LMFDB - Embedded newform 605.6.a.p.1.7

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			1.7
Root			$-5.37088$ 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)

$f(q)$	$=$	$q-5.37088 q^{2} -0.268292 q^{3} -3.15366 q^{4} -25.0000 q^{5} +1.44096 q^{6} +221.735 q^{7} +188.806 q^{8} -242.928 q^{9} +O(q^{10})$	\(q-5.37088 q^{2} -0.268292 q^{3} -3.15366 q^{4} -25.0000 q^{5} +1.44096 q^{6} +221.735 q^{7} +188.806 q^{8} -242.928 q^{9} +134.272 q^{10} +0.846102 q^{12} -491.994 q^{13} -1190.91 q^{14} +6.70730 q^{15} -913.137 q^{16} +1285.51 q^{17} +1304.74 q^{18} +1071.01 q^{19} +78.8415 q^{20} -59.4896 q^{21} -2916.56 q^{23} -50.6551 q^{24} +625.000 q^{25} +2642.44 q^{26} +130.371 q^{27} -699.276 q^{28} -2809.80 q^{29} -36.0241 q^{30} -3190.50 q^{31} -1137.44 q^{32} -6904.30 q^{34} -5543.37 q^{35} +766.112 q^{36} -3453.81 q^{37} -5752.27 q^{38} +131.998 q^{39} -4720.15 q^{40} +18113.0 q^{41} +319.512 q^{42} -9193.11 q^{43} +6073.20 q^{45} +15664.5 q^{46} -20216.7 q^{47} +244.987 q^{48} +32359.3 q^{49} -3356.80 q^{50} -344.891 q^{51} +1551.58 q^{52} +27357.7 q^{53} -700.204 q^{54} +41864.8 q^{56} -287.343 q^{57} +15091.1 q^{58} -2130.47 q^{59} -21.1525 q^{60} -3813.71 q^{61} +17135.8 q^{62} -53865.6 q^{63} +35329.5 q^{64} +12299.9 q^{65} +41640.1 q^{67} -4054.05 q^{68} +782.489 q^{69} +29772.8 q^{70} +45762.7 q^{71} -45866.3 q^{72} +41661.3 q^{73} +18550.0 q^{74} -167.682 q^{75} -3377.60 q^{76} -708.946 q^{78} -8358.28 q^{79} +22828.4 q^{80} +58996.5 q^{81} -97282.8 q^{82} -83900.1 q^{83} +187.610 q^{84} -32137.6 q^{85} +49375.1 q^{86} +753.846 q^{87} -92602.8 q^{89} -32618.4 q^{90} -109092. q^{91} +9197.83 q^{92} +855.984 q^{93} +108581. q^{94} -26775.3 q^{95} +305.167 q^{96} +44923.3 q^{97} -173798. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.37088	−0.949446	−0.474723	−	0.880135i	$-0.657452\pi$
$2$	−5.37088	−0.949446	−0.474723	+	0.880135i	$0.657452\pi$
$3$	−0.268292	−0.0172109	−0.00860547	−	0.999963i	$-0.502739\pi$
$3$	−0.268292	−0.0172109	−0.00860547	+	0.999963i	$0.502739\pi$
$4$	−3.15366	−0.0985519
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	1.44096	0.0163409
$7$	221.735	1.71036	0.855182	−	0.518328i	$-0.173445\pi$
$7$	221.735	1.71036	0.855182	+	0.518328i	$0.173445\pi$
$8$	188.806	1.04302
$9$	−242.928	−0.999704
$10$	134.272	0.424605
$11$	0	0
$11$	0	0
$12$	0.846102	0.00169617
$13$	−491.994	−0.807424	−0.403712	−	0.914886i	$-0.632280\pi$
$13$	−491.994	−0.807424	−0.403712	+	0.914886i	$0.632280\pi$
$14$	−1190.91	−1.62390
$15$	6.70730	0.00769696
$16$	−913.137	−0.891736
$17$	1285.51	1.07883	0.539413	−	0.842041i	$-0.318646\pi$
$17$	1285.51	1.07883	0.539413	+	0.842041i	$0.318646\pi$
$18$	1304.74	0.949165
$19$	1071.01	0.680628	0.340314	−	0.940312i	$-0.389467\pi$
$19$	1071.01	0.680628	0.340314	+	0.940312i	$0.389467\pi$
$20$	78.8415	0.0440737
$21$	−59.4896	−0.0294370
$22$	0	0
$23$	−2916.56	−1.14961	−0.574806	−	0.818290i	$-0.694922\pi$
$23$	−2916.56	−1.14961	−0.574806	+	0.818290i	$0.694922\pi$
$24$	−50.6551	−0.0179513
$25$	625.000	0.200000
$26$	2642.44	0.766606
$27$	130.371	0.0344168
$28$	−699.276	−0.168560
$29$	−2809.80	−0.620412	−0.310206	−	0.950669i	$-0.600398\pi$
$29$	−2809.80	−0.620412	−0.310206	+	0.950669i	$0.600398\pi$
$30$	−36.0241	−0.00730785
$31$	−3190.50	−0.596285	−0.298143	−	0.954521i	$-0.596367\pi$
$31$	−3190.50	−0.596285	−0.298143	+	0.954521i	$0.596367\pi$
$32$	−1137.44	−0.196361
$33$	0	0
$34$	−6904.30	−1.02429
$35$	−5543.37	−0.764898
$36$	766.112	0.0985227
$37$	−3453.81	−0.414758	−0.207379	−	0.978261i	$-0.566493\pi$
$37$	−3453.81	−0.414758	−0.207379	+	0.978261i	$0.566493\pi$
$38$	−5752.27	−0.646220
$39$	131.998	0.0138965
$40$	−4720.15	−0.466451
$41$	18113.0	1.68279	0.841397	−	0.540418i	$-0.181734\pi$
$41$	18113.0	1.68279	0.841397	+	0.540418i	$0.181734\pi$
$42$	319.512	0.0279488
$43$	−9193.11	−0.758213	−0.379106	−	0.925353i	$-0.623769\pi$
$43$	−9193.11	−0.758213	−0.379106	+	0.925353i	$0.623769\pi$
$44$	0	0
$45$	6073.20	0.447081
$46$	15664.5	1.09149
$47$	−20216.7	−1.33495	−0.667475	−	0.744632i	$-0.732625\pi$
$47$	−20216.7	−1.33495	−0.667475	+	0.744632i	$0.732625\pi$
$48$	244.987	0.0153476
$49$	32359.3	1.92534
$50$	−3356.80	−0.189889
$51$	−344.891	−0.0185676
$52$	1551.58	0.0795732
$53$	27357.7	1.33779	0.668897	−	0.743355i	$-0.266767\pi$
$53$	27357.7	1.33779	0.668897	+	0.743355i	$0.266767\pi$
$54$	−700.204	−0.0326769
$55$	0	0
$56$	41864.8	1.78394
$57$	−287.343	−0.0117142
$58$	15091.1	0.589048
$59$	−2130.47	−0.0796791	−0.0398396	−	0.999206i	$-0.512685\pi$
$59$	−2130.47	−0.0796791	−0.0398396	+	0.999206i	$0.512685\pi$
$60$	−21.1525	−0.000758550 0
$61$	−3813.71	−0.131227	−0.0656134	−	0.997845i	$-0.520900\pi$
$61$	−3813.71	−0.131227	−0.0656134	+	0.997845i	$0.520900\pi$
$62$	17135.8	0.566141
$63$	−53865.6	−1.70986
$64$	35329.5	1.07817
$65$	12299.9	0.361091
$66$	0	0
$67$	41640.1	1.13325	0.566623	−	0.823977i	$-0.308250\pi$
$67$	41640.1	1.13325	0.566623	+	0.823977i	$0.308250\pi$
$68$	−4054.05	−0.106320
$69$	782.489	0.0197859
$70$	29772.8	0.726230
$71$	45762.7	1.07737	0.538686	−	0.842507i	$-0.318921\pi$
$71$	45762.7	1.07737	0.538686	+	0.842507i	$0.318921\pi$
$72$	−45866.3	−1.04271
$73$	41661.3	0.915010	0.457505	−	0.889207i	$-0.348743\pi$
$73$	41661.3	0.915010	0.457505	+	0.889207i	$0.348743\pi$
$74$	18550.0	0.393790
$75$	−167.682	−0.00344219
$76$	−3377.60	−0.0670772
$77$	0	0
$78$	−708.946	−0.0131940
$79$	−8358.28	−0.150678	−0.0753389	−	0.997158i	$-0.524004\pi$
$79$	−8358.28	−0.150678	−0.0753389	+	0.997158i	$0.524004\pi$
$80$	22828.4	0.398796
$81$	58996.5	0.999111
$82$	−97282.8	−1.59772
$83$	−83900.1	−1.33680	−0.668401	−	0.743801i	$-0.733021\pi$
$83$	−83900.1	−1.33680	−0.668401	+	0.743801i	$0.733021\pi$
$84$	187.610	0.00290107
$85$	−32137.6	−0.482466
$86$	49375.1	0.719882
$87$	753.846	0.0106779
$88$	0	0
$89$	−92602.8	−1.23922	−0.619611	−	0.784909i	$-0.712710\pi$
$89$	−92602.8	−1.23922	−0.619611	+	0.784909i	$0.712710\pi$
$90$	−32618.4	−0.424479
$91$	−109092.	−1.38099
$92$	9197.83	0.113296
$93$	855.984	0.0102626
$94$	108581.	1.26746
$95$	−26775.3	−0.304386
$96$	305.167	0.00337955
$97$	44923.3	0.484777	0.242388	−	0.970179i	$-0.422069\pi$
$97$	44923.3	0.484777	0.242388	+	0.970179i	$0.422069\pi$
$98$	−173798.	−1.82801
$99$	0	0
$100$	−1971.04	−0.0197104
$101$	124891.	1.21823	0.609114	−	0.793083i	$-0.291525\pi$
$101$	124891.	1.21823	0.609114	+	0.793083i	$0.291525\pi$
$102$	1852.37	0.0176290
$103$	−46188.4	−0.428982	−0.214491	−	0.976726i	$-0.568809\pi$
$103$	−46188.4	−0.428982	−0.214491	+	0.976726i	$0.568809\pi$
$104$	−92891.5	−0.842156
$105$	1487.24	0.0131646
$106$	−146935.	−1.27016
$107$	150798.	1.27331	0.636657	−	0.771147i	$-0.280317\pi$
$107$	150798.	1.27331	0.636657	+	0.771147i	$0.280317\pi$
$108$	−411.144	−0.00339184
$109$	−148133.	−1.19422	−0.597110	−	0.802159i	$-0.703685\pi$
$109$	−148133.	−1.19422	−0.597110	+	0.802159i	$0.703685\pi$
$110$	0	0
$111$	926.630	0.00713837
$112$	−202474.	−1.52519
$113$	−194815.	−1.43525	−0.717624	−	0.696431i	$-0.754770\pi$
$113$	−194815.	−1.43525	−0.717624	+	0.696431i	$0.754770\pi$
$114$	1543.29	0.0111220
$115$	72913.9	0.514122
$116$	8861.15	0.0611428
$117$	119519.	0.807185
$118$	11442.5	0.0756510
$119$	285041.	1.84519
$120$	1266.38	0.00802806
$121$	0	0
$122$	20483.0	0.124593
$123$	−4859.57	−0.0289625
$124$	10061.7	0.0587650
$125$	−15625.0	−0.0894427
$126$	289305.	1.62342
$127$	−40455.3	−0.222570	−0.111285	−	0.993789i	$-0.535497\pi$
$127$	−40455.3	−0.222570	−0.111285	+	0.993789i	$0.535497\pi$
$128$	−153352.	−0.827303
$129$	2466.44	0.0130496
$130$	−66061.1	−0.342837
$131$	295391.	1.50390	0.751951	−	0.659219i	$-0.229113\pi$
$131$	295391.	1.50390	0.751951	+	0.659219i	$0.229113\pi$
$132$	0	0
$133$	237480.	1.16412
$134$	−223644.	−1.07596
$135$	−3259.26	−0.0153916
$136$	242711.	1.12523
$137$	−289922.	−1.31972	−0.659858	−	0.751391i	$-0.729383\pi$
$137$	−289922.	−1.31972	−0.659858	+	0.751391i	$0.729383\pi$
$138$	−4202.65	−0.0187856
$139$	−133041.	−0.584046	−0.292023	−	0.956411i	$-0.594328\pi$
$139$	−133041.	−0.584046	−0.292023	+	0.956411i	$0.594328\pi$
$140$	17481.9	0.0753821
$141$	5423.97	0.0229757
$142$	−245786.	−1.02291
$143$	0	0
$144$	221827.	0.891471
$145$	70244.9	0.277457
$146$	−223758.	−0.868753
$147$	−8681.73	−0.0331370
$148$	10892.1	0.0408751
$149$	−50252.2	−0.185434	−0.0927170	−	0.995693i	$-0.529555\pi$
$149$	−50252.2	−0.185434	−0.0927170	+	0.995693i	$0.529555\pi$
$150$	900.602	0.00326817
$151$	−404702.	−1.44442	−0.722210	−	0.691674i	$-0.756873\pi$
$151$	−404702.	−1.44442	−0.722210	+	0.691674i	$0.756873\pi$
$152$	202213.	0.709906
$153$	−312285.	−1.07851
$154$	0	0
$155$	79762.4	0.266667
$156$	−416.277	−0.00136953
$157$	−155288.	−0.502793	−0.251396	−	0.967884i	$-0.580890\pi$
$157$	−155288.	−0.502793	−0.251396	+	0.967884i	$0.580890\pi$
$158$	44891.3	0.143060
$159$	−7339.84	−0.0230247
$160$	28436.1	0.0878153
$161$	−646702.	−1.96625
$162$	−316863.	−0.948603
$163$	−480466.	−1.41643	−0.708213	−	0.705999i	$-0.750498\pi$
$163$	−480466.	−1.41643	−0.708213	+	0.705999i	$0.750498\pi$
$164$	−57122.3	−0.165842
$165$	0	0
$166$	450617.	1.26922
$167$	383961.	1.06536	0.532680	−	0.846317i	$-0.321185\pi$
$167$	383961.	1.06536	0.532680	+	0.846317i	$0.321185\pi$
$168$	−11232.0	−0.0307032
$169$	−129235.	−0.348066
$170$	172607.	0.458076
$171$	−260178.	−0.680426
$172$	28991.9	0.0747233
$173$	109985.	0.279395	0.139697	−	0.990194i	$-0.455387\pi$
$173$	109985.	0.279395	0.139697	+	0.990194i	$0.455387\pi$
$174$	−4048.82	−0.0101381
$175$	138584.	0.342073
$176$	0	0
$177$	571.587	0.00137135
$178$	497359.	1.17658
$179$	37994.3	0.0886311	0.0443156	−	0.999018i	$-0.485889\pi$
$179$	37994.3	0.0886311	0.0443156	+	0.999018i	$0.485889\pi$
$180$	−19152.8	−0.0440607
$181$	−668704.	−1.51718	−0.758590	−	0.651568i	$-0.774112\pi$
$181$	−668704.	−1.51718	−0.758590	+	0.651568i	$0.774112\pi$
$182$	585921.	1.31118
$183$	1023.19	0.00225854
$184$	−550664.	−1.19906
$185$	86345.3	0.185485
$186$	−4597.39	−0.00974381
$187$	0	0
$188$	63756.5	0.131562
$189$	28907.7	0.0588652
$190$	143807.	0.288998
$191$	−25621.6	−0.0508185	−0.0254093	−	0.999677i	$-0.508089\pi$
$191$	−25621.6	−0.0508185	−0.0254093	+	0.999677i	$0.508089\pi$
$192$	−9478.61	−0.0185563
$193$	589666.	1.13950	0.569748	−	0.821820i	$-0.307041\pi$
$193$	589666.	1.13950	0.569748	+	0.821820i	$0.307041\pi$
$194$	−241277.	−0.460270
$195$	−3299.95	−0.00621472
$196$	−102050.	−0.189746
$197$	−702167.	−1.28906	−0.644532	−	0.764577i	$-0.722948\pi$
$197$	−702167.	−1.28906	−0.644532	+	0.764577i	$0.722948\pi$
$198$	0	0
$199$	794060.	1.42141	0.710707	−	0.703488i	$-0.248375\pi$
$199$	794060.	1.42141	0.710707	+	0.703488i	$0.248375\pi$
$200$	118004.	0.208603
$201$	−11171.7	−0.0195042
$202$	−670776.	−1.15664
$203$	−623030.	−1.06113
$204$	1087.67	0.00182987
$205$	−452825.	−0.752568
$206$	248072.	0.407296
$207$	708514.	1.14927
$208$	449258.	0.720009
$209$	0	0
$210$	−7987.79	−0.0124991
$211$	−535197.	−0.827576	−0.413788	−	0.910373i	$-0.635794\pi$
$211$	−535197.	−0.827576	−0.413788	+	0.910373i	$0.635794\pi$
$212$	−86276.8	−0.131842
$213$	−12277.8	−0.0185426
$214$	−809916.	−1.20894
$215$	229828.	0.339083
$216$	24614.8	0.0358972
$217$	−707444.	−1.01986
$218$	795603.	1.13385
$219$	−11177.4	−0.0157482
$220$	0	0
$221$	−632462.	−0.871071
$222$	−4976.82	−0.00677749
$223$	−476745.	−0.641983	−0.320992	−	0.947082i	$-0.604016\pi$
$223$	−476745.	−0.641983	−0.320992	+	0.947082i	$0.604016\pi$
$224$	−252211.	−0.335849
$225$	−151830.	−0.199941
$226$	1.04633e6	1.36269
$227$	−1.12551e6	−1.44972	−0.724860	−	0.688896i	$-0.758096\pi$
$227$	−1.12551e6	−1.44972	−0.724860	+	0.688896i	$0.758096\pi$
$228$	906.184	0.00115446
$229$	−851597.	−1.07311	−0.536556	−	0.843865i	$-0.680275\pi$
$229$	−851597.	−1.07311	−0.536556	+	0.843865i	$0.680275\pi$
$230$	−391612.	−0.488131
$231$	0	0
$232$	−530507.	−0.647099
$233$	−1.57720e6	−1.90326	−0.951628	−	0.307254i	$-0.900590\pi$
$233$	−1.57720e6	−1.90326	−0.951628	+	0.307254i	$0.900590\pi$
$234$	−641923.	−0.766379
$235$	505417.	0.597008
$236$	6718.76	0.00785253
$237$	2242.46	0.00259331
$238$	−1.53092e6	−1.75191
$239$	−65445.9	−0.0741119	−0.0370560	−	0.999313i	$-0.511798\pi$
$239$	−65445.9	−0.0741119	−0.0370560	+	0.999313i	$0.511798\pi$
$240$	−6124.68	−0.00686366
$241$	−1.30310e6	−1.44522	−0.722612	−	0.691254i	$-0.757059\pi$
$241$	−1.30310e6	−1.44522	−0.722612	+	0.691254i	$0.757059\pi$
$242$	0	0
$243$	−47508.3	−0.0516124
$244$	12027.1	0.0129326
$245$	−808982.	−0.861040
$246$	26100.2	0.0274983
$247$	−526931.	−0.549555
$248$	−602385.	−0.621935
$249$	22509.7	0.0230076
$250$	83920.0	0.0849211
$251$	−1.51248e6	−1.51533	−0.757664	−	0.652645i	$-0.773659\pi$
$251$	−1.51248e6	−1.51533	−0.757664	+	0.652645i	$0.773659\pi$
$252$	169874.	0.168510
$253$	0	0
$254$	217280.	0.211318
$255$	8622.27	0.00830369
$256$	−306907.	−0.292690
$257$	480442.	0.453741	0.226871	−	0.973925i	$-0.427151\pi$
$257$	480442.	0.453741	0.226871	+	0.973925i	$0.427151\pi$
$258$	−13246.9	−0.0123898
$259$	−765830.	−0.709386
$260$	−38789.6	−0.0355862
$261$	682579.	0.620228
$262$	−1.58651e6	−1.42787
$263$	1.03939e6	0.926590	0.463295	−	0.886204i	$-0.346667\pi$
$263$	1.03939e6	0.926590	0.463295	+	0.886204i	$0.346667\pi$
$264$	0	0
$265$	−683942.	−0.598280
$266$	−1.27548e6	−1.10527
$267$	24844.6	0.0213282
$268$	−131319.	−0.111684
$269$	710322.	0.598515	0.299257	−	0.954172i	$-0.403261\pi$
$269$	710322.	0.598515	0.299257	+	0.954172i	$0.403261\pi$
$270$	17505.1	0.0146135
$271$	−976378.	−0.807598	−0.403799	−	0.914848i	$-0.632310\pi$
$271$	−976378.	−0.807598	−0.403799	+	0.914848i	$0.632310\pi$
$272$	−1.17384e6	−0.962028
$273$	29268.6	0.0237681
$274$	1.55714e6	1.25300
$275$	0	0
$276$	−2467.70	−0.00194994
$277$	1.90800e6	1.49410	0.747049	−	0.664769i	$-0.231470\pi$
$277$	1.90800e6	1.49410	0.747049	+	0.664769i	$0.231470\pi$
$278$	714545.	0.554521
$279$	775061.	0.596109
$280$	−1.04662e6	−0.797801
$281$	1.35132e6	1.02092	0.510460	−	0.859901i	$-0.329475\pi$
$281$	1.35132e6	1.02092	0.510460	+	0.859901i	$0.329475\pi$
$282$	−29131.5	−0.0218142
$283$	−1.66373e6	−1.23486	−0.617428	−	0.786628i	$-0.711825\pi$
$283$	−1.66373e6	−1.23486	−0.617428	+	0.786628i	$0.711825\pi$
$284$	−144320.	−0.106177
$285$	7183.59	0.00523877
$286$	0	0
$287$	4.01628e6	2.87819
$288$	276317.	0.196303
$289$	232668.	0.163867
$290$	−377277.	−0.263430
$291$	−12052.5	−0.00834346
$292$	−131386.	−0.0901760
$293$	628410.	0.427636	0.213818	−	0.976874i	$-0.431410\pi$
$293$	628410.	0.427636	0.213818	+	0.976874i	$0.431410\pi$
$294$	46628.5	0.0314618
$295$	53261.6	0.0356336
$296$	−652101.	−0.432599
$297$	0	0
$298$	269898.	0.176060
$299$	1.43493e6	0.928224
$300$	528.813	0.000339234 0
$301$	−2.03843e6	−1.29682
$302$	2.17361e6	1.37140
$303$	−33507.3	−0.0209668
$304$	−977980.	−0.606940
$305$	95342.6	0.0586864
$306$	1.67725e6	1.02398
$307$	896161.	0.542675	0.271338	−	0.962484i	$-0.412534\pi$
$307$	896161.	0.542675	0.271338	+	0.962484i	$0.412534\pi$
$308$	0	0
$309$	12392.0	0.00738319
$310$	−428394.	−0.253186
$311$	−365600.	−0.214341	−0.107170	−	0.994241i	$-0.534179\pi$
$311$	−365600.	−0.214341	−0.107170	+	0.994241i	$0.534179\pi$
$312$	24922.0	0.0144943
$313$	90979.4	0.0524907	0.0262453	−	0.999656i	$-0.491645\pi$
$313$	90979.4	0.0524907	0.0262453	+	0.999656i	$0.491645\pi$
$314$	834033.	0.477375
$315$	1.34664e6	0.764671
$316$	26359.2	0.0148496
$317$	1.36805e6	0.764632	0.382316	−	0.924032i	$-0.375127\pi$
$317$	1.36805e6	0.764632	0.382316	+	0.924032i	$0.375127\pi$
$318$	39421.4	0.0218607
$319$	0	0
$320$	−883237.	−0.482172
$321$	−40457.8	−0.0219149
$322$	3.47336e6	1.86685
$323$	1.37679e6	0.734280
$324$	−186055.	−0.0984643
$325$	−307497.	−0.161485
$326$	2.58053e6	1.34482
$327$	39742.8	0.0205537
$328$	3.41984e6	1.75518
$329$	−4.48274e6	−2.28325
$330$	0	0
$331$	−3.30977e6	−1.66046	−0.830229	−	0.557423i	$-0.811790\pi$
$331$	−3.30977e6	−1.66046	−0.830229	+	0.557423i	$0.811790\pi$
$332$	264592.	0.131744
$333$	839028.	0.414635
$334$	−2.06221e6	−1.01150
$335$	−1.04100e6	−0.506803
$336$	54322.2	0.0262500
$337$	1.23901e6	0.594292	0.297146	−	0.954832i	$-0.403965\pi$
$337$	1.23901e6	0.594292	0.297146	+	0.954832i	$0.403965\pi$
$338$	694103.	0.330470
$339$	52267.4	0.0247020
$340$	101351.	0.0475479
$341$	0	0
$342$	1.39739e6	0.646028
$343$	3.44848e6	1.58268
$344$	−1.73571e6	−0.790828
$345$	−19562.2	−0.00884852
$346$	−590716.	−0.265270
$347$	−817741.	−0.364579	−0.182290	−	0.983245i	$-0.558351\pi$
$347$	−817741.	−0.364579	−0.182290	+	0.983245i	$0.558351\pi$
$348$	−2377.37	−0.00105232
$349$	338460.	0.148746	0.0743728	−	0.997231i	$-0.476305\pi$
$349$	338460.	0.148746	0.0743728	+	0.997231i	$0.476305\pi$
$350$	−744319.	−0.324780
$351$	−64141.6	−0.0277889
$352$	0	0
$353$	245910.	0.105036	0.0525182	−	0.998620i	$-0.483275\pi$
$353$	245910.	0.105036	0.0525182	+	0.998620i	$0.483275\pi$
$354$	−3069.92	−0.00130203
$355$	−1.14407e6	−0.481815
$356$	292038.	0.122128
$357$	−76474.3	−0.0317574
$358$	−204063.	−0.0841505
$359$	2.13103e6	0.872677	0.436338	−	0.899783i	$-0.356275\pi$
$359$	2.13103e6	0.872677	0.436338	+	0.899783i	$0.356275\pi$
$360$	1.14666e6	0.466313
$361$	−1.32904e6	−0.536746
$362$	3.59153e6	1.44048
$363$	0	0
$364$	344040.	0.136099
$365$	−1.04153e6	−0.409205
$366$	−5495.41	−0.00214436
$367$	4.01426e6	1.55575	0.777877	−	0.628417i	$-0.216297\pi$
$367$	4.01426e6	1.55575	0.777877	+	0.628417i	$0.216297\pi$
$368$	2.66322e6	1.02515
$369$	−4.40016e6	−1.68230
$370$	−463750.	−0.176108
$371$	6.06614e6	2.28811
$372$	−2699.48	−0.00101140
$373$	−2.14645e6	−0.798820	−0.399410	−	0.916773i	$-0.630785\pi$
$373$	−2.14645e6	−0.798820	−0.399410	+	0.916773i	$0.630785\pi$
$374$	0	0
$375$	4192.06	0.00153939
$376$	−3.81703e6	−1.39237
$377$	1.38240e6	0.500936
$378$	−155260.	−0.0558893
$379$	4.41052e6	1.57722	0.788610	−	0.614894i	$-0.210801\pi$
$379$	4.41052e6	1.57722	0.788610	+	0.614894i	$0.210801\pi$
$380$	84440.1	0.0299978
$381$	10853.8	0.00383063
$382$	137610.	0.0482495
$383$	−4.73857e6	−1.65063	−0.825316	−	0.564671i	$-0.809003\pi$
$383$	−4.73857e6	−1.65063	−0.825316	+	0.564671i	$0.809003\pi$
$384$	41143.1	0.0142387
$385$	0	0
$386$	−3.16702e6	−1.08189
$387$	2.23326e6	0.757988
$388$	−141673.	−0.0477757
$389$	586812.	0.196619	0.0983093	−	0.995156i	$-0.468657\pi$
$389$	586812.	0.196619	0.0983093	+	0.995156i	$0.468657\pi$
$390$	17723.6	0.00590054
$391$	−3.74925e6	−1.24023
$392$	6.10963e6	2.00817
$393$	−79251.1	−0.0258836
$394$	3.77125e6	1.22390
$395$	208957.	0.0673852
$396$	0	0
$397$	−2.08583e6	−0.664205	−0.332103	−	0.943243i	$-0.607758\pi$
$397$	−2.08583e6	−0.664205	−0.332103	+	0.943243i	$0.607758\pi$
$398$	−4.26480e6	−1.34956
$399$	−63714.0	−0.0200356
$400$	−570711.	−0.178347
$401$	−3.55936e6	−1.10538	−0.552689	−	0.833388i	$-0.686398\pi$
$401$	−3.55936e6	−1.10538	−0.552689	+	0.833388i	$0.686398\pi$
$402$	60001.8	0.0185182
$403$	1.56971e6	0.481455
$404$	−393864.	−0.120059
$405$	−1.47491e6	−0.446816
$406$	3.34622e6	1.00749
$407$	0	0
$408$	−65117.5	−0.0193663
$409$	−3.22290e6	−0.952663	−0.476331	−	0.879266i	$-0.658034\pi$
$409$	−3.22290e6	−0.952663	−0.476331	+	0.879266i	$0.658034\pi$
$410$	2.43207e6	0.714523
$411$	77783.8	0.0227135
$412$	145662.	0.0422770
$413$	−472398.	−0.136280
$414$	−3.80534e6	−1.09117
$415$	2.09750e6	0.597836
$416$	559616.	0.158547
$417$	35693.7	0.0100520
$418$	0	0
$419$	1.18049e6	0.328494	0.164247	−	0.986419i	$-0.447481\pi$
$419$	1.18049e6	0.328494	0.164247	+	0.986419i	$0.447481\pi$
$420$	−4690.25	−0.00129740
$421$	−5.55803e6	−1.52832	−0.764162	−	0.645024i	$-0.776847\pi$
$421$	−5.55803e6	−1.52832	−0.764162	+	0.645024i	$0.776847\pi$
$422$	2.87448e6	0.785739
$423$	4.91119e6	1.33455
$424$	5.16529e6	1.39534
$425$	803441.	0.215765
$426$	65942.3	0.0176052
$427$	−845631.	−0.224446
$428$	−475565.	−0.125487
$429$	0	0
$430$	−1.23438e6	−0.321941
$431$	−1.40596e6	−0.364570	−0.182285	−	0.983246i	$-0.558349\pi$
$431$	−1.40596e6	−0.364570	−0.182285	+	0.983246i	$0.558349\pi$
$432$	−119046.	−0.0306907
$433$	−5.24455e6	−1.34428	−0.672138	−	0.740426i	$-0.734624\pi$
$433$	−5.24455e6	−1.34428	−0.672138	+	0.740426i	$0.734624\pi$
$434$	3.79959e6	0.968307
$435$	−18846.2	−0.00477529
$436$	467160.	0.117693
$437$	−3.12366e6	−0.782457
$438$	60032.4	0.0149520
$439$	6.18840e6	1.53256	0.766280	−	0.642507i	$-0.222106\pi$
$439$	6.18840e6	1.53256	0.766280	+	0.642507i	$0.222106\pi$
$440$	0	0
$441$	−7.86097e6	−1.92477
$442$	3.39688e6	0.827035
$443$	732225.	0.177270	0.0886350	−	0.996064i	$-0.471750\pi$
$443$	732225.	0.177270	0.0886350	+	0.996064i	$0.471750\pi$
$444$	−2922.28	−0.000703499 0
$445$	2.31507e6	0.554197
$446$	2.56054e6	0.609529
$447$	13482.3	0.00319149
$448$	7.83377e6	1.84406
$449$	5.73293e6	1.34203	0.671013	−	0.741445i	$-0.265859\pi$
$449$	5.73293e6	1.34203	0.671013	+	0.741445i	$0.265859\pi$
$450$	815461.	0.189833
$451$	0	0
$452$	614381.	0.141446
$453$	108578.	0.0248598
$454$	6.04497e6	1.37643
$455$	2.72731e6	0.617597
$456$	−54252.2	−0.0122181
$457$	−7.23974e6	−1.62156	−0.810779	−	0.585353i	$-0.800956\pi$
$457$	−7.23974e6	−1.62156	−0.810779	+	0.585353i	$0.800956\pi$
$458$	4.57382e6	1.01886
$459$	167592.	0.0371297
$460$	−229946.	−0.0506677
$461$	1.46657e6	0.321403	0.160701	−	0.987003i	$-0.448624\pi$
$461$	1.46657e6	0.321403	0.160701	+	0.987003i	$0.448624\pi$
$462$	0	0
$463$	−2.96908e6	−0.643678	−0.321839	−	0.946794i	$-0.604301\pi$
$463$	−2.96908e6	−0.643678	−0.321839	+	0.946794i	$0.604301\pi$
$464$	2.56573e6	0.553243
$465$	−21399.6	−0.00458959
$466$	8.47095e6	1.80704
$467$	−3.22009e6	−0.683244	−0.341622	−	0.939837i	$-0.610976\pi$
$467$	−3.22009e6	−0.683244	−0.341622	+	0.939837i	$0.610976\pi$
$468$	−376923.	−0.0795496
$469$	9.23304e6	1.93826
$470$	−2.71453e6	−0.566827
$471$	41662.5	0.00865353
$472$	−402245.	−0.0831066
$473$	0	0
$474$	−12044.0	−0.00246220
$475$	669382.	0.136126
$476$	−898923.	−0.181847
$477$	−6.64594e6	−1.33740
$478$	351502.	0.0703653
$479$	−9.28621e6	−1.84927	−0.924634	−	0.380857i	$-0.875629\pi$
$479$	−9.28621e6	−1.84927	−0.924634	+	0.380857i	$0.875629\pi$
$480$	−7629.17	−0.00151138
$481$	1.69926e6	0.334885
$482$	6.99879e6	1.37216
$483$	173505.	0.0338411
$484$	0	0
$485$	−1.12308e6	−0.216799
$486$	255162.	0.0490032
$487$	6.06521e6	1.15884	0.579420	−	0.815029i	$-0.303279\pi$
$487$	6.06521e6	1.15884	0.579420	+	0.815029i	$0.303279\pi$
$488$	−720051.	−0.136872
$489$	128905.	0.0243780
$490$	4.34494e6	0.817511
$491$	−5.44902e6	−1.02003	−0.510017	−	0.860164i	$-0.670361\pi$
$491$	−5.44902e6	−1.02003	−0.510017	+	0.860164i	$0.670361\pi$
$492$	15325.4	0.00285430
$493$	−3.61201e6	−0.669317
$494$	2.83008e6	0.521773
$495$	0	0
$496$	2.91336e6	0.531729
$497$	1.01472e7	1.84270
$498$	−120897.	−0.0218445
$499$	−1.99507e6	−0.358679	−0.179339	−	0.983787i	$-0.557396\pi$
$499$	−1.99507e6	−0.358679	−0.179339	+	0.983787i	$0.557396\pi$
$500$	49275.9	0.00881475
$501$	−103014.	−0.0183358
$502$	8.12337e6	1.43872
$503$	−2.53785e6	−0.447245	−0.223623	−	0.974676i	$-0.571788\pi$
$503$	−2.53785e6	−0.447245	−0.223623	+	0.974676i	$0.571788\pi$
$504$	−1.01701e7	−1.78341
$505$	−3.12228e6	−0.544808
$506$	0	0
$507$	34672.6	0.00599054
$508$	127582.	0.0219347
$509$	6.95659e6	1.19015	0.595075	−	0.803670i	$-0.297122\pi$
$509$	6.95659e6	1.19015	0.595075	+	0.803670i	$0.297122\pi$
$510$	−46309.2	−0.00788391
$511$	9.23776e6	1.56500
$512$	6.55563e6	1.10520
$513$	139628.	0.0234250
$514$	−2.58040e6	−0.430803
$515$	1.15471e6	0.191847
$516$	−7778.30	−0.00128606
$517$	0	0
$518$	4.11318e6	0.673524
$519$	−29508.1	−0.00480865
$520$	2.32229e6	0.376624
$521$	2.71739e6	0.438589	0.219294	−	0.975659i	$-0.429625\pi$
$521$	2.71739e6	0.438589	0.219294	+	0.975659i	$0.429625\pi$
$522$	−3.66605e6	−0.588873
$523$	−7.58306e6	−1.21224	−0.606122	−	0.795372i	$-0.707276\pi$
$523$	−7.58306e6	−1.21224	−0.606122	+	0.795372i	$0.707276\pi$
$524$	−931564.	−0.148212
$525$	−37181.0	−0.00588739
$526$	−5.58242e6	−0.879748
$527$	−4.10140e6	−0.643288
$528$	0	0
$529$	2.06996e6	0.321606
$530$	3.67337e6	0.568034
$531$	517550.	0.0796555
$532$	−748932.	−0.114726
$533$	−8.91150e6	−1.35873
$534$	−133437.	−0.0202500
$535$	−3.76994e6	−0.569443
$536$	7.86189e6	1.18199
$537$	−10193.6	−0.00152542
$538$	−3.81505e6	−0.568257
$539$	0	0
$540$	10278.6	0.00151688
$541$	−203390.	−0.0298770	−0.0149385	−	0.999888i	$-0.504755\pi$
$541$	−203390.	−0.0298770	−0.0149385	+	0.999888i	$0.504755\pi$
$542$	5.24401e6	0.766770
$543$	179408.	0.0261121
$544$	−1.46219e6	−0.211839
$545$	3.70332e6	0.534072
$546$	−157198.	−0.0225665
$547$	−9.67222e6	−1.38216	−0.691079	−	0.722779i	$-0.742864\pi$
$547$	−9.67222e6	−1.38216	−0.691079	+	0.722779i	$0.742864\pi$
$548$	914317.	0.130060
$549$	926456.	0.131188
$550$	0	0
$551$	−3.00932e6	−0.422270
$552$	147739.	0.0206370
$553$	−1.85332e6	−0.257714
$554$	−1.02476e7	−1.41857
$555$	−23165.7	−0.00319237
$556$	419565.	0.0575589
$557$	4.75973e6	0.650046	0.325023	−	0.945706i	$-0.394628\pi$
$557$	4.75973e6	0.650046	0.325023	+	0.945706i	$0.394628\pi$
$558$	−4.16276e6	−0.565973
$559$	4.52296e6	0.612199
$560$	5.06186e6	0.682087
$561$	0	0
$562$	−7.25777e6	−0.969309
$563$	−4.56293e6	−0.606698	−0.303349	−	0.952879i	$-0.598105\pi$
$563$	−4.56293e6	−0.606698	−0.303349	+	0.952879i	$0.598105\pi$
$564$	−17105.3	−0.00226430
$565$	4.87038e6	0.641863
$566$	8.93568e6	1.17243
$567$	1.30816e7	1.70884
$568$	8.64027e6	1.12372
$569$	7.11628e6	0.921451	0.460725	−	0.887543i	$-0.347589\pi$
$569$	7.11628e6	0.921451	0.460725	+	0.887543i	$0.347589\pi$
$570$	−38582.2	−0.00497393
$571$	7.87697e6	1.01104	0.505521	−	0.862814i	$-0.331300\pi$
$571$	7.87697e6	1.01104	0.505521	+	0.862814i	$0.331300\pi$
$572$	0	0
$573$	6874.06	0.000874635 0
$574$	−2.15710e7	−2.73269
$575$	−1.82285e6	−0.229922
$576$	−8.58252e6	−1.07785
$577$	−1.14810e7	−1.43562	−0.717812	−	0.696237i	$-0.754856\pi$
$577$	−1.14810e7	−1.43562	−0.717812	+	0.696237i	$0.754856\pi$
$578$	−1.24963e6	−0.155583
$579$	−158203.	−0.0196118
$580$	−221529.	−0.0273439
$581$	−1.86036e7	−2.28642
$582$	64732.8	0.00792167
$583$	0	0
$584$	7.86591e6	0.954370
$585$	−2.98798e6	−0.360984
$586$	−3.37512e6	−0.406017
$587$	−2.76883e6	−0.331666	−0.165833	−	0.986154i	$-0.553031\pi$
$587$	−2.76883e6	−0.331666	−0.165833	+	0.986154i	$0.553031\pi$
$588$	27379.2	0.00326571
$589$	−3.41706e6	−0.405848
$590$	−286062.	−0.0338322
$591$	188386.	0.0221860
$592$	3.15380e6	0.369854
$593$	1.02710e7	1.19943	0.599716	−	0.800213i	$-0.295280\pi$
$593$	1.02710e7	1.19943	0.599716	+	0.800213i	$0.295280\pi$
$594$	0	0
$595$	−7.12603e6	−0.825193
$596$	158478.	0.0182749
$597$	−213040.	−0.0244639
$598$	−7.70684e6	−0.881299
$599$	1.58174e6	0.180123	0.0900615	−	0.995936i	$-0.471294\pi$
$599$	1.58174e6	0.180123	0.0900615	+	0.995936i	$0.471294\pi$
$600$	−31659.5	−0.00359026
$601$	−8.87173e6	−1.00189	−0.500947	−	0.865478i	$-0.667015\pi$
$601$	−8.87173e6	−1.00189	−0.500947	+	0.865478i	$0.667015\pi$
$602$	1.09482e7	1.23126
$603$	−1.01155e7	−1.13291
$604$	1.27629e6	0.142350
$605$	0	0
$606$	179964.	0.0199069
$607$	8.96216e6	0.987281	0.493641	−	0.869666i	$-0.335666\pi$
$607$	8.96216e6	0.987281	0.493641	+	0.869666i	$0.335666\pi$
$608$	−1.21821e6	−0.133649
$609$	167154.	0.0182630
$610$	−512074.	−0.0557196
$611$	9.94648e6	1.07787
$612$	984842.	0.106289
$613$	−3.21264e6	−0.345311	−0.172655	−	0.984982i	$-0.555235\pi$
$613$	−3.21264e6	−0.345311	−0.172655	+	0.984982i	$0.555235\pi$
$614$	−4.81317e6	−0.515241
$615$	121489.	0.0129524
$616$	0	0
$617$	2.22623e6	0.235428	0.117714	−	0.993048i	$-0.462443\pi$
$617$	2.22623e6	0.235428	0.117714	+	0.993048i	$0.462443\pi$
$618$	−66555.7	−0.00700994
$619$	−1.15608e7	−1.21273	−0.606363	−	0.795188i	$-0.707372\pi$
$619$	−1.15608e7	−1.21273	−0.606363	+	0.795188i	$0.707372\pi$
$620$	−251544.	−0.0262805
$621$	−380233.	−0.0395659
$622$	1.96359e6	0.203505
$623$	−2.05333e7	−2.11952
$624$	−120532.	−0.0123920
$625$	390625.	0.0400000
$626$	−488639.	−0.0498371
$627$	0	0
$628$	489726.	0.0495512
$629$	−4.43990e6	−0.447452
$630$	−7.23264e6	−0.726014
$631$	1.38586e7	1.38562	0.692811	−	0.721120i	$-0.256372\pi$
$631$	1.38586e7	1.38562	0.692811	+	0.721120i	$0.256372\pi$
$632$	−1.57809e6	−0.157159
$633$	143589.	0.0142434
$634$	−7.34761e6	−0.725977
$635$	1.01138e6	0.0995362
$636$	23147.4	0.00226913
$637$	−1.59206e7	−1.55457
$638$	0	0
$639$	−1.11170e7	−1.07705
$640$	3.83380e6	0.369981
$641$	6.69506e6	0.643590	0.321795	−	0.946809i	$-0.395714\pi$
$641$	6.69506e6	0.643590	0.321795	+	0.946809i	$0.395714\pi$
$642$	217294.	0.0208070
$643$	4.42222e6	0.421806	0.210903	−	0.977507i	$-0.432360\pi$
$643$	4.42222e6	0.421806	0.210903	+	0.977507i	$0.432360\pi$
$644$	2.03948e6	0.193778
$645$	−61660.9	−0.00583594
$646$	−7.39457e6	−0.697159
$647$	−1.02767e7	−0.965148	−0.482574	−	0.875855i	$-0.660298\pi$
$647$	−1.02767e7	−0.965148	−0.482574	+	0.875855i	$0.660298\pi$
$648$	1.11389e7	1.04209
$649$	0	0
$650$	1.65153e6	0.153321
$651$	189801.	0.0175528
$652$	1.51523e6	0.139591
$653$	1.45186e7	1.33242	0.666212	−	0.745762i	$-0.267915\pi$
$653$	1.45186e7	1.33242	0.666212	+	0.745762i	$0.267915\pi$
$654$	−213454.	−0.0195146
$655$	−7.38478e6	−0.672565
$656$	−1.65397e7	−1.50061
$657$	−1.01207e7	−0.914739
$658$	2.40762e7	2.16782
$659$	−2.04237e7	−1.83198	−0.915991	−	0.401198i	$-0.868594\pi$
$659$	−2.04237e7	−1.83198	−0.915991	+	0.401198i	$0.868594\pi$
$660$	0	0
$661$	2.74176e6	0.244076	0.122038	−	0.992525i	$-0.461057\pi$
$661$	2.74176e6	0.244076	0.122038	+	0.992525i	$0.461057\pi$
$662$	1.77764e7	1.57652
$663$	169684.	0.0149919
$664$	−1.58408e7	−1.39431
$665$	−5.93700e6	−0.520611
$666$	−4.50632e6	−0.393673
$667$	8.19494e6	0.713232
$668$	−1.21088e6	−0.104993
$669$	127907.	0.0110491
$670$	5.59109e6	0.481182
$671$	0	0
$672$	67666.1	0.00578027
$673$	7.63514e6	0.649800	0.324900	−	0.945748i	$-0.394669\pi$
$673$	7.63514e6	0.649800	0.324900	+	0.945748i	$0.394669\pi$
$674$	−6.65457e6	−0.564248
$675$	81481.6	0.00688335
$676$	407562.	0.0343026
$677$	8.35682e6	0.700760	0.350380	−	0.936608i	$-0.386052\pi$
$677$	8.35682e6	0.700760	0.350380	+	0.936608i	$0.386052\pi$
$678$	−280722.	−0.0234532
$679$	9.96104e6	0.829145
$680$	−6.06778e6	−0.503220
$681$	301965.	0.0249510
$682$	0	0
$683$	−1.78314e6	−0.146262	−0.0731312	−	0.997322i	$-0.523299\pi$
$683$	−1.78314e6	−0.146262	−0.0731312	+	0.997322i	$0.523299\pi$
$684$	820515.	0.0670573
$685$	7.24806e6	0.590195
$686$	−1.85214e7	−1.50267
$687$	228477.	0.0184693
$688$	8.39457e6	0.676125
$689$	−1.34598e7	−1.08017
$690$	105066.	0.00840119
$691$	−681118.	−0.0542659	−0.0271330	−	0.999632i	$-0.508638\pi$
$691$	−681118.	−0.0542659	−0.0271330	+	0.999632i	$0.508638\pi$
$692$	−346855.	−0.0275349
$693$	0	0
$694$	4.39199e6	0.346149
$695$	3.32602e6	0.261193
$696$	142331.	0.0111372
$697$	2.32844e7	1.81544
$698$	−1.81783e6	−0.141226
$699$	423150.	0.0327568
$700$	−437047.	−0.0337119
$701$	−2.98657e6	−0.229551	−0.114775	−	0.993391i	$-0.536615\pi$
$701$	−2.98657e6	−0.229551	−0.114775	+	0.993391i	$0.536615\pi$
$702$	344497.	0.0263841
$703$	−3.69907e6	−0.282296
$704$	0	0
$705$	−135599.	−0.0102751
$706$	−1.32075e6	−0.0997264
$707$	2.76927e7	2.08361
$708$	−1802.59	−0.000135149 0
$709$	5.52759e6	0.412971	0.206486	−	0.978450i	$-0.433797\pi$
$709$	5.52759e6	0.412971	0.206486	+	0.978450i	$0.433797\pi$
$710$	6.14465e6	0.457458
$711$	2.03046e6	0.150633
$712$	−1.74840e7	−1.29253
$713$	9.30527e6	0.685496
$714$	410734.	0.0301519
$715$	0	0
$716$	−119821.	−0.00873477
$717$	17558.6	0.00127554
$718$	−1.14455e7	−0.828560
$719$	9.15469e6	0.660422	0.330211	−	0.943907i	$-0.392880\pi$
$719$	9.15469e6	0.660422	0.330211	+	0.943907i	$0.392880\pi$
$720$	−5.54567e6	−0.398678
$721$	−1.02416e7	−0.733716
$722$	7.13809e6	0.509611
$723$	349611.	0.0248737
$724$	2.10886e6	0.149521
$725$	−1.75612e6	−0.124082
$726$	0	0
$727$	75965.3	0.00533064	0.00266532	−	0.999996i	$-0.499152\pi$
$727$	75965.3	0.00533064	0.00266532	+	0.999996i	$0.499152\pi$
$728$	−2.05973e7	−1.44039
$729$	−1.43234e7	−0.998223
$730$	5.59395e6	0.388518
$731$	−1.18178e7	−0.817980
$732$	−3226.78	−0.000222583 0
$733$	−1.52622e7	−1.04920	−0.524600	−	0.851349i	$-0.675785\pi$
$733$	−1.52622e7	−1.04920	−0.524600	+	0.851349i	$0.675785\pi$
$734$	−2.15601e7	−1.47710
$735$	217043.	0.0148193
$736$	3.31742e6	0.225739
$737$	0	0
$738$	2.36327e7	1.59725
$739$	−1.02161e6	−0.0688138	−0.0344069	−	0.999408i	$-0.510954\pi$
$739$	−1.02161e6	−0.0688138	−0.0344069	+	0.999408i	$0.510954\pi$
$740$	−272304.	−0.0182799
$741$	141371.	0.00945836
$742$	−3.25805e7	−2.17244
$743$	2.24910e6	0.149464	0.0747319	−	0.997204i	$-0.476190\pi$
$743$	2.24910e6	0.149464	0.0747319	+	0.997204i	$0.476190\pi$
$744$	161615.	0.0107041
$745$	1.25630e6	0.0829286
$746$	1.15283e7	0.758436
$747$	2.03817e7	1.33641
$748$	0	0
$749$	3.34371e7	2.17783
$750$	−22515.1	−0.00146157
$751$	−1.34296e7	−0.868884	−0.434442	−	0.900700i	$-0.643054\pi$
$751$	−1.34296e7	−0.868884	−0.434442	+	0.900700i	$0.643054\pi$
$752$	1.84606e7	1.19042
$753$	405787.	0.0260802
$754$	−7.42473e6	−0.475611
$755$	1.01176e7	0.645964
$756$	−91165.0	−0.00580128
$757$	1.46205e6	0.0927302	0.0463651	−	0.998925i	$-0.485236\pi$
$757$	1.46205e6	0.0927302	0.0463651	+	0.998925i	$0.485236\pi$
$758$	−2.36884e7	−1.49748
$759$	0	0
$760$	−5.05533e6	−0.317480
$761$	−2.50525e7	−1.56816	−0.784079	−	0.620662i	$-0.786864\pi$
$761$	−2.50525e7	−1.56816	−0.784079	+	0.620662i	$0.786864\pi$
$762$	−58294.6	−0.00363698
$763$	−3.28461e7	−2.04255
$764$	80801.7	0.00500826
$765$	7.80713e6	0.482323
$766$	2.54503e7	1.56719
$767$	1.04818e6	0.0643348
$768$	82340.8	0.00503746
$769$	−6.89559e6	−0.420490	−0.210245	−	0.977649i	$-0.567426\pi$
$769$	−6.89559e6	−0.420490	−0.210245	+	0.977649i	$0.567426\pi$
$770$	0	0
$771$	−128899.	−0.00780931
$772$	−1.85961e6	−0.112299
$773$	825627.	0.0496976	0.0248488	−	0.999691i	$-0.492090\pi$
$773$	825627.	0.0496976	0.0248488	+	0.999691i	$0.492090\pi$
$774$	−1.19946e7	−0.719669
$775$	−1.99406e6	−0.119257
$776$	8.48178e6	0.505630
$777$	205466.	0.0122092
$778$	−3.15169e6	−0.186679
$779$	1.93992e7	1.14536
$780$	10406.9	0.000612472 0
$781$	0	0
$782$	2.01368e7	1.17753
$783$	−366315.	−0.0213526
$784$	−2.95485e7	−1.71690
$785$	3.88220e6	0.224856
$786$	425648.	0.0245750
$787$	−2.06984e7	−1.19124	−0.595621	−	0.803265i	$-0.703094\pi$
$787$	−2.06984e7	−1.19124	−0.595621	+	0.803265i	$0.703094\pi$
$788$	2.21439e6	0.127040
$789$	−278859.	−0.0159475
$790$	−1.12228e6	−0.0639786
$791$	−4.31973e7	−2.45480
$792$	0	0
$793$	1.87632e6	0.105956
$794$	1.12027e7	0.630627
$795$	183496.	0.0102970
$796$	−2.50420e6	−0.140083
$797$	5.24848e6	0.292676	0.146338	−	0.989235i	$-0.453251\pi$
$797$	5.24848e6	0.292676	0.146338	+	0.989235i	$0.453251\pi$
$798$	342200.	0.0190227
$799$	−2.59886e7	−1.44018
$800$	−710902.	−0.0392722
$801$	2.24958e7	1.23886
$802$	1.91169e7	1.04950
$803$	0	0
$804$	35231.7	0.00192218
$805$	1.61675e7	0.879335
$806$	−8.43070e6	−0.457116
$807$	−190574.	−0.0103010
$808$	2.35802e7	1.27063
$809$	−3.57950e7	−1.92287	−0.961437	−	0.275027i	$-0.911313\pi$
$809$	−3.57950e7	−1.92287	−0.961437	+	0.275027i	$0.911313\pi$
$810$	7.92158e6	0.424228
$811$	−1.70523e7	−0.910396	−0.455198	−	0.890390i	$-0.650432\pi$
$811$	−1.70523e7	−0.910396	−0.455198	+	0.890390i	$0.650432\pi$
$812$	1.96482e6	0.104576
$813$	261954.	0.0138995
$814$	0	0
$815$	1.20117e7	0.633445
$816$	314933.	0.0165574
$817$	−9.84591e6	−0.516061
$818$	1.73098e7	0.904502
$819$	2.65016e7	1.38058
$820$	1.42806e6	0.0741670
$821$	−2.07086e7	−1.07224	−0.536122	−	0.844141i	$-0.680111\pi$
$821$	−2.07086e7	−1.07224	−0.536122	+	0.844141i	$0.680111\pi$
$822$	−417767.	−0.0215653
$823$	1.02785e7	0.528967	0.264483	−	0.964390i	$-0.414799\pi$
$823$	1.02785e7	0.528967	0.264483	+	0.964390i	$0.414799\pi$
$824$	−8.72064e6	−0.447435
$825$	0	0
$826$	2.53719e6	0.129391
$827$	5.78581e6	0.294171	0.147086	−	0.989124i	$-0.453011\pi$
$827$	5.78581e6	0.294171	0.147086	+	0.989124i	$0.453011\pi$
$828$	−2.23441e6	−0.113263
$829$	−3.09169e6	−0.156246	−0.0781231	−	0.996944i	$-0.524893\pi$
$829$	−3.09169e6	−0.156246	−0.0781231	+	0.996944i	$0.524893\pi$
$830$	−1.12654e7	−0.567613
$831$	−511901.	−0.0257148
$832$	−1.73819e7	−0.870540
$833$	4.15980e7	2.07711
$834$	−191707.	−0.00954382
$835$	−9.59904e6	−0.476444
$836$	0	0
$837$	−415947.	−0.0205222
$838$	−6.34027e6	−0.311888
$839$	9.92910e6	0.486973	0.243486	−	0.969904i	$-0.421709\pi$
$839$	9.92910e6	0.486973	0.243486	+	0.969904i	$0.421709\pi$
$840$	280800.	0.0137309
$841$	−1.26162e7	−0.615089
$842$	2.98515e7	1.45106
$843$	−362548.	−0.0175710
$844$	1.68783e6	0.0815591
$845$	3.23086e6	0.155660
$846$	−2.63774e7	−1.26709
$847$	0	0
$848$	−2.49813e7	−1.19296
$849$	446365.	0.0212530
$850$	−4.31519e6	−0.204858
$851$	1.00732e7	0.476810
$852$	38719.9	0.00182741
$853$	−4.61784e6	−0.217303	−0.108652	−	0.994080i	$-0.534653\pi$
$853$	−4.61784e6	−0.217303	−0.108652	+	0.994080i	$0.534653\pi$
$854$	4.54178e6	0.213099
$855$	6.50446e6	0.304296
$856$	2.84715e7	1.32809
$857$	−2.66406e6	−0.123906	−0.0619529	−	0.998079i	$-0.519733\pi$
$857$	−2.66406e6	−0.123906	−0.0619529	+	0.998079i	$0.519733\pi$
$858$	0	0
$859$	−1.72516e7	−0.797711	−0.398855	−	0.917014i	$-0.630592\pi$
$859$	−1.72516e7	−0.797711	−0.398855	+	0.917014i	$0.630592\pi$
$860$	−724798.	−0.0334173
$861$	−1.07754e6	−0.0495363
$862$	7.55125e6	0.346139
$863$	2.63519e7	1.20444	0.602220	−	0.798330i	$-0.294283\pi$
$863$	2.63519e7	1.20444	0.602220	+	0.798330i	$0.294283\pi$
$864$	−148289.	−0.00675811
$865$	−2.74963e6	−0.124949
$866$	2.81678e7	1.27632
$867$	−62423.0	−0.00282031
$868$	2.23104e6	0.100510
$869$	0	0
$870$	101220.	0.00453388
$871$	−2.04867e7	−0.915011
$872$	−2.79683e7	−1.24559
$873$	−1.09131e7	−0.484633
$874$	1.67768e7	0.742901
$875$	−3.46460e6	−0.152980
$876$	35249.7	0.00155201
$877$	−1.41050e7	−0.619261	−0.309631	−	0.950857i	$-0.600205\pi$
$877$	−1.41050e7	−0.619261	−0.309631	+	0.950857i	$0.600205\pi$
$878$	−3.32372e7	−1.45508
$879$	−168597.	−0.00736001
$880$	0	0
$881$	−2.55930e7	−1.11092	−0.555458	−	0.831545i	$-0.687457\pi$
$881$	−2.55930e7	−1.11092	−0.555458	+	0.831545i	$0.687457\pi$
$882$	4.22203e7	1.82747
$883$	1.13583e7	0.490242	0.245121	−	0.969493i	$-0.421172\pi$
$883$	1.13583e7	0.490242	0.245121	+	0.969493i	$0.421172\pi$
$884$	1.99457e6	0.0858457
$885$	−14289.7	−0.000613287 0
$886$	−3.93269e6	−0.168308
$887$	−8.07174e6	−0.344476	−0.172238	−	0.985055i	$-0.555100\pi$
$887$	−8.07174e6	−0.344476	−0.172238	+	0.985055i	$0.555100\pi$
$888$	174953.	0.00744543
$889$	−8.97034e6	−0.380675
$890$	−1.24340e7	−0.526180
$891$	0	0
$892$	1.50349e6	0.0632687
$893$	−2.16523e7	−0.908604
$894$	−72411.6	−0.00303015
$895$	−949859.	−0.0396371
$896$	−3.40035e7	−1.41499
$897$	−384980.	−0.0159756
$898$	−3.07909e7	−1.27418
$899$	8.96465e6	0.369942
$900$	478820.	0.0197045
$901$	3.51684e7	1.44325
$902$	0	0
$903$	546894.	0.0223195
$904$	−3.67823e7	−1.49699
$905$	1.67176e7	0.678504
$906$	−583161.	−0.0236030
$907$	−2.03119e7	−0.819847	−0.409923	−	0.912120i	$-0.634445\pi$
$907$	−2.03119e7	−0.819847	−0.409923	+	0.912120i	$0.634445\pi$
$908$	3.54947e6	0.142873
$909$	−3.03396e7	−1.21787
$910$	−1.46480e7	−0.586375
$911$	3.04443e6	0.121537	0.0607686	−	0.998152i	$-0.480645\pi$
$911$	3.04443e6	0.121537	0.0607686	+	0.998152i	$0.480645\pi$
$912$	262384.	0.0104460
$913$	0	0
$914$	3.88837e7	1.53958
$915$	−25579.7	−0.00101005
$916$	2.68565e6	0.105757
$917$	6.54985e7	2.57222
$918$	−900117.	−0.0352527
$919$	1.22988e7	0.480367	0.240183	−	0.970728i	$-0.422792\pi$
$919$	1.22988e7	0.480367	0.240183	+	0.970728i	$0.422792\pi$
$920$	1.37666e7	0.536237
$921$	−240433.	−0.00933995
$922$	−7.87676e6	−0.305155
$923$	−2.25150e7	−0.869896
$924$	0	0
$925$	−2.15863e6	−0.0829515
$926$	1.59465e7	0.611138
$927$	1.12204e7	0.428855
$928$	3.19599e6	0.121825
$929$	3.76656e7	1.43188	0.715938	−	0.698164i	$-0.245999\pi$
$929$	3.76656e7	1.43188	0.715938	+	0.698164i	$0.245999\pi$
$930$	114935.	0.00435756
$931$	3.46571e7	1.31044
$932$	4.97395e6	0.187569
$933$	98087.5	0.00368901
$934$	1.72947e7	0.648703
$935$	0	0
$936$	2.25660e7	0.841907
$937$	4.17893e7	1.55495	0.777474	−	0.628915i	$-0.216501\pi$
$937$	4.17893e7	1.55495	0.777474	+	0.628915i	$0.216501\pi$
$938$	−4.95896e7	−1.84028
$939$	−24409.0	−0.000903413 0
$940$	−1.59391e6	−0.0588362
$941$	1.03572e7	0.381300	0.190650	−	0.981658i	$-0.438940\pi$
$941$	1.03572e7	0.381300	0.190650	+	0.981658i	$0.438940\pi$
$942$	−223764.	−0.00821606
$943$	−5.28276e7	−1.93456
$944$	1.94541e6	0.0710527
$945$	−722692.	−0.0263253
$946$	0	0
$947$	−5.12451e7	−1.85685	−0.928426	−	0.371518i	$-0.878837\pi$
$947$	−5.12451e7	−1.85685	−0.928426	+	0.371518i	$0.878837\pi$
$948$	−7071.95	−0.000255575 0
$949$	−2.04971e7	−0.738801
$950$	−3.59517e6	−0.129244
$951$	−367036.	−0.0131600
$952$	5.38175e7	1.92456
$953$	−3.38796e6	−0.120839	−0.0604193	−	0.998173i	$-0.519244\pi$
$953$	−3.38796e6	−0.120839	−0.0604193	+	0.998173i	$0.519244\pi$
$954$	3.56946e7	1.26979
$955$	640539.	0.0227267
$956$	206394.	0.00730387
$957$	0	0
$958$	4.98751e7	1.75578
$959$	−6.42858e7	−2.25719
$960$	236965.	0.00829863
$961$	−1.84499e7	−0.644444
$962$	−9.12650e6	−0.317956
$963$	−3.66330e7	−1.27294
$964$	4.10953e6	0.142430
$965$	−1.47416e7	−0.509598
$966$	−931874.	−0.0321303
$967$	1.05100e7	0.361440	0.180720	−	0.983535i	$-0.442157\pi$
$967$	1.05100e7	0.361440	0.180720	+	0.983535i	$0.442157\pi$
$968$	0	0
$969$	−369382.	−0.0126376
$970$	6.03193e6	0.205839
$971$	5.43381e6	0.184951	0.0924755	−	0.995715i	$-0.470522\pi$
$971$	5.43381e6	0.184951	0.0924755	+	0.995715i	$0.470522\pi$
$972$	149825.	0.00508650
$973$	−2.94997e7	−0.998932
$974$	−3.25755e7	−1.10026
$975$	82498.8	0.00277931
$976$	3.48244e6	0.117020
$977$	1.04317e7	0.349637	0.174818	−	0.984601i	$-0.444066\pi$
$977$	1.04317e7	0.349637	0.174818	+	0.984601i	$0.444066\pi$
$978$	−692334.	−0.0231456
$979$	0	0
$980$	2.55125e6	0.0848571
$981$	3.59856e7	1.19387
$982$	2.92660e7	0.968467
$983$	8.03649e6	0.265267	0.132633	−	0.991165i	$-0.457657\pi$
$983$	8.03649e6	0.265267	0.132633	+	0.991165i	$0.457657\pi$
$984$	−917517.	−0.0302083
$985$	1.75542e7	0.576487
$986$	1.93997e7	0.635480
$987$	1.20268e6	0.0392969
$988$	1.66176e6	0.0541597
$989$	2.68122e7	0.871650
$990$	0	0
$991$	5.32499e7	1.72240	0.861202	−	0.508263i	$-0.169712\pi$
$991$	5.32499e7	1.72240	0.861202	+	0.508263i	$0.169712\pi$
$992$	3.62901e6	0.117087
$993$	887985.	0.0285780
$994$	−5.44992e7	−1.74954
$995$	−1.98515e7	−0.635676
$996$	−70988.0	−0.00226744
$997$	1.68999e7	0.538451	0.269226	−	0.963077i	$-0.413232\pi$
$997$	1.68999e7	0.538451	0.269226	+	0.963077i	$0.413232\pi$
$998$	1.07153e7	0.340546
$999$	−450275.	−0.0142746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.7		20
11.5	even	5		55.6.g.b.36.7	yes	40
11.9	even	5		55.6.g.b.26.7	✓	40
11.10	odd	2		605.6.a.o.1.14		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.26.7	✓	40	11.9	even	5
55.6.g.b.36.7	yes	40	11.5	even	5
605.6.a.o.1.14		20	11.10	odd	2
605.6.a.p.1.7		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)

\(f(q)\)	\(=\)	\(q-5.37088 q^{2} -0.268292 q^{3} -3.15366 q^{4} -25.0000 q^{5} +1.44096 q^{6} +221.735 q^{7} +188.806 q^{8} -242.928 q^{9} +O(q^{10})\)	\(q-5.37088 q^{2} -0.268292 q^{3} -3.15366 q^{4} -25.0000 q^{5} +1.44096 q^{6} +221.735 q^{7} +188.806 q^{8} -242.928 q^{9} +134.272 q^{10} +0.846102 q^{12} -491.994 q^{13} -1190.91 q^{14} +6.70730 q^{15} -913.137 q^{16} +1285.51 q^{17} +1304.74 q^{18} +1071.01 q^{19} +78.8415 q^{20} -59.4896 q^{21} -2916.56 q^{23} -50.6551 q^{24} +625.000 q^{25} +2642.44 q^{26} +130.371 q^{27} -699.276 q^{28} -2809.80 q^{29} -36.0241 q^{30} -3190.50 q^{31} -1137.44 q^{32} -6904.30 q^{34} -5543.37 q^{35} +766.112 q^{36} -3453.81 q^{37} -5752.27 q^{38} +131.998 q^{39} -4720.15 q^{40} +18113.0 q^{41} +319.512 q^{42} -9193.11 q^{43} +6073.20 q^{45} +15664.5 q^{46} -20216.7 q^{47} +244.987 q^{48} +32359.3 q^{49} -3356.80 q^{50} -344.891 q^{51} +1551.58 q^{52} +27357.7 q^{53} -700.204 q^{54} +41864.8 q^{56} -287.343 q^{57} +15091.1 q^{58} -2130.47 q^{59} -21.1525 q^{60} -3813.71 q^{61} +17135.8 q^{62} -53865.6 q^{63} +35329.5 q^{64} +12299.9 q^{65} +41640.1 q^{67} -4054.05 q^{68} +782.489 q^{69} +29772.8 q^{70} +45762.7 q^{71} -45866.3 q^{72} +41661.3 q^{73} +18550.0 q^{74} -167.682 q^{75} -3377.60 q^{76} -708.946 q^{78} -8358.28 q^{79} +22828.4 q^{80} +58996.5 q^{81} -97282.8 q^{82} -83900.1 q^{83} +187.610 q^{84} -32137.6 q^{85} +49375.1 q^{86} +753.846 q^{87} -92602.8 q^{89} -32618.4 q^{90} -109092. q^{91} +9197.83 q^{92} +855.984 q^{93} +108581. q^{94} -26775.3 q^{95} +305.167 q^{96} +44923.3 q^{97} -173798. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 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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