LMFDB - Embedded newform 4022.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73177 q^{3} +1.00000 q^{4} +0.638996 q^{5} -1.73177 q^{6} +0.168919 q^{7} +1.00000 q^{8} -0.000964633 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.73177 q^{3} +1.00000 q^{4} +0.638996 q^{5} -1.73177 q^{6} +0.168919 q^{7} +1.00000 q^{8} -0.000964633 q^{9} +0.638996 q^{10} +0.464415 q^{11} -1.73177 q^{12} -2.40230 q^{13} +0.168919 q^{14} -1.10660 q^{15} +1.00000 q^{16} +5.16661 q^{17} -0.000964633 q^{18} -0.609350 q^{19} +0.638996 q^{20} -0.292528 q^{21} +0.464415 q^{22} -2.77010 q^{23} -1.73177 q^{24} -4.59168 q^{25} -2.40230 q^{26} +5.19699 q^{27} +0.168919 q^{28} +2.99910 q^{29} -1.10660 q^{30} +1.85295 q^{31} +1.00000 q^{32} -0.804261 q^{33} +5.16661 q^{34} +0.107938 q^{35} -0.000964633 q^{36} +4.53720 q^{37} -0.609350 q^{38} +4.16024 q^{39} +0.638996 q^{40} -3.94262 q^{41} -0.292528 q^{42} +2.57049 q^{43} +0.464415 q^{44} -0.000616396 q^{45} -2.77010 q^{46} +6.72279 q^{47} -1.73177 q^{48} -6.97147 q^{49} -4.59168 q^{50} -8.94739 q^{51} -2.40230 q^{52} +7.99260 q^{53} +5.19699 q^{54} +0.296759 q^{55} +0.168919 q^{56} +1.05525 q^{57} +2.99910 q^{58} +5.45010 q^{59} -1.10660 q^{60} +1.62623 q^{61} +1.85295 q^{62} -0.000162944 q^{63} +1.00000 q^{64} -1.53506 q^{65} -0.804261 q^{66} -6.88405 q^{67} +5.16661 q^{68} +4.79718 q^{69} +0.107938 q^{70} +7.90397 q^{71} -0.000964633 q^{72} -2.57324 q^{73} +4.53720 q^{74} +7.95175 q^{75} -0.609350 q^{76} +0.0784483 q^{77} +4.16024 q^{78} +6.80973 q^{79} +0.638996 q^{80} -8.99711 q^{81} -3.94262 q^{82} -3.11880 q^{83} -0.292528 q^{84} +3.30144 q^{85} +2.57049 q^{86} -5.19376 q^{87} +0.464415 q^{88} +15.0111 q^{89} -0.000616396 q^{90} -0.405794 q^{91} -2.77010 q^{92} -3.20889 q^{93} +6.72279 q^{94} -0.389372 q^{95} -1.73177 q^{96} -4.91004 q^{97} -6.97147 q^{98} -0.000447990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−1.73177	−0.999839	−0.499920	−	0.866072i	$-0.666637\pi$
$3$	−1.73177	−0.999839	−0.499920	+	0.866072i	$0.666637\pi$
$4$	1.00000	0.500000
$5$	0.638996	0.285768	0.142884	−	0.989739i	$-0.454362\pi$
$5$	0.638996	0.285768	0.142884	+	0.989739i	$0.454362\pi$
$6$	−1.73177	−0.706993
$7$	0.168919	0.0638452	0.0319226	−	0.999490i	$-0.489837\pi$
$7$	0.168919	0.0638452	0.0319226	+	0.999490i	$0.489837\pi$
$8$	1.00000	0.353553
$9$	−0.000964633 0	−0.000321544 0
$10$	0.638996	0.202068
$11$	0.464415	0.140026	0.0700132	−	0.997546i	$-0.477696\pi$
$11$	0.464415	0.140026	0.0700132	+	0.997546i	$0.477696\pi$
$12$	−1.73177	−0.499920
$13$	−2.40230	−0.666279	−0.333140	−	0.942878i	$-0.608108\pi$
$13$	−2.40230	−0.666279	−0.333140	+	0.942878i	$0.608108\pi$
$14$	0.168919	0.0451454
$15$	−1.10660	−0.285722
$16$	1.00000	0.250000
$17$	5.16661	1.25309	0.626543	−	0.779387i	$-0.284469\pi$
$17$	5.16661	1.25309	0.626543	+	0.779387i	$0.284469\pi$
$18$	−0.000964633 0	−0.000227366 0
$19$	−0.609350	−0.139794	−0.0698972	−	0.997554i	$-0.522267\pi$
$19$	−0.609350	−0.139794	−0.0698972	+	0.997554i	$0.522267\pi$
$20$	0.638996	0.142884
$21$	−0.292528	−0.0638349
$22$	0.464415	0.0990136
$23$	−2.77010	−0.577606	−0.288803	−	0.957389i	$-0.593257\pi$
$23$	−2.77010	−0.577606	−0.288803	+	0.957389i	$0.593257\pi$
$24$	−1.73177	−0.353497
$25$	−4.59168	−0.918337
$26$	−2.40230	−0.471131
$27$	5.19699	1.00016
$28$	0.168919	0.0319226
$29$	2.99910	0.556919	0.278460	−	0.960448i	$-0.410176\pi$
$29$	2.99910	0.556919	0.278460	+	0.960448i	$0.410176\pi$
$30$	−1.10660	−0.202036
$31$	1.85295	0.332800	0.166400	−	0.986058i	$-0.446786\pi$
$31$	1.85295	0.332800	0.166400	+	0.986058i	$0.446786\pi$
$32$	1.00000	0.176777
$33$	−0.804261	−0.140004
$34$	5.16661	0.886066
$35$	0.107938	0.0182449
$36$	−0.000964633 0	−0.000160772 0
$37$	4.53720	0.745911	0.372956	−	0.927849i	$-0.378344\pi$
$37$	4.53720	0.745911	0.372956	+	0.927849i	$0.378344\pi$
$38$	−0.609350	−0.0988496
$39$	4.16024	0.666172
$40$	0.638996	0.101034
$41$	−3.94262	−0.615733	−0.307867	−	0.951430i	$-0.599615\pi$
$41$	−3.94262	−0.615733	−0.307867	+	0.951430i	$0.599615\pi$
$42$	−0.292528	−0.0451381
$43$	2.57049	0.391996	0.195998	−	0.980604i	$-0.437205\pi$
$43$	2.57049	0.391996	0.195998	+	0.980604i	$0.437205\pi$
$44$	0.464415	0.0700132
$45$	−0.000616396 0	−9.18870e−5 0
$46$	−2.77010	−0.408429
$47$	6.72279	0.980620	0.490310	−	0.871548i	$-0.336884\pi$
$47$	6.72279	0.980620	0.490310	+	0.871548i	$0.336884\pi$
$48$	−1.73177	−0.249960
$49$	−6.97147	−0.995924
$50$	−4.59168	−0.649362
$51$	−8.94739	−1.25289
$52$	−2.40230	−0.333140
$53$	7.99260	1.09787	0.548934	−	0.835866i	$-0.315034\pi$
$53$	7.99260	1.09787	0.548934	+	0.835866i	$0.315034\pi$
$54$	5.19699	0.707220
$55$	0.296759	0.0400150
$56$	0.168919	0.0225727
$57$	1.05525	0.139772
$58$	2.99910	0.393801
$59$	5.45010	0.709542	0.354771	−	0.934953i	$-0.384559\pi$
$59$	5.45010	0.709542	0.354771	+	0.934953i	$0.384559\pi$
$60$	−1.10660	−0.142861
$61$	1.62623	0.208218	0.104109	−	0.994566i	$-0.466801\pi$
$61$	1.62623	0.208218	0.104109	+	0.994566i	$0.466801\pi$
$62$	1.85295	0.235325
$63$	−0.000162944 0	−2.05291e−5 0
$64$	1.00000	0.125000
$65$	−1.53506	−0.190401
$66$	−0.804261	−0.0989977
$67$	−6.88405	−0.841021	−0.420510	−	0.907288i	$-0.638149\pi$
$67$	−6.88405	−0.841021	−0.420510	+	0.907288i	$0.638149\pi$
$68$	5.16661	0.626543
$69$	4.79718	0.577513
$70$	0.107938	0.0129011
$71$	7.90397	0.938029	0.469014	−	0.883191i	$-0.344609\pi$
$71$	7.90397	0.938029	0.469014	+	0.883191i	$0.344609\pi$
$72$	−0.000964633 0	−0.000113683 0
$73$	−2.57324	−0.301174	−0.150587	−	0.988597i	$-0.548116\pi$
$73$	−2.57324	−0.301174	−0.150587	+	0.988597i	$0.548116\pi$
$74$	4.53720	0.527439
$75$	7.95175	0.918189
$76$	−0.609350	−0.0698972
$77$	0.0784483	0.00894002
$78$	4.16024	0.471055
$79$	6.80973	0.766154	0.383077	−	0.923716i	$-0.374864\pi$
$79$	6.80973	0.766154	0.383077	+	0.923716i	$0.374864\pi$
$80$	0.638996	0.0714419
$81$	−8.99711	−0.999678
$82$	−3.94262	−0.435389
$83$	−3.11880	−0.342333	−0.171167	−	0.985242i	$-0.554754\pi$
$83$	−3.11880	−0.342333	−0.171167	+	0.985242i	$0.554754\pi$
$84$	−0.292528	−0.0319175
$85$	3.30144	0.358092
$86$	2.57049	0.277183
$87$	−5.19376	−0.556830
$88$	0.464415	0.0495068
$89$	15.0111	1.59117	0.795586	−	0.605841i	$-0.207163\pi$
$89$	15.0111	1.59117	0.795586	+	0.605841i	$0.207163\pi$
$90$	−0.000616396 0	−6.49739e−5 0
$91$	−0.405794	−0.0425387
$92$	−2.77010	−0.288803
$93$	−3.20889	−0.332747
$94$	6.72279	0.693403
$95$	−0.389372	−0.0399487
$96$	−1.73177	−0.176748
$97$	−4.91004	−0.498539	−0.249270	−	0.968434i	$-0.580191\pi$
$97$	−4.91004	−0.498539	−0.249270	+	0.968434i	$0.580191\pi$
$98$	−6.97147	−0.704224
$99$	−0.000447990 0	−4.50247e−5 0
$100$	−4.59168	−0.459168
$101$	7.29988	0.726366	0.363183	−	0.931718i	$-0.381690\pi$
$101$	7.29988	0.726366	0.363183	+	0.931718i	$0.381690\pi$
$102$	−8.94739	−0.885924
$103$	5.74667	0.566236	0.283118	−	0.959085i	$-0.408631\pi$
$103$	5.74667	0.566236	0.283118	+	0.959085i	$0.408631\pi$
$104$	−2.40230	−0.235565
$105$	−0.186925	−0.0182420
$106$	7.99260	0.776310
$107$	3.47309	0.335757	0.167878	−	0.985808i	$-0.446308\pi$
$107$	3.47309	0.335757	0.167878	+	0.985808i	$0.446308\pi$
$108$	5.19699	0.500080
$109$	16.5005	1.58046	0.790229	−	0.612812i	$-0.209962\pi$
$109$	16.5005	1.58046	0.790229	+	0.612812i	$0.209962\pi$
$110$	0.296759	0.0282949
$111$	−7.85740	−0.745791
$112$	0.168919	0.0159613
$113$	−9.18200	−0.863770	−0.431885	−	0.901929i	$-0.642151\pi$
$113$	−9.18200	−0.863770	−0.431885	+	0.901929i	$0.642151\pi$
$114$	1.05525	0.0988337
$115$	−1.77008	−0.165061
$116$	2.99910	0.278460
$117$	0.00231734	0.000214238 0
$118$	5.45010	0.501722
$119$	0.872736	0.0800036
$120$	−1.10660	−0.101018
$121$	−10.7843	−0.980393
$122$	1.62623	0.147232
$123$	6.82771	0.615634
$124$	1.85295	0.166400
$125$	−6.12905	−0.548199
$126$	−0.000162944 0	−1.45162e−5 0
$127$	6.25652	0.555176	0.277588	−	0.960700i	$-0.410465\pi$
$127$	6.25652	0.555176	0.277588	+	0.960700i	$0.410465\pi$
$128$	1.00000	0.0883883
$129$	−4.45151	−0.391933
$130$	−1.53506	−0.134634
$131$	−21.8777	−1.91146	−0.955731	−	0.294241i	$-0.904933\pi$
$131$	−21.8777	−1.91146	−0.955731	+	0.294241i	$0.904933\pi$
$132$	−0.804261	−0.0700020
$133$	−0.102930	−0.00892520
$134$	−6.88405	−0.594692
$135$	3.32085	0.285814
$136$	5.16661	0.443033
$137$	10.3090	0.880758	0.440379	−	0.897812i	$-0.354844\pi$
$137$	10.3090	0.880758	0.440379	+	0.897812i	$0.354844\pi$
$138$	4.79718	0.408363
$139$	10.7601	0.912658	0.456329	−	0.889811i	$-0.349164\pi$
$139$	10.7601	0.912658	0.456329	+	0.889811i	$0.349164\pi$
$140$	0.107938	0.00912245
$141$	−11.6423	−0.980462
$142$	7.90397	0.663286
$143$	−1.11567	−0.0932967
$144$	−0.000964633 0	−8.03861e−5 0
$145$	1.91641	0.159150
$146$	−2.57324	−0.212962
$147$	12.0730	0.995764
$148$	4.53720	0.372956
$149$	13.8424	1.13401	0.567006	−	0.823714i	$-0.308102\pi$
$149$	13.8424	1.13401	0.567006	+	0.823714i	$0.308102\pi$
$150$	7.95175	0.649258
$151$	14.0609	1.14426	0.572129	−	0.820164i	$-0.306118\pi$
$151$	14.0609	1.14426	0.572129	+	0.820164i	$0.306118\pi$
$152$	−0.609350	−0.0494248
$153$	−0.00498388	−0.000402923 0
$154$	0.0784483	0.00632155
$155$	1.18403	0.0951036
$156$	4.16024	0.333086
$157$	−18.7876	−1.49941	−0.749707	−	0.661769i	$-0.769806\pi$
$157$	−18.7876	−1.49941	−0.749707	+	0.661769i	$0.769806\pi$
$158$	6.80973	0.541753
$159$	−13.8414	−1.09769
$160$	0.638996	0.0505171
$161$	−0.467921	−0.0368774
$162$	−8.99711	−0.706879
$163$	22.1114	1.73190	0.865948	−	0.500134i	$-0.166716\pi$
$163$	22.1114	1.73190	0.865948	+	0.500134i	$0.166716\pi$
$164$	−3.94262	−0.307867
$165$	−0.513920	−0.0400086
$166$	−3.11880	−0.242066
$167$	15.2555	1.18051	0.590253	−	0.807218i	$-0.299028\pi$
$167$	15.2555	1.18051	0.590253	+	0.807218i	$0.299028\pi$
$168$	−0.292528	−0.0225691
$169$	−7.22894	−0.556072
$170$	3.30144	0.253209
$171$	0.000587799 0	4.49501e−5 0
$172$	2.57049	0.195998
$173$	−4.42805	−0.336658	−0.168329	−	0.985731i	$-0.553837\pi$
$173$	−4.42805	−0.336658	−0.168329	+	0.985731i	$0.553837\pi$
$174$	−5.19376	−0.393738
$175$	−0.775621	−0.0586314
$176$	0.464415	0.0350066
$177$	−9.43833	−0.709428
$178$	15.0111	1.12513
$179$	20.7555	1.55134	0.775669	−	0.631139i	$-0.217412\pi$
$179$	20.7555	1.55134	0.775669	+	0.631139i	$0.217412\pi$
$180$	−0.000616396 0	−4.59435e−5 0
$181$	19.5602	1.45390	0.726949	−	0.686691i	$-0.240937\pi$
$181$	19.5602	1.45390	0.726949	+	0.686691i	$0.240937\pi$
$182$	−0.405794	−0.0300794
$183$	−2.81627	−0.208184
$184$	−2.77010	−0.204215
$185$	2.89925	0.213157
$186$	−3.20889	−0.235287
$187$	2.39945	0.175465
$188$	6.72279	0.490310
$189$	0.877867	0.0638555
$190$	−0.389372	−0.0282480
$191$	14.3966	1.04170	0.520851	−	0.853647i	$-0.325615\pi$
$191$	14.3966	1.04170	0.520851	+	0.853647i	$0.325615\pi$
$192$	−1.73177	−0.124980
$193$	−4.42194	−0.318298	−0.159149	−	0.987255i	$-0.550875\pi$
$193$	−4.42194	−0.318298	−0.159149	+	0.987255i	$0.550875\pi$
$194$	−4.91004	−0.352521
$195$	2.65838	0.190370
$196$	−6.97147	−0.497962
$197$	9.72302	0.692736	0.346368	−	0.938099i	$-0.387415\pi$
$197$	9.72302	0.692736	0.346368	+	0.938099i	$0.387415\pi$
$198$	−0.000447990 0	−3.18373e−5 0
$199$	−1.24385	−0.0881741	−0.0440871	−	0.999028i	$-0.514038\pi$
$199$	−1.24385	−0.0881741	−0.0440871	+	0.999028i	$0.514038\pi$
$200$	−4.59168	−0.324681
$201$	11.9216	0.840886
$202$	7.29988	0.513618
$203$	0.506604	0.0355566
$204$	−8.94739	−0.626443
$205$	−2.51932	−0.175957
$206$	5.74667	0.400390
$207$	0.00267213	0.000185726 0
$208$	−2.40230	−0.166570
$209$	−0.282991	−0.0195749
$210$	−0.186925	−0.0128990
$211$	−15.6794	−1.07942	−0.539708	−	0.841852i	$-0.681465\pi$
$211$	−15.6794	−1.07942	−0.539708	+	0.841852i	$0.681465\pi$
$212$	7.99260	0.548934
$213$	−13.6879	−0.937878
$214$	3.47309	0.237416
$215$	1.64253	0.112020
$216$	5.19699	0.353610
$217$	0.312998	0.0212477
$218$	16.5005	1.11755
$219$	4.45626	0.301126
$220$	0.296759	0.0200075
$221$	−12.4118	−0.834906
$222$	−7.85740	−0.527354
$223$	13.9900	0.936842	0.468421	−	0.883505i	$-0.344823\pi$
$223$	13.9900	0.936842	0.468421	+	0.883505i	$0.344823\pi$
$224$	0.168919	0.0112863
$225$	0.00442929	0.000295286 0
$226$	−9.18200	−0.610778
$227$	−23.8379	−1.58218	−0.791090	−	0.611700i	$-0.790486\pi$
$227$	−23.8379	−1.58218	−0.791090	+	0.611700i	$0.790486\pi$
$228$	1.05525	0.0698860
$229$	−15.3404	−1.01372	−0.506862	−	0.862027i	$-0.669194\pi$
$229$	−15.3404	−1.01372	−0.506862	+	0.862027i	$0.669194\pi$
$230$	−1.77008	−0.116716
$231$	−0.135855	−0.00893858
$232$	2.99910	0.196901
$233$	8.67901	0.568581	0.284290	−	0.958738i	$-0.408242\pi$
$233$	8.67901	0.568581	0.284290	+	0.958738i	$0.408242\pi$
$234$	0.00231734	0.000151489 0
$235$	4.29584	0.280230
$236$	5.45010	0.354771
$237$	−11.7929	−0.766031
$238$	0.872736	0.0565711
$239$	−6.37115	−0.412115	−0.206058	−	0.978540i	$-0.566063\pi$
$239$	−6.37115	−0.412115	−0.206058	+	0.978540i	$0.566063\pi$
$240$	−1.10660	−0.0714304
$241$	−6.27475	−0.404192	−0.202096	−	0.979366i	$-0.564775\pi$
$241$	−6.27475	−0.404192	−0.202096	+	0.979366i	$0.564775\pi$
$242$	−10.7843	−0.693242
$243$	−0.0100248	−0.000643088 0
$244$	1.62623	0.104109
$245$	−4.45474	−0.284603
$246$	6.82771	0.435319
$247$	1.46384	0.0931421
$248$	1.85295	0.117663
$249$	5.40106	0.342278
$250$	−6.12905	−0.387635
$251$	25.6398	1.61837	0.809185	−	0.587554i	$-0.199909\pi$
$251$	25.6398	1.61837	0.809185	+	0.587554i	$0.199909\pi$
$252$	−0.000162944 0	−1.02645e−5 0
$253$	−1.28648	−0.0808801
$254$	6.25652	0.392569
$255$	−5.71735	−0.358034
$256$	1.00000	0.0625000
$257$	2.69015	0.167807	0.0839035	−	0.996474i	$-0.473261\pi$
$257$	2.69015	0.167807	0.0839035	+	0.996474i	$0.473261\pi$
$258$	−4.45151	−0.277139
$259$	0.766417	0.0476228
$260$	−1.53506	−0.0952005
$261$	−0.00289303	−0.000179074 0
$262$	−21.8777	−1.35161
$263$	−0.640225	−0.0394780	−0.0197390	−	0.999805i	$-0.506284\pi$
$263$	−0.640225	−0.0394780	−0.0197390	+	0.999805i	$0.506284\pi$
$264$	−0.804261	−0.0494989
$265$	5.10724	0.313735
$266$	−0.102930	−0.00631107
$267$	−25.9958	−1.59092
$268$	−6.88405	−0.420510
$269$	1.78005	0.108531	0.0542657	−	0.998527i	$-0.482718\pi$
$269$	1.78005	0.108531	0.0542657	+	0.998527i	$0.482718\pi$
$270$	3.32085	0.202101
$271$	23.0397	1.39956	0.699782	−	0.714357i	$-0.253281\pi$
$271$	23.0397	1.39956	0.699782	+	0.714357i	$0.253281\pi$
$272$	5.16661	0.313272
$273$	0.702742	0.0425319
$274$	10.3090	0.622790
$275$	−2.13245	−0.128591
$276$	4.79718	0.288757
$277$	−20.4128	−1.22649	−0.613244	−	0.789893i	$-0.710136\pi$
$277$	−20.4128	−1.22649	−0.613244	+	0.789893i	$0.710136\pi$
$278$	10.7601	0.645347
$279$	−0.00178742	−0.000107010 0
$280$	0.107938	0.00645055
$281$	1.58203	0.0943762	0.0471881	−	0.998886i	$-0.484974\pi$
$281$	1.58203	0.0943762	0.0471881	+	0.998886i	$0.484974\pi$
$282$	−11.6423	−0.693291
$283$	−4.24059	−0.252077	−0.126038	−	0.992025i	$-0.540226\pi$
$283$	−4.24059	−0.252077	−0.126038	+	0.992025i	$0.540226\pi$
$284$	7.90397	0.469014
$285$	0.674304	0.0399423
$286$	−1.11567	−0.0659707
$287$	−0.665981	−0.0393116
$288$	−0.000964633 0	−5.68415e−5 0
$289$	9.69385	0.570226
$290$	1.91641	0.112536
$291$	8.50308	0.498459
$292$	−2.57324	−0.150587
$293$	23.7697	1.38864	0.694321	−	0.719666i	$-0.255705\pi$
$293$	23.7697	1.38864	0.694321	+	0.719666i	$0.255705\pi$
$294$	12.0730	0.704111
$295$	3.48259	0.202764
$296$	4.53720	0.263719
$297$	2.41356	0.140049
$298$	13.8424	0.801867
$299$	6.65462	0.384847
$300$	7.95175	0.459095
$301$	0.434204	0.0250271
$302$	14.0609	0.809113
$303$	−12.6417	−0.726249
$304$	−0.609350	−0.0349486
$305$	1.03916	0.0595019
$306$	−0.00498388	−0.000284909 0
$307$	−1.79874	−0.102660	−0.0513299	−	0.998682i	$-0.516346\pi$
$307$	−1.79874	−0.102660	−0.0513299	+	0.998682i	$0.516346\pi$
$308$	0.0784483	0.00447001
$309$	−9.95193	−0.566145
$310$	1.18403	0.0672484
$311$	25.3325	1.43647	0.718236	−	0.695800i	$-0.244950\pi$
$311$	25.3325	1.43647	0.718236	+	0.695800i	$0.244950\pi$
$312$	4.16024	0.235527
$313$	14.6579	0.828515	0.414258	−	0.910160i	$-0.364041\pi$
$313$	14.6579	0.828515	0.414258	+	0.910160i	$0.364041\pi$
$314$	−18.7876	−1.06025
$315$	−0.000104121 0	−5.86654e−6 0
$316$	6.80973	0.383077
$317$	−14.8186	−0.832297	−0.416148	−	0.909297i	$-0.636620\pi$
$317$	−14.8186	−0.832297	−0.416148	+	0.909297i	$0.636620\pi$
$318$	−13.8414	−0.776185
$319$	1.39283	0.0779834
$320$	0.638996	0.0357210
$321$	−6.01461	−0.335703
$322$	−0.467921	−0.0260762
$323$	−3.14827	−0.175174
$324$	−8.99711	−0.499839
$325$	11.0306	0.611869
$326$	22.1114	1.22464
$327$	−28.5750	−1.58020
$328$	−3.94262	−0.217695
$329$	1.13560	0.0626079
$330$	−0.513920	−0.0282904
$331$	−25.9904	−1.42856	−0.714281	−	0.699859i	$-0.753246\pi$
$331$	−25.9904	−1.42856	−0.714281	+	0.699859i	$0.753246\pi$
$332$	−3.11880	−0.171167
$333$	−0.00437673	−0.000239843 0
$334$	15.2555	0.834744
$335$	−4.39888	−0.240337
$336$	−0.292528	−0.0159587
$337$	18.8881	1.02890	0.514449	−	0.857521i	$-0.327996\pi$
$337$	18.8881	1.02890	0.514449	+	0.857521i	$0.327996\pi$
$338$	−7.22894	−0.393202
$339$	15.9011	0.863631
$340$	3.30144	0.179046
$341$	0.860540	0.0466008
$342$	0.000587799 0	3.17845e−5 0
$343$	−2.36004	−0.127430
$344$	2.57049	0.138592
$345$	3.06538	0.165035
$346$	−4.42805	−0.238053
$347$	23.8946	1.28273	0.641364	−	0.767237i	$-0.278369\pi$
$347$	23.8946	1.28273	0.641364	+	0.767237i	$0.278369\pi$
$348$	−5.19376	−0.278415
$349$	−10.4702	−0.560459	−0.280229	−	0.959933i	$-0.590411\pi$
$349$	−10.4702	−0.560459	−0.280229	+	0.959933i	$0.590411\pi$
$350$	−0.775621	−0.0414587
$351$	−12.4847	−0.666386
$352$	0.464415	0.0247534
$353$	−9.45917	−0.503461	−0.251730	−	0.967797i	$-0.581000\pi$
$353$	−9.45917	−0.503461	−0.251730	+	0.967797i	$0.581000\pi$
$354$	−9.43833	−0.501641
$355$	5.05061	0.268058
$356$	15.0111	0.795586
$357$	−1.51138	−0.0799907
$358$	20.7555	1.09696
$359$	10.4942	0.553862	0.276931	−	0.960890i	$-0.410683\pi$
$359$	10.4942	0.553862	0.276931	+	0.960890i	$0.410683\pi$
$360$	−0.000616396 0	−3.24869e−5 0
$361$	−18.6287	−0.980458
$362$	19.5602	1.02806
$363$	18.6760	0.980235
$364$	−0.405794	−0.0212694
$365$	−1.64429	−0.0860659
$366$	−2.81627	−0.147209
$367$	16.4759	0.860035	0.430017	−	0.902821i	$-0.358507\pi$
$367$	16.4759	0.860035	0.430017	+	0.902821i	$0.358507\pi$
$368$	−2.77010	−0.144401
$369$	0.00380318	0.000197985 0
$370$	2.89925	0.150725
$371$	1.35010	0.0700936
$372$	−3.20889	−0.166373
$373$	8.31136	0.430346	0.215173	−	0.976576i	$-0.430969\pi$
$373$	8.31136	0.430346	0.215173	+	0.976576i	$0.430969\pi$
$374$	2.39945	0.124073
$375$	10.6141	0.548111
$376$	6.72279	0.346701
$377$	−7.20475	−0.371064
$378$	0.877867	0.0451526
$379$	28.5039	1.46415	0.732075	−	0.681224i	$-0.238552\pi$
$379$	28.5039	1.46415	0.732075	+	0.681224i	$0.238552\pi$
$380$	−0.389372	−0.0199744
$381$	−10.8349	−0.555087
$382$	14.3966	0.736595
$383$	−13.4738	−0.688479	−0.344239	−	0.938882i	$-0.611863\pi$
$383$	−13.4738	−0.688479	−0.344239	+	0.938882i	$0.611863\pi$
$384$	−1.73177	−0.0883741
$385$	0.0501282	0.00255477
$386$	−4.42194	−0.225071
$387$	−0.00247958	−0.000126044 0
$388$	−4.91004	−0.249270
$389$	−9.81279	−0.497528	−0.248764	−	0.968564i	$-0.580024\pi$
$389$	−9.81279	−0.497528	−0.248764	+	0.968564i	$0.580024\pi$
$390$	2.65838	0.134612
$391$	−14.3120	−0.723790
$392$	−6.97147	−0.352112
$393$	37.8872	1.91116
$394$	9.72302	0.489839
$395$	4.35139	0.218942
$396$	−0.000447990 0	−2.25123e−5 0
$397$	−31.2956	−1.57068	−0.785342	−	0.619063i	$-0.787513\pi$
$397$	−31.2956	−1.57068	−0.785342	+	0.619063i	$0.787513\pi$
$398$	−1.24385	−0.0623485
$399$	0.178252	0.00892377
$400$	−4.59168	−0.229584
$401$	−29.7104	−1.48367	−0.741833	−	0.670585i	$-0.766043\pi$
$401$	−29.7104	−1.48367	−0.741833	+	0.670585i	$0.766043\pi$
$402$	11.9216	0.594596
$403$	−4.45136	−0.221738
$404$	7.29988	0.363183
$405$	−5.74911	−0.285676
$406$	0.506604	0.0251423
$407$	2.10714	0.104447
$408$	−8.94739	−0.442962
$409$	25.5211	1.26194	0.630970	−	0.775807i	$-0.282657\pi$
$409$	25.5211	1.26194	0.630970	+	0.775807i	$0.282657\pi$
$410$	−2.51932	−0.124420
$411$	−17.8528	−0.880616
$412$	5.74667	0.283118
$413$	0.920622	0.0453009
$414$	0.00267213	0.000131328 0
$415$	−1.99290	−0.0978278
$416$	−2.40230	−0.117783
$417$	−18.6340	−0.912511
$418$	−0.282991	−0.0138416
$419$	−6.51945	−0.318496	−0.159248	−	0.987239i	$-0.550907\pi$
$419$	−6.51945	−0.318496	−0.159248	+	0.987239i	$0.550907\pi$
$420$	−0.186925	−0.00912098
$421$	−24.4896	−1.19355	−0.596775	−	0.802409i	$-0.703551\pi$
$421$	−24.4896	−1.19355	−0.596775	+	0.802409i	$0.703551\pi$
$422$	−15.6794	−0.763262
$423$	−0.00648502	−0.000315313 0
$424$	7.99260	0.388155
$425$	−23.7234	−1.15076
$426$	−13.6879	−0.663180
$427$	0.274701	0.0132937
$428$	3.47309	0.167878
$429$	1.93208	0.0932817
$430$	1.64253	0.0792100
$431$	−21.3997	−1.03079	−0.515393	−	0.856954i	$-0.672354\pi$
$431$	−21.3997	−1.03079	−0.515393	+	0.856954i	$0.672354\pi$
$432$	5.19699	0.250040
$433$	36.1281	1.73621	0.868104	−	0.496383i	$-0.165339\pi$
$433$	36.1281	1.73621	0.868104	+	0.496383i	$0.165339\pi$
$434$	0.312998	0.0150244
$435$	−3.31879	−0.159124
$436$	16.5005	0.790229
$437$	1.68796	0.0807461
$438$	4.45626	0.212928
$439$	−14.9880	−0.715340	−0.357670	−	0.933848i	$-0.616429\pi$
$439$	−14.9880	−0.715340	−0.357670	+	0.933848i	$0.616429\pi$
$440$	0.296759	0.0141475
$441$	0.00672490	0.000320234 0
$442$	−12.4118	−0.590367
$443$	−16.9918	−0.807304	−0.403652	−	0.914913i	$-0.632259\pi$
$443$	−16.9918	−0.807304	−0.403652	+	0.914913i	$0.632259\pi$
$444$	−7.85740	−0.372896
$445$	9.59202	0.454705
$446$	13.9900	0.662447
$447$	−23.9718	−1.13383
$448$	0.168919	0.00798065
$449$	−32.9246	−1.55381	−0.776904	−	0.629620i	$-0.783211\pi$
$449$	−32.9246	−1.55381	−0.776904	+	0.629620i	$0.783211\pi$
$450$	0.00442929	0.000208799 0
$451$	−1.83101	−0.0862189
$452$	−9.18200	−0.431885
$453$	−24.3502	−1.14407
$454$	−23.8379	−1.11877
$455$	−0.259301	−0.0121562
$456$	1.05525	0.0494168
$457$	9.98962	0.467295	0.233647	−	0.972321i	$-0.424934\pi$
$457$	9.98962	0.467295	0.233647	+	0.972321i	$0.424934\pi$
$458$	−15.3404	−0.716810
$459$	26.8508	1.25329
$460$	−1.77008	−0.0825306
$461$	5.71130	0.266002	0.133001	−	0.991116i	$-0.457539\pi$
$461$	5.71130	0.266002	0.133001	+	0.991116i	$0.457539\pi$
$462$	−0.135855	−0.00632053
$463$	−11.8882	−0.552490	−0.276245	−	0.961087i	$-0.589090\pi$
$463$	−11.8882	−0.552490	−0.276245	+	0.961087i	$0.589090\pi$
$464$	2.99910	0.139230
$465$	−2.05047	−0.0950883
$466$	8.67901	0.402047
$467$	−22.4953	−1.04096	−0.520479	−	0.853874i	$-0.674247\pi$
$467$	−22.4953	−1.04096	−0.520479	+	0.853874i	$0.674247\pi$
$468$	0.00231734	0.000107119 0
$469$	−1.16284	−0.0536951
$470$	4.29584	0.198152
$471$	32.5359	1.49917
$472$	5.45010	0.250861
$473$	1.19378	0.0548899
$474$	−11.7929	−0.541666
$475$	2.79794	0.128378
$476$	0.872736	0.0400018
$477$	−0.00770992	−0.000353013 0
$478$	−6.37115	−0.291410
$479$	10.8105	0.493946	0.246973	−	0.969022i	$-0.420564\pi$
$479$	10.8105	0.493946	0.246973	+	0.969022i	$0.420564\pi$
$480$	−1.10660	−0.0505090
$481$	−10.8997	−0.496985
$482$	−6.27475	−0.285807
$483$	0.810333	0.0368714
$484$	−10.7843	−0.490196
$485$	−3.13750	−0.142466
$486$	−0.0100248	−0.000454732 0
$487$	−0.768909	−0.0348426	−0.0174213	−	0.999848i	$-0.505546\pi$
$487$	−0.768909	−0.0348426	−0.0174213	+	0.999848i	$0.505546\pi$
$488$	1.62623	0.0736161
$489$	−38.2918	−1.73162
$490$	−4.45474	−0.201245
$491$	−29.9174	−1.35015	−0.675077	−	0.737747i	$-0.735890\pi$
$491$	−29.9174	−1.35015	−0.675077	+	0.737747i	$0.735890\pi$
$492$	6.82771	0.307817
$493$	15.4952	0.697868
$494$	1.46384	0.0658614
$495$	−0.000286264 0	−1.28666e−5 0
$496$	1.85295	0.0832001
$497$	1.33513	0.0598886
$498$	5.40106	0.242027
$499$	24.2989	1.08777	0.543885	−	0.839160i	$-0.316953\pi$
$499$	24.2989	1.08777	0.543885	+	0.839160i	$0.316953\pi$
$500$	−6.12905	−0.274099
$501$	−26.4191	−1.18032
$502$	25.6398	1.14436
$503$	−9.80599	−0.437228	−0.218614	−	0.975811i	$-0.570154\pi$
$503$	−9.80599	−0.437228	−0.218614	+	0.975811i	$0.570154\pi$
$504$	−0.000162944 0	−7.25812e−6 0
$505$	4.66460	0.207572
$506$	−1.28648	−0.0571909
$507$	12.5189	0.555983
$508$	6.25652	0.277588
$509$	−4.09023	−0.181296	−0.0906480	−	0.995883i	$-0.528894\pi$
$509$	−4.09023	−0.181296	−0.0906480	+	0.995883i	$0.528894\pi$
$510$	−5.71735	−0.253168
$511$	−0.434667	−0.0192285
$512$	1.00000	0.0441942
$513$	−3.16678	−0.139817
$514$	2.69015	0.118657
$515$	3.67210	0.161812
$516$	−4.45151	−0.195967
$517$	3.12217	0.137313
$518$	0.766417	0.0336744
$519$	7.66838	0.336604
$520$	−1.53506	−0.0673170
$521$	24.5603	1.07601	0.538004	−	0.842942i	$-0.319179\pi$
$521$	24.5603	1.07601	0.538004	+	0.842942i	$0.319179\pi$
$522$	−0.00289303	−0.000126625 0
$523$	27.7534	1.21357	0.606786	−	0.794865i	$-0.292459\pi$
$523$	27.7534	1.21357	0.606786	+	0.794865i	$0.292459\pi$
$524$	−21.8777	−0.955731
$525$	1.34320	0.0586220
$526$	−0.640225	−0.0279151
$527$	9.57348	0.417028
$528$	−0.804261	−0.0350010
$529$	−15.3265	−0.666371
$530$	5.10724	0.221844
$531$	−0.00525734	−0.000228149 0
$532$	−0.102930	−0.00446260
$533$	9.47136	0.410250
$534$	−25.9958	−1.12495
$535$	2.21929	0.0959484
$536$	−6.88405	−0.297346
$537$	−35.9438	−1.55109
$538$	1.78005	0.0767434
$539$	−3.23765	−0.139456
$540$	3.32085	0.142907
$541$	−40.9214	−1.75935	−0.879675	−	0.475575i	$-0.842240\pi$
$541$	−40.9214	−1.75935	−0.879675	+	0.475575i	$0.842240\pi$
$542$	23.0397	0.989641
$543$	−33.8738	−1.45366
$544$	5.16661	0.221517
$545$	10.5437	0.451644
$546$	0.702742	0.0300746
$547$	14.5885	0.623758	0.311879	−	0.950122i	$-0.399042\pi$
$547$	14.5885	0.623758	0.311879	+	0.950122i	$0.399042\pi$
$548$	10.3090	0.440379
$549$	−0.00156872	−6.69513e−5 0
$550$	−2.13245	−0.0909279
$551$	−1.82750	−0.0778542
$552$	4.79718	0.204182
$553$	1.15029	0.0489153
$554$	−20.4128	−0.867259
$555$	−5.02085	−0.213123
$556$	10.7601	0.456329
$557$	−23.5417	−0.997496	−0.498748	−	0.866747i	$-0.666207\pi$
$557$	−23.5417	−0.997496	−0.498748	+	0.866747i	$0.666207\pi$
$558$	−0.00178742	−7.56675e−5 0
$559$	−6.17510	−0.261179
$560$	0.107938	0.00456122
$561$	−4.15530	−0.175437
$562$	1.58203	0.0667341
$563$	17.9313	0.755716	0.377858	−	0.925864i	$-0.376661\pi$
$563$	17.9313	0.755716	0.377858	+	0.925864i	$0.376661\pi$
$564$	−11.6423	−0.490231
$565$	−5.86726	−0.246838
$566$	−4.24059	−0.178245
$567$	−1.51978	−0.0638247
$568$	7.90397	0.331643
$569$	−36.4403	−1.52766	−0.763828	−	0.645420i	$-0.776682\pi$
$569$	−36.4403	−1.52766	−0.763828	+	0.645420i	$0.776682\pi$
$570$	0.674304	0.0282435
$571$	−43.6076	−1.82492	−0.912460	−	0.409167i	$-0.865819\pi$
$571$	−43.6076	−1.82492	−0.912460	+	0.409167i	$0.865819\pi$
$572$	−1.11567	−0.0466484
$573$	−24.9317	−1.04154
$574$	−0.665981	−0.0277975
$575$	12.7194	0.530437
$576$	−0.000964633 0	−4.01930e−5 0
$577$	7.58600	0.315809	0.157905	−	0.987454i	$-0.449526\pi$
$577$	7.58600	0.315809	0.157905	+	0.987454i	$0.449526\pi$
$578$	9.69385	0.403211
$579$	7.65780	0.318247
$580$	1.91641	0.0795748
$581$	−0.526824	−0.0218563
$582$	8.50308	0.352464
$583$	3.71188	0.153731
$584$	−2.57324	−0.106481
$585$	0.00148077	6.12224e−5 0
$586$	23.7697	0.981918
$587$	−9.32429	−0.384855	−0.192427	−	0.981311i	$-0.561636\pi$
$587$	−9.32429	−0.384855	−0.192427	+	0.981311i	$0.561636\pi$
$588$	12.0730	0.497882
$589$	−1.12910	−0.0465236
$590$	3.48259	0.143376
$591$	−16.8381	−0.692625
$592$	4.53720	0.186478
$593$	−2.79484	−0.114770	−0.0573852	−	0.998352i	$-0.518276\pi$
$593$	−2.79484	−0.114770	−0.0573852	+	0.998352i	$0.518276\pi$
$594$	2.41356	0.0990296
$595$	0.557675	0.0228624
$596$	13.8424	0.567006
$597$	2.15406	0.0881599
$598$	6.65462	0.272128
$599$	−39.2528	−1.60383	−0.801913	−	0.597441i	$-0.796184\pi$
$599$	−39.2528	−1.60383	−0.801913	+	0.597441i	$0.796184\pi$
$600$	7.95175	0.324629
$601$	33.9166	1.38349	0.691743	−	0.722144i	$-0.256843\pi$
$601$	33.9166	1.38349	0.691743	+	0.722144i	$0.256843\pi$
$602$	0.434204	0.0176968
$603$	0.00664058	0.000270425 0
$604$	14.0609	0.572129
$605$	−6.89114	−0.280165
$606$	−12.6417	−0.513536
$607$	17.2092	0.698501	0.349251	−	0.937029i	$-0.386436\pi$
$607$	17.2092	0.698501	0.349251	+	0.937029i	$0.386436\pi$
$608$	−0.609350	−0.0247124
$609$	−0.877323	−0.0355509
$610$	1.03916	0.0420742
$611$	−16.1502	−0.653367
$612$	−0.00498388	−0.000201461 0
$613$	−18.3187	−0.739884	−0.369942	−	0.929055i	$-0.620622\pi$
$613$	−18.3187	−0.739884	−0.369942	+	0.929055i	$0.620622\pi$
$614$	−1.79874	−0.0725914
$615$	4.36288	0.175928
$616$	0.0784483	0.00316077
$617$	40.7940	1.64230	0.821151	−	0.570710i	$-0.193332\pi$
$617$	40.7940	1.64230	0.821151	+	0.570710i	$0.193332\pi$
$618$	−9.95193	−0.400325
$619$	−31.1877	−1.25354	−0.626771	−	0.779204i	$-0.715624\pi$
$619$	−31.1877	−1.25354	−0.626771	+	0.779204i	$0.715624\pi$
$620$	1.18403	0.0475518
$621$	−14.3962	−0.577699
$622$	25.3325	1.01574
$623$	2.53565	0.101589
$624$	4.16024	0.166543
$625$	19.0420	0.761679
$626$	14.6579	0.585849
$627$	0.490076	0.0195718
$628$	−18.7876	−0.749707
$629$	23.4419	0.934691
$630$	−0.000104121 0	−4.14827e−6 0
$631$	−22.6668	−0.902352	−0.451176	−	0.892435i	$-0.648995\pi$
$631$	−22.6668	−0.902352	−0.451176	+	0.892435i	$0.648995\pi$
$632$	6.80973	0.270876
$633$	27.1532	1.07924
$634$	−14.8186	−0.588523
$635$	3.99789	0.158652
$636$	−13.8414	−0.548846
$637$	16.7476	0.663563
$638$	1.39283	0.0551426
$639$	−0.00762443	−0.000301618 0
$640$	0.638996	0.0252585
$641$	−0.954982	−0.0377195	−0.0188598	−	0.999822i	$-0.506004\pi$
$641$	−0.954982	−0.0377195	−0.0188598	+	0.999822i	$0.506004\pi$
$642$	−6.01461	−0.237378
$643$	44.6965	1.76266	0.881330	−	0.472502i	$-0.156649\pi$
$643$	44.6965	1.76266	0.881330	+	0.472502i	$0.156649\pi$
$644$	−0.467921	−0.0184387
$645$	−2.84450	−0.112002
$646$	−3.14827	−0.123867
$647$	9.37832	0.368700	0.184350	−	0.982861i	$-0.440982\pi$
$647$	9.37832	0.368700	0.184350	+	0.982861i	$0.440982\pi$
$648$	−8.99711	−0.353440
$649$	2.53111	0.0993547
$650$	11.0306	0.432657
$651$	−0.542041	−0.0212443
$652$	22.1114	0.865948
$653$	−16.6004	−0.649624	−0.324812	−	0.945779i	$-0.605301\pi$
$653$	−16.6004	−0.649624	−0.324812	+	0.945779i	$0.605301\pi$
$654$	−28.5750	−1.11737
$655$	−13.9798	−0.546234
$656$	−3.94262	−0.153933
$657$	0.00248223	9.68409e−5 0
$658$	1.13560	0.0442705
$659$	−32.6259	−1.27092	−0.635462	−	0.772132i	$-0.719190\pi$
$659$	−32.6259	−1.27092	−0.635462	+	0.772132i	$0.719190\pi$
$660$	−0.513920	−0.0200043
$661$	−32.6018	−1.26806	−0.634031	−	0.773308i	$-0.718601\pi$
$661$	−32.6018	−1.26806	−0.634031	+	0.773308i	$0.718601\pi$
$662$	−25.9904	−1.01015
$663$	21.4944	0.834771
$664$	−3.11880	−0.121033
$665$	−0.0657721	−0.00255053
$666$	−0.00437673	−0.000169595 0
$667$	−8.30781	−0.321680
$668$	15.2555	0.590253
$669$	−24.2276	−0.936691
$670$	−4.39888	−0.169944
$671$	0.755248	0.0291560
$672$	−0.292528	−0.0112845
$673$	−33.0438	−1.27374	−0.636872	−	0.770969i	$-0.719772\pi$
$673$	−33.0438	−1.27374	−0.636872	+	0.770969i	$0.719772\pi$
$674$	18.8881	0.727541
$675$	−23.8629	−0.918484
$676$	−7.22894	−0.278036
$677$	38.5833	1.48288	0.741438	−	0.671022i	$-0.234144\pi$
$677$	38.5833	1.48288	0.741438	+	0.671022i	$0.234144\pi$
$678$	15.9011	0.610680
$679$	−0.829397	−0.0318294
$680$	3.30144	0.126605
$681$	41.2819	1.58192
$682$	0.860540	0.0329518
$683$	−21.7860	−0.833620	−0.416810	−	0.908994i	$-0.636852\pi$
$683$	−21.7860	−0.833620	−0.416810	+	0.908994i	$0.636852\pi$
$684$	0.000587799 0	2.24750e−5 0
$685$	6.58741	0.251692
$686$	−2.36004	−0.0901067
$687$	26.5661	1.01356
$688$	2.57049	0.0979991
$689$	−19.2007	−0.731487
$690$	3.06538	0.116697
$691$	36.2171	1.37776	0.688882	−	0.724874i	$-0.258102\pi$
$691$	36.2171	1.37776	0.688882	+	0.724874i	$0.258102\pi$
$692$	−4.42805	−0.168329
$693$	−7.56738e−5 0	−2.87461e−6 0
$694$	23.8946	0.907026
$695$	6.87565	0.260808
$696$	−5.19376	−0.196869
$697$	−20.3700	−0.771567
$698$	−10.4702	−0.396304
$699$	−15.0301	−0.568490
$700$	−0.775621	−0.0293157
$701$	−37.0490	−1.39932	−0.699661	−	0.714475i	$-0.746666\pi$
$701$	−37.0490	−1.39932	−0.699661	+	0.714475i	$0.746666\pi$
$702$	−12.4847	−0.471206
$703$	−2.76474	−0.104274
$704$	0.464415	0.0175033
$705$	−7.43941	−0.280184
$706$	−9.45917	−0.356001
$707$	1.23309	0.0463750
$708$	−9.43833	−0.354714
$709$	−25.4532	−0.955913	−0.477957	−	0.878383i	$-0.658622\pi$
$709$	−25.4532	−0.955913	−0.477957	+	0.878383i	$0.658622\pi$
$710$	5.05061	0.189546
$711$	−0.00656888	−0.000246352 0
$712$	15.0111	0.562564
$713$	−5.13287	−0.192227
$714$	−1.51138	−0.0565620
$715$	−0.712906	−0.0266612
$716$	20.7555	0.775669
$717$	11.0334	0.412049
$718$	10.4942	0.391639
$719$	29.9738	1.11784	0.558918	−	0.829223i	$-0.311217\pi$
$719$	29.9738	1.11784	0.558918	+	0.829223i	$0.311217\pi$
$720$	−0.000616396 0	−2.29717e−5 0
$721$	0.970719	0.0361515
$722$	−18.6287	−0.693288
$723$	10.8664	0.404127
$724$	19.5602	0.726949
$725$	−13.7709	−0.511439
$726$	18.6760	0.693131
$727$	48.1488	1.78574	0.892871	−	0.450314i	$-0.148688\pi$
$727$	48.1488	1.78574	0.892871	+	0.450314i	$0.148688\pi$
$728$	−0.405794	−0.0150397
$729$	27.0087	1.00032
$730$	−1.64429	−0.0608578
$731$	13.2807	0.491205
$732$	−2.81627	−0.104092
$733$	−28.4205	−1.04974	−0.524868	−	0.851183i	$-0.675885\pi$
$733$	−28.4205	−1.04974	−0.524868	+	0.851183i	$0.675885\pi$
$734$	16.4759	0.608136
$735$	7.71459	0.284557
$736$	−2.77010	−0.102107
$737$	−3.19706	−0.117765
$738$	0.00380318	0.000139997 0
$739$	20.7730	0.764146	0.382073	−	0.924132i	$-0.375210\pi$
$739$	20.7730	0.764146	0.382073	+	0.924132i	$0.375210\pi$
$740$	2.89925	0.106579
$741$	−2.53504	−0.0931271
$742$	1.35010	0.0495637
$743$	−25.7063	−0.943073	−0.471537	−	0.881846i	$-0.656301\pi$
$743$	−25.7063	−0.943073	−0.471537	+	0.881846i	$0.656301\pi$
$744$	−3.20889	−0.117644
$745$	8.84522	0.324064
$746$	8.31136	0.304300
$747$	0.00300850	0.000110075 0
$748$	2.39945	0.0877326
$749$	0.586670	0.0214365
$750$	10.6141	0.387573
$751$	−22.1342	−0.807689	−0.403844	−	0.914828i	$-0.632326\pi$
$751$	−22.1342	−0.807689	−0.403844	+	0.914828i	$0.632326\pi$
$752$	6.72279	0.245155
$753$	−44.4023	−1.61811
$754$	−7.20475	−0.262382
$755$	8.98484	0.326992
$756$	0.877867	0.0319277
$757$	−13.6437	−0.495889	−0.247945	−	0.968774i	$-0.579755\pi$
$757$	−13.6437	−0.495889	−0.247945	+	0.968774i	$0.579755\pi$
$758$	28.5039	1.03531
$759$	2.22788	0.0808671
$760$	−0.389372	−0.0141240
$761$	−52.5584	−1.90524	−0.952620	−	0.304162i	$-0.901623\pi$
$761$	−52.5584	−1.90524	−0.952620	+	0.304162i	$0.901623\pi$
$762$	−10.8349	−0.392506
$763$	2.78723	0.100905
$764$	14.3966	0.520851
$765$	−0.00318468	−0.000115142 0
$766$	−13.4738	−0.486828
$767$	−13.0928	−0.472753
$768$	−1.73177	−0.0624900
$769$	−8.95075	−0.322772	−0.161386	−	0.986891i	$-0.551596\pi$
$769$	−8.95075	−0.322772	−0.161386	+	0.986891i	$0.551596\pi$
$770$	0.0501282	0.00180649
$771$	−4.65873	−0.167780
$772$	−4.42194	−0.159149
$773$	22.3739	0.804734	0.402367	−	0.915478i	$-0.368188\pi$
$773$	22.3739	0.804734	0.402367	+	0.915478i	$0.368188\pi$
$774$	−0.00247958	−8.91267e−5 0
$775$	−8.50818	−0.305623
$776$	−4.91004	−0.176260
$777$	−1.32726	−0.0476152
$778$	−9.81279	−0.351806
$779$	2.40243	0.0860760
$780$	2.65838	0.0951852
$781$	3.67072	0.131349
$782$	−14.3120	−0.511797
$783$	15.5863	0.557009
$784$	−6.97147	−0.248981
$785$	−12.0052	−0.428484
$786$	37.8872	1.35139
$787$	−26.2178	−0.934564	−0.467282	−	0.884108i	$-0.654767\pi$
$787$	−26.2178	−0.934564	−0.467282	+	0.884108i	$0.654767\pi$
$788$	9.72302	0.346368
$789$	1.10872	0.0394716
$790$	4.35139	0.154815
$791$	−1.55101	−0.0551476
$792$	−0.000447990 0	−1.59186e−5 0
$793$	−3.90671	−0.138731
$794$	−31.2956	−1.11064
$795$	−8.84458	−0.313685
$796$	−1.24385	−0.0440871
$797$	−17.0512	−0.603984	−0.301992	−	0.953311i	$-0.597652\pi$
$797$	−17.0512	−0.603984	−0.301992	+	0.953311i	$0.597652\pi$
$798$	0.178252	0.00631005
$799$	34.7340	1.22880
$800$	−4.59168	−0.162341
$801$	−0.0144802	−0.000511632 0
$802$	−29.7104	−1.04911
$803$	−1.19505	−0.0421724
$804$	11.9216	0.420443
$805$	−0.299000	−0.0105384
$806$	−4.45136	−0.156792
$807$	−3.08264	−0.108514
$808$	7.29988	0.256809
$809$	−9.08550	−0.319429	−0.159715	−	0.987163i	$-0.551057\pi$
$809$	−9.08550	−0.319429	−0.159715	+	0.987163i	$0.551057\pi$
$810$	−5.74911	−0.202003
$811$	−22.2371	−0.780851	−0.390425	−	0.920635i	$-0.627672\pi$
$811$	−22.2371	−0.780851	−0.390425	+	0.920635i	$0.627672\pi$
$812$	0.506604	0.0177783
$813$	−39.8995	−1.39934
$814$	2.10714	0.0738554
$815$	14.1291	0.494920
$816$	−8.94739	−0.313221
$817$	−1.56633	−0.0547989
$818$	25.5211	0.892326
$819$	0.000391442 0	1.36781e−5 0
$820$	−2.51932	−0.0879783
$821$	−17.6228	−0.615041	−0.307521	−	0.951541i	$-0.599499\pi$
$821$	−17.6228	−0.615041	−0.307521	+	0.951541i	$0.599499\pi$
$822$	−17.8528	−0.622690
$823$	29.3044	1.02149	0.510744	−	0.859733i	$-0.329370\pi$
$823$	29.3044	1.02149	0.510744	+	0.859733i	$0.329370\pi$
$824$	5.74667	0.200195
$825$	3.69291	0.128571
$826$	0.920622	0.0320326
$827$	−44.0601	−1.53212	−0.766059	−	0.642770i	$-0.777785\pi$
$827$	−44.0601	−1.53212	−0.766059	+	0.642770i	$0.777785\pi$
$828$	0.00267213	9.28629e−5 0
$829$	8.39663	0.291627	0.145813	−	0.989312i	$-0.453420\pi$
$829$	8.39663	0.291627	0.145813	+	0.989312i	$0.453420\pi$
$830$	−1.99290	−0.0691747
$831$	35.3504	1.22629
$832$	−2.40230	−0.0832849
$833$	−36.0188	−1.24798
$834$	−18.6340	−0.645243
$835$	9.74821	0.337351
$836$	−0.282991	−0.00978746
$837$	9.62977	0.332854
$838$	−6.51945	−0.225211
$839$	0.491767	0.0169777	0.00848884	−	0.999964i	$-0.497298\pi$
$839$	0.491767	0.0169777	0.00848884	+	0.999964i	$0.497298\pi$
$840$	−0.186925	−0.00644951
$841$	−20.0054	−0.689841
$842$	−24.4896	−0.843967
$843$	−2.73972	−0.0943610
$844$	−15.6794	−0.539708
$845$	−4.61926	−0.158907
$846$	−0.00648502	−0.000222960 0
$847$	−1.82167	−0.0625934
$848$	7.99260	0.274467
$849$	7.34374	0.252036
$850$	−23.7234	−0.813707
$851$	−12.5685	−0.430843
$852$	−13.6879	−0.468939
$853$	−44.3506	−1.51854	−0.759269	−	0.650777i	$-0.774443\pi$
$853$	−44.3506	−1.51854	−0.759269	+	0.650777i	$0.774443\pi$
$854$	0.274701	0.00940007
$855$	0.000375601 0	1.28453e−5 0
$856$	3.47309	0.118708
$857$	−16.5372	−0.564901	−0.282451	−	0.959282i	$-0.591147\pi$
$857$	−16.5372	−0.564901	−0.282451	+	0.959282i	$0.591147\pi$
$858$	1.93208	0.0659601
$859$	−37.9186	−1.29377	−0.646884	−	0.762589i	$-0.723928\pi$
$859$	−37.9186	−1.29377	−0.646884	+	0.762589i	$0.723928\pi$
$860$	1.64253	0.0560100
$861$	1.15333	0.0393053
$862$	−21.3997	−0.728876
$863$	−25.9519	−0.883413	−0.441707	−	0.897160i	$-0.645627\pi$
$863$	−25.9519	−0.883413	−0.441707	+	0.897160i	$0.645627\pi$
$864$	5.19699	0.176805
$865$	−2.82951	−0.0962061
$866$	36.1281	1.22768
$867$	−16.7875	−0.570135
$868$	0.312998	0.0106238
$869$	3.16254	0.107282
$870$	−3.31879	−0.112518
$871$	16.5376	0.560355
$872$	16.5005	0.558776
$873$	0.00473639	0.000160302 0
$874$	1.68796	0.0570961
$875$	−1.03531	−0.0349999
$876$	4.45626	0.150563
$877$	−28.4598	−0.961019	−0.480509	−	0.876990i	$-0.659548\pi$
$877$	−28.4598	−0.961019	−0.480509	+	0.876990i	$0.659548\pi$
$878$	−14.9880	−0.505821
$879$	−41.1637	−1.38842
$880$	0.296759	0.0100038
$881$	12.4603	0.419800	0.209900	−	0.977723i	$-0.432686\pi$
$881$	12.4603	0.419800	0.209900	+	0.977723i	$0.432686\pi$
$882$	0.00672490	0.000226439 0
$883$	36.7480	1.23667	0.618335	−	0.785915i	$-0.287808\pi$
$883$	36.7480	1.23667	0.618335	+	0.785915i	$0.287808\pi$
$884$	−12.4118	−0.417453
$885$	−6.03105	−0.202732
$886$	−16.9918	−0.570850
$887$	10.6502	0.357598	0.178799	−	0.983886i	$-0.442779\pi$
$887$	10.6502	0.357598	0.178799	+	0.983886i	$0.442779\pi$
$888$	−7.85740	−0.263677
$889$	1.05684	0.0354454
$890$	9.59202	0.321525
$891$	−4.17839	−0.139981
$892$	13.9900	0.468421
$893$	−4.09653	−0.137085
$894$	−23.9718	−0.801738
$895$	13.2627	0.443323
$896$	0.168919	0.00564317
$897$	−11.5243	−0.384785
$898$	−32.9246	−1.09871
$899$	5.55720	0.185343
$900$	0.00442929	0.000147643 0
$901$	41.2946	1.37572
$902$	−1.83101	−0.0609660
$903$	−0.751942	−0.0250231
$904$	−9.18200	−0.305389
$905$	12.4989	0.415477
$906$	−24.3502	−0.808982
$907$	3.82251	0.126924	0.0634621	−	0.997984i	$-0.479786\pi$
$907$	3.82251	0.126924	0.0634621	+	0.997984i	$0.479786\pi$
$908$	−23.8379	−0.791090
$909$	−0.00704171	−0.000233559 0
$910$	−0.259301	−0.00859573
$911$	−39.1958	−1.29861	−0.649307	−	0.760526i	$-0.724941\pi$
$911$	−39.1958	−1.29861	−0.649307	+	0.760526i	$0.724941\pi$
$912$	1.05525	0.0349430
$913$	−1.44842	−0.0479357
$914$	9.98962	0.330427
$915$	−1.79958	−0.0594924
$916$	−15.3404	−0.506862
$917$	−3.69555	−0.122038
$918$	26.8508	0.886208
$919$	10.5673	0.348582	0.174291	−	0.984694i	$-0.444237\pi$
$919$	10.5673	0.348582	0.174291	+	0.984694i	$0.444237\pi$
$920$	−1.77008	−0.0583579
$921$	3.11502	0.102643
$922$	5.71130	0.188092
$923$	−18.9877	−0.624989
$924$	−0.135855	−0.00446929
$925$	−20.8334	−0.684998
$926$	−11.8882	−0.390669
$927$	−0.00554343	−0.000182070 0
$928$	2.99910	0.0984503
$929$	27.9737	0.917789	0.458894	−	0.888491i	$-0.348246\pi$
$929$	27.9737	0.917789	0.458894	+	0.888491i	$0.348246\pi$
$930$	−2.05047	−0.0672376
$931$	4.24806	0.139225
$932$	8.67901	0.284290
$933$	−43.8701	−1.43624
$934$	−22.4953	−0.736069
$935$	1.53324	0.0501423
$936$	0.00231734	7.57447e−5 0
$937$	−19.5984	−0.640252	−0.320126	−	0.947375i	$-0.603725\pi$
$937$	−19.5984	−0.640252	−0.320126	+	0.947375i	$0.603725\pi$
$938$	−1.16284	−0.0379682
$939$	−25.3842	−0.828382
$940$	4.29584	0.140115
$941$	−18.9867	−0.618949	−0.309475	−	0.950908i	$-0.600153\pi$
$941$	−18.9867	−0.618949	−0.309475	+	0.950908i	$0.600153\pi$
$942$	32.5359	1.06008
$943$	10.9214	0.355651
$944$	5.45010	0.177386
$945$	0.560954	0.0182478
$946$	1.19378	0.0388130
$947$	27.5096	0.893943	0.446971	−	0.894548i	$-0.352503\pi$
$947$	27.5096	0.893943	0.446971	+	0.894548i	$0.352503\pi$
$948$	−11.7929	−0.383015
$949$	6.18169	0.200666
$950$	2.79794	0.0907772
$951$	25.6625	0.832163
$952$	0.872736	0.0282855
$953$	2.76956	0.0897149	0.0448574	−	0.998993i	$-0.485717\pi$
$953$	2.76956	0.0897149	0.0448574	+	0.998993i	$0.485717\pi$
$954$	−0.00770992	−0.000249618 0
$955$	9.19938	0.297685
$956$	−6.37115	−0.206058
$957$	−2.41206	−0.0779709
$958$	10.8105	0.349273
$959$	1.74138	0.0562322
$960$	−1.10660	−0.0357152
$961$	−27.5666	−0.889244
$962$	−10.8997	−0.351422
$963$	−0.00335026	−0.000107961 0
$964$	−6.27475	−0.202096
$965$	−2.82560	−0.0909594
$966$	0.810333	0.0260720
$967$	43.3730	1.39478	0.697390	−	0.716691i	$-0.254344\pi$
$967$	43.3730	1.39478	0.697390	+	0.716691i	$0.254344\pi$
$968$	−10.7843	−0.346621
$969$	5.45209	0.175146
$970$	−3.13750	−0.100739
$971$	41.0674	1.31792	0.658958	−	0.752180i	$-0.270998\pi$
$971$	41.0674	1.31792	0.658958	+	0.752180i	$0.270998\pi$
$972$	−0.0100248	−0.000321544 0
$973$	1.81758	0.0582688
$974$	−0.768909	−0.0246374
$975$	−19.1025	−0.611770
$976$	1.62623	0.0520545
$977$	47.5385	1.52089	0.760446	−	0.649402i	$-0.224981\pi$
$977$	47.5385	1.52089	0.760446	+	0.649402i	$0.224981\pi$
$978$	−38.2918	−1.22444
$979$	6.97137	0.222806
$980$	−4.45474	−0.142301
$981$	−0.0159169	−0.000508187 0
$982$	−29.9174	−0.954703
$983$	−3.99081	−0.127287	−0.0636436	−	0.997973i	$-0.520272\pi$
$983$	−3.99081	−0.127287	−0.0636436	+	0.997973i	$0.520272\pi$
$984$	6.82771	0.217660
$985$	6.21297	0.197962
$986$	15.4952	0.493467
$987$	−1.96661	−0.0625978
$988$	1.46384	0.0465710
$989$	−7.12052	−0.226419
$990$	−0.000286264 0	−9.09806e−6 0
$991$	10.8189	0.343674	0.171837	−	0.985125i	$-0.445030\pi$
$991$	10.8189	0.343674	0.171837	+	0.985125i	$0.445030\pi$
$992$	1.85295	0.0588313
$993$	45.0095	1.42833
$994$	1.33513	0.0423477
$995$	−0.794814	−0.0251973
$996$	5.40106	0.171139
$997$	−50.9530	−1.61370	−0.806849	−	0.590757i	$-0.798829\pi$
$997$	−50.9530	−1.61370	−0.806849	+	0.590757i	$0.798829\pi$
$998$	24.2989	0.769169
$999$	23.5798	0.746031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.10	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.10	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73177 q^{3} +1.00000 q^{4} +0.638996 q^{5} -1.73177 q^{6} +0.168919 q^{7} +1.00000 q^{8} -0.000964633 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73177 q^{3} +1.00000 q^{4} +0.638996 q^{5} -1.73177 q^{6} +0.168919 q^{7} +1.00000 q^{8} -0.000964633 q^{9} +0.638996 q^{10} +0.464415 q^{11} -1.73177 q^{12} -2.40230 q^{13} +0.168919 q^{14} -1.10660 q^{15} +1.00000 q^{16} +5.16661 q^{17} -0.000964633 q^{18} -0.609350 q^{19} +0.638996 q^{20} -0.292528 q^{21} +0.464415 q^{22} -2.77010 q^{23} -1.73177 q^{24} -4.59168 q^{25} -2.40230 q^{26} +5.19699 q^{27} +0.168919 q^{28} +2.99910 q^{29} -1.10660 q^{30} +1.85295 q^{31} +1.00000 q^{32} -0.804261 q^{33} +5.16661 q^{34} +0.107938 q^{35} -0.000964633 q^{36} +4.53720 q^{37} -0.609350 q^{38} +4.16024 q^{39} +0.638996 q^{40} -3.94262 q^{41} -0.292528 q^{42} +2.57049 q^{43} +0.464415 q^{44} -0.000616396 q^{45} -2.77010 q^{46} +6.72279 q^{47} -1.73177 q^{48} -6.97147 q^{49} -4.59168 q^{50} -8.94739 q^{51} -2.40230 q^{52} +7.99260 q^{53} +5.19699 q^{54} +0.296759 q^{55} +0.168919 q^{56} +1.05525 q^{57} +2.99910 q^{58} +5.45010 q^{59} -1.10660 q^{60} +1.62623 q^{61} +1.85295 q^{62} -0.000162944 q^{63} +1.00000 q^{64} -1.53506 q^{65} -0.804261 q^{66} -6.88405 q^{67} +5.16661 q^{68} +4.79718 q^{69} +0.107938 q^{70} +7.90397 q^{71} -0.000964633 q^{72} -2.57324 q^{73} +4.53720 q^{74} +7.95175 q^{75} -0.609350 q^{76} +0.0784483 q^{77} +4.16024 q^{78} +6.80973 q^{79} +0.638996 q^{80} -8.99711 q^{81} -3.94262 q^{82} -3.11880 q^{83} -0.292528 q^{84} +3.30144 q^{85} +2.57049 q^{86} -5.19376 q^{87} +0.464415 q^{88} +15.0111 q^{89} -0.000616396 q^{90} -0.405794 q^{91} -2.77010 q^{92} -3.20889 q^{93} +6.72279 q^{94} -0.389372 q^{95} -1.73177 q^{96} -4.91004 q^{97} -6.97147 q^{98} -0.000447990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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