LMFDB - Embedded newform 6013.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74380 q^{2} -2.93976 q^{3} +5.52843 q^{4} -4.29158 q^{5} +8.06610 q^{6} +1.00000 q^{7} -9.68130 q^{8} +5.64218 q^{9} +O(q^{10})$	\(q-2.74380 q^{2} -2.93976 q^{3} +5.52843 q^{4} -4.29158 q^{5} +8.06610 q^{6} +1.00000 q^{7} -9.68130 q^{8} +5.64218 q^{9} +11.7752 q^{10} -3.03501 q^{11} -16.2522 q^{12} -3.93107 q^{13} -2.74380 q^{14} +12.6162 q^{15} +15.5067 q^{16} -6.93125 q^{17} -15.4810 q^{18} -6.49537 q^{19} -23.7257 q^{20} -2.93976 q^{21} +8.32746 q^{22} -5.31036 q^{23} +28.4607 q^{24} +13.4177 q^{25} +10.7861 q^{26} -7.76736 q^{27} +5.52843 q^{28} +4.46167 q^{29} -34.6163 q^{30} +4.83839 q^{31} -23.1846 q^{32} +8.92220 q^{33} +19.0179 q^{34} -4.29158 q^{35} +31.1924 q^{36} -3.91184 q^{37} +17.8220 q^{38} +11.5564 q^{39} +41.5481 q^{40} +6.87869 q^{41} +8.06610 q^{42} -10.8125 q^{43} -16.7789 q^{44} -24.2138 q^{45} +14.5706 q^{46} -3.58884 q^{47} -45.5859 q^{48} +1.00000 q^{49} -36.8153 q^{50} +20.3762 q^{51} -21.7326 q^{52} +4.75734 q^{53} +21.3121 q^{54} +13.0250 q^{55} -9.68130 q^{56} +19.0948 q^{57} -12.2419 q^{58} -5.96851 q^{59} +69.7478 q^{60} -2.34530 q^{61} -13.2756 q^{62} +5.64218 q^{63} +32.6005 q^{64} +16.8705 q^{65} -24.4807 q^{66} -2.21749 q^{67} -38.3189 q^{68} +15.6112 q^{69} +11.7752 q^{70} -14.9464 q^{71} -54.6236 q^{72} -9.39835 q^{73} +10.7333 q^{74} -39.4446 q^{75} -35.9092 q^{76} -3.03501 q^{77} -31.7084 q^{78} -9.51904 q^{79} -66.5481 q^{80} +5.90762 q^{81} -18.8737 q^{82} +11.7757 q^{83} -16.2522 q^{84} +29.7460 q^{85} +29.6673 q^{86} -13.1162 q^{87} +29.3829 q^{88} -2.89418 q^{89} +66.4379 q^{90} -3.93107 q^{91} -29.3579 q^{92} -14.2237 q^{93} +9.84706 q^{94} +27.8754 q^{95} +68.1571 q^{96} +2.75287 q^{97} -2.74380 q^{98} -17.1241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.74380	−1.94016	−0.970079	−	0.242789i	$-0.921938\pi$
$2$	−2.74380	−1.94016	−0.970079	+	0.242789i	$0.921938\pi$
$3$	−2.93976	−1.69727	−0.848635	−	0.528979i	$-0.822575\pi$
$3$	−2.93976	−1.69727	−0.848635	+	0.528979i	$0.822575\pi$
$4$	5.52843	2.76421
$5$	−4.29158	−1.91925	−0.959626	−	0.281278i	$-0.909242\pi$
$5$	−4.29158	−1.91925	−0.959626	+	0.281278i	$0.909242\pi$
$6$	8.06610	3.29297
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.68130	−3.42286
$9$	5.64218	1.88073
$10$	11.7752	3.72365
$11$	−3.03501	−0.915091	−0.457545	−	0.889186i	$-0.651271\pi$
$11$	−3.03501	−0.915091	−0.457545	+	0.889186i	$0.651271\pi$
$12$	−16.2522	−4.69162
$13$	−3.93107	−1.09028	−0.545141	−	0.838344i	$-0.683524\pi$
$13$	−3.93107	−1.09028	−0.545141	+	0.838344i	$0.683524\pi$
$14$	−2.74380	−0.733311
$15$	12.6162	3.25749
$16$	15.5067	3.87667
$17$	−6.93125	−1.68107	−0.840537	−	0.541754i	$-0.817761\pi$
$17$	−6.93125	−1.68107	−0.840537	+	0.541754i	$0.817761\pi$
$18$	−15.4810	−3.64891
$19$	−6.49537	−1.49014	−0.745071	−	0.666986i	$-0.767584\pi$
$19$	−6.49537	−1.49014	−0.745071	+	0.666986i	$0.767584\pi$
$20$	−23.7257	−5.30523
$21$	−2.93976	−0.641508
$22$	8.32746	1.77542
$23$	−5.31036	−1.10729	−0.553643	−	0.832754i	$-0.686763\pi$
$23$	−5.31036	−1.10729	−0.553643	+	0.832754i	$0.686763\pi$
$24$	28.4607	5.80951
$25$	13.4177	2.68353
$26$	10.7861	2.11532
$27$	−7.76736	−1.49483
$28$	5.52843	1.04477
$29$	4.46167	0.828511	0.414255	−	0.910161i	$-0.364042\pi$
$29$	4.46167	0.828511	0.414255	+	0.910161i	$0.364042\pi$
$30$	−34.6163	−6.32005
$31$	4.83839	0.869001	0.434501	−	0.900672i	$-0.356925\pi$
$31$	4.83839	0.869001	0.434501	+	0.900672i	$0.356925\pi$
$32$	−23.1846	−4.09850
$33$	8.92220	1.55316
$34$	19.0179	3.26155
$35$	−4.29158	−0.725409
$36$	31.1924	5.19873
$37$	−3.91184	−0.643102	−0.321551	−	0.946892i	$-0.604204\pi$
$37$	−3.91184	−0.643102	−0.321551	+	0.946892i	$0.604204\pi$
$38$	17.8220	2.89111
$39$	11.5564	1.85050
$40$	41.5481	6.56933
$41$	6.87869	1.07427	0.537136	−	0.843496i	$-0.319506\pi$
$41$	6.87869	1.07427	0.537136	+	0.843496i	$0.319506\pi$
$42$	8.06610	1.24463
$43$	−10.8125	−1.64889	−0.824444	−	0.565944i	$-0.808512\pi$
$43$	−10.8125	−1.64889	−0.824444	+	0.565944i	$0.808512\pi$
$44$	−16.7789	−2.52951
$45$	−24.2138	−3.60959
$46$	14.5706	2.14831
$47$	−3.58884	−0.523486	−0.261743	−	0.965138i	$-0.584297\pi$
$47$	−3.58884	−0.523486	−0.261743	+	0.965138i	$0.584297\pi$
$48$	−45.5859	−6.57975
$49$	1.00000	0.142857
$50$	−36.8153	−5.20647
$51$	20.3762	2.85324
$52$	−21.7326	−3.01377
$53$	4.75734	0.653471	0.326736	−	0.945116i	$-0.394051\pi$
$53$	4.75734	0.653471	0.326736	+	0.945116i	$0.394051\pi$
$54$	21.3121	2.90020
$55$	13.0250	1.75629
$56$	−9.68130	−1.29372
$57$	19.0948	2.52917
$58$	−12.2419	−1.60744
$59$	−5.96851	−0.777034	−0.388517	−	0.921442i	$-0.627012\pi$
$59$	−5.96851	−0.777034	−0.388517	+	0.921442i	$0.627012\pi$
$60$	69.7478	9.00440
$61$	−2.34530	−0.300285	−0.150143	−	0.988664i	$-0.547973\pi$
$61$	−2.34530	−0.300285	−0.150143	+	0.988664i	$0.547973\pi$
$62$	−13.2756	−1.68600
$63$	5.64218	0.710847
$64$	32.6005	4.07506
$65$	16.8705	2.09253
$66$	−24.4807	−3.01337
$67$	−2.21749	−0.270909	−0.135455	−	0.990784i	$-0.543250\pi$
$67$	−2.21749	−0.270909	−0.135455	+	0.990784i	$0.543250\pi$
$68$	−38.3189	−4.64685
$69$	15.6112	1.87936
$70$	11.7752	1.40741
$71$	−14.9464	−1.77381	−0.886907	−	0.461947i	$-0.847151\pi$
$71$	−14.9464	−1.77381	−0.886907	+	0.461947i	$0.847151\pi$
$72$	−54.6236	−6.43745
$73$	−9.39835	−1.09999	−0.549997	−	0.835167i	$-0.685371\pi$
$73$	−9.39835	−1.09999	−0.549997	+	0.835167i	$0.685371\pi$
$74$	10.7333	1.24772
$75$	−39.4446	−4.55468
$76$	−35.9092	−4.11907
$77$	−3.03501	−0.345872
$78$	−31.7084	−3.59027
$79$	−9.51904	−1.07098	−0.535488	−	0.844543i	$-0.679872\pi$
$79$	−9.51904	−1.07098	−0.535488	+	0.844543i	$0.679872\pi$
$80$	−66.5481	−7.44031
$81$	5.90762	0.656403
$82$	−18.8737	−2.08426
$83$	11.7757	1.29255	0.646277	−	0.763103i	$-0.276325\pi$
$83$	11.7757	1.29255	0.646277	+	0.763103i	$0.276325\pi$
$84$	−16.2522	−1.77327
$85$	29.7460	3.22641
$86$	29.6673	3.19910
$87$	−13.1162	−1.40621
$88$	29.3829	3.13222
$89$	−2.89418	−0.306783	−0.153391	−	0.988166i	$-0.549019\pi$
$89$	−2.89418	−0.306783	−0.153391	+	0.988166i	$0.549019\pi$
$90$	66.4379	7.00317
$91$	−3.93107	−0.412088
$92$	−29.3579	−3.06078
$93$	−14.2237	−1.47493
$94$	9.84706	1.01565
$95$	27.8754	2.85996
$96$	68.1571	6.95625
$97$	2.75287	0.279511	0.139756	−	0.990186i	$-0.455368\pi$
$97$	2.75287	0.279511	0.139756	+	0.990186i	$0.455368\pi$
$98$	−2.74380	−0.277165
$99$	−17.1241	−1.72103
$100$	74.1785	7.41785
$101$	−8.75474	−0.871129	−0.435565	−	0.900157i	$-0.643451\pi$
$101$	−8.75474	−0.871129	−0.435565	+	0.900157i	$0.643451\pi$
$102$	−55.9082	−5.53573
$103$	4.42333	0.435843	0.217922	−	0.975966i	$-0.430072\pi$
$103$	4.42333	0.435843	0.217922	+	0.975966i	$0.430072\pi$
$104$	38.0579	3.73188
$105$	12.6162	1.23122
$106$	−13.0532	−1.26784
$107$	7.49101	0.724183	0.362092	−	0.932143i	$-0.382063\pi$
$107$	7.49101	0.724183	0.362092	+	0.932143i	$0.382063\pi$
$108$	−42.9413	−4.13203
$109$	4.85105	0.464646	0.232323	−	0.972639i	$-0.425367\pi$
$109$	4.85105	0.464646	0.232323	+	0.972639i	$0.425367\pi$
$110$	−35.7380	−3.40748
$111$	11.4999	1.09152
$112$	15.5067	1.46524
$113$	10.4913	0.986940	0.493470	−	0.869763i	$-0.335728\pi$
$113$	10.4913	0.986940	0.493470	+	0.869763i	$0.335728\pi$
$114$	−52.3924	−4.90699
$115$	22.7898	2.12516
$116$	24.6660	2.29018
$117$	−22.1798	−2.05052
$118$	16.3764	1.50757
$119$	−6.93125	−0.635387
$120$	−122.141	−11.1499
$121$	−1.78870	−0.162609
$122$	6.43503	0.582601
$123$	−20.2217	−1.82333
$124$	26.7487	2.40211
$125$	−36.1250	−3.23112
$126$	−15.4810	−1.37916
$127$	7.01140	0.622161	0.311081	−	0.950384i	$-0.399309\pi$
$127$	7.01140	0.622161	0.311081	+	0.950384i	$0.399309\pi$
$128$	−43.0800	−3.80777
$129$	31.7861	2.79861
$130$	−46.2892	−4.05983
$131$	0.833087	0.0727872	0.0363936	−	0.999338i	$-0.488413\pi$
$131$	0.833087	0.0727872	0.0363936	+	0.999338i	$0.488413\pi$
$132$	49.3258	4.29326
$133$	−6.49537	−0.563220
$134$	6.08434	0.525607
$135$	33.3342	2.86895
$136$	67.1035	5.75408
$137$	18.3842	1.57067	0.785333	−	0.619073i	$-0.212492\pi$
$137$	18.3842	1.57067	0.785333	+	0.619073i	$0.212492\pi$
$138$	−42.8339	−3.64626
$139$	8.12032	0.688757	0.344378	−	0.938831i	$-0.388090\pi$
$139$	8.12032	0.688757	0.344378	+	0.938831i	$0.388090\pi$
$140$	−23.7257	−2.00519
$141$	10.5503	0.888498
$142$	41.0100	3.44148
$143$	11.9308	0.997707
$144$	87.4914	7.29095
$145$	−19.1476	−1.59012
$146$	25.7872	2.13416
$147$	−2.93976	−0.242467
$148$	−21.6263	−1.77767
$149$	−18.1067	−1.48336	−0.741680	−	0.670753i	$-0.765971\pi$
$149$	−18.1067	−1.48336	−0.741680	+	0.670753i	$0.765971\pi$
$150$	108.228	8.83679
$151$	22.7339	1.85006	0.925031	−	0.379891i	$-0.124039\pi$
$151$	22.7339	1.85006	0.925031	+	0.379891i	$0.124039\pi$
$152$	62.8837	5.10054
$153$	−39.1073	−3.16164
$154$	8.32746	0.671046
$155$	−20.7644	−1.66783
$156$	63.8887	5.11519
$157$	16.8339	1.34349	0.671747	−	0.740781i	$-0.265544\pi$
$157$	16.8339	1.34349	0.671747	+	0.740781i	$0.265544\pi$
$158$	26.1183	2.07786
$159$	−13.9854	−1.10912
$160$	99.4985	7.86605
$161$	−5.31036	−0.418515
$162$	−16.2093	−1.27353
$163$	2.62612	0.205694	0.102847	−	0.994697i	$-0.467205\pi$
$163$	2.62612	0.205694	0.102847	+	0.994697i	$0.467205\pi$
$164$	38.0284	2.96952
$165$	−38.2903	−2.98090
$166$	−32.3102	−2.50776
$167$	−5.72984	−0.443388	−0.221694	−	0.975116i	$-0.571159\pi$
$167$	−5.72984	−0.443388	−0.221694	+	0.975116i	$0.571159\pi$
$168$	28.4607	2.19579
$169$	2.45330	0.188715
$170$	−81.6170	−6.25974
$171$	−36.6480	−2.80255
$172$	−59.7760	−4.55788
$173$	2.80304	0.213111	0.106556	−	0.994307i	$-0.466018\pi$
$173$	2.80304	0.213111	0.106556	+	0.994307i	$0.466018\pi$
$174$	35.9883	2.72826
$175$	13.4177	1.01428
$176$	−47.0630	−3.54750
$177$	17.5460	1.31884
$178$	7.94105	0.595207
$179$	8.87030	0.662997	0.331499	−	0.943456i	$-0.392446\pi$
$179$	8.87030	0.662997	0.331499	+	0.943456i	$0.392446\pi$
$180$	−133.865	−9.97767
$181$	15.0193	1.11638	0.558188	−	0.829715i	$-0.311497\pi$
$181$	15.0193	1.11638	0.558188	+	0.829715i	$0.311497\pi$
$182$	10.7861	0.799516
$183$	6.89462	0.509665
$184$	51.4112	3.79008
$185$	16.7880	1.23428
$186$	39.0270	2.86160
$187$	21.0364	1.53834
$188$	−19.8407	−1.44703
$189$	−7.76736	−0.564992
$190$	−76.4845	−5.54877
$191$	12.2613	0.887195	0.443598	−	0.896226i	$-0.353702\pi$
$191$	12.2613	0.887195	0.443598	+	0.896226i	$0.353702\pi$
$192$	−95.8376	−6.91648
$193$	4.19093	0.301670	0.150835	−	0.988559i	$-0.451804\pi$
$193$	4.19093	0.301670	0.150835	+	0.988559i	$0.451804\pi$
$194$	−7.55331	−0.542296
$195$	−49.5952	−3.55158
$196$	5.52843	0.394888
$197$	12.6600	0.901988	0.450994	−	0.892527i	$-0.351070\pi$
$197$	12.6600	0.901988	0.450994	+	0.892527i	$0.351070\pi$
$198$	46.9850	3.33908
$199$	−15.6289	−1.10791	−0.553953	−	0.832548i	$-0.686881\pi$
$199$	−15.6289	−1.10791	−0.553953	+	0.832548i	$0.686881\pi$
$200$	−129.900	−9.18534
$201$	6.51888	0.459806
$202$	24.0212	1.69013
$203$	4.46167	0.313148
$204$	112.648	7.88696
$205$	−29.5205	−2.06180
$206$	−12.1367	−0.845605
$207$	−29.9620	−2.08250
$208$	−60.9578	−4.22666
$209$	19.7135	1.36361
$210$	−34.6163	−2.38875
$211$	−7.15398	−0.492500	−0.246250	−	0.969206i	$-0.579198\pi$
$211$	−7.15398	−0.492500	−0.246250	+	0.969206i	$0.579198\pi$
$212$	26.3006	1.80633
$213$	43.9389	3.01064
$214$	−20.5538	−1.40503
$215$	46.4026	3.16463
$216$	75.1981	5.11658
$217$	4.83839	0.328452
$218$	−13.3103	−0.901487
$219$	27.6289	1.86699
$220$	72.0078	4.85476
$221$	27.2472	1.83285
$222$	−31.5533	−2.11772
$223$	−3.47019	−0.232381	−0.116191	−	0.993227i	$-0.537068\pi$
$223$	−3.47019	−0.232381	−0.116191	+	0.993227i	$0.537068\pi$
$224$	−23.1846	−1.54909
$225$	75.7048	5.04698
$226$	−28.7860	−1.91482
$227$	−16.6228	−1.10330	−0.551648	−	0.834077i	$-0.686001\pi$
$227$	−16.6228	−1.10330	−0.551648	+	0.834077i	$0.686001\pi$
$228$	105.564	6.99117
$229$	0.594437	0.0392815	0.0196407	−	0.999807i	$-0.493748\pi$
$229$	0.594437	0.0392815	0.0196407	+	0.999807i	$0.493748\pi$
$230$	−62.5307	−4.12315
$231$	8.92220	0.587038
$232$	−43.1947	−2.83587
$233$	−5.95044	−0.389826	−0.194913	−	0.980821i	$-0.562442\pi$
$233$	−5.95044	−0.389826	−0.194913	+	0.980821i	$0.562442\pi$
$234$	60.8568	3.97834
$235$	15.4018	1.00470
$236$	−32.9965	−2.14789
$237$	27.9837	1.81773
$238$	19.0179	1.23275
$239$	21.5512	1.39403	0.697017	−	0.717055i	$-0.254510\pi$
$239$	21.5512	1.39403	0.697017	+	0.717055i	$0.254510\pi$
$240$	195.635	12.6282
$241$	9.23940	0.595162	0.297581	−	0.954697i	$-0.403820\pi$
$241$	9.23940	0.595162	0.297581	+	0.954697i	$0.403820\pi$
$242$	4.90783	0.315487
$243$	5.93509	0.380736
$244$	−12.9658	−0.830053
$245$	−4.29158	−0.274179
$246$	55.4842	3.53755
$247$	25.5338	1.62467
$248$	−46.8419	−2.97447
$249$	−34.6178	−2.19381
$250$	99.1198	6.26888
$251$	−16.1361	−1.01850	−0.509250	−	0.860619i	$-0.670077\pi$
$251$	−16.1361	−1.01850	−0.509250	+	0.860619i	$0.670077\pi$
$252$	31.1924	1.96493
$253$	16.1170	1.01327
$254$	−19.2379	−1.20709
$255$	−87.4460	−5.47608
$256$	53.0018	3.31262
$257$	5.34462	0.333388	0.166694	−	0.986009i	$-0.446691\pi$
$257$	5.34462	0.333388	0.166694	+	0.986009i	$0.446691\pi$
$258$	−87.2146	−5.42974
$259$	−3.91184	−0.243070
$260$	93.2673	5.78419
$261$	25.1735	1.55820
$262$	−2.28582	−0.141219
$263$	22.4834	1.38638	0.693191	−	0.720754i	$-0.256204\pi$
$263$	22.4834	1.38638	0.693191	+	0.720754i	$0.256204\pi$
$264$	−86.3785	−5.31623
$265$	−20.4165	−1.25418
$266$	17.8220	1.09274
$267$	8.50819	0.520693
$268$	−12.2592	−0.748852
$269$	−9.95258	−0.606820	−0.303410	−	0.952860i	$-0.598125\pi$
$269$	−9.95258	−0.606820	−0.303410	+	0.952860i	$0.598125\pi$
$270$	−91.4624	−5.56623
$271$	−22.4571	−1.36417	−0.682085	−	0.731273i	$-0.738926\pi$
$271$	−22.4571	−1.36417	−0.682085	+	0.731273i	$0.738926\pi$
$272$	−107.481	−6.51697
$273$	11.5564	0.699425
$274$	−50.4425	−3.04734
$275$	−40.7227	−2.45567
$276$	86.3053	5.19497
$277$	−14.8314	−0.891134	−0.445567	−	0.895248i	$-0.646998\pi$
$277$	−14.8314	−0.891134	−0.445567	+	0.895248i	$0.646998\pi$
$278$	−22.2805	−1.33630
$279$	27.2991	1.63435
$280$	41.5481	2.48297
$281$	16.8865	1.00736	0.503681	−	0.863890i	$-0.331979\pi$
$281$	16.8865	1.00736	0.503681	+	0.863890i	$0.331979\pi$
$282$	−28.9480	−1.72383
$283$	28.8669	1.71596	0.857980	−	0.513683i	$-0.171719\pi$
$283$	28.8669	1.71596	0.857980	+	0.513683i	$0.171719\pi$
$284$	−82.6303	−4.90321
$285$	−81.9470	−4.85412
$286$	−32.7358	−1.93571
$287$	6.87869	0.406036
$288$	−130.812	−7.70814
$289$	31.0422	1.82601
$290$	52.5371	3.08509
$291$	−8.09276	−0.474406
$292$	−51.9581	−3.04062
$293$	−13.4623	−0.786479	−0.393239	−	0.919436i	$-0.628646\pi$
$293$	−13.4623	−0.786479	−0.393239	+	0.919436i	$0.628646\pi$
$294$	8.06610	0.470425
$295$	25.6143	1.49132
$296$	37.8717	2.20125
$297$	23.5740	1.36790
$298$	49.6812	2.87796
$299$	20.8754	1.20725
$300$	−218.067	−12.5901
$301$	−10.8125	−0.623221
$302$	−62.3774	−3.58941
$303$	25.7368	1.47854
$304$	−100.722	−5.77678
$305$	10.0650	0.576323
$306$	107.303	6.13408
$307$	−25.7963	−1.47227	−0.736137	−	0.676832i	$-0.763352\pi$
$307$	−25.7963	−1.47227	−0.736137	+	0.676832i	$0.763352\pi$
$308$	−16.7789	−0.956064
$309$	−13.0035	−0.739744
$310$	56.9732	3.23586
$311$	14.8718	0.843305	0.421653	−	0.906757i	$-0.361450\pi$
$311$	14.8718	0.843305	0.421653	+	0.906757i	$0.361450\pi$
$312$	−111.881	−6.33401
$313$	−30.3428	−1.71508	−0.857538	−	0.514420i	$-0.828007\pi$
$313$	−30.3428	−1.71508	−0.857538	+	0.514420i	$0.828007\pi$
$314$	−46.1889	−2.60659
$315$	−24.2138	−1.36430
$316$	−52.6253	−2.96041
$317$	−6.56589	−0.368777	−0.184389	−	0.982853i	$-0.559031\pi$
$317$	−6.56589	−0.368777	−0.184389	+	0.982853i	$0.559031\pi$
$318$	38.3732	2.15186
$319$	−13.5412	−0.758163
$320$	−139.908	−7.82107
$321$	−22.0218	−1.22913
$322$	14.5706	0.811985
$323$	45.0211	2.50504
$324$	32.6599	1.81444
$325$	−52.7457	−2.92581
$326$	−7.20554	−0.399078
$327$	−14.2609	−0.788630
$328$	−66.5947	−3.67708
$329$	−3.58884	−0.197859
$330$	105.061	5.78342
$331$	10.0579	0.552831	0.276416	−	0.961038i	$-0.410853\pi$
$331$	10.0579	0.552831	0.276416	+	0.961038i	$0.410853\pi$
$332$	65.1013	3.57290
$333$	−22.0713	−1.20950
$334$	15.7215	0.860243
$335$	9.51653	0.519943
$336$	−45.5859	−2.48691
$337$	24.6849	1.34467	0.672337	−	0.740245i	$-0.265290\pi$
$337$	24.6849	1.34467	0.672337	+	0.740245i	$0.265290\pi$
$338$	−6.73136	−0.366138
$339$	−30.8419	−1.67510
$340$	164.449	8.91848
$341$	−14.6846	−0.795215
$342$	100.555	5.43738
$343$	1.00000	0.0539949
$344$	104.679	5.64391
$345$	−66.9966	−3.60697
$346$	−7.69097	−0.413469
$347$	21.3120	1.14409	0.572044	−	0.820223i	$-0.306151\pi$
$347$	21.3120	1.14409	0.572044	+	0.820223i	$0.306151\pi$
$348$	−72.5121	−3.88706
$349$	−7.65815	−0.409932	−0.204966	−	0.978769i	$-0.565708\pi$
$349$	−7.65815	−0.409932	−0.204966	+	0.978769i	$0.565708\pi$
$350$	−36.8153	−1.96786
$351$	30.5340	1.62979
$352$	70.3655	3.75050
$353$	8.68319	0.462159	0.231080	−	0.972935i	$-0.425774\pi$
$353$	8.68319	0.462159	0.231080	+	0.972935i	$0.425774\pi$
$354$	−48.1426	−2.55875
$355$	64.1438	3.40440
$356$	−16.0003	−0.848013
$357$	20.3762	1.07842
$358$	−24.3383	−1.28632
$359$	10.2924	0.543211	0.271605	−	0.962409i	$-0.412445\pi$
$359$	10.2924	0.543211	0.271605	+	0.962409i	$0.412445\pi$
$360$	234.421	12.3551
$361$	23.1899	1.22052
$362$	−41.2099	−2.16594
$363$	5.25834	0.275991
$364$	−21.7326	−1.13910
$365$	40.3338	2.11117
$366$	−18.9174	−0.988831
$367$	15.5076	0.809489	0.404745	−	0.914430i	$-0.367360\pi$
$367$	15.5076	0.809489	0.404745	+	0.914430i	$0.367360\pi$
$368$	−82.3460	−4.29258
$369$	38.8108	2.02041
$370$	−46.0628	−2.39469
$371$	4.75734	0.246989
$372$	−78.6348	−4.07702
$373$	34.8683	1.80541	0.902707	−	0.430256i	$-0.141577\pi$
$373$	34.8683	1.80541	0.902707	+	0.430256i	$0.141577\pi$
$374$	−57.7197	−2.98462
$375$	106.199	5.48408
$376$	34.7447	1.79182
$377$	−17.5391	−0.903311
$378$	21.3121	1.09617
$379$	−22.4518	−1.15327	−0.576637	−	0.817001i	$-0.695635\pi$
$379$	−22.4518	−1.15327	−0.576637	+	0.817001i	$0.695635\pi$
$380$	154.107	7.90554
$381$	−20.6118	−1.05598
$382$	−33.6425	−1.72130
$383$	−1.53959	−0.0786694	−0.0393347	−	0.999226i	$-0.512524\pi$
$383$	−1.53959	−0.0786694	−0.0393347	+	0.999226i	$0.512524\pi$
$384$	126.645	6.46281
$385$	13.0250	0.663815
$386$	−11.4991	−0.585287
$387$	−61.0059	−3.10110
$388$	15.2190	0.772629
$389$	11.4548	0.580780	0.290390	−	0.956908i	$-0.406215\pi$
$389$	11.4548	0.580780	0.290390	+	0.956908i	$0.406215\pi$
$390$	136.079	6.89063
$391$	36.8074	1.86143
$392$	−9.68130	−0.488979
$393$	−2.44907	−0.123539
$394$	−34.7365	−1.75000
$395$	40.8517	2.05547
$396$	−94.6692	−4.75731
$397$	36.2496	1.81931	0.909657	−	0.415359i	$-0.136344\pi$
$397$	36.2496	1.81931	0.909657	+	0.415359i	$0.136344\pi$
$398$	42.8826	2.14951
$399$	19.0948	0.955937
$400$	208.063	10.4032
$401$	16.9275	0.845317	0.422659	−	0.906289i	$-0.361097\pi$
$401$	16.9275	0.845317	0.422659	+	0.906289i	$0.361097\pi$
$402$	−17.8865	−0.892097
$403$	−19.0201	−0.947457
$404$	−48.4000	−2.40799
$405$	−25.3530	−1.25980
$406$	−12.2419	−0.607556
$407$	11.8725	0.588497
$408$	−197.268	−9.76622
$409$	19.0831	0.943601	0.471800	−	0.881705i	$-0.343604\pi$
$409$	19.0831	0.943601	0.471800	+	0.881705i	$0.343604\pi$
$410$	80.9982	4.00021
$411$	−54.0450	−2.66585
$412$	24.4541	1.20476
$413$	−5.96851	−0.293691
$414$	82.2096	4.04038
$415$	−50.5365	−2.48074
$416$	91.1402	4.46852
$417$	−23.8718	−1.16901
$418$	−54.0900	−2.64563
$419$	11.9543	0.584007	0.292003	−	0.956417i	$-0.405678\pi$
$419$	11.9543	0.584007	0.292003	+	0.956417i	$0.405678\pi$
$420$	69.7478	3.40334
$421$	−13.5377	−0.659786	−0.329893	−	0.944018i	$-0.607013\pi$
$421$	−13.5377	−0.659786	−0.329893	+	0.944018i	$0.607013\pi$
$422$	19.6291	0.955529
$423$	−20.2489	−0.984534
$424$	−46.0573	−2.23674
$425$	−93.0011	−4.51121
$426$	−120.559	−5.84112
$427$	−2.34530	−0.113497
$428$	41.4135	2.00180
$429$	−35.0738	−1.69338
$430$	−127.319	−6.13989
$431$	27.5272	1.32594	0.662969	−	0.748647i	$-0.269296\pi$
$431$	27.5272	1.32594	0.662969	+	0.748647i	$0.269296\pi$
$432$	−120.446	−5.79496
$433$	−16.2073	−0.778871	−0.389436	−	0.921054i	$-0.627330\pi$
$433$	−16.2073	−0.778871	−0.389436	+	0.921054i	$0.627330\pi$
$434$	−13.2756	−0.637248
$435$	56.2893	2.69887
$436$	26.8187	1.28438
$437$	34.4928	1.65001
$438$	−75.8080	−3.62225
$439$	−0.118247	−0.00564364	−0.00282182	−	0.999996i	$-0.500898\pi$
$439$	−0.118247	−0.00564364	−0.00282182	+	0.999996i	$0.500898\pi$
$440$	−126.099	−6.01153
$441$	5.64218	0.268675
$442$	−74.7609	−3.55601
$443$	−7.73750	−0.367620	−0.183810	−	0.982962i	$-0.558843\pi$
$443$	−7.73750	−0.367620	−0.183810	+	0.982962i	$0.558843\pi$
$444$	63.5762	3.01719
$445$	12.4206	0.588793
$446$	9.52151	0.450857
$447$	53.2294	2.51766
$448$	32.6005	1.54023
$449$	−27.0703	−1.27753	−0.638764	−	0.769402i	$-0.720554\pi$
$449$	−27.0703	−1.27753	−0.638764	+	0.769402i	$0.720554\pi$
$450$	−207.719	−9.79195
$451$	−20.8769	−0.983056
$452$	58.0005	2.72811
$453$	−66.8323	−3.14006
$454$	45.6097	2.14057
$455$	16.8705	0.790901
$456$	−184.863	−8.65699
$457$	−25.7589	−1.20495	−0.602476	−	0.798137i	$-0.705819\pi$
$457$	−25.7589	−1.20495	−0.602476	+	0.798137i	$0.705819\pi$
$458$	−1.63102	−0.0762123
$459$	53.8375	2.51292
$460$	125.992	5.87441
$461$	19.2782	0.897876	0.448938	−	0.893563i	$-0.351802\pi$
$461$	19.2782	0.897876	0.448938	+	0.893563i	$0.351802\pi$
$462$	−24.4807	−1.13895
$463$	−13.9439	−0.648029	−0.324014	−	0.946052i	$-0.605033\pi$
$463$	−13.9439	−0.648029	−0.324014	+	0.946052i	$0.605033\pi$
$464$	69.1856	3.21186
$465$	61.0422	2.83076
$466$	16.3268	0.756325
$467$	−31.8916	−1.47577	−0.737884	−	0.674928i	$-0.764175\pi$
$467$	−31.8916	−1.47577	−0.737884	+	0.674928i	$0.764175\pi$
$468$	−122.619	−5.66808
$469$	−2.21749	−0.102394
$470$	−42.2594	−1.94928
$471$	−49.4877	−2.28027
$472$	57.7829	2.65968
$473$	32.8160	1.50888
$474$	−76.7815	−3.52669
$475$	−87.1527	−3.99884
$476$	−38.3189	−1.75634
$477$	26.8418	1.22900
$478$	−59.1322	−2.70465
$479$	30.6028	1.39828	0.699138	−	0.714987i	$-0.253567\pi$
$479$	30.6028	1.39828	0.699138	+	0.714987i	$0.253567\pi$
$480$	−292.502	−13.3508
$481$	15.3777	0.701163
$482$	−25.3510	−1.15471
$483$	15.6112	0.710333
$484$	−9.88869	−0.449486
$485$	−11.8141	−0.536453
$486$	−16.2847	−0.738689
$487$	−28.4315	−1.28835	−0.644177	−	0.764876i	$-0.722800\pi$
$487$	−28.4315	−1.28835	−0.644177	+	0.764876i	$0.722800\pi$
$488$	22.7056	1.02783
$489$	−7.72015	−0.349117
$490$	11.7752	0.531951
$491$	25.8254	1.16548	0.582741	−	0.812658i	$-0.301980\pi$
$491$	25.8254	1.16548	0.582741	+	0.812658i	$0.301980\pi$
$492$	−111.794	−5.04007
$493$	−30.9249	−1.39279
$494$	−70.0595	−3.15213
$495$	73.4893	3.30310
$496$	75.0274	3.36883
$497$	−14.9464	−0.670439
$498$	94.9843	4.25635
$499$	5.56113	0.248950	0.124475	−	0.992223i	$-0.460275\pi$
$499$	5.56113	0.248950	0.124475	+	0.992223i	$0.460275\pi$
$500$	−199.715	−8.93151
$501$	16.8443	0.752549
$502$	44.2741	1.97605
$503$	3.03245	0.135210	0.0676052	−	0.997712i	$-0.478464\pi$
$503$	3.03245	0.135210	0.0676052	+	0.997712i	$0.478464\pi$
$504$	−54.6236	−2.43313
$505$	37.5717	1.67192
$506$	−44.2218	−1.96590
$507$	−7.21211	−0.320301
$508$	38.7620	1.71979
$509$	−39.2718	−1.74069	−0.870345	−	0.492442i	$-0.836104\pi$
$509$	−39.2718	−1.74069	−0.870345	+	0.492442i	$0.836104\pi$
$510$	239.934	10.6245
$511$	−9.39835	−0.415758
$512$	−59.2664	−2.61923
$513$	50.4519	2.22751
$514$	−14.6646	−0.646826
$515$	−18.9831	−0.836494
$516$	175.727	7.73595
$517$	10.8922	0.479038
$518$	10.7333	0.471594
$519$	−8.24025	−0.361707
$520$	−163.328	−7.16242
$521$	−16.6533	−0.729592	−0.364796	−	0.931087i	$-0.618861\pi$
$521$	−16.6533	−0.729592	−0.364796	+	0.931087i	$0.618861\pi$
$522$	−69.0710	−3.02316
$523$	16.8219	0.735572	0.367786	−	0.929910i	$-0.380116\pi$
$523$	16.8219	0.735572	0.367786	+	0.929910i	$0.380116\pi$
$524$	4.60566	0.201199
$525$	−39.4446	−1.72151
$526$	−61.6898	−2.68980
$527$	−33.5361	−1.46086
$528$	138.354	6.02107
$529$	5.19992	0.226083
$530$	56.0188	2.43330
$531$	−33.6754	−1.46139
$532$	−35.9092	−1.55686
$533$	−27.0406	−1.17126
$534$	−23.3448	−1.01023
$535$	−32.1483	−1.38989
$536$	21.4682	0.927284
$537$	−26.0765	−1.12529
$538$	27.3079	1.17733
$539$	−3.03501	−0.130727
$540$	184.286	7.93040
$541$	−5.92095	−0.254562	−0.127281	−	0.991867i	$-0.540625\pi$
$541$	−5.92095	−0.254562	−0.127281	+	0.991867i	$0.540625\pi$
$542$	61.6177	2.64670
$543$	−44.1531	−1.89479
$544$	160.698	6.88988
$545$	−20.8187	−0.891773
$546$	−31.7084	−1.35699
$547$	−24.5541	−1.04986	−0.524929	−	0.851146i	$-0.675908\pi$
$547$	−24.5541	−1.04986	−0.524929	+	0.851146i	$0.675908\pi$
$548$	101.636	4.34166
$549$	−13.2326	−0.564754
$550$	111.735	4.76440
$551$	−28.9802	−1.23460
$552$	−151.136	−6.43279
$553$	−9.51904	−0.404791
$554$	40.6945	1.72894
$555$	−49.3526	−2.09490
$556$	44.8926	1.90387
$557$	26.9947	1.14380	0.571901	−	0.820323i	$-0.306206\pi$
$557$	26.9947	1.14380	0.571901	+	0.820323i	$0.306206\pi$
$558$	−74.9032	−3.17090
$559$	42.5046	1.79775
$560$	−66.5481	−2.81217
$561$	−61.8420	−2.61097
$562$	−46.3331	−1.95444
$563$	14.5528	0.613327	0.306664	−	0.951818i	$-0.400787\pi$
$563$	14.5528	0.613327	0.306664	+	0.951818i	$0.400787\pi$
$564$	58.3267	2.45600
$565$	−45.0243	−1.89419
$566$	−79.2050	−3.32923
$567$	5.90762	0.248097
$568$	144.701	6.07151
$569$	47.2866	1.98236	0.991179	−	0.132532i	$-0.0423107\pi$
$569$	47.2866	1.98236	0.991179	+	0.132532i	$0.0423107\pi$
$570$	224.846	9.41776
$571$	−0.474188	−0.0198441	−0.00992207	−	0.999951i	$-0.503158\pi$
$571$	−0.474188	−0.0198441	−0.00992207	+	0.999951i	$0.503158\pi$
$572$	65.9588	2.75788
$573$	−36.0452	−1.50581
$574$	−18.8737	−0.787775
$575$	−71.2525	−2.97144
$576$	183.938	7.66407
$577$	−3.30548	−0.137609	−0.0688044	−	0.997630i	$-0.521918\pi$
$577$	−3.30548	−0.137609	−0.0688044	+	0.997630i	$0.521918\pi$
$578$	−85.1736	−3.54275
$579$	−12.3203	−0.512015
$580$	−105.856	−4.39544
$581$	11.7757	0.488540
$582$	22.2049	0.920423
$583$	−14.4386	−0.597985
$584$	90.9882	3.76512
$585$	95.1863	3.93547
$586$	36.9380	1.52589
$587$	−16.3095	−0.673164	−0.336582	−	0.941654i	$-0.609271\pi$
$587$	−16.3095	−0.673164	−0.336582	+	0.941654i	$0.609271\pi$
$588$	−16.2522	−0.670231
$589$	−31.4272	−1.29493
$590$	−70.2806	−2.89341
$591$	−37.2173	−1.53092
$592$	−60.6596	−2.49309
$593$	37.2849	1.53111	0.765554	−	0.643371i	$-0.222465\pi$
$593$	37.2849	1.53111	0.765554	+	0.643371i	$0.222465\pi$
$594$	−64.6824	−2.65395
$595$	29.7460	1.21947
$596$	−100.102	−4.10033
$597$	45.9453	1.88041
$598$	−57.2779	−2.34227
$599$	−23.8871	−0.976002	−0.488001	−	0.872843i	$-0.662274\pi$
$599$	−23.8871	−0.976002	−0.488001	+	0.872843i	$0.662274\pi$
$600$	381.875	15.5900
$601$	−24.4579	−0.997659	−0.498830	−	0.866700i	$-0.666237\pi$
$601$	−24.4579	−0.997659	−0.498830	+	0.866700i	$0.666237\pi$
$602$	29.6673	1.20915
$603$	−12.5115	−0.509506
$604$	125.683	5.11397
$605$	7.67634	0.312088
$606$	−70.6166	−2.86861
$607$	−36.8853	−1.49713	−0.748565	−	0.663061i	$-0.769257\pi$
$607$	−36.8853	−1.49713	−0.748565	+	0.663061i	$0.769257\pi$
$608$	150.593	6.10734
$609$	−13.1162	−0.531496
$610$	−27.6165	−1.11816
$611$	14.1080	0.570748
$612$	−216.202	−8.73945
$613$	5.91120	0.238751	0.119376	−	0.992849i	$-0.461911\pi$
$613$	5.91120	0.238751	0.119376	+	0.992849i	$0.461911\pi$
$614$	70.7800	2.85645
$615$	86.7830	3.49943
$616$	29.3829	1.18387
$617$	−38.3202	−1.54271	−0.771356	−	0.636404i	$-0.780421\pi$
$617$	−38.3202	−1.54271	−0.771356	+	0.636404i	$0.780421\pi$
$618$	35.6790	1.43522
$619$	−8.74058	−0.351313	−0.175657	−	0.984451i	$-0.556205\pi$
$619$	−8.74058	−0.351313	−0.175657	+	0.984451i	$0.556205\pi$
$620$	−114.794	−4.61025
$621$	41.2475	1.65520
$622$	−40.8053	−1.63615
$623$	−2.89418	−0.115953
$624$	179.201	7.17379
$625$	87.9451	3.51780
$626$	83.2545	3.32752
$627$	−57.9530	−2.31442
$628$	93.0652	3.71371
$629$	27.1139	1.08110
$630$	66.4379	2.64695
$631$	−0.548985	−0.0218547	−0.0109274	−	0.999940i	$-0.503478\pi$
$631$	−0.548985	−0.0218547	−0.0109274	+	0.999940i	$0.503478\pi$
$632$	92.1566	3.66579
$633$	21.0310	0.835906
$634$	18.0155	0.715486
$635$	−30.0900	−1.19408
$636$	−77.3175	−3.06584
$637$	−3.93107	−0.155755
$638$	37.1544	1.47096
$639$	−84.3304	−3.33606
$640$	184.881	7.30807
$641$	−7.61209	−0.300659	−0.150330	−	0.988636i	$-0.548034\pi$
$641$	−7.61209	−0.300659	−0.150330	+	0.988636i	$0.548034\pi$
$642$	60.4233	2.38472
$643$	−4.43722	−0.174987	−0.0874934	−	0.996165i	$-0.527886\pi$
$643$	−4.43722	−0.174987	−0.0874934	+	0.996165i	$0.527886\pi$
$644$	−29.3579	−1.15687
$645$	−136.412	−5.37123
$646$	−123.529	−4.86017
$647$	−15.8700	−0.623915	−0.311958	−	0.950096i	$-0.600985\pi$
$647$	−15.8700	−0.623915	−0.311958	+	0.950096i	$0.600985\pi$
$648$	−57.1935	−2.24677
$649$	18.1145	0.711056
$650$	144.724	5.67653
$651$	−14.2237	−0.557471
$652$	14.5183	0.568581
$653$	−3.20409	−0.125386	−0.0626930	−	0.998033i	$-0.519969\pi$
$653$	−3.20409	−0.125386	−0.0626930	+	0.998033i	$0.519969\pi$
$654$	39.1291	1.53007
$655$	−3.57526	−0.139697
$656$	106.666	4.16459
$657$	−53.0271	−2.06879
$658$	9.84706	0.383878
$659$	−25.9172	−1.00959	−0.504795	−	0.863239i	$-0.668432\pi$
$659$	−25.9172	−1.00959	−0.504795	+	0.863239i	$0.668432\pi$
$660$	−211.685	−8.23984
$661$	14.8658	0.578214	0.289107	−	0.957297i	$-0.406642\pi$
$661$	14.8658	0.578214	0.289107	+	0.957297i	$0.406642\pi$
$662$	−27.5968	−1.07258
$663$	−80.1002	−3.11083
$664$	−114.004	−4.42423
$665$	27.8754	1.08096
$666$	60.5592	2.34662
$667$	−23.6931	−0.917399
$668$	−31.6770	−1.22562
$669$	10.2015	0.394414
$670$	−26.1114	−1.00877
$671$	7.11802	0.274788
$672$	68.1571	2.62922
$673$	13.9294	0.536940	0.268470	−	0.963288i	$-0.413482\pi$
$673$	13.9294	0.536940	0.268470	+	0.963288i	$0.413482\pi$
$674$	−67.7305	−2.60888
$675$	−104.220	−4.01142
$676$	13.5629	0.521650
$677$	−11.3758	−0.437208	−0.218604	−	0.975814i	$-0.570150\pi$
$677$	−11.3758	−0.437208	−0.218604	+	0.975814i	$0.570150\pi$
$678$	84.6240	3.24997
$679$	2.75287	0.105645
$680$	−287.980	−11.0435
$681$	48.8671	1.87259
$682$	40.2916	1.54284
$683$	−31.2058	−1.19406	−0.597029	−	0.802220i	$-0.703652\pi$
$683$	−31.2058	−1.19406	−0.597029	+	0.802220i	$0.703652\pi$
$684$	−202.606	−7.74684
$685$	−78.8972	−3.01451
$686$	−2.74380	−0.104759
$687$	−1.74750	−0.0666713
$688$	−167.666	−6.39219
$689$	−18.7014	−0.712468
$690$	183.825	6.99810
$691$	−34.5694	−1.31508	−0.657540	−	0.753420i	$-0.728403\pi$
$691$	−34.5694	−1.31508	−0.657540	+	0.753420i	$0.728403\pi$
$692$	15.4964	0.589085
$693$	−17.1241	−0.650490
$694$	−58.4758	−2.21971
$695$	−34.8490	−1.32190
$696$	126.982	4.81324
$697$	−47.6779	−1.80593
$698$	21.0124	0.795332
$699$	17.4928	0.661640
$700$	74.1785	2.80369
$701$	31.5665	1.19225	0.596124	−	0.802892i	$-0.296707\pi$
$701$	31.5665	1.19225	0.596124	+	0.802892i	$0.296707\pi$
$702$	−83.7792	−3.16204
$703$	25.4089	0.958313
$704$	−98.9429	−3.72905
$705$	−45.2776	−1.70525
$706$	−23.8249	−0.896662
$707$	−8.75474	−0.329256
$708$	97.0017	3.64555
$709$	−23.1382	−0.868972	−0.434486	−	0.900678i	$-0.643070\pi$
$709$	−23.1382	−0.868972	−0.434486	+	0.900678i	$0.643070\pi$
$710$	−175.998	−6.60507
$711$	−53.7081	−2.01421
$712$	28.0194	1.05007
$713$	−25.6936	−0.962233
$714$	−55.9082	−2.09231
$715$	−51.2022	−1.91485
$716$	49.0388	1.83267
$717$	−63.3554	−2.36605
$718$	−28.2402	−1.05391
$719$	14.6528	0.546459	0.273229	−	0.961949i	$-0.411908\pi$
$719$	14.6528	0.546459	0.273229	+	0.961949i	$0.411908\pi$
$720$	−375.476	−13.9932
$721$	4.42333	0.164733
$722$	−63.6284	−2.36800
$723$	−27.1616	−1.01015
$724$	83.0331	3.08590
$725$	59.8651	2.22333
$726$	−14.4278	−0.535467
$727$	26.0696	0.966866	0.483433	−	0.875381i	$-0.339390\pi$
$727$	26.0696	0.966866	0.483433	+	0.875381i	$0.339390\pi$
$728$	38.0579	1.41052
$729$	−35.1706	−1.30261
$730$	−110.668	−4.09599
$731$	74.9440	2.77190
$732$	38.1164	1.40882
$733$	−0.626922	−0.0231559	−0.0115780	−	0.999933i	$-0.503685\pi$
$733$	−0.626922	−0.0231559	−0.0115780	+	0.999933i	$0.503685\pi$
$734$	−42.5497	−1.57054
$735$	12.6162	0.465356
$736$	123.119	4.53821
$737$	6.73011	0.247907
$738$	−106.489	−3.91991
$739$	16.6908	0.613982	0.306991	−	0.951712i	$-0.400678\pi$
$739$	16.6908	0.613982	0.306991	+	0.951712i	$0.400678\pi$
$740$	92.8111	3.41180
$741$	−75.0631	−2.75751
$742$	−13.0532	−0.479198
$743$	−8.06730	−0.295961	−0.147980	−	0.988990i	$-0.547277\pi$
$743$	−8.06730	−0.295961	−0.147980	+	0.988990i	$0.547277\pi$
$744$	137.704	5.04847
$745$	77.7064	2.84694
$746$	−95.6717	−3.50279
$747$	66.4408	2.43094
$748$	116.298	4.25229
$749$	7.49101	0.273716
$750$	−291.388	−10.6400
$751$	−9.90200	−0.361329	−0.180665	−	0.983545i	$-0.557825\pi$
$751$	−9.90200	−0.361329	−0.180665	+	0.983545i	$0.557825\pi$
$752$	−55.6510	−2.02938
$753$	47.4362	1.72867
$754$	48.1238	1.75257
$755$	−97.5645	−3.55074
$756$	−42.9413	−1.56176
$757$	6.96049	0.252983	0.126492	−	0.991968i	$-0.459628\pi$
$757$	6.96049	0.252983	0.126492	+	0.991968i	$0.459628\pi$
$758$	61.6033	2.23753
$759$	−47.3801	−1.71979
$760$	−269.870	−9.78922
$761$	7.04117	0.255242	0.127621	−	0.991823i	$-0.459266\pi$
$761$	7.04117	0.255242	0.127621	+	0.991823i	$0.459266\pi$
$762$	56.5547	2.04876
$763$	4.85105	0.175620
$764$	67.7856	2.45240
$765$	167.832	6.06799
$766$	4.22432	0.152631
$767$	23.4626	0.847186
$768$	−155.813	−5.62240
$769$	9.37457	0.338056	0.169028	−	0.985611i	$-0.445937\pi$
$769$	9.37457	0.338056	0.169028	+	0.985611i	$0.445937\pi$
$770$	−35.7380	−1.28791
$771$	−15.7119	−0.565849
$772$	23.1692	0.833879
$773$	0.451616	0.0162435	0.00812175	−	0.999967i	$-0.497415\pi$
$773$	0.451616	0.0162435	0.00812175	+	0.999967i	$0.497415\pi$
$774$	167.388	6.01663
$775$	64.9199	2.33199
$776$	−26.6513	−0.956727
$777$	11.4999	0.412555
$778$	−31.4296	−1.12681
$779$	−44.6797	−1.60082
$780$	−274.183	−9.81734
$781$	45.3626	1.62320
$782$	−100.992	−3.61147
$783$	−34.6554	−1.23848
$784$	15.5067	0.553810
$785$	−72.2442	−2.57850
$786$	6.71977	0.239686
$787$	−0.649250	−0.0231433	−0.0115716	−	0.999933i	$-0.503683\pi$
$787$	−0.649250	−0.0231433	−0.0115716	+	0.999933i	$0.503683\pi$
$788$	69.9899	2.49329
$789$	−66.0956	−2.35307
$790$	−112.089	−3.98794
$791$	10.4913	0.373028
$792$	165.783	5.89085
$793$	9.21954	0.327396
$794$	−99.4616	−3.52976
$795$	60.0196	2.12868
$796$	−86.4034	−3.06249
$797$	−15.3682	−0.544369	−0.272185	−	0.962245i	$-0.587746\pi$
$797$	−15.3682	−0.544369	−0.272185	+	0.962245i	$0.587746\pi$
$798$	−52.3924	−1.85467
$799$	24.8752	0.880020
$800$	−311.083	−10.9984
$801$	−16.3295	−0.576974
$802$	−46.4455	−1.64005
$803$	28.5241	1.00659
$804$	36.0392	1.27100
$805$	22.7898	0.803236
$806$	52.1872	1.83822
$807$	29.2582	1.02994
$808$	84.7573	2.98175
$809$	−15.8470	−0.557152	−0.278576	−	0.960414i	$-0.589862\pi$
$809$	−15.8470	−0.557152	−0.278576	+	0.960414i	$0.589862\pi$
$810$	69.5636	2.44422
$811$	32.0067	1.12391	0.561953	−	0.827169i	$-0.310050\pi$
$811$	32.0067	1.12391	0.561953	+	0.827169i	$0.310050\pi$
$812$	24.6660	0.865607
$813$	66.0183	2.31536
$814$	−32.5757	−1.14178
$815$	−11.2702	−0.394778
$816$	315.967	11.0611
$817$	70.2311	2.45708
$818$	−52.3603	−1.83074
$819$	−22.1798	−0.775024
$820$	−163.202	−5.69925
$821$	−4.85373	−0.169397	−0.0846983	−	0.996407i	$-0.526993\pi$
$821$	−4.85373	−0.169397	−0.0846983	+	0.996407i	$0.526993\pi$
$822$	148.289	5.17216
$823$	35.2072	1.22724	0.613622	−	0.789600i	$-0.289712\pi$
$823$	35.2072	1.22724	0.613622	+	0.789600i	$0.289712\pi$
$824$	−42.8236	−1.49183
$825$	119.715	4.16794
$826$	16.3764	0.569807
$827$	23.7017	0.824188	0.412094	−	0.911141i	$-0.364798\pi$
$827$	23.7017	0.824188	0.412094	+	0.911141i	$0.364798\pi$
$828$	−165.643	−5.75648
$829$	0.0901997	0.00313276	0.00156638	−	0.999999i	$-0.499501\pi$
$829$	0.0901997	0.00313276	0.00156638	+	0.999999i	$0.499501\pi$
$830$	138.662	4.81303
$831$	43.6008	1.51250
$832$	−128.155	−4.44297
$833$	−6.93125	−0.240154
$834$	65.4993	2.26806
$835$	24.5900	0.850973
$836$	108.985	3.76932
$837$	−37.5815	−1.29901
$838$	−32.8002	−1.13307
$839$	−29.8429	−1.03029	−0.515145	−	0.857103i	$-0.672262\pi$
$839$	−29.8429	−1.03029	−0.515145	+	0.857103i	$0.672262\pi$
$840$	−122.141	−4.21427
$841$	−9.09353	−0.313570
$842$	37.1447	1.28009
$843$	−49.6421	−1.70977
$844$	−39.5503	−1.36138
$845$	−10.5285	−0.362192
$846$	55.5588	1.91015
$847$	−1.78870	−0.0614604
$848$	73.7706	2.53329
$849$	−84.8617	−2.91245
$850$	255.176	8.75247
$851$	20.7733	0.712099
$852$	242.913	8.32206
$853$	34.3528	1.17622	0.588109	−	0.808781i	$-0.299872\pi$
$853$	34.3528	1.17622	0.588109	+	0.808781i	$0.299872\pi$
$854$	6.43503	0.220202
$855$	157.278	5.37879
$856$	−72.5227	−2.47878
$857$	0.442500	0.0151155	0.00755776	−	0.999971i	$-0.497594\pi$
$857$	0.442500	0.0151155	0.00755776	+	0.999971i	$0.497594\pi$
$858$	96.2354	3.28542
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	256.534	8.74772
$861$	−20.2217	−0.689153
$862$	−75.5290	−2.57253
$863$	−32.1602	−1.09474	−0.547372	−	0.836889i	$-0.684372\pi$
$863$	−32.1602	−1.09474	−0.547372	+	0.836889i	$0.684372\pi$
$864$	180.083	6.12655
$865$	−12.0295	−0.409014
$866$	44.4695	1.51113
$867$	−91.2566	−3.09924
$868$	26.7487	0.907911
$869$	28.8904	0.980039
$870$	−154.446	−5.23623
$871$	8.71710	0.295368
$872$	−46.9645	−1.59042
$873$	15.5322	0.525684
$874$	−94.6412	−3.20129
$875$	−36.1250	−1.22125
$876$	152.744	5.16075
$877$	−37.5615	−1.26836	−0.634180	−	0.773185i	$-0.718662\pi$
$877$	−37.5615	−1.26836	−0.634180	+	0.773185i	$0.718662\pi$
$878$	0.324447	0.0109496
$879$	39.5760	1.33487
$880$	201.974	6.80856
$881$	39.9546	1.34611	0.673053	−	0.739594i	$-0.264983\pi$
$881$	39.9546	1.34611	0.673053	+	0.739594i	$0.264983\pi$
$882$	−15.4810	−0.521272
$883$	−27.1152	−0.912500	−0.456250	−	0.889852i	$-0.650808\pi$
$883$	−27.1152	−0.912500	−0.456250	+	0.889852i	$0.650808\pi$
$884$	150.634	5.06638
$885$	−75.2999	−2.53118
$886$	21.2301	0.713240
$887$	−37.1703	−1.24806	−0.624029	−	0.781401i	$-0.714505\pi$
$887$	−37.1703	−1.24806	−0.624029	+	0.781401i	$0.714505\pi$
$888$	−111.334	−3.73611
$889$	7.01140	0.235155
$890$	−34.0796	−1.14235
$891$	−17.9297	−0.600668
$892$	−19.1847	−0.642352
$893$	23.3109	0.780069
$894$	−146.051	−4.88467
$895$	−38.0676	−1.27246
$896$	−43.0800	−1.43920
$897$	−61.3686	−2.04904
$898$	74.2756	2.47861
$899$	21.5873	0.719977
$900$	418.528	13.9509
$901$	−32.9743	−1.09853
$902$	57.2821	1.90728
$903$	31.7861	1.05777
$904$	−101.570	−3.37815
$905$	−64.4565	−2.14261
$906$	183.374	6.09220
$907$	−20.7799	−0.689986	−0.344993	−	0.938605i	$-0.612119\pi$
$907$	−20.7799	−0.689986	−0.344993	+	0.938605i	$0.612119\pi$
$908$	−91.8981	−3.04975
$909$	−49.3958	−1.63836
$910$	−46.2892	−1.53447
$911$	−3.64247	−0.120681	−0.0603403	−	0.998178i	$-0.519219\pi$
$911$	−3.64247	−0.120681	−0.0603403	+	0.998178i	$0.519219\pi$
$912$	296.097	9.80476
$913$	−35.7395	−1.18280
$914$	70.6773	2.33780
$915$	−29.5888	−0.978176
$916$	3.28630	0.108582
$917$	0.833087	0.0275110
$918$	−147.719	−4.87546
$919$	33.0319	1.08962	0.544811	−	0.838559i	$-0.316601\pi$
$919$	33.0319	1.08962	0.544811	+	0.838559i	$0.316601\pi$
$920$	−220.635	−7.27413
$921$	75.8350	2.49885
$922$	−52.8955	−1.74202
$923$	58.7554	1.93396
$924$	49.3258	1.62270
$925$	−52.4877	−1.72578
$926$	38.2593	1.25728
$927$	24.9572	0.819702
$928$	−103.442	−3.39565
$929$	−29.0093	−0.951765	−0.475883	−	0.879509i	$-0.657871\pi$
$929$	−29.0093	−0.951765	−0.475883	+	0.879509i	$0.657871\pi$
$930$	−167.487	−5.49213
$931$	−6.49537	−0.212877
$932$	−32.8966	−1.07756
$933$	−43.7196	−1.43132
$934$	87.5041	2.86322
$935$	−90.2795	−2.95246
$936$	214.729	7.01864
$937$	15.1982	0.496504	0.248252	−	0.968695i	$-0.420144\pi$
$937$	15.1982	0.496504	0.248252	+	0.968695i	$0.420144\pi$
$938$	6.08434	0.198661
$939$	89.2005	2.91095
$940$	85.1478	2.77721
$941$	−36.0813	−1.17622	−0.588108	−	0.808782i	$-0.700127\pi$
$941$	−36.0813	−1.17622	−0.588108	+	0.808782i	$0.700127\pi$
$942$	135.784	4.42409
$943$	−36.5283	−1.18953
$944$	−92.5517	−3.01230
$945$	33.3342	1.08436
$946$	−90.0405	−2.92747
$947$	−45.4094	−1.47561	−0.737804	−	0.675015i	$-0.764137\pi$
$947$	−45.4094	−1.47561	−0.737804	+	0.675015i	$0.764137\pi$
$948$	154.706	5.02461
$949$	36.9455	1.19930
$950$	239.129	7.75838
$951$	19.3021	0.625915
$952$	67.1035	2.17484
$953$	48.9027	1.58411	0.792056	−	0.610448i	$-0.209011\pi$
$953$	48.9027	1.58411	0.792056	+	0.610448i	$0.209011\pi$
$954$	−73.6484	−2.38445
$955$	−52.6203	−1.70275
$956$	119.144	3.85341
$957$	39.8079	1.28681
$958$	−83.9678	−2.71288
$959$	18.3842	0.593656
$960$	411.294	13.2745
$961$	−7.58994	−0.244837
$962$	−42.1933	−1.36037
$963$	42.2656	1.36199
$964$	51.0794	1.64516
$965$	−17.9857	−0.578980
$966$	−42.8339	−1.37816
$967$	−25.3892	−0.816461	−0.408230	−	0.912879i	$-0.633854\pi$
$967$	−25.3892	−0.816461	−0.408230	+	0.912879i	$0.633854\pi$
$968$	17.3169	0.556587
$969$	−132.351	−4.25173
$970$	32.4156	1.04080
$971$	−5.04410	−0.161873	−0.0809365	−	0.996719i	$-0.525791\pi$
$971$	−5.04410	−0.161873	−0.0809365	+	0.996719i	$0.525791\pi$
$972$	32.8117	1.05244
$973$	8.12032	0.260326
$974$	78.0103	2.49961
$975$	155.060	4.96588
$976$	−36.3678	−1.16411
$977$	−28.8709	−0.923662	−0.461831	−	0.886968i	$-0.652807\pi$
$977$	−28.8709	−0.923662	−0.461831	+	0.886968i	$0.652807\pi$
$978$	21.1825	0.677343
$979$	8.78388	0.280734
$980$	−23.7257	−0.757889
$981$	27.3705	0.873872
$982$	−70.8596	−2.26122
$983$	48.5563	1.54870	0.774352	−	0.632755i	$-0.218076\pi$
$983$	48.5563	1.54870	0.774352	+	0.632755i	$0.218076\pi$
$984$	195.772	6.24099
$985$	−54.3314	−1.73114
$986$	84.8518	2.70223
$987$	10.5503	0.335821
$988$	141.162	4.49095
$989$	57.4182	1.82579
$990$	−201.640	−6.40854
$991$	−8.22028	−0.261126	−0.130563	−	0.991440i	$-0.541678\pi$
$991$	−8.22028	−0.261126	−0.130563	+	0.991440i	$0.541678\pi$
$992$	−112.176	−3.56160
$993$	−29.5677	−0.938304
$994$	41.0100	1.30076
$995$	67.0728	2.12635
$996$	−191.382	−6.06417
$997$	14.7896	0.468392	0.234196	−	0.972189i	$-0.424754\pi$
$997$	14.7896	0.468392	0.234196	+	0.972189i	$0.424754\pi$
$998$	−15.2586	−0.483003
$999$	30.3847	0.961328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.3	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.3	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74380 q^{2} -2.93976 q^{3} +5.52843 q^{4} -4.29158 q^{5} +8.06610 q^{6} +1.00000 q^{7} -9.68130 q^{8} +5.64218 q^{9} +O(q^{10})\)	\(q-2.74380 q^{2} -2.93976 q^{3} +5.52843 q^{4} -4.29158 q^{5} +8.06610 q^{6} +1.00000 q^{7} -9.68130 q^{8} +5.64218 q^{9} +11.7752 q^{10} -3.03501 q^{11} -16.2522 q^{12} -3.93107 q^{13} -2.74380 q^{14} +12.6162 q^{15} +15.5067 q^{16} -6.93125 q^{17} -15.4810 q^{18} -6.49537 q^{19} -23.7257 q^{20} -2.93976 q^{21} +8.32746 q^{22} -5.31036 q^{23} +28.4607 q^{24} +13.4177 q^{25} +10.7861 q^{26} -7.76736 q^{27} +5.52843 q^{28} +4.46167 q^{29} -34.6163 q^{30} +4.83839 q^{31} -23.1846 q^{32} +8.92220 q^{33} +19.0179 q^{34} -4.29158 q^{35} +31.1924 q^{36} -3.91184 q^{37} +17.8220 q^{38} +11.5564 q^{39} +41.5481 q^{40} +6.87869 q^{41} +8.06610 q^{42} -10.8125 q^{43} -16.7789 q^{44} -24.2138 q^{45} +14.5706 q^{46} -3.58884 q^{47} -45.5859 q^{48} +1.00000 q^{49} -36.8153 q^{50} +20.3762 q^{51} -21.7326 q^{52} +4.75734 q^{53} +21.3121 q^{54} +13.0250 q^{55} -9.68130 q^{56} +19.0948 q^{57} -12.2419 q^{58} -5.96851 q^{59} +69.7478 q^{60} -2.34530 q^{61} -13.2756 q^{62} +5.64218 q^{63} +32.6005 q^{64} +16.8705 q^{65} -24.4807 q^{66} -2.21749 q^{67} -38.3189 q^{68} +15.6112 q^{69} +11.7752 q^{70} -14.9464 q^{71} -54.6236 q^{72} -9.39835 q^{73} +10.7333 q^{74} -39.4446 q^{75} -35.9092 q^{76} -3.03501 q^{77} -31.7084 q^{78} -9.51904 q^{79} -66.5481 q^{80} +5.90762 q^{81} -18.8737 q^{82} +11.7757 q^{83} -16.2522 q^{84} +29.7460 q^{85} +29.6673 q^{86} -13.1162 q^{87} +29.3829 q^{88} -2.89418 q^{89} +66.4379 q^{90} -3.93107 q^{91} -29.3579 q^{92} -14.2237 q^{93} +9.84706 q^{94} +27.8754 q^{95} +68.1571 q^{96} +2.75287 q^{97} -2.74380 q^{98} -17.1241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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