LMFDB - Embedded newform 619.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +O(q^{10})$	\(q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +2.09786 q^{10} +6.08342 q^{11} -3.33328 q^{12} -6.72402 q^{13} -7.44689 q^{14} +1.82383 q^{15} -4.12905 q^{16} -5.23542 q^{17} +0.0539073 q^{18} -0.354999 q^{19} -2.04497 q^{20} -6.47416 q^{21} -12.0649 q^{22} +6.00028 q^{23} -0.228263 q^{24} -3.88108 q^{25} +13.3354 q^{26} +5.21942 q^{27} +7.25916 q^{28} +6.90103 q^{29} -3.61709 q^{30} -5.33395 q^{31} +7.92413 q^{32} -10.4889 q^{33} +10.3831 q^{34} -3.97191 q^{35} -0.0525484 q^{36} +5.05059 q^{37} +0.704048 q^{38} +11.5935 q^{39} -0.140040 q^{40} +9.63715 q^{41} +12.8398 q^{42} -0.0907075 q^{43} +11.7607 q^{44} +0.0287523 q^{45} -11.9000 q^{46} -4.97845 q^{47} +7.11925 q^{48} +7.09934 q^{49} +7.69711 q^{50} +9.02684 q^{51} -12.9992 q^{52} -6.61252 q^{53} -10.3514 q^{54} -6.43498 q^{55} +0.497107 q^{56} +0.612084 q^{57} -13.6864 q^{58} +6.12048 q^{59} +3.52591 q^{60} +1.72186 q^{61} +10.5785 q^{62} -0.102064 q^{63} -7.45736 q^{64} +7.11261 q^{65} +20.8021 q^{66} +11.6947 q^{67} -10.1214 q^{68} -10.3456 q^{69} +7.87726 q^{70} +10.5001 q^{71} -0.00359851 q^{72} -5.79254 q^{73} -10.0165 q^{74} +6.69170 q^{75} -0.686300 q^{76} +22.8427 q^{77} -22.9926 q^{78} +12.9226 q^{79} +4.36768 q^{80} -8.91772 q^{81} -19.1128 q^{82} +0.184214 q^{83} -12.5162 q^{84} +5.53798 q^{85} +0.179895 q^{86} -11.8987 q^{87} +0.805375 q^{88} -7.11052 q^{89} -0.0570227 q^{90} -25.2481 q^{91} +11.6000 q^{92} +9.19672 q^{93} +9.87346 q^{94} +0.375514 q^{95} -13.6627 q^{96} +13.5999 q^{97} -14.0797 q^{98} -0.165356 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.98324	−1.40236	−0.701182	−	0.712983i	$-0.747344\pi$
$2$	−1.98324	−1.40236	−0.701182	+	0.712983i	$0.747344\pi$
$3$	−1.72419	−0.995459	−0.497730	−	0.867332i	$-0.665833\pi$
$3$	−1.72419	−0.995459	−0.497730	+	0.867332i	$0.665833\pi$
$4$	1.93325	0.966623
$5$	−1.05779	−0.473059	−0.236529	−	0.971624i	$-0.576010\pi$
$5$	−1.05779	−0.473059	−0.236529	+	0.971624i	$0.576010\pi$
$6$	3.41948	1.39600
$7$	3.75491	1.41922	0.709611	−	0.704594i	$-0.248871\pi$
$7$	3.75491	1.41922	0.709611	+	0.704594i	$0.248871\pi$
$8$	0.132389	0.0468064
$9$	−0.0271814	−0.00906047
$10$	2.09786	0.663400
$11$	6.08342	1.83422	0.917109	−	0.398636i	$-0.130516\pi$
$11$	6.08342	1.83422	0.917109	+	0.398636i	$0.130516\pi$
$12$	−3.33328	−0.962234
$13$	−6.72402	−1.86491	−0.932454	−	0.361288i	$-0.882337\pi$
$13$	−6.72402	−1.86491	−0.932454	+	0.361288i	$0.882337\pi$
$14$	−7.44689	−1.99027
$15$	1.82383	0.470911
$16$	−4.12905	−1.03226
$17$	−5.23542	−1.26978	−0.634888	−	0.772604i	$-0.718954\pi$
$17$	−5.23542	−1.26978	−0.634888	+	0.772604i	$0.718954\pi$
$18$	0.0539073	0.0127061
$19$	−0.354999	−0.0814423	−0.0407211	−	0.999171i	$-0.512966\pi$
$19$	−0.354999	−0.0814423	−0.0407211	+	0.999171i	$0.512966\pi$
$20$	−2.04497	−0.457270
$21$	−6.47416	−1.41278
$22$	−12.0649	−2.57224
$23$	6.00028	1.25115	0.625573	−	0.780166i	$-0.284865\pi$
$23$	6.00028	1.25115	0.625573	+	0.780166i	$0.284865\pi$
$24$	−0.228263	−0.0465939
$25$	−3.88108	−0.776215
$26$	13.3354	2.61528
$27$	5.21942	1.00448
$28$	7.25916	1.37185
$29$	6.90103	1.28149	0.640745	−	0.767754i	$-0.278626\pi$
$29$	6.90103	1.28149	0.640745	+	0.767754i	$0.278626\pi$
$30$	−3.61709	−0.660388
$31$	−5.33395	−0.958005	−0.479003	−	0.877814i	$-0.659002\pi$
$31$	−5.33395	−0.958005	−0.479003	+	0.877814i	$0.659002\pi$
$32$	7.92413	1.40080
$33$	−10.4889	−1.82589
$34$	10.3831	1.78069
$35$	−3.97191	−0.671375
$36$	−0.0525484	−0.00875806
$37$	5.05059	0.830311	0.415156	−	0.909750i	$-0.363727\pi$
$37$	5.05059	0.830311	0.415156	+	0.909750i	$0.363727\pi$
$38$	0.704048	0.114212
$39$	11.5935	1.85644
$40$	−0.140040	−0.0221422
$41$	9.63715	1.50507	0.752535	−	0.658552i	$-0.228831\pi$
$41$	9.63715	1.50507	0.752535	+	0.658552i	$0.228831\pi$
$42$	12.8398	1.98123
$43$	−0.0907075	−0.0138328	−0.00691638	−	0.999976i	$-0.502202\pi$
$43$	−0.0907075	−0.0138328	−0.00691638	+	0.999976i	$0.502202\pi$
$44$	11.7607	1.77300
$45$	0.0287523	0.00428614
$46$	−11.9000	−1.75456
$47$	−4.97845	−0.726181	−0.363091	−	0.931754i	$-0.618278\pi$
$47$	−4.97845	−0.726181	−0.363091	+	0.931754i	$0.618278\pi$
$48$	7.11925	1.02758
$49$	7.09934	1.01419
$50$	7.69711	1.08854
$51$	9.02684	1.26401
$52$	−12.9992	−1.80266
$53$	−6.61252	−0.908300	−0.454150	−	0.890925i	$-0.650057\pi$
$53$	−6.61252	−0.908300	−0.454150	+	0.890925i	$0.650057\pi$
$54$	−10.3514	−1.40864
$55$	−6.43498	−0.867693
$56$	0.497107	0.0664287
$57$	0.612084	0.0810725
$58$	−13.6864	−1.79711
$59$	6.12048	0.796819	0.398409	−	0.917208i	$-0.369562\pi$
$59$	6.12048	0.796819	0.398409	+	0.917208i	$0.369562\pi$
$60$	3.52591	0.455193
$61$	1.72186	0.220462	0.110231	−	0.993906i	$-0.464841\pi$
$61$	1.72186	0.220462	0.110231	+	0.993906i	$0.464841\pi$
$62$	10.5785	1.34347
$63$	−0.102064	−0.0128588
$64$	−7.45736	−0.932170
$65$	7.11261	0.882211
$66$	20.8021	2.56056
$67$	11.6947	1.42873	0.714367	−	0.699771i	$-0.246715\pi$
$67$	11.6947	1.42873	0.714367	+	0.699771i	$0.246715\pi$
$68$	−10.1214	−1.22739
$69$	−10.3456	−1.24546
$70$	7.87726	0.941512
$71$	10.5001	1.24613	0.623066	−	0.782169i	$-0.285887\pi$
$71$	10.5001	1.24613	0.623066	+	0.782169i	$0.285887\pi$
$72$	−0.00359851	−0.000424089 0
$73$	−5.79254	−0.677965	−0.338983	−	0.940793i	$-0.610083\pi$
$73$	−5.79254	−0.677965	−0.338983	+	0.940793i	$0.610083\pi$
$74$	−10.0165	−1.16440
$75$	6.69170	0.772691
$76$	−0.686300	−0.0787240
$77$	22.8427	2.60316
$78$	−22.9926	−2.60340
$79$	12.9226	1.45391	0.726953	−	0.686687i	$-0.240936\pi$
$79$	12.9226	1.45391	0.726953	+	0.686687i	$0.240936\pi$
$80$	4.36768	0.488321
$81$	−8.91772	−0.990857
$82$	−19.1128	−2.11065
$83$	0.184214	0.0202201	0.0101101	−	0.999949i	$-0.496782\pi$
$83$	0.184214	0.0202201	0.0101101	+	0.999949i	$0.496782\pi$
$84$	−12.5162	−1.36562
$85$	5.53798	0.600678
$86$	0.179895	0.0193986
$87$	−11.8987	−1.27567
$88$	0.805375	0.0858533
$89$	−7.11052	−0.753714	−0.376857	−	0.926271i	$-0.622995\pi$
$89$	−7.11052	−0.753714	−0.376857	+	0.926271i	$0.622995\pi$
$90$	−0.0570227	−0.00601072
$91$	−25.2481	−2.64672
$92$	11.6000	1.20939
$93$	9.19672	0.953655
$94$	9.87346	1.01837
$95$	0.375514	0.0385270
$96$	−13.6627	−1.39444
$97$	13.5999	1.38086	0.690432	−	0.723398i	$-0.257421\pi$
$97$	13.5999	1.38086	0.690432	+	0.723398i	$0.257421\pi$
$98$	−14.0797	−1.42227
$99$	−0.165356	−0.0166189
$100$	−7.50308	−0.750308
$101$	13.8730	1.38041	0.690206	−	0.723613i	$-0.257520\pi$
$101$	13.8730	1.38041	0.690206	+	0.723613i	$0.257520\pi$
$102$	−17.9024	−1.77260
$103$	5.85475	0.576886	0.288443	−	0.957497i	$-0.406862\pi$
$103$	5.85475	0.576886	0.288443	+	0.957497i	$0.406862\pi$
$104$	−0.890184	−0.0872897
$105$	6.84831	0.668327
$106$	13.1142	1.27377
$107$	9.98693	0.965473	0.482737	−	0.875766i	$-0.339643\pi$
$107$	9.98693	0.965473	0.482737	+	0.875766i	$0.339643\pi$
$108$	10.0904	0.970952
$109$	−4.85404	−0.464933	−0.232466	−	0.972604i	$-0.574680\pi$
$109$	−4.85404	−0.464933	−0.232466	+	0.972604i	$0.574680\pi$
$110$	12.7621	1.21682
$111$	−8.70815	−0.826541
$112$	−15.5042	−1.46501
$113$	−3.36631	−0.316675	−0.158338	−	0.987385i	$-0.550613\pi$
$113$	−3.36631	−0.316675	−0.158338	+	0.987385i	$0.550613\pi$
$114$	−1.21391	−0.113693
$115$	−6.34705	−0.591865
$116$	13.3414	1.23872
$117$	0.182769	0.0168970
$118$	−12.1384	−1.11743
$119$	−19.6585	−1.80209
$120$	0.241454	0.0220417
$121$	26.0079	2.36436
$122$	−3.41486	−0.309167
$123$	−16.6162	−1.49824
$124$	−10.3118	−0.926030
$125$	9.39433	0.840254
$126$	0.202417	0.0180327
$127$	−7.17138	−0.636357	−0.318179	−	0.948031i	$-0.603071\pi$
$127$	−7.17138	−0.636357	−0.318179	+	0.948031i	$0.603071\pi$
$128$	−1.05852	−0.0935608
$129$	0.156397	0.0137700
$130$	−14.1060	−1.23718
$131$	−8.12631	−0.709999	−0.354999	−	0.934867i	$-0.615519\pi$
$131$	−8.12631	−0.709999	−0.354999	+	0.934867i	$0.615519\pi$
$132$	−20.2777	−1.76495
$133$	−1.33299	−0.115585
$134$	−23.1934	−2.00360
$135$	−5.52106	−0.475177
$136$	−0.693110	−0.0594337
$137$	−7.70090	−0.657933	−0.328966	−	0.944342i	$-0.606700\pi$
$137$	−7.70090	−0.657933	−0.328966	+	0.944342i	$0.606700\pi$
$138$	20.5178	1.74659
$139$	10.6370	0.902221	0.451110	−	0.892468i	$-0.351028\pi$
$139$	10.6370	0.902221	0.451110	+	0.892468i	$0.351028\pi$
$140$	−7.67868	−0.648967
$141$	8.58377	0.722884
$142$	−20.8242	−1.74753
$143$	−40.9050	−3.42065
$144$	0.112233	0.00935279
$145$	−7.29985	−0.606220
$146$	11.4880	0.950754
$147$	−12.2406	−1.00959
$148$	9.76403	0.802598
$149$	1.61152	0.132021	0.0660105	−	0.997819i	$-0.478973\pi$
$149$	1.61152	0.132021	0.0660105	+	0.997819i	$0.478973\pi$
$150$	−13.2713	−1.08359
$151$	19.9654	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$151$	19.9654	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$152$	−0.0469978	−0.00381202
$153$	0.142306	0.0115048
$154$	−45.3025	−3.65058
$155$	5.64220	0.453193
$156$	22.4130	1.79448
$157$	1.54108	0.122991	0.0614956	−	0.998107i	$-0.480413\pi$
$157$	1.54108	0.122991	0.0614956	+	0.998107i	$0.480413\pi$
$158$	−25.6286	−2.03891
$159$	11.4012	0.904176
$160$	−8.38207	−0.662661
$161$	22.5305	1.77565
$162$	17.6860	1.38954
$163$	−3.56264	−0.279048	−0.139524	−	0.990219i	$-0.544557\pi$
$163$	−3.56264	−0.279048	−0.139524	+	0.990219i	$0.544557\pi$
$164$	18.6310	1.45484
$165$	11.0951	0.863753
$166$	−0.365341	−0.0283559
$167$	−1.11339	−0.0861566	−0.0430783	−	0.999072i	$-0.513716\pi$
$167$	−1.11339	−0.0861566	−0.0430783	+	0.999072i	$0.513716\pi$
$168$	−0.857106	−0.0661271
$169$	32.2125	2.47788
$170$	−10.9832	−0.842369
$171$	0.00964937	0.000737906 0
$172$	−0.175360	−0.0133711
$173$	2.42857	0.184641	0.0923203	−	0.995729i	$-0.470572\pi$
$173$	2.42857	0.184641	0.0923203	+	0.995729i	$0.470572\pi$
$174$	23.5979	1.78895
$175$	−14.5731	−1.10162
$176$	−25.1187	−1.89340
$177$	−10.5528	−0.793201
$178$	14.1019	1.05698
$179$	20.2117	1.51069	0.755346	−	0.655326i	$-0.227469\pi$
$179$	20.2117	1.51069	0.755346	+	0.655326i	$0.227469\pi$
$180$	0.0555852	0.00414308
$181$	14.7095	1.09335	0.546676	−	0.837345i	$-0.315893\pi$
$181$	14.7095	1.09335	0.546676	+	0.837345i	$0.315893\pi$
$182$	50.0731	3.71166
$183$	−2.96881	−0.219461
$184$	0.794369	0.0585617
$185$	−5.34247	−0.392786
$186$	−18.2393	−1.33737
$187$	−31.8492	−2.32905
$188$	−9.62457	−0.701944
$189$	19.5985	1.42558
$190$	−0.744736	−0.0540288
$191$	−16.9898	−1.22934	−0.614670	−	0.788784i	$-0.710711\pi$
$191$	−16.9898	−1.22934	−0.614670	+	0.788784i	$0.710711\pi$
$192$	12.8579	0.927937
$193$	−24.0147	−1.72862	−0.864309	−	0.502961i	$-0.832244\pi$
$193$	−24.0147	−1.72862	−0.864309	+	0.502961i	$0.832244\pi$
$194$	−26.9719	−1.93647
$195$	−12.2635	−0.878205
$196$	13.7248	0.980341
$197$	−3.25339	−0.231794	−0.115897	−	0.993261i	$-0.536974\pi$
$197$	−3.25339	−0.231794	−0.115897	+	0.993261i	$0.536974\pi$
$198$	0.327941	0.0233057
$199$	−4.10164	−0.290758	−0.145379	−	0.989376i	$-0.546440\pi$
$199$	−4.10164	−0.290758	−0.145379	+	0.989376i	$0.546440\pi$
$200$	−0.513810	−0.0363319
$201$	−20.1638	−1.42225
$202$	−27.5134	−1.93584
$203$	25.9128	1.81872
$204$	17.4511	1.22182
$205$	−10.1941	−0.711986
$206$	−11.6114	−0.809004
$207$	−0.163096	−0.0113360
$208$	27.7638	1.92508
$209$	−2.15960	−0.149383
$210$	−13.5819	−0.937237
$211$	0.994439	0.0684600	0.0342300	−	0.999414i	$-0.489102\pi$
$211$	0.994439	0.0684600	0.0342300	+	0.999414i	$0.489102\pi$
$212$	−12.7836	−0.877984
$213$	−18.1041	−1.24047
$214$	−19.8065	−1.35394
$215$	0.0959496	0.00654371
$216$	0.690992	0.0470161
$217$	−20.0285	−1.35962
$218$	9.62673	0.652005
$219$	9.98742	0.674887
$220$	−12.4404	−0.838732
$221$	35.2031	2.36802
$222$	17.2704	1.15911
$223$	6.42942	0.430546	0.215273	−	0.976554i	$-0.430936\pi$
$223$	6.42942	0.430546	0.215273	+	0.976554i	$0.430936\pi$
$224$	29.7544	1.98805
$225$	0.105493	0.00703288
$226$	6.67620	0.444094
$227$	3.97251	0.263665	0.131832	−	0.991272i	$-0.457914\pi$
$227$	3.97251	0.263665	0.131832	+	0.991272i	$0.457914\pi$
$228$	1.18331	0.0783665
$229$	−6.23389	−0.411947	−0.205974	−	0.978558i	$-0.566036\pi$
$229$	−6.23389	−0.411947	−0.205974	+	0.978558i	$0.566036\pi$
$230$	12.5877	0.830010
$231$	−39.3850	−2.59134
$232$	0.913618	0.0599820
$233$	9.33323	0.611440	0.305720	−	0.952121i	$-0.401103\pi$
$233$	9.33323	0.611440	0.305720	+	0.952121i	$0.401103\pi$
$234$	−0.362474	−0.0236957
$235$	5.26616	0.343526
$236$	11.8324	0.770223
$237$	−22.2810	−1.44731
$238$	38.9876	2.52719
$239$	5.73841	0.371187	0.185594	−	0.982627i	$-0.440579\pi$
$239$	5.73841	0.371187	0.185594	+	0.982627i	$0.440579\pi$
$240$	−7.53069	−0.486104
$241$	−19.6426	−1.26529	−0.632644	−	0.774443i	$-0.718030\pi$
$241$	−19.6426	−1.26529	−0.632644	+	0.774443i	$0.718030\pi$
$242$	−51.5800	−3.31569
$243$	−0.282469	−0.0181204
$244$	3.32878	0.213103
$245$	−7.50962	−0.479772
$246$	32.9540	2.10107
$247$	2.38702	0.151882
$248$	−0.706154	−0.0448408
$249$	−0.317619	−0.0201283
$250$	−18.6312	−1.17834
$251$	7.09344	0.447734	0.223867	−	0.974620i	$-0.428132\pi$
$251$	7.09344	0.447734	0.223867	+	0.974620i	$0.428132\pi$
$252$	−0.197314	−0.0124296
$253$	36.5022	2.29487
$254$	14.2226	0.892404
$255$	−9.54851	−0.597951
$256$	17.0140	1.06338
$257$	19.4959	1.21612	0.608061	−	0.793890i	$-0.291948\pi$
$257$	19.4959	1.21612	0.608061	+	0.793890i	$0.291948\pi$
$258$	−0.310172	−0.0193105
$259$	18.9645	1.17840
$260$	13.7504	0.852766
$261$	−0.187580	−0.0116109
$262$	16.1164	0.995676
$263$	6.79551	0.419029	0.209514	−	0.977806i	$-0.432812\pi$
$263$	6.79551	0.419029	0.209514	+	0.977806i	$0.432812\pi$
$264$	−1.38862	−0.0854634
$265$	6.99467	0.429679
$266$	2.64364	0.162092
$267$	12.2599	0.750292
$268$	22.6087	1.38105
$269$	18.6646	1.13800	0.569001	−	0.822337i	$-0.307330\pi$
$269$	18.6646	1.13800	0.569001	+	0.822337i	$0.307330\pi$
$270$	10.9496	0.666371
$271$	−18.9261	−1.14968	−0.574840	−	0.818266i	$-0.694936\pi$
$271$	−18.9261	−1.14968	−0.574840	+	0.818266i	$0.694936\pi$
$272$	21.6173	1.31074
$273$	43.5324	2.63470
$274$	15.2727	0.922661
$275$	−23.6102	−1.42375
$276$	−20.0006	−1.20390
$277$	−17.9961	−1.08128	−0.540640	−	0.841254i	$-0.681818\pi$
$277$	−17.9961	−1.08128	−0.540640	+	0.841254i	$0.681818\pi$
$278$	−21.0958	−1.26524
$279$	0.144984	0.00867998
$280$	−0.525836	−0.0314247
$281$	−28.9297	−1.72580	−0.862900	−	0.505374i	$-0.831354\pi$
$281$	−28.9297	−1.72580	−0.862900	+	0.505374i	$0.831354\pi$
$282$	−17.0237	−1.01375
$283$	−28.9941	−1.72352	−0.861761	−	0.507315i	$-0.830638\pi$
$283$	−28.9941	−1.72352	−0.861761	+	0.507315i	$0.830638\pi$
$284$	20.2993	1.20454
$285$	−0.647457	−0.0383520
$286$	81.1245	4.79699
$287$	36.1866	2.13603
$288$	−0.215389	−0.0126919
$289$	10.4096	0.612330
$290$	14.4774	0.850141
$291$	−23.4488	−1.37459
$292$	−11.1984	−0.655337
$293$	9.64668	0.563565	0.281782	−	0.959478i	$-0.409074\pi$
$293$	9.64668	0.563565	0.281782	+	0.959478i	$0.409074\pi$
$294$	24.2760	1.41581
$295$	−6.47419	−0.376942
$296$	0.668640	0.0388639
$297$	31.7519	1.84243
$298$	−3.19604	−0.185142
$299$	−40.3460	−2.33327
$300$	12.9367	0.746901
$301$	−0.340598	−0.0196318
$302$	−39.5962	−2.27851
$303$	−23.9196	−1.37414
$304$	1.46581	0.0840698
$305$	−1.82137	−0.104291
$306$	−0.282227	−0.0161339
$307$	16.4730	0.940166	0.470083	−	0.882622i	$-0.344224\pi$
$307$	16.4730	0.940166	0.470083	+	0.882622i	$0.344224\pi$
$308$	44.1605	2.51628
$309$	−10.0947	−0.574267
$310$	−11.1899	−0.635541
$311$	24.5521	1.39222	0.696110	−	0.717935i	$-0.254913\pi$
$311$	24.5521	1.39222	0.696110	+	0.717935i	$0.254913\pi$
$312$	1.53484	0.0868934
$313$	−13.2228	−0.747395	−0.373698	−	0.927551i	$-0.621910\pi$
$313$	−13.2228	−0.747395	−0.373698	+	0.927551i	$0.621910\pi$
$314$	−3.05633	−0.172478
$315$	0.107962	0.00608298
$316$	24.9826	1.40538
$317$	11.4591	0.643607	0.321803	−	0.946807i	$-0.395711\pi$
$317$	11.4591	0.643607	0.321803	+	0.946807i	$0.395711\pi$
$318$	−22.6114	−1.26798
$319$	41.9819	2.35053
$320$	7.88833	0.440971
$321$	−17.2193	−0.961089
$322$	−44.6835	−2.49011
$323$	1.85857	0.103413
$324$	−17.2401	−0.957786
$325$	26.0965	1.44757
$326$	7.06558	0.391326
$327$	8.36927	0.462822
$328$	1.27585	0.0704470
$329$	−18.6936	−1.03061
$330$	−22.0043	−1.21130
$331$	26.1510	1.43739	0.718694	−	0.695326i	$-0.244740\pi$
$331$	26.1510	1.43739	0.718694	+	0.695326i	$0.244740\pi$
$332$	0.356131	0.0195452
$333$	−0.137282	−0.00752302
$334$	2.20812	0.120823
$335$	−12.3705	−0.675875
$336$	26.7322	1.45836
$337$	15.4634	0.842346	0.421173	−	0.906980i	$-0.361619\pi$
$337$	15.4634	0.842346	0.421173	+	0.906980i	$0.361619\pi$
$338$	−63.8851	−3.47489
$339$	5.80414	0.315237
$340$	10.7063	0.580630
$341$	−32.4486	−1.75719
$342$	−0.0191370	−0.00103481
$343$	0.373019	0.0201411
$344$	−0.0120086	−0.000647462 0
$345$	10.9435	0.589178
$346$	−4.81644	−0.258933
$347$	33.8444	1.81686	0.908432	−	0.418032i	$-0.137280\pi$
$347$	33.8444	1.81686	0.908432	+	0.418032i	$0.137280\pi$
$348$	−23.0031	−1.23309
$349$	26.7836	1.43369	0.716847	−	0.697230i	$-0.245584\pi$
$349$	26.7836	1.43369	0.716847	+	0.697230i	$0.245584\pi$
$350$	28.9020	1.54487
$351$	−35.0955	−1.87326
$352$	48.2058	2.56938
$353$	−24.0208	−1.27850	−0.639248	−	0.769000i	$-0.720754\pi$
$353$	−24.0208	−1.27850	−0.639248	+	0.769000i	$0.720754\pi$
$354$	20.9288	1.11236
$355$	−11.1069	−0.589494
$356$	−13.7464	−0.728557
$357$	33.8950	1.79391
$358$	−40.0846	−2.11854
$359$	−32.1070	−1.69454	−0.847271	−	0.531160i	$-0.821756\pi$
$359$	−32.1070	−1.69454	−0.847271	+	0.531160i	$0.821756\pi$
$360$	0.00380647	0.000200619 0
$361$	−18.8740	−0.993367
$362$	−29.1726	−1.53328
$363$	−44.8425	−2.35362
$364$	−48.8108	−2.55838
$365$	6.12730	0.320717
$366$	5.88786	0.307764
$367$	−15.2200	−0.794479	−0.397240	−	0.917715i	$-0.630032\pi$
$367$	−15.2200	−0.794479	−0.397240	+	0.917715i	$0.630032\pi$
$368$	−24.7755	−1.29151
$369$	−0.261951	−0.0136366
$370$	10.5954	0.550829
$371$	−24.8294	−1.28908
$372$	17.7795	0.921825
$373$	−21.1126	−1.09317	−0.546585	−	0.837403i	$-0.684073\pi$
$373$	−21.1126	−1.09317	−0.546585	+	0.837403i	$0.684073\pi$
$374$	63.1647	3.26617
$375$	−16.1976	−0.836439
$376$	−0.659090	−0.0339900
$377$	−46.4027	−2.38986
$378$	−38.8685	−1.99918
$379$	−10.1114	−0.519390	−0.259695	−	0.965691i	$-0.583622\pi$
$379$	−10.1114	−0.519390	−0.259695	+	0.965691i	$0.583622\pi$
$380$	0.725962	0.0372411
$381$	12.3648	0.633468
$382$	33.6949	1.72398
$383$	−14.6121	−0.746644	−0.373322	−	0.927702i	$-0.621781\pi$
$383$	−14.6121	−0.746644	−0.373322	+	0.927702i	$0.621781\pi$
$384$	1.82508	0.0931359
$385$	−24.1628	−1.23145
$386$	47.6270	2.42415
$387$	0.00246556	0.000125331 0
$388$	26.2920	1.33477
$389$	0.579277	0.0293705	0.0146853	−	0.999892i	$-0.495325\pi$
$389$	0.579277	0.0293705	0.0146853	+	0.999892i	$0.495325\pi$
$390$	24.3214	1.23156
$391$	−31.4140	−1.58867
$392$	0.939872	0.0474707
$393$	14.0113	0.706775
$394$	6.45225	0.325060
$395$	−13.6694	−0.687783
$396$	−0.319674	−0.0160642
$397$	−31.2076	−1.56626	−0.783132	−	0.621855i	$-0.786379\pi$
$397$	−31.2076	−1.56626	−0.783132	+	0.621855i	$0.786379\pi$
$398$	8.13455	0.407748
$399$	2.29832	0.115060
$400$	16.0252	0.801258
$401$	−10.9396	−0.546299	−0.273150	−	0.961972i	$-0.588065\pi$
$401$	−10.9396	−0.546299	−0.273150	+	0.961972i	$0.588065\pi$
$402$	39.9897	1.99451
$403$	35.8656	1.78659
$404$	26.8198	1.33434
$405$	9.43308	0.468734
$406$	−51.3912	−2.55050
$407$	30.7248	1.52297
$408$	1.19505	0.0591638
$409$	−5.13360	−0.253840	−0.126920	−	0.991913i	$-0.540509\pi$
$409$	−5.13360	−0.253840	−0.126920	+	0.991913i	$0.540509\pi$
$410$	20.2173	0.998464
$411$	13.2778	0.654945
$412$	11.3187	0.557631
$413$	22.9818	1.13086
$414$	0.323459	0.0158972
$415$	−0.194860	−0.00956530
$416$	−53.2820	−2.61237
$417$	−18.3402	−0.898124
$418$	4.28302	0.209489
$419$	2.80692	0.137127	0.0685636	−	0.997647i	$-0.478158\pi$
$419$	2.80692	0.137127	0.0685636	+	0.997647i	$0.478158\pi$
$420$	13.2395	0.646020
$421$	−22.1099	−1.07757	−0.538785	−	0.842443i	$-0.681116\pi$
$421$	−22.1099	−1.07757	−0.538785	+	0.842443i	$0.681116\pi$
$422$	−1.97221	−0.0960059
$423$	0.135321	0.00657955
$424$	−0.875423	−0.0425143
$425$	20.3191	0.985619
$426$	35.9049	1.73960
$427$	6.46543	0.312884
$428$	19.3072	0.933249
$429$	70.5279	3.40512
$430$	−0.190291	−0.00917666
$431$	2.65789	0.128026	0.0640130	−	0.997949i	$-0.479610\pi$
$431$	2.65789	0.128026	0.0640130	+	0.997949i	$0.479610\pi$
$432$	−21.5513	−1.03689
$433$	12.7709	0.613732	0.306866	−	0.951753i	$-0.400720\pi$
$433$	12.7709	0.613732	0.306866	+	0.951753i	$0.400720\pi$
$434$	39.7213	1.90668
$435$	12.5863	0.603467
$436$	−9.38406	−0.449415
$437$	−2.13009	−0.101896
$438$	−19.8075	−0.946437
$439$	−20.6371	−0.984954	−0.492477	−	0.870325i	$-0.663908\pi$
$439$	−20.6371	−0.984954	−0.492477	+	0.870325i	$0.663908\pi$
$440$	−0.851919	−0.0406136
$441$	−0.192970	−0.00918906
$442$	−69.8162	−3.32082
$443$	18.9329	0.899529	0.449764	−	0.893147i	$-0.351508\pi$
$443$	18.9329	0.899529	0.449764	+	0.893147i	$0.351508\pi$
$444$	−16.8350	−0.798954
$445$	7.52145	0.356551
$446$	−12.7511	−0.603782
$447$	−2.77857	−0.131422
$448$	−28.0017	−1.32296
$449$	−12.4002	−0.585203	−0.292602	−	0.956234i	$-0.594521\pi$
$449$	−12.4002	−0.585203	−0.292602	+	0.956234i	$0.594521\pi$
$450$	−0.209218	−0.00986265
$451$	58.6268	2.76063
$452$	−6.50790	−0.306106
$453$	−34.4241	−1.61738
$454$	−7.87845	−0.369754
$455$	26.7072	1.25205
$456$	0.0810329	0.00379471
$457$	−31.1873	−1.45888	−0.729440	−	0.684045i	$-0.760219\pi$
$457$	−31.1873	−1.45888	−0.729440	+	0.684045i	$0.760219\pi$
$458$	12.3633	0.577700
$459$	−27.3259	−1.27546
$460$	−12.2704	−0.572111
$461$	34.4152	1.60288	0.801439	−	0.598077i	$-0.204068\pi$
$461$	34.4152	1.60288	0.801439	+	0.598077i	$0.204068\pi$
$462$	78.1100	3.63401
$463$	6.32091	0.293758	0.146879	−	0.989154i	$-0.453077\pi$
$463$	6.32091	0.293758	0.146879	+	0.989154i	$0.453077\pi$
$464$	−28.4947	−1.32283
$465$	−9.72821	−0.451135
$466$	−18.5100	−0.857461
$467$	−10.0959	−0.467185	−0.233592	−	0.972335i	$-0.575048\pi$
$467$	−10.0959	−0.467185	−0.233592	+	0.972335i	$0.575048\pi$
$468$	0.353337	0.0163330
$469$	43.9125	2.02769
$470$	−10.4441	−0.481749
$471$	−2.65710	−0.122433
$472$	0.810282	0.0372962
$473$	−0.551811	−0.0253723
$474$	44.1886	2.02965
$475$	1.37778	0.0632167
$476$	−38.0048	−1.74195
$477$	0.179738	0.00822963
$478$	−11.3807	−0.520539
$479$	16.3802	0.748431	0.374216	−	0.927342i	$-0.377912\pi$
$479$	16.3802	0.748431	0.374216	+	0.927342i	$0.377912\pi$
$480$	14.4523	0.659652
$481$	−33.9603	−1.54845
$482$	38.9559	1.77439
$483$	−38.8468	−1.76759
$484$	50.2798	2.28544
$485$	−14.3859	−0.653229
$486$	0.560204	0.0254114
$487$	15.6438	0.708887	0.354443	−	0.935077i	$-0.384670\pi$
$487$	15.6438	0.708887	0.354443	+	0.935077i	$0.384670\pi$
$488$	0.227955	0.0103190
$489$	6.14266	0.277781
$490$	14.8934	0.672815
$491$	−25.0257	−1.12939	−0.564696	−	0.825299i	$-0.691007\pi$
$491$	−25.0257	−1.12939	−0.564696	+	0.825299i	$0.691007\pi$
$492$	−32.1233	−1.44823
$493$	−36.1298	−1.62720
$494$	−4.73403	−0.212994
$495$	0.174912	0.00786171
$496$	22.0241	0.988913
$497$	39.4269	1.76854
$498$	0.629916	0.0282272
$499$	−14.4100	−0.645081	−0.322541	−	0.946556i	$-0.604537\pi$
$499$	−14.4100	−0.645081	−0.322541	+	0.946556i	$0.604537\pi$
$500$	18.1615	0.812209
$501$	1.91969	0.0857654
$502$	−14.0680	−0.627885
$503$	28.2401	1.25917	0.629583	−	0.776933i	$-0.283226\pi$
$503$	28.2401	1.25917	0.629583	+	0.776933i	$0.283226\pi$
$504$	−0.0135121	−0.000601876 0
$505$	−14.6747	−0.653015
$506$	−72.3927	−3.21825
$507$	−55.5403	−2.46663
$508$	−13.8641	−0.615118
$509$	29.9612	1.32801	0.664003	−	0.747730i	$-0.268856\pi$
$509$	29.9612	1.32801	0.664003	+	0.747730i	$0.268856\pi$
$510$	18.9370	0.838545
$511$	−21.7505	−0.962184
$512$	−31.6259	−1.39768
$513$	−1.85289	−0.0818070
$514$	−38.6651	−1.70544
$515$	−6.19311	−0.272901
$516$	0.302353	0.0133104
$517$	−30.2860	−1.33198
$518$	−37.6112	−1.65254
$519$	−4.18730	−0.183802
$520$	0.941629	0.0412932
$521$	−2.37228	−0.103931	−0.0519657	−	0.998649i	$-0.516549\pi$
$521$	−2.37228	−0.103931	−0.0519657	+	0.998649i	$0.516549\pi$
$522$	0.372016	0.0162827
$523$	10.0656	0.440137	0.220068	−	0.975484i	$-0.429372\pi$
$523$	10.0656	0.440137	0.220068	+	0.975484i	$0.429372\pi$
$524$	−15.7102	−0.686301
$525$	25.1267	1.09662
$526$	−13.4771	−0.587631
$527$	27.9254	1.21645
$528$	43.3094	1.88480
$529$	13.0034	0.565366
$530$	−13.8721	−0.602566
$531$	−0.166363	−0.00721955
$532$	−2.57699	−0.111727
$533$	−64.8004	−2.80682
$534$	−24.3143	−1.05218
$535$	−10.5641	−0.456726
$536$	1.54824	0.0668740
$537$	−34.8487	−1.50383
$538$	−37.0165	−1.59589
$539$	43.1882	1.86025
$540$	−10.6736	−0.459318
$541$	−12.6292	−0.542971	−0.271486	−	0.962443i	$-0.587515\pi$
$541$	−12.6292	−0.542971	−0.271486	+	0.962443i	$0.587515\pi$
$542$	37.5351	1.61227
$543$	−25.3620	−1.08839
$544$	−41.4861	−1.77870
$545$	5.13456	0.219941
$546$	−86.3353	−3.69481
$547$	5.30868	0.226983	0.113491	−	0.993539i	$-0.463797\pi$
$547$	5.30868	0.226983	0.113491	+	0.993539i	$0.463797\pi$
$548$	−14.8877	−0.635973
$549$	−0.0468026	−0.00199749
$550$	46.8247	1.99661
$551$	−2.44986	−0.104367
$552$	−1.36964	−0.0582958
$553$	48.5232	2.06342
$554$	35.6906	1.51635
$555$	9.21141	0.391003
$556$	20.5640	0.872107
$557$	−9.22500	−0.390876	−0.195438	−	0.980716i	$-0.562613\pi$
$557$	−9.22500	−0.390876	−0.195438	+	0.980716i	$0.562613\pi$
$558$	−0.287539	−0.0121725
$559$	0.609919	0.0257968
$560$	16.4002	0.693036
$561$	54.9140	2.31847
$562$	57.3746	2.42020
$563$	28.4238	1.19792	0.598961	−	0.800778i	$-0.295581\pi$
$563$	28.4238	1.19792	0.598961	+	0.800778i	$0.295581\pi$
$564$	16.5945	0.698756
$565$	3.56085	0.149806
$566$	57.5023	2.41700
$567$	−33.4852	−1.40625
$568$	1.39009	0.0583271
$569$	−7.41846	−0.310998	−0.155499	−	0.987836i	$-0.549699\pi$
$569$	−7.41846	−0.310998	−0.155499	+	0.987836i	$0.549699\pi$
$570$	1.28406	0.0537835
$571$	−16.7408	−0.700581	−0.350291	−	0.936641i	$-0.613917\pi$
$571$	−16.7408	−0.700581	−0.350291	+	0.936641i	$0.613917\pi$
$572$	−79.0795	−3.30648
$573$	29.2936	1.22376
$574$	−71.7668	−2.99549
$575$	−23.2876	−0.971159
$576$	0.202702	0.00844590
$577$	9.51827	0.396251	0.198125	−	0.980177i	$-0.436515\pi$
$577$	9.51827	0.396251	0.198125	+	0.980177i	$0.436515\pi$
$578$	−20.6448	−0.858709
$579$	41.4059	1.72077
$580$	−14.1124	−0.585986
$581$	0.691707	0.0286968
$582$	46.5046	1.92768
$583$	−40.2267	−1.66602
$584$	−0.766866	−0.0317332
$585$	−0.193331	−0.00799325
$586$	−19.1317	−0.790323
$587$	−43.0662	−1.77753	−0.888765	−	0.458362i	$-0.848436\pi$
$587$	−43.0662	−1.77753	−0.888765	+	0.458362i	$0.848436\pi$
$588$	−23.6641	−0.975890
$589$	1.89354	0.0780221
$590$	12.8399	0.528610
$591$	5.60945	0.230742
$592$	−20.8541	−0.857100
$593$	16.0330	0.658396	0.329198	−	0.944261i	$-0.393222\pi$
$593$	16.0330	0.658396	0.329198	+	0.944261i	$0.393222\pi$
$594$	−62.9717	−2.58376
$595$	20.7946	0.852496
$596$	3.11547	0.127615
$597$	7.07200	0.289438
$598$	80.0159	3.27210
$599$	−38.5861	−1.57659	−0.788293	−	0.615301i	$-0.789035\pi$
$599$	−38.5861	−1.57659	−0.788293	+	0.615301i	$0.789035\pi$
$600$	0.885905	0.0361669
$601$	7.61906	0.310788	0.155394	−	0.987853i	$-0.450335\pi$
$601$	7.61906	0.310788	0.155394	+	0.987853i	$0.450335\pi$
$602$	0.675489	0.0275309
$603$	−0.317878	−0.0129450
$604$	38.5980	1.57053
$605$	−27.5110	−1.11848
$606$	47.4383	1.92705
$607$	−11.7127	−0.475402	−0.237701	−	0.971338i	$-0.576394\pi$
$607$	−11.7127	−0.475402	−0.237701	+	0.971338i	$0.576394\pi$
$608$	−2.81305	−0.114084
$609$	−44.6784	−1.81046
$610$	3.61221	0.146254
$611$	33.4752	1.35426
$612$	0.275113	0.0111208
$613$	−19.9221	−0.804647	−0.402323	−	0.915498i	$-0.631797\pi$
$613$	−19.9221	−0.804647	−0.402323	+	0.915498i	$0.631797\pi$
$614$	−32.6700	−1.31845
$615$	17.5765	0.708754
$616$	3.02411	0.121845
$617$	33.1161	1.33321	0.666603	−	0.745413i	$-0.267748\pi$
$617$	33.1161	1.33321	0.666603	+	0.745413i	$0.267748\pi$
$618$	20.0202	0.805331
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	10.9078	0.438067
$621$	31.3180	1.25675
$622$	−48.6927	−1.95240
$623$	−26.6994	−1.06969
$624$	−47.8700	−1.91633
$625$	9.46815	0.378726
$626$	26.2239	1.04812
$627$	3.72356	0.148705
$628$	2.97928	0.118886
$629$	−26.4419	−1.05431
$630$	−0.214115	−0.00853055
$631$	−23.1947	−0.923364	−0.461682	−	0.887045i	$-0.652754\pi$
$631$	−23.1947	−0.923364	−0.461682	+	0.887045i	$0.652754\pi$
$632$	1.71081	0.0680522
$633$	−1.71460	−0.0681492
$634$	−22.7261	−0.902571
$635$	7.58583	0.301034
$636$	22.0414	0.873997
$637$	−47.7361	−1.89137
$638$	−83.2602	−3.29630
$639$	−0.285408	−0.0112906
$640$	1.11969	0.0442597
$641$	−37.7299	−1.49024	−0.745121	−	0.666930i	$-0.767608\pi$
$641$	−37.7299	−1.49024	−0.745121	+	0.666930i	$0.767608\pi$
$642$	34.1501	1.34780
$643$	30.6859	1.21013	0.605066	−	0.796175i	$-0.293147\pi$
$643$	30.6859	1.21013	0.605066	+	0.796175i	$0.293147\pi$
$644$	43.5570	1.71639
$645$	−0.165435	−0.00651400
$646$	−3.68599	−0.145023
$647$	16.7802	0.659697	0.329849	−	0.944034i	$-0.393002\pi$
$647$	16.7802	0.659697	0.329849	+	0.944034i	$0.393002\pi$
$648$	−1.18060	−0.0463785
$649$	37.2334	1.46154
$650$	−51.7556	−2.03002
$651$	34.5328	1.35345
$652$	−6.88747	−0.269734
$653$	−22.3619	−0.875087	−0.437544	−	0.899197i	$-0.644151\pi$
$653$	−22.3619	−0.875087	−0.437544	+	0.899197i	$0.644151\pi$
$654$	−16.5983	−0.649044
$655$	8.59594	0.335871
$656$	−39.7923	−1.55363
$657$	0.157449	0.00614269
$658$	37.0740	1.44529
$659$	−18.9001	−0.736244	−0.368122	−	0.929777i	$-0.619999\pi$
$659$	−18.9001	−0.736244	−0.368122	+	0.929777i	$0.619999\pi$
$660$	21.4496	0.834924
$661$	−3.11133	−0.121017	−0.0605084	−	0.998168i	$-0.519272\pi$
$661$	−3.11133	−0.121017	−0.0605084	+	0.998168i	$0.519272\pi$
$662$	−51.8637	−2.01574
$663$	−60.6967	−2.35726
$664$	0.0243878	0.000946432 0
$665$	1.41002	0.0546783
$666$	0.272264	0.0105500
$667$	41.4082	1.60333
$668$	−2.15245	−0.0832809
$669$	−11.0855	−0.428591
$670$	24.5338	0.947823
$671$	10.4748	0.404375
$672$	−51.3021	−1.97902
$673$	2.56807	0.0989918	0.0494959	−	0.998774i	$-0.484239\pi$
$673$	2.56807	0.0989918	0.0494959	+	0.998774i	$0.484239\pi$
$674$	−30.6677	−1.18127
$675$	−20.2570	−0.779692
$676$	62.2747	2.39518
$677$	−22.1451	−0.851105	−0.425552	−	0.904934i	$-0.639920\pi$
$677$	−22.1451	−0.851105	−0.425552	+	0.904934i	$0.639920\pi$
$678$	−11.5110	−0.442077
$679$	51.0665	1.95975
$680$	0.733166	0.0281156
$681$	−6.84935	−0.262468
$682$	64.3534	2.46422
$683$	10.0367	0.384045	0.192023	−	0.981390i	$-0.438495\pi$
$683$	10.0367	0.384045	0.192023	+	0.981390i	$0.438495\pi$
$684$	0.0186546	0.000713277 0
$685$	8.14595	0.311241
$686$	−0.739786	−0.0282452
$687$	10.7484	0.410077
$688$	0.374536	0.0142790
$689$	44.4628	1.69390
$690$	−21.7036	−0.826242
$691$	46.8230	1.78123	0.890615	−	0.454759i	$-0.150275\pi$
$691$	46.8230	1.78123	0.890615	+	0.454759i	$0.150275\pi$
$692$	4.69502	0.178478
$693$	−0.620896	−0.0235859
$694$	−67.1217	−2.54790
$695$	−11.2518	−0.426803
$696$	−1.57525	−0.0597096
$697$	−50.4545	−1.91110
$698$	−53.1184	−2.01056
$699$	−16.0922	−0.608664
$700$	−28.1734	−1.06485
$701$	−19.9414	−0.753178	−0.376589	−	0.926381i	$-0.622903\pi$
$701$	−19.9414	−0.753178	−0.376589	+	0.926381i	$0.622903\pi$
$702$	69.6029	2.62699
$703$	−1.79295	−0.0676224
$704$	−45.3662	−1.70980
$705$	−9.07984	−0.341967
$706$	47.6390	1.79292
$707$	52.0917	1.95911
$708$	−20.4013	−0.766726
$709$	−24.8082	−0.931693	−0.465847	−	0.884865i	$-0.654250\pi$
$709$	−24.8082	−0.931693	−0.465847	+	0.884865i	$0.654250\pi$
$710$	22.0277	0.826685
$711$	−0.351255	−0.0131731
$712$	−0.941352	−0.0352787
$713$	−32.0052	−1.19860
$714$	−67.2219	−2.51572
$715$	43.2690	1.61817
$716$	39.0742	1.46027
$717$	−9.89410	−0.369502
$718$	63.6759	2.37636
$719$	11.7629	0.438681	0.219341	−	0.975648i	$-0.429609\pi$
$719$	11.7629	0.438681	0.219341	+	0.975648i	$0.429609\pi$
$720$	−0.118720	−0.00442442
$721$	21.9841	0.818730
$722$	37.4317	1.39306
$723$	33.8674	1.25954
$724$	28.4372	1.05686
$725$	−26.7834	−0.994712
$726$	88.9336	3.30063
$727$	10.6858	0.396315	0.198158	−	0.980170i	$-0.436504\pi$
$727$	10.6858	0.396315	0.198158	+	0.980170i	$0.436504\pi$
$728$	−3.34256	−0.123884
$729$	27.2402	1.00890
$730$	−12.1519	−0.449762
$731$	0.474892	0.0175645
$732$	−5.73944	−0.212136
$733$	7.03351	0.259789	0.129894	−	0.991528i	$-0.458536\pi$
$733$	7.03351	0.259789	0.129894	+	0.991528i	$0.458536\pi$
$734$	30.1850	1.11415
$735$	12.9480	0.477594
$736$	47.5470	1.75261
$737$	71.1437	2.62061
$738$	0.519513	0.0191235
$739$	−31.3859	−1.15455	−0.577274	−	0.816550i	$-0.695884\pi$
$739$	−31.3859	−1.15455	−0.577274	+	0.816550i	$0.695884\pi$
$740$	−10.3283	−0.379676
$741$	−4.11567	−0.151193
$742$	49.2427	1.80776
$743$	11.7765	0.432037	0.216019	−	0.976389i	$-0.430693\pi$
$743$	11.7765	0.432037	0.216019	+	0.976389i	$0.430693\pi$
$744$	1.21754	0.0446372
$745$	−1.70465	−0.0624537
$746$	41.8714	1.53302
$747$	−0.00500720	−0.000183204 0
$748$	−61.5724	−2.25131
$749$	37.5000	1.37022
$750$	32.1237	1.17299
$751$	−39.3469	−1.43579	−0.717894	−	0.696152i	$-0.754894\pi$
$751$	−39.3469	−1.43579	−0.717894	+	0.696152i	$0.754894\pi$
$752$	20.5563	0.749610
$753$	−12.2304	−0.445701
$754$	92.0278	3.35145
$755$	−21.1192	−0.768608
$756$	37.8887	1.37800
$757$	34.7833	1.26422	0.632111	−	0.774878i	$-0.282189\pi$
$757$	34.7833	1.26422	0.632111	+	0.774878i	$0.282189\pi$
$758$	20.0534	0.728373
$759$	−62.9366	−2.28445
$760$	0.0497138	0.00180331
$761$	15.7398	0.570568	0.285284	−	0.958443i	$-0.407912\pi$
$761$	15.7398	0.570568	0.285284	+	0.958443i	$0.407912\pi$
$762$	−24.5224	−0.888352
$763$	−18.2265	−0.659843
$764$	−32.8455	−1.18831
$765$	−0.150530	−0.00544243
$766$	28.9794	1.04707
$767$	−41.1542	−1.48599
$768$	−29.3353	−1.05855
$769$	21.2397	0.765924	0.382962	−	0.923764i	$-0.374904\pi$
$769$	21.2397	0.765924	0.382962	+	0.923764i	$0.374904\pi$
$770$	47.9206	1.72694
$771$	−33.6146	−1.21060
$772$	−46.4264	−1.67092
$773$	19.0417	0.684881	0.342441	−	0.939539i	$-0.388746\pi$
$773$	19.0417	0.684881	0.342441	+	0.939539i	$0.388746\pi$
$774$	−0.00488980	−0.000175760 0
$775$	20.7015	0.743618
$776$	1.80048	0.0646333
$777$	−32.6983	−1.17305
$778$	−1.14885	−0.0411881
$779$	−3.42117	−0.122576
$780$	−23.7083	−0.848894
$781$	63.8765	2.28568
$782$	62.3015	2.22790
$783$	36.0194	1.28723
$784$	−29.3135	−1.04691
$785$	−1.63014	−0.0581821
$786$	−27.7877	−0.991155
$787$	6.88251	0.245335	0.122668	−	0.992448i	$-0.460855\pi$
$787$	6.88251	0.245335	0.122668	+	0.992448i	$0.460855\pi$
$788$	−6.28960	−0.224058
$789$	−11.7167	−0.417126
$790$	27.1098	0.964522
$791$	−12.6402	−0.449433
$792$	−0.0218912	−0.000777871 0
$793$	−11.5778	−0.411141
$794$	61.8922	2.19647
$795$	−12.0601	−0.427728
$796$	−7.92949	−0.281053
$797$	−31.6062	−1.11955	−0.559774	−	0.828645i	$-0.689112\pi$
$797$	−31.6062	−1.11955	−0.559774	+	0.828645i	$0.689112\pi$
$798$	−4.55812	−0.161356
$799$	26.0643	0.922087
$800$	−30.7542	−1.08732
$801$	0.193274	0.00682901
$802$	21.6959	0.766110
$803$	−35.2384	−1.24354
$804$	−38.9817	−1.37478
$805$	−23.8326	−0.839988
$806$	−71.1301	−2.50545
$807$	−32.1813	−1.13284
$808$	1.83662	0.0646121
$809$	−3.63194	−0.127692	−0.0638460	−	0.997960i	$-0.520337\pi$
$809$	−3.63194	−0.127692	−0.0638460	+	0.997960i	$0.520337\pi$
$810$	−18.7081	−0.657335
$811$	−22.3667	−0.785402	−0.392701	−	0.919666i	$-0.628459\pi$
$811$	−22.3667	−0.785402	−0.392701	+	0.919666i	$0.628459\pi$
$812$	50.0957	1.75802
$813$	32.6322	1.14446
$814$	−60.9347	−2.13576
$815$	3.76853	0.132006
$816$	−37.2723	−1.30479
$817$	0.0322010	0.00112657
$818$	10.1812	0.355976
$819$	0.686279	0.0239805
$820$	−19.7077	−0.688222
$821$	7.83461	0.273430	0.136715	−	0.990610i	$-0.456346\pi$
$821$	7.83461	0.273430	0.136715	+	0.990610i	$0.456346\pi$
$822$	−26.3331	−0.918471
$823$	54.9563	1.91566	0.957829	−	0.287340i	$-0.0927708\pi$
$823$	54.9563	1.91566	0.957829	+	0.287340i	$0.0927708\pi$
$824$	0.775103	0.0270020
$825$	40.7084	1.41728
$826$	−45.5785	−1.58588
$827$	39.2858	1.36610	0.683050	−	0.730371i	$-0.260653\pi$
$827$	39.2858	1.36610	0.683050	+	0.730371i	$0.260653\pi$
$828$	−0.315305	−0.0109576
$829$	11.1466	0.387136	0.193568	−	0.981087i	$-0.437994\pi$
$829$	11.1466	0.387136	0.193568	+	0.981087i	$0.437994\pi$
$830$	0.386454	0.0134140
$831$	31.0286	1.07637
$832$	50.1434	1.73841
$833$	−37.1680	−1.28780
$834$	36.3731	1.25950
$835$	1.17773	0.0407571
$836$	−4.17505	−0.144397
$837$	−27.8401	−0.962296
$838$	−5.56681	−0.192302
$839$	−30.3701	−1.04849	−0.524247	−	0.851566i	$-0.675653\pi$
$839$	−30.3701	−1.04849	−0.524247	+	0.851566i	$0.675653\pi$
$840$	0.906639	0.0312820
$841$	18.6243	0.642216
$842$	43.8492	1.51114
$843$	49.8802	1.71796
$844$	1.92250	0.0661751
$845$	−34.0741	−1.17218
$846$	−0.268375	−0.00922691
$847$	97.6575	3.35555
$848$	27.3034	0.937604
$849$	49.9913	1.71570
$850$	−40.2976	−1.38220
$851$	30.3050	1.03884
$852$	−34.9998	−1.19907
$853$	40.0751	1.37214	0.686072	−	0.727533i	$-0.259333\pi$
$853$	40.0751	1.37214	0.686072	+	0.727533i	$0.259333\pi$
$854$	−12.8225	−0.438777
$855$	−0.0102070	−0.000349073 0
$856$	1.32216	0.0451904
$857$	44.1508	1.50816	0.754081	−	0.656781i	$-0.228083\pi$
$857$	44.1508	1.50816	0.754081	+	0.656781i	$0.228083\pi$
$858$	−139.874	−4.77521
$859$	0.132999	0.00453786	0.00226893	−	0.999997i	$-0.499278\pi$
$859$	0.132999	0.00453786	0.00226893	+	0.999997i	$0.499278\pi$
$860$	0.185494	0.00632530
$861$	−62.3925	−2.12633
$862$	−5.27124	−0.179539
$863$	−3.62727	−0.123474	−0.0617368	−	0.998092i	$-0.519664\pi$
$863$	−3.62727	−0.123474	−0.0617368	+	0.998092i	$0.519664\pi$
$864$	41.3594	1.40708
$865$	−2.56892	−0.0873459
$866$	−25.3279	−0.860675
$867$	−17.9481	−0.609550
$868$	−38.7200	−1.31424
$869$	78.6136	2.66678
$870$	−24.9617	−0.846281
$871$	−78.6354	−2.66446
$872$	−0.642620	−0.0217619
$873$	−0.369665	−0.0125113
$874$	4.22449	0.142895
$875$	35.2748	1.19251
$876$	19.3081	0.652362
$877$	−19.8824	−0.671382	−0.335691	−	0.941972i	$-0.608970\pi$
$877$	−19.8824	−0.671382	−0.335691	+	0.941972i	$0.608970\pi$
$878$	40.9283	1.38126
$879$	−16.6327	−0.561006
$880$	26.5704	0.895687
$881$	−27.5924	−0.929613	−0.464807	−	0.885412i	$-0.653876\pi$
$881$	−27.5924	−0.929613	−0.464807	+	0.885412i	$0.653876\pi$
$882$	0.382706	0.0128864
$883$	−29.7392	−1.00080	−0.500402	−	0.865793i	$-0.666815\pi$
$883$	−29.7392	−1.00080	−0.500402	+	0.865793i	$0.666815\pi$
$884$	68.0562	2.28898
$885$	11.1627	0.375230
$886$	−37.5485	−1.26147
$887$	13.4684	0.452225	0.226113	−	0.974101i	$-0.427398\pi$
$887$	13.4684	0.452225	0.226113	+	0.974101i	$0.427398\pi$
$888$	−1.15286	−0.0386875
$889$	−26.9279	−0.903133
$890$	−14.9169	−0.500014
$891$	−54.2502	−1.81745
$892$	12.4297	0.416176
$893$	1.76734	0.0591418
$894$	5.51057	0.184301
$895$	−21.3797	−0.714646
$896$	−3.97464	−0.132783
$897$	69.5641	2.32268
$898$	24.5927	0.820668
$899$	−36.8097	−1.22767
$900$	0.203944	0.00679814
$901$	34.6193	1.15334
$902$	−116.271	−3.87140
$903$	0.587255	0.0195426
$904$	−0.445660	−0.0148224
$905$	−15.5596	−0.517219
$906$	68.2713	2.26816
$907$	42.2875	1.40413	0.702067	−	0.712111i	$-0.252261\pi$
$907$	42.2875	1.40413	0.702067	+	0.712111i	$0.252261\pi$
$908$	7.67985	0.254865
$909$	−0.377087	−0.0125072
$910$	−52.9669	−1.75583
$911$	12.6596	0.419432	0.209716	−	0.977762i	$-0.432746\pi$
$911$	12.6596	0.419432	0.209716	+	0.977762i	$0.432746\pi$
$912$	−2.52733	−0.0836881
$913$	1.12065	0.0370881
$914$	61.8519	2.04588
$915$	3.14038	0.103818
$916$	−12.0517	−0.398198
$917$	−30.5135	−1.00765
$918$	54.1938	1.78866
$919$	22.2268	0.733195	0.366598	−	0.930380i	$-0.380523\pi$
$919$	22.2268	0.733195	0.366598	+	0.930380i	$0.380523\pi$
$920$	−0.840277	−0.0277031
$921$	−28.4026	−0.935897
$922$	−68.2537	−2.24782
$923$	−70.6029	−2.32392
$924$	−76.1410	−2.50485
$925$	−19.6017	−0.644501
$926$	−12.5359	−0.411955
$927$	−0.159141	−0.00522686
$928$	54.6847	1.79511
$929$	11.2819	0.370147	0.185074	−	0.982725i	$-0.440748\pi$
$929$	11.2819	0.370147	0.185074	+	0.982725i	$0.440748\pi$
$930$	19.2934	0.632655
$931$	−2.52026	−0.0825981
$932$	18.0434	0.591032
$933$	−42.3323	−1.38590
$934$	20.0227	0.655162
$935$	33.6898	1.10178
$936$	0.0241965	0.000790886 0
$937$	0.306358	0.0100083	0.00500413	−	0.999987i	$-0.498407\pi$
$937$	0.306358	0.0100083	0.00500413	+	0.999987i	$0.498407\pi$
$938$	−87.0891	−2.84356
$939$	22.7985	0.744001
$940$	10.1808	0.332061
$941$	−8.83306	−0.287950	−0.143975	−	0.989581i	$-0.545988\pi$
$941$	−8.83306	−0.287950	−0.143975	+	0.989581i	$0.545988\pi$
$942$	5.26968	0.171695
$943$	57.8256	1.88306
$944$	−25.2718	−0.822526
$945$	−20.7311	−0.674382
$946$	1.09438	0.0355812
$947$	−15.8861	−0.516230	−0.258115	−	0.966114i	$-0.583101\pi$
$947$	−15.8861	−0.516230	−0.258115	+	0.966114i	$0.583101\pi$
$948$	−43.0746	−1.39900
$949$	38.9492	1.26434
$950$	−2.73246	−0.0886528
$951$	−19.7576	−0.640684
$952$	−2.60256	−0.0843496
$953$	−45.8789	−1.48616	−0.743081	−	0.669201i	$-0.766637\pi$
$953$	−45.8789	−1.48616	−0.743081	+	0.669201i	$0.766637\pi$
$954$	−0.356463	−0.0115409
$955$	17.9717	0.581550
$956$	11.0938	0.358798
$957$	−72.3845	−2.33986
$958$	−32.4859	−1.04957
$959$	−28.9162	−0.933752
$960$	−13.6009	−0.438969
$961$	−2.54901	−0.0822262
$962$	67.3514	2.17150
$963$	−0.271459	−0.00874765
$964$	−37.9739	−1.22306
$965$	25.4026	0.817738
$966$	77.0426	2.47881
$967$	48.9246	1.57331	0.786654	−	0.617394i	$-0.211812\pi$
$967$	48.9246	1.57331	0.786654	+	0.617394i	$0.211812\pi$
$968$	3.44316	0.110667
$969$	−3.20451	−0.102944
$970$	28.5307	0.916065
$971$	32.6323	1.04722	0.523610	−	0.851958i	$-0.324585\pi$
$971$	32.6323	1.04722	0.523610	+	0.851958i	$0.324585\pi$
$972$	−0.546082	−0.0175156
$973$	39.9411	1.28045
$974$	−31.0254	−0.994117
$975$	−44.9951	−1.44100
$976$	−7.10965	−0.227574
$977$	−7.75796	−0.248199	−0.124100	−	0.992270i	$-0.539604\pi$
$977$	−7.75796	−0.248199	−0.124100	+	0.992270i	$0.539604\pi$
$978$	−12.1824	−0.389550
$979$	−43.2563	−1.38248
$980$	−14.5180	−0.463759
$981$	0.131940	0.00421251
$982$	49.6319	1.58382
$983$	−0.898497	−0.0286576	−0.0143288	−	0.999897i	$-0.504561\pi$
$983$	−0.898497	−0.0286576	−0.0143288	+	0.999897i	$0.504561\pi$
$984$	−2.19980	−0.0701271
$985$	3.44141	0.109652
$986$	71.6541	2.28193
$987$	32.2313	1.02593
$988$	4.61470	0.146813
$989$	−0.544271	−0.0173068
$990$	−0.346893	−0.0110250
$991$	1.90886	0.0606369	0.0303185	−	0.999540i	$-0.490348\pi$
$991$	1.90886	0.0606369	0.0303185	+	0.999540i	$0.490348\pi$
$992$	−42.2669	−1.34197
$993$	−45.0892	−1.43086
$994$	−78.1931	−2.48014
$995$	4.33868	0.137545
$996$	−0.614036	−0.0194565
$997$	20.8626	0.660724	0.330362	−	0.943854i	$-0.392829\pi$
$997$	20.8626	0.660724	0.330362	+	0.943854i	$0.392829\pi$
$998$	28.5786	0.904638
$999$	26.3612	0.834030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.4	✓	30
3.2	odd	2		5571.2.a.g.1.27		30
4.3	odd	2		9904.2.a.n.1.23		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.4	✓	30	1.1	even	1	trivial
5571.2.a.g.1.27		30	3.2	odd	2
9904.2.a.n.1.23		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +O(q^{10})\)	\(q-1.98324 q^{2} -1.72419 q^{3} +1.93325 q^{4} -1.05779 q^{5} +3.41948 q^{6} +3.75491 q^{7} +0.132389 q^{8} -0.0271814 q^{9} +2.09786 q^{10} +6.08342 q^{11} -3.33328 q^{12} -6.72402 q^{13} -7.44689 q^{14} +1.82383 q^{15} -4.12905 q^{16} -5.23542 q^{17} +0.0539073 q^{18} -0.354999 q^{19} -2.04497 q^{20} -6.47416 q^{21} -12.0649 q^{22} +6.00028 q^{23} -0.228263 q^{24} -3.88108 q^{25} +13.3354 q^{26} +5.21942 q^{27} +7.25916 q^{28} +6.90103 q^{29} -3.61709 q^{30} -5.33395 q^{31} +7.92413 q^{32} -10.4889 q^{33} +10.3831 q^{34} -3.97191 q^{35} -0.0525484 q^{36} +5.05059 q^{37} +0.704048 q^{38} +11.5935 q^{39} -0.140040 q^{40} +9.63715 q^{41} +12.8398 q^{42} -0.0907075 q^{43} +11.7607 q^{44} +0.0287523 q^{45} -11.9000 q^{46} -4.97845 q^{47} +7.11925 q^{48} +7.09934 q^{49} +7.69711 q^{50} +9.02684 q^{51} -12.9992 q^{52} -6.61252 q^{53} -10.3514 q^{54} -6.43498 q^{55} +0.497107 q^{56} +0.612084 q^{57} -13.6864 q^{58} +6.12048 q^{59} +3.52591 q^{60} +1.72186 q^{61} +10.5785 q^{62} -0.102064 q^{63} -7.45736 q^{64} +7.11261 q^{65} +20.8021 q^{66} +11.6947 q^{67} -10.1214 q^{68} -10.3456 q^{69} +7.87726 q^{70} +10.5001 q^{71} -0.00359851 q^{72} -5.79254 q^{73} -10.0165 q^{74} +6.69170 q^{75} -0.686300 q^{76} +22.8427 q^{77} -22.9926 q^{78} +12.9226 q^{79} +4.36768 q^{80} -8.91772 q^{81} -19.1128 q^{82} +0.184214 q^{83} -12.5162 q^{84} +5.53798 q^{85} +0.179895 q^{86} -11.8987 q^{87} +0.805375 q^{88} -7.11052 q^{89} -0.0570227 q^{90} -25.2481 q^{91} +11.6000 q^{92} +9.19672 q^{93} +9.87346 q^{94} +0.375514 q^{95} -13.6627 q^{96} +13.5999 q^{97} -14.0797 q^{98} -0.165356 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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