LMFDB - Embedded newform 1075.6.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,Mod(1,1075)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1075.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:	$172.412606299$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 $ x^10 - 2x^9 - 256x^8 + 266x^7 + 21986x^6 - 10450x^5 - 719484x^4 + 384582x^3 + 8437093x^2 - 5752252*x - 22734604
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$11.5305$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.5305 q^{2} -27.4953 q^{3} +78.8905 q^{4} -289.538 q^{6} +19.8137 q^{7} +493.778 q^{8} +512.989 q^{9} +O(q^{10})$	\(q+10.5305 q^{2} -27.4953 q^{3} +78.8905 q^{4} -289.538 q^{6} +19.8137 q^{7} +493.778 q^{8} +512.989 q^{9} -85.3712 q^{11} -2169.11 q^{12} +229.081 q^{13} +208.647 q^{14} +2675.21 q^{16} -1356.51 q^{17} +5402.01 q^{18} -2795.35 q^{19} -544.783 q^{21} -898.997 q^{22} +1856.11 q^{23} -13576.6 q^{24} +2412.33 q^{26} -7423.41 q^{27} +1563.11 q^{28} +7312.96 q^{29} -2937.36 q^{31} +12370.3 q^{32} +2347.30 q^{33} -14284.7 q^{34} +40469.9 q^{36} -2577.36 q^{37} -29436.3 q^{38} -6298.65 q^{39} -3532.54 q^{41} -5736.81 q^{42} -1849.00 q^{43} -6734.97 q^{44} +19545.7 q^{46} +7065.73 q^{47} -73555.6 q^{48} -16414.4 q^{49} +37297.6 q^{51} +18072.3 q^{52} +3852.63 q^{53} -78171.9 q^{54} +9783.57 q^{56} +76858.8 q^{57} +77008.8 q^{58} +27996.1 q^{59} -39244.4 q^{61} -30931.7 q^{62} +10164.2 q^{63} +44658.1 q^{64} +24718.2 q^{66} +14809.1 q^{67} -107016. q^{68} -51034.2 q^{69} +8956.13 q^{71} +253303. q^{72} -35168.6 q^{73} -27140.8 q^{74} -220526. q^{76} -1691.52 q^{77} -66327.6 q^{78} -13263.6 q^{79} +79452.3 q^{81} -37199.3 q^{82} +9812.47 q^{83} -42978.2 q^{84} -19470.8 q^{86} -201072. q^{87} -42154.4 q^{88} -87124.9 q^{89} +4538.95 q^{91} +146429. q^{92} +80763.5 q^{93} +74405.4 q^{94} -340124. q^{96} -83982.4 q^{97} -172851. q^{98} -43794.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9}+O(q^{10}) $ 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9} + 745 q^{11} - 4627 q^{12} - 1917 q^{13} + 1936 q^{14} + 5354 q^{16} - 4017 q^{17} + 2725 q^{18} - 2404 q^{19} - 228 q^{21} + 5836 q^{22} - 1733 q^{23} - 10711 q^{24} - 1484 q^{26} + 2324 q^{27} + 15028 q^{28} + 6996 q^{29} - 4899 q^{31} + 7554 q^{32} + 15734 q^{33} - 27033 q^{34} + 4433 q^{36} - 1466 q^{37} - 13905 q^{38} - 26542 q^{39} + 10297 q^{41} + 37642 q^{42} - 18490 q^{43} - 36140 q^{44} + 17991 q^{46} - 48592 q^{47} - 83607 q^{48} + 29458 q^{49} + 92972 q^{51} - 14232 q^{52} - 127165 q^{53} - 92002 q^{54} - 7780 q^{56} - 34060 q^{57} + 10305 q^{58} + 99372 q^{59} + 17408 q^{61} - 28265 q^{62} - 2244 q^{63} + 47202 q^{64} - 150292 q^{66} + 2021 q^{67} - 192151 q^{68} + 1654 q^{69} + 11286 q^{71} + 298365 q^{72} - 49892 q^{73} - 125431 q^{74} - 249803 q^{76} - 98144 q^{77} + 28494 q^{78} - 91524 q^{79} - 26450 q^{81} + 158909 q^{82} + 105203 q^{83} - 357682 q^{84} + 14792 q^{86} - 181200 q^{87} + 461824 q^{88} - 62682 q^{89} - 295304 q^{91} - 183783 q^{92} + 238430 q^{93} + 7259 q^{94} - 162399 q^{96} - 108383 q^{97} - 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9 + 745 * q^11 - 4627 * q^12 - 1917 * q^13 + 1936 * q^14 + 5354 * q^16 - 4017 * q^17 + 2725 * q^18 - 2404 * q^19 - 228 * q^21 + 5836 * q^22 - 1733 * q^23 - 10711 * q^24 - 1484 * q^26 + 2324 * q^27 + 15028 * q^28 + 6996 * q^29 - 4899 * q^31 + 7554 * q^32 + 15734 * q^33 - 27033 * q^34 + 4433 * q^36 - 1466 * q^37 - 13905 * q^38 - 26542 * q^39 + 10297 * q^41 + 37642 * q^42 - 18490 * q^43 - 36140 * q^44 + 17991 * q^46 - 48592 * q^47 - 83607 * q^48 + 29458 * q^49 + 92972 * q^51 - 14232 * q^52 - 127165 * q^53 - 92002 * q^54 - 7780 * q^56 - 34060 * q^57 + 10305 * q^58 + 99372 * q^59 + 17408 * q^61 - 28265 * q^62 - 2244 * q^63 + 47202 * q^64 - 150292 * q^66 + 2021 * q^67 - 192151 * q^68 + 1654 * q^69 + 11286 * q^71 + 298365 * q^72 - 49892 * q^73 - 125431 * q^74 - 249803 * q^76 - 98144 * q^77 + 28494 * q^78 - 91524 * q^79 - 26450 * q^81 + 158909 * q^82 + 105203 * q^83 - 357682 * q^84 + 14792 * q^86 - 181200 * q^87 + 461824 * q^88 - 62682 * q^89 - 295304 * q^91 - 183783 * q^92 + 238430 * q^93 + 7259 * q^94 - 162399 * q^96 - 108383 * q^97 - 354656 * q^98 - 270499 * q^99

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 $

$2$	10.5305	1.86154	0.930769	−	0.365607i	$-0.119138\pi$
$2$	10.5305	1.86154	0.930769	+	0.365607i	$0.119138\pi$
$3$	−27.4953	−1.76382	−0.881911	−	0.471417i	$-0.843743\pi$
$3$	−27.4953	−1.76382	−0.881911	+	0.471417i	$0.843743\pi$
$4$	78.8905	2.46533
$5$	0	0
$5$	0	0
$6$	−289.538	−3.28342
$7$	19.8137	0.152834	0.0764171	−	0.997076i	$-0.475652\pi$
$7$	19.8137	0.152834	0.0764171	+	0.997076i	$0.475652\pi$
$8$	493.778	2.72776
$9$	512.989	2.11107
$10$	0	0
$11$	−85.3712	−0.212730	−0.106365	−	0.994327i	$-0.533921\pi$
$11$	−85.3712	−0.212730	−0.106365	+	0.994327i	$0.533921\pi$
$12$	−2169.11	−4.34840
$13$	229.081	0.375951	0.187975	−	0.982174i	$-0.439807\pi$
$13$	229.081	0.375951	0.187975	+	0.982174i	$0.439807\pi$
$14$	208.647	0.284507
$15$	0	0
$16$	2675.21	2.61251
$17$	−1356.51	−1.13841	−0.569207	−	0.822194i	$-0.692750\pi$
$17$	−1356.51	−1.13841	−0.569207	+	0.822194i	$0.692750\pi$
$18$	5402.01	3.92983
$19$	−2795.35	−1.77645	−0.888223	−	0.459413i	$-0.848060\pi$
$19$	−2795.35	−1.77645	−0.888223	+	0.459413i	$0.848060\pi$
$20$	0	0
$21$	−544.783	−0.269572
$22$	−898.997	−0.396006
$23$	1856.11	0.731618	0.365809	−	0.930690i	$-0.380792\pi$
$23$	1856.11	0.731618	0.365809	+	0.930690i	$0.380792\pi$
$24$	−13576.6	−4.81129
$25$	0	0
$26$	2412.33	0.699847
$27$	−7423.41	−1.95972
$28$	1563.11	0.376786
$29$	7312.96	1.61472	0.807362	−	0.590057i	$-0.200895\pi$
$29$	7312.96	1.61472	0.807362	+	0.590057i	$0.200895\pi$
$30$	0	0
$31$	−2937.36	−0.548975	−0.274488	−	0.961591i	$-0.588508\pi$
$31$	−2937.36	−0.548975	−0.274488	+	0.961591i	$0.588508\pi$
$32$	12370.3	2.13553
$33$	2347.30	0.375218
$34$	−14284.7	−2.11920
$35$	0	0
$36$	40469.9	5.20447
$37$	−2577.36	−0.309507	−0.154754	−	0.987953i	$-0.549458\pi$
$37$	−2577.36	−0.309507	−0.154754	+	0.987953i	$0.549458\pi$
$38$	−29436.3	−3.30692
$39$	−6298.65	−0.663110
$40$	0	0
$41$	−3532.54	−0.328192	−0.164096	−	0.986444i	$-0.552471\pi$
$41$	−3532.54	−0.328192	−0.164096	+	0.986444i	$0.552471\pi$
$42$	−5736.81	−0.501819
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	−6734.97	−0.524450
$45$	0	0
$46$	19545.7	1.36194
$47$	7065.73	0.466566	0.233283	−	0.972409i	$-0.425053\pi$
$47$	7065.73	0.466566	0.233283	+	0.972409i	$0.425053\pi$
$48$	−73555.6	−4.60800
$49$	−16414.4	−0.976642
$50$	0	0
$51$	37297.6	2.00796
$52$	18072.3	0.926842
$53$	3852.63	0.188394	0.0941972	−	0.995554i	$-0.469972\pi$
$53$	3852.63	0.188394	0.0941972	+	0.995554i	$0.469972\pi$
$54$	−78171.9	−3.64810
$55$	0	0
$56$	9783.57	0.416896
$57$	76858.8	3.13333
$58$	77008.8	3.00587
$59$	27996.1	1.04705	0.523524	−	0.852011i	$-0.324617\pi$
$59$	27996.1	1.04705	0.523524	+	0.852011i	$0.324617\pi$
$60$	0	0
$61$	−39244.4	−1.35037	−0.675186	−	0.737648i	$-0.735937\pi$
$61$	−39244.4	−1.35037	−0.675186	+	0.737648i	$0.735937\pi$
$62$	−30931.7	−1.02194
$63$	10164.2	0.322643
$64$	44658.1	1.36286
$65$	0	0
$66$	24718.2	0.698484
$67$	14809.1	0.403034	0.201517	−	0.979485i	$-0.435413\pi$
$67$	14809.1	0.403034	0.201517	+	0.979485i	$0.435413\pi$
$68$	−107016.	−2.80656
$69$	−51034.2	−1.29044
$70$	0	0
$71$	8956.13	0.210850	0.105425	−	0.994427i	$-0.466380\pi$
$71$	8956.13	0.210850	0.105425	+	0.994427i	$0.466380\pi$
$72$	253303.	5.75849
$73$	−35168.6	−0.772411	−0.386205	−	0.922413i	$-0.626214\pi$
$73$	−35168.6	−0.772411	−0.386205	+	0.922413i	$0.626214\pi$
$74$	−27140.8	−0.576160
$75$	0	0
$76$	−220526.	−4.37952
$77$	−1691.52	−0.0325125
$78$	−66327.6	−1.23441
$79$	−13263.6	−0.239108	−0.119554	−	0.992828i	$-0.538146\pi$
$79$	−13263.6	−0.239108	−0.119554	+	0.992828i	$0.538146\pi$
$80$	0	0
$81$	79452.3	1.34553
$82$	−37199.3	−0.610942
$83$	9812.47	0.156345	0.0781724	−	0.996940i	$-0.475092\pi$
$83$	9812.47	0.156345	0.0781724	+	0.996940i	$0.475092\pi$
$84$	−42978.2	−0.664584
$85$	0	0
$86$	−19470.8	−0.283882
$87$	−201072.	−2.84808
$88$	−42154.4	−0.580278
$89$	−87124.9	−1.16592	−0.582958	−	0.812502i	$-0.698105\pi$
$89$	−87124.9	−1.16592	−0.582958	+	0.812502i	$0.698105\pi$
$90$	0	0
$91$	4538.95	0.0574581
$92$	146429.	1.80368
$93$	80763.5	0.968295
$94$	74405.4	0.868530
$95$	0	0
$96$	−340124.	−3.76669
$97$	−83982.4	−0.906272	−0.453136	−	0.891441i	$-0.649695\pi$
$97$	−83982.4	−0.906272	−0.453136	+	0.891441i	$0.649695\pi$
$98$	−172851.	−1.81806
$99$	−43794.5	−0.449088
$100$	0	0
$101$	74775.4	0.729382	0.364691	−	0.931129i	$-0.381175\pi$
$101$	74775.4	0.729382	0.364691	+	0.931129i	$0.381175\pi$
$102$	392760.	3.73789
$103$	−29400.7	−0.273064	−0.136532	−	0.990636i	$-0.543596\pi$
$103$	−29400.7	−0.273064	−0.136532	+	0.990636i	$0.543596\pi$
$104$	113115.	1.02551
$105$	0	0
$106$	40570.0	0.350704
$107$	199822.	1.68727	0.843635	−	0.536917i	$-0.180411\pi$
$107$	199822.	1.68727	0.843635	+	0.536917i	$0.180411\pi$
$108$	−585637.	−4.83135
$109$	−39465.7	−0.318166	−0.159083	−	0.987265i	$-0.550854\pi$
$109$	−39465.7	−0.318166	−0.159083	+	0.987265i	$0.550854\pi$
$110$	0	0
$111$	70865.2	0.545915
$112$	53005.8	0.399281
$113$	−41487.8	−0.305650	−0.152825	−	0.988253i	$-0.548837\pi$
$113$	−41487.8	−0.305650	−0.152825	+	0.988253i	$0.548837\pi$
$114$	809358.	5.83282
$115$	0	0
$116$	576923.	3.98082
$117$	117516.	0.793657
$118$	294811.	1.94912
$119$	−26877.5	−0.173989
$120$	0	0
$121$	−153763.	−0.954746
$122$	−413262.	−2.51377
$123$	97128.1	0.578871
$124$	−231730.	−1.35340
$125$	0	0
$126$	107034.	0.600612
$127$	−357769.	−1.96831	−0.984156	−	0.177305i	$-0.943262\pi$
$127$	−357769.	−1.96831	−0.984156	+	0.177305i	$0.943262\pi$
$128$	74420.5	0.401483
$129$	50838.7	0.268980
$130$	0	0
$131$	−61207.9	−0.311623	−0.155811	−	0.987787i	$-0.549799\pi$
$131$	−61207.9	−0.311623	−0.155811	+	0.987787i	$0.549799\pi$
$132$	185180.	0.925036
$133$	−55386.2	−0.271502
$134$	155946.	0.750263
$135$	0	0
$136$	−669814.	−3.10533
$137$	309777.	1.41009	0.705047	−	0.709161i	$-0.250926\pi$
$137$	309777.	1.41009	0.705047	+	0.709161i	$0.250926\pi$
$138$	−537414.	−2.40221
$139$	−193740.	−0.850517	−0.425259	−	0.905072i	$-0.639817\pi$
$139$	−193740.	−0.850517	−0.425259	+	0.905072i	$0.639817\pi$
$140$	0	0
$141$	−194274.	−0.822938
$142$	94312.1	0.392506
$143$	−19556.9	−0.0799762
$144$	1.37235e6	5.51518
$145$	0	0
$146$	−370342.	−1.43787
$147$	451319.	1.72262
$148$	−203329.	−0.763037
$149$	−455017.	−1.67904	−0.839521	−	0.543327i	$-0.817164\pi$
$149$	−455017.	−1.67904	−0.839521	+	0.543327i	$0.817164\pi$
$150$	0	0
$151$	−505868.	−1.80549	−0.902744	−	0.430179i	$-0.858451\pi$
$151$	−505868.	−1.80549	−0.902744	+	0.430179i	$0.858451\pi$
$152$	−1.38028e6	−4.84572
$153$	−695874.	−2.40327
$154$	−17812.5	−0.0605232
$155$	0	0
$156$	−496903.	−1.63478
$157$	−348495.	−1.12836	−0.564179	−	0.825652i	$-0.690807\pi$
$157$	−348495.	−1.12836	−0.564179	+	0.825652i	$0.690807\pi$
$158$	−139672.	−0.445108
$159$	−105929.	−0.332294
$160$	0	0
$161$	36776.4	0.111816
$162$	836669.	2.50476
$163$	−104915.	−0.309291	−0.154645	−	0.987970i	$-0.549424\pi$
$163$	−104915.	−0.309291	−0.154645	+	0.987970i	$0.549424\pi$
$164$	−278684.	−0.809100
$165$	0	0
$166$	103330.	0.291042
$167$	−186982.	−0.518809	−0.259405	−	0.965769i	$-0.583526\pi$
$167$	−186982.	−0.518809	−0.259405	+	0.965769i	$0.583526\pi$
$168$	−269002.	−0.735329
$169$	−318815.	−0.858661
$170$	0	0
$171$	−1.43398e6	−3.75019
$172$	−145868.	−0.375959
$173$	−491718.	−1.24911	−0.624555	−	0.780981i	$-0.714720\pi$
$173$	−491718.	−1.24911	−0.624555	+	0.780981i	$0.714720\pi$
$174$	−2.11738e6	−5.30182
$175$	0	0
$176$	−228386.	−0.555761
$177$	−769758.	−1.84681
$178$	−917464.	−2.17040
$179$	374509.	0.873634	0.436817	−	0.899550i	$-0.356106\pi$
$179$	374509.	0.873634	0.436817	+	0.899550i	$0.356106\pi$
$180$	0	0
$181$	460794.	1.04547	0.522733	−	0.852496i	$-0.324912\pi$
$181$	460794.	1.04547	0.522733	+	0.852496i	$0.324912\pi$
$182$	47797.2	0.106961
$183$	1.07904e6	2.38181
$184$	916507.	1.99568
$185$	0	0
$186$	850476.	1.80252
$187$	115807.	0.242175
$188$	557419.	1.15024
$189$	−147085.	−0.299512
$190$	0	0
$191$	−22464.4	−0.0445565	−0.0222783	−	0.999752i	$-0.507092\pi$
$191$	−22464.4	−0.0445565	−0.0222783	+	0.999752i	$0.507092\pi$
$192$	−1.22789e6	−2.40384
$193$	−830124.	−1.60417	−0.802083	−	0.597212i	$-0.796275\pi$
$193$	−830124.	−1.60417	−0.802083	+	0.597212i	$0.796275\pi$
$194$	−884372.	−1.68706
$195$	0	0
$196$	−1.29494e6	−2.40774
$197$	−802058.	−1.47245	−0.736224	−	0.676738i	$-0.763393\pi$
$197$	−802058.	−1.47245	−0.736224	+	0.676738i	$0.763393\pi$
$198$	−461176.	−0.835995
$199$	−187945.	−0.336432	−0.168216	−	0.985750i	$-0.553801\pi$
$199$	−187945.	−0.336432	−0.168216	+	0.985750i	$0.553801\pi$
$200$	0	0
$201$	−407180.	−0.710879
$202$	787419.	1.35777
$203$	144897.	0.246785
$204$	2.94242e6	4.95028
$205$	0	0
$206$	−309602.	−0.508319
$207$	952164.	1.54449
$208$	612841.	0.982176
$209$	238642.	0.377904
$210$	0	0
$211$	327613.	0.506589	0.253294	−	0.967389i	$-0.418486\pi$
$211$	327613.	0.506589	0.253294	+	0.967389i	$0.418486\pi$
$212$	303936.	0.464454
$213$	−246251.	−0.371902
$214$	2.10422e6	3.14092
$215$	0	0
$216$	−3.66552e6	−5.34566
$217$	−58200.0	−0.0839022
$218$	−415592.	−0.592278
$219$	966970.	1.36239
$220$	0	0
$221$	−310751.	−0.427988
$222$	746243.	1.01624
$223$	166692.	0.224467	0.112234	−	0.993682i	$-0.464199\pi$
$223$	166692.	0.224467	0.112234	+	0.993682i	$0.464199\pi$
$224$	245101.	0.326382
$225$	0	0
$226$	−436886.	−0.568980
$227$	155259.	0.199982	0.0999912	−	0.994988i	$-0.468119\pi$
$227$	155259.	0.199982	0.0999912	+	0.994988i	$0.468119\pi$
$228$	6.06343e6	7.72469
$229$	−1.01590e6	−1.28016	−0.640079	−	0.768309i	$-0.721098\pi$
$229$	−1.01590e6	−1.28016	−0.640079	+	0.768309i	$0.721098\pi$
$230$	0	0
$231$	46508.7	0.0573462
$232$	3.61098e6	4.40458
$233$	−23299.8	−0.0281166	−0.0140583	−	0.999901i	$-0.504475\pi$
$233$	−23299.8	−0.0281166	−0.0140583	+	0.999901i	$0.504475\pi$
$234$	1.23750e6	1.47742
$235$	0	0
$236$	2.20862e6	2.58132
$237$	364686.	0.421743
$238$	−283032.	−0.323887
$239$	4871.64	0.00551671	0.00275836	−	0.999996i	$-0.499122\pi$
$239$	4871.64	0.00551671	0.00275836	+	0.999996i	$0.499122\pi$
$240$	0	0
$241$	918873.	1.01909	0.509545	−	0.860444i	$-0.329814\pi$
$241$	918873.	1.01909	0.509545	+	0.860444i	$0.329814\pi$
$242$	−1.61919e6	−1.77730
$243$	−380672.	−0.413557
$244$	−3.09601e6	−3.32911
$245$	0	0
$246$	1.02280e6	1.07759
$247$	−640362.	−0.667856
$248$	−1.45040e6	−1.49748
$249$	−269796.	−0.275764
$250$	0	0
$251$	1.47118e6	1.47395	0.736973	−	0.675922i	$-0.236254\pi$
$251$	1.47118e6	1.47395	0.736973	+	0.675922i	$0.236254\pi$
$252$	801859.	0.795421
$253$	−158458.	−0.155637
$254$	−3.76747e6	−3.66409
$255$	0	0
$256$	−645377.	−0.615480
$257$	813506.	0.768295	0.384147	−	0.923272i	$-0.374495\pi$
$257$	813506.	0.768295	0.384147	+	0.923272i	$0.374495\pi$
$258$	535355.	0.500717
$259$	−51067.0	−0.0473033
$260$	0	0
$261$	3.75147e6	3.40879
$262$	−644546.	−0.580098
$263$	−691865.	−0.616782	−0.308391	−	0.951260i	$-0.599791\pi$
$263$	−691865.	−0.616782	−0.308391	+	0.951260i	$0.599791\pi$
$264$	1.15905e6	1.02351
$265$	0	0
$266$	−583242.	−0.505411
$267$	2.39552e6	2.05647
$268$	1.16830e6	0.993610
$269$	−759828.	−0.640228	−0.320114	−	0.947379i	$-0.603721\pi$
$269$	−759828.	−0.640228	−0.320114	+	0.947379i	$0.603721\pi$
$270$	0	0
$271$	954020.	0.789104	0.394552	−	0.918874i	$-0.370900\pi$
$271$	954020.	0.789104	0.394552	+	0.918874i	$0.370900\pi$
$272$	−3.62895e6	−2.97412
$273$	−124799.	−0.101346
$274$	3.26209e6	2.62494
$275$	0	0
$276$	−4.02611e6	−3.18136
$277$	−1.03398e6	−0.809680	−0.404840	−	0.914387i	$-0.632673\pi$
$277$	−1.03398e6	−0.809680	−0.404840	+	0.914387i	$0.632673\pi$
$278$	−2.04017e6	−1.58327
$279$	−1.50683e6	−1.15892
$280$	0	0
$281$	2.05117e6	1.54966	0.774829	−	0.632171i	$-0.217836\pi$
$281$	2.05117e6	1.54966	0.774829	+	0.632171i	$0.217836\pi$
$282$	−2.04580e6	−1.53193
$283$	2.37044e6	1.75940	0.879698	−	0.475533i	$-0.157745\pi$
$283$	2.37044e6	1.75940	0.879698	+	0.475533i	$0.157745\pi$
$284$	706553.	0.519815
$285$	0	0
$286$	−205943.	−0.148879
$287$	−69992.7	−0.0501589
$288$	6.34583e6	4.50824
$289$	420259.	0.295987
$290$	0	0
$291$	2.30912e6	1.59850
$292$	−2.77447e6	−1.90425
$293$	−1.48623e6	−1.01138	−0.505692	−	0.862714i	$-0.668763\pi$
$293$	−1.48623e6	−1.01138	−0.505692	+	0.862714i	$0.668763\pi$
$294$	4.75259e6	3.20673
$295$	0	0
$296$	−1.27264e6	−0.844263
$297$	633746.	0.416892
$298$	−4.79153e6	−3.12560
$299$	425200.	0.275052
$300$	0	0
$301$	−36635.5	−0.0233070
$302$	−5.32702e6	−3.36099
$303$	−2.05597e6	−1.28650
$304$	−7.47815e6	−4.64098
$305$	0	0
$306$	−7.32787e6	−4.47378
$307$	1.62571e6	0.984456	0.492228	−	0.870466i	$-0.336183\pi$
$307$	1.62571e6	0.984456	0.492228	+	0.870466i	$0.336183\pi$
$308$	−133445.	−0.0801539
$309$	808378.	0.481636
$310$	0	0
$311$	2.07269e6	1.21516	0.607581	−	0.794258i	$-0.292140\pi$
$311$	2.07269e6	1.21516	0.607581	+	0.794258i	$0.292140\pi$
$312$	−3.11013e6	−1.80881
$313$	345918.	0.199578	0.0997889	−	0.995009i	$-0.468183\pi$
$313$	345918.	0.199578	0.0997889	+	0.995009i	$0.468183\pi$
$314$	−3.66981e6	−2.10048
$315$	0	0
$316$	−1.04637e6	−0.589479
$317$	−574435.	−0.321065	−0.160532	−	0.987031i	$-0.551321\pi$
$317$	−574435.	−0.321065	−0.160532	+	0.987031i	$0.551321\pi$
$318$	−1.11548e6	−0.618579
$319$	−624316.	−0.343501
$320$	0	0
$321$	−5.49417e6	−2.97604
$322$	387272.	0.208150
$323$	3.79191e6	2.02233
$324$	6.26803e6	3.31718
$325$	0	0
$326$	−1.10480e6	−0.575757
$327$	1.08512e6	0.561187
$328$	−1.74429e6	−0.895229
$329$	139998.	0.0713072
$330$	0	0
$331$	−1.12898e6	−0.566393	−0.283196	−	0.959062i	$-0.591395\pi$
$331$	−1.12898e6	−0.566393	−0.283196	+	0.959062i	$0.591395\pi$
$332$	774111.	0.385441
$333$	−1.32216e6	−0.653390
$334$	−1.96900e6	−0.965784
$335$	0	0
$336$	−1.45741e6	−0.704260
$337$	370207.	0.177570	0.0887850	−	0.996051i	$-0.471702\pi$
$337$	370207.	0.177570	0.0887850	+	0.996051i	$0.471702\pi$
$338$	−3.35726e6	−1.59843
$339$	1.14072e6	0.539112
$340$	0	0
$341$	250766.	0.116784
$342$	−1.51005e7	−6.98113
$343$	−658239.	−0.302098
$344$	−912996.	−0.415980
$345$	0	0
$346$	−5.17801e6	−2.32527
$347$	−372676.	−0.166153	−0.0830764	−	0.996543i	$-0.526475\pi$
$347$	−372676.	−0.166153	−0.0830764	+	0.996543i	$0.526475\pi$
$348$	−1.58626e7	−7.02146
$349$	−2.14587e6	−0.943060	−0.471530	−	0.881850i	$-0.656298\pi$
$349$	−2.14587e6	−0.943060	−0.471530	+	0.881850i	$0.656298\pi$
$350$	0	0
$351$	−1.70056e6	−0.736759
$352$	−1.05607e6	−0.454292
$353$	2.87740e6	1.22903	0.614517	−	0.788904i	$-0.289351\pi$
$353$	2.87740e6	1.22903	0.614517	+	0.788904i	$0.289351\pi$
$354$	−8.10591e6	−3.43790
$355$	0	0
$356$	−6.87332e6	−2.87436
$357$	739003.	0.306885
$358$	3.94375e6	1.62630
$359$	647359.	0.265100	0.132550	−	0.991176i	$-0.457684\pi$
$359$	647359.	0.265100	0.132550	+	0.991176i	$0.457684\pi$
$360$	0	0
$361$	5.33787e6	2.15576
$362$	4.85237e6	1.94618
$363$	4.22775e6	1.68400
$364$	358080.	0.141653
$365$	0	0
$366$	1.13627e7	4.43384
$367$	−3.06021e6	−1.18600	−0.593001	−	0.805202i	$-0.702057\pi$
$367$	−3.06021e6	−1.18600	−0.593001	+	0.805202i	$0.702057\pi$
$368$	4.96549e6	1.91136
$369$	−1.81215e6	−0.692834
$370$	0	0
$371$	76335.0	0.0287931
$372$	6.37147e6	2.38716
$373$	−3.54156e6	−1.31802	−0.659010	−	0.752134i	$-0.729025\pi$
$373$	−3.54156e6	−1.31802	−0.659010	+	0.752134i	$0.729025\pi$
$374$	1.21950e6	0.450819
$375$	0	0
$376$	3.48890e6	1.27268
$377$	1.67526e6	0.607057
$378$	−1.54888e6	−0.557554
$379$	−3.92757e6	−1.40451	−0.702257	−	0.711923i	$-0.747824\pi$
$379$	−3.92757e6	−1.40451	−0.702257	+	0.711923i	$0.747824\pi$
$380$	0	0
$381$	9.83696e6	3.47175
$382$	−236560.	−0.0829437
$383$	1.29688e6	0.451754	0.225877	−	0.974156i	$-0.427475\pi$
$383$	1.29688e6	0.451754	0.225877	+	0.974156i	$0.427475\pi$
$384$	−2.04621e6	−0.708145
$385$	0	0
$386$	−8.74158e6	−2.98622
$387$	−948517.	−0.321934
$388$	−6.62541e6	−2.23426
$389$	−100541.	−0.0336874	−0.0168437	−	0.999858i	$-0.505362\pi$
$389$	−100541.	−0.0336874	−0.0168437	+	0.999858i	$0.505362\pi$
$390$	0	0
$391$	−2.51783e6	−0.832884
$392$	−8.10508e6	−2.66405
$393$	1.68293e6	0.549647
$394$	−8.44603e6	−2.74102
$395$	0	0
$396$	−3.45497e6	−1.10715
$397$	−3.36979e6	−1.07307	−0.536533	−	0.843879i	$-0.680266\pi$
$397$	−3.36979e6	−1.07307	−0.536533	+	0.843879i	$0.680266\pi$
$398$	−1.97914e6	−0.626281
$399$	1.52286e6	0.478880
$400$	0	0
$401$	4.73407e6	1.47019	0.735095	−	0.677964i	$-0.237138\pi$
$401$	4.73407e6	1.47019	0.735095	+	0.677964i	$0.237138\pi$
$402$	−4.28779e6	−1.32333
$403$	−672894.	−0.206388
$404$	5.89906e6	1.79817
$405$	0	0
$406$	1.52583e6	0.459400
$407$	220032.	0.0658416
$408$	1.84167e7	5.47724
$409$	−84169.8	−0.0248799	−0.0124399	−	0.999923i	$-0.503960\pi$
$409$	−84169.8	−0.0248799	−0.0124399	+	0.999923i	$0.503960\pi$
$410$	0	0
$411$	−8.51740e6	−2.48715
$412$	−2.31943e6	−0.673191
$413$	554705.	0.160025
$414$	1.00267e7	2.87513
$415$	0	0
$416$	2.83380e6	0.802854
$417$	5.32694e6	1.50016
$418$	2.51301e6	0.703483
$419$	−1.45191e6	−0.404022	−0.202011	−	0.979383i	$-0.564748\pi$
$419$	−1.45191e6	−0.404022	−0.202011	+	0.979383i	$0.564748\pi$
$420$	0	0
$421$	4.69910e6	1.29214	0.646070	−	0.763278i	$-0.276411\pi$
$421$	4.69910e6	1.29214	0.646070	+	0.763278i	$0.276411\pi$
$422$	3.44992e6	0.943034
$423$	3.62464e6	0.984950
$424$	1.90235e6	0.513896
$425$	0	0
$426$	−2.59314e6	−0.692311
$427$	−777577.	−0.206383
$428$	1.57641e7	4.15967
$429$	537723.	0.141064
$430$	0	0
$431$	3.34282e6	0.866803	0.433401	−	0.901201i	$-0.357313\pi$
$431$	3.34282e6	0.866803	0.433401	+	0.901201i	$0.357313\pi$
$432$	−1.98592e7	−5.11979
$433$	−629642.	−0.161389	−0.0806945	−	0.996739i	$-0.525714\pi$
$433$	−629642.	−0.161389	−0.0806945	+	0.996739i	$0.525714\pi$
$434$	−612872.	−0.156187
$435$	0	0
$436$	−3.11347e6	−0.784383
$437$	−5.18847e6	−1.29968
$438$	1.01826e7	2.53615
$439$	6.24963e6	1.54772	0.773861	−	0.633355i	$-0.218323\pi$
$439$	6.24963e6	1.54772	0.773861	+	0.633355i	$0.218323\pi$
$440$	0	0
$441$	−8.42041e6	−2.06175
$442$	−3.27235e6	−0.796716
$443$	−6.58305e6	−1.59374	−0.796871	−	0.604149i	$-0.793513\pi$
$443$	−6.58305e6	−1.59374	−0.796871	+	0.604149i	$0.793513\pi$
$444$	5.59059e6	1.34586
$445$	0	0
$446$	1.75534e6	0.417855
$447$	1.25108e7	2.96153
$448$	884842.	0.208291
$449$	1.62106e6	0.379476	0.189738	−	0.981835i	$-0.439236\pi$
$449$	1.62106e6	0.379476	0.189738	+	0.981835i	$0.439236\pi$
$450$	0	0
$451$	301577.	0.0698163
$452$	−3.27300e6	−0.753528
$453$	1.39090e7	3.18456
$454$	1.63495e6	0.372275
$455$	0	0
$456$	3.79512e7	8.54699
$457$	6.01194e6	1.34656	0.673278	−	0.739390i	$-0.264886\pi$
$457$	6.01194e6	1.34656	0.673278	+	0.739390i	$0.264886\pi$
$458$	−1.06979e7	−2.38306
$459$	1.00699e7	2.23097
$460$	0	0
$461$	−1.97072e6	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$461$	−1.97072e6	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$462$	489758.	0.106752
$463$	925538.	0.200651	0.100326	−	0.994955i	$-0.468012\pi$
$463$	925538.	0.200651	0.100326	+	0.994955i	$0.468012\pi$
$464$	1.95637e7	4.21848
$465$	0	0
$466$	−245357.	−0.0523401
$467$	−1.87994e6	−0.398890	−0.199445	−	0.979909i	$-0.563914\pi$
$467$	−1.87994e6	−0.398890	−0.199445	+	0.979909i	$0.563914\pi$
$468$	9.27090e6	1.95662
$469$	293423.	0.0615973
$470$	0	0
$471$	9.58195e6	1.99022
$472$	1.38238e7	2.85610
$473$	157851.	0.0324411
$474$	3.84031e6	0.785091
$475$	0	0
$476$	−2.12038e6	−0.428939
$477$	1.97636e6	0.397713
$478$	51300.6	0.0102696
$479$	8.18229e6	1.62943	0.814716	−	0.579860i	$-0.196893\pi$
$479$	8.18229e6	1.62943	0.814716	+	0.579860i	$0.196893\pi$
$480$	0	0
$481$	−590425.	−0.116360
$482$	9.67615e6	1.89708
$483$	−1.01118e6	−0.197224
$484$	−1.21304e7	−2.35376
$485$	0	0
$486$	−4.00865e6	−0.769853
$487$	1.84424e6	0.352367	0.176184	−	0.984357i	$-0.443625\pi$
$487$	1.84424e6	0.352367	0.176184	+	0.984357i	$0.443625\pi$
$488$	−1.93780e7	−3.68350
$489$	2.88465e6	0.545534
$490$	0	0
$491$	−4.29014e6	−0.803096	−0.401548	−	0.915838i	$-0.631528\pi$
$491$	−4.29014e6	−0.803096	−0.401548	+	0.915838i	$0.631528\pi$
$492$	7.66248e6	1.42711
$493$	−9.92009e6	−1.83822
$494$	−6.74330e6	−1.24324
$495$	0	0
$496$	−7.85806e6	−1.43420
$497$	177454.	0.0322252
$498$	−2.84108e6	−0.513346
$499$	−7.80338e6	−1.40291	−0.701457	−	0.712711i	$-0.747467\pi$
$499$	−7.80338e6	−1.40291	−0.701457	+	0.712711i	$0.747467\pi$
$500$	0	0
$501$	5.14111e6	0.915087
$502$	1.54922e7	2.74381
$503$	−673490.	−0.118689	−0.0593446	−	0.998238i	$-0.518901\pi$
$503$	−673490.	−0.118689	−0.0593446	+	0.998238i	$0.518901\pi$
$504$	5.01886e6	0.880094
$505$	0	0
$506$	−1.66864e6	−0.289725
$507$	8.76589e6	1.51452
$508$	−2.82246e7	−4.85253
$509$	9.44081e6	1.61516	0.807579	−	0.589760i	$-0.200778\pi$
$509$	9.44081e6	1.61516	0.807579	+	0.589760i	$0.200778\pi$
$510$	0	0
$511$	−696821.	−0.118051
$512$	−9.17757e6	−1.54722
$513$	2.07510e7	3.48134
$514$	8.56659e6	1.43021
$515$	0	0
$516$	4.01069e6	0.663124
$517$	−603210.	−0.0992527
$518$	−537759.	−0.0880569
$519$	1.35199e7	2.20321
$520$	0	0
$521$	−1.01037e7	−1.63074	−0.815369	−	0.578941i	$-0.803466\pi$
$521$	−1.01037e7	−1.63074	−0.815369	+	0.578941i	$0.803466\pi$
$522$	3.95046e7	6.34559
$523$	−1.22441e6	−0.195737	−0.0978687	−	0.995199i	$-0.531203\pi$
$523$	−1.22441e6	−0.195737	−0.0978687	+	0.995199i	$0.531203\pi$
$524$	−4.82872e6	−0.768252
$525$	0	0
$526$	−7.28565e6	−1.14816
$527$	3.98455e6	0.624961
$528$	6.27953e6	0.980262
$529$	−2.99120e6	−0.464735
$530$	0	0
$531$	1.43617e7	2.21039
$532$	−4.36944e6	−0.669340
$533$	−809239.	−0.123384
$534$	2.52259e7	3.82819
$535$	0	0
$536$	7.31240e6	1.09938
$537$	−1.02972e7	−1.54093
$538$	−8.00133e6	−1.19181
$539$	1.40132e6	0.207761
$540$	0	0
$541$	−2.66077e6	−0.390853	−0.195426	−	0.980718i	$-0.562609\pi$
$541$	−2.66077e6	−0.390853	−0.195426	+	0.980718i	$0.562609\pi$
$542$	1.00463e7	1.46895
$543$	−1.26696e7	−1.84402
$544$	−1.67804e7	−2.43112
$545$	0	0
$546$	−1.31420e6	−0.188659
$547$	−7.44368e6	−1.06370	−0.531850	−	0.846839i	$-0.678503\pi$
$547$	−7.44368e6	−1.06370	−0.531850	+	0.846839i	$0.678503\pi$
$548$	2.44385e7	3.47634
$549$	−2.01320e7	−2.85072
$550$	0	0
$551$	−2.04423e7	−2.86847
$552$	−2.51996e7	−3.52002
$553$	−262801.	−0.0365438
$554$	−1.08883e7	−1.50725
$555$	0	0
$556$	−1.52843e7	−2.09680
$557$	−5.55246e6	−0.758311	−0.379155	−	0.925333i	$-0.623785\pi$
$557$	−5.55246e6	−0.758311	−0.379155	+	0.925333i	$0.623785\pi$
$558$	−1.58676e7	−2.15738
$559$	−423571.	−0.0573320
$560$	0	0
$561$	−3.18414e6	−0.427154
$562$	2.15998e7	2.88475
$563$	2.05400e6	0.273105	0.136552	−	0.990633i	$-0.456398\pi$
$563$	2.05400e6	0.273105	0.136552	+	0.990633i	$0.456398\pi$
$564$	−1.53264e7	−2.02881
$565$	0	0
$566$	2.49618e7	3.27518
$567$	1.57424e6	0.205643
$568$	4.42234e6	0.575150
$569$	5.13151e6	0.664453	0.332227	−	0.943200i	$-0.392200\pi$
$569$	5.13151e6	0.664453	0.332227	+	0.943200i	$0.392200\pi$
$570$	0	0
$571$	−1.13394e7	−1.45546	−0.727730	−	0.685863i	$-0.759425\pi$
$571$	−1.13394e7	−1.45546	−0.727730	+	0.685863i	$0.759425\pi$
$572$	−1.54286e6	−0.197167
$573$	617664.	0.0785898
$574$	−737055.	−0.0933728
$575$	0	0
$576$	2.29091e7	2.87708
$577$	9.19195e6	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$577$	9.19195e6	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$578$	4.42552e6	0.550992
$579$	2.28245e7	2.82946
$580$	0	0
$581$	194421.	0.0238948
$582$	2.43160e7	2.97567
$583$	−328904.	−0.0400772
$584$	−1.73655e7	−2.10695
$585$	0	0
$586$	−1.56506e7	−1.88273
$587$	−7.32138e6	−0.876997	−0.438498	−	0.898732i	$-0.644490\pi$
$587$	−7.32138e6	−0.876997	−0.438498	+	0.898732i	$0.644490\pi$
$588$	3.56047e7	4.24683
$589$	8.21094e6	0.975225
$590$	0	0
$591$	2.20528e7	2.59714
$592$	−6.89498e6	−0.808591
$593$	−8.89330e6	−1.03855	−0.519274	−	0.854608i	$-0.673797\pi$
$593$	−8.89330e6	−1.03855	−0.519274	+	0.854608i	$0.673797\pi$
$594$	6.67363e6	0.776061
$595$	0	0
$596$	−3.58965e7	−4.13939
$597$	5.16758e6	0.593406
$598$	4.47755e6	0.512021
$599$	7.52622e6	0.857057	0.428529	−	0.903528i	$-0.359032\pi$
$599$	7.52622e6	0.857057	0.428529	+	0.903528i	$0.359032\pi$
$600$	0	0
$601$	1.53849e7	1.73743	0.868716	−	0.495311i	$-0.164946\pi$
$601$	1.53849e7	1.73743	0.868716	+	0.495311i	$0.164946\pi$
$602$	−385789.	−0.0433869
$603$	7.59690e6	0.850830
$604$	−3.99081e7	−4.45112
$605$	0	0
$606$	−2.16503e7	−2.39487
$607$	1.10155e7	1.21348	0.606740	−	0.794900i	$-0.292477\pi$
$607$	1.10155e7	1.21348	0.606740	+	0.794900i	$0.292477\pi$
$608$	−3.45793e7	−3.79365
$609$	−3.98397e6	−0.435285
$610$	0	0
$611$	1.61863e6	0.175406
$612$	−5.48978e7	−5.92484
$613$	8.89814e6	0.956419	0.478209	−	0.878246i	$-0.341286\pi$
$613$	8.89814e6	0.956419	0.478209	+	0.878246i	$0.341286\pi$
$614$	1.71194e7	1.83260
$615$	0	0
$616$	−835235.	−0.0886864
$617$	−7.40581e6	−0.783177	−0.391588	−	0.920140i	$-0.628074\pi$
$617$	−7.40581e6	−0.783177	−0.391588	+	0.920140i	$0.628074\pi$
$618$	8.51259e6	0.896583
$619$	1.41475e7	1.48406	0.742032	−	0.670364i	$-0.233862\pi$
$619$	1.41475e7	1.48406	0.742032	+	0.670364i	$0.233862\pi$
$620$	0	0
$621$	−1.37787e7	−1.43377
$622$	2.18264e7	2.26207
$623$	−1.72627e6	−0.178192
$624$	−1.68502e7	−1.73238
$625$	0	0
$626$	3.64267e6	0.371522
$627$	−6.56153e6	−0.666555
$628$	−2.74929e7	−2.78177
$629$	3.49621e6	0.352347
$630$	0	0
$631$	9.57148e6	0.956986	0.478493	−	0.878091i	$-0.341183\pi$
$631$	9.57148e6	0.956986	0.478493	+	0.878091i	$0.341183\pi$
$632$	−6.54927e6	−0.652229
$633$	−9.00781e6	−0.893532
$634$	−6.04906e6	−0.597675
$635$	0	0
$636$	−8.35680e6	−0.819214
$637$	−3.76023e6	−0.367169
$638$	−6.57433e6	−0.639440
$639$	4.59440e6	0.445119
$640$	0	0
$641$	−637566.	−0.0612887	−0.0306443	−	0.999530i	$-0.509756\pi$
$641$	−637566.	−0.0612887	−0.0306443	+	0.999530i	$0.509756\pi$
$642$	−5.78561e7	−5.54002
$643$	1.89702e7	1.80944	0.904718	−	0.426010i	$-0.140081\pi$
$643$	1.89702e7	1.80944	0.904718	+	0.426010i	$0.140081\pi$
$644$	2.90131e6	0.275664
$645$	0	0
$646$	3.99306e7	3.76465
$647$	−2.02807e7	−1.90468	−0.952338	−	0.305044i	$-0.901329\pi$
$647$	−2.02807e7	−1.90468	−0.952338	+	0.305044i	$0.901329\pi$
$648$	3.92318e7	3.67029
$649$	−2.39006e6	−0.222739
$650$	0	0
$651$	1.60022e6	0.147989
$652$	−8.27676e6	−0.762503
$653$	3.76628e6	0.345645	0.172822	−	0.984953i	$-0.444711\pi$
$653$	3.76628e6	0.345645	0.172822	+	0.984953i	$0.444711\pi$
$654$	1.14268e7	1.04467
$655$	0	0
$656$	−9.45029e6	−0.857404
$657$	−1.80411e7	−1.63061
$658$	1.47425e6	0.132741
$659$	−1.70994e7	−1.53379	−0.766897	−	0.641770i	$-0.778200\pi$
$659$	−1.70994e7	−1.53379	−0.766897	+	0.641770i	$0.778200\pi$
$660$	0	0
$661$	875240.	0.0779154	0.0389577	−	0.999241i	$-0.487596\pi$
$661$	875240.	0.0779154	0.0389577	+	0.999241i	$0.487596\pi$
$662$	−1.18887e7	−1.05436
$663$	8.54417e6	0.754894
$664$	4.84518e6	0.426472
$665$	0	0
$666$	−1.39229e7	−1.21631
$667$	1.35737e7	1.18136
$668$	−1.47511e7	−1.27904
$669$	−4.58324e6	−0.395920
$670$	0	0
$671$	3.35034e6	0.287265
$672$	−6.73913e6	−0.575679
$673$	1.59835e7	1.36030	0.680149	−	0.733074i	$-0.261915\pi$
$673$	1.59835e7	1.36030	0.680149	+	0.733074i	$0.261915\pi$
$674$	3.89844e6	0.330553
$675$	0	0
$676$	−2.51515e7	−2.11688
$677$	2.27744e7	1.90974	0.954871	−	0.297020i	$-0.0959926\pi$
$677$	2.27744e7	1.90974	0.954871	+	0.297020i	$0.0959926\pi$
$678$	1.20123e7	1.00358
$679$	−1.66400e6	−0.138509
$680$	0	0
$681$	−4.26888e6	−0.352733
$682$	2.64068e6	0.217398
$683$	1.16349e7	0.954354	0.477177	−	0.878807i	$-0.341660\pi$
$683$	1.16349e7	0.954354	0.477177	+	0.878807i	$0.341660\pi$
$684$	−1.13128e8	−9.24545
$685$	0	0
$686$	−6.93156e6	−0.562368
$687$	2.79325e7	2.25797
$688$	−4.94647e6	−0.398404
$689$	882566.	0.0708271
$690$	0	0
$691$	−5.50626e6	−0.438694	−0.219347	−	0.975647i	$-0.570393\pi$
$691$	−5.50626e6	−0.438694	−0.219347	+	0.975647i	$0.570393\pi$
$692$	−3.87918e7	−3.07946
$693$	−867731.	−0.0686360
$694$	−3.92444e6	−0.309300
$695$	0	0
$696$	−9.92848e7	−7.76890
$697$	4.79192e6	0.373618
$698$	−2.25970e7	−1.75554
$699$	640633.	0.0495926
$700$	0	0
$701$	−1.26842e7	−0.974916	−0.487458	−	0.873146i	$-0.662076\pi$
$701$	−1.26842e7	−0.974916	−0.487458	+	0.873146i	$0.662076\pi$
$702$	−1.79077e7	−1.37151
$703$	7.20462e6	0.549823
$704$	−3.81251e6	−0.289921
$705$	0	0
$706$	3.03004e7	2.28789
$707$	1.48158e6	0.111475
$708$	−6.07266e7	−4.55298
$709$	919145.	0.0686702	0.0343351	−	0.999410i	$-0.489069\pi$
$709$	919145.	0.0686702	0.0343351	+	0.999410i	$0.489069\pi$
$710$	0	0
$711$	−6.80408e6	−0.504772
$712$	−4.30203e7	−3.18034
$713$	−5.45207e6	−0.401640
$714$	7.78203e6	0.571278
$715$	0	0
$716$	2.95452e7	2.15379
$717$	−133947.	−0.00973049
$718$	6.81699e6	0.493493
$719$	7.21135e6	0.520228	0.260114	−	0.965578i	$-0.416240\pi$
$719$	7.21135e6	0.520228	0.260114	+	0.965578i	$0.416240\pi$
$720$	0	0
$721$	−582536.	−0.0417335
$722$	5.62102e7	4.01303
$723$	−2.52646e7	−1.79749
$724$	3.63522e7	2.57742
$725$	0	0
$726$	4.45201e7	3.13483
$727$	4.15671e6	0.291685	0.145842	−	0.989308i	$-0.453411\pi$
$727$	4.15671e6	0.291685	0.145842	+	0.989308i	$0.453411\pi$
$728$	2.24123e6	0.156732
$729$	−8.84023e6	−0.616091
$730$	0	0
$731$	2.50818e6	0.173607
$732$	8.51256e7	5.87195
$733$	−4.05351e6	−0.278658	−0.139329	−	0.990246i	$-0.544495\pi$
$733$	−4.05351e6	−0.278658	−0.139329	+	0.990246i	$0.544495\pi$
$734$	−3.22254e7	−2.20779
$735$	0	0
$736$	2.29606e7	1.56239
$737$	−1.26427e6	−0.0857375
$738$	−1.90828e7	−1.28974
$739$	1.27176e7	0.856629	0.428315	−	0.903630i	$-0.359108\pi$
$739$	1.27176e7	0.856629	0.428315	+	0.903630i	$0.359108\pi$
$740$	0	0
$741$	1.76069e7	1.17798
$742$	803842.	0.0535995
$743$	1.86660e6	0.124045	0.0620224	−	0.998075i	$-0.480245\pi$
$743$	1.86660e6	0.124045	0.0620224	+	0.998075i	$0.480245\pi$
$744$	3.98792e7	2.64128
$745$	0	0
$746$	−3.72942e7	−2.45355
$747$	5.03369e6	0.330054
$748$	9.13605e6	0.597041
$749$	3.95922e6	0.257873
$750$	0	0
$751$	2.61334e7	1.69081	0.845407	−	0.534122i	$-0.179358\pi$
$751$	2.61334e7	1.69081	0.845407	+	0.534122i	$0.179358\pi$
$752$	1.89023e7	1.21891
$753$	−4.04505e7	−2.59978
$754$	1.76413e7	1.13006
$755$	0	0
$756$	−1.16036e7	−0.738396
$757$	−1.20591e6	−0.0764846	−0.0382423	−	0.999268i	$-0.512176\pi$
$757$	−1.20591e6	−0.0764846	−0.0382423	+	0.999268i	$0.512176\pi$
$758$	−4.13591e7	−2.61456
$759$	4.35685e6	0.274516
$760$	0	0
$761$	−1.63050e6	−0.102061	−0.0510303	−	0.998697i	$-0.516251\pi$
$761$	−1.63050e6	−0.102061	−0.0510303	+	0.998697i	$0.516251\pi$
$762$	1.03588e8	6.46280
$763$	−781961.	−0.0486266
$764$	−1.77223e6	−0.109846
$765$	0	0
$766$	1.36567e7	0.840958
$767$	6.41337e6	0.393639
$768$	1.77448e7	1.08560
$769$	−3.03077e6	−0.184815	−0.0924074	−	0.995721i	$-0.529456\pi$
$769$	−3.03077e6	−0.184815	−0.0924074	+	0.995721i	$0.529456\pi$
$770$	0	0
$771$	−2.23676e7	−1.35513
$772$	−6.54888e7	−3.95480
$773$	−1.56440e7	−0.941669	−0.470834	−	0.882222i	$-0.656047\pi$
$773$	−1.56440e7	−0.941669	−0.470834	+	0.882222i	$0.656047\pi$
$774$	−9.98831e6	−0.599294
$775$	0	0
$776$	−4.14686e7	−2.47210
$777$	1.40410e6	0.0834346
$778$	−1.05874e6	−0.0627104
$779$	9.87468e6	0.583015
$780$	0	0
$781$	−764595.	−0.0448543
$782$	−2.65139e7	−1.55045
$783$	−5.42871e7	−3.16441
$784$	−4.39120e7	−2.55149
$785$	0	0
$786$	1.77220e7	1.02319
$787$	−2.77750e7	−1.59852	−0.799260	−	0.600986i	$-0.794775\pi$
$787$	−2.77750e7	−1.59852	−0.799260	+	0.600986i	$0.794775\pi$
$788$	−6.32747e7	−3.63007
$789$	1.90230e7	1.08789
$790$	0	0
$791$	−822028.	−0.0467138
$792$	−2.16247e7	−1.22501
$793$	−8.99016e6	−0.507673
$794$	−3.54854e7	−1.99756
$795$	0	0
$796$	−1.48270e7	−0.829414
$797$	646020.	0.0360247	0.0180123	−	0.999838i	$-0.494266\pi$
$797$	646020.	0.0360247	0.0180123	+	0.999838i	$0.494266\pi$
$798$	1.60364e7	0.891454
$799$	−9.58473e6	−0.531145
$800$	0	0
$801$	−4.46941e7	−2.46132
$802$	4.98519e7	2.73682
$803$	3.00239e6	0.164315
$804$	−3.21226e7	−1.75255
$805$	0	0
$806$	−7.08588e6	−0.384199
$807$	2.08917e7	1.12925
$808$	3.69224e7	1.98958
$809$	−1.67691e6	−0.0900823	−0.0450412	−	0.998985i	$-0.514342\pi$
$809$	−1.67691e6	−0.0900823	−0.0450412	+	0.998985i	$0.514342\pi$
$810$	0	0
$811$	1.09231e7	0.583169	0.291585	−	0.956545i	$-0.405817\pi$
$811$	1.09231e7	0.583169	0.291585	+	0.956545i	$0.405817\pi$
$812$	1.14310e7	0.608406
$813$	−2.62310e7	−1.39184
$814$	2.31704e6	0.122567
$815$	0	0
$816$	9.97789e7	5.24582
$817$	5.16860e6	0.270905
$818$	−886346.	−0.0463148
$819$	2.32843e6	0.121298
$820$	0	0
$821$	1.94364e7	1.00637	0.503186	−	0.864178i	$-0.332161\pi$
$821$	1.94364e7	1.00637	0.503186	+	0.864178i	$0.332161\pi$
$822$	−8.96921e7	−4.62993
$823$	3.08462e7	1.58746	0.793730	−	0.608271i	$-0.208136\pi$
$823$	3.08462e7	1.58746	0.793730	+	0.608271i	$0.208136\pi$
$824$	−1.45174e7	−0.744853
$825$	0	0
$826$	5.84130e6	0.297892
$827$	1.97925e7	1.00632	0.503161	−	0.864193i	$-0.332170\pi$
$827$	1.97925e7	1.00632	0.503161	+	0.864193i	$0.332170\pi$
$828$	7.51167e7	3.80768
$829$	−1.75755e7	−0.888223	−0.444111	−	0.895972i	$-0.646481\pi$
$829$	−1.75755e7	−0.888223	−0.444111	+	0.895972i	$0.646481\pi$
$830$	0	0
$831$	2.84296e7	1.42813
$832$	1.02303e7	0.512367
$833$	2.22663e7	1.11182
$834$	5.60951e7	2.79261
$835$	0	0
$836$	1.88266e7	0.931657
$837$	2.18052e7	1.07584
$838$	−1.52893e7	−0.752103
$839$	−1.50238e7	−0.736842	−0.368421	−	0.929659i	$-0.620101\pi$
$839$	−1.50238e7	−0.736842	−0.368421	+	0.929659i	$0.620101\pi$
$840$	0	0
$841$	3.29682e7	1.60733
$842$	4.94837e7	2.40537
$843$	−5.63974e7	−2.73332
$844$	2.58456e7	1.24891
$845$	0	0
$846$	3.81691e7	1.83352
$847$	−3.04661e6	−0.145918
$848$	1.03066e7	0.492183
$849$	−6.51759e7	−3.10326
$850$	0	0
$851$	−4.78387e6	−0.226441
$852$	−1.94269e7	−0.916861
$853$	−3.88390e7	−1.82766	−0.913829	−	0.406099i	$-0.866889\pi$
$853$	−3.88390e7	−1.82766	−0.913829	+	0.406099i	$0.866889\pi$
$854$	−8.18824e6	−0.384190
$855$	0	0
$856$	9.86679e7	4.60248
$857$	3.57330e6	0.166195	0.0830975	−	0.996541i	$-0.473519\pi$
$857$	3.57330e6	0.166195	0.0830975	+	0.996541i	$0.473519\pi$
$858$	5.66247e6	0.262596
$859$	3.27850e6	0.151598	0.0757988	−	0.997123i	$-0.475849\pi$
$859$	3.27850e6	0.151598	0.0757988	+	0.997123i	$0.475849\pi$
$860$	0	0
$861$	1.92447e6	0.0884713
$862$	3.52014e7	1.61359
$863$	−1.93441e7	−0.884139	−0.442070	−	0.896981i	$-0.645756\pi$
$863$	−1.93441e7	−0.884139	−0.442070	+	0.896981i	$0.645756\pi$
$864$	−9.18298e7	−4.18504
$865$	0	0
$866$	−6.63042e6	−0.300432
$867$	−1.15551e7	−0.522068
$868$	−4.59142e6	−0.206846
$869$	1.13233e6	0.0508655
$870$	0	0
$871$	3.39248e6	0.151521
$872$	−1.94873e7	−0.867881
$873$	−4.30820e7	−1.91320
$874$	−5.46370e7	−2.41940
$875$	0	0
$876$	7.62847e7	3.35875
$877$	2.57531e7	1.13066	0.565329	−	0.824866i	$-0.308749\pi$
$877$	2.57531e7	1.13066	0.565329	+	0.824866i	$0.308749\pi$
$878$	6.58114e7	2.88115
$879$	4.08642e7	1.78390
$880$	0	0
$881$	4.39384e6	0.190724	0.0953618	−	0.995443i	$-0.469599\pi$
$881$	4.39384e6	0.190724	0.0953618	+	0.995443i	$0.469599\pi$
$882$	−8.86708e7	−3.83804
$883$	−2.21529e7	−0.956156	−0.478078	−	0.878317i	$-0.658666\pi$
$883$	−2.21529e7	−0.956156	−0.478078	+	0.878317i	$0.658666\pi$
$884$	−2.45153e7	−1.05513
$885$	0	0
$886$	−6.93226e7	−2.96681
$887$	4.36187e7	1.86150	0.930750	−	0.365655i	$-0.119155\pi$
$887$	4.36187e7	1.86150	0.930750	+	0.365655i	$0.119155\pi$
$888$	3.49917e7	1.48913
$889$	−7.08874e6	−0.300825
$890$	0	0
$891$	−6.78294e6	−0.286236
$892$	1.31504e7	0.553385
$893$	−1.97512e7	−0.828828
$894$	1.31744e8	5.51300
$895$	0	0
$896$	1.47455e6	0.0613604
$897$	−1.16910e7	−0.485143
$898$	1.70705e7	0.706409
$899$	−2.14808e7	−0.886443
$900$	0	0
$901$	−5.22613e6	−0.214471
$902$	3.17574e6	0.129966
$903$	1.00730e6	0.0411094
$904$	−2.04858e7	−0.833742
$905$	0	0
$906$	1.46468e8	5.92818
$907$	−1.38621e7	−0.559515	−0.279758	−	0.960071i	$-0.590254\pi$
$907$	−1.38621e7	−0.559515	−0.279758	+	0.960071i	$0.590254\pi$
$908$	1.22484e7	0.493022
$909$	3.83589e7	1.53977
$910$	0	0
$911$	−2.31037e7	−0.922329	−0.461164	−	0.887315i	$-0.652568\pi$
$911$	−2.31037e7	−0.922329	−0.461164	+	0.887315i	$0.652568\pi$
$912$	2.05614e8	8.18587
$913$	−837702.	−0.0332593
$914$	6.33085e7	2.50666
$915$	0	0
$916$	−8.01451e7	−3.15601
$917$	−1.21275e6	−0.0476266
$918$	1.06041e8	4.15305
$919$	−2.27313e7	−0.887842	−0.443921	−	0.896066i	$-0.646413\pi$
$919$	−2.27313e7	−0.887842	−0.443921	+	0.896066i	$0.646413\pi$
$920$	0	0
$921$	−4.46992e7	−1.73640
$922$	−2.07526e7	−0.803978
$923$	2.05168e6	0.0792694
$924$	3.66910e6	0.141377
$925$	0	0
$926$	9.74634e6	0.373520
$927$	−1.50822e7	−0.576455
$928$	9.04635e7	3.44829
$929$	−3.32467e7	−1.26389	−0.631945	−	0.775013i	$-0.717743\pi$
$929$	−3.32467e7	−1.26389	−0.631945	+	0.775013i	$0.717743\pi$
$930$	0	0
$931$	4.58840e7	1.73495
$932$	−1.83813e6	−0.0693165
$933$	−5.69892e7	−2.14333
$934$	−1.97967e7	−0.742548
$935$	0	0
$936$	5.80269e7	2.16491
$937$	−1.72533e7	−0.641981	−0.320991	−	0.947082i	$-0.604016\pi$
$937$	−1.72533e7	−0.641981	−0.320991	+	0.947082i	$0.604016\pi$
$938$	3.08988e6	0.114666
$939$	−9.51110e6	−0.352019
$940$	0	0
$941$	1.12167e6	0.0412945	0.0206473	−	0.999787i	$-0.493427\pi$
$941$	1.12167e6	0.0412945	0.0206473	+	0.999787i	$0.493427\pi$
$942$	1.00902e8	3.70488
$943$	−6.55679e6	−0.240111
$944$	7.48954e7	2.73543
$945$	0	0
$946$	1.66225e6	0.0603903
$947$	−3.89113e7	−1.40994	−0.704970	−	0.709237i	$-0.749040\pi$
$947$	−3.89113e7	−1.40994	−0.704970	+	0.709237i	$0.749040\pi$
$948$	2.87702e7	1.03973
$949$	−8.05647e6	−0.290388
$950$	0	0
$951$	1.57942e7	0.566301
$952$	−1.32715e7	−0.474600
$953$	1.79943e7	0.641803	0.320902	−	0.947113i	$-0.396014\pi$
$953$	1.79943e7	0.641803	0.320902	+	0.947113i	$0.396014\pi$
$954$	2.08120e7	0.740358
$955$	0	0
$956$	384326.	0.0136005
$957$	1.71657e7	0.605874
$958$	8.61632e7	3.03325
$959$	6.13783e6	0.215510
$960$	0	0
$961$	−2.00011e7	−0.698626
$962$	−6.21744e6	−0.216608
$963$	1.02507e8	3.56194
$964$	7.24903e7	2.51239
$965$	0	0
$966$	−1.06482e7	−0.367140
$967$	−2.31110e7	−0.794791	−0.397395	−	0.917648i	$-0.630086\pi$
$967$	−2.31110e7	−0.794791	−0.397395	+	0.917648i	$0.630086\pi$
$968$	−7.59247e7	−2.60432
$969$	−1.04260e8	−3.56703
$970$	0	0
$971$	−3.50927e7	−1.19445	−0.597226	−	0.802073i	$-0.703730\pi$
$971$	−3.50927e7	−1.19445	−0.597226	+	0.802073i	$0.703730\pi$
$972$	−3.00314e7	−1.01955
$973$	−3.83871e6	−0.129988
$974$	1.94207e7	0.655945
$975$	0	0
$976$	−1.04987e8	−3.52786
$977$	−7.20029e6	−0.241331	−0.120666	−	0.992693i	$-0.538503\pi$
$977$	−7.20029e6	−0.241331	−0.120666	+	0.992693i	$0.538503\pi$
$978$	3.03767e7	1.01553
$979$	7.43795e6	0.248026
$980$	0	0
$981$	−2.02455e7	−0.671669
$982$	−4.51771e7	−1.49499
$983$	3.28324e7	1.08373	0.541863	−	0.840467i	$-0.317719\pi$
$983$	3.28324e7	1.08373	0.541863	+	0.840467i	$0.317719\pi$
$984$	4.79597e7	1.57902
$985$	0	0
$986$	−1.04463e8	−3.42193
$987$	−3.84929e6	−0.125773
$988$	−5.05184e7	−1.64648
$989$	−3.43195e6	−0.111571
$990$	0	0
$991$	5.19670e7	1.68090	0.840452	−	0.541885i	$-0.182289\pi$
$991$	5.19670e7	1.68090	0.840452	+	0.541885i	$0.182289\pi$
$992$	−3.63360e7	−1.17235
$993$	3.10417e7	0.999015
$994$	1.86867e6	0.0599884
$995$	0	0
$996$	−2.12844e7	−0.679849
$997$	5.30582e6	0.169050	0.0845249	−	0.996421i	$-0.473063\pi$
$997$	5.30582e6	0.169050	0.0845249	+	0.996421i	$0.473063\pi$
$998$	−8.21731e7	−2.61158
$999$	1.91328e7	0.606548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.b.1.10		10
5.4	even	2		43.6.a.b.1.1	✓	10
15.14	odd	2		387.6.a.e.1.10		10
20.19	odd	2		688.6.a.h.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.a.b.1.1	✓	10	5.4	even	2
387.6.a.e.1.10		10	15.14	odd	2
688.6.a.h.1.1		10	20.19	odd	2
1075.6.a.b.1.10		10	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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+10.5305 q^{2} -27.4953 q^{3} +78.8905 q^{4} -289.538 q^{6} +19.8137 q^{7} +493.778 q^{8} +512.989 q^{9} +O(q^{10})\)	\(q+10.5305 q^{2} -27.4953 q^{3} +78.8905 q^{4} -289.538 q^{6} +19.8137 q^{7} +493.778 q^{8} +512.989 q^{9} -85.3712 q^{11} -2169.11 q^{12} +229.081 q^{13} +208.647 q^{14} +2675.21 q^{16} -1356.51 q^{17} +5402.01 q^{18} -2795.35 q^{19} -544.783 q^{21} -898.997 q^{22} +1856.11 q^{23} -13576.6 q^{24} +2412.33 q^{26} -7423.41 q^{27} +1563.11 q^{28} +7312.96 q^{29} -2937.36 q^{31} +12370.3 q^{32} +2347.30 q^{33} -14284.7 q^{34} +40469.9 q^{36} -2577.36 q^{37} -29436.3 q^{38} -6298.65 q^{39} -3532.54 q^{41} -5736.81 q^{42} -1849.00 q^{43} -6734.97 q^{44} +19545.7 q^{46} +7065.73 q^{47} -73555.6 q^{48} -16414.4 q^{49} +37297.6 q^{51} +18072.3 q^{52} +3852.63 q^{53} -78171.9 q^{54} +9783.57 q^{56} +76858.8 q^{57} +77008.8 q^{58} +27996.1 q^{59} -39244.4 q^{61} -30931.7 q^{62} +10164.2 q^{63} +44658.1 q^{64} +24718.2 q^{66} +14809.1 q^{67} -107016. q^{68} -51034.2 q^{69} +8956.13 q^{71} +253303. q^{72} -35168.6 q^{73} -27140.8 q^{74} -220526. q^{76} -1691.52 q^{77} -66327.6 q^{78} -13263.6 q^{79} +79452.3 q^{81} -37199.3 q^{82} +9812.47 q^{83} -42978.2 q^{84} -19470.8 q^{86} -201072. q^{87} -42154.4 q^{88} -87124.9 q^{89} +4538.95 q^{91} +146429. q^{92} +80763.5 q^{93} +74405.4 q^{94} -340124. q^{96} -83982.4 q^{97} -172851. q^{98} -43794.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9}+O(q^{10}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9	\( 10 q - 8 q^{2} - 28 q^{3} + 202 q^{4} + 75 q^{6} - 60 q^{7} - 294 q^{8} + 1356 q^{9} + 745 q^{11} - 4627 q^{12} - 1917 q^{13} + 1936 q^{14} + 5354 q^{16} - 4017 q^{17} + 2725 q^{18} - 2404 q^{19} - 228 q^{21} + 5836 q^{22} - 1733 q^{23} - 10711 q^{24} - 1484 q^{26} + 2324 q^{27} + 15028 q^{28} + 6996 q^{29} - 4899 q^{31} + 7554 q^{32} + 15734 q^{33} - 27033 q^{34} + 4433 q^{36} - 1466 q^{37} - 13905 q^{38} - 26542 q^{39} + 10297 q^{41} + 37642 q^{42} - 18490 q^{43} - 36140 q^{44} + 17991 q^{46} - 48592 q^{47} - 83607 q^{48} + 29458 q^{49} + 92972 q^{51} - 14232 q^{52} - 127165 q^{53} - 92002 q^{54} - 7780 q^{56} - 34060 q^{57} + 10305 q^{58} + 99372 q^{59} + 17408 q^{61} - 28265 q^{62} - 2244 q^{63} + 47202 q^{64} - 150292 q^{66} + 2021 q^{67} - 192151 q^{68} + 1654 q^{69} + 11286 q^{71} + 298365 q^{72} - 49892 q^{73} - 125431 q^{74} - 249803 q^{76} - 98144 q^{77} + 28494 q^{78} - 91524 q^{79} - 26450 q^{81} + 158909 q^{82} + 105203 q^{83} - 357682 q^{84} + 14792 q^{86} - 181200 q^{87} + 461824 q^{88} - 62682 q^{89} - 295304 q^{91} - 183783 q^{92} + 238430 q^{93} + 7259 q^{94} - 162399 q^{96} - 108383 q^{97} - 354656 q^{98} - 270499 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 28 * q^3 + 202 * q^4 + 75 * q^6 - 60 * q^7 - 294 * q^8 + 1356 * q^9 + 745 * q^11 - 4627 * q^12 - 1917 * q^13 + 1936 * q^14 + 5354 * q^16 - 4017 * q^17 + 2725 * q^18 - 2404 * q^19 - 228 * q^21 + 5836 * q^22 - 1733 * q^23 - 10711 * q^24 - 1484 * q^26 + 2324 * q^27 + 15028 * q^28 + 6996 * q^29 - 4899 * q^31 + 7554 * q^32 + 15734 * q^33 - 27033 * q^34 + 4433 * q^36 - 1466 * q^37 - 13905 * q^38 - 26542 * q^39 + 10297 * q^41 + 37642 * q^42 - 18490 * q^43 - 36140 * q^44 + 17991 * q^46 - 48592 * q^47 - 83607 * q^48 + 29458 * q^49 + 92972 * q^51 - 14232 * q^52 - 127165 * q^53 - 92002 * q^54 - 7780 * q^56 - 34060 * q^57 + 10305 * q^58 + 99372 * q^59 + 17408 * q^61 - 28265 * q^62 - 2244 * q^63 + 47202 * q^64 - 150292 * q^66 + 2021 * q^67 - 192151 * q^68 + 1654 * q^69 + 11286 * q^71 + 298365 * q^72 - 49892 * q^73 - 125431 * q^74 - 249803 * q^76 - 98144 * q^77 + 28494 * q^78 - 91524 * q^79 - 26450 * q^81 + 158909 * q^82 + 105203 * q^83 - 357682 * q^84 + 14792 * q^86 - 181200 * q^87 + 461824 * q^88 - 62682 * q^89 - 295304 * q^91 - 183783 * q^92 + 238430 * q^93 + 7259 * q^94 - 162399 * q^96 - 108383 * q^97 - 354656 * q^98 - 270499 * q^99

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