LMFDB - Embedded newform 1027.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 8 x^{16} + 106 x^{15} - 57 x^{14} - 715 x^{13} + 859 x^{12} + 2323 x^{11} - 3741 x^{10} + \cdots + 8 $ x^18 - 6x^17 - 8x^16 + 106x^15 - 57x^14 - 715x^13 + 859x^12 + 2323x^11 - 3741x^10 - 3768x^9 + 7603x^8 + 2785x^7 - 7585x^6 - 510x^5 + 3292x^4 - 241x^3 - 361x^2 + 32*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.17251$ of defining polynomial
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17251 q^{2} +2.35329 q^{3} -0.625227 q^{4} -4.07505 q^{5} -2.75925 q^{6} -0.390573 q^{7} +3.07810 q^{8} +2.53797 q^{9} +O(q^{10})$	\(q-1.17251 q^{2} +2.35329 q^{3} -0.625227 q^{4} -4.07505 q^{5} -2.75925 q^{6} -0.390573 q^{7} +3.07810 q^{8} +2.53797 q^{9} +4.77802 q^{10} +5.79727 q^{11} -1.47134 q^{12} -1.00000 q^{13} +0.457949 q^{14} -9.58977 q^{15} -2.35864 q^{16} -5.92480 q^{17} -2.97579 q^{18} -0.102538 q^{19} +2.54783 q^{20} -0.919130 q^{21} -6.79734 q^{22} -0.876774 q^{23} +7.24365 q^{24} +11.6060 q^{25} +1.17251 q^{26} -1.08729 q^{27} +0.244197 q^{28} -9.55476 q^{29} +11.2441 q^{30} +4.62715 q^{31} -3.39068 q^{32} +13.6426 q^{33} +6.94687 q^{34} +1.59160 q^{35} -1.58681 q^{36} -4.79958 q^{37} +0.120227 q^{38} -2.35329 q^{39} -12.5434 q^{40} +0.995645 q^{41} +1.07769 q^{42} -7.84403 q^{43} -3.62461 q^{44} -10.3424 q^{45} +1.02802 q^{46} -4.91328 q^{47} -5.55055 q^{48} -6.84745 q^{49} -13.6082 q^{50} -13.9428 q^{51} +0.625227 q^{52} -11.9351 q^{53} +1.27486 q^{54} -23.6242 q^{55} -1.20222 q^{56} -0.241302 q^{57} +11.2030 q^{58} +9.46408 q^{59} +5.99579 q^{60} +7.00072 q^{61} -5.42536 q^{62} -0.991261 q^{63} +8.69286 q^{64} +4.07505 q^{65} -15.9961 q^{66} -7.41841 q^{67} +3.70435 q^{68} -2.06330 q^{69} -1.86617 q^{70} -1.18698 q^{71} +7.81212 q^{72} -10.2343 q^{73} +5.62754 q^{74} +27.3124 q^{75} +0.0641096 q^{76} -2.26425 q^{77} +2.75925 q^{78} -1.00000 q^{79} +9.61156 q^{80} -10.1726 q^{81} -1.16740 q^{82} -14.6408 q^{83} +0.574665 q^{84} +24.1439 q^{85} +9.19718 q^{86} -22.4851 q^{87} +17.8446 q^{88} +10.2822 q^{89} +12.1265 q^{90} +0.390573 q^{91} +0.548183 q^{92} +10.8890 q^{93} +5.76086 q^{94} +0.417848 q^{95} -7.97925 q^{96} +12.2998 q^{97} +8.02869 q^{98} +14.7133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.17251	−0.829088	−0.414544	−	0.910029i	$-0.636059\pi$
$2$	−1.17251	−0.829088	−0.414544	+	0.910029i	$0.636059\pi$
$3$	2.35329	1.35867	0.679336	−	0.733827i	$-0.262268\pi$
$3$	2.35329	1.35867	0.679336	+	0.733827i	$0.262268\pi$
$4$	−0.625227	−0.312614
$5$	−4.07505	−1.82242	−0.911209	−	0.411944i	$-0.864850\pi$
$5$	−4.07505	−1.82242	−0.911209	+	0.411944i	$0.864850\pi$
$6$	−2.75925	−1.12646
$7$	−0.390573	−0.147623	−0.0738113	−	0.997272i	$-0.523516\pi$
$7$	−0.390573	−0.147623	−0.0738113	+	0.997272i	$0.523516\pi$
$8$	3.07810	1.08827
$9$	2.53797	0.845990
$10$	4.77802	1.51094
$11$	5.79727	1.74794	0.873971	−	0.485978i	$-0.161537\pi$
$11$	5.79727	1.74794	0.873971	+	0.485978i	$0.161537\pi$
$12$	−1.47134	−0.424740
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.457949	0.122392
$15$	−9.58977	−2.47607
$16$	−2.35864	−0.589659
$17$	−5.92480	−1.43697	−0.718487	−	0.695540i	$-0.755165\pi$
$17$	−5.92480	−1.43697	−0.718487	+	0.695540i	$0.755165\pi$
$18$	−2.97579	−0.701400
$19$	−0.102538	−0.0235238	−0.0117619	−	0.999931i	$-0.503744\pi$
$19$	−0.102538	−0.0235238	−0.0117619	+	0.999931i	$0.503744\pi$
$20$	2.54783	0.569713
$21$	−0.919130	−0.200571
$22$	−6.79734	−1.44920
$23$	−0.876774	−0.182820	−0.0914101	−	0.995813i	$-0.529137\pi$
$23$	−0.876774	−0.182820	−0.0914101	+	0.995813i	$0.529137\pi$
$24$	7.24365	1.47860
$25$	11.6060	2.32121
$26$	1.17251	0.229948
$27$	−1.08729	−0.209249
$28$	0.244197	0.0461488
$29$	−9.55476	−1.77428	−0.887138	−	0.461505i	$-0.847310\pi$
$29$	−9.55476	−1.77428	−0.887138	+	0.461505i	$0.847310\pi$
$30$	11.2441	2.05288
$31$	4.62715	0.831060	0.415530	−	0.909579i	$-0.363596\pi$
$31$	4.62715	0.831060	0.415530	+	0.909579i	$0.363596\pi$
$32$	−3.39068	−0.599393
$33$	13.6426	2.37488
$34$	6.94687	1.19138
$35$	1.59160	0.269030
$36$	−1.58681	−0.264468
$37$	−4.79958	−0.789046	−0.394523	−	0.918886i	$-0.629090\pi$
$37$	−4.79958	−0.789046	−0.394523	+	0.918886i	$0.629090\pi$
$38$	0.120227	0.0195033
$39$	−2.35329	−0.376828
$40$	−12.5434	−1.98329
$41$	0.995645	0.155494	0.0777468	−	0.996973i	$-0.475227\pi$
$41$	0.995645	0.155494	0.0777468	+	0.996973i	$0.475227\pi$
$42$	1.07769	0.166291
$43$	−7.84403	−1.19620	−0.598102	−	0.801420i	$-0.704078\pi$
$43$	−7.84403	−1.19620	−0.598102	+	0.801420i	$0.704078\pi$
$44$	−3.62461	−0.546431
$45$	−10.3424	−1.54175
$46$	1.02802	0.151574
$47$	−4.91328	−0.716676	−0.358338	−	0.933592i	$-0.616657\pi$
$47$	−4.91328	−0.716676	−0.358338	+	0.933592i	$0.616657\pi$
$48$	−5.55055	−0.801153
$49$	−6.84745	−0.978208
$50$	−13.6082	−1.92448
$51$	−13.9428	−1.95238
$52$	0.625227	0.0867035
$53$	−11.9351	−1.63941	−0.819707	−	0.572783i	$-0.805864\pi$
$53$	−11.9351	−1.63941	−0.819707	+	0.572783i	$0.805864\pi$
$54$	1.27486	0.173486
$55$	−23.6242	−3.18548
$56$	−1.20222	−0.160653
$57$	−0.241302	−0.0319612
$58$	11.2030	1.47103
$59$	9.46408	1.23212	0.616059	−	0.787700i	$-0.288728\pi$
$59$	9.46408	1.23212	0.616059	+	0.787700i	$0.288728\pi$
$60$	5.99579	0.774053
$61$	7.00072	0.896351	0.448175	−	0.893946i	$-0.352074\pi$
$61$	7.00072	0.896351	0.448175	+	0.893946i	$0.352074\pi$
$62$	−5.42536	−0.689022
$63$	−0.991261	−0.124887
$64$	8.69286	1.08661
$65$	4.07505	0.505448
$66$	−15.9961	−1.96898
$67$	−7.41841	−0.906303	−0.453151	−	0.891434i	$-0.649700\pi$
$67$	−7.41841	−0.906303	−0.453151	+	0.891434i	$0.649700\pi$
$68$	3.70435	0.449218
$69$	−2.06330	−0.248393
$70$	−1.86617	−0.223049
$71$	−1.18698	−0.140869	−0.0704346	−	0.997516i	$-0.522439\pi$
$71$	−1.18698	−0.140869	−0.0704346	+	0.997516i	$0.522439\pi$
$72$	7.81212	0.920667
$73$	−10.2343	−1.19784	−0.598920	−	0.800809i	$-0.704403\pi$
$73$	−10.2343	−1.19784	−0.598920	+	0.800809i	$0.704403\pi$
$74$	5.62754	0.654188
$75$	27.3124	3.15376
$76$	0.0641096	0.00735388
$77$	−2.26425	−0.258036
$78$	2.75925	0.312423
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	9.61156	1.07460
$81$	−10.1726	−1.13029
$82$	−1.16740	−0.128918
$83$	−14.6408	−1.60704	−0.803521	−	0.595276i	$-0.797043\pi$
$83$	−14.6408	−1.60704	−0.803521	+	0.595276i	$0.797043\pi$
$84$	0.574665	0.0627011
$85$	24.1439	2.61877
$86$	9.19718	0.991758
$87$	−22.4851	−2.41066
$88$	17.8446	1.90224
$89$	10.2822	1.08991	0.544957	−	0.838464i	$-0.316546\pi$
$89$	10.2822	1.08991	0.544957	+	0.838464i	$0.316546\pi$
$90$	12.1265	1.27824
$91$	0.390573	0.0409431
$92$	0.548183	0.0571521
$93$	10.8890	1.12914
$94$	5.76086	0.594187
$95$	0.417848	0.0428703
$96$	−7.97925	−0.814378
$97$	12.2998	1.24886	0.624430	−	0.781081i	$-0.285331\pi$
$97$	12.2998	1.24886	0.624430	+	0.781081i	$0.285331\pi$
$98$	8.02869	0.811020
$99$	14.7133	1.47874
$100$	−7.25641	−0.725641
$101$	−16.6951	−1.66123	−0.830614	−	0.556848i	$-0.812011\pi$
$101$	−16.6951	−1.66123	−0.830614	+	0.556848i	$0.812011\pi$
$102$	16.3480	1.61869
$103$	5.82886	0.574335	0.287167	−	0.957880i	$-0.407286\pi$
$103$	5.82886	0.574335	0.287167	+	0.957880i	$0.407286\pi$
$104$	−3.07810	−0.301832
$105$	3.74550	0.365523
$106$	13.9940	1.35922
$107$	−4.84234	−0.468127	−0.234063	−	0.972221i	$-0.575202\pi$
$107$	−4.84234	−0.468127	−0.234063	+	0.972221i	$0.575202\pi$
$108$	0.679805	0.0654142
$109$	5.78559	0.554159	0.277079	−	0.960847i	$-0.410634\pi$
$109$	5.78559	0.554159	0.277079	+	0.960847i	$0.410634\pi$
$110$	27.6995	2.64104
$111$	−11.2948	−1.07205
$112$	0.921218	0.0870469
$113$	14.6139	1.37476	0.687378	−	0.726300i	$-0.258762\pi$
$113$	14.6139	1.37476	0.687378	+	0.726300i	$0.258762\pi$
$114$	0.282928	0.0264986
$115$	3.57290	0.333175
$116$	5.97390	0.554663
$117$	−2.53797	−0.234635
$118$	−11.0967	−1.02153
$119$	2.31406	0.212130
$120$	−29.5183	−2.69464
$121$	22.6083	2.05530
$122$	−8.20840	−0.743153
$123$	2.34304	0.211265
$124$	−2.89302	−0.259801
$125$	−26.9199	−2.40779
$126$	1.16226	0.103542
$127$	−4.44541	−0.394466	−0.197233	−	0.980357i	$-0.563196\pi$
$127$	−4.44541	−0.394466	−0.197233	+	0.980357i	$0.563196\pi$
$128$	−3.41109	−0.301500
$129$	−18.4593	−1.62525
$130$	−4.77802	−0.419061
$131$	8.89276	0.776964	0.388482	−	0.921456i	$-0.373000\pi$
$131$	8.89276	0.776964	0.388482	+	0.921456i	$0.373000\pi$
$132$	−8.52976	−0.742420
$133$	0.0400485	0.00347265
$134$	8.69813	0.751404
$135$	4.43077	0.381340
$136$	−18.2371	−1.56382
$137$	−18.0206	−1.53960	−0.769802	−	0.638283i	$-0.779645\pi$
$137$	−18.0206	−1.53960	−0.769802	+	0.638283i	$0.779645\pi$
$138$	2.41924	0.205939
$139$	−3.94733	−0.334808	−0.167404	−	0.985888i	$-0.553538\pi$
$139$	−3.94733	−0.334808	−0.167404	+	0.985888i	$0.553538\pi$
$140$	−0.995114	−0.0841025
$141$	−11.5624	−0.973728
$142$	1.39175	0.116793
$143$	−5.79727	−0.484792
$144$	−5.98614	−0.498845
$145$	38.9361	3.23347
$146$	11.9998	0.993114
$147$	−16.1140	−1.32906
$148$	3.00083	0.246666
$149$	−3.39301	−0.277966	−0.138983	−	0.990295i	$-0.544383\pi$
$149$	−3.39301	−0.277966	−0.138983	+	0.990295i	$0.544383\pi$
$150$	−32.0239	−2.61474
$151$	4.22487	0.343815	0.171908	−	0.985113i	$-0.445007\pi$
$151$	4.22487	0.343815	0.171908	+	0.985113i	$0.445007\pi$
$152$	−0.315622	−0.0256003
$153$	−15.0370	−1.21567
$154$	2.65485	0.213934
$155$	−18.8559	−1.51454
$156$	1.47134	0.117802
$157$	8.73977	0.697509	0.348755	−	0.937214i	$-0.386605\pi$
$157$	8.73977	0.697509	0.348755	+	0.937214i	$0.386605\pi$
$158$	1.17251	0.0932796
$159$	−28.0868	−2.22743
$160$	13.8172	1.09234
$161$	0.342444	0.0269884
$162$	11.9275	0.937110
$163$	16.1783	1.26718	0.633591	−	0.773668i	$-0.281580\pi$
$163$	16.1783	1.26718	0.633591	+	0.773668i	$0.281580\pi$
$164$	−0.622505	−0.0486095
$165$	−55.5945	−4.32802
$166$	17.1665	1.33238
$167$	−19.0426	−1.47356	−0.736780	−	0.676133i	$-0.763655\pi$
$167$	−19.0426	−1.47356	−0.736780	+	0.676133i	$0.763655\pi$
$168$	−2.82917	−0.218275
$169$	1.00000	0.0769231
$170$	−28.3088	−2.17119
$171$	−0.260238	−0.0199009
$172$	4.90430	0.373950
$173$	15.9545	1.21300	0.606500	−	0.795084i	$-0.292573\pi$
$173$	15.9545	1.21300	0.606500	+	0.795084i	$0.292573\pi$
$174$	26.3640	1.99865
$175$	−4.53300	−0.342662
$176$	−13.6736	−1.03069
$177$	22.2717	1.67404
$178$	−12.0560	−0.903633
$179$	−21.9408	−1.63993	−0.819965	−	0.572413i	$-0.806007\pi$
$179$	−21.9408	−1.63993	−0.819965	+	0.572413i	$0.806007\pi$
$180$	6.46632	0.481971
$181$	5.69930	0.423626	0.211813	−	0.977310i	$-0.432063\pi$
$181$	5.69930	0.423626	0.211813	+	0.977310i	$0.432063\pi$
$182$	−0.457949	−0.0339454
$183$	16.4747	1.21785
$184$	−2.69880	−0.198958
$185$	19.5585	1.43797
$186$	−12.7674	−0.936154
$187$	−34.3476	−2.51175
$188$	3.07192	0.224043
$189$	0.424666	0.0308899
$190$	−0.489929	−0.0355432
$191$	−3.14688	−0.227700	−0.113850	−	0.993498i	$-0.536318\pi$
$191$	−3.14688	−0.227700	−0.113850	+	0.993498i	$0.536318\pi$
$192$	20.4568	1.47634
$193$	25.5246	1.83730	0.918652	−	0.395068i	$-0.129279\pi$
$193$	25.5246	1.83730	0.918652	+	0.395068i	$0.129279\pi$
$194$	−14.4217	−1.03541
$195$	9.58977	0.686738
$196$	4.28122	0.305801
$197$	−10.3750	−0.739186	−0.369593	−	0.929194i	$-0.620503\pi$
$197$	−10.3750	−0.739186	−0.369593	+	0.929194i	$0.620503\pi$
$198$	−17.2514	−1.22601
$199$	3.71890	0.263626	0.131813	−	0.991275i	$-0.457920\pi$
$199$	3.71890	0.263626	0.131813	+	0.991275i	$0.457920\pi$
$200$	35.7245	2.52610
$201$	−17.4577	−1.23137
$202$	19.5752	1.37730
$203$	3.73183	0.261923
$204$	8.71740	0.610340
$205$	−4.05730	−0.283374
$206$	−6.83438	−0.476174
$207$	−2.22523	−0.154664
$208$	2.35864	0.163542
$209$	−0.594440	−0.0411183
$210$	−4.39163	−0.303051
$211$	19.6182	1.35057	0.675287	−	0.737555i	$-0.264020\pi$
$211$	19.6182	1.35057	0.675287	+	0.737555i	$0.264020\pi$
$212$	7.46216	0.512503
$213$	−2.79332	−0.191395
$214$	5.67768	0.388118
$215$	31.9648	2.17998
$216$	−3.34679	−0.227720
$217$	−1.80724	−0.122683
$218$	−6.78364	−0.459446
$219$	−24.0844	−1.62747
$220$	14.7705	0.995825
$221$	5.92480	0.398545
$222$	13.2432	0.888827
$223$	−7.13116	−0.477538	−0.238769	−	0.971076i	$-0.576744\pi$
$223$	−7.13116	−0.477538	−0.238769	+	0.971076i	$0.576744\pi$
$224$	1.32431	0.0884839
$225$	29.4558	1.96372
$226$	−17.1348	−1.13979
$227$	21.8285	1.44881	0.724403	−	0.689377i	$-0.242116\pi$
$227$	21.8285	1.44881	0.724403	+	0.689377i	$0.242116\pi$
$228$	0.150868	0.00999151
$229$	1.85200	0.122383	0.0611916	−	0.998126i	$-0.480510\pi$
$229$	1.85200	0.122383	0.0611916	+	0.998126i	$0.480510\pi$
$230$	−4.18925	−0.276231
$231$	−5.32844	−0.350586
$232$	−29.4105	−1.93089
$233$	−10.2237	−0.669779	−0.334889	−	0.942257i	$-0.608699\pi$
$233$	−10.2237	−0.669779	−0.334889	+	0.942257i	$0.608699\pi$
$234$	2.97579	0.194533
$235$	20.0219	1.30608
$236$	−5.91720	−0.385177
$237$	−2.35329	−0.152863
$238$	−2.71326	−0.175874
$239$	−23.7748	−1.53786	−0.768931	−	0.639331i	$-0.779211\pi$
$239$	−23.7748	−1.53786	−0.768931	+	0.639331i	$0.779211\pi$
$240$	22.6188	1.46004
$241$	16.2314	1.04556	0.522778	−	0.852469i	$-0.324896\pi$
$241$	16.2314	1.04556	0.522778	+	0.852469i	$0.324896\pi$
$242$	−26.5084	−1.70402
$243$	−20.6772	−1.32645
$244$	−4.37705	−0.280212
$245$	27.9037	1.78270
$246$	−2.74723	−0.175157
$247$	0.102538	0.00652434
$248$	14.2428	0.904419
$249$	−34.4541	−2.18344
$250$	31.5638	1.99627
$251$	−13.8858	−0.876465	−0.438232	−	0.898862i	$-0.644395\pi$
$251$	−13.8858	−0.876465	−0.438232	+	0.898862i	$0.644395\pi$
$252$	0.619764	0.0390414
$253$	−5.08290	−0.319559
$254$	5.21228	0.327047
$255$	56.8175	3.55805
$256$	−13.3862	−0.836638
$257$	−6.72625	−0.419572	−0.209786	−	0.977747i	$-0.567277\pi$
$257$	−6.72625	−0.419572	−0.209786	+	0.977747i	$0.567277\pi$
$258$	21.6436	1.34747
$259$	1.87458	0.116481
$260$	−2.54783	−0.158010
$261$	−24.2497	−1.50102
$262$	−10.4268	−0.644171
$263$	−7.08406	−0.436822	−0.218411	−	0.975857i	$-0.570087\pi$
$263$	−7.08406	−0.436822	−0.218411	+	0.975857i	$0.570087\pi$
$264$	41.9934	2.58451
$265$	48.6362	2.98770
$266$	−0.0469572	−0.00287913
$267$	24.1970	1.48083
$268$	4.63819	0.283323
$269$	4.39005	0.267666	0.133833	−	0.991004i	$-0.457271\pi$
$269$	4.39005	0.267666	0.133833	+	0.991004i	$0.457271\pi$
$270$	−5.19511	−0.316164
$271$	−18.1218	−1.10082	−0.550410	−	0.834894i	$-0.685529\pi$
$271$	−18.1218	−1.10082	−0.550410	+	0.834894i	$0.685529\pi$
$272$	13.9744	0.847325
$273$	0.919130	0.0556283
$274$	21.1293	1.27647
$275$	67.2833	4.05734
$276$	1.29003	0.0776509
$277$	−13.2593	−0.796673	−0.398337	−	0.917239i	$-0.630412\pi$
$277$	−13.2593	−0.796673	−0.398337	+	0.917239i	$0.630412\pi$
$278$	4.62827	0.277585
$279$	11.7436	0.703068
$280$	4.89911	0.292778
$281$	−4.57700	−0.273041	−0.136520	−	0.990637i	$-0.543592\pi$
$281$	−4.57700	−0.273041	−0.136520	+	0.990637i	$0.543592\pi$
$282$	13.5570	0.807306
$283$	8.33039	0.495190	0.247595	−	0.968864i	$-0.420360\pi$
$283$	8.33039	0.495190	0.247595	+	0.968864i	$0.420360\pi$
$284$	0.742136	0.0440376
$285$	0.983317	0.0582466
$286$	6.79734	0.401935
$287$	−0.388872	−0.0229544
$288$	−8.60544	−0.507080
$289$	18.1032	1.06490
$290$	−45.6529	−2.68083
$291$	28.9451	1.69679
$292$	6.39879	0.374461
$293$	11.6800	0.682353	0.341176	−	0.939999i	$-0.389175\pi$
$293$	11.6800	0.682353	0.341176	+	0.939999i	$0.389175\pi$
$294$	18.8938	1.10191
$295$	−38.5666	−2.24543
$296$	−14.7736	−0.858696
$297$	−6.30332	−0.365756
$298$	3.97833	0.230458
$299$	0.876774	0.0507052
$300$	−17.0764	−0.985909
$301$	3.06366	0.176587
$302$	−4.95369	−0.285053
$303$	−39.2885	−2.25706
$304$	0.241850	0.0138710
$305$	−28.5283	−1.63353
$306$	17.6309	1.00789
$307$	−12.1982	−0.696190	−0.348095	−	0.937459i	$-0.613171\pi$
$307$	−12.1982	−0.696190	−0.348095	+	0.937459i	$0.613171\pi$
$308$	1.41567	0.0806655
$309$	13.7170	0.780332
$310$	22.1086	1.25569
$311$	−5.84655	−0.331527	−0.165764	−	0.986165i	$-0.553009\pi$
$311$	−5.84655	−0.331527	−0.165764	+	0.986165i	$0.553009\pi$
$312$	−7.24365	−0.410091
$313$	−12.2290	−0.691225	−0.345612	−	0.938377i	$-0.612329\pi$
$313$	−12.2290	−0.691225	−0.345612	+	0.938377i	$0.612329\pi$
$314$	−10.2474	−0.578296
$315$	4.03944	0.227597
$316$	0.625227	0.0351718
$317$	16.5523	0.929670	0.464835	−	0.885397i	$-0.346114\pi$
$317$	16.5523	0.929670	0.464835	+	0.885397i	$0.346114\pi$
$318$	32.9319	1.84673
$319$	−55.3915	−3.10133
$320$	−35.4239	−1.98025
$321$	−11.3954	−0.636031
$322$	−0.401518	−0.0223757
$323$	0.607517	0.0338032
$324$	6.36020	0.353345
$325$	−11.6060	−0.643787
$326$	−18.9692	−1.05061
$327$	13.6152	0.752920
$328$	3.06469	0.169219
$329$	1.91899	0.105798
$330$	65.1849	3.58831
$331$	1.84791	0.101570	0.0507852	−	0.998710i	$-0.483828\pi$
$331$	1.84791	0.101570	0.0507852	+	0.998710i	$0.483828\pi$
$332$	9.15386	0.502383
$333$	−12.1812	−0.667524
$334$	22.3276	1.22171
$335$	30.2304	1.65166
$336$	2.16789	0.118268
$337$	29.2488	1.59328	0.796642	−	0.604451i	$-0.206608\pi$
$337$	29.2488	1.59328	0.796642	+	0.604451i	$0.206608\pi$
$338$	−1.17251	−0.0637760
$339$	34.3906	1.86784
$340$	−15.0954	−0.818663
$341$	26.8248	1.45264
$342$	0.305131	0.0164996
$343$	5.40843	0.292028
$344$	−24.1447	−1.30179
$345$	8.40807	0.452675
$346$	−18.7068	−1.00568
$347$	21.4469	1.15133	0.575665	−	0.817686i	$-0.304743\pi$
$347$	21.4469	1.15133	0.575665	+	0.817686i	$0.304743\pi$
$348$	14.0583	0.753605
$349$	−27.6330	−1.47916	−0.739580	−	0.673068i	$-0.764976\pi$
$349$	−27.6330	−1.47916	−0.739580	+	0.673068i	$0.764976\pi$
$350$	5.31497	0.284097
$351$	1.08729	0.0580353
$352$	−19.6567	−1.04770
$353$	24.5651	1.30747	0.653734	−	0.756725i	$-0.273202\pi$
$353$	24.5651	1.30747	0.653734	+	0.756725i	$0.273202\pi$
$354$	−26.1137	−1.38793
$355$	4.83702	0.256723
$356$	−6.42873	−0.340722
$357$	5.44566	0.288215
$358$	25.7257	1.35965
$359$	33.9082	1.78960	0.894802	−	0.446463i	$-0.147317\pi$
$359$	33.9082	1.78960	0.894802	+	0.446463i	$0.147317\pi$
$360$	−31.8348	−1.67784
$361$	−18.9895	−0.999447
$362$	−6.68247	−0.351223
$363$	53.2039	2.79248
$364$	−0.244197	−0.0127994
$365$	41.7055	2.18296
$366$	−19.3167	−1.00970
$367$	−8.55063	−0.446339	−0.223170	−	0.974780i	$-0.571640\pi$
$367$	−8.55063	−0.446339	−0.223170	+	0.974780i	$0.571640\pi$
$368$	2.06799	0.107802
$369$	2.52692	0.131546
$370$	−22.9325	−1.19220
$371$	4.66153	0.242014
$372$	−6.80811	−0.352984
$373$	17.2524	0.893294	0.446647	−	0.894710i	$-0.352618\pi$
$373$	17.2524	0.893294	0.446647	+	0.894710i	$0.352618\pi$
$374$	40.2729	2.08246
$375$	−63.3504	−3.27140
$376$	−15.1236	−0.779939
$377$	9.55476	0.492095
$378$	−0.497924	−0.0256105
$379$	−11.8672	−0.609576	−0.304788	−	0.952420i	$-0.598586\pi$
$379$	−11.8672	−0.609576	−0.304788	+	0.952420i	$0.598586\pi$
$380$	−0.261250	−0.0134018
$381$	−10.4613	−0.535951
$382$	3.68974	0.188783
$383$	−17.9522	−0.917315	−0.458657	−	0.888613i	$-0.651669\pi$
$383$	−17.9522	−0.917315	−0.458657	+	0.888613i	$0.651669\pi$
$384$	−8.02728	−0.409640
$385$	9.22695	0.470249
$386$	−29.9278	−1.52329
$387$	−19.9079	−1.01198
$388$	−7.69020	−0.390411
$389$	−17.2193	−0.873055	−0.436527	−	0.899691i	$-0.643792\pi$
$389$	−17.2193	−0.873055	−0.436527	+	0.899691i	$0.643792\pi$
$390$	−11.2441	−0.569366
$391$	5.19471	0.262708
$392$	−21.0771	−1.06456
$393$	20.9272	1.05564
$394$	12.1647	0.612850
$395$	4.07505	0.205038
$396$	−9.19915	−0.462275
$397$	26.7349	1.34178	0.670892	−	0.741555i	$-0.265911\pi$
$397$	26.7349	1.34178	0.670892	+	0.741555i	$0.265911\pi$
$398$	−4.36043	−0.218569
$399$	0.0942458	0.00471819
$400$	−27.3744	−1.36872
$401$	−18.3306	−0.915384	−0.457692	−	0.889111i	$-0.651324\pi$
$401$	−18.3306	−0.915384	−0.457692	+	0.889111i	$0.651324\pi$
$402$	20.4692	1.02091
$403$	−4.62715	−0.230495
$404$	10.4383	0.519323
$405$	41.4539	2.05986
$406$	−4.37559	−0.217157
$407$	−27.8244	−1.37921
$408$	−42.9172	−2.12472
$409$	−3.04453	−0.150542	−0.0752711	−	0.997163i	$-0.523982\pi$
$409$	−3.04453	−0.150542	−0.0752711	+	0.997163i	$0.523982\pi$
$410$	4.75722	0.234942
$411$	−42.4077	−2.09182
$412$	−3.64436	−0.179545
$413$	−3.69641	−0.181888
$414$	2.60909	0.128230
$415$	59.6622	2.92870
$416$	3.39068	0.166242
$417$	−9.28920	−0.454894
$418$	0.696986	0.0340907
$419$	−2.28291	−0.111527	−0.0557637	−	0.998444i	$-0.517759\pi$
$419$	−2.28291	−0.111527	−0.0557637	+	0.998444i	$0.517759\pi$
$420$	−2.34179	−0.114268
$421$	10.9629	0.534301	0.267150	−	0.963655i	$-0.413918\pi$
$421$	10.9629	0.534301	0.267150	+	0.963655i	$0.413918\pi$
$422$	−23.0025	−1.11974
$423$	−12.4698	−0.606301
$424$	−36.7374	−1.78413
$425$	−68.7634	−3.33552
$426$	3.27519	0.158683
$427$	−2.73429	−0.132322
$428$	3.02757	0.146343
$429$	−13.6426	−0.658673
$430$	−37.4790	−1.80740
$431$	3.68186	0.177349	0.0886744	−	0.996061i	$-0.471737\pi$
$431$	3.68186	0.177349	0.0886744	+	0.996061i	$0.471737\pi$
$432$	2.56453	0.123386
$433$	−20.8557	−1.00226	−0.501132	−	0.865371i	$-0.667083\pi$
$433$	−20.8557	−1.00226	−0.501132	+	0.865371i	$0.667083\pi$
$434$	2.11900	0.101715
$435$	91.6280	4.39323
$436$	−3.61731	−0.173238
$437$	0.0899027	0.00430063
$438$	28.2391	1.34932
$439$	7.38481	0.352458	0.176229	−	0.984349i	$-0.443610\pi$
$439$	7.38481	0.352458	0.176229	+	0.984349i	$0.443610\pi$
$440$	−72.7175	−3.46667
$441$	−17.3786	−0.827554
$442$	−6.94687	−0.330429
$443$	−12.1550	−0.577501	−0.288750	−	0.957404i	$-0.593240\pi$
$443$	−12.1550	−0.577501	−0.288750	+	0.957404i	$0.593240\pi$
$444$	7.06181	0.335139
$445$	−41.9006	−1.98628
$446$	8.36134	0.395921
$447$	−7.98473	−0.377665
$448$	−3.39519	−0.160408
$449$	2.24448	0.105924	0.0529618	−	0.998597i	$-0.483134\pi$
$449$	2.24448	0.105924	0.0529618	+	0.998597i	$0.483134\pi$
$450$	−34.5371	−1.62809
$451$	5.77202	0.271794
$452$	−9.13698	−0.429768
$453$	9.94235	0.467132
$454$	−25.5940	−1.20119
$455$	−1.59160	−0.0746155
$456$	−0.742750	−0.0347825
$457$	−32.5511	−1.52267	−0.761337	−	0.648356i	$-0.775457\pi$
$457$	−32.5511	−1.52267	−0.761337	+	0.648356i	$0.775457\pi$
$458$	−2.17148	−0.101466
$459$	6.44199	0.300686
$460$	−2.23388	−0.104155
$461$	25.5971	1.19218	0.596088	−	0.802919i	$-0.296721\pi$
$461$	25.5971	1.19218	0.596088	+	0.802919i	$0.296721\pi$
$462$	6.24764	0.290666
$463$	3.41217	0.158577	0.0792884	−	0.996852i	$-0.474735\pi$
$463$	3.41217	0.158577	0.0792884	+	0.996852i	$0.474735\pi$
$464$	22.5362	1.04622
$465$	−44.3733	−2.05776
$466$	11.9874	0.555305
$467$	2.19731	0.101680	0.0508398	−	0.998707i	$-0.483810\pi$
$467$	2.19731	0.101680	0.0508398	+	0.998707i	$0.483810\pi$
$468$	1.58681	0.0733502
$469$	2.89743	0.133791
$470$	−23.4758	−1.08286
$471$	20.5672	0.947686
$472$	29.1314	1.34088
$473$	−45.4739	−2.09089
$474$	2.75925	0.126736
$475$	−1.19006	−0.0546037
$476$	−1.44682	−0.0663147
$477$	−30.2910	−1.38693
$478$	27.8761	1.27502
$479$	18.6559	0.852408	0.426204	−	0.904627i	$-0.359850\pi$
$479$	18.6559	0.852408	0.426204	+	0.904627i	$0.359850\pi$
$480$	32.5158	1.48414
$481$	4.79958	0.218842
$482$	−19.0314	−0.866857
$483$	0.805870	0.0366683
$484$	−14.1353	−0.642515
$485$	−50.1225	−2.27594
$486$	24.2442	1.09974
$487$	2.78879	0.126372	0.0631860	−	0.998002i	$-0.479874\pi$
$487$	2.78879	0.126372	0.0631860	+	0.998002i	$0.479874\pi$
$488$	21.5489	0.975473
$489$	38.0722	1.72169
$490$	−32.7173	−1.47802
$491$	−20.9979	−0.947620	−0.473810	−	0.880627i	$-0.657122\pi$
$491$	−20.9979	−0.947620	−0.473810	+	0.880627i	$0.657122\pi$
$492$	−1.46493	−0.0660443
$493$	56.6101	2.54959
$494$	−0.120227	−0.00540925
$495$	−59.9574	−2.69488
$496$	−10.9138	−0.490042
$497$	0.463604	0.0207955
$498$	40.3977	1.81027
$499$	−12.8444	−0.574993	−0.287496	−	0.957782i	$-0.592823\pi$
$499$	−12.8444	−0.574993	−0.287496	+	0.957782i	$0.592823\pi$
$500$	16.8311	0.752709
$501$	−44.8127	−2.00208
$502$	16.2812	0.726666
$503$	4.94435	0.220458	0.110229	−	0.993906i	$-0.464842\pi$
$503$	4.94435	0.220458	0.110229	+	0.993906i	$0.464842\pi$
$504$	−3.05120	−0.135911
$505$	68.0335	3.02745
$506$	5.95973	0.264942
$507$	2.35329	0.104513
$508$	2.77939	0.123316
$509$	30.1003	1.33417	0.667087	−	0.744980i	$-0.267541\pi$
$509$	30.1003	1.33417	0.667087	+	0.744980i	$0.267541\pi$
$510$	−66.6189	−2.94993
$511$	3.99725	0.176828
$512$	22.5176	0.995147
$513$	0.111489	0.00492235
$514$	7.88657	0.347862
$515$	−23.7529	−1.04668
$516$	11.5412	0.508075
$517$	−28.4836	−1.25271
$518$	−2.19796	−0.0965729
$519$	37.5456	1.64807
$520$	12.5434	0.550065
$521$	4.10234	0.179727	0.0898634	−	0.995954i	$-0.471357\pi$
$521$	4.10234	0.179727	0.0898634	+	0.995954i	$0.471357\pi$
$522$	28.4329	1.24448
$523$	23.0712	1.00883	0.504417	−	0.863460i	$-0.331707\pi$
$523$	23.0712	1.00883	0.504417	+	0.863460i	$0.331707\pi$
$524$	−5.56000	−0.242890
$525$	−10.6675	−0.465566
$526$	8.30611	0.362164
$527$	−27.4149	−1.19421
$528$	−32.1780	−1.40037
$529$	−22.2313	−0.966577
$530$	−57.0263	−2.47706
$531$	24.0195	1.04236
$532$	−0.0250395	−0.00108560
$533$	−0.995645	−0.0431262
$534$	−28.3712	−1.22774
$535$	19.7328	0.853123
$536$	−22.8346	−0.986304
$537$	−51.6330	−2.22813
$538$	−5.14737	−0.221919
$539$	−39.6965	−1.70985
$540$	−2.77024	−0.119212
$541$	−28.6489	−1.23171	−0.615856	−	0.787859i	$-0.711190\pi$
$541$	−28.6489	−1.23171	−0.615856	+	0.787859i	$0.711190\pi$
$542$	21.2479	0.912677
$543$	13.4121	0.575568
$544$	20.0891	0.861313
$545$	−23.5766	−1.00991
$546$	−1.07769	−0.0461207
$547$	−27.9007	−1.19295	−0.596474	−	0.802632i	$-0.703432\pi$
$547$	−27.9007	−1.19295	−0.596474	+	0.802632i	$0.703432\pi$
$548$	11.2670	0.481301
$549$	17.7676	0.758304
$550$	−78.8901	−3.36389
$551$	0.979727	0.0417378
$552$	−6.35105	−0.270319
$553$	0.390573	0.0166088
$554$	15.5466	0.660512
$555$	46.0268	1.95373
$556$	2.46798	0.104666
$557$	15.4555	0.654871	0.327435	−	0.944874i	$-0.393816\pi$
$557$	15.4555	0.654871	0.327435	+	0.944874i	$0.393816\pi$
$558$	−13.7694	−0.582905
$559$	7.84403	0.331767
$560$	−3.75401	−0.158636
$561$	−80.8299	−3.41264
$562$	5.36656	0.226375
$563$	−20.5273	−0.865123	−0.432561	−	0.901604i	$-0.642390\pi$
$563$	−20.5273	−0.865123	−0.432561	+	0.901604i	$0.642390\pi$
$564$	7.22912	0.304401
$565$	−59.5522	−2.50538
$566$	−9.76744	−0.410556
$567$	3.97315	0.166856
$568$	−3.65366	−0.153304
$569$	40.9819	1.71805	0.859026	−	0.511932i	$-0.171070\pi$
$569$	40.9819	1.71805	0.859026	+	0.511932i	$0.171070\pi$
$570$	−1.15295	−0.0482916
$571$	44.9672	1.88182	0.940908	−	0.338661i	$-0.109974\pi$
$571$	44.9672	1.88182	0.940908	+	0.338661i	$0.109974\pi$
$572$	3.62461	0.151553
$573$	−7.40552	−0.309370
$574$	0.455955	0.0190312
$575$	−10.1759	−0.424363
$576$	22.0622	0.919259
$577$	19.6393	0.817596	0.408798	−	0.912625i	$-0.365948\pi$
$577$	19.6393	0.817596	0.408798	+	0.912625i	$0.365948\pi$
$578$	−21.2262	−0.882893
$579$	60.0668	2.49629
$580$	−24.3439	−1.01083
$581$	5.71831	0.237236
$582$	−33.9383	−1.40679
$583$	−69.1910	−2.86560
$584$	−31.5023	−1.30357
$585$	10.3424	0.427604
$586$	−13.6949	−0.565730
$587$	17.8469	0.736620	0.368310	−	0.929703i	$-0.379936\pi$
$587$	17.8469	0.736620	0.368310	+	0.929703i	$0.379936\pi$
$588$	10.0749	0.415483
$589$	−0.474459	−0.0195497
$590$	45.2196	1.86166
$591$	−24.4153	−1.00431
$592$	11.3205	0.465268
$593$	−15.3303	−0.629541	−0.314770	−	0.949168i	$-0.601927\pi$
$593$	−15.3303	−0.629541	−0.314770	+	0.949168i	$0.601927\pi$
$594$	7.39069	0.303244
$595$	−9.42993	−0.386589
$596$	2.12140	0.0868960
$597$	8.75164	0.358181
$598$	−1.02802	−0.0420390
$599$	16.6772	0.681414	0.340707	−	0.940170i	$-0.389334\pi$
$599$	16.6772	0.681414	0.340707	+	0.940170i	$0.389334\pi$
$600$	84.0701	3.43215
$601$	18.5377	0.756169	0.378085	−	0.925771i	$-0.376583\pi$
$601$	18.5377	0.756169	0.378085	+	0.925771i	$0.376583\pi$
$602$	−3.59217	−0.146406
$603$	−18.8277	−0.766723
$604$	−2.64151	−0.107481
$605$	−92.1300	−3.74562
$606$	46.0660	1.87130
$607$	−40.3728	−1.63868	−0.819340	−	0.573308i	$-0.805660\pi$
$607$	−40.3728	−1.63868	−0.819340	+	0.573308i	$0.805660\pi$
$608$	0.347674	0.0141000
$609$	8.78207	0.355867
$610$	33.4496	1.35434
$611$	4.91328	0.198770
$612$	9.40152	0.380034
$613$	−35.0296	−1.41483	−0.707417	−	0.706797i	$-0.750139\pi$
$613$	−35.0296	−1.41483	−0.707417	+	0.706797i	$0.750139\pi$
$614$	14.3025	0.577203
$615$	−9.54801	−0.385013
$616$	−6.96959	−0.280813
$617$	−15.1162	−0.608553	−0.304277	−	0.952584i	$-0.598415\pi$
$617$	−15.1162	−0.608553	−0.304277	+	0.952584i	$0.598415\pi$
$618$	−16.0833	−0.646964
$619$	−14.5491	−0.584779	−0.292389	−	0.956299i	$-0.594450\pi$
$619$	−14.5491	−0.584779	−0.292389	+	0.956299i	$0.594450\pi$
$620$	11.7892	0.473466
$621$	0.953310	0.0382550
$622$	6.85512	0.274865
$623$	−4.01595	−0.160896
$624$	5.55055	0.222200
$625$	51.6699	2.06680
$626$	14.3386	0.573086
$627$	−1.39889	−0.0558663
$628$	−5.46434	−0.218051
$629$	28.4365	1.13384
$630$	−4.73627	−0.188698
$631$	4.86723	0.193762	0.0968808	−	0.995296i	$-0.469113\pi$
$631$	4.86723	0.193762	0.0968808	+	0.995296i	$0.469113\pi$
$632$	−3.07810	−0.122440
$633$	46.1674	1.83499
$634$	−19.4077	−0.770778
$635$	18.1153	0.718883
$636$	17.5606	0.696324
$637$	6.84745	0.271306
$638$	64.9469	2.57127
$639$	−3.01253	−0.119174
$640$	13.9004	0.549460
$641$	−1.95652	−0.0772780	−0.0386390	−	0.999253i	$-0.512302\pi$
$641$	−1.95652	−0.0772780	−0.0386390	+	0.999253i	$0.512302\pi$
$642$	13.3612	0.527325
$643$	1.29541	0.0510859	0.0255430	−	0.999674i	$-0.491869\pi$
$643$	1.29541	0.0510859	0.0255430	+	0.999674i	$0.491869\pi$
$644$	−0.214105	−0.00843693
$645$	75.2225	2.96188
$646$	−0.712318	−0.0280258
$647$	26.3379	1.03545	0.517725	−	0.855547i	$-0.326779\pi$
$647$	26.3379	1.03545	0.517725	+	0.855547i	$0.326779\pi$
$648$	−31.3123	−1.23006
$649$	54.8658	2.15367
$650$	13.6082	0.533756
$651$	−4.25295	−0.166686
$652$	−10.1151	−0.396139
$653$	−13.6311	−0.533426	−0.266713	−	0.963776i	$-0.585938\pi$
$653$	−13.6311	−0.533426	−0.266713	+	0.963776i	$0.585938\pi$
$654$	−15.9639	−0.624237
$655$	−36.2385	−1.41595
$656$	−2.34836	−0.0916882
$657$	−25.9744	−1.01336
$658$	−2.25003	−0.0877155
$659$	−14.5569	−0.567055	−0.283527	−	0.958964i	$-0.591505\pi$
$659$	−14.5569	−0.567055	−0.283527	+	0.958964i	$0.591505\pi$
$660$	34.7592	1.35300
$661$	21.6885	0.843584	0.421792	−	0.906693i	$-0.361401\pi$
$661$	21.6885	0.843584	0.421792	+	0.906693i	$0.361401\pi$
$662$	−2.16669	−0.0842107
$663$	13.9428	0.541492
$664$	−45.0660	−1.74890
$665$	−0.163200	−0.00632862
$666$	14.2825	0.553436
$667$	8.37737	0.324373
$668$	11.9059	0.460655
$669$	−16.7817	−0.648818
$670$	−35.4453	−1.36937
$671$	40.5851	1.56677
$672$	3.11647	0.120221
$673$	−18.2194	−0.702308	−0.351154	−	0.936318i	$-0.614211\pi$
$673$	−18.2194	−0.702308	−0.351154	+	0.936318i	$0.614211\pi$
$674$	−34.2944	−1.32097
$675$	−12.6191	−0.485711
$676$	−0.625227	−0.0240472
$677$	−22.8130	−0.876776	−0.438388	−	0.898786i	$-0.644450\pi$
$677$	−22.8130	−0.876776	−0.438388	+	0.898786i	$0.644450\pi$
$678$	−40.3233	−1.54861
$679$	−4.80398	−0.184360
$680$	74.3171	2.84993
$681$	51.3687	1.96845
$682$	−31.4523	−1.20437
$683$	−8.24506	−0.315488	−0.157744	−	0.987480i	$-0.550422\pi$
$683$	−8.24506	−0.315488	−0.157744	+	0.987480i	$0.550422\pi$
$684$	0.162708	0.00622130
$685$	73.4349	2.80580
$686$	−6.34143	−0.242117
$687$	4.35828	0.166279
$688$	18.5012	0.705352
$689$	11.9351	0.454692
$690$	−9.85852	−0.375307
$691$	4.89426	0.186187	0.0930933	−	0.995657i	$-0.470325\pi$
$691$	4.89426	0.186187	0.0930933	+	0.995657i	$0.470325\pi$
$692$	−9.97521	−0.379200
$693$	−5.74660	−0.218295
$694$	−25.1466	−0.954554
$695$	16.0856	0.610160
$696$	−69.2114	−2.62345
$697$	−5.89900	−0.223440
$698$	32.3999	1.22635
$699$	−24.0594	−0.910010
$700$	2.83416	0.107121
$701$	−40.8095	−1.54135	−0.770677	−	0.637226i	$-0.780082\pi$
$701$	−40.8095	−1.54135	−0.770677	+	0.637226i	$0.780082\pi$
$702$	−1.27486	−0.0481164
$703$	0.492139	0.0185614
$704$	50.3949	1.89933
$705$	47.1173	1.77454
$706$	−28.8027	−1.08401
$707$	6.52066	0.245235
$708$	−13.9249	−0.523329
$709$	−7.43815	−0.279346	−0.139673	−	0.990198i	$-0.544605\pi$
$709$	−7.43815	−0.279346	−0.139673	+	0.990198i	$0.544605\pi$
$710$	−5.67144	−0.212845
$711$	−2.53797	−0.0951813
$712$	31.6497	1.18612
$713$	−4.05696	−0.151934
$714$	−6.38507	−0.238955
$715$	23.6242	0.883493
$716$	13.7180	0.512665
$717$	−55.9489	−2.08945
$718$	−39.7575	−1.48374
$719$	37.6906	1.40562	0.702811	−	0.711376i	$-0.251928\pi$
$719$	37.6906	1.40562	0.702811	+	0.711376i	$0.251928\pi$
$720$	24.3938	0.909105
$721$	−2.27659	−0.0847847
$722$	22.2653	0.828629
$723$	38.1971	1.42057
$724$	−3.56336	−0.132431
$725$	−110.893	−4.11846
$726$	−62.3819	−2.31521
$727$	22.3272	0.828072	0.414036	−	0.910261i	$-0.364119\pi$
$727$	22.3272	0.828072	0.414036	+	0.910261i	$0.364119\pi$
$728$	1.20222	0.0445572
$729$	−18.1417	−0.671913
$730$	−48.8999	−1.80987
$731$	46.4743	1.71891
$732$	−10.3005	−0.380716
$733$	13.8226	0.510549	0.255275	−	0.966869i	$-0.417834\pi$
$733$	13.8226	0.510549	0.255275	+	0.966869i	$0.417834\pi$
$734$	10.0257	0.370054
$735$	65.6655	2.42211
$736$	2.97286	0.109581
$737$	−43.0065	−1.58416
$738$	−2.96283	−0.109063
$739$	−50.8178	−1.86936	−0.934681	−	0.355488i	$-0.884315\pi$
$739$	−50.8178	−1.86936	−0.934681	+	0.355488i	$0.884315\pi$
$740$	−12.2285	−0.449529
$741$	0.241302	0.00886444
$742$	−5.46567	−0.200651
$743$	5.17738	0.189940	0.0949698	−	0.995480i	$-0.469725\pi$
$743$	5.17738	0.189940	0.0949698	+	0.995480i	$0.469725\pi$
$744$	33.5174	1.22881
$745$	13.8267	0.506571
$746$	−20.2285	−0.740619
$747$	−37.1580	−1.35954
$748$	21.4751	0.785207
$749$	1.89129	0.0691061
$750$	74.2788	2.71228
$751$	18.2533	0.666073	0.333037	−	0.942914i	$-0.391927\pi$
$751$	18.2533	0.666073	0.333037	+	0.942914i	$0.391927\pi$
$752$	11.5886	0.422595
$753$	−32.6773	−1.19083
$754$	−11.2030	−0.407990
$755$	−17.2166	−0.626575
$756$	−0.265513	−0.00965662
$757$	1.23515	0.0448924	0.0224462	−	0.999748i	$-0.492855\pi$
$757$	1.23515	0.0448924	0.0224462	+	0.999748i	$0.492855\pi$
$758$	13.9144	0.505392
$759$	−11.9615	−0.434176
$760$	1.28618	0.0466545
$761$	5.59152	0.202692	0.101346	−	0.994851i	$-0.467685\pi$
$761$	5.59152	0.202692	0.101346	+	0.994851i	$0.467685\pi$
$762$	12.2660	0.444350
$763$	−2.25969	−0.0818063
$764$	1.96752	0.0711822
$765$	61.2764	2.21545
$766$	21.0491	0.760534
$767$	−9.46408	−0.341728
$768$	−31.5016	−1.13672
$769$	−10.8606	−0.391643	−0.195822	−	0.980640i	$-0.562737\pi$
$769$	−10.8606	−0.391643	−0.195822	+	0.980640i	$0.562737\pi$
$770$	−10.8187	−0.389877
$771$	−15.8288	−0.570061
$772$	−15.9587	−0.574366
$773$	−7.12994	−0.256446	−0.128223	−	0.991745i	$-0.540927\pi$
$773$	−7.12994	−0.256446	−0.128223	+	0.991745i	$0.540927\pi$
$774$	23.3422	0.839017
$775$	53.7028	1.92906
$776$	37.8601	1.35910
$777$	4.41144	0.158259
$778$	20.1898	0.723839
$779$	−0.102092	−0.00365781
$780$	−5.99579	−0.214684
$781$	−6.88127	−0.246231
$782$	−6.09084	−0.217808
$783$	10.3888	0.371266
$784$	16.1506	0.576809
$785$	−35.6150	−1.27115
$786$	−24.5373	−0.875218
$787$	19.1287	0.681865	0.340933	−	0.940088i	$-0.389257\pi$
$787$	19.1287	0.681865	0.340933	+	0.940088i	$0.389257\pi$
$788$	6.48672	0.231080
$789$	−16.6708	−0.593498
$790$	−4.77802	−0.169994
$791$	−5.70777	−0.202945
$792$	45.2889	1.60927
$793$	−7.00072	−0.248603
$794$	−31.3468	−1.11246
$795$	114.455	4.05930
$796$	−2.32516	−0.0824130
$797$	−1.41114	−0.0499852	−0.0249926	−	0.999688i	$-0.507956\pi$
$797$	−1.41114	−0.0499852	−0.0249926	+	0.999688i	$0.507956\pi$
$798$	−0.110504	−0.00391179
$799$	29.1102	1.02985
$800$	−39.3523	−1.39132
$801$	26.0960	0.922055
$802$	21.4927	0.758934
$803$	−59.3312	−2.09375
$804$	10.9150	0.384943
$805$	−1.39548	−0.0491841
$806$	5.42536	0.191100
$807$	10.3311	0.363671
$808$	−51.3893	−1.80787
$809$	33.8952	1.19169	0.595846	−	0.803098i	$-0.296817\pi$
$809$	33.8952	1.19169	0.595846	+	0.803098i	$0.296817\pi$
$810$	−48.6050	−1.70781
$811$	−36.9310	−1.29682	−0.648412	−	0.761289i	$-0.724567\pi$
$811$	−36.9310	−1.29682	−0.648412	+	0.761289i	$0.724567\pi$
$812$	−2.33324	−0.0818807
$813$	−42.6458	−1.49565
$814$	32.6243	1.14348
$815$	−65.9274	−2.30934
$816$	32.8859	1.15124
$817$	0.804312	0.0281393
$818$	3.56973	0.124813
$819$	0.991261	0.0346375
$820$	2.53674	0.0885867
$821$	−14.4741	−0.505151	−0.252575	−	0.967577i	$-0.581278\pi$
$821$	−14.4741	−0.505151	−0.252575	+	0.967577i	$0.581278\pi$
$822$	49.7233	1.73430
$823$	−24.7005	−0.861005	−0.430503	−	0.902589i	$-0.641664\pi$
$823$	−24.7005	−0.861005	−0.430503	+	0.902589i	$0.641664\pi$
$824$	17.9418	0.625032
$825$	158.337	5.51259
$826$	4.33407	0.150801
$827$	34.7751	1.20925	0.604625	−	0.796510i	$-0.293323\pi$
$827$	34.7751	1.20925	0.604625	+	0.796510i	$0.293323\pi$
$828$	1.39127	0.0483501
$829$	7.34541	0.255117	0.127558	−	0.991831i	$-0.459286\pi$
$829$	7.34541	0.255117	0.127558	+	0.991831i	$0.459286\pi$
$830$	−69.9543	−2.42815
$831$	−31.2029	−1.08242
$832$	−8.69286	−0.301371
$833$	40.5698	1.40566
$834$	10.8916	0.377147
$835$	77.5995	2.68544
$836$	0.371661	0.0128541
$837$	−5.03106	−0.173899
$838$	2.67673	0.0924660
$839$	46.5926	1.60855	0.804277	−	0.594254i	$-0.202553\pi$
$839$	46.5926	1.60855	0.804277	+	0.594254i	$0.202553\pi$
$840$	11.5290	0.397789
$841$	62.2935	2.14805
$842$	−12.8541	−0.442982
$843$	−10.7710	−0.370973
$844$	−12.2659	−0.422208
$845$	−4.07505	−0.140186
$846$	14.6209	0.502676
$847$	−8.83018	−0.303409
$848$	28.1506	0.966695
$849$	19.6038	0.672801
$850$	80.6256	2.76544
$851$	4.20815	0.144253
$852$	1.74646	0.0598327
$853$	−49.4118	−1.69183	−0.845913	−	0.533321i	$-0.820944\pi$
$853$	−49.4118	−1.69183	−0.845913	+	0.533321i	$0.820944\pi$
$854$	3.20597	0.109706
$855$	1.06048	0.0362678
$856$	−14.9052	−0.509449
$857$	25.1975	0.860729	0.430364	−	0.902655i	$-0.358385\pi$
$857$	25.1975	0.860729	0.430364	+	0.902655i	$0.358385\pi$
$858$	15.9961	0.546098
$859$	53.0549	1.81021	0.905105	−	0.425189i	$-0.139792\pi$
$859$	53.0549	1.81021	0.905105	+	0.425189i	$0.139792\pi$
$860$	−19.9853	−0.681493
$861$	−0.915127	−0.0311875
$862$	−4.31700	−0.147038
$863$	−2.71604	−0.0924549	−0.0462275	−	0.998931i	$-0.514720\pi$
$863$	−2.71604	−0.0924549	−0.0462275	+	0.998931i	$0.514720\pi$
$864$	3.68666	0.125423
$865$	−65.0155	−2.21059
$866$	24.4535	0.830964
$867$	42.6022	1.44685
$868$	1.12993	0.0383524
$869$	−5.79727	−0.196659
$870$	−107.434	−3.64237
$871$	7.41841	0.251363
$872$	17.8086	0.603075
$873$	31.2166	1.05652
$874$	−0.105412	−0.00356560
$875$	10.5142	0.355444
$876$	15.0582	0.508770
$877$	−43.2815	−1.46151	−0.730756	−	0.682639i	$-0.760832\pi$
$877$	−43.2815	−1.46151	−0.730756	+	0.682639i	$0.760832\pi$
$878$	−8.65874	−0.292218
$879$	27.4864	0.927093
$880$	55.7208	1.87835
$881$	−47.2324	−1.59130	−0.795650	−	0.605756i	$-0.792871\pi$
$881$	−47.2324	−1.59130	−0.795650	+	0.605756i	$0.792871\pi$
$882$	20.3766	0.686114
$883$	−36.4171	−1.22553	−0.612766	−	0.790264i	$-0.709943\pi$
$883$	−36.4171	−1.22553	−0.612766	+	0.790264i	$0.709943\pi$
$884$	−3.70435	−0.124591
$885$	−90.7584	−3.05081
$886$	14.2518	0.478799
$887$	−25.2304	−0.847153	−0.423577	−	0.905860i	$-0.639226\pi$
$887$	−25.2304	−0.847153	−0.423577	+	0.905860i	$0.639226\pi$
$888$	−34.7665	−1.16669
$889$	1.73626	0.0582321
$890$	49.1287	1.64680
$891$	−58.9734	−1.97568
$892$	4.45860	0.149285
$893$	0.503799	0.0168590
$894$	9.36215	0.313117
$895$	89.4098	2.98864
$896$	1.33228	0.0445083
$897$	2.06330	0.0688917
$898$	−2.63167	−0.0878200
$899$	−44.2113	−1.47453
$900$	−18.4166	−0.613885
$901$	70.7131	2.35580
$902$	−6.76773	−0.225341
$903$	7.20968	0.239923
$904$	44.9829	1.49611
$905$	−23.2249	−0.772023
$906$	−11.6575	−0.387294
$907$	10.1835	0.338139	0.169069	−	0.985604i	$-0.445924\pi$
$907$	10.1835	0.338139	0.169069	+	0.985604i	$0.445924\pi$
$908$	−13.6478	−0.452917
$909$	−42.3718	−1.40538
$910$	1.86617	0.0618628
$911$	1.68816	0.0559312	0.0279656	−	0.999609i	$-0.491097\pi$
$911$	1.68816	0.0559312	0.0279656	+	0.999609i	$0.491097\pi$
$912$	0.569143	0.0188462
$913$	−84.8769	−2.80902
$914$	38.1663	1.26243
$915$	−67.1353	−2.21943
$916$	−1.15792	−0.0382587
$917$	−3.47327	−0.114697
$918$	−7.55327	−0.249295
$919$	19.8522	0.654863	0.327431	−	0.944875i	$-0.393817\pi$
$919$	19.8522	0.654863	0.327431	+	0.944875i	$0.393817\pi$
$920$	10.9977	0.362585
$921$	−28.7060	−0.945894
$922$	−30.0128	−0.988418
$923$	1.18698	0.0390701
$924$	3.33149	0.109598
$925$	−55.7041	−1.83154
$926$	−4.00079	−0.131474
$927$	14.7935	0.485881
$928$	32.3971	1.06349
$929$	21.4988	0.705354	0.352677	−	0.935745i	$-0.385271\pi$
$929$	21.4988	0.705354	0.352677	+	0.935745i	$0.385271\pi$
$930$	52.0280	1.70606
$931$	0.702125	0.0230112
$932$	6.39216	0.209382
$933$	−13.7586	−0.450437
$934$	−2.57637	−0.0843013
$935$	139.968	4.57746
$936$	−7.81212	−0.255347
$937$	−50.2938	−1.64303	−0.821514	−	0.570188i	$-0.806870\pi$
$937$	−50.2938	−1.64303	−0.821514	+	0.570188i	$0.806870\pi$
$938$	−3.39725	−0.110924
$939$	−28.7784	−0.939148
$940$	−12.5182	−0.408300
$941$	16.7677	0.546611	0.273306	−	0.961927i	$-0.411883\pi$
$941$	16.7677	0.546611	0.273306	+	0.961927i	$0.411883\pi$
$942$	−24.1152	−0.785715
$943$	−0.872956	−0.0284274
$944$	−22.3223	−0.726530
$945$	−1.73054	−0.0562944
$946$	53.3185	1.73353
$947$	0.321953	0.0104621	0.00523103	−	0.999986i	$-0.498335\pi$
$947$	0.321953	0.0104621	0.00523103	+	0.999986i	$0.498335\pi$
$948$	1.47134	0.0477869
$949$	10.2343	0.332221
$950$	1.39535	0.0452713
$951$	38.9524	1.26312
$952$	7.12291	0.230855
$953$	10.1199	0.327817	0.163908	−	0.986476i	$-0.447590\pi$
$953$	10.1199	0.327817	0.163908	+	0.986476i	$0.447590\pi$
$954$	35.5163	1.14988
$955$	12.8237	0.414965
$956$	14.8646	0.480757
$957$	−130.352	−4.21369
$958$	−21.8741	−0.706721
$959$	7.03835	0.227280
$960$	−83.3626	−2.69052
$961$	−9.58952	−0.309339
$962$	−5.62754	−0.181439
$963$	−12.2897	−0.396031
$964$	−10.1483	−0.326855
$965$	−104.014	−3.34834
$966$	−0.944888	−0.0304013
$967$	18.2513	0.586921	0.293461	−	0.955971i	$-0.405193\pi$
$967$	18.2513	0.586921	0.293461	+	0.955971i	$0.405193\pi$
$968$	69.5906	2.23673
$969$	1.42966	0.0459274
$970$	58.7690	1.88696
$971$	−52.2336	−1.67626	−0.838128	−	0.545474i	$-0.816350\pi$
$971$	−52.2336	−1.67626	−0.838128	+	0.545474i	$0.816350\pi$
$972$	12.9280	0.414665
$973$	1.54172	0.0494252
$974$	−3.26987	−0.104773
$975$	−27.3124	−0.874695
$976$	−16.5122	−0.528541
$977$	−5.35190	−0.171222	−0.0856112	−	0.996329i	$-0.527284\pi$
$977$	−5.35190	−0.171222	−0.0856112	+	0.996329i	$0.527284\pi$
$978$	−44.6400	−1.42743
$979$	59.6088	1.90510
$980$	−17.4462	−0.557297
$981$	14.6836	0.468813
$982$	24.6201	0.785660
$983$	36.4703	1.16322	0.581611	−	0.813467i	$-0.302423\pi$
$983$	36.4703	1.16322	0.581611	+	0.813467i	$0.302423\pi$
$984$	7.21211	0.229914
$985$	42.2785	1.34711
$986$	−66.3757	−2.11383
$987$	4.51595	0.143744
$988$	−0.0641096	−0.00203960
$989$	6.87745	0.218690
$990$	70.3004	2.23429
$991$	−39.4143	−1.25204	−0.626018	−	0.779809i	$-0.715316\pi$
$991$	−39.4143	−1.25204	−0.626018	+	0.779809i	$0.715316\pi$
$992$	−15.6892	−0.498131
$993$	4.34867	0.138001
$994$	−0.543579	−0.0172413
$995$	−15.1547	−0.480436
$996$	21.5417	0.682574
$997$	25.8846	0.819772	0.409886	−	0.912137i	$-0.365568\pi$
$997$	25.8846	0.819772	0.409886	+	0.912137i	$0.365568\pi$
$998$	15.0601	0.476719
$999$	5.21854	0.165107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.c.1.8	✓	18
3.2	odd	2		9243.2.a.m.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.c.1.8	✓	18	1.1	even	1	trivial
9243.2.a.m.1.11		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.17251 q^{2} +2.35329 q^{3} -0.625227 q^{4} -4.07505 q^{5} -2.75925 q^{6} -0.390573 q^{7} +3.07810 q^{8} +2.53797 q^{9} +O(q^{10})\)	\(q-1.17251 q^{2} +2.35329 q^{3} -0.625227 q^{4} -4.07505 q^{5} -2.75925 q^{6} -0.390573 q^{7} +3.07810 q^{8} +2.53797 q^{9} +4.77802 q^{10} +5.79727 q^{11} -1.47134 q^{12} -1.00000 q^{13} +0.457949 q^{14} -9.58977 q^{15} -2.35864 q^{16} -5.92480 q^{17} -2.97579 q^{18} -0.102538 q^{19} +2.54783 q^{20} -0.919130 q^{21} -6.79734 q^{22} -0.876774 q^{23} +7.24365 q^{24} +11.6060 q^{25} +1.17251 q^{26} -1.08729 q^{27} +0.244197 q^{28} -9.55476 q^{29} +11.2441 q^{30} +4.62715 q^{31} -3.39068 q^{32} +13.6426 q^{33} +6.94687 q^{34} +1.59160 q^{35} -1.58681 q^{36} -4.79958 q^{37} +0.120227 q^{38} -2.35329 q^{39} -12.5434 q^{40} +0.995645 q^{41} +1.07769 q^{42} -7.84403 q^{43} -3.62461 q^{44} -10.3424 q^{45} +1.02802 q^{46} -4.91328 q^{47} -5.55055 q^{48} -6.84745 q^{49} -13.6082 q^{50} -13.9428 q^{51} +0.625227 q^{52} -11.9351 q^{53} +1.27486 q^{54} -23.6242 q^{55} -1.20222 q^{56} -0.241302 q^{57} +11.2030 q^{58} +9.46408 q^{59} +5.99579 q^{60} +7.00072 q^{61} -5.42536 q^{62} -0.991261 q^{63} +8.69286 q^{64} +4.07505 q^{65} -15.9961 q^{66} -7.41841 q^{67} +3.70435 q^{68} -2.06330 q^{69} -1.86617 q^{70} -1.18698 q^{71} +7.81212 q^{72} -10.2343 q^{73} +5.62754 q^{74} +27.3124 q^{75} +0.0641096 q^{76} -2.26425 q^{77} +2.75925 q^{78} -1.00000 q^{79} +9.61156 q^{80} -10.1726 q^{81} -1.16740 q^{82} -14.6408 q^{83} +0.574665 q^{84} +24.1439 q^{85} +9.19718 q^{86} -22.4851 q^{87} +17.8446 q^{88} +10.2822 q^{89} +12.1265 q^{90} +0.390573 q^{91} +0.548183 q^{92} +10.8890 q^{93} +5.76086 q^{94} +0.417848 q^{95} -7.97925 q^{96} +12.2998 q^{97} +8.02869 q^{98} +14.7133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * q^99

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