LMFDB - Embedded newform 1849.4.a.g.1.16

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:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} +O(q^{10})$	\(q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} -3.03154 q^{10} +12.2621 q^{11} -8.54636 q^{12} +37.3046 q^{13} -5.61307 q^{14} -17.2360 q^{15} +63.1464 q^{16} +35.5003 q^{17} -4.87856 q^{18} -95.8018 q^{19} +127.926 q^{20} -31.9135 q^{21} +2.31431 q^{22} +123.383 q^{23} -3.23324 q^{24} +132.997 q^{25} +7.04074 q^{26} -56.7103 q^{27} +236.863 q^{28} +194.724 q^{29} -3.25306 q^{30} -64.0494 q^{31} +36.0225 q^{32} +13.1581 q^{33} +6.70021 q^{34} +477.696 q^{35} +205.867 q^{36} -286.712 q^{37} -18.0813 q^{38} +40.0306 q^{39} +48.3966 q^{40} +442.065 q^{41} -6.02324 q^{42} -97.6600 q^{44} +415.186 q^{45} +23.2869 q^{46} -463.616 q^{47} +67.7607 q^{48} +541.482 q^{49} +25.1013 q^{50} +38.0945 q^{51} -297.108 q^{52} -142.238 q^{53} -10.7033 q^{54} -196.957 q^{55} +89.6092 q^{56} -102.802 q^{57} +36.7516 q^{58} +496.417 q^{59} +137.274 q^{60} -144.960 q^{61} -12.0885 q^{62} +768.741 q^{63} -498.372 q^{64} -599.196 q^{65} +2.48342 q^{66} +713.903 q^{67} -282.738 q^{68} +132.399 q^{69} +90.1587 q^{70} +548.984 q^{71} +77.8832 q^{72} +514.562 q^{73} -54.1131 q^{74} +142.715 q^{75} +763.002 q^{76} -364.678 q^{77} +7.55523 q^{78} -1074.57 q^{79} -1014.27 q^{80} +637.056 q^{81} +83.4338 q^{82} +126.403 q^{83} +254.171 q^{84} -570.216 q^{85} +208.953 q^{87} -36.9464 q^{88} -77.2915 q^{89} +78.3608 q^{90} -1109.45 q^{91} -982.671 q^{92} -68.7297 q^{93} -87.5013 q^{94} +1538.79 q^{95} +38.6548 q^{96} -200.732 q^{97} +102.197 q^{98} -316.957 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * 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 $

$2$	0.188737	0.0667285	0.0333642	−	0.999443i	$-0.489378\pi$
$2$	0.188737	0.0667285	0.0333642	+	0.999443i	$0.489378\pi$
$3$	1.07307	0.206513	0.103257	−	0.994655i	$-0.467074\pi$
$3$	1.07307	0.206513	0.103257	+	0.994655i	$0.467074\pi$
$4$	−7.96438	−0.995547
$5$	−16.0623	−1.43665	−0.718327	−	0.695706i	$-0.755092\pi$
$5$	−16.0623	−1.43665	−0.718327	+	0.695706i	$0.755092\pi$
$6$	0.202528	0.0137803
$7$	−29.7402	−1.60582	−0.802911	−	0.596099i	$-0.796717\pi$
$7$	−29.7402	−1.60582	−0.802911	+	0.596099i	$0.796717\pi$
$8$	−3.01306	−0.133160
$9$	−25.8485	−0.957352
$10$	−3.03154	−0.0958657
$11$	12.2621	0.336105	0.168053	−	0.985778i	$-0.446252\pi$
$11$	12.2621	0.336105	0.168053	+	0.985778i	$0.446252\pi$
$12$	−8.54636	−0.205594
$13$	37.3046	0.795879	0.397940	−	0.917412i	$-0.369725\pi$
$13$	37.3046	0.795879	0.397940	+	0.917412i	$0.369725\pi$
$14$	−5.61307	−0.107154
$15$	−17.2360	−0.296688
$16$	63.1464	0.986662
$17$	35.5003	0.506476	0.253238	−	0.967404i	$-0.418504\pi$
$17$	35.5003	0.506476	0.253238	+	0.967404i	$0.418504\pi$
$18$	−4.87856	−0.0638826
$19$	−95.8018	−1.15676	−0.578380	−	0.815767i	$-0.696315\pi$
$19$	−95.8018	−1.15676	−0.578380	+	0.815767i	$0.696315\pi$
$20$	127.926	1.43026
$21$	−31.9135	−0.331623
$22$	2.31431	0.0224278
$23$	123.383	1.11857	0.559287	−	0.828974i	$-0.311075\pi$
$23$	123.383	1.11857	0.559287	+	0.828974i	$0.311075\pi$
$24$	−3.23324	−0.0274992
$25$	132.997	1.06397
$26$	7.04074	0.0531078
$27$	−56.7103	−0.404219
$28$	236.863	1.59867
$29$	194.724	1.24687	0.623437	−	0.781873i	$-0.285736\pi$
$29$	194.724	1.24687	0.623437	+	0.781873i	$0.285736\pi$
$30$	−3.25306	−0.0197975
$31$	−64.0494	−0.371084	−0.185542	−	0.982636i	$-0.559404\pi$
$31$	−64.0494	−0.371084	−0.185542	+	0.982636i	$0.559404\pi$
$32$	36.0225	0.198998
$33$	13.1581	0.0694102
$34$	6.70021	0.0337964
$35$	477.696	2.30701
$36$	205.867	0.953090
$37$	−286.712	−1.27392	−0.636962	−	0.770895i	$-0.719809\pi$
$37$	−286.712	−1.27392	−0.636962	+	0.770895i	$0.719809\pi$
$38$	−18.0813	−0.0771888
$39$	40.0306	0.164359
$40$	48.3966	0.191304
$41$	442.065	1.68388	0.841939	−	0.539573i	$-0.181414\pi$
$41$	442.065	1.68388	0.841939	+	0.539573i	$0.181414\pi$
$42$	−6.02324	−0.0221287
$43$	0	0
$43$	0	0
$44$	−97.6600	−0.334609
$45$	415.186	1.37538
$46$	23.2869	0.0746407
$47$	−463.616	−1.43884	−0.719418	−	0.694577i	$-0.755592\pi$
$47$	−463.616	−1.43884	−0.719418	+	0.694577i	$0.755592\pi$
$48$	67.7607	0.203759
$49$	541.482	1.57866
$50$	25.1013	0.0709973
$51$	38.0945	0.104594
$52$	−297.108	−0.792335
$53$	−142.238	−0.368640	−0.184320	−	0.982866i	$-0.559008\pi$
$53$	−142.238	−0.368640	−0.184320	+	0.982866i	$0.559008\pi$
$54$	−10.7033	−0.0269729
$55$	−196.957	−0.482867
$56$	89.6092	0.213831
$57$	−102.802	−0.238886
$58$	36.7516	0.0832020
$59$	496.417	1.09539	0.547695	−	0.836678i	$-0.315505\pi$
$59$	496.417	1.09539	0.547695	+	0.836678i	$0.315505\pi$
$60$	137.274	0.295367
$61$	−144.960	−0.304267	−0.152134	−	0.988360i	$-0.548614\pi$
$61$	−144.960	−0.304267	−0.152134	+	0.988360i	$0.548614\pi$
$62$	−12.0885	−0.0247619
$63$	768.741	1.53734
$64$	−498.372	−0.973383
$65$	−599.196	−1.14340
$66$	2.48342	0.00463163
$67$	713.903	1.30175	0.650874	−	0.759186i	$-0.274403\pi$
$67$	713.903	1.30175	0.650874	+	0.759186i	$0.274403\pi$
$68$	−282.738	−0.504221
$69$	132.399	0.231000
$70$	90.1587	0.153943
$71$	548.984	0.917640	0.458820	−	0.888529i	$-0.348272\pi$
$71$	548.984	0.917640	0.458820	+	0.888529i	$0.348272\pi$
$72$	77.8832	0.127481
$73$	514.562	0.824999	0.412499	−	0.910958i	$-0.364656\pi$
$73$	514.562	0.824999	0.412499	+	0.910958i	$0.364656\pi$
$74$	−54.1131	−0.0850070
$75$	142.715	0.219724
$76$	763.002	1.15161
$77$	−364.678	−0.539726
$78$	7.55523	0.0109675
$79$	−1074.57	−1.53036	−0.765180	−	0.643817i	$-0.777350\pi$
$79$	−1074.57	−1.53036	−0.765180	+	0.643817i	$0.777350\pi$
$80$	−1014.27	−1.41749
$81$	637.056	0.873876
$82$	83.4338	0.112363
$83$	126.403	0.167162	0.0835812	−	0.996501i	$-0.473364\pi$
$83$	126.403	0.167162	0.0835812	+	0.996501i	$0.473364\pi$
$84$	254.171	0.330147
$85$	−570.216	−0.727631
$86$	0	0
$87$	208.953	0.257496
$88$	−36.9464	−0.0447557
$89$	−77.2915	−0.0920548	−0.0460274	−	0.998940i	$-0.514656\pi$
$89$	−77.2915	−0.0920548	−0.0460274	+	0.998940i	$0.514656\pi$
$90$	78.3608	0.0917772
$91$	−1109.45	−1.27804
$92$	−982.671	−1.11359
$93$	−68.7297	−0.0766338
$94$	−87.5013	−0.0960114
$95$	1538.79	1.66186
$96$	38.6548	0.0410957
$97$	−200.732	−0.210116	−0.105058	−	0.994466i	$-0.533503\pi$
$97$	−200.732	−0.210116	−0.105058	+	0.994466i	$0.533503\pi$
$98$	102.197	0.105342
$99$	−316.957	−0.321771
$100$	−1059.24	−1.05924
$101$	1093.85	1.07765	0.538825	−	0.842418i	$-0.318868\pi$
$101$	1093.85	1.07765	0.538825	+	0.842418i	$0.318868\pi$
$102$	7.18982	0.00697940
$103$	−680.319	−0.650813	−0.325407	−	0.945574i	$-0.605501\pi$
$103$	−680.319	−0.650813	−0.325407	+	0.945574i	$0.605501\pi$
$104$	−112.401	−0.105979
$105$	512.603	0.476428
$106$	−26.8455	−0.0245987
$107$	510.574	0.461299	0.230650	−	0.973037i	$-0.425915\pi$
$107$	510.574	0.461299	0.230650	+	0.973037i	$0.425915\pi$
$108$	451.663	0.402419
$109$	−1738.31	−1.52752	−0.763761	−	0.645499i	$-0.776649\pi$
$109$	−1738.31	−1.52752	−0.763761	+	0.645499i	$0.776649\pi$
$110$	−37.1730	−0.0322210
$111$	−307.663	−0.263082
$112$	−1877.99	−1.58440
$113$	842.602	0.701463	0.350731	−	0.936476i	$-0.385933\pi$
$113$	842.602	0.701463	0.350731	+	0.936476i	$0.385933\pi$
$114$	−19.4026	−0.0159405
$115$	−1981.81	−1.60700
$116$	−1550.86	−1.24132
$117$	−964.268	−0.761937
$118$	93.6921	0.0730937
$119$	−1055.79	−0.813311
$120$	51.9331	0.0395069
$121$	−1180.64	−0.887033
$122$	−27.3593	−0.0203033
$123$	474.368	0.347743
$124$	510.114	0.369432
$125$	−128.443	−0.0919065
$126$	145.090	0.102584
$127$	−665.523	−0.465005	−0.232502	−	0.972596i	$-0.574691\pi$
$127$	−665.523	−0.465005	−0.232502	+	0.972596i	$0.574691\pi$
$128$	−382.241	−0.263951
$129$	0	0
$130$	−113.090	−0.0762975
$131$	−393.649	−0.262544	−0.131272	−	0.991346i	$-0.541906\pi$
$131$	−393.649	−0.262544	−0.131272	+	0.991346i	$0.541906\pi$
$132$	−104.796	−0.0691011
$133$	2849.17	1.85755
$134$	134.740	0.0868636
$135$	910.897	0.580722
$136$	−106.965	−0.0674423
$137$	3056.76	1.90625	0.953127	−	0.302570i	$-0.0978446\pi$
$137$	3056.76	1.90625	0.953127	+	0.302570i	$0.0978446\pi$
$138$	24.9886	0.0154143
$139$	−2297.91	−1.40220	−0.701102	−	0.713061i	$-0.747308\pi$
$139$	−2297.91	−1.40220	−0.701102	+	0.713061i	$0.747308\pi$
$140$	−3804.55	−2.29674
$141$	−497.494	−0.297139
$142$	103.613	0.0612327
$143$	457.432	0.267499
$144$	−1632.24	−0.944583
$145$	−3127.71	−1.79133
$146$	97.1167	0.0550509
$147$	581.050	0.326015
$148$	2283.48	1.26825
$149$	−862.754	−0.474359	−0.237180	−	0.971466i	$-0.576223\pi$
$149$	−862.754	−0.474359	−0.237180	+	0.971466i	$0.576223\pi$
$150$	26.9356	0.0146619
$151$	−1100.95	−0.593336	−0.296668	−	0.954981i	$-0.595875\pi$
$151$	−1100.95	−0.593336	−0.296668	+	0.954981i	$0.595875\pi$
$152$	288.657	0.154034
$153$	−917.631	−0.484876
$154$	−68.8280	−0.0360151
$155$	1028.78	0.533119
$156$	−318.819	−0.163628
$157$	567.708	0.288586	0.144293	−	0.989535i	$-0.453909\pi$
$157$	567.708	0.288586	0.144293	+	0.989535i	$0.453909\pi$
$158$	−202.810	−0.102118
$159$	−152.632	−0.0761289
$160$	−578.604	−0.285891
$161$	−3669.45	−1.79623
$162$	120.236	0.0583124
$163$	−1560.44	−0.749836	−0.374918	−	0.927058i	$-0.622329\pi$
$163$	−1560.44	−0.749836	−0.374918	+	0.927058i	$0.622329\pi$
$164$	−3520.77	−1.67638
$165$	−211.349	−0.0997184
$166$	23.8568	0.0111545
$167$	−2095.15	−0.970822	−0.485411	−	0.874286i	$-0.661330\pi$
$167$	−2095.15	−0.970822	−0.485411	+	0.874286i	$0.661330\pi$
$168$	96.1573	0.0441589
$169$	−805.368	−0.366576
$170$	−107.621	−0.0485537
$171$	2476.33	1.10743
$172$	0	0
$173$	832.450	0.365838	0.182919	−	0.983128i	$-0.441445\pi$
$173$	832.450	0.365838	0.182919	+	0.983128i	$0.441445\pi$
$174$	39.4371	0.0171823
$175$	−3955.35	−1.70855
$176$	774.307	0.331622
$177$	532.692	0.226212
$178$	−14.5877	−0.00614268
$179$	−2978.97	−1.24390	−0.621951	−	0.783056i	$-0.713660\pi$
$179$	−2978.97	−1.24390	−0.621951	+	0.783056i	$0.713660\pi$
$180$	−3306.70	−1.36926
$181$	4250.39	1.74546	0.872732	−	0.488200i	$-0.162346\pi$
$181$	4250.39	1.74546	0.872732	+	0.488200i	$0.162346\pi$
$182$	−209.393	−0.0852817
$183$	−155.553	−0.0628351
$184$	−371.761	−0.148949
$185$	4605.25	1.83019
$186$	−12.9718	−0.00511365
$187$	435.309	0.170230
$188$	3692.41	1.43243
$189$	1686.58	0.649104
$190$	290.427	0.110894
$191$	1087.10	0.411831	0.205916	−	0.978570i	$-0.433983\pi$
$191$	1087.10	0.411831	0.205916	+	0.978570i	$0.433983\pi$
$192$	−534.790	−0.201016
$193$	3796.24	1.41585	0.707926	−	0.706287i	$-0.249631\pi$
$193$	3796.24	1.41585	0.707926	+	0.706287i	$0.249631\pi$
$194$	−37.8855	−0.0140207
$195$	−642.982	−0.236128
$196$	−4312.57	−1.57164
$197$	4410.07	1.59495	0.797473	−	0.603355i	$-0.206170\pi$
$197$	4410.07	1.59495	0.797473	+	0.603355i	$0.206170\pi$
$198$	−59.8214	−0.0214713
$199$	−939.475	−0.334661	−0.167331	−	0.985901i	$-0.553515\pi$
$199$	−939.475	−0.334661	−0.167331	+	0.985901i	$0.553515\pi$
$200$	−400.727	−0.141678
$201$	766.070	0.268828
$202$	206.450	0.0719099
$203$	−5791.14	−2.00226
$204$	−303.399	−0.104128
$205$	−7100.57	−2.41915
$206$	−128.401	−0.0434278
$207$	−3189.27	−1.07087
$208$	2355.65	0.785264
$209$	−1174.73	−0.388793
$210$	96.7469	0.0317913
$211$	4083.91	1.33246	0.666228	−	0.745748i	$-0.267908\pi$
$211$	4083.91	1.33246	0.666228	+	0.745748i	$0.267908\pi$
$212$	1132.84	0.366998
$213$	589.100	0.189505
$214$	96.3639	0.0307818
$215$	0	0
$216$	170.872	0.0538257
$217$	1904.84	0.595895
$218$	−328.083	−0.101929
$219$	552.163	0.170373
$220$	1568.64	0.480717
$221$	1324.33	0.403094
$222$	−58.0673	−0.0175551
$223$	357.375	0.107317	0.0536583	−	0.998559i	$-0.482912\pi$
$223$	357.375	0.107317	0.0536583	+	0.998559i	$0.482912\pi$
$224$	−1071.32	−0.319556
$225$	−3437.76	−1.01860
$226$	159.030	0.0468075
$227$	−4410.09	−1.28946	−0.644731	−	0.764410i	$-0.723031\pi$
$227$	−4410.09	−1.28946	−0.644731	+	0.764410i	$0.723031\pi$
$228$	818.757	0.237822
$229$	2520.88	0.727444	0.363722	−	0.931508i	$-0.381506\pi$
$229$	2520.88	0.727444	0.363722	+	0.931508i	$0.381506\pi$
$230$	−374.041	−0.107233
$231$	−391.326	−0.111460
$232$	−586.716	−0.166034
$233$	−3707.94	−1.04255	−0.521277	−	0.853388i	$-0.674544\pi$
$233$	−3707.94	−1.04255	−0.521277	+	0.853388i	$0.674544\pi$
$234$	−181.993	−0.0508429
$235$	7446.73	2.06711
$236$	−3953.65	−1.09051
$237$	−1153.09	−0.316039
$238$	−199.266	−0.0542710
$239$	1160.46	0.314076	0.157038	−	0.987593i	$-0.449806\pi$
$239$	1160.46	0.314076	0.157038	+	0.987593i	$0.449806\pi$
$240$	−1088.39	−0.292730
$241$	989.096	0.264370	0.132185	−	0.991225i	$-0.457801\pi$
$241$	989.096	0.264370	0.132185	+	0.991225i	$0.457801\pi$
$242$	−222.830	−0.0591903
$243$	2214.79	0.584686
$244$	1154.52	0.302912
$245$	−8697.43	−2.26799
$246$	89.5306	0.0232043
$247$	−3573.85	−0.920641
$248$	192.985	0.0494135
$249$	135.639	0.0345212
$250$	−24.2419	−0.00613278
$251$	335.320	0.0843235	0.0421617	−	0.999111i	$-0.486576\pi$
$251$	335.320	0.0843235	0.0421617	+	0.999111i	$0.486576\pi$
$252$	−6122.54	−1.53049
$253$	1512.94	0.375959
$254$	−125.609	−0.0310291
$255$	−611.884	−0.150265
$256$	3914.83	0.955770
$257$	−938.359	−0.227756	−0.113878	−	0.993495i	$-0.536327\pi$
$257$	−938.359	−0.227756	−0.113878	+	0.993495i	$0.536327\pi$
$258$	0	0
$259$	8526.89	2.04570
$260$	4772.23	1.13831
$261$	−5033.33	−1.19370
$262$	−74.2959	−0.0175191
$263$	1594.82	0.373919	0.186960	−	0.982368i	$-0.440137\pi$
$263$	1594.82	0.373919	0.186960	+	0.982368i	$0.440137\pi$
$264$	−39.6463	−0.00924265
$265$	2284.67	0.529607
$266$	537.742	0.123951
$267$	−82.9394	−0.0190105
$268$	−5685.79	−1.29595
$269$	−1135.45	−0.257359	−0.128680	−	0.991686i	$-0.541074\pi$
$269$	−1135.45	−0.257359	−0.128680	+	0.991686i	$0.541074\pi$
$270$	171.920	0.0387507
$271$	3828.46	0.858163	0.429081	−	0.903266i	$-0.358837\pi$
$271$	3828.46	0.858163	0.429081	+	0.903266i	$0.358837\pi$
$272$	2241.72	0.499721
$273$	−1190.52	−0.263932
$274$	576.923	0.127201
$275$	1630.82	0.357607
$276$	−1054.48	−0.229971
$277$	−4491.44	−0.974240	−0.487120	−	0.873335i	$-0.661953\pi$
$277$	−4491.44	−0.974240	−0.487120	+	0.873335i	$0.661953\pi$
$278$	−433.700	−0.0935668
$279$	1655.58	0.355258
$280$	−1439.33	−0.307201
$281$	3495.10	0.741993	0.370997	−	0.928634i	$-0.379016\pi$
$281$	3495.10	0.741993	0.370997	+	0.928634i	$0.379016\pi$
$282$	−93.8953	−0.0198276
$283$	61.5992	0.0129388	0.00646942	−	0.999979i	$-0.497941\pi$
$283$	61.5992	0.0129388	0.00646942	+	0.999979i	$0.497941\pi$
$284$	−4372.32	−0.913554
$285$	1651.24	0.343196
$286$	86.3342	0.0178498
$287$	−13147.1	−2.70401
$288$	−931.129	−0.190511
$289$	−3652.73	−0.743482
$290$	−590.314	−0.119532
$291$	−215.400	−0.0433917
$292$	−4098.17	−0.821325
$293$	148.216	0.0295525	0.0147763	−	0.999891i	$-0.495296\pi$
$293$	148.216	0.0295525	0.0147763	+	0.999891i	$0.495296\pi$
$294$	109.665	0.0217545
$295$	−7973.59	−1.57370
$296$	863.882	0.169635
$297$	−695.387	−0.135860
$298$	−162.833	−0.0316533
$299$	4602.76	0.890249
$300$	−1136.64	−0.218746
$301$	0	0
$302$	−207.789	−0.0395924
$303$	1173.79	0.222549
$304$	−6049.53	−1.14133
$305$	2328.39	0.437126
$306$	−173.191	−0.0323551
$307$	5885.87	1.09422	0.547108	−	0.837062i	$-0.315729\pi$
$307$	5885.87	1.09422	0.547108	+	0.837062i	$0.315729\pi$
$308$	2904.43	0.537322
$309$	−730.032	−0.134402
$310$	194.168	0.0355742
$311$	6292.08	1.14724	0.573619	−	0.819122i	$-0.305539\pi$
$311$	6292.08	1.14724	0.573619	+	0.819122i	$0.305539\pi$
$312$	−120.615	−0.0218861
$313$	−4401.88	−0.794917	−0.397459	−	0.917620i	$-0.630108\pi$
$313$	−4401.88	−0.794917	−0.397459	+	0.917620i	$0.630108\pi$
$314$	107.147	0.0192569
$315$	−12347.7	−2.20862
$316$	8558.27	1.52354
$317$	9513.95	1.68567	0.842834	−	0.538173i	$-0.180885\pi$
$317$	9513.95	1.68567	0.842834	+	0.538173i	$0.180885\pi$
$318$	−28.8072	−0.00507996
$319$	2387.73	0.419081
$320$	8004.99	1.39841
$321$	547.883	0.0952643
$322$	−692.559	−0.119860
$323$	−3401.00	−0.585872
$324$	−5073.75	−0.869985
$325$	4961.38	0.846794
$326$	−294.512	−0.0500354
$327$	−1865.33	−0.315453
$328$	−1331.97	−0.224225
$329$	13788.1	2.31052
$330$	−39.8894	−0.00665405
$331$	1929.53	0.320412	0.160206	−	0.987084i	$-0.448784\pi$
$331$	1929.53	0.320412	0.160206	+	0.987084i	$0.448784\pi$
$332$	−1006.72	−0.166418
$333$	7411.08	1.21959
$334$	−395.431	−0.0647815
$335$	−11466.9	−1.87016
$336$	−2015.22	−0.327200
$337$	−6554.82	−1.05954	−0.529768	−	0.848142i	$-0.677721\pi$
$337$	−6554.82	−1.05954	−0.529768	+	0.848142i	$0.677721\pi$
$338$	−152.002	−0.0244611
$339$	904.173	0.144861
$340$	4541.42	0.724391
$341$	−785.380	−0.124723
$342$	467.375	0.0738969
$343$	−5902.90	−0.929233
$344$	0	0
$345$	−2126.63	−0.331867
$346$	157.114	0.0244118
$347$	3250.25	0.502832	0.251416	−	0.967879i	$-0.419104\pi$
$347$	3250.25	0.502832	0.251416	+	0.967879i	$0.419104\pi$
$348$	−1664.18	−0.256349
$349$	−11946.5	−1.83232	−0.916160	−	0.400814i	$-0.868727\pi$
$349$	−11946.5	−1.83232	−0.916160	+	0.400814i	$0.868727\pi$
$350$	−746.519	−0.114009
$351$	−2115.56	−0.321709
$352$	441.712	0.0668844
$353$	11585.6	1.74685	0.873427	−	0.486956i	$-0.161893\pi$
$353$	11585.6	1.74685	0.873427	+	0.486956i	$0.161893\pi$
$354$	100.538	0.0150948
$355$	−8817.93	−1.31833
$356$	615.579	0.0916450
$357$	−1132.94	−0.167959
$358$	−562.240	−0.0830036
$359$	−1265.03	−0.185977	−0.0929886	−	0.995667i	$-0.529642\pi$
$359$	−1265.03	−0.185977	−0.0929886	+	0.995667i	$0.529642\pi$
$360$	−1250.98	−0.183146
$361$	2318.99	0.338094
$362$	802.204	0.116472
$363$	−1266.91	−0.183184
$364$	8836.06	1.27235
$365$	−8265.03	−1.18524
$366$	−29.3586	−0.00419289
$367$	−1501.45	−0.213556	−0.106778	−	0.994283i	$-0.534053\pi$
$367$	−1501.45	−0.213556	−0.106778	+	0.994283i	$0.534053\pi$
$368$	7791.20	1.10365
$369$	−11426.7	−1.61206
$370$	869.179	0.122126
$371$	4230.19	0.591970
$372$	547.390	0.0762925
$373$	1196.30	0.166065	0.0830325	−	0.996547i	$-0.473539\pi$
$373$	1196.30	0.166065	0.0830325	+	0.996547i	$0.473539\pi$
$374$	82.1587	0.0113592
$375$	−137.829	−0.0189799
$376$	1396.90	0.191595
$377$	7264.10	0.992361
$378$	318.319	0.0433137
$379$	−1359.57	−0.184265	−0.0921326	−	0.995747i	$-0.529368\pi$
$379$	−1359.57	−0.184265	−0.0921326	+	0.995747i	$0.529368\pi$
$380$	−12255.5	−1.65446
$381$	−714.155	−0.0960296
$382$	205.175	0.0274809
$383$	10767.3	1.43651	0.718257	−	0.695778i	$-0.244940\pi$
$383$	10767.3	1.43651	0.718257	+	0.695778i	$0.244940\pi$
$384$	−410.173	−0.0545092
$385$	5857.55	0.775399
$386$	716.489	0.0944776
$387$	0	0
$388$	1598.71	0.209181
$389$	6353.89	0.828161	0.414081	−	0.910240i	$-0.364103\pi$
$389$	6353.89	0.828161	0.414081	+	0.910240i	$0.364103\pi$
$390$	−121.354	−0.0157564
$391$	4380.15	0.566531
$392$	−1631.52	−0.210215
$393$	−422.414	−0.0542187
$394$	832.341	0.106428
$395$	17260.0	2.19860
$396$	2524.36	0.320339
$397$	−14439.9	−1.82548	−0.912741	−	0.408538i	$-0.866039\pi$
$397$	−14439.9	−1.82548	−0.912741	+	0.408538i	$0.866039\pi$
$398$	−177.313	−0.0223314
$399$	3057.37	0.383609
$400$	8398.25	1.04978
$401$	−4528.96	−0.564004	−0.282002	−	0.959414i	$-0.590998\pi$
$401$	−4528.96	−0.564004	−0.282002	+	0.959414i	$0.590998\pi$
$402$	144.585	0.0179385
$403$	−2389.34	−0.295338
$404$	−8711.87	−1.07285
$405$	−10232.6	−1.25546
$406$	−1093.00	−0.133608
$407$	−3515.69	−0.428173
$408$	−114.781	−0.0139277
$409$	−1012.63	−0.122424	−0.0612120	−	0.998125i	$-0.519497\pi$
$409$	−1012.63	−0.122424	−0.0612120	+	0.998125i	$0.519497\pi$
$410$	−1340.14	−0.161426
$411$	3280.13	0.393666
$412$	5418.32	0.647916
$413$	−14763.6	−1.75900
$414$	−601.932	−0.0714574
$415$	−2030.31	−0.240154
$416$	1343.81	0.158379
$417$	−2465.83	−0.289573
$418$	−221.715	−0.0259436
$419$	2898.28	0.337924	0.168962	−	0.985623i	$-0.445958\pi$
$419$	2898.28	0.337924	0.168962	+	0.985623i	$0.445958\pi$
$420$	−4082.56	−0.474306
$421$	3294.97	0.381442	0.190721	−	0.981644i	$-0.438917\pi$
$421$	3294.97	0.381442	0.190721	+	0.981644i	$0.438917\pi$
$422$	770.784	0.0889127
$423$	11983.8	1.37747
$424$	428.572	0.0490880
$425$	4721.42	0.538877
$426$	111.185	0.0126453
$427$	4311.16	0.488599
$428$	−4066.40	−0.459245
$429$	490.858	0.0552421
$430$	0	0
$431$	−10692.3	−1.19496	−0.597480	−	0.801884i	$-0.703831\pi$
$431$	−10692.3	−1.19496	−0.597480	+	0.801884i	$0.703831\pi$
$432$	−3581.05	−0.398827
$433$	−8088.13	−0.897669	−0.448835	−	0.893615i	$-0.648161\pi$
$433$	−8088.13	−0.897669	−0.448835	+	0.893615i	$0.648161\pi$
$434$	359.514	0.0397632
$435$	−3356.26	−0.369932
$436$	13844.6	1.52072
$437$	−11820.3	−1.29392
$438$	104.213	0.0113687
$439$	1011.15	0.109930	0.0549651	−	0.998488i	$-0.482495\pi$
$439$	1011.15	0.109930	0.0549651	+	0.998488i	$0.482495\pi$
$440$	593.444	0.0642985
$441$	−13996.5	−1.51134
$442$	249.949	0.0268978
$443$	−10329.4	−1.10783	−0.553913	−	0.832575i	$-0.686866\pi$
$443$	−10329.4	−1.10783	−0.553913	+	0.832575i	$0.686866\pi$
$444$	2450.35	0.261911
$445$	1241.48	0.132251
$446$	67.4498	0.00716108
$447$	−925.798	−0.0979614
$448$	14821.7	1.56308
$449$	18981.4	1.99508	0.997539	−	0.0701154i	$-0.0223367\pi$
$449$	18981.4	1.99508	0.997539	+	0.0701154i	$0.0223367\pi$
$450$	−648.832	−0.0679694
$451$	5420.64	0.565960
$452$	−6710.80	−0.698339
$453$	−1181.40	−0.122532
$454$	−832.345	−0.0860438
$455$	17820.2	1.83610
$456$	309.750	0.0318100
$457$	1631.23	0.166971	0.0834857	−	0.996509i	$-0.473395\pi$
$457$	1631.23	0.166971	0.0834857	+	0.996509i	$0.473395\pi$
$458$	475.783	0.0485412
$459$	−2013.24	−0.204727
$460$	15783.9	1.59985
$461$	−11466.6	−1.15847	−0.579235	−	0.815160i	$-0.696649\pi$
$461$	−11466.6	−1.15847	−0.579235	+	0.815160i	$0.696649\pi$
$462$	−73.8575	−0.00743758
$463$	160.216	0.0160818	0.00804090	−	0.999968i	$-0.497440\pi$
$463$	160.216	0.0160818	0.00804090	+	0.999968i	$0.497440\pi$
$464$	12296.1	1.23024
$465$	1103.96	0.110096
$466$	−699.823	−0.0695680
$467$	−11139.9	−1.10384	−0.551920	−	0.833897i	$-0.686105\pi$
$467$	−11139.9	−1.10384	−0.551920	+	0.833897i	$0.686105\pi$
$468$	7679.80	0.758544
$469$	−21231.6	−2.09038
$470$	1405.47	0.137935
$471$	609.192	0.0595968
$472$	−1495.74	−0.145862
$473$	0	0
$474$	−217.630	−0.0210888
$475$	−12741.3	−1.23076
$476$	8408.70	0.809690
$477$	3676.64	0.352918
$478$	219.022	0.0209578
$479$	−13531.5	−1.29075	−0.645377	−	0.763864i	$-0.723300\pi$
$479$	−13531.5	−1.29075	−0.645377	+	0.763864i	$0.723300\pi$
$480$	−620.884	−0.0590403
$481$	−10695.7	−1.01389
$482$	186.679	0.0176410
$483$	−3937.59	−0.370945
$484$	9403.07	0.883083
$485$	3224.21	0.301864
$486$	418.011	0.0390152
$487$	3215.48	0.299194	0.149597	−	0.988747i	$-0.452202\pi$
$487$	3215.48	0.299194	0.149597	+	0.988747i	$0.452202\pi$
$488$	436.775	0.0405161
$489$	−1674.47	−0.154851
$490$	−1641.52	−0.151340
$491$	6495.70	0.597040	0.298520	−	0.954403i	$-0.403507\pi$
$491$	6495.70	0.597040	0.298520	+	0.954403i	$0.403507\pi$
$492$	−3778.05	−0.346194
$493$	6912.77	0.631512
$494$	−674.515	−0.0614330
$495$	5091.05	0.462274
$496$	−4044.49	−0.366135
$497$	−16326.9	−1.47357
$498$	25.6001	0.00230355
$499$	17673.8	1.58555	0.792775	−	0.609514i	$-0.208635\pi$
$499$	17673.8	1.58555	0.792775	+	0.609514i	$0.208635\pi$
$500$	1022.97	0.0914973
$501$	−2248.25	−0.200488
$502$	63.2871	0.00562678
$503$	−16367.1	−1.45084	−0.725420	−	0.688306i	$-0.758355\pi$
$503$	−16367.1	−1.45084	−0.725420	+	0.688306i	$0.758355\pi$
$504$	−2316.26	−0.204712
$505$	−17569.8	−1.54821
$506$	285.546	0.0250871
$507$	−864.219	−0.0757028
$508$	5300.48	0.462934
$509$	5525.13	0.481134	0.240567	−	0.970633i	$-0.422667\pi$
$509$	5525.13	0.481134	0.240567	+	0.970633i	$0.422667\pi$
$510$	−115.485	−0.0100270
$511$	−15303.2	−1.32480
$512$	3796.80	0.327728
$513$	5432.95	0.467584
$514$	−177.103	−0.0151978
$515$	10927.5	0.934993
$516$	0	0
$517$	−5684.90	−0.483601
$518$	1609.34	0.136506
$519$	893.281	0.0755504
$520$	1805.42	0.152255
$521$	18014.7	1.51485	0.757425	−	0.652922i	$-0.226457\pi$
$521$	18014.7	1.51485	0.757425	+	0.652922i	$0.226457\pi$
$522$	−949.973	−0.0796536
$523$	−2817.84	−0.235594	−0.117797	−	0.993038i	$-0.537583\pi$
$523$	−2817.84	−0.235594	−0.117797	+	0.993038i	$0.537583\pi$
$524$	3135.17	0.261375
$525$	−4244.38	−0.352838
$526$	301.001	0.0249510
$527$	−2273.78	−0.187945
$528$	830.888	0.0684844
$529$	3056.42	0.251206
$530$	431.200	0.0353399
$531$	−12831.6	−1.04867
$532$	−22691.9	−1.84928
$533$	16491.1	1.34016
$534$	−15.6537	−0.00126854
$535$	−8200.97	−0.662727
$536$	−2151.03	−0.173340
$537$	−3196.65	−0.256882
$538$	−214.301	−0.0171732
$539$	6639.70	0.530598
$540$	−7254.73	−0.578137
$541$	−5662.83	−0.450026	−0.225013	−	0.974356i	$-0.572242\pi$
$541$	−5662.83	−0.450026	−0.225013	+	0.974356i	$0.572242\pi$
$542$	722.570	0.0572639
$543$	4560.98	0.360461
$544$	1278.81	0.100788
$545$	27921.2	2.19452
$546$	−224.694	−0.0176118
$547$	8372.85	0.654474	0.327237	−	0.944942i	$-0.393882\pi$
$547$	8372.85	0.654474	0.327237	+	0.944942i	$0.393882\pi$
$548$	−24345.2	−1.89777
$549$	3747.01	0.291291
$550$	307.795	0.0238626
$551$	−18654.9	−1.44233
$552$	−398.927	−0.0307599
$553$	31957.9	2.45748
$554$	−847.699	−0.0650095
$555$	4941.77	0.377958
$556$	18301.4	1.39596
$557$	−9315.08	−0.708604	−0.354302	−	0.935131i	$-0.615282\pi$
$557$	−9315.08	−0.708604	−0.354302	+	0.935131i	$0.615282\pi$
$558$	312.469	0.0237058
$559$	0	0
$560$	30164.8	2.27624
$561$	467.118	0.0351546
$562$	659.653	0.0495121
$563$	−13652.0	−1.02196	−0.510980	−	0.859593i	$-0.670717\pi$
$563$	−13652.0	−1.02196	−0.510980	+	0.859593i	$0.670717\pi$
$564$	3962.23	0.295816
$565$	−13534.1	−1.00776
$566$	11.6260	0.000863389 0
$567$	−18946.2	−1.40329
$568$	−1654.12	−0.122193
$569$	11683.5	0.860808	0.430404	−	0.902636i	$-0.358371\pi$
$569$	11683.5	0.860808	0.430404	+	0.902636i	$0.358371\pi$
$570$	311.649	0.0229010
$571$	−13157.5	−0.964313	−0.482156	−	0.876085i	$-0.660146\pi$
$571$	−13157.5	−0.964313	−0.482156	+	0.876085i	$0.660146\pi$
$572$	−3643.16	−0.266308
$573$	1166.54	0.0850485
$574$	−2481.34	−0.180434
$575$	16409.5	1.19013
$576$	12882.2	0.931870
$577$	−11315.2	−0.816395	−0.408198	−	0.912894i	$-0.633843\pi$
$577$	−11315.2	−0.816395	−0.408198	+	0.912894i	$0.633843\pi$
$578$	−689.403	−0.0496114
$579$	4073.64	0.292392
$580$	24910.3	1.78335
$581$	−3759.24	−0.268433
$582$	−40.6539	−0.00289546
$583$	−1744.14	−0.123902
$584$	−1550.41	−0.109857
$585$	15488.3	1.09464
$586$	27.9739	0.00197200
$587$	−24594.5	−1.72934	−0.864669	−	0.502342i	$-0.832472\pi$
$587$	−24594.5	−1.72934	−0.864669	+	0.502342i	$0.832472\pi$
$588$	−4627.70	−0.324563
$589$	6136.05	0.429255
$590$	−1504.91	−0.105010
$591$	4732.33	0.329377
$592$	−18104.8	−1.25693
$593$	212.239	0.0146975	0.00734874	−	0.999973i	$-0.497661\pi$
$593$	212.239	0.0146975	0.00734874	+	0.999973i	$0.497661\pi$
$594$	−131.245	−0.00906574
$595$	16958.4	1.16845
$596$	6871.30	0.472247
$597$	−1008.13	−0.0691119
$598$	868.709	0.0594049
$599$	−12278.6	−0.837546	−0.418773	−	0.908091i	$-0.637540\pi$
$599$	−12278.6	−0.837546	−0.418773	+	0.908091i	$0.637540\pi$
$600$	−430.009	−0.0292584
$601$	−23050.4	−1.56447	−0.782235	−	0.622983i	$-0.785921\pi$
$601$	−23050.4	−1.56447	−0.782235	+	0.622983i	$0.785921\pi$
$602$	0	0
$603$	−18453.3	−1.24623
$604$	8768.35	0.590694
$605$	18963.8	1.27436
$606$	221.536	0.0148503
$607$	3484.20	0.232981	0.116490	−	0.993192i	$-0.462836\pi$
$607$	3484.20	0.232981	0.116490	+	0.993192i	$0.462836\pi$
$608$	−3451.02	−0.230193
$609$	−6214.32	−0.413493
$610$	439.453	0.0291688
$611$	−17295.0	−1.14514
$612$	7308.36	0.482717
$613$	15811.8	1.04182	0.520908	−	0.853613i	$-0.325593\pi$
$613$	15811.8	1.04182	0.520908	+	0.853613i	$0.325593\pi$
$614$	1110.88	0.0730154
$615$	−7619.43	−0.499586
$616$	1098.80	0.0718698
$617$	−6781.94	−0.442513	−0.221257	−	0.975216i	$-0.571016\pi$
$617$	−6781.94	−0.442513	−0.221257	+	0.975216i	$0.571016\pi$
$618$	−137.784	−0.00896840
$619$	−25032.1	−1.62540	−0.812702	−	0.582679i	$-0.802004\pi$
$619$	−25032.1	−1.62540	−0.812702	+	0.582679i	$0.802004\pi$
$620$	−8193.59	−0.530746
$621$	−6997.10	−0.452148
$622$	1187.55	0.0765534
$623$	2298.67	0.147824
$624$	2527.78	0.162167
$625$	−14561.5	−0.931935
$626$	−830.796	−0.0530436
$627$	−1260.57	−0.0802909
$628$	−4521.44	−0.287301
$629$	−10178.4	−0.645212
$630$	−2330.47	−0.147378
$631$	−13157.5	−0.830096	−0.415048	−	0.909800i	$-0.636235\pi$
$631$	−13157.5	−0.830096	−0.415048	+	0.909800i	$0.636235\pi$
$632$	3237.74	0.203782
$633$	4382.34	0.275170
$634$	1795.63	0.112482
$635$	10689.8	0.668051
$636$	1215.62	0.0757899
$637$	20199.8	1.25643
$638$	450.651	0.0279647
$639$	−14190.4	−0.878505
$640$	6139.66	0.379205
$641$	−17066.7	−1.05163	−0.525815	−	0.850599i	$-0.676240\pi$
$641$	−17066.7	−1.05163	−0.525815	+	0.850599i	$0.676240\pi$
$642$	103.406	0.00635684
$643$	−7417.34	−0.454916	−0.227458	−	0.973788i	$-0.573042\pi$
$643$	−7417.34	−0.454916	−0.227458	+	0.973788i	$0.573042\pi$
$644$	29224.9	1.78823
$645$	0	0
$646$	−641.893	−0.0390943
$647$	−18527.2	−1.12578	−0.562890	−	0.826532i	$-0.690310\pi$
$647$	−18527.2	−1.12578	−0.562890	+	0.826532i	$0.690310\pi$
$648$	−1919.49	−0.116365
$649$	6087.11	0.368167
$650$	936.394	0.0565052
$651$	2044.04	0.123060
$652$	12427.9	0.746497
$653$	−3103.90	−0.186011	−0.0930053	−	0.995666i	$-0.529647\pi$
$653$	−3103.90	−0.186011	−0.0930053	+	0.995666i	$0.529647\pi$
$654$	−352.057	−0.0210497
$655$	6322.89	0.377184
$656$	27914.8	1.66142
$657$	−13300.7	−0.789815
$658$	2602.31	0.154177
$659$	27085.9	1.60109	0.800545	−	0.599273i	$-0.204544\pi$
$659$	27085.9	1.60109	0.800545	+	0.599273i	$0.204544\pi$
$660$	1683.27	0.0992744
$661$	1700.11	0.100040	0.0500202	−	0.998748i	$-0.484071\pi$
$661$	1700.11	0.100040	0.0500202	+	0.998748i	$0.484071\pi$
$662$	364.172	0.0213806
$663$	1421.10	0.0832442
$664$	−380.859	−0.0222593
$665$	−45764.1	−2.66866
$666$	1398.74	0.0813816
$667$	24025.7	1.39472
$668$	16686.5	0.966500
$669$	383.490	0.0221623
$670$	−2164.22	−0.124793
$671$	−1777.52	−0.102266
$672$	−1149.60	−0.0659924
$673$	−21221.0	−1.21547	−0.607733	−	0.794141i	$-0.707921\pi$
$673$	−21221.0	−1.21547	−0.607733	+	0.794141i	$0.707921\pi$
$674$	−1237.13	−0.0707012
$675$	−7542.28	−0.430078
$676$	6414.26	0.364944
$677$	15266.7	0.866688	0.433344	−	0.901229i	$-0.357333\pi$
$677$	15266.7	0.866688	0.433344	+	0.901229i	$0.357333\pi$
$678$	170.651	0.00966637
$679$	5969.82	0.337409
$680$	1718.10	0.0968912
$681$	−4732.35	−0.266291
$682$	−148.230	−0.00832260
$683$	−6070.04	−0.340064	−0.170032	−	0.985439i	$-0.554387\pi$
$683$	−6070.04	−0.340064	−0.170032	+	0.985439i	$0.554387\pi$
$684$	−19722.5	−1.10250
$685$	−49098.6	−2.73863
$686$	−1114.09	−0.0620063
$687$	2705.09	0.150227
$688$	0	0
$689$	−5306.13	−0.293393
$690$	−401.373	−0.0221450
$691$	−13752.5	−0.757119	−0.378560	−	0.925577i	$-0.623580\pi$
$691$	−13752.5	−0.757119	−0.378560	+	0.925577i	$0.623580\pi$
$692$	−6629.95	−0.364209
$693$	9426.37	0.516708
$694$	613.441	0.0335532
$695$	36909.7	2.01448
$696$	−629.589	−0.0342881
$697$	15693.5	0.852844
$698$	−2254.73	−0.122268
$699$	−3978.89	−0.215301
$700$	31501.9	1.70094
$701$	−2208.71	−0.119004	−0.0595021	−	0.998228i	$-0.518951\pi$
$701$	−2208.71	−0.119004	−0.0595021	+	0.998228i	$0.518951\pi$
$702$	−399.283	−0.0214672
$703$	27467.5	1.47362
$704$	−6111.08	−0.327159
$705$	7990.88	0.426885
$706$	2186.63	0.116565
$707$	−32531.5	−1.73051
$708$	−4242.56	−0.225205
$709$	−12431.5	−0.658498	−0.329249	−	0.944243i	$-0.606796\pi$
$709$	−12431.5	−0.658498	−0.329249	+	0.944243i	$0.606796\pi$
$710$	−1664.27	−0.0879701
$711$	27776.0	1.46509
$712$	232.884	0.0122580
$713$	−7902.62	−0.415085
$714$	−213.827	−0.0112077
$715$	−7347.40	−0.384304
$716$	23725.6	1.23836
$717$	1245.26	0.0648608
$718$	−238.758	−0.0124100
$719$	31040.8	1.61005	0.805025	−	0.593241i	$-0.202152\pi$
$719$	31040.8	1.61005	0.805025	+	0.593241i	$0.202152\pi$
$720$	26217.5	1.35704
$721$	20232.8	1.04509
$722$	437.677	0.0225605
$723$	1061.37	0.0545960
$724$	−33851.7	−1.73769
$725$	25897.6	1.32664
$726$	−239.113	−0.0122236
$727$	27301.9	1.39281	0.696405	−	0.717649i	$-0.254782\pi$
$727$	27301.9	1.39281	0.696405	+	0.717649i	$0.254782\pi$
$728$	3342.83	0.170184
$729$	−14823.9	−0.753131
$730$	−1559.91	−0.0790891
$731$	0	0
$732$	1238.88	0.0625553
$733$	4837.03	0.243738	0.121869	−	0.992546i	$-0.461111\pi$
$733$	4837.03	0.243738	0.121869	+	0.992546i	$0.461111\pi$
$734$	−283.378	−0.0142502
$735$	−9332.98	−0.468370
$736$	4444.58	0.222594
$737$	8753.94	0.437525
$738$	−2156.64	−0.107571
$739$	7814.86	0.389005	0.194502	−	0.980902i	$-0.437691\pi$
$739$	7814.86	0.389005	0.194502	+	0.980902i	$0.437691\pi$
$740$	−36677.9	−1.82204
$741$	−3835.00	−0.190124
$742$	798.392	0.0395012
$743$	21269.6	1.05021	0.525106	−	0.851037i	$-0.324026\pi$
$743$	21269.6	1.05021	0.525106	+	0.851037i	$0.324026\pi$
$744$	207.087	0.0102045
$745$	13857.8	0.681490
$746$	225.786	0.0110813
$747$	−3267.32	−0.160033
$748$	−3466.96	−0.169472
$749$	−15184.6	−0.740765
$750$	−26.0134	−0.00126650
$751$	−14443.0	−0.701773	−0.350887	−	0.936418i	$-0.614120\pi$
$751$	−14443.0	−0.701773	−0.350887	+	0.936418i	$0.614120\pi$
$752$	−29275.7	−1.41965
$753$	359.823	0.0174139
$754$	1371.00	0.0662187
$755$	17683.7	0.852417
$756$	−13432.6	−0.646213
$757$	−24206.1	−1.16220	−0.581100	−	0.813832i	$-0.697378\pi$
$757$	−24206.1	−1.16220	−0.581100	+	0.813832i	$0.697378\pi$
$758$	−256.601	−0.0122957
$759$	1623.49	0.0776404
$760$	−4636.48	−0.221293
$761$	28668.2	1.36560	0.682801	−	0.730604i	$-0.260762\pi$
$761$	28668.2	1.36560	0.682801	+	0.730604i	$0.260762\pi$
$762$	−134.787	−0.00640791
$763$	51697.7	2.45293
$764$	−8658.07	−0.409997
$765$	14739.2	0.696599
$766$	2032.19	0.0958563
$767$	18518.6	0.871798
$768$	4200.90	0.197379
$769$	−26609.6	−1.24781	−0.623904	−	0.781501i	$-0.714455\pi$
$769$	−26609.6	−1.24781	−0.623904	+	0.781501i	$0.714455\pi$
$770$	1105.53	0.0517412
$771$	−1006.93	−0.0470346
$772$	−30234.7	−1.40955
$773$	−9132.09	−0.424914	−0.212457	−	0.977170i	$-0.568147\pi$
$773$	−9132.09	−0.424914	−0.212457	+	0.977170i	$0.568147\pi$
$774$	0	0
$775$	−8518.35	−0.394824
$776$	604.818	0.0279790
$777$	9149.98	0.422463
$778$	1199.21	0.0552619
$779$	−42350.6	−1.94784
$780$	5120.95	0.235076
$781$	6731.69	0.308424
$782$	826.694	0.0378037
$783$	−11042.9	−0.504010
$784$	34192.6	1.55761
$785$	−9118.67	−0.414598
$786$	−79.7249	−0.00361793
$787$	−1116.17	−0.0505557	−0.0252779	−	0.999680i	$-0.508047\pi$
$787$	−1116.17	−0.0505557	−0.0252779	+	0.999680i	$0.508047\pi$
$788$	−35123.5	−1.58784
$789$	1711.36	0.0772192
$790$	3257.59	0.146709
$791$	−25059.2	−1.12642
$792$	955.011	0.0428470
$793$	−5407.69	−0.242160
$794$	−2725.33	−0.121812
$795$	2451.61	0.109371
$796$	7482.33	0.333171
$797$	−21836.4	−0.970498	−0.485249	−	0.874376i	$-0.661271\pi$
$797$	−21836.4	−0.970498	−0.485249	+	0.874376i	$0.661271\pi$
$798$	577.037	0.0255976
$799$	−16458.5	−0.728737
$800$	4790.87	0.211729
$801$	1997.87	0.0881289
$802$	−854.780	−0.0376351
$803$	6309.61	0.277287
$804$	−6101.27	−0.267631
$805$	58939.7	2.58056
$806$	−450.955	−0.0197075
$807$	−1218.42	−0.0531481
$808$	−3295.85	−0.143500
$809$	27327.4	1.18761	0.593807	−	0.804607i	$-0.297624\pi$
$809$	27327.4	1.18761	0.593807	+	0.804607i	$0.297624\pi$
$810$	−1931.26	−0.0837747
$811$	29154.8	1.26235	0.631174	−	0.775641i	$-0.282573\pi$
$811$	29154.8	1.26235	0.631174	+	0.775641i	$0.282573\pi$
$812$	46122.8	1.99334
$813$	4108.21	0.177222
$814$	−663.540	−0.0285713
$815$	25064.2	1.07725
$816$	2405.53	0.103199
$817$	0	0
$818$	−191.121	−0.00816916
$819$	28677.6	1.22354
$820$	56551.6	2.40838
$821$	−30897.8	−1.31345	−0.656724	−	0.754131i	$-0.728058\pi$
$821$	−30897.8	−1.31345	−0.656724	+	0.754131i	$0.728058\pi$
$822$	619.081	0.0262688
$823$	−4597.16	−0.194711	−0.0973554	−	0.995250i	$-0.531038\pi$
$823$	−4597.16	−0.194711	−0.0973554	+	0.995250i	$0.531038\pi$
$824$	2049.84	0.0866622
$825$	1749.99	0.0738505
$826$	−2786.42	−0.117375
$827$	40709.2	1.71172	0.855862	−	0.517204i	$-0.173027\pi$
$827$	40709.2	1.71172	0.855862	+	0.517204i	$0.173027\pi$
$828$	25400.6	1.06610
$829$	6460.64	0.270672	0.135336	−	0.990800i	$-0.456789\pi$
$829$	6460.64	0.270672	0.135336	+	0.990800i	$0.456789\pi$
$830$	−383.194	−0.0160251
$831$	−4819.64	−0.201193
$832$	−18591.6	−0.774695
$833$	19222.8	0.799556
$834$	−465.392	−0.0193228
$835$	33652.8	1.39474
$836$	9356.00	0.387062
$837$	3632.26	0.149999
$838$	547.012	0.0225492
$839$	42238.9	1.73808	0.869039	−	0.494744i	$-0.164738\pi$
$839$	42238.9	1.73808	0.869039	+	0.494744i	$0.164738\pi$
$840$	−1544.50	−0.0634410
$841$	13528.5	0.554696
$842$	621.882	0.0254530
$843$	3750.50	0.153231
$844$	−32525.8	−1.32652
$845$	12936.0	0.526643
$846$	2261.78	0.0919167
$847$	35112.6	1.42442
$848$	−8981.81	−0.363723
$849$	66.1004	0.00267204
$850$	891.106	0.0359584
$851$	−35375.5	−1.42498
$852$	−4691.82	−0.188661
$853$	−5629.01	−0.225948	−0.112974	−	0.993598i	$-0.536038\pi$
$853$	−5629.01	−0.225948	−0.112974	+	0.993598i	$0.536038\pi$
$854$	813.674	0.0326034
$855$	−39775.6	−1.59099
$856$	−1538.39	−0.0614265
$857$	−26651.2	−1.06229	−0.531147	−	0.847280i	$-0.678239\pi$
$857$	−26651.2	−1.06229	−0.531147	+	0.847280i	$0.678239\pi$
$858$	92.6429	0.00368622
$859$	2148.00	0.0853187	0.0426593	−	0.999090i	$-0.486417\pi$
$859$	2148.00	0.0853187	0.0426593	+	0.999090i	$0.486417\pi$
$860$	0	0
$861$	−14107.8	−0.558413
$862$	−2018.02	−0.0797378
$863$	−14989.5	−0.591251	−0.295625	−	0.955304i	$-0.595528\pi$
$863$	−14989.5	−0.591251	−0.295625	+	0.955304i	$0.595528\pi$
$864$	−2042.85	−0.0804388
$865$	−13371.0	−0.525583
$866$	−1526.53	−0.0599001
$867$	−3919.64	−0.153539
$868$	−15170.9	−0.593242
$869$	−13176.5	−0.514362
$870$	−633.450	−0.0246850
$871$	26631.8	1.03603
$872$	5237.63	0.203404
$873$	5188.63	0.201155
$874$	−2230.93	−0.0863413
$875$	3819.93	0.147586
$876$	−4397.63	−0.169614
$877$	26925.9	1.03674	0.518370	−	0.855156i	$-0.326539\pi$
$877$	26925.9	1.03674	0.518370	+	0.855156i	$0.326539\pi$
$878$	190.840	0.00733548
$879$	159.047	0.00610299
$880$	−12437.1	−0.476426
$881$	14099.7	0.539197	0.269598	−	0.962973i	$-0.413109\pi$
$881$	14099.7	0.539197	0.269598	+	0.962973i	$0.413109\pi$
$882$	−2641.65	−0.100849
$883$	48023.0	1.83024	0.915120	−	0.403181i	$-0.132095\pi$
$883$	48023.0	1.83024	0.915120	+	0.403181i	$0.132095\pi$
$884$	−10547.4	−0.401299
$885$	−8556.24	−0.324989
$886$	−1949.54	−0.0739235
$887$	−9693.92	−0.366956	−0.183478	−	0.983024i	$-0.558736\pi$
$887$	−9693.92	−0.366956	−0.183478	+	0.983024i	$0.558736\pi$
$888$	927.008	0.0350319
$889$	19792.8	0.746715
$890$	234.312	0.00882490
$891$	7811.63	0.293714
$892$	−2846.27	−0.106839
$893$	44415.2	1.66439
$894$	−174.732	−0.00653681
$895$	47849.0	1.78705
$896$	11367.9	0.423858
$897$	4939.10	0.183848
$898$	3582.49	0.133128
$899$	−12472.0	−0.462696
$900$	27379.7	1.01406
$901$	−5049.50	−0.186707
$902$	1023.07	0.0377657
$903$	0	0
$904$	−2538.81	−0.0934066
$905$	−68270.9	−2.50763
$906$	−222.973	−0.00817634
$907$	18966.2	0.694334	0.347167	−	0.937803i	$-0.387144\pi$
$907$	18966.2	0.694334	0.347167	+	0.937803i	$0.387144\pi$
$908$	35123.6	1.28372
$909$	−28274.5	−1.03169
$910$	3363.33	0.122520
$911$	12247.3	0.445414	0.222707	−	0.974885i	$-0.428511\pi$
$911$	12247.3	0.445414	0.222707	+	0.974885i	$0.428511\pi$
$912$	−6491.59	−0.235700
$913$	1549.96	0.0561842
$914$	307.874	0.0111417
$915$	2498.54	0.0902723
$916$	−20077.3	−0.724205
$917$	11707.2	0.421599
$918$	−379.971	−0.0136611
$919$	−23177.0	−0.831926	−0.415963	−	0.909382i	$-0.636555\pi$
$919$	−23177.0	−0.831926	−0.415963	+	0.909382i	$0.636555\pi$
$920$	5971.33	0.213988
$921$	6315.97	0.225970
$922$	−2164.18	−0.0773029
$923$	20479.6	0.730330
$924$	3116.67	0.110964
$925$	−38131.7	−1.35542
$926$	30.2386	0.00107311
$927$	17585.2	0.623058
$928$	7014.45	0.248126
$929$	39323.8	1.38878	0.694388	−	0.719601i	$-0.255675\pi$
$929$	39323.8	1.38878	0.694388	+	0.719601i	$0.255675\pi$
$930$	208.357	0.00734655
$931$	−51875.0	−1.82614
$932$	29531.4	1.03791
$933$	6751.86	0.236920
$934$	−2102.51	−0.0736575
$935$	−6992.04	−0.244561
$936$	2905.40	0.101459
$937$	43289.9	1.50931	0.754653	−	0.656124i	$-0.227805\pi$
$937$	43289.9	1.50931	0.754653	+	0.656124i	$0.227805\pi$
$938$	−4007.19	−0.139488
$939$	−4723.54	−0.164161
$940$	−59308.5	−2.05791
$941$	28422.3	0.984635	0.492318	−	0.870416i	$-0.336150\pi$
$941$	28422.3	0.984635	0.492318	+	0.870416i	$0.336150\pi$
$942$	114.977	0.00397680
$943$	54543.4	1.88354
$944$	31346.9	1.08078
$945$	−27090.3	−0.932537
$946$	0	0
$947$	2201.51	0.0755431	0.0377716	−	0.999286i	$-0.487974\pi$
$947$	2201.51	0.0755431	0.0377716	+	0.999286i	$0.487974\pi$
$948$	9183.65	0.314632
$949$	19195.5	0.656599
$950$	−2404.75	−0.0821268
$951$	10209.2	0.348113
$952$	3181.16	0.108300
$953$	−10044.5	−0.341420	−0.170710	−	0.985321i	$-0.554606\pi$
$953$	−10044.5	−0.341420	−0.170710	+	0.985321i	$0.554606\pi$
$954$	693.917	0.0235497
$955$	−17461.3	−0.591659
$956$	−9242.37	−0.312677
$957$	2562.20	0.0865458
$958$	−2553.89	−0.0861300
$959$	−90908.9	−3.06111
$960$	8589.94	0.288791
$961$	−25688.7	−0.862296
$962$	−2018.67	−0.0676553
$963$	−13197.6	−0.441626
$964$	−7877.54	−0.263193
$965$	−60976.2	−2.03409
$966$	−743.167	−0.0247526
$967$	−28057.6	−0.933062	−0.466531	−	0.884505i	$-0.654496\pi$
$967$	−28057.6	−0.933062	−0.466531	+	0.884505i	$0.654496\pi$
$968$	3557.34	0.118117
$969$	−3649.52	−0.120990
$970$	608.527	0.0201429
$971$	38662.6	1.27780	0.638899	−	0.769290i	$-0.279390\pi$
$971$	38662.6	1.27780	0.638899	+	0.769290i	$0.279390\pi$
$972$	−17639.4	−0.582082
$973$	68340.4	2.25169
$974$	606.879	0.0199647
$975$	5323.93	0.174874
$976$	−9153.73	−0.300209
$977$	1575.15	0.0515798	0.0257899	−	0.999667i	$-0.491790\pi$
$977$	1575.15	0.0515798	0.0257899	+	0.999667i	$0.491790\pi$
$978$	−316.033	−0.0103330
$979$	−947.755	−0.0309401
$980$	69269.6	2.25790
$981$	44932.7	1.46238
$982$	1225.98	0.0398396
$983$	51323.9	1.66529	0.832644	−	0.553809i	$-0.186826\pi$
$983$	51323.9	1.66529	0.832644	+	0.553809i	$0.186826\pi$
$984$	−1429.30	−0.0463053
$985$	−70835.7	−2.29138
$986$	1304.69	0.0421399
$987$	14795.6	0.477152
$988$	28463.5	0.916542
$989$	0	0
$990$	960.867	0.0308468
$991$	−17395.6	−0.557609	−0.278804	−	0.960348i	$-0.589938\pi$
$991$	−17395.6	−0.557609	−0.278804	+	0.960348i	$0.589938\pi$
$992$	−2307.22	−0.0738451
$993$	2070.52	0.0661693
$994$	−3081.49	−0.0983288
$995$	15090.1	0.480792
$996$	−1080.28	−0.0343675
$997$	−9953.86	−0.316190	−0.158095	−	0.987424i	$-0.550535\pi$
$997$	−9953.86	−0.316190	−0.158095	+	0.987424i	$0.550535\pi$
$998$	3335.70	0.105801
$999$	16259.5	0.514944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.16		30
43.8	odd	14		43.4.e.a.21.6	✓	60
43.27	odd	14		43.4.e.a.41.6	yes	60
43.42	odd	2		1849.4.a.h.1.15		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.21.6	✓	60	43.8	odd	14
43.4.e.a.41.6	yes	60	43.27	odd	14
1849.4.a.g.1.16		30	1.1	even	1	trivial
1849.4.a.h.1.15		30	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)

\(f(q)\)	\(=\)	\(q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} +O(q^{10})\)	\(q+0.188737 q^{2} +1.07307 q^{3} -7.96438 q^{4} -16.0623 q^{5} +0.202528 q^{6} -29.7402 q^{7} -3.01306 q^{8} -25.8485 q^{9} -3.03154 q^{10} +12.2621 q^{11} -8.54636 q^{12} +37.3046 q^{13} -5.61307 q^{14} -17.2360 q^{15} +63.1464 q^{16} +35.5003 q^{17} -4.87856 q^{18} -95.8018 q^{19} +127.926 q^{20} -31.9135 q^{21} +2.31431 q^{22} +123.383 q^{23} -3.23324 q^{24} +132.997 q^{25} +7.04074 q^{26} -56.7103 q^{27} +236.863 q^{28} +194.724 q^{29} -3.25306 q^{30} -64.0494 q^{31} +36.0225 q^{32} +13.1581 q^{33} +6.70021 q^{34} +477.696 q^{35} +205.867 q^{36} -286.712 q^{37} -18.0813 q^{38} +40.0306 q^{39} +48.3966 q^{40} +442.065 q^{41} -6.02324 q^{42} -97.6600 q^{44} +415.186 q^{45} +23.2869 q^{46} -463.616 q^{47} +67.7607 q^{48} +541.482 q^{49} +25.1013 q^{50} +38.0945 q^{51} -297.108 q^{52} -142.238 q^{53} -10.7033 q^{54} -196.957 q^{55} +89.6092 q^{56} -102.802 q^{57} +36.7516 q^{58} +496.417 q^{59} +137.274 q^{60} -144.960 q^{61} -12.0885 q^{62} +768.741 q^{63} -498.372 q^{64} -599.196 q^{65} +2.48342 q^{66} +713.903 q^{67} -282.738 q^{68} +132.399 q^{69} +90.1587 q^{70} +548.984 q^{71} +77.8832 q^{72} +514.562 q^{73} -54.1131 q^{74} +142.715 q^{75} +763.002 q^{76} -364.678 q^{77} +7.55523 q^{78} -1074.57 q^{79} -1014.27 q^{80} +637.056 q^{81} +83.4338 q^{82} +126.403 q^{83} +254.171 q^{84} -570.216 q^{85} +208.953 q^{87} -36.9464 q^{88} -77.2915 q^{89} +78.3608 q^{90} -1109.45 q^{91} -982.671 q^{92} -68.7297 q^{93} -87.5013 q^{94} +1538.79 q^{95} +38.6548 q^{96} -200.732 q^{97} +102.197 q^{98} -316.957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} + 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} - 80 q^{18} - 254 q^{19} - 312 q^{20} - 548 q^{21} - 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} - 549 q^{26} + 10 q^{27} - 578 q^{28} - 793 q^{29} - 1560 q^{30} - 359 q^{31} - 676 q^{32} - 208 q^{33} - 1007 q^{34} - 514 q^{35} + 776 q^{36} - 510 q^{37} - 2066 q^{38} - 898 q^{39} - 1248 q^{40} - 270 q^{41} + 915 q^{42} + 3256 q^{44} - 807 q^{45} - 1960 q^{46} + 1421 q^{47} + 632 q^{48} + 386 q^{49} + 141 q^{50} - 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} - 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} - 1759 q^{61} - 395 q^{62} - 2204 q^{63} + 222 q^{64} - 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} - 1660 q^{69} - 1597 q^{70} - 727 q^{71} - 9100 q^{72} - 4623 q^{73} - 2649 q^{74} - 1027 q^{75} - 874 q^{76} - 3556 q^{77} - 4979 q^{78} + 546 q^{79} - 5809 q^{80} - 410 q^{81} + 4397 q^{82} - 492 q^{83} - 10611 q^{84} + 1723 q^{85} + 5937 q^{87} - 3974 q^{88} - 5218 q^{89} + 10492 q^{90} - 1104 q^{91} + 1060 q^{92} - 1997 q^{93} + 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} - 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 114 * q^4 - 27 * q^5 + 8 * q^6 - 48 * q^7 - 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 + 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 - 80 * q^18 - 254 * q^19 - 312 * q^20 - 548 * q^21 - 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 - 549 * q^26 + 10 * q^27 - 578 * q^28 - 793 * q^29 - 1560 * q^30 - 359 * q^31 - 676 * q^32 - 208 * q^33 - 1007 * q^34 - 514 * q^35 + 776 * q^36 - 510 * q^37 - 2066 * q^38 - 898 * q^39 - 1248 * q^40 - 270 * q^41 + 915 * q^42 + 3256 * q^44 - 807 * q^45 - 1960 * q^46 + 1421 * q^47 + 632 * q^48 + 386 * q^49 + 141 * q^50 - 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 - 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 - 1759 * q^61 - 395 * q^62 - 2204 * q^63 + 222 * q^64 - 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 - 1660 * q^69 - 1597 * q^70 - 727 * q^71 - 9100 * q^72 - 4623 * q^73 - 2649 * q^74 - 1027 * q^75 - 874 * q^76 - 3556 * q^77 - 4979 * q^78 + 546 * q^79 - 5809 * q^80 - 410 * q^81 + 4397 * q^82 - 492 * q^83 - 10611 * q^84 + 1723 * q^85 + 5937 * q^87 - 3974 * q^88 - 5218 * q^89 + 10492 * q^90 - 1104 * q^91 + 1060 * q^92 - 1997 * q^93 + 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 - 6270 * q^98 - 2693 * q^99

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