LMFDB - Embedded newform 1075.6.a.i.1.4

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-10.0422 q^{2} -25.6441 q^{3} +68.8458 q^{4} +257.523 q^{6} -86.6514 q^{7} -370.013 q^{8} +414.621 q^{9} +O(q^{10})$	\(q-10.0422 q^{2} -25.6441 q^{3} +68.8458 q^{4} +257.523 q^{6} -86.6514 q^{7} -370.013 q^{8} +414.621 q^{9} +160.181 q^{11} -1765.49 q^{12} -74.4649 q^{13} +870.171 q^{14} +1512.68 q^{16} -1729.17 q^{17} -4163.70 q^{18} -159.238 q^{19} +2222.10 q^{21} -1608.57 q^{22} -636.899 q^{23} +9488.67 q^{24} +747.792 q^{26} -4401.06 q^{27} -5965.59 q^{28} -4482.80 q^{29} -5062.18 q^{31} -3350.24 q^{32} -4107.69 q^{33} +17364.6 q^{34} +28544.9 q^{36} -3227.74 q^{37} +1599.11 q^{38} +1909.59 q^{39} -12413.9 q^{41} -22314.8 q^{42} -1849.00 q^{43} +11027.8 q^{44} +6395.87 q^{46} +14311.8 q^{47} -38791.4 q^{48} -9298.54 q^{49} +44342.9 q^{51} -5126.60 q^{52} +22772.9 q^{53} +44196.3 q^{54} +32062.2 q^{56} +4083.53 q^{57} +45017.2 q^{58} -16509.6 q^{59} +23864.7 q^{61} +50835.5 q^{62} -35927.5 q^{63} -14762.1 q^{64} +41250.2 q^{66} -2325.18 q^{67} -119046. q^{68} +16332.7 q^{69} +70430.0 q^{71} -153415. q^{72} -2642.20 q^{73} +32413.6 q^{74} -10962.9 q^{76} -13879.9 q^{77} -19176.5 q^{78} -8047.47 q^{79} +12108.5 q^{81} +124662. q^{82} -50560.2 q^{83} +152982. q^{84} +18568.0 q^{86} +114957. q^{87} -59268.9 q^{88} +31997.0 q^{89} +6452.49 q^{91} -43847.8 q^{92} +129815. q^{93} -143722. q^{94} +85913.9 q^{96} -36690.0 q^{97} +93377.8 q^{98} +66414.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * 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 $

$2$	−10.0422	−1.77523	−0.887614	−	0.460589i	$-0.847638\pi$
$2$	−10.0422	−1.77523	−0.887614	+	0.460589i	$0.847638\pi$
$3$	−25.6441	−1.64507	−0.822535	−	0.568714i	$-0.807441\pi$
$3$	−25.6441	−1.64507	−0.822535	+	0.568714i	$0.807441\pi$
$4$	68.8458	2.15143
$5$	0	0
$5$	0	0
$6$	257.523	2.92037
$7$	−86.6514	−0.668391	−0.334195	−	0.942504i	$-0.608465\pi$
$7$	−86.6514	−0.668391	−0.334195	+	0.942504i	$0.608465\pi$
$8$	−370.013	−2.04405
$9$	414.621	1.70626
$10$	0	0
$11$	160.181	0.399143	0.199571	−	0.979883i	$-0.436045\pi$
$11$	160.181	0.399143	0.199571	+	0.979883i	$0.436045\pi$
$12$	−1765.49	−3.53926
$13$	−74.4649	−0.122206	−0.0611031	−	0.998131i	$-0.519462\pi$
$13$	−74.4649	−0.122206	−0.0611031	+	0.998131i	$0.519462\pi$
$14$	870.171	1.18655
$15$	0	0
$16$	1512.68	1.47723
$17$	−1729.17	−1.45116	−0.725578	−	0.688140i	$-0.758428\pi$
$17$	−1729.17	−1.45116	−0.725578	+	0.688140i	$0.758428\pi$
$18$	−4163.70	−3.02900
$19$	−159.238	−0.101196	−0.0505981	−	0.998719i	$-0.516113\pi$
$19$	−159.238	−0.101196	−0.0505981	+	0.998719i	$0.516113\pi$
$20$	0	0
$21$	2222.10	1.09955
$22$	−1608.57	−0.708569
$23$	−636.899	−0.251045	−0.125522	−	0.992091i	$-0.540061\pi$
$23$	−636.899	−0.251045	−0.125522	+	0.992091i	$0.540061\pi$
$24$	9488.67	3.36261
$25$	0	0
$26$	747.792	0.216944
$27$	−4401.06	−1.16184
$28$	−5965.59	−1.43800
$29$	−4482.80	−0.989815	−0.494908	−	0.868946i	$-0.664798\pi$
$29$	−4482.80	−0.989815	−0.494908	+	0.868946i	$0.664798\pi$
$30$	0	0
$31$	−5062.18	−0.946093	−0.473046	−	0.881038i	$-0.656846\pi$
$31$	−5062.18	−0.946093	−0.473046	+	0.881038i	$0.656846\pi$
$32$	−3350.24	−0.578364
$33$	−4107.69	−0.656618
$34$	17364.6	2.57613
$35$	0	0
$36$	28544.9	3.67090
$37$	−3227.74	−0.387609	−0.193805	−	0.981040i	$-0.562083\pi$
$37$	−3227.74	−0.387609	−0.193805	+	0.981040i	$0.562083\pi$
$38$	1599.11	0.179646
$39$	1909.59	0.201038
$40$	0	0
$41$	−12413.9	−1.15331	−0.576656	−	0.816987i	$-0.695643\pi$
$41$	−12413.9	−1.15331	−0.576656	+	0.816987i	$0.695643\pi$
$42$	−22314.8	−1.95195
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	11027.8	0.858728
$45$	0	0
$46$	6395.87	0.445661
$47$	14311.8	0.945042	0.472521	−	0.881319i	$-0.343344\pi$
$47$	14311.8	0.945042	0.472521	+	0.881319i	$0.343344\pi$
$48$	−38791.4	−2.43015
$49$	−9298.54	−0.553254
$50$	0	0
$51$	44342.9	2.38726
$52$	−5126.60	−0.262918
$53$	22772.9	1.11360	0.556798	−	0.830648i	$-0.312030\pi$
$53$	22772.9	1.11360	0.556798	+	0.830648i	$0.312030\pi$
$54$	44196.3	2.06254
$55$	0	0
$56$	32062.2	1.36623
$57$	4083.53	0.166475
$58$	45017.2	1.75715
$59$	−16509.6	−0.617457	−0.308728	−	0.951150i	$-0.599903\pi$
$59$	−16509.6	−0.617457	−0.308728	+	0.951150i	$0.599903\pi$
$60$	0	0
$61$	23864.7	0.821165	0.410583	−	0.911823i	$-0.365325\pi$
$61$	23864.7	0.821165	0.410583	+	0.911823i	$0.365325\pi$
$62$	50835.5	1.67953
$63$	−35927.5	−1.14045
$64$	−14762.1	−0.450502
$65$	0	0
$66$	41250.2	1.16565
$67$	−2325.18	−0.0632806	−0.0316403	−	0.999499i	$-0.510073\pi$
$67$	−2325.18	−0.0632806	−0.0316403	+	0.999499i	$0.510073\pi$
$68$	−119046.	−3.12207
$69$	16332.7	0.412986
$70$	0	0
$71$	70430.0	1.65810	0.829052	−	0.559171i	$-0.188881\pi$
$71$	70430.0	1.65810	0.829052	+	0.559171i	$0.188881\pi$
$72$	−153415.	−3.48768
$73$	−2642.20	−0.0580308	−0.0290154	−	0.999579i	$-0.509237\pi$
$73$	−2642.20	−0.0580308	−0.0290154	+	0.999579i	$0.509237\pi$
$74$	32413.6	0.688095
$75$	0	0
$76$	−10962.9	−0.217717
$77$	−13879.9	−0.266783
$78$	−19176.5	−0.356888
$79$	−8047.47	−0.145075	−0.0725374	−	0.997366i	$-0.523110\pi$
$79$	−8047.47	−0.145075	−0.0725374	+	0.997366i	$0.523110\pi$
$80$	0	0
$81$	12108.5	0.205058
$82$	124662.	2.04739
$83$	−50560.2	−0.805590	−0.402795	−	0.915290i	$-0.631961\pi$
$83$	−50560.2	−0.805590	−0.402795	+	0.915290i	$0.631961\pi$
$84$	152982.	2.36561
$85$	0	0
$86$	18568.0	0.270720
$87$	114957.	1.62832
$88$	−59268.9	−0.815869
$89$	31997.0	0.428188	0.214094	−	0.976813i	$-0.431320\pi$
$89$	31997.0	0.428188	0.214094	+	0.976813i	$0.431320\pi$
$90$	0	0
$91$	6452.49	0.0816815
$92$	−43847.8	−0.540106
$93$	129815.	1.55639
$94$	−143722.	−1.67766
$95$	0	0
$96$	85913.9	0.951449
$97$	−36690.0	−0.395930	−0.197965	−	0.980209i	$-0.563433\pi$
$97$	−36690.0	−0.395930	−0.197965	+	0.980209i	$0.563433\pi$
$98$	93377.8	0.982151
$99$	66414.1	0.681040
$100$	0	0
$101$	−5398.29	−0.0526566	−0.0263283	−	0.999653i	$-0.508382\pi$
$101$	−5398.29	−0.0526566	−0.0263283	+	0.999653i	$0.508382\pi$
$102$	−445301.	−4.23792
$103$	−66139.6	−0.614283	−0.307142	−	0.951664i	$-0.599373\pi$
$103$	−66139.6	−0.614283	−0.307142	+	0.951664i	$0.599373\pi$
$104$	27553.0	0.249796
$105$	0	0
$106$	−228690.	−1.97689
$107$	−197766.	−1.66991	−0.834954	−	0.550320i	$-0.814506\pi$
$107$	−197766.	−1.66991	−0.834954	+	0.550320i	$0.814506\pi$
$108$	−302995.	−2.49963
$109$	33577.8	0.270698	0.135349	−	0.990798i	$-0.456784\pi$
$109$	33577.8	0.270698	0.135349	+	0.990798i	$0.456784\pi$
$110$	0	0
$111$	82772.5	0.637645
$112$	−131076.	−0.987367
$113$	−15251.3	−0.112360	−0.0561800	−	0.998421i	$-0.517892\pi$
$113$	−15251.3	−0.112360	−0.0561800	+	0.998421i	$0.517892\pi$
$114$	−41007.6	−0.295531
$115$	0	0
$116$	−308622.	−2.12952
$117$	−30874.7	−0.208515
$118$	165793.	1.09613
$119$	149835.	0.969940
$120$	0	0
$121$	−135393.	−0.840685
$122$	−239654.	−1.45776
$123$	318342.	1.89728
$124$	−348510.	−2.03545
$125$	0	0
$126$	360791.	2.02455
$127$	−34135.7	−0.187801	−0.0939007	−	0.995582i	$-0.529934\pi$
$127$	−34135.7	−0.187801	−0.0939007	+	0.995582i	$0.529934\pi$
$128$	255451.	1.37811
$129$	47416.0	0.250871
$130$	0	0
$131$	−255687.	−1.30176	−0.650880	−	0.759181i	$-0.725600\pi$
$131$	−255687.	−1.30176	−0.650880	+	0.759181i	$0.725600\pi$
$132$	−282797.	−1.41267
$133$	13798.2	0.0676386
$134$	23350.0	0.112337
$135$	0	0
$136$	639814.	2.96624
$137$	−11957.8	−0.0544316	−0.0272158	−	0.999630i	$-0.508664\pi$
$137$	−11957.8	−0.0544316	−0.0272158	+	0.999630i	$0.508664\pi$
$138$	−164016.	−0.733144
$139$	120963.	0.531024	0.265512	−	0.964107i	$-0.414459\pi$
$139$	120963.	0.531024	0.265512	+	0.964107i	$0.414459\pi$
$140$	0	0
$141$	−367015.	−1.55466
$142$	−707273.	−2.94351
$143$	−11927.8	−0.0487777
$144$	627190.	2.52053
$145$	0	0
$146$	26533.5	0.103018
$147$	238453.	0.910141
$148$	−222216.	−0.833915
$149$	−75320.1	−0.277936	−0.138968	−	0.990297i	$-0.544379\pi$
$149$	−75320.1	−0.277936	−0.138968	+	0.990297i	$0.544379\pi$
$150$	0	0
$151$	−423102.	−1.51009	−0.755044	−	0.655674i	$-0.772385\pi$
$151$	−423102.	−1.51009	−0.755044	+	0.655674i	$0.772385\pi$
$152$	58920.4	0.206850
$153$	−716948.	−2.47605
$154$	139384.	0.473601
$155$	0	0
$156$	131467.	0.432519
$157$	−86001.6	−0.278457	−0.139228	−	0.990260i	$-0.544462\pi$
$157$	−86001.6	−0.278457	−0.139228	+	0.990260i	$0.544462\pi$
$158$	80814.4	0.257541
$159$	−583990.	−1.83194
$160$	0	0
$161$	55188.2	0.167796
$162$	−121596.	−0.364024
$163$	−558009.	−1.64502	−0.822512	−	0.568748i	$-0.807428\pi$
$163$	−558009.	−1.64502	−0.822512	+	0.568748i	$0.807428\pi$
$164$	−854642.	−2.48127
$165$	0	0
$166$	507736.	1.43010
$167$	−155307.	−0.430924	−0.215462	−	0.976512i	$-0.569126\pi$
$167$	−155307.	−0.430924	−0.215462	+	0.976512i	$0.569126\pi$
$168$	−822206.	−2.24754
$169$	−365748.	−0.985066
$170$	0	0
$171$	−66023.6	−0.172667
$172$	−127296.	−0.328090
$173$	−737850.	−1.87436	−0.937179	−	0.348849i	$-0.886573\pi$
$173$	−737850.	−1.87436	−0.937179	+	0.348849i	$0.886573\pi$
$174$	−1.15443e6	−2.89063
$175$	0	0
$176$	242302.	0.589625
$177$	423374.	1.01576
$178$	−321320.	−0.760131
$179$	238943.	0.557394	0.278697	−	0.960379i	$-0.410097\pi$
$179$	238943.	0.557394	0.278697	+	0.960379i	$0.410097\pi$
$180$	0	0
$181$	−643357.	−1.45967	−0.729837	−	0.683621i	$-0.760404\pi$
$181$	−643357.	−1.45967	−0.729837	+	0.683621i	$0.760404\pi$
$182$	−64797.2	−0.145003
$183$	−611988.	−1.35088
$184$	235661.	0.513149
$185$	0	0
$186$	−1.30363e6	−2.76295
$187$	−276979.	−0.579218
$188$	985311.	2.03319
$189$	381358.	0.776566
$190$	0	0
$191$	−143807.	−0.285231	−0.142616	−	0.989778i	$-0.545551\pi$
$191$	−143807.	−0.285231	−0.142616	+	0.989778i	$0.545551\pi$
$192$	378560.	0.741108
$193$	326492.	0.630927	0.315464	−	0.948938i	$-0.397840\pi$
$193$	326492.	0.630927	0.315464	+	0.948938i	$0.397840\pi$
$194$	368449.	0.702866
$195$	0	0
$196$	−640165.	−1.19029
$197$	−354366.	−0.650559	−0.325279	−	0.945618i	$-0.605458\pi$
$197$	−354366.	−0.650559	−0.325279	+	0.945618i	$0.605458\pi$
$198$	−666944.	−1.20900
$199$	551822.	0.987794	0.493897	−	0.869520i	$-0.335572\pi$
$199$	551822.	0.987794	0.493897	+	0.869520i	$0.335572\pi$
$200$	0	0
$201$	59627.3	0.104101
$202$	54210.7	0.0934774
$203$	388441.	0.661584
$204$	3.05283e6	5.13602
$205$	0	0
$206$	664188.	1.09049
$207$	−264071.	−0.428347
$208$	−112642.	−0.180527
$209$	−25506.9	−0.0403917
$210$	0	0
$211$	−1.23038e6	−1.90254	−0.951269	−	0.308362i	$-0.900219\pi$
$211$	−1.23038e6	−1.90254	−0.951269	+	0.308362i	$0.900219\pi$
$212$	1.56782e6	2.39583
$213$	−1.80612e6	−2.72770
$214$	1.98601e6	2.96447
$215$	0	0
$216$	1.62845e6	2.37487
$217$	438645.	0.632360
$218$	−337195.	−0.480551
$219$	67756.9	0.0954647
$220$	0	0
$221$	128762.	0.177340
$222$	−831219.	−1.13196
$223$	303318.	0.408447	0.204224	−	0.978924i	$-0.434533\pi$
$223$	303318.	0.408447	0.204224	+	0.978924i	$0.434533\pi$
$224$	290303.	0.386573
$225$	0	0
$226$	153157.	0.199465
$227$	331610.	0.427133	0.213566	−	0.976929i	$-0.431492\pi$
$227$	331610.	0.427133	0.213566	+	0.976929i	$0.431492\pi$
$228$	281134.	0.358159
$229$	1.18359e6	1.49146	0.745732	−	0.666246i	$-0.232100\pi$
$229$	1.18359e6	1.49146	0.745732	+	0.666246i	$0.232100\pi$
$230$	0	0
$231$	355937.	0.438877
$232$	1.65870e6	2.02324
$233$	310185.	0.374309	0.187155	−	0.982330i	$-0.440073\pi$
$233$	310185.	0.374309	0.187155	+	0.982330i	$0.440073\pi$
$234$	310050.	0.370162
$235$	0	0
$236$	−1.13662e6	−1.32842
$237$	206370.	0.238658
$238$	−1.50467e6	−1.72186
$239$	−425578.	−0.481931	−0.240965	−	0.970534i	$-0.577464\pi$
$239$	−425578.	−0.481931	−0.240965	+	0.970534i	$0.577464\pi$
$240$	0	0
$241$	−338158.	−0.375039	−0.187520	−	0.982261i	$-0.560045\pi$
$241$	−338158.	−0.375039	−0.187520	+	0.982261i	$0.560045\pi$
$242$	1.35965e6	1.49241
$243$	758947.	0.824510
$244$	1.64298e6	1.76668
$245$	0	0
$246$	−3.19686e6	−3.36811
$247$	11857.7	0.0123668
$248$	1.87308e6	1.93387
$249$	1.29657e6	1.32525
$250$	0	0
$251$	−1.82682e6	−1.83026	−0.915128	−	0.403164i	$-0.867910\pi$
$251$	−1.82682e6	−1.83026	−0.915128	+	0.403164i	$0.867910\pi$
$252$	−2.47346e6	−2.45359
$253$	−102019.	−0.100203
$254$	342797.	0.333390
$255$	0	0
$256$	−2.09291e6	−1.99595
$257$	1.21139e6	1.14407	0.572035	−	0.820229i	$-0.306154\pi$
$257$	1.21139e6	1.14407	0.572035	+	0.820229i	$0.306154\pi$
$258$	−476161.	−0.445353
$259$	279688.	0.259075
$260$	0	0
$261$	−1.85866e6	−1.68888
$262$	2.56766e6	2.31092
$263$	−1.15619e6	−1.03072	−0.515359	−	0.856974i	$-0.672342\pi$
$263$	−1.15619e6	−1.03072	−0.515359	+	0.856974i	$0.672342\pi$
$264$	1.51990e6	1.34216
$265$	0	0
$266$	−138565.	−0.120074
$267$	−820535.	−0.704399
$268$	−160079.	−0.136144
$269$	−283495.	−0.238872	−0.119436	−	0.992842i	$-0.538109\pi$
$269$	−283495.	−0.238872	−0.119436	+	0.992842i	$0.538109\pi$
$270$	0	0
$271$	−143512.	−0.118704	−0.0593521	−	0.998237i	$-0.518903\pi$
$271$	−143512.	−0.118704	−0.0593521	+	0.998237i	$0.518903\pi$
$272$	−2.61568e6	−2.14369
$273$	−165468.	−0.134372
$274$	120083.	0.0966285
$275$	0	0
$276$	1.12444e6	0.888512
$277$	−458652.	−0.359157	−0.179578	−	0.983744i	$-0.557473\pi$
$277$	−458652.	−0.359157	−0.179578	+	0.983744i	$0.557473\pi$
$278$	−1.21473e6	−0.942689
$279$	−2.09889e6	−1.61428
$280$	0	0
$281$	−243421.	−0.183905	−0.0919523	−	0.995763i	$-0.529311\pi$
$281$	−243421.	−0.183905	−0.0919523	+	0.995763i	$0.529311\pi$
$282$	3.68564e6	2.75988
$283$	−947831.	−0.703501	−0.351750	−	0.936094i	$-0.614413\pi$
$283$	−947831.	−0.703501	−0.351750	+	0.936094i	$0.614413\pi$
$284$	4.84881e6	3.56730
$285$	0	0
$286$	119782.	0.0865915
$287$	1.07568e6	0.770864
$288$	−1.38908e6	−0.986837
$289$	1.57016e6	1.10586
$290$	0	0
$291$	940883.	0.651333
$292$	−181904.	−0.124849
$293$	2.55005e6	1.73532	0.867661	−	0.497156i	$-0.165622\pi$
$293$	2.55005e6	1.73532	0.867661	+	0.497156i	$0.165622\pi$
$294$	−2.39459e6	−1.61571
$295$	0	0
$296$	1.19431e6	0.792295
$297$	−704964.	−0.463741
$298$	756380.	0.493400
$299$	47426.6	0.0306792
$300$	0	0
$301$	160218.	0.101929
$302$	4.24887e6	2.68075
$303$	138434.	0.0866238
$304$	−240877.	−0.149490
$305$	0	0
$306$	7.19973e6	4.39555
$307$	2.96301e6	1.79426	0.897132	−	0.441762i	$-0.145646\pi$
$307$	2.96301e6	1.79426	0.897132	+	0.441762i	$0.145646\pi$
$308$	−955571.	−0.573966
$309$	1.69609e6	1.01054
$310$	0	0
$311$	−705956.	−0.413882	−0.206941	−	0.978353i	$-0.566351\pi$
$311$	−705956.	−0.413882	−0.206941	+	0.978353i	$0.566351\pi$
$312$	−706573.	−0.410932
$313$	1.00610e6	0.580473	0.290236	−	0.956955i	$-0.406266\pi$
$313$	1.00610e6	0.580473	0.290236	+	0.956955i	$0.406266\pi$
$314$	863646.	0.494324
$315$	0	0
$316$	−554035.	−0.312119
$317$	1.85740e6	1.03814	0.519071	−	0.854731i	$-0.326278\pi$
$317$	1.85740e6	1.03814	0.519071	+	0.854731i	$0.326278\pi$
$318$	5.86454e6	3.25212
$319$	−718057.	−0.395077
$320$	0	0
$321$	5.07154e6	2.74712
$322$	−554211.	−0.297876
$323$	275350.	0.146851
$324$	833617.	0.441168
$325$	0	0
$326$	5.60364e6	2.92029
$327$	−861072.	−0.445318
$328$	4.59329e6	2.35743
$329$	−1.24014e6	−0.631657
$330$	0	0
$331$	−2.50535e6	−1.25690	−0.628448	−	0.777852i	$-0.716309\pi$
$331$	−2.50535e6	−1.25690	−0.628448	+	0.777852i	$0.716309\pi$
$332$	−3.48086e6	−1.73317
$333$	−1.33829e6	−0.661361
$334$	1.55963e6	0.764988
$335$	0	0
$336$	3.36133e6	1.62429
$337$	−2.94917e6	−1.41457	−0.707286	−	0.706927i	$-0.750081\pi$
$337$	−2.94917e6	−1.41457	−0.707286	+	0.706927i	$0.750081\pi$
$338$	3.67292e6	1.74872
$339$	391107.	0.184840
$340$	0	0
$341$	−810863.	−0.377626
$342$	663022.	0.306523
$343$	2.26208e6	1.03818
$344$	684155.	0.311715
$345$	0	0
$346$	7.40963e6	3.32741
$347$	579524.	0.258373	0.129187	−	0.991620i	$-0.458763\pi$
$347$	579524.	0.258373	0.129187	+	0.991620i	$0.458763\pi$
$348$	7.91434e6	3.50321
$349$	−909270.	−0.399603	−0.199802	−	0.979836i	$-0.564030\pi$
$349$	−909270.	−0.399603	−0.199802	+	0.979836i	$0.564030\pi$
$350$	0	0
$351$	327724.	0.141985
$352$	−536643.	−0.230850
$353$	2.04684e6	0.874274	0.437137	−	0.899395i	$-0.355992\pi$
$353$	2.04684e6	0.874274	0.437137	+	0.899395i	$0.355992\pi$
$354$	−4.25161e6	−1.80320
$355$	0	0
$356$	2.20286e6	0.921217
$357$	−3.84238e6	−1.59562
$358$	−2.39952e6	−0.989501
$359$	−2.88758e6	−1.18249	−0.591246	−	0.806491i	$-0.701364\pi$
$359$	−2.88758e6	−1.18249	−0.591246	+	0.806491i	$0.701364\pi$
$360$	0	0
$361$	−2.45074e6	−0.989759
$362$	6.46072e6	2.59125
$363$	3.47204e6	1.38299
$364$	444227.	0.175732
$365$	0	0
$366$	6.14571e6	2.39811
$367$	−3.47823e6	−1.34801	−0.674005	−	0.738726i	$-0.735428\pi$
$367$	−3.47823e6	−1.34801	−0.674005	+	0.738726i	$0.735428\pi$
$368$	−963426.	−0.370850
$369$	−5.14704e6	−1.96785
$370$	0	0
$371$	−1.97330e6	−0.744318
$372$	8.93724e6	3.34847
$373$	−2.67314e6	−0.994833	−0.497416	−	0.867512i	$-0.665718\pi$
$373$	−2.67314e6	−0.994833	−0.497416	+	0.867512i	$0.665718\pi$
$374$	2.78148e6	1.02824
$375$	0	0
$376$	−5.29558e6	−1.93172
$377$	333811.	0.120962
$378$	−3.82967e6	−1.37858
$379$	−5.51561e6	−1.97240	−0.986201	−	0.165555i	$-0.947059\pi$
$379$	−5.51561e6	−1.97240	−0.986201	+	0.165555i	$0.947059\pi$
$380$	0	0
$381$	875379.	0.308947
$382$	1.44414e6	0.506350
$383$	−4.87225e6	−1.69720	−0.848600	−	0.529035i	$-0.822554\pi$
$383$	−4.87225e6	−1.69720	−0.848600	+	0.529035i	$0.822554\pi$
$384$	−6.55082e6	−2.26709
$385$	0	0
$386$	−3.27870e6	−1.12004
$387$	−766634.	−0.260202
$388$	−2.52595e6	−0.851817
$389$	−1.04630e6	−0.350575	−0.175287	−	0.984517i	$-0.556085\pi$
$389$	−1.04630e6	−0.350575	−0.175287	+	0.984517i	$0.556085\pi$
$390$	0	0
$391$	1.10130e6	0.364305
$392$	3.44058e6	1.13088
$393$	6.55687e6	2.14149
$394$	3.55861e6	1.15489
$395$	0	0
$396$	4.57234e6	1.46521
$397$	−4.96533e6	−1.58115	−0.790573	−	0.612367i	$-0.790217\pi$
$397$	−4.96533e6	−1.58115	−0.790573	+	0.612367i	$0.790217\pi$
$398$	−5.54151e6	−1.75356
$399$	−353844.	−0.111270
$400$	0	0
$401$	4.55036e6	1.41314	0.706570	−	0.707643i	$-0.250242\pi$
$401$	4.55036e6	1.41314	0.706570	+	0.707643i	$0.250242\pi$
$402$	−598789.	−0.184803
$403$	376955.	0.115618
$404$	−371650.	−0.113287
$405$	0	0
$406$	−3.90080e6	−1.17446
$407$	−517021.	−0.154711
$408$	−1.64075e7	−4.87968
$409$	2.74499e6	0.811396	0.405698	−	0.914007i	$-0.367028\pi$
$409$	2.74499e6	0.811396	0.405698	+	0.914007i	$0.367028\pi$
$410$	0	0
$411$	306648.	0.0895439
$412$	−4.55344e6	−1.32159
$413$	1.43058e6	0.412702
$414$	2.65186e6	0.760413
$415$	0	0
$416$	249475.	0.0706796
$417$	−3.10198e6	−0.873573
$418$	256145.	0.0717044
$419$	6.60205e6	1.83715	0.918574	−	0.395249i	$-0.129342\pi$
$419$	6.60205e6	1.83715	0.918574	+	0.395249i	$0.129342\pi$
$420$	0	0
$421$	−1.70052e6	−0.467601	−0.233801	−	0.972285i	$-0.575116\pi$
$421$	−1.70052e6	−0.467601	−0.233801	+	0.972285i	$0.575116\pi$
$422$	1.23557e7	3.37744
$423$	5.93399e6	1.61248
$424$	−8.42626e6	−2.27625
$425$	0	0
$426$	1.81374e7	4.84229
$427$	−2.06791e6	−0.548859
$428$	−1.36154e7	−3.59269
$429$	305879.	0.0802428
$430$	0	0
$431$	−176249.	−0.0457018	−0.0228509	−	0.999739i	$-0.507274\pi$
$431$	−176249.	−0.0457018	−0.0228509	+	0.999739i	$0.507274\pi$
$432$	−6.65741e6	−1.71631
$433$	2.62737e6	0.673444	0.336722	−	0.941604i	$-0.390682\pi$
$433$	2.62737e6	0.673444	0.336722	+	0.941604i	$0.390682\pi$
$434$	−4.40497e6	−1.12258
$435$	0	0
$436$	2.31169e6	0.582389
$437$	101419.	0.0254047
$438$	−680428.	−0.169472
$439$	4.20016e6	1.04017	0.520085	−	0.854115i	$-0.325900\pi$
$439$	4.20016e6	1.04017	0.520085	+	0.854115i	$0.325900\pi$
$440$	0	0
$441$	−3.85536e6	−0.943993
$442$	−1.29306e6	−0.314819
$443$	−5.29977e6	−1.28306	−0.641531	−	0.767097i	$-0.721700\pi$
$443$	−5.29977e6	−1.28306	−0.641531	+	0.767097i	$0.721700\pi$
$444$	5.69854e6	1.37185
$445$	0	0
$446$	−3.04598e6	−0.725087
$447$	1.93152e6	0.457225
$448$	1.27915e6	0.301112
$449$	4.27201e6	1.00004	0.500019	−	0.866015i	$-0.333326\pi$
$449$	4.27201e6	1.00004	0.500019	+	0.866015i	$0.333326\pi$
$450$	0	0
$451$	−1.98846e6	−0.460336
$452$	−1.04999e6	−0.241735
$453$	1.08501e7	2.48420
$454$	−3.33009e6	−0.758258
$455$	0	0
$456$	−1.51096e6	−0.340284
$457$	−6.27908e6	−1.40639	−0.703195	−	0.710997i	$-0.748244\pi$
$457$	−6.27908e6	−1.40639	−0.703195	+	0.710997i	$0.748244\pi$
$458$	−1.18859e7	−2.64769
$459$	7.61016e6	1.68602
$460$	0	0
$461$	−7.63968e6	−1.67426	−0.837130	−	0.547004i	$-0.815768\pi$
$461$	−7.63968e6	−1.67426	−0.837130	+	0.547004i	$0.815768\pi$
$462$	−3.57439e6	−0.779107
$463$	−5.68138e6	−1.23169	−0.615845	−	0.787868i	$-0.711185\pi$
$463$	−5.68138e6	−1.23169	−0.615845	+	0.787868i	$0.711185\pi$
$464$	−6.78105e6	−1.46218
$465$	0	0
$466$	−3.11494e6	−0.664484
$467$	5.14627e6	1.09194	0.545972	−	0.837803i	$-0.316160\pi$
$467$	5.14627e6	1.09194	0.545972	+	0.837803i	$0.316160\pi$
$468$	−2.12559e6	−0.448607
$469$	201481.	0.0422962
$470$	0	0
$471$	2.20544e6	0.458081
$472$	6.10877e6	1.26212
$473$	−296174.	−0.0608687
$474$	−2.07241e6	−0.423673
$475$	0	0
$476$	1.03155e7	2.08676
$477$	9.44209e6	1.90008
$478$	4.27374e6	0.855536
$479$	220697.	0.0439499	0.0219749	−	0.999759i	$-0.493005\pi$
$479$	220697.	0.0439499	0.0219749	+	0.999759i	$0.493005\pi$
$480$	0	0
$481$	240353.	0.0473683
$482$	3.39585e6	0.665780
$483$	−1.41525e6	−0.276036
$484$	−9.32126e6	−1.80868
$485$	0	0
$486$	−7.62150e6	−1.46369
$487$	−5.85223e6	−1.11815	−0.559074	−	0.829118i	$-0.688843\pi$
$487$	−5.85223e6	−1.11815	−0.559074	+	0.829118i	$0.688843\pi$
$488$	−8.83024e6	−1.67851
$489$	1.43096e7	2.70618
$490$	0	0
$491$	−4.83993e6	−0.906016	−0.453008	−	0.891506i	$-0.649649\pi$
$491$	−4.83993e6	−0.906016	−0.453008	+	0.891506i	$0.649649\pi$
$492$	2.19166e7	4.08187
$493$	7.75150e6	1.43638
$494$	−119077.	−0.0219539
$495$	0	0
$496$	−7.65748e6	−1.39760
$497$	−6.10286e6	−1.10826
$498$	−1.30204e7	−2.35262
$499$	1.00379e6	0.180464	0.0902319	−	0.995921i	$-0.471239\pi$
$499$	1.00379e6	0.180464	0.0902319	+	0.995921i	$0.471239\pi$
$500$	0	0
$501$	3.98272e6	0.708901
$502$	1.83453e7	3.24912
$503$	1.97660e6	0.348336	0.174168	−	0.984716i	$-0.444276\pi$
$503$	1.97660e6	0.348336	0.174168	+	0.984716i	$0.444276\pi$
$504$	1.32936e7	2.33114
$505$	0	0
$506$	1.02449e6	0.177882
$507$	9.37928e6	1.62050
$508$	−2.35010e6	−0.404042
$509$	3.12498e6	0.534630	0.267315	−	0.963609i	$-0.413864\pi$
$509$	3.12498e6	0.534630	0.267315	+	0.963609i	$0.413864\pi$
$510$	0	0
$511$	228950.	0.0387872
$512$	1.28430e7	2.16516
$513$	700818.	0.117574
$514$	−1.21651e7	−2.03098
$515$	0	0
$516$	3.26439e6	0.539732
$517$	2.29248e6	0.377206
$518$	−2.80869e6	−0.459916
$519$	1.89215e7	3.08345
$520$	0	0
$521$	−383430.	−0.0618859	−0.0309430	−	0.999521i	$-0.509851\pi$
$521$	−383430.	−0.0618859	−0.0309430	+	0.999521i	$0.509851\pi$
$522$	1.86650e7	2.99815
$523$	−1.00363e7	−1.60443	−0.802215	−	0.597036i	$-0.796345\pi$
$523$	−1.00363e7	−1.60443	−0.802215	+	0.597036i	$0.796345\pi$
$524$	−1.76030e7	−2.80065
$525$	0	0
$526$	1.16107e7	1.82976
$527$	8.75335e6	1.37293
$528$	−6.21363e6	−0.969975
$529$	−6.03070e6	−0.936977
$530$	0	0
$531$	−6.84522e6	−1.05354
$532$	949951.	0.145520
$533$	924397.	0.140942
$534$	8.23998e6	1.25047
$535$	0	0
$536$	860350.	0.129349
$537$	−6.12749e6	−0.916953
$538$	2.84691e6	0.424052
$539$	−1.48944e6	−0.220827
$540$	0	0
$541$	−3.52710e6	−0.518114	−0.259057	−	0.965862i	$-0.583412\pi$
$541$	−3.52710e6	−0.518114	−0.259057	+	0.965862i	$0.583412\pi$
$542$	1.44118e6	0.210727
$543$	1.64983e7	2.40127
$544$	5.79312e6	0.839296
$545$	0	0
$546$	1.66167e6	0.238541
$547$	1.31140e6	0.187398	0.0936992	−	0.995601i	$-0.470131\pi$
$547$	1.31140e6	0.187398	0.0936992	+	0.995601i	$0.470131\pi$
$548$	−823248.	−0.117106
$549$	9.89478e6	1.40112
$550$	0	0
$551$	713834.	0.100166
$552$	−6.04332e6	−0.844166
$553$	697325.	0.0969666
$554$	4.60588e6	0.637585
$555$	0	0
$556$	8.32778e6	1.14246
$557$	−1.34171e7	−1.83240	−0.916202	−	0.400717i	$-0.868761\pi$
$557$	−1.34171e7	−1.83240	−0.916202	+	0.400717i	$0.868761\pi$
$558$	2.10774e7	2.86571
$559$	137686.	0.0186363
$560$	0	0
$561$	7.10287e6	0.952855
$562$	2.44449e6	0.326473
$563$	1.23879e7	1.64712	0.823560	−	0.567229i	$-0.191985\pi$
$563$	1.23879e7	1.64712	0.823560	+	0.567229i	$0.191985\pi$
$564$	−2.52674e7	−3.34475
$565$	0	0
$566$	9.51831e6	1.24887
$567$	−1.04921e6	−0.137059
$568$	−2.60601e7	−3.38926
$569$	1.13384e7	1.46816	0.734078	−	0.679065i	$-0.237614\pi$
$569$	1.13384e7	1.46816	0.734078	+	0.679065i	$0.237614\pi$
$570$	0	0
$571$	1.03886e6	0.133341	0.0666707	−	0.997775i	$-0.478762\pi$
$571$	1.03886e6	0.133341	0.0666707	+	0.997775i	$0.478762\pi$
$572$	−821181.	−0.104942
$573$	3.68780e6	0.469225
$574$	−1.08022e7	−1.36846
$575$	0	0
$576$	−6.12066e6	−0.768673
$577$	2.50906e6	0.313741	0.156871	−	0.987619i	$-0.449859\pi$
$577$	2.50906e6	0.313741	0.156871	+	0.987619i	$0.449859\pi$
$578$	−1.57678e7	−1.96314
$579$	−8.37260e6	−1.03792
$580$	0	0
$581$	4.38112e6	0.538449
$582$	−9.44854e6	−1.15626
$583$	3.64777e6	0.444484
$584$	977649.	0.118618
$585$	0	0
$586$	−2.56082e7	−3.08059
$587$	−1.15377e6	−0.138205	−0.0691024	−	0.997610i	$-0.522014\pi$
$587$	−1.15377e6	−0.138205	−0.0691024	+	0.997610i	$0.522014\pi$
$588$	1.64165e7	1.95811
$589$	806094.	0.0957409
$590$	0	0
$591$	9.08740e6	1.07021
$592$	−4.88255e6	−0.572588
$593$	3.97163e6	0.463801	0.231901	−	0.972740i	$-0.425506\pi$
$593$	3.97163e6	0.463801	0.231901	+	0.972740i	$0.425506\pi$
$594$	7.07939e6	0.823246
$595$	0	0
$596$	−5.18547e6	−0.597961
$597$	−1.41510e7	−1.62499
$598$	−476268.	−0.0544626
$599$	−1.24121e7	−1.41345	−0.706724	−	0.707490i	$-0.749828\pi$
$599$	−1.24121e7	−1.41345	−0.706724	+	0.707490i	$0.749828\pi$
$600$	0	0
$601$	−891613.	−0.100691	−0.0503455	−	0.998732i	$-0.516032\pi$
$601$	−891613.	−0.100691	−0.0503455	+	0.998732i	$0.516032\pi$
$602$	−1.60895e6	−0.180947
$603$	−964070.	−0.107973
$604$	−2.91288e7	−3.24885
$605$	0	0
$606$	−1.39019e6	−0.153777
$607$	−1.53075e7	−1.68629	−0.843144	−	0.537687i	$-0.819298\pi$
$607$	−1.53075e7	−1.68629	−0.843144	+	0.537687i	$0.819298\pi$
$608$	533487.	0.0585282
$609$	−9.96122e6	−1.08835
$610$	0	0
$611$	−1.06573e6	−0.115490
$612$	−4.93589e7	−5.32705
$613$	−4.96083e6	−0.533216	−0.266608	−	0.963805i	$-0.585903\pi$
$613$	−4.96083e6	−0.533216	−0.266608	+	0.963805i	$0.585903\pi$
$614$	−2.97551e7	−3.18523
$615$	0	0
$616$	5.13574e6	0.545319
$617$	6.87842e6	0.727404	0.363702	−	0.931515i	$-0.381513\pi$
$617$	6.87842e6	0.727404	0.363702	+	0.931515i	$0.381513\pi$
$618$	−1.70325e7	−1.79394
$619$	7.24867e6	0.760382	0.380191	−	0.924908i	$-0.375858\pi$
$619$	7.24867e6	0.760382	0.380191	+	0.924908i	$0.375858\pi$
$620$	0	0
$621$	2.80303e6	0.291675
$622$	7.08935e6	0.734735
$623$	−2.77258e6	−0.286197
$624$	2.88860e6	0.296979
$625$	0	0
$626$	−1.01035e7	−1.03047
$627$	654102.	0.0664472
$628$	−5.92085e6	−0.599080
$629$	5.58130e6	0.562482
$630$	0	0
$631$	777481.	0.0777350	0.0388675	−	0.999244i	$-0.487625\pi$
$631$	777481.	0.0777350	0.0388675	+	0.999244i	$0.487625\pi$
$632$	2.97767e6	0.296541
$633$	3.15520e7	3.12981
$634$	−1.86524e7	−1.84294
$635$	0	0
$636$	−4.02053e7	−3.94131
$637$	692415.	0.0676110
$638$	7.21087e6	0.701352
$639$	2.92017e7	2.82915
$640$	0	0
$641$	1.98487e7	1.90804	0.954021	−	0.299740i	$-0.0968999\pi$
$641$	1.98487e7	1.90804	0.954021	+	0.299740i	$0.0968999\pi$
$642$	−5.09294e7	−4.87676
$643$	−1.28163e7	−1.22246	−0.611232	−	0.791451i	$-0.709326\pi$
$643$	−1.28163e7	−1.22246	−0.611232	+	0.791451i	$0.709326\pi$
$644$	3.79948e6	0.361002
$645$	0	0
$646$	−2.76512e6	−0.260695
$647$	1.29263e7	1.21399	0.606995	−	0.794706i	$-0.292375\pi$
$647$	1.29263e7	1.21399	0.606995	+	0.794706i	$0.292375\pi$
$648$	−4.48029e6	−0.419149
$649$	−2.64452e6	−0.246453
$650$	0	0
$651$	−1.12487e7	−1.04028
$652$	−3.84166e7	−3.53916
$653$	−1.47857e7	−1.35694	−0.678469	−	0.734629i	$-0.737356\pi$
$653$	−1.47857e7	−1.35694	−0.678469	+	0.734629i	$0.737356\pi$
$654$	8.64706e6	0.790540
$655$	0	0
$656$	−1.87782e7	−1.70371
$657$	−1.09551e6	−0.0990155
$658$	1.24538e7	1.12134
$659$	1.46140e7	1.31085	0.655427	−	0.755258i	$-0.272489\pi$
$659$	1.46140e7	1.31085	0.655427	+	0.755258i	$0.272489\pi$
$660$	0	0
$661$	3.22647e6	0.287227	0.143613	−	0.989634i	$-0.454128\pi$
$661$	3.22647e6	0.287227	0.143613	+	0.989634i	$0.454128\pi$
$662$	2.51593e7	2.23128
$663$	−3.30199e6	−0.291737
$664$	1.87080e7	1.64667
$665$	0	0
$666$	1.34394e7	1.17407
$667$	2.85509e6	0.248488
$668$	−1.06923e7	−0.927104
$669$	−7.77832e6	−0.671924
$670$	0	0
$671$	3.82265e6	0.327762
$672$	−7.44456e6	−0.635940
$673$	2.05649e6	0.175021	0.0875104	−	0.996164i	$-0.472109\pi$
$673$	2.05649e6	0.175021	0.0875104	+	0.996164i	$0.472109\pi$
$674$	2.96162e7	2.51119
$675$	0	0
$676$	−2.51802e7	−2.11930
$677$	−3.56527e6	−0.298965	−0.149483	−	0.988764i	$-0.547761\pi$
$677$	−3.56527e6	−0.298965	−0.149483	+	0.988764i	$0.547761\pi$
$678$	−3.92758e6	−0.328134
$679$	3.17924e6	0.264636
$680$	0	0
$681$	−8.50384e6	−0.702664
$682$	8.14285e6	0.670372
$683$	−114524.	−0.00939388	−0.00469694	−	0.999989i	$-0.501495\pi$
$683$	−114524.	−0.00939388	−0.00469694	+	0.999989i	$0.501495\pi$
$684$	−4.54545e6	−0.371481
$685$	0	0
$686$	−2.27163e7	−1.84301
$687$	−3.03521e7	−2.45356
$688$	−2.79695e6	−0.225275
$689$	−1.69578e6	−0.136088
$690$	0	0
$691$	−1.13623e7	−0.905254	−0.452627	−	0.891700i	$-0.649513\pi$
$691$	−1.13623e7	−0.905254	−0.452627	+	0.891700i	$0.649513\pi$
$692$	−5.07979e7	−4.03255
$693$	−5.75488e6	−0.455201
$694$	−5.81970e6	−0.458672
$695$	0	0
$696$	−4.25358e7	−3.32837
$697$	2.14656e7	1.67364
$698$	9.13107e6	0.709387
$699$	−7.95441e6	−0.615765
$700$	0	0
$701$	1.15161e7	0.885137	0.442569	−	0.896735i	$-0.354067\pi$
$701$	1.15161e7	0.885137	0.442569	+	0.896735i	$0.354067\pi$
$702$	−3.29108e6	−0.252055
$703$	513980.	0.0392246
$704$	−2.36460e6	−0.179815
$705$	0	0
$706$	−2.05548e7	−1.55204
$707$	467769.	0.0351952
$708$	2.91475e7	2.18534
$709$	9.15561e6	0.684025	0.342012	−	0.939695i	$-0.388892\pi$
$709$	9.15561e6	0.684025	0.342012	+	0.939695i	$0.388892\pi$
$710$	0	0
$711$	−3.33665e6	−0.247535
$712$	−1.18393e7	−0.875239
$713$	3.22410e6	0.237511
$714$	3.85859e7	2.83259
$715$	0	0
$716$	1.64503e7	1.19920
$717$	1.09136e7	0.792810
$718$	2.89977e7	2.09919
$719$	22286.6	0.00160776	0.000803882	−	1.00000i	$-0.499744\pi$
$719$	22286.6	0.00160776	0.000803882		1.00000i	$0.499744\pi$
$720$	0	0
$721$	5.73109e6	0.410581
$722$	2.46108e7	1.75705
$723$	8.67176e6	0.616966
$724$	−4.42925e7	−3.14039
$725$	0	0
$726$	−3.48669e7	−2.45512
$727$	−4.01960e6	−0.282064	−0.141032	−	0.990005i	$-0.545042\pi$
$727$	−4.01960e6	−0.282064	−0.141032	+	0.990005i	$0.545042\pi$
$728$	−2.38751e6	−0.166961
$729$	−2.24049e7	−1.56143
$730$	0	0
$731$	3.19723e6	0.221299
$732$	−4.21328e7	−2.90632
$733$	−2.55734e7	−1.75804	−0.879018	−	0.476789i	$-0.841801\pi$
$733$	−2.55734e7	−1.75804	−0.879018	+	0.476789i	$0.841801\pi$
$734$	3.49291e7	2.39303
$735$	0	0
$736$	2.13376e6	0.145195
$737$	−372449.	−0.0252580
$738$	5.16876e7	3.49338
$739$	5.47740e6	0.368947	0.184473	−	0.982838i	$-0.440942\pi$
$739$	5.47740e6	0.368947	0.184473	+	0.982838i	$0.440942\pi$
$740$	0	0
$741$	−304080.	−0.0203443
$742$	1.98163e7	1.32133
$743$	−1.84712e7	−1.22751	−0.613754	−	0.789498i	$-0.710341\pi$
$743$	−1.84712e7	−1.22751	−0.613754	+	0.789498i	$0.710341\pi$
$744$	−4.80334e7	−3.18134
$745$	0	0
$746$	2.68442e7	1.76605
$747$	−2.09633e7	−1.37454
$748$	−1.90688e7	−1.24615
$749$	1.71367e7	1.11615
$750$	0	0
$751$	−1.45484e7	−0.941271	−0.470636	−	0.882328i	$-0.655975\pi$
$751$	−1.45484e7	−0.941271	−0.470636	+	0.882328i	$0.655975\pi$
$752$	2.16493e7	1.39604
$753$	4.68472e7	3.01090
$754$	−3.35220e6	−0.214734
$755$	0	0
$756$	2.62549e7	1.67073
$757$	2.32740e7	1.47615	0.738075	−	0.674718i	$-0.235735\pi$
$757$	2.32740e7	1.47615	0.738075	+	0.674718i	$0.235735\pi$
$758$	5.53888e7	3.50146
$759$	2.61618e6	0.164840
$760$	0	0
$761$	1.35014e7	0.845117	0.422558	−	0.906336i	$-0.361132\pi$
$761$	1.35014e7	0.845117	0.422558	+	0.906336i	$0.361132\pi$
$762$	−8.79073e6	−0.548451
$763$	−2.90956e6	−0.180932
$764$	−9.90052e6	−0.613655
$765$	0	0
$766$	4.89282e7	3.01292
$767$	1.22939e6	0.0754570
$768$	5.36708e7	3.28348
$769$	814742.	0.0496826	0.0248413	−	0.999691i	$-0.492092\pi$
$769$	814742.	0.0496826	0.0248413	+	0.999691i	$0.492092\pi$
$770$	0	0
$771$	−3.10651e7	−1.88208
$772$	2.24776e7	1.35740
$773$	3.00770e7	1.81044	0.905222	−	0.424938i	$-0.139704\pi$
$773$	3.00770e7	1.81044	0.905222	+	0.424938i	$0.139704\pi$
$774$	7.69869e6	0.461917
$775$	0	0
$776$	1.35758e7	0.809303
$777$	−7.17236e6	−0.426196
$778$	1.05071e7	0.622350
$779$	1.97676e6	0.116711
$780$	0	0
$781$	1.12815e7	0.661820
$782$	−1.10595e7	−0.646724
$783$	1.97291e7	1.15001
$784$	−1.40657e7	−0.817283
$785$	0	0
$786$	−6.58455e7	−3.80163
$787$	−1.56743e7	−0.902094	−0.451047	−	0.892500i	$-0.648949\pi$
$787$	−1.56743e7	−0.902094	−0.451047	+	0.892500i	$0.648949\pi$
$788$	−2.43966e7	−1.39963
$789$	2.96495e7	1.69561
$790$	0	0
$791$	1.32155e6	0.0751004
$792$	−2.45741e7	−1.39208
$793$	−1.77708e6	−0.100352
$794$	4.98629e7	2.80690
$795$	0	0
$796$	3.79907e7	2.12517
$797$	2.65411e7	1.48004	0.740020	−	0.672585i	$-0.234816\pi$
$797$	2.65411e7	1.48004	0.740020	+	0.672585i	$0.234816\pi$
$798$	3.55337e6	0.197530
$799$	−2.47476e7	−1.37140
$800$	0	0
$801$	1.32666e7	0.730599
$802$	−4.56957e7	−2.50864
$803$	−423229.	−0.0231626
$804$	4.10509e6	0.223966
$805$	0	0
$806$	−3.78546e6	−0.205249
$807$	7.26998e6	0.392961
$808$	1.99744e6	0.107633
$809$	9.11078e6	0.489423	0.244712	−	0.969596i	$-0.421307\pi$
$809$	9.11078e6	0.489423	0.244712	+	0.969596i	$0.421307\pi$
$810$	0	0
$811$	1.73032e6	0.0923790	0.0461895	−	0.998933i	$-0.485292\pi$
$811$	1.73032e6	0.0923790	0.0461895	+	0.998933i	$0.485292\pi$
$812$	2.67425e7	1.42335
$813$	3.68025e6	0.195277
$814$	5.19203e6	0.274648
$815$	0	0
$816$	6.70768e7	3.52652
$817$	294432.	0.0154323
$818$	−2.75658e7	−1.44041
$819$	2.67534e6	0.139370
$820$	0	0
$821$	1.35640e7	0.702310	0.351155	−	0.936317i	$-0.385789\pi$
$821$	1.35640e7	0.702310	0.351155	+	0.936317i	$0.385789\pi$
$822$	−3.07942e6	−0.158961
$823$	−1.32595e7	−0.682381	−0.341191	−	0.939994i	$-0.610830\pi$
$823$	−1.32595e7	−0.682381	−0.341191	+	0.939994i	$0.610830\pi$
$824$	2.44725e7	1.25563
$825$	0	0
$826$	−1.43662e7	−0.732640
$827$	1.23788e7	0.629381	0.314691	−	0.949194i	$-0.398099\pi$
$827$	1.23788e7	0.629381	0.314691	+	0.949194i	$0.398099\pi$
$828$	−1.81802e7	−0.921559
$829$	−3.35004e7	−1.69303	−0.846514	−	0.532367i	$-0.821303\pi$
$829$	−3.35004e7	−1.69303	−0.846514	+	0.532367i	$0.821303\pi$
$830$	0	0
$831$	1.17617e7	0.590838
$832$	1.09926e6	0.0550542
$833$	1.60787e7	0.802858
$834$	3.11507e7	1.55079
$835$	0	0
$836$	−1.75604e6	−0.0869000
$837$	2.22790e7	1.09921
$838$	−6.62992e7	−3.26135
$839$	2.95491e6	0.144924	0.0724618	−	0.997371i	$-0.476914\pi$
$839$	2.95491e6	0.144924	0.0724618	+	0.997371i	$0.476914\pi$
$840$	0	0
$841$	−415667.	−0.0202654
$842$	1.70769e7	0.830098
$843$	6.24232e6	0.302536
$844$	−8.47066e7	−4.09318
$845$	0	0
$846$	−5.95903e7	−2.86253
$847$	1.17320e7	0.561906
$848$	3.44481e7	1.64504
$849$	2.43063e7	1.15731
$850$	0	0
$851$	2.05574e6	0.0973072
$852$	−1.24344e8	−5.86846
$853$	1.51567e7	0.713233	0.356616	−	0.934251i	$-0.383930\pi$
$853$	1.51567e7	0.713233	0.356616	+	0.934251i	$0.383930\pi$
$854$	2.07663e7	0.974350
$855$	0	0
$856$	7.31761e7	3.41338
$857$	−2.14886e7	−0.999441	−0.499720	−	0.866187i	$-0.666564\pi$
$857$	−2.14886e7	−0.999441	−0.499720	+	0.866187i	$0.666564\pi$
$858$	−3.07170e6	−0.142449
$859$	3.09910e7	1.43302	0.716511	−	0.697576i	$-0.245738\pi$
$859$	3.09910e7	1.43302	0.716511	+	0.697576i	$0.245738\pi$
$860$	0	0
$861$	−2.75848e7	−1.26813
$862$	1.76993e6	0.0811311
$863$	−4.13869e7	−1.89163	−0.945814	−	0.324709i	$-0.894734\pi$
$863$	−4.13869e7	−1.89163	−0.945814	+	0.324709i	$0.894734\pi$
$864$	1.47446e7	0.671968
$865$	0	0
$866$	−2.63846e7	−1.19552
$867$	−4.02653e7	−1.81921
$868$	3.01989e7	1.36048
$869$	−1.28905e6	−0.0579055
$870$	0	0
$871$	173145.	0.00773328
$872$	−1.24242e7	−0.553322
$873$	−1.52124e7	−0.675559
$874$	−1.01847e6	−0.0450992
$875$	0	0
$876$	4.66478e6	0.205386
$877$	8.16292e6	0.358382	0.179191	−	0.983814i	$-0.442652\pi$
$877$	8.16292e6	0.358382	0.179191	+	0.983814i	$0.442652\pi$
$878$	−4.21788e7	−1.84654
$879$	−6.53939e7	−2.85473
$880$	0	0
$881$	−7.19561e6	−0.312340	−0.156170	−	0.987730i	$-0.549915\pi$
$881$	−7.19561e6	−0.312340	−0.156170	+	0.987730i	$0.549915\pi$
$882$	3.87164e7	1.67580
$883$	4.13644e7	1.78535	0.892677	−	0.450696i	$-0.148824\pi$
$883$	4.13644e7	1.78535	0.892677	+	0.450696i	$0.148824\pi$
$884$	8.86474e6	0.381536
$885$	0	0
$886$	5.32213e7	2.27773
$887$	−2.87528e7	−1.22708	−0.613538	−	0.789665i	$-0.710254\pi$
$887$	−2.87528e7	−1.22708	−0.613538	+	0.789665i	$0.710254\pi$
$888$	−3.06269e7	−1.30338
$889$	2.95790e6	0.125525
$890$	0	0
$891$	1.93954e6	0.0818472
$892$	2.08822e7	0.878746
$893$	−2.27900e6	−0.0956346
$894$	−1.93967e7	−0.811678
$895$	0	0
$896$	−2.21352e7	−0.921115
$897$	−1.21621e6	−0.0504695
$898$	−4.29004e7	−1.77529
$899$	2.26927e7	0.936457
$900$	0	0
$901$	−3.93780e7	−1.61600
$902$	1.99685e7	0.817201
$903$	−4.10866e6	−0.167680
$904$	5.64320e6	0.229670
$905$	0	0
$906$	−1.08959e8	−4.41002
$907$	−1.38527e7	−0.559133	−0.279567	−	0.960126i	$-0.590191\pi$
$907$	−1.38527e7	−0.559133	−0.279567	+	0.960126i	$0.590191\pi$
$908$	2.28300e7	0.918947
$909$	−2.23824e6	−0.0898457
$910$	0	0
$911$	−8.40936e6	−0.335712	−0.167856	−	0.985812i	$-0.553684\pi$
$911$	−8.40936e6	−0.335712	−0.167856	+	0.985812i	$0.553684\pi$
$912$	6.17709e6	0.245922
$913$	−8.09877e6	−0.321545
$914$	6.30558e7	2.49666
$915$	0	0
$916$	8.14853e7	3.20878
$917$	2.21557e7	0.870084
$918$	−7.64228e7	−2.99306
$919$	1.71038e6	0.0668041	0.0334020	−	0.999442i	$-0.489366\pi$
$919$	1.71038e6	0.0668041	0.0334020	+	0.999442i	$0.489366\pi$
$920$	0	0
$921$	−7.59837e7	−2.95169
$922$	7.67192e7	2.97219
$923$	−5.24457e6	−0.202631
$924$	2.45048e7	0.944215
$925$	0	0
$926$	5.70535e7	2.18653
$927$	−2.74229e7	−1.04813
$928$	1.50185e7	0.572473
$929$	3.76430e7	1.43102	0.715509	−	0.698604i	$-0.246195\pi$
$929$	3.76430e7	1.43102	0.715509	+	0.698604i	$0.246195\pi$
$930$	0	0
$931$	1.48068e6	0.0559871
$932$	2.13549e7	0.805301
$933$	1.81036e7	0.680865
$934$	−5.16799e7	−1.93845
$935$	0	0
$936$	1.14240e7	0.426217
$937$	2.06587e7	0.768694	0.384347	−	0.923189i	$-0.374427\pi$
$937$	2.06587e7	0.768694	0.384347	+	0.923189i	$0.374427\pi$
$938$	−2.02331e6	−0.0750853
$939$	−2.58006e7	−0.954919
$940$	0	0
$941$	2.88381e7	1.06168	0.530840	−	0.847472i	$-0.321877\pi$
$941$	2.88381e7	1.06168	0.530840	+	0.847472i	$0.321877\pi$
$942$	−2.21474e7	−0.813197
$943$	7.90637e6	0.289533
$944$	−2.49738e7	−0.912125
$945$	0	0
$946$	2.97424e6	0.108056
$947$	3.57974e7	1.29711	0.648555	−	0.761168i	$-0.275374\pi$
$947$	3.57974e7	1.29711	0.648555	+	0.761168i	$0.275374\pi$
$948$	1.42077e7	0.513457
$949$	196751.	0.00709172
$950$	0	0
$951$	−4.76314e7	−1.70782
$952$	−5.54408e7	−1.98261
$953$	3.95404e7	1.41029	0.705146	−	0.709062i	$-0.250881\pi$
$953$	3.95404e7	1.41029	0.705146	+	0.709062i	$0.250881\pi$
$954$	−9.48194e7	−3.37308
$955$	0	0
$956$	−2.92993e7	−1.03684
$957$	1.84139e7	0.649930
$958$	−2.21628e6	−0.0780210
$959$	1.03616e6	0.0363816
$960$	0	0
$961$	−3.00345e6	−0.104909
$962$	−2.41368e6	−0.0840895
$963$	−8.19979e7	−2.84929
$964$	−2.32808e7	−0.806872
$965$	0	0
$966$	1.42122e7	0.490027
$967$	1.28993e7	0.443608	0.221804	−	0.975091i	$-0.428805\pi$
$967$	1.28993e7	0.443608	0.221804	+	0.975091i	$0.428805\pi$
$968$	5.00973e7	1.71841
$969$	−7.06110e6	−0.241581
$970$	0	0
$971$	−1.53201e7	−0.521452	−0.260726	−	0.965413i	$-0.583962\pi$
$971$	−1.53201e7	−0.521452	−0.260726	+	0.965413i	$0.583962\pi$
$972$	5.22503e7	1.77388
$973$	−1.04816e7	−0.354932
$974$	5.87693e7	1.98497
$975$	0	0
$976$	3.60997e7	1.21305
$977$	−361922.	−0.0121305	−0.00606524	−	0.999982i	$-0.501931\pi$
$977$	−361922.	−0.0121305	−0.00606524	+	0.999982i	$0.501931\pi$
$978$	−1.43700e8	−4.80409
$979$	5.12530e6	0.170908
$980$	0	0
$981$	1.39220e7	0.461881
$982$	4.86036e7	1.60838
$983$	−4.88750e6	−0.161325	−0.0806627	−	0.996741i	$-0.525704\pi$
$983$	−4.88750e6	−0.161325	−0.0806627	+	0.996741i	$0.525704\pi$
$984$	−1.17791e8	−3.87815
$985$	0	0
$986$	−7.78421e7	−2.54990
$987$	3.18023e7	1.03912
$988$	816352.	0.0266063
$989$	1.17763e6	0.0382839
$990$	0	0
$991$	−1.82277e7	−0.589587	−0.294793	−	0.955561i	$-0.595251\pi$
$991$	−1.82277e7	−0.589587	−0.294793	+	0.955561i	$0.595251\pi$
$992$	1.69595e7	0.547186
$993$	6.42476e7	2.06768
$994$	6.12862e7	1.96742
$995$	0	0
$996$	8.92636e7	2.85119
$997$	5.22203e6	0.166380	0.0831901	−	0.996534i	$-0.473489\pi$
$997$	5.22203e6	0.166380	0.0831901	+	0.996534i	$0.473489\pi$
$998$	−1.00802e7	−0.320364
$999$	1.42055e7	0.450342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.i.1.4	✓	37
5.4	even	2		1075.6.a.j.1.34	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.4	✓	37	1.1	even	1	trivial
1075.6.a.j.1.34	yes	37	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q-10.0422 q^{2} -25.6441 q^{3} +68.8458 q^{4} +257.523 q^{6} -86.6514 q^{7} -370.013 q^{8} +414.621 q^{9} +O(q^{10})\)	\(q-10.0422 q^{2} -25.6441 q^{3} +68.8458 q^{4} +257.523 q^{6} -86.6514 q^{7} -370.013 q^{8} +414.621 q^{9} +160.181 q^{11} -1765.49 q^{12} -74.4649 q^{13} +870.171 q^{14} +1512.68 q^{16} -1729.17 q^{17} -4163.70 q^{18} -159.238 q^{19} +2222.10 q^{21} -1608.57 q^{22} -636.899 q^{23} +9488.67 q^{24} +747.792 q^{26} -4401.06 q^{27} -5965.59 q^{28} -4482.80 q^{29} -5062.18 q^{31} -3350.24 q^{32} -4107.69 q^{33} +17364.6 q^{34} +28544.9 q^{36} -3227.74 q^{37} +1599.11 q^{38} +1909.59 q^{39} -12413.9 q^{41} -22314.8 q^{42} -1849.00 q^{43} +11027.8 q^{44} +6395.87 q^{46} +14311.8 q^{47} -38791.4 q^{48} -9298.54 q^{49} +44342.9 q^{51} -5126.60 q^{52} +22772.9 q^{53} +44196.3 q^{54} +32062.2 q^{56} +4083.53 q^{57} +45017.2 q^{58} -16509.6 q^{59} +23864.7 q^{61} +50835.5 q^{62} -35927.5 q^{63} -14762.1 q^{64} +41250.2 q^{66} -2325.18 q^{67} -119046. q^{68} +16332.7 q^{69} +70430.0 q^{71} -153415. q^{72} -2642.20 q^{73} +32413.6 q^{74} -10962.9 q^{76} -13879.9 q^{77} -19176.5 q^{78} -8047.47 q^{79} +12108.5 q^{81} +124662. q^{82} -50560.2 q^{83} +152982. q^{84} +18568.0 q^{86} +114957. q^{87} -59268.9 q^{88} +31997.0 q^{89} +6452.49 q^{91} -43847.8 q^{92} +129815. q^{93} -143722. q^{94} +85913.9 q^{96} -36690.0 q^{97} +93377.8 q^{98} +66414.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Introduction

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