LMFDB - Embedded newform 619.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, 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("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} +O(q^{10})$	\(q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} -2.82958 q^{10} +0.886722 q^{11} +7.77730 q^{12} -1.28594 q^{13} -3.64778 q^{14} +2.93116 q^{15} +0.154415 q^{16} +7.29839 q^{17} -6.09636 q^{18} -0.683286 q^{19} +4.03083 q^{20} +3.77874 q^{21} -2.03567 q^{22} +4.28827 q^{23} -6.93543 q^{24} -3.48083 q^{25} +2.95217 q^{26} -0.819191 q^{27} +5.19639 q^{28} -1.56489 q^{29} -6.72913 q^{30} +1.05127 q^{31} +5.47817 q^{32} +2.10875 q^{33} -16.7551 q^{34} +1.95845 q^{35} +8.68448 q^{36} -0.285339 q^{37} +1.56863 q^{38} -3.05815 q^{39} -3.59451 q^{40} +0.174292 q^{41} -8.67492 q^{42} -5.95067 q^{43} +2.89988 q^{44} +3.27306 q^{45} -9.84468 q^{46} -6.98344 q^{47} +0.367219 q^{48} -4.47524 q^{49} +7.99102 q^{50} +17.3566 q^{51} -4.20547 q^{52} +3.12955 q^{53} +1.88063 q^{54} +1.09293 q^{55} -4.63390 q^{56} -1.62495 q^{57} +3.59256 q^{58} +3.82207 q^{59} +9.58587 q^{60} -0.632482 q^{61} -2.41342 q^{62} +4.21950 q^{63} -12.8852 q^{64} -1.58499 q^{65} -4.84109 q^{66} -1.10009 q^{67} +23.8682 q^{68} +10.1981 q^{69} -4.49606 q^{70} +4.39889 q^{71} -7.74441 q^{72} +14.6478 q^{73} +0.655059 q^{74} -8.27789 q^{75} -2.23457 q^{76} +1.40896 q^{77} +7.02066 q^{78} +13.2226 q^{79} +0.190323 q^{80} -9.91474 q^{81} -0.400125 q^{82} +7.13246 q^{83} +12.3577 q^{84} +8.99559 q^{85} +13.6611 q^{86} -3.72153 q^{87} -2.58598 q^{88} +3.05862 q^{89} -7.51404 q^{90} -2.04330 q^{91} +14.0241 q^{92} +2.50006 q^{93} +16.0320 q^{94} -0.842181 q^{95} +13.0278 q^{96} -7.38986 q^{97} +10.2739 q^{98} +2.35472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	−2.29572	−1.62332	−0.811660	−	0.584130i	$-0.801436\pi$
$2$	−2.29572	−1.62332	−0.811660	+	0.584130i	$0.801436\pi$
$3$	2.37814	1.37302	0.686509	−	0.727121i	$-0.259142\pi$
$3$	2.37814	1.37302	0.686509	+	0.727121i	$0.259142\pi$
$4$	3.27033	1.63517
$5$	1.23255	0.551211	0.275606	−	0.961271i	$-0.411122\pi$
$5$	1.23255	0.551211	0.275606	+	0.961271i	$0.411122\pi$
$6$	−5.45954	−2.22885
$7$	1.58895	0.600566	0.300283	−	0.953850i	$-0.402919\pi$
$7$	1.58895	0.600566	0.300283	+	0.953850i	$0.402919\pi$
$8$	−2.91633	−1.03108
$9$	2.65553	0.885177
$10$	−2.82958	−0.894792
$11$	0.886722	0.267357	0.133678	−	0.991025i	$-0.457321\pi$
$11$	0.886722	0.267357	0.133678	+	0.991025i	$0.457321\pi$
$12$	7.77730	2.24511
$13$	−1.28594	−0.356657	−0.178328	−	0.983971i	$-0.557069\pi$
$13$	−1.28594	−0.356657	−0.178328	+	0.983971i	$0.557069\pi$
$14$	−3.64778	−0.974911
$15$	2.93116	0.756822
$16$	0.154415	0.0386037
$17$	7.29839	1.77012	0.885059	−	0.465478i	$-0.154118\pi$
$17$	7.29839	1.77012	0.885059	+	0.465478i	$0.154118\pi$
$18$	−6.09636	−1.43693
$19$	−0.683286	−0.156757	−0.0783783	−	0.996924i	$-0.524974\pi$
$19$	−0.683286	−0.156757	−0.0783783	+	0.996924i	$0.524974\pi$
$20$	4.03083	0.901322
$21$	3.77874	0.824588
$22$	−2.03567	−0.434006
$23$	4.28827	0.894167	0.447083	−	0.894492i	$-0.352463\pi$
$23$	4.28827	0.894167	0.447083	+	0.894492i	$0.352463\pi$
$24$	−6.93543	−1.41569
$25$	−3.48083	−0.696166
$26$	2.95217	0.578968
$27$	−0.819191	−0.157653
$28$	5.19639	0.982026
$29$	−1.56489	−0.290593	−0.145297	−	0.989388i	$-0.546414\pi$
$29$	−1.56489	−0.290593	−0.145297	+	0.989388i	$0.546414\pi$
$30$	−6.72913	−1.22856
$31$	1.05127	0.188814	0.0944068	−	0.995534i	$-0.469905\pi$
$31$	1.05127	0.188814	0.0944068	+	0.995534i	$0.469905\pi$
$32$	5.47817	0.968413
$33$	2.10875	0.367086
$34$	−16.7551	−2.87347
$35$	1.95845	0.331039
$36$	8.68448	1.44741
$37$	−0.285339	−0.0469095	−0.0234547	−	0.999725i	$-0.507467\pi$
$37$	−0.285339	−0.0469095	−0.0234547	+	0.999725i	$0.507467\pi$
$38$	1.56863	0.254466
$39$	−3.05815	−0.489696
$40$	−3.59451	−0.568342
$41$	0.174292	0.0272198	0.0136099	−	0.999907i	$-0.495668\pi$
$41$	0.174292	0.0272198	0.0136099	+	0.999907i	$0.495668\pi$
$42$	−8.67492	−1.33857
$43$	−5.95067	−0.907468	−0.453734	−	0.891137i	$-0.649908\pi$
$43$	−5.95067	−0.907468	−0.453734	+	0.891137i	$0.649908\pi$
$44$	2.89988	0.437173
$45$	3.27306	0.487920
$46$	−9.84468	−1.45152
$47$	−6.98344	−1.01864	−0.509320	−	0.860577i	$-0.670103\pi$
$47$	−6.98344	−1.01864	−0.509320	+	0.860577i	$0.670103\pi$
$48$	0.367219	0.0530036
$49$	−4.47524	−0.639320
$50$	7.99102	1.13010
$51$	17.3566	2.43040
$52$	−4.20547	−0.583194
$53$	3.12955	0.429877	0.214938	−	0.976628i	$-0.431045\pi$
$53$	3.12955	0.429877	0.214938	+	0.976628i	$0.431045\pi$
$54$	1.88063	0.255922
$55$	1.09293	0.147370
$56$	−4.63390	−0.619231
$57$	−1.62495	−0.215230
$58$	3.59256	0.471726
$59$	3.82207	0.497592	0.248796	−	0.968556i	$-0.419965\pi$
$59$	3.82207	0.497592	0.248796	+	0.968556i	$0.419965\pi$
$60$	9.58587	1.23753
$61$	−0.632482	−0.0809811	−0.0404905	−	0.999180i	$-0.512892\pi$
$61$	−0.632482	−0.0809811	−0.0404905	+	0.999180i	$0.512892\pi$
$62$	−2.41342	−0.306505
$63$	4.21950	0.531607
$64$	−12.8852	−1.61065
$65$	−1.58499	−0.196593
$66$	−4.84109	−0.595897
$67$	−1.10009	−0.134397	−0.0671986	−	0.997740i	$-0.521406\pi$
$67$	−1.10009	−0.134397	−0.0671986	+	0.997740i	$0.521406\pi$
$68$	23.8682	2.89444
$69$	10.1981	1.22771
$70$	−4.49606	−0.537381
$71$	4.39889	0.522052	0.261026	−	0.965332i	$-0.415939\pi$
$71$	4.39889	0.522052	0.261026	+	0.965332i	$0.415939\pi$
$72$	−7.74441	−0.912688
$73$	14.6478	1.71439	0.857197	−	0.514988i	$-0.172204\pi$
$73$	14.6478	1.71439	0.857197	+	0.514988i	$0.172204\pi$
$74$	0.655059	0.0761490
$75$	−8.27789	−0.955849
$76$	−2.23457	−0.256323
$77$	1.40896	0.160565
$78$	7.02066	0.794934
$79$	13.2226	1.48765	0.743827	−	0.668372i	$-0.233009\pi$
$79$	13.2226	1.48765	0.743827	+	0.668372i	$0.233009\pi$
$80$	0.190323	0.0212788
$81$	−9.91474	−1.10164
$82$	−0.400125	−0.0441864
$83$	7.13246	0.782889	0.391445	−	0.920202i	$-0.371975\pi$
$83$	7.13246	0.782889	0.391445	+	0.920202i	$0.371975\pi$
$84$	12.3577	1.34834
$85$	8.99559	0.975709
$86$	13.6611	1.47311
$87$	−3.72153	−0.398990
$88$	−2.58598	−0.275666
$89$	3.05862	0.324213	0.162106	−	0.986773i	$-0.448171\pi$
$89$	3.05862	0.324213	0.162106	+	0.986773i	$0.448171\pi$
$90$	−7.51404	−0.792049
$91$	−2.04330	−0.214196
$92$	14.0241	1.46211
$93$	2.50006	0.259244
$94$	16.0320	1.65358
$95$	−0.842181	−0.0864060
$96$	13.0278	1.32965
$97$	−7.38986	−0.750327	−0.375163	−	0.926959i	$-0.622413\pi$
$97$	−7.38986	−0.750327	−0.375163	+	0.926959i	$0.622413\pi$
$98$	10.2739	1.03782
$99$	2.35472	0.236658
$100$	−11.3835	−1.13835
$101$	3.26959	0.325336	0.162668	−	0.986681i	$-0.447990\pi$
$101$	3.26959	0.325336	0.162668	+	0.986681i	$0.447990\pi$
$102$	−39.8458	−3.94532
$103$	−6.32956	−0.623670	−0.311835	−	0.950136i	$-0.600944\pi$
$103$	−6.32956	−0.623670	−0.311835	+	0.950136i	$0.600944\pi$
$104$	3.75024	0.367741
$105$	4.65746	0.454522
$106$	−7.18458	−0.697828
$107$	2.25130	0.217641	0.108821	−	0.994061i	$-0.465293\pi$
$107$	2.25130	0.217641	0.108821	+	0.994061i	$0.465293\pi$
$108$	−2.67903	−0.257789
$109$	10.6348	1.01863	0.509316	−	0.860580i	$-0.329898\pi$
$109$	10.6348	1.01863	0.509316	+	0.860580i	$0.329898\pi$
$110$	−2.50905	−0.239229
$111$	−0.678575	−0.0644075
$112$	0.245357	0.0231841
$113$	−14.5105	−1.36503	−0.682515	−	0.730872i	$-0.739114\pi$
$113$	−14.5105	−1.36503	−0.682515	+	0.730872i	$0.739114\pi$
$114$	3.73043	0.349386
$115$	5.28549	0.492875
$116$	−5.11772	−0.475169
$117$	−3.41487	−0.315705
$118$	−8.77441	−0.807750
$119$	11.5968	1.06307
$120$	−8.54824	−0.780344
$121$	−10.2137	−0.928520
$122$	1.45200	0.131458
$123$	0.414489	0.0373732
$124$	3.43800	0.308742
$125$	−10.4530	−0.934946
$126$	−9.68680	−0.862969
$127$	−7.90271	−0.701252	−0.350626	−	0.936516i	$-0.614031\pi$
$127$	−7.90271	−0.701252	−0.350626	+	0.936516i	$0.614031\pi$
$128$	18.6244	1.64618
$129$	−14.1515	−1.24597
$130$	3.63868	0.319134
$131$	−6.84860	−0.598365	−0.299183	−	0.954196i	$-0.596714\pi$
$131$	−6.84860	−0.598365	−0.299183	+	0.954196i	$0.596714\pi$
$132$	6.89630	0.600246
$133$	−1.08571	−0.0941427
$134$	2.52550	0.218170
$135$	−1.00969	−0.0869002
$136$	−21.2845	−1.82513
$137$	−9.63629	−0.823284	−0.411642	−	0.911346i	$-0.635044\pi$
$137$	−9.63629	−0.823284	−0.411642	+	0.911346i	$0.635044\pi$
$138$	−23.4120	−1.99296
$139$	−5.24014	−0.444463	−0.222232	−	0.974994i	$-0.571334\pi$
$139$	−5.24014	−0.444463	−0.222232	+	0.974994i	$0.571334\pi$
$140$	6.40479	0.541303
$141$	−16.6076	−1.39861
$142$	−10.0986	−0.847457
$143$	−1.14028	−0.0953546
$144$	0.410054	0.0341711
$145$	−1.92880	−0.160178
$146$	−33.6272	−2.78301
$147$	−10.6427	−0.877798
$148$	−0.933154	−0.0767048
$149$	6.46539	0.529666	0.264833	−	0.964294i	$-0.414683\pi$
$149$	6.46539	0.529666	0.264833	+	0.964294i	$0.414683\pi$
$150$	19.0037	1.55165
$151$	−10.4038	−0.846652	−0.423326	−	0.905977i	$-0.639137\pi$
$151$	−10.4038	−0.846652	−0.423326	+	0.905977i	$0.639137\pi$
$152$	1.99269	0.161628
$153$	19.3811	1.56687
$154$	−3.23457	−0.260649
$155$	1.29574	0.104076
$156$	−10.0012	−0.800735
$157$	−10.7718	−0.859687	−0.429843	−	0.902903i	$-0.641431\pi$
$157$	−10.7718	−0.859687	−0.429843	+	0.902903i	$0.641431\pi$
$158$	−30.3553	−2.41494
$159$	7.44250	0.590229
$160$	6.75209	0.533800
$161$	6.81385	0.537006
$162$	22.7615	1.78831
$163$	3.38162	0.264869	0.132435	−	0.991192i	$-0.457721\pi$
$163$	3.38162	0.264869	0.132435	+	0.991192i	$0.457721\pi$
$164$	0.569991	0.0445089
$165$	2.59913	0.202342
$166$	−16.3741	−1.27088
$167$	−17.7906	−1.37667	−0.688337	−	0.725391i	$-0.741659\pi$
$167$	−17.7906	−1.37667	−0.688337	+	0.725391i	$0.741659\pi$
$168$	−11.0200	−0.850215
$169$	−11.3463	−0.872796
$170$	−20.6514	−1.58389
$171$	−1.81449	−0.138757
$172$	−19.4607	−1.48386
$173$	17.4205	1.32446	0.662228	−	0.749302i	$-0.269611\pi$
$173$	17.4205	1.32446	0.662228	+	0.749302i	$0.269611\pi$
$174$	8.54359	0.647688
$175$	−5.53086	−0.418094
$176$	0.136923	0.0103210
$177$	9.08941	0.683202
$178$	−7.02173	−0.526301
$179$	−4.36884	−0.326543	−0.163271	−	0.986581i	$-0.552205\pi$
$179$	−4.36884	−0.326543	−0.163271	+	0.986581i	$0.552205\pi$
$180$	10.7040	0.797830
$181$	24.1693	1.79649	0.898244	−	0.439496i	$-0.144843\pi$
$181$	24.1693	1.79649	0.898244	+	0.439496i	$0.144843\pi$
$182$	4.69085	0.347709
$183$	−1.50413	−0.111188
$184$	−12.5060	−0.921957
$185$	−0.351693	−0.0258570
$186$	−5.73945	−0.420837
$187$	6.47164	0.473253
$188$	−22.8382	−1.66565
$189$	−1.30165	−0.0946812
$190$	1.93341	0.140265
$191$	−3.26291	−0.236096	−0.118048	−	0.993008i	$-0.537664\pi$
$191$	−3.26291	−0.236096	−0.118048	+	0.993008i	$0.537664\pi$
$192$	−30.6427	−2.21145
$193$	−9.05710	−0.651945	−0.325972	−	0.945379i	$-0.605692\pi$
$193$	−9.05710	−0.651945	−0.325972	+	0.945379i	$0.605692\pi$
$194$	16.9651	1.21802
$195$	−3.76931	−0.269926
$196$	−14.6355	−1.04540
$197$	−21.7562	−1.55006	−0.775031	−	0.631923i	$-0.782266\pi$
$197$	−21.7562	−1.55006	−0.775031	+	0.631923i	$0.782266\pi$
$198$	−5.40578	−0.384172
$199$	−1.25088	−0.0886724	−0.0443362	−	0.999017i	$-0.514117\pi$
$199$	−1.25088	−0.0886724	−0.0443362	+	0.999017i	$0.514117\pi$
$200$	10.1513	0.717802
$201$	−2.61616	−0.184530
$202$	−7.50606	−0.528124
$203$	−2.48653	−0.174520
$204$	56.7617	3.97412
$205$	0.214822	0.0150038
$206$	14.5309	1.01242
$207$	11.3877	0.791496
$208$	−0.198569	−0.0137683
$209$	−0.605885	−0.0419099
$210$	−10.6922	−0.737834
$211$	0.992377	0.0683181	0.0341590	−	0.999416i	$-0.489125\pi$
$211$	0.992377	0.0683181	0.0341590	+	0.999416i	$0.489125\pi$
$212$	10.2347	0.702920
$213$	10.4612	0.716786
$214$	−5.16835	−0.353301
$215$	−7.33446	−0.500206
$216$	2.38903	0.162553
$217$	1.67041	0.113395
$218$	−24.4146	−1.65357
$219$	34.8345	2.35389
$220$	3.57423	0.240975
$221$	−9.38532	−0.631325
$222$	1.55782	0.104554
$223$	3.28542	0.220008	0.110004	−	0.993931i	$-0.464914\pi$
$223$	3.28542	0.220008	0.110004	+	0.993931i	$0.464914\pi$
$224$	8.70453	0.581596
$225$	−9.24346	−0.616231
$226$	33.3120	2.21588
$227$	18.7607	1.24519	0.622596	−	0.782543i	$-0.286078\pi$
$227$	18.7607	1.24519	0.622596	+	0.782543i	$0.286078\pi$
$228$	−5.31412	−0.351936
$229$	7.32209	0.483858	0.241929	−	0.970294i	$-0.422220\pi$
$229$	7.32209	0.483858	0.241929	+	0.970294i	$0.422220\pi$
$230$	−12.1340	−0.800093
$231$	3.35069	0.220459
$232$	4.56375	0.299625
$233$	2.94045	0.192635	0.0963176	−	0.995351i	$-0.469294\pi$
$233$	2.94045	0.192635	0.0963176	+	0.995351i	$0.469294\pi$
$234$	7.83958	0.512490
$235$	−8.60741	−0.561486
$236$	12.4995	0.813645
$237$	31.4450	2.04258
$238$	−26.6229	−1.72571
$239$	21.9756	1.42148	0.710740	−	0.703455i	$-0.248360\pi$
$239$	21.9756	1.42148	0.710740	+	0.703455i	$0.248360\pi$
$240$	0.452615	0.0292161
$241$	−6.85708	−0.441703	−0.220852	−	0.975307i	$-0.570884\pi$
$241$	−6.85708	−0.441703	−0.220852	+	0.975307i	$0.570884\pi$
$242$	23.4479	1.50729
$243$	−21.1210	−1.35492
$244$	−2.06843	−0.132418
$245$	−5.51594	−0.352400
$246$	−0.951551	−0.0606687
$247$	0.878668	0.0559083
$248$	−3.06585	−0.194682
$249$	16.9620	1.07492
$250$	23.9972	1.51772
$251$	4.78887	0.302271	0.151135	−	0.988513i	$-0.451707\pi$
$251$	4.78887	0.302271	0.151135	+	0.988513i	$0.451707\pi$
$252$	13.7992	0.869267
$253$	3.80251	0.239062
$254$	18.1424	1.13836
$255$	21.3927	1.33967
$256$	−16.9861	−1.06163
$257$	−22.0796	−1.37729	−0.688644	−	0.725099i	$-0.741794\pi$
$257$	−22.0796	−1.37729	−0.688644	+	0.725099i	$0.741794\pi$
$258$	32.4879	2.02261
$259$	−0.453389	−0.0281722
$260$	−5.18343	−0.321463
$261$	−4.15562	−0.257227
$262$	15.7225	0.971338
$263$	−13.2804	−0.818904	−0.409452	−	0.912332i	$-0.634280\pi$
$263$	−13.2804	−0.818904	−0.409452	+	0.912332i	$0.634280\pi$
$264$	−6.14980	−0.378494
$265$	3.85731	0.236953
$266$	2.49248	0.152824
$267$	7.27381	0.445150
$268$	−3.59766	−0.219762
$269$	−10.6510	−0.649401	−0.324700	−	0.945817i	$-0.605263\pi$
$269$	−10.6510	−0.649401	−0.324700	+	0.945817i	$0.605263\pi$
$270$	2.31797	0.141067
$271$	−26.8964	−1.63384	−0.816920	−	0.576752i	$-0.804320\pi$
$271$	−26.8964	−1.63384	−0.816920	+	0.576752i	$0.804320\pi$
$272$	1.12698	0.0683331
$273$	−4.85925	−0.294095
$274$	22.1222	1.33645
$275$	−3.08653	−0.186125
$276$	33.3512	2.00751
$277$	−21.0454	−1.26450	−0.632248	−	0.774766i	$-0.717867\pi$
$277$	−21.0454	−1.26450	−0.632248	+	0.774766i	$0.717867\pi$
$278$	12.0299	0.721506
$279$	2.79168	0.167134
$280$	−5.71149	−0.341327
$281$	6.75138	0.402753	0.201377	−	0.979514i	$-0.435458\pi$
$281$	6.75138	0.402753	0.201377	+	0.979514i	$0.435458\pi$
$282$	38.1264	2.27039
$283$	−30.4441	−1.80971	−0.904857	−	0.425716i	$-0.860022\pi$
$283$	−30.4441	−1.80971	−0.904857	+	0.425716i	$0.860022\pi$
$284$	14.3858	0.853642
$285$	−2.00282	−0.118637
$286$	2.61775	0.154791
$287$	0.276940	0.0163473
$288$	14.5475	0.857217
$289$	36.2664	2.13332
$290$	4.42799	0.260020
$291$	−17.5741	−1.03021
$292$	47.9032	2.80332
$293$	11.4521	0.669040	0.334520	−	0.942389i	$-0.391426\pi$
$293$	11.4521	0.669040	0.334520	+	0.942389i	$0.391426\pi$
$294$	24.4328	1.42495
$295$	4.71088	0.274278
$296$	0.832143	0.0483673
$297$	−0.726395	−0.0421497
$298$	−14.8427	−0.859817
$299$	−5.51448	−0.318911
$300$	−27.0715	−1.56297
$301$	−9.45530	−0.544994
$302$	23.8843	1.37439
$303$	7.77552	0.446692
$304$	−0.105510	−0.00605139
$305$	−0.779563	−0.0446377
$306$	−44.4936	−2.54353
$307$	−12.0514	−0.687808	−0.343904	−	0.939005i	$-0.611749\pi$
$307$	−12.0514	−0.687808	−0.343904	+	0.939005i	$0.611749\pi$
$308$	4.60775	0.262551
$309$	−15.0525	−0.856310
$310$	−2.97465	−0.168949
$311$	−26.8292	−1.52135	−0.760673	−	0.649136i	$-0.775131\pi$
$311$	−26.8292	−1.52135	−0.760673	+	0.649136i	$0.775131\pi$
$312$	8.91858	0.504915
$313$	1.71581	0.0969835	0.0484917	−	0.998824i	$-0.484559\pi$
$313$	1.71581	0.0969835	0.0484917	+	0.998824i	$0.484559\pi$
$314$	24.7292	1.39555
$315$	5.20073	0.293028
$316$	43.2422	2.43256
$317$	0.888576	0.0499074	0.0249537	−	0.999689i	$-0.492056\pi$
$317$	0.888576	0.0499074	0.0249537	+	0.999689i	$0.492056\pi$
$318$	−17.0859	−0.958130
$319$	−1.38763	−0.0776921
$320$	−15.8816	−0.887806
$321$	5.35390	0.298825
$322$	−15.6427	−0.871733
$323$	−4.98689	−0.277478
$324$	−32.4245	−1.80136
$325$	4.47616	0.248293
$326$	−7.76326	−0.429967
$327$	25.2911	1.39860
$328$	−0.508292	−0.0280657
$329$	−11.0963	−0.611760
$330$	−5.96687	−0.328465
$331$	−31.2292	−1.71651	−0.858256	−	0.513222i	$-0.828452\pi$
$331$	−31.2292	−1.71651	−0.858256	+	0.513222i	$0.828452\pi$
$332$	23.3255	1.28015
$333$	−0.757727	−0.0415232
$334$	40.8421	2.23478
$335$	−1.35591	−0.0740812
$336$	0.583493	0.0318321
$337$	−14.8366	−0.808202	−0.404101	−	0.914714i	$-0.632416\pi$
$337$	−14.8366	−0.808202	−0.404101	+	0.914714i	$0.632416\pi$
$338$	26.0480	1.41683
$339$	−34.5079	−1.87421
$340$	29.4186	1.59545
$341$	0.932184	0.0504806
$342$	4.16556	0.225248
$343$	−18.2336	−0.984520
$344$	17.3541	0.935671
$345$	12.5696	0.676726
$346$	−39.9926	−2.15002
$347$	14.5384	0.780461	0.390231	−	0.920717i	$-0.372395\pi$
$347$	14.5384	0.780461	0.390231	+	0.920717i	$0.372395\pi$
$348$	−12.1706	−0.652415
$349$	−2.48605	−0.133075	−0.0665375	−	0.997784i	$-0.521195\pi$
$349$	−2.48605	−0.133075	−0.0665375	+	0.997784i	$0.521195\pi$
$350$	12.6973	0.678700
$351$	1.05343	0.0562281
$352$	4.85761	0.258912
$353$	−11.3461	−0.603893	−0.301947	−	0.953325i	$-0.597636\pi$
$353$	−11.3461	−0.603893	−0.301947	+	0.953325i	$0.597636\pi$
$354$	−20.8667	−1.10906
$355$	5.42183	0.287761
$356$	10.0027	0.530142
$357$	27.5787	1.45962
$358$	10.0296	0.530083
$359$	8.73284	0.460902	0.230451	−	0.973084i	$-0.425980\pi$
$359$	8.73284	0.460902	0.230451	+	0.973084i	$0.425980\pi$
$360$	−9.54534	−0.503084
$361$	−18.5331	−0.975427
$362$	−55.4859	−2.91628
$363$	−24.2896	−1.27487
$364$	−6.68227	−0.350246
$365$	18.0541	0.944993
$366$	3.45306	0.180494
$367$	11.4963	0.600104	0.300052	−	0.953923i	$-0.402996\pi$
$367$	11.4963	0.600104	0.300052	+	0.953923i	$0.402996\pi$
$368$	0.662173	0.0345182
$369$	0.462837	0.0240943
$370$	0.807390	0.0419742
$371$	4.97269	0.258169
$372$	8.17604	0.423908
$373$	9.94088	0.514719	0.257360	−	0.966316i	$-0.417147\pi$
$373$	9.94088	0.514719	0.257360	+	0.966316i	$0.417147\pi$
$374$	−14.8571	−0.768241
$375$	−24.8587	−1.28370
$376$	20.3660	1.05030
$377$	2.01237	0.103642
$378$	2.98823	0.153698
$379$	25.8225	1.32641	0.663207	−	0.748436i	$-0.269195\pi$
$379$	25.8225	1.32641	0.663207	+	0.748436i	$0.269195\pi$
$380$	−2.75421	−0.141288
$381$	−18.7937	−0.962832
$382$	7.49072	0.383259
$383$	5.98909	0.306028	0.153014	−	0.988224i	$-0.451102\pi$
$383$	5.98909	0.306028	0.153014	+	0.988224i	$0.451102\pi$
$384$	44.2914	2.26024
$385$	1.73660	0.0885054
$386$	20.7926	1.05831
$387$	−15.8022	−0.803270
$388$	−24.1673	−1.22691
$389$	8.96719	0.454655	0.227327	−	0.973818i	$-0.427001\pi$
$389$	8.96719	0.454655	0.227327	+	0.973818i	$0.427001\pi$
$390$	8.65328	0.438176
$391$	31.2975	1.58278
$392$	13.0513	0.659190
$393$	−16.2869	−0.821566
$394$	49.9461	2.51625
$395$	16.2974	0.820011
$396$	7.70072	0.386976
$397$	35.7120	1.79233	0.896167	−	0.443717i	$-0.146340\pi$
$397$	35.7120	1.79233	0.896167	+	0.443717i	$0.146340\pi$
$398$	2.87167	0.143944
$399$	−2.58196	−0.129260
$400$	−0.537492	−0.0268746
$401$	29.9885	1.49755	0.748776	−	0.662823i	$-0.230642\pi$
$401$	29.9885	1.49755	0.748776	+	0.662823i	$0.230642\pi$
$402$	6.00597	0.299551
$403$	−1.35187	−0.0673417
$404$	10.6926	0.531979
$405$	−12.2204	−0.607235
$406$	5.70839	0.283303
$407$	−0.253017	−0.0125416
$408$	−50.6175	−2.50594
$409$	26.2183	1.29641	0.648206	−	0.761465i	$-0.275520\pi$
$409$	26.2183	1.29641	0.648206	+	0.761465i	$0.275520\pi$
$410$	−0.493172	−0.0243560
$411$	−22.9164	−1.13038
$412$	−20.6998	−1.01980
$413$	6.07308	0.298837
$414$	−26.1429	−1.28485
$415$	8.79108	0.431537
$416$	−7.04462	−0.345391
$417$	−12.4618	−0.610256
$418$	1.39094	0.0680332
$419$	−12.5753	−0.614344	−0.307172	−	0.951654i	$-0.599383\pi$
$419$	−12.5753	−0.614344	−0.307172	+	0.951654i	$0.599383\pi$
$420$	15.2315	0.743219
$421$	27.1337	1.32242	0.661208	−	0.750202i	$-0.270044\pi$
$421$	27.1337	1.32242	0.661208	+	0.750202i	$0.270044\pi$
$422$	−2.27822	−0.110902
$423$	−18.5448	−0.901677
$424$	−9.12681	−0.443237
$425$	−25.4045	−1.23230
$426$	−24.0159	−1.16357
$427$	−1.00498	−0.0486345
$428$	7.36250	0.355880
$429$	−2.71173	−0.130924
$430$	16.8379	0.811995
$431$	−4.65747	−0.224342	−0.112171	−	0.993689i	$-0.535780\pi$
$431$	−4.65747	−0.224342	−0.112171	+	0.993689i	$0.535780\pi$
$432$	−0.126495	−0.00608600
$433$	−1.07692	−0.0517535	−0.0258767	−	0.999665i	$-0.508238\pi$
$433$	−1.07692	−0.0517535	−0.0258767	+	0.999665i	$0.508238\pi$
$434$	−3.83480	−0.184076
$435$	−4.58695	−0.219928
$436$	34.7794	1.66563
$437$	−2.93012	−0.140167
$438$	−79.9702	−3.82112
$439$	5.07319	0.242130	0.121065	−	0.992645i	$-0.461369\pi$
$439$	5.07319	0.242130	0.121065	+	0.992645i	$0.461369\pi$
$440$	−3.18733	−0.151950
$441$	−11.8842	−0.565912
$442$	21.5461	1.02484
$443$	−35.8484	−1.70321	−0.851603	−	0.524187i	$-0.824369\pi$
$443$	−35.8484	−1.70321	−0.851603	+	0.524187i	$0.824369\pi$
$444$	−2.21917	−0.105317
$445$	3.76989	0.178710
$446$	−7.54240	−0.357143
$447$	15.3756	0.727240
$448$	−20.4739	−0.967300
$449$	27.4850	1.29710	0.648548	−	0.761174i	$-0.275377\pi$
$449$	27.4850	1.29710	0.648548	+	0.761174i	$0.275377\pi$
$450$	21.2204	1.00034
$451$	0.154548	0.00727739
$452$	−47.4541	−2.23205
$453$	−24.7417	−1.16247
$454$	−43.0694	−2.02135
$455$	−2.51846	−0.118067
$456$	4.73889	0.221919
$457$	−14.6879	−0.687072	−0.343536	−	0.939139i	$-0.611625\pi$
$457$	−14.6879	−0.687072	−0.343536	+	0.939139i	$0.611625\pi$
$458$	−16.8095	−0.785456
$459$	−5.97877	−0.279065
$460$	17.2853	0.805932
$461$	−6.30188	−0.293508	−0.146754	−	0.989173i	$-0.546883\pi$
$461$	−6.30188	−0.293508	−0.146754	+	0.989173i	$0.546883\pi$
$462$	−7.69225	−0.357876
$463$	29.8205	1.38587	0.692937	−	0.720998i	$-0.256316\pi$
$463$	29.8205	1.38587	0.692937	+	0.720998i	$0.256316\pi$
$464$	−0.241643	−0.0112180
$465$	3.08144	0.142898
$466$	−6.75045	−0.312709
$467$	−37.0003	−1.71217	−0.856085	−	0.516835i	$-0.827110\pi$
$467$	−37.0003	−1.71217	−0.856085	+	0.516835i	$0.827110\pi$
$468$	−11.1678	−0.516230
$469$	−1.74798	−0.0807144
$470$	19.7602	0.911470
$471$	−25.6169	−1.18037
$472$	−11.1464	−0.513056
$473$	−5.27659	−0.242618
$474$	−72.1891	−3.31575
$475$	2.37840	0.109129
$476$	37.9253	1.73830
$477$	8.31062	0.380517
$478$	−50.4497	−2.30752
$479$	−4.15963	−0.190058	−0.0950292	−	0.995474i	$-0.530294\pi$
$479$	−4.15963	−0.190058	−0.0950292	+	0.995474i	$0.530294\pi$
$480$	16.0574	0.732916
$481$	0.366930	0.0167306
$482$	15.7419	0.717026
$483$	16.2043	0.737319
$484$	−33.4023	−1.51829
$485$	−9.10834	−0.413588
$486$	48.4880	2.19946
$487$	−10.7350	−0.486448	−0.243224	−	0.969970i	$-0.578205\pi$
$487$	−10.7350	−0.486448	−0.243224	+	0.969970i	$0.578205\pi$
$488$	1.84453	0.0834979
$489$	8.04196	0.363670
$490$	12.6631	0.572059
$491$	25.8440	1.16632	0.583161	−	0.812357i	$-0.301816\pi$
$491$	25.8440	1.16632	0.583161	+	0.812357i	$0.301816\pi$
$492$	1.35552	0.0611114
$493$	−11.4212	−0.514385
$494$	−2.01718	−0.0907571
$495$	2.90230	0.130449
$496$	0.162332	0.00728891
$497$	6.98960	0.313527
$498$	−38.9399	−1.74494
$499$	−34.0984	−1.52645	−0.763226	−	0.646132i	$-0.776386\pi$
$499$	−34.0984	−1.52645	−0.763226	+	0.646132i	$0.776386\pi$
$500$	−34.1848	−1.52879
$501$	−42.3084	−1.89020
$502$	−10.9939	−0.490682
$503$	−6.79558	−0.303000	−0.151500	−	0.988457i	$-0.548410\pi$
$503$	−6.79558	−0.303000	−0.151500	+	0.988457i	$0.548410\pi$
$504$	−12.3055	−0.548129
$505$	4.02991	0.179329
$506$	−8.72949	−0.388073
$507$	−26.9832	−1.19836
$508$	−25.8445	−1.14666
$509$	24.6142	1.09101	0.545503	−	0.838109i	$-0.316338\pi$
$509$	24.6142	1.09101	0.545503	+	0.838109i	$0.316338\pi$
$510$	−49.1118	−2.17471
$511$	23.2746	1.02961
$512$	1.74656	0.0771878
$513$	0.559742	0.0247132
$514$	50.6886	2.23578
$515$	−7.80146	−0.343774
$516$	−46.2801	−2.03737
$517$	−6.19237	−0.272340
$518$	1.04085	0.0457325
$519$	41.4283	1.81850
$520$	4.62234	0.202703
$521$	43.9291	1.92457	0.962284	−	0.272047i	$-0.0877006\pi$
$521$	43.9291	1.92457	0.962284	+	0.272047i	$0.0877006\pi$
$522$	9.54015	0.417561
$523$	33.5193	1.46570	0.732849	−	0.680392i	$-0.238190\pi$
$523$	33.5193	1.46570	0.732849	+	0.680392i	$0.238190\pi$
$524$	−22.3972	−0.978427
$525$	−13.1531	−0.574050
$526$	30.4881	1.32934
$527$	7.67257	0.334223
$528$	0.325622	0.0141709
$529$	−4.61071	−0.200466
$530$	−8.85531	−0.384650
$531$	10.1496	0.440457
$532$	−3.55062	−0.153939
$533$	−0.224129	−0.00970812
$534$	−16.6986	−0.722621
$535$	2.77483	0.119966
$536$	3.20822	0.138574
$537$	−10.3897	−0.448349
$538$	24.4516	1.05419
$539$	−3.96830	−0.170927
$540$	−3.30202	−0.142096
$541$	0.414672	0.0178281	0.00891407	−	0.999960i	$-0.497163\pi$
$541$	0.414672	0.0178281	0.00891407	+	0.999960i	$0.497163\pi$
$542$	61.7466	2.65224
$543$	57.4778	2.46661
$544$	39.9818	1.71421
$545$	13.1079	0.561481
$546$	11.1555	0.477410
$547$	−36.8701	−1.57645	−0.788226	−	0.615386i	$-0.789000\pi$
$547$	−36.8701	−1.57645	−0.788226	+	0.615386i	$0.789000\pi$
$548$	−31.5139	−1.34621
$549$	−1.67958	−0.0716826
$550$	7.08581	0.302140
$551$	1.06927	0.0455524
$552$	−29.7410	−1.26586
$553$	21.0100	0.893434
$554$	48.3143	2.05268
$555$	−0.836375	−0.0355021
$556$	−17.1370	−0.726771
$557$	−0.0876469	−0.00371372	−0.00185686	−	0.999998i	$-0.500591\pi$
$557$	−0.0876469	−0.00371372	−0.00185686	+	0.999998i	$0.500591\pi$
$558$	−6.40892	−0.271311
$559$	7.65223	0.323655
$560$	0.302414	0.0127793
$561$	15.3904	0.649785
$562$	−15.4993	−0.653798
$563$	20.8536	0.878875	0.439437	−	0.898273i	$-0.355178\pi$
$563$	20.8536	0.878875	0.439437	+	0.898273i	$0.355178\pi$
$564$	−54.3123	−2.28696
$565$	−17.8848	−0.752419
$566$	69.8911	2.93774
$567$	−15.7540	−0.661606
$568$	−12.8286	−0.538276
$569$	−22.3044	−0.935049	−0.467525	−	0.883980i	$-0.654854\pi$
$569$	−22.3044	−0.935049	−0.467525	+	0.883980i	$0.654854\pi$
$570$	4.59792	0.192586
$571$	−15.7505	−0.659136	−0.329568	−	0.944132i	$-0.606903\pi$
$571$	−15.7505	−0.659136	−0.329568	+	0.944132i	$0.606903\pi$
$572$	−3.72908	−0.155921
$573$	−7.75964	−0.324164
$574$	−0.635777	−0.0265368
$575$	−14.9268	−0.622489
$576$	−34.2170	−1.42571
$577$	−4.92947	−0.205216	−0.102608	−	0.994722i	$-0.532719\pi$
$577$	−4.92947	−0.205216	−0.102608	+	0.994722i	$0.532719\pi$
$578$	−83.2576	−3.46306
$579$	−21.5390	−0.895131
$580$	−6.30782	−0.261918
$581$	11.3331	0.470177
$582$	40.3452	1.67236
$583$	2.77504	0.114931
$584$	−42.7178	−1.76768
$585$	−4.20898	−0.174020
$586$	−26.2909	−1.08607
$587$	−4.32731	−0.178607	−0.0893036	−	0.996004i	$-0.528464\pi$
$587$	−4.32731	−0.178607	−0.0893036	+	0.996004i	$0.528464\pi$
$588$	−34.8053	−1.43535
$589$	−0.718318	−0.0295978
$590$	−10.8149	−0.445241
$591$	−51.7391	−2.12826
$592$	−0.0440606	−0.00181088
$593$	−42.4209	−1.74202	−0.871009	−	0.491267i	$-0.836534\pi$
$593$	−42.4209	−1.74202	−0.871009	+	0.491267i	$0.836534\pi$
$594$	1.66760	0.0684224
$595$	14.2935	0.585978
$596$	21.1440	0.866092
$597$	−2.97476	−0.121749
$598$	12.6597	0.517694
$599$	−12.1937	−0.498222	−0.249111	−	0.968475i	$-0.580138\pi$
$599$	−12.1937	−0.498222	−0.249111	+	0.968475i	$0.580138\pi$
$600$	24.1411	0.985555
$601$	35.7522	1.45836	0.729182	−	0.684320i	$-0.239901\pi$
$601$	35.7522	1.45836	0.729182	+	0.684320i	$0.239901\pi$
$602$	21.7067	0.884700
$603$	−2.92132	−0.118965
$604$	−34.0240	−1.38442
$605$	−12.5889	−0.511811
$606$	−17.8504	−0.725124
$607$	38.1033	1.54656	0.773282	−	0.634062i	$-0.218614\pi$
$607$	38.1033	1.54656	0.773282	+	0.634062i	$0.218614\pi$
$608$	−3.74316	−0.151805
$609$	−5.91332	−0.239620
$610$	1.78966	0.0724612
$611$	8.98032	0.363305
$612$	63.3827	2.56209
$613$	46.0775	1.86105	0.930527	−	0.366224i	$-0.119349\pi$
$613$	46.0775	1.86105	0.930527	+	0.366224i	$0.119349\pi$
$614$	27.6666	1.11653
$615$	0.510877	0.0206005
$616$	−4.10898	−0.165556
$617$	−17.4268	−0.701575	−0.350788	−	0.936455i	$-0.614086\pi$
$617$	−17.4268	−0.701575	−0.350788	+	0.936455i	$0.614086\pi$
$618$	34.5564	1.39006
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	4.23749	0.170182
$621$	−3.51291	−0.140968
$622$	61.5924	2.46963
$623$	4.85999	0.194711
$624$	−0.472224	−0.0189041
$625$	4.52035	0.180814
$626$	−3.93903	−0.157435
$627$	−1.44088	−0.0575431
$628$	−35.2275	−1.40573
$629$	−2.08252	−0.0830353
$630$	−11.9394	−0.475678
$631$	−2.18545	−0.0870015	−0.0435008	−	0.999053i	$-0.513851\pi$
$631$	−2.18545	−0.0870015	−0.0435008	+	0.999053i	$0.513851\pi$
$632$	−38.5614	−1.53389
$633$	2.36001	0.0938019
$634$	−2.03992	−0.0810156
$635$	−9.74045	−0.386538
$636$	24.3395	0.965122
$637$	5.75492	0.228018
$638$	3.18560	0.126119
$639$	11.6814	0.462108
$640$	22.9555	0.907394
$641$	26.7023	1.05468	0.527339	−	0.849655i	$-0.323190\pi$
$641$	26.7023	1.05468	0.527339	+	0.849655i	$0.323190\pi$
$642$	−12.2910	−0.485089
$643$	−24.5173	−0.966867	−0.483434	−	0.875381i	$-0.660611\pi$
$643$	−24.5173	−0.966867	−0.483434	+	0.875381i	$0.660611\pi$
$644$	22.2835	0.878095
$645$	−17.4424	−0.686792
$646$	11.4485	0.450435
$647$	−5.35518	−0.210534	−0.105267	−	0.994444i	$-0.533570\pi$
$647$	−5.35518	−0.210534	−0.105267	+	0.994444i	$0.533570\pi$
$648$	28.9147	1.13588
$649$	3.38912	0.133034
$650$	−10.2760	−0.403058
$651$	3.97247	0.155693
$652$	11.0590	0.433105
$653$	31.0856	1.21648	0.608238	−	0.793755i	$-0.291877\pi$
$653$	31.0856	1.21648	0.608238	+	0.793755i	$0.291877\pi$
$654$	−58.0613	−2.27037
$655$	−8.44121	−0.329826
$656$	0.0269132	0.00105078
$657$	38.8977	1.51754
$658$	25.4741	0.993083
$659$	27.8723	1.08575	0.542875	−	0.839814i	$-0.317336\pi$
$659$	27.8723	1.08575	0.542875	+	0.839814i	$0.317336\pi$
$660$	8.50001	0.330862
$661$	39.9814	1.55510	0.777549	−	0.628822i	$-0.216463\pi$
$661$	39.9814	1.55510	0.777549	+	0.628822i	$0.216463\pi$
$662$	71.6935	2.78645
$663$	−22.3196	−0.866820
$664$	−20.8006	−0.807221
$665$	−1.33818	−0.0518925
$666$	1.73953	0.0674054
$667$	−6.71069	−0.259839
$668$	−58.1810	−2.25109
$669$	7.81317	0.302075
$670$	3.11279	0.120257
$671$	−0.560836	−0.0216508
$672$	20.7006	0.798541
$673$	3.95407	0.152418	0.0762092	−	0.997092i	$-0.475718\pi$
$673$	3.95407	0.152418	0.0762092	+	0.997092i	$0.475718\pi$
$674$	34.0607	1.31197
$675$	2.85147	0.109753
$676$	−37.1063	−1.42717
$677$	−15.9051	−0.611281	−0.305641	−	0.952147i	$-0.598871\pi$
$677$	−15.9051	−0.611281	−0.305641	+	0.952147i	$0.598871\pi$
$678$	79.2204	3.04244
$679$	−11.7421	−0.450621
$680$	−26.2341	−1.00603
$681$	44.6156	1.70967
$682$	−2.14003	−0.0819462
$683$	−45.2333	−1.73080	−0.865401	−	0.501079i	$-0.832937\pi$
$683$	−45.2333	−1.73080	−0.865401	+	0.501079i	$0.832937\pi$
$684$	−5.93398	−0.226892
$685$	−11.8772	−0.453803
$686$	41.8592	1.59819
$687$	17.4129	0.664345
$688$	−0.918871	−0.0350316
$689$	−4.02443	−0.153319
$690$	−28.8563	−1.09854
$691$	11.3211	0.430676	0.215338	−	0.976540i	$-0.430915\pi$
$691$	11.3211	0.430676	0.215338	+	0.976540i	$0.430915\pi$
$692$	56.9709	2.16571
$693$	3.74153	0.142129
$694$	−33.3761	−1.26694
$695$	−6.45871	−0.244993
$696$	10.8532	0.411390
$697$	1.27205	0.0481822
$698$	5.70727	0.216023
$699$	6.99279	0.264492
$700$	−18.0878	−0.683653
$701$	26.9662	1.01850	0.509251	−	0.860618i	$-0.329923\pi$
$701$	26.9662	1.01850	0.509251	+	0.860618i	$0.329923\pi$
$702$	−2.41839	−0.0912763
$703$	0.194968	0.00735337
$704$	−11.4256	−0.430617
$705$	−20.4696	−0.770930
$706$	26.0475	0.980311
$707$	5.19521	0.195386
$708$	29.7254	1.11715
$709$	32.3145	1.21360	0.606799	−	0.794855i	$-0.292453\pi$
$709$	32.3145	1.21360	0.606799	+	0.794855i	$0.292453\pi$
$710$	−12.4470	−0.467128
$711$	35.1129	1.31684
$712$	−8.91994	−0.334289
$713$	4.50813	0.168831
$714$	−63.3129	−2.36943
$715$	−1.40544	−0.0525605
$716$	−14.2876	−0.533952
$717$	52.2609	1.95172
$718$	−20.0482	−0.748191
$719$	−7.42994	−0.277090	−0.138545	−	0.990356i	$-0.544243\pi$
$719$	−7.42994	−0.277090	−0.138545	+	0.990356i	$0.544243\pi$
$720$	0.505410	0.0188355
$721$	−10.0573	−0.374555
$722$	42.5469	1.58343
$723$	−16.3071	−0.606466
$724$	79.0416	2.93756
$725$	5.44713	0.202301
$726$	55.7622	2.06953
$727$	−36.0936	−1.33864	−0.669318	−	0.742976i	$-0.733414\pi$
$727$	−36.0936	−1.33864	−0.669318	+	0.742976i	$0.733414\pi$
$728$	5.95894	0.220853
$729$	−20.4845	−0.758685
$730$	−41.4471	−1.53403
$731$	−43.4303	−1.60633
$732$	−4.91900	−0.181812
$733$	30.9713	1.14395	0.571975	−	0.820271i	$-0.306177\pi$
$733$	30.9713	1.14395	0.571975	+	0.820271i	$0.306177\pi$
$734$	−26.3924	−0.974160
$735$	−13.1177	−0.483852
$736$	23.4919	0.865923
$737$	−0.975473	−0.0359320
$738$	−1.06254	−0.0391128
$739$	19.8451	0.730013	0.365007	−	0.931005i	$-0.381067\pi$
$739$	19.8451	0.730013	0.365007	+	0.931005i	$0.381067\pi$
$740$	−1.15015	−0.0422805
$741$	2.08959	0.0767631
$742$	−11.4159	−0.419092
$743$	−38.6318	−1.41726	−0.708631	−	0.705579i	$-0.750687\pi$
$743$	−38.6318	−1.41726	−0.708631	+	0.705579i	$0.750687\pi$
$744$	−7.29101	−0.267301
$745$	7.96889	0.291957
$746$	−22.8215	−0.835554
$747$	18.9405	0.692996
$748$	21.1644	0.773848
$749$	3.57720	0.130708
$750$	57.0686	2.08385
$751$	−12.4844	−0.455562	−0.227781	−	0.973712i	$-0.573147\pi$
$751$	−12.4844	−0.455562	−0.227781	+	0.973712i	$0.573147\pi$
$752$	−1.07835	−0.0393233
$753$	11.3886	0.415023
$754$	−4.61983	−0.168244
$755$	−12.8232	−0.466684
$756$	−4.25684	−0.154820
$757$	−3.77413	−0.137173	−0.0685865	−	0.997645i	$-0.521849\pi$
$757$	−3.77413	−0.137173	−0.0685865	+	0.997645i	$0.521849\pi$
$758$	−59.2813	−2.15319
$759$	9.04288	0.328236
$760$	2.45608	0.0890914
$761$	24.0444	0.871608	0.435804	−	0.900041i	$-0.356464\pi$
$761$	24.0444	0.871608	0.435804	+	0.900041i	$0.356464\pi$
$762$	43.1451	1.56298
$763$	16.8982	0.611756
$764$	−10.6708	−0.386056
$765$	23.8881	0.863676
$766$	−13.7493	−0.496781
$767$	−4.91497	−0.177469
$768$	−40.3953	−1.45764
$769$	48.4431	1.74690	0.873451	−	0.486913i	$-0.161877\pi$
$769$	48.4431	1.74690	0.873451	+	0.486913i	$0.161877\pi$
$770$	−3.98675	−0.143673
$771$	−52.5083	−1.89104
$772$	−29.6197	−1.06604
$773$	27.3322	0.983070	0.491535	−	0.870858i	$-0.336436\pi$
$773$	27.3322	0.983070	0.491535	+	0.870858i	$0.336436\pi$
$774$	36.2774	1.30396
$775$	−3.65929	−0.131446
$776$	21.5513	0.773646
$777$	−1.07822	−0.0386810
$778$	−20.5862	−0.738050
$779$	−0.119091	−0.00426688
$780$	−12.3269	−0.441374
$781$	3.90059	0.139574
$782$	−71.8503	−2.56936
$783$	1.28195	0.0458130
$784$	−0.691044	−0.0246801
$785$	−13.2768	−0.473869
$786$	37.3902	1.33366
$787$	48.7456	1.73759	0.868797	−	0.495168i	$-0.164894\pi$
$787$	48.7456	1.73759	0.868797	+	0.495168i	$0.164894\pi$
$788$	−71.1499	−2.53461
$789$	−31.5826	−1.12437
$790$	−37.4143	−1.33114
$791$	−23.0564	−0.819790
$792$	−6.86714	−0.244013
$793$	0.813337	0.0288825
$794$	−81.9848	−2.90953
$795$	9.17322	0.325341
$796$	−4.09079	−0.144994
$797$	1.26368	0.0447620	0.0223810	−	0.999750i	$-0.492875\pi$
$797$	1.26368	0.0447620	0.0223810	+	0.999750i	$0.492875\pi$
$798$	5.92745	0.209830
$799$	−50.9679	−1.80311
$800$	−19.0686	−0.674176
$801$	8.12226	0.286986
$802$	−68.8452	−2.43101
$803$	12.9885	0.458355
$804$	−8.55572	−0.301737
$805$	8.39837	0.296004
$806$	3.10353	0.109317
$807$	−25.3294	−0.891639
$808$	−9.53520	−0.335447
$809$	51.9851	1.82770	0.913850	−	0.406053i	$-0.133095\pi$
$809$	51.9851	1.82770	0.913850	+	0.406053i	$0.133095\pi$
$810$	28.0546	0.985737
$811$	−34.5911	−1.21466	−0.607329	−	0.794450i	$-0.707759\pi$
$811$	−34.5911	−1.21466	−0.607329	+	0.794450i	$0.707759\pi$
$812$	−8.13180	−0.285370
$813$	−63.9633	−2.24329
$814$	0.580855	0.0203590
$815$	4.16800	0.145999
$816$	2.68011	0.0938226
$817$	4.06601	0.142252
$818$	−60.1899	−2.10449
$819$	−5.42605	−0.189601
$820$	0.702540	0.0245338
$821$	−15.5898	−0.544089	−0.272044	−	0.962285i	$-0.587700\pi$
$821$	−15.5898	−0.544089	−0.272044	+	0.962285i	$0.587700\pi$
$822$	52.6097	1.83497
$823$	42.7901	1.49157	0.745784	−	0.666188i	$-0.232075\pi$
$823$	42.7901	1.49157	0.745784	+	0.666188i	$0.232075\pi$
$824$	18.4591	0.643053
$825$	−7.34019	−0.255553
$826$	−13.9421	−0.485107
$827$	47.0912	1.63752	0.818761	−	0.574135i	$-0.194662\pi$
$827$	47.0912	1.63752	0.818761	+	0.574135i	$0.194662\pi$
$828$	37.2414	1.29423
$829$	−17.7774	−0.617436	−0.308718	−	0.951154i	$-0.599900\pi$
$829$	−17.7774	−0.617436	−0.308718	+	0.951154i	$0.599900\pi$
$830$	−20.1819	−0.700523
$831$	−50.0488	−1.73617
$832$	16.5696	0.574448
$833$	−32.6621	−1.13167
$834$	28.6087	0.990640
$835$	−21.9277	−0.758838
$836$	−1.98145	−0.0685298
$837$	−0.861190	−0.0297671
$838$	28.8694	0.997277
$839$	33.1147	1.14325	0.571624	−	0.820516i	$-0.306314\pi$
$839$	33.1147	1.14325	0.571624	+	0.820516i	$0.306314\pi$
$840$	−13.5827	−0.468648
$841$	−26.5511	−0.915556
$842$	−62.2914	−2.14670
$843$	16.0557	0.552988
$844$	3.24541	0.111711
$845$	−13.9849	−0.481095
$846$	42.5736	1.46371
$847$	−16.2291	−0.557638
$848$	0.483249	0.0165948
$849$	−72.4002	−2.48477
$850$	58.3215	2.00041
$851$	−1.22361	−0.0419449
$852$	34.2115	1.17207
$853$	37.2476	1.27533	0.637666	−	0.770313i	$-0.279900\pi$
$853$	37.2476	1.27533	0.637666	+	0.770313i	$0.279900\pi$
$854$	2.30716	0.0789493
$855$	−2.23644	−0.0764846
$856$	−6.56553	−0.224405
$857$	−48.8641	−1.66916	−0.834582	−	0.550883i	$-0.814291\pi$
$857$	−48.8641	−1.66916	−0.834582	+	0.550883i	$0.814291\pi$
$858$	6.22538	0.212531
$859$	−51.1884	−1.74652	−0.873262	−	0.487250i	$-0.838000\pi$
$859$	−51.1884	−1.74652	−0.873262	+	0.487250i	$0.838000\pi$
$860$	−23.9861	−0.817921
$861$	0.658602	0.0224451
$862$	10.6922	0.364179
$863$	−5.69769	−0.193951	−0.0969757	−	0.995287i	$-0.530917\pi$
$863$	−5.69769	−0.193951	−0.0969757	+	0.995287i	$0.530917\pi$
$864$	−4.48767	−0.152673
$865$	21.4716	0.730055
$866$	2.47231	0.0840124
$867$	86.2466	2.92909
$868$	5.46281	0.185420
$869$	11.7247	0.397734
$870$	10.5304	0.357013
$871$	1.41465	0.0479337
$872$	−31.0147	−1.05029
$873$	−19.6240	−0.664173
$874$	6.72673	0.227535
$875$	−16.6093	−0.561497
$876$	113.920	3.84901
$877$	−19.4427	−0.656533	−0.328266	−	0.944585i	$-0.606464\pi$
$877$	−19.4427	−0.656533	−0.328266	+	0.944585i	$0.606464\pi$
$878$	−11.6466	−0.393054
$879$	27.2347	0.918603
$880$	0.168764	0.00568903
$881$	5.37476	0.181080	0.0905401	−	0.995893i	$-0.471141\pi$
$881$	5.37476	0.181080	0.0905401	+	0.995893i	$0.471141\pi$
$882$	27.2827	0.918656
$883$	−9.77223	−0.328862	−0.164431	−	0.986389i	$-0.552579\pi$
$883$	−9.77223	−0.328862	−0.164431	+	0.986389i	$0.552579\pi$
$884$	−30.6931	−1.03232
$885$	11.2031	0.376588
$886$	82.2978	2.76485
$887$	36.0013	1.20881	0.604403	−	0.796679i	$-0.293412\pi$
$887$	36.0013	1.20881	0.604403	+	0.796679i	$0.293412\pi$
$888$	1.97895	0.0664092
$889$	−12.5570	−0.421148
$890$	−8.65460	−0.290103
$891$	−8.79162	−0.294530
$892$	10.7444	0.359749
$893$	4.77169	0.159679
$894$	−35.2980	−1.18054
$895$	−5.38480	−0.179994
$896$	29.5933	0.988641
$897$	−13.1142	−0.437870
$898$	−63.0978	−2.10560
$899$	−1.64512	−0.0548680
$900$	−30.2292	−1.00764
$901$	22.8407	0.760933
$902$	−0.354799	−0.0118135
$903$	−22.4860	−0.748287
$904$	42.3173	1.40745
$905$	29.7897	0.990244
$906$	56.8001	1.88706
$907$	−47.8956	−1.59035	−0.795174	−	0.606381i	$-0.792621\pi$
$907$	−47.8956	−1.59035	−0.795174	+	0.606381i	$0.792621\pi$
$908$	61.3538	2.03610
$909$	8.68250	0.287980
$910$	5.78168	0.191661
$911$	−33.6374	−1.11446	−0.557229	−	0.830359i	$-0.688135\pi$
$911$	−33.6374	−1.11446	−0.557229	+	0.830359i	$0.688135\pi$
$912$	−0.250916	−0.00830866
$913$	6.32451	0.209311
$914$	33.7194	1.11534
$915$	−1.85391	−0.0612883
$916$	23.9457	0.791188
$917$	−10.8821	−0.359358
$918$	13.7256	0.453012
$919$	2.11560	0.0697872	0.0348936	−	0.999391i	$-0.488891\pi$
$919$	2.11560	0.0697872	0.0348936	+	0.999391i	$0.488891\pi$
$920$	−15.4142	−0.508193
$921$	−28.6598	−0.944373
$922$	14.4674	0.476457
$923$	−5.65672	−0.186193
$924$	10.9579	0.360487
$925$	0.993218	0.0326568
$926$	−68.4595	−2.24972
$927$	−16.8083	−0.552058
$928$	−8.57275	−0.281414
$929$	11.7523	0.385580	0.192790	−	0.981240i	$-0.438246\pi$
$929$	11.7523	0.385580	0.192790	+	0.981240i	$0.438246\pi$
$930$	−7.07413	−0.231970
$931$	3.05787	0.100218
$932$	9.61625	0.314991
$933$	−63.8035	−2.08883
$934$	84.9424	2.77940
$935$	7.97659	0.260862
$936$	9.95889	0.325516
$937$	17.1081	0.558898	0.279449	−	0.960160i	$-0.409848\pi$
$937$	17.1081	0.558898	0.279449	+	0.960160i	$0.409848\pi$
$938$	4.01288	0.131025
$939$	4.08044	0.133160
$940$	−28.1491	−0.918122
$941$	24.0508	0.784034	0.392017	−	0.919958i	$-0.371777\pi$
$941$	24.0508	0.784034	0.392017	+	0.919958i	$0.371777\pi$
$942$	58.8093	1.91611
$943$	0.747410	0.0243390
$944$	0.590185	0.0192089
$945$	−1.60434	−0.0521893
$946$	12.1136	0.393846
$947$	−5.70842	−0.185499	−0.0927494	−	0.995689i	$-0.529566\pi$
$947$	−5.70842	−0.185499	−0.0927494	+	0.995689i	$0.529566\pi$
$948$	102.836	3.33995
$949$	−18.8363	−0.611451
$950$	−5.46015	−0.177151
$951$	2.11315	0.0685237
$952$	−33.8200	−1.09611
$953$	56.3967	1.82687	0.913435	−	0.406985i	$-0.133420\pi$
$953$	56.3967	1.82687	0.913435	+	0.406985i	$0.133420\pi$
$954$	−19.0789	−0.617701
$955$	−4.02168	−0.130139
$956$	71.8674	2.32436
$957$	−3.29996	−0.106673
$958$	9.54936	0.308526
$959$	−15.3116	−0.494436
$960$	−37.7685	−1.21897
$961$	−29.8948	−0.964349
$962$	−0.842370	−0.0271591
$963$	5.97840	0.192651
$964$	−22.4249	−0.722258
$965$	−11.1633	−0.359359
$966$	−37.2004	−1.19690
$967$	−20.5830	−0.661906	−0.330953	−	0.943647i	$-0.607370\pi$
$967$	−20.5830	−0.661906	−0.330953	+	0.943647i	$0.607370\pi$
$968$	29.7866	0.957378
$969$	−11.8595	−0.380982
$970$	20.9102	0.671386
$971$	−9.40675	−0.301877	−0.150938	−	0.988543i	$-0.548230\pi$
$971$	−9.40675	−0.301877	−0.150938	+	0.988543i	$0.548230\pi$
$972$	−69.0729	−2.21551
$973$	−8.32631	−0.266929
$974$	24.6445	0.789661
$975$	10.6449	0.340910
$976$	−0.0976646	−0.00312617
$977$	30.9387	0.989816	0.494908	−	0.868945i	$-0.335202\pi$
$977$	30.9387	0.989816	0.494908	+	0.868945i	$0.335202\pi$
$978$	−18.4621	−0.590353
$979$	2.71214	0.0866805
$980$	−18.0390	−0.576234
$981$	28.2411	0.901670
$982$	−59.3305	−1.89331
$983$	18.0662	0.576222	0.288111	−	0.957597i	$-0.406973\pi$
$983$	18.0662	0.576222	0.288111	+	0.957597i	$0.406973\pi$
$984$	−1.20879	−0.0385347
$985$	−26.8155	−0.854412
$986$	26.2199	0.835011
$987$	−26.3886	−0.839958
$988$	2.87354	0.0914194
$989$	−25.5181	−0.811428
$990$	−6.66287	−0.211760
$991$	−36.4417	−1.15761	−0.578804	−	0.815467i	$-0.696480\pi$
$991$	−36.4417	−1.15761	−0.578804	+	0.815467i	$0.696480\pi$
$992$	5.75903	0.182850
$993$	−74.2673	−2.35680
$994$	−16.0462	−0.508954
$995$	−1.54176	−0.0488772
$996$	55.4713	1.75767
$997$	12.7205	0.402861	0.201431	−	0.979503i	$-0.435441\pi$
$997$	12.7205	0.402861	0.201431	+	0.979503i	$0.435441\pi$
$998$	78.2803	2.47792
$999$	0.233747	0.00739543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.3	✓	30
3.2	odd	2		5571.2.a.g.1.28		30
4.3	odd	2		9904.2.a.n.1.7		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.3	✓	30	1.1	even	1	trivial
5571.2.a.g.1.28		30	3.2	odd	2
9904.2.a.n.1.7		30	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} +O(q^{10})\)	\(q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} -2.82958 q^{10} +0.886722 q^{11} +7.77730 q^{12} -1.28594 q^{13} -3.64778 q^{14} +2.93116 q^{15} +0.154415 q^{16} +7.29839 q^{17} -6.09636 q^{18} -0.683286 q^{19} +4.03083 q^{20} +3.77874 q^{21} -2.03567 q^{22} +4.28827 q^{23} -6.93543 q^{24} -3.48083 q^{25} +2.95217 q^{26} -0.819191 q^{27} +5.19639 q^{28} -1.56489 q^{29} -6.72913 q^{30} +1.05127 q^{31} +5.47817 q^{32} +2.10875 q^{33} -16.7551 q^{34} +1.95845 q^{35} +8.68448 q^{36} -0.285339 q^{37} +1.56863 q^{38} -3.05815 q^{39} -3.59451 q^{40} +0.174292 q^{41} -8.67492 q^{42} -5.95067 q^{43} +2.89988 q^{44} +3.27306 q^{45} -9.84468 q^{46} -6.98344 q^{47} +0.367219 q^{48} -4.47524 q^{49} +7.99102 q^{50} +17.3566 q^{51} -4.20547 q^{52} +3.12955 q^{53} +1.88063 q^{54} +1.09293 q^{55} -4.63390 q^{56} -1.62495 q^{57} +3.59256 q^{58} +3.82207 q^{59} +9.58587 q^{60} -0.632482 q^{61} -2.41342 q^{62} +4.21950 q^{63} -12.8852 q^{64} -1.58499 q^{65} -4.84109 q^{66} -1.10009 q^{67} +23.8682 q^{68} +10.1981 q^{69} -4.49606 q^{70} +4.39889 q^{71} -7.74441 q^{72} +14.6478 q^{73} +0.655059 q^{74} -8.27789 q^{75} -2.23457 q^{76} +1.40896 q^{77} +7.02066 q^{78} +13.2226 q^{79} +0.190323 q^{80} -9.91474 q^{81} -0.400125 q^{82} +7.13246 q^{83} +12.3577 q^{84} +8.99559 q^{85} +13.6611 q^{86} -3.72153 q^{87} -2.58598 q^{88} +3.05862 q^{89} -7.51404 q^{90} -2.04330 q^{91} +14.0241 q^{92} +2.50006 q^{93} +16.0320 q^{94} -0.842181 q^{95} +13.0278 q^{96} -7.38986 q^{97} +10.2739 q^{98} +2.35472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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