LMFDB - Embedded newform 4033.2.a.d.1.60

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			1.60
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)

$f(q)$	$=$	$q+1.44999 q^{2} +1.38793 q^{3} +0.102465 q^{4} +2.53458 q^{5} +2.01248 q^{6} -3.56931 q^{7} -2.75140 q^{8} -1.07366 q^{9} +O(q^{10})$	\(q+1.44999 q^{2} +1.38793 q^{3} +0.102465 q^{4} +2.53458 q^{5} +2.01248 q^{6} -3.56931 q^{7} -2.75140 q^{8} -1.07366 q^{9} +3.67511 q^{10} -4.30525 q^{11} +0.142214 q^{12} +4.95808 q^{13} -5.17545 q^{14} +3.51782 q^{15} -4.19443 q^{16} +3.28211 q^{17} -1.55679 q^{18} -3.22908 q^{19} +0.259705 q^{20} -4.95394 q^{21} -6.24256 q^{22} -0.272413 q^{23} -3.81875 q^{24} +1.42411 q^{25} +7.18915 q^{26} -5.65394 q^{27} -0.365728 q^{28} +1.82542 q^{29} +5.10079 q^{30} -7.36449 q^{31} -0.579067 q^{32} -5.97537 q^{33} +4.75901 q^{34} -9.04671 q^{35} -0.110012 q^{36} -1.00000 q^{37} -4.68212 q^{38} +6.88145 q^{39} -6.97366 q^{40} -1.48023 q^{41} -7.18316 q^{42} -10.1833 q^{43} -0.441136 q^{44} -2.72127 q^{45} -0.394995 q^{46} +8.13762 q^{47} -5.82157 q^{48} +5.73996 q^{49} +2.06494 q^{50} +4.55533 q^{51} +0.508028 q^{52} +1.79271 q^{53} -8.19815 q^{54} -10.9120 q^{55} +9.82061 q^{56} -4.48173 q^{57} +2.64683 q^{58} -3.18224 q^{59} +0.360452 q^{60} -13.5137 q^{61} -10.6784 q^{62} +3.83221 q^{63} +7.54922 q^{64} +12.5667 q^{65} -8.66422 q^{66} -10.6812 q^{67} +0.336300 q^{68} -0.378089 q^{69} -13.1176 q^{70} +7.99980 q^{71} +2.95406 q^{72} +1.48477 q^{73} -1.44999 q^{74} +1.97656 q^{75} -0.330866 q^{76} +15.3668 q^{77} +9.97802 q^{78} -17.6318 q^{79} -10.6311 q^{80} -4.62630 q^{81} -2.14631 q^{82} -15.3175 q^{83} -0.507604 q^{84} +8.31877 q^{85} -14.7656 q^{86} +2.53355 q^{87} +11.8455 q^{88} -7.26451 q^{89} -3.94581 q^{90} -17.6969 q^{91} -0.0279127 q^{92} -10.2214 q^{93} +11.7995 q^{94} -8.18436 q^{95} -0.803703 q^{96} +5.45132 q^{97} +8.32288 q^{98} +4.62235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.44999	1.02530	0.512648	−	0.858599i	$-0.328665\pi$
$2$	1.44999	1.02530	0.512648	+	0.858599i	$0.328665\pi$
$3$	1.38793	0.801321	0.400660	−	0.916227i	$-0.368781\pi$
$3$	1.38793	0.801321	0.400660	+	0.916227i	$0.368781\pi$
$4$	0.102465	0.0512323
$5$	2.53458	1.13350	0.566750	−	0.823890i	$-0.308201\pi$
$5$	2.53458	1.13350	0.566750	+	0.823890i	$0.308201\pi$
$6$	2.01248	0.821591
$7$	−3.56931	−1.34907	−0.674536	−	0.738242i	$-0.735656\pi$
$7$	−3.56931	−1.34907	−0.674536	+	0.738242i	$0.735656\pi$
$8$	−2.75140	−0.972768
$9$	−1.07366	−0.357885
$10$	3.67511	1.16217
$11$	−4.30525	−1.29808	−0.649041	−	0.760754i	$-0.724829\pi$
$11$	−4.30525	−1.29808	−0.649041	+	0.760754i	$0.724829\pi$
$12$	0.142214	0.0410535
$13$	4.95808	1.37512	0.687561	−	0.726126i	$-0.258681\pi$
$13$	4.95808	1.37512	0.687561	+	0.726126i	$0.258681\pi$
$14$	−5.17545	−1.38320
$15$	3.51782	0.908297
$16$	−4.19443	−1.04861
$17$	3.28211	0.796028	0.398014	−	0.917379i	$-0.369700\pi$
$17$	3.28211	0.796028	0.398014	+	0.917379i	$0.369700\pi$
$18$	−1.55679	−0.366938
$19$	−3.22908	−0.740801	−0.370400	−	0.928872i	$-0.620780\pi$
$19$	−3.22908	−0.740801	−0.370400	+	0.928872i	$0.620780\pi$
$20$	0.259705	0.0580719
$21$	−4.95394	−1.08104
$22$	−6.24256	−1.33092
$23$	−0.272413	−0.0568020	−0.0284010	−	0.999597i	$-0.509042\pi$
$23$	−0.272413	−0.0568020	−0.0284010	+	0.999597i	$0.509042\pi$
$24$	−3.81875	−0.779499
$25$	1.42411	0.284822
$26$	7.18915	1.40991
$27$	−5.65394	−1.08810
$28$	−0.365728	−0.0691161
$29$	1.82542	0.338971	0.169486	−	0.985533i	$-0.445789\pi$
$29$	1.82542	0.338971	0.169486	+	0.985533i	$0.445789\pi$
$30$	5.10079	0.931273
$31$	−7.36449	−1.32270	−0.661351	−	0.750077i	$-0.730017\pi$
$31$	−7.36449	−1.32270	−0.661351	+	0.750077i	$0.730017\pi$
$32$	−0.579067	−0.102366
$33$	−5.97537	−1.04018
$34$	4.75901	0.816164
$35$	−9.04671	−1.52917
$36$	−0.110012	−0.0183353
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−4.68212	−0.759540
$39$	6.88145	1.10191
$40$	−6.97366	−1.10263
$41$	−1.48023	−0.231173	−0.115586	−	0.993297i	$-0.536875\pi$
$41$	−1.48023	−0.231173	−0.115586	+	0.993297i	$0.536875\pi$
$42$	−7.18316	−1.10839
$43$	−10.1833	−1.55294	−0.776468	−	0.630157i	$-0.782991\pi$
$43$	−10.1833	−1.55294	−0.776468	+	0.630157i	$0.782991\pi$
$44$	−0.441136	−0.0665037
$45$	−2.72127	−0.405663
$46$	−0.394995	−0.0582388
$47$	8.13762	1.18699	0.593497	−	0.804836i	$-0.297747\pi$
$47$	8.13762	1.18699	0.593497	+	0.804836i	$0.297747\pi$
$48$	−5.82157	−0.840271
$49$	5.73996	0.819995
$50$	2.06494	0.292027
$51$	4.55533	0.637873
$52$	0.508028	0.0704508
$53$	1.79271	0.246248	0.123124	−	0.992391i	$-0.460709\pi$
$53$	1.79271	0.246248	0.123124	+	0.992391i	$0.460709\pi$
$54$	−8.19815	−1.11563
$55$	−10.9120	−1.47137
$56$	9.82061	1.31233
$57$	−4.48173	−0.593619
$58$	2.64683	0.347546
$59$	−3.18224	−0.414293	−0.207146	−	0.978310i	$-0.566418\pi$
$59$	−3.18224	−0.414293	−0.207146	+	0.978310i	$0.566418\pi$
$60$	0.360452	0.0465342
$61$	−13.5137	−1.73026	−0.865128	−	0.501551i	$-0.832763\pi$
$61$	−13.5137	−1.73026	−0.865128	+	0.501551i	$0.832763\pi$
$62$	−10.6784	−1.35616
$63$	3.83221	0.482813
$64$	7.54922	0.943653
$65$	12.5667	1.55870
$66$	−8.66422	−1.06649
$67$	−10.6812	−1.30492	−0.652460	−	0.757823i	$-0.726263\pi$
$67$	−10.6812	−1.30492	−0.652460	+	0.757823i	$0.726263\pi$
$68$	0.336300	0.0407824
$69$	−0.378089	−0.0455166
$70$	−13.1176	−1.56786
$71$	7.99980	0.949401	0.474701	−	0.880147i	$-0.342556\pi$
$71$	7.99980	0.949401	0.474701	+	0.880147i	$0.342556\pi$
$72$	2.95406	0.348139
$73$	1.48477	0.173779	0.0868894	−	0.996218i	$-0.472307\pi$
$73$	1.48477	0.173779	0.0868894	+	0.996218i	$0.472307\pi$
$74$	−1.44999	−0.168558
$75$	1.97656	0.228234
$76$	−0.330866	−0.0379530
$77$	15.3668	1.75120
$78$	9.97802	1.12979
$79$	−17.6318	−1.98373	−0.991865	−	0.127295i	$-0.959371\pi$
$79$	−17.6318	−1.98373	−0.991865	+	0.127295i	$0.959371\pi$
$80$	−10.6311	−1.18860
$81$	−4.62630	−0.514033
$82$	−2.14631	−0.237021
$83$	−15.3175	−1.68131	−0.840657	−	0.541568i	$-0.817831\pi$
$83$	−15.3175	−1.68131	−0.840657	+	0.541568i	$0.817831\pi$
$84$	−0.507604	−0.0553842
$85$	8.31877	0.902297
$86$	−14.7656	−1.59222
$87$	2.53355	0.271625
$88$	11.8455	1.26273
$89$	−7.26451	−0.770037	−0.385018	−	0.922909i	$-0.625805\pi$
$89$	−7.26451	−0.770037	−0.385018	+	0.922909i	$0.625805\pi$
$90$	−3.94581	−0.415925
$91$	−17.6969	−1.85514
$92$	−0.0279127	−0.00291010
$93$	−10.2214	−1.05991
$94$	11.7995	1.21702
$95$	−8.18436	−0.839698
$96$	−0.803703	−0.0820276
$97$	5.45132	0.553497	0.276749	−	0.960942i	$-0.410743\pi$
$97$	5.45132	0.553497	0.276749	+	0.960942i	$0.410743\pi$
$98$	8.32288	0.840738
$99$	4.62235	0.464564
$100$	0.145921	0.0145921
$101$	7.81382	0.777504	0.388752	−	0.921342i	$-0.372906\pi$
$101$	7.81382	0.777504	0.388752	+	0.921342i	$0.372906\pi$
$102$	6.60517	0.654009
$103$	−3.60557	−0.355267	−0.177634	−	0.984097i	$-0.556844\pi$
$103$	−3.60557	−0.355267	−0.177634	+	0.984097i	$0.556844\pi$
$104$	−13.6417	−1.33768
$105$	−12.5562	−1.22536
$106$	2.59941	0.252477
$107$	16.6749	1.61202	0.806011	−	0.591901i	$-0.201622\pi$
$107$	16.6749	1.61202	0.806011	+	0.591901i	$0.201622\pi$
$108$	−0.579329	−0.0557460
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−15.8223	−1.50860
$111$	−1.38793	−0.131736
$112$	14.9712	1.41465
$113$	4.17974	0.393197	0.196599	−	0.980484i	$-0.437010\pi$
$113$	4.17974	0.393197	0.196599	+	0.980484i	$0.437010\pi$
$114$	−6.49845	−0.608635
$115$	−0.690452	−0.0643850
$116$	0.187041	0.0173663
$117$	−5.32327	−0.492136
$118$	−4.61422	−0.424773
$119$	−11.7148	−1.07390
$120$	−9.67894	−0.883562
$121$	7.53516	0.685015
$122$	−19.5948	−1.77403
$123$	−2.05445	−0.185244
$124$	−0.754600	−0.0677651
$125$	−9.06339	−0.810654
$126$	5.55666	0.495026
$127$	1.83376	0.162720	0.0813600	−	0.996685i	$-0.474074\pi$
$127$	1.83376	0.162720	0.0813600	+	0.996685i	$0.474074\pi$
$128$	12.1044	1.06989
$129$	−14.1337	−1.24440
$130$	18.2215	1.59813
$131$	12.3232	1.07669	0.538343	−	0.842726i	$-0.319051\pi$
$131$	12.3232	1.07669	0.538343	+	0.842726i	$0.319051\pi$
$132$	−0.612265	−0.0532908
$133$	11.5256	0.999394
$134$	−15.4877	−1.33793
$135$	−14.3304	−1.23336
$136$	−9.03040	−0.774350
$137$	−13.5961	−1.16159	−0.580795	−	0.814050i	$-0.697258\pi$
$137$	−13.5961	−1.16159	−0.580795	+	0.814050i	$0.697258\pi$
$138$	−0.548225	−0.0466680
$139$	−8.06705	−0.684238	−0.342119	−	0.939657i	$-0.611145\pi$
$139$	−8.06705	−0.684238	−0.342119	+	0.939657i	$0.611145\pi$
$140$	−0.926968	−0.0783431
$141$	11.2944	0.951163
$142$	11.5996	0.973417
$143$	−21.3457	−1.78502
$144$	4.50337	0.375281
$145$	4.62667	0.384224
$146$	2.15289	0.178175
$147$	7.96666	0.657079
$148$	−0.102465	−0.00842255
$149$	6.23571	0.510850	0.255425	−	0.966829i	$-0.417785\pi$
$149$	6.23571	0.510850	0.255425	+	0.966829i	$0.417785\pi$
$150$	2.86599	0.234007
$151$	24.2808	1.97594	0.987972	−	0.154631i	$-0.0494188\pi$
$151$	24.2808	1.97594	0.987972	+	0.154631i	$0.0494188\pi$
$152$	8.88449	0.720627
$153$	−3.52385	−0.284887
$154$	22.2816	1.79550
$155$	−18.6659	−1.49928
$156$	0.705106	0.0564537
$157$	−3.48695	−0.278289	−0.139145	−	0.990272i	$-0.544435\pi$
$157$	−3.48695	−0.278289	−0.139145	+	0.990272i	$0.544435\pi$
$158$	−25.5659	−2.03391
$159$	2.48816	0.197324
$160$	−1.46769	−0.116031
$161$	0.972325	0.0766299
$162$	−6.70807	−0.527036
$163$	13.4901	1.05662	0.528312	−	0.849050i	$-0.322825\pi$
$163$	13.4901	1.05662	0.528312	+	0.849050i	$0.322825\pi$
$164$	−0.151671	−0.0118435
$165$	−15.1451	−1.17904
$166$	−22.2102	−1.72384
$167$	10.3032	0.797289	0.398645	−	0.917105i	$-0.369481\pi$
$167$	10.3032	0.797289	0.398645	+	0.917105i	$0.369481\pi$
$168$	13.6303	1.05160
$169$	11.5825	0.890963
$170$	12.0621	0.925122
$171$	3.46692	0.265122
$172$	−1.04343	−0.0795605
$173$	20.9305	1.59132	0.795659	−	0.605744i	$-0.207125\pi$
$173$	20.9305	1.59132	0.795659	+	0.605744i	$0.207125\pi$
$174$	3.67361	0.278496
$175$	−5.08309	−0.384246
$176$	18.0581	1.36118
$177$	−4.41673	−0.331981
$178$	−10.5335	−0.789516
$179$	−0.00348101	−0.000260183 0	−0.000130091	−	1.00000i	$-0.500041\pi$
$179$	−0.00348101	−0.000260183 0	−0.000130091		1.00000i	$0.500041\pi$
$180$	−0.278834	−0.0207831
$181$	−7.42469	−0.551873	−0.275936	−	0.961176i	$-0.588988\pi$
$181$	−7.42469	−0.551873	−0.275936	+	0.961176i	$0.588988\pi$
$182$	−25.6603	−1.90207
$183$	−18.7561	−1.38649
$184$	0.749517	0.0552551
$185$	−2.53458	−0.186346
$186$	−14.8209	−1.08672
$187$	−14.1303	−1.03331
$188$	0.833819	0.0608125
$189$	20.1807	1.46793
$190$	−11.8672	−0.860939
$191$	−16.8820	−1.22154	−0.610769	−	0.791809i	$-0.709139\pi$
$191$	−16.8820	−1.22154	−0.610769	+	0.791809i	$0.709139\pi$
$192$	10.4778	0.756168
$193$	−10.8740	−0.782726	−0.391363	−	0.920236i	$-0.627996\pi$
$193$	−10.8740	−0.782726	−0.391363	+	0.920236i	$0.627996\pi$
$194$	7.90434	0.567499
$195$	17.4416	1.24902
$196$	0.588144	0.0420103
$197$	−4.51927	−0.321984	−0.160992	−	0.986956i	$-0.551469\pi$
$197$	−4.51927	−0.321984	−0.160992	+	0.986956i	$0.551469\pi$
$198$	6.70236	0.476316
$199$	8.48841	0.601727	0.300864	−	0.953667i	$-0.402725\pi$
$199$	8.48841	0.601727	0.300864	+	0.953667i	$0.402725\pi$
$200$	−3.91830	−0.277066
$201$	−14.8248	−1.04566
$202$	11.3299	0.797172
$203$	−6.51548	−0.457297
$204$	0.466760	0.0326798
$205$	−3.75176	−0.262034
$206$	−5.22803	−0.364254
$207$	0.292477	0.0203286
$208$	−20.7963	−1.44196
$209$	13.9020	0.961620
$210$	−18.2063	−1.25635
$211$	−12.6552	−0.871222	−0.435611	−	0.900135i	$-0.643468\pi$
$211$	−12.6552	−0.871222	−0.435611	+	0.900135i	$0.643468\pi$
$212$	0.183690	0.0126159
$213$	11.1031	0.760775
$214$	24.1784	1.65280
$215$	−25.8104	−1.76025
$216$	15.5563	1.05847
$217$	26.2861	1.78442
$218$	−1.44999	−0.0982056
$219$	2.06075	0.139253
$220$	−1.11810	−0.0753820
$221$	16.2729	1.09464
$222$	−2.01248	−0.135069
$223$	9.97022	0.667655	0.333828	−	0.942634i	$-0.391660\pi$
$223$	9.97022	0.667655	0.333828	+	0.942634i	$0.391660\pi$
$224$	2.06687	0.138098
$225$	−1.52900	−0.101934
$226$	6.06058	0.403144
$227$	−2.38111	−0.158040	−0.0790199	−	0.996873i	$-0.525179\pi$
$227$	−2.38111	−0.158040	−0.0790199	+	0.996873i	$0.525179\pi$
$228$	−0.459219	−0.0304125
$229$	19.7795	1.30707	0.653534	−	0.756897i	$-0.273286\pi$
$229$	19.7795	1.30707	0.653534	+	0.756897i	$0.273286\pi$
$230$	−1.00115	−0.0660137
$231$	21.3280	1.40328
$232$	−5.02246	−0.329741
$233$	7.81551	0.512011	0.256006	−	0.966675i	$-0.417593\pi$
$233$	7.81551	0.512011	0.256006	+	0.966675i	$0.417593\pi$
$234$	−7.71867	−0.504585
$235$	20.6255	1.34546
$236$	−0.326068	−0.0212252
$237$	−24.4716	−1.58960
$238$	−16.9864	−1.10106
$239$	−8.38682	−0.542499	−0.271249	−	0.962509i	$-0.587437\pi$
$239$	−8.38682	−0.542499	−0.271249	+	0.962509i	$0.587437\pi$
$240$	−14.7552	−0.952447
$241$	−8.39039	−0.540472	−0.270236	−	0.962794i	$-0.587102\pi$
$241$	−8.39039	−0.540472	−0.270236	+	0.962794i	$0.587102\pi$
$242$	10.9259	0.702343
$243$	10.5409	0.676196
$244$	−1.38468	−0.0886451
$245$	14.5484	0.929464
$246$	−2.97893	−0.189930
$247$	−16.0100	−1.01869
$248$	20.2627	1.28668
$249$	−21.2596	−1.34727
$250$	−13.1418	−0.831160
$251$	18.1722	1.14702	0.573509	−	0.819199i	$-0.305582\pi$
$251$	18.1722	1.14702	0.573509	+	0.819199i	$0.305582\pi$
$252$	0.392666	0.0247356
$253$	1.17280	0.0737335
$254$	2.65893	0.166836
$255$	11.5459	0.723030
$256$	2.45281	0.153301
$257$	−3.79073	−0.236459	−0.118230	−	0.992986i	$-0.537722\pi$
$257$	−3.79073	−0.236459	−0.118230	+	0.992986i	$0.537722\pi$
$258$	−20.4936	−1.27588
$259$	3.56931	0.221786
$260$	1.28764	0.0798559
$261$	−1.95987	−0.121313
$262$	17.8685	1.10392
$263$	15.9656	0.984481	0.492240	−	0.870459i	$-0.336178\pi$
$263$	15.9656	0.984481	0.492240	+	0.870459i	$0.336178\pi$
$264$	16.4407	1.01185
$265$	4.54378	0.279122
$266$	16.7119	1.02467
$267$	−10.0826	−0.617046
$268$	−1.09445	−0.0668541
$269$	25.6094	1.56143	0.780716	−	0.624886i	$-0.214855\pi$
$269$	25.6094	1.56143	0.780716	+	0.624886i	$0.214855\pi$
$270$	−20.7789	−1.26456
$271$	13.8200	0.839505	0.419752	−	0.907639i	$-0.362117\pi$
$271$	13.8200	0.839505	0.419752	+	0.907639i	$0.362117\pi$
$272$	−13.7666	−0.834721
$273$	−24.5620	−1.48656
$274$	−19.7141	−1.19097
$275$	−6.13115	−0.369722
$276$	−0.0387408	−0.00233192
$277$	16.8448	1.01210	0.506051	−	0.862503i	$-0.331105\pi$
$277$	16.8448	1.01210	0.506051	+	0.862503i	$0.331105\pi$
$278$	−11.6971	−0.701547
$279$	7.90693	0.473375
$280$	24.8911	1.48753
$281$	19.3356	1.15347	0.576733	−	0.816933i	$-0.304327\pi$
$281$	19.3356	1.15347	0.576733	+	0.816933i	$0.304327\pi$
$282$	16.3768	0.975224
$283$	−31.0436	−1.84535	−0.922674	−	0.385580i	$-0.874001\pi$
$283$	−31.0436	−1.84535	−0.922674	+	0.385580i	$0.874001\pi$
$284$	0.819697	0.0486400
$285$	−11.3593	−0.672867
$286$	−30.9511	−1.83018
$287$	5.28339	0.311869
$288$	0.621718	0.0366351
$289$	−6.22778	−0.366340
$290$	6.70862	0.393944
$291$	7.56604	0.443529
$292$	0.152136	0.00890310
$293$	21.1671	1.23659	0.618296	−	0.785945i	$-0.287823\pi$
$293$	21.1671	1.23659	0.618296	+	0.785945i	$0.287823\pi$
$294$	11.5516	0.673700
$295$	−8.06566	−0.469601
$296$	2.75140	0.159922
$297$	24.3416	1.41244
$298$	9.04171	0.523772
$299$	−1.35064	−0.0781097
$300$	0.202528	0.0116930
$301$	36.3473	2.09502
$302$	35.2069	2.02593
$303$	10.8450	0.623030
$304$	13.5441	0.776810
$305$	−34.2517	−1.96125
$306$	−5.10954	−0.292093
$307$	18.7565	1.07049	0.535244	−	0.844697i	$-0.320219\pi$
$307$	18.7565	1.07049	0.535244	+	0.844697i	$0.320219\pi$
$308$	1.57455	0.0897183
$309$	−5.00427	−0.284683
$310$	−27.0654	−1.53721
$311$	−12.4045	−0.703396	−0.351698	−	0.936114i	$-0.614396\pi$
$311$	−12.4045	−0.703396	−0.351698	+	0.936114i	$0.614396\pi$
$312$	−18.9337	−1.07191
$313$	−10.5787	−0.597943	−0.298972	−	0.954262i	$-0.596644\pi$
$313$	−10.5787	−0.597943	−0.298972	+	0.954262i	$0.596644\pi$
$314$	−5.05604	−0.285329
$315$	9.71305	0.547268
$316$	−1.80663	−0.101631
$317$	32.2794	1.81299	0.906496	−	0.422215i	$-0.138747\pi$
$317$	32.2794	1.81299	0.906496	+	0.422215i	$0.138747\pi$
$318$	3.60780	0.202315
$319$	−7.85887	−0.440012
$320$	19.1341	1.06963
$321$	23.1435	1.29175
$322$	1.40986	0.0785684
$323$	−10.5982	−0.589698
$324$	−0.474032	−0.0263351
$325$	7.06085	0.391666
$326$	19.5604	1.08335
$327$	−1.38793	−0.0767526
$328$	4.07271	0.224878
$329$	−29.0457	−1.60134
$330$	−21.9602	−1.20887
$331$	−5.25248	−0.288702	−0.144351	−	0.989527i	$-0.546109\pi$
$331$	−5.25248	−0.288702	−0.144351	+	0.989527i	$0.546109\pi$
$332$	−1.56950	−0.0861376
$333$	1.07366	0.0588360
$334$	14.9396	0.817458
$335$	−27.0725	−1.47913
$336$	20.7790	1.13359
$337$	1.25539	0.0683853	0.0341926	−	0.999415i	$-0.489114\pi$
$337$	1.25539	0.0683853	0.0341926	+	0.999415i	$0.489114\pi$
$338$	16.7945	0.913501
$339$	5.80119	0.315077
$340$	0.852380	0.0462268
$341$	31.7060	1.71697
$342$	5.02699	0.271828
$343$	4.49746	0.242840
$344$	28.0183	1.51065
$345$	−0.958298	−0.0515930
$346$	30.3490	1.63157
$347$	−5.97721	−0.320873	−0.160437	−	0.987046i	$-0.551290\pi$
$347$	−5.97721	−0.320873	−0.160437	+	0.987046i	$0.551290\pi$
$348$	0.259599	0.0139160
$349$	−30.1788	−1.61543	−0.807717	−	0.589571i	$-0.799297\pi$
$349$	−30.1788	−1.61543	−0.807717	+	0.589571i	$0.799297\pi$
$350$	−7.37042	−0.393966
$351$	−28.0327	−1.49627
$352$	2.49303	0.132879
$353$	29.3065	1.55982	0.779912	−	0.625889i	$-0.215264\pi$
$353$	29.3065	1.55982	0.779912	+	0.625889i	$0.215264\pi$
$354$	−6.40420	−0.340379
$355$	20.2761	1.07615
$356$	−0.744356	−0.0394508
$357$	−16.2594	−0.860537
$358$	−0.00504742	−0.000266764 0
$359$	−8.61342	−0.454599	−0.227299	−	0.973825i	$-0.572990\pi$
$359$	−8.61342	−0.454599	−0.227299	+	0.973825i	$0.572990\pi$
$360$	7.48731	0.394616
$361$	−8.57306	−0.451214
$362$	−10.7657	−0.565833
$363$	10.4583	0.548916
$364$	−1.81331	−0.0950432
$365$	3.76327	0.196978
$366$	−27.1961	−1.42156
$367$	13.5562	0.707630	0.353815	−	0.935315i	$-0.384884\pi$
$367$	13.5562	0.707630	0.353815	+	0.935315i	$0.384884\pi$
$368$	1.14262	0.0595630
$369$	1.58926	0.0827333
$370$	−3.67511	−0.191060
$371$	−6.39875	−0.332206
$372$	−1.04733	−0.0543016
$373$	−8.49043	−0.439618	−0.219809	−	0.975543i	$-0.570543\pi$
$373$	−8.49043	−0.439618	−0.219809	+	0.975543i	$0.570543\pi$
$374$	−20.4887	−1.05945
$375$	−12.5793	−0.649594
$376$	−22.3899	−1.15467
$377$	9.05056	0.466127
$378$	29.2617	1.50506
$379$	−21.5198	−1.10540	−0.552698	−	0.833382i	$-0.686402\pi$
$379$	−21.5198	−1.10540	−0.552698	+	0.833382i	$0.686402\pi$
$380$	−0.838608	−0.0430197
$381$	2.54513	0.130391
$382$	−24.4787	−1.25244
$383$	20.9328	1.06962	0.534808	−	0.844974i	$-0.320384\pi$
$383$	20.9328	1.06962	0.534808	+	0.844974i	$0.320384\pi$
$384$	16.8001	0.857324
$385$	38.9483	1.98499
$386$	−15.7671	−0.802526
$387$	10.9333	0.555773
$388$	0.558568	0.0283570
$389$	−35.3162	−1.79060	−0.895302	−	0.445459i	$-0.853041\pi$
$389$	−35.3162	−1.79060	−0.895302	+	0.445459i	$0.853041\pi$
$390$	25.2901	1.28062
$391$	−0.894087	−0.0452159
$392$	−15.7930	−0.797665
$393$	17.1038	0.862771
$394$	−6.55288	−0.330129
$395$	−44.6892	−2.24856
$396$	0.473628	0.0238007
$397$	13.9538	0.700320	0.350160	−	0.936690i	$-0.386127\pi$
$397$	13.9538	0.700320	0.350160	+	0.936690i	$0.386127\pi$
$398$	12.3081	0.616949
$399$	15.9967	0.800835
$400$	−5.97333	−0.298667
$401$	−34.9345	−1.74454	−0.872272	−	0.489020i	$-0.837354\pi$
$401$	−34.9345	−1.74454	−0.872272	+	0.489020i	$0.837354\pi$
$402$	−21.4958	−1.07211
$403$	−36.5137	−1.81888
$404$	0.800640	0.0398333
$405$	−11.7257	−0.582656
$406$	−9.44736	−0.468865
$407$	4.30525	0.213403
$408$	−12.5335	−0.620503
$409$	−28.7770	−1.42293	−0.711466	−	0.702721i	$-0.751968\pi$
$409$	−28.7770	−1.42293	−0.711466	+	0.702721i	$0.751968\pi$
$410$	−5.44001	−0.268663
$411$	−18.8704	−0.930806
$412$	−0.369444	−0.0182012
$413$	11.3584	0.558911
$414$	0.424089	0.0208428
$415$	−38.8235	−1.90577
$416$	−2.87106	−0.140765
$417$	−11.1965	−0.548294
$418$	20.1577	0.985945
$419$	−19.7175	−0.963265	−0.481633	−	0.876373i	$-0.659956\pi$
$419$	−19.7175	−0.963265	−0.481633	+	0.876373i	$0.659956\pi$
$420$	−1.28657	−0.0627780
$421$	12.6673	0.617367	0.308683	−	0.951165i	$-0.400112\pi$
$421$	12.6673	0.617367	0.308683	+	0.951165i	$0.400112\pi$
$422$	−18.3499	−0.893260
$423$	−8.73700	−0.424808
$424$	−4.93248	−0.239542
$425$	4.67408	0.226726
$426$	16.0994	0.780019
$427$	48.2347	2.33424
$428$	1.70859	0.0825876
$429$	−29.6264	−1.43037
$430$	−37.4247	−1.80478
$431$	−30.2273	−1.45600	−0.727999	−	0.685578i	$-0.759550\pi$
$431$	−30.2273	−1.45600	−0.727999	+	0.685578i	$0.759550\pi$
$432$	23.7151	1.14099
$433$	−38.8989	−1.86936	−0.934680	−	0.355490i	$-0.884314\pi$
$433$	−38.8989	−1.86936	−0.934680	+	0.355490i	$0.884314\pi$
$434$	38.1146	1.82956
$435$	6.42149	0.307887
$436$	−0.102465	−0.00490717
$437$	0.879641	0.0420789
$438$	2.98806	0.142775
$439$	−8.57932	−0.409469	−0.204734	−	0.978818i	$-0.565633\pi$
$439$	−8.57932	−0.409469	−0.204734	+	0.978818i	$0.565633\pi$
$440$	30.0233	1.43131
$441$	−6.16274	−0.293464
$442$	23.5956	1.12233
$443$	−0.610995	−0.0290293	−0.0145146	−	0.999895i	$-0.504620\pi$
$443$	−0.610995	−0.0290293	−0.0145146	+	0.999895i	$0.504620\pi$
$444$	−0.142214	−0.00674916
$445$	−18.4125	−0.872837
$446$	14.4567	0.684545
$447$	8.65472	0.409354
$448$	−26.9455	−1.27306
$449$	−8.68698	−0.409964	−0.204982	−	0.978766i	$-0.565714\pi$
$449$	−8.68698	−0.409964	−0.204982	+	0.978766i	$0.565714\pi$
$450$	−2.21704	−0.104512
$451$	6.37275	0.300081
$452$	0.428276	0.0201444
$453$	33.7000	1.58337
$454$	−3.45258	−0.162038
$455$	−44.8543	−2.10280
$456$	12.3310	0.577454
$457$	−36.4607	−1.70556	−0.852780	−	0.522270i	$-0.825085\pi$
$457$	−36.4607	−1.70556	−0.852780	+	0.522270i	$0.825085\pi$
$458$	28.6801	1.34013
$459$	−18.5568	−0.866159
$460$	−0.0707470	−0.00329860
$461$	−4.76636	−0.221992	−0.110996	−	0.993821i	$-0.535404\pi$
$461$	−4.76636	−0.221992	−0.110996	+	0.993821i	$0.535404\pi$
$462$	30.9253	1.43877
$463$	26.8262	1.24672	0.623360	−	0.781935i	$-0.285767\pi$
$463$	26.8262	1.24672	0.623360	+	0.781935i	$0.285767\pi$
$464$	−7.65659	−0.355448
$465$	−25.9070	−1.20141
$466$	11.3324	0.524963
$467$	−15.7947	−0.730892	−0.365446	−	0.930833i	$-0.619084\pi$
$467$	−15.7947	−0.730892	−0.365446	+	0.930833i	$0.619084\pi$
$468$	−0.545447	−0.0252133
$469$	38.1246	1.76043
$470$	29.9067	1.37949
$471$	−4.83964	−0.222999
$472$	8.75564	0.403011
$473$	43.8415	2.01584
$474$	−35.4836	−1.62981
$475$	−4.59856	−0.210997
$476$	−1.20036	−0.0550183
$477$	−1.92476	−0.0881285
$478$	−12.1608	−0.556222
$479$	−37.9605	−1.73446	−0.867230	−	0.497909i	$-0.834102\pi$
$479$	−37.9605	−1.73446	−0.867230	+	0.497909i	$0.834102\pi$
$480$	−2.03705	−0.0929783
$481$	−4.95808	−0.226069
$482$	−12.1660	−0.554144
$483$	1.34952	0.0614051
$484$	0.772088	0.0350949
$485$	13.8168	0.627389
$486$	15.2841	0.693301
$487$	38.3950	1.73984	0.869922	−	0.493190i	$-0.164169\pi$
$487$	38.3950	1.73984	0.869922	+	0.493190i	$0.164169\pi$
$488$	37.1817	1.68314
$489$	18.7232	0.846694
$490$	21.0950	0.952976
$491$	15.8623	0.715857	0.357929	−	0.933749i	$-0.383483\pi$
$491$	15.8623	0.715857	0.357929	+	0.933749i	$0.383483\pi$
$492$	−0.210509	−0.00949046
$493$	5.99121	0.269831
$494$	−23.2143	−1.04446
$495$	11.7157	0.526583
$496$	30.8898	1.38700
$497$	−28.5537	−1.28081
$498$	−30.8261	−1.38135
$499$	−21.7212	−0.972377	−0.486188	−	0.873854i	$-0.661613\pi$
$499$	−21.7212	−0.972377	−0.486188	+	0.873854i	$0.661613\pi$
$500$	−0.928677	−0.0415317
$501$	14.3002	0.638884
$502$	26.3494	1.17603
$503$	−10.0617	−0.448627	−0.224314	−	0.974517i	$-0.572014\pi$
$503$	−10.0617	−0.448627	−0.224314	+	0.974517i	$0.572014\pi$
$504$	−10.5439	−0.469665
$505$	19.8048	0.881301
$506$	1.70055	0.0755987
$507$	16.0757	0.713947
$508$	0.187896	0.00833653
$509$	−38.4700	−1.70515	−0.852576	−	0.522604i	$-0.824961\pi$
$509$	−38.4700	−1.70515	−0.852576	+	0.522604i	$0.824961\pi$
$510$	16.7413	0.741319
$511$	−5.29959	−0.234440
$512$	−20.6523	−0.912711
$513$	18.2570	0.806067
$514$	−5.49651	−0.242441
$515$	−9.13861	−0.402695
$516$	−1.44820	−0.0637535
$517$	−35.0345	−1.54081
$518$	5.17545	0.227396
$519$	29.0501	1.27516
$520$	−34.5759	−1.51625
$521$	26.4116	1.15711	0.578557	−	0.815642i	$-0.303616\pi$
$521$	26.4116	1.15711	0.578557	+	0.815642i	$0.303616\pi$
$522$	−2.84179	−0.124382
$523$	−12.3920	−0.541865	−0.270932	−	0.962598i	$-0.587332\pi$
$523$	−12.3920	−0.541865	−0.270932	+	0.962598i	$0.587332\pi$
$524$	1.26270	0.0551611
$525$	−7.05497	−0.307904
$526$	23.1499	1.00938
$527$	−24.1710	−1.05291
$528$	25.0633	1.09074
$529$	−22.9258	−0.996774
$530$	6.58843	0.286183
$531$	3.41663	0.148269
$532$	1.18096	0.0512013
$533$	−7.33909	−0.317891
$534$	−14.6197	−0.632655
$535$	42.2639	1.82723
$536$	29.3884	1.26938
$537$	−0.00483139	−0.000208490 0
$538$	37.1333	1.60093
$539$	−24.7120	−1.06442
$540$	−1.46836	−0.0631881
$541$	−9.70675	−0.417326	−0.208663	−	0.977988i	$-0.566911\pi$
$541$	−9.70675	−0.417326	−0.208663	+	0.977988i	$0.566911\pi$
$542$	20.0388	0.860741
$543$	−10.3049	−0.442227
$544$	−1.90056	−0.0814858
$545$	−2.53458	−0.108570
$546$	−35.6146	−1.52417
$547$	−36.3966	−1.55620	−0.778102	−	0.628138i	$-0.783817\pi$
$547$	−36.3966	−1.55620	−0.778102	+	0.628138i	$0.783817\pi$
$548$	−1.39312	−0.0595110
$549$	14.5091	0.619233
$550$	−8.89010	−0.379075
$551$	−5.89441	−0.251110
$552$	1.04028	0.0442771
$553$	62.9333	2.67619
$554$	24.4247	1.03771
$555$	−3.51782	−0.149323
$556$	−0.826588	−0.0350551
$557$	−1.27464	−0.0540084	−0.0270042	−	0.999635i	$-0.508597\pi$
$557$	−1.27464	−0.0540084	−0.0270042	+	0.999635i	$0.508597\pi$
$558$	11.4649	0.485350
$559$	−50.4895	−2.13548
$560$	37.9458	1.60350
$561$	−19.6118	−0.828011
$562$	28.0364	1.18264
$563$	19.9440	0.840540	0.420270	−	0.907399i	$-0.361935\pi$
$563$	19.9440	0.840540	0.420270	+	0.907399i	$0.361935\pi$
$564$	1.15728	0.0487303
$565$	10.5939	0.445689
$566$	−45.0128	−1.89203
$567$	16.5127	0.693467
$568$	−22.0107	−0.923547
$569$	−2.27489	−0.0953683	−0.0476842	−	0.998862i	$-0.515184\pi$
$569$	−2.27489	−0.0953683	−0.0476842	+	0.998862i	$0.515184\pi$
$570$	−16.4709	−0.689888
$571$	−14.9547	−0.625834	−0.312917	−	0.949780i	$-0.601306\pi$
$571$	−14.9547	−0.625834	−0.312917	+	0.949780i	$0.601306\pi$
$572$	−2.18719	−0.0914508
$573$	−23.4310	−0.978843
$574$	7.66085	0.319758
$575$	−0.387946	−0.0161785
$576$	−8.10526	−0.337719
$577$	−6.15289	−0.256148	−0.128074	−	0.991765i	$-0.540880\pi$
$577$	−6.15289	−0.256148	−0.128074	+	0.991765i	$0.540880\pi$
$578$	−9.03020	−0.375607
$579$	−15.0923	−0.627214
$580$	0.474071	0.0196847
$581$	54.6729	2.26821
$582$	10.9707	0.454748
$583$	−7.71807	−0.319650
$584$	−4.08519	−0.169046
$585$	−13.4923	−0.557836
$586$	30.6920	1.26787
$587$	−31.4016	−1.29608	−0.648041	−	0.761605i	$-0.724412\pi$
$587$	−31.4016	−1.29608	−0.648041	+	0.761605i	$0.724412\pi$
$588$	0.816301	0.0336637
$589$	23.7805	0.979859
$590$	−11.6951	−0.481480
$591$	−6.27242	−0.258013
$592$	4.19443	0.172390
$593$	25.7222	1.05628	0.528142	−	0.849156i	$-0.322889\pi$
$593$	25.7222	1.05628	0.528142	+	0.849156i	$0.322889\pi$
$594$	35.2951	1.44817
$595$	−29.6923	−1.21726
$596$	0.638941	0.0261720
$597$	11.7813	0.482177
$598$	−1.95841	−0.0800855
$599$	−7.51628	−0.307107	−0.153553	−	0.988140i	$-0.549072\pi$
$599$	−7.51628	−0.307107	−0.153553	+	0.988140i	$0.549072\pi$
$600$	−5.43832	−0.222019
$601$	−32.0566	−1.30762	−0.653809	−	0.756660i	$-0.726830\pi$
$601$	−32.0566	−1.30762	−0.653809	+	0.756660i	$0.726830\pi$
$602$	52.7031	2.14802
$603$	11.4680	0.467012
$604$	2.48793	0.101232
$605$	19.0985	0.776464
$606$	15.7251	0.638790
$607$	21.8141	0.885408	0.442704	−	0.896668i	$-0.354019\pi$
$607$	21.8141	0.885408	0.442704	+	0.896668i	$0.354019\pi$
$608$	1.86985	0.0758325
$609$	−9.04301	−0.366441
$610$	−49.6645	−2.01086
$611$	40.3469	1.63226
$612$	−0.361070	−0.0145954
$613$	−16.4873	−0.665916	−0.332958	−	0.942942i	$-0.608047\pi$
$613$	−16.4873	−0.665916	−0.332958	+	0.942942i	$0.608047\pi$
$614$	27.1967	1.09757
$615$	−5.20718	−0.209974
$616$	−42.2801	−1.70352
$617$	−34.7330	−1.39830	−0.699149	−	0.714976i	$-0.746437\pi$
$617$	−34.7330	−1.39830	−0.699149	+	0.714976i	$0.746437\pi$
$618$	−7.25613	−0.291884
$619$	−14.5981	−0.586749	−0.293375	−	0.955998i	$-0.594778\pi$
$619$	−14.5981	−0.586749	−0.293375	+	0.955998i	$0.594778\pi$
$620$	−1.91260	−0.0768118
$621$	1.54020	0.0618063
$622$	−17.9864	−0.721189
$623$	25.9293	1.03883
$624$	−28.8638	−1.15548
$625$	−30.0925	−1.20370
$626$	−15.3390	−0.613069
$627$	19.2949	0.770566
$628$	−0.357289	−0.0142574
$629$	−3.28211	−0.130866
$630$	14.0838	0.561112
$631$	−35.8579	−1.42748	−0.713740	−	0.700410i	$-0.753000\pi$
$631$	−35.8579	−1.42748	−0.713740	+	0.700410i	$0.753000\pi$
$632$	48.5121	1.92971
$633$	−17.5645	−0.698128
$634$	46.8047	1.85885
$635$	4.64782	0.184443
$636$	0.254948	0.0101094
$637$	28.4592	1.12759
$638$	−11.3953	−0.451143
$639$	−8.58902	−0.339777
$640$	30.6796	1.21272
$641$	−27.5749	−1.08914	−0.544572	−	0.838714i	$-0.683308\pi$
$641$	−27.5749	−1.08914	−0.544572	+	0.838714i	$0.683308\pi$
$642$	33.5578	1.32442
$643$	12.1141	0.477733	0.238867	−	0.971052i	$-0.423224\pi$
$643$	12.1141	0.477733	0.238867	+	0.971052i	$0.423224\pi$
$644$	0.0996289	0.00392593
$645$	−35.8229	−1.41053
$646$	−15.3672	−0.604615
$647$	5.93008	0.233135	0.116568	−	0.993183i	$-0.462811\pi$
$647$	5.93008	0.233135	0.116568	+	0.993183i	$0.462811\pi$
$648$	12.7288	0.500035
$649$	13.7004	0.537786
$650$	10.2381	0.401573
$651$	36.4833	1.42989
$652$	1.38226	0.0541333
$653$	41.2660	1.61486	0.807431	−	0.589962i	$-0.200857\pi$
$653$	41.2660	1.61486	0.807431	+	0.589962i	$0.200857\pi$
$654$	−2.01248	−0.0786942
$655$	31.2343	1.22042
$656$	6.20872	0.242410
$657$	−1.59413	−0.0621929
$658$	−42.1159	−1.64185
$659$	22.6453	0.882135	0.441068	−	0.897474i	$-0.354600\pi$
$659$	22.6453	0.882135	0.441068	+	0.897474i	$0.354600\pi$
$660$	−1.55184	−0.0604052
$661$	29.3534	1.14172	0.570858	−	0.821049i	$-0.306611\pi$
$661$	29.3534	1.14172	0.570858	+	0.821049i	$0.306611\pi$
$662$	−7.61603	−0.296005
$663$	22.5857	0.877154
$664$	42.1446	1.63553
$665$	29.2125	1.13281
$666$	1.55679	0.0603243
$667$	−0.497267	−0.0192542
$668$	1.05572	0.0408470
$669$	13.8380	0.535006
$670$	−39.2548	−1.51654
$671$	58.1800	2.24601
$672$	2.86866	0.110661
$673$	−46.2860	−1.78419	−0.892097	−	0.451844i	$-0.850766\pi$
$673$	−46.2860	−1.78419	−0.892097	+	0.451844i	$0.850766\pi$
$674$	1.82030	0.0701151
$675$	−8.05184	−0.309915
$676$	1.18680	0.0456461
$677$	−5.86756	−0.225508	−0.112754	−	0.993623i	$-0.535967\pi$
$677$	−5.86756	−0.225508	−0.112754	+	0.993623i	$0.535967\pi$
$678$	8.41165	0.323047
$679$	−19.4574	−0.746708
$680$	−22.8883	−0.877726
$681$	−3.30481	−0.126641
$682$	45.9733	1.76041
$683$	31.7042	1.21313	0.606563	−	0.795035i	$-0.292548\pi$
$683$	31.7042	1.21313	0.606563	+	0.795035i	$0.292548\pi$
$684$	0.355237	0.0135828
$685$	−34.4603	−1.31666
$686$	6.52126	0.248983
$687$	27.4526	1.04738
$688$	42.7131	1.62842
$689$	8.88841	0.338621
$690$	−1.38952	−0.0528981
$691$	−29.6200	−1.12680	−0.563399	−	0.826185i	$-0.690506\pi$
$691$	−29.6200	−1.12680	−0.563399	+	0.826185i	$0.690506\pi$
$692$	2.14464	0.0815270
$693$	−16.4986	−0.626730
$694$	−8.66687	−0.328990
$695$	−20.4466	−0.775584
$696$	−6.97081	−0.264228
$697$	−4.85827	−0.184020
$698$	−43.7589	−1.65630
$699$	10.8474	0.410285
$700$	−0.520838	−0.0196858
$701$	−39.8238	−1.50412	−0.752062	−	0.659092i	$-0.770941\pi$
$701$	−39.8238	−1.50412	−0.752062	+	0.659092i	$0.770941\pi$
$702$	−40.6470	−1.53412
$703$	3.22908	0.121787
$704$	−32.5013	−1.22494
$705$	28.6267	1.07814
$706$	42.4940	1.59928
$707$	−27.8899	−1.04891
$708$	−0.452559	−0.0170082
$709$	−23.3291	−0.876144	−0.438072	−	0.898940i	$-0.644339\pi$
$709$	−23.3291	−0.876144	−0.438072	+	0.898940i	$0.644339\pi$
$710$	29.4002	1.10337
$711$	18.9305	0.709948
$712$	19.9876	0.749067
$713$	2.00618	0.0751320
$714$	−23.5759	−0.882305
$715$	−54.1026	−2.02332
$716$	−0.000356680 0	−1.33298e−5 0
$717$	−11.6403	−0.434715
$718$	−12.4894	−0.466099
$719$	−9.02594	−0.336611	−0.168305	−	0.985735i	$-0.553829\pi$
$719$	−9.02594	−0.336611	−0.168305	+	0.985735i	$0.553829\pi$
$720$	11.4142	0.425381
$721$	12.8694	0.479281
$722$	−12.4308	−0.462628
$723$	−11.6453	−0.433092
$724$	−0.760768	−0.0282737
$725$	2.59960	0.0965466
$726$	15.1644	0.562802
$727$	23.3758	0.866961	0.433481	−	0.901163i	$-0.357285\pi$
$727$	23.3758	0.866961	0.433481	+	0.901163i	$0.357285\pi$
$728$	48.6913	1.80462
$729$	28.5088	1.05588
$730$	5.45669	0.201961
$731$	−33.4226	−1.23618
$732$	−1.92184	−0.0710332
$733$	6.92693	0.255852	0.127926	−	0.991784i	$-0.459168\pi$
$733$	6.92693	0.255852	0.127926	+	0.991784i	$0.459168\pi$
$734$	19.6564	0.725531
$735$	20.1922	0.744799
$736$	0.157745	0.00581456
$737$	45.9854	1.69389
$738$	2.30440	0.0848262
$739$	−6.83024	−0.251254	−0.125627	−	0.992078i	$-0.540094\pi$
$739$	−6.83024	−0.251254	−0.125627	+	0.992078i	$0.540094\pi$
$740$	−0.259705	−0.00954696
$741$	−22.2207	−0.816299
$742$	−9.27810	−0.340610
$743$	32.5923	1.19569	0.597847	−	0.801610i	$-0.296023\pi$
$743$	32.5923	1.19569	0.597847	+	0.801610i	$0.296023\pi$
$744$	28.1232	1.03104
$745$	15.8049	0.579048
$746$	−12.3110	−0.450738
$747$	16.4457	0.601717
$748$	−1.44785	−0.0529388
$749$	−59.5178	−2.17473
$750$	−18.2399	−0.666026
$751$	−10.6095	−0.387146	−0.193573	−	0.981086i	$-0.562008\pi$
$751$	−10.6095	−0.387146	−0.193573	+	0.981086i	$0.562008\pi$
$752$	−34.1327	−1.24469
$753$	25.2217	0.919129
$754$	13.1232	0.477919
$755$	61.5417	2.23973
$756$	2.06781	0.0752054
$757$	29.8095	1.08345	0.541723	−	0.840557i	$-0.317772\pi$
$757$	29.8095	1.08345	0.541723	+	0.840557i	$0.317772\pi$
$758$	−31.2034	−1.13336
$759$	1.62777	0.0590842
$760$	22.5185	0.816831
$761$	12.2769	0.445037	0.222518	−	0.974929i	$-0.428572\pi$
$761$	12.2769	0.445037	0.222518	+	0.974929i	$0.428572\pi$
$762$	3.69041	0.133689
$763$	3.56931	0.129218
$764$	−1.72981	−0.0625822
$765$	−8.93149	−0.322919
$766$	30.3523	1.09667
$767$	−15.7778	−0.569704
$768$	3.40432	0.122843
$769$	−16.0059	−0.577188	−0.288594	−	0.957452i	$-0.593188\pi$
$769$	−16.0059	−0.577188	−0.288594	+	0.957452i	$0.593188\pi$
$770$	56.4746	2.03520
$771$	−5.26126	−0.189480
$772$	−1.11420	−0.0401009
$773$	−11.9892	−0.431223	−0.215612	−	0.976479i	$-0.569175\pi$
$773$	−11.9892	−0.431223	−0.215612	+	0.976479i	$0.569175\pi$
$774$	15.8532	0.569832
$775$	−10.4879	−0.376735
$776$	−14.9988	−0.538424
$777$	4.95394	0.177722
$778$	−51.2081	−1.83590
$779$	4.77977	0.171253
$780$	1.78715	0.0639902
$781$	−34.4411	−1.23240
$782$	−1.29642	−0.0463597
$783$	−10.3208	−0.368835
$784$	−24.0759	−0.859853
$785$	−8.83797	−0.315441
$786$	24.8002	0.884596
$787$	38.7212	1.38026	0.690131	−	0.723684i	$-0.257553\pi$
$787$	38.7212	1.38026	0.690131	+	0.723684i	$0.257553\pi$
$788$	−0.463065	−0.0164960
$789$	22.1591	0.788885
$790$	−64.7988	−2.30544
$791$	−14.9188	−0.530451
$792$	−12.7180	−0.451913
$793$	−67.0021	−2.37932
$794$	20.2328	0.718036
$795$	6.30644	0.223666
$796$	0.869762	0.0308279
$797$	−10.4443	−0.369957	−0.184978	−	0.982743i	$-0.559222\pi$
$797$	−10.4443	−0.369957	−0.184978	+	0.982743i	$0.559222\pi$
$798$	23.1950	0.821093
$799$	26.7085	0.944880
$800$	−0.824655	−0.0291560
$801$	7.79958	0.275585
$802$	−50.6546	−1.78868
$803$	−6.39229	−0.225579
$804$	−1.51902	−0.0535716
$805$	2.46444	0.0868600
$806$	−52.9444	−1.86489
$807$	35.5440	1.25121
$808$	−21.4990	−0.756331
$809$	4.37087	0.153672	0.0768359	−	0.997044i	$-0.475518\pi$
$809$	4.37087	0.153672	0.0768359	+	0.997044i	$0.475518\pi$
$810$	−17.0022	−0.597395
$811$	12.9850	0.455965	0.227983	−	0.973665i	$-0.426787\pi$
$811$	12.9850	0.455965	0.227983	+	0.973665i	$0.426787\pi$
$812$	−0.667606	−0.0234284
$813$	19.1812	0.672713
$814$	6.24256	0.218802
$815$	34.1917	1.19768
$816$	−19.1070	−0.668879
$817$	32.8826	1.15042
$818$	−41.7263	−1.45893
$819$	19.0004	0.663927
$820$	−0.384423	−0.0134246
$821$	53.1506	1.85497	0.927485	−	0.373861i	$-0.121966\pi$
$821$	53.1506	1.85497	0.927485	+	0.373861i	$0.121966\pi$
$822$	−27.3618	−0.954352
$823$	30.2688	1.05510	0.527552	−	0.849522i	$-0.323110\pi$
$823$	30.2688	1.05510	0.527552	+	0.849522i	$0.323110\pi$
$824$	9.92037	0.345593
$825$	−8.50960	−0.296266
$826$	16.4696	0.573049
$827$	36.6182	1.27334	0.636669	−	0.771137i	$-0.280312\pi$
$827$	36.6182	1.27334	0.636669	+	0.771137i	$0.280312\pi$
$828$	0.0299686	0.00104148
$829$	4.41219	0.153242	0.0766208	−	0.997060i	$-0.475587\pi$
$829$	4.41219	0.153242	0.0766208	+	0.997060i	$0.475587\pi$
$830$	−56.2935	−1.95398
$831$	23.3793	0.811019
$832$	37.4296	1.29764
$833$	18.8392	0.652739
$834$	−16.2348	−0.562164
$835$	26.1144	0.903727
$836$	1.42446	0.0492660
$837$	41.6384	1.43923
$838$	−28.5902	−0.987632
$839$	14.7597	0.509562	0.254781	−	0.966999i	$-0.417997\pi$
$839$	14.7597	0.509562	0.254781	+	0.966999i	$0.417997\pi$
$840$	34.5471	1.19199
$841$	−25.6679	−0.885098
$842$	18.3674	0.632984
$843$	26.8364	0.924296
$844$	−1.29671	−0.0446347
$845$	29.3568	1.00991
$846$	−12.6685	−0.435554
$847$	−26.8953	−0.924134
$848$	−7.51941	−0.258218
$849$	−43.0862	−1.47872
$850$	6.77736	0.232462
$851$	0.272413	0.00933818
$852$	1.13768	0.0389763
$853$	−32.8244	−1.12389	−0.561944	−	0.827176i	$-0.689946\pi$
$853$	−32.8244	−1.12389	−0.561944	+	0.827176i	$0.689946\pi$
$854$	69.9397	2.39329
$855$	8.78719	0.300515
$856$	−45.8793	−1.56812
$857$	52.1539	1.78154	0.890772	−	0.454451i	$-0.150165\pi$
$857$	52.1539	1.78154	0.890772	+	0.454451i	$0.150165\pi$
$858$	−42.9579	−1.46656
$859$	31.4148	1.07186	0.535929	−	0.844263i	$-0.319962\pi$
$859$	31.4148	1.07186	0.535929	+	0.844263i	$0.319962\pi$
$860$	−2.64465	−0.0901819
$861$	7.33297	0.249907
$862$	−43.8292	−1.49283
$863$	−45.6333	−1.55338	−0.776689	−	0.629885i	$-0.783102\pi$
$863$	−45.6333	−1.55338	−0.776689	+	0.629885i	$0.783102\pi$
$864$	3.27401	0.111384
$865$	53.0502	1.80376
$866$	−56.4029	−1.91665
$867$	−8.64371	−0.293556
$868$	2.69340	0.0914200
$869$	75.9092	2.57504
$870$	9.31108	0.315675
$871$	−52.9584	−1.79443
$872$	2.75140	0.0931743
$873$	−5.85284	−0.198088
$874$	1.27547	0.0431434
$875$	32.3500	1.09363
$876$	0.211154	0.00713424
$877$	−2.85482	−0.0964003	−0.0482002	−	0.998838i	$-0.515349\pi$
$877$	−2.85482	−0.0964003	−0.0482002	+	0.998838i	$0.515349\pi$
$878$	−12.4399	−0.419827
$879$	29.3783	0.990907
$880$	45.7697	1.54289
$881$	37.9369	1.27813	0.639064	−	0.769154i	$-0.279322\pi$
$881$	37.9369	1.27813	0.639064	+	0.769154i	$0.279322\pi$
$882$	−8.93590	−0.300888
$883$	34.0889	1.14718	0.573591	−	0.819142i	$-0.305550\pi$
$883$	34.0889	1.14718	0.573591	+	0.819142i	$0.305550\pi$
$884$	1.66740	0.0560808
$885$	−11.1946	−0.376301
$886$	−0.885936	−0.0297636
$887$	−16.1264	−0.541472	−0.270736	−	0.962654i	$-0.587267\pi$
$887$	−16.1264	−0.541472	−0.270736	+	0.962654i	$0.587267\pi$
$888$	3.81875	0.128149
$889$	−6.54526	−0.219521
$890$	−26.6979	−0.894916
$891$	19.9174	0.667257
$892$	1.02160	0.0342056
$893$	−26.2770	−0.879326
$894$	12.5492	0.419710
$895$	−0.00882290	−0.000294917 0
$896$	−43.2044	−1.44336
$897$	−1.87459	−0.0625909
$898$	−12.5960	−0.420334
$899$	−13.4433	−0.448358
$900$	−0.156669	−0.00522230
$901$	5.88387	0.196020
$902$	9.24041	0.307672
$903$	50.4474	1.67878
$904$	−11.5002	−0.382490
$905$	−18.8185	−0.625548
$906$	48.8646	1.62342
$907$	−50.9918	−1.69316	−0.846578	−	0.532265i	$-0.821341\pi$
$907$	−50.9918	−1.69316	−0.846578	+	0.532265i	$0.821341\pi$
$908$	−0.243980	−0.00809675
$909$	−8.38935	−0.278257
$910$	−65.0381	−2.15599
$911$	7.99408	0.264856	0.132428	−	0.991193i	$-0.457723\pi$
$911$	7.99408	0.264856	0.132428	+	0.991193i	$0.457723\pi$
$912$	18.7983	0.622474
$913$	65.9456	2.18248
$914$	−52.8676	−1.74871
$915$	−47.5389	−1.57159
$916$	2.02670	0.0669641
$917$	−43.9854	−1.45253
$918$	−26.9072	−0.888069
$919$	−39.2623	−1.29515	−0.647573	−	0.762004i	$-0.724216\pi$
$919$	−39.2623	−1.29515	−0.647573	+	0.762004i	$0.724216\pi$
$920$	1.89971	0.0626317
$921$	26.0326	0.857805
$922$	−6.91117	−0.227607
$923$	39.6636	1.30554
$924$	2.18536	0.0718932
$925$	−1.42411	−0.0468245
$926$	38.8977	1.27826
$927$	3.87114	0.127145
$928$	−1.05704	−0.0346990
$929$	30.7151	1.00773	0.503865	−	0.863783i	$-0.331911\pi$
$929$	30.7151	1.00773	0.503865	+	0.863783i	$0.331911\pi$
$930$	−37.5648	−1.23180
$931$	−18.5348	−0.607453
$932$	0.800814	0.0262315
$933$	−17.2166	−0.563645
$934$	−22.9021	−0.749381
$935$	−35.8144	−1.17126
$936$	14.6464	0.478734
$937$	7.30135	0.238525	0.119262	−	0.992863i	$-0.461947\pi$
$937$	7.30135	0.238525	0.119262	+	0.992863i	$0.461947\pi$
$938$	55.2802	1.80496
$939$	−14.6825	−0.479144
$940$	2.11338	0.0689310
$941$	11.9010	0.387963	0.193981	−	0.981005i	$-0.437860\pi$
$941$	11.9010	0.387963	0.193981	+	0.981005i	$0.437860\pi$
$942$	−7.01742	−0.228640
$943$	0.403233	0.0131311
$944$	13.3477	0.434431
$945$	51.1496	1.66390
$946$	63.5697	2.06683
$947$	−19.7521	−0.641858	−0.320929	−	0.947103i	$-0.603995\pi$
$947$	−19.7521	−0.641858	−0.320929	+	0.947103i	$0.603995\pi$
$948$	−2.50748	−0.0814391
$949$	7.36159	0.238967
$950$	−6.66786	−0.216334
$951$	44.8015	1.45279
$952$	32.2323	1.04465
$953$	12.3878	0.401279	0.200639	−	0.979665i	$-0.435698\pi$
$953$	12.3878	0.401279	0.200639	+	0.979665i	$0.435698\pi$
$954$	−2.79087	−0.0903579
$955$	−42.7888	−1.38461
$956$	−0.859353	−0.0277935
$957$	−10.9076	−0.352591
$958$	−55.0422	−1.77833
$959$	48.5285	1.56707
$960$	26.5568	0.857117
$961$	23.2357	0.749540
$962$	−7.18915	−0.231787
$963$	−17.9031	−0.576919
$964$	−0.859718	−0.0276897
$965$	−27.5610	−0.887220
$966$	1.95678	0.0629585
$967$	−20.3485	−0.654364	−0.327182	−	0.944961i	$-0.606099\pi$
$967$	−20.3485	−0.654364	−0.327182	+	0.944961i	$0.606099\pi$
$968$	−20.7323	−0.666360
$969$	−14.7095	−0.472537
$970$	20.0342	0.643260
$971$	47.1777	1.51401	0.757003	−	0.653412i	$-0.226663\pi$
$971$	47.1777	1.51401	0.757003	+	0.653412i	$0.226663\pi$
$972$	1.08007	0.0346431
$973$	28.7938	0.923087
$974$	55.6723	1.78386
$975$	9.79995	0.313850
$976$	56.6824	1.81436
$977$	−31.5094	−1.00807	−0.504037	−	0.863682i	$-0.668152\pi$
$977$	−31.5094	−1.00807	−0.504037	+	0.863682i	$0.668152\pi$
$978$	27.1485	0.868113
$979$	31.2755	0.999570
$980$	1.49070	0.0476186
$981$	1.07366	0.0342792
$982$	23.0002	0.733966
$983$	−2.90781	−0.0927447	−0.0463724	−	0.998924i	$-0.514766\pi$
$983$	−2.90781	−0.0927447	−0.0463724	+	0.998924i	$0.514766\pi$
$984$	5.65262	0.180199
$985$	−11.4545	−0.364969
$986$	8.68719	0.276656
$987$	−40.3133	−1.28319
$988$	−1.64046	−0.0521900
$989$	2.77405	0.0882098
$990$	16.9877	0.539904
$991$	−8.58261	−0.272636	−0.136318	−	0.990665i	$-0.543527\pi$
$991$	−8.58261	−0.272636	−0.136318	+	0.990665i	$0.543527\pi$
$992$	4.26453	0.135399
$993$	−7.29006	−0.231343
$994$	−41.4026	−1.31321
$995$	21.5146	0.682058
$996$	−2.17836	−0.0690239
$997$	−32.4228	−1.02684	−0.513420	−	0.858138i	$-0.671622\pi$
$997$	−32.4228	−1.02684	−0.513420	+	0.858138i	$0.671622\pi$
$998$	−31.4955	−0.996974
$999$	5.65394	0.178883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.60	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.60	✓	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)

\(f(q)\)	\(=\)	\(q+1.44999 q^{2} +1.38793 q^{3} +0.102465 q^{4} +2.53458 q^{5} +2.01248 q^{6} -3.56931 q^{7} -2.75140 q^{8} -1.07366 q^{9} +O(q^{10})\)	\(q+1.44999 q^{2} +1.38793 q^{3} +0.102465 q^{4} +2.53458 q^{5} +2.01248 q^{6} -3.56931 q^{7} -2.75140 q^{8} -1.07366 q^{9} +3.67511 q^{10} -4.30525 q^{11} +0.142214 q^{12} +4.95808 q^{13} -5.17545 q^{14} +3.51782 q^{15} -4.19443 q^{16} +3.28211 q^{17} -1.55679 q^{18} -3.22908 q^{19} +0.259705 q^{20} -4.95394 q^{21} -6.24256 q^{22} -0.272413 q^{23} -3.81875 q^{24} +1.42411 q^{25} +7.18915 q^{26} -5.65394 q^{27} -0.365728 q^{28} +1.82542 q^{29} +5.10079 q^{30} -7.36449 q^{31} -0.579067 q^{32} -5.97537 q^{33} +4.75901 q^{34} -9.04671 q^{35} -0.110012 q^{36} -1.00000 q^{37} -4.68212 q^{38} +6.88145 q^{39} -6.97366 q^{40} -1.48023 q^{41} -7.18316 q^{42} -10.1833 q^{43} -0.441136 q^{44} -2.72127 q^{45} -0.394995 q^{46} +8.13762 q^{47} -5.82157 q^{48} +5.73996 q^{49} +2.06494 q^{50} +4.55533 q^{51} +0.508028 q^{52} +1.79271 q^{53} -8.19815 q^{54} -10.9120 q^{55} +9.82061 q^{56} -4.48173 q^{57} +2.64683 q^{58} -3.18224 q^{59} +0.360452 q^{60} -13.5137 q^{61} -10.6784 q^{62} +3.83221 q^{63} +7.54922 q^{64} +12.5667 q^{65} -8.66422 q^{66} -10.6812 q^{67} +0.336300 q^{68} -0.378089 q^{69} -13.1176 q^{70} +7.99980 q^{71} +2.95406 q^{72} +1.48477 q^{73} -1.44999 q^{74} +1.97656 q^{75} -0.330866 q^{76} +15.3668 q^{77} +9.97802 q^{78} -17.6318 q^{79} -10.6311 q^{80} -4.62630 q^{81} -2.14631 q^{82} -15.3175 q^{83} -0.507604 q^{84} +8.31877 q^{85} -14.7656 q^{86} +2.53355 q^{87} +11.8455 q^{88} -7.26451 q^{89} -3.94581 q^{90} -17.6969 q^{91} -0.0279127 q^{92} -10.2214 q^{93} +11.7995 q^{94} -8.18436 q^{95} -0.803703 q^{96} +5.45132 q^{97} +8.32288 q^{98} +4.62235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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