LMFDB - Embedded newform 2671.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, 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("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65824 q^{2} -2.83500 q^{3} +5.06626 q^{4} +1.38285 q^{5} +7.53611 q^{6} +2.52336 q^{7} -8.15086 q^{8} +5.03721 q^{9} +O(q^{10})$	\(q-2.65824 q^{2} -2.83500 q^{3} +5.06626 q^{4} +1.38285 q^{5} +7.53611 q^{6} +2.52336 q^{7} -8.15086 q^{8} +5.03721 q^{9} -3.67595 q^{10} -2.03718 q^{11} -14.3628 q^{12} +3.33406 q^{13} -6.70772 q^{14} -3.92037 q^{15} +11.5344 q^{16} +3.26579 q^{17} -13.3901 q^{18} +3.35017 q^{19} +7.00586 q^{20} -7.15373 q^{21} +5.41532 q^{22} +5.28495 q^{23} +23.1077 q^{24} -3.08773 q^{25} -8.86275 q^{26} -5.77548 q^{27} +12.7840 q^{28} -6.15230 q^{29} +10.4213 q^{30} -6.61927 q^{31} -14.3596 q^{32} +5.77540 q^{33} -8.68125 q^{34} +3.48943 q^{35} +25.5198 q^{36} -11.2815 q^{37} -8.90555 q^{38} -9.45206 q^{39} -11.2714 q^{40} -6.18312 q^{41} +19.0164 q^{42} +9.68651 q^{43} -10.3209 q^{44} +6.96569 q^{45} -14.0487 q^{46} -12.0615 q^{47} -32.7001 q^{48} -0.632633 q^{49} +8.20794 q^{50} -9.25849 q^{51} +16.8912 q^{52} -6.76440 q^{53} +15.3526 q^{54} -2.81711 q^{55} -20.5676 q^{56} -9.49771 q^{57} +16.3543 q^{58} -3.60878 q^{59} -19.8616 q^{60} -3.84866 q^{61} +17.5956 q^{62} +12.7107 q^{63} +15.1025 q^{64} +4.61051 q^{65} -15.3524 q^{66} +4.14333 q^{67} +16.5453 q^{68} -14.9828 q^{69} -9.27575 q^{70} -15.0815 q^{71} -41.0576 q^{72} +8.58453 q^{73} +29.9889 q^{74} +8.75371 q^{75} +16.9728 q^{76} -5.14055 q^{77} +25.1259 q^{78} +3.83739 q^{79} +15.9504 q^{80} +1.26184 q^{81} +16.4362 q^{82} -2.12271 q^{83} -36.2426 q^{84} +4.51609 q^{85} -25.7491 q^{86} +17.4417 q^{87} +16.6048 q^{88} -2.20518 q^{89} -18.5165 q^{90} +8.41306 q^{91} +26.7749 q^{92} +18.7656 q^{93} +32.0624 q^{94} +4.63277 q^{95} +40.7095 q^{96} -14.0363 q^{97} +1.68169 q^{98} -10.2617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	−2.65824	−1.87966	−0.939831	−	0.341640i	$-0.889018\pi$
$2$	−2.65824	−1.87966	−0.939831	+	0.341640i	$0.889018\pi$
$3$	−2.83500	−1.63679	−0.818393	−	0.574659i	$-0.805135\pi$
$3$	−2.83500	−1.63679	−0.818393	+	0.574659i	$0.805135\pi$
$4$	5.06626	2.53313
$5$	1.38285	0.618429	0.309214	−	0.950992i	$-0.399934\pi$
$5$	1.38285	0.618429	0.309214	+	0.950992i	$0.399934\pi$
$6$	7.53611	3.07660
$7$	2.52336	0.953742	0.476871	−	0.878973i	$-0.341771\pi$
$7$	2.52336	0.953742	0.476871	+	0.878973i	$0.341771\pi$
$8$	−8.15086	−2.88176
$9$	5.03721	1.67907
$10$	−3.67595	−1.16244
$11$	−2.03718	−0.614233	−0.307117	−	0.951672i	$-0.599364\pi$
$11$	−2.03718	−0.614233	−0.307117	+	0.951672i	$0.599364\pi$
$12$	−14.3628	−4.14619
$13$	3.33406	0.924703	0.462352	−	0.886697i	$-0.347006\pi$
$13$	3.33406	0.924703	0.462352	+	0.886697i	$0.347006\pi$
$14$	−6.70772	−1.79271
$15$	−3.92037	−1.01224
$16$	11.5344	2.88361
$17$	3.26579	0.792069	0.396035	−	0.918236i	$-0.370386\pi$
$17$	3.26579	0.792069	0.396035	+	0.918236i	$0.370386\pi$
$18$	−13.3901	−3.15608
$19$	3.35017	0.768581	0.384290	−	0.923212i	$-0.374446\pi$
$19$	3.35017	0.768581	0.384290	+	0.923212i	$0.374446\pi$
$20$	7.00586	1.56656
$21$	−7.15373	−1.56107
$22$	5.41532	1.15455
$23$	5.28495	1.10199	0.550994	−	0.834509i	$-0.314249\pi$
$23$	5.28495	1.10199	0.550994	+	0.834509i	$0.314249\pi$
$24$	23.1077	4.71683
$25$	−3.08773	−0.617546
$26$	−8.86275	−1.73813
$27$	−5.77548	−1.11149
$28$	12.7840	2.41595
$29$	−6.15230	−1.14245	−0.571227	−	0.820792i	$-0.693532\pi$
$29$	−6.15230	−1.14245	−0.571227	+	0.820792i	$0.693532\pi$
$30$	10.4213	1.90266
$31$	−6.61927	−1.18886	−0.594428	−	0.804149i	$-0.702621\pi$
$31$	−6.61927	−1.18886	−0.594428	+	0.804149i	$0.702621\pi$
$32$	−14.3596	−2.53845
$33$	5.77540	1.00537
$34$	−8.68125	−1.48882
$35$	3.48943	0.589821
$36$	25.5198	4.25330
$37$	−11.2815	−1.85466	−0.927330	−	0.374245i	$-0.877902\pi$
$37$	−11.2815	−1.85466	−0.927330	+	0.374245i	$0.877902\pi$
$38$	−8.90555	−1.44467
$39$	−9.45206	−1.51354
$40$	−11.2714	−1.78216
$41$	−6.18312	−0.965642	−0.482821	−	0.875719i	$-0.660388\pi$
$41$	−6.18312	−0.965642	−0.482821	+	0.875719i	$0.660388\pi$
$42$	19.0164	2.93429
$43$	9.68651	1.47718	0.738590	−	0.674155i	$-0.235492\pi$
$43$	9.68651	1.47718	0.738590	+	0.674155i	$0.235492\pi$
$44$	−10.3209	−1.55593
$45$	6.96569	1.03838
$46$	−14.0487	−2.07136
$47$	−12.0615	−1.75935	−0.879675	−	0.475575i	$-0.842240\pi$
$47$	−12.0615	−1.75935	−0.879675	+	0.475575i	$0.842240\pi$
$48$	−32.7001	−4.71985
$49$	−0.632633	−0.0903761
$50$	8.20794	1.16078
$51$	−9.25849	−1.29645
$52$	16.8912	2.34239
$53$	−6.76440	−0.929161	−0.464581	−	0.885531i	$-0.653795\pi$
$53$	−6.76440	−0.929161	−0.464581	+	0.885531i	$0.653795\pi$
$54$	15.3526	2.08923
$55$	−2.81711	−0.379859
$56$	−20.5676	−2.74846
$57$	−9.49771	−1.25800
$58$	16.3543	2.14743
$59$	−3.60878	−0.469823	−0.234912	−	0.972017i	$-0.575480\pi$
$59$	−3.60878	−0.469823	−0.234912	+	0.972017i	$0.575480\pi$
$60$	−19.8616	−2.56412
$61$	−3.84866	−0.492771	−0.246385	−	0.969172i	$-0.579243\pi$
$61$	−3.84866	−0.492771	−0.246385	+	0.969172i	$0.579243\pi$
$62$	17.5956	2.23465
$63$	12.7107	1.60140
$64$	15.1025	1.88782
$65$	4.61051	0.571863
$66$	−15.3524	−1.88975
$67$	4.14333	0.506189	0.253094	−	0.967442i	$-0.418552\pi$
$67$	4.14333	0.506189	0.253094	+	0.967442i	$0.418552\pi$
$68$	16.5453	2.00641
$69$	−14.9828	−1.80372
$70$	−9.27575	−1.10866
$71$	−15.0815	−1.78985	−0.894924	−	0.446219i	$-0.852770\pi$
$71$	−15.0815	−1.78985	−0.894924	+	0.446219i	$0.852770\pi$
$72$	−41.0576	−4.83868
$73$	8.58453	1.00474	0.502372	−	0.864652i	$-0.332461\pi$
$73$	8.58453	1.00474	0.502372	+	0.864652i	$0.332461\pi$
$74$	29.9889	3.48613
$75$	8.75371	1.01079
$76$	16.9728	1.94691
$77$	−5.14055	−0.585820
$78$	25.1259	2.84495
$79$	3.83739	0.431740	0.215870	−	0.976422i	$-0.430741\pi$
$79$	3.83739	0.431740	0.215870	+	0.976422i	$0.430741\pi$
$80$	15.9504	1.78331
$81$	1.26184	0.140204
$82$	16.4362	1.81508
$83$	−2.12271	−0.232998	−0.116499	−	0.993191i	$-0.537167\pi$
$83$	−2.12271	−0.232998	−0.116499	+	0.993191i	$0.537167\pi$
$84$	−36.2426	−3.95440
$85$	4.51609	0.489838
$86$	−25.7491	−2.77660
$87$	17.4417	1.86995
$88$	16.6048	1.77007
$89$	−2.20518	−0.233749	−0.116874	−	0.993147i	$-0.537288\pi$
$89$	−2.20518	−0.233749	−0.116874	+	0.993147i	$0.537288\pi$
$90$	−18.5165	−1.95181
$91$	8.41306	0.881928
$92$	26.7749	2.79148
$93$	18.7656	1.94590
$94$	32.0624	3.30698
$95$	4.63277	0.475312
$96$	40.7095	4.15490
$97$	−14.0363	−1.42517	−0.712586	−	0.701585i	$-0.752476\pi$
$97$	−14.0363	−1.42517	−0.712586	+	0.701585i	$0.752476\pi$
$98$	1.68169	0.169876
$99$	−10.2617	−1.03134
$100$	−15.6432	−1.56432
$101$	−11.7255	−1.16673	−0.583367	−	0.812209i	$-0.698265\pi$
$101$	−11.7255	−1.16673	−0.583367	+	0.812209i	$0.698265\pi$
$102$	24.6113	2.43688
$103$	17.0964	1.68456	0.842279	−	0.539043i	$-0.181214\pi$
$103$	17.0964	1.68456	0.842279	+	0.539043i	$0.181214\pi$
$104$	−27.1755	−2.66477
$105$	−9.89252	−0.965411
$106$	17.9814	1.74651
$107$	9.86654	0.953834	0.476917	−	0.878948i	$-0.341754\pi$
$107$	9.86654	0.953834	0.476917	+	0.878948i	$0.341754\pi$
$108$	−29.2600	−2.81555
$109$	0.198909	0.0190521	0.00952603	−	0.999955i	$-0.496968\pi$
$109$	0.198909	0.0190521	0.00952603	+	0.999955i	$0.496968\pi$
$110$	7.48857	0.714007
$111$	31.9829	3.03568
$112$	29.1056	2.75022
$113$	6.32705	0.595199	0.297600	−	0.954691i	$-0.403814\pi$
$113$	6.32705	0.595199	0.297600	+	0.954691i	$0.403814\pi$
$114$	25.2472	2.36462
$115$	7.30828	0.681501
$116$	−31.1691	−2.89398
$117$	16.7944	1.55264
$118$	9.59302	0.883109
$119$	8.24077	0.755430
$120$	31.9544	2.91702
$121$	−6.84989	−0.622718
$122$	10.2307	0.926242
$123$	17.5291	1.58055
$124$	−33.5349	−3.01152
$125$	−11.1841	−1.00034
$126$	−33.7882	−3.01009
$127$	−1.10061	−0.0976629	−0.0488315	−	0.998807i	$-0.515550\pi$
$127$	−1.10061	−0.0976629	−0.0488315	+	0.998807i	$0.515550\pi$
$128$	−11.4269	−1.01001
$129$	−27.4612	−2.41783
$130$	−12.2558	−1.07491
$131$	14.9206	1.30362	0.651810	−	0.758382i	$-0.274010\pi$
$131$	14.9206	1.30362	0.651810	+	0.758382i	$0.274010\pi$
$132$	29.2597	2.54673
$133$	8.45369	0.733028
$134$	−11.0140	−0.951464
$135$	−7.98661	−0.687378
$136$	−26.6190	−2.28256
$137$	−14.6787	−1.25409	−0.627045	−	0.778983i	$-0.715736\pi$
$137$	−14.6787	−1.25409	−0.627045	+	0.778983i	$0.715736\pi$
$138$	39.8279	3.39038
$139$	−1.99986	−0.169626	−0.0848130	−	0.996397i	$-0.527029\pi$
$139$	−1.99986	−0.169626	−0.0848130	+	0.996397i	$0.527029\pi$
$140$	17.6783	1.49409
$141$	34.1943	2.87968
$142$	40.0904	3.36431
$143$	−6.79209	−0.567983
$144$	58.1014	4.84178
$145$	−8.50769	−0.706526
$146$	−22.8198	−1.88858
$147$	1.79351	0.147926
$148$	−57.1547	−4.69809
$149$	4.05360	0.332084	0.166042	−	0.986119i	$-0.446901\pi$
$149$	4.05360	0.332084	0.166042	+	0.986119i	$0.446901\pi$
$150$	−23.2695	−1.89995
$151$	8.21724	0.668709	0.334355	−	0.942447i	$-0.391482\pi$
$151$	8.21724	0.668709	0.334355	+	0.942447i	$0.391482\pi$
$152$	−27.3067	−2.21487
$153$	16.4504	1.32994
$154$	13.6648	1.10114
$155$	−9.15344	−0.735222
$156$	−47.8866	−3.83399
$157$	−12.4796	−0.995980	−0.497990	−	0.867183i	$-0.665928\pi$
$157$	−12.4796	−0.995980	−0.497990	+	0.867183i	$0.665928\pi$
$158$	−10.2007	−0.811524
$159$	19.1770	1.52084
$160$	−19.8572	−1.56985
$161$	13.3358	1.05101
$162$	−3.35427	−0.263536
$163$	−8.68982	−0.680639	−0.340320	−	0.940310i	$-0.610535\pi$
$163$	−8.68982	−0.680639	−0.340320	+	0.940310i	$0.610535\pi$
$164$	−31.3253	−2.44609
$165$	7.98651	0.621749
$166$	5.64269	0.437958
$167$	−4.60365	−0.356241	−0.178121	−	0.984009i	$-0.557002\pi$
$167$	−4.60365	−0.356241	−0.178121	+	0.984009i	$0.557002\pi$
$168$	58.3090	4.49864
$169$	−1.88401	−0.144924
$170$	−12.0049	−0.920730
$171$	16.8755	1.29050
$172$	49.0744	3.74188
$173$	2.60457	0.198021	0.0990107	−	0.995086i	$-0.468432\pi$
$173$	2.60457	0.198021	0.0990107	+	0.995086i	$0.468432\pi$
$174$	−46.3644	−3.51488
$175$	−7.79147	−0.588980
$176$	−23.4978	−1.77121
$177$	10.2309	0.769000
$178$	5.86191	0.439369
$179$	−6.60463	−0.493653	−0.246827	−	0.969060i	$-0.579388\pi$
$179$	−6.60463	−0.493653	−0.246827	+	0.969060i	$0.579388\pi$
$180$	35.2900	2.63036
$181$	13.5752	1.00903	0.504517	−	0.863402i	$-0.331671\pi$
$181$	13.5752	1.00903	0.504517	+	0.863402i	$0.331671\pi$
$182$	−22.3640	−1.65773
$183$	10.9109	0.806560
$184$	−43.0768	−3.17567
$185$	−15.6005	−1.14697
$186$	−49.8835	−3.65764
$187$	−6.65300	−0.486515
$188$	−61.1067	−4.45666
$189$	−14.5736	−1.06008
$190$	−12.3150	−0.893426
$191$	−25.9572	−1.87820	−0.939098	−	0.343650i	$-0.888337\pi$
$191$	−25.9572	−1.87820	−0.939098	+	0.343650i	$0.888337\pi$
$192$	−42.8156	−3.08995
$193$	−23.5101	−1.69230	−0.846148	−	0.532948i	$-0.821084\pi$
$193$	−23.5101	−1.69230	−0.846148	+	0.532948i	$0.821084\pi$
$194$	37.3119	2.67884
$195$	−13.0708	−0.936017
$196$	−3.20508	−0.228934
$197$	16.1629	1.15156	0.575779	−	0.817605i	$-0.304699\pi$
$197$	16.1629	1.15156	0.575779	+	0.817605i	$0.304699\pi$
$198$	27.2781	1.93857
$199$	5.72320	0.405707	0.202853	−	0.979209i	$-0.434979\pi$
$199$	5.72320	0.405707	0.202853	+	0.979209i	$0.434979\pi$
$200$	25.1676	1.77962
$201$	−11.7463	−0.828523
$202$	31.1693	2.19306
$203$	−15.5245	−1.08961
$204$	−46.9059	−3.28407
$205$	−8.55032	−0.597180
$206$	−45.4464	−3.16640
$207$	26.6214	1.85031
$208$	38.4566	2.66648
$209$	−6.82489	−0.472088
$210$	26.2967	1.81465
$211$	14.6785	1.01051	0.505256	−	0.862969i	$-0.331398\pi$
$211$	14.6785	1.01051	0.505256	+	0.862969i	$0.331398\pi$
$212$	−34.2702	−2.35368
$213$	42.7561	2.92960
$214$	−26.2277	−1.79289
$215$	13.3950	0.913530
$216$	47.0751	3.20305
$217$	−16.7028	−1.13386
$218$	−0.528749	−0.0358114
$219$	−24.3371	−1.64455
$220$	−14.2722	−0.962233
$221$	10.8883	0.732429
$222$	−85.0183	−5.70605
$223$	−11.6143	−0.777754	−0.388877	−	0.921290i	$-0.627137\pi$
$223$	−11.6143	−0.777754	−0.388877	+	0.921290i	$0.627137\pi$
$224$	−36.2346	−2.42103
$225$	−15.5535	−1.03690
$226$	−16.8188	−1.11877
$227$	−8.05871	−0.534876	−0.267438	−	0.963575i	$-0.586177\pi$
$227$	−8.05871	−0.534876	−0.267438	+	0.963575i	$0.586177\pi$
$228$	−48.1178	−3.18668
$229$	25.0866	1.65777	0.828886	−	0.559417i	$-0.188975\pi$
$229$	25.0866	1.65777	0.828886	+	0.559417i	$0.188975\pi$
$230$	−19.4272	−1.28099
$231$	14.5734	0.958862
$232$	50.1465	3.29228
$233$	−2.53476	−0.166058	−0.0830289	−	0.996547i	$-0.526459\pi$
$233$	−2.53476	−0.166058	−0.0830289	+	0.996547i	$0.526459\pi$
$234$	−44.6435	−2.91844
$235$	−16.6792	−1.08803
$236$	−18.2830	−1.19012
$237$	−10.8790	−0.706665
$238$	−21.9060	−1.41995
$239$	−19.1036	−1.23571	−0.617853	−	0.786293i	$-0.711997\pi$
$239$	−19.1036	−1.23571	−0.617853	+	0.786293i	$0.711997\pi$
$240$	−45.2193	−2.91889
$241$	−20.8596	−1.34368	−0.671841	−	0.740695i	$-0.734496\pi$
$241$	−20.8596	−1.34368	−0.671841	+	0.740695i	$0.734496\pi$
$242$	18.2087	1.17050
$243$	13.7491	0.882007
$244$	−19.4983	−1.24825
$245$	−0.874835	−0.0558911
$246$	−46.5967	−2.97090
$247$	11.1697	0.710709
$248$	53.9527	3.42600
$249$	6.01789	0.381368
$250$	29.7301	1.88029
$251$	20.0012	1.26246	0.631231	−	0.775595i	$-0.282550\pi$
$251$	20.0012	1.26246	0.631231	+	0.775595i	$0.282550\pi$
$252$	64.3957	4.05655
$253$	−10.7664	−0.676877
$254$	2.92568	0.183573
$255$	−12.8031	−0.801761
$256$	0.170484	0.0106552
$257$	28.4505	1.77469	0.887346	−	0.461105i	$-0.152547\pi$
$257$	28.4505	1.77469	0.887346	+	0.461105i	$0.152547\pi$
$258$	72.9986	4.54470
$259$	−28.4672	−1.76887
$260$	23.3580	1.44860
$261$	−30.9904	−1.91826
$262$	−39.6626	−2.45036
$263$	20.2374	1.24789	0.623946	−	0.781468i	$-0.285529\pi$
$263$	20.2374	1.24789	0.623946	+	0.781468i	$0.285529\pi$
$264$	−47.0745	−2.89723
$265$	−9.35413	−0.574620
$266$	−22.4720	−1.37784
$267$	6.25169	0.382597
$268$	20.9912	1.28224
$269$	−0.716358	−0.0436771	−0.0218386	−	0.999762i	$-0.506952\pi$
$269$	−0.716358	−0.0436771	−0.0218386	+	0.999762i	$0.506952\pi$
$270$	21.2303	1.29204
$271$	13.4773	0.818691	0.409345	−	0.912380i	$-0.365757\pi$
$271$	13.4773	0.818691	0.409345	+	0.912380i	$0.365757\pi$
$272$	37.6690	2.28402
$273$	−23.8510	−1.44353
$274$	39.0197	2.35727
$275$	6.29027	0.379317
$276$	−75.9067	−4.56905
$277$	21.5137	1.29264	0.646318	−	0.763068i	$-0.276308\pi$
$277$	21.5137	1.29264	0.646318	+	0.763068i	$0.276308\pi$
$278$	5.31612	0.318839
$279$	−33.3426	−1.99617
$280$	−28.4418	−1.69973
$281$	−11.1982	−0.668031	−0.334015	−	0.942568i	$-0.608404\pi$
$281$	−11.1982	−0.668031	−0.334015	+	0.942568i	$0.608404\pi$
$282$	−90.8968	−5.41283
$283$	−8.70658	−0.517552	−0.258776	−	0.965937i	$-0.583319\pi$
$283$	−8.70658	−0.517552	−0.258776	+	0.965937i	$0.583319\pi$
$284$	−76.4069	−4.53391
$285$	−13.1339	−0.777984
$286$	18.0550	1.06762
$287$	−15.6023	−0.920973
$288$	−72.3325	−4.26223
$289$	−6.33464	−0.372626
$290$	22.6155	1.32803
$291$	39.7929	2.33270
$292$	43.4914	2.54514
$293$	−10.4275	−0.609182	−0.304591	−	0.952483i	$-0.598520\pi$
$293$	−10.4275	−0.609182	−0.304591	+	0.952483i	$0.598520\pi$
$294$	−4.76759	−0.278051
$295$	−4.99040	−0.290552
$296$	91.9535	5.34469
$297$	11.7657	0.682715
$298$	−10.7754	−0.624205
$299$	17.6204	1.01901
$300$	44.3485	2.56046
$301$	24.4426	1.40885
$302$	−21.8434	−1.25695
$303$	33.2418	1.90969
$304$	38.6423	2.21629
$305$	−5.32211	−0.304743
$306$	−43.7293	−2.49984
$307$	−2.78686	−0.159055	−0.0795273	−	0.996833i	$-0.525341\pi$
$307$	−2.78686	−0.159055	−0.0795273	+	0.996833i	$0.525341\pi$
$308$	−26.0433	−1.48396
$309$	−48.4682	−2.75726
$310$	24.3321	1.38197
$311$	−8.03620	−0.455691	−0.227846	−	0.973697i	$-0.573168\pi$
$311$	−8.03620	−0.455691	−0.227846	+	0.973697i	$0.573168\pi$
$312$	77.0424	4.36167
$313$	−21.9528	−1.24085	−0.620424	−	0.784267i	$-0.713039\pi$
$313$	−21.9528	−1.24085	−0.620424	+	0.784267i	$0.713039\pi$
$314$	33.1738	1.87211
$315$	17.5770	0.990351
$316$	19.4412	1.09365
$317$	−3.44907	−0.193719	−0.0968594	−	0.995298i	$-0.530880\pi$
$317$	−3.44907	−0.193719	−0.0968594	+	0.995298i	$0.530880\pi$
$318$	−50.9772	−2.85866
$319$	12.5333	0.701733
$320$	20.8845	1.16748
$321$	−27.9716	−1.56122
$322$	−35.4499	−1.97555
$323$	10.9409	0.608769
$324$	6.39279	0.355155
$325$	−10.2947	−0.571047
$326$	23.0997	1.27937
$327$	−0.563907	−0.0311841
$328$	50.3977	2.78275
$329$	−30.4356	−1.67797
$330$	−21.2301	−1.16868
$331$	−17.9767	−0.988091	−0.494046	−	0.869436i	$-0.664482\pi$
$331$	−17.9767	−0.988091	−0.494046	+	0.869436i	$0.664482\pi$
$332$	−10.7542	−0.590214
$333$	−56.8270	−3.11410
$334$	12.2376	0.669614
$335$	5.72960	0.313042
$336$	−82.5143	−4.50152
$337$	1.98011	0.107863	0.0539316	−	0.998545i	$-0.482825\pi$
$337$	1.98011	0.107863	0.0539316	+	0.998545i	$0.482825\pi$
$338$	5.00817	0.272408
$339$	−17.9372	−0.974214
$340$	22.8797	1.24082
$341$	13.4846	0.730234
$342$	−44.8591	−2.42570
$343$	−19.2599	−1.03994
$344$	−78.9534	−4.25688
$345$	−20.7189	−1.11547
$346$	−6.92357	−0.372213
$347$	−28.7274	−1.54217	−0.771085	−	0.636732i	$-0.780286\pi$
$347$	−28.7274	−1.54217	−0.771085	+	0.636732i	$0.780286\pi$
$348$	88.3644	4.73683
$349$	9.64451	0.516259	0.258129	−	0.966110i	$-0.416894\pi$
$349$	9.64451	0.516259	0.258129	+	0.966110i	$0.416894\pi$
$350$	20.7116	1.10708
$351$	−19.2558	−1.02780
$352$	29.2532	1.55920
$353$	13.7963	0.734305	0.367153	−	0.930161i	$-0.380333\pi$
$353$	13.7963	0.734305	0.367153	+	0.930161i	$0.380333\pi$
$354$	−27.1962	−1.44546
$355$	−20.8555	−1.10689
$356$	−11.1720	−0.592116
$357$	−23.3626	−1.23648
$358$	17.5567	0.927902
$359$	−6.70529	−0.353892	−0.176946	−	0.984221i	$-0.556622\pi$
$359$	−6.70529	−0.353892	−0.176946	+	0.984221i	$0.556622\pi$
$360$	−56.7764	−2.99238
$361$	−7.77639	−0.409284
$362$	−36.0861	−1.89664
$363$	19.4194	1.01926
$364$	42.6227	2.23404
$365$	11.8711	0.621362
$366$	−29.0039	−1.51606
$367$	23.5513	1.22937	0.614685	−	0.788773i	$-0.289283\pi$
$367$	23.5513	1.22937	0.614685	+	0.788773i	$0.289283\pi$
$368$	60.9589	3.17770
$369$	−31.1457	−1.62138
$370$	41.4700	2.15592
$371$	−17.0690	−0.886180
$372$	95.0713	4.92922
$373$	7.72031	0.399743	0.199871	−	0.979822i	$-0.435948\pi$
$373$	7.72031	0.399743	0.199871	+	0.979822i	$0.435948\pi$
$374$	17.6853	0.914484
$375$	31.7069	1.63734
$376$	98.3116	5.07003
$377$	−20.5122	−1.05643
$378$	38.7403	1.99258
$379$	−17.9944	−0.924308	−0.462154	−	0.886800i	$-0.652923\pi$
$379$	−17.9944	−0.924308	−0.462154	+	0.886800i	$0.652923\pi$
$380$	23.4708	1.20403
$381$	3.12021	0.159853
$382$	69.0005	3.53037
$383$	−11.3548	−0.580204	−0.290102	−	0.956996i	$-0.593689\pi$
$383$	−11.3548	−0.580204	−0.290102	+	0.956996i	$0.593689\pi$
$384$	32.3953	1.65317
$385$	−7.10860	−0.362288
$386$	62.4956	3.18094
$387$	48.7930	2.48029
$388$	−71.1116	−3.61014
$389$	11.8524	0.600942	0.300471	−	0.953791i	$-0.402856\pi$
$389$	11.8524	0.600942	0.300471	+	0.953791i	$0.402856\pi$
$390$	34.7453	1.75940
$391$	17.2595	0.872851
$392$	5.15650	0.260442
$393$	−42.2999	−2.13375
$394$	−42.9649	−2.16454
$395$	5.30652	0.267000
$396$	−51.9884	−2.61252
$397$	−30.9115	−1.55140	−0.775702	−	0.631099i	$-0.782604\pi$
$397$	−30.9115	−1.55140	−0.775702	+	0.631099i	$0.782604\pi$
$398$	−15.2137	−0.762591
$399$	−23.9662	−1.19981
$400$	−35.6153	−1.78076
$401$	16.4299	0.820472	0.410236	−	0.911979i	$-0.365446\pi$
$401$	16.4299	0.820472	0.410236	+	0.911979i	$0.365446\pi$
$402$	31.2246	1.55734
$403$	−22.0691	−1.09934
$404$	−59.4045	−2.95549
$405$	1.74493	0.0867062
$406$	41.2679	2.04809
$407$	22.9824	1.13919
$408$	75.4646	3.73606
$409$	4.82273	0.238469	0.119234	−	0.992866i	$-0.461956\pi$
$409$	4.82273	0.238469	0.119234	+	0.992866i	$0.461956\pi$
$410$	22.7288	1.12250
$411$	41.6142	2.05268
$412$	86.6147	4.26720
$413$	−9.10627	−0.448090
$414$	−70.7661	−3.47796
$415$	−2.93539	−0.144093
$416$	−47.8760	−2.34731
$417$	5.66960	0.277641
$418$	18.1422	0.887365
$419$	33.5884	1.64090	0.820449	−	0.571719i	$-0.193723\pi$
$419$	33.5884	1.64090	0.820449	+	0.571719i	$0.193723\pi$
$420$	−50.1181	−2.44551
$421$	−16.4684	−0.802620	−0.401310	−	0.915942i	$-0.631445\pi$
$421$	−16.4684	−0.802620	−0.401310	+	0.915942i	$0.631445\pi$
$422$	−39.0191	−1.89942
$423$	−60.7563	−2.95407
$424$	55.1356	2.67762
$425$	−10.0839	−0.489139
$426$	−113.656	−5.50665
$427$	−9.71157	−0.469976
$428$	49.9864	2.41618
$429$	19.2556	0.929667
$430$	−35.6071	−1.71713
$431$	−2.53374	−0.122046	−0.0610230	−	0.998136i	$-0.519436\pi$
$431$	−2.53374	−0.122046	−0.0610230	+	0.998136i	$0.519436\pi$
$432$	−66.6169	−3.20511
$433$	−17.7558	−0.853290	−0.426645	−	0.904419i	$-0.640305\pi$
$433$	−17.7558	−0.853290	−0.426645	+	0.904419i	$0.640305\pi$
$434$	44.4002	2.13128
$435$	24.1193	1.15643
$436$	1.00773	0.0482613
$437$	17.7054	0.846966
$438$	64.6940	3.09120
$439$	6.64959	0.317368	0.158684	−	0.987329i	$-0.449275\pi$
$439$	6.64959	0.317368	0.158684	+	0.987329i	$0.449275\pi$
$440$	22.9619	1.09466
$441$	−3.18670	−0.151748
$442$	−28.9439	−1.37672
$443$	−16.9192	−0.803855	−0.401928	−	0.915671i	$-0.631660\pi$
$443$	−16.9192	−0.803855	−0.401928	+	0.915671i	$0.631660\pi$
$444$	162.034	7.68977
$445$	−3.04943	−0.144557
$446$	30.8737	1.46191
$447$	−11.4919	−0.543550
$448$	38.1092	1.80049
$449$	29.9975	1.41567	0.707836	−	0.706377i	$-0.249672\pi$
$449$	29.9975	1.41567	0.707836	+	0.706377i	$0.249672\pi$
$450$	41.3451	1.94903
$451$	12.5961	0.593129
$452$	32.0545	1.50772
$453$	−23.2958	−1.09453
$454$	21.4220	1.00539
$455$	11.6340	0.545410
$456$	77.4145	3.62526
$457$	−5.45971	−0.255394	−0.127697	−	0.991813i	$-0.540759\pi$
$457$	−5.45971	−0.255394	−0.127697	+	0.991813i	$0.540759\pi$
$458$	−66.6864	−3.11605
$459$	−18.8615	−0.880378
$460$	37.0256	1.72633
$461$	−5.34459	−0.248922	−0.124461	−	0.992224i	$-0.539720\pi$
$461$	−5.34459	−0.248922	−0.124461	+	0.992224i	$0.539720\pi$
$462$	−38.7398	−1.80234
$463$	−32.1131	−1.49242	−0.746211	−	0.665710i	$-0.768129\pi$
$463$	−32.1131	−1.49242	−0.746211	+	0.665710i	$0.768129\pi$
$464$	−70.9633	−3.29439
$465$	25.9500	1.20340
$466$	6.73802	0.312133
$467$	−16.9232	−0.783111	−0.391555	−	0.920155i	$-0.628063\pi$
$467$	−16.9232	−0.783111	−0.391555	+	0.920155i	$0.628063\pi$
$468$	85.0846	3.93304
$469$	10.4551	0.482774
$470$	44.3374	2.04513
$471$	35.3796	1.63021
$472$	29.4146	1.35392
$473$	−19.7332	−0.907333
$474$	28.9190	1.32829
$475$	−10.3444	−0.474634
$476$	41.7498	1.91360
$477$	−34.0737	−1.56013
$478$	50.7819	2.32271
$479$	−10.9928	−0.502273	−0.251137	−	0.967952i	$-0.580804\pi$
$479$	−10.9928	−0.502273	−0.251137	+	0.967952i	$0.580804\pi$
$480$	56.2951	2.56951
$481$	−37.6131	−1.71501
$482$	55.4498	2.52567
$483$	−37.8071	−1.72028
$484$	−34.7033	−1.57742
$485$	−19.4101	−0.881367
$486$	−36.5485	−1.65787
$487$	2.01603	0.0913550	0.0456775	−	0.998956i	$-0.485455\pi$
$487$	2.01603	0.0913550	0.0456775	+	0.998956i	$0.485455\pi$
$488$	31.3699	1.42005
$489$	24.6356	1.11406
$490$	2.32552	0.105056
$491$	−13.0352	−0.588271	−0.294136	−	0.955764i	$-0.595032\pi$
$491$	−13.0352	−0.588271	−0.294136	+	0.955764i	$0.595032\pi$
$492$	88.8071	4.00373
$493$	−20.0921	−0.904902
$494$	−29.6917	−1.33589
$495$	−14.1904	−0.637810
$496$	−76.3495	−3.42820
$497$	−38.0562	−1.70705
$498$	−15.9970	−0.716843
$499$	21.7819	0.975093	0.487547	−	0.873097i	$-0.337892\pi$
$499$	21.7819	0.975093	0.487547	+	0.873097i	$0.337892\pi$
$500$	−56.6615	−2.53398
$501$	13.0513	0.583091
$502$	−53.1680	−2.37300
$503$	14.0252	0.625355	0.312677	−	0.949859i	$-0.398774\pi$
$503$	14.0252	0.625355	0.312677	+	0.949859i	$0.398774\pi$
$504$	−103.603	−4.61485
$505$	−16.2146	−0.721541
$506$	28.6197	1.27230
$507$	5.34117	0.237210
$508$	−5.57595	−0.247393
$509$	−23.1033	−1.02404	−0.512018	−	0.858975i	$-0.671102\pi$
$509$	−23.1033	−1.02404	−0.512018	+	0.858975i	$0.671102\pi$
$510$	34.0337	1.50704
$511$	21.6619	0.958266
$512$	22.4007	0.989979
$513$	−19.3488	−0.854271
$514$	−75.6283	−3.33582
$515$	23.6417	1.04178
$516$	−139.126	−6.12466
$517$	24.5715	1.08065
$518$	75.6728	3.32487
$519$	−7.38393	−0.324119
$520$	−37.5796	−1.64797
$521$	8.33329	0.365088	0.182544	−	0.983198i	$-0.441567\pi$
$521$	8.33329	0.365088	0.182544	+	0.983198i	$0.441567\pi$
$522$	82.3800	3.60568
$523$	2.69645	0.117908	0.0589538	−	0.998261i	$-0.481224\pi$
$523$	2.69645	0.117908	0.0589538	+	0.998261i	$0.481224\pi$
$524$	75.5916	3.30224
$525$	22.0888	0.964034
$526$	−53.7959	−2.34561
$527$	−21.6171	−0.941656
$528$	66.6161	2.89909
$529$	4.93066	0.214376
$530$	24.8656	1.08009
$531$	−18.1782	−0.788866
$532$	42.8286	1.85685
$533$	−20.6149	−0.892932
$534$	−16.6185	−0.719153
$535$	13.6439	0.589878
$536$	−33.7717	−1.45872
$537$	18.7241	0.808005
$538$	1.90425	0.0820982
$539$	1.28879	0.0555120
$540$	−40.4622	−1.74122
$541$	−5.07262	−0.218089	−0.109044	−	0.994037i	$-0.534779\pi$
$541$	−5.07262	−0.218089	−0.109044	+	0.994037i	$0.534779\pi$
$542$	−35.8261	−1.53886
$543$	−38.4856	−1.65157
$544$	−46.8955	−2.01063
$545$	0.275061	0.0117823
$546$	63.4018	2.71334
$547$	32.2782	1.38011	0.690057	−	0.723755i	$-0.257585\pi$
$547$	32.2782	1.38011	0.690057	+	0.723755i	$0.257585\pi$
$548$	−74.3663	−3.17677
$549$	−19.3865	−0.827396
$550$	−16.7211	−0.712988
$551$	−20.6112	−0.878067
$552$	122.123	5.19789
$553$	9.68312	0.411768
$554$	−57.1888	−2.42972
$555$	44.2275	1.87735
$556$	−10.1318	−0.429684
$557$	3.96832	0.168143	0.0840716	−	0.996460i	$-0.473208\pi$
$557$	3.96832	0.168143	0.0840716	+	0.996460i	$0.473208\pi$
$558$	88.6328	3.75212
$559$	32.2955	1.36595
$560$	40.2486	1.70082
$561$	18.8612	0.796322
$562$	29.7676	1.25567
$563$	16.4208	0.692054	0.346027	−	0.938224i	$-0.387530\pi$
$563$	16.4208	0.692054	0.346027	+	0.938224i	$0.387530\pi$
$564$	173.237	7.29460
$565$	8.74936	0.368088
$566$	23.1442	0.972823
$567$	3.18408	0.133719
$568$	122.927	5.15792
$569$	−8.15245	−0.341769	−0.170884	−	0.985291i	$-0.554662\pi$
$569$	−8.15245	−0.341769	−0.170884	+	0.985291i	$0.554662\pi$
$570$	34.9131	1.46235
$571$	−26.6141	−1.11377	−0.556883	−	0.830591i	$-0.688003\pi$
$571$	−26.6141	−1.11377	−0.556883	+	0.830591i	$0.688003\pi$
$572$	−34.4105	−1.43877
$573$	73.5885	3.07420
$574$	41.4746	1.73112
$575$	−16.3185	−0.680528
$576$	76.0746	3.16978
$577$	23.7734	0.989698	0.494849	−	0.868979i	$-0.335223\pi$
$577$	23.7734	0.989698	0.494849	+	0.868979i	$0.335223\pi$
$578$	16.8390	0.700411
$579$	66.6511	2.76993
$580$	−43.1022	−1.78972
$581$	−5.35638	−0.222220
$582$	−105.779	−4.38469
$583$	13.7803	0.570722
$584$	−69.9713	−2.89543
$585$	23.2241	0.960197
$586$	27.7189	1.14506
$587$	−40.1008	−1.65514	−0.827568	−	0.561365i	$-0.810276\pi$
$587$	−40.1008	−1.65514	−0.827568	+	0.561365i	$0.810276\pi$
$588$	9.08639	0.374716
$589$	−22.1756	−0.913731
$590$	13.2657	0.546140
$591$	−45.8218	−1.88485
$592$	−130.125	−5.34812
$593$	2.02118	0.0830000	0.0415000	−	0.999139i	$-0.486786\pi$
$593$	2.02118	0.0830000	0.0415000	+	0.999139i	$0.486786\pi$
$594$	−31.2761	−1.28327
$595$	11.3957	0.467179
$596$	20.5366	0.841210
$597$	−16.2252	−0.664055
$598$	−46.8392	−1.91540
$599$	36.7195	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$599$	36.7195	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$600$	−71.3502	−2.91286
$601$	−0.572555	−0.0233550	−0.0116775	−	0.999932i	$-0.503717\pi$
$601$	−0.572555	−0.0233550	−0.0116775	+	0.999932i	$0.503717\pi$
$602$	−64.9744	−2.64816
$603$	20.8708	0.849926
$604$	41.6306	1.69393
$605$	−9.47236	−0.385106
$606$	−88.3649	−3.58958
$607$	−10.2532	−0.416165	−0.208083	−	0.978111i	$-0.566722\pi$
$607$	−10.2532	−0.416165	−0.208083	+	0.978111i	$0.566722\pi$
$608$	−48.1072	−1.95100
$609$	44.0119	1.78345
$610$	14.1475	0.572814
$611$	−40.2138	−1.62688
$612$	83.3422	3.36891
$613$	15.5061	0.626284	0.313142	−	0.949706i	$-0.398618\pi$
$613$	15.5061	0.626284	0.313142	+	0.949706i	$0.398618\pi$
$614$	7.40815	0.298969
$615$	24.2401	0.977457
$616$	41.8999	1.68819
$617$	24.9018	1.00251	0.501254	−	0.865300i	$-0.332872\pi$
$617$	24.9018	1.00251	0.501254	+	0.865300i	$0.332872\pi$
$618$	128.840	5.18272
$619$	−47.2909	−1.90078	−0.950391	−	0.311057i	$-0.899317\pi$
$619$	−47.2909	−1.90078	−0.950391	+	0.311057i	$0.899317\pi$
$620$	−46.3737	−1.86241
$621$	−30.5231	−1.22485
$622$	21.3622	0.856545
$623$	−5.56448	−0.222936
$624$	−109.024	−4.36446
$625$	−0.0272650	−0.00109060
$626$	58.3560	2.33237
$627$	19.3486	0.772707
$628$	−63.2248	−2.52295
$629$	−36.8428	−1.46902
$630$	−46.7239	−1.86152
$631$	−8.12301	−0.323372	−0.161686	−	0.986842i	$-0.551693\pi$
$631$	−8.12301	−0.323372	−0.161686	+	0.986842i	$0.551693\pi$
$632$	−31.2780	−1.24417
$633$	−41.6136	−1.65399
$634$	9.16846	0.364126
$635$	−1.52197	−0.0603975
$636$	97.1558	3.85248
$637$	−2.10924	−0.0835710
$638$	−33.3167	−1.31902
$639$	−75.9688	−3.00528
$640$	−15.8017	−0.624617
$641$	7.41333	0.292809	0.146404	−	0.989225i	$-0.453230\pi$
$641$	7.41333	0.292809	0.146404	+	0.989225i	$0.453230\pi$
$642$	74.3553	2.93457
$643$	24.1316	0.951656	0.475828	−	0.879538i	$-0.342148\pi$
$643$	24.1316	0.951656	0.475828	+	0.879538i	$0.342148\pi$
$644$	67.5628	2.66235
$645$	−37.9747	−1.49525
$646$	−29.0836	−1.14428
$647$	36.1616	1.42166	0.710829	−	0.703365i	$-0.248320\pi$
$647$	36.1616	1.42166	0.710829	+	0.703365i	$0.248320\pi$
$648$	−10.2851	−0.404035
$649$	7.35174	0.288581
$650$	27.3658	1.07337
$651$	47.3524	1.85589
$652$	−44.0249	−1.72415
$653$	31.6399	1.23816	0.619082	−	0.785326i	$-0.287505\pi$
$653$	31.6399	1.23816	0.619082	+	0.785326i	$0.287505\pi$
$654$	1.49900	0.0586156
$655$	20.6329	0.806196
$656$	−71.3189	−2.78453
$657$	43.2421	1.68703
$658$	80.9051	3.15401
$659$	−26.9047	−1.04806	−0.524029	−	0.851700i	$-0.675572\pi$
$659$	−26.9047	−1.04806	−0.524029	+	0.851700i	$0.675572\pi$
$660$	40.4617	1.57497
$661$	32.8494	1.27769	0.638847	−	0.769334i	$-0.279412\pi$
$661$	32.8494	1.27769	0.638847	+	0.769334i	$0.279412\pi$
$662$	47.7866	1.85728
$663$	−30.8684	−1.19883
$664$	17.3019	0.671445
$665$	11.6902	0.453325
$666$	151.060	5.85346
$667$	−32.5146	−1.25897
$668$	−23.3233	−0.902405
$669$	32.9266	1.27302
$670$	−15.2307	−0.588412
$671$	7.84042	0.302676
$672$	102.725	3.96270
$673$	−34.2823	−1.32148	−0.660742	−	0.750613i	$-0.729758\pi$
$673$	−34.2823	−1.32148	−0.660742	+	0.750613i	$0.729758\pi$
$674$	−5.26360	−0.202746
$675$	17.8331	0.686397
$676$	−9.54490	−0.367111
$677$	−20.9522	−0.805258	−0.402629	−	0.915363i	$-0.631904\pi$
$677$	−20.9522	−0.805258	−0.402629	+	0.915363i	$0.631904\pi$
$678$	47.6814	1.83119
$679$	−35.4187	−1.35925
$680$	−36.8100	−1.41160
$681$	22.8464	0.875477
$682$	−35.8455	−1.37259
$683$	50.7499	1.94189	0.970945	−	0.239302i	$-0.0769187\pi$
$683$	50.7499	1.94189	0.970945	+	0.239302i	$0.0769187\pi$
$684$	85.4955	3.26900
$685$	−20.2985	−0.775565
$686$	51.1975	1.95473
$687$	−71.1206	−2.71342
$688$	111.729	4.25961
$689$	−22.5529	−0.859198
$690$	55.0760	2.09671
$691$	46.0624	1.75230	0.876148	−	0.482043i	$-0.160105\pi$
$691$	46.0624	1.75230	0.876148	+	0.482043i	$0.160105\pi$
$692$	13.1954	0.501614
$693$	−25.8940	−0.983632
$694$	76.3645	2.89876
$695$	−2.76550	−0.104902
$696$	−142.165	−5.38876
$697$	−20.1928	−0.764855
$698$	−25.6374	−0.970391
$699$	7.18605	0.271801
$700$	−39.4736	−1.49196
$701$	−48.7876	−1.84268	−0.921340	−	0.388757i	$-0.872905\pi$
$701$	−48.7876	−1.84268	−0.921340	+	0.388757i	$0.872905\pi$
$702$	51.1866	1.93192
$703$	−37.7947	−1.42546
$704$	−30.7666	−1.15956
$705$	47.2856	1.78088
$706$	−36.6740	−1.38025
$707$	−29.5878	−1.11276
$708$	51.8323	1.94798
$709$	1.10316	0.0414299	0.0207150	−	0.999785i	$-0.493406\pi$
$709$	1.10316	0.0414299	0.0207150	+	0.999785i	$0.493406\pi$
$710$	55.4389	2.08058
$711$	19.3297	0.724921
$712$	17.9741	0.673609
$713$	−34.9825	−1.31010
$714$	62.1033	2.32416
$715$	−9.39243	−0.351257
$716$	−33.4608	−1.25049
$717$	54.1585	2.02259
$718$	17.8243	0.665197
$719$	−13.7923	−0.514365	−0.257182	−	0.966363i	$-0.582794\pi$
$719$	−13.7923	−0.514365	−0.257182	+	0.966363i	$0.582794\pi$
$720$	80.3454	2.99430
$721$	43.1404	1.60663
$722$	20.6715	0.769315
$723$	59.1368	2.19932
$724$	68.7753	2.55601
$725$	18.9966	0.705517
$726$	−51.6216	−1.91586
$727$	−0.573070	−0.0212540	−0.0106270	−	0.999944i	$-0.503383\pi$
$727$	−0.573070	−0.0212540	−0.0106270	+	0.999944i	$0.503383\pi$
$728$	−68.5736	−2.54151
$729$	−42.7642	−1.58386
$730$	−31.5563	−1.16795
$731$	31.6341	1.17003
$732$	55.2776	2.04312
$733$	51.5290	1.90327	0.951633	−	0.307236i	$-0.0994040\pi$
$733$	51.5290	1.90327	0.951633	+	0.307236i	$0.0994040\pi$
$734$	−62.6051	−2.31080
$735$	2.48015	0.0914819
$736$	−75.8899	−2.79734
$737$	−8.44072	−0.310918
$738$	82.7928	3.04764
$739$	−12.2360	−0.450108	−0.225054	−	0.974346i	$-0.572256\pi$
$739$	−12.2360	−0.450108	−0.225054	+	0.974346i	$0.572256\pi$
$740$	−79.0363	−2.90543
$741$	−31.6660	−1.16328
$742$	45.3736	1.66572
$743$	35.9763	1.31984	0.659921	−	0.751335i	$-0.270590\pi$
$743$	35.9763	1.31984	0.659921	+	0.751335i	$0.270590\pi$
$744$	−152.956	−5.60763
$745$	5.60551	0.205370
$746$	−20.5225	−0.751381
$747$	−10.6925	−0.391220
$748$	−33.7058	−1.23241
$749$	24.8969	0.909712
$750$	−84.2847	−3.07764
$751$	52.3561	1.91050	0.955250	−	0.295799i	$-0.0955857\pi$
$751$	52.3561	1.91050	0.955250	+	0.295799i	$0.0955857\pi$
$752$	−139.123	−5.07328
$753$	−56.7033	−2.06638
$754$	54.5263	1.98573
$755$	11.3632	0.413549
$756$	−73.8338	−2.68531
$757$	−40.0366	−1.45516	−0.727578	−	0.686025i	$-0.759354\pi$
$757$	−40.0366	−1.45516	−0.727578	+	0.686025i	$0.759354\pi$
$758$	47.8334	1.73739
$759$	30.5227	1.10790
$760$	−37.7610	−1.36974
$761$	−12.6416	−0.458257	−0.229129	−	0.973396i	$-0.573588\pi$
$761$	−12.6416	−0.458257	−0.229129	+	0.973396i	$0.573588\pi$
$762$	−8.29428	−0.300470
$763$	0.501921	0.0181707
$764$	−131.506	−4.75771
$765$	22.7485	0.822473
$766$	30.1838	1.09059
$767$	−12.0319	−0.434447
$768$	−0.483321	−0.0174404
$769$	−44.4687	−1.60358	−0.801790	−	0.597605i	$-0.796119\pi$
$769$	−44.4687	−1.60358	−0.801790	+	0.597605i	$0.796119\pi$
$770$	18.8964	0.680979
$771$	−80.6570	−2.90479
$772$	−119.108	−4.28680
$773$	−11.6346	−0.418467	−0.209234	−	0.977866i	$-0.567097\pi$
$773$	−11.6346	−0.418467	−0.209234	+	0.977866i	$0.567097\pi$
$774$	−129.704	−4.66210
$775$	20.4385	0.734173
$776$	114.408	4.10701
$777$	80.7045	2.89526
$778$	−31.5067	−1.12957
$779$	−20.7145	−0.742173
$780$	−66.2199	−2.37105
$781$	30.7238	1.09938
$782$	−45.8800	−1.64066
$783$	35.5325	1.26983
$784$	−7.29706	−0.260609
$785$	−17.2574	−0.615942
$786$	112.443	4.01072
$787$	32.3867	1.15446	0.577230	−	0.816581i	$-0.304134\pi$
$787$	32.3867	1.15446	0.577230	+	0.816581i	$0.304134\pi$
$788$	81.8854	2.91705
$789$	−57.3730	−2.04253
$790$	−14.1060	−0.501870
$791$	15.9655	0.567666
$792$	83.6417	2.97208
$793$	−12.8317	−0.455666
$794$	82.1703	2.91612
$795$	26.5189	0.940530
$796$	28.9952	1.02771
$797$	−3.40693	−0.120680	−0.0603399	−	0.998178i	$-0.519218\pi$
$797$	−3.40693	−0.120680	−0.0603399	+	0.998178i	$0.519218\pi$
$798$	63.7079	2.25524
$799$	−39.3903	−1.39353
$800$	44.3387	1.56761
$801$	−11.1080	−0.392481
$802$	−43.6748	−1.54221
$803$	−17.4882	−0.617147
$804$	−59.5100	−2.09876
$805$	18.4415	0.649976
$806$	58.6649	2.06638
$807$	2.03087	0.0714901
$808$	95.5731	3.36225
$809$	7.66215	0.269387	0.134693	−	0.990887i	$-0.456995\pi$
$809$	7.66215	0.269387	0.134693	+	0.990887i	$0.456995\pi$
$810$	−4.63845	−0.162978
$811$	2.15049	0.0755138	0.0377569	−	0.999287i	$-0.487979\pi$
$811$	2.15049	0.0755138	0.0377569	+	0.999287i	$0.487979\pi$
$812$	−78.6510	−2.76011
$813$	−38.2082	−1.34002
$814$	−61.0927	−2.14130
$815$	−12.0167	−0.420927
$816$	−106.792	−3.73845
$817$	32.4514	1.13533
$818$	−12.8200	−0.448240
$819$	42.3783	1.48082
$820$	−43.3181	−1.51273
$821$	56.7004	1.97886	0.989430	−	0.145014i	$-0.0463227\pi$
$821$	56.7004	1.97886	0.989430	+	0.145014i	$0.0463227\pi$
$822$	−110.621	−3.85834
$823$	−40.0302	−1.39536	−0.697682	−	0.716408i	$-0.745785\pi$
$823$	−40.0302	−1.39536	−0.697682	+	0.716408i	$0.745785\pi$
$824$	−139.350	−4.85449
$825$	−17.8329	−0.620861
$826$	24.2067	0.842258
$827$	−42.6249	−1.48221	−0.741107	−	0.671387i	$-0.765699\pi$
$827$	−42.6249	−1.48221	−0.741107	+	0.671387i	$0.765699\pi$
$828$	134.871	4.68708
$829$	−55.6017	−1.93113	−0.965563	−	0.260170i	$-0.916222\pi$
$829$	−55.6017	−1.93113	−0.965563	+	0.260170i	$0.916222\pi$
$830$	7.80298	0.270845
$831$	−60.9914	−2.11577
$832$	50.3528	1.74567
$833$	−2.06604	−0.0715841
$834$	−15.0712	−0.521872
$835$	−6.36616	−0.220310
$836$	−34.5767	−1.19586
$837$	38.2294	1.32140
$838$	−89.2860	−3.08433
$839$	−9.71588	−0.335429	−0.167715	−	0.985836i	$-0.553639\pi$
$839$	−9.71588	−0.335429	−0.167715	+	0.985836i	$0.553639\pi$
$840$	80.6325	2.78209
$841$	8.85077	0.305199
$842$	43.7770	1.50865
$843$	31.7470	1.09342
$844$	74.3653	2.55976
$845$	−2.60531	−0.0896252
$846$	161.505	5.55266
$847$	−17.2848	−0.593912
$848$	−78.0235	−2.67934
$849$	24.6831	0.847122
$850$	26.8054	0.919417
$851$	−59.6219	−2.04381
$852$	216.613	7.42105
$853$	−39.8558	−1.36464	−0.682319	−	0.731055i	$-0.739028\pi$
$853$	−39.8558	−1.36464	−0.682319	+	0.731055i	$0.739028\pi$
$854$	25.8157	0.883396
$855$	23.3362	0.798082
$856$	−80.4207	−2.74872
$857$	26.5213	0.905950	0.452975	−	0.891523i	$-0.350363\pi$
$857$	26.5213	0.905950	0.452975	+	0.891523i	$0.350363\pi$
$858$	−51.1860	−1.74746
$859$	10.2187	0.348658	0.174329	−	0.984687i	$-0.444224\pi$
$859$	10.2187	0.348658	0.174329	+	0.984687i	$0.444224\pi$
$860$	67.8624	2.31409
$861$	44.2324	1.50744
$862$	6.73530	0.229405
$863$	−21.5513	−0.733614	−0.366807	−	0.930297i	$-0.619549\pi$
$863$	−21.5513	−0.733614	−0.366807	+	0.930297i	$0.619549\pi$
$864$	82.9338	2.82147
$865$	3.60172	0.122462
$866$	47.1993	1.60390
$867$	17.9587	0.609909
$868$	−84.6208	−2.87222
$869$	−7.81745	−0.265189
$870$	−64.1149	−2.17370
$871$	13.8141	0.468074
$872$	−1.62128	−0.0549035
$873$	−70.7038	−2.39296
$874$	−47.0654	−1.59201
$875$	−28.2216	−0.954063
$876$	−123.298	−4.16586
$877$	20.5883	0.695216	0.347608	−	0.937640i	$-0.386994\pi$
$877$	20.5883	0.695216	0.347608	+	0.937640i	$0.386994\pi$
$878$	−17.6762	−0.596544
$879$	29.5620	0.997101
$880$	−32.4938	−1.09537
$881$	−42.3428	−1.42656	−0.713282	−	0.700877i	$-0.752792\pi$
$881$	−42.3428	−1.42656	−0.713282	+	0.700877i	$0.752792\pi$
$882$	8.47103	0.285234
$883$	39.0663	1.31469	0.657344	−	0.753591i	$-0.271680\pi$
$883$	39.0663	1.31469	0.657344	+	0.753591i	$0.271680\pi$
$884$	55.1631	1.85534
$885$	14.1478	0.475572
$886$	44.9753	1.51098
$887$	37.2306	1.25008	0.625040	−	0.780593i	$-0.285083\pi$
$887$	37.2306	1.25008	0.625040	+	0.780593i	$0.285083\pi$
$888$	−260.688	−8.74811
$889$	−2.77723	−0.0931452
$890$	8.10613	0.271718
$891$	−2.57059	−0.0861181
$892$	−58.8412	−1.97015
$893$	−40.4080	−1.35220
$894$	30.5484	1.02169
$895$	−9.13321	−0.305289
$896$	−28.8343	−0.963287
$897$	−49.9536	−1.66790
$898$	−79.7408	−2.66098
$899$	40.7237	1.35821
$900$	−78.7982	−2.62661
$901$	−22.0911	−0.735960
$902$	−33.4836	−1.11488
$903$	−69.2947	−2.30598
$904$	−51.5709	−1.71522
$905$	18.7724	0.624016
$906$	61.9260	2.05735
$907$	21.4753	0.713075	0.356538	−	0.934281i	$-0.383957\pi$
$907$	21.4753	0.713075	0.356538	+	0.934281i	$0.383957\pi$
$908$	−40.8275	−1.35491
$909$	−59.0639	−1.95903
$910$	−30.9260	−1.02519
$911$	−8.39941	−0.278285	−0.139142	−	0.990272i	$-0.544435\pi$
$911$	−8.39941	−0.278285	−0.139142	+	0.990272i	$0.544435\pi$
$912$	−109.551	−3.62759
$913$	4.32435	0.143115
$914$	14.5132	0.480055
$915$	15.0882	0.498800
$916$	127.095	4.19935
$917$	37.6501	1.24332
$918$	50.1384	1.65481
$919$	−29.3253	−0.967351	−0.483676	−	0.875247i	$-0.660699\pi$
$919$	−29.3253	−0.967351	−0.483676	+	0.875247i	$0.660699\pi$
$920$	−59.5687	−1.96392
$921$	7.90074	0.260338
$922$	14.2072	0.467890
$923$	−50.2828	−1.65508
$924$	73.8328	2.42892
$925$	34.8341	1.14534
$926$	85.3644	2.80525
$927$	86.1181	2.82849
$928$	88.3448	2.90006
$929$	−9.00741	−0.295523	−0.147762	−	0.989023i	$-0.547207\pi$
$929$	−9.00741	−0.295523	−0.147762	+	0.989023i	$0.547207\pi$
$930$	−68.9813	−2.26199
$931$	−2.11942	−0.0694613
$932$	−12.8418	−0.420646
$933$	22.7826	0.745869
$934$	44.9859	1.47198
$935$	−9.20009	−0.300875
$936$	−136.889	−4.47434
$937$	−17.7039	−0.578361	−0.289181	−	0.957275i	$-0.593383\pi$
$937$	−17.7039	−0.578361	−0.289181	+	0.957275i	$0.593383\pi$
$938$	−27.7923	−0.907451
$939$	62.2362	2.03100
$940$	−84.5012	−2.75613
$941$	8.72349	0.284378	0.142189	−	0.989840i	$-0.454586\pi$
$941$	8.72349	0.284378	0.142189	+	0.989840i	$0.454586\pi$
$942$	−94.0476	−3.06424
$943$	−32.6775	−1.06413
$944$	−41.6253	−1.35479
$945$	−20.1531	−0.655581
$946$	52.4556	1.70548
$947$	23.0076	0.747647	0.373824	−	0.927500i	$-0.378047\pi$
$947$	23.0076	0.747647	0.373824	+	0.927500i	$0.378047\pi$
$948$	−55.1157	−1.79007
$949$	28.6214	0.929089
$950$	27.4980	0.892151
$951$	9.77809	0.317076
$952$	−67.1693	−2.17697
$953$	37.8828	1.22714	0.613572	−	0.789639i	$-0.289732\pi$
$953$	37.8828	1.22714	0.613572	+	0.789639i	$0.289732\pi$
$954$	90.5761	2.93251
$955$	−35.8948	−1.16153
$956$	−96.7835	−3.13020
$957$	−35.5320	−1.14859
$958$	29.2215	0.944104
$959$	−37.0398	−1.19608
$960$	−59.2075	−1.91092
$961$	12.8147	0.413377
$962$	99.9848	3.22364
$963$	49.6998	1.60155
$964$	−105.680	−3.40372
$965$	−32.5109	−1.04656
$966$	100.500	3.23355
$967$	−46.5325	−1.49638	−0.748192	−	0.663482i	$-0.769078\pi$
$967$	−46.5325	−1.49638	−0.748192	+	0.663482i	$0.769078\pi$
$968$	55.8325	1.79452
$969$	−31.0175	−0.996425
$970$	51.5967	1.65667
$971$	−21.1382	−0.678358	−0.339179	−	0.940722i	$-0.610149\pi$
$971$	−21.1382	−0.678358	−0.339179	+	0.940722i	$0.610149\pi$
$972$	69.6566	2.23424
$973$	−5.04638	−0.161779
$974$	−5.35909	−0.171716
$975$	29.1854	0.934682
$976$	−44.3922	−1.42096
$977$	−10.9329	−0.349773	−0.174887	−	0.984589i	$-0.555956\pi$
$977$	−10.9329	−0.349773	−0.174887	+	0.984589i	$0.555956\pi$
$978$	−65.4874	−2.09406
$979$	4.49236	0.143576
$980$	−4.43214	−0.141579
$981$	1.00195	0.0319897
$982$	34.6508	1.10575
$983$	−21.6546	−0.690675	−0.345337	−	0.938479i	$-0.612235\pi$
$983$	−21.6546	−0.690675	−0.345337	+	0.938479i	$0.612235\pi$
$984$	−142.877	−4.55477
$985$	22.3508	0.712157
$986$	53.4097	1.70091
$987$	86.2847	2.74647
$988$	56.5884	1.80032
$989$	51.1927	1.62783
$990$	37.7215	1.19887
$991$	1.64691	0.0523160	0.0261580	−	0.999658i	$-0.491673\pi$
$991$	1.64691	0.0523160	0.0261580	+	0.999658i	$0.491673\pi$
$992$	95.0503	3.01785
$993$	50.9640	1.61729
$994$	101.163	3.20868
$995$	7.91431	0.250901
$996$	30.4882	0.966054
$997$	50.0524	1.58518	0.792588	−	0.609758i	$-0.208733\pi$
$997$	50.0524	1.58518	0.792588	+	0.609758i	$0.208733\pi$
$998$	−57.9017	−1.83285
$999$	65.1558	2.06144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.4	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.4	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65824 q^{2} -2.83500 q^{3} +5.06626 q^{4} +1.38285 q^{5} +7.53611 q^{6} +2.52336 q^{7} -8.15086 q^{8} +5.03721 q^{9} +O(q^{10})\)	\(q-2.65824 q^{2} -2.83500 q^{3} +5.06626 q^{4} +1.38285 q^{5} +7.53611 q^{6} +2.52336 q^{7} -8.15086 q^{8} +5.03721 q^{9} -3.67595 q^{10} -2.03718 q^{11} -14.3628 q^{12} +3.33406 q^{13} -6.70772 q^{14} -3.92037 q^{15} +11.5344 q^{16} +3.26579 q^{17} -13.3901 q^{18} +3.35017 q^{19} +7.00586 q^{20} -7.15373 q^{21} +5.41532 q^{22} +5.28495 q^{23} +23.1077 q^{24} -3.08773 q^{25} -8.86275 q^{26} -5.77548 q^{27} +12.7840 q^{28} -6.15230 q^{29} +10.4213 q^{30} -6.61927 q^{31} -14.3596 q^{32} +5.77540 q^{33} -8.68125 q^{34} +3.48943 q^{35} +25.5198 q^{36} -11.2815 q^{37} -8.90555 q^{38} -9.45206 q^{39} -11.2714 q^{40} -6.18312 q^{41} +19.0164 q^{42} +9.68651 q^{43} -10.3209 q^{44} +6.96569 q^{45} -14.0487 q^{46} -12.0615 q^{47} -32.7001 q^{48} -0.632633 q^{49} +8.20794 q^{50} -9.25849 q^{51} +16.8912 q^{52} -6.76440 q^{53} +15.3526 q^{54} -2.81711 q^{55} -20.5676 q^{56} -9.49771 q^{57} +16.3543 q^{58} -3.60878 q^{59} -19.8616 q^{60} -3.84866 q^{61} +17.5956 q^{62} +12.7107 q^{63} +15.1025 q^{64} +4.61051 q^{65} -15.3524 q^{66} +4.14333 q^{67} +16.5453 q^{68} -14.9828 q^{69} -9.27575 q^{70} -15.0815 q^{71} -41.0576 q^{72} +8.58453 q^{73} +29.9889 q^{74} +8.75371 q^{75} +16.9728 q^{76} -5.14055 q^{77} +25.1259 q^{78} +3.83739 q^{79} +15.9504 q^{80} +1.26184 q^{81} +16.4362 q^{82} -2.12271 q^{83} -36.2426 q^{84} +4.51609 q^{85} -25.7491 q^{86} +17.4417 q^{87} +16.6048 q^{88} -2.20518 q^{89} -18.5165 q^{90} +8.41306 q^{91} +26.7749 q^{92} +18.7656 q^{93} +32.0624 q^{94} +4.63277 q^{95} +40.7095 q^{96} -14.0363 q^{97} +1.68169 q^{98} -10.2617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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