LMFDB - Embedded newform 1150.4.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 179x^{7} + 380x^{6} + 10197x^{5} - 8259x^{4} - 205207x^{3} - 105750x^{2} + 525560x + 178000 $ x^9 - 3x^8 - 179x^7 + 380x^6 + 10197x^5 - 8259x^4 - 205207x^3 - 105750x^2 + 525560x + 178000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.56723$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +1.56723 q^{3} +4.00000 q^{4} +3.13447 q^{6} -3.11755 q^{7} +8.00000 q^{8} -24.5438 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +1.56723 q^{3} +4.00000 q^{4} +3.13447 q^{6} -3.11755 q^{7} +8.00000 q^{8} -24.5438 q^{9} -7.96901 q^{11} +6.26894 q^{12} +86.3933 q^{13} -6.23510 q^{14} +16.0000 q^{16} +129.666 q^{17} -49.0876 q^{18} -100.925 q^{19} -4.88593 q^{21} -15.9380 q^{22} -23.0000 q^{23} +12.5379 q^{24} +172.787 q^{26} -80.7812 q^{27} -12.4702 q^{28} -152.889 q^{29} +285.339 q^{31} +32.0000 q^{32} -12.4893 q^{33} +259.332 q^{34} -98.1751 q^{36} -20.8025 q^{37} -201.849 q^{38} +135.399 q^{39} +143.296 q^{41} -9.77186 q^{42} +125.836 q^{43} -31.8760 q^{44} -46.0000 q^{46} -174.447 q^{47} +25.0757 q^{48} -333.281 q^{49} +203.217 q^{51} +345.573 q^{52} +393.767 q^{53} -161.562 q^{54} -24.9404 q^{56} -158.172 q^{57} -305.778 q^{58} +824.318 q^{59} +17.4020 q^{61} +570.678 q^{62} +76.5164 q^{63} +64.0000 q^{64} -24.9786 q^{66} +753.226 q^{67} +518.664 q^{68} -36.0464 q^{69} +687.723 q^{71} -196.350 q^{72} +139.400 q^{73} -41.6051 q^{74} -403.698 q^{76} +24.8438 q^{77} +270.797 q^{78} +1044.06 q^{79} +536.079 q^{81} +286.591 q^{82} +764.278 q^{83} -19.5437 q^{84} +251.671 q^{86} -239.613 q^{87} -63.7521 q^{88} -502.692 q^{89} -269.335 q^{91} -92.0000 q^{92} +447.193 q^{93} -348.893 q^{94} +50.1515 q^{96} -239.739 q^{97} -666.562 q^{98} +195.590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) $ 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	1.56723	0.301614	0.150807	−	0.988563i	$-0.451813\pi$
$3$	1.56723	0.301614	0.150807	+	0.988563i	$0.451813\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	3.13447	0.213274
$7$	−3.11755	−0.168332	−0.0841659	−	0.996452i	$-0.526823\pi$
$7$	−3.11755	−0.168332	−0.0841659	+	0.996452i	$0.526823\pi$
$8$	8.00000	0.353553
$9$	−24.5438	−0.909029
$10$	0	0
$11$	−7.96901	−0.218432	−0.109216	−	0.994018i	$-0.534834\pi$
$11$	−7.96901	−0.218432	−0.109216	+	0.994018i	$0.534834\pi$
$12$	6.26894	0.150807
$13$	86.3933	1.84317	0.921584	−	0.388178i	$-0.126895\pi$
$13$	86.3933	1.84317	0.921584	+	0.388178i	$0.126895\pi$
$14$	−6.23510	−0.119029
$15$	0	0
$16$	16.0000	0.250000
$17$	129.666	1.84992	0.924960	−	0.380064i	$-0.124098\pi$
$17$	129.666	1.84992	0.924960	+	0.380064i	$0.124098\pi$
$18$	−49.0876	−0.642780
$19$	−100.925	−1.21862	−0.609308	−	0.792934i	$-0.708553\pi$
$19$	−100.925	−1.21862	−0.609308	+	0.792934i	$0.708553\pi$
$20$	0	0
$21$	−4.88593	−0.0507713
$22$	−15.9380	−0.154454
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	12.5379	0.106637
$25$	0	0
$26$	172.787	1.30332
$27$	−80.7812	−0.575790
$28$	−12.4702	−0.0841659
$29$	−152.889	−0.978992	−0.489496	−	0.872006i	$-0.662819\pi$
$29$	−152.889	−0.978992	−0.489496	+	0.872006i	$0.662819\pi$
$30$	0	0
$31$	285.339	1.65318	0.826588	−	0.562808i	$-0.190279\pi$
$31$	285.339	1.65318	0.826588	+	0.562808i	$0.190279\pi$
$32$	32.0000	0.176777
$33$	−12.4893	−0.0658821
$34$	259.332	1.30809
$35$	0	0
$36$	−98.1751	−0.454514
$37$	−20.8025	−0.0924302	−0.0462151	−	0.998932i	$-0.514716\pi$
$37$	−20.8025	−0.0924302	−0.0462151	+	0.998932i	$0.514716\pi$
$38$	−201.849	−0.861691
$39$	135.399	0.555926
$40$	0	0
$41$	143.296	0.545829	0.272915	−	0.962038i	$-0.412012\pi$
$41$	143.296	0.545829	0.272915	+	0.962038i	$0.412012\pi$
$42$	−9.77186	−0.0359007
$43$	125.836	0.446273	0.223137	−	0.974787i	$-0.428370\pi$
$43$	125.836	0.446273	0.223137	+	0.974787i	$0.428370\pi$
$44$	−31.8760	−0.109216
$45$	0	0
$46$	−46.0000	−0.147442
$47$	−174.447	−0.541397	−0.270698	−	0.962664i	$-0.587255\pi$
$47$	−174.447	−0.541397	−0.270698	+	0.962664i	$0.587255\pi$
$48$	25.0757	0.0754036
$49$	−333.281	−0.971664
$50$	0	0
$51$	203.217	0.557963
$52$	345.573	0.921584
$53$	393.767	1.02053	0.510264	−	0.860018i	$-0.329548\pi$
$53$	393.767	1.02053	0.510264	+	0.860018i	$0.329548\pi$
$54$	−161.562	−0.407145
$55$	0	0
$56$	−24.9404	−0.0595143
$57$	−158.172	−0.367552
$58$	−305.778	−0.692252
$59$	824.318	1.81893	0.909467	−	0.415777i	$-0.136490\pi$
$59$	824.318	1.81893	0.909467	+	0.415777i	$0.136490\pi$
$60$	0	0
$61$	17.4020	0.0365263	0.0182631	−	0.999833i	$-0.494186\pi$
$61$	17.4020	0.0365263	0.0182631	+	0.999833i	$0.494186\pi$
$62$	570.678	1.16897
$63$	76.5164	0.153019
$64$	64.0000	0.125000
$65$	0	0
$66$	−24.9786	−0.0465857
$67$	753.226	1.37345	0.686725	−	0.726917i	$-0.259048\pi$
$67$	753.226	1.37345	0.686725	+	0.726917i	$0.259048\pi$
$68$	518.664	0.924960
$69$	−36.0464	−0.0628909
$70$	0	0
$71$	687.723	1.14955	0.574773	−	0.818313i	$-0.305091\pi$
$71$	687.723	1.14955	0.574773	+	0.818313i	$0.305091\pi$
$72$	−196.350	−0.321390
$73$	139.400	0.223501	0.111750	−	0.993736i	$-0.464354\pi$
$73$	139.400	0.223501	0.111750	+	0.993736i	$0.464354\pi$
$74$	−41.6051	−0.0653580
$75$	0	0
$76$	−403.698	−0.609308
$77$	24.8438	0.0367690
$78$	270.797	0.393099
$79$	1044.06	1.48691	0.743455	−	0.668786i	$-0.233186\pi$
$79$	1044.06	1.48691	0.743455	+	0.668786i	$0.233186\pi$
$80$	0	0
$81$	536.079	0.735362
$82$	286.591	0.385960
$83$	764.278	1.01073	0.505364	−	0.862906i	$-0.331358\pi$
$83$	764.278	1.01073	0.505364	+	0.862906i	$0.331358\pi$
$84$	−19.5437	−0.0253857
$85$	0	0
$86$	251.671	0.315563
$87$	−239.613	−0.295278
$88$	−63.7521	−0.0772272
$89$	−502.692	−0.598711	−0.299355	−	0.954142i	$-0.596772\pi$
$89$	−502.692	−0.598711	−0.299355	+	0.954142i	$0.596772\pi$
$90$	0	0
$91$	−269.335	−0.310264
$92$	−92.0000	−0.104257
$93$	447.193	0.498621
$94$	−348.893	−0.382825
$95$	0	0
$96$	50.1515	0.0533184
$97$	−239.739	−0.250947	−0.125473	−	0.992097i	$-0.540045\pi$
$97$	−239.739	−0.250947	−0.125473	+	0.992097i	$0.540045\pi$
$98$	−666.562	−0.687070
$99$	195.590	0.198561
$100$	0	0
$101$	−957.560	−0.943375	−0.471687	−	0.881766i	$-0.656355\pi$
$101$	−957.560	−0.943375	−0.471687	+	0.881766i	$0.656355\pi$
$102$	406.434	0.394539
$103$	890.192	0.851585	0.425792	−	0.904821i	$-0.359995\pi$
$103$	890.192	0.851585	0.425792	+	0.904821i	$0.359995\pi$
$104$	691.147	0.651659
$105$	0	0
$106$	787.534	0.721623
$107$	−624.094	−0.563864	−0.281932	−	0.959434i	$-0.590975\pi$
$107$	−624.094	−0.563864	−0.281932	+	0.959434i	$0.590975\pi$
$108$	−323.125	−0.287895
$109$	319.022	0.280337	0.140168	−	0.990128i	$-0.455236\pi$
$109$	319.022	0.280337	0.140168	+	0.990128i	$0.455236\pi$
$110$	0	0
$111$	−32.6025	−0.0278783
$112$	−49.8808	−0.0420830
$113$	−495.599	−0.412584	−0.206292	−	0.978490i	$-0.566140\pi$
$113$	−495.599	−0.412584	−0.206292	+	0.978490i	$0.566140\pi$
$114$	−316.345	−0.259898
$115$	0	0
$116$	−611.556	−0.489496
$117$	−2120.42	−1.67549
$118$	1648.64	1.28618
$119$	−404.240	−0.311401
$120$	0	0
$121$	−1267.49	−0.952288
$122$	34.8041	0.0258280
$123$	224.578	0.164630
$124$	1141.36	0.826588
$125$	0	0
$126$	153.033	0.108200
$127$	−1945.56	−1.35937	−0.679686	−	0.733503i	$-0.737884\pi$
$127$	−1945.56	−1.35937	−0.679686	+	0.733503i	$0.737884\pi$
$128$	128.000	0.0883883
$129$	197.214	0.134602
$130$	0	0
$131$	1841.34	1.22808	0.614041	−	0.789274i	$-0.289543\pi$
$131$	1841.34	1.22808	0.614041	+	0.789274i	$0.289543\pi$
$132$	−49.9572	−0.0329410
$133$	314.637	0.205132
$134$	1506.45	0.971176
$135$	0	0
$136$	1037.33	0.654046
$137$	3060.51	1.90859	0.954295	−	0.298866i	$-0.0966082\pi$
$137$	3060.51	1.90859	0.954295	+	0.298866i	$0.0966082\pi$
$138$	−72.0928	−0.0444706
$139$	−2404.60	−1.46731	−0.733654	−	0.679523i	$-0.762187\pi$
$139$	−2404.60	−1.46731	−0.733654	+	0.679523i	$0.762187\pi$
$140$	0	0
$141$	−273.399	−0.163293
$142$	1375.45	0.812851
$143$	−688.469	−0.402606
$144$	−392.700	−0.227257
$145$	0	0
$146$	278.801	0.158039
$147$	−522.329	−0.293068
$148$	−83.2102	−0.0462151
$149$	−2257.35	−1.24113	−0.620567	−	0.784153i	$-0.713098\pi$
$149$	−2257.35	−1.24113	−0.620567	+	0.784153i	$0.713098\pi$
$150$	0	0
$151$	2942.13	1.58561	0.792804	−	0.609477i	$-0.208620\pi$
$151$	2942.13	1.58561	0.792804	+	0.609477i	$0.208620\pi$
$152$	−807.397	−0.430846
$153$	−3182.50	−1.68163
$154$	49.6876	0.0259996
$155$	0	0
$156$	541.594	0.277963
$157$	1265.63	0.643362	0.321681	−	0.946848i	$-0.395752\pi$
$157$	1265.63	0.643362	0.321681	+	0.946848i	$0.395752\pi$
$158$	2088.12	1.05140
$159$	617.125	0.307806
$160$	0	0
$161$	71.7036	0.0350996
$162$	1072.16	0.519980
$163$	1590.74	0.764396	0.382198	−	0.924080i	$-0.375167\pi$
$163$	1590.74	0.764396	0.382198	+	0.924080i	$0.375167\pi$
$164$	573.182	0.272915
$165$	0	0
$166$	1528.56	0.714692
$167$	−1435.87	−0.665334	−0.332667	−	0.943044i	$-0.607949\pi$
$167$	−1435.87	−0.665334	−0.332667	+	0.943044i	$0.607949\pi$
$168$	−39.0874	−0.0179504
$169$	5266.81	2.39727
$170$	0	0
$171$	2477.07	1.10776
$172$	503.342	0.223137
$173$	−2823.10	−1.24067	−0.620336	−	0.784336i	$-0.713004\pi$
$173$	−2823.10	−1.24067	−0.620336	+	0.784336i	$0.713004\pi$
$174$	−479.225	−0.208793
$175$	0	0
$176$	−127.504	−0.0546079
$177$	1291.90	0.548616
$178$	−1005.38	−0.423352
$179$	1366.22	0.570483	0.285241	−	0.958456i	$-0.407926\pi$
$179$	1366.22	0.570483	0.285241	+	0.958456i	$0.407926\pi$
$180$	0	0
$181$	2755.29	1.13149	0.565743	−	0.824581i	$-0.308589\pi$
$181$	2755.29	1.13149	0.565743	+	0.824581i	$0.308589\pi$
$182$	−538.671	−0.219390
$183$	27.2730	0.0110168
$184$	−184.000	−0.0737210
$185$	0	0
$186$	894.387	0.352579
$187$	−1033.31	−0.404081
$188$	−697.786	−0.270698
$189$	251.839	0.0969239
$190$	0	0
$191$	−989.523	−0.374866	−0.187433	−	0.982277i	$-0.560017\pi$
$191$	−989.523	−0.374866	−0.187433	+	0.982277i	$0.560017\pi$
$192$	100.303	0.0377018
$193$	−3221.11	−1.20135	−0.600674	−	0.799494i	$-0.705101\pi$
$193$	−3221.11	−1.20135	−0.600674	+	0.799494i	$0.705101\pi$
$194$	−479.479	−0.177446
$195$	0	0
$196$	−1333.12	−0.485832
$197$	2674.84	0.967383	0.483692	−	0.875239i	$-0.339296\pi$
$197$	2674.84	0.967383	0.483692	+	0.875239i	$0.339296\pi$
$198$	391.179	0.140404
$199$	−1699.87	−0.605531	−0.302766	−	0.953065i	$-0.597910\pi$
$199$	−1699.87	−0.605531	−0.302766	+	0.953065i	$0.597910\pi$
$200$	0	0
$201$	1180.48	0.414252
$202$	−1915.12	−0.667067
$203$	476.639	0.164796
$204$	812.868	0.278981
$205$	0	0
$206$	1780.38	0.602161
$207$	564.507	0.189546
$208$	1382.29	0.460792
$209$	804.269	0.266184
$210$	0	0
$211$	−1107.10	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$211$	−1107.10	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$212$	1575.07	0.510264
$213$	1077.82	0.346719
$214$	−1248.19	−0.398712
$215$	0	0
$216$	−646.249	−0.203573
$217$	−889.559	−0.278282
$218$	638.043	0.198228
$219$	218.473	0.0674111
$220$	0	0
$221$	11202.3	3.40972
$222$	−65.2049	−0.0197129
$223$	−4899.29	−1.47121	−0.735606	−	0.677409i	$-0.763103\pi$
$223$	−4899.29	−1.47121	−0.735606	+	0.677409i	$0.763103\pi$
$224$	−99.7616	−0.0297571
$225$	0	0
$226$	−991.197	−0.291741
$227$	−2912.21	−0.851498	−0.425749	−	0.904841i	$-0.639989\pi$
$227$	−2912.21	−0.851498	−0.425749	+	0.904841i	$0.639989\pi$
$228$	−632.690	−0.183776
$229$	−3007.44	−0.867849	−0.433924	−	0.900949i	$-0.642872\pi$
$229$	−3007.44	−0.867849	−0.433924	+	0.900949i	$0.642872\pi$
$230$	0	0
$231$	38.9360	0.0110901
$232$	−1223.11	−0.346126
$233$	−1197.66	−0.336744	−0.168372	−	0.985723i	$-0.553851\pi$
$233$	−1197.66	−0.336744	−0.168372	+	0.985723i	$0.553851\pi$
$234$	−4240.84	−1.18475
$235$	0	0
$236$	3297.27	0.909467
$237$	1636.29	0.448473
$238$	−808.481	−0.220193
$239$	1822.84	0.493346	0.246673	−	0.969099i	$-0.420663\pi$
$239$	1822.84	0.493346	0.246673	+	0.969099i	$0.420663\pi$
$240$	0	0
$241$	−6667.59	−1.78215	−0.891073	−	0.453860i	$-0.850047\pi$
$241$	−6667.59	−1.78215	−0.891073	+	0.453860i	$0.850047\pi$
$242$	−2534.99	−0.673369
$243$	3021.25	0.797586
$244$	69.6081	0.0182631
$245$	0	0
$246$	449.155	0.116411
$247$	−8719.21	−2.24611
$248$	2282.71	0.584486
$249$	1197.80	0.304850
$250$	0	0
$251$	2805.39	0.705476	0.352738	−	0.935722i	$-0.385251\pi$
$251$	2805.39	0.705476	0.352738	+	0.935722i	$0.385251\pi$
$252$	306.066	0.0765093
$253$	183.287	0.0455461
$254$	−3891.11	−0.961221
$255$	0	0
$256$	256.000	0.0625000
$257$	−1270.78	−0.308440	−0.154220	−	0.988037i	$-0.549287\pi$
$257$	−1270.78	−0.308440	−0.154220	+	0.988037i	$0.549287\pi$
$258$	394.428	0.0951783
$259$	64.8530	0.0155589
$260$	0	0
$261$	3752.47	0.889932
$262$	3682.68	0.868385
$263$	−3056.51	−0.716625	−0.358312	−	0.933602i	$-0.616648\pi$
$263$	−3056.51	−0.716625	−0.358312	+	0.933602i	$0.616648\pi$
$264$	−99.9144	−0.0232928
$265$	0	0
$266$	629.275	0.145050
$267$	−787.836	−0.180580
$268$	3012.90	0.686725
$269$	4822.45	1.09305	0.546524	−	0.837444i	$-0.315951\pi$
$269$	4822.45	1.09305	0.546524	+	0.837444i	$0.315951\pi$
$270$	0	0
$271$	−5939.02	−1.33125	−0.665626	−	0.746285i	$-0.731836\pi$
$271$	−5939.02	−1.33125	−0.665626	+	0.746285i	$0.731836\pi$
$272$	2074.66	0.462480
$273$	−422.112	−0.0935801
$274$	6121.02	1.34958
$275$	0	0
$276$	−144.186	−0.0314455
$277$	−769.611	−0.166937	−0.0834683	−	0.996510i	$-0.526600\pi$
$277$	−769.611	−0.166937	−0.0834683	+	0.996510i	$0.526600\pi$
$278$	−4809.21	−1.03754
$279$	−7003.30	−1.50278
$280$	0	0
$281$	−2169.65	−0.460606	−0.230303	−	0.973119i	$-0.573972\pi$
$281$	−2169.65	−0.460606	−0.230303	+	0.973119i	$0.573972\pi$
$282$	−546.797	−0.115466
$283$	5902.49	1.23981	0.619906	−	0.784676i	$-0.287171\pi$
$283$	5902.49	1.23981	0.619906	+	0.784676i	$0.287171\pi$
$284$	2750.89	0.574773
$285$	0	0
$286$	−1376.94	−0.284686
$287$	−446.731	−0.0918805
$288$	−785.401	−0.160695
$289$	11900.3	2.42221
$290$	0	0
$291$	−375.728	−0.0756892
$292$	557.601	0.111750
$293$	−2271.30	−0.452870	−0.226435	−	0.974026i	$-0.572707\pi$
$293$	−2271.30	−0.452870	−0.226435	+	0.974026i	$0.572707\pi$
$294$	−1044.66	−0.207230
$295$	0	0
$296$	−166.420	−0.0326790
$297$	643.746	0.125771
$298$	−4514.69	−0.877615
$299$	−1987.05	−0.384327
$300$	0	0
$301$	−392.299	−0.0751220
$302$	5884.25	1.12119
$303$	−1500.72	−0.284535
$304$	−1614.79	−0.304654
$305$	0	0
$306$	−6364.99	−1.18909
$307$	1787.91	0.332383	0.166191	−	0.986094i	$-0.446853\pi$
$307$	1787.91	0.332383	0.166191	+	0.986094i	$0.446853\pi$
$308$	99.3751	0.0183845
$309$	1395.14	0.256850
$310$	0	0
$311$	8231.75	1.50090	0.750450	−	0.660927i	$-0.229837\pi$
$311$	8231.75	1.50090	0.750450	+	0.660927i	$0.229837\pi$
$312$	1083.19	0.196550
$313$	3717.33	0.671296	0.335648	−	0.941987i	$-0.391045\pi$
$313$	3717.33	0.671296	0.335648	+	0.941987i	$0.391045\pi$
$314$	2531.25	0.454926
$315$	0	0
$316$	4176.24	0.743455
$317$	−10682.0	−1.89263	−0.946315	−	0.323247i	$-0.895226\pi$
$317$	−10682.0	−1.89263	−0.946315	+	0.323247i	$0.895226\pi$
$318$	1234.25	0.217652
$319$	1218.37	0.213843
$320$	0	0
$321$	−978.101	−0.170069
$322$	143.407	0.0248192
$323$	−13086.5	−2.25434
$324$	2144.32	0.367681
$325$	0	0
$326$	3181.48	0.540509
$327$	499.981	0.0845536
$328$	1146.36	0.192980
$329$	543.846	0.0911343
$330$	0	0
$331$	−10625.3	−1.76441	−0.882206	−	0.470864i	$-0.843942\pi$
$331$	−10625.3	−1.76441	−0.882206	+	0.470864i	$0.843942\pi$
$332$	3057.11	0.505364
$333$	510.573	0.0840217
$334$	−2871.74	−0.470462
$335$	0	0
$336$	−78.1749	−0.0126928
$337$	11792.4	1.90615	0.953077	−	0.302728i	$-0.0978973\pi$
$337$	11792.4	1.90615	0.953077	+	0.302728i	$0.0978973\pi$
$338$	10533.6	1.69513
$339$	−776.719	−0.124441
$340$	0	0
$341$	−2273.87	−0.361106
$342$	4954.14	0.783302
$343$	2108.34	0.331894
$344$	1006.68	0.157781
$345$	0	0
$346$	−5646.20	−0.877287
$347$	6564.40	1.01555	0.507774	−	0.861490i	$-0.330468\pi$
$347$	6564.40	1.01555	0.507774	+	0.861490i	$0.330468\pi$
$348$	−958.451	−0.147639
$349$	−2849.37	−0.437030	−0.218515	−	0.975834i	$-0.570121\pi$
$349$	−2849.37	−0.437030	−0.218515	+	0.975834i	$0.570121\pi$
$350$	0	0
$351$	−6978.95	−1.06128
$352$	−255.008	−0.0386136
$353$	−8212.73	−1.23830	−0.619149	−	0.785273i	$-0.712522\pi$
$353$	−8212.73	−1.23830	−0.619149	+	0.785273i	$0.712522\pi$
$354$	2583.80	0.387930
$355$	0	0
$356$	−2010.77	−0.299355
$357$	−633.539	−0.0939229
$358$	2732.45	0.403392
$359$	−843.840	−0.124056	−0.0620281	−	0.998074i	$-0.519757\pi$
$359$	−843.840	−0.124056	−0.0620281	+	0.998074i	$0.519757\pi$
$360$	0	0
$361$	3326.77	0.485023
$362$	5510.58	0.800082
$363$	−1986.46	−0.287224
$364$	−1077.34	−0.155132
$365$	0	0
$366$	54.5461	0.00779008
$367$	−9048.21	−1.28695	−0.643477	−	0.765465i	$-0.722509\pi$
$367$	−9048.21	−1.28695	−0.643477	+	0.765465i	$0.722509\pi$
$368$	−368.000	−0.0521286
$369$	−3517.01	−0.496175
$370$	0	0
$371$	−1227.59	−0.171788
$372$	1788.77	0.249311
$373$	−6713.72	−0.931966	−0.465983	−	0.884794i	$-0.654299\pi$
$373$	−6713.72	−0.931966	−0.465983	+	0.884794i	$0.654299\pi$
$374$	−2066.62	−0.285728
$375$	0	0
$376$	−1395.57	−0.191413
$377$	−13208.6	−1.80445
$378$	503.679	0.0685355
$379$	9396.18	1.27348	0.636741	−	0.771078i	$-0.280282\pi$
$379$	9396.18	1.27348	0.636741	+	0.771078i	$0.280282\pi$
$380$	0	0
$381$	−3049.14	−0.410006
$382$	−1979.05	−0.265070
$383$	6658.52	0.888341	0.444171	−	0.895942i	$-0.353498\pi$
$383$	6658.52	0.888341	0.444171	+	0.895942i	$0.353498\pi$
$384$	200.606	0.0266592
$385$	0	0
$386$	−6442.21	−0.849482
$387$	−3088.48	−0.405675
$388$	−958.958	−0.125473
$389$	−6104.01	−0.795592	−0.397796	−	0.917474i	$-0.630225\pi$
$389$	−6104.01	−0.795592	−0.397796	+	0.917474i	$0.630225\pi$
$390$	0	0
$391$	−2982.32	−0.385735
$392$	−2666.25	−0.343535
$393$	2885.81	0.370407
$394$	5349.68	0.684043
$395$	0	0
$396$	782.358	0.0992803
$397$	−5891.58	−0.744810	−0.372405	−	0.928070i	$-0.621467\pi$
$397$	−5891.58	−0.744810	−0.372405	+	0.928070i	$0.621467\pi$
$398$	−3399.74	−0.428175
$399$	493.110	0.0618707
$400$	0	0
$401$	2292.08	0.285439	0.142719	−	0.989763i	$-0.454415\pi$
$401$	2292.08	0.285439	0.142719	+	0.989763i	$0.454415\pi$
$402$	2360.96	0.292921
$403$	24651.4	3.04708
$404$	−3830.24	−0.471687
$405$	0	0
$406$	953.278	0.116528
$407$	165.776	0.0201897
$408$	1625.74	0.197270
$409$	−7522.24	−0.909415	−0.454707	−	0.890641i	$-0.650256\pi$
$409$	−7522.24	−0.909415	−0.454707	+	0.890641i	$0.650256\pi$
$410$	0	0
$411$	4796.53	0.575658
$412$	3560.77	0.425792
$413$	−2569.85	−0.306184
$414$	1129.01	0.134029
$415$	0	0
$416$	2764.59	0.325829
$417$	−3768.58	−0.442561
$418$	1608.54	0.188220
$419$	1959.44	0.228460	0.114230	−	0.993454i	$-0.463560\pi$
$419$	1959.44	0.228460	0.114230	+	0.993454i	$0.463560\pi$
$420$	0	0
$421$	−1163.78	−0.134725	−0.0673627	−	0.997729i	$-0.521458\pi$
$421$	−1163.78	−0.134725	−0.0673627	+	0.997729i	$0.521458\pi$
$422$	−2214.19	−0.255415
$423$	4281.58	0.492145
$424$	3150.13	0.360811
$425$	0	0
$426$	2155.65	0.245168
$427$	−54.2517	−0.00614853
$428$	−2496.38	−0.281932
$429$	−1078.99	−0.121432
$430$	0	0
$431$	769.323	0.0859791	0.0429896	−	0.999076i	$-0.486312\pi$
$431$	769.323	0.0859791	0.0429896	+	0.999076i	$0.486312\pi$
$432$	−1292.50	−0.143948
$433$	−9948.62	−1.10416	−0.552079	−	0.833792i	$-0.686165\pi$
$433$	−9948.62	−1.10416	−0.552079	+	0.833792i	$0.686165\pi$
$434$	−1779.12	−0.196775
$435$	0	0
$436$	1276.09	0.140168
$437$	2321.27	0.254099
$438$	436.946	0.0476668
$439$	2097.68	0.228056	0.114028	−	0.993478i	$-0.463625\pi$
$439$	2097.68	0.228056	0.114028	+	0.993478i	$0.463625\pi$
$440$	0	0
$441$	8179.97	0.883271
$442$	22404.6	2.41103
$443$	8269.16	0.886862	0.443431	−	0.896309i	$-0.353761\pi$
$443$	8269.16	0.886862	0.443431	+	0.896309i	$0.353761\pi$
$444$	−130.410	−0.0139391
$445$	0	0
$446$	−9798.57	−1.04030
$447$	−3537.79	−0.374344
$448$	−199.523	−0.0210415
$449$	−11658.2	−1.22535	−0.612676	−	0.790334i	$-0.709907\pi$
$449$	−11658.2	−1.22535	−0.612676	+	0.790334i	$0.709907\pi$
$450$	0	0
$451$	−1141.92	−0.119226
$452$	−1982.39	−0.206292
$453$	4611.00	0.478242
$454$	−5824.42	−0.602100
$455$	0	0
$456$	−1265.38	−0.129949
$457$	−4933.63	−0.505001	−0.252501	−	0.967597i	$-0.581253\pi$
$457$	−4933.63	−0.505001	−0.252501	+	0.967597i	$0.581253\pi$
$458$	−6014.88	−0.613662
$459$	−10474.6	−1.06517
$460$	0	0
$461$	−8271.13	−0.835629	−0.417814	−	0.908532i	$-0.637204\pi$
$461$	−8271.13	−0.835629	−0.417814	+	0.908532i	$0.637204\pi$
$462$	77.8720	0.00784185
$463$	6685.81	0.671093	0.335546	−	0.942024i	$-0.391079\pi$
$463$	6685.81	0.671093	0.335546	+	0.942024i	$0.391079\pi$
$464$	−2446.22	−0.244748
$465$	0	0
$466$	−2395.32	−0.238114
$467$	−9503.72	−0.941712	−0.470856	−	0.882210i	$-0.656055\pi$
$467$	−9503.72	−0.941712	−0.470856	+	0.882210i	$0.656055\pi$
$468$	−8481.67	−0.837747
$469$	−2348.22	−0.231195
$470$	0	0
$471$	1983.53	0.194047
$472$	6594.55	0.643090
$473$	−1002.79	−0.0974802
$474$	3272.57	0.317119
$475$	0	0
$476$	−1616.96	−0.155700
$477$	−9664.52	−0.927690
$478$	3645.68	0.348848
$479$	−8791.21	−0.838582	−0.419291	−	0.907852i	$-0.637721\pi$
$479$	−8791.21	−0.838582	−0.419291	+	0.907852i	$0.637721\pi$
$480$	0	0
$481$	−1797.20	−0.170364
$482$	−13335.2	−1.26017
$483$	112.376	0.0105865
$484$	−5069.98	−0.476144
$485$	0	0
$486$	6042.51	0.563979
$487$	6534.37	0.608009	0.304005	−	0.952671i	$-0.401676\pi$
$487$	6534.37	0.608009	0.304005	+	0.952671i	$0.401676\pi$
$488$	139.216	0.0129140
$489$	2493.06	0.230553
$490$	0	0
$491$	−8856.72	−0.814050	−0.407025	−	0.913417i	$-0.633434\pi$
$491$	−8856.72	−0.814050	−0.407025	+	0.913417i	$0.633434\pi$
$492$	898.311	0.0823150
$493$	−19824.5	−1.81106
$494$	−17438.4	−1.58824
$495$	0	0
$496$	4565.43	0.413294
$497$	−2144.01	−0.193505
$498$	2395.60	0.215561
$499$	−15617.3	−1.40106	−0.700529	−	0.713623i	$-0.747053\pi$
$499$	−15617.3	−1.40106	−0.700529	+	0.713623i	$0.747053\pi$
$500$	0	0
$501$	−2250.34	−0.200674
$502$	5610.77	0.498847
$503$	−3449.82	−0.305805	−0.152903	−	0.988241i	$-0.548862\pi$
$503$	−3449.82	−0.305805	−0.152903	+	0.988241i	$0.548862\pi$
$504$	612.132	0.0541002
$505$	0	0
$506$	366.574	0.0322060
$507$	8254.32	0.723051
$508$	−7782.23	−0.679686
$509$	5599.41	0.487602	0.243801	−	0.969825i	$-0.421606\pi$
$509$	5599.41	0.487602	0.243801	+	0.969825i	$0.421606\pi$
$510$	0	0
$511$	−434.587	−0.0376223
$512$	512.000	0.0441942
$513$	8152.81	0.701667
$514$	−2541.56	−0.218100
$515$	0	0
$516$	788.855	0.0673012
$517$	1390.17	0.118258
$518$	129.706	0.0110018
$519$	−4424.46	−0.374204
$520$	0	0
$521$	−10637.0	−0.894467	−0.447233	−	0.894417i	$-0.647591\pi$
$521$	−10637.0	−0.894467	−0.447233	+	0.894417i	$0.647591\pi$
$522$	7504.94	0.629277
$523$	2221.92	0.185770	0.0928850	−	0.995677i	$-0.470391\pi$
$523$	2221.92	0.185770	0.0928850	+	0.995677i	$0.470391\pi$
$524$	7365.36	0.614041
$525$	0	0
$526$	−6113.02	−0.506730
$527$	36998.8	3.05824
$528$	−199.829	−0.0164705
$529$	529.000	0.0434783
$530$	0	0
$531$	−20231.9	−1.65346
$532$	1258.55	0.102566
$533$	12379.8	1.00606
$534$	−1575.67	−0.127689
$535$	0	0
$536$	6025.81	0.485588
$537$	2141.19	0.172066
$538$	9644.89	0.772901
$539$	2655.92	0.212242
$540$	0	0
$541$	−14960.5	−1.18892	−0.594458	−	0.804127i	$-0.702633\pi$
$541$	−14960.5	−1.18892	−0.594458	+	0.804127i	$0.702633\pi$
$542$	−11878.0	−0.941338
$543$	4318.18	0.341273
$544$	4149.32	0.327023
$545$	0	0
$546$	−844.223	−0.0661711
$547$	775.411	0.0606109	0.0303055	−	0.999541i	$-0.490352\pi$
$547$	775.411	0.0606109	0.0303055	+	0.999541i	$0.490352\pi$
$548$	12242.0	0.954295
$549$	−427.111	−0.0332034
$550$	0	0
$551$	15430.3	1.19301
$552$	−288.371	−0.0222353
$553$	−3254.91	−0.250294
$554$	−1539.22	−0.118042
$555$	0	0
$556$	−9618.42	−0.733654
$557$	−3234.70	−0.246066	−0.123033	−	0.992403i	$-0.539262\pi$
$557$	−3234.70	−0.246066	−0.123033	+	0.992403i	$0.539262\pi$
$558$	−14006.6	−1.06263
$559$	10871.4	0.822557
$560$	0	0
$561$	−1619.44	−0.121877
$562$	−4339.30	−0.325698
$563$	2308.49	0.172809	0.0864043	−	0.996260i	$-0.472462\pi$
$563$	2308.49	0.172809	0.0864043	+	0.996260i	$0.472462\pi$
$564$	−1093.59	−0.0816465
$565$	0	0
$566$	11805.0	0.876680
$567$	−1671.25	−0.123785
$568$	5501.78	0.406426
$569$	24312.5	1.79127	0.895637	−	0.444786i	$-0.146720\pi$
$569$	24312.5	1.79127	0.895637	+	0.444786i	$0.146720\pi$
$570$	0	0
$571$	11902.2	0.872316	0.436158	−	0.899870i	$-0.356339\pi$
$571$	11902.2	0.872316	0.436158	+	0.899870i	$0.356339\pi$
$572$	−2753.88	−0.201303
$573$	−1550.81	−0.113065
$574$	−893.462	−0.0649693
$575$	0	0
$576$	−1570.80	−0.113629
$577$	24035.6	1.73417	0.867084	−	0.498161i	$-0.165991\pi$
$577$	24035.6	1.73417	0.867084	+	0.498161i	$0.165991\pi$
$578$	23800.6	1.71276
$579$	−5048.23	−0.362344
$580$	0	0
$581$	−2382.67	−0.170138
$582$	−751.456	−0.0535203
$583$	−3137.93	−0.222916
$584$	1115.20	0.0790195
$585$	0	0
$586$	−4542.61	−0.320228
$587$	−24831.6	−1.74602	−0.873008	−	0.487706i	$-0.837834\pi$
$587$	−24831.6	−1.74602	−0.873008	+	0.487706i	$0.837834\pi$
$588$	−2089.32	−0.146534
$589$	−28797.7	−2.01458
$590$	0	0
$591$	4192.10	0.291777
$592$	−332.841	−0.0231075
$593$	14820.9	1.02635	0.513173	−	0.858285i	$-0.328470\pi$
$593$	14820.9	1.02635	0.513173	+	0.858285i	$0.328470\pi$
$594$	1287.49	0.0889334
$595$	0	0
$596$	−9029.39	−0.620567
$597$	−2664.10	−0.182637
$598$	−3974.09	−0.271760
$599$	23113.5	1.57661	0.788306	−	0.615284i	$-0.210959\pi$
$599$	23113.5	1.57661	0.788306	+	0.615284i	$0.210959\pi$
$600$	0	0
$601$	−3429.23	−0.232748	−0.116374	−	0.993205i	$-0.537127\pi$
$601$	−3429.23	−0.232748	−0.116374	+	0.993205i	$0.537127\pi$
$602$	−784.598	−0.0531193
$603$	−18487.0	−1.24851
$604$	11768.5	0.792804
$605$	0	0
$606$	−3001.44	−0.201197
$607$	2839.08	0.189843	0.0949214	−	0.995485i	$-0.469740\pi$
$607$	2839.08	0.189843	0.0949214	+	0.995485i	$0.469740\pi$
$608$	−3229.59	−0.215423
$609$	747.005	0.0497047
$610$	0	0
$611$	−15071.0	−0.997886
$612$	−12730.0	−0.840815
$613$	−11863.1	−0.781643	−0.390822	−	0.920466i	$-0.627809\pi$
$613$	−11863.1	−0.781643	−0.390822	+	0.920466i	$0.627809\pi$
$614$	3575.82	0.235030
$615$	0	0
$616$	198.750	0.0129998
$617$	5506.18	0.359271	0.179636	−	0.983733i	$-0.442508\pi$
$617$	5506.18	0.359271	0.179636	+	0.983733i	$0.442508\pi$
$618$	2790.28	0.181620
$619$	13654.1	0.886602	0.443301	−	0.896373i	$-0.353807\pi$
$619$	13654.1	0.886602	0.443301	+	0.896373i	$0.353807\pi$
$620$	0	0
$621$	1857.97	0.120061
$622$	16463.5	1.06130
$623$	1567.17	0.100782
$624$	2166.38	0.138982
$625$	0	0
$626$	7434.65	0.474678
$627$	1260.48	0.0802849
$628$	5062.50	0.321681
$629$	−2697.38	−0.170989
$630$	0	0
$631$	−11706.0	−0.738522	−0.369261	−	0.929326i	$-0.620389\pi$
$631$	−11706.0	−0.738522	−0.369261	+	0.929326i	$0.620389\pi$
$632$	8352.48	0.525702
$633$	−1735.08	−0.108947
$634$	−21364.1	−1.33829
$635$	0	0
$636$	2468.50	0.153903
$637$	−28793.2	−1.79094
$638$	2436.75	0.151210
$639$	−16879.3	−1.04497
$640$	0	0
$641$	−21484.6	−1.32385	−0.661926	−	0.749569i	$-0.730261\pi$
$641$	−21484.6	−1.32385	−0.661926	+	0.749569i	$0.730261\pi$
$642$	−1956.20	−0.120257
$643$	−7277.79	−0.446358	−0.223179	−	0.974778i	$-0.571643\pi$
$643$	−7277.79	−0.446358	−0.223179	+	0.974778i	$0.571643\pi$
$644$	286.815	0.0175498
$645$	0	0
$646$	−26173.0	−1.59406
$647$	−4415.65	−0.268311	−0.134156	−	0.990960i	$-0.542832\pi$
$647$	−4415.65	−0.268311	−0.134156	+	0.990960i	$0.542832\pi$
$648$	4288.63	0.259990
$649$	−6569.00	−0.397312
$650$	0	0
$651$	−1394.15	−0.0839339
$652$	6362.97	0.382198
$653$	−12318.5	−0.738222	−0.369111	−	0.929385i	$-0.620338\pi$
$653$	−12318.5	−0.738222	−0.369111	+	0.929385i	$0.620338\pi$
$654$	999.963	0.0597884
$655$	0	0
$656$	2292.73	0.136457
$657$	−3421.41	−0.203169
$658$	1087.69	0.0644417
$659$	26934.6	1.59214	0.796071	−	0.605203i	$-0.206908\pi$
$659$	26934.6	1.59214	0.796071	+	0.605203i	$0.206908\pi$
$660$	0	0
$661$	12605.6	0.741756	0.370878	−	0.928682i	$-0.379057\pi$
$661$	12605.6	0.741756	0.370878	+	0.928682i	$0.379057\pi$
$662$	−21250.6	−1.24763
$663$	17556.6	1.02842
$664$	6114.22	0.357346
$665$	0	0
$666$	1021.15	0.0594123
$667$	3516.45	0.204134
$668$	−5743.47	−0.332667
$669$	−7678.33	−0.443739
$670$	0	0
$671$	−138.677	−0.00797848
$672$	−156.350	−0.00897518
$673$	6858.98	0.392859	0.196430	−	0.980518i	$-0.437065\pi$
$673$	6858.98	0.392859	0.196430	+	0.980518i	$0.437065\pi$
$674$	23584.8	1.34785
$675$	0	0
$676$	21067.2	1.19864
$677$	−7453.70	−0.423144	−0.211572	−	0.977362i	$-0.567858\pi$
$677$	−7453.70	−0.423144	−0.211572	+	0.977362i	$0.567858\pi$
$678$	−1553.44	−0.0879933
$679$	747.399	0.0422424
$680$	0	0
$681$	−4564.11	−0.256824
$682$	−4547.74	−0.255340
$683$	−18575.3	−1.04065	−0.520326	−	0.853968i	$-0.674190\pi$
$683$	−18575.3	−1.04065	−0.520326	+	0.853968i	$0.674190\pi$
$684$	9908.28	0.553878
$685$	0	0
$686$	4216.68	0.234684
$687$	−4713.37	−0.261756
$688$	2013.37	0.111568
$689$	34018.8	1.88101
$690$	0	0
$691$	−3918.04	−0.215701	−0.107850	−	0.994167i	$-0.534397\pi$
$691$	−3918.04	−0.215701	−0.107850	+	0.994167i	$0.534397\pi$
$692$	−11292.4	−0.620336
$693$	−609.760	−0.0334241
$694$	13128.8	0.718102
$695$	0	0
$696$	−1916.90	−0.104397
$697$	18580.6	1.00974
$698$	−5698.75	−0.309027
$699$	−1877.02	−0.101567
$700$	0	0
$701$	11109.1	0.598550	0.299275	−	0.954167i	$-0.403255\pi$
$701$	11109.1	0.598550	0.299275	+	0.954167i	$0.403255\pi$
$702$	−13957.9	−0.750438
$703$	2099.49	0.112637
$704$	−510.017	−0.0273039
$705$	0	0
$706$	−16425.5	−0.875610
$707$	2985.24	0.158800
$708$	5167.60	0.274308
$709$	−10738.1	−0.568796	−0.284398	−	0.958706i	$-0.591794\pi$
$709$	−10738.1	−0.568796	−0.284398	+	0.958706i	$0.591794\pi$
$710$	0	0
$711$	−25625.2	−1.35164
$712$	−4021.54	−0.211676
$713$	−6562.80	−0.344711
$714$	−1267.08	−0.0664135
$715$	0	0
$716$	5464.90	0.285241
$717$	2856.82	0.148800
$718$	−1687.68	−0.0877210
$719$	−789.164	−0.0409330	−0.0204665	−	0.999791i	$-0.506515\pi$
$719$	−789.164	−0.0409330	−0.0204665	+	0.999791i	$0.506515\pi$
$720$	0	0
$721$	−2775.22	−0.143349
$722$	6653.54	0.342963
$723$	−10449.7	−0.537521
$724$	11021.2	0.565743
$725$	0	0
$726$	−3972.92	−0.203098
$727$	−30131.0	−1.53714	−0.768569	−	0.639767i	$-0.779031\pi$
$727$	−30131.0	−1.53714	−0.768569	+	0.639767i	$0.779031\pi$
$728$	−2154.68	−0.109695
$729$	−9739.12	−0.494799
$730$	0	0
$731$	16316.6	0.825570
$732$	109.092	0.00550842
$733$	4233.17	0.213309	0.106655	−	0.994296i	$-0.465986\pi$
$733$	4233.17	0.213309	0.106655	+	0.994296i	$0.465986\pi$
$734$	−18096.4	−0.910015
$735$	0	0
$736$	−736.000	−0.0368605
$737$	−6002.46	−0.300005
$738$	−7034.03	−0.350848
$739$	−15379.7	−0.765561	−0.382781	−	0.923839i	$-0.625033\pi$
$739$	−15379.7	−0.765561	−0.382781	+	0.923839i	$0.625033\pi$
$740$	0	0
$741$	−13665.0	−0.677460
$742$	−2455.17	−0.121472
$743$	−8271.25	−0.408402	−0.204201	−	0.978929i	$-0.565460\pi$
$743$	−8271.25	−0.408402	−0.204201	+	0.978929i	$0.565460\pi$
$744$	3577.55	0.176289
$745$	0	0
$746$	−13427.4	−0.659000
$747$	−18758.3	−0.918781
$748$	−4133.24	−0.202040
$749$	1945.64	0.0949163
$750$	0	0
$751$	3363.70	0.163440	0.0817199	−	0.996655i	$-0.473959\pi$
$751$	3363.70	0.163440	0.0817199	+	0.996655i	$0.473959\pi$
$752$	−2791.14	−0.135349
$753$	4396.70	0.212782
$754$	−26417.2	−1.27594
$755$	0	0
$756$	1007.36	0.0484619
$757$	14292.5	0.686222	0.343111	−	0.939295i	$-0.388519\pi$
$757$	14292.5	0.686222	0.343111	+	0.939295i	$0.388519\pi$
$758$	18792.4	0.900487
$759$	287.254	0.0137374
$760$	0	0
$761$	24279.4	1.15654	0.578271	−	0.815845i	$-0.303728\pi$
$761$	24279.4	1.15654	0.578271	+	0.815845i	$0.303728\pi$
$762$	−6098.28	−0.289918
$763$	−994.565	−0.0471896
$764$	−3958.09	−0.187433
$765$	0	0
$766$	13317.0	0.628152
$767$	71215.6	3.35260
$768$	401.212	0.0188509
$769$	−15096.5	−0.707923	−0.353962	−	0.935260i	$-0.615166\pi$
$769$	−15096.5	−0.707923	−0.353962	+	0.935260i	$0.615166\pi$
$770$	0	0
$771$	−1991.61	−0.0930300
$772$	−12884.4	−0.600674
$773$	23237.6	1.08124	0.540619	−	0.841267i	$-0.318190\pi$
$773$	23237.6	1.08124	0.540619	+	0.841267i	$0.318190\pi$
$774$	−6176.96	−0.286856
$775$	0	0
$776$	−1917.92	−0.0887231
$777$	101.640	0.00469280
$778$	−12208.0	−0.562569
$779$	−14462.0	−0.665156
$780$	0	0
$781$	−5480.47	−0.251097
$782$	−5964.64	−0.272756
$783$	12350.5	0.563694
$784$	−5332.49	−0.242916
$785$	0	0
$786$	5771.62	0.261917
$787$	24861.6	1.12607	0.563037	−	0.826432i	$-0.309633\pi$
$787$	24861.6	1.12607	0.563037	+	0.826432i	$0.309633\pi$
$788$	10699.4	0.483692
$789$	−4790.26	−0.216144
$790$	0	0
$791$	1545.05	0.0694511
$792$	1564.72	0.0702018
$793$	1503.42	0.0673240
$794$	−11783.2	−0.526660
$795$	0	0
$796$	−6799.48	−0.302766
$797$	14402.3	0.640093	0.320046	−	0.947402i	$-0.396301\pi$
$797$	14402.3	0.640093	0.320046	+	0.947402i	$0.396301\pi$
$798$	986.221	0.0437492
$799$	−22619.8	−1.00154
$800$	0	0
$801$	12338.0	0.544245
$802$	4584.16	0.201836
$803$	−1110.88	−0.0488197
$804$	4721.92	0.207126
$805$	0	0
$806$	49302.8	2.15461
$807$	7557.90	0.329679
$808$	−7660.48	−0.333533
$809$	15497.0	0.673478	0.336739	−	0.941598i	$-0.390676\pi$
$809$	15497.0	0.673478	0.336739	+	0.941598i	$0.390676\pi$
$810$	0	0
$811$	1004.10	0.0434755	0.0217378	−	0.999764i	$-0.493080\pi$
$811$	1004.10	0.0434755	0.0217378	+	0.999764i	$0.493080\pi$
$812$	1906.56	0.0823978
$813$	−9307.83	−0.401525
$814$	331.551	0.0142763
$815$	0	0
$816$	3251.47	0.139491
$817$	−12699.9	−0.543835
$818$	−15044.5	−0.643053
$819$	6610.51	0.282039
$820$	0	0
$821$	−18966.4	−0.806251	−0.403125	−	0.915145i	$-0.632076\pi$
$821$	−18966.4	−0.806251	−0.403125	+	0.915145i	$0.632076\pi$
$822$	9593.07	0.407052
$823$	22587.4	0.956681	0.478340	−	0.878175i	$-0.341239\pi$
$823$	22587.4	0.956681	0.478340	+	0.878175i	$0.341239\pi$
$824$	7121.54	0.301081
$825$	0	0
$826$	−5139.71	−0.216505
$827$	38206.5	1.60649	0.803247	−	0.595647i	$-0.203104\pi$
$827$	38206.5	1.60649	0.803247	+	0.595647i	$0.203104\pi$
$828$	2258.03	0.0947728
$829$	13118.6	0.549610	0.274805	−	0.961500i	$-0.411387\pi$
$829$	13118.6	0.549610	0.274805	+	0.961500i	$0.411387\pi$
$830$	0	0
$831$	−1206.16	−0.0503505
$832$	5529.17	0.230396
$833$	−43215.2	−1.79750
$834$	−7537.16	−0.312938
$835$	0	0
$836$	3217.08	0.133092
$837$	−23050.0	−0.951883
$838$	3918.87	0.161546
$839$	17272.0	0.710723	0.355362	−	0.934729i	$-0.384358\pi$
$839$	17272.0	0.710723	0.355362	+	0.934729i	$0.384358\pi$
$840$	0	0
$841$	−1013.97	−0.0415750
$842$	−2327.57	−0.0952653
$843$	−3400.35	−0.138925
$844$	−4428.38	−0.180606
$845$	0	0
$846$	8563.15	0.347999
$847$	3951.48	0.160300
$848$	6300.27	0.255132
$849$	9250.59	0.373945
$850$	0	0
$851$	478.459	0.0192730
$852$	4311.29	0.173360
$853$	−23894.2	−0.959111	−0.479555	−	0.877512i	$-0.659202\pi$
$853$	−23894.2	−0.959111	−0.479555	+	0.877512i	$0.659202\pi$
$854$	−108.503	−0.00434767
$855$	0	0
$856$	−4992.75	−0.199356
$857$	−11143.2	−0.444161	−0.222080	−	0.975028i	$-0.571285\pi$
$857$	−11143.2	−0.444161	−0.222080	+	0.975028i	$0.571285\pi$
$858$	−2157.98	−0.0858652
$859$	−16101.3	−0.639545	−0.319773	−	0.947494i	$-0.603607\pi$
$859$	−16101.3	−0.639545	−0.319773	+	0.947494i	$0.603607\pi$
$860$	0	0
$861$	−700.132	−0.0277125
$862$	1538.65	0.0607964
$863$	−23591.6	−0.930555	−0.465277	−	0.885165i	$-0.654045\pi$
$863$	−23591.6	−0.930555	−0.465277	+	0.885165i	$0.654045\pi$
$864$	−2585.00	−0.101786
$865$	0	0
$866$	−19897.2	−0.780757
$867$	18650.5	0.730572
$868$	−3558.24	−0.139141
$869$	−8320.12	−0.324788
$870$	0	0
$871$	65073.7	2.53150
$872$	2552.17	0.0991141
$873$	5884.11	0.228118
$874$	4642.53	0.179675
$875$	0	0
$876$	873.891	0.0337055
$877$	−15583.6	−0.600024	−0.300012	−	0.953935i	$-0.596991\pi$
$877$	−15583.6	−0.600024	−0.300012	+	0.953935i	$0.596991\pi$
$878$	4195.36	0.161260
$879$	−3559.66	−0.136592
$880$	0	0
$881$	47051.7	1.79933	0.899667	−	0.436578i	$-0.143810\pi$
$881$	47051.7	1.79933	0.899667	+	0.436578i	$0.143810\pi$
$882$	16359.9	0.624567
$883$	−26672.3	−1.01653	−0.508265	−	0.861201i	$-0.669713\pi$
$883$	−26672.3	−1.01653	−0.508265	+	0.861201i	$0.669713\pi$
$884$	44809.1	1.70486
$885$	0	0
$886$	16538.3	0.627106
$887$	−14245.9	−0.539267	−0.269634	−	0.962963i	$-0.586903\pi$
$887$	−14245.9	−0.539267	−0.269634	+	0.962963i	$0.586903\pi$
$888$	−260.820	−0.00985646
$889$	6065.37	0.228826
$890$	0	0
$891$	−4272.02	−0.160626
$892$	−19597.1	−0.735606
$893$	17605.9	0.659754
$894$	−7075.58	−0.264701
$895$	0	0
$896$	−399.046	−0.0148786
$897$	−3114.17	−0.115919
$898$	−23316.3	−0.866455
$899$	−43625.2	−1.61845
$900$	0	0
$901$	51058.2	1.88790
$902$	−2283.85	−0.0843058
$903$	−614.824	−0.0226579
$904$	−3964.79	−0.145871
$905$	0	0
$906$	9222.00	0.338168
$907$	33851.5	1.23927	0.619637	−	0.784888i	$-0.287280\pi$
$907$	33851.5	1.23927	0.619637	+	0.784888i	$0.287280\pi$
$908$	−11648.8	−0.425749
$909$	23502.2	0.857555
$910$	0	0
$911$	−50223.9	−1.82656	−0.913278	−	0.407338i	$-0.866457\pi$
$911$	−50223.9	−1.82656	−0.913278	+	0.407338i	$0.866457\pi$
$912$	−2530.76	−0.0918879
$913$	−6090.54	−0.220775
$914$	−9867.27	−0.357090
$915$	0	0
$916$	−12029.8	−0.433924
$917$	−5740.47	−0.206725
$918$	−20949.2	−0.753186
$919$	32253.2	1.15771	0.578854	−	0.815431i	$-0.303500\pi$
$919$	32253.2	1.15771	0.578854	+	0.815431i	$0.303500\pi$
$920$	0	0
$921$	2802.08	0.100251
$922$	−16542.3	−0.590879
$923$	59414.7	2.11881
$924$	155.744	0.00554503
$925$	0	0
$926$	13371.6	0.474534
$927$	−21848.7	−0.774115
$928$	−4892.45	−0.173063
$929$	8180.31	0.288899	0.144450	−	0.989512i	$-0.453859\pi$
$929$	8180.31	0.288899	0.144450	+	0.989512i	$0.453859\pi$
$930$	0	0
$931$	33636.2	1.18408
$932$	−4790.65	−0.168372
$933$	12901.1	0.452693
$934$	−19007.4	−0.665891
$935$	0	0
$936$	−16963.3	−0.592376
$937$	−15875.2	−0.553488	−0.276744	−	0.960944i	$-0.589255\pi$
$937$	−15875.2	−0.553488	−0.276744	+	0.960944i	$0.589255\pi$
$938$	−4696.44	−0.163480
$939$	5825.92	0.202473
$940$	0	0
$941$	13107.5	0.454082	0.227041	−	0.973885i	$-0.427095\pi$
$941$	13107.5	0.454082	0.227041	+	0.973885i	$0.427095\pi$
$942$	3967.06	0.137212
$943$	−3295.80	−0.113813
$944$	13189.1	0.454733
$945$	0	0
$946$	−2005.57	−0.0689289
$947$	−30992.3	−1.06348	−0.531740	−	0.846908i	$-0.678461\pi$
$947$	−30992.3	−1.06348	−0.531740	+	0.846908i	$0.678461\pi$
$948$	6545.14	0.224237
$949$	12043.3	0.411950
$950$	0	0
$951$	−16741.3	−0.570844
$952$	−3233.92	−0.110097
$953$	−33417.7	−1.13589	−0.567946	−	0.823066i	$-0.692262\pi$
$953$	−33417.7	−1.13589	−0.567946	+	0.823066i	$0.692262\pi$
$954$	−19329.0	−0.655976
$955$	0	0
$956$	7291.36	0.246673
$957$	1909.48	0.0644980
$958$	−17582.4	−0.592967
$959$	−9541.29	−0.321277
$960$	0	0
$961$	51627.5	1.73299
$962$	−3594.40	−0.120466
$963$	15317.6	0.512568
$964$	−26670.4	−0.891073
$965$	0	0
$966$	224.753	0.00748582
$967$	2073.56	0.0689568	0.0344784	−	0.999405i	$-0.489023\pi$
$967$	2073.56	0.0689568	0.0344784	+	0.999405i	$0.489023\pi$
$968$	−10140.0	−0.336685
$969$	−20509.6	−0.679942
$970$	0	0
$971$	−21966.2	−0.725982	−0.362991	−	0.931793i	$-0.618244\pi$
$971$	−21966.2	−0.725982	−0.362991	+	0.931793i	$0.618244\pi$
$972$	12085.0	0.398793
$973$	7496.48	0.246995
$974$	13068.7	0.429927
$975$	0	0
$976$	278.432	0.00913156
$977$	21230.2	0.695203	0.347602	−	0.937642i	$-0.386996\pi$
$977$	21230.2	0.695203	0.347602	+	0.937642i	$0.386996\pi$
$978$	4986.13	0.163025
$979$	4005.96	0.130777
$980$	0	0
$981$	−7829.99	−0.254834
$982$	−17713.4	−0.575620
$983$	−38862.8	−1.26097	−0.630483	−	0.776203i	$-0.717143\pi$
$983$	−38862.8	−1.26097	−0.630483	+	0.776203i	$0.717143\pi$
$984$	1796.62	0.0582055
$985$	0	0
$986$	−39649.0	−1.28061
$987$	852.334	0.0274874
$988$	−34876.8	−1.12306
$989$	−2894.22	−0.0930544
$990$	0	0
$991$	4502.76	0.144334	0.0721669	−	0.997393i	$-0.477009\pi$
$991$	4502.76	0.144334	0.0721669	+	0.997393i	$0.477009\pi$
$992$	9130.85	0.292243
$993$	−16652.4	−0.532172
$994$	−4288.02	−0.136829
$995$	0	0
$996$	4791.21	0.152425
$997$	−25980.7	−0.825294	−0.412647	−	0.910891i	$-0.635396\pi$
$997$	−25980.7	−0.825294	−0.412647	+	0.910891i	$0.635396\pi$
$998$	−31234.7	−0.990698
$999$	1680.45	0.0532204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.bb.1.6		9
5.2	odd	4		230.4.b.b.139.13	yes	18
5.3	odd	4		230.4.b.b.139.6	✓	18
5.4	even	2		1150.4.a.ba.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.b.139.6	✓	18	5.3	odd	4
230.4.b.b.139.13	yes	18	5.2	odd	4
1150.4.a.ba.1.4		9	5.4	even	2
1150.4.a.bb.1.6		9	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +1.56723 q^{3} +4.00000 q^{4} +3.13447 q^{6} -3.11755 q^{7} +8.00000 q^{8} -24.5438 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +1.56723 q^{3} +4.00000 q^{4} +3.13447 q^{6} -3.11755 q^{7} +8.00000 q^{8} -24.5438 q^{9} -7.96901 q^{11} +6.26894 q^{12} +86.3933 q^{13} -6.23510 q^{14} +16.0000 q^{16} +129.666 q^{17} -49.0876 q^{18} -100.925 q^{19} -4.88593 q^{21} -15.9380 q^{22} -23.0000 q^{23} +12.5379 q^{24} +172.787 q^{26} -80.7812 q^{27} -12.4702 q^{28} -152.889 q^{29} +285.339 q^{31} +32.0000 q^{32} -12.4893 q^{33} +259.332 q^{34} -98.1751 q^{36} -20.8025 q^{37} -201.849 q^{38} +135.399 q^{39} +143.296 q^{41} -9.77186 q^{42} +125.836 q^{43} -31.8760 q^{44} -46.0000 q^{46} -174.447 q^{47} +25.0757 q^{48} -333.281 q^{49} +203.217 q^{51} +345.573 q^{52} +393.767 q^{53} -161.562 q^{54} -24.9404 q^{56} -158.172 q^{57} -305.778 q^{58} +824.318 q^{59} +17.4020 q^{61} +570.678 q^{62} +76.5164 q^{63} +64.0000 q^{64} -24.9786 q^{66} +753.226 q^{67} +518.664 q^{68} -36.0464 q^{69} +687.723 q^{71} -196.350 q^{72} +139.400 q^{73} -41.6051 q^{74} -403.698 q^{76} +24.8438 q^{77} +270.797 q^{78} +1044.06 q^{79} +536.079 q^{81} +286.591 q^{82} +764.278 q^{83} -19.5437 q^{84} +251.671 q^{86} -239.613 q^{87} -63.7521 q^{88} -502.692 q^{89} -269.335 q^{91} -92.0000 q^{92} +447.193 q^{93} -348.893 q^{94} +50.1515 q^{96} -239.739 q^{97} -666.562 q^{98} +195.590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * q^99

Introduction

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