LMFDB - Embedded newform 4033.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +O(q^{10})$	\(q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +4.46684 q^{10} +3.88769 q^{11} +17.6881 q^{12} +3.80642 q^{13} +9.25654 q^{14} -5.03714 q^{15} +16.7659 q^{16} +1.84146 q^{17} -18.6820 q^{18} -6.95397 q^{19} -9.14036 q^{20} -10.4384 q^{21} -10.7636 q^{22} +4.09671 q^{23} -31.6839 q^{24} -2.39705 q^{25} -10.5386 q^{26} +11.7008 q^{27} -18.9414 q^{28} +3.22497 q^{29} +13.9461 q^{30} +1.83556 q^{31} -26.1224 q^{32} +12.1379 q^{33} -5.09834 q^{34} +5.39404 q^{35} +38.2284 q^{36} +1.00000 q^{37} +19.2531 q^{38} +11.8841 q^{39} +16.3727 q^{40} -2.86442 q^{41} +28.9001 q^{42} -1.93334 q^{43} +22.0253 q^{44} -10.8865 q^{45} -11.3423 q^{46} +7.27647 q^{47} +52.3453 q^{48} +4.17796 q^{49} +6.63657 q^{50} +5.74927 q^{51} +21.5648 q^{52} +5.78810 q^{53} -32.3954 q^{54} -6.27227 q^{55} +33.9288 q^{56} -21.7112 q^{57} -8.92879 q^{58} -12.5053 q^{59} -28.5374 q^{60} +7.02458 q^{61} -5.08200 q^{62} -22.5599 q^{63} +38.7920 q^{64} -6.14115 q^{65} -33.6055 q^{66} +14.0937 q^{67} +10.4326 q^{68} +12.7905 q^{69} -14.9342 q^{70} +2.13334 q^{71} -68.4769 q^{72} -3.64184 q^{73} -2.76864 q^{74} -7.48390 q^{75} -39.3970 q^{76} -12.9979 q^{77} -32.9029 q^{78} -9.58443 q^{79} -27.0495 q^{80} +16.2884 q^{81} +7.93055 q^{82} +9.85300 q^{83} -59.1374 q^{84} -2.97094 q^{85} +5.35272 q^{86} +10.0688 q^{87} -39.4530 q^{88} +14.5544 q^{89} +30.1409 q^{90} -12.7262 q^{91} +23.2095 q^{92} +5.73085 q^{93} -20.1460 q^{94} +11.2193 q^{95} -81.5577 q^{96} +2.55129 q^{97} -11.5673 q^{98} +26.2330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−2.76864	−1.95773	−0.978864	−	0.204514i	$-0.934439\pi$
$2$	−2.76864	−1.95773	−0.978864	+	0.204514i	$0.934439\pi$
$3$	3.12213	1.80256	0.901282	−	0.433233i	$-0.142627\pi$
$3$	3.12213	1.80256	0.901282	+	0.433233i	$0.142627\pi$
$4$	5.66539	2.83270
$5$	−1.61337	−0.721520	−0.360760	−	0.932659i	$-0.617483\pi$
$5$	−1.61337	−0.721520	−0.360760	+	0.932659i	$0.617483\pi$
$6$	−8.64407	−3.52893
$7$	−3.34335	−1.26367	−0.631833	−	0.775105i	$-0.717697\pi$
$7$	−3.34335	−1.26367	−0.631833	+	0.775105i	$0.717697\pi$
$8$	−10.1482	−3.58792
$9$	6.74771	2.24924
$10$	4.46684	1.41254
$11$	3.88769	1.17218	0.586092	−	0.810245i	$-0.300666\pi$
$11$	3.88769	1.17218	0.586092	+	0.810245i	$0.300666\pi$
$12$	17.6881	5.10611
$13$	3.80642	1.05571	0.527855	−	0.849334i	$-0.322996\pi$
$13$	3.80642	1.05571	0.527855	+	0.849334i	$0.322996\pi$
$14$	9.25654	2.47391
$15$	−5.03714	−1.30058
$16$	16.7659	4.19147
$17$	1.84146	0.446619	0.223309	−	0.974748i	$-0.428314\pi$
$17$	1.84146	0.446619	0.223309	+	0.974748i	$0.428314\pi$
$18$	−18.6820	−4.40339
$19$	−6.95397	−1.59535	−0.797676	−	0.603087i	$-0.793937\pi$
$19$	−6.95397	−1.59535	−0.797676	+	0.603087i	$0.793937\pi$
$20$	−9.14036	−2.04385
$21$	−10.4384	−2.27784
$22$	−10.7636	−2.29482
$23$	4.09671	0.854223	0.427112	−	0.904199i	$-0.359531\pi$
$23$	4.09671	0.854223	0.427112	+	0.904199i	$0.359531\pi$
$24$	−31.6839	−6.46745
$25$	−2.39705	−0.479409
$26$	−10.5386	−2.06679
$27$	11.7008	2.25183
$28$	−18.9414	−3.57958
$29$	3.22497	0.598861	0.299431	−	0.954118i	$-0.403203\pi$
$29$	3.22497	0.598861	0.299431	+	0.954118i	$0.403203\pi$
$30$	13.9461	2.54619
$31$	1.83556	0.329676	0.164838	−	0.986321i	$-0.447290\pi$
$31$	1.83556	0.329676	0.164838	+	0.986321i	$0.447290\pi$
$32$	−26.1224	−4.61784
$33$	12.1379	2.11293
$34$	−5.09834	−0.874357
$35$	5.39404	0.911760
$36$	38.2284	6.37140
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	19.2531	3.12326
$39$	11.8841	1.90298
$40$	16.3727	2.58875
$41$	−2.86442	−0.447347	−0.223673	−	0.974664i	$-0.571805\pi$
$41$	−2.86442	−0.447347	−0.223673	+	0.974664i	$0.571805\pi$
$42$	28.9001	4.45939
$43$	−1.93334	−0.294831	−0.147416	−	0.989075i	$-0.547095\pi$
$43$	−1.93334	−0.294831	−0.147416	+	0.989075i	$0.547095\pi$
$44$	22.0253	3.32044
$45$	−10.8865	−1.62287
$46$	−11.3423	−1.67234
$47$	7.27647	1.06138	0.530691	−	0.847565i	$-0.321932\pi$
$47$	7.27647	1.06138	0.530691	+	0.847565i	$0.321932\pi$
$48$	52.3453	7.55539
$49$	4.17796	0.596852
$50$	6.63657	0.938553
$51$	5.74927	0.805058
$52$	21.5648	2.99051
$53$	5.78810	0.795057	0.397528	−	0.917590i	$-0.369868\pi$
$53$	5.78810	0.795057	0.397528	+	0.917590i	$0.369868\pi$
$54$	−32.3954	−4.40846
$55$	−6.27227	−0.845753
$56$	33.9288	4.53393
$57$	−21.7112	−2.87572
$58$	−8.92879	−1.17241
$59$	−12.5053	−1.62805	−0.814023	−	0.580832i	$-0.802727\pi$
$59$	−12.5053	−1.62805	−0.814023	+	0.580832i	$0.802727\pi$
$60$	−28.5374	−3.68416
$61$	7.02458	0.899405	0.449703	−	0.893178i	$-0.351530\pi$
$61$	7.02458	0.899405	0.449703	+	0.893178i	$0.351530\pi$
$62$	−5.08200	−0.645415
$63$	−22.5599	−2.84228
$64$	38.7920	4.84900
$65$	−6.14115	−0.761716
$66$	−33.6055	−4.13655
$67$	14.0937	1.72182	0.860909	−	0.508759i	$-0.169896\pi$
$67$	14.0937	1.72182	0.860909	+	0.508759i	$0.169896\pi$
$68$	10.4326	1.26513
$69$	12.7905	1.53979
$70$	−14.9342	−1.78498
$71$	2.13334	0.253181	0.126590	−	0.991955i	$-0.459597\pi$
$71$	2.13334	0.253181	0.126590	+	0.991955i	$0.459597\pi$
$72$	−68.4769	−8.07008
$73$	−3.64184	−0.426245	−0.213123	−	0.977025i	$-0.568363\pi$
$73$	−3.64184	−0.426245	−0.213123	+	0.977025i	$0.568363\pi$
$74$	−2.76864	−0.321848
$75$	−7.48390	−0.864166
$76$	−39.3970	−4.51915
$77$	−12.9979	−1.48125
$78$	−32.9029	−3.72553
$79$	−9.58443	−1.07833	−0.539166	−	0.842199i	$-0.681261\pi$
$79$	−9.58443	−1.07833	−0.539166	+	0.842199i	$0.681261\pi$
$80$	−27.0495	−3.02423
$81$	16.2884	1.80982
$82$	7.93055	0.875783
$83$	9.85300	1.08151	0.540754	−	0.841181i	$-0.318139\pi$
$83$	9.85300	1.08151	0.540754	+	0.841181i	$0.318139\pi$
$84$	−59.1374	−6.45242
$85$	−2.97094	−0.322244
$86$	5.35272	0.577199
$87$	10.0688	1.07949
$88$	−39.4530	−4.20570
$89$	14.5544	1.54277	0.771383	−	0.636371i	$-0.219565\pi$
$89$	14.5544	1.54277	0.771383	+	0.636371i	$0.219565\pi$
$90$	30.1409	3.17713
$91$	−12.7262	−1.33407
$92$	23.2095	2.41976
$93$	5.73085	0.594261
$94$	−20.1460	−2.07790
$95$	11.2193	1.15108
$96$	−81.5577	−8.32395
$97$	2.55129	0.259045	0.129522	−	0.991577i	$-0.458656\pi$
$97$	2.55129	0.259045	0.129522	+	0.991577i	$0.458656\pi$
$98$	−11.5673	−1.16847
$99$	26.2330	2.63652
$100$	−13.5802	−1.35802
$101$	1.73108	0.172249	0.0861246	−	0.996284i	$-0.472552\pi$
$101$	1.73108	0.172249	0.0861246	+	0.996284i	$0.472552\pi$
$102$	−15.9177	−1.57608
$103$	−14.2240	−1.40153	−0.700767	−	0.713390i	$-0.747159\pi$
$103$	−14.2240	−1.40153	−0.700767	+	0.713390i	$0.747159\pi$
$104$	−38.6282	−3.78780
$105$	16.8409	1.64350
$106$	−16.0252	−1.55650
$107$	9.11248	0.880937	0.440468	−	0.897768i	$-0.354812\pi$
$107$	9.11248	0.880937	0.440468	+	0.897768i	$0.354812\pi$
$108$	66.2898	6.37874
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	17.3657	1.65575
$111$	3.12213	0.296340
$112$	−56.0542	−5.29662
$113$	−3.16377	−0.297622	−0.148811	−	0.988866i	$-0.547545\pi$
$113$	−3.16377	−0.297622	−0.148811	+	0.988866i	$0.547545\pi$
$114$	60.1107	5.62988
$115$	−6.60950	−0.616339
$116$	18.2707	1.69639
$117$	25.6846	2.37454
$118$	34.6226	3.18727
$119$	−6.15662	−0.564377
$120$	51.1178	4.66639
$121$	4.11415	0.374014
$122$	−19.4486	−1.76079
$123$	−8.94309	−0.806371
$124$	10.3991	0.933871
$125$	11.9342	1.06742
$126$	62.4604	5.56441
$127$	14.3425	1.27269	0.636346	−	0.771404i	$-0.280445\pi$
$127$	14.3425	1.27269	0.636346	+	0.771404i	$0.280445\pi$
$128$	−55.1563	−4.87518
$129$	−6.03613	−0.531452
$130$	17.0027	1.49123
$131$	−9.83339	−0.859147	−0.429574	−	0.903032i	$-0.641336\pi$
$131$	−9.83339	−0.859147	−0.429574	+	0.903032i	$0.641336\pi$
$132$	68.7659	5.98530
$133$	23.2495	2.01599
$134$	−39.0204	−3.37085
$135$	−18.8777	−1.62474
$136$	−18.6874	−1.60243
$137$	−8.50721	−0.726820	−0.363410	−	0.931629i	$-0.618388\pi$
$137$	−8.50721	−0.726820	−0.363410	+	0.931629i	$0.618388\pi$
$138$	−35.4123	−3.01449
$139$	10.1041	0.857019	0.428509	−	0.903537i	$-0.359039\pi$
$139$	10.1041	0.857019	0.428509	+	0.903537i	$0.359039\pi$
$140$	30.5594	2.58274
$141$	22.7181	1.91321
$142$	−5.90646	−0.495659
$143$	14.7982	1.23749
$144$	113.131	9.42761
$145$	−5.20306	−0.432090
$146$	10.0830	0.834472
$147$	13.0441	1.07586
$148$	5.66539	0.465692
$149$	14.7565	1.20890	0.604450	−	0.796643i	$-0.293393\pi$
$149$	14.7565	1.20890	0.604450	+	0.796643i	$0.293393\pi$
$150$	20.7203	1.69180
$151$	−18.5105	−1.50636	−0.753182	−	0.657813i	$-0.771482\pi$
$151$	−18.5105	−1.50636	−0.753182	+	0.657813i	$0.771482\pi$
$152$	70.5701	5.72399
$153$	12.4256	1.00455
$154$	35.9866	2.89988
$155$	−2.96143	−0.237867
$156$	67.3283	5.39058
$157$	1.29859	0.103639	0.0518195	−	0.998656i	$-0.483498\pi$
$157$	1.29859	0.103639	0.0518195	+	0.998656i	$0.483498\pi$
$158$	26.5359	2.11108
$159$	18.0712	1.43314
$160$	42.1451	3.33186
$161$	−13.6967	−1.07945
$162$	−45.0968	−3.54314
$163$	−10.0122	−0.784213	−0.392106	−	0.919920i	$-0.628254\pi$
$163$	−10.0122	−0.784213	−0.392106	+	0.919920i	$0.628254\pi$
$164$	−16.2280	−1.26720
$165$	−19.5829	−1.52452
$166$	−27.2795	−2.11730
$167$	24.2850	1.87923	0.939614	−	0.342237i	$-0.111185\pi$
$167$	24.2850	1.87923	0.939614	+	0.342237i	$0.111185\pi$
$168$	105.930	8.17270
$169$	1.48881	0.114524
$170$	8.22549	0.630866
$171$	−46.9234	−3.58832
$172$	−10.9531	−0.835167
$173$	−25.2346	−1.91855	−0.959275	−	0.282473i	$-0.908845\pi$
$173$	−25.2346	−1.91855	−0.959275	+	0.282473i	$0.908845\pi$
$174$	−27.8769	−2.11334
$175$	8.01416	0.605813
$176$	65.1806	4.91317
$177$	−39.0431	−2.93466
$178$	−40.2960	−3.02031
$179$	23.2089	1.73472	0.867358	−	0.497685i	$-0.165817\pi$
$179$	23.2089	1.73472	0.867358	+	0.497685i	$0.165817\pi$
$180$	−61.6764	−4.59709
$181$	12.8021	0.951574	0.475787	−	0.879560i	$-0.342163\pi$
$181$	12.8021	0.951574	0.475787	+	0.879560i	$0.342163\pi$
$182$	35.2342	2.61174
$183$	21.9317	1.62123
$184$	−41.5741	−3.06488
$185$	−1.61337	−0.118617
$186$	−15.8667	−1.16340
$187$	7.15901	0.523519
$188$	41.2241	3.00658
$189$	−39.1199	−2.84556
$190$	−31.0623	−2.25350
$191$	21.2022	1.53414	0.767068	−	0.641566i	$-0.221715\pi$
$191$	21.2022	1.53414	0.767068	+	0.641566i	$0.221715\pi$
$192$	121.114	8.74063
$193$	−8.81889	−0.634798	−0.317399	−	0.948292i	$-0.602809\pi$
$193$	−8.81889	−0.634798	−0.317399	+	0.948292i	$0.602809\pi$
$194$	−7.06362	−0.507139
$195$	−19.1735	−1.37304
$196$	23.6698	1.69070
$197$	17.5294	1.24892	0.624461	−	0.781056i	$-0.285319\pi$
$197$	17.5294	1.24892	0.624461	+	0.781056i	$0.285319\pi$
$198$	−72.6299	−5.16158
$199$	−14.0884	−0.998697	−0.499348	−	0.866401i	$-0.666427\pi$
$199$	−14.0884	−0.998697	−0.499348	+	0.866401i	$0.666427\pi$
$200$	24.3256	1.72008
$201$	44.0023	3.10369
$202$	−4.79275	−0.337217
$203$	−10.7822	−0.756761
$204$	32.5718	2.28049
$205$	4.62136	0.322769
$206$	39.3813	2.74382
$207$	27.6434	1.92135
$208$	63.8180	4.42498
$209$	−27.0349	−1.87004
$210$	−46.6265	−3.21753
$211$	−16.2991	−1.12208	−0.561038	−	0.827790i	$-0.689598\pi$
$211$	−16.2991	−1.12208	−0.561038	+	0.827790i	$0.689598\pi$
$212$	32.7919	2.25215
$213$	6.66057	0.456375
$214$	−25.2292	−1.72463
$215$	3.11918	0.212726
$216$	−118.742	−8.07937
$217$	−6.13690	−0.416600
$218$	2.76864	0.187516
$219$	−11.3703	−0.768335
$220$	−35.5349	−2.39576
$221$	7.00935	0.471500
$222$	−8.64407	−0.580152
$223$	11.5553	0.773797	0.386899	−	0.922122i	$-0.373546\pi$
$223$	11.5553	0.773797	0.386899	+	0.922122i	$0.373546\pi$
$224$	87.3364	5.83541
$225$	−16.1746	−1.07830
$226$	8.75934	0.582663
$227$	0.204192	0.0135527	0.00677635	−	0.999977i	$-0.497843\pi$
$227$	0.204192	0.0135527	0.00677635	+	0.999977i	$0.497843\pi$
$228$	−123.003	−8.14605
$229$	4.75914	0.314493	0.157246	−	0.987559i	$-0.449738\pi$
$229$	4.75914	0.314493	0.157246	+	0.987559i	$0.449738\pi$
$230$	18.2994	1.20662
$231$	−40.5812	−2.67004
$232$	−32.7275	−2.14867
$233$	−20.4066	−1.33688	−0.668442	−	0.743764i	$-0.733038\pi$
$233$	−20.4066	−1.33688	−0.668442	+	0.743764i	$0.733038\pi$
$234$	−71.1115	−4.64870
$235$	−11.7396	−0.765809
$236$	−70.8472	−4.61176
$237$	−29.9238	−1.94376
$238$	17.0455	1.10490
$239$	23.8903	1.54534	0.772668	−	0.634811i	$-0.218922\pi$
$239$	23.8903	1.54534	0.772668	+	0.634811i	$0.218922\pi$
$240$	−84.4522	−5.45136
$241$	−10.3426	−0.666224	−0.333112	−	0.942887i	$-0.608099\pi$
$241$	−10.3426	−0.666224	−0.333112	+	0.942887i	$0.608099\pi$
$242$	−11.3906	−0.732217
$243$	15.7521	1.01050
$244$	39.7970	2.54774
$245$	−6.74059	−0.430640
$246$	24.7602	1.57865
$247$	−26.4697	−1.68423
$248$	−18.6275	−1.18285
$249$	30.7624	1.94949
$250$	−33.0414	−2.08972
$251$	1.75869	0.111008	0.0555038	−	0.998458i	$-0.482323\pi$
$251$	1.75869	0.111008	0.0555038	+	0.998458i	$0.482323\pi$
$252$	−127.811	−8.05132
$253$	15.9268	1.00131
$254$	−39.7093	−2.49158
$255$	−9.27568	−0.580865
$256$	75.1243	4.69527
$257$	30.8732	1.92582	0.962908	−	0.269828i	$-0.0869670\pi$
$257$	30.8732	1.92582	0.962908	+	0.269828i	$0.0869670\pi$
$258$	16.7119	1.04044
$259$	−3.34335	−0.207745
$260$	−34.7920	−2.15771
$261$	21.7611	1.34698
$262$	27.2252	1.68198
$263$	7.80846	0.481491	0.240745	−	0.970588i	$-0.422608\pi$
$263$	7.80846	0.481491	0.240745	+	0.970588i	$0.422608\pi$
$264$	−123.177	−7.58104
$265$	−9.33833	−0.573649
$266$	−64.3697	−3.94676
$267$	45.4408	2.78093
$268$	79.8462	4.87739
$269$	11.2276	0.684558	0.342279	−	0.939598i	$-0.388801\pi$
$269$	11.2276	0.684558	0.342279	+	0.939598i	$0.388801\pi$
$270$	52.2657	3.18079
$271$	0.492152	0.0298961	0.0149480	−	0.999888i	$-0.495242\pi$
$271$	0.492152	0.0298961	0.0149480	+	0.999888i	$0.495242\pi$
$272$	30.8736	1.87199
$273$	−39.7328	−2.40474
$274$	23.5534	1.42291
$275$	−9.31898	−0.561956
$276$	72.4630	4.36176
$277$	26.2559	1.57757	0.788783	−	0.614672i	$-0.210712\pi$
$277$	26.2559	1.57757	0.788783	+	0.614672i	$0.210712\pi$
$278$	−27.9747	−1.67781
$279$	12.3858	0.741518
$280$	−54.7397	−3.27132
$281$	−18.9457	−1.13021	−0.565103	−	0.825021i	$-0.691163\pi$
$281$	−18.9457	−1.13021	−0.565103	+	0.825021i	$0.691163\pi$
$282$	−62.8984	−3.74554
$283$	22.5710	1.34170	0.670852	−	0.741591i	$-0.265928\pi$
$283$	22.5710	1.34170	0.670852	+	0.741591i	$0.265928\pi$
$284$	12.0862	0.717185
$285$	35.0282	2.07489
$286$	−40.9709	−2.42266
$287$	9.57674	0.565297
$288$	−176.267	−10.3866
$289$	−13.6090	−0.800532
$290$	14.4054	0.845915
$291$	7.96547	0.466944
$292$	−20.6325	−1.20742
$293$	19.5955	1.14478	0.572392	−	0.819980i	$-0.306016\pi$
$293$	19.5955	1.14478	0.572392	+	0.819980i	$0.306016\pi$
$294$	−36.1146	−2.10625
$295$	20.1756	1.17467
$296$	−10.1482	−0.589850
$297$	45.4892	2.63955
$298$	−40.8555	−2.36670
$299$	15.5938	0.901812
$300$	−42.3992	−2.44792
$301$	6.46381	0.372568
$302$	51.2490	2.94905
$303$	5.40467	0.310490
$304$	−116.590	−6.68687
$305$	−11.3332	−0.648938
$306$	−34.4021	−1.96664
$307$	33.6617	1.92117	0.960586	−	0.277982i	$-0.0896657\pi$
$307$	33.6617	1.92117	0.960586	+	0.277982i	$0.0896657\pi$
$308$	−73.6382	−4.19593
$309$	−44.4093	−2.52635
$310$	8.19914	0.465680
$311$	−0.765802	−0.0434246	−0.0217123	−	0.999764i	$-0.506912\pi$
$311$	−0.765802	−0.0434246	−0.0217123	+	0.999764i	$0.506912\pi$
$312$	−120.602	−6.82776
$313$	−8.97560	−0.507331	−0.253665	−	0.967292i	$-0.581636\pi$
$313$	−8.97560	−0.507331	−0.253665	+	0.967292i	$0.581636\pi$
$314$	−3.59534	−0.202897
$315$	36.3974	2.05076
$316$	−54.2995	−3.05459
$317$	−11.1037	−0.623645	−0.311823	−	0.950140i	$-0.600939\pi$
$317$	−11.1037	−0.623645	−0.311823	+	0.950140i	$0.600939\pi$
$318$	−50.0328	−2.80570
$319$	12.5377	0.701975
$320$	−62.5857	−3.49865
$321$	28.4504	1.58794
$322$	37.9214	2.11327
$323$	−12.8054	−0.712513
$324$	92.2803	5.12668
$325$	−9.12416	−0.506117
$326$	27.7201	1.53527
$327$	−3.12213	−0.172654
$328$	29.0686	1.60504
$329$	−24.3278	−1.34123
$330$	54.2180	2.98460
$331$	18.3752	1.00999	0.504996	−	0.863122i	$-0.331494\pi$
$331$	18.3752	1.00999	0.504996	+	0.863122i	$0.331494\pi$
$332$	55.8211	3.06358
$333$	6.74771	0.369772
$334$	−67.2364	−3.67901
$335$	−22.7383	−1.24233
$336$	−175.008	−9.54749
$337$	20.6948	1.12732	0.563658	−	0.826008i	$-0.309394\pi$
$337$	20.6948	1.12732	0.563658	+	0.826008i	$0.309394\pi$
$338$	−4.12199	−0.224207
$339$	−9.87769	−0.536483
$340$	−16.8316	−0.912819
$341$	7.13608	0.386440
$342$	129.914	7.02495
$343$	9.43505	0.509445
$344$	19.6198	1.05783
$345$	−20.6357	−1.11099
$346$	69.8656	3.75600
$347$	−0.106910	−0.00573921	−0.00286961	−	0.999996i	$-0.500913\pi$
$347$	−0.106910	−0.00573921	−0.00286961	+	0.999996i	$0.500913\pi$
$348$	57.0436	3.05786
$349$	−27.1790	−1.45486	−0.727429	−	0.686183i	$-0.759285\pi$
$349$	−27.1790	−1.45486	−0.727429	+	0.686183i	$0.759285\pi$
$350$	−22.1884	−1.18602
$351$	44.5382	2.37728
$352$	−101.556	−5.41295
$353$	−30.9054	−1.64493	−0.822463	−	0.568819i	$-0.807401\pi$
$353$	−30.9054	−1.64493	−0.822463	+	0.568819i	$0.807401\pi$
$354$	108.096	5.74526
$355$	−3.44186	−0.182675
$356$	82.4565	4.37019
$357$	−19.2218	−1.01732
$358$	−64.2572	−3.39610
$359$	32.8630	1.73444	0.867221	−	0.497924i	$-0.165904\pi$
$359$	32.8630	1.73444	0.867221	+	0.497924i	$0.165904\pi$
$360$	110.478	5.82272
$361$	29.3578	1.54515
$362$	−35.4445	−1.86292
$363$	12.8449	0.674184
$364$	−72.0987	−3.77900
$365$	5.87563	0.307544
$366$	−60.7210	−3.17394
$367$	−16.4096	−0.856572	−0.428286	−	0.903643i	$-0.640882\pi$
$367$	−16.4096	−0.856572	−0.428286	+	0.903643i	$0.640882\pi$
$368$	68.6850	3.58045
$369$	−19.3282	−1.00619
$370$	4.46684	0.232220
$371$	−19.3516	−1.00469
$372$	32.4675	1.68336
$373$	−27.6209	−1.43016	−0.715079	−	0.699043i	$-0.753609\pi$
$373$	−27.6209	−1.43016	−0.715079	+	0.699043i	$0.753609\pi$
$374$	−19.8208	−1.02491
$375$	37.2600	1.92410
$376$	−73.8429	−3.80816
$377$	12.2756	0.632224
$378$	108.309	5.57082
$379$	−11.3449	−0.582749	−0.291374	−	0.956609i	$-0.594113\pi$
$379$	−11.3449	−0.582749	−0.291374	+	0.956609i	$0.594113\pi$
$380$	63.5618	3.26065
$381$	44.7792	2.29411
$382$	−58.7013	−3.00342
$383$	37.6711	1.92490	0.962452	−	0.271452i	$-0.0875040\pi$
$383$	37.6711	1.92490	0.962452	+	0.271452i	$0.0875040\pi$
$384$	−172.205	−8.78782
$385$	20.9704	1.06875
$386$	24.4164	1.24276
$387$	−13.0456	−0.663144
$388$	14.4541	0.733794
$389$	3.22236	0.163380	0.0816902	−	0.996658i	$-0.473968\pi$
$389$	3.22236	0.163380	0.0816902	+	0.996658i	$0.473968\pi$
$390$	53.0845	2.68804
$391$	7.54391	0.381512
$392$	−42.3987	−2.14146
$393$	−30.7011	−1.54867
$394$	−48.5328	−2.44505
$395$	15.4632	0.778038
$396$	148.620	7.46845
$397$	−3.41350	−0.171319	−0.0856594	−	0.996324i	$-0.527300\pi$
$397$	−3.41350	−0.171319	−0.0856594	+	0.996324i	$0.527300\pi$
$398$	39.0056	1.95518
$399$	72.5881	3.63395
$400$	−40.1886	−2.00943
$401$	−27.5181	−1.37419	−0.687095	−	0.726568i	$-0.741114\pi$
$401$	−27.5181	−1.37419	−0.687095	+	0.726568i	$0.741114\pi$
$402$	−121.827	−6.07617
$403$	6.98689	0.348042
$404$	9.80726	0.487929
$405$	−26.2792	−1.30582
$406$	29.8520	1.48153
$407$	3.88769	0.192706
$408$	−58.3445	−2.88848
$409$	12.6710	0.626540	0.313270	−	0.949664i	$-0.398575\pi$
$409$	12.6710	0.626540	0.313270	+	0.949664i	$0.398575\pi$
$410$	−12.7949	−0.631895
$411$	−26.5606	−1.31014
$412$	−80.5847	−3.97012
$413$	41.8094	2.05731
$414$	−76.5348	−3.76148
$415$	−15.8965	−0.780329
$416$	−99.4329	−4.87510
$417$	31.5463	1.54483
$418$	74.8501	3.66104
$419$	−24.5440	−1.19905	−0.599527	−	0.800355i	$-0.704645\pi$
$419$	−24.5440	−1.19905	−0.599527	+	0.800355i	$0.704645\pi$
$420$	95.4104	4.65555
$421$	21.5089	1.04828	0.524140	−	0.851632i	$-0.324387\pi$
$421$	21.5089	1.04828	0.524140	+	0.851632i	$0.324387\pi$
$422$	45.1264	2.19672
$423$	49.0995	2.38730
$424$	−58.7386	−2.85260
$425$	−4.41406	−0.214113
$426$	−18.4407	−0.893457
$427$	−23.4856	−1.13655
$428$	51.6258	2.49543
$429$	46.2019	2.23065
$430$	−8.63590	−0.416460
$431$	−20.0907	−0.967734	−0.483867	−	0.875142i	$-0.660768\pi$
$431$	−20.0907	−0.967734	−0.483867	+	0.875142i	$0.660768\pi$
$432$	196.175	9.43847
$433$	12.6758	0.609158	0.304579	−	0.952487i	$-0.401484\pi$
$433$	12.6758	0.609158	0.304579	+	0.952487i	$0.401484\pi$
$434$	16.9909	0.815589
$435$	−16.2446	−0.778870
$436$	−5.66539	−0.271323
$437$	−28.4884	−1.36279
$438$	31.4804	1.50419
$439$	−17.8879	−0.853742	−0.426871	−	0.904313i	$-0.640384\pi$
$439$	−17.8879	−0.853742	−0.426871	+	0.904313i	$0.640384\pi$
$440$	63.6521	3.03449
$441$	28.1917	1.34246
$442$	−19.4064	−0.923068
$443$	2.23203	0.106047	0.0530235	−	0.998593i	$-0.483114\pi$
$443$	2.23203	0.106047	0.0530235	+	0.998593i	$0.483114\pi$
$444$	17.6881	0.839440
$445$	−23.4816	−1.11314
$446$	−31.9924	−1.51488
$447$	46.0717	2.17912
$448$	−129.695	−6.12751
$449$	−34.4729	−1.62688	−0.813438	−	0.581652i	$-0.802407\pi$
$449$	−34.4729	−1.62688	−0.813438	+	0.581652i	$0.802407\pi$
$450$	44.7816	2.11103
$451$	−11.1360	−0.524372
$452$	−17.9240	−0.843073
$453$	−57.7922	−2.71532
$454$	−0.565335	−0.0265325
$455$	20.5320	0.962554
$456$	220.329	10.3179
$457$	17.3065	0.809562	0.404781	−	0.914414i	$-0.367348\pi$
$457$	17.3065	0.809562	0.404781	+	0.914414i	$0.367348\pi$
$458$	−13.1764	−0.615691
$459$	21.5466	1.00571
$460$	−37.4454	−1.74590
$461$	21.8186	1.01619	0.508097	−	0.861300i	$-0.330349\pi$
$461$	21.8186	1.01619	0.508097	+	0.861300i	$0.330349\pi$
$462$	112.355	5.22722
$463$	36.0980	1.67762	0.838809	−	0.544426i	$-0.183252\pi$
$463$	36.0980	1.67762	0.838809	+	0.544426i	$0.183252\pi$
$464$	54.0694	2.51011
$465$	−9.24596	−0.428771
$466$	56.4988	2.61725
$467$	7.60070	0.351718	0.175859	−	0.984415i	$-0.443730\pi$
$467$	7.60070	0.351718	0.175859	+	0.984415i	$0.443730\pi$
$468$	145.513	6.72635
$469$	−47.1201	−2.17580
$470$	32.5028	1.49924
$471$	4.05438	0.186816
$472$	126.905	5.84130
$473$	−7.51622	−0.345596
$474$	82.8485	3.80536
$475$	16.6690	0.764827
$476$	−34.8797	−1.59871
$477$	39.0564	1.78827
$478$	−66.1438	−3.02534
$479$	−22.9636	−1.04923	−0.524616	−	0.851339i	$-0.675791\pi$
$479$	−22.9636	−1.04923	−0.524616	+	0.851339i	$0.675791\pi$
$480$	131.583	6.00589
$481$	3.80642	0.173558
$482$	28.6349	1.30428
$483$	−42.7630	−1.94578
$484$	23.3083	1.05947
$485$	−4.11617	−0.186906
$486$	−43.6119	−1.97828
$487$	23.7112	1.07446	0.537229	−	0.843436i	$-0.319471\pi$
$487$	23.7112	1.07446	0.537229	+	0.843436i	$0.319471\pi$
$488$	−71.2866	−3.22699
$489$	−31.2593	−1.41359
$490$	18.6623	0.843076
$491$	−6.19229	−0.279454	−0.139727	−	0.990190i	$-0.544623\pi$
$491$	−6.19229	−0.279454	−0.139727	+	0.990190i	$0.544623\pi$
$492$	−50.6661	−2.28420
$493$	5.93863	0.267463
$494$	73.2853	3.29726
$495$	−42.3235	−1.90230
$496$	30.7747	1.38183
$497$	−7.13249	−0.319936
$498$	−85.1701	−3.81656
$499$	−40.9988	−1.83536	−0.917680	−	0.397321i	$-0.869940\pi$
$499$	−40.9988	−1.83536	−0.917680	+	0.397321i	$0.869940\pi$
$500$	67.6116	3.02368
$501$	75.8209	3.38743
$502$	−4.86919	−0.217323
$503$	18.0643	0.805446	0.402723	−	0.915322i	$-0.368064\pi$
$503$	18.0643	0.805446	0.402723	+	0.915322i	$0.368064\pi$
$504$	228.942	10.1979
$505$	−2.79287	−0.124281
$506$	−44.0955	−1.96028
$507$	4.64827	0.206437
$508$	81.2560	3.60515
$509$	21.2323	0.941103	0.470552	−	0.882373i	$-0.344055\pi$
$509$	21.2323	0.941103	0.470552	+	0.882373i	$0.344055\pi$
$510$	25.6810	1.13718
$511$	12.1759	0.538632
$512$	−97.6798	−4.31688
$513$	−81.3673	−3.59245
$514$	−85.4769	−3.77022
$515$	22.9486	1.01123
$516$	−34.1971	−1.50544
$517$	28.2887	1.24414
$518$	9.25654	0.406709
$519$	−78.7857	−3.45831
$520$	62.3214	2.73297
$521$	−10.1868	−0.446292	−0.223146	−	0.974785i	$-0.571633\pi$
$521$	−10.1868	−0.446292	−0.223146	+	0.974785i	$0.571633\pi$
$522$	−60.2488	−2.63702
$523$	−12.5749	−0.549863	−0.274932	−	0.961464i	$-0.588655\pi$
$523$	−12.5749	−0.549863	−0.274932	+	0.961464i	$0.588655\pi$
$524$	−55.7100	−2.43370
$525$	25.0213	1.09202
$526$	−21.6189	−0.942627
$527$	3.38010	0.147239
$528$	203.502	8.85631
$529$	−6.21696	−0.270302
$530$	25.8545	1.12305
$531$	−84.3818	−3.66186
$532$	131.718	5.71069
$533$	−10.9032	−0.472269
$534$	−125.809	−5.44431
$535$	−14.7018	−0.635613
$536$	−143.025	−6.17774
$537$	72.4613	3.12693
$538$	−31.0852	−1.34018
$539$	16.2426	0.699620
$540$	−106.950	−4.60239
$541$	−32.3227	−1.38966	−0.694831	−	0.719173i	$-0.744521\pi$
$541$	−32.3227	−1.38966	−0.694831	+	0.719173i	$0.744521\pi$
$542$	−1.36259	−0.0585284
$543$	39.9699	1.71527
$544$	−48.1033	−2.06241
$545$	1.61337	0.0691090
$546$	110.006	4.70782
$547$	19.7943	0.846342	0.423171	−	0.906050i	$-0.360917\pi$
$547$	19.7943	0.846342	0.423171	+	0.906050i	$0.360917\pi$
$548$	−48.1967	−2.05886
$549$	47.3998	2.02297
$550$	25.8010	1.10016
$551$	−22.4263	−0.955394
$552$	−129.800	−5.52465
$553$	32.0441	1.36265
$554$	−72.6933	−3.08844
$555$	−5.03714	−0.213815
$556$	57.2437	2.42767
$557$	−28.9516	−1.22672	−0.613358	−	0.789805i	$-0.710182\pi$
$557$	−28.9516	−1.22672	−0.613358	+	0.789805i	$0.710182\pi$
$558$	−34.2919	−1.45169
$559$	−7.35909	−0.311256
$560$	90.4359	3.82162
$561$	22.3514	0.943676
$562$	52.4539	2.21263
$563$	−0.477589	−0.0201280	−0.0100640	−	0.999949i	$-0.503204\pi$
$563$	−0.477589	−0.0201280	−0.0100640	+	0.999949i	$0.503204\pi$
$564$	128.707	5.41954
$565$	5.10431	0.214740
$566$	−62.4910	−2.62669
$567$	−54.4578	−2.28701
$568$	−21.6495	−0.908393
$569$	−12.6469	−0.530186	−0.265093	−	0.964223i	$-0.585403\pi$
$569$	−12.6469	−0.530186	−0.265093	+	0.964223i	$0.585403\pi$
$570$	−96.9806	−4.06207
$571$	20.4305	0.854990	0.427495	−	0.904018i	$-0.359396\pi$
$571$	20.4305	0.854990	0.427495	+	0.904018i	$0.359396\pi$
$572$	83.8375	3.50542
$573$	66.1960	2.76538
$574$	−26.5146	−1.10670
$575$	−9.82001	−0.409523
$576$	261.757	10.9065
$577$	34.5195	1.43706	0.718532	−	0.695494i	$-0.244814\pi$
$577$	34.5195	1.43706	0.718532	+	0.695494i	$0.244814\pi$
$578$	37.6786	1.56722
$579$	−27.5337	−1.14426
$580$	−29.4774	−1.22398
$581$	−32.9420	−1.36666
$582$	−22.0536	−0.914149
$583$	22.5024	0.931952
$584$	36.9580	1.52933
$585$	−41.4387	−1.71328
$586$	−54.2531	−2.24117
$587$	5.38327	0.222191	0.111096	−	0.993810i	$-0.464564\pi$
$587$	5.38327	0.222191	0.111096	+	0.993810i	$0.464564\pi$
$588$	73.9002	3.04759
$589$	−12.7644	−0.525949
$590$	−55.8590	−2.29968
$591$	54.7292	2.25126
$592$	16.7659	0.689074
$593$	−13.9864	−0.574353	−0.287176	−	0.957878i	$-0.592717\pi$
$593$	−13.9864	−0.574353	−0.287176	+	0.957878i	$0.592717\pi$
$594$	−125.944	−5.16752
$595$	9.93289	0.407209
$596$	83.6013	3.42444
$597$	−43.9857	−1.80021
$598$	−43.1737	−1.76550
$599$	−42.3275	−1.72945	−0.864727	−	0.502241i	$-0.832509\pi$
$599$	−42.3275	−1.72945	−0.864727	+	0.502241i	$0.832509\pi$
$600$	75.9479	3.10056
$601$	15.3659	0.626789	0.313394	−	0.949623i	$-0.398534\pi$
$601$	15.3659	0.626789	0.313394	+	0.949623i	$0.398534\pi$
$602$	−17.8960	−0.729386
$603$	95.1000	3.87277
$604$	−104.869	−4.26707
$605$	−6.63764	−0.269858
$606$	−14.9636	−0.607855
$607$	−30.1097	−1.22211	−0.611057	−	0.791587i	$-0.709255\pi$
$607$	−30.1097	−1.22211	−0.611057	+	0.791587i	$0.709255\pi$
$608$	181.655	7.36708
$609$	−33.6634	−1.36411
$610$	31.3777	1.27044
$611$	27.6973	1.12051
$612$	70.3959	2.84559
$613$	−46.3485	−1.87200	−0.936000	−	0.352000i	$-0.885502\pi$
$613$	−46.3485	−1.87200	−0.936000	+	0.352000i	$0.885502\pi$
$614$	−93.1972	−3.76113
$615$	14.4285	0.581812
$616$	131.905	5.31460
$617$	24.7591	0.996764	0.498382	−	0.866957i	$-0.333928\pi$
$617$	24.7591	0.996764	0.498382	+	0.866957i	$0.333928\pi$
$618$	122.953	4.94591
$619$	13.7396	0.552240	0.276120	−	0.961123i	$-0.410951\pi$
$619$	13.7396	0.552240	0.276120	+	0.961123i	$0.410951\pi$
$620$	−16.7776	−0.673806
$621$	47.9349	1.92356
$622$	2.12023	0.0850136
$623$	−48.6605	−1.94954
$624$	199.248	7.97631
$625$	−7.26893	−0.290757
$626$	24.8502	0.993215
$627$	−84.4066	−3.37087
$628$	7.35704	0.293578
$629$	1.84146	0.0734236
$630$	−100.772	−4.01483
$631$	8.02661	0.319534	0.159767	−	0.987155i	$-0.448926\pi$
$631$	8.02661	0.319534	0.159767	+	0.987155i	$0.448926\pi$
$632$	97.2644	3.86897
$633$	−50.8879	−2.02261
$634$	30.7422	1.22093
$635$	−23.1397	−0.918273
$636$	102.380	4.05965
$637$	15.9031	0.630102
$638$	−34.7124	−1.37428
$639$	14.3952	0.569463
$640$	88.9874	3.51754
$641$	12.9124	0.510009	0.255005	−	0.966940i	$-0.417923\pi$
$641$	12.9124	0.510009	0.255005	+	0.966940i	$0.417923\pi$
$642$	−78.7689	−3.10876
$643$	4.69458	0.185136	0.0925681	−	0.995706i	$-0.470492\pi$
$643$	4.69458	0.185136	0.0925681	+	0.995706i	$0.470492\pi$
$644$	−77.5973	−3.05776
$645$	9.73849	0.383453
$646$	35.4537	1.39491
$647$	−28.9482	−1.13807	−0.569036	−	0.822313i	$-0.692683\pi$
$647$	−28.9482	−1.13807	−0.569036	+	0.822313i	$0.692683\pi$
$648$	−165.298	−6.49350
$649$	−48.6166	−1.90837
$650$	25.2616	0.990840
$651$	−19.1602	−0.750948
$652$	−56.7228	−2.22144
$653$	−35.6751	−1.39607	−0.698037	−	0.716062i	$-0.745943\pi$
$653$	−35.6751	−1.39607	−0.698037	+	0.716062i	$0.745943\pi$
$654$	8.64407	0.338010
$655$	15.8649	0.619892
$656$	−48.0245	−1.87504
$657$	−24.5741	−0.958726
$658$	67.3550	2.62577
$659$	−12.1829	−0.474578	−0.237289	−	0.971439i	$-0.576259\pi$
$659$	−12.1829	−0.474578	−0.237289	+	0.971439i	$0.576259\pi$
$660$	−110.945	−4.31851
$661$	34.9982	1.36127	0.680635	−	0.732622i	$-0.261704\pi$
$661$	34.9982	1.36127	0.680635	+	0.732622i	$0.261704\pi$
$662$	−50.8744	−1.97729
$663$	21.8841	0.849908
$664$	−99.9900	−3.88036
$665$	−37.5100	−1.45458
$666$	−18.6820	−0.723913
$667$	13.2118	0.511561
$668$	137.584	5.32328
$669$	36.0770	1.39482
$670$	62.9542	2.43213
$671$	27.3094	1.05427
$672$	272.676	10.5187
$673$	28.9217	1.11485	0.557424	−	0.830228i	$-0.311790\pi$
$673$	28.9217	1.11485	0.557424	+	0.830228i	$0.311790\pi$
$674$	−57.2965	−2.20698
$675$	−28.0474	−1.07955
$676$	8.43471	0.324412
$677$	2.75805	0.106000	0.0530002	−	0.998595i	$-0.483122\pi$
$677$	2.75805	0.106000	0.0530002	+	0.998595i	$0.483122\pi$
$678$	27.3478	1.05029
$679$	−8.52985	−0.327346
$680$	30.1496	1.15619
$681$	0.637514	0.0244296
$682$	−19.7573	−0.756545
$683$	9.78543	0.374429	0.187215	−	0.982319i	$-0.440054\pi$
$683$	9.78543	0.374429	0.187215	+	0.982319i	$0.440054\pi$
$684$	−265.839	−10.1646
$685$	13.7252	0.524415
$686$	−26.1223	−0.997354
$687$	14.8587	0.566893
$688$	−32.4141	−1.23578
$689$	22.0319	0.839349
$690$	57.1330	2.17502
$691$	−3.52814	−0.134217	−0.0671084	−	0.997746i	$-0.521377\pi$
$691$	−3.52814	−0.134217	−0.0671084	+	0.997746i	$0.521377\pi$
$692$	−142.964	−5.43467
$693$	−87.7060	−3.33168
$694$	0.295995	0.0112358
$695$	−16.3016	−0.618356
$696$	−102.180	−3.87311
$697$	−5.27470	−0.199793
$698$	75.2489	2.84821
$699$	−63.7122	−2.40982
$700$	45.4034	1.71609
$701$	35.7474	1.35016	0.675081	−	0.737744i	$-0.264109\pi$
$701$	35.7474	1.35016	0.675081	+	0.737744i	$0.264109\pi$
$702$	−123.311	−4.65406
$703$	−6.95397	−0.262274
$704$	150.811	5.68392
$705$	−36.6526	−1.38042
$706$	85.5659	3.22032
$707$	−5.78761	−0.217665
$708$	−221.194	−8.31299
$709$	3.75615	0.141065	0.0705325	−	0.997509i	$-0.477530\pi$
$709$	3.75615	0.141065	0.0705325	+	0.997509i	$0.477530\pi$
$710$	9.52929	0.357628
$711$	−64.6729	−2.42542
$712$	−147.701	−5.53532
$713$	7.51975	0.281617
$714$	53.2183	1.99164
$715$	−23.8749	−0.892870
$716$	131.488	4.91392
$717$	74.5887	2.78556
$718$	−90.9859	−3.39556
$719$	−1.18679	−0.0442599	−0.0221300	−	0.999755i	$-0.507045\pi$
$719$	−1.18679	−0.0442599	−0.0221300	+	0.999755i	$0.507045\pi$
$720$	−182.522	−6.80220
$721$	47.5558	1.77107
$722$	−81.2812	−3.02497
$723$	−32.2909	−1.20091
$724$	72.5290	2.69552
$725$	−7.73040	−0.287100
$726$	−35.5630	−1.31987
$727$	18.0752	0.670370	0.335185	−	0.942152i	$-0.391201\pi$
$727$	18.0752	0.670370	0.335185	+	0.942152i	$0.391201\pi$
$728$	129.147	4.78652
$729$	0.314846	0.0116610
$730$	−16.2675	−0.602088
$731$	−3.56015	−0.131677
$732$	124.251	4.59247
$733$	−10.7342	−0.396478	−0.198239	−	0.980154i	$-0.563522\pi$
$733$	−10.7342	−0.396478	−0.198239	+	0.980154i	$0.563522\pi$
$734$	45.4323	1.67694
$735$	−21.0450	−0.776256
$736$	−107.016	−3.94467
$737$	54.7919	2.01829
$738$	53.5130	1.96984
$739$	15.1219	0.556270	0.278135	−	0.960542i	$-0.410284\pi$
$739$	15.1219	0.556270	0.278135	+	0.960542i	$0.410284\pi$
$740$	−9.14036	−0.336006
$741$	−82.6420	−3.03593
$742$	53.5778	1.96690
$743$	21.9608	0.805664	0.402832	−	0.915274i	$-0.368026\pi$
$743$	21.9608	0.805664	0.402832	+	0.915274i	$0.368026\pi$
$744$	−58.1576	−2.13216
$745$	−23.8076	−0.872245
$746$	76.4726	2.79986
$747$	66.4852	2.43257
$748$	40.5586	1.48297
$749$	−30.4662	−1.11321
$750$	−103.160	−3.76686
$751$	−1.79937	−0.0656599	−0.0328299	−	0.999461i	$-0.510452\pi$
$751$	−1.79937	−0.0656599	−0.0328299	+	0.999461i	$0.510452\pi$
$752$	121.997	4.44876
$753$	5.49087	0.200098
$754$	−33.9867	−1.23772
$755$	29.8642	1.08687
$756$	−221.630	−8.06060
$757$	−27.8513	−1.01227	−0.506136	−	0.862454i	$-0.668927\pi$
$757$	−27.8513	−1.01227	−0.506136	+	0.862454i	$0.668927\pi$
$758$	31.4100	1.14086
$759$	49.7254	1.80492
$760$	−113.855	−4.12997
$761$	−44.4277	−1.61050	−0.805252	−	0.592932i	$-0.797970\pi$
$761$	−44.4277	−1.61050	−0.805252	+	0.592932i	$0.797970\pi$
$762$	−123.978	−4.49124
$763$	3.34335	0.121037
$764$	120.119	4.34574
$765$	−20.0470	−0.724803
$766$	−104.298	−3.76844
$767$	−47.6002	−1.71875
$768$	234.548	8.46352
$769$	8.70981	0.314084	0.157042	−	0.987592i	$-0.449804\pi$
$769$	8.70981	0.314084	0.157042	+	0.987592i	$0.449804\pi$
$770$	−58.0595	−2.09232
$771$	96.3902	3.47141
$772$	−49.9625	−1.79819
$773$	4.26867	0.153533	0.0767667	−	0.997049i	$-0.475540\pi$
$773$	4.26867	0.153533	0.0767667	+	0.997049i	$0.475540\pi$
$774$	36.1186	1.29826
$775$	−4.39992	−0.158050
$776$	−25.8909	−0.929431
$777$	−10.4384	−0.374474
$778$	−8.92158	−0.319854
$779$	19.9191	0.713675
$780$	−108.625	−3.88941
$781$	8.29377	0.296774
$782$	−20.8864	−0.746896
$783$	37.7348	1.34853
$784$	70.0472	2.50169
$785$	−2.09511	−0.0747775
$786$	85.0005	3.03187
$787$	4.68347	0.166948	0.0834739	−	0.996510i	$-0.473398\pi$
$787$	4.68347	0.166948	0.0834739	+	0.996510i	$0.473398\pi$
$788$	99.3112	3.53781
$789$	24.3791	0.867917
$790$	−42.8121	−1.52319
$791$	10.5776	0.376095
$792$	−266.217	−9.45961
$793$	26.7385	0.949511
$794$	9.45078	0.335396
$795$	−29.1555	−1.03404
$796$	−79.8160	−2.82900
$797$	−40.8931	−1.44851	−0.724254	−	0.689533i	$-0.757816\pi$
$797$	−40.8931	−1.44851	−0.724254	+	0.689533i	$0.757816\pi$
$798$	−200.971	−7.11429
$799$	13.3993	0.474033
$800$	62.6167	2.21384
$801$	98.2090	3.47004
$802$	76.1879	2.69029
$803$	−14.1584	−0.499638
$804$	249.290	8.79180
$805$	22.0978	0.778846
$806$	−19.3442	−0.681371
$807$	35.0540	1.23396
$808$	−17.5673	−0.618016
$809$	−48.1269	−1.69205	−0.846025	−	0.533143i	$-0.821011\pi$
$809$	−48.1269	−1.69205	−0.846025	+	0.533143i	$0.821011\pi$
$810$	72.7577	2.55645
$811$	30.7336	1.07920	0.539601	−	0.841921i	$-0.318575\pi$
$811$	30.7336	1.07920	0.539601	+	0.841921i	$0.318575\pi$
$812$	−61.0853	−2.14367
$813$	1.53656	0.0538896
$814$	−10.7636	−0.377265
$815$	16.1533	0.565825
$816$	96.3915	3.37438
$817$	13.4444	0.470359
$818$	−35.0815	−1.22660
$819$	−85.8725	−3.00063
$820$	26.1818	0.914308
$821$	−6.34502	−0.221443	−0.110721	−	0.993851i	$-0.535316\pi$
$821$	−6.34502	−0.221443	−0.110721	+	0.993851i	$0.535316\pi$
$822$	73.5369	2.56489
$823$	−33.4548	−1.16616	−0.583080	−	0.812415i	$-0.698153\pi$
$823$	−33.4548	−1.16616	−0.583080	+	0.812415i	$0.698153\pi$
$824$	144.348	5.02859
$825$	−29.0951	−1.01296
$826$	−115.755	−4.02765
$827$	−0.434651	−0.0151143	−0.00755715	−	0.999971i	$-0.502406\pi$
$827$	−0.434651	−0.0151143	−0.00755715	+	0.999971i	$0.502406\pi$
$828$	156.611	5.44260
$829$	16.1239	0.560006	0.280003	−	0.959999i	$-0.409664\pi$
$829$	16.1239	0.560006	0.280003	+	0.959999i	$0.409664\pi$
$830$	44.0118	1.52767
$831$	81.9745	2.84366
$832$	147.658	5.11914
$833$	7.69353	0.266565
$834$	−87.3406	−3.02436
$835$	−39.1806	−1.35590
$836$	−153.163	−5.29727
$837$	21.4775	0.742372
$838$	67.9537	2.34742
$839$	−34.2038	−1.18085	−0.590423	−	0.807094i	$-0.701039\pi$
$839$	−34.2038	−1.18085	−0.590423	+	0.807094i	$0.701039\pi$
$840$	−170.904	−5.89676
$841$	−18.5996	−0.641365
$842$	−59.5505	−2.05224
$843$	−59.1509	−2.03727
$844$	−92.3408	−3.17850
$845$	−2.40200	−0.0826314
$846$	−135.939	−4.67368
$847$	−13.7550	−0.472629
$848$	97.0426	3.33246
$849$	70.4695	2.41851
$850$	12.2210	0.419175
$851$	4.09671	0.140433
$852$	37.7347	1.29277
$853$	−7.51665	−0.257365	−0.128683	−	0.991686i	$-0.541075\pi$
$853$	−7.51665	−0.257365	−0.128683	+	0.991686i	$0.541075\pi$
$854$	65.0233	2.22505
$855$	75.7046	2.58904
$856$	−92.4750	−3.16073
$857$	44.7278	1.52787	0.763937	−	0.645291i	$-0.223264\pi$
$857$	44.7278	1.52787	0.763937	+	0.645291i	$0.223264\pi$
$858$	−127.917	−4.36700
$859$	−2.95019	−0.100659	−0.0503296	−	0.998733i	$-0.516027\pi$
$859$	−2.95019	−0.100659	−0.0503296	+	0.998733i	$0.516027\pi$
$860$	17.6714	0.602589
$861$	29.8998	1.01898
$862$	55.6240	1.89456
$863$	−19.7700	−0.672980	−0.336490	−	0.941687i	$-0.609240\pi$
$863$	−19.7700	−0.672980	−0.336490	+	0.941687i	$0.609240\pi$
$864$	−305.654	−10.3986
$865$	40.7127	1.38427
$866$	−35.0947	−1.19257
$867$	−42.4892	−1.44301
$868$	−34.7680	−1.18010
$869$	−37.2613	−1.26400
$870$	44.9756	1.52482
$871$	53.6464	1.81774
$872$	10.1482	0.343660
$873$	17.2154	0.582652
$874$	78.8743	2.66796
$875$	−39.9000	−1.34887
$876$	−64.4173	−2.17646
$877$	−28.3201	−0.956303	−0.478152	−	0.878277i	$-0.658693\pi$
$877$	−28.3201	−0.956303	−0.478152	+	0.878277i	$0.658693\pi$
$878$	49.5252	1.67139
$879$	61.1799	2.06355
$880$	−105.160	−3.54495
$881$	−21.2395	−0.715577	−0.357789	−	0.933803i	$-0.616469\pi$
$881$	−21.2395	−0.715577	−0.357789	+	0.933803i	$0.616469\pi$
$882$	−78.0527	−2.62817
$883$	31.3857	1.05621	0.528107	−	0.849178i	$-0.322902\pi$
$883$	31.3857	1.05621	0.528107	+	0.849178i	$0.322902\pi$
$884$	39.7107	1.33562
$885$	62.9908	2.11741
$886$	−6.17970	−0.207611
$887$	−10.5544	−0.354381	−0.177191	−	0.984177i	$-0.556701\pi$
$887$	−10.5544	−0.354381	−0.177191	+	0.984177i	$0.556701\pi$
$888$	−31.6839	−1.06324
$889$	−47.9520	−1.60826
$890$	65.0123	2.17922
$891$	63.3244	2.12145
$892$	65.4651	2.19193
$893$	−50.6004	−1.69328
$894$	−127.556	−4.26612
$895$	−37.4445	−1.25163
$896$	184.407	6.16060
$897$	48.6859	1.62557
$898$	95.4431	3.18498
$899$	5.91961	0.197430
$900$	−91.6353	−3.05451
$901$	10.6585	0.355087
$902$	30.8315	1.02658
$903$	20.1809	0.671577
$904$	32.1064	1.06784
$905$	−20.6545	−0.686579
$906$	160.006	5.31585
$907$	−37.3604	−1.24053	−0.620266	−	0.784391i	$-0.712975\pi$
$907$	−37.3604	−1.24053	−0.620266	+	0.784391i	$0.712975\pi$
$908$	1.15683	0.0383907
$909$	11.6808	0.387429
$910$	−56.8458	−1.88442
$911$	−20.8312	−0.690169	−0.345085	−	0.938572i	$-0.612150\pi$
$911$	−20.8312	−0.690169	−0.345085	+	0.938572i	$0.612150\pi$
$912$	−364.008	−12.0535
$913$	38.3055	1.26773
$914$	−47.9154	−1.58490
$915$	−35.3838	−1.16975
$916$	26.9624	0.890862
$917$	32.8764	1.08568
$918$	−59.6548	−1.96890
$919$	49.6950	1.63929	0.819643	−	0.572874i	$-0.194172\pi$
$919$	49.6950	1.63929	0.819643	+	0.572874i	$0.194172\pi$
$920$	67.0743	2.21137
$921$	105.096	3.46304
$922$	−60.4080	−1.98943
$923$	8.12038	0.267286
$924$	−229.908	−7.56342
$925$	−2.39705	−0.0788144
$926$	−99.9426	−3.28432
$927$	−95.9795	−3.15238
$928$	−84.2440	−2.76545
$929$	25.5061	0.836827	0.418414	−	0.908257i	$-0.362586\pi$
$929$	25.5061	0.836827	0.418414	+	0.908257i	$0.362586\pi$
$930$	25.5988	0.839417
$931$	−29.0534	−0.952188
$932$	−115.612	−3.78699
$933$	−2.39093	−0.0782756
$934$	−21.0436	−0.688569
$935$	−11.5501	−0.377729
$936$	−260.652	−8.51966
$937$	7.39228	0.241495	0.120748	−	0.992683i	$-0.461471\pi$
$937$	7.39228	0.241495	0.120748	+	0.992683i	$0.461471\pi$
$938$	130.459	4.25963
$939$	−28.0230	−0.914496
$940$	−66.5096	−2.16930
$941$	−28.9448	−0.943574	−0.471787	−	0.881712i	$-0.656391\pi$
$941$	−28.9448	−0.943574	−0.471787	+	0.881712i	$0.656391\pi$
$942$	−11.2251	−0.365734
$943$	−11.7347	−0.382134
$944$	−209.662	−6.82391
$945$	63.1148	2.05312
$946$	20.8097	0.676583
$947$	0.591774	0.0192301	0.00961504	−	0.999954i	$-0.496939\pi$
$947$	0.591774	0.0192301	0.00961504	+	0.999954i	$0.496939\pi$
$948$	−169.530	−5.50609
$949$	−13.8624	−0.449992
$950$	−46.1506	−1.49732
$951$	−34.6672	−1.12416
$952$	62.4784	2.02494
$953$	−34.2049	−1.10801	−0.554003	−	0.832515i	$-0.686900\pi$
$953$	−34.2049	−1.10801	−0.554003	+	0.832515i	$0.686900\pi$
$954$	−108.133	−3.50094
$955$	−34.2069	−1.10691
$956$	135.348	4.37747
$957$	39.1443	1.26536
$958$	63.5780	2.05411
$959$	28.4425	0.918457
$960$	−195.401	−6.30653
$961$	−27.6307	−0.891314
$962$	−10.5386	−0.339779
$963$	61.4883	1.98143
$964$	−58.5947	−1.88721
$965$	14.2281	0.458019
$966$	118.395	3.80931
$967$	−2.83106	−0.0910406	−0.0455203	−	0.998963i	$-0.514495\pi$
$967$	−2.83106	−0.0910406	−0.0455203	+	0.998963i	$0.514495\pi$
$968$	−41.7511	−1.34193
$969$	−39.9803	−1.28435
$970$	11.3962	0.365910
$971$	10.2022	0.327404	0.163702	−	0.986510i	$-0.447656\pi$
$971$	10.2022	0.327404	0.163702	+	0.986510i	$0.447656\pi$
$972$	89.2418	2.86243
$973$	−33.7815	−1.08299
$974$	−65.6480	−2.10350
$975$	−28.4868	−0.912309
$976$	117.773	3.76983
$977$	18.4032	0.588771	0.294386	−	0.955687i	$-0.404885\pi$
$977$	18.4032	0.588771	0.294386	+	0.955687i	$0.404885\pi$
$978$	86.5458	2.76743
$979$	56.5831	1.80840
$980$	−38.1881	−1.21987
$981$	−6.74771	−0.215438
$982$	17.1443	0.547095
$983$	−22.6528	−0.722512	−0.361256	−	0.932467i	$-0.617652\pi$
$983$	−22.6528	−0.722512	−0.361256	+	0.932467i	$0.617652\pi$
$984$	90.7560	2.89319
$985$	−28.2814	−0.901121
$986$	−16.4420	−0.523619
$987$	−75.9545	−2.41766
$988$	−149.961	−4.77091
$989$	−7.92032	−0.251852
$990$	117.179	3.72418
$991$	−24.9346	−0.792073	−0.396036	−	0.918235i	$-0.629615\pi$
$991$	−24.9346	−0.792073	−0.396036	+	0.918235i	$0.629615\pi$
$992$	−47.9492	−1.52239
$993$	57.3698	1.82058
$994$	19.7473	0.626348
$995$	22.7297	0.720579
$996$	174.281	5.52230
$997$	6.20822	0.196616	0.0983082	−	0.995156i	$-0.468657\pi$
$997$	6.20822	0.196616	0.0983082	+	0.995156i	$0.468657\pi$
$998$	113.511	3.59313
$999$	11.7008	0.370198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.1	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.1	✓	85	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +O(q^{10})\)	\(q-2.76864 q^{2} +3.12213 q^{3} +5.66539 q^{4} -1.61337 q^{5} -8.64407 q^{6} -3.34335 q^{7} -10.1482 q^{8} +6.74771 q^{9} +4.46684 q^{10} +3.88769 q^{11} +17.6881 q^{12} +3.80642 q^{13} +9.25654 q^{14} -5.03714 q^{15} +16.7659 q^{16} +1.84146 q^{17} -18.6820 q^{18} -6.95397 q^{19} -9.14036 q^{20} -10.4384 q^{21} -10.7636 q^{22} +4.09671 q^{23} -31.6839 q^{24} -2.39705 q^{25} -10.5386 q^{26} +11.7008 q^{27} -18.9414 q^{28} +3.22497 q^{29} +13.9461 q^{30} +1.83556 q^{31} -26.1224 q^{32} +12.1379 q^{33} -5.09834 q^{34} +5.39404 q^{35} +38.2284 q^{36} +1.00000 q^{37} +19.2531 q^{38} +11.8841 q^{39} +16.3727 q^{40} -2.86442 q^{41} +28.9001 q^{42} -1.93334 q^{43} +22.0253 q^{44} -10.8865 q^{45} -11.3423 q^{46} +7.27647 q^{47} +52.3453 q^{48} +4.17796 q^{49} +6.63657 q^{50} +5.74927 q^{51} +21.5648 q^{52} +5.78810 q^{53} -32.3954 q^{54} -6.27227 q^{55} +33.9288 q^{56} -21.7112 q^{57} -8.92879 q^{58} -12.5053 q^{59} -28.5374 q^{60} +7.02458 q^{61} -5.08200 q^{62} -22.5599 q^{63} +38.7920 q^{64} -6.14115 q^{65} -33.6055 q^{66} +14.0937 q^{67} +10.4326 q^{68} +12.7905 q^{69} -14.9342 q^{70} +2.13334 q^{71} -68.4769 q^{72} -3.64184 q^{73} -2.76864 q^{74} -7.48390 q^{75} -39.3970 q^{76} -12.9979 q^{77} -32.9029 q^{78} -9.58443 q^{79} -27.0495 q^{80} +16.2884 q^{81} +7.93055 q^{82} +9.85300 q^{83} -59.1374 q^{84} -2.97094 q^{85} +5.35272 q^{86} +10.0688 q^{87} -39.4530 q^{88} +14.5544 q^{89} +30.1409 q^{90} -12.7262 q^{91} +23.2095 q^{92} +5.73085 q^{93} -20.1460 q^{94} +11.2193 q^{95} -81.5577 q^{96} +2.55129 q^{97} -11.5673 q^{98} +26.2330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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