LMFDB - Embedded newform 4033.2.a.d.1.6

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			1.6
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65601 q^{2} -2.08930 q^{3} +5.05439 q^{4} -0.388260 q^{5} +5.54922 q^{6} -5.15918 q^{7} -8.11249 q^{8} +1.36520 q^{9} +O(q^{10})$	\(q-2.65601 q^{2} -2.08930 q^{3} +5.05439 q^{4} -0.388260 q^{5} +5.54922 q^{6} -5.15918 q^{7} -8.11249 q^{8} +1.36520 q^{9} +1.03122 q^{10} +3.34161 q^{11} -10.5602 q^{12} +5.68872 q^{13} +13.7028 q^{14} +0.811194 q^{15} +11.4381 q^{16} -6.13070 q^{17} -3.62597 q^{18} +2.07318 q^{19} -1.96242 q^{20} +10.7791 q^{21} -8.87535 q^{22} -3.39201 q^{23} +16.9495 q^{24} -4.84925 q^{25} -15.1093 q^{26} +3.41561 q^{27} -26.0765 q^{28} +1.48595 q^{29} -2.15454 q^{30} -7.78032 q^{31} -14.1547 q^{32} -6.98164 q^{33} +16.2832 q^{34} +2.00310 q^{35} +6.90023 q^{36} -1.00000 q^{37} -5.50639 q^{38} -11.8855 q^{39} +3.14976 q^{40} +4.76687 q^{41} -28.6294 q^{42} -0.146580 q^{43} +16.8898 q^{44} -0.530051 q^{45} +9.00922 q^{46} -5.10022 q^{47} -23.8976 q^{48} +19.6171 q^{49} +12.8797 q^{50} +12.8089 q^{51} +28.7530 q^{52} +1.00969 q^{53} -9.07188 q^{54} -1.29741 q^{55} +41.8538 q^{56} -4.33150 q^{57} -3.94671 q^{58} -1.03977 q^{59} +4.10009 q^{60} -3.25158 q^{61} +20.6646 q^{62} -7.04329 q^{63} +14.7188 q^{64} -2.20870 q^{65} +18.5433 q^{66} +11.9498 q^{67} -30.9870 q^{68} +7.08694 q^{69} -5.32027 q^{70} -3.61312 q^{71} -11.0751 q^{72} +12.4513 q^{73} +2.65601 q^{74} +10.1316 q^{75} +10.4787 q^{76} -17.2400 q^{77} +31.5679 q^{78} +4.12486 q^{79} -4.44095 q^{80} -11.2318 q^{81} -12.6609 q^{82} -15.9117 q^{83} +54.4818 q^{84} +2.38031 q^{85} +0.389319 q^{86} -3.10461 q^{87} -27.1088 q^{88} +9.37787 q^{89} +1.40782 q^{90} -29.3491 q^{91} -17.1445 q^{92} +16.2555 q^{93} +13.5462 q^{94} -0.804933 q^{95} +29.5734 q^{96} +0.428035 q^{97} -52.1033 q^{98} +4.56195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.65601	−1.87808	−0.939041	−	0.343804i	$-0.888284\pi$
$2$	−2.65601	−1.87808	−0.939041	+	0.343804i	$0.888284\pi$
$3$	−2.08930	−1.20626	−0.603130	−	0.797643i	$-0.706080\pi$
$3$	−2.08930	−1.20626	−0.603130	+	0.797643i	$0.706080\pi$
$4$	5.05439	2.52720
$5$	−0.388260	−0.173635	−0.0868177	−	0.996224i	$-0.527670\pi$
$5$	−0.388260	−0.173635	−0.0868177	+	0.996224i	$0.527670\pi$
$6$	5.54922	2.26546
$7$	−5.15918	−1.94999	−0.974993	−	0.222235i	$-0.928665\pi$
$7$	−5.15918	−1.94999	−0.974993	+	0.222235i	$0.928665\pi$
$8$	−8.11249	−2.86820
$9$	1.36520	0.455065
$10$	1.03122	0.326102
$11$	3.34161	1.00753	0.503766	−	0.863840i	$-0.331947\pi$
$11$	3.34161	1.00753	0.503766	+	0.863840i	$0.331947\pi$
$12$	−10.5602	−3.04846
$13$	5.68872	1.57777	0.788883	−	0.614543i	$-0.210660\pi$
$13$	5.68872	1.57777	0.788883	+	0.614543i	$0.210660\pi$
$14$	13.7028	3.66224
$15$	0.811194	0.209449
$16$	11.4381	2.85952
$17$	−6.13070	−1.48691	−0.743457	−	0.668784i	$-0.766815\pi$
$17$	−6.13070	−1.48691	−0.743457	+	0.668784i	$0.766815\pi$
$18$	−3.62597	−0.854650
$19$	2.07318	0.475620	0.237810	−	0.971312i	$-0.423570\pi$
$19$	2.07318	0.475620	0.237810	+	0.971312i	$0.423570\pi$
$20$	−1.96242	−0.438810
$21$	10.7791	2.35219
$22$	−8.87535	−1.89223
$23$	−3.39201	−0.707283	−0.353642	−	0.935381i	$-0.615057\pi$
$23$	−3.39201	−0.707283	−0.353642	+	0.935381i	$0.615057\pi$
$24$	16.9495	3.45980
$25$	−4.84925	−0.969851
$26$	−15.1093	−2.96318
$27$	3.41561	0.657334
$28$	−26.0765	−4.92800
$29$	1.48595	0.275935	0.137967	−	0.990437i	$-0.455943\pi$
$29$	1.48595	0.275935	0.137967	+	0.990437i	$0.455943\pi$
$30$	−2.15454	−0.393363
$31$	−7.78032	−1.39739	−0.698694	−	0.715421i	$-0.746235\pi$
$31$	−7.78032	−1.39739	−0.698694	+	0.715421i	$0.746235\pi$
$32$	−14.1547	−2.50222
$33$	−6.98164	−1.21535
$34$	16.2832	2.79255
$35$	2.00310	0.338586
$36$	6.90023	1.15004
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.50639	−0.893254
$39$	−11.8855	−1.90320
$40$	3.14976	0.498021
$41$	4.76687	0.744460	0.372230	−	0.928140i	$-0.378593\pi$
$41$	4.76687	0.744460	0.372230	+	0.928140i	$0.378593\pi$
$42$	−28.6294	−4.41761
$43$	−0.146580	−0.0223533	−0.0111766	−	0.999938i	$-0.503558\pi$
$43$	−0.146580	−0.0223533	−0.0111766	+	0.999938i	$0.503558\pi$
$44$	16.8898	2.54623
$45$	−0.530051	−0.0790154
$46$	9.00922	1.32834
$47$	−5.10022	−0.743944	−0.371972	−	0.928244i	$-0.621318\pi$
$47$	−5.10022	−0.743944	−0.371972	+	0.928244i	$0.621318\pi$
$48$	−23.8976	−3.44933
$49$	19.6171	2.80245
$50$	12.8797	1.82146
$51$	12.8089	1.79361
$52$	28.7530	3.98732
$53$	1.00969	0.138691	0.0693455	−	0.997593i	$-0.477909\pi$
$53$	1.00969	0.138691	0.0693455	+	0.997593i	$0.477909\pi$
$54$	−9.07188	−1.23453
$55$	−1.29741	−0.174943
$56$	41.8538	5.59295
$57$	−4.33150	−0.573722
$58$	−3.94671	−0.518229
$59$	−1.03977	−0.135367	−0.0676833	−	0.997707i	$-0.521561\pi$
$59$	−1.03977	−0.135367	−0.0676833	+	0.997707i	$0.521561\pi$
$60$	4.10009	0.529320
$61$	−3.25158	−0.416322	−0.208161	−	0.978095i	$-0.566748\pi$
$61$	−3.25158	−0.416322	−0.208161	+	0.978095i	$0.566748\pi$
$62$	20.6646	2.62441
$63$	−7.04329	−0.887371
$64$	14.7188	1.83985
$65$	−2.20870	−0.273956
$66$	18.5433	2.28252
$67$	11.9498	1.45990	0.729949	−	0.683502i	$-0.239544\pi$
$67$	11.9498	1.45990	0.729949	+	0.683502i	$0.239544\pi$
$68$	−30.9870	−3.75772
$69$	7.08694	0.853168
$70$	−5.32027	−0.635893
$71$	−3.61312	−0.428798	−0.214399	−	0.976746i	$-0.568779\pi$
$71$	−3.61312	−0.428798	−0.214399	+	0.976746i	$0.568779\pi$
$72$	−11.0751	−1.30522
$73$	12.4513	1.45731	0.728656	−	0.684880i	$-0.240145\pi$
$73$	12.4513	1.45731	0.728656	+	0.684880i	$0.240145\pi$
$74$	2.65601	0.308755
$75$	10.1316	1.16989
$76$	10.4787	1.20198
$77$	−17.2400	−1.96468
$78$	31.5679	3.57436
$79$	4.12486	0.464083	0.232041	−	0.972706i	$-0.425460\pi$
$79$	4.12486	0.464083	0.232041	+	0.972706i	$0.425460\pi$
$80$	−4.44095	−0.496514
$81$	−11.2318	−1.24798
$82$	−12.6609	−1.39816
$83$	−15.9117	−1.74654	−0.873269	−	0.487239i	$-0.838004\pi$
$83$	−15.9117	−1.74654	−0.873269	+	0.487239i	$0.838004\pi$
$84$	54.4818	5.94445
$85$	2.38031	0.258181
$86$	0.389319	0.0419813
$87$	−3.10461	−0.332849
$88$	−27.1088	−2.88981
$89$	9.37787	0.994052	0.497026	−	0.867736i	$-0.334425\pi$
$89$	9.37787	0.994052	0.497026	+	0.867736i	$0.334425\pi$
$90$	1.40782	0.148397
$91$	−29.3491	−3.07662
$92$	−17.1445	−1.78744
$93$	16.2555	1.68561
$94$	13.5462	1.39719
$95$	−0.804933	−0.0825844
$96$	29.5734	3.01833
$97$	0.428035	0.0434604	0.0217302	−	0.999764i	$-0.493083\pi$
$97$	0.428035	0.0434604	0.0217302	+	0.999764i	$0.493083\pi$
$98$	−52.1033	−5.26323
$99$	4.56195	0.458493
$100$	−24.5100	−2.45100
$101$	11.8608	1.18020	0.590098	−	0.807331i	$-0.299089\pi$
$101$	11.8608	1.18020	0.590098	+	0.807331i	$0.299089\pi$
$102$	−34.0206	−3.36854
$103$	10.4568	1.03034	0.515170	−	0.857088i	$-0.327729\pi$
$103$	10.4568	1.03034	0.515170	+	0.857088i	$0.327729\pi$
$104$	−46.1497	−4.52535
$105$	−4.18510	−0.408424
$106$	−2.68174	−0.260473
$107$	−11.0742	−1.07058	−0.535291	−	0.844668i	$-0.679798\pi$
$107$	−11.0742	−1.07058	−0.535291	+	0.844668i	$0.679798\pi$
$108$	17.2638	1.66121
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	3.44595	0.328558
$111$	2.08930	0.198308
$112$	−59.0111	−5.57603
$113$	10.7037	1.00692	0.503460	−	0.864019i	$-0.332060\pi$
$113$	10.7037	1.00692	0.503460	+	0.864019i	$0.332060\pi$
$114$	11.5045	1.07750
$115$	1.31698	0.122809
$116$	7.51060	0.697341
$117$	7.76621	0.717986
$118$	2.76164	0.254230
$119$	31.6294	2.89946
$120$	−6.58081	−0.600743
$121$	0.166349	0.0151226
$122$	8.63623	0.781888
$123$	−9.95945	−0.898013
$124$	−39.3248	−3.53147
$125$	3.82408	0.342036
$126$	18.7070	1.66656
$127$	10.5588	0.936939	0.468470	−	0.883480i	$-0.344806\pi$
$127$	10.5588	0.936939	0.468470	+	0.883480i	$0.344806\pi$
$128$	−10.7839	−0.953175
$129$	0.306251	0.0269639
$130$	5.86634	0.514512
$131$	−8.79055	−0.768034	−0.384017	−	0.923326i	$-0.625460\pi$
$131$	−8.79055	−0.768034	−0.384017	+	0.923326i	$0.625460\pi$
$132$	−35.2879	−3.07142
$133$	−10.6959	−0.927452
$134$	−31.7387	−2.74181
$135$	−1.32614	−0.114136
$136$	49.7353	4.26476
$137$	12.4239	1.06145	0.530723	−	0.847545i	$-0.321920\pi$
$137$	12.4239	1.06145	0.530723	+	0.847545i	$0.321920\pi$
$138$	−18.8230	−1.60232
$139$	3.42117	0.290180	0.145090	−	0.989418i	$-0.453653\pi$
$139$	3.42117	0.290180	0.145090	+	0.989418i	$0.453653\pi$
$140$	10.1245	0.855674
$141$	10.6559	0.897390
$142$	9.59648	0.805319
$143$	19.0095	1.58965
$144$	15.6152	1.30127
$145$	−0.576937	−0.0479120
$146$	−33.0707	−2.73695
$147$	−40.9861	−3.38048
$148$	−5.05439	−0.415468
$149$	−3.31490	−0.271568	−0.135784	−	0.990738i	$-0.543355\pi$
$149$	−3.31490	−0.271568	−0.135784	+	0.990738i	$0.543355\pi$
$150$	−26.9096	−2.19716
$151$	4.56254	0.371295	0.185647	−	0.982616i	$-0.440562\pi$
$151$	4.56254	0.371295	0.185647	+	0.982616i	$0.440562\pi$
$152$	−16.8187	−1.36417
$153$	−8.36961	−0.676642
$154$	45.7895	3.68982
$155$	3.02079	0.242636
$156$	−60.0738	−4.80975
$157$	−4.77233	−0.380874	−0.190437	−	0.981699i	$-0.560990\pi$
$157$	−4.77233	−0.380874	−0.190437	+	0.981699i	$0.560990\pi$
$158$	−10.9557	−0.871586
$159$	−2.10954	−0.167298
$160$	5.49570	0.434473
$161$	17.5000	1.37919
$162$	29.8318	2.34381
$163$	15.2403	1.19371	0.596856	−	0.802348i	$-0.296416\pi$
$163$	15.2403	1.19371	0.596856	+	0.802348i	$0.296416\pi$
$164$	24.0936	1.88140
$165$	2.71069	0.211027
$166$	42.2617	3.28014
$167$	10.8866	0.842430	0.421215	−	0.906961i	$-0.361604\pi$
$167$	10.8866	0.842430	0.421215	+	0.906961i	$0.361604\pi$
$168$	−87.4453	−6.74655
$169$	19.3615	1.48935
$170$	−6.32212	−0.484885
$171$	2.83029	0.216438
$172$	−0.740874	−0.0564911
$173$	12.5545	0.954500	0.477250	−	0.878768i	$-0.341634\pi$
$173$	12.5545	0.954500	0.477250	+	0.878768i	$0.341634\pi$
$174$	8.24588	0.625119
$175$	25.0182	1.89120
$176$	38.2216	2.88106
$177$	2.17240	0.163287
$178$	−24.9077	−1.86691
$179$	−8.29324	−0.619866	−0.309933	−	0.950758i	$-0.600307\pi$
$179$	−8.29324	−0.619866	−0.309933	+	0.950758i	$0.600307\pi$
$180$	−2.67909	−0.199687
$181$	11.3354	0.842555	0.421278	−	0.906932i	$-0.361582\pi$
$181$	11.3354	0.842555	0.421278	+	0.906932i	$0.361582\pi$
$182$	77.9515	5.77815
$183$	6.79354	0.502193
$184$	27.5177	2.02863
$185$	0.388260	0.0285455
$186$	−43.1747	−3.16572
$187$	−20.4864	−1.49811
$188$	−25.7785	−1.88009
$189$	−17.6217	−1.28179
$190$	2.13791	0.155100
$191$	−3.10667	−0.224790	−0.112395	−	0.993664i	$-0.535852\pi$
$191$	−3.10667	−0.224790	−0.112395	+	0.993664i	$0.535852\pi$
$192$	−30.7521	−2.21934
$193$	−23.9669	−1.72517	−0.862586	−	0.505911i	$-0.831157\pi$
$193$	−23.9669	−1.72517	−0.862586	+	0.505911i	$0.831157\pi$
$194$	−1.13687	−0.0816222
$195$	4.61465	0.330462
$196$	99.1526	7.08233
$197$	−14.0619	−1.00187	−0.500936	−	0.865484i	$-0.667011\pi$
$197$	−14.0619	−1.00187	−0.500936	+	0.865484i	$0.667011\pi$
$198$	−12.1166	−0.861088
$199$	5.07826	0.359988	0.179994	−	0.983668i	$-0.442392\pi$
$199$	5.07826	0.359988	0.179994	+	0.983668i	$0.442392\pi$
$200$	39.3395	2.78173
$201$	−24.9667	−1.76102
$202$	−31.5025	−2.21651
$203$	−7.66631	−0.538069
$204$	64.7412	4.53279
$205$	−1.85079	−0.129265
$206$	−27.7734	−1.93506
$207$	−4.63076	−0.321860
$208$	65.0680	4.51165
$209$	6.92775	0.479203
$210$	11.1157	0.767053
$211$	23.4351	1.61334	0.806670	−	0.591002i	$-0.201267\pi$
$211$	23.4351	1.61334	0.806670	+	0.591002i	$0.201267\pi$
$212$	5.10335	0.350499
$213$	7.54891	0.517243
$214$	29.4131	2.01064
$215$	0.0569113	0.00388132
$216$	−27.7091	−1.88536
$217$	40.1401	2.72489
$218$	2.65601	0.179888
$219$	−26.0145	−1.75790
$220$	−6.55764	−0.442116
$221$	−34.8758	−2.34600
$222$	−5.54922	−0.372439
$223$	−8.30504	−0.556147	−0.278073	−	0.960560i	$-0.589696\pi$
$223$	−8.30504	−0.556147	−0.278073	+	0.960560i	$0.589696\pi$
$224$	73.0265	4.87929
$225$	−6.62018	−0.441345
$226$	−28.4291	−1.89108
$227$	19.8147	1.31514	0.657572	−	0.753391i	$-0.271583\pi$
$227$	19.8147	1.31514	0.657572	+	0.753391i	$0.271583\pi$
$228$	−21.8931	−1.44991
$229$	1.36045	0.0899009	0.0449504	−	0.998989i	$-0.485687\pi$
$229$	1.36045	0.0899009	0.0449504	+	0.998989i	$0.485687\pi$
$230$	−3.49792	−0.230646
$231$	36.0195	2.36991
$232$	−12.0548	−0.791436
$233$	−22.7565	−1.49083	−0.745413	−	0.666603i	$-0.767748\pi$
$233$	−22.7565	−1.49083	−0.745413	+	0.666603i	$0.767748\pi$
$234$	−20.6271	−1.34844
$235$	1.98021	0.129175
$236$	−5.25541	−0.342098
$237$	−8.61809	−0.559805
$238$	−84.0080	−5.44543
$239$	−17.0020	−1.09977	−0.549883	−	0.835242i	$-0.685328\pi$
$239$	−17.0020	−1.09977	−0.549883	+	0.835242i	$0.685328\pi$
$240$	9.27851	0.598925
$241$	12.2345	0.788096	0.394048	−	0.919090i	$-0.371074\pi$
$241$	12.2345	0.788096	0.394048	+	0.919090i	$0.371074\pi$
$242$	−0.441824	−0.0284015
$243$	13.2199	0.848057
$244$	−16.4348	−1.05213
$245$	−7.61655	−0.486604
$246$	26.4524	1.68654
$247$	11.7937	0.750417
$248$	63.1178	4.00799
$249$	33.2444	2.10678
$250$	−10.1568	−0.642371
$251$	−27.0144	−1.70513	−0.852565	−	0.522620i	$-0.824955\pi$
$251$	−27.0144	−1.70513	−0.852565	+	0.522620i	$0.824955\pi$
$252$	−35.5995	−2.24256
$253$	−11.3348	−0.712611
$254$	−28.0442	−1.75965
$255$	−4.97319	−0.311433
$256$	−0.795343	−0.0497090
$257$	4.74317	0.295871	0.147935	−	0.988997i	$-0.452737\pi$
$257$	4.74317	0.295871	0.147935	+	0.988997i	$0.452737\pi$
$258$	−0.813406	−0.0506404
$259$	5.15918	0.320576
$260$	−11.1636	−0.692340
$261$	2.02862	0.125568
$262$	23.3478	1.44243
$263$	18.4637	1.13852	0.569260	−	0.822157i	$-0.307230\pi$
$263$	18.4637	1.13852	0.569260	+	0.822157i	$0.307230\pi$
$264$	56.6385	3.48586
$265$	−0.392021	−0.0240817
$266$	28.4084	1.74183
$267$	−19.5932	−1.19909
$268$	60.3988	3.68945
$269$	16.9574	1.03391	0.516956	−	0.856012i	$-0.327065\pi$
$269$	16.9574	1.03391	0.516956	+	0.856012i	$0.327065\pi$
$270$	3.52225	0.214358
$271$	−16.8030	−1.02071	−0.510353	−	0.859965i	$-0.670485\pi$
$271$	−16.8030	−1.02071	−0.510353	+	0.859965i	$0.670485\pi$
$272$	−70.1235	−4.25186
$273$	61.3192	3.71121
$274$	−32.9980	−1.99348
$275$	−16.2043	−0.977157
$276$	35.8202	2.15612
$277$	26.7697	1.60843	0.804217	−	0.594335i	$-0.202585\pi$
$277$	26.7697	1.60843	0.804217	+	0.594335i	$0.202585\pi$
$278$	−9.08667	−0.544982
$279$	−10.6217	−0.635902
$280$	−16.2502	−0.971133
$281$	−14.4970	−0.864817	−0.432409	−	0.901678i	$-0.642336\pi$
$281$	−14.4970	−0.864817	−0.432409	+	0.901678i	$0.642336\pi$
$282$	−28.3022	−1.68537
$283$	5.84731	0.347587	0.173793	−	0.984782i	$-0.444398\pi$
$283$	5.84731	0.347587	0.173793	+	0.984782i	$0.444398\pi$
$284$	−18.2621	−1.08366
$285$	1.68175	0.0996184
$286$	−50.4893	−2.98550
$287$	−24.5931	−1.45169
$288$	−19.3239	−1.13867
$289$	20.5855	1.21091
$290$	1.53235	0.0899828
$291$	−0.894296	−0.0524245
$292$	62.9336	3.68291
$293$	−29.2028	−1.70605	−0.853023	−	0.521873i	$-0.825233\pi$
$293$	−29.2028	−1.70605	−0.853023	+	0.521873i	$0.825233\pi$
$294$	108.860	6.34882
$295$	0.403702	0.0235044
$296$	8.11249	0.471529
$297$	11.4136	0.662285
$298$	8.80442	0.510026
$299$	−19.2962	−1.11593
$300$	51.2089	2.95655
$301$	0.756234	0.0435886
$302$	−12.1182	−0.697322
$303$	−24.7809	−1.42362
$304$	23.7132	1.36004
$305$	1.26246	0.0722882
$306$	22.2298	1.27079
$307$	30.9561	1.76676	0.883380	−	0.468657i	$-0.155262\pi$
$307$	30.9561	1.76676	0.883380	+	0.468657i	$0.155262\pi$
$308$	−87.1375	−4.96512
$309$	−21.8474	−1.24286
$310$	−8.02325	−0.455690
$311$	−28.1625	−1.59695	−0.798475	−	0.602028i	$-0.794360\pi$
$311$	−28.1625	−1.59695	−0.798475	+	0.602028i	$0.794360\pi$
$312$	96.4207	5.45875
$313$	5.94883	0.336248	0.168124	−	0.985766i	$-0.446229\pi$
$313$	5.94883	0.336248	0.168124	+	0.985766i	$0.446229\pi$
$314$	12.6754	0.715313
$315$	2.73463	0.154079
$316$	20.8486	1.17283
$317$	−0.629417	−0.0353516	−0.0176758	−	0.999844i	$-0.505627\pi$
$317$	−0.629417	−0.0353516	−0.0176758	+	0.999844i	$0.505627\pi$
$318$	5.60296	0.314199
$319$	4.96548	0.278014
$320$	−5.71473	−0.319463
$321$	23.1373	1.29140
$322$	−46.4801	−2.59024
$323$	−12.7100	−0.707206
$324$	−56.7700	−3.15389
$325$	−27.5860	−1.53020
$326$	−40.4784	−2.24189
$327$	2.08930	0.115539
$328$	−38.6712	−2.13526
$329$	26.3129	1.45068
$330$	−7.19963	−0.396327
$331$	−14.5595	−0.800261	−0.400131	−	0.916458i	$-0.631035\pi$
$331$	−14.5595	−0.800261	−0.400131	+	0.916458i	$0.631035\pi$
$332$	−80.4240	−4.41384
$333$	−1.36520	−0.0748122
$334$	−28.9149	−1.58215
$335$	−4.63962	−0.253490
$336$	123.292	6.72614
$337$	8.00070	0.435826	0.217913	−	0.975968i	$-0.430075\pi$
$337$	8.00070	0.435826	0.217913	+	0.975968i	$0.430075\pi$
$338$	−51.4243	−2.79711
$339$	−22.3633	−1.21461
$340$	12.0310	0.652473
$341$	−25.9988	−1.40791
$342$	−7.51729	−0.406489
$343$	−65.0940	−3.51474
$344$	1.18913	0.0641137
$345$	−2.75158	−0.148140
$346$	−33.3448	−1.79263
$347$	8.64749	0.464222	0.232111	−	0.972689i	$-0.425437\pi$
$347$	8.64749	0.464222	0.232111	+	0.972689i	$0.425437\pi$
$348$	−15.6919	−0.841176
$349$	14.8611	0.795498	0.397749	−	0.917494i	$-0.369791\pi$
$349$	14.8611	0.795498	0.397749	+	0.917494i	$0.369791\pi$
$350$	−66.4485	−3.55182
$351$	19.4304	1.03712
$352$	−47.2994	−2.52107
$353$	34.0815	1.81397	0.906987	−	0.421159i	$-0.138377\pi$
$353$	34.0815	1.81397	0.906987	+	0.421159i	$0.138377\pi$
$354$	−5.76991	−0.306667
$355$	1.40283	0.0744545
$356$	47.3994	2.51216
$357$	−66.0834	−3.49751
$358$	22.0269	1.16416
$359$	−17.4266	−0.919743	−0.459872	−	0.887985i	$-0.652105\pi$
$359$	−17.4266	−0.919743	−0.459872	+	0.887985i	$0.652105\pi$
$360$	4.30004	0.226632
$361$	−14.7019	−0.773786
$362$	−30.1070	−1.58239
$363$	−0.347554	−0.0182418
$364$	−148.342	−7.77522
$365$	−4.83434	−0.253041
$366$	−18.0437	−0.943160
$367$	−12.0249	−0.627693	−0.313846	−	0.949474i	$-0.601618\pi$
$367$	−12.0249	−0.627693	−0.313846	+	0.949474i	$0.601618\pi$
$368$	−38.7981	−2.02249
$369$	6.50771	0.338778
$370$	−1.03122	−0.0536108
$371$	−5.20915	−0.270446
$372$	82.1615	4.25987
$373$	−14.3303	−0.741996	−0.370998	−	0.928634i	$-0.620984\pi$
$373$	−14.3303	−0.741996	−0.370998	+	0.928634i	$0.620984\pi$
$374$	54.4121	2.81358
$375$	−7.98966	−0.412584
$376$	41.3755	2.13378
$377$	8.45318	0.435361
$378$	46.8035	2.40731
$379$	22.8997	1.17628	0.588140	−	0.808759i	$-0.299860\pi$
$379$	22.8997	1.17628	0.588140	+	0.808759i	$0.299860\pi$
$380$	−4.06845	−0.208707
$381$	−22.0605	−1.13019
$382$	8.25134	0.422175
$383$	−28.1694	−1.43939	−0.719694	−	0.694292i	$-0.755718\pi$
$383$	−28.1694	−1.43939	−0.719694	+	0.694292i	$0.755718\pi$
$384$	22.5310	1.14978
$385$	6.69359	0.341137
$386$	63.6562	3.24002
$387$	−0.200111	−0.0101722
$388$	2.16346	0.109833
$389$	−17.0133	−0.862608	−0.431304	−	0.902207i	$-0.641946\pi$
$389$	−17.0133	−0.862608	−0.431304	+	0.902207i	$0.641946\pi$
$390$	−12.2566	−0.620636
$391$	20.7954	1.05167
$392$	−159.144	−8.03797
$393$	18.3661	0.926449
$394$	37.3487	1.88160
$395$	−1.60152	−0.0805812
$396$	23.0579	1.15870
$397$	−29.5925	−1.48520	−0.742602	−	0.669733i	$-0.766408\pi$
$397$	−29.5925	−1.48520	−0.742602	+	0.669733i	$0.766408\pi$
$398$	−13.4879	−0.676088
$399$	22.3470	1.11875
$400$	−55.4662	−2.77331
$401$	8.70057	0.434486	0.217243	−	0.976118i	$-0.430294\pi$
$401$	8.70057	0.434486	0.217243	+	0.976118i	$0.430294\pi$
$402$	66.3119	3.30734
$403$	−44.2601	−2.20475
$404$	59.9493	2.98259
$405$	4.36087	0.216694
$406$	20.3618	1.01054
$407$	−3.34161	−0.165637
$408$	−103.912	−5.14442
$409$	−28.2420	−1.39648	−0.698238	−	0.715866i	$-0.746032\pi$
$409$	−28.2420	−1.39648	−0.698238	+	0.715866i	$0.746032\pi$
$410$	4.91571	0.242770
$411$	−25.9573	−1.28038
$412$	52.8528	2.60387
$413$	5.36436	0.263963
$414$	12.2993	0.604479
$415$	6.17789	0.303261
$416$	−80.5220	−3.94791
$417$	−7.14788	−0.350033
$418$	−18.4002	−0.899982
$419$	−16.7877	−0.820131	−0.410065	−	0.912056i	$-0.634494\pi$
$419$	−16.7877	−0.820131	−0.410065	+	0.912056i	$0.634494\pi$
$420$	−21.1531	−1.03217
$421$	38.2317	1.86330	0.931650	−	0.363357i	$-0.118369\pi$
$421$	38.2317	1.86330	0.931650	+	0.363357i	$0.118369\pi$
$422$	−62.2439	−3.02999
$423$	−6.96280	−0.338543
$424$	−8.19107	−0.397793
$425$	29.7293	1.44208
$426$	−20.0500	−0.971424
$427$	16.7755	0.811822
$428$	−55.9732	−2.70557
$429$	−39.7166	−1.91753
$430$	−0.151157	−0.00728944
$431$	23.4730	1.13065	0.565327	−	0.824867i	$-0.308750\pi$
$431$	23.4730	1.13065	0.565327	+	0.824867i	$0.308750\pi$
$432$	39.0680	1.87966
$433$	−29.7683	−1.43057	−0.715286	−	0.698832i	$-0.753704\pi$
$433$	−29.7683	−1.43057	−0.715286	+	0.698832i	$0.753704\pi$
$434$	−106.612	−5.11756
$435$	1.20540	0.0577944
$436$	−5.05439	−0.242061
$437$	−7.03225	−0.336398
$438$	69.0948	3.30148
$439$	−0.179125	−0.00854918	−0.00427459	−	0.999991i	$-0.501361\pi$
$439$	−0.179125	−0.00854918	−0.00427459	+	0.999991i	$0.501361\pi$
$440$	10.5253	0.501772
$441$	26.7812	1.27530
$442$	92.6305	4.40599
$443$	−6.71034	−0.318818	−0.159409	−	0.987213i	$-0.550959\pi$
$443$	−6.71034	−0.318818	−0.159409	+	0.987213i	$0.550959\pi$
$444$	10.5602	0.501163
$445$	−3.64106	−0.172603
$446$	22.0583	1.04449
$447$	6.92585	0.327581
$448$	−75.9370	−3.58768
$449$	32.8327	1.54947	0.774735	−	0.632286i	$-0.217883\pi$
$449$	32.8327	1.54947	0.774735	+	0.632286i	$0.217883\pi$
$450$	17.5833	0.828883
$451$	15.9290	0.750068
$452$	54.1007	2.54468
$453$	−9.53255	−0.447878
$454$	−52.6279	−2.46995
$455$	11.3951	0.534210
$456$	35.1393	1.64555
$457$	−7.85022	−0.367218	−0.183609	−	0.982999i	$-0.558778\pi$
$457$	−7.85022	−0.367218	−0.183609	+	0.982999i	$0.558778\pi$
$458$	−3.61336	−0.168841
$459$	−20.9401	−0.977398
$460$	6.65655	0.310363
$461$	−31.5277	−1.46839	−0.734195	−	0.678938i	$-0.762440\pi$
$461$	−31.5277	−1.46839	−0.734195	+	0.678938i	$0.762440\pi$
$462$	−95.6682	−4.45089
$463$	−4.86170	−0.225942	−0.112971	−	0.993598i	$-0.536037\pi$
$463$	−4.86170	−0.225942	−0.112971	+	0.993598i	$0.536037\pi$
$464$	16.9965	0.789042
$465$	−6.31135	−0.292682
$466$	60.4414	2.79989
$467$	−32.1157	−1.48614	−0.743068	−	0.669216i	$-0.766630\pi$
$467$	−32.1157	−1.48614	−0.743068	+	0.669216i	$0.766630\pi$
$468$	39.2535	1.81449
$469$	−61.6510	−2.84678
$470$	−5.25947	−0.242601
$471$	9.97086	0.459433
$472$	8.43513	0.388258
$473$	−0.489814	−0.0225217
$474$	22.8897	1.05136
$475$	−10.0534	−0.461280
$476$	159.867	7.32750
$477$	1.37842	0.0631134
$478$	45.1574	2.06545
$479$	−5.96834	−0.272700	−0.136350	−	0.990661i	$-0.543537\pi$
$479$	−5.96834	−0.272700	−0.136350	+	0.990661i	$0.543537\pi$
$480$	−11.4822	−0.524088
$481$	−5.68872	−0.259383
$482$	−32.4951	−1.48011
$483$	−36.5628	−1.66367
$484$	0.840792	0.0382178
$485$	−0.166189	−0.00754626
$486$	−35.1122	−1.59272
$487$	−39.0549	−1.76975	−0.884874	−	0.465831i	$-0.845755\pi$
$487$	−39.0549	−1.76975	−0.884874	+	0.465831i	$0.845755\pi$
$488$	26.3784	1.19409
$489$	−31.8416	−1.43993
$490$	20.2296	0.913882
$491$	−8.38870	−0.378577	−0.189288	−	0.981922i	$-0.560618\pi$
$491$	−8.38870	−0.378577	−0.189288	+	0.981922i	$0.560618\pi$
$492$	−50.3389	−2.26945
$493$	−9.10995	−0.410291
$494$	−31.3243	−1.40935
$495$	−1.77122	−0.0796106
$496$	−88.9920	−3.99586
$497$	18.6407	0.836151
$498$	−88.2975	−3.95671
$499$	13.0397	0.583736	0.291868	−	0.956459i	$-0.405723\pi$
$499$	13.0397	0.583736	0.291868	+	0.956459i	$0.405723\pi$
$500$	19.3284	0.864391
$501$	−22.7454	−1.01619
$502$	71.7504	3.20238
$503$	−20.1155	−0.896905	−0.448452	−	0.893807i	$-0.648025\pi$
$503$	−20.1155	−0.896905	−0.448452	+	0.893807i	$0.648025\pi$
$504$	57.1386	2.54516
$505$	−4.60509	−0.204924
$506$	30.1053	1.33834
$507$	−40.4521	−1.79654
$508$	53.3681	2.36783
$509$	−20.5829	−0.912321	−0.456160	−	0.889898i	$-0.650776\pi$
$509$	−20.5829	−0.912321	−0.456160	+	0.889898i	$0.650776\pi$
$510$	13.2088	0.584898
$511$	−64.2384	−2.84174
$512$	23.6803	1.04653
$513$	7.08116	0.312641
$514$	−12.5979	−0.555670
$515$	−4.05996	−0.178903
$516$	1.54791	0.0681430
$517$	−17.0429	−0.749548
$518$	−13.7028	−0.602068
$519$	−26.2301	−1.15138
$520$	17.9181	0.785760
$521$	23.6057	1.03419	0.517093	−	0.855929i	$-0.327014\pi$
$521$	23.6057	1.03419	0.517093	+	0.855929i	$0.327014\pi$
$522$	−5.38803	−0.235828
$523$	−36.7479	−1.60687	−0.803436	−	0.595392i	$-0.796997\pi$
$523$	−36.7479	−1.60687	−0.803436	+	0.595392i	$0.796997\pi$
$524$	−44.4309	−1.94097
$525$	−52.2706	−2.28127
$526$	−49.0398	−2.13824
$527$	47.6988	2.07779
$528$	−79.8566	−3.47531
$529$	−11.4943	−0.499751
$530$	1.04121	0.0452274
$531$	−1.41949	−0.0616006
$532$	−54.0613	−2.34385
$533$	27.1174	1.17458
$534$	52.0398	2.25198
$535$	4.29966	0.185891
$536$	−96.9424	−4.18728
$537$	17.3271	0.747720
$538$	−45.0391	−1.94177
$539$	65.5527	2.82356
$540$	−6.70285	−0.288445
$541$	−20.6879	−0.889443	−0.444721	−	0.895669i	$-0.646697\pi$
$541$	−20.6879	−0.889443	−0.444721	+	0.895669i	$0.646697\pi$
$542$	44.6288	1.91697
$543$	−23.6832	−1.01634
$544$	86.7781	3.72058
$545$	0.388260	0.0166312
$546$	−162.864	−6.96996
$547$	22.5572	0.964477	0.482239	−	0.876040i	$-0.339824\pi$
$547$	22.5572	0.964477	0.482239	+	0.876040i	$0.339824\pi$
$548$	62.7953	2.68248
$549$	−4.43904	−0.189454
$550$	43.0388	1.83518
$551$	3.08065	0.131240
$552$	−57.4928	−2.44706
$553$	−21.2809	−0.904955
$554$	−71.1006	−3.02077
$555$	−0.811194	−0.0344333
$556$	17.2920	0.733342
$557$	−25.1567	−1.06592	−0.532962	−	0.846139i	$-0.678921\pi$
$557$	−25.1567	−1.06592	−0.532962	+	0.846139i	$0.678921\pi$
$558$	28.2112	1.19428
$559$	−0.833854	−0.0352683
$560$	22.9117	0.968195
$561$	42.8024	1.80712
$562$	38.5041	1.62420
$563$	−8.79634	−0.370722	−0.185361	−	0.982671i	$-0.559345\pi$
$563$	−8.79634	−0.370722	−0.185361	+	0.982671i	$0.559345\pi$
$564$	53.8592	2.26788
$565$	−4.15582	−0.174837
$566$	−15.5305	−0.652797
$567$	57.9470	2.43355
$568$	29.3114	1.22988
$569$	−3.94240	−0.165274	−0.0826370	−	0.996580i	$-0.526334\pi$
$569$	−3.94240	−0.165274	−0.0826370	+	0.996580i	$0.526334\pi$
$570$	−4.46675	−0.187092
$571$	−46.2781	−1.93668	−0.968340	−	0.249635i	$-0.919689\pi$
$571$	−46.2781	−1.93668	−0.968340	+	0.249635i	$0.919689\pi$
$572$	96.0813	4.01736
$573$	6.49077	0.271156
$574$	65.3196	2.72639
$575$	16.4487	0.685959
$576$	20.0940	0.837252
$577$	16.6682	0.693908	0.346954	−	0.937882i	$-0.387216\pi$
$577$	16.6682	0.693908	0.346954	+	0.937882i	$0.387216\pi$
$578$	−54.6753	−2.27419
$579$	50.0741	2.08101
$580$	−2.91607	−0.121083
$581$	82.0914	3.40572
$582$	2.37526	0.0984576
$583$	3.37397	0.139736
$584$	−101.011	−4.17986
$585$	−3.01531	−0.124668
$586$	77.5630	3.20410
$587$	16.3788	0.676027	0.338013	−	0.941141i	$-0.390245\pi$
$587$	16.3788	0.676027	0.338013	+	0.941141i	$0.390245\pi$
$588$	−207.160	−8.54313
$589$	−16.1300	−0.664625
$590$	−1.07224	−0.0441432
$591$	29.3797	1.20852
$592$	−11.4381	−0.470102
$593$	−23.8823	−0.980729	−0.490365	−	0.871517i	$-0.663136\pi$
$593$	−23.8823	−0.980729	−0.490365	+	0.871517i	$0.663136\pi$
$594$	−30.3147	−1.24383
$595$	−12.2804	−0.503449
$596$	−16.7548	−0.686304
$597$	−10.6100	−0.434240
$598$	51.2509	2.09580
$599$	−34.9562	−1.42827	−0.714137	−	0.700006i	$-0.753181\pi$
$599$	−34.9562	−1.42827	−0.714137	+	0.700006i	$0.753181\pi$
$600$	−82.1923	−3.35549
$601$	16.6126	0.677641	0.338821	−	0.940851i	$-0.389972\pi$
$601$	16.6126	0.677641	0.338821	+	0.940851i	$0.389972\pi$
$602$	−2.00857	−0.0818630
$603$	16.3138	0.664348
$604$	23.0609	0.938334
$605$	−0.0645867	−0.00262582
$606$	65.8183	2.67369
$607$	34.2242	1.38912	0.694558	−	0.719437i	$-0.255600\pi$
$607$	34.2242	1.38912	0.694558	+	0.719437i	$0.255600\pi$
$608$	−29.3452	−1.19010
$609$	16.0173	0.649052
$610$	−3.35311	−0.135763
$611$	−29.0137	−1.17377
$612$	−42.3033	−1.71001
$613$	35.4481	1.43174	0.715868	−	0.698236i	$-0.246031\pi$
$613$	35.4481	1.43174	0.715868	+	0.698236i	$0.246031\pi$
$614$	−82.2198	−3.31812
$615$	3.86686	0.155927
$616$	139.859	5.63508
$617$	4.92562	0.198298	0.0991491	−	0.995073i	$-0.468388\pi$
$617$	4.92562	0.198298	0.0991491	+	0.995073i	$0.468388\pi$
$618$	58.0270	2.33419
$619$	−11.0179	−0.442845	−0.221423	−	0.975178i	$-0.571070\pi$
$619$	−11.0179	−0.442845	−0.221423	+	0.975178i	$0.571070\pi$
$620$	15.2683	0.613188
$621$	−11.5858	−0.464921
$622$	74.8000	2.99921
$623$	−48.3821	−1.93839
$624$	−135.947	−5.44223
$625$	22.7615	0.910461
$626$	−15.8002	−0.631501
$627$	−14.4742	−0.578043
$628$	−24.1212	−0.962542
$629$	6.13070	0.244447
$630$	−7.26320	−0.289373
$631$	27.9488	1.11262	0.556312	−	0.830973i	$-0.312216\pi$
$631$	27.9488	1.11262	0.556312	+	0.830973i	$0.312216\pi$
$632$	−33.4629	−1.33108
$633$	−48.9631	−1.94611
$634$	1.67174	0.0663932
$635$	−4.09955	−0.162686
$636$	−10.6624	−0.422794
$637$	111.596	4.42160
$638$	−13.1884	−0.522132
$639$	−4.93261	−0.195131
$640$	4.18698	0.165505
$641$	11.9897	0.473565	0.236782	−	0.971563i	$-0.423907\pi$
$641$	11.9897	0.473565	0.236782	+	0.971563i	$0.423907\pi$
$642$	−61.4530	−2.42536
$643$	−26.7114	−1.05340	−0.526698	−	0.850052i	$-0.676570\pi$
$643$	−26.7114	−1.05340	−0.526698	+	0.850052i	$0.676570\pi$
$644$	88.4518	3.48549
$645$	−0.118905	−0.00468189
$646$	33.7580	1.32819
$647$	−2.25540	−0.0886688	−0.0443344	−	0.999017i	$-0.514117\pi$
$647$	−2.25540	−0.0886688	−0.0443344	+	0.999017i	$0.514117\pi$
$648$	91.1181	3.57946
$649$	−3.47451	−0.136386
$650$	73.2688	2.87384
$651$	−83.8649	−3.28692
$652$	77.0304	3.01675
$653$	−5.46563	−0.213887	−0.106943	−	0.994265i	$-0.534106\pi$
$653$	−5.46563	−0.213887	−0.106943	+	0.994265i	$0.534106\pi$
$654$	−5.54922	−0.216991
$655$	3.41302	0.133358
$656$	54.5239	2.12880
$657$	16.9984	0.663172
$658$	−69.8875	−2.72450
$659$	−0.0101999	−0.000397333 0	−0.000198667	−	1.00000i	$-0.500063\pi$
$659$	−0.0101999	−0.000397333 0	−0.000198667		1.00000i	$0.500063\pi$
$660$	13.7009	0.533307
$661$	−7.01228	−0.272746	−0.136373	−	0.990658i	$-0.543545\pi$
$661$	−7.01228	−0.272746	−0.136373	+	0.990658i	$0.543545\pi$
$662$	38.6701	1.50296
$663$	72.8662	2.82989
$664$	129.084	5.00942
$665$	4.15279	0.161038
$666$	3.62597	0.140504
$667$	−5.04038	−0.195164
$668$	55.0251	2.12899
$669$	17.3518	0.670858
$670$	12.3229	0.476075
$671$	−10.8655	−0.419458
$672$	−152.575	−5.88569
$673$	44.2075	1.70407	0.852037	−	0.523482i	$-0.175367\pi$
$673$	44.2075	1.70407	0.852037	+	0.523482i	$0.175367\pi$
$674$	−21.2499	−0.818517
$675$	−16.5631	−0.637516
$676$	97.8605	3.76387
$677$	0.556036	0.0213702	0.0106851	−	0.999943i	$-0.496599\pi$
$677$	0.556036	0.0213702	0.0106851	+	0.999943i	$0.496599\pi$
$678$	59.3972	2.28113
$679$	−2.20831	−0.0847471
$680$	−19.3102	−0.740514
$681$	−41.3988	−1.58641
$682$	69.0531	2.64418
$683$	−23.8061	−0.910915	−0.455457	−	0.890258i	$-0.650524\pi$
$683$	−23.8061	−0.910915	−0.455457	+	0.890258i	$0.650524\pi$
$684$	14.3054	0.546981
$685$	−4.82371	−0.184305
$686$	172.890	6.60098
$687$	−2.84239	−0.108444
$688$	−1.67660	−0.0639197
$689$	5.74382	0.218822
$690$	7.30822	0.278219
$691$	−7.49145	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$691$	−7.49145	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$692$	63.4553	2.41221
$693$	−23.5359	−0.894055
$694$	−22.9678	−0.871847
$695$	−1.32831	−0.0503855
$696$	25.1862	0.954679
$697$	−29.2243	−1.10695
$698$	−39.4713	−1.49401
$699$	47.5452	1.79832
$700$	126.452	4.77942
$701$	6.91924	0.261336	0.130668	−	0.991426i	$-0.458288\pi$
$701$	6.91924	0.261336	0.130668	+	0.991426i	$0.458288\pi$
$702$	−51.6074	−1.94779
$703$	−2.07318	−0.0781914
$704$	49.1845	1.85371
$705$	−4.13727	−0.155819
$706$	−90.5207	−3.40679
$707$	−61.1921	−2.30137
$708$	10.9801	0.412659
$709$	25.2609	0.948693	0.474346	−	0.880338i	$-0.342684\pi$
$709$	25.2609	0.948693	0.474346	+	0.880338i	$0.342684\pi$
$710$	−3.72593	−0.139832
$711$	5.63124	0.211188
$712$	−76.0779	−2.85114
$713$	26.3909	0.988348
$714$	175.518	6.56861
$715$	−7.38062	−0.276020
$716$	−41.9173	−1.56652
$717$	35.5223	1.32660
$718$	46.2854	1.72735
$719$	−25.6853	−0.957898	−0.478949	−	0.877843i	$-0.658982\pi$
$719$	−25.6853	−0.957898	−0.478949	+	0.877843i	$0.658982\pi$
$720$	−6.06277	−0.225946
$721$	−53.9485	−2.00915
$722$	39.0485	1.45323
$723$	−25.5617	−0.950649
$724$	57.2936	2.12930
$725$	−7.20577	−0.267616
$726$	0.923106	0.0342597
$727$	5.54617	0.205696	0.102848	−	0.994697i	$-0.467204\pi$
$727$	5.54617	0.205696	0.102848	+	0.994697i	$0.467204\pi$
$728$	238.094	8.82436
$729$	6.07509	0.225003
$730$	12.8401	0.475232
$731$	0.898640	0.0332374
$732$	34.3372	1.26914
$733$	24.6819	0.911647	0.455824	−	0.890070i	$-0.349345\pi$
$733$	24.6819	0.911647	0.455824	+	0.890070i	$0.349345\pi$
$734$	31.9382	1.17886
$735$	15.9133	0.586971
$736$	48.0128	1.76978
$737$	39.9315	1.47089
$738$	−17.2845	−0.636253
$739$	−14.2579	−0.524486	−0.262243	−	0.965002i	$-0.584462\pi$
$739$	−14.2579	−0.524486	−0.262243	+	0.965002i	$0.584462\pi$
$740$	1.96242	0.0721400
$741$	−24.6407	−0.905199
$742$	13.8356	0.507919
$743$	−10.4747	−0.384281	−0.192140	−	0.981367i	$-0.561543\pi$
$743$	−10.4747	−0.384281	−0.192140	+	0.981367i	$0.561543\pi$
$744$	−131.872	−4.83468
$745$	1.28705	0.0471537
$746$	38.0615	1.39353
$747$	−21.7226	−0.794788
$748$	−103.546	−3.78603
$749$	57.1337	2.08762
$750$	21.2206	0.774867
$751$	−14.1270	−0.515502	−0.257751	−	0.966211i	$-0.582981\pi$
$751$	−14.1270	−0.515502	−0.257751	+	0.966211i	$0.582981\pi$
$752$	−58.3367	−2.12732
$753$	56.4412	2.05683
$754$	−22.4517	−0.817643
$755$	−1.77146	−0.0644699
$756$	−89.0670	−3.23934
$757$	29.0280	1.05504	0.527520	−	0.849543i	$-0.323122\pi$
$757$	29.0280	1.05504	0.527520	+	0.849543i	$0.323122\pi$
$758$	−60.8219	−2.20915
$759$	23.6818	0.859595
$760$	6.53002	0.236869
$761$	37.4531	1.35767	0.678836	−	0.734289i	$-0.262485\pi$
$761$	37.4531	1.35767	0.678836	+	0.734289i	$0.262485\pi$
$762$	58.5929	2.12260
$763$	5.15918	0.186775
$764$	−15.7023	−0.568089
$765$	3.24959	0.117489
$766$	74.8181	2.70329
$767$	−5.91496	−0.213577
$768$	1.66171	0.0599620
$769$	−36.0923	−1.30152	−0.650760	−	0.759284i	$-0.725550\pi$
$769$	−36.0923	−1.30152	−0.650760	+	0.759284i	$0.725550\pi$
$770$	−17.7782	−0.640684
$771$	−9.90992	−0.356897
$772$	−121.138	−4.35985
$773$	−17.1352	−0.616312	−0.308156	−	0.951336i	$-0.599712\pi$
$773$	−17.1352	−0.616312	−0.308156	+	0.951336i	$0.599712\pi$
$774$	0.531496	0.0191042
$775$	37.7288	1.35526
$776$	−3.47243	−0.124653
$777$	−10.7791	−0.386698
$778$	45.1875	1.62005
$779$	9.88258	0.354080
$780$	23.3243	0.835143
$781$	−12.0736	−0.432028
$782$	−55.2328	−1.97512
$783$	5.07544	0.181381
$784$	224.382	8.01365
$785$	1.85291	0.0661331
$786$	−48.7806	−1.73995
$787$	−45.9996	−1.63971	−0.819854	−	0.572572i	$-0.805946\pi$
$787$	−45.9996	−1.63971	−0.819854	+	0.572572i	$0.805946\pi$
$788$	−71.0745	−2.53193
$789$	−38.5763	−1.37335
$790$	4.25365	0.151338
$791$	−55.2223	−1.96348
$792$	−37.0088	−1.31505
$793$	−18.4973	−0.656859
$794$	78.5979	2.78934
$795$	0.819051	0.0290488
$796$	25.6675	0.909760
$797$	−46.5794	−1.64993	−0.824964	−	0.565185i	$-0.808805\pi$
$797$	−46.5794	−1.64993	−0.824964	+	0.565185i	$0.808805\pi$
$798$	−59.3539	−2.10110
$799$	31.2679	1.10618
$800$	68.6396	2.42678
$801$	12.8026	0.452358
$802$	−23.1088	−0.816000
$803$	41.6073	1.46829
$804$	−126.192	−4.45043
$805$	−6.79455	−0.239476
$806$	117.555	4.14070
$807$	−35.4292	−1.24717
$808$	−96.2209	−3.38504
$809$	−44.6231	−1.56887	−0.784433	−	0.620214i	$-0.787046\pi$
$809$	−44.6231	−1.56887	−0.784433	+	0.620214i	$0.787046\pi$
$810$	−11.5825	−0.406968
$811$	5.33051	0.187180	0.0935898	−	0.995611i	$-0.470166\pi$
$811$	5.33051	0.187180	0.0935898	+	0.995611i	$0.470166\pi$
$812$	−38.7485	−1.35981
$813$	35.1065	1.23124
$814$	8.87535	0.311081
$815$	−5.91721	−0.207271
$816$	146.509	5.12885
$817$	−0.303887	−0.0106317
$818$	75.0110	2.62270
$819$	−40.0673	−1.40006
$820$	−9.35460	−0.326677
$821$	−38.8784	−1.35686	−0.678432	−	0.734663i	$-0.737340\pi$
$821$	−38.8784	−1.35686	−0.678432	+	0.734663i	$0.737340\pi$
$822$	68.9430	2.40466
$823$	−50.4227	−1.75763	−0.878813	−	0.477166i	$-0.841664\pi$
$823$	−50.4227	−1.75763	−0.878813	+	0.477166i	$0.841664\pi$
$824$	−84.8307	−2.95522
$825$	33.8557	1.17871
$826$	−14.2478	−0.495744
$827$	46.7702	1.62636	0.813180	−	0.582012i	$-0.197734\pi$
$827$	46.7702	1.62636	0.813180	+	0.582012i	$0.197734\pi$
$828$	−23.4057	−0.813403
$829$	−43.5682	−1.51319	−0.756593	−	0.653886i	$-0.773138\pi$
$829$	−43.5682	−1.51319	−0.756593	+	0.653886i	$0.773138\pi$
$830$	−16.4085	−0.569548
$831$	−55.9300	−1.94019
$832$	83.7311	2.90285
$833$	−120.267	−4.16699
$834$	18.9848	0.657391
$835$	−4.22683	−0.146276
$836$	35.0156	1.21104
$837$	−26.5745	−0.918550
$838$	44.5882	1.54027
$839$	44.9404	1.55152	0.775758	−	0.631031i	$-0.217368\pi$
$839$	44.9404	1.55152	0.775758	+	0.631031i	$0.217368\pi$
$840$	33.9516	1.17144
$841$	−26.7919	−0.923860
$842$	−101.544	−3.49943
$843$	30.2886	1.04319
$844$	118.450	4.07723
$845$	−7.51730	−0.258603
$846$	18.4933	0.635811
$847$	−0.858224	−0.0294889
$848$	11.5489	0.396590
$849$	−12.2168	−0.419280
$850$	−78.9614	−2.70835
$851$	3.39201	0.116277
$852$	38.1551	1.30717
$853$	36.7761	1.25919	0.629595	−	0.776924i	$-0.283221\pi$
$853$	36.7761	1.25919	0.629595	+	0.776924i	$0.283221\pi$
$854$	−44.5559	−1.52467
$855$	−1.09889	−0.0375813
$856$	89.8392	3.07064
$857$	44.5555	1.52199	0.760993	−	0.648760i	$-0.224712\pi$
$857$	44.5555	1.52199	0.760993	+	0.648760i	$0.224712\pi$
$858$	105.488	3.60129
$859$	17.2291	0.587848	0.293924	−	0.955829i	$-0.405039\pi$
$859$	17.2291	0.587848	0.293924	+	0.955829i	$0.405039\pi$
$860$	0.287652	0.00980886
$861$	51.3826	1.75111
$862$	−62.3445	−2.12346
$863$	27.6354	0.940720	0.470360	−	0.882475i	$-0.344124\pi$
$863$	27.6354	0.940720	0.470360	+	0.882475i	$0.344124\pi$
$864$	−48.3468	−1.64479
$865$	−4.87441	−0.165735
$866$	79.0649	2.68673
$867$	−43.0094	−1.46068
$868$	202.884	6.88632
$869$	13.7837	0.467579
$870$	−3.20155	−0.108543
$871$	67.9789	2.30338
$872$	8.11249	0.274724
$873$	0.584351	0.0197773
$874$	18.6777	0.631783
$875$	−19.7291	−0.666965
$876$	−131.488	−4.44255
$877$	26.8448	0.906483	0.453241	−	0.891388i	$-0.350268\pi$
$877$	26.8448	0.906483	0.453241	+	0.891388i	$0.350268\pi$
$878$	0.475758	0.0160561
$879$	61.0136	2.05794
$880$	−14.8399	−0.500254
$881$	−11.4946	−0.387263	−0.193631	−	0.981074i	$-0.562027\pi$
$881$	−11.4946	−0.387263	−0.193631	+	0.981074i	$0.562027\pi$
$882$	−71.1311	−2.39511
$883$	−19.5982	−0.659531	−0.329766	−	0.944063i	$-0.606970\pi$
$883$	−19.5982	−0.659531	−0.329766	+	0.944063i	$0.606970\pi$
$884$	−176.276	−5.92880
$885$	−0.843456	−0.0283525
$886$	17.8227	0.598766
$887$	−38.9538	−1.30794	−0.653970	−	0.756521i	$-0.726898\pi$
$887$	−38.9538	−1.30794	−0.653970	+	0.756521i	$0.726898\pi$
$888$	−16.9495	−0.568787
$889$	−54.4746	−1.82702
$890$	9.67068	0.324162
$891$	−37.5324	−1.25738
$892$	−41.9769	−1.40549
$893$	−10.5737	−0.353834
$894$	−18.3951	−0.615225
$895$	3.21994	0.107631
$896$	55.6363	1.85868
$897$	40.3156	1.34610
$898$	−87.2039	−2.91003
$899$	−11.5612	−0.385588
$900$	−33.4610	−1.11537
$901$	−6.19008	−0.206222
$902$	−42.3076	−1.40869
$903$	−1.58000	−0.0525792
$904$	−86.8337	−2.88805
$905$	−4.40110	−0.146297
$906$	25.3185	0.841152
$907$	−22.3346	−0.741610	−0.370805	−	0.928711i	$-0.620918\pi$
$907$	−22.3346	−0.741610	−0.370805	+	0.928711i	$0.620918\pi$
$908$	100.151	3.32363
$909$	16.1923	0.537066
$910$	−30.2655	−1.00329
$911$	−32.1384	−1.06479	−0.532397	−	0.846495i	$-0.678709\pi$
$911$	−32.1384	−1.06479	−0.532397	+	0.846495i	$0.678709\pi$
$912$	−49.5441	−1.64057
$913$	−53.1707	−1.75969
$914$	20.8503	0.689665
$915$	−2.63766	−0.0871985
$916$	6.87623	0.227197
$917$	45.3520	1.49765
$918$	55.6170	1.83564
$919$	−3.27716	−0.108103	−0.0540517	−	0.998538i	$-0.517214\pi$
$919$	−3.27716	−0.108103	−0.0540517	+	0.998538i	$0.517214\pi$
$920$	−10.6840	−0.352242
$921$	−64.6768	−2.13117
$922$	83.7379	2.75776
$923$	−20.5540	−0.676543
$924$	182.057	5.98923
$925$	4.84925	0.159442
$926$	12.9127	0.424339
$927$	14.2756	0.468871
$928$	−21.0332	−0.690449
$929$	48.6914	1.59751	0.798756	−	0.601655i	$-0.205492\pi$
$929$	48.6914	1.59751	0.798756	+	0.601655i	$0.205492\pi$
$930$	16.7630	0.549681
$931$	40.6698	1.33290
$932$	−115.020	−3.76761
$933$	58.8401	1.92634
$934$	85.2995	2.79109
$935$	7.95406	0.260126
$936$	−63.0033	−2.05933
$937$	0.209857	0.00685572	0.00342786	−	0.999994i	$-0.498909\pi$
$937$	0.209857	0.00685572	0.00342786	+	0.999994i	$0.498909\pi$
$938$	163.746	5.34649
$939$	−12.4289	−0.405602
$940$	10.0088	0.326450
$941$	4.74724	0.154756	0.0773778	−	0.997002i	$-0.475345\pi$
$941$	4.74724	0.154756	0.0773778	+	0.997002i	$0.475345\pi$
$942$	−26.4827	−0.862853
$943$	−16.1693	−0.526544
$944$	−11.8930	−0.387083
$945$	6.84182	0.222564
$946$	1.30095	0.0422976
$947$	−1.18813	−0.0386090	−0.0193045	−	0.999814i	$-0.506145\pi$
$947$	−1.18813	−0.0386090	−0.0193045	+	0.999814i	$0.506145\pi$
$948$	−43.5592	−1.41474
$949$	70.8318	2.29930
$950$	26.7019	0.866323
$951$	1.31504	0.0426432
$952$	−256.593	−8.31623
$953$	37.2390	1.20629	0.603145	−	0.797631i	$-0.293914\pi$
$953$	37.2390	1.20629	0.603145	+	0.797631i	$0.293914\pi$
$954$	−3.66109	−0.118532
$955$	1.20620	0.0390316
$956$	−85.9346	−2.77932
$957$	−10.3744	−0.335357
$958$	15.8520	0.512154
$959$	−64.0972	−2.06981
$960$	11.9398	0.385356
$961$	29.5334	0.952691
$962$	15.1093	0.487143
$963$	−15.1184	−0.487184
$964$	61.8381	1.99167
$965$	9.30538	0.299551
$966$	97.1112	3.12450
$967$	−1.63756	−0.0526604	−0.0263302	−	0.999653i	$-0.508382\pi$
$967$	−1.63756	−0.0526604	−0.0263302	+	0.999653i	$0.508382\pi$
$968$	−1.34950	−0.0433747
$969$	26.5552	0.853075
$970$	0.441400	0.0141725
$971$	−23.2630	−0.746544	−0.373272	−	0.927722i	$-0.621764\pi$
$971$	−23.2630	−0.746544	−0.373272	+	0.927722i	$0.621764\pi$
$972$	66.8185	2.14321
$973$	−17.6504	−0.565847
$974$	103.730	3.32373
$975$	57.6356	1.84582
$976$	−37.1918	−1.19048
$977$	−50.5322	−1.61667	−0.808334	−	0.588724i	$-0.799631\pi$
$977$	−50.5322	−1.61667	−0.808334	+	0.588724i	$0.799631\pi$
$978$	84.5717	2.70431
$979$	31.3372	1.00154
$980$	−38.4970	−1.22974
$981$	−1.36520	−0.0435873
$982$	22.2805	0.710998
$983$	−16.5154	−0.526759	−0.263379	−	0.964692i	$-0.584837\pi$
$983$	−16.5154	−0.526759	−0.263379	+	0.964692i	$0.584837\pi$
$984$	80.7959	2.57568
$985$	5.45969	0.173960
$986$	24.1961	0.770561
$987$	−54.9758	−1.74990
$988$	59.6101	1.89645
$989$	0.497202	0.0158101
$990$	4.70439	0.149515
$991$	−27.1342	−0.861947	−0.430973	−	0.902365i	$-0.641830\pi$
$991$	−27.1342	−0.861947	−0.430973	+	0.902365i	$0.641830\pi$
$992$	110.128	3.49657
$993$	30.4192	0.965324
$994$	−49.5100	−1.57036
$995$	−1.97169	−0.0625067
$996$	168.030	5.32424
$997$	−44.8201	−1.41947	−0.709733	−	0.704471i	$-0.751185\pi$
$997$	−44.8201	−1.41947	−0.709733	+	0.704471i	$0.751185\pi$
$998$	−34.6335	−1.09630
$999$	−3.41561	−0.108065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.6	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.6	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65601 q^{2} -2.08930 q^{3} +5.05439 q^{4} -0.388260 q^{5} +5.54922 q^{6} -5.15918 q^{7} -8.11249 q^{8} +1.36520 q^{9} +O(q^{10})\)	\(q-2.65601 q^{2} -2.08930 q^{3} +5.05439 q^{4} -0.388260 q^{5} +5.54922 q^{6} -5.15918 q^{7} -8.11249 q^{8} +1.36520 q^{9} +1.03122 q^{10} +3.34161 q^{11} -10.5602 q^{12} +5.68872 q^{13} +13.7028 q^{14} +0.811194 q^{15} +11.4381 q^{16} -6.13070 q^{17} -3.62597 q^{18} +2.07318 q^{19} -1.96242 q^{20} +10.7791 q^{21} -8.87535 q^{22} -3.39201 q^{23} +16.9495 q^{24} -4.84925 q^{25} -15.1093 q^{26} +3.41561 q^{27} -26.0765 q^{28} +1.48595 q^{29} -2.15454 q^{30} -7.78032 q^{31} -14.1547 q^{32} -6.98164 q^{33} +16.2832 q^{34} +2.00310 q^{35} +6.90023 q^{36} -1.00000 q^{37} -5.50639 q^{38} -11.8855 q^{39} +3.14976 q^{40} +4.76687 q^{41} -28.6294 q^{42} -0.146580 q^{43} +16.8898 q^{44} -0.530051 q^{45} +9.00922 q^{46} -5.10022 q^{47} -23.8976 q^{48} +19.6171 q^{49} +12.8797 q^{50} +12.8089 q^{51} +28.7530 q^{52} +1.00969 q^{53} -9.07188 q^{54} -1.29741 q^{55} +41.8538 q^{56} -4.33150 q^{57} -3.94671 q^{58} -1.03977 q^{59} +4.10009 q^{60} -3.25158 q^{61} +20.6646 q^{62} -7.04329 q^{63} +14.7188 q^{64} -2.20870 q^{65} +18.5433 q^{66} +11.9498 q^{67} -30.9870 q^{68} +7.08694 q^{69} -5.32027 q^{70} -3.61312 q^{71} -11.0751 q^{72} +12.4513 q^{73} +2.65601 q^{74} +10.1316 q^{75} +10.4787 q^{76} -17.2400 q^{77} +31.5679 q^{78} +4.12486 q^{79} -4.44095 q^{80} -11.2318 q^{81} -12.6609 q^{82} -15.9117 q^{83} +54.4818 q^{84} +2.38031 q^{85} +0.389319 q^{86} -3.10461 q^{87} -27.1088 q^{88} +9.37787 q^{89} +1.40782 q^{90} -29.3491 q^{91} -17.1445 q^{92} +16.2555 q^{93} +13.5462 q^{94} -0.804933 q^{95} +29.5734 q^{96} +0.428035 q^{97} -52.1033 q^{98} +4.56195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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