LMFDB - Embedded newform 605.6.a.p.1.4

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			1.4
Root			$-9.34075$ 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)

$f(q)$	$=$	$q-9.34075 q^{2} -29.7904 q^{3} +55.2496 q^{4} -25.0000 q^{5} +278.265 q^{6} +104.862 q^{7} -217.169 q^{8} +644.469 q^{9} +O(q^{10})$	\(q-9.34075 q^{2} -29.7904 q^{3} +55.2496 q^{4} -25.0000 q^{5} +278.265 q^{6} +104.862 q^{7} -217.169 q^{8} +644.469 q^{9} +233.519 q^{10} -1645.91 q^{12} +683.403 q^{13} -979.490 q^{14} +744.760 q^{15} +260.530 q^{16} +2095.97 q^{17} -6019.82 q^{18} -662.705 q^{19} -1381.24 q^{20} -3123.88 q^{21} +207.184 q^{23} +6469.54 q^{24} +625.000 q^{25} -6383.49 q^{26} -11959.9 q^{27} +5793.59 q^{28} -3372.53 q^{29} -6956.62 q^{30} -3793.08 q^{31} +4515.85 q^{32} -19577.9 q^{34} -2621.55 q^{35} +35606.6 q^{36} -5022.86 q^{37} +6190.16 q^{38} -20358.9 q^{39} +5429.21 q^{40} -6028.54 q^{41} +29179.4 q^{42} -64.4041 q^{43} -16111.7 q^{45} -1935.25 q^{46} +1149.81 q^{47} -7761.31 q^{48} -5810.95 q^{49} -5837.97 q^{50} -62439.7 q^{51} +37757.7 q^{52} +28877.1 q^{53} +111715. q^{54} -22772.7 q^{56} +19742.2 q^{57} +31501.9 q^{58} -2046.07 q^{59} +41147.7 q^{60} +3097.34 q^{61} +35430.2 q^{62} +67580.3 q^{63} -50518.4 q^{64} -17085.1 q^{65} -22927.8 q^{67} +115801. q^{68} -6172.09 q^{69} +24487.3 q^{70} +56733.0 q^{71} -139958. q^{72} +144.174 q^{73} +46917.3 q^{74} -18619.0 q^{75} -36614.2 q^{76} +190167. q^{78} -81151.0 q^{79} -6513.26 q^{80} +199685. q^{81} +56311.0 q^{82} -61854.8 q^{83} -172593. q^{84} -52399.2 q^{85} +601.582 q^{86} +100469. q^{87} +70326.0 q^{89} +150495. q^{90} +71663.0 q^{91} +11446.8 q^{92} +112997. q^{93} -10740.1 q^{94} +16567.6 q^{95} -134529. q^{96} +146247. q^{97} +54278.6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.34075	−1.65123	−0.825613	−	0.564236i	$-0.809171\pi$
$2$	−9.34075	−1.65123	−0.825613	+	0.564236i	$0.809171\pi$
$3$	−29.7904	−1.91106	−0.955528	−	0.294901i	$-0.904713\pi$
$3$	−29.7904	−1.91106	−0.955528	+	0.294901i	$0.904713\pi$
$4$	55.2496	1.72655
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	278.265	3.15559
$7$	104.862	0.808860	0.404430	−	0.914569i	$-0.367470\pi$
$7$	104.862	0.808860	0.404430	+	0.914569i	$0.367470\pi$
$8$	−217.169	−1.19970
$9$	644.469	2.65213
$10$	233.519	0.738451
$11$	0	0
$11$	0	0
$12$	−1645.91	−3.29953
$13$	683.403	1.12155	0.560775	−	0.827968i	$-0.310503\pi$
$13$	683.403	1.12155	0.560775	+	0.827968i	$0.310503\pi$
$14$	−979.490	−1.33561
$15$	744.760	0.854650
$16$	260.530	0.254424
$17$	2095.97	1.75899	0.879493	−	0.475912i	$-0.157882\pi$
$17$	2095.97	1.75899	0.879493	+	0.475912i	$0.157882\pi$
$18$	−6019.82	−4.37927
$19$	−662.705	−0.421149	−0.210575	−	0.977578i	$-0.567534\pi$
$19$	−662.705	−0.421149	−0.210575	+	0.977578i	$0.567534\pi$
$20$	−1381.24	−0.772137
$21$	−3123.88	−1.54578
$22$	0	0
$23$	207.184	0.0816651	0.0408325	−	0.999166i	$-0.486999\pi$
$23$	207.184	0.0816651	0.0408325	+	0.999166i	$0.486999\pi$
$24$	6469.54	2.29269
$25$	625.000	0.200000
$26$	−6383.49	−1.85193
$27$	−11959.9	−3.15732
$28$	5793.59	1.39654
$29$	−3372.53	−0.744665	−0.372332	−	0.928099i	$-0.621442\pi$
$29$	−3372.53	−0.744665	−0.372332	+	0.928099i	$0.621442\pi$
$30$	−6956.62	−1.41122
$31$	−3793.08	−0.708904	−0.354452	−	0.935074i	$-0.615333\pi$
$31$	−3793.08	−0.708904	−0.354452	+	0.935074i	$0.615333\pi$
$32$	4515.85	0.779586
$33$	0	0
$34$	−19577.9	−2.90448
$35$	−2621.55	−0.361733
$36$	35606.6	4.57904
$37$	−5022.86	−0.603180	−0.301590	−	0.953438i	$-0.597517\pi$
$37$	−5022.86	−0.603180	−0.301590	+	0.953438i	$0.597517\pi$
$38$	6190.16	0.695413
$39$	−20358.9	−2.14334
$40$	5429.21	0.536521
$41$	−6028.54	−0.560083	−0.280041	−	0.959988i	$-0.590348\pi$
$41$	−6028.54	−0.560083	−0.280041	+	0.959988i	$0.590348\pi$
$42$	29179.4	2.55243
$43$	−64.4041	−0.00531180	−0.00265590	−	0.999996i	$-0.500845\pi$
$43$	−64.4041	−0.00531180	−0.00265590	+	0.999996i	$0.500845\pi$
$44$	0	0
$45$	−16111.7	−1.18607
$46$	−1935.25	−0.134848
$47$	1149.81	0.0759243	0.0379621	−	0.999279i	$-0.487913\pi$
$47$	1149.81	0.0759243	0.0379621	+	0.999279i	$0.487913\pi$
$48$	−7761.31	−0.486219
$49$	−5810.95	−0.345746
$50$	−5837.97	−0.330245
$51$	−62439.7	−3.36152
$52$	37757.7	1.93641
$53$	28877.1	1.41210	0.706048	−	0.708164i	$-0.250476\pi$
$53$	28877.1	1.41210	0.706048	+	0.708164i	$0.250476\pi$
$54$	111715.	5.21345
$55$	0	0
$56$	−22772.7	−0.970388
$57$	19742.2	0.804840
$58$	31501.9	1.22961
$59$	−2046.07	−0.0765226	−0.0382613	−	0.999268i	$-0.512182\pi$
$59$	−2046.07	−0.0765226	−0.0382613	+	0.999268i	$0.512182\pi$
$60$	41147.7	1.47560
$61$	3097.34	0.106577	0.0532886	−	0.998579i	$-0.483030\pi$
$61$	3097.34	0.106577	0.0532886	+	0.998579i	$0.483030\pi$
$62$	35430.2	1.17056
$63$	67580.3	2.14520
$64$	−50518.4	−1.54170
$65$	−17085.1	−0.501572
$66$	0	0
$67$	−22927.8	−0.623986	−0.311993	−	0.950084i	$-0.600996\pi$
$67$	−22927.8	−0.623986	−0.311993	+	0.950084i	$0.600996\pi$
$68$	115801.	3.03698
$69$	−6172.09	−0.156067
$70$	24487.3	0.597303
$71$	56733.0	1.33564	0.667820	−	0.744322i	$-0.267227\pi$
$71$	56733.0	1.33564	0.667820	+	0.744322i	$0.267227\pi$
$72$	−139958.	−3.18176
$73$	144.174	0.00316651	0.00158325	−	0.999999i	$-0.499496\pi$
$73$	144.174	0.00316651	0.00158325	+	0.999999i	$0.499496\pi$
$74$	46917.3	0.995987
$75$	−18619.0	−0.382211
$76$	−36614.2	−0.727135
$77$	0	0
$78$	190167.	3.53915
$79$	−81151.0	−1.46294	−0.731469	−	0.681874i	$-0.761165\pi$
$79$	−81151.0	−1.46294	−0.731469	+	0.681874i	$0.761165\pi$
$80$	−6513.26	−0.113782
$81$	199685.	3.38168
$82$	56311.0	0.924824
$83$	−61854.8	−0.985548	−0.492774	−	0.870157i	$-0.664017\pi$
$83$	−61854.8	−0.985548	−0.492774	+	0.870157i	$0.664017\pi$
$84$	−172593.	−2.66886
$85$	−52399.2	−0.786642
$86$	601.582	0.00877099
$87$	100469.	1.42310
$88$	0	0
$89$	70326.0	0.941111	0.470555	−	0.882370i	$-0.344054\pi$
$89$	70326.0	0.941111	0.470555	+	0.882370i	$0.344054\pi$
$90$	150495.	1.95847
$91$	71663.0	0.907176
$92$	11446.8	0.140999
$93$	112997.	1.35476
$94$	−10740.1	−0.125368
$95$	16567.6	0.188344
$96$	−134529.	−1.48983
$97$	146247.	1.57819	0.789093	−	0.614273i	$-0.210551\pi$
$97$	146247.	1.57819	0.789093	+	0.614273i	$0.210551\pi$
$98$	54278.6	0.570905
$99$	0	0
$100$	34531.0	0.345310
$101$	341.925	0.00333524	0.00166762	−	0.999999i	$-0.499469\pi$
$101$	341.925	0.00333524	0.00166762	+	0.999999i	$0.499469\pi$
$102$	583234.	5.55063
$103$	−80265.7	−0.745482	−0.372741	−	0.927935i	$-0.621582\pi$
$103$	−80265.7	−0.745482	−0.372741	+	0.927935i	$0.621582\pi$
$104$	−148414.	−1.34552
$105$	78097.1	0.691292
$106$	−269734.	−2.33169
$107$	−131409.	−1.10960	−0.554800	−	0.831984i	$-0.687205\pi$
$107$	−131409.	−1.10960	−0.554800	+	0.831984i	$0.687205\pi$
$108$	−660780.	−5.45127
$109$	−164257.	−1.32421	−0.662106	−	0.749411i	$-0.730337\pi$
$109$	−164257.	−1.32421	−0.662106	+	0.749411i	$0.730337\pi$
$110$	0	0
$111$	149633.	1.15271
$112$	27319.8	0.205794
$113$	−195740.	−1.44206	−0.721032	−	0.692902i	$-0.756332\pi$
$113$	−195740.	−1.44206	−0.721032	+	0.692902i	$0.756332\pi$
$114$	−184407.	−1.32897
$115$	−5179.60	−0.0365217
$116$	−186331.	−1.28570
$117$	440432.	2.97450
$118$	19111.8	0.126356
$119$	219787.	1.42277
$120$	−161739.	−1.02532
$121$	0	0
$122$	−28931.5	−0.175983
$123$	179593.	1.07035
$124$	−209566.	−1.22396
$125$	−15625.0	−0.0894427
$126$	−631251.	−3.54222
$127$	83790.3	0.460983	0.230491	−	0.973074i	$-0.425967\pi$
$127$	83790.3	0.460983	0.230491	+	0.973074i	$0.425967\pi$
$128$	327372.	1.76611
$129$	1918.62	0.0101512
$130$	159587.	0.828209
$131$	43116.7	0.219516	0.109758	−	0.993958i	$-0.464992\pi$
$131$	43116.7	0.219516	0.109758	+	0.993958i	$0.464992\pi$
$132$	0	0
$133$	−69492.6	−0.340651
$134$	214162.	1.03034
$135$	298998.	1.41200
$136$	−455178.	−2.11025
$137$	274031.	1.24738	0.623690	−	0.781672i	$-0.285633\pi$
$137$	274031.	1.24738	0.623690	+	0.781672i	$0.285633\pi$
$138$	57652.0	0.257701
$139$	−363170.	−1.59431	−0.797156	−	0.603773i	$-0.793663\pi$
$139$	−363170.	−1.59431	−0.797156	+	0.603773i	$0.793663\pi$
$140$	−144840.	−0.624550
$141$	−34253.3	−0.145096
$142$	−529928.	−2.20545
$143$	0	0
$144$	167904.	0.674767
$145$	84313.2	0.333024
$146$	−1346.70	−0.00522862
$147$	173111.	0.660740
$148$	−277511.	−1.04142
$149$	314344.	1.15995	0.579975	−	0.814635i	$-0.303062\pi$
$149$	314344.	1.15995	0.579975	+	0.814635i	$0.303062\pi$
$150$	173915.	0.631117
$151$	175604.	0.626748	0.313374	−	0.949630i	$-0.398541\pi$
$151$	175604.	0.626748	0.313374	+	0.949630i	$0.398541\pi$
$152$	143919.	0.505252
$153$	1.35079e6	4.66507
$154$	0	0
$155$	94827.0	0.317032
$156$	−1.12482e6	−3.70059
$157$	−485538.	−1.57208	−0.786039	−	0.618177i	$-0.787871\pi$
$157$	−485538.	−1.57208	−0.786039	+	0.618177i	$0.787871\pi$
$158$	758011.	2.41564
$159$	−860261.	−2.69859
$160$	−112896.	−0.348642
$161$	21725.7	0.0660556
$162$	−1.86521e6	−5.58392
$163$	174562.	0.514613	0.257307	−	0.966330i	$-0.417165\pi$
$163$	174562.	0.514613	0.257307	+	0.966330i	$0.417165\pi$
$164$	−333074.	−0.967011
$165$	0	0
$166$	577770.	1.62736
$167$	−492246.	−1.36581	−0.682906	−	0.730506i	$-0.739284\pi$
$167$	−492246.	−1.36581	−0.682906	+	0.730506i	$0.739284\pi$
$168$	678409.	1.85447
$169$	95746.4	0.257873
$170$	489448.	1.29892
$171$	−427092.	−1.11694
$172$	−3558.30	−0.00917109
$173$	11927.0	0.0302982	0.0151491	−	0.999885i	$-0.495178\pi$
$173$	11927.0	0.0302982	0.0151491	+	0.999885i	$0.495178\pi$
$174$	−938456.	−2.34985
$175$	65538.8	0.161772
$176$	0	0
$177$	60953.2	0.146239
$178$	−656897.	−1.55399
$179$	−363325.	−0.847545	−0.423773	−	0.905769i	$-0.639294\pi$
$179$	−363325.	−0.847545	−0.423773	+	0.905769i	$0.639294\pi$
$180$	−890166.	−2.04781
$181$	−542986.	−1.23195	−0.615974	−	0.787766i	$-0.711237\pi$
$181$	−542986.	−1.23195	−0.615974	+	0.787766i	$0.711237\pi$
$182$	−669386.	−1.49795
$183$	−92271.0	−0.203675
$184$	−44993.8	−0.0979735
$185$	125572.	0.269750
$186$	−1.05548e6	−2.23701
$187$	0	0
$188$	63526.4	0.131087
$189$	−1.25414e6	−2.55383
$190$	−154754.	−0.310998
$191$	−246664.	−0.489241	−0.244621	−	0.969619i	$-0.578663\pi$
$191$	−246664.	−0.489241	−0.244621	+	0.969619i	$0.578663\pi$
$192$	1.50496e6	2.94627
$193$	−3125.20	−0.00603927	−0.00301964	−	0.999995i	$-0.500961\pi$
$193$	−3125.20	−0.00603927	−0.00301964	+	0.999995i	$0.500961\pi$
$194$	−1.36606e6	−2.60594
$195$	508971.	0.958532
$196$	−321053.	−0.596947
$197$	−590532.	−1.08412	−0.542061	−	0.840339i	$-0.682356\pi$
$197$	−590532.	−1.08412	−0.542061	+	0.840339i	$0.682356\pi$
$198$	0	0
$199$	−553859.	−0.991440	−0.495720	−	0.868483i	$-0.665096\pi$
$199$	−553859.	−0.991440	−0.495720	+	0.868483i	$0.665096\pi$
$200$	−135730.	−0.239940
$201$	683027.	1.19247
$202$	−3193.84	−0.00550724
$203$	−353650.	−0.602329
$204$	−3.44977e6	−5.80383
$205$	150713.	0.250477
$206$	749742.	1.23096
$207$	133524.	0.216587
$208$	178047.	0.285349
$209$	0	0
$210$	−729485.	−1.14148
$211$	347594.	0.537485	0.268743	−	0.963212i	$-0.413392\pi$
$211$	347594.	0.537485	0.268743	+	0.963212i	$0.413392\pi$
$212$	1.59545e6	2.43805
$213$	−1.69010e6	−2.55248
$214$	1.22746e6	1.83220
$215$	1610.10	0.00237551
$216$	2.59732e6	3.78783
$217$	−397750.	−0.573404
$218$	1.53428e6	2.18657
$219$	−4295.01	−0.00605137
$220$	0	0
$221$	1.43239e6	1.97279
$222$	−1.39769e6	−1.90339
$223$	888308.	1.19619	0.598096	−	0.801424i	$-0.295924\pi$
$223$	888308.	1.19619	0.598096	+	0.801424i	$0.295924\pi$
$224$	473541.	0.630576
$225$	402793.	0.530427
$226$	1.82836e6	2.38117
$227$	989082.	1.27399	0.636997	−	0.770866i	$-0.280176\pi$
$227$	989082.	1.27399	0.636997	+	0.770866i	$0.280176\pi$
$228$	1.09075e6	1.38960
$229$	−537761.	−0.677642	−0.338821	−	0.940851i	$-0.610028\pi$
$229$	−537761.	−0.677642	−0.338821	+	0.940851i	$0.610028\pi$
$230$	48381.3	0.0603057
$231$	0	0
$232$	732407.	0.893373
$233$	1086.32	0.00131090	0.000655449	−	1.00000i	$-0.499791\pi$
$233$	1086.32	0.00131090	0.000655449		1.00000i	$0.499791\pi$
$234$	−4.11396e6	−4.91157
$235$	−28745.2	−0.0339544
$236$	−113044.	−0.132120
$237$	2.41752e6	2.79576
$238$	−2.05298e6	−2.34932
$239$	397160.	0.449750	0.224875	−	0.974388i	$-0.427803\pi$
$239$	397160.	0.449750	0.224875	+	0.974388i	$0.427803\pi$
$240$	194033.	0.217444
$241$	−2776.01	−0.00307878	−0.00153939	−	0.999999i	$-0.500490\pi$
$241$	−2776.01	−0.00307878	−0.00153939	+	0.999999i	$0.500490\pi$
$242$	0	0
$243$	−3.04244e6	−3.30526
$244$	171127.	0.184011
$245$	145274.	0.154622
$246$	−1.67753e6	−1.76739
$247$	−452894.	−0.472340
$248$	823738.	0.850471
$249$	1.84268e6	1.88344
$250$	145949.	0.147690
$251$	1.65722e6	1.66034	0.830170	−	0.557511i	$-0.188244\pi$
$251$	1.65722e6	1.66034	0.830170	+	0.557511i	$0.188244\pi$
$252$	3.73378e6	3.70380
$253$	0	0
$254$	−782665.	−0.761187
$255$	1.56099e6	1.50332
$256$	−1.44131e6	−1.37454
$257$	−1.60605e6	−1.51679	−0.758396	−	0.651794i	$-0.774017\pi$
$257$	−1.60605e6	−1.51679	−0.758396	+	0.651794i	$0.774017\pi$
$258$	−17921.4	−0.0167619
$259$	−526708.	−0.487888
$260$	−943943.	−0.865989
$261$	−2.17349e6	−1.97495
$262$	−402742.	−0.362471
$263$	344452.	0.307072	0.153536	−	0.988143i	$-0.450934\pi$
$263$	344452.	0.307072	0.153536	+	0.988143i	$0.450934\pi$
$264$	0	0
$265$	−721928.	−0.631509
$266$	649113.	0.562492
$267$	−2.09504e6	−1.79851
$268$	−1.26675e6	−1.07734
$269$	852598.	0.718396	0.359198	−	0.933261i	$-0.383050\pi$
$269$	852598.	0.718396	0.359198	+	0.933261i	$0.383050\pi$
$270$	−2.79286e6	−2.33153
$271$	644255.	0.532887	0.266443	−	0.963851i	$-0.414151\pi$
$271$	644255.	0.532887	0.266443	+	0.963851i	$0.414151\pi$
$272$	546063.	0.447529
$273$	−2.13487e6	−1.73366
$274$	−2.55966e6	−2.05971
$275$	0	0
$276$	−341006.	−0.269457
$277$	759126.	0.594448	0.297224	−	0.954808i	$-0.403939\pi$
$277$	759126.	0.594448	0.297224	+	0.954808i	$0.403939\pi$
$278$	3.39228e6	2.63257
$279$	−2.44452e6	−1.88011
$280$	569319.	0.433971
$281$	−278537.	−0.210434	−0.105217	−	0.994449i	$-0.533554\pi$
$281$	−278537.	−0.210434	−0.105217	+	0.994449i	$0.533554\pi$
$282$	319951.	0.239586
$283$	−942755.	−0.699734	−0.349867	−	0.936799i	$-0.613773\pi$
$283$	−942755.	−0.699734	−0.349867	+	0.936799i	$0.613773\pi$
$284$	3.13447e6	2.30605
$285$	−493556.	−0.359935
$286$	0	0
$287$	−632165.	−0.453028
$288$	2.91032e6	2.06757
$289$	2.97322e6	2.09403
$290$	−787549.	−0.549898
$291$	−4.35677e6	−3.01600
$292$	7965.57	0.00546713
$293$	1.43929e6	0.979444	0.489722	−	0.871879i	$-0.337098\pi$
$293$	1.43929e6	0.979444	0.489722	+	0.871879i	$0.337098\pi$
$294$	−1.61698e6	−1.09103
$295$	51151.7	0.0342219
$296$	1.09081e6	0.723634
$297$	0	0
$298$	−2.93620e6	−1.91534
$299$	141590.	0.0915914
$300$	−1.02869e6	−0.659907
$301$	−6753.54	−0.00429650
$302$	−1.64028e6	−1.03490
$303$	−10186.1	−0.00637384
$304$	−172655.	−0.107151
$305$	−77433.5	−0.0476628
$306$	−1.26173e7	−7.70308
$307$	−2.55503e6	−1.54721	−0.773607	−	0.633666i	$-0.781549\pi$
$307$	−2.55503e6	−1.54721	−0.773607	+	0.633666i	$0.781549\pi$
$308$	0	0
$309$	2.39115e6	1.42466
$310$	−885755.	−0.523491
$311$	1.96609e6	1.15267	0.576333	−	0.817215i	$-0.304483\pi$
$311$	1.96609e6	1.15267	0.576333	+	0.817215i	$0.304483\pi$
$312$	4.42130e6	2.57137
$313$	318885.	0.183981	0.0919905	−	0.995760i	$-0.470677\pi$
$313$	318885.	0.183981	0.0919905	+	0.995760i	$0.470677\pi$
$314$	4.53529e6	2.59586
$315$	−1.68951e6	−0.959365
$316$	−4.48356e6	−2.52584
$317$	2.25781e6	1.26194	0.630970	−	0.775807i	$-0.282657\pi$
$317$	2.25781e6	1.26194	0.630970	+	0.775807i	$0.282657\pi$
$318$	8.03549e6	4.45599
$319$	0	0
$320$	1.26296e6	0.689468
$321$	3.91473e6	2.12051
$322$	−202935.	−0.109073
$323$	−1.38901e6	−0.740796
$324$	1.10325e7	5.83864
$325$	427127.	0.224310
$326$	−1.63054e6	−0.849743
$327$	4.89328e6	2.53064
$328$	1.30921e6	0.671930
$329$	120571.	0.0614121
$330$	0	0
$331$	−387029.	−0.194166	−0.0970830	−	0.995276i	$-0.530951\pi$
$331$	−387029.	−0.194166	−0.0970830	+	0.995276i	$0.530951\pi$
$332$	−3.41745e6	−1.70160
$333$	−3.23708e6	−1.59971
$334$	4.59795e6	2.25527
$335$	573194.	0.279055
$336$	−813867.	−0.393283
$337$	141741.	0.0679861	0.0339931	−	0.999422i	$-0.489178\pi$
$337$	141741.	0.0679861	0.0339931	+	0.999422i	$0.489178\pi$
$338$	−894343.	−0.425807
$339$	5.83119e6	2.75586
$340$	−2.89503e6	−1.35818
$341$	0	0
$342$	3.98936e6	1.84433
$343$	−2.37176e6	−1.08852
$344$	13986.5	0.00637256
$345$	154302.	0.0697951
$346$	−111407.	−0.0500292
$347$	791412.	0.352841	0.176420	−	0.984315i	$-0.443548\pi$
$347$	791412.	0.352841	0.176420	+	0.984315i	$0.443548\pi$
$348$	5.55087e6	2.45705
$349$	696453.	0.306075	0.153038	−	0.988220i	$-0.451094\pi$
$349$	696453.	0.306075	0.153038	+	0.988220i	$0.451094\pi$
$350$	−612181.	−0.267122
$351$	−8.17344e6	−3.54109
$352$	0	0
$353$	−93568.5	−0.0399662	−0.0199831	−	0.999800i	$-0.506361\pi$
$353$	−93568.5	−0.0399662	−0.0199831	+	0.999800i	$0.506361\pi$
$354$	−569348.	−0.241474
$355$	−1.41832e6	−0.597317
$356$	3.88548e6	1.62487
$357$	−6.54756e6	−2.71900
$358$	3.39373e6	1.39949
$359$	−3.64252e6	−1.49165	−0.745823	−	0.666144i	$-0.767944\pi$
$359$	−3.64252e6	−1.49165	−0.745823	+	0.666144i	$0.767944\pi$
$360$	3.49896e6	1.42293
$361$	−2.03692e6	−0.822633
$362$	5.07190e6	2.03423
$363$	0	0
$364$	3.95935e6	1.56628
$365$	−3604.36	−0.00141611
$366$	861880.	0.336313
$367$	4.00150e6	1.55081	0.775404	−	0.631465i	$-0.217546\pi$
$367$	4.00150e6	1.55081	0.775404	+	0.631465i	$0.217546\pi$
$368$	53977.7	0.0207776
$369$	−3.88520e6	−1.48541
$370$	−1.17293e6	−0.445419
$371$	3.02811e6	1.14219
$372$	6.24306e6	2.33905
$373$	213017.	0.0792762	0.0396381	−	0.999214i	$-0.487379\pi$
$373$	213017.	0.0792762	0.0396381	+	0.999214i	$0.487379\pi$
$374$	0	0
$375$	465475.	0.170930
$376$	−249702.	−0.0910862
$377$	−2.30480e6	−0.835178
$378$	1.17146e7	4.21695
$379$	301370.	0.107771	0.0538856	−	0.998547i	$-0.482839\pi$
$379$	301370.	0.107771	0.0538856	+	0.998547i	$0.482839\pi$
$380$	915354.	0.325185
$381$	−2.49615e6	−0.880964
$382$	2.30403e6	0.807848
$383$	−2.90449e6	−1.01175	−0.505875	−	0.862607i	$-0.668830\pi$
$383$	−2.90449e6	−1.01175	−0.505875	+	0.862607i	$0.668830\pi$
$384$	−9.75255e6	−3.37513
$385$	0	0
$386$	29191.7	0.00997221
$387$	−41506.4	−0.0140876
$388$	8.08010e6	2.72482
$389$	−2.94751e6	−0.987602	−0.493801	−	0.869575i	$-0.664393\pi$
$389$	−2.94751e6	−0.987602	−0.493801	+	0.869575i	$0.664393\pi$
$390$	−4.75417e6	−1.58275
$391$	434251.	0.143648
$392$	1.26196e6	0.414791
$393$	−1.28446e6	−0.419508
$394$	5.51601e6	1.79013
$395$	2.02877e6	0.654246
$396$	0	0
$397$	2.39527e6	0.762744	0.381372	−	0.924422i	$-0.375452\pi$
$397$	2.39527e6	0.762744	0.381372	+	0.924422i	$0.375452\pi$
$398$	5.17345e6	1.63709
$399$	2.07021e6	0.651003
$400$	162832.	0.0508849
$401$	−1.76385e6	−0.547773	−0.273887	−	0.961762i	$-0.588309\pi$
$401$	−1.76385e6	−0.547773	−0.273887	+	0.961762i	$0.588309\pi$
$402$	−6.37999e6	−1.96904
$403$	−2.59220e6	−0.795071
$404$	18891.2	0.00575846
$405$	−4.99212e6	−1.51233
$406$	3.30336e6	0.994582
$407$	0	0
$408$	1.35600e7	4.03281
$409$	4.19571e6	1.24022	0.620108	−	0.784516i	$-0.287089\pi$
$409$	4.19571e6	1.24022	0.620108	+	0.784516i	$0.287089\pi$
$410$	−1.40778e6	−0.413594
$411$	−8.16350e6	−2.38381
$412$	−4.43465e6	−1.28711
$413$	−214555.	−0.0618960
$414$	−1.24721e6	−0.357634
$415$	1.54637e6	0.440751
$416$	3.08614e6	0.874344
$417$	1.08190e7	3.04682
$418$	0	0
$419$	−776757.	−0.216147	−0.108074	−	0.994143i	$-0.534468\pi$
$419$	−776757.	−0.216147	−0.108074	+	0.994143i	$0.534468\pi$
$420$	4.31483e6	1.19355
$421$	−445405.	−0.122476	−0.0612378	−	0.998123i	$-0.519505\pi$
$421$	−445405.	−0.122476	−0.0612378	+	0.998123i	$0.519505\pi$
$422$	−3.24679e6	−0.887510
$423$	741015.	0.201361
$424$	−6.27121e6	−1.69409
$425$	1.30998e6	0.351797
$426$	1.57868e7	4.21473
$427$	324793.	0.0862060
$428$	−7.26030e6	−1.91578
$429$	0	0
$430$	−15039.6	−0.00392251
$431$	−7.13276e6	−1.84954	−0.924771	−	0.380524i	$-0.875744\pi$
$431$	−7.13276e6	−1.84954	−0.924771	+	0.380524i	$0.875744\pi$
$432$	−3.11592e6	−0.803299
$433$	848625.	0.217518	0.108759	−	0.994068i	$-0.465312\pi$
$433$	848625.	0.217518	0.108759	+	0.994068i	$0.465312\pi$
$434$	3.71528e6	0.946820
$435$	−2.51173e6	−0.636428
$436$	−9.07512e6	−2.28632
$437$	−137302.	−0.0343932
$438$	40118.6	0.00999219
$439$	1.62886e6	0.403388	0.201694	−	0.979449i	$-0.435355\pi$
$439$	1.62886e6	0.403388	0.201694	+	0.979449i	$0.435355\pi$
$440$	0	0
$441$	−3.74498e6	−0.916964
$442$	−1.33796e7	−3.25752
$443$	6.48432e6	1.56984	0.784920	−	0.619598i	$-0.212704\pi$
$443$	6.48432e6	1.56984	0.784920	+	0.619598i	$0.212704\pi$
$444$	8.26717e6	1.99021
$445$	−1.75815e6	−0.420877
$446$	−8.29746e6	−1.97519
$447$	−9.36442e6	−2.21673
$448$	−5.29746e6	−1.24702
$449$	−4.41854e6	−1.03434	−0.517169	−	0.855883i	$-0.673014\pi$
$449$	−4.41854e6	−1.03434	−0.517169	+	0.855883i	$0.673014\pi$
$450$	−3.76239e6	−0.875855
$451$	0	0
$452$	−1.08146e7	−2.48979
$453$	−5.23133e6	−1.19775
$454$	−9.23877e6	−2.10365
$455$	−1.79158e6	−0.405701
$456$	−4.28740e6	−0.965565
$457$	7.11622e6	1.59389	0.796946	−	0.604051i	$-0.206448\pi$
$457$	7.11622e6	1.59389	0.796946	+	0.604051i	$0.206448\pi$
$458$	5.02309e6	1.11894
$459$	−2.50676e7	−5.55368
$460$	−286171.	−0.0630566
$461$	−4.80786e6	−1.05366	−0.526828	−	0.849972i	$-0.676619\pi$
$461$	−4.80786e6	−1.05366	−0.526828	+	0.849972i	$0.676619\pi$
$462$	0	0
$463$	−1.68139e6	−0.364516	−0.182258	−	0.983251i	$-0.558341\pi$
$463$	−1.68139e6	−0.364516	−0.182258	+	0.983251i	$0.558341\pi$
$464$	−878646.	−0.189461
$465$	−2.82493e6	−0.605865
$466$	−10147.1	−0.00216459
$467$	3.56867e6	0.757205	0.378603	−	0.925559i	$-0.376405\pi$
$467$	3.56867e6	0.757205	0.378603	+	0.925559i	$0.376405\pi$
$468$	2.43337e7	5.13562
$469$	−2.40425e6	−0.504717
$470$	268502.	0.0560664
$471$	1.44644e7	3.00433
$472$	444341.	0.0918040
$473$	0	0
$474$	−2.25815e7	−4.61643
$475$	−414191.	−0.0842299
$476$	1.21432e7	2.45649
$477$	1.86104e7	3.74507
$478$	−3.70977e6	−0.742639
$479$	1.61470e6	0.321554	0.160777	−	0.986991i	$-0.448600\pi$
$479$	1.61470e6	0.321554	0.160777	+	0.986991i	$0.448600\pi$
$480$	3.36322e6	0.666273
$481$	−3.43264e6	−0.676496
$482$	25930.0	0.00508377
$483$	−647218.	−0.126236
$484$	0	0
$485$	−3.65618e6	−0.705786
$486$	2.84186e7	5.45774
$487$	−3.70843e6	−0.708546	−0.354273	−	0.935142i	$-0.615272\pi$
$487$	−3.70843e6	−0.708546	−0.354273	+	0.935142i	$0.615272\pi$
$488$	−672645.	−0.127860
$489$	−5.20027e6	−0.983454
$490$	−1.35697e6	−0.255316
$491$	4.20205e6	0.786607	0.393304	−	0.919409i	$-0.371332\pi$
$491$	4.20205e6	0.786607	0.393304	+	0.919409i	$0.371332\pi$
$492$	9.92242e6	1.84801
$493$	−7.06871e6	−1.30985
$494$	4.23037e6	0.779940
$495$	0	0
$496$	−988212.	−0.180362
$497$	5.94914e6	1.08035
$498$	−1.72120e7	−3.10998
$499$	8.79479e6	1.58115	0.790577	−	0.612362i	$-0.209781\pi$
$499$	8.79479e6	1.58115	0.790577	+	0.612362i	$0.209781\pi$
$500$	−863275.	−0.154427
$501$	1.46642e7	2.61014
$502$	−1.54797e7	−2.74160
$503$	−4.61218e6	−0.812804	−0.406402	−	0.913694i	$-0.633217\pi$
$503$	−4.61218e6	−0.812804	−0.406402	+	0.913694i	$0.633217\pi$
$504$	−1.46763e7	−2.57360
$505$	−8548.13	−0.00149157
$506$	0	0
$507$	−2.85232e6	−0.492809
$508$	4.62938e6	0.795910
$509$	2.86854e6	0.490758	0.245379	−	0.969427i	$-0.421088\pi$
$509$	2.86854e6	0.490758	0.245379	+	0.969427i	$0.421088\pi$
$510$	−1.45808e7	−2.48232
$511$	15118.4	0.00256126
$512$	2.98704e6	0.503578
$513$	7.92589e6	1.32970
$514$	1.50017e7	2.50457
$515$	2.00664e6	0.333390
$516$	106003.	0.0175265
$517$	0	0
$518$	4.91984e6	0.805614
$519$	−355311.	−0.0579016
$520$	3.71034e6	0.601735
$521$	−1.15236e7	−1.85991	−0.929957	−	0.367669i	$-0.880156\pi$
$521$	−1.15236e7	−1.85991	−0.929957	+	0.367669i	$0.880156\pi$
$522$	2.03020e7	3.26109
$523$	−7.59004e6	−1.21336	−0.606680	−	0.794946i	$-0.707499\pi$
$523$	−7.59004e6	−1.21336	−0.606680	+	0.794946i	$0.707499\pi$
$524$	2.38218e6	0.379006
$525$	−1.95243e6	−0.309155
$526$	−3.21744e6	−0.507045
$527$	−7.95017e6	−1.24695
$528$	0	0
$529$	−6.39342e6	−0.993331
$530$	6.74335e6	1.04276
$531$	−1.31863e6	−0.202948
$532$	−3.83944e6	−0.588150
$533$	−4.11992e6	−0.628160
$534$	1.95692e7	2.96976
$535$	3.28523e6	0.496228
$536$	4.97919e6	0.748595
$537$	1.08236e7	1.61971
$538$	−7.96390e6	−1.18623
$539$	0	0
$540$	1.65195e7	2.43788
$541$	−2.71563e6	−0.398913	−0.199456	−	0.979907i	$-0.563918\pi$
$541$	−2.71563e6	−0.398913	−0.199456	+	0.979907i	$0.563918\pi$
$542$	−6.01783e6	−0.879917
$543$	1.61758e7	2.35432
$544$	9.46507e6	1.37128
$545$	4.10642e6	0.592205
$546$	1.99413e7	2.86267
$547$	−1.16215e7	−1.66071	−0.830356	−	0.557234i	$-0.811863\pi$
$547$	−1.16215e7	−1.66071	−0.830356	+	0.557234i	$0.811863\pi$
$548$	1.51401e7	2.15366
$549$	1.99614e6	0.282657
$550$	0	0
$551$	2.23499e6	0.313615
$552$	1.34038e6	0.187233
$553$	−8.50966e6	−1.18331
$554$	−7.09080e6	−0.981569
$555$	−3.74083e6	−0.515508
$556$	−2.00650e7	−2.75266
$557$	7.22788e6	0.987127	0.493563	−	0.869710i	$-0.335694\pi$
$557$	7.22788e6	0.987127	0.493563	+	0.869710i	$0.335694\pi$
$558$	2.28336e7	3.10449
$559$	−44013.9	−0.00595745
$560$	−682994.	−0.0920337
$561$	0	0
$562$	2.60174e6	0.347475
$563$	−1.01745e7	−1.35283	−0.676413	−	0.736522i	$-0.736467\pi$
$563$	−1.01745e7	−1.35283	−0.676413	+	0.736522i	$0.736467\pi$
$564$	−1.89248e6	−0.250515
$565$	4.89351e6	0.644911
$566$	8.80604e6	1.15542
$567$	2.09394e7	2.73531
$568$	−1.23206e7	−1.60237
$569$	4.86972e6	0.630556	0.315278	−	0.948999i	$-0.397902\pi$
$569$	4.86972e6	0.630556	0.315278	+	0.948999i	$0.397902\pi$
$570$	4.61018e6	0.594335
$571$	3.37580e6	0.433298	0.216649	−	0.976250i	$-0.430487\pi$
$571$	3.37580e6	0.433298	0.216649	+	0.976250i	$0.430487\pi$
$572$	0	0
$573$	7.34823e6	0.934967
$574$	5.90489e6	0.748053
$575$	129490.	0.0163330
$576$	−3.25575e7	−4.08879
$577$	5.48923e6	0.686392	0.343196	−	0.939264i	$-0.388491\pi$
$577$	5.48923e6	0.686392	0.343196	+	0.939264i	$0.388491\pi$
$578$	−2.77721e7	−3.45772
$579$	93101.0	0.0115414
$580$	4.65827e6	0.574983
$581$	−6.48622e6	−0.797170
$582$	4.06955e7	4.98010
$583$	0	0
$584$	−31310.1	−0.00379885
$585$	−1.10108e7	−1.33024
$586$	−1.34441e7	−1.61728
$587$	1.05225e6	0.126044	0.0630220	−	0.998012i	$-0.479926\pi$
$587$	1.05225e6	0.126044	0.0630220	+	0.998012i	$0.479926\pi$
$588$	9.56429e6	1.14080
$589$	2.51369e6	0.298555
$590$	−477795.	−0.0565082
$591$	1.75922e7	2.07182
$592$	−1.30861e6	−0.153464
$593$	1.15552e7	1.34940	0.674698	−	0.738094i	$-0.264274\pi$
$593$	1.15552e7	1.34940	0.674698	+	0.738094i	$0.264274\pi$
$594$	0	0
$595$	−5.49469e6	−0.636283
$596$	1.73674e7	2.00271
$597$	1.64997e7	1.89470
$598$	−1.32256e6	−0.151238
$599$	4.19175e6	0.477340	0.238670	−	0.971101i	$-0.423289\pi$
$599$	4.19175e6	0.477340	0.238670	+	0.971101i	$0.423289\pi$
$600$	4.04346e6	0.458538
$601$	−7.83492e6	−0.884807	−0.442403	−	0.896816i	$-0.645874\pi$
$601$	−7.83492e6	−0.884807	−0.442403	+	0.896816i	$0.645874\pi$
$602$	63083.1	0.00709450
$603$	−1.47762e7	−1.65489
$604$	9.70207e6	1.08211
$605$	0	0
$606$	95145.7	0.0105247
$607$	2.87782e6	0.317024	0.158512	−	0.987357i	$-0.449330\pi$
$607$	2.87782e6	0.317024	0.158512	+	0.987357i	$0.449330\pi$
$608$	−2.99267e6	−0.328322
$609$	1.05354e7	1.15108
$610$	723287.	0.0787020
$611$	785782.	0.0851528
$612$	7.46303e7	8.05447
$613$	−1.53432e7	−1.64916	−0.824581	−	0.565743i	$-0.808589\pi$
$613$	−1.53432e7	−1.64916	−0.824581	+	0.565743i	$0.808589\pi$
$614$	2.38659e7	2.55480
$615$	−4.48981e6	−0.478675
$616$	0	0
$617$	5.04227e6	0.533228	0.266614	−	0.963803i	$-0.414095\pi$
$617$	5.04227e6	0.533228	0.266614	+	0.963803i	$0.414095\pi$
$618$	−2.23351e7	−2.35243
$619$	−1.36560e7	−1.43250	−0.716251	−	0.697842i	$-0.754144\pi$
$619$	−1.36560e7	−1.43250	−0.716251	+	0.697842i	$0.754144\pi$
$620$	5.23915e6	0.547371
$621$	−2.47790e6	−0.257843
$622$	−1.83648e7	−1.90331
$623$	7.37452e6	0.761227
$624$	−5.30410e6	−0.545319
$625$	390625.	0.0400000
$626$	−2.97862e6	−0.303794
$627$	0	0
$628$	−2.68258e7	−2.71427
$629$	−1.05278e7	−1.06098
$630$	1.57813e7	1.58413
$631$	4.41300e6	0.441225	0.220613	−	0.975361i	$-0.429194\pi$
$631$	4.41300e6	0.441225	0.220613	+	0.975361i	$0.429194\pi$
$632$	1.76234e7	1.75508
$633$	−1.03550e7	−1.02716
$634$	−2.10896e7	−2.08375
$635$	−2.09476e6	−0.206158
$636$	−4.75291e7	−4.65926
$637$	−3.97122e6	−0.387771
$638$	0	0
$639$	3.65626e7	3.54230
$640$	−8.18431e6	−0.789827
$641$	7.77884e6	0.747773	0.373887	−	0.927474i	$-0.378025\pi$
$641$	7.77884e6	0.747773	0.373887	+	0.927474i	$0.378025\pi$
$642$	−3.65666e7	−3.50144
$643$	3.23688e6	0.308745	0.154372	−	0.988013i	$-0.450664\pi$
$643$	3.23688e6	0.308745	0.154372	+	0.988013i	$0.450664\pi$
$644$	1.20034e6	0.114048
$645$	−47965.6	−0.00453973
$646$	1.29744e7	1.22322
$647$	3.96862e6	0.372717	0.186358	−	0.982482i	$-0.440331\pi$
$647$	3.96862e6	0.372717	0.186358	+	0.982482i	$0.440331\pi$
$648$	−4.33653e7	−4.05700
$649$	0	0
$650$	−3.98968e6	−0.370386
$651$	1.18491e7	1.09581
$652$	9.64448e6	0.888505
$653$	−1.55061e7	−1.42305	−0.711523	−	0.702663i	$-0.751994\pi$
$653$	−1.55061e7	−1.42305	−0.711523	+	0.702663i	$0.751994\pi$
$654$	−4.57069e7	−4.17866
$655$	−1.07792e6	−0.0981707
$656$	−1.57062e6	−0.142499
$657$	92915.8	0.00839800
$658$	−1.12623e6	−0.101405
$659$	−1.31062e7	−1.17561	−0.587805	−	0.809002i	$-0.700008\pi$
$659$	−1.31062e7	−1.17561	−0.587805	+	0.809002i	$0.700008\pi$
$660$	0	0
$661$	−1.12843e7	−1.00454	−0.502272	−	0.864710i	$-0.667502\pi$
$661$	−1.12843e7	−1.00454	−0.502272	+	0.864710i	$0.667502\pi$
$662$	3.61514e6	0.320612
$663$	−4.26715e7	−3.77011
$664$	1.34329e7	1.18236
$665$	1.73731e6	0.152344
$666$	3.02367e7	2.64149
$667$	−698734.	−0.0608131
$668$	−2.71964e7	−2.35814
$669$	−2.64630e7	−2.28599
$670$	−5.35406e6	−0.460783
$671$	0	0
$672$	−1.41070e7	−1.20507
$673$	−1.36969e7	−1.16570	−0.582848	−	0.812581i	$-0.698062\pi$
$673$	−1.36969e7	−1.16570	−0.582848	+	0.812581i	$0.698062\pi$
$674$	−1.32397e6	−0.112261
$675$	−7.47495e6	−0.631464
$676$	5.28995e6	0.445230
$677$	−1.43243e7	−1.20116	−0.600581	−	0.799564i	$-0.705064\pi$
$677$	−1.43243e7	−1.20116	−0.600581	+	0.799564i	$0.705064\pi$
$678$	−5.44677e7	−4.55056
$679$	1.53358e7	1.27653
$680$	1.13795e7	0.943734
$681$	−2.94652e7	−2.43468
$682$	0	0
$683$	−2.27710e7	−1.86780	−0.933899	−	0.357536i	$-0.883617\pi$
$683$	−2.27710e7	−1.86780	−0.933899	+	0.357536i	$0.883617\pi$
$684$	−2.35967e7	−1.92846
$685$	−6.85078e6	−0.557845
$686$	2.21541e7	1.79739
$687$	1.60201e7	1.29501
$688$	−16779.2	−0.00135145
$689$	1.97347e7	1.58374
$690$	−1.44130e6	−0.115247
$691$	−9.23545e6	−0.735805	−0.367903	−	0.929864i	$-0.619924\pi$
$691$	−9.23545e6	−0.735805	−0.367903	+	0.929864i	$0.619924\pi$
$692$	658963.	0.0523114
$693$	0	0
$694$	−7.39238e6	−0.582620
$695$	9.07926e6	0.712998
$696$	−2.18187e7	−1.70729
$697$	−1.26356e7	−0.985178
$698$	−6.50539e6	−0.505400
$699$	−32362.0	−0.00250520
$700$	3.62099e6	0.279307
$701$	−1.45466e7	−1.11806	−0.559032	−	0.829146i	$-0.688827\pi$
$701$	−1.45466e7	−1.11806	−0.559032	+	0.829146i	$0.688827\pi$
$702$	7.63460e7	5.84714
$703$	3.32867e6	0.254029
$704$	0	0
$705$	856331.	0.0648887
$706$	874000.	0.0659933
$707$	35855.0	0.00269774
$708$	3.36764e6	0.252489
$709$	−9.73838e6	−0.727564	−0.363782	−	0.931484i	$-0.618515\pi$
$709$	−9.73838e6	−0.727564	−0.363782	+	0.931484i	$0.618515\pi$
$710$	1.32482e7	0.986305
$711$	−5.22993e7	−3.87991
$712$	−1.52726e7	−1.12905
$713$	−785865.	−0.0578927
$714$	6.11591e7	4.48968
$715$	0	0
$716$	−2.00736e7	−1.46333
$717$	−1.18316e7	−0.859497
$718$	3.40239e7	2.46305
$719$	2.11010e7	1.52224	0.761118	−	0.648614i	$-0.224651\pi$
$719$	2.11010e7	1.52224	0.761118	+	0.648614i	$0.224651\pi$
$720$	−4.19759e6	−0.301765
$721$	−8.41683e6	−0.602990
$722$	1.90264e7	1.35835
$723$	82698.6	0.00588372
$724$	−2.99998e7	−2.12702
$725$	−2.10783e6	−0.148933
$726$	0	0
$727$	8.13887e6	0.571121	0.285561	−	0.958361i	$-0.407820\pi$
$727$	8.13887e6	0.571121	0.285561	+	0.958361i	$0.407820\pi$
$728$	−1.55630e7	−1.08834
$729$	4.21120e7	2.93486
$730$	33667.4	0.00233831
$731$	−134989.	−0.00934339
$732$	−5.09793e6	−0.351655
$733$	−5.73509e6	−0.394258	−0.197129	−	0.980378i	$-0.563162\pi$
$733$	−5.73509e6	−0.394258	−0.197129	+	0.980378i	$0.563162\pi$
$734$	−3.73771e7	−2.56074
$735$	−4.32777e6	−0.295492
$736$	935610.	0.0636650
$737$	0	0
$738$	3.62907e7	2.45276
$739$	−1.02238e7	−0.688655	−0.344328	−	0.938850i	$-0.611893\pi$
$739$	−1.02238e7	−0.688655	−0.344328	+	0.938850i	$0.611893\pi$
$740$	6.93778e6	0.465737
$741$	1.34919e7	0.902668
$742$	−2.82849e7	−1.88601
$743$	−434315.	−0.0288624	−0.0144312	−	0.999896i	$-0.504594\pi$
$743$	−434315.	−0.0288624	−0.0144312	+	0.999896i	$0.504594\pi$
$744$	−2.45395e7	−1.62530
$745$	−7.85859e6	−0.518745
$746$	−1.98974e6	−0.130903
$747$	−3.98635e7	−2.61381
$748$	0	0
$749$	−1.37798e7	−0.897511
$750$	−4.34789e6	−0.282244
$751$	−8.19147e6	−0.529983	−0.264992	−	0.964251i	$-0.585369\pi$
$751$	−8.19147e6	−0.529983	−0.264992	+	0.964251i	$0.585369\pi$
$752$	299560.	0.0193170
$753$	−4.93694e7	−3.17300
$754$	2.15285e7	1.37907
$755$	−4.39011e6	−0.280290
$756$	−6.92908e7	−4.40931
$757$	2.63265e7	1.66976	0.834879	−	0.550433i	$-0.185537\pi$
$757$	2.63265e7	1.66976	0.834879	+	0.550433i	$0.185537\pi$
$758$	−2.81503e6	−0.177955
$759$	0	0
$760$	−3.59797e6	−0.225956
$761$	−1.14234e7	−0.715044	−0.357522	−	0.933905i	$-0.616378\pi$
$761$	−1.14234e7	−0.715044	−0.357522	+	0.933905i	$0.616378\pi$
$762$	2.33159e7	1.45467
$763$	−1.72243e7	−1.07110
$764$	−1.36281e7	−0.844699
$765$	−3.37696e7	−2.08628
$766$	2.71301e7	1.67063
$767$	−1.39829e6	−0.0858239
$768$	4.29373e7	2.62683
$769$	3.21542e6	0.196075	0.0980374	−	0.995183i	$-0.468744\pi$
$769$	3.21542e6	0.196075	0.0980374	+	0.995183i	$0.468744\pi$
$770$	0	0
$771$	4.78449e7	2.89868
$772$	−172666.	−0.0104271
$773$	1.16045e7	0.698519	0.349259	−	0.937026i	$-0.386433\pi$
$773$	1.16045e7	0.698519	0.349259	+	0.937026i	$0.386433\pi$
$774$	387701.	0.0232619
$775$	−2.37067e6	−0.141781
$776$	−3.17603e7	−1.89335
$777$	1.56908e7	0.932381
$778$	2.75320e7	1.63075
$779$	3.99514e6	0.235878
$780$	2.81205e7	1.65495
$781$	0	0
$782$	−4.05623e6	−0.237195
$783$	4.03352e7	2.35114
$784$	−1.51393e6	−0.0879661
$785$	1.21384e7	0.703054
$786$	1.19978e7	0.692703
$787$	−6.55803e6	−0.377430	−0.188715	−	0.982032i	$-0.560432\pi$
$787$	−6.55803e6	−0.377430	−0.188715	+	0.982032i	$0.560432\pi$
$788$	−3.26267e7	−1.87179
$789$	−1.02614e7	−0.586831
$790$	−1.89503e7	−1.08031
$791$	−2.05257e7	−1.16643
$792$	0	0
$793$	2.11673e6	0.119532
$794$	−2.23736e7	−1.25946
$795$	2.15065e7	1.20685
$796$	−3.06005e7	−1.71177
$797$	1.54212e7	0.859946	0.429973	−	0.902842i	$-0.358523\pi$
$797$	1.54212e7	0.859946	0.429973	+	0.902842i	$0.358523\pi$
$798$	−1.93373e7	−1.07495
$799$	2.40996e6	0.133550
$800$	2.82240e6	0.155917
$801$	4.53229e7	2.49595
$802$	1.64757e7	0.904497
$803$	0	0
$804$	3.77370e7	2.05886
$805$	−543143.	−0.0295410
$806$	2.42131e7	1.31284
$807$	−2.53992e7	−1.37289
$808$	−74255.4	−0.00400129
$809$	6.46922e6	0.347520	0.173760	−	0.984788i	$-0.444408\pi$
$809$	6.46922e6	0.347520	0.173760	+	0.984788i	$0.444408\pi$
$810$	4.66302e7	2.49721
$811$	−6.77971e6	−0.361959	−0.180979	−	0.983487i	$-0.557927\pi$
$811$	−6.77971e6	−0.361959	−0.180979	+	0.983487i	$0.557927\pi$
$812$	−1.95390e7	−1.03995
$813$	−1.91926e7	−1.01838
$814$	0	0
$815$	−4.36405e6	−0.230142
$816$	−1.62675e7	−0.855252
$817$	42680.9	0.00223706
$818$	−3.91911e7	−2.04788
$819$	4.61846e7	2.40595
$820$	8.32685e6	0.432460
$821$	−8.59771e6	−0.445169	−0.222584	−	0.974913i	$-0.571449\pi$
$821$	−8.59771e6	−0.445169	−0.222584	+	0.974913i	$0.571449\pi$
$822$	7.62532e7	3.93621
$823$	−1.12980e7	−0.581434	−0.290717	−	0.956809i	$-0.593894\pi$
$823$	−1.12980e7	−0.581434	−0.290717	+	0.956809i	$0.593894\pi$
$824$	1.74312e7	0.894353
$825$	0	0
$826$	2.00410e6	0.102204
$827$	−1.41631e7	−0.720101	−0.360050	−	0.932933i	$-0.617241\pi$
$827$	−1.41631e7	−0.720101	−0.360050	+	0.932933i	$0.617241\pi$
$828$	7.37712e6	0.373948
$829$	−3.49665e7	−1.76712	−0.883559	−	0.468320i	$-0.844859\pi$
$829$	−3.49665e7	−1.76712	−0.883559	+	0.468320i	$0.844859\pi$
$830$	−1.44442e7	−0.727779
$831$	−2.26147e7	−1.13602
$832$	−3.45244e7	−1.72909
$833$	−1.21796e7	−0.608162
$834$	−1.01058e8	−5.03099
$835$	1.23062e7	0.610810
$836$	0	0
$837$	4.53649e7	2.23824
$838$	7.25549e6	0.356908
$839$	−2.98370e7	−1.46336	−0.731678	−	0.681650i	$-0.761263\pi$
$839$	−2.98370e7	−1.46336	−0.731678	+	0.681650i	$0.761263\pi$
$840$	−1.69602e7	−0.829342
$841$	−9.13720e6	−0.445475
$842$	4.16041e6	0.202235
$843$	8.29772e6	0.402152
$844$	1.92044e7	0.927995
$845$	−2.39366e6	−0.115324
$846$	−6.92164e6	−0.332493
$847$	0	0
$848$	7.52337e6	0.359272
$849$	2.80851e7	1.33723
$850$	−1.22362e7	−0.580897
$851$	−1.04066e6	−0.0492587
$852$	−9.33773e7	−4.40699
$853$	1.01487e7	0.477573	0.238787	−	0.971072i	$-0.423250\pi$
$853$	1.01487e7	0.477573	0.238787	+	0.971072i	$0.423250\pi$
$854$	−3.03381e6	−0.142346
$855$	1.06773e7	0.499513
$856$	2.85380e7	1.33118
$857$	1.78177e7	0.828707	0.414353	−	0.910116i	$-0.364008\pi$
$857$	1.78177e7	0.828707	0.414353	+	0.910116i	$0.364008\pi$
$858$	0	0
$859$	452913.	0.0209426	0.0104713	−	0.999945i	$-0.496667\pi$
$859$	452913.	0.0209426	0.0104713	+	0.999945i	$0.496667\pi$
$860$	88957.4	0.00410144
$861$	1.88324e7	0.865763
$862$	6.66253e7	3.05401
$863$	3.81836e7	1.74522	0.872609	−	0.488419i	$-0.162426\pi$
$863$	3.81836e7	1.74522	0.872609	+	0.488419i	$0.162426\pi$
$864$	−5.40091e7	−2.46140
$865$	−298176.	−0.0135498
$866$	−7.92679e6	−0.359172
$867$	−8.85736e7	−4.00181
$868$	−2.19755e7	−0.990011
$869$	0	0
$870$	2.34614e7	1.05089
$871$	−1.56689e7	−0.699831
$872$	3.56714e7	1.58865
$873$	9.42518e7	4.18556
$874$	1.28250e6	0.0567910
$875$	−1.63847e6	−0.0723466
$876$	−237298.	−0.0104480
$877$	2.01771e7	0.885850	0.442925	−	0.896559i	$-0.353941\pi$
$877$	2.01771e7	0.885850	0.442925	+	0.896559i	$0.353941\pi$
$878$	−1.52148e7	−0.666085
$879$	−4.28771e7	−1.87177
$880$	0	0
$881$	3.80559e7	1.65190	0.825948	−	0.563747i	$-0.190641\pi$
$881$	3.80559e7	1.65190	0.825948	+	0.563747i	$0.190641\pi$
$882$	3.49809e7	1.51412
$883$	−3.30098e7	−1.42476	−0.712379	−	0.701795i	$-0.752382\pi$
$883$	−3.30098e7	−1.42476	−0.712379	+	0.701795i	$0.752382\pi$
$884$	7.91390e7	3.40612
$885$	−1.52383e6	−0.0654000
$886$	−6.05684e7	−2.59216
$887$	3.42147e7	1.46017	0.730086	−	0.683355i	$-0.239480\pi$
$887$	3.42147e7	1.46017	0.730086	+	0.683355i	$0.239480\pi$
$888$	−3.24956e7	−1.38291
$889$	8.78643e6	0.372870
$890$	1.64224e7	0.694964
$891$	0	0
$892$	4.90786e7	2.06529
$893$	−761983.	−0.0319755
$894$	8.74707e7	3.66032
$895$	9.08313e6	0.379034
$896$	3.43289e7	1.42853
$897$	−4.21803e6	−0.175036
$898$	4.12724e7	1.70793
$899$	1.27923e7	0.527896
$900$	2.22541e7	0.915808
$901$	6.05255e7	2.48386
$902$	0	0
$903$	201191.	0.00821086
$904$	4.25087e7	1.73004
$905$	1.35747e7	0.550944
$906$	4.88645e7	1.97776
$907$	−8.84992e6	−0.357208	−0.178604	−	0.983921i	$-0.557158\pi$
$907$	−8.84992e6	−0.357208	−0.178604	+	0.983921i	$0.557158\pi$
$908$	5.46464e7	2.19962
$909$	220360.	0.00884551
$910$	1.67347e7	0.669905
$911$	2.74128e6	0.109435	0.0547176	−	0.998502i	$-0.482574\pi$
$911$	2.74128e6	0.109435	0.0547176	+	0.998502i	$0.482574\pi$
$912$	5.14346e6	0.204771
$913$	0	0
$914$	−6.64708e7	−2.63188
$915$	2.30677e6	0.0910862
$916$	−2.97111e7	−1.16998
$917$	4.52130e6	0.177558
$918$	2.34150e8	9.17039
$919$	2.17296e7	0.848718	0.424359	−	0.905494i	$-0.360499\pi$
$919$	2.17296e7	0.848718	0.424359	+	0.905494i	$0.360499\pi$
$920$	1.12485e6	0.0438151
$921$	7.61154e7	2.95681
$922$	4.49090e7	1.73983
$923$	3.87715e7	1.49799
$924$	0	0
$925$	−3.13929e6	−0.120636
$926$	1.57055e7	0.601899
$927$	−5.17287e7	−1.97712
$928$	−1.52298e7	−0.580530
$929$	1.45227e6	0.0552087	0.0276043	−	0.999619i	$-0.491212\pi$
$929$	1.45227e6	0.0552087	0.0276043	+	0.999619i	$0.491212\pi$
$930$	2.63870e7	1.00042
$931$	3.85095e6	0.145611
$932$	60018.9	0.00226333
$933$	−5.85708e7	−2.20281
$934$	−3.33340e7	−1.25032
$935$	0	0
$936$	−9.56479e7	−3.56850
$937$	−3.77408e6	−0.140431	−0.0702153	−	0.997532i	$-0.522369\pi$
$937$	−3.77408e6	−0.140431	−0.0702153	+	0.997532i	$0.522369\pi$
$938$	2.24575e7	0.833402
$939$	−9.49971e6	−0.351598
$940$	−1.58816e6	−0.0586239
$941$	2.28386e7	0.840807	0.420403	−	0.907337i	$-0.361889\pi$
$941$	2.28386e7	0.840807	0.420403	+	0.907337i	$0.361889\pi$
$942$	−1.35108e8	−4.96083
$943$	−1.24902e6	−0.0457392
$944$	−533063.	−0.0194692
$945$	3.13535e7	1.14211
$946$	0	0
$947$	2.88815e7	1.04651	0.523256	−	0.852175i	$-0.324717\pi$
$947$	2.88815e7	1.04651	0.523256	+	0.852175i	$0.324717\pi$
$948$	1.33567e8	4.82701
$949$	98529.1	0.00355139
$950$	3.86885e6	0.139083
$951$	−6.72611e7	−2.41164
$952$	−4.77309e7	−1.70690
$953$	964733.	0.0344092	0.0172046	−	0.999852i	$-0.494523\pi$
$953$	964733.	0.0344092	0.0172046	+	0.999852i	$0.494523\pi$
$954$	−1.73835e8	−6.18396
$955$	6.16661e6	0.218795
$956$	2.19429e7	0.776515
$957$	0	0
$958$	−1.50825e7	−0.530958
$959$	2.87355e7	1.00895
$960$	−3.76241e7	−1.31761
$961$	−1.42417e7	−0.497455
$962$	3.20634e7	1.11705
$963$	−8.46891e7	−2.94281
$964$	−153374.	−0.00531567
$965$	78130.0	0.00270084
$966$	6.04550e6	0.208444
$967$	−2.66005e7	−0.914796	−0.457398	−	0.889262i	$-0.651218\pi$
$967$	−2.66005e7	−0.914796	−0.457398	+	0.889262i	$0.651218\pi$
$968$	0	0
$969$	4.13791e7	1.41570
$970$	3.41515e7	1.16541
$971$	4.84553e7	1.64928	0.824638	−	0.565661i	$-0.191379\pi$
$971$	4.84553e7	1.64928	0.824638	+	0.565661i	$0.191379\pi$
$972$	−1.68093e8	−5.70670
$973$	−3.80828e7	−1.28958
$974$	3.46395e7	1.16997
$975$	−1.27243e7	−0.428669
$976$	806951.	0.0271158
$977$	−2.81308e7	−0.942858	−0.471429	−	0.881904i	$-0.656262\pi$
$977$	−2.81308e7	−0.942858	−0.471429	+	0.881904i	$0.656262\pi$
$978$	4.85745e7	1.62391
$979$	0	0
$980$	8.02632e6	0.266963
$981$	−1.05858e8	−3.51199
$982$	−3.92503e7	−1.29887
$983$	−3.35067e7	−1.10598	−0.552991	−	0.833187i	$-0.686514\pi$
$983$	−3.35067e7	−1.10598	−0.552991	+	0.833187i	$0.686514\pi$
$984$	−3.90019e7	−1.28410
$985$	1.47633e7	0.484834
$986$	6.60271e7	2.16287
$987$	−3.59187e6	−0.117362
$988$	−2.50222e7	−0.815518
$989$	−13343.5	−0.000433789 0
$990$	0	0
$991$	−6.78574e6	−0.219489	−0.109745	−	0.993960i	$-0.535003\pi$
$991$	−6.78574e6	−0.219489	−0.109745	+	0.993960i	$0.535003\pi$
$992$	−1.71290e7	−0.552652
$993$	1.15297e7	0.371062
$994$	−5.55694e7	−1.78390
$995$	1.38465e7	0.443385
$996$	1.01807e8	3.25185
$997$	−3.74712e6	−0.119388	−0.0596939	−	0.998217i	$-0.519012\pi$
$997$	−3.74712e6	−0.119388	−0.0596939	+	0.998217i	$0.519012\pi$
$998$	−8.21499e7	−2.61084
$999$	6.00730e7	1.90443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.4		20
11.3	even	5		55.6.g.b.31.2	yes	40
11.4	even	5		55.6.g.b.16.2	✓	40
11.10	odd	2		605.6.a.o.1.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.2	✓	40	11.4	even	5
55.6.g.b.31.2	yes	40	11.3	even	5
605.6.a.o.1.17		20	11.10	odd	2
605.6.a.p.1.4		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)

\(f(q)\)	\(=\)	\(q-9.34075 q^{2} -29.7904 q^{3} +55.2496 q^{4} -25.0000 q^{5} +278.265 q^{6} +104.862 q^{7} -217.169 q^{8} +644.469 q^{9} +O(q^{10})\)	\(q-9.34075 q^{2} -29.7904 q^{3} +55.2496 q^{4} -25.0000 q^{5} +278.265 q^{6} +104.862 q^{7} -217.169 q^{8} +644.469 q^{9} +233.519 q^{10} -1645.91 q^{12} +683.403 q^{13} -979.490 q^{14} +744.760 q^{15} +260.530 q^{16} +2095.97 q^{17} -6019.82 q^{18} -662.705 q^{19} -1381.24 q^{20} -3123.88 q^{21} +207.184 q^{23} +6469.54 q^{24} +625.000 q^{25} -6383.49 q^{26} -11959.9 q^{27} +5793.59 q^{28} -3372.53 q^{29} -6956.62 q^{30} -3793.08 q^{31} +4515.85 q^{32} -19577.9 q^{34} -2621.55 q^{35} +35606.6 q^{36} -5022.86 q^{37} +6190.16 q^{38} -20358.9 q^{39} +5429.21 q^{40} -6028.54 q^{41} +29179.4 q^{42} -64.4041 q^{43} -16111.7 q^{45} -1935.25 q^{46} +1149.81 q^{47} -7761.31 q^{48} -5810.95 q^{49} -5837.97 q^{50} -62439.7 q^{51} +37757.7 q^{52} +28877.1 q^{53} +111715. q^{54} -22772.7 q^{56} +19742.2 q^{57} +31501.9 q^{58} -2046.07 q^{59} +41147.7 q^{60} +3097.34 q^{61} +35430.2 q^{62} +67580.3 q^{63} -50518.4 q^{64} -17085.1 q^{65} -22927.8 q^{67} +115801. q^{68} -6172.09 q^{69} +24487.3 q^{70} +56733.0 q^{71} -139958. q^{72} +144.174 q^{73} +46917.3 q^{74} -18619.0 q^{75} -36614.2 q^{76} +190167. q^{78} -81151.0 q^{79} -6513.26 q^{80} +199685. q^{81} +56311.0 q^{82} -61854.8 q^{83} -172593. q^{84} -52399.2 q^{85} +601.582 q^{86} +100469. q^{87} +70326.0 q^{89} +150495. q^{90} +71663.0 q^{91} +11446.8 q^{92} +112997. q^{93} -10740.1 q^{94} +16567.6 q^{95} -134529. q^{96} +146247. q^{97} +54278.6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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