LMFDB - Embedded newform 425.4.b.f.324.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,4,Mod(324,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("425.324");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	425.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$25.0758117524$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.27793984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{3} + 49x^{2} - 14x + 2 $ x^6 - 2x^3 + 49x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.5
Root			$0.143705 + 0.143705i$ of defining polynomial
Character	$\chi$	$=$	425.324
Dual form			425.4.b.f.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.67129i q^{2} +7.62999i q^{3} -13.8209 q^{4} -35.6419 q^{6} +26.1222i q^{7} -27.1912i q^{8} -31.2167 q^{9} +O(q^{10})$	\(q+4.67129i q^{2} +7.62999i q^{3} -13.8209 q^{4} -35.6419 q^{6} +26.1222i q^{7} -27.1912i q^{8} -31.2167 q^{9} -3.24412 q^{11} -105.453i q^{12} +20.0515i q^{13} -122.024 q^{14} +16.4506 q^{16} -17.0000i q^{17} -145.822i q^{18} -57.3466 q^{19} -199.312 q^{21} -15.1542i q^{22} -77.0438i q^{23} +207.469 q^{24} -93.6662 q^{26} -32.1732i q^{27} -361.033i q^{28} +286.162 q^{29} -8.54816 q^{31} -140.684i q^{32} -24.7526i q^{33} +79.4119 q^{34} +431.443 q^{36} +357.982i q^{37} -267.882i q^{38} -152.992 q^{39} +194.467 q^{41} -931.044i q^{42} +74.2619i q^{43} +44.8367 q^{44} +359.894 q^{46} +23.6130i q^{47} +125.518i q^{48} -339.369 q^{49} +129.710 q^{51} -277.130i q^{52} -104.330i q^{53} +150.290 q^{54} +710.295 q^{56} -437.553i q^{57} +1336.75i q^{58} -249.363 q^{59} -370.384 q^{61} -39.9309i q^{62} -815.448i q^{63} +788.781 q^{64} +115.626 q^{66} +939.650i q^{67} +234.956i q^{68} +587.843 q^{69} -520.197 q^{71} +848.820i q^{72} -348.741i q^{73} -1672.24 q^{74} +792.583 q^{76} -84.7434i q^{77} -714.672i q^{78} +953.827 q^{79} -597.369 q^{81} +908.412i q^{82} +1414.28i q^{83} +2754.68 q^{84} -346.899 q^{86} +2183.41i q^{87} +88.2115i q^{88} +486.132 q^{89} -523.788 q^{91} +1064.82i q^{92} -65.2223i q^{93} -110.303 q^{94} +1073.42 q^{96} -685.281i q^{97} -1585.29i q^{98} +101.271 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 50 q^{4} - 148 q^{6} - 118 q^{9}+O(q^{10}) $ 6 * q - 50 * q^4 - 148 * q^6 - 118 * q^9	$ 6 q - 50 q^{4} - 148 q^{6} - 118 q^{9} - 56 q^{11} - 184 q^{14} + 274 q^{16} - 160 q^{19} - 384 q^{21} + 1332 q^{24} + 52 q^{26} + 912 q^{29} + 460 q^{31} + 34 q^{34} + 2626 q^{36} - 536 q^{39} - 588 q^{41} + 2244 q^{44} - 1408 q^{46} + 538 q^{49} - 136 q^{51} + 2200 q^{54} + 1368 q^{56} - 1272 q^{59} - 168 q^{61} + 1838 q^{64} + 4936 q^{66} - 1152 q^{69} - 804 q^{71} - 1672 q^{74} - 1816 q^{76} + 1188 q^{79} - 1010 q^{81} + 4080 q^{84} - 2528 q^{86} + 340 q^{89} - 2032 q^{91} + 4032 q^{94} + 1356 q^{96} + 5840 q^{99}+O(q^{100}) $ 6 * q - 50 * q^4 - 148 * q^6 - 118 * q^9 - 56 * q^11 - 184 * q^14 + 274 * q^16 - 160 * q^19 - 384 * q^21 + 1332 * q^24 + 52 * q^26 + 912 * q^29 + 460 * q^31 + 34 * q^34 + 2626 * q^36 - 536 * q^39 - 588 * q^41 + 2244 * q^44 - 1408 * q^46 + 538 * q^49 - 136 * q^51 + 2200 * q^54 + 1368 * q^56 - 1272 * q^59 - 168 * q^61 + 1838 * q^64 + 4936 * q^66 - 1152 * q^69 - 804 * q^71 - 1672 * q^74 - 1816 * q^76 + 1188 * q^79 - 1010 * q^81 + 4080 * q^84 - 2528 * q^86 + 340 * q^89 - 2032 * q^91 + 4032 * q^94 + 1356 * q^96 + 5840 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$1$

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 $

$2$	4.67129i	1.65155i	0.564000	+	0.825775i	$0.309262\pi$
$2$	4.67129i	1.65155i	−0.564000	+	0.825775i	$0.690738\pi$
$3$	7.62999i	1.46839i	0.678938	+	0.734196i	$0.262441\pi$
$3$	7.62999i	1.46839i	−0.678938	+	0.734196i	$0.737559\pi$
$4$	−13.8209	−1.72762
$5$	0	0
$5$	0	0
$6$	−35.6419	−2.42512
$7$	26.1222i	1.41047i	0.708975	+	0.705233i	$0.249158\pi$
$7$	26.1222i	1.41047i	−0.708975	+	0.705233i	$0.750842\pi$
$8$	− 27.1912i	− 1.20169i
$9$	−31.2167	−1.15617
$10$	0	0
$11$	−3.24412	−0.0889216	−0.0444608	−	0.999011i	$-0.514157\pi$
$11$	−3.24412	−0.0889216	−0.0444608	+	0.999011i	$0.514157\pi$
$12$	− 105.453i	− 2.53682i
$13$	20.0515i	0.427790i	0.976857	+	0.213895i	$0.0686151\pi$
$13$	20.0515i	0.427790i	−0.976857	+	0.213895i	$0.931385\pi$
$14$	−122.024	−2.32945
$15$	0	0
$16$	16.4506	0.257041
$17$	− 17.0000i	− 0.242536i
$17$	− 17.0000i	− 0.242536i
$18$	− 145.822i	− 1.90948i
$19$	−57.3466	−0.692432	−0.346216	−	0.938155i	$-0.612534\pi$
$19$	−57.3466	−0.692432	−0.346216	+	0.938155i	$0.612534\pi$
$20$	0	0
$21$	−199.312	−2.07112
$22$	− 15.1542i	− 0.146858i
$23$	− 77.0438i	− 0.698467i	−0.937036	−	0.349233i	$-0.886442\pi$
$23$	− 77.0438i	− 0.698467i	0.937036	−	0.349233i	$-0.113558\pi$
$24$	207.469	1.76456
$25$	0	0
$26$	−93.6662	−0.706517
$27$	− 32.1732i	− 0.229323i
$28$	− 361.033i	− 2.43674i
$29$	286.162	1.83238	0.916190	−	0.400744i	$-0.131248\pi$
$29$	286.162	1.83238	0.916190	+	0.400744i	$0.131248\pi$
$30$	0	0
$31$	−8.54816	−0.0495256	−0.0247628	−	0.999693i	$-0.507883\pi$
$31$	−8.54816	−0.0495256	−0.0247628	+	0.999693i	$0.507883\pi$
$32$	− 140.684i	− 0.777178i
$33$	− 24.7526i	− 0.130572i
$34$	79.4119	0.400560
$35$	0	0
$36$	431.443	1.99742
$37$	357.982i	1.59059i	0.606221	+	0.795296i	$0.292685\pi$
$37$	357.982i	1.59059i	−0.606221	+	0.795296i	$0.707315\pi$
$38$	− 267.882i	− 1.14359i
$39$	−152.992	−0.628164
$40$	0	0
$41$	194.467	0.740748	0.370374	−	0.928883i	$-0.379230\pi$
$41$	194.467	0.740748	0.370374	+	0.928883i	$0.379230\pi$
$42$	− 931.044i	− 3.42055i
$43$	74.2619i	0.263368i	0.991292	+	0.131684i	$0.0420384\pi$
$43$	74.2619i	0.263368i	−0.991292	+	0.131684i	$0.957962\pi$
$44$	44.8367	0.153622
$45$	0	0
$46$	359.894	1.15355
$47$	23.6130i	0.0732831i	0.999328	+	0.0366416i	$0.0116660\pi$
$47$	23.6130i	0.0732831i	−0.999328	+	0.0366416i	$0.988334\pi$
$48$	125.518i	0.377437i
$49$	−339.369	−0.989415
$50$	0	0
$51$	129.710	0.356137
$52$	− 277.130i	− 0.739058i
$53$	− 104.330i	− 0.270393i	−0.990819	−	0.135197i	$-0.956833\pi$
$53$	− 104.330i	− 0.270393i	0.990819	−	0.135197i	$-0.0431666\pi$
$54$	150.290	0.378739
$55$	0	0
$56$	710.295	1.69495
$57$	− 437.553i	− 1.01676i
$58$	1336.75i	3.02627i
$59$	−249.363	−0.550243	−0.275122	−	0.961409i	$-0.588718\pi$
$59$	−249.363	−0.550243	−0.275122	+	0.961409i	$0.588718\pi$
$60$	0	0
$61$	−370.384	−0.777424	−0.388712	−	0.921359i	$-0.627080\pi$
$61$	−370.384	−0.777424	−0.388712	+	0.921359i	$0.627080\pi$
$62$	− 39.9309i	− 0.0817940i
$63$	− 815.448i	− 1.63074i
$64$	788.781	1.54059
$65$	0	0
$66$	115.626	0.215646
$67$	939.650i	1.71338i	0.515830	+	0.856691i	$0.327483\pi$
$67$	939.650i	1.71338i	−0.515830	+	0.856691i	$0.672517\pi$
$68$	234.956i	0.419008i
$69$	587.843	1.02562
$70$	0	0
$71$	−520.197	−0.869522	−0.434761	−	0.900546i	$-0.643167\pi$
$71$	−520.197	−0.869522	−0.434761	+	0.900546i	$0.643167\pi$
$72$	848.820i	1.38937i
$73$	− 348.741i	− 0.559137i	−0.960126	−	0.279568i	$-0.909809\pi$
$73$	− 348.741i	− 0.559137i	0.960126	−	0.279568i	$-0.0901914\pi$
$74$	−1672.24	−2.62694
$75$	0	0
$76$	792.583	1.19626
$77$	− 84.7434i	− 0.125421i
$78$	− 714.672i	− 1.03744i
$79$	953.827	1.35840	0.679202	−	0.733951i	$-0.262326\pi$
$79$	953.827	1.35840	0.679202	+	0.733951i	$0.262326\pi$
$80$	0	0
$81$	−597.369	−0.819437
$82$	908.412i	1.22338i
$83$	1414.28i	1.87033i	0.354211	+	0.935166i	$0.384750\pi$
$83$	1414.28i	1.87033i	−0.354211	+	0.935166i	$0.615250\pi$
$84$	2754.68	3.57809
$85$	0	0
$86$	−346.899	−0.434966
$87$	2183.41i	2.69065i
$88$	88.2115i	0.106857i
$89$	486.132	0.578987	0.289493	−	0.957180i	$-0.406513\pi$
$89$	486.132	0.578987	0.289493	+	0.957180i	$0.406513\pi$
$90$	0	0
$91$	−523.788	−0.603384
$92$	1064.82i	1.20668i
$93$	− 65.2223i	− 0.0727230i
$94$	−110.303	−0.121031
$95$	0	0
$96$	1073.42	1.14120
$97$	− 685.281i	− 0.717317i	−0.933469	−	0.358659i	$-0.883234\pi$
$97$	− 685.281i	− 0.717317i	0.933469	−	0.358659i	$-0.116766\pi$
$98$	− 1585.29i	− 1.63407i
$99$	101.271	0.102809
$100$	0	0
$101$	864.755	0.851944	0.425972	−	0.904736i	$-0.359932\pi$
$101$	864.755	0.851944	0.425972	+	0.904736i	$0.359932\pi$
$102$	605.912i	0.588178i
$103$	− 1880.91i	− 1.79933i	−0.436580	−	0.899665i	$-0.643810\pi$
$103$	− 1880.91i	− 1.79933i	0.436580	−	0.899665i	$-0.356190\pi$
$104$	545.224	0.514073
$105$	0	0
$106$	487.355	0.446567
$107$	− 32.8149i	− 0.0296480i	−0.999890	−	0.0148240i	$-0.995281\pi$
$107$	− 32.8149i	− 0.0296480i	0.999890	−	0.0148240i	$-0.00471880\pi$
$108$	444.663i	0.396183i
$109$	−528.727	−0.464613	−0.232307	−	0.972643i	$-0.574627\pi$
$109$	−528.727	−0.464613	−0.232307	+	0.972643i	$0.574627\pi$
$110$	0	0
$111$	−2731.40	−2.33561
$112$	429.727i	0.362548i
$113$	− 414.691i	− 0.345229i	−0.984989	−	0.172614i	$-0.944779\pi$
$113$	− 414.691i	− 0.345229i	0.984989	−	0.172614i	$-0.0552215\pi$
$114$	2043.94	1.67923
$115$	0	0
$116$	−3955.03	−3.16565
$117$	− 625.940i	− 0.494600i
$118$	− 1164.85i	− 0.908754i
$119$	444.077	0.342088
$120$	0	0
$121$	−1320.48	−0.992093
$122$	− 1730.17i	− 1.28395i
$123$	1483.78i	1.08771i
$124$	118.143	0.0855613
$125$	0	0
$126$	3809.19	2.69325
$127$	596.093i	0.416494i	0.978076	+	0.208247i	$0.0667758\pi$
$127$	596.093i	0.416494i	−0.978076	+	0.208247i	$0.933224\pi$
$128$	2559.15i	1.76718i
$129$	−566.617	−0.386728
$130$	0	0
$131$	121.819	0.0812472	0.0406236	−	0.999175i	$-0.487066\pi$
$131$	121.819	0.0812472	0.0406236	+	0.999175i	$0.487066\pi$
$132$	342.103i	0.225578i
$133$	− 1498.02i	− 0.976652i
$134$	−4389.38	−2.82973
$135$	0	0
$136$	−462.251	−0.291454
$137$	− 897.365i	− 0.559614i	−0.960056	−	0.279807i	$-0.909730\pi$
$137$	− 897.365i	− 0.559614i	0.960056	−	0.279807i	$-0.0902705\pi$
$138$	2745.98i	1.69387i
$139$	2113.61	1.28974	0.644871	−	0.764292i	$-0.276911\pi$
$139$	2113.61	1.28974	0.644871	+	0.764292i	$0.276911\pi$
$140$	0	0
$141$	−180.167	−0.107608
$142$	− 2429.99i	− 1.43606i
$143$	− 65.0493i	− 0.0380398i
$144$	−513.534	−0.297184
$145$	0	0
$146$	1629.07	0.923442
$147$	− 2589.38i	− 1.45285i
$148$	− 4947.65i	− 2.74793i
$149$	−2580.76	−1.41895	−0.709476	−	0.704729i	$-0.751068\pi$
$149$	−2580.76	−1.41895	−0.709476	+	0.704729i	$0.751068\pi$
$150$	0	0
$151$	1342.77	0.723662	0.361831	−	0.932244i	$-0.382152\pi$
$151$	1342.77	0.723662	0.361831	+	0.932244i	$0.382152\pi$
$152$	1559.32i	0.832091i
$153$	530.683i	0.280413i
$154$	395.861	0.207139
$155$	0	0
$156$	2114.50	1.08523
$157$	− 2495.82i	− 1.26871i	−0.773041	−	0.634357i	$-0.781265\pi$
$157$	− 2495.82i	− 1.26871i	0.773041	−	0.634357i	$-0.218735\pi$
$158$	4455.60i	2.24347i
$159$	796.036	0.397043
$160$	0	0
$161$	2012.55	0.985164
$162$	− 2790.48i	− 1.35334i
$163$	− 1961.58i	− 0.942595i	−0.881974	−	0.471297i	$-0.843786\pi$
$163$	− 1961.58i	− 0.942595i	0.881974	−	0.471297i	$-0.156214\pi$
$164$	−2687.72	−1.27973
$165$	0	0
$166$	−6606.51	−3.08894
$167$	2179.24i	1.00979i	0.863182	+	0.504894i	$0.168468\pi$
$167$	2179.24i	1.00979i	−0.863182	+	0.504894i	$0.831532\pi$
$168$	5419.54i	2.48885i
$169$	1794.94	0.816995
$170$	0	0
$171$	1790.17	0.800571
$172$	− 1026.37i	− 0.454999i
$173$	− 3111.45i	− 1.36739i	−0.729766	−	0.683697i	$-0.760371\pi$
$173$	− 3111.45i	− 1.36739i	0.729766	−	0.683697i	$-0.239629\pi$
$174$	−10199.4	−4.44374
$175$	0	0
$176$	−53.3677	−0.0228565
$177$	− 1902.64i	− 0.807972i
$178$	2270.86i	0.956226i
$179$	−810.106	−0.338269	−0.169135	−	0.985593i	$-0.554097\pi$
$179$	−810.106	−0.338269	−0.169135	+	0.985593i	$0.554097\pi$
$180$	0	0
$181$	−3356.23	−1.37827	−0.689134	−	0.724634i	$-0.742009\pi$
$181$	−3356.23	−1.37827	−0.689134	+	0.724634i	$0.742009\pi$
$182$	− 2446.77i	− 0.996519i
$183$	− 2826.03i	− 1.14156i
$184$	−2094.92	−0.839343
$185$	0	0
$186$	304.672	0.120106
$187$	55.1500i	0.0215667i
$188$	− 326.353i	− 0.126605i
$189$	840.434	0.323453
$190$	0	0
$191$	1338.41	0.507038	0.253519	−	0.967330i	$-0.418412\pi$
$191$	1338.41	0.507038	0.253519	+	0.967330i	$0.418412\pi$
$192$	6018.39i	2.26219i
$193$	227.465i	0.0848358i	0.999100	+	0.0424179i	$0.0135061\pi$
$193$	227.465i	0.0848358i	−0.999100	+	0.0424179i	$0.986494\pi$
$194$	3201.15	1.18468
$195$	0	0
$196$	4690.40	1.70933
$197$	815.549i	0.294952i	0.989066	+	0.147476i	$0.0471148\pi$
$197$	815.549i	0.294952i	−0.989066	+	0.147476i	$0.952885\pi$
$198$	473.064i	0.169794i
$199$	−1866.90	−0.665030	−0.332515	−	0.943098i	$-0.607897\pi$
$199$	−1866.90	−0.665030	−0.332515	+	0.943098i	$0.607897\pi$
$200$	0	0
$201$	−7169.52	−2.51591
$202$	4039.52i	1.40703i
$203$	7475.19i	2.58451i
$204$	−1792.71	−0.615268
$205$	0	0
$206$	8786.25	2.97168
$207$	2405.05i	0.807549i
$208$	329.859i	0.109960i
$209$	186.039	0.0615721
$210$	0	0
$211$	−1102.88	−0.359836	−0.179918	−	0.983682i	$-0.557583\pi$
$211$	−1102.88	−0.359836	−0.179918	+	0.983682i	$0.557583\pi$
$212$	1441.94i	0.467135i
$213$	− 3969.10i	− 1.27680i
$214$	153.288	0.0489651
$215$	0	0
$216$	−874.828	−0.275576
$217$	− 223.297i	− 0.0698542i
$218$	− 2469.84i	− 0.767332i
$219$	2660.89	0.821032
$220$	0	0
$221$	340.875	0.103754
$222$	− 12759.2i	− 3.85738i
$223$	568.848i	0.170820i	0.996346	+	0.0854100i	$0.0272200\pi$
$223$	568.848i	0.170820i	−0.996346	+	0.0854100i	$0.972780\pi$
$224$	3674.98	1.09618
$225$	0	0
$226$	1937.14	0.570163
$227$	2106.99i	0.616061i	0.951377	+	0.308030i	$0.0996698\pi$
$227$	2106.99i	0.616061i	−0.951377	+	0.308030i	$0.900330\pi$
$228$	6047.39i	1.75657i
$229$	−4336.30	−1.25131	−0.625656	−	0.780099i	$-0.715169\pi$
$229$	−4336.30	−1.25131	−0.625656	+	0.780099i	$0.715169\pi$
$230$	0	0
$231$	646.591	0.184167
$232$	− 7781.11i	− 2.20196i
$233$	4517.39i	1.27014i	0.772453	+	0.635072i	$0.219030\pi$
$233$	4517.39i	1.27014i	−0.772453	+	0.635072i	$0.780970\pi$
$234$	2923.95	0.816856
$235$	0	0
$236$	3446.43	0.950609
$237$	7277.69i	1.99467i
$238$	2074.41i	0.564976i
$239$	−5300.88	−1.43467	−0.717333	−	0.696731i	$-0.754637\pi$
$239$	−5300.88	−1.43467	−0.717333	+	0.696731i	$0.754637\pi$
$240$	0	0
$241$	−1368.82	−0.365864	−0.182932	−	0.983126i	$-0.558559\pi$
$241$	−1368.82	−0.365864	−0.182932	+	0.983126i	$0.558559\pi$
$242$	− 6168.32i	− 1.63849i
$243$	− 5426.60i	− 1.43258i
$244$	5119.05	1.34309
$245$	0	0
$246$	−6931.17	−1.79640
$247$	− 1149.88i	− 0.296216i
$248$	232.435i	0.0595146i
$249$	−10790.9	−2.74638
$250$	0	0
$251$	−5547.63	−1.39507	−0.697536	−	0.716549i	$-0.745720\pi$
$251$	−5547.63	−1.39507	−0.697536	+	0.716549i	$0.745720\pi$
$252$	11270.3i	2.81730i
$253$	249.939i	0.0621088i
$254$	−2784.52	−0.687860
$255$	0	0
$256$	−5644.28	−1.37800
$257$	− 193.949i	− 0.0470748i	−0.999723	−	0.0235374i	$-0.992507\pi$
$257$	− 193.949i	− 0.0470748i	0.999723	−	0.0235374i	$-0.00749288\pi$
$258$	− 2646.83i	− 0.638700i
$259$	−9351.29	−2.24348
$260$	0	0
$261$	−8933.04	−2.11855
$262$	569.052i	0.134184i
$263$	1345.63i	0.315494i	0.987480	+	0.157747i	$0.0504231\pi$
$263$	1345.63i	0.315494i	−0.987480	+	0.157747i	$0.949577\pi$
$264$	−673.052	−0.156907
$265$	0	0
$266$	6997.67	1.61299
$267$	3709.18i	0.850180i
$268$	− 12986.8i	− 2.96007i
$269$	3083.04	0.698797	0.349398	−	0.936974i	$-0.386386\pi$
$269$	3083.04	0.698797	0.349398	+	0.936974i	$0.386386\pi$
$270$	0	0
$271$	−422.163	−0.0946294	−0.0473147	−	0.998880i	$-0.515066\pi$
$271$	−422.163	−0.0946294	−0.0473147	+	0.998880i	$0.515066\pi$
$272$	− 279.661i	− 0.0623416i
$273$	− 3996.50i	− 0.886004i
$274$	4191.85	0.924230
$275$	0	0
$276$	−8124.54	−1.77188
$277$	− 8260.00i	− 1.79168i	−0.444377	−	0.895840i	$-0.646575\pi$
$277$	− 8260.00i	− 1.79168i	0.444377	−	0.895840i	$-0.353425\pi$
$278$	9873.28i	2.13007i
$279$	266.845	0.0572602
$280$	0	0
$281$	3321.91	0.705226	0.352613	−	0.935769i	$-0.385293\pi$
$281$	3321.91	0.705226	0.352613	+	0.935769i	$0.385293\pi$
$282$	− 841.611i	− 0.177721i
$283$	7954.43i	1.67082i	0.549629	+	0.835409i	$0.314769\pi$
$283$	7954.43i	1.67082i	−0.549629	+	0.835409i	$0.685231\pi$
$284$	7189.61	1.50220
$285$	0	0
$286$	303.864	0.0628246
$287$	5079.91i	1.04480i
$288$	4391.69i	0.898552i
$289$	−289.000	−0.0588235
$290$	0	0
$291$	5228.69	1.05330
$292$	4819.92i	0.965974i
$293$	1171.99i	0.233681i	0.993151	+	0.116841i	$0.0372767\pi$
$293$	1171.99i	0.233681i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	12095.8	2.39945
$295$	0	0
$296$	9733.98	1.91141
$297$	104.374i	0.0203918i
$298$	− 12055.5i	− 2.34347i
$299$	1544.84	0.298798
$300$	0	0
$301$	−1939.88	−0.371472
$302$	6272.46i	1.19516i
$303$	6598.07i	1.25099i
$304$	−943.387	−0.177983
$305$	0	0
$306$	−2478.98	−0.463116
$307$	865.763i	0.160950i	0.996757	+	0.0804751i	$0.0256438\pi$
$307$	865.763i	0.160950i	−0.996757	+	0.0804751i	$0.974356\pi$
$308$	1171.23i	0.216679i
$309$	14351.3	2.64212
$310$	0	0
$311$	6994.83	1.27537	0.637685	−	0.770297i	$-0.279892\pi$
$311$	6994.83	1.27537	0.637685	+	0.770297i	$0.279892\pi$
$312$	4160.05i	0.754861i
$313$	− 3442.33i	− 0.621635i	−0.950470	−	0.310818i	$-0.899397\pi$
$313$	− 3442.33i	− 0.621635i	0.950470	−	0.310818i	$-0.100603\pi$
$314$	11658.7	2.09534
$315$	0	0
$316$	−13182.8	−2.34680
$317$	2066.15i	0.366078i	0.983106	+	0.183039i	$0.0585935\pi$
$317$	2066.15i	0.366078i	−0.983106	+	0.183039i	$0.941407\pi$
$318$	3718.52i	0.655736i
$319$	−928.344	−0.162938
$320$	0	0
$321$	250.377	0.0435349
$322$	9401.21i	1.62705i
$323$	974.892i	0.167939i
$324$	8256.20	1.41567
$325$	0	0
$326$	9163.11	1.55674
$327$	− 4034.18i	− 0.682234i
$328$	− 5287.80i	− 0.890152i
$329$	−616.823	−0.103363
$330$	0	0
$331$	9027.44	1.49907	0.749536	−	0.661964i	$-0.230277\pi$
$331$	9027.44	1.49907	0.749536	+	0.661964i	$0.230277\pi$
$332$	− 19546.7i	− 3.23121i
$333$	− 11175.0i	− 1.83900i
$334$	−10179.8	−1.66771
$335$	0	0
$336$	−3278.81	−0.532362
$337$	204.309i	0.0330250i	0.999864	+	0.0165125i	$0.00525633\pi$
$337$	204.309i	0.0330250i	−0.999864	+	0.0165125i	$0.994744\pi$
$338$	8384.67i	1.34931i
$339$	3164.09	0.506931
$340$	0	0
$341$	27.7312	0.00440390
$342$	8362.39i	1.32218i
$343$	94.8397i	0.0149296i
$344$	2019.27	0.316488
$345$	0	0
$346$	14534.5	2.25832
$347$	143.063i	0.0221326i	0.999939	+	0.0110663i	$0.00352259\pi$
$347$	143.063i	0.0221326i	−0.999939	+	0.0110663i	$0.996477\pi$
$348$	− 30176.8i	− 4.64841i
$349$	3998.42	0.613268	0.306634	−	0.951828i	$-0.400797\pi$
$349$	3998.42	0.613268	0.306634	+	0.951828i	$0.400797\pi$
$350$	0	0
$351$	645.119	0.0981024
$352$	456.396i	0.0691079i
$353$	5809.57i	0.875956i	0.898986	+	0.437978i	$0.144305\pi$
$353$	5809.57i	0.875956i	−0.898986	+	0.437978i	$0.855695\pi$
$354$	8887.77	1.33441
$355$	0	0
$356$	−6718.79	−1.00027
$357$	3388.30i	0.502320i
$358$	− 3784.24i	− 0.558668i
$359$	4895.37	0.719687	0.359844	−	0.933013i	$-0.382830\pi$
$359$	4895.37	0.719687	0.359844	+	0.933013i	$0.382830\pi$
$360$	0	0
$361$	−3570.37	−0.520538
$362$	− 15677.9i	− 2.27628i
$363$	− 10075.2i	− 1.45678i
$364$	7239.24	1.04242
$365$	0	0
$366$	13201.2	1.88535
$367$	528.151i	0.0751206i	0.999294	+	0.0375603i	$0.0119586\pi$
$367$	528.151i	0.0751206i	−0.999294	+	0.0375603i	$0.988041\pi$
$368$	− 1267.42i	− 0.179535i
$369$	−6070.62	−0.856433
$370$	0	0
$371$	2725.33	0.381380
$372$	901.433i	0.125637i
$373$	10113.5i	1.40390i	0.712226	+	0.701950i	$0.247687\pi$
$373$	10113.5i	1.40390i	−0.712226	+	0.701950i	$0.752313\pi$
$374$	−257.621	−0.0356184
$375$	0	0
$376$	642.066	0.0880639
$377$	5737.98i	0.783875i
$378$	3925.91i	0.534198i
$379$	−729.385	−0.0988548	−0.0494274	−	0.998778i	$-0.515740\pi$
$379$	−729.385	−0.0988548	−0.0494274	+	0.998778i	$0.515740\pi$
$380$	0	0
$381$	−4548.18	−0.611576
$382$	6252.12i	0.837399i
$383$	1608.08i	0.214540i	0.994230	+	0.107270i	$0.0342109\pi$
$383$	1608.08i	0.214540i	−0.994230	+	0.107270i	$0.965789\pi$
$384$	−19526.3	−2.59491
$385$	0	0
$386$	−1062.56	−0.140111
$387$	− 2318.21i	− 0.304499i
$388$	9471.22i	1.23925i
$389$	−9824.09	−1.28047	−0.640233	−	0.768181i	$-0.721162\pi$
$389$	−9824.09	−1.28047	−0.640233	+	0.768181i	$0.721162\pi$
$390$	0	0
$391$	−1309.74	−0.169403
$392$	9227.87i	1.18897i
$393$	929.478i	0.119303i
$394$	−3809.66	−0.487127
$395$	0	0
$396$	−1399.65	−0.177614
$397$	2876.88i	0.363694i	0.983327	+	0.181847i	$0.0582076\pi$
$397$	2876.88i	0.363694i	−0.983327	+	0.181847i	$0.941792\pi$
$398$	− 8720.82i	− 1.09833i
$399$	11429.9	1.43411
$400$	0	0
$401$	−6515.91	−0.811444	−0.405722	−	0.913996i	$-0.632980\pi$
$401$	−6515.91	−0.811444	−0.405722	+	0.913996i	$0.632980\pi$
$402$	− 33490.9i	− 4.15516i
$403$	− 171.403i	− 0.0211866i
$404$	−11951.7	−1.47183
$405$	0	0
$406$	−34918.8	−4.26845
$407$	− 1161.34i	− 0.141438i
$408$	− 3526.97i	− 0.427968i
$409$	8870.10	1.07237	0.536183	−	0.844101i	$-0.319866\pi$
$409$	8870.10	1.07237	0.536183	+	0.844101i	$0.319866\pi$
$410$	0	0
$411$	6846.89	0.821732
$412$	25995.9i	3.10855i
$413$	− 6513.92i	− 0.776099i
$414$	−11234.7	−1.33371
$415$	0	0
$416$	2820.93	0.332469
$417$	16126.8i	1.89385i
$418$	869.041i	0.101689i
$419$	1009.53	0.117706	0.0588531	−	0.998267i	$-0.481256\pi$
$419$	1009.53	0.117706	0.0588531	+	0.998267i	$0.481256\pi$
$420$	0	0
$421$	−3253.60	−0.376652	−0.188326	−	0.982107i	$-0.560306\pi$
$421$	−3253.60	−0.376652	−0.188326	+	0.982107i	$0.560306\pi$
$422$	− 5151.87i	− 0.594287i
$423$	− 737.119i	− 0.0847280i
$424$	−2836.86	−0.324930
$425$	0	0
$426$	18540.8	2.10870
$427$	− 9675.25i	− 1.09653i
$428$	453.532i	0.0512203i
$429$	496.325	0.0558573
$430$	0	0
$431$	−2352.51	−0.262915	−0.131457	−	0.991322i	$-0.541966\pi$
$431$	−2352.51	−0.262915	−0.131457	+	0.991322i	$0.541966\pi$
$432$	− 529.269i	− 0.0589455i
$433$	5860.51i	0.650434i	0.945639	+	0.325217i	$0.105437\pi$
$433$	5860.51i	0.650434i	−0.945639	+	0.325217i	$0.894563\pi$
$434$	1043.08	0.115368
$435$	0	0
$436$	7307.50	0.802674
$437$	4418.20i	0.483641i
$438$	12429.8i	1.35597i
$439$	−2894.17	−0.314650	−0.157325	−	0.987547i	$-0.550287\pi$
$439$	−2894.17	−0.314650	−0.157325	+	0.987547i	$0.550287\pi$
$440$	0	0
$441$	10594.0	1.14394
$442$	1592.32i	0.171356i
$443$	8256.85i	0.885541i	0.896635	+	0.442771i	$0.146004\pi$
$443$	8256.85i	0.885541i	−0.896635	+	0.442771i	$0.853996\pi$
$444$	37750.5	4.03504
$445$	0	0
$446$	−2657.25	−0.282118
$447$	− 19691.1i	− 2.08358i
$448$	20604.7i	2.17295i
$449$	−15487.1	−1.62779	−0.813897	−	0.581009i	$-0.802658\pi$
$449$	−15487.1	−1.62779	−0.813897	+	0.581009i	$0.802658\pi$
$450$	0	0
$451$	−630.874	−0.0658685
$452$	5731.42i	0.596423i
$453$	10245.3i	1.06262i
$454$	−9842.35	−1.01745
$455$	0	0
$456$	−11897.6	−1.22184
$457$	− 16055.6i	− 1.64343i	−0.569897	−	0.821716i	$-0.693017\pi$
$457$	− 16055.6i	− 1.64343i	0.569897	−	0.821716i	$-0.306983\pi$
$458$	− 20256.1i	− 2.06661i
$459$	−546.944	−0.0556191
$460$	0	0
$461$	14064.0	1.42088	0.710440	−	0.703758i	$-0.248496\pi$
$461$	14064.0	1.42088	0.710440	+	0.703758i	$0.248496\pi$
$462$	3020.41i	0.304161i
$463$	8071.30i	0.810162i	0.914281	+	0.405081i	$0.132757\pi$
$463$	8071.30i	0.810162i	−0.914281	+	0.405081i	$0.867243\pi$
$464$	4707.55	0.470997
$465$	0	0
$466$	−21102.0	−2.09771
$467$	8582.41i	0.850421i	0.905094	+	0.425211i	$0.139800\pi$
$467$	8582.41i	0.850421i	−0.905094	+	0.425211i	$0.860200\pi$
$468$	8651.07i	0.854479i
$469$	−24545.7	−2.41667
$470$	0	0
$471$	19043.1	1.86297
$472$	6780.49i	0.661224i
$473$	− 240.914i	− 0.0234191i
$474$	−33996.2	−3.29429
$475$	0	0
$476$	−6137.56	−0.590997
$477$	3256.84i	0.312621i
$478$	− 24761.9i	− 2.36942i
$479$	6320.96	0.602948	0.301474	−	0.953474i	$-0.402521\pi$
$479$	6320.96	0.602948	0.301474	+	0.953474i	$0.402521\pi$
$480$	0	0
$481$	−7178.07	−0.680441
$482$	− 6394.13i	− 0.604242i
$483$	15355.8i	1.44661i
$484$	18250.2	1.71396
$485$	0	0
$486$	25349.2	2.36597
$487$	7336.47i	0.682643i	0.939947	+	0.341321i	$0.110874\pi$
$487$	7336.47i	0.682643i	−0.939947	+	0.341321i	$0.889126\pi$
$488$	10071.2i	0.934225i
$489$	14966.8	1.38410
$490$	0	0
$491$	6672.53	0.613294	0.306647	−	0.951823i	$-0.400793\pi$
$491$	6672.53	0.613294	0.306647	+	0.951823i	$0.400793\pi$
$492$	− 20507.2i	− 1.87914i
$493$	− 4864.76i	− 0.444417i
$494$	5371.43	0.489215
$495$	0	0
$496$	−140.623	−0.0127301
$497$	− 13588.7i	− 1.22643i
$498$	− 50407.6i	− 4.53578i
$499$	−17920.9	−1.60772	−0.803858	−	0.594821i	$-0.797223\pi$
$499$	−17920.9	−1.60772	−0.803858	+	0.594821i	$0.797223\pi$
$500$	0	0
$501$	−16627.6	−1.48276
$502$	− 25914.6i	− 2.30403i
$503$	11325.3i	1.00392i	0.864891	+	0.501959i	$0.167387\pi$
$503$	11325.3i	1.00392i	−0.864891	+	0.501959i	$0.832613\pi$
$504$	−22173.0	−1.95965
$505$	0	0
$506$	−1167.54	−0.102576
$507$	13695.4i	1.19967i
$508$	− 8238.56i	− 0.719541i
$509$	8313.78	0.723972	0.361986	−	0.932184i	$-0.382099\pi$
$509$	8313.78	0.723972	0.361986	+	0.932184i	$0.382099\pi$
$510$	0	0
$511$	9109.87	0.788644
$512$	− 5892.85i	− 0.508651i
$513$	1845.02i	0.158791i
$514$	905.993	0.0777464
$515$	0	0
$516$	7831.17	0.668117
$517$	− 76.6033i	− 0.00651646i
$518$	− 43682.6i	− 3.70521i
$519$	23740.3	2.00787
$520$	0	0
$521$	5121.64	0.430677	0.215339	−	0.976539i	$-0.430914\pi$
$521$	5121.64	0.430677	0.215339	+	0.976539i	$0.430914\pi$
$522$	− 41728.8i	− 3.49889i
$523$	− 13378.5i	− 1.11855i	−0.828982	−	0.559275i	$-0.811080\pi$
$523$	− 13378.5i	− 1.11855i	0.828982	−	0.559275i	$-0.188920\pi$
$524$	−1683.65	−0.140364
$525$	0	0
$526$	−6285.81	−0.521054
$527$	145.319i	0.0120117i
$528$	− 407.195i	− 0.0335623i
$529$	6231.26	0.512144
$530$	0	0
$531$	7784.29	0.636176
$532$	20704.0i	1.68728i
$533$	3899.35i	0.316885i
$534$	−17326.6	−1.40411
$535$	0	0
$536$	25550.2	2.05896
$537$	− 6181.10i	− 0.496712i
$538$	14401.8i	1.15410i
$539$	1100.95	0.0879804
$540$	0	0
$541$	9906.81	0.787296	0.393648	−	0.919261i	$-0.371213\pi$
$541$	9906.81	0.787296	0.393648	+	0.919261i	$0.371213\pi$
$542$	− 1972.04i	− 0.156285i
$543$	− 25608.0i	− 2.02384i
$544$	−2391.63	−0.188493
$545$	0	0
$546$	18668.8	1.46328
$547$	16399.6i	1.28189i	0.767585	+	0.640947i	$0.221458\pi$
$547$	16399.6i	1.28189i	−0.767585	+	0.640947i	$0.778542\pi$
$548$	12402.4i	0.966798i
$549$	11562.2	0.898836
$550$	0	0
$551$	−16410.4	−1.26880
$552$	− 15984.2i	− 1.23248i
$553$	24916.1i	1.91598i
$554$	38584.8	2.95905
$555$	0	0
$556$	−29212.0	−2.22818
$557$	22044.3i	1.67692i	0.544962	+	0.838461i	$0.316544\pi$
$557$	22044.3i	1.67692i	−0.544962	+	0.838461i	$0.683456\pi$
$558$	1246.51i	0.0945681i
$559$	−1489.06	−0.112666
$560$	0	0
$561$	−420.793	−0.0316683
$562$	15517.6i	1.16472i
$563$	− 12048.8i	− 0.901947i	−0.892537	−	0.450973i	$-0.851077\pi$
$563$	− 12048.8i	− 0.901947i	0.892537	−	0.450973i	$-0.148923\pi$
$564$	2490.07	0.185906
$565$	0	0
$566$	−37157.4	−2.75944
$567$	− 15604.6i	− 1.15579i
$568$	14144.8i	1.04490i
$569$	23785.4	1.75243	0.876217	−	0.481916i	$-0.160059\pi$
$569$	23785.4	1.75243	0.876217	+	0.481916i	$0.160059\pi$
$570$	0	0
$571$	−10878.3	−0.797271	−0.398635	−	0.917110i	$-0.630516\pi$
$571$	−10878.3	−0.797271	−0.398635	+	0.917110i	$0.630516\pi$
$572$	899.041i	0.0657182i
$573$	10212.1i	0.744531i
$574$	−23729.7	−1.72554
$575$	0	0
$576$	−24623.1	−1.78119
$577$	6315.86i	0.455689i	0.973698	+	0.227845i	$0.0731678\pi$
$577$	6315.86i	0.455689i	−0.973698	+	0.227845i	$0.926832\pi$
$578$	− 1350.00i	− 0.0971500i
$579$	−1735.56	−0.124572
$580$	0	0
$581$	−36944.1	−2.63804
$582$	24424.7i	1.73958i
$583$	338.459i	0.0240438i
$584$	−9482.69	−0.671912
$585$	0	0
$586$	−5474.72	−0.385936
$587$	18192.1i	1.27916i	0.768724	+	0.639581i	$0.220892\pi$
$587$	18192.1i	1.27916i	−0.768724	+	0.639581i	$0.779108\pi$
$588$	35787.7i	2.50996i
$589$	490.207	0.0342931
$590$	0	0
$591$	−6222.63	−0.433104
$592$	5889.03i	0.408848i
$593$	9828.72i	0.680636i	0.940310	+	0.340318i	$0.110535\pi$
$593$	9828.72i	0.680636i	−0.940310	+	0.340318i	$0.889465\pi$
$594$	−487.559	−0.0336781
$595$	0	0
$596$	35668.5	2.45140
$597$	− 14244.4i	− 0.976524i
$598$	7216.40i	0.493479i
$599$	−4662.57	−0.318043	−0.159021	−	0.987275i	$-0.550834\pi$
$599$	−4662.57	−0.318043	−0.159021	+	0.987275i	$0.550834\pi$
$600$	0	0
$601$	21658.6	1.47000	0.735001	−	0.678066i	$-0.237182\pi$
$601$	21658.6	1.47000	0.735001	+	0.678066i	$0.237182\pi$
$602$	− 9061.76i	− 0.613504i
$603$	− 29332.8i	− 1.98097i
$604$	−18558.3	−1.25021
$605$	0	0
$606$	−30821.5	−2.06607
$607$	25764.7i	1.72283i	0.507902	+	0.861415i	$0.330421\pi$
$607$	25764.7i	1.72283i	−0.507902	+	0.861415i	$0.669579\pi$
$608$	8067.76i	0.538143i
$609$	−57035.6	−3.79507
$610$	0	0
$611$	−473.475	−0.0313498
$612$	− 7334.54i	− 0.484446i
$613$	− 16018.1i	− 1.05541i	−0.849428	−	0.527705i	$-0.823053\pi$
$613$	− 16018.1i	− 1.05541i	0.849428	−	0.527705i	$-0.176947\pi$
$614$	−4044.23	−0.265817
$615$	0	0
$616$	−2304.28	−0.150718
$617$	22250.3i	1.45180i	0.687798	+	0.725902i	$0.258578\pi$
$617$	22250.3i	1.45180i	−0.687798	+	0.725902i	$0.741422\pi$
$618$	67038.9i	4.36360i
$619$	3765.95	0.244534	0.122267	−	0.992497i	$-0.460984\pi$
$619$	3765.95	0.244534	0.122267	+	0.992497i	$0.460984\pi$
$620$	0	0
$621$	−2478.74	−0.160175
$622$	32674.9i	2.10634i
$623$	12698.8i	0.816642i
$624$	−2516.82	−0.161464
$625$	0	0
$626$	16080.1	1.02666
$627$	1419.47i	0.0904120i
$628$	34494.5i	2.19185i
$629$	6085.70	0.385775
$630$	0	0
$631$	−20806.5	−1.31267	−0.656334	−	0.754470i	$-0.727894\pi$
$631$	−20806.5	−1.31267	−0.656334	+	0.754470i	$0.727894\pi$
$632$	− 25935.7i	− 1.63239i
$633$	− 8414.96i	− 0.528380i
$634$	−9651.60	−0.604596
$635$	0	0
$636$	−11002.0	−0.685937
$637$	− 6804.85i	− 0.423262i
$638$	− 4336.56i	− 0.269100i
$639$	16238.8	1.00532
$640$	0	0
$641$	2439.58	0.150324	0.0751620	−	0.997171i	$-0.476053\pi$
$641$	2439.58	0.150324	0.0751620	+	0.997171i	$0.476053\pi$
$642$	1169.58i	0.0719000i
$643$	19320.1i	1.18493i	0.805595	+	0.592466i	$0.201846\pi$
$643$	19320.1i	1.18493i	−0.805595	+	0.592466i	$0.798154\pi$
$644$	−27815.4	−1.70199
$645$	0	0
$646$	−4554.00	−0.277360
$647$	− 14067.1i	− 0.854766i	−0.904071	−	0.427383i	$-0.859436\pi$
$647$	− 14067.1i	− 0.854766i	0.904071	−	0.427383i	$-0.140564\pi$
$648$	16243.2i	0.984712i
$649$	808.963	0.0489285
$650$	0	0
$651$	1703.75	0.102573
$652$	27110.9i	1.62844i
$653$	− 15893.7i	− 0.952478i	−0.879316	−	0.476239i	$-0.842000\pi$
$653$	− 15893.7i	− 0.952478i	0.879316	−	0.476239i	$-0.158000\pi$
$654$	18844.8	1.12674
$655$	0	0
$656$	3199.11	0.190403
$657$	10886.5i	0.646459i
$658$	− 2881.36i	− 0.170710i
$659$	9653.54	0.570635	0.285318	−	0.958433i	$-0.407901\pi$
$659$	9653.54	0.570635	0.285318	+	0.958433i	$0.407901\pi$
$660$	0	0
$661$	5389.06	0.317111	0.158555	−	0.987350i	$-0.449316\pi$
$661$	5389.06	0.317111	0.158555	+	0.987350i	$0.449316\pi$
$662$	42169.7i	2.47579i
$663$	2600.87i	0.152352i
$664$	38456.0	2.24757
$665$	0	0
$666$	52201.7	3.03720
$667$	− 22047.0i	− 1.27986i
$668$	− 30119.1i	− 1.74453i
$669$	−4340.30	−0.250831
$670$	0	0
$671$	1201.57	0.0691297
$672$	28040.1i	1.60963i
$673$	3032.18i	0.173673i	0.996223	+	0.0868366i	$0.0276758\pi$
$673$	3032.18i	0.173673i	−0.996223	+	0.0868366i	$0.972324\pi$
$674$	−954.386	−0.0545424
$675$	0	0
$676$	−24807.7	−1.41145
$677$	− 22029.2i	− 1.25059i	−0.780388	−	0.625295i	$-0.784979\pi$
$677$	− 22029.2i	− 1.25059i	0.780388	−	0.625295i	$-0.215021\pi$
$678$	14780.4i	0.837222i
$679$	17901.1	1.01175
$680$	0	0
$681$	−16076.3	−0.904618
$682$	129.540i	0.00727326i
$683$	9040.72i	0.506491i	0.967402	+	0.253246i	$0.0814980\pi$
$683$	9040.72i	0.506491i	−0.967402	+	0.253246i	$0.918502\pi$
$684$	−24741.8	−1.38308
$685$	0	0
$686$	−443.023	−0.0246570
$687$	− 33085.9i	− 1.83742i
$688$	1221.65i	0.0676964i
$689$	2091.97	0.115672
$690$	0	0
$691$	−22863.5	−1.25871	−0.629355	−	0.777118i	$-0.716681\pi$
$691$	−22863.5	−1.25871	−0.629355	+	0.777118i	$0.716681\pi$
$692$	43003.1i	2.36233i
$693$	2645.41i	0.145008i
$694$	−668.288	−0.0365531
$695$	0	0
$696$	59369.7	3.23334
$697$	− 3305.94i	− 0.179658i
$698$	18677.8i	1.01284i
$699$	−34467.6	−1.86507
$700$	0	0
$701$	1753.00	0.0944507	0.0472253	−	0.998884i	$-0.484962\pi$
$701$	1753.00	0.0944507	0.0472253	+	0.998884i	$0.484962\pi$
$702$	3013.54i	0.162021i
$703$	− 20529.1i	− 1.10138i
$704$	−2558.90	−0.136992
$705$	0	0
$706$	−27138.2	−1.44668
$707$	22589.3i	1.20164i
$708$	26296.2i	1.39587i
$709$	−11547.0	−0.611645	−0.305823	−	0.952089i	$-0.598931\pi$
$709$	−11547.0	−0.611645	−0.305823	+	0.952089i	$0.598931\pi$
$710$	0	0
$711$	−29775.3	−1.57055
$712$	− 13218.5i	− 0.695765i
$713$	658.582i	0.0345920i
$714$	−15827.7	−0.829606
$715$	0	0
$716$	11196.4	0.584399
$717$	− 40445.6i	− 2.10665i
$718$	22867.7i	1.18860i
$719$	10289.8	0.533720	0.266860	−	0.963735i	$-0.414014\pi$
$719$	10289.8	0.533720	0.266860	+	0.963735i	$0.414014\pi$
$720$	0	0
$721$	49133.4	2.53790
$722$	− 16678.2i	− 0.859695i
$723$	− 10444.0i	− 0.537231i
$724$	46386.2	2.38112
$725$	0	0
$726$	47064.2	2.40595
$727$	2950.10i	0.150499i	0.997165	+	0.0752497i	$0.0239754\pi$
$727$	2950.10i	0.150499i	−0.997165	+	0.0752497i	$0.976025\pi$
$728$	14242.5i	0.725083i
$729$	25275.9	1.28415
$730$	0	0
$731$	1262.45	0.0638762
$732$	39058.3i	1.97218i
$733$	− 24348.2i	− 1.22691i	−0.789731	−	0.613453i	$-0.789780\pi$
$733$	− 24348.2i	− 1.22691i	0.789731	−	0.613453i	$-0.210220\pi$
$734$	−2467.15	−0.124065
$735$	0	0
$736$	−10838.8	−0.542833
$737$	− 3048.33i	− 0.152357i
$738$	− 28357.6i	− 1.41444i
$739$	29233.5	1.45517	0.727585	−	0.686017i	$-0.240642\pi$
$739$	29233.5	1.45517	0.727585	+	0.686017i	$0.240642\pi$
$740$	0	0
$741$	8773.59	0.434961
$742$	12730.8i	0.629868i
$743$	− 15340.6i	− 0.757457i	−0.925508	−	0.378729i	$-0.876361\pi$
$743$	− 15340.6i	− 0.757457i	0.925508	−	0.378729i	$-0.123639\pi$
$744$	−1773.47	−0.0873908
$745$	0	0
$746$	−47242.9	−2.31861
$747$	− 44149.2i	− 2.16243i
$748$	− 762.224i	− 0.0372589i
$749$	857.197	0.0418175
$750$	0	0
$751$	39862.6	1.93689	0.968446	−	0.249223i	$-0.0801752\pi$
$751$	39862.6	1.93689	0.968446	+	0.249223i	$0.0801752\pi$
$752$	388.448i	0.0188368i
$753$	− 42328.3i	− 2.04851i
$754$	−26803.7	−1.29461
$755$	0	0
$756$	−11615.6	−0.558802
$757$	26375.1i	1.26634i	0.774013	+	0.633169i	$0.218246\pi$
$757$	26375.1i	1.26634i	−0.774013	+	0.633169i	$0.781754\pi$
$758$	− 3407.17i	− 0.163264i
$759$	−1907.03	−0.0912000
$760$	0	0
$761$	7848.63	0.373867	0.186933	−	0.982373i	$-0.440145\pi$
$761$	7848.63	0.373867	0.186933	+	0.982373i	$0.440145\pi$
$762$	− 21245.9i	− 1.01005i
$763$	− 13811.5i	− 0.655322i
$764$	−18498.1	−0.875967
$765$	0	0
$766$	−7511.78	−0.354323
$767$	− 5000.10i	− 0.235389i
$768$	− 43065.8i	− 2.02344i
$769$	−31818.9	−1.49209	−0.746046	−	0.665895i	$-0.768050\pi$
$769$	−31818.9	−1.49209	−0.746046	+	0.665895i	$0.768050\pi$
$770$	0	0
$771$	1479.83	0.0691242
$772$	− 3143.78i	− 0.146564i
$773$	29559.8i	1.37541i	0.725990	+	0.687706i	$0.241382\pi$
$773$	29559.8i	1.37541i	−0.725990	+	0.687706i	$0.758618\pi$
$774$	10829.0	0.502896
$775$	0	0
$776$	−18633.6	−0.861996
$777$	− 71350.2i	− 3.29430i
$778$	− 45891.2i	− 2.11475i
$779$	−11152.0	−0.512917
$780$	0	0
$781$	1687.58	0.0773193
$782$	− 6118.19i	− 0.279778i
$783$	− 9206.75i	− 0.420208i
$784$	−5582.84	−0.254320
$785$	0	0
$786$	−4341.86	−0.197034
$787$	− 28038.7i	− 1.26998i	−0.772521	−	0.634989i	$-0.781005\pi$
$787$	− 28038.7i	− 1.26998i	0.772521	−	0.634989i	$-0.218995\pi$
$788$	− 11271.6i	− 0.509563i
$789$	−10267.1	−0.463269
$790$	0	0
$791$	10832.6	0.486934
$792$	− 2753.67i	− 0.123545i
$793$	− 7426.75i	− 0.332574i
$794$	−13438.7	−0.600659
$795$	0	0
$796$	25802.3	1.14892
$797$	5320.45i	0.236462i	0.992986	+	0.118231i	$0.0377223\pi$
$797$	5320.45i	0.236462i	−0.992986	+	0.118231i	$0.962278\pi$
$798$	53392.2i	2.36850i
$799$	401.421	0.0177738
$800$	0	0
$801$	−15175.4	−0.669409
$802$	− 30437.7i	− 1.34014i
$803$	1131.35i	0.0497194i
$804$	99089.4	4.34653
$805$	0	0
$806$	800.673	0.0349907
$807$	23523.6i	1.02611i
$808$	− 23513.8i	− 1.02378i
$809$	−30934.0	−1.34435	−0.672177	−	0.740390i	$-0.734641\pi$
$809$	−30934.0	−1.34435	−0.672177	+	0.740390i	$0.734641\pi$
$810$	0	0
$811$	−40364.5	−1.74771	−0.873854	−	0.486189i	$-0.838387\pi$
$811$	−40364.5	−1.74771	−0.873854	+	0.486189i	$0.838387\pi$
$812$	− 103314.i	− 4.46504i
$813$	− 3221.10i	− 0.138953i
$814$	5424.94	0.233592
$815$	0	0
$816$	2133.81	0.0915419
$817$	− 4258.66i	− 0.182364i
$818$	41434.8i	1.77107i
$819$	16350.9	0.697616
$820$	0	0
$821$	19799.7	0.841672	0.420836	−	0.907137i	$-0.361737\pi$
$821$	19799.7	0.841672	0.420836	+	0.907137i	$0.361737\pi$
$822$	31983.8i	1.35713i
$823$	− 18756.4i	− 0.794419i	−0.917728	−	0.397210i	$-0.869979\pi$
$823$	− 18756.4i	− 0.794419i	0.917728	−	0.397210i	$-0.130021\pi$
$824$	−51144.1	−2.16225
$825$	0	0
$826$	30428.4	1.28177
$827$	20958.0i	0.881234i	0.897695	+	0.440617i	$0.145240\pi$
$827$	20958.0i	0.881234i	−0.897695	+	0.440617i	$0.854760\pi$
$828$	− 33240.0i	− 1.39513i
$829$	31320.3	1.31218	0.656091	−	0.754682i	$-0.272209\pi$
$829$	31320.3	1.31218	0.656091	+	0.754682i	$0.272209\pi$
$830$	0	0
$831$	63023.7	2.63089
$832$	15816.2i	0.659049i
$833$	5769.28i	0.239968i
$834$	−75333.0	−3.12778
$835$	0	0
$836$	−2571.23	−0.106373
$837$	275.021i	0.0113574i
$838$	4715.82i	0.194398i
$839$	30290.6	1.24642	0.623212	−	0.782053i	$-0.285827\pi$
$839$	30290.6	1.24642	0.623212	+	0.782053i	$0.285827\pi$
$840$	0	0
$841$	57499.9	2.35762
$842$	− 15198.5i	− 0.622060i
$843$	25346.1i	1.03555i
$844$	15242.8	0.621659
$845$	0	0
$846$	3443.29	0.139933
$847$	− 34493.7i	− 1.39931i
$848$	− 1716.29i	− 0.0695021i
$849$	−60692.2	−2.45342
$850$	0	0
$851$	27580.3	1.11098
$852$	54856.6i	2.20582i
$853$	21111.8i	0.847425i	0.905797	+	0.423712i	$0.139273\pi$
$853$	21111.8i	0.847425i	−0.905797	+	0.423712i	$0.860727\pi$
$854$	45195.9	1.81097
$855$	0	0
$856$	−892.277	−0.0356278
$857$	− 39983.0i	− 1.59369i	−0.604184	−	0.796845i	$-0.706501\pi$
$857$	− 39983.0i	− 1.59369i	0.604184	−	0.796845i	$-0.293499\pi$
$858$	2318.48i	0.0922512i
$859$	39503.3	1.56907	0.784537	−	0.620082i	$-0.212901\pi$
$859$	39503.3	1.56907	0.784537	+	0.620082i	$0.212901\pi$
$860$	0	0
$861$	−38759.6	−1.53418
$862$	− 10989.2i	− 0.434217i
$863$	− 26019.9i	− 1.02634i	−0.858288	−	0.513168i	$-0.828472\pi$
$863$	− 26019.9i	− 1.02634i	0.858288	−	0.513168i	$-0.171528\pi$
$864$	−4526.26	−0.178225
$865$	0	0
$866$	−27376.1	−1.07422
$867$	− 2205.07i	− 0.0863760i
$868$	3086.17i	0.120681i
$869$	−3094.33	−0.120791
$870$	0	0
$871$	−18841.4	−0.732968
$872$	14376.7i	0.558323i
$873$	21392.2i	0.829343i
$874$	−20638.7	−0.798757
$875$	0	0
$876$	−36775.9	−1.41843
$877$	15038.3i	0.579027i	0.957174	+	0.289514i	$0.0934935\pi$
$877$	15038.3i	0.579027i	−0.957174	+	0.289514i	$0.906506\pi$
$878$	− 13519.5i	− 0.519660i
$879$	−8942.30	−0.343136
$880$	0	0
$881$	−18334.3	−0.701133	−0.350567	−	0.936538i	$-0.614011\pi$
$881$	−18334.3	−0.701133	−0.350567	+	0.936538i	$0.614011\pi$
$882$	49487.5i	1.88927i
$883$	− 26659.5i	− 1.01604i	−0.861345	−	0.508020i	$-0.830378\pi$
$883$	− 26659.5i	− 1.01604i	0.861345	−	0.508020i	$-0.169622\pi$
$884$	−4711.21	−0.179248
$885$	0	0
$886$	−38570.1	−1.46251
$887$	11473.7i	0.434327i	0.976135	+	0.217163i	$0.0696804\pi$
$887$	11473.7i	0.434327i	−0.976135	+	0.217163i	$0.930320\pi$
$888$	74270.1i	2.80669i
$889$	−15571.3	−0.587450
$890$	0	0
$891$	1937.94	0.0728656
$892$	− 7862.01i	− 0.295111i
$893$	− 1354.12i	− 0.0507436i
$894$	91983.0	3.44113
$895$	0	0
$896$	−66850.7	−2.49255
$897$	11787.1i	0.438752i
$898$	− 72344.6i	− 2.68838i
$899$	−2446.16	−0.0907498
$900$	0	0
$901$	−1773.61	−0.0655799
$902$	− 2946.99i	− 0.108785i
$903$	− 14801.3i	− 0.545466i
$904$	−11276.0	−0.414860
$905$	0	0
$906$	−47858.8	−1.75497
$907$	− 20361.6i	− 0.745421i	−0.927948	−	0.372710i	$-0.878429\pi$
$907$	− 20361.6i	− 0.745421i	0.927948	−	0.372710i	$-0.121571\pi$
$908$	− 29120.5i	− 1.06432i
$909$	−26994.8	−0.984995
$910$	0	0
$911$	−19261.9	−0.700523	−0.350262	−	0.936652i	$-0.613907\pi$
$911$	−19261.9	−0.700523	−0.350262	+	0.936652i	$0.613907\pi$
$912$	− 7198.03i	− 0.261349i
$913$	− 4588.09i	− 0.166313i
$914$	75000.3	2.71421
$915$	0	0
$916$	59931.7	2.16179
$917$	3182.18i	0.114596i
$918$	− 2554.93i	− 0.0918577i
$919$	21191.8	0.760666	0.380333	−	0.924850i	$-0.375809\pi$
$919$	21191.8	0.760666	0.380333	+	0.924850i	$0.375809\pi$
$920$	0	0
$921$	−6605.76	−0.236338
$922$	65697.0i	2.34665i
$923$	− 10430.7i	− 0.371973i
$924$	−8936.49	−0.318170
$925$	0	0
$926$	−37703.4	−1.33802
$927$	58715.6i	2.08034i
$928$	− 40258.5i	− 1.42409i
$929$	−40815.0	−1.44144	−0.720719	−	0.693227i	$-0.756188\pi$
$929$	−40815.0	−1.44144	−0.720719	+	0.693227i	$0.756188\pi$
$930$	0	0
$931$	19461.7	0.685102
$932$	− 62434.5i	− 2.19432i
$933$	53370.4i	1.87274i
$934$	−40090.9	−1.40451
$935$	0	0
$936$	−17020.1	−0.594358
$937$	− 38439.1i	− 1.34018i	−0.742278	−	0.670092i	$-0.766255\pi$
$937$	− 38439.1i	− 1.34018i	0.742278	−	0.670092i	$-0.233745\pi$
$938$	− 114660.i	− 3.99124i
$939$	26264.9	0.912804
$940$	0	0
$941$	−2244.08	−0.0777415	−0.0388708	−	0.999244i	$-0.512376\pi$
$941$	−2244.08	−0.0777415	−0.0388708	+	0.999244i	$0.512376\pi$
$942$	88955.6i	3.07678i
$943$	− 14982.5i	− 0.517388i
$944$	−4102.18	−0.141435
$945$	0	0
$946$	1125.38	0.0386778
$947$	− 42289.0i	− 1.45112i	−0.688160	−	0.725559i	$-0.741581\pi$
$947$	− 42289.0i	− 1.45112i	0.688160	−	0.725559i	$-0.258419\pi$
$948$	− 100584.i	− 3.44602i
$949$	6992.76	0.239193
$950$	0	0
$951$	−15764.7	−0.537546
$952$	− 12075.0i	− 0.411085i
$953$	− 37426.2i	− 1.27214i	−0.771629	−	0.636072i	$-0.780558\pi$
$953$	− 37426.2i	− 1.27214i	0.771629	−	0.636072i	$-0.219442\pi$
$954$	−15213.6	−0.516309
$955$	0	0
$956$	73263.0	2.47855
$957$	− 7083.25i	− 0.239257i
$958$	29527.0i	0.995799i
$959$	23441.2	0.789317
$960$	0	0
$961$	−29717.9	−0.997547
$962$	− 33530.8i	− 1.12378i
$963$	1024.37i	0.0342782i
$964$	18918.3	0.632072
$965$	0	0
$966$	−71731.1	−2.38914
$967$	1088.56i	0.0362003i	0.999836	+	0.0181001i	$0.00576177\pi$
$967$	1088.56i	0.0362003i	−0.999836	+	0.0181001i	$0.994238\pi$
$968$	35905.4i	1.19219i
$969$	−7438.41	−0.246601
$970$	0	0
$971$	39506.5	1.30569	0.652845	−	0.757491i	$-0.273575\pi$
$971$	39506.5	1.30569	0.652845	+	0.757491i	$0.273575\pi$
$972$	75000.6i	2.47494i
$973$	55212.1i	1.81914i
$974$	−34270.8	−1.12742
$975$	0	0
$976$	−6093.05	−0.199830
$977$	− 43326.8i	− 1.41878i	−0.704817	−	0.709389i	$-0.748971\pi$
$977$	− 43326.8i	− 1.41878i	0.704817	−	0.709389i	$-0.251029\pi$
$978$	69914.4i	2.28591i
$979$	−1577.07	−0.0514845
$980$	0	0
$981$	16505.1	0.537174
$982$	31169.3i	1.01288i
$983$	− 10664.1i	− 0.346014i	−0.984921	−	0.173007i	$-0.944652\pi$
$983$	− 10664.1i	− 0.346014i	0.984921	−	0.173007i	$-0.0553483\pi$
$984$	40345.9	1.30709
$985$	0	0
$986$	22724.7	0.733977
$987$	− 4706.35i	− 0.151778i
$988$	15892.4i	0.511747i
$989$	5721.42	0.183954
$990$	0	0
$991$	15461.4	0.495609	0.247804	−	0.968810i	$-0.420291\pi$
$991$	15461.4	0.495609	0.247804	+	0.968810i	$0.420291\pi$
$992$	1202.59i	0.0384902i
$993$	68879.2i	2.20122i
$994$	63476.7	2.02551
$995$	0	0
$996$	149141.	4.74469
$997$	46061.1i	1.46316i	0.681756	+	0.731579i	$0.261216\pi$
$997$	46061.1i	1.46316i	−0.681756	+	0.731579i	$0.738784\pi$
$998$	− 83713.7i	− 2.65522i
$999$	11517.4	0.364760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.b.f.324.5		6
5.2	odd	4		425.4.a.g.1.1		3
5.3	odd	4		17.4.a.b.1.3	✓	3
5.4	even	2	inner	425.4.b.f.324.2		6
15.8	even	4		153.4.a.g.1.1		3
20.3	even	4		272.4.a.h.1.3		3
35.13	even	4		833.4.a.d.1.3		3
40.3	even	4		1088.4.a.x.1.1		3
40.13	odd	4		1088.4.a.v.1.3		3
55.43	even	4		2057.4.a.e.1.1		3
60.23	odd	4		2448.4.a.bi.1.3		3
85.13	odd	4		289.4.b.b.288.1		6
85.33	odd	4		289.4.a.b.1.3		3
85.38	odd	4		289.4.b.b.288.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.3	✓	3	5.3	odd	4
153.4.a.g.1.1		3	15.8	even	4
272.4.a.h.1.3		3	20.3	even	4
289.4.a.b.1.3		3	85.33	odd	4
289.4.b.b.288.1		6	85.13	odd	4
289.4.b.b.288.2		6	85.38	odd	4
425.4.a.g.1.1		3	5.2	odd	4
425.4.b.f.324.2		6	5.4	even	2	inner
425.4.b.f.324.5		6	1.1	even	1	trivial
833.4.a.d.1.3		3	35.13	even	4
1088.4.a.v.1.3		3	40.13	odd	4
1088.4.a.x.1.1		3	40.3	even	4
2057.4.a.e.1.1		3	55.43	even	4
2448.4.a.bi.1.3		3	60.23	odd	4

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.67129i q^{2} +7.62999i q^{3} -13.8209 q^{4} -35.6419 q^{6} +26.1222i q^{7} -27.1912i q^{8} -31.2167 q^{9} +O(q^{10})\)	\(q+4.67129i q^{2} +7.62999i q^{3} -13.8209 q^{4} -35.6419 q^{6} +26.1222i q^{7} -27.1912i q^{8} -31.2167 q^{9} -3.24412 q^{11} -105.453i q^{12} +20.0515i q^{13} -122.024 q^{14} +16.4506 q^{16} -17.0000i q^{17} -145.822i q^{18} -57.3466 q^{19} -199.312 q^{21} -15.1542i q^{22} -77.0438i q^{23} +207.469 q^{24} -93.6662 q^{26} -32.1732i q^{27} -361.033i q^{28} +286.162 q^{29} -8.54816 q^{31} -140.684i q^{32} -24.7526i q^{33} +79.4119 q^{34} +431.443 q^{36} +357.982i q^{37} -267.882i q^{38} -152.992 q^{39} +194.467 q^{41} -931.044i q^{42} +74.2619i q^{43} +44.8367 q^{44} +359.894 q^{46} +23.6130i q^{47} +125.518i q^{48} -339.369 q^{49} +129.710 q^{51} -277.130i q^{52} -104.330i q^{53} +150.290 q^{54} +710.295 q^{56} -437.553i q^{57} +1336.75i q^{58} -249.363 q^{59} -370.384 q^{61} -39.9309i q^{62} -815.448i q^{63} +788.781 q^{64} +115.626 q^{66} +939.650i q^{67} +234.956i q^{68} +587.843 q^{69} -520.197 q^{71} +848.820i q^{72} -348.741i q^{73} -1672.24 q^{74} +792.583 q^{76} -84.7434i q^{77} -714.672i q^{78} +953.827 q^{79} -597.369 q^{81} +908.412i q^{82} +1414.28i q^{83} +2754.68 q^{84} -346.899 q^{86} +2183.41i q^{87} +88.2115i q^{88} +486.132 q^{89} -523.788 q^{91} +1064.82i q^{92} -65.2223i q^{93} -110.303 q^{94} +1073.42 q^{96} -685.281i q^{97} -1585.29i q^{98} +101.271 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 50 q^{4} - 148 q^{6} - 118 q^{9}+O(q^{10}) \) 6 * q - 50 * q^4 - 148 * q^6 - 118 * q^9	\( 6 q - 50 q^{4} - 148 q^{6} - 118 q^{9} - 56 q^{11} - 184 q^{14} + 274 q^{16} - 160 q^{19} - 384 q^{21} + 1332 q^{24} + 52 q^{26} + 912 q^{29} + 460 q^{31} + 34 q^{34} + 2626 q^{36} - 536 q^{39} - 588 q^{41} + 2244 q^{44} - 1408 q^{46} + 538 q^{49} - 136 q^{51} + 2200 q^{54} + 1368 q^{56} - 1272 q^{59} - 168 q^{61} + 1838 q^{64} + 4936 q^{66} - 1152 q^{69} - 804 q^{71} - 1672 q^{74} - 1816 q^{76} + 1188 q^{79} - 1010 q^{81} + 4080 q^{84} - 2528 q^{86} + 340 q^{89} - 2032 q^{91} + 4032 q^{94} + 1356 q^{96} + 5840 q^{99}+O(q^{100}) \) 6 * q - 50 * q^4 - 148 * q^6 - 118 * q^9 - 56 * q^11 - 184 * q^14 + 274 * q^16 - 160 * q^19 - 384 * q^21 + 1332 * q^24 + 52 * q^26 + 912 * q^29 + 460 * q^31 + 34 * q^34 + 2626 * q^36 - 536 * q^39 - 588 * q^41 + 2244 * q^44 - 1408 * q^46 + 538 * q^49 - 136 * q^51 + 2200 * q^54 + 1368 * q^56 - 1272 * q^59 - 168 * q^61 + 1838 * q^64 + 4936 * q^66 - 1152 * q^69 - 804 * q^71 - 1672 * q^74 - 1816 * q^76 + 1188 * q^79 - 1010 * q^81 + 4080 * q^84 - 2528 * q^86 + 340 * q^89 - 2032 * q^91 + 4032 * q^94 + 1356 * q^96 + 5840 * q^99

Introduction

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