LMFDB - Embedded newform 1849.4.a.d.1.7

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:	$0$
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			1.7
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	$-0.389606\pi$
$2$	1.92278	0.679807	0.339903	+	0.940460i	$0.389606\pi$
$3$	8.37832	1.61241	0.806205	−	0.591637i	$-0.201518\pi$
$3$	8.37832	1.61241	0.806205	+	0.591637i	$0.201518\pi$
$4$	−4.30290	−0.537862
$5$	0.0702257	0.00628118	0.00314059	−	0.999995i	$-0.499000\pi$
$5$	0.0702257	0.00628118	0.00314059	+	0.999995i	$0.499000\pi$
$6$	16.1097	1.09613
$7$	−23.4425	−1.26578	−0.632888	−	0.774243i	$-0.718131\pi$
$7$	−23.4425	−1.26578	−0.632888	+	0.774243i	$0.718131\pi$
$8$	−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	$-0.589283\pi$
$19$	−45.8530	−0.553653	−0.276826	+	0.960920i	$0.589283\pi$
$20$	−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	$-0.357455\pi$
$29$	135.243	0.866002	0.433001	+	0.901393i	$0.357455\pi$
$30$	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	$-0.192844\pi$
$37$	370.014	1.64405	0.822025	+	0.569451i	$0.192844\pi$
$38$	−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	$-0.299797\pi$
$61$	560.563	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$62$	−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	$-0.335311\pi$
$71$	591.806	0.989217	0.494608	+	0.869116i	$0.335311\pi$
$72$	−1021.84	−1.67258
$73$	704.727	1.12989	0.564946	−	0.825128i	$-0.308897\pi$
$73$	704.727	1.12989	0.564946	+	0.825128i	$0.308897\pi$
$74$	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	$-0.571958\pi$
$89$	−376.390	−0.448283	−0.224142	+	0.974557i	$0.571958\pi$
$90$	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	$-0.363460\pi$
$113$	999.212	0.831840	0.415920	+	0.909401i	$0.363460\pi$
$114$	−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	$-0.675057\pi$
$131$	−1567.29	−1.04530	−0.522651	+	0.852547i	$0.675057\pi$
$132$	−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	$-0.562942\pi$
$137$	−630.037	−0.392903	−0.196452	+	0.980514i	$0.562942\pi$
$138$	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	$-0.261846\pi$
$149$	2474.66	1.36062	0.680309	+	0.732926i	$0.261846\pi$
$150$	−2013.63	−1.09608
$151$	2083.60	1.12292	0.561459	−	0.827504i	$-0.310240\pi$
$151$	2083.60	1.12292	0.561459	+	0.827504i	$0.310240\pi$
$152$	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	$-0.264126\pi$
$157$	2655.89	1.35008	0.675042	+	0.737780i	$0.264126\pi$
$158$	−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	$-0.408473\pi$
$163$	1180.34	0.567188	0.283594	+	0.958944i	$0.408473\pi$
$164$	−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	$-0.484208\pi$
$179$	237.525	0.0991813	0.0495906	+	0.998770i	$0.484208\pi$
$180$	−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	$-0.399862\pi$
$191$	1633.59	0.618861	0.309430	+	0.950922i	$0.399862\pi$
$192$	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	$-0.445218\pi$
$199$	961.504	0.342508	0.171254	+	0.985227i	$0.445218\pi$
$200$	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	$-0.688189\pi$
$211$	−3416.62	−1.11474	−0.557370	+	0.830264i	$0.688189\pi$
$212$	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	$-0.293415\pi$
$223$	4025.40	1.20879	0.604396	+	0.796684i	$0.293415\pi$
$224$	−3937.80	−1.17458
$225$	−5399.32	−1.59980
$226$	1921.27	0.565491
$227$	−2703.95	−0.790605	−0.395303	−	0.918551i	$-0.629360\pi$
$227$	−2703.95	−0.790605	−0.395303	+	0.918551i	$0.629360\pi$
$228$	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	$-0.560171\pi$
$233$	−1336.62	−0.375816	−0.187908	+	0.982187i	$0.560171\pi$
$234$	−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	$-0.468444\pi$
$241$	740.596	0.197950	0.0989750	+	0.995090i	$0.468444\pi$
$242$	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	$-0.320450\pi$
$257$	4405.40	1.06927	0.534633	+	0.845084i	$0.320450\pi$
$258$	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	$-0.511232\pi$
$263$	−300.950	−0.0705603	−0.0352802	+	0.999377i	$0.511232\pi$
$264$	−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	$-0.541770\pi$
$277$	−1206.48	−0.261699	−0.130849	+	0.991402i	$0.541770\pi$
$278$	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	$-0.760182\pi$
$313$	−8077.72	−1.45872	−0.729361	+	0.684130i	$0.760182\pi$
$314$	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	$-0.767930\pi$
$331$	−8982.38	−1.49159	−0.745795	+	0.666176i	$0.767930\pi$
$332$	−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	$-0.574780\pi$
$347$	−3009.24	−0.465546	−0.232773	+	0.972531i	$0.574780\pi$
$348$	−4875.67	−0.751044
$349$	5833.59	0.894742	0.447371	−	0.894348i	$-0.352360\pi$
$349$	5833.59	0.894742	0.447371	+	0.894348i	$0.352360\pi$
$350$	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	$-0.476120\pi$
$373$	1079.87	0.149903	0.0749514	+	0.997187i	$0.476120\pi$
$374$	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	$-0.714961\pi$
$383$	−9371.54	−1.25030	−0.625148	+	0.780506i	$0.714961\pi$
$384$	−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	$-0.578215\pi$
$389$	−3732.64	−0.486510	−0.243255	+	0.969962i	$0.578215\pi$
$390$	−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	$-0.463013\pi$
$409$	1917.96	0.231875	0.115937	+	0.993257i	$0.463013\pi$
$410$	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	$-0.316427\pi$
$419$	9353.24	1.09054	0.545269	+	0.838261i	$0.316427\pi$
$420$	59.3497	0.00689516
$421$	3476.89	0.402502	0.201251	−	0.979540i	$-0.435499\pi$
$421$	3476.89	0.402502	0.201251	+	0.979540i	$0.435499\pi$
$422$	−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	$-0.277585\pi$
$433$	11591.6	1.28650	0.643251	+	0.765655i	$0.277585\pi$
$434$	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	$-0.697014\pi$
$449$	−11039.6	−1.16034	−0.580170	+	0.814495i	$0.697014\pi$
$450$	−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	$-0.723505\pi$
$457$	−12619.7	−1.29174	−0.645870	+	0.763447i	$0.723505\pi$
$458$	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	$-0.504712\pi$
$463$	−294.968	−0.0296076	−0.0148038	+	0.999890i	$0.504712\pi$
$464$	−1496.04	−0.149681
$465$	−128.296	−0.0127948
$466$	−2570.04	−0.255482
$467$	−5598.67	−0.554766	−0.277383	−	0.960759i	$-0.589467\pi$
$467$	−5598.67	−0.554766	−0.277383	+	0.960759i	$0.589467\pi$
$468$	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	$-0.323717\pi$
$491$	11444.1	1.05186	0.525931	+	0.850527i	$0.323717\pi$
$492$	−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	$-0.480273\pi$
$499$	1380.77	0.123871	0.0619356	+	0.998080i	$0.480273\pi$
$500$	75.5421	0.00675669
$501$	−23969.4	−2.13747
$502$	2524.77	0.224475
$503$	−9663.44	−0.856603	−0.428302	−	0.903636i	$-0.640888\pi$
$503$	−9663.44	−0.856603	−0.428302	+	0.903636i	$0.640888\pi$
$504$	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	$-0.436447\pi$
$521$	4717.21	0.396670	0.198335	+	0.980134i	$0.436447\pi$
$522$	11232.9	0.941862
$523$	−6886.07	−0.575730	−0.287865	−	0.957671i	$-0.592945\pi$
$523$	−6886.07	−0.575730	−0.287865	+	0.957671i	$0.592945\pi$
$524$	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	$-0.535553\pi$
$571$	−3041.59	−0.222919	−0.111459	+	0.993769i	$0.535553\pi$
$572$	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	$-0.199836\pi$
$577$	22434.4	1.61864	0.809319	+	0.587369i	$0.199836\pi$
$578$	−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	$-0.0972931\pi$
$587$	27125.4	1.90730	0.953650	+	0.300918i	$0.0972931\pi$
$588$	−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	$-0.632164\pi$
$593$	−11650.0	−0.806756	−0.403378	+	0.915033i	$0.632164\pi$
$594$	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	$-0.339628\pi$
$601$	14226.2	0.965553	0.482777	+	0.875744i	$0.339628\pi$
$602$	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	$-0.287319\pi$
$607$	18530.3	1.23908	0.619541	+	0.784964i	$0.287319\pi$
$608$	−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	$-0.648022\pi$
$631$	−14216.2	−0.896892	−0.448446	+	0.893810i	$0.648022\pi$
$632$	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	$-0.729792\pi$
$641$	−21448.7	−1.32164	−0.660821	+	0.750543i	$0.729792\pi$
$642$	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	$-0.505179\pi$
$647$	−535.525	−0.0325404	−0.0162702	+	0.999868i	$0.505179\pi$
$648$	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	$-0.498757\pi$
$653$	130.350	0.00781159	0.00390580	+	0.999992i	$0.498757\pi$
$654$	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	$-0.598906\pi$
$673$	−10676.1	−0.611494	−0.305747	+	0.952113i	$0.598906\pi$
$674$	6755.97	0.386098
$675$	−16961.6	−0.967186
$676$	6131.90	0.348879
$677$	−6422.42	−0.364599	−0.182300	−	0.983243i	$-0.558354\pi$
$677$	−6422.42	−0.364599	−0.182300	+	0.983243i	$0.558354\pi$
$678$	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	$-0.423494\pi$
$691$	8647.75	0.476087	0.238043	+	0.971255i	$0.423494\pi$
$692$	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	$-0.292004\pi$
$727$	23833.0	1.21584	0.607920	+	0.793999i	$0.292004\pi$
$728$	−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	$-0.486304\pi$
$733$	1707.21	0.0860261	0.0430130	+	0.999075i	$0.486304\pi$
$734$	−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	$-0.643802\pi$
$739$	−17540.3	−0.873111	−0.436556	+	0.899677i	$0.643802\pi$
$740$	−111.809	−0.00555428
$741$	10673.7	0.529163
$742$	12587.1	0.622758
$743$	−8710.93	−0.430112	−0.215056	−	0.976602i	$-0.568993\pi$
$743$	−8710.93	−0.430112	−0.215056	+	0.976602i	$0.568993\pi$
$744$	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	$-0.287025\pi$
$751$	25530.9	1.24053	0.620264	+	0.784393i	$0.287025\pi$
$752$	−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	$-0.842456\pi$
$757$	−36656.9	−1.76000	−0.879998	+	0.474978i	$0.842456\pi$
$758$	−10113.2	−0.484602
$759$	58476.3	2.79652
$760$	76.1732	0.00363565
$761$	15174.7	0.722840	0.361420	−	0.932403i	$-0.382292\pi$
$761$	15174.7	0.722840	0.361420	+	0.932403i	$0.382292\pi$
$762$	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	$-0.445464\pi$
$773$	7328.29	0.340983	0.170492	+	0.985359i	$0.445464\pi$
$774$	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	$-0.644110\pi$
$811$	−20205.3	−0.874852	−0.437426	+	0.899254i	$0.644110\pi$
$812$	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	$-0.222765\pi$
$829$	36516.9	1.52989	0.764947	+	0.644093i	$0.222765\pi$
$830$	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	$-0.559852\pi$
$839$	−9085.26	−0.373847	−0.186924	+	0.982374i	$0.559852\pi$
$840$	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	$-0.484675\pi$
$859$	2423.33	0.0962549	0.0481275	+	0.998841i	$0.484675\pi$
$860$	0	0
$861$	−70188.0	−2.77817
$862$	−9307.86	−0.367781
$863$	859.671	0.0339091	0.0169545	−	0.999856i	$-0.494603\pi$
$863$	859.671	0.0339091	0.0169545	+	0.999856i	$0.494603\pi$
$864$	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	$-0.382142\pi$
$887$	19118.6	0.723721	0.361861	+	0.932232i	$0.382142\pi$
$888$	−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	$-0.391913\pi$
$911$	18316.9	0.666154	0.333077	+	0.942900i	$0.391913\pi$
$912$	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	$-0.744432\pi$
$929$	−39337.6	−1.38926	−0.694631	+	0.719366i	$0.744432\pi$
$930$	−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	$-0.245934\pi$
$937$	41077.3	1.43216	0.716082	+	0.698017i	$0.245934\pi$
$938$	−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	$-0.355172\pi$
$953$	25857.2	0.878907	0.439453	+	0.898265i	$0.355172\pi$
$954$	−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	$-0.377864\pi$
$983$	23075.1	0.748711	0.374356	+	0.927285i	$0.377864\pi$
$984$	−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	$-0.624317\pi$
$991$	−23753.3	−0.761401	−0.380701	+	0.924698i	$0.624317\pi$
$992$	−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	$-0.504457\pi$
$997$	−881.578	−0.0280039	−0.0140019	+	0.999902i	$0.504457\pi$
$998$	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.d.1.7		10
43.6	even	3		43.4.c.a.36.7	yes	20
43.36	even	3		43.4.c.a.6.7	✓	20
43.42	odd	2		1849.4.a.f.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.7	✓	20	43.36	even	3
43.4.c.a.36.7	yes	20	43.6	even	3
1849.4.a.d.1.7		10	1.1	even	1	trivial
1849.4.a.f.1.4		10	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
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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