LMFDB - Embedded newform 4235.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.15952.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 1 $ x^4 - 6x^2 - 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.275377$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} -0.724623 q^{6} +1.00000 q^{7} +1.08063 q^{8} +3.92417 q^{9} +O(q^{10})$	\(q-0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} -0.724623 q^{6} +1.00000 q^{7} +1.08063 q^{8} +3.92417 q^{9} -0.275377 q^{10} -5.06322 q^{12} -7.06322 q^{13} -0.275377 q^{14} +2.63138 q^{15} +3.55075 q^{16} -3.76771 q^{17} -1.08063 q^{18} +4.83093 q^{19} -1.92417 q^{20} +2.63138 q^{21} -3.35600 q^{23} +2.84354 q^{24} +1.00000 q^{25} +1.94505 q^{26} +2.43184 q^{27} -1.92417 q^{28} -9.81352 q^{29} -0.724623 q^{30} -8.10630 q^{31} -3.13905 q^{32} +1.03754 q^{34} +1.00000 q^{35} -7.55075 q^{36} -9.51726 q^{37} -1.33033 q^{38} -18.5860 q^{39} +1.08063 q^{40} -3.74203 q^{41} -0.724623 q^{42} -10.0680 q^{43} +3.92417 q^{45} +0.924167 q^{46} +5.30105 q^{47} +9.34339 q^{48} +1.00000 q^{49} -0.275377 q^{50} -9.91428 q^{51} +13.5908 q^{52} +11.9068 q^{53} -0.669673 q^{54} +1.08063 q^{56} +12.7120 q^{57} +2.70242 q^{58} -2.02013 q^{59} -5.06322 q^{60} +2.96246 q^{61} +2.23229 q^{62} +3.92417 q^{63} -6.23709 q^{64} -7.06322 q^{65} +12.0680 q^{67} +7.24970 q^{68} -8.83093 q^{69} -0.275377 q^{70} +5.57568 q^{71} +4.24056 q^{72} +7.92896 q^{73} +2.62084 q^{74} +2.63138 q^{75} -9.29551 q^{76} +5.11817 q^{78} +4.37341 q^{79} +3.55075 q^{80} -5.37341 q^{81} +1.03047 q^{82} -15.6694 q^{83} -5.06322 q^{84} -3.76771 q^{85} +2.77250 q^{86} -25.8231 q^{87} -4.79611 q^{89} -1.08063 q^{90} -7.06322 q^{91} +6.45751 q^{92} -21.3308 q^{93} -1.45979 q^{94} +4.83093 q^{95} -8.26004 q^{96} -2.30540 q^{97} -0.275377 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9} - 8 q^{12} - 16 q^{13} - 2 q^{15} + 12 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 2 q^{23} + 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} + 4 q^{28} - 12 q^{29} - 4 q^{30} - 6 q^{31} - 12 q^{32} + 8 q^{34} + 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} - 6 q^{40} - 18 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} - 4 q^{51} - 30 q^{52} + 34 q^{53} + 2 q^{54} - 6 q^{56} + 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} + 8 q^{61} + 22 q^{62} + 4 q^{63} - 16 q^{64} - 16 q^{65} + 14 q^{67} + 44 q^{68} - 10 q^{69} + 12 q^{72} - 2 q^{73} - 48 q^{74} - 2 q^{75} - 38 q^{76} + 14 q^{78} + 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} + 10 q^{83} - 8 q^{84} - 2 q^{85} - 24 q^{86} - 32 q^{87} + 10 q^{89} + 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} - 54 q^{94} - 6 q^{95} - 8 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9 - 8 * q^12 - 16 * q^13 - 2 * q^15 + 12 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 2 * q^23 + 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 + 4 * q^28 - 12 * q^29 - 4 * q^30 - 6 * q^31 - 12 * q^32 + 8 * q^34 + 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 - 6 * q^40 - 18 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 - 4 * q^51 - 30 * q^52 + 34 * q^53 + 2 * q^54 - 6 * q^56 + 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 + 22 * q^62 + 4 * q^63 - 16 * q^64 - 16 * q^65 + 14 * q^67 + 44 * q^68 - 10 * q^69 + 12 * q^72 - 2 * q^73 - 48 * q^74 - 2 * q^75 - 38 * q^76 + 14 * q^78 + 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 + 10 * q^83 - 8 * q^84 - 2 * q^85 - 24 * q^86 - 32 * q^87 + 10 * q^89 + 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 - 54 * q^94 - 6 * q^95 - 8 * q^96 - 34 * q^97

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 $

$2$	−0.275377	−0.194721	−0.0973606	−	0.995249i	$-0.531040\pi$
$2$	−0.275377	−0.194721	−0.0973606	+	0.995249i	$0.531040\pi$
$3$	2.63138	1.51923	0.759614	−	0.650374i	$-0.225388\pi$
$3$	2.63138	1.51923	0.759614	+	0.650374i	$0.225388\pi$
$4$	−1.92417	−0.962084
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.724623	−0.295826
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.08063	0.382059
$9$	3.92417	1.30806
$10$	−0.275377	−0.0870820
$11$	0	0
$11$	0	0
$12$	−5.06322	−1.46163
$13$	−7.06322	−1.95898	−0.979492	−	0.201483i	$-0.935424\pi$
$13$	−7.06322	−1.95898	−0.979492	+	0.201483i	$0.935424\pi$
$14$	−0.275377	−0.0735977
$15$	2.63138	0.679420
$16$	3.55075	0.887689
$17$	−3.76771	−0.913803	−0.456902	−	0.889517i	$-0.651041\pi$
$17$	−3.76771	−0.913803	−0.456902	+	0.889517i	$0.651041\pi$
$18$	−1.08063	−0.254706
$19$	4.83093	1.10829	0.554145	−	0.832420i	$-0.313045\pi$
$19$	4.83093	1.10829	0.554145	+	0.832420i	$0.313045\pi$
$20$	−1.92417	−0.430257
$21$	2.63138	0.574214
$22$	0	0
$23$	−3.35600	−0.699775	−0.349888	−	0.936792i	$-0.613780\pi$
$23$	−3.35600	−0.699775	−0.349888	+	0.936792i	$0.613780\pi$
$24$	2.84354	0.580435
$25$	1.00000	0.200000
$26$	1.94505	0.381456
$27$	2.43184	0.468007
$28$	−1.92417	−0.363633
$29$	−9.81352	−1.82232	−0.911162	−	0.412048i	$-0.864814\pi$
$29$	−9.81352	−1.82232	−0.911162	+	0.412048i	$0.864814\pi$
$30$	−0.724623	−0.132297
$31$	−8.10630	−1.45594	−0.727968	−	0.685612i	$-0.759535\pi$
$31$	−8.10630	−1.45594	−0.727968	+	0.685612i	$0.759535\pi$
$32$	−3.13905	−0.554911
$33$	0	0
$34$	1.03754	0.177937
$35$	1.00000	0.169031
$36$	−7.55075	−1.25846
$37$	−9.51726	−1.56463	−0.782314	−	0.622885i	$-0.785961\pi$
$37$	−9.51726	−1.56463	−0.782314	+	0.622885i	$0.785961\pi$
$38$	−1.33033	−0.215808
$39$	−18.5860	−2.97614
$40$	1.08063	0.170862
$41$	−3.74203	−0.584407	−0.292204	−	0.956356i	$-0.594388\pi$
$41$	−3.74203	−0.584407	−0.292204	+	0.956356i	$0.594388\pi$
$42$	−0.724623	−0.111812
$43$	−10.0680	−1.53536	−0.767679	−	0.640835i	$-0.778588\pi$
$43$	−10.0680	−1.53536	−0.767679	+	0.640835i	$0.778588\pi$
$44$	0	0
$45$	3.92417	0.584980
$46$	0.924167	0.136261
$47$	5.30105	0.773238	0.386619	−	0.922239i	$-0.373643\pi$
$47$	5.30105	0.773238	0.386619	+	0.922239i	$0.373643\pi$
$48$	9.34339	1.34860
$49$	1.00000	0.142857
$50$	−0.275377	−0.0389442
$51$	−9.91428	−1.38828
$52$	13.5908	1.88471
$53$	11.9068	1.63552	0.817760	−	0.575560i	$-0.195216\pi$
$53$	11.9068	1.63552	0.817760	+	0.575560i	$0.195216\pi$
$54$	−0.669673	−0.0911309
$55$	0	0
$56$	1.08063	0.144405
$57$	12.7120	1.68375
$58$	2.70242	0.354845
$59$	−2.02013	−0.262999	−0.131499	−	0.991316i	$-0.541979\pi$
$59$	−2.02013	−0.262999	−0.131499	+	0.991316i	$0.541979\pi$
$60$	−5.06322	−0.653659
$61$	2.96246	0.379304	0.189652	−	0.981851i	$-0.439264\pi$
$61$	2.96246	0.379304	0.189652	+	0.981851i	$0.439264\pi$
$62$	2.23229	0.283501
$63$	3.92417	0.494399
$64$	−6.23709	−0.779636
$65$	−7.06322	−0.876084
$66$	0	0
$67$	12.0680	1.47434	0.737171	−	0.675706i	$-0.236161\pi$
$67$	12.0680	1.47434	0.737171	+	0.675706i	$0.236161\pi$
$68$	7.24970	0.879155
$69$	−8.83093	−1.06312
$70$	−0.275377	−0.0329139
$71$	5.57568	0.661712	0.330856	−	0.943681i	$-0.392663\pi$
$71$	5.57568	0.661712	0.330856	+	0.943681i	$0.392663\pi$
$72$	4.24056	0.499755
$73$	7.92896	0.928015	0.464007	−	0.885831i	$-0.346411\pi$
$73$	7.92896	0.928015	0.464007	+	0.885831i	$0.346411\pi$
$74$	2.62084	0.304666
$75$	2.63138	0.303846
$76$	−9.29551	−1.06627
$77$	0	0
$78$	5.11817	0.579518
$79$	4.37341	0.492047	0.246024	−	0.969264i	$-0.420876\pi$
$79$	4.37341	0.492047	0.246024	+	0.969264i	$0.420876\pi$
$80$	3.55075	0.396986
$81$	−5.37341	−0.597046
$82$	1.03047	0.113796
$83$	−15.6694	−1.71994	−0.859968	−	0.510347i	$-0.829517\pi$
$83$	−15.6694	−1.71994	−0.859968	+	0.510347i	$0.829517\pi$
$84$	−5.06322	−0.552442
$85$	−3.76771	−0.408665
$86$	2.77250	0.298967
$87$	−25.8231	−2.76853
$88$	0	0
$89$	−4.79611	−0.508386	−0.254193	−	0.967153i	$-0.581810\pi$
$89$	−4.79611	−0.508386	−0.254193	+	0.967153i	$0.581810\pi$
$90$	−1.08063	−0.113908
$91$	−7.06322	−0.740426
$92$	6.45751	0.673242
$93$	−21.3308	−2.21190
$94$	−1.45979	−0.150566
$95$	4.83093	0.495643
$96$	−8.26004	−0.843037
$97$	−2.30540	−0.234078	−0.117039	−	0.993127i	$-0.537340\pi$
$97$	−2.30540	−0.234078	−0.117039	+	0.993127i	$0.537340\pi$
$98$	−0.275377	−0.0278173
$99$	0	0
$100$	−1.92417	−0.192417
$101$	0.657058	0.0653797	0.0326898	−	0.999466i	$-0.489593\pi$
$101$	0.657058	0.0653797	0.0326898	+	0.999466i	$0.489593\pi$
$102$	2.73017	0.270327
$103$	−0.343692	−0.0338650	−0.0169325	−	0.999857i	$-0.505390\pi$
$103$	−0.343692	−0.0338650	−0.0169325	+	0.999857i	$0.505390\pi$
$104$	−7.63270	−0.748448
$105$	2.63138	0.256797
$106$	−3.27885	−0.318470
$107$	16.5603	1.60095	0.800474	−	0.599367i	$-0.204581\pi$
$107$	16.5603	1.60095	0.800474	+	0.599367i	$0.204581\pi$
$108$	−4.67926	−0.450262
$109$	−11.5354	−1.10489	−0.552446	−	0.833549i	$-0.686306\pi$
$109$	−11.5354	−1.10489	−0.552446	+	0.833549i	$0.686306\pi$
$110$	0	0
$111$	−25.0435	−2.37703
$112$	3.55075	0.335515
$113$	−2.89849	−0.272667	−0.136334	−	0.990663i	$-0.543532\pi$
$113$	−2.89849	−0.272667	−0.136334	+	0.990663i	$0.543532\pi$
$114$	−3.50060	−0.327861
$115$	−3.35600	−0.312949
$116$	18.8828	1.75323
$117$	−27.7172	−2.56246
$118$	0.556299	0.0512114
$119$	−3.76771	−0.345385
$120$	2.84354	0.259579
$121$	0	0
$122$	−0.815794	−0.0738585
$123$	−9.84671	−0.887848
$124$	15.5979	1.40073
$125$	1.00000	0.0894427
$126$	−1.08063	−0.0962699
$127$	−6.23784	−0.553518	−0.276759	−	0.960939i	$-0.589260\pi$
$127$	−6.23784	−0.553518	−0.276759	+	0.960939i	$0.589260\pi$
$128$	7.99565	0.706723
$129$	−26.4928	−2.33256
$130$	1.94505	0.170592
$131$	1.42402	0.124417	0.0622084	−	0.998063i	$-0.480186\pi$
$131$	1.42402	0.124417	0.0622084	+	0.998063i	$0.480186\pi$
$132$	0	0
$133$	4.83093	0.418894
$134$	−3.32326	−0.287086
$135$	2.43184	0.209299
$136$	−4.07149	−0.349127
$137$	18.5019	1.58073	0.790363	−	0.612639i	$-0.209892\pi$
$137$	18.5019	1.58073	0.790363	+	0.612639i	$0.209892\pi$
$138$	2.43184	0.207012
$139$	−4.16125	−0.352953	−0.176476	−	0.984305i	$-0.556470\pi$
$139$	−4.16125	−0.352953	−0.176476	+	0.984305i	$0.556470\pi$
$140$	−1.92417	−0.162622
$141$	13.9491	1.17473
$142$	−1.53542	−0.128849
$143$	0	0
$144$	13.9338	1.16115
$145$	−9.81352	−0.814968
$146$	−2.18346	−0.180704
$147$	2.63138	0.217033
$148$	18.3128	1.50530
$149$	−17.1111	−1.40180	−0.700898	−	0.713262i	$-0.747217\pi$
$149$	−17.1111	−1.40180	−0.700898	+	0.713262i	$0.747217\pi$
$150$	−0.724623	−0.0591652
$151$	−5.90883	−0.480854	−0.240427	−	0.970667i	$-0.577287\pi$
$151$	−5.90883	−0.480854	−0.240427	+	0.970667i	$0.577287\pi$
$152$	5.22043	0.423433
$153$	−14.7851	−1.19531
$154$	0	0
$155$	−8.10630	−0.651114
$156$	35.7626	2.86330
$157$	5.69460	0.454478	0.227239	−	0.973839i	$-0.427030\pi$
$157$	5.69460	0.454478	0.227239	+	0.973839i	$0.427030\pi$
$158$	−1.20434	−0.0958120
$159$	31.3312	2.48473
$160$	−3.13905	−0.248164
$161$	−3.35600	−0.264490
$162$	1.47972	0.116257
$163$	−1.23502	−0.0967339	−0.0483669	−	0.998830i	$-0.515402\pi$
$163$	−1.23502	−0.0967339	−0.0483669	+	0.998830i	$0.515402\pi$
$164$	7.20029	0.562249
$165$	0	0
$166$	4.31499	0.334908
$167$	−1.49158	−0.115422	−0.0577110	−	0.998333i	$-0.518380\pi$
$167$	−1.49158	−0.115422	−0.0577110	+	0.998333i	$0.518380\pi$
$168$	2.84354	0.219384
$169$	36.8890	2.83762
$170$	1.03754	0.0795758
$171$	18.9574	1.44971
$172$	19.3725	1.47714
$173$	−6.47972	−0.492644	−0.246322	−	0.969188i	$-0.579222\pi$
$173$	−6.47972	−0.492644	−0.246322	+	0.969188i	$0.579222\pi$
$174$	7.11110	0.539091
$175$	1.00000	0.0755929
$176$	0	0
$177$	−5.31574	−0.399555
$178$	1.32074	0.0989936
$179$	−14.5255	−1.08569	−0.542844	−	0.839833i	$-0.682653\pi$
$179$	−14.5255	−1.08569	−0.542844	+	0.839833i	$0.682653\pi$
$180$	−7.55075	−0.562800
$181$	−4.30540	−0.320018	−0.160009	−	0.987116i	$-0.551152\pi$
$181$	−4.30540	−0.320018	−0.160009	+	0.987116i	$0.551152\pi$
$182$	1.94505	0.144177
$183$	7.79536	0.576249
$184$	−3.62659	−0.267356
$185$	−9.51726	−0.699723
$186$	5.87401	0.430703
$187$	0	0
$188$	−10.2001	−0.743920
$189$	2.43184	0.176890
$190$	−1.33033	−0.0965121
$191$	−5.05974	−0.366110	−0.183055	−	0.983103i	$-0.558599\pi$
$191$	−5.05974	−0.366110	−0.183055	+	0.983103i	$0.558599\pi$
$192$	−16.4122	−1.18444
$193$	−7.28637	−0.524484	−0.262242	−	0.965002i	$-0.584462\pi$
$193$	−7.28637	−0.524484	−0.262242	+	0.965002i	$0.584462\pi$
$194$	0.634855	0.0455799
$195$	−18.5860	−1.33097
$196$	−1.92417	−0.137441
$197$	15.8467	1.12903	0.564516	−	0.825422i	$-0.309063\pi$
$197$	15.8467	1.12903	0.564516	+	0.825422i	$0.309063\pi$
$198$	0	0
$199$	−4.37689	−0.310269	−0.155135	−	0.987893i	$-0.549581\pi$
$199$	−4.37689	−0.310269	−0.155135	+	0.987893i	$0.549581\pi$
$200$	1.08063	0.0764118
$201$	31.7555	2.23986
$202$	−0.180939	−0.0127308
$203$	−9.81352	−0.688774
$204$	19.0767	1.33564
$205$	−3.74203	−0.261355
$206$	0.0946450	0.00659423
$207$	−13.1695	−0.915345
$208$	−25.0798	−1.73897
$209$	0	0
$210$	−0.724623	−0.0500037
$211$	16.6868	1.14877	0.574383	−	0.818587i	$-0.305242\pi$
$211$	16.6868	1.14877	0.574383	+	0.818587i	$0.305242\pi$
$212$	−22.9106	−1.57351
$213$	14.6717	1.00529
$214$	−4.56034	−0.311739
$215$	−10.0680	−0.686633
$216$	2.62791	0.178806
$217$	−8.10630	−0.550292
$218$	3.17659	0.215146
$219$	20.8641	1.40987
$220$	0	0
$221$	26.6121	1.79013
$222$	6.89642	0.462857
$223$	−6.70796	−0.449198	−0.224599	−	0.974451i	$-0.572107\pi$
$223$	−6.70796	−0.449198	−0.224599	+	0.974451i	$0.572107\pi$
$224$	−3.13905	−0.209737
$225$	3.92417	0.261611
$226$	0.798179	0.0530940
$227$	−25.0360	−1.66170	−0.830849	−	0.556497i	$-0.812145\pi$
$227$	−25.0360	−1.66170	−0.830849	+	0.556497i	$0.812145\pi$
$228$	−24.4600	−1.61991
$229$	2.04027	0.134825	0.0674123	−	0.997725i	$-0.478526\pi$
$229$	2.04027	0.134825	0.0674123	+	0.997725i	$0.478526\pi$
$230$	0.924167	0.0609378
$231$	0	0
$232$	−10.6047	−0.696236
$233$	−9.36559	−0.613560	−0.306780	−	0.951780i	$-0.599252\pi$
$233$	−9.36559	−0.613560	−0.306780	+	0.951780i	$0.599252\pi$
$234$	7.63270	0.498965
$235$	5.30105	0.345803
$236$	3.88707	0.253027
$237$	11.5081	0.747532
$238$	1.03754	0.0672538
$239$	5.41443	0.350230	0.175115	−	0.984548i	$-0.443970\pi$
$239$	5.41443	0.350230	0.175115	+	0.984548i	$0.443970\pi$
$240$	9.34339	0.603113
$241$	25.4703	1.64068	0.820342	−	0.571873i	$-0.193783\pi$
$241$	25.4703	1.64068	0.820342	+	0.571873i	$0.193783\pi$
$242$	0	0
$243$	−21.4350	−1.37506
$244$	−5.70027	−0.364922
$245$	1.00000	0.0638877
$246$	2.71156	0.172883
$247$	−34.1219	−2.17112
$248$	−8.75989	−0.556253
$249$	−41.2321	−2.61298
$250$	−0.275377	−0.0174164
$251$	−7.12164	−0.449514	−0.224757	−	0.974415i	$-0.572159\pi$
$251$	−7.12164	−0.449514	−0.224757	+	0.974415i	$0.572159\pi$
$252$	−7.55075	−0.475653
$253$	0	0
$254$	1.71776	0.107782
$255$	−9.91428	−0.620856
$256$	10.2724	0.642022
$257$	15.4733	0.965198	0.482599	−	0.875841i	$-0.339693\pi$
$257$	15.4733	0.965198	0.482599	+	0.875841i	$0.339693\pi$
$258$	7.29551	0.454199
$259$	−9.51726	−0.591374
$260$	13.5908	0.842866
$261$	−38.5099	−2.38370
$262$	−0.392142	−0.0242266
$263$	−14.6772	−0.905034	−0.452517	−	0.891756i	$-0.649474\pi$
$263$	−14.6772	−0.905034	−0.452517	+	0.891756i	$0.649474\pi$
$264$	0	0
$265$	11.9068	0.731426
$266$	−1.33033	−0.0815676
$267$	−12.6204	−0.772355
$268$	−23.2209	−1.41844
$269$	−14.1244	−0.861178	−0.430589	−	0.902548i	$-0.641694\pi$
$269$	−14.1244	−0.861178	−0.430589	+	0.902548i	$0.641694\pi$
$270$	−0.669673	−0.0407550
$271$	16.0958	0.977748	0.488874	−	0.872354i	$-0.337408\pi$
$271$	16.0958	0.977748	0.488874	+	0.872354i	$0.337408\pi$
$272$	−13.3782	−0.811173
$273$	−18.5860	−1.12488
$274$	−5.09501	−0.307801
$275$	0	0
$276$	16.9922	1.02281
$277$	15.4059	0.925648	0.462824	−	0.886450i	$-0.346836\pi$
$277$	15.4059	0.925648	0.462824	+	0.886450i	$0.346836\pi$
$278$	1.14591	0.0687274
$279$	−31.8105	−1.90444
$280$	1.08063	0.0645798
$281$	5.51019	0.328710	0.164355	−	0.986401i	$-0.447446\pi$
$281$	5.51019	0.328710	0.164355	+	0.986401i	$0.447446\pi$
$282$	−3.84126	−0.228744
$283$	−4.27810	−0.254307	−0.127153	−	0.991883i	$-0.540584\pi$
$283$	−4.27810	−0.254307	−0.127153	+	0.991883i	$0.540584\pi$
$284$	−10.7285	−0.636622
$285$	12.7120	0.752994
$286$	0	0
$287$	−3.74203	−0.220885
$288$	−12.3182	−0.725855
$289$	−2.80438	−0.164963
$290$	2.70242	0.158692
$291$	−6.06639	−0.355618
$292$	−15.2566	−0.892828
$293$	7.27375	0.424937	0.212469	−	0.977168i	$-0.431850\pi$
$293$	7.27375	0.424937	0.212469	+	0.977168i	$0.431850\pi$
$294$	−0.724623	−0.0422609
$295$	−2.02013	−0.117617
$296$	−10.2846	−0.597780
$297$	0	0
$298$	4.71201	0.272959
$299$	23.7042	1.37085
$300$	−5.06322	−0.292325
$301$	−10.0680	−0.580311
$302$	1.62716	0.0936324
$303$	1.72897	0.0993267
$304$	17.1534	0.983817
$305$	2.96246	0.169630
$306$	4.07149	0.232751
$307$	9.23546	0.527096	0.263548	−	0.964646i	$-0.415107\pi$
$307$	9.23546	0.527096	0.263548	+	0.964646i	$0.415107\pi$
$308$	0	0
$309$	−0.904385	−0.0514487
$310$	2.23229	0.126786
$311$	−13.2153	−0.749373	−0.374686	−	0.927152i	$-0.622250\pi$
$311$	−13.2153	−0.749373	−0.374686	+	0.927152i	$0.622250\pi$
$312$	−20.0845	−1.13706
$313$	26.5351	1.49985	0.749927	−	0.661521i	$-0.230089\pi$
$313$	26.5351	1.49985	0.749927	+	0.661521i	$0.230089\pi$
$314$	−1.56816	−0.0884966
$315$	3.92417	0.221102
$316$	−8.41518	−0.473391
$317$	15.7315	0.883568	0.441784	−	0.897121i	$-0.354346\pi$
$317$	15.7315	0.883568	0.441784	+	0.897121i	$0.354346\pi$
$318$	−8.62791	−0.483829
$319$	0	0
$320$	−6.23709	−0.348664
$321$	43.5766	2.43221
$322$	0.924167	0.0515018
$323$	−18.2015	−1.01276
$324$	10.3393	0.574408
$325$	−7.06322	−0.391797
$326$	0.340095	0.0188361
$327$	−30.3541	−1.67858
$328$	−4.04374	−0.223278
$329$	5.30105	0.292257
$330$	0	0
$331$	1.53128	0.0841665	0.0420833	−	0.999114i	$-0.486601\pi$
$331$	1.53128	0.0841665	0.0420833	+	0.999114i	$0.486601\pi$
$332$	30.1505	1.65472
$333$	−37.3473	−2.04662
$334$	0.410747	0.0224751
$335$	12.0680	0.659346
$336$	9.34339	0.509724
$337$	−0.770432	−0.0419681	−0.0209840	−	0.999780i	$-0.506680\pi$
$337$	−0.770432	−0.0419681	−0.0209840	+	0.999780i	$0.506680\pi$
$338$	−10.1584	−0.552544
$339$	−7.62703	−0.414244
$340$	7.24970	0.393170
$341$	0	0
$342$	−5.22043	−0.282288
$343$	1.00000	0.0539949
$344$	−10.8798	−0.586597
$345$	−8.83093	−0.475441
$346$	1.78437	0.0959282
$347$	6.16982	0.331214	0.165607	−	0.986192i	$-0.447042\pi$
$347$	6.16982	0.331214	0.165607	+	0.986192i	$0.447042\pi$
$348$	49.6880	2.66356
$349$	−0.945923	−0.0506341	−0.0253171	−	0.999679i	$-0.508060\pi$
$349$	−0.945923	−0.0506341	−0.0253171	+	0.999679i	$0.508060\pi$
$350$	−0.275377	−0.0147195
$351$	−17.1766	−0.916819
$352$	0	0
$353$	28.1012	1.49568	0.747838	−	0.663881i	$-0.231092\pi$
$353$	28.1012	1.49568	0.747838	+	0.663881i	$0.231092\pi$
$354$	1.46383	0.0778019
$355$	5.57568	0.295926
$356$	9.22852	0.489110
$357$	−9.91428	−0.524719
$358$	4.00000	0.211407
$359$	−3.93406	−0.207632	−0.103816	−	0.994597i	$-0.533105\pi$
$359$	−3.93406	−0.207632	−0.103816	+	0.994597i	$0.533105\pi$
$360$	4.24056	0.223497
$361$	4.33785	0.228308
$362$	1.18561	0.0623143
$363$	0	0
$364$	13.5908	0.712352
$365$	7.92896	0.415021
$366$	−2.14666	−0.112208
$367$	−9.74455	−0.508661	−0.254331	−	0.967117i	$-0.581855\pi$
$367$	−9.74455	−0.508661	−0.254331	+	0.967117i	$0.581855\pi$
$368$	−11.9163	−0.621183
$369$	−14.6844	−0.764437
$370$	2.62084	0.136251
$371$	11.9068	0.618168
$372$	41.0440	2.12803
$373$	−23.3560	−1.20933	−0.604664	−	0.796481i	$-0.706693\pi$
$373$	−23.3560	−1.20933	−0.604664	+	0.796481i	$0.706693\pi$
$374$	0	0
$375$	2.63138	0.135884
$376$	5.72846	0.295423
$377$	69.3150	3.56990
$378$	−0.669673	−0.0344442
$379$	−15.2375	−0.782699	−0.391350	−	0.920242i	$-0.627992\pi$
$379$	−15.2375	−0.782699	−0.391350	+	0.920242i	$0.627992\pi$
$380$	−9.29551	−0.476850
$381$	−16.4141	−0.840921
$382$	1.39334	0.0712894
$383$	−23.9455	−1.22356	−0.611779	−	0.791029i	$-0.709546\pi$
$383$	−23.9455	−1.22356	−0.611779	+	0.791029i	$0.709546\pi$
$384$	21.0396	1.07367
$385$	0	0
$386$	2.00650	0.102128
$387$	−39.5086	−2.00833
$388$	4.43598	0.225203
$389$	−30.5516	−1.54903	−0.774515	−	0.632555i	$-0.782006\pi$
$389$	−30.5516	−1.54903	−0.774515	+	0.632555i	$0.782006\pi$
$390$	5.11817	0.259169
$391$	12.6444	0.639457
$392$	1.08063	0.0545799
$393$	3.74713	0.189018
$394$	−4.36382	−0.219846
$395$	4.37341	0.220050
$396$	0	0
$397$	−26.7709	−1.34359	−0.671796	−	0.740736i	$-0.734477\pi$
$397$	−26.7709	−1.34359	−0.671796	+	0.740736i	$0.734477\pi$
$398$	1.20530	0.0604160
$399$	12.7120	0.636396
$400$	3.55075	0.177538
$401$	−30.5099	−1.52359	−0.761795	−	0.647818i	$-0.775682\pi$
$401$	−30.5099	−1.52359	−0.761795	+	0.647818i	$0.775682\pi$
$402$	−8.74476	−0.436149
$403$	57.2566	2.85215
$404$	−1.26429	−0.0629007
$405$	−5.37341	−0.267007
$406$	2.70242	0.134119
$407$	0	0
$408$	−10.7136	−0.530404
$409$	−1.64834	−0.0815053	−0.0407527	−	0.999169i	$-0.512976\pi$
$409$	−1.64834	−0.0815053	−0.0407527	+	0.999169i	$0.512976\pi$
$410$	1.03047	0.0508913
$411$	48.6856	2.40148
$412$	0.661321	0.0325810
$413$	−2.02013	−0.0994042
$414$	3.62659	0.178237
$415$	−15.6694	−0.769179
$416$	22.1718	1.08706
$417$	−10.9498	−0.536216
$418$	0	0
$419$	−18.2949	−0.893762	−0.446881	−	0.894593i	$-0.647465\pi$
$419$	−18.2949	−0.893762	−0.446881	+	0.894593i	$0.647465\pi$
$420$	−5.06322	−0.247060
$421$	−18.5109	−0.902168	−0.451084	−	0.892482i	$-0.648962\pi$
$421$	−18.5109	−0.902168	−0.451084	+	0.892482i	$0.648962\pi$
$422$	−4.59516	−0.223689
$423$	20.8022	1.01144
$424$	12.8668	0.624865
$425$	−3.76771	−0.182761
$426$	−4.04027	−0.195751
$427$	2.96246	0.143363
$428$	−31.8649	−1.54025
$429$	0	0
$430$	2.77250	0.133702
$431$	8.25656	0.397705	0.198852	−	0.980029i	$-0.436279\pi$
$431$	8.25656	0.397705	0.198852	+	0.980029i	$0.436279\pi$
$432$	8.63486	0.415445
$433$	−2.86781	−0.137818	−0.0689092	−	0.997623i	$-0.521952\pi$
$433$	−2.86781	−0.137818	−0.0689092	+	0.997623i	$0.521952\pi$
$434$	2.23229	0.107153
$435$	−25.8231	−1.23812
$436$	22.1961	1.06300
$437$	−16.2126	−0.775554
$438$	−5.74551	−0.274531
$439$	−22.8733	−1.09168	−0.545841	−	0.837889i	$-0.683790\pi$
$439$	−22.8733	−1.09168	−0.545841	+	0.837889i	$0.683790\pi$
$440$	0	0
$441$	3.92417	0.186865
$442$	−7.32838	−0.348576
$443$	−10.2458	−0.486793	−0.243396	−	0.969927i	$-0.578262\pi$
$443$	−10.2458	−0.486793	−0.243396	+	0.969927i	$0.578262\pi$
$444$	48.1879	2.28690
$445$	−4.79611	−0.227357
$446$	1.84722	0.0874685
$447$	−45.0258	−2.12965
$448$	−6.23709	−0.294675
$449$	−27.7443	−1.30934	−0.654668	−	0.755917i	$-0.727192\pi$
$449$	−27.7443	−1.30934	−0.654668	+	0.755917i	$0.727192\pi$
$450$	−1.08063	−0.0509412
$451$	0	0
$452$	5.57718	0.262329
$453$	−15.5484	−0.730527
$454$	6.89435	0.323568
$455$	−7.06322	−0.331129
$456$	13.7369	0.643291
$457$	32.7145	1.53032	0.765160	−	0.643840i	$-0.222660\pi$
$457$	32.7145	1.53032	0.765160	+	0.643840i	$0.222660\pi$
$458$	−0.561843	−0.0262532
$459$	−9.16245	−0.427667
$460$	6.45751	0.301083
$461$	5.33425	0.248441	0.124220	−	0.992255i	$-0.460357\pi$
$461$	5.33425	0.248441	0.124220	+	0.992255i	$0.460357\pi$
$462$	0	0
$463$	7.22262	0.335664	0.167832	−	0.985816i	$-0.446323\pi$
$463$	7.22262	0.335664	0.167832	+	0.985816i	$0.446323\pi$
$464$	−34.8454	−1.61766
$465$	−21.3308	−0.989191
$466$	2.57907	0.119473
$467$	28.0704	1.29894	0.649472	−	0.760385i	$-0.274990\pi$
$467$	28.0704	1.29894	0.649472	+	0.760385i	$0.274990\pi$
$468$	53.3326	2.46530
$469$	12.0680	0.557249
$470$	−1.45979	−0.0673351
$471$	14.9847	0.690457
$472$	−2.18301	−0.100481
$473$	0	0
$474$	−3.16907	−0.145560
$475$	4.83093	0.221658
$476$	7.24970	0.332289
$477$	46.7241	2.13935
$478$	−1.49101	−0.0681972
$479$	−17.2744	−0.789288	−0.394644	−	0.918834i	$-0.629132\pi$
$479$	−17.2744	−0.789288	−0.394644	+	0.918834i	$0.629132\pi$
$480$	−8.26004	−0.377017
$481$	67.2225	3.06508
$482$	−7.01393	−0.319476
$483$	−8.83093	−0.401821
$484$	0	0
$485$	−2.30540	−0.104683
$486$	5.90271	0.267753
$487$	−22.5587	−1.02223	−0.511117	−	0.859511i	$-0.670768\pi$
$487$	−22.5587	−1.02223	−0.511117	+	0.859511i	$0.670768\pi$
$488$	3.20131	0.144917
$489$	−3.24980	−0.146961
$490$	−0.275377	−0.0124403
$491$	20.6959	0.933994	0.466997	−	0.884259i	$-0.345336\pi$
$491$	20.6959	0.933994	0.466997	+	0.884259i	$0.345336\pi$
$492$	18.9467	0.854184
$493$	36.9745	1.66525
$494$	9.39639	0.422764
$495$	0	0
$496$	−28.7835	−1.29242
$497$	5.57568	0.250103
$498$	11.3544	0.508802
$499$	0.781643	0.0349911	0.0174956	−	0.999847i	$-0.494431\pi$
$499$	0.781643	0.0349911	0.0174956	+	0.999847i	$0.494431\pi$
$500$	−1.92417	−0.0860514
$501$	−3.92492	−0.175352
$502$	1.96114	0.0875299
$503$	38.4066	1.71247	0.856233	−	0.516590i	$-0.172799\pi$
$503$	38.4066	1.71247	0.856233	+	0.516590i	$0.172799\pi$
$504$	4.24056	0.188890
$505$	0.657058	0.0292387
$506$	0	0
$507$	97.0691	4.31099
$508$	12.0026	0.532531
$509$	23.5450	1.04361	0.521807	−	0.853064i	$-0.325258\pi$
$509$	23.5450	1.04361	0.521807	+	0.853064i	$0.325258\pi$
$510$	2.73017	0.120894
$511$	7.92896	0.350757
$512$	−18.8201	−0.831738
$513$	11.7480	0.518688
$514$	−4.26100	−0.187944
$515$	−0.343692	−0.0151449
$516$	50.9765	2.24412
$517$	0	0
$518$	2.62084	0.115153
$519$	−17.0506	−0.748438
$520$	−7.63270	−0.334716
$521$	−10.4832	−0.459277	−0.229638	−	0.973276i	$-0.573754\pi$
$521$	−10.4832	−0.459277	−0.229638	+	0.973276i	$0.573754\pi$
$522$	10.6047	0.464157
$523$	−16.3979	−0.717031	−0.358515	−	0.933524i	$-0.616717\pi$
$523$	−16.3979	−0.717031	−0.358515	+	0.933524i	$0.616717\pi$
$524$	−2.74004	−0.119699
$525$	2.63138	0.114843
$526$	4.04177	0.176229
$527$	30.5422	1.33044
$528$	0	0
$529$	−11.7372	−0.510315
$530$	−3.27885	−0.142424
$531$	−7.92734	−0.344017
$532$	−9.29551	−0.403011
$533$	26.4308	1.14484
$534$	3.47537	0.150394
$535$	16.5603	0.715966
$536$	13.0410	0.563286
$537$	−38.2222	−1.64941
$538$	3.88953	0.167690
$539$	0	0
$540$	−4.67926	−0.201363
$541$	14.8898	0.640162	0.320081	−	0.947390i	$-0.396290\pi$
$541$	14.8898	0.640162	0.320081	+	0.947390i	$0.396290\pi$
$542$	−4.43241	−0.190388
$543$	−11.3292	−0.486180
$544$	11.8270	0.507080
$545$	−11.5354	−0.494123
$546$	5.11817	0.219037
$547$	25.0012	1.06897	0.534487	−	0.845177i	$-0.320505\pi$
$547$	25.0012	1.06897	0.534487	+	0.845177i	$0.320505\pi$
$548$	−35.6008	−1.52079
$549$	11.6252	0.496151
$550$	0	0
$551$	−47.4084	−2.01966
$552$	−9.54293	−0.406174
$553$	4.37341	0.185976
$554$	−4.24242	−0.180243
$555$	−25.0435	−1.06304
$556$	8.00695	0.339570
$557$	−38.3557	−1.62518	−0.812592	−	0.582833i	$-0.801944\pi$
$557$	−38.3557	−1.62518	−0.812592	+	0.582833i	$0.801944\pi$
$558$	8.75989	0.370836
$559$	71.1126	3.00774
$560$	3.55075	0.150047
$561$	0	0
$562$	−1.51738	−0.0640068
$563$	−10.7886	−0.454685	−0.227342	−	0.973815i	$-0.573004\pi$
$563$	−10.7886	−0.454685	−0.227342	+	0.973815i	$0.573004\pi$
$564$	−26.8404	−1.13018
$565$	−2.89849	−0.121940
$566$	1.17809	0.0495189
$567$	−5.37341	−0.225662
$568$	6.02523	0.252813
$569$	31.9757	1.34049	0.670245	−	0.742140i	$-0.266189\pi$
$569$	31.9757	1.34049	0.670245	+	0.742140i	$0.266189\pi$
$570$	−3.50060	−0.146624
$571$	18.8384	0.788364	0.394182	−	0.919032i	$-0.371028\pi$
$571$	18.8384	0.788364	0.394182	+	0.919032i	$0.371028\pi$
$572$	0	0
$573$	−13.3141	−0.556205
$574$	1.03047	0.0430110
$575$	−3.35600	−0.139955
$576$	−24.4754	−1.01981
$577$	−26.0946	−1.08633	−0.543166	−	0.839625i	$-0.682775\pi$
$577$	−26.0946	−1.08633	−0.543166	+	0.839625i	$0.682775\pi$
$578$	0.772262	0.0321218
$579$	−19.1732	−0.796812
$580$	18.8828	0.784068
$581$	−15.6694	−0.650075
$582$	1.67055	0.0692464
$583$	0	0
$584$	8.56825	0.354557
$585$	−27.7172	−1.14597
$586$	−2.00303	−0.0827443
$587$	8.40313	0.346834	0.173417	−	0.984848i	$-0.444519\pi$
$587$	8.40313	0.346834	0.173417	+	0.984848i	$0.444519\pi$
$588$	−5.06322	−0.208804
$589$	−39.1610	−1.61360
$590$	0.556299	0.0229025
$591$	41.6987	1.71526
$592$	−33.7934	−1.38890
$593$	22.8365	0.937781	0.468891	−	0.883256i	$-0.344654\pi$
$593$	22.8365	0.937781	0.468891	+	0.883256i	$0.344654\pi$
$594$	0	0
$595$	−3.76771	−0.154461
$596$	32.9246	1.34864
$597$	−11.5173	−0.471370
$598$	−6.52760	−0.266933
$599$	−23.9330	−0.977876	−0.488938	−	0.872319i	$-0.662616\pi$
$599$	−23.9330	−0.977876	−0.488938	+	0.872319i	$0.662616\pi$
$600$	2.84354	0.116087
$601$	−21.6637	−0.883681	−0.441840	−	0.897094i	$-0.645674\pi$
$601$	−21.6637	−0.883681	−0.441840	+	0.897094i	$0.645674\pi$
$602$	2.77250	0.112999
$603$	47.3569	1.92852
$604$	11.3696	0.462621
$605$	0	0
$606$	−0.476119	−0.0193410
$607$	−25.6790	−1.04228	−0.521138	−	0.853472i	$-0.674492\pi$
$607$	−25.6790	−1.04228	−0.521138	+	0.853472i	$0.674492\pi$
$608$	−15.1645	−0.615003
$609$	−25.8231	−1.04641
$610$	−0.815794	−0.0330305
$611$	−37.4425	−1.51476
$612$	28.4490	1.14998
$613$	30.4680	1.23059	0.615295	−	0.788297i	$-0.289037\pi$
$613$	30.4680	1.23059	0.615295	+	0.788297i	$0.289037\pi$
$614$	−2.54324	−0.102637
$615$	−9.84671	−0.397058
$616$	0	0
$617$	−24.9619	−1.00493	−0.502465	−	0.864597i	$-0.667573\pi$
$617$	−24.9619	−1.00493	−0.502465	+	0.864597i	$0.667573\pi$
$618$	0.249047	0.0100181
$619$	−18.7301	−0.752825	−0.376413	−	0.926452i	$-0.622842\pi$
$619$	−18.7301	−0.752825	−0.376413	+	0.926452i	$0.622842\pi$
$620$	15.5979	0.626426
$621$	−8.16125	−0.327500
$622$	3.63920	0.145919
$623$	−4.79611	−0.192152
$624$	−65.9944	−2.64189
$625$	1.00000	0.0400000
$626$	−7.30717	−0.292053
$627$	0	0
$628$	−10.9574	−0.437246
$629$	35.8582	1.42976
$630$	−1.08063	−0.0430532
$631$	26.0862	1.03847	0.519237	−	0.854630i	$-0.326216\pi$
$631$	26.0862	1.03847	0.519237	+	0.854630i	$0.326216\pi$
$632$	4.72603	0.187991
$633$	43.9093	1.74524
$634$	−4.33209	−0.172049
$635$	−6.23784	−0.247541
$636$	−60.2865	−2.39052
$637$	−7.06322	−0.279855
$638$	0	0
$639$	21.8799	0.865556
$640$	7.99565	0.316056
$641$	49.8455	1.96878	0.984390	−	0.176000i	$-0.0563159\pi$
$641$	49.8455	1.96878	0.984390	+	0.176000i	$0.0563159\pi$
$642$	−12.0000	−0.473602
$643$	−35.9365	−1.41720	−0.708598	−	0.705612i	$-0.750672\pi$
$643$	−35.9365	−1.41720	−0.708598	+	0.705612i	$0.750672\pi$
$644$	6.45751	0.254462
$645$	−26.4928	−1.04315
$646$	5.01229	0.197206
$647$	14.1284	0.555445	0.277723	−	0.960661i	$-0.410420\pi$
$647$	14.1284	0.555445	0.277723	+	0.960661i	$0.410420\pi$
$648$	−5.80665	−0.228107
$649$	0	0
$650$	1.94505	0.0762911
$651$	−21.3308	−0.836019
$652$	2.37638	0.0930661
$653$	29.9844	1.17338	0.586689	−	0.809812i	$-0.300431\pi$
$653$	29.9844	1.17338	0.586689	+	0.809812i	$0.300431\pi$
$654$	8.35882	0.326856
$655$	1.42402	0.0556409
$656$	−13.2870	−0.518772
$657$	31.1146	1.21390
$658$	−1.45979	−0.0569085
$659$	42.8430	1.66893	0.834464	−	0.551063i	$-0.185778\pi$
$659$	42.8430	1.66893	0.834464	+	0.551063i	$0.185778\pi$
$660$	0	0
$661$	−13.6528	−0.531034	−0.265517	−	0.964106i	$-0.585543\pi$
$661$	−13.6528	−0.531034	−0.265517	+	0.964106i	$0.585543\pi$
$662$	−0.421679	−0.0163890
$663$	70.0267	2.71961
$664$	−16.9327	−0.657118
$665$	4.83093	0.187335
$666$	10.2846	0.398520
$667$	32.9342	1.27522
$668$	2.87005	0.111046
$669$	−17.6512	−0.682435
$670$	−3.32326	−0.128389
$671$	0	0
$672$	−8.26004	−0.318638
$673$	−19.4352	−0.749173	−0.374586	−	0.927192i	$-0.622215\pi$
$673$	−19.4352	−0.749173	−0.374586	+	0.927192i	$0.622215\pi$
$674$	0.212159	0.00817208
$675$	2.43184	0.0936014
$676$	−70.9807	−2.73003
$677$	41.1836	1.58281	0.791407	−	0.611289i	$-0.209349\pi$
$677$	41.1836	1.58281	0.791407	+	0.611289i	$0.209349\pi$
$678$	2.10031	0.0806620
$679$	−2.30540	−0.0884732
$680$	−4.07149	−0.156134
$681$	−65.8793	−2.52450
$682$	0	0
$683$	21.4320	0.820072	0.410036	−	0.912069i	$-0.365516\pi$
$683$	21.4320	0.820072	0.410036	+	0.912069i	$0.365516\pi$
$684$	−36.4771	−1.39474
$685$	18.5019	0.706922
$686$	−0.275377	−0.0105140
$687$	5.36872	0.204829
$688$	−35.7490	−1.36292
$689$	−84.1000	−3.20396
$690$	2.43184	0.0925784
$691$	−39.5576	−1.50484	−0.752421	−	0.658682i	$-0.771114\pi$
$691$	−39.5576	−1.50484	−0.752421	+	0.658682i	$0.771114\pi$
$692$	12.4681	0.473964
$693$	0	0
$694$	−1.69903	−0.0644943
$695$	−4.16125	−0.157845
$696$	−27.9051	−1.05774
$697$	14.0989	0.534033
$698$	0.260486	0.00985953
$699$	−24.6444	−0.932138
$700$	−1.92417	−0.0727267
$701$	22.7381	0.858807	0.429404	−	0.903113i	$-0.358724\pi$
$701$	22.7381	0.858807	0.429404	+	0.903113i	$0.358724\pi$
$702$	4.73004	0.178524
$703$	−45.9772	−1.73406
$704$	0	0
$705$	13.9491	0.525353
$706$	−7.73843	−0.291240
$707$	0.657058	0.0247112
$708$	10.2284	0.384406
$709$	7.18618	0.269883	0.134941	−	0.990854i	$-0.456915\pi$
$709$	7.18618	0.269883	0.134941	+	0.990854i	$0.456915\pi$
$710$	−1.53542	−0.0576231
$711$	17.1620	0.643625
$712$	−5.18280	−0.194234
$713$	27.2048	1.01883
$714$	2.73017	0.102174
$715$	0	0
$716$	27.9495	1.04452
$717$	14.2474	0.532080
$718$	1.08335	0.0404303
$719$	−10.3351	−0.385435	−0.192717	−	0.981254i	$-0.561730\pi$
$719$	−10.3351	−0.385435	−0.192717	+	0.981254i	$0.561730\pi$
$720$	13.9338	0.519280
$721$	−0.343692	−0.0127998
$722$	−1.19454	−0.0444563
$723$	67.0220	2.49257
$724$	8.28431	0.307884
$725$	−9.81352	−0.364465
$726$	0	0
$727$	32.4887	1.20494	0.602470	−	0.798141i	$-0.294183\pi$
$727$	32.4887	1.20494	0.602470	+	0.798141i	$0.294183\pi$
$728$	−7.63270	−0.282887
$729$	−40.2834	−1.49198
$730$	−2.18346	−0.0808133
$731$	37.9333	1.40301
$732$	−14.9996	−0.554400
$733$	−18.9260	−0.699048	−0.349524	−	0.936927i	$-0.613657\pi$
$733$	−18.9260	−0.699048	−0.349524	+	0.936927i	$0.613657\pi$
$734$	2.68343	0.0990471
$735$	2.63138	0.0970600
$736$	10.5347	0.388313
$737$	0	0
$738$	4.04374	0.148852
$739$	−31.3237	−1.15226	−0.576131	−	0.817358i	$-0.695438\pi$
$739$	−31.3237	−1.15226	−0.576131	+	0.817358i	$0.695438\pi$
$740$	18.3128	0.673192
$741$	−89.7877	−3.29843
$742$	−3.27885	−0.120370
$743$	14.6970	0.539180	0.269590	−	0.962975i	$-0.413112\pi$
$743$	14.6970	0.539180	0.269590	+	0.962975i	$0.413112\pi$
$744$	−23.0506	−0.845076
$745$	−17.1111	−0.626902
$746$	6.43171	0.235482
$747$	−61.4892	−2.24977
$748$	0	0
$749$	16.5603	0.605102
$750$	−0.724623	−0.0264595
$751$	−3.42946	−0.125143	−0.0625714	−	0.998040i	$-0.519930\pi$
$751$	−3.42946	−0.125143	−0.0625714	+	0.998040i	$0.519930\pi$
$752$	18.8227	0.686395
$753$	−18.7398	−0.682915
$754$	−19.0878	−0.695136
$755$	−5.90883	−0.215044
$756$	−4.67926	−0.170183
$757$	38.7675	1.40903	0.704514	−	0.709690i	$-0.251165\pi$
$757$	38.7675	1.40903	0.704514	+	0.709690i	$0.251165\pi$
$758$	4.19607	0.152408
$759$	0	0
$760$	5.22043	0.189365
$761$	−7.06427	−0.256080	−0.128040	−	0.991769i	$-0.540869\pi$
$761$	−7.06427	−0.256080	−0.128040	+	0.991769i	$0.540869\pi$
$762$	4.52008	0.163745
$763$	−11.5354	−0.417610
$764$	9.73579	0.352229
$765$	−14.7851	−0.534557
$766$	6.59405	0.238253
$767$	14.2686	0.515211
$768$	27.0305	0.975378
$769$	37.5651	1.35463	0.677317	−	0.735692i	$-0.263143\pi$
$769$	37.5651	1.35463	0.677317	+	0.735692i	$0.263143\pi$
$770$	0	0
$771$	40.7161	1.46636
$772$	14.0202	0.504598
$773$	−31.3414	−1.12727	−0.563636	−	0.826023i	$-0.690598\pi$
$773$	−31.3414	−1.12727	−0.563636	+	0.826023i	$0.690598\pi$
$774$	10.8798	0.391065
$775$	−8.10630	−0.291187
$776$	−2.49128	−0.0894317
$777$	−25.0435	−0.898432
$778$	8.41323	0.301629
$779$	−18.0775	−0.647693
$780$	35.7626	1.28051
$781$	0	0
$782$	−3.48199	−0.124516
$783$	−23.8649	−0.852861
$784$	3.55075	0.126813
$785$	5.69460	0.203249
$786$	−1.03187	−0.0368057
$787$	18.0165	0.642220	0.321110	−	0.947042i	$-0.395944\pi$
$787$	18.0165	0.642220	0.321110	+	0.947042i	$0.395944\pi$
$788$	−30.4917	−1.08622
$789$	−38.6213	−1.37495
$790$	−1.20434	−0.0428484
$791$	−2.89849	−0.103058
$792$	0	0
$793$	−20.9245	−0.743050
$794$	7.37209	0.261626
$795$	31.3312	1.11120
$796$	8.42186	0.298505
$797$	19.0381	0.674364	0.337182	−	0.941440i	$-0.390526\pi$
$797$	19.0381	0.674364	0.337182	+	0.941440i	$0.390526\pi$
$798$	−3.50060	−0.123920
$799$	−19.9728	−0.706588
$800$	−3.13905	−0.110982
$801$	−18.8207	−0.664998
$802$	8.40173	0.296675
$803$	0	0
$804$	−61.1030	−2.15494
$805$	−3.35600	−0.118284
$806$	−15.7672	−0.555375
$807$	−37.1666	−1.30833
$808$	0.710034	0.0249789
$809$	−45.3736	−1.59525	−0.797625	−	0.603154i	$-0.793910\pi$
$809$	−45.3736	−1.59525	−0.797625	+	0.603154i	$0.793910\pi$
$810$	1.47972	0.0519919
$811$	20.9739	0.736493	0.368247	−	0.929728i	$-0.379958\pi$
$811$	20.9739	0.736493	0.368247	+	0.929728i	$0.379958\pi$
$812$	18.8828	0.662658
$813$	42.3541	1.48542
$814$	0	0
$815$	−1.23502	−0.0432607
$816$	−35.2032	−1.23236
$817$	−48.6378	−1.70162
$818$	0.453916	0.0158708
$819$	−27.7172	−0.968519
$820$	7.20029	0.251445
$821$	−25.3681	−0.885353	−0.442677	−	0.896681i	$-0.645971\pi$
$821$	−25.3681	−0.885353	−0.442677	+	0.896681i	$0.645971\pi$
$822$	−13.4069	−0.467620
$823$	−50.3694	−1.75577	−0.877884	−	0.478873i	$-0.841045\pi$
$823$	−50.3694	−1.75577	−0.877884	+	0.478873i	$0.841045\pi$
$824$	−0.371403	−0.0129384
$825$	0	0
$826$	0.556299	0.0193561
$827$	−28.8505	−1.00323	−0.501616	−	0.865090i	$-0.667261\pi$
$827$	−28.8505	−1.00323	−0.501616	+	0.865090i	$0.667261\pi$
$828$	25.3404	0.880638
$829$	7.66185	0.266107	0.133054	−	0.991109i	$-0.457522\pi$
$829$	7.66185	0.266107	0.133054	+	0.991109i	$0.457522\pi$
$830$	4.31499	0.149775
$831$	40.5387	1.40627
$832$	44.0539	1.52729
$833$	−3.76771	−0.130543
$834$	3.01534	0.104413
$835$	−1.49158	−0.0516183
$836$	0	0
$837$	−19.7132	−0.681388
$838$	5.03799	0.174034
$839$	24.1802	0.834794	0.417397	−	0.908724i	$-0.362943\pi$
$839$	24.1802	0.834794	0.417397	+	0.908724i	$0.362943\pi$
$840$	2.84354	0.0981115
$841$	67.3051	2.32087
$842$	5.09749	0.175671
$843$	14.4994	0.499386
$844$	−32.1082	−1.10521
$845$	36.8890	1.26902
$846$	−5.72846	−0.196949
$847$	0	0
$848$	42.2780	1.45183
$849$	−11.2573	−0.386350
$850$	1.03754	0.0355874
$851$	31.9400	1.09489
$852$	−28.2309	−0.967174
$853$	−18.7338	−0.641432	−0.320716	−	0.947175i	$-0.603923\pi$
$853$	−18.7338	−0.641432	−0.320716	+	0.947175i	$0.603923\pi$
$854$	−0.815794	−0.0279159
$855$	18.9574	0.648328
$856$	17.8955	0.611657
$857$	39.2820	1.34185	0.670924	−	0.741526i	$-0.265898\pi$
$857$	39.2820	1.34185	0.670924	+	0.741526i	$0.265898\pi$
$858$	0	0
$859$	−33.2018	−1.13283	−0.566415	−	0.824120i	$-0.691670\pi$
$859$	−33.2018	−1.13283	−0.566415	+	0.824120i	$0.691670\pi$
$860$	19.3725	0.660598
$861$	−9.84671	−0.335575
$862$	−2.27367	−0.0774415
$863$	−8.10828	−0.276009	−0.138004	−	0.990432i	$-0.544069\pi$
$863$	−8.10828	−0.276009	−0.138004	+	0.990432i	$0.544069\pi$
$864$	−7.63366	−0.259702
$865$	−6.47972	−0.220317
$866$	0.789731	0.0268361
$867$	−7.37938	−0.250617
$868$	15.5979	0.529427
$869$	0	0
$870$	7.11110	0.241089
$871$	−85.2390	−2.88821
$872$	−12.4655	−0.422134
$873$	−9.04678	−0.306187
$874$	4.46458	0.151017
$875$	1.00000	0.0338062
$876$	−40.1461	−1.35641
$877$	−25.0623	−0.846292	−0.423146	−	0.906061i	$-0.639074\pi$
$877$	−25.0623	−0.846292	−0.423146	+	0.906061i	$0.639074\pi$
$878$	6.29878	0.212573
$879$	19.1400	0.645577
$880$	0	0
$881$	15.0435	0.506829	0.253415	−	0.967358i	$-0.418446\pi$
$881$	15.0435	0.506829	0.253415	+	0.967358i	$0.418446\pi$
$882$	−1.08063	−0.0363866
$883$	14.6536	0.493132	0.246566	−	0.969126i	$-0.420698\pi$
$883$	14.6536	0.493132	0.246566	+	0.969126i	$0.420698\pi$
$884$	−51.2062	−1.72225
$885$	−5.31574	−0.178687
$886$	2.82146	0.0947888
$887$	53.8754	1.80896	0.904479	−	0.426519i	$-0.140260\pi$
$887$	53.8754	1.80896	0.904479	+	0.426519i	$0.140260\pi$
$888$	−27.0627	−0.908165
$889$	−6.23784	−0.209210
$890$	1.32074	0.0442713
$891$	0	0
$892$	12.9072	0.432167
$893$	25.6090	0.856972
$894$	12.3991	0.414688
$895$	−14.5255	−0.485535
$896$	7.99565	0.267116
$897$	62.3748	2.08263
$898$	7.64016	0.254955
$899$	79.5513	2.65319
$900$	−7.55075	−0.251692
$901$	−44.8612	−1.49454
$902$	0	0
$903$	−26.4928	−0.881624
$904$	−3.13219	−0.104175
$905$	−4.30540	−0.143116
$906$	4.28167	0.142249
$907$	46.1536	1.53250	0.766252	−	0.642540i	$-0.222119\pi$
$907$	46.1536	1.53250	0.766252	+	0.642540i	$0.222119\pi$
$908$	48.1735	1.59869
$909$	2.57840	0.0855203
$910$	1.94505	0.0644778
$911$	−17.6784	−0.585711	−0.292856	−	0.956157i	$-0.594606\pi$
$911$	−17.6784	−0.585711	−0.292856	+	0.956157i	$0.594606\pi$
$912$	45.1372	1.49464
$913$	0	0
$914$	−9.00884	−0.297986
$915$	7.79536	0.257707
$916$	−3.92581	−0.129712
$917$	1.42402	0.0470251
$918$	2.52313	0.0832757
$919$	7.21141	0.237882	0.118941	−	0.992901i	$-0.462050\pi$
$919$	7.21141	0.237882	0.118941	+	0.992901i	$0.462050\pi$
$920$	−3.62659	−0.119565
$921$	24.3020	0.800779
$922$	−1.46893	−0.0483767
$923$	−39.3823	−1.29628
$924$	0	0
$925$	−9.51726	−0.312925
$926$	−1.98895	−0.0653608
$927$	−1.34871	−0.0442973
$928$	30.8051	1.01123
$929$	26.9991	0.885813	0.442906	−	0.896568i	$-0.353947\pi$
$929$	26.9991	0.885813	0.442906	+	0.896568i	$0.353947\pi$
$930$	5.87401	0.192616
$931$	4.83093	0.158327
$932$	18.0210	0.590296
$933$	−34.7746	−1.13847
$934$	−7.72996	−0.252932
$935$	0	0
$936$	−29.9520	−0.979012
$937$	−35.1590	−1.14859	−0.574297	−	0.818647i	$-0.694724\pi$
$937$	−35.1590	−1.14859	−0.574297	+	0.818647i	$0.694724\pi$
$938$	−3.32326	−0.108508
$939$	69.8240	2.27862
$940$	−10.2001	−0.332691
$941$	3.73541	0.121771	0.0608854	−	0.998145i	$-0.480608\pi$
$941$	3.73541	0.121771	0.0608854	+	0.998145i	$0.480608\pi$
$942$	−4.12644	−0.134447
$943$	12.5583	0.408954
$944$	−7.17299	−0.233461
$945$	2.43184	0.0791077
$946$	0	0
$947$	−47.2263	−1.53465	−0.767325	−	0.641259i	$-0.778412\pi$
$947$	−47.2263	−1.53465	−0.767325	+	0.641259i	$0.778412\pi$
$948$	−22.1435	−0.719189
$949$	−56.0040	−1.81797
$950$	−1.33033	−0.0431615
$951$	41.3955	1.34234
$952$	−4.07149	−0.131958
$953$	−9.60888	−0.311262	−0.155631	−	0.987815i	$-0.549741\pi$
$953$	−9.60888	−0.311262	−0.155631	+	0.987815i	$0.549741\pi$
$954$	−12.8668	−0.416577
$955$	−5.05974	−0.163729
$956$	−10.4183	−0.336951
$957$	0	0
$958$	4.75698	0.153691
$959$	18.5019	0.597458
$960$	−16.4122	−0.529700
$961$	34.7122	1.11975
$962$	−18.5115	−0.596836
$963$	64.9856	2.09413
$964$	−49.0091	−1.57848
$965$	−7.28637	−0.234557
$966$	2.43184	0.0782431
$967$	−46.2737	−1.48806	−0.744030	−	0.668146i	$-0.767088\pi$
$967$	−46.2737	−1.48806	−0.744030	+	0.668146i	$0.767088\pi$
$968$	0	0
$969$	−47.8951	−1.53861
$970$	0.634855	0.0203840
$971$	20.7910	0.667215	0.333608	−	0.942712i	$-0.391734\pi$
$971$	20.7910	0.667215	0.333608	+	0.942712i	$0.391734\pi$
$972$	41.2445	1.32292
$973$	−4.16125	−0.133404
$974$	6.21216	0.199050
$975$	−18.5860	−0.595229
$976$	10.5190	0.336704
$977$	−8.65891	−0.277023	−0.138512	−	0.990361i	$-0.544232\pi$
$977$	−8.65891	−0.277023	−0.138512	+	0.990361i	$0.544232\pi$
$978$	0.894920	0.0286164
$979$	0	0
$980$	−1.92417	−0.0614653
$981$	−45.2669	−1.44526
$982$	−5.69919	−0.181868
$983$	10.0007	0.318972	0.159486	−	0.987200i	$-0.449016\pi$
$983$	10.0007	0.318972	0.159486	+	0.987200i	$0.449016\pi$
$984$	−10.6406	−0.339211
$985$	15.8467	0.504918
$986$	−10.1819	−0.324259
$987$	13.9491	0.444005
$988$	65.6562	2.08880
$989$	33.7883	1.07441
$990$	0	0
$991$	18.3793	0.583838	0.291919	−	0.956443i	$-0.405706\pi$
$991$	18.3793	0.583838	0.291919	+	0.956443i	$0.405706\pi$
$992$	25.4461	0.807914
$993$	4.02937	0.127868
$994$	−1.53542	−0.0487004
$995$	−4.37689	−0.138757
$996$	79.3374	2.51390
$997$	36.3472	1.15113	0.575564	−	0.817757i	$-0.304783\pi$
$997$	36.3472	1.15113	0.575564	+	0.817757i	$0.304783\pi$
$998$	−0.215247	−0.00681352
$999$	−23.1444	−0.732257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.u.1.2	✓	4
11.10	odd	2		4235.2.a.v.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.u.1.2	✓	4	1.1	even	1	trivial
4235.2.a.v.1.3	yes	4	11.10	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} -0.724623 q^{6} +1.00000 q^{7} +1.08063 q^{8} +3.92417 q^{9} +O(q^{10})\)	\(q-0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} -0.724623 q^{6} +1.00000 q^{7} +1.08063 q^{8} +3.92417 q^{9} -0.275377 q^{10} -5.06322 q^{12} -7.06322 q^{13} -0.275377 q^{14} +2.63138 q^{15} +3.55075 q^{16} -3.76771 q^{17} -1.08063 q^{18} +4.83093 q^{19} -1.92417 q^{20} +2.63138 q^{21} -3.35600 q^{23} +2.84354 q^{24} +1.00000 q^{25} +1.94505 q^{26} +2.43184 q^{27} -1.92417 q^{28} -9.81352 q^{29} -0.724623 q^{30} -8.10630 q^{31} -3.13905 q^{32} +1.03754 q^{34} +1.00000 q^{35} -7.55075 q^{36} -9.51726 q^{37} -1.33033 q^{38} -18.5860 q^{39} +1.08063 q^{40} -3.74203 q^{41} -0.724623 q^{42} -10.0680 q^{43} +3.92417 q^{45} +0.924167 q^{46} +5.30105 q^{47} +9.34339 q^{48} +1.00000 q^{49} -0.275377 q^{50} -9.91428 q^{51} +13.5908 q^{52} +11.9068 q^{53} -0.669673 q^{54} +1.08063 q^{56} +12.7120 q^{57} +2.70242 q^{58} -2.02013 q^{59} -5.06322 q^{60} +2.96246 q^{61} +2.23229 q^{62} +3.92417 q^{63} -6.23709 q^{64} -7.06322 q^{65} +12.0680 q^{67} +7.24970 q^{68} -8.83093 q^{69} -0.275377 q^{70} +5.57568 q^{71} +4.24056 q^{72} +7.92896 q^{73} +2.62084 q^{74} +2.63138 q^{75} -9.29551 q^{76} +5.11817 q^{78} +4.37341 q^{79} +3.55075 q^{80} -5.37341 q^{81} +1.03047 q^{82} -15.6694 q^{83} -5.06322 q^{84} -3.76771 q^{85} +2.77250 q^{86} -25.8231 q^{87} -4.79611 q^{89} -1.08063 q^{90} -7.06322 q^{91} +6.45751 q^{92} -21.3308 q^{93} -1.45979 q^{94} +4.83093 q^{95} -8.26004 q^{96} -2.30540 q^{97} -0.275377 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9} - 8 q^{12} - 16 q^{13} - 2 q^{15} + 12 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 2 q^{23} + 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} + 4 q^{28} - 12 q^{29} - 4 q^{30} - 6 q^{31} - 12 q^{32} + 8 q^{34} + 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} - 6 q^{40} - 18 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} - 4 q^{51} - 30 q^{52} + 34 q^{53} + 2 q^{54} - 6 q^{56} + 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} + 8 q^{61} + 22 q^{62} + 4 q^{63} - 16 q^{64} - 16 q^{65} + 14 q^{67} + 44 q^{68} - 10 q^{69} + 12 q^{72} - 2 q^{73} - 48 q^{74} - 2 q^{75} - 38 q^{76} + 14 q^{78} + 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} + 10 q^{83} - 8 q^{84} - 2 q^{85} - 24 q^{86} - 32 q^{87} + 10 q^{89} + 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} - 54 q^{94} - 6 q^{95} - 8 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9 - 8 * q^12 - 16 * q^13 - 2 * q^15 + 12 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 2 * q^23 + 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 + 4 * q^28 - 12 * q^29 - 4 * q^30 - 6 * q^31 - 12 * q^32 + 8 * q^34 + 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 - 6 * q^40 - 18 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 - 4 * q^51 - 30 * q^52 + 34 * q^53 + 2 * q^54 - 6 * q^56 + 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 + 22 * q^62 + 4 * q^63 - 16 * q^64 - 16 * q^65 + 14 * q^67 + 44 * q^68 - 10 * q^69 + 12 * q^72 - 2 * q^73 - 48 * q^74 - 2 * q^75 - 38 * q^76 + 14 * q^78 + 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 + 10 * q^83 - 8 * q^84 - 2 * q^85 - 24 * q^86 - 32 * q^87 + 10 * q^89 + 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 - 54 * q^94 - 6 * q^95 - 8 * q^96 - 34 * q^97

Introduction

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