LMFDB - Embedded newform 4033.2.a.d.1.54

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			1.54
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)

$f(q)$	$=$	$q+1.01006 q^{2} -3.14082 q^{3} -0.979773 q^{4} -0.344760 q^{5} -3.17243 q^{6} -0.0177090 q^{7} -3.00976 q^{8} +6.86476 q^{9} +O(q^{10})$	\(q+1.01006 q^{2} -3.14082 q^{3} -0.979773 q^{4} -0.344760 q^{5} -3.17243 q^{6} -0.0177090 q^{7} -3.00976 q^{8} +6.86476 q^{9} -0.348229 q^{10} +4.61234 q^{11} +3.07729 q^{12} -6.41156 q^{13} -0.0178872 q^{14} +1.08283 q^{15} -1.08050 q^{16} -5.15472 q^{17} +6.93384 q^{18} +4.19222 q^{19} +0.337787 q^{20} +0.0556207 q^{21} +4.65875 q^{22} -1.23182 q^{23} +9.45311 q^{24} -4.88114 q^{25} -6.47608 q^{26} -12.1385 q^{27} +0.0173508 q^{28} +8.05637 q^{29} +1.09373 q^{30} +6.30626 q^{31} +4.92815 q^{32} -14.4865 q^{33} -5.20660 q^{34} +0.00610535 q^{35} -6.72591 q^{36} -1.00000 q^{37} +4.23440 q^{38} +20.1376 q^{39} +1.03764 q^{40} +7.42677 q^{41} +0.0561804 q^{42} -2.30684 q^{43} -4.51905 q^{44} -2.36670 q^{45} -1.24421 q^{46} +6.49822 q^{47} +3.39365 q^{48} -6.99969 q^{49} -4.93026 q^{50} +16.1901 q^{51} +6.28188 q^{52} +11.6805 q^{53} -12.2607 q^{54} -1.59015 q^{55} +0.0532997 q^{56} -13.1670 q^{57} +8.13744 q^{58} -7.23856 q^{59} -1.06093 q^{60} -0.319797 q^{61} +6.36972 q^{62} -0.121568 q^{63} +7.13873 q^{64} +2.21045 q^{65} -14.6323 q^{66} +0.600660 q^{67} +5.05046 q^{68} +3.86892 q^{69} +0.00616679 q^{70} +14.9719 q^{71} -20.6613 q^{72} -0.166623 q^{73} -1.01006 q^{74} +15.3308 q^{75} -4.10742 q^{76} -0.0816798 q^{77} +20.3402 q^{78} -14.4223 q^{79} +0.372513 q^{80} +17.5306 q^{81} +7.50151 q^{82} +3.04147 q^{83} -0.0544957 q^{84} +1.77714 q^{85} -2.33005 q^{86} -25.3036 q^{87} -13.8820 q^{88} +6.69691 q^{89} -2.39051 q^{90} +0.113542 q^{91} +1.20690 q^{92} -19.8068 q^{93} +6.56361 q^{94} -1.44531 q^{95} -15.4784 q^{96} -5.23939 q^{97} -7.07012 q^{98} +31.6626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.01006	0.714222	0.357111	−	0.934062i	$-0.383762\pi$
$2$	1.01006	0.714222	0.357111	+	0.934062i	$0.383762\pi$
$3$	−3.14082	−1.81335	−0.906677	−	0.421825i	$-0.861390\pi$
$3$	−3.14082	−1.81335	−0.906677	+	0.421825i	$0.861390\pi$
$4$	−0.979773	−0.489887
$5$	−0.344760	−0.154181	−0.0770907	−	0.997024i	$-0.524563\pi$
$5$	−0.344760	−0.154181	−0.0770907	+	0.997024i	$0.524563\pi$
$6$	−3.17243	−1.29514
$7$	−0.0177090	−0.00669336	−0.00334668	−	0.999994i	$-0.501065\pi$
$7$	−0.0177090	−0.00669336	−0.00334668	+	0.999994i	$0.501065\pi$
$8$	−3.00976	−1.06411
$9$	6.86476	2.28825
$10$	−0.348229	−0.110120
$11$	4.61234	1.39067	0.695336	−	0.718685i	$-0.255256\pi$
$11$	4.61234	1.39067	0.695336	+	0.718685i	$0.255256\pi$
$12$	3.07729	0.888338
$13$	−6.41156	−1.77825	−0.889124	−	0.457667i	$-0.848685\pi$
$13$	−6.41156	−1.77825	−0.889124	+	0.457667i	$0.848685\pi$
$14$	−0.0178872	−0.00478055
$15$	1.08283	0.279586
$16$	−1.08050	−0.270125
$17$	−5.15472	−1.25020	−0.625102	−	0.780543i	$-0.714943\pi$
$17$	−5.15472	−1.25020	−0.625102	+	0.780543i	$0.714943\pi$
$18$	6.93384	1.63432
$19$	4.19222	0.961761	0.480880	−	0.876786i	$-0.340317\pi$
$19$	4.19222	0.961761	0.480880	+	0.876786i	$0.340317\pi$
$20$	0.337787	0.0755314
$21$	0.0556207	0.0121374
$22$	4.65875	0.993249
$23$	−1.23182	−0.256852	−0.128426	−	0.991719i	$-0.540992\pi$
$23$	−1.23182	−0.256852	−0.128426	+	0.991719i	$0.540992\pi$
$24$	9.45311	1.92961
$25$	−4.88114	−0.976228
$26$	−6.47608	−1.27006
$27$	−12.1385	−2.33606
$28$	0.0173508	0.00327899
$29$	8.05637	1.49603	0.748015	−	0.663682i	$-0.231007\pi$
$29$	8.05637	1.49603	0.748015	+	0.663682i	$0.231007\pi$
$30$	1.09373	0.199686
$31$	6.30626	1.13264	0.566319	−	0.824186i	$-0.308367\pi$
$31$	6.30626	1.13264	0.566319	+	0.824186i	$0.308367\pi$
$32$	4.92815	0.871181
$33$	−14.4865	−2.52178
$34$	−5.20660	−0.892924
$35$	0.00610535	0.00103199
$36$	−6.72591	−1.12098
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.23440	0.686911
$39$	20.1376	3.22459
$40$	1.03764	0.164066
$41$	7.42677	1.15987	0.579933	−	0.814664i	$-0.303079\pi$
$41$	7.42677	1.15987	0.579933	+	0.814664i	$0.303079\pi$
$42$	0.0561804	0.00866883
$43$	−2.30684	−0.351790	−0.175895	−	0.984409i	$-0.556282\pi$
$43$	−2.30684	−0.351790	−0.175895	+	0.984409i	$0.556282\pi$
$44$	−4.51905	−0.681272
$45$	−2.36670	−0.352806
$46$	−1.24421	−0.183449
$47$	6.49822	0.947863	0.473931	−	0.880562i	$-0.342834\pi$
$47$	6.49822	0.947863	0.473931	+	0.880562i	$0.342834\pi$
$48$	3.39365	0.489831
$49$	−6.99969	−0.999955
$50$	−4.93026	−0.697244
$51$	16.1901	2.26706
$52$	6.28188	0.871140
$53$	11.6805	1.60443	0.802217	−	0.597032i	$-0.203654\pi$
$53$	11.6805	1.60443	0.802217	+	0.597032i	$0.203654\pi$
$54$	−12.2607	−1.66847
$55$	−1.59015	−0.214416
$56$	0.0532997	0.00712248
$57$	−13.1670	−1.74401
$58$	8.13744	1.06850
$59$	−7.23856	−0.942381	−0.471190	−	0.882032i	$-0.656176\pi$
$59$	−7.23856	−0.942381	−0.471190	+	0.882032i	$0.656176\pi$
$60$	−1.06093	−0.136965
$61$	−0.319797	−0.0409458	−0.0204729	−	0.999790i	$-0.506517\pi$
$61$	−0.319797	−0.0409458	−0.0204729	+	0.999790i	$0.506517\pi$
$62$	6.36972	0.808955
$63$	−0.121568	−0.0153161
$64$	7.13873	0.892342
$65$	2.21045	0.274173
$66$	−14.6323	−1.80111
$67$	0.600660	0.0733823	0.0366912	−	0.999327i	$-0.488318\pi$
$67$	0.600660	0.0733823	0.0366912	+	0.999327i	$0.488318\pi$
$68$	5.05046	0.612458
$69$	3.86892	0.465764
$70$	0.00616679	0.000737072 0
$71$	14.9719	1.77683	0.888417	−	0.459036i	$-0.151805\pi$
$71$	14.9719	1.77683	0.888417	+	0.459036i	$0.151805\pi$
$72$	−20.6613	−2.43495
$73$	−0.166623	−0.0195018	−0.00975088	−	0.999952i	$-0.503104\pi$
$73$	−0.166623	−0.0195018	−0.00975088	+	0.999952i	$0.503104\pi$
$74$	−1.01006	−0.117417
$75$	15.3308	1.77025
$76$	−4.10742	−0.471154
$77$	−0.0816798	−0.00930828
$78$	20.3402	2.30308
$79$	−14.4223	−1.62263	−0.811316	−	0.584608i	$-0.801248\pi$
$79$	−14.4223	−1.62263	−0.811316	+	0.584608i	$0.801248\pi$
$80$	0.372513	0.0416482
$81$	17.5306	1.94785
$82$	7.50151	0.828403
$83$	3.04147	0.333845	0.166923	−	0.985970i	$-0.446617\pi$
$83$	3.04147	0.333845	0.166923	+	0.985970i	$0.446617\pi$
$84$	−0.0544957	−0.00594597
$85$	1.77714	0.192758
$86$	−2.33005	−0.251256
$87$	−25.3036	−2.71283
$88$	−13.8820	−1.47983
$89$	6.69691	0.709871	0.354935	−	0.934891i	$-0.384503\pi$
$89$	6.69691	0.709871	0.354935	+	0.934891i	$0.384503\pi$
$90$	−2.39051	−0.251982
$91$	0.113542	0.0119025
$92$	1.20690	0.125828
$93$	−19.8068	−2.05387
$94$	6.56361	0.676985
$95$	−1.44531	−0.148286
$96$	−15.4784	−1.57976
$97$	−5.23939	−0.531979	−0.265990	−	0.963976i	$-0.585699\pi$
$97$	−5.23939	−0.531979	−0.265990	+	0.963976i	$0.585699\pi$
$98$	−7.07012	−0.714190
$99$	31.6626	3.18221
$100$	4.78241	0.478241
$101$	−19.0295	−1.89351	−0.946755	−	0.321954i	$-0.895660\pi$
$101$	−19.0295	−1.89351	−0.946755	+	0.321954i	$0.895660\pi$
$102$	16.3530	1.61919
$103$	−0.159461	−0.0157121	−0.00785606	−	0.999969i	$-0.502501\pi$
$103$	−0.159461	−0.0157121	−0.00785606	+	0.999969i	$0.502501\pi$
$104$	19.2973	1.89225
$105$	−0.0191758	−0.00187137
$106$	11.7980	1.14592
$107$	1.22497	0.118422	0.0592110	−	0.998245i	$-0.481142\pi$
$107$	1.22497	0.118422	0.0592110	+	0.998245i	$0.481142\pi$
$108$	11.8930	1.14440
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−1.60615	−0.153141
$111$	3.14082	0.298114
$112$	0.0191345	0.00180804
$113$	−16.5956	−1.56118	−0.780590	−	0.625043i	$-0.785081\pi$
$113$	−16.5956	−1.56118	−0.780590	+	0.625043i	$0.785081\pi$
$114$	−13.2995	−1.24561
$115$	0.424682	0.0396018
$116$	−7.89341	−0.732885
$117$	−44.0138	−4.06908
$118$	−7.31140	−0.673069
$119$	0.0912849	0.00836807
$120$	−3.25906	−0.297510
$121$	10.2737	0.933969
$122$	−0.323015	−0.0292444
$123$	−23.3262	−2.10325
$124$	−6.17871	−0.554864
$125$	3.40662	0.304698
$126$	−0.122791	−0.0109391
$127$	3.67993	0.326541	0.163271	−	0.986581i	$-0.447796\pi$
$127$	3.67993	0.326541	0.163271	+	0.986581i	$0.447796\pi$
$128$	−2.64572	−0.233851
$129$	7.24537	0.637920
$130$	2.23269	0.195820
$131$	−22.7946	−1.99157	−0.995785	−	0.0917149i	$-0.970765\pi$
$131$	−22.7946	−1.99157	−0.995785	+	0.0917149i	$0.970765\pi$
$132$	14.1935	1.23539
$133$	−0.0742399	−0.00643741
$134$	0.606705	0.0524113
$135$	4.18488	0.360177
$136$	15.5145	1.33036
$137$	−0.130928	−0.0111859	−0.00559295	−	0.999984i	$-0.501780\pi$
$137$	−0.130928	−0.0111859	−0.00559295	+	0.999984i	$0.501780\pi$
$138$	3.90786	0.332659
$139$	−5.24349	−0.444747	−0.222373	−	0.974962i	$-0.571380\pi$
$139$	−5.24349	−0.444747	−0.222373	+	0.974962i	$0.571380\pi$
$140$	−0.00598186	−0.000505559 0
$141$	−20.4098	−1.71881
$142$	15.1225	1.26905
$143$	−29.5723	−2.47296
$144$	−7.41736	−0.618113
$145$	−2.77751	−0.230660
$146$	−0.168300	−0.0139286
$147$	21.9848	1.81327
$148$	0.979773	0.0805369
$149$	19.7141	1.61504	0.807520	−	0.589840i	$-0.200809\pi$
$149$	19.7141	1.61504	0.807520	+	0.589840i	$0.200809\pi$
$150$	15.4851	1.26435
$151$	−16.6343	−1.35368	−0.676842	−	0.736128i	$-0.736652\pi$
$151$	−16.6343	−1.35368	−0.676842	+	0.736128i	$0.736652\pi$
$152$	−12.6176	−1.02342
$153$	−35.3859	−2.86078
$154$	−0.0825017	−0.00664818
$155$	−2.17415	−0.174632
$156$	−19.7303	−1.57968
$157$	−2.59718	−0.207277	−0.103639	−	0.994615i	$-0.533049\pi$
$157$	−2.59718	−0.207277	−0.103639	+	0.994615i	$0.533049\pi$
$158$	−14.5674	−1.15892
$159$	−36.6862	−2.90941
$160$	−1.69903	−0.134320
$161$	0.0218143	0.00171920
$162$	17.7071	1.39120
$163$	−24.5852	−1.92567	−0.962833	−	0.270099i	$-0.912944\pi$
$163$	−24.5852	−1.92567	−0.962833	+	0.270099i	$0.912944\pi$
$164$	−7.27655	−0.568203
$165$	4.99438	0.388812
$166$	3.07208	0.238440
$167$	0.504795	0.0390622	0.0195311	−	0.999809i	$-0.493783\pi$
$167$	0.504795	0.0390622	0.0195311	+	0.999809i	$0.493783\pi$
$168$	−0.167405	−0.0129156
$169$	28.1081	2.16216
$170$	1.79503	0.137672
$171$	28.7786	2.20075
$172$	2.26018	0.172337
$173$	−6.26541	−0.476351	−0.238175	−	0.971222i	$-0.576549\pi$
$173$	−6.26541	−0.476351	−0.238175	+	0.971222i	$0.576549\pi$
$174$	−25.5582	−1.93756
$175$	0.0864400	0.00653425
$176$	−4.98362	−0.375655
$177$	22.7350	1.70887
$178$	6.76430	0.507005
$179$	3.88927	0.290698	0.145349	−	0.989380i	$-0.453570\pi$
$179$	3.88927	0.290698	0.145349	+	0.989380i	$0.453570\pi$
$180$	2.31882	0.172835
$181$	7.40022	0.550054	0.275027	−	0.961436i	$-0.411313\pi$
$181$	7.40022	0.550054	0.275027	+	0.961436i	$0.411313\pi$
$182$	0.114685	0.00850100
$183$	1.00443	0.0742493
$184$	3.70748	0.273319
$185$	0.344760	0.0253473
$186$	−20.0062	−1.46692
$187$	−23.7753	−1.73862
$188$	−6.36678	−0.464345
$189$	0.214961	0.0156361
$190$	−1.45985	−0.105909
$191$	−13.4218	−0.971169	−0.485585	−	0.874190i	$-0.661393\pi$
$191$	−13.4218	−0.971169	−0.485585	+	0.874190i	$0.661393\pi$
$192$	−22.4215	−1.61813
$193$	5.96408	0.429304	0.214652	−	0.976691i	$-0.431138\pi$
$193$	5.96408	0.429304	0.214652	+	0.976691i	$0.431138\pi$
$194$	−5.29211	−0.379951
$195$	−6.94263	−0.497172
$196$	6.85811	0.489865
$197$	−8.22073	−0.585703	−0.292851	−	0.956158i	$-0.594604\pi$
$197$	−8.22073	−0.585703	−0.292851	+	0.956158i	$0.594604\pi$
$198$	31.9812	2.27281
$199$	1.86102	0.131924	0.0659621	−	0.997822i	$-0.478988\pi$
$199$	1.86102	0.131924	0.0659621	+	0.997822i	$0.478988\pi$
$200$	14.6911	1.03881
$201$	−1.88657	−0.133068
$202$	−19.2210	−1.35239
$203$	−0.142670	−0.0100135
$204$	−15.8626	−1.11060
$205$	−2.56046	−0.178830
$206$	−0.161065	−0.0112219
$207$	−8.45614	−0.587742
$208$	6.92768	0.480348
$209$	19.3359	1.33749
$210$	−0.0193688	−0.00133657
$211$	−9.85662	−0.678558	−0.339279	−	0.940686i	$-0.610183\pi$
$211$	−9.85662	−0.678558	−0.339279	+	0.940686i	$0.610183\pi$
$212$	−11.4442	−0.785991
$213$	−47.0240	−3.22203
$214$	1.23729	0.0845797
$215$	0.795307	0.0542395
$216$	36.5340	2.48582
$217$	−0.111677	−0.00758116
$218$	−1.01006	−0.0684101
$219$	0.523334	0.0353636
$220$	1.55799	0.105039
$221$	33.0498	2.22317
$222$	3.17243	0.212919
$223$	12.2132	0.817859	0.408930	−	0.912566i	$-0.365902\pi$
$223$	12.2132	0.817859	0.408930	+	0.912566i	$0.365902\pi$
$224$	−0.0872724	−0.00583113
$225$	−33.5079	−2.23386
$226$	−16.7626	−1.11503
$227$	15.5051	1.02911	0.514556	−	0.857457i	$-0.327957\pi$
$227$	15.5051	1.02911	0.514556	+	0.857457i	$0.327957\pi$
$228$	12.9007	0.854368
$229$	5.67788	0.375205	0.187602	−	0.982245i	$-0.439928\pi$
$229$	5.67788	0.375205	0.187602	+	0.982245i	$0.439928\pi$
$230$	0.428956	0.0282845
$231$	0.256542	0.0168792
$232$	−24.2477	−1.59194
$233$	15.3192	1.00360	0.501798	−	0.864985i	$-0.332672\pi$
$233$	15.3192	1.00360	0.501798	+	0.864985i	$0.332672\pi$
$234$	−44.4567	−2.90623
$235$	−2.24033	−0.146143
$236$	7.09215	0.461660
$237$	45.2978	2.94241
$238$	0.0922035	0.00597666
$239$	13.8311	0.894657	0.447328	−	0.894370i	$-0.352376\pi$
$239$	13.8311	0.894657	0.447328	+	0.894370i	$0.352376\pi$
$240$	−1.17000	−0.0755229
$241$	−27.5980	−1.77774	−0.888870	−	0.458159i	$-0.848509\pi$
$241$	−27.5980	−1.77774	−0.888870	+	0.458159i	$0.848509\pi$
$242$	10.3770	0.667062
$243$	−18.6451	−1.19608
$244$	0.313329	0.0200588
$245$	2.41321	0.154175
$246$	−23.5609	−1.50219
$247$	−26.8787	−1.71025
$248$	−18.9803	−1.20525
$249$	−9.55273	−0.605379
$250$	3.44090	0.217622
$251$	−23.9447	−1.51137	−0.755687	−	0.654933i	$-0.772697\pi$
$251$	−23.9447	−1.51137	−0.755687	+	0.654933i	$0.772697\pi$
$252$	0.119109	0.00750316
$253$	−5.68157	−0.357197
$254$	3.71696	0.233223
$255$	−5.58169	−0.349539
$256$	−16.9498	−1.05936
$257$	−18.7703	−1.17086	−0.585429	−	0.810724i	$-0.699074\pi$
$257$	−18.7703	−1.17086	−0.585429	+	0.810724i	$0.699074\pi$
$258$	7.31828	0.455616
$259$	0.0177090	0.00110038
$260$	−2.16574	−0.134314
$261$	55.3050	3.42329
$262$	−23.0239	−1.42242
$263$	16.7073	1.03022	0.515108	−	0.857125i	$-0.327752\pi$
$263$	16.7073	1.03022	0.515108	+	0.857125i	$0.327752\pi$
$264$	43.6010	2.68345
$265$	−4.02696	−0.247374
$266$	−0.0749869	−0.00459774
$267$	−21.0338	−1.28725
$268$	−0.588511	−0.0359490
$269$	−14.7979	−0.902246	−0.451123	−	0.892462i	$-0.648976\pi$
$269$	−14.7979	−0.902246	−0.451123	+	0.892462i	$0.648976\pi$
$270$	4.22699	0.257246
$271$	−31.9975	−1.94371	−0.971854	−	0.235582i	$-0.924300\pi$
$271$	−31.9975	−1.94371	−0.971854	+	0.235582i	$0.924300\pi$
$272$	5.56967	0.337711
$273$	−0.356616	−0.0215834
$274$	−0.132245	−0.00798922
$275$	−22.5135	−1.35761
$276$	−3.79067	−0.228171
$277$	−27.0604	−1.62590	−0.812951	−	0.582332i	$-0.802141\pi$
$277$	−27.0604	−1.62590	−0.812951	+	0.582332i	$0.802141\pi$
$278$	−5.29625	−0.317648
$279$	43.2910	2.59176
$280$	−0.0183756	−0.00109815
$281$	−15.3377	−0.914970	−0.457485	−	0.889217i	$-0.651250\pi$
$281$	−15.3377	−0.914970	−0.457485	+	0.889217i	$0.651250\pi$
$282$	−20.6151	−1.22761
$283$	−24.5438	−1.45898	−0.729489	−	0.683993i	$-0.760242\pi$
$283$	−24.5438	−1.45898	−0.729489	+	0.683993i	$0.760242\pi$
$284$	−14.6690	−0.870448
$285$	4.53946	0.268894
$286$	−29.8699	−1.76624
$287$	−0.131521	−0.00776341
$288$	33.8305	1.99348
$289$	9.57119	0.563011
$290$	−2.80546	−0.164742
$291$	16.4560	0.964667
$292$	0.163253	0.00955365
$293$	20.8869	1.22023	0.610114	−	0.792313i	$-0.291124\pi$
$293$	20.8869	1.22023	0.610114	+	0.792313i	$0.291124\pi$
$294$	22.2060	1.29508
$295$	2.49557	0.145298
$296$	3.00976	0.174939
$297$	−55.9870	−3.24869
$298$	19.9125	1.15350
$299$	7.89789	0.456747
$300$	−15.0207	−0.867220
$301$	0.0408518	0.00235466
$302$	−16.8017	−0.966831
$303$	59.7684	3.43361
$304$	−4.52968	−0.259795
$305$	0.110253	0.00631309
$306$	−35.7420	−2.04324
$307$	2.78843	0.159144	0.0795721	−	0.996829i	$-0.474645\pi$
$307$	2.78843	0.159144	0.0795721	+	0.996829i	$0.474645\pi$
$308$	0.0800277	0.00456000
$309$	0.500837	0.0284916
$310$	−2.19603	−0.124726
$311$	−30.2106	−1.71309	−0.856544	−	0.516073i	$-0.827393\pi$
$311$	−30.2106	−1.71309	−0.856544	+	0.516073i	$0.827393\pi$
$312$	−60.6092	−3.43132
$313$	18.2208	1.02990	0.514952	−	0.857219i	$-0.327810\pi$
$313$	18.2208	1.02990	0.514952	+	0.857219i	$0.327810\pi$
$314$	−2.62331	−0.148042
$315$	0.0419118	0.00236146
$316$	14.1305	0.794905
$317$	−18.0583	−1.01426	−0.507128	−	0.861871i	$-0.669293\pi$
$317$	−18.0583	−1.01426	−0.507128	+	0.861871i	$0.669293\pi$
$318$	−37.0554	−2.07796
$319$	37.1587	2.08049
$320$	−2.46115	−0.137582
$321$	−3.84740	−0.214741
$322$	0.0220338	0.00122789
$323$	−21.6097	−1.20240
$324$	−17.1761	−0.954225
$325$	31.2957	1.73598
$326$	−24.8326	−1.37535
$327$	3.14082	0.173688
$328$	−22.3528	−1.23423
$329$	−0.115077	−0.00634439
$330$	5.04464	0.277698
$331$	2.97039	0.163268	0.0816338	−	0.996662i	$-0.473986\pi$
$331$	2.97039	0.163268	0.0816338	+	0.996662i	$0.473986\pi$
$332$	−2.97995	−0.163546
$333$	−6.86476	−0.376187
$334$	0.509874	0.0278991
$335$	−0.207084	−0.0113142
$336$	−0.0600981	−0.00327862
$337$	19.1859	1.04513	0.522563	−	0.852601i	$-0.324976\pi$
$337$	19.1859	1.04513	0.522563	+	0.852601i	$0.324976\pi$
$338$	28.3910	1.54427
$339$	52.1237	2.83097
$340$	−1.74120	−0.0944297
$341$	29.0866	1.57513
$342$	29.0682	1.57183
$343$	0.247920	0.0133864
$344$	6.94303	0.374343
$345$	−1.33385	−0.0718121
$346$	−6.32846	−0.340220
$347$	10.4814	0.562669	0.281334	−	0.959610i	$-0.409223\pi$
$347$	10.4814	0.562669	0.281334	+	0.959610i	$0.409223\pi$
$348$	24.7918	1.32898
$349$	15.9996	0.856440	0.428220	−	0.903675i	$-0.359141\pi$
$349$	15.9996	0.856440	0.428220	+	0.903675i	$0.359141\pi$
$350$	0.0873098	0.00466691
$351$	77.8269	4.15409
$352$	22.7303	1.21153
$353$	15.6196	0.831347	0.415673	−	0.909514i	$-0.363546\pi$
$353$	15.6196	0.831347	0.415673	+	0.909514i	$0.363546\pi$
$354$	22.9638	1.22051
$355$	−5.16171	−0.273955
$356$	−6.56145	−0.347756
$357$	−0.286710	−0.0151743
$358$	3.92841	0.207623
$359$	10.7911	0.569534	0.284767	−	0.958597i	$-0.408084\pi$
$359$	10.7911	0.569534	0.284767	+	0.958597i	$0.408084\pi$
$360$	7.12318	0.375425
$361$	−1.42532	−0.0750166
$362$	7.47469	0.392861
$363$	−32.2677	−1.69362
$364$	−0.111246	−0.00583086
$365$	0.0574450	0.00300681
$366$	1.01453	0.0530305
$367$	−10.6042	−0.553536	−0.276768	−	0.960937i	$-0.589263\pi$
$367$	−10.6042	−0.553536	−0.276768	+	0.960937i	$0.589263\pi$
$368$	1.33098	0.0693820
$369$	50.9830	2.65407
$370$	0.348229	0.0181036
$371$	−0.206849	−0.0107391
$372$	19.4062	1.00617
$373$	29.3767	1.52107	0.760535	−	0.649297i	$-0.224937\pi$
$373$	29.3767	1.52107	0.760535	+	0.649297i	$0.224937\pi$
$374$	−24.0146	−1.24176
$375$	−10.6996	−0.552525
$376$	−19.5581	−1.00863
$377$	−51.6539	−2.66031
$378$	0.217124	0.0111676
$379$	−8.87960	−0.456114	−0.228057	−	0.973648i	$-0.573237\pi$
$379$	−8.87960	−0.456114	−0.228057	+	0.973648i	$0.573237\pi$
$380$	1.41608	0.0726431
$381$	−11.5580	−0.592135
$382$	−13.5569	−0.693631
$383$	−25.1912	−1.28721	−0.643605	−	0.765358i	$-0.722562\pi$
$383$	−25.1912	−1.28721	−0.643605	+	0.765358i	$0.722562\pi$
$384$	8.30974	0.424055
$385$	0.0281599	0.00143516
$386$	6.02410	0.306619
$387$	−15.8359	−0.804984
$388$	5.13341	0.260609
$389$	16.1355	0.818100	0.409050	−	0.912512i	$-0.365860\pi$
$389$	16.1355	0.818100	0.409050	+	0.912512i	$0.365860\pi$
$390$	−7.01249	−0.355091
$391$	6.34969	0.321118
$392$	21.0674	1.06406
$393$	71.5937	3.61142
$394$	−8.30345	−0.418322
$395$	4.97222	0.250180
$396$	−31.0222	−1.55892
$397$	5.69868	0.286008	0.143004	−	0.989722i	$-0.454324\pi$
$397$	5.69868	0.286008	0.143004	+	0.989722i	$0.454324\pi$
$398$	1.87975	0.0942233
$399$	0.233174	0.0116733
$400$	5.27406	0.263703
$401$	6.28377	0.313796	0.156898	−	0.987615i	$-0.449851\pi$
$401$	6.28377	0.313796	0.156898	+	0.987615i	$0.449851\pi$
$402$	−1.90555	−0.0950402
$403$	−40.4330	−2.01411
$404$	18.6446	0.927606
$405$	−6.04387	−0.300322
$406$	−0.144106	−0.00715185
$407$	−4.61234	−0.228625
$408$	−48.7282	−2.41240
$409$	−22.0116	−1.08840	−0.544201	−	0.838955i	$-0.683167\pi$
$409$	−22.0116	−1.08840	−0.544201	+	0.838955i	$0.683167\pi$
$410$	−2.58622	−0.127724
$411$	0.411220	0.0202840
$412$	0.156235	0.00769716
$413$	0.128188	0.00630770
$414$	−8.54123	−0.419779
$415$	−1.04858	−0.0514727
$416$	−31.5971	−1.54918
$417$	16.4689	0.806483
$418$	19.5305	0.955268
$419$	36.9903	1.80709	0.903546	−	0.428490i	$-0.140954\pi$
$419$	36.9903	1.80709	0.903546	+	0.428490i	$0.140954\pi$
$420$	0.0187879	0.000916758 0
$421$	8.21720	0.400482	0.200241	−	0.979747i	$-0.435828\pi$
$421$	8.21720	0.400482	0.200241	+	0.979747i	$0.435828\pi$
$422$	−9.95581	−0.484641
$423$	44.6087	2.16895
$424$	−35.1554	−1.70729
$425$	25.1609	1.22048
$426$	−47.4972	−2.30125
$427$	0.00566328	0.000274065 0
$428$	−1.20019	−0.0580134
$429$	92.8813	4.48435
$430$	0.803310	0.0387390
$431$	13.6342	0.656737	0.328368	−	0.944550i	$-0.393501\pi$
$431$	13.6342	0.656737	0.328368	+	0.944550i	$0.393501\pi$
$432$	13.1156	0.631027
$433$	−1.02901	−0.0494511	−0.0247255	−	0.999694i	$-0.507871\pi$
$433$	−1.02901	−0.0494511	−0.0247255	+	0.999694i	$0.507871\pi$
$434$	−0.112801	−0.00541463
$435$	8.72368	0.418268
$436$	0.979773	0.0469226
$437$	−5.16405	−0.247030
$438$	0.528600	0.0252575
$439$	−13.0996	−0.625209	−0.312604	−	0.949883i	$-0.601201\pi$
$439$	−13.0996	−0.625209	−0.312604	+	0.949883i	$0.601201\pi$
$440$	4.78597	0.228162
$441$	−48.0512	−2.28815
$442$	33.3824	1.58784
$443$	19.8422	0.942733	0.471366	−	0.881937i	$-0.343761\pi$
$443$	19.8422	0.942733	0.471366	+	0.881937i	$0.343761\pi$
$444$	−3.07729	−0.146042
$445$	−2.30883	−0.109449
$446$	12.3361	0.584133
$447$	−61.9184	−2.92864
$448$	−0.126420	−0.00597277
$449$	7.00214	0.330451	0.165226	−	0.986256i	$-0.447165\pi$
$449$	7.00214	0.330451	0.165226	+	0.986256i	$0.447165\pi$
$450$	−33.8450	−1.59547
$451$	34.2548	1.61299
$452$	16.2599	0.764801
$453$	52.2455	2.45471
$454$	15.6612	0.735015
$455$	−0.0391448	−0.00183514
$456$	39.6295	1.85582
$457$	−26.4903	−1.23916	−0.619582	−	0.784932i	$-0.712698\pi$
$457$	−26.4903	−1.23916	−0.619582	+	0.784932i	$0.712698\pi$
$458$	5.73501	0.267979
$459$	62.5707	2.92055
$460$	−0.416092	−0.0194004
$461$	9.99978	0.465736	0.232868	−	0.972508i	$-0.425189\pi$
$461$	9.99978	0.465736	0.232868	+	0.972508i	$0.425189\pi$
$462$	0.259123	0.0120555
$463$	−16.9288	−0.786746	−0.393373	−	0.919379i	$-0.628692\pi$
$463$	−16.9288	−0.786746	−0.393373	+	0.919379i	$0.628692\pi$
$464$	−8.70489	−0.404114
$465$	6.82861	0.316669
$466$	15.4734	0.716790
$467$	9.44918	0.437256	0.218628	−	0.975808i	$-0.429842\pi$
$467$	9.44918	0.437256	0.218628	+	0.975808i	$0.429842\pi$
$468$	43.1236	1.99339
$469$	−0.0106371	−0.000491175 0
$470$	−2.26287	−0.104378
$471$	8.15728	0.375867
$472$	21.7863	1.00280
$473$	−10.6399	−0.489224
$474$	45.7536	2.10153
$475$	−20.4628	−0.938898
$476$	−0.0894385	−0.00409941
$477$	80.1835	3.67135
$478$	13.9702	0.638984
$479$	36.7922	1.68108	0.840540	−	0.541750i	$-0.182238\pi$
$479$	36.7922	1.68108	0.840540	+	0.541750i	$0.182238\pi$
$480$	5.33634	0.243570
$481$	6.41156	0.292342
$482$	−27.8757	−1.26970
$483$	−0.0685147	−0.00311753
$484$	−10.0659	−0.457539
$485$	1.80633	0.0820213
$486$	−18.8327	−0.854268
$487$	−17.5995	−0.797508	−0.398754	−	0.917058i	$-0.630557\pi$
$487$	−17.5995	−0.797508	−0.398754	+	0.917058i	$0.630557\pi$
$488$	0.962512	0.0435709
$489$	77.2179	3.49191
$490$	2.43750	0.110115
$491$	−11.9916	−0.541173	−0.270587	−	0.962696i	$-0.587218\pi$
$491$	−11.9916	−0.541173	−0.270587	+	0.962696i	$0.587218\pi$
$492$	22.8544	1.03035
$493$	−41.5284	−1.87034
$494$	−27.1491	−1.22150
$495$	−10.9160	−0.490638
$496$	−6.81390	−0.305953
$497$	−0.265137	−0.0118930
$498$	−9.64885	−0.432375
$499$	26.9702	1.20735	0.603676	−	0.797230i	$-0.293702\pi$
$499$	26.9702	1.20735	0.603676	+	0.797230i	$0.293702\pi$
$500$	−3.33772	−0.149267
$501$	−1.58547	−0.0708336
$502$	−24.1856	−1.07946
$503$	−6.97727	−0.311101	−0.155551	−	0.987828i	$-0.549715\pi$
$503$	−6.97727	−0.311101	−0.155551	+	0.987828i	$0.549715\pi$
$504$	0.365890	0.0162980
$505$	6.56063	0.291944
$506$	−5.73874	−0.255118
$507$	−88.2826	−3.92077
$508$	−3.60550	−0.159968
$509$	7.91506	0.350829	0.175414	−	0.984495i	$-0.443873\pi$
$509$	7.91506	0.350829	0.175414	+	0.984495i	$0.443873\pi$
$510$	−5.63786	−0.249649
$511$	0.00295073	0.000130532 0
$512$	−11.8289	−0.522770
$513$	−50.8873	−2.24673
$514$	−18.9592	−0.836253
$515$	0.0549757	0.00242252
$516$	−7.09882	−0.312508
$517$	29.9720	1.31817
$518$	0.0178872	0.000785918 0
$519$	19.6785	0.863792
$520$	−6.65292	−0.291750
$521$	−39.3807	−1.72530	−0.862649	−	0.505803i	$-0.831196\pi$
$521$	−39.3807	−1.72530	−0.862649	+	0.505803i	$0.831196\pi$
$522$	55.8615	2.44499
$523$	−44.4185	−1.94229	−0.971143	−	0.238498i	$-0.923345\pi$
$523$	−44.4185	−1.94229	−0.971143	+	0.238498i	$0.923345\pi$
$524$	22.3335	0.975644
$525$	−0.271493	−0.0118489
$526$	16.8754	0.735803
$527$	−32.5070	−1.41603
$528$	15.6527	0.681195
$529$	−21.4826	−0.934027
$530$	−4.06748	−0.176680
$531$	−49.6910	−2.15641
$532$	0.0727382	0.00315360
$533$	−47.6172	−2.06253
$534$	−21.2454	−0.919380
$535$	−0.422320	−0.0182585
$536$	−1.80784	−0.0780869
$537$	−12.2155	−0.527138
$538$	−14.9468	−0.644404
$539$	−32.2849	−1.39061
$540$	−4.10023	−0.176446
$541$	33.0794	1.42219	0.711096	−	0.703094i	$-0.248199\pi$
$541$	33.0794	1.42219	0.711096	+	0.703094i	$0.248199\pi$
$542$	−32.3195	−1.38824
$543$	−23.2428	−0.997443
$544$	−25.4032	−1.08915
$545$	0.344760	0.0147679
$546$	−0.360204	−0.0154153
$547$	11.8918	0.508459	0.254229	−	0.967144i	$-0.418178\pi$
$547$	11.8918	0.508459	0.254229	+	0.967144i	$0.418178\pi$
$548$	0.128279	0.00547982
$549$	−2.19533	−0.0936944
$550$	−22.7400	−0.969638
$551$	33.7740	1.43882
$552$	−11.6445	−0.495624
$553$	0.255404	0.0108609
$554$	−27.3327	−1.16126
$555$	−1.08283	−0.0459636
$556$	5.13743	0.217876
$557$	23.2875	0.986724	0.493362	−	0.869824i	$-0.335768\pi$
$557$	23.2875	0.986724	0.493362	+	0.869824i	$0.335768\pi$
$558$	43.7266	1.85109
$559$	14.7905	0.625569
$560$	−0.00659682	−0.000278766 0
$561$	74.6741	3.15274
$562$	−15.4920	−0.653492
$563$	−27.8624	−1.17426	−0.587131	−	0.809492i	$-0.699743\pi$
$563$	−27.8624	−1.17426	−0.587131	+	0.809492i	$0.699743\pi$
$564$	19.9969	0.842023
$565$	5.72149	0.240705
$566$	−24.7908	−1.04203
$567$	−0.310450	−0.0130377
$568$	−45.0617	−1.89075
$569$	−2.32253	−0.0973656	−0.0486828	−	0.998814i	$-0.515502\pi$
$569$	−2.32253	−0.0973656	−0.0486828	+	0.998814i	$0.515502\pi$
$570$	4.58514	0.192050
$571$	−20.0638	−0.839643	−0.419821	−	0.907607i	$-0.637907\pi$
$571$	−20.0638	−0.839643	−0.419821	+	0.907607i	$0.637907\pi$
$572$	28.9741	1.21147
$573$	42.1556	1.76107
$574$	−0.132844	−0.00554480
$575$	6.01268	0.250746
$576$	49.0057	2.04190
$577$	−8.85730	−0.368734	−0.184367	−	0.982857i	$-0.559024\pi$
$577$	−8.85730	−0.368734	−0.184367	+	0.982857i	$0.559024\pi$
$578$	9.66750	0.402115
$579$	−18.7321	−0.778480
$580$	2.72133	0.112997
$581$	−0.0538614	−0.00223455
$582$	16.6216	0.688986
$583$	53.8742	2.23124
$584$	0.501495	0.0207520
$585$	15.1742	0.627377
$586$	21.0971	0.871514
$587$	10.6576	0.439887	0.219943	−	0.975513i	$-0.429413\pi$
$587$	10.6576	0.439887	0.219943	+	0.975513i	$0.429413\pi$
$588$	−21.5401	−0.888298
$589$	26.4372	1.08933
$590$	2.52068	0.103775
$591$	25.8198	1.06209
$592$	1.08050	0.0444082
$593$	−28.3853	−1.16564	−0.582822	−	0.812600i	$-0.698052\pi$
$593$	−28.3853	−1.16564	−0.582822	+	0.812600i	$0.698052\pi$
$594$	−56.5503	−2.32029
$595$	−0.0314714	−0.00129020
$596$	−19.3153	−0.791187
$597$	−5.84514	−0.239225
$598$	7.97736	0.326219
$599$	−35.1493	−1.43616	−0.718081	−	0.695960i	$-0.754979\pi$
$599$	−35.1493	−1.43616	−0.718081	+	0.695960i	$0.754979\pi$
$600$	−46.1420	−1.88374
$601$	−7.86750	−0.320922	−0.160461	−	0.987042i	$-0.551298\pi$
$601$	−7.86750	−0.320922	−0.160461	+	0.987042i	$0.551298\pi$
$602$	0.0412629	0.00168175
$603$	4.12339	0.167917
$604$	16.2979	0.663152
$605$	−3.54195	−0.144001
$606$	60.3699	2.45236
$607$	−32.3286	−1.31218	−0.656089	−	0.754684i	$-0.727790\pi$
$607$	−32.3286	−1.31218	−0.656089	+	0.754684i	$0.727790\pi$
$608$	20.6599	0.837868
$609$	0.448101	0.0181580
$610$	0.111363	0.00450895
$611$	−41.6638	−1.68553
$612$	34.6702	1.40146
$613$	−32.4074	−1.30892	−0.654462	−	0.756095i	$-0.727105\pi$
$613$	−32.4074	−1.30892	−0.654462	+	0.756095i	$0.727105\pi$
$614$	2.81649	0.113664
$615$	8.04193	0.324282
$616$	0.245836	0.00990503
$617$	6.95054	0.279818	0.139909	−	0.990164i	$-0.455319\pi$
$617$	6.95054	0.279818	0.139909	+	0.990164i	$0.455319\pi$
$618$	0.505877	0.0203494
$619$	−9.89069	−0.397540	−0.198770	−	0.980046i	$-0.563695\pi$
$619$	−9.89069	−0.397540	−0.198770	+	0.980046i	$0.563695\pi$
$620$	2.13017	0.0855497
$621$	14.9525	0.600022
$622$	−30.5147	−1.22353
$623$	−0.118595	−0.00475142
$624$	−21.7586	−0.871042
$625$	23.2312	0.929249
$626$	18.4042	0.735580
$627$	−60.7307	−2.42535
$628$	2.54465	0.101542
$629$	5.15472	0.205532
$630$	0.0423335	0.00168661
$631$	28.4701	1.13338	0.566688	−	0.823932i	$-0.308225\pi$
$631$	28.4701	1.13338	0.566688	+	0.823932i	$0.308225\pi$
$632$	43.4075	1.72666
$633$	30.9579	1.23047
$634$	−18.2400	−0.724403
$635$	−1.26869	−0.0503466
$636$	35.9442	1.42528
$637$	44.8789	1.77817
$638$	37.5326	1.48593
$639$	102.778	4.06585
$640$	0.912140	0.0360555
$641$	−16.8595	−0.665912	−0.332956	−	0.942942i	$-0.608046\pi$
$641$	−16.8595	−0.665912	−0.332956	+	0.942942i	$0.608046\pi$
$642$	−3.88612	−0.153373
$643$	−1.37305	−0.0541478	−0.0270739	−	0.999633i	$-0.508619\pi$
$643$	−1.37305	−0.0541478	−0.0270739	+	0.999633i	$0.508619\pi$
$644$	−0.0213730	−0.000842215 0
$645$	−2.49792	−0.0983554
$646$	−21.8272	−0.858779
$647$	−36.3159	−1.42773	−0.713863	−	0.700286i	$-0.753056\pi$
$647$	−36.3159	−1.42773	−0.713863	+	0.700286i	$0.753056\pi$
$648$	−52.7630	−2.07273
$649$	−33.3867	−1.31054
$650$	31.6107	1.23987
$651$	0.350759	0.0137473
$652$	24.0880	0.943358
$653$	−24.2819	−0.950223	−0.475112	−	0.879926i	$-0.657592\pi$
$653$	−24.2819	−0.950223	−0.475112	+	0.879926i	$0.657592\pi$
$654$	3.17243	0.124052
$655$	7.85866	0.307063
$656$	−8.02461	−0.313309
$657$	−1.14383	−0.0446250
$658$	−0.116235	−0.00453131
$659$	33.6411	1.31047	0.655236	−	0.755424i	$-0.272569\pi$
$659$	33.6411	1.31047	0.655236	+	0.755424i	$0.272569\pi$
$660$	−4.89336	−0.190474
$661$	−37.1306	−1.44421	−0.722107	−	0.691782i	$-0.756826\pi$
$661$	−37.1306	−1.44421	−0.722107	+	0.691782i	$0.756826\pi$
$662$	3.00028	0.116609
$663$	−103.804	−4.03140
$664$	−9.15410	−0.355248
$665$	0.0255950	0.000992530 0
$666$	−6.93384	−0.268681
$667$	−9.92399	−0.384258
$668$	−0.494584	−0.0191360
$669$	−38.3596	−1.48307
$670$	−0.209168	−0.00808085
$671$	−1.47501	−0.0569422
$672$	0.274107	0.0105739
$673$	15.9182	0.613603	0.306801	−	0.951774i	$-0.400741\pi$
$673$	15.9182	0.613603	0.306801	+	0.951774i	$0.400741\pi$
$674$	19.3790	0.746452
$675$	59.2498	2.28053
$676$	−27.5396	−1.05922
$677$	42.3989	1.62952	0.814762	−	0.579796i	$-0.196868\pi$
$677$	42.3989	1.62952	0.814762	+	0.579796i	$0.196868\pi$
$678$	52.6483	2.02194
$679$	0.0927842	0.00356073
$680$	−5.34877	−0.205116
$681$	−48.6989	−1.86614
$682$	29.3793	1.12499
$683$	−9.74097	−0.372728	−0.186364	−	0.982481i	$-0.559670\pi$
$683$	−9.74097	−0.372728	−0.186364	+	0.982481i	$0.559670\pi$
$684$	−28.1965	−1.07812
$685$	0.0451386	0.00172466
$686$	0.250415	0.00956089
$687$	−17.8332	−0.680379
$688$	2.49254	0.0950271
$689$	−74.8900	−2.85308
$690$	−1.34727	−0.0512898
$691$	−21.3939	−0.813863	−0.406931	−	0.913459i	$-0.633401\pi$
$691$	−21.3939	−0.813863	−0.406931	+	0.913459i	$0.633401\pi$
$692$	6.13868	0.233358
$693$	−0.560712	−0.0212997
$694$	10.5868	0.401870
$695$	1.80775	0.0685717
$696$	76.1577	2.88675
$697$	−38.2830	−1.45007
$698$	16.1606	0.611688
$699$	−48.1149	−1.81987
$700$	−0.0846916	−0.00320104
$701$	−6.11190	−0.230843	−0.115422	−	0.993317i	$-0.536822\pi$
$701$	−6.11190	−0.230843	−0.115422	+	0.993317i	$0.536822\pi$
$702$	78.6100	2.96694
$703$	−4.19222	−0.158112
$704$	32.9262	1.24095
$705$	7.03647	0.265009
$706$	15.7768	0.593766
$707$	0.336994	0.0126740
$708$	−22.2752	−0.837152
$709$	38.2583	1.43682	0.718411	−	0.695619i	$-0.244870\pi$
$709$	38.2583	1.43682	0.718411	+	0.695619i	$0.244870\pi$
$710$	−5.21365	−0.195665
$711$	−99.0054	−3.71299
$712$	−20.1561	−0.755381
$713$	−7.76817	−0.290920
$714$	−0.289595	−0.0108378
$715$	10.1953	0.381284
$716$	−3.81060	−0.142409
$717$	−43.4409	−1.62233
$718$	10.8997	0.406774
$719$	−37.0979	−1.38352	−0.691758	−	0.722129i	$-0.743164\pi$
$719$	−37.0979	−1.38352	−0.691758	+	0.722129i	$0.743164\pi$
$720$	2.55721	0.0953016
$721$	0.00282389	0.000105167 0
$722$	−1.43966	−0.0535785
$723$	86.6802	3.22367
$724$	−7.25054	−0.269464
$725$	−39.3243	−1.46047
$726$	−32.5924	−1.20962
$727$	44.5085	1.65073	0.825364	−	0.564601i	$-0.190970\pi$
$727$	44.5085	1.65073	0.825364	+	0.564601i	$0.190970\pi$
$728$	−0.341735	−0.0126655
$729$	5.96889	0.221070
$730$	0.0580231	0.00214753
$731$	11.8911	0.439809
$732$	−0.984110	−0.0363737
$733$	15.1635	0.560078	0.280039	−	0.959989i	$-0.409653\pi$
$733$	15.1635	0.560078	0.280039	+	0.959989i	$0.409653\pi$
$734$	−10.7109	−0.395348
$735$	−7.57947	−0.279573
$736$	−6.07058	−0.223765
$737$	2.77045	0.102051
$738$	51.4960	1.89560
$739$	3.65459	0.134436	0.0672181	−	0.997738i	$-0.478588\pi$
$739$	3.65459	0.134436	0.0672181	+	0.997738i	$0.478588\pi$
$740$	−0.337787	−0.0124173
$741$	84.4211	3.10129
$742$	−0.208930	−0.00767008
$743$	−28.6522	−1.05115	−0.525573	−	0.850749i	$-0.676149\pi$
$743$	−28.6522	−1.05115	−0.525573	+	0.850749i	$0.676149\pi$
$744$	59.6138	2.18555
$745$	−6.79663	−0.249009
$746$	29.6723	1.08638
$747$	20.8790	0.763922
$748$	23.2944	0.851729
$749$	−0.0216929	−0.000792642 0
$750$	−10.8073	−0.394625
$751$	−14.3383	−0.523211	−0.261605	−	0.965175i	$-0.584252\pi$
$751$	−14.3383	−0.523211	−0.261605	+	0.965175i	$0.584252\pi$
$752$	−7.02132	−0.256041
$753$	75.2059	2.74066
$754$	−52.1737	−1.90005
$755$	5.73486	0.208713
$756$	−0.210613	−0.00765991
$757$	30.3873	1.10445	0.552223	−	0.833696i	$-0.313780\pi$
$757$	30.3873	1.10445	0.552223	+	0.833696i	$0.313780\pi$
$758$	−8.96895	−0.325767
$759$	17.8448	0.647725
$760$	4.35003	0.157792
$761$	11.6903	0.423772	0.211886	−	0.977294i	$-0.432039\pi$
$761$	11.6903	0.423772	0.211886	+	0.977294i	$0.432039\pi$
$762$	−11.6743	−0.422916
$763$	0.0177090	0.000641108 0
$764$	13.1503	0.475763
$765$	12.1997	0.441080
$766$	−25.4447	−0.919354
$767$	46.4105	1.67579
$768$	53.2363	1.92100
$769$	−13.2167	−0.476607	−0.238304	−	0.971191i	$-0.576591\pi$
$769$	−13.2167	−0.476607	−0.238304	+	0.971191i	$0.576591\pi$
$770$	0.0284433	0.00102503
$771$	58.9541	2.12318
$772$	−5.84345	−0.210310
$773$	22.2151	0.799020	0.399510	−	0.916729i	$-0.369180\pi$
$773$	22.2151	0.799020	0.399510	+	0.916729i	$0.369180\pi$
$774$	−15.9953	−0.574938
$775$	−30.7817	−1.10571
$776$	15.7693	0.566084
$777$	−0.0556207	−0.00199538
$778$	16.2978	0.584306
$779$	31.1346	1.11551
$780$	6.80221	0.243558
$781$	69.0554	2.47099
$782$	6.41358	0.229349
$783$	−97.7924	−3.49481
$784$	7.56315	0.270112
$785$	0.895404	0.0319583
$786$	72.3141	2.57936
$787$	6.29369	0.224346	0.112173	−	0.993689i	$-0.464219\pi$
$787$	6.29369	0.224346	0.112173	+	0.993689i	$0.464219\pi$
$788$	8.05445	0.286928
$789$	−52.4746	−1.86815
$790$	5.02226	0.178684
$791$	0.293891	0.0104496
$792$	−95.2967	−3.38622
$793$	2.05040	0.0728118
$794$	5.75602	0.204274
$795$	12.6480	0.448577
$796$	−1.82338	−0.0646279
$797$	−38.0292	−1.34706	−0.673532	−	0.739158i	$-0.735224\pi$
$797$	−38.0292	−1.34706	−0.673532	+	0.739158i	$0.735224\pi$
$798$	0.235521	0.00833734
$799$	−33.4965	−1.18502
$800$	−24.0550	−0.850472
$801$	45.9726	1.62436
$802$	6.34700	0.224120
$803$	−0.768522	−0.0271206
$804$	1.84841	0.0651883
$805$	−0.00752069	−0.000265069 0
$806$	−40.8399	−1.43852
$807$	46.4777	1.63609
$808$	57.2743	2.01490
$809$	−50.2829	−1.76785	−0.883925	−	0.467628i	$-0.845109\pi$
$809$	−50.2829	−1.76785	−0.883925	+	0.467628i	$0.845109\pi$
$810$	−6.10469	−0.214497
$811$	−36.8465	−1.29386	−0.646928	−	0.762551i	$-0.723947\pi$
$811$	−36.8465	−1.29386	−0.646928	+	0.762551i	$0.723947\pi$
$812$	0.139784	0.00490547
$813$	100.498	3.52463
$814$	−4.65875	−0.163289
$815$	8.47601	0.296902
$816$	−17.4933	−0.612389
$817$	−9.67078	−0.338338
$818$	−22.2330	−0.777360
$819$	0.779440	0.0272358
$820$	2.50867	0.0876064
$821$	−29.3803	−1.02538	−0.512689	−	0.858574i	$-0.671351\pi$
$821$	−29.3803	−1.02538	−0.512689	+	0.858574i	$0.671351\pi$
$822$	0.415358	0.0144873
$823$	20.9621	0.730692	0.365346	−	0.930872i	$-0.380951\pi$
$823$	20.9621	0.730692	0.365346	+	0.930872i	$0.380951\pi$
$824$	0.479938	0.0167194
$825$	70.7108	2.46183
$826$	0.129477	0.00450510
$827$	27.9892	0.973279	0.486640	−	0.873603i	$-0.338222\pi$
$827$	27.9892	0.973279	0.486640	+	0.873603i	$0.338222\pi$
$828$	8.28510	0.287927
$829$	−7.68442	−0.266891	−0.133445	−	0.991056i	$-0.542604\pi$
$829$	−7.68442	−0.266891	−0.133445	+	0.991056i	$0.542604\pi$
$830$	−1.05913	−0.0367630
$831$	84.9919	2.94834
$832$	−45.7704	−1.58680
$833$	36.0815	1.25015
$834$	16.6346	0.576008
$835$	−0.174033	−0.00602266
$836$	−18.9448	−0.655220
$837$	−76.5487	−2.64591
$838$	37.3625	1.29067
$839$	9.32581	0.321963	0.160981	−	0.986957i	$-0.448534\pi$
$839$	9.32581	0.321963	0.160981	+	0.986957i	$0.448534\pi$
$840$	0.0577146	0.00199134
$841$	35.9051	1.23811
$842$	8.29989	0.286033
$843$	48.1730	1.65916
$844$	9.65726	0.332416
$845$	−9.69056	−0.333366
$846$	45.0576	1.54911
$847$	−0.181936	−0.00625140
$848$	−12.6207	−0.433397
$849$	77.0877	2.64564
$850$	25.4141	0.871697
$851$	1.23182	0.0422262
$852$	46.0728	1.57843
$853$	−3.76760	−0.129000	−0.0645000	−	0.997918i	$-0.520545\pi$
$853$	−3.76760	−0.129000	−0.0645000	+	0.997918i	$0.520545\pi$
$854$	0.00572027	0.000195744 0
$855$	−9.92170	−0.339315
$856$	−3.68686	−0.126014
$857$	38.6528	1.32035	0.660176	−	0.751111i	$-0.270482\pi$
$857$	38.6528	1.32035	0.660176	+	0.751111i	$0.270482\pi$
$858$	93.8159	3.20282
$859$	19.6633	0.670905	0.335452	−	0.942057i	$-0.391111\pi$
$859$	19.6633	0.670905	0.335452	+	0.942057i	$0.391111\pi$
$860$	−0.779220	−0.0265712
$861$	0.413083	0.0140778
$862$	13.7714	0.469056
$863$	−43.1484	−1.46879	−0.734395	−	0.678722i	$-0.762534\pi$
$863$	−43.1484	−1.46879	−0.734395	+	0.678722i	$0.762534\pi$
$864$	−59.8204	−2.03513
$865$	2.16007	0.0734444
$866$	−1.03936	−0.0353190
$867$	−30.0614	−1.02094
$868$	0.109419	0.00371391
$869$	−66.5204	−2.25655
$870$	8.81146	0.298736
$871$	−3.85117	−0.130492
$872$	3.00976	0.101923
$873$	−35.9671	−1.21730
$874$	−5.21602	−0.176434
$875$	−0.0603278	−0.00203945
$876$	−0.512748	−0.0173242
$877$	28.1664	0.951112	0.475556	−	0.879685i	$-0.342247\pi$
$877$	28.1664	0.951112	0.475556	+	0.879685i	$0.342247\pi$
$878$	−13.2314	−0.446538
$879$	−65.6022	−2.21271
$880$	1.71815	0.0579190
$881$	−25.0323	−0.843358	−0.421679	−	0.906745i	$-0.638559\pi$
$881$	−25.0323	−0.843358	−0.421679	+	0.906745i	$0.638559\pi$
$882$	−48.5347	−1.63425
$883$	7.42645	0.249920	0.124960	−	0.992162i	$-0.460120\pi$
$883$	7.42645	0.249920	0.124960	+	0.992162i	$0.460120\pi$
$884$	−32.3813	−1.08910
$885$	−7.83813	−0.263476
$886$	20.0419	0.673321
$887$	−50.2996	−1.68890	−0.844448	−	0.535637i	$-0.820072\pi$
$887$	−50.2996	−1.68890	−0.844448	+	0.535637i	$0.820072\pi$
$888$	−9.45311	−0.317226
$889$	−0.0651678	−0.00218566
$890$	−2.33206	−0.0781708
$891$	80.8573	2.70882
$892$	−11.9662	−0.400658
$893$	27.2420	0.911617
$894$	−62.5415	−2.09170
$895$	−1.34087	−0.0448202
$896$	0.0468530	0.00156525
$897$	−24.8058	−0.828243
$898$	7.07260	0.236016
$899$	50.8056	1.69446
$900$	32.8301	1.09434
$901$	−60.2095	−2.00587
$902$	34.5995	1.15204
$903$	−0.128308	−0.00426983
$904$	49.9487	1.66127
$905$	−2.55130	−0.0848081
$906$	52.7713	1.75321
$907$	−16.2388	−0.539199	−0.269599	−	0.962973i	$-0.586891\pi$
$907$	−16.2388	−0.539199	−0.269599	+	0.962973i	$0.586891\pi$
$908$	−15.1915	−0.504148
$909$	−130.633	−4.33283
$910$	−0.0395387	−0.00131070
$911$	−38.8691	−1.28779	−0.643895	−	0.765114i	$-0.722682\pi$
$911$	−38.8691	−1.28779	−0.643895	+	0.765114i	$0.722682\pi$
$912$	14.2269	0.471101
$913$	14.0283	0.464269
$914$	−26.7568	−0.885038
$915$	−0.346286	−0.0114479
$916$	−5.56303	−0.183808
$917$	0.403669	0.0133303
$918$	63.2004	2.08592
$919$	15.4153	0.508505	0.254253	−	0.967138i	$-0.418171\pi$
$919$	15.4153	0.508505	0.254253	+	0.967138i	$0.418171\pi$
$920$	−1.27819	−0.0421407
$921$	−8.75797	−0.288585
$922$	10.1004	0.332639
$923$	−95.9931	−3.15965
$924$	−0.251353	−0.00826889
$925$	4.88114	0.160491
$926$	−17.0991	−0.561911
$927$	−1.09466	−0.0359533
$928$	39.7029	1.30331
$929$	21.3257	0.699675	0.349837	−	0.936810i	$-0.386237\pi$
$929$	21.3257	0.699675	0.349837	+	0.936810i	$0.386237\pi$
$930$	6.89732	0.226172
$931$	−29.3442	−0.961717
$932$	−15.0094	−0.491648
$933$	94.8863	3.10644
$934$	9.54427	0.312298
$935$	8.19679	0.268064
$936$	132.471	4.32995
$937$	34.7108	1.13395	0.566976	−	0.823734i	$-0.308113\pi$
$937$	34.7108	1.13395	0.566976	+	0.823734i	$0.308113\pi$
$938$	−0.0107441	−0.000350808 0
$939$	−57.2284	−1.86758
$940$	2.19501	0.0715934
$941$	41.4015	1.34965	0.674825	−	0.737978i	$-0.264219\pi$
$941$	41.4015	1.34965	0.674825	+	0.737978i	$0.264219\pi$
$942$	8.23936	0.268453
$943$	−9.14844	−0.297914
$944$	7.82125	0.254560
$945$	−0.0741099	−0.00241080
$946$	−10.7470	−0.349415
$947$	55.6126	1.80717	0.903584	−	0.428412i	$-0.140927\pi$
$947$	55.6126	1.80717	0.903584	+	0.428412i	$0.140927\pi$
$948$	−44.3815	−1.44144
$949$	1.06831	0.0346790
$950$	−20.6687	−0.670582
$951$	56.7179	1.83920
$952$	−0.274745	−0.00890455
$953$	−25.7840	−0.835226	−0.417613	−	0.908625i	$-0.637133\pi$
$953$	−25.7840	−0.835226	−0.417613	+	0.908625i	$0.637133\pi$
$954$	80.9904	2.62216
$955$	4.62731	0.149736
$956$	−13.5513	−0.438280
$957$	−116.709	−3.77266
$958$	37.1625	1.20066
$959$	0.00231859	7.48713e−5 0
$960$	7.73003	0.249486
$961$	8.76892	0.282869
$962$	6.47608	0.208797
$963$	8.40911	0.270980
$964$	27.0397	0.870891
$965$	−2.05618	−0.0661907
$966$	−0.0692041	−0.00222661
$967$	−44.3484	−1.42615	−0.713074	−	0.701089i	$-0.752698\pi$
$967$	−44.3484	−1.42615	−0.713074	+	0.701089i	$0.752698\pi$
$968$	−30.9212	−0.993846
$969$	67.8723	2.18037
$970$	1.82451	0.0585814
$971$	−14.4124	−0.462515	−0.231257	−	0.972893i	$-0.574284\pi$
$971$	−14.4124	−0.462515	−0.231257	+	0.972893i	$0.574284\pi$
$972$	18.2679	0.585944
$973$	0.0928568	0.00297685
$974$	−17.7766	−0.569598
$975$	−98.2943	−3.14794
$976$	0.345540	0.0110605
$977$	52.0202	1.66427	0.832137	−	0.554570i	$-0.187117\pi$
$977$	52.0202	1.66427	0.832137	+	0.554570i	$0.187117\pi$
$978$	77.9949	2.49400
$979$	30.8884	0.987197
$980$	−2.36440	−0.0755280
$981$	−6.86476	−0.219175
$982$	−12.1123	−0.386518
$983$	−3.66485	−0.116891	−0.0584453	−	0.998291i	$-0.518614\pi$
$983$	−3.66485	−0.116891	−0.0584453	+	0.998291i	$0.518614\pi$
$984$	70.2061	2.23809
$985$	2.83418	0.0903044
$986$	−41.9462	−1.33584
$987$	0.361436	0.0115046
$988$	26.3350	0.837828
$989$	2.84161	0.0903579
$990$	−11.0258	−0.350424
$991$	−21.9345	−0.696772	−0.348386	−	0.937351i	$-0.613270\pi$
$991$	−21.9345	−0.696772	−0.348386	+	0.937351i	$0.613270\pi$
$992$	31.0782	0.986733
$993$	−9.32948	−0.296062
$994$	−0.267805	−0.00849425
$995$	−0.641606	−0.0203403
$996$	9.35950	0.296567
$997$	−15.4991	−0.490863	−0.245431	−	0.969414i	$-0.578930\pi$
$997$	−15.4991	−0.490863	−0.245431	+	0.969414i	$0.578930\pi$
$998$	27.2416	0.862317
$999$	12.1385	0.384046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.54	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.54	✓	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)

\(f(q)\)	\(=\)	\(q+1.01006 q^{2} -3.14082 q^{3} -0.979773 q^{4} -0.344760 q^{5} -3.17243 q^{6} -0.0177090 q^{7} -3.00976 q^{8} +6.86476 q^{9} +O(q^{10})\)	\(q+1.01006 q^{2} -3.14082 q^{3} -0.979773 q^{4} -0.344760 q^{5} -3.17243 q^{6} -0.0177090 q^{7} -3.00976 q^{8} +6.86476 q^{9} -0.348229 q^{10} +4.61234 q^{11} +3.07729 q^{12} -6.41156 q^{13} -0.0178872 q^{14} +1.08283 q^{15} -1.08050 q^{16} -5.15472 q^{17} +6.93384 q^{18} +4.19222 q^{19} +0.337787 q^{20} +0.0556207 q^{21} +4.65875 q^{22} -1.23182 q^{23} +9.45311 q^{24} -4.88114 q^{25} -6.47608 q^{26} -12.1385 q^{27} +0.0173508 q^{28} +8.05637 q^{29} +1.09373 q^{30} +6.30626 q^{31} +4.92815 q^{32} -14.4865 q^{33} -5.20660 q^{34} +0.00610535 q^{35} -6.72591 q^{36} -1.00000 q^{37} +4.23440 q^{38} +20.1376 q^{39} +1.03764 q^{40} +7.42677 q^{41} +0.0561804 q^{42} -2.30684 q^{43} -4.51905 q^{44} -2.36670 q^{45} -1.24421 q^{46} +6.49822 q^{47} +3.39365 q^{48} -6.99969 q^{49} -4.93026 q^{50} +16.1901 q^{51} +6.28188 q^{52} +11.6805 q^{53} -12.2607 q^{54} -1.59015 q^{55} +0.0532997 q^{56} -13.1670 q^{57} +8.13744 q^{58} -7.23856 q^{59} -1.06093 q^{60} -0.319797 q^{61} +6.36972 q^{62} -0.121568 q^{63} +7.13873 q^{64} +2.21045 q^{65} -14.6323 q^{66} +0.600660 q^{67} +5.05046 q^{68} +3.86892 q^{69} +0.00616679 q^{70} +14.9719 q^{71} -20.6613 q^{72} -0.166623 q^{73} -1.01006 q^{74} +15.3308 q^{75} -4.10742 q^{76} -0.0816798 q^{77} +20.3402 q^{78} -14.4223 q^{79} +0.372513 q^{80} +17.5306 q^{81} +7.50151 q^{82} +3.04147 q^{83} -0.0544957 q^{84} +1.77714 q^{85} -2.33005 q^{86} -25.3036 q^{87} -13.8820 q^{88} +6.69691 q^{89} -2.39051 q^{90} +0.113542 q^{91} +1.20690 q^{92} -19.8068 q^{93} +6.56361 q^{94} -1.44531 q^{95} -15.4784 q^{96} -5.23939 q^{97} -7.07012 q^{98} +31.6626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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