LMFDB - Embedded newform 605.6.a.p.1.12

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			1.12
Root			$1.84684$ 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)

$f(q)$	$=$	$q+1.84684 q^{2} -21.5804 q^{3} -28.5892 q^{4} -25.0000 q^{5} -39.8555 q^{6} -85.4988 q^{7} -111.898 q^{8} +222.716 q^{9} +O(q^{10})$	\(q+1.84684 q^{2} -21.5804 q^{3} -28.5892 q^{4} -25.0000 q^{5} -39.8555 q^{6} -85.4988 q^{7} -111.898 q^{8} +222.716 q^{9} -46.1709 q^{10} +616.968 q^{12} -1015.48 q^{13} -157.902 q^{14} +539.511 q^{15} +708.196 q^{16} -849.161 q^{17} +411.319 q^{18} +955.100 q^{19} +714.730 q^{20} +1845.10 q^{21} +4452.75 q^{23} +2414.82 q^{24} +625.000 q^{25} -1875.43 q^{26} +437.748 q^{27} +2444.34 q^{28} -3076.30 q^{29} +996.389 q^{30} +232.709 q^{31} +4888.67 q^{32} -1568.26 q^{34} +2137.47 q^{35} -6367.26 q^{36} -3498.48 q^{37} +1763.91 q^{38} +21914.6 q^{39} +2797.46 q^{40} -4118.93 q^{41} +3407.60 q^{42} +9689.44 q^{43} -5567.89 q^{45} +8223.49 q^{46} +1494.84 q^{47} -15283.2 q^{48} -9496.96 q^{49} +1154.27 q^{50} +18325.3 q^{51} +29031.8 q^{52} +35609.0 q^{53} +808.449 q^{54} +9567.17 q^{56} -20611.5 q^{57} -5681.43 q^{58} +12009.0 q^{59} -15424.2 q^{60} +45752.8 q^{61} +429.775 q^{62} -19041.9 q^{63} -13633.7 q^{64} +25387.1 q^{65} +62687.0 q^{67} +24276.8 q^{68} -96092.2 q^{69} +3947.56 q^{70} -48606.7 q^{71} -24921.5 q^{72} -18920.9 q^{73} -6461.12 q^{74} -13487.8 q^{75} -27305.5 q^{76} +40472.6 q^{78} -76255.6 q^{79} -17704.9 q^{80} -63566.7 q^{81} -7607.00 q^{82} +70349.1 q^{83} -52750.0 q^{84} +21229.0 q^{85} +17894.8 q^{86} +66388.0 q^{87} -32826.4 q^{89} -10283.0 q^{90} +86822.5 q^{91} -127300. q^{92} -5021.96 q^{93} +2760.72 q^{94} -23877.5 q^{95} -105500. q^{96} -55019.4 q^{97} -17539.3 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.84684	0.326478	0.163239	−	0.986587i	$-0.447806\pi$
$2$	1.84684	0.326478	0.163239	+	0.986587i	$0.447806\pi$
$3$	−21.5804	−1.38439	−0.692193	−	0.721712i	$-0.743355\pi$
$3$	−21.5804	−1.38439	−0.692193	+	0.721712i	$0.743355\pi$
$4$	−28.5892	−0.893412
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−39.8555	−0.451971
$7$	−85.4988	−0.659500	−0.329750	−	0.944068i	$-0.606964\pi$
$7$	−85.4988	−0.659500	−0.329750	+	0.944068i	$0.606964\pi$
$8$	−111.898	−0.618157
$9$	222.716	0.916525
$10$	−46.1709	−0.146005
$11$	0	0
$11$	0	0
$12$	616.968	1.23683
$13$	−1015.48	−1.66653	−0.833267	−	0.552871i	$-0.813532\pi$
$13$	−1015.48	−1.66653	−0.833267	+	0.552871i	$0.813532\pi$
$14$	−157.902	−0.215312
$15$	539.511	0.619116
$16$	708.196	0.691598
$17$	−849.161	−0.712636	−0.356318	−	0.934365i	$-0.615968\pi$
$17$	−849.161	−0.712636	−0.356318	+	0.934365i	$0.615968\pi$
$18$	411.319	0.299225
$19$	955.100	0.606966	0.303483	−	0.952837i	$-0.401850\pi$
$19$	955.100	0.606966	0.303483	+	0.952837i	$0.401850\pi$
$20$	714.730	0.399546
$21$	1845.10	0.913003
$22$	0	0
$23$	4452.75	1.75513	0.877563	−	0.479461i	$-0.159168\pi$
$23$	4452.75	1.75513	0.877563	+	0.479461i	$0.159168\pi$
$24$	2414.82	0.855768
$25$	625.000	0.200000
$26$	−1875.43	−0.544086
$27$	437.748	0.115562
$28$	2444.34	0.589205
$29$	−3076.30	−0.679257	−0.339629	−	0.940560i	$-0.610301\pi$
$29$	−3076.30	−0.679257	−0.339629	+	0.940560i	$0.610301\pi$
$30$	996.389	0.202128
$31$	232.709	0.0434919	0.0217460	−	0.999764i	$-0.493078\pi$
$31$	232.709	0.0434919	0.0217460	+	0.999764i	$0.493078\pi$
$32$	4888.67	0.843948
$33$	0	0
$34$	−1568.26	−0.232660
$35$	2137.47	0.294937
$36$	−6367.26	−0.818835
$37$	−3498.48	−0.420122	−0.210061	−	0.977688i	$-0.567366\pi$
$37$	−3498.48	−0.420122	−0.210061	+	0.977688i	$0.567366\pi$
$38$	1763.91	0.198161
$39$	21914.6	2.30713
$40$	2797.46	0.276448
$41$	−4118.93	−0.382671	−0.191335	−	0.981525i	$-0.561282\pi$
$41$	−4118.93	−0.382671	−0.191335	+	0.981525i	$0.561282\pi$
$42$	3407.60	0.298075
$43$	9689.44	0.799148	0.399574	−	0.916701i	$-0.369158\pi$
$43$	9689.44	0.799148	0.399574	+	0.916701i	$0.369158\pi$
$44$	0	0
$45$	−5567.89	−0.409882
$46$	8223.49	0.573009
$47$	1494.84	0.0987072	0.0493536	−	0.998781i	$-0.484284\pi$
$47$	1494.84	0.0987072	0.0493536	+	0.998781i	$0.484284\pi$
$48$	−15283.2	−0.957439
$49$	−9496.96	−0.565060
$50$	1154.27	0.0652955
$51$	18325.3	0.986563
$52$	29031.8	1.48890
$53$	35609.0	1.74129	0.870643	−	0.491916i	$-0.163703\pi$
$53$	35609.0	1.74129	0.870643	+	0.491916i	$0.163703\pi$
$54$	808.449	0.0377284
$55$	0	0
$56$	9567.17	0.407674
$57$	−20611.5	−0.840276
$58$	−5681.43	−0.221762
$59$	12009.0	0.449135	0.224567	−	0.974459i	$-0.427903\pi$
$59$	12009.0	0.449135	0.224567	+	0.974459i	$0.427903\pi$
$60$	−15424.2	−0.553126
$61$	45752.8	1.57432	0.787161	−	0.616748i	$-0.211550\pi$
$61$	45752.8	1.57432	0.787161	+	0.616748i	$0.211550\pi$
$62$	429.775	0.0141991
$63$	−19041.9	−0.604448
$64$	−13633.7	−0.416068
$65$	25387.1	0.745297
$66$	0	0
$67$	62687.0	1.70605	0.853023	−	0.521873i	$-0.174767\pi$
$67$	62687.0	1.70605	0.853023	+	0.521873i	$0.174767\pi$
$68$	24276.8	0.636678
$69$	−96092.2	−2.42977
$70$	3947.56	0.0962904
$71$	−48606.7	−1.14433	−0.572163	−	0.820140i	$-0.693896\pi$
$71$	−48606.7	−1.14433	−0.572163	+	0.820140i	$0.693896\pi$
$72$	−24921.5	−0.566556
$73$	−18920.9	−0.415560	−0.207780	−	0.978176i	$-0.566624\pi$
$73$	−18920.9	−0.415560	−0.207780	+	0.978176i	$0.566624\pi$
$74$	−6461.12	−0.137160
$75$	−13487.8	−0.276877
$76$	−27305.5	−0.542271
$77$	0	0
$78$	40472.6	0.753225
$79$	−76255.6	−1.37469	−0.687344	−	0.726332i	$-0.741223\pi$
$79$	−76255.6	−1.37469	−0.687344	+	0.726332i	$0.741223\pi$
$80$	−17704.9	−0.309292
$81$	−63566.7	−1.07651
$82$	−7607.00	−0.124933
$83$	70349.1	1.12089	0.560445	−	0.828191i	$-0.310630\pi$
$83$	70349.1	1.12089	0.560445	+	0.828191i	$0.310630\pi$
$84$	−52750.0	−0.815688
$85$	21229.0	0.318701
$86$	17894.8	0.260904
$87$	66388.0	0.940354
$88$	0	0
$89$	−32826.4	−0.439287	−0.219643	−	0.975580i	$-0.570489\pi$
$89$	−32826.4	−0.439287	−0.219643	+	0.975580i	$0.570489\pi$
$90$	−10283.0	−0.133817
$91$	86822.5	1.09908
$92$	−127300.	−1.56805
$93$	−5021.96	−0.0602096
$94$	2760.72	0.0322257
$95$	−23877.5	−0.271444
$96$	−105500.	−1.16835
$97$	−55019.4	−0.593726	−0.296863	−	0.954920i	$-0.595940\pi$
$97$	−55019.4	−0.593726	−0.296863	+	0.954920i	$0.595940\pi$
$98$	−17539.3	−0.184479
$99$	0	0
$100$	−17868.2	−0.178682
$101$	42273.6	0.412350	0.206175	−	0.978515i	$-0.433898\pi$
$101$	42273.6	0.412350	0.206175	+	0.978515i	$0.433898\pi$
$102$	33843.8	0.322091
$103$	167774.	1.55823	0.779113	−	0.626884i	$-0.215670\pi$
$103$	167774.	1.55823	0.779113	+	0.626884i	$0.215670\pi$
$104$	113631.	1.03018
$105$	−46127.5	−0.408307
$106$	65764.0	0.568491
$107$	−170586.	−1.44041	−0.720203	−	0.693764i	$-0.755951\pi$
$107$	−170586.	−1.44041	−0.720203	+	0.693764i	$0.755951\pi$
$108$	−12514.9	−0.103244
$109$	−193422.	−1.55934	−0.779668	−	0.626193i	$-0.784612\pi$
$109$	−193422.	−1.55934	−0.779668	+	0.626193i	$0.784612\pi$
$110$	0	0
$111$	75498.8	0.581611
$112$	−60549.9	−0.456109
$113$	−3028.82	−0.0223140	−0.0111570	−	0.999938i	$-0.503551\pi$
$113$	−3028.82	−0.0223140	−0.0111570	+	0.999938i	$0.503551\pi$
$114$	−38066.0	−0.274331
$115$	−111319.	−0.784916
$116$	87949.0	0.606857
$117$	−226164.	−1.52742
$118$	22178.7	0.146633
$119$	72602.2	0.469983
$120$	−60370.4	−0.382711
$121$	0	0
$122$	84498.0	0.513981
$123$	88888.4	0.529764
$124$	−6652.95	−0.0388562
$125$	−15625.0	−0.0894427
$126$	−35167.3	−0.197339
$127$	19219.0	0.105736	0.0528679	−	0.998602i	$-0.483164\pi$
$127$	19219.0	0.105736	0.0528679	+	0.998602i	$0.483164\pi$
$128$	−181617.	−0.979785
$129$	−209102.	−1.10633
$130$	46885.8	0.243323
$131$	−271500.	−1.38227	−0.691133	−	0.722727i	$-0.742888\pi$
$131$	−271500.	−1.38227	−0.691133	+	0.722727i	$0.742888\pi$
$132$	0	0
$133$	−81659.8	−0.400294
$134$	115773.	0.556986
$135$	−10943.7	−0.0516809
$136$	95019.7	0.440521
$137$	−15513.3	−0.0706160	−0.0353080	−	0.999376i	$-0.511241\pi$
$137$	−15513.3	−0.0706160	−0.0353080	+	0.999376i	$0.511241\pi$
$138$	−177467.	−0.793266
$139$	−86669.1	−0.380476	−0.190238	−	0.981738i	$-0.560926\pi$
$139$	−86669.1	−0.380476	−0.190238	+	0.981738i	$0.560926\pi$
$140$	−61108.5	−0.263501
$141$	−32259.2	−0.136649
$142$	−89768.5	−0.373597
$143$	0	0
$144$	157726.	0.633867
$145$	76907.6	0.303773
$146$	−34943.7	−0.135671
$147$	204949.	0.782261
$148$	100019.	0.375342
$149$	−171768.	−0.633836	−0.316918	−	0.948453i	$-0.602648\pi$
$149$	−171768.	−0.633836	−0.316918	+	0.948453i	$0.602648\pi$
$150$	−24909.7	−0.0903942
$151$	243414.	0.868768	0.434384	−	0.900728i	$-0.356966\pi$
$151$	243414.	0.868768	0.434384	+	0.900728i	$0.356966\pi$
$152$	−106874.	−0.375200
$153$	−189121.	−0.653149
$154$	0	0
$155$	−5817.72	−0.0194502
$156$	−626520.	−2.06122
$157$	−251491.	−0.814279	−0.407140	−	0.913366i	$-0.633474\pi$
$157$	−251491.	−0.814279	−0.407140	+	0.913366i	$0.633474\pi$
$158$	−140832.	−0.448805
$159$	−768458.	−2.41061
$160$	−122217.	−0.377425
$161$	−380704.	−1.15751
$162$	−117397.	−0.351455
$163$	−356823.	−1.05192	−0.525961	−	0.850509i	$-0.676294\pi$
$163$	−356823.	−1.05192	−0.525961	+	0.850509i	$0.676294\pi$
$164$	117757.	0.341883
$165$	0	0
$166$	129923.	0.365946
$167$	446497.	1.23888	0.619438	−	0.785046i	$-0.287361\pi$
$167$	446497.	1.23888	0.619438	+	0.785046i	$0.287361\pi$
$168$	−206464.	−0.564379
$169$	659913.	1.77734
$170$	39206.5	0.104049
$171$	212716.	0.556300
$172$	−277013.	−0.713969
$173$	473469.	1.20275	0.601377	−	0.798965i	$-0.294619\pi$
$173$	473469.	1.20275	0.601377	+	0.798965i	$0.294619\pi$
$174$	122608.	0.307005
$175$	−53436.7	−0.131900
$176$	0	0
$177$	−259160.	−0.621776
$178$	−60625.0	−0.143417
$179$	313327.	0.730912	0.365456	−	0.930829i	$-0.380913\pi$
$179$	313327.	0.730912	0.365456	+	0.930829i	$0.380913\pi$
$180$	159181.	0.366194
$181$	43279.7	0.0981946	0.0490973	−	0.998794i	$-0.484366\pi$
$181$	43279.7	0.0981946	0.0490973	+	0.998794i	$0.484366\pi$
$182$	160347.	0.358825
$183$	−987366.	−2.17947
$184$	−498255.	−1.08494
$185$	87462.1	0.187884
$186$	−9274.73	−0.0196571
$187$	0	0
$188$	−42736.1	−0.0881862
$189$	−37426.9	−0.0762131
$190$	−44097.8	−0.0886203
$191$	−886049.	−1.75742	−0.878708	−	0.477360i	$-0.841594\pi$
$191$	−886049.	−1.75742	−0.878708	+	0.477360i	$0.841594\pi$
$192$	294222.	0.575999
$193$	67432.1	0.130309	0.0651543	−	0.997875i	$-0.479246\pi$
$193$	67432.1	0.130309	0.0651543	+	0.997875i	$0.479246\pi$
$194$	−101612.	−0.193838
$195$	−547864.	−1.03178
$196$	271510.	0.504831
$197$	−285003.	−0.523220	−0.261610	−	0.965174i	$-0.584253\pi$
$197$	−285003.	−0.523220	−0.261610	+	0.965174i	$0.584253\pi$
$198$	0	0
$199$	549780.	0.984139	0.492070	−	0.870556i	$-0.336241\pi$
$199$	549780.	0.984139	0.492070	+	0.870556i	$0.336241\pi$
$200$	−69936.5	−0.123631
$201$	−1.35281e6	−2.36183
$202$	78072.4	0.134623
$203$	263020.	0.447970
$204$	−523905.	−0.881408
$205$	102973.	0.171136
$206$	309850.	0.508726
$207$	991696.	1.60862
$208$	−719161.	−1.15257
$209$	0	0
$210$	−85190.0	−0.133303
$211$	801491.	1.23935	0.619673	−	0.784860i	$-0.287265\pi$
$211$	801491.	1.23935	0.619673	+	0.784860i	$0.287265\pi$
$212$	−1.01803e6	−1.55569
$213$	1.04895e6	1.58419
$214$	−315045.	−0.470260
$215$	−242236.	−0.357390
$216$	−48983.3	−0.0714354
$217$	−19896.3	−0.0286829
$218$	−357219.	−0.509088
$219$	408320.	0.575295
$220$	0	0
$221$	862309.	1.18763
$222$	139434.	0.189883
$223$	317595.	0.427673	0.213836	−	0.976869i	$-0.431404\pi$
$223$	317595.	0.427673	0.213836	+	0.976869i	$0.431404\pi$
$224$	−417975.	−0.556584
$225$	139197.	0.183305
$226$	−5593.73	−0.00728502
$227$	937563.	1.20764	0.603818	−	0.797122i	$-0.293645\pi$
$227$	937563.	1.20764	0.603818	+	0.797122i	$0.293645\pi$
$228$	589265.	0.750713
$229$	1.52446e6	1.92100	0.960499	−	0.278282i	$-0.0897649\pi$
$229$	1.52446e6	1.92100	0.960499	+	0.278282i	$0.0897649\pi$
$230$	−205587.	−0.256258
$231$	0	0
$232$	344233.	0.419887
$233$	346251.	0.417831	0.208916	−	0.977934i	$-0.433007\pi$
$233$	346251.	0.417831	0.208916	+	0.977934i	$0.433007\pi$
$234$	−417688.	−0.498668
$235$	−37370.9	−0.0441432
$236$	−343328.	−0.401263
$237$	1.64563e6	1.90310
$238$	134084.	0.153439
$239$	−934589.	−1.05834	−0.529171	−	0.848515i	$-0.677497\pi$
$239$	−934589.	−1.05834	−0.529171	+	0.848515i	$0.677497\pi$
$240$	382080.	0.428180
$241$	731491.	0.811272	0.405636	−	0.914035i	$-0.367050\pi$
$241$	731491.	0.811272	0.405636	+	0.914035i	$0.367050\pi$
$242$	0	0
$243$	1.26542e6	1.37474
$244$	−1.30804e6	−1.40652
$245$	237424.	0.252702
$246$	164162.	0.172956
$247$	−969887.	−1.01153
$248$	−26039.7	−0.0268848
$249$	−1.51816e6	−1.55175
$250$	−28856.8	−0.0292010
$251$	891620.	0.893296	0.446648	−	0.894710i	$-0.352618\pi$
$251$	891620.	0.893296	0.446648	+	0.894710i	$0.352618\pi$
$252$	544393.	0.540021
$253$	0	0
$254$	35494.4	0.0345204
$255$	−458132.	−0.441205
$256$	100863.	0.0961901
$257$	248272.	0.234474	0.117237	−	0.993104i	$-0.462596\pi$
$257$	248272.	0.234474	0.117237	+	0.993104i	$0.462596\pi$
$258$	−386178.	−0.361192
$259$	299116.	0.277070
$260$	−725796.	−0.665857
$261$	−685141.	−0.622556
$262$	−501416.	−0.451279
$263$	−1.15245e6	−1.02739	−0.513694	−	0.857973i	$-0.671723\pi$
$263$	−1.15245e6	−1.02739	−0.513694	+	0.857973i	$0.671723\pi$
$264$	0	0
$265$	−890225.	−0.778727
$266$	−150812.	−0.130687
$267$	708408.	0.608143
$268$	−1.79217e6	−1.52420
$269$	−1.25963e6	−1.06136	−0.530679	−	0.847573i	$-0.678063\pi$
$269$	−1.25963e6	−1.06136	−0.530679	+	0.847573i	$0.678063\pi$
$270$	−20211.2	−0.0168726
$271$	1.51506e6	1.25316	0.626578	−	0.779359i	$-0.284455\pi$
$271$	1.51506e6	1.25316	0.626578	+	0.779359i	$0.284455\pi$
$272$	−601373.	−0.492858
$273$	−1.87367e6	−1.52155
$274$	−28650.6	−0.0230545
$275$	0	0
$276$	2.74720e6	2.17079
$277$	−111549.	−0.0873503	−0.0436751	−	0.999046i	$-0.513907\pi$
$277$	−111549.	−0.0873503	−0.0436751	+	0.999046i	$0.513907\pi$
$278$	−160064.	−0.124217
$279$	51827.8	0.0398614
$280$	−239179.	−0.182318
$281$	1.96391e6	1.48373	0.741867	−	0.670547i	$-0.233941\pi$
$281$	1.96391e6	1.48373	0.741867	+	0.670547i	$0.233941\pi$
$282$	−59577.5	−0.0446128
$283$	−679729.	−0.504510	−0.252255	−	0.967661i	$-0.581172\pi$
$283$	−679729.	−0.504510	−0.252255	+	0.967661i	$0.581172\pi$
$284$	1.38963e6	1.02236
$285$	515287.	0.375783
$286$	0	0
$287$	352164.	0.252371
$288$	1.08878e6	0.773499
$289$	−698782.	−0.492150
$290$	142036.	0.0991751
$291$	1.18734e6	0.821946
$292$	540932.	0.371266
$293$	1.65970e6	1.12943	0.564716	−	0.825285i	$-0.308986\pi$
$293$	1.65970e6	1.12943	0.564716	+	0.825285i	$0.308986\pi$
$294$	378506.	0.255391
$295$	−300225.	−0.200859
$296$	391474.	0.259701
$297$	0	0
$298$	−317228.	−0.206933
$299$	−4.52169e6	−2.92498
$300$	385605.	0.247366
$301$	−828435.	−0.527038
$302$	449547.	0.283633
$303$	−912283.	−0.570851
$304$	676398.	0.419777
$305$	−1.14382e6	−0.704058
$306$	−349276.	−0.213238
$307$	−626785.	−0.379553	−0.189777	−	0.981827i	$-0.560776\pi$
$307$	−626785.	−0.379553	−0.189777	+	0.981827i	$0.560776\pi$
$308$	0	0
$309$	−3.62063e6	−2.15719
$310$	−10744.4	−0.00635004
$311$	1.82212e6	1.06826	0.534129	−	0.845403i	$-0.320640\pi$
$311$	1.82212e6	1.06826	0.534129	+	0.845403i	$0.320640\pi$
$312$	−2.45220e6	−1.42617
$313$	2.55497e6	1.47409	0.737047	−	0.675841i	$-0.236220\pi$
$313$	2.55497e6	1.47409	0.737047	+	0.675841i	$0.236220\pi$
$314$	−464463.	−0.265844
$315$	476048.	0.270317
$316$	2.18009e6	1.22816
$317$	−902842.	−0.504619	−0.252310	−	0.967647i	$-0.581190\pi$
$317$	−902842.	−0.504619	−0.252310	+	0.967647i	$0.581190\pi$
$318$	−1.41922e6	−0.787011
$319$	0	0
$320$	340843.	0.186071
$321$	3.68133e6	1.99408
$322$	−703099.	−0.377900
$323$	−811033.	−0.432546
$324$	1.81732e6	0.961765
$325$	−634677.	−0.333307
$326$	−658993.	−0.343429
$327$	4.17413e6	2.15872
$328$	460902.	0.236551
$329$	−127807.	−0.0650974
$330$	0	0
$331$	−893304.	−0.448156	−0.224078	−	0.974571i	$-0.571937\pi$
$331$	−893304.	−0.448156	−0.224078	+	0.974571i	$0.571937\pi$
$332$	−2.01122e6	−1.00142
$333$	−779166.	−0.385052
$334$	824607.	0.404465
$335$	−1.56718e6	−0.762967
$336$	1.30669e6	0.631431
$337$	−916481.	−0.439591	−0.219795	−	0.975546i	$-0.570539\pi$
$337$	−916481.	−0.439591	−0.219795	+	0.975546i	$0.570539\pi$
$338$	1.21875e6	0.580261
$339$	65363.3	0.0308912
$340$	−606921.	−0.284731
$341$	0	0
$342$	392851.	0.181619
$343$	2.24896e6	1.03216
$344$	−1.08423e6	−0.493999
$345$	2.40231e6	1.08663
$346$	874421.	0.392672
$347$	−1.89211e6	−0.843575	−0.421787	−	0.906695i	$-0.638597\pi$
$347$	−1.89211e6	−0.843575	−0.421787	+	0.906695i	$0.638597\pi$
$348$	−1.89798e6	−0.840124
$349$	−4.10253e6	−1.80297	−0.901485	−	0.432811i	$-0.857522\pi$
$349$	−4.10253e6	−1.80297	−0.901485	+	0.432811i	$0.857522\pi$
$350$	−98688.9	−0.0430624
$351$	−444526.	−0.192588
$352$	0	0
$353$	1.94656e6	0.831442	0.415721	−	0.909492i	$-0.363529\pi$
$353$	1.94656e6	0.831442	0.415721	+	0.909492i	$0.363529\pi$
$354$	−478625.	−0.202996
$355$	1.21517e6	0.511758
$356$	938480.	0.392464
$357$	−1.56679e6	−0.650639
$358$	578664.	0.238627
$359$	220819.	0.0904275	0.0452138	−	0.998977i	$-0.485603\pi$
$359$	220819.	0.0904275	0.0452138	+	0.998977i	$0.485603\pi$
$360$	623037.	0.253372
$361$	−1.56388e6	−0.631592
$362$	79930.5	0.0320583
$363$	0	0
$364$	−2.48219e6	−0.981931
$365$	473021.	0.185844
$366$	−1.82350e6	−0.711548
$367$	2.53101e6	0.980909	0.490455	−	0.871467i	$-0.336831\pi$
$367$	2.53101e6	0.980909	0.490455	+	0.871467i	$0.336831\pi$
$368$	3.15342e6	1.21384
$369$	−917351.	−0.350727
$370$	161528.	0.0613400
$371$	−3.04453e6	−1.14838
$372$	143574.	0.0537920
$373$	−19740.2	−0.00734649	−0.00367325	−	0.999993i	$-0.501169\pi$
$373$	−19740.2	−0.00734649	−0.00367325	+	0.999993i	$0.501169\pi$
$374$	0	0
$375$	337194.	0.123823
$376$	−167270.	−0.0610165
$377$	3.12393e6	1.13201
$378$	−69121.4	−0.0248819
$379$	−2.42182e6	−0.866053	−0.433027	−	0.901381i	$-0.642554\pi$
$379$	−2.42182e6	−0.866053	−0.433027	+	0.901381i	$0.642554\pi$
$380$	682638.	0.242511
$381$	−414755.	−0.146379
$382$	−1.63639e6	−0.573757
$383$	−4.32927e6	−1.50806	−0.754029	−	0.656841i	$-0.771892\pi$
$383$	−4.32927e6	−1.50806	−0.754029	+	0.656841i	$0.771892\pi$
$384$	3.91937e6	1.35640
$385$	0	0
$386$	124536.	0.0425429
$387$	2.15799e6	0.732439
$388$	1.57296e6	0.530442
$389$	−546163.	−0.182999	−0.0914994	−	0.995805i	$-0.529166\pi$
$389$	−546163.	−0.182999	−0.0914994	+	0.995805i	$0.529166\pi$
$390$	−1.01182e6	−0.336853
$391$	−3.78110e6	−1.25077
$392$	1.06269e6	0.349296
$393$	5.85909e6	1.91359
$394$	−526354.	−0.170819
$395$	1.90639e6	0.614779
$396$	0	0
$397$	−3.13342e6	−0.997796	−0.498898	−	0.866661i	$-0.666262\pi$
$397$	−3.13342e6	−0.997796	−0.498898	+	0.866661i	$0.666262\pi$
$398$	1.01535e6	0.321299
$399$	1.76226e6	0.554162
$400$	442623.	0.138320
$401$	1.37233e6	0.426186	0.213093	−	0.977032i	$-0.431646\pi$
$401$	1.37233e6	0.426186	0.213093	+	0.977032i	$0.431646\pi$
$402$	−2.49843e6	−0.771084
$403$	−236312.	−0.0724807
$404$	−1.20857e6	−0.368398
$405$	1.58917e6	0.481429
$406$	485755.	0.146252
$407$	0	0
$408$	−2.05057e6	−0.609851
$409$	3.79066e6	1.12049	0.560244	−	0.828328i	$-0.310707\pi$
$409$	3.79066e6	1.12049	0.560244	+	0.828328i	$0.310707\pi$
$410$	190175.	0.0558719
$411$	334784.	0.0977598
$412$	−4.79651e6	−1.39214
$413$	−1.02675e6	−0.296205
$414$	1.83150e6	0.525177
$415$	−1.75873e6	−0.501278
$416$	−4.96436e6	−1.40647
$417$	1.87036e6	0.526726
$418$	0	0
$419$	−3.73663e6	−1.03979	−0.519894	−	0.854231i	$-0.674029\pi$
$419$	−3.73663e6	−1.03979	−0.519894	+	0.854231i	$0.674029\pi$
$420$	1.31875e6	0.364787
$421$	6.67850e6	1.83643	0.918213	−	0.396087i	$-0.129632\pi$
$421$	6.67850e6	1.83643	0.918213	+	0.396087i	$0.129632\pi$
$422$	1.48022e6	0.404619
$423$	332923.	0.0904676
$424$	−3.98459e6	−1.07639
$425$	−530726.	−0.142527
$426$	1.93724e6	0.517202
$427$	−3.91181e6	−1.03826
$428$	4.87693e6	1.28688
$429$	0	0
$430$	−447370.	−0.116680
$431$	−1.78388e6	−0.462566	−0.231283	−	0.972887i	$-0.574292\pi$
$431$	−1.78388e6	−0.462566	−0.231283	+	0.972887i	$0.574292\pi$
$432$	310012.	0.0799224
$433$	1.97669e6	0.506663	0.253332	−	0.967379i	$-0.418474\pi$
$433$	1.97669e6	0.506663	0.253332	+	0.967379i	$0.418474\pi$
$434$	−36745.2	−0.00936433
$435$	−1.65970e6	−0.420539
$436$	5.52978e6	1.39313
$437$	4.25282e6	1.06530
$438$	754101.	0.187821
$439$	−2.13844e6	−0.529584	−0.264792	−	0.964306i	$-0.585303\pi$
$439$	−2.13844e6	−0.529584	−0.264792	+	0.964306i	$0.585303\pi$
$440$	0	0
$441$	−2.11512e6	−0.517891
$442$	1.59254e6	0.387735
$443$	−2.75102e6	−0.666015	−0.333007	−	0.942924i	$-0.608063\pi$
$443$	−2.75102e6	−0.666015	−0.333007	+	0.942924i	$0.608063\pi$
$444$	−2.15845e6	−0.519618
$445$	820660.	0.196455
$446$	586546.	0.139626
$447$	3.70683e6	0.877474
$448$	1.16567e6	0.274397
$449$	1.79974e6	0.421302	0.210651	−	0.977561i	$-0.432442\pi$
$449$	1.79974e6	0.421302	0.210651	+	0.977561i	$0.432442\pi$
$450$	257074.	0.0598450
$451$	0	0
$452$	86591.5	0.0199356
$453$	−5.25299e6	−1.20271
$454$	1.73153e6	0.394266
$455$	−2.17056e6	−0.491523
$456$	2.30639e6	0.519422
$457$	6.51731e6	1.45975	0.729874	−	0.683582i	$-0.239579\pi$
$457$	6.51731e6	1.45975	0.729874	+	0.683582i	$0.239579\pi$
$458$	2.81543e6	0.627163
$459$	−371719.	−0.0823536
$460$	3.18251e6	0.701254
$461$	−4.04106e6	−0.885611	−0.442806	−	0.896618i	$-0.646017\pi$
$461$	−4.04106e6	−0.885611	−0.442806	+	0.896618i	$0.646017\pi$
$462$	0	0
$463$	−7.41853e6	−1.60829	−0.804147	−	0.594430i	$-0.797378\pi$
$463$	−7.41853e6	−1.60829	−0.804147	+	0.594430i	$0.797378\pi$
$464$	−2.17863e6	−0.469773
$465$	125549.	0.0269265
$466$	639469.	0.136413
$467$	4.71925e6	1.00134	0.500669	−	0.865639i	$-0.333087\pi$
$467$	4.71925e6	1.00134	0.500669	+	0.865639i	$0.333087\pi$
$468$	6.46584e6	1.36462
$469$	−5.35967e6	−1.12514
$470$	−69017.9	−0.0144118
$471$	5.42729e6	1.12728
$472$	−1.34379e6	−0.277636
$473$	0	0
$474$	3.03921e6	0.621319
$475$	596937.	0.121393
$476$	−2.07564e6	−0.419889
$477$	7.93067e6	1.59593
$478$	−1.72603e6	−0.345525
$479$	−8.42121e6	−1.67701	−0.838505	−	0.544894i	$-0.816570\pi$
$479$	−8.42121e6	−1.67701	−0.838505	+	0.544894i	$0.816570\pi$
$480$	2.63749e6	0.522502
$481$	3.55265e6	0.700148
$482$	1.35094e6	0.264862
$483$	8.21577e6	1.60243
$484$	0	0
$485$	1.37548e6	0.265522
$486$	2.33703e6	0.448822
$487$	6.67431e6	1.27522	0.637609	−	0.770360i	$-0.279924\pi$
$487$	6.67431e6	1.27522	0.637609	+	0.770360i	$0.279924\pi$
$488$	−5.11966e6	−0.973177
$489$	7.70039e6	1.45627
$490$	438483.	0.0825017
$491$	−2.97941e6	−0.557733	−0.278866	−	0.960330i	$-0.589959\pi$
$491$	−2.97941e6	−0.557733	−0.278866	+	0.960330i	$0.589959\pi$
$492$	−2.54125e6	−0.473298
$493$	2.61228e6	0.484063
$494$	−1.79122e6	−0.330242
$495$	0	0
$496$	164803.	0.0300789
$497$	4.15581e6	0.754683
$498$	−2.80380e6	−0.506610
$499$	−1.53445e6	−0.275869	−0.137934	−	0.990441i	$-0.544046\pi$
$499$	−1.53445e6	−0.275869	−0.137934	+	0.990441i	$0.544046\pi$
$500$	446706.	0.0799092
$501$	−9.63561e6	−1.71508
$502$	1.64668e6	0.291641
$503$	5.24604e6	0.924509	0.462255	−	0.886747i	$-0.347041\pi$
$503$	5.24604e6	0.924509	0.462255	+	0.886747i	$0.347041\pi$
$504$	2.13076e6	0.373644
$505$	−1.05684e6	−0.184408
$506$	0	0
$507$	−1.42412e7	−2.46052
$508$	−549457.	−0.0944657
$509$	−3.41159e6	−0.583663	−0.291831	−	0.956470i	$-0.594265\pi$
$509$	−3.41159e6	−0.583663	−0.291831	+	0.956470i	$0.594265\pi$
$510$	−846094.	−0.144043
$511$	1.61771e6	0.274062
$512$	5.99801e6	1.01119
$513$	418093.	0.0701422
$514$	458518.	0.0765506
$515$	−4.19434e6	−0.696860
$516$	5.97807e6	0.988409
$517$	0	0
$518$	552418.	0.0904573
$519$	−1.02177e7	−1.66508
$520$	−2.84077e6	−0.460710
$521$	−1.09388e7	−1.76554	−0.882769	−	0.469806i	$-0.844324\pi$
$521$	−1.09388e7	−1.76554	−0.882769	+	0.469806i	$0.844324\pi$
$522$	−1.26534e6	−0.203251
$523$	4.54821e6	0.727087	0.363543	−	0.931577i	$-0.381567\pi$
$523$	4.54821e6	0.727087	0.363543	+	0.931577i	$0.381567\pi$
$524$	7.76197e6	1.23493
$525$	1.15319e6	0.182601
$526$	−2.12840e6	−0.335419
$527$	−197607.	−0.0309939
$528$	0	0
$529$	1.33906e7	2.08047
$530$	−1.64410e6	−0.254237
$531$	2.67459e6	0.411643
$532$	2.33459e6	0.357628
$533$	4.18271e6	0.637734
$534$	1.30831e6	0.198545
$535$	4.26466e6	0.644169
$536$	−7.01458e6	−1.05460
$537$	−6.76174e6	−1.01186
$538$	−2.32633e6	−0.346510
$539$	0	0
$540$	312872.	0.0461723
$541$	−9.52761e6	−1.39956	−0.699779	−	0.714359i	$-0.746718\pi$
$541$	−9.52761e6	−1.39956	−0.699779	+	0.714359i	$0.746718\pi$
$542$	2.79806e6	0.409127
$543$	−933995.	−0.135939
$544$	−4.15127e6	−0.601428
$545$	4.83555e6	0.697356
$546$	−3.46036e6	−0.496752
$547$	−6.10841e6	−0.872891	−0.436445	−	0.899731i	$-0.643763\pi$
$547$	−6.10841e6	−0.872891	−0.436445	+	0.899731i	$0.643763\pi$
$548$	443513.	0.0630892
$549$	1.01899e7	1.44290
$550$	0	0
$551$	−2.93818e6	−0.412286
$552$	1.07526e7	1.50198
$553$	6.51976e6	0.906606
$554$	−206012.	−0.0285179
$555$	−1.88747e6	−0.260104
$556$	2.47780e6	0.339922
$557$	6.21112e6	0.848265	0.424133	−	0.905600i	$-0.360579\pi$
$557$	6.21112e6	0.848265	0.424133	+	0.905600i	$0.360579\pi$
$558$	95717.5	0.0130139
$559$	−9.83946e6	−1.33181
$560$	1.51375e6	0.203978
$561$	0	0
$562$	3.62702e6	0.484406
$563$	−4.22641e6	−0.561954	−0.280977	−	0.959715i	$-0.590658\pi$
$563$	−4.22641e6	−0.561954	−0.280977	+	0.959715i	$0.590658\pi$
$564$	922265.	0.122084
$565$	75720.5	0.00997912
$566$	−1.25535e6	−0.164711
$567$	5.43487e6	0.709956
$568$	5.43900e6	0.707373
$569$	1.30241e7	1.68642	0.843211	−	0.537582i	$-0.180662\pi$
$569$	1.30241e7	1.68642	0.843211	+	0.537582i	$0.180662\pi$
$570$	951650.	0.122685
$571$	−6.57751e6	−0.844250	−0.422125	−	0.906538i	$-0.638716\pi$
$571$	−6.57751e6	−0.844250	−0.422125	+	0.906538i	$0.638716\pi$
$572$	0	0
$573$	1.91213e7	2.43294
$574$	650389.	0.0823936
$575$	2.78297e6	0.351025
$576$	−3.03644e6	−0.381337
$577$	62120.7	0.00776778	0.00388389	−	0.999992i	$-0.498764\pi$
$577$	62120.7	0.00776778	0.00388389	+	0.999992i	$0.498764\pi$
$578$	−1.29054e6	−0.160676
$579$	−1.45521e6	−0.180397
$580$	−2.19873e6	−0.271395
$581$	−6.01476e6	−0.739227
$582$	2.19283e6	0.268347
$583$	0	0
$584$	2.11721e6	0.256881
$585$	5.65410e6	0.683083
$586$	3.06519e6	0.368735
$587$	1.08901e6	0.130448	0.0652240	−	0.997871i	$-0.479224\pi$
$587$	1.08901e6	0.130448	0.0652240	+	0.997871i	$0.479224\pi$
$588$	−5.85932e6	−0.698882
$589$	222260.	0.0263981
$590$	−554466.	−0.0655761
$591$	6.15049e6	0.724338
$592$	−2.47761e6	−0.290556
$593$	−5.81621e6	−0.679208	−0.339604	−	0.940568i	$-0.610293\pi$
$593$	−5.81621e6	−0.679208	−0.339604	+	0.940568i	$0.610293\pi$
$594$	0	0
$595$	−1.81506e6	−0.210183
$596$	4.91071e6	0.566277
$597$	−1.18645e7	−1.36243
$598$	−8.35082e6	−0.954940
$599$	6.01591e6	0.685069	0.342534	−	0.939505i	$-0.388715\pi$
$599$	6.01591e6	0.685069	0.342534	+	0.939505i	$0.388715\pi$
$600$	1.50926e6	0.171154
$601$	1.26834e7	1.43235	0.716175	−	0.697921i	$-0.245891\pi$
$601$	1.26834e7	1.43235	0.716175	+	0.697921i	$0.245891\pi$
$602$	−1.52998e6	−0.172066
$603$	1.39614e7	1.56363
$604$	−6.95902e6	−0.776169
$605$	0	0
$606$	−1.68484e6	−0.186370
$607$	3.76601e6	0.414868	0.207434	−	0.978249i	$-0.433489\pi$
$607$	3.76601e6	0.414868	0.207434	+	0.978249i	$0.433489\pi$
$608$	4.66917e6	0.512248
$609$	−5.67609e6	−0.620163
$610$	−2.11245e6	−0.229859
$611$	−1.51798e6	−0.164499
$612$	5.40683e6	0.583531
$613$	−1.18326e7	−1.27183	−0.635915	−	0.771759i	$-0.719377\pi$
$613$	−1.18326e7	−1.27183	−0.635915	+	0.771759i	$0.719377\pi$
$614$	−1.15757e6	−0.123916
$615$	−2.22221e6	−0.236918
$616$	0	0
$617$	−1.26897e7	−1.34195	−0.670977	−	0.741478i	$-0.734125\pi$
$617$	−1.26897e7	−1.34195	−0.670977	+	0.741478i	$0.734125\pi$
$618$	−6.68671e6	−0.704273
$619$	−8.72018e6	−0.914742	−0.457371	−	0.889276i	$-0.651209\pi$
$619$	−8.72018e6	−0.914742	−0.457371	+	0.889276i	$0.651209\pi$
$620$	166324.	0.0173770
$621$	1.94918e6	0.202826
$622$	3.36516e6	0.348762
$623$	2.80662e6	0.289710
$624$	1.55198e7	1.59560
$625$	390625.	0.0400000
$626$	4.71861e6	0.481259
$627$	0	0
$628$	7.18992e6	0.727487
$629$	2.97078e6	0.299394
$630$	879182.	0.0882526
$631$	1.93216e7	1.93183	0.965917	−	0.258853i	$-0.0833446\pi$
$631$	1.93216e7	1.93183	0.965917	+	0.258853i	$0.0833446\pi$
$632$	8.53287e6	0.849772
$633$	−1.72965e7	−1.71573
$634$	−1.66740e6	−0.164747
$635$	−480476.	−0.0472865
$636$	2.19696e7	2.15367
$637$	9.64400e6	0.941691
$638$	0	0
$639$	−1.08255e7	−1.04880
$640$	4.54042e6	0.438173
$641$	326009.	0.0313390	0.0156695	−	0.999877i	$-0.495012\pi$
$641$	326009.	0.0313390	0.0156695	+	0.999877i	$0.495012\pi$
$642$	6.79881e6	0.651022
$643$	1.18052e7	1.12602	0.563012	−	0.826449i	$-0.309643\pi$
$643$	1.18052e7	1.12602	0.563012	+	0.826449i	$0.309643\pi$
$644$	1.08840e7	1.03413
$645$	5.22756e6	0.494766
$646$	−1.49785e6	−0.141217
$647$	1.68565e7	1.58309	0.791546	−	0.611109i	$-0.209276\pi$
$647$	1.68565e7	1.58309	0.791546	+	0.611109i	$0.209276\pi$
$648$	7.11300e6	0.665450
$649$	0	0
$650$	−1.17214e6	−0.108817
$651$	429371.	0.0397082
$652$	1.02013e7	0.939800
$653$	−9.24716e6	−0.848644	−0.424322	−	0.905511i	$-0.639487\pi$
$653$	−9.24716e6	−0.848644	−0.424322	+	0.905511i	$0.639487\pi$
$654$	7.70894e6	0.704775
$655$	6.78750e6	0.618169
$656$	−2.91701e6	−0.264654
$657$	−4.21397e6	−0.380871
$658$	−236038.	−0.0212528
$659$	−1.01552e7	−0.910905	−0.455453	−	0.890260i	$-0.650523\pi$
$659$	−1.01552e7	−0.910905	−0.455453	+	0.890260i	$0.650523\pi$
$660$	0	0
$661$	1.32719e7	1.18149	0.590745	−	0.806858i	$-0.298834\pi$
$661$	1.32719e7	1.18149	0.590745	+	0.806858i	$0.298834\pi$
$662$	−1.64979e6	−0.146313
$663$	−1.86090e7	−1.64414
$664$	−7.87194e6	−0.692886
$665$	2.04150e6	0.179017
$666$	−1.43899e6	−0.125711
$667$	−1.36980e7	−1.19218
$668$	−1.27650e7	−1.10683
$669$	−6.85384e6	−0.592064
$670$	−2.89432e6	−0.249092
$671$	0	0
$672$	9.02009e6	0.770527
$673$	−1.12684e7	−0.959014	−0.479507	−	0.877538i	$-0.659185\pi$
$673$	−1.12684e7	−0.959014	−0.479507	+	0.877538i	$0.659185\pi$
$674$	−1.69259e6	−0.143517
$675$	273593.	0.0231124
$676$	−1.88664e7	−1.58789
$677$	−2.21349e7	−1.85612	−0.928059	−	0.372432i	$-0.878524\pi$
$677$	−2.21349e7	−1.85612	−0.928059	+	0.372432i	$0.878524\pi$
$678$	120715.	0.0100853
$679$	4.70409e6	0.391562
$680$	−2.37549e6	−0.197007
$681$	−2.02330e7	−1.67183
$682$	0	0
$683$	−2.94478e6	−0.241547	−0.120774	−	0.992680i	$-0.538537\pi$
$683$	−2.94478e6	−0.241547	−0.120774	+	0.992680i	$0.538537\pi$
$684$	−6.08137e6	−0.497005
$685$	387833.	0.0315804
$686$	4.15345e6	0.336976
$687$	−3.28985e7	−2.65940
$688$	6.86202e6	0.552689
$689$	−3.61603e7	−2.90191
$690$	4.43667e6	0.354759
$691$	−869351.	−0.0692628	−0.0346314	−	0.999400i	$-0.511026\pi$
$691$	−869351.	−0.0692628	−0.0346314	+	0.999400i	$0.511026\pi$
$692$	−1.35361e7	−1.07456
$693$	0	0
$694$	−3.49443e6	−0.275408
$695$	2.16673e6	0.170154
$696$	−7.42870e6	−0.581286
$697$	3.49764e6	0.272705
$698$	−7.57670e6	−0.588629
$699$	−7.47225e6	−0.578440
$700$	1.52771e6	0.117841
$701$	−1.26507e7	−0.972341	−0.486171	−	0.873864i	$-0.661607\pi$
$701$	−1.26507e7	−0.972341	−0.486171	+	0.873864i	$0.661607\pi$
$702$	−820966.	−0.0628756
$703$	−3.34140e6	−0.255000
$704$	0	0
$705$	806480.	0.0611112
$706$	3.59499e6	0.271447
$707$	−3.61434e6	−0.271945
$708$	7.40916e6	0.555503
$709$	1.88497e7	1.40828	0.704140	−	0.710061i	$-0.251333\pi$
$709$	1.88497e7	1.40828	0.704140	+	0.710061i	$0.251333\pi$
$710$	2.24421e6	0.167078
$711$	−1.69833e7	−1.25994
$712$	3.67322e6	0.271548
$713$	1.03619e6	0.0763338
$714$	−2.89360e6	−0.212419
$715$	0	0
$716$	−8.95777e6	−0.653006
$717$	2.01688e7	1.46515
$718$	407817.	0.0295226
$719$	−3.33675e6	−0.240714	−0.120357	−	0.992731i	$-0.538404\pi$
$719$	−3.33675e6	−0.240714	−0.120357	+	0.992731i	$0.538404\pi$
$720$	−3.94316e6	−0.283474
$721$	−1.43444e7	−1.02765
$722$	−2.88824e6	−0.206201
$723$	−1.57859e7	−1.12311
$724$	−1.23733e6	−0.0877283
$725$	−1.92269e6	−0.135851
$726$	0	0
$727$	2.74122e6	0.192357	0.0961785	−	0.995364i	$-0.469338\pi$
$727$	2.74122e6	0.192357	0.0961785	+	0.995364i	$0.469338\pi$
$728$	−9.71530e6	−0.679403
$729$	−1.18617e7	−0.826663
$730$	873593.	0.0606739
$731$	−8.22789e6	−0.569502
$732$	2.82280e7	1.94716
$733$	−2.49850e7	−1.71759	−0.858794	−	0.512321i	$-0.828786\pi$
$733$	−2.49850e7	−1.71759	−0.858794	+	0.512321i	$0.828786\pi$
$734$	4.67436e6	0.320245
$735$	−5.12372e6	−0.349838
$736$	2.17680e7	1.48124
$737$	0	0
$738$	−1.69420e6	−0.114505
$739$	−2.23536e7	−1.50569	−0.752845	−	0.658198i	$-0.771319\pi$
$739$	−2.23536e7	−1.50569	−0.752845	+	0.658198i	$0.771319\pi$
$740$	−2.50047e6	−0.167858
$741$	2.09306e7	1.40035
$742$	−5.62274e6	−0.374920
$743$	−1.56954e7	−1.04304	−0.521520	−	0.853239i	$-0.674635\pi$
$743$	−1.56954e7	−1.04304	−0.521520	+	0.853239i	$0.674635\pi$
$744$	561949.	0.0372190
$745$	4.29420e6	0.283460
$746$	−36457.0	−0.00239846
$747$	1.56678e7	1.02732
$748$	0	0
$749$	1.45849e7	0.949947
$750$	622743.	0.0404255
$751$	−2.34346e6	−0.151621	−0.0758103	−	0.997122i	$-0.524154\pi$
$751$	−2.34346e6	−0.151621	−0.0758103	+	0.997122i	$0.524154\pi$
$752$	1.05864e6	0.0682657
$753$	−1.92415e7	−1.23667
$754$	5.76939e6	0.369574
$755$	−6.08536e6	−0.388525
$756$	1.07001e6	0.0680897
$757$	−1.09000e7	−0.691329	−0.345665	−	0.938358i	$-0.612347\pi$
$757$	−1.09000e7	−0.691329	−0.345665	+	0.938358i	$0.612347\pi$
$758$	−4.47271e6	−0.282747
$759$	0	0
$760$	2.67185e6	0.167795
$761$	1.44056e7	0.901715	0.450858	−	0.892596i	$-0.351118\pi$
$761$	1.44056e7	0.901715	0.450858	+	0.892596i	$0.351118\pi$
$762$	−765985.	−0.0477895
$763$	1.65374e7	1.02838
$764$	2.53314e7	1.57010
$765$	4.72803e6	0.292097
$766$	−7.99546e6	−0.492347
$767$	−1.21949e7	−0.748499
$768$	−2.17666e6	−0.133164
$769$	57342.5	0.00349672	0.00174836	−	0.999998i	$-0.499443\pi$
$769$	57342.5	0.00349672	0.00174836	+	0.999998i	$0.499443\pi$
$770$	0	0
$771$	−5.35782e6	−0.324603
$772$	−1.92783e6	−0.116419
$773$	1.65767e7	0.997811	0.498905	−	0.866656i	$-0.333735\pi$
$773$	1.65767e7	0.997811	0.498905	+	0.866656i	$0.333735\pi$
$774$	3.98545e6	0.239125
$775$	145443.	0.00869838
$776$	6.15657e6	0.367016
$777$	−6.45505e6	−0.383572
$778$	−1.00867e6	−0.0597450
$779$	−3.93399e6	−0.232268
$780$	1.56630e7	0.921804
$781$	0	0
$782$	−6.98307e6	−0.408347
$783$	−1.34665e6	−0.0784963
$784$	−6.72571e6	−0.390794
$785$	6.28727e6	0.364157
$786$	1.08208e7	0.624745
$787$	−3.20182e7	−1.84272	−0.921362	−	0.388706i	$-0.872922\pi$
$787$	−3.20182e7	−1.84272	−0.921362	+	0.388706i	$0.872922\pi$
$788$	8.14801e6	0.467451
$789$	2.48705e7	1.42230
$790$	3.52079e6	0.200712
$791$	258960.	0.0147161
$792$	0	0
$793$	−4.64612e7	−2.62366
$794$	−5.78691e6	−0.325758
$795$	1.92114e7	1.07806
$796$	−1.57178e7	−0.879242
$797$	−2.18129e7	−1.21637	−0.608187	−	0.793793i	$-0.708103\pi$
$797$	−2.18129e7	−1.21637	−0.608187	+	0.793793i	$0.708103\pi$
$798$	3.25460e6	0.180921
$799$	−1.26936e6	−0.0703423
$800$	3.05542e6	0.168790
$801$	−7.31095e6	−0.402617
$802$	2.53448e6	0.139140
$803$	0	0
$804$	3.86759e7	2.11009
$805$	9.51761e6	0.517652
$806$	−436429.	−0.0236633
$807$	2.71833e7	1.46933
$808$	−4.73034e6	−0.254897
$809$	−940848.	−0.0505415	−0.0252708	−	0.999681i	$-0.508045\pi$
$809$	−940848.	−0.0505415	−0.0252708	+	0.999681i	$0.508045\pi$
$810$	2.93493e6	0.157176
$811$	−3.40004e7	−1.81523	−0.907616	−	0.419801i	$-0.862100\pi$
$811$	−3.40004e7	−1.81523	−0.907616	+	0.419801i	$0.862100\pi$
$812$	−7.51954e6	−0.400222
$813$	−3.26956e7	−1.73485
$814$	0	0
$815$	8.92057e6	0.470434
$816$	1.29779e7	0.682305
$817$	9.25438e6	0.485056
$818$	7.00073e6	0.365814
$819$	1.93367e7	1.00733
$820$	−2.94393e6	−0.152895
$821$	−5.44954e6	−0.282164	−0.141082	−	0.989998i	$-0.545058\pi$
$821$	−5.44954e6	−0.282164	−0.141082	+	0.989998i	$0.545058\pi$
$822$	618292.	0.0319164
$823$	3.21039e7	1.65218	0.826092	−	0.563536i	$-0.190559\pi$
$823$	3.21039e7	1.65218	0.826092	+	0.563536i	$0.190559\pi$
$824$	−1.87736e7	−0.963228
$825$	0	0
$826$	−1.89625e6	−0.0967041
$827$	2.63221e7	1.33831	0.669156	−	0.743122i	$-0.266656\pi$
$827$	2.63221e7	1.33831	0.669156	+	0.743122i	$0.266656\pi$
$828$	−2.83518e7	−1.43716
$829$	−2.14109e7	−1.08205	−0.541026	−	0.841006i	$-0.681964\pi$
$829$	−2.14109e7	−1.08205	−0.541026	+	0.841006i	$0.681964\pi$
$830$	−3.24808e6	−0.163656
$831$	2.40727e6	0.120927
$832$	1.38448e7	0.693391
$833$	8.06445e6	0.402682
$834$	3.45424e6	0.171964
$835$	−1.11624e7	−0.554042
$836$	0	0
$837$	101868.	0.00502601
$838$	−6.90094e6	−0.339468
$839$	−1.98063e7	−0.971399	−0.485700	−	0.874126i	$-0.661435\pi$
$839$	−1.98063e7	−0.971399	−0.485700	+	0.874126i	$0.661435\pi$
$840$	5.16159e6	0.252398
$841$	−1.10475e7	−0.538610
$842$	1.23341e7	0.599552
$843$	−4.23821e7	−2.05406
$844$	−2.29140e7	−1.10725
$845$	−1.64978e7	−0.794849
$846$	614854.	0.0295356
$847$	0	0
$848$	2.52182e7	1.20427
$849$	1.46688e7	0.698436
$850$	−980163.	−0.0465319
$851$	−1.55779e7	−0.737367
$852$	−2.99887e7	−1.41533
$853$	2.21558e6	0.104259	0.0521296	−	0.998640i	$-0.483399\pi$
$853$	2.21558e6	0.104259	0.0521296	+	0.998640i	$0.483399\pi$
$854$	−7.22447e6	−0.338970
$855$	−5.31789e6	−0.248785
$856$	1.90883e7	0.890396
$857$	−2.56229e7	−1.19173	−0.595863	−	0.803086i	$-0.703190\pi$
$857$	−2.56229e7	−1.19173	−0.595863	+	0.803086i	$0.703190\pi$
$858$	0	0
$859$	1.69523e7	0.783872	0.391936	−	0.919992i	$-0.371805\pi$
$859$	1.69523e7	0.783872	0.391936	+	0.919992i	$0.371805\pi$
$860$	6.92533e6	0.319297
$861$	−7.59985e6	−0.349379
$862$	−3.29454e6	−0.151017
$863$	5.42456e6	0.247935	0.123968	−	0.992286i	$-0.460438\pi$
$863$	5.42456e6	0.247935	0.123968	+	0.992286i	$0.460438\pi$
$864$	2.14001e6	0.0975283
$865$	−1.18367e7	−0.537888
$866$	3.65063e6	0.165414
$867$	1.50800e7	0.681325
$868$	568819.	0.0256257
$869$	0	0
$870$	−3.06519e6	−0.137297
$871$	−6.36576e7	−2.84318
$872$	2.16436e7	0.963914
$873$	−1.22537e7	−0.544165
$874$	7.85426e6	0.347798
$875$	1.33592e6	0.0589875
$876$	−1.16735e7	−0.513976
$877$	−1.67149e7	−0.733846	−0.366923	−	0.930251i	$-0.619589\pi$
$877$	−1.67149e7	−0.733846	−0.366923	+	0.930251i	$0.619589\pi$
$878$	−3.94934e6	−0.172897
$879$	−3.58171e7	−1.56357
$880$	0	0
$881$	1.36326e7	0.591752	0.295876	−	0.955226i	$-0.404389\pi$
$881$	1.36326e7	0.591752	0.295876	+	0.955226i	$0.404389\pi$
$882$	−3.90628e6	−0.169080
$883$	−2.87301e7	−1.24004	−0.620021	−	0.784586i	$-0.712876\pi$
$883$	−2.87301e7	−1.24004	−0.620021	+	0.784586i	$0.712876\pi$
$884$	−2.46527e7	−1.06105
$885$	6.47899e6	0.278067
$886$	−5.08068e6	−0.217439
$887$	2.90808e7	1.24107	0.620537	−	0.784177i	$-0.286915\pi$
$887$	2.90808e7	1.24107	0.620537	+	0.784177i	$0.286915\pi$
$888$	−8.44819e6	−0.359527
$889$	−1.64320e6	−0.0697328
$890$	1.51562e6	0.0641382
$891$	0	0
$892$	−9.07979e6	−0.382088
$893$	1.42772e6	0.0599119
$894$	6.84591e6	0.286476
$895$	−7.83318e6	−0.326874
$896$	1.55280e7	0.646168
$897$	9.75800e7	4.04930
$898$	3.32382e6	0.137546
$899$	−715883.	−0.0295422
$900$	−3.97954e6	−0.163767
$901$	−3.02378e7	−1.24090
$902$	0	0
$903$	1.78780e7	0.729624
$904$	338920.	0.0137935
$905$	−1.08199e6	−0.0439140
$906$	−9.70142e6	−0.392658
$907$	−3.40477e7	−1.37426	−0.687132	−	0.726533i	$-0.741131\pi$
$907$	−3.40477e7	−1.37426	−0.687132	+	0.726533i	$0.741131\pi$
$908$	−2.68042e7	−1.07892
$909$	9.41498e6	0.377929
$910$	−4.00868e6	−0.160471
$911$	−3.17126e7	−1.26601	−0.633004	−	0.774148i	$-0.718178\pi$
$911$	−3.17126e7	−1.26601	−0.633004	+	0.774148i	$0.718178\pi$
$912$	−1.45970e7	−0.581133
$913$	0	0
$914$	1.20364e7	0.476575
$915$	2.46842e7	0.974688
$916$	−4.35831e7	−1.71624
$917$	2.32129e7	0.911605
$918$	−686503.	−0.0268866
$919$	−5.88046e6	−0.229680	−0.114840	−	0.993384i	$-0.536635\pi$
$919$	−5.88046e6	−0.229680	−0.114840	+	0.993384i	$0.536635\pi$
$920$	1.24564e7	0.485201
$921$	1.35263e7	0.525448
$922$	−7.46318e6	−0.289132
$923$	4.93592e7	1.90706
$924$	0	0
$925$	−2.18655e6	−0.0840244
$926$	−1.37008e7	−0.525072
$927$	3.73658e7	1.42815
$928$	−1.50390e7	−0.573258
$929$	−5.33835e6	−0.202940	−0.101470	−	0.994839i	$-0.532355\pi$
$929$	−5.33835e6	−0.202940	−0.101470	+	0.994839i	$0.532355\pi$
$930$	231868.	0.00879091
$931$	−9.07054e6	−0.342972
$932$	−9.89903e6	−0.373296
$933$	−3.93222e7	−1.47888
$934$	8.71569e6	0.326915
$935$	0	0
$936$	2.53074e7	0.944185
$937$	3.23255e7	1.20281	0.601405	−	0.798945i	$-0.294608\pi$
$937$	3.23255e7	1.20281	0.601405	+	0.798945i	$0.294608\pi$
$938$	−9.89842e6	−0.367332
$939$	−5.51374e7	−2.04072
$940$	1.06840e6	0.0394381
$941$	1.70985e7	0.629481	0.314741	−	0.949178i	$-0.398082\pi$
$941$	1.70985e7	0.629481	0.314741	+	0.949178i	$0.398082\pi$
$942$	1.00233e7	0.368031
$943$	−1.83406e7	−0.671636
$944$	8.50473e6	0.310621
$945$	935673.	0.0340835
$946$	0	0
$947$	1.45681e7	0.527873	0.263936	−	0.964540i	$-0.414979\pi$
$947$	1.45681e7	0.527873	0.263936	+	0.964540i	$0.414979\pi$
$948$	−4.70472e7	−1.70025
$949$	1.92138e7	0.692545
$950$	1.10245e6	0.0396322
$951$	1.94837e7	0.698588
$952$	−8.12407e6	−0.290523
$953$	−5.02636e6	−0.179276	−0.0896379	−	0.995974i	$-0.528571\pi$
$953$	−5.02636e6	−0.179276	−0.0896379	+	0.995974i	$0.528571\pi$
$954$	1.46467e7	0.521036
$955$	2.21512e7	0.785940
$956$	2.67191e7	0.945535
$957$	0	0
$958$	−1.55526e7	−0.547506
$959$	1.32637e6	0.0465713
$960$	−7.35554e6	−0.257594
$961$	−2.85750e7	−0.998108
$962$	6.56116e6	0.228583
$963$	−3.79922e7	−1.32017
$964$	−2.09127e7	−0.724800
$965$	−1.68580e6	−0.0582758
$966$	1.51732e7	0.523159
$967$	2.03055e7	0.698308	0.349154	−	0.937065i	$-0.386469\pi$
$967$	2.03055e7	0.698308	0.349154	+	0.937065i	$0.386469\pi$
$968$	0	0
$969$	1.75025e7	0.598811
$970$	2.54029e6	0.0866871
$971$	3.22865e7	1.09894	0.549468	−	0.835515i	$-0.314830\pi$
$971$	3.22865e7	1.09894	0.549468	+	0.835515i	$0.314830\pi$
$972$	−3.61775e7	−1.22821
$973$	7.41010e6	0.250924
$974$	1.23264e7	0.416330
$975$	1.36966e7	0.461425
$976$	3.24020e7	1.08880
$977$	−6.50868e6	−0.218151	−0.109075	−	0.994033i	$-0.534789\pi$
$977$	−6.50868e6	−0.218151	−0.109075	+	0.994033i	$0.534789\pi$
$978$	1.42214e7	0.475438
$979$	0	0
$980$	−6.78776e6	−0.225767
$981$	−4.30781e7	−1.42917
$982$	−5.50248e6	−0.182087
$983$	3.25402e7	1.07408	0.537040	−	0.843557i	$-0.319543\pi$
$983$	3.25402e7	1.07408	0.537040	+	0.843557i	$0.319543\pi$
$984$	−9.94647e6	−0.327477
$985$	7.12508e6	0.233991
$986$	4.82445e6	0.158036
$987$	2.75812e6	0.0901199
$988$	2.77283e7	0.903714
$989$	4.31446e7	1.40261
$990$	0	0
$991$	6.90974e6	0.223500	0.111750	−	0.993736i	$-0.464354\pi$
$991$	6.90974e6	0.223500	0.111750	+	0.993736i	$0.464354\pi$
$992$	1.13764e6	0.0367049
$993$	1.92779e7	0.620421
$994$	7.67510e6	0.246387
$995$	−1.37445e7	−0.440120
$996$	4.34031e7	1.38635
$997$	4.69004e7	1.49430	0.747151	−	0.664654i	$-0.231421\pi$
$997$	4.69004e7	1.49430	0.747151	+	0.664654i	$0.231421\pi$
$998$	−2.83388e6	−0.0900649
$999$	−1.53145e6	−0.0485501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.12		20
11.5	even	5		55.6.g.b.36.5	yes	40
11.9	even	5		55.6.g.b.26.5	✓	40
11.10	odd	2		605.6.a.o.1.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.26.5	✓	40	11.9	even	5
55.6.g.b.36.5	yes	40	11.5	even	5
605.6.a.o.1.9		20	11.10	odd	2
605.6.a.p.1.12		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)

\(f(q)\)	\(=\)	\(q+1.84684 q^{2} -21.5804 q^{3} -28.5892 q^{4} -25.0000 q^{5} -39.8555 q^{6} -85.4988 q^{7} -111.898 q^{8} +222.716 q^{9} +O(q^{10})\)	\(q+1.84684 q^{2} -21.5804 q^{3} -28.5892 q^{4} -25.0000 q^{5} -39.8555 q^{6} -85.4988 q^{7} -111.898 q^{8} +222.716 q^{9} -46.1709 q^{10} +616.968 q^{12} -1015.48 q^{13} -157.902 q^{14} +539.511 q^{15} +708.196 q^{16} -849.161 q^{17} +411.319 q^{18} +955.100 q^{19} +714.730 q^{20} +1845.10 q^{21} +4452.75 q^{23} +2414.82 q^{24} +625.000 q^{25} -1875.43 q^{26} +437.748 q^{27} +2444.34 q^{28} -3076.30 q^{29} +996.389 q^{30} +232.709 q^{31} +4888.67 q^{32} -1568.26 q^{34} +2137.47 q^{35} -6367.26 q^{36} -3498.48 q^{37} +1763.91 q^{38} +21914.6 q^{39} +2797.46 q^{40} -4118.93 q^{41} +3407.60 q^{42} +9689.44 q^{43} -5567.89 q^{45} +8223.49 q^{46} +1494.84 q^{47} -15283.2 q^{48} -9496.96 q^{49} +1154.27 q^{50} +18325.3 q^{51} +29031.8 q^{52} +35609.0 q^{53} +808.449 q^{54} +9567.17 q^{56} -20611.5 q^{57} -5681.43 q^{58} +12009.0 q^{59} -15424.2 q^{60} +45752.8 q^{61} +429.775 q^{62} -19041.9 q^{63} -13633.7 q^{64} +25387.1 q^{65} +62687.0 q^{67} +24276.8 q^{68} -96092.2 q^{69} +3947.56 q^{70} -48606.7 q^{71} -24921.5 q^{72} -18920.9 q^{73} -6461.12 q^{74} -13487.8 q^{75} -27305.5 q^{76} +40472.6 q^{78} -76255.6 q^{79} -17704.9 q^{80} -63566.7 q^{81} -7607.00 q^{82} +70349.1 q^{83} -52750.0 q^{84} +21229.0 q^{85} +17894.8 q^{86} +66388.0 q^{87} -32826.4 q^{89} -10283.0 q^{90} +86822.5 q^{91} -127300. q^{92} -5021.96 q^{93} +2760.72 q^{94} -23877.5 q^{95} -105500. q^{96} -55019.4 q^{97} -17539.3 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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