$	408721.	0.843397
$189$	−349926.	−0.712560
$190$	129067.	0.259376
$191$	−988176.	−1.95998	−0.979989	−	0.199054i	$-0.936213\pi$
$191$	−988176.	−1.95998	−0.979989	+	0.199054i	$0.936213\pi$
$192$	−35958.2	−0.0703955
$193$	−158668.	−0.306617	−0.153308	−	0.988178i	$-0.548993\pi$
$193$	−158668.	−0.306617	−0.153308	+	0.988178i	$0.548993\pi$
$194$	−514620.	−0.981709
$195$	−90484.3	−0.170407
$196$	−116689.	−0.216966
$197$	−71920.8	−0.132035	−0.0660175	−	0.997818i	$-0.521029\pi$
$197$	−71920.8	−0.132035	−0.0660175	+	0.997818i	$0.521029\pi$
$198$	0	0
$199$	335394.	0.600376	0.300188	−	0.953880i	$-0.402951\pi$
$199$	335394.	0.600376	0.300188	+	0.953880i	$0.402951\pi$
$200$	69288.5	0.122486
$201$	−463960.	−0.810009
$202$	102272.	0.176351
$203$	424998.	0.723847
$204$	−46187.2	−0.0777045
$205$	175343.	0.291410
$206$	−558841.	−0.917531
$207$	455319.	0.738567
$208$	528256.	0.846615
$209$	0	0
$210$	148154.	0.231827
$211$	−953230.	−1.47398	−0.736990	−	0.675904i	$-0.763753\pi$
$211$	−953230.	−1.47398	−0.736990	+	0.675904i	$0.763753\pi$
$212$	48456.3	0.0740476
$213$	−200051.	−0.302128
$214$	978181.	1.46011
$215$	−415414.	−0.612893
$216$	397737.	0.580045
$217$	−636631.	−0.917779
$218$	−412148.	−0.587370
$219$	232258.	0.327235
$220$	0	0
$221$	−135858.	−0.187114
$222$	−680410.	−0.926592
$223$	−298153.	−0.401492	−0.200746	−	0.979643i	$-0.564337\pi$
$223$	−298153.	−0.401492	−0.200746	+	0.979643i	$0.564337\pi$
$224$	−518922.	−0.691006
$225$	−103805.	−0.136697
$226$	−1.22880e6	−1.60034
$227$	566566.	0.729769	0.364885	−	0.931053i	$-0.381108\pi$
$227$	566566.	0.729769	0.364885	+	0.931053i	$0.381108\pi$
$228$	−104552.	−0.133197
$229$	841691.	1.06063	0.530315	−	0.847801i	$-0.322074\pi$
$229$	841691.	1.06063	0.530315	+	0.847801i	$0.322074\pi$
$230$	−474823.	−0.591851
$231$	0	0
$232$	−483066.	−0.589233
$233$	586519.	0.707770	0.353885	−	0.935289i	$-0.384860\pi$
$233$	586519.	0.707770	0.353885	+	0.935289i	$0.384860\pi$
$234$	−474879.	−0.566949
$235$	−638698.	−0.754442
$236$	413843.	0.483677
$237$	−843077.	−0.974981
$238$	222446.	0.254556
$239$	−88676.8	−0.100419	−0.0502094	−	0.998739i	$-0.515989\pi$
$239$	−88676.8	−0.100419	−0.0502094	+	0.998739i	$0.515989\pi$
$240$	−280640.	−0.314500
$241$	−1.59243e6	−1.76611	−0.883054	−	0.469271i	$-0.844517\pi$
$241$	−1.59243e6	−1.76611	−0.883054	+	0.469271i	$0.844517\pi$
$242$	0	0
$243$	−949820.	−1.03187
$244$	−500099.	−0.537751
$245$	182348.	0.194082
$246$	−426148.	−0.448975
$247$	−307536.	−0.320741
$248$	723615.	0.747100
$249$	111504.	0.113971
$250$	108251.	0.109542
$251$	−914619.	−0.916338	−0.458169	−	0.888865i	$-0.651495\pi$
$251$	−914619.	−0.916338	−0.458169	+	0.888865i	$0.651495\pi$
$252$	259160.	0.257079
$253$	0	0
$254$	−1.23526e6	−1.20136
$255$	72175.6	0.0695088
$256$	1.24511e6	1.18743
$257$	−348609.	−0.329235	−0.164617	−	0.986358i	$-0.552639\pi$
$257$	−348609.	−0.329235	−0.164617	+	0.986358i	$0.552639\pi$
$258$	1.00961e6	0.944285
$259$	1.09225e6	1.01174
$260$	165061.	0.151430
$261$	723706.	0.657599
$262$	182736.	0.164464
$263$	1.57116e6	1.40065	0.700326	−	0.713823i	$-0.253038\pi$
$263$	1.57116e6	1.40065	0.700326	+	0.713823i	$0.253038\pi$
$264$	0	0
$265$	−75721.6	−0.0662376
$266$	503542.	0.436346
$267$	−530809.	−0.455680
$268$	846355.	0.719806
$269$	−404828.	−0.341107	−0.170553	−	0.985348i	$-0.554556\pi$
$269$	−404828.	−0.341107	−0.170553	+	0.985348i	$0.554556\pi$
$270$	621395.	0.518750
$271$	−1.61283e6	−1.33403	−0.667015	−	0.745044i	$-0.732428\pi$
$271$	−1.61283e6	−1.33403	−0.667015	+	0.745044i	$0.732428\pi$
$272$	−421368.	−0.345334
$273$	−353016.	−0.286674
$274$	−339613.	−0.273280
$275$	0	0
$276$	384636.	0.303932
$277$	−1.13751e6	−0.890752	−0.445376	−	0.895344i	$-0.646930\pi$
$277$	−1.13751e6	−0.890752	−0.445376	+	0.895344i	$0.646930\pi$
$278$	640225.	0.496844
$279$	−1.08408e6	−0.833782
$280$	270323.	0.206057
$281$	2.06644e6	1.56119	0.780596	−	0.625036i	$-0.214916\pi$
$281$	2.06644e6	1.56119	0.780596	+	0.625036i	$0.214916\pi$
$282$	1.55227e6	1.16237
$283$	−1.04088e6	−0.772562	−0.386281	−	0.922381i	$-0.626240\pi$
$283$	−1.04088e6	−0.772562	−0.386281	+	0.922381i	$0.626240\pi$
$284$	364932.	0.268483
$285$	163381.	0.119149
$286$	0	0
$287$	684084.	0.490236
$288$	−883645.	−0.627764
$289$	−1.31149e6	−0.923676
$290$	−754706.	−0.526967
$291$	−651438.	−0.450963
$292$	−423684.	−0.290794
$293$	1.32727e6	0.903216	0.451608	−	0.892217i	$-0.350851\pi$
$293$	1.32727e6	0.903216	0.451608	+	0.892217i	$0.350851\pi$
$294$	−443171.	−0.299022
$295$	−646702.	−0.432662
$296$	−1.24148e6	−0.823591
$297$	0	0
$298$	1.05697e6	0.689483
$299$	1.13139e6	0.731873
$300$	−87690.0	−0.0562532
$301$	−1.62070e6	−1.03106
$302$	990778.	0.625114
$303$	129462.	0.0810097
$304$	−953832.	−0.591954
$305$	781493.	0.481034
$306$	378792.	0.231258
$307$	2.32241e6	1.40635	0.703175	−	0.711017i	$-0.251765\pi$
$307$	2.32241e6	1.40635	0.703175	+	0.711017i	$0.251765\pi$
$308$	0	0
$309$	−707416.	−0.421482
$310$	1.13052e6	0.668151
$311$	688254.	0.403504	0.201752	−	0.979437i	$-0.435337\pi$
$311$	688254.	0.403504	0.201752	+	0.979437i	$0.435337\pi$
$312$	401249.	0.233361
$313$	−2.40289e6	−1.38635	−0.693175	−	0.720769i	$-0.743789\pi$
$313$	−2.40289e6	−1.38635	−0.693175	+	0.720769i	$0.743789\pi$
$314$	−3.75673e6	−2.15023
$315$	−404984.	−0.229965
$316$	1.53794e6	0.866406
$317$	1.74472e6	0.975161	0.487581	−	0.873078i	$-0.337880\pi$
$317$	1.74472e6	0.975161	0.487581	+	0.873078i	$0.337880\pi$
$318$	184031.	0.102052
$319$	0	0
$320$	−102504.	−0.0559582
$321$	1.23824e6	0.670723
$322$	−1.85248e6	−0.995665
$323$	245309.	0.130830
$324$	142308.	0.0753123
$325$	−257937.	−0.135458
$326$	1.20640e6	0.628703
$327$	−521722.	−0.269817
$328$	−777553.	−0.399067
$329$	−2.49182e6	−1.26919
$330$	0	0
$331$	1.70336e6	0.854546	0.427273	−	0.904123i	$-0.359474\pi$
$331$	1.70336e6	0.854546	0.427273	+	0.904123i	$0.359474\pi$
$332$	−203406.	−0.101279
$333$	1.85993e6	0.919148
$334$	3.33081e6	1.63374
$335$	−1.32258e6	−0.643886
$336$	−1.09489e6	−0.529080
$337$	−3.00186e6	−1.43984	−0.719922	−	0.694055i	$-0.755823\pi$
$337$	−3.00186e6	−1.43984	−0.719922	+	0.694055i	$0.755823\pi$
$338$	1.39235e6	0.662912
$339$	−1.55550e6	−0.735139
$340$	−131663.	−0.0617683
$341$	0	0
$342$	857454.	0.396411
$343$	2.35068e6	1.07884
$344$	1.84214e6	0.839318
$345$	−601061.	−0.271876
$346$	−1.06458e6	−0.478064
$347$	2.59348e6	1.15627	0.578135	−	0.815941i	$-0.303781\pi$
$347$	2.59348e6	1.15627	0.578135	+	0.815941i	$0.303781\pi$
$348$	611358.	0.270612
$349$	−2.94017e6	−1.29214	−0.646070	−	0.763279i	$-0.723588\pi$
$349$	−2.94017e6	−1.29214	−0.646070	+	0.763279i	$0.723588\pi$
$350$	422332.	0.184282
$351$	−1.48064e6	−0.641478
$352$	0	0
$353$	−419329.	−0.179109	−0.0895547	−	0.995982i	$-0.528544\pi$
$353$	−419329.	−0.179109	−0.0895547	+	0.995982i	$0.528544\pi$
$354$	1.57172e6	0.666603
$355$	−570271.	−0.240165
$356$	968302.	0.404935
$357$	281586.	0.116934
$358$	1.83030e6	0.754770
$359$	2.61176e6	1.06954	0.534770	−	0.844998i	$-0.320398\pi$
$359$	2.61176e6	1.06954	0.534770	+	0.844998i	$0.320398\pi$
$360$	460318.	0.187198
$361$	−1.92080e6	−0.775738
$362$	5.42070e6	2.17412
$363$	0	0
$364$	643971.	0.254749
$365$	662081.	0.260123
$366$	−1.89931e6	−0.741129
$367$	2.45230e6	0.950404	0.475202	−	0.879877i	$-0.342375\pi$
$367$	2.45230e6	0.950404	0.475202	+	0.879877i	$0.342375\pi$
$368$	3.50905e6	1.35073
$369$	1.16489e6	0.445368
$370$	−1.93960e6	−0.736559
$371$	−295420.	−0.111431
$372$	−915791.	−0.343115
$373$	286790.	0.106731	0.0533657	−	0.998575i	$-0.483005\pi$
$373$	286790.	0.106731	0.0533657	+	0.998575i	$0.483005\pi$
$374$	0	0
$375$	137031.	0.0503200
$376$	2.83228e6	1.03316
$377$	1.79829e6	0.651638
$378$	2.42431e6	0.872688
$379$	2.93968e6	1.05124	0.525620	−	0.850720i	$-0.323833\pi$
$379$	2.93968e6	1.05124	0.525620	+	0.850720i	$0.323833\pi$
$380$	−298039.	−0.105880
$381$	−1.56367e6	−0.551865
$382$	6.84616e6	2.40043
$383$	3.75887e6	1.30936	0.654681	−	0.755905i	$-0.272803\pi$
$383$	3.75887e6	1.30936	0.654681	+	0.755905i	$0.272803\pi$
$384$	1.74222e6	0.602943
$385$	0	0
$386$	1.09926e6	0.375520
$387$	−2.75980e6	−0.936699
$388$	1.18835e6	0.400743
$389$	4.99193e6	1.67261	0.836304	−	0.548265i	$-0.184712\pi$
$389$	4.99193e6	1.67261	0.836304	+	0.548265i	$0.184712\pi$
$390$	626882.	0.208701
$391$	−902466.	−0.298531
$392$	−808614.	−0.265782
$393$	231319.	0.0755492
$394$	498273.	0.161706
$395$	−2.40330e6	−0.775025
$396$	0	0
$397$	−1.33592e6	−0.425406	−0.212703	−	0.977117i	$-0.568227\pi$
$397$	−1.33592e6	−0.425406	−0.212703	+	0.977117i	$0.568227\pi$
$398$	−2.32364e6	−0.735293
$399$	637414.	0.200442
$400$	−800000.	−0.250000
$401$	−5.90548e6	−1.83398	−0.916990	−	0.398911i	$-0.869388\pi$
$401$	−5.90548e6	−1.83398	−0.916990	+	0.398911i	$0.869388\pi$
$402$	3.21435e6	0.992036
$403$	−2.69377e6	−0.826225
$404$	−236165.	−0.0719884
$405$	−222381.	−0.0673690
$406$	−2.94442e6	−0.886511
$407$	0	0
$408$	−320060.	−0.0951878
$409$	−5.08742e6	−1.50380	−0.751899	−	0.659278i	$-0.770862\pi$
$409$	−5.08742e6	−1.50380	−0.751899	+	0.659278i	$0.770862\pi$
$410$	−1.21479e6	−0.356896
$411$	−429903.	−0.125535
$412$	1.29047e6	0.374545
$413$	−2.52305e6	−0.727864
$414$	−3.15449e6	−0.904540
$415$	317857.	0.0905966
$416$	−2.19571e6	−0.622074
$417$	810436.	0.228233
$418$	0	0
$419$	−4.99006e6	−1.38858	−0.694290	−	0.719695i	$-0.744281\pi$
$419$	−4.99006e6	−1.38858	−0.694290	+	0.719695i	$0.744281\pi$
$420$	−342114.	−0.0946341
$421$	5.18209e6	1.42495	0.712475	−	0.701698i	$-0.247574\pi$
$421$	5.18209e6	1.42495	0.712475	+	0.701698i	$0.247574\pi$
$422$	6.60405e6	1.80522
$423$	−4.24318e6	−1.15303
$424$	335785.	0.0907081
$425$	205746.	0.0552534
$426$	1.38597e6	0.370023
$427$	3.04892e6	0.809238
$428$	−2.25880e6	−0.596031
$429$	0	0
$430$	2.87802e6	0.750624
$431$	6.86906e6	1.78116	0.890582	−	0.454823i	$-0.150297\pi$
$431$	6.86906e6	1.78116	0.890582	+	0.454823i	$0.150297\pi$
$432$	−4.59224e6	−1.18390
$433$	5.11781e6	1.31179	0.655895	−	0.754853i	$-0.272292\pi$
$433$	5.11781e6	1.31179	0.655895	+	0.754853i	$0.272292\pi$
$434$	4.41062e6	1.12402
$435$	−955354.	−0.242070
$436$	951725.	0.239770
$437$	−2.04287e6	−0.511726
$438$	−1.60910e6	−0.400772
$439$	−3.38097e6	−0.837299	−0.418649	−	0.908148i	$-0.637496\pi$
$439$	−3.38097e6	−0.837299	−0.418649	+	0.908148i	$0.637496\pi$
$440$	0	0
$441$	1.21142e6	0.296620
$442$	941236.	0.229162
$443$	−3.02094e6	−0.731362	−0.365681	−	0.930740i	$-0.619164\pi$
$443$	−3.02094e6	−0.731362	−0.365681	+	0.930740i	$0.619164\pi$
$444$	1.57119e6	0.378244
$445$	−1.51314e6	−0.362226
$446$	2.06562e6	0.491716
$447$	1.33798e6	0.316724
$448$	−399908.	−0.0941380
$449$	6.35481e6	1.48760	0.743801	−	0.668402i	$-0.233021\pi$
$449$	6.35481e6	1.48760	0.743801	+	0.668402i	$0.233021\pi$
$450$	719166.	0.167416
$451$	0	0
$452$	2.83753e6	0.653273
$453$	1.25419e6	0.287156
$454$	−3.92521e6	−0.893765
$455$	−1.00632e6	−0.227880
$456$	−724506.	−0.163166
$457$	1.96164e6	0.439368	0.219684	−	0.975571i	$-0.429497\pi$
$457$	1.96164e6	0.439368	0.219684	+	0.975571i	$0.429497\pi$
$458$	−5.83129e6	−1.29898
$459$	1.18105e6	0.261658
$460$	1.09645e6	0.241600
$461$	328999.	0.0721012	0.0360506	−	0.999350i	$-0.488522\pi$
$461$	328999.	0.0721012	0.0360506	+	0.999350i	$0.488522\pi$
$462$	0	0
$463$	−2.33428e6	−0.506059	−0.253030	−	0.967459i	$-0.581427\pi$
$463$	−2.33428e6	−0.506059	−0.253030	+	0.967459i	$0.581427\pi$
$464$	5.57745e6	1.20265
$465$	1.43108e6	0.306926
$466$	−4.06344e6	−0.866821
$467$	−2.28204e6	−0.484206	−0.242103	−	0.970251i	$-0.577837\pi$
$467$	−2.28204e6	−0.484206	−0.242103	+	0.970251i	$0.577837\pi$
$468$	1.09658e6	0.231434
$469$	−5.15991e6	−1.08320
$470$	4.42494e6	0.923981
$471$	−4.75550e6	−0.987743
$472$	2.86778e6	0.592503
$473$	0	0
$474$	5.84090e6	1.19408
$475$	465738.	0.0947126
$476$	−513669.	−0.103912
$477$	−503056.	−0.101233
$478$	614360.	0.122985
$479$	5.71067e6	1.13723	0.568615	−	0.822604i	$-0.307479\pi$
$479$	5.71067e6	1.13723	0.568615	+	0.822604i	$0.307479\pi$
$480$	1.16649e6	0.231088
$481$	4.62162e6	0.910817
$482$	1.10325e7	2.16299
$483$	−2.34498e6	−0.457374
$484$	0	0
$485$	−1.85701e6	−0.358476
$486$	6.58042e6	1.26376
$487$	−4.07084e6	−0.777789	−0.388895	−	0.921282i	$-0.627143\pi$
$487$	−4.07084e6	−0.777789	−0.388895	+	0.921282i	$0.627143\pi$
$488$	−3.46550e6	−0.658744
$489$	1.52713e6	0.288804
$490$	−1.26332e6	−0.237696
$491$	−1.85323e6	−0.346917	−0.173459	−	0.984841i	$-0.555494\pi$
$491$	−1.85323e6	−0.346917	−0.173459	+	0.984841i	$0.555494\pi$
$492$	984053.	0.183276
$493$	−1.43442e6	−0.265803
$494$	2.13063e6	0.392818
$495$	0	0
$496$	−8.35481e6	−1.52487
$497$	−2.22486e6	−0.404028
$498$	−772509.	−0.139582
$499$	5.50169e6	0.989110	0.494555	−	0.869146i	$-0.335331\pi$
$499$	5.50169e6	0.989110	0.494555	+	0.869146i	$0.335331\pi$
$500$	−249972.	−0.0447163
$501$	4.21634e6	0.750484
$502$	6.33655e6	1.12226
$503$	−6.97396e6	−1.22902	−0.614511	−	0.788909i	$-0.710646\pi$
$503$	−6.97396e6	−1.22902	−0.614511	+	0.788909i	$0.710646\pi$
$504$	1.79589e6	0.314922
$505$	369050.	0.0643957
$506$	0	0
$507$	1.76252e6	0.304519
$508$	2.85245e6	0.490409
$509$	−2.33628e6	−0.399697	−0.199848	−	0.979827i	$-0.564045\pi$
$509$	−2.33628e6	−0.399697	−0.199848	+	0.979827i	$0.564045\pi$
$510$	−500038.	−0.0851290
$511$	2.58305e6	0.437603
$512$	−2.26917e6	−0.382554
$513$	2.67348e6	0.448522
$514$	2.41519e6	0.403221
$515$	−2.01658e6	−0.335041
$516$	−2.33137e6	−0.385467
$517$	0	0
$518$	−7.56716e6	−1.23911
$519$	−1.34761e6	−0.219606
$520$	1.14381e6	0.185501
$521$	−9.84555e6	−1.58908	−0.794540	−	0.607212i	$-0.792288\pi$
$521$	−9.84555e6	−1.58908	−0.794540	+	0.607212i	$0.792288\pi$
$522$	−5.01389e6	−0.805375
$523$	6.24599e6	0.998498	0.499249	−	0.866459i	$-0.333609\pi$
$523$	6.24599e6	0.998498	0.499249	+	0.866459i	$0.333609\pi$
$524$	−421972.	−0.0671359
$525$	534613.	0.0846529
$526$	−1.08851e7	−1.71541
$527$	2.14871e6	0.337017
$528$	0	0
$529$	1.07917e6	0.167669
$530$	524604.	0.0811227
$531$	−4.29636e6	−0.661248
$532$	−1.16277e6	−0.178121
$533$	2.89456e6	0.441331
$534$	3.67748e6	0.558082
$535$	3.52977e6	0.533166
$536$	5.86493e6	0.881760
$537$	2.31691e6	0.346715
$538$	2.80468e6	0.417761
$539$	0	0
$540$	−1.43491e6	−0.211759
$541$	2.09170e6	0.307260	0.153630	−	0.988128i	$-0.450904\pi$
$541$	2.09170e6	0.307260	0.153630	+	0.988128i	$0.450904\pi$
$542$	1.11738e7	1.63382
$543$	6.86185e6	0.998716
$544$	1.75143e6	0.253744
$545$	−1.48724e6	−0.214481
$546$	2.44572e6	0.351095
$547$	1.39294e6	0.199050	0.0995252	−	0.995035i	$-0.468268\pi$
$547$	1.39294e6	0.199050	0.0995252	+	0.995035i	$0.468268\pi$
$548$	784229.	0.111556
$549$	5.19184e6	0.735175
$550$	0	0
$551$	−3.24704e6	−0.455626
$552$	2.66538e6	0.372316
$553$	−9.37625e6	−1.30382
$554$	7.88077e6	1.09092
$555$	−2.45526e6	−0.338350
$556$	−1.47840e6	−0.202817
$557$	1.22063e7	1.66704	0.833518	−	0.552492i	$-0.186323\pi$
$557$	1.22063e7	1.66704	0.833518	+	0.552492i	$0.186323\pi$
$558$	7.51062e6	1.02115
$559$	−6.85765e6	−0.928209
$560$	−3.12112e6	−0.420573
$561$	0	0
$562$	−1.43164e7	−1.91203
$563$	−8.93896e6	−1.18855	−0.594273	−	0.804263i	$-0.702560\pi$
$563$	−8.93896e6	−1.18855	−0.594273	+	0.804263i	$0.702560\pi$
$564$	−3.58447e6	−0.474491
$565$	−4.43415e6	−0.584371
$566$	7.21127e6	0.946173
$567$	−867598.	−0.113334
$568$	2.52885e6	0.328891
$569$	−8.92494e6	−1.15565	−0.577823	−	0.816162i	$-0.696097\pi$
$569$	−8.92494e6	−1.15565	−0.577823	+	0.816162i	$0.696097\pi$
$570$	−1.13191e6	−0.145924
$571$	−1.40113e7	−1.79841	−0.899203	−	0.437531i	$-0.855853\pi$
$571$	−1.40113e7	−1.79841	−0.899203	+	0.437531i	$0.855853\pi$
$572$	0	0
$573$	8.66629e6	1.10267
$574$	−4.73939e6	−0.600402
$575$	−1.71340e6	−0.216117
$576$	−680982.	−0.0855223
$577$	9.59582e6	1.19989	0.599947	−	0.800040i	$-0.295188\pi$
$577$	9.59582e6	1.19989	0.599947	+	0.800040i	$0.295188\pi$
$578$	9.08609e6	1.13125
$579$	1.39152e6	0.172501
$580$	1.74276e6	0.215113
$581$	1.24009e6	0.152410
$582$	4.51321e6	0.552304
$583$	0	0
$584$	−2.93598e6	−0.356222
$585$	−1.71361e6	−0.207024
$586$	−9.19545e6	−1.10619
$587$	1.11952e6	0.134102	0.0670510	−	0.997750i	$-0.478641\pi$
$587$	1.11952e6	0.134102	0.0670510	+	0.997750i	$0.478641\pi$
$588$	1.02336e6	0.122064
$589$	4.86394e6	0.577697
$590$	4.48040e6	0.529891
$591$	630744.	0.0742822
$592$	1.43341e7	1.68099
$593$	−4.86477e6	−0.568101	−0.284050	−	0.958809i	$-0.591678\pi$
$593$	−4.86477e6	−0.568101	−0.284050	+	0.958809i	$0.591678\pi$
$594$	0	0
$595$	802699.	0.0929523
$596$	−2.44075e6	−0.281454
$597$	−2.94140e6	−0.337768
$598$	−7.83838e6	−0.896341
$599$	7.28602e6	0.829704	0.414852	−	0.909889i	$-0.363833\pi$
$599$	7.28602e6	0.829704	0.414852	+	0.909889i	$0.363833\pi$
$600$	−607659.	−0.0689100
$601$	−3.43060e6	−0.387422	−0.193711	−	0.981059i	$-0.562052\pi$
$601$	−3.43060e6	−0.387422	−0.193711	+	0.981059i	$0.562052\pi$
$602$	1.12283e7	1.26277
$603$	−8.78654e6	−0.984067
$604$	−2.28789e6	−0.255178
$605$	0	0
$606$	−896925.	−0.0992144
$607$	−9.12658e6	−1.00539	−0.502697	−	0.864463i	$-0.667659\pi$
$607$	−9.12658e6	−1.00539	−0.502697	+	0.864463i	$0.667659\pi$
$608$	3.96463e6	0.434955
$609$	−3.72722e6	−0.407232
$610$	−5.41424e6	−0.589132
$611$	−1.05436e7	−1.14258
$612$	−874700.	−0.0944019
$613$	−1.05611e7	−1.13516	−0.567581	−	0.823317i	$-0.692121\pi$
$613$	−1.05611e7	−1.13516	−0.567581	+	0.823317i	$0.692121\pi$
$614$	−1.60898e7	−1.72239
$615$	−1.53776e6	−0.163946
$616$	0	0
$617$	6.71725e6	0.710360	0.355180	−	0.934798i	$-0.384420\pi$
$617$	6.71725e6	0.710360	0.355180	+	0.934798i	$0.384420\pi$
$618$	4.90103e6	0.516198
$619$	−1.27690e7	−1.33946	−0.669730	−	0.742604i	$-0.733590\pi$
$619$	−1.27690e7	−1.33946	−0.669730	+	0.742604i	$0.733590\pi$
$620$	−2.61058e6	−0.272746
$621$	−9.83545e6	−1.02345
$622$	−4.76827e6	−0.494180
$623$	−5.90338e6	−0.609369
$624$	−4.63280e6	−0.476301
$625$	390625.	0.0400000
$626$	1.66474e7	1.69789
$627$	0	0
$628$	8.67498e6	0.877747
$629$	−3.68647e6	−0.371522
$630$	2.80576e6	0.281643
$631$	−1.34469e6	−0.134447	−0.0672233	−	0.997738i	$-0.521414\pi$
$631$	−1.34469e6	−0.134447	−0.0672233	+	0.997738i	$0.521414\pi$
$632$	1.06574e7	1.06135
$633$	8.35981e6	0.829253
$634$	−1.20875e7	−1.19430
$635$	−4.45745e6	−0.438684
$636$	−424961.	−0.0416588
$637$	3.01019e6	0.293931
$638$	0	0
$639$	−3.78859e6	−0.367050
$640$	4.96644e6	0.479287
$641$	−253932.	−0.0244103	−0.0122051	−	0.999926i	$-0.503885\pi$
$641$	−253932.	−0.0244103	−0.0122051	+	0.999926i	$0.503885\pi$
$642$	−8.57863e6	−0.821449
$643$	−1.37861e7	−1.31496	−0.657482	−	0.753470i	$-0.728378\pi$
$643$	−1.37861e7	−1.31496	−0.657482	+	0.753470i	$0.728378\pi$
$644$	4.27771e6	0.406440
$645$	3.64317e6	0.344811
$646$	−1.69952e6	−0.160230
$647$	1.68990e7	1.58709	0.793544	−	0.608513i	$-0.208234\pi$
$647$	1.68990e7	1.58709	0.793544	+	0.608513i	$0.208234\pi$
$648$	986140.	0.0922574
$649$	0	0
$650$	1.78701e6	0.165899
$651$	5.58324e6	0.516338
$652$	−2.78579e6	−0.256643
$653$	9.90887e6	0.909371	0.454685	−	0.890652i	$-0.349752\pi$
$653$	9.90887e6	0.909371	0.454685	+	0.890652i	$0.349752\pi$
$654$	3.61453e6	0.330451
$655$	659405.	0.0600550
$656$	8.97757e6	0.814515
$657$	4.39853e6	0.397552
$658$	1.72635e7	1.55440
$659$	−2.04546e6	−0.183476	−0.0917378	−	0.995783i	$-0.529242\pi$
$659$	−2.04546e6	−0.183476	−0.0917378	+	0.995783i	$0.529242\pi$
$660$	0	0
$661$	1.21559e6	0.108214	0.0541070	−	0.998535i	$-0.482769\pi$
$661$	1.21559e6	0.108214	0.0541070	+	0.998535i	$0.482769\pi$
$662$	−1.18010e7	−1.04658
$663$	1.19147e6	0.105269
$664$	−1.40953e6	−0.124066
$665$	1.81703e6	0.159334
$666$	−1.28857e7	−1.12570
$667$	1.19455e7	1.03966
$668$	−7.69145e6	−0.666910
$669$	2.61480e6	0.225877
$670$	9.16292e6	0.788582
$671$	0	0
$672$	4.55094e6	0.388757
$673$	−1.48030e7	−1.25983	−0.629917	−	0.776662i	$-0.716911\pi$
$673$	−1.48030e7	−1.25983	−0.629917	+	0.776662i	$0.716911\pi$
$674$	2.07971e7	1.76341
$675$	2.24231e6	0.189424
$676$	−3.21519e6	−0.270607
$677$	1.70600e7	1.43056	0.715282	−	0.698836i	$-0.246298\pi$
$677$	1.70600e7	1.43056	0.715282	+	0.698836i	$0.246298\pi$
$678$	1.07766e7	0.900341
$679$	−7.24495e6	−0.603061
$680$	−912374.	−0.0756660
$681$	−4.96877e6	−0.410565
$682$	0	0
$683$	−2.30891e6	−0.189389	−0.0946946	−	0.995506i	$-0.530187\pi$
$683$	−2.30891e6	−0.189389	−0.0946946	+	0.995506i	$0.530187\pi$
$684$	−1.98002e6	−0.161819
$685$	−1.22550e6	−0.0997896
$686$	−1.62857e7	−1.32128
$687$	−7.38162e6	−0.596705
$688$	−2.12692e7	−1.71309
$689$	−1.25001e6	−0.100315
$690$	4.16419e6	0.332972
$691$	3.55307e6	0.283080	0.141540	−	0.989933i	$-0.454795\pi$
$691$	3.55307e6	0.283080	0.141540	+	0.989933i	$0.454795\pi$
$692$	2.45830e6	0.195151
$693$	0	0
$694$	−1.79678e7	−1.41611
$695$	2.31026e6	0.181425
$696$	4.23649e6	0.331499
$697$	−2.30887e6	−0.180019
$698$	2.03697e7	1.58251
$699$	−5.14376e6	−0.398188
$700$	−975242.	−0.0752258
$701$	−1.21007e7	−0.930066	−0.465033	−	0.885293i	$-0.653958\pi$
$701$	−1.21007e7	−0.930066	−0.465033	+	0.885293i	$0.653958\pi$
$702$	1.02580e7	0.785632
$703$	−8.34490e6	−0.636844
$704$	0	0
$705$	5.60137e6	0.424445
$706$	2.90514e6	0.219359
$707$	1.43981e6	0.108332
$708$	−3.62940e6	−0.272114
$709$	−2.15898e7	−1.61300	−0.806499	−	0.591235i	$-0.798640\pi$
$709$	−2.15898e7	−1.61300	−0.806499	+	0.591235i	$0.798640\pi$
$710$	3.95088e6	0.294136
$711$	−1.59663e7	−1.18449
$712$	6.70997e6	0.496045
$713$	−1.78939e7	−1.31820
$714$	−1.95085e6	−0.143212
$715$	0	0
$716$	−4.22650e6	−0.308105
$717$	777694.	0.0564951
$718$	−1.80945e7	−1.30989
$719$	−1.84555e6	−0.133139	−0.0665694	−	0.997782i	$-0.521205\pi$
$719$	−1.84555e6	−0.133139	−0.0665694	+	0.997782i	$0.521205\pi$
$720$	−5.31480e6	−0.382081
$721$	−7.86751e6	−0.563636
$722$	1.33075e7	0.950063
$723$	1.39656e7	0.993603
$724$	−1.25174e7	−0.887498
$725$	−2.72336e6	−0.192425
$726$	0	0
$727$	8.91402e6	0.625515	0.312757	−	0.949833i	$-0.398747\pi$
$727$	8.91402e6	0.625515	0.312757	+	0.949833i	$0.398747\pi$
$728$	4.46248e6	0.312067
$729$	6.16836e6	0.429884
$730$	−4.58695e6	−0.318579
$731$	5.47007e6	0.378616
$732$	4.38586e6	0.302536
$733$	−1.34201e7	−0.922561	−0.461280	−	0.887254i	$-0.652610\pi$
$733$	−1.34201e7	−0.922561	−0.461280	+	0.887254i	$0.652610\pi$
$734$	−1.69897e7	−1.16398
$735$	−1.59919e6	−0.109189
$736$	−1.45855e7	−0.992490
$737$	0	0
$738$	−8.07045e6	−0.545452
$739$	−9.47994e6	−0.638550	−0.319275	−	0.947662i	$-0.603439\pi$
$739$	−9.47994e6	−0.638550	−0.319275	+	0.947662i	$0.603439\pi$
$740$	4.47889e6	0.300671
$741$	2.69709e6	0.180447
$742$	2.04669e6	0.136472
$743$	−2.38018e7	−1.58175	−0.790873	−	0.611980i	$-0.790373\pi$
$743$	−2.38018e7	−1.58175	−0.790873	+	0.611980i	$0.790373\pi$
$744$	−6.34610e6	−0.420314
$745$	3.81409e6	0.251768
$746$	−1.98690e6	−0.130716
$747$	2.11168e6	0.138461
$748$	0	0
$749$	1.37711e7	0.896940
$750$	−949361.	−0.0616280
$751$	1.39390e7	0.901844	0.450922	−	0.892563i	$-0.351095\pi$
$751$	1.39390e7	0.901844	0.450922	+	0.892563i	$0.351095\pi$
$752$	−3.27013e7	−2.10873
$753$	8.02119e6	0.515527
$754$	−1.24587e7	−0.798076
$755$	3.57523e6	0.228264
$756$	−5.59818e6	−0.356240
$757$	−1.29170e7	−0.819260	−0.409630	−	0.912252i	$-0.634342\pi$
$757$	−1.29170e7	−0.819260	−0.409630	+	0.912252i	$0.634342\pi$
$758$	−2.03663e7	−1.28748
$759$	0	0
$760$	−2.06530e6	−0.129703
$761$	−1.64266e7	−1.02822	−0.514109	−	0.857725i	$-0.671877\pi$
$761$	−1.64266e7	−1.02822	−0.514109	+	0.857725i	$0.671877\pi$
$762$	1.08332e7	0.675881
$763$	−5.80232e6	−0.360820
$764$	−1.58090e7	−0.979878
$765$	1.36687e6	0.0844451
$766$	−2.60417e7	−1.60360
$767$	−1.06758e7	−0.655255
$768$	−1.09196e7	−0.668042
$769$	−6.91944e6	−0.421944	−0.210972	−	0.977492i	$-0.567663\pi$
$769$	−6.91944e6	−0.421944	−0.210972	+	0.977492i	$0.567663\pi$
$770$	0	0
$771$	3.05729e6	0.185226
$772$	−2.53840e6	−0.153291
$773$	1.38589e7	0.834219	0.417110	−	0.908856i	$-0.363043\pi$
$773$	1.38589e7	0.834219	0.417110	+	0.908856i	$0.363043\pi$
$774$	1.91201e7	1.14720
$775$	4.07950e6	0.243979
$776$	8.23485e6	0.490909
$777$	−9.57898e6	−0.569202
$778$	−3.45845e7	−2.04848
$779$	−5.22650e6	−0.308579
$780$	−1.44759e6	−0.0851938
$781$	0	0
$782$	6.25235e6	0.365617
$783$	−1.56329e7	−0.911247
$784$	9.33619e6	0.542475
$785$	−1.35562e7	−0.785169
$786$	−1.60259e6	−0.0925267
$787$	−2.82924e7	−1.62829	−0.814146	−	0.580660i	$-0.802795\pi$
$787$	−2.82924e7	−1.62829	−0.814146	+	0.580660i	$0.802795\pi$
$788$	−1.15060e6	−0.0660101
$789$	−1.37790e7	−0.787999
$790$	1.66502e7	0.949190
$791$	−1.72994e7	−0.983082
$792$	0	0
$793$	1.29009e7	0.728511
$794$	9.25535e6	0.521004
$795$	664077.	0.0372650
$796$	5.36571e6	0.300154
$797$	−2.18451e7	−1.21817	−0.609085	−	0.793105i	$-0.708463\pi$
$797$	−2.18451e7	−1.21817	−0.609085	+	0.793105i	$0.708463\pi$
$798$	−4.41605e6	−0.245486
$799$	8.41021e6	0.466058
$800$	3.32523e6	0.183695
$801$	−1.00525e7	−0.553598
$802$	4.09136e7	2.24611
$803$	0	0
$804$	−7.42252e6	−0.404959
$805$	−6.68468e6	−0.363572
$806$	1.86627e7	1.01190
$807$	3.55034e6	0.191905
$808$	−1.63654e6	−0.0881856
$809$	−5.74207e6	−0.308459	−0.154229	−	0.988035i	$-0.549289\pi$
$809$	−5.74207e6	−0.308459	−0.154229	+	0.988035i	$0.549289\pi$
$810$	1.54067e6	0.0825083
$811$	2.42174e7	1.29293	0.646464	−	0.762944i	$-0.276247\pi$
$811$	2.42174e7	1.29293	0.646464	+	0.762944i	$0.276247\pi$
$812$	6.79920e6	0.361883
$813$	1.41445e7	0.750519
$814$	0	0
$815$	4.35329e6	0.229574
$816$	3.69539e6	0.194283
$817$	1.23824e7	0.649005
$818$	3.52460e7	1.84173
$819$	−6.68547e6	−0.348275
$820$	2.80517e6	0.145688
$821$	2.75893e7	1.42851	0.714254	−	0.699887i	$-0.246766\pi$
$821$	2.75893e7	1.42851	0.714254	+	0.699887i	$0.246766\pi$
$822$	2.97840e6	0.153746
$823$	−1.89005e7	−0.972687	−0.486343	−	0.873768i	$-0.661670\pi$
$823$	−1.89005e7	−0.972687	−0.486343	+	0.873768i	$0.661670\pi$
$824$	8.94247e6	0.458817
$825$	0	0
$826$	1.74799e7	0.891431
$827$	2.14401e7	1.09009	0.545046	−	0.838406i	$-0.316512\pi$
$827$	2.14401e7	1.09009	0.545046	+	0.838406i	$0.316512\pi$
$828$	7.28429e6	0.369242
$829$	2.98594e7	1.50902	0.754509	−	0.656289i	$-0.227875\pi$
$829$	2.98594e7	1.50902	0.754509	+	0.656289i	$0.227875\pi$
$830$	−2.20214e6	−0.110956
$831$	9.97597e6	0.501133
$832$	−1.69213e6	−0.0847471
$833$	−2.40111e6	−0.119894
$834$	−5.61476e6	−0.279522
$835$	1.20192e7	0.596569
$836$	0	0
$837$	2.34175e7	1.15539
$838$	3.45715e7	1.70062
$839$	1.87577e7	0.919972	0.459986	−	0.887926i	$-0.347854\pi$
$839$	1.87577e7	0.919972	0.459986	+	0.887926i	$0.347854\pi$
$840$	−2.37072e6	−0.115927
$841$	−1.52438e6	−0.0743194
$842$	−3.59019e7	−1.74517
$843$	−1.81226e7	−0.878319
$844$	−1.52500e7	−0.736907
$845$	5.02430e6	0.242066
$846$	2.93971e7	1.41214
$847$	0	0
$848$	−3.87694e6	−0.185140
$849$	9.12847e6	0.434639
$850$	−1.42542e6	−0.0676701
$851$	3.07000e7	1.45317
$852$	−3.20045e6	−0.151047
$853$	−2.87871e7	−1.35465	−0.677323	−	0.735686i	$-0.736860\pi$
$853$	−2.87871e7	−1.35465	−0.677323	+	0.735686i	$0.736860\pi$
$854$	−2.11231e7	−0.991092
$855$	3.09413e6	0.144752
$856$	−1.56527e7	−0.730136
$857$	1.22533e7	0.569905	0.284952	−	0.958542i	$-0.408022\pi$
$857$	1.22533e7	0.569905	0.284952	+	0.958542i	$0.408022\pi$
$858$	0	0
$859$	1.59234e7	0.736298	0.368149	−	0.929767i	$-0.379992\pi$
$859$	1.59234e7	0.736298	0.368149	+	0.929767i	$0.379992\pi$
$860$	−6.64588e6	−0.306412
$861$	−5.99941e6	−0.275804
$862$	−4.75893e7	−2.18143
$863$	1.45962e7	0.667132	0.333566	−	0.942727i	$-0.391748\pi$
$863$	1.45962e7	0.667132	0.333566	+	0.942727i	$0.391748\pi$
$864$	1.90878e7	0.869905
$865$	−3.84153e6	−0.174568
$866$	−3.54565e7	−1.60658
$867$	1.15017e7	0.519656
$868$	−1.01849e7	−0.458838
$869$	0	0
$870$	6.61876e6	0.296469
$871$	−2.18331e7	−0.975147
$872$	6.59511e6	0.293718
$873$	−1.23370e7	−0.547867
$874$	1.41532e7	0.626723
$875$	1.52399e6	0.0672916
$876$	3.71571e6	0.163599
$877$	3.97331e7	1.74443	0.872214	−	0.489125i	$-0.162684\pi$
$877$	3.97331e7	1.74443	0.872214	+	0.489125i	$0.162684\pi$
$878$	2.34236e7	1.02546
$879$	−1.16402e7	−0.508144
$880$	0	0
$881$	2.15286e7	0.934491	0.467246	−	0.884128i	$-0.345246\pi$
$881$	2.15286e7	0.934491	0.467246	+	0.884128i	$0.345246\pi$
$882$	−8.39284e6	−0.363277
$883$	−3.79705e6	−0.163887	−0.0819435	−	0.996637i	$-0.526113\pi$
$883$	−3.79705e6	−0.163887	−0.0819435	+	0.996637i	$0.526113\pi$
$884$	−2.17349e6	−0.0935463
$885$	5.67157e6	0.243414
$886$	2.09293e7	0.895715
$887$	2.16740e7	0.924975	0.462487	−	0.886626i	$-0.346957\pi$
$887$	2.16740e7	0.924975	0.462487	+	0.886626i	$0.346957\pi$
$888$	1.08878e7	0.463348
$889$	−1.73903e7	−0.737994
$890$	1.04832e7	0.443626
$891$	0	0
$892$	−4.76991e6	−0.200723
$893$	1.90378e7	0.798893
$894$	−9.26964e6	−0.387899
$895$	6.60465e6	0.275608
$896$	1.93761e7	0.806299
$897$	−9.92231e6	−0.411748
$898$	−4.40266e7	−1.82190
$899$	−2.84415e7	−1.17369
$900$	−1.66069e6	−0.0683410
$901$	997082.	0.0409184
$902$	0	0
$903$	1.42135e7	0.580072
$904$	1.96631e7	0.800258
$905$	1.95606e7	0.793891
$906$	−8.68911e6	−0.351686
$907$	−8.87651e6	−0.358281	−0.179141	−	0.983823i	$-0.557332\pi$
$907$	−8.87651e6	−0.358281	−0.179141	+	0.983823i	$0.557332\pi$
$908$	9.06403e6	0.364844
$909$	2.45178e6	0.0984174
$910$	6.97185e6	0.279090
$911$	3.94519e7	1.57497	0.787484	−	0.616335i	$-0.211383\pi$
$911$	3.94519e7	1.57497	0.787484	+	0.616335i	$0.211383\pi$
$912$	8.36509e6	0.333030
$913$	0	0
$914$	−1.35904e7	−0.538103
$915$	−6.85368e6	−0.270627
$916$	1.34655e7	0.530255
$917$	2.57261e6	0.101030
$918$	−8.18237e6	−0.320459
$919$	−416597.	−0.0162715	−0.00813574	−	0.999967i	$-0.502590\pi$
$919$	−416597.	−0.0162715	−0.00813574	+	0.999967i	$0.502590\pi$
$920$	7.59803e6	0.295959
$921$	−2.03675e7	−0.791205
$922$	−2.27933e6	−0.0883039
$923$	−9.41402e6	−0.363723
$924$	0	0
$925$	−6.99906e6	−0.268958
$926$	1.61721e7	0.619782
$927$	−1.33972e7	−0.512051
$928$	−2.31828e7	−0.883684
$929$	3.69499e7	1.40467	0.702334	−	0.711848i	$-0.252141\pi$
$929$	3.69499e7	1.40467	0.702334	+	0.711848i	$0.252141\pi$
$930$	−9.91466e6	−0.375898
$931$	−5.43528e6	−0.205517
$932$	9.38324e6	0.353845
$933$	−6.03597e6	−0.227009
$934$	1.58101e7	0.593018
$935$	0	0
$936$	7.59893e6	0.283506
$937$	−2.65436e7	−0.987668	−0.493834	−	0.869556i	$-0.664405\pi$
$937$	−2.65436e7	−0.987668	−0.493834	+	0.869556i	$0.664405\pi$
$938$	3.57482e7	1.32662
$939$	2.10733e7	0.779953
$940$	−1.02180e7	−0.377178
$941$	−3.74014e7	−1.37693	−0.688467	−	0.725267i	$-0.741716\pi$
$941$	−3.74014e7	−1.37693	−0.688467	+	0.725267i	$0.741716\pi$
$942$	3.29464e7	1.20971
$943$	1.92277e7	0.704123
$944$	−3.31111e7	−1.20933
$945$	8.74814e6	0.318667
$946$	0	0
$947$	2.42486e7	0.878641	0.439321	−	0.898330i	$-0.355219\pi$
$947$	2.42486e7	0.878641	0.439321	+	0.898330i	$0.355219\pi$
$948$	−1.34877e7	−0.487436
$949$	1.09296e7	0.393949
$950$	−3.22667e6	−0.115997
$951$	−1.53011e7	−0.548621
$952$	−3.55954e6	−0.127292
$953$	4.47391e7	1.59571	0.797857	−	0.602847i	$-0.205967\pi$
$953$	4.47391e7	1.59571	0.797857	+	0.602847i	$0.205967\pi$
$954$	3.48521e6	0.123982
$955$	2.47044e7	0.876528
$956$	−1.41867e6	−0.0502038
$957$	0	0
$958$	−3.95640e7	−1.39279
$959$	−4.78116e6	−0.167875
$960$	898955.	0.0314818
$961$	1.39751e7	0.488143
$962$	−3.20189e7	−1.11550
$963$	2.34500e7	0.814850
$964$	−2.54760e7	−0.882955
$965$	3.96670e6	0.137123
$966$	1.62462e7	0.560156
$967$	−3.79989e7	−1.30679	−0.653394	−	0.757018i	$-0.726656\pi$
$967$	−3.79989e7	−1.30679	−0.653394	+	0.757018i	$0.726656\pi$
$968$	0	0
$969$	−2.15136e6	−0.0736043
$970$	1.28655e7	0.439033
$971$	−1.22365e7	−0.416495	−0.208247	−	0.978076i	$-0.566776\pi$
$971$	−1.22365e7	−0.416495	−0.208247	+	0.978076i	$0.566776\pi$
$972$	−1.51954e7	−0.515878
$973$	9.01324e6	0.305210
$974$	2.82031e7	0.952575
$975$	2.26211e6	0.0762082
$976$	4.00124e7	1.34453
$977$	−3.30015e7	−1.10611	−0.553054	−	0.833145i	$-0.686538\pi$
$977$	−3.30015e7	−1.10611	−0.553054	+	0.833145i	$0.686538\pi$
$978$	−1.05801e7	−0.353705
$979$	0	0
$980$	2.91723e6	0.0970300
$981$	−9.88046e6	−0.327797
$982$	1.28393e7	0.424877
$983$	−1.31541e7	−0.434187	−0.217093	−	0.976151i	$-0.569658\pi$
$983$	−1.31541e7	−0.434187	−0.217093	+	0.976151i	$0.569658\pi$
$984$	6.81913e6	0.224513
$985$	1.79802e6	0.0590478
$986$	9.93779e6	0.325535
$987$	2.18532e7	0.714040
$988$	−4.92003e6	−0.160352
$989$	−4.55534e7	−1.48091
$990$	0	0
$991$	1.14642e7	0.370818	0.185409	−	0.982661i	$-0.440639\pi$
$991$	1.14642e7	0.370818	0.185409	+	0.982661i	$0.440639\pi$
$992$	3.47270e7	1.12044
$993$	−1.49384e7	−0.480763
$994$	1.54140e7	0.494821
$995$	−8.38486e6	−0.268496
$996$	1.78387e6	0.0569789
$997$	2.17229e7	0.692119	0.346060	−	0.938213i	$-0.387520\pi$
$997$	2.17229e7	0.692119	0.346060	+	0.938213i	$0.387520\pi$
$998$	−3.81161e7	−1.21139
$999$	−4.01767e7	−1.27368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.5		20
11.3	even	5		55.6.g.b.31.3	yes	40
11.4	even	5		55.6.g.b.16.3	✓	40
11.10	odd	2		605.6.a.o.1.16		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.3	✓	40	11.4	even	5
55.6.g.b.31.3	yes	40	11.3	even	5
605.6.a.o.1.16		20	11.10	odd	2
605.6.a.p.1.5		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)

\(f(q)\)	\(=\)	\(q-6.92807 q^{2} -8.76999 q^{3} +15.9982 q^{4} -25.0000 q^{5} +60.7591 q^{6} -97.5351 q^{7} +110.862 q^{8} -166.087 q^{9} +O(q^{10})\)	\(q-6.92807 q^{2} -8.76999 q^{3} +15.9982 q^{4} -25.0000 q^{5} +60.7591 q^{6} -97.5351 q^{7} +110.862 q^{8} -166.087 q^{9} +173.202 q^{10} -140.304 q^{12} -412.700 q^{13} +675.730 q^{14} +219.250 q^{15} -1280.00 q^{16} +329.194 q^{17} +1150.67 q^{18} +745.181 q^{19} -399.955 q^{20} +855.382 q^{21} -2741.44 q^{23} -972.255 q^{24} +625.000 q^{25} +2859.22 q^{26} +3587.69 q^{27} -1560.39 q^{28} -4357.38 q^{29} -1518.98 q^{30} +6527.19 q^{31} +5320.36 q^{32} -2280.68 q^{34} +2438.38 q^{35} -2657.10 q^{36} -11198.5 q^{37} -5162.67 q^{38} +3619.37 q^{39} -2771.54 q^{40} -7013.72 q^{41} -5926.15 q^{42} +16616.6 q^{43} +4152.18 q^{45} +18992.9 q^{46} +25547.9 q^{47} +11225.6 q^{48} -7293.90 q^{49} -4330.05 q^{50} -2887.02 q^{51} -6602.46 q^{52} +3028.86 q^{53} -24855.8 q^{54} -10812.9 q^{56} -6535.23 q^{57} +30188.3 q^{58} +25868.1 q^{59} +3507.60 q^{60} -31259.7 q^{61} -45220.9 q^{62} +16199.3 q^{63} +4100.14 q^{64} +10317.5 q^{65} +52903.1 q^{67} +5266.51 q^{68} +24042.4 q^{69} -16893.3 q^{70} +22810.8 q^{71} -18412.7 q^{72} -26483.2 q^{73} +77584.0 q^{74} -5481.24 q^{75} +11921.6 q^{76} -25075.3 q^{78} +96132.1 q^{79} +32000.0 q^{80} +8895.24 q^{81} +48591.6 q^{82} -12714.3 q^{83} +13684.6 q^{84} -8229.84 q^{85} -115121. q^{86} +38214.2 q^{87} +60525.7 q^{89} -28766.6 q^{90} +40252.7 q^{91} -43858.2 q^{92} -57243.4 q^{93} -176998. q^{94} -18629.5 q^{95} -46659.5 q^{96} +74280.4 q^{97} +50532.7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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