LMFDB - Embedded newform 605.6.a.p.1.16

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			1.16
Root			$8.03981$ 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)

$f(q)$	$=$	$q+8.03981 q^{2} +5.09012 q^{3} +32.6385 q^{4} -25.0000 q^{5} +40.9236 q^{6} +87.3874 q^{7} +5.13363 q^{8} -217.091 q^{9} +O(q^{10})$	\(q+8.03981 q^{2} +5.09012 q^{3} +32.6385 q^{4} -25.0000 q^{5} +40.9236 q^{6} +87.3874 q^{7} +5.13363 q^{8} -217.091 q^{9} -200.995 q^{10} +166.134 q^{12} +275.400 q^{13} +702.578 q^{14} -127.253 q^{15} -1003.16 q^{16} -535.605 q^{17} -1745.37 q^{18} +1657.77 q^{19} -815.963 q^{20} +444.812 q^{21} -45.1551 q^{23} +26.1308 q^{24} +625.000 q^{25} +2214.16 q^{26} -2341.92 q^{27} +2852.20 q^{28} +3133.95 q^{29} -1023.09 q^{30} -9702.05 q^{31} -8229.49 q^{32} -4306.16 q^{34} -2184.69 q^{35} -7085.52 q^{36} -10320.4 q^{37} +13328.2 q^{38} +1401.82 q^{39} -128.341 q^{40} -17365.6 q^{41} +3576.21 q^{42} +761.702 q^{43} +5427.27 q^{45} -363.038 q^{46} +11860.0 q^{47} -5106.20 q^{48} -9170.44 q^{49} +5024.88 q^{50} -2726.29 q^{51} +8988.64 q^{52} -37185.3 q^{53} -18828.6 q^{54} +448.614 q^{56} +8438.25 q^{57} +25196.4 q^{58} -18356.4 q^{59} -4153.35 q^{60} -5929.76 q^{61} -78002.7 q^{62} -18971.0 q^{63} -34062.4 q^{64} -6884.99 q^{65} +13531.2 q^{67} -17481.4 q^{68} -229.845 q^{69} -17564.5 q^{70} -14728.1 q^{71} -1114.46 q^{72} -14294.7 q^{73} -82974.3 q^{74} +3181.32 q^{75} +54107.2 q^{76} +11270.3 q^{78} -30544.5 q^{79} +25079.0 q^{80} +40832.4 q^{81} -139616. q^{82} +99114.1 q^{83} +14518.0 q^{84} +13390.1 q^{85} +6123.94 q^{86} +15952.2 q^{87} -8353.16 q^{89} +43634.2 q^{90} +24066.5 q^{91} -1473.79 q^{92} -49384.6 q^{93} +95352.1 q^{94} -41444.3 q^{95} -41889.1 q^{96} -25957.0 q^{97} -73728.6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.03981	1.42125	0.710625	−	0.703571i	$-0.248412\pi$
$2$	8.03981	1.42125	0.710625	+	0.703571i	$0.248412\pi$
$3$	5.09012	0.326531	0.163266	−	0.986582i	$-0.447797\pi$
$3$	5.09012	0.326531	0.163266	+	0.986582i	$0.447797\pi$
$4$	32.6385	1.01995
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	40.9236	0.464083
$7$	87.3874	0.674068	0.337034	−	0.941492i	$-0.390576\pi$
$7$	87.3874	0.674068	0.337034	+	0.941492i	$0.390576\pi$
$8$	5.13363	0.0283595
$9$	−217.091	−0.893377
$10$	−200.995	−0.635603
$11$	0	0
$11$	0	0
$12$	166.134	0.333047
$13$	275.400	0.451965	0.225983	−	0.974131i	$-0.427441\pi$
$13$	275.400	0.451965	0.225983	+	0.974131i	$0.427441\pi$
$14$	702.578	0.958020
$15$	−127.253	−0.146029
$16$	−1003.16	−0.979648
$17$	−535.605	−0.449493	−0.224746	−	0.974417i	$-0.572155\pi$
$17$	−535.605	−0.449493	−0.224746	+	0.974417i	$0.572155\pi$
$18$	−1745.37	−1.26971
$19$	1657.77	1.05351	0.526757	−	0.850016i	$-0.323408\pi$
$19$	1657.77	1.05351	0.526757	+	0.850016i	$0.323408\pi$
$20$	−815.963	−0.456137
$21$	444.812	0.220104
$22$	0	0
$23$	−45.1551	−0.0177986	−0.00889932	−	0.999960i	$-0.502833\pi$
$23$	−45.1551	−0.0177986	−0.00889932	+	0.999960i	$0.502833\pi$
$24$	26.1308	0.00926028
$25$	625.000	0.200000
$26$	2214.16	0.642356
$27$	−2341.92	−0.618247
$28$	2852.20	0.687518
$29$	3133.95	0.691986	0.345993	−	0.938237i	$-0.387542\pi$
$29$	3133.95	0.691986	0.345993	+	0.938237i	$0.387542\pi$
$30$	−1023.09	−0.207544
$31$	−9702.05	−1.81326	−0.906629	−	0.421929i	$-0.861353\pi$
$31$	−9702.05	−1.81326	−0.906629	+	0.421929i	$0.861353\pi$
$32$	−8229.49	−1.42068
$33$	0	0
$34$	−4306.16	−0.638842
$35$	−2184.69	−0.301452
$36$	−7085.52	−0.911204
$37$	−10320.4	−1.23935	−0.619675	−	0.784859i	$-0.712735\pi$
$37$	−10320.4	−1.23935	−0.619675	+	0.784859i	$0.712735\pi$
$38$	13328.2	1.49731
$39$	1401.82	0.147581
$40$	−128.341	−0.0126828
$41$	−17365.6	−1.61336	−0.806680	−	0.590989i	$-0.798738\pi$
$41$	−17365.6	−1.61336	−0.806680	+	0.590989i	$0.798738\pi$
$42$	3576.21	0.312823
$43$	761.702	0.0628223	0.0314111	−	0.999507i	$-0.490000\pi$
$43$	761.702	0.0628223	0.0314111	+	0.999507i	$0.490000\pi$
$44$	0	0
$45$	5427.27	0.399530
$46$	−363.038	−0.0252963
$47$	11860.0	0.783141	0.391570	−	0.920148i	$-0.371932\pi$
$47$	11860.0	0.783141	0.391570	+	0.920148i	$0.371932\pi$
$48$	−5106.20	−0.319886
$49$	−9170.44	−0.545632
$50$	5024.88	0.284250
$51$	−2726.29	−0.146773
$52$	8988.64	0.460984
$53$	−37185.3	−1.81836	−0.909182	−	0.416398i	$-0.863292\pi$
$53$	−37185.3	−1.81836	−0.909182	+	0.416398i	$0.863292\pi$
$54$	−18828.6	−0.878684
$55$	0	0
$56$	448.614	0.0191163
$57$	8438.25	0.344006
$58$	25196.4	0.983486
$59$	−18356.4	−0.686528	−0.343264	−	0.939239i	$-0.611533\pi$
$59$	−18356.4	−0.686528	−0.343264	+	0.939239i	$0.611533\pi$
$60$	−4153.35	−0.148943
$61$	−5929.76	−0.204039	−0.102019	−	0.994782i	$-0.532530\pi$
$61$	−5929.76	−0.204039	−0.102019	+	0.994782i	$0.532530\pi$
$62$	−78002.7	−2.57709
$63$	−18971.0	−0.602197
$64$	−34062.4	−1.03950
$65$	−6884.99	−0.202125
$66$	0	0
$67$	13531.2	0.368256	0.184128	−	0.982902i	$-0.441054\pi$
$67$	13531.2	0.368256	0.184128	+	0.982902i	$0.441054\pi$
$68$	−17481.4	−0.458462
$69$	−229.845	−0.00581181
$70$	−17564.5	−0.428439
$71$	−14728.1	−0.346737	−0.173368	−	0.984857i	$-0.555465\pi$
$71$	−14728.1	−0.346737	−0.173368	+	0.984857i	$0.555465\pi$
$72$	−1114.46	−0.0253358
$73$	−14294.7	−0.313956	−0.156978	−	0.987602i	$-0.550175\pi$
$73$	−14294.7	−0.313956	−0.156978	+	0.987602i	$0.550175\pi$
$74$	−82974.3	−1.76143
$75$	3181.32	0.0653063
$76$	54107.2	1.07454
$77$	0	0
$78$	11270.3	0.209749
$79$	−30544.5	−0.550637	−0.275318	−	0.961353i	$-0.588783\pi$
$79$	−30544.5	−0.550637	−0.275318	+	0.961353i	$0.588783\pi$
$80$	25079.0	0.438112
$81$	40832.4	0.691500
$82$	−139616.	−2.29299
$83$	99114.1	1.57921	0.789606	−	0.613615i	$-0.210285\pi$
$83$	99114.1	1.57921	0.789606	+	0.613615i	$0.210285\pi$
$84$	14518.0	0.224496
$85$	13390.1	0.201019
$86$	6123.94	0.0892862
$87$	15952.2	0.225955
$88$	0	0
$89$	−8353.16	−0.111783	−0.0558915	−	0.998437i	$-0.517800\pi$
$89$	−8353.16	−0.111783	−0.0558915	+	0.998437i	$0.517800\pi$
$90$	43634.2	0.567833
$91$	24066.5	0.304655
$92$	−1473.79	−0.0181538
$93$	−49384.6	−0.592085
$94$	95352.1	1.11304
$95$	−41444.3	−0.471146
$96$	−41889.1	−0.463898
$97$	−25957.0	−0.280107	−0.140054	−	0.990144i	$-0.544728\pi$
$97$	−25957.0	−0.280107	−0.140054	+	0.990144i	$0.544728\pi$
$98$	−73728.6	−0.775480
$99$	0	0
$100$	20399.1	0.203991
$101$	126372.	1.23267	0.616334	−	0.787485i	$-0.288617\pi$
$101$	126372.	1.23267	0.616334	+	0.787485i	$0.288617\pi$
$102$	−21918.9	−0.208602
$103$	−104864.	−0.973943	−0.486972	−	0.873418i	$-0.661899\pi$
$103$	−104864.	−0.973943	−0.486972	+	0.873418i	$0.661899\pi$
$104$	1413.80	0.0128175
$105$	−11120.3	−0.0984336
$106$	−298962.	−2.58435
$107$	12435.4	0.105002	0.0525012	−	0.998621i	$-0.483281\pi$
$107$	12435.4	0.105002	0.0525012	+	0.998621i	$0.483281\pi$
$108$	−76436.7	−0.630583
$109$	159686.	1.28736	0.643680	−	0.765295i	$-0.277407\pi$
$109$	159686.	1.28736	0.643680	+	0.765295i	$0.277407\pi$
$110$	0	0
$111$	−52532.3	−0.404686
$112$	−87663.5	−0.660349
$113$	−210310.	−1.54940	−0.774701	−	0.632328i	$-0.782100\pi$
$113$	−210310.	−1.54940	−0.774701	+	0.632328i	$0.782100\pi$
$114$	67841.9	0.488918
$115$	1128.88	0.00795979
$116$	102288.	0.705794
$117$	−59786.7	−0.403776
$118$	−147582.	−0.975729
$119$	−46805.2	−0.302989
$120$	−653.269	−0.00414132
$121$	0	0
$122$	−47674.1	−0.289990
$123$	−88393.2	−0.526812
$124$	−316661.	−1.84944
$125$	−15625.0	−0.0894427
$126$	−152523.	−0.855873
$127$	101449.	0.558134	0.279067	−	0.960272i	$-0.409975\pi$
$127$	101449.	0.558134	0.279067	+	0.960272i	$0.409975\pi$
$128$	−10511.6	−0.0567078
$129$	3877.15	0.0205134
$130$	−55354.0	−0.287270
$131$	−17033.7	−0.0867222	−0.0433611	−	0.999059i	$-0.513807\pi$
$131$	−17033.7	−0.0867222	−0.0433611	+	0.999059i	$0.513807\pi$
$132$	0	0
$133$	144868.	0.710141
$134$	108788.	0.523384
$135$	58547.9	0.276488
$136$	−2749.60	−0.0127474
$137$	−46136.9	−0.210013	−0.105007	−	0.994472i	$-0.533486\pi$
$137$	−46136.9	−0.210013	−0.105007	+	0.994472i	$0.533486\pi$
$138$	−1847.91	−0.00826005
$139$	−412953.	−1.81286	−0.906428	−	0.422360i	$-0.861202\pi$
$139$	−412953.	−1.81286	−0.906428	+	0.422360i	$0.861202\pi$
$140$	−71304.9	−0.307468
$141$	60368.8	0.255720
$142$	−118411.	−0.492800
$143$	0	0
$144$	217777.	0.875195
$145$	−78348.8	−0.309466
$146$	−114927.	−0.446210
$147$	−46678.6	−0.178166
$148$	−336844.	−1.26408
$149$	−31348.5	−0.115678	−0.0578390	−	0.998326i	$-0.518421\pi$
$149$	−31348.5	−0.115678	−0.0578390	+	0.998326i	$0.518421\pi$
$150$	25577.2	0.0928166
$151$	−82417.5	−0.294156	−0.147078	−	0.989125i	$-0.546987\pi$
$151$	−82417.5	−0.294156	−0.147078	+	0.989125i	$0.546987\pi$
$152$	8510.38	0.0298772
$153$	116275.	0.401567
$154$	0	0
$155$	242551.	0.810913
$156$	45753.3	0.150526
$157$	75295.5	0.243792	0.121896	−	0.992543i	$-0.461103\pi$
$157$	75295.5	0.243792	0.121896	+	0.992543i	$0.461103\pi$
$158$	−245572.	−0.782593
$159$	−189277.	−0.593753
$160$	205737.	0.635350
$161$	−3945.98	−0.0119975
$162$	328285.	0.982795
$163$	470786.	1.38789	0.693944	−	0.720029i	$-0.255871\pi$
$163$	470786.	1.38789	0.693944	+	0.720029i	$0.255871\pi$
$164$	−566789.	−1.64555
$165$	0	0
$166$	796859.	2.24446
$167$	92495.6	0.256643	0.128322	−	0.991733i	$-0.459041\pi$
$167$	92495.6	0.256643	0.128322	+	0.991733i	$0.459041\pi$
$168$	2283.50	0.00624206
$169$	−295448.	−0.795727
$170$	107654.	0.285699
$171$	−359887.	−0.941186
$172$	24860.8	0.0640758
$173$	−303811.	−0.771771	−0.385886	−	0.922547i	$-0.626104\pi$
$173$	−303811.	−0.771771	−0.385886	+	0.922547i	$0.626104\pi$
$174$	128253.	0.321139
$175$	54617.1	0.134814
$176$	0	0
$177$	−93436.4	−0.224173
$178$	−67157.8	−0.158872
$179$	245854.	0.573516	0.286758	−	0.958003i	$-0.407422\pi$
$179$	245854.	0.573516	0.286758	+	0.958003i	$0.407422\pi$
$180$	177138.	0.407503
$181$	740026.	1.67900	0.839499	−	0.543361i	$-0.182849\pi$
$181$	740026.	1.67900	0.839499	+	0.543361i	$0.182849\pi$
$182$	193490.	0.432992
$183$	−30183.2	−0.0666250
$184$	−231.809	−0.000504761 0
$185$	258011.	0.554254
$186$	−397043.	−0.841502
$187$	0	0
$188$	387093.	0.798767
$189$	−204654.	−0.416741
$190$	−333204.	−0.669617
$191$	686745.	1.36211	0.681054	−	0.732233i	$-0.261522\pi$
$191$	686745.	1.36211	0.681054	+	0.732233i	$0.261522\pi$
$192$	−173382.	−0.339430
$193$	516092.	0.997319	0.498659	−	0.866798i	$-0.333826\pi$
$193$	516092.	0.997319	0.498659	+	0.866798i	$0.333826\pi$
$194$	−208689.	−0.398103
$195$	−35045.4	−0.0660001
$196$	−299310.	−0.556520
$197$	−856193.	−1.57183	−0.785916	−	0.618334i	$-0.787808\pi$
$197$	−856193.	−1.57183	−0.785916	+	0.618334i	$0.787808\pi$
$198$	0	0
$199$	−561060.	−1.00433	−0.502165	−	0.864772i	$-0.667463\pi$
$199$	−561060.	−1.00433	−0.502165	+	0.864772i	$0.667463\pi$
$200$	3208.52	0.00567191
$201$	68875.4	0.120247
$202$	1.01600e6	1.75193
$203$	273868.	0.466446
$204$	−88982.2	−0.149702
$205$	434141.	0.721516
$206$	−843087.	−1.38422
$207$	9802.74	0.0159009
$208$	−276270.	−0.442767
$209$	0	0
$210$	−89405.1	−0.139899
$211$	133963.	0.207148	0.103574	−	0.994622i	$-0.466972\pi$
$211$	133963.	0.207148	0.103574	+	0.994622i	$0.466972\pi$
$212$	−1.21367e6	−1.85465
$213$	−74967.6	−0.113220
$214$	99978.0	0.149235
$215$	−19042.5	−0.0280950
$216$	−12022.5	−0.0175332
$217$	−847837.	−1.22226
$218$	1.28384e6	1.82966
$219$	−72761.9	−0.102516
$220$	0	0
$221$	−147506.	−0.203155
$222$	−422349.	−0.575161
$223$	−18382.2	−0.0247534	−0.0123767	−	0.999923i	$-0.503940\pi$
$223$	−18382.2	−0.0247534	−0.0123767	+	0.999923i	$0.503940\pi$
$224$	−719153.	−0.957638
$225$	−135682.	−0.178675
$226$	−1.69085e6	−2.20209
$227$	−795189.	−1.02425	−0.512125	−	0.858911i	$-0.671141\pi$
$227$	−795189.	−1.02425	−0.512125	+	0.858911i	$0.671141\pi$
$228$	275412.	0.350870
$229$	369120.	0.465135	0.232567	−	0.972580i	$-0.425287\pi$
$229$	369120.	0.465135	0.232567	+	0.972580i	$0.425287\pi$
$230$	9075.95	0.0113129
$231$	0	0
$232$	16088.5	0.0196244
$233$	−915467.	−1.10472	−0.552361	−	0.833605i	$-0.686273\pi$
$233$	−915467.	−1.10472	−0.552361	+	0.833605i	$0.686273\pi$
$234$	−480674.	−0.573866
$235$	−296500.	−0.350231
$236$	−599127.	−0.700227
$237$	−155475.	−0.179800
$238$	−376305.	−0.430623
$239$	1.56244e6	1.76932	0.884662	−	0.466233i	$-0.154389\pi$
$239$	1.56244e6	1.76932	0.884662	+	0.466233i	$0.154389\pi$
$240$	127655.	0.143057
$241$	−1.39175e6	−1.54354	−0.771772	−	0.635899i	$-0.780630\pi$
$241$	−1.39175e6	−1.54354	−0.771772	+	0.635899i	$0.780630\pi$
$242$	0	0
$243$	776928.	0.844043
$244$	−193539.	−0.208110
$245$	229261.	0.244014
$246$	−710664.	−0.748732
$247$	456550.	0.476152
$248$	−49806.7	−0.0514231
$249$	504503.	0.515662
$250$	−125622.	−0.127121
$251$	1.59069e6	1.59368	0.796838	−	0.604193i	$-0.206504\pi$
$251$	1.59069e6	1.59368	0.796838	+	0.604193i	$0.206504\pi$
$252$	−619185.	−0.614213
$253$	0	0
$254$	815630.	0.793248
$255$	68157.4	0.0656391
$256$	1.00549e6	0.958906
$257$	1.53132e6	1.44622	0.723109	−	0.690734i	$-0.242712\pi$
$257$	1.53132e6	1.44622	0.723109	+	0.690734i	$0.242712\pi$
$258$	31171.6	0.0291547
$259$	−901876.	−0.835406
$260$	−224716.	−0.206158
$261$	−680352.	−0.618205
$262$	−136948.	−0.123254
$263$	2.22509e6	1.98362	0.991809	−	0.127730i	$-0.0407690\pi$
$263$	2.22509e6	1.98362	0.991809	+	0.127730i	$0.0407690\pi$
$264$	0	0
$265$	929631.	0.813198
$266$	1.16471e6	1.00929
$267$	−42518.6	−0.0365006
$268$	441638.	0.375604
$269$	256201.	0.215874	0.107937	−	0.994158i	$-0.465576\pi$
$269$	256201.	0.215874	0.107937	+	0.994158i	$0.465576\pi$
$270$	470714.	0.392959
$271$	−1.13482e6	−0.938649	−0.469324	−	0.883026i	$-0.655503\pi$
$271$	−1.13482e6	−0.938649	−0.469324	+	0.883026i	$0.655503\pi$
$272$	537298.	0.440345
$273$	122501.	0.0994795
$274$	−370932.	−0.298482
$275$	0	0
$276$	−7501.79	−0.00592778
$277$	−1.88729e6	−1.47788	−0.738939	−	0.673772i	$-0.764673\pi$
$277$	−1.88729e6	−1.47788	−0.738939	+	0.673772i	$0.764673\pi$
$278$	−3.32006e6	−2.57652
$279$	2.10623e6	1.61992
$280$	−11215.4	−0.00854905
$281$	−412628.	−0.311740	−0.155870	−	0.987778i	$-0.549818\pi$
$281$	−412628.	−0.311740	−0.155870	+	0.987778i	$0.549818\pi$
$282$	485353.	0.363442
$283$	2.02423e6	1.50243	0.751213	−	0.660059i	$-0.229469\pi$
$283$	2.02423e6	1.50243	0.751213	+	0.660059i	$0.229469\pi$
$284$	−480703.	−0.353656
$285$	−210956.	−0.153844
$286$	0	0
$287$	−1.51754e6	−1.08751
$288$	1.78654e6	1.26921
$289$	−1.13298e6	−0.797956
$290$	−629910.	−0.439828
$291$	−132124.	−0.0914638
$292$	−466559.	−0.320221
$293$	1.10170e6	0.749715	0.374858	−	0.927082i	$-0.377692\pi$
$293$	1.10170e6	0.749715	0.374858	+	0.927082i	$0.377692\pi$
$294$	−375287.	−0.253219
$295$	458911.	0.307025
$296$	−52981.3	−0.0351474
$297$	0	0
$298$	−252036.	−0.164407
$299$	−12435.7	−0.00804437
$300$	103834.	0.0666094
$301$	66563.1	0.0423465
$302$	−662621.	−0.418069
$303$	643247.	0.402505
$304$	−1.66301e6	−1.03207
$305$	148244.	0.0912489
$306$	934828.	0.570727
$307$	884228.	0.535449	0.267725	−	0.963495i	$-0.413728\pi$
$307$	884228.	0.535449	0.267725	+	0.963495i	$0.413728\pi$
$308$	0	0
$309$	−533771.	−0.318023
$310$	1.95007e6	1.15251
$311$	2.16567e6	1.26967	0.634835	−	0.772647i	$-0.281068\pi$
$311$	2.16567e6	1.26967	0.634835	+	0.772647i	$0.281068\pi$
$312$	7196.40	0.00418532
$313$	−843167.	−0.486466	−0.243233	−	0.969968i	$-0.578208\pi$
$313$	−843167.	−0.486466	−0.243233	+	0.969968i	$0.578208\pi$
$314$	605361.	0.346490
$315$	474275.	0.269311
$316$	−996927.	−0.561624
$317$	−1.79691e6	−1.00434	−0.502168	−	0.864770i	$-0.667464\pi$
$317$	−1.79691e6	−1.00434	−0.502168	+	0.864770i	$0.667464\pi$
$318$	−1.52175e6	−0.843872
$319$	0	0
$320$	851560.	0.464879
$321$	63297.5	0.0342866
$322$	−31725.0	−0.0170515
$323$	−887911.	−0.473547
$324$	1.33271e6	0.705298
$325$	172125.	0.0903931
$326$	3.78503e6	1.97254
$327$	812820.	0.420363
$328$	−89148.7	−0.0457541
$329$	1.03641e6	0.527890
$330$	0	0
$331$	1.42608e6	0.715440	0.357720	−	0.933829i	$-0.383554\pi$
$331$	1.42608e6	0.715440	0.357720	+	0.933829i	$0.383554\pi$
$332$	3.23494e6	1.61072
$333$	2.24047e6	1.10721
$334$	743647.	0.364754
$335$	−338280.	−0.164689
$336$	−446218.	−0.215625
$337$	−3.75169e6	−1.79950	−0.899750	−	0.436405i	$-0.856252\pi$
$337$	−3.75169e6	−1.79950	−0.899750	+	0.436405i	$0.856252\pi$
$338$	−2.37535e6	−1.13093
$339$	−1.07050e6	−0.505928
$340$	437034.	0.205030
$341$	0	0
$342$	−2.89342e6	−1.33766
$343$	−2.27010e6	−1.04186
$344$	3910.29	0.00178161
$345$	5746.12	0.00259912
$346$	−2.44258e6	−1.09688
$347$	1.72014e6	0.766902	0.383451	−	0.923561i	$-0.374735\pi$
$347$	1.72014e6	0.766902	0.383451	+	0.923561i	$0.374735\pi$
$348$	520656.	0.230464
$349$	−785863.	−0.345369	−0.172684	−	0.984977i	$-0.555244\pi$
$349$	−785863.	−0.345369	−0.172684	+	0.984977i	$0.555244\pi$
$350$	439111.	0.191604
$351$	−644963.	−0.279426
$352$	0	0
$353$	−1.14065e6	−0.487208	−0.243604	−	0.969875i	$-0.578330\pi$
$353$	−1.14065e6	−0.487208	−0.243604	+	0.969875i	$0.578330\pi$
$354$	−751211.	−0.318606
$355$	368202.	0.155065
$356$	−272635.	−0.114014
$357$	−238244.	−0.0989353
$358$	1.97662e6	0.815110
$359$	−1.03014e6	−0.421851	−0.210925	−	0.977502i	$-0.567648\pi$
$359$	−1.03014e6	−0.421851	−0.210925	+	0.977502i	$0.567648\pi$
$360$	27861.6	0.0113305
$361$	272106.	0.109893
$362$	5.94966e6	2.38628
$363$	0	0
$364$	785494.	0.310734
$365$	357368.	0.140405
$366$	−242667.	−0.0946908
$367$	−3.91817e6	−1.51851	−0.759255	−	0.650793i	$-0.774437\pi$
$367$	−3.91817e6	−1.51851	−0.759255	+	0.650793i	$0.774437\pi$
$368$	45297.7	0.0174364
$369$	3.76992e6	1.44134
$370$	2.07436e6	0.787734
$371$	−3.24952e6	−1.22570
$372$	−1.61184e6	−0.603900
$373$	233503.	0.0869001	0.0434501	−	0.999056i	$-0.486165\pi$
$373$	233503.	0.0869001	0.0434501	+	0.999056i	$0.486165\pi$
$374$	0	0
$375$	−79533.1	−0.0292058
$376$	60884.8	0.0222095
$377$	863090.	0.312754
$378$	−1.64538e6	−0.592293
$379$	4.90258e6	1.75318	0.876591	−	0.481236i	$-0.159812\pi$
$379$	4.90258e6	1.75318	0.876591	+	0.481236i	$0.159812\pi$
$380$	−1.35268e6	−0.480547
$381$	516387.	0.182248
$382$	5.52130e6	1.93590
$383$	−3.13825e6	−1.09318	−0.546589	−	0.837401i	$-0.684074\pi$
$383$	−3.13825e6	−1.09318	−0.546589	+	0.837401i	$0.684074\pi$
$384$	−53505.2	−0.0185169
$385$	0	0
$386$	4.14928e6	1.41744
$387$	−165358.	−0.0561240
$388$	−847197.	−0.285697
$389$	−3.90309e6	−1.30778	−0.653890	−	0.756590i	$-0.726864\pi$
$389$	−3.90309e6	−1.30778	−0.653890	+	0.756590i	$0.726864\pi$
$390$	−281759.	−0.0938028
$391$	24185.3	0.00800036
$392$	−47077.6	−0.0154739
$393$	−86703.5	−0.0283175
$394$	−6.88362e6	−2.23397
$395$	763612.	0.246252
$396$	0	0
$397$	−5.14540e6	−1.63849	−0.819243	−	0.573446i	$-0.805606\pi$
$397$	−5.14540e6	−1.63849	−0.819243	+	0.573446i	$0.805606\pi$
$398$	−4.51081e6	−1.42741
$399$	737397.	0.231883
$400$	−626975.	−0.195930
$401$	3.35592e6	1.04220	0.521100	−	0.853496i	$-0.325522\pi$
$401$	3.35592e6	1.04220	0.521100	+	0.853496i	$0.325522\pi$
$402$	553745.	0.170901
$403$	−2.67194e6	−0.819529
$404$	4.12459e6	1.25727
$405$	−1.02081e6	−0.309248
$406$	2.20185e6	0.662937
$407$	0	0
$408$	−13995.8	−0.00416243
$409$	−3.97766e6	−1.17576	−0.587881	−	0.808947i	$-0.700038\pi$
$409$	−3.97766e6	−1.17576	−0.587881	+	0.808947i	$0.700038\pi$
$410$	3.49041e6	1.02546
$411$	−234842.	−0.0685759
$412$	−3.42261e6	−0.993377
$413$	−1.60412e6	−0.462767
$414$	78812.2	0.0225992
$415$	−2.47785e6	−0.706245
$416$	−2.26640e6	−0.642100
$417$	−2.10198e6	−0.591954
$418$	0	0
$419$	−4.09304e6	−1.13897	−0.569483	−	0.822003i	$-0.692856\pi$
$419$	−4.09304e6	−1.13897	−0.569483	+	0.822003i	$0.692856\pi$
$420$	−362950.	−0.100398
$421$	6.41144e6	1.76299	0.881496	−	0.472192i	$-0.156537\pi$
$421$	6.41144e6	1.76299	0.881496	+	0.472192i	$0.156537\pi$
$422$	1.07704e6	0.294409
$423$	−2.57469e6	−0.699640
$424$	−190895.	−0.0515680
$425$	−334753.	−0.0898985
$426$	−602726.	−0.160915
$427$	−518186.	−0.137536
$428$	405872.	0.107098
$429$	0	0
$430$	−153098.	−0.0399300
$431$	6.51513e6	1.68939	0.844694	−	0.535249i	$-0.179782\pi$
$431$	6.51513e6	1.68939	0.844694	+	0.535249i	$0.179782\pi$
$432$	2.34932e6	0.605664
$433$	1.77674e6	0.455412	0.227706	−	0.973730i	$-0.426878\pi$
$433$	1.77674e6	0.455412	0.227706	+	0.973730i	$0.426878\pi$
$434$	−6.81645e6	−1.73714
$435$	−398805.	−0.101050
$436$	5.21191e6	1.31305
$437$	−74856.8	−0.0187511
$438$	−584992.	−0.145702
$439$	−1.00751e6	−0.249511	−0.124755	−	0.992188i	$-0.539815\pi$
$439$	−1.00751e6	−0.249511	−0.124755	+	0.992188i	$0.539815\pi$
$440$	0	0
$441$	1.99082e6	0.487455
$442$	−1.18592e6	−0.288734
$443$	6.25518e6	1.51436	0.757182	−	0.653203i	$-0.226575\pi$
$443$	6.25518e6	1.51436	0.757182	+	0.653203i	$0.226575\pi$
$444$	−1.71458e6	−0.412761
$445$	208829.	0.0499909
$446$	−147789.	−0.0351808
$447$	−159567.	−0.0377725
$448$	−2.97662e6	−0.700695
$449$	2.80210e6	0.655946	0.327973	−	0.944687i	$-0.393634\pi$
$449$	2.80210e6	0.655946	0.327973	+	0.944687i	$0.393634\pi$
$450$	−1.09085e6	−0.253943
$451$	0	0
$452$	−6.86421e6	−1.58032
$453$	−419515.	−0.0960510
$454$	−6.39317e6	−1.45572
$455$	−601662.	−0.136246
$456$	43318.8	0.00975584
$457$	3.57246e6	0.800159	0.400080	−	0.916480i	$-0.368982\pi$
$457$	3.57246e6	0.800159	0.400080	+	0.916480i	$0.368982\pi$
$458$	2.96765e6	0.661073
$459$	1.25434e6	0.277897
$460$	36844.9	0.00811862
$461$	4.42703e6	0.970197	0.485098	−	0.874460i	$-0.338784\pi$
$461$	4.42703e6	0.970197	0.485098	+	0.874460i	$0.338784\pi$
$462$	0	0
$463$	−3.54436e6	−0.768395	−0.384198	−	0.923251i	$-0.625522\pi$
$463$	−3.54436e6	−0.768395	−0.384198	+	0.923251i	$0.625522\pi$
$464$	−3.14386e6	−0.677903
$465$	1.23462e6	0.264789
$466$	−7.36018e6	−1.57009
$467$	2.55917e6	0.543009	0.271504	−	0.962437i	$-0.412479\pi$
$467$	2.55917e6	0.543009	0.271504	+	0.962437i	$0.412479\pi$
$468$	−1.95135e6	−0.411832
$469$	1.18246e6	0.248229
$470$	−2.38380e6	−0.497766
$471$	383263.	0.0796058
$472$	−94235.1	−0.0194696
$473$	0	0
$474$	−1.24999e6	−0.255541
$475$	1.03611e6	0.210703
$476$	−1.52765e6	−0.309034
$477$	8.07257e6	1.62449
$478$	1.25617e7	2.51465
$479$	−2.79272e6	−0.556147	−0.278073	−	0.960560i	$-0.589696\pi$
$479$	−2.79272e6	−0.556147	−0.278073	+	0.960560i	$0.589696\pi$
$480$	1.04723e6	0.207462
$481$	−2.84225e6	−0.560143
$482$	−1.11894e7	−2.19376
$483$	−20085.5	−0.00391756
$484$	0	0
$485$	648924.	0.125268
$486$	6.24635e6	1.19960
$487$	−5.05901e6	−0.966592	−0.483296	−	0.875457i	$-0.660560\pi$
$487$	−5.05901e6	−0.966592	−0.483296	+	0.875457i	$0.660560\pi$
$488$	−30441.2	−0.00578644
$489$	2.39636e6	0.453189
$490$	1.84321e6	0.346805
$491$	3.29137e6	0.616130	0.308065	−	0.951365i	$-0.400319\pi$
$491$	3.29137e6	0.616130	0.308065	+	0.951365i	$0.400319\pi$
$492$	−2.88502e6	−0.537324
$493$	−1.67856e6	−0.311043
$494$	3.67057e6	0.676732
$495$	0	0
$496$	9.73271e6	1.77635
$497$	−1.28705e6	−0.233724
$498$	4.05611e6	0.732885
$499$	6.89582e6	1.23975	0.619876	−	0.784700i	$-0.287183\pi$
$499$	6.89582e6	1.23975	0.619876	+	0.784700i	$0.287183\pi$
$500$	−509977.	−0.0912275
$501$	470813.	0.0838020
$502$	1.27888e7	2.26501
$503$	−1.98657e6	−0.350094	−0.175047	−	0.984560i	$-0.556008\pi$
$503$	−1.98657e6	−0.350094	−0.175047	+	0.984560i	$0.556008\pi$
$504$	−97390.0	−0.0170780
$505$	−3.15929e6	−0.551266
$506$	0	0
$507$	−1.50387e6	−0.259830
$508$	3.31114e6	0.569271
$509$	4.62803e6	0.791775	0.395887	−	0.918299i	$-0.370437\pi$
$509$	4.62803e6	0.791775	0.395887	+	0.918299i	$0.370437\pi$
$510$	547972.	0.0932896
$511$	−1.24918e6	−0.211628
$512$	8.42028e6	1.41955
$513$	−3.88236e6	−0.651332
$514$	1.23115e7	2.05544
$515$	2.62160e6	0.435561
$516$	126545.	0.0209228
$517$	0	0
$518$	−7.25091e6	−1.18732
$519$	−1.54644e6	−0.252007
$520$	−35345.0	−0.00573217
$521$	−7.44421e6	−1.20150	−0.600750	−	0.799437i	$-0.705131\pi$
$521$	−7.44421e6	−1.20150	−0.600750	+	0.799437i	$0.705131\pi$
$522$	−5.46990e6	−0.878624
$523$	−1.03729e7	−1.65823	−0.829117	−	0.559074i	$-0.811157\pi$
$523$	−1.03729e7	−1.65823	−0.829117	+	0.559074i	$0.811157\pi$
$524$	−555954.	−0.0884527
$525$	278008.	0.0440209
$526$	1.78893e7	2.81922
$527$	5.19647e6	0.815046
$528$	0	0
$529$	−6.43430e6	−0.999683
$530$	7.47406e6	1.15576
$531$	3.98501e6	0.613329
$532$	4.72829e6	0.724311
$533$	−4.78249e6	−0.729182
$534$	−341841.	−0.0518766
$535$	−310884.	−0.0469585
$536$	69464.1	0.0104436
$537$	1.25143e6	0.187271
$538$	2.05980e6	0.306811
$539$	0	0
$540$	1.91092e6	0.282005
$541$	1.54545e6	0.227019	0.113510	−	0.993537i	$-0.463791\pi$
$541$	1.54545e6	0.227019	0.113510	+	0.993537i	$0.463791\pi$
$542$	−9.12372e6	−1.33406
$543$	3.76682e6	0.548246
$544$	4.40776e6	0.638587
$545$	−3.99214e6	−0.575725
$546$	984886.	0.141385
$547$	9.47273e6	1.35365	0.676826	−	0.736143i	$-0.263355\pi$
$547$	9.47273e6	1.35365	0.676826	+	0.736143i	$0.263355\pi$
$548$	−1.50584e6	−0.214204
$549$	1.28730e6	0.182284
$550$	0	0
$551$	5.19538e6	0.729018
$552$	−1179.94	−0.000164820 0
$553$	−2.66920e6	−0.371167
$554$	−1.51734e7	−2.10044
$555$	1.31331e6	0.180981
$556$	−1.34782e7	−1.84903
$557$	−381869.	−0.0521527	−0.0260763	−	0.999660i	$-0.508301\pi$
$557$	−381869.	−0.0521527	−0.0260763	+	0.999660i	$0.508301\pi$
$558$	1.69337e7	2.30232
$559$	209772.	0.0283935
$560$	2.19159e6	0.295317
$561$	0	0
$562$	−3.31745e6	−0.443061
$563$	2.58638e6	0.343891	0.171945	−	0.985106i	$-0.444995\pi$
$563$	2.58638e6	0.343891	0.171945	+	0.985106i	$0.444995\pi$
$564$	1.97035e6	0.260823
$565$	5.25775e6	0.692913
$566$	1.62744e7	2.13533
$567$	3.56824e6	0.466118
$568$	−75608.4	−0.00983330
$569$	2.29229e6	0.296817	0.148408	−	0.988926i	$-0.452585\pi$
$569$	2.29229e6	0.296817	0.148408	+	0.988926i	$0.452585\pi$
$570$	−1.69605e6	−0.218651
$571$	5.85181e6	0.751103	0.375552	−	0.926801i	$-0.377453\pi$
$571$	5.85181e6	0.751103	0.375552	+	0.926801i	$0.377453\pi$
$572$	0	0
$573$	3.49561e6	0.444771
$574$	−1.22007e7	−1.54563
$575$	−28221.9	−0.00355973
$576$	7.39463e6	0.928667
$577$	−8.15004e6	−1.01911	−0.509554	−	0.860439i	$-0.670190\pi$
$577$	−8.15004e6	−1.01911	−0.509554	+	0.860439i	$0.670190\pi$
$578$	−9.10897e6	−1.13410
$579$	2.62697e6	0.325656
$580$	−2.55719e6	−0.315641
$581$	8.66133e6	1.06450
$582$	−1.06225e6	−0.129993
$583$	0	0
$584$	−73383.8	−0.00890365
$585$	1.49467e6	0.180574
$586$	8.85750e6	1.06553
$587$	1.01684e7	1.21803	0.609016	−	0.793158i	$-0.291565\pi$
$587$	1.01684e7	1.21803	0.609016	+	0.793158i	$0.291565\pi$
$588$	−1.52352e6	−0.181721
$589$	−1.60838e7	−1.91029
$590$	3.68956e6	0.436359
$591$	−4.35812e6	−0.513252
$592$	1.03530e7	1.21413
$593$	−1.05687e7	−1.23420	−0.617102	−	0.786883i	$-0.711693\pi$
$593$	−1.05687e7	−1.23420	−0.617102	+	0.786883i	$0.711693\pi$
$594$	0	0
$595$	1.17013e6	0.135501
$596$	−1.02317e6	−0.117986
$597$	−2.85586e6	−0.327945
$598$	−99980.6	−0.0114331
$599$	1.09021e7	1.24149	0.620745	−	0.784013i	$-0.286830\pi$
$599$	1.09021e7	1.24149	0.620745	+	0.784013i	$0.286830\pi$
$600$	16331.7	0.00185206
$601$	1.69087e6	0.190952	0.0954759	−	0.995432i	$-0.469563\pi$
$601$	1.69087e6	0.190952	0.0954759	+	0.995432i	$0.469563\pi$
$602$	535155.	0.0601850
$603$	−2.93750e6	−0.328991
$604$	−2.68999e6	−0.300025
$605$	0	0
$606$	5.17158e6	0.572060
$607$	−5.14594e6	−0.566882	−0.283441	−	0.958990i	$-0.591476\pi$
$607$	−5.14594e6	−0.566882	−0.283441	+	0.958990i	$0.591476\pi$
$608$	−1.36426e7	−1.49671
$609$	1.39402e6	0.152309
$610$	1.19185e6	0.129688
$611$	3.26624e6	0.353952
$612$	3.79504e6	0.409579
$613$	7.86343e6	0.845203	0.422601	−	0.906316i	$-0.361117\pi$
$613$	7.86343e6	0.845203	0.422601	+	0.906316i	$0.361117\pi$
$614$	7.10902e6	0.761008
$615$	2.20983e6	0.235598
$616$	0	0
$617$	−1.57505e7	−1.66564	−0.832819	−	0.553545i	$-0.813275\pi$
$617$	−1.57505e7	−1.66564	−0.832819	+	0.553545i	$0.813275\pi$
$618$	−4.29141e6	−0.451990
$619$	−2.06935e6	−0.217074	−0.108537	−	0.994092i	$-0.534617\pi$
$619$	−2.06935e6	−0.217074	−0.108537	+	0.994092i	$0.534617\pi$
$620$	7.91652e6	0.827094
$621$	105749.	0.0110040
$622$	1.74116e7	1.80452
$623$	−729961.	−0.0753493
$624$	−1.40625e6	−0.144577
$625$	390625.	0.0400000
$626$	−6.77890e6	−0.691391
$627$	0	0
$628$	2.45753e6	0.248657
$629$	5.52768e6	0.557078
$630$	3.81308e6	0.382758
$631$	8.15762e6	0.815624	0.407812	−	0.913066i	$-0.366292\pi$
$631$	8.15762e6	0.815624	0.407812	+	0.913066i	$0.366292\pi$
$632$	−156804.	−0.0156158
$633$	681890.	0.0676402
$634$	−1.44468e7	−1.42741
$635$	−2.53622e6	−0.249605
$636$	−6.17773e6	−0.605601
$637$	−2.52554e6	−0.246607
$638$	0	0
$639$	3.19733e6	0.309767
$640$	262789.	0.0253605
$641$	−5.78445e6	−0.556054	−0.278027	−	0.960573i	$-0.589681\pi$
$641$	−5.78445e6	−0.556054	−0.278027	+	0.960573i	$0.589681\pi$
$642$	508900.	0.0487298
$643$	1.18216e7	1.12759	0.563794	−	0.825916i	$-0.309341\pi$
$643$	1.18216e7	1.12759	0.563794	+	0.825916i	$0.309341\pi$
$644$	−128791.	−0.0122369
$645$	−96928.8	−0.00917389
$646$	−7.13864e6	−0.673029
$647$	4.96683e6	0.466464	0.233232	−	0.972421i	$-0.425070\pi$
$647$	4.96683e6	0.466464	0.233232	+	0.972421i	$0.425070\pi$
$648$	209618.	0.0196106
$649$	0	0
$650$	1.38385e6	0.128471
$651$	−4.31559e6	−0.399106
$652$	1.53658e7	1.41558
$653$	−1.13495e6	−0.104158	−0.0520792	−	0.998643i	$-0.516585\pi$
$653$	−1.13495e6	−0.104158	−0.0520792	+	0.998643i	$0.516585\pi$
$654$	6.53491e6	0.597442
$655$	425842.	0.0387834
$656$	1.74205e7	1.58052
$657$	3.10325e6	0.280481
$658$	8.33257e6	0.750264
$659$	2.83539e6	0.254331	0.127166	−	0.991881i	$-0.459412\pi$
$659$	2.83539e6	0.254331	0.127166	+	0.991881i	$0.459412\pi$
$660$	0	0
$661$	1.26094e7	1.12251	0.561255	−	0.827643i	$-0.310319\pi$
$661$	1.26094e7	1.12251	0.561255	+	0.827643i	$0.310319\pi$
$662$	1.14654e7	1.01682
$663$	−750821.	−0.0663365
$664$	508815.	0.0447857
$665$	−3.62171e6	−0.317585
$666$	1.80130e7	1.57362
$667$	−141514.	−0.0123164
$668$	3.01892e6	0.261764
$669$	−93567.5	−0.00808276
$670$	−2.71971e6	−0.234064
$671$	0	0
$672$	−3.66058e6	−0.312699
$673$	−2.27449e6	−0.193574	−0.0967868	−	0.995305i	$-0.530857\pi$
$673$	−2.27449e6	−0.193574	−0.0967868	+	0.995305i	$0.530857\pi$
$674$	−3.01629e7	−2.55754
$675$	−1.46370e6	−0.123649
$676$	−9.64299e6	−0.811605
$677$	−1.07738e7	−0.903439	−0.451719	−	0.892160i	$-0.649189\pi$
$677$	−1.07738e7	−0.903439	−0.451719	+	0.892160i	$0.649189\pi$
$678$	−8.60664e6	−0.719051
$679$	−2.26831e6	−0.188811
$680$	68739.9	0.00570081
$681$	−4.04761e6	−0.334449
$682$	0	0
$683$	−2.09650e7	−1.71966	−0.859832	−	0.510577i	$-0.829432\pi$
$683$	−2.09650e7	−1.71966	−0.859832	+	0.510577i	$0.829432\pi$
$684$	−1.17462e7	−0.959966
$685$	1.15342e6	0.0939208
$686$	−1.82512e7	−1.48075
$687$	1.87886e6	0.151881
$688$	−764108.	−0.0615437
$689$	−1.02408e7	−0.821838
$690$	46197.7	0.00369400
$691$	−7.59878e6	−0.605409	−0.302705	−	0.953084i	$-0.597890\pi$
$691$	−7.59878e6	−0.605409	−0.302705	+	0.953084i	$0.597890\pi$
$692$	−9.91595e6	−0.787171
$693$	0	0
$694$	1.38296e7	1.08996
$695$	1.03238e7	0.810734
$696$	81892.6	0.00640799
$697$	9.30113e6	0.725193
$698$	−6.31818e6	−0.490856
$699$	−4.65984e6	−0.360726
$700$	1.78262e6	0.137504
$701$	−9.70668e6	−0.746064	−0.373032	−	0.927819i	$-0.621682\pi$
$701$	−9.70668e6	−0.746064	−0.373032	+	0.927819i	$0.621682\pi$
$702$	−5.18538e6	−0.397135
$703$	−1.71089e7	−1.30567
$704$	0	0
$705$	−1.50922e6	−0.114361
$706$	−9.17059e6	−0.692445
$707$	1.10433e7	0.830903
$708$	−3.04963e6	−0.228646
$709$	−1.76055e7	−1.31532	−0.657662	−	0.753313i	$-0.728454\pi$
$709$	−1.76055e7	−1.31532	−0.657662	+	0.753313i	$0.728454\pi$
$710$	2.96027e6	0.220387
$711$	6.63093e6	0.491926
$712$	−42882.0	−0.00317011
$713$	438097.	0.0322735
$714$	−1.91543e6	−0.140612
$715$	0	0
$716$	8.02433e6	0.584960
$717$	7.95298e6	0.577740
$718$	−8.28211e6	−0.599556
$719$	−1.42502e7	−1.02801	−0.514005	−	0.857787i	$-0.671839\pi$
$719$	−1.42502e7	−1.02801	−0.514005	+	0.857787i	$0.671839\pi$
$720$	−5.44441e6	−0.391399
$721$	−9.16380e6	−0.656504
$722$	2.18768e6	0.156186
$723$	−7.08418e6	−0.504016
$724$	2.41533e7	1.71250
$725$	1.95872e6	0.138397
$726$	0	0
$727$	1.12384e7	0.788618	0.394309	−	0.918978i	$-0.370984\pi$
$727$	1.12384e7	0.788618	0.394309	+	0.918978i	$0.370984\pi$
$728$	123548.	0.00863989
$729$	−5.96762e6	−0.415894
$730$	2.87317e6	0.199551
$731$	−407971.	−0.0282382
$732$	−985134.	−0.0679544
$733$	−5.45485e6	−0.374993	−0.187497	−	0.982265i	$-0.560037\pi$
$733$	−5.45485e6	−0.374993	−0.187497	+	0.982265i	$0.560037\pi$
$734$	−3.15013e7	−2.15818
$735$	1.16697e6	0.0796783
$736$	371603.	0.0252863
$737$	0	0
$738$	3.03094e7	2.04850
$739$	−1.63170e7	−1.09908	−0.549539	−	0.835468i	$-0.685197\pi$
$739$	−1.63170e7	−1.09908	−0.549539	+	0.835468i	$0.685197\pi$
$740$	8.42110e6	0.565313
$741$	2.32389e6	0.155479
$742$	−2.61255e7	−1.74203
$743$	426899.	0.0283696	0.0141848	−	0.999899i	$-0.495485\pi$
$743$	426899.	0.0283696	0.0141848	+	0.999899i	$0.495485\pi$
$744$	−253522.	−0.0167913
$745$	783712.	0.0517328
$746$	1.87732e6	0.123507
$747$	−2.15168e7	−1.41083
$748$	0	0
$749$	1.08669e6	0.0707788
$750$	−639431.	−0.0415088
$751$	1.74812e6	0.113102	0.0565511	−	0.998400i	$-0.481990\pi$
$751$	1.74812e6	0.113102	0.0565511	+	0.998400i	$0.481990\pi$
$752$	−1.18975e7	−0.767202
$753$	8.09678e6	0.520385
$754$	6.93908e6	0.444502
$755$	2.06044e6	0.131550
$756$	−6.67960e6	−0.425056
$757$	−2.45676e7	−1.55820	−0.779100	−	0.626900i	$-0.784323\pi$
$757$	−2.45676e7	−1.55820	−0.779100	+	0.626900i	$0.784323\pi$
$758$	3.94158e7	2.49171
$759$	0	0
$760$	−212759.	−0.0133615
$761$	1.57134e7	0.983575	0.491788	−	0.870715i	$-0.336344\pi$
$761$	1.57134e7	0.983575	0.491788	+	0.870715i	$0.336344\pi$
$762$	4.15166e6	0.259020
$763$	1.39545e7	0.867768
$764$	2.24143e7	1.38929
$765$	−2.90687e6	−0.179586
$766$	−2.52309e7	−1.55368
$767$	−5.05536e6	−0.310287
$768$	5.11804e6	0.313113
$769$	−1.81574e7	−1.10723	−0.553615	−	0.832773i	$-0.686752\pi$
$769$	−1.81574e7	−1.10723	−0.553615	+	0.832773i	$0.686752\pi$
$770$	0	0
$771$	7.79461e6	0.472236
$772$	1.68445e7	1.01722
$773$	402350.	0.0242190	0.0121095	−	0.999927i	$-0.496145\pi$
$773$	402350.	0.0242190	0.0121095	+	0.999927i	$0.496145\pi$
$774$	−1.32945e6	−0.0797663
$775$	−6.06378e6	−0.362652
$776$	−133253.	−0.00794371
$777$	−4.59066e6	−0.272786
$778$	−3.13801e7	−1.85868
$779$	−2.87882e7	−1.69970
$780$	−1.14383e6	−0.0673171
$781$	0	0
$782$	194445.	0.0113705
$783$	−7.33946e6	−0.427819
$784$	9.19942e6	0.534528
$785$	−1.88239e6	−0.109027
$786$	−697080.	−0.0402463
$787$	1.13823e7	0.655079	0.327539	−	0.944837i	$-0.393781\pi$
$787$	1.13823e7	0.655079	0.327539	+	0.944837i	$0.393781\pi$
$788$	−2.79449e7	−1.60320
$789$	1.13260e7	0.647713
$790$	6.13930e6	0.349986
$791$	−1.83785e7	−1.04440
$792$	0	0
$793$	−1.63305e6	−0.0922184
$794$	−4.13680e7	−2.32870
$795$	4.73193e6	0.265534
$796$	−1.83122e7	−1.02437
$797$	−2.06350e7	−1.15069	−0.575345	−	0.817911i	$-0.695132\pi$
$797$	−2.06350e7	−1.15069	−0.575345	+	0.817911i	$0.695132\pi$
$798$	5.92853e6	0.329564
$799$	−6.35228e6	−0.352016
$800$	−5.14343e6	−0.284137
$801$	1.81339e6	0.0998644
$802$	2.69810e7	1.48123
$803$	0	0
$804$	2.24799e6	0.122646
$805$	98649.6	0.00536544
$806$	−2.14819e7	−1.16476
$807$	1.30409e6	0.0704895
$808$	648745.	0.0349579
$809$	−9.49711e6	−0.510176	−0.255088	−	0.966918i	$-0.582104\pi$
$809$	−9.49711e6	−0.510176	−0.255088	+	0.966918i	$0.582104\pi$
$810$	−8.20712e6	−0.439519
$811$	2.31598e7	1.23647	0.618235	−	0.785993i	$-0.287848\pi$
$811$	2.31598e7	1.23647	0.618235	+	0.785993i	$0.287848\pi$
$812$	8.93865e6	0.475753
$813$	−5.77636e6	−0.306498
$814$	0	0
$815$	−1.17696e7	−0.620683
$816$	2.73491e6	0.143786
$817$	1.26273e6	0.0661842
$818$	−3.19796e7	−1.67105
$819$	−5.22461e6	−0.272172
$820$	1.41697e7	0.735913
$821$	−3.61026e7	−1.86931	−0.934653	−	0.355561i	$-0.884290\pi$
$821$	−3.61026e7	−1.86931	−0.934653	+	0.355561i	$0.884290\pi$
$822$	−1.88809e6	−0.0974636
$823$	−1.59854e7	−0.822664	−0.411332	−	0.911486i	$-0.634936\pi$
$823$	−1.59854e7	−0.822664	−0.411332	+	0.911486i	$0.634936\pi$
$824$	−538333.	−0.0276206
$825$	0	0
$826$	−1.28968e7	−0.657708
$827$	3.19040e7	1.62211	0.811057	−	0.584967i	$-0.198893\pi$
$827$	3.19040e7	1.62211	0.811057	+	0.584967i	$0.198893\pi$
$828$	319947.	0.0162182
$829$	−6.06216e6	−0.306366	−0.153183	−	0.988198i	$-0.548952\pi$
$829$	−6.06216e6	−0.306366	−0.153183	+	0.988198i	$0.548952\pi$
$830$	−1.99215e7	−1.00375
$831$	−9.60652e6	−0.482574
$832$	−9.38077e6	−0.469819
$833$	4.91174e6	0.245258
$834$	−1.68995e7	−0.841316
$835$	−2.31239e6	−0.114774
$836$	0	0
$837$	2.27214e7	1.12104
$838$	−3.29072e7	−1.61876
$839$	−2.67128e7	−1.31013	−0.655066	−	0.755572i	$-0.727359\pi$
$839$	−2.67128e7	−1.31013	−0.655066	+	0.755572i	$0.727359\pi$
$840$	−57087.5	−0.00279153
$841$	−1.06895e7	−0.521155
$842$	5.15467e7	2.50565
$843$	−2.10033e6	−0.101793
$844$	4.37237e6	0.211281
$845$	7.38620e6	0.355860
$846$	−2.07000e7	−0.994364
$847$	0	0
$848$	3.73027e7	1.78136
$849$	1.03036e7	0.490589
$850$	−2.69135e6	−0.127768
$851$	466020.	0.0220587
$852$	−2.44683e6	−0.115480
$853$	3.48299e7	1.63900	0.819502	−	0.573077i	$-0.194250\pi$
$853$	3.48299e7	1.63900	0.819502	+	0.573077i	$0.194250\pi$
$854$	−4.16612e6	−0.195473
$855$	8.99717e6	0.420911
$856$	63838.5	0.00297782
$857$	3.82451e7	1.77878	0.889392	−	0.457145i	$-0.151128\pi$
$857$	3.82451e7	1.77878	0.889392	+	0.457145i	$0.151128\pi$
$858$	0	0
$859$	−2.39157e6	−0.110586	−0.0552929	−	0.998470i	$-0.517609\pi$
$859$	−2.39157e6	−0.110586	−0.0552929	+	0.998470i	$0.517609\pi$
$860$	−621520.	−0.0286556
$861$	−7.72445e6	−0.355107
$862$	5.23804e7	2.40105
$863$	703921.	0.0321734	0.0160867	−	0.999871i	$-0.494879\pi$
$863$	703921.	0.0321734	0.0160867	+	0.999871i	$0.494879\pi$
$864$	1.92728e7	0.878334
$865$	7.59528e6	0.345147
$866$	1.42847e7	0.647255
$867$	−5.76702e6	−0.260558
$868$	−2.76722e7	−1.24665
$869$	0	0
$870$	−3.20632e6	−0.143618
$871$	3.72649e6	0.166439
$872$	819767.	0.0365089
$873$	5.63501e6	0.250242
$874$	−601834.	−0.0266501
$875$	−1.36543e6	−0.0602905
$876$	−2.37484e6	−0.104562
$877$	−3.89143e7	−1.70848	−0.854241	−	0.519877i	$-0.825978\pi$
$877$	−3.89143e7	−1.70848	−0.854241	+	0.519877i	$0.825978\pi$
$878$	−8.10022e6	−0.354618
$879$	5.60781e6	0.244805
$880$	0	0
$881$	−4.17191e7	−1.81090	−0.905452	−	0.424448i	$-0.860468\pi$
$881$	−4.17191e7	−1.81090	−0.905452	+	0.424448i	$0.860468\pi$
$882$	1.60058e7	0.692797
$883$	−2.13389e7	−0.921022	−0.460511	−	0.887654i	$-0.652334\pi$
$883$	−2.13389e7	−0.921022	−0.460511	+	0.887654i	$0.652334\pi$
$884$	−4.81436e6	−0.207209
$885$	2.33591e6	0.100253
$886$	5.02905e7	2.15229
$887$	−1.55581e7	−0.663970	−0.331985	−	0.943285i	$-0.607718\pi$
$887$	−1.55581e7	−0.663970	−0.331985	+	0.943285i	$0.607718\pi$
$888$	−269681.	−0.0114767
$889$	8.86536e6	0.376220
$890$	1.67895e6	0.0710496
$891$	0	0
$892$	−599967.	−0.0252473
$893$	1.96612e7	0.825050
$894$	−1.28289e6	−0.0536842
$895$	−6.14636e6	−0.256484
$896$	−918579.	−0.0382249
$897$	−63299.1	−0.00262674
$898$	2.25284e7	0.932264
$899$	−3.04058e7	−1.25475
$900$	−4.42845e6	−0.182241
$901$	1.99166e7	0.817342
$902$	0	0
$903$	338814.	0.0138275
$904$	−1.07965e6	−0.0439403
$905$	−1.85006e7	−0.750871
$906$	−3.37282e6	−0.136513
$907$	−2.54429e7	−1.02695	−0.513475	−	0.858105i	$-0.671642\pi$
$907$	−2.54429e7	−1.02695	−0.513475	+	0.858105i	$0.671642\pi$
$908$	−2.59538e7	−1.04469
$909$	−2.74341e7	−1.10124
$910$	−4.83724e6	−0.193640
$911$	−3.56469e7	−1.42307	−0.711534	−	0.702652i	$-0.751999\pi$
$911$	−3.56469e7	−1.42307	−0.711534	+	0.702652i	$0.751999\pi$
$912$	−8.46491e6	−0.337004
$913$	0	0
$914$	2.87219e7	1.13723
$915$	754579.	0.0297956
$916$	1.20475e7	0.474416
$917$	−1.48853e6	−0.0584567
$918$	1.00847e7	0.394962
$919$	−3.06863e7	−1.19855	−0.599275	−	0.800543i	$-0.704544\pi$
$919$	−3.06863e7	−1.19855	−0.599275	+	0.800543i	$0.704544\pi$
$920$	5795.23	0.000225736 0
$921$	4.50083e6	0.174841
$922$	3.55925e7	1.37889
$923$	−4.05611e6	−0.156713
$924$	0	0
$925$	−6.45027e6	−0.247870
$926$	−2.84959e7	−1.09208
$927$	2.27650e7	0.870099
$928$	−2.57908e7	−0.983095
$929$	2.19520e7	0.834515	0.417258	−	0.908788i	$-0.362991\pi$
$929$	2.19520e7	0.834515	0.417258	+	0.908788i	$0.362991\pi$
$930$	9.92607e6	0.376331
$931$	−1.52025e7	−0.574832
$932$	−2.98795e7	−1.12677
$933$	1.10235e7	0.414587
$934$	2.05752e7	0.771751
$935$	0	0
$936$	−306923.	−0.0114509
$937$	3.13082e7	1.16495	0.582477	−	0.812847i	$-0.302084\pi$
$937$	3.13082e7	1.16495	0.582477	+	0.812847i	$0.302084\pi$
$938$	9.50672e6	0.352796
$939$	−4.29182e6	−0.158846
$940$	−9.67732e6	−0.357220
$941$	−4.85670e7	−1.78800	−0.893999	−	0.448069i	$-0.852112\pi$
$941$	−4.85670e7	−1.78800	−0.893999	+	0.448069i	$0.852112\pi$
$942$	3.08136e6	0.113140
$943$	784146.	0.0287156
$944$	1.84144e7	0.672556
$945$	5.11635e6	0.186372
$946$	0	0
$947$	−1.75692e7	−0.636614	−0.318307	−	0.947988i	$-0.603114\pi$
$947$	−1.75692e7	−0.636614	−0.318307	+	0.947988i	$0.603114\pi$
$948$	−5.07448e6	−0.183388
$949$	−3.93676e6	−0.141897
$950$	8.33010e6	0.299462
$951$	−9.14650e6	−0.327947
$952$	−240280.	−0.00859262
$953$	−6.77413e6	−0.241614	−0.120807	−	0.992676i	$-0.538548\pi$
$953$	−6.77413e6	−0.241614	−0.120807	+	0.992676i	$0.538548\pi$
$954$	6.49019e7	2.30880
$955$	−1.71686e7	−0.609154
$956$	5.09956e7	1.80463
$957$	0	0
$958$	−2.24530e7	−0.790424
$959$	−4.03178e6	−0.141563
$960$	4.33454e6	0.151798
$961$	6.55007e7	2.28790
$962$	−2.28511e7	−0.796104
$963$	−2.69960e6	−0.0938068
$964$	−4.54247e7	−1.57434
$965$	−1.29023e7	−0.446014
$966$	−161484.	−0.00556783
$967$	−4.11545e7	−1.41531	−0.707654	−	0.706559i	$-0.750246\pi$
$967$	−4.11545e7	−1.41531	−0.707654	+	0.706559i	$0.750246\pi$
$968$	0	0
$969$	−4.51957e6	−0.154628
$970$	5.21722e6	0.178037
$971$	−2.56885e7	−0.874359	−0.437180	−	0.899374i	$-0.644023\pi$
$971$	−2.56885e7	−0.874359	−0.437180	+	0.899374i	$0.644023\pi$
$972$	2.53578e7	0.860885
$973$	−3.60869e7	−1.22199
$974$	−4.06735e7	−1.37377
$975$	876136.	0.0295162
$976$	5.94849e6	0.199886
$977$	−2.42595e7	−0.813102	−0.406551	−	0.913628i	$-0.633269\pi$
$977$	−2.42595e7	−0.813102	−0.406551	+	0.913628i	$0.633269\pi$
$978$	1.92663e7	0.644095
$979$	0	0
$980$	7.48274e6	0.248883
$981$	−3.46663e7	−1.15010
$982$	2.64620e7	0.875675
$983$	−4.99585e7	−1.64902	−0.824510	−	0.565848i	$-0.808549\pi$
$983$	−4.99585e7	−1.64902	−0.824510	+	0.565848i	$0.808549\pi$
$984$	−453777.	−0.0149402
$985$	2.14048e7	0.702944
$986$	−1.34953e7	−0.442070
$987$	5.27547e6	0.172373
$988$	1.49011e7	0.485653
$989$	−34394.7	−0.00111815
$990$	0	0
$991$	−1.30996e7	−0.423715	−0.211857	−	0.977301i	$-0.567951\pi$
$991$	−1.30996e7	−0.423715	−0.211857	+	0.977301i	$0.567951\pi$
$992$	7.98429e7	2.57607
$993$	7.25891e6	0.233614
$994$	−1.03476e7	−0.332181
$995$	1.40265e7	0.449150
$996$	1.64662e7	0.525951
$997$	4.82210e7	1.53638	0.768190	−	0.640222i	$-0.221158\pi$
$997$	4.82210e7	1.53638	0.768190	+	0.640222i	$0.221158\pi$
$998$	5.54411e7	1.76200
$999$	2.41696e7	0.766224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.16		20
11.5	even	5		55.6.g.b.36.3	yes	40
11.9	even	5		55.6.g.b.26.3	✓	40
11.10	odd	2		605.6.a.o.1.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.26.3	✓	40	11.9	even	5
55.6.g.b.36.3	yes	40	11.5	even	5
605.6.a.o.1.5		20	11.10	odd	2
605.6.a.p.1.16		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)

\(f(q)\)	\(=\)	\(q+8.03981 q^{2} +5.09012 q^{3} +32.6385 q^{4} -25.0000 q^{5} +40.9236 q^{6} +87.3874 q^{7} +5.13363 q^{8} -217.091 q^{9} +O(q^{10})\)	\(q+8.03981 q^{2} +5.09012 q^{3} +32.6385 q^{4} -25.0000 q^{5} +40.9236 q^{6} +87.3874 q^{7} +5.13363 q^{8} -217.091 q^{9} -200.995 q^{10} +166.134 q^{12} +275.400 q^{13} +702.578 q^{14} -127.253 q^{15} -1003.16 q^{16} -535.605 q^{17} -1745.37 q^{18} +1657.77 q^{19} -815.963 q^{20} +444.812 q^{21} -45.1551 q^{23} +26.1308 q^{24} +625.000 q^{25} +2214.16 q^{26} -2341.92 q^{27} +2852.20 q^{28} +3133.95 q^{29} -1023.09 q^{30} -9702.05 q^{31} -8229.49 q^{32} -4306.16 q^{34} -2184.69 q^{35} -7085.52 q^{36} -10320.4 q^{37} +13328.2 q^{38} +1401.82 q^{39} -128.341 q^{40} -17365.6 q^{41} +3576.21 q^{42} +761.702 q^{43} +5427.27 q^{45} -363.038 q^{46} +11860.0 q^{47} -5106.20 q^{48} -9170.44 q^{49} +5024.88 q^{50} -2726.29 q^{51} +8988.64 q^{52} -37185.3 q^{53} -18828.6 q^{54} +448.614 q^{56} +8438.25 q^{57} +25196.4 q^{58} -18356.4 q^{59} -4153.35 q^{60} -5929.76 q^{61} -78002.7 q^{62} -18971.0 q^{63} -34062.4 q^{64} -6884.99 q^{65} +13531.2 q^{67} -17481.4 q^{68} -229.845 q^{69} -17564.5 q^{70} -14728.1 q^{71} -1114.46 q^{72} -14294.7 q^{73} -82974.3 q^{74} +3181.32 q^{75} +54107.2 q^{76} +11270.3 q^{78} -30544.5 q^{79} +25079.0 q^{80} +40832.4 q^{81} -139616. q^{82} +99114.1 q^{83} +14518.0 q^{84} +13390.1 q^{85} +6123.94 q^{86} +15952.2 q^{87} -8353.16 q^{89} +43634.2 q^{90} +24066.5 q^{91} -1473.79 q^{92} -49384.6 q^{93} +95352.1 q^{94} -41444.3 q^{95} -41889.1 q^{96} -25957.0 q^{97} -73728.6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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