LMFDB - Embedded newform 4015.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41139 q^{2} -3.18109 q^{3} +3.81483 q^{4} +1.00000 q^{5} +7.67086 q^{6} -3.73754 q^{7} -4.37626 q^{8} +7.11932 q^{9} +O(q^{10})$	\(q-2.41139 q^{2} -3.18109 q^{3} +3.81483 q^{4} +1.00000 q^{5} +7.67086 q^{6} -3.73754 q^{7} -4.37626 q^{8} +7.11932 q^{9} -2.41139 q^{10} +1.00000 q^{11} -12.1353 q^{12} +1.00745 q^{13} +9.01269 q^{14} -3.18109 q^{15} +2.92324 q^{16} +3.53876 q^{17} -17.1675 q^{18} +5.00704 q^{19} +3.81483 q^{20} +11.8895 q^{21} -2.41139 q^{22} -0.391364 q^{23} +13.9213 q^{24} +1.00000 q^{25} -2.42936 q^{26} -13.1039 q^{27} -14.2581 q^{28} +5.23389 q^{29} +7.67086 q^{30} +0.906270 q^{31} +1.70343 q^{32} -3.18109 q^{33} -8.53336 q^{34} -3.73754 q^{35} +27.1590 q^{36} +9.23637 q^{37} -12.0739 q^{38} -3.20479 q^{39} -4.37626 q^{40} -3.85837 q^{41} -28.6702 q^{42} +10.8492 q^{43} +3.81483 q^{44} +7.11932 q^{45} +0.943734 q^{46} -5.91517 q^{47} -9.29910 q^{48} +6.96922 q^{49} -2.41139 q^{50} -11.2571 q^{51} +3.84325 q^{52} +9.74202 q^{53} +31.5988 q^{54} +1.00000 q^{55} +16.3565 q^{56} -15.9278 q^{57} -12.6210 q^{58} +8.90242 q^{59} -12.1353 q^{60} +10.3735 q^{61} -2.18537 q^{62} -26.6088 q^{63} -9.95412 q^{64} +1.00745 q^{65} +7.67086 q^{66} +5.52814 q^{67} +13.4998 q^{68} +1.24496 q^{69} +9.01269 q^{70} -8.76327 q^{71} -31.1560 q^{72} +1.00000 q^{73} -22.2725 q^{74} -3.18109 q^{75} +19.1010 q^{76} -3.73754 q^{77} +7.72801 q^{78} -5.30661 q^{79} +2.92324 q^{80} +20.3268 q^{81} +9.30405 q^{82} +5.31245 q^{83} +45.3562 q^{84} +3.53876 q^{85} -26.1618 q^{86} -16.6495 q^{87} -4.37626 q^{88} +7.61286 q^{89} -17.1675 q^{90} -3.76539 q^{91} -1.49299 q^{92} -2.88293 q^{93} +14.2638 q^{94} +5.00704 q^{95} -5.41875 q^{96} +14.7533 q^{97} -16.8055 q^{98} +7.11932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−2.41139	−1.70511	−0.852557	−	0.522634i	$-0.824949\pi$
$2$	−2.41139	−1.70511	−0.852557	+	0.522634i	$0.824949\pi$
$3$	−3.18109	−1.83660	−0.918301	−	0.395883i	$-0.870439\pi$
$3$	−3.18109	−1.83660	−0.918301	+	0.395883i	$0.870439\pi$
$4$	3.81483	1.90741
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.67086	3.13162
$7$	−3.73754	−1.41266	−0.706329	−	0.707884i	$-0.749650\pi$
$7$	−3.73754	−1.41266	−0.706329	+	0.707884i	$0.749650\pi$
$8$	−4.37626	−1.54724
$9$	7.11932	2.37311
$10$	−2.41139	−0.762550
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−12.1353	−3.50316
$13$	1.00745	0.279416	0.139708	−	0.990193i	$-0.455384\pi$
$13$	1.00745	0.279416	0.139708	+	0.990193i	$0.455384\pi$
$14$	9.01269	2.40874
$15$	−3.18109	−0.821354
$16$	2.92324	0.730811
$17$	3.53876	0.858276	0.429138	−	0.903239i	$-0.358817\pi$
$17$	3.53876	0.858276	0.429138	+	0.903239i	$0.358817\pi$
$18$	−17.1675	−4.04642
$19$	5.00704	1.14869	0.574347	−	0.818612i	$-0.305256\pi$
$19$	5.00704	1.14869	0.574347	+	0.818612i	$0.305256\pi$
$20$	3.81483	0.853021
$21$	11.8895	2.59449
$22$	−2.41139	−0.514111
$23$	−0.391364	−0.0816051	−0.0408025	−	0.999167i	$-0.512991\pi$
$23$	−0.391364	−0.0816051	−0.0408025	+	0.999167i	$0.512991\pi$
$24$	13.9213	2.84167
$25$	1.00000	0.200000
$26$	−2.42936	−0.476437
$27$	−13.1039	−2.52185
$28$	−14.2581	−2.69452
$29$	5.23389	0.971909	0.485954	−	0.873984i	$-0.338472\pi$
$29$	5.23389	0.971909	0.485954	+	0.873984i	$0.338472\pi$
$30$	7.67086	1.40050
$31$	0.906270	0.162771	0.0813854	−	0.996683i	$-0.474066\pi$
$31$	0.906270	0.162771	0.0813854	+	0.996683i	$0.474066\pi$
$32$	1.70343	0.301126
$33$	−3.18109	−0.553756
$34$	−8.53336	−1.46346
$35$	−3.73754	−0.631760
$36$	27.1590	4.52650
$37$	9.23637	1.51845	0.759225	−	0.650828i	$-0.225578\pi$
$37$	9.23637	1.51845	0.759225	+	0.650828i	$0.225578\pi$
$38$	−12.0739	−1.95865
$39$	−3.20479	−0.513177
$40$	−4.37626	−0.691948
$41$	−3.85837	−0.602576	−0.301288	−	0.953533i	$-0.597417\pi$
$41$	−3.85837	−0.602576	−0.301288	+	0.953533i	$0.597417\pi$
$42$	−28.6702	−4.42390
$43$	10.8492	1.65449	0.827246	−	0.561839i	$-0.189906\pi$
$43$	10.8492	1.65449	0.827246	+	0.561839i	$0.189906\pi$
$44$	3.81483	0.575107
$45$	7.11932	1.06129
$46$	0.943734	0.139146
$47$	−5.91517	−0.862817	−0.431408	−	0.902157i	$-0.641983\pi$
$47$	−5.91517	−0.862817	−0.431408	+	0.902157i	$0.641983\pi$
$48$	−9.29910	−1.34221
$49$	6.96922	0.995602
$50$	−2.41139	−0.341023
$51$	−11.2571	−1.57631
$52$	3.84325	0.532962
$53$	9.74202	1.33817	0.669084	−	0.743186i	$-0.266686\pi$
$53$	9.74202	1.33817	0.669084	+	0.743186i	$0.266686\pi$
$54$	31.5988	4.30005
$55$	1.00000	0.134840
$56$	16.3565	2.18572
$57$	−15.9278	−2.10969
$58$	−12.6210	−1.65721
$59$	8.90242	1.15900	0.579498	−	0.814974i	$-0.303249\pi$
$59$	8.90242	1.15900	0.579498	+	0.814974i	$0.303249\pi$
$60$	−12.1353	−1.56666
$61$	10.3735	1.32819	0.664093	−	0.747650i	$-0.268818\pi$
$61$	10.3735	1.32819	0.664093	+	0.747650i	$0.268818\pi$
$62$	−2.18537	−0.277543
$63$	−26.6088	−3.35239
$64$	−9.95412	−1.24427
$65$	1.00745	0.124959
$66$	7.67086	0.944218
$67$	5.52814	0.675370	0.337685	−	0.941259i	$-0.390356\pi$
$67$	5.52814	0.675370	0.337685	+	0.941259i	$0.390356\pi$
$68$	13.4998	1.63709
$69$	1.24496	0.149876
$70$	9.01269	1.07722
$71$	−8.76327	−1.04001	−0.520004	−	0.854164i	$-0.674070\pi$
$71$	−8.76327	−1.04001	−0.520004	+	0.854164i	$0.674070\pi$
$72$	−31.1560	−3.67177
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−22.2725	−2.58913
$75$	−3.18109	−0.367320
$76$	19.1010	2.19103
$77$	−3.73754	−0.425932
$78$	7.72801	0.875024
$79$	−5.30661	−0.597041	−0.298520	−	0.954403i	$-0.596493\pi$
$79$	−5.30661	−0.597041	−0.298520	+	0.954403i	$0.596493\pi$
$80$	2.92324	0.326829
$81$	20.3268	2.25853
$82$	9.30405	1.02746
$83$	5.31245	0.583118	0.291559	−	0.956553i	$-0.405826\pi$
$83$	5.31245	0.583118	0.291559	+	0.956553i	$0.405826\pi$
$84$	45.3562	4.94877
$85$	3.53876	0.383833
$86$	−26.1618	−2.82110
$87$	−16.6495	−1.78501
$88$	−4.37626	−0.466511
$89$	7.61286	0.806961	0.403481	−	0.914988i	$-0.367800\pi$
$89$	7.61286	0.806961	0.403481	+	0.914988i	$0.367800\pi$
$90$	−17.1675	−1.80961
$91$	−3.76539	−0.394720
$92$	−1.49299	−0.155655
$93$	−2.88293	−0.298945
$94$	14.2638	1.47120
$95$	5.00704	0.513711
$96$	−5.41875	−0.553049
$97$	14.7533	1.49797	0.748987	−	0.662585i	$-0.230541\pi$
$97$	14.7533	1.49797	0.748987	+	0.662585i	$0.230541\pi$
$98$	−16.8055	−1.69762
$99$	7.11932	0.715519
$100$	3.81483	0.381483
$101$	−4.83677	−0.481276	−0.240638	−	0.970615i	$-0.577357\pi$
$101$	−4.83677	−0.481276	−0.240638	+	0.970615i	$0.577357\pi$
$102$	27.1454	2.68779
$103$	−5.61388	−0.553152	−0.276576	−	0.960992i	$-0.589200\pi$
$103$	−5.61388	−0.553152	−0.276576	+	0.960992i	$0.589200\pi$
$104$	−4.40886	−0.432325
$105$	11.8895	1.16029
$106$	−23.4919	−2.28173
$107$	14.8416	1.43479	0.717396	−	0.696666i	$-0.245334\pi$
$107$	14.8416	1.43479	0.717396	+	0.696666i	$0.245334\pi$
$108$	−49.9892	−4.81022
$109$	−11.1637	−1.06929	−0.534646	−	0.845076i	$-0.679555\pi$
$109$	−11.1637	−1.06929	−0.534646	+	0.845076i	$0.679555\pi$
$110$	−2.41139	−0.229917
$111$	−29.3817	−2.78879
$112$	−10.9257	−1.03239
$113$	−0.838480	−0.0788775	−0.0394388	−	0.999222i	$-0.512557\pi$
$113$	−0.838480	−0.0788775	−0.0394388	+	0.999222i	$0.512557\pi$
$114$	38.4083	3.59727
$115$	−0.391364	−0.0364949
$116$	19.9664	1.85383
$117$	7.17236	0.663085
$118$	−21.4672	−1.97622
$119$	−13.2263	−1.21245
$120$	13.9213	1.27083
$121$	1.00000	0.0909091
$122$	−25.0145	−2.26471
$123$	12.2738	1.10669
$124$	3.45726	0.310471
$125$	1.00000	0.0894427
$126$	64.1643	5.71621
$127$	−17.4581	−1.54915	−0.774576	−	0.632480i	$-0.782037\pi$
$127$	−17.4581	−1.54915	−0.774576	+	0.632480i	$0.782037\pi$
$128$	20.5965	1.82049
$129$	−34.5124	−3.03865
$130$	−2.42936	−0.213069
$131$	9.97137	0.871203	0.435601	−	0.900140i	$-0.356536\pi$
$131$	9.97137	0.871203	0.435601	+	0.900140i	$0.356536\pi$
$132$	−12.1353	−1.05624
$133$	−18.7140	−1.62271
$134$	−13.3305	−1.15158
$135$	−13.1039	−1.12781
$136$	−15.4866	−1.32796
$137$	5.70726	0.487604	0.243802	−	0.969825i	$-0.421605\pi$
$137$	5.70726	0.487604	0.243802	+	0.969825i	$0.421605\pi$
$138$	−3.00210	−0.255556
$139$	4.01965	0.340942	0.170471	−	0.985363i	$-0.445471\pi$
$139$	4.01965	0.340942	0.170471	+	0.985363i	$0.445471\pi$
$140$	−14.2581	−1.20503
$141$	18.8167	1.58465
$142$	21.1317	1.77333
$143$	1.00745	0.0842472
$144$	20.8115	1.73429
$145$	5.23389	0.434651
$146$	−2.41139	−0.199568
$147$	−22.1697	−1.82853
$148$	35.2352	2.89631
$149$	4.11039	0.336737	0.168368	−	0.985724i	$-0.446150\pi$
$149$	4.11039	0.336737	0.168368	+	0.985724i	$0.446150\pi$
$150$	7.67086	0.626323
$151$	−20.7200	−1.68617	−0.843085	−	0.537781i	$-0.819263\pi$
$151$	−20.7200	−1.68617	−0.843085	+	0.537781i	$0.819263\pi$
$152$	−21.9121	−1.77731
$153$	25.1936	2.03678
$154$	9.01269	0.726263
$155$	0.906270	0.0727934
$156$	−12.2257	−0.978840
$157$	−14.8987	−1.18905	−0.594525	−	0.804077i	$-0.702660\pi$
$157$	−14.8987	−1.18905	−0.594525	+	0.804077i	$0.702660\pi$
$158$	12.7963	1.01802
$159$	−30.9902	−2.45768
$160$	1.70343	0.134668
$161$	1.46274	0.115280
$162$	−49.0160	−3.85106
$163$	−20.1088	−1.57505	−0.787523	−	0.616285i	$-0.788637\pi$
$163$	−20.1088	−1.57505	−0.787523	+	0.616285i	$0.788637\pi$
$164$	−14.7190	−1.14936
$165$	−3.18109	−0.247647
$166$	−12.8104	−0.994282
$167$	5.97801	0.462592	0.231296	−	0.972883i	$-0.425703\pi$
$167$	5.97801	0.462592	0.231296	+	0.972883i	$0.425703\pi$
$168$	−52.0313	−4.01431
$169$	−11.9850	−0.921927
$170$	−8.53336	−0.654479
$171$	35.6467	2.72597
$172$	41.3879	3.15580
$173$	−17.0353	−1.29517	−0.647585	−	0.761993i	$-0.724221\pi$
$173$	−17.0353	−1.29517	−0.647585	+	0.761993i	$0.724221\pi$
$174$	40.1484	3.04364
$175$	−3.73754	−0.282532
$176$	2.92324	0.220348
$177$	−28.3194	−2.12861
$178$	−18.3576	−1.37596
$179$	2.61486	0.195443	0.0977217	−	0.995214i	$-0.468844\pi$
$179$	2.61486	0.195443	0.0977217	+	0.995214i	$0.468844\pi$
$180$	27.1590	2.02431
$181$	−19.0515	−1.41609	−0.708045	−	0.706167i	$-0.750423\pi$
$181$	−19.0515	−1.41609	−0.708045	+	0.706167i	$0.750423\pi$
$182$	9.07983	0.673042
$183$	−32.9989	−2.43935
$184$	1.71271	0.126263
$185$	9.23637	0.679072
$186$	6.95187	0.509736
$187$	3.53876	0.258780
$188$	−22.5654	−1.64575
$189$	48.9765	3.56252
$190$	−12.0739	−0.875936
$191$	−20.6531	−1.49440	−0.747202	−	0.664597i	$-0.768603\pi$
$191$	−20.6531	−1.49440	−0.747202	+	0.664597i	$0.768603\pi$
$192$	31.6649	2.28522
$193$	−15.4506	−1.11216	−0.556079	−	0.831129i	$-0.687695\pi$
$193$	−15.4506	−1.11216	−0.556079	+	0.831129i	$0.687695\pi$
$194$	−35.5761	−2.55422
$195$	−3.20479	−0.229500
$196$	26.5863	1.89902
$197$	−17.7491	−1.26457	−0.632287	−	0.774734i	$-0.717884\pi$
$197$	−17.7491	−1.26457	−0.632287	+	0.774734i	$0.717884\pi$
$198$	−17.1675	−1.22004
$199$	3.54686	0.251430	0.125715	−	0.992066i	$-0.459878\pi$
$199$	3.54686	0.251430	0.125715	+	0.992066i	$0.459878\pi$
$200$	−4.37626	−0.309448
$201$	−17.5855	−1.24039
$202$	11.6634	0.820631
$203$	−19.5619	−1.37297
$204$	−42.9440	−3.00668
$205$	−3.85837	−0.269480
$206$	13.5373	0.943186
$207$	−2.78625	−0.193658
$208$	2.94502	0.204201
$209$	5.00704	0.346344
$210$	−28.6702	−1.97843
$211$	21.5730	1.48515	0.742573	−	0.669765i	$-0.233605\pi$
$211$	21.5730	1.48515	0.742573	+	0.669765i	$0.233605\pi$
$212$	37.1641	2.55244
$213$	27.8767	1.91008
$214$	−35.7890	−2.44648
$215$	10.8492	0.739912
$216$	57.3462	3.90192
$217$	−3.38722	−0.229940
$218$	26.9202	1.82326
$219$	−3.18109	−0.214958
$220$	3.81483	0.257196
$221$	3.56513	0.239816
$222$	70.8509	4.75520
$223$	−11.2708	−0.754751	−0.377375	−	0.926060i	$-0.623173\pi$
$223$	−11.2708	−0.754751	−0.377375	+	0.926060i	$0.623173\pi$
$224$	−6.36663	−0.425388
$225$	7.11932	0.474622
$226$	2.02191	0.134495
$227$	26.1049	1.73265	0.866323	−	0.499484i	$-0.166477\pi$
$227$	26.1049	1.73265	0.866323	+	0.499484i	$0.166477\pi$
$228$	−60.7619	−4.02406
$229$	−3.59417	−0.237509	−0.118755	−	0.992924i	$-0.537890\pi$
$229$	−3.59417	−0.237509	−0.118755	+	0.992924i	$0.537890\pi$
$230$	0.943734	0.0622280
$231$	11.8895	0.782268
$232$	−22.9049	−1.50378
$233$	30.2333	1.98065	0.990324	−	0.138774i	$-0.0443162\pi$
$233$	30.2333	1.98065	0.990324	+	0.138774i	$0.0443162\pi$
$234$	−17.2954	−1.13064
$235$	−5.91517	−0.385863
$236$	33.9612	2.21068
$237$	16.8808	1.09653
$238$	31.8938	2.06737
$239$	−6.77695	−0.438364	−0.219182	−	0.975684i	$-0.570339\pi$
$239$	−6.77695	−0.438364	−0.219182	+	0.975684i	$0.570339\pi$
$240$	−9.29910	−0.600254
$241$	15.3658	0.989797	0.494899	−	0.868951i	$-0.335205\pi$
$241$	15.3658	0.989797	0.494899	+	0.868951i	$0.335205\pi$
$242$	−2.41139	−0.155010
$243$	−25.3496	−1.62617
$244$	39.5730	2.53340
$245$	6.96922	0.445247
$246$	−29.5970	−1.88704
$247$	5.04434	0.320964
$248$	−3.96607	−0.251846
$249$	−16.8994	−1.07096
$250$	−2.41139	−0.152510
$251$	10.9549	0.691466	0.345733	−	0.938333i	$-0.387630\pi$
$251$	10.9549	0.691466	0.345733	+	0.938333i	$0.387630\pi$
$252$	−101.508	−6.39439
$253$	−0.391364	−0.0246049
$254$	42.0983	2.64148
$255$	−11.2571	−0.704948
$256$	−29.7580	−1.85987
$257$	−20.8440	−1.30021	−0.650107	−	0.759842i	$-0.725276\pi$
$257$	−20.8440	−1.30021	−0.650107	+	0.759842i	$0.725276\pi$
$258$	83.2230	5.18124
$259$	−34.5213	−2.14505
$260$	3.84325	0.238348
$261$	37.2618	2.30644
$262$	−24.0449	−1.48550
$263$	10.3355	0.637316	0.318658	−	0.947870i	$-0.396768\pi$
$263$	10.3355	0.637316	0.318658	+	0.947870i	$0.396768\pi$
$264$	13.9213	0.856795
$265$	9.74202	0.598447
$266$	45.1269	2.76691
$267$	−24.2172	−1.48207
$268$	21.0889	1.28821
$269$	5.53726	0.337613	0.168806	−	0.985649i	$-0.446009\pi$
$269$	5.53726	0.337613	0.168806	+	0.985649i	$0.446009\pi$
$270$	31.5988	1.92304
$271$	16.4191	0.997392	0.498696	−	0.866777i	$-0.333812\pi$
$271$	16.4191	0.997392	0.498696	+	0.866777i	$0.333812\pi$
$272$	10.3447	0.627238
$273$	11.9780	0.724943
$274$	−13.7624	−0.831420
$275$	1.00000	0.0603023
$276$	4.74932	0.285876
$277$	−9.72236	−0.584160	−0.292080	−	0.956394i	$-0.594347\pi$
$277$	−9.72236	−0.584160	−0.292080	+	0.956394i	$0.594347\pi$
$278$	−9.69297	−0.581346
$279$	6.45203	0.386273
$280$	16.3565	0.977485
$281$	29.3091	1.74843	0.874217	−	0.485535i	$-0.161375\pi$
$281$	29.3091	1.74843	0.874217	+	0.485535i	$0.161375\pi$
$282$	−45.3745	−2.70201
$283$	3.31945	0.197321	0.0986604	−	0.995121i	$-0.468544\pi$
$283$	3.31945	0.197321	0.0986604	+	0.995121i	$0.468544\pi$
$284$	−33.4303	−1.98373
$285$	−15.9278	−0.943483
$286$	−2.42936	−0.143651
$287$	14.4208	0.851233
$288$	12.1272	0.714605
$289$	−4.47715	−0.263362
$290$	−12.6210	−0.741129
$291$	−46.9317	−2.75118
$292$	3.81483	0.223246
$293$	18.2054	1.06357	0.531787	−	0.846878i	$-0.321521\pi$
$293$	18.2054	1.06357	0.531787	+	0.846878i	$0.321521\pi$
$294$	53.4599	3.11784
$295$	8.90242	0.518319
$296$	−40.4208	−2.34941
$297$	−13.1039	−0.760367
$298$	−9.91178	−0.574174
$299$	−0.394280	−0.0228018
$300$	−12.1353	−0.700632
$301$	−40.5495	−2.33723
$302$	49.9641	2.87511
$303$	15.3862	0.883913
$304$	14.6368	0.839478
$305$	10.3735	0.593983
$306$	−60.7517	−3.47295
$307$	10.1773	0.580849	0.290425	−	0.956898i	$-0.406203\pi$
$307$	10.1773	0.580849	0.290425	+	0.956898i	$0.406203\pi$
$308$	−14.2581	−0.812429
$309$	17.8582	1.01592
$310$	−2.18537	−0.124121
$311$	29.4742	1.67133	0.835665	−	0.549240i	$-0.185083\pi$
$311$	29.4742	1.67133	0.835665	+	0.549240i	$0.185083\pi$
$312$	14.0250	0.794009
$313$	−6.00846	−0.339618	−0.169809	−	0.985477i	$-0.554315\pi$
$313$	−6.00846	−0.339618	−0.169809	+	0.985477i	$0.554315\pi$
$314$	35.9268	2.02746
$315$	−26.6088	−1.49923
$316$	−20.2438	−1.13880
$317$	2.45441	0.137854	0.0689268	−	0.997622i	$-0.478043\pi$
$317$	2.45441	0.137854	0.0689268	+	0.997622i	$0.478043\pi$
$318$	74.7297	4.19063
$319$	5.23389	0.293042
$320$	−9.95412	−0.556452
$321$	−47.2125	−2.63514
$322$	−3.52724	−0.196566
$323$	17.7187	0.985896
$324$	77.5432	4.30796
$325$	1.00745	0.0558833
$326$	48.4903	2.68563
$327$	35.5128	1.96386
$328$	16.8852	0.932331
$329$	22.1082	1.21886
$330$	7.67086	0.422267
$331$	−21.8185	−1.19925	−0.599627	−	0.800279i	$-0.704685\pi$
$331$	−21.8185	−1.19925	−0.599627	+	0.800279i	$0.704685\pi$
$332$	20.2661	1.11225
$333$	65.7567	3.60345
$334$	−14.4153	−0.788773
$335$	5.52814	0.302035
$336$	34.7558	1.89608
$337$	1.44864	0.0789125	0.0394562	−	0.999221i	$-0.487437\pi$
$337$	1.44864	0.0789125	0.0394562	+	0.999221i	$0.487437\pi$
$338$	28.9007	1.57199
$339$	2.66728	0.144867
$340$	13.4998	0.732128
$341$	0.906270	0.0490773
$342$	−85.9583	−4.64809
$343$	0.115053	0.00621230
$344$	−47.4791	−2.55990
$345$	1.24496	0.0670266
$346$	41.0788	2.20841
$347$	6.32104	0.339331	0.169666	−	0.985502i	$-0.445731\pi$
$347$	6.32104	0.339331	0.169666	+	0.985502i	$0.445731\pi$
$348$	−63.5148	−3.40475
$349$	10.3609	0.554606	0.277303	−	0.960782i	$-0.410559\pi$
$349$	10.3609	0.554606	0.277303	+	0.960782i	$0.410559\pi$
$350$	9.01269	0.481748
$351$	−13.2016	−0.704647
$352$	1.70343	0.0907930
$353$	12.1889	0.648747	0.324374	−	0.945929i	$-0.394846\pi$
$353$	12.1889	0.648747	0.324374	+	0.945929i	$0.394846\pi$
$354$	68.2892	3.62953
$355$	−8.76327	−0.465106
$356$	29.0417	1.53921
$357$	42.0740	2.22679
$358$	−6.30545	−0.333253
$359$	−23.1284	−1.22067	−0.610336	−	0.792143i	$-0.708966\pi$
$359$	−23.1284	−1.22067	−0.610336	+	0.792143i	$0.708966\pi$
$360$	−31.1560	−1.64207
$361$	6.07043	0.319496
$362$	45.9408	2.41459
$363$	−3.18109	−0.166964
$364$	−14.3643	−0.752893
$365$	1.00000	0.0523424
$366$	79.5735	4.15937
$367$	−21.8153	−1.13875	−0.569374	−	0.822079i	$-0.692814\pi$
$367$	−21.8153	−1.13875	−0.569374	+	0.822079i	$0.692814\pi$
$368$	−1.14405	−0.0596379
$369$	−27.4690	−1.42998
$370$	−22.2725	−1.15789
$371$	−36.4112	−1.89038
$372$	−10.9979	−0.570212
$373$	14.6544	0.758775	0.379387	−	0.925238i	$-0.376135\pi$
$373$	14.6544	0.758775	0.379387	+	0.925238i	$0.376135\pi$
$374$	−8.53336	−0.441249
$375$	−3.18109	−0.164271
$376$	25.8863	1.33499
$377$	5.27288	0.271567
$378$	−118.102	−6.07450
$379$	22.8573	1.17410	0.587051	−	0.809550i	$-0.300289\pi$
$379$	22.8573	1.17410	0.587051	+	0.809550i	$0.300289\pi$
$380$	19.1010	0.979860
$381$	55.5356	2.84518
$382$	49.8027	2.54813
$383$	3.99951	0.204365	0.102183	−	0.994766i	$-0.467417\pi$
$383$	3.99951	0.204365	0.102183	+	0.994766i	$0.467417\pi$
$384$	−65.5192	−3.34351
$385$	−3.73754	−0.190483
$386$	37.2575	1.89636
$387$	77.2392	3.92629
$388$	56.2814	2.85726
$389$	−13.5828	−0.688677	−0.344339	−	0.938846i	$-0.611897\pi$
$389$	−13.5828	−0.688677	−0.344339	+	0.938846i	$0.611897\pi$
$390$	7.72801	0.391323
$391$	−1.38495	−0.0700397
$392$	−30.4991	−1.54044
$393$	−31.7198	−1.60005
$394$	42.8002	2.15624
$395$	−5.30661	−0.267005
$396$	27.1590	1.36479
$397$	−18.6172	−0.934368	−0.467184	−	0.884160i	$-0.654732\pi$
$397$	−18.6172	−0.934368	−0.467184	+	0.884160i	$0.654732\pi$
$398$	−8.55287	−0.428717
$399$	59.5309	2.98027
$400$	2.92324	0.146162
$401$	21.4575	1.07154	0.535768	−	0.844365i	$-0.320022\pi$
$401$	21.4575	1.07154	0.535768	+	0.844365i	$0.320022\pi$
$402$	42.4056	2.11500
$403$	0.913021	0.0454808
$404$	−18.4514	−0.917993
$405$	20.3268	1.01005
$406$	47.1714	2.34108
$407$	9.23637	0.457830
$408$	49.2641	2.43894
$409$	6.93930	0.343127	0.171563	−	0.985173i	$-0.445118\pi$
$409$	6.93930	0.343127	0.171563	+	0.985173i	$0.445118\pi$
$410$	9.30405	0.459494
$411$	−18.1553	−0.895534
$412$	−21.4160	−1.05509
$413$	−33.2732	−1.63726
$414$	6.71875	0.330208
$415$	5.31245	0.260778
$416$	1.71612	0.0841396
$417$	−12.7869	−0.626176
$418$	−12.0739	−0.590556
$419$	−4.60237	−0.224840	−0.112420	−	0.993661i	$-0.535860\pi$
$419$	−4.60237	−0.224840	−0.112420	+	0.993661i	$0.535860\pi$
$420$	45.3562	2.21316
$421$	−8.05668	−0.392659	−0.196329	−	0.980538i	$-0.562902\pi$
$421$	−8.05668	−0.392659	−0.196329	+	0.980538i	$0.562902\pi$
$422$	−52.0210	−2.53234
$423$	−42.1120	−2.04756
$424$	−42.6336	−2.07047
$425$	3.53876	0.171655
$426$	−67.2218	−3.25691
$427$	−38.7713	−1.87627
$428$	56.6181	2.73674
$429$	−3.20479	−0.154729
$430$	−26.1618	−1.26163
$431$	5.62186	0.270796	0.135398	−	0.990791i	$-0.456769\pi$
$431$	5.62186	0.270796	0.135398	+	0.990791i	$0.456769\pi$
$432$	−38.3060	−1.84300
$433$	−2.91109	−0.139898	−0.0699491	−	0.997551i	$-0.522284\pi$
$433$	−2.91109	−0.139898	−0.0699491	+	0.997551i	$0.522284\pi$
$434$	8.16793	0.392073
$435$	−16.6495	−0.798281
$436$	−42.5877	−2.03958
$437$	−1.95958	−0.0937392
$438$	7.67086	0.366528
$439$	−3.83236	−0.182909	−0.0914543	−	0.995809i	$-0.529152\pi$
$439$	−3.83236	−0.182909	−0.0914543	+	0.995809i	$0.529152\pi$
$440$	−4.37626	−0.208630
$441$	49.6161	2.36267
$442$	−8.59693	−0.408914
$443$	−41.4547	−1.96957	−0.984786	−	0.173771i	$-0.944405\pi$
$443$	−41.4547	−1.96957	−0.984786	+	0.173771i	$0.944405\pi$
$444$	−112.086	−5.31937
$445$	7.61286	0.360884
$446$	27.1784	1.28694
$447$	−13.0755	−0.618451
$448$	37.2040	1.75772
$449$	21.4808	1.01374	0.506872	−	0.862021i	$-0.330802\pi$
$449$	21.4808	1.01374	0.506872	+	0.862021i	$0.330802\pi$
$450$	−17.1675	−0.809284
$451$	−3.85837	−0.181683
$452$	−3.19865	−0.150452
$453$	65.9122	3.09682
$454$	−62.9493	−2.95436
$455$	−3.76539	−0.176524
$456$	69.7044	3.26421
$457$	31.2183	1.46033	0.730164	−	0.683271i	$-0.239443\pi$
$457$	31.2183	1.46033	0.730164	+	0.683271i	$0.239443\pi$
$458$	8.66695	0.404980
$459$	−46.3717	−2.16445
$460$	−1.49299	−0.0696108
$461$	11.7578	0.547616	0.273808	−	0.961784i	$-0.411717\pi$
$461$	11.7578	0.547616	0.273808	+	0.961784i	$0.411717\pi$
$462$	−28.6702	−1.33386
$463$	17.1003	0.794720	0.397360	−	0.917663i	$-0.369926\pi$
$463$	17.1003	0.794720	0.397360	+	0.917663i	$0.369926\pi$
$464$	15.2999	0.710282
$465$	−2.88293	−0.133692
$466$	−72.9044	−3.37723
$467$	−12.1055	−0.560177	−0.280089	−	0.959974i	$-0.590364\pi$
$467$	−12.1055	−0.560177	−0.280089	+	0.959974i	$0.590364\pi$
$468$	27.3613	1.26478
$469$	−20.6617	−0.954067
$470$	14.2638	0.657941
$471$	47.3942	2.18381
$472$	−38.9593	−1.79325
$473$	10.8492	0.498848
$474$	−40.7063	−1.86970
$475$	5.00704	0.229739
$476$	−50.4560	−2.31264
$477$	69.3566	3.17562
$478$	16.3419	0.747461
$479$	39.0017	1.78203	0.891017	−	0.453971i	$-0.149993\pi$
$479$	39.0017	1.78203	0.891017	+	0.453971i	$0.149993\pi$
$480$	−5.41875	−0.247331
$481$	9.30518	0.424280
$482$	−37.0530	−1.68772
$483$	−4.65311	−0.211724
$484$	3.81483	0.173401
$485$	14.7533	0.669914
$486$	61.1278	2.77281
$487$	27.7762	1.25866	0.629331	−	0.777138i	$-0.283329\pi$
$487$	27.7762	1.25866	0.629331	+	0.777138i	$0.283329\pi$
$488$	−45.3970	−2.05503
$489$	63.9680	2.89273
$490$	−16.8055	−0.759197
$491$	−12.0816	−0.545236	−0.272618	−	0.962122i	$-0.587890\pi$
$491$	−12.0816	−0.545236	−0.272618	+	0.962122i	$0.587890\pi$
$492$	46.8224	2.11092
$493$	18.5215	0.834166
$494$	−12.1639	−0.547279
$495$	7.11932	0.319990
$496$	2.64925	0.118955
$497$	32.7531	1.46918
$498$	40.7511	1.82610
$499$	21.4509	0.960276	0.480138	−	0.877193i	$-0.340587\pi$
$499$	21.4509	0.960276	0.480138	+	0.877193i	$0.340587\pi$
$500$	3.81483	0.170604
$501$	−19.0166	−0.849598
$502$	−26.4166	−1.17903
$503$	−8.21145	−0.366131	−0.183065	−	0.983101i	$-0.558602\pi$
$503$	−8.21145	−0.366131	−0.183065	+	0.983101i	$0.558602\pi$
$504$	116.447	5.18696
$505$	−4.83677	−0.215233
$506$	0.943734	0.0419541
$507$	38.1255	1.69321
$508$	−66.5995	−2.95487
$509$	−33.8208	−1.49908	−0.749541	−	0.661958i	$-0.769726\pi$
$509$	−33.8208	−1.49908	−0.749541	+	0.661958i	$0.769726\pi$
$510$	27.1454	1.20202
$511$	−3.73754	−0.165339
$512$	30.5653	1.35081
$513$	−65.6119	−2.89684
$514$	50.2632	2.21701
$515$	−5.61388	−0.247377
$516$	−131.659	−5.79595
$517$	−5.91517	−0.260149
$518$	83.2446	3.65756
$519$	54.1908	2.37871
$520$	−4.40886	−0.193341
$521$	29.3099	1.28409	0.642045	−	0.766667i	$-0.278086\pi$
$521$	29.3099	1.28409	0.642045	+	0.766667i	$0.278086\pi$
$522$	−89.8528	−3.93275
$523$	−44.5521	−1.94813	−0.974064	−	0.226274i	$-0.927346\pi$
$523$	−44.5521	−1.94813	−0.974064	+	0.226274i	$0.927346\pi$
$524$	38.0390	1.66174
$525$	11.8895	0.518898
$526$	−24.9230	−1.08670
$527$	3.20708	0.139702
$528$	−9.29910	−0.404691
$529$	−22.8468	−0.993341
$530$	−23.4919	−1.02042
$531$	63.3792	2.75042
$532$	−71.3907	−3.09518
$533$	−3.88711	−0.168369
$534$	58.3972	2.52709
$535$	14.8416	0.641658
$536$	−24.1926	−1.04496
$537$	−8.31809	−0.358952
$538$	−13.3525	−0.575668
$539$	6.96922	0.300185
$540$	−49.9892	−2.15119
$541$	19.3367	0.831352	0.415676	−	0.909513i	$-0.363545\pi$
$541$	19.3367	0.831352	0.415676	+	0.909513i	$0.363545\pi$
$542$	−39.5930	−1.70067
$543$	60.6046	2.60079
$544$	6.02803	0.258450
$545$	−11.1637	−0.478202
$546$	−28.8837	−1.23611
$547$	1.41250	0.0603940	0.0301970	−	0.999544i	$-0.490387\pi$
$547$	1.41250	0.0603940	0.0301970	+	0.999544i	$0.490387\pi$
$548$	21.7722	0.930062
$549$	73.8521	3.15193
$550$	−2.41139	−0.102822
$551$	26.2063	1.11643
$552$	−5.44829	−0.231895
$553$	19.8337	0.843414
$554$	23.4445	0.996059
$555$	−29.3817	−1.24718
$556$	15.3343	0.650318
$557$	−36.0610	−1.52795	−0.763977	−	0.645244i	$-0.776756\pi$
$557$	−36.0610	−1.52795	−0.763977	+	0.645244i	$0.776756\pi$
$558$	−15.5584	−0.658639
$559$	10.9301	0.462292
$560$	−10.9257	−0.461697
$561$	−11.2571	−0.475276
$562$	−70.6758	−2.98128
$563$	10.6282	0.447927	0.223963	−	0.974598i	$-0.428100\pi$
$563$	10.6282	0.447927	0.223963	+	0.974598i	$0.428100\pi$
$564$	71.7824	3.02258
$565$	−0.838480	−0.0352751
$566$	−8.00450	−0.336454
$567$	−75.9723	−3.19054
$568$	38.3504	1.60915
$569$	−29.2742	−1.22724	−0.613619	−	0.789603i	$-0.710287\pi$
$569$	−29.2742	−1.22724	−0.613619	+	0.789603i	$0.710287\pi$
$570$	38.4083	1.60875
$571$	27.3944	1.14642	0.573209	−	0.819409i	$-0.305698\pi$
$571$	27.3944	1.14642	0.573209	+	0.819409i	$0.305698\pi$
$572$	3.84325	0.160694
$573$	65.6993	2.74463
$574$	−34.7743	−1.45145
$575$	−0.391364	−0.0163210
$576$	−70.8666	−2.95278
$577$	23.7670	0.989431	0.494716	−	0.869055i	$-0.335272\pi$
$577$	23.7670	0.989431	0.494716	+	0.869055i	$0.335272\pi$
$578$	10.7962	0.449061
$579$	49.1497	2.04259
$580$	19.9664	0.829059
$581$	−19.8555	−0.823746
$582$	113.171	4.69108
$583$	9.74202	0.403473
$584$	−4.37626	−0.181091
$585$	7.17236	0.296541
$586$	−43.9005	−1.81351
$587$	9.63677	0.397752	0.198876	−	0.980025i	$-0.436271\pi$
$587$	9.63677	0.397752	0.198876	+	0.980025i	$0.436271\pi$
$588$	−84.5735	−3.48775
$589$	4.53773	0.186974
$590$	−21.4672	−0.883792
$591$	56.4616	2.32252
$592$	27.0002	1.10970
$593$	−31.8303	−1.30711	−0.653557	−	0.756878i	$-0.726724\pi$
$593$	−31.8303	−1.30711	−0.653557	+	0.756878i	$0.726724\pi$
$594$	31.5988	1.29651
$595$	−13.2263	−0.542225
$596$	15.6804	0.642296
$597$	−11.2829	−0.461777
$598$	0.950764	0.0388796
$599$	−1.04975	−0.0428915	−0.0214457	−	0.999770i	$-0.506827\pi$
$599$	−1.04975	−0.0428915	−0.0214457	+	0.999770i	$0.506827\pi$
$600$	13.9213	0.568334
$601$	33.2189	1.35503	0.677513	−	0.735511i	$-0.263058\pi$
$601$	33.2189	1.35503	0.677513	+	0.735511i	$0.263058\pi$
$602$	97.7808	3.98525
$603$	39.3566	1.60273
$604$	−79.0432	−3.21622
$605$	1.00000	0.0406558
$606$	−37.1022	−1.50717
$607$	−6.82799	−0.277140	−0.138570	−	0.990353i	$-0.544251\pi$
$607$	−6.82799	−0.277140	−0.138570	+	0.990353i	$0.544251\pi$
$608$	8.52912	0.345902
$609$	62.2281	2.52161
$610$	−25.0145	−1.01281
$611$	−5.95924	−0.241085
$612$	96.1092	3.88499
$613$	−36.1779	−1.46121	−0.730606	−	0.682800i	$-0.760762\pi$
$613$	−36.1779	−1.46121	−0.730606	+	0.682800i	$0.760762\pi$
$614$	−24.5415	−0.990414
$615$	12.2738	0.494928
$616$	16.3565	0.659021
$617$	−8.30213	−0.334231	−0.167116	−	0.985937i	$-0.553445\pi$
$617$	−8.30213	−0.334231	−0.167116	+	0.985937i	$0.553445\pi$
$618$	−43.0633	−1.73226
$619$	−33.2151	−1.33503	−0.667514	−	0.744598i	$-0.732641\pi$
$619$	−33.2151	−1.33503	−0.667514	+	0.744598i	$0.732641\pi$
$620$	3.45726	0.138847
$621$	5.12841	0.205796
$622$	−71.0740	−2.84981
$623$	−28.4534	−1.13996
$624$	−9.36838	−0.375035
$625$	1.00000	0.0400000
$626$	14.4888	0.579088
$627$	−15.9278	−0.636096
$628$	−56.8361	−2.26801
$629$	32.6853	1.30325
$630$	64.1643	2.55637
$631$	−29.6197	−1.17914	−0.589572	−	0.807716i	$-0.700703\pi$
$631$	−29.6197	−1.17914	−0.589572	+	0.807716i	$0.700703\pi$
$632$	23.2231	0.923767
$633$	−68.6256	−2.72762
$634$	−5.91856	−0.235056
$635$	−17.4581	−0.692802
$636$	−118.222	−4.68782
$637$	7.02114	0.278188
$638$	−12.6210	−0.499669
$639$	−62.3885	−2.46805
$640$	20.5965	0.814147
$641$	5.15751	0.203710	0.101855	−	0.994799i	$-0.467522\pi$
$641$	5.15751	0.203710	0.101855	+	0.994799i	$0.467522\pi$
$642$	113.848	4.49322
$643$	5.44285	0.214645	0.107323	−	0.994224i	$-0.465772\pi$
$643$	5.44285	0.214645	0.107323	+	0.994224i	$0.465772\pi$
$644$	5.58010	0.219887
$645$	−34.5124	−1.35892
$646$	−42.7269	−1.68107
$647$	−27.8285	−1.09405	−0.547026	−	0.837116i	$-0.684240\pi$
$647$	−27.8285	−1.09405	−0.547026	+	0.837116i	$0.684240\pi$
$648$	−88.9554	−3.49450
$649$	8.90242	0.349450
$650$	−2.42936	−0.0952873
$651$	10.7751	0.422308
$652$	−76.7117	−3.00426
$653$	36.1732	1.41557	0.707784	−	0.706429i	$-0.249695\pi$
$653$	36.1732	1.41557	0.707784	+	0.706429i	$0.249695\pi$
$654$	−85.6355	−3.34861
$655$	9.97137	0.389614
$656$	−11.2789	−0.440369
$657$	7.11932	0.277751
$658$	−53.3116	−2.07830
$659$	−42.9499	−1.67309	−0.836546	−	0.547897i	$-0.815429\pi$
$659$	−42.9499	−1.67309	−0.836546	+	0.547897i	$0.815429\pi$
$660$	−12.1353	−0.472366
$661$	10.6102	0.412687	0.206344	−	0.978480i	$-0.433843\pi$
$661$	10.6102	0.412687	0.206344	+	0.978480i	$0.433843\pi$
$662$	52.6131	2.04487
$663$	−11.3410	−0.440447
$664$	−23.2487	−0.902224
$665$	−18.7140	−0.725698
$666$	−158.565	−6.14429
$667$	−2.04836	−0.0793127
$668$	22.8051	0.882355
$669$	35.8535	1.38618
$670$	−13.3305	−0.515004
$671$	10.3735	0.400463
$672$	20.2528	0.781269
$673$	−19.2915	−0.743633	−0.371817	−	0.928306i	$-0.621265\pi$
$673$	−19.2915	−0.743633	−0.371817	+	0.928306i	$0.621265\pi$
$674$	−3.49325	−0.134555
$675$	−13.1039	−0.504371
$676$	−45.7209	−1.75849
$677$	29.1030	1.11852	0.559259	−	0.828993i	$-0.311086\pi$
$677$	29.1030	1.11852	0.559259	+	0.828993i	$0.311086\pi$
$678$	−6.43186	−0.247014
$679$	−55.1412	−2.11612
$680$	−15.4866	−0.593882
$681$	−83.0422	−3.18218
$682$	−2.18537	−0.0836823
$683$	36.1708	1.38404	0.692019	−	0.721879i	$-0.256721\pi$
$683$	36.1708	1.38404	0.692019	+	0.721879i	$0.256721\pi$
$684$	135.986	5.19956
$685$	5.70726	0.218063
$686$	−0.277439	−0.0105927
$687$	11.4334	0.436210
$688$	31.7150	1.20912
$689$	9.81459	0.373906
$690$	−3.00210	−0.114288
$691$	−12.2018	−0.464178	−0.232089	−	0.972695i	$-0.574556\pi$
$691$	−12.2018	−0.464178	−0.232089	+	0.972695i	$0.574556\pi$
$692$	−64.9867	−2.47042
$693$	−26.6088	−1.01078
$694$	−15.2425	−0.578599
$695$	4.01965	0.152474
$696$	72.8624	2.76184
$697$	−13.6539	−0.517177
$698$	−24.9842	−0.945667
$699$	−96.1747	−3.63766
$700$	−14.2581	−0.538904
$701$	15.7866	0.596251	0.298125	−	0.954527i	$-0.403639\pi$
$701$	15.7866	0.596251	0.298125	+	0.954527i	$0.403639\pi$
$702$	31.8342	1.20150
$703$	46.2469	1.74423
$704$	−9.95412	−0.375160
$705$	18.8167	0.708677
$706$	−29.3921	−1.10619
$707$	18.0776	0.679879
$708$	−108.033	−4.06015
$709$	−41.8273	−1.57086	−0.785428	−	0.618953i	$-0.787557\pi$
$709$	−41.8273	−1.57086	−0.785428	+	0.618953i	$0.787557\pi$
$710$	21.1317	0.793059
$711$	−37.7795	−1.41684
$712$	−33.3159	−1.24856
$713$	−0.354682	−0.0132829
$714$	−101.457	−3.79693
$715$	1.00745	0.0376765
$716$	9.97522	0.372791
$717$	21.5581	0.805101
$718$	55.7718	2.08138
$719$	−0.866060	−0.0322986	−0.0161493	−	0.999870i	$-0.505141\pi$
$719$	−0.866060	−0.0322986	−0.0161493	+	0.999870i	$0.505141\pi$
$720$	20.8115	0.775600
$721$	20.9821	0.781414
$722$	−14.6382	−0.544778
$723$	−48.8799	−1.81786
$724$	−72.6783	−2.70107
$725$	5.23389	0.194382
$726$	7.67086	0.284692
$727$	7.80317	0.289404	0.144702	−	0.989475i	$-0.453778\pi$
$727$	7.80317	0.289404	0.144702	+	0.989475i	$0.453778\pi$
$728$	16.4783	0.610727
$729$	19.6588	0.728103
$730$	−2.41139	−0.0892497
$731$	38.3929	1.42001
$732$	−125.885	−4.65285
$733$	6.07759	0.224481	0.112240	−	0.993681i	$-0.464197\pi$
$733$	6.07759	0.224481	0.112240	+	0.993681i	$0.464197\pi$
$734$	52.6052	1.94169
$735$	−22.1697	−0.817742
$736$	−0.666660	−0.0245734
$737$	5.52814	0.203632
$738$	66.2385	2.43827
$739$	−19.8288	−0.729414	−0.364707	−	0.931122i	$-0.618831\pi$
$739$	−19.8288	−0.729414	−0.364707	+	0.931122i	$0.618831\pi$
$740$	35.2352	1.29527
$741$	−16.0465	−0.589483
$742$	87.8018	3.22330
$743$	21.2868	0.780936	0.390468	−	0.920617i	$-0.372313\pi$
$743$	21.2868	0.780936	0.390468	+	0.920617i	$0.372313\pi$
$744$	12.6164	0.462541
$745$	4.11039	0.150593
$746$	−35.3375	−1.29380
$747$	37.8211	1.38380
$748$	13.4998	0.493600
$749$	−55.4711	−2.02687
$750$	7.67086	0.280100
$751$	50.8748	1.85645	0.928223	−	0.372024i	$-0.121336\pi$
$751$	50.8748	1.85645	0.928223	+	0.372024i	$0.121336\pi$
$752$	−17.2915	−0.630556
$753$	−34.8485	−1.26995
$754$	−12.7150	−0.463053
$755$	−20.7200	−0.754078
$756$	186.837	6.79519
$757$	28.2930	1.02833	0.514163	−	0.857693i	$-0.328103\pi$
$757$	28.2930	1.02833	0.514163	+	0.857693i	$0.328103\pi$
$758$	−55.1181	−2.00198
$759$	1.24496	0.0451893
$760$	−21.9121	−0.794836
$761$	18.3474	0.665094	0.332547	−	0.943087i	$-0.392092\pi$
$761$	18.3474	0.665094	0.332547	+	0.943087i	$0.392092\pi$
$762$	−133.918	−4.85135
$763$	41.7249	1.51054
$764$	−78.7879	−2.85045
$765$	25.1936	0.910877
$766$	−9.64439	−0.348466
$767$	8.96874	0.323842
$768$	94.6628	3.41585
$769$	−41.5561	−1.49855	−0.749275	−	0.662259i	$-0.769598\pi$
$769$	−41.5561	−1.49855	−0.749275	+	0.662259i	$0.769598\pi$
$770$	9.01269	0.324795
$771$	66.3067	2.38798
$772$	−58.9414	−2.12135
$773$	9.25444	0.332859	0.166430	−	0.986053i	$-0.446776\pi$
$773$	9.25444	0.332859	0.166430	+	0.986053i	$0.446776\pi$
$774$	−186.254	−6.69477
$775$	0.906270	0.0325542
$776$	−64.5645	−2.31773
$777$	109.815	3.93961
$778$	32.7536	1.17427
$779$	−19.3190	−0.692175
$780$	−12.2257	−0.437750
$781$	−8.76327	−0.313574
$782$	3.33965	0.119426
$783$	−68.5845	−2.45101
$784$	20.3727	0.727597
$785$	−14.8987	−0.531759
$786$	76.4890	2.72827
$787$	29.6165	1.05572	0.527858	−	0.849333i	$-0.322996\pi$
$787$	29.6165	1.05572	0.527858	+	0.849333i	$0.322996\pi$
$788$	−67.7099	−2.41207
$789$	−32.8782	−1.17050
$790$	12.7963	0.455273
$791$	3.13385	0.111427
$792$	−31.1560	−1.10708
$793$	10.4508	0.371117
$794$	44.8933	1.59320
$795$	−30.9902	−1.09911
$796$	13.5306	0.479581
$797$	15.2819	0.541313	0.270656	−	0.962676i	$-0.412759\pi$
$797$	15.2819	0.541313	0.270656	+	0.962676i	$0.412759\pi$
$798$	−143.553	−5.08171
$799$	−20.9324	−0.740535
$800$	1.70343	0.0602252
$801$	54.1984	1.91501
$802$	−51.7425	−1.82709
$803$	1.00000	0.0352892
$804$	−67.0857	−2.36593
$805$	1.46274	0.0515548
$806$	−2.20166	−0.0775500
$807$	−17.6145	−0.620060
$808$	21.1670	0.744651
$809$	−17.1012	−0.601246	−0.300623	−	0.953743i	$-0.597195\pi$
$809$	−17.1012	−0.601246	−0.300623	+	0.953743i	$0.597195\pi$
$810$	−49.0160	−1.72224
$811$	15.3172	0.537860	0.268930	−	0.963160i	$-0.413330\pi$
$811$	15.3172	0.537860	0.268930	+	0.963160i	$0.413330\pi$
$812$	−74.6252	−2.61883
$813$	−52.2307	−1.83181
$814$	−22.2725	−0.780652
$815$	−20.1088	−0.704382
$816$	−32.9073	−1.15199
$817$	54.3225	1.90050
$818$	−16.7334	−0.585070
$819$	−26.8070	−0.936712
$820$	−14.7190	−0.514010
$821$	−1.62592	−0.0567449	−0.0283725	−	0.999597i	$-0.509032\pi$
$821$	−1.62592	−0.0567449	−0.0283725	+	0.999597i	$0.509032\pi$
$822$	43.7796	1.52699
$823$	−53.2751	−1.85705	−0.928526	−	0.371268i	$-0.878923\pi$
$823$	−53.2751	−1.85705	−0.928526	+	0.371268i	$0.878923\pi$
$824$	24.5678	0.855860
$825$	−3.18109	−0.110751
$826$	80.2347	2.79172
$827$	25.4849	0.886195	0.443098	−	0.896473i	$-0.353879\pi$
$827$	25.4849	0.886195	0.443098	+	0.896473i	$0.353879\pi$
$828$	−10.6291	−0.369385
$829$	−23.2328	−0.806908	−0.403454	−	0.915000i	$-0.632190\pi$
$829$	−23.2328	−0.806908	−0.403454	+	0.915000i	$0.632190\pi$
$830$	−12.8104	−0.444656
$831$	30.9277	1.07287
$832$	−10.0283	−0.347668
$833$	24.6624	0.854502
$834$	30.8342	1.06770
$835$	5.97801	0.206878
$836$	19.1010	0.660621
$837$	−11.8757	−0.410484
$838$	11.0981	0.383379
$839$	−13.3284	−0.460147	−0.230073	−	0.973173i	$-0.573897\pi$
$839$	−13.3284	−0.460147	−0.230073	+	0.973173i	$0.573897\pi$
$840$	−52.0313	−1.79525
$841$	−1.60641	−0.0553934
$842$	19.4278	0.669528
$843$	−93.2348	−3.21118
$844$	82.2972	2.83279
$845$	−11.9850	−0.412298
$846$	101.549	3.49132
$847$	−3.73754	−0.128423
$848$	28.4783	0.977949
$849$	−10.5595	−0.362400
$850$	−8.53336	−0.292692
$851$	−3.61479	−0.123913
$852$	106.345	3.64332
$853$	42.5793	1.45789	0.728944	−	0.684573i	$-0.240011\pi$
$853$	42.5793	1.45789	0.728944	+	0.684573i	$0.240011\pi$
$854$	93.4929	3.19926
$855$	35.6467	1.21909
$856$	−64.9507	−2.21997
$857$	−7.05880	−0.241124	−0.120562	−	0.992706i	$-0.538470\pi$
$857$	−7.05880	−0.241124	−0.120562	+	0.992706i	$0.538470\pi$
$858$	7.72801	0.263830
$859$	40.3688	1.37737	0.688683	−	0.725063i	$-0.258189\pi$
$859$	40.3688	1.37737	0.688683	+	0.725063i	$0.258189\pi$
$860$	41.3879	1.41132
$861$	−45.8739	−1.56338
$862$	−13.5565	−0.461737
$863$	−54.9782	−1.87148	−0.935741	−	0.352689i	$-0.885267\pi$
$863$	−54.9782	−1.87148	−0.935741	+	0.352689i	$0.885267\pi$
$864$	−22.3216	−0.759396
$865$	−17.0353	−0.579218
$866$	7.01980	0.238542
$867$	14.2422	0.483690
$868$	−12.9217	−0.438590
$869$	−5.30661	−0.180015
$870$	40.1484	1.36116
$871$	5.56933	0.188709
$872$	48.8554	1.65445
$873$	105.034	3.55485
$874$	4.72531	0.159836
$875$	−3.73754	−0.126352
$876$	−12.1353	−0.410014
$877$	−13.3797	−0.451799	−0.225900	−	0.974151i	$-0.572532\pi$
$877$	−13.3797	−0.451799	−0.225900	+	0.974151i	$0.572532\pi$
$878$	9.24134	0.311880
$879$	−57.9131	−1.95336
$880$	2.92324	0.0985425
$881$	−22.2446	−0.749438	−0.374719	−	0.927138i	$-0.622261\pi$
$881$	−22.2446	−0.749438	−0.374719	+	0.927138i	$0.622261\pi$
$882$	−119.644	−4.02862
$883$	−29.0128	−0.976359	−0.488180	−	0.872743i	$-0.662339\pi$
$883$	−29.0128	−0.976359	−0.488180	+	0.872743i	$0.662339\pi$
$884$	13.6003	0.457429
$885$	−28.3194	−0.951945
$886$	99.9636	3.35834
$887$	54.2574	1.82178	0.910892	−	0.412644i	$-0.135395\pi$
$887$	54.2574	1.82178	0.910892	+	0.412644i	$0.135395\pi$
$888$	128.582	4.31493
$889$	65.2502	2.18842
$890$	−18.3576	−0.615348
$891$	20.3268	0.680974
$892$	−42.9963	−1.43962
$893$	−29.6175	−0.991112
$894$	31.5303	1.05453
$895$	2.61486	0.0874050
$896$	−76.9802	−2.57173
$897$	1.25424	0.0418778
$898$	−51.7988	−1.72855
$899$	4.74332	0.158198
$900$	27.1590	0.905299
$901$	34.4747	1.14852
$902$	9.30405	0.309791
$903$	128.991	4.29257
$904$	3.66941	0.122043
$905$	−19.0515	−0.633295
$906$	−158.940	−5.28044
$907$	−6.44343	−0.213951	−0.106975	−	0.994262i	$-0.534117\pi$
$907$	−6.44343	−0.213951	−0.106975	+	0.994262i	$0.534117\pi$
$908$	99.5858	3.30487
$909$	−34.4345	−1.14212
$910$	9.07983	0.300993
$911$	17.1200	0.567213	0.283606	−	0.958941i	$-0.408469\pi$
$911$	17.1200	0.567213	0.283606	+	0.958941i	$0.408469\pi$
$912$	−46.5609	−1.54179
$913$	5.31245	0.175817
$914$	−75.2796	−2.49003
$915$	−32.9989	−1.09091
$916$	−13.7111	−0.453028
$917$	−37.2684	−1.23071
$918$	111.821	3.69063
$919$	40.2048	1.32623	0.663117	−	0.748516i	$-0.269233\pi$
$919$	40.2048	1.32623	0.663117	+	0.748516i	$0.269233\pi$
$920$	1.71271	0.0564665
$921$	−32.3749	−1.06679
$922$	−28.3527	−0.933747
$923$	−8.82855	−0.290595
$924$	45.3562	1.49211
$925$	9.23637	0.303690
$926$	−41.2357	−1.35509
$927$	−39.9670	−1.31269
$928$	8.91555	0.292667
$929$	−11.7905	−0.386835	−0.193418	−	0.981117i	$-0.561957\pi$
$929$	−11.7905	−0.386835	−0.193418	+	0.981117i	$0.561957\pi$
$930$	6.95187	0.227961
$931$	34.8951	1.14364
$932$	115.335	3.77791
$933$	−93.7601	−3.06957
$934$	29.1912	0.955166
$935$	3.53876	0.115730
$936$	−31.3881	−1.02595
$937$	9.31105	0.304179	0.152089	−	0.988367i	$-0.451400\pi$
$937$	9.31105	0.304179	0.152089	+	0.988367i	$0.451400\pi$
$938$	49.8234	1.62679
$939$	19.1134	0.623744
$940$	−22.5654	−0.736001
$941$	5.53201	0.180338	0.0901692	−	0.995926i	$-0.471259\pi$
$941$	5.53201	0.180338	0.0901692	+	0.995926i	$0.471259\pi$
$942$	−114.286	−3.72365
$943$	1.51003	0.0491732
$944$	26.0239	0.847007
$945$	48.9765	1.59321
$946$	−26.1618	−0.850593
$947$	14.4653	0.470058	0.235029	−	0.971988i	$-0.424482\pi$
$947$	14.4653	0.470058	0.235029	+	0.971988i	$0.424482\pi$
$948$	64.3973	2.09153
$949$	1.00745	0.0327032
$950$	−12.0739	−0.391731
$951$	−7.80770	−0.253182
$952$	57.8817	1.87596
$953$	−23.6932	−0.767497	−0.383749	−	0.923438i	$-0.625367\pi$
$953$	−23.6932	−0.767497	−0.383749	+	0.923438i	$0.625367\pi$
$954$	−167.246	−5.41479
$955$	−20.6531	−0.668318
$956$	−25.8529	−0.836142
$957$	−16.6495	−0.538201
$958$	−94.0485	−3.03857
$959$	−21.3311	−0.688817
$960$	31.6649	1.02198
$961$	−30.1787	−0.973506
$962$	−22.4385	−0.723445
$963$	105.662	3.40492
$964$	58.6178	1.88795
$965$	−15.4506	−0.497372
$966$	11.2205	0.361013
$967$	−22.9106	−0.736754	−0.368377	−	0.929677i	$-0.620086\pi$
$967$	−22.9106	−0.736754	−0.368377	+	0.929677i	$0.620086\pi$
$968$	−4.37626	−0.140658
$969$	−56.3648	−1.81070
$970$	−35.5761	−1.14228
$971$	−26.5866	−0.853205	−0.426603	−	0.904439i	$-0.640290\pi$
$971$	−26.5866	−0.853205	−0.426603	+	0.904439i	$0.640290\pi$
$972$	−96.7041	−3.10179
$973$	−15.0236	−0.481635
$974$	−66.9795	−2.14616
$975$	−3.20479	−0.102635
$976$	30.3242	0.970654
$977$	45.8303	1.46624	0.733120	−	0.680099i	$-0.238063\pi$
$977$	45.8303	1.46624	0.733120	+	0.680099i	$0.238063\pi$
$978$	−154.252	−4.93244
$979$	7.61286	0.243308
$980$	26.5863	0.849270
$981$	−79.4783	−2.53755
$982$	29.1336	0.929690
$983$	−36.5768	−1.16662	−0.583310	−	0.812250i	$-0.698243\pi$
$983$	−36.5768	−1.16662	−0.583310	+	0.812250i	$0.698243\pi$
$984$	−53.7134	−1.71232
$985$	−17.7491	−0.565535
$986$	−44.6627	−1.42235
$987$	−70.3282	−2.23857
$988$	19.2433	0.612210
$989$	−4.24600	−0.135015
$990$	−17.1675	−0.545619
$991$	18.2871	0.580907	0.290454	−	0.956889i	$-0.406194\pi$
$991$	18.2871	0.580907	0.290454	+	0.956889i	$0.406194\pi$
$992$	1.54376	0.0490146
$993$	69.4067	2.20255
$994$	−78.9806	−2.50511
$995$	3.54686	0.112443
$996$	−64.4682	−2.04275
$997$	11.9290	0.377795	0.188898	−	0.981997i	$-0.439509\pi$
$997$	11.9290	0.377795	0.188898	+	0.981997i	$0.439509\pi$
$998$	−51.7267	−1.63738
$999$	−121.033	−3.82931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.4	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.4	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41139 q^{2} -3.18109 q^{3} +3.81483 q^{4} +1.00000 q^{5} +7.67086 q^{6} -3.73754 q^{7} -4.37626 q^{8} +7.11932 q^{9} +O(q^{10})\)	\(q-2.41139 q^{2} -3.18109 q^{3} +3.81483 q^{4} +1.00000 q^{5} +7.67086 q^{6} -3.73754 q^{7} -4.37626 q^{8} +7.11932 q^{9} -2.41139 q^{10} +1.00000 q^{11} -12.1353 q^{12} +1.00745 q^{13} +9.01269 q^{14} -3.18109 q^{15} +2.92324 q^{16} +3.53876 q^{17} -17.1675 q^{18} +5.00704 q^{19} +3.81483 q^{20} +11.8895 q^{21} -2.41139 q^{22} -0.391364 q^{23} +13.9213 q^{24} +1.00000 q^{25} -2.42936 q^{26} -13.1039 q^{27} -14.2581 q^{28} +5.23389 q^{29} +7.67086 q^{30} +0.906270 q^{31} +1.70343 q^{32} -3.18109 q^{33} -8.53336 q^{34} -3.73754 q^{35} +27.1590 q^{36} +9.23637 q^{37} -12.0739 q^{38} -3.20479 q^{39} -4.37626 q^{40} -3.85837 q^{41} -28.6702 q^{42} +10.8492 q^{43} +3.81483 q^{44} +7.11932 q^{45} +0.943734 q^{46} -5.91517 q^{47} -9.29910 q^{48} +6.96922 q^{49} -2.41139 q^{50} -11.2571 q^{51} +3.84325 q^{52} +9.74202 q^{53} +31.5988 q^{54} +1.00000 q^{55} +16.3565 q^{56} -15.9278 q^{57} -12.6210 q^{58} +8.90242 q^{59} -12.1353 q^{60} +10.3735 q^{61} -2.18537 q^{62} -26.6088 q^{63} -9.95412 q^{64} +1.00745 q^{65} +7.67086 q^{66} +5.52814 q^{67} +13.4998 q^{68} +1.24496 q^{69} +9.01269 q^{70} -8.76327 q^{71} -31.1560 q^{72} +1.00000 q^{73} -22.2725 q^{74} -3.18109 q^{75} +19.1010 q^{76} -3.73754 q^{77} +7.72801 q^{78} -5.30661 q^{79} +2.92324 q^{80} +20.3268 q^{81} +9.30405 q^{82} +5.31245 q^{83} +45.3562 q^{84} +3.53876 q^{85} -26.1618 q^{86} -16.6495 q^{87} -4.37626 q^{88} +7.61286 q^{89} -17.1675 q^{90} -3.76539 q^{91} -1.49299 q^{92} -2.88293 q^{93} +14.2638 q^{94} +5.00704 q^{95} -5.41875 q^{96} +14.7533 q^{97} -16.8055 q^{98} +7.11932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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