LMFDB - Embedded newform 4033.2.a.d.1.71

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.71
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.16094 q^{2} -3.21639 q^{3} +2.66965 q^{4} -2.39427 q^{5} -6.95041 q^{6} -3.11050 q^{7} +1.44706 q^{8} +7.34515 q^{9} +O(q^{10})$	\(q+2.16094 q^{2} -3.21639 q^{3} +2.66965 q^{4} -2.39427 q^{5} -6.95041 q^{6} -3.11050 q^{7} +1.44706 q^{8} +7.34515 q^{9} -5.17387 q^{10} +1.44819 q^{11} -8.58662 q^{12} +3.41513 q^{13} -6.72160 q^{14} +7.70091 q^{15} -2.21228 q^{16} +0.750832 q^{17} +15.8724 q^{18} +1.44335 q^{19} -6.39186 q^{20} +10.0046 q^{21} +3.12945 q^{22} +7.06412 q^{23} -4.65431 q^{24} +0.732547 q^{25} +7.37988 q^{26} -13.9757 q^{27} -8.30394 q^{28} +9.01907 q^{29} +16.6412 q^{30} -7.76930 q^{31} -7.67473 q^{32} -4.65794 q^{33} +1.62250 q^{34} +7.44740 q^{35} +19.6090 q^{36} -1.00000 q^{37} +3.11898 q^{38} -10.9844 q^{39} -3.46466 q^{40} +11.3734 q^{41} +21.6193 q^{42} -1.14049 q^{43} +3.86615 q^{44} -17.5863 q^{45} +15.2651 q^{46} -8.94165 q^{47} +7.11556 q^{48} +2.67523 q^{49} +1.58299 q^{50} -2.41497 q^{51} +9.11719 q^{52} -2.13412 q^{53} -30.2006 q^{54} -3.46736 q^{55} -4.50109 q^{56} -4.64236 q^{57} +19.4896 q^{58} -6.49795 q^{59} +20.5587 q^{60} -1.70109 q^{61} -16.7890 q^{62} -22.8471 q^{63} -12.1600 q^{64} -8.17676 q^{65} -10.0655 q^{66} -12.2920 q^{67} +2.00446 q^{68} -22.7209 q^{69} +16.0934 q^{70} -2.93774 q^{71} +10.6289 q^{72} -2.98794 q^{73} -2.16094 q^{74} -2.35616 q^{75} +3.85322 q^{76} -4.50460 q^{77} -23.7366 q^{78} +4.79812 q^{79} +5.29681 q^{80} +22.9158 q^{81} +24.5772 q^{82} -0.950412 q^{83} +26.7087 q^{84} -1.79770 q^{85} -2.46452 q^{86} -29.0088 q^{87} +2.09562 q^{88} -7.26605 q^{89} -38.0029 q^{90} -10.6228 q^{91} +18.8587 q^{92} +24.9891 q^{93} -19.3223 q^{94} -3.45577 q^{95} +24.6849 q^{96} +0.686069 q^{97} +5.78100 q^{98} +10.6372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	2.16094	1.52801	0.764006	−	0.645209i	$-0.223230\pi$
$2$	2.16094	1.52801	0.764006	+	0.645209i	$0.223230\pi$
$3$	−3.21639	−1.85698	−0.928491	−	0.371354i	$-0.878894\pi$
$3$	−3.21639	−1.85698	−0.928491	+	0.371354i	$0.878894\pi$
$4$	2.66965	1.33482
$5$	−2.39427	−1.07075	−0.535376	−	0.844614i	$-0.679830\pi$
$5$	−2.39427	−1.07075	−0.535376	+	0.844614i	$0.679830\pi$
$6$	−6.95041	−2.83749
$7$	−3.11050	−1.17566	−0.587830	−	0.808985i	$-0.700018\pi$
$7$	−3.11050	−1.17566	−0.587830	+	0.808985i	$0.700018\pi$
$8$	1.44706	0.511614
$9$	7.34515	2.44838
$10$	−5.17387	−1.63612
$11$	1.44819	0.436646	0.218323	−	0.975877i	$-0.429941\pi$
$11$	1.44819	0.436646	0.218323	+	0.975877i	$0.429941\pi$
$12$	−8.58662	−2.47874
$13$	3.41513	0.947186	0.473593	−	0.880744i	$-0.342957\pi$
$13$	3.41513	0.947186	0.473593	+	0.880744i	$0.342957\pi$
$14$	−6.72160	−1.79642
$15$	7.70091	1.98837
$16$	−2.21228	−0.553071
$17$	0.750832	0.182104	0.0910518	−	0.995846i	$-0.470977\pi$
$17$	0.750832	0.182104	0.0910518	+	0.995846i	$0.470977\pi$
$18$	15.8724	3.74116
$19$	1.44335	0.331126	0.165563	−	0.986199i	$-0.447056\pi$
$19$	1.44335	0.331126	0.165563	+	0.986199i	$0.447056\pi$
$20$	−6.39186	−1.42926
$21$	10.0046	2.18318
$22$	3.12945	0.667200
$23$	7.06412	1.47297	0.736485	−	0.676454i	$-0.236484\pi$
$23$	7.06412	1.47297	0.736485	+	0.676454i	$0.236484\pi$
$24$	−4.65431	−0.950058
$25$	0.732547	0.146509
$26$	7.37988	1.44731
$27$	−13.9757	−2.68963
$28$	−8.30394	−1.56930
$29$	9.01907	1.67480	0.837400	−	0.546591i	$-0.184075\pi$
$29$	9.01907	1.67480	0.837400	+	0.546591i	$0.184075\pi$
$30$	16.6412	3.03825
$31$	−7.76930	−1.39541	−0.697704	−	0.716386i	$-0.745795\pi$
$31$	−7.76930	−1.39541	−0.697704	+	0.716386i	$0.745795\pi$
$32$	−7.67473	−1.35671
$33$	−4.65794	−0.810843
$34$	1.62250	0.278256
$35$	7.44740	1.25884
$36$	19.6090	3.26816
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.11898	0.505965
$39$	−10.9844	−1.75891
$40$	−3.46466	−0.547811
$41$	11.3734	1.77623	0.888114	−	0.459624i	$-0.152016\pi$
$41$	11.3734	1.77623	0.888114	+	0.459624i	$0.152016\pi$
$42$	21.6193	3.33593
$43$	−1.14049	−0.173922	−0.0869612	−	0.996212i	$-0.527716\pi$
$43$	−1.14049	−0.173922	−0.0869612	+	0.996212i	$0.527716\pi$
$44$	3.86615	0.582844
$45$	−17.5863	−2.62161
$46$	15.2651	2.25072
$47$	−8.94165	−1.30427	−0.652137	−	0.758101i	$-0.726127\pi$
$47$	−8.94165	−1.30427	−0.652137	+	0.758101i	$0.726127\pi$
$48$	7.11556	1.02704
$49$	2.67523	0.382176
$50$	1.58299	0.223868
$51$	−2.41497	−0.338163
$52$	9.11719	1.26433
$53$	−2.13412	−0.293144	−0.146572	−	0.989200i	$-0.546824\pi$
$53$	−2.13412	−0.293144	−0.146572	+	0.989200i	$0.546824\pi$
$54$	−30.2006	−4.10978
$55$	−3.46736	−0.467539
$56$	−4.50109	−0.601484
$57$	−4.64236	−0.614896
$58$	19.4896	2.55912
$59$	−6.49795	−0.845961	−0.422981	−	0.906139i	$-0.639016\pi$
$59$	−6.49795	−0.845961	−0.422981	+	0.906139i	$0.639016\pi$
$60$	20.5587	2.65412
$61$	−1.70109	−0.217803	−0.108901	−	0.994053i	$-0.534733\pi$
$61$	−1.70109	−0.217803	−0.108901	+	0.994053i	$0.534733\pi$
$62$	−16.7890	−2.13220
$63$	−22.8471	−2.87847
$64$	−12.1600	−1.52000
$65$	−8.17676	−1.01420
$66$	−10.0655	−1.23898
$67$	−12.2920	−1.50170	−0.750852	−	0.660470i	$-0.770357\pi$
$67$	−12.2920	−1.50170	−0.750852	+	0.660470i	$0.770357\pi$
$68$	2.00446	0.243076
$69$	−22.7209	−2.73528
$70$	16.0934	1.92352
$71$	−2.93774	−0.348646	−0.174323	−	0.984689i	$-0.555774\pi$
$71$	−2.93774	−0.348646	−0.174323	+	0.984689i	$0.555774\pi$
$72$	10.6289	1.25263
$73$	−2.98794	−0.349711	−0.174856	−	0.984594i	$-0.555946\pi$
$73$	−2.98794	−0.349711	−0.174856	+	0.984594i	$0.555946\pi$
$74$	−2.16094	−0.251204
$75$	−2.35616	−0.272066
$76$	3.85322	0.441995
$77$	−4.50460	−0.513347
$78$	−23.7366	−2.68764
$79$	4.79812	0.539831	0.269915	−	0.962884i	$-0.413004\pi$
$79$	4.79812	0.539831	0.269915	+	0.962884i	$0.413004\pi$
$80$	5.29681	0.592202
$81$	22.9158	2.54620
$82$	24.5772	2.71410
$83$	−0.950412	−0.104321	−0.0521606	−	0.998639i	$-0.516611\pi$
$83$	−0.950412	−0.104321	−0.0521606	+	0.998639i	$0.516611\pi$
$84$	26.7087	2.91416
$85$	−1.79770	−0.194988
$86$	−2.46452	−0.265756
$87$	−29.0088	−3.11007
$88$	2.09562	0.223394
$89$	−7.26605	−0.770200	−0.385100	−	0.922875i	$-0.625833\pi$
$89$	−7.26605	−0.770200	−0.385100	+	0.922875i	$0.625833\pi$
$90$	−38.0029	−4.00586
$91$	−10.6228	−1.11357
$92$	18.8587	1.96615
$93$	24.9891	2.59125
$94$	−19.3223	−1.99295
$95$	−3.45577	−0.354554
$96$	24.6849	2.51939
$97$	0.686069	0.0696598	0.0348299	−	0.999393i	$-0.488911\pi$
$97$	0.686069	0.0696598	0.0348299	+	0.999393i	$0.488911\pi$
$98$	5.78100	0.583970
$99$	10.6372	1.06908
$100$	1.95564	0.195564
$101$	−8.44893	−0.840700	−0.420350	−	0.907362i	$-0.638093\pi$
$101$	−8.44893	−0.840700	−0.420350	+	0.907362i	$0.638093\pi$
$102$	−5.21859	−0.516717
$103$	0.607391	0.0598480	0.0299240	−	0.999552i	$-0.490473\pi$
$103$	0.607391	0.0598480	0.0299240	+	0.999552i	$0.490473\pi$
$104$	4.94190	0.484594
$105$	−23.9537	−2.33764
$106$	−4.61170	−0.447928
$107$	16.6248	1.60718	0.803591	−	0.595182i	$-0.202920\pi$
$107$	16.6248	1.60718	0.803591	+	0.595182i	$0.202920\pi$
$108$	−37.3102	−3.59017
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−7.49275	−0.714406
$111$	3.21639	0.305286
$112$	6.88131	0.650223
$113$	17.0037	1.59957	0.799785	−	0.600286i	$-0.204947\pi$
$113$	17.0037	1.59957	0.799785	+	0.600286i	$0.204947\pi$
$114$	−10.0318	−0.939569
$115$	−16.9134	−1.57719
$116$	24.0777	2.23556
$117$	25.0847	2.31908
$118$	−14.0417	−1.29264
$119$	−2.33547	−0.214092
$120$	11.1437	1.01728
$121$	−8.90275	−0.809341
$122$	−3.67596	−0.332805
$123$	−36.5813	−3.29842
$124$	−20.7413	−1.86262
$125$	10.2175	0.913877
$126$	−49.3712	−4.39834
$127$	−14.8865	−1.32096	−0.660480	−	0.750844i	$-0.729647\pi$
$127$	−14.8865	−1.32096	−0.660480	+	0.750844i	$0.729647\pi$
$128$	−10.9276	−0.965872
$129$	3.66824	0.322971
$130$	−17.6694	−1.54971
$131$	−3.26307	−0.285095	−0.142548	−	0.989788i	$-0.545529\pi$
$131$	−3.26307	−0.285095	−0.142548	+	0.989788i	$0.545529\pi$
$132$	−12.4350	−1.08233
$133$	−4.48953	−0.389292
$134$	−26.5622	−2.29462
$135$	33.4617	2.87992
$136$	1.08650	0.0931666
$137$	−0.908447	−0.0776139	−0.0388069	−	0.999247i	$-0.512356\pi$
$137$	−0.908447	−0.0776139	−0.0388069	+	0.999247i	$0.512356\pi$
$138$	−49.0985	−4.17954
$139$	−16.1902	−1.37323	−0.686616	−	0.727021i	$-0.740904\pi$
$139$	−16.1902	−1.37323	−0.686616	+	0.727021i	$0.740904\pi$
$140$	19.8819	1.68033
$141$	28.7598	2.42201
$142$	−6.34827	−0.532735
$143$	4.94575	0.413585
$144$	−16.2496	−1.35413
$145$	−21.5941	−1.79330
$146$	−6.45674	−0.534364
$147$	−8.60458	−0.709694
$148$	−2.66965	−0.219444
$149$	−0.400808	−0.0328355	−0.0164178	−	0.999865i	$-0.505226\pi$
$149$	−0.400808	−0.0328355	−0.0164178	+	0.999865i	$0.505226\pi$
$150$	−5.09151	−0.415720
$151$	22.2154	1.80786	0.903931	−	0.427679i	$-0.140669\pi$
$151$	22.2154	1.80786	0.903931	+	0.427679i	$0.140669\pi$
$152$	2.08861	0.169409
$153$	5.51498	0.445859
$154$	−9.73415	−0.784400
$155$	18.6018	1.49414
$156$	−29.3244	−2.34783
$157$	−16.9452	−1.35237	−0.676187	−	0.736730i	$-0.736369\pi$
$157$	−16.9452	−1.35237	−0.676187	+	0.736730i	$0.736369\pi$
$158$	10.3684	0.824868
$159$	6.86417	0.544364
$160$	18.3754	1.45270
$161$	−21.9730	−1.73171
$162$	49.5197	3.89063
$163$	0.327363	0.0256411	0.0128205	−	0.999918i	$-0.495919\pi$
$163$	0.327363	0.0256411	0.0128205	+	0.999918i	$0.495919\pi$
$164$	30.3630	2.37095
$165$	11.1524	0.868212
$166$	−2.05378	−0.159404
$167$	−1.62788	−0.125969	−0.0629846	−	0.998014i	$-0.520062\pi$
$167$	−1.62788	−0.125969	−0.0629846	+	0.998014i	$0.520062\pi$
$168$	14.4773	1.11694
$169$	−1.33689	−0.102838
$170$	−3.88471	−0.297944
$171$	10.6016	0.810725
$172$	−3.04469	−0.232156
$173$	−16.1920	−1.23106	−0.615529	−	0.788115i	$-0.711057\pi$
$173$	−16.1920	−1.23106	−0.615529	+	0.788115i	$0.711057\pi$
$174$	−62.6863	−4.75223
$175$	−2.27859	−0.172245
$176$	−3.20380	−0.241496
$177$	20.8999	1.57094
$178$	−15.7015	−1.17688
$179$	16.6431	1.24396	0.621982	−	0.783032i	$-0.286328\pi$
$179$	16.6431	1.24396	0.621982	+	0.783032i	$0.286328\pi$
$180$	−46.9492	−3.49939
$181$	−5.32013	−0.395442	−0.197721	−	0.980258i	$-0.563354\pi$
$181$	−5.32013	−0.395442	−0.197721	+	0.980258i	$0.563354\pi$
$182$	−22.9551	−1.70155
$183$	5.47138	0.404456
$184$	10.2222	0.753592
$185$	2.39427	0.176031
$186$	53.9999	3.95946
$187$	1.08735	0.0795147
$188$	−23.8710	−1.74097
$189$	43.4715	3.16208
$190$	−7.46769	−0.541763
$191$	−17.4425	−1.26209	−0.631046	−	0.775745i	$-0.717374\pi$
$191$	−17.4425	−1.26209	−0.631046	+	0.775745i	$0.717374\pi$
$192$	39.1114	2.82262
$193$	−18.0574	−1.29980	−0.649901	−	0.760019i	$-0.725190\pi$
$193$	−18.0574	−1.29980	−0.649901	+	0.760019i	$0.725190\pi$
$194$	1.48255	0.106441
$195$	26.2996	1.88335
$196$	7.14192	0.510137
$197$	−16.9570	−1.20814	−0.604070	−	0.796932i	$-0.706455\pi$
$197$	−16.9570	−1.20814	−0.604070	+	0.796932i	$0.706455\pi$
$198$	22.9863	1.63356
$199$	−27.1675	−1.92585	−0.962925	−	0.269770i	$-0.913052\pi$
$199$	−27.1675	−1.92585	−0.962925	+	0.269770i	$0.913052\pi$
$200$	1.06004	0.0749562
$201$	39.5358	2.78864
$202$	−18.2576	−1.28460
$203$	−28.0539	−1.96899
$204$	−6.44711	−0.451388
$205$	−27.2310	−1.90190
$206$	1.31253	0.0914486
$207$	51.8870	3.60640
$208$	−7.55523	−0.523861
$209$	2.09024	0.144585
$210$	−51.7625	−3.57195
$211$	15.5404	1.06985	0.534924	−	0.844900i	$-0.320340\pi$
$211$	15.5404	1.06985	0.534924	+	0.844900i	$0.320340\pi$
$212$	−5.69735	−0.391296
$213$	9.44892	0.647429
$214$	35.9252	2.45580
$215$	2.73063	0.186228
$216$	−20.2237	−1.37605
$217$	24.1664	1.64053
$218$	−2.16094	−0.146357
$219$	9.61036	0.649408
$220$	−9.25663	−0.624082
$221$	2.56419	0.172486
$222$	6.95041	0.466481
$223$	3.47236	0.232526	0.116263	−	0.993218i	$-0.462908\pi$
$223$	3.47236	0.232526	0.116263	+	0.993218i	$0.462908\pi$
$224$	23.8723	1.59503
$225$	5.38067	0.358712
$226$	36.7438	2.44416
$227$	3.45725	0.229466	0.114733	−	0.993396i	$-0.463399\pi$
$227$	3.45725	0.229466	0.114733	+	0.993396i	$0.463399\pi$
$228$	−12.3935	−0.820777
$229$	27.4984	1.81714	0.908571	−	0.417730i	$-0.137174\pi$
$229$	27.4984	1.81714	0.908571	+	0.417730i	$0.137174\pi$
$230$	−36.5488	−2.40996
$231$	14.4885	0.953276
$232$	13.0512	0.856850
$233$	−5.61544	−0.367880	−0.183940	−	0.982938i	$-0.558885\pi$
$233$	−5.61544	−0.367880	−0.183940	+	0.982938i	$0.558885\pi$
$234$	54.2063	3.54358
$235$	21.4088	1.39655
$236$	−17.3472	−1.12921
$237$	−15.4326	−1.00246
$238$	−5.04679	−0.327135
$239$	−11.7596	−0.760668	−0.380334	−	0.924849i	$-0.624191\pi$
$239$	−11.7596	−0.760668	−0.380334	+	0.924849i	$0.624191\pi$
$240$	−17.0366	−1.09971
$241$	18.1141	1.16683	0.583415	−	0.812174i	$-0.301716\pi$
$241$	18.1141	1.16683	0.583415	+	0.812174i	$0.301716\pi$
$242$	−19.2383	−1.23668
$243$	−31.7791	−2.03863
$244$	−4.54132	−0.290728
$245$	−6.40524	−0.409216
$246$	−79.0498	−5.04003
$247$	4.92921	0.313638
$248$	−11.2427	−0.713910
$249$	3.05689	0.193723
$250$	22.0793	1.39641
$251$	−14.5542	−0.918653	−0.459327	−	0.888267i	$-0.651909\pi$
$251$	−14.5542	−0.918653	−0.459327	+	0.888267i	$0.651909\pi$
$252$	−60.9937	−3.84224
$253$	10.2302	0.643166
$254$	−32.1687	−2.01844
$255$	5.78209	0.362089
$256$	0.706220	0.0441387
$257$	6.11516	0.381453	0.190727	−	0.981643i	$-0.438916\pi$
$257$	6.11516	0.381453	0.190727	+	0.981643i	$0.438916\pi$
$258$	7.92684	0.493504
$259$	3.11050	0.193277
$260$	−21.8290	−1.35378
$261$	66.2465	4.10055
$262$	−7.05128	−0.435629
$263$	−28.1573	−1.73625	−0.868126	−	0.496344i	$-0.834676\pi$
$263$	−28.1573	−1.73625	−0.868126	+	0.496344i	$0.834676\pi$
$264$	−6.74033	−0.414838
$265$	5.10967	0.313885
$266$	−9.70159	−0.594843
$267$	23.3704	1.43025
$268$	−32.8152	−2.00451
$269$	9.37114	0.571368	0.285684	−	0.958324i	$-0.407779\pi$
$269$	9.37114	0.571368	0.285684	+	0.958324i	$0.407779\pi$
$270$	72.3085	4.40056
$271$	1.38326	0.0840269	0.0420135	−	0.999117i	$-0.486623\pi$
$271$	1.38326	0.0840269	0.0420135	+	0.999117i	$0.486623\pi$
$272$	−1.66105	−0.100716
$273$	34.1670	2.06788
$274$	−1.96310	−0.118595
$275$	1.06087	0.0639727
$276$	−60.6569	−3.65111
$277$	−27.8732	−1.67474	−0.837368	−	0.546639i	$-0.815907\pi$
$277$	−27.8732	−1.67474	−0.837368	+	0.546639i	$0.815907\pi$
$278$	−34.9859	−2.09831
$279$	−57.0667	−3.41650
$280$	10.7768	0.644040
$281$	7.00205	0.417707	0.208854	−	0.977947i	$-0.433027\pi$
$281$	7.00205	0.417707	0.208854	+	0.977947i	$0.433027\pi$
$282$	62.1481	3.70087
$283$	15.3848	0.914530	0.457265	−	0.889331i	$-0.348829\pi$
$283$	15.3848	0.914530	0.457265	+	0.889331i	$0.348829\pi$
$284$	−7.84273	−0.465380
$285$	11.1151	0.658401
$286$	10.6875	0.631963
$287$	−35.3770	−2.08824
$288$	−56.3721	−3.32176
$289$	−16.4363	−0.966838
$290$	−46.6635	−2.74018
$291$	−2.20667	−0.129357
$292$	−7.97673	−0.466803
$293$	18.6904	1.09191	0.545953	−	0.837816i	$-0.316168\pi$
$293$	18.6904	1.09191	0.545953	+	0.837816i	$0.316168\pi$
$294$	−18.5940	−1.08442
$295$	15.5579	0.905815
$296$	−1.44706	−0.0841088
$297$	−20.2395	−1.17441
$298$	−0.866122	−0.0501731
$299$	24.1249	1.39518
$300$	−6.29010	−0.363159
$301$	3.54748	0.204474
$302$	48.0060	2.76243
$303$	27.1750	1.56117
$304$	−3.19309	−0.183136
$305$	4.07289	0.233213
$306$	11.9175	0.681279
$307$	3.91847	0.223639	0.111819	−	0.993729i	$-0.464332\pi$
$307$	3.91847	0.223639	0.111819	+	0.993729i	$0.464332\pi$
$308$	−12.0257	−0.685227
$309$	−1.95361	−0.111137
$310$	40.1974	2.28306
$311$	12.9812	0.736095	0.368048	−	0.929807i	$-0.380026\pi$
$311$	12.9812	0.736095	0.368048	+	0.929807i	$0.380026\pi$
$312$	−15.8951	−0.899882
$313$	−6.17220	−0.348873	−0.174437	−	0.984668i	$-0.555810\pi$
$313$	−6.17220	−0.348873	−0.174437	+	0.984668i	$0.555810\pi$
$314$	−36.6175	−2.06645
$315$	54.7023	3.08212
$316$	12.8093	0.720578
$317$	5.62442	0.315899	0.157949	−	0.987447i	$-0.449512\pi$
$317$	5.62442	0.315899	0.157949	+	0.987447i	$0.449512\pi$
$318$	14.8330	0.831795
$319$	13.0613	0.731294
$320$	29.1144	1.62755
$321$	−53.4719	−2.98451
$322$	−47.4822	−2.64608
$323$	1.08371	0.0602993
$324$	61.1772	3.39873
$325$	2.50174	0.138772
$326$	0.707411	0.0391799
$327$	3.21639	0.177867
$328$	16.4580	0.908742
$329$	27.8130	1.53338
$330$	24.0996	1.32664
$331$	12.4192	0.682623	0.341311	−	0.939950i	$-0.389129\pi$
$331$	12.4192	0.682623	0.341311	+	0.939950i	$0.389129\pi$
$332$	−2.53726	−0.139250
$333$	−7.34515	−0.402512
$334$	−3.51775	−0.192483
$335$	29.4304	1.60795
$336$	−22.1330	−1.20745
$337$	−27.8013	−1.51443	−0.757217	−	0.653164i	$-0.773441\pi$
$337$	−27.8013	−1.51443	−0.757217	+	0.653164i	$0.773441\pi$
$338$	−2.88894	−0.157137
$339$	−54.6904	−2.97037
$340$	−4.79922	−0.260274
$341$	−11.2514	−0.609299
$342$	22.9094	1.23880
$343$	13.4522	0.726351
$344$	−1.65035	−0.0889811
$345$	54.4002	2.92881
$346$	−34.9899	−1.88107
$347$	−13.4106	−0.719918	−0.359959	−	0.932968i	$-0.617209\pi$
$347$	−13.4106	−0.719918	−0.359959	+	0.932968i	$0.617209\pi$
$348$	−77.4433	−4.15140
$349$	−33.6001	−1.79857	−0.899285	−	0.437363i	$-0.855912\pi$
$349$	−33.6001	−1.79857	−0.899285	+	0.437363i	$0.855912\pi$
$350$	−4.92389	−0.263193
$351$	−47.7288	−2.54758
$352$	−11.1145	−0.592403
$353$	−20.2588	−1.07827	−0.539133	−	0.842221i	$-0.681248\pi$
$353$	−20.2588	−1.07827	−0.539133	+	0.842221i	$0.681248\pi$
$354$	45.1634	2.40041
$355$	7.03376	0.373313
$356$	−19.3978	−1.02808
$357$	7.51176	0.397565
$358$	35.9647	1.90079
$359$	−3.31805	−0.175120	−0.0875601	−	0.996159i	$-0.527907\pi$
$359$	−3.31805	−0.175120	−0.0875601	+	0.996159i	$0.527907\pi$
$360$	−25.4485	−1.34125
$361$	−16.9168	−0.890355
$362$	−11.4965	−0.604241
$363$	28.6347	1.50293
$364$	−28.3590	−1.48642
$365$	7.15394	0.374454
$366$	11.8233	0.618014
$367$	−26.8382	−1.40094	−0.700471	−	0.713681i	$-0.747027\pi$
$367$	−26.8382	−1.40094	−0.700471	+	0.713681i	$0.747027\pi$
$368$	−15.6278	−0.814657
$369$	83.5394	4.34889
$370$	5.17387	0.268977
$371$	6.63819	0.344638
$372$	66.7120	3.45886
$373$	−16.4836	−0.853490	−0.426745	−	0.904372i	$-0.640340\pi$
$373$	−16.4836	−0.853490	−0.426745	+	0.904372i	$0.640340\pi$
$374$	2.34969	0.121499
$375$	−32.8633	−1.69705
$376$	−12.9391	−0.667284
$377$	30.8013	1.58635
$378$	93.9391	4.83171
$379$	20.0510	1.02995	0.514976	−	0.857205i	$-0.327801\pi$
$379$	20.0510	1.02995	0.514976	+	0.857205i	$0.327801\pi$
$380$	−9.22567	−0.473267
$381$	47.8806	2.45300
$382$	−37.6921	−1.92849
$383$	−33.7649	−1.72531	−0.862653	−	0.505796i	$-0.831199\pi$
$383$	−33.7649	−1.72531	−0.862653	+	0.505796i	$0.831199\pi$
$384$	35.1474	1.79361
$385$	10.7852	0.549667
$386$	−39.0209	−1.98611
$387$	−8.37704	−0.425829
$388$	1.83156	0.0929835
$389$	10.5522	0.535016	0.267508	−	0.963556i	$-0.413800\pi$
$389$	10.5522	0.535016	0.267508	+	0.963556i	$0.413800\pi$
$390$	56.8318	2.87779
$391$	5.30397	0.268233
$392$	3.87122	0.195526
$393$	10.4953	0.529417
$394$	−36.6431	−1.84605
$395$	−11.4880	−0.578025
$396$	28.3975	1.42703
$397$	1.09160	0.0547859	0.0273930	−	0.999625i	$-0.491279\pi$
$397$	1.09160	0.0547859	0.0273930	+	0.999625i	$0.491279\pi$
$398$	−58.7071	−2.94272
$399$	14.4401	0.722908
$400$	−1.62060	−0.0810301
$401$	−0.821093	−0.0410034	−0.0205017	−	0.999790i	$-0.506526\pi$
$401$	−0.821093	−0.0410034	−0.0205017	+	0.999790i	$0.506526\pi$
$402$	85.4343	4.26108
$403$	−26.5332	−1.32171
$404$	−22.5557	−1.12219
$405$	−54.8668	−2.72635
$406$	−60.6226	−3.00865
$407$	−1.44819	−0.0717841
$408$	−3.49461	−0.173009
$409$	33.9503	1.67873	0.839367	−	0.543564i	$-0.182926\pi$
$409$	33.9503	1.67873	0.839367	+	0.543564i	$0.182926\pi$
$410$	−58.8446	−2.90613
$411$	2.92192	0.144128
$412$	1.62152	0.0798865
$413$	20.2119	0.994563
$414$	112.125	5.51062
$415$	2.27555	0.111702
$416$	−26.2102	−1.28506
$417$	52.0738	2.55007
$418$	4.51687	0.220927
$419$	−1.94222	−0.0948836	−0.0474418	−	0.998874i	$-0.515107\pi$
$419$	−1.94222	−0.0948836	−0.0474418	+	0.998874i	$0.515107\pi$
$420$	−63.9480	−3.12034
$421$	26.1959	1.27671	0.638356	−	0.769741i	$-0.279615\pi$
$421$	26.1959	1.27671	0.638356	+	0.769741i	$0.279615\pi$
$422$	33.5819	1.63474
$423$	−65.6778	−3.19336
$424$	−3.08821	−0.149977
$425$	0.550020	0.0266799
$426$	20.4185	0.989280
$427$	5.29126	0.256062
$428$	44.3824	2.14530
$429$	−15.9075	−0.768020
$430$	5.90073	0.284558
$431$	8.80335	0.424042	0.212021	−	0.977265i	$-0.431995\pi$
$431$	8.80335	0.424042	0.212021	+	0.977265i	$0.431995\pi$
$432$	30.9182	1.48755
$433$	28.5914	1.37401	0.687007	−	0.726651i	$-0.258924\pi$
$433$	28.5914	1.37401	0.687007	+	0.726651i	$0.258924\pi$
$434$	52.2222	2.50674
$435$	69.4551	3.33012
$436$	−2.66965	−0.127853
$437$	10.1960	0.487739
$438$	20.7674	0.992304
$439$	40.9958	1.95662	0.978312	−	0.207139i	$-0.0664152\pi$
$439$	40.9958	1.95662	0.978312	+	0.207139i	$0.0664152\pi$
$440$	−5.01749	−0.239199
$441$	19.6500	0.935714
$442$	5.54105	0.263561
$443$	−23.6699	−1.12459	−0.562294	−	0.826937i	$-0.690081\pi$
$443$	−23.6699	−1.12459	−0.562294	+	0.826937i	$0.690081\pi$
$444$	8.58662	0.407503
$445$	17.3969	0.824693
$446$	7.50354	0.355303
$447$	1.28916	0.0609750
$448$	37.8238	1.78701
$449$	−4.11590	−0.194242	−0.0971208	−	0.995273i	$-0.530963\pi$
$449$	−4.11590	−0.194242	−0.0971208	+	0.995273i	$0.530963\pi$
$450$	11.6273	0.548116
$451$	16.4708	0.775582
$452$	45.3938	2.13514
$453$	−71.4533	−3.35717
$454$	7.47090	0.350627
$455$	25.4338	1.19236
$456$	−6.71778	−0.314589
$457$	11.0947	0.518989	0.259495	−	0.965745i	$-0.416444\pi$
$457$	11.0947	0.518989	0.259495	+	0.965745i	$0.416444\pi$
$458$	59.4222	2.77662
$459$	−10.4934	−0.489790
$460$	−45.1529	−2.10526
$461$	19.8392	0.924004	0.462002	−	0.886879i	$-0.347131\pi$
$461$	19.8392	0.924004	0.462002	+	0.886879i	$0.347131\pi$
$462$	31.3088	1.45662
$463$	−20.9195	−0.972214	−0.486107	−	0.873899i	$-0.661583\pi$
$463$	−20.9195	−0.972214	−0.486107	+	0.873899i	$0.661583\pi$
$464$	−19.9527	−0.926283
$465$	−59.8308	−2.77458
$466$	−12.1346	−0.562125
$467$	−22.6099	−1.04626	−0.523131	−	0.852252i	$-0.675236\pi$
$467$	−22.6099	−1.04626	−0.523131	+	0.852252i	$0.675236\pi$
$468$	66.9671	3.09556
$469$	38.2342	1.76549
$470$	46.2629	2.13395
$471$	54.5024	2.51134
$472$	−9.40294	−0.432805
$473$	−1.65164	−0.0759424
$474$	−33.3489	−1.53177
$475$	1.05732	0.0485131
$476$	−6.23487	−0.285775
$477$	−15.6755	−0.717730
$478$	−25.4119	−1.16231
$479$	−31.7109	−1.44891	−0.724454	−	0.689323i	$-0.757908\pi$
$479$	−31.7109	−1.44891	−0.724454	+	0.689323i	$0.757908\pi$
$480$	−59.1024	−2.69764
$481$	−3.41513	−0.155716
$482$	39.1434	1.78293
$483$	70.6736	3.21576
$484$	−23.7672	−1.08033
$485$	−1.64264	−0.0745883
$486$	−68.6726	−3.11505
$487$	5.22804	0.236905	0.118453	−	0.992960i	$-0.462207\pi$
$487$	5.22804	0.236905	0.118453	+	0.992960i	$0.462207\pi$
$488$	−2.46159	−0.111431
$489$	−1.05293	−0.0476150
$490$	−13.8413	−0.625287
$491$	−6.73138	−0.303783	−0.151892	−	0.988397i	$-0.548536\pi$
$491$	−6.73138	−0.303783	−0.151892	+	0.988397i	$0.548536\pi$
$492$	−97.6591	−4.40281
$493$	6.77181	0.304987
$494$	10.6517	0.479243
$495$	−25.4683	−1.14472
$496$	17.1879	0.771759
$497$	9.13785	0.409889
$498$	6.60575	0.296011
$499$	24.5167	1.09752	0.548758	−	0.835981i	$-0.315101\pi$
$499$	24.5167	1.09752	0.548758	+	0.835981i	$0.315101\pi$
$500$	27.2770	1.21986
$501$	5.23590	0.233923
$502$	−31.4507	−1.40371
$503$	−9.98767	−0.445328	−0.222664	−	0.974895i	$-0.571475\pi$
$503$	−9.98767	−0.445328	−0.222664	+	0.974895i	$0.571475\pi$
$504$	−33.0612	−1.47266
$505$	20.2291	0.900181
$506$	22.1068	0.982766
$507$	4.29996	0.190968
$508$	−39.7416	−1.76325
$509$	−15.6560	−0.693939	−0.346970	−	0.937876i	$-0.612789\pi$
$509$	−15.6560	−0.693939	−0.346970	+	0.937876i	$0.612789\pi$
$510$	12.4947	0.553276
$511$	9.29399	0.411142
$512$	23.3813	1.03332
$513$	−20.1718	−0.890606
$514$	13.2145	0.582865
$515$	−1.45426	−0.0640824
$516$	9.79291	0.431109
$517$	−12.9492	−0.569505
$518$	6.72160	0.295330
$519$	52.0799	2.28605
$520$	−11.8323	−0.518879
$521$	−5.49491	−0.240736	−0.120368	−	0.992729i	$-0.538408\pi$
$521$	−5.49491	−0.240736	−0.120368	+	0.992729i	$0.538408\pi$
$522$	143.154	6.26570
$523$	−16.8562	−0.737071	−0.368536	−	0.929614i	$-0.620141\pi$
$523$	−16.8562	−0.737071	−0.368536	+	0.929614i	$0.620141\pi$
$524$	−8.71123	−0.380552
$525$	7.32883	0.319857
$526$	−60.8461	−2.65302
$527$	−5.83344	−0.254109
$528$	10.3047	0.448454
$529$	26.9018	1.16964
$530$	11.0417	0.479620
$531$	−47.7285	−2.07124
$532$	−11.9855	−0.519636
$533$	38.8416	1.68242
$534$	50.5020	2.18544
$535$	−39.8044	−1.72089
$536$	−17.7873	−0.768292
$537$	−53.5307	−2.31002
$538$	20.2504	0.873058
$539$	3.87424	0.166875
$540$	89.3308	3.84419
$541$	−21.5061	−0.924618	−0.462309	−	0.886719i	$-0.652979\pi$
$541$	−21.5061	−0.924618	−0.462309	+	0.886719i	$0.652979\pi$
$542$	2.98913	0.128394
$543$	17.1116	0.734330
$544$	−5.76243	−0.247062
$545$	2.39427	0.102559
$546$	73.8326	3.15974
$547$	22.2513	0.951399	0.475699	−	0.879608i	$-0.342195\pi$
$547$	22.2513	0.951399	0.475699	+	0.879608i	$0.342195\pi$
$548$	−2.42523	−0.103601
$549$	−12.4948	−0.533265
$550$	2.29247	0.0977511
$551$	13.0176	0.554570
$552$	−32.8786	−1.39941
$553$	−14.9246	−0.634657
$554$	−60.2322	−2.55902
$555$	−7.70091	−0.326886
$556$	−43.2220	−1.83302
$557$	14.3744	0.609064	0.304532	−	0.952502i	$-0.401500\pi$
$557$	14.3744	0.609064	0.304532	+	0.952502i	$0.401500\pi$
$558$	−123.318	−5.22045
$559$	−3.89491	−0.164737
$560$	−16.4757	−0.696227
$561$	−3.49733	−0.147657
$562$	15.1310	0.638262
$563$	23.9451	1.00917	0.504583	−	0.863363i	$-0.331646\pi$
$563$	23.9451	1.00917	0.504583	+	0.863363i	$0.331646\pi$
$564$	76.7785	3.23296
$565$	−40.7114	−1.71274
$566$	33.2455	1.39741
$567$	−71.2798	−2.99347
$568$	−4.25109	−0.178372
$569$	−5.13571	−0.215300	−0.107650	−	0.994189i	$-0.534333\pi$
$569$	−5.13571	−0.215300	−0.107650	+	0.994189i	$0.534333\pi$
$570$	24.0190	1.00604
$571$	−38.2268	−1.59974	−0.799870	−	0.600173i	$-0.795098\pi$
$571$	−38.2268	−1.59974	−0.799870	+	0.600173i	$0.795098\pi$
$572$	13.2034	0.552062
$573$	56.1018	2.34368
$574$	−76.4475	−3.19086
$575$	5.17480	0.215804
$576$	−89.3173	−3.72155
$577$	−23.4827	−0.977598	−0.488799	−	0.872396i	$-0.662565\pi$
$577$	−23.4827	−0.977598	−0.488799	+	0.872396i	$0.662565\pi$
$578$	−35.5177	−1.47734
$579$	58.0797	2.41371
$580$	−57.6487	−2.39373
$581$	2.95626	0.122646
$582$	−4.76846	−0.197659
$583$	−3.09061	−0.128000
$584$	−4.32373	−0.178917
$585$	−60.0595	−2.48316
$586$	40.3888	1.66845
$587$	−43.8312	−1.80911	−0.904553	−	0.426361i	$-0.859795\pi$
$587$	−43.8312	−1.80911	−0.904553	+	0.426361i	$0.859795\pi$
$588$	−22.9712	−0.947316
$589$	−11.2138	−0.462056
$590$	33.6196	1.38410
$591$	54.5404	2.24349
$592$	2.21228	0.0909243
$593$	−33.1022	−1.35934	−0.679672	−	0.733516i	$-0.737878\pi$
$593$	−33.1022	−1.35934	−0.679672	+	0.733516i	$0.737878\pi$
$594$	−43.7362	−1.79452
$595$	5.59174	0.229239
$596$	−1.07002	−0.0438296
$597$	87.3811	3.57627
$598$	52.1323	2.13185
$599$	−22.1816	−0.906314	−0.453157	−	0.891431i	$-0.649702\pi$
$599$	−22.1816	−0.906314	−0.453157	+	0.891431i	$0.649702\pi$
$600$	−3.40951	−0.139192
$601$	−20.1350	−0.821323	−0.410661	−	0.911788i	$-0.634702\pi$
$601$	−20.1350	−0.821323	−0.410661	+	0.911788i	$0.634702\pi$
$602$	7.66589	0.312438
$603$	−90.2865	−3.67675
$604$	59.3072	2.41317
$605$	21.3156	0.866603
$606$	58.7235	2.38548
$607$	0.398251	0.0161645	0.00808226	−	0.999967i	$-0.497427\pi$
$607$	0.398251	0.0161645	0.00808226	+	0.999967i	$0.497427\pi$
$608$	−11.0773	−0.449243
$609$	90.2321	3.65639
$610$	8.80125	0.356352
$611$	−30.5369	−1.23539
$612$	14.7230	0.595143
$613$	−10.0213	−0.404755	−0.202378	−	0.979308i	$-0.564867\pi$
$613$	−10.0213	−0.404755	−0.202378	+	0.979308i	$0.564867\pi$
$614$	8.46757	0.341723
$615$	87.5856	3.53179
$616$	−6.51843	−0.262635
$617$	−12.8546	−0.517508	−0.258754	−	0.965943i	$-0.583312\pi$
$617$	−12.8546	−0.517508	−0.258754	+	0.965943i	$0.583312\pi$
$618$	−4.22162	−0.169818
$619$	−20.9505	−0.842072	−0.421036	−	0.907044i	$-0.638333\pi$
$619$	−20.9505	−0.842072	−0.421036	+	0.907044i	$0.638333\pi$
$620$	49.6603	1.99441
$621$	−98.7260	−3.96174
$622$	28.0515	1.12476
$623$	22.6011	0.905493
$624$	24.3006	0.972801
$625$	−28.1261	−1.12504
$626$	−13.3377	−0.533083
$627$	−6.72302	−0.268492
$628$	−45.2377	−1.80518
$629$	−0.750832	−0.0299376
$630$	118.208	4.70953
$631$	−34.7839	−1.38473	−0.692363	−	0.721549i	$-0.743430\pi$
$631$	−34.7839	−1.38473	−0.692363	+	0.721549i	$0.743430\pi$
$632$	6.94318	0.276185
$633$	−49.9841	−1.98669
$634$	12.1540	0.482698
$635$	35.6423	1.41442
$636$	18.3249	0.726629
$637$	9.13626	0.361992
$638$	28.2247	1.11743
$639$	−21.5782	−0.853619
$640$	26.1637	1.03421
$641$	−29.2567	−1.15557	−0.577784	−	0.816189i	$-0.696083\pi$
$641$	−29.2567	−1.15557	−0.577784	+	0.816189i	$0.696083\pi$
$642$	−115.549	−4.56037
$643$	12.6068	0.497164	0.248582	−	0.968611i	$-0.420035\pi$
$643$	12.6068	0.497164	0.248582	+	0.968611i	$0.420035\pi$
$644$	−58.6600	−2.31153
$645$	−8.78278	−0.345822
$646$	2.34183	0.0921380
$647$	16.2146	0.637463	0.318732	−	0.947845i	$-0.396743\pi$
$647$	16.2146	0.637463	0.318732	+	0.947845i	$0.396743\pi$
$648$	33.1606	1.30267
$649$	−9.41026	−0.369385
$650$	5.40611	0.212045
$651$	−77.7287	−3.04643
$652$	0.873944	0.0342263
$653$	37.5475	1.46935	0.734673	−	0.678421i	$-0.237336\pi$
$653$	37.5475	1.46935	0.734673	+	0.678421i	$0.237336\pi$
$654$	6.95041	0.271783
$655$	7.81268	0.305266
$656$	−25.1612	−0.982379
$657$	−21.9469	−0.856228
$658$	60.1022	2.34303
$659$	43.2651	1.68537	0.842684	−	0.538408i	$-0.180974\pi$
$659$	43.2651	1.68537	0.842684	+	0.538408i	$0.180974\pi$
$660$	29.7729	1.15891
$661$	−32.9952	−1.28337	−0.641683	−	0.766970i	$-0.721763\pi$
$661$	−32.9952	−1.28337	−0.641683	+	0.766970i	$0.721763\pi$
$662$	26.8372	1.04306
$663$	−8.24743	−0.320303
$664$	−1.37531	−0.0533722
$665$	10.7492	0.416835
$666$	−15.8724	−0.615043
$667$	63.7118	2.46693
$668$	−4.34587	−0.168147
$669$	−11.1684	−0.431797
$670$	63.5972	2.45697
$671$	−2.46351	−0.0951026
$672$	−76.7825	−2.96195
$673$	6.43691	0.248125	0.124062	−	0.992274i	$-0.460408\pi$
$673$	6.43691	0.248125	0.124062	+	0.992274i	$0.460408\pi$
$674$	−60.0768	−2.31407
$675$	−10.2379	−0.394056
$676$	−3.56903	−0.137270
$677$	−5.75305	−0.221108	−0.110554	−	0.993870i	$-0.535262\pi$
$677$	−5.75305	−0.221108	−0.110554	+	0.993870i	$0.535262\pi$
$678$	−118.182	−4.53877
$679$	−2.13402	−0.0818962
$680$	−2.60138	−0.0997583
$681$	−11.1199	−0.426114
$682$	−24.3136	−0.931016
$683$	−31.2302	−1.19499	−0.597495	−	0.801873i	$-0.703837\pi$
$683$	−31.2302	−1.19499	−0.597495	+	0.801873i	$0.703837\pi$
$684$	28.3025	1.08217
$685$	2.17507	0.0831052
$686$	29.0694	1.10987
$687$	−88.4454	−3.37440
$688$	2.52308	0.0961914
$689$	−7.28830	−0.277662
$690$	117.555	4.47525
$691$	−24.7132	−0.940135	−0.470068	−	0.882630i	$-0.655770\pi$
$691$	−24.7132	−0.940135	−0.470068	+	0.882630i	$0.655770\pi$
$692$	−43.2270	−1.64324
$693$	−33.0870	−1.25687
$694$	−28.9794	−1.10004
$695$	38.7637	1.47039
$696$	−41.9776	−1.59116
$697$	8.53952	0.323457
$698$	−72.6076	−2.74824
$699$	18.0614	0.683146
$700$	−6.08303	−0.229917
$701$	39.1208	1.47757	0.738786	−	0.673940i	$-0.235399\pi$
$701$	39.1208	1.47757	0.738786	+	0.673940i	$0.235399\pi$
$702$	−103.139	−3.89273
$703$	−1.44335	−0.0544368
$704$	−17.6100	−0.663703
$705$	−68.8589	−2.59337
$706$	−43.7779	−1.64760
$707$	26.2804	0.988377
$708$	55.7954	2.09692
$709$	38.9061	1.46115	0.730575	−	0.682832i	$-0.239252\pi$
$709$	38.9061	1.46115	0.730575	+	0.682832i	$0.239252\pi$
$710$	15.1995	0.570427
$711$	35.2429	1.32171
$712$	−10.5144	−0.394045
$713$	−54.8833	−2.05539
$714$	16.2324	0.607484
$715$	−11.8415	−0.442847
$716$	44.4312	1.66047
$717$	37.8236	1.41255
$718$	−7.17010	−0.267586
$719$	−22.6699	−0.845443	−0.422721	−	0.906260i	$-0.638925\pi$
$719$	−22.6699	−0.845443	−0.422721	+	0.906260i	$0.638925\pi$
$720$	38.9059	1.44994
$721$	−1.88929	−0.0703609
$722$	−36.5560	−1.36047
$723$	−58.2619	−2.16678
$724$	−14.2029	−0.527845
$725$	6.60690	0.245374
$726$	61.8777	2.29650
$727$	20.3832	0.755972	0.377986	−	0.925811i	$-0.376617\pi$
$727$	20.3832	0.755972	0.377986	+	0.925811i	$0.376617\pi$
$728$	−15.3718	−0.569717
$729$	33.4664	1.23950
$730$	15.4592	0.572171
$731$	−0.856313	−0.0316719
$732$	14.6066	0.539877
$733$	−5.37970	−0.198704	−0.0993519	−	0.995052i	$-0.531677\pi$
$733$	−5.37970	−0.198704	−0.0993519	+	0.995052i	$0.531677\pi$
$734$	−57.9956	−2.14066
$735$	20.6017	0.759906
$736$	−54.2152	−1.99840
$737$	−17.8011	−0.655713
$738$	180.523	6.64516
$739$	20.2488	0.744864	0.372432	−	0.928059i	$-0.378524\pi$
$739$	20.2488	0.744864	0.372432	+	0.928059i	$0.378524\pi$
$740$	6.39186	0.234970
$741$	−15.8543	−0.582421
$742$	14.3447	0.526611
$743$	12.3869	0.454431	0.227216	−	0.973844i	$-0.427038\pi$
$743$	12.3869	0.454431	0.227216	+	0.973844i	$0.427038\pi$
$744$	36.1608	1.32572
$745$	0.959645	0.0351587
$746$	−35.6201	−1.30414
$747$	−6.98092	−0.255419
$748$	2.90283	0.106138
$749$	−51.7116	−1.88950
$750$	−71.0155	−2.59312
$751$	−27.8489	−1.01622	−0.508111	−	0.861292i	$-0.669656\pi$
$751$	−27.8489	−1.01622	−0.508111	+	0.861292i	$0.669656\pi$
$752$	19.7815	0.721355
$753$	46.8120	1.70592
$754$	66.5597	2.42396
$755$	−53.1897	−1.93577
$756$	116.053	4.22082
$757$	19.4286	0.706143	0.353072	−	0.935596i	$-0.385137\pi$
$757$	19.4286	0.706143	0.353072	+	0.935596i	$0.385137\pi$
$758$	43.3290	1.57378
$759$	−32.9042	−1.19435
$760$	−5.00071	−0.181395
$761$	−6.55690	−0.237687	−0.118844	−	0.992913i	$-0.537919\pi$
$761$	−6.55690	−0.237687	−0.118844	+	0.992913i	$0.537919\pi$
$762$	103.467	3.74821
$763$	3.11050	0.112608
$764$	−46.5652	−1.68467
$765$	−13.2044	−0.477405
$766$	−72.9638	−2.63629
$767$	−22.1913	−0.801283
$768$	−2.27148	−0.0819649
$769$	44.1558	1.59230	0.796150	−	0.605100i	$-0.206867\pi$
$769$	44.1558	1.59230	0.796150	+	0.605100i	$0.206867\pi$
$770$	23.3062	0.839898
$771$	−19.6687	−0.708352
$772$	−48.2069	−1.73500
$773$	−17.2537	−0.620573	−0.310286	−	0.950643i	$-0.600425\pi$
$773$	−17.2537	−0.620573	−0.310286	+	0.950643i	$0.600425\pi$
$774$	−18.1023	−0.650672
$775$	−5.69138	−0.204441
$776$	0.992785	0.0356389
$777$	−10.0046	−0.358913
$778$	22.8026	0.817511
$779$	16.4158	0.588156
$780$	70.2107	2.51395
$781$	−4.25441	−0.152235
$782$	11.4615	0.409864
$783$	−126.048	−4.50458
$784$	−5.91837	−0.211370
$785$	40.5715	1.44806
$786$	22.6797	0.808956
$787$	2.62493	0.0935687	0.0467843	−	0.998905i	$-0.485103\pi$
$787$	2.62493	0.0935687	0.0467843	+	0.998905i	$0.485103\pi$
$788$	−45.2693	−1.61265
$789$	90.5648	3.22419
$790$	−24.8249	−0.883229
$791$	−52.8900	−1.88055
$792$	15.3927	0.546954
$793$	−5.80946	−0.206300
$794$	2.35888	0.0837136
$795$	−16.4347	−0.582878
$796$	−72.5275	−2.57067
$797$	41.6689	1.47599	0.737994	−	0.674807i	$-0.235773\pi$
$797$	41.6689	1.47599	0.737994	+	0.674807i	$0.235773\pi$
$798$	31.2041	1.10461
$799$	−6.71367	−0.237513
$800$	−5.62210	−0.198771
$801$	−53.3703	−1.88575
$802$	−1.77433	−0.0626538
$803$	−4.32710	−0.152700
$804$	105.547	3.72234
$805$	52.6093	1.85423
$806$	−57.3365	−2.01959
$807$	−30.1412	−1.06102
$808$	−12.2261	−0.430114
$809$	55.8878	1.96491	0.982456	−	0.186495i	$-0.0597128\pi$
$809$	55.8878	1.96491	0.982456	+	0.186495i	$0.0597128\pi$
$810$	−118.564	−4.16590
$811$	6.74946	0.237006	0.118503	−	0.992954i	$-0.462191\pi$
$811$	6.74946	0.237006	0.118503	+	0.992954i	$0.462191\pi$
$812$	−74.8939	−2.62826
$813$	−4.44909	−0.156037
$814$	−3.12945	−0.109687
$815$	−0.783797	−0.0274552
$816$	5.34259	0.187028
$817$	−1.64612	−0.0575903
$818$	73.3645	2.56513
$819$	−78.0259	−2.72645
$820$	−72.6972	−2.53870
$821$	24.8473	0.867177	0.433588	−	0.901111i	$-0.357247\pi$
$821$	24.8473	0.867177	0.433588	+	0.901111i	$0.357247\pi$
$822$	6.31408	0.220229
$823$	9.98986	0.348225	0.174112	−	0.984726i	$-0.444294\pi$
$823$	9.98986	0.348225	0.174112	+	0.984726i	$0.444294\pi$
$824$	0.878933	0.0306191
$825$	−3.41216	−0.118796
$826$	43.6766	1.51970
$827$	−56.7857	−1.97463	−0.987317	−	0.158764i	$-0.949249\pi$
$827$	−56.7857	−1.97463	−0.987317	+	0.158764i	$0.949249\pi$
$828$	138.520	4.81390
$829$	−1.11162	−0.0386081	−0.0193040	−	0.999814i	$-0.506145\pi$
$829$	−1.11162	−0.0386081	−0.0193040	+	0.999814i	$0.506145\pi$
$830$	4.91731	0.170682
$831$	89.6510	3.10996
$832$	−41.5281	−1.43973
$833$	2.00865	0.0695956
$834$	112.528	3.89653
$835$	3.89759	0.134882
$836$	5.58020	0.192995
$837$	108.582	3.75313
$838$	−4.19701	−0.144983
$839$	7.23851	0.249901	0.124951	−	0.992163i	$-0.460123\pi$
$839$	7.23851	0.249901	0.124951	+	0.992163i	$0.460123\pi$
$840$	−34.6625	−1.19597
$841$	52.3437	1.80495
$842$	56.6077	1.95083
$843$	−22.5213	−0.775675
$844$	41.4875	1.42806
$845$	3.20088	0.110114
$846$	−141.925	−4.87950
$847$	27.6920	0.951509
$848$	4.72128	0.162129
$849$	−49.4834	−1.69827
$850$	1.18856	0.0407672
$851$	−7.06412	−0.242155
$852$	25.2253	0.864203
$853$	−0.817859	−0.0280030	−0.0140015	−	0.999902i	$-0.504457\pi$
$853$	−0.817859	−0.0280030	−0.0140015	+	0.999902i	$0.504457\pi$
$854$	11.4341	0.391266
$855$	−25.3831	−0.868085
$856$	24.0571	0.822256
$857$	−42.3458	−1.44651	−0.723253	−	0.690584i	$-0.757354\pi$
$857$	−42.3458	−1.44651	−0.723253	+	0.690584i	$0.757354\pi$
$858$	−34.3750	−1.17354
$859$	10.9190	0.372551	0.186275	−	0.982498i	$-0.440358\pi$
$859$	10.9190	0.372551	0.186275	+	0.982498i	$0.440358\pi$
$860$	7.28983	0.248581
$861$	113.786	3.87782
$862$	19.0235	0.647942
$863$	−12.5026	−0.425594	−0.212797	−	0.977096i	$-0.568257\pi$
$863$	−12.5026	−0.425594	−0.212797	+	0.977096i	$0.568257\pi$
$864$	107.260	3.64905
$865$	38.7682	1.31816
$866$	61.7842	2.09951
$867$	52.8654	1.79540
$868$	64.5159	2.18981
$869$	6.94859	0.235715
$870$	150.088	5.08846
$871$	−41.9787	−1.42239
$872$	−1.44706	−0.0490037
$873$	5.03929	0.170554
$874$	22.0328	0.745272
$875$	−31.7814	−1.07441
$876$	25.6563	0.866845
$877$	11.1871	0.377760	0.188880	−	0.982000i	$-0.439514\pi$
$877$	11.1871	0.377760	0.188880	+	0.982000i	$0.439514\pi$
$878$	88.5893	2.98975
$879$	−60.1157	−2.02765
$880$	7.67079	0.258582
$881$	−41.6095	−1.40186	−0.700930	−	0.713230i	$-0.747231\pi$
$881$	−41.6095	−1.40186	−0.700930	+	0.713230i	$0.747231\pi$
$882$	42.4624	1.42978
$883$	8.20270	0.276043	0.138021	−	0.990429i	$-0.455926\pi$
$883$	8.20270	0.276043	0.138021	+	0.990429i	$0.455926\pi$
$884$	6.84547	0.230238
$885$	−50.0402	−1.68208
$886$	−51.1490	−1.71839
$887$	0.739710	0.0248370	0.0124185	−	0.999923i	$-0.496047\pi$
$887$	0.739710	0.0248370	0.0124185	+	0.999923i	$0.496047\pi$
$888$	4.65431	0.156189
$889$	46.3044	1.55300
$890$	37.5936	1.26014
$891$	33.1865	1.11179
$892$	9.26996	0.310381
$893$	−12.9059	−0.431879
$894$	2.78578	0.0931705
$895$	−39.8481	−1.33198
$896$	33.9903	1.13554
$897$	−77.5950	−2.59082
$898$	−8.89421	−0.296803
$899$	−70.0719	−2.33703
$900$	14.3645	0.478816
$901$	−1.60237	−0.0533826
$902$	35.5924	1.18510
$903$	−11.4101	−0.379704
$904$	24.6054	0.818362
$905$	12.7379	0.423421
$906$	−154.406	−5.12979
$907$	−34.1461	−1.13380	−0.566901	−	0.823786i	$-0.691858\pi$
$907$	−34.1461	−1.13380	−0.566901	+	0.823786i	$0.691858\pi$
$908$	9.22963	0.306296
$909$	−62.0587	−2.05836
$910$	54.9609	1.82194
$911$	−33.3334	−1.10438	−0.552192	−	0.833717i	$-0.686208\pi$
$911$	−33.3334	−1.10438	−0.552192	+	0.833717i	$0.686208\pi$
$912$	10.2702	0.340081
$913$	−1.37638	−0.0455514
$914$	23.9750	0.793022
$915$	−13.1000	−0.433072
$916$	73.4109	2.42556
$917$	10.1498	0.335175
$918$	−22.6756	−0.748406
$919$	−12.4257	−0.409887	−0.204943	−	0.978774i	$-0.565701\pi$
$919$	−12.4257	−0.409887	−0.204943	+	0.978774i	$0.565701\pi$
$920$	−24.4748	−0.806910
$921$	−12.6033	−0.415294
$922$	42.8713	1.41189
$923$	−10.0328	−0.330232
$924$	38.6793	1.27245
$925$	−0.732547	−0.0240860
$926$	−45.2058	−1.48555
$927$	4.46138	0.146531
$928$	−69.2189	−2.27222
$929$	−54.0281	−1.77261	−0.886303	−	0.463106i	$-0.846735\pi$
$929$	−54.0281	−1.77261	−0.886303	+	0.463106i	$0.846735\pi$
$930$	−129.290	−4.23960
$931$	3.86128	0.126548
$932$	−14.9912	−0.491054
$933$	−41.7525	−1.36692
$934$	−48.8586	−1.59870
$935$	−2.60341	−0.0851405
$936$	36.2990	1.18647
$937$	−14.2330	−0.464973	−0.232487	−	0.972600i	$-0.574686\pi$
$937$	−14.2330	−0.464973	−0.232487	+	0.972600i	$0.574686\pi$
$938$	82.6218	2.69770
$939$	19.8522	0.647852
$940$	57.1538	1.86415
$941$	−12.4422	−0.405605	−0.202802	−	0.979220i	$-0.565005\pi$
$941$	−12.4422	−0.405605	−0.202802	+	0.979220i	$0.565005\pi$
$942$	117.776	3.83735
$943$	80.3431	2.61633
$944$	14.3753	0.467876
$945$	−104.083	−3.38581
$946$	−3.56909	−0.116041
$947$	19.4121	0.630808	0.315404	−	0.948958i	$-0.397860\pi$
$947$	19.4121	0.630808	0.315404	+	0.948958i	$0.397860\pi$
$948$	−41.1996	−1.33810
$949$	−10.2042	−0.331242
$950$	2.28480	0.0741287
$951$	−18.0903	−0.586619
$952$	−3.37956	−0.109532
$953$	−10.6130	−0.343789	−0.171895	−	0.985115i	$-0.554989\pi$
$953$	−10.6130	−0.343789	−0.171895	+	0.985115i	$0.554989\pi$
$954$	−33.8737	−1.09670
$955$	41.7620	1.35139
$956$	−31.3941	−1.01536
$957$	−42.0103	−1.35800
$958$	−68.5252	−2.21395
$959$	2.82573	0.0912475
$960$	−93.6433	−3.02233
$961$	29.3621	0.947164
$962$	−7.37988	−0.237937
$963$	122.112	3.93500
$964$	48.3582	1.55751
$965$	43.2344	1.39176
$966$	152.721	4.91372
$967$	−4.46380	−0.143546	−0.0717730	−	0.997421i	$-0.522866\pi$
$967$	−4.46380	−0.143546	−0.0717730	+	0.997421i	$0.522866\pi$
$968$	−12.8828	−0.414070
$969$	−3.48563	−0.111975
$970$	−3.54964	−0.113972
$971$	−2.47887	−0.0795506	−0.0397753	−	0.999209i	$-0.512664\pi$
$971$	−2.47887	−0.0795506	−0.0397753	+	0.999209i	$0.512664\pi$
$972$	−84.8389	−2.72121
$973$	50.3595	1.61445
$974$	11.2975	0.361994
$975$	−8.04658	−0.257697
$976$	3.76330	0.120460
$977$	35.5197	1.13638	0.568188	−	0.822899i	$-0.307645\pi$
$977$	35.5197	1.13638	0.568188	+	0.822899i	$0.307645\pi$
$978$	−2.27531	−0.0727563
$979$	−10.5226	−0.336304
$980$	−17.0997	−0.546230
$981$	−7.34515	−0.234513
$982$	−14.5461	−0.464184
$983$	21.7317	0.693133	0.346566	−	0.938025i	$-0.387348\pi$
$983$	21.7317	0.693133	0.346566	+	0.938025i	$0.387348\pi$
$984$	−52.9354	−1.68752
$985$	40.5998	1.29362
$986$	14.6334	0.466024
$987$	−89.4575	−2.84746
$988$	13.1593	0.418652
$989$	−8.05652	−0.256183
$990$	−55.0354	−1.74914
$991$	29.4205	0.934572	0.467286	−	0.884106i	$-0.345232\pi$
$991$	29.4205	0.934572	0.467286	+	0.884106i	$0.345232\pi$
$992$	59.6273	1.89317
$993$	−39.9451	−1.26762
$994$	19.7463	0.626315
$995$	65.0463	2.06211
$996$	8.16083	0.258586
$997$	0.635455	0.0201251	0.0100625	−	0.999949i	$-0.496797\pi$
$997$	0.635455	0.0201251	0.0100625	+	0.999949i	$0.496797\pi$
$998$	52.9789	1.67702
$999$	13.9757	0.442172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.71	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.71	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+2.16094 q^{2} -3.21639 q^{3} +2.66965 q^{4} -2.39427 q^{5} -6.95041 q^{6} -3.11050 q^{7} +1.44706 q^{8} +7.34515 q^{9} +O(q^{10})\)	\(q+2.16094 q^{2} -3.21639 q^{3} +2.66965 q^{4} -2.39427 q^{5} -6.95041 q^{6} -3.11050 q^{7} +1.44706 q^{8} +7.34515 q^{9} -5.17387 q^{10} +1.44819 q^{11} -8.58662 q^{12} +3.41513 q^{13} -6.72160 q^{14} +7.70091 q^{15} -2.21228 q^{16} +0.750832 q^{17} +15.8724 q^{18} +1.44335 q^{19} -6.39186 q^{20} +10.0046 q^{21} +3.12945 q^{22} +7.06412 q^{23} -4.65431 q^{24} +0.732547 q^{25} +7.37988 q^{26} -13.9757 q^{27} -8.30394 q^{28} +9.01907 q^{29} +16.6412 q^{30} -7.76930 q^{31} -7.67473 q^{32} -4.65794 q^{33} +1.62250 q^{34} +7.44740 q^{35} +19.6090 q^{36} -1.00000 q^{37} +3.11898 q^{38} -10.9844 q^{39} -3.46466 q^{40} +11.3734 q^{41} +21.6193 q^{42} -1.14049 q^{43} +3.86615 q^{44} -17.5863 q^{45} +15.2651 q^{46} -8.94165 q^{47} +7.11556 q^{48} +2.67523 q^{49} +1.58299 q^{50} -2.41497 q^{51} +9.11719 q^{52} -2.13412 q^{53} -30.2006 q^{54} -3.46736 q^{55} -4.50109 q^{56} -4.64236 q^{57} +19.4896 q^{58} -6.49795 q^{59} +20.5587 q^{60} -1.70109 q^{61} -16.7890 q^{62} -22.8471 q^{63} -12.1600 q^{64} -8.17676 q^{65} -10.0655 q^{66} -12.2920 q^{67} +2.00446 q^{68} -22.7209 q^{69} +16.0934 q^{70} -2.93774 q^{71} +10.6289 q^{72} -2.98794 q^{73} -2.16094 q^{74} -2.35616 q^{75} +3.85322 q^{76} -4.50460 q^{77} -23.7366 q^{78} +4.79812 q^{79} +5.29681 q^{80} +22.9158 q^{81} +24.5772 q^{82} -0.950412 q^{83} +26.7087 q^{84} -1.79770 q^{85} -2.46452 q^{86} -29.0088 q^{87} +2.09562 q^{88} -7.26605 q^{89} -38.0029 q^{90} -10.6228 q^{91} +18.8587 q^{92} +24.9891 q^{93} -19.3223 q^{94} -3.45577 q^{95} +24.6849 q^{96} +0.686069 q^{97} +5.78100 q^{98} +10.6372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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