LMFDB - Embedded newform 8002.2.a.d.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.766862 q^{3} +1.00000 q^{4} -0.616141 q^{5} -0.766862 q^{6} +2.92795 q^{7} +1.00000 q^{8} -2.41192 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.766862 q^{3} +1.00000 q^{4} -0.616141 q^{5} -0.766862 q^{6} +2.92795 q^{7} +1.00000 q^{8} -2.41192 q^{9} -0.616141 q^{10} +0.437600 q^{11} -0.766862 q^{12} +1.61489 q^{13} +2.92795 q^{14} +0.472496 q^{15} +1.00000 q^{16} +3.33181 q^{17} -2.41192 q^{18} +2.22577 q^{19} -0.616141 q^{20} -2.24533 q^{21} +0.437600 q^{22} -8.61666 q^{23} -0.766862 q^{24} -4.62037 q^{25} +1.61489 q^{26} +4.15020 q^{27} +2.92795 q^{28} -6.74177 q^{29} +0.472496 q^{30} -0.598772 q^{31} +1.00000 q^{32} -0.335579 q^{33} +3.33181 q^{34} -1.80403 q^{35} -2.41192 q^{36} -10.0409 q^{37} +2.22577 q^{38} -1.23840 q^{39} -0.616141 q^{40} -7.62206 q^{41} -2.24533 q^{42} -2.87507 q^{43} +0.437600 q^{44} +1.48608 q^{45} -8.61666 q^{46} -9.15550 q^{47} -0.766862 q^{48} +1.57288 q^{49} -4.62037 q^{50} -2.55504 q^{51} +1.61489 q^{52} +8.70758 q^{53} +4.15020 q^{54} -0.269623 q^{55} +2.92795 q^{56} -1.70686 q^{57} -6.74177 q^{58} -9.42202 q^{59} +0.472496 q^{60} +4.26039 q^{61} -0.598772 q^{62} -7.06198 q^{63} +1.00000 q^{64} -0.995002 q^{65} -0.335579 q^{66} +8.54059 q^{67} +3.33181 q^{68} +6.60779 q^{69} -1.80403 q^{70} -13.1916 q^{71} -2.41192 q^{72} +7.08650 q^{73} -10.0409 q^{74} +3.54319 q^{75} +2.22577 q^{76} +1.28127 q^{77} -1.23840 q^{78} +7.30002 q^{79} -0.616141 q^{80} +4.05313 q^{81} -7.62206 q^{82} +15.3060 q^{83} -2.24533 q^{84} -2.05287 q^{85} -2.87507 q^{86} +5.17001 q^{87} +0.437600 q^{88} +2.62820 q^{89} +1.48608 q^{90} +4.72832 q^{91} -8.61666 q^{92} +0.459176 q^{93} -9.15550 q^{94} -1.37139 q^{95} -0.766862 q^{96} +8.11949 q^{97} +1.57288 q^{98} -1.05546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.766862	−0.442748	−0.221374	−	0.975189i	$-0.571054\pi$
$3$	−0.766862	−0.442748	−0.221374	+	0.975189i	$0.571054\pi$
$4$	1.00000	0.500000
$5$	−0.616141	−0.275547	−0.137773	−	0.990464i	$-0.543995\pi$
$5$	−0.616141	−0.275547	−0.137773	+	0.990464i	$0.543995\pi$
$6$	−0.766862	−0.313070
$7$	2.92795	1.10666	0.553330	−	0.832962i	$-0.313357\pi$
$7$	2.92795	1.10666	0.553330	+	0.832962i	$0.313357\pi$
$8$	1.00000	0.353553
$9$	−2.41192	−0.803974
$10$	−0.616141	−0.194841
$11$	0.437600	0.131941	0.0659707	−	0.997822i	$-0.478986\pi$
$11$	0.437600	0.131941	0.0659707	+	0.997822i	$0.478986\pi$
$12$	−0.766862	−0.221374
$13$	1.61489	0.447891	0.223945	−	0.974602i	$-0.428106\pi$
$13$	1.61489	0.447891	0.223945	+	0.974602i	$0.428106\pi$
$14$	2.92795	0.782527
$15$	0.472496	0.121998
$16$	1.00000	0.250000
$17$	3.33181	0.808083	0.404042	−	0.914741i	$-0.367605\pi$
$17$	3.33181	0.808083	0.404042	+	0.914741i	$0.367605\pi$
$18$	−2.41192	−0.568496
$19$	2.22577	0.510627	0.255314	−	0.966858i	$-0.417821\pi$
$19$	2.22577	0.510627	0.255314	+	0.966858i	$0.417821\pi$
$20$	−0.616141	−0.137773
$21$	−2.24533	−0.489972
$22$	0.437600	0.0932966
$23$	−8.61666	−1.79670	−0.898349	−	0.439282i	$-0.855233\pi$
$23$	−8.61666	−1.79670	−0.898349	+	0.439282i	$0.855233\pi$
$24$	−0.766862	−0.156535
$25$	−4.62037	−0.924074
$26$	1.61489	0.316707
$27$	4.15020	0.798706
$28$	2.92795	0.553330
$29$	−6.74177	−1.25192	−0.625958	−	0.779857i	$-0.715292\pi$
$29$	−6.74177	−1.25192	−0.625958	+	0.779857i	$0.715292\pi$
$30$	0.472496	0.0862655
$31$	−0.598772	−0.107543	−0.0537713	−	0.998553i	$-0.517124\pi$
$31$	−0.598772	−0.107543	−0.0537713	+	0.998553i	$0.517124\pi$
$32$	1.00000	0.176777
$33$	−0.335579	−0.0584168
$34$	3.33181	0.571401
$35$	−1.80403	−0.304937
$36$	−2.41192	−0.401987
$37$	−10.0409	−1.65072	−0.825359	−	0.564608i	$-0.809028\pi$
$37$	−10.0409	−1.65072	−0.825359	+	0.564608i	$0.809028\pi$
$38$	2.22577	0.361068
$39$	−1.23840	−0.198303
$40$	−0.616141	−0.0974205
$41$	−7.62206	−1.19037	−0.595183	−	0.803590i	$-0.702920\pi$
$41$	−7.62206	−1.19037	−0.595183	+	0.803590i	$0.702920\pi$
$42$	−2.24533	−0.346462
$43$	−2.87507	−0.438444	−0.219222	−	0.975675i	$-0.570352\pi$
$43$	−2.87507	−0.438444	−0.219222	+	0.975675i	$0.570352\pi$
$44$	0.437600	0.0659707
$45$	1.48608	0.221532
$46$	−8.61666	−1.27046
$47$	−9.15550	−1.33547	−0.667734	−	0.744400i	$-0.732735\pi$
$47$	−9.15550	−1.33547	−0.667734	+	0.744400i	$0.732735\pi$
$48$	−0.766862	−0.110687
$49$	1.57288	0.224697
$50$	−4.62037	−0.653419
$51$	−2.55504	−0.357777
$52$	1.61489	0.223945
$53$	8.70758	1.19608	0.598039	−	0.801467i	$-0.295947\pi$
$53$	8.70758	1.19608	0.598039	+	0.801467i	$0.295947\pi$
$54$	4.15020	0.564771
$55$	−0.269623	−0.0363560
$56$	2.92795	0.391263
$57$	−1.70686	−0.226079
$58$	−6.74177	−0.885238
$59$	−9.42202	−1.22664	−0.613321	−	0.789834i	$-0.710167\pi$
$59$	−9.42202	−1.22664	−0.613321	+	0.789834i	$0.710167\pi$
$60$	0.472496	0.0609989
$61$	4.26039	0.545487	0.272744	−	0.962087i	$-0.412069\pi$
$61$	4.26039	0.545487	0.272744	+	0.962087i	$0.412069\pi$
$62$	−0.598772	−0.0760442
$63$	−7.06198	−0.889726
$64$	1.00000	0.125000
$65$	−0.995002	−0.123415
$66$	−0.335579	−0.0413069
$67$	8.54059	1.04340	0.521700	−	0.853129i	$-0.325298\pi$
$67$	8.54059	1.04340	0.521700	+	0.853129i	$0.325298\pi$
$68$	3.33181	0.404042
$69$	6.60779	0.795485
$70$	−1.80403	−0.215623
$71$	−13.1916	−1.56555	−0.782775	−	0.622304i	$-0.786197\pi$
$71$	−13.1916	−1.56555	−0.782775	+	0.622304i	$0.786197\pi$
$72$	−2.41192	−0.284248
$73$	7.08650	0.829412	0.414706	−	0.909956i	$-0.363884\pi$
$73$	7.08650	0.829412	0.414706	+	0.909956i	$0.363884\pi$
$74$	−10.0409	−1.16723
$75$	3.54319	0.409132
$76$	2.22577	0.255314
$77$	1.28127	0.146014
$78$	−1.23840	−0.140221
$79$	7.30002	0.821316	0.410658	−	0.911789i	$-0.365299\pi$
$79$	7.30002	0.821316	0.410658	+	0.911789i	$0.365299\pi$
$80$	−0.616141	−0.0688867
$81$	4.05313	0.450348
$82$	−7.62206	−0.841715
$83$	15.3060	1.68006	0.840028	−	0.542544i	$-0.182539\pi$
$83$	15.3060	1.68006	0.840028	+	0.542544i	$0.182539\pi$
$84$	−2.24533	−0.244986
$85$	−2.05287	−0.222665
$86$	−2.87507	−0.310027
$87$	5.17001	0.554284
$88$	0.437600	0.0466483
$89$	2.62820	0.278589	0.139294	−	0.990251i	$-0.455517\pi$
$89$	2.62820	0.278589	0.139294	+	0.990251i	$0.455517\pi$
$90$	1.48608	0.156647
$91$	4.72832	0.495663
$92$	−8.61666	−0.898349
$93$	0.459176	0.0476143
$94$	−9.15550	−0.944318
$95$	−1.37139	−0.140702
$96$	−0.766862	−0.0782676
$97$	8.11949	0.824409	0.412204	−	0.911091i	$-0.364759\pi$
$97$	8.11949	0.824409	0.412204	+	0.911091i	$0.364759\pi$
$98$	1.57288	0.158885
$99$	−1.05546	−0.106077
$100$	−4.62037	−0.462037
$101$	−7.56838	−0.753082	−0.376541	−	0.926400i	$-0.622887\pi$
$101$	−7.56838	−0.753082	−0.376541	+	0.926400i	$0.622887\pi$
$102$	−2.55504	−0.252987
$103$	2.61511	0.257674	0.128837	−	0.991666i	$-0.458876\pi$
$103$	2.61511	0.257674	0.128837	+	0.991666i	$0.458876\pi$
$104$	1.61489	0.158353
$105$	1.38344	0.135010
$106$	8.70758	0.845755
$107$	−18.0826	−1.74811	−0.874054	−	0.485830i	$-0.838518\pi$
$107$	−18.0826	−1.74811	−0.874054	+	0.485830i	$0.838518\pi$
$108$	4.15020	0.399353
$109$	3.07925	0.294938	0.147469	−	0.989067i	$-0.452887\pi$
$109$	3.07925	0.294938	0.147469	+	0.989067i	$0.452887\pi$
$110$	−0.269623	−0.0257076
$111$	7.70001	0.730853
$112$	2.92795	0.276665
$113$	3.37331	0.317334	0.158667	−	0.987332i	$-0.449280\pi$
$113$	3.37331	0.317334	0.158667	+	0.987332i	$0.449280\pi$
$114$	−1.70686	−0.159862
$115$	5.30908	0.495074
$116$	−6.74177	−0.625958
$117$	−3.89500	−0.360092
$118$	−9.42202	−0.867367
$119$	9.75538	0.894274
$120$	0.472496	0.0431327
$121$	−10.8085	−0.982591
$122$	4.26039	0.385718
$123$	5.84507	0.527032
$124$	−0.598772	−0.0537713
$125$	5.92751	0.530172
$126$	−7.06198	−0.629131
$127$	−10.7084	−0.950221	−0.475111	−	0.879926i	$-0.657592\pi$
$127$	−10.7084	−0.950221	−0.475111	+	0.879926i	$0.657592\pi$
$128$	1.00000	0.0883883
$129$	2.20478	0.194120
$130$	−0.995002	−0.0872675
$131$	12.6963	1.10928	0.554639	−	0.832091i	$-0.312856\pi$
$131$	12.6963	1.10928	0.554639	+	0.832091i	$0.312856\pi$
$132$	−0.335579	−0.0292084
$133$	6.51695	0.565091
$134$	8.54059	0.737795
$135$	−2.55711	−0.220081
$136$	3.33181	0.285701
$137$	−6.67293	−0.570107	−0.285053	−	0.958512i	$-0.592011\pi$
$137$	−6.67293	−0.570107	−0.285053	+	0.958512i	$0.592011\pi$
$138$	6.60779	0.562493
$139$	6.01600	0.510271	0.255135	−	0.966905i	$-0.417880\pi$
$139$	6.01600	0.510271	0.255135	+	0.966905i	$0.417880\pi$
$140$	−1.80403	−0.152468
$141$	7.02101	0.591276
$142$	−13.1916	−1.10701
$143$	0.706677	0.0590953
$144$	−2.41192	−0.200994
$145$	4.15389	0.344961
$146$	7.08650	0.586483
$147$	−1.20618	−0.0994841
$148$	−10.0409	−0.825359
$149$	−16.6214	−1.36168	−0.680839	−	0.732433i	$-0.738385\pi$
$149$	−16.6214	−1.36168	−0.680839	+	0.732433i	$0.738385\pi$
$150$	3.54319	0.289300
$151$	3.46036	0.281600	0.140800	−	0.990038i	$-0.455033\pi$
$151$	3.46036	0.281600	0.140800	+	0.990038i	$0.455033\pi$
$152$	2.22577	0.180534
$153$	−8.03607	−0.649678
$154$	1.28127	0.103248
$155$	0.368928	0.0296330
$156$	−1.23840	−0.0991514
$157$	7.15372	0.570929	0.285465	−	0.958389i	$-0.407852\pi$
$157$	7.15372	0.570929	0.285465	+	0.958389i	$0.407852\pi$
$158$	7.30002	0.580758
$159$	−6.67752	−0.529562
$160$	−0.616141	−0.0487102
$161$	−25.2291	−1.98833
$162$	4.05313	0.318444
$163$	−17.9620	−1.40689	−0.703447	−	0.710748i	$-0.748357\pi$
$163$	−17.9620	−1.40689	−0.703447	+	0.710748i	$0.748357\pi$
$164$	−7.62206	−0.595183
$165$	0.206764	0.0160966
$166$	15.3060	1.18798
$167$	−12.5392	−0.970314	−0.485157	−	0.874427i	$-0.661238\pi$
$167$	−12.5392	−0.970314	−0.485157	+	0.874427i	$0.661238\pi$
$168$	−2.24533	−0.173231
$169$	−10.3921	−0.799394
$170$	−2.05287	−0.157448
$171$	−5.36839	−0.410531
$172$	−2.87507	−0.219222
$173$	6.11583	0.464978	0.232489	−	0.972599i	$-0.425313\pi$
$173$	6.11583	0.464978	0.232489	+	0.972599i	$0.425313\pi$
$174$	5.17001	0.391938
$175$	−13.5282	−1.02264
$176$	0.437600	0.0329853
$177$	7.22539	0.543094
$178$	2.62820	0.196992
$179$	−13.3903	−1.00084	−0.500419	−	0.865783i	$-0.666821\pi$
$179$	−13.3903	−1.00084	−0.500419	+	0.865783i	$0.666821\pi$
$180$	1.48608	0.110766
$181$	11.2694	0.837647	0.418824	−	0.908068i	$-0.362443\pi$
$181$	11.2694	0.837647	0.418824	+	0.908068i	$0.362443\pi$
$182$	4.72832	0.350486
$183$	−3.26713	−0.241513
$184$	−8.61666	−0.635229
$185$	6.18663	0.454850
$186$	0.459176	0.0336684
$187$	1.45800	0.106620
$188$	−9.15550	−0.667734
$189$	12.1516	0.883896
$190$	−1.37139	−0.0994911
$191$	18.8725	1.36556	0.682782	−	0.730622i	$-0.260770\pi$
$191$	18.8725	1.36556	0.682782	+	0.730622i	$0.260770\pi$
$192$	−0.766862	−0.0553435
$193$	−12.6870	−0.913229	−0.456614	−	0.889665i	$-0.650938\pi$
$193$	−12.6870	−0.913229	−0.456614	+	0.889665i	$0.650938\pi$
$194$	8.11949	0.582945
$195$	0.763030	0.0546417
$196$	1.57288	0.112348
$197$	−9.36446	−0.667190	−0.333595	−	0.942716i	$-0.608262\pi$
$197$	−9.36446	−0.667190	−0.333595	+	0.942716i	$0.608262\pi$
$198$	−1.05546	−0.0750081
$199$	−20.1131	−1.42578	−0.712890	−	0.701275i	$-0.752614\pi$
$199$	−20.1131	−1.42578	−0.712890	+	0.701275i	$0.752614\pi$
$200$	−4.62037	−0.326709
$201$	−6.54946	−0.461963
$202$	−7.56838	−0.532509
$203$	−19.7396	−1.38545
$204$	−2.55504	−0.178889
$205$	4.69626	0.328001
$206$	2.61511	0.182203
$207$	20.7827	1.44450
$208$	1.61489	0.111973
$209$	0.973998	0.0673728
$210$	1.38344	0.0954666
$211$	−17.9822	−1.23795	−0.618973	−	0.785412i	$-0.712451\pi$
$211$	−17.9822	−1.23795	−0.618973	+	0.785412i	$0.712451\pi$
$212$	8.70758	0.598039
$213$	10.1161	0.693145
$214$	−18.0826	−1.23610
$215$	1.77145	0.120812
$216$	4.15020	0.282385
$217$	−1.75317	−0.119013
$218$	3.07925	0.208553
$219$	−5.43437	−0.367221
$220$	−0.269623	−0.0181780
$221$	5.38052	0.361933
$222$	7.70001	0.516791
$223$	15.9503	1.06811	0.534055	−	0.845450i	$-0.320668\pi$
$223$	15.9503	1.06811	0.534055	+	0.845450i	$0.320668\pi$
$224$	2.92795	0.195632
$225$	11.1440	0.742932
$226$	3.37331	0.224389
$227$	−15.8698	−1.05332	−0.526659	−	0.850077i	$-0.676555\pi$
$227$	−15.8698	−1.05332	−0.526659	+	0.850077i	$0.676555\pi$
$228$	−1.70686	−0.113040
$229$	−2.46288	−0.162752	−0.0813759	−	0.996683i	$-0.525931\pi$
$229$	−2.46288	−0.162752	−0.0813759	+	0.996683i	$0.525931\pi$
$230$	5.30908	0.350070
$231$	−0.982557	−0.0646475
$232$	−6.74177	−0.442619
$233$	−13.0365	−0.854049	−0.427024	−	0.904240i	$-0.640438\pi$
$233$	−13.0365	−0.854049	−0.427024	+	0.904240i	$0.640438\pi$
$234$	−3.89500	−0.254624
$235$	5.64108	0.367984
$236$	−9.42202	−0.613321
$237$	−5.59811	−0.363636
$238$	9.75538	0.632347
$239$	−9.14910	−0.591806	−0.295903	−	0.955218i	$-0.595620\pi$
$239$	−9.14910	−0.591806	−0.295903	+	0.955218i	$0.595620\pi$
$240$	0.472496	0.0304995
$241$	7.72515	0.497621	0.248810	−	0.968552i	$-0.419960\pi$
$241$	7.72515	0.497621	0.248810	+	0.968552i	$0.419960\pi$
$242$	−10.8085	−0.694797
$243$	−15.5588	−0.998097
$244$	4.26039	0.272744
$245$	−0.969115	−0.0619145
$246$	5.84507	0.372668
$247$	3.59438	0.228705
$248$	−0.598772	−0.0380221
$249$	−11.7376	−0.743841
$250$	5.92751	0.374888
$251$	2.00287	0.126420	0.0632101	−	0.998000i	$-0.479866\pi$
$251$	2.00287	0.126420	0.0632101	+	0.998000i	$0.479866\pi$
$252$	−7.06198	−0.444863
$253$	−3.77065	−0.237059
$254$	−10.7084	−0.671908
$255$	1.57427	0.0985844
$256$	1.00000	0.0625000
$257$	1.98861	0.124046	0.0620231	−	0.998075i	$-0.480245\pi$
$257$	1.98861	0.124046	0.0620231	+	0.998075i	$0.480245\pi$
$258$	2.20478	0.137264
$259$	−29.3993	−1.82678
$260$	−0.995002	−0.0617074
$261$	16.2606	1.00651
$262$	12.6963	0.784378
$263$	29.8585	1.84115	0.920576	−	0.390565i	$-0.127720\pi$
$263$	29.8585	1.84115	0.920576	+	0.390565i	$0.127720\pi$
$264$	−0.335579	−0.0206535
$265$	−5.36510	−0.329576
$266$	6.51695	0.399580
$267$	−2.01547	−0.123345
$268$	8.54059	0.521700
$269$	27.6318	1.68474	0.842369	−	0.538901i	$-0.181160\pi$
$269$	27.6318	1.68474	0.842369	+	0.538901i	$0.181160\pi$
$270$	−2.55711	−0.155621
$271$	−5.73479	−0.348364	−0.174182	−	0.984713i	$-0.555728\pi$
$271$	−5.73479	−0.348364	−0.174182	+	0.984713i	$0.555728\pi$
$272$	3.33181	0.202021
$273$	−3.62597	−0.219454
$274$	−6.67293	−0.403126
$275$	−2.02187	−0.121924
$276$	6.60779	0.397742
$277$	25.1197	1.50930	0.754649	−	0.656129i	$-0.227807\pi$
$277$	25.1197	1.50930	0.754649	+	0.656129i	$0.227807\pi$
$278$	6.01600	0.360816
$279$	1.44419	0.0864615
$280$	−1.80403	−0.107811
$281$	−29.2006	−1.74196	−0.870982	−	0.491316i	$-0.836516\pi$
$281$	−29.2006	−1.74196	−0.870982	+	0.491316i	$0.836516\pi$
$282$	7.02101	0.418095
$283$	−29.0652	−1.72775	−0.863875	−	0.503707i	$-0.831969\pi$
$283$	−29.0652	−1.72775	−0.863875	+	0.503707i	$0.831969\pi$
$284$	−13.1916	−0.782775
$285$	1.05167	0.0622954
$286$	0.706677	0.0417867
$287$	−22.3170	−1.31733
$288$	−2.41192	−0.142124
$289$	−5.89902	−0.347001
$290$	4.15389	0.243925
$291$	−6.22653	−0.365006
$292$	7.08650	0.414706
$293$	4.66058	0.272274	0.136137	−	0.990690i	$-0.456531\pi$
$293$	4.66058	0.272274	0.136137	+	0.990690i	$0.456531\pi$
$294$	−1.20618	−0.0703459
$295$	5.80530	0.337997
$296$	−10.0409	−0.583617
$297$	1.81613	0.105382
$298$	−16.6214	−0.962852
$299$	−13.9150	−0.804724
$300$	3.54319	0.204566
$301$	−8.41805	−0.485208
$302$	3.46036	0.199121
$303$	5.80390	0.333426
$304$	2.22577	0.127657
$305$	−2.62500	−0.150307
$306$	−8.03607	−0.459392
$307$	−9.67702	−0.552297	−0.276148	−	0.961115i	$-0.589058\pi$
$307$	−9.67702	−0.552297	−0.276148	+	0.961115i	$0.589058\pi$
$308$	1.28127	0.0730071
$309$	−2.00543	−0.114085
$310$	0.368928	0.0209537
$311$	−13.6019	−0.771296	−0.385648	−	0.922646i	$-0.626022\pi$
$311$	−13.6019	−0.771296	−0.385648	+	0.922646i	$0.626022\pi$
$312$	−1.23840	−0.0701106
$313$	−16.1397	−0.912268	−0.456134	−	0.889911i	$-0.650766\pi$
$313$	−16.1397	−0.912268	−0.456134	+	0.889911i	$0.650766\pi$
$314$	7.15372	0.403708
$315$	4.35118	0.245161
$316$	7.30002	0.410658
$317$	−18.1372	−1.01869	−0.509343	−	0.860564i	$-0.670111\pi$
$317$	−18.1372	−1.01869	−0.509343	+	0.860564i	$0.670111\pi$
$318$	−6.67752	−0.374457
$319$	−2.95020	−0.165179
$320$	−0.616141	−0.0344433
$321$	13.8668	0.773971
$322$	−25.2291	−1.40596
$323$	7.41586	0.412629
$324$	4.05313	0.225174
$325$	−7.46140	−0.413884
$326$	−17.9620	−0.994824
$327$	−2.36136	−0.130583
$328$	−7.62206	−0.420858
$329$	−26.8068	−1.47791
$330$	0.206764	0.0113820
$331$	7.28584	0.400466	0.200233	−	0.979748i	$-0.435830\pi$
$331$	7.28584	0.400466	0.200233	+	0.979748i	$0.435830\pi$
$332$	15.3060	0.840028
$333$	24.2179	1.32714
$334$	−12.5392	−0.686116
$335$	−5.26221	−0.287505
$336$	−2.24533	−0.122493
$337$	33.8354	1.84313	0.921567	−	0.388219i	$-0.126910\pi$
$337$	33.8354	1.84313	0.921567	+	0.388219i	$0.126910\pi$
$338$	−10.3921	−0.565257
$339$	−2.58686	−0.140499
$340$	−2.05287	−0.111332
$341$	−0.262023	−0.0141893
$342$	−5.36839	−0.290289
$343$	−15.8903	−0.857997
$344$	−2.87507	−0.155013
$345$	−4.07133	−0.219193
$346$	6.11583	0.328789
$347$	12.3446	0.662690	0.331345	−	0.943510i	$-0.392498\pi$
$347$	12.3446	0.662690	0.331345	+	0.943510i	$0.392498\pi$
$348$	5.17001	0.277142
$349$	6.48284	0.347018	0.173509	−	0.984832i	$-0.444489\pi$
$349$	6.48284	0.347018	0.173509	+	0.984832i	$0.444489\pi$
$350$	−13.5282	−0.723113
$351$	6.70213	0.357733
$352$	0.437600	0.0233242
$353$	9.15287	0.487158	0.243579	−	0.969881i	$-0.421678\pi$
$353$	9.15287	0.487158	0.243579	+	0.969881i	$0.421678\pi$
$354$	7.22539	0.384025
$355$	8.12787	0.431382
$356$	2.62820	0.139294
$357$	−7.48103	−0.395938
$358$	−13.3903	−0.707700
$359$	1.59171	0.0840074	0.0420037	−	0.999117i	$-0.486626\pi$
$359$	1.59171	0.0840074	0.0420037	+	0.999117i	$0.486626\pi$
$360$	1.48608	0.0783235
$361$	−14.0459	−0.739260
$362$	11.2694	0.592306
$363$	8.28864	0.435041
$364$	4.72832	0.247831
$365$	−4.36628	−0.228542
$366$	−3.26713	−0.170776
$367$	25.4807	1.33008	0.665042	−	0.746806i	$-0.268414\pi$
$367$	25.4807	1.33008	0.665042	+	0.746806i	$0.268414\pi$
$368$	−8.61666	−0.449175
$369$	18.3838	0.957023
$370$	6.18663	0.321628
$371$	25.4954	1.32365
$372$	0.459176	0.0238072
$373$	−17.4650	−0.904303	−0.452151	−	0.891941i	$-0.649343\pi$
$373$	−17.4650	−0.904303	−0.452151	+	0.891941i	$0.649343\pi$
$374$	1.45800	0.0753914
$375$	−4.54558	−0.234733
$376$	−9.15550	−0.472159
$377$	−10.8872	−0.560722
$378$	12.1516	0.625009
$379$	0.364107	0.0187029	0.00935145	−	0.999956i	$-0.497023\pi$
$379$	0.364107	0.0187029	0.00935145	+	0.999956i	$0.497023\pi$
$380$	−1.37139	−0.0703509
$381$	8.21191	0.420709
$382$	18.8725	0.965599
$383$	0.659034	0.0336751	0.0168375	−	0.999858i	$-0.494640\pi$
$383$	0.659034	0.0336751	0.0168375	+	0.999858i	$0.494640\pi$
$384$	−0.766862	−0.0391338
$385$	−0.789443	−0.0402337
$386$	−12.6870	−0.645750
$387$	6.93444	0.352497
$388$	8.11949	0.412204
$389$	−4.10725	−0.208246	−0.104123	−	0.994564i	$-0.533204\pi$
$389$	−4.10725	−0.208246	−0.104123	+	0.994564i	$0.533204\pi$
$390$	0.763030	0.0386375
$391$	−28.7091	−1.45188
$392$	1.57288	0.0794423
$393$	−9.73629	−0.491131
$394$	−9.36446	−0.471775
$395$	−4.49784	−0.226311
$396$	−1.05546	−0.0530387
$397$	0.685920	0.0344254	0.0172127	−	0.999852i	$-0.494521\pi$
$397$	0.685920	0.0344254	0.0172127	+	0.999852i	$0.494521\pi$
$398$	−20.1131	−1.00818
$399$	−4.99760	−0.250193
$400$	−4.62037	−0.231018
$401$	−20.0831	−1.00290	−0.501450	−	0.865187i	$-0.667200\pi$
$401$	−20.0831	−1.00290	−0.501450	+	0.865187i	$0.667200\pi$
$402$	−6.54946	−0.326657
$403$	−0.966953	−0.0481674
$404$	−7.56838	−0.376541
$405$	−2.49730	−0.124092
$406$	−19.7396	−0.979658
$407$	−4.39391	−0.217798
$408$	−2.55504	−0.126493
$409$	−15.4507	−0.763988	−0.381994	−	0.924165i	$-0.624762\pi$
$409$	−15.4507	−0.763988	−0.381994	+	0.924165i	$0.624762\pi$
$410$	4.69626	0.231932
$411$	5.11722	0.252414
$412$	2.61511	0.128837
$413$	−27.5872	−1.35748
$414$	20.7827	1.02141
$415$	−9.43068	−0.462934
$416$	1.61489	0.0791766
$417$	−4.61344	−0.225921
$418$	0.973998	0.0476398
$419$	6.86464	0.335359	0.167680	−	0.985842i	$-0.446373\pi$
$419$	6.86464	0.335359	0.167680	+	0.985842i	$0.446373\pi$
$420$	1.38344	0.0675051
$421$	1.87491	0.0913773	0.0456887	−	0.998956i	$-0.485452\pi$
$421$	1.87491	0.0913773	0.0456887	+	0.998956i	$0.485452\pi$
$422$	−17.9822	−0.875360
$423$	22.0824	1.07368
$424$	8.70758	0.422878
$425$	−15.3942	−0.746729
$426$	10.1161	0.490127
$427$	12.4742	0.603669
$428$	−18.0826	−0.874054
$429$	−0.541924	−0.0261643
$430$	1.77145	0.0854268
$431$	9.28403	0.447196	0.223598	−	0.974681i	$-0.428220\pi$
$431$	9.28403	0.447196	0.223598	+	0.974681i	$0.428220\pi$
$432$	4.15020	0.199677
$433$	29.4226	1.41396	0.706979	−	0.707234i	$-0.250057\pi$
$433$	29.4226	1.41396	0.706979	+	0.707234i	$0.250057\pi$
$434$	−1.75317	−0.0841550
$435$	−3.18546	−0.152731
$436$	3.07925	0.147469
$437$	−19.1787	−0.917443
$438$	−5.43437	−0.259664
$439$	−14.2371	−0.679501	−0.339751	−	0.940516i	$-0.610343\pi$
$439$	−14.2371	−0.679501	−0.339751	+	0.940516i	$0.610343\pi$
$440$	−0.269623	−0.0128538
$441$	−3.79366	−0.180650
$442$	5.38052	0.255925
$443$	−18.0500	−0.857583	−0.428792	−	0.903403i	$-0.641061\pi$
$443$	−18.0500	−0.857583	−0.428792	+	0.903403i	$0.641061\pi$
$444$	7.70001	0.365426
$445$	−1.61934	−0.0767643
$446$	15.9503	0.755267
$447$	12.7463	0.602881
$448$	2.92795	0.138333
$449$	−0.533358	−0.0251707	−0.0125854	−	0.999921i	$-0.504006\pi$
$449$	−0.533358	−0.0251707	−0.0125854	+	0.999921i	$0.504006\pi$
$450$	11.1440	0.525332
$451$	−3.33541	−0.157058
$452$	3.37331	0.158667
$453$	−2.65362	−0.124678
$454$	−15.8698	−0.744808
$455$	−2.91331	−0.136578
$456$	−1.70686	−0.0799311
$457$	21.5088	1.00614	0.503071	−	0.864245i	$-0.332204\pi$
$457$	21.5088	1.00614	0.503071	+	0.864245i	$0.332204\pi$
$458$	−2.46288	−0.115083
$459$	13.8277	0.645421
$460$	5.30908	0.247537
$461$	24.2611	1.12995	0.564977	−	0.825107i	$-0.308885\pi$
$461$	24.2611	1.12995	0.564977	+	0.825107i	$0.308885\pi$
$462$	−0.982557	−0.0457127
$463$	−4.31881	−0.200712	−0.100356	−	0.994952i	$-0.531998\pi$
$463$	−4.31881	−0.200712	−0.100356	+	0.994952i	$0.531998\pi$
$464$	−6.74177	−0.312979
$465$	−0.282917	−0.0131200
$466$	−13.0365	−0.603904
$467$	27.4536	1.27040	0.635201	−	0.772347i	$-0.280917\pi$
$467$	27.4536	1.27040	0.635201	+	0.772347i	$0.280917\pi$
$468$	−3.89500	−0.180046
$469$	25.0064	1.15469
$470$	5.64108	0.260204
$471$	−5.48592	−0.252778
$472$	−9.42202	−0.433684
$473$	−1.25813	−0.0578488
$474$	−5.59811	−0.257130
$475$	−10.2839	−0.471857
$476$	9.75538	0.447137
$477$	−21.0020	−0.961616
$478$	−9.14910	−0.418470
$479$	−32.9787	−1.50683	−0.753417	−	0.657543i	$-0.771596\pi$
$479$	−32.9787	−1.50683	−0.753417	+	0.657543i	$0.771596\pi$
$480$	0.472496	0.0215664
$481$	−16.2150	−0.739342
$482$	7.72515	0.351871
$483$	19.3473	0.880331
$484$	−10.8085	−0.491296
$485$	−5.00275	−0.227163
$486$	−15.5588	−0.705761
$487$	39.9832	1.81181	0.905906	−	0.423478i	$-0.139191\pi$
$487$	39.9832	1.81181	0.905906	+	0.423478i	$0.139191\pi$
$488$	4.26039	0.192859
$489$	13.7744	0.622899
$490$	−0.969115	−0.0437801
$491$	32.7809	1.47938	0.739692	−	0.672946i	$-0.234971\pi$
$491$	32.7809	1.47938	0.739692	+	0.672946i	$0.234971\pi$
$492$	5.84507	0.263516
$493$	−22.4623	−1.01165
$494$	3.59438	0.161719
$495$	0.650311	0.0292293
$496$	−0.598772	−0.0268857
$497$	−38.6242	−1.73253
$498$	−11.7376	−0.525975
$499$	−43.3993	−1.94282	−0.971409	−	0.237411i	$-0.923701\pi$
$499$	−43.3993	−1.94282	−0.971409	+	0.237411i	$0.923701\pi$
$500$	5.92751	0.265086
$501$	9.61586	0.429605
$502$	2.00287	0.0893926
$503$	−0.242159	−0.0107973	−0.00539867	−	0.999985i	$-0.501718\pi$
$503$	−0.242159	−0.0107973	−0.00539867	+	0.999985i	$0.501718\pi$
$504$	−7.06198	−0.314566
$505$	4.66319	0.207509
$506$	−3.77065	−0.167626
$507$	7.96933	0.353930
$508$	−10.7084	−0.475111
$509$	−9.94851	−0.440960	−0.220480	−	0.975392i	$-0.570762\pi$
$509$	−9.94851	−0.440960	−0.220480	+	0.975392i	$0.570762\pi$
$510$	1.57427	0.0697097
$511$	20.7489	0.917877
$512$	1.00000	0.0441942
$513$	9.23740	0.407841
$514$	1.98861	0.0877139
$515$	−1.61127	−0.0710012
$516$	2.20478	0.0970601
$517$	−4.00645	−0.176203
$518$	−29.3993	−1.29173
$519$	−4.69000	−0.205868
$520$	−0.995002	−0.0436337
$521$	14.0005	0.613374	0.306687	−	0.951810i	$-0.400780\pi$
$521$	14.0005	0.613374	0.306687	+	0.951810i	$0.400780\pi$
$522$	16.2606	0.711709
$523$	10.6073	0.463826	0.231913	−	0.972737i	$-0.425502\pi$
$523$	10.6073	0.463826	0.231913	+	0.972737i	$0.425502\pi$
$524$	12.6963	0.554639
$525$	10.3743	0.452770
$526$	29.8585	1.30189
$527$	−1.99500	−0.0869035
$528$	−0.335579	−0.0146042
$529$	51.2468	2.22812
$530$	−5.36510	−0.233045
$531$	22.7252	0.986189
$532$	6.51695	0.282545
$533$	−12.3088	−0.533154
$534$	−2.01547	−0.0872179
$535$	11.1414	0.481685
$536$	8.54059	0.368897
$537$	10.2685	0.443120
$538$	27.6318	1.19129
$539$	0.688291	0.0296468
$540$	−2.55711	−0.110040
$541$	−6.39674	−0.275017	−0.137509	−	0.990501i	$-0.543909\pi$
$541$	−6.39674	−0.275017	−0.137509	+	0.990501i	$0.543909\pi$
$542$	−5.73479	−0.246330
$543$	−8.64207	−0.370867
$544$	3.33181	0.142850
$545$	−1.89725	−0.0812693
$546$	−3.62597	−0.155177
$547$	24.7024	1.05620	0.528098	−	0.849183i	$-0.322905\pi$
$547$	24.7024	1.05620	0.528098	+	0.849183i	$0.322905\pi$
$548$	−6.67293	−0.285053
$549$	−10.2757	−0.438558
$550$	−2.02187	−0.0862130
$551$	−15.0057	−0.639263
$552$	6.60779	0.281246
$553$	21.3741	0.908918
$554$	25.1197	1.06723
$555$	−4.74430	−0.201384
$556$	6.01600	0.255135
$557$	−10.6777	−0.452431	−0.226215	−	0.974077i	$-0.572635\pi$
$557$	−10.6777	−0.452431	−0.226215	+	0.974077i	$0.572635\pi$
$558$	1.44419	0.0611375
$559$	−4.64293	−0.196375
$560$	−1.80403	−0.0762342
$561$	−1.11809	−0.0472056
$562$	−29.2006	−1.23175
$563$	5.45787	0.230022	0.115011	−	0.993364i	$-0.463310\pi$
$563$	5.45787	0.230022	0.115011	+	0.993364i	$0.463310\pi$
$564$	7.02101	0.295638
$565$	−2.07843	−0.0874404
$566$	−29.0652	−1.22170
$567$	11.8674	0.498383
$568$	−13.1916	−0.553506
$569$	3.23014	0.135414	0.0677072	−	0.997705i	$-0.478432\pi$
$569$	3.23014	0.135414	0.0677072	+	0.997705i	$0.478432\pi$
$570$	1.05167	0.0440495
$571$	−15.8764	−0.664407	−0.332204	−	0.943208i	$-0.607792\pi$
$571$	−15.8764	−0.664407	−0.332204	+	0.943208i	$0.607792\pi$
$572$	0.706677	0.0295476
$573$	−14.4726	−0.604601
$574$	−22.3170	−0.931493
$575$	39.8122	1.66028
$576$	−2.41192	−0.100497
$577$	−10.7562	−0.447786	−0.223893	−	0.974614i	$-0.571877\pi$
$577$	−10.7562	−0.447786	−0.223893	+	0.974614i	$0.571877\pi$
$578$	−5.89902	−0.245367
$579$	9.72916	0.404330
$580$	4.15389	0.172481
$581$	44.8153	1.85925
$582$	−6.22653	−0.258098
$583$	3.81044	0.157812
$584$	7.08650	0.293241
$585$	2.39987	0.0992223
$586$	4.66058	0.192527
$587$	37.1223	1.53220	0.766101	−	0.642720i	$-0.222194\pi$
$587$	37.1223	1.53220	0.766101	+	0.642720i	$0.222194\pi$
$588$	−1.20618	−0.0497421
$589$	−1.33273	−0.0549142
$590$	5.80530	0.239000
$591$	7.18125	0.295397
$592$	−10.0409	−0.412680
$593$	−26.9097	−1.10505	−0.552525	−	0.833496i	$-0.686336\pi$
$593$	−26.9097	−1.10505	−0.552525	+	0.833496i	$0.686336\pi$
$594$	1.81613	0.0745166
$595$	−6.01069	−0.246414
$596$	−16.6214	−0.680839
$597$	15.4240	0.631262
$598$	−13.9150	−0.569026
$599$	−1.03692	−0.0423673	−0.0211837	−	0.999776i	$-0.506743\pi$
$599$	−1.03692	−0.0423673	−0.0211837	+	0.999776i	$0.506743\pi$
$600$	3.54319	0.144650
$601$	15.0379	0.613407	0.306704	−	0.951805i	$-0.400774\pi$
$601$	15.0379	0.613407	0.306704	+	0.951805i	$0.400774\pi$
$602$	−8.41805	−0.343094
$603$	−20.5992	−0.838866
$604$	3.46036	0.140800
$605$	6.65957	0.270750
$606$	5.80390	0.235767
$607$	39.8857	1.61891	0.809456	−	0.587180i	$-0.199762\pi$
$607$	39.8857	1.61891	0.809456	+	0.587180i	$0.199762\pi$
$608$	2.22577	0.0902670
$609$	15.1375	0.613404
$610$	−2.62500	−0.106283
$611$	−14.7852	−0.598143
$612$	−8.03607	−0.324839
$613$	−34.7239	−1.40249	−0.701243	−	0.712922i	$-0.747371\pi$
$613$	−34.7239	−1.40249	−0.701243	+	0.712922i	$0.747371\pi$
$614$	−9.67702	−0.390533
$615$	−3.60139	−0.145222
$616$	1.28127	0.0516238
$617$	11.6065	0.467260	0.233630	−	0.972326i	$-0.424940\pi$
$617$	11.6065	0.467260	0.233630	+	0.972326i	$0.424940\pi$
$618$	−2.00543	−0.0806701
$619$	42.6069	1.71252	0.856258	−	0.516549i	$-0.172784\pi$
$619$	42.6069	1.71252	0.856258	+	0.516549i	$0.172784\pi$
$620$	0.368928	0.0148165
$621$	−35.7609	−1.43503
$622$	−13.6019	−0.545388
$623$	7.69524	0.308303
$624$	−1.23840	−0.0495757
$625$	19.4497	0.777987
$626$	−16.1397	−0.645071
$627$	−0.746922	−0.0298292
$628$	7.15372	0.285465
$629$	−33.4545	−1.33392
$630$	4.35118	0.173355
$631$	−21.3715	−0.850786	−0.425393	−	0.905009i	$-0.639864\pi$
$631$	−21.3715	−0.850786	−0.425393	+	0.905009i	$0.639864\pi$
$632$	7.30002	0.290379
$633$	13.7899	0.548099
$634$	−18.1372	−0.720319
$635$	6.59792	0.261830
$636$	−6.67752	−0.264781
$637$	2.54003	0.100640
$638$	−2.95020	−0.116800
$639$	31.8170	1.25866
$640$	−0.616141	−0.0243551
$641$	−10.5800	−0.417884	−0.208942	−	0.977928i	$-0.567002\pi$
$641$	−10.5800	−0.417884	−0.208942	+	0.977928i	$0.567002\pi$
$642$	13.8668	0.547280
$643$	−32.5221	−1.28255	−0.641274	−	0.767312i	$-0.721594\pi$
$643$	−32.5221	−1.28255	−0.641274	+	0.767312i	$0.721594\pi$
$644$	−25.2291	−0.994167
$645$	−1.35846	−0.0534892
$646$	7.41586	0.291773
$647$	32.6466	1.28347	0.641736	−	0.766926i	$-0.278214\pi$
$647$	32.6466	1.28347	0.641736	+	0.766926i	$0.278214\pi$
$648$	4.05313	0.159222
$649$	−4.12307	−0.161845
$650$	−7.46140	−0.292660
$651$	1.34444	0.0526929
$652$	−17.9620	−0.703447
$653$	16.4557	0.643962	0.321981	−	0.946746i	$-0.395651\pi$
$653$	16.4557	0.643962	0.321981	+	0.946746i	$0.395651\pi$
$654$	−2.36136	−0.0923364
$655$	−7.82269	−0.305658
$656$	−7.62206	−0.297591
$657$	−17.0921	−0.666826
$658$	−26.8068	−1.04504
$659$	13.0553	0.508563	0.254282	−	0.967130i	$-0.418161\pi$
$659$	13.0553	0.508563	0.254282	+	0.967130i	$0.418161\pi$
$660$	0.206764	0.00804828
$661$	0.423191	0.0164602	0.00823010	−	0.999966i	$-0.497380\pi$
$661$	0.423191	0.0164602	0.00823010	+	0.999966i	$0.497380\pi$
$662$	7.28584	0.283172
$663$	−4.12612	−0.160245
$664$	15.3060	0.593989
$665$	−4.01536	−0.155709
$666$	24.2179	0.938426
$667$	58.0916	2.24932
$668$	−12.5392	−0.485157
$669$	−12.2317	−0.472903
$670$	−5.26221	−0.203297
$671$	1.86435	0.0719723
$672$	−2.24533	−0.0866156
$673$	−18.1101	−0.698094	−0.349047	−	0.937105i	$-0.613495\pi$
$673$	−18.1101	−0.698094	−0.349047	+	0.937105i	$0.613495\pi$
$674$	33.8354	1.30329
$675$	−19.1755	−0.738064
$676$	−10.3921	−0.399697
$677$	−38.7786	−1.49038	−0.745191	−	0.666851i	$-0.767642\pi$
$677$	−38.7786	−1.49038	−0.745191	+	0.666851i	$0.767642\pi$
$678$	−2.58686	−0.0993479
$679$	23.7734	0.912341
$680$	−2.05287	−0.0787239
$681$	12.1700	0.466355
$682$	−0.262023	−0.0100334
$683$	−27.7061	−1.06014	−0.530072	−	0.847952i	$-0.677835\pi$
$683$	−27.7061	−1.06014	−0.530072	+	0.847952i	$0.677835\pi$
$684$	−5.36839	−0.205266
$685$	4.11147	0.157091
$686$	−15.8903	−0.606696
$687$	1.88869	0.0720580
$688$	−2.87507	−0.109611
$689$	14.0618	0.535712
$690$	−4.07133	−0.154993
$691$	−26.2341	−0.997992	−0.498996	−	0.866604i	$-0.666298\pi$
$691$	−26.2341	−0.997992	−0.498996	+	0.866604i	$0.666298\pi$
$692$	6.11583	0.232489
$693$	−3.09032	−0.117392
$694$	12.3446	0.468593
$695$	−3.70671	−0.140603
$696$	5.17001	0.195969
$697$	−25.3953	−0.961915
$698$	6.48284	0.245379
$699$	9.99719	0.378129
$700$	−13.5282	−0.511318
$701$	−12.4496	−0.470213	−0.235107	−	0.971970i	$-0.575544\pi$
$701$	−12.4496	−0.470213	−0.235107	+	0.971970i	$0.575544\pi$
$702$	6.70213	0.252955
$703$	−22.3488	−0.842902
$704$	0.437600	0.0164927
$705$	−4.32593	−0.162924
$706$	9.15287	0.344473
$707$	−22.1598	−0.833406
$708$	7.22539	0.271547
$709$	−40.4489	−1.51909	−0.759544	−	0.650456i	$-0.774578\pi$
$709$	−40.4489	−1.51909	−0.759544	+	0.650456i	$0.774578\pi$
$710$	8.12787	0.305033
$711$	−17.6071	−0.660317
$712$	2.62820	0.0984961
$713$	5.15942	0.193222
$714$	−7.48103	−0.279971
$715$	−0.435413	−0.0162835
$716$	−13.3903	−0.500419
$717$	7.01610	0.262021
$718$	1.59171	0.0594022
$719$	−16.5779	−0.618251	−0.309126	−	0.951021i	$-0.600036\pi$
$719$	−16.5779	−0.618251	−0.309126	+	0.951021i	$0.600036\pi$
$720$	1.48608	0.0553831
$721$	7.65689	0.285158
$722$	−14.0459	−0.522736
$723$	−5.92413	−0.220321
$724$	11.2694	0.418824
$725$	31.1495	1.15686
$726$	8.28864	0.307620
$727$	−39.8468	−1.47784	−0.738918	−	0.673796i	$-0.764663\pi$
$727$	−39.8468	−1.47784	−0.738918	+	0.673796i	$0.764663\pi$
$728$	4.72832	0.175243
$729$	−0.227951	−0.00844264
$730$	−4.36628	−0.161603
$731$	−9.57919	−0.354299
$732$	−3.26713	−0.120757
$733$	−0.468952	−0.0173211	−0.00866057	−	0.999962i	$-0.502757\pi$
$733$	−0.468952	−0.0173211	−0.00866057	+	0.999962i	$0.502757\pi$
$734$	25.4807	0.940511
$735$	0.743178	0.0274125
$736$	−8.61666	−0.317614
$737$	3.73736	0.137668
$738$	18.3838	0.676717
$739$	−7.55388	−0.277874	−0.138937	−	0.990301i	$-0.544369\pi$
$739$	−7.55388	−0.277874	−0.138937	+	0.990301i	$0.544369\pi$
$740$	6.18663	0.227425
$741$	−2.75640	−0.101259
$742$	25.4954	0.935964
$743$	−3.88921	−0.142681	−0.0713407	−	0.997452i	$-0.522728\pi$
$743$	−3.88921	−0.142681	−0.0713407	+	0.997452i	$0.522728\pi$
$744$	0.459176	0.0168342
$745$	10.2411	0.375206
$746$	−17.4650	−0.639439
$747$	−36.9170	−1.35072
$748$	1.45800	0.0533098
$749$	−52.9448	−1.93456
$750$	−4.54558	−0.165981
$751$	5.35837	0.195530	0.0977648	−	0.995210i	$-0.468831\pi$
$751$	5.35837	0.195530	0.0977648	+	0.995210i	$0.468831\pi$
$752$	−9.15550	−0.333867
$753$	−1.53593	−0.0559723
$754$	−10.8872	−0.396490
$755$	−2.13207	−0.0775939
$756$	12.1516	0.441948
$757$	50.6693	1.84161	0.920804	−	0.390026i	$-0.127534\pi$
$757$	50.6693	1.84161	0.920804	+	0.390026i	$0.127534\pi$
$758$	0.364107	0.0132249
$759$	2.89157	0.104957
$760$	−1.37139	−0.0497456
$761$	45.3463	1.64380	0.821902	−	0.569629i	$-0.192913\pi$
$761$	45.3463	1.64380	0.821902	+	0.569629i	$0.192913\pi$
$762$	8.21191	0.297486
$763$	9.01587	0.326396
$764$	18.8725	0.682782
$765$	4.95136	0.179017
$766$	0.659034	0.0238119
$767$	−15.2156	−0.549402
$768$	−0.766862	−0.0276718
$769$	−2.81977	−0.101683	−0.0508417	−	0.998707i	$-0.516190\pi$
$769$	−2.81977	−0.101683	−0.0508417	+	0.998707i	$0.516190\pi$
$770$	−0.789443	−0.0284496
$771$	−1.52499	−0.0549212
$772$	−12.6870	−0.456614
$773$	−43.6400	−1.56962	−0.784811	−	0.619735i	$-0.787240\pi$
$773$	−43.6400	−1.56962	−0.784811	+	0.619735i	$0.787240\pi$
$774$	6.93444	0.249253
$775$	2.76655	0.0993774
$776$	8.11949	0.291473
$777$	22.5452	0.808806
$778$	−4.10725	−0.147252
$779$	−16.9650	−0.607833
$780$	0.763030	0.0273208
$781$	−5.77263	−0.206561
$782$	−28.7091	−1.02664
$783$	−27.9797	−0.999913
$784$	1.57288	0.0561742
$785$	−4.40770	−0.157318
$786$	−9.73629	−0.347282
$787$	−1.67151	−0.0595828	−0.0297914	−	0.999556i	$-0.509484\pi$
$787$	−1.67151	−0.0595828	−0.0297914	+	0.999556i	$0.509484\pi$
$788$	−9.36446	−0.333595
$789$	−22.8973	−0.815166
$790$	−4.49784	−0.160026
$791$	9.87687	0.351181
$792$	−1.05546	−0.0375040
$793$	6.88008	0.244319
$794$	0.685920	0.0243424
$795$	4.11430	0.145919
$796$	−20.1131	−0.712890
$797$	−24.6368	−0.872681	−0.436341	−	0.899782i	$-0.643726\pi$
$797$	−24.6368	−0.872681	−0.436341	+	0.899782i	$0.643726\pi$
$798$	−4.99760	−0.176913
$799$	−30.5044	−1.07917
$800$	−4.62037	−0.163355
$801$	−6.33902	−0.223978
$802$	−20.0831	−0.709157
$803$	3.10105	0.109434
$804$	−6.54946	−0.230982
$805$	15.5447	0.547879
$806$	−0.966953	−0.0340595
$807$	−21.1898	−0.745915
$808$	−7.56838	−0.266255
$809$	−19.6625	−0.691298	−0.345649	−	0.938364i	$-0.612341\pi$
$809$	−19.6625	−0.691298	−0.345649	+	0.938364i	$0.612341\pi$
$810$	−2.49730	−0.0877463
$811$	−49.1453	−1.72572	−0.862862	−	0.505439i	$-0.831331\pi$
$811$	−49.1453	−1.72572	−0.862862	+	0.505439i	$0.831331\pi$
$812$	−19.7396	−0.692723
$813$	4.39780	0.154237
$814$	−4.39391	−0.154006
$815$	11.0671	0.387665
$816$	−2.55504	−0.0894444
$817$	−6.39925	−0.223881
$818$	−15.4507	−0.540221
$819$	−11.4043	−0.398500
$820$	4.69626	0.164001
$821$	31.5321	1.10048	0.550238	−	0.835008i	$-0.314537\pi$
$821$	31.5321	1.10048	0.550238	+	0.835008i	$0.314537\pi$
$822$	5.11722	0.178483
$823$	27.8370	0.970336	0.485168	−	0.874421i	$-0.338758\pi$
$823$	27.8370	0.970336	0.485168	+	0.874421i	$0.338758\pi$
$824$	2.61511	0.0911015
$825$	1.55050	0.0539814
$826$	−27.5872	−0.959881
$827$	16.8504	0.585944	0.292972	−	0.956121i	$-0.405356\pi$
$827$	16.8504	0.585944	0.292972	+	0.956121i	$0.405356\pi$
$828$	20.7827	0.722249
$829$	2.26828	0.0787807	0.0393904	−	0.999224i	$-0.487458\pi$
$829$	2.26828	0.0787807	0.0393904	+	0.999224i	$0.487458\pi$
$830$	−9.43068	−0.327344
$831$	−19.2634	−0.668239
$832$	1.61489	0.0559863
$833$	5.24053	0.181574
$834$	−4.61344	−0.159751
$835$	7.72593	0.267367
$836$	0.973998	0.0336864
$837$	−2.48502	−0.0858950
$838$	6.86464	0.237135
$839$	−40.0275	−1.38190	−0.690951	−	0.722902i	$-0.742808\pi$
$839$	−40.0275	−1.38190	−0.690951	+	0.722902i	$0.742808\pi$
$840$	1.38344	0.0477333
$841$	16.4515	0.567294
$842$	1.87491	0.0646135
$843$	22.3929	0.771251
$844$	−17.9822	−0.618973
$845$	6.40302	0.220270
$846$	22.0824	0.759207
$847$	−31.6467	−1.08739
$848$	8.70758	0.299020
$849$	22.2890	0.764958
$850$	−15.3942	−0.528017
$851$	86.5193	2.96584
$852$	10.1161	0.346572
$853$	32.1803	1.10183	0.550916	−	0.834561i	$-0.314278\pi$
$853$	32.1803	1.10183	0.550916	+	0.834561i	$0.314278\pi$
$854$	12.4742	0.426858
$855$	3.30769	0.113121
$856$	−18.0826	−0.618049
$857$	−38.1836	−1.30433	−0.652163	−	0.758079i	$-0.726138\pi$
$857$	−38.1836	−1.30433	−0.652163	+	0.758079i	$0.726138\pi$
$858$	−0.541924	−0.0185010
$859$	29.3007	0.999728	0.499864	−	0.866104i	$-0.333383\pi$
$859$	29.3007	0.999728	0.499864	+	0.866104i	$0.333383\pi$
$860$	1.77145	0.0604059
$861$	17.1141	0.583245
$862$	9.28403	0.316215
$863$	51.4988	1.75304	0.876520	−	0.481366i	$-0.159859\pi$
$863$	51.4988	1.75304	0.876520	+	0.481366i	$0.159859\pi$
$864$	4.15020	0.141193
$865$	−3.76821	−0.128123
$866$	29.4226	0.999820
$867$	4.52374	0.153634
$868$	−1.75317	−0.0595066
$869$	3.19449	0.108366
$870$	−3.18546	−0.107997
$871$	13.7921	0.467329
$872$	3.07925	0.104276
$873$	−19.5836	−0.662803
$874$	−19.1787	−0.648730
$875$	17.3554	0.586721
$876$	−5.43437	−0.183610
$877$	24.3645	0.822730	0.411365	−	0.911471i	$-0.365052\pi$
$877$	24.3645	0.822730	0.411365	+	0.911471i	$0.365052\pi$
$878$	−14.2371	−0.480480
$879$	−3.57402	−0.120549
$880$	−0.269623	−0.00908900
$881$	7.28451	0.245421	0.122711	−	0.992442i	$-0.460841\pi$
$881$	7.28451	0.245421	0.122711	+	0.992442i	$0.460841\pi$
$882$	−3.79366	−0.127739
$883$	−17.0258	−0.572963	−0.286481	−	0.958086i	$-0.592486\pi$
$883$	−17.0258	−0.572963	−0.286481	+	0.958086i	$0.592486\pi$
$884$	5.38052	0.180967
$885$	−4.45186	−0.149648
$886$	−18.0500	−0.606403
$887$	29.6283	0.994820	0.497410	−	0.867516i	$-0.334285\pi$
$887$	29.6283	0.994820	0.497410	+	0.867516i	$0.334285\pi$
$888$	7.70001	0.258395
$889$	−31.3538	−1.05157
$890$	−1.61934	−0.0542805
$891$	1.77365	0.0594196
$892$	15.9503	0.534055
$893$	−20.3781	−0.681926
$894$	12.7463	0.426301
$895$	8.25032	0.275778
$896$	2.92795	0.0978159
$897$	10.6709	0.356290
$898$	−0.533358	−0.0177984
$899$	4.03679	0.134634
$900$	11.1440	0.371466
$901$	29.0120	0.966531
$902$	−3.33541	−0.111057
$903$	6.45548	0.214825
$904$	3.37331	0.112195
$905$	−6.94354	−0.230811
$906$	−2.65362	−0.0881605
$907$	11.9674	0.397371	0.198686	−	0.980063i	$-0.436333\pi$
$907$	11.9674	0.397371	0.198686	+	0.980063i	$0.436333\pi$
$908$	−15.8698	−0.526659
$909$	18.2543	0.605458
$910$	−2.91331	−0.0965754
$911$	0.468905	0.0155355	0.00776776	−	0.999970i	$-0.497527\pi$
$911$	0.468905	0.0155355	0.00776776	+	0.999970i	$0.497527\pi$
$912$	−1.70686	−0.0565198
$913$	6.69792	0.221669
$914$	21.5088	0.711449
$915$	2.01302	0.0665483
$916$	−2.46288	−0.0813759
$917$	37.1740	1.22759
$918$	13.8277	0.456382
$919$	−40.2653	−1.32823	−0.664116	−	0.747630i	$-0.731192\pi$
$919$	−40.2653	−1.32823	−0.664116	+	0.747630i	$0.731192\pi$
$920$	5.30908	0.175035
$921$	7.42094	0.244528
$922$	24.2611	0.798998
$923$	−21.3030	−0.701195
$924$	−0.982557	−0.0323238
$925$	46.3928	1.52539
$926$	−4.31881	−0.141925
$927$	−6.30743	−0.207163
$928$	−6.74177	−0.221310
$929$	11.3963	0.373899	0.186950	−	0.982370i	$-0.440140\pi$
$929$	11.3963	0.373899	0.186950	+	0.982370i	$0.440140\pi$
$930$	−0.282917	−0.00927722
$931$	3.50087	0.114736
$932$	−13.0365	−0.427024
$933$	10.4308	0.341490
$934$	27.4536	0.898310
$935$	−0.898335	−0.0293787
$936$	−3.89500	−0.127312
$937$	26.0594	0.851322	0.425661	−	0.904883i	$-0.360042\pi$
$937$	26.0594	0.851322	0.425661	+	0.904883i	$0.360042\pi$
$938$	25.0064	0.816488
$939$	12.3769	0.403905
$940$	5.64108	0.183992
$941$	39.7978	1.29737	0.648686	−	0.761056i	$-0.275319\pi$
$941$	39.7978	1.29737	0.648686	+	0.761056i	$0.275319\pi$
$942$	−5.48592	−0.178741
$943$	65.6767	2.13873
$944$	−9.42202	−0.306661
$945$	−7.48708	−0.243555
$946$	−1.25813	−0.0409053
$947$	−20.0473	−0.651450	−0.325725	−	0.945465i	$-0.605608\pi$
$947$	−20.0473	−0.651450	−0.325725	+	0.945465i	$0.605608\pi$
$948$	−5.59811	−0.181818
$949$	11.4439	0.371486
$950$	−10.2839	−0.333654
$951$	13.9087	0.451021
$952$	9.75538	0.316174
$953$	−34.4190	−1.11494	−0.557470	−	0.830197i	$-0.688228\pi$
$953$	−34.4190	−1.11494	−0.557470	+	0.830197i	$0.688228\pi$
$954$	−21.0020	−0.679965
$955$	−11.6281	−0.376277
$956$	−9.14910	−0.295903
$957$	2.26240	0.0731329
$958$	−32.9787	−1.06549
$959$	−19.5380	−0.630914
$960$	0.472496	0.0152497
$961$	−30.6415	−0.988435
$962$	−16.2150	−0.522793
$963$	43.6137	1.40543
$964$	7.72515	0.248810
$965$	7.81697	0.251637
$966$	19.3473	0.622488
$967$	−47.5266	−1.52835	−0.764176	−	0.645008i	$-0.776854\pi$
$967$	−47.5266	−1.52835	−0.764176	+	0.645008i	$0.776854\pi$
$968$	−10.8085	−0.347399
$969$	−5.68694	−0.182691
$970$	−5.00275	−0.160629
$971$	−33.8191	−1.08531	−0.542653	−	0.839957i	$-0.682580\pi$
$971$	−33.8191	−1.08531	−0.542653	+	0.839957i	$0.682580\pi$
$972$	−15.5588	−0.499049
$973$	17.6145	0.564696
$974$	39.9832	1.28115
$975$	5.72187	0.183246
$976$	4.26039	0.136372
$977$	−9.75881	−0.312212	−0.156106	−	0.987740i	$-0.549894\pi$
$977$	−9.75881	−0.312212	−0.156106	+	0.987740i	$0.549894\pi$
$978$	13.7744	0.440456
$979$	1.15010	0.0367574
$980$	−0.969115	−0.0309572
$981$	−7.42690	−0.237123
$982$	32.7809	1.04608
$983$	21.5120	0.686126	0.343063	−	0.939312i	$-0.388536\pi$
$983$	21.5120	0.686126	0.343063	+	0.939312i	$0.388536\pi$
$984$	5.84507	0.186334
$985$	5.76983	0.183842
$986$	−22.4623	−0.715346
$987$	20.5571	0.654341
$988$	3.59438	0.114353
$989$	24.7735	0.787751
$990$	0.650311	0.0206682
$991$	54.8476	1.74229	0.871145	−	0.491025i	$-0.163378\pi$
$991$	54.8476	1.74229	0.871145	+	0.491025i	$0.163378\pi$
$992$	−0.598772	−0.0190110
$993$	−5.58724	−0.177306
$994$	−38.6242	−1.22509
$995$	12.3925	0.392869
$996$	−11.7376	−0.371921
$997$	28.9217	0.915958	0.457979	−	0.888963i	$-0.348573\pi$
$997$	28.9217	0.915958	0.457979	+	0.888963i	$0.348573\pi$
$998$	−43.3993	−1.37378
$999$	−41.6719	−1.31844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.32	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.32	✓	69	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.766862 q^{3} +1.00000 q^{4} -0.616141 q^{5} -0.766862 q^{6} +2.92795 q^{7} +1.00000 q^{8} -2.41192 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.766862 q^{3} +1.00000 q^{4} -0.616141 q^{5} -0.766862 q^{6} +2.92795 q^{7} +1.00000 q^{8} -2.41192 q^{9} -0.616141 q^{10} +0.437600 q^{11} -0.766862 q^{12} +1.61489 q^{13} +2.92795 q^{14} +0.472496 q^{15} +1.00000 q^{16} +3.33181 q^{17} -2.41192 q^{18} +2.22577 q^{19} -0.616141 q^{20} -2.24533 q^{21} +0.437600 q^{22} -8.61666 q^{23} -0.766862 q^{24} -4.62037 q^{25} +1.61489 q^{26} +4.15020 q^{27} +2.92795 q^{28} -6.74177 q^{29} +0.472496 q^{30} -0.598772 q^{31} +1.00000 q^{32} -0.335579 q^{33} +3.33181 q^{34} -1.80403 q^{35} -2.41192 q^{36} -10.0409 q^{37} +2.22577 q^{38} -1.23840 q^{39} -0.616141 q^{40} -7.62206 q^{41} -2.24533 q^{42} -2.87507 q^{43} +0.437600 q^{44} +1.48608 q^{45} -8.61666 q^{46} -9.15550 q^{47} -0.766862 q^{48} +1.57288 q^{49} -4.62037 q^{50} -2.55504 q^{51} +1.61489 q^{52} +8.70758 q^{53} +4.15020 q^{54} -0.269623 q^{55} +2.92795 q^{56} -1.70686 q^{57} -6.74177 q^{58} -9.42202 q^{59} +0.472496 q^{60} +4.26039 q^{61} -0.598772 q^{62} -7.06198 q^{63} +1.00000 q^{64} -0.995002 q^{65} -0.335579 q^{66} +8.54059 q^{67} +3.33181 q^{68} +6.60779 q^{69} -1.80403 q^{70} -13.1916 q^{71} -2.41192 q^{72} +7.08650 q^{73} -10.0409 q^{74} +3.54319 q^{75} +2.22577 q^{76} +1.28127 q^{77} -1.23840 q^{78} +7.30002 q^{79} -0.616141 q^{80} +4.05313 q^{81} -7.62206 q^{82} +15.3060 q^{83} -2.24533 q^{84} -2.05287 q^{85} -2.87507 q^{86} +5.17001 q^{87} +0.437600 q^{88} +2.62820 q^{89} +1.48608 q^{90} +4.72832 q^{91} -8.61666 q^{92} +0.459176 q^{93} -9.15550 q^{94} -1.37139 q^{95} -0.766862 q^{96} +8.11949 q^{97} +1.57288 q^{98} -1.05546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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