LMFDB - Embedded newform 1875.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.5125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 6x^{2} + 7x + 11 $ x^4 - 2x^3 - 6x^2 + 7*x + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.70636$ of defining polynomial
Character	$\chi$	$=$	1875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70636 q^{2} -1.00000 q^{3} +0.911672 q^{4} -1.70636 q^{6} +3.94243 q^{7} -1.85708 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.70636 q^{2} -1.00000 q^{3} +0.911672 q^{4} -1.70636 q^{6} +3.94243 q^{7} -1.85708 q^{8} +1.00000 q^{9} -5.90869 q^{11} -0.911672 q^{12} -3.29066 q^{13} +6.72721 q^{14} -4.99220 q^{16} -2.70636 q^{17} +1.70636 q^{18} -2.35813 q^{19} -3.94243 q^{21} -10.0824 q^{22} +0.584296 q^{23} +1.85708 q^{24} -5.61505 q^{26} -1.00000 q^{27} +3.59420 q^{28} -3.91167 q^{29} +2.70934 q^{31} -4.80433 q^{32} +5.90869 q^{33} -4.61803 q^{34} +0.911672 q^{36} +0.0208515 q^{37} -4.02383 q^{38} +3.29066 q^{39} +1.47214 q^{41} -6.72721 q^{42} -1.27279 q^{43} -5.38679 q^{44} +0.997020 q^{46} -5.43358 q^{47} +4.99220 q^{48} +8.54276 q^{49} +2.70636 q^{51} -3.00000 q^{52} -2.81554 q^{53} -1.70636 q^{54} -7.32142 q^{56} +2.35813 q^{57} -6.67473 q^{58} -4.69033 q^{59} +5.58132 q^{61} +4.62312 q^{62} +3.94243 q^{63} +1.78646 q^{64} +10.0824 q^{66} -6.03076 q^{67} -2.46731 q^{68} -0.584296 q^{69} -8.10138 q^{71} -1.85708 q^{72} -13.3166 q^{73} +0.0355801 q^{74} -2.14984 q^{76} -23.2946 q^{77} +5.61505 q^{78} +16.6648 q^{79} +1.00000 q^{81} +2.51200 q^{82} -0.781641 q^{83} -3.59420 q^{84} -2.17183 q^{86} +3.91167 q^{87} +10.9729 q^{88} -3.47327 q^{89} -12.9732 q^{91} +0.532686 q^{92} -2.70934 q^{93} -9.27165 q^{94} +4.80433 q^{96} +2.45443 q^{97} +14.5770 q^{98} -5.90869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} - 2 q^{7} - 15 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 - 2 * q^7 - 15 * q^8 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} - 2 q^{7} - 15 q^{8} + 4 q^{9} - 7 q^{11} - 8 q^{12} - q^{13} + 16 q^{14} + 4 q^{16} - 2 q^{17} - 2 q^{18} + 5 q^{19} + 2 q^{21} + 6 q^{22} - q^{23} + 15 q^{24} + 3 q^{26} - 4 q^{27} - 9 q^{28} - 20 q^{29} + 23 q^{31} - 12 q^{32} + 7 q^{33} - 14 q^{34} + 8 q^{36} - 2 q^{37} - 35 q^{38} + q^{39} - 12 q^{41} - 16 q^{42} - 16 q^{43} - 29 q^{44} - 17 q^{46} - 2 q^{47} - 4 q^{48} + 8 q^{49} + 2 q^{51} - 12 q^{52} + 4 q^{53} + 2 q^{54} + 5 q^{56} - 5 q^{57} + 25 q^{58} - 15 q^{59} - 2 q^{61} - 9 q^{62} - 2 q^{63} + 23 q^{64} - 6 q^{66} - 2 q^{67} + 11 q^{68} + q^{69} - 2 q^{71} - 15 q^{72} - 16 q^{73} - 19 q^{74} + 40 q^{76} - 19 q^{77} - 3 q^{78} + 35 q^{79} + 4 q^{81} + 6 q^{82} - 16 q^{83} + 9 q^{84} + 3 q^{86} + 20 q^{87} + 30 q^{88} - 35 q^{89} - 12 q^{91} + 23 q^{92} - 23 q^{93} - 9 q^{94} + 12 q^{96} - 12 q^{97} + q^{98} - 7 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 - 2 * q^7 - 15 * q^8 + 4 * q^9 - 7 * q^11 - 8 * q^12 - q^13 + 16 * q^14 + 4 * q^16 - 2 * q^17 - 2 * q^18 + 5 * q^19 + 2 * q^21 + 6 * q^22 - q^23 + 15 * q^24 + 3 * q^26 - 4 * q^27 - 9 * q^28 - 20 * q^29 + 23 * q^31 - 12 * q^32 + 7 * q^33 - 14 * q^34 + 8 * q^36 - 2 * q^37 - 35 * q^38 + q^39 - 12 * q^41 - 16 * q^42 - 16 * q^43 - 29 * q^44 - 17 * q^46 - 2 * q^47 - 4 * q^48 + 8 * q^49 + 2 * q^51 - 12 * q^52 + 4 * q^53 + 2 * q^54 + 5 * q^56 - 5 * q^57 + 25 * q^58 - 15 * q^59 - 2 * q^61 - 9 * q^62 - 2 * q^63 + 23 * q^64 - 6 * q^66 - 2 * q^67 + 11 * q^68 + q^69 - 2 * q^71 - 15 * q^72 - 16 * q^73 - 19 * q^74 + 40 * q^76 - 19 * q^77 - 3 * q^78 + 35 * q^79 + 4 * q^81 + 6 * q^82 - 16 * q^83 + 9 * q^84 + 3 * q^86 + 20 * q^87 + 30 * q^88 - 35 * q^89 - 12 * q^91 + 23 * q^92 - 23 * q^93 - 9 * q^94 + 12 * q^96 - 12 * q^97 + q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.70636	1.20658	0.603290	−	0.797522i	$-0.293856\pi$
$2$	1.70636	1.20658	0.603290	+	0.797522i	$0.293856\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.911672	0.455836
$5$	0	0
$5$	0	0
$6$	−1.70636	−0.696619
$7$	3.94243	1.49010	0.745049	−	0.667009i	$-0.232426\pi$
$7$	3.94243	1.49010	0.745049	+	0.667009i	$0.232426\pi$
$8$	−1.85708	−0.656578
$9$	1.00000	0.333333
$10$	0	0
$11$	−5.90869	−1.78154	−0.890769	−	0.454457i	$-0.849833\pi$
$11$	−5.90869	−1.78154	−0.890769	+	0.454457i	$0.849833\pi$
$12$	−0.911672	−0.263177
$13$	−3.29066	−0.912664	−0.456332	−	0.889810i	$-0.650837\pi$
$13$	−3.29066	−0.912664	−0.456332	+	0.889810i	$0.650837\pi$
$14$	6.72721	1.79792
$15$	0	0
$16$	−4.99220	−1.24805
$17$	−2.70636	−0.656389	−0.328195	−	0.944610i	$-0.606440\pi$
$17$	−2.70636	−0.656389	−0.328195	+	0.944610i	$0.606440\pi$
$18$	1.70636	0.402193
$19$	−2.35813	−0.540993	−0.270497	−	0.962721i	$-0.587188\pi$
$19$	−2.35813	−0.540993	−0.270497	+	0.962721i	$0.587188\pi$
$20$	0	0
$21$	−3.94243	−0.860309
$22$	−10.0824	−2.14957
$23$	0.584296	0.121834	0.0609170	−	0.998143i	$-0.480597\pi$
$23$	0.584296	0.121834	0.0609170	+	0.998143i	$0.480597\pi$
$24$	1.85708	0.379075
$25$	0	0
$26$	−5.61505	−1.10120
$27$	−1.00000	−0.192450
$28$	3.59420	0.679240
$29$	−3.91167	−0.726379	−0.363190	−	0.931715i	$-0.618312\pi$
$29$	−3.91167	−0.726379	−0.363190	+	0.931715i	$0.618312\pi$
$30$	0	0
$31$	2.70934	0.486612	0.243306	−	0.969950i	$-0.421768\pi$
$31$	2.70934	0.486612	0.243306	+	0.969950i	$0.421768\pi$
$32$	−4.80433	−0.849294
$33$	5.90869	1.02857
$34$	−4.61803	−0.791986
$35$	0	0
$36$	0.911672	0.151945
$37$	0.0208515	0.00342796	0.00171398	−	0.999999i	$-0.499454\pi$
$37$	0.0208515	0.00342796	0.00171398	+	0.999999i	$0.499454\pi$
$38$	−4.02383	−0.652752
$39$	3.29066	0.526927
$40$	0	0
$41$	1.47214	0.229909	0.114955	−	0.993371i	$-0.463328\pi$
$41$	1.47214	0.229909	0.114955	+	0.993371i	$0.463328\pi$
$42$	−6.72721	−1.03803
$43$	−1.27279	−0.194098	−0.0970491	−	0.995280i	$-0.530940\pi$
$43$	−1.27279	−0.194098	−0.0970491	+	0.995280i	$0.530940\pi$
$44$	−5.38679	−0.812089
$45$	0	0
$46$	0.997020	0.147003
$47$	−5.43358	−0.792568	−0.396284	−	0.918128i	$-0.629701\pi$
$47$	−5.43358	−0.792568	−0.396284	+	0.918128i	$0.629701\pi$
$48$	4.99220	0.720562
$49$	8.54276	1.22039
$50$	0	0
$51$	2.70636	0.378967
$52$	−3.00000	−0.416025
$53$	−2.81554	−0.386744	−0.193372	−	0.981125i	$-0.561942\pi$
$53$	−2.81554	−0.386744	−0.193372	+	0.981125i	$0.561942\pi$
$54$	−1.70636	−0.232206
$55$	0	0
$56$	−7.32142	−0.978365
$57$	2.35813	0.312343
$58$	−6.67473	−0.876435
$59$	−4.69033	−0.610629	−0.305315	−	0.952252i	$-0.598762\pi$
$59$	−4.69033	−0.610629	−0.305315	+	0.952252i	$0.598762\pi$
$60$	0	0
$61$	5.58132	0.714614	0.357307	−	0.933987i	$-0.383695\pi$
$61$	5.58132	0.714614	0.357307	+	0.933987i	$0.383695\pi$
$62$	4.62312	0.587137
$63$	3.94243	0.496700
$64$	1.78646	0.223308
$65$	0	0
$66$	10.0824	1.24105
$67$	−6.03076	−0.736774	−0.368387	−	0.929672i	$-0.620090\pi$
$67$	−6.03076	−0.736774	−0.368387	+	0.929672i	$0.620090\pi$
$68$	−2.46731	−0.299206
$69$	−0.584296	−0.0703409
$70$	0	0
$71$	−8.10138	−0.961457	−0.480728	−	0.876870i	$-0.659628\pi$
$71$	−8.10138	−0.961457	−0.480728	+	0.876870i	$0.659628\pi$
$72$	−1.85708	−0.218859
$73$	−13.3166	−1.55859	−0.779295	−	0.626658i	$-0.784422\pi$
$73$	−13.3166	−1.55859	−0.779295	+	0.626658i	$0.784422\pi$
$74$	0.0355801	0.00413611
$75$	0	0
$76$	−2.14984	−0.246604
$77$	−23.2946	−2.65467
$78$	5.61505	0.635780
$79$	16.6648	1.87494	0.937469	−	0.348067i	$-0.113162\pi$
$79$	16.6648	1.87494	0.937469	+	0.348067i	$0.113162\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.51200	0.277404
$83$	−0.781641	−0.0857962	−0.0428981	−	0.999079i	$-0.513659\pi$
$83$	−0.781641	−0.0857962	−0.0428981	+	0.999079i	$0.513659\pi$
$84$	−3.59420	−0.392160
$85$	0	0
$86$	−2.17183	−0.234195
$87$	3.91167	0.419375
$88$	10.9729	1.16972
$89$	−3.47327	−0.368166	−0.184083	−	0.982911i	$-0.558932\pi$
$89$	−3.47327	−0.368166	−0.184083	+	0.982911i	$0.558932\pi$
$90$	0	0
$91$	−12.9732	−1.35996
$92$	0.532686	0.0555363
$93$	−2.70934	−0.280946
$94$	−9.27165	−0.956297
$95$	0	0
$96$	4.80433	0.490340
$97$	2.45443	0.249209	0.124605	−	0.992206i	$-0.460234\pi$
$97$	2.45443	0.249209	0.124605	+	0.992206i	$0.460234\pi$
$98$	14.5770	1.47250
$99$	−5.90869	−0.593846
$100$	0	0
$101$	−6.87495	−0.684083	−0.342042	−	0.939685i	$-0.611118\pi$
$101$	−6.87495	−0.684083	−0.342042	+	0.939685i	$0.611118\pi$
$102$	4.61803	0.457254
$103$	−11.7532	−1.15807	−0.579036	−	0.815302i	$-0.696571\pi$
$103$	−11.7532	−1.15807	−0.579036	+	0.815302i	$0.696571\pi$
$104$	6.11102	0.599235
$105$	0	0
$106$	−4.80433	−0.466638
$107$	−5.66780	−0.547927	−0.273964	−	0.961740i	$-0.588335\pi$
$107$	−5.66780	−0.547927	−0.273964	+	0.961740i	$0.588335\pi$
$108$	−0.911672	−0.0877257
$109$	−1.36128	−0.130387	−0.0651934	−	0.997873i	$-0.520766\pi$
$109$	−1.36128	−0.130387	−0.0651934	+	0.997873i	$0.520766\pi$
$110$	0	0
$111$	−0.0208515	−0.00197913
$112$	−19.6814	−1.85972
$113$	10.6857	1.00522	0.502612	−	0.864512i	$-0.332373\pi$
$113$	10.6857	1.00522	0.502612	+	0.864512i	$0.332373\pi$
$114$	4.02383	0.376866
$115$	0	0
$116$	−3.56616	−0.331110
$117$	−3.29066	−0.304221
$118$	−8.00341	−0.736773
$119$	−10.6696	−0.978085
$120$	0	0
$121$	23.9126	2.17388
$122$	9.52375	0.862239
$123$	−1.47214	−0.132738
$124$	2.47003	0.221815
$125$	0	0
$126$	6.72721	0.599308
$127$	13.5428	1.20173	0.600863	−	0.799352i	$-0.294824\pi$
$127$	13.5428	1.20173	0.600863	+	0.799352i	$0.294824\pi$
$128$	12.6570	1.11873
$129$	1.27279	0.112063
$130$	0	0
$131$	4.59236	0.401236	0.200618	−	0.979670i	$-0.435705\pi$
$131$	4.59236	0.401236	0.200618	+	0.979670i	$0.435705\pi$
$132$	5.38679	0.468860
$133$	−9.29678	−0.806133
$134$	−10.2907	−0.888977
$135$	0	0
$136$	5.02594	0.430970
$137$	−15.2620	−1.30392	−0.651961	−	0.758253i	$-0.726053\pi$
$137$	−15.2620	−1.30392	−0.651961	+	0.758253i	$0.726053\pi$
$138$	−0.997020	−0.0848720
$139$	18.2382	1.54694	0.773471	−	0.633832i	$-0.218519\pi$
$139$	18.2382	1.54694	0.773471	+	0.633832i	$0.218519\pi$
$140$	0	0
$141$	5.43358	0.457590
$142$	−13.8239	−1.16007
$143$	19.4435	1.62595
$144$	−4.99220	−0.416017
$145$	0	0
$146$	−22.7229	−1.88056
$147$	−8.54276	−0.704595
$148$	0.0190097	0.00156259
$149$	14.7323	1.20692	0.603458	−	0.797394i	$-0.293789\pi$
$149$	14.7323	1.20692	0.603458	+	0.797394i	$0.293789\pi$
$150$	0	0
$151$	−17.4354	−1.41887	−0.709437	−	0.704769i	$-0.751051\pi$
$151$	−17.4354	−1.41887	−0.709437	+	0.704769i	$0.751051\pi$
$152$	4.37925	0.355204
$153$	−2.70636	−0.218796
$154$	−39.7490	−3.20307
$155$	0	0
$156$	3.00000	0.240192
$157$	−17.9105	−1.42942	−0.714708	−	0.699423i	$-0.753440\pi$
$157$	−17.9105	−1.42942	−0.714708	+	0.699423i	$0.753440\pi$
$158$	28.4362	2.26226
$159$	2.81554	0.223287
$160$	0	0
$161$	2.30354	0.181545
$162$	1.70636	0.134064
$163$	−21.7598	−1.70436	−0.852180	−	0.523249i	$-0.824720\pi$
$163$	−21.7598	−1.70436	−0.852180	+	0.523249i	$0.824720\pi$
$164$	1.34210	0.104801
$165$	0	0
$166$	−1.33376	−0.103520
$167$	22.6030	1.74907	0.874535	−	0.484962i	$-0.161167\pi$
$167$	22.6030	1.74907	0.874535	+	0.484962i	$0.161167\pi$
$168$	7.32142	0.564860
$169$	−2.17157	−0.167044
$170$	0	0
$171$	−2.35813	−0.180331
$172$	−1.16036	−0.0884769
$173$	−12.9117	−0.981656	−0.490828	−	0.871256i	$-0.663306\pi$
$173$	−12.9117	−0.981656	−0.490828	+	0.871256i	$0.663306\pi$
$174$	6.67473	0.506010
$175$	0	0
$176$	29.4974	2.22345
$177$	4.69033	0.352547
$178$	−5.92666	−0.444222
$179$	−6.43060	−0.480645	−0.240323	−	0.970693i	$-0.577253\pi$
$179$	−6.43060	−0.480645	−0.240323	+	0.970693i	$0.577253\pi$
$180$	0	0
$181$	14.7071	1.09317	0.546584	−	0.837404i	$-0.315928\pi$
$181$	14.7071	1.09317	0.546584	+	0.837404i	$0.315928\pi$
$182$	−22.1370	−1.64090
$183$	−5.58132	−0.412583
$184$	−1.08508	−0.0799935
$185$	0	0
$186$	−4.62312	−0.338984
$187$	15.9911	1.16938
$188$	−4.95364	−0.361281
$189$	−3.94243	−0.286770
$190$	0	0
$191$	6.71303	0.485737	0.242869	−	0.970059i	$-0.421912\pi$
$191$	6.71303	0.485737	0.242869	+	0.970059i	$0.421912\pi$
$192$	−1.78646	−0.128927
$193$	−4.82817	−0.347539	−0.173769	−	0.984786i	$-0.555595\pi$
$193$	−4.82817	−0.347539	−0.173769	+	0.984786i	$0.555595\pi$
$194$	4.18814	0.300691
$195$	0	0
$196$	7.78819	0.556299
$197$	14.3841	1.02482	0.512411	−	0.858740i	$-0.328752\pi$
$197$	14.3841	1.02482	0.512411	+	0.858740i	$0.328752\pi$
$198$	−10.0824	−0.716523
$199$	−8.72608	−0.618575	−0.309288	−	0.950969i	$-0.600091\pi$
$199$	−8.72608	−0.618575	−0.309288	+	0.950969i	$0.600091\pi$
$200$	0	0
$201$	6.03076	0.425377
$202$	−11.7312	−0.825402
$203$	−15.4215	−1.08238
$204$	2.46731	0.172747
$205$	0	0
$206$	−20.0551	−1.39731
$207$	0.584296	0.0406114
$208$	16.4276	1.13905
$209$	13.9335	0.963800
$210$	0	0
$211$	2.97617	0.204888	0.102444	−	0.994739i	$-0.467334\pi$
$211$	2.97617	0.204888	0.102444	+	0.994739i	$0.467334\pi$
$212$	−2.56685	−0.176292
$213$	8.10138	0.555097
$214$	−9.67132	−0.661118
$215$	0	0
$216$	1.85708	0.126358
$217$	10.6814	0.725100
$218$	−2.32283	−0.157322
$219$	13.3166	0.899852
$220$	0	0
$221$	8.90571	0.599063
$222$	−0.0355801	−0.00238798
$223$	0.304683	0.0204031	0.0102015	−	0.999948i	$-0.496753\pi$
$223$	0.304683	0.0204031	0.0102015	+	0.999948i	$0.496753\pi$
$224$	−18.9408	−1.26553
$225$	0	0
$226$	18.2336	1.21288
$227$	9.57221	0.635330	0.317665	−	0.948203i	$-0.397101\pi$
$227$	9.57221	0.635330	0.317665	+	0.948203i	$0.397101\pi$
$228$	2.14984	0.142377
$229$	12.1292	0.801517	0.400759	−	0.916184i	$-0.368747\pi$
$229$	12.1292	0.801517	0.400759	+	0.916184i	$0.368747\pi$
$230$	0	0
$231$	23.2946	1.53267
$232$	7.26430	0.476924
$233$	−20.1002	−1.31681	−0.658405	−	0.752664i	$-0.728769\pi$
$233$	−20.1002	−1.31681	−0.658405	+	0.752664i	$0.728769\pi$
$234$	−5.61505	−0.367068
$235$	0	0
$236$	−4.27604	−0.278347
$237$	−16.6648	−1.08250
$238$	−18.2063	−1.18014
$239$	17.6637	1.14257	0.571284	−	0.820752i	$-0.306445\pi$
$239$	17.6637	1.14257	0.571284	+	0.820752i	$0.306445\pi$
$240$	0	0
$241$	29.5387	1.90276	0.951379	−	0.308024i	$-0.0996676\pi$
$241$	29.5387	1.90276	0.951379	+	0.308024i	$0.0996676\pi$
$242$	40.8036	2.62296
$243$	−1.00000	−0.0641500
$244$	5.08833	0.325747
$245$	0	0
$246$	−2.51200	−0.160159
$247$	7.75981	0.493745
$248$	−5.03147	−0.319499
$249$	0.781641	0.0495345
$250$	0	0
$251$	1.89396	0.119546	0.0597729	−	0.998212i	$-0.480962\pi$
$251$	1.89396	0.119546	0.0597729	+	0.998212i	$0.480962\pi$
$252$	3.59420	0.226413
$253$	−3.45242	−0.217052
$254$	23.1088	1.44998
$255$	0	0
$256$	18.0245	1.12653
$257$	−22.1211	−1.37988	−0.689938	−	0.723869i	$-0.742362\pi$
$257$	−22.1211	−1.37988	−0.689938	+	0.723869i	$0.742362\pi$
$258$	2.17183	0.135213
$259$	0.0822054	0.00510799
$260$	0	0
$261$	−3.91167	−0.242126
$262$	7.83623	0.484124
$263$	19.7153	1.21570	0.607849	−	0.794053i	$-0.292033\pi$
$263$	19.7153	1.21570	0.607849	+	0.794053i	$0.292033\pi$
$264$	−10.9729	−0.675337
$265$	0	0
$266$	−15.8637	−0.972664
$267$	3.47327	0.212561
$268$	−5.49807	−0.335848
$269$	18.1647	1.10752	0.553762	−	0.832675i	$-0.313192\pi$
$269$	18.1647	1.10752	0.553762	+	0.832675i	$0.313192\pi$
$270$	0	0
$271$	22.5695	1.37100	0.685500	−	0.728073i	$-0.259584\pi$
$271$	22.5695	1.37100	0.685500	+	0.728073i	$0.259584\pi$
$272$	13.5107	0.819206
$273$	12.9732	0.785173
$274$	−26.0425	−1.57329
$275$	0	0
$276$	−0.532686	−0.0320639
$277$	−8.25491	−0.495990	−0.247995	−	0.968761i	$-0.579772\pi$
$277$	−8.25491	−0.495990	−0.247995	+	0.968761i	$0.579772\pi$
$278$	31.1209	1.86651
$279$	2.70934	0.162204
$280$	0	0
$281$	1.28129	0.0764355	0.0382177	−	0.999269i	$-0.487832\pi$
$281$	1.28129	0.0764355	0.0382177	+	0.999269i	$0.487832\pi$
$282$	9.27165	0.552119
$283$	−2.67132	−0.158794	−0.0793968	−	0.996843i	$-0.525299\pi$
$283$	−2.67132	−0.158794	−0.0793968	+	0.996843i	$0.525299\pi$
$284$	−7.38580	−0.438266
$285$	0	0
$286$	33.1776	1.96183
$287$	5.80379	0.342587
$288$	−4.80433	−0.283098
$289$	−9.67560	−0.569153
$290$	0	0
$291$	−2.45443	−0.143881
$292$	−12.1404	−0.710461
$293$	−17.6605	−1.03174	−0.515870	−	0.856667i	$-0.672531\pi$
$293$	−17.6605	−1.03174	−0.515870	+	0.856667i	$0.672531\pi$
$294$	−14.5770	−0.850150
$295$	0	0
$296$	−0.0387229	−0.00225072
$297$	5.90869	0.342857
$298$	25.1386	1.45624
$299$	−1.92272	−0.111194
$300$	0	0
$301$	−5.01787	−0.289225
$302$	−29.7511	−1.71199
$303$	6.87495	0.394956
$304$	11.7723	0.675186
$305$	0	0
$306$	−4.61803	−0.263995
$307$	28.5593	1.62997	0.814983	−	0.579484i	$-0.196746\pi$
$307$	28.5593	1.62997	0.814983	+	0.579484i	$0.196746\pi$
$308$	−21.2370	−1.21009
$309$	11.7532	0.668613
$310$	0	0
$311$	−29.3283	−1.66306	−0.831529	−	0.555482i	$-0.812534\pi$
$311$	−29.3283	−1.66306	−0.831529	+	0.555482i	$0.812534\pi$
$312$	−6.11102	−0.345968
$313$	17.4933	0.988777	0.494388	−	0.869241i	$-0.335392\pi$
$313$	17.4933	0.988777	0.494388	+	0.869241i	$0.335392\pi$
$314$	−30.5619	−1.72471
$315$	0	0
$316$	15.1928	0.854665
$317$	−3.91763	−0.220036	−0.110018	−	0.993930i	$-0.535091\pi$
$317$	−3.91763	−0.220036	−0.110018	+	0.993930i	$0.535091\pi$
$318$	4.80433	0.269414
$319$	23.1129	1.29407
$320$	0	0
$321$	5.66780	0.316346
$322$	3.93068	0.219048
$323$	6.38197	0.355102
$324$	0.911672	0.0506484
$325$	0	0
$326$	−37.1301	−2.05645
$327$	1.36128	0.0752788
$328$	−2.73388	−0.150953
$329$	−21.4215	−1.18101
$330$	0	0
$331$	−17.5534	−0.964820	−0.482410	−	0.875945i	$-0.660238\pi$
$331$	−17.5534	−0.964820	−0.482410	+	0.875945i	$0.660238\pi$
$332$	−0.712600	−0.0391090
$333$	0.0208515	0.00114265
$334$	38.5689	2.11039
$335$	0	0
$336$	19.6814	1.07371
$337$	14.0476	0.765221	0.382611	−	0.923910i	$-0.375025\pi$
$337$	14.0476	0.765221	0.382611	+	0.923910i	$0.375025\pi$
$338$	−3.70549	−0.201552
$339$	−10.6857	−0.580366
$340$	0	0
$341$	−16.0087	−0.866918
$342$	−4.02383	−0.217584
$343$	6.08221	0.328408
$344$	2.36367	0.127440
$345$	0	0
$346$	−22.0320	−1.18445
$347$	1.03050	0.0553199	0.0276599	−	0.999617i	$-0.491194\pi$
$347$	1.03050	0.0553199	0.0276599	+	0.999617i	$0.491194\pi$
$348$	3.56616	0.191166
$349$	21.5626	1.15422	0.577109	−	0.816667i	$-0.304181\pi$
$349$	21.5626	1.15422	0.577109	+	0.816667i	$0.304181\pi$
$350$	0	0
$351$	3.29066	0.175642
$352$	28.3873	1.51305
$353$	−7.15625	−0.380888	−0.190444	−	0.981698i	$-0.560993\pi$
$353$	−7.15625	−0.380888	−0.190444	+	0.981698i	$0.560993\pi$
$354$	8.00341	0.425376
$355$	0	0
$356$	−3.16649	−0.167823
$357$	10.6696	0.564697
$358$	−10.9729	−0.579937
$359$	27.1518	1.43302	0.716510	−	0.697577i	$-0.245738\pi$
$359$	27.1518	1.43302	0.716510	+	0.697577i	$0.245738\pi$
$360$	0	0
$361$	−13.4392	−0.707326
$362$	25.0956	1.31899
$363$	−23.9126	−1.25509
$364$	−11.8273	−0.619918
$365$	0	0
$366$	−9.52375	−0.497814
$367$	−21.4423	−1.11928	−0.559641	−	0.828735i	$-0.689061\pi$
$367$	−21.4423	−1.11928	−0.559641	+	0.828735i	$0.689061\pi$
$368$	−2.91692	−0.152055
$369$	1.47214	0.0766363
$370$	0	0
$371$	−11.1001	−0.576287
$372$	−2.47003	−0.128065
$373$	−6.39073	−0.330900	−0.165450	−	0.986218i	$-0.552908\pi$
$373$	−6.39073	−0.330900	−0.165450	+	0.986218i	$0.552908\pi$
$374$	27.2865	1.41095
$375$	0	0
$376$	10.0906	0.520383
$377$	12.8720	0.662940
$378$	−6.72721	−0.346011
$379$	−0.154667	−0.00794469	−0.00397235	−	0.999992i	$-0.501264\pi$
$379$	−0.154667	−0.00794469	−0.00397235	+	0.999992i	$0.501264\pi$
$380$	0	0
$381$	−13.5428	−0.693816
$382$	11.4549	0.586081
$383$	4.25508	0.217424	0.108712	−	0.994073i	$-0.465327\pi$
$383$	4.25508	0.217424	0.108712	+	0.994073i	$0.465327\pi$
$384$	−12.6570	−0.645901
$385$	0	0
$386$	−8.23860	−0.419334
$387$	−1.27279	−0.0646994
$388$	2.23763	0.113599
$389$	−20.3682	−1.03271	−0.516354	−	0.856375i	$-0.672711\pi$
$389$	−20.3682	−1.03271	−0.516354	+	0.856375i	$0.672711\pi$
$390$	0	0
$391$	−1.58132	−0.0799706
$392$	−15.8646	−0.801283
$393$	−4.59236	−0.231654
$394$	24.5444	1.23653
$395$	0	0
$396$	−5.38679	−0.270696
$397$	1.95716	0.0982270	0.0491135	−	0.998793i	$-0.484360\pi$
$397$	1.95716	0.0982270	0.0491135	+	0.998793i	$0.484360\pi$
$398$	−14.8898	−0.746360
$399$	9.29678	0.465421
$400$	0	0
$401$	−32.8337	−1.63964	−0.819818	−	0.572624i	$-0.805925\pi$
$401$	−32.8337	−1.63964	−0.819818	+	0.572624i	$0.805925\pi$
$402$	10.2907	0.513251
$403$	−8.91552	−0.444114
$404$	−6.26770	−0.311830
$405$	0	0
$406$	−26.3147	−1.30597
$407$	−0.123205	−0.00610704
$408$	−5.02594	−0.248821
$409$	−39.5764	−1.95693	−0.978464	−	0.206417i	$-0.933820\pi$
$409$	−39.5764	−1.95693	−0.978464	+	0.206417i	$0.933820\pi$
$410$	0	0
$411$	15.2620	0.752819
$412$	−10.7150	−0.527891
$413$	−18.4913	−0.909898
$414$	0.997020	0.0490009
$415$	0	0
$416$	15.8094	0.775121
$417$	−18.2382	−0.893127
$418$	23.7756	1.16290
$419$	19.5595	0.955544	0.477772	−	0.878484i	$-0.341445\pi$
$419$	19.5595	0.955544	0.477772	+	0.878484i	$0.341445\pi$
$420$	0	0
$421$	−40.3325	−1.96568	−0.982842	−	0.184451i	$-0.940949\pi$
$421$	−40.3325	−1.96568	−0.982842	+	0.184451i	$0.940949\pi$
$422$	5.07842	0.247214
$423$	−5.43358	−0.264189
$424$	5.22869	0.253928
$425$	0	0
$426$	13.8239	0.669769
$427$	22.0039	1.06485
$428$	−5.16718	−0.249765
$429$	−19.4435	−0.938740
$430$	0	0
$431$	13.7370	0.661689	0.330844	−	0.943685i	$-0.392666\pi$
$431$	13.7370	0.661689	0.330844	+	0.943685i	$0.392666\pi$
$432$	4.99220	0.240187
$433$	12.4253	0.597124	0.298562	−	0.954390i	$-0.403493\pi$
$433$	12.4253	0.597124	0.298562	+	0.954390i	$0.403493\pi$
$434$	18.2263	0.874892
$435$	0	0
$436$	−1.24104	−0.0594349
$437$	−1.37785	−0.0659114
$438$	22.7229	1.08574
$439$	10.9654	0.523349	0.261675	−	0.965156i	$-0.415725\pi$
$439$	10.9654	0.523349	0.261675	+	0.965156i	$0.415725\pi$
$440$	0	0
$441$	8.54276	0.406798
$442$	15.1964	0.722818
$443$	−8.13187	−0.386357	−0.193178	−	0.981164i	$-0.561880\pi$
$443$	−8.13187	−0.386357	−0.193178	+	0.981164i	$0.561880\pi$
$444$	−0.0190097	−0.000902160 0
$445$	0	0
$446$	0.519899	0.0246180
$447$	−14.7323	−0.696814
$448$	7.04300	0.332751
$449$	−32.9503	−1.55502	−0.777511	−	0.628869i	$-0.783518\pi$
$449$	−32.9503	−1.55502	−0.777511	+	0.628869i	$0.783518\pi$
$450$	0	0
$451$	−8.69840	−0.409592
$452$	9.74183	0.458217
$453$	17.4354	0.819187
$454$	16.3337	0.766577
$455$	0	0
$456$	−4.37925	−0.205077
$457$	22.8800	1.07028	0.535142	−	0.844762i	$-0.320258\pi$
$457$	22.8800	1.07028	0.535142	+	0.844762i	$0.320258\pi$
$458$	20.6967	0.967095
$459$	2.70636	0.126322
$460$	0	0
$461$	12.0425	0.560875	0.280438	−	0.959872i	$-0.409520\pi$
$461$	12.0425	0.560875	0.280438	+	0.959872i	$0.409520\pi$
$462$	39.7490	1.84929
$463$	27.2002	1.26410	0.632049	−	0.774928i	$-0.282214\pi$
$463$	27.2002	1.26410	0.632049	+	0.774928i	$0.282214\pi$
$464$	19.5278	0.906557
$465$	0	0
$466$	−34.2983	−1.58884
$467$	3.94243	0.182434	0.0912170	−	0.995831i	$-0.470924\pi$
$467$	3.94243	0.182434	0.0912170	+	0.995831i	$0.470924\pi$
$468$	−3.00000	−0.138675
$469$	−23.7758	−1.09787
$470$	0	0
$471$	17.9105	0.825274
$472$	8.71033	0.400926
$473$	7.52050	0.345793
$474$	−28.4362	−1.30612
$475$	0	0
$476$	−9.72721	−0.445846
$477$	−2.81554	−0.128915
$478$	30.1406	1.37860
$479$	19.9493	0.911505	0.455752	−	0.890107i	$-0.349370\pi$
$479$	19.9493	0.911505	0.455752	+	0.890107i	$0.349370\pi$
$480$	0	0
$481$	−0.0686150	−0.00312857
$482$	50.4038	2.29583
$483$	−2.30354	−0.104815
$484$	21.8005	0.990931
$485$	0	0
$486$	−1.70636	−0.0774022
$487$	11.0023	0.498560	0.249280	−	0.968431i	$-0.419806\pi$
$487$	11.0023	0.498560	0.249280	+	0.968431i	$0.419806\pi$
$488$	−10.3650	−0.469200
$489$	21.7598	0.984013
$490$	0	0
$491$	−33.2933	−1.50251	−0.751253	−	0.660014i	$-0.770550\pi$
$491$	−33.2933	−1.50251	−0.751253	+	0.660014i	$0.770550\pi$
$492$	−1.34210	−0.0605068
$493$	10.5864	0.476788
$494$	13.2411	0.595743
$495$	0	0
$496$	−13.5256	−0.607316
$497$	−31.9391	−1.43267
$498$	1.33376	0.0597673
$499$	−41.1448	−1.84189	−0.920946	−	0.389690i	$-0.872582\pi$
$499$	−41.1448	−1.84189	−0.920946	+	0.389690i	$0.872582\pi$
$500$	0	0
$501$	−22.6030	−1.00983
$502$	3.23179	0.144242
$503$	−32.0761	−1.43020	−0.715102	−	0.699020i	$-0.753620\pi$
$503$	−32.0761	−1.43020	−0.715102	+	0.699020i	$0.753620\pi$
$504$	−7.32142	−0.326122
$505$	0	0
$506$	−5.89108	−0.261891
$507$	2.17157	0.0964429
$508$	12.3465	0.547790
$509$	−27.0953	−1.20098	−0.600489	−	0.799633i	$-0.705028\pi$
$509$	−27.0953	−1.20098	−0.600489	+	0.799633i	$0.705028\pi$
$510$	0	0
$511$	−52.4997	−2.32245
$512$	5.44234	0.240520
$513$	2.35813	0.104114
$514$	−37.7466	−1.66493
$515$	0	0
$516$	1.16036	0.0510822
$517$	32.1053	1.41199
$518$	0.140272	0.00616321
$519$	12.9117	0.566759
$520$	0	0
$521$	25.9556	1.13714	0.568569	−	0.822636i	$-0.307497\pi$
$521$	25.9556	1.13714	0.568569	+	0.822636i	$0.307497\pi$
$522$	−6.67473	−0.292145
$523$	1.79382	0.0784381	0.0392190	−	0.999231i	$-0.487513\pi$
$523$	1.79382	0.0784381	0.0392190	+	0.999231i	$0.487513\pi$
$524$	4.18673	0.182898
$525$	0	0
$526$	33.6414	1.46684
$527$	−7.33246	−0.319407
$528$	−29.4974	−1.28371
$529$	−22.6586	−0.985156
$530$	0	0
$531$	−4.69033	−0.203543
$532$	−8.47561	−0.367464
$533$	−4.84430	−0.209830
$534$	5.92666	0.256472
$535$	0	0
$536$	11.1996	0.483750
$537$	6.43060	0.277501
$538$	30.9956	1.33632
$539$	−50.4765	−2.17418
$540$	0	0
$541$	−7.43542	−0.319674	−0.159837	−	0.987143i	$-0.551097\pi$
$541$	−7.43542	−0.319674	−0.159837	+	0.987143i	$0.551097\pi$
$542$	38.5117	1.65422
$543$	−14.7071	−0.631141
$544$	13.0023	0.557468
$545$	0	0
$546$	22.1370	0.947374
$547$	−19.4868	−0.833194	−0.416597	−	0.909091i	$-0.636777\pi$
$547$	−19.4868	−0.833194	−0.416597	+	0.909091i	$0.636777\pi$
$548$	−13.9139	−0.594374
$549$	5.58132	0.238205
$550$	0	0
$551$	9.22425	0.392966
$552$	1.08508	0.0461843
$553$	65.6999	2.79384
$554$	−14.0859	−0.598451
$555$	0	0
$556$	16.6272	0.705152
$557$	26.3285	1.11557	0.557787	−	0.829984i	$-0.311650\pi$
$557$	26.3285	1.11557	0.557787	+	0.829984i	$0.311650\pi$
$558$	4.62312	0.195712
$559$	4.18830	0.177146
$560$	0	0
$561$	−15.9911	−0.675143
$562$	2.18635	0.0922255
$563$	−36.7708	−1.54971	−0.774853	−	0.632141i	$-0.782176\pi$
$563$	−36.7708	−1.54971	−0.774853	+	0.632141i	$0.782176\pi$
$564$	4.95364	0.208586
$565$	0	0
$566$	−4.55824	−0.191597
$567$	3.94243	0.165567
$568$	15.0449	0.631271
$569$	−36.2823	−1.52103	−0.760516	−	0.649320i	$-0.775054\pi$
$569$	−36.2823	−1.52103	−0.760516	+	0.649320i	$0.775054\pi$
$570$	0	0
$571$	−3.36442	−0.140797	−0.0703983	−	0.997519i	$-0.522427\pi$
$571$	−3.36442	−0.140797	−0.0703983	+	0.997519i	$0.522427\pi$
$572$	17.7261	0.741164
$573$	−6.71303	−0.280441
$574$	9.90337	0.413359
$575$	0	0
$576$	1.78646	0.0744359
$577$	6.88442	0.286602	0.143301	−	0.989679i	$-0.454228\pi$
$577$	6.88442	0.286602	0.143301	+	0.989679i	$0.454228\pi$
$578$	−16.5101	−0.686729
$579$	4.82817	0.200652
$580$	0	0
$581$	−3.08156	−0.127845
$582$	−4.18814	−0.173604
$583$	16.6362	0.689000
$584$	24.7300	1.02334
$585$	0	0
$586$	−30.1353	−1.24488
$587$	14.7377	0.608288	0.304144	−	0.952626i	$-0.401630\pi$
$587$	14.7377	0.608288	0.304144	+	0.952626i	$0.401630\pi$
$588$	−7.78819	−0.321180
$589$	−6.38899	−0.263254
$590$	0	0
$591$	−14.3841	−0.591682
$592$	−0.104095	−0.00427826
$593$	−5.82561	−0.239229	−0.119615	−	0.992820i	$-0.538166\pi$
$593$	−5.82561	−0.239229	−0.119615	+	0.992820i	$0.538166\pi$
$594$	10.0824	0.413685
$595$	0	0
$596$	13.4310	0.550156
$597$	8.72608	0.357134
$598$	−3.28085	−0.134164
$599$	−27.1527	−1.10943	−0.554715	−	0.832040i	$-0.687173\pi$
$599$	−27.1527	−1.10943	−0.554715	+	0.832040i	$0.687173\pi$
$600$	0	0
$601$	20.9140	0.853101	0.426551	−	0.904464i	$-0.359729\pi$
$601$	20.9140	0.853101	0.426551	+	0.904464i	$0.359729\pi$
$602$	−8.56231	−0.348974
$603$	−6.03076	−0.245591
$604$	−15.8954	−0.646774
$605$	0	0
$606$	11.7312	0.476546
$607$	−1.46424	−0.0594318	−0.0297159	−	0.999558i	$-0.509460\pi$
$607$	−1.46424	−0.0594318	−0.0297159	+	0.999558i	$0.509460\pi$
$608$	11.3293	0.459462
$609$	15.4215	0.624910
$610$	0	0
$611$	17.8800	0.723349
$612$	−2.46731	−0.0997353
$613$	−34.7105	−1.40194	−0.700971	−	0.713189i	$-0.747250\pi$
$613$	−34.7105	−1.40194	−0.700971	+	0.713189i	$0.747250\pi$
$614$	48.7326	1.96669
$615$	0	0
$616$	43.2600	1.74299
$617$	−41.9038	−1.68698	−0.843492	−	0.537142i	$-0.819504\pi$
$617$	−41.9038	−1.68698	−0.843492	+	0.537142i	$0.819504\pi$
$618$	20.0551	0.806736
$619$	−18.7614	−0.754083	−0.377042	−	0.926196i	$-0.623059\pi$
$619$	−18.7614	−0.754083	−0.377042	+	0.926196i	$0.623059\pi$
$620$	0	0
$621$	−0.584296	−0.0234470
$622$	−50.0448	−2.00661
$623$	−13.6931	−0.548604
$624$	−16.4276	−0.657631
$625$	0	0
$626$	29.8498	1.19304
$627$	−13.9335	−0.556450
$628$	−16.3285	−0.651579
$629$	−0.0564316	−0.00225007
$630$	0	0
$631$	9.88888	0.393670	0.196835	−	0.980437i	$-0.436934\pi$
$631$	9.88888	0.393670	0.196835	+	0.980437i	$0.436934\pi$
$632$	−30.9479	−1.23104
$633$	−2.97617	−0.118292
$634$	−6.68490	−0.265491
$635$	0	0
$636$	2.56685	0.101782
$637$	−28.1113	−1.11381
$638$	39.4389	1.56140
$639$	−8.10138	−0.320486
$640$	0	0
$641$	−1.81266	−0.0715959	−0.0357979	−	0.999359i	$-0.511397\pi$
$641$	−1.81266	−0.0715959	−0.0357979	+	0.999359i	$0.511397\pi$
$642$	9.67132	0.381697
$643$	−45.7391	−1.80377	−0.901886	−	0.431974i	$-0.857817\pi$
$643$	−45.7391	−1.80377	−0.901886	+	0.431974i	$0.857817\pi$
$644$	2.10008	0.0827546
$645$	0	0
$646$	10.8899	0.428459
$647$	25.6771	1.00947	0.504736	−	0.863274i	$-0.331590\pi$
$647$	25.6771	1.00947	0.504736	+	0.863274i	$0.331590\pi$
$648$	−1.85708	−0.0729531
$649$	27.7137	1.08786
$650$	0	0
$651$	−10.6814	−0.418637
$652$	−19.8378	−0.776909
$653$	−35.9684	−1.40755	−0.703775	−	0.710422i	$-0.748504\pi$
$653$	−35.9684	−1.40755	−0.703775	+	0.710422i	$0.748504\pi$
$654$	2.32283	0.0908299
$655$	0	0
$656$	−7.34919	−0.286938
$657$	−13.3166	−0.519530
$658$	−36.5528	−1.42498
$659$	−32.0924	−1.25014	−0.625072	−	0.780567i	$-0.714930\pi$
$659$	−32.0924	−1.25014	−0.625072	+	0.780567i	$0.714930\pi$
$660$	0	0
$661$	16.2064	0.630357	0.315179	−	0.949032i	$-0.397936\pi$
$661$	16.2064	0.630357	0.315179	+	0.949032i	$0.397936\pi$
$662$	−29.9524	−1.16413
$663$	−8.90571	−0.345869
$664$	1.45157	0.0563319
$665$	0	0
$666$	0.0355801	0.00137870
$667$	−2.28557	−0.0884977
$668$	20.6065	0.797289
$669$	−0.304683	−0.0117797
$670$	0	0
$671$	−32.9783	−1.27311
$672$	18.9408	0.730655
$673$	−34.1608	−1.31680	−0.658401	−	0.752667i	$-0.728767\pi$
$673$	−34.1608	−1.31680	−0.658401	+	0.752667i	$0.728767\pi$
$674$	23.9703	0.923301
$675$	0	0
$676$	−1.97976	−0.0761446
$677$	−9.17514	−0.352629	−0.176315	−	0.984334i	$-0.556418\pi$
$677$	−9.17514	−0.352629	−0.176315	+	0.984334i	$0.556418\pi$
$678$	−18.2336	−0.700258
$679$	9.67641	0.371346
$680$	0	0
$681$	−9.57221	−0.366808
$682$	−27.3166	−1.04601
$683$	−19.5007	−0.746173	−0.373087	−	0.927797i	$-0.621701\pi$
$683$	−19.5007	−0.746173	−0.373087	+	0.927797i	$0.621701\pi$
$684$	−2.14984	−0.0822014
$685$	0	0
$686$	10.3784	0.396251
$687$	−12.1292	−0.462756
$688$	6.35400	0.242244
$689$	9.26498	0.352968
$690$	0	0
$691$	29.0458	1.10495	0.552477	−	0.833528i	$-0.313683\pi$
$691$	29.0458	1.10495	0.552477	+	0.833528i	$0.313683\pi$
$692$	−11.7712	−0.447474
$693$	−23.2946	−0.884889
$694$	1.75840	0.0667479
$695$	0	0
$696$	−7.26430	−0.275352
$697$	−3.98413	−0.150910
$698$	36.7936	1.39266
$699$	20.1002	0.760261
$700$	0	0
$701$	−20.4085	−0.770820	−0.385410	−	0.922745i	$-0.625940\pi$
$701$	−20.4085	−0.770820	−0.385410	+	0.922745i	$0.625940\pi$
$702$	5.61505	0.211927
$703$	−0.0491705	−0.00185450
$704$	−10.5557	−0.397831
$705$	0	0
$706$	−12.2111	−0.459573
$707$	−27.1040	−1.01935
$708$	4.27604	0.160704
$709$	16.4810	0.618956	0.309478	−	0.950907i	$-0.399846\pi$
$709$	16.4810	0.618956	0.309478	+	0.950907i	$0.399846\pi$
$710$	0	0
$711$	16.6648	0.624980
$712$	6.45016	0.241730
$713$	1.58306	0.0592859
$714$	18.2063	0.681353
$715$	0	0
$716$	−5.86259	−0.219095
$717$	−17.6637	−0.659662
$718$	46.3309	1.72905
$719$	31.0813	1.15914	0.579569	−	0.814923i	$-0.303221\pi$
$719$	31.0813	1.15914	0.579569	+	0.814923i	$0.303221\pi$
$720$	0	0
$721$	−46.3360	−1.72564
$722$	−22.9321	−0.853446
$723$	−29.5387	−1.09856
$724$	13.4080	0.498305
$725$	0	0
$726$	−40.8036	−1.51436
$727$	0.953049	0.0353466	0.0176733	−	0.999844i	$-0.494374\pi$
$727$	0.953049	0.0353466	0.0176733	+	0.999844i	$0.494374\pi$
$728$	24.0923	0.892919
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.44462	0.127404
$732$	−5.08833	−0.188070
$733$	15.3751	0.567893	0.283947	−	0.958840i	$-0.408356\pi$
$733$	15.3751	0.567893	0.283947	+	0.958840i	$0.408356\pi$
$734$	−36.5884	−1.35050
$735$	0	0
$736$	−2.80715	−0.103473
$737$	35.6339	1.31259
$738$	2.51200	0.0924679
$739$	5.19285	0.191022	0.0955110	−	0.995428i	$-0.469551\pi$
$739$	5.19285	0.191022	0.0955110	+	0.995428i	$0.469551\pi$
$740$	0	0
$741$	−7.75981	−0.285064
$742$	−18.9408	−0.695337
$743$	42.3399	1.55330	0.776650	−	0.629932i	$-0.216917\pi$
$743$	42.3399	1.55330	0.776650	+	0.629932i	$0.216917\pi$
$744$	5.03147	0.184463
$745$	0	0
$746$	−10.9049	−0.399257
$747$	−0.781641	−0.0285987
$748$	14.5786	0.533046
$749$	−22.3449	−0.816465
$750$	0	0
$751$	22.2461	0.811773	0.405887	−	0.913923i	$-0.366963\pi$
$751$	22.2461	0.811773	0.405887	+	0.913923i	$0.366963\pi$
$752$	27.1255	0.989165
$753$	−1.89396	−0.0690199
$754$	21.9642	0.799891
$755$	0	0
$756$	−3.59420	−0.130720
$757$	9.27680	0.337171	0.168585	−	0.985687i	$-0.446080\pi$
$757$	9.27680	0.337171	0.168585	+	0.985687i	$0.446080\pi$
$758$	−0.263917	−0.00958591
$759$	3.45242	0.125315
$760$	0	0
$761$	−17.4122	−0.631191	−0.315596	−	0.948894i	$-0.602204\pi$
$761$	−17.4122	−0.631191	−0.315596	+	0.948894i	$0.602204\pi$
$762$	−23.1088	−0.837145
$763$	−5.36674	−0.194289
$764$	6.12008	0.221417
$765$	0	0
$766$	7.26070	0.262340
$767$	15.4343	0.557300
$768$	−18.0245	−0.650404
$769$	−23.1912	−0.836297	−0.418148	−	0.908379i	$-0.637321\pi$
$769$	−23.1912	−0.836297	−0.418148	+	0.908379i	$0.637321\pi$
$770$	0	0
$771$	22.1211	0.796672
$772$	−4.40170	−0.158421
$773$	5.50798	0.198108	0.0990541	−	0.995082i	$-0.468418\pi$
$773$	5.50798	0.198108	0.0990541	+	0.995082i	$0.468418\pi$
$774$	−2.17183	−0.0780650
$775$	0	0
$776$	−4.55807	−0.163625
$777$	−0.0822054	−0.00294910
$778$	−34.7555	−1.24605
$779$	−3.47149	−0.124379
$780$	0	0
$781$	47.8685	1.71287
$782$	−2.69830	−0.0964909
$783$	3.91167	0.139792
$784$	−42.6471	−1.52311
$785$	0	0
$786$	−7.83623	−0.279509
$787$	−25.7971	−0.919568	−0.459784	−	0.888031i	$-0.652073\pi$
$787$	−25.7971	−0.919568	−0.459784	+	0.888031i	$0.652073\pi$
$788$	13.1136	0.467151
$789$	−19.7153	−0.701883
$790$	0	0
$791$	42.1275	1.49788
$792$	10.9729	0.389906
$793$	−18.3662	−0.652203
$794$	3.33962	0.118519
$795$	0	0
$796$	−7.95532	−0.281969
$797$	−3.70988	−0.131411	−0.0657054	−	0.997839i	$-0.520930\pi$
$797$	−3.70988	−0.131411	−0.0657054	+	0.997839i	$0.520930\pi$
$798$	15.8637	0.561568
$799$	14.7052	0.520233
$800$	0	0
$801$	−3.47327	−0.122722
$802$	−56.0261	−1.97835
$803$	78.6837	2.77669
$804$	5.49807	0.193902
$805$	0	0
$806$	−15.2131	−0.535859
$807$	−18.1647	−0.639429
$808$	12.7674	0.449154
$809$	37.5040	1.31857	0.659286	−	0.751893i	$-0.270859\pi$
$809$	37.5040	1.31857	0.659286	+	0.751893i	$0.270859\pi$
$810$	0	0
$811$	45.6159	1.60179	0.800896	−	0.598804i	$-0.204357\pi$
$811$	45.6159	1.60179	0.800896	+	0.598804i	$0.204357\pi$
$812$	−14.0593	−0.493386
$813$	−22.5695	−0.791547
$814$	−0.210232	−0.00736863
$815$	0	0
$816$	−13.5107	−0.472969
$817$	3.00140	0.105006
$818$	−67.5317	−2.36119
$819$	−12.9732	−0.453320
$820$	0	0
$821$	45.0511	1.57229	0.786147	−	0.618039i	$-0.212073\pi$
$821$	45.0511	1.57229	0.786147	+	0.618039i	$0.212073\pi$
$822$	26.0425	0.908337
$823$	41.4573	1.44511	0.722556	−	0.691312i	$-0.242967\pi$
$823$	41.4573	1.44511	0.722556	+	0.691312i	$0.242967\pi$
$824$	21.8266	0.760364
$825$	0	0
$826$	−31.5529	−1.09786
$827$	38.6933	1.34550	0.672749	−	0.739871i	$-0.265113\pi$
$827$	38.6933	1.34550	0.672749	+	0.739871i	$0.265113\pi$
$828$	0.532686	0.0185121
$829$	24.1258	0.837922	0.418961	−	0.908004i	$-0.362394\pi$
$829$	24.1258	0.837922	0.418961	+	0.908004i	$0.362394\pi$
$830$	0	0
$831$	8.25491	0.286360
$832$	−5.87864	−0.203805
$833$	−23.1198	−0.801053
$834$	−31.1209	−1.07763
$835$	0	0
$836$	12.7028	0.439334
$837$	−2.70934	−0.0936486
$838$	33.3756	1.15294
$839$	−17.7858	−0.614032	−0.307016	−	0.951704i	$-0.599331\pi$
$839$	−17.7858	−0.614032	−0.307016	+	0.951704i	$0.599331\pi$
$840$	0	0
$841$	−13.6988	−0.472373
$842$	−68.8218	−2.37175
$843$	−1.28129	−0.0441300
$844$	2.71329	0.0933953
$845$	0	0
$846$	−9.27165	−0.318766
$847$	94.2739	3.23929
$848$	14.0557	0.482676
$849$	2.67132	0.0916796
$850$	0	0
$851$	0.0121834	0.000417642 0
$852$	7.38580	0.253033
$853$	−12.8433	−0.439745	−0.219872	−	0.975529i	$-0.570564\pi$
$853$	−12.8433	−0.439745	−0.219872	+	0.975529i	$0.570564\pi$
$854$	37.5467	1.28482
$855$	0	0
$856$	10.5256	0.359757
$857$	15.6015	0.532936	0.266468	−	0.963844i	$-0.414143\pi$
$857$	15.6015	0.532936	0.266468	+	0.963844i	$0.414143\pi$
$858$	−33.1776	−1.13267
$859$	4.82843	0.164744	0.0823719	−	0.996602i	$-0.473750\pi$
$859$	4.82843	0.164744	0.0823719	+	0.996602i	$0.473750\pi$
$860$	0	0
$861$	−5.80379	−0.197793
$862$	23.4403	0.798381
$863$	13.1548	0.447796	0.223898	−	0.974613i	$-0.428122\pi$
$863$	13.1548	0.447796	0.223898	+	0.974613i	$0.428122\pi$
$864$	4.80433	0.163447
$865$	0	0
$866$	21.2021	0.720478
$867$	9.67560	0.328601
$868$	9.73792	0.330527
$869$	−98.4673	−3.34027
$870$	0	0
$871$	19.8452	0.672428
$872$	2.52800	0.0856090
$873$	2.45443	0.0830698
$874$	−2.35111	−0.0795274
$875$	0	0
$876$	12.1404	0.410185
$877$	−6.25253	−0.211133	−0.105567	−	0.994412i	$-0.533666\pi$
$877$	−6.25253	−0.211133	−0.105567	+	0.994412i	$0.533666\pi$
$878$	18.7109	0.631463
$879$	17.6605	0.595675
$880$	0	0
$881$	−16.7801	−0.565335	−0.282667	−	0.959218i	$-0.591219\pi$
$881$	−16.7801	−0.565335	−0.282667	+	0.959218i	$0.591219\pi$
$882$	14.5770	0.490834
$883$	−16.2367	−0.546407	−0.273203	−	0.961956i	$-0.588083\pi$
$883$	−16.2367	−0.546407	−0.273203	+	0.961956i	$0.588083\pi$
$884$	8.11909	0.273074
$885$	0	0
$886$	−13.8759	−0.466171
$887$	−57.6873	−1.93695	−0.968476	−	0.249108i	$-0.919863\pi$
$887$	−57.6873	−1.93695	−0.968476	+	0.249108i	$0.919863\pi$
$888$	0.0387229	0.00129945
$889$	53.3914	1.79069
$890$	0	0
$891$	−5.90869	−0.197949
$892$	0.277771	0.00930046
$893$	12.8131	0.428774
$894$	−25.1386	−0.840762
$895$	0	0
$896$	49.8994	1.66702
$897$	1.92272	0.0641977
$898$	−56.2252	−1.87626
$899$	−10.5981	−0.353465
$900$	0	0
$901$	7.61988	0.253855
$902$	−14.8426	−0.494205
$903$	5.01787	0.166984
$904$	−19.8442	−0.660007
$905$	0	0
$906$	29.7511	0.988415
$907$	−9.00465	−0.298995	−0.149497	−	0.988762i	$-0.547766\pi$
$907$	−9.00465	−0.298995	−0.149497	+	0.988762i	$0.547766\pi$
$908$	8.72672	0.289606
$909$	−6.87495	−0.228028
$910$	0	0
$911$	29.9503	0.992298	0.496149	−	0.868237i	$-0.334747\pi$
$911$	29.9503	0.992298	0.496149	+	0.868237i	$0.334747\pi$
$912$	−11.7723	−0.389819
$913$	4.61847	0.152849
$914$	39.0416	1.29138
$915$	0	0
$916$	11.0578	0.365360
$917$	18.1051	0.597882
$918$	4.61803	0.152418
$919$	8.93560	0.294758	0.147379	−	0.989080i	$-0.452916\pi$
$919$	8.93560	0.294758	0.147379	+	0.989080i	$0.452916\pi$
$920$	0	0
$921$	−28.5593	−0.941062
$922$	20.5489	0.676741
$923$	26.6589	0.877487
$924$	21.2370	0.698647
$925$	0	0
$926$	46.4133	1.52524
$927$	−11.7532	−0.386024
$928$	18.7930	0.616910
$929$	−41.4596	−1.36025	−0.680123	−	0.733098i	$-0.738074\pi$
$929$	−41.4596	−1.36025	−0.680123	+	0.733098i	$0.738074\pi$
$930$	0	0
$931$	−20.1450	−0.660225
$932$	−18.3248	−0.600250
$933$	29.3283	0.960167
$934$	6.72721	0.220121
$935$	0	0
$936$	6.11102	0.199745
$937$	−20.8585	−0.681417	−0.340709	−	0.940169i	$-0.610667\pi$
$937$	−20.8585	−0.681417	−0.340709	+	0.940169i	$0.610667\pi$
$938$	−40.5702	−1.32466
$939$	−17.4933	−0.570871
$940$	0	0
$941$	3.67382	0.119763	0.0598816	−	0.998205i	$-0.480928\pi$
$941$	3.67382	0.119763	0.0598816	+	0.998205i	$0.480928\pi$
$942$	30.5619	0.995759
$943$	0.860163	0.0280107
$944$	23.4151	0.762096
$945$	0	0
$946$	12.8327	0.417227
$947$	31.6997	1.03010	0.515051	−	0.857160i	$-0.327773\pi$
$947$	31.6997	1.03010	0.515051	+	0.857160i	$0.327773\pi$
$948$	−15.1928	−0.493441
$949$	43.8204	1.42247
$950$	0	0
$951$	3.91763	0.127038
$952$	19.8144	0.642189
$953$	−25.6214	−0.829960	−0.414980	−	0.909831i	$-0.636211\pi$
$953$	−25.6214	−0.829960	−0.414980	+	0.909831i	$0.636211\pi$
$954$	−4.80433	−0.155546
$955$	0	0
$956$	16.1035	0.520824
$957$	−23.1129	−0.747133
$958$	34.0407	1.09980
$959$	−60.1694	−1.94297
$960$	0	0
$961$	−23.6595	−0.763209
$962$	−0.117082	−0.00377488
$963$	−5.66780	−0.182642
$964$	26.9296	0.867345
$965$	0	0
$966$	−3.93068	−0.126468
$967$	29.0166	0.933112	0.466556	−	0.884492i	$-0.345495\pi$
$967$	29.0166	0.933112	0.466556	+	0.884492i	$0.345495\pi$
$968$	−44.4077	−1.42732
$969$	−6.38197	−0.205018
$970$	0	0
$971$	−3.77287	−0.121077	−0.0605386	−	0.998166i	$-0.519282\pi$
$971$	−3.77287	−0.121077	−0.0605386	+	0.998166i	$0.519282\pi$
$972$	−0.911672	−0.0292419
$973$	71.9027	2.30510
$974$	18.7739	0.601553
$975$	0	0
$976$	−27.8630	−0.891874
$977$	−36.7167	−1.17467	−0.587336	−	0.809343i	$-0.699823\pi$
$977$	−36.7167	−1.17467	−0.587336	+	0.809343i	$0.699823\pi$
$978$	37.1301	1.18729
$979$	20.5225	0.655902
$980$	0	0
$981$	−1.36128	−0.0434622
$982$	−56.8104	−1.81289
$983$	−23.5627	−0.751534	−0.375767	−	0.926714i	$-0.622621\pi$
$983$	−23.5627	−0.751534	−0.375767	+	0.926714i	$0.622621\pi$
$984$	2.73388	0.0871528
$985$	0	0
$986$	18.0642	0.575282
$987$	21.4215	0.681854
$988$	7.07440	0.225067
$989$	−0.743684	−0.0236478
$990$	0	0
$991$	29.1375	0.925583	0.462791	−	0.886467i	$-0.346848\pi$
$991$	29.1375	0.925583	0.462791	+	0.886467i	$0.346848\pi$
$992$	−13.0166	−0.413277
$993$	17.5534	0.557039
$994$	−54.4997	−1.72863
$995$	0	0
$996$	0.712600	0.0225796
$997$	−43.9240	−1.39109	−0.695544	−	0.718484i	$-0.744836\pi$
$997$	−43.9240	−1.39109	−0.695544	+	0.718484i	$0.744836\pi$
$998$	−70.2078	−2.22239
$999$	−0.0208515	−0.000659711 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.a.e.1.4		4
3.2	odd	2		5625.2.a.n.1.1		4
5.2	odd	4		1875.2.b.c.1249.6		8
5.3	odd	4		1875.2.b.c.1249.3		8
5.4	even	2		1875.2.a.h.1.1		4
15.14	odd	2		5625.2.a.i.1.4		4
25.3	odd	20		375.2.i.b.49.2		16
25.4	even	10		75.2.g.b.16.2	✓	8
25.6	even	5		375.2.g.b.301.1		8
25.8	odd	20		375.2.i.b.199.3		16
25.17	odd	20		375.2.i.b.199.2		16
25.19	even	10		75.2.g.b.61.2	yes	8
25.21	even	5		375.2.g.b.76.1		8
25.22	odd	20		375.2.i.b.49.3		16
75.29	odd	10		225.2.h.c.91.1		8
75.44	odd	10		225.2.h.c.136.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.16.2	✓	8	25.4	even	10
75.2.g.b.61.2	yes	8	25.19	even	10
225.2.h.c.91.1		8	75.29	odd	10
225.2.h.c.136.1		8	75.44	odd	10
375.2.g.b.76.1		8	25.21	even	5
375.2.g.b.301.1		8	25.6	even	5
375.2.i.b.49.2		16	25.3	odd	20
375.2.i.b.49.3		16	25.22	odd	20
375.2.i.b.199.2		16	25.17	odd	20
375.2.i.b.199.3		16	25.8	odd	20
1875.2.a.e.1.4		4	1.1	even	1	trivial
1875.2.a.h.1.1		4	5.4	even	2
1875.2.b.c.1249.3		8	5.3	odd	4
1875.2.b.c.1249.6		8	5.2	odd	4
5625.2.a.i.1.4		4	15.14	odd	2
5625.2.a.n.1.1		4	3.2	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70636 q^{2} -1.00000 q^{3} +0.911672 q^{4} -1.70636 q^{6} +3.94243 q^{7} -1.85708 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.70636 q^{2} -1.00000 q^{3} +0.911672 q^{4} -1.70636 q^{6} +3.94243 q^{7} -1.85708 q^{8} +1.00000 q^{9} -5.90869 q^{11} -0.911672 q^{12} -3.29066 q^{13} +6.72721 q^{14} -4.99220 q^{16} -2.70636 q^{17} +1.70636 q^{18} -2.35813 q^{19} -3.94243 q^{21} -10.0824 q^{22} +0.584296 q^{23} +1.85708 q^{24} -5.61505 q^{26} -1.00000 q^{27} +3.59420 q^{28} -3.91167 q^{29} +2.70934 q^{31} -4.80433 q^{32} +5.90869 q^{33} -4.61803 q^{34} +0.911672 q^{36} +0.0208515 q^{37} -4.02383 q^{38} +3.29066 q^{39} +1.47214 q^{41} -6.72721 q^{42} -1.27279 q^{43} -5.38679 q^{44} +0.997020 q^{46} -5.43358 q^{47} +4.99220 q^{48} +8.54276 q^{49} +2.70636 q^{51} -3.00000 q^{52} -2.81554 q^{53} -1.70636 q^{54} -7.32142 q^{56} +2.35813 q^{57} -6.67473 q^{58} -4.69033 q^{59} +5.58132 q^{61} +4.62312 q^{62} +3.94243 q^{63} +1.78646 q^{64} +10.0824 q^{66} -6.03076 q^{67} -2.46731 q^{68} -0.584296 q^{69} -8.10138 q^{71} -1.85708 q^{72} -13.3166 q^{73} +0.0355801 q^{74} -2.14984 q^{76} -23.2946 q^{77} +5.61505 q^{78} +16.6648 q^{79} +1.00000 q^{81} +2.51200 q^{82} -0.781641 q^{83} -3.59420 q^{84} -2.17183 q^{86} +3.91167 q^{87} +10.9729 q^{88} -3.47327 q^{89} -12.9732 q^{91} +0.532686 q^{92} -2.70934 q^{93} -9.27165 q^{94} +4.80433 q^{96} +2.45443 q^{97} +14.5770 q^{98} -5.90869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} - 2 q^{7} - 15 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 - 2 * q^7 - 15 * q^8 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 8 q^{4} + 2 q^{6} - 2 q^{7} - 15 q^{8} + 4 q^{9} - 7 q^{11} - 8 q^{12} - q^{13} + 16 q^{14} + 4 q^{16} - 2 q^{17} - 2 q^{18} + 5 q^{19} + 2 q^{21} + 6 q^{22} - q^{23} + 15 q^{24} + 3 q^{26} - 4 q^{27} - 9 q^{28} - 20 q^{29} + 23 q^{31} - 12 q^{32} + 7 q^{33} - 14 q^{34} + 8 q^{36} - 2 q^{37} - 35 q^{38} + q^{39} - 12 q^{41} - 16 q^{42} - 16 q^{43} - 29 q^{44} - 17 q^{46} - 2 q^{47} - 4 q^{48} + 8 q^{49} + 2 q^{51} - 12 q^{52} + 4 q^{53} + 2 q^{54} + 5 q^{56} - 5 q^{57} + 25 q^{58} - 15 q^{59} - 2 q^{61} - 9 q^{62} - 2 q^{63} + 23 q^{64} - 6 q^{66} - 2 q^{67} + 11 q^{68} + q^{69} - 2 q^{71} - 15 q^{72} - 16 q^{73} - 19 q^{74} + 40 q^{76} - 19 q^{77} - 3 q^{78} + 35 q^{79} + 4 q^{81} + 6 q^{82} - 16 q^{83} + 9 q^{84} + 3 q^{86} + 20 q^{87} + 30 q^{88} - 35 q^{89} - 12 q^{91} + 23 q^{92} - 23 q^{93} - 9 q^{94} + 12 q^{96} - 12 q^{97} + q^{98} - 7 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 + 2 * q^6 - 2 * q^7 - 15 * q^8 + 4 * q^9 - 7 * q^11 - 8 * q^12 - q^13 + 16 * q^14 + 4 * q^16 - 2 * q^17 - 2 * q^18 + 5 * q^19 + 2 * q^21 + 6 * q^22 - q^23 + 15 * q^24 + 3 * q^26 - 4 * q^27 - 9 * q^28 - 20 * q^29 + 23 * q^31 - 12 * q^32 + 7 * q^33 - 14 * q^34 + 8 * q^36 - 2 * q^37 - 35 * q^38 + q^39 - 12 * q^41 - 16 * q^42 - 16 * q^43 - 29 * q^44 - 17 * q^46 - 2 * q^47 - 4 * q^48 + 8 * q^49 + 2 * q^51 - 12 * q^52 + 4 * q^53 + 2 * q^54 + 5 * q^56 - 5 * q^57 + 25 * q^58 - 15 * q^59 - 2 * q^61 - 9 * q^62 - 2 * q^63 + 23 * q^64 - 6 * q^66 - 2 * q^67 + 11 * q^68 + q^69 - 2 * q^71 - 15 * q^72 - 16 * q^73 - 19 * q^74 + 40 * q^76 - 19 * q^77 - 3 * q^78 + 35 * q^79 + 4 * q^81 + 6 * q^82 - 16 * q^83 + 9 * q^84 + 3 * q^86 + 20 * q^87 + 30 * q^88 - 35 * q^89 - 12 * q^91 + 23 * q^92 - 23 * q^93 - 9 * q^94 + 12 * q^96 - 12 * q^97 + q^98 - 7 * q^99

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