LMFDB - Embedded newform 325.4.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,4,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, 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("325.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.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:	$19.1756207519$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56155 q^{2} -8.68466 q^{3} -5.56155 q^{4} -13.5616 q^{6} +27.1771 q^{7} -21.1771 q^{8} +48.4233 q^{9} +O(q^{10})$	\(q+1.56155 q^{2} -8.68466 q^{3} -5.56155 q^{4} -13.5616 q^{6} +27.1771 q^{7} -21.1771 q^{8} +48.4233 q^{9} +15.2614 q^{11} +48.3002 q^{12} +13.0000 q^{13} +42.4384 q^{14} +11.4233 q^{16} -44.5464 q^{17} +75.6155 q^{18} +23.9697 q^{19} -236.024 q^{21} +23.8314 q^{22} -122.739 q^{23} +183.916 q^{24} +20.3002 q^{26} -186.054 q^{27} -151.147 q^{28} -219.909 q^{29} +27.0928 q^{31} +187.255 q^{32} -132.540 q^{33} -69.5616 q^{34} -269.309 q^{36} -94.1922 q^{37} +37.4299 q^{38} -112.901 q^{39} -160.354 q^{41} -368.563 q^{42} +151.302 q^{43} -84.8769 q^{44} -191.663 q^{46} -466.948 q^{47} -99.2074 q^{48} +395.594 q^{49} +386.870 q^{51} -72.3002 q^{52} +120.847 q^{53} -290.533 q^{54} -575.531 q^{56} -208.169 q^{57} -343.400 q^{58} -439.633 q^{59} -137.305 q^{61} +42.3068 q^{62} +1316.00 q^{63} +201.022 q^{64} -206.968 q^{66} -512.280 q^{67} +247.747 q^{68} +1065.94 q^{69} +410.719 q^{71} -1025.46 q^{72} +308.004 q^{73} -147.086 q^{74} -133.309 q^{76} +414.759 q^{77} -176.300 q^{78} -586.462 q^{79} +308.386 q^{81} -250.401 q^{82} -1354.20 q^{83} +1312.66 q^{84} +236.266 q^{86} +1909.84 q^{87} -323.191 q^{88} +439.882 q^{89} +353.302 q^{91} +682.617 q^{92} -235.292 q^{93} -729.164 q^{94} -1626.24 q^{96} +1511.27 q^{97} +617.740 q^{98} +739.006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 5 q^{3} - 7 q^{4} - 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9}+O(q^{10}) $ 2 * q - q^2 - 5 * q^3 - 7 * q^4 - 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9	$ 2 q - q^{2} - 5 q^{3} - 7 q^{4} - 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9} + 80 q^{11} + 43 q^{12} + 26 q^{13} + 89 q^{14} - 39 q^{16} - 19 q^{17} + 110 q^{18} - 84 q^{19} - 303 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 13 q^{26} - 335 q^{27} - 125 q^{28} - 44 q^{29} - 86 q^{31} + 123 q^{32} + 106 q^{33} - 135 q^{34} - 250 q^{36} - 209 q^{37} + 314 q^{38} - 65 q^{39} - 230 q^{41} - 197 q^{42} - 287 q^{43} - 178 q^{44} - 4 q^{46} - 435 q^{47} - 285 q^{48} + 383 q^{49} + 481 q^{51} - 91 q^{52} + 118 q^{53} + 91 q^{54} - 1015 q^{56} - 606 q^{57} - 794 q^{58} - 368 q^{59} - 1058 q^{61} + 332 q^{62} + 1560 q^{63} + 769 q^{64} - 818 q^{66} - 68 q^{67} + 211 q^{68} + 796 q^{69} - 131 q^{71} - 1350 q^{72} - 456 q^{73} + 147 q^{74} + 22 q^{76} - 762 q^{77} - 299 q^{78} - 1008 q^{79} + 122 q^{81} - 72 q^{82} - 1958 q^{83} + 1409 q^{84} + 1359 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 117 q^{91} + 788 q^{92} - 652 q^{93} - 811 q^{94} - 1863 q^{96} + 928 q^{97} + 650 q^{98} - 130 q^{99}+O(q^{100}) $ 2 * q - q^2 - 5 * q^3 - 7 * q^4 - 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9 + 80 * q^11 + 43 * q^12 + 26 * q^13 + 89 * q^14 - 39 * q^16 - 19 * q^17 + 110 * q^18 - 84 * q^19 - 303 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 13 * q^26 - 335 * q^27 - 125 * q^28 - 44 * q^29 - 86 * q^31 + 123 * q^32 + 106 * q^33 - 135 * q^34 - 250 * q^36 - 209 * q^37 + 314 * q^38 - 65 * q^39 - 230 * q^41 - 197 * q^42 - 287 * q^43 - 178 * q^44 - 4 * q^46 - 435 * q^47 - 285 * q^48 + 383 * q^49 + 481 * q^51 - 91 * q^52 + 118 * q^53 + 91 * q^54 - 1015 * q^56 - 606 * q^57 - 794 * q^58 - 368 * q^59 - 1058 * q^61 + 332 * q^62 + 1560 * q^63 + 769 * q^64 - 818 * q^66 - 68 * q^67 + 211 * q^68 + 796 * q^69 - 131 * q^71 - 1350 * q^72 - 456 * q^73 + 147 * q^74 + 22 * q^76 - 762 * q^77 - 299 * q^78 - 1008 * q^79 + 122 * q^81 - 72 * q^82 - 1958 * q^83 + 1409 * q^84 + 1359 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 117 * q^91 + 788 * q^92 - 652 * q^93 - 811 * q^94 - 1863 * q^96 + 928 * q^97 + 650 * q^98 - 130 * 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 $

$2$	1.56155	0.552092	0.276046	−	0.961144i	$-0.410976\pi$
$2$	1.56155	0.552092	0.276046	+	0.961144i	$0.410976\pi$
$3$	−8.68466	−1.67136	−0.835682	−	0.549214i	$-0.814927\pi$
$3$	−8.68466	−1.67136	−0.835682	+	0.549214i	$0.814927\pi$
$4$	−5.56155	−0.695194
$5$	0	0
$5$	0	0
$6$	−13.5616	−0.922747
$7$	27.1771	1.46742	0.733712	−	0.679460i	$-0.237786\pi$
$7$	27.1771	1.46742	0.733712	+	0.679460i	$0.237786\pi$
$8$	−21.1771	−0.935904
$9$	48.4233	1.79346
$10$	0	0
$11$	15.2614	0.418316	0.209158	−	0.977882i	$-0.432928\pi$
$11$	15.2614	0.418316	0.209158	+	0.977882i	$0.432928\pi$
$12$	48.3002	1.16192
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	42.4384	0.810154
$15$	0	0
$16$	11.4233	0.178489
$17$	−44.5464	−0.635535	−0.317767	−	0.948169i	$-0.602933\pi$
$17$	−44.5464	−0.635535	−0.317767	+	0.948169i	$0.602933\pi$
$18$	75.6155	0.990153
$19$	23.9697	0.289422	0.144711	−	0.989474i	$-0.453775\pi$
$19$	23.9697	0.289422	0.144711	+	0.989474i	$0.453775\pi$
$20$	0	0
$21$	−236.024	−2.45260
$22$	23.8314	0.230949
$23$	−122.739	−1.11273	−0.556365	−	0.830938i	$-0.687804\pi$
$23$	−122.739	−1.11273	−0.556365	+	0.830938i	$0.687804\pi$
$24$	183.916	1.56423
$25$	0	0
$26$	20.3002	0.153123
$27$	−186.054	−1.32615
$28$	−151.147	−1.02014
$29$	−219.909	−1.40814	−0.704071	−	0.710130i	$-0.748636\pi$
$29$	−219.909	−1.40814	−0.704071	+	0.710130i	$0.748636\pi$
$30$	0	0
$31$	27.0928	0.156968	0.0784840	−	0.996915i	$-0.474992\pi$
$31$	27.0928	0.156968	0.0784840	+	0.996915i	$0.474992\pi$
$32$	187.255	1.03445
$33$	−132.540	−0.699158
$34$	−69.5616	−0.350874
$35$	0	0
$36$	−269.309	−1.24680
$37$	−94.1922	−0.418516	−0.209258	−	0.977860i	$-0.567105\pi$
$37$	−94.1922	−0.418516	−0.209258	+	0.977860i	$0.567105\pi$
$38$	37.4299	0.159788
$39$	−112.901	−0.463553
$40$	0	0
$41$	−160.354	−0.610808	−0.305404	−	0.952223i	$-0.598791\pi$
$41$	−160.354	−0.610808	−0.305404	+	0.952223i	$0.598791\pi$
$42$	−368.563	−1.35406
$43$	151.302	0.536589	0.268295	−	0.963337i	$-0.413540\pi$
$43$	151.302	0.536589	0.268295	+	0.963337i	$0.413540\pi$
$44$	−84.8769	−0.290811
$45$	0	0
$46$	−191.663	−0.614329
$47$	−466.948	−1.44918	−0.724589	−	0.689181i	$-0.757970\pi$
$47$	−466.948	−1.44918	−0.724589	+	0.689181i	$0.757970\pi$
$48$	−99.2074	−0.298320
$49$	395.594	1.15333
$50$	0	0
$51$	386.870	1.06221
$52$	−72.3002	−0.192812
$53$	120.847	0.313199	0.156600	−	0.987662i	$-0.449947\pi$
$53$	120.847	0.313199	0.156600	+	0.987662i	$0.449947\pi$
$54$	−290.533	−0.732158
$55$	0	0
$56$	−575.531	−1.37337
$57$	−208.169	−0.483730
$58$	−343.400	−0.777424
$59$	−439.633	−0.970090	−0.485045	−	0.874489i	$-0.661197\pi$
$59$	−439.633	−0.970090	−0.485045	+	0.874489i	$0.661197\pi$
$60$	0	0
$61$	−137.305	−0.288198	−0.144099	−	0.989563i	$-0.546028\pi$
$61$	−137.305	−0.288198	−0.144099	+	0.989563i	$0.546028\pi$
$62$	42.3068	0.0866609
$63$	1316.00	2.63176
$64$	201.022	0.392621
$65$	0	0
$66$	−206.968	−0.386000
$67$	−512.280	−0.934104	−0.467052	−	0.884230i	$-0.654684\pi$
$67$	−512.280	−0.934104	−0.467052	+	0.884230i	$0.654684\pi$
$68$	247.747	0.441820
$69$	1065.94	1.85977
$70$	0	0
$71$	410.719	0.686526	0.343263	−	0.939239i	$-0.388468\pi$
$71$	410.719	0.686526	0.343263	+	0.939239i	$0.388468\pi$
$72$	−1025.46	−1.67850
$73$	308.004	0.493823	0.246912	−	0.969038i	$-0.420584\pi$
$73$	308.004	0.493823	0.246912	+	0.969038i	$0.420584\pi$
$74$	−147.086	−0.231060
$75$	0	0
$76$	−133.309	−0.201205
$77$	414.759	0.613847
$78$	−176.300	−0.255924
$79$	−586.462	−0.835217	−0.417608	−	0.908627i	$-0.637132\pi$
$79$	−586.462	−0.835217	−0.417608	+	0.908627i	$0.637132\pi$
$80$	0	0
$81$	308.386	0.423027
$82$	−250.401	−0.337222
$83$	−1354.20	−1.79088	−0.895440	−	0.445182i	$-0.853139\pi$
$83$	−1354.20	−1.79088	−0.895440	+	0.445182i	$0.853139\pi$
$84$	1312.66	1.70503
$85$	0	0
$86$	236.266	0.296247
$87$	1909.84	2.35352
$88$	−323.191	−0.391503
$89$	439.882	0.523904	0.261952	−	0.965081i	$-0.415634\pi$
$89$	439.882	0.523904	0.261952	+	0.965081i	$0.415634\pi$
$90$	0	0
$91$	353.302	0.406990
$92$	682.617	0.773563
$93$	−235.292	−0.262351
$94$	−729.164	−0.800080
$95$	0	0
$96$	−1626.24	−1.72894
$97$	1511.27	1.58192	0.790959	−	0.611869i	$-0.209582\pi$
$97$	1511.27	1.58192	0.790959	+	0.611869i	$0.209582\pi$
$98$	617.740	0.636747
$99$	739.006	0.750231
$100$	0	0
$101$	336.260	0.331278	0.165639	−	0.986186i	$-0.447031\pi$
$101$	336.260	0.331278	0.165639	+	0.986186i	$0.447031\pi$
$102$	604.118	0.586438
$103$	−322.712	−0.308716	−0.154358	−	0.988015i	$-0.549331\pi$
$103$	−322.712	−0.308716	−0.154358	+	0.988015i	$0.549331\pi$
$104$	−275.302	−0.259573
$105$	0	0
$106$	188.708	0.172915
$107$	−1434.62	−1.29617	−0.648083	−	0.761570i	$-0.724429\pi$
$107$	−1434.62	−1.29617	−0.648083	+	0.761570i	$0.724429\pi$
$108$	1034.75	0.921933
$109$	849.147	0.746179	0.373089	−	0.927795i	$-0.378298\pi$
$109$	849.147	0.746179	0.373089	+	0.927795i	$0.378298\pi$
$110$	0	0
$111$	818.027	0.699493
$112$	310.452	0.261919
$113$	−1614.53	−1.34409	−0.672044	−	0.740511i	$-0.734583\pi$
$113$	−1614.53	−1.34409	−0.672044	+	0.740511i	$0.734583\pi$
$114$	−325.066	−0.267064
$115$	0	0
$116$	1223.04	0.978931
$117$	629.503	0.497415
$118$	−686.509	−0.535579
$119$	−1210.64	−0.932599
$120$	0	0
$121$	−1098.09	−0.825012
$122$	−214.409	−0.159112
$123$	1392.62	1.02088
$124$	−150.678	−0.109123
$125$	0	0
$126$	2055.01	1.45297
$127$	−865.174	−0.604502	−0.302251	−	0.953228i	$-0.597738\pi$
$127$	−865.174	−0.604502	−0.302251	+	0.953228i	$0.597738\pi$
$128$	−1184.13	−0.817683
$129$	−1314.01	−0.896836
$130$	0	0
$131$	−281.400	−0.187680	−0.0938400	−	0.995587i	$-0.529914\pi$
$131$	−281.400	−0.187680	−0.0938400	+	0.995587i	$0.529914\pi$
$132$	737.127	0.486050
$133$	651.426	0.424705
$134$	−799.953	−0.515712
$135$	0	0
$136$	943.363	0.594799
$137$	2641.43	1.64725	0.823624	−	0.567137i	$-0.191949\pi$
$137$	2641.43	1.64725	0.823624	+	0.567137i	$0.191949\pi$
$138$	1664.53	1.02677
$139$	−1998.64	−1.21958	−0.609791	−	0.792562i	$-0.708747\pi$
$139$	−1998.64	−1.21958	−0.609791	+	0.792562i	$0.708747\pi$
$140$	0	0
$141$	4055.28	2.42210
$142$	641.359	0.379026
$143$	198.398	0.116020
$144$	553.153	0.320112
$145$	0	0
$146$	480.964	0.272636
$147$	−3435.60	−1.92764
$148$	523.855	0.290950
$149$	−1752.98	−0.963824	−0.481912	−	0.876220i	$-0.660058\pi$
$149$	−1752.98	−0.963824	−0.481912	+	0.876220i	$0.660058\pi$
$150$	0	0
$151$	−2794.64	−1.50613	−0.753063	−	0.657949i	$-0.771424\pi$
$151$	−2794.64	−1.50613	−0.753063	+	0.657949i	$0.771424\pi$
$152$	−507.608	−0.270871
$153$	−2157.08	−1.13980
$154$	647.669	0.338900
$155$	0	0
$156$	627.902	0.322259
$157$	−3244.87	−1.64949	−0.824743	−	0.565508i	$-0.808680\pi$
$157$	−3244.87	−1.64949	−0.824743	+	0.565508i	$0.808680\pi$
$158$	−915.792	−0.461117
$159$	−1049.51	−0.523470
$160$	0	0
$161$	−3335.68	−1.63285
$162$	481.562	0.233550
$163$	−3281.47	−1.57684	−0.788418	−	0.615139i	$-0.789100\pi$
$163$	−3281.47	−1.57684	−0.788418	+	0.615139i	$0.789100\pi$
$164$	891.818	0.424630
$165$	0	0
$166$	−2114.66	−0.988731
$167$	3126.52	1.44873	0.724364	−	0.689418i	$-0.242134\pi$
$167$	3126.52	1.44873	0.724364	+	0.689418i	$0.242134\pi$
$168$	4998.29	2.29540
$169$	169.000	0.0769231
$170$	0	0
$171$	1160.69	0.519066
$172$	−841.474	−0.373034
$173$	−97.5698	−0.0428792	−0.0214396	−	0.999770i	$-0.506825\pi$
$173$	−97.5698	−0.0428792	−0.0214396	+	0.999770i	$0.506825\pi$
$174$	2982.31	1.29936
$175$	0	0
$176$	174.335	0.0746648
$177$	3818.06	1.62137
$178$	686.900	0.289243
$179$	−34.7150	−0.0144956	−0.00724782	−	0.999974i	$-0.502307\pi$
$179$	−34.7150	−0.0144956	−0.00724782	+	0.999974i	$0.502307\pi$
$180$	0	0
$181$	−1229.35	−0.504843	−0.252422	−	0.967617i	$-0.581227\pi$
$181$	−1229.35	−0.504843	−0.252422	+	0.967617i	$0.581227\pi$
$182$	551.700	0.224696
$183$	1192.45	0.481684
$184$	2599.25	1.04141
$185$	0	0
$186$	−367.420	−0.144842
$187$	−679.839	−0.265854
$188$	2596.96	1.00746
$189$	−5056.40	−1.94603
$190$	0	0
$191$	4280.80	1.62172	0.810858	−	0.585243i	$-0.199001\pi$
$191$	4280.80	1.62172	0.810858	+	0.585243i	$0.199001\pi$
$192$	−1745.81	−0.656212
$193$	−472.320	−0.176157	−0.0880786	−	0.996114i	$-0.528073\pi$
$193$	−472.320	−0.176157	−0.0880786	+	0.996114i	$0.528073\pi$
$194$	2359.93	0.873365
$195$	0	0
$196$	−2200.12	−0.801791
$197$	4484.37	1.62182	0.810908	−	0.585173i	$-0.198974\pi$
$197$	4484.37	1.62182	0.810908	+	0.585173i	$0.198974\pi$
$198$	1154.00	0.414197
$199$	−366.240	−0.130463	−0.0652314	−	0.997870i	$-0.520779\pi$
$199$	−366.240	−0.130463	−0.0652314	+	0.997870i	$0.520779\pi$
$200$	0	0
$201$	4448.98	1.56123
$202$	525.087	0.182896
$203$	−5976.49	−2.06634
$204$	−2151.60	−0.738442
$205$	0	0
$206$	−503.932	−0.170440
$207$	−5943.41	−1.99563
$208$	148.503	0.0495039
$209$	365.810	0.121070
$210$	0	0
$211$	2122.55	0.692524	0.346262	−	0.938138i	$-0.387451\pi$
$211$	2122.55	0.692524	0.346262	+	0.938138i	$0.387451\pi$
$212$	−672.095	−0.217734
$213$	−3566.95	−1.14743
$214$	−2240.23	−0.715603
$215$	0	0
$216$	3940.08	1.24115
$217$	736.303	0.230339
$218$	1325.99	0.411960
$219$	−2674.91	−0.825358
$220$	0	0
$221$	−579.103	−0.176266
$222$	1277.39	0.386185
$223$	5926.42	1.77965	0.889826	−	0.456301i	$-0.150826\pi$
$223$	5926.42	1.77965	0.889826	+	0.456301i	$0.150826\pi$
$224$	5089.04	1.51797
$225$	0	0
$226$	−2521.17	−0.742060
$227$	895.661	0.261881	0.130941	−	0.991390i	$-0.458200\pi$
$227$	895.661	0.261881	0.130941	+	0.991390i	$0.458200\pi$
$228$	1157.74	0.336286
$229$	627.717	0.181138	0.0905692	−	0.995890i	$-0.471131\pi$
$229$	627.717	0.181138	0.0905692	+	0.995890i	$0.471131\pi$
$230$	0	0
$231$	−3602.04	−1.02596
$232$	4657.03	1.31788
$233$	−2303.72	−0.647734	−0.323867	−	0.946103i	$-0.604983\pi$
$233$	−2303.72	−0.647734	−0.323867	+	0.946103i	$0.604983\pi$
$234$	983.002	0.274619
$235$	0	0
$236$	2445.04	0.674401
$237$	5093.22	1.39595
$238$	−1890.48	−0.514881
$239$	544.622	0.147400	0.0737001	−	0.997280i	$-0.476519\pi$
$239$	544.622	0.147400	0.0737001	+	0.997280i	$0.476519\pi$
$240$	0	0
$241$	5426.10	1.45031	0.725157	−	0.688584i	$-0.241767\pi$
$241$	5426.10	1.45031	0.725157	+	0.688584i	$0.241767\pi$
$242$	−1714.73	−0.455483
$243$	2345.23	0.619121
$244$	763.629	0.200354
$245$	0	0
$246$	2174.65	0.563621
$247$	311.606	0.0802713
$248$	−573.746	−0.146907
$249$	11760.8	2.99321
$250$	0	0
$251$	−5221.22	−1.31299	−0.656494	−	0.754331i	$-0.727961\pi$
$251$	−5221.22	−1.31299	−0.656494	+	0.754331i	$0.727961\pi$
$252$	−7319.02	−1.82958
$253$	−1873.16	−0.465472
$254$	−1351.02	−0.333741
$255$	0	0
$256$	−3457.26	−0.844057
$257$	−658.206	−0.159758	−0.0798789	−	0.996805i	$-0.525453\pi$
$257$	−658.206	−0.159758	−0.0798789	+	0.996805i	$0.525453\pi$
$258$	−2051.89	−0.495136
$259$	−2559.87	−0.614141
$260$	0	0
$261$	−10648.7	−2.52544
$262$	−439.422	−0.103617
$263$	−3246.45	−0.761160	−0.380580	−	0.924748i	$-0.624276\pi$
$263$	−3246.45	−0.761160	−0.380580	+	0.924748i	$0.624276\pi$
$264$	2806.81	0.654344
$265$	0	0
$266$	1017.24	0.234477
$267$	−3820.23	−0.875634
$268$	2849.07	0.649384
$269$	−2585.80	−0.586093	−0.293047	−	0.956098i	$-0.594669\pi$
$269$	−2585.80	−0.586093	−0.293047	+	0.956098i	$0.594669\pi$
$270$	0	0
$271$	988.933	0.221673	0.110836	−	0.993839i	$-0.464647\pi$
$271$	988.933	0.221673	0.110836	+	0.993839i	$0.464647\pi$
$272$	−508.867	−0.113436
$273$	−3068.31	−0.680229
$274$	4124.74	0.909433
$275$	0	0
$276$	−5928.30	−1.29290
$277$	−8142.40	−1.76617	−0.883086	−	0.469211i	$-0.844538\pi$
$277$	−8142.40	−1.76617	−0.883086	+	0.469211i	$0.844538\pi$
$278$	−3120.97	−0.673322
$279$	1311.92	0.281515
$280$	0	0
$281$	1534.21	0.325705	0.162853	−	0.986650i	$-0.447930\pi$
$281$	1534.21	0.325705	0.162853	+	0.986650i	$0.447930\pi$
$282$	6332.54	1.33722
$283$	6965.00	1.46299	0.731495	−	0.681847i	$-0.238823\pi$
$283$	6965.00	1.46299	0.731495	+	0.681847i	$0.238823\pi$
$284$	−2284.23	−0.477269
$285$	0	0
$286$	309.809	0.0640537
$287$	−4357.96	−0.896314
$288$	9067.49	1.85523
$289$	−2928.62	−0.596096
$290$	0	0
$291$	−13124.9	−2.64396
$292$	−1712.98	−0.343303
$293$	−640.029	−0.127614	−0.0638070	−	0.997962i	$-0.520324\pi$
$293$	−640.029	−0.127614	−0.0638070	+	0.997962i	$0.520324\pi$
$294$	−5364.87	−1.06424
$295$	0	0
$296$	1994.72	0.391691
$297$	−2839.44	−0.554750
$298$	−2737.37	−0.532120
$299$	−1595.60	−0.308616
$300$	0	0
$301$	4111.95	0.787404
$302$	−4363.99	−0.831520
$303$	−2920.30	−0.553686
$304$	273.813	0.0516587
$305$	0	0
$306$	−3368.40	−0.629276
$307$	100.406	0.0186660	0.00933299	−	0.999956i	$-0.497029\pi$
$307$	100.406	0.0186660	0.00933299	+	0.999956i	$0.497029\pi$
$308$	−2306.71	−0.426743
$309$	2802.64	0.515977
$310$	0	0
$311$	−3878.92	−0.707245	−0.353623	−	0.935388i	$-0.615050\pi$
$311$	−3878.92	−0.707245	−0.353623	+	0.935388i	$0.615050\pi$
$312$	2390.90	0.433841
$313$	3789.39	0.684311	0.342155	−	0.939643i	$-0.388843\pi$
$313$	3789.39	0.684311	0.342155	+	0.939643i	$0.388843\pi$
$314$	−5067.04	−0.910668
$315$	0	0
$316$	3261.64	0.580638
$317$	−4406.81	−0.780791	−0.390396	−	0.920647i	$-0.627662\pi$
$317$	−4406.81	−0.780791	−0.390396	+	0.920647i	$0.627662\pi$
$318$	−1638.87	−0.289004
$319$	−3356.11	−0.589048
$320$	0	0
$321$	12459.2	2.16636
$322$	−5208.84	−0.901482
$323$	−1067.76	−0.183938
$324$	−1715.11	−0.294086
$325$	0	0
$326$	−5124.19	−0.870559
$327$	−7374.55	−1.24714
$328$	3395.83	0.571657
$329$	−12690.3	−2.12656
$330$	0	0
$331$	−4131.49	−0.686064	−0.343032	−	0.939324i	$-0.611454\pi$
$331$	−4131.49	−0.686064	−0.343032	+	0.939324i	$0.611454\pi$
$332$	7531.47	1.24501
$333$	−4561.10	−0.750591
$334$	4882.23	0.799831
$335$	0	0
$336$	−2696.17	−0.437762
$337$	4560.82	0.737221	0.368611	−	0.929584i	$-0.379834\pi$
$337$	4560.82	0.737221	0.368611	+	0.929584i	$0.379834\pi$
$338$	263.902	0.0424686
$339$	14021.6	2.24646
$340$	0	0
$341$	413.473	0.0656622
$342$	1812.48	0.286572
$343$	1429.34	0.225007
$344$	−3204.14	−0.502196
$345$	0	0
$346$	−152.360	−0.0236733
$347$	−10069.4	−1.55779	−0.778896	−	0.627153i	$-0.784220\pi$
$347$	−10069.4	−1.55779	−0.778896	+	0.627153i	$0.784220\pi$
$348$	−10621.6	−1.63615
$349$	5879.32	0.901757	0.450878	−	0.892585i	$-0.351111\pi$
$349$	5879.32	0.901757	0.450878	+	0.892585i	$0.351111\pi$
$350$	0	0
$351$	−2418.70	−0.367808
$352$	2857.76	0.432725
$353$	9142.56	1.37850	0.689249	−	0.724525i	$-0.257941\pi$
$353$	9142.56	1.37850	0.689249	+	0.724525i	$0.257941\pi$
$354$	5962.10	0.895147
$355$	0	0
$356$	−2446.43	−0.364215
$357$	10514.0	1.55871
$358$	−54.2093	−0.00800293
$359$	−2754.32	−0.404924	−0.202462	−	0.979290i	$-0.564894\pi$
$359$	−2754.32	−0.404924	−0.202462	+	0.979290i	$0.564894\pi$
$360$	0	0
$361$	−6284.45	−0.916235
$362$	−1919.69	−0.278720
$363$	9536.54	1.37889
$364$	−1964.91	−0.282937
$365$	0	0
$366$	1862.07	0.265934
$367$	−3040.19	−0.432416	−0.216208	−	0.976347i	$-0.569369\pi$
$367$	−3040.19	−0.432416	−0.216208	+	0.976347i	$0.569369\pi$
$368$	−1402.08	−0.198610
$369$	−7764.88	−1.09546
$370$	0	0
$371$	3284.26	0.459596
$372$	1308.59	0.182385
$373$	5384.72	0.747481	0.373740	−	0.927533i	$-0.378075\pi$
$373$	5384.72	0.747481	0.373740	+	0.927533i	$0.378075\pi$
$374$	−1061.60	−0.146776
$375$	0	0
$376$	9888.59	1.35629
$377$	−2858.82	−0.390548
$378$	−7895.84	−1.07439
$379$	−3424.27	−0.464097	−0.232049	−	0.972704i	$-0.574543\pi$
$379$	−3424.27	−0.464097	−0.232049	+	0.972704i	$0.574543\pi$
$380$	0	0
$381$	7513.74	1.01034
$382$	6684.69	0.895336
$383$	382.985	0.0510956	0.0255478	−	0.999674i	$-0.491867\pi$
$383$	382.985	0.0510956	0.0255478	+	0.999674i	$0.491867\pi$
$384$	10283.8	1.36665
$385$	0	0
$386$	−737.553	−0.0972551
$387$	7326.54	0.962349
$388$	−8405.00	−1.09974
$389$	8588.34	1.11940	0.559699	−	0.828696i	$-0.310917\pi$
$389$	8588.34	1.11940	0.559699	+	0.828696i	$0.310917\pi$
$390$	0	0
$391$	5467.56	0.707178
$392$	−8377.52	−1.07941
$393$	2443.87	0.313681
$394$	7002.57	0.895392
$395$	0	0
$396$	−4110.02	−0.521556
$397$	7239.16	0.915171	0.457586	−	0.889166i	$-0.348714\pi$
$397$	7239.16	0.915171	0.457586	+	0.889166i	$0.348714\pi$
$398$	−571.904	−0.0720275
$399$	−5657.41	−0.709837
$400$	0	0
$401$	4269.62	0.531708	0.265854	−	0.964013i	$-0.414346\pi$
$401$	4269.62	0.531708	0.265854	+	0.964013i	$0.414346\pi$
$402$	6947.32	0.861942
$403$	352.206	0.0435351
$404$	−1870.12	−0.230302
$405$	0	0
$406$	−9332.60	−1.14081
$407$	−1437.50	−0.175072
$408$	−8192.78	−0.994125
$409$	13562.5	1.63967	0.819834	−	0.572602i	$-0.194066\pi$
$409$	13562.5	1.63967	0.819834	+	0.572602i	$0.194066\pi$
$410$	0	0
$411$	−22939.9	−2.75315
$412$	1794.78	0.214618
$413$	−11947.9	−1.42353
$414$	−9280.95	−1.10177
$415$	0	0
$416$	2434.31	0.286904
$417$	17357.5	2.03837
$418$	571.232	0.0668418
$419$	−14576.9	−1.69959	−0.849794	−	0.527114i	$-0.823274\pi$
$419$	−14576.9	−1.69959	−0.849794	+	0.527114i	$0.823274\pi$
$420$	0	0
$421$	15848.4	1.83469	0.917343	−	0.398099i	$-0.130330\pi$
$421$	15848.4	1.83469	0.917343	+	0.398099i	$0.130330\pi$
$422$	3314.48	0.382337
$423$	−22611.2	−2.59904
$424$	−2559.18	−0.293124
$425$	0	0
$426$	−5569.98	−0.633490
$427$	−3731.55	−0.422909
$428$	7978.70	0.901087
$429$	−1723.02	−0.193912
$430$	0	0
$431$	10694.7	1.19524	0.597618	−	0.801781i	$-0.296114\pi$
$431$	10694.7	1.19524	0.597618	+	0.801781i	$0.296114\pi$
$432$	−2125.35	−0.236703
$433$	16079.0	1.78454	0.892272	−	0.451498i	$-0.149110\pi$
$433$	16079.0	1.78454	0.892272	+	0.451498i	$0.149110\pi$
$434$	1149.78	0.127168
$435$	0	0
$436$	−4722.57	−0.518739
$437$	−2942.01	−0.322049
$438$	−4177.01	−0.455674
$439$	6035.80	0.656203	0.328101	−	0.944643i	$-0.393591\pi$
$439$	6035.80	0.656203	0.328101	+	0.944643i	$0.393591\pi$
$440$	0	0
$441$	19156.0	2.06845
$442$	−904.300	−0.0973149
$443$	−10201.3	−1.09409	−0.547043	−	0.837105i	$-0.684247\pi$
$443$	−10201.3	−1.09409	−0.547043	+	0.837105i	$0.684247\pi$
$444$	−4549.50	−0.486283
$445$	0	0
$446$	9254.41	0.982532
$447$	15224.0	1.61090
$448$	5463.19	0.576141
$449$	−5822.54	−0.611988	−0.305994	−	0.952033i	$-0.598989\pi$
$449$	−5822.54	−0.611988	−0.305994	+	0.952033i	$0.598989\pi$
$450$	0	0
$451$	−2447.22	−0.255511
$452$	8979.27	0.934402
$453$	24270.5	2.51728
$454$	1398.62	0.144583
$455$	0	0
$456$	4408.40	0.452724
$457$	−4621.60	−0.473062	−0.236531	−	0.971624i	$-0.576010\pi$
$457$	−4621.60	−0.473062	−0.236531	+	0.971624i	$0.576010\pi$
$458$	980.213	0.100005
$459$	8288.03	0.842816
$460$	0	0
$461$	5127.77	0.518056	0.259028	−	0.965870i	$-0.416598\pi$
$461$	5127.77	0.518056	0.259028	+	0.965870i	$0.416598\pi$
$462$	−5624.78	−0.566425
$463$	−6486.27	−0.651064	−0.325532	−	0.945531i	$-0.605543\pi$
$463$	−6486.27	−0.651064	−0.325532	+	0.945531i	$0.605543\pi$
$464$	−2512.09	−0.251338
$465$	0	0
$466$	−3597.39	−0.357609
$467$	−12978.0	−1.28598	−0.642990	−	0.765875i	$-0.722306\pi$
$467$	−12978.0	−1.28598	−0.642990	+	0.765875i	$0.722306\pi$
$468$	−3501.01	−0.345800
$469$	−13922.3	−1.37073
$470$	0	0
$471$	28180.6	2.75689
$472$	9310.13	0.907910
$473$	2309.08	0.224464
$474$	7953.34	0.770694
$475$	0	0
$476$	6733.04	0.648337
$477$	5851.79	0.561709
$478$	850.456	0.0813786
$479$	−5808.96	−0.554109	−0.277055	−	0.960854i	$-0.589358\pi$
$479$	−5808.96	−0.554109	−0.277055	+	0.960854i	$0.589358\pi$
$480$	0	0
$481$	−1224.50	−0.116076
$482$	8473.14	0.800707
$483$	28969.2	2.72908
$484$	6107.09	0.573543
$485$	0	0
$486$	3662.20	0.341812
$487$	5387.14	0.501262	0.250631	−	0.968083i	$-0.419362\pi$
$487$	5387.14	0.501262	0.250631	+	0.968083i	$0.419362\pi$
$488$	2907.72	0.269726
$489$	28498.4	2.63547
$490$	0	0
$491$	15259.1	1.40251	0.701255	−	0.712911i	$-0.252624\pi$
$491$	15259.1	1.40251	0.701255	+	0.712911i	$0.252624\pi$
$492$	−7745.14	−0.709711
$493$	9796.16	0.894922
$494$	486.589	0.0443172
$495$	0	0
$496$	309.489	0.0280171
$497$	11162.1	1.00742
$498$	18365.1	1.65253
$499$	1856.04	0.166509	0.0832544	−	0.996528i	$-0.473469\pi$
$499$	1856.04	0.166509	0.0832544	+	0.996528i	$0.473469\pi$
$500$	0	0
$501$	−27152.8	−2.42135
$502$	−8153.20	−0.724891
$503$	−1049.46	−0.0930283	−0.0465142	−	0.998918i	$-0.514811\pi$
$503$	−1049.46	−0.0930283	−0.0465142	+	0.998918i	$0.514811\pi$
$504$	−27869.1	−2.46307
$505$	0	0
$506$	−2925.04	−0.256984
$507$	−1467.71	−0.128566
$508$	4811.71	0.420246
$509$	−551.106	−0.0479909	−0.0239954	−	0.999712i	$-0.507639\pi$
$509$	−551.106	−0.0479909	−0.0239954	+	0.999712i	$0.507639\pi$
$510$	0	0
$511$	8370.64	0.724649
$512$	4074.36	0.351686
$513$	−4459.66	−0.383818
$514$	−1027.82	−0.0882010
$515$	0	0
$516$	7307.92	0.623475
$517$	−7126.26	−0.606214
$518$	−3997.37	−0.339063
$519$	847.361	0.0716667
$520$	0	0
$521$	−8995.30	−0.756413	−0.378206	−	0.925721i	$-0.623459\pi$
$521$	−8995.30	−0.756413	−0.378206	+	0.925721i	$0.623459\pi$
$522$	−16628.5	−1.39427
$523$	−2663.91	−0.222724	−0.111362	−	0.993780i	$-0.535521\pi$
$523$	−2663.91	−0.222724	−0.111362	+	0.993780i	$0.535521\pi$
$524$	1565.02	0.130474
$525$	0	0
$526$	−5069.51	−0.420230
$527$	−1206.89	−0.0997586
$528$	−1514.04	−0.124792
$529$	2897.77	0.238167
$530$	0	0
$531$	−21288.5	−1.73981
$532$	−3622.94	−0.295253
$533$	−2084.60	−0.169408
$534$	−5965.49	−0.483431
$535$	0	0
$536$	10848.6	0.874232
$537$	301.488	0.0242275
$538$	−4037.86	−0.323577
$539$	6037.30	0.482458
$540$	0	0
$541$	−6169.23	−0.490270	−0.245135	−	0.969489i	$-0.578832\pi$
$541$	−6169.23	−0.490270	−0.245135	+	0.969489i	$0.578832\pi$
$542$	1544.27	0.122384
$543$	10676.5	0.843776
$544$	−8341.52	−0.657426
$545$	0	0
$546$	−4791.32	−0.375549
$547$	−5140.42	−0.401807	−0.200904	−	0.979611i	$-0.564388\pi$
$547$	−5140.42	−0.401807	−0.200904	+	0.979611i	$0.564388\pi$
$548$	−14690.5	−1.14516
$549$	−6648.76	−0.516871
$550$	0	0
$551$	−5271.15	−0.407547
$552$	−22573.6	−1.74057
$553$	−15938.3	−1.22562
$554$	−12714.8	−0.975090
$555$	0	0
$556$	11115.5	0.847847
$557$	−2778.56	−0.211367	−0.105683	−	0.994400i	$-0.533703\pi$
$557$	−2778.56	−0.211367	−0.105683	+	0.994400i	$0.533703\pi$
$558$	2048.64	0.155422
$559$	1966.93	0.148823
$560$	0	0
$561$	5904.17	0.444339
$562$	2395.75	0.179819
$563$	−4906.14	−0.367263	−0.183632	−	0.982995i	$-0.558785\pi$
$563$	−4906.14	−0.367263	−0.183632	+	0.982995i	$0.558785\pi$
$564$	−22553.7	−1.68383
$565$	0	0
$566$	10876.2	0.807706
$567$	8381.04	0.620759
$568$	−8697.82	−0.642522
$569$	−9363.15	−0.689849	−0.344924	−	0.938631i	$-0.612095\pi$
$569$	−9363.15	−0.689849	−0.344924	+	0.938631i	$0.612095\pi$
$570$	0	0
$571$	7199.32	0.527640	0.263820	−	0.964572i	$-0.415018\pi$
$571$	7199.32	0.527640	0.263820	+	0.964572i	$0.415018\pi$
$572$	−1103.40	−0.0806564
$573$	−37177.3	−2.71048
$574$	−6805.18	−0.494848
$575$	0	0
$576$	9734.14	0.704148
$577$	11449.6	0.826086	0.413043	−	0.910711i	$-0.364466\pi$
$577$	11449.6	0.826086	0.413043	+	0.910711i	$0.364466\pi$
$578$	−4573.19	−0.329100
$579$	4101.94	0.294423
$580$	0	0
$581$	−36803.3	−2.62798
$582$	−20495.2	−1.45971
$583$	1844.28	0.131016
$584$	−6522.62	−0.462171
$585$	0	0
$586$	−999.439	−0.0704547
$587$	5439.39	0.382466	0.191233	−	0.981545i	$-0.438751\pi$
$587$	5439.39	0.382466	0.191233	+	0.981545i	$0.438751\pi$
$588$	19107.3	1.34008
$589$	649.406	0.0454301
$590$	0	0
$591$	−38945.2	−2.71064
$592$	−1075.99	−0.0747006
$593$	28405.8	1.96709	0.983547	−	0.180651i	$-0.0578204\pi$
$593$	28405.8	1.96709	0.983547	+	0.180651i	$0.0578204\pi$
$594$	−4433.93	−0.306273
$595$	0	0
$596$	9749.30	0.670045
$597$	3180.67	0.218051
$598$	−2491.62	−0.170384
$599$	−10482.3	−0.715020	−0.357510	−	0.933909i	$-0.616374\pi$
$599$	−10482.3	−0.715020	−0.357510	+	0.933909i	$0.616374\pi$
$600$	0	0
$601$	3199.54	0.217158	0.108579	−	0.994088i	$-0.465370\pi$
$601$	3199.54	0.217158	0.108579	+	0.994088i	$0.465370\pi$
$602$	6421.02	0.434720
$603$	−24806.3	−1.67527
$604$	15542.6	1.04705
$605$	0	0
$606$	−4560.20	−0.305686
$607$	−11342.8	−0.758468	−0.379234	−	0.925301i	$-0.623812\pi$
$607$	−11342.8	−0.758468	−0.379234	+	0.925301i	$0.623812\pi$
$608$	4488.44	0.299392
$609$	51903.7	3.45361
$610$	0	0
$611$	−6070.32	−0.401930
$612$	11996.7	0.792384
$613$	−14385.4	−0.947831	−0.473916	−	0.880570i	$-0.657160\pi$
$613$	−14385.4	−0.947831	−0.473916	+	0.880570i	$0.657160\pi$
$614$	156.789	0.0103053
$615$	0	0
$616$	−8783.39	−0.574502
$617$	−22056.8	−1.43918	−0.719588	−	0.694401i	$-0.755669\pi$
$617$	−22056.8	−1.43918	−0.719588	+	0.694401i	$0.755669\pi$
$618$	4376.48	0.284867
$619$	13621.4	0.884477	0.442238	−	0.896898i	$-0.354185\pi$
$619$	13621.4	0.884477	0.442238	+	0.896898i	$0.354185\pi$
$620$	0	0
$621$	22836.0	1.47565
$622$	−6057.14	−0.390465
$623$	11954.7	0.768789
$624$	−1289.70	−0.0827390
$625$	0	0
$626$	5917.34	0.377803
$627$	−3176.94	−0.202352
$628$	18046.5	1.14671
$629$	4195.92	0.265982
$630$	0	0
$631$	−18737.5	−1.18214	−0.591068	−	0.806622i	$-0.701293\pi$
$631$	−18737.5	−1.18214	−0.591068	+	0.806622i	$0.701293\pi$
$632$	12419.6	0.781683
$633$	−18433.7	−1.15746
$634$	−6881.46	−0.431069
$635$	0	0
$636$	5836.91	0.363913
$637$	5142.72	0.319877
$638$	−5240.75	−0.325209
$639$	19888.4	1.23125
$640$	0	0
$641$	29798.7	1.83616	0.918081	−	0.396394i	$-0.129739\pi$
$641$	29798.7	1.83616	0.918081	+	0.396394i	$0.129739\pi$
$642$	19455.6	1.19603
$643$	22983.5	1.40961	0.704807	−	0.709399i	$-0.251034\pi$
$643$	22983.5	1.40961	0.704807	+	0.709399i	$0.251034\pi$
$644$	18551.5	1.13515
$645$	0	0
$646$	−1667.37	−0.101551
$647$	24905.4	1.51334	0.756672	−	0.653794i	$-0.226824\pi$
$647$	24905.4	1.51334	0.756672	+	0.653794i	$0.226824\pi$
$648$	−6530.72	−0.395912
$649$	−6709.39	−0.405804
$650$	0	0
$651$	−6394.54	−0.384980
$652$	18250.1	1.09621
$653$	−10077.8	−0.603946	−0.301973	−	0.953316i	$-0.597645\pi$
$653$	−10077.8	−0.603946	−0.301973	+	0.953316i	$0.597645\pi$
$654$	−11515.7	−0.688534
$655$	0	0
$656$	−1831.77	−0.109022
$657$	14914.6	0.885650
$658$	−19816.5	−1.17406
$659$	12334.6	0.729116	0.364558	−	0.931181i	$-0.381220\pi$
$659$	12334.6	0.729116	0.364558	+	0.931181i	$0.381220\pi$
$660$	0	0
$661$	−12749.1	−0.750202	−0.375101	−	0.926984i	$-0.622392\pi$
$661$	−12749.1	−0.750202	−0.375101	+	0.926984i	$0.622392\pi$
$662$	−6451.54	−0.378771
$663$	5029.31	0.294604
$664$	28678.1	1.67609
$665$	0	0
$666$	−7122.40	−0.414395
$667$	26991.3	1.56688
$668$	−17388.3	−1.00715
$669$	−51468.9	−2.97444
$670$	0	0
$671$	−2095.46	−0.120558
$672$	−44196.5	−2.53708
$673$	13618.2	0.780007	0.390004	−	0.920813i	$-0.372474\pi$
$673$	13618.2	0.780007	0.390004	+	0.920813i	$0.372474\pi$
$674$	7121.96	0.407014
$675$	0	0
$676$	−939.902	−0.0534765
$677$	−9655.67	−0.548150	−0.274075	−	0.961708i	$-0.588372\pi$
$677$	−9655.67	−0.548150	−0.274075	+	0.961708i	$0.588372\pi$
$678$	21895.5	1.24025
$679$	41071.9	2.32135
$680$	0	0
$681$	−7778.51	−0.437699
$682$	645.660	0.0362516
$683$	−16316.8	−0.914119	−0.457060	−	0.889436i	$-0.651097\pi$
$683$	−16316.8	−0.914119	−0.457060	+	0.889436i	$0.651097\pi$
$684$	−6455.25	−0.360852
$685$	0	0
$686$	2232.00	0.124225
$687$	−5451.51	−0.302748
$688$	1728.37	0.0957753
$689$	1571.01	0.0868658
$690$	0	0
$691$	2350.84	0.129421	0.0647106	−	0.997904i	$-0.479388\pi$
$691$	2350.84	0.129421	0.0647106	+	0.997904i	$0.479388\pi$
$692$	542.640	0.0298093
$693$	20084.0	1.10091
$694$	−15723.9	−0.860045
$695$	0	0
$696$	−40444.7	−2.20266
$697$	7143.20	0.388189
$698$	9180.88	0.497853
$699$	20007.1	1.08260
$700$	0	0
$701$	−8076.90	−0.435179	−0.217589	−	0.976040i	$-0.569819\pi$
$701$	−8076.90	−0.435179	−0.217589	+	0.976040i	$0.569819\pi$
$702$	−3776.93	−0.203064
$703$	−2257.76	−0.121128
$704$	3067.87	0.164239
$705$	0	0
$706$	14276.6	0.761058
$707$	9138.55	0.486125
$708$	−21234.3	−1.12717
$709$	−13624.9	−0.721712	−0.360856	−	0.932622i	$-0.617515\pi$
$709$	−13624.9	−0.721712	−0.360856	+	0.932622i	$0.617515\pi$
$710$	0	0
$711$	−28398.4	−1.49792
$712$	−9315.43	−0.490324
$713$	−3325.33	−0.174663
$714$	16418.2	0.860553
$715$	0	0
$716$	193.069	0.0100773
$717$	−4729.86	−0.246359
$718$	−4301.02	−0.223555
$719$	16235.8	0.842131	0.421066	−	0.907030i	$-0.361656\pi$
$719$	16235.8	0.842131	0.421066	+	0.907030i	$0.361656\pi$
$720$	0	0
$721$	−8770.37	−0.453018
$722$	−9813.51	−0.505846
$723$	−47123.8	−2.42400
$724$	6837.08	0.350964
$725$	0	0
$726$	14891.8	0.761277
$727$	−24181.2	−1.23361	−0.616803	−	0.787118i	$-0.711572\pi$
$727$	−24181.2	−1.23361	−0.616803	+	0.787118i	$0.711572\pi$
$728$	−7481.91	−0.380904
$729$	−28693.9	−1.45780
$730$	0	0
$731$	−6739.96	−0.341021
$732$	−6631.86	−0.334864
$733$	−3053.70	−0.153876	−0.0769379	−	0.997036i	$-0.524514\pi$
$733$	−3053.70	−0.153876	−0.0769379	+	0.997036i	$0.524514\pi$
$734$	−4747.41	−0.238733
$735$	0	0
$736$	−22983.4	−1.15106
$737$	−7818.10	−0.390751
$738$	−12125.3	−0.604793
$739$	−8033.62	−0.399894	−0.199947	−	0.979807i	$-0.564077\pi$
$739$	−8033.62	−0.399894	−0.199947	+	0.979807i	$0.564077\pi$
$740$	0	0
$741$	−2706.19	−0.134163
$742$	5128.54	0.253739
$743$	16139.6	0.796912	0.398456	−	0.917187i	$-0.369546\pi$
$743$	16139.6	0.796912	0.398456	+	0.917187i	$0.369546\pi$
$744$	4982.79	0.245535
$745$	0	0
$746$	8408.53	0.412678
$747$	−65574.9	−3.21186
$748$	3780.96	0.184820
$749$	−38988.7	−1.90202
$750$	0	0
$751$	−18491.1	−0.898469	−0.449235	−	0.893414i	$-0.648303\pi$
$751$	−18491.1	−0.898469	−0.449235	+	0.893414i	$0.648303\pi$
$752$	−5334.08	−0.258662
$753$	45344.5	2.19448
$754$	−4464.20	−0.215619
$755$	0	0
$756$	28121.5	1.35287
$757$	−160.630	−0.00771227	−0.00385613	−	0.999993i	$-0.501227\pi$
$757$	−160.630	−0.00771227	−0.00385613	+	0.999993i	$0.501227\pi$
$758$	−5347.17	−0.256224
$759$	16267.7	0.777973
$760$	0	0
$761$	26799.1	1.27656	0.638282	−	0.769803i	$-0.279645\pi$
$761$	26799.1	1.27656	0.638282	+	0.769803i	$0.279645\pi$
$762$	11733.1	0.557803
$763$	23077.3	1.09496
$764$	−23807.9	−1.12741
$765$	0	0
$766$	598.052	0.0282095
$767$	−5715.22	−0.269054
$768$	30025.1	1.41073
$769$	−5145.82	−0.241304	−0.120652	−	0.992695i	$-0.538499\pi$
$769$	−5145.82	−0.241304	−0.120652	+	0.992695i	$0.538499\pi$
$770$	0	0
$771$	5716.29	0.267013
$772$	2626.83	0.122463
$773$	−12810.6	−0.596072	−0.298036	−	0.954555i	$-0.596332\pi$
$773$	−12810.6	−0.596072	−0.298036	+	0.954555i	$0.596332\pi$
$774$	11440.8	0.531306
$775$	0	0
$776$	−32004.3	−1.48052
$777$	22231.6	1.02645
$778$	13411.1	0.618011
$779$	−3843.64	−0.176781
$780$	0	0
$781$	6268.13	0.287185
$782$	8537.89	0.390428
$783$	40915.0	1.86741
$784$	4518.98	0.205857
$785$	0	0
$786$	3816.23	0.173181
$787$	−28073.0	−1.27153	−0.635764	−	0.771883i	$-0.719315\pi$
$787$	−28073.0	−1.27153	−0.635764	+	0.771883i	$0.719315\pi$
$788$	−24940.0	−1.12748
$789$	28194.3	1.27217
$790$	0	0
$791$	−43878.1	−1.97235
$792$	−15650.0	−0.702144
$793$	−1784.96	−0.0799318
$794$	11304.3	0.505259
$795$	0	0
$796$	2036.87	0.0906970
$797$	−30093.1	−1.33746	−0.668729	−	0.743507i	$-0.733161\pi$
$797$	−30093.1	−1.33746	−0.668729	+	0.743507i	$0.733161\pi$
$798$	−8834.35	−0.391896
$799$	20800.8	0.921003
$800$	0	0
$801$	21300.6	0.939598
$802$	6667.24	0.293552
$803$	4700.56	0.206574
$804$	−24743.2	−1.08536
$805$	0	0
$806$	549.989	0.0240354
$807$	22456.8	0.979575
$808$	−7120.99	−0.310044
$809$	−24337.1	−1.05766	−0.528831	−	0.848727i	$-0.677369\pi$
$809$	−24337.1	−1.05766	−0.528831	+	0.848727i	$0.677369\pi$
$810$	0	0
$811$	19078.7	0.826071	0.413035	−	0.910715i	$-0.364469\pi$
$811$	19078.7	0.826071	0.413035	+	0.910715i	$0.364469\pi$
$812$	33238.5	1.43651
$813$	−8588.54	−0.370496
$814$	−2244.74	−0.0966559
$815$	0	0
$816$	4419.33	0.189593
$817$	3626.66	0.155301
$818$	21178.6	0.905248
$819$	17108.0	0.729919
$820$	0	0
$821$	2013.92	0.0856104	0.0428052	−	0.999083i	$-0.486371\pi$
$821$	2013.92	0.0856104	0.0428052	+	0.999083i	$0.486371\pi$
$822$	−35821.9	−1.51999
$823$	7692.10	0.325795	0.162898	−	0.986643i	$-0.447916\pi$
$823$	7692.10	0.325795	0.162898	+	0.986643i	$0.447916\pi$
$824$	6834.10	0.288929
$825$	0	0
$826$	−18657.3	−0.785922
$827$	4762.76	0.200263	0.100131	−	0.994974i	$-0.468074\pi$
$827$	4762.76	0.200263	0.100131	+	0.994974i	$0.468074\pi$
$828$	33054.6	1.38735
$829$	19977.7	0.836976	0.418488	−	0.908222i	$-0.362560\pi$
$829$	19977.7	0.836976	0.418488	+	0.908222i	$0.362560\pi$
$830$	0	0
$831$	70714.0	2.95191
$832$	2613.28	0.108893
$833$	−17622.3	−0.732984
$834$	27104.6	1.12537
$835$	0	0
$836$	−2034.47	−0.0841671
$837$	−5040.72	−0.208164
$838$	−22762.6	−0.938330
$839$	−30615.8	−1.25980	−0.629901	−	0.776676i	$-0.716905\pi$
$839$	−30615.8	−1.25980	−0.629901	+	0.776676i	$0.716905\pi$
$840$	0	0
$841$	23971.0	0.982861
$842$	24748.1	1.01292
$843$	−13324.1	−0.544372
$844$	−11804.7	−0.481439
$845$	0	0
$846$	−35308.5	−1.43491
$847$	−29842.9	−1.21064
$848$	1380.47	0.0559026
$849$	−60488.6	−2.44519
$850$	0	0
$851$	11561.0	0.465696
$852$	19837.8	0.797690
$853$	−5660.88	−0.227227	−0.113614	−	0.993525i	$-0.536243\pi$
$853$	−5660.88	−0.227227	−0.113614	+	0.993525i	$0.536243\pi$
$854$	−5827.01	−0.233485
$855$	0	0
$856$	30381.0	1.21309
$857$	−41346.1	−1.64802	−0.824012	−	0.566572i	$-0.808269\pi$
$857$	−41346.1	−1.64802	−0.824012	+	0.566572i	$0.808269\pi$
$858$	−2690.58	−0.107057
$859$	−34810.5	−1.38268	−0.691339	−	0.722530i	$-0.742979\pi$
$859$	−34810.5	−1.38268	−0.691339	+	0.722530i	$0.742979\pi$
$860$	0	0
$861$	37847.4	1.49807
$862$	16700.4	0.659880
$863$	8360.51	0.329774	0.164887	−	0.986312i	$-0.447274\pi$
$863$	8360.51	0.329774	0.164887	+	0.986312i	$0.447274\pi$
$864$	−34839.5	−1.37183
$865$	0	0
$866$	25108.2	0.985233
$867$	25434.1	0.996293
$868$	−4094.99	−0.160130
$869$	−8950.21	−0.349385
$870$	0	0
$871$	−6659.64	−0.259074
$872$	−17982.4	−0.698352
$873$	73180.6	2.83710
$874$	−4594.10	−0.177801
$875$	0	0
$876$	14876.6	0.573784
$877$	40579.3	1.56245	0.781223	−	0.624251i	$-0.214596\pi$
$877$	40579.3	1.56245	0.781223	+	0.624251i	$0.214596\pi$
$878$	9425.22	0.362285
$879$	5558.43	0.213289
$880$	0	0
$881$	10445.2	0.399442	0.199721	−	0.979853i	$-0.435996\pi$
$881$	10445.2	0.399442	0.199721	+	0.979853i	$0.435996\pi$
$882$	29913.0	1.14198
$883$	−18227.6	−0.694685	−0.347343	−	0.937738i	$-0.612916\pi$
$883$	−18227.6	−0.694685	−0.347343	+	0.937738i	$0.612916\pi$
$884$	3220.71	0.122539
$885$	0	0
$886$	−15929.9	−0.604036
$887$	23517.7	0.890245	0.445122	−	0.895470i	$-0.353160\pi$
$887$	23517.7	0.890245	0.445122	+	0.895470i	$0.353160\pi$
$888$	−17323.4	−0.654658
$889$	−23512.9	−0.887061
$890$	0	0
$891$	4706.40	0.176959
$892$	−32960.1	−1.23720
$893$	−11192.6	−0.419424
$894$	23773.1	0.889366
$895$	0	0
$896$	−32181.2	−1.19989
$897$	13857.3	0.515809
$898$	−9092.21	−0.337874
$899$	−5957.95	−0.221033
$900$	0	0
$901$	−5383.28	−0.199049
$902$	−3821.47	−0.141065
$903$	−35710.9	−1.31604
$904$	34191.0	1.25794
$905$	0	0
$906$	37899.7	1.38977
$907$	30564.6	1.11894	0.559471	−	0.828850i	$-0.311004\pi$
$907$	30564.6	1.11894	0.559471	+	0.828850i	$0.311004\pi$
$908$	−4981.26	−0.182058
$909$	16282.8	0.594132
$910$	0	0
$911$	−32766.5	−1.19166	−0.595831	−	0.803110i	$-0.703177\pi$
$911$	−32766.5	−1.19166	−0.595831	+	0.803110i	$0.703177\pi$
$912$	−2377.97	−0.0863404
$913$	−20667.0	−0.749154
$914$	−7216.87	−0.261174
$915$	0	0
$916$	−3491.08	−0.125926
$917$	−7647.64	−0.275406
$918$	12942.2	0.465312
$919$	20686.7	0.742538	0.371269	−	0.928525i	$-0.378923\pi$
$919$	20686.7	0.742538	0.371269	+	0.928525i	$0.378923\pi$
$920$	0	0
$921$	−871.989	−0.0311976
$922$	8007.28	0.286015
$923$	5339.34	0.190408
$924$	20033.0	0.713242
$925$	0	0
$926$	−10128.6	−0.359447
$927$	−15626.8	−0.553669
$928$	−41179.0	−1.45665
$929$	45632.2	1.61156	0.805782	−	0.592212i	$-0.201745\pi$
$929$	45632.2	1.61156	0.805782	+	0.592212i	$0.201745\pi$
$930$	0	0
$931$	9482.26	0.333801
$932$	12812.3	0.450301
$933$	33687.1	1.18206
$934$	−20265.9	−0.709979
$935$	0	0
$936$	−13331.0	−0.465532
$937$	17761.4	0.619253	0.309626	−	0.950858i	$-0.399796\pi$
$937$	17761.4	0.619253	0.309626	+	0.950858i	$0.399796\pi$
$938$	−21740.4	−0.756768
$939$	−32909.6	−1.14373
$940$	0	0
$941$	−44888.3	−1.55507	−0.777534	−	0.628841i	$-0.783530\pi$
$941$	−44888.3	−1.55507	−0.777534	+	0.628841i	$0.783530\pi$
$942$	44005.5	1.52206
$943$	19681.7	0.679664
$944$	−5022.05	−0.173150
$945$	0	0
$946$	3605.74	0.123925
$947$	−16069.6	−0.551415	−0.275708	−	0.961242i	$-0.588912\pi$
$947$	−16069.6	−0.551415	−0.275708	+	0.961242i	$0.588912\pi$
$948$	−28326.2	−0.970457
$949$	4004.05	0.136962
$950$	0	0
$951$	38271.6	1.30499
$952$	25637.8	0.872823
$953$	−3512.03	−0.119377	−0.0596883	−	0.998217i	$-0.519011\pi$
$953$	−3512.03	−0.119377	−0.0596883	+	0.998217i	$0.519011\pi$
$954$	9137.88	0.310115
$955$	0	0
$956$	−3028.94	−0.102472
$957$	29146.7	0.984513
$958$	−9071.00	−0.305919
$959$	71786.5	2.41721
$960$	0	0
$961$	−29057.0	−0.975361
$962$	−1912.12	−0.0640844
$963$	−69468.9	−2.32461
$964$	−30177.5	−1.00825
$965$	0	0
$966$	45237.0	1.50670
$967$	37011.9	1.23084	0.615421	−	0.788199i	$-0.288986\pi$
$967$	37011.9	1.23084	0.615421	+	0.788199i	$0.288986\pi$
$968$	23254.4	0.772132
$969$	9273.16	0.307427
$970$	0	0
$971$	19532.3	0.645542	0.322771	−	0.946477i	$-0.395386\pi$
$971$	19532.3	0.645542	0.322771	+	0.946477i	$0.395386\pi$
$972$	−13043.1	−0.430409
$973$	−54317.1	−1.78965
$974$	8412.30	0.276743
$975$	0	0
$976$	−1568.47	−0.0514402
$977$	−30201.2	−0.988970	−0.494485	−	0.869186i	$-0.664643\pi$
$977$	−30201.2	−0.988970	−0.494485	+	0.869186i	$0.664643\pi$
$978$	44501.8	1.45502
$979$	6713.21	0.219157
$980$	0	0
$981$	41118.5	1.33824
$982$	23827.8	0.774315
$983$	38774.9	1.25812	0.629058	−	0.777359i	$-0.283441\pi$
$983$	38774.9	1.25812	0.629058	+	0.777359i	$0.283441\pi$
$984$	−29491.7	−0.955447
$985$	0	0
$986$	15297.2	0.494080
$987$	110211.	3.55425
$988$	−1733.01	−0.0558041
$989$	−18570.6	−0.597079
$990$	0	0
$991$	−27728.9	−0.888838	−0.444419	−	0.895819i	$-0.646590\pi$
$991$	−27728.9	−0.888838	−0.444419	+	0.895819i	$0.646590\pi$
$992$	5073.25	0.162375
$993$	35880.6	1.14666
$994$	17430.3	0.556192
$995$	0	0
$996$	−65408.2	−2.08086
$997$	48918.2	1.55392	0.776958	−	0.629552i	$-0.216761\pi$
$997$	48918.2	1.55392	0.776958	+	0.629552i	$0.216761\pi$
$998$	2898.31	0.0919283
$999$	17524.8	0.555016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.a.f.1.2		2
5.2	odd	4		325.4.b.e.274.3		4
5.3	odd	4		325.4.b.e.274.2		4
5.4	even	2		13.4.a.b.1.1	✓	2
15.14	odd	2		117.4.a.d.1.2		2
20.19	odd	2		208.4.a.h.1.1		2
35.34	odd	2		637.4.a.b.1.1		2
40.19	odd	2		832.4.a.z.1.2		2
40.29	even	2		832.4.a.s.1.1		2
55.54	odd	2		1573.4.a.b.1.2		2
60.59	even	2		1872.4.a.bb.1.2		2
65.4	even	6		169.4.c.j.146.1		4
65.9	even	6		169.4.c.g.146.2		4
65.19	odd	12		169.4.e.f.23.3		8
65.24	odd	12		169.4.e.f.147.3		8
65.29	even	6		169.4.c.g.22.2		4
65.34	odd	4		169.4.b.f.168.2		4
65.44	odd	4		169.4.b.f.168.3		4
65.49	even	6		169.4.c.j.22.1		4
65.54	odd	12		169.4.e.f.147.2		8
65.59	odd	12		169.4.e.f.23.2		8
65.64	even	2		169.4.a.g.1.2		2
195.194	odd	2		1521.4.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.1	✓	2	5.4	even	2
117.4.a.d.1.2		2	15.14	odd	2
169.4.a.g.1.2		2	65.64	even	2
169.4.b.f.168.2		4	65.34	odd	4
169.4.b.f.168.3		4	65.44	odd	4
169.4.c.g.22.2		4	65.29	even	6
169.4.c.g.146.2		4	65.9	even	6
169.4.c.j.22.1		4	65.49	even	6
169.4.c.j.146.1		4	65.4	even	6
169.4.e.f.23.2		8	65.59	odd	12
169.4.e.f.23.3		8	65.19	odd	12
169.4.e.f.147.2		8	65.54	odd	12
169.4.e.f.147.3		8	65.24	odd	12
208.4.a.h.1.1		2	20.19	odd	2
325.4.a.f.1.2		2	1.1	even	1	trivial
325.4.b.e.274.2		4	5.3	odd	4
325.4.b.e.274.3		4	5.2	odd	4
637.4.a.b.1.1		2	35.34	odd	2
832.4.a.s.1.1		2	40.29	even	2
832.4.a.z.1.2		2	40.19	odd	2
1521.4.a.r.1.1		2	195.194	odd	2
1573.4.a.b.1.2		2	55.54	odd	2
1872.4.a.bb.1.2		2	60.59	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56155 q^{2} -8.68466 q^{3} -5.56155 q^{4} -13.5616 q^{6} +27.1771 q^{7} -21.1771 q^{8} +48.4233 q^{9} +O(q^{10})\)	\(q+1.56155 q^{2} -8.68466 q^{3} -5.56155 q^{4} -13.5616 q^{6} +27.1771 q^{7} -21.1771 q^{8} +48.4233 q^{9} +15.2614 q^{11} +48.3002 q^{12} +13.0000 q^{13} +42.4384 q^{14} +11.4233 q^{16} -44.5464 q^{17} +75.6155 q^{18} +23.9697 q^{19} -236.024 q^{21} +23.8314 q^{22} -122.739 q^{23} +183.916 q^{24} +20.3002 q^{26} -186.054 q^{27} -151.147 q^{28} -219.909 q^{29} +27.0928 q^{31} +187.255 q^{32} -132.540 q^{33} -69.5616 q^{34} -269.309 q^{36} -94.1922 q^{37} +37.4299 q^{38} -112.901 q^{39} -160.354 q^{41} -368.563 q^{42} +151.302 q^{43} -84.8769 q^{44} -191.663 q^{46} -466.948 q^{47} -99.2074 q^{48} +395.594 q^{49} +386.870 q^{51} -72.3002 q^{52} +120.847 q^{53} -290.533 q^{54} -575.531 q^{56} -208.169 q^{57} -343.400 q^{58} -439.633 q^{59} -137.305 q^{61} +42.3068 q^{62} +1316.00 q^{63} +201.022 q^{64} -206.968 q^{66} -512.280 q^{67} +247.747 q^{68} +1065.94 q^{69} +410.719 q^{71} -1025.46 q^{72} +308.004 q^{73} -147.086 q^{74} -133.309 q^{76} +414.759 q^{77} -176.300 q^{78} -586.462 q^{79} +308.386 q^{81} -250.401 q^{82} -1354.20 q^{83} +1312.66 q^{84} +236.266 q^{86} +1909.84 q^{87} -323.191 q^{88} +439.882 q^{89} +353.302 q^{91} +682.617 q^{92} -235.292 q^{93} -729.164 q^{94} -1626.24 q^{96} +1511.27 q^{97} +617.740 q^{98} +739.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 5 q^{3} - 7 q^{4} - 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9}+O(q^{10}) \) 2 * q - q^2 - 5 * q^3 - 7 * q^4 - 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9	\( 2 q - q^{2} - 5 q^{3} - 7 q^{4} - 23 q^{6} + 9 q^{7} + 3 q^{8} + 35 q^{9} + 80 q^{11} + 43 q^{12} + 26 q^{13} + 89 q^{14} - 39 q^{16} - 19 q^{17} + 110 q^{18} - 84 q^{19} - 303 q^{21} - 142 q^{22} - 196 q^{23} + 273 q^{24} - 13 q^{26} - 335 q^{27} - 125 q^{28} - 44 q^{29} - 86 q^{31} + 123 q^{32} + 106 q^{33} - 135 q^{34} - 250 q^{36} - 209 q^{37} + 314 q^{38} - 65 q^{39} - 230 q^{41} - 197 q^{42} - 287 q^{43} - 178 q^{44} - 4 q^{46} - 435 q^{47} - 285 q^{48} + 383 q^{49} + 481 q^{51} - 91 q^{52} + 118 q^{53} + 91 q^{54} - 1015 q^{56} - 606 q^{57} - 794 q^{58} - 368 q^{59} - 1058 q^{61} + 332 q^{62} + 1560 q^{63} + 769 q^{64} - 818 q^{66} - 68 q^{67} + 211 q^{68} + 796 q^{69} - 131 q^{71} - 1350 q^{72} - 456 q^{73} + 147 q^{74} + 22 q^{76} - 762 q^{77} - 299 q^{78} - 1008 q^{79} + 122 q^{81} - 72 q^{82} - 1958 q^{83} + 1409 q^{84} + 1359 q^{86} + 2558 q^{87} + 1242 q^{88} - 720 q^{89} + 117 q^{91} + 788 q^{92} - 652 q^{93} - 811 q^{94} - 1863 q^{96} + 928 q^{97} + 650 q^{98} - 130 q^{99}+O(q^{100}) \) 2 * q - q^2 - 5 * q^3 - 7 * q^4 - 23 * q^6 + 9 * q^7 + 3 * q^8 + 35 * q^9 + 80 * q^11 + 43 * q^12 + 26 * q^13 + 89 * q^14 - 39 * q^16 - 19 * q^17 + 110 * q^18 - 84 * q^19 - 303 * q^21 - 142 * q^22 - 196 * q^23 + 273 * q^24 - 13 * q^26 - 335 * q^27 - 125 * q^28 - 44 * q^29 - 86 * q^31 + 123 * q^32 + 106 * q^33 - 135 * q^34 - 250 * q^36 - 209 * q^37 + 314 * q^38 - 65 * q^39 - 230 * q^41 - 197 * q^42 - 287 * q^43 - 178 * q^44 - 4 * q^46 - 435 * q^47 - 285 * q^48 + 383 * q^49 + 481 * q^51 - 91 * q^52 + 118 * q^53 + 91 * q^54 - 1015 * q^56 - 606 * q^57 - 794 * q^58 - 368 * q^59 - 1058 * q^61 + 332 * q^62 + 1560 * q^63 + 769 * q^64 - 818 * q^66 - 68 * q^67 + 211 * q^68 + 796 * q^69 - 131 * q^71 - 1350 * q^72 - 456 * q^73 + 147 * q^74 + 22 * q^76 - 762 * q^77 - 299 * q^78 - 1008 * q^79 + 122 * q^81 - 72 * q^82 - 1958 * q^83 + 1409 * q^84 + 1359 * q^86 + 2558 * q^87 + 1242 * q^88 - 720 * q^89 + 117 * q^91 + 788 * q^92 - 652 * q^93 - 811 * q^94 - 1863 * q^96 + 928 * q^97 + 650 * q^98 - 130 * q^99

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