LMFDB - Embedded newform 625.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(1,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("625.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.8.6152203125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 $ x^8 - 3x^7 - 8x^6 + 20x^5 + 26x^4 - 35x^3 - 27x^2 + 16*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.32610$ of defining polynomial
Character	$\chi$	$=$	625.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32610 q^{2} -2.30231 q^{3} +3.41075 q^{4} -5.35542 q^{6} +3.59425 q^{7} +3.28154 q^{8} +2.30065 q^{9} +O(q^{10})$	\(q+2.32610 q^{2} -2.30231 q^{3} +3.41075 q^{4} -5.35542 q^{6} +3.59425 q^{7} +3.28154 q^{8} +2.30065 q^{9} -0.497788 q^{11} -7.85261 q^{12} +2.64789 q^{13} +8.36058 q^{14} +0.811708 q^{16} +5.10719 q^{17} +5.35154 q^{18} -0.987277 q^{19} -8.27508 q^{21} -1.15790 q^{22} +6.41382 q^{23} -7.55514 q^{24} +6.15926 q^{26} +1.61013 q^{27} +12.2591 q^{28} -5.57001 q^{29} +6.05507 q^{31} -4.67497 q^{32} +1.14606 q^{33} +11.8798 q^{34} +7.84693 q^{36} -4.59612 q^{37} -2.29651 q^{38} -6.09627 q^{39} -2.87475 q^{41} -19.2487 q^{42} -9.48858 q^{43} -1.69783 q^{44} +14.9192 q^{46} +5.36834 q^{47} -1.86881 q^{48} +5.91861 q^{49} -11.7583 q^{51} +9.03129 q^{52} -0.307600 q^{53} +3.74532 q^{54} +11.7947 q^{56} +2.27302 q^{57} -12.9564 q^{58} -1.26645 q^{59} -6.22625 q^{61} +14.0847 q^{62} +8.26910 q^{63} -12.4979 q^{64} +2.66586 q^{66} -5.28626 q^{67} +17.4193 q^{68} -14.7666 q^{69} -0.151963 q^{71} +7.54968 q^{72} -14.8741 q^{73} -10.6910 q^{74} -3.36735 q^{76} -1.78917 q^{77} -14.1805 q^{78} -16.5886 q^{79} -10.6090 q^{81} -6.68696 q^{82} +14.5960 q^{83} -28.2242 q^{84} -22.0714 q^{86} +12.8239 q^{87} -1.63351 q^{88} +11.3822 q^{89} +9.51717 q^{91} +21.8759 q^{92} -13.9407 q^{93} +12.4873 q^{94} +10.7633 q^{96} +0.849192 q^{97} +13.7673 q^{98} -1.14523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9	$ 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9} + q^{11} + 10 q^{12} + 10 q^{13} - 8 q^{14} + 13 q^{16} + 15 q^{17} - 5 q^{18} - 10 q^{19} - 14 q^{21} - 5 q^{22} + 30 q^{23} + 5 q^{24} + 11 q^{26} + 20 q^{27} - 5 q^{28} + 10 q^{29} - 9 q^{31} + 30 q^{32} + 5 q^{33} + 7 q^{34} + 3 q^{36} - 10 q^{37} + 20 q^{38} + 8 q^{39} - 4 q^{41} - 35 q^{42} - 18 q^{44} - 9 q^{46} + 30 q^{47} + 5 q^{48} - 4 q^{49} - 14 q^{51} + 5 q^{52} + 10 q^{53} - 20 q^{54} - 10 q^{57} - 30 q^{58} - 5 q^{59} + 6 q^{61} + 10 q^{62} - 9 q^{64} - 18 q^{66} + 10 q^{67} + 40 q^{68} + 3 q^{69} - 9 q^{71} - 15 q^{72} - 18 q^{74} - 10 q^{76} + 5 q^{77} - 30 q^{78} - 20 q^{79} + 8 q^{81} - 45 q^{82} + 40 q^{83} - 28 q^{84} - 24 q^{86} + 40 q^{87} - 40 q^{88} - 5 q^{89} + 6 q^{91} + 15 q^{92} - 40 q^{93} + 47 q^{94} + 71 q^{96} - 30 q^{98} - 22 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9 + q^11 + 10 * q^12 + 10 * q^13 - 8 * q^14 + 13 * q^16 + 15 * q^17 - 5 * q^18 - 10 * q^19 - 14 * q^21 - 5 * q^22 + 30 * q^23 + 5 * q^24 + 11 * q^26 + 20 * q^27 - 5 * q^28 + 10 * q^29 - 9 * q^31 + 30 * q^32 + 5 * q^33 + 7 * q^34 + 3 * q^36 - 10 * q^37 + 20 * q^38 + 8 * q^39 - 4 * q^41 - 35 * q^42 - 18 * q^44 - 9 * q^46 + 30 * q^47 + 5 * q^48 - 4 * q^49 - 14 * q^51 + 5 * q^52 + 10 * q^53 - 20 * q^54 - 10 * q^57 - 30 * q^58 - 5 * q^59 + 6 * q^61 + 10 * q^62 - 9 * q^64 - 18 * q^66 + 10 * q^67 + 40 * q^68 + 3 * q^69 - 9 * q^71 - 15 * q^72 - 18 * q^74 - 10 * q^76 + 5 * q^77 - 30 * q^78 - 20 * q^79 + 8 * q^81 - 45 * q^82 + 40 * q^83 - 28 * q^84 - 24 * q^86 + 40 * q^87 - 40 * q^88 - 5 * q^89 + 6 * q^91 + 15 * q^92 - 40 * q^93 + 47 * q^94 + 71 * q^96 - 30 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.32610	1.64480	0.822401	−	0.568908i	$-0.192634\pi$
$2$	2.32610	1.64480	0.822401	+	0.568908i	$0.192634\pi$
$3$	−2.30231	−1.32924	−0.664621	−	0.747181i	$-0.731407\pi$
$3$	−2.30231	−1.32924	−0.664621	+	0.747181i	$0.731407\pi$
$4$	3.41075	1.70537
$5$	0	0
$5$	0	0
$6$	−5.35542	−2.18634
$7$	3.59425	1.35850	0.679249	−	0.733908i	$-0.262306\pi$
$7$	3.59425	1.35850	0.679249	+	0.733908i	$0.262306\pi$
$8$	3.28154	1.16020
$9$	2.30065	0.766883
$10$	0	0
$11$	−0.497788	−0.150089	−0.0750443	−	0.997180i	$-0.523910\pi$
$11$	−0.497788	−0.150089	−0.0750443	+	0.997180i	$0.523910\pi$
$12$	−7.85261	−2.26685
$13$	2.64789	0.734392	0.367196	−	0.930143i	$-0.380318\pi$
$13$	2.64789	0.734392	0.367196	+	0.930143i	$0.380318\pi$
$14$	8.36058	2.23446
$15$	0	0
$16$	0.811708	0.202927
$17$	5.10719	1.23867	0.619337	−	0.785125i	$-0.287401\pi$
$17$	5.10719	1.23867	0.619337	+	0.785125i	$0.287401\pi$
$18$	5.35154	1.26137
$19$	−0.987277	−0.226497	−0.113248	−	0.993567i	$-0.536126\pi$
$19$	−0.987277	−0.226497	−0.113248	+	0.993567i	$0.536126\pi$
$20$	0	0
$21$	−8.27508	−1.80577
$22$	−1.15790	−0.246866
$23$	6.41382	1.33737	0.668687	−	0.743544i	$-0.266857\pi$
$23$	6.41382	1.33737	0.668687	+	0.743544i	$0.266857\pi$
$24$	−7.55514	−1.54219
$25$	0	0
$26$	6.15926	1.20793
$27$	1.61013	0.309869
$28$	12.2591	2.31675
$29$	−5.57001	−1.03432	−0.517162	−	0.855887i	$-0.673012\pi$
$29$	−5.57001	−1.03432	−0.517162	+	0.855887i	$0.673012\pi$
$30$	0	0
$31$	6.05507	1.08752	0.543762	−	0.839240i	$-0.317000\pi$
$31$	6.05507	1.08752	0.543762	+	0.839240i	$0.317000\pi$
$32$	−4.67497	−0.826426
$33$	1.14606	0.199504
$34$	11.8798	2.03738
$35$	0	0
$36$	7.84693	1.30782
$37$	−4.59612	−0.755598	−0.377799	−	0.925888i	$-0.623319\pi$
$37$	−4.59612	−0.755598	−0.377799	+	0.925888i	$0.623319\pi$
$38$	−2.29651	−0.372543
$39$	−6.09627	−0.976185
$40$	0	0
$41$	−2.87475	−0.448960	−0.224480	−	0.974479i	$-0.572068\pi$
$41$	−2.87475	−0.448960	−0.224480	+	0.974479i	$0.572068\pi$
$42$	−19.2487	−2.97014
$43$	−9.48858	−1.44700	−0.723498	−	0.690327i	$-0.757467\pi$
$43$	−9.48858	−1.44700	−0.723498	+	0.690327i	$0.757467\pi$
$44$	−1.69783	−0.255957
$45$	0	0
$46$	14.9192	2.19972
$47$	5.36834	0.783053	0.391527	−	0.920167i	$-0.371947\pi$
$47$	5.36834	0.783053	0.391527	+	0.920167i	$0.371947\pi$
$48$	−1.86881	−0.269739
$49$	5.91861	0.845515
$50$	0	0
$51$	−11.7583	−1.64650
$52$	9.03129	1.25241
$53$	−0.307600	−0.0422521	−0.0211261	−	0.999777i	$-0.506725\pi$
$53$	−0.307600	−0.0422521	−0.0211261	+	0.999777i	$0.506725\pi$
$54$	3.74532	0.509673
$55$	0	0
$56$	11.7947	1.57613
$57$	2.27302	0.301069
$58$	−12.9564	−1.70126
$59$	−1.26645	−0.164878	−0.0824389	−	0.996596i	$-0.526271\pi$
$59$	−1.26645	−0.164878	−0.0824389	+	0.996596i	$0.526271\pi$
$60$	0	0
$61$	−6.22625	−0.797190	−0.398595	−	0.917127i	$-0.630502\pi$
$61$	−6.22625	−0.797190	−0.398595	+	0.917127i	$0.630502\pi$
$62$	14.0847	1.78876
$63$	8.26910	1.04181
$64$	−12.4979	−1.56223
$65$	0	0
$66$	2.66586	0.328145
$67$	−5.28626	−0.645819	−0.322910	−	0.946430i	$-0.604661\pi$
$67$	−5.28626	−0.645819	−0.322910	+	0.946430i	$0.604661\pi$
$68$	17.4193	2.11240
$69$	−14.7666	−1.77769
$70$	0	0
$71$	−0.151963	−0.0180347	−0.00901734	−	0.999959i	$-0.502870\pi$
$71$	−0.151963	−0.0180347	−0.00901734	+	0.999959i	$0.502870\pi$
$72$	7.54968	0.889738
$73$	−14.8741	−1.74088	−0.870439	−	0.492276i	$-0.836165\pi$
$73$	−14.8741	−1.74088	−0.870439	+	0.492276i	$0.836165\pi$
$74$	−10.6910	−1.24281
$75$	0	0
$76$	−3.36735	−0.386262
$77$	−1.78917	−0.203895
$78$	−14.1805	−1.60563
$79$	−16.5886	−1.86636	−0.933181	−	0.359406i	$-0.882979\pi$
$79$	−16.5886	−1.86636	−0.933181	+	0.359406i	$0.882979\pi$
$80$	0	0
$81$	−10.6090	−1.17877
$82$	−6.68696	−0.738451
$83$	14.5960	1.60212	0.801058	−	0.598587i	$-0.204271\pi$
$83$	14.5960	1.60212	0.801058	+	0.598587i	$0.204271\pi$
$84$	−28.2242	−3.07952
$85$	0	0
$86$	−22.0714	−2.38002
$87$	12.8239	1.37487
$88$	−1.63351	−0.174133
$89$	11.3822	1.20652	0.603258	−	0.797546i	$-0.293869\pi$
$89$	11.3822	1.20652	0.603258	+	0.797546i	$0.293869\pi$
$90$	0	0
$91$	9.51717	0.997670
$92$	21.8759	2.28072
$93$	−13.9407	−1.44558
$94$	12.4873	1.28797
$95$	0	0
$96$	10.7633	1.09852
$97$	0.849192	0.0862223	0.0431112	−	0.999070i	$-0.486273\pi$
$97$	0.849192	0.0862223	0.0431112	+	0.999070i	$0.486273\pi$
$98$	13.7673	1.39070
$99$	−1.14523	−0.115100
$100$	0	0
$101$	−13.2498	−1.31841	−0.659203	−	0.751965i	$-0.729106\pi$
$101$	−13.2498	−1.31841	−0.659203	+	0.751965i	$0.729106\pi$
$102$	−27.3511	−2.70816
$103$	0.830909	0.0818719	0.0409360	−	0.999162i	$-0.486966\pi$
$103$	0.830909	0.0818719	0.0409360	+	0.999162i	$0.486966\pi$
$104$	8.68917	0.852043
$105$	0	0
$106$	−0.715509	−0.0694964
$107$	−0.0722844	−0.00698800	−0.00349400	−	0.999994i	$-0.501112\pi$
$107$	−0.0722844	−0.00698800	−0.00349400	+	0.999994i	$0.501112\pi$
$108$	5.49174	0.528443
$109$	5.59621	0.536020	0.268010	−	0.963416i	$-0.413634\pi$
$109$	5.59621	0.536020	0.268010	+	0.963416i	$0.413634\pi$
$110$	0	0
$111$	10.5817	1.00437
$112$	2.91748	0.275676
$113$	−2.60239	−0.244812	−0.122406	−	0.992480i	$-0.539061\pi$
$113$	−2.60239	−0.244812	−0.122406	+	0.992480i	$0.539061\pi$
$114$	5.28728	0.495199
$115$	0	0
$116$	−18.9979	−1.76391
$117$	6.09186	0.563193
$118$	−2.94589	−0.271191
$119$	18.3565	1.68274
$120$	0	0
$121$	−10.7522	−0.977473
$122$	−14.4829	−1.31122
$123$	6.61857	0.596777
$124$	20.6523	1.85463
$125$	0	0
$126$	19.2348	1.71357
$127$	4.94483	0.438783	0.219391	−	0.975637i	$-0.429593\pi$
$127$	4.94483	0.438783	0.219391	+	0.975637i	$0.429593\pi$
$128$	−19.7214	−1.74314
$129$	21.8457	1.92341
$130$	0	0
$131$	2.70342	0.236199	0.118099	−	0.993002i	$-0.462320\pi$
$131$	2.70342	0.236199	0.118099	+	0.993002i	$0.462320\pi$
$132$	3.90893	0.340229
$133$	−3.54852	−0.307695
$134$	−12.2964	−1.06224
$135$	0	0
$136$	16.7595	1.43711
$137$	−2.24838	−0.192092	−0.0960459	−	0.995377i	$-0.530620\pi$
$137$	−2.24838	−0.192092	−0.0960459	+	0.995377i	$0.530620\pi$
$138$	−34.3487	−2.92395
$139$	−10.8032	−0.916317	−0.458159	−	0.888870i	$-0.651491\pi$
$139$	−10.8032	−0.916317	−0.458159	+	0.888870i	$0.651491\pi$
$140$	0	0
$141$	−12.3596	−1.04087
$142$	−0.353481	−0.0296635
$143$	−1.31809	−0.110224
$144$	1.86745	0.155621
$145$	0	0
$146$	−34.5986	−2.86340
$147$	−13.6265	−1.12389
$148$	−15.6762	−1.28858
$149$	12.1878	0.998460	0.499230	−	0.866469i	$-0.333616\pi$
$149$	12.1878	0.998460	0.499230	+	0.866469i	$0.333616\pi$
$150$	0	0
$151$	17.0860	1.39044	0.695220	−	0.718797i	$-0.255307\pi$
$151$	17.0860	1.39044	0.695220	+	0.718797i	$0.255307\pi$
$152$	−3.23979	−0.262782
$153$	11.7498	0.949918
$154$	−4.16179	−0.335367
$155$	0	0
$156$	−20.7929	−1.66476
$157$	−7.49835	−0.598433	−0.299217	−	0.954185i	$-0.596725\pi$
$157$	−7.49835	−0.598433	−0.299217	+	0.954185i	$0.596725\pi$
$158$	−38.5868	−3.06980
$159$	0.708192	0.0561633
$160$	0	0
$161$	23.0529	1.81682
$162$	−24.6775	−1.93885
$163$	1.95259	0.152939	0.0764693	−	0.997072i	$-0.475635\pi$
$163$	1.95259	0.152939	0.0764693	+	0.997072i	$0.475635\pi$
$164$	−9.80504	−0.765645
$165$	0	0
$166$	33.9517	2.63516
$167$	−0.356578	−0.0275928	−0.0137964	−	0.999905i	$-0.504392\pi$
$167$	−0.356578	−0.0275928	−0.0137964	+	0.999905i	$0.504392\pi$
$168$	−27.1550	−2.09506
$169$	−5.98868	−0.460668
$170$	0	0
$171$	−2.27138	−0.173697
$172$	−32.3632	−2.46767
$173$	−9.95032	−0.756509	−0.378254	−	0.925702i	$-0.623476\pi$
$173$	−9.95032	−0.756509	−0.378254	+	0.925702i	$0.623476\pi$
$174$	29.8297	2.26138
$175$	0	0
$176$	−0.404058	−0.0304570
$177$	2.91577	0.219162
$178$	26.4763	1.98448
$179$	15.3824	1.14973	0.574867	−	0.818247i	$-0.305054\pi$
$179$	15.3824	1.14973	0.574867	+	0.818247i	$0.305054\pi$
$180$	0	0
$181$	8.91917	0.662957	0.331478	−	0.943463i	$-0.392453\pi$
$181$	8.91917	0.662957	0.331478	+	0.943463i	$0.392453\pi$
$182$	22.1379	1.64097
$183$	14.3348	1.05966
$184$	21.0472	1.55162
$185$	0	0
$186$	−32.4274	−2.37769
$187$	−2.54230	−0.185911
$188$	18.3101	1.33540
$189$	5.78719	0.420956
$190$	0	0
$191$	−11.3887	−0.824056	−0.412028	−	0.911171i	$-0.635179\pi$
$191$	−11.3887	−0.824056	−0.412028	+	0.911171i	$0.635179\pi$
$192$	28.7740	2.07659
$193$	17.3321	1.24759	0.623795	−	0.781588i	$-0.285590\pi$
$193$	17.3321	1.24759	0.623795	+	0.781588i	$0.285590\pi$
$194$	1.97531	0.141819
$195$	0	0
$196$	20.1869	1.44192
$197$	25.9609	1.84964	0.924820	−	0.380405i	$-0.124215\pi$
$197$	25.9609	1.84964	0.924820	+	0.380405i	$0.124215\pi$
$198$	−2.66393	−0.189317
$199$	−8.38571	−0.594447	−0.297223	−	0.954808i	$-0.596061\pi$
$199$	−8.38571	−0.594447	−0.297223	+	0.954808i	$0.596061\pi$
$200$	0	0
$201$	12.1706	0.858450
$202$	−30.8204	−2.16852
$203$	−20.0200	−1.40513
$204$	−40.1048	−2.80790
$205$	0	0
$206$	1.93278	0.134663
$207$	14.7559	1.02561
$208$	2.14931	0.149028
$209$	0.491454	0.0339946
$210$	0	0
$211$	15.9135	1.09553	0.547765	−	0.836632i	$-0.315479\pi$
$211$	15.9135	1.09553	0.547765	+	0.836632i	$0.315479\pi$
$212$	−1.04915	−0.0720557
$213$	0.349866	0.0239724
$214$	−0.168141	−0.0114939
$215$	0	0
$216$	5.28370	0.359510
$217$	21.7634	1.47740
$218$	13.0174	0.881647
$219$	34.2448	2.31405
$220$	0	0
$221$	13.5233	0.909674
$222$	24.6142	1.65199
$223$	−0.379706	−0.0254270	−0.0127135	−	0.999919i	$-0.504047\pi$
$223$	−0.379706	−0.0254270	−0.0127135	+	0.999919i	$0.504047\pi$
$224$	−16.8030	−1.12270
$225$	0	0
$226$	−6.05343	−0.402668
$227$	20.3009	1.34742	0.673710	−	0.738996i	$-0.264700\pi$
$227$	20.3009	1.34742	0.673710	+	0.738996i	$0.264700\pi$
$228$	7.75270	0.513435
$229$	−11.9107	−0.787078	−0.393539	−	0.919308i	$-0.628749\pi$
$229$	−11.9107	−0.787078	−0.393539	+	0.919308i	$0.628749\pi$
$230$	0	0
$231$	4.11923	0.271026
$232$	−18.2782	−1.20002
$233$	−19.0610	−1.24873	−0.624364	−	0.781133i	$-0.714642\pi$
$233$	−19.0610	−1.24873	−0.624364	+	0.781133i	$0.714642\pi$
$234$	14.1703	0.926341
$235$	0	0
$236$	−4.31954	−0.281178
$237$	38.1922	2.48085
$238$	42.6991	2.76777
$239$	4.12493	0.266819	0.133410	−	0.991061i	$-0.457407\pi$
$239$	4.12493	0.266819	0.133410	+	0.991061i	$0.457407\pi$
$240$	0	0
$241$	16.1858	1.04262	0.521310	−	0.853367i	$-0.325444\pi$
$241$	16.1858	1.04262	0.521310	+	0.853367i	$0.325444\pi$
$242$	−25.0107	−1.60775
$243$	19.5948	1.25701
$244$	−21.2362	−1.35951
$245$	0	0
$246$	15.3955	0.981580
$247$	−2.61420	−0.166338
$248$	19.8700	1.26175
$249$	−33.6045	−2.12960
$250$	0	0
$251$	11.8718	0.749344	0.374672	−	0.927157i	$-0.377755\pi$
$251$	11.8718	0.749344	0.374672	+	0.927157i	$0.377755\pi$
$252$	28.2038	1.77667
$253$	−3.19272	−0.200725
$254$	11.5022	0.721711
$255$	0	0
$256$	−20.8782	−1.30489
$257$	−18.9164	−1.17997	−0.589986	−	0.807414i	$-0.700867\pi$
$257$	−18.9164	−1.17997	−0.589986	+	0.807414i	$0.700867\pi$
$258$	50.8153	3.16362
$259$	−16.5196	−1.02648
$260$	0	0
$261$	−12.8146	−0.793206
$262$	6.28843	0.388501
$263$	−6.74703	−0.416040	−0.208020	−	0.978125i	$-0.566702\pi$
$263$	−6.74703	−0.416040	−0.208020	+	0.978125i	$0.566702\pi$
$264$	3.76086	0.231465
$265$	0	0
$266$	−8.25421	−0.506098
$267$	−26.2055	−1.60375
$268$	−18.0301	−1.10136
$269$	−25.3329	−1.54457	−0.772286	−	0.635275i	$-0.780887\pi$
$269$	−25.3329	−1.54457	−0.772286	+	0.635275i	$0.780887\pi$
$270$	0	0
$271$	9.40735	0.571456	0.285728	−	0.958311i	$-0.407765\pi$
$271$	9.40735	0.571456	0.285728	+	0.958311i	$0.407765\pi$
$272$	4.14555	0.251361
$273$	−21.9115	−1.32614
$274$	−5.22995	−0.315953
$275$	0	0
$276$	−50.3653	−3.03163
$277$	−5.96736	−0.358544	−0.179272	−	0.983800i	$-0.557374\pi$
$277$	−5.96736	−0.358544	−0.179272	+	0.983800i	$0.557374\pi$
$278$	−25.1294	−1.50716
$279$	13.9306	0.834003
$280$	0	0
$281$	11.0723	0.660516	0.330258	−	0.943891i	$-0.392864\pi$
$281$	11.0723	0.660516	0.330258	+	0.943891i	$0.392864\pi$
$282$	−28.7497	−1.71202
$283$	−3.02406	−0.179762	−0.0898810	−	0.995953i	$-0.528649\pi$
$283$	−3.02406	−0.179762	−0.0898810	+	0.995953i	$0.528649\pi$
$284$	−0.518307	−0.0307559
$285$	0	0
$286$	−3.06600	−0.181297
$287$	−10.3326	−0.609911
$288$	−10.7555	−0.633772
$289$	9.08337	0.534316
$290$	0	0
$291$	−1.95511	−0.114610
$292$	−50.7317	−2.96885
$293$	6.26426	0.365962	0.182981	−	0.983116i	$-0.441425\pi$
$293$	6.26426	0.365962	0.182981	+	0.983116i	$0.441425\pi$
$294$	−31.6966	−1.84858
$295$	0	0
$296$	−15.0824	−0.876646
$297$	−0.801501	−0.0465078
$298$	28.3500	1.64227
$299$	16.9831	0.982158
$300$	0	0
$301$	−34.1043	−1.96574
$302$	39.7438	2.28700
$303$	30.5052	1.75248
$304$	−0.801381	−0.0459623
$305$	0	0
$306$	27.3313	1.56243
$307$	25.8734	1.47667	0.738337	−	0.674432i	$-0.235612\pi$
$307$	25.8734	1.47667	0.738337	+	0.674432i	$0.235612\pi$
$308$	−6.10241	−0.347717
$309$	−1.91301	−0.108828
$310$	0	0
$311$	−9.00277	−0.510500	−0.255250	−	0.966875i	$-0.582158\pi$
$311$	−9.00277	−0.510500	−0.255250	+	0.966875i	$0.582158\pi$
$312$	−20.0052	−1.13257
$313$	−33.2274	−1.87812	−0.939062	−	0.343748i	$-0.888304\pi$
$313$	−33.2274	−1.87812	−0.939062	+	0.343748i	$0.888304\pi$
$314$	−17.4419	−0.984304
$315$	0	0
$316$	−56.5795	−3.18285
$317$	−25.9693	−1.45858	−0.729290	−	0.684204i	$-0.760150\pi$
$317$	−25.9693	−1.45858	−0.729290	+	0.684204i	$0.760150\pi$
$318$	1.64733	0.0923774
$319$	2.77268	0.155240
$320$	0	0
$321$	0.166421	0.00928874
$322$	53.6233	2.98831
$323$	−5.04221	−0.280556
$324$	−36.1845	−2.01025
$325$	0	0
$326$	4.54192	0.251554
$327$	−12.8842	−0.712500
$328$	−9.43361	−0.520884
$329$	19.2951	1.06378
$330$	0	0
$331$	12.1284	0.666636	0.333318	−	0.942814i	$-0.391832\pi$
$331$	12.1284	0.666636	0.333318	+	0.942814i	$0.391832\pi$
$332$	49.7832	2.73221
$333$	−10.5741	−0.579455
$334$	−0.829436	−0.0453847
$335$	0	0
$336$	−6.71695	−0.366440
$337$	−30.2519	−1.64793	−0.823963	−	0.566644i	$-0.808241\pi$
$337$	−30.2519	−1.64793	−0.823963	+	0.566644i	$0.808241\pi$
$338$	−13.9303	−0.757707
$339$	5.99152	0.325415
$340$	0	0
$341$	−3.01414	−0.163225
$342$	−5.28345	−0.285696
$343$	−3.88680	−0.209867
$344$	−31.1372	−1.67881
$345$	0	0
$346$	−23.1455	−1.24431
$347$	−13.3283	−0.715502	−0.357751	−	0.933817i	$-0.616456\pi$
$347$	−13.3283	−0.715502	−0.357751	+	0.933817i	$0.616456\pi$
$348$	43.7391	2.34466
$349$	−27.4444	−1.46906	−0.734532	−	0.678574i	$-0.762598\pi$
$349$	−27.4444	−1.46906	−0.734532	+	0.678574i	$0.762598\pi$
$350$	0	0
$351$	4.26344	0.227566
$352$	2.32714	0.124037
$353$	15.5564	0.827983	0.413992	−	0.910281i	$-0.364134\pi$
$353$	15.5564	0.827983	0.413992	+	0.910281i	$0.364134\pi$
$354$	6.78237	0.360479
$355$	0	0
$356$	38.8220	2.05756
$357$	−42.2624	−2.23676
$358$	35.7810	1.89109
$359$	−21.9829	−1.16021	−0.580107	−	0.814540i	$-0.696989\pi$
$359$	−21.9829	−1.16021	−0.580107	+	0.814540i	$0.696989\pi$
$360$	0	0
$361$	−18.0253	−0.948699
$362$	20.7469	1.09043
$363$	24.7550	1.29930
$364$	32.4607	1.70140
$365$	0	0
$366$	33.3442	1.74293
$367$	12.1103	0.632155	0.316078	−	0.948733i	$-0.397634\pi$
$367$	12.1103	0.632155	0.316078	+	0.948733i	$0.397634\pi$
$368$	5.20615	0.271389
$369$	−6.61379	−0.344300
$370$	0	0
$371$	−1.10559	−0.0573994
$372$	−47.5481	−2.46526
$373$	7.08604	0.366901	0.183451	−	0.983029i	$-0.441273\pi$
$373$	7.08604	0.366901	0.183451	+	0.983029i	$0.441273\pi$
$374$	−5.91364	−0.305787
$375$	0	0
$376$	17.6164	0.908499
$377$	−14.7488	−0.759600
$378$	13.4616	0.692390
$379$	−21.5030	−1.10453	−0.552266	−	0.833668i	$-0.686237\pi$
$379$	−21.5030	−1.10453	−0.552266	+	0.833668i	$0.686237\pi$
$380$	0	0
$381$	−11.3845	−0.583248
$382$	−26.4912	−1.35541
$383$	24.8816	1.27139	0.635696	−	0.771940i	$-0.280713\pi$
$383$	24.8816	1.27139	0.635696	+	0.771940i	$0.280713\pi$
$384$	45.4048	2.31706
$385$	0	0
$386$	40.3161	2.05204
$387$	−21.8299	−1.10968
$388$	2.89638	0.147041
$389$	−35.4142	−1.79557	−0.897785	−	0.440434i	$-0.854825\pi$
$389$	−35.4142	−1.79557	−0.897785	+	0.440434i	$0.854825\pi$
$390$	0	0
$391$	32.7566	1.65657
$392$	19.4222	0.980967
$393$	−6.22412	−0.313965
$394$	60.3878	3.04229
$395$	0	0
$396$	−3.90611	−0.196289
$397$	5.49705	0.275889	0.137944	−	0.990440i	$-0.455950\pi$
$397$	5.49705	0.275889	0.137944	+	0.990440i	$0.455950\pi$
$398$	−19.5060	−0.977748
$399$	8.16980	0.409001
$400$	0	0
$401$	24.8463	1.24077	0.620383	−	0.784299i	$-0.286977\pi$
$401$	24.8463	1.24077	0.620383	+	0.784299i	$0.286977\pi$
$402$	28.3101	1.41198
$403$	16.0332	0.798669
$404$	−45.1918	−2.24838
$405$	0	0
$406$	−46.5685	−2.31116
$407$	2.28789	0.113407
$408$	−38.5855	−1.91027
$409$	3.93157	0.194404	0.0972019	−	0.995265i	$-0.469011\pi$
$409$	3.93157	0.194404	0.0972019	+	0.995265i	$0.469011\pi$
$410$	0	0
$411$	5.17647	0.255336
$412$	2.83402	0.139622
$413$	−4.55194	−0.223986
$414$	34.3238	1.68692
$415$	0	0
$416$	−12.3788	−0.606921
$417$	24.8724	1.21801
$418$	1.14317	0.0559144
$419$	−4.76604	−0.232836	−0.116418	−	0.993200i	$-0.537141\pi$
$419$	−4.76604	−0.232836	−0.116418	+	0.993200i	$0.537141\pi$
$420$	0	0
$421$	16.0581	0.782625	0.391312	−	0.920258i	$-0.372021\pi$
$421$	16.0581	0.782625	0.391312	+	0.920258i	$0.372021\pi$
$422$	37.0164	1.80193
$423$	12.3507	0.600510
$424$	−1.00940	−0.0490209
$425$	0	0
$426$	0.813824	0.0394299
$427$	−22.3787	−1.08298
$428$	−0.246544	−0.0119172
$429$	3.03465	0.146514
$430$	0	0
$431$	−41.3693	−1.99269	−0.996344	−	0.0854360i	$-0.972772\pi$
$431$	−41.3693	−1.99269	−0.996344	+	0.0854360i	$0.972772\pi$
$432$	1.30695	0.0628808
$433$	15.1854	0.729763	0.364881	−	0.931054i	$-0.381110\pi$
$433$	15.1854	0.729763	0.364881	+	0.931054i	$0.381110\pi$
$434$	50.6239	2.43003
$435$	0	0
$436$	19.0873	0.914115
$437$	−6.33222	−0.302911
$438$	79.6568	3.80615
$439$	17.1194	0.817063	0.408532	−	0.912744i	$-0.366041\pi$
$439$	17.1194	0.817063	0.408532	+	0.912744i	$0.366041\pi$
$440$	0	0
$441$	13.6166	0.648411
$442$	31.4565	1.49623
$443$	35.3909	1.68147	0.840736	−	0.541445i	$-0.182123\pi$
$443$	35.3909	1.68147	0.840736	+	0.541445i	$0.182123\pi$
$444$	36.0916	1.71283
$445$	0	0
$446$	−0.883234	−0.0418223
$447$	−28.0601	−1.32719
$448$	−44.9204	−2.12229
$449$	20.6830	0.976090	0.488045	−	0.872818i	$-0.337710\pi$
$449$	20.6830	0.976090	0.488045	+	0.872818i	$0.337710\pi$
$450$	0	0
$451$	1.43101	0.0673838
$452$	−8.87610	−0.417497
$453$	−39.3374	−1.84823
$454$	47.2220	2.21624
$455$	0	0
$456$	7.45902	0.349301
$457$	41.7664	1.95375	0.976876	−	0.213807i	$-0.0685863\pi$
$457$	41.7664	1.95375	0.976876	+	0.213807i	$0.0685863\pi$
$458$	−27.7054	−1.29459
$459$	8.22322	0.383827
$460$	0	0
$461$	−10.6783	−0.497340	−0.248670	−	0.968588i	$-0.579993\pi$
$461$	−10.6783	−0.497340	−0.248670	+	0.968588i	$0.579993\pi$
$462$	9.58176	0.445784
$463$	−7.83033	−0.363906	−0.181953	−	0.983307i	$-0.558242\pi$
$463$	−7.83033	−0.363906	−0.181953	+	0.983307i	$0.558242\pi$
$464$	−4.52122	−0.209892
$465$	0	0
$466$	−44.3379	−2.05391
$467$	4.98100	0.230493	0.115246	−	0.993337i	$-0.463234\pi$
$467$	4.98100	0.230493	0.115246	+	0.993337i	$0.463234\pi$
$468$	20.7778	0.960455
$469$	−19.0001	−0.877344
$470$	0	0
$471$	17.2635	0.795462
$472$	−4.15591	−0.191291
$473$	4.72330	0.217178
$474$	88.8388	4.08050
$475$	0	0
$476$	62.6094	2.86970
$477$	−0.707679	−0.0324024
$478$	9.59500	0.438865
$479$	−16.3981	−0.749247	−0.374623	−	0.927177i	$-0.622228\pi$
$479$	−16.3981	−0.749247	−0.374623	+	0.927177i	$0.622228\pi$
$480$	0	0
$481$	−12.1700	−0.554906
$482$	37.6498	1.71490
$483$	−53.0749	−2.41499
$484$	−36.6731	−1.66696
$485$	0	0
$486$	45.5794	2.06753
$487$	0.876508	0.0397184	0.0198592	−	0.999803i	$-0.493678\pi$
$487$	0.876508	0.0397184	0.0198592	+	0.999803i	$0.493678\pi$
$488$	−20.4317	−0.924901
$489$	−4.49547	−0.203292
$490$	0	0
$491$	12.2118	0.551112	0.275556	−	0.961285i	$-0.411138\pi$
$491$	12.2118	0.551112	0.275556	+	0.961285i	$0.411138\pi$
$492$	22.5743	1.01773
$493$	−28.4471	−1.28119
$494$	−6.08090	−0.273592
$495$	0	0
$496$	4.91495	0.220688
$497$	−0.546192	−0.0245001
$498$	−78.1675	−3.50277
$499$	−3.34603	−0.149789	−0.0748945	−	0.997191i	$-0.523862\pi$
$499$	−3.34603	−0.149789	−0.0748945	+	0.997191i	$0.523862\pi$
$500$	0	0
$501$	0.820954	0.0366775
$502$	27.6151	1.23252
$503$	11.8820	0.529792	0.264896	−	0.964277i	$-0.414662\pi$
$503$	11.8820	0.529792	0.264896	+	0.964277i	$0.414662\pi$
$504$	27.1354	1.20871
$505$	0	0
$506$	−7.42660	−0.330152
$507$	13.7878	0.612339
$508$	16.8656	0.748289
$509$	36.3183	1.60978	0.804890	−	0.593424i	$-0.202224\pi$
$509$	36.3183	1.60978	0.804890	+	0.593424i	$0.202224\pi$
$510$	0	0
$511$	−53.4611	−2.36498
$512$	−9.12203	−0.403140
$513$	−1.58964	−0.0701844
$514$	−44.0014	−1.94082
$515$	0	0
$516$	74.5102	3.28013
$517$	−2.67229	−0.117527
$518$	−38.4263	−1.68835
$519$	22.9088	1.00558
$520$	0	0
$521$	0.204224	0.00894722	0.00447361	−	0.999990i	$-0.498576\pi$
$521$	0.204224	0.00894722	0.00447361	+	0.999990i	$0.498576\pi$
$522$	−29.8081	−1.30467
$523$	28.0312	1.22572	0.612859	−	0.790192i	$-0.290019\pi$
$523$	28.0312	1.22572	0.612859	+	0.790192i	$0.290019\pi$
$524$	9.22069	0.402808
$525$	0	0
$526$	−15.6943	−0.684303
$527$	30.9244	1.34709
$528$	0.930269	0.0404848
$529$	18.1371	0.788570
$530$	0	0
$531$	−2.91366	−0.126442
$532$	−12.1031	−0.524736
$533$	−7.61202	−0.329713
$534$	−60.9567	−2.63785
$535$	0	0
$536$	−17.3471	−0.749280
$537$	−35.4151	−1.52827
$538$	−58.9268	−2.54052
$539$	−2.94621	−0.126902
$540$	0	0
$541$	−9.32216	−0.400791	−0.200396	−	0.979715i	$-0.564223\pi$
$541$	−9.32216	−0.400791	−0.200396	+	0.979715i	$0.564223\pi$
$542$	21.8824	0.939931
$543$	−20.5347	−0.881230
$544$	−23.8760	−1.02367
$545$	0	0
$546$	−50.9684	−2.18125
$547$	−20.0378	−0.856755	−0.428378	−	0.903600i	$-0.640915\pi$
$547$	−20.0378	−0.856755	−0.428378	+	0.903600i	$0.640915\pi$
$548$	−7.66865	−0.327588
$549$	−14.3244	−0.611351
$550$	0	0
$551$	5.49914	0.234271
$552$	−48.4573	−2.06248
$553$	−59.6235	−2.53545
$554$	−13.8807	−0.589734
$555$	0	0
$556$	−36.8471	−1.56266
$557$	−28.9839	−1.22809	−0.614043	−	0.789272i	$-0.710458\pi$
$557$	−28.9839	−1.22809	−0.614043	+	0.789272i	$0.710458\pi$
$558$	32.4040	1.37177
$559$	−25.1247	−1.06266
$560$	0	0
$561$	5.85316	0.247121
$562$	25.7552	1.08642
$563$	13.7025	0.577492	0.288746	−	0.957406i	$-0.406762\pi$
$563$	13.7025	0.577492	0.288746	+	0.957406i	$0.406762\pi$
$564$	−42.1555	−1.77507
$565$	0	0
$566$	−7.03428	−0.295673
$567$	−38.1312	−1.60136
$568$	−0.498673	−0.0209239
$569$	34.6152	1.45115	0.725573	−	0.688146i	$-0.241575\pi$
$569$	34.6152	1.45115	0.725573	+	0.688146i	$0.241575\pi$
$570$	0	0
$571$	−42.4197	−1.77521	−0.887604	−	0.460607i	$-0.847632\pi$
$571$	−42.4197	−1.77521	−0.887604	+	0.460607i	$0.847632\pi$
$572$	−4.49566	−0.187973
$573$	26.2203	1.09537
$574$	−24.0346	−1.00318
$575$	0	0
$576$	−28.7532	−1.19805
$577$	−34.3049	−1.42813	−0.714067	−	0.700078i	$-0.753149\pi$
$577$	−34.3049	−1.42813	−0.714067	+	0.700078i	$0.753149\pi$
$578$	21.1288	0.878844
$579$	−39.9039	−1.65835
$580$	0	0
$581$	52.4615	2.17647
$582$	−4.54777	−0.188511
$583$	0.153120	0.00634156
$584$	−48.8099	−2.01977
$585$	0	0
$586$	14.5713	0.601935
$587$	29.7521	1.22800	0.614001	−	0.789305i	$-0.289559\pi$
$587$	29.7521	1.22800	0.614001	+	0.789305i	$0.289559\pi$
$588$	−46.4765	−1.91666
$589$	−5.97803	−0.246321
$590$	0	0
$591$	−59.7702	−2.45862
$592$	−3.73071	−0.153331
$593$	−14.8105	−0.608195	−0.304098	−	0.952641i	$-0.598355\pi$
$593$	−14.8105	−0.608195	−0.304098	+	0.952641i	$0.598355\pi$
$594$	−1.86437	−0.0764962
$595$	0	0
$596$	41.5694	1.70275
$597$	19.3065	0.790163
$598$	39.5044	1.61545
$599$	27.2394	1.11297	0.556486	−	0.830857i	$-0.312149\pi$
$599$	27.2394	1.11297	0.556486	+	0.830857i	$0.312149\pi$
$600$	0	0
$601$	33.1682	1.35296	0.676480	−	0.736461i	$-0.263505\pi$
$601$	33.1682	1.35296	0.676480	+	0.736461i	$0.263505\pi$
$602$	−79.3301	−3.23325
$603$	−12.1618	−0.495268
$604$	58.2761	2.37122
$605$	0	0
$606$	70.9583	2.88248
$607$	5.79849	0.235353	0.117677	−	0.993052i	$-0.462455\pi$
$607$	5.79849	0.235353	0.117677	+	0.993052i	$0.462455\pi$
$608$	4.61549	0.187183
$609$	46.0923	1.86775
$610$	0	0
$611$	14.2148	0.575068
$612$	40.0758	1.61997
$613$	4.04653	0.163438	0.0817189	−	0.996655i	$-0.473959\pi$
$613$	4.04653	0.163438	0.0817189	+	0.996655i	$0.473959\pi$
$614$	60.1842	2.42884
$615$	0	0
$616$	−5.87125	−0.236559
$617$	37.1749	1.49661	0.748303	−	0.663357i	$-0.230869\pi$
$617$	37.1749	1.49661	0.748303	+	0.663357i	$0.230869\pi$
$618$	−4.44986	−0.179000
$619$	−37.7118	−1.51576	−0.757882	−	0.652391i	$-0.773766\pi$
$619$	−37.7118	−1.51576	−0.757882	+	0.652391i	$0.773766\pi$
$620$	0	0
$621$	10.3271	0.414411
$622$	−20.9413	−0.839672
$623$	40.9106	1.63905
$624$	−4.94839	−0.198094
$625$	0	0
$626$	−77.2903	−3.08914
$627$	−1.13148	−0.0451870
$628$	−25.5750	−1.02055
$629$	−23.4733	−0.935940
$630$	0	0
$631$	18.5225	0.737368	0.368684	−	0.929555i	$-0.379808\pi$
$631$	18.5225	0.737368	0.368684	+	0.929555i	$0.379808\pi$
$632$	−54.4362	−2.16536
$633$	−36.6379	−1.45622
$634$	−60.4072	−2.39908
$635$	0	0
$636$	2.41546	0.0957794
$637$	15.6718	0.620940
$638$	6.44954	0.255340
$639$	−0.349613	−0.0138305
$640$	0	0
$641$	−19.7116	−0.778560	−0.389280	−	0.921120i	$-0.627276\pi$
$641$	−19.7116	−0.778560	−0.389280	+	0.921120i	$0.627276\pi$
$642$	0.387113	0.0152781
$643$	42.5897	1.67957	0.839787	−	0.542916i	$-0.182680\pi$
$643$	42.5897	1.67957	0.839787	+	0.542916i	$0.182680\pi$
$644$	78.6275	3.09836
$645$	0	0
$646$	−11.7287	−0.461459
$647$	27.4018	1.07728	0.538638	−	0.842537i	$-0.318939\pi$
$647$	27.4018	1.07728	0.538638	+	0.842537i	$0.318939\pi$
$648$	−34.8138	−1.36761
$649$	0.630424	0.0247463
$650$	0	0
$651$	−50.1062	−1.96382
$652$	6.65979	0.260818
$653$	21.4414	0.839068	0.419534	−	0.907740i	$-0.362193\pi$
$653$	21.4414	0.839068	0.419534	+	0.907740i	$0.362193\pi$
$654$	−29.9701	−1.17192
$655$	0	0
$656$	−2.33346	−0.0911062
$657$	−34.2200	−1.33505
$658$	44.8825	1.74970
$659$	−36.7342	−1.43096	−0.715480	−	0.698633i	$-0.753792\pi$
$659$	−36.7342	−1.43096	−0.715480	+	0.698633i	$0.753792\pi$
$660$	0	0
$661$	−15.7515	−0.612664	−0.306332	−	0.951925i	$-0.599102\pi$
$661$	−15.7515	−0.612664	−0.306332	+	0.951925i	$0.599102\pi$
$662$	28.2118	1.09648
$663$	−31.1348	−1.20918
$664$	47.8973	1.85878
$665$	0	0
$666$	−24.5963	−0.953089
$667$	−35.7250	−1.38328
$668$	−1.21620	−0.0470561
$669$	0.874201	0.0337986
$670$	0	0
$671$	3.09935	0.119649
$672$	38.6858	1.49234
$673$	31.0107	1.19537	0.597687	−	0.801730i	$-0.296087\pi$
$673$	31.0107	1.19537	0.597687	+	0.801730i	$0.296087\pi$
$674$	−70.3690	−2.71051
$675$	0	0
$676$	−20.4259	−0.785611
$677$	−9.59882	−0.368912	−0.184456	−	0.982841i	$-0.559052\pi$
$677$	−9.59882	−0.368912	−0.184456	+	0.982841i	$0.559052\pi$
$678$	13.9369	0.535243
$679$	3.05220	0.117133
$680$	0	0
$681$	−46.7391	−1.79105
$682$	−7.01120	−0.268473
$683$	−0.868350	−0.0332265	−0.0166132	−	0.999862i	$-0.505288\pi$
$683$	−0.868350	−0.0332265	−0.0166132	+	0.999862i	$0.505288\pi$
$684$	−7.74710	−0.296218
$685$	0	0
$686$	−9.04109	−0.345190
$687$	27.4221	1.04622
$688$	−7.70196	−0.293635
$689$	−0.814491	−0.0310296
$690$	0	0
$691$	−13.1375	−0.499772	−0.249886	−	0.968275i	$-0.580393\pi$
$691$	−13.1375	−0.499772	−0.249886	+	0.968275i	$0.580393\pi$
$692$	−33.9380	−1.29013
$693$	−4.11625	−0.156364
$694$	−31.0030	−1.17686
$695$	0	0
$696$	42.0822	1.59512
$697$	−14.6819	−0.556116
$698$	−63.8384	−2.41632
$699$	43.8844	1.65986
$700$	0	0
$701$	7.13602	0.269524	0.134762	−	0.990878i	$-0.456973\pi$
$701$	7.13602	0.269524	0.134762	+	0.990878i	$0.456973\pi$
$702$	9.91719	0.374300
$703$	4.53765	0.171141
$704$	6.22129	0.234474
$705$	0	0
$706$	36.1858	1.36187
$707$	−47.6231	−1.79105
$708$	9.94495	0.373754
$709$	−8.00513	−0.300639	−0.150319	−	0.988637i	$-0.548030\pi$
$709$	−8.00513	−0.300639	−0.150319	+	0.988637i	$0.548030\pi$
$710$	0	0
$711$	−38.1645	−1.43128
$712$	37.3513	1.39980
$713$	38.8362	1.45443
$714$	−98.3066	−3.67903
$715$	0	0
$716$	52.4655	1.96073
$717$	−9.49688	−0.354667
$718$	−51.1345	−1.90832
$719$	−41.2567	−1.53861	−0.769307	−	0.638879i	$-0.779398\pi$
$719$	−41.2567	−1.53861	−0.769307	+	0.638879i	$0.779398\pi$
$720$	0	0
$721$	2.98649	0.111223
$722$	−41.9286	−1.56042
$723$	−37.2648	−1.38589
$724$	30.4210	1.13059
$725$	0	0
$726$	57.5825	2.13709
$727$	39.2602	1.45608	0.728040	−	0.685534i	$-0.240431\pi$
$727$	39.2602	1.45608	0.728040	+	0.685534i	$0.240431\pi$
$728$	31.2310	1.15750
$729$	−13.2864	−0.492090
$730$	0	0
$731$	−48.4600	−1.79236
$732$	48.8924	1.80711
$733$	0.912055	0.0336875	0.0168438	−	0.999858i	$-0.494638\pi$
$733$	0.912055	0.0336875	0.0168438	+	0.999858i	$0.494638\pi$
$734$	28.1699	1.03977
$735$	0	0
$736$	−29.9844	−1.10524
$737$	2.63143	0.0969301
$738$	−15.3843	−0.566305
$739$	−11.6941	−0.430174	−0.215087	−	0.976595i	$-0.569003\pi$
$739$	−11.6941	−0.430174	−0.215087	+	0.976595i	$0.569003\pi$
$740$	0	0
$741$	6.01871	0.221103
$742$	−2.57171	−0.0944106
$743$	11.5631	0.424211	0.212105	−	0.977247i	$-0.431968\pi$
$743$	11.5631	0.424211	0.212105	+	0.977247i	$0.431968\pi$
$744$	−45.7470	−1.67716
$745$	0	0
$746$	16.4828	0.603480
$747$	33.5802	1.22863
$748$	−8.67113	−0.317048
$749$	−0.259808	−0.00949318
$750$	0	0
$751$	−27.2430	−0.994112	−0.497056	−	0.867718i	$-0.665586\pi$
$751$	−27.2430	−0.994112	−0.497056	+	0.867718i	$0.665586\pi$
$752$	4.35753	0.158903
$753$	−27.3327	−0.996059
$754$	−34.3071	−1.24939
$755$	0	0
$756$	19.7387	0.717888
$757$	17.1080	0.621800	0.310900	−	0.950443i	$-0.399370\pi$
$757$	17.1080	0.621800	0.310900	+	0.950443i	$0.399370\pi$
$758$	−50.0181	−1.81674
$759$	7.35065	0.266812
$760$	0	0
$761$	37.7173	1.36725	0.683625	−	0.729833i	$-0.260402\pi$
$761$	37.7173	1.36725	0.683625	+	0.729833i	$0.260402\pi$
$762$	−26.4816	−0.959328
$763$	20.1142	0.728182
$764$	−38.8439	−1.40532
$765$	0	0
$766$	57.8772	2.09119
$767$	−3.35342	−0.121085
$768$	48.0682	1.73451
$769$	−5.93347	−0.213966	−0.106983	−	0.994261i	$-0.534119\pi$
$769$	−5.93347	−0.213966	−0.106983	+	0.994261i	$0.534119\pi$
$770$	0	0
$771$	43.5514	1.56847
$772$	59.1153	2.12761
$773$	23.5908	0.848503	0.424252	−	0.905544i	$-0.360537\pi$
$773$	23.5908	0.848503	0.424252	+	0.905544i	$0.360537\pi$
$774$	−50.7786	−1.82520
$775$	0	0
$776$	2.78666	0.100035
$777$	38.0333	1.36444
$778$	−82.3770	−2.95336
$779$	2.83817	0.101688
$780$	0	0
$781$	0.0756453	0.00270680
$782$	76.1952	2.72473
$783$	−8.96842	−0.320505
$784$	4.80418	0.171578
$785$	0	0
$786$	−14.4779	−0.516411
$787$	−18.2307	−0.649854	−0.324927	−	0.945739i	$-0.605340\pi$
$787$	−18.2307	−0.649854	−0.324927	+	0.945739i	$0.605340\pi$
$788$	88.5462	3.15433
$789$	15.5338	0.553017
$790$	0	0
$791$	−9.35364	−0.332577
$792$	−3.75814	−0.133540
$793$	−16.4864	−0.585451
$794$	12.7867	0.453783
$795$	0	0
$796$	−28.6015	−1.01375
$797$	−10.8296	−0.383603	−0.191801	−	0.981434i	$-0.561433\pi$
$797$	−10.8296	−0.383603	−0.191801	+	0.981434i	$0.561433\pi$
$798$	19.0038	0.672727
$799$	27.4171	0.969948
$800$	0	0
$801$	26.1865	0.925256
$802$	57.7950	2.04081
$803$	7.40413	0.261286
$804$	41.5109	1.46398
$805$	0	0
$806$	37.2948	1.31365
$807$	58.3242	2.05311
$808$	−43.4799	−1.52962
$809$	44.8177	1.57571	0.787854	−	0.615863i	$-0.211192\pi$
$809$	44.8177	1.57571	0.787854	+	0.615863i	$0.211192\pi$
$810$	0	0
$811$	−3.06296	−0.107555	−0.0537775	−	0.998553i	$-0.517126\pi$
$811$	−3.06296	−0.107555	−0.0537775	+	0.998553i	$0.517126\pi$
$812$	−68.2831	−2.39627
$813$	−21.6587	−0.759602
$814$	5.32187	0.186532
$815$	0	0
$816$	−9.54435	−0.334119
$817$	9.36786	0.327740
$818$	9.14524	0.319756
$819$	21.8957	0.765096
$820$	0	0
$821$	20.3210	0.709208	0.354604	−	0.935017i	$-0.384616\pi$
$821$	20.3210	0.709208	0.354604	+	0.935017i	$0.384616\pi$
$822$	12.0410	0.419978
$823$	−50.0369	−1.74418	−0.872089	−	0.489348i	$-0.837235\pi$
$823$	−50.0369	−1.74418	−0.872089	+	0.489348i	$0.837235\pi$
$824$	2.72666	0.0949879
$825$	0	0
$826$	−10.5883	−0.368413
$827$	−31.6293	−1.09986	−0.549929	−	0.835211i	$-0.685345\pi$
$827$	−31.6293	−1.09986	−0.549929	+	0.835211i	$0.685345\pi$
$828$	50.3288	1.74905
$829$	33.1369	1.15089	0.575446	−	0.817840i	$-0.304829\pi$
$829$	33.1369	1.15089	0.575446	+	0.817840i	$0.304829\pi$
$830$	0	0
$831$	13.7387	0.476591
$832$	−33.0930	−1.14729
$833$	30.2274	1.04732
$834$	57.8557	2.00338
$835$	0	0
$836$	1.67623	0.0579735
$837$	9.74944	0.336990
$838$	−11.0863	−0.382970
$839$	10.3854	0.358543	0.179271	−	0.983800i	$-0.442626\pi$
$839$	10.3854	0.358543	0.179271	+	0.983800i	$0.442626\pi$
$840$	0	0
$841$	2.02500	0.0698275
$842$	37.3528	1.28726
$843$	−25.4918	−0.877986
$844$	54.2769	1.86829
$845$	0	0
$846$	28.7289	0.987720
$847$	−38.6461	−1.32790
$848$	−0.249681	−0.00857410
$849$	6.96235	0.238947
$850$	0	0
$851$	−29.4787	−1.01052
$852$	1.19331	0.0408820
$853$	−9.31456	−0.318924	−0.159462	−	0.987204i	$-0.550976\pi$
$853$	−9.31456	−0.318924	−0.159462	+	0.987204i	$0.550976\pi$
$854$	−52.0551	−1.78129
$855$	0	0
$856$	−0.237204	−0.00810748
$857$	−34.0314	−1.16249	−0.581245	−	0.813729i	$-0.697434\pi$
$857$	−34.0314	−1.16249	−0.581245	+	0.813729i	$0.697434\pi$
$858$	7.05890	0.240987
$859$	33.4243	1.14042	0.570211	−	0.821498i	$-0.306861\pi$
$859$	33.4243	1.14042	0.570211	+	0.821498i	$0.306861\pi$
$860$	0	0
$861$	23.7888	0.810719
$862$	−96.2291	−3.27758
$863$	16.5900	0.564730	0.282365	−	0.959307i	$-0.408881\pi$
$863$	16.5900	0.564730	0.282365	+	0.959307i	$0.408881\pi$
$864$	−7.52730	−0.256084
$865$	0	0
$866$	35.3227	1.20032
$867$	−20.9128	−0.710235
$868$	74.2296	2.51952
$869$	8.25760	0.280120
$870$	0	0
$871$	−13.9974	−0.474285
$872$	18.3642	0.621891
$873$	1.95369	0.0661224
$874$	−14.7294	−0.498229
$875$	0	0
$876$	116.800	3.94632
$877$	−32.9538	−1.11277	−0.556385	−	0.830925i	$-0.687812\pi$
$877$	−32.9538	−1.11277	−0.556385	+	0.830925i	$0.687812\pi$
$878$	39.8214	1.34391
$879$	−14.4223	−0.486452
$880$	0	0
$881$	−50.0755	−1.68709	−0.843544	−	0.537061i	$-0.819535\pi$
$881$	−50.0755	−1.68709	−0.843544	+	0.537061i	$0.819535\pi$
$882$	31.6737	1.06651
$883$	12.5335	0.421786	0.210893	−	0.977509i	$-0.432363\pi$
$883$	12.5335	0.421786	0.210893	+	0.977509i	$0.432363\pi$
$884$	46.1245	1.55133
$885$	0	0
$886$	82.3228	2.76569
$887$	26.9358	0.904415	0.452207	−	0.891913i	$-0.350637\pi$
$887$	26.9358	0.904415	0.452207	+	0.891913i	$0.350637\pi$
$888$	34.7244	1.16527
$889$	17.7729	0.596085
$890$	0	0
$891$	5.28101	0.176921
$892$	−1.29508	−0.0433625
$893$	−5.30004	−0.177359
$894$	−65.2705	−2.18297
$895$	0	0
$896$	−70.8835	−2.36805
$897$	−39.1004	−1.30552
$898$	48.1107	1.60548
$899$	−33.7268	−1.12485
$900$	0	0
$901$	−1.57097	−0.0523366
$902$	3.32869	0.110833
$903$	78.5188	2.61294
$904$	−8.53986	−0.284032
$905$	0	0
$906$	−91.5027	−3.03997
$907$	−28.6510	−0.951342	−0.475671	−	0.879623i	$-0.657795\pi$
$907$	−28.6510	−0.951342	−0.475671	+	0.879623i	$0.657795\pi$
$908$	69.2414	2.29786
$909$	−30.4832	−1.01106
$910$	0	0
$911$	−8.90071	−0.294894	−0.147447	−	0.989070i	$-0.547106\pi$
$911$	−8.90071	−0.294894	−0.147447	+	0.989070i	$0.547106\pi$
$912$	1.84503	0.0610950
$913$	−7.26569	−0.240459
$914$	97.1530	3.21354
$915$	0	0
$916$	−40.6242	−1.34226
$917$	9.71676	0.320876
$918$	19.1280	0.631320
$919$	17.1901	0.567049	0.283525	−	0.958965i	$-0.408496\pi$
$919$	17.1901	0.567049	0.283525	+	0.958965i	$0.408496\pi$
$920$	0	0
$921$	−59.5687	−1.96286
$922$	−24.8389	−0.818025
$923$	−0.402381	−0.0132445
$924$	14.0497	0.462200
$925$	0	0
$926$	−18.2141	−0.598554
$927$	1.91163	0.0627861
$928$	26.0396	0.854793
$929$	34.7789	1.14106	0.570530	−	0.821277i	$-0.306738\pi$
$929$	34.7789	1.14106	0.570530	+	0.821277i	$0.306738\pi$
$930$	0	0
$931$	−5.84330	−0.191507
$932$	−65.0123	−2.12955
$933$	20.7272	0.678578
$934$	11.5863	0.379115
$935$	0	0
$936$	19.9907	0.653417
$937$	−16.5386	−0.540292	−0.270146	−	0.962819i	$-0.587072\pi$
$937$	−16.5386	−0.540292	−0.270146	+	0.962819i	$0.587072\pi$
$938$	−44.1962	−1.44306
$939$	76.4999	2.49648
$940$	0	0
$941$	41.1982	1.34302	0.671512	−	0.740994i	$-0.265645\pi$
$941$	41.1982	1.34302	0.671512	+	0.740994i	$0.265645\pi$
$942$	40.1568	1.30838
$943$	−18.4381	−0.600428
$944$	−1.02799	−0.0334582
$945$	0	0
$946$	10.9869	0.357214
$947$	−37.1110	−1.20594	−0.602972	−	0.797762i	$-0.706017\pi$
$947$	−37.1110	−1.20594	−0.602972	+	0.797762i	$0.706017\pi$
$948$	130.264	4.23077
$949$	−39.3849	−1.27849
$950$	0	0
$951$	59.7895	1.93881
$952$	60.2376	1.95231
$953$	20.8962	0.676895	0.338447	−	0.940985i	$-0.390098\pi$
$953$	20.8962	0.676895	0.338447	+	0.940985i	$0.390098\pi$
$954$	−1.64613	−0.0532956
$955$	0	0
$956$	14.0691	0.455027
$957$	−6.38358	−0.206352
$958$	−38.1436	−1.23236
$959$	−8.08122	−0.260956
$960$	0	0
$961$	5.66391	0.182707
$962$	−28.3087	−0.912710
$963$	−0.166301	−0.00535897
$964$	55.2057	1.77806
$965$	0	0
$966$	−123.458	−3.97218
$967$	8.28057	0.266285	0.133143	−	0.991097i	$-0.457493\pi$
$967$	8.28057	0.266285	0.133143	+	0.991097i	$0.457493\pi$
$968$	−35.2838	−1.13407
$969$	11.6087	0.372927
$970$	0	0
$971$	−26.4077	−0.847463	−0.423731	−	0.905788i	$-0.639280\pi$
$971$	−26.4077	−0.847463	−0.423731	+	0.905788i	$0.639280\pi$
$972$	66.8329	2.14366
$973$	−38.8294	−1.24481
$974$	2.03885	0.0653289
$975$	0	0
$976$	−5.05390	−0.161771
$977$	25.3280	0.810314	0.405157	−	0.914247i	$-0.367217\pi$
$977$	25.3280	0.810314	0.405157	+	0.914247i	$0.367217\pi$
$978$	−10.4569	−0.334376
$979$	−5.66594	−0.181084
$980$	0	0
$981$	12.8749	0.411065
$982$	28.4059	0.906470
$983$	−5.12811	−0.163561	−0.0817807	−	0.996650i	$-0.526061\pi$
$983$	−5.12811	−0.163561	−0.0817807	+	0.996650i	$0.526061\pi$
$984$	21.7191	0.692381
$985$	0	0
$986$	−66.1708	−2.10731
$987$	−44.4235	−1.41401
$988$	−8.91638	−0.283668
$989$	−60.8581	−1.93517
$990$	0	0
$991$	−26.5396	−0.843059	−0.421530	−	0.906815i	$-0.638507\pi$
$991$	−26.5396	−0.843059	−0.421530	+	0.906815i	$0.638507\pi$
$992$	−28.3073	−0.898758
$993$	−27.9233	−0.886120
$994$	−1.27050	−0.0402978
$995$	0	0
$996$	−114.616	−3.63176
$997$	44.4973	1.40924	0.704622	−	0.709583i	$-0.251117\pi$
$997$	44.4973	1.40924	0.704622	+	0.709583i	$0.251117\pi$
$998$	−7.78321	−0.246373
$999$	−7.40034	−0.234136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.a.g.1.6	yes	8
3.2	odd	2		5625.2.a.s.1.3		8
4.3	odd	2		10000.2.a.be.1.8		8
5.2	odd	4		625.2.b.d.624.14		16
5.3	odd	4		625.2.b.d.624.3		16
5.4	even	2		625.2.a.e.1.3	✓	8
15.14	odd	2		5625.2.a.be.1.6		8
20.19	odd	2		10000.2.a.bn.1.1		8
25.2	odd	20		625.2.e.k.124.7		32
25.3	odd	20		625.2.e.j.249.2		32
25.4	even	10		625.2.d.q.376.3		16
25.6	even	5		625.2.d.m.251.2		16
25.8	odd	20		625.2.e.j.374.7		32
25.9	even	10		625.2.d.p.126.2		16
25.11	even	5		625.2.d.n.501.3		16
25.12	odd	20		625.2.e.k.499.2		32
25.13	odd	20		625.2.e.k.499.7		32
25.14	even	10		625.2.d.p.501.2		16
25.16	even	5		625.2.d.n.126.3		16
25.17	odd	20		625.2.e.j.374.2		32
25.19	even	10		625.2.d.q.251.3		16
25.21	even	5		625.2.d.m.376.2		16
25.22	odd	20		625.2.e.j.249.7		32
25.23	odd	20		625.2.e.k.124.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.3	✓	8	5.4	even	2
625.2.a.g.1.6	yes	8	1.1	even	1	trivial
625.2.b.d.624.3		16	5.3	odd	4
625.2.b.d.624.14		16	5.2	odd	4
625.2.d.m.251.2		16	25.6	even	5
625.2.d.m.376.2		16	25.21	even	5
625.2.d.n.126.3		16	25.16	even	5
625.2.d.n.501.3		16	25.11	even	5
625.2.d.p.126.2		16	25.9	even	10
625.2.d.p.501.2		16	25.14	even	10
625.2.d.q.251.3		16	25.19	even	10
625.2.d.q.376.3		16	25.4	even	10
625.2.e.j.249.2		32	25.3	odd	20
625.2.e.j.249.7		32	25.22	odd	20
625.2.e.j.374.2		32	25.17	odd	20
625.2.e.j.374.7		32	25.8	odd	20
625.2.e.k.124.2		32	25.23	odd	20
625.2.e.k.124.7		32	25.2	odd	20
625.2.e.k.499.2		32	25.12	odd	20
625.2.e.k.499.7		32	25.13	odd	20
5625.2.a.s.1.3		8	3.2	odd	2
5625.2.a.be.1.6		8	15.14	odd	2
10000.2.a.be.1.8		8	4.3	odd	2
10000.2.a.bn.1.1		8	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.a (trivial)

\(f(q)\)	\(=\)	\(q+2.32610 q^{2} -2.30231 q^{3} +3.41075 q^{4} -5.35542 q^{6} +3.59425 q^{7} +3.28154 q^{8} +2.30065 q^{9} +O(q^{10})\)	\(q+2.32610 q^{2} -2.30231 q^{3} +3.41075 q^{4} -5.35542 q^{6} +3.59425 q^{7} +3.28154 q^{8} +2.30065 q^{9} -0.497788 q^{11} -7.85261 q^{12} +2.64789 q^{13} +8.36058 q^{14} +0.811708 q^{16} +5.10719 q^{17} +5.35154 q^{18} -0.987277 q^{19} -8.27508 q^{21} -1.15790 q^{22} +6.41382 q^{23} -7.55514 q^{24} +6.15926 q^{26} +1.61013 q^{27} +12.2591 q^{28} -5.57001 q^{29} +6.05507 q^{31} -4.67497 q^{32} +1.14606 q^{33} +11.8798 q^{34} +7.84693 q^{36} -4.59612 q^{37} -2.29651 q^{38} -6.09627 q^{39} -2.87475 q^{41} -19.2487 q^{42} -9.48858 q^{43} -1.69783 q^{44} +14.9192 q^{46} +5.36834 q^{47} -1.86881 q^{48} +5.91861 q^{49} -11.7583 q^{51} +9.03129 q^{52} -0.307600 q^{53} +3.74532 q^{54} +11.7947 q^{56} +2.27302 q^{57} -12.9564 q^{58} -1.26645 q^{59} -6.22625 q^{61} +14.0847 q^{62} +8.26910 q^{63} -12.4979 q^{64} +2.66586 q^{66} -5.28626 q^{67} +17.4193 q^{68} -14.7666 q^{69} -0.151963 q^{71} +7.54968 q^{72} -14.8741 q^{73} -10.6910 q^{74} -3.36735 q^{76} -1.78917 q^{77} -14.1805 q^{78} -16.5886 q^{79} -10.6090 q^{81} -6.68696 q^{82} +14.5960 q^{83} -28.2242 q^{84} -22.0714 q^{86} +12.8239 q^{87} -1.63351 q^{88} +11.3822 q^{89} +9.51717 q^{91} +21.8759 q^{92} -13.9407 q^{93} +12.4873 q^{94} +10.7633 q^{96} +0.849192 q^{97} +13.7673 q^{98} -1.14523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9	\( 8 q + 5 q^{2} + 5 q^{3} + 11 q^{4} - 4 q^{6} + 10 q^{7} + 15 q^{8} + 9 q^{9} + q^{11} + 10 q^{12} + 10 q^{13} - 8 q^{14} + 13 q^{16} + 15 q^{17} - 5 q^{18} - 10 q^{19} - 14 q^{21} - 5 q^{22} + 30 q^{23} + 5 q^{24} + 11 q^{26} + 20 q^{27} - 5 q^{28} + 10 q^{29} - 9 q^{31} + 30 q^{32} + 5 q^{33} + 7 q^{34} + 3 q^{36} - 10 q^{37} + 20 q^{38} + 8 q^{39} - 4 q^{41} - 35 q^{42} - 18 q^{44} - 9 q^{46} + 30 q^{47} + 5 q^{48} - 4 q^{49} - 14 q^{51} + 5 q^{52} + 10 q^{53} - 20 q^{54} - 10 q^{57} - 30 q^{58} - 5 q^{59} + 6 q^{61} + 10 q^{62} - 9 q^{64} - 18 q^{66} + 10 q^{67} + 40 q^{68} + 3 q^{69} - 9 q^{71} - 15 q^{72} - 18 q^{74} - 10 q^{76} + 5 q^{77} - 30 q^{78} - 20 q^{79} + 8 q^{81} - 45 q^{82} + 40 q^{83} - 28 q^{84} - 24 q^{86} + 40 q^{87} - 40 q^{88} - 5 q^{89} + 6 q^{91} + 15 q^{92} - 40 q^{93} + 47 q^{94} + 71 q^{96} - 30 q^{98} - 22 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 + 11 * q^4 - 4 * q^6 + 10 * q^7 + 15 * q^8 + 9 * q^9 + q^11 + 10 * q^12 + 10 * q^13 - 8 * q^14 + 13 * q^16 + 15 * q^17 - 5 * q^18 - 10 * q^19 - 14 * q^21 - 5 * q^22 + 30 * q^23 + 5 * q^24 + 11 * q^26 + 20 * q^27 - 5 * q^28 + 10 * q^29 - 9 * q^31 + 30 * q^32 + 5 * q^33 + 7 * q^34 + 3 * q^36 - 10 * q^37 + 20 * q^38 + 8 * q^39 - 4 * q^41 - 35 * q^42 - 18 * q^44 - 9 * q^46 + 30 * q^47 + 5 * q^48 - 4 * q^49 - 14 * q^51 + 5 * q^52 + 10 * q^53 - 20 * q^54 - 10 * q^57 - 30 * q^58 - 5 * q^59 + 6 * q^61 + 10 * q^62 - 9 * q^64 - 18 * q^66 + 10 * q^67 + 40 * q^68 + 3 * q^69 - 9 * q^71 - 15 * q^72 - 18 * q^74 - 10 * q^76 + 5 * q^77 - 30 * q^78 - 20 * q^79 + 8 * q^81 - 45 * q^82 + 40 * q^83 - 28 * q^84 - 24 * q^86 + 40 * q^87 - 40 * q^88 - 5 * q^89 + 6 * q^91 + 15 * q^92 - 40 * q^93 + 47 * q^94 + 71 * q^96 - 30 * q^98 - 22 * q^99

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