LMFDB - Embedded newform 1849.4.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 $ x^10 - x^9 - 59x^8 + 42x^7 + 1187x^6 - 541x^5 - 9389x^4 + 2180x^3 + 22676x^2 - 320x - 768
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.92278$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92278 q^{2} -8.37832 q^{3} -4.30290 q^{4} -0.0702257 q^{5} +16.1097 q^{6} +23.4425 q^{7} +23.6558 q^{8} +43.1963 q^{9} +O(q^{10})$	\(q-1.92278 q^{2} -8.37832 q^{3} -4.30290 q^{4} -0.0702257 q^{5} +16.1097 q^{6} +23.4425 q^{7} +23.6558 q^{8} +43.1963 q^{9} +0.135029 q^{10} +55.0459 q^{11} +36.0511 q^{12} -27.7838 q^{13} -45.0749 q^{14} +0.588374 q^{15} -11.0619 q^{16} +29.4207 q^{17} -83.0572 q^{18} +45.8530 q^{19} +0.302174 q^{20} -196.409 q^{21} -105.841 q^{22} +126.794 q^{23} -198.196 q^{24} -124.995 q^{25} +53.4222 q^{26} -135.698 q^{27} -100.871 q^{28} -135.243 q^{29} -1.13132 q^{30} -218.051 q^{31} -167.977 q^{32} -461.192 q^{33} -56.5696 q^{34} -1.64627 q^{35} -185.869 q^{36} -370.014 q^{37} -88.1655 q^{38} +232.781 q^{39} -1.66125 q^{40} +357.357 q^{41} +377.652 q^{42} -236.857 q^{44} -3.03349 q^{45} -243.797 q^{46} +442.020 q^{47} +92.6798 q^{48} +206.551 q^{49} +240.339 q^{50} -246.496 q^{51} +119.551 q^{52} -279.248 q^{53} +260.918 q^{54} -3.86564 q^{55} +554.552 q^{56} -384.172 q^{57} +260.044 q^{58} +413.803 q^{59} -2.53171 q^{60} -560.563 q^{61} +419.265 q^{62} +1012.63 q^{63} +411.478 q^{64} +1.95114 q^{65} +886.773 q^{66} +179.328 q^{67} -126.594 q^{68} -1062.32 q^{69} +3.16542 q^{70} -591.806 q^{71} +1021.84 q^{72} -704.727 q^{73} +711.457 q^{74} +1047.25 q^{75} -197.301 q^{76} +1290.41 q^{77} -447.589 q^{78} -597.771 q^{79} +0.776827 q^{80} -29.3797 q^{81} -687.120 q^{82} +37.8912 q^{83} +845.128 q^{84} -2.06609 q^{85} +1133.11 q^{87} +1302.16 q^{88} +376.390 q^{89} +5.83275 q^{90} -651.321 q^{91} -545.581 q^{92} +1826.90 q^{93} -849.909 q^{94} -3.22006 q^{95} +1407.37 q^{96} -1659.85 q^{97} -397.153 q^{98} +2377.78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) $ 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.92278	−0.679807	−0.339903	−	0.940460i	$-0.610394\pi$
$2$	−1.92278	−0.679807	−0.339903	+	0.940460i	$0.610394\pi$
$3$	−8.37832	−1.61241	−0.806205	−	0.591637i	$-0.798482\pi$
$3$	−8.37832	−1.61241	−0.806205	+	0.591637i	$0.798482\pi$
$4$	−4.30290	−0.537862
$5$	−0.0702257	−0.00628118	−0.00314059	−	0.999995i	$-0.501000\pi$
$5$	−0.0702257	−0.00628118	−0.00314059	+	0.999995i	$0.501000\pi$
$6$	16.1097	1.09613
$7$	23.4425	1.26578	0.632888	−	0.774243i	$-0.281869\pi$
$7$	23.4425	1.26578	0.632888	+	0.774243i	$0.281869\pi$
$8$	23.6558	1.04545
$9$	43.1963	1.59986
$10$	0.135029	0.00426999
$11$	55.0459	1.50881	0.754407	−	0.656407i	$-0.227925\pi$
$11$	55.0459	1.50881	0.754407	+	0.656407i	$0.227925\pi$
$12$	36.0511	0.867254
$13$	−27.7838	−0.592756	−0.296378	−	0.955071i	$-0.595779\pi$
$13$	−27.7838	−0.592756	−0.296378	+	0.955071i	$0.595779\pi$
$14$	−45.0749	−0.860483
$15$	0.588374	0.0101278
$16$	−11.0619	−0.172841
$17$	29.4207	0.419739	0.209870	−	0.977729i	$-0.432696\pi$
$17$	29.4207	0.419739	0.209870	+	0.977729i	$0.432696\pi$
$18$	−83.0572	−1.08760
$19$	45.8530	0.553653	0.276826	−	0.960920i	$-0.410717\pi$
$19$	45.8530	0.553653	0.276826	+	0.960920i	$0.410717\pi$
$20$	0.302174	0.00337841
$21$	−196.409	−2.04095
$22$	−105.841	−1.02570
$23$	126.794	1.14949	0.574747	−	0.818331i	$-0.305101\pi$
$23$	126.794	1.14949	0.574747	+	0.818331i	$0.305101\pi$
$24$	−198.196	−1.68569
$25$	−124.995	−0.999961
$26$	53.4222	0.402960
$27$	−135.698	−0.967225
$28$	−100.871	−0.680813
$29$	−135.243	−0.866002	−0.433001	−	0.901393i	$-0.642545\pi$
$29$	−135.243	−0.866002	−0.433001	+	0.901393i	$0.642545\pi$
$30$	−1.13132	−0.00688497
$31$	−218.051	−1.26333	−0.631663	−	0.775243i	$-0.717627\pi$
$31$	−218.051	−1.26333	−0.631663	+	0.775243i	$0.717627\pi$
$32$	−167.977	−0.927951
$33$	−461.192	−2.43283
$34$	−56.5696	−0.285341
$35$	−1.64627	−0.00795057
$36$	−185.869	−0.860506
$37$	−370.014	−1.64405	−0.822025	−	0.569451i	$-0.807156\pi$
$37$	−370.014	−1.64405	−0.822025	+	0.569451i	$0.807156\pi$
$38$	−88.1655	−0.376377
$39$	232.781	0.955766
$40$	−1.66125	−0.00656666
$41$	357.357	1.36121	0.680606	−	0.732649i	$-0.261716\pi$
$41$	357.357	1.36121	0.680606	+	0.732649i	$0.261716\pi$
$42$	377.652	1.38745
$43$	0	0
$43$	0	0
$44$	−236.857	−0.811534
$45$	−3.03349	−0.0100490
$46$	−243.797	−0.781434
$47$	442.020	1.37181	0.685907	−	0.727689i	$-0.259406\pi$
$47$	442.020	1.37181	0.685907	+	0.727689i	$0.259406\pi$
$48$	92.6798	0.278691
$49$	206.551	0.602189
$50$	240.339	0.679780
$51$	−246.496	−0.676791
$52$	119.551	0.318821
$53$	−279.248	−0.723730	−0.361865	−	0.932230i	$-0.617860\pi$
$53$	−279.248	−0.723730	−0.361865	+	0.932230i	$0.617860\pi$
$54$	260.918	0.657526
$55$	−3.86564	−0.00947713
$56$	554.552	1.32331
$57$	−384.172	−0.892715
$58$	260.044	0.588714
$59$	413.803	0.913095	0.456547	−	0.889699i	$-0.349086\pi$
$59$	413.803	0.913095	0.456547	+	0.889699i	$0.349086\pi$
$60$	−2.53171	−0.00544738
$61$	−560.563	−1.17660	−0.588301	−	0.808642i	$-0.700203\pi$
$61$	−560.563	−1.17660	−0.588301	+	0.808642i	$0.700203\pi$
$62$	419.265	0.858818
$63$	1012.63	2.02507
$64$	411.478	0.803669
$65$	1.95114	0.00372321
$66$	886.773	1.65385
$67$	179.328	0.326991	0.163495	−	0.986544i	$-0.447723\pi$
$67$	179.328	0.326991	0.163495	+	0.986544i	$0.447723\pi$
$68$	−126.594	−0.225762
$69$	−1062.32	−1.85345
$70$	3.16542	0.00540485
$71$	−591.806	−0.989217	−0.494608	−	0.869116i	$-0.664689\pi$
$71$	−591.806	−0.989217	−0.494608	+	0.869116i	$0.664689\pi$
$72$	1021.84	1.67258
$73$	−704.727	−1.12989	−0.564946	−	0.825128i	$-0.691103\pi$
$73$	−704.727	−1.12989	−0.564946	+	0.825128i	$0.691103\pi$
$74$	711.457	1.11764
$75$	1047.25	1.61235
$76$	−197.301	−0.297789
$77$	1290.41	1.90982
$78$	−447.589	−0.649736
$79$	−597.771	−0.851323	−0.425661	−	0.904882i	$-0.639959\pi$
$79$	−597.771	−0.851323	−0.425661	+	0.904882i	$0.639959\pi$
$80$	0.776827	0.00108565
$81$	−29.3797	−0.0403013
$82$	−687.120	−0.925362
$83$	37.8912	0.0501096	0.0250548	−	0.999686i	$-0.492024\pi$
$83$	37.8912	0.0501096	0.0250548	+	0.999686i	$0.492024\pi$
$84$	845.128	1.09775
$85$	−2.06609	−0.00263646
$86$	0	0
$87$	1133.11	1.39635
$88$	1302.16	1.57739
$89$	376.390	0.448283	0.224142	−	0.974557i	$-0.428042\pi$
$89$	376.390	0.448283	0.224142	+	0.974557i	$0.428042\pi$
$90$	5.83275	0.00683140
$91$	−651.321	−0.750297
$92$	−545.581	−0.618270
$93$	1826.90	2.03700
$94$	−849.909	−0.932569
$95$	−3.22006	−0.00347759
$96$	1407.37	1.49624
$97$	−1659.85	−1.73745	−0.868723	−	0.495298i	$-0.835059\pi$
$97$	−1659.85	−1.73745	−0.868723	+	0.495298i	$0.835059\pi$
$98$	−397.153	−0.409372
$99$	2377.78	2.41390
$100$	537.841	0.537841
$101$	−1022.45	−1.00730	−0.503652	−	0.863907i	$-0.668011\pi$
$101$	−1022.45	−1.00730	−0.503652	+	0.863907i	$0.668011\pi$
$102$	473.959	0.460087
$103$	−66.6363	−0.0637463	−0.0318732	−	0.999492i	$-0.510147\pi$
$103$	−66.6363	−0.0637463	−0.0318732	+	0.999492i	$0.510147\pi$
$104$	−657.248	−0.619697
$105$	13.7930	0.0128196
$106$	536.934	0.491997
$107$	1282.02	1.15830	0.579148	−	0.815222i	$-0.303385\pi$
$107$	1282.02	1.15830	0.579148	+	0.815222i	$0.303385\pi$
$108$	583.894	0.520234
$109$	1587.05	1.39461	0.697303	−	0.716776i	$-0.254383\pi$
$109$	1587.05	1.39461	0.697303	+	0.716776i	$0.254383\pi$
$110$	7.43279	0.00644262
$111$	3100.09	2.65088
$112$	−259.318	−0.218779
$113$	−999.212	−0.831840	−0.415920	−	0.909401i	$-0.636540\pi$
$113$	−999.212	−0.831840	−0.415920	+	0.909401i	$0.636540\pi$
$114$	738.679	0.606874
$115$	−8.90420	−0.00722018
$116$	581.939	0.465790
$117$	−1200.16	−0.948329
$118$	−795.654	−0.620728
$119$	689.694	0.531296
$120$	13.9185	0.0105881
$121$	1699.05	1.27652
$122$	1077.84	0.799862
$123$	−2994.05	−2.19483
$124$	938.252	0.679496
$125$	17.5561	0.0125621
$126$	−1947.07	−1.37666
$127$	1275.21	0.890994	0.445497	−	0.895284i	$-0.353027\pi$
$127$	1275.21	0.890994	0.445497	+	0.895284i	$0.353027\pi$
$128$	552.632	0.381611
$129$	0	0
$130$	−3.75161	−0.00253106
$131$	1567.29	1.04530	0.522651	−	0.852547i	$-0.324943\pi$
$131$	1567.29	1.04530	0.522651	+	0.852547i	$0.324943\pi$
$132$	1984.46	1.30853
$133$	1074.91	0.700801
$134$	−344.809	−0.222290
$135$	9.52948	0.00607531
$136$	695.970	0.438816
$137$	630.037	0.392903	0.196452	−	0.980514i	$-0.437058\pi$
$137$	630.037	0.392903	0.196452	+	0.980514i	$0.437058\pi$
$138$	2042.61	1.25999
$139$	599.524	0.365834	0.182917	−	0.983128i	$-0.441446\pi$
$139$	599.524	0.365834	0.182917	+	0.983128i	$0.441446\pi$
$140$	7.08372	0.00427631
$141$	−3703.39	−2.21193
$142$	1137.91	0.672477
$143$	−1529.38	−0.894359
$144$	−477.831	−0.276523
$145$	9.49757	0.00543952
$146$	1355.04	0.768108
$147$	−1730.55	−0.970975
$148$	1592.13	0.884273
$149$	−2474.66	−1.36062	−0.680309	−	0.732926i	$-0.738154\pi$
$149$	−2474.66	−1.36062	−0.680309	+	0.732926i	$0.738154\pi$
$150$	−2013.63	−1.09608
$151$	−2083.60	−1.12292	−0.561459	−	0.827504i	$-0.689760\pi$
$151$	−2083.60	−1.12292	−0.561459	+	0.827504i	$0.689760\pi$
$152$	1084.69	0.578816
$153$	1270.86	0.671525
$154$	−2481.19	−1.29831
$155$	15.3128	0.00793518
$156$	−1001.64	−0.514071
$157$	−2655.89	−1.35008	−0.675042	−	0.737780i	$-0.735874\pi$
$157$	−2655.89	−1.35008	−0.675042	+	0.737780i	$0.735874\pi$
$158$	1149.39	0.578735
$159$	2339.63	1.16695
$160$	11.7963	0.00582863
$161$	2972.37	1.45500
$162$	56.4908	0.0273971
$163$	−1180.34	−0.567188	−0.283594	−	0.958944i	$-0.591527\pi$
$163$	−1180.34	−0.567188	−0.283594	+	0.958944i	$0.591527\pi$
$164$	−1537.67	−0.732145
$165$	32.3876	0.0152810
$166$	−72.8566	−0.0340649
$167$	−2860.88	−1.32564	−0.662819	−	0.748780i	$-0.730640\pi$
$167$	−2860.88	−1.32564	−0.662819	+	0.748780i	$0.730640\pi$
$168$	−4646.21	−2.13371
$169$	−1425.06	−0.648640
$170$	3.97264	0.00179228
$171$	1980.68	0.885769
$172$	0	0
$173$	−315.057	−0.138459	−0.0692293	−	0.997601i	$-0.522054\pi$
$173$	−315.057	−0.138459	−0.0692293	+	0.997601i	$0.522054\pi$
$174$	−2178.73	−0.949248
$175$	−2930.20	−1.26573
$176$	−608.909	−0.260786
$177$	−3466.98	−1.47228
$178$	−723.716	−0.304746
$179$	−237.525	−0.0991813	−0.0495906	−	0.998770i	$-0.515792\pi$
$179$	−237.525	−0.0991813	−0.0495906	+	0.998770i	$0.515792\pi$
$180$	13.0528	0.00540500
$181$	−213.864	−0.0878254	−0.0439127	−	0.999035i	$-0.513982\pi$
$181$	−213.864	−0.0878254	−0.0439127	+	0.999035i	$0.513982\pi$
$182$	1252.35	0.510057
$183$	4696.58	1.89716
$184$	2999.41	1.20174
$185$	25.9845	0.0103266
$186$	−3512.74	−1.38477
$187$	1619.49	0.633308
$188$	−1901.97	−0.737847
$189$	−3181.10	−1.22429
$190$	6.19149	0.00236409
$191$	−1633.59	−0.618861	−0.309430	−	0.950922i	$-0.600138\pi$
$191$	−1633.59	−0.618861	−0.309430	+	0.950922i	$0.600138\pi$
$192$	−3447.50	−1.29584
$193$	−4902.71	−1.82852	−0.914261	−	0.405126i	$-0.867228\pi$
$193$	−4902.71	−1.82852	−0.914261	+	0.405126i	$0.867228\pi$
$194$	3191.53	1.18113
$195$	−16.3472	−0.00600334
$196$	−888.767	−0.323895
$197$	4431.04	1.60253	0.801265	−	0.598309i	$-0.204161\pi$
$197$	4431.04	1.60253	0.801265	+	0.598309i	$0.204161\pi$
$198$	−4571.95	−1.64098
$199$	−961.504	−0.342508	−0.171254	−	0.985227i	$-0.554782\pi$
$199$	−961.504	−0.342508	−0.171254	+	0.985227i	$0.554782\pi$
$200$	−2956.86	−1.04541
$201$	−1502.47	−0.527242
$202$	1965.95	0.684772
$203$	−3170.44	−1.09616
$204$	1060.65	0.364020
$205$	−25.0956	−0.00855002
$206$	128.127	0.0433352
$207$	5477.03	1.83903
$208$	307.340	0.102453
$209$	2524.02	0.835359
$210$	−26.5209	−0.00871483
$211$	3416.62	1.11474	0.557370	−	0.830264i	$-0.311811\pi$
$211$	3416.62	1.11474	0.557370	+	0.830264i	$0.311811\pi$
$212$	1201.58	0.389267
$213$	4958.34	1.59502
$214$	−2465.05	−0.787418
$215$	0	0
$216$	−3210.04	−1.01118
$217$	−5111.66	−1.59909
$218$	−3051.56	−0.948063
$219$	5904.43	1.82185
$220$	16.6334	0.00509739
$221$	−817.418	−0.248803
$222$	−5960.81	−1.80209
$223$	−4025.40	−1.20879	−0.604396	−	0.796684i	$-0.706585\pi$
$223$	−4025.40	−1.20879	−0.604396	+	0.796684i	$0.706585\pi$
$224$	−3937.80	−1.17458
$225$	−5399.32	−1.59980
$226$	1921.27	0.565491
$227$	2703.95	0.790605	0.395303	−	0.918551i	$-0.370640\pi$
$227$	2703.95	0.790605	0.395303	+	0.918551i	$0.370640\pi$
$228$	1653.05	0.480158
$229$	2876.31	0.830007	0.415004	−	0.909820i	$-0.363780\pi$
$229$	2876.31	0.830007	0.415004	+	0.909820i	$0.363780\pi$
$230$	17.1208	0.00490833
$231$	−10811.5	−3.07941
$232$	−3199.29	−0.905362
$233$	1336.62	0.375816	0.187908	−	0.982187i	$-0.439829\pi$
$233$	1336.62	0.375816	0.187908	+	0.982187i	$0.439829\pi$
$234$	2307.64	0.644681
$235$	−31.0412	−0.00861661
$236$	−1780.55	−0.491119
$237$	5008.32	1.37268
$238$	−1326.13	−0.361178
$239$	3444.74	0.932308	0.466154	−	0.884704i	$-0.345639\pi$
$239$	3444.74	0.932308	0.466154	+	0.884704i	$0.345639\pi$
$240$	−6.50851	−0.00175051
$241$	−740.596	−0.197950	−0.0989750	−	0.995090i	$-0.531556\pi$
$241$	−740.596	−0.197950	−0.0989750	+	0.995090i	$0.531556\pi$
$242$	−3266.90	−0.867787
$243$	3909.99	1.03221
$244$	2412.05	0.632850
$245$	−14.5052	−0.00378246
$246$	5756.91	1.49206
$247$	−1273.97	−0.328181
$248$	−5158.18	−1.32074
$249$	−317.465	−0.0807972
$250$	−33.7566	−0.00853981
$251$	1313.08	0.330203	0.165102	−	0.986277i	$-0.447205\pi$
$251$	1313.08	0.330203	0.165102	+	0.986277i	$0.447205\pi$
$252$	−4357.24	−1.08921
$253$	6979.48	1.73437
$254$	−2451.95	−0.605704
$255$	17.3104	0.00425105
$256$	−4354.42	−1.06309
$257$	−4405.40	−1.06927	−0.534633	−	0.845084i	$-0.679550\pi$
$257$	−4405.40	−1.06927	−0.534633	+	0.845084i	$0.679550\pi$
$258$	0	0
$259$	−8674.05	−2.08100
$260$	−8.39554	−0.00200258
$261$	−5842.01	−1.38549
$262$	−3013.56	−0.710604
$263$	300.950	0.0705603	0.0352802	−	0.999377i	$-0.488768\pi$
$263$	300.950	0.0705603	0.0352802	+	0.999377i	$0.488768\pi$
$264$	−10909.9	−2.54340
$265$	19.6104	0.00454588
$266$	−2066.82	−0.476409
$267$	−3153.51	−0.722816
$268$	−771.629	−0.175876
$269$	−2216.51	−0.502389	−0.251195	−	0.967937i	$-0.580823\pi$
$269$	−2216.51	−0.502389	−0.251195	+	0.967937i	$0.580823\pi$
$270$	−18.3231	−0.00413004
$271$	129.247	0.0289712	0.0144856	−	0.999895i	$-0.495389\pi$
$271$	129.247	0.0289712	0.0144856	+	0.999895i	$0.495389\pi$
$272$	−325.447	−0.0725483
$273$	5456.98	1.20979
$274$	−1211.43	−0.267098
$275$	−6880.46	−1.50875
$276$	4571.06	0.996903
$277$	1206.48	0.261699	0.130849	−	0.991402i	$-0.458230\pi$
$277$	1206.48	0.261699	0.130849	+	0.991402i	$0.458230\pi$
$278$	−1152.75	−0.248697
$279$	−9419.00	−2.02115
$280$	−38.9438	−0.00831192
$281$	−7942.09	−1.68607	−0.843034	−	0.537860i	$-0.819233\pi$
$281$	−7942.09	−1.68607	−0.843034	+	0.537860i	$0.819233\pi$
$282$	7120.82	1.50368
$283$	−3506.49	−0.736535	−0.368267	−	0.929720i	$-0.620049\pi$
$283$	−3506.49	−0.736535	−0.368267	+	0.929720i	$0.620049\pi$
$284$	2546.48	0.532063
$285$	26.9787	0.00560730
$286$	2940.67	0.607992
$287$	8377.33	1.72299
$288$	−7255.99	−1.48459
$289$	−4047.42	−0.823819
$290$	−18.2618	−0.00369782
$291$	13906.8	2.80147
$292$	3032.37	0.607726
$293$	5419.92	1.08067	0.540333	−	0.841451i	$-0.318298\pi$
$293$	5419.92	1.08067	0.540333	+	0.841451i	$0.318298\pi$
$294$	3327.47	0.660076
$295$	−29.0596	−0.00573531
$296$	−8752.98	−1.71877
$297$	−7469.61	−1.45936
$298$	4758.24	0.924957
$299$	−3522.81	−0.681370
$300$	−4506.21	−0.867220
$301$	0	0
$302$	4006.31	0.763368
$303$	8566.43	1.62419
$304$	−507.220	−0.0956942
$305$	39.3659	0.00739045
$306$	−2443.60	−0.456507
$307$	5756.16	1.07010	0.535051	−	0.844820i	$-0.320292\pi$
$307$	5756.16	1.07010	0.535051	+	0.844820i	$0.320292\pi$
$308$	−5552.52	−1.02722
$309$	558.301	0.102785
$310$	−29.4432	−0.00539439
$311$	−489.709	−0.0892888	−0.0446444	−	0.999003i	$-0.514215\pi$
$311$	−489.709	−0.0892888	−0.0446444	+	0.999003i	$0.514215\pi$
$312$	5506.64	0.999205
$313$	8077.72	1.45872	0.729361	−	0.684130i	$-0.239818\pi$
$313$	8077.72	1.45872	0.729361	+	0.684130i	$0.239818\pi$
$314$	5106.70	0.917796
$315$	−71.1126	−0.0127198
$316$	2572.15	0.457895
$317$	−4400.14	−0.779610	−0.389805	−	0.920897i	$-0.627458\pi$
$317$	−4400.14	−0.779610	−0.389805	+	0.920897i	$0.627458\pi$
$318$	−4498.61	−0.793300
$319$	−7444.59	−1.30664
$320$	−28.8964	−0.00504799
$321$	−10741.2	−1.86765
$322$	−5715.22	−0.989120
$323$	1349.03	0.232390
$324$	126.418	0.0216766
$325$	3472.84	0.592733
$326$	2269.55	0.385578
$327$	−13296.8	−2.24868
$328$	8453.57	1.42308
$329$	10362.1	1.73641
$330$	−62.2743	−0.0103881
$331$	8982.38	1.49159	0.745795	−	0.666176i	$-0.232070\pi$
$331$	8982.38	1.49159	0.745795	+	0.666176i	$0.232070\pi$
$332$	−163.042	−0.0269521
$333$	−15983.2	−2.63026
$334$	5500.85	0.901178
$335$	−12.5934	−0.00205389
$336$	2172.65	0.352761
$337$	3513.64	0.567952	0.283976	−	0.958831i	$-0.408346\pi$
$337$	3513.64	0.567952	0.283976	+	0.958831i	$0.408346\pi$
$338$	2740.09	0.440950
$339$	8371.72	1.34127
$340$	8.89017	0.00141805
$341$	−12002.8	−1.90612
$342$	−3808.42	−0.602152
$343$	−3198.71	−0.503540
$344$	0	0
$345$	74.6022	0.0116419
$346$	605.787	0.0941251
$347$	3009.24	0.465546	0.232773	−	0.972531i	$-0.425220\pi$
$347$	3009.24	0.465546	0.232773	+	0.972531i	$0.425220\pi$
$348$	−4875.67	−0.751044
$349$	−5833.59	−0.894742	−0.447371	−	0.894348i	$-0.647640\pi$
$349$	−5833.59	−0.894742	−0.447371	+	0.894348i	$0.647640\pi$
$350$	5634.14	0.860449
$351$	3770.20	0.573329
$352$	−9246.44	−1.40011
$353$	6183.54	0.932342	0.466171	−	0.884695i	$-0.345633\pi$
$353$	6183.54	0.932342	0.466171	+	0.884695i	$0.345633\pi$
$354$	6666.25	1.00087
$355$	41.5600	0.00621345
$356$	−1619.57	−0.241115
$357$	−5778.48	−0.856666
$358$	456.709	0.0674241
$359$	−4308.93	−0.633472	−0.316736	−	0.948514i	$-0.602587\pi$
$359$	−4308.93	−0.633472	−0.316736	+	0.948514i	$0.602587\pi$
$360$	−71.7598	−0.0105058
$361$	−4756.50	−0.693468
$362$	411.215	0.0597043
$363$	−14235.2	−2.05827
$364$	2802.57	0.403557
$365$	49.4900	0.00709705
$366$	−9030.51	−1.28971
$367$	−695.735	−0.0989566	−0.0494783	−	0.998775i	$-0.515756\pi$
$367$	−695.735	−0.0989566	−0.0494783	+	0.998775i	$0.515756\pi$
$368$	−1402.58	−0.198680
$369$	15436.5	2.17775
$370$	−49.9626	−0.00702008
$371$	−6546.28	−0.916081
$372$	−7860.97	−1.09563
$373$	−1079.87	−0.149903	−0.0749514	−	0.997187i	$-0.523880\pi$
$373$	−1079.87	−0.149903	−0.0749514	+	0.997187i	$0.523880\pi$
$374$	−3113.92	−0.430527
$375$	−147.091	−0.0202553
$376$	10456.4	1.43416
$377$	3757.57	0.513328
$378$	6116.56	0.832281
$379$	−5259.67	−0.712853	−0.356426	−	0.934323i	$-0.616005\pi$
$379$	−5259.67	−0.712853	−0.356426	+	0.934323i	$0.616005\pi$
$380$	13.8556	0.00187047
$381$	−10684.1	−1.43665
$382$	3141.04	0.420706
$383$	9371.54	1.25030	0.625148	−	0.780506i	$-0.285039\pi$
$383$	9371.54	1.25030	0.625148	+	0.780506i	$0.285039\pi$
$384$	−4630.13	−0.615313
$385$	−90.6202	−0.0119959
$386$	9426.85	1.24304
$387$	0	0
$388$	7142.17	0.934507
$389$	3732.64	0.486510	0.243255	−	0.969962i	$-0.421785\pi$
$389$	3732.64	0.486510	0.243255	+	0.969962i	$0.421785\pi$
$390$	31.4322	0.00408111
$391$	3730.36	0.482487
$392$	4886.13	0.629558
$393$	−13131.2	−1.68545
$394$	−8519.93	−1.08941
$395$	41.9789	0.00534731
$396$	−10231.3	−1.29834
$397$	4906.86	0.620323	0.310161	−	0.950684i	$-0.399617\pi$
$397$	4906.86	0.620323	0.310161	+	0.950684i	$0.399617\pi$
$398$	1848.76	0.232840
$399$	−9005.94	−1.12998
$400$	1382.68	0.172835
$401$	−1871.94	−0.233118	−0.116559	−	0.993184i	$-0.537186\pi$
$401$	−1871.94	−0.233118	−0.116559	+	0.993184i	$0.537186\pi$
$402$	2888.92	0.358423
$403$	6058.28	0.748845
$404$	4399.51	0.541791
$405$	2.06321	0.000253140 0
$406$	6096.08	0.745181
$407$	−20367.7	−2.48057
$408$	−5831.07	−0.707551
$409$	−1917.96	−0.231875	−0.115937	−	0.993257i	$-0.536987\pi$
$409$	−1917.96	−0.231875	−0.115937	+	0.993257i	$0.536987\pi$
$410$	48.2535	0.00581237
$411$	−5278.66	−0.633520
$412$	286.729	0.0342868
$413$	9700.58	1.15577
$414$	−10531.1	−1.25019
$415$	−2.66094	−0.000314747 0
$416$	4667.04	0.550049
$417$	−5023.00	−0.589874
$418$	−4853.15	−0.567883
$419$	−9353.24	−1.09054	−0.545269	−	0.838261i	$-0.683573\pi$
$419$	−9353.24	−1.09054	−0.545269	+	0.838261i	$0.683573\pi$
$420$	−59.3497	−0.00689516
$421$	−3476.89	−0.402502	−0.201251	−	0.979540i	$-0.564501\pi$
$421$	−3476.89	−0.402502	−0.201251	+	0.979540i	$0.564501\pi$
$422$	−6569.43	−0.757808
$423$	19093.6	2.19471
$424$	−6605.85	−0.756624
$425$	−3677.44	−0.419722
$426$	−9533.82	−1.08431
$427$	−13141.0	−1.48931
$428$	−5516.41	−0.623004
$429$	12813.7	1.44207
$430$	0	0
$431$	−4840.83	−0.541008	−0.270504	−	0.962719i	$-0.587190\pi$
$431$	−4840.83	−0.541008	−0.270504	+	0.962719i	$0.587190\pi$
$432$	1501.07	0.167177
$433$	−11591.6	−1.28650	−0.643251	−	0.765655i	$-0.722415\pi$
$433$	−11591.6	−1.28650	−0.643251	+	0.765655i	$0.722415\pi$
$434$	9828.62	1.08707
$435$	−79.5737	−0.00877073
$436$	−6828.93	−0.750107
$437$	5813.88	0.636421
$438$	−11352.9	−1.23850
$439$	−4477.72	−0.486811	−0.243405	−	0.969925i	$-0.578265\pi$
$439$	−4477.72	−0.486811	−0.243405	+	0.969925i	$0.578265\pi$
$440$	−91.4448	−0.00990786
$441$	8922.23	0.963420
$442$	1571.72	0.169138
$443$	4418.43	0.473874	0.236937	−	0.971525i	$-0.423857\pi$
$443$	4418.43	0.473874	0.236937	+	0.971525i	$0.423857\pi$
$444$	−13339.4	−1.42581
$445$	−26.4322	−0.00281575
$446$	7739.97	0.821745
$447$	20733.5	2.19387
$448$	9646.08	1.01726
$449$	11039.6	1.16034	0.580170	−	0.814495i	$-0.302986\pi$
$449$	11039.6	1.16034	0.580170	+	0.814495i	$0.302986\pi$
$450$	10381.7	1.08756
$451$	19671.0	2.05382
$452$	4299.51	0.447416
$453$	17457.1	1.81060
$454$	−5199.11	−0.537459
$455$	45.7395	0.00471275
$456$	−9087.89	−0.933289
$457$	12619.7	1.29174	0.645870	−	0.763447i	$-0.276495\pi$
$457$	12619.7	1.29174	0.645870	+	0.763447i	$0.276495\pi$
$458$	−5530.52	−0.564245
$459$	−3992.32	−0.405982
$460$	38.3139	0.00388346
$461$	−6864.96	−0.693564	−0.346782	−	0.937946i	$-0.612726\pi$
$461$	−6864.96	−0.693564	−0.346782	+	0.937946i	$0.612726\pi$
$462$	20788.2	2.09341
$463$	294.968	0.0296076	0.0148038	−	0.999890i	$-0.495288\pi$
$463$	294.968	0.0296076	0.0148038	+	0.999890i	$0.495288\pi$
$464$	1496.04	0.149681
$465$	−128.296	−0.0127948
$466$	−2570.04	−0.255482
$467$	5598.67	0.554766	0.277383	−	0.960759i	$-0.410533\pi$
$467$	5598.67	0.554766	0.277383	+	0.960759i	$0.410533\pi$
$468$	5164.15	0.510071
$469$	4203.89	0.413897
$470$	59.6855	0.00585763
$471$	22251.9	2.17689
$472$	9788.86	0.954595
$473$	0	0
$474$	−9629.92	−0.933158
$475$	−5731.40	−0.553631
$476$	−2967.69	−0.285764
$477$	−12062.5	−1.15787
$478$	−6623.49	−0.633789
$479$	6372.78	0.607891	0.303946	−	0.952689i	$-0.401696\pi$
$479$	6372.78	0.607891	0.303946	+	0.952689i	$0.401696\pi$
$480$	−98.8333	−0.00939813
$481$	10280.4	0.974522
$482$	1424.01	0.134568
$483$	−24903.4	−2.34606
$484$	−7310.83	−0.686592
$485$	116.564	0.0109132
$486$	−7518.08	−0.701701
$487$	−15966.6	−1.48566	−0.742830	−	0.669480i	$-0.766517\pi$
$487$	−15966.6	−1.48566	−0.742830	+	0.669480i	$0.766517\pi$
$488$	−13260.6	−1.23008
$489$	9889.30	0.914539
$490$	27.8903	0.00257134
$491$	−11444.1	−1.05186	−0.525931	−	0.850527i	$-0.676283\pi$
$491$	−11444.1	−1.05186	−0.525931	+	0.850527i	$0.676283\pi$
$492$	12883.1	1.18052
$493$	−3978.95	−0.363495
$494$	2449.57	0.223100
$495$	−166.981	−0.0151621
$496$	2412.05	0.218355
$497$	−13873.4	−1.25213
$498$	610.416	0.0549265
$499$	−1380.77	−0.123871	−0.0619356	−	0.998080i	$-0.519727\pi$
$499$	−1380.77	−0.123871	−0.0619356	+	0.998080i	$0.519727\pi$
$500$	−75.5421	−0.00675669
$501$	23969.4	2.13747
$502$	−2524.77	−0.224475
$503$	9663.44	0.856603	0.428302	−	0.903636i	$-0.359112\pi$
$503$	9663.44	0.856603	0.428302	+	0.903636i	$0.359112\pi$
$504$	23954.6	2.11711
$505$	71.8024	0.00632706
$506$	−13420.0	−1.17904
$507$	11939.6	1.04587
$508$	−5487.08	−0.479232
$509$	−7566.30	−0.658881	−0.329441	−	0.944176i	$-0.606860\pi$
$509$	−7566.30	−0.658881	−0.329441	+	0.944176i	$0.606860\pi$
$510$	−33.2841	−0.00288989
$511$	−16520.6	−1.43019
$512$	3951.56	0.341085
$513$	−6222.16	−0.535507
$514$	8470.64	0.726894
$515$	4.67958	0.000400402 0
$516$	0	0
$517$	24331.4	2.06981
$518$	16678.3	1.41468
$519$	2639.65	0.223252
$520$	46.1557	0.00389243
$521$	−4717.21	−0.396670	−0.198335	−	0.980134i	$-0.563553\pi$
$521$	−4717.21	−0.396670	−0.198335	+	0.980134i	$0.563553\pi$
$522$	11232.9	0.941862
$523$	6886.07	0.575730	0.287865	−	0.957671i	$-0.407055\pi$
$523$	6886.07	0.575730	0.287865	+	0.957671i	$0.407055\pi$
$524$	−6743.88	−0.562229
$525$	24550.1	2.04087
$526$	−578.662	−0.0479674
$527$	−6415.21	−0.530267
$528$	5101.64	0.420493
$529$	3909.69	0.321336
$530$	−37.7066	−0.00309032
$531$	17874.8	1.46083
$532$	−4625.23	−0.376934
$533$	−9928.72	−0.806868
$534$	6063.53	0.491376
$535$	−90.0309	−0.00727547
$536$	4242.14	0.341852
$537$	1990.06	0.159921
$538$	4261.86	0.341528
$539$	11369.8	0.908591
$540$	−41.0044	−0.00326768
$541$	1060.61	0.0842871	0.0421435	−	0.999112i	$-0.486581\pi$
$541$	1060.61	0.0842871	0.0421435	+	0.999112i	$0.486581\pi$
$542$	−248.514	−0.0196949
$543$	1791.82	0.141611
$544$	−4942.00	−0.389497
$545$	−111.452	−0.00875978
$546$	−10492.6	−0.822421
$547$	13123.1	1.02578	0.512890	−	0.858454i	$-0.328575\pi$
$547$	13123.1	1.02578	0.512890	+	0.858454i	$0.328575\pi$
$548$	−2710.99	−0.211328
$549$	−24214.2	−1.88240
$550$	13229.6	1.02566
$551$	−6201.32	−0.479465
$552$	−25130.1	−1.93769
$553$	−14013.3	−1.07758
$554$	−2319.81	−0.177905
$555$	−217.706	−0.0166507
$556$	−2579.69	−0.196768
$557$	−10395.9	−0.790826	−0.395413	−	0.918504i	$-0.629398\pi$
$557$	−10395.9	−0.790826	−0.395413	+	0.918504i	$0.629398\pi$
$558$	18110.7	1.37399
$559$	0	0
$560$	18.2108	0.00137419
$561$	−13568.6	−1.02115
$562$	15270.9	1.14620
$563$	−10043.6	−0.751844	−0.375922	−	0.926651i	$-0.622674\pi$
$563$	−10043.6	−0.751844	−0.375922	+	0.926651i	$0.622674\pi$
$564$	15935.3	1.18971
$565$	70.1704	0.00522494
$566$	6742.23	0.500701
$567$	−688.733	−0.0510124
$568$	−13999.6	−1.03418
$569$	6375.58	0.469733	0.234867	−	0.972028i	$-0.424535\pi$
$569$	6375.58	0.469733	0.234867	+	0.972028i	$0.424535\pi$
$570$	−51.8743	−0.00381188
$571$	3041.59	0.222919	0.111459	−	0.993769i	$-0.464447\pi$
$571$	3041.59	0.222919	0.111459	+	0.993769i	$0.464447\pi$
$572$	6580.78	0.481042
$573$	13686.7	0.997856
$574$	−16107.8	−1.17130
$575$	−15848.6	−1.14945
$576$	17774.3	1.28576
$577$	−22434.4	−1.61864	−0.809319	−	0.587369i	$-0.800164\pi$
$577$	−22434.4	−1.61864	−0.809319	+	0.587369i	$0.800164\pi$
$578$	7782.32	0.560038
$579$	41076.5	2.94832
$580$	−40.8671	−0.00292571
$581$	888.264	0.0634275
$582$	−26739.7	−1.90446
$583$	−15371.5	−1.09197
$584$	−16670.9	−1.18124
$585$	84.2819	0.00595663
$586$	−10421.3	−0.734644
$587$	−27125.4	−1.90730	−0.953650	−	0.300918i	$-0.902707\pi$
$587$	−27125.4	−1.90730	−0.953650	+	0.300918i	$0.902707\pi$
$588$	7446.38	0.522251
$589$	−9998.30	−0.699444
$590$	55.8754	0.00389891
$591$	−37124.7	−2.58393
$592$	4093.04	0.284160
$593$	11650.0	0.806756	0.403378	−	0.915033i	$-0.367836\pi$
$593$	11650.0	0.806756	0.403378	+	0.915033i	$0.367836\pi$
$594$	14362.4	0.992084
$595$	−48.4343	−0.00333716
$596$	10648.2	0.731825
$597$	8055.79	0.552264
$598$	6773.61	0.463200
$599$	20342.1	1.38757	0.693786	−	0.720181i	$-0.255941\pi$
$599$	20342.1	1.38757	0.693786	+	0.720181i	$0.255941\pi$
$600$	24773.5	1.68563
$601$	−14226.2	−0.965553	−0.482777	−	0.875744i	$-0.660372\pi$
$601$	−14226.2	−0.965553	−0.482777	+	0.875744i	$0.660372\pi$
$602$	0	0
$603$	7746.29	0.523140
$604$	8965.51	0.603976
$605$	−119.317	−0.00801805
$606$	−16471.4	−1.10413
$607$	−18530.3	−1.23908	−0.619541	−	0.784964i	$-0.712681\pi$
$607$	−18530.3	−1.23908	−0.619541	+	0.784964i	$0.712681\pi$
$608$	−7702.26	−0.513763
$609$	26563.0	1.76747
$610$	−75.6922	−0.00502408
$611$	−12281.0	−0.813152
$612$	−5468.40	−0.361188
$613$	−10295.0	−0.678321	−0.339160	−	0.940729i	$-0.610143\pi$
$613$	−10295.0	−0.678321	−0.339160	+	0.940729i	$0.610143\pi$
$614$	−11067.9	−0.727463
$615$	210.259	0.0137861
$616$	30525.8	1.99662
$617$	6789.02	0.442975	0.221487	−	0.975163i	$-0.428909\pi$
$617$	6789.02	0.442975	0.221487	+	0.975163i	$0.428909\pi$
$618$	−1073.49	−0.0698741
$619$	28847.0	1.87311	0.936557	−	0.350514i	$-0.113993\pi$
$619$	28847.0	1.87311	0.936557	+	0.350514i	$0.113993\pi$
$620$	−65.8894	−0.00426804
$621$	−17205.7	−1.11182
$622$	941.604	0.0606992
$623$	8823.52	0.567426
$624$	−2574.99	−0.165196
$625$	15623.2	0.999882
$626$	−15531.7	−0.991649
$627$	−21147.1	−1.34694
$628$	11428.0	0.726159
$629$	−10886.1	−0.690072
$630$	136.734	0.00864702
$631$	14216.2	0.896892	0.448446	−	0.893810i	$-0.351978\pi$
$631$	14216.2	0.896892	0.448446	+	0.893810i	$0.351978\pi$
$632$	−14140.8	−0.890015
$633$	−28625.6	−1.79742
$634$	8460.51	0.529984
$635$	−89.5522	−0.00559649
$636$	−10067.2	−0.627658
$637$	−5738.76	−0.356951
$638$	14314.3	0.888260
$639$	−25563.8	−1.58261
$640$	−38.8090	−0.00239697
$641$	21448.7	1.32164	0.660821	−	0.750543i	$-0.270208\pi$
$641$	21448.7	1.32164	0.660821	+	0.750543i	$0.270208\pi$
$642$	20653.0	1.26964
$643$	−26733.7	−1.63961	−0.819807	−	0.572639i	$-0.805920\pi$
$643$	−26733.7	−1.63961	−0.819807	+	0.572639i	$0.805920\pi$
$644$	−12789.8	−0.782591
$645$	0	0
$646$	−2593.89	−0.157980
$647$	535.525	0.0325404	0.0162702	−	0.999868i	$-0.494821\pi$
$647$	535.525	0.0325404	0.0162702	+	0.999868i	$0.494821\pi$
$648$	−695.000	−0.0421330
$649$	22778.2	1.37769
$650$	−6677.51	−0.402944
$651$	42827.1	2.57838
$652$	5078.90	0.305069
$653$	−130.350	−0.00781159	−0.00390580	−	0.999992i	$-0.501243\pi$
$653$	−130.350	−0.00781159	−0.00390580	+	0.999992i	$0.501243\pi$
$654$	25567.0	1.52867
$655$	−110.064	−0.00656573
$656$	−3953.03	−0.235274
$657$	−30441.6	−1.80767
$658$	−19924.0	−1.18042
$659$	27788.9	1.64265	0.821323	−	0.570464i	$-0.193237\pi$
$659$	27788.9	1.64265	0.821323	+	0.570464i	$0.193237\pi$
$660$	−139.360	−0.00821908
$661$	21026.7	1.23729	0.618643	−	0.785673i	$-0.287683\pi$
$661$	21026.7	1.23729	0.618643	+	0.785673i	$0.287683\pi$
$662$	−17271.2	−1.01399
$663$	6848.59	0.401172
$664$	896.347	0.0523871
$665$	−75.4863	−0.00440186
$666$	30732.3	1.78807
$667$	−17148.0	−0.995464
$668$	12310.1	0.713011
$669$	33726.1	1.94907
$670$	24.2144	0.00139625
$671$	−30856.7	−1.77527
$672$	32992.2	1.89390
$673$	10676.1	0.611494	0.305747	−	0.952113i	$-0.401094\pi$
$673$	10676.1	0.611494	0.305747	+	0.952113i	$0.401094\pi$
$674$	−6755.97	−0.386098
$675$	16961.6	0.967186
$676$	6131.90	0.348879
$677$	6422.42	0.364599	0.182300	−	0.983243i	$-0.441646\pi$
$677$	6422.42	0.364599	0.182300	+	0.983243i	$0.441646\pi$
$678$	−16097.0	−0.911802
$679$	−38911.0	−2.19922
$680$	−48.8750	−0.00275628
$681$	−22654.6	−1.27478
$682$	23078.8	1.29580
$683$	−2695.62	−0.151017	−0.0755087	−	0.997145i	$-0.524058\pi$
$683$	−2695.62	−0.151017	−0.0755087	+	0.997145i	$0.524058\pi$
$684$	−8522.67	−0.476422
$685$	−44.2448	−0.00246789
$686$	6150.43	0.342310
$687$	−24098.6	−1.33831
$688$	0	0
$689$	7758.57	0.428996
$690$	−143.444	−0.00791423
$691$	−8647.75	−0.476087	−0.238043	−	0.971255i	$-0.576506\pi$
$691$	−8647.75	−0.476087	−0.238043	+	0.971255i	$0.576506\pi$
$692$	1355.66	0.0744717
$693$	55741.1	3.05545
$694$	−5786.12	−0.316482
$695$	−42.1020	−0.00229787
$696$	26804.7	1.45981
$697$	10513.7	0.571354
$698$	11216.7	0.608252
$699$	−11198.7	−0.605969
$700$	12608.3	0.680787
$701$	−13509.0	−0.727855	−0.363927	−	0.931427i	$-0.618564\pi$
$701$	−13509.0	−0.727855	−0.363927	+	0.931427i	$0.618564\pi$
$702$	−7249.28	−0.389753
$703$	−16966.2	−0.910233
$704$	22650.2	1.21259
$705$	260.073	0.0138935
$706$	−11889.6	−0.633813
$707$	−23968.8	−1.27502
$708$	14918.1	0.791885
$709$	−5130.31	−0.271753	−0.135877	−	0.990726i	$-0.543385\pi$
$709$	−5130.31	−0.271753	−0.135877	+	0.990726i	$0.543385\pi$
$710$	−79.9109	−0.00422395
$711$	−25821.5	−1.36200
$712$	8903.81	0.468658
$713$	−27647.5	−1.45219
$714$	11110.8	0.582367
$715$	107.402	0.00561763
$716$	1022.05	0.0533459
$717$	−28861.1	−1.50326
$718$	8285.14	0.430639
$719$	−26587.1	−1.37904	−0.689521	−	0.724265i	$-0.742179\pi$
$719$	−26587.1	−1.37904	−0.689521	+	0.724265i	$0.742179\pi$
$720$	33.5560	0.00173689
$721$	−1562.12	−0.0806886
$722$	9145.72	0.471425
$723$	6204.95	0.319176
$724$	920.236	0.0472380
$725$	16904.8	0.865968
$726$	27371.2	1.39923
$727$	−23833.0	−1.21584	−0.607920	−	0.793999i	$-0.707996\pi$
$727$	−23833.0	−1.21584	−0.607920	+	0.793999i	$0.707996\pi$
$728$	−15407.5	−0.784398
$729$	−31965.9	−1.62404
$730$	−95.1586	−0.00482462
$731$	0	0
$732$	−20208.9	−1.02041
$733$	−1707.21	−0.0860261	−0.0430130	−	0.999075i	$-0.513696\pi$
$733$	−1707.21	−0.0860261	−0.0430130	+	0.999075i	$0.513696\pi$
$734$	1337.75	0.0672714
$735$	121.529	0.00609887
$736$	−21298.5	−1.06667
$737$	9871.25	0.493368
$738$	−29681.0	−1.48045
$739$	17540.3	0.873111	0.436556	−	0.899677i	$-0.356198\pi$
$739$	17540.3	0.873111	0.436556	+	0.899677i	$0.356198\pi$
$740$	−111.809	−0.00555428
$741$	10673.7	0.529163
$742$	12587.1	0.622758
$743$	8710.93	0.430112	0.215056	−	0.976602i	$-0.431007\pi$
$743$	8710.93	0.430112	0.215056	+	0.976602i	$0.431007\pi$
$744$	43216.9	2.12958
$745$	173.785	0.00854628
$746$	2076.36	0.101905
$747$	1636.76	0.0801685
$748$	−6968.49	−0.340633
$749$	30053.8	1.46614
$750$	282.823	0.0137697
$751$	−25530.9	−1.24053	−0.620264	−	0.784393i	$-0.712975\pi$
$751$	−25530.9	−1.24053	−0.620264	+	0.784393i	$0.712975\pi$
$752$	−4889.56	−0.237106
$753$	−11001.4	−0.532423
$754$	−7225.00	−0.348964
$755$	146.322	0.00705326
$756$	13687.9	0.658500
$757$	36656.9	1.76000	0.879998	−	0.474978i	$-0.157544\pi$
$757$	36656.9	1.76000	0.879998	+	0.474978i	$0.157544\pi$
$758$	10113.2	0.484602
$759$	−58476.3	−2.79652
$760$	−76.1732	−0.00363565
$761$	−15174.7	−0.722840	−0.361420	−	0.932403i	$-0.617708\pi$
$761$	−15174.7	−0.722840	−0.361420	+	0.932403i	$0.617708\pi$
$762$	20543.2	0.976642
$763$	37204.5	1.76526
$764$	7029.17	0.332862
$765$	−89.2474	−0.00421797
$766$	−18019.4	−0.849959
$767$	−11497.0	−0.541243
$768$	36482.7	1.71414
$769$	−11275.3	−0.528737	−0.264369	−	0.964422i	$-0.585164\pi$
$769$	−11275.3	−0.528737	−0.264369	+	0.964422i	$0.585164\pi$
$770$	174.243	0.00815492
$771$	36909.9	1.72409
$772$	21095.9	0.983493
$773$	−7328.29	−0.340983	−0.170492	−	0.985359i	$-0.554536\pi$
$773$	−7328.29	−0.340983	−0.170492	+	0.985359i	$0.554536\pi$
$774$	0	0
$775$	27255.3	1.26328
$776$	−39265.1	−1.81641
$777$	72674.0	3.35542
$778$	−7177.06	−0.330733
$779$	16385.9	0.753640
$780$	70.3406	0.00322897
$781$	−32576.5	−1.49254
$782$	−7172.68	−0.327998
$783$	18352.2	0.837619
$784$	−2284.84	−0.104083
$785$	186.512	0.00848012
$786$	25248.6	1.14578
$787$	−11509.0	−0.521285	−0.260642	−	0.965435i	$-0.583934\pi$
$787$	−11509.0	−0.521285	−0.260642	+	0.965435i	$0.583934\pi$
$788$	−19066.3	−0.861941
$789$	−2521.46	−0.113772
$790$	−80.7164	−0.00363514
$791$	−23424.0	−1.05292
$792$	56248.3	2.52361
$793$	15574.6	0.697438
$794$	−9434.83	−0.421700
$795$	−164.302	−0.00732982
$796$	4137.25	0.184222
$797$	7631.02	0.339153	0.169576	−	0.985517i	$-0.445760\pi$
$797$	7631.02	0.339153	0.169576	+	0.985517i	$0.445760\pi$
$798$	17316.5	0.768167
$799$	13004.5	0.575804
$800$	20996.3	0.927914
$801$	16258.6	0.717192
$802$	3599.34	0.158475
$803$	−38792.3	−1.70480
$804$	6464.96	0.283584
$805$	−208.737	−0.00913913
$806$	−11648.8	−0.509070
$807$	18570.6	0.810057
$808$	−24186.9	−1.05309
$809$	7806.54	0.339262	0.169631	−	0.985508i	$-0.445742\pi$
$809$	7806.54	0.339262	0.169631	+	0.985508i	$0.445742\pi$
$810$	−3.96710	−0.000172086 0
$811$	20205.3	0.874852	0.437426	−	0.899254i	$-0.355890\pi$
$811$	20205.3	0.874852	0.437426	+	0.899254i	$0.355890\pi$
$812$	13642.1	0.589586
$813$	−1082.87	−0.0467135
$814$	39162.7	1.68631
$815$	82.8905	0.00356261
$816$	2726.70	0.116978
$817$	0	0
$818$	3687.82	0.157630
$819$	−28134.7	−1.20037
$820$	107.984	0.00459874
$821$	9050.07	0.384713	0.192357	−	0.981325i	$-0.438387\pi$
$821$	9050.07	0.384713	0.192357	+	0.981325i	$0.438387\pi$
$822$	10149.7	0.430672
$823$	−31551.3	−1.33634	−0.668171	−	0.744008i	$-0.732923\pi$
$823$	−31551.3	−1.33634	−0.668171	+	0.744008i	$0.732923\pi$
$824$	−1576.34	−0.0666436
$825$	57646.7	2.43273
$826$	−18652.1	−0.785703
$827$	25419.2	1.06882	0.534410	−	0.845226i	$-0.320534\pi$
$827$	25419.2	1.06882	0.534410	+	0.845226i	$0.320534\pi$
$828$	−23567.1	−0.989147
$829$	−36516.9	−1.52989	−0.764947	−	0.644093i	$-0.777235\pi$
$829$	−36516.9	−1.52989	−0.764947	+	0.644093i	$0.777235\pi$
$830$	5.11641	0.000213968 0
$831$	−10108.3	−0.421966
$832$	−11432.4	−0.476380
$833$	6076.87	0.252762
$834$	9658.15	0.401001
$835$	200.907	0.00832657
$836$	−10860.6	−0.449308
$837$	29589.1	1.22192
$838$	17984.3	0.741355
$839$	9085.26	0.373847	0.186924	−	0.982374i	$-0.440148\pi$
$839$	9085.26	0.373847	0.186924	+	0.982374i	$0.440148\pi$
$840$	326.284	0.0134022
$841$	−6098.23	−0.250040
$842$	6685.31	0.273624
$843$	66541.4	2.71863
$844$	−14701.4	−0.599577
$845$	100.076	0.00407422
$846$	−36712.9	−1.49198
$847$	39829.9	1.61579
$848$	3089.00	0.125091
$849$	29378.5	1.18760
$850$	7070.92	0.285330
$851$	−46915.5	−1.88983
$852$	−21335.2	−0.857903
$853$	22536.8	0.904625	0.452313	−	0.891859i	$-0.350599\pi$
$853$	22536.8	0.904625	0.452313	+	0.891859i	$0.350599\pi$
$854$	25267.3	1.01245
$855$	−139.095	−0.00556367
$856$	30327.3	1.21094
$857$	−27300.1	−1.08816	−0.544080	−	0.839033i	$-0.683121\pi$
$857$	−27300.1	−1.08816	−0.544080	+	0.839033i	$0.683121\pi$
$858$	−24637.9	−0.980331
$859$	−2423.33	−0.0962549	−0.0481275	−	0.998841i	$-0.515325\pi$
$859$	−2423.33	−0.0962549	−0.0481275	+	0.998841i	$0.515325\pi$
$860$	0	0
$861$	−70188.0	−2.77817
$862$	9307.86	0.367781
$863$	−859.671	−0.0339091	−0.0169545	−	0.999856i	$-0.505397\pi$
$863$	−859.671	−0.0339091	−0.0169545	+	0.999856i	$0.505397\pi$
$864$	22794.1	0.897537
$865$	22.1251	0.000869684 0
$866$	22288.1	0.874573
$867$	33910.6	1.32833
$868$	21995.0	0.860089
$869$	−32904.8	−1.28449
$870$	153.003	0.00596240
$871$	−4982.40	−0.193826
$872$	37543.1	1.45799
$873$	−71699.4	−2.77968
$874$	−11178.8	−0.432643
$875$	411.559	0.0159008
$876$	−25406.2	−0.979903
$877$	−17566.8	−0.676385	−0.338192	−	0.941077i	$-0.609815\pi$
$877$	−17566.8	−0.676385	−0.338192	+	0.941077i	$0.609815\pi$
$878$	8609.69	0.330937
$879$	−45409.9	−1.74248
$880$	42.7611	0.00163804
$881$	−25664.9	−0.981469	−0.490734	−	0.871309i	$-0.663271\pi$
$881$	−25664.9	−0.981469	−0.490734	+	0.871309i	$0.663271\pi$
$882$	−17155.5	−0.654940
$883$	−38817.2	−1.47939	−0.739695	−	0.672942i	$-0.765030\pi$
$883$	−38817.2	−1.47939	−0.739695	+	0.672942i	$0.765030\pi$
$884$	3517.27	0.133822
$885$	243.471	0.00924767
$886$	−8495.69	−0.322143
$887$	−19118.6	−0.723721	−0.361861	−	0.932232i	$-0.617858\pi$
$887$	−19118.6	−0.723721	−0.361861	+	0.932232i	$0.617858\pi$
$888$	73335.3	2.77136
$889$	29894.0	1.12780
$890$	50.8235	0.00191417
$891$	−1617.23	−0.0608072
$892$	17320.9	0.650164
$893$	20268.0	0.759509
$894$	−39866.0	−1.49141
$895$	16.6804	0.000622975 0
$896$	12955.1	0.483034
$897$	29515.3	1.09865
$898$	−21226.8	−0.788808
$899$	29490.0	1.09404
$900$	23232.8	0.860472
$901$	−8215.68	−0.303778
$902$	−37823.1	−1.39620
$903$	0	0
$904$	−23637.2	−0.869647
$905$	15.0188	0.000551647 0
$906$	−33566.2	−1.23086
$907$	−9172.98	−0.335814	−0.167907	−	0.985803i	$-0.553701\pi$
$907$	−9172.98	−0.335814	−0.167907	+	0.985803i	$0.553701\pi$
$908$	−11634.8	−0.425237
$909$	−44166.1	−1.61155
$910$	−87.9472	−0.00320376
$911$	−18316.9	−0.666154	−0.333077	−	0.942900i	$-0.608087\pi$
$911$	−18316.9	−0.666154	−0.333077	+	0.942900i	$0.608087\pi$
$912$	4249.65	0.154298
$913$	2085.75	0.0756061
$914$	−24265.0	−0.878134
$915$	−329.821	−0.0119164
$916$	−12376.5	−0.446430
$917$	36741.2	1.32312
$918$	7676.38	0.275989
$919$	23462.4	0.842168	0.421084	−	0.907022i	$-0.361650\pi$
$919$	23462.4	0.842168	0.421084	+	0.907022i	$0.361650\pi$
$920$	−210.636	−0.00754833
$921$	−48227.0	−1.72544
$922$	13199.8	0.471490
$923$	16442.6	0.586365
$924$	46520.8	1.65630
$925$	46249.9	1.64399
$926$	−567.159	−0.0201274
$927$	−2878.44	−0.101985
$928$	22717.8	0.803608
$929$	39337.6	1.38926	0.694631	−	0.719366i	$-0.255568\pi$
$929$	39337.6	1.38926	0.694631	+	0.719366i	$0.255568\pi$
$930$	246.685	0.00869796
$931$	9470.98	0.333404
$932$	−5751.36	−0.202137
$933$	4102.94	0.143970
$934$	−10765.0	−0.377134
$935$	−113.730	−0.00397792
$936$	−28390.7	−0.991430
$937$	−41077.3	−1.43216	−0.716082	−	0.698017i	$-0.754066\pi$
$937$	−41077.3	−1.43216	−0.716082	+	0.698017i	$0.754066\pi$
$938$	−8083.17	−0.281370
$939$	−67677.7	−2.35206
$940$	133.567	0.00463455
$941$	−38488.3	−1.33335	−0.666675	−	0.745348i	$-0.732283\pi$
$941$	−38488.3	−1.33335	−0.666675	+	0.745348i	$0.732283\pi$
$942$	−42785.6	−1.47986
$943$	45310.6	1.56471
$944$	−4577.43	−0.157821
$945$	223.395	0.00768998
$946$	0	0
$947$	24162.6	0.829122	0.414561	−	0.910022i	$-0.363935\pi$
$947$	24162.6	0.829122	0.414561	+	0.910022i	$0.363935\pi$
$948$	−21550.3	−0.738313
$949$	19580.0	0.669750
$950$	11020.3	0.376362
$951$	36865.8	1.25705
$952$	16315.3	0.555443
$953$	−25857.2	−0.878907	−0.439453	−	0.898265i	$-0.644828\pi$
$953$	−25857.2	−0.878907	−0.439453	+	0.898265i	$0.644828\pi$
$954$	23193.6	0.787128
$955$	114.720	0.00388717
$956$	−14822.4	−0.501453
$957$	62373.2	2.10683
$958$	−12253.5	−0.413249
$959$	14769.6	0.497327
$960$	242.103	0.00813942
$961$	17755.2	0.595993
$962$	−19766.9	−0.662487
$963$	55378.6	1.85312
$964$	3186.71	0.106470
$965$	344.296	0.0114853
$966$	47884.0	1.59487
$967$	−42638.6	−1.41796	−0.708979	−	0.705230i	$-0.750844\pi$
$967$	−42638.6	−1.41796	−0.708979	+	0.705230i	$0.750844\pi$
$968$	40192.4	1.33454
$969$	−11302.6	−0.374707
$970$	−224.128	−0.00741888
$971$	−49198.6	−1.62601	−0.813007	−	0.582254i	$-0.802171\pi$
$971$	−49198.6	−1.62601	−0.813007	+	0.582254i	$0.802171\pi$
$972$	−16824.3	−0.555185
$973$	14054.3	0.463064
$974$	30700.4	1.00996
$975$	−29096.5	−0.955728
$976$	6200.87	0.203366
$977$	42001.4	1.37538	0.687688	−	0.726006i	$-0.258626\pi$
$977$	42001.4	1.37538	0.687688	+	0.726006i	$0.258626\pi$
$978$	−19015.0	−0.621710
$979$	20718.7	0.676376
$980$	62.4144	0.00203444
$981$	68554.8	2.23118
$982$	22004.5	0.715063
$983$	−23075.1	−0.748711	−0.374356	−	0.927285i	$-0.622136\pi$
$983$	−23075.1	−0.748711	−0.374356	+	0.927285i	$0.622136\pi$
$984$	−70826.7	−2.29459
$985$	−311.173	−0.0100658
$986$	7650.67	0.247106
$987$	−86816.7	−2.79980
$988$	5481.77	0.176516
$989$	0	0
$990$	321.069	0.0103073
$991$	23753.3	0.761401	0.380701	−	0.924698i	$-0.375683\pi$
$991$	23753.3	0.761401	0.380701	+	0.924698i	$0.375683\pi$
$992$	36627.6	1.17230
$993$	−75257.3	−2.40505
$994$	26675.6	0.851205
$995$	67.5223	0.00215136
$996$	1366.02	0.0434578
$997$	881.578	0.0280039	0.0140019	−	0.999902i	$-0.495543\pi$
$997$	881.578	0.0280039	0.0140019	+	0.999902i	$0.495543\pi$
$998$	2654.92	0.0842085
$999$	50210.1	1.59017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.f.1.4		10
43.7	odd	6		43.4.c.a.6.7	✓	20
43.37	odd	6		43.4.c.a.36.7	yes	20
43.42	odd	2		1849.4.a.d.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.7	✓	20	43.7	odd	6
43.4.c.a.36.7	yes	20	43.37	odd	6
1849.4.a.d.1.7		10	43.42	odd	2
1849.4.a.f.1.4		10	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-1.92278 q^{2} -8.37832 q^{3} -4.30290 q^{4} -0.0702257 q^{5} +16.1097 q^{6} +23.4425 q^{7} +23.6558 q^{8} +43.1963 q^{9} +O(q^{10})\)	\(q-1.92278 q^{2} -8.37832 q^{3} -4.30290 q^{4} -0.0702257 q^{5} +16.1097 q^{6} +23.4425 q^{7} +23.6558 q^{8} +43.1963 q^{9} +0.135029 q^{10} +55.0459 q^{11} +36.0511 q^{12} -27.7838 q^{13} -45.0749 q^{14} +0.588374 q^{15} -11.0619 q^{16} +29.4207 q^{17} -83.0572 q^{18} +45.8530 q^{19} +0.302174 q^{20} -196.409 q^{21} -105.841 q^{22} +126.794 q^{23} -198.196 q^{24} -124.995 q^{25} +53.4222 q^{26} -135.698 q^{27} -100.871 q^{28} -135.243 q^{29} -1.13132 q^{30} -218.051 q^{31} -167.977 q^{32} -461.192 q^{33} -56.5696 q^{34} -1.64627 q^{35} -185.869 q^{36} -370.014 q^{37} -88.1655 q^{38} +232.781 q^{39} -1.66125 q^{40} +357.357 q^{41} +377.652 q^{42} -236.857 q^{44} -3.03349 q^{45} -243.797 q^{46} +442.020 q^{47} +92.6798 q^{48} +206.551 q^{49} +240.339 q^{50} -246.496 q^{51} +119.551 q^{52} -279.248 q^{53} +260.918 q^{54} -3.86564 q^{55} +554.552 q^{56} -384.172 q^{57} +260.044 q^{58} +413.803 q^{59} -2.53171 q^{60} -560.563 q^{61} +419.265 q^{62} +1012.63 q^{63} +411.478 q^{64} +1.95114 q^{65} +886.773 q^{66} +179.328 q^{67} -126.594 q^{68} -1062.32 q^{69} +3.16542 q^{70} -591.806 q^{71} +1021.84 q^{72} -704.727 q^{73} +711.457 q^{74} +1047.25 q^{75} -197.301 q^{76} +1290.41 q^{77} -447.589 q^{78} -597.771 q^{79} +0.776827 q^{80} -29.3797 q^{81} -687.120 q^{82} +37.8912 q^{83} +845.128 q^{84} -2.06609 q^{85} +1133.11 q^{87} +1302.16 q^{88} +376.390 q^{89} +5.83275 q^{90} -651.321 q^{91} -545.581 q^{92} +1826.90 q^{93} -849.909 q^{94} -3.22006 q^{95} +1407.37 q^{96} -1659.85 q^{97} -397.153 q^{98} +2377.78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9}+O(q^{10}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9	\( 10 q + q^{2} - 5 q^{3} + 39 q^{4} - 19 q^{5} - 15 q^{6} - 51 q^{7} + 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} - 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 9 q^{21} - 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} - 21 q^{26} + 97 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} - 253 q^{31} + 399 q^{32} - 424 q^{33} - 231 q^{34} + 355 q^{35} + 1092 q^{36} - 129 q^{37} + 854 q^{38} - 691 q^{39} - 1345 q^{40} + 391 q^{41} - 31 q^{42} + 377 q^{44} - 944 q^{45} - 40 q^{46} - 334 q^{47} - 2401 q^{48} + 115 q^{49} + 424 q^{50} - 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} - 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 738 q^{64} + 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} - 3503 q^{69} + 85 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} + 2232 q^{74} - 82 q^{75} - 252 q^{76} + 1448 q^{77} + 2822 q^{78} + 1405 q^{79} - 3157 q^{80} - 974 q^{81} - 3304 q^{82} - 543 q^{83} + 3652 q^{84} - 973 q^{85} + 1409 q^{87} + 2686 q^{88} - 2196 q^{89} - 742 q^{90} - 3513 q^{91} - 2629 q^{92} - 983 q^{93} - 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} - 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 10 * q + q^2 - 5 * q^3 + 39 * q^4 - 19 * q^5 - 15 * q^6 - 51 * q^7 + 36 * q^8 + 117 * q^9 - 27 * q^10 + 27 * q^11 - 72 * q^12 + 15 * q^13 - 96 * q^14 - 65 * q^15 + 67 * q^16 + 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 9 * q^21 - 190 * q^22 + 61 * q^23 - 202 * q^24 + 151 * q^25 - 21 * q^26 + 97 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 - 253 * q^31 + 399 * q^32 - 424 * q^33 - 231 * q^34 + 355 * q^35 + 1092 * q^36 - 129 * q^37 + 854 * q^38 - 691 * q^39 - 1345 * q^40 + 391 * q^41 - 31 * q^42 + 377 * q^44 - 944 * q^45 - 40 * q^46 - 334 * q^47 - 2401 * q^48 + 115 * q^49 + 424 * q^50 - 795 * q^51 + 564 * q^52 - 773 * q^53 + 182 * q^54 - 1242 * q^55 + 923 * q^56 + 765 * q^57 - 1328 * q^58 - 1483 * q^59 + 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 738 * q^64 + 1063 * q^65 - 1483 * q^66 + 642 * q^67 + 1052 * q^68 - 3503 * q^69 + 85 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 + 2232 * q^74 - 82 * q^75 - 252 * q^76 + 1448 * q^77 + 2822 * q^78 + 1405 * q^79 - 3157 * q^80 - 974 * q^81 - 3304 * q^82 - 543 * q^83 + 3652 * q^84 - 973 * q^85 + 1409 * q^87 + 2686 * q^88 - 2196 * q^89 - 742 * q^90 - 3513 * q^91 - 2629 * q^92 - 983 * q^93 - 4939 * q^94 + 149 * q^95 - 3540 * q^96 - 425 * q^97 - 213 * q^98 + 3181 * q^99

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