LMFDB - Embedded newform 425.4.b.f.324.4

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			324.4
Root			$-1.93854 - 1.93854i$ of defining polynomial
Character	$\chi$	$=$	425.324
Dual form			425.4.b.f.324.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36122i q^{2} -3.15463i q^{3} +6.14708 q^{4} +4.29415 q^{6} -7.94049i q^{7} +19.2573i q^{8} +17.0483 q^{9} +O(q^{10})$	\(q+1.36122i q^{2} -3.15463i q^{3} +6.14708 q^{4} +4.29415 q^{6} -7.94049i q^{7} +19.2573i q^{8} +17.0483 q^{9} +27.6161 q^{11} -19.3918i q^{12} -58.1117i q^{13} +10.8088 q^{14} +22.9632 q^{16} -17.0000i q^{17} +23.2065i q^{18} -89.1688 q^{19} -25.0493 q^{21} +37.5916i q^{22} +115.269i q^{23} +60.7497 q^{24} +79.1029 q^{26} -138.956i q^{27} -48.8108i q^{28} +128.558 q^{29} +273.460 q^{31} +185.316i q^{32} -87.1187i q^{33} +23.1408 q^{34} +104.797 q^{36} -132.351i q^{37} -121.379i q^{38} -183.321 q^{39} -470.559 q^{41} -34.0977i q^{42} -352.642i q^{43} +169.758 q^{44} -156.907 q^{46} +152.598i q^{47} -72.4403i q^{48} +279.949 q^{49} -53.6287 q^{51} -357.217i q^{52} -527.614i q^{53} +189.150 q^{54} +152.912 q^{56} +281.295i q^{57} +174.995i q^{58} +292.020 q^{59} -53.8962 q^{61} +372.239i q^{62} -135.372i q^{63} -68.5514 q^{64} +118.588 q^{66} +52.9572i q^{67} -104.500i q^{68} +363.632 q^{69} +788.400 q^{71} +328.304i q^{72} -295.780i q^{73} +180.159 q^{74} -548.127 q^{76} -219.285i q^{77} -249.541i q^{78} +720.325 q^{79} +21.9487 q^{81} -640.535i q^{82} +116.051i q^{83} -153.980 q^{84} +480.024 q^{86} -405.552i q^{87} +531.812i q^{88} +813.329 q^{89} -461.435 q^{91} +708.569i q^{92} -862.664i q^{93} -207.720 q^{94} +584.605 q^{96} +794.693i q^{97} +381.072i q^{98} +470.808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36122i	0.481264i	0.970616	+	0.240632i	$0.0773548\pi$
$2$	1.36122i	0.481264i	−0.970616	+	0.240632i	$0.922645\pi$
$3$	− 3.15463i	− 0.607109i	−0.952814	−	0.303555i	$-0.901827\pi$
$3$	− 3.15463i	− 0.607109i	0.952814	−	0.303555i	$-0.0981735\pi$
$4$	6.14708	0.768385
$5$	0	0
$5$	0	0
$6$	4.29415	0.292180
$7$	− 7.94049i	− 0.428746i	−0.976752	−	0.214373i	$-0.931229\pi$
$7$	− 7.94049i	− 0.428746i	0.976752	−	0.214373i	$-0.0687708\pi$
$8$	19.2573i	0.851061i
$9$	17.0483	0.631419
$10$	0	0
$11$	27.6161	0.756961	0.378481	−	0.925609i	$-0.376447\pi$
$11$	27.6161	0.756961	0.378481	+	0.925609i	$0.376447\pi$
$12$	− 19.3918i	− 0.466493i
$13$	− 58.1117i	− 1.23979i	−0.784684	−	0.619896i	$-0.787175\pi$
$13$	− 58.1117i	− 1.23979i	0.784684	−	0.619896i	$-0.212825\pi$
$14$	10.8088	0.206340
$15$	0	0
$16$	22.9632	0.358799
$17$	− 17.0000i	− 0.242536i
$17$	− 17.0000i	− 0.242536i
$18$	23.2065i	0.303879i
$19$	−89.1688	−1.07667	−0.538335	−	0.842731i	$-0.680946\pi$
$19$	−89.1688	−1.07667	−0.538335	+	0.842731i	$0.680946\pi$
$20$	0	0
$21$	−25.0493	−0.260296
$22$	37.5916i	0.364298i
$23$	115.269i	1.04501i	0.852635	+	0.522507i	$0.175003\pi$
$23$	115.269i	1.04501i	−0.852635	+	0.522507i	$0.824997\pi$
$24$	60.7497	0.516687
$25$	0	0
$26$	79.1029	0.596668
$27$	− 138.956i	− 0.990449i
$28$	− 48.8108i	− 0.329442i
$29$	128.558	0.823191	0.411596	−	0.911367i	$-0.364972\pi$
$29$	128.558	0.823191	0.411596	+	0.911367i	$0.364972\pi$
$30$	0	0
$31$	273.460	1.58435	0.792174	−	0.610295i	$-0.208949\pi$
$31$	273.460	1.58435	0.792174	+	0.610295i	$0.208949\pi$
$32$	185.316i	1.02374i
$33$	− 87.1187i	− 0.459558i
$34$	23.1408	0.116724
$35$	0	0
$36$	104.797	0.485172
$37$	− 132.351i	− 0.588063i	−0.955796	−	0.294031i	$-0.905003\pi$
$37$	− 132.351i	− 0.588063i	0.955796	−	0.294031i	$-0.0949970\pi$
$38$	− 121.379i	− 0.518163i
$39$	−183.321	−0.752689
$40$	0	0
$41$	−470.559	−1.79241	−0.896207	−	0.443636i	$-0.853688\pi$
$41$	−470.559	−1.79241	−0.896207	+	0.443636i	$0.853688\pi$
$42$	− 34.0977i	− 0.125271i
$43$	− 352.642i	− 1.25064i	−0.780370	−	0.625318i	$-0.784969\pi$
$43$	− 352.642i	− 1.25064i	0.780370	−	0.625318i	$-0.215031\pi$
$44$	169.758	0.581637
$45$	0	0
$46$	−156.907	−0.502928
$47$	152.598i	0.473589i	0.971560	+	0.236795i	$0.0760969\pi$
$47$	152.598i	0.473589i	−0.971560	+	0.236795i	$0.923903\pi$
$48$	− 72.4403i	− 0.217830i
$49$	279.949	0.816177
$50$	0	0
$51$	−53.6287	−0.147246
$52$	− 357.217i	− 0.952637i
$53$	− 527.614i	− 1.36742i	−0.729753	−	0.683711i	$-0.760365\pi$
$53$	− 527.614i	− 1.36742i	0.729753	−	0.683711i	$-0.239635\pi$
$54$	189.150	0.476668
$55$	0	0
$56$	152.912	0.364889
$57$	281.295i	0.653656i
$58$	174.995i	0.396173i
$59$	292.020	0.644368	0.322184	−	0.946677i	$-0.395583\pi$
$59$	292.020	0.644368	0.322184	+	0.946677i	$0.395583\pi$
$60$	0	0
$61$	−53.8962	−0.113126	−0.0565632	−	0.998399i	$-0.518014\pi$
$61$	−53.8962	−0.113126	−0.0565632	+	0.998399i	$0.518014\pi$
$62$	372.239i	0.762490i
$63$	− 135.372i	− 0.270718i
$64$	−68.5514	−0.133889
$65$	0	0
$66$	118.588	0.221169
$67$	52.9572i	0.0965635i	0.998834	+	0.0482817i	$0.0153745\pi$
$67$	52.9572i	0.0965635i	−0.998834	+	0.0482817i	$0.984625\pi$
$68$	− 104.500i	− 0.186361i
$69$	363.632	0.634437
$70$	0	0
$71$	788.400	1.31783	0.658915	−	0.752218i	$-0.271016\pi$
$71$	788.400	1.31783	0.658915	+	0.752218i	$0.271016\pi$
$72$	328.304i	0.537375i
$73$	− 295.780i	− 0.474224i	−0.971482	−	0.237112i	$-0.923799\pi$
$73$	− 295.780i	− 0.474224i	0.971482	−	0.237112i	$-0.0762009\pi$
$74$	180.159	0.283014
$75$	0	0
$76$	−548.127	−0.827296
$77$	− 219.285i	− 0.324544i
$78$	− 249.541i	− 0.362242i
$79$	720.325	1.02586	0.512930	−	0.858430i	$-0.328560\pi$
$79$	720.325	1.02586	0.512930	+	0.858430i	$0.328560\pi$
$80$	0	0
$81$	21.9487	0.0301079
$82$	− 640.535i	− 0.862625i
$83$	116.051i	0.153473i	0.997051	+	0.0767363i	$0.0244500\pi$
$83$	116.051i	0.153473i	−0.997051	+	0.0767363i	$0.975550\pi$
$84$	−153.980	−0.200007
$85$	0	0
$86$	480.024	0.601887
$87$	− 405.552i	− 0.499767i
$88$	531.812i	0.644220i
$89$	813.329	0.968682	0.484341	−	0.874879i	$-0.339059\pi$
$89$	813.329	0.968682	0.484341	+	0.874879i	$0.339059\pi$
$90$	0	0
$91$	−461.435	−0.531556
$92$	708.569i	0.802972i
$93$	− 862.664i	− 0.961872i
$94$	−207.720	−0.227922
$95$	0	0
$96$	584.605	0.621521
$97$	794.693i	0.831844i	0.909400	+	0.415922i	$0.136541\pi$
$97$	794.693i	0.831844i	−0.909400	+	0.415922i	$0.863459\pi$
$98$	381.072i	0.392797i
$99$	470.808	0.477959
$100$	0	0
$101$	265.513	0.261579	0.130790	−	0.991410i	$-0.458249\pi$
$101$	265.513	0.261579	0.130790	+	0.991410i	$0.458249\pi$
$102$	− 73.0006i	− 0.0708641i
$103$	− 523.107i	− 0.500420i	−0.968192	−	0.250210i	$-0.919500\pi$
$103$	− 523.107i	− 0.500420i	0.968192	−	0.250210i	$-0.0804996\pi$
$104$	1119.07	1.05514
$105$	0	0
$106$	718.199	0.658091
$107$	− 986.039i	− 0.890878i	−0.895312	−	0.445439i	$-0.853048\pi$
$107$	− 986.039i	− 0.890878i	0.895312	−	0.445439i	$-0.146952\pi$
$108$	− 854.174i	− 0.761046i
$109$	−1814.39	−1.59438	−0.797188	−	0.603732i	$-0.793680\pi$
$109$	−1814.39	−1.59438	−0.797188	+	0.603732i	$0.793680\pi$
$110$	0	0
$111$	−417.518	−0.357018
$112$	− 182.339i	− 0.153834i
$113$	707.339i	0.588857i	0.955673	+	0.294429i	$0.0951293\pi$
$113$	707.339i	0.588857i	−0.955673	+	0.294429i	$0.904871\pi$
$114$	−382.904	−0.314581
$115$	0	0
$116$	790.253	0.632527
$117$	− 990.706i	− 0.782827i
$118$	397.503i	0.310112i
$119$	−134.988	−0.103986
$120$	0	0
$121$	−568.350	−0.427010
$122$	− 73.3647i	− 0.0544437i
$123$	1484.44i	1.08819i
$124$	1680.98	1.21739
$125$	0	0
$126$	184.271	0.130287
$127$	2648.18i	1.85030i	0.379600	+	0.925151i	$0.376062\pi$
$127$	2648.18i	1.85030i	−0.379600	+	0.925151i	$0.623938\pi$
$128$	1389.22i	0.959302i
$129$	−1112.46	−0.759273
$130$	0	0
$131$	−1979.08	−1.31995	−0.659974	−	0.751289i	$-0.729433\pi$
$131$	−1979.08	−1.31995	−0.659974	+	0.751289i	$0.729433\pi$
$132$	− 535.525i	− 0.353117i
$133$	708.044i	0.461618i
$134$	−72.0865	−0.0464726
$135$	0	0
$136$	327.374	0.206413
$137$	3141.92i	1.95936i	0.200570	+	0.979679i	$0.435721\pi$
$137$	3141.92i	1.95936i	−0.200570	+	0.979679i	$0.564279\pi$
$138$	494.984i	0.305332i
$139$	−1468.07	−0.895830	−0.447915	−	0.894076i	$-0.647833\pi$
$139$	−1468.07	−0.895830	−0.447915	+	0.894076i	$0.647833\pi$
$140$	0	0
$141$	481.390	0.287520
$142$	1073.19i	0.634224i
$143$	− 1604.82i	− 0.938474i
$144$	391.483	0.226553
$145$	0	0
$146$	402.621	0.228227
$147$	− 883.135i	− 0.495508i
$148$	− 813.570i	− 0.451858i
$149$	286.027	0.157263	0.0786316	−	0.996904i	$-0.474945\pi$
$149$	286.027	0.157263	0.0786316	+	0.996904i	$0.474945\pi$
$150$	0	0
$151$	−669.626	−0.360883	−0.180442	−	0.983586i	$-0.557753\pi$
$151$	−669.626	−0.360883	−0.180442	+	0.983586i	$0.557753\pi$
$152$	− 1717.15i	− 0.916311i
$153$	− 289.821i	− 0.153141i
$154$	298.496	0.156191
$155$	0	0
$156$	−1126.89	−0.578354
$157$	720.809i	0.366413i	0.983074	+	0.183206i	$0.0586476\pi$
$157$	720.809i	0.366413i	−0.983074	+	0.183206i	$0.941352\pi$
$158$	980.522i	0.493710i
$159$	−1664.43	−0.830174
$160$	0	0
$161$	915.294	0.448045
$162$	29.8770i	0.0144899i
$163$	676.599i	0.325125i	0.986698	+	0.162562i	$0.0519759\pi$
$163$	676.599i	0.325125i	−0.986698	+	0.162562i	$0.948024\pi$
$164$	−2892.56	−1.37726
$165$	0	0
$166$	−157.971	−0.0738609
$167$	− 2835.67i	− 1.31396i	−0.753909	−	0.656979i	$-0.771834\pi$
$167$	− 2835.67i	− 1.31396i	0.753909	−	0.656979i	$-0.228166\pi$
$168$	− 482.382i	− 0.221527i
$169$	−1179.97	−0.537083
$170$	0	0
$171$	−1520.18	−0.679829
$172$	− 2167.72i	− 0.960970i
$173$	177.314i	0.0779243i	0.999241	+	0.0389621i	$0.0124052\pi$
$173$	177.314i	0.0779243i	−0.999241	+	0.0389621i	$0.987595\pi$
$174$	552.046	0.240520
$175$	0	0
$176$	634.153	0.271597
$177$	− 921.214i	− 0.391202i
$178$	1107.12i	0.466192i
$179$	1023.76	0.427483	0.213741	−	0.976890i	$-0.431435\pi$
$179$	1023.76	0.427483	0.213741	+	0.976890i	$0.431435\pi$
$180$	0	0
$181$	−3450.21	−1.41686	−0.708432	−	0.705779i	$-0.750597\pi$
$181$	−3450.21	−1.41686	−0.708432	+	0.705779i	$0.750597\pi$
$182$	− 628.116i	− 0.255819i
$183$	170.023i	0.0686800i
$184$	−2219.78	−0.889370
$185$	0	0
$186$	1174.28	0.462915
$187$	− 469.474i	− 0.183590i
$188$	938.031i	0.363899i
$189$	−1103.38	−0.424651
$190$	0	0
$191$	−490.894	−0.185968	−0.0929839	−	0.995668i	$-0.529640\pi$
$191$	−490.894	−0.185968	−0.0929839	+	0.995668i	$0.529640\pi$
$192$	216.254i	0.0812855i
$193$	3548.80i	1.32357i	0.749696	+	0.661783i	$0.230200\pi$
$193$	3548.80i	1.32357i	−0.749696	+	0.661783i	$0.769800\pi$
$194$	−1081.75	−0.400337
$195$	0	0
$196$	1720.87	0.627138
$197$	1363.15i	0.492996i	0.969143	+	0.246498i	$0.0792799\pi$
$197$	1363.15i	0.492996i	−0.969143	+	0.246498i	$0.920720\pi$
$198$	640.874i	0.230025i
$199$	−3737.46	−1.33137	−0.665683	−	0.746235i	$-0.731860\pi$
$199$	−3737.46	−1.33137	−0.665683	+	0.746235i	$0.731860\pi$
$200$	0	0
$201$	167.060	0.0586246
$202$	361.422i	0.125889i
$203$	− 1020.81i	− 0.352940i
$204$	−329.660	−0.113141
$205$	0	0
$206$	712.064	0.240834
$207$	1965.15i	0.659841i
$208$	− 1334.43i	− 0.444836i
$209$	−2462.50	−0.814997
$210$	0	0
$211$	−5266.12	−1.71817	−0.859087	−	0.511829i	$-0.828968\pi$
$211$	−5266.12	−1.71817	−0.859087	+	0.511829i	$0.828968\pi$
$212$	− 3243.28i	− 1.05071i
$213$	− 2487.11i	− 0.800066i
$214$	1342.22	0.428748
$215$	0	0
$216$	2675.92	0.842932
$217$	− 2171.40i	− 0.679283i
$218$	− 2469.78i	− 0.767316i
$219$	−933.075	−0.287906
$220$	0	0
$221$	−987.899	−0.300694
$222$	− 568.334i	− 0.171820i
$223$	− 704.546i	− 0.211569i	−0.994389	−	0.105785i	$-0.966265\pi$
$223$	− 704.546i	− 0.211569i	0.994389	−	0.105785i	$-0.0337354\pi$
$224$	1471.50	0.438923
$225$	0	0
$226$	−962.845	−0.283396
$227$	− 2151.26i	− 0.629006i	−0.949256	−	0.314503i	$-0.898162\pi$
$227$	− 2151.26i	− 0.629006i	0.949256	−	0.314503i	$-0.101838\pi$
$228$	1729.14i	0.502259i
$229$	3916.94	1.13030	0.565149	−	0.824989i	$-0.308819\pi$
$229$	3916.94	1.13030	0.565149	+	0.824989i	$0.308819\pi$
$230$	0	0
$231$	−691.764	−0.197034
$232$	2475.67i	0.700586i
$233$	5192.74i	1.46003i	0.683429	+	0.730017i	$0.260488\pi$
$233$	5192.74i	1.46003i	−0.683429	+	0.730017i	$0.739512\pi$
$234$	1348.57	0.376747
$235$	0	0
$236$	1795.07	0.495123
$237$	− 2272.36i	− 0.622809i
$238$	− 183.749i	− 0.0500448i
$239$	−334.305	−0.0904786	−0.0452393	−	0.998976i	$-0.514405\pi$
$239$	−334.305	−0.0904786	−0.0452393	+	0.998976i	$0.514405\pi$
$240$	0	0
$241$	−1918.45	−0.512773	−0.256386	−	0.966574i	$-0.582532\pi$
$241$	−1918.45	−0.512773	−0.256386	+	0.966574i	$0.582532\pi$
$242$	− 773.651i	− 0.205505i
$243$	− 3821.06i	− 1.00873i
$244$	−331.304	−0.0869245
$245$	0	0
$246$	−2020.65	−0.523708
$247$	5181.75i	1.33485i
$248$	5266.09i	1.34838i
$249$	366.097	0.0931746
$250$	0	0
$251$	7695.71	1.93525	0.967627	−	0.252385i	$-0.0812148\pi$
$251$	7695.71	1.93525	0.967627	+	0.252385i	$0.0812148\pi$
$252$	− 832.141i	− 0.208016i
$253$	3183.29i	0.791035i
$254$	−3604.76	−0.890484
$255$	0	0
$256$	−2439.44	−0.595567
$257$	5335.10i	1.29492i	0.762099	+	0.647460i	$0.224169\pi$
$257$	5335.10i	1.29492i	−0.762099	+	0.647460i	$0.775831\pi$
$258$	− 1514.30i	− 0.365411i
$259$	−1050.93	−0.252130
$260$	0	0
$261$	2191.69	0.519778
$262$	− 2693.97i	− 0.635244i
$263$	− 3934.15i	− 0.922396i	−0.887297	−	0.461198i	$-0.847420\pi$
$263$	− 3934.15i	− 0.922396i	0.887297	−	0.461198i	$-0.152580\pi$
$264$	1677.67	0.391112
$265$	0	0
$266$	−963.804	−0.222160
$267$	− 2565.75i	− 0.588095i
$268$	325.532i	0.0741979i
$269$	−3424.04	−0.776088	−0.388044	−	0.921641i	$-0.626849\pi$
$269$	−3424.04	−0.776088	−0.388044	+	0.921641i	$0.626849\pi$
$270$	0	0
$271$	549.034	0.123068	0.0615340	−	0.998105i	$-0.480401\pi$
$271$	549.034	0.123068	0.0615340	+	0.998105i	$0.480401\pi$
$272$	− 390.374i	− 0.0870216i
$273$	1455.66i	0.322712i
$274$	−4276.85	−0.942970
$275$	0	0
$276$	2235.27	0.487492
$277$	5203.65i	1.12873i	0.825527	+	0.564363i	$0.190878\pi$
$277$	5203.65i	1.12873i	−0.825527	+	0.564363i	$0.809122\pi$
$278$	− 1998.37i	− 0.431131i
$279$	4662.02	1.00039
$280$	0	0
$281$	−1986.73	−0.421774	−0.210887	−	0.977510i	$-0.567635\pi$
$281$	−1986.73	−0.421774	−0.210887	+	0.977510i	$0.567635\pi$
$282$	655.279i	0.138373i
$283$	− 753.696i	− 0.158313i	−0.996862	−	0.0791565i	$-0.974777\pi$
$283$	− 753.696i	− 0.158313i	0.996862	−	0.0791565i	$-0.0252227\pi$
$284$	4846.36	1.01260
$285$	0	0
$286$	2184.51	0.451654
$287$	3736.47i	0.768490i
$288$	3159.33i	0.646407i
$289$	−289.000	−0.0588235
$290$	0	0
$291$	2506.96	0.505020
$292$	− 1818.18i	− 0.364387i
$293$	7202.22i	1.43603i	0.696025	+	0.718017i	$0.254950\pi$
$293$	7202.22i	1.43603i	−0.696025	+	0.718017i	$0.745050\pi$
$294$	1202.14	0.238471
$295$	0	0
$296$	2548.72	0.500477
$297$	− 3837.43i	− 0.749731i
$298$	389.345i	0.0756852i
$299$	6698.50	1.29560
$300$	0	0
$301$	−2800.15	−0.536205
$302$	− 911.509i	− 0.173680i
$303$	− 837.595i	− 0.158807i
$304$	−2047.60	−0.386308
$305$	0	0
$306$	394.511	0.0737016
$307$	2425.71i	0.450953i	0.974249	+	0.225477i	$0.0723940\pi$
$307$	2425.71i	0.450953i	−0.974249	+	0.225477i	$0.927606\pi$
$308$	− 1347.96i	− 0.249375i
$309$	−1650.21	−0.303809
$310$	0	0
$311$	−9544.94	−1.74033	−0.870167	−	0.492757i	$-0.835989\pi$
$311$	−9544.94	−1.74033	−0.870167	+	0.492757i	$0.835989\pi$
$312$	− 3530.27i	− 0.640584i
$313$	− 588.379i	− 0.106253i	−0.998588	−	0.0531264i	$-0.983081\pi$
$313$	− 588.379i	− 0.106253i	0.998588	−	0.0531264i	$-0.0169186\pi$
$314$	−981.180	−0.176341
$315$	0	0
$316$	4427.89	0.788255
$317$	7653.31i	1.35600i	0.735061	+	0.678001i	$0.237154\pi$
$317$	7653.31i	1.35600i	−0.735061	+	0.678001i	$0.762846\pi$
$318$	− 2265.65i	− 0.399533i
$319$	3550.26	0.623124
$320$	0	0
$321$	−3110.59	−0.540860
$322$	1245.92i	0.215628i
$323$	1515.87i	0.261131i
$324$	134.920	0.0231345
$325$	0	0
$326$	−921.001	−0.156471
$327$	5723.73i	0.967960i
$328$	− 9061.70i	− 1.52545i
$329$	1211.70	0.203050
$330$	0	0
$331$	752.266	0.124919	0.0624597	−	0.998047i	$-0.480106\pi$
$331$	752.266	0.124919	0.0624597	+	0.998047i	$0.480106\pi$
$332$	713.373i	0.117926i
$333$	− 2256.36i	− 0.371314i
$334$	3859.98	0.632361
$335$	0	0
$336$	−575.211	−0.0933939
$337$	− 1968.57i	− 0.318204i	−0.987262	−	0.159102i	$-0.949140\pi$
$337$	− 1968.57i	− 0.318204i	0.987262	−	0.159102i	$-0.0508598\pi$
$338$	− 1606.20i	− 0.258479i
$339$	2231.39	0.357501
$340$	0	0
$341$	7551.89	1.19929
$342$	− 2069.30i	− 0.327178i
$343$	− 4946.52i	− 0.778678i
$344$	6790.93	1.06437
$345$	0	0
$346$	−241.363	−0.0375022
$347$	3983.10i	0.616207i	0.951353	+	0.308104i	$0.0996944\pi$
$347$	3983.10i	0.616207i	−0.951353	+	0.308104i	$0.900306\pi$
$348$	− 2492.96i	− 0.384013i
$349$	−1495.61	−0.229393	−0.114697	−	0.993401i	$-0.536590\pi$
$349$	−1495.61	−0.229393	−0.114697	+	0.993401i	$0.536590\pi$
$350$	0	0
$351$	−8074.98	−1.22795
$352$	5117.72i	0.774930i
$353$	− 6482.49i	− 0.977417i	−0.872447	−	0.488708i	$-0.837468\pi$
$353$	− 6482.49i	− 0.977417i	0.872447	−	0.488708i	$-0.162532\pi$
$354$	1253.98	0.188272
$355$	0	0
$356$	4999.59	0.744320
$357$	425.838i	0.0631309i
$358$	1393.56i	0.205732i
$359$	4943.42	0.726751	0.363376	−	0.931643i	$-0.381624\pi$
$359$	4943.42	0.726751	0.363376	+	0.931643i	$0.381624\pi$
$360$	0	0
$361$	1092.08	0.159218
$362$	− 4696.50i	− 0.681886i
$363$	1792.94i	0.259242i
$364$	−2836.48	−0.408439
$365$	0	0
$366$	−231.439	−0.0330533
$367$	− 14.8871i	− 0.00211743i	−0.999999	−	0.00105872i	$-0.999663\pi$
$367$	− 14.8871i	− 0.00211743i	0.999999	−	0.00105872i	$-0.000337000\pi$
$368$	2646.95i	0.374950i
$369$	−8022.23	−1.13176
$370$	0	0
$371$	−4189.51	−0.586276
$372$	− 5302.86i	− 0.739088i
$373$	− 1923.18i	− 0.266966i	−0.991051	−	0.133483i	$-0.957384\pi$
$373$	− 1923.18i	− 0.266966i	0.991051	−	0.133483i	$-0.0426162\pi$
$374$	639.058	0.0883554
$375$	0	0
$376$	−2938.63	−0.403053
$377$	− 7470.70i	− 1.02059i
$378$	− 1501.94i	− 0.204369i
$379$	9592.87	1.30014	0.650069	−	0.759875i	$-0.274740\pi$
$379$	9592.87	1.30014	0.650069	+	0.759875i	$0.274740\pi$
$380$	0	0
$381$	8354.04	1.12333
$382$	− 668.215i	− 0.0894996i
$383$	9083.77i	1.21190i	0.795502	+	0.605951i	$0.207207\pi$
$383$	9083.77i	1.21190i	−0.795502	+	0.605951i	$0.792793\pi$
$384$	4382.47	0.582401
$385$	0	0
$386$	−4830.70	−0.636985
$387$	− 6011.95i	− 0.789675i
$388$	4885.04i	0.639176i
$389$	1143.78	0.149079	0.0745396	−	0.997218i	$-0.476251\pi$
$389$	1143.78	0.149079	0.0745396	+	0.997218i	$0.476251\pi$
$390$	0	0
$391$	1959.58	0.253453
$392$	5391.06i	0.694616i
$393$	6243.27i	0.801352i
$394$	−1855.55	−0.237262
$395$	0	0
$396$	2894.09	0.367256
$397$	10604.5i	1.34061i	0.742084	+	0.670307i	$0.233838\pi$
$397$	10604.5i	1.34061i	−0.742084	+	0.670307i	$0.766162\pi$
$398$	− 5087.51i	− 0.640739i
$399$	2233.62	0.280252
$400$	0	0
$401$	13785.4	1.71674	0.858368	−	0.513035i	$-0.171479\pi$
$401$	13785.4	1.71674	0.858368	+	0.513035i	$0.171479\pi$
$402$	227.406i	0.0282139i
$403$	− 15891.2i	− 1.96426i
$404$	1632.13	0.200993
$405$	0	0
$406$	1389.55	0.169857
$407$	− 3655.01i	− 0.445141i
$408$	− 1032.74i	− 0.125315i
$409$	9505.94	1.14924	0.574619	−	0.818421i	$-0.305150\pi$
$409$	9505.94	1.14924	0.574619	+	0.818421i	$0.305150\pi$
$410$	0	0
$411$	9911.59	1.18954
$412$	− 3215.58i	− 0.384515i
$413$	− 2318.78i	− 0.276270i
$414$	−2675.00	−0.317558
$415$	0	0
$416$	10769.1	1.26922
$417$	4631.23i	0.543866i
$418$	− 3352.00i	− 0.392229i
$419$	−9680.86	−1.12874	−0.564369	−	0.825523i	$-0.690880\pi$
$419$	−9680.86	−1.12874	−0.564369	+	0.825523i	$0.690880\pi$
$420$	0	0
$421$	−12360.3	−1.43089	−0.715444	−	0.698671i	$-0.753775\pi$
$421$	−12360.3	−1.43089	−0.715444	+	0.698671i	$0.753775\pi$
$422$	− 7168.36i	− 0.826897i
$423$	2601.54i	0.299033i
$424$	10160.4	1.16376
$425$	0	0
$426$	3385.51	0.385043
$427$	427.962i	0.0485025i
$428$	− 6061.25i	− 0.684537i
$429$	−5062.61	−0.569756
$430$	0	0
$431$	2970.58	0.331990	0.165995	−	0.986127i	$-0.446916\pi$
$431$	2970.58	0.331990	0.165995	+	0.986127i	$0.446916\pi$
$432$	− 3190.87i	− 0.355372i
$433$	− 6131.50i	− 0.680510i	−0.940333	−	0.340255i	$-0.889487\pi$
$433$	− 6131.50i	− 0.680510i	0.940333	−	0.340255i	$-0.110513\pi$
$434$	2955.76	0.326915
$435$	0	0
$436$	−11153.2	−1.22509
$437$	− 10278.4i	− 1.12513i
$438$	− 1270.12i	− 0.138559i
$439$	2544.91	0.276679	0.138339	−	0.990385i	$-0.455824\pi$
$439$	2544.91	0.276679	0.138339	+	0.990385i	$0.455824\pi$
$440$	0	0
$441$	4772.65	0.515349
$442$	− 1344.75i	− 0.144713i
$443$	− 8529.82i	− 0.914817i	−0.889257	−	0.457408i	$-0.848778\pi$
$443$	− 8529.82i	− 0.914817i	0.889257	−	0.457408i	$-0.151222\pi$
$444$	−2566.51	−0.274327
$445$	0	0
$446$	959.043	0.101821
$447$	− 902.308i	− 0.0954759i
$448$	544.331i	0.0574046i
$449$	−8855.74	−0.930798	−0.465399	−	0.885101i	$-0.654089\pi$
$449$	−8855.74	−0.930798	−0.465399	+	0.885101i	$0.654089\pi$
$450$	0	0
$451$	−12995.0	−1.35679
$452$	4348.07i	0.452469i
$453$	2112.42i	0.219095i
$454$	2928.35	0.302718
$455$	0	0
$456$	−5416.98	−0.556301
$457$	− 7154.78i	− 0.732356i	−0.930545	−	0.366178i	$-0.880666\pi$
$457$	− 7154.78i	− 0.732356i	0.930545	−	0.366178i	$-0.119334\pi$
$458$	5331.82i	0.543973i
$459$	−2362.25	−0.240219
$460$	0	0
$461$	−7263.06	−0.733784	−0.366892	−	0.930264i	$-0.619578\pi$
$461$	−7263.06	−0.733784	−0.366892	+	0.930264i	$0.619578\pi$
$462$	− 941.645i	− 0.0948253i
$463$	− 352.898i	− 0.0354224i	−0.999843	−	0.0177112i	$-0.994362\pi$
$463$	− 352.898i	− 0.0354224i	0.999843	−	0.0177112i	$-0.00563794\pi$
$464$	2952.09	0.295360
$465$	0	0
$466$	−7068.47	−0.702662
$467$	1483.02i	0.146951i	0.997297	+	0.0734753i	$0.0234090\pi$
$467$	1483.02i	0.146951i	−0.997297	+	0.0734753i	$0.976591\pi$
$468$	− 6089.94i	− 0.601512i
$469$	420.506	0.0414012
$470$	0	0
$471$	2273.89	0.222452
$472$	5623.51i	0.548396i
$473$	− 9738.60i	− 0.946683i
$474$	3093.19	0.299736
$475$	0	0
$476$	−829.783	−0.0799014
$477$	− 8994.92i	− 0.863415i
$478$	− 455.063i	− 0.0435441i
$479$	9990.10	0.952942	0.476471	−	0.879190i	$-0.341916\pi$
$479$	9990.10	0.952942	0.476471	+	0.879190i	$0.341916\pi$
$480$	0	0
$481$	−7691.13	−0.729075
$482$	− 2611.44i	− 0.246779i
$483$	− 2887.42i	− 0.272012i
$484$	−3493.69	−0.328108
$485$	0	0
$486$	5201.30	0.485465
$487$	− 1129.88i	− 0.105133i	−0.998617	−	0.0525663i	$-0.983260\pi$
$487$	− 1129.88i	− 0.105133i	0.998617	−	0.0525663i	$-0.0167401\pi$
$488$	− 1037.90i	− 0.0962774i
$489$	2134.42	0.197386
$490$	0	0
$491$	18774.9	1.72566	0.862832	−	0.505491i	$-0.168689\pi$
$491$	18774.9	1.72566	0.862832	+	0.505491i	$0.168689\pi$
$492$	9124.97i	0.836149i
$493$	− 2185.48i	− 0.199653i
$494$	−7053.51	−0.642414
$495$	0	0
$496$	6279.49	0.568463
$497$	− 6260.28i	− 0.565014i
$498$	498.339i	0.0448416i
$499$	−17329.1	−1.55462	−0.777310	−	0.629118i	$-0.783416\pi$
$499$	−17329.1	−1.55462	−0.777310	+	0.629118i	$0.783416\pi$
$500$	0	0
$501$	−8945.50	−0.797716
$502$	10475.6i	0.931369i
$503$	20837.0i	1.84707i	0.383518	+	0.923533i	$0.374712\pi$
$503$	20837.0i	1.84707i	−0.383518	+	0.923533i	$0.625288\pi$
$504$	2606.90	0.230398
$505$	0	0
$506$	−4333.16	−0.380697
$507$	3722.37i	0.326068i
$508$	16278.6i	1.42174i
$509$	−11835.0	−1.03060	−0.515301	−	0.857009i	$-0.672320\pi$
$509$	−11835.0	−1.03060	−0.515301	+	0.857009i	$0.672320\pi$
$510$	0	0
$511$	−2348.63	−0.203322
$512$	7793.12i	0.672676i
$513$	12390.6i	1.06639i
$514$	−7262.26	−0.623199
$515$	0	0
$516$	−6838.35	−0.583414
$517$	4214.16i	0.358489i
$518$	− 1430.55i	− 0.121341i
$519$	559.359	0.0473086
$520$	0	0
$521$	7686.37	0.646346	0.323173	−	0.946340i	$-0.395250\pi$
$521$	7686.37	0.646346	0.323173	+	0.946340i	$0.395250\pi$
$522$	2983.37i	0.250151i
$523$	− 11476.4i	− 0.959518i	−0.877400	−	0.479759i	$-0.840724\pi$
$523$	− 11476.4i	− 0.959518i	0.877400	−	0.479759i	$-0.159276\pi$
$524$	−12165.6	−1.01423
$525$	0	0
$526$	5355.25	0.443916
$527$	− 4648.81i	− 0.384261i
$528$	− 2000.52i	− 0.164889i
$529$	−1120.01	−0.0920535
$530$	0	0
$531$	4978.44	0.406866
$532$	4352.40i	0.354700i
$533$	27345.0i	2.22222i
$534$	3492.56	0.283029
$535$	0	0
$536$	−1019.81	−0.0821814
$537$	− 3229.59i	− 0.259529i
$538$	− 4660.88i	− 0.373504i
$539$	7731.09	0.617814
$540$	0	0
$541$	−546.481	−0.0434289	−0.0217145	−	0.999764i	$-0.506912\pi$
$541$	−546.481	−0.0434289	−0.0217145	+	0.999764i	$0.506912\pi$
$542$	747.357i	0.0592283i
$543$	10884.1i	0.860191i
$544$	3150.38	0.248293
$545$	0	0
$546$	−1981.47	−0.155310
$547$	8397.33i	0.656388i	0.944610	+	0.328194i	$0.106440\pi$
$547$	8397.33i	0.656388i	−0.944610	+	0.328194i	$0.893560\pi$
$548$	19313.6i	1.50554i
$549$	−918.839	−0.0714301
$550$	0	0
$551$	−11463.3	−0.886305
$552$	7002.58i	0.539945i
$553$	− 5719.73i	− 0.439833i
$554$	−7083.32	−0.543215
$555$	0	0
$556$	−9024.36	−0.688342
$557$	− 4881.65i	− 0.371350i	−0.982611	−	0.185675i	$-0.940553\pi$
$557$	− 4881.65i	− 0.371350i	0.982611	−	0.185675i	$-0.0594472\pi$
$558$	6346.04i	0.481451i
$559$	−20492.6	−1.55053
$560$	0	0
$561$	−1481.02	−0.111459
$562$	− 2704.38i	− 0.202985i
$563$	− 7198.57i	− 0.538870i	−0.963019	−	0.269435i	$-0.913163\pi$
$563$	− 7198.57i	− 0.538870i	0.963019	−	0.269435i	$-0.0868369\pi$
$564$	2959.14	0.220926
$565$	0	0
$566$	1025.95	0.0761904
$567$	− 174.283i	− 0.0129087i
$568$	15182.5i	1.12155i
$569$	23946.9	1.76433	0.882167	−	0.470937i	$-0.156084\pi$
$569$	23946.9	1.76433	0.882167	+	0.470937i	$0.156084\pi$
$570$	0	0
$571$	1593.15	0.116763	0.0583813	−	0.998294i	$-0.481406\pi$
$571$	1593.15	0.116763	0.0583813	+	0.998294i	$0.481406\pi$
$572$	− 9864.95i	− 0.721109i
$573$	1548.59i	0.112903i
$574$	−5086.16	−0.369847
$575$	0	0
$576$	−1168.69	−0.0845403
$577$	12937.4i	0.933435i	0.884406	+	0.466717i	$0.154564\pi$
$577$	12937.4i	0.933435i	−0.884406	+	0.466717i	$0.845436\pi$
$578$	− 393.393i	− 0.0283097i
$579$	11195.2	0.803549
$580$	0	0
$581$	921.499	0.0658007
$582$	3412.53i	0.243048i
$583$	− 14570.6i	− 1.03508i
$584$	5695.92	0.403594
$585$	0	0
$586$	−9803.82	−0.691112
$587$	− 12899.2i	− 0.906998i	−0.891257	−	0.453499i	$-0.850176\pi$
$587$	− 12899.2i	− 0.906998i	0.891257	−	0.453499i	$-0.149824\pi$
$588$	− 5428.70i	− 0.380741i
$589$	−24384.1	−1.70582
$590$	0	0
$591$	4300.23	0.299302
$592$	− 3039.19i	− 0.210997i
$593$	− 4357.13i	− 0.301730i	−0.988554	−	0.150865i	$-0.951794\pi$
$593$	− 4357.13i	− 0.301730i	0.988554	−	0.150865i	$-0.0482058\pi$
$594$	5223.59	0.360819
$595$	0	0
$596$	1758.23	0.120839
$597$	11790.3i	0.808284i
$598$	9118.14i	0.623526i
$599$	−13726.8	−0.936328	−0.468164	−	0.883642i	$-0.655084\pi$
$599$	−13726.8	−0.936328	−0.468164	+	0.883642i	$0.655084\pi$
$600$	0	0
$601$	2531.41	0.171811	0.0859056	−	0.996303i	$-0.472622\pi$
$601$	2531.41	0.171811	0.0859056	+	0.996303i	$0.472622\pi$
$602$	− 3811.62i	− 0.258057i
$603$	902.830i	0.0609720i
$604$	−4116.24	−0.277297
$605$	0	0
$606$	1140.15	0.0764283
$607$	185.004i	0.0123708i	0.999981	+	0.00618540i	$0.00196889\pi$
$607$	185.004i	0.0123708i	−0.999981	+	0.00618540i	$0.998031\pi$
$608$	− 16524.4i	− 1.10223i
$609$	−3220.28	−0.214273
$610$	0	0
$611$	8867.73	0.587152
$612$	− 1781.55i	− 0.117672i
$613$	17706.9i	1.16668i	0.812228	+	0.583339i	$0.198254\pi$
$613$	17706.9i	1.16668i	−0.812228	+	0.583339i	$0.801746\pi$
$614$	−3301.93	−0.217028
$615$	0	0
$616$	4222.84	0.276207
$617$	− 6183.89i	− 0.403491i	−0.979438	−	0.201746i	$-0.935339\pi$
$617$	− 6183.89i	− 0.403491i	0.979438	−	0.201746i	$-0.0646614\pi$
$618$	− 2246.30i	− 0.146213i
$619$	1247.51	0.0810046	0.0405023	−	0.999179i	$-0.487104\pi$
$619$	1247.51	0.0810046	0.0405023	+	0.999179i	$0.487104\pi$
$620$	0	0
$621$	16017.4	1.03503
$622$	− 12992.8i	− 0.837561i
$623$	− 6458.23i	− 0.415318i
$624$	−4209.63	−0.270064
$625$	0	0
$626$	800.914	0.0511357
$627$	7768.27i	0.494792i
$628$	4430.87i	0.281546i
$629$	−2249.96	−0.142626
$630$	0	0
$631$	24053.3	1.51750	0.758752	−	0.651379i	$-0.225809\pi$
$631$	24053.3	1.51750	0.758752	+	0.651379i	$0.225809\pi$
$632$	13871.5i	0.873069i
$633$	16612.7i	1.04312i
$634$	−10417.8	−0.652596
$635$	0	0
$636$	−10231.4	−0.637893
$637$	− 16268.3i	− 1.01189i
$638$	4832.69i	0.299887i
$639$	13440.9	0.832102
$640$	0	0
$641$	−21286.8	−1.31167	−0.655834	−	0.754905i	$-0.727683\pi$
$641$	−21286.8	−1.31167	−0.655834	+	0.754905i	$0.727683\pi$
$642$	− 4234.20i	− 0.260297i
$643$	1789.41i	0.109747i	0.998493	+	0.0548736i	$0.0174756\pi$
$643$	1789.41i	0.109747i	−0.998493	+	0.0548736i	$0.982524\pi$
$644$	5626.38	0.344271
$645$	0	0
$646$	−2063.43	−0.125673
$647$	− 4378.61i	− 0.266060i	−0.991112	−	0.133030i	$-0.957529\pi$
$647$	− 4378.61i	− 0.266060i	0.991112	−	0.133030i	$-0.0424707\pi$
$648$	422.672i	0.0256237i
$649$	8064.45	0.487762
$650$	0	0
$651$	−6849.97	−0.412399
$652$	4159.11i	0.249821i
$653$	7665.15i	0.459358i	0.973266	+	0.229679i	$0.0737676\pi$
$653$	7665.15i	0.459358i	−0.973266	+	0.229679i	$0.926232\pi$
$654$	−7791.26	−0.465845
$655$	0	0
$656$	−10805.5	−0.643117
$657$	− 5042.54i	− 0.299434i
$658$	1649.39i	0.0977205i
$659$	4710.22	0.278428	0.139214	−	0.990262i	$-0.455542\pi$
$659$	4710.22	0.278428	0.139214	+	0.990262i	$0.455542\pi$
$660$	0	0
$661$	−31266.6	−1.83983	−0.919916	−	0.392116i	$-0.871743\pi$
$661$	−31266.6	−1.83983	−0.919916	+	0.392116i	$0.871743\pi$
$662$	1024.00i	0.0601192i
$663$	3116.46i	0.182554i
$664$	−2234.82	−0.130614
$665$	0	0
$666$	3071.40	0.178700
$667$	14818.7i	0.860246i
$668$	− 17431.1i	− 1.00962i
$669$	−2222.58	−0.128446
$670$	0	0
$671$	−1488.40	−0.0856322
$672$	− 4642.05i	− 0.266474i
$673$	− 11723.0i	− 0.671454i	−0.941959	−	0.335727i	$-0.891018\pi$
$673$	− 11723.0i	− 0.671454i	0.941959	−	0.335727i	$-0.108982\pi$
$674$	2679.65	0.153140
$675$	0	0
$676$	−7253.37	−0.412686
$677$	− 289.531i	− 0.0164366i	−0.999966	−	0.00821829i	$-0.997384\pi$
$677$	− 289.531i	− 0.0164366i	0.999966	−	0.00821829i	$-0.00261599\pi$
$678$	3037.42i	0.172052i
$679$	6310.25	0.356650
$680$	0	0
$681$	−6786.45	−0.381875
$682$	10279.8i	0.577175i
$683$	− 1720.10i	− 0.0963660i	−0.998839	−	0.0481830i	$-0.984657\pi$
$683$	− 1720.10i	− 0.0963660i	0.998839	−	0.0481830i	$-0.0153431\pi$
$684$	−9344.64	−0.522370
$685$	0	0
$686$	6733.30	0.374750
$687$	− 12356.5i	− 0.686215i
$688$	− 8097.77i	− 0.448728i
$689$	−30660.5	−1.69532
$690$	0	0
$691$	−16777.7	−0.923665	−0.461832	−	0.886967i	$-0.652808\pi$
$691$	−16777.7	−0.923665	−0.461832	+	0.886967i	$0.652808\pi$
$692$	1089.96i	0.0598758i
$693$	− 3738.44i	− 0.204923i
$694$	−5421.88	−0.296559
$695$	0	0
$696$	7809.84	0.425332
$697$	7999.50i	0.434724i
$698$	− 2035.86i	− 0.110399i
$699$	16381.2	0.886400
$700$	0	0
$701$	23981.1	1.29209	0.646043	−	0.763301i	$-0.276423\pi$
$701$	23981.1	1.29209	0.646043	+	0.763301i	$0.276423\pi$
$702$	− 10991.8i	− 0.590969i
$703$	11801.6i	0.633150i
$704$	−1893.12	−0.101349
$705$	0	0
$706$	8824.10	0.470396
$707$	− 2108.30i	− 0.112151i
$708$	− 5662.78i	− 0.300593i
$709$	7709.28	0.408361	0.204181	−	0.978933i	$-0.434547\pi$
$709$	7709.28	0.408361	0.204181	+	0.978933i	$0.434547\pi$
$710$	0	0
$711$	12280.3	0.647747
$712$	15662.5i	0.824407i
$713$	31521.5i	1.65567i
$714$	−579.660	−0.0303827
$715$	0	0
$716$	6293.13	0.328471
$717$	1054.61i	0.0549304i
$718$	6729.09i	0.349760i
$719$	11976.5	0.621209	0.310605	−	0.950539i	$-0.399468\pi$
$719$	11976.5	0.621209	0.310605	+	0.950539i	$0.399468\pi$
$720$	0	0
$721$	−4153.72	−0.214553
$722$	1486.56i	0.0766260i
$723$	6052.00i	0.311309i
$724$	−21208.7	−1.08870
$725$	0	0
$726$	−2440.58	−0.124764
$727$	− 18597.3i	− 0.948745i	−0.880324	−	0.474372i	$-0.842675\pi$
$727$	− 18597.3i	− 0.948745i	0.880324	−	0.474372i	$-0.157325\pi$
$728$	− 8886.00i	− 0.452386i
$729$	−11461.4	−0.582300
$730$	0	0
$731$	−5994.91	−0.303324
$732$	1045.14i	0.0527727i
$733$	23569.5i	1.18767i	0.804588	+	0.593833i	$0.202386\pi$
$733$	23569.5i	1.18767i	−0.804588	+	0.593833i	$0.797614\pi$
$734$	20.2646	0.00101905
$735$	0	0
$736$	−21361.3	−1.06982
$737$	1462.47i	0.0730948i
$738$	− 10920.0i	− 0.544678i
$739$	−10149.1	−0.505199	−0.252599	−	0.967571i	$-0.581285\pi$
$739$	−10149.1	−0.505199	−0.252599	+	0.967571i	$0.581285\pi$
$740$	0	0
$741$	16346.5	0.810397
$742$	− 5702.85i	− 0.282154i
$743$	− 27758.0i	− 1.37058i	−0.728269	−	0.685291i	$-0.759675\pi$
$743$	− 27758.0i	− 1.37058i	0.728269	−	0.685291i	$-0.240325\pi$
$744$	16612.6	0.818611
$745$	0	0
$746$	2617.87	0.128481
$747$	1978.47i	0.0969054i
$748$	− 2885.89i	− 0.141068i
$749$	−7829.63	−0.381960
$750$	0	0
$751$	−815.225	−0.0396112	−0.0198056	−	0.999804i	$-0.506305\pi$
$751$	−815.225	−0.0396112	−0.0198056	+	0.999804i	$0.506305\pi$
$752$	3504.13i	0.169924i
$753$	− 24277.1i	− 1.17491i
$754$	10169.3	0.491172
$755$	0	0
$756$	−6782.56	−0.326295
$757$	− 13239.4i	− 0.635659i	−0.948148	−	0.317829i	$-0.897046\pi$
$757$	− 13239.4i	− 0.635659i	0.948148	−	0.317829i	$-0.102954\pi$
$758$	13058.0i	0.625710i
$759$	10042.1	0.480244
$760$	0	0
$761$	−11028.2	−0.525324	−0.262662	−	0.964888i	$-0.584600\pi$
$761$	−11028.2	−0.525324	−0.262662	+	0.964888i	$0.584600\pi$
$762$	11371.7i	0.540621i
$763$	14407.1i	0.683582i
$764$	−3017.56	−0.142895
$765$	0	0
$766$	−12365.0	−0.583246
$767$	− 16969.8i	− 0.798882i
$768$	7695.55i	0.361574i
$769$	18921.2	0.887277	0.443639	−	0.896206i	$-0.353687\pi$
$769$	18921.2	0.887277	0.443639	+	0.896206i	$0.353687\pi$
$770$	0	0
$771$	16830.3	0.786158
$772$	21814.7i	1.01701i
$773$	− 38728.6i	− 1.80203i	−0.433786	−	0.901016i	$-0.642823\pi$
$773$	− 38728.6i	− 1.80203i	0.433786	−	0.901016i	$-0.357177\pi$
$774$	8183.59	0.380043
$775$	0	0
$776$	−15303.6	−0.707949
$777$	3315.29i	0.153070i
$778$	1556.93i	0.0717465i
$779$	41959.2	1.92984
$780$	0	0
$781$	21772.5	0.997545
$782$	2667.42i	0.121978i
$783$	− 17863.9i	− 0.815329i
$784$	6428.50	0.292844
$785$	0	0
$786$	−8498.47	−0.385662
$787$	− 20587.3i	− 0.932477i	−0.884659	−	0.466239i	$-0.845609\pi$
$787$	− 20587.3i	− 0.932477i	0.884659	−	0.466239i	$-0.154391\pi$
$788$	8379.37i	0.378811i
$789$	−12410.8	−0.559995
$790$	0	0
$791$	5616.62	0.252470
$792$	9066.49i	0.406772i
$793$	3132.00i	0.140253i
$794$	−14435.0	−0.645190
$795$	0	0
$796$	−22974.5	−1.02300
$797$	− 15871.4i	− 0.705385i	−0.935739	−	0.352693i	$-0.885266\pi$
$797$	− 15871.4i	− 0.705385i	0.935739	−	0.352693i	$-0.114734\pi$
$798$	3040.45i	0.134876i
$799$	2594.17	0.114862
$800$	0	0
$801$	13865.9	0.611644
$802$	18765.0i	0.826204i
$803$	− 8168.28i	− 0.358969i
$804$	1026.93	0.0450462
$805$	0	0
$806$	21631.4	0.945329
$807$	10801.6i	0.471170i
$808$	5113.06i	0.222620i
$809$	−39667.1	−1.72388	−0.861942	−	0.507007i	$-0.830752\pi$
$809$	−39667.1	−1.72388	−0.861942	+	0.507007i	$0.830752\pi$
$810$	0	0
$811$	8003.87	0.346552	0.173276	−	0.984873i	$-0.444565\pi$
$811$	8003.87	0.346552	0.173276	+	0.984873i	$0.444565\pi$
$812$	− 6275.00i	− 0.271194i
$813$	− 1732.00i	− 0.0747157i
$814$	4975.28	0.214230
$815$	0	0
$816$	−1231.48	−0.0528316
$817$	31444.7i	1.34652i
$818$	12939.7i	0.553088i
$819$	−7866.69	−0.335634
$820$	0	0
$821$	−13279.1	−0.564489	−0.282244	−	0.959343i	$-0.591079\pi$
$821$	−13279.1	−0.564489	−0.282244	+	0.959343i	$0.591079\pi$
$822$	13491.9i	0.572486i
$823$	− 28934.0i	− 1.22549i	−0.790281	−	0.612745i	$-0.790065\pi$
$823$	− 28934.0i	− 1.22549i	0.790281	−	0.612745i	$-0.209935\pi$
$824$	10073.6	0.425887
$825$	0	0
$826$	3156.37	0.132959
$827$	− 13679.6i	− 0.575193i	−0.957752	−	0.287597i	$-0.907144\pi$
$827$	− 13679.6i	− 0.575193i	0.957752	−	0.287597i	$-0.0928563\pi$
$828$	12079.9i	0.507012i
$829$	−16514.5	−0.691886	−0.345943	−	0.938256i	$-0.612441\pi$
$829$	−16514.5	−0.691886	−0.345943	+	0.938256i	$0.612441\pi$
$830$	0	0
$831$	16415.6	0.685260
$832$	3983.64i	0.165995i
$833$	− 4759.13i	− 0.197952i
$834$	−6304.13	−0.261744
$835$	0	0
$836$	−15137.1	−0.626231
$837$	− 37998.9i	− 1.56922i
$838$	− 13177.8i	− 0.543221i
$839$	87.9839	0.00362043	0.00181022	−	0.999998i	$-0.499424\pi$
$839$	87.9839	0.00362043	0.00181022	+	0.999998i	$0.499424\pi$
$840$	0	0
$841$	−7861.94	−0.322356
$842$	− 16825.1i	− 0.688635i
$843$	6267.41i	0.256063i
$844$	−32371.3	−1.32022
$845$	0	0
$846$	−3541.27	−0.143914
$847$	4512.98i	0.183079i
$848$	− 12115.7i	− 0.490630i
$849$	−2377.63	−0.0961133
$850$	0	0
$851$	15256.0	0.614534
$852$	− 15288.5i	− 0.614758i
$853$	− 8162.96i	− 0.327660i	−0.986489	−	0.163830i	$-0.947615\pi$
$853$	− 8162.96i	− 0.327660i	0.986489	−	0.163830i	$-0.0523849\pi$
$854$	−582.551	−0.0233425
$855$	0	0
$856$	18988.4	0.758191
$857$	18724.9i	0.746361i	0.927759	+	0.373181i	$0.121733\pi$
$857$	18724.9i	0.746361i	−0.927759	+	0.373181i	$0.878267\pi$
$858$	− 6891.34i	− 0.274203i
$859$	46422.5	1.84391	0.921953	−	0.387301i	$-0.126593\pi$
$859$	46422.5	1.84391	0.921953	+	0.387301i	$0.126593\pi$
$860$	0	0
$861$	11787.2	0.466557
$862$	4043.61i	0.159775i
$863$	− 29112.3i	− 1.14831i	−0.818746	−	0.574157i	$-0.805330\pi$
$863$	− 29112.3i	− 1.14831i	0.818746	−	0.574157i	$-0.194670\pi$
$864$	25750.8	1.01396
$865$	0	0
$866$	8346.33	0.327505
$867$	911.688i	0.0357123i
$868$	− 13347.8i	− 0.521950i
$869$	19892.6	0.776536
$870$	0	0
$871$	3077.43	0.119719
$872$	− 34940.2i	− 1.35691i
$873$	13548.2i	0.525241i
$874$	13991.2	0.541487
$875$	0	0
$876$	−5735.69	−0.221222
$877$	39163.0i	1.50791i	0.656924	+	0.753957i	$0.271857\pi$
$877$	39163.0i	1.50791i	−0.656924	+	0.753957i	$0.728143\pi$
$878$	3464.19i	0.133156i
$879$	22720.3	0.871830
$880$	0	0
$881$	−35073.2	−1.34125	−0.670627	−	0.741795i	$-0.733975\pi$
$881$	−35073.2	−1.34125	−0.670627	+	0.741795i	$0.733975\pi$
$882$	6496.63i	0.248019i
$883$	48775.7i	1.85893i	0.368915	+	0.929463i	$0.379729\pi$
$883$	48775.7i	1.85893i	−0.368915	+	0.929463i	$0.620271\pi$
$884$	−6072.69	−0.231048
$885$	0	0
$886$	11611.0	0.440269
$887$	13296.0i	0.503309i	0.967817	+	0.251654i	$0.0809746\pi$
$887$	13296.0i	0.503309i	−0.967817	+	0.251654i	$0.919025\pi$
$888$	− 8040.27i	− 0.303844i
$889$	21027.9	0.793309
$890$	0	0
$891$	606.137	0.0227905
$892$	− 4330.90i	− 0.162566i
$893$	− 13607.0i	− 0.509899i
$894$	1228.24	0.0459492
$895$	0	0
$896$	11031.1	0.411297
$897$	− 21131.3i	− 0.786570i
$898$	− 12054.6i	− 0.447960i
$899$	35155.3	1.30422
$900$	0	0
$901$	−8969.43	−0.331648
$902$	− 17689.1i	− 0.652974i
$903$	8833.44i	0.325535i
$904$	−13621.4	−0.501153
$905$	0	0
$906$	−2875.47	−0.105443
$907$	− 11675.0i	− 0.427410i	−0.976898	−	0.213705i	$-0.931447\pi$
$907$	− 11675.0i	− 0.427410i	0.976898	−	0.213705i	$-0.0685532\pi$
$908$	− 13224.0i	− 0.483319i
$909$	4526.54	0.165166
$910$	0	0
$911$	18552.9	0.674738	0.337369	−	0.941372i	$-0.390463\pi$
$911$	18552.9	0.674738	0.337369	+	0.941372i	$0.390463\pi$
$912$	6459.41i	0.234531i
$913$	3204.87i	0.116173i
$914$	9739.24	0.352457
$915$	0	0
$916$	24077.7	0.868504
$917$	15714.9i	0.565922i
$918$	− 3215.55i	− 0.115609i
$919$	−33956.8	−1.21886	−0.609429	−	0.792841i	$-0.708601\pi$
$919$	−33956.8	−1.21886	−0.609429	+	0.792841i	$0.708601\pi$
$920$	0	0
$921$	7652.23	0.273778
$922$	− 9886.63i	− 0.353144i
$923$	− 45815.3i	− 1.63383i
$924$	−4252.33	−0.151398
$925$	0	0
$926$	480.372	0.0170475
$927$	− 8918.08i	− 0.315974i
$928$	23823.8i	0.842732i
$929$	23695.3	0.836832	0.418416	−	0.908256i	$-0.362585\pi$
$929$	23695.3	0.836832	0.418416	+	0.908256i	$0.362585\pi$
$930$	0	0
$931$	−24962.7	−0.878753
$932$	31920.2i	1.12187i
$933$	30110.8i	1.05657i
$934$	−2018.72	−0.0707221
$935$	0	0
$936$	19078.3	0.666234
$937$	7990.62i	0.278593i	0.990251	+	0.139297i	$0.0444842\pi$
$937$	7990.62i	0.278593i	−0.990251	+	0.139297i	$0.955516\pi$
$938$	572.402i	0.0199249i
$939$	−1856.12	−0.0645071
$940$	0	0
$941$	24385.9	0.844799	0.422400	−	0.906410i	$-0.361188\pi$
$941$	24385.9	0.844799	0.422400	+	0.906410i	$0.361188\pi$
$942$	3095.26i	0.107058i
$943$	− 54241.0i	− 1.87310i
$944$	6705.69	0.231199
$945$	0	0
$946$	13256.4	0.455605
$947$	− 1174.62i	− 0.0403064i	−0.999797	−	0.0201532i	$-0.993585\pi$
$947$	− 1174.62i	− 0.0403064i	0.999797	−	0.0201532i	$-0.00641539\pi$
$948$	− 13968.4i	− 0.478557i
$949$	−17188.3	−0.587939
$950$	0	0
$951$	24143.4	0.823241
$952$	− 2599.51i	− 0.0884985i
$953$	33546.9i	1.14029i	0.821546	+	0.570143i	$0.193112\pi$
$953$	33546.9i	1.14029i	−0.821546	+	0.570143i	$0.806888\pi$
$954$	12244.1	0.415531
$955$	0	0
$956$	−2055.00	−0.0695224
$957$	− 11199.8i	− 0.378304i
$958$	13598.7i	0.458617i
$959$	24948.4	0.840067
$960$	0	0
$961$	44989.1	1.51016
$962$	− 10469.3i	− 0.350878i
$963$	− 16810.3i	− 0.562517i
$964$	−11792.9	−0.394007
$965$	0	0
$966$	3930.41	0.130910
$967$	24766.8i	0.823625i	0.911269	+	0.411813i	$0.135104\pi$
$967$	24766.8i	0.823625i	−0.911269	+	0.411813i	$0.864896\pi$
$968$	− 10944.9i	− 0.363411i
$969$	4782.01	0.158535
$970$	0	0
$971$	42324.3	1.39882	0.699409	−	0.714721i	$-0.253447\pi$
$971$	42324.3	1.39882	0.699409	+	0.714721i	$0.253447\pi$
$972$	− 23488.3i	− 0.775091i
$973$	11657.2i	0.384083i
$974$	1538.01	0.0505966
$975$	0	0
$976$	−1237.63	−0.0405896
$977$	− 11320.4i	− 0.370698i	−0.982673	−	0.185349i	$-0.940658\pi$
$977$	− 11320.4i	− 0.370698i	0.982673	−	0.185349i	$-0.0593416\pi$
$978$	2905.42i	0.0949949i
$979$	22461.0	0.733254
$980$	0	0
$981$	−30932.2	−1.00672
$982$	25556.8i	0.830500i
$983$	11311.9i	0.367032i	0.983017	+	0.183516i	$0.0587478\pi$
$983$	11311.9i	0.367032i	−0.983017	+	0.183516i	$0.941252\pi$
$984$	−28586.3	−0.926116
$985$	0	0
$986$	2974.92	0.0960860
$987$	− 3822.47i	− 0.123273i
$988$	31852.6i	1.02568i
$989$	40648.8	1.30693
$990$	0	0
$991$	−29405.5	−0.942580	−0.471290	−	0.881978i	$-0.656212\pi$
$991$	−29405.5	−0.942580	−0.471290	+	0.881978i	$0.656212\pi$
$992$	50676.5i	1.62196i
$993$	− 2373.12i	− 0.0758397i
$994$	8521.63	0.271921
$995$	0	0
$996$	2250.43	0.0715939
$997$	− 54905.9i	− 1.74412i	−0.489398	−	0.872060i	$-0.662784\pi$
$997$	− 54905.9i	− 1.74412i	0.489398	−	0.872060i	$-0.337216\pi$
$998$	− 23588.7i	− 0.748183i
$999$	−18390.9	−0.582446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.4.b.f.324.4		6
5.2	odd	4		425.4.a.g.1.2		3
5.3	odd	4		17.4.a.b.1.2	✓	3
5.4	even	2	inner	425.4.b.f.324.3		6
15.8	even	4		153.4.a.g.1.2		3
20.3	even	4		272.4.a.h.1.2		3
35.13	even	4		833.4.a.d.1.2		3
40.3	even	4		1088.4.a.x.1.2		3
40.13	odd	4		1088.4.a.v.1.2		3
55.43	even	4		2057.4.a.e.1.2		3
60.23	odd	4		2448.4.a.bi.1.1		3
85.13	odd	4		289.4.b.b.288.4		6
85.33	odd	4		289.4.a.b.1.2		3
85.38	odd	4		289.4.b.b.288.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.4.a.b.1.2	✓	3	5.3	odd	4
153.4.a.g.1.2		3	15.8	even	4
272.4.a.h.1.2		3	20.3	even	4
289.4.a.b.1.2		3	85.33	odd	4
289.4.b.b.288.3		6	85.38	odd	4
289.4.b.b.288.4		6	85.13	odd	4
425.4.a.g.1.2		3	5.2	odd	4
425.4.b.f.324.3		6	5.4	even	2	inner
425.4.b.f.324.4		6	1.1	even	1	trivial
833.4.a.d.1.2		3	35.13	even	4
1088.4.a.v.1.2		3	40.13	odd	4
1088.4.a.x.1.2		3	40.3	even	4
2057.4.a.e.1.2		3	55.43	even	4
2448.4.a.bi.1.1		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)

\(f(q)\)	\(=\)	\(q+1.36122i q^{2} -3.15463i q^{3} +6.14708 q^{4} +4.29415 q^{6} -7.94049i q^{7} +19.2573i q^{8} +17.0483 q^{9} +O(q^{10})\)	\(q+1.36122i q^{2} -3.15463i q^{3} +6.14708 q^{4} +4.29415 q^{6} -7.94049i q^{7} +19.2573i q^{8} +17.0483 q^{9} +27.6161 q^{11} -19.3918i q^{12} -58.1117i q^{13} +10.8088 q^{14} +22.9632 q^{16} -17.0000i q^{17} +23.2065i q^{18} -89.1688 q^{19} -25.0493 q^{21} +37.5916i q^{22} +115.269i q^{23} +60.7497 q^{24} +79.1029 q^{26} -138.956i q^{27} -48.8108i q^{28} +128.558 q^{29} +273.460 q^{31} +185.316i q^{32} -87.1187i q^{33} +23.1408 q^{34} +104.797 q^{36} -132.351i q^{37} -121.379i q^{38} -183.321 q^{39} -470.559 q^{41} -34.0977i q^{42} -352.642i q^{43} +169.758 q^{44} -156.907 q^{46} +152.598i q^{47} -72.4403i q^{48} +279.949 q^{49} -53.6287 q^{51} -357.217i q^{52} -527.614i q^{53} +189.150 q^{54} +152.912 q^{56} +281.295i q^{57} +174.995i q^{58} +292.020 q^{59} -53.8962 q^{61} +372.239i q^{62} -135.372i q^{63} -68.5514 q^{64} +118.588 q^{66} +52.9572i q^{67} -104.500i q^{68} +363.632 q^{69} +788.400 q^{71} +328.304i q^{72} -295.780i q^{73} +180.159 q^{74} -548.127 q^{76} -219.285i q^{77} -249.541i q^{78} +720.325 q^{79} +21.9487 q^{81} -640.535i q^{82} +116.051i q^{83} -153.980 q^{84} +480.024 q^{86} -405.552i q^{87} +531.812i q^{88} +813.329 q^{89} -461.435 q^{91} +708.569i q^{92} -862.664i q^{93} -207.720 q^{94} +584.605 q^{96} +794.693i q^{97} +381.072i q^{98} +470.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 50 q^{4} - 148 q^{6} - 118 q^{9}+O(q^{10}) \) 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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