LMFDB - Embedded newform 4235.2.a.z.1.3

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:	$5$
Coefficient field:	5.5.270017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 7x^{2} + 7x - 3 $ x^5 - 2x^4 - 5x^3 + 7x^2 + 7x - 3
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			1.3
Root			$-1.11334$ 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)

$f(q)$	$=$	$q-0.352882 q^{2} -1.11334 q^{3} -1.87547 q^{4} +1.00000 q^{5} +0.392879 q^{6} -1.00000 q^{7} +1.36758 q^{8} -1.76046 q^{9} +O(q^{10})$	\(q-0.352882 q^{2} -1.11334 q^{3} -1.87547 q^{4} +1.00000 q^{5} +0.392879 q^{6} -1.00000 q^{7} +1.36758 q^{8} -1.76046 q^{9} -0.352882 q^{10} +2.08805 q^{12} +1.18669 q^{13} +0.352882 q^{14} -1.11334 q^{15} +3.26835 q^{16} -2.58016 q^{17} +0.621235 q^{18} +2.84851 q^{19} -1.87547 q^{20} +1.11334 q^{21} -2.43927 q^{23} -1.52259 q^{24} +1.00000 q^{25} -0.418762 q^{26} +5.30004 q^{27} +1.87547 q^{28} +0.595940 q^{29} +0.392879 q^{30} -5.79734 q^{31} -3.88851 q^{32} +0.910491 q^{34} -1.00000 q^{35} +3.30170 q^{36} -1.54955 q^{37} -1.00519 q^{38} -1.32120 q^{39} +1.36758 q^{40} +1.81683 q^{41} -0.392879 q^{42} +5.14216 q^{43} -1.76046 q^{45} +0.860772 q^{46} +8.24886 q^{47} -3.63880 q^{48} +1.00000 q^{49} -0.352882 q^{50} +2.87261 q^{51} -2.22561 q^{52} +3.28426 q^{53} -1.87029 q^{54} -1.36758 q^{56} -3.17138 q^{57} -0.210296 q^{58} -4.07501 q^{59} +2.08805 q^{60} +3.64174 q^{61} +2.04577 q^{62} +1.76046 q^{63} -5.16452 q^{64} +1.18669 q^{65} -0.843325 q^{67} +4.83902 q^{68} +2.71574 q^{69} +0.352882 q^{70} +10.7292 q^{71} -2.40758 q^{72} -4.54124 q^{73} +0.546809 q^{74} -1.11334 q^{75} -5.34231 q^{76} +0.466227 q^{78} -0.402859 q^{79} +3.26835 q^{80} -0.619380 q^{81} -0.641126 q^{82} +0.473203 q^{83} -2.08805 q^{84} -2.58016 q^{85} -1.81457 q^{86} -0.663487 q^{87} -1.45319 q^{89} +0.621235 q^{90} -1.18669 q^{91} +4.57478 q^{92} +6.45443 q^{93} -2.91087 q^{94} +2.84851 q^{95} +4.32925 q^{96} +6.40638 q^{97} -0.352882 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	$ 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * q^98

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 $

$2$	−0.352882	−0.249525	−0.124763	−	0.992187i	$-0.539817\pi$
$2$	−0.352882	−0.249525	−0.124763	+	0.992187i	$0.539817\pi$
$3$	−1.11334	−0.642790	−0.321395	−	0.946945i	$-0.604152\pi$
$3$	−1.11334	−0.642790	−0.321395	+	0.946945i	$0.604152\pi$
$4$	−1.87547	−0.937737
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.392879	0.160392
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.36758	0.483514
$9$	−1.76046	−0.586821
$10$	−0.352882	−0.111591
$11$	0	0
$11$	0	0
$12$	2.08805	0.602768
$13$	1.18669	0.329129	0.164565	−	0.986366i	$-0.447378\pi$
$13$	1.18669	0.329129	0.164565	+	0.986366i	$0.447378\pi$
$14$	0.352882	0.0943116
$15$	−1.11334	−0.287464
$16$	3.26835	0.817088
$17$	−2.58016	−0.625781	−0.312890	−	0.949789i	$-0.601297\pi$
$17$	−2.58016	−0.625781	−0.312890	+	0.949789i	$0.601297\pi$
$18$	0.621235	0.146427
$19$	2.84851	0.653494	0.326747	−	0.945112i	$-0.394048\pi$
$19$	2.84851	0.653494	0.326747	+	0.945112i	$0.394048\pi$
$20$	−1.87547	−0.419369
$21$	1.11334	0.242952
$22$	0	0
$23$	−2.43927	−0.508622	−0.254311	−	0.967122i	$-0.581849\pi$
$23$	−2.43927	−0.508622	−0.254311	+	0.967122i	$0.581849\pi$
$24$	−1.52259	−0.310798
$25$	1.00000	0.200000
$26$	−0.418762	−0.0821260
$27$	5.30004	1.01999
$28$	1.87547	0.354431
$29$	0.595940	0.110663	0.0553317	−	0.998468i	$-0.482378\pi$
$29$	0.595940	0.110663	0.0553317	+	0.998468i	$0.482378\pi$
$30$	0.392879	0.0717296
$31$	−5.79734	−1.04123	−0.520616	−	0.853791i	$-0.674298\pi$
$31$	−5.79734	−1.04123	−0.520616	+	0.853791i	$0.674298\pi$
$32$	−3.88851	−0.687398
$33$	0	0
$34$	0.910491	0.156148
$35$	−1.00000	−0.169031
$36$	3.30170	0.550284
$37$	−1.54955	−0.254745	−0.127373	−	0.991855i	$-0.540654\pi$
$37$	−1.54955	−0.254745	−0.127373	+	0.991855i	$0.540654\pi$
$38$	−1.00519	−0.163063
$39$	−1.32120	−0.211561
$40$	1.36758	0.216234
$41$	1.81683	0.283741	0.141871	−	0.989885i	$-0.454688\pi$
$41$	1.81683	0.283741	0.141871	+	0.989885i	$0.454688\pi$
$42$	−0.392879	−0.0606226
$43$	5.14216	0.784172	0.392086	−	0.919929i	$-0.371754\pi$
$43$	5.14216	0.784172	0.392086	+	0.919929i	$0.371754\pi$
$44$	0	0
$45$	−1.76046	−0.262434
$46$	0.860772	0.126914
$47$	8.24886	1.20322	0.601610	−	0.798790i	$-0.294526\pi$
$47$	8.24886	1.20322	0.601610	+	0.798790i	$0.294526\pi$
$48$	−3.63880	−0.525216
$49$	1.00000	0.142857
$50$	−0.352882	−0.0499050
$51$	2.87261	0.402245
$52$	−2.22561	−0.308637
$53$	3.28426	0.451127	0.225564	−	0.974228i	$-0.427578\pi$
$53$	3.28426	0.451127	0.225564	+	0.974228i	$0.427578\pi$
$54$	−1.87029	−0.254514
$55$	0	0
$56$	−1.36758	−0.182751
$57$	−3.17138	−0.420059
$58$	−0.210296	−0.0276133
$59$	−4.07501	−0.530522	−0.265261	−	0.964177i	$-0.585458\pi$
$59$	−4.07501	−0.530522	−0.265261	+	0.964177i	$0.585458\pi$
$60$	2.08805	0.269566
$61$	3.64174	0.466277	0.233138	−	0.972444i	$-0.425100\pi$
$61$	3.64174	0.466277	0.233138	+	0.972444i	$0.425100\pi$
$62$	2.04577	0.259814
$63$	1.76046	0.221798
$64$	−5.16452	−0.645565
$65$	1.18669	0.147191
$66$	0	0
$67$	−0.843325	−0.103029	−0.0515143	−	0.998672i	$-0.516405\pi$
$67$	−0.843325	−0.103029	−0.0515143	+	0.998672i	$0.516405\pi$
$68$	4.83902	0.586818
$69$	2.71574	0.326937
$70$	0.352882	0.0421774
$71$	10.7292	1.27332	0.636661	−	0.771144i	$-0.280315\pi$
$71$	10.7292	1.27332	0.636661	+	0.771144i	$0.280315\pi$
$72$	−2.40758	−0.283736
$73$	−4.54124	−0.531512	−0.265756	−	0.964040i	$-0.585622\pi$
$73$	−4.54124	−0.531512	−0.265756	+	0.964040i	$0.585622\pi$
$74$	0.546809	0.0635653
$75$	−1.11334	−0.128558
$76$	−5.34231	−0.612805
$77$	0	0
$78$	0.466227	0.0527898
$79$	−0.402859	−0.0453252	−0.0226626	−	0.999743i	$-0.507214\pi$
$79$	−0.402859	−0.0453252	−0.0226626	+	0.999743i	$0.507214\pi$
$80$	3.26835	0.365413
$81$	−0.619380	−0.0688200
$82$	−0.641126	−0.0708005
$83$	0.473203	0.0519408	0.0259704	−	0.999663i	$-0.491732\pi$
$83$	0.473203	0.0519408	0.0259704	+	0.999663i	$0.491732\pi$
$84$	−2.08805	−0.227825
$85$	−2.58016	−0.279858
$86$	−1.81457	−0.195671
$87$	−0.663487	−0.0711333
$88$	0	0
$89$	−1.45319	−0.154038	−0.0770190	−	0.997030i	$-0.524540\pi$
$89$	−1.45319	−0.154038	−0.0770190	+	0.997030i	$0.524540\pi$
$90$	0.621235	0.0654839
$91$	−1.18669	−0.124399
$92$	4.57478	0.476954
$93$	6.45443	0.669294
$94$	−2.91087	−0.300233
$95$	2.84851	0.292251
$96$	4.32925	0.441853
$97$	6.40638	0.650469	0.325235	−	0.945633i	$-0.394557\pi$
$97$	6.40638	0.650469	0.325235	+	0.945633i	$0.394557\pi$
$98$	−0.352882	−0.0356464
$99$	0	0
$100$	−1.87547	−0.187547
$101$	3.79900	0.378015	0.189007	−	0.981976i	$-0.439473\pi$
$101$	3.79900	0.378015	0.189007	+	0.981976i	$0.439473\pi$
$102$	−1.01369	−0.100370
$103$	−14.4936	−1.42810	−0.714048	−	0.700097i	$-0.753140\pi$
$103$	−14.4936	−1.42810	−0.714048	+	0.700097i	$0.753140\pi$
$104$	1.62290	0.159139
$105$	1.11334	0.108651
$106$	−1.15895	−0.112568
$107$	−2.10716	−0.203707	−0.101854	−	0.994799i	$-0.532477\pi$
$107$	−2.10716	−0.203707	−0.101854	+	0.994799i	$0.532477\pi$
$108$	−9.94008	−0.956485
$109$	−10.0307	−0.960764	−0.480382	−	0.877059i	$-0.659502\pi$
$109$	−10.0307	−0.960764	−0.480382	+	0.877059i	$0.659502\pi$
$110$	0	0
$111$	1.72519	0.163748
$112$	−3.26835	−0.308830
$113$	7.97489	0.750215	0.375107	−	0.926981i	$-0.377606\pi$
$113$	7.97489	0.750215	0.375107	+	0.926981i	$0.377606\pi$
$114$	1.11912	0.104815
$115$	−2.43927	−0.227463
$116$	−1.11767	−0.103773
$117$	−2.08913	−0.193140
$118$	1.43800	0.132378
$119$	2.58016	0.236523
$120$	−1.52259	−0.138993
$121$	0	0
$122$	−1.28510	−0.116348
$123$	−2.02276	−0.182386
$124$	10.8728	0.976402
$125$	1.00000	0.0894427
$126$	−0.621235	−0.0553440
$127$	−9.22608	−0.818682	−0.409341	−	0.912381i	$-0.634241\pi$
$127$	−9.22608	−0.818682	−0.409341	+	0.912381i	$0.634241\pi$
$128$	9.59949	0.848483
$129$	−5.72500	−0.504058
$130$	−0.418762	−0.0367279
$131$	−8.90201	−0.777772	−0.388886	−	0.921286i	$-0.627140\pi$
$131$	−8.90201	−0.777772	−0.388886	+	0.921286i	$0.627140\pi$
$132$	0	0
$133$	−2.84851	−0.246997
$134$	0.297594	0.0257082
$135$	5.30004	0.456155
$136$	−3.52859	−0.302574
$137$	−7.86948	−0.672335	−0.336168	−	0.941802i	$-0.609131\pi$
$137$	−7.86948	−0.672335	−0.336168	+	0.941802i	$0.609131\pi$
$138$	−0.958336	−0.0815790
$139$	−12.1276	−1.02865	−0.514327	−	0.857594i	$-0.671958\pi$
$139$	−12.1276	−1.02865	−0.514327	+	0.857594i	$0.671958\pi$
$140$	1.87547	0.158507
$141$	−9.18383	−0.773418
$142$	−3.78614	−0.317726
$143$	0	0
$144$	−5.75382	−0.479485
$145$	0.595940	0.0494901
$146$	1.60252	0.132626
$147$	−1.11334	−0.0918271
$148$	2.90615	0.238884
$149$	−23.0530	−1.88858	−0.944290	−	0.329115i	$-0.893249\pi$
$149$	−23.0530	−1.88858	−0.944290	+	0.329115i	$0.893249\pi$
$150$	0.392879	0.0320784
$151$	16.8038	1.36747	0.683737	−	0.729729i	$-0.260354\pi$
$151$	16.8038	1.36747	0.683737	+	0.729729i	$0.260354\pi$
$152$	3.89558	0.315973
$153$	4.54228	0.367221
$154$	0	0
$155$	−5.79734	−0.465653
$156$	2.47787	0.198389
$157$	0.610454	0.0487195	0.0243598	−	0.999703i	$-0.492245\pi$
$157$	0.610454	0.0487195	0.0243598	+	0.999703i	$0.492245\pi$
$158$	0.142162	0.0113098
$159$	−3.65651	−0.289980
$160$	−3.88851	−0.307414
$161$	2.43927	0.192241
$162$	0.218568	0.0171723
$163$	25.3370	1.98455	0.992273	−	0.124077i	$-0.0395971\pi$
$163$	25.3370	1.98455	0.992273	+	0.124077i	$0.0395971\pi$
$164$	−3.40742	−0.266075
$165$	0	0
$166$	−0.166985	−0.0129605
$167$	−19.4165	−1.50250	−0.751248	−	0.660020i	$-0.770548\pi$
$167$	−19.4165	−1.50250	−0.751248	+	0.660020i	$0.770548\pi$
$168$	1.52259	0.117471
$169$	−11.5918	−0.891674
$170$	0.910491	0.0698315
$171$	−5.01470	−0.383484
$172$	−9.64399	−0.735348
$173$	−3.26643	−0.248342	−0.124171	−	0.992261i	$-0.539627\pi$
$173$	−3.26643	−0.248342	−0.124171	+	0.992261i	$0.539627\pi$
$174$	0.234132	0.0177495
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	4.53690	0.341014
$178$	0.512804	0.0384363
$179$	6.99215	0.522618	0.261309	−	0.965255i	$-0.415846\pi$
$179$	6.99215	0.522618	0.261309	+	0.965255i	$0.415846\pi$
$180$	3.30170	0.246094
$181$	23.6246	1.75600	0.878000	−	0.478661i	$-0.158878\pi$
$181$	23.6246	1.75600	0.878000	+	0.478661i	$0.158878\pi$
$182$	0.418762	0.0310407
$183$	−4.05451	−0.299718
$184$	−3.33590	−0.245926
$185$	−1.54955	−0.113925
$186$	−2.27765	−0.167006
$187$	0	0
$188$	−15.4705	−1.12830
$189$	−5.30004	−0.385521
$190$	−1.00519	−0.0729240
$191$	−10.6841	−0.773075	−0.386538	−	0.922274i	$-0.626329\pi$
$191$	−10.6841	−0.773075	−0.386538	+	0.922274i	$0.626329\pi$
$192$	5.74990	0.414963
$193$	−21.0095	−1.51230	−0.756149	−	0.654400i	$-0.772921\pi$
$193$	−21.0095	−1.51230	−0.756149	+	0.654400i	$0.772921\pi$
$194$	−2.26069	−0.162308
$195$	−1.32120	−0.0946130
$196$	−1.87547	−0.133962
$197$	5.39044	0.384053	0.192026	−	0.981390i	$-0.438494\pi$
$197$	5.39044	0.384053	0.192026	+	0.981390i	$0.438494\pi$
$198$	0	0
$199$	−10.3487	−0.733603	−0.366802	−	0.930299i	$-0.619547\pi$
$199$	−10.3487	−0.733603	−0.366802	+	0.930299i	$0.619547\pi$
$200$	1.36758	0.0967028
$201$	0.938911	0.0662257
$202$	−1.34060	−0.0943242
$203$	−0.595940	−0.0418268
$204$	−5.38750	−0.377201
$205$	1.81683	0.126893
$206$	5.11452	0.356346
$207$	4.29424	0.298470
$208$	3.87853	0.268928
$209$	0	0
$210$	−0.392879	−0.0271112
$211$	8.49238	0.584640	0.292320	−	0.956321i	$-0.405573\pi$
$211$	8.49238	0.584640	0.292320	+	0.956321i	$0.405573\pi$
$212$	−6.15954	−0.423039
$213$	−11.9453	−0.818478
$214$	0.743580	0.0508300
$215$	5.14216	0.350693
$216$	7.24825	0.493181
$217$	5.79734	0.393549
$218$	3.53964	0.239735
$219$	5.05597	0.341651
$220$	0	0
$221$	−3.06186	−0.205963
$222$	−0.608787	−0.0408591
$223$	1.86383	0.124811	0.0624056	−	0.998051i	$-0.480123\pi$
$223$	1.86383	0.124811	0.0624056	+	0.998051i	$0.480123\pi$
$224$	3.88851	0.259812
$225$	−1.76046	−0.117364
$226$	−2.81419	−0.187197
$227$	−20.8417	−1.38331	−0.691657	−	0.722226i	$-0.743119\pi$
$227$	−20.8417	−1.38331	−0.691657	+	0.722226i	$0.743119\pi$
$228$	5.94784	0.393905
$229$	7.60360	0.502460	0.251230	−	0.967927i	$-0.419165\pi$
$229$	7.60360	0.502460	0.251230	+	0.967927i	$0.419165\pi$
$230$	0.860772	0.0567576
$231$	0	0
$232$	0.814999	0.0535073
$233$	−12.5717	−0.823600	−0.411800	−	0.911274i	$-0.635100\pi$
$233$	−12.5717	−0.823600	−0.411800	+	0.911274i	$0.635100\pi$
$234$	0.737215	0.0481933
$235$	8.24886	0.538096
$236$	7.64258	0.497490
$237$	0.448521	0.0291346
$238$	−0.910491	−0.0590184
$239$	−27.9975	−1.81101	−0.905503	−	0.424341i	$-0.860506\pi$
$239$	−27.9975	−1.81101	−0.905503	+	0.424341i	$0.860506\pi$
$240$	−3.63880	−0.234884
$241$	−11.3347	−0.730129	−0.365065	−	0.930982i	$-0.618953\pi$
$241$	−11.3347	−0.730129	−0.365065	+	0.930982i	$0.618953\pi$
$242$	0	0
$243$	−15.2105	−0.975756
$244$	−6.82999	−0.437245
$245$	1.00000	0.0638877
$246$	0.713794	0.0455099
$247$	3.38031	0.215084
$248$	−7.92834	−0.503450
$249$	−0.526839	−0.0333870
$250$	−0.352882	−0.0223182
$251$	20.7489	1.30966	0.654829	−	0.755777i	$-0.272741\pi$
$251$	20.7489	1.30966	0.654829	+	0.755777i	$0.272741\pi$
$252$	−3.30170	−0.207988
$253$	0	0
$254$	3.25571	0.204282
$255$	2.87261	0.179890
$256$	6.94156	0.433848
$257$	−16.2581	−1.01415	−0.507077	−	0.861901i	$-0.669274\pi$
$257$	−16.2581	−1.01415	−0.507077	+	0.861901i	$0.669274\pi$
$258$	2.02025	0.125775
$259$	1.54955	0.0962846
$260$	−2.22561	−0.138027
$261$	−1.04913	−0.0649396
$262$	3.14136	0.194074
$263$	21.8823	1.34932	0.674660	−	0.738129i	$-0.264290\pi$
$263$	21.8823	1.34932	0.674660	+	0.738129i	$0.264290\pi$
$264$	0	0
$265$	3.28426	0.201750
$266$	1.00519	0.0616320
$267$	1.61790	0.0990140
$268$	1.58163	0.0966137
$269$	−24.8098	−1.51268	−0.756341	−	0.654178i	$-0.773015\pi$
$269$	−24.8098	−1.51268	−0.756341	+	0.654178i	$0.773015\pi$
$270$	−1.87029	−0.113822
$271$	−27.7811	−1.68758	−0.843792	−	0.536671i	$-0.819682\pi$
$271$	−27.7811	−1.68758	−0.843792	+	0.536671i	$0.819682\pi$
$272$	−8.43287	−0.511318
$273$	1.32120	0.0799625
$274$	2.77700	0.167764
$275$	0	0
$276$	−5.09331	−0.306581
$277$	−14.0869	−0.846398	−0.423199	−	0.906037i	$-0.639093\pi$
$277$	−14.0869	−0.846398	−0.423199	+	0.906037i	$0.639093\pi$
$278$	4.27963	0.256675
$279$	10.2060	0.611017
$280$	−1.36758	−0.0817288
$281$	−19.4150	−1.15820	−0.579102	−	0.815255i	$-0.696597\pi$
$281$	−19.4150	−1.15820	−0.579102	+	0.815255i	$0.696597\pi$
$282$	3.24080	0.192987
$283$	21.7126	1.29068	0.645341	−	0.763895i	$-0.276715\pi$
$283$	21.7126	1.29068	0.645341	+	0.763895i	$0.276715\pi$
$284$	−20.1223	−1.19404
$285$	−3.17138	−0.187856
$286$	0	0
$287$	−1.81683	−0.107244
$288$	6.84558	0.403380
$289$	−10.3428	−0.608399
$290$	−0.210296	−0.0123490
$291$	−7.13251	−0.418115
$292$	8.51698	0.498419
$293$	−10.1146	−0.590902	−0.295451	−	0.955358i	$-0.595470\pi$
$293$	−10.1146	−0.590902	−0.295451	+	0.955358i	$0.595470\pi$
$294$	0.392879	0.0229132
$295$	−4.07501	−0.237256
$296$	−2.11915	−0.123173
$297$	0	0
$298$	8.13500	0.471248
$299$	−2.89466	−0.167402
$300$	2.08805	0.120554
$301$	−5.14216	−0.296389
$302$	−5.92975	−0.341219
$303$	−4.22960	−0.242984
$304$	9.30995	0.533962
$305$	3.64174	0.208525
$306$	−1.60289	−0.0916309
$307$	7.80558	0.445488	0.222744	−	0.974877i	$-0.428499\pi$
$307$	7.80558	0.445488	0.222744	+	0.974877i	$0.428499\pi$
$308$	0	0
$309$	16.1364	0.917965
$310$	2.04577	0.116192
$311$	−19.0963	−1.08285	−0.541426	−	0.840748i	$-0.682116\pi$
$311$	−19.0963	−1.08285	−0.541426	+	0.840748i	$0.682116\pi$
$312$	−1.80685	−0.102293
$313$	5.90347	0.333684	0.166842	−	0.985984i	$-0.446643\pi$
$313$	5.90347	0.333684	0.166842	+	0.985984i	$0.446643\pi$
$314$	−0.215418	−0.0121567
$315$	1.76046	0.0991909
$316$	0.755552	0.0425031
$317$	11.9526	0.671322	0.335661	−	0.941983i	$-0.391040\pi$
$317$	11.9526	0.671322	0.335661	+	0.941983i	$0.391040\pi$
$318$	1.29032	0.0723573
$319$	0	0
$320$	−5.16452	−0.288706
$321$	2.34600	0.130941
$322$	−0.860772	−0.0479690
$323$	−7.34962	−0.408944
$324$	1.16163	0.0645351
$325$	1.18669	0.0658259
$326$	−8.94096	−0.495194
$327$	11.1676	0.617570
$328$	2.48467	0.137193
$329$	−8.24886	−0.454774
$330$	0	0
$331$	−9.14026	−0.502394	−0.251197	−	0.967936i	$-0.580824\pi$
$331$	−9.14026	−0.502394	−0.251197	+	0.967936i	$0.580824\pi$
$332$	−0.887481	−0.0487069
$333$	2.72793	0.149490
$334$	6.85174	0.374910
$335$	−0.843325	−0.0460758
$336$	3.63880	0.198513
$337$	−24.0294	−1.30896	−0.654481	−	0.756078i	$-0.727113\pi$
$337$	−24.0294	−1.30896	−0.654481	+	0.756078i	$0.727113\pi$
$338$	4.09052	0.222495
$339$	−8.87881	−0.482231
$340$	4.83902	0.262433
$341$	0	0
$342$	1.76960	0.0956888
$343$	−1.00000	−0.0539949
$344$	7.03234	0.379158
$345$	2.71574	0.146211
$346$	1.15266	0.0619675
$347$	−15.7292	−0.844388	−0.422194	−	0.906506i	$-0.638740\pi$
$347$	−15.7292	−0.844388	−0.422194	+	0.906506i	$0.638740\pi$
$348$	1.24435	0.0667043
$349$	−23.5916	−1.26283	−0.631416	−	0.775444i	$-0.717526\pi$
$349$	−23.5916	−1.26283	−0.631416	+	0.775444i	$0.717526\pi$
$350$	0.352882	0.0188623
$351$	6.28951	0.335709
$352$	0	0
$353$	−2.18904	−0.116511	−0.0582554	−	0.998302i	$-0.518554\pi$
$353$	−2.18904	−0.116511	−0.0582554	+	0.998302i	$0.518554\pi$
$354$	−1.60099	−0.0850915
$355$	10.7292	0.569447
$356$	2.72542	0.144447
$357$	−2.87261	−0.152035
$358$	−2.46740	−0.130406
$359$	26.2299	1.38436	0.692181	−	0.721724i	$-0.256650\pi$
$359$	26.2299	1.38436	0.692181	+	0.721724i	$0.256650\pi$
$360$	−2.40758	−0.126891
$361$	−10.8860	−0.572946
$362$	−8.33668	−0.438166
$363$	0	0
$364$	2.22561	0.116654
$365$	−4.54124	−0.237699
$366$	1.43076	0.0747872
$367$	−19.6317	−1.02477	−0.512383	−	0.858757i	$-0.671237\pi$
$367$	−19.6317	−1.02477	−0.512383	+	0.858757i	$0.671237\pi$
$368$	−7.97238	−0.415589
$369$	−3.19846	−0.166505
$370$	0.546809	0.0284273
$371$	−3.28426	−0.170510
$372$	−12.1051	−0.627622
$373$	−1.64233	−0.0850366	−0.0425183	−	0.999096i	$-0.513538\pi$
$373$	−1.64233	−0.0850366	−0.0425183	+	0.999096i	$0.513538\pi$
$374$	0	0
$375$	−1.11334	−0.0574929
$376$	11.2810	0.581774
$377$	0.707198	0.0364225
$378$	1.87029	0.0961971
$379$	1.67946	0.0862679	0.0431339	−	0.999069i	$-0.486266\pi$
$379$	1.67946	0.0862679	0.0431339	+	0.999069i	$0.486266\pi$
$380$	−5.34231	−0.274055
$381$	10.2718	0.526241
$382$	3.77023	0.192902
$383$	32.9917	1.68580	0.842898	−	0.538073i	$-0.180848\pi$
$383$	32.9917	1.68580	0.842898	+	0.538073i	$0.180848\pi$
$384$	−10.6875	−0.545396
$385$	0	0
$386$	7.41387	0.377356
$387$	−9.05259	−0.460169
$388$	−12.0150	−0.609969
$389$	4.86341	0.246585	0.123292	−	0.992370i	$-0.460655\pi$
$389$	4.86341	0.246585	0.123292	+	0.992370i	$0.460655\pi$
$390$	0.466227	0.0236083
$391$	6.29369	0.318286
$392$	1.36758	0.0690734
$393$	9.91101	0.499944
$394$	−1.90219	−0.0958308
$395$	−0.402859	−0.0202700
$396$	0	0
$397$	20.9337	1.05063	0.525316	−	0.850907i	$-0.323947\pi$
$397$	20.9337	1.05063	0.525316	+	0.850907i	$0.323947\pi$
$398$	3.65188	0.183052
$399$	3.17138	0.158767
$400$	3.26835	0.163418
$401$	29.7163	1.48396	0.741981	−	0.670421i	$-0.233886\pi$
$401$	29.7163	1.48396	0.741981	+	0.670421i	$0.233886\pi$
$402$	−0.331325	−0.0165250
$403$	−6.87965	−0.342700
$404$	−7.12493	−0.354479
$405$	−0.619380	−0.0307772
$406$	0.210296	0.0104368
$407$	0	0
$408$	3.92853	0.194491
$409$	−31.9815	−1.58138	−0.790691	−	0.612215i	$-0.790279\pi$
$409$	−31.9815	−1.58138	−0.790691	+	0.612215i	$0.790279\pi$
$410$	−0.641126	−0.0316629
$411$	8.76145	0.432170
$412$	27.1823	1.33918
$413$	4.07501	0.200518
$414$	−1.51536	−0.0744758
$415$	0.473203	0.0232286
$416$	−4.61447	−0.226243
$417$	13.5023	0.661208
$418$	0	0
$419$	13.6139	0.665083	0.332541	−	0.943089i	$-0.392094\pi$
$419$	13.6139	0.665083	0.332541	+	0.943089i	$0.392094\pi$
$420$	−2.08805	−0.101886
$421$	−29.8370	−1.45417	−0.727083	−	0.686550i	$-0.759124\pi$
$421$	−29.8370	−1.45417	−0.727083	+	0.686550i	$0.759124\pi$
$422$	−2.99681	−0.145882
$423$	−14.5218	−0.706075
$424$	4.49150	0.218126
$425$	−2.58016	−0.125156
$426$	4.21528	0.204231
$427$	−3.64174	−0.176236
$428$	3.95193	0.191024
$429$	0	0
$430$	−1.81457	−0.0875066
$431$	−25.2412	−1.21582	−0.607912	−	0.794004i	$-0.707993\pi$
$431$	−25.2412	−1.21582	−0.607912	+	0.794004i	$0.707993\pi$
$432$	17.3224	0.833424
$433$	−14.8370	−0.713023	−0.356511	−	0.934291i	$-0.616034\pi$
$433$	−14.8370	−0.713023	−0.356511	+	0.934291i	$0.616034\pi$
$434$	−2.04577	−0.0982003
$435$	−0.663487	−0.0318118
$436$	18.8123	0.900944
$437$	−6.94828	−0.332381
$438$	−1.78416	−0.0852504
$439$	−31.1242	−1.48548	−0.742739	−	0.669581i	$-0.766474\pi$
$439$	−31.1242	−1.48548	−0.742739	+	0.669581i	$0.766474\pi$
$440$	0	0
$441$	−1.76046	−0.0838316
$442$	1.08047	0.0513929
$443$	−7.32038	−0.347802	−0.173901	−	0.984763i	$-0.555637\pi$
$443$	−7.32038	−0.347802	−0.173901	+	0.984763i	$0.555637\pi$
$444$	−3.23555	−0.153552
$445$	−1.45319	−0.0688878
$446$	−0.657711	−0.0311435
$447$	25.6660	1.21396
$448$	5.16452	0.244001
$449$	−38.1191	−1.79895	−0.899476	−	0.436970i	$-0.856052\pi$
$449$	−38.1191	−1.79895	−0.899476	+	0.436970i	$0.856052\pi$
$450$	0.621235	0.0292853
$451$	0	0
$452$	−14.9567	−0.703504
$453$	−18.7084	−0.878998
$454$	7.35467	0.345172
$455$	−1.18669	−0.0556330
$456$	−4.33713	−0.203105
$457$	16.8813	0.789673	0.394836	−	0.918751i	$-0.370801\pi$
$457$	16.8813	0.789673	0.394836	+	0.918751i	$0.370801\pi$
$458$	−2.68317	−0.125376
$459$	−13.6749	−0.638292
$460$	4.57478	0.213300
$461$	−31.6815	−1.47556	−0.737778	−	0.675044i	$-0.764125\pi$
$461$	−31.6815	−1.47556	−0.737778	+	0.675044i	$0.764125\pi$
$462$	0	0
$463$	15.6645	0.727990	0.363995	−	0.931401i	$-0.381413\pi$
$463$	15.6645	0.727990	0.363995	+	0.931401i	$0.381413\pi$
$464$	1.94774	0.0904217
$465$	6.45443	0.299317
$466$	4.43632	0.205509
$467$	−14.2450	−0.659179	−0.329590	−	0.944124i	$-0.606910\pi$
$467$	−14.2450	−0.659179	−0.329590	+	0.944124i	$0.606910\pi$
$468$	3.91811	0.181115
$469$	0.843325	0.0389411
$470$	−2.91087	−0.134268
$471$	−0.679646	−0.0313164
$472$	−5.57292	−0.256515
$473$	0	0
$474$	−0.158275	−0.00726981
$475$	2.84851	0.130699
$476$	−4.83902	−0.221796
$477$	−5.78181	−0.264731
$478$	9.87979	0.451891
$479$	0.765774	0.0349891	0.0174945	−	0.999847i	$-0.494431\pi$
$479$	0.765774	0.0349891	0.0174945	+	0.999847i	$0.494431\pi$
$480$	4.32925	0.197602
$481$	−1.83884	−0.0838441
$482$	3.99979	0.182186
$483$	−2.71574	−0.123571
$484$	0	0
$485$	6.40638	0.290899
$486$	5.36752	0.243476
$487$	−31.7898	−1.44054	−0.720268	−	0.693696i	$-0.755981\pi$
$487$	−31.7898	−1.44054	−0.720268	+	0.693696i	$0.755981\pi$
$488$	4.98038	0.225451
$489$	−28.2088	−1.27565
$490$	−0.352882	−0.0159416
$491$	−20.8195	−0.939569	−0.469785	−	0.882781i	$-0.655668\pi$
$491$	−20.8195	−0.939569	−0.469785	+	0.882781i	$0.655668\pi$
$492$	3.79363	0.171030
$493$	−1.53762	−0.0692510
$494$	−1.19285	−0.0536688
$495$	0	0
$496$	−18.9477	−0.850779
$497$	−10.7292	−0.481270
$498$	0.185912	0.00833090
$499$	22.0571	0.987413	0.493707	−	0.869629i	$-0.335642\pi$
$499$	22.0571	0.987413	0.493707	+	0.869629i	$0.335642\pi$
$500$	−1.87547	−0.0838738
$501$	21.6173	0.965789
$502$	−7.32190	−0.326792
$503$	8.67739	0.386906	0.193453	−	0.981110i	$-0.438031\pi$
$503$	8.67739	0.386906	0.193453	+	0.981110i	$0.438031\pi$
$504$	2.40758	0.107242
$505$	3.79900	0.169053
$506$	0	0
$507$	12.9056	0.573159
$508$	17.3033	0.767709
$509$	24.9791	1.10718	0.553589	−	0.832790i	$-0.313258\pi$
$509$	24.9791	1.10718	0.553589	+	0.832790i	$0.313258\pi$
$510$	−1.01369	−0.0448870
$511$	4.54124	0.200893
$512$	−21.6485	−0.956739
$513$	15.0972	0.666559
$514$	5.73720	0.253057
$515$	−14.4936	−0.638664
$516$	10.7371	0.472674
$517$	0	0
$518$	−0.546809	−0.0240254
$519$	3.63666	0.159632
$520$	1.62290	0.0711689
$521$	−17.6782	−0.774496	−0.387248	−	0.921976i	$-0.626574\pi$
$521$	−17.6782	−0.774496	−0.387248	+	0.921976i	$0.626574\pi$
$522$	0.370219	0.0162041
$523$	42.3826	1.85326	0.926631	−	0.375973i	$-0.122692\pi$
$523$	42.3826	1.85326	0.926631	+	0.375973i	$0.122692\pi$
$524$	16.6955	0.729346
$525$	1.11334	0.0485904
$526$	−7.72186	−0.336689
$527$	14.9580	0.651583
$528$	0	0
$529$	−17.0500	−0.741304
$530$	−1.15895	−0.0503417
$531$	7.17391	0.311321
$532$	5.34231	0.231619
$533$	2.15602	0.0933875
$534$	−0.570928	−0.0247065
$535$	−2.10716	−0.0911006
$536$	−1.15332	−0.0498157
$537$	−7.78468	−0.335934
$538$	8.75493	0.377452
$539$	0	0
$540$	−9.94008	−0.427753
$541$	−25.7272	−1.10610	−0.553049	−	0.833149i	$-0.686536\pi$
$541$	−25.7272	−1.10610	−0.553049	+	0.833149i	$0.686536\pi$
$542$	9.80345	0.421094
$543$	−26.3023	−1.12874
$544$	10.0330	0.430160
$545$	−10.0307	−0.429667
$546$	−0.466227	−0.0199527
$547$	13.9978	0.598502	0.299251	−	0.954174i	$-0.403263\pi$
$547$	13.9978	0.598502	0.299251	+	0.954174i	$0.403263\pi$
$548$	14.7590	0.630474
$549$	−6.41115	−0.273621
$550$	0	0
$551$	1.69754	0.0723178
$552$	3.71401	0.158079
$553$	0.402859	0.0171313
$554$	4.97100	0.211198
$555$	1.72519	0.0732302
$556$	22.7451	0.964607
$557$	35.7726	1.51573	0.757866	−	0.652410i	$-0.226242\pi$
$557$	35.7726	1.51573	0.757866	+	0.652410i	$0.226242\pi$
$558$	−3.60151	−0.152464
$559$	6.10216	0.258094
$560$	−3.26835	−0.138113
$561$	0	0
$562$	6.85121	0.289001
$563$	29.5190	1.24408	0.622040	−	0.782986i	$-0.286304\pi$
$563$	29.5190	1.24408	0.622040	+	0.782986i	$0.286304\pi$
$564$	17.2240	0.725263
$565$	7.97489	0.335506
$566$	−7.66199	−0.322057
$567$	0.619380	0.0260115
$568$	14.6731	0.615669
$569$	−22.5643	−0.945944	−0.472972	−	0.881077i	$-0.656819\pi$
$569$	−22.5643	−0.945944	−0.472972	+	0.881077i	$0.656819\pi$
$570$	1.11912	0.0468748
$571$	23.0601	0.965033	0.482517	−	0.875887i	$-0.339723\pi$
$571$	23.0601	0.965033	0.482517	+	0.875887i	$0.339723\pi$
$572$	0	0
$573$	11.8951	0.496925
$574$	0.641126	0.0267601
$575$	−2.43927	−0.101724
$576$	9.09195	0.378831
$577$	7.64775	0.318380	0.159190	−	0.987248i	$-0.449112\pi$
$577$	7.64775	0.318380	0.159190	+	0.987248i	$0.449112\pi$
$578$	3.64978	0.151811
$579$	23.3908	0.972090
$580$	−1.11767	−0.0464088
$581$	−0.473203	−0.0196318
$582$	2.51693	0.104330
$583$	0	0
$584$	−6.21053	−0.256993
$585$	−2.08913	−0.0863748
$586$	3.56926	0.147445
$587$	24.0891	0.994265	0.497132	−	0.867675i	$-0.334386\pi$
$587$	24.0891	0.994265	0.497132	+	0.867675i	$0.334386\pi$
$588$	2.08805	0.0861097
$589$	−16.5138	−0.680439
$590$	1.43800	0.0592014
$591$	−6.00141	−0.246865
$592$	−5.06449	−0.208149
$593$	16.8875	0.693485	0.346743	−	0.937960i	$-0.387288\pi$
$593$	16.8875	0.693485	0.346743	+	0.937960i	$0.387288\pi$
$594$	0	0
$595$	2.58016	0.105776
$596$	43.2354	1.77099
$597$	11.5217	0.471553
$598$	1.02147	0.0417711
$599$	−23.9030	−0.976652	−0.488326	−	0.872661i	$-0.662392\pi$
$599$	−23.9030	−0.976652	−0.488326	+	0.872661i	$0.662392\pi$
$600$	−1.52259	−0.0621596
$601$	1.65944	0.0676901	0.0338451	−	0.999427i	$-0.489225\pi$
$601$	1.65944	0.0676901	0.0338451	+	0.999427i	$0.489225\pi$
$602$	1.81457	0.0739565
$603$	1.48464	0.0604593
$604$	−31.5151	−1.28233
$605$	0	0
$606$	1.49255	0.0606306
$607$	−4.69099	−0.190402	−0.0952008	−	0.995458i	$-0.530349\pi$
$607$	−4.69099	−0.190402	−0.0952008	+	0.995458i	$0.530349\pi$
$608$	−11.0765	−0.449210
$609$	0.663487	0.0268859
$610$	−1.28510	−0.0520323
$611$	9.78886	0.396015
$612$	−8.51892	−0.344357
$613$	35.8278	1.44707	0.723536	−	0.690287i	$-0.242516\pi$
$613$	35.8278	1.44707	0.723536	+	0.690287i	$0.242516\pi$
$614$	−2.75445	−0.111160
$615$	−2.02276	−0.0815655
$616$	0	0
$617$	21.7486	0.875564	0.437782	−	0.899081i	$-0.355764\pi$
$617$	21.7486	0.875564	0.437782	+	0.899081i	$0.355764\pi$
$618$	−5.69423	−0.229055
$619$	−17.6796	−0.710602	−0.355301	−	0.934752i	$-0.615622\pi$
$619$	−17.6796	−0.710602	−0.355301	+	0.934752i	$0.615622\pi$
$620$	10.8728	0.436660
$621$	−12.9282	−0.518791
$622$	6.73874	0.270199
$623$	1.45319	0.0582209
$624$	−4.31814	−0.172864
$625$	1.00000	0.0400000
$626$	−2.08323	−0.0832625
$627$	0	0
$628$	−1.14489	−0.0456861
$629$	3.99810	0.159415
$630$	−0.621235	−0.0247506
$631$	−23.5814	−0.938762	−0.469381	−	0.882996i	$-0.655523\pi$
$631$	−23.5814	−0.938762	−0.469381	+	0.882996i	$0.655523\pi$
$632$	−0.550944	−0.0219154
$633$	−9.45495	−0.375801
$634$	−4.21784	−0.167512
$635$	−9.22608	−0.366126
$636$	6.85769	0.271925
$637$	1.18669	0.0470185
$638$	0	0
$639$	−18.8884	−0.747212
$640$	9.59949	0.379453
$641$	−12.7447	−0.503386	−0.251693	−	0.967807i	$-0.580987\pi$
$641$	−12.7447	−0.503386	−0.251693	+	0.967807i	$0.580987\pi$
$642$	−0.827860	−0.0326730
$643$	10.5098	0.414465	0.207232	−	0.978292i	$-0.433554\pi$
$643$	10.5098	0.414465	0.207232	+	0.978292i	$0.433554\pi$
$644$	−4.57478	−0.180272
$645$	−5.72500	−0.225422
$646$	2.59355	0.102042
$647$	−2.19644	−0.0863509	−0.0431755	−	0.999068i	$-0.513747\pi$
$647$	−2.19644	−0.0863509	−0.0431755	+	0.999068i	$0.513747\pi$
$648$	−0.847054	−0.0332754
$649$	0	0
$650$	−0.418762	−0.0164252
$651$	−6.45443	−0.252969
$652$	−47.5189	−1.86098
$653$	8.77272	0.343303	0.171652	−	0.985158i	$-0.445090\pi$
$653$	8.77272	0.343303	0.171652	+	0.985158i	$0.445090\pi$
$654$	−3.94084	−0.154099
$655$	−8.90201	−0.347830
$656$	5.93804	0.231842
$657$	7.99469	0.311902
$658$	2.91087	0.113478
$659$	43.8609	1.70858	0.854288	−	0.519799i	$-0.173993\pi$
$659$	43.8609	1.70858	0.854288	+	0.519799i	$0.173993\pi$
$660$	0	0
$661$	18.2226	0.708776	0.354388	−	0.935098i	$-0.384689\pi$
$661$	18.2226	0.708776	0.354388	+	0.935098i	$0.384689\pi$
$662$	3.22543	0.125360
$663$	3.40890	0.132391
$664$	0.647146	0.0251141
$665$	−2.84851	−0.110461
$666$	−0.962638	−0.0373015
$667$	−1.45366	−0.0562858
$668$	36.4152	1.40895
$669$	−2.07508	−0.0802274
$670$	0.297594	0.0114971
$671$	0	0
$672$	−4.32925	−0.167005
$673$	41.5422	1.60133	0.800666	−	0.599111i	$-0.204479\pi$
$673$	41.5422	1.60133	0.800666	+	0.599111i	$0.204479\pi$
$674$	8.47952	0.326619
$675$	5.30004	0.203999
$676$	21.7401	0.836156
$677$	36.0516	1.38558	0.692788	−	0.721141i	$-0.256382\pi$
$677$	36.0516	1.38558	0.692788	+	0.721141i	$0.256382\pi$
$678$	3.13317	0.120329
$679$	−6.40638	−0.245854
$680$	−3.52859	−0.135315
$681$	23.2040	0.889181
$682$	0	0
$683$	3.52687	0.134952	0.0674760	−	0.997721i	$-0.478505\pi$
$683$	3.52687	0.134952	0.0674760	+	0.997721i	$0.478505\pi$
$684$	9.40495	0.359607
$685$	−7.86948	−0.300677
$686$	0.352882	0.0134731
$687$	−8.46543	−0.322976
$688$	16.8064	0.640738
$689$	3.89740	0.148479
$690$	−0.958336	−0.0364832
$691$	42.0941	1.60134	0.800668	−	0.599109i	$-0.204478\pi$
$691$	42.0941	1.60134	0.800668	+	0.599109i	$0.204478\pi$
$692$	6.12610	0.232880
$693$	0	0
$694$	5.55055	0.210696
$695$	−12.1276	−0.460028
$696$	−0.907374	−0.0343939
$697$	−4.68771	−0.177560
$698$	8.32506	0.315108
$699$	13.9966	0.529402
$700$	1.87547	0.0708863
$701$	4.43150	0.167375	0.0836877	−	0.996492i	$-0.473330\pi$
$701$	4.43150	0.167375	0.0836877	+	0.996492i	$0.473330\pi$
$702$	−2.21945	−0.0837679
$703$	−4.41393	−0.166474
$704$	0	0
$705$	−9.18383	−0.345883
$706$	0.772472	0.0290723
$707$	−3.79900	−0.142876
$708$	−8.50883	−0.319782
$709$	−2.03577	−0.0764550	−0.0382275	−	0.999269i	$-0.512171\pi$
$709$	−2.03577	−0.0764550	−0.0382275	+	0.999269i	$0.512171\pi$
$710$	−3.78614	−0.142091
$711$	0.709219	0.0265978
$712$	−1.98736	−0.0744795
$713$	14.1412	0.529594
$714$	1.01369	0.0379364
$715$	0	0
$716$	−13.1136	−0.490078
$717$	31.1708	1.16410
$718$	−9.25605	−0.345433
$719$	8.99711	0.335536	0.167768	−	0.985827i	$-0.446344\pi$
$719$	8.99711	0.335536	0.167768	+	0.985827i	$0.446344\pi$
$720$	−5.75382	−0.214432
$721$	14.4936	0.539769
$722$	3.84146	0.142964
$723$	12.6194	0.469320
$724$	−44.3073	−1.64667
$725$	0.595940	0.0221327
$726$	0	0
$727$	24.2651	0.899944	0.449972	−	0.893043i	$-0.351434\pi$
$727$	24.2651	0.899944	0.449972	+	0.893043i	$0.351434\pi$
$728$	−1.62290	−0.0601487
$729$	18.7927	0.696026
$730$	1.60252	0.0593120
$731$	−13.2676	−0.490720
$732$	7.60413	0.281057
$733$	−4.78930	−0.176897	−0.0884485	−	0.996081i	$-0.528191\pi$
$733$	−4.78930	−0.176897	−0.0884485	+	0.996081i	$0.528191\pi$
$734$	6.92766	0.255705
$735$	−1.11334	−0.0410663
$736$	9.48511	0.349626
$737$	0	0
$738$	1.12868	0.0415472
$739$	25.2262	0.927962	0.463981	−	0.885845i	$-0.346421\pi$
$739$	25.2262	0.927962	0.463981	+	0.885845i	$0.346421\pi$
$740$	2.90615	0.106832
$741$	−3.76345	−0.138254
$742$	1.15895	0.0425465
$743$	1.76835	0.0648746	0.0324373	−	0.999474i	$-0.489673\pi$
$743$	1.76835	0.0648746	0.0324373	+	0.999474i	$0.489673\pi$
$744$	8.82698	0.323613
$745$	−23.0530	−0.844598
$746$	0.579548	0.0212188
$747$	−0.833057	−0.0304800
$748$	0	0
$749$	2.10716	0.0769941
$750$	0.392879	0.0143459
$751$	−38.2105	−1.39432	−0.697161	−	0.716915i	$-0.745554\pi$
$751$	−38.2105	−1.39432	−0.697161	+	0.716915i	$0.745554\pi$
$752$	26.9602	0.983137
$753$	−23.1007	−0.841835
$754$	−0.249557	−0.00908834
$755$	16.8038	0.611553
$756$	9.94008	0.361517
$757$	−45.1642	−1.64152	−0.820760	−	0.571273i	$-0.806450\pi$
$757$	−45.1642	−1.64152	−0.820760	+	0.571273i	$0.806450\pi$
$758$	−0.592650	−0.0215260
$759$	0	0
$760$	3.89558	0.141308
$761$	−4.70935	−0.170714	−0.0853570	−	0.996350i	$-0.527203\pi$
$761$	−4.70935	−0.170714	−0.0853570	+	0.996350i	$0.527203\pi$
$762$	−3.62473	−0.131310
$763$	10.0307	0.363135
$764$	20.0378	0.724941
$765$	4.54228	0.164226
$766$	−11.6422	−0.420648
$767$	−4.83579	−0.174610
$768$	−7.72835	−0.278873
$769$	−36.4290	−1.31366	−0.656831	−	0.754038i	$-0.728104\pi$
$769$	−36.4290	−1.31366	−0.656831	+	0.754038i	$0.728104\pi$
$770$	0	0
$771$	18.1009	0.651889
$772$	39.4028	1.41814
$773$	−28.2151	−1.01483	−0.507413	−	0.861703i	$-0.669398\pi$
$773$	−28.2151	−1.01483	−0.507413	+	0.861703i	$0.669398\pi$
$774$	3.19449	0.114824
$775$	−5.79734	−0.208246
$776$	8.76126	0.314511
$777$	−1.72519	−0.0618908
$778$	−1.71621	−0.0615290
$779$	5.17526	0.185423
$780$	2.47787	0.0887221
$781$	0	0
$782$	−2.22093	−0.0794203
$783$	3.15851	0.112876
$784$	3.26835	0.116727
$785$	0.610454	0.0217880
$786$	−3.49741	−0.124749
$787$	3.88204	0.138380	0.0691899	−	0.997604i	$-0.477959\pi$
$787$	3.88204	0.138380	0.0691899	+	0.997604i	$0.477959\pi$
$788$	−10.1096	−0.360140
$789$	−24.3625	−0.867329
$790$	0.142162	0.00505788
$791$	−7.97489	−0.283555
$792$	0	0
$793$	4.32162	0.153465
$794$	−7.38712	−0.262159
$795$	−3.65651	−0.129683
$796$	19.4088	0.687927
$797$	2.64421	0.0936626	0.0468313	−	0.998903i	$-0.485088\pi$
$797$	2.64421	0.0936626	0.0468313	+	0.998903i	$0.485088\pi$
$798$	−1.11912	−0.0396165
$799$	−21.2834	−0.752952
$800$	−3.88851	−0.137480
$801$	2.55829	0.0903927
$802$	−10.4863	−0.370286
$803$	0	0
$804$	−1.76090	−0.0621023
$805$	2.43927	0.0859728
$806$	2.42770	0.0855122
$807$	27.6219	0.972337
$808$	5.19545	0.182775
$809$	5.47143	0.192365	0.0961826	−	0.995364i	$-0.469337\pi$
$809$	5.47143	0.192365	0.0961826	+	0.995364i	$0.469337\pi$
$810$	0.218568	0.00767969
$811$	−0.0416824	−0.00146367	−0.000731834	−	1.00000i	$-0.500233\pi$
$811$	−0.0416824	−0.00146367	−0.000731834		1.00000i	$0.500233\pi$
$812$	1.11767	0.0392226
$813$	30.9300	1.08476
$814$	0	0
$815$	25.3370	0.887516
$816$	9.38870	0.328670
$817$	14.6475	0.512452
$818$	11.2857	0.394595
$819$	2.08913	0.0730001
$820$	−3.40742	−0.118992
$821$	−14.6990	−0.512998	−0.256499	−	0.966544i	$-0.582569\pi$
$821$	−14.6990	−0.512998	−0.256499	+	0.966544i	$0.582569\pi$
$822$	−3.09175	−0.107837
$823$	17.8374	0.621771	0.310885	−	0.950447i	$-0.399374\pi$
$823$	17.8374	0.621771	0.310885	+	0.950447i	$0.399374\pi$
$824$	−19.8212	−0.690504
$825$	0	0
$826$	−1.43800	−0.0500343
$827$	21.6802	0.753893	0.376946	−	0.926235i	$-0.376974\pi$
$827$	21.6802	0.753893	0.376946	+	0.926235i	$0.376974\pi$
$828$	−8.05373	−0.279887
$829$	50.5878	1.75699	0.878493	−	0.477756i	$-0.158550\pi$
$829$	50.5878	1.75699	0.878493	+	0.477756i	$0.158550\pi$
$830$	−0.166985	−0.00579613
$831$	15.6835	0.544056
$832$	−6.12870	−0.212474
$833$	−2.58016	−0.0893972
$834$	−4.76470	−0.164988
$835$	−19.4165	−0.671937
$836$	0	0
$837$	−30.7261	−1.06205
$838$	−4.80410	−0.165955
$839$	37.3508	1.28949	0.644747	−	0.764396i	$-0.276963\pi$
$839$	37.3508	1.28949	0.644747	+	0.764396i	$0.276963\pi$
$840$	1.52259	0.0525344
$841$	−28.6449	−0.987754
$842$	10.5289	0.362851
$843$	21.6156	0.744481
$844$	−15.9272	−0.548239
$845$	−11.5918	−0.398769
$846$	5.12448	0.176183
$847$	0	0
$848$	10.7341	0.368611
$849$	−24.1736	−0.829637
$850$	0.910491	0.0312296
$851$	3.77977	0.129569
$852$	22.4031	0.767518
$853$	28.3123	0.969395	0.484698	−	0.874682i	$-0.338930\pi$
$853$	28.3123	0.969395	0.484698	+	0.874682i	$0.338930\pi$
$854$	1.28510	0.0439753
$855$	−5.01470	−0.171499
$856$	−2.88172	−0.0984953
$857$	50.2023	1.71488	0.857440	−	0.514584i	$-0.172054\pi$
$857$	50.2023	1.71488	0.857440	+	0.514584i	$0.172054\pi$
$858$	0	0
$859$	−3.55378	−0.121253	−0.0606267	−	0.998161i	$-0.519310\pi$
$859$	−3.55378	−0.121253	−0.0606267	+	0.998161i	$0.519310\pi$
$860$	−9.64399	−0.328857
$861$	2.02276	0.0689354
$862$	8.90715	0.303379
$863$	−32.9311	−1.12099	−0.560494	−	0.828159i	$-0.689389\pi$
$863$	−32.9311	−1.12099	−0.560494	+	0.828159i	$0.689389\pi$
$864$	−20.6093	−0.701141
$865$	−3.26643	−0.111062
$866$	5.23572	0.177917
$867$	11.5151	0.391073
$868$	−10.8728	−0.369045
$869$	0	0
$870$	0.234132	0.00793783
$871$	−1.00077	−0.0339097
$872$	−13.7178	−0.464543
$873$	−11.2782	−0.381709
$874$	2.45192	0.0829375
$875$	−1.00000	−0.0338062
$876$	−9.48234	−0.320378
$877$	−26.1737	−0.883824	−0.441912	−	0.897058i	$-0.645700\pi$
$877$	−26.1737	−0.883824	−0.441912	+	0.897058i	$0.645700\pi$
$878$	10.9832	0.370664
$879$	11.2611	0.379826
$880$	0	0
$881$	10.2923	0.346756	0.173378	−	0.984855i	$-0.444532\pi$
$881$	10.2923	0.346756	0.173378	+	0.984855i	$0.444532\pi$
$882$	0.621235	0.0209181
$883$	−54.9538	−1.84934	−0.924671	−	0.380767i	$-0.875660\pi$
$883$	−54.9538	−1.84934	−0.924671	+	0.380767i	$0.875660\pi$
$884$	5.74243	0.193139
$885$	4.53690	0.152506
$886$	2.58323	0.0867852
$887$	35.7428	1.20012	0.600062	−	0.799953i	$-0.295143\pi$
$887$	35.7428	1.20012	0.600062	+	0.799953i	$0.295143\pi$
$888$	2.35934	0.0791743
$889$	9.22608	0.309433
$890$	0.512804	0.0171892
$891$	0	0
$892$	−3.49556	−0.117040
$893$	23.4970	0.786297
$894$	−9.05706	−0.302913
$895$	6.99215	0.233722
$896$	−9.59949	−0.320696
$897$	3.22275	0.107605
$898$	13.4515	0.448884
$899$	−3.45487	−0.115226
$900$	3.30170	0.110057
$901$	−8.47391	−0.282307
$902$	0	0
$903$	5.72500	0.190516
$904$	10.9063	0.362739
$905$	23.6246	0.785307
$906$	6.60186	0.219332
$907$	−15.4698	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$907$	−15.4698	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$908$	39.0882	1.29719
$909$	−6.68800	−0.221827
$910$	0.418762	0.0138818
$911$	14.8688	0.492624	0.246312	−	0.969191i	$-0.420781\pi$
$911$	14.8688	0.492624	0.246312	+	0.969191i	$0.420781\pi$
$912$	−10.3652	−0.343226
$913$	0	0
$914$	−5.95709	−0.197043
$915$	−4.05451	−0.134038
$916$	−14.2604	−0.471175
$917$	8.90201	0.293970
$918$	4.82564	0.159270
$919$	2.19254	0.0723252	0.0361626	−	0.999346i	$-0.488487\pi$
$919$	2.19254	0.0723252	0.0361626	+	0.999346i	$0.488487\pi$
$920$	−3.33590	−0.109981
$921$	−8.69030	−0.286355
$922$	11.1798	0.368188
$923$	12.7323	0.419087
$924$	0	0
$925$	−1.54955	−0.0509490
$926$	−5.52771	−0.181652
$927$	25.5154	0.838036
$928$	−2.31732	−0.0760698
$929$	−24.0592	−0.789358	−0.394679	−	0.918819i	$-0.629144\pi$
$929$	−24.0592	−0.789358	−0.394679	+	0.918819i	$0.629144\pi$
$930$	−2.27765	−0.0746871
$931$	2.84851	0.0933562
$932$	23.5779	0.772320
$933$	21.2608	0.696047
$934$	5.02679	0.164482
$935$	0	0
$936$	−2.85706	−0.0933859
$937$	−23.0089	−0.751666	−0.375833	−	0.926687i	$-0.622643\pi$
$937$	−23.0089	−0.751666	−0.375833	+	0.926687i	$0.622643\pi$
$938$	−0.297594	−0.00971679
$939$	−6.57260	−0.214489
$940$	−15.4705	−0.504593
$941$	−18.5589	−0.605003	−0.302501	−	0.953149i	$-0.597822\pi$
$941$	−18.5589	−0.605003	−0.302501	+	0.953149i	$0.597822\pi$
$942$	0.239835	0.00781423
$943$	−4.43173	−0.144317
$944$	−13.3186	−0.433483
$945$	−5.30004	−0.172410
$946$	0	0
$947$	−39.8686	−1.29555	−0.647777	−	0.761830i	$-0.724301\pi$
$947$	−39.8686	−1.29555	−0.647777	+	0.761830i	$0.724301\pi$
$948$	−0.841190	−0.0273206
$949$	−5.38906	−0.174936
$950$	−1.00519	−0.0326126
$951$	−13.3073	−0.431519
$952$	3.52859	0.114362
$953$	−53.0777	−1.71936	−0.859678	−	0.510837i	$-0.829336\pi$
$953$	−53.0777	−1.71936	−0.859678	+	0.510837i	$0.829336\pi$
$954$	2.04030	0.0660570
$955$	−10.6841	−0.345730
$956$	52.5085	1.69825
$957$	0	0
$958$	−0.270228	−0.00873065
$959$	7.86948	0.254119
$960$	5.74990	0.185577
$961$	2.60909	0.0841643
$962$	0.648895	0.0209212
$963$	3.70958	0.119540
$964$	21.2579	0.684669
$965$	−21.0095	−0.676320
$966$	0.958336	0.0308340
$967$	34.1191	1.09720	0.548599	−	0.836086i	$-0.315162\pi$
$967$	34.1191	1.09720	0.548599	+	0.836086i	$0.315162\pi$
$968$	0	0
$969$	8.18266	0.262865
$970$	−2.26069	−0.0725865
$971$	10.2137	0.327774	0.163887	−	0.986479i	$-0.447597\pi$
$971$	10.2137	0.327774	0.163887	+	0.986479i	$0.447597\pi$
$972$	28.5270	0.915003
$973$	12.1276	0.388795
$974$	11.2181	0.359450
$975$	−1.32120	−0.0423122
$976$	11.9025	0.380989
$977$	10.2119	0.326707	0.163354	−	0.986568i	$-0.447769\pi$
$977$	10.2119	0.326707	0.163354	+	0.986568i	$0.447769\pi$
$978$	9.95437	0.318306
$979$	0	0
$980$	−1.87547	−0.0599098
$981$	17.6586	0.563797
$982$	7.34681	0.234446
$983$	20.5190	0.654454	0.327227	−	0.944946i	$-0.393886\pi$
$983$	20.5190	0.654454	0.327227	+	0.944946i	$0.393886\pi$
$984$	−2.76629	−0.0881861
$985$	5.39044	0.171754
$986$	0.542598	0.0172799
$987$	9.18383	0.292324
$988$	−6.33968	−0.201692
$989$	−12.5431	−0.398847
$990$	0	0
$991$	34.0510	1.08167	0.540833	−	0.841130i	$-0.318109\pi$
$991$	34.0510	1.08167	0.540833	+	0.841130i	$0.318109\pi$
$992$	22.5430	0.715741
$993$	10.1763	0.322934
$994$	3.78614	0.120089
$995$	−10.3487	−0.328077
$996$	0.988072	0.0313083
$997$	−49.3278	−1.56223	−0.781113	−	0.624389i	$-0.785348\pi$
$997$	−49.3278	−1.56223	−0.781113	+	0.624389i	$0.785348\pi$
$998$	−7.78356	−0.246384
$999$	−8.21269	−0.259838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.z.1.3	✓	5
11.10	odd	2		4235.2.a.bf.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.z.1.3	✓	5	1.1	even	1	trivial
4235.2.a.bf.1.3	yes	5	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)

\(f(q)\)	\(=\)	\(q-0.352882 q^{2} -1.11334 q^{3} -1.87547 q^{4} +1.00000 q^{5} +0.392879 q^{6} -1.00000 q^{7} +1.36758 q^{8} -1.76046 q^{9} +O(q^{10})\)	\(q-0.352882 q^{2} -1.11334 q^{3} -1.87547 q^{4} +1.00000 q^{5} +0.392879 q^{6} -1.00000 q^{7} +1.36758 q^{8} -1.76046 q^{9} -0.352882 q^{10} +2.08805 q^{12} +1.18669 q^{13} +0.352882 q^{14} -1.11334 q^{15} +3.26835 q^{16} -2.58016 q^{17} +0.621235 q^{18} +2.84851 q^{19} -1.87547 q^{20} +1.11334 q^{21} -2.43927 q^{23} -1.52259 q^{24} +1.00000 q^{25} -0.418762 q^{26} +5.30004 q^{27} +1.87547 q^{28} +0.595940 q^{29} +0.392879 q^{30} -5.79734 q^{31} -3.88851 q^{32} +0.910491 q^{34} -1.00000 q^{35} +3.30170 q^{36} -1.54955 q^{37} -1.00519 q^{38} -1.32120 q^{39} +1.36758 q^{40} +1.81683 q^{41} -0.392879 q^{42} +5.14216 q^{43} -1.76046 q^{45} +0.860772 q^{46} +8.24886 q^{47} -3.63880 q^{48} +1.00000 q^{49} -0.352882 q^{50} +2.87261 q^{51} -2.22561 q^{52} +3.28426 q^{53} -1.87029 q^{54} -1.36758 q^{56} -3.17138 q^{57} -0.210296 q^{58} -4.07501 q^{59} +2.08805 q^{60} +3.64174 q^{61} +2.04577 q^{62} +1.76046 q^{63} -5.16452 q^{64} +1.18669 q^{65} -0.843325 q^{67} +4.83902 q^{68} +2.71574 q^{69} +0.352882 q^{70} +10.7292 q^{71} -2.40758 q^{72} -4.54124 q^{73} +0.546809 q^{74} -1.11334 q^{75} -5.34231 q^{76} +0.466227 q^{78} -0.402859 q^{79} +3.26835 q^{80} -0.619380 q^{81} -0.641126 q^{82} +0.473203 q^{83} -2.08805 q^{84} -2.58016 q^{85} -1.81457 q^{86} -0.663487 q^{87} -1.45319 q^{89} +0.621235 q^{90} -1.18669 q^{91} +4.57478 q^{92} +6.45443 q^{93} -2.91087 q^{94} +2.84851 q^{95} +4.32925 q^{96} +6.40638 q^{97} -0.352882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9	\( 5 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 5 q^{5} + q^{6} - 5 q^{7} - q^{9} - 2 q^{10} - 3 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 6 q^{17} - 11 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 3 q^{23} + 6 q^{24} + 5 q^{25} - 15 q^{26} + 5 q^{27} - 4 q^{28} - 17 q^{29} + q^{30} + 12 q^{31} + 3 q^{32} - 12 q^{34} - 5 q^{35} - 3 q^{36} - 2 q^{37} + 21 q^{38} - 14 q^{39} - 5 q^{41} - q^{42} - 4 q^{43} - q^{45} - 2 q^{46} - 12 q^{48} + 5 q^{49} - 2 q^{50} - 14 q^{51} - 2 q^{52} + 8 q^{53} - 22 q^{54} - 4 q^{57} + 6 q^{58} - 16 q^{59} - 3 q^{60} - 24 q^{61} - 9 q^{62} + q^{63} - 38 q^{64} - 8 q^{65} - 9 q^{67} - 19 q^{68} + 22 q^{69} + 2 q^{70} - 10 q^{71} - 4 q^{72} - 11 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 5 q^{78} - 9 q^{79} + 2 q^{80} - 19 q^{81} + 44 q^{82} - 10 q^{83} + 3 q^{84} - 6 q^{85} + 15 q^{86} + 2 q^{87} - 9 q^{89} - 11 q^{90} + 8 q^{91} - 26 q^{92} - q^{93} - 34 q^{94} - 7 q^{95} + 18 q^{96} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 5 * q^5 + q^6 - 5 * q^7 - q^9 - 2 * q^10 - 3 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 6 * q^17 - 11 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 3 * q^23 + 6 * q^24 + 5 * q^25 - 15 * q^26 + 5 * q^27 - 4 * q^28 - 17 * q^29 + q^30 + 12 * q^31 + 3 * q^32 - 12 * q^34 - 5 * q^35 - 3 * q^36 - 2 * q^37 + 21 * q^38 - 14 * q^39 - 5 * q^41 - q^42 - 4 * q^43 - q^45 - 2 * q^46 - 12 * q^48 + 5 * q^49 - 2 * q^50 - 14 * q^51 - 2 * q^52 + 8 * q^53 - 22 * q^54 - 4 * q^57 + 6 * q^58 - 16 * q^59 - 3 * q^60 - 24 * q^61 - 9 * q^62 + q^63 - 38 * q^64 - 8 * q^65 - 9 * q^67 - 19 * q^68 + 22 * q^69 + 2 * q^70 - 10 * q^71 - 4 * q^72 - 11 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 5 * q^78 - 9 * q^79 + 2 * q^80 - 19 * q^81 + 44 * q^82 - 10 * q^83 + 3 * q^84 - 6 * q^85 + 15 * q^86 + 2 * q^87 - 9 * q^89 - 11 * q^90 + 8 * q^91 - 26 * q^92 - q^93 - 34 * q^94 - 7 * q^95 + 18 * q^96 + 11 * q^97 - 2 * q^98

Introduction

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